Properties

Label 294.2.e.f.67.1
Level 294294
Weight 22
Character 294.67
Analytic conductor 2.3482.348
Analytic rank 00
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] = [294,2,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("294.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 294=2372 294 = 2 \cdot 3 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 294.e (of order 33, degree 22, not 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: 2.347601819432.34760181943
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: no (minimal twist has level 42)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 67.1
Root 0.500000+0.866025i0.500000 + 0.866025i of defining polynomial
Character χ\chi == 294.67
Dual form 294.2.e.f.79.1

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+(0.500000+0.866025i)q2+(0.5000000.866025i)q3+(0.500000+0.866025i)q4+(1.50000+2.59808i)q5+1.00000q61.00000q8+(0.5000000.866025i)q9+(1.50000+2.59808i)q10+(1.50000+2.59808i)q11+(0.500000+0.866025i)q12+4.00000q13+3.00000q15+(0.5000000.866025i)q16+(0.5000000.866025i)q18+(2.000003.46410i)q193.00000q203.00000q22+(0.500000+0.866025i)q24+(2.00000+3.46410i)q25+(2.00000+3.46410i)q261.00000q27+9.00000q29+(1.50000+2.59808i)q30+(0.500000+0.866025i)q31+(0.5000000.866025i)q32+(1.50000+2.59808i)q33+1.00000q36+(4.000006.92820i)q37+(2.000003.46410i)q38+(2.000003.46410i)q39+(1.500002.59808i)q4010.0000q43+(1.500002.59808i)q44+(1.500002.59808i)q45+(3.000005.19615i)q471.00000q484.00000q50+(2.00000+3.46410i)q52+(1.500002.59808i)q53+(0.5000000.866025i)q549.00000q554.00000q57+(4.50000+7.79423i)q58+(1.500002.59808i)q59+(1.50000+2.59808i)q60+(5.000008.66025i)q611.00000q62+1.00000q64+(6.00000+10.3923i)q65+(1.50000+2.59808i)q66+(5.000008.66025i)q676.00000q71+(0.500000+0.866025i)q72+(1.000001.73205i)q73+(4.000006.92820i)q74+(2.00000+3.46410i)q75+4.00000q76+4.00000q78+(0.500000+0.866025i)q79+(1.500002.59808i)q80+(0.500000+0.866025i)q81+9.00000q83+(5.000008.66025i)q86+(4.500007.79423i)q87+(1.500002.59808i)q88+(3.00000+5.19615i)q89+3.00000q90+(0.500000+0.866025i)q93+(3.000005.19615i)q94+(6.0000010.3923i)q95+(0.5000000.866025i)q96+1.00000q97+3.00000q99+O(q100)q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} +4.00000 q^{13} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{18} +(-2.00000 - 3.46410i) q^{19} -3.00000 q^{20} -3.00000 q^{22} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(2.00000 + 3.46410i) q^{26} -1.00000 q^{27} +9.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(-0.500000 + 0.866025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +1.00000 q^{36} +(-4.00000 - 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(2.00000 - 3.46410i) q^{39} +(-1.50000 - 2.59808i) q^{40} -10.0000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(1.50000 - 2.59808i) q^{45} +(-3.00000 - 5.19615i) q^{47} -1.00000 q^{48} -4.00000 q^{50} +(-2.00000 + 3.46410i) q^{52} +(1.50000 - 2.59808i) q^{53} +(-0.500000 - 0.866025i) q^{54} -9.00000 q^{55} -4.00000 q^{57} +(4.50000 + 7.79423i) q^{58} +(1.50000 - 2.59808i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(-5.00000 - 8.66025i) q^{61} -1.00000 q^{62} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(-1.50000 + 2.59808i) q^{66} +(5.00000 - 8.66025i) q^{67} -6.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(4.00000 - 6.92820i) q^{74} +(2.00000 + 3.46410i) q^{75} +4.00000 q^{76} +4.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +9.00000 q^{83} +(-5.00000 - 8.66025i) q^{86} +(4.50000 - 7.79423i) q^{87} +(1.50000 - 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +3.00000 q^{90} +(0.500000 + 0.866025i) q^{93} +(3.00000 - 5.19615i) q^{94} +(6.00000 - 10.3923i) q^{95} +(-0.500000 - 0.866025i) q^{96} +1.00000 q^{97} +3.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q2+q3q4+3q5+2q62q8q93q103q11+q12+8q13+6q15q16+q184q196q206q22q244q25+4q26++6q99+O(q100) 2 q + q^{2} + q^{3} - q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{8} - q^{9} - 3 q^{10} - 3 q^{11} + q^{12} + 8 q^{13} + 6 q^{15} - q^{16} + q^{18} - 4 q^{19} - 6 q^{20} - 6 q^{22} - q^{24} - 4 q^{25} + 4 q^{26}+ \cdots + 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/294Z)×\left(\mathbb{Z}/294\mathbb{Z}\right)^\times.

nn 197197 199199
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 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i 0.0673912π0.0673912\pi
−0.306851 + 0.951757i 0.599275π0.599275\pi
66 1.00000 0.408248
77 0 0
88 −1.00000 −0.353553
99 −0.500000 0.866025i −0.166667 0.288675i
1010 −1.50000 + 2.59808i −0.474342 + 0.821584i
1111 −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i 0.982718π-0.982718\pi
0.546259 + 0.837616i 0.316051π0.316051\pi
1212 0.500000 + 0.866025i 0.144338 + 0.250000i
1313 4.00000 1.10940 0.554700 0.832050i 0.312833π-0.312833\pi
0.554700 + 0.832050i 0.312833π0.312833\pi
1414 0 0
1515 3.00000 0.774597
1616 −0.500000 0.866025i −0.125000 0.216506i
1717 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
1818 0.500000 0.866025i 0.117851 0.204124i
1919 −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i 0.318398π-0.318398\pi
−0.998899 + 0.0469020i 0.985065π0.985065\pi
2020 −3.00000 −0.670820
2121 0 0
2222 −3.00000 −0.639602
2323 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
2424 −0.500000 + 0.866025i −0.102062 + 0.176777i
2525 −2.00000 + 3.46410i −0.400000 + 0.692820i
2626 2.00000 + 3.46410i 0.392232 + 0.679366i
2727 −1.00000 −0.192450
2828 0 0
2929 9.00000 1.67126 0.835629 0.549294i 0.185103π-0.185103\pi
0.835629 + 0.549294i 0.185103π0.185103\pi
3030 1.50000 + 2.59808i 0.273861 + 0.474342i
3131 −0.500000 + 0.866025i −0.0898027 + 0.155543i −0.907428 0.420208i 0.861957π-0.861957\pi
0.817625 + 0.575751i 0.195290π0.195290\pi
3232 0.500000 0.866025i 0.0883883 0.153093i
3333 1.50000 + 2.59808i 0.261116 + 0.452267i
3434 0 0
3535 0 0
3636 1.00000 0.166667
3737 −4.00000 6.92820i −0.657596 1.13899i −0.981236 0.192809i 0.938240π-0.938240\pi
0.323640 0.946180i 0.395093π-0.395093\pi
3838 2.00000 3.46410i 0.324443 0.561951i
3939 2.00000 3.46410i 0.320256 0.554700i
4040 −1.50000 2.59808i −0.237171 0.410792i
4141 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4242 0 0
4343 −10.0000 −1.52499 −0.762493 0.646997i 0.776025π-0.776025\pi
−0.762493 + 0.646997i 0.776025π0.776025\pi
4444 −1.50000 2.59808i −0.226134 0.391675i
4545 1.50000 2.59808i 0.223607 0.387298i
4646 0 0
4747 −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i 0.310836π-0.310836\pi
−0.997503 + 0.0706177i 0.977503π0.977503\pi
4848 −1.00000 −0.144338
4949 0 0
5050 −4.00000 −0.565685
