Properties

Label 285.2.i.a.106.1
Level 285285
Weight 22
Character 285.106
Analytic conductor 2.2762.276
Analytic rank 11
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [285,2,Mod(106,285)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(285, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("285.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 285=3519 285 = 3 \cdot 5 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 285.i (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: 2.275736457612.27573645761
Analytic rank: 11
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 106.1
Root 0.500000+0.866025i0.500000 + 0.866025i of defining polynomial
Character χ\chi == 285.106
Dual form 285.2.i.a.121.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.00000+1.73205i)q2+(0.500000+0.866025i)q3+(1.000001.73205i)q4+(0.5000000.866025i)q5+(1.000001.73205i)q62.00000q7+(0.5000000.866025i)q9+(1.00000+1.73205i)q103.00000q11+2.00000q12+(3.000005.19615i)q13+(2.000003.46410i)q14+(0.500000+0.866025i)q15+(2.000003.46410i)q16+(3.00000+5.19615i)q17+2.00000q18+(3.500002.59808i)q192.00000q20+(1.000001.73205i)q21+(3.000005.19615i)q22+(4.00000+6.92820i)q23+(0.5000000.866025i)q25+12.0000q26+1.00000q27+(2.00000+3.46410i)q28+(3.500006.06218i)q292.00000q30+9.00000q31+(4.00000+6.92820i)q32+(1.500002.59808i)q33+(6.0000010.3923i)q34+(1.00000+1.73205i)q35+(1.00000+1.73205i)q362.00000q37+(8.000003.46410i)q38+6.00000q39+(3.00000+5.19615i)q41+(2.00000+3.46410i)q42+(5.00000+8.66025i)q43+(3.00000+5.19615i)q441.00000q4516.0000q46+(2.000003.46410i)q47+(2.00000+3.46410i)q483.00000q49+2.00000q50+(3.000005.19615i)q51+(6.00000+10.3923i)q52+(7.0000012.1244i)q53+(1.00000+1.73205i)q54+(1.50000+2.59808i)q55+(4.000001.73205i)q57+14.0000q58+(1.50000+2.59808i)q59+(1.000001.73205i)q60+(3.50000+6.06218i)q61+(9.00000+15.5885i)q62+(1.00000+1.73205i)q638.00000q646.00000q65+(3.00000+5.19615i)q66+(2.000003.46410i)q67+12.0000q688.00000q69+(2.000003.46410i)q70+(3.50000+6.06218i)q71+(1.00000+1.73205i)q73+(2.000003.46410i)q74+1.00000q75+(1.00000+8.66025i)q76+6.00000q77+(6.00000+10.3923i)q78+(2.50000+4.33013i)q79+(2.000003.46410i)q80+(0.500000+0.866025i)q81+(6.0000010.3923i)q826.00000q834.00000q84+(3.00000+5.19615i)q85+(10.000017.3205i)q86+7.00000q87+(1.500002.59808i)q89+(1.000001.73205i)q90+(6.00000+10.3923i)q91+(8.0000013.8564i)q92+(4.50000+7.79423i)q93+8.00000q94+(4.00000+1.73205i)q958.00000q96+(6.0000010.3923i)q97+(3.000005.19615i)q98+(1.50000+2.59808i)q99+O(q100)q+(-1.00000 + 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{6} -2.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} -3.00000 q^{11} +2.00000 q^{12} +(-3.00000 - 5.19615i) q^{13} +(2.00000 - 3.46410i) q^{14} +(0.500000 + 0.866025i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-3.00000 + 5.19615i) q^{17} +2.00000 q^{18} +(-3.50000 - 2.59808i) q^{19} -2.00000 q^{20} +(1.00000 - 1.73205i) q^{21} +(3.00000 - 5.19615i) q^{22} +(4.00000 + 6.92820i) q^{23} +(-0.500000 - 0.866025i) q^{25} +12.0000 q^{26} +1.00000 q^{27} +(2.00000 + 3.46410i) q^{28} +(-3.50000 - 6.06218i) q^{29} -2.00000 q^{30} +9.00000 q^{31} +(4.00000 + 6.92820i) q^{32} +(1.50000 - 2.59808i) q^{33} +(-6.00000 - 10.3923i) q^{34} +(-1.00000 + 1.73205i) q^{35} +(-1.00000 + 1.73205i) q^{36} -2.00000 q^{37} +(8.00000 - 3.46410i) q^{38} +6.00000 q^{39} +(-3.00000 + 5.19615i) q^{41} +(2.00000 + 3.46410i) q^{42} +(-5.00000 + 8.66025i) q^{43} +(3.00000 + 5.19615i) q^{44} -1.00000 q^{45} -16.0000 q^{46} +(-2.00000 - 3.46410i) q^{47} +(2.00000 + 3.46410i) q^{48} -3.00000 q^{49} +2.00000 q^{50} +(-3.00000 - 5.19615i) q^{51} +(-6.00000 + 10.3923i) q^{52} +(-7.00000 - 12.1244i) q^{53} +(-1.00000 + 1.73205i) q^{54} +(-1.50000 + 2.59808i) q^{55} +(4.00000 - 1.73205i) q^{57} +14.0000 q^{58} +(-1.50000 + 2.59808i) q^{59} +(1.00000 - 1.73205i) q^{60} +(3.50000 + 6.06218i) q^{61} +(-9.00000 + 15.5885i) q^{62} +(1.00000 + 1.73205i) q^{63} -8.00000 q^{64} -6.00000 q^{65} +(3.00000 + 5.19615i) q^{66} +(-2.00000 - 3.46410i) q^{67} +12.0000 q^{68} -8.00000 q^{69} +(-2.00000 - 3.46410i) q^{70} +(-3.50000 + 6.06218i) q^{71} +(-1.00000 + 1.73205i) q^{73} +(2.00000 - 3.46410i) q^{74} +1.00000 q^{75} +(-1.00000 + 8.66025i) q^{76} +6.00000 q^{77} +(-6.00000 + 10.3923i) q^{78} +(-2.50000 + 4.33013i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.00000 - 10.3923i) q^{82} -6.00000 q^{83} -4.00000 q^{84} +(3.00000 + 5.19615i) q^{85} +(-10.0000 - 17.3205i) q^{86} +7.00000 q^{87} +(-1.50000 - 2.59808i) q^{89} +(1.00000 - 1.73205i) q^{90} +(6.00000 + 10.3923i) q^{91} +(8.00000 - 13.8564i) q^{92} +(-4.50000 + 7.79423i) q^{93} +8.00000 q^{94} +(-4.00000 + 1.73205i) q^{95} -8.00000 q^{96} +(6.00000 - 10.3923i) q^{97} +(3.00000 - 5.19615i) q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q2q32q4+q52q64q7q9+2q106q11+4q126q13+4q14+q15+4q166q17+4q187q194q20+2q21++3q99+O(q100) 2 q - 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 4 q^{7} - q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 6 q^{13} + 4 q^{14} + q^{15} + 4 q^{16} - 6 q^{17} + 4 q^{18} - 7 q^{19} - 4 q^{20} + 2 q^{21}+ \cdots + 3 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/285Z)×\left(\mathbb{Z}/285\mathbb{Z}\right)^\times.

nn 172172 191191 211211
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 −1.00000 + 1.73205i −0.707107 + 1.22474i 0.258819 + 0.965926i 0.416667π0.416667\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
33 −0.500000 + 0.866025i −0.288675 + 0.500000i
44 −1.00000 1.73205i −0.500000 0.866025i
55 0.500000 0.866025i 0.223607 0.387298i
66 −1.00000 1.73205i −0.408248 0.707107i
77 −2.00000 −0.755929 −0.377964 0.925820i 0.623376π-0.623376\pi
−0.377964 + 0.925820i 0.623376π0.623376\pi
88 0 0
99 −0.500000 0.866025i −0.166667 0.288675i
1010 1.00000 + 1.73205i 0.316228 + 0.547723i
1111 −3.00000 −0.904534 −0.452267 0.891883i 0.649385π-0.649385\pi
−0.452267 + 0.891883i 0.649385π0.649385\pi
1212 2.00000 0.577350
1313 −3.00000 5.19615i −0.832050 1.44115i −0.896410 0.443227i 0.853834π-0.853834\pi
0.0643593 0.997927i 0.479500π-0.479500\pi
1414 2.00000 3.46410i 0.534522 0.925820i
1515 0.500000 + 0.866025i 0.129099 + 0.223607i
1616 2.00000 3.46410i 0.500000 0.866025i
1717 −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i 0.426034π0.426034\pi
−0.957892 + 0.287129i 0.907299π0.907299\pi
1818 2.00000 0.471405
1919 −3.50000 2.59808i −0.802955 0.596040i
2020 −2.00000 −0.447214
2121 1.00000 1.73205i 0.218218 0.377964i
2222 3.00000 5.19615i 0.639602 1.10782i
2323 4.00000 + 6.92820i 0.834058 + 1.44463i 0.894795 + 0.446476i 0.147321π0.147321\pi
−0.0607377 + 0.998154i 0.519345π0.519345\pi
2424 0 0
2525 −0.500000 0.866025i −0.100000 0.173205i
2626 12.0000 2.35339
2727 1.00000 0.192450
2828 2.00000 + 3.46410i 0.377964 + 0.654654i
2929 −3.50000 6.06218i −0.649934 1.12572i −0.983138 0.182864i 0.941463π-0.941463\pi
0.333205 0.942855i 0.391870π-0.391870\pi
3030 −2.00000 −0.365148
3131 9.00000 1.61645 0.808224 0.588875i 0.200429π-0.200429\pi
0.808224 + 0.588875i 0.200429π0.200429\pi
3232 4.00000 + 6.92820i 0.707107 + 1.22474i
3333 1.50000 2.59808i 0.261116 0.452267i
