Properties

Label 114.2.e.b.49.1
Level 114114
Weight 22
Character 114.49
Analytic conductor 0.9100.910
Analytic rank 00
Dimension 22
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [114,2,Mod(7,114)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(114, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("114.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 114=2319 114 = 2 \cdot 3 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 114.e (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: 0.9102945830430.910294583043
Analytic rank: 00
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]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 49.1
Root 0.500000+0.866025i0.500000 + 0.866025i of defining polynomial
Character χ\chi == 114.49
Dual form 114.2.e.b.7.1

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+(0.5000000.866025i)q2+(0.5000000.866025i)q3+(0.5000000.866025i)q4+(0.5000000.866025i)q6+1.00000q71.00000q8+(0.5000000.866025i)q92.00000q111.00000q12+(1.50000+2.59808i)q13+(0.5000000.866025i)q14+(0.500000+0.866025i)q16+(2.00000+3.46410i)q171.00000q18+(4.00000+1.73205i)q19+(0.5000000.866025i)q21+(1.00000+1.73205i)q22+(2.000003.46410i)q23+(0.500000+0.866025i)q24+(2.50000+4.33013i)q25+3.00000q261.00000q27+(0.5000000.866025i)q283.00000q31+(0.500000+0.866025i)q32+(1.00000+1.73205i)q33+(2.00000+3.46410i)q34+(0.500000+0.866025i)q365.00000q37+(3.500002.59808i)q38+3.00000q39+(2.00000+3.46410i)q41+(0.5000000.866025i)q42+(4.500007.79423i)q43+(1.00000+1.73205i)q444.00000q46+(5.000008.66025i)q47+(0.500000+0.866025i)q486.00000q49+5.00000q50+(2.00000+3.46410i)q51+(1.500002.59808i)q52+(2.00000+3.46410i)q53+(0.500000+0.866025i)q541.00000q56+(3.500002.59808i)q57+(7.0000012.1244i)q59+(5.500009.52628i)q61+(1.50000+2.59808i)q62+(0.5000000.866025i)q63+1.00000q64+(1.00000+1.73205i)q66+(1.500002.59808i)q67+4.00000q684.00000q69+(7.00000+12.1244i)q71+(0.500000+0.866025i)q72+(5.500009.52628i)q73+(2.50000+4.33013i)q74+5.00000q75+(0.5000004.33013i)q762.00000q77+(1.500002.59808i)q78+(0.500000+0.866025i)q79+(0.500000+0.866025i)q81+(2.00000+3.46410i)q82+8.00000q831.00000q84+(4.500007.79423i)q86+2.00000q88+(7.00000+12.1244i)q89+(1.50000+2.59808i)q91+(2.00000+3.46410i)q92+(1.50000+2.59808i)q9310.0000q94+1.00000q96+(1.00000+1.73205i)q97+(3.00000+5.19615i)q98+(1.00000+1.73205i)q99+O(q100)q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -2.00000 q^{11} -1.00000 q^{12} +(1.50000 + 2.59808i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} -1.00000 q^{18} +(4.00000 + 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +3.00000 q^{26} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} -3.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(2.00000 + 3.46410i) q^{34} +(-0.500000 + 0.866025i) q^{36} -5.00000 q^{37} +(3.50000 - 2.59808i) q^{38} +3.00000 q^{39} +(-2.00000 + 3.46410i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(4.50000 - 7.79423i) q^{43} +(1.00000 + 1.73205i) q^{44} -4.00000 q^{46} +(-5.00000 - 8.66025i) q^{47} +(0.500000 + 0.866025i) q^{48} -6.00000 q^{49} +5.00000 q^{50} +(2.00000 + 3.46410i) q^{51} +(1.50000 - 2.59808i) q^{52} +(2.00000 + 3.46410i) q^{53} +(-0.500000 + 0.866025i) q^{54} -1.00000 q^{56} +(3.50000 - 2.59808i) q^{57} +(7.00000 - 12.1244i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(-1.50000 + 2.59808i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{66} +(-1.50000 - 2.59808i) q^{67} +4.00000 q^{68} -4.00000 q^{69} +(-7.00000 + 12.1244i) q^{71} +(0.500000 + 0.866025i) q^{72} +(5.50000 - 9.52628i) q^{73} +(-2.50000 + 4.33013i) q^{74} +5.00000 q^{75} +(-0.500000 - 4.33013i) q^{76} -2.00000 q^{77} +(1.50000 - 2.59808i) q^{78} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.00000 + 3.46410i) q^{82} +8.00000 q^{83} -1.00000 q^{84} +(-4.50000 - 7.79423i) q^{86} +2.00000 q^{88} +(7.00000 + 12.1244i) q^{89} +(1.50000 + 2.59808i) q^{91} +(-2.00000 + 3.46410i) q^{92} +(-1.50000 + 2.59808i) q^{93} -10.0000 q^{94} +1.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(1.00000 + 1.73205i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q2+q3q4q6+2q72q8q94q112q12+3q13+q14q164q172q18+8q19+q212q224q23q24+5q25++2q99+O(q100) 2 q + q^{2} + q^{3} - q^{4} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9} - 4 q^{11} - 2 q^{12} + 3 q^{13} + q^{14} - q^{16} - 4 q^{17} - 2 q^{18} + 8 q^{19} + q^{21} - 2 q^{22} - 4 q^{23} - q^{24} + 5 q^{25}+ \cdots + 2 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/114Z)×\left(\mathbb{Z}/114\mathbb{Z}\right)^\times.

nn 7777 9797
χ(n)\chi(n) 11 e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.500000 0.866025i 0.353553 0.612372i
33 0.500000 0.866025i 0.288675 0.500000i
44 −0.500000 0.866025i −0.250000 0.433013i
55 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
66 −0.500000 0.866025i −0.204124 0.353553i
77 1.00000 0.377964 0.188982 0.981981i 0.439481π-0.439481\pi
0.188982 + 0.981981i 0.439481π0.439481\pi
88 −1.00000 −0.353553
99 −0.500000 0.866025i −0.166667 0.288675i
1010 0 0
1111 −2.00000 −0.603023 −0.301511 0.953463i 0.597491π-0.597491\pi
−0.301511 + 0.953463i 0.597491π0.597491\pi
1212 −1.00000 −0.288675
1313 1.50000 + 2.59808i 0.416025 + 0.720577i 0.995535 0.0943882i 0.0300895π-0.0300895\pi
−0.579510 + 0.814965i 0.696756π0.696756\pi
1414 0.500000 0.866025i 0.133631 0.231455i
1515 0 0
1616 −0.500000 + 0.866025i −0.125000 + 0.216506i
1717 −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i 0.994540π-0.994540\pi
0.514782 + 0.857321i 0.327873π0.327873\pi
1818 −1.00000 −0.235702
1919 4.00000 + 1.73205i 0.917663 + 0.397360i
2020 0 0
2121 0.500000 0.866025i 0.109109 0.188982i
2222 −1.00000 + 1.73205i −0.213201 + 0.369274i
2323 −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i 0.303595π-0.303595\pi
−0.995639 + 0.0932891i 0.970262π0.970262\pi
2424 −0.500000 + 0.866025i −0.102062 + 0.176777i
2525 2.50000 + 4.33013i 0.500000 + 0.866025i
2626 3.00000 0.588348
2727 −1.00000 −0.192450
2828 −0.500000 0.866025i −0.0944911 0.163663i
2929 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
3030 0 0
3131 −3.00000 −0.538816 −0.269408 0.963026i 0.586828π-0.586828\pi
−0.269408 + 0.963026i 0.586828π0.586828\pi
3232 0.500000 + 0.866025i 0.0883883 + 0.153093i
3333 −1.00000 + 1.73205i −0.174078 + 0.301511i
3434 2.00000 + 3.46410i 0.342997 + 0.594089i
3535 0 0
3636 −0.500000 + 0.866025i −0.0833333 + 0.144338i
3737 −5.00000 −0.821995 −0.410997 0.911636i 0.634819π-0.634819\pi
−0.410997 + 0.911636i 0.634819π0.634819\pi
3838 3.50000 2.59808i 0.567775 0.421464i
3939 3.00000 0.480384
4040 0 0
4141 −2.00000 + 3.46410i −0.312348 + 0.541002i −0.978870 0.204483i 0.934449π-0.934449\pi
0.666523 + 0.745485i 0.267782π0.267782\pi
