Properties

Label 1638.2.bj.h.1135.1
Level 16381638
Weight 22
Character 1638.1135
Analytic conductor 13.07913.079
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1638,2,Mod(127,1638)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.127");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1638=232713 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1638.bj (of order 66, 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: 13.079495851113.0794958511
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x162x15+2x14+18x13+143x12148x11+172x10+1612x9++97344 x^{16} - 2 x^{15} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + \cdots + 97344 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 22 2^{2}
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 1135.1
Root 2.027982.02798i-2.02798 - 2.02798i of defining polynomial
Character χ\chi == 1638.1135
Dual form 1638.2.bj.h.127.4

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+(0.8660250.500000i)q2+(0.500000+0.866025i)q42.19147iq5+(0.8660250.500000i)q71.00000iq8+(1.09573+1.89787i)q10+(3.541952.04495i)q11+(3.53557+0.706919i)q131.00000q14+(0.500000+0.866025i)q16+(2.85204+4.93987i)q17+(6.696123.86601i)q19+(1.897871.09573i)q20+(2.04495+3.54195i)q22+(1.23791+2.14412i)q23+0.197462q25+(2.708442.38000i)q26+(0.866025+0.500000i)q28+(4.908888.50243i)q29+7.19507iq31+(0.8660250.500000i)q325.70407iq34+(1.095731.89787i)q35+(8.794255.07736i)q377.73201q382.19147q40+(3.140931.81341i)q41+(1.377692.38624i)q434.08989iq44+(2.144121.23791i)q467.70008iq47+(0.5000000.866025i)q49+(0.1710070.0987308i)q50+(1.15558+3.41535i)q52+6.31111q53+(4.48144+7.76207i)q55+(0.5000000.866025i)q56+(8.50243+4.90888i)q58+(4.207812.42938i)q59+(5.63434+9.75896i)q61+(3.597546.23112i)q621.00000q64+(1.549197.74810i)q65+(5.490943.17020i)q67+(2.85204+4.93987i)q68+2.19147iq70+(7.21341+4.16466i)q717.37805iq73+(5.07736+8.79425i)q74+(6.69612+3.86601i)q764.08989q77+3.45834q79+(1.89787+1.09573i)q80+(1.81341+3.14093i)q82+0.332783iq83+(10.82566.25015i)q85+2.75539iq86+(2.04495+3.54195i)q88+(11.71516.76374i)q89+(3.415351.15558i)q912.47582q92+(3.85004+6.66847i)q94+(8.4722314.6743i)q95+(10.06005.80816i)q97+(0.866025+0.500000i)q98+O(q100)q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -2.19147i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-1.09573 + 1.89787i) q^{10} +(-3.54195 - 2.04495i) q^{11} +(3.53557 + 0.706919i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.85204 + 4.93987i) q^{17} +(6.69612 - 3.86601i) q^{19} +(1.89787 - 1.09573i) q^{20} +(2.04495 + 3.54195i) q^{22} +(-1.23791 + 2.14412i) q^{23} +0.197462 q^{25} +(-2.70844 - 2.38000i) q^{26} +(0.866025 + 0.500000i) q^{28} +(4.90888 - 8.50243i) q^{29} +7.19507i q^{31} +(0.866025 - 0.500000i) q^{32} -5.70407i q^{34} +(-1.09573 - 1.89787i) q^{35} +(-8.79425 - 5.07736i) q^{37} -7.73201 q^{38} -2.19147 q^{40} +(-3.14093 - 1.81341i) q^{41} +(-1.37769 - 2.38624i) q^{43} -4.08989i q^{44} +(2.14412 - 1.23791i) q^{46} -7.70008i q^{47} +(0.500000 - 0.866025i) q^{49} +(-0.171007 - 0.0987308i) q^{50} +(1.15558 + 3.41535i) q^{52} +6.31111 q^{53} +(-4.48144 + 7.76207i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-8.50243 + 4.90888i) q^{58} +(4.20781 - 2.42938i) q^{59} +(5.63434 + 9.75896i) q^{61} +(3.59754 - 6.23112i) q^{62} -1.00000 q^{64} +(1.54919 - 7.74810i) q^{65} +(-5.49094 - 3.17020i) q^{67} +(-2.85204 + 4.93987i) q^{68} +2.19147i q^{70} +(-7.21341 + 4.16466i) q^{71} -7.37805i q^{73} +(5.07736 + 8.79425i) q^{74} +(6.69612 + 3.86601i) q^{76} -4.08989 q^{77} +3.45834 q^{79} +(1.89787 + 1.09573i) q^{80} +(1.81341 + 3.14093i) q^{82} +0.332783i q^{83} +(10.8256 - 6.25015i) q^{85} +2.75539i q^{86} +(-2.04495 + 3.54195i) q^{88} +(-11.7151 - 6.76374i) q^{89} +(3.41535 - 1.15558i) q^{91} -2.47582 q^{92} +(-3.85004 + 6.66847i) q^{94} +(-8.47223 - 14.6743i) q^{95} +(10.0600 - 5.80816i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+8q4+2q1012q11+10q1316q148q166q174q2212q2320q252q26+16q29+2q356q37+4q40+12q416q43+6q46+24q97+O(q100) 16 q + 8 q^{4} + 2 q^{10} - 12 q^{11} + 10 q^{13} - 16 q^{14} - 8 q^{16} - 6 q^{17} - 4 q^{22} - 12 q^{23} - 20 q^{25} - 2 q^{26} + 16 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{40} + 12 q^{41} - 6 q^{43} + 6 q^{46}+ \cdots - 24 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1638Z)×\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times.

nn 379379 703703 911911
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) 11 11

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.866025 0.500000i −0.612372 0.353553i
33 0 0
44 0.500000 + 0.866025i 0.250000 + 0.433013i
55 2.19147i 0.980055i −0.871707 0.490027i 0.836987π-0.836987\pi
0.871707 0.490027i 0.163013π-0.163013\pi
66 0 0
77 0.866025 0.500000i 0.327327 0.188982i
88 1.00000i 0.353553i
99 0 0
1010 −1.09573 + 1.89787i −0.346502 + 0.600159i
1111 −3.54195 2.04495i −1.06794 0.616574i −0.140321 0.990106i 0.544813π-0.544813\pi
−0.927617 + 0.373532i 0.878147π0.878147\pi
1212 0 0
1313 3.53557 + 0.706919i 0.980591 + 0.196064i
1414 −1.00000 −0.267261
1515 0 0
1616 −0.500000 + 0.866025i −0.125000 + 0.216506i
1717 2.85204 + 4.93987i 0.691720 + 1.19809i 0.971274 + 0.237965i 0.0764803π0.0764803\pi
−0.279553 + 0.960130i 0.590186π0.590186\pi
1818 0 0
1919 6.69612 3.86601i 1.53620 0.886923i 0.537139 0.843494i 0.319505π-0.319505\pi
0.999057 0.0434286i 0.0138281π-0.0138281\pi
2020 1.89787 1.09573i 0.424376 0.245014i
2121 0 0
2222 2.04495 + 3.54195i 0.435984 + 0.755146i
2323 −1.23791 + 2.14412i −0.258122 + 0.447080i −0.965739 0.259516i 0.916437π-0.916437\pi
0.707617 + 0.706596i 0.249770π0.249770\pi
2424 0 0
2525 0.197462 0.0394923
2626 −2.70844 2.38000i −0.531168 0.466755i
2727 0 0
2828 0.866025 + 0.500000i 0.163663 + 0.0944911i
2929 4.90888 8.50243i 0.911556 1.57886i 0.0996903 0.995019i 0.468215π-0.468215\pi
0.811866 0.583844i 0.198452π-0.198452\pi
3030 0 0
3131 7.19507i 1.29227i 0.763222 + 0.646137i 0.223616π0.223616\pi
−0.763222 + 0.646137i 0.776384π0.776384\pi
3232 0.866025 0.500000i 0.153093 0.0883883i
3333 0 0
3434 5.70407i 0.978240i
3535 −1.09573 1.89787i −0.185213 0.320798i
3636 0 0