3434 −6.00000 10.3923i −1.02899 1.78227i
3535 −1.00000 + 1.73205i −0.169031 + 0.292770i
3636 −1.00000 + 1.73205i −0.166667 + 0.288675i
3737 −2.00000 −0.328798 −0.164399 0.986394i 0.552568π-0.552568\pi
−0.164399 + 0.986394i 0.552568π0.552568\pi
3838 8.00000 3.46410i 1.29777 0.561951i
3939 6.00000 0.960769
4040 0 0
4141 −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i 0.988546π-0.988546\pi
0.530831 + 0.847477i 0.321880π0.321880\pi
4242 2.00000 + 3.46410i 0.308607 + 0.534522i
4343 −5.00000 + 8.66025i −0.762493 + 1.32068i 0.179069 + 0.983836i 0.442691π0.442691\pi
−0.941562 + 0.336840i 0.890642π0.890642\pi
4444 3.00000 + 5.19615i 0.452267 + 0.783349i
4545 −1.00000 −0.149071
4646 −16.0000 −2.35907
4747 −2.00000 3.46410i −0.291730 0.505291i 0.682489 0.730896i 0.260898π-0.260898\pi
−0.974219 + 0.225605i 0.927564π0.927564\pi
4848 2.00000 + 3.46410i 0.288675 + 0.500000i
4949 −3.00000 −0.428571
5050 2.00000 0.282843
5151 −3.00000 5.19615i −0.420084 0.727607i
5252 −6.00000 + 10.3923i −0.832050 + 1.44115i
5353 −7.00000 12.1244i −0.961524 1.66541i −0.718677 0.695344i 0.755252π-0.755252\pi
−0.242846 0.970065i 0.578081π-0.578081\pi
5454 −1.00000 + 1.73205i −0.136083 + 0.235702i
5555 −1.50000 + 2.59808i −0.202260 + 0.350325i
5656 0 0
5757 4.00000 1.73205i 0.529813 0.229416i
5858 14.0000 1.83829
5959 −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i 0.895896π-0.895896\pi
0.751710 + 0.659494i 0.229229π0.229229\pi
6060 1.00000 1.73205i 0.129099 0.223607i
6161 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i 0.0187572π-0.0187572\pi
−0.550135 + 0.835076i 0.685424π0.685424\pi
6262 −9.00000 + 15.5885i −1.14300 + 1.97974i
6363 1.00000 + 1.73205i 0.125988 + 0.218218i
6464 −8.00000 −1.00000
6565 −6.00000 −0.744208
6666 3.00000 + 5.19615i 0.369274 + 0.639602i
6767 −2.00000 3.46410i −0.244339 0.423207i 0.717607 0.696449i 0.245238π-0.245238\pi
−0.961946 + 0.273241i 0.911904π0.911904\pi
6868 12.0000 1.45521
6969 −8.00000 −0.963087
7070 −2.00000 3.46410i −0.239046 0.414039i
7171 −3.50000 + 6.06218i −0.415374 + 0.719448i −0.995468 0.0951014i 0.969682π-0.969682\pi
0.580094 + 0.814550i 0.303016π0.303016\pi
7272 0 0
7373 −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i 0.870674π-0.870674\pi
0.801553 + 0.597924i 0.204008π0.204008\pi
7474 2.00000 3.46410i 0.232495 0.402694i
7575 1.00000 0.115470
7676 −1.00000 + 8.66025i −0.114708 + 0.993399i
7777 6.00000 0.683763
7878 −6.00000 + 10.3923i −0.679366 + 1.17670i
7979 −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i 0.924090π-0.924090\pi
0.690426 + 0.723403i 0.257423π0.257423\pi
8080 −2.00000 3.46410i −0.223607 0.387298i
8181 −0.500000 + 0.866025i −0.0555556 + 0.0962250i
8282 −6.00000 10.3923i −0.662589 1.14764i
8383 −6.00000 −0.658586 −0.329293 0.944228i 0.606810π-0.606810\pi
−0.329293 + 0.944228i 0.606810π0.606810\pi
8484 −4.00000 −0.436436
8585 3.00000 + 5.19615i 0.325396 + 0.563602i
8686 −10.0000 17.3205i −1.07833 1.86772i
8787 7.00000 0.750479
8888 0 0
8989 −1.50000 2.59808i −0.159000 0.275396i 0.775509 0.631337i 0.217494π-0.217494\pi
−0.934508 + 0.355942i 0.884160π0.884160\pi
9090 1.00000 1.73205i 0.105409 0.182574i
9191 6.00000 + 10.3923i 0.628971 + 1.08941i
9292 8.00000 13.8564i 0.834058 1.44463i
9393 −4.50000 + 7.79423i −0.466628 + 0.808224i
9494 8.00000 0.825137
9595 −4.00000 + 1.73205i −0.410391 + 0.177705i
9696 −8.00000 −0.816497
9797 6.00000 10.3923i 0.609208 1.05518i −0.382164 0.924095i 0.624821π-0.624821\pi
0.991371 0.131084i 0.0418458π-0.0418458\pi
9898 3.00000 5.19615i 0.303046 0.524891i
9999 1.50000 + 2.59808i 0.150756 + 0.261116i
100100 −1.00000 + 1.73205i −0.100000 + 0.173205i
101101 1.50000 + 2.59808i 0.149256 + 0.258518i 0.930953 0.365140i 0.118979π-0.118979\pi
−0.781697 + 0.623658i 0.785646π0.785646\pi
102102 12.0000 1.18818
103103 −8.00000 −0.788263 −0.394132 0.919054i 0.628955π-0.628955\pi
−0.394132 + 0.919054i 0.628955π0.628955\pi
104104 0 0
105105 −1.00000 1.73205i −0.0975900 0.169031i
106106 28.0000 2.71960
107107 12.0000 1.16008 0.580042 0.814587i 0.303036π-0.303036\pi
0.580042 + 0.814587i 0.303036π0.303036\pi
108108 −1.00000 1.73205i −0.0962250 0.166667i
109109 −1.50000 + 2.59808i −0.143674 + 0.248851i −0.928877 0.370387i 0.879225π-0.879225\pi
0.785203 + 0.619238i 0.212558π0.212558\pi
110110 −3.00000 5.19615i −0.286039 0.495434i
111111 1.00000 1.73205i 0.0949158 0.164399i
112112 −4.00000 + 6.92820i −0.377964 + 0.654654i
113113 6.00000 0.564433 0.282216 0.959351i 0.408930π-0.408930\pi
0.282216 + 0.959351i 0.408930π0.408930\pi
114114 −1.00000 + 8.66025i −0.0936586 + 0.811107i
115115 8.00000 0.746004
116116 −7.00000 + 12.1244i −0.649934 + 1.12572i
117117 −3.00000 + 5.19615i −0.277350 + 0.480384i
118118 −3.00000 5.19615i −0.276172 0.478345i
119119 6.00000 10.3923i 0.550019 0.952661i
120120 0 0
121121 −2.00000 −0.181818
122122 −14.0000 −1.26750
123123 −3.00000 5.19615i −0.270501 0.468521i
124124 −9.00000 15.5885i −0.808224 1.39988i
125125 −1.00000 −0.0894427
126126 −4.00000 −0.356348
127127 4.00000 + 6.92820i 0.354943 + 0.614779i 0.987108 0.160055i 0.0511671π-0.0511671\pi
−0.632166 + 0.774833i 0.717834π0.717834\pi
128128 0 0
129129 −5.00000 8.66025i −0.440225 0.762493i
130130 6.00000 10.3923i 0.526235 0.911465i
131131 4.00000 6.92820i 0.349482 0.605320i −0.636676 0.771132i 0.719691π-0.719691\pi
0.986157 + 0.165812i 0.0530244π0.0530244\pi
132132 −6.00000 −0.522233
133133 7.00000 + 5.19615i 0.606977 + 0.450564i
134134 8.00000 0.691095
135135 0.500000 0.866025i 0.0430331 0.0745356i
136136 0 0
137137 −1.00000 1.73205i −0.0854358 0.147979i 0.820141 0.572161i 0.193895π-0.193895\pi
−0.905577 + 0.424182i 0.860562π0.860562\pi
138138 8.00000 13.8564i 0.681005 1.17954i
139139 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i 0.112407π-0.112407\pi
−0.768655 + 0.639664i 0.779074π0.779074\pi
140140 4.00000 0.338062
141141 4.00000 0.336861
142142 −7.00000 12.1244i −0.587427 1.01745i
143143 9.00000 + 15.5885i 0.752618 + 1.30357i
144144 −4.00000 −0.333333
145145 −7.00000 −0.581318
146146 −2.00000 3.46410i −0.165521 0.286691i
147147 1.50000 2.59808i 0.123718 0.214286i
148148 2.00000 + 3.46410i 0.164399 + 0.284747i
149149 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i 0.794119π-0.794119\pi
0.920904 + 0.389789i 0.127452π0.127452\pi
150150 −1.00000 + 1.73205i −0.0816497 + 0.141421i
151151 5.00000 0.406894 0.203447 0.979086i 0.434786π-0.434786\pi
0.203447 + 0.979086i 0.434786π0.434786\pi
152152 0 0
153153 6.00000 0.485071
154154 −6.00000 + 10.3923i −0.483494 + 0.837436i
155155 4.50000 7.79423i 0.361449 0.626048i
156156 −6.00000 10.3923i −0.480384 0.832050i
157157 10.0000 17.3205i 0.798087 1.38233i −0.122774 0.992435i 0.539179π-0.539179\pi
0.920860 0.389892i 0.127488π-0.127488\pi
158158 −5.00000 8.66025i −0.397779 0.688973i
159159 14.0000 1.11027
160160 8.00000 0.632456
161161 −8.00000 13.8564i −0.630488 1.09204i
162162 −1.00000 1.73205i −0.0785674 0.136083i
163163 −10.0000 −0.783260 −0.391630 0.920123i 0.628089π-0.628089\pi
−0.391630 + 0.920123i 0.628089π0.628089\pi
164164 12.0000 0.937043
165165 −1.50000 2.59808i −0.116775 0.202260i
166166 6.00000 10.3923i 0.465690 0.806599i