4242 −0.500000 0.866025i −0.0771517 0.133631i
4343 4.50000 7.79423i 0.686244 1.18861i −0.286801 0.957990i 0.592592π-0.592592\pi
0.973044 0.230618i 0.0740749π-0.0740749\pi
4444 1.00000 + 1.73205i 0.150756 + 0.261116i
4545 0 0
4646 −4.00000 −0.589768
4747 −5.00000 8.66025i −0.729325 1.26323i −0.957169 0.289530i 0.906501π-0.906501\pi
0.227844 0.973698i 0.426832π-0.426832\pi
4848 0.500000 + 0.866025i 0.0721688 + 0.125000i
4949 −6.00000 −0.857143
5050 5.00000 0.707107
5151 2.00000 + 3.46410i 0.280056 + 0.485071i
5252 1.50000 2.59808i 0.208013 0.360288i
5353 2.00000 + 3.46410i 0.274721 + 0.475831i 0.970065 0.242846i 0.0780811π-0.0780811\pi
−0.695344 + 0.718677i 0.744748π0.744748\pi
5454 −0.500000 + 0.866025i −0.0680414 + 0.117851i
5555 0 0
5656 −1.00000 −0.133631
5757 3.50000 2.59808i 0.463586 0.344124i
5858 0 0
5959 7.00000 12.1244i 0.911322 1.57846i 0.0991242 0.995075i 0.468396π-0.468396\pi
0.812198 0.583382i 0.198271π-0.198271\pi
6060 0 0
6161 −5.50000 9.52628i −0.704203 1.21972i −0.966978 0.254858i 0.917971π-0.917971\pi
0.262776 0.964857i 0.415362π-0.415362\pi
6262 −1.50000 + 2.59808i −0.190500 + 0.329956i
6363 −0.500000 0.866025i −0.0629941 0.109109i
6464 1.00000 0.125000
6565 0 0
6666 1.00000 + 1.73205i 0.123091 + 0.213201i
6767 −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i 0.225330π-0.225330\pi
−0.942987 + 0.332830i 0.891996π0.891996\pi
6868 4.00000 0.485071
6969 −4.00000 −0.481543
7070 0 0
7171 −7.00000 + 12.1244i −0.830747 + 1.43890i 0.0666994 + 0.997773i 0.478753π0.478753\pi
−0.897447 + 0.441123i 0.854580π0.854580\pi
7272 0.500000 + 0.866025i 0.0589256 + 0.102062i
7373 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i 0.610721π-0.610721\pi
0.984594 0.174855i 0.0559458π-0.0559458\pi
7474 −2.50000 + 4.33013i −0.290619 + 0.503367i
7575 5.00000 0.577350
7676 −0.500000 4.33013i −0.0573539 0.496700i
7777 −2.00000 −0.227921
7878 1.50000 2.59808i 0.169842 0.294174i
7979 −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i 0.851249π-0.851249\pi
0.836527 + 0.547926i 0.184582π0.184582\pi
8080 0 0
8181 −0.500000 + 0.866025i −0.0555556 + 0.0962250i
8282 2.00000 + 3.46410i 0.220863 + 0.382546i
8383 8.00000 0.878114 0.439057 0.898459i 0.355313π-0.355313\pi
0.439057 + 0.898459i 0.355313π0.355313\pi
8484 −1.00000 −0.109109
8585 0 0
8686 −4.50000 7.79423i −0.485247 0.840473i
8787 0 0
8888 2.00000 0.213201
8989 7.00000 + 12.1244i 0.741999 + 1.28518i 0.951584 + 0.307389i 0.0994552π0.0994552\pi
−0.209585 + 0.977790i 0.567211π0.567211\pi
9090 0 0
9191 1.50000 + 2.59808i 0.157243 + 0.272352i
9292 −2.00000 + 3.46410i −0.208514 + 0.361158i
9393 −1.50000 + 2.59808i −0.155543 + 0.269408i
9494 −10.0000 −1.03142
9595 0 0
9696 1.00000 0.102062
9797 −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i 0.865709π-0.865709\pi
0.810782 + 0.585348i 0.199042π0.199042\pi
9898 −3.00000 + 5.19615i −0.303046 + 0.524891i
9999 1.00000 + 1.73205i 0.100504 + 0.174078i
100100 2.50000 4.33013i 0.250000 0.433013i
101101 5.00000 + 8.66025i 0.497519 + 0.861727i 0.999996 0.00286291i 0.000911295π-0.000911295\pi
−0.502477 + 0.864590i 0.667578π0.667578\pi
102102 4.00000 0.396059
103103 −3.00000 −0.295599 −0.147799 0.989017i 0.547219π-0.547219\pi
−0.147799 + 0.989017i 0.547219π0.547219\pi
104104 −1.50000 2.59808i −0.147087 0.254762i
105105 0 0
106106 4.00000 0.388514
107107 −10.0000 −0.966736 −0.483368 0.875417i 0.660587π-0.660587\pi
−0.483368 + 0.875417i 0.660587π0.660587\pi
108108 0.500000 + 0.866025i 0.0481125 + 0.0833333i
109109 −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i 0.400578π0.400578\pi
−0.977769 + 0.209687i 0.932756π0.932756\pi
110110 0 0
111111 −2.50000 + 4.33013i −0.237289 + 0.410997i
112112 −0.500000 + 0.866025i −0.0472456 + 0.0818317i
113113 10.0000 0.940721 0.470360 0.882474i 0.344124π-0.344124\pi
0.470360 + 0.882474i 0.344124π0.344124\pi
114114 −0.500000 4.33013i −0.0468293 0.405554i
115115 0 0
116116 0 0
117117 1.50000 2.59808i 0.138675 0.240192i
118118 −7.00000 12.1244i −0.644402 1.11614i
119119 −2.00000 + 3.46410i −0.183340 + 0.317554i
120120 0 0
121121 −7.00000 −0.636364
122122 −11.0000 −0.995893
123123 2.00000 + 3.46410i 0.180334 + 0.312348i
124124 1.50000 + 2.59808i 0.134704 + 0.233314i
125125 0 0
126126 −1.00000 −0.0890871
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 0.500000 0.866025i 0.0441942 0.0765466i
129129 −4.50000 7.79423i −0.396203 0.686244i
130130 0 0
131131 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i 0.748915π-0.748915\pi
0.966803 + 0.255524i 0.0822479π0.0822479\pi
132132 2.00000 0.174078
133133 4.00000 + 1.73205i 0.346844 + 0.150188i
134134 −3.00000 −0.259161
135135 0 0
136136 2.00000 3.46410i 0.171499 0.297044i
137137 3.00000 + 5.19615i 0.256307 + 0.443937i 0.965250 0.261329i 0.0841608π-0.0841608\pi
−0.708942 + 0.705266i 0.750827π0.750827\pi
138138 −2.00000 + 3.46410i −0.170251 + 0.294884i
139139 9.50000 + 16.4545i 0.805779 + 1.39565i 0.915764 + 0.401718i 0.131587π0.131587\pi
−0.109984 + 0.993933i 0.535080π0.535080\pi
140140 0 0
141141 −10.0000 −0.842152
142142 7.00000 + 12.1244i 0.587427 + 1.01745i
143143 −3.00000 5.19615i −0.250873 0.434524i
144144 1.00000 0.0833333
145145 0 0
146146 −5.50000 9.52628i −0.455183 0.788400i
147147 −3.00000 + 5.19615i −0.247436 + 0.428571i
148148 2.50000 + 4.33013i 0.205499 + 0.355934i
149149 11.0000 19.0526i 0.901155 1.56085i 0.0751583 0.997172i 0.476054π-0.476054\pi
0.825997 0.563675i 0.190613π-0.190613\pi
150150 2.50000 4.33013i 0.204124 0.353553i
151151 −20.0000 −1.62758 −0.813788 0.581161i 0.802599π-0.802599\pi
−0.813788 + 0.581161i 0.802599π0.802599\pi
152152 −4.00000 1.73205i −0.324443 0.140488i
153153 4.00000 0.323381
154154 −1.00000 + 1.73205i −0.0805823 + 0.139573i
155155 0 0
156156 −1.50000 2.59808i −0.120096 0.208013i
157157 10.5000 18.1865i 0.837991 1.45144i −0.0535803 0.998564i 0.517063π-0.517063\pi
0.891572 0.452880i 0.149603π-0.149603\pi
158158 0.500000 + 0.866025i 0.0397779 + 0.0688973i
159159 4.00000 0.317221
160160 0 0
161161 −2.00000 3.46410i −0.157622 0.273009i
162162 0.500000 + 0.866025i 0.0392837 + 0.0680414i
163163 11.0000 0.861586 0.430793 0.902451i 0.358234π-0.358234\pi
0.430793 + 0.902451i 0.358234π0.358234\pi
164164 4.00000 0.312348
165165 0 0
166166 4.00000 6.92820i 0.310460 0.537733i
167167 −3.00000 5.19615i −0.232147 0.402090i 0.726293 0.687386i 0.241242π-0.241242\pi
−0.958440 + 0.285295i 0.907908π0.907908\pi
168168 −0.500000 + 0.866025i −0.0385758 + 0.0668153i
169169 2.00000 3.46410i 0.153846 0.266469i
170170 0 0
171171 −0.500000 4.33013i −0.0382360 0.331133i
172172 −9.00000 −0.686244
173173 12.0000 20.7846i 0.912343 1.58022i 0.101598 0.994826i 0.467605π-0.467605\pi