3737 −8.79425 5.07736i −1.44577 0.834713i −0.447540 0.894264i 0.647700π-0.647700\pi
−0.998225 + 0.0595505i 0.981033π0.981033\pi
3838 −7.73201 −1.25430
3939 0 0
4040 −2.19147 −0.346502
4141 −3.14093 1.81341i −0.490530 0.283208i 0.234264 0.972173i 0.424732π-0.424732\pi
−0.724794 + 0.688965i 0.758065π0.758065\pi
4242 0 0
4343 −1.37769 2.38624i −0.210096 0.363897i 0.741648 0.670789i 0.234044π-0.234044\pi
−0.951744 + 0.306892i 0.900711π0.900711\pi
4444 4.08989i 0.616574i
4545 0 0
4646 2.14412 1.23791i 0.316133 0.182520i
4747 7.70008i 1.12317i −0.827418 0.561586i 0.810191π-0.810191\pi
0.827418 0.561586i 0.189809π-0.189809\pi
4848 0 0
4949 0.500000 0.866025i 0.0714286 0.123718i
5050 −0.171007 0.0987308i −0.0241840 0.0139626i
5151 0 0
5252 1.15558 + 3.41535i 0.160250 + 0.473624i
5353 6.31111 0.866898 0.433449 0.901178i 0.357296π-0.357296\pi
0.433449 + 0.901178i 0.357296π0.357296\pi
5454 0 0
5555 −4.48144 + 7.76207i −0.604277 + 1.04664i
5656 −0.500000 0.866025i −0.0668153 0.115728i
5757 0 0
5858 −8.50243 + 4.90888i −1.11642 + 0.644568i
5959 4.20781 2.42938i 0.547810 0.316278i −0.200428 0.979708i 0.564233π-0.564233\pi
0.748238 + 0.663430i 0.230900π0.230900\pi
6060 0 0
6161 5.63434 + 9.75896i 0.721403 + 1.24951i 0.960438 + 0.278496i 0.0898357π0.0898357\pi
−0.239035 + 0.971011i 0.576831π0.576831\pi
6262 3.59754 6.23112i 0.456888 0.791353i
6363 0 0
6464 −1.00000 −0.125000
6565 1.54919 7.74810i 0.192153 0.961033i
6666 0 0
6767 −5.49094 3.17020i −0.670825 0.387301i 0.125564 0.992086i 0.459926π-0.459926\pi
−0.796389 + 0.604784i 0.793259π0.793259\pi
6868 −2.85204 + 4.93987i −0.345860 + 0.599047i
6969 0 0
7070 2.19147i 0.261931i
7171 −7.21341 + 4.16466i −0.856074 + 0.494255i −0.862696 0.505723i 0.831226π-0.831226\pi
0.00662155 + 0.999978i 0.497892π0.497892\pi
7272 0 0
7373 7.37805i 0.863536i −0.901985 0.431768i 0.857890π-0.857890\pi
0.901985 0.431768i 0.142110π-0.142110\pi
7474 5.07736 + 8.79425i 0.590231 + 1.02231i
7575 0 0
7676 6.69612 + 3.86601i 0.768098 + 0.443461i
7777 −4.08989 −0.466086
7878 0 0
7979 3.45834 0.389094 0.194547 0.980893i 0.437676π-0.437676\pi
0.194547 + 0.980893i 0.437676π0.437676\pi
8080 1.89787 + 1.09573i 0.212188 + 0.122507i
8181 0 0
8282 1.81341 + 3.14093i 0.200258 + 0.346857i
8383 0.332783i 0.0365277i 0.999833 + 0.0182638i 0.00581389π0.00581389\pi
−0.999833 + 0.0182638i 0.994186π0.994186\pi
8484 0 0
8585 10.8256 6.25015i 1.17420 0.677924i
8686 2.75539i 0.297121i
8787 0 0
8888 −2.04495 + 3.54195i −0.217992 + 0.377573i
8989 −11.7151 6.76374i −1.24180 0.716956i −0.272342 0.962200i 0.587798π-0.587798\pi
−0.969461 + 0.245245i 0.921132π0.921132\pi
9090 0 0
9191 3.41535 1.15558i 0.358026 0.121137i
9292 −2.47582 −0.258122
9393 0 0
9494 −3.85004 + 6.66847i −0.397101 + 0.687800i
9595 −8.47223 14.6743i −0.869233 1.50556i
9696 0 0
9797 10.0600 5.80816i 1.02144 0.589729i 0.106920 0.994268i 0.465901π-0.465901\pi
0.914521 + 0.404539i 0.132568π0.132568\pi
9898 −0.866025 + 0.500000i −0.0874818 + 0.0505076i
9999 0 0
100100 0.0987308 + 0.171007i 0.00987308 + 0.0171007i
101101 1.12692 1.95189i 0.112133 0.194220i −0.804497 0.593957i 0.797565π-0.797565\pi
0.916630 + 0.399737i 0.130898π0.130898\pi
102102 0 0
103103 −16.0325 −1.57973 −0.789867 0.613278i 0.789850π-0.789850\pi
−0.789867 + 0.613278i 0.789850π0.789850\pi
104104 0.706919 3.53557i 0.0693191 0.346691i
105105 0 0
106106 −5.46559 3.15556i −0.530865 0.306495i
107107 4.30793 7.46156i 0.416464 0.721336i −0.579117 0.815244i 0.696603π-0.696603\pi
0.995581 + 0.0939082i 0.0299360π0.0299360\pi
108108 0 0
109109 10.0318i 0.960870i −0.877030 0.480435i 0.840479π-0.840479\pi
0.877030 0.480435i 0.159521π-0.159521\pi
110110 7.76207 4.48144i 0.740085 0.427288i
111111 0 0
112112 1.00000i 0.0944911i
113113 9.27760 + 16.0693i 0.872763 + 1.51167i 0.859127 + 0.511763i 0.171007π0.171007\pi
0.0136363 + 0.999907i 0.495659π0.495659\pi
114114 0 0
115115 4.69878 + 2.71284i 0.438163 + 0.252974i
116116 9.81776 0.911556
117117 0 0
118118 −4.85876 −0.447285
119119 4.93987 + 2.85204i 0.452837 + 0.261446i
120120 0 0
121121 2.86360 + 4.95991i 0.260328 + 0.450901i
122122 11.2687i 1.02022i
123123 0 0
124124 −6.23112 + 3.59754i −0.559571 + 0.323068i
125125 11.3901i 1.01876i
126126 0 0
127127 −0.132439 + 0.229390i −0.0117520 + 0.0203551i −0.871842 0.489788i 0.837074π-0.837074\pi
0.860090 + 0.510143i 0.170408π0.170408\pi
128128 0.866025 + 0.500000i 0.0765466 + 0.0441942i
129129 0 0
130130 −5.21569 + 5.93545i −0.457446 + 0.520574i
131131 5.10237 0.445796 0.222898 0.974842i 0.428448π-0.428448\pi
0.222898 + 0.974842i 0.428448π0.428448\pi
132132 0 0
133133 3.86601 6.69612i 0.335225 0.580627i
134134 3.17020 + 5.49094i 0.273863 + 0.474345i
135135 0 0
136136 4.93987 2.85204i 0.423591 0.244560i
137137 −18.8812 + 10.9011i −1.61313 + 0.931342i −0.624493 + 0.781030i 0.714694π0.714694\pi
−0.988639 + 0.150312i 0.951972π0.951972\pi
138138 0 0
139139 −8.22455 14.2453i −0.697597 1.20827i −0.969297 0.245892i 0.920919π-0.920919\pi
0.271700 0.962382i 0.412414π-0.412414\pi
140140 1.09573 1.89787i 0.0926065 0.160399i
141141 0 0
142142 8.32933 0.698982
143143 −11.0772 9.73392i −0.926322 0.813991i
144144 0 0
145145 −18.6328 10.7577i −1.54737 0.893375i
146146 −3.68903 + 6.38958i −0.305306 + 0.528806i
147147 0 0
148148 10.1547i 0.834713i
149149 12.8023 7.39139i 1.04880 0.605526i 0.126489 0.991968i 0.459629π-0.459629\pi
0.922314 + 0.386442i 0.126296π0.126296\pi
150150 0 0
151151 18.9896i 1.54535i −0.634803 0.772674i 0.718919π-0.718919\pi
0.634803 0.772674i 0.281081π-0.281081\pi
152152 −3.86601 6.69612i −0.313575 0.543127i
153153 0 0
154154 3.54195 + 2.04495i 0.285418 + 0.164786i
155155 15.7678 1.26650
156156 0 0
157157 −13.5474 −1.08120 −0.540601 0.841279i 0.681803π-0.681803\pi
−0.540601 + 0.841279i 0.681803π0.681803\pi
158158 −2.99501 1.72917i −0.238270 0.137565i
159159 0 0
160160 −1.09573 1.89787i −0.0866254 0.150040i
161161 2.47582i 0.195122i
162162 0 0
163163 −3.86502 + 2.23147i −0.302732 + 0.174782i −0.643670 0.765304i 0.722589π-0.722589\pi
0.340938 + 0.940086i 0.389256π0.389256\pi
164164 3.62683i 0.283208i
165165 0 0
166166 0.166392 0.288199i 0.0129145 0.0223685i
167167 2.86448 + 1.65381i 0.221660 + 0.127976i 0.606719 0.794917i 0.292485π-0.292485\pi
