Properties

Label 1800.2.f.f.649.1
Level 18001800
Weight 22
Character 1800.649
Analytic conductor 14.37314.373
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] = [1800,2,Mod(649,1800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1800.649");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1800=233252 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1800.f (of order 22, degree 11, 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: 14.373072363814.3730723638
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,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 200)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 649.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 1800.649
Dual form 1800.2.f.f.649.2

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) == q2.00000iq71.00000q11+4.00000iq13+5.00000iq171.00000q19+2.00000iq238.00000q29+10.0000q31+6.00000iq37+3.00000q41+4.00000iq43+4.00000iq47+3.00000q496.00000iq53+8.00000q59+10.0000q61+1.00000iq67+12.0000q71+3.00000iq73+2.00000iq776.00000q79+13.0000iq839.00000q89+8.00000q91+14.0000iq97+O(q100)q-2.00000i q^{7} -1.00000 q^{11} +4.00000i q^{13} +5.00000i q^{17} -1.00000 q^{19} +2.00000i q^{23} -8.00000 q^{29} +10.0000 q^{31} +6.00000i q^{37} +3.00000 q^{41} +4.00000i q^{43} +4.00000i q^{47} +3.00000 q^{49} -6.00000i q^{53} +8.00000 q^{59} +10.0000 q^{61} +1.00000i q^{67} +12.0000 q^{71} +3.00000i q^{73} +2.00000i q^{77} -6.00000 q^{79} +13.0000i q^{83} -9.00000 q^{89} +8.00000 q^{91} +14.0000i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q112q1916q29+20q31+6q41+6q49+16q59+20q61+24q7112q7918q89+16q91+O(q100) 2 q - 2 q^{11} - 2 q^{19} - 16 q^{29} + 20 q^{31} + 6 q^{41} + 6 q^{49} + 16 q^{59} + 20 q^{61} + 24 q^{71} - 12 q^{79} - 18 q^{89} + 16 q^{91}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1800Z)×\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times.

nn 577577 901901 10011001 13511351
χ(n)\chi(n) 1-1 11 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 0 0
33 0 0
44 0 0
55 0 0
66 0 0
77 − 2.00000i − 0.755929i −0.925820 0.377964i 0.876624π-0.876624\pi
0.925820 0.377964i 0.123376π-0.123376\pi
88 0 0
99 0 0
1010 0 0
1111 −1.00000 −0.301511 −0.150756 0.988571i 0.548171π-0.548171\pi
−0.150756 + 0.988571i 0.548171π0.548171\pi
1212 0 0
1313 4.00000i 1.10940i 0.832050 + 0.554700i 0.187167π0.187167\pi
−0.832050 + 0.554700i 0.812833π0.812833\pi
1414 0 0
1515 0 0
1616 0 0
1717 5.00000i 1.21268i 0.795206 + 0.606339i 0.207363π0.207363\pi
−0.795206 + 0.606339i 0.792637π0.792637\pi
1818 0 0
1919 −1.00000 −0.229416 −0.114708 0.993399i 0.536593π-0.536593\pi
−0.114708 + 0.993399i 0.536593π0.536593\pi
2020 0 0
2121 0 0
2222 0 0
2323 2.00000i 0.417029i 0.978019 + 0.208514i 0.0668628π0.0668628\pi
−0.978019 + 0.208514i 0.933137π0.933137\pi
2424 0 0
2525 0 0
2626 0 0
2727 0 0
2828 0 0
2929 −8.00000 −1.48556 −0.742781 0.669534i 0.766494π-0.766494\pi
−0.742781 + 0.669534i 0.766494π0.766494\pi
3030 0 0
3131 10.0000 1.79605 0.898027 0.439941i 0.145001π-0.145001\pi
0.898027 + 0.439941i 0.145001π0.145001\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0 0
3737 6.00000i 0.986394i 0.869918 + 0.493197i 0.164172π0.164172\pi
−0.869918 + 0.493197i 0.835828π0.835828\pi
3838 0 0
3939 0 0
4040 0 0
4141 3.00000 0.468521 0.234261 0.972174i 0.424733π-0.424733\pi
0.234261 + 0.972174i 0.424733π0.424733\pi
4242 0 0
4343 4.00000i 0.609994i 0.952353 + 0.304997i 0.0986555π0.0986555\pi
−0.952353 + 0.304997i 0.901344π0.901344\pi
4444 0 0
4545 0 0
4646 0 0
4747 4.00000i 0.583460i 0.956501 + 0.291730i 0.0942309π0.0942309\pi
−0.956501 + 0.291730i 0.905769π0.905769\pi
4848 0 0
4949 3.00000 0.428571
5050 0 0
5151 0 0
5252 0 0
5353 − 6.00000i − 0.824163i −0.911147 0.412082i 0.864802π-0.864802\pi
0.911147 0.412082i 0.135198π-0.135198\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 0 0
5959 8.00000 1.04151 0.520756 0.853706i 0.325650π-0.325650\pi
0.520756 + 0.853706i 0.325650π0.325650\pi
6060 0 0