0.810745 0.585399i 0.199062π-0.199062\pi
174174 0 0
175175 2.50000 + 4.33013i 0.188982 + 0.327327i
176176 1.00000 1.73205i 0.0753778 0.130558i
177177 −7.00000 12.1244i −0.526152 0.911322i
178178 14.0000 1.04934
179179 4.00000 0.298974 0.149487 0.988764i 0.452238π-0.452238\pi
0.149487 + 0.988764i 0.452238π0.452238\pi
180180 0 0
181181 9.00000 + 15.5885i 0.668965 + 1.15868i 0.978194 + 0.207693i 0.0665956π0.0665956\pi
−0.309229 + 0.950988i 0.600071π0.600071\pi
182182 3.00000 0.222375
183183 −11.0000 −0.813143
184184 2.00000 + 3.46410i 0.147442 + 0.255377i
185185 0 0
186186 1.50000 + 2.59808i 0.109985 + 0.190500i
187187 4.00000 6.92820i 0.292509 0.506640i
188188 −5.00000 + 8.66025i −0.364662 + 0.631614i
189189 −1.00000 −0.0727393
190190 0 0
191191 −8.00000 −0.578860 −0.289430 0.957199i 0.593466π-0.593466\pi
−0.289430 + 0.957199i 0.593466π0.593466\pi
192192 0.500000 0.866025i 0.0360844 0.0625000i
193193 6.50000 11.2583i 0.467880 0.810392i −0.531446 0.847092i 0.678351π-0.678351\pi
0.999326 + 0.0366998i 0.0116845π0.0116845\pi
194194 1.00000 + 1.73205i 0.0717958 + 0.124354i
195195 0 0
196196 3.00000 + 5.19615i 0.214286 + 0.371154i
197197 −2.00000 −0.142494 −0.0712470 0.997459i 0.522698π-0.522698\pi
−0.0712470 + 0.997459i 0.522698π0.522698\pi
198198 2.00000 0.142134
199199 −2.50000 4.33013i −0.177220 0.306955i 0.763707 0.645563i 0.223377π-0.223377\pi
−0.940927 + 0.338608i 0.890044π0.890044\pi
200200 −2.50000 4.33013i −0.176777 0.306186i
201201 −3.00000 −0.211604
202202 10.0000 0.703598
203203 0 0
204204 2.00000 3.46410i 0.140028 0.242536i
205205 0 0
206206 −1.50000 + 2.59808i −0.104510 + 0.181017i
207207 −2.00000 + 3.46410i −0.139010 + 0.240772i
208208 −3.00000 −0.208013
209209 −8.00000 3.46410i −0.553372 0.239617i
210210 0 0
211211 −12.5000 + 21.6506i −0.860535 + 1.49049i 0.0108774 + 0.999941i 0.496538π0.496538\pi
−0.871413 + 0.490550i 0.836796π0.836796\pi
212212 2.00000 3.46410i 0.137361 0.237915i
213213 7.00000 + 12.1244i 0.479632 + 0.830747i
214214 −5.00000 + 8.66025i −0.341793 + 0.592003i
215215 0 0
216216 1.00000 0.0680414
217217 −3.00000 −0.203653
218218 7.00000 + 12.1244i 0.474100 + 0.821165i
219219 −5.50000 9.52628i −0.371656 0.643726i
220220 0 0
221221 −12.0000 −0.807207
222222 2.50000 + 4.33013i 0.167789 + 0.290619i
223223 −4.50000 + 7.79423i −0.301342 + 0.521940i −0.976440 0.215788i 0.930768π-0.930768\pi
0.675098 + 0.737728i 0.264101π0.264101\pi
224224 0.500000 + 0.866025i 0.0334077 + 0.0578638i
225225 2.50000 4.33013i 0.166667 0.288675i
226226 5.00000 8.66025i 0.332595 0.576072i
227227 8.00000 0.530979 0.265489 0.964114i 0.414466π-0.414466\pi
0.265489 + 0.964114i 0.414466π0.414466\pi
228228 −4.00000 1.73205i −0.264906 0.114708i
229229 −11.0000 −0.726900 −0.363450 0.931614i 0.618401π-0.618401\pi
−0.363450 + 0.931614i 0.618401π0.618401\pi
230230 0 0
231231 −1.00000 + 1.73205i −0.0657952 + 0.113961i
232232 0 0
233233 −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i 0.367385π0.367385\pi
−0.994283 + 0.106773i 0.965948π0.965948\pi
234234 −1.50000 2.59808i −0.0980581 0.169842i
235235 0 0
236236 −14.0000 −0.911322
237237 0.500000 + 0.866025i 0.0324785 + 0.0562544i
238238 2.00000 + 3.46410i 0.129641 + 0.224544i
239239 −12.0000 −0.776215 −0.388108 0.921614i 0.626871π-0.626871\pi
−0.388108 + 0.921614i 0.626871π0.626871\pi
240240 0 0
241241 −12.5000 21.6506i −0.805196 1.39464i −0.916159 0.400815i 0.868727π-0.868727\pi
0.110963 0.993825i 0.464606π-0.464606\pi
242242 −3.50000 + 6.06218i −0.224989 + 0.389692i
243243 0.500000 + 0.866025i 0.0320750 + 0.0555556i
244244 −5.50000 + 9.52628i −0.352101 + 0.609858i
245245 0 0
246246 4.00000 0.255031
247247 1.50000 + 12.9904i 0.0954427 + 0.826558i
248248 3.00000 0.190500
249249 4.00000 6.92820i 0.253490 0.439057i
250250 0 0
251251 9.00000 + 15.5885i 0.568075 + 0.983935i 0.996756 + 0.0804789i 0.0256450π0.0256450\pi
−0.428681 + 0.903456i 0.641022π0.641022\pi
252252 −0.500000 + 0.866025i −0.0314970 + 0.0545545i
253253 4.00000 + 6.92820i 0.251478 + 0.435572i
254254 8.00000 0.501965
255255 0 0
256256 −0.500000 0.866025i −0.0312500 0.0541266i
257257 6.00000 + 10.3923i 0.374270 + 0.648254i 0.990217 0.139533i 0.0445601π-0.0445601\pi
−0.615948 + 0.787787i 0.711227π0.711227\pi
258258 −9.00000 −0.560316
259259 −5.00000 −0.310685
260260 0 0
261261 0 0
262262 −3.00000 5.19615i −0.185341 0.321019i
263263 −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i 0.353935π0.353935\pi
−0.997906 + 0.0646755i 0.979399π0.979399\pi
264264 1.00000 1.73205i 0.0615457 0.106600i
265265 0 0
266266 3.50000 2.59808i 0.214599 0.159298i
267267 14.0000 0.856786
268268 −1.50000 + 2.59808i −0.0916271 + 0.158703i
269269 −1.00000 + 1.73205i −0.0609711 + 0.105605i −0.894900 0.446267i 0.852753π-0.852753\pi
0.833929 + 0.551872i 0.186086π0.186086\pi
270270 0 0
271271 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i 0.671801π-0.671801\pi
0.999870 + 0.0161307i 0.00513477π0.00513477\pi
272272 −2.00000 3.46410i −0.121268 0.210042i
273273 3.00000 0.181568
274274 6.00000 0.362473
275275 −5.00000 8.66025i −0.301511 0.522233i
276276 2.00000 + 3.46410i 0.120386 + 0.208514i
277277 −2.00000 −0.120168 −0.0600842 0.998193i 0.519137π-0.519137\pi
−0.0600842 + 0.998193i 0.519137π0.519137\pi
278278 19.0000 1.13954
279279 1.50000 + 2.59808i 0.0898027 + 0.155543i
280280 0 0
281281 4.00000 + 6.92820i 0.238620 + 0.413302i 0.960319 0.278906i 0.0899716π-0.0899716\pi
−0.721699 + 0.692207i 0.756638π0.756638\pi
282282 −5.00000 + 8.66025i −0.297746 + 0.515711i
283283 10.0000 17.3205i 0.594438 1.02960i −0.399188 0.916869i 0.630708π-0.630708\pi
0.993626 0.112728i 0.0359589π-0.0359589\pi
284284 14.0000 0.830747
285285 0 0
286286 −6.00000 −0.354787
287287 −2.00000 + 3.46410i −0.118056 + 0.204479i
288288 0.500000 0.866025i 0.0294628 0.0510310i
289289 0.500000 + 0.866025i 0.0294118 + 0.0509427i
290290 0 0
291291 1.00000 + 1.73205i 0.0586210 + 0.101535i
292292 −11.0000 −0.643726
293293 14.0000 0.817889 0.408944 0.912559i 0.365897π-0.365897\pi
0.408944 + 0.912559i 0.365897π0.365897\pi
294294 3.00000 + 5.19615i 0.174964 + 0.303046i
295295 0 0
296296 5.00000 0.290619
297297 2.00000 0.116052
298298 −11.0000 19.0526i −0.637213 1.10369i
299299 6.00000 10.3923i 0.346989 0.601003i
300300 −2.50000 4.33013i −0.144338 0.250000i
301301 4.50000 7.79423i 0.259376 0.449252i
302302 −10.0000 + 17.3205i −0.575435 + 0.996683i
303303 10.0000 0.574485
304304 −3.50000 + 2.59808i −0.200739 + 0.149010i
305305 0 0
306306 2.00000 3.46410i 0.114332 0.198030i
307307 6.00000 10.3923i 0.342438 0.593120i −0.642447 0.766330i 0.722081π-0.722081\pi
0.984885 + 0.173210i 0.0554140π0.0554140\pi
308308 1.00000 + 1.73205i 0.0569803 + 0.0986928i
