Properties

Label 1183.2.e.b.508.1
Level 11831183
Weight 22
Character 1183.508
Analytic conductor 9.4469.446
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] = [1183,2,Mod(170,1183)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1183.170");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1183=7132 1183 = 7 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1183.e (of order 33, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 9.446302559129.44630255912
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 91)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 508.1
Root 0.500000+0.866025i0.500000 + 0.866025i of defining polynomial
Character χ\chi == 1183.508
Dual form 1183.2.e.b.170.1

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)q4+(0.500000+2.59808i)q7+3.00000q8+(1.50000+2.59808i)q9+(1.50000+2.59808i)q11+(2.50000+0.866025i)q14+(0.500000+0.866025i)q16+(3.50000+6.06218i)q17+(1.50000+2.59808i)q18+(3.500006.06218i)q193.00000q22+(3.00000+5.19615i)q23+(2.500004.33013i)q25+(2.00000+1.73205i)q285.00000q29+(2.500004.33013i)q327.00000q34+3.00000q36+(4.00000+6.92820i)q37+(3.500006.06218i)q38+2.00000q43+(1.50000+2.59808i)q44+(3.00000+5.19615i)q46+(3.50000+6.06218i)q47+(6.500002.59808i)q49+5.00000q50+(1.500002.59808i)q53+(1.50000+7.79423i)q56+(2.500004.33013i)q58+(3.50000+6.06218i)q59+(3.50000+6.06218i)q61+(7.50000+2.59808i)q63+7.00000q64+(1.50000+2.59808i)q67+(3.50000+6.06218i)q68+5.00000q71+(4.50000+7.79423i)q72+(7.0000012.1244i)q73+(4.00000+6.92820i)q747.00000q76+(6.000005.19615i)q77+(3.00000+5.19615i)q79+(4.50000+7.79423i)q81+(1.00000+1.73205i)q86+(4.50000+7.79423i)q88+6.00000q92+(3.50000+6.06218i)q94+14.0000q97+(1.000006.92820i)q989.00000q99+O(q100)q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-2.50000 + 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(-3.50000 - 6.06218i) q^{19} -3.00000 q^{22} +(3.00000 + 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +(2.00000 + 1.73205i) q^{28} -5.00000 q^{29} +(2.50000 - 4.33013i) q^{32} -7.00000 q^{34} +3.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(3.50000 - 6.06218i) q^{38} +2.00000 q^{43} +(1.50000 + 2.59808i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(3.50000 + 6.06218i) q^{47} +(-6.50000 - 2.59808i) q^{49} +5.00000 q^{50} +(1.50000 - 2.59808i) q^{53} +(-1.50000 + 7.79423i) q^{56} +(-2.50000 - 4.33013i) q^{58} +(-3.50000 + 6.06218i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-7.50000 + 2.59808i) q^{63} +7.00000 q^{64} +(-1.50000 + 2.59808i) q^{67} +(3.50000 + 6.06218i) q^{68} +5.00000 q^{71} +(4.50000 + 7.79423i) q^{72} +(7.00000 - 12.1244i) q^{73} +(-4.00000 + 6.92820i) q^{74} -7.00000 q^{76} +(-6.00000 - 5.19615i) q^{77} +(3.00000 + 5.19615i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(1.00000 + 1.73205i) q^{86} +(-4.50000 + 7.79423i) q^{88} +6.00000 q^{92} +(-3.50000 + 6.06218i) q^{94} +14.0000 q^{97} +(-1.00000 - 6.92820i) q^{98} -9.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q2+q4q7+6q8+3q93q115q14+q167q173q187q196q22+6q23+5q25+4q2810q29+5q3214q34+6q36+18q99+O(q100) 2 q + q^{2} + q^{4} - q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{11} - 5 q^{14} + q^{16} - 7 q^{17} - 3 q^{18} - 7 q^{19} - 6 q^{22} + 6 q^{23} + 5 q^{25} + 4 q^{28} - 10 q^{29} + 5 q^{32} - 14 q^{34} + 6 q^{36}+ \cdots - 18 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1183Z)×\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times.

nn 339339 10161016
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.500000 + 0.866025i 0.353553 + 0.612372i 0.986869 0.161521i 0.0516399π-0.0516399\pi
−0.633316 + 0.773893i 0.718307π0.718307\pi
33 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
44 0.500000 0.866025i 0.250000 0.433013i
55 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
66 0 0
77 −0.500000 + 2.59808i −0.188982 + 0.981981i
88 3.00000 1.06066
99 1.50000 + 2.59808i 0.500000 + 0.866025i
1010 0 0
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 0
1313 0 0
1414 −2.50000 + 0.866025i −0.668153 + 0.231455i
1515 0 0
1616 0.500000 + 0.866025i 0.125000 + 0.216506i
1717 −3.50000 + 6.06218i −0.848875 + 1.47029i 0.0333386 + 0.999444i 0.489386π0.489386\pi
−0.882213 + 0.470850i 0.843947π0.843947\pi
1818 −1.50000 + 2.59808i −0.353553 + 0.612372i
1919 −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i 0.869927π-0.869927\pi
0.114708 0.993399i 0.463407π-0.463407\pi
2020 0 0
2121 0 0
2222 −3.00000 −0.639602
2323 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i 0.0484560π0.0484560\pi
−0.362892 + 0.931831i 0.618211π0.618211\pi
2424 0 0
2525 2.50000 4.33013i 0.500000 0.866025i
2626 0 0
2727 0 0
2828 2.00000 + 1.73205i 0.377964 + 0.327327i
2929 −5.00000 −0.928477 −0.464238 0.885710i 0.653672π-0.653672\pi
−0.464238 + 0.885710i 0.653672π0.653672\pi
3030 0 0
3131 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
3232 2.50000 4.33013i 0.441942 0.765466i
3333 0 0
3434 −7.00000 −1.20049
3535 0 0
3636 3.00000 0.500000
3737 4.00000 + 6.92820i 0.657596 + 1.13899i 0.981236 + 0.192809i 0.0617599π0.0617599\pi
−0.323640 + 0.946180i 0.604907π0.604907\pi
3838 3.50000 6.06218i 0.567775 0.983415i
3939 0 0
4040 0 0
4141 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4242 0 0
4343 2.00000 0.304997 0.152499 0.988304i 0.451268π-0.451268\pi
0.152499 + 0.988304i 0.451268π0.451268\pi
4444 1.50000 + 2.59808i 0.226134 + 0.391675i
4545 0 0
4646 −3.00000 + 5.19615i −0.442326 + 0.766131i
