Properties

Label 240.4.f.g.49.3
Level 240240
Weight 44
Character 240.49
Analytic conductor 14.16014.160
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [240,4,Mod(49,240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(240, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("240.49");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 240=2435 240 = 2^{4} \cdot 3 \cdot 5
Weight: k k == 4 4
Character orbit: [χ][\chi] == 240.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: 14.160458401414.1604584014
Analytic rank: 00
Dimension: 44
Coefficient field: Q(i,129)\Q(i, \sqrt{129})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+65x2+1024 x^{4} + 65x^{2} + 1024 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 49.3
Root 6.17891i-6.17891i of defining polynomial
Character χ\chi == 240.49
Dual form 240.4.f.g.49.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+3.00000iq3+(0.178908+11.1789i)q5+35.0735iq79.00000q925.6422q1137.6422iq13+(33.53670.536725i)q1595.7891iq17+50.8625q19105.220q21+110.863iq23+(124.9364.00000i)q2527.0000iq27+54.5047q29198.441q3176.9265iq33+(392.0836.27493i)q35+266.945iq37+112.927q39+103.853q41+108.000iq43+(1.61018100.610i)q45597.009iq47887.147q49+287.367q51+305.642iq53+(4.58760286.652i)q55+152.588iq57223.533q59+485.450q61315.661iq63+(420.799+6.73450i)q65+876.166iq67332.588q69585.597q71+1137.60iq73+(12.0000374.808i)q75899.360iq77+685.009q79+81.0000q81+305.725iq83+(1070.82+17.1375i)q85+163.514iq87887.175q89+1320.24q91595.322iq93+(9.09973+568.588i)q95556.550iq97+230.780q99+O(q100)q+3.00000i q^{3} +(-0.178908 + 11.1789i) q^{5} +35.0735i q^{7} -9.00000 q^{9} -25.6422 q^{11} -37.6422i q^{13} +(-33.5367 - 0.536725i) q^{15} -95.7891i q^{17} +50.8625 q^{19} -105.220 q^{21} +110.863i q^{23} +(-124.936 - 4.00000i) q^{25} -27.0000i q^{27} +54.5047 q^{29} -198.441 q^{31} -76.9265i q^{33} +(-392.083 - 6.27493i) q^{35} +266.945i q^{37} +112.927 q^{39} +103.853 q^{41} +108.000i q^{43} +(1.61018 - 100.610i) q^{45} -597.009i q^{47} -887.147 q^{49} +287.367 q^{51} +305.642i q^{53} +(4.58760 - 286.652i) q^{55} +152.588i q^{57} -223.533 q^{59} +485.450 q^{61} -315.661i q^{63} +(420.799 + 6.73450i) q^{65} +876.166i q^{67} -332.588 q^{69} -585.597 q^{71} +1137.60i q^{73} +(12.0000 - 374.808i) q^{75} -899.360i q^{77} +685.009 q^{79} +81.0000 q^{81} +305.725i q^{83} +(1070.82 + 17.1375i) q^{85} +163.514i q^{87} -887.175 q^{89} +1320.24 q^{91} -595.322i q^{93} +(-9.09973 + 568.588i) q^{95} -556.550i q^{97} +230.780 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+22q536q9148q1166q15160q1912q21100q29+24q31796q35+588q39+688q41198q453276q49+468q511072q55+1332q59++1332q99+O(q100) 4 q + 22 q^{5} - 36 q^{9} - 148 q^{11} - 66 q^{15} - 160 q^{19} - 12 q^{21} - 100 q^{29} + 24 q^{31} - 796 q^{35} + 588 q^{39} + 688 q^{41} - 198 q^{45} - 3276 q^{49} + 468 q^{51} - 1072 q^{55} + 1332 q^{59}+ \cdots + 1332 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/240Z)×\left(\mathbb{Z}/240\mathbb{Z}\right)^\times.

