Properties

Label 200.4.c.a.49.1
Level 200200
Weight 44
Character 200.49
Analytic conductor 11.80011.800
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] = [200,4,Mod(49,200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("200.49");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 200=2352 200 = 2^{3} \cdot 5^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 200.c (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: 11.800382001111.8003820011
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: 2 2
Twist minimal: no (minimal twist has level 40)
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 == 200.49
Dual form 200.4.c.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) == q10.0000iq318.0000iq773.0000q916.0000q11+6.00000iq136.00000iq17+124.000q19180.000q2142.0000iq23+460.000iq27142.000q29188.000q31+160.000iq33+202.000iq37+60.0000q39+54.0000q4166.0000iq43+38.0000iq47+19.0000q4960.0000q51738.000iq531240.00iq57564.000q59262.000q61+1314.00iq63554.000iq67420.000q69+140.000q71882.000iq73+288.000iq77+1160.00q79+2629.00q81642.000iq83+1420.00iq87+854.000q89+108.000q91+1880.00iq93478.000iq97+1168.00q99+O(q100)q-10.0000i q^{3} -18.0000i q^{7} -73.0000 q^{9} -16.0000 q^{11} +6.00000i q^{13} -6.00000i q^{17} +124.000 q^{19} -180.000 q^{21} -42.0000i q^{23} +460.000i q^{27} -142.000 q^{29} -188.000 q^{31} +160.000i q^{33} +202.000i q^{37} +60.0000 q^{39} +54.0000 q^{41} -66.0000i q^{43} +38.0000i q^{47} +19.0000 q^{49} -60.0000 q^{51} -738.000i q^{53} -1240.00i q^{57} -564.000 q^{59} -262.000 q^{61} +1314.00i q^{63} -554.000i q^{67} -420.000 q^{69} +140.000 q^{71} -882.000i q^{73} +288.000i q^{77} +1160.00 q^{79} +2629.00 q^{81} -642.000i q^{83} +1420.00i q^{87} +854.000 q^{89} +108.000 q^{91} +1880.00i q^{93} -478.000i q^{97} +1168.00 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q146q932q11+248q19360q21284q29376q31+120q39+108q41+38q49120q511128q59524q61840q69+280q71+2320q79+5258q81++2336q99+O(q100) 2 q - 146 q^{9} - 32 q^{11} + 248 q^{19} - 360 q^{21} - 284 q^{29} - 376 q^{31} + 120 q^{39} + 108 q^{41} + 38 q^{49} - 120 q^{51} - 1128 q^{59} - 524 q^{61} - 840 q^{69} + 280 q^{71} + 2320 q^{79} + 5258 q^{81}+ \cdots + 2336 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/200Z)×\left(\mathbb{Z}/200\mathbb{Z}\right)^\times.

nn 101101 151151 177177
χ(n)\chi(n) 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 − 10.0000i − 1.92450i −0.272166 0.962250i 0.587740π-0.587740\pi
0.272166 0.962250i 0.412260π-0.412260\pi
44 0 0
55 0 0
66 0 0
77 − 18.0000i − 0.971909i −0.873984 0.485954i 0.838472π-0.838472\pi
0.873984 0.485954i 0.161528π-0.161528\pi
88 0 0
99 −73.0000 −2.70370
1010 0 0
1111 −16.0000 −0.438562 −0.219281 0.975662i 0.570371π-0.570371\pi
−0.219281 + 0.975662i 0.570371π0.570371\pi
1212 0 0
1313 6.00000i 0.128008i 0.997950 + 0.0640039i 0.0203870π0.0203870\pi
−0.997950 + 0.0640039i 0.979613π0.979613\pi
1414 0 0
1515 0 0
1616 0 0
1717 − 6.00000i − 0.0856008i −0.999084 0.0428004i 0.986372π-0.986372\pi
0.999084 0.0428004i 0.0136280π-0.0136280\pi
1818 0 0
1919 124.000 1.49724 0.748620 0.663000i 0.230717π-0.230717\pi
0.748620 + 0.663000i 0.230717π0.230717\pi
2020 0 0
2121 −180.000 −1.87044
2222 0 0
2323 − 42.0000i − 0.380765i −0.981710 0.190383i 0.939027π-0.939027\pi
0.981710 0.190383i 0.0609729π-0.0609729\pi
2424 0 0
2525 0 0
2626 0 0
2727 460.000i 3.27878i
2828 0 0
2929 −142.000 −0.909267 −0.454633 0.890679i 0.650230π-0.650230\pi
−0.454633 + 0.890679i 0.650230π0.650230\pi
3030 0 0
3131 −188.000 −1.08922 −0.544610 0.838690i 0.683322π-0.683322\pi
−0.544610 + 0.838690i 0.683322π0.683322\pi
3232 0 0
3333 160.000i 0.844013i
3434 0 0
3535 0 0
3636 0 0
3737 202.000i 0.897530i 0.893650 + 0.448765i 0.148136π0.148136\pi
−0.893650 + 0.448765i 0.851864π0.851864\pi
3838 0 0
3939 60.0000 0.246351
4040 0 0
4141 54.0000 0.205692 0.102846 0.994697i 0.467205π-0.467205\pi
0.102846 + 0.994697i 0.467205π0.467205\pi
4242 0 0
4343 − 66.0000i − 0.234068i −0.993128 0.117034i 0.962661π-0.962661\pi
0.993128 0.117034i 0.0373386π-0.0373386\pi
4444 0 0
4545 0 0
4646 0 0
4747 38.0000i 0.117933i 0.998260 + 0.0589667i 0.0187806π0.0187806\pi
−0.998260 + 0.0589667i 0.981219π0.981219\pi
4848 0 0
4949 19.0000 0.0553936
5050 0 0
5151 −60.0000 −0.164739
5252 0 0
5353 − 738.000i − 1.91268i −0.292255 0.956341i 0.594405π-0.594405\pi
0.292255 0.956341i 0.405595π-0.405595\pi
