Properties

Label 832.2.i.b.705.1
Level 832832
Weight 22
Character 832.705
Analytic conductor 6.6446.644
Analytic rank 11
Dimension 22
Inner twists 22

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [832,2,Mod(321,832)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(832, 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("832.321");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 832=2613 832 = 2^{6} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 832.i (of order 33, degree 22, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.643553448176.64355344817
Analytic rank: 11
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 416)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 705.1
Root 0.5000000.866025i0.500000 - 0.866025i of defining polynomial
Character χ\chi == 832.705
Dual form 832.2.i.b.321.1

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+(1.000001.73205i)q31.00000q5+(0.500000+0.866025i)q9+(2.000003.46410i)q11+(2.50000+2.59808i)q13+(1.00000+1.73205i)q15+(1.50000+2.59808i)q17+(1.000001.73205i)q19+(1.00000+1.73205i)q234.00000q254.00000q27+(2.50000+4.33013i)q292.00000q31+(4.00000+6.92820i)q33+(2.50000+4.33013i)q37+(7.00000+1.73205i)q39+(1.500002.59808i)q41+(2.000003.46410i)q43+(0.5000000.866025i)q456.00000q47+(3.50000+6.06218i)q49+6.00000q5113.0000q53+(2.00000+3.46410i)q554.00000q57+(6.00000+10.3923i)q59+(3.50000+6.06218i)q61+(2.500002.59808i)q65+(7.00000+12.1244i)q67+(2.000003.46410i)q69+(3.000005.19615i)q71+7.00000q73+(4.00000+6.92820i)q758.00000q79+(5.50000+9.52628i)q81+4.00000q83+(1.500002.59808i)q85+(5.000008.66025i)q87+(7.0000012.1244i)q89+(2.00000+3.46410i)q93+(1.00000+1.73205i)q95+(1.000001.73205i)q97+4.00000q99+O(q100)q+(-1.00000 - 1.73205i) q^{3} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{9} +(-2.00000 - 3.46410i) q^{11} +(-2.50000 + 2.59808i) q^{13} +(1.00000 + 1.73205i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(1.00000 - 1.73205i) q^{19} +(1.00000 + 1.73205i) q^{23} -4.00000 q^{25} -4.00000 q^{27} +(2.50000 + 4.33013i) q^{29} -2.00000 q^{31} +(-4.00000 + 6.92820i) q^{33} +(2.50000 + 4.33013i) q^{37} +(7.00000 + 1.73205i) q^{39} +(-1.50000 - 2.59808i) q^{41} +(2.00000 - 3.46410i) q^{43} +(0.500000 - 0.866025i) q^{45} -6.00000 q^{47} +(3.50000 + 6.06218i) q^{49} +6.00000 q^{51} -13.0000 q^{53} +(2.00000 + 3.46410i) q^{55} -4.00000 q^{57} +(-6.00000 + 10.3923i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(2.50000 - 2.59808i) q^{65} +(7.00000 + 12.1244i) q^{67} +(2.00000 - 3.46410i) q^{69} +(3.00000 - 5.19615i) q^{71} +7.00000 q^{73} +(4.00000 + 6.92820i) q^{75} -8.00000 q^{79} +(5.50000 + 9.52628i) q^{81} +4.00000 q^{83} +(1.50000 - 2.59808i) q^{85} +(5.00000 - 8.66025i) q^{87} +(-7.00000 - 12.1244i) q^{89} +(2.00000 + 3.46410i) q^{93} +(-1.00000 + 1.73205i) q^{95} +(1.00000 - 1.73205i) q^{97} +4.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q32q5q94q115q13+2q153q17+2q19+2q238q258q27+5q294q318q33+5q37+14q393q41+4q43+q45++8q99+O(q100) 2 q - 2 q^{3} - 2 q^{5} - q^{9} - 4 q^{11} - 5 q^{13} + 2 q^{15} - 3 q^{17} + 2 q^{19} + 2 q^{23} - 8 q^{25} - 8 q^{27} + 5 q^{29} - 4 q^{31} - 8 q^{33} + 5 q^{37} + 14 q^{39} - 3 q^{41} + 4 q^{43} + q^{45}+ \cdots + 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/832Z)×\left(\mathbb{Z}/832\mathbb{Z}\right)^\times.

nn 261261 703703 769769
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 0 0
33 −1.00000 1.73205i −0.577350 1.00000i −0.995782 0.0917517i 0.970753π-0.970753\pi
0.418432 0.908248i 0.362580π-0.362580\pi
44 0 0
55 −1.00000 −0.447214 −0.223607 0.974679i 0.571783π-0.571783\pi
−0.223607 + 0.974679i 0.571783π0.571783\pi
66 0 0
77 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
88 0 0
99 −0.500000 + 0.866025i −0.166667 + 0.288675i
1010 0 0
1111 −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i 0.960630π-0.960630\pi
0.389338 0.921095i 0.372704π-0.372704\pi
1212 0 0
1313 −2.50000 + 2.59808i −0.693375 + 0.720577i
1414 0 0
1515 1.00000 + 1.73205i 0.258199 + 0.447214i
1616 0 0
1717 −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i 0.951855π-0.951855\pi
0.624780 + 0.780801i 0.285189π0.285189\pi
1818 0 0
1919 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i 0.759652π-0.759652\pi
0.957635 + 0.287984i 0.0929851π0.0929851\pi
2020 0 0
2121 0 0
2222 0 0
2323 1.00000 + 1.73205i 0.208514 + 0.361158i 0.951247 0.308431i 0.0998038π-0.0998038\pi
−0.742732 + 0.669588i 0.766471π0.766471\pi
2424 0 0
2525 −4.00000 −0.800000
2626 0 0
2727 −4.00000 −0.769800
2828 0 0
2929 2.50000 + 4.33013i 0.464238 + 0.804084i 0.999167 0.0408130i 0.0129948π-0.0129948\pi
−0.534928 + 0.844897i 0.679661π0.679661\pi
3030 0 0
3131 −2.00000 −0.359211 −0.179605 0.983739i 0.557482π-0.557482\pi
−0.179605 + 0.983739i 0.557482π0.557482\pi
3232 0 0
3333 −4.00000 + 6.92820i −0.696311 + 1.20605i
3434 0 0
3535 0 0
3636 0 0
3737 2.50000 + 4.33013i 0.410997 + 0.711868i 0.994999 0.0998840i 0.0318472π-0.0318472\pi
−0.584002 + 0.811752i 0.698514π0.698514\pi
3838 0 0
3939 7.00000 + 1.73205i 1.12090 + 0.277350i
4040 0 0
4141 −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i 0.241934π-0.241934\pi
−0.959058 + 0.283211i 0.908600π0.908600\pi
4242 0 0