5151 0 0
5252 −2.00000 + 3.46410i −0.277350 + 0.480384i
5353 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i 0.767275π-0.767275\pi
0.950464 + 0.310835i 0.100609π0.100609\pi
5454 −0.500000 0.866025i −0.0680414 0.117851i
5555 −9.00000 −1.21356
5656 0 0
5757 −4.00000 −0.529813
5858 4.50000 + 7.79423i 0.590879 + 1.02343i
5959 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i 0.770771π-0.770771\pi
0.946993 + 0.321253i 0.104104π0.104104\pi
6060 −1.50000 + 2.59808i −0.193649 + 0.335410i
6161 −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i 0.945525π-0.945525\pi
0.345207 0.938527i 0.387809π-0.387809\pi
6262 −1.00000 −0.127000
6363 0 0
6464 1.00000 0.125000
6565 6.00000 + 10.3923i 0.744208 + 1.28901i
6666 −1.50000 + 2.59808i −0.184637 + 0.319801i
6767 5.00000 8.66025i 0.610847 1.05802i −0.380251 0.924883i 0.624162π-0.624162\pi
0.991098 0.133135i 0.0425044π-0.0425044\pi
6868 0 0
6969 0 0
7070 0 0
7171 −6.00000 −0.712069 −0.356034 0.934473i 0.615871π-0.615871\pi
−0.356034 + 0.934473i 0.615871π0.615871\pi
7272 0.500000 + 0.866025i 0.0589256 + 0.102062i
7373 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i 0.795992π-0.795992\pi
0.918594 + 0.395203i 0.129326π0.129326\pi
7474 4.00000 6.92820i 0.464991 0.805387i
7575 2.00000 + 3.46410i 0.230940 + 0.400000i
7676 4.00000 0.458831
7777 0 0
7878 4.00000 0.452911
7979 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i 0.148751π-0.148751\pi
−0.836527 + 0.547926i 0.815418π0.815418\pi
8080 1.50000 2.59808i 0.167705 0.290474i
8181 −0.500000 + 0.866025i −0.0555556 + 0.0962250i
8282 0 0
8383 9.00000 0.987878 0.493939 0.869496i 0.335557π-0.335557\pi
0.493939 + 0.869496i 0.335557π0.335557\pi
8484 0 0
8585 0 0
8686 −5.00000 8.66025i −0.539164 0.933859i
8787 4.50000 7.79423i 0.482451 0.835629i
8888 1.50000 2.59808i 0.159901 0.276956i
8989 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i 0.0636557π-0.0636557\pi
−0.662071 + 0.749441i 0.730322π0.730322\pi
9090 3.00000 0.316228
9191 0 0
9292 0 0
9393 0.500000 + 0.866025i 0.0518476 + 0.0898027i
9494 3.00000 5.19615i 0.309426 0.535942i
9595 6.00000 10.3923i 0.615587 1.06623i
9696 −0.500000 0.866025i −0.0510310 0.0883883i
9797 1.00000 0.101535 0.0507673 0.998711i 0.483833π-0.483833\pi
0.0507673 + 0.998711i 0.483833π0.483833\pi
9898 0 0
9999 3.00000 0.301511
100100 −2.00000 3.46410i −0.200000 0.346410i
101101 −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i 0.519872π0.519872\pi
−0.833143 + 0.553058i 0.813461π0.813461\pi
102102 0 0
103103 4.00000 + 6.92820i 0.394132 + 0.682656i 0.992990 0.118199i 0.0377120π-0.0377120\pi
−0.598858 + 0.800855i 0.704379π0.704379\pi
104104 −4.00000 −0.392232
105105 0 0
106106 3.00000 0.291386
107107 1.50000 + 2.59808i 0.145010 + 0.251166i 0.929377 0.369132i 0.120345π-0.120345\pi
−0.784366 + 0.620298i 0.787012π0.787012\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 −4.50000 7.79423i −0.429058 0.743151i
111111 −8.00000 −0.759326
112112 0 0
113113 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
114114 −2.00000 3.46410i −0.187317 0.324443i
115115 0 0
116116 −4.50000 + 7.79423i −0.417815 + 0.723676i
117117 −2.00000 3.46410i −0.184900 0.320256i
118118 3.00000 0.276172
119119 0 0
120120 −3.00000 −0.273861
121121 1.00000 + 1.73205i 0.0909091 + 0.157459i
122122 5.00000 8.66025i 0.452679 0.784063i
123123 0 0
124124 −0.500000 0.866025i −0.0449013 0.0777714i
125125 3.00000 0.268328
126126 0 0
127127 5.00000 0.443678 0.221839 0.975083i 0.428794π-0.428794\pi
0.221839 + 0.975083i 0.428794π0.428794\pi
128128 0.500000 + 0.866025i 0.0441942 + 0.0765466i
129129 −5.00000 + 8.66025i −0.440225 + 0.762493i
130130 −6.00000 + 10.3923i −0.526235 + 0.911465i
131131 −4.50000 7.79423i −0.393167 0.680985i 0.599699 0.800226i 0.295287π-0.295287\pi
−0.992865 + 0.119241i 0.961954π0.961954\pi
132132 −3.00000 −0.261116
133133 0 0
134134 10.0000 0.863868
135135 −1.50000 2.59808i −0.129099 0.223607i
136136 0 0
137137 −9.00000 + 15.5885i −0.768922 + 1.33181i 0.169226 + 0.985577i 0.445873π0.445873\pi
−0.938148 + 0.346235i 0.887460π0.887460\pi
138138 0 0
139139 −2.00000 −0.169638 −0.0848189 0.996396i 0.527031π-0.527031\pi
−0.0848189 + 0.996396i 0.527031π0.527031\pi
140140 0 0
141141 −6.00000 −0.505291
142142 −3.00000 5.19615i −0.251754 0.436051i
143143 −6.00000 + 10.3923i −0.501745 + 0.869048i
144144 −0.500000 + 0.866025i −0.0416667 + 0.0721688i
145145 13.5000 + 23.3827i 1.12111 + 1.94183i
146146 2.00000 0.165521
147147 0 0
148148 8.00000 0.657596
149149 −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i 0.902763π-0.902763\pi
0.216394 0.976306i 0.430570π-0.430570\pi
150150 −2.00000 + 3.46410i −0.163299 + 0.282843i
151151 0.500000 0.866025i 0.0406894 0.0704761i −0.844963 0.534824i 0.820378π-0.820378\pi
0.885653 + 0.464348i 0.153711π0.153711\pi
152152 2.00000 + 3.46410i 0.162221 + 0.280976i
153153 0 0
154154 0 0
155155 −3.00000 −0.240966
156156 2.00000 + 3.46410i 0.160128 + 0.277350i
157157 −2.00000 + 3.46410i −0.159617 + 0.276465i −0.934731 0.355357i 0.884359π-0.884359\pi
0.775113 + 0.631822i 0.217693π0.217693\pi
158158 −0.500000 + 0.866025i −0.0397779 + 0.0688973i
159159 −1.50000 2.59808i −0.118958 0.206041i
160160 3.00000 0.237171
161161 0 0
162162 −1.00000 −0.0785674
163163 8.00000 + 13.8564i 0.626608 + 1.08532i 0.988227 + 0.152992i 0.0488907π0.0488907\pi
−0.361619 + 0.932326i 0.617776π0.617776\pi
164164 0 0
165165 −4.50000 + 7.79423i −0.350325 + 0.606780i
166166 4.50000 + 7.79423i 0.349268 + 0.604949i
167167 −6.00000 −0.464294 −0.232147 0.972681i 0.574575π-0.574575\pi
−0.232147 + 0.972681i 0.574575π0.574575\pi
168168 0 0
169169 3.00000 0.230769
170170 0 0
171171 −2.00000 + 3.46410i −0.152944 + 0.264906i
172172 5.00000 8.66025i 0.381246 0.660338i
173173 9.00000 + 15.5885i 0.684257 + 1.18517i 0.973670 + 0.227964i 0.0732068π0.0732068\pi
−0.289412 + 0.957205i 0.593460π0.593460\pi
174174 9.00000 0.682288
175175 0 0
176176 3.00000 0.226134
177177 −1.50000 2.59808i −0.112747 0.195283i
178178 −3.00000 + 5.19615i −0.224860 + 0.389468i
179179 −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i 0.981361π-0.981361\pi
0.549825 + 0.835280i 0.314694π0.314694\pi
180180 1.50000 + 2.59808i 0.111803 + 0.193649i
181181 −8.00000 −0.594635 −0.297318 0.954779i 0.596092π-0.596092\pi
−0.297318 + 0.954779i 0.596092π0.596092\pi
182182 0 0
183183 −10.0000 −0.739221
184184 0 0
185185 12.0000 20.7846i 0.882258 1.52811i
186186 −0.500000 + 0.866025i −0.0366618 + 0.0635001i
187187 0 0
188188 6.00000 0.437595
189189 0 0
190190 12.0000 0.870572
191191 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
