Properties

Label 525.2.i.a.226.1
Level 525525
Weight 22
Character 525.226
Analytic conductor 4.1924.192
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] = [525,2,Mod(151,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 525=3527 525 = 3 \cdot 5^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 525.i (of order 33, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.192146106124.19214610612
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,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 226.1
Root 0.5000000.866025i0.500000 - 0.866025i of defining polynomial
Character χ\chi == 525.226
Dual form 525.2.i.a.151.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.00000+1.73205i)q2+(0.500000+0.866025i)q3+(1.000001.73205i)q42.00000q6+(0.500000+2.59808i)q7+(0.500000+0.866025i)q9+(3.00000+5.19615i)q11+(1.000001.73205i)q12+3.00000q13+(5.000001.73205i)q14+(2.000003.46410i)q16+(2.000003.46410i)q17+(1.000001.73205i)q18+(0.500000+0.866025i)q19+(2.00000+1.73205i)q2112.0000q22+(2.00000+3.46410i)q23+(3.00000+5.19615i)q261.00000q27+(4.000003.46410i)q288.00000q29+(0.5000000.866025i)q31+(4.00000+6.92820i)q32+(3.00000+5.19615i)q33+8.00000q34+2.00000q36+(3.500006.06218i)q37+(1.000001.73205i)q38+(1.50000+2.59808i)q396.00000q41+(1.000005.19615i)q421.00000q43+(6.0000010.3923i)q44+(4.000006.92820i)q46+(1.000001.73205i)q47+4.00000q48+(6.50000+2.59808i)q49+(2.000003.46410i)q51+(3.000005.19615i)q52+(2.00000+3.46410i)q53+(1.000001.73205i)q541.00000q57+(8.0000013.8564i)q58+(4.00000+6.92820i)q59+(7.0000012.1244i)q61+2.00000q62+(2.500000.866025i)q638.00000q64+(6.0000010.3923i)q66+(3.50000+6.06218i)q67+(4.00000+6.92820i)q684.00000q69+6.00000q71+(0.500000+0.866025i)q73+(7.00000+12.1244i)q74+2.00000q76+(12.0000+10.3923i)q776.00000q78+(0.5000000.866025i)q79+(0.5000000.866025i)q81+(6.0000010.3923i)q822.00000q83+(5.00000+1.73205i)q84+(1.000001.73205i)q86+(4.000006.92820i)q87+(6.0000010.3923i)q89+(1.50000+7.79423i)q91+8.00000q92+(0.5000000.866025i)q93+(2.00000+3.46410i)q94+(4.00000+6.92820i)q96+6.00000q97+(2.0000013.8564i)q986.00000q99+O(q100)q+(-1.00000 + 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.00000 + 5.19615i) q^{11} +(1.00000 - 1.73205i) q^{12} +3.00000 q^{13} +(-5.00000 - 1.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-2.00000 + 1.73205i) q^{21} -12.0000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(-3.00000 + 5.19615i) q^{26} -1.00000 q^{27} +(4.00000 - 3.46410i) q^{28} -8.00000 q^{29} +(-0.500000 - 0.866025i) q^{31} +(4.00000 + 6.92820i) q^{32} +(-3.00000 + 5.19615i) q^{33} +8.00000 q^{34} +2.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{39} -6.00000 q^{41} +(-1.00000 - 5.19615i) q^{42} -1.00000 q^{43} +(6.00000 - 10.3923i) q^{44} +(-4.00000 - 6.92820i) q^{46} +(1.00000 - 1.73205i) q^{47} +4.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{51} +(-3.00000 - 5.19615i) q^{52} +(2.00000 + 3.46410i) q^{53} +(1.00000 - 1.73205i) q^{54} -1.00000 q^{57} +(8.00000 - 13.8564i) q^{58} +(4.00000 + 6.92820i) q^{59} +(7.00000 - 12.1244i) q^{61} +2.00000 q^{62} +(-2.50000 - 0.866025i) q^{63} -8.00000 q^{64} +(-6.00000 - 10.3923i) q^{66} +(3.50000 + 6.06218i) q^{67} +(-4.00000 + 6.92820i) q^{68} -4.00000 q^{69} +6.00000 q^{71} +(0.500000 + 0.866025i) q^{73} +(7.00000 + 12.1244i) q^{74} +2.00000 q^{76} +(-12.0000 + 10.3923i) q^{77} -6.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} -2.00000 q^{83} +(5.00000 + 1.73205i) q^{84} +(1.00000 - 1.73205i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(6.00000 - 10.3923i) q^{89} +(1.50000 + 7.79423i) q^{91} +8.00000 q^{92} +(0.500000 - 0.866025i) q^{93} +(2.00000 + 3.46410i) q^{94} +(-4.00000 + 6.92820i) q^{96} +6.00000 q^{97} +(2.00000 - 13.8564i) q^{98} -6.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q2+q32q44q6+q7q9+6q11+2q12+6q1310q14+4q164q172q18q194q2124q224q236q262q27+12q99+O(q100) 2 q - 2 q^{2} + q^{3} - 2 q^{4} - 4 q^{6} + q^{7} - q^{9} + 6 q^{11} + 2 q^{12} + 6 q^{13} - 10 q^{14} + 4 q^{16} - 4 q^{17} - 2 q^{18} - q^{19} - 4 q^{21} - 24 q^{22} - 4 q^{23} - 6 q^{26} - 2 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/525Z)×\left(\mathbb{Z}/525\mathbb{Z}\right)^\times.

nn 127127 176176 451451
χ(n)\chi(n) 11 11 e(13)e\left(\frac{1}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.00000 + 1.73205i −0.707107 + 1.22474i 0.258819 + 0.965926i 0.416667π0.416667\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
33 0.500000 + 0.866025i 0.288675 + 0.500000i
44 −1.00000 1.73205i −0.500000 0.866025i
55 0 0
66 −2.00000 −0.816497
77 0.500000 + 2.59808i 0.188982 + 0.981981i
88 0 0
99 −0.500000 + 0.866025i −0.166667 + 0.288675i
1010 0 0
1111 3.00000 + 5.19615i 0.904534 + 1.56670i 0.821541 + 0.570149i 0.193114π0.193114\pi
0.0829925 + 0.996550i 0.473552π0.473552\pi
1212 1.00000 1.73205i 0.288675 0.500000i
1313 3.00000 0.832050 0.416025 0.909353i 0.363423π-0.363423\pi
0.416025 + 0.909353i 0.363423π0.363423\pi
1414 −5.00000 1.73205i −1.33631 0.462910i
1515 0 0
1616 2.00000 3.46410i 0.500000 0.866025i
1717 −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i 0.327873π-0.327873\pi
−0.999853 + 0.0171533i 0.994540π0.994540\pi
1818 −1.00000 1.73205i −0.235702 0.408248i
1919 −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i 0.869927π-0.869927\pi
0.802955 + 0.596040i 0.203260π0.203260\pi
2020 0 0
2121 −2.00000 + 1.73205i −0.436436 + 0.377964i
2222 −12.0000 −2.55841
2323 −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i 0.970262π-0.970262\pi
0.578610 + 0.815604i 0.303595π0.303595\pi
2424 0 0
2525 0 0
2626 −3.00000 + 5.19615i −0.588348 + 1.01905i
2727 −1.00000 −0.192450
2828 4.00000 3.46410i 0.755929 0.654654i
2929 −8.00000 −1.48556 −0.742781 0.669534i 0.766494π-0.766494\pi
−0.742781 + 0.669534i 0.766494π0.766494\pi
3030 0 0
3131 −0.500000 0.866025i −0.0898027 0.155543i 0.817625 0.575751i 0.195290π-0.195290\pi
−0.907428 + 0.420208i 0.861957π0.861957\pi
3232 4.00000 + 6.92820i 0.707107 + 1.22474i
3333 −3.00000 + 5.19615i −0.522233 + 0.904534i
3434 8.00000 1.37199
3535 0 0
3636 2.00000 0.333333
3737 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i 0.638181π-0.638181\pi
0.995998 0.0893706i 0.0284856π-0.0284856\pi
3838 −1.00000 1.73205i −0.162221 0.280976i
3939 1.50000 + 2.59808i 0.240192 + 0.416025i
4040 0 0
4141 −6.00000 −0.937043 −0.468521 0.883452i 0.655213π-0.655213\pi
−0.468521 + 0.883452i 0.655213π0.655213\pi
4242 −1.00000 5.19615i −0.154303 0.801784i
4343 −1.00000 −0.152499 −0.0762493 0.997089i 0.524294π-0.524294\pi