4343 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i 0.734678π-0.734678\pi
0.977261 + 0.212041i 0.0680112π0.0680112\pi
4444 0 0
4545 0.500000 0.866025i 0.0745356 0.129099i
4646 0 0
4747 −6.00000 −0.875190 −0.437595 0.899172i 0.644170π-0.644170\pi
−0.437595 + 0.899172i 0.644170π0.644170\pi
4848 0 0
4949 3.50000 + 6.06218i 0.500000 + 0.866025i
5050 0 0
5151 6.00000 0.840168
5252 0 0
5353 −13.0000 −1.78569 −0.892844 0.450367i 0.851293π-0.851293\pi
−0.892844 + 0.450367i 0.851293π0.851293\pi
5454 0 0
5555 2.00000 + 3.46410i 0.269680 + 0.467099i
5656 0 0
5757 −4.00000 −0.529813
5858 0 0
5959 −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i 0.452025π0.452025\pi
−0.931282 + 0.364299i 0.881308π0.881308\pi
6060 0 0
6161 −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i 0.981243π-0.981243\pi
0.550135 + 0.835076i 0.314576π0.314576\pi
6262 0 0
6363 0 0
6464 0 0
6565 2.50000 2.59808i 0.310087 0.322252i
6666 0 0
6767 7.00000 + 12.1244i 0.855186 + 1.48123i 0.876472 + 0.481452i 0.159891π0.159891\pi
−0.0212861 + 0.999773i 0.506776π0.506776\pi
6868 0 0
6969 2.00000 3.46410i 0.240772 0.417029i
7070 0 0
7171 3.00000 5.19615i 0.356034 0.616670i −0.631260 0.775571i 0.717462π-0.717462\pi
0.987294 + 0.158901i 0.0507952π0.0507952\pi
7272 0 0
7373 7.00000 0.819288 0.409644 0.912245i 0.365653π-0.365653\pi
0.409644 + 0.912245i 0.365653π0.365653\pi
7474 0 0
7575 4.00000 + 6.92820i 0.461880 + 0.800000i
7676 0 0
7777 0 0
7878 0 0
7979 −8.00000 −0.900070 −0.450035 0.893011i 0.648589π-0.648589\pi
−0.450035 + 0.893011i 0.648589π0.648589\pi
8080 0 0
8181 5.50000 + 9.52628i 0.611111 + 1.05848i
8282 0 0
8383 4.00000 0.439057 0.219529 0.975606i 0.429548π-0.429548\pi
0.219529 + 0.975606i 0.429548π0.429548\pi
8484 0 0
8585 1.50000 2.59808i 0.162698 0.281801i
8686 0 0
8787 5.00000 8.66025i 0.536056 0.928477i
8888 0 0
8989 −7.00000 12.1244i −0.741999 1.28518i −0.951584 0.307389i 0.900545π-0.900545\pi
0.209585 0.977790i 0.432789π-0.432789\pi
9090 0 0
9191 0 0
9292 0 0
9393 2.00000 + 3.46410i 0.207390 + 0.359211i
9494 0 0
9595 −1.00000 + 1.73205i −0.102598 + 0.177705i
9696 0 0
9797 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i 0.800958π-0.800958\pi
0.912317 + 0.409484i 0.134291π0.134291\pi
9898 0 0
9999 4.00000 0.402015
100100 0 0
101101 −5.50000 9.52628i −0.547270 0.947900i −0.998460 0.0554722i 0.982334π-0.982334\pi
0.451190 0.892428i 0.351000π-0.351000\pi
102102 0 0
103103 −14.0000 −1.37946 −0.689730 0.724066i 0.742271π-0.742271\pi
−0.689730 + 0.724066i 0.742271π0.742271\pi
104104 0 0
105105 0 0
106106 0 0
107107 −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i 0.260329π-0.260329\pi
−0.973814 + 0.227345i 0.926996π0.926996\pi
108108 0 0
109109 10.0000 0.957826 0.478913 0.877862i 0.341031π-0.341031\pi
0.478913 + 0.877862i 0.341031π0.341031\pi
110110 0 0
111111 5.00000 8.66025i 0.474579 0.821995i
112112 0 0
113113 4.50000 7.79423i 0.423324 0.733219i −0.572938 0.819599i 0.694196π-0.694196\pi
0.996262 + 0.0863794i 0.0275297π0.0275297\pi
114114 0 0
115115 −1.00000 1.73205i −0.0932505 0.161515i
116116 0 0
117117 −1.00000 3.46410i −0.0924500 0.320256i
118118 0 0
119119 0 0
120120 0 0
121121 −2.50000 + 4.33013i −0.227273 + 0.393648i
122122 0 0
123123 −3.00000 + 5.19615i −0.270501 + 0.468521i
124124 0 0
125125 9.00000 0.804984
126126 0 0
127127 −11.0000 19.0526i −0.976092 1.69064i −0.676283 0.736642i 0.736410π-0.736410\pi
−0.299809 0.953999i 0.596923π-0.596923\pi
128128 0 0
129129 −8.00000 −0.704361
130130 0 0
131131 −18.0000 −1.57267 −0.786334 0.617802i 0.788023π-0.788023\pi
−0.786334 + 0.617802i 0.788023π0.788023\pi
132132 0 0
133133 0 0
134134 0 0
135135 4.00000 0.344265
136136 0 0
137137 0.500000 0.866025i 0.0427179 0.0739895i −0.843876 0.536538i 0.819732π-0.819732\pi
0.886594 + 0.462549i 0.153065π0.153065\pi
138138 0 0
139139 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i 0.595942π-0.595942\pi
0.975417 0.220366i 0.0707252π-0.0707252\pi
140140 0 0
141141 6.00000 + 10.3923i 0.505291 + 0.875190i
142142 0 0
143143 14.0000 + 3.46410i 1.17074 + 0.289683i
144144 0 0
145145 −2.50000 4.33013i −0.207614 0.359597i
146146 0 0
147147 7.00000 12.1244i 0.577350 1.00000i
148148 0 0
149149 10.5000 18.1865i 0.860194 1.48990i −0.0115483 0.999933i 0.503676π-0.503676\pi
0.871742 0.489966i 0.162991π-0.162991\pi
150150 0 0
151151 −22.0000 −1.79033 −0.895167 0.445730i 0.852944π-0.852944\pi
−0.895167 + 0.445730i 0.852944π0.852944\pi
152152 0 0
153153 −1.50000 2.59808i −0.121268 0.210042i
154154 0 0
155155 2.00000 0.160644
156156 0 0
157157 −5.00000 −0.399043 −0.199522 0.979893i 0.563939π-0.563939\pi
−0.199522 + 0.979893i 0.563939π0.563939\pi
158158 0 0
159159 13.0000 + 22.5167i 1.03097 + 1.78569i
160160 0 0
161161 0 0
162162 0 0
163163 −8.00000 + 13.8564i −0.626608 + 1.08532i 0.361619 + 0.932326i 0.382224π0.382224\pi
−0.988227 + 0.152992i 0.951109π0.951109\pi
164164 0 0
165165 4.00000 6.92820i 0.311400 0.539360i
166166 0 0
167167 −2.00000 3.46410i −0.154765 0.268060i 0.778209 0.628006i 0.216129π-0.216129\pi
−0.932973 + 0.359946i 0.882795π0.882795\pi
168168 0 0
169169 −0.500000 12.9904i −0.0384615 0.999260i
170170 0 0
171171 1.00000 + 1.73205i 0.0764719 + 0.132453i
172172 0 0