192192 0.500000 0.866025i 0.0360844 0.0625000i
193193 9.50000 16.4545i 0.683825 1.18442i −0.289980 0.957033i 0.593649π-0.593649\pi
0.973805 0.227387i 0.0730182π-0.0730182\pi
194194 0.500000 + 0.866025i 0.0358979 + 0.0621770i
195195 12.0000 0.859338
196196 0 0
197197 6.00000 0.427482 0.213741 0.976890i 0.431435π-0.431435\pi
0.213741 + 0.976890i 0.431435π0.431435\pi
198198 1.50000 + 2.59808i 0.106600 + 0.184637i
199199 10.0000 17.3205i 0.708881 1.22782i −0.256391 0.966573i 0.582534π-0.582534\pi
0.965272 0.261245i 0.0841331π-0.0841331\pi
200200 2.00000 3.46410i 0.141421 0.244949i
201201 −5.00000 8.66025i −0.352673 0.610847i
202202 −18.0000 −1.26648
203203 0 0
204204 0 0
205205 0 0
206206 −4.00000 + 6.92820i −0.278693 + 0.482711i
207207 0 0
208208 −2.00000 3.46410i −0.138675 0.240192i
209209 12.0000 0.830057
210210 0 0
211211 14.0000 0.963800 0.481900 0.876226i 0.339947π-0.339947\pi
0.481900 + 0.876226i 0.339947π0.339947\pi
212212 1.50000 + 2.59808i 0.103020 + 0.178437i
213213 −3.00000 + 5.19615i −0.205557 + 0.356034i
214214 −1.50000 + 2.59808i −0.102538 + 0.177601i
215215 −15.0000 25.9808i −1.02299 1.77187i
216216 1.00000 0.0680414
217217 0 0
218218 −14.0000 −0.948200
219219 −1.00000 1.73205i −0.0675737 0.117041i
220220 4.50000 7.79423i 0.303390 0.525487i
221221 0 0
222222 −4.00000 6.92820i −0.268462 0.464991i
223223 19.0000 1.27233 0.636167 0.771551i 0.280519π-0.280519\pi
0.636167 + 0.771551i 0.280519π0.280519\pi
224224 0 0
225225 4.00000 0.266667
226226 0 0
227227 −13.5000 + 23.3827i −0.896026 + 1.55196i −0.0634974 + 0.997982i 0.520225π0.520225\pi
−0.832529 + 0.553981i 0.813108π0.813108\pi
228228 2.00000 3.46410i 0.132453 0.229416i
229229 −2.00000 3.46410i −0.132164 0.228914i 0.792347 0.610071i 0.208859π-0.208859\pi
−0.924510 + 0.381157i 0.875526π0.875526\pi
230230 0 0
231231 0 0
232232 −9.00000 −0.590879
233233 12.0000 + 20.7846i 0.786146 + 1.36165i 0.928312 + 0.371802i 0.121260π0.121260\pi
−0.142166 + 0.989843i 0.545407π0.545407\pi
234234 2.00000 3.46410i 0.130744 0.226455i
235235 9.00000 15.5885i 0.587095 1.01688i
236236 1.50000 + 2.59808i 0.0976417 + 0.169120i
237237 1.00000 0.0649570
238238 0 0
239239 −24.0000 −1.55243 −0.776215 0.630468i 0.782863π-0.782863\pi
−0.776215 + 0.630468i 0.782863π0.782863\pi
240240 −1.50000 2.59808i −0.0968246 0.167705i
241241 −0.500000 + 0.866025i −0.0322078 + 0.0557856i −0.881680 0.471848i 0.843587π-0.843587\pi
0.849472 + 0.527633i 0.176921π0.176921\pi
242242 −1.00000 + 1.73205i −0.0642824 + 0.111340i
243243 0.500000 + 0.866025i 0.0320750 + 0.0555556i
244244 10.0000 0.640184
245245 0 0
246246 0 0
247247 −8.00000 13.8564i −0.509028 0.881662i
248248 0.500000 0.866025i 0.0317500 0.0549927i
249249 4.50000 7.79423i 0.285176 0.493939i
250250 1.50000 + 2.59808i 0.0948683 + 0.164317i
251251 −27.0000 −1.70422 −0.852112 0.523359i 0.824679π-0.824679\pi
−0.852112 + 0.523359i 0.824679π0.824679\pi
252252 0 0
253253 0 0
254254 2.50000 + 4.33013i 0.156864 + 0.271696i
255255 0 0
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i 0.106747π-0.106747\pi
−0.757159 + 0.653231i 0.773413π0.773413\pi
258258 −10.0000 −0.622573
259259 0 0
260260 −12.0000 −0.744208
261261 −4.50000 7.79423i −0.278543 0.482451i
262262 4.50000 7.79423i 0.278011 0.481529i
263263 3.00000 5.19615i 0.184988 0.320408i −0.758585 0.651575i 0.774109π-0.774109\pi
0.943572 + 0.331166i 0.107442π0.107442\pi
264264 −1.50000 2.59808i −0.0923186 0.159901i
265265 9.00000 0.552866
266266 0 0
267267 6.00000 0.367194
268268 5.00000 + 8.66025i 0.305424 + 0.529009i
269269 10.5000 18.1865i 0.640196 1.10885i −0.345192 0.938532i 0.612186π-0.612186\pi
0.985389 0.170321i 0.0544803π-0.0544803\pi
270270 1.50000 2.59808i 0.0912871 0.158114i
271271 5.50000 + 9.52628i 0.334101 + 0.578680i 0.983312 0.181928i 0.0582339π-0.0582339\pi
−0.649211 + 0.760609i 0.724901π0.724901\pi
272272 0 0
273273 0 0
274274 −18.0000 −1.08742
275275 −6.00000 10.3923i −0.361814 0.626680i
276276 0 0
277277 −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i 0.910591π-0.910591\pi
0.720473 + 0.693482i 0.243925π0.243925\pi
278278 −1.00000 1.73205i −0.0599760 0.103882i
279279 1.00000 0.0598684
280280 0 0
281281 6.00000 0.357930 0.178965 0.983855i 0.442725π-0.442725\pi
0.178965 + 0.983855i 0.442725π0.442725\pi
282282 −3.00000 5.19615i −0.178647 0.309426i
283283 7.00000 12.1244i 0.416107 0.720718i −0.579437 0.815017i 0.696728π-0.696728\pi
0.995544 + 0.0942988i 0.0300609π0.0300609\pi
284284 3.00000 5.19615i 0.178017 0.308335i
285285 −6.00000 10.3923i −0.355409 0.615587i
286286 −12.0000 −0.709575
287287 0 0
288288 −1.00000 −0.0589256
289289 8.50000 + 14.7224i 0.500000 + 0.866025i
290290 −13.5000 + 23.3827i −0.792747 + 1.37308i
291291 0.500000 0.866025i 0.0293105 0.0507673i
292292 1.00000 + 1.73205i 0.0585206 + 0.101361i
293293 −33.0000 −1.92788 −0.963940 0.266119i 0.914259π-0.914259\pi
−0.963940 + 0.266119i 0.914259π0.914259\pi
294294 0 0
295295 9.00000 0.524000
296296 4.00000 + 6.92820i 0.232495 + 0.402694i
297297 1.50000 2.59808i 0.0870388 0.150756i
298298 9.00000 15.5885i 0.521356 0.903015i
299299 0 0
300300 −4.00000 −0.230940
301301 0 0
302302 1.00000 0.0575435
303303 9.00000 + 15.5885i 0.517036 + 0.895533i
304304 −2.00000 + 3.46410i −0.114708 + 0.198680i
305305 15.0000 25.9808i 0.858898 1.48765i
306306 0 0
307307 −8.00000 −0.456584 −0.228292 0.973593i 0.573314π-0.573314\pi
−0.228292 + 0.973593i 0.573314π0.573314\pi
308308 0 0
309309 8.00000 0.455104
310310 −1.50000 2.59808i −0.0851943 0.147561i
311311 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i 0.595114π-0.595114\pi
0.974841 0.222900i 0.0715523π-0.0715523\pi
312312 −2.00000 + 3.46410i −0.113228 + 0.196116i
313313 −15.5000 26.8468i −0.876112 1.51747i −0.855574 0.517681i 0.826795π-0.826795\pi
−0.0205381 0.999789i 0.506538π-0.506538\pi
314314 −4.00000 −0.225733
315315 0 0
316316 −1.00000 −0.0562544
317317 −4.50000 7.79423i −0.252745 0.437767i 0.711535 0.702650i 0.248000π-0.248000\pi
−0.964281 + 0.264883i 0.914667π0.914667\pi
318318 1.50000 2.59808i 0.0841158 0.145693i
319319 −13.5000 + 23.3827i −0.755855 + 1.30918i
320320 1.50000 + 2.59808i 0.0838525 + 0.145237i
321321 3.00000 0.167444
322322 0 0
323323 0 0
324324 −0.500000 0.866025i −0.0277778 0.0481125i
325325 −8.00000 + 13.8564i −0.443760 + 0.768615i
326326 −8.00000 + 13.8564i −0.443079 + 0.767435i
327327 7.00000 + 12.1244i 0.387101 + 0.670478i
328328 0 0
329329 0 0
330330 −9.00000 −0.495434
331331 −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i 0.981428π-0.981428\pi
0.448649 0.893708i 0.351905π-0.351905\pi