4747 3.50000 + 6.06218i 0.510527 + 0.884260i 0.999926 + 0.0121990i 0.00388317π0.00388317\pi
−0.489398 + 0.872060i 0.662783π0.662783\pi
4848 0 0
4949 −6.50000 2.59808i −0.928571 0.371154i
5050 5.00000 0.707107
5151 0 0
5252 0 0
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 0
5555 0 0
5656 −1.50000 + 7.79423i −0.200446 + 1.04155i
5757 0 0
5858 −2.50000 4.33013i −0.328266 0.568574i
5959 −3.50000 + 6.06218i −0.455661 + 0.789228i −0.998726 0.0504625i 0.983930π-0.983930\pi
0.543065 + 0.839691i 0.317264π0.317264\pi
6060 0 0
6161 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i 0.0187572π-0.0187572\pi
−0.550135 + 0.835076i 0.685424π0.685424\pi
6262 0 0
6363 −7.50000 + 2.59808i −0.944911 + 0.327327i
6464 7.00000 0.875000
6565 0 0
6666 0 0
6767 −1.50000 + 2.59808i −0.183254 + 0.317406i −0.942987 0.332830i 0.891996π-0.891996\pi
0.759733 + 0.650236i 0.225330π0.225330\pi
6868 3.50000 + 6.06218i 0.424437 + 0.735147i
6969 0 0
7070 0 0
7171 5.00000 0.593391 0.296695 0.954972i 0.404115π-0.404115\pi
0.296695 + 0.954972i 0.404115π0.404115\pi
7272 4.50000 + 7.79423i 0.530330 + 0.918559i
7373 7.00000 12.1244i 0.819288 1.41905i −0.0869195 0.996215i 0.527702π-0.527702\pi
0.906208 0.422833i 0.138964π-0.138964\pi
7474 −4.00000 + 6.92820i −0.464991 + 0.805387i
7575 0 0
7676 −7.00000 −0.802955
7777 −6.00000 5.19615i −0.683763 0.592157i
7878 0 0
7979 3.00000 + 5.19615i 0.337526 + 0.584613i 0.983967 0.178352i 0.0570765π-0.0570765\pi
−0.646440 + 0.762964i 0.723743π0.723743\pi
8080 0 0
8181 −4.50000 + 7.79423i −0.500000 + 0.866025i
8282 0 0
8383 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
8484 0 0
8585 0 0
8686 1.00000 + 1.73205i 0.107833 + 0.186772i
8787 0 0
8888 −4.50000 + 7.79423i −0.479702 + 0.830868i
8989 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
9090 0 0
9191 0 0
9292 6.00000 0.625543
9393 0 0
9494 −3.50000 + 6.06218i −0.360997 + 0.625266i
9595 0 0
9696 0 0
9797 14.0000 1.42148 0.710742 0.703452i 0.248359π-0.248359\pi
0.710742 + 0.703452i 0.248359π0.248359\pi
9898 −1.00000 6.92820i −0.101015 0.699854i
9999 −9.00000 −0.904534
100100 −2.50000 4.33013i −0.250000 0.433013i
101101 7.00000 12.1244i 0.696526 1.20642i −0.273138 0.961975i 0.588061π-0.588061\pi
0.969664 0.244443i 0.0786053π-0.0786053\pi
102102 0 0
103103 −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i 0.924396π-0.924396\pi
0.282194 0.959357i 0.408938π-0.408938\pi
104104 0 0
105105 0 0
106106 3.00000 0.291386
107107 −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i 0.293050π-0.293050\pi
−0.992003 + 0.126217i 0.959717π0.959717\pi
108108 0 0
109109 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i 0.771977π-0.771977\pi
0.945769 + 0.324840i 0.105310π0.105310\pi
110110 0 0
111111 0 0
112112 −2.50000 + 0.866025i −0.236228 + 0.0818317i
113113 9.00000 0.846649 0.423324 0.905978i 0.360863π-0.360863\pi
0.423324 + 0.905978i 0.360863π0.360863\pi
114114 0 0
115115 0 0
116116 −2.50000 + 4.33013i −0.232119 + 0.402042i
117117 0 0
118118 −7.00000 −0.644402
119119 −14.0000 12.1244i −1.28338 1.11144i
120120 0 0
121121 1.00000 + 1.73205i 0.0909091 + 0.157459i
122122 −3.50000 + 6.06218i −0.316875 + 0.548844i
123123 0 0
124124 0 0
125125 0 0
126126 −6.00000 5.19615i −0.534522 0.462910i
127127 2.00000 0.177471 0.0887357 0.996055i 0.471717π-0.471717\pi
0.0887357 + 0.996055i 0.471717π0.471717\pi
128128 −1.50000 2.59808i −0.132583 0.229640i
129129 0 0
130130 0 0
131131 −7.00000 12.1244i −0.611593 1.05931i −0.990972 0.134069i 0.957196π-0.957196\pi
0.379379 0.925241i 0.376138π-0.376138\pi
132132 0 0
133133 17.5000 6.06218i 1.51744 0.525657i
134134 −3.00000 −0.259161
135135 0 0
136136 −10.5000 + 18.1865i −0.900368 + 1.55948i
137137 2.00000 3.46410i 0.170872 0.295958i −0.767853 0.640626i 0.778675π-0.778675\pi
0.938725 + 0.344668i 0.112008π0.112008\pi
138138 0 0
139139 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
140140 0 0
141141 0 0
142142 2.50000 + 4.33013i 0.209795 + 0.363376i
143143 0 0
144144 −1.50000 + 2.59808i −0.125000 + 0.216506i
145145 0 0
146146 14.0000 1.15865
147147 0 0
148148 8.00000 0.657596
149149 −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i 0.245707π-0.245707\pi
−0.962348 + 0.271821i 0.912374π0.912374\pi
150150 0 0
151151 −1.50000 + 2.59808i −0.122068 + 0.211428i −0.920583 0.390547i 0.872286π-0.872286\pi
0.798515 + 0.601975i 0.205619π0.205619\pi
152152 −10.5000 18.1865i −0.851662 1.47512i
153153 −21.0000 −1.69775
154154 1.50000 7.79423i 0.120873 0.628077i
155155 0 0
156156 0 0
157157 −3.50000 + 6.06218i −0.279330 + 0.483814i −0.971219 0.238190i 0.923446π-0.923446\pi
0.691888 + 0.722005i 0.256779π0.256779\pi
158158 −3.00000 + 5.19615i −0.238667 + 0.413384i
159159 0 0
160160 0 0
161161 −15.0000 + 5.19615i −1.18217 + 0.409514i
162162 −9.00000 −0.707107
163163 −6.50000 11.2583i −0.509119 0.881820i −0.999944 0.0105623i 0.996638π-0.996638\pi
0.490825 0.871258i 0.336695π-0.336695\pi
164164 0 0
165165 0 0
166166 0 0
167167 7.00000 0.541676 0.270838 0.962625i 0.412699π-0.412699\pi
0.270838 + 0.962625i 0.412699π0.412699\pi
168168 0 0
169169 0 0
170170 0 0
171171 10.5000 18.1865i 0.802955 1.39076i
172172 1.00000 1.73205i 0.0762493 0.132068i
173173 −3.50000 6.06218i −0.266100 0.460899i 0.701751 0.712422i 0.252402π-0.252402\pi
−0.967851 + 0.251523i 0.919068π0.919068\pi
174174 0 0
175175 10.0000 + 8.66025i 0.755929 + 0.654654i
176176 −3.00000 −0.226134
177177 0 0
178178 0 0
179179 5.00000 8.66025i 0.373718 0.647298i −0.616417 0.787420i 0.711416π-0.711416\pi