−0.0762493 + 0.997089i 0.524294π0.524294\pi
4444 6.00000 10.3923i 0.904534 1.56670i
4545 0 0
4646 −4.00000 6.92820i −0.589768 1.02151i
4747 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i 0.786737π-0.786737\pi
0.929695 + 0.368329i 0.120070π0.120070\pi
4848 4.00000 0.577350
4949 −6.50000 + 2.59808i −0.928571 + 0.371154i
5050 0 0
5151 2.00000 3.46410i 0.280056 0.485071i
5252 −3.00000 5.19615i −0.416025 0.720577i
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 1.00000 1.73205i 0.136083 0.235702i
5555 0 0
5656 0 0
5757 −1.00000 −0.132453
5858 8.00000 13.8564i 1.05045 1.81944i
5959 4.00000 + 6.92820i 0.520756 + 0.901975i 0.999709 + 0.0241347i 0.00768307π0.00768307\pi
−0.478953 + 0.877841i 0.658984π0.658984\pi
6060 0 0
6161 7.00000 12.1244i 0.896258 1.55236i 0.0640184 0.997949i 0.479608π-0.479608\pi
0.832240 0.554416i 0.187058π-0.187058\pi
6262 2.00000 0.254000
6363 −2.50000 0.866025i −0.314970 0.109109i
6464 −8.00000 −1.00000
6565 0 0
6666 −6.00000 10.3923i −0.738549 1.27920i
6767 3.50000 + 6.06218i 0.427593 + 0.740613i 0.996659 0.0816792i 0.0260283π-0.0260283\pi
−0.569066 + 0.822292i 0.692695π0.692695\pi
6868 −4.00000 + 6.92820i −0.485071 + 0.840168i
6969 −4.00000 −0.481543
7070 0 0
7171 6.00000 0.712069 0.356034 0.934473i 0.384129π-0.384129\pi
0.356034 + 0.934473i 0.384129π0.384129\pi
7272 0 0
7373 0.500000 + 0.866025i 0.0585206 + 0.101361i 0.893801 0.448463i 0.148028π-0.148028\pi
−0.835281 + 0.549823i 0.814695π0.814695\pi
7474 7.00000 + 12.1244i 0.813733 + 1.40943i
7575 0 0
7676 2.00000 0.229416
7777 −12.0000 + 10.3923i −1.36753 + 1.18431i
7878 −6.00000 −0.679366
7979 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i 0.815418π-0.815418\pi
0.892781 + 0.450490i 0.148751π0.148751\pi
8080 0 0
8181 −0.500000 0.866025i −0.0555556 0.0962250i
8282 6.00000 10.3923i 0.662589 1.14764i
8383 −2.00000 −0.219529 −0.109764 0.993958i 0.535010π-0.535010\pi
−0.109764 + 0.993958i 0.535010π0.535010\pi
8484 5.00000 + 1.73205i 0.545545 + 0.188982i
8585 0 0
8686 1.00000 1.73205i 0.107833 0.186772i
8787 −4.00000 6.92820i −0.428845 0.742781i
8888 0 0
8989 6.00000 10.3923i 0.635999 1.10158i −0.350304 0.936636i 0.613922π-0.613922\pi
0.986303 0.164946i 0.0527450π-0.0527450\pi
9090 0 0
9191 1.50000 + 7.79423i 0.157243 + 0.817057i
9292 8.00000 0.834058
9393 0.500000 0.866025i 0.0518476 0.0898027i
9494 2.00000 + 3.46410i 0.206284 + 0.357295i
9595 0 0
9696 −4.00000 + 6.92820i −0.408248 + 0.707107i
9797 6.00000 0.609208 0.304604 0.952479i 0.401476π-0.401476\pi
0.304604 + 0.952479i 0.401476π0.401476\pi
9898 2.00000 13.8564i 0.202031 1.39971i
9999 −6.00000 −0.603023
100100 0 0
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 + 6.92820i 0.396059 + 0.685994i
103103 −9.50000 + 16.4545i −0.936063 + 1.62131i −0.163335 + 0.986571i 0.552225π0.552225\pi
−0.772728 + 0.634738i 0.781108π0.781108\pi
104104 0 0
105105 0 0
106106 −8.00000 −0.777029
107107 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i 0.636370π-0.636370\pi
0.995474 0.0950377i 0.0302972π-0.0302972\pi
108108 1.00000 + 1.73205i 0.0962250 + 0.166667i
109109 7.50000 + 12.9904i 0.718370 + 1.24425i 0.961645 + 0.274296i 0.0884447π0.0884447\pi
−0.243276 + 0.969957i 0.578222π0.578222\pi
110110 0 0
111111 7.00000 0.664411
112112 10.0000 + 3.46410i 0.944911 + 0.327327i
113113 6.00000 0.564433 0.282216 0.959351i 0.408930π-0.408930\pi
0.282216 + 0.959351i 0.408930π0.408930\pi
114114 1.00000 1.73205i 0.0936586 0.162221i
115115 0 0
116116 8.00000 + 13.8564i 0.742781 + 1.28654i
117117 −1.50000 + 2.59808i −0.138675 + 0.240192i
118118 −16.0000 −1.47292
119119 8.00000 6.92820i 0.733359 0.635107i
120120 0 0
121121 −12.5000 + 21.6506i −1.13636 + 1.96824i
122122 14.0000 + 24.2487i 1.26750 + 2.19538i
123123 −3.00000 5.19615i −0.270501 0.468521i
124124 −1.00000 + 1.73205i −0.0898027 + 0.155543i
125125 0 0
126126 4.00000 3.46410i 0.356348 0.308607i
127127 −5.00000 −0.443678 −0.221839 0.975083i 0.571206π-0.571206\pi
−0.221839 + 0.975083i 0.571206π0.571206\pi
128128 0 0
129129 −0.500000 0.866025i −0.0440225 0.0762493i
130130 0 0
131131 −1.00000 + 1.73205i −0.0873704 + 0.151330i −0.906399 0.422423i 0.861180π-0.861180\pi
0.819028 + 0.573753i 0.194513π0.194513\pi
132132 12.0000 1.04447
133133 −2.50000 0.866025i −0.216777 0.0750939i
134134 −14.0000 −1.20942
135135 0 0
136136 0 0
137137 4.00000 + 6.92820i 0.341743 + 0.591916i 0.984757 0.173939i 0.0556494π-0.0556494\pi
−0.643013 + 0.765855i 0.722316π0.722316\pi
138138 4.00000 6.92820i 0.340503 0.589768i
139139 21.0000 1.78120 0.890598 0.454791i 0.150286π-0.150286\pi
0.890598 + 0.454791i 0.150286π0.150286\pi
140140 0 0
141141 2.00000 0.168430
142142 −6.00000 + 10.3923i −0.503509 + 0.872103i
143143 9.00000 + 15.5885i 0.752618 + 1.30357i
144144 2.00000 + 3.46410i 0.166667 + 0.288675i
145145 0 0
146146 −2.00000 −0.165521
147147 −5.50000 4.33013i −0.453632 0.357143i
148148 −14.0000 −1.15079
149149 2.00000 3.46410i 0.163846 0.283790i −0.772399 0.635138i 0.780943π-0.780943\pi
0.936245 + 0.351348i 0.114277π0.114277\pi
150150 0 0
151151 −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i 0.272204π-0.272204\pi
−0.981617 + 0.190864i 0.938871π0.938871\pi
152152 0 0
153153 4.00000 0.323381
154154 −6.00000 31.1769i −0.483494 2.51231i
155155 0 0
156156 3.00000 5.19615i 0.240192 0.416025i
157157 5.00000 + 8.66025i 0.399043 + 0.691164i 0.993608 0.112884i 0.0360089π-0.0360089\pi
−0.594565 + 0.804048i 0.702676π0.702676\pi
158158 1.00000 + 1.73205i 0.0795557 + 0.137795i
159159 −2.00000 + 3.46410i −0.158610 + 0.274721i
160160 0 0
161161 −10.0000 3.46410i −0.788110 0.273009i
162162 2.00000 0.157135
163163 −6.00000 + 10.3923i −0.469956 + 0.813988i −0.999410 0.0343508i 0.989064π-0.989064\pi
0.529454 + 0.848339i 0.322397π0.322397\pi
164164 6.00000 + 10.3923i 0.468521 + 0.811503i
165165 0 0
166166 2.00000 3.46410i 0.155230 0.268866i
167167 10.0000 0.773823 0.386912 0.922117i 0.373542π-0.373542\pi
0.386912 + 0.922117i 0.373542π0.373542\pi
168168 0 0
169169 −4.00000 −0.307692
170170 0 0
171171 −0.500000 0.866025i −0.0382360 0.0662266i
172172 1.00000 + 1.73205i 0.0762493 + 0.132068i
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 16.0000 1.21296
175175 0 0
176176 24.0000 1.80907
177177 −4.00000 + 6.92820i −0.300658 + 0.520756i
178178 12.0000 + 20.7846i 0.899438 + 1.55787i
179179 −9.00000 15.5885i −0.672692 1.16514i −0.977138 0.212607i 0.931805π-0.931805\pi
0.304446 0.952529i 0.401529π-0.401529\pi
180180 0 0