309309 −1.50000 + 2.59808i −0.0853320 + 0.147799i
310310 0 0
311311 10.0000 0.567048 0.283524 0.958965i 0.408496π-0.408496\pi
0.283524 + 0.958965i 0.408496π0.408496\pi
312312 −3.00000 −0.169842
313313 −3.00000 5.19615i −0.169570 0.293704i 0.768699 0.639611i 0.220905π-0.220905\pi
−0.938269 + 0.345907i 0.887571π0.887571\pi
314314 −10.5000 18.1865i −0.592549 1.02633i
315315 0 0
316316 1.00000 0.0562544
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 2.00000 3.46410i 0.112154 0.194257i
319319 0 0
320320 0 0
321321 −5.00000 + 8.66025i −0.279073 + 0.483368i
322322 −4.00000 −0.222911
323323 −14.0000 + 10.3923i −0.778981 + 0.578243i
324324 1.00000 0.0555556
325325 −7.50000 + 12.9904i −0.416025 + 0.720577i
326326 5.50000 9.52628i 0.304617 0.527612i
327327 7.00000 + 12.1244i 0.387101 + 0.670478i
328328 2.00000 3.46410i 0.110432 0.191273i
329329 −5.00000 8.66025i −0.275659 0.477455i
330330 0 0
331331 15.0000 0.824475 0.412237 0.911077i 0.364747π-0.364747\pi
0.412237 + 0.911077i 0.364747π0.364747\pi
332332 −4.00000 6.92820i −0.219529 0.380235i
333333 2.50000 + 4.33013i 0.136999 + 0.237289i
334334 −6.00000 −0.328305
335335 0 0
336336 0.500000 + 0.866025i 0.0272772 + 0.0472456i
337337 9.50000 16.4545i 0.517498 0.896333i −0.482295 0.876009i 0.660197π-0.660197\pi
0.999793 0.0203242i 0.00646983π-0.00646983\pi
338338 −2.00000 3.46410i −0.108786 0.188422i
339339 5.00000 8.66025i 0.271563 0.470360i
340340 0 0
341341 6.00000 0.324918
342342 −4.00000 1.73205i −0.216295 0.0936586i
343343 −13.0000 −0.701934
344344 −4.50000 + 7.79423i −0.242624 + 0.420237i
345345 0 0
346346 −12.0000 20.7846i −0.645124 1.11739i
347347 −8.00000 + 13.8564i −0.429463 + 0.743851i −0.996826 0.0796169i 0.974630π-0.974630\pi
0.567363 + 0.823468i 0.307964π0.307964\pi
348348 0 0
349349 −29.0000 −1.55233 −0.776167 0.630527i 0.782839π-0.782839\pi
−0.776167 + 0.630527i 0.782839π0.782839\pi
350350 5.00000 0.267261
351351 −1.50000 2.59808i −0.0800641 0.138675i
352352 −1.00000 1.73205i −0.0533002 0.0923186i
353353 −12.0000 −0.638696 −0.319348 0.947638i 0.603464π-0.603464\pi
−0.319348 + 0.947638i 0.603464π0.603464\pi
354354 −14.0000 −0.744092
355355 0 0
356356 7.00000 12.1244i 0.370999 0.642590i
357357 2.00000 + 3.46410i 0.105851 + 0.183340i
358358 2.00000 3.46410i 0.105703 0.183083i
359359 18.0000 31.1769i 0.950004 1.64545i 0.204595 0.978847i 0.434412π-0.434412\pi
0.745409 0.666608i 0.232254π-0.232254\pi
360360 0 0
361361 13.0000 + 13.8564i 0.684211 + 0.729285i
362362 18.0000 0.946059
363363 −3.50000 + 6.06218i −0.183702 + 0.318182i
364364 1.50000 2.59808i 0.0786214 0.136176i
365365 0 0
366366 −5.50000 + 9.52628i −0.287490 + 0.497947i
367367 −11.5000 19.9186i −0.600295 1.03974i −0.992776 0.119982i 0.961716π-0.961716\pi
0.392481 0.919760i 0.371617π-0.371617\pi
368368 4.00000 0.208514
369369 4.00000 0.208232
370370 0 0
371371 2.00000 + 3.46410i 0.103835 + 0.179847i
372372 3.00000 0.155543
373373 26.0000 1.34623 0.673114 0.739538i 0.264956π-0.264956\pi
0.673114 + 0.739538i 0.264956π0.264956\pi
374374 −4.00000 6.92820i −0.206835 0.358249i
375375 0 0
376376 5.00000 + 8.66025i 0.257855 + 0.446619i
377377 0 0
378378 −0.500000 + 0.866025i −0.0257172 + 0.0445435i
379379 −13.0000 −0.667765 −0.333883 0.942615i 0.608359π-0.608359\pi
−0.333883 + 0.942615i 0.608359π0.608359\pi
380380 0 0
381381 8.00000 0.409852
382382 −4.00000 + 6.92820i −0.204658 + 0.354478i
383383 −7.00000 + 12.1244i −0.357683 + 0.619526i −0.987573 0.157159i 0.949767π-0.949767\pi
0.629890 + 0.776684i 0.283100π0.283100\pi
384384 −0.500000 0.866025i −0.0255155 0.0441942i
385385 0 0
386386 −6.50000 11.2583i −0.330841 0.573034i
387387 −9.00000 −0.457496
388388 2.00000 0.101535
389389 8.00000 + 13.8564i 0.405616 + 0.702548i 0.994393 0.105748i 0.0337237π-0.0337237\pi
−0.588777 + 0.808296i 0.700390π0.700390\pi
390390 0 0
391391 16.0000 0.809155
392392 6.00000 0.303046
393393 −3.00000 5.19615i −0.151330 0.262111i
394394 −1.00000 + 1.73205i −0.0503793 + 0.0872595i
395395 0 0
396396 1.00000 1.73205i 0.0502519 0.0870388i
397397 −7.50000 + 12.9904i −0.376414 + 0.651969i −0.990538 0.137241i 0.956176π-0.956176\pi
0.614123 + 0.789210i 0.289510π0.289510\pi
398398 −5.00000 −0.250627
399399 3.50000 2.59808i 0.175219 0.130066i
400400 −5.00000 −0.250000
401401 −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i 0.981709π-0.981709\pi
0.548911 + 0.835881i 0.315043π0.315043\pi
402402 −1.50000 + 2.59808i −0.0748132 + 0.129580i
403403 −4.50000 7.79423i −0.224161 0.388258i
404404 5.00000 8.66025i 0.248759 0.430864i
405405 0 0
406406 0 0
407407 10.0000 0.495682
408408 −2.00000 3.46410i −0.0990148 0.171499i
409409 15.0000 + 25.9808i 0.741702 + 1.28467i 0.951720 + 0.306968i 0.0993146π0.0993146\pi
−0.210017 + 0.977698i 0.567352π0.567352\pi
410410 0 0
411411 6.00000 0.295958
412412 1.50000 + 2.59808i 0.0738997 + 0.127998i
413413 7.00000 12.1244i 0.344447 0.596601i
414414 2.00000 + 3.46410i 0.0982946 + 0.170251i
415415 0 0
416416 −1.50000 + 2.59808i −0.0735436 + 0.127381i
417417 19.0000 0.930434
418418 −7.00000 + 5.19615i −0.342381 + 0.254152i
419419 18.0000 0.879358 0.439679 0.898155i 0.355092π-0.355092\pi
0.439679 + 0.898155i 0.355092π0.355092\pi
420420 0 0
421421 −5.00000 + 8.66025i −0.243685 + 0.422075i −0.961761 0.273890i 0.911690π-0.911690\pi
0.718076 + 0.695965i 0.245023π0.245023\pi
422422 12.5000 + 21.6506i 0.608490 + 1.05394i
423423 −5.00000 + 8.66025i −0.243108 + 0.421076i
424424 −2.00000 3.46410i −0.0971286 0.168232i
425425 −20.0000 −0.970143
426426 14.0000 0.678302
427427 −5.50000 9.52628i −0.266164 0.461009i
428428 5.00000 + 8.66025i 0.241684 + 0.418609i
429429 −6.00000 −0.289683
430430 0 0
431431 5.00000 + 8.66025i 0.240842 + 0.417150i 0.960954 0.276707i 0.0892433π-0.0892433\pi
−0.720113 + 0.693857i 0.755910π0.755910\pi
432432 0.500000 0.866025i 0.0240563 0.0416667i
433433 4.50000 + 7.79423i 0.216256 + 0.374567i 0.953660 0.300885i 0.0972820π-0.0972820\pi
−0.737404 + 0.675452i 0.763949π0.763949\pi
434434 −1.50000 + 2.59808i −0.0720023 + 0.124712i
435435 0 0
436436 14.0000 0.670478
437437 −2.00000 17.3205i −0.0956730 0.828552i
438438 −11.0000 −0.525600
439439 −9.50000 + 16.4545i −0.453410 + 0.785330i −0.998595 0.0529862i 0.983126π-0.983126\pi
0.545185 + 0.838316i 0.316459π0.316459\pi
440440 0 0
441441 3.00000 + 5.19615i 0.142857 + 0.247436i
442442 −6.00000 + 10.3923i −0.285391 + 0.494312i
443443 −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i 0.973557π-0.973557\pi
0.426414 0.904528i 0.359777π-0.359777\pi
444444 5.00000 0.237289
445445 0 0
446446 4.50000 + 7.79423i 0.213081 + 0.369067i
447447 −11.0000 19.0526i −0.520282 0.901155i
448448 1.00000 0.0472456
449449 −36.0000 −1.69895 −0.849473 0.527633i 0.823080π-0.823080\pi
