Properties

Label 1400.4.g.e.449.1
Level 14001400
Weight 44
Character 1400.449
Analytic conductor 82.60382.603
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1400,4,Mod(449,1400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1400, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1400.449");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 1400=23527 1400 = 2^{3} \cdot 5^{2} \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 1400.g (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: 82.602674008082.6026740080
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,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 449.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 1400.449
Dual form 1400.4.g.e.449.2

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) == q4.00000iq37.00000iq7+11.0000q9+20.0000q1110.0000iq13+14.0000iq1712.0000q1928.0000q21+104.000iq23152.000iq27+122.000q29+224.000q3180.0000iq33158.000iq3740.0000q39+378.000q41+404.000iq43112.000iq4749.0000q49+56.0000q51+270.000iq53+48.0000iq57324.000q59186.000q6177.0000iq63156.000iq67+416.000q69360.000q71102.000iq73140.000iq77+912.000q79311.000q81+1068.00iq83488.000iq87+1590.00q8970.0000q91896.000iq93866.000iq97+220.000q99+O(q100)q-4.00000i q^{3} -7.00000i q^{7} +11.0000 q^{9} +20.0000 q^{11} -10.0000i q^{13} +14.0000i q^{17} -12.0000 q^{19} -28.0000 q^{21} +104.000i q^{23} -152.000i q^{27} +122.000 q^{29} +224.000 q^{31} -80.0000i q^{33} -158.000i q^{37} -40.0000 q^{39} +378.000 q^{41} +404.000i q^{43} -112.000i q^{47} -49.0000 q^{49} +56.0000 q^{51} +270.000i q^{53} +48.0000i q^{57} -324.000 q^{59} -186.000 q^{61} -77.0000i q^{63} -156.000i q^{67} +416.000 q^{69} -360.000 q^{71} -102.000i q^{73} -140.000i q^{77} +912.000 q^{79} -311.000 q^{81} +1068.00i q^{83} -488.000i q^{87} +1590.00 q^{89} -70.0000 q^{91} -896.000i q^{93} -866.000i q^{97} +220.000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+22q9+40q1124q1956q21+244q29+448q3180q39+756q4198q49+112q51648q59372q61+832q69720q71+1824q79622q81++440q99+O(q100) 2 q + 22 q^{9} + 40 q^{11} - 24 q^{19} - 56 q^{21} + 244 q^{29} + 448 q^{31} - 80 q^{39} + 756 q^{41} - 98 q^{49} + 112 q^{51} - 648 q^{59} - 372 q^{61} + 832 q^{69} - 720 q^{71} + 1824 q^{79} - 622 q^{81}+ \cdots + 440 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1400Z)×\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times.

nn 351351 701701 801801 11771177
χ(n)\chi(n) 11 11 11 1-1

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 − 4.00000i − 0.769800i −0.922958 0.384900i 0.874236π-0.874236\pi
0.922958 0.384900i 0.125764π-0.125764\pi
44 0 0
55 0 0
66 0 0
77 − 7.00000i − 0.377964i
88 0 0
99 11.0000 0.407407
1010 0 0
1111 20.0000 0.548202 0.274101 0.961701i 0.411620π-0.411620\pi
0.274101 + 0.961701i 0.411620π0.411620\pi
1212 0 0
1313 − 10.0000i − 0.213346i −0.994294 0.106673i 0.965980π-0.965980\pi
0.994294 0.106673i 0.0340198π-0.0340198\pi
1414 0 0
1515 0 0
1616 0 0
1717 14.0000i 0.199735i 0.995001 + 0.0998676i 0.0318419π0.0318419\pi
−0.995001 + 0.0998676i 0.968158π0.968158\pi
1818 0 0
1919 −12.0000 −0.144894 −0.0724471 0.997372i 0.523081π-0.523081\pi
−0.0724471 + 0.997372i 0.523081π0.523081\pi
2020 0 0
2121 −28.0000 −0.290957
2222 0 0
2323 104.000i 0.942848i 0.881907 + 0.471424i 0.156260π0.156260\pi
−0.881907 + 0.471424i 0.843740π0.843740\pi
2424 0 0
2525 0 0
2626 0 0
2727 − 152.000i − 1.08342i
2828 0 0
2929 122.000 0.781201 0.390601 0.920560i 0.372267π-0.372267\pi
0.390601 + 0.920560i 0.372267π0.372267\pi
3030 0 0
3131 224.000 1.29779 0.648897 0.760877i 0.275231π-0.275231\pi
0.648897 + 0.760877i 0.275231π0.275231\pi
3232 0 0
3333 − 80.0000i − 0.422006i
3434 0 0
3535 0 0
3636 0 0
3737 − 158.000i − 0.702028i −0.936370 0.351014i 0.885837π-0.885837\pi
0.936370 0.351014i 0.114163π-0.114163\pi
3838 0 0
3939 −40.0000 −0.164234
4040 0 0
4141 378.000 1.43985 0.719923 0.694054i 0.244177π-0.244177\pi
0.719923 + 0.694054i 0.244177π0.244177\pi
4242 0 0
4343 404.000i 1.43278i 0.697701 + 0.716389i 0.254206π0.254206\pi
−0.697701 + 0.716389i 0.745794π0.745794\pi
4444 0 0
4545 0 0
4646 0 0
4747 − 112.000i − 0.347593i −0.984782 0.173797i 0.944396π-0.944396\pi
0.984782 0.173797i 0.0556035π-0.0556035\pi
4848 0 0
4949 −49.0000 −0.142857
5050 0 0
5151 56.0000 0.153756
5252 0 0
