Properties

Label 1530.2.d.g.919.4
Level 15301530
Weight 22
Character 1530.919
Analytic conductor 12.21712.217
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1530,2,Mod(919,1530)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1530, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1530.919");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1530=232517 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1530.d (of order 22, degree 11, 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: 12.217111509312.2171115093
Analytic rank: 00
Dimension: 66
Coefficient field: 6.0.5161984.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x64x3+25x220x+8 x^{6} - 4x^{3} + 25x^{2} - 20x + 8 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 170)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 919.4
Root 1.320011.32001i1.32001 - 1.32001i of defining polynomial
Character χ\chi == 1530.919
Dual form 1530.2.d.g.919.1

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+1.00000iq21.00000q4+(1.804871.32001i)q52.64002iq71.00000iq8+(1.320011.80487i)q102.00000q11+0.484862iq13+2.64002q14+1.00000q16+1.00000iq175.76491q19+(1.80487+1.32001i)q202.00000iq22+1.35998iq23+(1.51514+4.76491i)q250.484862q26+2.64002iq28+8.15516q292.09461q31+1.00000iq321.00000q34+(3.48486+4.76491i)q35+11.1396iq375.76491iq38+(1.32001+1.80487i)q40+0.249771q41+1.03028iq43+2.00000q441.35998q46+6.01468iq47+0.0302761q49+(4.76491+1.51514i)q500.484862iq52+7.70436iq53+(3.60975+2.64002i)q552.64002q56+8.15516iq58+8.73463q5911.3747q612.09461iq621.00000q64+(0.6400230.875115i)q65+4.96972iq671.00000iq68+(4.764913.48486i)q708.34438q71+0.484862iq7311.1396q74+5.76491q76+5.28005iq779.85952q79+(1.804871.32001i)q80+0.249771iq82+17.5298iq83+(1.320011.80487i)q851.03028q86+2.00000iq888.73463q89+1.28005q911.35998iq926.01468q94+(10.4049+7.60975i)q956.73463iq97+0.0302761iq98+O(q100)q+1.00000i q^{2} -1.00000 q^{4} +(-1.80487 - 1.32001i) q^{5} -2.64002i q^{7} -1.00000i q^{8} +(1.32001 - 1.80487i) q^{10} -2.00000 q^{11} +0.484862i q^{13} +2.64002 q^{14} +1.00000 q^{16} +1.00000i q^{17} -5.76491 q^{19} +(1.80487 + 1.32001i) q^{20} -2.00000i q^{22} +1.35998i q^{23} +(1.51514 + 4.76491i) q^{25} -0.484862 q^{26} +2.64002i q^{28} +8.15516 q^{29} -2.09461 q^{31} +1.00000i q^{32} -1.00000 q^{34} +(-3.48486 + 4.76491i) q^{35} +11.1396i q^{37} -5.76491i q^{38} +(-1.32001 + 1.80487i) q^{40} +0.249771 q^{41} +1.03028i q^{43} +2.00000 q^{44} -1.35998 q^{46} +6.01468i q^{47} +0.0302761 q^{49} +(-4.76491 + 1.51514i) q^{50} -0.484862i q^{52} +7.70436i q^{53} +(3.60975 + 2.64002i) q^{55} -2.64002 q^{56} +8.15516i q^{58} +8.73463 q^{59} -11.3747 q^{61} -2.09461i q^{62} -1.00000 q^{64} +(0.640023 - 0.875115i) q^{65} +4.96972i q^{67} -1.00000i q^{68} +(-4.76491 - 3.48486i) q^{70} -8.34438 q^{71} +0.484862i q^{73} -11.1396 q^{74} +5.76491 q^{76} +5.28005i q^{77} -9.85952 q^{79} +(-1.80487 - 1.32001i) q^{80} +0.249771i q^{82} +17.5298i q^{83} +(1.32001 - 1.80487i) q^{85} -1.03028 q^{86} +2.00000i q^{88} -8.73463 q^{89} +1.28005 q^{91} -1.35998i q^{92} -6.01468 q^{94} +(10.4049 + 7.60975i) q^{95} -6.73463i q^{97} +0.0302761i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q6q42q512q11+6q162q19+2q20+10q252q26+34q29+6q316q3420q3532q41+12q4424q46+2q49+4q50+4q55++14q95+O(q100) 6 q - 6 q^{4} - 2 q^{5} - 12 q^{11} + 6 q^{16} - 2 q^{19} + 2 q^{20} + 10 q^{25} - 2 q^{26} + 34 q^{29} + 6 q^{31} - 6 q^{34} - 20 q^{35} - 32 q^{41} + 12 q^{44} - 24 q^{46} + 2 q^{49} + 4 q^{50} + 4 q^{55}+ \cdots + 14 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1530Z)×\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times.

nn 307307 12611261 13611361
χ(n)\chi(n) 1-1 11 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 1.00000i 0.707107i
33 0 0
44 −1.00000 −0.500000
55 −1.80487 1.32001i −0.807164 0.590327i
66 0 0
77 2.64002i 0.997835i −0.866649 0.498918i 0.833731π-0.833731\pi
0.866649 0.498918i 0.166269π-0.166269\pi
88 1.00000i 0.353553i
99 0 0
1010 1.32001 1.80487i 0.417424 0.570751i
1111 −2.00000 −0.603023 −0.301511 0.953463i 0.597491π-0.597491\pi
−0.301511 + 0.953463i 0.597491π0.597491\pi
1212 0 0
1313 0.484862i 0.134477i 0.997737 + 0.0672383i 0.0214188π0.0214188\pi
−0.997737 + 0.0672383i 0.978581π0.978581\pi
1414 2.64002 0.705576
1515 0 0
1616 1.00000 0.250000
1717 1.00000i 0.242536i
1818 0 0
1919 −5.76491 −1.32256 −0.661280 0.750139i 0.729987π-0.729987\pi
−0.661280 + 0.750139i 0.729987π0.729987\pi
2020 1.80487 + 1.32001i 0.403582 + 0.295164i
2121 0 0
2222 2.00000i 0.426401i
2323 1.35998i 0.283575i 0.989897 + 0.141787i 0.0452849π0.0452849\pi
−0.989897 + 0.141787i 0.954715π0.954715\pi
2424 0 0
2525 1.51514 + 4.76491i 0.303028 + 0.952982i
2626 −0.484862 −0.0950893
2727 0 0
2828 2.64002i 0.498918i
2929 8.15516 1.51438 0.757188 0.653197i 0.226573π-0.226573\pi
0.757188 + 0.653197i 0.226573π0.226573\pi
3030 0 0
3131 −2.09461 −0.376203 −0.188101 0.982150i 0.560233π-0.560233\pi
−0.188101 + 0.982150i 0.560233π0.560233\pi
3232 1.00000i 0.176777i
3333 0 0
3434 −1.00000 −0.171499
3535 −3.48486 + 4.76491i −0.589049 + 0.805417i
3636 0 0
3737 11.1396i 1.83133i 0.401939 + 0.915667i 0.368337π0.368337\pi
−0.401939 + 0.915667i 0.631663π0.631663\pi
3838 5.76491i 0.935192i
3939 0 0
4040 −1.32001 + 1.80487i −0.208712 + 0.285376i