−0.849473 + 0.527633i 0.823080π0.823080\pi
450450 −2.50000 4.33013i −0.117851 0.204124i
451451 4.00000 6.92820i 0.188353 0.326236i
452452 −5.00000 8.66025i −0.235180 0.407344i
453453 −10.0000 + 17.3205i −0.469841 + 0.813788i
454454 4.00000 6.92820i 0.187729 0.325157i
455455 0 0
456456 −3.50000 + 2.59808i −0.163903 + 0.121666i
457457 5.00000 0.233890 0.116945 0.993138i 0.462690π-0.462690\pi
0.116945 + 0.993138i 0.462690π0.462690\pi
458458 −5.50000 + 9.52628i −0.256998 + 0.445134i
459459 2.00000 3.46410i 0.0933520 0.161690i
460460 0 0
461461 −3.00000 + 5.19615i −0.139724 + 0.242009i −0.927392 0.374091i 0.877955π-0.877955\pi
0.787668 + 0.616100i 0.211288π0.211288\pi
462462 1.00000 + 1.73205i 0.0465242 + 0.0805823i
463463 −9.00000 −0.418265 −0.209133 0.977887i 0.567064π-0.567064\pi
−0.209133 + 0.977887i 0.567064π0.567064\pi
464464 0 0
465465 0 0
466466 9.00000 + 15.5885i 0.416917 + 0.722121i
467467 8.00000 0.370196 0.185098 0.982720i 0.440740π-0.440740\pi
0.185098 + 0.982720i 0.440740π0.440740\pi
468468 −3.00000 −0.138675
469469 −1.50000 2.59808i −0.0692636 0.119968i
470470 0 0
471471 −10.5000 18.1865i −0.483814 0.837991i
472472 −7.00000 + 12.1244i −0.322201 + 0.558069i
473473 −9.00000 + 15.5885i −0.413820 + 0.716758i
474474 1.00000 0.0459315
475475 2.50000 + 21.6506i 0.114708 + 0.993399i
476476 4.00000 0.183340
477477 2.00000 3.46410i 0.0915737 0.158610i
478478 −6.00000 + 10.3923i −0.274434 + 0.475333i
479479 −3.00000 5.19615i −0.137073 0.237418i 0.789314 0.613990i 0.210436π-0.210436\pi
−0.926388 + 0.376571i 0.877103π0.877103\pi
480480 0 0
481481 −7.50000 12.9904i −0.341971 0.592310i
482482 −25.0000 −1.13872
483483 −4.00000 −0.182006
484484 3.50000 + 6.06218i 0.159091 + 0.275554i
485485 0 0
486486 1.00000 0.0453609
487487 32.0000 1.45006 0.725029 0.688718i 0.241826π-0.241826\pi
0.725029 + 0.688718i 0.241826π0.241826\pi
488488 5.50000 + 9.52628i 0.248973 + 0.431234i
489489 5.50000 9.52628i 0.248719 0.430793i
490490 0 0
491491 −15.0000 + 25.9808i −0.676941 + 1.17250i 0.298957 + 0.954267i 0.403361π0.403361\pi
−0.975898 + 0.218229i 0.929972π0.929972\pi
492492 2.00000 3.46410i 0.0901670 0.156174i
493493 0 0
494494 12.0000 + 5.19615i 0.539906 + 0.233786i
495495 0 0
496496 1.50000 2.59808i 0.0673520 0.116657i
497497 −7.00000 + 12.1244i −0.313993 + 0.543852i
498498 −4.00000 6.92820i −0.179244 0.310460i
499499 −2.50000 + 4.33013i −0.111915 + 0.193843i −0.916542 0.399937i 0.869032π-0.869032\pi
0.804627 + 0.593780i 0.202365π0.202365\pi
500500 0 0
501501 −6.00000 −0.268060
502502 18.0000 0.803379
503503 −8.00000 13.8564i −0.356702 0.617827i 0.630705 0.776022i 0.282766π-0.282766\pi
−0.987408 + 0.158196i 0.949432π0.949432\pi
504504 0.500000 + 0.866025i 0.0222718 + 0.0385758i
505505 0 0
506506 8.00000 0.355643
507507 −2.00000 3.46410i −0.0888231 0.153846i
508508 4.00000 6.92820i 0.177471 0.307389i
509509 −13.0000 22.5167i −0.576215 0.998033i −0.995908 0.0903676i 0.971196π-0.971196\pi
0.419694 0.907666i 0.362138π-0.362138\pi
510510 0 0
511511 5.50000 9.52628i 0.243306 0.421418i
512512 −1.00000 −0.0441942
513513 −4.00000 1.73205i −0.176604 0.0764719i
514514 12.0000 0.529297
515515 0 0
516516 −4.50000 + 7.79423i −0.198101 + 0.343122i
517517 10.0000 + 17.3205i 0.439799 + 0.761755i
518518 −2.50000 + 4.33013i −0.109844 + 0.190255i
519519 −12.0000 20.7846i −0.526742 0.912343i
520520 0 0
521521 34.0000 1.48957 0.744784 0.667306i 0.232553π-0.232553\pi
0.744784 + 0.667306i 0.232553π0.232553\pi
522522 0 0
523523 −18.5000 32.0429i −0.808949 1.40114i −0.913593 0.406630i 0.866704π-0.866704\pi
0.104644 0.994510i 0.466630π-0.466630\pi
524524 −6.00000 −0.262111
525525 5.00000 0.218218
526526 9.00000 + 15.5885i 0.392419 + 0.679689i
527527 6.00000 10.3923i 0.261364 0.452696i
528528 −1.00000 1.73205i −0.0435194 0.0753778i
529529 3.50000 6.06218i 0.152174 0.263573i
530530 0 0
531531 −14.0000 −0.607548
532532 −0.500000 4.33013i −0.0216777 0.187735i
533533 −12.0000 −0.519778
534534 7.00000 12.1244i 0.302920 0.524672i
535535 0 0
536536 1.50000 + 2.59808i 0.0647901 + 0.112220i
537537 2.00000 3.46410i 0.0863064 0.149487i
538538 1.00000 + 1.73205i 0.0431131 + 0.0746740i
539539 12.0000 0.516877
540540 0 0
541541 15.5000 + 26.8468i 0.666397 + 1.15423i 0.978905 + 0.204318i 0.0654977π0.0654977\pi
−0.312507 + 0.949915i 0.601169π0.601169\pi
542542 −8.00000 13.8564i −0.343629 0.595184i
543543 18.0000 0.772454
544544 −4.00000 −0.171499
545545 0 0
546546 1.50000 2.59808i 0.0641941 0.111187i
547547 −5.50000 9.52628i −0.235163 0.407314i 0.724157 0.689635i 0.242229π-0.242229\pi
−0.959320 + 0.282321i 0.908896π0.908896\pi
548548 3.00000 5.19615i 0.128154 0.221969i
549549 −5.50000 + 9.52628i −0.234734 + 0.406572i
550550 −10.0000 −0.426401
551551 0 0
552552 4.00000 0.170251
553553 −0.500000 + 0.866025i −0.0212622 + 0.0368271i
554554 −1.00000 + 1.73205i −0.0424859 + 0.0735878i
555555 0 0
556556 9.50000 16.4545i 0.402890 0.697826i
557557 −17.0000 29.4449i −0.720313 1.24762i −0.960874 0.276985i 0.910665π-0.910665\pi
0.240561 0.970634i 0.422669π-0.422669\pi
558558 3.00000 0.127000
559559 27.0000 1.14198
560560 0 0
561561 −4.00000 6.92820i −0.168880 0.292509i
562562 8.00000 0.337460
563563 −6.00000 −0.252870 −0.126435 0.991975i 0.540353π-0.540353\pi
−0.126435 + 0.991975i 0.540353π0.540353\pi
564564 5.00000 + 8.66025i 0.210538 + 0.364662i
565565 0 0
566566 −10.0000 17.3205i −0.420331 0.728035i
567567 −0.500000 + 0.866025i −0.0209980 + 0.0363696i
568568 7.00000 12.1244i 0.293713 0.508727i
569569 24.0000 1.00613 0.503066 0.864248i 0.332205π-0.332205\pi
0.503066 + 0.864248i 0.332205π0.332205\pi
570570 0 0
571571 −7.00000 −0.292941 −0.146470 0.989215i 0.546791π-0.546791\pi
−0.146470 + 0.989215i 0.546791π0.546791\pi
572572 −3.00000 + 5.19615i −0.125436 + 0.217262i
573573 −4.00000 + 6.92820i −0.167102 + 0.289430i
574574 2.00000 + 3.46410i 0.0834784 + 0.144589i
575575 10.0000 17.3205i 0.417029 0.722315i
576576 −0.500000 0.866025i −0.0208333 0.0360844i
577577 −14.0000 −0.582828 −0.291414 0.956597i 0.594126π-0.594126\pi
−0.291414 + 0.956597i 0.594126π0.594126\pi
578578 1.00000 0.0415945
579579 −6.50000 11.2583i −0.270131 0.467880i
580580 0 0
581581 8.00000 0.331896
582582 2.00000 0.0829027
583583 −4.00000 6.92820i −0.165663 0.286937i
584584 −5.50000 + 9.52628i −0.227592 + 0.394200i
585585 0 0
586586 7.00000 12.1244i 0.289167 0.500853i
587587 1.00000 1.73205i 0.0412744 0.0714894i −0.844650 0.535319i 0.820192π-0.820192\pi
0.885925 + 0.463829i 0.153525π0.153525\pi
588588 6.00000 0.247436
589589 −12.0000 5.19615i −0.494451 0.214104i
590590 0 0
591591 −1.00000 + 1.73205i −0.0411345 + 0.0712470i
592592 2.50000 4.33013i 0.102749 0.177967i