nn 3131 9797 161161 181181
χ(n)\chi(n) 11 1-1 11 11

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 3.00000i 0.577350i
44 0 0
55 −0.178908 + 11.1789i −0.0160020 + 0.999872i
66 0 0
77 35.0735i 1.89379i 0.321545 + 0.946894i 0.395798π0.395798\pi
−0.321545 + 0.946894i 0.604202π0.604202\pi
88 0 0
99 −9.00000 −0.333333
1010 0 0
1111 −25.6422 −0.702855 −0.351428 0.936215i 0.614304π-0.614304\pi
−0.351428 + 0.936215i 0.614304π0.614304\pi
1212 0 0
1313 37.6422i 0.803082i −0.915841 0.401541i 0.868475π-0.868475\pi
0.915841 0.401541i 0.131525π-0.131525\pi
1414 0 0
1515 −33.5367 0.536725i −0.577276 0.00923879i
1616 0 0
1717 95.7891i 1.36660i −0.730136 0.683302i 0.760543π-0.760543\pi
0.730136 0.683302i 0.239457π-0.239457\pi
1818 0 0
1919 50.8625 0.614140 0.307070 0.951687i 0.400651π-0.400651\pi
0.307070 + 0.951687i 0.400651π0.400651\pi
2020 0 0
2121 −105.220 −1.09338
2222 0 0
2323 110.863i 1.00506i 0.864559 + 0.502531i 0.167598π0.167598\pi
−0.864559 + 0.502531i 0.832402π0.832402\pi
2424 0 0
2525 −124.936 4.00000i −0.999488 0.0320000i
2626 0 0
2727 27.0000i 0.192450i
2828 0 0
2929 54.5047 0.349009 0.174505 0.984656i 0.444168π-0.444168\pi
0.174505 + 0.984656i 0.444168π0.444168\pi
3030 0 0
3131 −198.441 −1.14971 −0.574855 0.818255i 0.694941π-0.694941\pi
−0.574855 + 0.818255i 0.694941π0.694941\pi
3232 0 0
3333 76.9265i 0.405794i
3434 0 0
3535 −392.083 6.27493i −1.89355 0.0303045i
3636 0 0
3737 266.945i 1.18610i 0.805167 + 0.593048i 0.202076π0.202076\pi
−0.805167 + 0.593048i 0.797924π0.797924\pi
3838 0 0
3939 112.927 0.463659
4040 0 0
4141 103.853 0.395589 0.197794 0.980244i 0.436622π-0.436622\pi
0.197794 + 0.980244i 0.436622π0.436622\pi
4242 0 0
4343 108.000i 0.383020i 0.981491 + 0.191510i 0.0613384π0.0613384\pi
−0.981491 + 0.191510i 0.938662π0.938662\pi
4444 0 0
4545 1.61018 100.610i 0.00533402 0.333291i
4646 0 0
4747 597.009i 1.85283i −0.376510 0.926413i 0.622876π-0.622876\pi
0.376510 0.926413i 0.377124π-0.377124\pi
4848 0 0
4949 −887.147 −2.58643
5050 0 0
5151 287.367 0.789009
5252 0 0
5353 305.642i 0.792136i 0.918221 + 0.396068i 0.129625π0.129625\pi
−0.918221 + 0.396068i 0.870375π0.870375\pi
5454 0 0
5555 4.58760 286.652i 0.0112471 0.702765i
5656 0 0
5757 152.588i 0.354574i
5858 0 0
5959 −223.533 −0.493246 −0.246623 0.969111i 0.579321π-0.579321\pi
−0.246623 + 0.969111i 0.579321π0.579321\pi
6060 0 0
6161 485.450 1.01894 0.509471 0.860488i 0.329841π-0.329841\pi
0.509471 + 0.860488i 0.329841π0.329841\pi
6262 0 0
6363 315.661i 0.631263i
6464 0 0
6565 420.799 + 6.73450i 0.802979 + 0.0128510i
6666 0 0
6767 876.166i 1.59762i 0.601582 + 0.798811i 0.294537π0.294537\pi
−0.601582 + 0.798811i 0.705463π0.705463\pi