4141 0.249771 0.0390077 0.0195038 0.999810i 0.493791π-0.493791\pi
0.0195038 + 0.999810i 0.493791π0.493791\pi
4242 0 0
4343 1.03028i 0.157116i 0.996910 + 0.0785578i 0.0250315π0.0250315\pi
−0.996910 + 0.0785578i 0.974968π0.974968\pi
4444 2.00000 0.301511
4545 0 0
4646 −1.35998 −0.200518
4747 6.01468i 0.877331i 0.898650 + 0.438666i 0.144549π0.144549\pi
−0.898650 + 0.438666i 0.855451π0.855451\pi
4848 0 0
4949 0.0302761 0.00432516
5050 −4.76491 + 1.51514i −0.673860 + 0.214273i
5151 0 0
5252 0.484862i 0.0672383i
5353 7.70436i 1.05827i 0.848536 + 0.529137i 0.177484π0.177484\pi
−0.848536 + 0.529137i 0.822516π0.822516\pi
5454 0 0
5555 3.60975 + 2.64002i 0.486738 + 0.355981i
5656 −2.64002 −0.352788
5757 0 0
5858 8.15516i 1.07083i
5959 8.73463 1.13715 0.568576 0.822631i 0.307494π-0.307494\pi
0.568576 + 0.822631i 0.307494π0.307494\pi
6060 0 0
6161 −11.3747 −1.45638 −0.728188 0.685378i 0.759637π-0.759637\pi
−0.728188 + 0.685378i 0.759637π0.759637\pi
6262 2.09461i 0.266016i
6363 0 0
6464 −1.00000 −0.125000
6565 0.640023 0.875115i 0.0793851 0.108545i
6666 0 0
6767 4.96972i 0.607148i 0.952808 + 0.303574i 0.0981800π0.0981800\pi
−0.952808 + 0.303574i 0.901820π0.901820\pi
6868 1.00000i 0.121268i
6969 0 0
7070 −4.76491 3.48486i −0.569516 0.416521i
7171 −8.34438 −0.990296 −0.495148 0.868809i 0.664886π-0.664886\pi
−0.495148 + 0.868809i 0.664886π0.664886\pi
7272 0 0
7373 0.484862i 0.0567488i 0.999597 + 0.0283744i 0.00903306π0.00903306\pi
−0.999597 + 0.0283744i 0.990967π0.990967\pi
7474 −11.1396 −1.29495
7575 0 0
7676 5.76491 0.661280
7777 5.28005i 0.601717i
7878 0 0
7979 −9.85952 −1.10928 −0.554641 0.832090i 0.687144π-0.687144\pi
−0.554641 + 0.832090i 0.687144π0.687144\pi
8080 −1.80487 1.32001i −0.201791 0.147582i
8181 0 0
8282 0.249771i 0.0275826i
8383 17.5298i 1.92415i 0.272790 + 0.962074i 0.412054π0.412054\pi
−0.272790 + 0.962074i 0.587946π0.587946\pi
8484 0 0
8585 1.32001 1.80487i 0.143175 0.195766i
8686 −1.03028 −0.111098
8787 0 0
8888 2.00000i 0.213201i
8989 −8.73463 −0.925869 −0.462935 0.886392i 0.653204π-0.653204\pi
−0.462935 + 0.886392i 0.653204π0.653204\pi
9090 0 0
9191 1.28005 0.134185
9292 1.35998i 0.141787i
9393 0 0
9494 −6.01468 −0.620367
9595 10.4049 + 7.60975i 1.06752 + 0.780744i
9696 0 0
9797 6.73463i 0.683798i −0.939737 0.341899i 0.888930π-0.888930\pi
0.939737 0.341899i 0.111070π-0.111070\pi
9898 0.0302761i 0.00305835i
9999 0 0
100100 −1.51514 4.76491i −0.151514 0.476491i
101101 −13.5298 −1.34627 −0.673134 0.739521i 0.735052π-0.735052\pi
−0.673134 + 0.739521i 0.735052π0.735052\pi
102102 0 0
103103 11.2195i 1.10549i −0.833351 0.552745i 0.813580π-0.813580\pi
0.833351 0.552745i 0.186420π-0.186420\pi
104104 0.484862 0.0475446
105105 0 0
106106 −7.70436 −0.748313
107107 19.4693i 1.88216i −0.338177 0.941082i 0.609810π-0.609810\pi
0.338177 0.941082i 0.390190π-0.390190\pi
108108 0 0
109109 12.6547 1.21210 0.606050 0.795426i 0.292753π-0.292753\pi
0.606050 + 0.795426i 0.292753π0.292753\pi
110110 −2.64002 + 3.60975i −0.251716 + 0.344176i
111111 0 0
112112 2.64002i 0.249459i
113113 7.51514i 0.706965i −0.935441 0.353482i 0.884997π-0.884997\pi
0.935441 0.353482i 0.115003π-0.115003\pi
114114 0 0
115115 1.79518 2.45459i 0.167402 0.228891i
116116 −8.15516 −0.757188
117117 0 0
118118 8.73463i 0.804088i
119119 2.64002 0.242011
120120 0 0
121121 −7.00000 −0.636364
122122 11.3747i 1.02981i
123123 0 0
124124 2.09461 0.188101
125125 3.55510 10.6001i 0.317978 0.948098i
126126 0 0
127127 14.7952i 1.31286i 0.754387 + 0.656430i 0.227934π0.227934\pi
−0.754387 + 0.656430i 0.772066π0.772066\pi
128128 1.00000i 0.0883883i
129129 0 0
130130 0.875115 + 0.640023i 0.0767526 + 0.0561338i
131131 2.49954 0.218386 0.109193 0.994021i 0.465173π-0.465173\pi
0.109193 + 0.994021i 0.465173π0.465173\pi
132132 0 0
133133 15.2195i 1.31970i
134134 −4.96972 −0.429319
135135 0 0
136136 1.00000 0.0857493
137137 2.06055i 0.176045i 0.996118 + 0.0880224i 0.0280547π0.0280547\pi
−0.996118 + 0.0880224i 0.971945π0.971945\pi
138138 0 0
139139 15.5904 1.32236 0.661179 0.750228i 0.270056π-0.270056\pi
0.661179 + 0.750228i 0.270056π0.270056\pi
140140 3.48486 4.76491i 0.294525 0.402708i
141141 0 0
142142 8.34438i 0.700245i
143143 0.969724i 0.0810924i
144144 0 0
145145 −14.7190 10.7649i −1.22235 0.893977i
146146 −0.484862 −0.0401275
147147 0 0
148148 11.1396i 0.915667i
149149 10.0000 0.819232 0.409616 0.912258i 0.365663π-0.365663\pi
0.409616 + 0.912258i 0.365663π0.365663\pi
150150 0 0
151151 −15.8401 −1.28905 −0.644526 0.764582i 0.722945π-0.722945\pi
−0.644526 + 0.764582i 0.722945π0.722945\pi
152152 5.76491i 0.467596i
153153 0 0
154154 −5.28005 −0.425478
155155 3.78051 + 2.76491i 0.303657 + 0.222083i
156156 0 0
157157 1.34060i 0.106991i −0.998568 0.0534957i 0.982964π-0.982964\pi
0.998568 0.0534957i 0.0170364π-0.0170364\pi
158158 9.85952i 0.784381i
159159 0 0
160160 1.32001 1.80487i 0.104356 0.142688i
161161 3.59037 0.282961
162162 0 0
163163 16.2498i 1.27278i 0.771367 + 0.636390i 0.219573π0.219573\pi
−0.771367 + 0.636390i 0.780427π0.780427\pi
164164 −0.249771 −0.0195038
165165 0 0
166166 −17.5298 −1.36058
167167 2.95035i 0.228305i −0.993463 0.114152i 0.963585π-0.963585\pi
0.993463 0.114152i 0.0364152π-0.0364152\pi
168168 0 0
169169 12.7649 0.981916
170170 1.80487 + 1.32001i 0.138427 + 0.101240i