5454 0 0
5555 0 0
5656 0 0
5757 − 1240.00i − 2.88144i
5858 0 0
5959 −564.000 −1.24452 −0.622259 0.782812i 0.713785π-0.713785\pi
−0.622259 + 0.782812i 0.713785π0.713785\pi
6060 0 0
6161 −262.000 −0.549929 −0.274964 0.961454i 0.588666π-0.588666\pi
−0.274964 + 0.961454i 0.588666π0.588666\pi
6262 0 0
6363 1314.00i 2.62775i
6464 0 0
6565 0 0
6666 0 0
6767 − 554.000i − 1.01018i −0.863067 0.505089i 0.831460π-0.831460\pi
0.863067 0.505089i 0.168540π-0.168540\pi
6868 0 0
6969 −420.000 −0.732783
7070 0 0
7171 140.000 0.234013 0.117007 0.993131i 0.462670π-0.462670\pi
0.117007 + 0.993131i 0.462670π0.462670\pi
7272 0 0
7373 − 882.000i − 1.41411i −0.707157 0.707057i 0.750023π-0.750023\pi
0.707157 0.707057i 0.249977π-0.249977\pi
7474 0 0
7575 0 0
7676 0 0
7777 288.000i 0.426242i
7878 0 0
7979 1160.00 1.65203 0.826014 0.563650i 0.190603π-0.190603\pi
0.826014 + 0.563650i 0.190603π0.190603\pi
8080 0 0
8181 2629.00 3.60631
8282 0 0
8383 − 642.000i − 0.849020i −0.905423 0.424510i 0.860446π-0.860446\pi
0.905423 0.424510i 0.139554π-0.139554\pi
8484 0 0
8585 0 0
8686 0 0
8787 1420.00i 1.74988i
8888 0 0
8989 854.000 1.01712 0.508561 0.861026i 0.330178π-0.330178\pi
0.508561 + 0.861026i 0.330178π0.330178\pi
9090 0 0
9191 108.000 0.124412
9292 0 0
9393 1880.00i 2.09620i
9494 0 0
9595 0 0
9696 0 0
9797 − 478.000i − 0.500346i −0.968201 0.250173i 0.919513π-0.919513\pi
0.968201 0.250173i 0.0804875π-0.0804875\pi
9898 0 0
9999 1168.00 1.18574
100100 0 0
101101 −1794.00 −1.76742 −0.883711 0.468033i 0.844963π-0.844963\pi
−0.883711 + 0.468033i 0.844963π0.844963\pi
102102 0 0
103103 − 642.000i − 0.614157i −0.951684 0.307078i 0.900649π-0.900649\pi
0.951684 0.307078i 0.0993514π-0.0993514\pi
104104 0 0
105105 0 0
106106 0 0
107107 − 850.000i − 0.767968i −0.923340 0.383984i 0.874552π-0.874552\pi
0.923340 0.383984i 0.125448π-0.125448\pi
108108 0 0
109109 −666.000 −0.585241 −0.292620 0.956229i 0.594527π-0.594527\pi
−0.292620 + 0.956229i 0.594527π0.594527\pi
110110 0 0
111111 2020.00 1.72730
112112 0 0
113113 1446.00i 1.20379i 0.798575 + 0.601895i 0.205587π0.205587\pi
−0.798575 + 0.601895i 0.794413π0.794413\pi
114114 0 0
115115 0 0
116116 0 0
117117 − 438.000i − 0.346095i
118118 0 0
119119 −108.000 −0.0831962
120120 0 0
121121 −1075.00 −0.807663
122122 0 0
123123 − 540.000i − 0.395855i
124124 0 0
125125 0 0
126126 0 0
127127 − 1154.00i − 0.806307i −0.915132 0.403153i 0.867914π-0.867914\pi
0.915132 0.403153i 0.132086π-0.132086\pi
128128 0 0
129129 −660.000 −0.450463
130130 0 0
131131 −368.000 −0.245437 −0.122719 0.992441i 0.539161π-0.539161\pi
−0.122719 + 0.992441i 0.539161π0.539161\pi
132132 0 0
133133 − 2232.00i − 1.45518i
134134 0 0
135135 0 0
136136 0 0
137137 − 670.000i − 0.417825i −0.977934 0.208912i 0.933008π-0.933008\pi
0.977934 0.208912i 0.0669923π-0.0669923\pi
138138 0 0
139139 572.000 0.349039 0.174519 0.984654i 0.444163π-0.444163\pi
0.174519 + 0.984654i 0.444163π0.444163\pi
140140 0 0
141141 380.000 0.226963
142142 0 0
143143 − 96.0000i − 0.0561393i
144144 0 0
145145 0 0
146146 0 0
147147 − 190.000i − 0.106605i
148148 0 0
149149 −1730.00 −0.951189 −0.475594 0.879665i 0.657767π-0.657767\pi
−0.475594 + 0.879665i 0.657767π0.657767\pi
150150 0 0
151151 1324.00 0.713547 0.356773 0.934191i 0.383877π-0.383877\pi
0.356773 + 0.934191i 0.383877π0.383877\pi
152152 0 0
153153 438.000i 0.231439i
154154 0 0
155155 0 0
156156 0 0
157157 2946.00i 1.49756i 0.662820 + 0.748778i 0.269359π0.269359\pi
−0.662820 + 0.748778i 0.730641π0.730641\pi
158158 0 0
159159 −7380.00 −3.68096
160160 0 0
161161 −756.000 −0.370069
162162 0 0
163163 − 2098.00i − 1.00815i −0.863661 0.504074i 0.831834π-0.831834\pi
0.863661 0.504074i 0.168166π-0.168166\pi
164164 0 0
165165 0 0
166166 0 0
167167 − 866.000i − 0.401276i −0.979665 0.200638i 0.935699π-0.935699\pi
0.979665 0.200638i 0.0643015π-0.0643015\pi
168168 0 0
169169 2161.00 0.983614
170170 0 0
171171 −9052.00 −4.04809
172172 0 0
173173 1678.00i 0.737433i 0.929542 + 0.368717i 0.120203π0.120203\pi
−0.929542 + 0.368717i 0.879797π0.879797\pi
174174 0 0
175175 0 0
176176 0 0
177177 5640.00i 2.39508i
178178 0 0
179179 1620.00 0.676450 0.338225 0.941065i 0.390174π-0.390174\pi
0.338225 + 0.941065i 0.390174π0.390174\pi
180180 0 0
181181 2510.00 1.03076 0.515378 0.856963i 0.327652π-0.327652\pi
0.515378 + 0.856963i 0.327652π0.327652\pi
182182 0 0
183183 2620.00i 1.05834i