5353 270.000i 0.699761i 0.936794 + 0.349881i 0.113778π0.113778\pi
−0.936794 + 0.349881i 0.886222π0.886222\pi
5454 0 0
5555 0 0
5656 0 0
5757 48.0000i 0.111540i
5858 0 0
5959 −324.000 −0.714936 −0.357468 0.933925i 0.616360π-0.616360\pi
−0.357468 + 0.933925i 0.616360π0.616360\pi
6060 0 0
6161 −186.000 −0.390408 −0.195204 0.980763i 0.562537π-0.562537\pi
−0.195204 + 0.980763i 0.562537π0.562537\pi
6262 0 0
6363 − 77.0000i − 0.153986i
6464 0 0
6565 0 0
6666 0 0
6767 − 156.000i − 0.284454i −0.989834 0.142227i 0.954574π-0.954574\pi
0.989834 0.142227i 0.0454263π-0.0454263\pi
6868 0 0
6969 416.000 0.725805
7070 0 0
7171 −360.000 −0.601748 −0.300874 0.953664i 0.597278π-0.597278\pi
−0.300874 + 0.953664i 0.597278π0.597278\pi
7272 0 0
7373 − 102.000i − 0.163537i −0.996651 0.0817685i 0.973943π-0.973943\pi
0.996651 0.0817685i 0.0260568π-0.0260568\pi
7474 0 0
7575 0 0
7676 0 0
7777 − 140.000i − 0.207201i
7878 0 0
7979 912.000 1.29884 0.649418 0.760432i 0.275013π-0.275013\pi
0.649418 + 0.760432i 0.275013π0.275013\pi
8080 0 0
8181 −311.000 −0.426612
8282 0 0
8383 1068.00i 1.41239i 0.708018 + 0.706194i 0.249589π0.249589\pi
−0.708018 + 0.706194i 0.750411π0.750411\pi
8484 0 0
8585 0 0
8686 0 0
8787 − 488.000i − 0.601369i
8888 0 0
8989 1590.00 1.89370 0.946852 0.321669i 0.104244π-0.104244\pi
0.946852 + 0.321669i 0.104244π0.104244\pi
9090 0 0
9191 −70.0000 −0.0806373
9292 0 0
9393 − 896.000i − 0.999042i
9494 0 0
9595 0 0
9696 0 0
9797 − 866.000i − 0.906484i −0.891387 0.453242i 0.850267π-0.850267\pi
0.891387 0.453242i 0.149733π-0.149733\pi
9898 0 0
9999 220.000 0.223342
100100 0 0
101101 702.000 0.691600 0.345800 0.938308i 0.387608π-0.387608\pi
0.345800 + 0.938308i 0.387608π0.387608\pi
102102 0 0
103103 − 296.000i − 0.283163i −0.989927 0.141581i 0.954781π-0.954781\pi
0.989927 0.141581i 0.0452187π-0.0452187\pi
104104 0 0
105105 0 0
106106 0 0
107107 44.0000i 0.0397537i 0.999802 + 0.0198768i 0.00632741π0.00632741\pi
−0.999802 + 0.0198768i 0.993673π0.993673\pi
108108 0 0
109109 650.000 0.571181 0.285590 0.958352i 0.407810π-0.407810\pi
0.285590 + 0.958352i 0.407810π0.407810\pi
110110 0 0
111111 −632.000 −0.540421
112112 0 0
113113 − 942.000i − 0.784212i −0.919920 0.392106i 0.871747π-0.871747\pi
0.919920 0.392106i 0.128253π-0.128253\pi
114114 0 0
115115 0 0
116116 0 0
117117 − 110.000i − 0.0869188i
118118 0 0
119119 98.0000 0.0754928
120120 0 0
121121 −931.000 −0.699474
122122 0 0
123123 − 1512.00i − 1.10839i
124124 0 0
125125 0 0
126126 0 0
127127 − 736.000i − 0.514248i −0.966378 0.257124i 0.917225π-0.917225\pi
0.966378 0.257124i 0.0827748π-0.0827748\pi
128128 0 0
129129 1616.00 1.10295
130130 0 0
131131 924.000 0.616261 0.308131 0.951344i 0.400297π-0.400297\pi
0.308131 + 0.951344i 0.400297π0.400297\pi
132132 0 0
133133 84.0000i 0.0547648i
134134 0 0
135135 0 0
136136 0 0
137137 − 474.000i − 0.295595i −0.989018 0.147798i 0.952782π-0.952782\pi
0.989018 0.147798i 0.0472184π-0.0472184\pi
138138 0 0
139139 −1012.00 −0.617530 −0.308765 0.951138i 0.599916π-0.599916\pi
−0.308765 + 0.951138i 0.599916π0.599916\pi
140140 0 0
141141 −448.000 −0.267577
142142 0 0
143143 − 200.000i − 0.116957i
144144 0 0
145145 0 0
146146 0 0
147147 196.000i 0.109971i
148148 0 0
149149 −302.000 −0.166046 −0.0830228 0.996548i 0.526457π-0.526457\pi
−0.0830228 + 0.996548i 0.526457π0.526457\pi
150150 0 0
151151 −2104.00 −1.13391 −0.566957 0.823747i 0.691880π-0.691880\pi
−0.566957 + 0.823747i 0.691880π0.691880\pi
152152 0 0
153153 154.000i 0.0813736i
154154 0 0
155155 0 0
156156 0 0
157157 − 1190.00i − 0.604919i −0.953162 0.302460i 0.902192π-0.902192\pi
0.953162 0.302460i 0.0978078π-0.0978078\pi
158158 0 0
159159 1080.00 0.538677
160160 0 0
161161 728.000 0.356363
162162 0 0
163163 − 1732.00i − 0.832274i −0.909302 0.416137i 0.863384π-0.863384\pi
0.909302 0.416137i 0.136616π-0.136616\pi
164164 0 0
165165 0 0
166166 0 0
167167 − 2264.00i − 1.04906i −0.851391 0.524532i 0.824240π-0.824240\pi
0.851391 0.524532i 0.175760π-0.175760\pi
168168 0 0
169169 2097.00 0.954483
170170 0 0
171171 −132.000 −0.0590309
172172 0 0
173173 − 1066.00i − 0.468477i −0.972179 0.234238i 0.924740π-0.924740\pi
0.972179 0.234238i 0.0752596π-0.0752596\pi
174174 0 0
175175 0 0
176176 0 0
177177 1296.00i 0.550358i
178178 0 0
179179 2356.00 0.983775 0.491887 0.870659i 0.336307π-0.336307\pi