173173 −1.00000 + 1.73205i −0.0760286 + 0.131685i −0.901533 0.432710i 0.857557π-0.857557\pi
0.825505 + 0.564396i 0.190891π0.190891\pi
174174 0 0
175175 0 0
176176 0 0
177177 24.0000 1.80395
178178 0 0
179179 −8.00000 13.8564i −0.597948 1.03568i −0.993124 0.117071i 0.962650π-0.962650\pi
0.395175 0.918606i 0.370684π-0.370684\pi
180180 0 0
181181 −5.00000 −0.371647 −0.185824 0.982583i 0.559495π-0.559495\pi
−0.185824 + 0.982583i 0.559495π0.559495\pi
182182 0 0
183183 14.0000 1.03491
184184 0 0
185185 −2.50000 4.33013i −0.183804 0.318357i
186186 0 0
187187 12.0000 0.877527
188188 0 0
189189 0 0
190190 0 0
191191 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i 0.763683π-0.763683\pi
0.953912 + 0.300088i 0.0970159π0.0970159\pi
192192 0 0
193193 10.5000 + 18.1865i 0.755807 + 1.30910i 0.944972 + 0.327150i 0.106088π0.106088\pi
−0.189166 + 0.981945i 0.560578π0.560578\pi
194194 0 0
195195 −7.00000 1.73205i −0.501280 0.124035i
196196 0 0
197197 −9.00000 15.5885i −0.641223 1.11063i −0.985160 0.171639i 0.945094π-0.945094\pi
0.343937 0.938993i 0.388239π-0.388239\pi
198198 0 0
199199 −7.00000 + 12.1244i −0.496217 + 0.859473i −0.999990 0.00436292i 0.998611π-0.998611\pi
0.503774 + 0.863836i 0.331945π0.331945\pi
200200 0 0
201201 14.0000 24.2487i 0.987484 1.71037i
202202 0 0
203203 0 0
204204 0 0
205205 1.50000 + 2.59808i 0.104765 + 0.181458i
206206 0 0
207207 −2.00000 −0.139010
208208 0 0
209209 −8.00000 −0.553372
210210 0 0
211211 −9.00000 15.5885i −0.619586 1.07315i −0.989561 0.144112i 0.953967π-0.953967\pi
0.369976 0.929041i 0.379366π-0.379366\pi
212212 0 0
213213 −12.0000 −0.822226
214214 0 0
215215 −2.00000 + 3.46410i −0.136399 + 0.236250i
216216 0 0
217217 0 0
218218 0 0
219219 −7.00000 12.1244i −0.473016 0.819288i
220220 0 0
221221 −3.00000 10.3923i −0.201802 0.699062i
222222 0 0
223223 9.00000 + 15.5885i 0.602685 + 1.04388i 0.992413 + 0.122950i 0.0392356π0.0392356\pi
−0.389728 + 0.920930i 0.627431π0.627431\pi
224224 0 0
225225 2.00000 3.46410i 0.133333 0.230940i
226226 0 0
227227 −9.00000 + 15.5885i −0.597351 + 1.03464i 0.395860 + 0.918311i 0.370447π0.370447\pi
−0.993210 + 0.116331i 0.962887π0.962887\pi
228228 0 0
229229 18.0000 1.18947 0.594737 0.803921i 0.297256π-0.297256\pi
0.594737 + 0.803921i 0.297256π0.297256\pi
230230 0 0
231231 0 0
232232 0 0
233233 6.00000 0.393073 0.196537 0.980497i 0.437031π-0.437031\pi
0.196537 + 0.980497i 0.437031π0.437031\pi
234234 0 0
235235 6.00000 0.391397
236236 0 0
237237 8.00000 + 13.8564i 0.519656 + 0.900070i
238238 0 0
239239 12.0000 0.776215 0.388108 0.921614i 0.373129π-0.373129\pi
0.388108 + 0.921614i 0.373129π0.373129\pi
240240 0 0
241241 −3.50000 + 6.06218i −0.225455 + 0.390499i −0.956456 0.291877i 0.905720π-0.905720\pi
0.731001 + 0.682376i 0.239053π0.239053\pi
242242 0 0
243243 5.00000 8.66025i 0.320750 0.555556i
244244 0 0
245245 −3.50000 6.06218i −0.223607 0.387298i
246246 0 0
247247 2.00000 + 6.92820i 0.127257 + 0.440831i
248248 0 0
249249 −4.00000 6.92820i −0.253490 0.439057i
250250 0 0
251251 11.0000 19.0526i 0.694314 1.20259i −0.276098 0.961130i 0.589041π-0.589041\pi
0.970411 0.241457i 0.0776254π-0.0776254\pi
252252 0 0
253253 4.00000 6.92820i 0.251478 0.435572i
254254 0 0
255255 −6.00000 −0.375735
256256 0 0
257257 −5.50000 9.52628i −0.343081 0.594233i 0.641923 0.766769i 0.278137π-0.278137\pi
−0.985003 + 0.172536i 0.944804π0.944804\pi
258258 0 0
259259 0 0
260260 0 0
261261 −5.00000 −0.309492
262262 0 0
263263 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i 0.0984850π0.0984850\pi
−0.212565 + 0.977147i 0.568182π0.568182\pi
264264 0 0
265265 13.0000 0.798584
266266 0 0
267267 −14.0000 + 24.2487i −0.856786 + 1.48400i
268268 0 0
269269 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i 0.692975π-0.692975\pi
0.996586 + 0.0825561i 0.0263084π0.0263084\pi
270270 0 0
271271 6.00000 + 10.3923i 0.364474 + 0.631288i 0.988692 0.149963i 0.0479155π-0.0479155\pi
−0.624218 + 0.781251i 0.714582π0.714582\pi
272272 0 0
273273 0 0
274274 0 0
275275 8.00000 + 13.8564i 0.482418 + 0.835573i
276276 0 0
277277 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i 0.823769π-0.823769\pi
0.880656 + 0.473757i 0.157103π0.157103\pi
278278 0 0
279279 1.00000 1.73205i 0.0598684 0.103695i
280280 0 0
281281 −21.0000 −1.25275 −0.626377 0.779520i 0.715463π-0.715463\pi
−0.626377 + 0.779520i 0.715463π0.715463\pi
282282 0 0
283283 10.0000 + 17.3205i 0.594438 + 1.02960i 0.993626 + 0.112728i 0.0359589π0.0359589\pi
−0.399188 + 0.916869i 0.630708π0.630708\pi
284284 0 0
285285 4.00000 0.236940
286286 0 0
287287 0 0
288288 0 0
289289 4.00000 + 6.92820i 0.235294 + 0.407541i
290290 0 0
291291 −4.00000 −0.234484
292292 0 0
293293 −9.50000 + 16.4545i −0.554996 + 0.961281i 0.442908 + 0.896567i 0.353947π0.353947\pi
−0.997904 + 0.0647140i 0.979386π0.979386\pi
294294 0 0
295295 6.00000 10.3923i 0.349334 0.605063i
296296 0 0
297297 8.00000 + 13.8564i 0.464207 + 0.804030i
298298 0 0
299299 −7.00000 1.73205i −0.404820 0.100167i
300300 0 0
301301 0 0
302302 0 0
303303 −11.0000 + 19.0526i −0.631933 + 1.09454i
304304 0 0
305305 3.50000 6.06218i 0.200409 0.347119i
306306 0 0
307307 26.0000 1.48390 0.741949 0.670456i 0.233902π-0.233902\pi
0.741949 + 0.670456i 0.233902π0.233902\pi
308308 0 0