6868 0 0
6969 −332.588 −0.580273
7070 0 0
7171 −585.597 −0.978839 −0.489420 0.872048i 0.662791π-0.662791\pi
−0.489420 + 0.872048i 0.662791π0.662791\pi
7272 0 0
7373 1137.60i 1.82391i 0.410287 + 0.911957i 0.365429π0.365429\pi
−0.410287 + 0.911957i 0.634571π0.634571\pi
7474 0 0
7575 12.0000 374.808i 0.0184752 0.577055i
7676 0 0
7777 899.360i 1.33106i
7878 0 0
7979 685.009 0.975564 0.487782 0.872965i 0.337806π-0.337806\pi
0.487782 + 0.872965i 0.337806π0.337806\pi
8080 0 0
8181 81.0000 0.111111
8282 0 0
8383 305.725i 0.404309i 0.979354 + 0.202155i 0.0647944π0.0647944\pi
−0.979354 + 0.202155i 0.935206π0.935206\pi
8484 0 0
8585 1070.82 + 17.1375i 1.36643 + 0.0218685i
8686 0 0
8787 163.514i 0.201501i
8888 0 0
8989 −887.175 −1.05663 −0.528317 0.849047i 0.677177π-0.677177\pi
−0.528317 + 0.849047i 0.677177π0.677177\pi
9090 0 0
9191 1320.24 1.52087
9292 0 0
9393 595.322i 0.663785i
9494 0 0
9595 −9.09973 + 568.588i −0.00982750 + 0.614062i
9696 0 0
9797 556.550i 0.582568i −0.956637 0.291284i 0.905918π-0.905918\pi
0.956637 0.291284i 0.0940824π-0.0940824\pi
9898 0 0
9999 230.780 0.234285
100100 0 0
101101 1591.09 1.56752 0.783760 0.621063i 0.213299π-0.213299\pi
0.783760 + 0.621063i 0.213299π0.213299\pi
102102 0 0
103103 1350.95i 1.29236i 0.763187 + 0.646178i 0.223634π0.223634\pi
−0.763187 + 0.646178i 0.776366π0.776366\pi
104104 0 0
105105 18.8248 1176.25i 0.0174963 1.09324i
106106 0 0
107107 1333.51i 1.20481i −0.798190 0.602406i 0.794209π-0.794209\pi
0.798190 0.602406i 0.205791π-0.205791\pi
108108 0 0
109109 609.910 0.535952 0.267976 0.963426i 0.413645π-0.413645\pi
0.267976 + 0.963426i 0.413645π0.413645\pi
110110 0 0
111111 −800.836 −0.684793
112112 0 0
113113 241.808i 0.201304i −0.994922 0.100652i 0.967907π-0.967907\pi
0.994922 0.100652i 0.0320929π-0.0320929\pi
114114 0 0
115115 −1239.32 19.8342i −1.00493 0.0160831i
116116 0 0
117117 338.780i 0.267694i
118118 0 0
119119 3359.65 2.58806
120120 0 0
121121 −673.478 −0.505994
122122 0 0
123123 311.559i 0.228393i
124124 0 0
125125 67.0677 1395.93i 0.0479898 0.998848i
126126 0 0
127127 1045.94i 0.730802i 0.930850 + 0.365401i 0.119068π0.119068\pi
−0.930850 + 0.365401i 0.880932π0.880932\pi
128128 0 0
129129 −324.000 −0.221137
130130 0 0
131131 886.524 0.591267 0.295633 0.955301i 0.404469π-0.404469\pi
0.295633 + 0.955301i 0.404469π0.404469\pi
132132 0 0
133133 1783.92i 1.16305i
134134 0 0
135135 301.831 + 4.83053i 0.192425 + 0.00307960i
136136 0 0
137137 160.723i 0.100230i −0.998743 0.0501150i 0.984041π-0.984041\pi
0.998743 0.0501150i 0.0159588π-0.0159588\pi
138138 0 0
139139 −57.2655 −0.0349439 −0.0174719 0.999847i 0.505562π-0.505562\pi
