Properties

Label 60.2.d.a.49.1
Level 6060
Weight 22
Character 60.49
Analytic conductor 0.4790.479
Analytic rank 00
Dimension 22
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [60,2,Mod(49,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 60=2235 60 = 2^{2} \cdot 3 \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 60.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: 0.4791024121280.479102412128
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 49.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 60.49
Dual form 60.2.d.a.49.2

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) == q1.00000iq3+(1.000002.00000i)q5+4.00000iq71.00000q94.00000q11+(2.000001.00000i)q15+4.00000iq17+4.00000q214.00000iq23+(3.000004.00000i)q25+1.00000iq27+6.00000q29+4.00000q31+4.00000iq33+(8.00000+4.00000i)q358.00000iq3710.0000q414.00000iq43+(1.00000+2.00000i)q454.00000iq479.00000q49+4.00000q51+12.0000iq53+(4.00000+8.00000i)q554.00000q59+2.00000q614.00000iq634.00000iq674.00000q69+8.00000iq73+(4.00000+3.00000i)q7516.0000iq77+12.0000q79+1.00000q814.00000iq83+(8.00000+4.00000i)q856.00000iq87+10.0000q894.00000iq93+8.00000iq97+4.00000q99+O(q100)q-1.00000i q^{3} +(1.00000 - 2.00000i) q^{5} +4.00000i q^{7} -1.00000 q^{9} -4.00000 q^{11} +(-2.00000 - 1.00000i) q^{15} +4.00000i q^{17} +4.00000 q^{21} -4.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} +1.00000i q^{27} +6.00000 q^{29} +4.00000 q^{31} +4.00000i q^{33} +(8.00000 + 4.00000i) q^{35} -8.00000i q^{37} -10.0000 q^{41} -4.00000i q^{43} +(-1.00000 + 2.00000i) q^{45} -4.00000i q^{47} -9.00000 q^{49} +4.00000 q^{51} +12.0000i q^{53} +(-4.00000 + 8.00000i) q^{55} -4.00000 q^{59} +2.00000 q^{61} -4.00000i q^{63} -4.00000i q^{67} -4.00000 q^{69} +8.00000i q^{73} +(-4.00000 + 3.00000i) q^{75} -16.0000i q^{77} +12.0000 q^{79} +1.00000 q^{81} -4.00000i q^{83} +(8.00000 + 4.00000i) q^{85} -6.00000i q^{87} +10.0000 q^{89} -4.00000i q^{93} +8.00000i q^{97} +4.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q52q98q114q15+8q216q25+12q29+8q31+16q3520q412q4518q49+8q518q558q59+4q618q698q75++8q99+O(q100) 2 q + 2 q^{5} - 2 q^{9} - 8 q^{11} - 4 q^{15} + 8 q^{21} - 6 q^{25} + 12 q^{29} + 8 q^{31} + 16 q^{35} - 20 q^{41} - 2 q^{45} - 18 q^{49} + 8 q^{51} - 8 q^{55} - 8 q^{59} + 4 q^{61} - 8 q^{69} - 8 q^{75}+ \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/60Z)×\left(\mathbb{Z}/60\mathbb{Z}\right)^\times.

nn 3131 3737 4141
χ(n)\chi(n) 11 1-1 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 0
33 1.00000i 0.577350i
44 0 0
55 1.00000 2.00000i 0.447214 0.894427i
66 0 0
77 4.00000i 1.51186i 0.654654 + 0.755929i 0.272814π0.272814\pi
−0.654654 + 0.755929i 0.727186π0.727186\pi
88 0 0
99 −1.00000 −0.333333
1010 0 0
1111 −4.00000 −1.20605 −0.603023 0.797724i 0.706037π-0.706037\pi
−0.603023 + 0.797724i 0.706037π0.706037\pi
1212 0 0
1313 0 0 1.00000 00
−1.00000 π\pi
1414 0 0
1515 −2.00000 1.00000i −0.516398 0.258199i
1616 0 0
1717 4.00000i 0.970143i 0.874475 + 0.485071i 0.161206π0.161206\pi
−0.874475 + 0.485071i 0.838794π0.838794\pi
1818 0 0
1919 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2020 0 0
2121 4.00000 0.872872
2222 0 0
2323 4.00000i 0.834058i −0.908893 0.417029i 0.863071π-0.863071\pi
0.908893 0.417029i 0.136929π-0.136929\pi
2424 0 0
2525 −3.00000 4.00000i −0.600000 0.800000i
2626 0 0
2727 1.00000i 0.192450i
2828 0 0
2929 6.00000 1.11417 0.557086 0.830455i 0.311919π-0.311919\pi
0.557086 + 0.830455i 0.311919π0.311919\pi
3030 0 0
3131 4.00000 0.718421 0.359211 0.933257i 0.383046π-0.383046\pi
0.359211 + 0.933257i 0.383046π0.383046\pi
3232 0 0
3333 4.00000i 0.696311i
3434 0 0
3535 8.00000 + 4.00000i 1.35225 + 0.676123i
3636 0 0
3737 8.00000i 1.31519i −0.753371 0.657596i 0.771573π-0.771573\pi
0.753371 0.657596i 0.228427π-0.228427\pi
3838 0 0
3939 0 0
4040 0 0
4141 −10.0000 −1.56174 −0.780869 0.624695i 0.785223π-0.785223\pi
−0.780869 + 0.624695i 0.785223π0.785223\pi
4242 0 0
4343 4.00000i 0.609994i −0.952353 0.304997i 0.901344π-0.901344\pi
0.952353 0.304997i 0.0986555π-0.0986555\pi
4444 0 0
4545 −1.00000 + 2.00000i −0.149071 + 0.298142i
4646 0 0
4747 4.00000i 0.583460i −0.956501 0.291730i 0.905769π-0.905769\pi
0.956501 0.291730i 0.0942309π-0.0942309\pi
4848 0 0
4949 −9.00000 −1.28571
5050 0 0
5151 4.00000 0.560112
5252 0 0
5353 12.0000i 1.64833i 0.566352 + 0.824163i 0.308354π0.308354\pi
−0.566352 + 0.824163i 0.691646π0.691646\pi
5454 0 0
5555 −4.00000 + 8.00000i −0.539360 + 1.07872i
5656 0 0
5757 0 0
5858 0 0
5959 −4.00000 −0.520756 −0.260378 0.965507i 0.583847π-0.583847\pi
−0.260378 + 0.965507i 0.583847π0.583847\pi
6060 0 0
6161 2.00000 0.256074 0.128037 0.991769i 0.459132π-0.459132\pi
0.128037 + 0.991769i 0.459132π0.459132\pi
6262 0 0
6363 4.00000i 0.503953i
6464 0 0
6565 0 0
6666 0 0
6767 4.00000i 0.488678i −0.969690 0.244339i 0.921429π-0.921429\pi