309309 14.0000 + 24.2487i 0.796432 + 1.37946i
310310 0 0
311311 −10.0000 −0.567048 −0.283524 0.958965i 0.591504π-0.591504\pi
−0.283524 + 0.958965i 0.591504π0.591504\pi
312312 0 0
313313 −34.0000 −1.92179 −0.960897 0.276907i 0.910691π-0.910691\pi
−0.960897 + 0.276907i 0.910691π0.910691\pi
314314 0 0
315315 0 0
316316 0 0
317317 3.00000 0.168497 0.0842484 0.996445i 0.473151π-0.473151\pi
0.0842484 + 0.996445i 0.473151π0.473151\pi
318318 0 0
319319 10.0000 17.3205i 0.559893 0.969762i
320320 0 0
321321 −6.00000 + 10.3923i −0.334887 + 0.580042i
322322 0 0
323323 3.00000 + 5.19615i 0.166924 + 0.289122i
324324 0 0
325325 10.0000 10.3923i 0.554700 0.576461i
326326 0 0
327327 −10.0000 17.3205i −0.553001 0.957826i
328328 0 0
329329 0 0
330330 0 0
331331 4.00000 6.92820i 0.219860 0.380808i −0.734905 0.678170i 0.762773π-0.762773\pi
0.954765 + 0.297361i 0.0961066π0.0961066\pi
332332 0 0
333333 −5.00000 −0.273998
334334 0 0
335335 −7.00000 12.1244i −0.382451 0.662424i
336336 0 0
337337 −1.00000 −0.0544735 −0.0272367 0.999629i 0.508671π-0.508671\pi
−0.0272367 + 0.999629i 0.508671π0.508671\pi
338338 0 0
339339 −18.0000 −0.977626
340340 0 0
341341 4.00000 + 6.92820i 0.216612 + 0.375183i
342342 0 0
343343 0 0
344344 0 0
345345 −2.00000 + 3.46410i −0.107676 + 0.186501i
346346 0 0
347347 −5.00000 + 8.66025i −0.268414 + 0.464907i −0.968452 0.249198i 0.919833π-0.919833\pi
0.700038 + 0.714105i 0.253166π0.253166\pi
348348 0 0
349349 −5.00000 8.66025i −0.267644 0.463573i 0.700609 0.713545i 0.252912π-0.252912\pi
−0.968253 + 0.249973i 0.919578π0.919578\pi
350350 0 0
351351 10.0000 10.3923i 0.533761 0.554700i
352352 0 0
353353 −1.50000 2.59808i −0.0798369 0.138282i 0.823343 0.567545i 0.192107π-0.192107\pi
−0.903179 + 0.429263i 0.858773π0.858773\pi
354354 0 0
355355 −3.00000 + 5.19615i −0.159223 + 0.275783i
356356 0 0
357357 0 0
358358 0 0
359359 −20.0000 −1.05556 −0.527780 0.849381i 0.676975π-0.676975\pi
−0.527780 + 0.849381i 0.676975π0.676975\pi
360360 0 0
361361 7.50000 + 12.9904i 0.394737 + 0.683704i
362362 0 0
363363 10.0000 0.524864
364364 0 0
365365 −7.00000 −0.366397
366366 0 0
367367 −11.0000 19.0526i −0.574195 0.994535i −0.996129 0.0879086i 0.971982π-0.971982\pi
0.421933 0.906627i 0.361352π-0.361352\pi
368368 0 0
369369 3.00000 0.156174
370370 0 0
371371 0 0
372372 0 0
373373 −1.50000 + 2.59808i −0.0776671 + 0.134523i −0.902243 0.431228i 0.858080π-0.858080\pi
0.824576 + 0.565751i 0.191414π0.191414\pi
374374 0 0
375375 −9.00000 15.5885i −0.464758 0.804984i
376376 0 0
377377 −17.5000 4.33013i −0.901296 0.223013i
378378 0 0
379379 −1.00000 1.73205i −0.0513665 0.0889695i 0.839199 0.543825i 0.183024π-0.183024\pi
−0.890565 + 0.454855i 0.849691π0.849691\pi
380380 0 0
381381 −22.0000 + 38.1051i −1.12709 + 1.95218i
382382 0 0
383383 2.00000 3.46410i 0.102195 0.177007i −0.810394 0.585886i 0.800747π-0.800747\pi
0.912589 + 0.408879i 0.134080π0.134080\pi
384384 0 0
385385 0 0
386386 0 0
387387 2.00000 + 3.46410i 0.101666 + 0.176090i
388388 0 0
389389 −33.0000 −1.67317 −0.836583 0.547840i 0.815450π-0.815450\pi
−0.836583 + 0.547840i 0.815450π0.815450\pi
390390 0 0
391391 −6.00000 −0.303433
392392 0 0
393393 18.0000 + 31.1769i 0.907980 + 1.57267i
394394 0 0
395395 8.00000 0.402524
396396 0 0
397397 −17.0000 + 29.4449i −0.853206 + 1.47780i 0.0250943 + 0.999685i 0.492011π0.492011\pi
−0.878300 + 0.478110i 0.841322π0.841322\pi
398398 0 0
399399 0 0
400400 0 0
401401 16.5000 + 28.5788i 0.823971 + 1.42716i 0.902703 + 0.430263i 0.141579π0.141579\pi
−0.0787327 + 0.996896i 0.525087π0.525087\pi
402402 0 0
403403 5.00000 5.19615i 0.249068 0.258839i
404404 0 0
405405 −5.50000 9.52628i −0.273297 0.473365i
406406 0 0
407407 10.0000 17.3205i 0.495682 0.858546i
408408 0 0
409409 4.50000 7.79423i 0.222511 0.385400i −0.733059 0.680165i 0.761908π-0.761908\pi
0.955570 + 0.294765i 0.0952414π0.0952414\pi
410410 0 0
411411 −2.00000 −0.0986527
412412 0 0
413413 0 0
414414 0 0
415415 −4.00000 −0.196352
416416 0 0
417417 −32.0000 −1.56705
418418 0 0
419419 −7.00000 12.1244i −0.341972 0.592314i 0.642827 0.766012i 0.277762π-0.277762\pi
−0.984799 + 0.173698i 0.944428π0.944428\pi
420420 0 0
421421 −9.00000 −0.438633 −0.219317 0.975654i 0.570383π-0.570383\pi
−0.219317 + 0.975654i 0.570383π0.570383\pi
422422 0 0
423423 3.00000 5.19615i 0.145865 0.252646i
424424 0 0
425425 6.00000 10.3923i 0.291043 0.504101i
426426 0 0
427427 0 0
428428 0 0
429429 −8.00000 27.7128i −0.386244 1.33799i
430430 0 0
431431 −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i 0.259993π-0.259993\pi
−0.973574 + 0.228373i 0.926659π0.926659\pi
432432 0 0
433433 0.500000 0.866025i 0.0240285 0.0416185i −0.853761 0.520665i 0.825684π-0.825684\pi
0.877790 + 0.479046i 0.159017π0.159017\pi
434434 0 0
435435 −5.00000 + 8.66025i −0.239732 + 0.415227i
436436 0 0
437437 4.00000 0.191346
438438 0 0
439439 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i 0.105523π-0.105523\pi
−0.754642 + 0.656136i 0.772190π0.772190\pi
440440 0 0
441441 −7.00000 −0.333333
442442 0 0
443443 −4.00000 −0.190046 −0.0950229 0.995475i 0.530292π-0.530292\pi
−0.0950229 + 0.995475i 0.530292π0.530292\pi
444444 0 0
445445 7.00000 + 12.1244i 0.331832 + 0.574750i
446446 0 0
447447 −42.0000 −1.98653