0.491887 + 0.870659i 0.336307π0.336307\pi
180180 0 0
181181 2158.00 0.886204 0.443102 0.896471i 0.353878π-0.353878\pi
0.443102 + 0.896471i 0.353878π0.353878\pi
182182 0 0
183183 744.000i 0.300536i
184184 0 0
185185 0 0
186186 0 0
187187 280.000i 0.109495i
188188 0 0
189189 −1064.00 −0.409495
190190 0 0
191191 −2688.00 −1.01831 −0.509154 0.860675i 0.670042π-0.670042\pi
−0.509154 + 0.860675i 0.670042π0.670042\pi
192192 0 0
193193 − 4414.00i − 1.64625i −0.567859 0.823126i 0.692228π-0.692228\pi
0.567859 0.823126i 0.307772π-0.307772\pi
194194 0 0
195195 0 0
196196 0 0
197197 − 3774.00i − 1.36491i −0.730930 0.682453i 0.760913π-0.760913\pi
0.730930 0.682453i 0.239087π-0.239087\pi
198198 0 0
199199 −664.000 −0.236531 −0.118266 0.992982i 0.537733π-0.537733\pi
−0.118266 + 0.992982i 0.537733π0.537733\pi
200200 0 0
201201 −624.000 −0.218973
202202 0 0
203203 − 854.000i − 0.295266i
204204 0 0
205205 0 0
206206 0 0
207207 1144.00i 0.384123i
208208 0 0
209209 −240.000 −0.0794313
210210 0 0
211211 1260.00 0.411099 0.205550 0.978647i 0.434102π-0.434102\pi
0.205550 + 0.978647i 0.434102π0.434102\pi
212212 0 0
213213 1440.00i 0.463226i
214214 0 0
215215 0 0
216216 0 0
217217 − 1568.00i − 0.490520i
218218 0 0
219219 −408.000 −0.125891
220220 0 0
221221 140.000 0.0426128
222222 0 0
223223 − 1152.00i − 0.345936i −0.984927 0.172968i 0.944664π-0.944664\pi
0.984927 0.172968i 0.0553356π-0.0553356\pi
224224 0 0
225225 0 0
226226 0 0
227227 − 2588.00i − 0.756703i −0.925662 0.378352i 0.876491π-0.876491\pi
0.925662 0.378352i 0.123509π-0.123509\pi
228228 0 0
229229 −766.000 −0.221042 −0.110521 0.993874i 0.535252π-0.535252\pi
−0.110521 + 0.993874i 0.535252π0.535252\pi
230230 0 0
231231 −560.000 −0.159503
232232 0 0
233233 6138.00i 1.72581i 0.505366 + 0.862905i 0.331357π0.331357\pi
−0.505366 + 0.862905i 0.668643π0.668643\pi
234234 0 0
235235 0 0
236236 0 0
237237 − 3648.00i − 0.999844i
238238 0 0
239239 −3856.00 −1.04361 −0.521807 0.853063i 0.674742π-0.674742\pi
−0.521807 + 0.853063i 0.674742π0.674742\pi
240240 0 0
241241 2578.00 0.689060 0.344530 0.938775i 0.388038π-0.388038\pi
0.344530 + 0.938775i 0.388038π0.388038\pi
242242 0 0
243243 − 2860.00i − 0.755017i
244244 0 0
245245 0 0
246246 0 0
247247 120.000i 0.0309126i
248248 0 0
249249 4272.00 1.08726
250250 0 0
251251 −1404.00 −0.353067 −0.176533 0.984295i 0.556488π-0.556488\pi
−0.176533 + 0.984295i 0.556488π0.556488\pi
252252 0 0
253253 2080.00i 0.516871i
254254 0 0
255255 0 0
256256 0 0
257257 − 2946.00i − 0.715044i −0.933905 0.357522i 0.883622π-0.883622\pi
0.933905 0.357522i 0.116378π-0.116378\pi
258258 0 0
259259 −1106.00 −0.265342
260260 0 0
261261 1342.00 0.318267
262262 0 0
263263 − 3080.00i − 0.722133i −0.932540 0.361066i 0.882413π-0.882413\pi
0.932540 0.361066i 0.117587π-0.117587\pi
264264 0 0
265265 0 0
266266 0 0
267267 − 6360.00i − 1.45777i
268268 0 0
269269 −2294.00 −0.519954 −0.259977 0.965615i 0.583715π-0.583715\pi
−0.259977 + 0.965615i 0.583715π0.583715\pi
270270 0 0
271271 −3728.00 −0.835645 −0.417823 0.908529i 0.637207π-0.637207\pi
−0.417823 + 0.908529i 0.637207π0.637207\pi
272272 0 0
273273 280.000i 0.0620746i
274274 0 0
275275 0 0
276276 0 0
277277 − 2734.00i − 0.593033i −0.955028 0.296516i 0.904175π-0.904175\pi
0.955028 0.296516i 0.0958250π-0.0958250\pi
278278 0 0
279279 2464.00 0.528731
280280 0 0
281281 1034.00 0.219513 0.109757 0.993958i 0.464993π-0.464993\pi
0.109757 + 0.993958i 0.464993π0.464993\pi
282282 0 0
283283 − 5180.00i − 1.08805i −0.839068 0.544027i 0.816899π-0.816899\pi
0.839068 0.544027i 0.183101π-0.183101\pi
284284 0 0
285285 0 0
286286 0 0
287287 − 2646.00i − 0.544211i
288288 0 0
289289 4717.00 0.960106
290290 0 0
291291 −3464.00 −0.697812
292292 0 0
293293 7934.00i 1.58194i 0.611853 + 0.790971i 0.290424π0.290424\pi
−0.611853 + 0.790971i 0.709576π0.709576\pi
294294 0 0
295295 0 0
296296 0 0
297297 − 3040.00i − 0.593935i
298298 0 0
299299 1040.00 0.201153
300300 0 0
301301 2828.00 0.541539
302302 0 0
303303 − 2808.00i − 0.532394i
304304 0 0
305305 0 0
306306 0 0
307307 3444.00i 0.640259i 0.947374 + 0.320129i 0.103726π0.103726\pi
−0.947374 + 0.320129i 0.896274π0.896274\pi
308308 0 0
309309 −1184.00 −0.217979
310310 0 0
311311 7656.00 1.39592 0.697961 0.716135i 0.254091π-0.254091\pi
0.697961 + 0.716135i 0.254091π0.254091\pi