−0.0174719 + 0.999847i 0.505562π0.505562\pi
140140 0 0
141141 1791.03 1.06973
142142 0 0
143143 965.228i 0.564450i
144144 0 0
145145 −9.75135 + 609.303i −0.00558487 + 0.348965i
146146 0 0
147147 2661.44i 1.49328i
148148 0 0
149149 1105.15 0.607633 0.303817 0.952731i 0.401739π-0.401739\pi
0.303817 + 0.952731i 0.401739π0.401739\pi
150150 0 0
151151 −2289.63 −1.23396 −0.616980 0.786979i 0.711644π-0.711644\pi
−0.616980 + 0.786979i 0.711644π0.711644\pi
152152 0 0
153153 862.102i 0.455535i
154154 0 0
155155 35.5027 2218.35i 0.0183977 1.14956i
156156 0 0
157157 161.514i 0.0821034i −0.999157 0.0410517i 0.986929π-0.986929\pi
0.999157 0.0410517i 0.0130708π-0.0130708\pi
158158 0 0
159159 −916.927 −0.457340
160160 0 0
161161 −3888.33 −1.90338
162162 0 0
163163 1594.15i 0.766032i 0.923742 + 0.383016i 0.125115π0.125115\pi
−0.923742 + 0.383016i 0.874885π0.874885\pi
164164 0 0
165165 859.955 + 13.7628i 0.405742 + 0.00649353i
166166 0 0
167167 1017.39i 0.471427i −0.971823 0.235713i 0.924257π-0.924257\pi
0.971823 0.235713i 0.0757427π-0.0757427\pi
168168 0 0
169169 780.066 0.355060
170170 0 0
171171 −457.763 −0.204713
172172 0 0
173173 2444.49i 1.07428i 0.843492 + 0.537142i 0.180496π0.180496\pi
−0.843492 + 0.537142i 0.819504π0.819504\pi
174174 0 0
175175 140.294 4381.94i 0.0606012 1.89282i
176176 0 0
177177 670.599i 0.284776i
178178 0 0
179179 222.780 0.0930242 0.0465121 0.998918i 0.485189π-0.485189\pi
0.0465121 + 0.998918i 0.485189π0.485189\pi
180180 0 0
181181 −100.034 −0.0410798 −0.0205399 0.999789i 0.506539π-0.506539\pi
−0.0205399 + 0.999789i 0.506539π0.506539\pi
182182 0 0
183183 1456.35i 0.588287i
184184 0 0
185185 −2984.16 47.7588i −1.18594 0.0189800i
186186 0 0
187187 2456.24i 0.960525i
188188 0 0
189189 946.983 0.364460
190190 0 0
191191 −702.403 −0.266095 −0.133047 0.991110i 0.542476π-0.542476\pi
−0.133047 + 0.991110i 0.542476π0.542476\pi
192192 0 0
193193 4126.63i 1.53907i 0.638602 + 0.769537i 0.279513π0.279513\pi
−0.638602 + 0.769537i 0.720487π0.720487\pi
194194 0 0
195195 −20.2035 + 1262.40i −0.00741950 + 0.463600i
196196 0 0
197197 3104.45i 1.12276i 0.827559 + 0.561378i 0.189729π0.189729\pi
−0.827559 + 0.561378i 0.810271π0.810271\pi
198198 0 0
199199 −367.616 −0.130953 −0.0654764 0.997854i 0.520857π-0.520857\pi
−0.0654764 + 0.997854i 0.520857π0.520857\pi
200200 0 0
201201 −2628.50 −0.922388
202202 0 0
203203 1911.67i 0.660950i
204204 0 0
205205 −18.5802 + 1160.96i −0.00633023 + 0.395538i
206206 0 0
207207 997.763i 0.335021i
208208 0 0
209209 −1304.23 −0.431652
210210 0 0
211211 −2594.85 −0.846619 −0.423310 0.905985i 0.639132π-0.639132\pi
−0.423310 + 0.905985i 0.639132π0.639132\pi
212212 0 0