332332 −4.50000 + 7.79423i −0.246970 + 0.427764i
333333 −4.00000 + 6.92820i −0.219199 + 0.379663i
334334 −3.00000 5.19615i −0.164153 0.284321i
335335 30.0000 1.63908
336336 0 0
337337 −7.00000 −0.381314 −0.190657 0.981657i 0.561062π-0.561062\pi
−0.190657 + 0.981657i 0.561062π0.561062\pi
338338 1.50000 + 2.59808i 0.0815892 + 0.141317i
339339 0 0
340340 0 0
341341 −1.50000 2.59808i −0.0812296 0.140694i
342342 −4.00000 −0.216295
343343 0 0
344344 10.0000 0.539164
345345 0 0
346346 −9.00000 + 15.5885i −0.483843 + 0.838041i
347347 −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i 0.937721π-0.937721\pi
0.658824 + 0.752297i 0.271054π0.271054\pi
348348 4.50000 + 7.79423i 0.241225 + 0.417815i
349349 −26.0000 −1.39175 −0.695874 0.718164i 0.744983π-0.744983\pi
−0.695874 + 0.718164i 0.744983π0.744983\pi
350350 0 0
351351 −4.00000 −0.213504
352352 1.50000 + 2.59808i 0.0799503 + 0.138478i
353353 12.0000 20.7846i 0.638696 1.10625i −0.347024 0.937856i 0.612808π-0.612808\pi
0.985719 0.168397i 0.0538590π-0.0538590\pi
354354 1.50000 2.59808i 0.0797241 0.138086i
355355 −9.00000 15.5885i −0.477670 0.827349i
356356 −6.00000 −0.317999
357357 0 0
358358 −12.0000 −0.634220
359359 −15.0000 25.9808i −0.791670 1.37121i −0.924932 0.380131i 0.875879π-0.875879\pi
0.133263 0.991081i 0.457455π-0.457455\pi
360360 −1.50000 + 2.59808i −0.0790569 + 0.136931i
361361 1.50000 2.59808i 0.0789474 0.136741i
362362 −4.00000 6.92820i −0.210235 0.364138i
363363 2.00000 0.104973
364364 0 0
365365 6.00000 0.314054
366366 −5.00000 8.66025i −0.261354 0.452679i
367367 −9.50000 + 16.4545i −0.495896 + 0.858917i −0.999989 0.00473247i 0.998494π-0.998494\pi
0.504093 + 0.863649i 0.331827π0.331827\pi
368368 0 0
369369 0 0
370370 24.0000 1.24770
371371 0 0
372372 −1.00000 −0.0518476
373373 −4.00000 6.92820i −0.207112 0.358729i 0.743691 0.668523i 0.233073π-0.233073\pi
−0.950804 + 0.309794i 0.899740π0.899740\pi
374374 0 0
375375 1.50000 2.59808i 0.0774597 0.134164i
376376 3.00000 + 5.19615i 0.154713 + 0.267971i
377377 36.0000 1.85409
378378 0 0
379379 8.00000 0.410932 0.205466 0.978664i 0.434129π-0.434129\pi
0.205466 + 0.978664i 0.434129π0.434129\pi
380380 6.00000 + 10.3923i 0.307794 + 0.533114i
381381 2.50000 4.33013i 0.128079 0.221839i
382382 0 0
383383 9.00000 + 15.5885i 0.459879 + 0.796533i 0.998954 0.0457244i 0.0145596π-0.0145596\pi
−0.539076 + 0.842257i 0.681226π0.681226\pi
384384 1.00000 0.0510310
385385 0 0
386386 19.0000 0.967075
387387 5.00000 + 8.66025i 0.254164 + 0.440225i
388388 −0.500000 + 0.866025i −0.0253837 + 0.0439658i
389389 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i 0.784728π-0.784728\pi
0.932002 + 0.362454i 0.118061π0.118061\pi
390390 6.00000 + 10.3923i 0.303822 + 0.526235i
391391 0 0
392392 0 0
393393 −9.00000 −0.453990
394394 3.00000 + 5.19615i 0.151138 + 0.261778i
395395 −1.50000 + 2.59808i −0.0754732 + 0.130723i
396396 −1.50000 + 2.59808i −0.0753778 + 0.130558i
397397 −2.00000 3.46410i −0.100377 0.173858i 0.811463 0.584404i 0.198672π-0.198672\pi
−0.911840 + 0.410546i 0.865338π0.865338\pi
398398 20.0000 1.00251
399399 0 0
400400 4.00000 0.200000
401401 −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i 0.962132π-0.962132\pi
0.393680 0.919247i 0.371202π-0.371202\pi
402402 5.00000 8.66025i 0.249377 0.431934i
403403 −2.00000 + 3.46410i −0.0996271 + 0.172559i
404404 −9.00000 15.5885i −0.447767 0.775555i
405405 −3.00000 −0.149071
406406 0 0
407407 24.0000 1.18964
408408 0 0
409409 −12.5000 + 21.6506i −0.618085 + 1.07056i 0.371750 + 0.928333i 0.378758π0.378758\pi
−0.989835 + 0.142222i 0.954575π0.954575\pi
410410 0 0
411411 9.00000 + 15.5885i 0.443937 + 0.768922i
412412 −8.00000 −0.394132
413413 0 0
414414 0 0
415415 13.5000 + 23.3827i 0.662689 + 1.14781i
416416 2.00000 3.46410i 0.0980581 0.169842i
417417 −1.00000 + 1.73205i −0.0489702 + 0.0848189i
418418 6.00000 + 10.3923i 0.293470 + 0.508304i
419419 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
420420 0 0
421421 −22.0000 −1.07221 −0.536107 0.844150i 0.680106π-0.680106\pi
−0.536107 + 0.844150i 0.680106π0.680106\pi
422422 7.00000 + 12.1244i 0.340755 + 0.590204i
423423 −3.00000 + 5.19615i −0.145865 + 0.252646i
424424 −1.50000 + 2.59808i −0.0728464 + 0.126174i
425425 0 0
426426 −6.00000 −0.290701
427427 0 0
428428 −3.00000 −0.145010
429429 6.00000 + 10.3923i 0.289683 + 0.501745i
430430 15.0000 25.9808i 0.723364 1.25290i
431431 −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i 0.926659π-0.926659\pi
0.684564 + 0.728953i 0.259993π0.259993\pi
432432 0.500000 + 0.866025i 0.0240563 + 0.0416667i
433433 34.0000 1.63394 0.816968 0.576683i 0.195653π-0.195653\pi
0.816968 + 0.576683i 0.195653π0.195653\pi
434434 0 0
435435 27.0000 1.29455
436436 −7.00000 12.1244i −0.335239 0.580651i
437437 0 0
438438 1.00000 1.73205i 0.0477818 0.0827606i
439439 17.5000 + 30.3109i 0.835229 + 1.44666i 0.893843 + 0.448379i 0.147999π0.147999\pi
−0.0586141 + 0.998281i 0.518668π0.518668\pi
440440 9.00000 0.429058
441441 0 0
442442 0 0
443443 16.5000 + 28.5788i 0.783939 + 1.35782i 0.929631 + 0.368492i 0.120126π0.120126\pi
−0.145692 + 0.989330i 0.546541π0.546541\pi
444444 4.00000 6.92820i 0.189832 0.328798i
445445 −9.00000 + 15.5885i −0.426641 + 0.738964i
446446 9.50000 + 16.4545i 0.449838 + 0.779142i
447447 −18.0000 −0.851371
448448 0 0
449449 12.0000 0.566315 0.283158 0.959073i 0.408618π-0.408618\pi
0.283158 + 0.959073i 0.408618π0.408618\pi
450450 2.00000 + 3.46410i 0.0942809 + 0.163299i
451451 0 0
452452 0 0
453453 −0.500000 0.866025i −0.0234920 0.0406894i
454454 −27.0000 −1.26717
455455 0 0
456456 4.00000 0.187317
457457 0.500000 + 0.866025i 0.0233890 + 0.0405110i 0.877483 0.479608i 0.159221π-0.159221\pi
−0.854094 + 0.520119i 0.825888π0.825888\pi
458458 2.00000 3.46410i 0.0934539 0.161867i
459459 0 0
460460 0 0
461461 −30.0000 −1.39724 −0.698620 0.715493i 0.746202π-0.746202\pi
−0.698620 + 0.715493i 0.746202π0.746202\pi
462462 0 0
463463 8.00000 0.371792 0.185896 0.982569i 0.440481π-0.440481\pi
0.185896 + 0.982569i 0.440481π0.440481\pi
464464 −4.50000 7.79423i −0.208907 0.361838i
465465 −1.50000 + 2.59808i −0.0695608 + 0.120483i
466466 −12.0000 + 20.7846i −0.555889 + 0.962828i
467467 18.0000 + 31.1769i 0.832941 + 1.44270i 0.895696 + 0.444667i 0.146678π0.146678\pi
−0.0627555 + 0.998029i 0.519989π0.519989\pi
468468 4.00000 0.184900
469469 0 0
470470 18.0000 0.830278
471471 2.00000 + 3.46410i 0.0921551 + 0.159617i
472472 −1.50000 + 2.59808i −0.0690431 + 0.119586i
473473 15.0000 25.9808i 0.689701 1.19460i
474474 0.500000 + 0.866025i 0.0229658 + 0.0397779i
475475 16.0000 0.734130
476476 0 0
477477 −3.00000 −0.137361