0.969690 0.244339i 0.0785709π-0.0785709\pi
6868 0 0
6969 −4.00000 −0.481543
7070 0 0
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 0 0
7373 8.00000i 0.936329i 0.883641 + 0.468165i 0.155085π0.155085\pi
−0.883641 + 0.468165i 0.844915π0.844915\pi
7474 0 0
7575 −4.00000 + 3.00000i −0.461880 + 0.346410i
7676 0 0
7777 16.0000i 1.82337i
7878 0 0
7979 12.0000 1.35011 0.675053 0.737769i 0.264121π-0.264121\pi
0.675053 + 0.737769i 0.264121π0.264121\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 4.00000i 0.439057i −0.975606 0.219529i 0.929548π-0.929548\pi
0.975606 0.219529i 0.0704519π-0.0704519\pi
8484 0 0
8585 8.00000 + 4.00000i 0.867722 + 0.433861i
8686 0 0
8787 6.00000i 0.643268i
8888 0 0
8989 10.0000 1.06000 0.529999 0.847998i 0.322192π-0.322192\pi
0.529999 + 0.847998i 0.322192π0.322192\pi
9090 0 0
9191 0 0
9292 0 0
9393 4.00000i 0.414781i
9494 0 0
9595 0 0
9696 0 0
9797 8.00000i 0.812277i 0.913812 + 0.406138i 0.133125π0.133125\pi
−0.913812 + 0.406138i 0.866875π0.866875\pi
9898 0 0
9999 4.00000 0.402015
100100 0 0
101101 −2.00000 −0.199007 −0.0995037 0.995037i 0.531726π-0.531726\pi
−0.0995037 + 0.995037i 0.531726π0.531726\pi
102102 0 0
103103 4.00000i 0.394132i 0.980390 + 0.197066i 0.0631413π0.0631413\pi
−0.980390 + 0.197066i 0.936859π0.936859\pi
104104 0 0
105105 4.00000 8.00000i 0.390360 0.780720i
106106 0 0
107107 12.0000i 1.16008i 0.814587 + 0.580042i 0.196964π0.196964\pi
−0.814587 + 0.580042i 0.803036π0.803036\pi
108108 0 0
109109 2.00000 0.191565 0.0957826 0.995402i 0.469465π-0.469465\pi
0.0957826 + 0.995402i 0.469465π0.469465\pi
110110 0 0
111111 −8.00000 −0.759326
112112 0 0
113113 12.0000i 1.12887i −0.825479 0.564433i 0.809095π-0.809095\pi
0.825479 0.564433i 0.190905π-0.190905\pi
114114 0 0
115115 −8.00000 4.00000i −0.746004 0.373002i
116116 0 0
117117 0 0
118118 0 0
119119 −16.0000 −1.46672
120120 0 0
121121 5.00000 0.454545
122122 0 0
123123 10.0000i 0.901670i
124124 0 0
125125 −11.0000 + 2.00000i −0.983870 + 0.178885i
126126 0 0
127127 4.00000i 0.354943i 0.984126 + 0.177471i 0.0567917π0.0567917\pi
−0.984126 + 0.177471i 0.943208π0.943208\pi
128128 0 0
129129 −4.00000 −0.352180
130130 0 0
131131 12.0000 1.04844 0.524222 0.851581i 0.324356π-0.324356\pi
0.524222 + 0.851581i 0.324356π0.324356\pi
132132 0 0
133133 0 0
134134 0 0
135135 2.00000 + 1.00000i 0.172133 + 0.0860663i
136136 0 0
137137 12.0000i 1.02523i 0.858619 + 0.512615i 0.171323π0.171323\pi
−0.858619 + 0.512615i 0.828677π0.828677\pi
138138 0 0
139139 −16.0000 −1.35710 −0.678551 0.734553i 0.737392π-0.737392\pi
−0.678551 + 0.734553i 0.737392π0.737392\pi
140140 0 0
141141 −4.00000 −0.336861
142142 0 0
143143 0 0
144144 0 0
145145 6.00000 12.0000i 0.498273 0.996546i
146146 0 0
147147 9.00000i 0.742307i
148148 0 0
149149 2.00000 0.163846 0.0819232 0.996639i 0.473894π-0.473894\pi
0.0819232 + 0.996639i 0.473894π0.473894\pi
150150 0 0
151151 −20.0000 −1.62758 −0.813788 0.581161i 0.802599π-0.802599\pi
−0.813788 + 0.581161i 0.802599π0.802599\pi
152152 0 0
153153 4.00000i 0.323381i
154154 0 0
155155 4.00000 8.00000i 0.321288 0.642575i
156156 0 0
157157 8.00000i 0.638470i 0.947676 + 0.319235i 0.103426π0.103426\pi
−0.947676 + 0.319235i 0.896574π0.896574\pi
158158 0 0
159159 12.0000 0.951662
160160 0 0
161161 16.0000 1.26098
162162 0 0
163163 20.0000i 1.56652i −0.621694 0.783260i 0.713555π-0.713555\pi
0.621694 0.783260i 0.286445π-0.286445\pi
164164 0 0
165165 8.00000 + 4.00000i 0.622799 + 0.311400i
166166 0 0
167167 12.0000i 0.928588i 0.885681 + 0.464294i 0.153692π0.153692\pi
−0.885681 + 0.464294i 0.846308π0.846308\pi
168168 0 0
169169 13.0000 1.00000
170170 0 0
171171 0 0
172172 0 0
173173 4.00000i 0.304114i 0.988372 + 0.152057i 0.0485898π0.0485898\pi
−0.988372 + 0.152057i 0.951410π0.951410\pi
174174 0 0
175175 16.0000 12.0000i 1.20949 0.907115i
176176 0 0
177177 4.00000i 0.300658i
178178 0 0
179179 −4.00000 −0.298974 −0.149487 0.988764i 0.547762π-0.547762\pi
−0.149487 + 0.988764i 0.547762π0.547762\pi
180180 0 0
181181 −10.0000 −0.743294 −0.371647 0.928374i 0.621207π-0.621207\pi
−0.371647 + 0.928374i 0.621207π0.621207\pi
182182 0 0
183183 2.00000i 0.147844i
184184 0 0
185185 −16.0000 8.00000i −1.17634 0.588172i
186186 0 0
187187 16.0000i 1.17004i
188188 0 0
189189 −4.00000 −0.290957
190190 0 0
191191 24.0000 1.73658 0.868290 0.496058i 0.165220π-0.165220\pi
0.868290 + 0.496058i 0.165220π0.165220\pi
192192 0 0
193193 16.0000i 1.15171i −0.817554 0.575853i 0.804670π-0.804670\pi
0.817554 0.575853i 0.195330π-0.195330\pi
194194 0 0
195195 0 0
196196 0 0
197197 4.00000i 0.284988i −0.989796 0.142494i 0.954488π-0.954488\pi
0.989796 0.142494i 0.0455122π-0.0455122\pi
198198 0 0
199199 12.0000 0.850657 0.425329 0.905039i 0.360158π-0.360158\pi
0.425329 + 0.905039i 0.360158π0.360158\pi
200200 0 0
201201 −4.00000 −0.282138
202202 0 0