184184 0 0
185185 0 0
186186 0 0
187187 96.0000i 0.0375413i
188188 0 0
189189 8280.00 3.18667
190190 0 0
191191 −372.000 −0.140927 −0.0704633 0.997514i 0.522448π-0.522448\pi
−0.0704633 + 0.997514i 0.522448π0.522448\pi
192192 0 0
193193 − 2938.00i − 1.09576i −0.836557 0.547880i 0.815435π-0.815435\pi
0.836557 0.547880i 0.184565π-0.184565\pi
194194 0 0
195195 0 0
196196 0 0
197197 2234.00i 0.807949i 0.914770 + 0.403974i 0.132372π0.132372\pi
−0.914770 + 0.403974i 0.867628π0.867628\pi
198198 0 0
199199 3048.00 1.08576 0.542882 0.839809i 0.317333π-0.317333\pi
0.542882 + 0.839809i 0.317333π0.317333\pi
200200 0 0
201201 −5540.00 −1.94409
202202 0 0
203203 2556.00i 0.883724i
204204 0 0
205205 0 0
206206 0 0
207207 3066.00i 1.02948i
208208 0 0
209209 −1984.00 −0.656632
210210 0 0
211211 4896.00 1.59741 0.798707 0.601720i 0.205518π-0.205518\pi
0.798707 + 0.601720i 0.205518π0.205518\pi
212212 0 0
213213 − 1400.00i − 0.450359i
214214 0 0
215215 0 0
216216 0 0
217217 3384.00i 1.05862i
218218 0 0
219219 −8820.00 −2.72146
220220 0 0
221221 36.0000 0.0109576
222222 0 0
223223 5302.00i 1.59214i 0.605202 + 0.796072i 0.293092π0.293092\pi
−0.605202 + 0.796072i 0.706908π0.706908\pi
224224 0 0
225225 0 0
226226 0 0
227227 − 3778.00i − 1.10465i −0.833630 0.552323i 0.813741π-0.813741\pi
0.833630 0.552323i 0.186259π-0.186259\pi
228228 0 0
229229 3034.00 0.875513 0.437756 0.899094i 0.355773π-0.355773\pi
0.437756 + 0.899094i 0.355773π0.355773\pi
230230 0 0
231231 2880.00 0.820303
232232 0 0
233233 3478.00i 0.977903i 0.872311 + 0.488951i 0.162620π0.162620\pi
−0.872311 + 0.488951i 0.837380π0.837380\pi
234234 0 0
235235 0 0
236236 0 0
237237 − 11600.0i − 3.17933i
238238 0 0
239239 −1560.00 −0.422209 −0.211105 0.977463i 0.567706π-0.567706\pi
−0.211105 + 0.977463i 0.567706π0.567706\pi
240240 0 0
241241 −3218.00 −0.860123 −0.430061 0.902800i 0.641508π-0.641508\pi
−0.430061 + 0.902800i 0.641508π0.641508\pi
242242 0 0
243243 − 13870.0i − 3.66157i
244244 0 0
245245 0 0
246246 0 0
247247 744.000i 0.191658i
248248 0 0
249249 −6420.00 −1.63394
250250 0 0
251251 688.000 0.173013 0.0865063 0.996251i 0.472430π-0.472430\pi
0.0865063 + 0.996251i 0.472430π0.472430\pi
252252 0 0
253253 672.000i 0.166989i
254254 0 0
255255 0 0
256256 0 0
257257 2170.00i 0.526696i 0.964701 + 0.263348i 0.0848267π0.0848267\pi
−0.964701 + 0.263348i 0.915173π0.915173\pi
258258 0 0
259259 3636.00 0.872317
260260 0 0
261261 10366.0 2.45839
262262 0 0
263263 − 2274.00i − 0.533159i −0.963813 0.266580i 0.914106π-0.914106\pi
0.963813 0.266580i 0.0858935π-0.0858935\pi
264264 0 0
265265 0 0
266266 0 0
267267 − 8540.00i − 1.95745i
268268 0 0
269269 −7146.00 −1.61970 −0.809850 0.586637i 0.800452π-0.800452\pi
−0.809850 + 0.586637i 0.800452π0.800452\pi
270270 0 0
271271 2604.00 0.583696 0.291848 0.956465i 0.405730π-0.405730\pi
0.291848 + 0.956465i 0.405730π0.405730\pi
272272 0 0
273273 − 1080.00i − 0.239431i
274274 0 0
275275 0 0
276276 0 0
277277 − 5150.00i − 1.11709i −0.829475 0.558544i 0.811360π-0.811360\pi
0.829475 0.558544i 0.188640π-0.188640\pi
278278 0 0
279279 13724.0 2.94493
280280 0 0
281281 5270.00 1.11880 0.559398 0.828899i 0.311032π-0.311032\pi
0.559398 + 0.828899i 0.311032π0.311032\pi
282282 0 0
283283 − 3434.00i − 0.721308i −0.932700 0.360654i 0.882554π-0.882554\pi
0.932700 0.360654i 0.117446π-0.117446\pi
284284 0 0
285285 0 0
286286 0 0
287287 − 972.000i − 0.199914i
288288 0 0
289289 4877.00 0.992673
290290 0 0
291291 −4780.00 −0.962916
292292 0 0
293293 9878.00i 1.96955i 0.173826 + 0.984776i 0.444387π0.444387\pi
−0.173826 + 0.984776i 0.555613π0.555613\pi
294294 0 0
295295 0 0
296296 0 0
297297 − 7360.00i − 1.43795i
298298 0 0
299299 252.000 0.0487409
300300 0 0
301301 −1188.00 −0.227492
302302 0 0
303303 17940.0i 3.40141i
304304 0 0
305305 0 0
306306 0 0
307307 8054.00i 1.49728i 0.662975 + 0.748642i 0.269294π0.269294\pi
−0.662975 + 0.748642i 0.730706π0.730706\pi
308308 0 0
309309 −6420.00 −1.18195
310310 0 0
311311 5492.00 1.00136 0.500680 0.865633i 0.333083π-0.333083\pi
0.500680 + 0.865633i 0.333083π0.333083\pi
312312 0 0
313313 422.000i 0.0762072i 0.999274 + 0.0381036i 0.0121317π0.0121317\pi
−0.999274 + 0.0381036i 0.987868π0.987868\pi
314314 0 0
315315 0 0
316316 0 0
317317 6194.00i 1.09744i 0.836005 + 0.548722i 0.184885π0.184885\pi
−0.836005 + 0.548722i 0.815115π0.815115\pi
318318 0 0
319319 2272.00 0.398770
320320 0 0