593593 −17.0000 29.4449i −0.698106 1.20916i −0.969122 0.246581i 0.920693π-0.920693\pi
0.271016 0.962575i 0.412640π-0.412640\pi
594594 1.00000 1.73205i 0.0410305 0.0710669i
595595 0 0
596596 −22.0000 −0.901155
597597 −5.00000 −0.204636
598598 −6.00000 10.3923i −0.245358 0.424973i
599599 23.0000 + 39.8372i 0.939755 + 1.62770i 0.765928 + 0.642926i 0.222280π0.222280\pi
0.173826 + 0.984776i 0.444387π0.444387\pi
600600 −5.00000 −0.204124
601601 27.0000 1.10135 0.550676 0.834719i 0.314370π-0.314370\pi
0.550676 + 0.834719i 0.314370π0.314370\pi
602602 −4.50000 7.79423i −0.183406 0.317669i
603603 −1.50000 + 2.59808i −0.0610847 + 0.105802i
604604 10.0000 + 17.3205i 0.406894 + 0.704761i
605605 0 0
606606 5.00000 8.66025i 0.203111 0.351799i
607607 5.00000 0.202944 0.101472 0.994838i 0.467645π-0.467645\pi
0.101472 + 0.994838i 0.467645π0.467645\pi
608608 0.500000 + 4.33013i 0.0202777 + 0.175610i
609609 0 0
610610 0 0
611611 15.0000 25.9808i 0.606835 1.05107i
612612 −2.00000 3.46410i −0.0808452 0.140028i
613613 −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i 0.846193π-0.846193\pi
0.845124 + 0.534570i 0.179527π0.179527\pi
614614 −6.00000 10.3923i −0.242140 0.419399i
615615 0 0
616616 2.00000 0.0805823
617617 21.0000 + 36.3731i 0.845428 + 1.46432i 0.885249 + 0.465118i 0.153988π0.153988\pi
−0.0398207 + 0.999207i 0.512679π0.512679\pi
618618 1.50000 + 2.59808i 0.0603388 + 0.104510i
619619 1.00000 0.0401934 0.0200967 0.999798i 0.493603π-0.493603\pi
0.0200967 + 0.999798i 0.493603π0.493603\pi
620620 0 0
621621 2.00000 + 3.46410i 0.0802572 + 0.139010i
622622 5.00000 8.66025i 0.200482 0.347245i
623623 7.00000 + 12.1244i 0.280449 + 0.485752i
624624 −1.50000 + 2.59808i −0.0600481 + 0.104006i
625625 −12.5000 + 21.6506i −0.500000 + 0.866025i
626626 −6.00000 −0.239808
627627 −7.00000 + 5.19615i −0.279553 + 0.207514i
628628 −21.0000 −0.837991
629629 10.0000 17.3205i 0.398726 0.690614i
630630 0 0
631631 −8.50000 14.7224i −0.338380 0.586091i 0.645748 0.763550i 0.276545π-0.276545\pi
−0.984128 + 0.177459i 0.943212π0.943212\pi
632632 0.500000 0.866025i 0.0198889 0.0344486i
633633 12.5000 + 21.6506i 0.496830 + 0.860535i
634634 −12.0000 −0.476581
635635 0 0
636636 −2.00000 3.46410i −0.0793052 0.137361i
637637 −9.00000 15.5885i −0.356593 0.617637i
638638 0 0
639639 14.0000 0.553831
640640 0 0
641641 7.00000 12.1244i 0.276483 0.478883i −0.694025 0.719951i 0.744164π-0.744164\pi
0.970508 + 0.241068i 0.0774976π0.0774976\pi
642642 5.00000 + 8.66025i 0.197334 + 0.341793i
643643 −18.5000 + 32.0429i −0.729569 + 1.26365i 0.227497 + 0.973779i 0.426946π0.426946\pi
−0.957066 + 0.289871i 0.906387π0.906387\pi
644644 −2.00000 + 3.46410i −0.0788110 + 0.136505i
645645 0 0
646646 2.00000 + 17.3205i 0.0786889 + 0.681466i
647647 48.0000 1.88707 0.943537 0.331266i 0.107476π-0.107476\pi
0.943537 + 0.331266i 0.107476π0.107476\pi
648648 0.500000 0.866025i 0.0196419 0.0340207i
649649 −14.0000 + 24.2487i −0.549548 + 0.951845i
650650 7.50000 + 12.9904i 0.294174 + 0.509525i
651651 −1.50000 + 2.59808i −0.0587896 + 0.101827i
652652 −5.50000 9.52628i −0.215397 0.373078i
653653 −42.0000 −1.64359 −0.821794 0.569785i 0.807026π-0.807026\pi
−0.821794 + 0.569785i 0.807026π0.807026\pi
654654 14.0000 0.547443
655655 0 0
656656 −2.00000 3.46410i −0.0780869 0.135250i
657657 −11.0000 −0.429151
658658 −10.0000 −0.389841
659659 7.00000 + 12.1244i 0.272681 + 0.472298i 0.969548 0.244903i 0.0787562π-0.0787562\pi
−0.696866 + 0.717201i 0.745423π0.745423\pi
660660 0 0
661661 −5.00000 8.66025i −0.194477 0.336845i 0.752252 0.658876i 0.228968π-0.228968\pi
−0.946729 + 0.322031i 0.895634π0.895634\pi
662662 7.50000 12.9904i 0.291496 0.504885i
663663 −6.00000 + 10.3923i −0.233021 + 0.403604i
664664 −8.00000 −0.310460
665665 0 0
666666 5.00000 0.193746
667667 0 0
668668 −3.00000 + 5.19615i −0.116073 + 0.201045i
669669 4.50000 + 7.79423i 0.173980 + 0.301342i
670670 0 0
671671 11.0000 + 19.0526i 0.424650 + 0.735516i
672672 1.00000 0.0385758
673673 −1.00000 −0.0385472 −0.0192736 0.999814i 0.506135π-0.506135\pi
−0.0192736 + 0.999814i 0.506135π0.506135\pi
674674 −9.50000 16.4545i −0.365926 0.633803i
675675 −2.50000 4.33013i −0.0962250 0.166667i
676676 −4.00000 −0.153846
677677 18.0000 0.691796 0.345898 0.938272i 0.387574π-0.387574\pi
0.345898 + 0.938272i 0.387574π0.387574\pi
678678 −5.00000 8.66025i −0.192024 0.332595i
679679 −1.00000 + 1.73205i −0.0383765 + 0.0664700i
680680 0 0
681681 4.00000 6.92820i 0.153280 0.265489i
682682 3.00000 5.19615i 0.114876 0.198971i
683683 −36.0000 −1.37750 −0.688751 0.724998i 0.741841π-0.741841\pi
−0.688751 + 0.724998i 0.741841π0.741841\pi
684684 −3.50000 + 2.59808i −0.133826 + 0.0993399i
685685 0 0
686686 −6.50000 + 11.2583i −0.248171 + 0.429845i
687687 −5.50000 + 9.52628i −0.209838 + 0.363450i
688688 4.50000 + 7.79423i 0.171561 + 0.297152i
689689 −6.00000 + 10.3923i −0.228582 + 0.395915i
690690 0 0
691691 4.00000 0.152167 0.0760836 0.997101i 0.475758π-0.475758\pi
0.0760836 + 0.997101i 0.475758π0.475758\pi
692692 −24.0000 −0.912343
693693 1.00000 + 1.73205i 0.0379869 + 0.0657952i
694694 8.00000 + 13.8564i 0.303676 + 0.525982i
695695 0 0
696696 0 0
697697 −8.00000 13.8564i −0.303022 0.524849i
698698 −14.5000 + 25.1147i −0.548833 + 0.950607i
699699 9.00000 + 15.5885i 0.340411 + 0.589610i
700700 2.50000 4.33013i 0.0944911 0.163663i
701701 22.0000 38.1051i 0.830929 1.43921i −0.0663742 0.997795i 0.521143π-0.521143\pi
0.897303 0.441416i 0.145524π-0.145524\pi
702702 −3.00000 −0.113228
703703 −20.0000 8.66025i −0.754314 0.326628i
704704 −2.00000 −0.0753778
705705 0 0
706706 −6.00000 + 10.3923i −0.225813 + 0.391120i
707707 5.00000 + 8.66025i 0.188044 + 0.325702i
708708 −7.00000 + 12.1244i −0.263076 + 0.455661i
709709 15.5000 + 26.8468i 0.582115 + 1.00825i 0.995228 + 0.0975728i 0.0311079π0.0311079\pi
−0.413114 + 0.910679i 0.635559π0.635559\pi
710710 0 0
711711 1.00000 0.0375029
712712 −7.00000 12.1244i −0.262336 0.454379i
713713 6.00000 + 10.3923i 0.224702 + 0.389195i
714714 4.00000 0.149696
715715 0 0
716716 −2.00000 3.46410i −0.0747435 0.129460i
717717 −6.00000 + 10.3923i −0.224074 + 0.388108i
718718 −18.0000 31.1769i −0.671754 1.16351i
719719 −20.0000 + 34.6410i −0.745874 + 1.29189i 0.203911 + 0.978989i 0.434635π0.434635\pi
−0.949785 + 0.312903i 0.898699π0.898699\pi
720720 0 0
721721 −3.00000 −0.111726
722722 18.5000 4.33013i 0.688499 0.161151i
723723 −25.0000 −0.929760
724724 9.00000 15.5885i 0.334482 0.579340i
725725 0 0
726726 3.50000 + 6.06218i 0.129897 + 0.224989i
727727 −8.50000 + 14.7224i −0.315248 + 0.546025i −0.979490 0.201492i 0.935421π-0.935421\pi
0.664243 + 0.747517i 0.268754π0.268754\pi
728728 −1.50000 2.59808i −0.0555937 0.0962911i