213213 1756.79i 0.565133i
214214 0 0
215215 −1207.32 19.3221i −0.382971 0.00612910i
216216 0 0
217217 6960.00i 2.17731i
218218 0 0
219219 −3412.79 −1.05304
220220 0 0
221221 −3605.71 −1.09749
222222 0 0
223223 1834.41i 0.550857i −0.961321 0.275429i 0.911180π-0.911180\pi
0.961321 0.275429i 0.0888198π-0.0888198\pi
224224 0 0
225225 1124.42 + 36.0000i 0.333163 + 0.0106667i
226226 0 0
227227 175.811i 0.0514053i −0.999670 0.0257027i 0.991818π-0.991818\pi
0.999670 0.0257027i 0.00818231π-0.00818231\pi
228228 0 0
229229 −1622.35 −0.468158 −0.234079 0.972218i 0.575207π-0.575207\pi
−0.234079 + 0.972218i 0.575207π0.575207\pi
230230 0 0
231231 2698.08 0.768487
232232 0 0
233233 3965.65i 1.11501i −0.830172 0.557507i 0.811758π-0.811758\pi
0.830172 0.557507i 0.188242π-0.188242\pi
234234 0 0
235235 6673.91 + 106.810i 1.85259 + 0.0296490i
236236 0 0
237237 2055.03i 0.563242i
238238 0 0
239239 −6323.25 −1.71137 −0.855685 0.517497i 0.826864π-0.826864\pi
−0.855685 + 0.517497i 0.826864π0.826864\pi
240240 0 0
241241 3407.51 0.910775 0.455388 0.890293i 0.349501π-0.349501\pi
0.455388 + 0.890293i 0.349501π0.349501\pi
242242 0 0
243243 243.000i 0.0641500i
244244 0 0
245245 158.718 9917.33i 0.0413882 2.58610i
246246 0 0
247247 1914.58i 0.493205i
248248 0 0
249249 −917.175 −0.233428
250250 0 0
251251 −1345.81 −0.338433 −0.169216 0.985579i 0.554124π-0.554124\pi
−0.169216 + 0.985579i 0.554124π0.554124\pi
252252 0 0
253253 2842.76i 0.706414i
254254 0 0
255255 −51.4124 + 3212.45i −0.0126258 + 0.788908i
256256 0 0
257257 4697.19i 1.14009i 0.821614 + 0.570044i 0.193074π0.193074\pi
−0.821614 + 0.570044i 0.806926π0.806926\pi
258258 0 0
259259 −9362.70 −2.24621
260260 0 0
261261 −490.542 −0.116336
262262 0 0
263263 4700.66i 1.10211i 0.834468 + 0.551056i 0.185775π0.185775\pi
−0.834468 + 0.551056i 0.814225π0.814225\pi
264264 0 0
265265 −3416.75 54.6819i −0.792034 0.0126758i
266266 0 0
267267 2661.53i 0.610048i
268268 0 0
269269 7962.67 1.80481 0.902403 0.430894i 0.141802π-0.141802\pi
0.902403 + 0.430894i 0.141802π0.141802\pi
270270 0 0
271271 6122.73 1.37243 0.686217 0.727397i 0.259270π-0.259270\pi
0.686217 + 0.727397i 0.259270π0.259270\pi
272272 0 0
273273 3960.72i 0.878073i
274274 0 0
275275 3203.63 + 102.569i 0.702495 + 0.0224914i
276276 0 0
277277 8417.57i 1.82586i −0.408117 0.912930i 0.633814π-0.633814\pi
0.408117 0.912930i 0.366186π-0.366186\pi
278278 0 0
279279 1785.97 0.383237
280280 0 0
281281 3030.99 0.643466 0.321733 0.946830i 0.395735π-0.395735\pi
0.321733 + 0.946830i 0.395735π0.395735\pi
282282 0 0
283283 2890.81i 0.607211i 0.952798 + 0.303606i 0.0981905π0.0981905\pi
−0.952798 + 0.303606i 0.901809π0.901809\pi