181181 13.0000 0.966282 0.483141 0.875542i 0.339496π-0.339496\pi
0.483141 + 0.875542i 0.339496π0.339496\pi
182182 −15.0000 5.19615i −1.11187 0.385164i
183183 14.0000 1.03491
184184 0 0
185185 0 0
186186 1.00000 + 1.73205i 0.0733236 + 0.127000i
187187 12.0000 20.7846i 0.877527 1.51992i
188188 −4.00000 −0.291730
189189 −0.500000 2.59808i −0.0363696 0.188982i
190190 0 0
191191 −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i 0.951167π-0.951167\pi
0.626468 + 0.779447i 0.284500π0.284500\pi
192192 −4.00000 6.92820i −0.288675 0.500000i
193193 −4.50000 7.79423i −0.323917 0.561041i 0.657376 0.753563i 0.271667π-0.271667\pi
−0.981293 + 0.192522i 0.938333π0.938333\pi
194194 −6.00000 + 10.3923i −0.430775 + 0.746124i
195195 0 0
196196 11.0000 + 8.66025i 0.785714 + 0.618590i
197197 −12.0000 −0.854965 −0.427482 0.904024i 0.640599π-0.640599\pi
−0.427482 + 0.904024i 0.640599π0.640599\pi
198198 6.00000 10.3923i 0.426401 0.738549i
199199 −4.00000 6.92820i −0.283552 0.491127i 0.688705 0.725042i 0.258180π-0.258180\pi
−0.972257 + 0.233915i 0.924846π0.924846\pi
200200 0 0
201201 −3.50000 + 6.06218i −0.246871 + 0.427593i
202202 −20.0000 −1.40720
203203 −4.00000 20.7846i −0.280745 1.45879i
204204 −8.00000 −0.560112
205205 0 0
206206 −19.0000 32.9090i −1.32379 2.29288i
207207 −2.00000 3.46410i −0.139010 0.240772i
208208 6.00000 10.3923i 0.416025 0.720577i
209209 −6.00000 −0.415029
210210 0 0
211211 −20.0000 −1.37686 −0.688428 0.725304i 0.741699π-0.741699\pi
−0.688428 + 0.725304i 0.741699π0.741699\pi
212212 4.00000 6.92820i 0.274721 0.475831i
213213 3.00000 + 5.19615i 0.205557 + 0.356034i
214214 12.0000 + 20.7846i 0.820303 + 1.42081i
215215 0 0
216216 0 0
217217 2.00000 1.73205i 0.135769 0.117579i
218218 −30.0000 −2.03186
219219 −0.500000 + 0.866025i −0.0337869 + 0.0585206i
220220 0 0
221221 −6.00000 10.3923i −0.403604 0.699062i
222222 −7.00000 + 12.1244i −0.469809 + 0.813733i
223223 24.0000 1.60716 0.803579 0.595198i 0.202926π-0.202926\pi
0.803579 + 0.595198i 0.202926π0.202926\pi
224224 −16.0000 + 13.8564i −1.06904 + 0.925820i
225225 0 0
226226 −6.00000 + 10.3923i −0.399114 + 0.691286i
227227 −5.00000 8.66025i −0.331862 0.574801i 0.651015 0.759065i 0.274343π-0.274343\pi
−0.982877 + 0.184263i 0.941010π0.941010\pi
228228 1.00000 + 1.73205i 0.0662266 + 0.114708i
229229 −6.50000 + 11.2583i −0.429532 + 0.743971i −0.996832 0.0795401i 0.974655π-0.974655\pi
0.567300 + 0.823511i 0.307988π0.307988\pi
230230 0 0
231231 −15.0000 5.19615i −0.986928 0.341882i
232232 0 0
233233 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i 0.770364π-0.770364\pi
0.947403 + 0.320043i 0.103697π0.103697\pi
234234 −3.00000 5.19615i −0.196116 0.339683i
235235 0 0
236236 8.00000 13.8564i 0.520756 0.901975i
237237 1.00000 0.0649570
238238 4.00000 + 20.7846i 0.259281 + 1.34727i
239239 14.0000 0.905585 0.452792 0.891616i 0.350428π-0.350428\pi
0.452792 + 0.891616i 0.350428π0.350428\pi
240240 0 0
241241 9.00000 + 15.5885i 0.579741 + 1.00414i 0.995509 + 0.0946700i 0.0301796π0.0301796\pi
−0.415768 + 0.909471i 0.636487π0.636487\pi
242242 −25.0000 43.3013i −1.60706 2.78351i
243243 0.500000 0.866025i 0.0320750 0.0555556i
244244 −28.0000 −1.79252
245245 0 0
246246 12.0000 0.765092
247247 −1.50000 + 2.59808i −0.0954427 + 0.165312i
248248 0 0
249249 −1.00000 1.73205i −0.0633724 0.109764i
250250 0 0
251251 12.0000 0.757433 0.378717 0.925513i 0.376365π-0.376365\pi
0.378717 + 0.925513i 0.376365π0.376365\pi
252252 1.00000 + 5.19615i 0.0629941 + 0.327327i
253253 −24.0000 −1.50887
254254 5.00000 8.66025i 0.313728 0.543393i
255255 0 0
256256 −8.00000 13.8564i −0.500000 0.866025i
257257 −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i 0.356405π0.356405\pi
−0.997374 + 0.0724199i 0.976928π0.976928\pi
258258 2.00000 0.124515
259259 17.5000 + 6.06218i 1.08740 + 0.376685i
260260 0 0
261261 4.00000 6.92820i 0.247594 0.428845i
262262 −2.00000 3.46410i −0.123560 0.214013i
263263 2.00000 + 3.46410i 0.123325 + 0.213606i 0.921077 0.389380i 0.127311π-0.127311\pi
−0.797752 + 0.602986i 0.793977π0.793977\pi
264264 0 0
265265 0 0
266266 4.00000 3.46410i 0.245256 0.212398i
267267 12.0000 0.734388
268268 7.00000 12.1244i 0.427593 0.740613i
269269 5.00000 + 8.66025i 0.304855 + 0.528025i 0.977229 0.212187i 0.0680585π-0.0680585\pi
−0.672374 + 0.740212i 0.734725π0.734725\pi
270270 0 0
271271 12.0000 20.7846i 0.728948 1.26258i −0.228380 0.973572i 0.573343π-0.573343\pi
0.957328 0.289003i 0.0933238π-0.0933238\pi
272272 −16.0000 −0.970143
273273 −6.00000 + 5.19615i −0.363137 + 0.314485i
274274 −16.0000 −0.966595
275275 0 0
276276 4.00000 + 6.92820i 0.240772 + 0.417029i
277277 −3.50000 6.06218i −0.210295 0.364241i 0.741512 0.670940i 0.234109π-0.234109\pi
−0.951807 + 0.306699i 0.900776π0.900776\pi
278278 −21.0000 + 36.3731i −1.25950 + 2.18151i
279279 1.00000 0.0598684
280280 0 0
281281 −12.0000 −0.715860 −0.357930 0.933748i 0.616517π-0.616517\pi
−0.357930 + 0.933748i 0.616517π0.616517\pi
282282 −2.00000 + 3.46410i −0.119098 + 0.206284i
283283 −3.50000 6.06218i −0.208053 0.360359i 0.743048 0.669238i 0.233379π-0.233379\pi
−0.951101 + 0.308879i 0.900046π0.900046\pi
284284 −6.00000 10.3923i −0.356034 0.616670i
285285 0 0
286286 −36.0000 −2.12872
287287 −3.00000 15.5885i −0.177084 0.920158i
288288 −8.00000 −0.471405
289289 0.500000 0.866025i 0.0294118 0.0509427i
290290 0 0
291291 3.00000 + 5.19615i 0.175863 + 0.304604i
292292 1.00000 1.73205i 0.0585206 0.101361i
293293 16.0000 0.934730 0.467365 0.884064i 0.345203π-0.345203\pi
0.467365 + 0.884064i 0.345203π0.345203\pi
294294 13.0000 5.19615i 0.758175 0.303046i
295295 0 0
296296 0 0
297297 −3.00000 5.19615i −0.174078 0.301511i
298298 4.00000 + 6.92820i 0.231714 + 0.401340i
299299 −6.00000 + 10.3923i −0.346989 + 0.601003i
300300 0 0
301301 −0.500000 2.59808i −0.0288195 0.149751i
302302 16.0000 0.920697
303303 −5.00000 + 8.66025i −0.287242 + 0.497519i
304304 2.00000 + 3.46410i 0.114708 + 0.198680i
305305 0 0
306306 −4.00000 + 6.92820i −0.228665 + 0.396059i
307307 −3.00000 −0.171219 −0.0856095 0.996329i 0.527284π-0.527284\pi
−0.0856095 + 0.996329i 0.527284π0.527284\pi
308308 30.0000 + 10.3923i 1.70941 + 0.592157i
309309 −19.0000 −1.08087
310310 0 0
311311 −3.00000 5.19615i −0.170114 0.294647i 0.768345 0.640036i 0.221080π-0.221080\pi
−0.938460 + 0.345389i 0.887747π0.887747\pi
312312 0 0
313313 5.50000 9.52628i 0.310878 0.538457i −0.667674 0.744453i 0.732710π-0.732710\pi
0.978553 + 0.205996i 0.0660435π0.0660435\pi
314314 −20.0000 −1.12867
315315 0 0
316316 −2.00000 −0.112509