0.990134 + 0.140122i 0.0447496π0.0447496\pi
180180 0 0
181181 −7.00000 −0.520306 −0.260153 0.965567i 0.583773π-0.583773\pi
−0.260153 + 0.965567i 0.583773π0.583773\pi
182182 0 0
183183 0 0
184184 9.00000 + 15.5885i 0.663489 + 1.14920i
185185 0 0
186186 0 0
187187 −10.5000 18.1865i −0.767836 1.32993i
188188 7.00000 0.510527
189189 0 0
190190 0 0
191191 10.0000 + 17.3205i 0.723575 + 1.25327i 0.959558 + 0.281511i 0.0908356π0.0908356\pi
−0.235983 + 0.971757i 0.575831π0.575831\pi
192192 0 0
193193 2.00000 3.46410i 0.143963 0.249351i −0.785022 0.619467i 0.787349π-0.787349\pi
0.928986 + 0.370116i 0.120682π0.120682\pi
194194 7.00000 + 12.1244i 0.502571 + 0.870478i
195195 0 0
196196 −5.50000 + 4.33013i −0.392857 + 0.309295i
197197 −2.00000 −0.142494 −0.0712470 0.997459i 0.522698π-0.522698\pi
−0.0712470 + 0.997459i 0.522698π0.522698\pi
198198 −4.50000 7.79423i −0.319801 0.553912i
199199 7.00000 12.1244i 0.496217 0.859473i −0.503774 0.863836i 0.668055π-0.668055\pi
0.999990 + 0.00436292i 0.00138876π0.00138876\pi
200200 7.50000 12.9904i 0.530330 0.918559i
201201 0 0
202202 14.0000 0.985037
203203 2.50000 12.9904i 0.175466 0.911746i
204204 0 0
205205 0 0
206206 7.00000 12.1244i 0.487713 0.844744i
207207 −9.00000 + 15.5885i −0.625543 + 1.08347i
208208 0 0
209209 21.0000 1.45260
210210 0 0
211211 −26.0000 −1.78991 −0.894957 0.446153i 0.852794π-0.852794\pi
−0.894957 + 0.446153i 0.852794π0.852794\pi
212212 −1.50000 2.59808i −0.103020 0.178437i
213213 0 0
214214 4.00000 6.92820i 0.273434 0.473602i
215215 0 0
216216 0 0
217217 0 0
218218 4.00000 0.270914
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 −21.0000 −1.40626 −0.703132 0.711059i 0.748216π-0.748216\pi
−0.703132 + 0.711059i 0.748216π0.748216\pi
224224 10.0000 + 8.66025i 0.668153 + 0.578638i
225225 15.0000 1.00000
226226 4.50000 + 7.79423i 0.299336 + 0.518464i
227227 −14.0000 + 24.2487i −0.929213 + 1.60944i −0.144571 + 0.989494i 0.546180π0.546180\pi
−0.784642 + 0.619949i 0.787153π0.787153\pi
228228 0 0
229229 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i 0.0135930π-0.0135930\pi
−0.536515 + 0.843891i 0.680260π0.680260\pi
230230 0 0
231231 0 0
232232 −15.0000 −0.984798
233233 13.5000 + 23.3827i 0.884414 + 1.53185i 0.846383 + 0.532574i 0.178775π0.178775\pi
0.0380310 + 0.999277i 0.487891π0.487891\pi
234234 0 0
235235 0 0
236236 3.50000 + 6.06218i 0.227831 + 0.394614i
237237 0 0
238238 3.50000 18.1865i 0.226871 1.17886i
239239 19.0000 1.22901 0.614504 0.788914i 0.289356π-0.289356\pi
0.614504 + 0.788914i 0.289356π0.289356\pi
240240 0 0
241241 14.0000 24.2487i 0.901819 1.56200i 0.0766885 0.997055i 0.475565π-0.475565\pi
0.825131 0.564942i 0.191101π-0.191101\pi
242242 −1.00000 + 1.73205i −0.0642824 + 0.111340i
243243 0 0
244244 7.00000 0.448129
245245 0 0
246246 0 0
247247 0 0
248248 0 0
249249 0 0
250250 0 0
251251 −14.0000 −0.883672 −0.441836 0.897096i 0.645673π-0.645673\pi
−0.441836 + 0.897096i 0.645673π0.645673\pi
252252 −1.50000 + 7.79423i −0.0944911 + 0.490990i
253253 −18.0000 −1.13165
254254 1.00000 + 1.73205i 0.0627456 + 0.108679i
255255 0 0
256256 8.50000 14.7224i 0.531250 0.920152i
257257 7.00000 + 12.1244i 0.436648 + 0.756297i 0.997429 0.0716680i 0.0228322π-0.0228322\pi
−0.560781 + 0.827964i 0.689499π0.689499\pi
258258 0 0
259259 −20.0000 + 6.92820i −1.24274 + 0.430498i
260260 0 0
261261 −7.50000 12.9904i −0.464238 0.804084i
262262 7.00000 12.1244i 0.432461 0.749045i
263263 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i 0.568182π-0.568182\pi
0.952517 0.304487i 0.0984850π-0.0984850\pi
264264 0 0
265265 0 0
266266 14.0000 + 12.1244i 0.858395 + 0.743392i
267267 0 0
268268 1.50000 + 2.59808i 0.0916271 + 0.158703i
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 0 0
271271 −3.50000 6.06218i −0.212610 0.368251i 0.739921 0.672694i 0.234863π-0.234863\pi
−0.952531 + 0.304443i 0.901530π0.901530\pi
272272 −7.00000 −0.424437
273273 0 0
274274 4.00000 0.241649
275275 7.50000 + 12.9904i 0.452267 + 0.783349i
276276 0 0
277277 8.50000 14.7224i 0.510716 0.884585i −0.489207 0.872167i 0.662714π-0.662714\pi
0.999923 0.0124177i 0.00395278π-0.00395278\pi
278278 0 0
279279 0 0
280280 0 0
281281 12.0000 0.715860 0.357930 0.933748i 0.383483π-0.383483\pi
0.357930 + 0.933748i 0.383483π0.383483\pi
282282 0 0
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 2.50000 4.33013i 0.148348 0.256946i
285285 0 0
286286 0 0
287287 0 0
288288 15.0000 0.883883
289289 −16.0000 27.7128i −0.941176 1.63017i
290290 0 0
291291 0 0
292292 −7.00000 12.1244i −0.409644 0.709524i
293293 −14.0000 −0.817889 −0.408944 0.912559i 0.634103π-0.634103\pi
−0.408944 + 0.912559i 0.634103π0.634103\pi
294294 0 0
295295 0 0
296296 12.0000 + 20.7846i 0.697486 + 1.20808i
297297 0 0
298298 3.00000 5.19615i 0.173785 0.301005i
299299 0 0
300300 0 0
301301 −1.00000 + 5.19615i −0.0576390 + 0.299501i
302302 −3.00000 −0.172631
303303 0 0
304304 3.50000 6.06218i 0.200739 0.347690i
305305 0 0
306306 −10.5000 18.1865i −0.600245 1.03965i
307307 −21.0000 −1.19853 −0.599267 0.800549i 0.704541π-0.704541\pi
−0.599267 + 0.800549i 0.704541π0.704541\pi
308308 −7.50000 + 2.59808i −0.427352 + 0.148039i
309309 0 0
310310 0 0
311311 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
312312 0 0
313313 7.00000 + 12.1244i 0.395663 + 0.685309i 0.993186 0.116543i 0.0371814π-0.0371814\pi
−0.597522 + 0.801852i 0.703848π0.703848\pi
314314 −7.00000 −0.395033
315315 0 0
316316 6.00000 0.337526
317317 −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i 0.220558π-0.220558\pi