284284 0 0
285285 −1705.76 27.2992i −0.354529 0.00567391i
286286 0 0
287287 3642.49i 0.749161i
288288 0 0
289289 −4262.55 −0.867606
290290 0 0
291291 1669.65 0.336346
292292 0 0
293293 8966.75i 1.78786i 0.448206 + 0.893930i 0.352063π0.352063\pi
−0.448206 + 0.893930i 0.647937π0.647937\pi
294294 0 0
295295 39.9919 2498.86i 0.00789295 0.493183i
296296 0 0
297297 692.339i 0.135265i
298298 0 0
299299 4173.11 0.807147
300300 0 0
301301 −3787.93 −0.725358
302302 0 0
303303 4773.28i 0.905009i
304304 0 0
305305 −86.8511 + 5426.80i −0.0163052 + 1.01881i
306306 0 0
307307 3298.42i 0.613194i 0.951839 + 0.306597i 0.0991904π0.0991904\pi
−0.951839 + 0.306597i 0.900810π0.900810\pi
308308 0 0
309309 −4052.84 −0.746142
310310 0 0
311311 3394.92 0.618998 0.309499 0.950900i 0.399839π-0.399839\pi
0.309499 + 0.950900i 0.399839π0.399839\pi
312312 0 0
313313 5946.95i 1.07393i 0.843603 + 0.536967i 0.180430π0.180430\pi
−0.843603 + 0.536967i 0.819570π0.819570\pi
314314 0 0
315315 3528.75 + 56.4744i 0.631182 + 0.0101015i
316316 0 0
317317 2520.83i 0.446637i 0.974746 + 0.223318i 0.0716889π0.0716889\pi
−0.974746 + 0.223318i 0.928311π0.928311\pi
318318 0 0
319319 −1397.62 −0.245303
320320 0 0
321321 4000.52 0.695599
322322 0 0
323323 4872.08i 0.839286i
324324 0 0
325325 −150.569 + 4702.86i −0.0256986 + 0.802671i
326326 0 0
327327 1829.73i 0.309432i
328328 0 0
329329 20939.2 3.50886
330330 0 0
331331 4586.86 0.761682 0.380841 0.924641i 0.375635π-0.375635\pi
0.380841 + 0.924641i 0.375635π0.375635\pi
332332 0 0
333333 2402.51i 0.395365i
334334 0 0
335335 −9794.58 156.753i −1.59742 0.0255652i
336336 0 0
337337 8582.12i 1.38723i −0.720344 0.693617i 0.756016π-0.756016\pi
0.720344 0.693617i 0.243984π-0.243984\pi
338338 0 0
339339 725.424 0.116223
340340 0 0
341341 5088.45 0.808080
342342 0 0
343343 19085.1i 3.00437i
344344 0 0
345345 59.5027 3717.97i 0.00928556 0.580199i
346346 0 0
347347 2539.38i 0.392857i −0.980518 0.196428i 0.937066π-0.937066\pi
0.980518 0.196428i 0.0629343π-0.0629343\pi
348348 0 0
349349 9002.82 1.38083 0.690415 0.723413i 0.257428π-0.257428\pi
0.690415 + 0.723413i 0.257428π0.257428\pi
350350 0 0
351351 −1016.34 −0.154553
352352 0 0
353353 3928.08i 0.592267i −0.955146 0.296134i 0.904303π-0.904303\pi
0.955146 0.296134i 0.0956974π-0.0956974\pi
354354 0 0
355355 104.768 6546.34i 0.0156634 0.978714i
356356 0 0
357357 10079.0i 1.49422i
358358 0 0
359359 10001.7 1.47039 0.735197 0.677854i 0.237090π-0.237090\pi
0.735197 + 0.677854i 0.237090π0.237090\pi
360360 0 0
361361 −4272.00 −0.622832
362362 0 0
363363 2020.44i 0.292136i
364364 0 0
365365 −12717.1 203.526i −1.82368 0.0291863i
366366 0 0