317317 10.0000 17.3205i 0.561656 0.972817i −0.435696 0.900094i 0.643498π-0.643498\pi
0.997352 0.0727229i 0.0231689π-0.0231689\pi
318318 −4.00000 6.92820i −0.224309 0.388514i
319319 −24.0000 41.5692i −1.34374 2.32743i
320320 0 0
321321 12.0000 0.669775
322322 16.0000 13.8564i 0.891645 0.772187i
323323 4.00000 0.222566
324324 −1.00000 + 1.73205i −0.0555556 + 0.0962250i
325325 0 0
326326 −12.0000 20.7846i −0.664619 1.15115i
327327 −7.50000 + 12.9904i −0.414751 + 0.718370i
328328 0 0
329329 5.00000 + 1.73205i 0.275659 + 0.0954911i
330330 0 0
331331 4.50000 7.79423i 0.247342 0.428410i −0.715445 0.698669i 0.753776π-0.753776\pi
0.962788 + 0.270259i 0.0871094π0.0871094\pi
332332 2.00000 + 3.46410i 0.109764 + 0.190117i
333333 3.50000 + 6.06218i 0.191799 + 0.332205i
334334 −10.0000 + 17.3205i −0.547176 + 0.947736i
335335 0 0
336336 2.00000 + 10.3923i 0.109109 + 0.566947i
337337 −25.0000 −1.36184 −0.680918 0.732359i 0.738419π-0.738419\pi
−0.680918 + 0.732359i 0.738419π0.738419\pi
338338 4.00000 6.92820i 0.217571 0.376845i
339339 3.00000 + 5.19615i 0.162938 + 0.282216i
340340 0 0
341341 3.00000 5.19615i 0.162459 0.281387i
342342 2.00000 0.108148
343343 −10.0000 15.5885i −0.539949 0.841698i
344344 0 0
345345 0 0
346346 24.0000 + 41.5692i 1.29025 + 2.23478i
347347 8.00000 + 13.8564i 0.429463 + 0.743851i 0.996826 0.0796169i 0.0253697π-0.0253697\pi
−0.567363 + 0.823468i 0.692036π0.692036\pi
348348 −8.00000 + 13.8564i −0.428845 + 0.742781i
349349 2.00000 0.107058 0.0535288 0.998566i 0.482953π-0.482953\pi
0.0535288 + 0.998566i 0.482953π0.482953\pi
350350 0 0
351351 −3.00000 −0.160128
352352 −24.0000 + 41.5692i −1.27920 + 2.21565i
353353 −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i 0.325675π-0.325675\pi
−0.999711 + 0.0240566i 0.992342π0.992342\pi
354354 −8.00000 13.8564i −0.425195 0.736460i
355355 0 0
356356 −24.0000 −1.27200
357357 10.0000 + 3.46410i 0.529256 + 0.183340i
358358 36.0000 1.90266
359359 12.0000 20.7846i 0.633336 1.09697i −0.353529 0.935423i 0.615019π-0.615019\pi
0.986865 0.161546i 0.0516481π-0.0516481\pi
360360 0 0
361361 9.00000 + 15.5885i 0.473684 + 0.820445i
362362 −13.0000 + 22.5167i −0.683265 + 1.18345i
363363 −25.0000 −1.31216
364364 12.0000 10.3923i 0.628971 0.544705i
365365 0 0
366366 −14.0000 + 24.2487i −0.731792 + 1.26750i
367367 9.50000 + 16.4545i 0.495896 + 0.858917i 0.999989 0.00473247i 0.00150640π-0.00150640\pi
−0.504093 + 0.863649i 0.668173π0.668173\pi
368368 8.00000 + 13.8564i 0.417029 + 0.722315i
369369 3.00000 5.19615i 0.156174 0.270501i
370370 0 0
371371 −8.00000 + 6.92820i −0.415339 + 0.359694i
372372 −2.00000 −0.103695
373373 5.50000 9.52628i 0.284779 0.493252i −0.687776 0.725923i 0.741413π-0.741413\pi
0.972556 + 0.232671i 0.0747464π0.0747464\pi
374374 24.0000 + 41.5692i 1.24101 + 2.14949i
375375 0 0
376376 0 0
377377 −24.0000 −1.23606
378378 5.00000 + 1.73205i 0.257172 + 0.0890871i
379379 11.0000 0.565032 0.282516 0.959263i 0.408831π-0.408831\pi
0.282516 + 0.959263i 0.408831π0.408831\pi
380380 0 0
381381 −2.50000 4.33013i −0.128079 0.221839i
382382 −10.0000 17.3205i −0.511645 0.886194i
383383 14.0000 24.2487i 0.715367 1.23905i −0.247451 0.968900i 0.579593π-0.579593\pi
0.962818 0.270151i 0.0870736π-0.0870736\pi
384384 0 0
385385 0 0
386386 18.0000 0.916176
387387 0.500000 0.866025i 0.0254164 0.0440225i
388388 −6.00000 10.3923i −0.304604 0.527589i
389389 −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i 0.215272π-0.215272\pi
−0.932002 + 0.362454i 0.881939π0.881939\pi
390390 0 0
391391 16.0000 0.809155
392392 0 0
393393 −2.00000 −0.100887
394394 12.0000 20.7846i 0.604551 1.04711i
395395 0 0
396396 6.00000 + 10.3923i 0.301511 + 0.522233i
397397 −18.5000 + 32.0429i −0.928488 + 1.60819i −0.142636 + 0.989775i 0.545558π0.545558\pi
−0.785853 + 0.618414i 0.787776π0.787776\pi
398398 16.0000 0.802008
399399 −0.500000 2.59808i −0.0250313 0.130066i
400400 0 0
401401 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i 0.736472π-0.736472\pi
0.976050 + 0.217545i 0.0698049π0.0698049\pi
402402 −7.00000 12.1244i −0.349128 0.604708i
403403 −1.50000 2.59808i −0.0747203 0.129419i
404404 10.0000 17.3205i 0.497519 0.861727i
405405 0 0
406406 40.0000 + 13.8564i 1.98517 + 0.687682i
407407 42.0000 2.08186
408408 0 0
409409 −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i 0.206116π-0.206116\pi
−0.921192 + 0.389109i 0.872783π0.872783\pi
410410 0 0
411411 −4.00000 + 6.92820i −0.197305 + 0.341743i
412412 38.0000 1.87213
413413 −16.0000 + 13.8564i −0.787309 + 0.681829i
414414 8.00000 0.393179
415415 0 0
416416 12.0000 + 20.7846i 0.588348 + 1.01905i
417417 10.5000 + 18.1865i 0.514187 + 0.890598i
418418 6.00000 10.3923i 0.293470 0.508304i
419419 6.00000 0.293119 0.146560 0.989202i 0.453180π-0.453180\pi
0.146560 + 0.989202i 0.453180π0.453180\pi
420420 0 0
421421 1.00000 0.0487370 0.0243685 0.999703i 0.492242π-0.492242\pi
0.0243685 + 0.999703i 0.492242π0.492242\pi
422422 20.0000 34.6410i 0.973585 1.68630i
423423 1.00000 + 1.73205i 0.0486217 + 0.0842152i
424424 0 0
425425 0 0
426426 −12.0000 −0.581402
427427 35.0000 + 12.1244i 1.69377 + 0.586739i
428428 −24.0000 −1.16008
429429 −9.00000 + 15.5885i −0.434524 + 0.752618i
430430 0 0
431431 1.00000 + 1.73205i 0.0481683 + 0.0834300i 0.889104 0.457705i 0.151328π-0.151328\pi
−0.840936 + 0.541135i 0.817995π0.817995\pi
432432 −2.00000 + 3.46410i −0.0962250 + 0.166667i
433433 5.00000 0.240285 0.120142 0.992757i 0.461665π-0.461665\pi
0.120142 + 0.992757i 0.461665π0.461665\pi
434434 1.00000 + 5.19615i 0.0480015 + 0.249423i
435435 0 0
436436 15.0000 25.9808i 0.718370 1.24425i
437437 −2.00000 3.46410i −0.0956730 0.165710i
438438 −1.00000 1.73205i −0.0477818 0.0827606i
439439 −8.00000 + 13.8564i −0.381819 + 0.661330i −0.991322 0.131453i 0.958036π-0.958036\pi
0.609503 + 0.792784i 0.291369π0.291369\pi
440440 0 0
441441 1.00000 6.92820i 0.0476190 0.329914i
442442 24.0000 1.14156
443443 −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i 0.493236π0.493236\pi
−0.876454 + 0.481486i 0.840097π0.840097\pi
444444 −7.00000 12.1244i −0.332205 0.575396i
445445 0 0
446446 −24.0000 + 41.5692i −1.13643 + 1.96836i
447447 4.00000 0.189194
448448 −4.00000 20.7846i −0.188982 0.981981i
449449 30.0000 1.41579 0.707894 0.706319i 0.249646π-0.249646\pi
0.707894 + 0.706319i 0.249646π0.249646\pi
450450 0 0
451451 −18.0000 31.1769i −0.847587 1.46806i
452452 −6.00000 10.3923i −0.282216 0.488813i
453453 4.00000 6.92820i 0.187936 0.325515i
454454 20.0000 0.938647
455455 0 0