6161 10.0000 1.28037 0.640184 0.768221i 0.278858π-0.278858\pi
0.640184 + 0.768221i 0.278858π0.278858\pi
6262 0 0
6363 0 0
6464 0 0
6565 0 0
6666 0 0
6767 1.00000i 0.122169i 0.998133 + 0.0610847i 0.0194560π0.0194560\pi
−0.998133 + 0.0610847i 0.980544π0.980544\pi
6868 0 0
6969 0 0
7070 0 0
7171 12.0000 1.42414 0.712069 0.702109i 0.247758π-0.247758\pi
0.712069 + 0.702109i 0.247758π0.247758\pi
7272 0 0
7373 3.00000i 0.351123i 0.984468 + 0.175562i 0.0561742π0.0561742\pi
−0.984468 + 0.175562i 0.943826π0.943826\pi
7474 0 0
7575 0 0
7676 0 0
7777 2.00000i 0.227921i
7878 0 0
7979 −6.00000 −0.675053 −0.337526 0.941316i 0.609590π-0.609590\pi
−0.337526 + 0.941316i 0.609590π0.609590\pi
8080 0 0
8181 0 0
8282 0 0
8383 13.0000i 1.42694i 0.700688 + 0.713468i 0.252876π0.252876\pi
−0.700688 + 0.713468i 0.747124π0.747124\pi
8484 0 0
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 −9.00000 −0.953998 −0.476999 0.878904i 0.658275π-0.658275\pi
−0.476999 + 0.878904i 0.658275π0.658275\pi
9090 0 0
9191 8.00000 0.838628
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 14.0000i 1.42148i 0.703452 + 0.710742i 0.251641π0.251641\pi
−0.703452 + 0.710742i 0.748359π0.748359\pi
9898 0 0
9999 0 0
100100 0 0
101101 −6.00000 −0.597022 −0.298511 0.954406i 0.596490π-0.596490\pi
−0.298511 + 0.954406i 0.596490π0.596490\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 0 0
106106 0 0
107107 − 15.0000i − 1.45010i −0.688694 0.725052i 0.741816π-0.741816\pi
0.688694 0.725052i 0.258184π-0.258184\pi
108108 0 0
109109 −14.0000 −1.34096 −0.670478 0.741929i 0.733911π-0.733911\pi
−0.670478 + 0.741929i 0.733911π0.733911\pi
110110 0 0
111111 0 0
112112 0 0
113113 9.00000i 0.846649i 0.905978 + 0.423324i 0.139137π0.139137\pi
−0.905978 + 0.423324i 0.860863π0.860863\pi
114114 0 0
115115 0 0
116116 0 0
117117 0 0
118118 0 0
119119 10.0000 0.916698
120120 0 0
121121 −10.0000 −0.909091
122122 0 0
123123 0 0
124124 0 0
125125 0 0
126126 0 0
127127 6.00000i 0.532414i 0.963916 + 0.266207i 0.0857705π0.0857705\pi
−0.963916 + 0.266207i 0.914230π0.914230\pi
128128 0 0
129129 0 0
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 2.00000i 0.173422i
134134 0 0
135135 0 0
136136 0 0
137137 13.0000i 1.11066i 0.831628 + 0.555332i 0.187409π0.187409\pi
−0.831628 + 0.555332i 0.812591π0.812591\pi
138138 0 0
139139 −9.00000 −0.763370 −0.381685 0.924292i 0.624656π-0.624656\pi
−0.381685 + 0.924292i 0.624656π0.624656\pi
140140 0 0
141141 0 0
142142 0 0
143143 − 4.00000i − 0.334497i
144144 0 0
145145 0 0
146146 0 0
147147 0 0
148148 0 0
149149 8.00000 0.655386 0.327693 0.944784i 0.393729π-0.393729\pi
0.327693 + 0.944784i 0.393729π0.393729\pi
150150 0 0
151151 2.00000 0.162758 0.0813788 0.996683i 0.474068π-0.474068\pi
0.0813788 + 0.996683i 0.474068π0.474068\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 0 0
157157 14.0000i 1.11732i 0.829396 + 0.558661i 0.188685π0.188685\pi
−0.829396 + 0.558661i 0.811315π0.811315\pi
158158 0 0
159159 0 0
160160 0 0
161161 4.00000 0.315244
162162 0 0
163163 7.00000i 0.548282i 0.961689 + 0.274141i 0.0883936π0.0883936\pi
−0.961689 + 0.274141i 0.911606π0.911606\pi
164164 0 0
165165 0 0
166166 0 0
167167 − 12.0000i − 0.928588i −0.885681 0.464294i 0.846308π-0.846308\pi
0.885681 0.464294i 0.153692π-0.153692\pi
168168 0 0
169169 −3.00000 −0.230769
170170 0 0
171171 0 0
172172 0 0
173173 − 8.00000i − 0.608229i −0.952636 0.304114i 0.901639π-0.901639\pi
0.952636 0.304114i 0.0983605π-0.0983605\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 −19.0000 −1.42013 −0.710063 0.704138i 0.751334π-0.751334\pi
−0.710063 + 0.704138i 0.751334π0.751334\pi
180180 0 0
181181 2.00000 0.148659 0.0743294 0.997234i 0.476318π-0.476318\pi
0.0743294 + 0.997234i 0.476318π0.476318\pi
182182 0 0
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 − 5.00000i − 0.365636i
188188 0 0
189189 0 0
190190 0 0
191191 10.0000 0.723575 0.361787 0.932261i 0.382167π-0.382167\pi
0.361787 + 0.932261i 0.382167π0.382167\pi
192192 0 0