448448 0 0
449449 5.00000 8.66025i 0.235965 0.408703i −0.723588 0.690232i 0.757508π-0.757508\pi
0.959553 + 0.281529i 0.0908417π0.0908417\pi
450450 0 0
451451 −6.00000 + 10.3923i −0.282529 + 0.489355i
452452 0 0
453453 22.0000 + 38.1051i 1.03365 + 1.79033i
454454 0 0
455455 0 0
456456 0 0
457457 12.5000 + 21.6506i 0.584725 + 1.01277i 0.994910 + 0.100771i 0.0321310π0.0321310\pi
−0.410184 + 0.912003i 0.634536π0.634536\pi
458458 0 0
459459 6.00000 10.3923i 0.280056 0.485071i
460460 0 0
461461 10.5000 18.1865i 0.489034 0.847031i −0.510887 0.859648i 0.670683π-0.670683\pi
0.999920 + 0.0126168i 0.00401615π0.00401615\pi
462462 0 0
463463 20.0000 0.929479 0.464739 0.885448i 0.346148π-0.346148\pi
0.464739 + 0.885448i 0.346148π0.346148\pi
464464 0 0
465465 −2.00000 3.46410i −0.0927478 0.160644i
466466 0 0
467467 24.0000 1.11059 0.555294 0.831654i 0.312606π-0.312606\pi
0.555294 + 0.831654i 0.312606π0.312606\pi
468468 0 0
469469 0 0
470470 0 0
471471 5.00000 + 8.66025i 0.230388 + 0.399043i
472472 0 0
473473 −16.0000 −0.735681
474474 0 0
475475 −4.00000 + 6.92820i −0.183533 + 0.317888i
476476 0 0
477477 6.50000 11.2583i 0.297615 0.515484i
478478 0 0
479479 3.00000 + 5.19615i 0.137073 + 0.237418i 0.926388 0.376571i 0.122897π-0.122897\pi
−0.789314 + 0.613990i 0.789564π0.789564\pi
480480 0 0
481481 −17.5000 4.33013i −0.797931 0.197437i
482482 0 0
483483 0 0
484484 0 0
485485 −1.00000 + 1.73205i −0.0454077 + 0.0786484i
486486 0 0
487487 16.0000 27.7128i 0.725029 1.25579i −0.233933 0.972253i 0.575160π-0.575160\pi
0.958962 0.283535i 0.0915071π-0.0915071\pi
488488 0 0
489489 32.0000 1.44709
490490 0 0
491491 8.00000 + 13.8564i 0.361035 + 0.625331i 0.988131 0.153611i 0.0490902π-0.0490902\pi
−0.627096 + 0.778942i 0.715757π0.715757\pi
492492 0 0
493493 −15.0000 −0.675566
494494 0 0
495495 −4.00000 −0.179787
496496 0 0
497497 0 0
498498 0 0
499499 −14.0000 −0.626726 −0.313363 0.949633i 0.601456π-0.601456\pi
−0.313363 + 0.949633i 0.601456π0.601456\pi
500500 0 0
501501 −4.00000 + 6.92820i −0.178707 + 0.309529i
502502 0 0
503503 −14.0000 + 24.2487i −0.624229 + 1.08120i 0.364460 + 0.931219i 0.381254π0.381254\pi
−0.988689 + 0.149978i 0.952080π0.952080\pi
504504 0 0
505505 5.50000 + 9.52628i 0.244747 + 0.423914i
506506 0 0
507507 −22.0000 + 13.8564i −0.977054 + 0.615385i
508508 0 0
509509 −1.50000 2.59808i −0.0664863 0.115158i 0.830866 0.556473i 0.187846π-0.187846\pi
−0.897352 + 0.441315i 0.854512π0.854512\pi
510510 0 0
511511 0 0
512512 0 0
513513 −4.00000 + 6.92820i −0.176604 + 0.305888i
514514 0 0
515515 14.0000 0.616914
516516 0 0
517517 12.0000 + 20.7846i 0.527759 + 0.914106i
518518 0 0
519519 4.00000 0.175581
520520 0 0
521521 −25.0000 −1.09527 −0.547635 0.836717i 0.684472π-0.684472\pi
−0.547635 + 0.836717i 0.684472π0.684472\pi
522522 0 0
523523 −8.00000 13.8564i −0.349816 0.605898i 0.636401 0.771358i 0.280422π-0.280422\pi
−0.986216 + 0.165460i 0.947089π0.947089\pi
524524 0 0
525525 0 0
526526 0 0
527527 3.00000 5.19615i 0.130682 0.226348i
528528 0 0
529529 9.50000 16.4545i 0.413043 0.715412i
530530 0 0
531531 −6.00000 10.3923i −0.260378 0.450988i
532532 0 0
533533 10.5000 + 2.59808i 0.454805 + 0.112535i
534534 0 0
535535 3.00000 + 5.19615i 0.129701 + 0.224649i
536536 0 0
537537 −16.0000 + 27.7128i −0.690451 + 1.19590i
538538 0 0
539539 14.0000 24.2487i 0.603023 1.04447i
540540 0 0
541541 23.0000 0.988847 0.494424 0.869221i 0.335379π-0.335379\pi
0.494424 + 0.869221i 0.335379π0.335379\pi
542542 0 0
543543 5.00000 + 8.66025i 0.214571 + 0.371647i
544544 0 0
545545 −10.0000 −0.428353
546546 0 0
547547 22.0000 0.940652 0.470326 0.882493i 0.344136π-0.344136\pi
0.470326 + 0.882493i 0.344136π0.344136\pi
548548 0 0
549549 −3.50000 6.06218i −0.149376 0.258727i
550550 0 0
551551 10.0000 0.426014
552552 0 0
553553 0 0
554554 0 0
555555 −5.00000 + 8.66025i −0.212238 + 0.367607i
556556 0 0
557557 −11.5000 19.9186i −0.487271 0.843978i 0.512622 0.858614i 0.328674π-0.328674\pi
−0.999893 + 0.0146368i 0.995341π0.995341\pi
558558 0 0
559559 4.00000 + 13.8564i 0.169182 + 0.586064i
560560 0 0
561561 −12.0000 20.7846i −0.506640 0.877527i
562562 0 0
563563 −12.0000 + 20.7846i −0.505740 + 0.875967i 0.494238 + 0.869326i 0.335447π0.335447\pi
−0.999978 + 0.00664037i 0.997886π0.997886\pi
564564 0 0
565565 −4.50000 + 7.79423i −0.189316 + 0.327906i
566566 0 0
567567 0 0
568568 0 0
569569 −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i 0.206806π-0.206806\pi
−0.922032 + 0.387113i 0.873472π0.873472\pi
570570 0 0
571571 −20.0000 −0.836974 −0.418487 0.908223i 0.637439π-0.637439\pi
−0.418487 + 0.908223i 0.637439π0.637439\pi
572572 0 0
573573 −12.0000 −0.501307
574574 0 0
575575 −4.00000 6.92820i −0.166812 0.288926i
576576 0 0
577577 −29.0000 −1.20729 −0.603643 0.797255i 0.706285π-0.706285\pi
−0.603643 + 0.797255i 0.706285π0.706285\pi
578578 0 0
579579 21.0000 36.3731i 0.872730 1.51161i
580580 0 0
581581 0 0
582582 0 0
583583 26.0000 + 45.0333i 1.07681 + 1.86509i
584584 0 0
585585 1.00000 + 3.46410i 0.0413449 + 0.143223i
586586 0 0
587587 −8.00000 13.8564i −0.330195 0.571915i 0.652355 0.757914i 0.273781π-0.273781\pi
−0.982550 + 0.185999i 0.940448π0.940448\pi
588588 0 0
589589 −2.00000 + 3.46410i −0.0824086 + 0.142736i