456456 0 0
457457 −7.50000 + 12.9904i −0.350835 + 0.607664i −0.986396 0.164386i 0.947436π-0.947436\pi
0.635561 + 0.772051i 0.280769π0.280769\pi
458458 −13.0000 22.5167i −0.607450 1.05213i
459459 2.00000 + 3.46410i 0.0933520 + 0.161690i
460460 0 0
461461 −8.00000 −0.372597 −0.186299 0.982493i 0.559649π-0.559649\pi
−0.186299 + 0.982493i 0.559649π0.559649\pi
462462 24.0000 20.7846i 1.11658 0.966988i
463463 −3.00000 −0.139422 −0.0697109 0.997567i 0.522208π-0.522208\pi
−0.0697109 + 0.997567i 0.522208π0.522208\pi
464464 −16.0000 + 27.7128i −0.742781 + 1.28654i
465465 0 0
466466 6.00000 + 10.3923i 0.277945 + 0.481414i
467467 11.0000 19.0526i 0.509019 0.881647i −0.490926 0.871201i 0.663342π-0.663342\pi
0.999945 0.0104461i 0.00332515π-0.00332515\pi
468468 6.00000 0.277350
469469 −14.0000 + 12.1244i −0.646460 + 0.559851i
470470 0 0
471471 −5.00000 + 8.66025i −0.230388 + 0.399043i
472472 0 0
473473 −3.00000 5.19615i −0.137940 0.238919i
474474 −1.00000 + 1.73205i −0.0459315 + 0.0795557i
475475 0 0
476476 −20.0000 6.92820i −0.916698 0.317554i
477477 −4.00000 −0.183147
478478 −14.0000 + 24.2487i −0.640345 + 1.10911i
479479 2.00000 + 3.46410i 0.0913823 + 0.158279i 0.908093 0.418769i 0.137538π-0.137538\pi
−0.816711 + 0.577047i 0.804205π0.804205\pi
480480 0 0
481481 10.5000 18.1865i 0.478759 0.829235i
482482 −36.0000 −1.63976
483483 −2.00000 10.3923i −0.0910032 0.472866i
484484 50.0000 2.27273
485485 0 0
486486 1.00000 + 1.73205i 0.0453609 + 0.0785674i
487487 −6.50000 11.2583i −0.294543 0.510164i 0.680335 0.732901i 0.261834π-0.261834\pi
−0.974879 + 0.222737i 0.928501π0.928501\pi
488488 0 0
489489 −12.0000 −0.542659
490490 0 0
491491 −12.0000 −0.541552 −0.270776 0.962642i 0.587280π-0.587280\pi
−0.270776 + 0.962642i 0.587280π0.587280\pi
492492 −6.00000 + 10.3923i −0.270501 + 0.468521i
493493 16.0000 + 27.7128i 0.720604 + 1.24812i
494494 −3.00000 5.19615i −0.134976 0.233786i
495495 0 0
496496 −4.00000 −0.179605
497497 3.00000 + 15.5885i 0.134568 + 0.699238i
498498 4.00000 0.179244
499499 −14.5000 + 25.1147i −0.649109 + 1.12429i 0.334227 + 0.942493i 0.391525π0.391525\pi
−0.983336 + 0.181797i 0.941809π0.941809\pi
500500 0 0
501501 5.00000 + 8.66025i 0.223384 + 0.386912i
502502 −12.0000 + 20.7846i −0.535586 + 0.927663i
503503 2.00000 0.0891756 0.0445878 0.999005i 0.485803π-0.485803\pi
0.0445878 + 0.999005i 0.485803π0.485803\pi
504504 0 0
505505 0 0
506506 24.0000 41.5692i 1.06693 1.84798i
507507 −2.00000 3.46410i −0.0888231 0.153846i
508508 5.00000 + 8.66025i 0.221839 + 0.384237i
509509 −5.00000 + 8.66025i −0.221621 + 0.383859i −0.955300 0.295637i 0.904468π-0.904468\pi
0.733679 + 0.679496i 0.237801π0.237801\pi
510510 0 0
511511 −2.00000 + 1.73205i −0.0884748 + 0.0766214i
512512 32.0000 1.41421
513513 0.500000 0.866025i 0.0220755 0.0382360i
514514 −18.0000 31.1769i −0.793946 1.37515i
515515 0 0
516516 −1.00000 + 1.73205i −0.0440225 + 0.0762493i
517517 12.0000 0.527759
518518 −28.0000 + 24.2487i −1.23025 + 1.06543i
519519 24.0000 1.05348
520520 0 0
521521 −2.00000 3.46410i −0.0876216 0.151765i 0.818884 0.573959i 0.194593π-0.194593\pi
−0.906505 + 0.422194i 0.861260π0.861260\pi
522522 8.00000 + 13.8564i 0.350150 + 0.606478i
523523 5.50000 9.52628i 0.240498 0.416555i −0.720358 0.693602i 0.756023π-0.756023\pi
0.960856 + 0.277047i 0.0893559π0.0893559\pi
524524 4.00000 0.174741
525525 0 0
526526 −8.00000 −0.348817
527527 −2.00000 + 3.46410i −0.0871214 + 0.150899i
528528 12.0000 + 20.7846i 0.522233 + 0.904534i
529529 3.50000 + 6.06218i 0.152174 + 0.263573i
530530 0 0
531531 −8.00000 −0.347170
532532 1.00000 + 5.19615i 0.0433555 + 0.225282i
533533 −18.0000 −0.779667
534534 −12.0000 + 20.7846i −0.519291 + 0.899438i
535535 0 0
536536 0 0
537537 9.00000 15.5885i 0.388379 0.672692i
538538 −20.0000 −0.862261
539539 −33.0000 25.9808i −1.42141 1.11907i
540540 0 0
541541 1.50000 2.59808i 0.0644900 0.111700i −0.831978 0.554809i 0.812791π-0.812791\pi
0.896468 + 0.443109i 0.146125π0.146125\pi
542542 24.0000 + 41.5692i 1.03089 + 1.78555i
543543 6.50000 + 11.2583i 0.278942 + 0.483141i
544544 16.0000 27.7128i 0.685994 1.18818i
545545 0 0
546546 −3.00000 15.5885i −0.128388 0.667124i
547547 −36.0000 −1.53925 −0.769624 0.638497i 0.779557π-0.779557\pi
−0.769624 + 0.638497i 0.779557π0.779557\pi
548548 8.00000 13.8564i 0.341743 0.591916i
549549 7.00000 + 12.1244i 0.298753 + 0.517455i
550550 0 0
551551 4.00000 6.92820i 0.170406 0.295151i
552552 0 0
553553 2.50000 + 0.866025i 0.106311 + 0.0368271i
554554 14.0000 0.594803
555555 0 0
556556 −21.0000 36.3731i −0.890598 1.54256i
557557 −5.00000 8.66025i −0.211857 0.366947i 0.740439 0.672124i 0.234618π-0.234618\pi
−0.952296 + 0.305177i 0.901284π0.901284\pi
558558 −1.00000 + 1.73205i −0.0423334 + 0.0733236i
559559 −3.00000 −0.126886
560560 0 0
561561 24.0000 1.01328
562562 12.0000 20.7846i 0.506189 0.876746i
563563 −13.0000 22.5167i −0.547885 0.948964i −0.998419 0.0562051i 0.982100π-0.982100\pi
0.450535 0.892759i 0.351233π-0.351233\pi
564564 −2.00000 3.46410i −0.0842152 0.145865i
565565 0 0
566566 14.0000 0.588464
567567 2.00000 1.73205i 0.0839921 0.0727393i
568568 0 0
569569 −9.00000 + 15.5885i −0.377300 + 0.653502i −0.990668 0.136295i 0.956481π-0.956481\pi
0.613369 + 0.789797i 0.289814π0.289814\pi
570570 0 0
571571 1.50000 + 2.59808i 0.0627730 + 0.108726i 0.895704 0.444651i 0.146672π-0.146672\pi
−0.832931 + 0.553377i 0.813339π0.813339\pi
572572 18.0000 31.1769i 0.752618 1.30357i
573573 −10.0000 −0.417756
574574 30.0000 + 10.3923i 1.25218 + 0.433766i
575575 0 0
576576 4.00000 6.92820i 0.166667 0.288675i
577577 −14.5000 25.1147i −0.603643 1.04554i −0.992264 0.124143i 0.960382π-0.960382\pi
0.388621 0.921397i 0.372951π-0.372951\pi
578578 1.00000 + 1.73205i 0.0415945 + 0.0720438i
579579 4.50000 7.79423i 0.187014 0.323917i
580580 0 0
581581 −1.00000 5.19615i −0.0414870 0.215573i
582582 −12.0000 −0.497416
583583 −12.0000 + 20.7846i −0.496989 + 0.860811i
584584 0 0
585585 0 0
586586 −16.0000 + 27.7128i −0.660954 + 1.14481i
587587 −12.0000 −0.495293 −0.247647 0.968850i 0.579657π-0.579657\pi
−0.247647 + 0.968850i 0.579657π0.579657\pi
588588 −2.00000 + 13.8564i −0.0824786 + 0.571429i
589589 1.00000 0.0412043
590590 0 0
591591 −6.00000 10.3923i −0.246807 0.427482i
592592 −14.0000 24.2487i −0.575396 0.996616i
593593 −9.00000 + 15.5885i −0.369586 + 0.640141i −0.989501 0.144528i 0.953834π-0.953834\pi
0.619915 + 0.784669i 0.287167π0.287167\pi
594594 12.0000 0.492366
595595 0 0
596596 −8.00000 −0.327693
597597 4.00000 6.92820i 0.163709 0.283552i