171171 0 0
172172 1.03028i 0.0785578i
173173 6.14048i 0.466852i 0.972375 + 0.233426i 0.0749937π0.0749937\pi
−0.972375 + 0.233426i 0.925006π0.925006\pi
174174 0 0
175175 12.5795 4.00000i 0.950919 0.302372i
176176 −2.00000 −0.150756
177177 0 0
178178 8.73463i 0.654688i
179179 −15.5904 −1.16528 −0.582639 0.812731i 0.697980π-0.697980\pi
−0.582639 + 0.812731i 0.697980π0.697980\pi
180180 0 0
181181 4.10929 0.305441 0.152721 0.988269i 0.451197π-0.451197\pi
0.152721 + 0.988269i 0.451197π0.451197\pi
182182 1.28005i 0.0948834i
183183 0 0
184184 1.35998 0.100259
185185 14.7044 20.1055i 1.08109 1.47819i
186186 0 0
187187 2.00000i 0.146254i
188188 6.01468i 0.438666i
189189 0 0
190190 −7.60975 + 10.4049i −0.552069 + 0.754853i
191191 −6.06055 −0.438526 −0.219263 0.975666i 0.570365π-0.570365\pi
−0.219263 + 0.975666i 0.570365π0.570365\pi
192192 0 0
193193 12.5601i 0.904095i 0.891994 + 0.452048i 0.149306π0.149306\pi
−0.891994 + 0.452048i 0.850694π0.850694\pi
194194 6.73463 0.483518
195195 0 0
196196 −0.0302761 −0.00216258
197197 26.0487i 1.85590i 0.372710 + 0.927948i 0.378429π0.378429\pi
−0.372710 + 0.927948i 0.621571π0.621571\pi
198198 0 0
199199 −3.37466 −0.239223 −0.119612 0.992821i 0.538165π-0.538165\pi
−0.119612 + 0.992821i 0.538165π0.538165\pi
200200 4.76491 1.51514i 0.336930 0.107136i
201201 0 0
202202 13.5298i 0.951955i
203203 21.5298i 1.51110i
204204 0 0
205205 −0.450805 0.329700i −0.0314856 0.0230273i
206206 11.2195 0.781699
207207 0 0
208208 0.484862i 0.0336191i
209209 11.5298 0.797534
210210 0 0
211211 18.0294 1.24119 0.620596 0.784130i 0.286891π-0.286891\pi
0.620596 + 0.784130i 0.286891π0.286891\pi
212212 7.70436i 0.529137i
213213 0 0
214214 19.4693 1.33089
215215 1.35998 1.85952i 0.0927496 0.126818i
216216 0 0
217217 5.52982i 0.375388i
218218 12.6547i 0.857085i
219219 0 0
220220 −3.60975 2.64002i −0.243369 0.177990i
221221 −0.484862 −0.0326153
222222 0 0
223223 23.2947i 1.55993i −0.625823 0.779965i 0.715237π-0.715237\pi
0.625823 0.779965i 0.284763π-0.284763\pi
224224 2.64002 0.176394
225225 0 0
226226 7.51514 0.499900
227227 17.4839i 1.16045i −0.814456 0.580225i 0.802965π-0.802965\pi
0.814456 0.580225i 0.197035π-0.197035\pi
228228 0 0
229229 −0.719953 −0.0475758 −0.0237879 0.999717i 0.507573π-0.507573\pi
−0.0237879 + 0.999717i 0.507573π0.507573\pi
230230 2.45459 + 1.79518i 0.161851 + 0.118371i
231231 0 0
232232 8.15516i 0.535413i
233233 11.0450i 0.723579i 0.932260 + 0.361790i 0.117834π0.117834\pi
−0.932260 + 0.361790i 0.882166π0.882166\pi
234234 0 0
235235 7.93945 10.8557i 0.517912 0.708150i
236236 −8.73463 −0.568576
237237 0 0
238238 2.64002i 0.171127i
239239 −5.59037 −0.361611 −0.180805 0.983519i 0.557870π-0.557870\pi
−0.180805 + 0.983519i 0.557870π0.557870\pi
240240 0 0
241241 −8.37088 −0.539215 −0.269608 0.962970i 0.586894π-0.586894\pi
−0.269608 + 0.962970i 0.586894π0.586894\pi
242242 7.00000i 0.449977i
243243 0 0
244244 11.3747 0.728188
245245 −0.0546445 0.0399648i −0.00349111 0.00255326i
246246 0 0
247247 2.79518i 0.177853i
248248 2.09461i 0.133008i
249249 0 0
250250 10.6001 + 3.55510i 0.670407 + 0.224844i
251251 −19.4693 −1.22889 −0.614445 0.788960i 0.710620π-0.710620\pi
−0.614445 + 0.788960i 0.710620π0.710620\pi
252252 0 0
253253 2.71995i 0.171002i
254254 −14.7952 −0.928332
255255 0 0
256256 1.00000 0.0625000
257257 13.9394i 0.869519i 0.900547 + 0.434759i 0.143167π0.143167\pi
−0.900547 + 0.434759i 0.856833π0.856833\pi
258258 0 0
259259 29.4087 1.82737
260260 −0.640023 + 0.875115i −0.0396926 + 0.0542723i
261261 0 0
262262 2.49954i 0.154422i
263263 16.2645i 1.00291i 0.865184 + 0.501454i 0.167202π0.167202\pi
−0.865184 + 0.501454i 0.832798π0.832798\pi
264264 0 0
265265 10.1698 13.9054i 0.624728 0.854201i
266266 −15.2195 −0.933167
267267 0 0
268268 4.96972i 0.303574i
269269 10.4049 0.634400 0.317200 0.948359i 0.397257π-0.397257\pi
0.317200 + 0.948359i 0.397257π0.397257\pi
270270 0 0
271271 −24.0294 −1.45968 −0.729840 0.683618i 0.760405π-0.760405\pi
−0.729840 + 0.683618i 0.760405π0.760405\pi
272272 1.00000i 0.0606339i
273273 0 0
274274 −2.06055 −0.124483
275275 −3.03028 9.52982i −0.182733 0.574670i
276276 0 0
277277 18.9503i 1.13862i −0.822124 0.569308i 0.807211π-0.807211\pi
0.822124 0.569308i 0.192789π-0.192789\pi
278278 15.5904i 0.935048i
279279 0 0
280280 4.76491 + 3.48486i 0.284758 + 0.208260i
281281 −19.6438 −1.17185 −0.585926 0.810365i 0.699269π-0.699269\pi
−0.585926 + 0.810365i 0.699269π0.699269\pi
282282 0 0
283283 25.7943i 1.53331i 0.642059 + 0.766655i 0.278080π0.278080\pi
−0.642059 + 0.766655i 0.721920π0.721920\pi
284284 8.34438 0.495148
285285 0 0
286286 0.969724 0.0573410
287287 0.659401i 0.0389232i
288288 0 0
289289 −1.00000 −0.0588235
290290 10.7649 14.7190i 0.632137 0.864332i
291291 0 0
292292 0.484862i 0.0283744i
293293 22.9239i 1.33923i 0.742710 + 0.669613i 0.233540π0.233540\pi
−0.742710 + 0.669613i 0.766460π0.766460\pi
294294 0 0
295295 −15.7649 11.5298i −0.917868 0.671292i
296296 11.1396 0.647474
297297 0 0
298298 10.0000i 0.579284i
299299 −0.659401 −0.0381341
300300 0 0
301301 2.71995 0.156775
302302 15.8401i 0.911498i
303303 0 0
304304 −5.76491 −0.330640
305305 20.5298 + 15.0147i 1.17553 + 0.859738i
306306 0 0
307307 10.4702i 0.597565i 0.954321 + 0.298782i 0.0965805π0.0965805\pi