167167 −11.0000 19.0526i −0.851206 1.47433i −0.880121 0.474749i 0.842539π-0.842539\pi
0.0289155 0.999582i 0.490795π-0.490795\pi
168168 0 0
169169 −11.5000 + 19.9186i −0.884615 + 1.53220i
170170 −12.0000 −0.920358
171171 −0.500000 + 4.33013i −0.0382360 + 0.331133i
172172 20.0000 1.52499
173173 −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i 0.906580π-0.906580\pi
0.729155 + 0.684349i 0.239913π0.239913\pi
174174 −7.00000 + 12.1244i −0.530669 + 0.919145i
175175 1.00000 + 1.73205i 0.0755929 + 0.130931i
176176 −6.00000 + 10.3923i −0.452267 + 0.783349i
177177 −1.50000 2.59808i −0.112747 0.195283i
178178 6.00000 0.449719
179179 1.00000 0.0747435 0.0373718 0.999301i 0.488101π-0.488101\pi
0.0373718 + 0.999301i 0.488101π0.488101\pi
180180 1.00000 + 1.73205i 0.0745356 + 0.129099i
181181 7.00000 + 12.1244i 0.520306 + 0.901196i 0.999721 + 0.0236082i 0.00751541π0.00751541\pi
−0.479415 + 0.877588i 0.659151π0.659151\pi
182182 −24.0000 −1.77900
183183 −7.00000 −0.517455
184184 0 0
185185 −1.00000 + 1.73205i −0.0735215 + 0.127343i
186186 −9.00000 15.5885i −0.659912 1.14300i
187187 9.00000 15.5885i 0.658145 1.13994i
188188 −4.00000 + 6.92820i −0.291730 + 0.505291i
189189 −2.00000 −0.145479
190190 1.00000 8.66025i 0.0725476 0.628281i
191191 −5.00000 −0.361787 −0.180894 0.983503i 0.557899π-0.557899\pi
−0.180894 + 0.983503i 0.557899π0.557899\pi
192192 4.00000 6.92820i 0.288675 0.500000i
193193 9.00000 15.5885i 0.647834 1.12208i −0.335805 0.941932i 0.609008π-0.609008\pi
0.983639 0.180150i 0.0576584π-0.0576584\pi
194194 12.0000 + 20.7846i 0.861550 + 1.49225i
195195 3.00000 5.19615i 0.214834 0.372104i
196196 3.00000 + 5.19615i 0.214286 + 0.371154i
197197 −18.0000 −1.28245 −0.641223 0.767354i 0.721573π-0.721573\pi
−0.641223 + 0.767354i 0.721573π0.721573\pi
198198 −6.00000 −0.426401
199199 5.50000 + 9.52628i 0.389885 + 0.675300i 0.992434 0.122782i 0.0391815π-0.0391815\pi
−0.602549 + 0.798082i 0.705848π0.705848\pi
200200 0 0
201201 4.00000 0.282138
202202 −6.00000 −0.422159
203203 7.00000 + 12.1244i 0.491304 + 0.850963i
204204 −6.00000 + 10.3923i −0.420084 + 0.727607i
205205 3.00000 + 5.19615i 0.209529 + 0.362915i
206206 8.00000 13.8564i 0.557386 0.965422i
207207 4.00000 6.92820i 0.278019 0.481543i
208208 −24.0000 −1.66410
209209 10.5000 + 7.79423i 0.726300 + 0.539138i
210210 4.00000 0.276026
211211 −6.50000 + 11.2583i −0.447478 + 0.775055i −0.998221 0.0596196i 0.981011π-0.981011\pi
0.550743 + 0.834675i 0.314345π0.314345\pi
212212 −14.0000 + 24.2487i −0.961524 + 1.66541i
213213 −3.50000 6.06218i −0.239816 0.415374i
214214 −12.0000 + 20.7846i −0.820303 + 1.42081i
215215 5.00000 + 8.66025i 0.340997 + 0.590624i
216216 0 0
217217 −18.0000 −1.22192
218218 −3.00000 5.19615i −0.203186 0.351928i
219219 −1.00000 1.73205i −0.0675737 0.117041i
220220 6.00000 0.404520
221221 36.0000 2.42162
222222 2.00000 + 3.46410i 0.134231 + 0.232495i
223223 −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i 0.919650π-0.919650\pi
0.700449 + 0.713702i 0.252983π0.252983\pi
224224 −8.00000 13.8564i −0.534522 0.925820i
225225 −0.500000 + 0.866025i −0.0333333 + 0.0577350i
226226 −6.00000 + 10.3923i −0.399114 + 0.691286i
227227 14.0000 0.929213 0.464606 0.885517i 0.346196π-0.346196\pi
0.464606 + 0.885517i 0.346196π0.346196\pi
228228 −7.00000 5.19615i −0.463586 0.344124i
229229 29.0000 1.91637 0.958187 0.286143i 0.0923732π-0.0923732\pi
0.958187 + 0.286143i 0.0923732π0.0923732\pi
230230 −8.00000 + 13.8564i −0.527504 + 0.913664i
231231 −3.00000 + 5.19615i −0.197386 + 0.341882i
232232 0 0
233233 −8.00000 + 13.8564i −0.524097 + 0.907763i 0.475509 + 0.879711i 0.342264π0.342264\pi
−0.999606 + 0.0280525i 0.991069π0.991069\pi
234234 −6.00000 10.3923i −0.392232 0.679366i
235235 −4.00000 −0.260931
236236 6.00000 0.390567
237237 −2.50000 4.33013i −0.162392 0.281272i
238238 12.0000 + 20.7846i 0.777844 + 1.34727i
239239 −9.00000 −0.582162 −0.291081 0.956698i 0.594015π-0.594015\pi
−0.291081 + 0.956698i 0.594015π0.594015\pi
240240 4.00000 0.258199
241241 −10.5000 18.1865i −0.676364 1.17150i −0.976068 0.217465i 0.930221π-0.930221\pi
0.299704 0.954032i 0.403112π-0.403112\pi
242242 2.00000 3.46410i 0.128565 0.222681i
243243 −0.500000 0.866025i −0.0320750 0.0555556i
244244 7.00000 12.1244i 0.448129 0.776182i
245245 −1.50000 + 2.59808i −0.0958315 + 0.165985i
246246 12.0000 0.765092
247247 −3.00000 + 25.9808i −0.190885 + 1.65312i
248248 0 0
249249 3.00000 5.19615i 0.190117 0.329293i
250250 1.00000 1.73205i 0.0632456 0.109545i
251251 −1.50000 2.59808i −0.0946792 0.163989i 0.814795 0.579748i 0.196849π-0.196849\pi
−0.909475 + 0.415759i 0.863516π0.863516\pi
252252 2.00000 3.46410i 0.125988 0.218218i
253253 −12.0000 20.7846i −0.754434 1.30672i
254254 −16.0000 −1.00393
255255 −6.00000 −0.375735
256256 −8.00000 13.8564i −0.500000 0.866025i
257257 −1.00000 1.73205i −0.0623783 0.108042i 0.833150 0.553047i 0.186535π-0.186535\pi
−0.895528 + 0.445005i 0.853202π0.853202\pi
258258 20.0000 1.24515
259259 4.00000 0.248548
260260 6.00000 + 10.3923i 0.372104 + 0.644503i
261261 −3.50000 + 6.06218i −0.216645 + 0.375239i
262262 8.00000 + 13.8564i 0.494242 + 0.856052i
263263 −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i 0.953967π-0.953967\pi
0.619586 + 0.784929i 0.287301π0.287301\pi
264264 0 0
265265 −14.0000 −0.860013
266266 −16.0000 + 6.92820i −0.981023 + 0.424795i
267267 3.00000 0.183597
268268 −4.00000 + 6.92820i −0.244339 + 0.423207i
269269 −10.5000 + 18.1865i −0.640196 + 1.10885i 0.345192 + 0.938532i 0.387814π0.387814\pi
−0.985389 + 0.170321i 0.945520π0.945520\pi
270270 1.00000 + 1.73205i 0.0608581 + 0.105409i
271271 2.50000 4.33013i 0.151864 0.263036i −0.780049 0.625719i 0.784806π-0.784806\pi
0.931913 + 0.362682i 0.118139π0.118139\pi
272272 12.0000 + 20.7846i 0.727607 + 1.26025i
273273 −12.0000 −0.726273
274274 4.00000 0.241649
275275 1.50000 + 2.59808i 0.0904534 + 0.156670i
276276 8.00000 + 13.8564i 0.481543 + 0.834058i
277277 16.0000 0.961347 0.480673 0.876900i 0.340392π-0.340392\pi
0.480673 + 0.876900i 0.340392π0.340392\pi
278278 −8.00000 −0.479808
279279 −4.50000 7.79423i −0.269408 0.466628i
280280 0 0
281281 −7.00000 12.1244i −0.417585 0.723278i 0.578111 0.815958i 0.303790π-0.303790\pi
−0.995696 + 0.0926797i 0.970457π0.970457\pi
282282 −4.00000 + 6.92820i −0.238197 + 0.412568i
283283 13.0000 22.5167i 0.772770 1.33848i −0.163270 0.986581i 0.552204π-0.552204\pi
0.936039 0.351895i 0.114463π-0.114463\pi
284284 14.0000 0.830747
285285 0.500000 4.33013i 0.0296174 0.256495i
286286 −36.0000 −2.12872
287287 6.00000 10.3923i 0.354169 0.613438i
288288 4.00000 6.92820i 0.235702 0.408248i
289289 −9.50000 16.4545i −0.558824 0.967911i
290290 7.00000 12.1244i 0.411054 0.711967i
291291 6.00000 + 10.3923i 0.351726 + 0.609208i
292292 4.00000 0.234082
293293 −12.0000 −0.701047 −0.350524 0.936554i 0.613996π-0.613996\pi
−0.350524 + 0.936554i 0.613996π0.613996\pi
294294 3.00000 + 5.19615i 0.174964 + 0.303046i
295295 1.50000 + 2.59808i 0.0873334 + 0.151266i
296296 0 0
297297 −3.00000 −0.174078
298298 3.00000 + 5.19615i 0.173785 + 0.301005i
299299 24.0000 41.5692i 1.38796 2.40401i
300300 −1.00000 1.73205i −0.0577350 0.100000i
301301 10.0000 17.3205i 0.576390 0.998337i