193193 − 11.0000i − 0.791797i −0.918294 0.395899i 0.870433π-0.870433\pi
0.918294 0.395899i 0.129567π-0.129567\pi
194194 0 0
195195 0 0
196196 0 0
197197 − 2.00000i − 0.142494i −0.997459 0.0712470i 0.977302π-0.977302\pi
0.997459 0.0712470i 0.0226979π-0.0226979\pi
198198 0 0
199199 28.0000 1.98487 0.992434 0.122782i 0.0391815π-0.0391815\pi
0.992434 + 0.122782i 0.0391815π0.0391815\pi
200200 0 0
201201 0 0
202202 0 0
203203 16.0000i 1.12298i
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 1.00000 0.0691714
210210 0 0
211211 −1.00000 −0.0688428 −0.0344214 0.999407i 0.510959π-0.510959\pi
−0.0344214 + 0.999407i 0.510959π0.510959\pi
212212 0 0
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 − 20.0000i − 1.35769i
218218 0 0
219219 0 0
220220 0 0
221221 −20.0000 −1.34535
222222 0 0
223223 − 4.00000i − 0.267860i −0.990991 0.133930i 0.957240π-0.957240\pi
0.990991 0.133930i 0.0427597π-0.0427597\pi
224224 0 0
225225 0 0
226226 0 0
227227 − 12.0000i − 0.796468i −0.917284 0.398234i 0.869623π-0.869623\pi
0.917284 0.398234i 0.130377π-0.130377\pi
228228 0 0
229229 −4.00000 −0.264327 −0.132164 0.991228i 0.542192π-0.542192\pi
−0.132164 + 0.991228i 0.542192π0.542192\pi
230230 0 0
231231 0 0
232232 0 0
233233 − 6.00000i − 0.393073i −0.980497 0.196537i 0.937031π-0.937031\pi
0.980497 0.196537i 0.0629694π-0.0629694\pi
234234 0 0
235235 0 0
236236 0 0
237237 0 0
238238 0 0
239239 24.0000 1.55243 0.776215 0.630468i 0.217137π-0.217137\pi
0.776215 + 0.630468i 0.217137π0.217137\pi
240240 0 0
241241 −7.00000 −0.450910 −0.225455 0.974254i 0.572387π-0.572387\pi
−0.225455 + 0.974254i 0.572387π0.572387\pi
242242 0 0
243243 0 0
244244 0 0
245245 0 0
246246 0 0
247247 − 4.00000i − 0.254514i
248248 0 0
249249 0 0
250250 0 0
251251 −15.0000 −0.946792 −0.473396 0.880850i 0.656972π-0.656972\pi
−0.473396 + 0.880850i 0.656972π0.656972\pi
252252 0 0
253253 − 2.00000i − 0.125739i
254254 0 0
255255 0 0
256256 0 0
257257 30.0000i 1.87135i 0.352865 + 0.935674i 0.385208π0.385208\pi
−0.352865 + 0.935674i 0.614792π0.614792\pi
258258 0 0
259259 12.0000 0.745644
260260 0 0
261261 0 0
262262 0 0
263263 − 30.0000i − 1.84988i −0.380114 0.924940i 0.624115π-0.624115\pi
0.380114 0.924940i 0.375885π-0.375885\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 0 0
269269 −16.0000 −0.975537 −0.487769 0.872973i 0.662189π-0.662189\pi
−0.487769 + 0.872973i 0.662189π0.662189\pi
270270 0 0
271271 −6.00000 −0.364474 −0.182237 0.983255i 0.558334π-0.558334\pi
−0.182237 + 0.983255i 0.558334π0.558334\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 − 8.00000i − 0.480673i −0.970690 0.240337i 0.922742π-0.922742\pi
0.970690 0.240337i 0.0772579π-0.0772579\pi
278278 0 0
279279 0 0
280280 0 0
281281 2.00000 0.119310 0.0596550 0.998219i 0.481000π-0.481000\pi
0.0596550 + 0.998219i 0.481000π0.481000\pi
282282 0 0
283283 − 1.00000i − 0.0594438i −0.999558 0.0297219i 0.990538π-0.990538\pi
0.999558 0.0297219i 0.00946217π-0.00946217\pi
284284 0 0
285285 0 0
286286 0 0
287287 − 6.00000i − 0.354169i
288288 0 0
289289 −8.00000 −0.470588
290290 0 0
291291 0 0
292292 0 0
293293 2.00000i 0.116841i 0.998292 + 0.0584206i 0.0186065π0.0186065\pi
−0.998292 + 0.0584206i 0.981394π0.981394\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 −8.00000 −0.462652
300300 0 0
301301 8.00000 0.461112
302302 0 0
303303 0 0
304304 0 0
305305 0 0
306306 0 0
307307 − 13.0000i − 0.741949i −0.928643 0.370975i 0.879024π-0.879024\pi
0.928643 0.370975i 0.120976π-0.120976\pi
308308 0 0
309309 0 0
310310 0 0
311311 −14.0000 −0.793867 −0.396934 0.917847i 0.629926π-0.629926\pi
−0.396934 + 0.917847i 0.629926π0.629926\pi
312312 0 0
313313 − 22.0000i − 1.24351i −0.783210 0.621757i 0.786419π-0.786419\pi
0.783210 0.621757i 0.213581π-0.213581\pi
314314 0 0
315315 0 0
316316 0 0
317317 12.0000i 0.673987i 0.941507 + 0.336994i 0.109410π0.109410\pi
−0.941507 + 0.336994i 0.890590π0.890590\pi
318318 0 0
319319 8.00000 0.447914
320320 0 0
321321 0 0
322322 0 0