590590 0 0
591591 −18.0000 + 31.1769i −0.740421 + 1.28245i
592592 0 0
593593 −1.00000 −0.0410651 −0.0205325 0.999789i 0.506536π-0.506536\pi
−0.0205325 + 0.999789i 0.506536π0.506536\pi
594594 0 0
595595 0 0
596596 0 0
597597 28.0000 1.14596
598598 0 0
599599 30.0000 1.22577 0.612883 0.790173i 0.290010π-0.290010\pi
0.612883 + 0.790173i 0.290010π0.290010\pi
600600 0 0
601601 4.50000 + 7.79423i 0.183559 + 0.317933i 0.943090 0.332538i 0.107905π-0.107905\pi
−0.759531 + 0.650471i 0.774572π0.774572\pi
602602 0 0
603603 −14.0000 −0.570124
604604 0 0
605605 2.50000 4.33013i 0.101639 0.176045i
606606 0 0
607607 −17.0000 + 29.4449i −0.690009 + 1.19513i 0.281826 + 0.959466i 0.409060π0.409060\pi
−0.971834 + 0.235665i 0.924273π0.924273\pi
608608 0 0
609609 0 0
610610 0 0
611611 15.0000 15.5885i 0.606835 0.630641i
612612 0 0
613613 0.500000 + 0.866025i 0.0201948 + 0.0349784i 0.875946 0.482409i 0.160238π-0.160238\pi
−0.855751 + 0.517387i 0.826905π0.826905\pi
614614 0 0
615615 3.00000 5.19615i 0.120972 0.209529i
616616 0 0
617617 18.5000 32.0429i 0.744782 1.29000i −0.205515 0.978654i 0.565887π-0.565887\pi
0.950297 0.311346i 0.100780π-0.100780\pi
618618 0 0
619619 −36.0000 −1.44696 −0.723481 0.690344i 0.757459π-0.757459\pi
−0.723481 + 0.690344i 0.757459π0.757459\pi
620620 0 0
621621 −4.00000 6.92820i −0.160514 0.278019i
622622 0 0
623623 0 0
624624 0 0
625625 11.0000 0.440000
626626 0 0
627627 8.00000 + 13.8564i 0.319489 + 0.553372i
628628 0 0
629629 −15.0000 −0.598089
630630 0 0
631631 10.0000 17.3205i 0.398094 0.689519i −0.595397 0.803432i 0.703005π-0.703005\pi
0.993491 + 0.113913i 0.0363385π0.0363385\pi
632632 0 0
633633 −18.0000 + 31.1769i −0.715436 + 1.23917i
634634 0 0
635635 11.0000 + 19.0526i 0.436522 + 0.756078i
636636 0 0
637637 −24.5000 6.06218i −0.970725 0.240192i
638638 0 0
639639 3.00000 + 5.19615i 0.118678 + 0.205557i
640640 0 0
641641 8.50000 14.7224i 0.335730 0.581501i −0.647895 0.761730i 0.724350π-0.724350\pi
0.983625 + 0.180229i 0.0576838π0.0576838\pi
642642 0 0
643643 2.00000 3.46410i 0.0788723 0.136611i −0.823891 0.566748i 0.808201π-0.808201\pi
0.902764 + 0.430137i 0.141535π0.141535\pi
644644 0 0
645645 8.00000 0.315000
646646 0 0
647647 19.0000 + 32.9090i 0.746967 + 1.29378i 0.949270 + 0.314462i 0.101824π0.101824\pi
−0.202303 + 0.979323i 0.564843π0.564843\pi
648648 0 0
649649 48.0000 1.88416
650650 0 0
651651 0 0
652652 0 0
653653 7.00000 + 12.1244i 0.273931 + 0.474463i 0.969865 0.243643i 0.0783426π-0.0783426\pi
−0.695934 + 0.718106i 0.745009π0.745009\pi
654654 0 0
655655 18.0000 0.703318
656656 0 0
657657 −3.50000 + 6.06218i −0.136548 + 0.236508i
658658 0 0
659659 −14.0000 + 24.2487i −0.545363 + 0.944596i 0.453221 + 0.891398i 0.350275π0.350275\pi
−0.998584 + 0.0531977i 0.983059π0.983059\pi
660660 0 0
661661 6.50000 + 11.2583i 0.252821 + 0.437898i 0.964301 0.264807i 0.0853084π-0.0853084\pi
−0.711481 + 0.702706i 0.751975π0.751975\pi
662662 0 0
663663 −15.0000 + 15.5885i −0.582552 + 0.605406i
664664 0 0
665665 0 0
666666 0 0
667667 −5.00000 + 8.66025i −0.193601 + 0.335326i
668668 0 0
669669 18.0000 31.1769i 0.695920 1.20537i
670670 0 0
671671 28.0000 1.08093
672672 0 0
673673 2.50000 + 4.33013i 0.0963679 + 0.166914i 0.910179 0.414216i 0.135944π-0.135944\pi
−0.813811 + 0.581130i 0.802611π0.802611\pi
674674 0 0
675675 16.0000 0.615840
676676 0 0
677677 −26.0000 −0.999261 −0.499631 0.866239i 0.666531π-0.666531\pi
−0.499631 + 0.866239i 0.666531π0.666531\pi
678678 0 0
679679 0 0
680680 0 0
681681 36.0000 1.37952
682682 0 0
683683 19.0000 32.9090i 0.727015 1.25923i −0.231125 0.972924i 0.574240π-0.574240\pi
0.958139 0.286302i 0.0924262π-0.0924262\pi
684684 0 0
685685 −0.500000 + 0.866025i −0.0191040 + 0.0330891i
686686 0 0
687687 −18.0000 31.1769i −0.686743 1.18947i
688688 0 0
689689 32.5000 33.7750i 1.23815 1.28672i
690690 0 0
691691 −10.0000 17.3205i −0.380418 0.658903i 0.610704 0.791859i 0.290887π-0.290887\pi
−0.991122 + 0.132956i 0.957553π0.957553\pi
692692 0 0
693693 0 0
694694 0 0
695695 −8.00000 + 13.8564i −0.303457 + 0.525603i
696696 0 0
697697 9.00000 0.340899
698698 0 0
699699 −6.00000 10.3923i −0.226941 0.393073i
700700 0 0
701701 10.0000 0.377695 0.188847 0.982006i 0.439525π-0.439525\pi
0.188847 + 0.982006i 0.439525π0.439525\pi
702702 0 0
703703 10.0000 0.377157
704704 0 0
705705 −6.00000 10.3923i −0.225973 0.391397i
706706 0 0
707707 0 0
708708 0 0
709709 10.5000 18.1865i 0.394336 0.683010i −0.598680 0.800988i 0.704308π-0.704308\pi
0.993016 + 0.117978i 0.0376414π0.0376414\pi
710710 0 0
711711 4.00000 6.92820i 0.150012 0.259828i
712712 0 0
713713 −2.00000 3.46410i −0.0749006 0.129732i
714714 0 0
715715 −14.0000 3.46410i −0.523570 0.129550i
716716 0 0
717717 −12.0000 20.7846i −0.448148 0.776215i
718718 0 0
719719 −24.0000 + 41.5692i −0.895049 + 1.55027i −0.0613050 + 0.998119i 0.519526π0.519526\pi
−0.833744 + 0.552151i 0.813807π0.813807\pi
720720 0 0
721721 0 0
722722 0 0
723723 14.0000 0.520666
724724 0 0
725725 −10.0000 17.3205i −0.371391 0.643268i
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 13.0000 0.481481
730730 0 0
731731 6.00000 + 10.3923i 0.221918 + 0.384373i
732732 0 0
733733 −1.00000 −0.0369358 −0.0184679 0.999829i 0.505879π-0.505879\pi