321321 −8500.00 −1.47796
322322 0 0
323323 − 744.000i − 0.128165i
324324 0 0
325325 0 0
326326 0 0
327327 6660.00i 1.12630i
328328 0 0
329329 684.000 0.114620
330330 0 0
331331 7688.00 1.27665 0.638324 0.769768i 0.279628π-0.279628\pi
0.638324 + 0.769768i 0.279628π0.279628\pi
332332 0 0
333333 − 14746.0i − 2.42665i
334334 0 0
335335 0 0
336336 0 0
337337 − 1438.00i − 0.232442i −0.993223 0.116221i 0.962922π-0.962922\pi
0.993223 0.116221i 0.0370780π-0.0370780\pi
338338 0 0
339339 14460.0 2.31669
340340 0 0
341341 3008.00 0.477690
342342 0 0
343343 − 6516.00i − 1.02575i
344344 0 0
345345 0 0
346346 0 0
347347 8838.00i 1.36729i 0.729816 + 0.683644i 0.239606π0.239606\pi
−0.729816 + 0.683644i 0.760394π0.760394\pi
348348 0 0
349349 7810.00 1.19788 0.598939 0.800794i 0.295589π-0.295589\pi
0.598939 + 0.800794i 0.295589π0.295589\pi
350350 0 0
351351 −2760.00 −0.419709
352352 0 0
353353 − 5906.00i − 0.890495i −0.895408 0.445247i 0.853116π-0.853116\pi
0.895408 0.445247i 0.146884π-0.146884\pi
354354 0 0
355355 0 0
356356 0 0
357357 1080.00i 0.160111i
358358 0 0
359359 −8904.00 −1.30901 −0.654506 0.756057i 0.727123π-0.727123\pi
−0.654506 + 0.756057i 0.727123π0.727123\pi
360360 0 0
361361 8517.00 1.24173
362362 0 0
363363 10750.0i 1.55435i
364364 0 0
365365 0 0
366366 0 0
367367 − 7370.00i − 1.04826i −0.851639 0.524129i 0.824391π-0.824391\pi
0.851639 0.524129i 0.175609π-0.175609\pi
368368 0 0
369369 −3942.00 −0.556131
370370 0 0
371371 −13284.0 −1.85895
372372 0 0
373373 734.000i 0.101890i 0.998701 + 0.0509451i 0.0162234π0.0162234\pi
−0.998701 + 0.0509451i 0.983777π0.983777\pi
374374 0 0
375375 0 0
376376 0 0
377377 − 852.000i − 0.116393i
378378 0 0
379379 −10300.0 −1.39598 −0.697989 0.716109i 0.745921π-0.745921\pi
−0.697989 + 0.716109i 0.745921π0.745921\pi
380380 0 0
381381 −11540.0 −1.55174
382382 0 0
383383 − 2682.00i − 0.357817i −0.983866 0.178908i 0.942743π-0.942743\pi
0.983866 0.178908i 0.0572566π-0.0572566\pi
384384 0 0
385385 0 0
386386 0 0
387387 4818.00i 0.632849i
388388 0 0
389389 −6114.00 −0.796895 −0.398447 0.917191i 0.630451π-0.630451\pi
−0.398447 + 0.917191i 0.630451π0.630451\pi
390390 0 0
391391 −252.000 −0.0325938
392392 0 0
393393 3680.00i 0.472345i
394394 0 0
395395 0 0
396396 0 0
397397 − 7174.00i − 0.906934i −0.891273 0.453467i 0.850187π-0.850187\pi
0.891273 0.453467i 0.149813π-0.149813\pi
398398 0 0
399399 −22320.0 −2.80050
400400 0 0
401401 10498.0 1.30734 0.653672 0.756778i 0.273228π-0.273228\pi
0.653672 + 0.756778i 0.273228π0.273228\pi
402402 0 0
403403 − 1128.00i − 0.139428i
404404 0 0
405405 0 0
406406 0 0
407407 − 3232.00i − 0.393622i
408408 0 0
409409 1810.00 0.218823 0.109412 0.993997i 0.465103π-0.465103\pi
0.109412 + 0.993997i 0.465103π0.465103\pi
410410 0 0
411411 −6700.00 −0.804104
412412 0 0
413413 10152.0i 1.20956i
414414 0 0
415415 0 0
416416 0 0
417417 − 5720.00i − 0.671726i
418418 0 0
419419 3396.00 0.395956 0.197978 0.980206i 0.436563π-0.436563\pi
0.197978 + 0.980206i 0.436563π0.436563\pi
420420 0 0
421421 −14974.0 −1.73346 −0.866732 0.498775i 0.833784π-0.833784\pi
−0.866732 + 0.498775i 0.833784π0.833784\pi
422422 0 0
423423 − 2774.00i − 0.318857i
424424 0 0
425425 0 0
426426 0 0
427427 4716.00i 0.534481i
428428 0 0
429429 −960.000 −0.108040
430430 0 0
431431 −13540.0 −1.51322 −0.756611 0.653865i 0.773146π-0.773146\pi
−0.756611 + 0.653865i 0.773146π0.773146\pi
432432 0 0
433433 − 15426.0i − 1.71207i −0.516918 0.856035i 0.672921π-0.672921\pi
0.516918 0.856035i 0.327079π-0.327079\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 5208.00i − 0.570097i
438438 0 0
439439 10472.0 1.13850 0.569250 0.822165i 0.307234π-0.307234\pi
0.569250 + 0.822165i 0.307234π0.307234\pi
440440 0 0
441441 −1387.00 −0.149768
442442 0 0
443443 − 722.000i − 0.0774340i −0.999250 0.0387170i 0.987673π-0.987673\pi
0.999250 0.0387170i 0.0123271π-0.0123271\pi
444444 0 0
445445 0 0
446446 0 0
447447 17300.0i 1.83056i
448448 0 0
449449 11898.0 1.25056 0.625280 0.780401i 0.284985π-0.284985\pi
0.625280 + 0.780401i 0.284985π0.284985\pi
450450 0 0
451451 −864.000 −0.0902088
452452 0 0
453453 − 13240.0i − 1.37322i
454454 0 0
455455 0 0
456456 0 0
457457 − 790.000i − 0.0808635i −0.999182 0.0404318i 0.987127π-0.987127\pi
0.999182 0.0404318i 0.0128733π-0.0128733\pi
458458 0 0
459459 2760.00 0.280666
460460 0 0
461461 −3418.00 −0.345319 −0.172660 0.984982i 0.555236π-0.555236\pi