302302 −5.00000 + 8.66025i −0.287718 + 0.498342i
303303 −3.00000 −0.172345
304304 −16.0000 + 6.92820i −0.917663 + 0.397360i
305305 7.00000 0.400819
306306 −6.00000 + 10.3923i −0.342997 + 0.594089i
307307 −8.00000 + 13.8564i −0.456584 + 0.790827i −0.998778 0.0494267i 0.984261π-0.984261\pi
0.542194 + 0.840254i 0.317594π0.317594\pi
308308 −6.00000 10.3923i −0.341882 0.592157i
309309 4.00000 6.92820i 0.227552 0.394132i
310310 9.00000 + 15.5885i 0.511166 + 0.885365i
311311 −8.00000 −0.453638 −0.226819 0.973937i 0.572833π-0.572833\pi
−0.226819 + 0.973937i 0.572833π0.572833\pi
312312 0 0
313313 4.00000 + 6.92820i 0.226093 + 0.391605i 0.956647 0.291250i 0.0940712π-0.0940712\pi
−0.730554 + 0.682855i 0.760738π0.760738\pi
314314 20.0000 + 34.6410i 1.12867 + 1.95491i
315315 2.00000 0.112687
316316 10.0000 0.562544
317317 −6.00000 10.3923i −0.336994 0.583690i 0.646872 0.762598i 0.276077π-0.276077\pi
−0.983866 + 0.178908i 0.942743π0.942743\pi
318318 −14.0000 + 24.2487i −0.785081 + 1.35980i
319319 10.5000 + 18.1865i 0.587887 + 1.01825i
320320 −4.00000 + 6.92820i −0.223607 + 0.387298i
321321 −6.00000 + 10.3923i −0.334887 + 0.580042i
322322 32.0000 1.78329
323323 24.0000 10.3923i 1.33540 0.578243i
324324 2.00000 0.111111
325325 −3.00000 + 5.19615i −0.166410 + 0.288231i
326326 10.0000 17.3205i 0.553849 0.959294i
327327 −1.50000 2.59808i −0.0829502 0.143674i
328328 0 0
329329 4.00000 + 6.92820i 0.220527 + 0.381964i
330330 6.00000 0.330289
331331 −8.00000 −0.439720 −0.219860 0.975531i 0.570560π-0.570560\pi
−0.219860 + 0.975531i 0.570560π0.570560\pi
332332 6.00000 + 10.3923i 0.329293 + 0.570352i
333333 1.00000 + 1.73205i 0.0547997 + 0.0949158i
334334 44.0000 2.40757
335335 −4.00000 −0.218543
336336 −4.00000 6.92820i −0.218218 0.377964i
337337 6.00000 10.3923i 0.326841 0.566105i −0.655042 0.755592i 0.727349π-0.727349\pi
0.981883 + 0.189487i 0.0606826π0.0606826\pi
338338 −23.0000 39.8372i −1.25104 2.16686i
339339 −3.00000 + 5.19615i −0.162938 + 0.282216i
340340 6.00000 10.3923i 0.325396 0.563602i
341341 −27.0000 −1.46213
342342 −7.00000 5.19615i −0.378517 0.280976i
343343 20.0000 1.07990
344344 0 0
345345 −4.00000 + 6.92820i −0.215353 + 0.373002i
346346 −6.00000 10.3923i −0.322562 0.558694i
347347 −1.00000 + 1.73205i −0.0536828 + 0.0929814i −0.891618 0.452788i 0.850429π-0.850429\pi
0.837935 + 0.545770i 0.183763π0.183763\pi
348348 −7.00000 12.1244i −0.375239 0.649934i
349349 −2.00000 −0.107058 −0.0535288 0.998566i 0.517047π-0.517047\pi
−0.0535288 + 0.998566i 0.517047π0.517047\pi
350350 −4.00000 −0.213809
351351 −3.00000 5.19615i −0.160128 0.277350i
352352 −12.0000 20.7846i −0.639602 1.10782i
353353 2.00000 0.106449 0.0532246 0.998583i 0.483050π-0.483050\pi
0.0532246 + 0.998583i 0.483050π0.483050\pi
354354 6.00000 0.318896
355355 3.50000 + 6.06218i 0.185761 + 0.321747i
356356 −3.00000 + 5.19615i −0.159000 + 0.275396i
357357 6.00000 + 10.3923i 0.317554 + 0.550019i
358358 −1.00000 + 1.73205i −0.0528516 + 0.0915417i
359359 16.0000 27.7128i 0.844448 1.46263i −0.0416523 0.999132i 0.513262π-0.513262\pi
0.886100 0.463494i 0.153404π-0.153404\pi
360360 0 0
361361 5.50000 + 18.1865i 0.289474 + 0.957186i
362362 −28.0000 −1.47165
363363 1.00000 1.73205i 0.0524864 0.0909091i
364364 12.0000 20.7846i 0.628971 1.08941i
365365 1.00000 + 1.73205i 0.0523424 + 0.0906597i
366366 7.00000 12.1244i 0.365896 0.633750i
367367 10.0000 + 17.3205i 0.521996 + 0.904123i 0.999673 + 0.0255875i 0.00814566π0.00814566\pi
−0.477677 + 0.878536i 0.658521π0.658521\pi
368368 32.0000 1.66812
369369 6.00000 0.312348
370370 −2.00000 3.46410i −0.103975 0.180090i
371371 14.0000 + 24.2487i 0.726844 + 1.25893i
372372 18.0000 0.933257
373373 −24.0000 −1.24267 −0.621336 0.783544i 0.713410π-0.713410\pi
−0.621336 + 0.783544i 0.713410π0.713410\pi
374374 18.0000 + 31.1769i 0.930758 + 1.61212i
375375 0.500000 0.866025i 0.0258199 0.0447214i
376376 0 0
377377 −21.0000 + 36.3731i −1.08156 + 1.87331i
378378 2.00000 3.46410i 0.102869 0.178174i
379379 −25.0000 −1.28416 −0.642082 0.766636i 0.721929π-0.721929\pi
−0.642082 + 0.766636i 0.721929π0.721929\pi
380380 7.00000 + 5.19615i 0.359092 + 0.266557i
381381 −8.00000 −0.409852
382382 5.00000 8.66025i 0.255822 0.443097i
383383 17.0000 29.4449i 0.868659 1.50456i 0.00529229 0.999986i 0.498315π-0.498315\pi
0.863367 0.504576i 0.168351π-0.168351\pi
384384 0 0
385385 3.00000 5.19615i 0.152894 0.264820i
386386 18.0000 + 31.1769i 0.916176 + 1.58686i
387387 10.0000 0.508329
388388 −24.0000 −1.21842
389389 −18.5000 32.0429i −0.937987 1.62464i −0.769218 0.638986i 0.779354π-0.779354\pi
−0.168769 0.985656i 0.553979π-0.553979\pi
390390 6.00000 + 10.3923i 0.303822 + 0.526235i
391391 −48.0000 −2.42746
392392 0 0
393393 4.00000 + 6.92820i 0.201773 + 0.349482i
394394 18.0000 31.1769i 0.906827 1.57067i
395395 2.50000 + 4.33013i 0.125789 + 0.217872i
396396 3.00000 5.19615i 0.150756 0.261116i
397397 −6.00000 + 10.3923i −0.301131 + 0.521575i −0.976392 0.216004i 0.930698π-0.930698\pi
0.675261 + 0.737579i 0.264031π0.264031\pi
398398 −22.0000 −1.10276
399399 −8.00000 + 3.46410i −0.400501 + 0.173422i
400400 −4.00000 −0.200000
401401 11.5000 19.9186i 0.574283 0.994687i −0.421837 0.906672i 0.638614π-0.638614\pi
0.996119 0.0880147i 0.0280523π-0.0280523\pi
402402 −4.00000 + 6.92820i −0.199502 + 0.345547i
403403 −27.0000 46.7654i −1.34497 2.32955i
404404 3.00000 5.19615i 0.149256 0.258518i
405405 0.500000 + 0.866025i 0.0248452 + 0.0430331i
406406 −28.0000 −1.38962
407407 6.00000 0.297409
408408 0 0
409409 −5.50000 9.52628i −0.271957 0.471044i 0.697406 0.716677i 0.254338π-0.254338\pi
−0.969363 + 0.245633i 0.921004π0.921004\pi
410410 −12.0000 −0.592638
411411 2.00000 0.0986527
412412 8.00000 + 13.8564i 0.394132 + 0.682656i
413413 3.00000 5.19615i 0.147620 0.255686i
414414 8.00000 + 13.8564i 0.393179 + 0.681005i
415415 −3.00000 + 5.19615i −0.147264 + 0.255069i
416416 24.0000 41.5692i 1.17670 2.03810i
417417 −4.00000 −0.195881
418418 −24.0000 + 10.3923i −1.17388 + 0.508304i
419419 −9.00000 −0.439679 −0.219839 0.975536i 0.570553π-0.570553\pi
−0.219839 + 0.975536i 0.570553π0.570553\pi
420420 −2.00000 + 3.46410i −0.0975900 + 0.169031i
421421 −4.50000 + 7.79423i −0.219317 + 0.379867i −0.954599 0.297893i 0.903716π-0.903716\pi
0.735283 + 0.677761i 0.237049π0.237049\pi
422422 −13.0000 22.5167i −0.632830 1.09609i
423423 −2.00000 + 3.46410i −0.0972433 + 0.168430i
424424 0 0
425425 6.00000 0.291043
426426 14.0000 0.678302
427427 −7.00000 12.1244i −0.338754 0.586739i
428428 −12.0000 20.7846i −0.580042 1.00466i
429429 −18.0000 −0.869048
430430 −20.0000 −0.964486
431431 10.5000 + 18.1865i 0.505767 + 0.876014i 0.999978 + 0.00667224i 0.00212386π0.00212386\pi
−0.494211 + 0.869342i 0.664543π0.664543\pi
432432 2.00000 3.46410i 0.0962250 0.166667i
433433 5.00000 + 8.66025i 0.240285 + 0.416185i 0.960795 0.277259i 0.0894259π-0.0894259\pi
−0.720511 + 0.693444i 0.756093π0.756093\pi
434434 18.0000 31.1769i 0.864028 1.49654i
435435 3.50000 6.06218i 0.167812 0.290659i
436436 6.00000 0.287348
437437 4.00000 34.6410i 0.191346 1.65710i
438438 4.00000 0.191127
439439 4.50000 7.79423i 0.214773 0.371998i −0.738429 0.674331i 0.764432π-0.764432\pi