203203 24.0000i 1.68447i
204204 0 0
205205 −10.0000 + 20.0000i −0.698430 + 1.39686i
206206 0 0
207207 4.00000i 0.278019i
208208 0 0
209209 0 0
210210 0 0
211211 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
212212 0 0
213213 0 0
214214 0 0
215215 −8.00000 4.00000i −0.545595 0.272798i
216216 0 0
217217 16.0000i 1.08615i
218218 0 0
219219 8.00000 0.540590
220220 0 0
221221 0 0
222222 0 0
223223 20.0000i 1.33930i 0.742677 + 0.669650i 0.233556π0.233556\pi
−0.742677 + 0.669650i 0.766444π0.766444\pi
224224 0 0
225225 3.00000 + 4.00000i 0.200000 + 0.266667i
226226 0 0
227227 20.0000i 1.32745i −0.747978 0.663723i 0.768975π-0.768975\pi
0.747978 0.663723i 0.231025π-0.231025\pi
228228 0 0
229229 −26.0000 −1.71813 −0.859064 0.511868i 0.828954π-0.828954\pi
−0.859064 + 0.511868i 0.828954π0.828954\pi
230230 0 0
231231 −16.0000 −1.05272
232232 0 0
233233 20.0000i 1.31024i −0.755523 0.655122i 0.772617π-0.772617\pi
0.755523 0.655122i 0.227383π-0.227383\pi
234234 0 0
235235 −8.00000 4.00000i −0.521862 0.260931i
236236 0 0
237237 12.0000i 0.779484i
238238 0 0
239239 −8.00000 −0.517477 −0.258738 0.965947i 0.583307π-0.583307\pi
−0.258738 + 0.965947i 0.583307π0.583307\pi
240240 0 0
241241 −2.00000 −0.128831 −0.0644157 0.997923i 0.520518π-0.520518\pi
−0.0644157 + 0.997923i 0.520518π0.520518\pi
242242 0 0
243243 1.00000i 0.0641500i
244244 0 0
245245 −9.00000 + 18.0000i −0.574989 + 1.14998i
246246 0 0
247247 0 0
248248 0 0
249249 −4.00000 −0.253490
250250 0 0
251251 −12.0000 −0.757433 −0.378717 0.925513i 0.623635π-0.623635\pi
−0.378717 + 0.925513i 0.623635π0.623635\pi
252252 0 0
253253 16.0000i 1.00591i
254254 0 0
255255 4.00000 8.00000i 0.250490 0.500979i
256256 0 0
257257 12.0000i 0.748539i 0.927320 + 0.374270i 0.122107π0.122107\pi
−0.927320 + 0.374270i 0.877893π0.877893\pi
258258 0 0
259259 32.0000 1.98838
260260 0 0
261261 −6.00000 −0.371391
262262 0 0
263263 4.00000i 0.246651i −0.992366 0.123325i 0.960644π-0.960644\pi
0.992366 0.123325i 0.0393559π-0.0393559\pi
264264 0 0
265265 24.0000 + 12.0000i 1.47431 + 0.737154i
266266 0 0
267267 10.0000i 0.611990i
268268 0 0
269269 −6.00000 −0.365826 −0.182913 0.983129i 0.558553π-0.558553\pi
−0.182913 + 0.983129i 0.558553π0.558553\pi
270270 0 0
271271 4.00000 0.242983 0.121491 0.992592i 0.461232π-0.461232\pi
0.121491 + 0.992592i 0.461232π0.461232\pi
272272 0 0
273273 0 0
274274 0 0
275275 12.0000 + 16.0000i 0.723627 + 0.964836i
276276 0 0
277277 32.0000i 1.92269i −0.275340 0.961347i 0.588791π-0.588791\pi
0.275340 0.961347i 0.411209π-0.411209\pi
278278 0 0
279279 −4.00000 −0.239474
280280 0 0
281281 6.00000 0.357930 0.178965 0.983855i 0.442725π-0.442725\pi
0.178965 + 0.983855i 0.442725π0.442725\pi
282282 0 0
283283 28.0000i 1.66443i 0.554455 + 0.832214i 0.312927π0.312927\pi
−0.554455 + 0.832214i 0.687073π0.687073\pi
284284 0 0
285285 0 0
286286 0 0
287287 40.0000i 2.36113i
288288 0 0
289289 1.00000 0.0588235
290290 0 0
291291 8.00000 0.468968
292292 0 0
293293 12.0000i 0.701047i −0.936554 0.350524i 0.886004π-0.886004\pi
0.936554 0.350524i 0.113996π-0.113996\pi
294294 0 0
295295 −4.00000 + 8.00000i −0.232889 + 0.465778i
296296 0 0
297297 4.00000i 0.232104i
298298 0 0
299299 0 0
300300 0 0
301301 16.0000 0.922225
302302 0 0
303303 2.00000i 0.114897i
304304 0 0
305305 2.00000 4.00000i 0.114520 0.229039i
306306 0 0
307307 12.0000i 0.684876i 0.939540 + 0.342438i 0.111253π0.111253\pi
−0.939540 + 0.342438i 0.888747π0.888747\pi
308308 0 0
309309 4.00000 0.227552
310310 0 0
311311 24.0000 1.36092 0.680458 0.732787i 0.261781π-0.261781\pi
0.680458 + 0.732787i 0.261781π0.261781\pi
312312 0 0
313313 16.0000i 0.904373i −0.891923 0.452187i 0.850644π-0.850644\pi
0.891923 0.452187i 0.149356π-0.149356\pi
314314 0 0
315315 −8.00000 4.00000i −0.450749 0.225374i
316316 0 0
317317 4.00000i 0.224662i 0.993671 + 0.112331i 0.0358318π0.0358318\pi
−0.993671 + 0.112331i 0.964168π0.964168\pi
318318 0 0
319319 −24.0000 −1.34374
320320 0 0
321321 12.0000 0.669775
322322 0 0
323323 0 0
324324 0 0
325325 0 0
326326 0 0
327327 2.00000i 0.110600i
328328 0 0
329329 16.0000 0.882109
330330 0 0
331331 −8.00000 −0.439720 −0.219860 0.975531i 0.570560π-0.570560\pi
−0.219860 + 0.975531i 0.570560π0.570560\pi
332332 0 0
333333 8.00000i 0.438397i
334334 0 0
335335 −8.00000 4.00000i −0.437087 0.218543i
336336 0 0
337337 8.00000i 0.435788i −0.975972 0.217894i 0.930081π-0.930081\pi
0.975972 0.217894i 0.0699187π-0.0699187\pi
338338 0 0
339339 −12.0000 −0.651751
340340 0 0
341341 −16.0000 −0.866449
342342 0 0
343343 8.00000i 0.431959i
344344 0 0
345345 −4.00000 + 8.00000i −0.215353 + 0.430706i
346346 0 0
347347 12.0000i 0.644194i 0.946707 + 0.322097i 0.104388π0.104388\pi
−0.946707 + 0.322097i 0.895612π0.895612\pi
348348 0 0
349349 14.0000 0.749403 0.374701 0.927146i 0.377745π-0.377745\pi
0.374701 + 0.927146i 0.377745π0.377745\pi