312312 0 0
313313 − 3798.00i − 0.685865i −0.939360 0.342932i 0.888580π-0.888580\pi
0.939360 0.342932i 0.111420π-0.111420\pi
314314 0 0
315315 0 0
316316 0 0
317317 − 6822.00i − 1.20871i −0.796714 0.604356i 0.793430π-0.793430\pi
0.796714 0.604356i 0.206570π-0.206570\pi
318318 0 0
319319 2440.00 0.428256
320320 0 0
321321 176.000 0.0306024
322322 0 0
323323 − 168.000i − 0.0289405i
324324 0 0
325325 0 0
326326 0 0
327327 − 2600.00i − 0.439695i
328328 0 0
329329 −784.000 −0.131378
330330 0 0
331331 −6572.00 −1.09133 −0.545664 0.838004i 0.683723π-0.683723\pi
−0.545664 + 0.838004i 0.683723π0.683723\pi
332332 0 0
333333 − 1738.00i − 0.286011i
334334 0 0
335335 0 0
336336 0 0
337337 11022.0i 1.78162i 0.454374 + 0.890811i 0.349863π0.349863\pi
−0.454374 + 0.890811i 0.650137π0.650137\pi
338338 0 0
339339 −3768.00 −0.603686
340340 0 0
341341 4480.00 0.711453
342342 0 0
343343 343.000i 0.0539949i
344344 0 0
345345 0 0
346346 0 0
347347 10908.0i 1.68753i 0.536715 + 0.843764i 0.319665π0.319665\pi
−0.536715 + 0.843764i 0.680335π0.680335\pi
348348 0 0
349349 12058.0 1.84943 0.924713 0.380664i 0.124305π-0.124305\pi
0.924713 + 0.380664i 0.124305π0.124305\pi
350350 0 0
351351 −1520.00 −0.231144
352352 0 0
353353 1570.00i 0.236721i 0.992971 + 0.118361i 0.0377639π0.0377639\pi
−0.992971 + 0.118361i 0.962236π0.962236\pi
354354 0 0
355355 0 0
356356 0 0
357357 − 392.000i − 0.0581144i
358358 0 0
359359 −120.000 −0.0176417 −0.00882083 0.999961i 0.502808π-0.502808\pi
−0.00882083 + 0.999961i 0.502808π0.502808\pi
360360 0 0
361361 −6715.00 −0.979006
362362 0 0
363363 3724.00i 0.538455i
364364 0 0
365365 0 0
366366 0 0
367367 − 4336.00i − 0.616723i −0.951269 0.308362i 0.900219π-0.900219\pi
0.951269 0.308362i 0.0997806π-0.0997806\pi
368368 0 0
369369 4158.00 0.586604
370370 0 0
371371 1890.00 0.264485
372372 0 0
373373 7758.00i 1.07693i 0.842649 + 0.538464i 0.180995π0.180995\pi
−0.842649 + 0.538464i 0.819005π0.819005\pi
374374 0 0
375375 0 0
376376 0 0
377377 − 1220.00i − 0.166666i
378378 0 0
379379 −10660.0 −1.44477 −0.722384 0.691492i 0.756954π-0.756954\pi
−0.722384 + 0.691492i 0.756954π0.756954\pi
380380 0 0
381381 −2944.00 −0.395868
382382 0 0
383383 − 14304.0i − 1.90836i −0.299240 0.954178i 0.596733π-0.596733\pi
0.299240 0.954178i 0.403267π-0.403267\pi
384384 0 0
385385 0 0
386386 0 0
387387 4444.00i 0.583724i
388388 0 0
389389 11970.0 1.56016 0.780081 0.625678i 0.215178π-0.215178\pi
0.780081 + 0.625678i 0.215178π0.215178\pi
390390 0 0
391391 −1456.00 −0.188320
392392 0 0
393393 − 3696.00i − 0.474398i
394394 0 0
395395 0 0
396396 0 0
397397 4106.00i 0.519079i 0.965733 + 0.259539i 0.0835707π0.0835707\pi
−0.965733 + 0.259539i 0.916429π0.916429\pi
398398 0 0
399399 336.000 0.0421580
400400 0 0
401401 −3790.00 −0.471979 −0.235989 0.971756i 0.575833π-0.575833\pi
−0.235989 + 0.971756i 0.575833π0.575833\pi
402402 0 0
403403 − 2240.00i − 0.276879i
404404 0 0
405405 0 0
406406 0 0
407407 − 3160.00i − 0.384854i
408408 0 0
409409 13366.0 1.61591 0.807954 0.589246i 0.200575π-0.200575\pi
0.807954 + 0.589246i 0.200575π0.200575\pi
410410 0 0
411411 −1896.00 −0.227549
412412 0 0
413413 2268.00i 0.270220i
414414 0 0
415415 0 0
416416 0 0
417417 4048.00i 0.475375i
418418 0 0
419419 −6524.00 −0.760664 −0.380332 0.924850i 0.624190π-0.624190\pi
−0.380332 + 0.924850i 0.624190π0.624190\pi
420420 0 0
421421 −2978.00 −0.344748 −0.172374 0.985032i 0.555144π-0.555144\pi
−0.172374 + 0.985032i 0.555144π0.555144\pi
422422 0 0
423423 − 1232.00i − 0.141612i
424424 0 0
425425 0 0
426426 0 0
427427 1302.00i 0.147560i
428428 0 0
429429 −800.000 −0.0900335
430430 0 0
431431 15760.0 1.76133 0.880664 0.473741i 0.157097π-0.157097\pi
0.880664 + 0.473741i 0.157097π0.157097\pi
432432 0 0
433433 10322.0i 1.14560i 0.819696 + 0.572799i 0.194142π0.194142\pi
−0.819696 + 0.572799i 0.805858π0.805858\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 1248.00i − 0.136613i
438438 0 0
439439 344.000 0.0373991 0.0186996 0.999825i 0.494047π-0.494047\pi
0.0186996 + 0.999825i 0.494047π0.494047\pi
440440 0 0
441441 −539.000 −0.0582011
442442 0 0
443443 − 252.000i − 0.0270268i −0.999909 0.0135134i 0.995698π-0.995698\pi
0.999909 0.0135134i 0.00430158π-0.00430158\pi
444444 0 0
445445 0 0
446446 0 0
447447 1208.00i 0.127822i
448448 0 0