0.953202 + 0.302333i 0.0977654π0.0977654\pi
440440 0 0
441441 1.50000 + 2.59808i 0.0714286 + 0.123718i
442442 −36.0000 + 62.3538i −1.71235 + 2.96587i
443443 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
444444 −4.00000 −0.189832
445445 −3.00000 −0.142214
446446 −8.00000 13.8564i −0.378811 0.656120i
447447 1.50000 + 2.59808i 0.0709476 + 0.122885i
448448 16.0000 0.755929
449449 13.0000 0.613508 0.306754 0.951789i 0.400757π-0.400757\pi
0.306754 + 0.951789i 0.400757π0.400757\pi
450450 −1.00000 1.73205i −0.0471405 0.0816497i
451451 9.00000 15.5885i 0.423793 0.734032i
452452 −6.00000 10.3923i −0.282216 0.488813i
453453 −2.50000 + 4.33013i −0.117460 + 0.203447i
454454 −14.0000 + 24.2487i −0.657053 + 1.13805i
455455 12.0000 0.562569
456456 0 0
457457 12.0000 0.561336 0.280668 0.959805i 0.409444π-0.409444\pi
0.280668 + 0.959805i 0.409444π0.409444\pi
458458 −29.0000 + 50.2295i −1.35508 + 2.34707i
459459 −3.00000 + 5.19615i −0.140028 + 0.242536i
460460 −8.00000 13.8564i −0.373002 0.646058i
461461 −16.5000 + 28.5788i −0.768482 + 1.33105i 0.169904 + 0.985461i 0.445654π0.445654\pi
−0.938386 + 0.345589i 0.887679π0.887679\pi
462462 −6.00000 10.3923i −0.279145 0.483494i
463463 −26.0000 −1.20832 −0.604161 0.796862i 0.706492π-0.706492\pi
−0.604161 + 0.796862i 0.706492π0.706492\pi
464464 −28.0000 −1.29987
465465 4.50000 + 7.79423i 0.208683 + 0.361449i
466466 −16.0000 27.7128i −0.741186 1.28377i
467467 −18.0000 −0.832941 −0.416470 0.909149i 0.636733π-0.636733\pi
−0.416470 + 0.909149i 0.636733π0.636733\pi
468468 12.0000 0.554700
469469 4.00000 + 6.92820i 0.184703 + 0.319915i
470470 4.00000 6.92820i 0.184506 0.319574i
471471 10.0000 + 17.3205i 0.460776 + 0.798087i
472472 0 0
473473 15.0000 25.9808i 0.689701 1.19460i
474474 10.0000 0.459315
475475 −0.500000 + 4.33013i −0.0229416 + 0.198680i
476476 −24.0000 −1.10004
477477 −7.00000 + 12.1244i −0.320508 + 0.555136i
478478 9.00000 15.5885i 0.411650 0.712999i
479479 7.50000 + 12.9904i 0.342684 + 0.593546i 0.984930 0.172953i 0.0553307π-0.0553307\pi
−0.642246 + 0.766498i 0.721997π0.721997\pi
480480 −4.00000 + 6.92820i −0.182574 + 0.316228i
481481 6.00000 + 10.3923i 0.273576 + 0.473848i
482482 42.0000 1.91305
483483 16.0000 0.728025
484484 2.00000 + 3.46410i 0.0909091 + 0.157459i
485485 −6.00000 10.3923i −0.272446 0.471890i
486486 2.00000 0.0907218
487487 −22.0000 −0.996915 −0.498458 0.866914i 0.666100π-0.666100\pi
−0.498458 + 0.866914i 0.666100π0.666100\pi
488488 0 0
489489 5.00000 8.66025i 0.226108 0.391630i
490490 −3.00000 5.19615i −0.135526 0.234738i
491491 2.50000 4.33013i 0.112823 0.195416i −0.804084 0.594515i 0.797344π-0.797344\pi
0.916908 + 0.399100i 0.130677π0.130677\pi
492492 −6.00000 + 10.3923i −0.270501 + 0.468521i
493493 42.0000 1.89158
494494 −42.0000 31.1769i −1.88967 1.40272i
495495 3.00000 0.134840
496496 18.0000 31.1769i 0.808224 1.39988i
497497 7.00000 12.1244i 0.313993 0.543852i
498498 6.00000 + 10.3923i 0.268866 + 0.465690i
499499 −6.00000 + 10.3923i −0.268597 + 0.465223i −0.968500 0.249015i 0.919893π-0.919893\pi
0.699903 + 0.714238i 0.253227π0.253227\pi
500500 1.00000 + 1.73205i 0.0447214 + 0.0774597i
501501 22.0000 0.982888
502502 6.00000 0.267793
503503 12.0000 + 20.7846i 0.535054 + 0.926740i 0.999161 + 0.0409609i 0.0130419π0.0130419\pi
−0.464107 + 0.885779i 0.653625π0.653625\pi
504504 0 0
505505 3.00000 0.133498
506506 48.0000 2.13386
507507 −11.5000 19.9186i −0.510733 0.884615i
508508 8.00000 13.8564i 0.354943 0.614779i
509509 15.0000 + 25.9808i 0.664863 + 1.15158i 0.979322 + 0.202306i 0.0648436π0.0648436\pi
−0.314459 + 0.949271i 0.601823π0.601823\pi
510510 6.00000 10.3923i 0.265684 0.460179i
511511 2.00000 3.46410i 0.0884748 0.153243i
512512 32.0000 1.41421
513513 −3.50000 2.59808i −0.154529 0.114708i
514514 4.00000 0.176432
515515 −4.00000 + 6.92820i −0.176261 + 0.305293i
516516 −10.0000 + 17.3205i −0.440225 + 0.762493i
517517 6.00000 + 10.3923i 0.263880 + 0.457053i
518518 −4.00000 + 6.92820i −0.175750 + 0.304408i
519519 −3.00000 5.19615i −0.131685 0.228086i
520520 0 0
521521 −7.00000 −0.306676 −0.153338 0.988174i 0.549002π-0.549002\pi
−0.153338 + 0.988174i 0.549002π0.549002\pi
522522 −7.00000 12.1244i −0.306382 0.530669i
523523 11.0000 + 19.0526i 0.480996 + 0.833110i 0.999762 0.0218062i 0.00694167π-0.00694167\pi
−0.518766 + 0.854916i 0.673608π0.673608\pi
524524 −16.0000 −0.698963
525525 −2.00000 −0.0872872
526526 −12.0000 20.7846i −0.523225 0.906252i
527527 −27.0000 + 46.7654i −1.17614 + 2.03713i
528528 −6.00000 10.3923i −0.261116 0.452267i
529529 −20.5000 + 35.5070i −0.891304 + 1.54378i
530530 14.0000 24.2487i 0.608121 1.05330i
531531 3.00000 0.130189
532532 2.00000 17.3205i 0.0867110 0.750939i
533533 36.0000 1.55933
534534 −3.00000 + 5.19615i −0.129823 + 0.224860i
535535 6.00000 10.3923i 0.259403 0.449299i
536536 0 0
537537 −0.500000 + 0.866025i −0.0215766 + 0.0373718i
538538 −21.0000 36.3731i −0.905374 1.56815i
539539 9.00000 0.387657
540540 −2.00000 −0.0860663
541541 4.50000 + 7.79423i 0.193470 + 0.335100i 0.946398 0.323003i 0.104692π-0.104692\pi
−0.752928 + 0.658103i 0.771359π0.771359\pi
542542 5.00000 + 8.66025i 0.214768 + 0.371990i
543543 −14.0000 −0.600798
544544 −48.0000 −2.05798
545545 1.50000 + 2.59808i 0.0642529 + 0.111289i
546546 12.0000 20.7846i 0.513553 0.889499i
547547 −14.0000 24.2487i −0.598597 1.03680i −0.993028 0.117875i 0.962392π-0.962392\pi
0.394432 0.918925i 0.370941π-0.370941\pi
548548 −2.00000 + 3.46410i −0.0854358 + 0.147979i
549549 3.50000 6.06218i 0.149376 0.258727i
550550 −6.00000 −0.255841
551551 −3.50000 + 30.3109i −0.149105 + 1.29129i
552552 0 0
553553 5.00000 8.66025i 0.212622 0.368271i
554554 −16.0000 + 27.7128i −0.679775 + 1.17740i
555555 −1.00000 1.73205i −0.0424476 0.0735215i
556556 4.00000 6.92820i 0.169638 0.293821i
557557 −6.00000 10.3923i −0.254228 0.440336i 0.710457 0.703740i 0.248488π-0.248488\pi
−0.964686 + 0.263404i 0.915155π0.915155\pi
558558 18.0000 0.762001
559559 60.0000 2.53773
560560 4.00000 + 6.92820i 0.169031 + 0.292770i
561561 9.00000 + 15.5885i 0.379980 + 0.658145i
562562 28.0000 1.18111
563563 −18.0000 −0.758610 −0.379305 0.925272i 0.623837π-0.623837\pi
−0.379305 + 0.925272i 0.623837π0.623837\pi
564564 −4.00000 6.92820i −0.168430 0.291730i
565565 3.00000 5.19615i 0.126211 0.218604i
566566 26.0000 + 45.0333i 1.09286 + 1.89289i
567567 1.00000 1.73205i 0.0419961 0.0727393i
568568 0 0
569569 −11.0000 −0.461144 −0.230572 0.973055i 0.574060π-0.574060\pi
−0.230572 + 0.973055i 0.574060π0.574060\pi
570570 7.00000 + 5.19615i 0.293198 + 0.217643i
571571 −15.0000 −0.627730 −0.313865 0.949468i 0.601624π-0.601624\pi
−0.313865 + 0.949468i 0.601624π0.601624\pi
572572 18.0000 31.1769i 0.752618 1.30357i
573573 2.50000 4.33013i 0.104439 0.180894i
574574 12.0000 + 20.7846i 0.500870 + 0.867533i
575575 4.00000 6.92820i 0.166812 0.288926i
576576 4.00000 + 6.92820i 0.166667 + 0.288675i
577577 32.0000 1.33218 0.666089 0.745873i 0.267967π-0.267967\pi
0.666089 + 0.745873i 0.267967π0.267967\pi
578578 38.0000 1.58059
579579 9.00000 + 15.5885i 0.374027 + 0.647834i
580580 7.00000 + 12.1244i 0.290659 + 0.503436i
581581 12.0000 0.497844