323323 − 5.00000i − 0.278207i
324324 0 0
325325 0 0
326326 0 0
327327 0 0
328328 0 0
329329 8.00000 0.441054
330330 0 0
331331 −27.0000 −1.48405 −0.742027 0.670370i 0.766135π-0.766135\pi
−0.742027 + 0.670370i 0.766135π0.766135\pi
332332 0 0
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 − 19.0000i − 1.03500i −0.855684 0.517498i 0.826864π-0.826864\pi
0.855684 0.517498i 0.173136π-0.173136\pi
338338 0 0
339339 0 0
340340 0 0
341341 −10.0000 −0.541530
342342 0 0
343343 − 20.0000i − 1.07990i
344344 0 0
345345 0 0
346346 0 0
347347 17.0000i 0.912608i 0.889824 + 0.456304i 0.150827π0.150827\pi
−0.889824 + 0.456304i 0.849173π0.849173\pi
348348 0 0
349349 18.0000 0.963518 0.481759 0.876304i 0.339998π-0.339998\pi
0.481759 + 0.876304i 0.339998π0.339998\pi
350350 0 0
351351 0 0
352352 0 0
353353 10.0000i 0.532246i 0.963939 + 0.266123i 0.0857428π0.0857428\pi
−0.963939 + 0.266123i 0.914257π0.914257\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 −18.0000 −0.950004 −0.475002 0.879985i 0.657553π-0.657553\pi
−0.475002 + 0.879985i 0.657553π0.657553\pi
360360 0 0
361361 −18.0000 −0.947368
362362 0 0
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 − 20.0000i − 1.04399i −0.852948 0.521996i 0.825188π-0.825188\pi
0.852948 0.521996i 0.174812π-0.174812\pi
368368 0 0
369369 0 0
370370 0 0
371371 −12.0000 −0.623009
372372 0 0
373373 10.0000i 0.517780i 0.965907 + 0.258890i 0.0833568π0.0833568\pi
−0.965907 + 0.258890i 0.916643π0.916643\pi
374374 0 0
375375 0 0
376376 0 0
377377 − 32.0000i − 1.64808i
378378 0 0
379379 5.00000 0.256833 0.128416 0.991720i 0.459011π-0.459011\pi
0.128416 + 0.991720i 0.459011π0.459011\pi
380380 0 0
381381 0 0
382382 0 0
383383 − 6.00000i − 0.306586i −0.988181 0.153293i 0.951012π-0.951012\pi
0.988181 0.153293i 0.0489878π-0.0489878\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 30.0000 1.52106 0.760530 0.649303i 0.224939π-0.224939\pi
0.760530 + 0.649303i 0.224939π0.224939\pi
390390 0 0
391391 −10.0000 −0.505722
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 − 4.00000i − 0.200754i −0.994949 0.100377i 0.967995π-0.967995\pi
0.994949 0.100377i 0.0320049π-0.0320049\pi
398398 0 0
399399 0 0
400400 0 0
401401 −21.0000 −1.04869 −0.524345 0.851506i 0.675690π-0.675690\pi
−0.524345 + 0.851506i 0.675690π0.675690\pi
402402 0 0
403403 40.0000i 1.99254i
404404 0 0
405405 0 0
406406 0 0
407407 − 6.00000i − 0.297409i
408408 0 0
409409 11.0000 0.543915 0.271957 0.962309i 0.412329π-0.412329\pi
0.271957 + 0.962309i 0.412329π0.412329\pi
410410 0 0
411411 0 0
412412 0 0
413413 − 16.0000i − 0.787309i
414414 0 0
415415 0 0
416416 0 0
417417 0 0
418418 0 0
419419 −3.00000 −0.146560 −0.0732798 0.997311i 0.523347π-0.523347\pi
−0.0732798 + 0.997311i 0.523347π0.523347\pi
420420 0 0
421421 −12.0000 −0.584844 −0.292422 0.956289i 0.594461π-0.594461\pi
−0.292422 + 0.956289i 0.594461π0.594461\pi
422422 0 0
423423 0 0
424424 0 0
425425 0 0
426426 0 0
427427 − 20.0000i − 0.967868i
428428 0 0
429429 0 0
430430 0 0
431431 34.0000 1.63772 0.818861 0.573992i 0.194606π-0.194606\pi
0.818861 + 0.573992i 0.194606π0.194606\pi
432432 0 0
433433 5.00000i 0.240285i 0.992757 + 0.120142i 0.0383351π0.0383351\pi
−0.992757 + 0.120142i 0.961665π0.961665\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 2.00000i − 0.0956730i
438438 0 0
439439 −16.0000 −0.763638 −0.381819 0.924237i 0.624702π-0.624702\pi
−0.381819 + 0.924237i 0.624702π0.624702\pi
440440 0 0
441441 0 0
442442 0 0
443443 21.0000i 0.997740i 0.866677 + 0.498870i 0.166252π0.166252\pi
−0.866677 + 0.498870i 0.833748π0.833748\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 −39.0000 −1.84052 −0.920262 0.391303i 0.872024π-0.872024\pi
−0.920262 + 0.391303i 0.872024π0.872024\pi
450450 0 0
451451 −3.00000 −0.141264
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 − 1.00000i − 0.0467780i −0.999726 0.0233890i 0.992554π-0.992554\pi
0.999726 0.0233890i 0.00744563π-0.00744563\pi
458458 0 0
459459 0 0
460460 0 0