−0.172660 + 0.984982i 0.555236π0.555236\pi
462462 0 0
463463 7534.00i 0.756230i 0.925759 + 0.378115i 0.123428π0.123428\pi
−0.925759 + 0.378115i 0.876572π0.876572\pi
464464 0 0
465465 0 0
466466 0 0
467467 − 14314.0i − 1.41836i −0.705029 0.709179i 0.749066π-0.749066\pi
0.705029 0.709179i 0.250934π-0.250934\pi
468468 0 0
469469 −9972.00 −0.981800
470470 0 0
471471 29460.0 2.88205
472472 0 0
473473 1056.00i 0.102653i
474474 0 0
475475 0 0
476476 0 0
477477 53874.0i 5.17132i
478478 0 0
479479 7016.00 0.669247 0.334623 0.942352i 0.391391π-0.391391\pi
0.334623 + 0.942352i 0.391391π0.391391\pi
480480 0 0
481481 −1212.00 −0.114891
482482 0 0
483483 7560.00i 0.712199i
484484 0 0
485485 0 0
486486 0 0
487487 15190.0i 1.41340i 0.707515 + 0.706699i 0.249816π0.249816\pi
−0.707515 + 0.706699i 0.750184π0.750184\pi
488488 0 0
489489 −20980.0 −1.94018
490490 0 0
491491 −12624.0 −1.16031 −0.580156 0.814505i 0.697008π-0.697008\pi
−0.580156 + 0.814505i 0.697008π0.697008\pi
492492 0 0
493493 852.000i 0.0778340i
494494 0 0
495495 0 0
496496 0 0
497497 − 2520.00i − 0.227440i
498498 0 0
499499 2492.00 0.223562 0.111781 0.993733i 0.464345π-0.464345\pi
0.111781 + 0.993733i 0.464345π0.464345\pi
500500 0 0
501501 −8660.00 −0.772256
502502 0 0
503503 − 11714.0i − 1.03837i −0.854661 0.519186i 0.826235π-0.826235\pi
0.854661 0.519186i 0.173765π-0.173765\pi
504504 0 0
505505 0 0
506506 0 0
507507 − 21610.0i − 1.89297i
508508 0 0
509509 5618.00 0.489221 0.244610 0.969621i 0.421340π-0.421340\pi
0.244610 + 0.969621i 0.421340π0.421340\pi
510510 0 0
511511 −15876.0 −1.37439
512512 0 0
513513 57040.0i 4.90912i
514514 0 0
515515 0 0
516516 0 0
517517 − 608.000i − 0.0517211i
518518 0 0
519519 16780.0 1.41919
520520 0 0
521521 13770.0 1.15792 0.578958 0.815357i 0.303459π-0.303459\pi
0.578958 + 0.815357i 0.303459π0.303459\pi
522522 0 0
523523 − 6986.00i − 0.584085i −0.956405 0.292042i 0.905665π-0.905665\pi
0.956405 0.292042i 0.0943349π-0.0943349\pi
524524 0 0
525525 0 0
526526 0 0
527527 1128.00i 0.0932380i
528528 0 0
529529 10403.0 0.855018
530530 0 0
531531 41172.0 3.36481
532532 0 0
533533 324.000i 0.0263302i
534534 0 0
535535 0 0
536536 0 0
537537 − 16200.0i − 1.30183i
538538 0 0
539539 −304.000 −0.0242935
540540 0 0
541541 11958.0 0.950304 0.475152 0.879904i 0.342393π-0.342393\pi
0.475152 + 0.879904i 0.342393π0.342393\pi
542542 0 0
543543 − 25100.0i − 1.98369i
544544 0 0
545545 0 0
546546 0 0
547547 − 4194.00i − 0.327829i −0.986475 0.163915i 0.947588π-0.947588\pi
0.986475 0.163915i 0.0524121π-0.0524121\pi
548548 0 0
549549 19126.0 1.48684
550550 0 0
551551 −17608.0 −1.36139
552552 0 0
553553 − 20880.0i − 1.60562i
554554 0 0
555555 0 0
556556 0 0
557557 − 5382.00i − 0.409412i −0.978823 0.204706i 0.934376π-0.934376\pi
0.978823 0.204706i 0.0656239π-0.0656239\pi
558558 0 0
559559 396.000 0.0299625
560560 0 0
561561 960.000 0.0722482
562562 0 0
563563 − 15418.0i − 1.15416i −0.816688 0.577079i 0.804192π-0.804192\pi
0.816688 0.577079i 0.195808π-0.195808\pi
564564 0 0
565565 0 0
566566 0 0
567567 − 47322.0i − 3.50500i
568568 0 0
569569 5778.00 0.425705 0.212853 0.977084i 0.431725π-0.431725\pi
0.212853 + 0.977084i 0.431725π0.431725\pi
570570 0 0
571571 6024.00 0.441500 0.220750 0.975330i 0.429149π-0.429149\pi
0.220750 + 0.975330i 0.429149π0.429149\pi
572572 0 0
573573 3720.00i 0.271213i
574574 0 0
575575 0 0
576576 0 0
577577 554.000i 0.0399711i 0.999800 + 0.0199855i 0.00636202π0.00636202\pi
−0.999800 + 0.0199855i 0.993638π0.993638\pi
578578 0 0
579579 −29380.0 −2.10879
580580 0 0
581581 −11556.0 −0.825170
582582 0 0
583583 11808.0i 0.838829i
584584 0 0
585585 0 0
586586 0 0
587587 − 2386.00i − 0.167770i −0.996475 0.0838848i 0.973267π-0.973267\pi
0.996475 0.0838848i 0.0267328π-0.0267328\pi
588588 0 0
589589 −23312.0 −1.63082
590590 0 0
591591 22340.0 1.55490
592592 0 0
593593 846.000i 0.0585853i 0.999571 + 0.0292926i 0.00932547π0.00932547\pi
−0.999571 + 0.0292926i 0.990675π0.990675\pi
594594 0 0
595595 0 0
596596 0 0
597597 − 30480.0i − 2.08955i
598598 0 0
599599 −22304.0 −1.52140 −0.760698 0.649105i 0.775143π-0.775143\pi
−0.760698 + 0.649105i 0.775143π0.775143\pi
600600 0 0
601601 5510.00 0.373973 0.186986 0.982363i 0.440128π-0.440128\pi
0.186986 + 0.982363i 0.440128π0.440128\pi
602602 0 0
603603 40442.0i 2.73122i
604604 0 0
605605 0 0
606606 0 0
607607 − 8234.00i − 0.550589i −0.961360 0.275295i 0.911225π-0.911225\pi