449449 11966.0 1.25771 0.628854 0.777524i 0.283525π-0.283525\pi
0.628854 + 0.777524i 0.283525π0.283525\pi
450450 0 0
451451 7560.00 0.789327
452452 0 0
453453 8416.00i 0.872888i
454454 0 0
455455 0 0
456456 0 0
457457 15846.0i 1.62198i 0.585060 + 0.810990i 0.301071π0.301071\pi
−0.585060 + 0.810990i 0.698929π0.698929\pi
458458 0 0
459459 2128.00 0.216398
460460 0 0
461461 5430.00 0.548591 0.274295 0.961645i 0.411555π-0.411555\pi
0.274295 + 0.961645i 0.411555π0.411555\pi
462462 0 0
463463 8912.00i 0.894548i 0.894397 + 0.447274i 0.147605π0.147605\pi
−0.894397 + 0.447274i 0.852395π0.852395\pi
464464 0 0
465465 0 0
466466 0 0
467467 11028.0i 1.09275i 0.837540 + 0.546376i 0.183993π0.183993\pi
−0.837540 + 0.546376i 0.816007π0.816007\pi
468468 0 0
469469 −1092.00 −0.107514
470470 0 0
471471 −4760.00 −0.465667
472472 0 0
473473 8080.00i 0.785452i
474474 0 0
475475 0 0
476476 0 0
477477 2970.00i 0.285088i
478478 0 0
479479 −5856.00 −0.558596 −0.279298 0.960204i 0.590102π-0.590102\pi
−0.279298 + 0.960204i 0.590102π0.590102\pi
480480 0 0
481481 −1580.00 −0.149775
482482 0 0
483483 − 2912.00i − 0.274328i
484484 0 0
485485 0 0
486486 0 0
487487 − 10264.0i − 0.955044i −0.878620 0.477522i 0.841535π-0.841535\pi
0.878620 0.477522i 0.158465π-0.158465\pi
488488 0 0
489489 −6928.00 −0.640685
490490 0 0
491491 2804.00 0.257725 0.128862 0.991663i 0.458867π-0.458867\pi
0.128862 + 0.991663i 0.458867π0.458867\pi
492492 0 0
493493 1708.00i 0.156033i
494494 0 0
495495 0 0
496496 0 0
497497 2520.00i 0.227440i
498498 0 0
499499 −8716.00 −0.781927 −0.390964 0.920406i 0.627858π-0.627858\pi
−0.390964 + 0.920406i 0.627858π0.627858\pi
500500 0 0
501501 −9056.00 −0.807569
502502 0 0
503503 2504.00i 0.221964i 0.993822 + 0.110982i 0.0353996π0.0353996\pi
−0.993822 + 0.110982i 0.964600π0.964600\pi
504504 0 0
505505 0 0
506506 0 0
507507 − 8388.00i − 0.734762i
508508 0 0
509509 −17094.0 −1.48856 −0.744281 0.667866i 0.767208π-0.767208\pi
−0.744281 + 0.667866i 0.767208π0.767208\pi
510510 0 0
511511 −714.000 −0.0618112
512512 0 0
513513 1824.00i 0.156982i
514514 0 0
515515 0 0
516516 0 0
517517 − 2240.00i − 0.190551i
518518 0 0
519519 −4264.00 −0.360634
520520 0 0
521521 9882.00 0.830976 0.415488 0.909599i 0.363611π-0.363611\pi
0.415488 + 0.909599i 0.363611π0.363611\pi
522522 0 0
523523 − 7532.00i − 0.629735i −0.949136 0.314867i 0.898040π-0.898040\pi
0.949136 0.314867i 0.101960π-0.101960\pi
524524 0 0
525525 0 0
526526 0 0
527527 3136.00i 0.259215i
528528 0 0
529529 1351.00 0.111038
530530 0 0
531531 −3564.00 −0.291270
532532 0 0
533533 − 3780.00i − 0.307186i
534534 0 0
535535 0 0
536536 0 0
537537 − 9424.00i − 0.757310i
538538 0 0
539539 −980.000 −0.0783146
540540 0 0
541541 −17338.0 −1.37785 −0.688927 0.724831i 0.741918π-0.741918\pi
−0.688927 + 0.724831i 0.741918π0.741918\pi
542542 0 0
543543 − 8632.00i − 0.682200i
544544 0 0
545545 0 0
546546 0 0
547547 − 764.000i − 0.0597190i −0.999554 0.0298595i 0.990494π-0.990494\pi
0.999554 0.0298595i 0.00950598π-0.00950598\pi
548548 0 0
549549 −2046.00 −0.159055
550550 0 0
551551 −1464.00 −0.113191
552552 0 0
553553 − 6384.00i − 0.490914i
554554 0 0
555555 0 0
556556 0 0
557557 2442.00i 0.185765i 0.995677 + 0.0928823i 0.0296080π0.0296080\pi
−0.995677 + 0.0928823i 0.970392π0.970392\pi
558558 0 0
559559 4040.00 0.305678
560560 0 0
561561 1120.00 0.0842895
562562 0 0
563563 8972.00i 0.671625i 0.941929 + 0.335812i 0.109011π0.109011\pi
−0.941929 + 0.335812i 0.890989π0.890989\pi
564564 0 0
565565 0 0
566566 0 0
567567 2177.00i 0.161244i
568568 0 0
569569 −8682.00 −0.639663 −0.319832 0.947474i 0.603626π-0.603626\pi
−0.319832 + 0.947474i 0.603626π0.603626\pi
570570 0 0
571571 15524.0 1.13776 0.568878 0.822422i 0.307377π-0.307377\pi
0.568878 + 0.822422i 0.307377π0.307377\pi
572572 0 0
573573 10752.0i 0.783894i
574574 0 0
575575 0 0
576576 0 0
577577 19774.0i 1.42669i 0.700811 + 0.713347i 0.252822π0.252822\pi
−0.700811 + 0.713347i 0.747178π0.747178\pi
578578 0 0
579579 −17656.0 −1.26729
580580 0 0
581581 7476.00 0.533833
582582 0 0
583583 5400.00i 0.383611i
584584 0 0
585585 0 0
586586 0 0
587587 6700.00i 0.471105i 0.971862 + 0.235552i 0.0756899π0.0756899\pi
−0.971862 + 0.235552i 0.924310π0.924310\pi
588588 0 0
589589 −2688.00 −0.188043
590590 0 0
591591 −15096.0 −1.05070
592592 0 0