−0.937892 + 0.346929i 0.887225π0.887225\pi
318318 0 0
319319 7.50000 12.9904i 0.419919 0.727322i
320320 0 0
321321 0 0
322322 −12.0000 10.3923i −0.668734 0.579141i
323323 49.0000 2.72643
324324 4.50000 + 7.79423i 0.250000 + 0.433013i
325325 0 0
326326 6.50000 11.2583i 0.360002 0.623541i
327327 0 0
328328 0 0
329329 −17.5000 + 6.06218i −0.964806 + 0.334219i
330330 0 0
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 0 0
333333 −12.0000 + 20.7846i −0.657596 + 1.13899i
334334 3.50000 + 6.06218i 0.191511 + 0.331708i
335335 0 0
336336 0 0
337337 23.0000 1.25289 0.626445 0.779466i 0.284509π-0.284509\pi
0.626445 + 0.779466i 0.284509π0.284509\pi
338338 0 0
339339 0 0
340340 0 0
341341 0 0
342342 21.0000 1.13555
343343 10.0000 15.5885i 0.539949 0.841698i
344344 6.00000 0.323498
345345 0 0
346346 3.50000 6.06218i 0.188161 0.325905i
347347 −2.00000 + 3.46410i −0.107366 + 0.185963i −0.914702 0.404128i 0.867575π-0.867575\pi
0.807337 + 0.590091i 0.200908π0.200908\pi
348348 0 0
349349 −14.0000 −0.749403 −0.374701 0.927146i 0.622255π-0.622255\pi
−0.374701 + 0.927146i 0.622255π0.622255\pi
350350 −2.50000 + 12.9904i −0.133631 + 0.694365i
351351 0 0
352352 7.50000 + 12.9904i 0.399751 + 0.692390i
353353 7.00000 12.1244i 0.372572 0.645314i −0.617388 0.786659i 0.711809π-0.711809\pi
0.989960 + 0.141344i 0.0451425π0.0451425\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 10.0000 0.528516
359359 4.00000 + 6.92820i 0.211112 + 0.365657i 0.952063 0.305903i 0.0989582π-0.0989582\pi
−0.740951 + 0.671559i 0.765625π0.765625\pi
360360 0 0
361361 −15.0000 + 25.9808i −0.789474 + 1.36741i
362362 −3.50000 6.06218i −0.183956 0.318621i
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 −7.00000 + 12.1244i −0.365397 + 0.632886i −0.988840 0.148983i 0.952400π-0.952400\pi
0.623443 + 0.781869i 0.285733π0.285733\pi
368368 −3.00000 + 5.19615i −0.156386 + 0.270868i
369369 0 0
370370 0 0
371371 6.00000 + 5.19615i 0.311504 + 0.269771i
372372 0 0
373373 −7.50000 12.9904i −0.388335 0.672616i 0.603890 0.797067i 0.293616π-0.293616\pi
−0.992226 + 0.124451i 0.960283π0.960283\pi
374374 10.5000 18.1865i 0.542942 0.940403i
375375 0 0
376376 10.5000 + 18.1865i 0.541496 + 0.937899i
377377 0 0
378378 0 0
379379 12.0000 0.616399 0.308199 0.951322i 0.400274π-0.400274\pi
0.308199 + 0.951322i 0.400274π0.400274\pi
380380 0 0
381381 0 0
382382 −10.0000 + 17.3205i −0.511645 + 0.886194i
383383 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
384384 0 0
385385 0 0
386386 4.00000 0.203595
387387 3.00000 + 5.19615i 0.152499 + 0.264135i
388388 7.00000 12.1244i 0.355371 0.615521i
389389 1.50000 2.59808i 0.0760530 0.131728i −0.825491 0.564416i 0.809102π-0.809102\pi
0.901544 + 0.432688i 0.142435π0.142435\pi
390390 0 0
391391 −42.0000 −2.12403
392392 −19.5000 7.79423i −0.984899 0.393668i
393393 0 0
394394 −1.00000 1.73205i −0.0503793 0.0872595i
395395 0 0
396396 −4.50000 + 7.79423i −0.226134 + 0.391675i
397397 7.00000 + 12.1244i 0.351320 + 0.608504i 0.986481 0.163876i 0.0523996π-0.0523996\pi
−0.635161 + 0.772380i 0.719066π0.719066\pi
398398 14.0000 0.701757
399399 0 0
400400 5.00000 0.250000
401401 11.0000 + 19.0526i 0.549314 + 0.951439i 0.998322 + 0.0579116i 0.0184442π0.0184442\pi
−0.449008 + 0.893528i 0.648223π0.648223\pi
402402 0 0
403403 0 0
404404 −7.00000 12.1244i −0.348263 0.603209i
405405 0 0
406406 12.5000 4.33013i 0.620365 0.214901i
407407 −24.0000 −1.18964
408408 0 0
409409 −14.0000 + 24.2487i −0.692255 + 1.19902i 0.278842 + 0.960337i 0.410050π0.410050\pi
−0.971097 + 0.238685i 0.923284π0.923284\pi
410410 0 0
411411 0 0
412412 −14.0000 −0.689730
413413 −14.0000 12.1244i −0.688895 0.596601i
414414 −18.0000 −0.884652
415415 0 0
416416 0 0
417417 0 0
418418 10.5000 + 18.1865i 0.513572 + 0.889532i
419419 14.0000 0.683945 0.341972 0.939710i 0.388905π-0.388905\pi
0.341972 + 0.939710i 0.388905π0.388905\pi
420420 0 0
421421 −30.0000 −1.46211 −0.731055 0.682318i 0.760972π-0.760972\pi
−0.731055 + 0.682318i 0.760972π0.760972\pi
422422 −13.0000 22.5167i −0.632830 1.09609i
423423 −10.5000 + 18.1865i −0.510527 + 0.884260i
424424 4.50000 7.79423i 0.218539 0.378521i
425425 17.5000 + 30.3109i 0.848875 + 1.47029i
426426 0 0
427427 −17.5000 + 6.06218i −0.846884 + 0.293369i
428428 −8.00000 −0.386695
429429 0 0
430430 0 0
431431 −12.0000 + 20.7846i −0.578020 + 1.00116i 0.417687 + 0.908591i 0.362841π0.362841\pi
−0.995706 + 0.0925683i 0.970492π0.970492\pi
432432 0 0
433433 21.0000 1.00920 0.504598 0.863355i 0.331641π-0.331641\pi
0.504598 + 0.863355i 0.331641π0.331641\pi
434434 0 0
435435 0 0
436436 −2.00000 3.46410i −0.0957826 0.165900i
437437 21.0000 36.3731i 1.00457 1.73996i
438438 0 0
439439 −7.00000 12.1244i −0.334092 0.578664i 0.649218 0.760602i 0.275096π-0.275096\pi
−0.983310 + 0.181938i 0.941763π0.941763\pi
440440 0 0
441441 −3.00000 20.7846i −0.142857 0.989743i
442442 0 0
443443 10.0000 + 17.3205i 0.475114 + 0.822922i 0.999594 0.0285009i 0.00907336π-0.00907336\pi
−0.524479 + 0.851423i 0.675740π0.675740\pi
444444 0 0
445445 0 0
446446 −10.5000 18.1865i −0.497189 0.861157i
447447 0 0
448448 −3.50000 + 18.1865i −0.165359 + 0.859233i
449449 12.0000 0.566315 0.283158 0.959073i 0.408618π-0.408618\pi
0.283158 + 0.959073i 0.408618π0.408618\pi
450450 7.50000 + 12.9904i 0.353553 + 0.612372i
451451 0 0
452452 4.50000 7.79423i 0.211662 0.366610i
453453 0 0
454454 −28.0000 −1.31411
455455 0 0
456456 0 0
457457 −3.00000 5.19615i −0.140334 0.243066i 0.787288 0.616585i 0.211484π-0.211484\pi