−0.385059 + 0.922892i 0.625819π0.625819\pi
168168 0 0
169169 12.0005 + 4.99872i 0.923118 + 0.384517i
170170 −12.5003 −0.958729
171171 0 0
172172 1.37769 2.38624i 0.105048 0.181949i
173173 −5.06107 8.76603i −0.384786 0.666469i 0.606953 0.794737i 0.292391π-0.292391\pi
−0.991740 + 0.128268i 0.959058π0.959058\pi
174174 0 0
175175 0.171007 0.0987308i 0.0129269 0.00746335i
176176 3.54195 2.04495i 0.266984 0.154144i
177177 0 0
178178 6.76374 + 11.7151i 0.506964 + 0.878088i
179179 −4.62579 + 8.01210i −0.345748 + 0.598853i −0.985489 0.169737i 0.945708π-0.945708\pi
0.639742 + 0.768590i 0.279041π0.279041\pi
180180 0 0
181181 23.2645 1.72923 0.864617 0.502431i 0.167561π-0.167561\pi
0.864617 + 0.502431i 0.167561π0.167561\pi
182182 −3.53557 0.706919i −0.262074 0.0524003i
183183 0 0
184184 2.14412 + 1.23791i 0.158067 + 0.0912598i
185185 −11.1269 + 19.2723i −0.818065 + 1.41693i
186186 0 0
187187 23.3290i 1.70599i
188188 6.66847 3.85004i 0.486348 0.280793i
189189 0 0
190190 16.9445i 1.22928i
191191 −4.45096 7.70929i −0.322060 0.557825i 0.658853 0.752272i 0.271042π-0.271042\pi
−0.980913 + 0.194447i 0.937709π0.937709\pi
192192 0 0
193193 7.69754 + 4.44417i 0.554081 + 0.319899i 0.750766 0.660568i 0.229684π-0.229684\pi
−0.196685 + 0.980467i 0.563018π0.563018\pi
194194 −11.6163 −0.834003
195195 0 0
196196 1.00000 0.0714286
197197 20.2586 + 11.6963i 1.44336 + 0.833326i 0.998072 0.0620596i 0.0197669π-0.0197669\pi
0.445291 + 0.895386i 0.353100π0.353100\pi
198198 0 0
199199 −1.96804 3.40875i −0.139511 0.241640i 0.787801 0.615930i 0.211220π-0.211220\pi
−0.927312 + 0.374290i 0.877886π0.877886\pi
200200 0.197462i 0.0139626i
201201 0 0
202202 −1.95189 + 1.12692i −0.137334 + 0.0792900i
203203 9.81776i 0.689072i
204204 0 0
205205 −3.97404 + 6.88324i −0.277559 + 0.480747i
206206 13.8846 + 8.01627i 0.967385 + 0.558520i
207207 0 0
208208 −2.38000 + 2.70844i −0.165023 + 0.187796i
209209 −31.6231 −2.18741
210210 0 0
211211 −6.40104 + 11.0869i −0.440666 + 0.763256i −0.997739 0.0672076i 0.978591π-0.978591\pi
0.557073 + 0.830464i 0.311924π0.311924\pi
212212 3.15556 + 5.46559i 0.216725 + 0.375378i
213213 0 0
214214 −7.46156 + 4.30793i −0.510062 + 0.294484i
215215 −5.22936 + 3.01917i −0.356639 + 0.205906i
216216 0 0
217217 3.59754 + 6.23112i 0.244217 + 0.422996i
218218 −5.01589 + 8.68777i −0.339719 + 0.588410i
219219 0 0
220220 −8.96287 −0.604277
221221 6.59149 + 19.4814i 0.443392 + 1.31046i
222222 0 0
223223 16.3236 + 9.42444i 1.09311 + 0.631107i 0.934403 0.356218i 0.115934π-0.115934\pi
0.158707 + 0.987326i 0.449267π0.449267\pi
224224 0.500000 0.866025i 0.0334077 0.0578638i
225225 0 0
226226 18.5552i 1.23427i
227227 1.14246 0.659599i 0.0758276 0.0437791i −0.461607 0.887085i 0.652727π-0.652727\pi
0.537434 + 0.843306i 0.319394π0.319394\pi
228228 0 0
229229 4.34109i 0.286867i 0.989660 + 0.143434i 0.0458143π0.0458143\pi
−0.989660 + 0.143434i 0.954186π0.954186\pi
230230 −2.71284 4.69878i −0.178879 0.309828i
231231 0 0
232232 −8.50243 4.90888i −0.558212 0.322284i
233233 5.76422 0.377627 0.188813 0.982013i 0.439536π-0.439536\pi
0.188813 + 0.982013i 0.439536π0.439536\pi
234234 0 0
235235 −16.8745 −1.10077
236236 4.20781 + 2.42938i 0.273905 + 0.158139i
237237 0 0
238238 −2.85204 4.93987i −0.184870 0.320204i
239239 13.0951i 0.847049i 0.905885 + 0.423525i 0.139207π0.139207\pi
−0.905885 + 0.423525i 0.860793π0.860793\pi
240240 0 0
241241 −0.389769 + 0.225033i −0.0251072 + 0.0144957i −0.512501 0.858687i 0.671281π-0.671281\pi
0.487394 + 0.873182i 0.337948π0.337948\pi
242242 5.72721i 0.368159i
243243 0 0
244244 −5.63434 + 9.75896i −0.360701 + 0.624753i
245245 −1.89787 1.09573i −0.121250 0.0700039i
246246 0 0
247247 26.4076 8.93493i 1.68027 0.568516i
248248 7.19507 0.456888
249249 0 0
250250 −5.69504 + 9.86410i −0.360186 + 0.623860i
251251 −9.35111 16.1966i −0.590237 1.02232i −0.994200 0.107545i 0.965701π-0.965701\pi
0.403963 0.914775i 0.367632π-0.367632\pi
252252 0 0
253253 8.76922 5.06291i 0.551316 0.318303i
254254 0.229390 0.132439i 0.0143932 0.00830994i
255255 0 0
256256 −0.500000 0.866025i −0.0312500 0.0541266i
257257 −9.88929 + 17.1287i −0.616877 + 1.06846i 0.373175 + 0.927761i 0.378269π0.378269\pi
−0.990052 + 0.140701i 0.955064π0.955064\pi
258258 0 0
259259 −10.1547 −0.630984
260260 7.48464 2.53241i 0.464178 0.157053i
261261 0 0
262262 −4.41878 2.55119i −0.272993 0.157613i
263263 11.7723 20.3903i 0.725914 1.25732i −0.232683 0.972553i 0.574750π-0.574750\pi
0.958597 0.284767i 0.0919162π-0.0919162\pi
264264 0 0
265265 13.8306i 0.849608i
266266 −6.69612 + 3.86601i −0.410565 + 0.237040i
267267 0 0
268268 6.34039i 0.387301i
269269 11.4216 + 19.7827i 0.696384 + 1.20617i 0.969712 + 0.244252i 0.0785424π0.0785424\pi
−0.273327 + 0.961921i 0.588124π0.588124\pi
270270 0 0
271271 −11.2562 6.49877i −0.683766 0.394772i 0.117507 0.993072i 0.462510π-0.462510\pi
−0.801272 + 0.598300i 0.795843π0.795843\pi
272272 −5.70407 −0.345860
273273 0 0
274274 21.8022 1.31712
275275 −0.699399 0.403798i −0.0421753 0.0243499i
276276 0 0
277277 −13.4753 23.3399i −0.809652 1.40236i −0.913105 0.407724i 0.866323π-0.866323\pi
0.103453 0.994634i 0.467011π-0.467011\pi
278278 16.4491i 0.986551i
279279 0 0
280280 −1.89787 + 1.09573i −0.113419 + 0.0654827i
281281 0.0773961i 0.00461706i 0.999997 + 0.00230853i 0.000734829π0.000734829\pi
−0.999997 + 0.00230853i 0.999265π0.999265\pi
282282 0 0
283283 11.1534 19.3183i 0.663002 1.14835i −0.316821 0.948485i 0.602616π-0.602616\pi
0.979823 0.199867i 0.0640511π-0.0640511\pi
284284 −7.21341 4.16466i −0.428037 0.247127i
285285 0 0
286286 4.72618 + 13.9684i 0.279465 + 0.825970i
287287 −3.62683 −0.214085
288288 0 0
289289 −7.76822 + 13.4550i −0.456954 + 0.791468i
290290 10.7577 + 18.6328i 0.631712 + 1.09416i
291291 0 0
292292 6.38958 3.68903i 0.373922 0.215884i
293293 −5.16126 + 2.97986i −0.301524 + 0.174085i −0.643127 0.765759i 0.722363π-0.722363\pi
0.341603 + 0.939844i 0.389030π0.389030\pi
294294 0 0
295295 −5.32391 9.22128i −0.309970 0.536884i
296296 −5.07736 + 8.79425i −0.295116 + 0.511155i
297297 0 0
298298 −14.7828 −0.856344
299299 −5.89243 + 6.70559i −0.340768 + 0.387794i
300300 0 0
301301 −2.38624 1.37769i −0.137540 0.0794089i