0.961360 0.275295i 0.0887754π-0.0887754\pi
608608 0 0
609609 25560.0 1.70073
610610 0 0
611611 −228.000 −0.0150964
612612 0 0
613613 1046.00i 0.0689193i 0.999406 + 0.0344597i 0.0109710π0.0109710\pi
−0.999406 + 0.0344597i 0.989029π0.989029\pi
614614 0 0
615615 0 0
616616 0 0
617617 − 3862.00i − 0.251991i −0.992031 0.125995i 0.959788π-0.959788\pi
0.992031 0.125995i 0.0402124π-0.0402124\pi
618618 0 0
619619 −13964.0 −0.906721 −0.453361 0.891327i 0.649775π-0.649775\pi
−0.453361 + 0.891327i 0.649775π0.649775\pi
620620 0 0
621621 19320.0 1.24845
622622 0 0
623623 − 15372.0i − 0.988549i
624624 0 0
625625 0 0
626626 0 0
627627 19840.0i 1.26369i
628628 0 0
629629 1212.00 0.0768293
630630 0 0
631631 −14884.0 −0.939022 −0.469511 0.882927i 0.655570π-0.655570\pi
−0.469511 + 0.882927i 0.655570π0.655570\pi
632632 0 0
633633 − 48960.0i − 3.07423i
634634 0 0
635635 0 0
636636 0 0
637637 114.000i 0.00709081i
638638 0 0
639639 −10220.0 −0.632703
640640 0 0
641641 17838.0 1.09916 0.549578 0.835443i 0.314789π-0.314789\pi
0.549578 + 0.835443i 0.314789π0.314789\pi
642642 0 0
643643 7814.00i 0.479244i 0.970866 + 0.239622i 0.0770236π0.0770236\pi
−0.970866 + 0.239622i 0.922976π0.922976\pi
644644 0 0
645645 0 0
646646 0 0
647647 774.000i 0.0470310i 0.999723 + 0.0235155i 0.00748591π0.00748591\pi
−0.999723 + 0.0235155i 0.992514π0.992514\pi
648648 0 0
649649 9024.00 0.545798
650650 0 0
651651 33840.0 2.03732
652652 0 0
653653 23422.0i 1.40364i 0.712357 + 0.701818i 0.247628π0.247628\pi
−0.712357 + 0.701818i 0.752372π0.752372\pi
654654 0 0
655655 0 0
656656 0 0
657657 64386.0i 3.82334i
658658 0 0
659659 13508.0 0.798478 0.399239 0.916847i 0.369274π-0.369274\pi
0.399239 + 0.916847i 0.369274π0.369274\pi
660660 0 0
661661 −6222.00 −0.366124 −0.183062 0.983101i 0.558601π-0.558601\pi
−0.183062 + 0.983101i 0.558601π0.558601\pi
662662 0 0
663663 − 360.000i − 0.0210878i
664664 0 0
665665 0 0
666666 0 0
667667 5964.00i 0.346217i
668668 0 0
669669 53020.0 3.06408
670670 0 0
671671 4192.00 0.241178
672672 0 0
673673 15566.0i 0.891568i 0.895141 + 0.445784i 0.147075π0.147075\pi
−0.895141 + 0.445784i 0.852925π0.852925\pi
674674 0 0
675675 0 0
676676 0 0
677677 2234.00i 0.126824i 0.997987 + 0.0634118i 0.0201982π0.0201982\pi
−0.997987 + 0.0634118i 0.979802π0.979802\pi
678678 0 0
679679 −8604.00 −0.486290
680680 0 0
681681 −37780.0 −2.12589
682682 0 0
683683 − 13282.0i − 0.744102i −0.928212 0.372051i 0.878655π-0.878655\pi
0.928212 0.372051i 0.121345π-0.121345\pi
684684 0 0
685685 0 0
686686 0 0
687687 − 30340.0i − 1.68492i
688688 0 0
689689 4428.00 0.244838
690690 0 0
691691 −27416.0 −1.50934 −0.754670 0.656105i 0.772203π-0.772203\pi
−0.754670 + 0.656105i 0.772203π0.772203\pi
692692 0 0
693693 − 21024.0i − 1.15243i
694694 0 0
695695 0 0
696696 0 0
697697 − 324.000i − 0.0176074i
698698 0 0
699699 34780.0 1.88197
700700 0 0
701701 25626.0 1.38071 0.690357 0.723469i 0.257453π-0.257453\pi
0.690357 + 0.723469i 0.257453π0.257453\pi
702702 0 0
703703 25048.0i 1.34382i
704704 0 0
705705 0 0
706706 0 0
707707 32292.0i 1.71777i
708708 0 0
709709 −11702.0 −0.619856 −0.309928 0.950760i 0.600305π-0.600305\pi
−0.309928 + 0.950760i 0.600305π0.600305\pi
710710 0 0
711711 −84680.0 −4.46659
712712 0 0
713713 7896.00i 0.414737i
714714 0 0
715715 0 0
716716 0 0
717717 15600.0i 0.812542i
718718 0 0
719719 28008.0 1.45274 0.726371 0.687302i 0.241205π-0.241205\pi
0.726371 + 0.687302i 0.241205π0.241205\pi
720720 0 0
721721 −11556.0 −0.596904
722722 0 0
723723 32180.0i 1.65531i
724724 0 0
725725 0 0
726726 0 0
727727 − 7682.00i − 0.391898i −0.980614 0.195949i 0.937221π-0.937221\pi
0.980614 0.195949i 0.0627787π-0.0627787\pi
728728 0 0
729729 −67717.0 −3.44038
730730 0 0
731731 −396.000 −0.0200364
732732 0 0
733733 14270.0i 0.719065i 0.933133 + 0.359532i 0.117064π0.117064\pi
−0.933133 + 0.359532i 0.882936π0.882936\pi
734734 0 0
735735 0 0
736736 0 0
737737 8864.00i 0.443025i
738738 0 0
739739 −29324.0 −1.45968 −0.729838 0.683620i 0.760405π-0.760405\pi
−0.729838 + 0.683620i 0.760405π0.760405\pi
740740 0 0
741741 7440.00 0.368846
742742 0 0
743743 − 29258.0i − 1.44465i −0.691556 0.722323i 0.743074π-0.743074\pi
0.691556 0.722323i 0.256926π-0.256926\pi
744744 0 0
745745 0 0
746746 0 0
747747 46866.0i 2.29550i
748748 0 0
749749 −15300.0 −0.746395
750750 0 0
751751 19076.0 0.926888 0.463444 0.886126i 0.346613π-0.346613\pi