−0.927622 + 0.373519i 0.878151π0.878151\pi
458458 −7.00000 + 12.1244i −0.327089 + 0.566534i
459459 0 0
460460 0 0
461461 28.0000 1.30409 0.652045 0.758180i 0.273911π-0.273911\pi
0.652045 + 0.758180i 0.273911π0.273911\pi
462462 0 0
463463 −16.0000 −0.743583 −0.371792 0.928316i 0.621256π-0.621256\pi
−0.371792 + 0.928316i 0.621256π0.621256\pi
464464 −2.50000 4.33013i −0.116060 0.201021i
465465 0 0
466466 −13.5000 + 23.3827i −0.625375 + 1.08318i
467467 −7.00000 12.1244i −0.323921 0.561048i 0.657372 0.753566i 0.271668π-0.271668\pi
−0.981293 + 0.192518i 0.938335π0.938335\pi
468468 0 0
469469 −6.00000 5.19615i −0.277054 0.239936i
470470 0 0
471471 0 0
472472 −10.5000 + 18.1865i −0.483302 + 0.837103i
473473 −3.00000 + 5.19615i −0.137940 + 0.238919i
474474 0 0
475475 −35.0000 −1.60591
476476 −17.5000 + 6.06218i −0.802111 + 0.277859i
477477 9.00000 0.412082
478478 9.50000 + 16.4545i 0.434520 + 0.752611i
479479 3.50000 6.06218i 0.159919 0.276988i −0.774920 0.632059i 0.782210π-0.782210\pi
0.934839 + 0.355071i 0.115543π0.115543\pi
480480 0 0
481481 0 0
482482 28.0000 1.27537
483483 0 0
484484 2.00000 0.0909091
485485 0 0
486486 0 0
487487 12.5000 21.6506i 0.566429 0.981084i −0.430486 0.902597i 0.641658π-0.641658\pi
0.996915 0.0784867i 0.0250088π-0.0250088\pi
488488 10.5000 + 18.1865i 0.475313 + 0.823266i
489489 0 0
490490 0 0
491491 30.0000 1.35388 0.676941 0.736038i 0.263305π-0.263305\pi
0.676941 + 0.736038i 0.263305π0.263305\pi
492492 0 0
493493 17.5000 30.3109i 0.788160 1.36513i
494494 0 0
495495 0 0
496496 0 0
497497 −2.50000 + 12.9904i −0.112140 + 0.582698i
498498 0 0
499499 4.00000 + 6.92820i 0.179065 + 0.310149i 0.941560 0.336844i 0.109360π-0.109360\pi
−0.762496 + 0.646993i 0.776026π0.776026\pi
500500 0 0
501501 0 0
502502 −7.00000 12.1244i −0.312425 0.541136i
503503 −28.0000 −1.24846 −0.624229 0.781241i 0.714587π-0.714587\pi
−0.624229 + 0.781241i 0.714587π0.714587\pi
504504 −22.5000 + 7.79423i −1.00223 + 0.347183i
505505 0 0
506506 −9.00000 15.5885i −0.400099 0.692991i
507507 0 0
508508 1.00000 1.73205i 0.0443678 0.0768473i
509509 −14.0000 24.2487i −0.620539 1.07481i −0.989385 0.145315i 0.953580π-0.953580\pi
0.368846 0.929490i 0.379753π-0.379753\pi
510510 0 0
511511 28.0000 + 24.2487i 1.23865 + 1.07270i
512512 11.0000 0.486136
513513 0 0
514514 −7.00000 + 12.1244i −0.308757 + 0.534782i
515515 0 0
516516 0 0
517517 −21.0000 −0.923579
518518 −16.0000 13.8564i −0.703000 0.608816i
519519 0 0
520520 0 0
521521 7.00000 12.1244i 0.306676 0.531178i −0.670957 0.741496i 0.734117π-0.734117\pi
0.977633 + 0.210318i 0.0674500π0.0674500\pi
522522 7.50000 12.9904i 0.328266 0.568574i
523523 7.00000 + 12.1244i 0.306089 + 0.530161i 0.977503 0.210921i 0.0676463π-0.0676463\pi
−0.671414 + 0.741082i 0.734313π0.734313\pi
524524 −14.0000 −0.611593
525525 0 0
526526 24.0000 1.04645
527527 0 0
528528 0 0
529529 −6.50000 + 11.2583i −0.282609 + 0.489493i
530530 0 0
531531 −21.0000 −0.911322
532532 3.50000 18.1865i 0.151744 0.788486i
533533 0 0
534534 0 0
535535 0 0
536536 −4.50000 + 7.79423i −0.194370 + 0.336659i
537537 0 0
538538 21.0000 0.905374
539539 16.5000 12.9904i 0.710705 0.559535i
540540 0 0
541541 4.00000 + 6.92820i 0.171973 + 0.297867i 0.939110 0.343617i 0.111652π-0.111652\pi
−0.767136 + 0.641484i 0.778319π0.778319\pi
542542 3.50000 6.06218i 0.150338 0.260393i
543543 0 0
544544 17.5000 + 30.3109i 0.750306 + 1.29957i
545545 0 0
546546 0 0
547547 2.00000 0.0855138 0.0427569 0.999086i 0.486386π-0.486386\pi
0.0427569 + 0.999086i 0.486386π0.486386\pi
548548 −2.00000 3.46410i −0.0854358 0.147979i
549549 −10.5000 + 18.1865i −0.448129 + 0.776182i
550550 −7.50000 + 12.9904i −0.319801 + 0.553912i
551551 17.5000 + 30.3109i 0.745525 + 1.29129i
552552 0 0
553553 −15.0000 + 5.19615i −0.637865 + 0.220963i
554554 17.0000 0.722261
555555 0 0
556556 0 0
557557 9.00000 15.5885i 0.381342 0.660504i −0.609912 0.792469i 0.708795π-0.708795\pi
0.991254 + 0.131965i 0.0421286π0.0421286\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 6.00000 + 10.3923i 0.253095 + 0.438373i
563563 −14.0000 + 24.2487i −0.590030 + 1.02196i 0.404198 + 0.914671i 0.367551π0.367551\pi
−0.994228 + 0.107290i 0.965783π0.965783\pi
564564 0 0
565565 0 0
566566 14.0000 0.588464
567567 −18.0000 15.5885i −0.755929 0.654654i
568568 15.0000 0.629386
569569 −0.500000 0.866025i −0.0209611 0.0363057i 0.855355 0.518043i 0.173339π-0.173339\pi
−0.876316 + 0.481737i 0.840006π0.840006\pi
570570 0 0
571571 −2.00000 + 3.46410i −0.0836974 + 0.144968i −0.904835 0.425762i 0.860006π-0.860006\pi
0.821138 + 0.570730i 0.193340π0.193340\pi
572572 0 0
573573 0 0
574574 0 0
575575 30.0000 1.25109
576576 10.5000 + 18.1865i 0.437500 + 0.757772i
577577 7.00000 12.1244i 0.291414 0.504744i −0.682730 0.730670i 0.739208π-0.739208\pi
0.974144 + 0.225927i 0.0725410π0.0725410\pi
578578 16.0000 27.7128i 0.665512 1.15270i
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 4.50000 + 7.79423i 0.186371 + 0.322804i
584584 21.0000 36.3731i 0.868986 1.50513i
585585 0 0
586586 −7.00000 12.1244i −0.289167 0.500853i
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 0 0
590590 0 0
591591 0 0
592592 −4.00000 + 6.92820i −0.164399 + 0.284747i
593593 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
594594 0 0
595595 0 0
596596 −6.00000 −0.245770
597597 0 0
598598 0 0
599599 −16.0000 + 27.7128i −0.653742 + 1.13231i 0.328465 + 0.944516i 0.393469π0.393469\pi
−0.982208 + 0.187799i 0.939865π0.939865\pi
600600 0 0