302302 −9.49478 + 16.4454i −0.546363 + 0.946329i
303303 0 0
304304 7.73201i 0.443461i
305305 21.3865 12.3475i 1.22459 0.707015i
306306 0 0
307307 31.1089i 1.77548i 0.460349 + 0.887738i 0.347724π0.347724\pi
−0.460349 + 0.887738i 0.652276π0.652276\pi
308308 −2.04495 3.54195i −0.116522 0.201821i
309309 0 0
310310 −13.6553 7.88389i −0.775569 0.447775i
311311 −3.48435 −0.197579 −0.0987896 0.995108i 0.531497π-0.531497\pi
−0.0987896 + 0.995108i 0.531497π0.531497\pi
312312 0 0
313313 10.2750 0.580779 0.290389 0.956909i 0.406215π-0.406215\pi
0.290389 + 0.956909i 0.406215π0.406215\pi
314314 11.7324 + 6.77371i 0.662098 + 0.382262i
315315 0 0
316316 1.72917 + 2.99501i 0.0972734 + 0.168483i
317317 26.5282i 1.48997i 0.667080 + 0.744986i 0.267544π0.267544\pi
−0.667080 + 0.744986i 0.732456π0.732456\pi
318318 0 0
319319 −34.7740 + 20.0768i −1.94697 + 1.12408i
320320 2.19147i 0.122507i
321321 0 0
322322 1.23791 2.14412i 0.0689860 0.119487i
323323 38.1951 + 22.0520i 2.12523 + 1.22700i
324324 0 0
325325 0.698140 + 0.139589i 0.0387258 + 0.00774302i
326326 4.46294 0.247180
327327 0 0
328328 −1.81341 + 3.14093i −0.100129 + 0.173429i
329329 −3.85004 6.66847i −0.212260 0.367645i
330330 0 0
331331 −24.8329 + 14.3373i −1.36494 + 0.788048i −0.990277 0.139113i 0.955575π-0.955575\pi
−0.374663 + 0.927161i 0.622242π0.622242\pi
332332 −0.288199 + 0.166392i −0.0158170 + 0.00913192i
333333 0 0
334334 −1.65381 2.86448i −0.0904924 0.156737i
335335 −6.94739 + 12.0332i −0.379576 + 0.657445i
336336 0 0
337337 4.82923 0.263065 0.131532 0.991312i 0.458010π-0.458010\pi
0.131532 + 0.991312i 0.458010π0.458010\pi
338338 −7.89340 10.3293i −0.429345 0.561839i
339339 0 0
340340 10.8256 + 6.25015i 0.587099 + 0.338962i
341341 14.7135 25.4846i 0.796783 1.38007i
342342 0 0
343343 1.00000i 0.0539949i
344344 −2.38624 + 1.37769i −0.128657 + 0.0742803i
345345 0 0
346346 10.1221i 0.544170i
347347 15.2594 + 26.4300i 0.819167 + 1.41884i 0.906297 + 0.422642i 0.138897π0.138897\pi
−0.0871296 + 0.996197i 0.527769π0.527769\pi
348348 0 0
349349 −4.60570 2.65910i −0.246537 0.142338i 0.371640 0.928377i 0.378795π-0.378795\pi
−0.618178 + 0.786038i 0.712129π0.712129\pi
350350 −0.197462 −0.0105548
351351 0 0
352352 −4.08989 −0.217992
353353 24.4457 + 14.1137i 1.30111 + 0.751199i 0.980595 0.196043i 0.0628094π-0.0628094\pi
0.320519 + 0.947242i 0.396143π0.396143\pi
354354 0 0
355355 9.12673 + 15.8080i 0.484397 + 0.839000i
356356 13.5275i 0.716956i
357357 0 0
358358 8.01210 4.62579i 0.423453 0.244481i
359359 7.58573i 0.400359i 0.979759 + 0.200180i 0.0641526π0.0641526\pi
−0.979759 + 0.200180i 0.935847π0.935847\pi
360360 0 0
361361 20.3920 35.3200i 1.07326 1.85895i
362362 −20.1476 11.6322i −1.05894 0.611377i
363363 0 0
364364 2.70844 + 2.38000i 0.141961 + 0.124746i
365365 −16.1688 −0.846313
366366 0 0
367367 5.92558 10.2634i 0.309313 0.535746i −0.668899 0.743353i 0.733234π-0.733234\pi
0.978212 + 0.207607i 0.0665676π0.0665676\pi
368368 −1.23791 2.14412i −0.0645305 0.111770i
369369 0 0
370370 19.2723 11.1269i 1.00192 0.578459i
371371 5.46559 3.15556i 0.283759 0.163828i
372372 0 0
373373 14.9133 + 25.8306i 0.772182 + 1.33746i 0.936365 + 0.351028i 0.114168π0.114168\pi
−0.164183 + 0.986430i 0.552499π0.552499\pi
374374 −11.6645 + 20.2035i −0.603158 + 1.04470i
375375 0 0
376376 −7.70008 −0.397101
377377 23.3662 26.5908i 1.20342 1.36949i
378378 0 0
379379 −1.55298 0.896611i −0.0797711 0.0460558i 0.459584 0.888134i 0.347999π-0.347999\pi
−0.539355 + 0.842079i 0.681332π0.681332\pi
380380 8.47223 14.6743i 0.434616 0.752778i
381381 0 0
382382 8.90192i 0.455462i
383383 −14.4611 + 8.34912i −0.738927 + 0.426620i −0.821679 0.569950i 0.806962π-0.806962\pi
0.0827518 + 0.996570i 0.473629π0.473629\pi
384384 0 0
385385 8.96287i 0.456790i
386386 −4.44417 7.69754i −0.226203 0.391794i
387387 0 0
388388 10.0600 + 5.80816i 0.510720 + 0.294864i
389389 −15.6288 −0.792413 −0.396207 0.918161i 0.629674π-0.629674\pi
−0.396207 + 0.918161i 0.629674π0.629674\pi
390390 0 0
391391 −14.1222 −0.714192
392392 −0.866025 0.500000i −0.0437409 0.0252538i
393393 0 0
394394 −11.6963 20.2586i −0.589251 1.02061i
395395 7.57885i 0.381333i
396396 0 0
397397 4.86182 2.80697i 0.244008 0.140878i −0.373010 0.927827i 0.621674π-0.621674\pi
0.617017 + 0.786950i 0.288341π0.288341\pi
398398 3.93608i 0.197298i
399399 0 0
400400 −0.0987308 + 0.171007i −0.00493654 + 0.00855034i
401401 −21.8559 12.6185i −1.09143 0.630139i −0.157475 0.987523i 0.550335π-0.550335\pi
−0.933957 + 0.357384i 0.883669π0.883669\pi
402402 0 0
403403 −5.08633 + 25.4387i −0.253368 + 1.26719i
404404 2.25385 0.112133
405405 0 0
406406 −4.90888 + 8.50243i −0.243624 + 0.421969i
407407 20.7659 + 35.9675i 1.02933 + 1.78284i
408408 0 0
409409 25.0467 14.4607i 1.23848 0.715037i 0.269697 0.962945i 0.413076π-0.413076\pi
0.968784 + 0.247908i 0.0797430π0.0797430\pi
410410 6.88324 3.97404i 0.339939 0.196264i
411411 0 0
412412 −8.01627 13.8846i −0.394933 0.684045i
413413 2.42938 4.20781i 0.119542 0.207053i
414414 0 0
415415 0.729284 0.0357991
416416 3.41535 1.15558i 0.167452 0.0566568i
417417 0 0
418418 27.3864 + 15.8115i 1.33951 + 0.773368i
419419 −16.0468 + 27.7939i −0.783938 + 1.35782i 0.145693 + 0.989330i 0.453459π0.453459\pi
−0.929631 + 0.368491i 0.879875π0.879875\pi
420420 0 0
421421 1.02963i 0.0501810i 0.999685 + 0.0250905i 0.00798740π0.00798740\pi
−0.999685 + 0.0250905i 0.992013π0.992013\pi
422422 11.0869 6.40104i 0.539703 0.311598i
423423 0 0
424424 6.31111i 0.306495i
425425 0.563168 + 0.975435i 0.0273176 + 0.0473155i
426426 0 0
427427 9.75896 + 5.63434i 0.472269 + 0.272665i
428428 8.61586 0.416464
429429 0 0
430430 6.03835 0.291195
431431 30.5908 + 17.6616i 1.47350 + 0.850728i 0.999555 0.0298236i 0.00949455π-0.00949455\pi
0.473950 + 0.880552i 0.342828π0.342828\pi
432432 0 0
433433 10.0469 + 17.4018i 0.482824 + 0.836276i 0.999806 0.0197204i 0.00627760π-0.00627760\pi
−0.516981 + 0.855997i 0.672944π0.672944\pi
434434 7.19507i 0.345375i
435435 0 0
436436 8.68777 5.01589i 0.416069 0.240217i
437437 19.1431i 0.915736i
438438 0 0
439439 6.52940 11.3093i 0.311631 0.539761i −0.667084 0.744982i 0.732458π-0.732458\pi
0.978716 + 0.205221i 0.0657913π0.0657913\pi