582582 −24.0000 −0.994832
583583 21.0000 + 36.3731i 0.869731 + 1.50642i
584584 0 0
585585 3.00000 + 5.19615i 0.124035 + 0.214834i
586586 12.0000 20.7846i 0.495715 0.858604i
587587 −11.0000 + 19.0526i −0.454019 + 0.786383i −0.998631 0.0523045i 0.983343π-0.983343\pi
0.544613 + 0.838688i 0.316677π0.316677\pi
588588 −6.00000 −0.247436
589589 −31.5000 23.3827i −1.29793 0.963467i
590590 −6.00000 −0.247016
591591 9.00000 15.5885i 0.370211 0.641223i
592592 −4.00000 + 6.92820i −0.164399 + 0.284747i
593593 5.00000 + 8.66025i 0.205325 + 0.355634i 0.950236 0.311530i 0.100841π-0.100841\pi
−0.744911 + 0.667164i 0.767508π0.767508\pi
594594 3.00000 5.19615i 0.123091 0.213201i
595595 −6.00000 10.3923i −0.245976 0.426043i
596596 −6.00000 −0.245770
597597 −11.0000 −0.450200
598598 48.0000 + 83.1384i 1.96287 + 3.39978i
599599 −2.00000 3.46410i −0.0817178 0.141539i 0.822270 0.569097i 0.192707π-0.192707\pi
−0.903988 + 0.427558i 0.859374π0.859374\pi
600600 0 0
601601 1.00000 0.0407909 0.0203954 0.999792i 0.493507π-0.493507\pi
0.0203954 + 0.999792i 0.493507π0.493507\pi
602602 20.0000 + 34.6410i 0.815139 + 1.41186i
603603 −2.00000 + 3.46410i −0.0814463 + 0.141069i
604604 −5.00000 8.66025i −0.203447 0.352381i
605605 −1.00000 + 1.73205i −0.0406558 + 0.0704179i
606606 3.00000 5.19615i 0.121867 0.211079i
607607 −14.0000 −0.568242 −0.284121 0.958788i 0.591702π-0.591702\pi
−0.284121 + 0.958788i 0.591702π0.591702\pi
608608 4.00000 34.6410i 0.162221 1.40488i
609609 −14.0000 −0.567309
610610 −7.00000 + 12.1244i −0.283422 + 0.490901i
611611 −12.0000 + 20.7846i −0.485468 + 0.840855i
612612 −6.00000 10.3923i −0.242536 0.420084i
613613 19.0000 32.9090i 0.767403 1.32918i −0.171564 0.985173i 0.554882π-0.554882\pi
0.938967 0.344008i 0.111785π-0.111785\pi
614614 −16.0000 27.7128i −0.645707 1.11840i
615615 −6.00000 −0.241943
616616 0 0
617617 −14.0000 24.2487i −0.563619 0.976216i −0.997177 0.0750907i 0.976075π-0.976075\pi
0.433558 0.901126i 0.357258π-0.357258\pi
618618 8.00000 + 13.8564i 0.321807 + 0.557386i
619619 −16.0000 −0.643094 −0.321547 0.946894i 0.604203π-0.604203\pi
−0.321547 + 0.946894i 0.604203π0.604203\pi
620620 −18.0000 −0.722897
621621 4.00000 + 6.92820i 0.160514 + 0.278019i
622622 8.00000 13.8564i 0.320771 0.555591i
623623 3.00000 + 5.19615i 0.120192 + 0.208179i
624624 12.0000 20.7846i 0.480384 0.832050i
625625 −0.500000 + 0.866025i −0.0200000 + 0.0346410i
626626 −16.0000 −0.639489
627627 −12.0000 + 5.19615i −0.479234 + 0.207514i
628628 −40.0000 −1.59617
629629 6.00000 10.3923i 0.239236 0.414368i
630630 −2.00000 + 3.46410i −0.0796819 + 0.138013i
631631 −14.5000 25.1147i −0.577236 0.999802i −0.995795 0.0916122i 0.970798π-0.970798\pi
0.418559 0.908190i 0.362535π-0.362535\pi
632632 0 0
633633 −6.50000 11.2583i −0.258352 0.447478i
634634 24.0000 0.953162
635635 8.00000 0.317470
636636 −14.0000 24.2487i −0.555136 0.961524i
637637 9.00000 + 15.5885i 0.356593 + 0.617637i
638638 −42.0000 −1.66280
639639 7.00000 0.276916
640640 0 0
641641 −9.50000 + 16.4545i −0.375227 + 0.649913i −0.990361 0.138510i 0.955769π-0.955769\pi
0.615134 + 0.788423i 0.289102π0.289102\pi
642642 −12.0000 20.7846i −0.473602 0.820303i
643643 −16.0000 + 27.7128i −0.630978 + 1.09289i 0.356374 + 0.934344i 0.384013π0.384013\pi
−0.987352 + 0.158543i 0.949320π0.949320\pi
644644 −16.0000 + 27.7128i −0.630488 + 1.09204i
645645 −10.0000 −0.393750
646646 −6.00000 + 51.9615i −0.236067 + 2.04440i
647647 2.00000 0.0786281 0.0393141 0.999227i 0.487483π-0.487483\pi
0.0393141 + 0.999227i 0.487483π0.487483\pi
648648 0 0
649649 4.50000 7.79423i 0.176640 0.305950i
650650 −6.00000 10.3923i −0.235339 0.407620i
651651 9.00000 15.5885i 0.352738 0.610960i
652652 10.0000 + 17.3205i 0.391630 + 0.678323i
653653 −18.0000 −0.704394 −0.352197 0.935926i 0.614565π-0.614565\pi
−0.352197 + 0.935926i 0.614565π0.614565\pi
654654 6.00000 0.234619
655655 −4.00000 6.92820i −0.156293 0.270707i
656656 12.0000 + 20.7846i 0.468521 + 0.811503i
657657 2.00000 0.0780274
658658 −16.0000 −0.623745
659659 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
660660 −3.00000 + 5.19615i −0.116775 + 0.202260i
661661 −8.50000 14.7224i −0.330612 0.572636i 0.652020 0.758202i 0.273922π-0.273922\pi
−0.982632 + 0.185565i 0.940588π0.940588\pi
662662 8.00000 13.8564i 0.310929 0.538545i
663663 −18.0000 + 31.1769i −0.699062 + 1.21081i
664664 0 0
665665 8.00000 3.46410i 0.310227 0.134332i
666666 −4.00000 −0.154997
667667 28.0000 48.4974i 1.08416 1.87783i
668668 −22.0000 + 38.1051i −0.851206 + 1.47433i
669669 −4.00000 6.92820i −0.154649 0.267860i
670670 4.00000 6.92820i 0.154533 0.267660i
671671 −10.5000 18.1865i −0.405348 0.702083i
672672 16.0000 0.617213
673673 −36.0000 −1.38770 −0.693849 0.720121i 0.744086π-0.744086\pi
−0.693849 + 0.720121i 0.744086π0.744086\pi
674674 12.0000 + 20.7846i 0.462223 + 0.800593i
675675 −0.500000 0.866025i −0.0192450 0.0333333i
676676 46.0000 1.76923
677677 30.0000 1.15299 0.576497 0.817099i 0.304419π-0.304419\pi
0.576497 + 0.817099i 0.304419π0.304419\pi
678678 −6.00000 10.3923i −0.230429 0.399114i
679679 −12.0000 + 20.7846i −0.460518 + 0.797640i
680680 0 0
681681 −7.00000 + 12.1244i −0.268241 + 0.464606i
682682 27.0000 46.7654i 1.03388 1.79074i
683683 −36.0000 −1.37750 −0.688751 0.724998i 0.741841π-0.741841\pi
−0.688751 + 0.724998i 0.741841π0.741841\pi
684684 8.00000 3.46410i 0.305888 0.132453i
685685 −2.00000 −0.0764161
686686 −20.0000 + 34.6410i −0.763604 + 1.32260i
687687 −14.5000 + 25.1147i −0.553210 + 0.958187i
688688 20.0000 + 34.6410i 0.762493 + 1.32068i
689689 −42.0000 + 72.7461i −1.60007 + 2.77141i
690690 −8.00000 13.8564i −0.304555 0.527504i
691691 −1.00000 −0.0380418 −0.0190209 0.999819i 0.506055π-0.506055\pi
−0.0190209 + 0.999819i 0.506055π0.506055\pi
692692 12.0000 0.456172
693693 −3.00000 5.19615i −0.113961 0.197386i
694694 −2.00000 3.46410i −0.0759190 0.131495i
695695 4.00000 0.151729
696696 0 0
697697 −18.0000 31.1769i −0.681799 1.18091i
698698 2.00000 3.46410i 0.0757011 0.131118i
699699 −8.00000 13.8564i −0.302588 0.524097i
700700 2.00000 3.46410i 0.0755929 0.130931i
701701 −9.00000 + 15.5885i −0.339925 + 0.588768i −0.984418 0.175842i 0.943735π-0.943735\pi
0.644493 + 0.764610i 0.277068π0.277068\pi
702702 12.0000 0.452911
703703 7.00000 + 5.19615i 0.264010 + 0.195977i
704704 24.0000 0.904534
705705 2.00000 3.46410i 0.0753244 0.130466i
706706 −2.00000 + 3.46410i −0.0752710 + 0.130373i
707707 −3.00000 5.19615i −0.112827 0.195421i
708708 −3.00000 + 5.19615i −0.112747 + 0.195283i
709709 17.5000 + 30.3109i 0.657226 + 1.13835i 0.981331 + 0.192328i 0.0616038π0.0616038\pi
−0.324104 + 0.946021i 0.605063π0.605063\pi
710710 −14.0000 −0.525411
711711 5.00000 0.187515
712712 0 0
713713 36.0000 + 62.3538i 1.34821 + 2.33517i
714714 −24.0000 −0.898177
715715 18.0000 0.673162
716716 −1.00000 1.73205i −0.0373718 0.0647298i
717717 4.50000 7.79423i 0.168056 0.291081i
718718 32.0000 + 55.4256i 1.19423 + 2.06847i
719719 −16.5000 + 28.5788i −0.615346 + 1.06581i 0.374978 + 0.927034i 0.377650π0.377650\pi
−0.990324 + 0.138777i 0.955683π0.955683\pi
720720 −2.00000 + 3.46410i −0.0745356 + 0.129099i
721721 16.0000 0.595871