593593 − 1294.00i − 0.0896091i −0.998996 0.0448046i 0.985733π-0.985733\pi
0.998996 0.0448046i 0.0142665π-0.0142665\pi
594594 0 0
595595 0 0
596596 0 0
597597 2656.00i 0.182082i
598598 0 0
599599 −19720.0 −1.34514 −0.672569 0.740035i 0.734809π-0.734809\pi
−0.672569 + 0.740035i 0.734809π0.734809\pi
600600 0 0
601601 21450.0 1.45585 0.727923 0.685659i 0.240486π-0.240486\pi
0.727923 + 0.685659i 0.240486π0.240486\pi
602602 0 0
603603 − 1716.00i − 0.115889i
604604 0 0
605605 0 0
606606 0 0
607607 19264.0i 1.28814i 0.764966 + 0.644071i 0.222756π0.222756\pi
−0.764966 + 0.644071i 0.777244π0.777244\pi
608608 0 0
609609 −3416.00 −0.227296
610610 0 0
611611 −1120.00 −0.0741577
612612 0 0
613613 13150.0i 0.866433i 0.901290 + 0.433217i 0.142621π0.142621\pi
−0.901290 + 0.433217i 0.857379π0.857379\pi
614614 0 0
615615 0 0
616616 0 0
617617 15238.0i 0.994261i 0.867676 + 0.497130i 0.165613π0.165613\pi
−0.867676 + 0.497130i 0.834387π0.834387\pi
618618 0 0
619619 −23764.0 −1.54306 −0.771531 0.636191i 0.780509π-0.780509\pi
−0.771531 + 0.636191i 0.780509π0.780509\pi
620620 0 0
621621 15808.0 1.02150
622622 0 0
623623 − 11130.0i − 0.715753i
624624 0 0
625625 0 0
626626 0 0
627627 960.000i 0.0611463i
628628 0 0
629629 2212.00 0.140220
630630 0 0
631631 −2008.00 −0.126683 −0.0633417 0.997992i 0.520176π-0.520176\pi
−0.0633417 + 0.997992i 0.520176π0.520176\pi
632632 0 0
633633 − 5040.00i − 0.316464i
634634 0 0
635635 0 0
636636 0 0
637637 490.000i 0.0304780i
638638 0 0
639639 −3960.00 −0.245157
640640 0 0
641641 13058.0 0.804618 0.402309 0.915504i 0.368208π-0.368208\pi
0.402309 + 0.915504i 0.368208π0.368208\pi
642642 0 0
643643 24188.0i 1.48349i 0.670684 + 0.741743i 0.266001π0.266001\pi
−0.670684 + 0.741743i 0.733999π0.733999\pi
644644 0 0
645645 0 0
646646 0 0
647647 − 6648.00i − 0.403956i −0.979390 0.201978i 0.935263π-0.935263\pi
0.979390 0.201978i 0.0647370π-0.0647370\pi
648648 0 0
649649 −6480.00 −0.391930
650650 0 0
651651 −6272.00 −0.377602
652652 0 0
653653 9814.00i 0.588134i 0.955785 + 0.294067i 0.0950089π0.0950089\pi
−0.955785 + 0.294067i 0.904991π0.904991\pi
654654 0 0
655655 0 0
656656 0 0
657657 − 1122.00i − 0.0666262i
658658 0 0
659659 −26540.0 −1.56882 −0.784409 0.620243i 0.787034π-0.787034\pi
−0.784409 + 0.620243i 0.787034π0.787034\pi
660660 0 0
661661 −1330.00 −0.0782617 −0.0391309 0.999234i 0.512459π-0.512459\pi
−0.0391309 + 0.999234i 0.512459π0.512459\pi
662662 0 0
663663 − 560.000i − 0.0328033i
664664 0 0
665665 0 0
666666 0 0
667667 12688.0i 0.736554i
668668 0 0
669669 −4608.00 −0.266301
670670 0 0
671671 −3720.00 −0.214022
672672 0 0
673673 − 17950.0i − 1.02812i −0.857756 0.514058i 0.828142π-0.828142\pi
0.857756 0.514058i 0.171858π-0.171858\pi
674674 0 0
675675 0 0
676676 0 0
677677 − 23742.0i − 1.34783i −0.738810 0.673914i 0.764612π-0.764612\pi
0.738810 0.673914i 0.235388π-0.235388\pi
678678 0 0
679679 −6062.00 −0.342619
680680 0 0
681681 −10352.0 −0.582510
682682 0 0
683683 6356.00i 0.356084i 0.984023 + 0.178042i 0.0569763π0.0569763\pi
−0.984023 + 0.178042i 0.943024π0.943024\pi
684684 0 0
685685 0 0
686686 0 0
687687 3064.00i 0.170159i
688688 0 0
689689 2700.00 0.149291
690690 0 0
691691 −3156.00 −0.173748 −0.0868740 0.996219i 0.527688π-0.527688\pi
−0.0868740 + 0.996219i 0.527688π0.527688\pi
692692 0 0
693693 − 1540.00i − 0.0844152i
694694 0 0
695695 0 0
696696 0 0
697697 5292.00i 0.287588i
698698 0 0
699699 24552.0 1.32853
700700 0 0
701701 −18330.0 −0.987610 −0.493805 0.869573i 0.664394π-0.664394\pi
−0.493805 + 0.869573i 0.664394π0.664394\pi
702702 0 0
703703 1896.00i 0.101720i
704704 0 0
705705 0 0
706706 0 0
707707 − 4914.00i − 0.261400i
708708 0 0
709709 −19070.0 −1.01014 −0.505070 0.863079i 0.668533π-0.668533\pi
−0.505070 + 0.863079i 0.668533π0.668533\pi
710710 0 0
711711 10032.0 0.529155
712712 0 0
713713 23296.0i 1.22362i
714714 0 0
715715 0 0
716716 0 0
717717 15424.0i 0.803375i
718718 0 0
719719 4176.00 0.216604 0.108302 0.994118i 0.465459π-0.465459\pi
0.108302 + 0.994118i 0.465459π0.465459\pi
720720 0 0
721721 −2072.00 −0.107025
722722 0 0
723723 − 10312.0i − 0.530439i
724724 0 0
725725 0 0
726726 0 0
727727 10520.0i 0.536678i 0.963324 + 0.268339i 0.0864748π0.0864748\pi
−0.963324 + 0.268339i 0.913525π0.913525\pi
728728 0 0
729729 −19837.0 −1.00782
730730 0 0
731731 −5656.00 −0.286176