440440 7.76207 + 4.48144i 0.370042 + 0.213644i
441441 0 0
442442 4.03232 20.1672i 0.191798 0.959254i
443443 −7.46148 −0.354506 −0.177253 0.984165i 0.556721π-0.556721\pi
−0.177253 + 0.984165i 0.556721π0.556721\pi
444444 0 0
445445 −14.8225 + 25.6734i −0.702656 + 1.21704i
446446 −9.42444 16.3236i −0.446260 0.772945i
447447 0 0
448448 −0.866025 + 0.500000i −0.0409159 + 0.0236228i
449449 8.28796 4.78506i 0.391133 0.225821i −0.291518 0.956565i 0.594160π-0.594160\pi
0.682651 + 0.730745i 0.260827π0.260827\pi
450450 0 0
451451 7.41667 + 12.8460i 0.349237 + 0.604897i
452452 −9.27760 + 16.0693i −0.436382 + 0.755835i
453453 0 0
454454 −1.31920 −0.0619130
455455 −2.53241 7.48464i −0.118721 0.350886i
456456 0 0
457457 22.3679 + 12.9141i 1.04633 + 0.604097i 0.921619 0.388097i 0.126867π-0.126867\pi
0.124708 + 0.992194i 0.460201π0.460201\pi
458458 2.17054 3.75949i 0.101423 0.175670i
459459 0 0
460460 5.42568i 0.252974i
461461 1.35535 0.782512i 0.0631250 0.0364452i −0.468105 0.883673i 0.655063π-0.655063\pi
0.531230 + 0.847227i 0.321730π0.321730\pi
462462 0 0
463463 20.4863i 0.952080i 0.879424 + 0.476040i 0.157928π0.157928\pi
−0.879424 + 0.476040i 0.842072π0.842072\pi
464464 4.90888 + 8.50243i 0.227889 + 0.394716i
465465 0 0
466466 −4.99196 2.88211i −0.231248 0.133511i
467467 3.80822 0.176224 0.0881118 0.996111i 0.471917π-0.471917\pi
0.0881118 + 0.996111i 0.471917π0.471917\pi
468468 0 0
469469 −6.34039 −0.292772
470470 14.6137 + 8.43725i 0.674082 + 0.389181i
471471 0 0
472472 −2.42938 4.20781i −0.111821 0.193680i
473473 11.2692i 0.518160i
474474 0 0
475475 1.32223 0.763388i 0.0606679 0.0350266i
476476 5.70407i 0.261446i
477477 0 0
478478 6.54753 11.3407i 0.299477 0.518710i
479479 20.8886 + 12.0600i 0.954425 + 0.551037i 0.894453 0.447163i 0.147566π-0.147566\pi
0.0599720 + 0.998200i 0.480899π0.480899\pi
480480 0 0
481481 −27.5034 24.1682i −1.25405 1.10197i
482482 0.450067 0.0205000
483483 0 0
484484 −2.86360 + 4.95991i −0.130164 + 0.225450i
485485 −12.7284 22.0462i −0.577967 1.00107i
486486 0 0
487487 −6.65422 + 3.84182i −0.301532 + 0.174089i −0.643131 0.765756i 0.722365π-0.722365\pi
0.341599 + 0.939846i 0.389031π0.389031\pi
488488 9.75896 5.63434i 0.441767 0.255054i
489489 0 0
490490 1.09573 + 1.89787i 0.0495002 + 0.0857369i
491491 −16.2767 + 28.1921i −0.734557 + 1.27229i 0.220360 + 0.975419i 0.429277π0.429277\pi
−0.954917 + 0.296872i 0.904056π0.904056\pi
492492 0 0
493493 56.0012 2.52217
494494 −27.3371 5.46590i −1.22995 0.245923i
495495 0 0
496496 −6.23112 3.59754i −0.279785 0.161534i
497497 −4.16466 + 7.21341i −0.186811 + 0.323566i
498498 0 0
499499 5.87524i 0.263012i 0.991315 + 0.131506i 0.0419813π0.0419813\pi
−0.991315 + 0.131506i 0.958019π0.958019\pi
500500 9.86410 5.69504i 0.441136 0.254690i
501501 0 0
502502 18.7022i 0.834721i
503503 11.0238 + 19.0939i 0.491529 + 0.851353i 0.999952 0.00975426i 0.00310493π-0.00310493\pi
−0.508424 + 0.861107i 0.669772π0.669772\pi
504504 0 0
505505 −4.27750 2.46962i −0.190346 0.109897i
506506 −10.1258 −0.450148
507507 0 0
508508 −0.264877 −0.0117520
509509 5.86940 + 3.38870i 0.260156 + 0.150201i 0.624406 0.781100i 0.285341π-0.285341\pi
−0.364249 + 0.931301i 0.618674π0.618674\pi
510510 0 0
511511 −3.68903 6.38958i −0.163193 0.282658i
512512 1.00000i 0.0441942i
513513 0 0
514514 17.1287 9.88929i 0.755517 0.436198i
515515 35.1348i 1.54823i
516516 0 0
517517 −15.7463 + 27.2733i −0.692519 + 1.19948i
518518 8.79425 + 5.07736i 0.386397 + 0.223086i
519519 0 0
520520 −7.74810 1.54919i −0.339777 0.0679365i
521521 2.61232 0.114448 0.0572240 0.998361i 0.481775π-0.481775\pi
0.0572240 + 0.998361i 0.481775π0.481775\pi
522522 0 0
523523 −4.02060 + 6.96388i −0.175809 + 0.304509i −0.940441 0.339957i 0.889587π-0.889587\pi
0.764632 + 0.644467i 0.222921π0.222921\pi
524524 2.55119 + 4.41878i 0.111449 + 0.193035i
525525 0 0
526526 −20.3903 + 11.7723i −0.889059 + 0.513299i
527527 −35.5427 + 20.5206i −1.54827 + 0.893892i
528528 0 0
529529 8.43516 + 14.6101i 0.366746 + 0.635223i
530530 −6.91531 + 11.9777i −0.300382 + 0.520276i
531531 0 0
532532 7.73201 0.335225
533533 −9.82303 8.63184i −0.425483 0.373886i
534534 0 0
535535 −16.3518 9.44070i −0.706949 0.408157i
536536 −3.17020 + 5.49094i −0.136932 + 0.237172i
537537 0 0
538538 22.8431i 0.984836i
539539 −3.54195 + 2.04495i −0.152563 + 0.0880820i
540540 0 0
541541 21.6552i 0.931029i −0.885040 0.465514i 0.845869π-0.845869\pi
0.885040 0.465514i 0.154131π-0.154131\pi
542542 6.49877 + 11.2562i 0.279146 + 0.483495i
543543 0 0
544544 4.93987 + 2.85204i 0.211795 + 0.122280i
545545 −21.9843 −0.941705
546546 0 0
547547 −32.9495 −1.40882 −0.704409 0.709795i 0.748788π-0.748788\pi
−0.704409 + 0.709795i 0.748788π0.748788\pi
548548 −18.8812 10.9011i −0.806566 0.465671i
549549 0 0
550550 0.403798 + 0.699399i 0.0172180 + 0.0298225i
551551 75.9111i 3.23392i
552552 0 0
553553 2.99501 1.72917i 0.127361 0.0735318i
554554 26.9506i 1.14502i
555555 0 0
556556 8.22455 14.2453i 0.348799 0.604137i
557557 0.280535 + 0.161967i 0.0118866 + 0.00686276i 0.505932 0.862574i 0.331149π-0.331149\pi
−0.494045 + 0.869436i 0.664482π0.664482\pi
558558 0 0
559559 −3.18406 9.41062i −0.134671 0.398027i
560560 2.19147 0.0926065
561561 0 0
562562 0.0386980 0.0670270i 0.00163238 0.00282736i
563563 −18.3668 31.8123i −0.774070 1.34073i −0.935316 0.353815i 0.884884π-0.884884\pi
0.161245 0.986914i 0.448449π-0.448449\pi
564564 0 0
565565 35.2153 20.3316i 1.48152 0.855356i
566566 −19.3183 + 11.1534i −0.812008 + 0.468813i
567567 0 0
568568 4.16466 + 7.21341i 0.174745 + 0.302668i
569569 1.32995 2.30354i 0.0557544 0.0965695i −0.836801 0.547507i 0.815577π-0.815577\pi
0.892556 + 0.450937i 0.148910π0.148910\pi
570570 0 0
571571 4.29994 0.179947 0.0899735 0.995944i 0.471322π-0.471322\pi
0.0899735 + 0.995944i 0.471322π0.471322\pi
572572 2.89122 14.4601i 0.120888 0.604607i
573573 0 0
574574 3.14093 + 1.81341i 0.131100 + 0.0756905i
575575 −0.244439 + 0.423381i −0.0101938 + 0.0176562i
576576 0 0
577577 2.08429i 0.0867702i −0.999058 0.0433851i 0.986186π-0.986186\pi
0.999058 0.0433851i 0.0138142π-0.0138142\pi
578578 13.4550 7.76822i 0.559652 0.323115i
579579 0 0
580580 21.5153i 0.893375i