461461 −12.0000 −0.558896 −0.279448 0.960161i 0.590151π-0.590151\pi
−0.279448 + 0.960161i 0.590151π0.590151\pi
462462 0 0
463463 − 36.0000i − 1.67306i −0.547920 0.836531i 0.684580π-0.684580\pi
0.547920 0.836531i 0.315420π-0.315420\pi
464464 0 0
465465 0 0
466466 0 0
467467 − 28.0000i − 1.29569i −0.761774 0.647843i 0.775671π-0.775671\pi
0.761774 0.647843i 0.224329π-0.224329\pi
468468 0 0
469469 2.00000 0.0923514
470470 0 0
471471 0 0
472472 0 0
473473 − 4.00000i − 0.183920i
474474 0 0
475475 0 0
476476 0 0
477477 0 0
478478 0 0
479479 22.0000 1.00521 0.502603 0.864517i 0.332376π-0.332376\pi
0.502603 + 0.864517i 0.332376π0.332376\pi
480480 0 0
481481 −24.0000 −1.09431
482482 0 0
483483 0 0
484484 0 0
485485 0 0
486486 0 0
487487 38.0000i 1.72194i 0.508652 + 0.860972i 0.330144π0.330144\pi
−0.508652 + 0.860972i 0.669856π0.669856\pi
488488 0 0
489489 0 0
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 − 40.0000i − 1.80151i
494494 0 0
495495 0 0
496496 0 0
497497 − 24.0000i − 1.07655i
498498 0 0
499499 4.00000 0.179065 0.0895323 0.995984i 0.471463π-0.471463\pi
0.0895323 + 0.995984i 0.471463π0.471463\pi
500500 0 0
501501 0 0
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 0 0
506506 0 0
507507 0 0
508508 0 0
509509 34.0000 1.50702 0.753512 0.657434i 0.228358π-0.228358\pi
0.753512 + 0.657434i 0.228358π0.228358\pi
510510 0 0
511511 6.00000 0.265424
512512 0 0
513513 0 0
514514 0 0
515515 0 0
516516 0 0
517517 − 4.00000i − 0.175920i
518518 0 0
519519 0 0
520520 0 0
521521 35.0000 1.53338 0.766689 0.642019i 0.221903π-0.221903\pi
0.766689 + 0.642019i 0.221903π0.221903\pi
522522 0 0
523523 − 35.0000i − 1.53044i −0.643767 0.765222i 0.722629π-0.722629\pi
0.643767 0.765222i 0.277371π-0.277371\pi
524524 0 0
525525 0 0
526526 0 0
527527 50.0000i 2.17803i
528528 0 0
529529 19.0000 0.826087
530530 0 0
531531 0 0
532532 0 0
533533 12.0000i 0.519778i
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 0 0
539539 −3.00000 −0.129219
540540 0 0
541541 −32.0000 −1.37579 −0.687894 0.725811i 0.741464π-0.741464\pi
−0.687894 + 0.725811i 0.741464π0.741464\pi
542542 0 0
543543 0 0
544544 0 0
545545 0 0
546546 0 0
547547 19.0000i 0.812381i 0.913788 + 0.406191i 0.133143π0.133143\pi
−0.913788 + 0.406191i 0.866857π0.866857\pi
548548 0 0
549549 0 0
550550 0 0
551551 8.00000 0.340811
552552 0 0
553553 12.0000i 0.510292i
554554 0 0
555555 0 0
556556 0 0
557557 − 28.0000i − 1.18640i −0.805056 0.593199i 0.797865π-0.797865\pi
0.805056 0.593199i 0.202135π-0.202135\pi
558558 0 0
559559 −16.0000 −0.676728
560560 0 0
561561 0 0
562562 0 0
563563 32.0000i 1.34864i 0.738440 + 0.674320i 0.235563π0.235563\pi
−0.738440 + 0.674320i 0.764437π0.764437\pi
564564 0 0
565565 0 0
566566 0 0
567567 0 0
568568 0 0
569569 17.0000 0.712677 0.356339 0.934357i 0.384025π-0.384025\pi
0.356339 + 0.934357i 0.384025π0.384025\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 0 0
574574 0 0
575575 0 0
576576 0 0
577577 13.0000i 0.541197i 0.962692 + 0.270599i 0.0872216π0.0872216\pi
−0.962692 + 0.270599i 0.912778π0.912778\pi
578578 0 0
579579 0 0
580580 0 0
581581 26.0000 1.07866
582582 0 0
583583 6.00000i 0.248495i
584584 0 0
585585 0 0
586586 0 0
587587 3.00000i 0.123823i 0.998082 + 0.0619116i 0.0197197π0.0197197\pi
−0.998082 + 0.0619116i 0.980280π0.980280\pi
588588 0 0
589589 −10.0000 −0.412043
590590 0 0
591591 0 0
592592 0 0
593593 − 39.0000i − 1.60154i −0.598973 0.800769i 0.704424π-0.704424\pi
0.598973 0.800769i 0.295576π-0.295576\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
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 43.0000 1.75401 0.877003 0.480484i 0.159539π-0.159539\pi
0.877003 + 0.480484i 0.159539π0.159539\pi
602602 0 0
603603 0 0
604604 0 0
605605 0 0
606606 0 0
607607 0 0 1.00000 00
−1.00000 π\pi
608608 0 0
609609 0 0
610610 0 0
611611 −16.0000 −0.647291
612612 0 0
613613 30.0000i 1.21169i 0.795583 + 0.605844i 0.207165π0.207165\pi
−0.795583 + 0.605844i 0.792835π0.792835\pi
614614 0 0
615615 0 0
616616 0 0