722722 −37.0000 8.66025i −1.37700 0.322301i
723723 21.0000 0.780998
724724 14.0000 24.2487i 0.520306 0.901196i
725725 −3.50000 + 6.06218i −0.129987 + 0.225144i
726726 2.00000 + 3.46410i 0.0742270 + 0.128565i
727727 −7.00000 + 12.1244i −0.259616 + 0.449667i −0.966139 0.258022i 0.916929π-0.916929\pi
0.706523 + 0.707690i 0.250263π0.250263\pi
728728 0 0
729729 1.00000 0.0370370
730730 −4.00000 −0.148047
731731 −30.0000 51.9615i −1.10959 1.92187i
732732 7.00000 + 12.1244i 0.258727 + 0.448129i
733733 14.0000 0.517102 0.258551 0.965998i 0.416755π-0.416755\pi
0.258551 + 0.965998i 0.416755π0.416755\pi
734734 −40.0000 −1.47643
735735 −1.50000 2.59808i −0.0553283 0.0958315i
736736 −32.0000 + 55.4256i −1.17954 + 2.04302i
737737 6.00000 + 10.3923i 0.221013 + 0.382805i
738738 −6.00000 + 10.3923i −0.220863 + 0.382546i
739739 14.5000 25.1147i 0.533391 0.923861i −0.465848 0.884865i 0.654251π-0.654251\pi
0.999239 0.0389959i 0.0124159π-0.0124159\pi
740740 4.00000 0.147043
741741 −21.0000 15.5885i −0.771454 0.572656i
742742 −56.0000 −2.05582
743743 3.00000 5.19615i 0.110059 0.190628i −0.805735 0.592277i 0.798229π-0.798229\pi
0.915794 + 0.401648i 0.131563π0.131563\pi
744744 0 0
745745 −1.50000 2.59808i −0.0549557 0.0951861i
746746 24.0000 41.5692i 0.878702 1.52196i
747747 3.00000 + 5.19615i 0.109764 + 0.190117i
748748 −36.0000 −1.31629
749749 −24.0000 −0.876941
750750 1.00000 + 1.73205i 0.0365148 + 0.0632456i
751751 −14.5000 25.1147i −0.529113 0.916450i −0.999424 0.0339490i 0.989192π-0.989192\pi
0.470311 0.882501i 0.344142π-0.344142\pi
752752 −16.0000 −0.583460
753753 3.00000 0.109326
754754 −42.0000 72.7461i −1.52955 2.64926i
755755 2.50000 4.33013i 0.0909843 0.157589i
756756 2.00000 + 3.46410i 0.0727393 + 0.125988i
757757 −23.0000 + 39.8372i −0.835949 + 1.44791i 0.0573060 + 0.998357i 0.481749π0.481749\pi
−0.893255 + 0.449550i 0.851584π0.851584\pi
758758 25.0000 43.3013i 0.908041 1.57277i
759759 24.0000 0.871145
760760 0 0
761761 −30.0000 −1.08750 −0.543750 0.839248i 0.682996π-0.682996\pi
−0.543750 + 0.839248i 0.682996π0.682996\pi
762762 8.00000 13.8564i 0.289809 0.501965i
763763 3.00000 5.19615i 0.108607 0.188113i
764764 5.00000 + 8.66025i 0.180894 + 0.313317i
765765 3.00000 5.19615i 0.108465 0.187867i
766766 34.0000 + 58.8897i 1.22847 + 2.12777i
767767 18.0000 0.649942
768768 16.0000 0.577350
769769 −6.50000 11.2583i −0.234396 0.405986i 0.724701 0.689063i 0.241978π-0.241978\pi
−0.959097 + 0.283078i 0.908645π0.908645\pi
770770 6.00000 + 10.3923i 0.216225 + 0.374513i
771771 2.00000 0.0720282
772772 −36.0000 −1.29567
773773 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
774774 −10.0000 + 17.3205i −0.359443 + 0.622573i
775775 −4.50000 7.79423i −0.161645 0.279977i
776776 0 0
777777 −2.00000 + 3.46410i −0.0717496 + 0.124274i
778778 74.0000 2.65303
779779 24.0000 10.3923i 0.859889 0.372343i
780780 −12.0000 −0.429669
781781 10.5000 18.1865i 0.375720 0.650765i
782782 48.0000 83.1384i 1.71648 2.97302i
783783 −3.50000 6.06218i −0.125080 0.216645i
784784 −6.00000 + 10.3923i −0.214286 + 0.371154i
785785 −10.0000 17.3205i −0.356915 0.618195i
786786 −16.0000 −0.570701
787787 −28.0000 −0.998092 −0.499046 0.866575i 0.666316π-0.666316\pi
−0.499046 + 0.866575i 0.666316π0.666316\pi
788788 18.0000 + 31.1769i 0.641223 + 1.11063i
789789 −6.00000 10.3923i −0.213606 0.369976i
790790 −10.0000 −0.355784
791791 −12.0000 −0.426671
792792 0 0
793793 21.0000 36.3731i 0.745732 1.29165i
794794 −12.0000 20.7846i −0.425864 0.737618i
795795 7.00000 12.1244i 0.248264 0.430007i
796796 11.0000 19.0526i 0.389885 0.675300i
797797 34.0000 1.20434 0.602171 0.798367i 0.294303π-0.294303\pi
0.602171 + 0.798367i 0.294303π0.294303\pi
798798 2.00000 17.3205i 0.0707992 0.613139i
799799 24.0000 0.849059
800800 4.00000 6.92820i 0.141421 0.244949i
801801 −1.50000 + 2.59808i −0.0529999 + 0.0917985i
802802 23.0000 + 39.8372i 0.812158 + 1.40670i
803803 3.00000 5.19615i 0.105868 0.183368i
804804 −4.00000 6.92820i −0.141069 0.244339i
805805 −16.0000 −0.563926
806806 108.000 3.80414
807807 −10.5000 18.1865i −0.369618 0.640196i
808808 0 0
809809 −37.0000 −1.30085 −0.650425 0.759570i 0.725409π-0.725409\pi
−0.650425 + 0.759570i 0.725409π0.725409\pi
810810 −2.00000 −0.0702728
811811 3.50000 + 6.06218i 0.122902 + 0.212872i 0.920911 0.389774i 0.127447π-0.127447\pi
−0.798009 + 0.602645i 0.794113π0.794113\pi
812812 14.0000 24.2487i 0.491304 0.850963i
813813 2.50000 + 4.33013i 0.0876788 + 0.151864i
814814 −6.00000 + 10.3923i −0.210300 + 0.364250i
815815 −5.00000 + 8.66025i −0.175142 + 0.303355i
816816 −24.0000 −0.840168
817817 40.0000 17.3205i 1.39942 0.605968i
818818 22.0000 0.769212
819819 6.00000 10.3923i 0.209657 0.363137i
820820 6.00000 10.3923i 0.209529 0.362915i
821821 −7.50000 12.9904i −0.261752 0.453367i 0.704956 0.709251i 0.250967π-0.250967\pi
−0.966708 + 0.255884i 0.917634π0.917634\pi
822822 −2.00000 + 3.46410i −0.0697580 + 0.120824i
823823 −8.00000 13.8564i −0.278862 0.483004i 0.692240 0.721668i 0.256624π-0.256624\pi
−0.971102 + 0.238664i 0.923291π0.923291\pi
824824 0 0
825825 −3.00000 −0.104447
826826 6.00000 + 10.3923i 0.208767 + 0.361595i
827827 −24.0000 41.5692i −0.834562 1.44550i −0.894387 0.447295i 0.852388π-0.852388\pi
0.0598250 0.998209i 0.480946π-0.480946\pi
828828 −16.0000 −0.556038
829829 −6.00000 −0.208389 −0.104194 0.994557i 0.533226π-0.533226\pi
−0.104194 + 0.994557i 0.533226π0.533226\pi
830830 −6.00000 10.3923i −0.208263 0.360722i
831831 −8.00000 + 13.8564i −0.277517 + 0.480673i
832832 24.0000 + 41.5692i 0.832050 + 1.44115i
833833 9.00000 15.5885i 0.311832 0.540108i
834834 4.00000 6.92820i 0.138509 0.239904i
835835 −22.0000 −0.761341
836836 3.00000 25.9808i 0.103757 0.898563i
837837 9.00000 0.311086
838838 9.00000 15.5885i 0.310900 0.538494i
839839 8.00000 13.8564i 0.276191 0.478376i −0.694244 0.719740i 0.744261π-0.744261\pi
0.970435 + 0.241363i 0.0775945π0.0775945\pi
840840 0 0
841841 −10.0000 + 17.3205i −0.344828 + 0.597259i
842842 −9.00000 15.5885i −0.310160 0.537214i
843843 14.0000 0.482186
844844 26.0000 0.894957
845845 11.5000 + 19.9186i 0.395612 + 0.685220i
846846 −4.00000 6.92820i −0.137523 0.238197i
847847 4.00000 0.137442
848848 −56.0000 −1.92305
849849 13.0000 + 22.5167i 0.446159 + 0.772770i
850850 −6.00000 + 10.3923i −0.205798 + 0.356453i
851851 −8.00000 13.8564i −0.274236 0.474991i
852852 −7.00000 + 12.1244i −0.239816 + 0.415374i
853853 17.0000 29.4449i 0.582069 1.00817i −0.413165 0.910656i 0.635577π-0.635577\pi
0.995234 0.0975167i 0.0310899π-0.0310899\pi
854854 28.0000 0.958140
855855 3.50000 + 2.59808i 0.119697 + 0.0888523i
856856 0 0
857857 13.0000 22.5167i 0.444072 0.769154i −0.553915 0.832573i 0.686867π-0.686867\pi
0.997987 + 0.0634184i 0.0202003π0.0202003\pi
858858 18.0000 31.1769i 0.614510 1.06436i
859859 −2.50000 4.33013i −0.0852989 0.147742i 0.820220 0.572049i 0.193851π-0.193851\pi
−0.905519 + 0.424307i 0.860518π0.860518\pi
860860 10.0000 17.3205i 0.340997 0.590624i
861861 6.00000 + 10.3923i 0.204479 + 0.354169i
862862 −42.0000 −1.43053
863863 −6.00000 −0.204242 −0.102121 0.994772i 0.532563π-0.532563\pi
−0.102121 + 0.994772i 0.532563π0.532563\pi
864864 4.00000 + 6.92820i 0.136083 + 0.235702i