729729 1.00000 0.0370370
730730 0 0
731731 18.0000 + 31.1769i 0.665754 + 1.15312i
732732 5.50000 + 9.52628i 0.203286 + 0.352101i
733733 −2.00000 −0.0738717 −0.0369358 0.999318i 0.511760π-0.511760\pi
−0.0369358 + 0.999318i 0.511760π0.511760\pi
734734 −23.0000 −0.848945
735735 0 0
736736 2.00000 3.46410i 0.0737210 0.127688i
737737 3.00000 + 5.19615i 0.110506 + 0.191403i
738738 2.00000 3.46410i 0.0736210 0.127515i
739739 2.50000 4.33013i 0.0919640 0.159286i −0.816373 0.577524i 0.804019π-0.804019\pi
0.908337 + 0.418238i 0.137352π0.137352\pi
740740 0 0
741741 12.0000 + 5.19615i 0.440831 + 0.190885i
742742 4.00000 0.146845
743743 9.00000 15.5885i 0.330178 0.571885i −0.652369 0.757902i 0.726225π-0.726225\pi
0.982547 + 0.186017i 0.0595579π0.0595579\pi
744744 1.50000 2.59808i 0.0549927 0.0952501i
745745 0 0
746746 13.0000 22.5167i 0.475964 0.824394i
747747 −4.00000 6.92820i −0.146352 0.253490i
748748 −8.00000 −0.292509
749749 −10.0000 −0.365392
750750 0 0
751751 −6.50000 11.2583i −0.237188 0.410822i 0.722718 0.691143i 0.242893π-0.242893\pi
−0.959906 + 0.280321i 0.909559π0.909559\pi
752752 10.0000 0.364662
753753 18.0000 0.655956
754754 0 0
755755 0 0
756756 0.500000 + 0.866025i 0.0181848 + 0.0314970i
757757 −2.50000 + 4.33013i −0.0908640 + 0.157381i −0.907875 0.419241i 0.862296π-0.862296\pi
0.817011 + 0.576622i 0.195630π0.195630\pi
758758 −6.50000 + 11.2583i −0.236091 + 0.408921i
759759 8.00000 0.290382
760760 0 0
761761 −34.0000 −1.23250 −0.616250 0.787551i 0.711349π-0.711349\pi
−0.616250 + 0.787551i 0.711349π0.711349\pi
762762 4.00000 6.92820i 0.144905 0.250982i
763763 −7.00000 + 12.1244i −0.253417 + 0.438931i
764764 4.00000 + 6.92820i 0.144715 + 0.250654i
765765 0 0
766766 7.00000 + 12.1244i 0.252920 + 0.438071i
767767 42.0000 1.51653
768768 −1.00000 −0.0360844
769769 −13.5000 23.3827i −0.486822 0.843201i 0.513063 0.858351i 0.328511π-0.328511\pi
−0.999885 + 0.0151499i 0.995177π0.995177\pi
770770 0 0
771771 12.0000 0.432169
772772 −13.0000 −0.467880
773773 9.00000 + 15.5885i 0.323708 + 0.560678i 0.981250 0.192740i 0.0617373π-0.0617373\pi
−0.657542 + 0.753418i 0.728404π0.728404\pi
774774 −4.50000 + 7.79423i −0.161749 + 0.280158i
775775 −7.50000 12.9904i −0.269408 0.466628i
776776 1.00000 1.73205i 0.0358979 0.0621770i
777777 −2.50000 + 4.33013i −0.0896870 + 0.155342i
778778 16.0000 0.573628
779779 −14.0000 + 10.3923i −0.501602 + 0.372343i
780780 0 0
781781 14.0000 24.2487i 0.500959 0.867687i
782782 8.00000 13.8564i 0.286079 0.495504i
783783 0 0
784784 3.00000 5.19615i 0.107143 0.185577i
785785 0 0
786786 −6.00000 −0.214013
787787 −47.0000 −1.67537 −0.837685 0.546154i 0.816091π-0.816091\pi
−0.837685 + 0.546154i 0.816091π0.816091\pi
788788 1.00000 + 1.73205i 0.0356235 + 0.0617018i
789789 9.00000 + 15.5885i 0.320408 + 0.554964i
790790 0 0
791791 10.0000 0.355559
792792 −1.00000 1.73205i −0.0355335 0.0615457i
793793 16.5000 28.5788i 0.585932 1.01486i
794794 7.50000 + 12.9904i 0.266165 + 0.461011i
795795 0 0
796796 −2.50000 + 4.33013i −0.0886102 + 0.153477i
797797 26.0000 0.920967 0.460484 0.887668i 0.347676π-0.347676\pi
0.460484 + 0.887668i 0.347676π0.347676\pi
798798 −0.500000 4.33013i −0.0176998 0.153285i
799799 40.0000 1.41510
800800 −2.50000 + 4.33013i −0.0883883 + 0.153093i
801801 7.00000 12.1244i 0.247333 0.428393i
802802 9.00000 + 15.5885i 0.317801 + 0.550448i
803803 −11.0000 + 19.0526i −0.388182 + 0.672350i
804804 1.50000 + 2.59808i 0.0529009 + 0.0916271i
805805 0 0
806806 −9.00000 −0.317011
807807 1.00000 + 1.73205i 0.0352017 + 0.0609711i
808808 −5.00000 8.66025i −0.175899 0.304667i
809809 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
810810 0 0
811811 −2.00000 3.46410i −0.0702295 0.121641i 0.828772 0.559586i 0.189040π-0.189040\pi
−0.899002 + 0.437945i 0.855706π0.855706\pi
812812 0 0
813813 −8.00000 13.8564i −0.280572 0.485965i
814814 5.00000 8.66025i 0.175250 0.303542i
815815 0 0
816816 −4.00000 −0.140028
817817 31.5000 23.3827i 1.10205 0.818057i
818818 30.0000 1.04893
819819 1.50000 2.59808i 0.0524142 0.0907841i
820820 0 0
821821 −24.0000 41.5692i −0.837606 1.45078i −0.891891 0.452250i 0.850621π-0.850621\pi
0.0542853 0.998525i 0.482712π-0.482712\pi
822822 3.00000 5.19615i 0.104637 0.181237i
823823 −2.00000 3.46410i −0.0697156 0.120751i 0.829060 0.559159i 0.188876π-0.188876\pi
−0.898776 + 0.438408i 0.855543π0.855543\pi
824824 3.00000 0.104510
825825 −10.0000 −0.348155
826826 −7.00000 12.1244i −0.243561 0.421860i
827827 −18.0000 31.1769i −0.625921 1.08413i −0.988362 0.152121i 0.951390π-0.951390\pi
0.362441 0.932007i 0.381944π-0.381944\pi
828828 4.00000 0.139010
829829 −31.0000 −1.07667 −0.538337 0.842729i 0.680947π-0.680947\pi
−0.538337 + 0.842729i 0.680947π0.680947\pi
830830 0 0
831831 −1.00000 + 1.73205i −0.0346896 + 0.0600842i
832832 1.50000 + 2.59808i 0.0520031 + 0.0900721i
833833 12.0000 20.7846i 0.415775 0.720144i
834834 9.50000 16.4545i 0.328958 0.569772i
835835 0 0
836836 1.00000 + 8.66025i 0.0345857 + 0.299521i
837837 3.00000 0.103695
838838 9.00000 15.5885i 0.310900 0.538494i
839839 6.00000 10.3923i 0.207143 0.358782i −0.743670 0.668546i 0.766917π-0.766917\pi
0.950813 + 0.309764i 0.100250π0.100250\pi
840840 0 0
841841 14.5000 25.1147i 0.500000 0.866025i
842842 5.00000 + 8.66025i 0.172311 + 0.298452i
843843 8.00000 0.275535
844844 25.0000 0.860535
845845 0 0
846846 5.00000 + 8.66025i 0.171904 + 0.297746i
847847 −7.00000 −0.240523
848848 −4.00000 −0.137361
849849 −10.0000 17.3205i −0.343199 0.594438i
850850 −10.0000 + 17.3205i −0.342997 + 0.594089i
851851 10.0000 + 17.3205i 0.342796 + 0.593739i
852852 7.00000 12.1244i 0.239816 0.415374i
853853 −1.50000 + 2.59808i −0.0513590 + 0.0889564i −0.890562 0.454862i 0.849689π-0.849689\pi
0.839203 + 0.543818i 0.183022π0.183022\pi
854854 −11.0000 −0.376412
855855 0 0
856856 10.0000 0.341793
857857 −21.0000 + 36.3731i −0.717346 + 1.24248i 0.244701 + 0.969599i 0.421310π0.421310\pi
−0.962048 + 0.272882i 0.912023π0.912023\pi
858858 −3.00000 + 5.19615i −0.102418 + 0.177394i
859859 −3.50000 6.06218i −0.119418 0.206839i 0.800119 0.599841i 0.204770π-0.204770\pi
−0.919537 + 0.393003i 0.871436π0.871436\pi
860860 0 0
861861 2.00000 + 3.46410i 0.0681598 + 0.118056i
862862 10.0000 0.340601
863863 −22.0000 −0.748889 −0.374444 0.927249i 0.622167π-0.622167\pi
−0.374444 + 0.927249i 0.622167π0.622167\pi
864864 −0.500000 0.866025i −0.0170103 0.0294628i
865865 0 0
866866 9.00000 0.305832
867867 1.00000 0.0339618
868868 1.50000 + 2.59808i 0.0509133 + 0.0881845i
869869 1.00000 1.73205i 0.0339227 0.0587558i
870870 0 0
871871 4.50000 7.79423i 0.152477 0.264097i
872872 7.00000 12.1244i 0.237050 0.410582i
873873 2.00000 0.0676897
874874 −16.0000 6.92820i −0.541208 0.234350i