617617 − 18.0000i − 0.724653i −0.932051 0.362326i 0.881983π-0.881983\pi
0.932051 0.362326i 0.118017π-0.118017\pi
618618 0 0
619619 −44.0000 −1.76851 −0.884255 0.467005i 0.845333π-0.845333\pi
−0.884255 + 0.467005i 0.845333π0.845333\pi
620620 0 0
621621 0 0
622622 0 0
623623 18.0000i 0.721155i
624624 0 0
625625 0 0
626626 0 0
627627 0 0
628628 0 0
629629 −30.0000 −1.19618
630630 0 0
631631 10.0000 0.398094 0.199047 0.979990i 0.436215π-0.436215\pi
0.199047 + 0.979990i 0.436215π0.436215\pi
632632 0 0
633633 0 0
634634 0 0
635635 0 0
636636 0 0
637637 12.0000i 0.475457i
638638 0 0
639639 0 0
640640 0 0
641641 6.00000 0.236986 0.118493 0.992955i 0.462194π-0.462194\pi
0.118493 + 0.992955i 0.462194π0.462194\pi
642642 0 0
643643 − 12.0000i − 0.473234i −0.971603 0.236617i 0.923961π-0.923961\pi
0.971603 0.236617i 0.0760386π-0.0760386\pi
644644 0 0
645645 0 0
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 −8.00000 −0.314027
650650 0 0
651651 0 0
652652 0 0
653653 34.0000i 1.33052i 0.746611 + 0.665261i 0.231680π0.231680\pi
−0.746611 + 0.665261i 0.768320π0.768320\pi
654654 0 0
655655 0 0
656656 0 0
657657 0 0
658658 0 0
659659 −21.0000 −0.818044 −0.409022 0.912525i 0.634130π-0.634130\pi
−0.409022 + 0.912525i 0.634130π0.634130\pi
660660 0 0
661661 24.0000 0.933492 0.466746 0.884391i 0.345426π-0.345426\pi
0.466746 + 0.884391i 0.345426π0.345426\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 − 16.0000i − 0.619522i
668668 0 0
669669 0 0
670670 0 0
671671 −10.0000 −0.386046
672672 0 0
673673 − 6.00000i − 0.231283i −0.993291 0.115642i 0.963108π-0.963108\pi
0.993291 0.115642i 0.0368924π-0.0368924\pi
674674 0 0
675675 0 0
676676 0 0
677677 − 32.0000i − 1.22986i −0.788582 0.614930i 0.789184π-0.789184\pi
0.788582 0.614930i 0.210816π-0.210816\pi
678678 0 0
679679 28.0000 1.07454
680680 0 0
681681 0 0
682682 0 0
683683 3.00000i 0.114792i 0.998351 + 0.0573959i 0.0182797π0.0182797\pi
−0.998351 + 0.0573959i 0.981720π0.981720\pi
684684 0 0
685685 0 0
686686 0 0
687687 0 0
688688 0 0
689689 24.0000 0.914327
690690 0 0
691691 −19.0000 −0.722794 −0.361397 0.932412i 0.617700π-0.617700\pi
−0.361397 + 0.932412i 0.617700π0.617700\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 15.0000i 0.568166i
698698 0 0
699699 0 0
700700 0 0
701701 28.0000 1.05755 0.528773 0.848763i 0.322652π-0.322652\pi
0.528773 + 0.848763i 0.322652π0.322652\pi
702702 0 0
703703 − 6.00000i − 0.226294i
704704 0 0
705705 0 0
706706 0 0
707707 12.0000i 0.451306i
708708 0 0
709709 28.0000 1.05156 0.525781 0.850620i 0.323773π-0.323773\pi
0.525781 + 0.850620i 0.323773π0.323773\pi
710710 0 0
711711 0 0
712712 0 0
713713 20.0000i 0.749006i
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 −14.0000 −0.522112 −0.261056 0.965324i 0.584071π-0.584071\pi
−0.261056 + 0.965324i 0.584071π0.584071\pi
720720 0 0
721721 8.00000 0.297936
722722 0 0
723723 0 0
724724 0 0
725725 0 0
726726 0 0
727727 − 8.00000i − 0.296704i −0.988935 0.148352i 0.952603π-0.952603\pi
0.988935 0.148352i 0.0473968π-0.0473968\pi
728728 0 0
729729 0 0
730730 0 0
731731 −20.0000 −0.739727
732732 0 0
733733 36.0000i 1.32969i 0.746981 + 0.664845i 0.231502π0.231502\pi
−0.746981 + 0.664845i 0.768498π0.768498\pi
734734 0 0
735735 0 0
736736 0 0
737737 − 1.00000i − 0.0368355i
738738 0 0
739739 −12.0000 −0.441427 −0.220714 0.975339i 0.570839π-0.570839\pi
−0.220714 + 0.975339i 0.570839π0.570839\pi
740740 0 0
741741 0 0
742742 0 0
743743 − 30.0000i − 1.10059i −0.834969 0.550297i 0.814515π-0.814515\pi
0.834969 0.550297i 0.185485π-0.185485\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 −30.0000 −1.09618
750750 0 0
751751 24.0000 0.875772 0.437886 0.899030i 0.355727π-0.355727\pi
0.437886 + 0.899030i 0.355727π0.355727\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 − 32.0000i − 1.16306i −0.813525 0.581530i 0.802454π-0.802454\pi
0.813525 0.581530i 0.197546π-0.197546\pi
758758 0 0
759759 0 0
760760 0 0
761761 3.00000 0.108750 0.0543750 0.998521i 0.482683π-0.482683\pi