350350 0 0
351351 0 0
352352 0 0
353353 28.0000i 1.49029i 0.666903 + 0.745145i 0.267620π0.267620\pi
−0.666903 + 0.745145i 0.732380π0.732380\pi
354354 0 0
355355 0 0
356356 0 0
357357 16.0000i 0.846810i
358358 0 0
359359 −24.0000 −1.26667 −0.633336 0.773877i 0.718315π-0.718315\pi
−0.633336 + 0.773877i 0.718315π0.718315\pi
360360 0 0
361361 −19.0000 −1.00000
362362 0 0
363363 5.00000i 0.262432i
364364 0 0
365365 16.0000 + 8.00000i 0.837478 + 0.418739i
366366 0 0
367367 4.00000i 0.208798i 0.994535 + 0.104399i 0.0332919π0.0332919\pi
−0.994535 + 0.104399i 0.966708π0.966708\pi
368368 0 0
369369 10.0000 0.520579
370370 0 0
371371 −48.0000 −2.49204
372372 0 0
373373 24.0000i 1.24267i −0.783544 0.621336i 0.786590π-0.786590\pi
0.783544 0.621336i 0.213410π-0.213410\pi
374374 0 0
375375 2.00000 + 11.0000i 0.103280 + 0.568038i
376376 0 0
377377 0 0
378378 0 0
379379 −8.00000 −0.410932 −0.205466 0.978664i 0.565871π-0.565871\pi
−0.205466 + 0.978664i 0.565871π0.565871\pi
380380 0 0
381381 4.00000 0.204926
382382 0 0
383383 28.0000i 1.43073i 0.698749 + 0.715367i 0.253740π0.253740\pi
−0.698749 + 0.715367i 0.746260π0.746260\pi
384384 0 0
385385 −32.0000 16.0000i −1.63087 0.815436i
386386 0 0
387387 4.00000i 0.203331i
388388 0 0
389389 34.0000 1.72387 0.861934 0.507020i 0.169253π-0.169253\pi
0.861934 + 0.507020i 0.169253π0.169253\pi
390390 0 0
391391 16.0000 0.809155
392392 0 0
393393 12.0000i 0.605320i
394394 0 0
395395 12.0000 24.0000i 0.603786 1.20757i
396396 0 0
397397 8.00000i 0.401508i −0.979642 0.200754i 0.935661π-0.935661\pi
0.979642 0.200754i 0.0643393π-0.0643393\pi
398398 0 0
399399 0 0
400400 0 0
401401 −14.0000 −0.699127 −0.349563 0.936913i 0.613670π-0.613670\pi
−0.349563 + 0.936913i 0.613670π0.613670\pi
402402 0 0
403403 0 0
404404 0 0
405405 1.00000 2.00000i 0.0496904 0.0993808i
406406 0 0
407407 32.0000i 1.58618i
408408 0 0
409409 −26.0000 −1.28562 −0.642809 0.766027i 0.722231π-0.722231\pi
−0.642809 + 0.766027i 0.722231π0.722231\pi
410410 0 0
411411 12.0000 0.591916
412412 0 0
413413 16.0000i 0.787309i
414414 0 0
415415 −8.00000 4.00000i −0.392705 0.196352i
416416 0 0
417417 16.0000i 0.783523i
418418 0 0
419419 28.0000 1.36789 0.683945 0.729534i 0.260263π-0.260263\pi
0.683945 + 0.729534i 0.260263π0.260263\pi
420420 0 0
421421 10.0000 0.487370 0.243685 0.969854i 0.421644π-0.421644\pi
0.243685 + 0.969854i 0.421644π0.421644\pi
422422 0 0
423423 4.00000i 0.194487i
424424 0 0
425425 16.0000 12.0000i 0.776114 0.582086i
426426 0 0
427427 8.00000i 0.387147i
428428 0 0
429429 0 0
430430 0 0
431431 8.00000 0.385346 0.192673 0.981263i 0.438284π-0.438284\pi
0.192673 + 0.981263i 0.438284π0.438284\pi
432432 0 0
433433 16.0000i 0.768911i −0.923144 0.384455i 0.874389π-0.874389\pi
0.923144 0.384455i 0.125611π-0.125611\pi
434434 0 0
435435 −12.0000 6.00000i −0.575356 0.287678i
436436 0 0
437437 0 0
438438 0 0
439439 12.0000 0.572729 0.286364 0.958121i 0.407553π-0.407553\pi
0.286364 + 0.958121i 0.407553π0.407553\pi
440440 0 0
441441 9.00000 0.428571
442442 0 0
443443 36.0000i 1.71041i −0.518289 0.855206i 0.673431π-0.673431\pi
0.518289 0.855206i 0.326569π-0.326569\pi
444444 0 0
445445 10.0000 20.0000i 0.474045 0.948091i
446446 0 0
447447 2.00000i 0.0945968i
448448 0 0
449449 −18.0000 −0.849473 −0.424736 0.905317i 0.639633π-0.639633\pi
−0.424736 + 0.905317i 0.639633π0.639633\pi
450450 0 0
451451 40.0000 1.88353
452452 0 0
453453 20.0000i 0.939682i
454454 0 0
455455 0 0
456456 0 0
457457 40.0000i 1.87112i 0.353166 + 0.935561i 0.385105π0.385105\pi
−0.353166 + 0.935561i 0.614895π0.614895\pi
458458 0 0
459459 −4.00000 −0.186704
460460 0 0
461461 6.00000 0.279448 0.139724 0.990190i 0.455378π-0.455378\pi
0.139724 + 0.990190i 0.455378π0.455378\pi
462462 0 0
463463 12.0000i 0.557687i −0.960337 0.278844i 0.910049π-0.910049\pi
0.960337 0.278844i 0.0899511π-0.0899511\pi
464464 0 0
465465 −8.00000 4.00000i −0.370991 0.185496i
466466 0 0
467467 12.0000i 0.555294i 0.960683 + 0.277647i 0.0895545π0.0895545\pi
−0.960683 + 0.277647i 0.910445π0.910445\pi
468468 0 0
469469 16.0000 0.738811
470470 0 0
471471 8.00000 0.368621
472472 0 0
473473 16.0000i 0.735681i
474474 0 0
475475 0 0
476476 0 0
477477 12.0000i 0.549442i
478478 0 0
479479 16.0000 0.731059 0.365529 0.930800i 0.380888π-0.380888\pi
0.365529 + 0.930800i 0.380888π0.380888\pi
480480 0 0
481481 0 0
482482 0 0
483483 16.0000i 0.728025i
484484 0 0
485485 16.0000 + 8.00000i 0.726523 + 0.363261i
486486 0 0
487487 12.0000i 0.543772i −0.962329 0.271886i 0.912353π-0.912353\pi
0.962329 0.271886i 0.0876473π-0.0876473\pi
488488 0 0
489489 −20.0000 −0.904431
490490 0 0
491491 −36.0000 −1.62466 −0.812329 0.583200i 0.801800π-0.801800\pi
−0.812329 + 0.583200i 0.801800π0.801800\pi
492492 0 0
493493 24.0000i 1.08091i
494494 0 0
495495 4.00000 8.00000i 0.179787 0.359573i
496496 0 0
497497 0 0
498498 0 0