732732 0 0
733733 − 6874.00i − 0.346381i −0.984888 0.173190i 0.944592π-0.944592\pi
0.984888 0.173190i 0.0554076π-0.0554076\pi
734734 0 0
735735 0 0
736736 0 0
737737 − 3120.00i − 0.155939i
738738 0 0
739739 −11804.0 −0.587574 −0.293787 0.955871i 0.594916π-0.594916\pi
−0.293787 + 0.955871i 0.594916π0.594916\pi
740740 0 0
741741 480.000 0.0237965
742742 0 0
743743 − 20648.0i − 1.01952i −0.860317 0.509759i 0.829735π-0.829735\pi
0.860317 0.509759i 0.170265π-0.170265\pi
744744 0 0
745745 0 0
746746 0 0
747747 11748.0i 0.575417i
748748 0 0
749749 308.000 0.0150255
750750 0 0
751751 1232.00 0.0598619 0.0299310 0.999552i 0.490471π-0.490471\pi
0.0299310 + 0.999552i 0.490471π0.490471\pi
752752 0 0
753753 5616.00i 0.271791i
754754 0 0
755755 0 0
756756 0 0
757757 11250.0i 0.540143i 0.962840 + 0.270071i 0.0870473π0.0870473\pi
−0.962840 + 0.270071i 0.912953π0.912953\pi
758758 0 0
759759 8320.00 0.397888
760760 0 0
761761 14698.0 0.700134 0.350067 0.936725i 0.386159π-0.386159\pi
0.350067 + 0.936725i 0.386159π0.386159\pi
762762 0 0
763763 − 4550.00i − 0.215886i
764764 0 0
765765 0 0
766766 0 0
767767 3240.00i 0.152529i
768768 0 0
769769 30014.0 1.40745 0.703727 0.710470i 0.251518π-0.251518\pi
0.703727 + 0.710470i 0.251518π0.251518\pi
770770 0 0
771771 −11784.0 −0.550441
772772 0 0
773773 − 34018.0i − 1.58285i −0.611267 0.791425i 0.709340π-0.709340\pi
0.611267 0.791425i 0.290660π-0.290660\pi
774774 0 0
775775 0 0
776776 0 0
777777 4424.00i 0.204260i
778778 0 0
779779 −4536.00 −0.208625
780780 0 0
781781 −7200.00 −0.329880
782782 0 0
783783 − 18544.0i − 0.846371i
784784 0 0
785785 0 0
786786 0 0
787787 18516.0i 0.838658i 0.907834 + 0.419329i 0.137735π0.137735\pi
−0.907834 + 0.419329i 0.862265π0.862265\pi
788788 0 0
789789 −12320.0 −0.555898
790790 0 0
791791 −6594.00 −0.296404
792792 0 0
793793 1860.00i 0.0832920i
794794 0 0
795795 0 0
796796 0 0
797797 38618.0i 1.71634i 0.513369 + 0.858168i 0.328397π0.328397\pi
−0.513369 + 0.858168i 0.671603π0.671603\pi
798798 0 0
799799 1568.00 0.0694266
800800 0 0
801801 17490.0 0.771509
802802 0 0
803803 − 2040.00i − 0.0896514i
804804 0 0
805805 0 0
806806 0 0
807807 9176.00i 0.400261i
808808 0 0
809809 −19514.0 −0.848054 −0.424027 0.905650i 0.639384π-0.639384\pi
−0.424027 + 0.905650i 0.639384π0.639384\pi
810810 0 0
811811 −31020.0 −1.34311 −0.671553 0.740956i 0.734373π-0.734373\pi
−0.671553 + 0.740956i 0.734373π0.734373\pi
812812 0 0
813813 14912.0i 0.643280i
814814 0 0
815815 0 0
816816 0 0
817817 − 4848.00i − 0.207601i
818818 0 0
819819 −770.000 −0.0328522
820820 0 0
821821 3726.00 0.158390 0.0791951 0.996859i 0.474765π-0.474765\pi
0.0791951 + 0.996859i 0.474765π0.474765\pi
822822 0 0
823823 32904.0i 1.39363i 0.717249 + 0.696817i 0.245401π0.245401\pi
−0.717249 + 0.696817i 0.754599π0.754599\pi
824824 0 0
825825 0 0
826826 0 0
827827 39868.0i 1.67636i 0.545397 + 0.838178i 0.316379π0.316379\pi
−0.545397 + 0.838178i 0.683621π0.683621\pi
828828 0 0
829829 26810.0 1.12322 0.561610 0.827402i 0.310182π-0.310182\pi
0.561610 + 0.827402i 0.310182π0.310182\pi
830830 0 0
831831 −10936.0 −0.456517
832832 0 0
833833 − 686.000i − 0.0285336i
834834 0 0
835835 0 0
836836 0 0
837837 − 34048.0i − 1.40606i
838838 0 0
839839 37096.0 1.52646 0.763228 0.646130i 0.223613π-0.223613\pi
0.763228 + 0.646130i 0.223613π0.223613\pi
840840 0 0
841841 −9505.00 −0.389725
842842 0 0
843843 − 4136.00i − 0.168982i
844844 0 0
845845 0 0
846846 0 0
847847 6517.00i 0.264376i
848848 0 0
849849 −20720.0 −0.837584
850850 0 0
851851 16432.0 0.661906
852852 0 0
853853 − 14386.0i − 0.577453i −0.957412 0.288726i 0.906768π-0.906768\pi
0.957412 0.288726i 0.0932318π-0.0932318\pi
854854 0 0
855855 0 0
856856 0 0
857857 118.000i 0.00470339i 0.999997 + 0.00235169i 0.000748568π0.000748568\pi
−0.999997 + 0.00235169i 0.999251π0.999251\pi
858858 0 0
859859 25116.0 0.997610 0.498805 0.866714i 0.333772π-0.333772\pi
0.498805 + 0.866714i 0.333772π0.333772\pi
860860 0 0
861861 −10584.0 −0.418934
862862 0 0
863863 − 11776.0i − 0.464496i −0.972657 0.232248i 0.925392π-0.925392\pi
0.972657 0.232248i 0.0746080π-0.0746080\pi
864864 0 0
865865 0 0
866866 0 0
867867 − 18868.0i − 0.739090i
868868 0 0
869869 18240.0 0.712025
870870 0 0
871871 −1560.00 −0.0606872
872872 0 0
873873 − 9526.00i − 0.369308i
874874 0 0
875875 0 0