0.0543750 + 0.998521i 0.482683π0.482683\pi
762762 0 0
763763 28.0000i 1.01367i
764764 0 0
765765 0 0
766766 0 0
767767 32.0000i 1.15545i
768768 0 0
769769 −13.0000 −0.468792 −0.234396 0.972141i 0.575311π-0.575311\pi
−0.234396 + 0.972141i 0.575311π0.575311\pi
770770 0 0
771771 0 0
772772 0 0
773773 0 0 1.00000 00
−1.00000 π\pi
774774 0 0
775775 0 0
776776 0 0
777777 0 0
778778 0 0
779779 −3.00000 −0.107486
780780 0 0
781781 −12.0000 −0.429394
782782 0 0
783783 0 0
784784 0 0
785785 0 0
786786 0 0
787787 52.0000i 1.85360i 0.375555 + 0.926800i 0.377452π0.377452\pi
−0.375555 + 0.926800i 0.622548π0.622548\pi
788788 0 0
789789 0 0
790790 0 0
791791 18.0000 0.640006
792792 0 0
793793 40.0000i 1.42044i
794794 0 0
795795 0 0
796796 0 0
797797 42.0000i 1.48772i 0.668338 + 0.743858i 0.267006π0.267006\pi
−0.668338 + 0.743858i 0.732994π0.732994\pi
798798 0 0
799799 −20.0000 −0.707549
800800 0 0
801801 0 0
802802 0 0
803803 − 3.00000i − 0.105868i
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 18.0000 0.632846 0.316423 0.948618i 0.397518π-0.397518\pi
0.316423 + 0.948618i 0.397518π0.397518\pi
810810 0 0
811811 44.0000 1.54505 0.772524 0.634985i 0.218994π-0.218994\pi
0.772524 + 0.634985i 0.218994π0.218994\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 − 4.00000i − 0.139942i
818818 0 0
819819 0 0
820820 0 0
821821 38.0000 1.32621 0.663105 0.748527i 0.269238π-0.269238\pi
0.663105 + 0.748527i 0.269238π0.269238\pi
822822 0 0
823823 28.0000i 0.976019i 0.872838 + 0.488009i 0.162277π0.162277\pi
−0.872838 + 0.488009i 0.837723π0.837723\pi
824824 0 0
825825 0 0
826826 0 0
827827 3.00000i 0.104320i 0.998639 + 0.0521601i 0.0166106π0.0166106\pi
−0.998639 + 0.0521601i 0.983389π0.983389\pi
828828 0 0
829829 20.0000 0.694629 0.347314 0.937749i 0.387094π-0.387094\pi
0.347314 + 0.937749i 0.387094π0.387094\pi
830830 0 0
831831 0 0
832832 0 0
833833 15.0000i 0.519719i
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 −16.0000 −0.552381 −0.276191 0.961103i 0.589072π-0.589072\pi
−0.276191 + 0.961103i 0.589072π0.589072\pi
840840 0 0
841841 35.0000 1.20690
842842 0 0
843843 0 0
844844 0 0
845845 0 0
846846 0 0
847847 20.0000i 0.687208i
848848 0 0
849849 0 0
850850 0 0
851851 −12.0000 −0.411355
852852 0 0
853853 − 22.0000i − 0.753266i −0.926363 0.376633i 0.877082π-0.877082\pi
0.926363 0.376633i 0.122918π-0.122918\pi
854854 0 0
855855 0 0
856856 0 0
857857 − 3.00000i − 0.102478i −0.998686 0.0512390i 0.983683π-0.983683\pi
0.998686 0.0512390i 0.0163170π-0.0163170\pi
858858 0 0
859859 −41.0000 −1.39890 −0.699451 0.714681i 0.746572π-0.746572\pi
−0.699451 + 0.714681i 0.746572π0.746572\pi
860860 0 0
861861 0 0
862862 0 0
863863 − 48.0000i − 1.63394i −0.576681 0.816970i 0.695652π-0.695652\pi
0.576681 0.816970i 0.304348π-0.304348\pi
864864 0 0
865865 0 0
866866 0 0
867867 0 0
868868 0 0
869869 6.00000 0.203536
870870 0 0
871871 −4.00000 −0.135535
872872 0 0
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 − 4.00000i − 0.135070i −0.997717 0.0675352i 0.978487π-0.978487\pi
0.997717 0.0675352i 0.0215135π-0.0215135\pi
878878 0 0
879879 0 0
880880 0 0
881881 −30.0000 −1.01073 −0.505363 0.862907i 0.668641π-0.668641\pi
−0.505363 + 0.862907i 0.668641π0.668641\pi
882882 0 0
883883 5.00000i 0.168263i 0.996455 + 0.0841317i 0.0268116π0.0268116\pi
−0.996455 + 0.0841317i 0.973188π0.973188\pi
884884 0 0
885885 0 0
886886 0 0
887887 28.0000i 0.940148i 0.882627 + 0.470074i 0.155773π0.155773\pi
−0.882627 + 0.470074i 0.844227π0.844227\pi
888888 0 0
889889 12.0000 0.402467
890890 0 0
891891 0 0
892892 0 0
893893 − 4.00000i − 0.133855i
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 −80.0000 −2.66815
900900 0 0
901901 30.0000 0.999445
902902 0 0
903903 0 0
904904 0 0
905905 0 0
906906 0 0
907907 − 12.0000i − 0.398453i −0.979953 0.199227i 0.936157π-0.936157\pi
0.979953 0.199227i 0.0638430π-0.0638430\pi
908908 0 0
909909 0 0
910910 0 0
911911 −28.0000 −0.927681 −0.463841 0.885919i 0.653529π-0.653529\pi