581581 0.166392 + 0.288199i 0.00690308 + 0.0119565i
582582 0 0
583583 −22.3536 12.9059i −0.925793 0.534507i
584584 −7.37805 −0.305306
585585 0 0
586586 5.95971 0.246193
587587 −12.9028 7.44945i −0.532556 0.307472i 0.209500 0.977809i 0.432816π-0.432816\pi
−0.742057 + 0.670337i 0.766150π0.766150\pi
588588 0 0
589589 27.8162 + 48.1791i 1.14615 + 1.98518i
590590 10.6478i 0.438364i
591591 0 0
592592 8.79425 5.07736i 0.361441 0.208678i
593593 1.36361i 0.0559968i −0.999608 0.0279984i 0.991087π-0.991087\pi
0.999608 0.0279984i 0.00891334π-0.00891334\pi
594594 0 0
595595 6.25015 10.8256i 0.256231 0.443805i
596596 12.8023 + 7.39139i 0.524401 + 0.302763i
597597 0 0
598598 8.45579 2.86100i 0.345783 0.116995i
599599 −18.0030 −0.735581 −0.367790 0.929909i 0.619886π-0.619886\pi
−0.367790 + 0.929909i 0.619886π0.619886\pi
600600 0 0
601601 6.76892 11.7241i 0.276110 0.478237i −0.694305 0.719681i 0.744288π-0.744288\pi
0.970415 + 0.241445i 0.0776213π0.0776213\pi
602602 1.37769 + 2.38624i 0.0561506 + 0.0972557i
603603 0 0
604604 16.4454 9.49478i 0.669155 0.386337i
605605 10.8695 6.27550i 0.441907 0.255135i
606606 0 0
607607 1.10556 + 1.91489i 0.0448733 + 0.0777228i 0.887590 0.460635i 0.152378π-0.152378\pi
−0.842716 + 0.538358i 0.819045π0.819045\pi
608608 3.86601 6.69612i 0.156787 0.271563i
609609 0 0
610610 −24.6950 −0.999870
611611 5.44333 27.2242i 0.220214 1.10137i
612612 0 0
613613 22.5849 + 13.0394i 0.912195 + 0.526656i 0.881137 0.472862i 0.156779π-0.156779\pi
0.0310579 + 0.999518i 0.490112π0.490112\pi
614614 15.5544 26.9411i 0.627726 1.08725i
615615 0 0
616616 4.08989i 0.164786i
617617 24.5921 14.1983i 0.990042 0.571601i 0.0847549 0.996402i 0.472989π-0.472989\pi
0.905287 + 0.424801i 0.139656π0.139656\pi
618618 0 0
619619 14.7197i 0.591633i 0.955245 + 0.295817i 0.0955918π0.0955918\pi
−0.955245 + 0.295817i 0.904408π0.904408\pi
620620 7.88389 + 13.6553i 0.316625 + 0.548410i
621621 0 0
622622 3.01753 + 1.74217i 0.120992 + 0.0698548i
623623 −13.5275 −0.541967
624624 0 0
625625 −23.9737 −0.958948
626626 −8.89843 5.13751i −0.355653 0.205336i
627627 0 0
628628 −6.77371 11.7324i −0.270300 0.468174i
629629 57.9233i 2.30955i
630630 0 0
631631 −24.3684 + 14.0691i −0.970090 + 0.560082i −0.899264 0.437407i 0.855897π-0.855897\pi
−0.0708262 + 0.997489i 0.522564π0.522564\pi
632632 3.45834i 0.137565i
633633 0 0
634634 13.2641 22.9741i 0.526785 0.912418i
635635 0.502702 + 0.290235i 0.0199491 + 0.0115176i
636636 0 0
637637 2.38000 2.70844i 0.0942988 0.107312i
638638 40.1536 1.58970
639639 0 0
640640 1.09573 1.89787i 0.0433127 0.0750198i
641641 −3.89572 6.74758i −0.153872 0.266513i 0.778776 0.627302i 0.215841π-0.215841\pi
−0.932648 + 0.360789i 0.882508π0.882508\pi
642642 0 0
643643 −29.3656 + 16.9542i −1.15807 + 0.668610i −0.950840 0.309683i 0.899777π-0.899777\pi
−0.207227 + 0.978293i 0.566444π0.566444\pi
644644 −2.14412 + 1.23791i −0.0844902 + 0.0487804i
645645 0 0
646646 −22.0520 38.1951i −0.867624 1.50277i
647647 −2.20290 + 3.81554i −0.0866050 + 0.150004i −0.906074 0.423119i 0.860935π-0.860935\pi
0.819469 + 0.573123i 0.194268π0.194268\pi
648648 0 0
649649 −19.8718 −0.780036
650650 −0.534812 0.469958i −0.0209771 0.0184333i
651651 0 0
652652 −3.86502 2.23147i −0.151366 0.0873912i
653653 13.8081 23.9163i 0.540352 0.935916i −0.458532 0.888678i 0.651625π-0.651625\pi
0.998884 0.0472385i 0.0150421π-0.0150421\pi
654654 0 0
655655 11.1817i 0.436905i
656656 3.14093 1.81341i 0.122633 0.0708019i
657657 0 0
658658 7.70008i 0.300181i
659659 3.72022 + 6.44362i 0.144919 + 0.251008i 0.929343 0.369218i 0.120374π-0.120374\pi
−0.784423 + 0.620226i 0.787041π0.787041\pi
660660 0 0
661661 1.02781 + 0.593407i 0.0399772 + 0.0230809i 0.519855 0.854254i 0.325986π-0.325986\pi
−0.479878 + 0.877335i 0.659319π0.659319\pi
662662 28.6746 1.11447
663663 0 0
664664 0.332783 0.0129145
665665 −14.6743 8.47223i −0.569047 0.328539i
666666 0 0
667667 12.1535 + 21.0505i 0.470585 + 0.815077i
668668 3.30762i 0.127976i
669669 0 0
670670 12.0332 6.94739i 0.464884 0.268401i
671671 46.0876i 1.77919i
672672 0 0
673673 −1.14981 + 1.99153i −0.0443219 + 0.0767678i −0.887335 0.461125i 0.847446π-0.847446\pi
0.843013 + 0.537893i 0.180779π0.180779\pi
674674 −4.18223 2.41461i −0.161094 0.0930074i
675675 0 0
676676 1.67124 + 12.8921i 0.0642786 + 0.495851i
677677 −6.12752 −0.235500 −0.117750 0.993043i 0.537568π-0.537568\pi
−0.117750 + 0.993043i 0.537568π0.537568\pi
678678 0 0
679679 5.80816 10.0600i 0.222897 0.386068i
680680 −6.25015 10.8256i −0.239682 0.415142i
681681 0 0
682682 −25.4846 + 14.7135i −0.975855 + 0.563410i
683683 8.69462 5.01984i 0.332691 0.192079i −0.324344 0.945939i 0.605144π-0.605144\pi
0.657035 + 0.753860i 0.271810π0.271810\pi
684684 0 0
685685 23.8894 + 41.3776i 0.912766 + 1.58096i
686686 −0.500000 + 0.866025i −0.0190901 + 0.0330650i
687687 0 0
688688 2.75539 0.105048
689689 22.3134 + 4.46144i 0.850073 + 0.169967i
690690 0 0
691691 −19.2007 11.0855i −0.730428 0.421713i 0.0881509 0.996107i 0.471904π-0.471904\pi
−0.818579 + 0.574394i 0.805238π0.805238\pi
692692 5.06107 8.76603i 0.192393 0.333235i
693693 0 0
694694 30.5188i 1.15848i
695695 −31.2182 + 18.0238i −1.18417 + 0.683684i
696696 0 0
697697 20.6877i 0.783602i
698698 2.65910 + 4.60570i 0.100648 + 0.174328i
699699 0 0
700700 0.171007 + 0.0987308i 0.00646345 + 0.00373167i
701701 −21.3510 −0.806416 −0.403208 0.915108i 0.632105π-0.632105\pi
−0.403208 + 0.915108i 0.632105π0.632105\pi
702702 0 0
703703 −78.5165 −2.96130
704704 3.54195 + 2.04495i 0.133492 + 0.0770718i
705705 0 0
706706 −14.1137 24.4457i −0.531178 0.920027i
707707 2.25385i 0.0847646i
708708 0 0
709709 21.5442 12.4385i 0.809109 0.467139i −0.0375376 0.999295i 0.511951π-0.511951\pi
0.846646 + 0.532156i 0.178618π0.178618\pi
710710 18.2535i 0.685040i
711711 0 0
712712 −6.76374 + 11.7151i −0.253482 + 0.439044i
713713 −15.4271 8.90685i −0.577750 0.333564i
714714 0 0
715715 −21.3316 + 24.2754i −0.797756 + 0.907847i
716716 −9.25158 −0.345748
717717 0 0
718718 3.79286 6.56943i 0.141548 0.245169i
719719 −11.5010 19.9203i −0.428914 0.742901i 0.567863 0.823123i 0.307770π-0.307770\pi
−0.996777 + 0.0802222i 0.974437π0.974437\pi
720720 0 0