478478 −12.0000 20.7846i −0.548867 0.950666i
479479 −9.00000 + 15.5885i −0.411220 + 0.712255i −0.995023 0.0996406i 0.968231π-0.968231\pi
0.583803 + 0.811895i 0.301564π0.301564\pi
480480 1.50000 2.59808i 0.0684653 0.118585i
481481 −16.0000 27.7128i −0.729537 1.26360i
482482 −1.00000 −0.0455488
483483 0 0
484484 −2.00000 −0.0909091
485485 1.50000 + 2.59808i 0.0681115 + 0.117973i
486486 −0.500000 + 0.866025i −0.0226805 + 0.0392837i
487487 −20.5000 + 35.5070i −0.928944 + 1.60898i −0.143851 + 0.989599i 0.545949π0.545949\pi
−0.785093 + 0.619378i 0.787385π0.787385\pi
488488 5.00000 + 8.66025i 0.226339 + 0.392031i
489489 16.0000 0.723545
490490 0 0
491491 −33.0000 −1.48927 −0.744635 0.667472i 0.767376π-0.767376\pi
−0.744635 + 0.667472i 0.767376π0.767376\pi
492492 0 0
493493 0 0
494494 8.00000 13.8564i 0.359937 0.623429i
495495 4.50000 + 7.79423i 0.202260 + 0.350325i
496496 1.00000 0.0449013
497497 0 0
498498 9.00000 0.403300
499499 −1.00000 1.73205i −0.0447661 0.0775372i 0.842774 0.538267i 0.180921π-0.180921\pi
−0.887540 + 0.460730i 0.847588π0.847588\pi
500500 −1.50000 + 2.59808i −0.0670820 + 0.116190i
501501 −3.00000 + 5.19615i −0.134030 + 0.232147i
502502 −13.5000 23.3827i −0.602534 1.04362i
503503 12.0000 0.535054 0.267527 0.963550i 0.413794π-0.413794\pi
0.267527 + 0.963550i 0.413794π0.413794\pi
504504 0 0
505505 −54.0000 −2.40297
506506 0 0
507507 1.50000 2.59808i 0.0666173 0.115385i
508508 −2.50000 + 4.33013i −0.110920 + 0.192118i
509509 −1.50000 2.59808i −0.0664863 0.115158i 0.830866 0.556473i 0.187846π-0.187846\pi
−0.897352 + 0.441315i 0.854512π0.854512\pi
510510 0 0
511511 0 0
512512 −1.00000 −0.0441942
513513 2.00000 + 3.46410i 0.0883022 + 0.152944i
514514 −3.00000 + 5.19615i −0.132324 + 0.229192i
515515 −12.0000 + 20.7846i −0.528783 + 0.915879i
516516 −5.00000 8.66025i −0.220113 0.381246i
517517 18.0000 0.791639
518518 0 0
519519 18.0000 0.790112
520520 −6.00000 10.3923i −0.263117 0.455733i
521521 −9.00000 + 15.5885i −0.394297 + 0.682943i −0.993011 0.118020i 0.962345π-0.962345\pi
0.598714 + 0.800963i 0.295679π0.295679\pi
522522 4.50000 7.79423i 0.196960 0.341144i
523523 −2.00000 3.46410i −0.0874539 0.151475i 0.818980 0.573822i 0.194540π-0.194540\pi
−0.906434 + 0.422347i 0.861206π0.861206\pi
524524 9.00000 0.393167
525525 0 0
526526 6.00000 0.261612
527527 0 0
528528 1.50000 2.59808i 0.0652791 0.113067i
529529 11.5000 19.9186i 0.500000 0.866025i
530530 4.50000 + 7.79423i 0.195468 + 0.338560i
531531 −3.00000 −0.130189
532532 0 0
533533 0 0
534534 3.00000 + 5.19615i 0.129823 + 0.224860i
535535 −4.50000 + 7.79423i −0.194552 + 0.336974i
536536 −5.00000 + 8.66025i −0.215967 + 0.374066i
537537 6.00000 + 10.3923i 0.258919 + 0.448461i
538538 21.0000 0.905374
539539 0 0
540540 3.00000 0.129099
541541 −13.0000 22.5167i −0.558914 0.968067i −0.997587 0.0694205i 0.977885π-0.977885\pi
0.438674 0.898646i 0.355448π-0.355448\pi
542542 −5.50000 + 9.52628i −0.236245 + 0.409189i
543543 −4.00000 + 6.92820i −0.171656 + 0.297318i
544544 0 0
545545 −42.0000 −1.79908
546546 0 0
547547 8.00000 0.342055 0.171028 0.985266i 0.445291π-0.445291\pi
0.171028 + 0.985266i 0.445291π0.445291\pi
548548 −9.00000 15.5885i −0.384461 0.665906i
549549 −5.00000 + 8.66025i −0.213395 + 0.369611i
550550 6.00000 10.3923i 0.255841 0.443129i
551551 −18.0000 31.1769i −0.766826 1.32818i
552552 0 0
553553 0 0
554554 −8.00000 −0.339887
555555 −12.0000 20.7846i −0.509372 0.882258i
556556 1.00000 1.73205i 0.0424094 0.0734553i
557557 −1.50000 + 2.59808i −0.0635570 + 0.110084i −0.896053 0.443947i 0.853578π-0.853578\pi
0.832496 + 0.554031i 0.186911π0.186911\pi
558558 0.500000 + 0.866025i 0.0211667 + 0.0366618i
559559 −40.0000 −1.69182
560560 0 0
561561 0 0
562562 3.00000 + 5.19615i 0.126547 + 0.219186i
563563 19.5000 33.7750i 0.821827 1.42345i −0.0824933 0.996592i 0.526288π-0.526288\pi
0.904320 0.426855i 0.140378π-0.140378\pi
564564 3.00000 5.19615i 0.126323 0.218797i
565565 0 0
566566 14.0000 0.588464
567567 0 0
568568 6.00000 0.251754
569569 18.0000 + 31.1769i 0.754599 + 1.30700i 0.945573 + 0.325409i 0.105502π0.105502\pi
−0.190974 + 0.981595i 0.561165π0.561165\pi
570570 6.00000 10.3923i 0.251312 0.435286i
571571 17.0000 29.4449i 0.711428 1.23223i −0.252893 0.967494i 0.581382π-0.581382\pi
0.964321 0.264735i 0.0852845π-0.0852845\pi
572572 −6.00000 10.3923i −0.250873 0.434524i
573573 0 0
574574 0 0
575575 0 0
576576 −0.500000 0.866025i −0.0208333 0.0360844i
577577 11.5000 19.9186i 0.478751 0.829222i −0.520952 0.853586i 0.674423π-0.674423\pi
0.999703 + 0.0243645i 0.00775624π0.00775624\pi
578578 −8.50000 + 14.7224i −0.353553 + 0.612372i
579579 −9.50000 16.4545i −0.394807 0.683825i
580580 −27.0000 −1.12111
581581 0 0
582582 1.00000 0.0414513
583583 4.50000 + 7.79423i 0.186371 + 0.322804i
584584 −1.00000 + 1.73205i −0.0413803 + 0.0716728i
585585 6.00000 10.3923i 0.248069 0.429669i
586586 −16.5000 28.5788i −0.681609 1.18058i
587587 −21.0000 −0.866763 −0.433381 0.901211i 0.642680π-0.642680\pi
−0.433381 + 0.901211i 0.642680π0.642680\pi
588588 0 0
589589 4.00000 0.164817
590590 4.50000 + 7.79423i 0.185262 + 0.320883i
591591 3.00000 5.19615i 0.123404 0.213741i
592592 −4.00000 + 6.92820i −0.164399 + 0.284747i
593593 12.0000 + 20.7846i 0.492781 + 0.853522i 0.999965 0.00831589i 0.00264706π-0.00264706\pi
−0.507184 + 0.861838i 0.669314π0.669314\pi
594594 3.00000 0.123091
595595 0 0
596596 18.0000 0.737309
597597 −10.0000 17.3205i −0.409273 0.708881i
598598 0 0
599599 9.00000 15.5885i 0.367730 0.636927i −0.621480 0.783430i 0.713468π-0.713468\pi
0.989210 + 0.146503i 0.0468017π0.0468017\pi
600600 −2.00000 3.46410i −0.0816497 0.141421i
601601 −11.0000 −0.448699 −0.224350 0.974509i 0.572026π-0.572026\pi
−0.224350 + 0.974509i 0.572026π0.572026\pi
602602 0 0
603603 −10.0000 −0.407231
604604 0.500000 + 0.866025i 0.0203447 + 0.0352381i
605605 −3.00000 + 5.19615i −0.121967 + 0.211254i
606606 −9.00000 + 15.5885i −0.365600 + 0.633238i
607607 −3.50000 6.06218i −0.142061 0.246056i 0.786212 0.617957i 0.212039π-0.212039\pi
−0.928272 + 0.371901i 0.878706π0.878706\pi
608608 −4.00000 −0.162221
609609 0 0
610610 30.0000 1.21466
611611 −12.0000 20.7846i −0.485468 0.840855i
612612 0 0
613613 8.00000 13.8564i 0.323117 0.559655i −0.658012 0.753007i 0.728603π-0.728603\pi
0.981129 + 0.193352i 0.0619359π0.0619359\pi
614614 −4.00000 6.92820i −0.161427 0.279600i
615615 0 0
616616 0 0
617617 −6.00000 −0.241551 −0.120775 0.992680i 0.538538π-0.538538\pi
−0.120775 + 0.992680i 0.538538π0.538538\pi
618618 4.00000 + 6.92820i 0.160904 + 0.278693i