0.463444 + 0.886126i 0.346613π0.346613\pi
752752 0 0
753753 − 6880.00i − 0.332963i
754754 0 0
755755 0 0
756756 0 0
757757 − 22670.0i − 1.08845i −0.838940 0.544224i 0.816824π-0.816824\pi
0.838940 0.544224i 0.183176π-0.183176\pi
758758 0 0
759759 6720.00 0.321371
760760 0 0
761761 −23206.0 −1.10541 −0.552705 0.833377i 0.686404π-0.686404\pi
−0.552705 + 0.833377i 0.686404π0.686404\pi
762762 0 0
763763 11988.0i 0.568800i
764764 0 0
765765 0 0
766766 0 0
767767 − 3384.00i − 0.159308i
768768 0 0
769769 1854.00 0.0869401 0.0434701 0.999055i 0.486159π-0.486159\pi
0.0434701 + 0.999055i 0.486159π0.486159\pi
770770 0 0
771771 21700.0 1.01363
772772 0 0
773773 − 6474.00i − 0.301234i −0.988592 0.150617i 0.951874π-0.951874\pi
0.988592 0.150617i 0.0481260π-0.0481260\pi
774774 0 0
775775 0 0
776776 0 0
777777 − 36360.0i − 1.67877i
778778 0 0
779779 6696.00 0.307971
780780 0 0
781781 −2240.00 −0.102629
782782 0 0
783783 − 65320.0i − 2.98129i
784784 0 0
785785 0 0
786786 0 0
787787 − 20354.0i − 0.921908i −0.887424 0.460954i 0.847507π-0.847507\pi
0.887424 0.460954i 0.152493π-0.152493\pi
788788 0 0
789789 −22740.0 −1.02607
790790 0 0
791791 26028.0 1.16997
792792 0 0
793793 − 1572.00i − 0.0703952i
794794 0 0
795795 0 0
796796 0 0
797797 − 1886.00i − 0.0838213i −0.999121 0.0419106i 0.986656π-0.986656\pi
0.999121 0.0419106i 0.0133445π-0.0133445\pi
798798 0 0
799799 228.000 0.0100952
800800 0 0
801801 −62342.0 −2.75000
802802 0 0
803803 14112.0i 0.620176i
804804 0 0
805805 0 0
806806 0 0
807807 71460.0i 3.11711i
808808 0 0
809809 9462.00 0.411207 0.205603 0.978635i 0.434084π-0.434084\pi
0.205603 + 0.978635i 0.434084π0.434084\pi
810810 0 0
811811 24512.0 1.06132 0.530661 0.847584i 0.321944π-0.321944\pi
0.530661 + 0.847584i 0.321944π0.321944\pi
812812 0 0
813813 − 26040.0i − 1.12332i
814814 0 0
815815 0 0
816816 0 0
817817 − 8184.00i − 0.350455i
818818 0 0
819819 −7884.00 −0.336373
820820 0 0
821821 36242.0 1.54063 0.770313 0.637666i 0.220100π-0.220100\pi
0.770313 + 0.637666i 0.220100π0.220100\pi
822822 0 0
823823 17718.0i 0.750438i 0.926936 + 0.375219i 0.122433π0.122433\pi
−0.926936 + 0.375219i 0.877567π0.877567\pi
824824 0 0
825825 0 0
826826 0 0
827827 6726.00i 0.282812i 0.989952 + 0.141406i 0.0451624π0.0451624\pi
−0.989952 + 0.141406i 0.954838π0.954838\pi
828828 0 0
829829 −41722.0 −1.74797 −0.873984 0.485955i 0.838472π-0.838472\pi
−0.873984 + 0.485955i 0.838472π0.838472\pi
830830 0 0
831831 −51500.0 −2.14984
832832 0 0
833833 − 114.000i − 0.00474174i
834834 0 0
835835 0 0
836836 0 0
837837 − 86480.0i − 3.57131i
838838 0 0
839839 −16720.0 −0.688008 −0.344004 0.938968i 0.611783π-0.611783\pi
−0.344004 + 0.938968i 0.611783π0.611783\pi
840840 0 0
841841 −4225.00 −0.173234
842842 0 0
843843 − 52700.0i − 2.15313i
844844 0 0
845845 0 0
846846 0 0
847847 19350.0i 0.784975i
848848 0 0
849849 −34340.0 −1.38816
850850 0 0
851851 8484.00 0.341748
852852 0 0
853853 33286.0i 1.33610i 0.744118 + 0.668049i 0.232870π0.232870\pi
−0.744118 + 0.668049i 0.767130π0.767130\pi
854854 0 0
855855 0 0
856856 0 0
857857 38978.0i 1.55363i 0.629727 + 0.776816i 0.283167π0.283167\pi
−0.629727 + 0.776816i 0.716833π0.716833\pi
858858 0 0
859859 1916.00 0.0761037 0.0380518 0.999276i 0.487885π-0.487885\pi
0.0380518 + 0.999276i 0.487885π0.487885\pi
860860 0 0
861861 −9720.00 −0.384735
862862 0 0
863863 2374.00i 0.0936407i 0.998903 + 0.0468203i 0.0149088π0.0149088\pi
−0.998903 + 0.0468203i 0.985091π0.985091\pi
864864 0 0
865865 0 0
866866 0 0
867867 − 48770.0i − 1.91040i
868868 0 0
869869 −18560.0 −0.724517
870870 0 0
871871 3324.00 0.129310
872872 0 0
873873 34894.0i 1.35279i
874874 0 0
875875 0 0
876876 0 0
877877 32722.0i 1.25991i 0.776631 + 0.629956i 0.216927π0.216927\pi
−0.776631 + 0.629956i 0.783073π0.783073\pi
878878 0 0
879879 98780.0 3.79041
880880 0 0
881881 5390.00 0.206122 0.103061 0.994675i 0.467136π-0.467136\pi
0.103061 + 0.994675i 0.467136π0.467136\pi
882882 0 0
883883 43238.0i 1.64788i 0.566680 + 0.823938i 0.308228π0.308228\pi
−0.566680 + 0.823938i 0.691772π0.691772\pi
884884 0 0
885885 0 0
886886 0 0
887887 − 11010.0i − 0.416775i −0.978046 0.208388i 0.933178π-0.933178\pi
0.978046 0.208388i 0.0668215π-0.0668215\pi
888888 0 0
889889 −20772.0 −0.783656
890890 0 0
891891 −42064.0 −1.58159
892892 0 0
893893 4712.00i 0.176575i
894894 0 0
895895 0 0
896896 0 0
897897 − 2520.00i − 0.0938020i