598598 −12.0000 20.7846i −0.490716 0.849946i
599599 2.00000 + 3.46410i 0.0817178 + 0.141539i 0.903988 0.427558i 0.140626π-0.140626\pi
−0.822270 + 0.569097i 0.807293π0.807293\pi
600600 0 0
601601 −33.0000 −1.34610 −0.673049 0.739598i 0.735016π-0.735016\pi
−0.673049 + 0.739598i 0.735016π0.735016\pi
602602 5.00000 + 1.73205i 0.203785 + 0.0705931i
603603 −7.00000 −0.285062
604604 −8.00000 + 13.8564i −0.325515 + 0.563809i
605605 0 0
606606 −10.0000 17.3205i −0.406222 0.703598i
607607 17.5000 30.3109i 0.710303 1.23028i −0.254440 0.967088i 0.581891π-0.581891\pi
0.964743 0.263193i 0.0847754π-0.0847754\pi
608608 −8.00000 −0.324443
609609 16.0000 13.8564i 0.648353 0.561490i
610610 0 0
611611 3.00000 5.19615i 0.121367 0.210214i
612612 −4.00000 6.92820i −0.161690 0.280056i
613613 −15.0000 25.9808i −0.605844 1.04935i −0.991917 0.126885i 0.959502π-0.959502\pi
0.386073 0.922468i 0.373831π-0.373831\pi
614614 3.00000 5.19615i 0.121070 0.209700i
615615 0 0
616616 0 0
617617 −18.0000 −0.724653 −0.362326 0.932051i 0.618017π-0.618017\pi
−0.362326 + 0.932051i 0.618017π0.618017\pi
618618 19.0000 32.9090i 0.764292 1.32379i
619619 −1.50000 2.59808i −0.0602901 0.104425i 0.834305 0.551303i 0.185869π-0.185869\pi
−0.894595 + 0.446878i 0.852536π0.852536\pi
620620 0 0
621621 2.00000 3.46410i 0.0802572 0.139010i
622622 12.0000 0.481156
623623 30.0000 + 10.3923i 1.20192 + 0.416359i
624624 12.0000 0.480384
625625 0 0
626626 11.0000 + 19.0526i 0.439648 + 0.761493i
627627 −3.00000 5.19615i −0.119808 0.207514i
628628 10.0000 17.3205i 0.399043 0.691164i
629629 −28.0000 −1.11643
630630 0 0
631631 24.0000 0.955425 0.477712 0.878516i 0.341466π-0.341466\pi
0.477712 + 0.878516i 0.341466π0.341466\pi
632632 0 0
633633 −10.0000 17.3205i −0.397464 0.688428i
634634 20.0000 + 34.6410i 0.794301 + 1.37577i
635635 0 0
636636 8.00000 0.317221
637637 −19.5000 + 7.79423i −0.772618 + 0.308819i
638638 96.0000 3.80068
639639 −3.00000 + 5.19615i −0.118678 + 0.205557i
640640 0 0
641641 −6.00000 10.3923i −0.236986 0.410471i 0.722862 0.690992i 0.242826π-0.242826\pi
−0.959848 + 0.280521i 0.909493π0.909493\pi
642642 −12.0000 + 20.7846i −0.473602 + 0.820303i
643643 −1.00000 −0.0394362 −0.0197181 0.999806i 0.506277π-0.506277\pi
−0.0197181 + 0.999806i 0.506277π0.506277\pi
644644 4.00000 + 20.7846i 0.157622 + 0.819028i
645645 0 0
646646 −4.00000 + 6.92820i −0.157378 + 0.272587i
647647 15.0000 + 25.9808i 0.589711 + 1.02141i 0.994270 + 0.106897i 0.0340916π0.0340916\pi
−0.404559 + 0.914512i 0.632575π0.632575\pi
648648 0 0
649649 −24.0000 + 41.5692i −0.942082 + 1.63173i
650650 0 0
651651 2.50000 + 0.866025i 0.0979827 + 0.0339422i
652652 24.0000 0.939913
653653 7.00000 12.1244i 0.273931 0.474463i −0.695934 0.718106i 0.745009π-0.745009\pi
0.969865 + 0.243643i 0.0783426π0.0783426\pi
654654 −15.0000 25.9808i −0.586546 1.01593i
655655 0 0
656656 −12.0000 + 20.7846i −0.468521 + 0.811503i
657657 −1.00000 −0.0390137
658658 −8.00000 + 6.92820i −0.311872 + 0.270089i
659659 −12.0000 −0.467454 −0.233727 0.972302i 0.575092π-0.575092\pi
−0.233727 + 0.972302i 0.575092π0.575092\pi
660660 0 0
661661 −11.5000 19.9186i −0.447298 0.774743i 0.550911 0.834564i 0.314280π-0.314280\pi
−0.998209 + 0.0598209i 0.980947π0.980947\pi
662662 9.00000 + 15.5885i 0.349795 + 0.605863i
663663 6.00000 10.3923i 0.233021 0.403604i
664664 0 0
665665 0 0
666666 −14.0000 −0.542489
667667 16.0000 27.7128i 0.619522 1.07304i
668668 −10.0000 17.3205i −0.386912 0.670151i
669669 12.0000 + 20.7846i 0.463947 + 0.803579i
670670 0 0
671671 84.0000 3.24278
672672 −20.0000 6.92820i −0.771517 0.267261i
673673 37.0000 1.42625 0.713123 0.701039i 0.247280π-0.247280\pi
0.713123 + 0.701039i 0.247280π0.247280\pi
674674 25.0000 43.3013i 0.962964 1.66790i
675675 0 0
676676 4.00000 + 6.92820i 0.153846 + 0.266469i
677677 8.00000 13.8564i 0.307465 0.532545i −0.670342 0.742052i 0.733853π-0.733853\pi
0.977807 + 0.209507i 0.0671860π0.0671860\pi
678678 −12.0000 −0.460857
679679 3.00000 + 15.5885i 0.115129 + 0.598230i
680680 0 0
681681 5.00000 8.66025i 0.191600 0.331862i
682682 6.00000 + 10.3923i 0.229752 + 0.397942i
683683 −24.0000 41.5692i −0.918334 1.59060i −0.801945 0.597398i 0.796201π-0.796201\pi
−0.116390 0.993204i 0.537132π-0.537132\pi
684684 −1.00000 + 1.73205i −0.0382360 + 0.0662266i
685685 0 0
686686 37.0000 1.73205i 1.41267 0.0661300i
687687 −13.0000 −0.495981
688688 −2.00000 + 3.46410i −0.0762493 + 0.132068i
689689 6.00000 + 10.3923i 0.228582 + 0.395915i
690690 0 0
691691 −13.5000 + 23.3827i −0.513564 + 0.889519i 0.486312 + 0.873785i 0.338342π0.338342\pi
−0.999876 + 0.0157341i 0.994991π0.994991\pi
692692 −48.0000 −1.82469
693693 −3.00000 15.5885i −0.113961 0.592157i
694694 −32.0000 −1.21470
695695 0 0
696696 0 0
697697 12.0000 + 20.7846i 0.454532 + 0.787273i
698698 −2.00000 + 3.46410i −0.0757011 + 0.131118i
699699 6.00000 0.226941
700700 0 0
701701 −44.0000 −1.66186 −0.830929 0.556379i 0.812190π-0.812190\pi
−0.830929 + 0.556379i 0.812190π0.812190\pi
702702 3.00000 5.19615i 0.113228 0.196116i
703703 3.50000 + 6.06218i 0.132005 + 0.228639i
704704 −24.0000 41.5692i −0.904534 1.56670i
705705 0 0
706706 36.0000 1.35488
707707 −20.0000 + 17.3205i −0.752177 + 0.651405i
708708 16.0000 0.601317
709709 13.0000 22.5167i 0.488225 0.845631i −0.511683 0.859174i 0.670978π-0.670978\pi
0.999908 + 0.0135434i 0.00431112π0.00431112\pi
710710 0 0
711711 0.500000 + 0.866025i 0.0187515 + 0.0324785i
712712 0 0
713713 4.00000 0.149801
714714 −16.0000 + 13.8564i −0.598785 + 0.518563i
715715 0 0
716716 −18.0000 + 31.1769i −0.672692 + 1.16514i
717717 7.00000 + 12.1244i 0.261420 + 0.452792i
718718 24.0000 + 41.5692i 0.895672 + 1.55135i
719719 17.0000 29.4449i 0.633993 1.09811i −0.352735 0.935723i 0.614748π-0.614748\pi
0.986728 0.162385i 0.0519185π-0.0519185\pi
720720 0 0
721721 −47.5000 16.4545i −1.76899 0.612797i
722722 −36.0000 −1.33978
723723 −9.00000 + 15.5885i −0.334714 + 0.579741i
724724 −13.0000 22.5167i −0.483141 0.836825i
725725 0 0
726726 25.0000 43.3013i 0.927837 1.60706i
727727 −7.00000 −0.259616 −0.129808 0.991539i 0.541436π-0.541436\pi
−0.129808 + 0.991539i 0.541436π0.541436\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 2.00000 + 3.46410i 0.0739727 + 0.128124i
732732 −14.0000 24.2487i −0.517455 0.896258i
733733 −21.5000 + 37.2391i −0.794121 + 1.37546i 0.129275 + 0.991609i 0.458735π0.458735\pi
−0.923396 + 0.383849i 0.874598π0.874598\pi
734734 −38.0000 −1.40261
735735 0 0
736736 −32.0000 −1.17954