499499 −24.0000 −1.07439 −0.537194 0.843459i 0.680516π-0.680516\pi
−0.537194 + 0.843459i 0.680516π0.680516\pi
500500 0 0
501501 12.0000 0.536120
502502 0 0
503503 36.0000i 1.60516i −0.596544 0.802580i 0.703460π-0.703460\pi
0.596544 0.802580i 0.296540π-0.296540\pi
504504 0 0
505505 −2.00000 + 4.00000i −0.0889988 + 0.177998i
506506 0 0
507507 13.0000i 0.577350i
508508 0 0
509509 −42.0000 −1.86162 −0.930809 0.365507i 0.880896π-0.880896\pi
−0.930809 + 0.365507i 0.880896π0.880896\pi
510510 0 0
511511 −32.0000 −1.41560
512512 0 0
513513 0 0
514514 0 0
515515 8.00000 + 4.00000i 0.352522 + 0.176261i
516516 0 0
517517 16.0000i 0.703679i
518518 0 0
519519 4.00000 0.175581
520520 0 0
521521 −38.0000 −1.66481 −0.832405 0.554168i 0.813037π-0.813037\pi
−0.832405 + 0.554168i 0.813037π0.813037\pi
522522 0 0
523523 28.0000i 1.22435i 0.790721 + 0.612177i 0.209706π0.209706\pi
−0.790721 + 0.612177i 0.790294π0.790294\pi
524524 0 0
525525 −12.0000 16.0000i −0.523723 0.698297i
526526 0 0
527527 16.0000i 0.696971i
528528 0 0
529529 7.00000 0.304348
530530 0 0
531531 4.00000 0.173585
532532 0 0
533533 0 0
534534 0 0
535535 24.0000 + 12.0000i 1.03761 + 0.518805i
536536 0 0
537537 4.00000i 0.172613i
538538 0 0
539539 36.0000 1.55063
540540 0 0
541541 −2.00000 −0.0859867 −0.0429934 0.999075i 0.513689π-0.513689\pi
−0.0429934 + 0.999075i 0.513689π0.513689\pi
542542 0 0
543543 10.0000i 0.429141i
544544 0 0
545545 2.00000 4.00000i 0.0856706 0.171341i
546546 0 0
547547 28.0000i 1.19719i 0.801050 + 0.598597i 0.204275π0.204275\pi
−0.801050 + 0.598597i 0.795725π0.795725\pi
548548 0 0
549549 −2.00000 −0.0853579
550550 0 0
551551 0 0
552552 0 0
553553 48.0000i 2.04117i
554554 0 0
555555 −8.00000 + 16.0000i −0.339581 + 0.679162i
556556 0 0
557557 12.0000i 0.508456i −0.967144 0.254228i 0.918179π-0.918179\pi
0.967144 0.254228i 0.0818214π-0.0818214\pi
558558 0 0
559559 0 0
560560 0 0
561561 −16.0000 −0.675521
562562 0 0
563563 20.0000i 0.842900i −0.906852 0.421450i 0.861521π-0.861521\pi
0.906852 0.421450i 0.138479π-0.138479\pi
564564 0 0
565565 −24.0000 12.0000i −1.00969 0.504844i
566566 0 0
567567 4.00000i 0.167984i
568568 0 0
569569 −26.0000 −1.08998 −0.544988 0.838444i 0.683466π-0.683466\pi
−0.544988 + 0.838444i 0.683466π0.683466\pi
570570 0 0
571571 40.0000 1.67395 0.836974 0.547243i 0.184323π-0.184323\pi
0.836974 + 0.547243i 0.184323π0.184323\pi
572572 0 0
573573 24.0000i 1.00261i
574574 0 0
575575 −16.0000 + 12.0000i −0.667246 + 0.500435i
576576 0 0
577577 32.0000i 1.33218i −0.745873 0.666089i 0.767967π-0.767967\pi
0.745873 0.666089i 0.232033π-0.232033\pi
578578 0 0
579579 −16.0000 −0.664937
580580 0 0
581581 16.0000 0.663792
582582 0 0
583583 48.0000i 1.98796i
584584 0 0
585585 0 0
586586 0 0
587587 36.0000i 1.48588i −0.669359 0.742940i 0.733431π-0.733431\pi
0.669359 0.742940i 0.266569π-0.266569\pi
588588 0 0
589589 0 0
590590 0 0
591591 −4.00000 −0.164538
592592 0 0
593593 36.0000i 1.47834i 0.673517 + 0.739171i 0.264783π0.264783\pi
−0.673517 + 0.739171i 0.735217π0.735217\pi
594594 0 0
595595 −16.0000 + 32.0000i −0.655936 + 1.31187i
596596 0 0
597597 12.0000i 0.491127i
598598 0 0
599599 24.0000 0.980613 0.490307 0.871550i 0.336885π-0.336885\pi
0.490307 + 0.871550i 0.336885π0.336885\pi
600600 0 0
601601 38.0000 1.55005 0.775026 0.631929i 0.217737π-0.217737\pi
0.775026 + 0.631929i 0.217737π0.217737\pi
602602 0 0
603603 4.00000i 0.162893i
604604 0 0
605605 5.00000 10.0000i 0.203279 0.406558i
606606 0 0
607607 28.0000i 1.13648i −0.822861 0.568242i 0.807624π-0.807624\pi
0.822861 0.568242i 0.192376π-0.192376\pi
608608 0 0
609609 24.0000 0.972529
610610 0 0
611611 0 0
612612 0 0
613613 8.00000i 0.323117i 0.986863 + 0.161558i 0.0516520π0.0516520\pi
−0.986863 + 0.161558i 0.948348π0.948348\pi
614614 0 0
615615 20.0000 + 10.0000i 0.806478 + 0.403239i
616616 0 0
617617 44.0000i 1.77137i −0.464283 0.885687i 0.653688π-0.653688\pi
0.464283 0.885687i 0.346312π-0.346312\pi
618618 0 0
619619 16.0000 0.643094 0.321547 0.946894i 0.395797π-0.395797\pi
0.321547 + 0.946894i 0.395797π0.395797\pi
620620 0 0
621621 4.00000 0.160514
622622 0 0
623623 40.0000i 1.60257i
624624 0 0
625625 −7.00000 + 24.0000i −0.280000 + 0.960000i
626626 0 0
627627 0 0
628628 0 0
629629 32.0000 1.27592
630630 0 0
631631 −28.0000 −1.11466 −0.557331 0.830290i 0.688175π-0.688175\pi
−0.557331 + 0.830290i 0.688175π0.688175\pi
632632 0 0
633633 0 0
634634 0 0
635635 8.00000 + 4.00000i 0.317470 + 0.158735i
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 14.0000 0.552967 0.276483 0.961019i 0.410831π-0.410831\pi
0.276483 + 0.961019i 0.410831π0.410831\pi
642642 0 0
643643 36.0000i 1.41970i −0.704352 0.709851i 0.748762π-0.748762\pi
0.704352 0.709851i 0.251238π-0.251238\pi
644644 0 0
645645 −4.00000 + 8.00000i −0.157500 + 0.315000i
646646 0 0
647647 12.0000i 0.471769i 0.971781 + 0.235884i 0.0757987π0.0757987\pi