875875 0 0
876876 −5.50000 + 9.52628i −0.185828 + 0.321863i
877877 12.5000 21.6506i 0.422095 0.731090i −0.574049 0.818821i 0.694628π-0.694628\pi
0.996144 + 0.0877308i 0.0279615π0.0279615\pi
878878 9.50000 + 16.4545i 0.320609 + 0.555312i
879879 7.00000 12.1244i 0.236104 0.408944i
880880 0 0
881881 36.0000 1.21287 0.606435 0.795133i 0.292599π-0.292599\pi
0.606435 + 0.795133i 0.292599π0.292599\pi
882882 6.00000 0.202031
883883 4.50000 + 7.79423i 0.151437 + 0.262297i 0.931756 0.363085i 0.118277π-0.118277\pi
−0.780319 + 0.625382i 0.784943π0.784943\pi
884884 6.00000 + 10.3923i 0.201802 + 0.349531i
885885 0 0
886886 −24.0000 −0.806296
887887 −9.00000 15.5885i −0.302190 0.523409i 0.674441 0.738328i 0.264385π-0.264385\pi
−0.976632 + 0.214919i 0.931051π0.931051\pi
888888 2.50000 4.33013i 0.0838945 0.145310i
889889 4.00000 + 6.92820i 0.134156 + 0.232364i
890890 0 0
891891 1.00000 1.73205i 0.0335013 0.0580259i
892892 9.00000 0.301342
893893 −5.00000 43.3013i −0.167319 1.44902i
894894 −22.0000 −0.735790
895895 0 0
896896 0.500000 0.866025i 0.0167038 0.0289319i
897897 −6.00000 10.3923i −0.200334 0.346989i
898898 −18.0000 + 31.1769i −0.600668 + 1.04039i
899899 0 0
900900 −5.00000 −0.166667
901901 −16.0000 −0.533037
902902 −4.00000 6.92820i −0.133185 0.230684i
903903 −4.50000 7.79423i −0.149751 0.259376i
904904 −10.0000 −0.332595
905905 0 0
906906 10.0000 + 17.3205i 0.332228 + 0.575435i
907907 −26.0000 + 45.0333i −0.863316 + 1.49531i 0.00539395 + 0.999985i 0.498283π0.498283\pi
−0.868710 + 0.495321i 0.835050π0.835050\pi
908908 −4.00000 6.92820i −0.132745 0.229920i
909909 5.00000 8.66025i 0.165840 0.287242i
910910 0 0
911911 −60.0000 −1.98789 −0.993944 0.109885i 0.964952π-0.964952\pi
−0.993944 + 0.109885i 0.964952π0.964952\pi
912912 0.500000 + 4.33013i 0.0165567 + 0.143385i
913913 −16.0000 −0.529523
914914 2.50000 4.33013i 0.0826927 0.143228i
915915 0 0
916916 5.50000 + 9.52628i 0.181725 + 0.314757i
917917 3.00000 5.19615i 0.0990687 0.171592i
918918 −2.00000 3.46410i −0.0660098 0.114332i
919919 55.0000 1.81428 0.907141 0.420826i 0.138260π-0.138260\pi
0.907141 + 0.420826i 0.138260π0.138260\pi
920920 0 0
921921 −6.00000 10.3923i −0.197707 0.342438i
922922 3.00000 + 5.19615i 0.0987997 + 0.171126i
923923 −42.0000 −1.38245
924924 2.00000 0.0657952
925925 −12.5000 21.6506i −0.410997 0.711868i
926926 −4.50000 + 7.79423i −0.147879 + 0.256134i
927927 1.50000 + 2.59808i 0.0492665 + 0.0853320i
928928 0 0
929929 −6.00000 + 10.3923i −0.196854 + 0.340960i −0.947507 0.319736i 0.896406π-0.896406\pi
0.750653 + 0.660697i 0.229739π0.229739\pi
930930 0 0
931931 −24.0000 10.3923i −0.786568 0.340594i
932932 18.0000 0.589610
933933 5.00000 8.66025i 0.163693 0.283524i
934934 4.00000 6.92820i 0.130884 0.226698i
935935 0 0
936936 −1.50000 + 2.59808i −0.0490290 + 0.0849208i
937937 12.5000 + 21.6506i 0.408357 + 0.707295i 0.994706 0.102763i 0.0327685π-0.0327685\pi
−0.586349 + 0.810059i 0.699435π0.699435\pi
938938 −3.00000 −0.0979535
939939 −6.00000 −0.195803
940940 0 0
941941 16.0000 + 27.7128i 0.521585 + 0.903412i 0.999685 + 0.0251063i 0.00799243π0.00799243\pi
−0.478100 + 0.878306i 0.658674π0.658674\pi
942942 −21.0000 −0.684217
943943 16.0000 0.521032
944944 7.00000 + 12.1244i 0.227831 + 0.394614i
945945 0 0
946946 9.00000 + 15.5885i 0.292615 + 0.506824i
947947 −5.00000 + 8.66025i −0.162478 + 0.281420i −0.935757 0.352646i 0.885282π-0.885282\pi
0.773279 + 0.634066i 0.218615π0.218615\pi
948948 0.500000 0.866025i 0.0162392 0.0281272i
949949 33.0000 1.07123
950950 20.0000 + 8.66025i 0.648886 + 0.280976i
951951 −12.0000 −0.389127
952952 2.00000 3.46410i 0.0648204 0.112272i
953953 15.0000 25.9808i 0.485898 0.841599i −0.513971 0.857808i 0.671826π-0.671826\pi
0.999869 + 0.0162081i 0.00515944π0.00515944\pi
954954 −2.00000 3.46410i −0.0647524 0.112154i
955955 0 0
956956 6.00000 + 10.3923i 0.194054 + 0.336111i
957957 0 0
958958 −6.00000 −0.193851
959959 3.00000 + 5.19615i 0.0968751 + 0.167793i
960960 0 0
961961 −22.0000 −0.709677
962962 −15.0000 −0.483619
963963 5.00000 + 8.66025i 0.161123 + 0.279073i
964964 −12.5000 + 21.6506i −0.402598 + 0.697320i
965965 0 0
966966 −2.00000 + 3.46410i −0.0643489 + 0.111456i
967967 −25.5000 + 44.1673i −0.820025 + 1.42032i 0.0856383 + 0.996326i 0.472707π0.472707\pi
−0.905663 + 0.423998i 0.860626π0.860626\pi
968968 7.00000 0.224989
969969 2.00000 + 17.3205i 0.0642493 + 0.556415i
970970 0 0
971971 −3.00000 + 5.19615i −0.0962746 + 0.166752i −0.910140 0.414301i 0.864026π-0.864026\pi
0.813865 + 0.581054i 0.197359π0.197359\pi
972972 0.500000 0.866025i 0.0160375 0.0277778i
973973 9.50000 + 16.4545i 0.304556 + 0.527506i
974974 16.0000 27.7128i 0.512673 0.887976i
975975 7.50000 + 12.9904i 0.240192 + 0.416025i
976976 11.0000 0.352101
977977 −42.0000 −1.34370 −0.671850 0.740688i 0.734500π-0.734500\pi
−0.671850 + 0.740688i 0.734500π0.734500\pi
978978 −5.50000 9.52628i −0.175871 0.304617i
979979 −14.0000 24.2487i −0.447442 0.774992i
980980 0 0
981981 14.0000 0.446986
982982 15.0000 + 25.9808i 0.478669 + 0.829079i
983983 3.00000 5.19615i 0.0956851 0.165732i −0.814209 0.580572i 0.802829π-0.802829\pi
0.909894 + 0.414840i 0.136162π0.136162\pi
984984 −2.00000 3.46410i −0.0637577 0.110432i
985985 0 0
986986 0 0
987987 −10.0000 −0.318304
988988 10.5000 7.79423i 0.334050 0.247967i
989989 −36.0000 −1.14473
990990 0 0
991991 8.50000 14.7224i 0.270011 0.467673i −0.698853 0.715265i 0.746306π-0.746306\pi
0.968864 + 0.247592i 0.0796392π0.0796392\pi
992992 −1.50000 2.59808i −0.0476250 0.0824890i
993993 7.50000 12.9904i 0.238005 0.412237i
994994 7.00000 + 12.1244i 0.222027 + 0.384561i
995995 0 0
996996 −8.00000 −0.253490
997997 24.5000 + 42.4352i 0.775923 + 1.34394i 0.934274 + 0.356555i 0.116049π0.116049\pi
−0.158352 + 0.987383i 0.550618π0.550618\pi
998998 2.50000 + 4.33013i 0.0791361 + 0.137068i
999999 5.00000 0.158193
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 114.2.e.b.49.1 yes 2
3.2 odd 2 342.2.g.c.163.1 2
4.3 odd 2 912.2.q.b.49.1 2
12.11 even 2 2736.2.s.k.1873.1 2
19.7 even 3 inner 114.2.e.b.7.1 2
19.8 odd 6 2166.2.a.h.1.1 1
19.11 even 3 2166.2.a.b.1.1 1
57.8 even 6 6498.2.a.g.1.1 1
57.11 odd 6 6498.2.a.u.1.1 1
57.26 odd 6 342.2.g.c.235.1 2
76.7 odd 6 912.2.q.b.577.1 2
228.83 even 6 2736.2.s.k.577.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.2.e.b.7.1 2 19.7 even 3 inner
114.2.e.b.49.1 yes 2 1.1 even 1 trivial
342.2.g.c.163.1 2 3.2 odd 2
342.2.g.c.235.1 2 57.26 odd 6
912.2.q.b.49.1 2 4.3 odd 2
912.2.q.b.577.1 2 76.7 odd 6
2166.2.a.b.1.1 1 19.11 even 3
2166.2.a.h.1.1 1 19.8 odd 6
2736.2.s.k.577.1 2 228.83 even 6
2736.2.s.k.1873.1 2 12.11 even 2
6498.2.a.g.1.1 1 57.8 even 6
6498.2.a.u.1.1 1 57.11 odd 6