721721 −13.8846 + 8.01627i −0.517089 + 0.298542i
722722 −35.3200 + 20.3920i −1.31447 + 0.758912i
723723 0 0
724724 11.6322 + 20.1476i 0.432309 + 0.748781i
725725 0.969316 1.67890i 0.0359995 0.0623529i
726726 0 0
727727 −3.42508 −0.127029 −0.0635146 0.997981i 0.520231π-0.520231\pi
−0.0635146 + 0.997981i 0.520231π0.520231\pi
728728 −1.15558 3.41535i −0.0428285 0.126581i
729729 0 0
730730 14.0026 + 8.08439i 0.518258 + 0.299217i
731731 7.85846 13.6113i 0.290656 0.503431i
732732 0 0
733733 21.6929i 0.801247i 0.916243 + 0.400624i 0.131206π0.131206\pi
−0.916243 + 0.400624i 0.868794π0.868794\pi
734734 −10.2634 + 5.92558i −0.378829 + 0.218717i
735735 0 0
736736 2.47582i 0.0912598i
737737 12.9658 + 22.4573i 0.477600 + 0.827227i
738738 0 0
739739 −44.6284 25.7662i −1.64168 0.947826i −0.980236 0.197833i 0.936610π-0.936610\pi
−0.661447 0.749992i 0.730057π-0.730057\pi
740740 −22.2538 −0.818065
741741 0 0
742742 −6.31111 −0.231688
743743 41.6540 + 24.0489i 1.52814 + 0.882270i 0.999440 + 0.0334593i 0.0106524π0.0106524\pi
0.528697 + 0.848811i 0.322681π0.322681\pi
744744 0 0
745745 −16.1980 28.0558i −0.593449 1.02788i
746746 29.8266i 1.09203i
747747 0 0
748748 20.2035 11.6645i 0.738714 0.426497i
749749 8.61586i 0.314817i
750750 0 0
751751 −14.7133 + 25.4842i −0.536896 + 0.929931i 0.462173 + 0.886790i 0.347070π0.347070\pi
−0.999069 + 0.0431415i 0.986263π0.986263\pi
752752 6.66847 + 3.85004i 0.243174 + 0.140397i
753753 0 0
754754 −33.5311 + 11.3452i −1.22113 + 0.413167i
755755 −41.6150 −1.51453
756756 0 0
757757 10.0541 17.4142i 0.365423 0.632931i −0.623421 0.781886i 0.714258π-0.714258\pi
0.988844 + 0.148955i 0.0475911π0.0475911\pi
758758 0.896611 + 1.55298i 0.0325664 + 0.0564067i
759759 0 0
760760 −14.6743 + 8.47223i −0.532294 + 0.307320i
761761 −28.0939 + 16.2200i −1.01840 + 0.587976i −0.913642 0.406521i 0.866742π-0.866742\pi
−0.104763 + 0.994497i 0.533409π0.533409\pi
762762 0 0
763763 −5.01589 8.68777i −0.181587 0.314518i
764764 4.45096 7.70929i 0.161030 0.278912i
765765 0 0
766766 16.6982 0.603332
767767 16.5944 5.61466i 0.599188 0.202734i
768768 0 0
769769 −37.1542 21.4510i −1.33982 0.773543i −0.353036 0.935610i 0.614851π-0.614851\pi
−0.986780 + 0.162067i 0.948184π0.948184\pi
770770 4.48144 7.76207i 0.161500 0.279726i
771771 0 0
772772 8.88835i 0.319899i
773773 −12.8157 + 7.39912i −0.460947 + 0.266128i −0.712442 0.701731i 0.752411π-0.752411\pi
0.251495 + 0.967858i 0.419078π0.419078\pi
774774 0 0
775775 1.42075i 0.0510349i
776776 −5.80816 10.0600i −0.208501 0.361134i
777777 0 0
778778 13.5350 + 7.81441i 0.485252 + 0.280160i
779779 −28.0427 −1.00473
780780 0 0
781781 34.0660 1.21898
782782 12.2302 + 7.06112i 0.437352 + 0.252505i
783783 0 0
784784 0.500000 + 0.866025i 0.0178571 + 0.0309295i
785785 29.6887i 1.05964i
786786 0 0
787787 24.2123 13.9790i 0.863076 0.498297i −0.00196533 0.999998i 0.500626π-0.500626\pi
0.865041 + 0.501701i 0.167292π0.167292\pi
788788 23.3926i 0.833326i
789789 0 0
790790 −3.78942 + 6.56347i −0.134822 + 0.233518i
791791 16.0693 + 9.27760i 0.571358 + 0.329873i
792792 0 0
793793 13.0218 + 38.4865i 0.462418 + 1.36670i
794794 −5.61394 −0.199231
795795 0 0
796796 1.96804 3.40875i 0.0697554 0.120820i
797797 8.78182 + 15.2106i 0.311068 + 0.538786i 0.978594 0.205801i 0.0659800π-0.0659800\pi
−0.667526 + 0.744587i 0.732647π0.732647\pi
798798 0 0
799799 38.0374 21.9609i 1.34567 0.776921i
800800 0.171007 0.0987308i 0.00604600 0.00349066i
801801 0 0
802802 12.6185 + 21.8559i 0.445575 + 0.771759i
803803 −15.0877 + 26.1327i −0.532434 + 0.922203i
804804 0 0
805805 5.42568 0.191230
806806 17.1242 19.4874i 0.603176 0.686414i
807807 0 0
808808 −1.95189 1.12692i −0.0686672 0.0396450i
809809 5.97749 10.3533i 0.210157 0.364003i −0.741606 0.670835i 0.765936π-0.765936\pi
0.951764 + 0.306832i 0.0992690π0.0992690\pi
810810 0 0
811811 5.88549i 0.206667i −0.994647 0.103334i 0.967049π-0.967049\pi
0.994647 0.103334i 0.0329510π-0.0329510\pi
812812 8.50243 4.90888i 0.298377 0.172268i
813813 0 0
814814 41.5317i 1.45569i
815815 4.89020 + 8.47008i 0.171296 + 0.296694i
816816 0 0
817817 −18.4504 10.6523i −0.645498 0.372678i
818818 −28.9215 −1.01122
819819 0 0
820820 −7.94809 −0.277559
821821 26.2172 + 15.1365i 0.914987 + 0.528268i 0.882032 0.471189i 0.156175π-0.156175\pi
0.0329546 + 0.999457i 0.489508π0.489508\pi
822822 0 0
823823 18.2981 + 31.6932i 0.637831 + 1.10476i 0.985908 + 0.167290i 0.0535016π0.0535016\pi
−0.348076 + 0.937466i 0.613165π0.613165\pi
824824 16.0325i 0.558520i
825825 0 0
826826 −4.20781 + 2.42938i −0.146408 + 0.0845289i
827827 43.4520i 1.51098i −0.655163 0.755488i 0.727400π-0.727400\pi
0.655163 0.755488i 0.272600π-0.272600\pi
828828 0 0
829829 −0.418633 + 0.725093i −0.0145397 + 0.0251835i −0.873204 0.487355i 0.837962π-0.837962\pi
0.858664 + 0.512539i 0.171295π0.171295\pi
830830 −0.631578 0.364642i −0.0219224 0.0126569i
831831 0 0
832832 −3.53557 0.706919i −0.122574 0.0245080i
833833 5.70407 0.197634
834834 0 0
835835 3.62427 6.27742i 0.125423 0.217239i
836836 −15.8115 27.3864i −0.546854 0.947178i
837837 0 0
838838 27.7939 16.0468i 0.960124 0.554328i
839839 33.2964 19.2237i 1.14952 0.663675i 0.200749 0.979643i 0.435663π-0.435663\pi
0.948770 + 0.315968i 0.102329π0.102329\pi
840840 0 0
841841 −33.6942 58.3601i −1.16187 2.01242i
842842 0.514814 0.891684i 0.0177417 0.0307295i
843843 0 0
844844 −12.8021 −0.440666
845845 10.9545 26.2988i 0.376848 0.904706i
846846 0 0
847847 4.95991 + 2.86360i 0.170424 + 0.0983946i
848848 −3.15556 + 5.46559i −0.108362 + 0.187689i
849849 0 0
850850 1.12634i 0.0386330i
851851 21.7730 12.5706i 0.746367 0.430915i
852852 0 0
853853 32.9422i 1.12792i 0.825803 + 0.563959i 0.190722π0.190722\pi
−0.825803 + 0.563959i 0.809278π0.809278\pi
854854 −5.63434 9.75896i −0.192803 0.333945i
855855 0 0
856856 −7.46156 4.30793i −0.255031 0.147242i
857857 22.1242 0.755750 0.377875 0.925857i 0.376655π-0.376655\pi
0.377875 + 0.925857i 0.376655π0.376655\pi
858858 0 0
859859 18.4476 0.629425 0.314712 0.949187i 0.398092π-0.398092\pi
0.314712 + 0.949187i 0.398092π0.398092\pi
860860 −5.22936 3.01917i −0.178320 0.102953i
861861 0 0
862862 −17.6616 30.5908i −0.601556 1.04193i
863863 45.1859i 1.53814i −0.639162 0.769072i 0.720719π-0.720719\pi