601601 −7.00000 −0.285536 −0.142768 0.989756i 0.545600π-0.545600\pi
−0.142768 + 0.989756i 0.545600π0.545600\pi
602602 −5.00000 + 1.73205i −0.203785 + 0.0705931i
603603 −9.00000 −0.366508
604604 1.50000 + 2.59808i 0.0610341 + 0.105714i
605605 0 0
606606 0 0
607607 −7.00000 12.1244i −0.284121 0.492112i 0.688274 0.725450i 0.258368π-0.258368\pi
−0.972396 + 0.233338i 0.925035π0.925035\pi
608608 −35.0000 −1.41944
609609 0 0
610610 0 0
611611 0 0
612612 −10.5000 + 18.1865i −0.424437 + 0.735147i
613613 16.0000 27.7128i 0.646234 1.11931i −0.337781 0.941225i 0.609676π-0.609676\pi
0.984015 0.178085i 0.0569903π-0.0569903\pi
614614 −10.5000 18.1865i −0.423746 0.733949i
615615 0 0
616616 −18.0000 15.5885i −0.725241 0.628077i
617617 −30.0000 −1.20775 −0.603877 0.797077i 0.706378π-0.706378\pi
−0.603877 + 0.797077i 0.706378π0.706378\pi
618618 0 0
619619 −14.0000 + 24.2487i −0.562708 + 0.974638i 0.434551 + 0.900647i 0.356907π0.356907\pi
−0.997259 + 0.0739910i 0.976426π0.976426\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 −12.5000 21.6506i −0.500000 0.866025i
626626 −7.00000 + 12.1244i −0.279776 + 0.484587i
627627 0 0
628628 3.50000 + 6.06218i 0.139665 + 0.241907i
629629 −56.0000 −2.23287
630630 0 0
631631 −16.0000 −0.636950 −0.318475 0.947931i 0.603171π-0.603171\pi
−0.318475 + 0.947931i 0.603171π0.603171\pi
632632 9.00000 + 15.5885i 0.358001 + 0.620076i
633633 0 0
634634 3.00000 5.19615i 0.119145 0.206366i
635635 0 0
636636 0 0
637637 0 0
638638 15.0000 0.593856
639639 7.50000 + 12.9904i 0.296695 + 0.513892i
640640 0 0
641641 −9.00000 + 15.5885i −0.355479 + 0.615707i −0.987200 0.159489i 0.949015π-0.949015\pi
0.631721 + 0.775196i 0.282349π0.282349\pi
642642 0 0
643643 7.00000 0.276053 0.138027 0.990429i 0.455924π-0.455924\pi
0.138027 + 0.990429i 0.455924π0.455924\pi
644644 −3.00000 + 15.5885i −0.118217 + 0.614271i
645645 0 0
646646 24.5000 + 42.4352i 0.963940 + 1.66959i
647647 21.0000 36.3731i 0.825595 1.42997i −0.0758684 0.997118i 0.524173π-0.524173\pi
0.901464 0.432855i 0.142494π-0.142494\pi
648648 −13.5000 + 23.3827i −0.530330 + 0.918559i
649649 −10.5000 18.1865i −0.412161 0.713884i
650650 0 0
651651 0 0
652652 −13.0000 −0.509119
653653 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i 0.129211π-0.129211\pi
−0.801337 + 0.598213i 0.795878π0.795878\pi
654654 0 0
655655 0 0
656656 0 0
657657 42.0000 1.63858
658658 −14.0000 12.1244i −0.545777 0.472657i
659659 −40.0000 −1.55818 −0.779089 0.626913i 0.784318π-0.784318\pi
−0.779089 + 0.626913i 0.784318π0.784318\pi
660660 0 0
661661 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
662662 10.0000 17.3205i 0.388661 0.673181i
663663 0 0
664664 0 0
665665 0 0
666666 −24.0000 −0.929981
667667 −15.0000 25.9808i −0.580802 1.00598i
668668 3.50000 6.06218i 0.135419 0.234553i
669669 0 0
670670 0 0
671671 −21.0000 −0.810696
672672 0 0
673673 −26.0000 −1.00223 −0.501113 0.865382i 0.667076π-0.667076\pi
−0.501113 + 0.865382i 0.667076π0.667076\pi
674674 11.5000 + 19.9186i 0.442963 + 0.767235i
675675 0 0
676676 0 0
677677 17.5000 + 30.3109i 0.672580 + 1.16494i 0.977170 + 0.212459i 0.0681471π0.0681471\pi
−0.304590 + 0.952483i 0.598520π0.598520\pi
678678 0 0
679679 −7.00000 + 36.3731i −0.268635 + 1.39587i
680680 0 0
681681 0 0
682682 0 0
683683 −12.0000 + 20.7846i −0.459167 + 0.795301i −0.998917 0.0465244i 0.985185π-0.985185\pi
0.539750 + 0.841825i 0.318519π0.318519\pi
684684 −10.5000 18.1865i −0.401478 0.695379i
685685 0 0
686686 18.5000 + 0.866025i 0.706333 + 0.0330650i
687687 0 0
688688 1.00000 + 1.73205i 0.0381246 + 0.0660338i
689689 0 0
690690 0 0
691691 17.5000 + 30.3109i 0.665731 + 1.15308i 0.979086 + 0.203445i 0.0652137π0.0652137\pi
−0.313355 + 0.949636i 0.601453π0.601453\pi
692692 −7.00000 −0.266100
693693 4.50000 23.3827i 0.170941 0.888235i
694694 −4.00000 −0.151838
695695 0 0
696696 0 0
697697 0 0
698698 −7.00000 12.1244i −0.264954 0.458914i
699699 0 0
700700 12.5000 4.33013i 0.472456 0.163663i
701701 30.0000 1.13308 0.566542 0.824033i 0.308281π-0.308281\pi
0.566542 + 0.824033i 0.308281π0.308281\pi
702702 0 0
703703 28.0000 48.4974i 1.05604 1.82911i
704704 −10.5000 + 18.1865i −0.395734 + 0.685431i
705705 0 0
706706 14.0000 0.526897
707707 28.0000 + 24.2487i 1.05305 + 0.911967i
708708 0 0
709709 25.0000 + 43.3013i 0.938895 + 1.62621i 0.767537 + 0.641004i 0.221482π0.221482\pi
0.171358 + 0.985209i 0.445185π0.445185\pi
710710 0 0
711711 −9.00000 + 15.5885i −0.337526 + 0.584613i
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 −5.00000 8.66025i −0.186859 0.323649i
717717 0 0
718718 −4.00000 + 6.92820i −0.149279 + 0.258558i
719719 21.0000 + 36.3731i 0.783168 + 1.35649i 0.930087 + 0.367338i 0.119731π0.119731\pi
−0.146920 + 0.989148i 0.546936π0.546936\pi
720720 0 0
721721 35.0000 12.1244i 1.30347 0.451535i
722722 −30.0000 −1.11648
723723 0 0
724724 −3.50000 + 6.06218i −0.130076 + 0.225299i
725725 −12.5000 + 21.6506i −0.464238 + 0.804084i
726726 0 0
727727 28.0000 1.03846 0.519231 0.854634i 0.326218π-0.326218\pi
0.519231 + 0.854634i 0.326218π0.326218\pi
728728 0 0
729729 −27.0000 −1.00000
730730 0 0
731731 −7.00000 + 12.1244i −0.258904 + 0.448435i
732732 0 0
733733 21.0000 + 36.3731i 0.775653 + 1.34347i 0.934427 + 0.356155i 0.115912π0.115912\pi
−0.158774 + 0.987315i 0.550754π0.550754\pi
734734 −14.0000 −0.516749
735735 0 0
736736 30.0000 1.10581
737737 −4.50000 7.79423i −0.165760 0.287104i
738738 0 0
739739 2.00000 3.46410i 0.0735712 0.127429i −0.826893 0.562360i 0.809894π-0.809894\pi
0.900464 + 0.434930i 0.143227π0.143227\pi