619619 −17.0000 + 29.4449i −0.683288 + 1.18349i 0.290684 + 0.956819i 0.406117π0.406117\pi
−0.973972 + 0.226670i 0.927216π0.927216\pi
620620 1.50000 2.59808i 0.0602414 0.104341i
621621 0 0
622622 24.0000 0.962312
623623 0 0
624624 −4.00000 −0.160128
625625 14.5000 + 25.1147i 0.580000 + 1.00459i
626626 15.5000 26.8468i 0.619505 1.07301i
627627 6.00000 10.3923i 0.239617 0.415029i
628628 −2.00000 3.46410i −0.0798087 0.138233i
629629 0 0
630630 0 0
631631 −7.00000 −0.278666 −0.139333 0.990246i 0.544496π-0.544496\pi
−0.139333 + 0.990246i 0.544496π0.544496\pi
632632 −0.500000 0.866025i −0.0198889 0.0344486i
633633 7.00000 12.1244i 0.278225 0.481900i
634634 4.50000 7.79423i 0.178718 0.309548i
635635 7.50000 + 12.9904i 0.297628 + 0.515508i
636636 3.00000 0.118958
637637 0 0
638638 −27.0000 −1.06894
639639 3.00000 + 5.19615i 0.118678 + 0.205557i
640640 −1.50000 + 2.59808i −0.0592927 + 0.102698i
641641 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i 0.631488π-0.631488\pi
0.993899 0.110291i 0.0351782π-0.0351782\pi
642642 1.50000 + 2.59808i 0.0592003 + 0.102538i
643643 34.0000 1.34083 0.670415 0.741987i 0.266116π-0.266116\pi
0.670415 + 0.741987i 0.266116π0.266116\pi
644644 0 0
645645 −30.0000 −1.18125
646646 0 0
647647 −9.00000 + 15.5885i −0.353827 + 0.612845i −0.986916 0.161233i 0.948453π-0.948453\pi
0.633090 + 0.774078i 0.281786π0.281786\pi
648648 0.500000 0.866025i 0.0196419 0.0340207i
649649 4.50000 + 7.79423i 0.176640 + 0.305950i
650650 −16.0000 −0.627572
651651 0 0
652652 −16.0000 −0.626608
653653 −1.50000 2.59808i −0.0586995 0.101671i 0.835182 0.549973i 0.185362π-0.185362\pi
−0.893882 + 0.448303i 0.852029π0.852029\pi
654654 −7.00000 + 12.1244i −0.273722 + 0.474100i
655655 13.5000 23.3827i 0.527489 0.913637i
656656 0 0
657657 −2.00000 −0.0780274
658658 0 0
659659 −24.0000 −0.934907 −0.467454 0.884018i 0.654829π-0.654829\pi
−0.467454 + 0.884018i 0.654829π0.654829\pi
660660 −4.50000 7.79423i −0.175162 0.303390i
661661 7.00000 12.1244i 0.272268 0.471583i −0.697174 0.716902i 0.745559π-0.745559\pi
0.969442 + 0.245319i 0.0788928π0.0788928\pi
662662 10.0000 17.3205i 0.388661 0.673181i
663663 0 0
664664 −9.00000 −0.349268
665665 0 0
666666 −8.00000 −0.309994
667667 0 0
668668 3.00000 5.19615i 0.116073 0.201045i
669669 9.50000 16.4545i 0.367291 0.636167i
670670 15.0000 + 25.9808i 0.579501 + 1.00372i
671671 30.0000 1.15814
672672 0 0
673673 29.0000 1.11787 0.558934 0.829212i 0.311211π-0.311211\pi
0.558934 + 0.829212i 0.311211π0.311211\pi
674674 −3.50000 6.06218i −0.134815 0.233506i
675675 2.00000 3.46410i 0.0769800 0.133333i
676676 −1.50000 + 2.59808i −0.0576923 + 0.0999260i
677677 −16.5000 28.5788i −0.634147 1.09837i −0.986695 0.162581i 0.948018π-0.948018\pi
0.352549 0.935793i 0.385315π-0.385315\pi
678678 0 0
679679 0 0
680680 0 0
681681 13.5000 + 23.3827i 0.517321 + 0.896026i
682682 1.50000 2.59808i 0.0574380 0.0994855i
683683 −16.5000 + 28.5788i −0.631355 + 1.09354i 0.355920 + 0.934516i 0.384168π0.384168\pi
−0.987275 + 0.159022i 0.949166π0.949166\pi
684684 −2.00000 3.46410i −0.0764719 0.132453i
685685 −54.0000 −2.06323
686686 0 0
687687 −4.00000 −0.152610
688688 5.00000 + 8.66025i 0.190623 + 0.330169i
689689 6.00000 10.3923i 0.228582 0.395915i
690690 0 0
691691 4.00000 + 6.92820i 0.152167 + 0.263561i 0.932024 0.362397i 0.118041π-0.118041\pi
−0.779857 + 0.625958i 0.784708π0.784708\pi
692692 −18.0000 −0.684257
693693 0 0
694694 −12.0000 −0.455514
695695 −3.00000 5.19615i −0.113796 0.197101i
696696 −4.50000 + 7.79423i −0.170572 + 0.295439i
697697 0 0
698698 −13.0000 22.5167i −0.492057 0.852268i
699699 24.0000 0.907763
700700 0 0
701701 −15.0000 −0.566542 −0.283271 0.959040i 0.591420π-0.591420\pi
−0.283271 + 0.959040i 0.591420π0.591420\pi
702702 −2.00000 3.46410i −0.0754851 0.130744i
703703 −16.0000 + 27.7128i −0.603451 + 1.04521i
704704 −1.50000 + 2.59808i −0.0565334 + 0.0979187i
705705 −9.00000 15.5885i −0.338960 0.587095i
706706 24.0000 0.903252
707707 0 0
708708 3.00000 0.112747
709709 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i 0.106538π-0.106538\pi
−0.756730 + 0.653727i 0.773204π0.773204\pi
710710 9.00000 15.5885i 0.337764 0.585024i
711711 0.500000 0.866025i 0.0187515 0.0324785i
712712 −3.00000 5.19615i −0.112430 0.194734i
713713 0 0
714714 0 0
715715 −36.0000 −1.34632
716716 −6.00000 10.3923i −0.224231 0.388379i
717717 −12.0000 + 20.7846i −0.448148 + 0.776215i
718718 15.0000 25.9808i 0.559795 0.969593i
719719 −9.00000 15.5885i −0.335643 0.581351i 0.647965 0.761670i 0.275620π-0.275620\pi
−0.983608 + 0.180319i 0.942287π0.942287\pi
720720 −3.00000 −0.111803
721721 0 0
722722 3.00000 0.111648
723723 0.500000 + 0.866025i 0.0185952 + 0.0322078i
724724 4.00000 6.92820i 0.148659 0.257485i
725725 −18.0000 + 31.1769i −0.668503 + 1.15788i
726726 1.00000 + 1.73205i 0.0371135 + 0.0642824i
727727 13.0000 0.482143 0.241072 0.970507i 0.422501π-0.422501\pi
0.241072 + 0.970507i 0.422501π0.422501\pi
728728 0 0
729729 1.00000 0.0370370
730730 3.00000 + 5.19615i 0.111035 + 0.192318i
731731 0 0
732732 5.00000 8.66025i 0.184805 0.320092i
733733 −5.00000 8.66025i −0.184679 0.319874i 0.758789 0.651336i 0.225791π-0.225791\pi
−0.943468 + 0.331463i 0.892458π0.892458\pi
734734 −19.0000 −0.701303
735735 0 0
736736 0 0
737737 15.0000 + 25.9808i 0.552532 + 0.957014i
738738 0 0
739739 −25.0000 + 43.3013i −0.919640 + 1.59286i −0.119677 + 0.992813i 0.538186π0.538186\pi
−0.799962 + 0.600050i 0.795147π0.795147\pi
740740 12.0000 + 20.7846i 0.441129 + 0.764057i
741741 −16.0000 −0.587775
742742 0 0
743743 42.0000 1.54083 0.770415 0.637542i 0.220049π-0.220049\pi
0.770415 + 0.637542i 0.220049π0.220049\pi
744744 −0.500000 0.866025i −0.0183309 0.0317500i
745745 27.0000 46.7654i 0.989203 1.71335i
746746 4.00000 6.92820i 0.146450 0.253660i
747747 −4.50000 7.79423i −0.164646 0.285176i
748748 0 0
749749 0 0
750750 3.00000 0.109545
751751 3.50000 + 6.06218i 0.127717 + 0.221212i 0.922792 0.385299i 0.125902π-0.125902\pi
−0.795075 + 0.606511i 0.792568π0.792568\pi
752752 −3.00000 + 5.19615i −0.109399 + 0.189484i
753753 −13.5000 + 23.3827i −0.491967 + 0.852112i
754754 18.0000 + 31.1769i 0.655521 + 1.13540i
755755 3.00000 0.109181
756756 0 0
757757 38.0000 1.38113 0.690567 0.723269i 0.257361π-0.257361\pi
0.690567 + 0.723269i 0.257361π0.257361\pi
758758 4.00000 + 6.92820i 0.145287 + 0.251644i
759759 0 0
760760 −6.00000 + 10.3923i −0.217643 + 0.376969i
761761 6.00000 + 10.3923i 0.217500 + 0.376721i 0.954043 0.299670i 0.0968765π-0.0968765\pi
−0.736543 + 0.676391i 0.763543π0.763543\pi
762762 5.00000 0.181131
763763 0 0
764764 0 0
765765 0 0
766766 −9.00000 + 15.5885i −0.325183 + 0.563234i