−0.971781 + 0.235884i 0.924201π0.924201\pi
648648 0 0
649649 16.0000 0.628055
650650 0 0
651651 16.0000 0.627089
652652 0 0
653653 4.00000i 0.156532i −0.996933 0.0782660i 0.975062π-0.975062\pi
0.996933 0.0782660i 0.0249384π-0.0249384\pi
654654 0 0
655655 12.0000 24.0000i 0.468879 0.937758i
656656 0 0
657657 8.00000i 0.312110i
658658 0 0
659659 −28.0000 −1.09073 −0.545363 0.838200i 0.683608π-0.683608\pi
−0.545363 + 0.838200i 0.683608π0.683608\pi
660660 0 0
661661 −22.0000 −0.855701 −0.427850 0.903850i 0.640729π-0.640729\pi
−0.427850 + 0.903850i 0.640729π0.640729\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 24.0000i 0.929284i
668668 0 0
669669 20.0000 0.773245
670670 0 0
671671 −8.00000 −0.308837
672672 0 0
673673 0 0 1.00000 00
−1.00000 π\pi
674674 0 0
675675 4.00000 3.00000i 0.153960 0.115470i
676676 0 0
677677 4.00000i 0.153732i 0.997041 + 0.0768662i 0.0244914π0.0244914\pi
−0.997041 + 0.0768662i 0.975509π0.975509\pi
678678 0 0
679679 −32.0000 −1.22805
680680 0 0
681681 −20.0000 −0.766402
682682 0 0
683683 44.0000i 1.68361i 0.539779 + 0.841807i 0.318508π0.318508\pi
−0.539779 + 0.841807i 0.681492π0.681492\pi
684684 0 0
685685 24.0000 + 12.0000i 0.916993 + 0.458496i
686686 0 0
687687 26.0000i 0.991962i
688688 0 0
689689 0 0
690690 0 0
691691 −32.0000 −1.21734 −0.608669 0.793424i 0.708296π-0.708296\pi
−0.608669 + 0.793424i 0.708296π0.708296\pi
692692 0 0
693693 16.0000i 0.607790i
694694 0 0
695695 −16.0000 + 32.0000i −0.606915 + 1.21383i
696696 0 0
697697 40.0000i 1.51511i
698698 0 0
699699 −20.0000 −0.756469
700700 0 0
701701 26.0000 0.982006 0.491003 0.871158i 0.336630π-0.336630\pi
0.491003 + 0.871158i 0.336630π0.336630\pi
702702 0 0
703703 0 0
704704 0 0
705705 −4.00000 + 8.00000i −0.150649 + 0.301297i
706706 0 0
707707 8.00000i 0.300871i
708708 0 0
709709 6.00000 0.225335 0.112667 0.993633i 0.464061π-0.464061\pi
0.112667 + 0.993633i 0.464061π0.464061\pi
710710 0 0
711711 −12.0000 −0.450035
712712 0 0
713713 16.0000i 0.599205i
714714 0 0
715715 0 0
716716 0 0
717717 8.00000i 0.298765i
718718 0 0
719719 −8.00000 −0.298350 −0.149175 0.988811i 0.547662π-0.547662\pi
−0.149175 + 0.988811i 0.547662π0.547662\pi
720720 0 0
721721 −16.0000 −0.595871
722722 0 0
723723 2.00000i 0.0743808i
724724 0 0
725725 −18.0000 24.0000i −0.668503 0.891338i
726726 0 0
727727 12.0000i 0.445055i −0.974926 0.222528i 0.928569π-0.928569\pi
0.974926 0.222528i 0.0714308π-0.0714308\pi
728728 0 0
729729 −1.00000 −0.0370370
730730 0 0
731731 16.0000 0.591781
732732 0 0
733733 16.0000i 0.590973i 0.955347 + 0.295487i 0.0954818π0.0954818\pi
−0.955347 + 0.295487i 0.904518π0.904518\pi
734734 0 0
735735 18.0000 + 9.00000i 0.663940 + 0.331970i
736736 0 0
737737 16.0000i 0.589368i
738738 0 0
739739 −40.0000 −1.47142 −0.735712 0.677295i 0.763152π-0.763152\pi
−0.735712 + 0.677295i 0.763152π0.763152\pi
740740 0 0
741741 0 0
742742 0 0
743743 36.0000i 1.32071i −0.750953 0.660356i 0.770405π-0.770405\pi
0.750953 0.660356i 0.229595π-0.229595\pi
744744 0 0
745745 2.00000 4.00000i 0.0732743 0.146549i
746746 0 0
747747 4.00000i 0.146352i
748748 0 0
749749 −48.0000 −1.75388
750750 0 0
751751 −28.0000 −1.02173 −0.510867 0.859660i 0.670676π-0.670676\pi
−0.510867 + 0.859660i 0.670676π0.670676\pi
752752 0 0
753753 12.0000i 0.437304i
754754 0 0
755755 −20.0000 + 40.0000i −0.727875 + 1.45575i
756756 0 0
757757 16.0000i 0.581530i 0.956795 + 0.290765i 0.0939098π0.0939098\pi
−0.956795 + 0.290765i 0.906090π0.906090\pi
758758 0 0
759759 16.0000 0.580763
760760 0 0
761761 42.0000 1.52250 0.761249 0.648459i 0.224586π-0.224586\pi
0.761249 + 0.648459i 0.224586π0.224586\pi
762762 0 0
763763 8.00000i 0.289619i
764764 0 0
765765 −8.00000 4.00000i −0.289241 0.144620i
766766 0 0
767767 0 0
768768 0 0
769769 18.0000 0.649097 0.324548 0.945869i 0.394788π-0.394788\pi
0.324548 + 0.945869i 0.394788π0.394788\pi
770770 0 0
771771 12.0000 0.432169
772772 0 0
773773 12.0000i 0.431610i 0.976436 + 0.215805i 0.0692376π0.0692376\pi
−0.976436 + 0.215805i 0.930762π0.930762\pi
774774 0 0
775775 −12.0000 16.0000i −0.431053 0.574737i
776776 0 0
777777 32.0000i 1.14799i
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 6.00000i 0.214423i
784784 0 0
785785 16.0000 + 8.00000i 0.571064 + 0.285532i
786786 0 0
787787 28.0000i 0.998092i 0.866575 + 0.499046i 0.166316π0.166316\pi
−0.866575 + 0.499046i 0.833684π0.833684\pi
788788 0 0
789789 −4.00000 −0.142404
790790 0 0
791791 48.0000 1.70668
792792 0 0
793793 0 0
794794 0 0
795795 12.0000 24.0000i 0.425596 0.851192i
796796 0 0
797797 28.0000i 0.991811i 0.868377 + 0.495905i 0.165164π0.165164\pi
−0.868377 + 0.495905i 0.834836π0.834836\pi
798798 0 0
799799 16.0000 0.566039
800800 0 0
801801 −10.0000 −0.353333
802802 0 0
803803 32.0000i 1.12926i
804804 0 0
805805 16.0000 32.0000i 0.563926 1.12785i
806806 0 0