−0.463841 + 0.885919i 0.653529π0.653529\pi
912912 0 0
913913 − 13.0000i − 0.430237i
914914 0 0
915915 0 0
916916 0 0
917917 − 24.0000i − 0.792550i
918918 0 0
919919 34.0000 1.12156 0.560778 0.827966i 0.310502π-0.310502\pi
0.560778 + 0.827966i 0.310502π0.310502\pi
920920 0 0
921921 0 0
922922 0 0
923923 48.0000i 1.57994i
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 −2.00000 −0.0656179 −0.0328089 0.999462i 0.510445π-0.510445\pi
−0.0328089 + 0.999462i 0.510445π0.510445\pi
930930 0 0
931931 −3.00000 −0.0983210
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 5.00000i 0.163343i 0.996659 + 0.0816714i 0.0260258π0.0260258\pi
−0.996659 + 0.0816714i 0.973974π0.973974\pi
938938 0 0
939939 0 0
940940 0 0
941941 −4.00000 −0.130396 −0.0651981 0.997872i 0.520768π-0.520768\pi
−0.0651981 + 0.997872i 0.520768π0.520768\pi
942942 0 0
943943 6.00000i 0.195387i
944944 0 0
945945 0 0
946946 0 0
947947 40.0000i 1.29983i 0.760009 + 0.649913i 0.225195π0.225195\pi
−0.760009 + 0.649913i 0.774805π0.774805\pi
948948 0 0
949949 −12.0000 −0.389536
950950 0 0
951951 0 0
952952 0 0
953953 39.0000i 1.26333i 0.775240 + 0.631667i 0.217629π0.217629\pi
−0.775240 + 0.631667i 0.782371π0.782371\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 26.0000 0.839584
960960 0 0
961961 69.0000 2.22581
962962 0 0
963963 0 0
964964 0 0
965965 0 0
966966 0 0
967967 0 0 1.00000 00
−1.00000 π\pi
968968 0 0
969969 0 0
970970 0 0
971971 31.0000 0.994837 0.497419 0.867511i 0.334281π-0.334281\pi
0.497419 + 0.867511i 0.334281π0.334281\pi
972972 0 0
973973 18.0000i 0.577054i
974974 0 0
975975 0 0
976976 0 0
977977 17.0000i 0.543878i 0.962314 + 0.271939i 0.0876649π0.0876649\pi
−0.962314 + 0.271939i 0.912335π0.912335\pi
978978 0 0
979979 9.00000 0.287641
980980 0 0
981981 0 0
982982 0 0
983983 − 6.00000i − 0.191370i −0.995412 0.0956851i 0.969496π-0.969496\pi
0.995412 0.0956851i 0.0305042π-0.0305042\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 −8.00000 −0.254385
990990 0 0
991991 38.0000 1.20711 0.603555 0.797321i 0.293750π-0.293750\pi
0.603555 + 0.797321i 0.293750π0.293750\pi
992992 0 0
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 12.0000i 0.380044i 0.981780 + 0.190022i 0.0608559π0.0608559\pi
−0.981780 + 0.190022i 0.939144π0.939144\pi
998998 0 0
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 1800.2.f.f.649.1 2
3.2 odd 2 200.2.c.a.49.1 2
4.3 odd 2 3600.2.f.n.2449.2 2
5.2 odd 4 1800.2.a.r.1.1 1
5.3 odd 4 1800.2.a.h.1.1 1
5.4 even 2 inner 1800.2.f.f.649.2 2
12.11 even 2 400.2.c.a.49.2 2
15.2 even 4 200.2.a.a.1.1 1
15.8 even 4 200.2.a.e.1.1 yes 1
15.14 odd 2 200.2.c.a.49.2 2
20.3 even 4 3600.2.a.bf.1.1 1
20.7 even 4 3600.2.a.m.1.1 1
20.19 odd 2 3600.2.f.n.2449.1 2
24.5 odd 2 1600.2.c.a.449.2 2
24.11 even 2 1600.2.c.b.449.1 2
60.23 odd 4 400.2.a.a.1.1 1
60.47 odd 4 400.2.a.h.1.1 1
60.59 even 2 400.2.c.a.49.1 2
105.62 odd 4 9800.2.a.bq.1.1 1
105.83 odd 4 9800.2.a.c.1.1 1
120.29 odd 2 1600.2.c.a.449.1 2
120.53 even 4 1600.2.a.a.1.1 1
120.59 even 2 1600.2.c.b.449.2 2
120.77 even 4 1600.2.a.x.1.1 1
120.83 odd 4 1600.2.a.y.1.1 1
120.107 odd 4 1600.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.2.a.a.1.1 1 15.2 even 4
200.2.a.e.1.1 yes 1 15.8 even 4
200.2.c.a.49.1 2 3.2 odd 2
200.2.c.a.49.2 2 15.14 odd 2
400.2.a.a.1.1 1 60.23 odd 4
400.2.a.h.1.1 1 60.47 odd 4
400.2.c.a.49.1 2 60.59 even 2
400.2.c.a.49.2 2 12.11 even 2
1600.2.a.a.1.1 1 120.53 even 4
1600.2.a.b.1.1 1 120.107 odd 4
1600.2.a.x.1.1 1 120.77 even 4
1600.2.a.y.1.1 1 120.83 odd 4
1600.2.c.a.449.1 2 120.29 odd 2
1600.2.c.a.449.2 2 24.5 odd 2
1600.2.c.b.449.1 2 24.11 even 2
1600.2.c.b.449.2 2 120.59 even 2
1800.2.a.h.1.1 1 5.3 odd 4
1800.2.a.r.1.1 1 5.2 odd 4
1800.2.f.f.649.1 2 1.1 even 1 trivial
1800.2.f.f.649.2 2 5.4 even 2 inner
3600.2.a.m.1.1 1 20.7 even 4
3600.2.a.bf.1.1 1 20.3 even 4
3600.2.f.n.2449.1 2 20.19 odd 2
3600.2.f.n.2449.2 2 4.3 odd 2
9800.2.a.c.1.1 1 105.83 odd 4
9800.2.a.bq.1.1 1 105.62 odd 4