767767 6.00000 10.3923i 0.216647 0.375244i
768768 0.500000 + 0.866025i 0.0180422 + 0.0312500i
769769 19.0000 0.685158 0.342579 0.939489i 0.388700π-0.388700\pi
0.342579 + 0.939489i 0.388700π0.388700\pi
770770 0 0
771771 6.00000 0.216085
772772 9.50000 + 16.4545i 0.341912 + 0.592210i
773773 3.00000 5.19615i 0.107903 0.186893i −0.807018 0.590527i 0.798920π-0.798920\pi
0.914920 + 0.403634i 0.132253π0.132253\pi
774774 −5.00000 + 8.66025i −0.179721 + 0.311286i
775775 −2.00000 3.46410i −0.0718421 0.124434i
776776 −1.00000 −0.0358979
777777 0 0
778778 6.00000 0.215110
779779 0 0
780780 −6.00000 + 10.3923i −0.214834 + 0.372104i
781781 9.00000 15.5885i 0.322045 0.557799i
782782 0 0
783783 −9.00000 −0.321634
784784 0 0
785785 −12.0000 −0.428298
786786 −4.50000 7.79423i −0.160510 0.278011i
787787 25.0000 43.3013i 0.891154 1.54352i 0.0526599 0.998613i 0.483230π-0.483230\pi
0.838494 0.544911i 0.183437π-0.183437\pi
788788 −3.00000 + 5.19615i −0.106871 + 0.185105i
789789 −3.00000 5.19615i −0.106803 0.184988i
790790 −3.00000 −0.106735
791791 0 0
792792 −3.00000 −0.106600
793793 −20.0000 34.6410i −0.710221 1.23014i
794794 2.00000 3.46410i 0.0709773 0.122936i
795795 4.50000 7.79423i 0.159599 0.276433i
796796 10.0000 + 17.3205i 0.354441 + 0.613909i
797797 33.0000 1.16892 0.584460 0.811423i 0.301306π-0.301306\pi
0.584460 + 0.811423i 0.301306π0.301306\pi
798798 0 0
799799 0 0
800800 2.00000 + 3.46410i 0.0707107 + 0.122474i
801801 3.00000 5.19615i 0.106000 0.183597i
802802 12.0000 20.7846i 0.423735 0.733930i
803803 3.00000 + 5.19615i 0.105868 + 0.183368i
804804 10.0000 0.352673
805805 0 0
806806 −4.00000 −0.140894
807807 −10.5000 18.1865i −0.369618 0.640196i
808808 9.00000 15.5885i 0.316619 0.548400i
809809 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
810810 −1.50000 2.59808i −0.0527046 0.0912871i
811811 −2.00000 −0.0702295 −0.0351147 0.999383i 0.511180π-0.511180\pi
−0.0351147 + 0.999383i 0.511180π0.511180\pi
812812 0 0
813813 11.0000 0.385787
814814 12.0000 + 20.7846i 0.420600 + 0.728500i
815815 −24.0000 + 41.5692i −0.840683 + 1.45611i
816816 0 0
817817 20.0000 + 34.6410i 0.699711 + 1.21194i
818818 −25.0000 −0.874105
819819 0 0
820820 0 0
821821 1.50000 + 2.59808i 0.0523504 + 0.0906735i 0.891013 0.453978i 0.149995π-0.149995\pi
−0.838663 + 0.544651i 0.816662π0.816662\pi
822822 −9.00000 + 15.5885i −0.313911 + 0.543710i
823823 20.0000 34.6410i 0.697156 1.20751i −0.272292 0.962215i 0.587782π-0.587782\pi
0.969448 0.245295i 0.0788849π-0.0788849\pi
824824 −4.00000 6.92820i −0.139347 0.241355i
825825 −12.0000 −0.417786
826826 0 0
827827 15.0000 0.521601 0.260801 0.965393i 0.416014π-0.416014\pi
0.260801 + 0.965393i 0.416014π0.416014\pi
828828 0 0
829829 −2.00000 + 3.46410i −0.0694629 + 0.120313i −0.898665 0.438636i 0.855462π-0.855462\pi
0.829202 + 0.558949i 0.188795π0.188795\pi
830830 −13.5000 + 23.3827i −0.468592 + 0.811625i
831831 4.00000 + 6.92820i 0.138758 + 0.240337i
832832 4.00000 0.138675
833833 0 0
834834 −2.00000 −0.0692543
835835 −9.00000 15.5885i −0.311458 0.539461i
836836 −6.00000 + 10.3923i −0.207514 + 0.359425i
837837 0.500000 0.866025i 0.0172825 0.0299342i
838838 0 0
839839 24.0000 0.828572 0.414286 0.910147i 0.364031π-0.364031\pi
0.414286 + 0.910147i 0.364031π0.364031\pi
840840 0 0
841841 52.0000 1.79310
842842 −11.0000 19.0526i −0.379085 0.656595i
843843 3.00000 5.19615i 0.103325 0.178965i
844844 −7.00000 + 12.1244i −0.240950 + 0.417338i
845845 4.50000 + 7.79423i 0.154805 + 0.268130i
846846 −6.00000 −0.206284
847847 0 0
848848 −3.00000 −0.103020
849849 −7.00000 12.1244i −0.240239 0.416107i
850850 0 0
851851 0 0
852852 −3.00000 5.19615i −0.102778 0.178017i
853853 10.0000 0.342393 0.171197 0.985237i 0.445237π-0.445237\pi
0.171197 + 0.985237i 0.445237π0.445237\pi
854854 0 0
855855 −12.0000 −0.410391
856856 −1.50000 2.59808i −0.0512689 0.0888004i
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 −6.00000 + 10.3923i −0.204837 + 0.354787i
859859 25.0000 + 43.3013i 0.852989 + 1.47742i 0.878498 + 0.477746i 0.158546π0.158546\pi
−0.0255092 + 0.999675i 0.508121π0.508121\pi
860860 30.0000 1.02299
861861 0 0
862862 −12.0000 −0.408722
863863 −3.00000 5.19615i −0.102121 0.176879i 0.810437 0.585826i 0.199230π-0.199230\pi
−0.912558 + 0.408946i 0.865896π0.865896\pi
864864 −0.500000 + 0.866025i −0.0170103 + 0.0294628i
865865 −27.0000 + 46.7654i −0.918028 + 1.59007i
866866 17.0000 + 29.4449i 0.577684 + 1.00058i
867867 17.0000 0.577350
868868 0 0
869869 −3.00000 −0.101768
870870 13.5000 + 23.3827i 0.457693 + 0.792747i
871871 20.0000 34.6410i 0.677674 1.17377i
872872 7.00000 12.1244i 0.237050 0.410582i
873873 −0.500000 0.866025i −0.0169224 0.0293105i
874874 0 0
875875 0 0
876876 2.00000 0.0675737
877877 −16.0000 27.7128i −0.540282 0.935795i −0.998888 0.0471555i 0.984984π-0.984984\pi
0.458606 0.888640i 0.348349π-0.348349\pi
878878 −17.5000 + 30.3109i −0.590596 + 1.02294i
879879 −16.5000 + 28.5788i −0.556531 + 0.963940i
880880 4.50000 + 7.79423i 0.151695 + 0.262743i
881881 6.00000 0.202145 0.101073 0.994879i 0.467773π-0.467773\pi
0.101073 + 0.994879i 0.467773π0.467773\pi
882882 0 0
883883 32.0000 1.07689 0.538443 0.842662i 0.319013π-0.319013\pi
0.538443 + 0.842662i 0.319013π0.319013\pi
884884 0 0
885885 4.50000 7.79423i 0.151266 0.262000i
886886 −16.5000 + 28.5788i −0.554328 + 0.960125i
887887 −12.0000 20.7846i −0.402921 0.697879i 0.591156 0.806557i 0.298672π-0.298672\pi
−0.994077 + 0.108678i 0.965338π0.965338\pi
888888 8.00000 0.268462
889889 0 0
890890 −18.0000 −0.603361
891891 −1.50000 2.59808i −0.0502519 0.0870388i
892892 −9.50000 + 16.4545i −0.318084 + 0.550937i
893893 −12.0000 + 20.7846i −0.401565 + 0.695530i
894894 −9.00000 15.5885i −0.301005 0.521356i
895895 −36.0000 −1.20335
896896 0 0
897897 0 0
898898 6.00000 + 10.3923i 0.200223 + 0.346796i
899899 −4.50000 + 7.79423i −0.150083 + 0.259952i
900900 −2.00000 + 3.46410i −0.0666667 + 0.115470i
901901 0 0
902902 0 0
903903 0 0
904904 0 0
905905 −12.0000 20.7846i −0.398893 0.690904i
906906 0.500000 0.866025i 0.0166114 0.0287718i
907907 −4.00000 + 6.92820i −0.132818 + 0.230047i −0.924762 0.380547i 0.875736π-0.875736\pi
0.791944 + 0.610594i 0.209069π0.209069\pi
908908 −13.5000 23.3827i −0.448013 0.775982i
909909 18.0000 0.597022
910910 0 0
911911 6.00000 0.198789 0.0993944 0.995048i 0.468309π-0.468309\pi
0.0993944 + 0.995048i 0.468309π0.468309\pi
912912 2.00000 + 3.46410i 0.0662266 + 0.114708i
913913 −13.5000 + 23.3827i −0.446785 + 0.773854i
914914 −0.500000 + 0.866025i −0.0165385 + 0.0286456i
915915 −15.0000 25.9808i −0.495885 0.858898i
916916 4.00000 0.132164