876876 0 0
877877 − 24694.0i − 0.950806i −0.879768 0.475403i 0.842302π-0.842302\pi
0.879768 0.475403i 0.157698π-0.157698\pi
878878 0 0
879879 31736.0 1.21778
880880 0 0
881881 32850.0 1.25624 0.628118 0.778118i 0.283825π-0.283825\pi
0.628118 + 0.778118i 0.283825π0.283825\pi
882882 0 0
883883 47340.0i 1.80421i 0.431516 + 0.902105i 0.357979π0.357979\pi
−0.431516 + 0.902105i 0.642021π0.642021\pi
884884 0 0
885885 0 0
886886 0 0
887887 − 1992.00i − 0.0754057i −0.999289 0.0377028i 0.987996π-0.987996\pi
0.999289 0.0377028i 0.0120040π-0.0120040\pi
888888 0 0
889889 −5152.00 −0.194367
890890 0 0
891891 −6220.00 −0.233870
892892 0 0
893893 1344.00i 0.0503642i
894894 0 0
895895 0 0
896896 0 0
897897 − 4160.00i − 0.154848i
898898 0 0
899899 27328.0 1.01384
900900 0 0
901901 −3780.00 −0.139767
902902 0 0
903903 − 11312.0i − 0.416877i
904904 0 0
905905 0 0
906906 0 0
907907 13516.0i 0.494809i 0.968912 + 0.247404i 0.0795776π0.0795776\pi
−0.968912 + 0.247404i 0.920422π0.920422\pi
908908 0 0
909909 7722.00 0.281763
910910 0 0
911911 −3408.00 −0.123943 −0.0619715 0.998078i 0.519739π-0.519739\pi
−0.0619715 + 0.998078i 0.519739π0.519739\pi
912912 0 0
913913 21360.0i 0.774275i
914914 0 0
915915 0 0
916916 0 0
917917 − 6468.00i − 0.232925i
918918 0 0
919919 −39240.0 −1.40850 −0.704248 0.709954i 0.748716π-0.748716\pi
−0.704248 + 0.709954i 0.748716π0.748716\pi
920920 0 0
921921 13776.0 0.492871
922922 0 0
923923 3600.00i 0.128381i
924924 0 0
925925 0 0
926926 0 0
927927 − 3256.00i − 0.115363i
928928 0 0
929929 −21922.0 −0.774206 −0.387103 0.922036i 0.626524π-0.626524\pi
−0.387103 + 0.922036i 0.626524π0.626524\pi
930930 0 0
931931 588.000 0.0206992
932932 0 0
933933 − 30624.0i − 1.07458i
934934 0 0
935935 0 0
936936 0 0
937937 − 186.000i − 0.00648490i −0.999995 0.00324245i 0.998968π-0.998968\pi
0.999995 0.00324245i 0.00103211π-0.00103211\pi
938938 0 0
939939 −15192.0 −0.527979
940940 0 0
941941 −18282.0 −0.633343 −0.316672 0.948535i 0.602565π-0.602565\pi
−0.316672 + 0.948535i 0.602565π0.602565\pi
942942 0 0
943943 39312.0i 1.35756i
944944 0 0
945945 0 0
946946 0 0
947947 16980.0i 0.582657i 0.956623 + 0.291328i 0.0940972π0.0940972\pi
−0.956623 + 0.291328i 0.905903π0.905903\pi
948948 0 0
949949 −1020.00 −0.0348900
950950 0 0
951951 −27288.0 −0.930467
952952 0 0
953953 − 44310.0i − 1.50613i −0.657946 0.753065i 0.728575π-0.728575\pi
0.657946 0.753065i 0.271425π-0.271425\pi
954954 0 0
955955 0 0
956956 0 0
957957 − 9760.00i − 0.329672i
958958 0 0
959959 −3318.00 −0.111725
960960 0 0
961961 20385.0 0.684267
962962 0 0
963963 484.000i 0.0161959i
964964 0 0
965965 0 0
966966 0 0
967967 − 51512.0i − 1.71304i −0.516110 0.856522i 0.672620π-0.672620\pi
0.516110 0.856522i 0.327380π-0.327380\pi
968968 0 0
969969 −672.000 −0.0222784
970970 0 0
971971 1844.00 0.0609442 0.0304721 0.999536i 0.490299π-0.490299\pi
0.0304721 + 0.999536i 0.490299π0.490299\pi
972972 0 0
973973 7084.00i 0.233405i
974974 0 0
975975 0 0
976976 0 0
977977 − 34162.0i − 1.11867i −0.828942 0.559334i 0.811057π-0.811057\pi
0.828942 0.559334i 0.188943π-0.188943\pi
978978 0 0
979979 31800.0 1.03813
980980 0 0
981981 7150.00 0.232703
982982 0 0
983983 − 216.000i − 0.00700847i −0.999994 0.00350424i 0.998885π-0.998885\pi
0.999994 0.00350424i 0.00111544π-0.00111544\pi
984984 0 0
985985 0 0
986986 0 0
987987 3136.00i 0.101135i
988988 0 0
989989 −42016.0 −1.35089
990990 0 0
991991 52832.0 1.69351 0.846753 0.531987i 0.178554π-0.178554\pi
0.846753 + 0.531987i 0.178554π0.178554\pi
992992 0 0
993993 26288.0i 0.840105i
994994 0 0
995995 0 0
996996 0 0
997997 − 5054.00i − 0.160543i −0.996773 0.0802717i 0.974421π-0.974421\pi
0.996773 0.0802717i 0.0255788π-0.0255788\pi
998998 0 0
999999 −24016.0 −0.760593
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 1400.4.g.e.449.1 2
5.2 odd 4 280.4.a.a.1.1 1
5.3 odd 4 1400.4.a.g.1.1 1
5.4 even 2 inner 1400.4.g.e.449.2 2
20.7 even 4 560.4.a.l.1.1 1
35.27 even 4 1960.4.a.g.1.1 1
40.27 even 4 2240.4.a.l.1.1 1
40.37 odd 4 2240.4.a.z.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.4.a.a.1.1 1 5.2 odd 4
560.4.a.l.1.1 1 20.7 even 4
1400.4.a.g.1.1 1 5.3 odd 4
1400.4.g.e.449.1 2 1.1 even 1 trivial
1400.4.g.e.449.2 2 5.4 even 2 inner
1960.4.a.g.1.1 1 35.27 even 4
2240.4.a.l.1.1 1 40.27 even 4
2240.4.a.z.1.1 1 40.37 odd 4