−0.954321 + 0.298782i 0.903420π0.903420\pi
308308 5.28005i 0.300859i
309309 0 0
310310 −2.76491 + 3.78051i −0.157036 + 0.214718i
311311 9.73841 0.552215 0.276107 0.961127i 0.410955π-0.410955\pi
0.276107 + 0.961127i 0.410955π0.410955\pi
312312 0 0
313313 9.50046i 0.536998i 0.963280 + 0.268499i 0.0865275π0.0865275\pi
−0.963280 + 0.268499i 0.913472π0.913472\pi
314314 1.34060 0.0756544
315315 0 0
316316 9.85952 0.554641
317317 13.0790i 0.734591i 0.930104 + 0.367295i 0.119716π0.119716\pi
−0.930104 + 0.367295i 0.880284π0.880284\pi
318318 0 0
319319 −16.3103 −0.913203
320320 1.80487 + 1.32001i 0.100896 + 0.0737909i
321321 0 0
322322 3.59037i 0.200083i
323323 5.76491i 0.320768i
324324 0 0
325325 −2.31032 + 0.734633i −0.128154 + 0.0407501i
326326 −16.2498 −0.899992
327327 0 0
328328 0.249771i 0.0137913i
329329 15.8789 0.875432
330330 0 0
331331 24.8851 1.36781 0.683904 0.729572i 0.260281π-0.260281\pi
0.683904 + 0.729572i 0.260281π0.260281\pi
332332 17.5298i 0.962074i
333333 0 0
334334 2.95035 0.161436
335335 6.56009 8.96972i 0.358416 0.490068i
336336 0 0
337337 27.5445i 1.50044i −0.661186 0.750222i 0.729947π-0.729947\pi
0.661186 0.750222i 0.270053π-0.270053\pi
338338 12.7649i 0.694320i
339339 0 0
340340 −1.32001 + 1.80487i −0.0715877 + 0.0978830i
341341 4.18922 0.226859
342342 0 0
343343 18.5601i 1.00215i
344344 1.03028 0.0555488
345345 0 0
346346 −6.14048 −0.330114
347347 4.48486i 0.240760i 0.992728 + 0.120380i 0.0384113π0.0384113\pi
−0.992728 + 0.120380i 0.961589π0.961589\pi
348348 0 0
349349 −34.2186 −1.83168 −0.915839 0.401545i 0.868473π-0.868473\pi
−0.915839 + 0.401545i 0.868473π0.868473\pi
350350 4.00000 + 12.5795i 0.213809 + 0.672401i
351351 0 0
352352 2.00000i 0.106600i
353353 4.90917i 0.261289i 0.991429 + 0.130644i 0.0417046π0.0417046\pi
−0.991429 + 0.130644i 0.958295π0.958295\pi
354354 0 0
355355 15.0606 + 11.0147i 0.799331 + 0.584599i
356356 8.73463 0.462935
357357 0 0
358358 15.5904i 0.823977i
359359 −13.7796 −0.727259 −0.363629 0.931544i 0.618463π-0.618463\pi
−0.363629 + 0.931544i 0.618463π0.618463\pi
360360 0 0
361361 14.2342 0.749167
362362 4.10929i 0.215979i
363363 0 0
364364 −1.28005 −0.0670927
365365 0.640023 0.875115i 0.0335004 0.0458056i
366366 0 0
367367 4.39025i 0.229169i 0.993413 + 0.114585i 0.0365537π0.0365537\pi
−0.993413 + 0.114585i 0.963446π0.963446\pi
368368 1.35998i 0.0708937i
369369 0 0
370370 20.1055 + 14.7044i 1.04524 + 0.764443i
371371 20.3397 1.05598
372372 0 0
373373 0.220411i 0.0114125i 0.999984 + 0.00570623i 0.00181636π0.00181636\pi
−0.999984 + 0.00570623i 0.998184π0.998184\pi
374374 2.00000 0.103418
375375 0 0
376376 6.01468 0.310183
377377 3.95413i 0.203648i
378378 0 0
379379 −26.3103 −1.35147 −0.675735 0.737144i 0.736174π-0.736174\pi
−0.675735 + 0.737144i 0.736174π0.736174\pi
380380 −10.4049 7.60975i −0.533762 0.390372i
381381 0 0
382382 6.06055i 0.310085i
383383 36.1433i 1.84684i −0.383793 0.923419i 0.625382π-0.625382\pi
0.383793 0.923419i 0.374618π-0.374618\pi
384384 0 0
385385 6.96972 9.52982i 0.355210 0.485684i
386386 −12.5601 −0.639292
387387 0 0
388388 6.73463i 0.341899i
389389 3.77959 0.191633 0.0958164 0.995399i 0.469454π-0.469454\pi
0.0958164 + 0.995399i 0.469454π0.469454\pi
390390 0 0
391391 −1.35998 −0.0687770
392392 0.0302761i 0.00152917i
393393 0 0
394394 −26.0487 −1.31232
395395 17.7952 + 13.0147i 0.895373 + 0.654840i
396396 0 0
397397 12.2304i 0.613826i 0.951738 + 0.306913i 0.0992960π0.0992960\pi
−0.951738 + 0.306913i 0.900704π0.900704\pi
398398 3.37466i 0.169156i
399399 0 0
400400 1.51514 + 4.76491i 0.0757569 + 0.238245i
401401 11.7796 0.588245 0.294122 0.955768i 0.404973π-0.404973\pi
0.294122 + 0.955768i 0.404973π0.404973\pi
402402 0 0
403403 1.01560i 0.0505905i
404404 13.5298 0.673134
405405 0 0
406406 21.5298 1.06851
407407 22.2791i 1.10434i
408408 0 0
409409 15.7649 0.779525 0.389762 0.920916i 0.372557π-0.372557\pi
0.389762 + 0.920916i 0.372557π0.372557\pi
410410 0.329700 0.450805i 0.0162827 0.0222637i
411411 0 0
412412 11.2195i 0.552745i
413413 23.0596i 1.13469i
414414 0 0
415415 23.1396 31.6391i 1.13588 1.55310i
416416 −0.484862 −0.0237723
417417 0 0
418418 11.5298i 0.563942i
419419 18.1892 0.888601 0.444301 0.895878i 0.353452π-0.353452\pi
0.444301 + 0.895878i 0.353452π0.353452\pi
420420 0 0
421421 9.03028 0.440109 0.220054 0.975488i 0.429377π-0.429377\pi
0.220054 + 0.975488i 0.429377π0.429377\pi
422422 18.0294i 0.877655i
423423 0 0
424424 7.70436 0.374157
425425 −4.76491 + 1.51514i −0.231132 + 0.0734950i
426426 0 0
427427 30.0294i 1.45322i
428428 19.4693i 0.941082i
429429 0 0
430430 1.85952 + 1.35998i 0.0896739 + 0.0655839i
431431 −20.4196 −0.983578 −0.491789 0.870714i 0.663657π-0.663657\pi
−0.491789 + 0.870714i 0.663657π0.663657\pi
432432 0 0
433433 11.5904i 0.556998i −0.960437 0.278499i 0.910163π-0.910163\pi
0.960437 0.278499i 0.0898368π-0.0898368\pi
434434 −5.52982 −0.265440
435435 0 0
436436 −12.6547 −0.606050
437437 7.84014i 0.375045i
438438 0 0
439439 2.01938 0.0963796 0.0481898 0.998838i 0.484655π-0.484655\pi
0.0481898 + 0.998838i 0.484655π0.484655\pi
440440 2.64002 3.60975i 0.125858 0.172088i
441441 0 0
442442 0.484862i 0.0230625i
443443 27.4087i 1.30223i −0.758980 0.651114i 0.774302π-0.774302\pi
0.758980 0.651114i 0.225698π-0.225698\pi
444444 0 0