737737 −21.0000 + 36.3731i −0.773545 + 1.33982i
738738 6.00000 + 10.3923i 0.220863 + 0.382546i
739739 −20.5000 35.5070i −0.754105 1.30615i −0.945818 0.324697i 0.894738π-0.894738\pi
0.191714 0.981451i 0.438596π-0.438596\pi
740740 0 0
741741 −3.00000 −0.110208
742742 −4.00000 20.7846i −0.146845 0.763027i
743743 −6.00000 −0.220119 −0.110059 0.993925i 0.535104π-0.535104\pi
−0.110059 + 0.993925i 0.535104π0.535104\pi
744744 0 0
745745 0 0
746746 11.0000 + 19.0526i 0.402739 + 0.697564i
747747 1.00000 1.73205i 0.0365881 0.0633724i
748748 −48.0000 −1.75505
749749 30.0000 + 10.3923i 1.09618 + 0.379727i
750750 0 0
751751 −14.5000 + 25.1147i −0.529113 + 0.916450i 0.470311 + 0.882501i 0.344142π0.344142\pi
−0.999424 + 0.0339490i 0.989192π0.989192\pi
752752 −4.00000 6.92820i −0.145865 0.252646i
753753 6.00000 + 10.3923i 0.218652 + 0.378717i
754754 24.0000 41.5692i 0.874028 1.51386i
755755 0 0
756756 −4.00000 + 3.46410i −0.145479 + 0.125988i
757757 22.0000 0.799604 0.399802 0.916602i 0.369079π-0.369079\pi
0.399802 + 0.916602i 0.369079π0.369079\pi
758758 −11.0000 + 19.0526i −0.399538 + 0.692020i
759759 −12.0000 20.7846i −0.435572 0.754434i
760760 0 0
761761 6.00000 10.3923i 0.217500 0.376721i −0.736543 0.676391i 0.763543π-0.763543\pi
0.954043 + 0.299670i 0.0968765π0.0968765\pi
762762 10.0000 0.362262
763763 −30.0000 + 25.9808i −1.08607 + 0.940567i
764764 20.0000 0.723575
765765 0 0
766766 28.0000 + 48.4974i 1.01168 + 1.75228i
767767 12.0000 + 20.7846i 0.433295 + 0.750489i
768768 8.00000 13.8564i 0.288675 0.500000i
769769 −49.0000 −1.76699 −0.883493 0.468445i 0.844814π-0.844814\pi
−0.883493 + 0.468445i 0.844814π0.844814\pi
770770 0 0
771771 −18.0000 −0.648254
772772 −9.00000 + 15.5885i −0.323917 + 0.561041i
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 1.00000 + 1.73205i 0.0359443 + 0.0622573i
775775 0 0
776776 0 0
777777 3.50000 + 18.1865i 0.125562 + 0.652438i
778778 12.0000 0.430221
779779 3.00000 5.19615i 0.107486 0.186171i
780780 0 0
781781 18.0000 + 31.1769i 0.644091 + 1.11560i
782782 −16.0000 + 27.7128i −0.572159 + 0.991008i
783783 8.00000 0.285897
784784 −4.00000 + 27.7128i −0.142857 + 0.989743i
785785 0 0
786786 2.00000 3.46410i 0.0713376 0.123560i
787787 −16.0000 27.7128i −0.570338 0.987855i −0.996531 0.0832226i 0.973479π-0.973479\pi
0.426193 0.904632i 0.359855π-0.359855\pi
788788 12.0000 + 20.7846i 0.427482 + 0.740421i
789789 −2.00000 + 3.46410i −0.0712019 + 0.123325i
790790 0 0
791791 3.00000 + 15.5885i 0.106668 + 0.554262i
792792 0 0
793793 21.0000 36.3731i 0.745732 1.29165i
794794 −37.0000 64.0859i −1.31308 2.27432i
795795 0 0
796796 −8.00000 + 13.8564i −0.283552 + 0.491127i
797797 36.0000 1.27519 0.637593 0.770374i 0.279930π-0.279930\pi
0.637593 + 0.770374i 0.279930π0.279930\pi
798798 5.00000 + 1.73205i 0.176998 + 0.0613139i
799799 −8.00000 −0.283020
800800 0 0
801801 6.00000 + 10.3923i 0.212000 + 0.367194i
802802 12.0000 + 20.7846i 0.423735 + 0.733930i
803803 −3.00000 + 5.19615i −0.105868 + 0.183368i
804804 14.0000 0.493742
805805 0 0
806806 6.00000 0.211341
807807 −5.00000 + 8.66025i −0.176008 + 0.304855i
808808 0 0
809809 21.0000 + 36.3731i 0.738321 + 1.27881i 0.953251 + 0.302180i 0.0977142π0.0977142\pi
−0.214930 + 0.976629i 0.568952π0.568952\pi
810810 0 0
811811 −48.0000 −1.68551 −0.842754 0.538299i 0.819067π-0.819067\pi
−0.842754 + 0.538299i 0.819067π0.819067\pi
812812 −32.0000 + 27.7128i −1.12298 + 0.972529i
813813 24.0000 0.841717
814814 −42.0000 + 72.7461i −1.47210 + 2.54975i
815815 0 0
816816 −8.00000 13.8564i −0.280056 0.485071i
817817 0.500000 0.866025i 0.0174928 0.0302984i
818818 10.0000 0.349642
819819 −7.50000 2.59808i −0.262071 0.0907841i
820820 0 0
821821 −27.0000 + 46.7654i −0.942306 + 1.63212i −0.181250 + 0.983437i 0.558014π0.558014\pi
−0.761056 + 0.648686i 0.775319π0.775319\pi
822822 −8.00000 13.8564i −0.279032 0.483298i
823823 4.00000 + 6.92820i 0.139431 + 0.241502i 0.927281 0.374365i 0.122139π-0.122139\pi
−0.787850 + 0.615867i 0.788806π0.788806\pi
824824 0 0
825825 0 0
826826 −8.00000 41.5692i −0.278356 1.44638i
827827 30.0000 1.04320 0.521601 0.853189i 0.325335π-0.325335\pi
0.521601 + 0.853189i 0.325335π0.325335\pi
828828 −4.00000 + 6.92820i −0.139010 + 0.240772i
829829 −28.5000 49.3634i −0.989846 1.71446i −0.618024 0.786159i 0.712066π-0.712066\pi
−0.371822 0.928304i 0.621267π-0.621267\pi
830830 0 0
831831 3.50000 6.06218i 0.121414 0.210295i
832832 −24.0000 −0.832050
833833 22.0000 + 17.3205i 0.762255 + 0.600120i
834834 −42.0000 −1.45434
835835 0 0
836836 6.00000 + 10.3923i 0.207514 + 0.359425i
837837 0.500000 + 0.866025i 0.0172825 + 0.0299342i
838838 −6.00000 + 10.3923i −0.207267 + 0.358996i
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 35.0000 1.20690
842842 −1.00000 + 1.73205i −0.0344623 + 0.0596904i
843843 −6.00000 10.3923i −0.206651 0.357930i
844844 20.0000 + 34.6410i 0.688428 + 1.19239i
845845 0 0
846846 −4.00000 −0.137523
847847 −62.5000 21.6506i −2.14753 0.743925i
848848 16.0000 0.549442
849849 3.50000 6.06218i 0.120120 0.208053i
850850 0 0
851851 14.0000 + 24.2487i 0.479914 + 0.831235i
852852 6.00000 10.3923i 0.205557 0.356034i
853853 9.00000 0.308154 0.154077 0.988059i 0.450760π-0.450760\pi
0.154077 + 0.988059i 0.450760π0.450760\pi
854854 −56.0000 + 48.4974i −1.91628 + 1.65955i
855855 0 0
856856 0 0
857857 −6.00000 10.3923i −0.204956 0.354994i 0.745163 0.666883i 0.232372π-0.232372\pi
−0.950119 + 0.311888i 0.899038π0.899038\pi
858858 −18.0000 31.1769i −0.614510 1.06436i
859859 20.0000 34.6410i 0.682391 1.18194i −0.291858 0.956462i 0.594273π-0.594273\pi
0.974249 0.225475i 0.0723932π-0.0723932\pi
860860 0 0
861861 12.0000 10.3923i 0.408959 0.354169i
862862 −4.00000 −0.136241
863863 −3.00000 + 5.19615i −0.102121 + 0.176879i −0.912558 0.408946i 0.865896π-0.865896\pi
0.810437 + 0.585826i 0.199230π0.199230\pi
864864 −4.00000 6.92820i −0.136083 0.235702i
865865 0 0
866866 −5.00000 + 8.66025i −0.169907 + 0.294287i
867867 1.00000 0.0339618
868868 −5.00000 1.73205i −0.169711 0.0587896i
869869 6.00000 0.203536
870870 0 0
871871 10.5000 + 18.1865i 0.355779 + 0.616227i
872872 0 0
873873 −3.00000 + 5.19615i −0.101535 + 0.175863i
874874 8.00000 0.270604
875875 0 0
876876 2.00000 0.0675737
877877 −11.0000 + 19.0526i −0.371444 + 0.643359i −0.989788 0.142548i 0.954470π-0.954470\pi
0.618344 + 0.785907i 0.287804π0.287804\pi
878878 −16.0000 27.7128i −0.539974 0.935262i
879879 8.00000 + 13.8564i 0.269833 + 0.467365i
880880 0 0
881881 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