−0.0184679 + 0.999829i 0.505879π0.505879\pi
734734 0 0
735735 −7.00000 + 12.1244i −0.258199 + 0.447214i
736736 0 0
737737 28.0000 48.4974i 1.03139 1.78643i
738738 0 0
739739 −10.0000 17.3205i −0.367856 0.637145i 0.621374 0.783514i 0.286575π-0.286575\pi
−0.989230 + 0.146369i 0.953241π0.953241\pi
740740 0 0
741741 10.0000 10.3923i 0.367359 0.381771i
742742 0 0
743743 −24.0000 41.5692i −0.880475 1.52503i −0.850814 0.525467i 0.823891π-0.823891\pi
−0.0296605 0.999560i 0.509443π-0.509443\pi
744744 0 0
745745 −10.5000 + 18.1865i −0.384690 + 0.666303i
746746 0 0
747747 −2.00000 + 3.46410i −0.0731762 + 0.126745i
748748 0 0
749749 0 0
750750 0 0
751751 −10.0000 17.3205i −0.364905 0.632034i 0.623856 0.781540i 0.285565π-0.285565\pi
−0.988761 + 0.149505i 0.952232π0.952232\pi
752752 0 0
753753 −44.0000 −1.60345
754754 0 0
755755 22.0000 0.800662
756756 0 0
757757 19.0000 + 32.9090i 0.690567 + 1.19610i 0.971652 + 0.236414i 0.0759722π0.0759722\pi
−0.281086 + 0.959683i 0.590695π0.590695\pi
758758 0 0
759759 −16.0000 −0.580763
760760 0 0
761761 −19.0000 + 32.9090i −0.688749 + 1.19295i 0.283493 + 0.958974i 0.408507π0.408507\pi
−0.972243 + 0.233975i 0.924827π0.924827\pi
762762 0 0
763763 0 0
764764 0 0
765765 1.50000 + 2.59808i 0.0542326 + 0.0939336i
766766 0 0
767767 −12.0000 41.5692i −0.433295 1.50098i
768768 0 0
769769 −19.0000 32.9090i −0.685158 1.18673i −0.973387 0.229166i 0.926400π-0.926400\pi
0.288230 0.957561i 0.406933π-0.406933\pi
770770 0 0
771771 −11.0000 + 19.0526i −0.396155 + 0.686161i
772772 0 0
773773 −3.00000 + 5.19615i −0.107903 + 0.186893i −0.914920 0.403634i 0.867747π-0.867747\pi
0.807018 + 0.590527i 0.201080π0.201080\pi
774774 0 0
775775 8.00000 0.287368
776776 0 0
777777 0 0
778778 0 0
779779 −6.00000 −0.214972
780780 0 0
781781 −24.0000 −0.858788
782782 0 0
783783 −10.0000 17.3205i −0.357371 0.618984i
784784 0 0
785785 5.00000 0.178458
786786 0 0
787787 −11.0000 + 19.0526i −0.392108 + 0.679150i −0.992727 0.120384i 0.961587π-0.961587\pi
0.600620 + 0.799535i 0.294921π0.294921\pi
788788 0 0
789789 24.0000 41.5692i 0.854423 1.47990i
790790 0 0
791791 0 0
792792 0 0
793793 −7.00000 24.2487i −0.248577 0.861097i
794794 0 0
795795 −13.0000 22.5167i −0.461062 0.798584i
796796 0 0
797797 15.0000 25.9808i 0.531327 0.920286i −0.468004 0.883726i 0.655027π-0.655027\pi
0.999331 0.0365596i 0.0116399π-0.0116399\pi
798798 0 0
799799 9.00000 15.5885i 0.318397 0.551480i
800800 0 0
801801 14.0000 0.494666
802802 0 0
803803 −14.0000 24.2487i −0.494049 0.855718i
804804 0 0
805805 0 0
806806 0 0
807807 −28.0000 −0.985647
808808 0 0
809809 12.5000 + 21.6506i 0.439477 + 0.761196i 0.997649 0.0685291i 0.0218306π-0.0218306\pi
−0.558173 + 0.829725i 0.688497π0.688497\pi
810810 0 0
811811 −2.00000 −0.0702295 −0.0351147 0.999383i 0.511180π-0.511180\pi
−0.0351147 + 0.999383i 0.511180π0.511180\pi
812812 0 0
813813 12.0000 20.7846i 0.420858 0.728948i
814814 0 0
815815 8.00000 13.8564i 0.280228 0.485369i
816816 0 0
817817 −4.00000 6.92820i −0.139942 0.242387i
818818 0 0
819819 0 0
820820 0 0
821821 15.0000 + 25.9808i 0.523504 + 0.906735i 0.999626 + 0.0273557i 0.00870868π0.00870868\pi
−0.476122 + 0.879379i 0.657958π0.657958\pi
822822 0 0
823823 26.0000 45.0333i 0.906303 1.56976i 0.0871445 0.996196i 0.472226π-0.472226\pi
0.819159 0.573567i 0.194441π-0.194441\pi
824824 0 0
825825 16.0000 27.7128i 0.557048 0.964836i
826826 0 0
827827 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
828828 0 0
829829 −15.5000 26.8468i −0.538337 0.932427i −0.998994 0.0448490i 0.985719π-0.985719\pi
0.460657 0.887578i 0.347614π-0.347614\pi
830830 0 0
831831 −2.00000 −0.0693792
832832 0 0
833833 −21.0000 −0.727607
834834 0 0
835835 2.00000 + 3.46410i 0.0692129 + 0.119880i
836836 0 0
837837 8.00000 0.276520
838838 0 0
839839 −13.0000 + 22.5167i −0.448810 + 0.777361i −0.998309 0.0581329i 0.981485π-0.981485\pi
0.549499 + 0.835494i 0.314819π0.314819\pi
840840 0 0
841841 2.00000 3.46410i 0.0689655 0.119452i
842842 0 0
843843 21.0000 + 36.3731i 0.723278 + 1.25275i
844844 0 0
845845 0.500000 + 12.9904i 0.0172005 + 0.446883i
846846 0 0
847847 0 0
848848 0 0
849849 20.0000 34.6410i 0.686398 1.18888i
850850 0 0
851851 −5.00000 + 8.66025i −0.171398 + 0.296870i
852852 0 0
853853 39.0000 1.33533 0.667667 0.744460i 0.267293π-0.267293\pi
0.667667 + 0.744460i 0.267293π0.267293\pi
854854 0 0
855855 −1.00000 1.73205i −0.0341993 0.0592349i
856856 0 0
857857 −21.0000 −0.717346 −0.358673 0.933463i 0.616771π-0.616771\pi
−0.358673 + 0.933463i 0.616771π0.616771\pi
858858 0 0
859859 50.0000 1.70598 0.852989 0.521929i 0.174787π-0.174787\pi
0.852989 + 0.521929i 0.174787π0.174787\pi
860860 0 0
861861 0 0
862862 0 0
863863 −24.0000 −0.816970 −0.408485 0.912765i 0.633943π-0.633943\pi
−0.408485 + 0.912765i 0.633943π0.633943\pi
864864 0 0
865865 1.00000 1.73205i 0.0340010 0.0588915i
866866 0 0
867867 8.00000 13.8564i 0.271694 0.470588i
868868 0 0
869869 16.0000 + 27.7128i 0.542763 + 0.940093i
870870 0 0
871871 −49.0000 12.1244i −1.66030 0.410818i
872872 0 0
873873 1.00000 + 1.73205i 0.0338449 + 0.0586210i
874874 0 0
875875 0 0
876876 0 0
877877 20.5000 35.5070i 0.692236 1.19899i −0.278868 0.960329i 0.589959π-0.589959\pi
0.971104 0.238658i 0.0767075π-0.0767075\pi