445445 15.7649 + 11.5298i 0.747328 + 0.546566i
446446 23.2947 1.10304
447447 0 0
448448 2.64002i 0.124729i
449449 29.7190 1.40253 0.701264 0.712902i 0.252619π-0.252619\pi
0.701264 + 0.712902i 0.252619π0.252619\pi
450450 0 0
451451 −0.499542 −0.0235225
452452 7.51514i 0.353482i
453453 0 0
454454 17.4839 0.820562
455455 −2.31032 1.68968i −0.108310 0.0792133i
456456 0 0
457457 39.4693i 1.84629i 0.384447 + 0.923147i 0.374392π0.374392\pi
−0.384447 + 0.923147i 0.625608π0.625608\pi
458458 0.719953i 0.0336412i
459459 0 0
460460 −1.79518 + 2.45459i −0.0837009 + 0.114446i
461461 −14.6888 −0.684124 −0.342062 0.939677i 0.611125π-0.611125\pi
−0.342062 + 0.939677i 0.611125π0.611125\pi
462462 0 0
463463 35.1055i 1.63149i −0.578411 0.815746i 0.696327π-0.696327\pi
0.578411 0.815746i 0.303673π-0.303673\pi
464464 8.15516 0.378594
465465 0 0
466466 −11.0450 −0.511648
467467 9.96881i 0.461301i 0.973037 + 0.230651i 0.0740855π0.0740855\pi
−0.973037 + 0.230651i 0.925915π0.925915\pi
468468 0 0
469469 13.1202 0.605834
470470 10.8557 + 7.93945i 0.500738 + 0.366219i
471471 0 0
472472 8.73463i 0.402044i
473473 2.06055i 0.0947443i
474474 0 0
475475 −8.73463 27.4693i −0.400772 1.26038i
476476 −2.64002 −0.121005
477477 0 0
478478 5.59037i 0.255698i
479479 −2.28383 −0.104351 −0.0521754 0.998638i 0.516615π-0.516615\pi
−0.0521754 + 0.998638i 0.516615π0.516615\pi
480480 0 0
481481 −5.40115 −0.246271
482482 8.37088i 0.381283i
483483 0 0
484484 7.00000 0.318182
485485 −8.88979 + 12.1552i −0.403665 + 0.551937i
486486 0 0
487487 10.8292i 0.490720i −0.969432 0.245360i 0.921094π-0.921094\pi
0.969432 0.245360i 0.0789061π-0.0789061\pi
488488 11.3747i 0.514906i
489489 0 0
490490 0.0399648 0.0546445i 0.00180543 0.00246859i
491491 −24.7952 −1.11899 −0.559496 0.828833i 0.689005π-0.689005\pi
−0.559496 + 0.828833i 0.689005π0.689005\pi
492492 0 0
493493 8.15516i 0.367290i
494494 2.79518 0.125761
495495 0 0
496496 −2.09461 −0.0940507
497497 22.0294i 0.988152i
498498 0 0
499499 −5.15138 −0.230607 −0.115304 0.993330i 0.536784π-0.536784\pi
−0.115304 + 0.993330i 0.536784π0.536784\pi
500500 −3.55510 + 10.6001i −0.158989 + 0.474049i
501501 0 0
502502 19.4693i 0.868956i
503503 29.0109i 1.29353i −0.762688 0.646766i 0.776121π-0.776121\pi
0.762688 0.646766i 0.223879π-0.223879\pi
504504 0 0
505505 24.4196 + 17.8595i 1.08666 + 0.794738i
506506 2.71995 0.120917
507507 0 0
508508 14.7952i 0.656430i
509509 −27.4693 −1.21755 −0.608777 0.793341i 0.708340π-0.708340\pi
−0.608777 + 0.793341i 0.708340π0.708340\pi
510510 0 0
511511 1.28005 0.0566259
512512 1.00000i 0.0441942i
513513 0 0
514514 −13.9394 −0.614843
515515 −14.8099 + 20.2498i −0.652601 + 0.892312i
516516 0 0
517517 12.0294i 0.529051i
518518 29.4087i 1.29214i
519519 0 0
520520 −0.875115 0.640023i −0.0383763 0.0280669i
521521 −5.68968 −0.249269 −0.124635 0.992203i 0.539776π-0.539776\pi
−0.124635 + 0.992203i 0.539776π0.539776\pi
522522 0 0
523523 7.52982i 0.329256i −0.986356 0.164628i 0.947358π-0.947358\pi
0.986356 0.164628i 0.0526424π-0.0526424\pi
524524 −2.49954 −0.109193
525525 0 0
526526 −16.2645 −0.709164
527527 2.09461i 0.0912426i
528528 0 0
529529 21.1505 0.919585
530530 13.9054 + 10.1698i 0.604012 + 0.441750i
531531 0 0
532532 15.2195i 0.659849i
533533 0.121104i 0.00524561i
534534 0 0
535535 −25.6997 + 35.1396i −1.11109 + 1.51922i
536536 4.96972 0.214659
537537 0 0
538538 10.4049i 0.448588i
539539 −0.0605522 −0.00260817
540540 0 0
541541 26.0100 1.11826 0.559128 0.829081i 0.311136π-0.311136\pi
0.559128 + 0.829081i 0.311136π0.311136\pi
542542 24.0294i 1.03215i
543543 0 0
544544 −1.00000 −0.0428746
545545 −22.8401 16.7044i −0.978364 0.715536i
546546 0 0
547547 11.5833i 0.495264i −0.968854 0.247632i 0.920348π-0.920348\pi
0.968854 0.247632i 0.0796524π-0.0796524\pi
548548 2.06055i 0.0880224i
549549 0 0
550550 9.52982 3.03028i 0.406353 0.129211i
551551 −47.0138 −2.00285
552552 0 0
553553 26.0294i 1.10688i
554554 18.9503 0.805123
555555 0 0
556556 −15.5904 −0.661179
557557 5.95413i 0.252284i −0.992012 0.126142i 0.959740π-0.959740\pi
0.992012 0.126142i 0.0402596π-0.0402596\pi
558558 0 0
559559 −0.499542 −0.0211284
560560 −3.48486 + 4.76491i −0.147262 + 0.201354i
561561 0 0
562562 19.6438i 0.828624i
563563 34.5289i 1.45522i −0.685991 0.727610i 0.740631π-0.740631\pi
0.685991 0.727610i 0.259369π-0.259369\pi
564564 0 0
565565 −9.92007 + 13.5639i −0.417340 + 0.570637i
566566 −25.7943 −1.08421
567567 0 0
568568 8.34438i 0.350122i
569569 12.7952 0.536402 0.268201 0.963363i 0.413571π-0.413571\pi
0.268201 + 0.963363i 0.413571π0.413571\pi
570570 0 0
571571 −4.22041 −0.176619 −0.0883094 0.996093i 0.528146π-0.528146\pi
−0.0883094 + 0.996093i 0.528146π0.528146\pi
572572 0.969724i 0.0405462i
573573 0 0
574574 0.659401 0.0275229
575575 −6.48016 + 2.06055i −0.270242 + 0.0859310i
576576 0 0
577577 35.5592i 1.48035i −0.672415 0.740174i 0.734743π-0.734743\pi
0.672415 0.740174i 0.265257π-0.265257\pi
578578 1.00000i 0.0415945i
579579 0 0
580580 14.7190 + 10.7649i 0.611175 + 0.446989i
581581 46.2791 1.91998
582582 0 0
583583 15.4087i 0.638164i
584584 0.484862 0.0200637
585585 0 0
586586 −22.9239 −0.946976
587587 43.6803i 1.80288i 0.432906 + 0.901439i 0.357488π0.357488\pi
−0.432906 + 0.901439i 0.642512π0.642512\pi
588588 0 0
589589 12.0752 0.497551
590590 11.5298 15.7649i 0.474675 0.649031i