898898 0 0
899899 26696.0 0.990391
900900 0 0
901901 −4428.00 −0.163727
902902 0 0
903903 11880.0i 0.437809i
904904 0 0
905905 0 0
906906 0 0
907907 − 74.0000i − 0.00270907i −0.999999 0.00135454i 0.999569π-0.999569\pi
0.999999 0.00135454i 0.000431163π-0.000431163\pi
908908 0 0
909909 130962. 4.77859
910910 0 0
911911 17460.0 0.634990 0.317495 0.948260i 0.397158π-0.397158\pi
0.317495 + 0.948260i 0.397158π0.397158\pi
912912 0 0
913913 10272.0i 0.372348i
914914 0 0
915915 0 0
916916 0 0
917917 6624.00i 0.238543i
918918 0 0
919919 −17072.0 −0.612789 −0.306395 0.951905i 0.599123π-0.599123\pi
−0.306395 + 0.951905i 0.599123π0.599123\pi
920920 0 0
921921 80540.0 2.88152
922922 0 0
923923 840.000i 0.0299555i
924924 0 0
925925 0 0
926926 0 0
927927 46866.0i 1.66050i
928928 0 0
929929 14826.0 0.523601 0.261800 0.965122i 0.415684π-0.415684\pi
0.261800 + 0.965122i 0.415684π0.415684\pi
930930 0 0
931931 2356.00 0.0829375
932932 0 0
933933 − 54920.0i − 1.92712i
934934 0 0
935935 0 0
936936 0 0
937937 3354.00i 0.116937i 0.998289 + 0.0584687i 0.0186218π0.0186218\pi
−0.998289 + 0.0584687i 0.981378π0.981378\pi
938938 0 0
939939 4220.00 0.146661
940940 0 0
941941 −15434.0 −0.534680 −0.267340 0.963602i 0.586145π-0.586145\pi
−0.267340 + 0.963602i 0.586145π0.586145\pi
942942 0 0
943943 − 2268.00i − 0.0783205i
944944 0 0
945945 0 0
946946 0 0
947947 − 9306.00i − 0.319329i −0.987171 0.159664i 0.948959π-0.948959\pi
0.987171 0.159664i 0.0510412π-0.0510412\pi
948948 0 0
949949 5292.00 0.181017
950950 0 0
951951 61940.0 2.11203
952952 0 0
953953 − 12202.0i − 0.414755i −0.978261 0.207378i 0.933507π-0.933507\pi
0.978261 0.207378i 0.0664928π-0.0664928\pi
954954 0 0
955955 0 0
956956 0 0
957957 − 22720.0i − 0.767433i
958958 0 0
959959 −12060.0 −0.406087
960960 0 0
961961 5553.00 0.186399
962962 0 0
963963 62050.0i 2.07636i
964964 0 0
965965 0 0
966966 0 0
967967 17478.0i 0.581235i 0.956839 + 0.290618i 0.0938608π0.0938608\pi
−0.956839 + 0.290618i 0.906139π0.906139\pi
968968 0 0
969969 −7440.00 −0.246653
970970 0 0
971971 10920.0 0.360906 0.180453 0.983584i 0.442244π-0.442244\pi
0.180453 + 0.983584i 0.442244π0.442244\pi
972972 0 0
973973 − 10296.0i − 0.339234i
974974 0 0
975975 0 0
976976 0 0
977977 10834.0i 0.354770i 0.984142 + 0.177385i 0.0567638π0.0567638\pi
−0.984142 + 0.177385i 0.943236π0.943236\pi
978978 0 0
979979 −13664.0 −0.446071
980980 0 0
981981 48618.0 1.58232
982982 0 0
983983 36862.0i 1.19605i 0.801478 + 0.598024i 0.204047π0.204047\pi
−0.801478 + 0.598024i 0.795953π0.795953\pi
984984 0 0
985985 0 0
986986 0 0
987987 − 6840.00i − 0.220587i
988988 0 0
989989 −2772.00 −0.0891248
990990 0 0
991991 5380.00 0.172453 0.0862267 0.996276i 0.472519π-0.472519\pi
0.0862267 + 0.996276i 0.472519π0.472519\pi
992992 0 0
993993 − 76880.0i − 2.45691i
994994 0 0
995995 0 0
996996 0 0
997997 31266.0i 0.993184i 0.867984 + 0.496592i 0.165415π0.165415\pi
−0.867984 + 0.496592i 0.834585π0.834585\pi
998998 0 0
999999 −92920.0 −2.94280
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 200.4.c.a.49.1 2
3.2 odd 2 1800.4.f.n.649.1 2
4.3 odd 2 400.4.c.a.49.2 2
5.2 odd 4 200.4.a.a.1.1 1
5.3 odd 4 40.4.a.c.1.1 1
5.4 even 2 inner 200.4.c.a.49.2 2
15.2 even 4 1800.4.a.bd.1.1 1
15.8 even 4 360.4.a.i.1.1 1
15.14 odd 2 1800.4.f.n.649.2 2
20.3 even 4 80.4.a.a.1.1 1
20.7 even 4 400.4.a.u.1.1 1
20.19 odd 2 400.4.c.a.49.1 2
35.13 even 4 1960.4.a.a.1.1 1
40.3 even 4 320.4.a.n.1.1 1
40.13 odd 4 320.4.a.a.1.1 1
40.27 even 4 1600.4.a.a.1.1 1
40.37 odd 4 1600.4.a.ca.1.1 1
60.23 odd 4 720.4.a.ba.1.1 1
80.3 even 4 1280.4.d.b.641.1 2
80.13 odd 4 1280.4.d.o.641.2 2
80.43 even 4 1280.4.d.b.641.2 2
80.53 odd 4 1280.4.d.o.641.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.4.a.c.1.1 1 5.3 odd 4
80.4.a.a.1.1 1 20.3 even 4
200.4.a.a.1.1 1 5.2 odd 4
200.4.c.a.49.1 2 1.1 even 1 trivial
200.4.c.a.49.2 2 5.4 even 2 inner
320.4.a.a.1.1 1 40.13 odd 4
320.4.a.n.1.1 1 40.3 even 4
360.4.a.i.1.1 1 15.8 even 4
400.4.a.u.1.1 1 20.7 even 4
400.4.c.a.49.1 2 20.19 odd 2
400.4.c.a.49.2 2 4.3 odd 2
720.4.a.ba.1.1 1 60.23 odd 4
1280.4.d.b.641.1 2 80.3 even 4
1280.4.d.b.641.2 2 80.43 even 4
1280.4.d.o.641.1 2 80.53 odd 4
1280.4.d.o.641.2 2 80.13 odd 4
1600.4.a.a.1.1 1 40.27 even 4
1600.4.a.ca.1.1 1 40.37 odd 4
1800.4.a.bd.1.1 1 15.2 even 4
1800.4.f.n.649.1 2 3.2 odd 2
1800.4.f.n.649.2 2 15.14 odd 2
1960.4.a.a.1.1 1 35.13 even 4