740740 0 0
741741 0 0
742742 −1.50000 + 7.79423i −0.0550667 + 0.286135i
743743 −9.00000 −0.330178 −0.165089 0.986279i 0.552791π-0.552791\pi
−0.165089 + 0.986279i 0.552791π0.552791\pi
744744 0 0
745745 0 0
746746 7.50000 12.9904i 0.274595 0.475612i
747747 0 0
748748 −21.0000 −0.767836
749749 20.0000 6.92820i 0.730784 0.253151i
750750 0 0
751751 10.0000 + 17.3205i 0.364905 + 0.632034i 0.988761 0.149505i 0.0477681π-0.0477681\pi
−0.623856 + 0.781540i 0.714435π0.714435\pi
752752 −3.50000 + 6.06218i −0.127632 + 0.221065i
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 9.00000 0.327111 0.163555 0.986534i 0.447704π-0.447704\pi
0.163555 + 0.986534i 0.447704π0.447704\pi
758758 6.00000 + 10.3923i 0.217930 + 0.377466i
759759 0 0
760760 0 0
761761 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
762762 0 0
763763 8.00000 + 6.92820i 0.289619 + 0.250818i
764764 20.0000 0.723575
765765 0 0
766766 0 0
767767 0 0
768768 0 0
769769 14.0000 0.504853 0.252426 0.967616i 0.418771π-0.418771\pi
0.252426 + 0.967616i 0.418771π0.418771\pi
770770 0 0
771771 0 0
772772 −2.00000 3.46410i −0.0719816 0.124676i
773773 21.0000 36.3731i 0.755318 1.30825i −0.189899 0.981804i 0.560816π-0.560816\pi
0.945216 0.326445i 0.105851π-0.105851\pi
774774 −3.00000 + 5.19615i −0.107833 + 0.186772i
775775 0 0
776776 42.0000 1.50771
777777 0 0
778778 3.00000 0.107555
779779 0 0
780780 0 0
781781 −7.50000 + 12.9904i −0.268371 + 0.464832i
782782 −21.0000 36.3731i −0.750958 1.30070i
783783 0 0
784784 −1.00000 6.92820i −0.0357143 0.247436i
785785 0 0
786786 0 0
787787 3.50000 6.06218i 0.124762 0.216093i −0.796878 0.604140i 0.793517π-0.793517\pi
0.921640 + 0.388047i 0.126850π0.126850\pi
788788 −1.00000 + 1.73205i −0.0356235 + 0.0617018i
789789 0 0
790790 0 0
791791 −4.50000 + 23.3827i −0.160002 + 0.831393i
792792 −27.0000 −0.959403
793793 0 0
794794 −7.00000 + 12.1244i −0.248421 + 0.430277i
795795 0 0
796796 −7.00000 12.1244i −0.248108 0.429736i
797797 −42.0000 −1.48772 −0.743858 0.668338i 0.767006π-0.767006\pi
−0.743858 + 0.668338i 0.767006π0.767006\pi
798798 0 0
799799 −49.0000 −1.73350
800800 −12.5000 21.6506i −0.441942 0.765466i
801801 0 0
802802 −11.0000 + 19.0526i −0.388424 + 0.672769i
803803 21.0000 + 36.3731i 0.741074 + 1.28358i
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 21.0000 36.3731i 0.738777 1.27960i
809809 15.5000 26.8468i 0.544951 0.943883i −0.453659 0.891175i 0.649882π-0.649882\pi
0.998610 0.0527074i 0.0167851π-0.0167851\pi
810810 0 0
811811 28.0000 0.983213 0.491606 0.870817i 0.336410π-0.336410\pi
0.491606 + 0.870817i 0.336410π0.336410\pi
812812 −10.0000 8.66025i −0.350931 0.303915i
813813 0 0
814814 −12.0000 20.7846i −0.420600 0.728500i
815815 0 0
816816 0 0
817817 −7.00000 12.1244i −0.244899 0.424178i
818818 −28.0000 −0.978997
819819 0 0
820820 0 0
821821 18.0000 + 31.1769i 0.628204 + 1.08808i 0.987912 + 0.155017i 0.0495431π0.0495431\pi
−0.359708 + 0.933065i 0.617124π0.617124\pi
822822 0 0
823823 −2.00000 + 3.46410i −0.0697156 + 0.120751i −0.898776 0.438408i 0.855543π-0.855543\pi
0.829060 + 0.559159i 0.188876π0.188876\pi
824824 −21.0000 36.3731i −0.731570 1.26712i
825825 0 0
826826 3.50000 18.1865i 0.121781 0.632790i
827827 5.00000 0.173867 0.0869335 0.996214i 0.472293π-0.472293\pi
0.0869335 + 0.996214i 0.472293π0.472293\pi
828828 9.00000 + 15.5885i 0.312772 + 0.541736i
829829 −17.5000 + 30.3109i −0.607800 + 1.05274i 0.383802 + 0.923415i 0.374614π0.374614\pi
−0.991602 + 0.129325i 0.958719π0.958719\pi
830830 0 0
831831 0 0
832832 0 0
833833 38.5000 30.3109i 1.33395 1.05021i
834834 0 0
835835 0 0
836836 10.5000 18.1865i 0.363150 0.628994i
837837 0 0
838838 7.00000 + 12.1244i 0.241811 + 0.418829i
839839 −7.00000 −0.241667 −0.120833 0.992673i 0.538557π-0.538557\pi
−0.120833 + 0.992673i 0.538557π0.538557\pi
840840 0 0
841841 −4.00000 −0.137931
842842 −15.0000 25.9808i −0.516934 0.895356i
843843 0 0
844844 −13.0000 + 22.5167i −0.447478 + 0.775055i
845845 0 0
846846 −21.0000 −0.721995
847847 −5.00000 + 1.73205i −0.171802 + 0.0595140i
848848 3.00000 0.103020
849849 0 0
850850 −17.5000 + 30.3109i −0.600245 + 1.03965i
851851 −24.0000 + 41.5692i −0.822709 + 1.42497i
852852 0 0
853853 42.0000 1.43805 0.719026 0.694983i 0.244588π-0.244588\pi
0.719026 + 0.694983i 0.244588π0.244588\pi
854854 −14.0000 12.1244i −0.479070 0.414887i
855855 0 0
856856 −12.0000 20.7846i −0.410152 0.710403i
857857 −10.5000 + 18.1865i −0.358673 + 0.621240i −0.987739 0.156112i 0.950104π-0.950104\pi
0.629066 + 0.777352i 0.283437π0.283437\pi
858858 0 0
859859 28.0000 + 48.4974i 0.955348 + 1.65471i 0.733571 + 0.679613i 0.237852π0.237852\pi
0.221777 + 0.975097i 0.428814π0.428814\pi
860860 0 0
861861 0 0
862862 −24.0000 −0.817443
863863 −10.0000 17.3205i −0.340404 0.589597i 0.644104 0.764938i 0.277230π-0.277230\pi
−0.984508 + 0.175341i 0.943897π0.943897\pi
864864 0 0
865865 0 0
866866 10.5000 + 18.1865i 0.356805 + 0.618004i
867867 0 0
868868 0 0
869869 −18.0000 −0.610608
870870 0 0
871871 0 0
872872 6.00000 10.3923i 0.203186 0.351928i
873873 21.0000 + 36.3731i 0.710742 + 1.23104i
874874 42.0000 1.42067
875875 0 0
876876 0 0
877877 −24.0000 41.5692i −0.810422 1.40369i −0.912569 0.408923i 0.865904π-0.865904\pi
0.102146 0.994769i 0.467429π-0.467429\pi
878878 7.00000 12.1244i 0.236239 0.409177i
879879 0 0
880880 0 0
881881 42.0000 1.41502 0.707508 0.706705i 0.249819π-0.249819\pi
0.707508 + 0.706705i 0.249819π0.249819\pi
882882 16.5000 12.9904i 0.555584 0.437409i