591591 0 0
592592 11.1396i 0.457833i
593593 20.1505i 0.827480i 0.910395 + 0.413740i 0.135778π0.135778\pi
−0.910395 + 0.413740i 0.864222π0.864222\pi
594594 0 0
595595 −4.76491 3.48486i −0.195342 0.142865i
596596 −10.0000 −0.409616
597597 0 0
598598 0.659401i 0.0269649i
599599 33.4986 1.36872 0.684358 0.729146i 0.260082π-0.260082\pi
0.684358 + 0.729146i 0.260082π0.260082\pi
600600 0 0
601601 7.93945 0.323857 0.161928 0.986803i 0.448229π-0.448229\pi
0.161928 + 0.986803i 0.448229π0.448229\pi
602602 2.71995i 0.110857i
603603 0 0
604604 15.8401 0.644526
605605 12.6341 + 9.24008i 0.513650 + 0.375663i
606606 0 0
607607 38.9797i 1.58214i 0.611727 + 0.791069i 0.290475π0.290475\pi
−0.611727 + 0.791069i 0.709525π0.709525\pi
608608 5.76491i 0.233798i
609609 0 0
610610 −15.0147 + 20.5298i −0.607927 + 0.831228i
611611 −2.91629 −0.117980
612612 0 0
613613 28.5142i 1.15168i −0.817563 0.575839i 0.804675π-0.804675\pi
0.817563 0.575839i 0.195325π-0.195325\pi
614614 −10.4702 −0.422542
615615 0 0
616616 5.28005 0.212739
617617 1.07615i 0.0433241i 0.999765 + 0.0216621i 0.00689579π0.00689579\pi
−0.999765 + 0.0216621i 0.993104π0.993104\pi
618618 0 0
619619 0.719953 0.0289374 0.0144687 0.999895i 0.495394π-0.495394\pi
0.0144687 + 0.999895i 0.495394π0.495394\pi
620620 −3.78051 2.76491i −0.151829 0.111041i
621621 0 0
622622 9.73841i 0.390475i
623623 23.0596i 0.923865i
624624 0 0
625625 −20.4087 + 14.4390i −0.816349 + 0.577560i
626626 −9.50046 −0.379715
627627 0 0
628628 1.34060i 0.0534957i
629629 −11.1396 −0.444164
630630 0 0
631631 3.81078 0.151705 0.0758524 0.997119i 0.475832π-0.475832\pi
0.0758524 + 0.997119i 0.475832π0.475832\pi
632632 9.85952i 0.392191i
633633 0 0
634634 −13.0790 −0.519434
635635 19.5298 26.7034i 0.775017 1.05969i
636636 0 0
637637 0.0146797i 0.000581632i
638638 16.3103i 0.645732i
639639 0 0
640640 −1.32001 + 1.80487i −0.0521780 + 0.0713439i
641641 −35.7796 −1.41321 −0.706604 0.707609i 0.749774π-0.749774\pi
−0.706604 + 0.707609i 0.749774π0.749774\pi
642642 0 0
643643 11.3094i 0.445999i −0.974819 0.223000i 0.928415π-0.928415\pi
0.974819 0.223000i 0.0715849π-0.0715849\pi
644644 −3.59037 −0.141480
645645 0 0
646646 5.76491 0.226817
647647 49.4528i 1.94419i −0.234591 0.972094i 0.575375π-0.575375\pi
0.234591 0.972094i 0.424625π-0.424625\pi
648648 0 0
649649 −17.4693 −0.685729
650650 −0.734633 2.31032i −0.0288147 0.0906183i
651651 0 0
652652 16.2498i 0.636390i
653653 46.1311i 1.80525i −0.430429 0.902624i 0.641638π-0.641638\pi
0.430429 0.902624i 0.358362π-0.358362\pi
654654 0 0
655655 −4.51136 3.29942i −0.176273 0.128919i
656656 0.249771 0.00975191
657657 0 0
658658 15.8789i 0.619024i
659659 −23.6732 −0.922176 −0.461088 0.887355i 0.652541π-0.652541\pi
−0.461088 + 0.887355i 0.652541π0.652541\pi
660660 0 0
661661 −32.1287 −1.24966 −0.624830 0.780761i 0.714832π-0.714832\pi
−0.624830 + 0.780761i 0.714832π0.714832\pi
662662 24.8851i 0.967187i
663663 0 0
664664 17.5298 0.680289
665665 20.0899 27.4693i 0.779053 1.06521i
666666 0 0
667667 11.0908i 0.429439i
668668 2.95035i 0.114152i
669669 0 0
670670 8.96972 + 6.56009i 0.346531 + 0.253439i
671671 22.7493 0.878227
672672 0 0
673673 47.7631i 1.84113i 0.390588 + 0.920566i 0.372272π0.372272\pi
−0.390588 + 0.920566i 0.627728π0.627728\pi
674674 27.5445 1.06097
675675 0 0
676676 −12.7649 −0.490958
677677 8.82168i 0.339045i −0.985526 0.169522i 0.945778π-0.945778\pi
0.985526 0.169522i 0.0542225π-0.0542225\pi
678678 0 0
679679 −17.7796 −0.682318
680680 −1.80487 1.32001i −0.0692137 0.0506201i
681681 0 0
682682 4.18922i 0.160413i
683683 28.5142i 1.09107i 0.838089 + 0.545533i 0.183673π0.183673\pi
−0.838089 + 0.545533i 0.816327π0.816327\pi
684684 0 0
685685 2.71995 3.71904i 0.103924 0.142097i
686686 18.5601 0.708628
687687 0 0
688688 1.03028i 0.0392789i
689689 −3.73555 −0.142313
690690 0 0
691691 −50.4078 −1.91760 −0.958801 0.284077i 0.908313π-0.908313\pi
−0.958801 + 0.284077i 0.908313π0.908313\pi
692692 6.14048i 0.233426i
693693 0 0
694694 −4.48486 −0.170243
695695 −28.1386 20.5795i −1.06736 0.780624i
696696 0 0
697697 0.249771i 0.00946075i
698698 34.2186i 1.29519i
699699 0 0
700700 −12.5795 + 4.00000i −0.475459 + 0.151186i
701701 −10.4702 −0.395453 −0.197727 0.980257i 0.563356π-0.563356\pi
−0.197727 + 0.980257i 0.563356π0.563356\pi
702702 0 0
703703 64.2186i 2.42205i
704704 2.00000 0.0753778
705705 0 0
706706 −4.90917 −0.184759
707707 35.7190i 1.34335i
708708 0 0
709709 5.90539 0.221782 0.110891 0.993833i 0.464630π-0.464630\pi
0.110891 + 0.993833i 0.464630π0.464630\pi
710710 −11.0147 + 15.0606i −0.413374 + 0.565212i
711711 0 0
712712 8.73463i 0.327344i
713713 2.84862i 0.106682i
714714 0 0
715715 −1.28005 + 1.75023i −0.0478710 + 0.0654549i
716716 15.5904 0.582639
717717 0 0
718718 13.7796i 0.514250i
719719 −43.8354 −1.63479 −0.817393 0.576080i 0.804582π-0.804582\pi
−0.817393 + 0.576080i 0.804582π0.804582\pi
720720 0 0
721721 −29.6197 −1.10310
722722 14.2342i 0.529741i
723723 0 0
724724 −4.10929 −0.152721
725725 12.3562 + 38.8586i 0.458898 + 1.44317i
726726 0 0
727727 6.60597i 0.245002i 0.992468 + 0.122501i 0.0390914π0.0390914\pi
−0.992468 + 0.122501i 0.960909π0.960909\pi
728728 1.28005i 0.0474417i
729729 0 0
730730 0.875115 + 0.640023i 0.0323894 + 0.0236883i
731731 −1.03028 −0.0381061