0.639162 0.769072i 0.279281π-0.279281\pi
864864 0 0
865865 −19.2105 + 11.0912i −0.653176 + 0.377112i
866866 20.0939i 0.682817i
867867 0 0
868868 −3.59754 + 6.23112i −0.122108 + 0.211498i
869869 −12.2493 7.07212i −0.415528 0.239905i
870870 0 0
871871 −17.1725 15.0901i −0.581869 0.511309i
872872 −10.0318 −0.339719
873873 0 0
874874 9.57153 16.5784i 0.323762 0.560772i
875875 −5.69504 9.86410i −0.192527 0.333467i
876876 0 0
877877 15.2612 8.81106i 0.515334 0.297528i −0.219689 0.975570i 0.570504π-0.570504\pi
0.735024 + 0.678041i 0.237171π0.237171\pi
878878 −11.3093 + 6.52940i −0.381669 + 0.220357i
879879 0 0
880880 −4.48144 7.76207i −0.151069 0.261659i
881881 −1.23560 + 2.14012i −0.0416283 + 0.0721023i −0.886089 0.463515i 0.846588π-0.846588\pi
0.844461 + 0.535618i 0.179921π0.179921\pi
882882 0 0
883883 −3.93880 −0.132551 −0.0662756 0.997801i 0.521112π-0.521112\pi
−0.0662756 + 0.997801i 0.521112π0.521112\pi
884884 −13.5757 + 15.4491i −0.456599 + 0.519610i
885885 0 0
886886 6.46183 + 3.73074i 0.217089 + 0.125337i
887887 −3.57140 + 6.18584i −0.119916 + 0.207700i −0.919734 0.392542i 0.871596π-0.871596\pi
0.799818 + 0.600242i 0.204929π0.204929\pi
888888 0 0
889889 0.264877i 0.00888370i
890890 25.6734 14.8225i 0.860574 0.496853i
891891 0 0
892892 18.8489i 0.631107i
893893 −29.7686 51.5607i −0.996167 1.72541i
894894 0 0
895895 17.5583 + 10.1373i 0.586908 + 0.338852i
896896 1.00000 0.0334077
897897 0 0
898898 −9.57011 −0.319359
899899 61.1756 + 35.3198i 2.04032 + 1.17798i
900900 0 0
901901 17.9995 + 31.1761i 0.599651 + 1.03863i
902902 14.8333i 0.493896i
903903 0 0
904904 16.0693 9.27760i 0.534456 0.308568i
905905 50.9834i 1.69474i
906906 0 0
907907 3.67909 6.37237i 0.122162 0.211591i −0.798458 0.602051i 0.794351π-0.794351\pi
0.920620 + 0.390459i 0.127684π0.127684\pi
908908 1.14246 + 0.659599i 0.0379138 + 0.0218895i
909909 0 0
910910 −1.54919 + 7.74810i −0.0513552 + 0.256847i
911911 23.9499 0.793497 0.396748 0.917927i 0.370139π-0.370139\pi
0.396748 + 0.917927i 0.370139π0.370139\pi
912912 0 0
913913 0.680523 1.17870i 0.0225220 0.0390093i
914914 −12.9141 22.3679i −0.427161 0.739864i
915915 0 0
916916 −3.75949 + 2.17054i −0.124217 + 0.0717168i
917917 4.41878 2.55119i 0.145921 0.0842476i
918918 0 0
919919 18.9710 + 32.8588i 0.625797 + 1.08391i 0.988386 + 0.151963i 0.0485595π0.0485595\pi
−0.362589 + 0.931949i 0.618107π0.618107\pi
920920 2.71284 4.69878i 0.0894397 0.154914i
921921 0 0
922922 −1.56502 −0.0515413
923923 −28.4476 + 9.62517i −0.936364 + 0.316816i
924924 0 0
925925 −1.73653 1.00258i −0.0570966 0.0329648i
926926 10.2432 17.7417i 0.336611 0.583027i
927927 0 0
928928 9.81776i 0.322284i
929929 −5.58551 + 3.22479i −0.183254 + 0.105802i −0.588821 0.808264i 0.700408π-0.700408\pi
0.405566 + 0.914066i 0.367074π0.367074\pi
930930 0 0
931931 7.73201i 0.253406i
932932 2.88211 + 4.99196i 0.0944067 + 0.163517i
933933 0 0
934934 −3.29802 1.90411i −0.107914 0.0623044i
935935 −51.1249 −1.67196
936936 0 0
937937 −29.8183 −0.974120 −0.487060 0.873368i 0.661931π-0.661931\pi
−0.487060 + 0.873368i 0.661931π0.661931\pi
938938 5.49094 + 3.17020i 0.179286 + 0.103511i
939939 0 0
940940 −8.43725 14.6137i −0.275193 0.476648i
941941 21.5581i 0.702774i 0.936230 + 0.351387i 0.114290π0.114290\pi
−0.936230 + 0.351387i 0.885710π0.885710\pi
942942 0 0
943943 7.77636 4.48968i 0.253233 0.146204i
944944 4.85876i 0.158139i
945945 0 0
946946 5.63462 9.75944i 0.183197 0.317307i
947947 26.4885 + 15.2932i 0.860762 + 0.496961i 0.864267 0.503033i 0.167783π-0.167783\pi
−0.00350556 + 0.999994i 0.501116π0.501116\pi
948948 0 0
949949 5.21568 26.0856i 0.169308 0.846776i
950950 −1.52678 −0.0495351
951951 0 0
952952 2.85204 4.93987i 0.0924350 0.160102i
953953 2.64767 + 4.58590i 0.0857664 + 0.148552i 0.905718 0.423882i 0.139333π-0.139333\pi
−0.819951 + 0.572434i 0.805999π0.805999\pi
954954 0 0
955955 −16.8947 + 9.75414i −0.546699 + 0.315637i
956956 −11.3407 + 6.54753i −0.366783 + 0.211762i
957957 0 0
958958 −12.0600 20.8886i −0.389642 0.674880i
959959 −10.9011 + 18.8812i −0.352014 + 0.609706i
960960 0 0
961961 −20.7691 −0.669971
962962 11.7346 + 34.6820i 0.378337 + 1.11819i
963963 0 0
964964 −0.389769 0.225033i −0.0125536 0.00724784i
965965 9.73927 16.8689i 0.313518 0.543030i
966966 0 0
967967 46.8612i 1.50695i 0.657474 + 0.753477i 0.271625π0.271625\pi
−0.657474 + 0.753477i 0.728375π0.728375\pi
968968 4.95991 2.86360i 0.159417 0.0920397i
969969 0 0
970970 25.4568i 0.817368i
971971 −23.5583 40.8042i −0.756023 1.30947i −0.944864 0.327463i 0.893806π-0.893806\pi
0.188841 0.982008i 0.439527π-0.439527\pi
972972 0 0
973973 −14.2453 8.22455i −0.456685 0.263667i
974974 7.68364 0.246200
975975 0 0
976976 −11.2687 −0.360701
977977 4.49153 + 2.59319i 0.143697 + 0.0829635i 0.570125 0.821558i 0.306895π-0.306895\pi
−0.426428 + 0.904522i 0.640228π0.640228\pi
978978 0 0
979979 27.6630 + 47.9137i 0.884113 + 1.53133i
980980 2.19147i 0.0700039i
981981 0 0
982982 28.1921 16.2767i 0.899645 0.519411i
983983 12.1664i 0.388046i 0.980997 + 0.194023i 0.0621537π0.0621537\pi
−0.980997 + 0.194023i 0.937846π0.937846\pi
984984 0 0
985985 25.6321 44.3960i 0.816706 1.41458i
986986 −48.4985 28.0006i −1.54451 0.891721i
987987 0 0
988988 20.9417 + 18.4022i 0.666243 + 0.585450i
989989 6.82184 0.216922
990990 0 0
991991 22.1272 38.3254i 0.702894 1.21745i −0.264553 0.964371i 0.585224π-0.585224\pi
0.967446 0.253076i 0.0814424π-0.0814424\pi
992992 3.59754 + 6.23112i 0.114222 + 0.197838i
993993 0 0
994994 7.21341 4.16466i 0.228795 0.132095i
995995 −7.47016 + 4.31290i −0.236820 + 0.136728i
996996 0 0
997997 −18.4175 31.9001i −0.583289 1.01029i −0.995086 0.0990113i 0.968432π-0.968432\pi
0.411797 0.911276i 0.364901π-0.364901\pi
998998 2.93762 5.08811i 0.0929888 0.161061i
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 1638.2.bj.h.1135.1 yes 16
3.2 odd 2 1638.2.bj.i.1135.8 yes 16
13.10 even 6 inner 1638.2.bj.h.127.4 16
39.23 odd 6 1638.2.bj.i.127.5 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1638.2.bj.h.127.4 16 13.10 even 6 inner
1638.2.bj.h.1135.1 yes 16 1.1 even 1 trivial
1638.2.bj.i.127.5 yes 16 39.23 odd 6
1638.2.bj.i.1135.8 yes 16 3.2 odd 2