807807 6.00000i 0.211210i
808808 0 0
809809 −6.00000 −0.210949 −0.105474 0.994422i 0.533636π-0.533636\pi
−0.105474 + 0.994422i 0.533636π0.533636\pi
810810 0 0
811811 40.0000 1.40459 0.702295 0.711886i 0.252159π-0.252159\pi
0.702295 + 0.711886i 0.252159π0.252159\pi
812812 0 0
813813 4.00000i 0.140286i
814814 0 0
815815 −40.0000 20.0000i −1.40114 0.700569i
816816 0 0
817817 0 0
818818 0 0
819819 0 0
820820 0 0
821821 −14.0000 −0.488603 −0.244302 0.969699i 0.578559π-0.578559\pi
−0.244302 + 0.969699i 0.578559π0.578559\pi
822822 0 0
823823 12.0000i 0.418294i −0.977884 0.209147i 0.932931π-0.932931\pi
0.977884 0.209147i 0.0670687π-0.0670687\pi
824824 0 0
825825 16.0000 12.0000i 0.557048 0.417786i
826826 0 0
827827 28.0000i 0.973655i 0.873498 + 0.486828i 0.161846π0.161846\pi
−0.873498 + 0.486828i 0.838154π0.838154\pi
828828 0 0
829829 18.0000 0.625166 0.312583 0.949890i 0.398806π-0.398806\pi
0.312583 + 0.949890i 0.398806π0.398806\pi
830830 0 0
831831 −32.0000 −1.11007
832832 0 0
833833 36.0000i 1.24733i
834834 0 0
835835 24.0000 + 12.0000i 0.830554 + 0.415277i
836836 0 0
837837 4.00000i 0.138260i
838838 0 0
839839 56.0000 1.93333 0.966667 0.256036i 0.0824164π-0.0824164\pi
0.966667 + 0.256036i 0.0824164π0.0824164\pi
840840 0 0
841841 7.00000 0.241379
842842 0 0
843843 6.00000i 0.206651i
844844 0 0
845845 13.0000 26.0000i 0.447214 0.894427i
846846 0 0
847847 20.0000i 0.687208i
848848 0 0
849849 28.0000 0.960958
850850 0 0
851851 −32.0000 −1.09695
852852 0 0
853853 8.00000i 0.273915i −0.990577 0.136957i 0.956268π-0.956268\pi
0.990577 0.136957i 0.0437323π-0.0437323\pi
854854 0 0
855855 0 0
856856 0 0
857857 12.0000i 0.409912i −0.978771 0.204956i 0.934295π-0.934295\pi
0.978771 0.204956i 0.0657052π-0.0657052\pi
858858 0 0
859859 40.0000 1.36478 0.682391 0.730987i 0.260940π-0.260940\pi
0.682391 + 0.730987i 0.260940π0.260940\pi
860860 0 0
861861 −40.0000 −1.36320
862862 0 0
863863 12.0000i 0.408485i 0.978920 + 0.204242i 0.0654731π0.0654731\pi
−0.978920 + 0.204242i 0.934527π0.934527\pi
864864 0 0
865865 8.00000 + 4.00000i 0.272008 + 0.136004i
866866 0 0
867867 1.00000i 0.0339618i
868868 0 0
869869 −48.0000 −1.62829
870870 0 0
871871 0 0
872872 0 0
873873 8.00000i 0.270759i
874874 0 0
875875 −8.00000 44.0000i −0.270449 1.48747i
876876 0 0
877877 56.0000i 1.89099i 0.325643 + 0.945493i 0.394419π0.394419\pi
−0.325643 + 0.945493i 0.605581π0.605581\pi
878878 0 0
879879 −12.0000 −0.404750
880880 0 0
881881 30.0000 1.01073 0.505363 0.862907i 0.331359π-0.331359\pi
0.505363 + 0.862907i 0.331359π0.331359\pi
882882 0 0
883883 12.0000i 0.403832i 0.979403 + 0.201916i 0.0647168π0.0647168\pi
−0.979403 + 0.201916i 0.935283π0.935283\pi
884884 0 0
885885 8.00000 + 4.00000i 0.268917 + 0.134459i
886886 0 0
887887 36.0000i 1.20876i −0.796696 0.604381i 0.793421π-0.793421\pi
0.796696 0.604381i 0.206579π-0.206579\pi
888888 0 0
889889 −16.0000 −0.536623
890890 0 0
891891 −4.00000 −0.134005
892892 0 0
893893 0 0
894894 0 0
895895 −4.00000 + 8.00000i −0.133705 + 0.267411i
896896 0 0
897897 0 0
898898 0 0
899899 24.0000 0.800445
900900 0 0
901901 −48.0000 −1.59911
902902 0 0
903903 16.0000i 0.532447i
904904 0 0
905905 −10.0000 + 20.0000i −0.332411 + 0.664822i
906906 0 0
907907 12.0000i 0.398453i 0.979953 + 0.199227i 0.0638430π0.0638430\pi
−0.979953 + 0.199227i 0.936157π0.936157\pi
908908 0 0
909909 2.00000 0.0663358
910910 0 0
911911 48.0000 1.59031 0.795155 0.606406i 0.207389π-0.207389\pi
0.795155 + 0.606406i 0.207389π0.207389\pi
912912 0 0
913913 16.0000i 0.529523i
914914 0 0
915915 −4.00000 2.00000i −0.132236 0.0661180i
916916 0 0
917917 48.0000i 1.58510i
918918 0 0
919919 12.0000 0.395843 0.197922 0.980218i 0.436581π-0.436581\pi
0.197922 + 0.980218i 0.436581π0.436581\pi
920920 0 0
921921 12.0000 0.395413
922922 0 0
923923 0 0
924924 0 0
925925 −32.0000 + 24.0000i −1.05215 + 0.789115i
926926 0 0
927927 4.00000i 0.131377i
928928 0 0
929929 −18.0000 −0.590561 −0.295280 0.955411i 0.595413π-0.595413\pi
−0.295280 + 0.955411i 0.595413π0.595413\pi
930930 0 0
931931 0 0
932932 0 0
933933 24.0000i 0.785725i
934934 0 0
935935 −32.0000 16.0000i −1.04651 0.523256i
936936 0 0
937937 32.0000i 1.04539i 0.852518 + 0.522697i 0.175074π0.175074\pi
−0.852518 + 0.522697i 0.824926π0.824926\pi
938938 0 0
939939 −16.0000 −0.522140
940940 0 0
941941 −10.0000 −0.325991 −0.162995 0.986627i 0.552116π-0.552116\pi
−0.162995 + 0.986627i 0.552116π0.552116\pi
942942 0 0
943943 40.0000i 1.30258i
944944 0 0
945945 −4.00000 + 8.00000i −0.130120 + 0.260240i
946946 0 0
947947 12.0000i 0.389948i 0.980808 + 0.194974i 0.0624622π0.0624622\pi
−0.980808 + 0.194974i 0.937538π0.937538\pi
948948 0 0
949949 0 0
950950 0 0
951951 4.00000 0.129709
952952 0 0
953953 4.00000i 0.129573i 0.997899 + 0.0647864i 0.0206366π0.0206366\pi
−0.997899 + 0.0647864i 0.979363π0.979363\pi
954954 0 0