883883 −40.0000 −1.34611 −0.673054 0.739594i 0.735018π-0.735018\pi
−0.673054 + 0.739594i 0.735018π0.735018\pi
884884 0 0
885885 0 0
886886 −10.0000 + 17.3205i −0.335957 + 0.581894i
887887 −21.0000 36.3731i −0.705111 1.22129i −0.966651 0.256096i 0.917564π-0.917564\pi
0.261540 0.965193i 0.415770π-0.415770\pi
888888 0 0
889889 −1.00000 + 5.19615i −0.0335389 + 0.174273i
890890 0 0
891891 −13.5000 23.3827i −0.452267 0.783349i
892892 −10.5000 + 18.1865i −0.351566 + 0.608930i
893893 24.5000 42.4352i 0.819861 1.42004i
894894 0 0
895895 0 0
896896 7.50000 2.59808i 0.250557 0.0867956i
897897 0 0
898898 6.00000 + 10.3923i 0.200223 + 0.346796i
899899 0 0
900900 7.50000 12.9904i 0.250000 0.433013i
901901 10.5000 + 18.1865i 0.349806 + 0.605881i
902902 0 0
903903 0 0
904904 27.0000 0.898007
905905 0 0
906906 0 0
907907 19.0000 32.9090i 0.630885 1.09272i −0.356487 0.934300i 0.616025π-0.616025\pi
0.987371 0.158424i 0.0506412π-0.0506412\pi
908908 14.0000 + 24.2487i 0.464606 + 0.804722i
909909 42.0000 1.39305
910910 0 0
911911 −54.0000 −1.78910 −0.894550 0.446968i 0.852504π-0.852504\pi
−0.894550 + 0.446968i 0.852504π0.852504\pi
912912 0 0
913913 0 0
914914 3.00000 5.19615i 0.0992312 0.171873i
915915 0 0
916916 14.0000 0.462573
917917 35.0000 12.1244i 1.15580 0.400381i
918918 0 0
919919 −25.0000 43.3013i −0.824674 1.42838i −0.902168 0.431384i 0.858025π-0.858025\pi
0.0774944 0.996993i 0.475308π-0.475308\pi
920920 0 0
921921 0 0
922922 14.0000 + 24.2487i 0.461065 + 0.798589i
923923 0 0
924924 0 0
925925 40.0000 1.31519
926926 −8.00000 13.8564i −0.262896 0.455350i
927927 21.0000 36.3731i 0.689730 1.19465i
928928 −12.5000 + 21.6506i −0.410333 + 0.710717i
929929 7.00000 + 12.1244i 0.229663 + 0.397787i 0.957708 0.287742i 0.0929044π-0.0929044\pi
−0.728046 + 0.685529i 0.759571π0.759571\pi
930930 0 0
931931 7.00000 + 48.4974i 0.229416 + 1.58944i
932932 27.0000 0.884414
933933 0 0
934934 7.00000 12.1244i 0.229047 0.396721i
935935 0 0
936936 0 0
937937 7.00000 0.228680 0.114340 0.993442i 0.463525π-0.463525\pi
0.114340 + 0.993442i 0.463525π0.463525\pi
938938 1.50000 7.79423i 0.0489767 0.254491i
939939 0 0
940940 0 0
941941 14.0000 24.2487i 0.456387 0.790485i −0.542380 0.840133i 0.682477π-0.682477\pi
0.998767 + 0.0496480i 0.0158099π0.0158099\pi
942942 0 0
943943 0 0
944944 −7.00000 −0.227831
945945 0 0
946946 −6.00000 −0.195077
947947 −13.5000 23.3827i −0.438691 0.759835i 0.558898 0.829237i 0.311224π-0.311224\pi
−0.997589 + 0.0694014i 0.977891π0.977891\pi
948948 0 0
949949 0 0
950950 −17.5000 30.3109i −0.567775 0.983415i
951951 0 0
952952 −42.0000 36.3731i −1.36123 1.17886i
953953 9.00000 0.291539 0.145769 0.989319i 0.453434π-0.453434\pi
0.145769 + 0.989319i 0.453434π0.453434\pi
954954 4.50000 + 7.79423i 0.145693 + 0.252347i
955955 0 0
956956 9.50000 16.4545i 0.307252 0.532176i
957957 0 0
958958 7.00000 0.226160
959959 8.00000 + 6.92820i 0.258333 + 0.223723i
960960 0 0
961961 15.5000 + 26.8468i 0.500000 + 0.866025i
962962 0 0
963963 12.0000 20.7846i 0.386695 0.669775i
964964 −14.0000 24.2487i −0.450910 0.780998i
965965 0 0
966966 0 0
967967 5.00000 0.160789 0.0803946 0.996763i 0.474382π-0.474382\pi
0.0803946 + 0.996763i 0.474382π0.474382\pi
968968 3.00000 + 5.19615i 0.0964237 + 0.167011i
969969 0 0
970970 0 0
971971 14.0000 + 24.2487i 0.449281 + 0.778178i 0.998339 0.0576061i 0.0183467π-0.0183467\pi
−0.549058 + 0.835784i 0.685013π0.685013\pi
972972 0 0
973973 0 0
974974 25.0000 0.801052
975975 0 0
976976 −3.50000 + 6.06218i −0.112032 + 0.194046i
977977 −19.0000 + 32.9090i −0.607864 + 1.05285i 0.383728 + 0.923446i 0.374640π0.374640\pi
−0.991592 + 0.129405i 0.958693π0.958693\pi
978978 0 0
979979 0 0
980980 0 0
981981 12.0000 0.383131
982982 15.0000 + 25.9808i 0.478669 + 0.829079i
983983 −3.50000 + 6.06218i −0.111633 + 0.193353i −0.916429 0.400198i 0.868941π-0.868941\pi
0.804796 + 0.593551i 0.202275π0.202275\pi
984984 0 0
985985 0 0
986986 35.0000 1.11463
987987 0 0
988988 0 0
989989 6.00000 + 10.3923i 0.190789 + 0.330456i
990990 0 0
991991 −2.00000 + 3.46410i −0.0635321 + 0.110041i −0.896042 0.443969i 0.853570π-0.853570\pi
0.832510 + 0.554010i 0.186903π0.186903\pi
992992 0 0
993993 0 0
994994 −12.5000 + 4.33013i −0.396476 + 0.137343i
995995 0 0
996996 0 0
997997 3.50000 6.06218i 0.110846 0.191991i −0.805266 0.592914i 0.797977π-0.797977\pi
0.916112 + 0.400923i 0.131311π0.131311\pi
998998 −4.00000 + 6.92820i −0.126618 + 0.219308i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1183.2.e.b.508.1 2
7.2 even 3 inner 1183.2.e.b.170.1 2
7.3 odd 6 8281.2.a.e.1.1 1
7.4 even 3 8281.2.a.f.1.1 1
13.12 even 2 91.2.e.a.53.1 2
39.38 odd 2 819.2.j.b.235.1 2
52.51 odd 2 1456.2.r.g.417.1 2
91.12 odd 6 637.2.e.a.79.1 2
91.25 even 6 637.2.a.c.1.1 1
91.38 odd 6 637.2.a.d.1.1 1
91.51 even 6 91.2.e.a.79.1 yes 2
91.90 odd 2 637.2.e.a.508.1 2
273.38 even 6 5733.2.a.d.1.1 1
273.116 odd 6 5733.2.a.c.1.1 1
273.233 odd 6 819.2.j.b.352.1 2
364.51 odd 6 1456.2.r.g.625.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.e.a.53.1 2 13.12 even 2
91.2.e.a.79.1 yes 2 91.51 even 6
637.2.a.c.1.1 1 91.25 even 6
637.2.a.d.1.1 1 91.38 odd 6
637.2.e.a.79.1 2 91.12 odd 6
637.2.e.a.508.1 2 91.90 odd 2
819.2.j.b.235.1 2 39.38 odd 2
819.2.j.b.352.1 2 273.233 odd 6
1183.2.e.b.170.1 2 7.2 even 3 inner
1183.2.e.b.508.1 2 1.1 even 1 trivial
1456.2.r.g.417.1 2 52.51 odd 2
1456.2.r.g.625.1 2 364.51 odd 6
5733.2.a.c.1.1 1 273.116 odd 6
5733.2.a.d.1.1 1 273.38 even 6
8281.2.a.e.1.1 1 7.3 odd 6
8281.2.a.f.1.1 1 7.4 even 3