732732 0 0
733733 44.6188i 1.64803i 0.566565 + 0.824017i 0.308272π0.308272\pi
−0.566565 + 0.824017i 0.691728π0.691728\pi
734734 −4.39025 −0.162047
735735 0 0
736736 −1.35998 −0.0501294
737737 9.93945i 0.366124i
738738 0 0
739739 −34.4149 −1.26597 −0.632987 0.774163i 0.718171π-0.718171\pi
−0.632987 + 0.774163i 0.718171π0.718171\pi
740740 −14.7044 + 20.1055i −0.540543 + 0.739093i
741741 0 0
742742 20.3397i 0.746693i
743743 28.0412i 1.02873i 0.857571 + 0.514365i 0.171973π0.171973\pi
−0.857571 + 0.514365i 0.828027π0.828027\pi
744744 0 0
745745 −18.0487 13.2001i −0.661255 0.483615i
746746 −0.220411 −0.00806983
747747 0 0
748748 2.00000i 0.0731272i
749749 −51.3993 −1.87809
750750 0 0
751751 −47.4040 −1.72980 −0.864899 0.501947i 0.832617π-0.832617\pi
−0.864899 + 0.501947i 0.832617π0.832617\pi
752752 6.01468i 0.219333i
753753 0 0
754754 −3.95413 −0.144001
755755 28.5895 + 20.9092i 1.04048 + 0.760963i
756756 0 0
757757 35.9759i 1.30757i 0.756682 + 0.653784i 0.226819π0.226819\pi
−0.756682 + 0.653784i 0.773181π0.773181\pi
758758 26.3103i 0.955634i
759759 0 0
760760 7.60975 10.4049i 0.276035 0.377427i
761761 −13.1807 −0.477801 −0.238901 0.971044i 0.576787π-0.576787\pi
−0.238901 + 0.971044i 0.576787π0.576787\pi
762762 0 0
763763 33.4087i 1.20948i
764764 6.06055 0.219263
765765 0 0
766766 36.1433 1.30591
767767 4.23509i 0.152920i
768768 0 0
769769 6.11399 0.220476 0.110238 0.993905i 0.464839π-0.464839\pi
0.110238 + 0.993905i 0.464839π0.464839\pi
770770 9.52982 + 6.96972i 0.343431 + 0.251171i
771771 0 0
772772 12.5601i 0.452048i
773773 44.5601i 1.60272i 0.598186 + 0.801358i 0.295889π0.295889\pi
−0.598186 + 0.801358i 0.704111π0.704111\pi
774774 0 0
775775 −3.17362 9.98062i −0.114000 0.358515i
776776 −6.73463 −0.241759
777777 0 0
778778 3.77959i 0.135505i
779779 −1.43991 −0.0515900
780780 0 0
781781 16.6888 0.597171
782782 1.35998i 0.0486327i
783783 0 0
784784 0.0302761 0.00108129
785785 −1.76961 + 2.41961i −0.0631600 + 0.0863597i
786786 0 0
787787 26.3856i 0.940543i −0.882522 0.470272i 0.844156π-0.844156\pi
0.882522 0.470272i 0.155844π-0.155844\pi
788788 26.0487i 0.927948i
789789 0 0
790790 −13.0147 + 17.7952i −0.463042 + 0.633124i
791791 −19.8401 −0.705434
792792 0 0
793793 5.51514i 0.195848i
794794 −12.2304 −0.434040
795795 0 0
796796 3.37466 0.119612
797797 12.4390i 0.440612i −0.975431 0.220306i 0.929294π-0.929294\pi
0.975431 0.220306i 0.0707055π-0.0707055\pi
798798 0 0
799799 −6.01468 −0.212784
800800 −4.76491 + 1.51514i −0.168465 + 0.0535682i
801801 0 0
802802 11.7796i 0.415952i
803803 0.969724i 0.0342208i
804804 0 0
805805 −6.48016 4.73933i −0.228396 0.167039i
806806 1.01560 0.0357729
807807 0 0
808808 13.5298i 0.475977i
809809 5.96125 0.209586 0.104793 0.994494i 0.466582π-0.466582\pi
0.104793 + 0.994494i 0.466582π0.466582\pi
810810 0 0
811811 −27.8089 −0.976504 −0.488252 0.872703i 0.662365π-0.662365\pi
−0.488252 + 0.872703i 0.662365π0.662365\pi
812812 21.5298i 0.755548i
813813 0 0
814814 22.2791 0.780883
815815 21.4499 29.3288i 0.751357 1.02734i
816816 0 0
817817 5.93945i 0.207795i
818818 15.7649i 0.551207i
819819 0 0
820820 0.450805 + 0.329700i 0.0157428 + 0.0115136i
821821 9.05677 0.316083 0.158042 0.987432i 0.449482π-0.449482\pi
0.158042 + 0.987432i 0.449482π0.449482\pi
822822 0 0
823823 6.54828i 0.228259i 0.993466 + 0.114129i 0.0364078π0.0364078\pi
−0.993466 + 0.114129i 0.963592π0.963592\pi
824824 −11.2195 −0.390850
825825 0 0
826826 23.0596 0.802347
827827 15.7115i 0.546341i −0.961966 0.273171i 0.911928π-0.911928\pi
0.961966 0.273171i 0.0880724π-0.0880724\pi
828828 0 0
829829 1.87890 0.0652567 0.0326284 0.999468i 0.489612π-0.489612\pi
0.0326284 + 0.999468i 0.489612π0.489612\pi
830830 31.6391 + 23.1396i 1.09821 + 0.803186i
831831 0 0
832832 0.484862i 0.0168096i
833833 0.0302761i 0.00104900i
834834 0 0
835835 −3.89449 + 5.32500i −0.134774 + 0.184279i
836836 −11.5298 −0.398767
837837 0 0
838838 18.1892i 0.628336i
839839 −48.6841 −1.68076 −0.840380 0.541997i 0.817668π-0.817668\pi
−0.840380 + 0.541997i 0.817668π0.817668\pi
840840 0 0
841841 37.5067 1.29333
842842 9.03028i 0.311204i
843843 0 0
844844 −18.0294 −0.620596
845845 −23.0390 16.8498i −0.792567 0.579652i
846846 0 0
847847 18.4802i 0.634986i
848848 7.70436i 0.264569i
849849 0 0
850850 −1.51514 4.76491i −0.0519688 0.163435i
851851 −15.1495 −0.519320
852852 0 0
853853 35.9494i 1.23089i −0.788182 0.615443i 0.788977π-0.788977\pi
0.788182 0.615443i 0.211023π-0.211023\pi
854854 −30.0294 −1.02758
855855 0 0
856856 −19.4693 −0.665446
857857 13.4158i 0.458276i 0.973394 + 0.229138i 0.0735907π0.0735907\pi
−0.973394 + 0.229138i 0.926409π0.926409\pi
858858 0 0
859859 23.8860 0.814980 0.407490 0.913210i 0.366404π-0.366404\pi
0.407490 + 0.913210i 0.366404π0.366404\pi
860860 −1.35998 + 1.85952i −0.0463748 + 0.0634090i
861861 0 0
862862 20.4196i 0.695495i
863863 15.5979i 0.530960i −0.964116 0.265480i 0.914470π-0.914470\pi
0.964116 0.265480i 0.0855304π-0.0855304\pi
864864 0 0
865865 8.10551 11.0828i 0.275596 0.376826i
866866 11.5904 0.393857
867867 0 0
868868 5.52982i 0.187694i
869869 19.7190 0.668922
870870 0 0
871871 −2.40963 −0.0816472
872872 12.6547i 0.428542i
873873 0 0
874874 7.84014 0.265197
875875 −27.9844 9.38555i −0.946046 0.317290i
876876 0 0