955955 24.0000 48.0000i 0.776622 1.55324i
956956 0 0
957957 24.0000i 0.775810i
958958 0 0
959959 −48.0000 −1.55000
960960 0 0
961961 −15.0000 −0.483871
962962 0 0
963963 12.0000i 0.386695i
964964 0 0
965965 −32.0000 16.0000i −1.03012 0.515058i
966966 0 0
967967 20.0000i 0.643157i 0.946883 + 0.321578i 0.104213π0.104213\pi
−0.946883 + 0.321578i 0.895787π0.895787\pi
968968 0 0
969969 0 0
970970 0 0
971971 −12.0000 −0.385098 −0.192549 0.981287i 0.561675π-0.561675\pi
−0.192549 + 0.981287i 0.561675π0.561675\pi
972972 0 0
973973 64.0000i 2.05175i
974974 0 0
975975 0 0
976976 0 0
977977 12.0000i 0.383914i −0.981403 0.191957i 0.938517π-0.938517\pi
0.981403 0.191957i 0.0614834π-0.0614834\pi
978978 0 0
979979 −40.0000 −1.27841
980980 0 0
981981 −2.00000 −0.0638551
982982 0 0
983983 28.0000i 0.893061i 0.894768 + 0.446531i 0.147341π0.147341\pi
−0.894768 + 0.446531i 0.852659π0.852659\pi
984984 0 0
985985 −8.00000 4.00000i −0.254901 0.127451i
986986 0 0
987987 16.0000i 0.509286i
988988 0 0
989989 −16.0000 −0.508770
990990 0 0
991991 28.0000 0.889449 0.444725 0.895667i 0.353302π-0.353302\pi
0.444725 + 0.895667i 0.353302π0.353302\pi
992992 0 0
993993 8.00000i 0.253872i
994994 0 0
995995 12.0000 24.0000i 0.380426 0.760851i
996996 0 0
997997 24.0000i 0.760088i −0.924968 0.380044i 0.875909π-0.875909\pi
0.924968 0.380044i 0.124091π-0.124091\pi
998998 0 0
999999 8.00000 0.253109
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 60.2.d.a.49.1 2
3.2 odd 2 180.2.d.a.109.2 2
4.3 odd 2 240.2.f.b.49.2 2
5.2 odd 4 300.2.a.a.1.1 1
5.3 odd 4 300.2.a.d.1.1 1
5.4 even 2 inner 60.2.d.a.49.2 yes 2
7.2 even 3 2940.2.bb.d.949.2 4
7.3 odd 6 2940.2.bb.e.1549.2 4
7.4 even 3 2940.2.bb.d.1549.1 4
7.5 odd 6 2940.2.bb.e.949.1 4
7.6 odd 2 2940.2.k.c.589.2 2
8.3 odd 2 960.2.f.c.769.1 2
8.5 even 2 960.2.f.f.769.2 2
9.2 odd 6 1620.2.r.d.109.1 4
9.4 even 3 1620.2.r.c.1189.1 4
9.5 odd 6 1620.2.r.d.1189.2 4
9.7 even 3 1620.2.r.c.109.2 4
12.11 even 2 720.2.f.c.289.2 2
15.2 even 4 900.2.a.a.1.1 1
15.8 even 4 900.2.a.h.1.1 1
15.14 odd 2 180.2.d.a.109.1 2
16.3 odd 4 3840.2.d.b.2689.1 2
16.5 even 4 3840.2.d.o.2689.2 2
16.11 odd 4 3840.2.d.be.2689.2 2
16.13 even 4 3840.2.d.r.2689.1 2
20.3 even 4 1200.2.a.a.1.1 1
20.7 even 4 1200.2.a.s.1.1 1
20.19 odd 2 240.2.f.b.49.1 2
24.5 odd 2 2880.2.f.l.1729.1 2
24.11 even 2 2880.2.f.p.1729.1 2
35.4 even 6 2940.2.bb.d.1549.2 4
35.9 even 6 2940.2.bb.d.949.1 4
35.19 odd 6 2940.2.bb.e.949.2 4
35.24 odd 6 2940.2.bb.e.1549.1 4
35.34 odd 2 2940.2.k.c.589.1 2
40.3 even 4 4800.2.a.bk.1.1 1
40.13 odd 4 4800.2.a.bj.1.1 1
40.19 odd 2 960.2.f.c.769.2 2
40.27 even 4 4800.2.a.bf.1.1 1
40.29 even 2 960.2.f.f.769.1 2
40.37 odd 4 4800.2.a.bn.1.1 1
45.4 even 6 1620.2.r.c.1189.2 4
45.14 odd 6 1620.2.r.d.1189.1 4
45.29 odd 6 1620.2.r.d.109.2 4
45.34 even 6 1620.2.r.c.109.1 4
60.23 odd 4 3600.2.a.d.1.1 1
60.47 odd 4 3600.2.a.bm.1.1 1
60.59 even 2 720.2.f.c.289.1 2
80.19 odd 4 3840.2.d.be.2689.1 2
80.29 even 4 3840.2.d.o.2689.1 2
80.59 odd 4 3840.2.d.b.2689.2 2
80.69 even 4 3840.2.d.r.2689.2 2
120.29 odd 2 2880.2.f.l.1729.2 2
120.59 even 2 2880.2.f.p.1729.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.2.d.a.49.1 2 1.1 even 1 trivial
60.2.d.a.49.2 yes 2 5.4 even 2 inner
180.2.d.a.109.1 2 15.14 odd 2
180.2.d.a.109.2 2 3.2 odd 2
240.2.f.b.49.1 2 20.19 odd 2
240.2.f.b.49.2 2 4.3 odd 2
300.2.a.a.1.1 1 5.2 odd 4
300.2.a.d.1.1 1 5.3 odd 4
720.2.f.c.289.1 2 60.59 even 2
720.2.f.c.289.2 2 12.11 even 2
900.2.a.a.1.1 1 15.2 even 4
900.2.a.h.1.1 1 15.8 even 4
960.2.f.c.769.1 2 8.3 odd 2
960.2.f.c.769.2 2 40.19 odd 2
960.2.f.f.769.1 2 40.29 even 2
960.2.f.f.769.2 2 8.5 even 2
1200.2.a.a.1.1 1 20.3 even 4
1200.2.a.s.1.1 1 20.7 even 4
1620.2.r.c.109.1 4 45.34 even 6
1620.2.r.c.109.2 4 9.7 even 3
1620.2.r.c.1189.1 4 9.4 even 3
1620.2.r.c.1189.2 4 45.4 even 6
1620.2.r.d.109.1 4 9.2 odd 6
1620.2.r.d.109.2 4 45.29 odd 6
1620.2.r.d.1189.1 4 45.14 odd 6
1620.2.r.d.1189.2 4 9.5 odd 6
2880.2.f.l.1729.1 2 24.5 odd 2
2880.2.f.l.1729.2 2 120.29 odd 2
2880.2.f.p.1729.1 2 24.11 even 2
2880.2.f.p.1729.2 2 120.59 even 2
2940.2.k.c.589.1 2 35.34 odd 2
2940.2.k.c.589.2 2 7.6 odd 2
2940.2.bb.d.949.1 4 35.9 even 6
2940.2.bb.d.949.2 4 7.2 even 3
2940.2.bb.d.1549.1 4 7.4 even 3
2940.2.bb.d.1549.2 4 35.4 even 6
2940.2.bb.e.949.1 4 7.5 odd 6
2940.2.bb.e.949.2 4 35.19 odd 6
2940.2.bb.e.1549.1 4 35.24 odd 6
2940.2.bb.e.1549.2 4 7.3 odd 6
3600.2.a.d.1.1 1 60.23 odd 4
3600.2.a.bm.1.1 1 60.47 odd 4
3840.2.d.b.2689.1 2 16.3 odd 4
3840.2.d.b.2689.2 2 80.59 odd 4
3840.2.d.o.2689.1 2 80.29 even 4
3840.2.d.o.2689.2 2 16.5 even 4
3840.2.d.r.2689.1 2 16.13 even 4
3840.2.d.r.2689.2 2 80.69 even 4
3840.2.d.be.2689.1 2 80.19 odd 4
3840.2.d.be.2689.2 2 16.11 odd 4
4800.2.a.bf.1.1 1 40.27 even 4
4800.2.a.bj.1.1 1 40.13 odd 4
4800.2.a.bk.1.1 1 40.3 even 4
4800.2.a.bn.1.1 1 40.37 odd 4