882882 11.0000 + 8.66025i 0.370389 + 0.291606i
883883 −7.00000 −0.235569 −0.117784 0.993039i 0.537579π-0.537579\pi
−0.117784 + 0.993039i 0.537579π0.537579\pi
884884 −12.0000 + 20.7846i −0.403604 + 0.699062i
885885 0 0
886886 −36.0000 62.3538i −1.20944 2.09482i
887887 5.00000 8.66025i 0.167884 0.290783i −0.769792 0.638295i 0.779640π-0.779640\pi
0.937676 + 0.347512i 0.112973π0.112973\pi
888888 0 0
889889 −2.50000 12.9904i −0.0838473 0.435683i
890890 0 0
891891 3.00000 5.19615i 0.100504 0.174078i
892892 −24.0000 41.5692i −0.803579 1.39184i
893893 1.00000 + 1.73205i 0.0334637 + 0.0579609i
894894 −4.00000 + 6.92820i −0.133780 + 0.231714i
895895 0 0
896896 0 0
897897 −12.0000 −0.400668
898898 −30.0000 + 51.9615i −1.00111 + 1.73398i
899899 4.00000 + 6.92820i 0.133407 + 0.231069i
900900 0 0
901901 8.00000 13.8564i 0.266519 0.461624i
902902 72.0000 2.39734
903903 2.00000 1.73205i 0.0665558 0.0576390i
904904 0 0
905905 0 0
906906 8.00000 + 13.8564i 0.265782 + 0.460348i
907907 15.5000 + 26.8468i 0.514669 + 0.891433i 0.999855 + 0.0170220i 0.00541854π0.00541854\pi
−0.485186 + 0.874411i 0.661248π0.661248\pi
908908 −10.0000 + 17.3205i −0.331862 + 0.574801i
909909 −10.0000 −0.331679
910910 0 0
911911 12.0000 0.397578 0.198789 0.980042i 0.436299π-0.436299\pi
0.198789 + 0.980042i 0.436299π0.436299\pi
912912 −2.00000 + 3.46410i −0.0662266 + 0.114708i
913913 −6.00000 10.3923i −0.198571 0.343935i
914914 −15.0000 25.9808i −0.496156 0.859367i
915915 0 0
916916 26.0000 0.859064
917917 −5.00000 1.73205i −0.165115 0.0571974i
918918 −8.00000 −0.264039
919919 4.50000 7.79423i 0.148441 0.257108i −0.782210 0.623015i 0.785908π-0.785908\pi
0.930652 + 0.365907i 0.119241π0.119241\pi
920920 0 0
921921 −1.50000 2.59808i −0.0494267 0.0856095i
922922 8.00000 13.8564i 0.263466 0.456336i
923923 18.0000 0.592477
924924 6.00000 + 31.1769i 0.197386 + 1.02565i
925925 0 0
926926 3.00000 5.19615i 0.0985861 0.170756i
927927 −9.50000 16.4545i −0.312021 0.540436i
928928 −32.0000 55.4256i −1.05045 1.81944i
929929 7.00000 12.1244i 0.229663 0.397787i −0.728046 0.685529i 0.759571π-0.759571\pi
0.957708 + 0.287742i 0.0929044π0.0929044\pi
930930 0 0
931931 1.00000 6.92820i 0.0327737 0.227063i
932932 −12.0000 −0.393073
933933 3.00000 5.19615i 0.0982156 0.170114i
934934 22.0000 + 38.1051i 0.719862 + 1.24684i
935935 0 0
936936 0 0
937937 29.0000 0.947389 0.473694 0.880689i 0.342920π-0.342920\pi
0.473694 + 0.880689i 0.342920π0.342920\pi
938938 −7.00000 36.3731i −0.228558 1.18762i
939939 11.0000 0.358971
940940 0 0
941941 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
942942 −10.0000 17.3205i −0.325818 0.564333i
943943 12.0000 20.7846i 0.390774 0.676840i
944944 32.0000 1.04151
945945 0 0
946946 12.0000 0.390154
947947 13.0000 22.5167i 0.422443 0.731693i −0.573735 0.819041i 0.694506π-0.694506\pi
0.996178 + 0.0873481i 0.0278392π0.0278392\pi
948948 −1.00000 1.73205i −0.0324785 0.0562544i
949949 1.50000 + 2.59808i 0.0486921 + 0.0843371i
950950 0 0
951951 20.0000 0.648544
952952 0 0
953953 −4.00000 −0.129573 −0.0647864 0.997899i 0.520637π-0.520637\pi
−0.0647864 + 0.997899i 0.520637π0.520637\pi
954954 4.00000 6.92820i 0.129505 0.224309i
955955 0 0
956956 −14.0000 24.2487i −0.452792 0.784259i
957957 24.0000 41.5692i 0.775810 1.34374i
958958 −8.00000 −0.258468
959959 −16.0000 + 13.8564i −0.516667 + 0.447447i
960960 0 0
961961 15.0000 25.9808i 0.483871 0.838089i
962962 21.0000 + 36.3731i 0.677067 + 1.17271i
963963 6.00000 + 10.3923i 0.193347 + 0.334887i
964964 18.0000 31.1769i 0.579741 1.00414i
965965 0 0
966966 20.0000 + 6.92820i 0.643489 + 0.222911i
967967 −55.0000 −1.76868 −0.884340 0.466843i 0.845391π-0.845391\pi
−0.884340 + 0.466843i 0.845391π0.845391\pi
968968 0 0
969969 2.00000 + 3.46410i 0.0642493 + 0.111283i
970970 0 0
971971 26.0000 45.0333i 0.834380 1.44519i −0.0601548 0.998189i 0.519159π-0.519159\pi
0.894534 0.446999i 0.147507π-0.147507\pi
972972 −2.00000 −0.0641500
973973 10.5000 + 54.5596i 0.336615 + 1.74910i
974974 26.0000 0.833094
975975 0 0
976976 −28.0000 48.4974i −0.896258 1.55236i
977977 −11.0000 19.0526i −0.351921 0.609545i 0.634665 0.772787i 0.281138π-0.281138\pi
−0.986586 + 0.163242i 0.947805π0.947805\pi
978978 12.0000 20.7846i 0.383718 0.664619i
979979 72.0000 2.30113
980980 0 0
981981 −15.0000 −0.478913
982982 12.0000 20.7846i 0.382935 0.663264i
983983 16.0000 + 27.7128i 0.510321 + 0.883901i 0.999928 + 0.0119587i 0.00380665π0.00380665\pi
−0.489608 + 0.871943i 0.662860π0.662860\pi
984984 0 0
985985 0 0
986986 −64.0000 −2.03818
987987 1.00000 + 5.19615i 0.0318304 + 0.165395i
988988 6.00000 0.190885
989989 2.00000 3.46410i 0.0635963 0.110152i
990990 0 0
991991 7.50000 + 12.9904i 0.238245 + 0.412653i 0.960211 0.279276i 0.0900944π-0.0900944\pi
−0.721966 + 0.691929i 0.756761π0.756761\pi
992992 4.00000 6.92820i 0.127000 0.219971i
993993 9.00000 0.285606
994994 −30.0000 10.3923i −0.951542 0.329624i
995995 0 0
996996 −2.00000 + 3.46410i −0.0633724 + 0.109764i
997997 −12.5000 21.6506i −0.395879 0.685682i 0.597334 0.801993i 0.296227π-0.296227\pi
−0.993213 + 0.116310i 0.962893π0.962893\pi
998998 −29.0000 50.2295i −0.917979 1.58999i
999999 −3.50000 + 6.06218i −0.110735 + 0.191799i
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 525.2.i.a.226.1 2
5.2 odd 4 525.2.r.d.499.1 4
5.3 odd 4 525.2.r.d.499.2 4
5.4 even 2 105.2.i.b.16.1 2
7.2 even 3 3675.2.a.o.1.1 1
7.4 even 3 inner 525.2.i.a.151.1 2
7.5 odd 6 3675.2.a.p.1.1 1
15.14 odd 2 315.2.j.a.226.1 2
20.19 odd 2 1680.2.bg.l.961.1 2
35.4 even 6 105.2.i.b.46.1 yes 2
35.9 even 6 735.2.a.b.1.1 1
35.18 odd 12 525.2.r.d.424.1 4
35.19 odd 6 735.2.a.a.1.1 1
35.24 odd 6 735.2.i.f.361.1 2
35.32 odd 12 525.2.r.d.424.2 4
35.34 odd 2 735.2.i.f.226.1 2
105.44 odd 6 2205.2.a.k.1.1 1
105.74 odd 6 315.2.j.a.46.1 2
105.89 even 6 2205.2.a.m.1.1 1
140.39 odd 6 1680.2.bg.l.1201.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.i.b.16.1 2 5.4 even 2
105.2.i.b.46.1 yes 2 35.4 even 6
315.2.j.a.46.1 2 105.74 odd 6
315.2.j.a.226.1 2 15.14 odd 2
525.2.i.a.151.1 2 7.4 even 3 inner
525.2.i.a.226.1 2 1.1 even 1 trivial
525.2.r.d.424.1 4 35.18 odd 12
525.2.r.d.424.2 4 35.32 odd 12
525.2.r.d.499.1 4 5.2 odd 4
525.2.r.d.499.2 4 5.3 odd 4
735.2.a.a.1.1 1 35.19 odd 6
735.2.a.b.1.1 1 35.9 even 6
735.2.i.f.226.1 2 35.34 odd 2
735.2.i.f.361.1 2 35.24 odd 6
1680.2.bg.l.961.1 2 20.19 odd 2
1680.2.bg.l.1201.1 2 140.39 odd 6
2205.2.a.k.1.1 1 105.44 odd 6
2205.2.a.m.1.1 1 105.89 even 6
3675.2.a.o.1.1 1 7.2 even 3
3675.2.a.p.1.1 1 7.5 odd 6