865865 3.00000 + 5.19615i 0.102003 + 0.176674i
866866 −20.0000 −0.679628
867867 19.0000 0.645274
868868 18.0000 + 31.1769i 0.610960 + 1.05821i
869869 7.50000 12.9904i 0.254420 0.440668i
870870 7.00000 + 12.1244i 0.237322 + 0.411054i
871871 −12.0000 + 20.7846i −0.406604 + 0.704260i
872872 0 0
873873 −12.0000 −0.406138
874874 56.0000 + 41.5692i 1.89423 + 1.40610i
875875 2.00000 0.0676123
876876 −2.00000 + 3.46410i −0.0675737 + 0.117041i
877877 −6.00000 + 10.3923i −0.202606 + 0.350923i −0.949367 0.314169i 0.898274π-0.898274\pi
0.746762 + 0.665092i 0.231608π0.231608\pi
878878 9.00000 + 15.5885i 0.303735 + 0.526085i
879879 6.00000 10.3923i 0.202375 0.350524i
880880 6.00000 + 10.3923i 0.202260 + 0.350325i
881881 3.00000 0.101073 0.0505363 0.998722i 0.483907π-0.483907\pi
0.0505363 + 0.998722i 0.483907π0.483907\pi
882882 −6.00000 −0.202031
883883 −10.0000 17.3205i −0.336527 0.582882i 0.647250 0.762278i 0.275919π-0.275919\pi
−0.983777 + 0.179396i 0.942586π0.942586\pi
884884 −36.0000 62.3538i −1.21081 2.09719i
885885 −3.00000 −0.100844
886886 0 0
887887 6.00000 + 10.3923i 0.201460 + 0.348939i 0.948999 0.315279i 0.102098π-0.102098\pi
−0.747539 + 0.664218i 0.768765π0.768765\pi
888888 0 0
889889 −8.00000 13.8564i −0.268311 0.464729i
890890 3.00000 5.19615i 0.100560 0.174175i
891891 1.50000 2.59808i 0.0502519 0.0870388i
892892 16.0000 0.535720
893893 −2.00000 + 17.3205i −0.0669274 + 0.579609i
894894 −6.00000 −0.200670
895895 0.500000 0.866025i 0.0167132 0.0289480i
896896 0 0
897897 24.0000 + 41.5692i 0.801337 + 1.38796i
898898 −13.0000 + 22.5167i −0.433816 + 0.751391i
899899 −31.5000 54.5596i −1.05058 1.81966i
900900 2.00000 0.0666667
901901 84.0000 2.79845
902902 18.0000 + 31.1769i 0.599334 + 1.03808i
903903 10.0000 + 17.3205i 0.332779 + 0.576390i
904904 0 0
905905 14.0000 0.465376
906906 −5.00000 8.66025i −0.166114 0.287718i
907907 2.00000 3.46410i 0.0664089 0.115024i −0.830909 0.556408i 0.812179π-0.812179\pi
0.897318 + 0.441384i 0.145512π0.145512\pi
908908 −14.0000 24.2487i −0.464606 0.804722i
909909 1.50000 2.59808i 0.0497519 0.0861727i
910910 −12.0000 + 20.7846i −0.397796 + 0.689003i
911911 −45.0000 −1.49092 −0.745458 0.666552i 0.767769π-0.767769\pi
−0.745458 + 0.666552i 0.767769π0.767769\pi
912912 2.00000 17.3205i 0.0662266 0.573539i
913913 18.0000 0.595713
914914 −12.0000 + 20.7846i −0.396925 + 0.687494i
915915 −3.50000 + 6.06218i −0.115706 + 0.200409i
916916 −29.0000 50.2295i −0.958187 1.65963i
917917 −8.00000 + 13.8564i −0.264183 + 0.457579i
918918 −6.00000 10.3923i −0.198030 0.342997i
919919 −40.0000 −1.31948 −0.659739 0.751495i 0.729333π-0.729333\pi
−0.659739 + 0.751495i 0.729333π0.729333\pi
920920 0 0
921921 −8.00000 13.8564i −0.263609 0.456584i
922922 −33.0000 57.1577i −1.08680 1.88239i
923923 42.0000 1.38245
924924 12.0000 0.394771
925925 1.00000 + 1.73205i 0.0328798 + 0.0569495i
926926 26.0000 45.0333i 0.854413 1.47989i
927927 4.00000 + 6.92820i 0.131377 + 0.227552i
928928 28.0000 48.4974i 0.919145 1.59201i
929929 7.50000 12.9904i 0.246067 0.426201i −0.716364 0.697727i 0.754195π-0.754195\pi
0.962431 + 0.271526i 0.0875283π0.0875283\pi
930930 −18.0000 −0.590243
931931 10.5000 + 7.79423i 0.344124 + 0.255446i
932932 32.0000 1.04819
933933 4.00000 6.92820i 0.130954 0.226819i
934934 18.0000 31.1769i 0.588978 1.02014i
935935 −9.00000 15.5885i −0.294331 0.509797i
936936 0 0
937937 −15.0000 25.9808i −0.490029 0.848755i 0.509906 0.860230i 0.329680π-0.329680\pi
−0.999934 + 0.0114759i 0.996347π0.996347\pi
938938 −16.0000 −0.522419
939939 −8.00000 −0.261070
940940 4.00000 + 6.92820i 0.130466 + 0.225973i
941941 −8.50000 14.7224i −0.277092 0.479938i 0.693569 0.720390i 0.256037π-0.256037\pi
−0.970661 + 0.240453i 0.922704π0.922704\pi
942942 −40.0000 −1.30327
943943 −48.0000 −1.56310
944944 6.00000 + 10.3923i 0.195283 + 0.338241i
945945 −1.00000 + 1.73205i −0.0325300 + 0.0563436i
946946 30.0000 + 51.9615i 0.975384 + 1.68941i
947947 12.0000 20.7846i 0.389948 0.675409i −0.602494 0.798123i 0.705826π-0.705826\pi
0.992442 + 0.122714i 0.0391598π0.0391598\pi
948948 −5.00000 + 8.66025i −0.162392 + 0.281272i
949949 12.0000 0.389536
950950 −7.00000 5.19615i −0.227110 0.168585i
951951 12.0000 0.389127
952952 0 0
953953 −12.0000 + 20.7846i −0.388718 + 0.673280i −0.992277 0.124039i 0.960415π-0.960415\pi
0.603559 + 0.797318i 0.293749π0.293749\pi
954954 −14.0000 24.2487i −0.453267 0.785081i
955955 −2.50000 + 4.33013i −0.0808981 + 0.140120i
956956 9.00000 + 15.5885i 0.291081 + 0.504167i
957957 −21.0000 −0.678834
958958 −30.0000 −0.969256
959959 2.00000 + 3.46410i 0.0645834 + 0.111862i
960960 −4.00000 6.92820i −0.129099 0.223607i
961961 50.0000 1.61290
962962 −24.0000 −0.773791
963963 −6.00000 10.3923i −0.193347 0.334887i
964964 −21.0000 + 36.3731i −0.676364 + 1.17150i
965965 −9.00000 15.5885i −0.289720 0.501810i
966966 −16.0000 + 27.7128i −0.514792 + 0.891645i
967967 −20.0000 + 34.6410i −0.643157 + 1.11398i 0.341567 + 0.939857i 0.389042π0.389042\pi
−0.984724 + 0.174123i 0.944291π0.944291\pi
968968 0 0
969969 −3.00000 + 25.9808i −0.0963739 + 0.834622i
970970 24.0000 0.770594
971971 16.0000 27.7128i 0.513464 0.889346i −0.486414 0.873729i 0.661695π-0.661695\pi
0.999878 0.0156178i 0.00497150π-0.00497150\pi
972972 −1.00000 + 1.73205i −0.0320750 + 0.0555556i
973973 −4.00000 6.92820i −0.128234 0.222108i
974974 22.0000 38.1051i 0.704925 1.22097i
975975 −3.00000 5.19615i −0.0960769 0.166410i
976976 28.0000 0.896258
977977 42.0000 1.34370 0.671850 0.740688i 0.265500π-0.265500\pi
0.671850 + 0.740688i 0.265500π0.265500\pi
978978 10.0000 + 17.3205i 0.319765 + 0.553849i
979979 4.50000 + 7.79423i 0.143821 + 0.249105i
980980 6.00000 0.191663
981981 3.00000 0.0957826
982982 5.00000 + 8.66025i 0.159556 + 0.276360i
983983 −13.0000 + 22.5167i −0.414636 + 0.718170i −0.995390 0.0959088i 0.969424π-0.969424\pi
0.580755 + 0.814079i 0.302758π0.302758\pi
984984 0 0
985985 −9.00000 + 15.5885i −0.286764 + 0.496690i
986986 −42.0000 + 72.7461i −1.33755 + 2.31671i
987987 −8.00000 −0.254643
988988 48.0000 20.7846i 1.52708 0.661247i
989989 −80.0000 −2.54385
990990 −3.00000 + 5.19615i −0.0953463 + 0.165145i
991991 −28.0000 + 48.4974i −0.889449 + 1.54057i −0.0489218 + 0.998803i 0.515578π0.515578\pi
−0.840528 + 0.541769i 0.817755π0.817755\pi
992992 36.0000 + 62.3538i 1.14300 + 1.97974i
993993 4.00000 6.92820i 0.126936 0.219860i
994994 14.0000 + 24.2487i 0.444053 + 0.769122i
995995 11.0000 0.348723
996996 −12.0000 −0.380235
997997 20.0000 + 34.6410i 0.633406 + 1.09709i 0.986850 + 0.161636i 0.0516771π0.0516771\pi
−0.353444 + 0.935456i 0.614990π0.614990\pi
998998 −12.0000 20.7846i −0.379853 0.657925i
999999 −2.00000 −0.0632772
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 285.2.i.a.106.1 2
3.2 odd 2 855.2.k.d.676.1 2
19.7 even 3 inner 285.2.i.a.121.1 yes 2
19.8 odd 6 5415.2.a.a.1.1 1
19.11 even 3 5415.2.a.k.1.1 1
57.26 odd 6 855.2.k.d.406.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
285.2.i.a.106.1 2 1.1 even 1 trivial
285.2.i.a.121.1 yes 2 19.7 even 3 inner
855.2.k.d.406.1 2 57.26 odd 6
855.2.k.d.676.1 2 3.2 odd 2
5415.2.a.a.1.1 1 19.8 odd 6
5415.2.a.k.1.1 1 19.11 even 3