917917 0 0
918918 0 0
919919 −4.00000 6.92820i −0.131948 0.228540i 0.792480 0.609898i 0.208790π-0.208790\pi
−0.924427 + 0.381358i 0.875456π0.875456\pi
920920 0 0
921921 −4.00000 + 6.92820i −0.131804 + 0.228292i
922922 −15.0000 25.9808i −0.493999 0.855631i
923923 −24.0000 −0.789970
924924 0 0
925925 32.0000 1.05215
926926 4.00000 + 6.92820i 0.131448 + 0.227675i
927927 4.00000 6.92820i 0.131377 0.227552i
928928 4.50000 7.79423i 0.147720 0.255858i
929929 −3.00000 5.19615i −0.0984268 0.170480i 0.812607 0.582812i 0.198048π-0.198048\pi
−0.911034 + 0.412332i 0.864714π0.864714\pi
930930 −3.00000 −0.0983739
931931 0 0
932932 −24.0000 −0.786146
933933 −12.0000 20.7846i −0.392862 0.680458i
934934 −18.0000 + 31.1769i −0.588978 + 1.02014i
935935 0 0
936936 2.00000 + 3.46410i 0.0653720 + 0.113228i
937937 −35.0000 −1.14340 −0.571700 0.820463i 0.693716π-0.693716\pi
−0.571700 + 0.820463i 0.693716π0.693716\pi
938938 0 0
939939 −31.0000 −1.01165
940940 9.00000 + 15.5885i 0.293548 + 0.508439i
941941 −4.50000 + 7.79423i −0.146696 + 0.254085i −0.930004 0.367549i 0.880197π-0.880197\pi
0.783309 + 0.621633i 0.213531π0.213531\pi
942942 −2.00000 + 3.46410i −0.0651635 + 0.112867i
943943 0 0
944944 −3.00000 −0.0976417
945945 0 0
946946 30.0000 0.975384
947947 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
948948 −0.500000 + 0.866025i −0.0162392 + 0.0281272i
949949 4.00000 6.92820i 0.129845 0.224899i
950950 8.00000 + 13.8564i 0.259554 + 0.449561i
951951 −9.00000 −0.291845
952952 0 0
953953 −6.00000 −0.194359 −0.0971795 0.995267i 0.530982π-0.530982\pi
−0.0971795 + 0.995267i 0.530982π0.530982\pi
954954 −1.50000 2.59808i −0.0485643 0.0841158i
955955 0 0
956956 12.0000 20.7846i 0.388108 0.672222i
957957 13.5000 + 23.3827i 0.436393 + 0.755855i
958958 −18.0000 −0.581554
959959 0 0
960960 3.00000 0.0968246
961961 15.0000 + 25.9808i 0.483871 + 0.838089i
962962 16.0000 27.7128i 0.515861 0.893497i
963963 1.50000 2.59808i 0.0483368 0.0837218i
964964 −0.500000 0.866025i −0.0161039 0.0278928i
965965 57.0000 1.83489
966966 0 0
967967 −1.00000 −0.0321578 −0.0160789 0.999871i 0.505118π-0.505118\pi
−0.0160789 + 0.999871i 0.505118π0.505118\pi
968968 −1.00000 1.73205i −0.0321412 0.0556702i
969969 0 0
970970 −1.50000 + 2.59808i −0.0481621 + 0.0834192i
971971 −19.5000 33.7750i −0.625785 1.08389i −0.988389 0.151948i 0.951445π-0.951445\pi
0.362604 0.931943i 0.381888π-0.381888\pi
972972 −1.00000 −0.0320750
973973 0 0
974974 −41.0000 −1.31372
975975 8.00000 + 13.8564i 0.256205 + 0.443760i
976976 −5.00000 + 8.66025i −0.160046 + 0.277208i
977977 −21.0000 + 36.3731i −0.671850 + 1.16368i 0.305530 + 0.952183i 0.401167π0.401167\pi
−0.977379 + 0.211495i 0.932167π0.932167\pi
978978 8.00000 + 13.8564i 0.255812 + 0.443079i
979979 −18.0000 −0.575282
980980 0 0
981981 14.0000 0.446986
982982 −16.5000 28.5788i −0.526536 0.911987i
983983 18.0000 31.1769i 0.574111 0.994389i −0.422027 0.906583i 0.638681π-0.638681\pi
0.996138 0.0878058i 0.0279855π-0.0279855\pi
984984 0 0
985985 9.00000 + 15.5885i 0.286764 + 0.496690i
986986 0 0
987987 0 0
988988 16.0000 0.509028
989989 0 0
990990 −4.50000 + 7.79423i −0.143019 + 0.247717i
991991 6.50000 11.2583i 0.206479 0.357633i −0.744124 0.668042i 0.767133π-0.767133\pi
0.950603 + 0.310409i 0.100466π0.100466\pi
992992 0.500000 + 0.866025i 0.0158750 + 0.0274963i
993993 −20.0000 −0.634681
994994 0 0
995995 60.0000 1.90213
996996 4.50000 + 7.79423i 0.142588 + 0.246970i
997997 7.00000 12.1244i 0.221692 0.383982i −0.733630 0.679549i 0.762175π-0.762175\pi
0.955322 + 0.295567i 0.0955086π0.0955086\pi
998998 1.00000 1.73205i 0.0316544 0.0548271i
999999 4.00000 + 6.92820i 0.126554 + 0.219199i
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 294.2.e.f.67.1 2
3.2 odd 2 882.2.g.b.361.1 2
4.3 odd 2 2352.2.q.m.1537.1 2
7.2 even 3 inner 294.2.e.f.79.1 2
7.3 odd 6 294.2.a.d.1.1 1
7.4 even 3 294.2.a.a.1.1 1
7.5 odd 6 42.2.e.b.37.1 yes 2
7.6 odd 2 42.2.e.b.25.1 2
21.2 odd 6 882.2.g.b.667.1 2
21.5 even 6 126.2.g.b.37.1 2
21.11 odd 6 882.2.a.k.1.1 1
21.17 even 6 882.2.a.g.1.1 1
21.20 even 2 126.2.g.b.109.1 2
28.3 even 6 2352.2.a.m.1.1 1
28.11 odd 6 2352.2.a.n.1.1 1
28.19 even 6 336.2.q.d.289.1 2
28.23 odd 6 2352.2.q.m.961.1 2
28.27 even 2 336.2.q.d.193.1 2
35.4 even 6 7350.2.a.cw.1.1 1
35.12 even 12 1050.2.o.b.499.2 4
35.13 even 4 1050.2.o.b.949.2 4
35.19 odd 6 1050.2.i.e.751.1 2
35.24 odd 6 7350.2.a.ce.1.1 1
35.27 even 4 1050.2.o.b.949.1 4
35.33 even 12 1050.2.o.b.499.1 4
35.34 odd 2 1050.2.i.e.151.1 2
56.3 even 6 9408.2.a.bu.1.1 1
56.5 odd 6 1344.2.q.v.961.1 2
56.11 odd 6 9408.2.a.bm.1.1 1
56.13 odd 2 1344.2.q.v.193.1 2
56.19 even 6 1344.2.q.j.961.1 2
56.27 even 2 1344.2.q.j.193.1 2
56.45 odd 6 9408.2.a.d.1.1 1
56.53 even 6 9408.2.a.db.1.1 1
63.5 even 6 1134.2.h.a.541.1 2
63.13 odd 6 1134.2.e.a.865.1 2
63.20 even 6 1134.2.h.a.109.1 2
63.34 odd 6 1134.2.h.p.109.1 2
63.40 odd 6 1134.2.h.p.541.1 2
63.41 even 6 1134.2.e.p.865.1 2
63.47 even 6 1134.2.e.p.919.1 2
63.61 odd 6 1134.2.e.a.919.1 2
84.11 even 6 7056.2.a.bz.1.1 1
84.47 odd 6 1008.2.s.n.289.1 2
84.59 odd 6 7056.2.a.g.1.1 1
84.83 odd 2 1008.2.s.n.865.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.2.e.b.25.1 2 7.6 odd 2
42.2.e.b.37.1 yes 2 7.5 odd 6
126.2.g.b.37.1 2 21.5 even 6
126.2.g.b.109.1 2 21.20 even 2
294.2.a.a.1.1 1 7.4 even 3
294.2.a.d.1.1 1 7.3 odd 6
294.2.e.f.67.1 2 1.1 even 1 trivial
294.2.e.f.79.1 2 7.2 even 3 inner
336.2.q.d.193.1 2 28.27 even 2
336.2.q.d.289.1 2 28.19 even 6
882.2.a.g.1.1 1 21.17 even 6
882.2.a.k.1.1 1 21.11 odd 6
882.2.g.b.361.1 2 3.2 odd 2
882.2.g.b.667.1 2 21.2 odd 6
1008.2.s.n.289.1 2 84.47 odd 6
1008.2.s.n.865.1 2 84.83 odd 2
1050.2.i.e.151.1 2 35.34 odd 2
1050.2.i.e.751.1 2 35.19 odd 6
1050.2.o.b.499.1 4 35.33 even 12
1050.2.o.b.499.2 4 35.12 even 12
1050.2.o.b.949.1 4 35.27 even 4
1050.2.o.b.949.2 4 35.13 even 4
1134.2.e.a.865.1 2 63.13 odd 6
1134.2.e.a.919.1 2 63.61 odd 6
1134.2.e.p.865.1 2 63.41 even 6
1134.2.e.p.919.1 2 63.47 even 6
1134.2.h.a.109.1 2 63.20 even 6
1134.2.h.a.541.1 2 63.5 even 6
1134.2.h.p.109.1 2 63.34 odd 6
1134.2.h.p.541.1 2 63.40 odd 6
1344.2.q.j.193.1 2 56.27 even 2
1344.2.q.j.961.1 2 56.19 even 6
1344.2.q.v.193.1 2 56.13 odd 2
1344.2.q.v.961.1 2 56.5 odd 6
2352.2.a.m.1.1 1 28.3 even 6
2352.2.a.n.1.1 1 28.11 odd 6
2352.2.q.m.961.1 2 28.23 odd 6
2352.2.q.m.1537.1 2 4.3 odd 2
7056.2.a.g.1.1 1 84.59 odd 6
7056.2.a.bz.1.1 1 84.11 even 6
7350.2.a.ce.1.1 1 35.24 odd 6
7350.2.a.cw.1.1 1 35.4 even 6
9408.2.a.d.1.1 1 56.45 odd 6
9408.2.a.bm.1.1 1 56.11 odd 6
9408.2.a.bu.1.1 1 56.3 even 6
9408.2.a.db.1.1 1 56.53 even 6