877877 33.3893i 1.12748i 0.825953 + 0.563739i 0.190638π0.190638\pi
−0.825953 + 0.563739i 0.809362π0.809362\pi
878878 2.01938i 0.0681507i
879879 0 0
880880 3.60975 + 2.64002i 0.121685 + 0.0889952i
881881 35.1202 1.18323 0.591615 0.806221i 0.298491π-0.298491\pi
0.591615 + 0.806221i 0.298491π0.298491\pi
882882 0 0
883883 22.2110i 0.747460i 0.927537 + 0.373730i 0.121921π0.121921\pi
−0.927537 + 0.373730i 0.878079π0.878079\pi
884884 0.484862 0.0163077
885885 0 0
886886 27.4087 0.920814
887887 5.17076i 0.173617i 0.996225 + 0.0868085i 0.0276668π0.0276668\pi
−0.996225 + 0.0868085i 0.972333π0.972333\pi
888888 0 0
889889 39.0596 1.31002
890890 −11.5298 + 15.7649i −0.386480 + 0.528441i
891891 0 0
892892 23.2947i 0.779965i
893893 34.6741i 1.16032i
894894 0 0
895895 28.1386 + 20.5795i 0.940571 + 0.687896i
896896 −2.64002 −0.0881970
897897 0 0
898898 29.7190i 0.991737i
899899 −17.0819 −0.569713
900900 0 0
901901 −7.70436 −0.256669
902902 0.499542i 0.0166329i
903903 0 0
904904 −7.51514 −0.249950
905905 −7.41675 5.42431i −0.246541 0.180310i
906906 0 0
907907 3.85482i 0.127997i −0.997950 0.0639986i 0.979615π-0.979615\pi
0.997950 0.0639986i 0.0203853π-0.0203853\pi
908908 17.4839i 0.580225i
909909 0 0
910910 1.68968 2.31032i 0.0560122 0.0765865i
911911 22.6400 0.750097 0.375049 0.927005i 0.377626π-0.377626\pi
0.375049 + 0.927005i 0.377626π0.377626\pi
912912 0 0
913913 35.0596i 1.16030i
914914 −39.4693 −1.30553
915915 0 0
916916 0.719953 0.0237879
917917 6.59885i 0.217913i
918918 0 0
919919 −31.5298 −1.04007 −0.520036 0.854144i 0.674082π-0.674082\pi
−0.520036 + 0.854144i 0.674082π0.674082\pi
920920 −2.45459 1.79518i −0.0809253 0.0591855i
921921 0 0
922922 14.6888i 0.483749i
923923 4.04587i 0.133172i
924924 0 0
925925 −53.0790 + 16.8780i −1.74523 + 0.554945i
926926 35.1055 1.15364
927927 0 0
928928 8.15516i 0.267706i
929929 −11.1589 −0.366113 −0.183057 0.983102i 0.558599π-0.558599\pi
−0.183057 + 0.983102i 0.558599π0.558599\pi
930930 0 0
931931 −0.174539 −0.00572028
932932 11.0450i 0.361790i
933933 0 0
934934 −9.96881 −0.326189
935935 −2.64002 + 3.60975i −0.0863380 + 0.118051i
936936 0 0
937937 24.5307i 0.801384i 0.916213 + 0.400692i 0.131230π0.131230\pi
−0.916213 + 0.400692i 0.868770π0.868770\pi
938938 13.1202i 0.428389i
939939 0 0
940940 −7.93945 + 10.8557i −0.258956 + 0.354075i
941941 −35.3747 −1.15318 −0.576590 0.817033i 0.695617π-0.695617\pi
−0.576590 + 0.817033i 0.695617π0.695617\pi
942942 0 0
943943 0.339682i 0.0110616i
944944 8.73463 0.284288
945945 0 0
946946 2.06055 0.0669943
947947 2.23509i 0.0726307i 0.999340 + 0.0363154i 0.0115621π0.0115621\pi
−0.999340 + 0.0363154i 0.988438π0.988438\pi
948948 0 0
949949 −0.235091 −0.00763138
950950 27.4693 8.73463i 0.891221 0.283389i
951951 0 0
952952 2.64002i 0.0855637i
953953 5.65092i 0.183051i 0.995803 + 0.0915257i 0.0291744π0.0291744\pi
−0.995803 + 0.0915257i 0.970826π0.970826\pi
954954 0 0
955955 10.9385 + 8.00000i 0.353963 + 0.258874i
956956 5.59037 0.180805
957957 0 0
958958 2.28383i 0.0737871i
959959 5.43991 0.175664
960960 0 0
961961 −26.6126 −0.858471
962962 5.40115i 0.174140i
963963 0 0
964964 8.37088 0.269608
965965 16.5795 22.6694i 0.533712 0.729753i
966966 0 0
967967 40.9991i 1.31844i 0.751949 + 0.659221i 0.229114π0.229114\pi
−0.751949 + 0.659221i 0.770886π0.770886\pi
968968 7.00000i 0.224989i
969969 0 0
970970 −12.1552 8.88979i −0.390279 0.285434i
971971 45.3846 1.45646 0.728231 0.685332i 0.240343π-0.240343\pi
0.728231 + 0.685332i 0.240343π0.240343\pi
972972 0 0
973973 41.1589i 1.31950i
974974 10.8292 0.346991
975975 0 0
976976 −11.3747 −0.364094
977977 4.72752i 0.151247i 0.997136 + 0.0756233i 0.0240946π0.0240946\pi
−0.997136 + 0.0756233i 0.975905π0.975905\pi
978978 0 0
979979 17.4693 0.558320
980980 0.0546445 + 0.0399648i 0.00174556 + 0.00127663i
981981 0 0
982982 24.7952i 0.791246i
983983 14.3297i 0.457046i 0.973538 + 0.228523i 0.0733897π0.0733897\pi
−0.973538 + 0.228523i 0.926610π0.926610\pi
984984 0 0
985985 34.3846 47.0147i 1.09559 1.49801i
986986 −8.15516 −0.259713
987987 0 0
988988 2.79518i 0.0889267i
989989 −1.40115 −0.0445540
990990 0 0
991991 16.8827 0.536296 0.268148 0.963378i 0.413588π-0.413588\pi
0.268148 + 0.963378i 0.413588π0.413588\pi
992992 2.09461i 0.0665039i
993993 0 0
994994 −22.0294 −0.698729
995995 6.09083 + 4.45459i 0.193092 + 0.141220i
996996 0 0
997997 18.5189i 0.586500i 0.956036 + 0.293250i 0.0947368π0.0947368\pi
−0.956036 + 0.293250i 0.905263π0.905263\pi
998998 5.15138i 0.163064i
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 1530.2.d.g.919.4 6
3.2 odd 2 170.2.c.b.69.2 6
5.2 odd 4 7650.2.a.dj.1.3 3
5.3 odd 4 7650.2.a.do.1.1 3
5.4 even 2 inner 1530.2.d.g.919.1 6
12.11 even 2 1360.2.e.c.1089.3 6
15.2 even 4 850.2.a.q.1.2 3
15.8 even 4 850.2.a.p.1.2 3
15.14 odd 2 170.2.c.b.69.5 yes 6
60.23 odd 4 6800.2.a.bp.1.2 3
60.47 odd 4 6800.2.a.bk.1.2 3
60.59 even 2 1360.2.e.c.1089.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.c.b.69.2 6 3.2 odd 2
170.2.c.b.69.5 yes 6 15.14 odd 2
850.2.a.p.1.2 3 15.8 even 4
850.2.a.q.1.2 3 15.2 even 4
1360.2.e.c.1089.3 6 12.11 even 2
1360.2.e.c.1089.4 6 60.59 even 2
1530.2.d.g.919.1 6 5.4 even 2 inner
1530.2.d.g.919.4 6 1.1 even 1 trivial
6800.2.a.bk.1.2 3 60.47 odd 4
6800.2.a.bp.1.2 3 60.23 odd 4
7650.2.a.dj.1.3 3 5.2 odd 4
7650.2.a.do.1.1 3 5.3 odd 4