878878 0 0
879879 38.0000 1.28171
880880 0 0
881881 14.5000 + 25.1147i 0.488517 + 0.846137i 0.999913 0.0132086i 0.00420455π-0.00420455\pi
−0.511395 + 0.859346i 0.670871π0.670871\pi
882882 0 0
883883 −58.0000 −1.95186 −0.975928 0.218094i 0.930016π-0.930016\pi
−0.975928 + 0.218094i 0.930016π0.930016\pi
884884 0 0
885885 −24.0000 −0.806751
886886 0 0
887887 −28.0000 48.4974i −0.940148 1.62838i −0.765186 0.643809i 0.777353π-0.777353\pi
−0.174962 0.984575i 0.555980π-0.555980\pi
888888 0 0
889889 0 0
890890 0 0
891891 22.0000 38.1051i 0.737028 1.27657i
892892 0 0
893893 −6.00000 + 10.3923i −0.200782 + 0.347765i
894894 0 0
895895 8.00000 + 13.8564i 0.267411 + 0.463169i
896896 0 0
897897 4.00000 + 13.8564i 0.133556 + 0.462652i
898898 0 0
899899 −5.00000 8.66025i −0.166759 0.288836i
900900 0 0
901901 19.5000 33.7750i 0.649639 1.12521i
902902 0 0
903903 0 0
904904 0 0
905905 5.00000 0.166206
906906 0 0
907907 8.00000 + 13.8564i 0.265636 + 0.460094i 0.967730 0.251990i 0.0810849π-0.0810849\pi
−0.702094 + 0.712084i 0.747752π0.747752\pi
908908 0 0
909909 11.0000 0.364847
910910 0 0
911911 32.0000 1.06021 0.530104 0.847933i 0.322153π-0.322153\pi
0.530104 + 0.847933i 0.322153π0.322153\pi
912912 0 0
913913 −8.00000 13.8564i −0.264761 0.458580i
914914 0 0
915915 −14.0000 −0.462826
916916 0 0
917917 0 0
918918 0 0
919919 −15.0000 + 25.9808i −0.494804 + 0.857026i −0.999982 0.00598907i 0.998094π-0.998094\pi
0.505178 + 0.863015i 0.331427π0.331427\pi
920920 0 0
921921 −26.0000 45.0333i −0.856729 1.48390i
922922 0 0
923923 6.00000 + 20.7846i 0.197492 + 0.684134i
924924 0 0
925925 −10.0000 17.3205i −0.328798 0.569495i
926926 0 0
927927 7.00000 12.1244i 0.229910 0.398216i
928928 0 0
929929 −1.50000 + 2.59808i −0.0492134 + 0.0852401i −0.889583 0.456774i 0.849005π-0.849005\pi
0.840369 + 0.542014i 0.182338π0.182338\pi
930930 0 0
931931 14.0000 0.458831
932932 0 0
933933 10.0000 + 17.3205i 0.327385 + 0.567048i
934934 0 0
935935 −12.0000 −0.392442
936936 0 0
937937 55.0000 1.79677 0.898386 0.439207i 0.144741π-0.144741\pi
0.898386 + 0.439207i 0.144741π0.144741\pi
938938 0 0
939939 34.0000 + 58.8897i 1.10955 + 1.92179i
940940 0 0
941941 46.0000 1.49956 0.749779 0.661689i 0.230160π-0.230160\pi
0.749779 + 0.661689i 0.230160π0.230160\pi
942942 0 0
943943 3.00000 5.19615i 0.0976934 0.169210i
944944 0 0
945945 0 0
946946 0 0
947947 19.0000 + 32.9090i 0.617417 + 1.06940i 0.989955 + 0.141381i 0.0451542π0.0451542\pi
−0.372538 + 0.928017i 0.621512π0.621512\pi
948948 0 0
949949 −17.5000 + 18.1865i −0.568074 + 0.590360i
950950 0 0
951951 −3.00000 5.19615i −0.0972817 0.168497i
952952 0 0
953953 −21.0000 + 36.3731i −0.680257 + 1.17824i 0.294646 + 0.955607i 0.404798π0.404798\pi
−0.974902 + 0.222633i 0.928535π0.928535\pi
954954 0 0
955955 −3.00000 + 5.19615i −0.0970777 + 0.168144i
956956 0 0
957957 −40.0000 −1.29302
958958 0 0
959959 0 0
960960 0 0
961961 −27.0000 −0.870968
962962 0 0
963963 6.00000 0.193347
964964 0 0
965965 −10.5000 18.1865i −0.338007 0.585445i
966966 0 0
967967 38.0000 1.22200 0.610999 0.791632i 0.290768π-0.290768\pi
0.610999 + 0.791632i 0.290768π0.290768\pi
968968 0 0
969969 6.00000 10.3923i 0.192748 0.333849i
970970 0 0
971971 −9.00000 + 15.5885i −0.288824 + 0.500257i −0.973529 0.228562i 0.926597π-0.926597\pi
0.684706 + 0.728820i 0.259931π0.259931\pi
972972 0 0
973973 0 0
974974 0 0
975975 −28.0000 6.92820i −0.896718 0.221880i
976976 0 0
977977 8.50000 + 14.7224i 0.271939 + 0.471012i 0.969358 0.245651i 0.0790017π-0.0790017\pi
−0.697419 + 0.716663i 0.745668π0.745668\pi
978978 0 0
979979 −28.0000 + 48.4974i −0.894884 + 1.54998i
980980 0 0
981981 −5.00000 + 8.66025i −0.159638 + 0.276501i
982982 0 0
983983 −18.0000 −0.574111 −0.287055 0.957914i 0.592676π-0.592676\pi
−0.287055 + 0.957914i 0.592676π0.592676\pi
984984 0 0
985985 9.00000 + 15.5885i 0.286764 + 0.496690i
986986 0 0
987987 0 0
988988 0 0
989989 8.00000 0.254385
990990 0 0
991991 −1.00000 1.73205i −0.0317660 0.0550204i 0.849705 0.527258i 0.176780π-0.176780\pi
−0.881471 + 0.472237i 0.843446π0.843446\pi
992992 0 0
993993 −16.0000 −0.507745
994994 0 0
995995 7.00000 12.1244i 0.221915 0.384368i
996996 0 0
997997 −27.5000 + 47.6314i −0.870934 + 1.50850i −0.00990158 + 0.999951i 0.503152π0.503152\pi
−0.861032 + 0.508551i 0.830182π0.830182\pi
998998 0 0
999999 −10.0000 17.3205i −0.316386 0.547997i
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 832.2.i.b.705.1 2
4.3 odd 2 832.2.i.h.705.1 2
8.3 odd 2 416.2.i.a.289.1 2
8.5 even 2 416.2.i.b.289.1 yes 2
13.9 even 3 inner 832.2.i.b.321.1 2
52.35 odd 6 832.2.i.h.321.1 2
104.3 odd 6 5408.2.a.k.1.1 1
104.29 even 6 5408.2.a.d.1.1 1
104.35 odd 6 416.2.i.a.321.1 yes 2
104.61 even 6 416.2.i.b.321.1 yes 2
104.75 odd 6 5408.2.a.j.1.1 1
104.101 even 6 5408.2.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
416.2.i.a.289.1 2 8.3 odd 2
416.2.i.a.321.1 yes 2 104.35 odd 6
416.2.i.b.289.1 yes 2 8.5 even 2
416.2.i.b.321.1 yes 2 104.61 even 6
832.2.i.b.321.1 2 13.9 even 3 inner
832.2.i.b.705.1 2 1.1 even 1 trivial
832.2.i.h.321.1 2 52.35 odd 6
832.2.i.h.705.1 2 4.3 odd 2
5408.2.a.c.1.1 1 104.101 even 6
5408.2.a.d.1.1 1 104.29 even 6
5408.2.a.j.1.1 1 104.75 odd 6
5408.2.a.k.1.1 1 104.3 odd 6