367367 5967.79i 0.848818i −0.905471 0.424409i 0.860482π-0.860482\pi
0.905471 0.424409i 0.139518π-0.139518\pi
368368 0 0
369369 −934.678 −0.131863
370370 0 0
371371 −10719.9 −1.50014
372372 0 0
373373 6931.55i 0.962204i −0.876665 0.481102i 0.840237π-0.840237\pi
0.876665 0.481102i 0.159763π-0.159763\pi
374374 0 0
375375 4187.80 + 201.203i 0.576685 + 0.0277069i
376376 0 0
377377 2051.68i 0.280283i
378378 0 0
379379 9711.70 1.31624 0.658122 0.752911i 0.271351π-0.271351\pi
0.658122 + 0.752911i 0.271351π0.271351\pi
380380 0 0
381381 −3137.81 −0.421929
382382 0 0
383383 5664.84i 0.755769i 0.925853 + 0.377885i 0.123348π0.123348\pi
−0.925853 + 0.377885i 0.876652π0.876652\pi
384384 0 0
385385 10053.9 + 160.903i 1.33089 + 0.0212997i
386386 0 0
387387 972.000i 0.127673i
388388 0 0
389389 −8918.17 −1.16239 −0.581195 0.813765i 0.697414π-0.697414\pi
−0.581195 + 0.813765i 0.697414π0.697414\pi
390390 0 0
391391 10619.4 1.37352
392392 0 0
393393 2659.57i 0.341368i
394394 0 0
395395 −122.554 + 7657.66i −0.0156110 + 0.975439i
396396 0 0
397397 12849.9i 1.62448i 0.583321 + 0.812242i 0.301753π0.301753\pi
−0.583321 + 0.812242i 0.698247π0.698247\pi
398398 0 0
399399 −5351.77 −0.671488
400400 0 0
401401 3563.08 0.443721 0.221860 0.975078i 0.428787π-0.428787\pi
0.221860 + 0.975078i 0.428787π0.428787\pi
402402 0 0
403403 7469.74i 0.923311i
404404 0 0
405405 −14.4916 + 905.492i −0.00177801 + 0.111097i
406406 0 0
407407 6845.06i 0.833654i
408408 0 0
409409 2026.69 0.245020 0.122510 0.992467i 0.460906π-0.460906\pi
0.122510 + 0.992467i 0.460906π0.460906\pi
410410 0 0
411411 482.169 0.0578678
412412 0 0
413413 7840.07i 0.934104i
414414 0 0
415415 −3417.67 54.6968i −0.404258 0.00646978i
416416 0 0
417417 171.796i 0.0201748i
418418 0 0
419419 −1670.39 −0.194759 −0.0973793 0.995247i 0.531046π-0.531046\pi
−0.0973793 + 0.995247i 0.531046π0.531046\pi
420420 0 0
421421 6079.66 0.703812 0.351906 0.936035i 0.385534π-0.385534\pi
0.351906 + 0.936035i 0.385534π0.385534\pi
422422 0 0
423423 5373.08i 0.617608i
424424 0 0
425425 −383.156 + 11967.5i −0.0437313 + 1.36590i
426426 0 0
427427 17026.4i 1.92966i
428428 0 0
429429 −2895.68 −0.325886
430430 0 0
431431 −1719.37 −0.192155 −0.0960777 0.995374i 0.530630π-0.530630\pi
−0.0960777 + 0.995374i 0.530630π0.530630\pi
432432 0 0
433433 12024.9i 1.33459i −0.744792 0.667296i 0.767451π-0.767451\pi
0.744792 0.667296i 0.232549π-0.232549\pi
434434 0 0
435435 −1827.91 29.2540i −0.201475 0.00322442i
436436 0 0
437437 5638.75i 0.617249i
438438 0 0
439439 −7542.97 −0.820060 −0.410030 0.912072i 0.634482π-0.634482\pi
−0.410030 + 0.912072i 0.634482π0.634482\pi
440440 0 0
441441 7984.32 0.862145
442442 0 0
443443 4578.13i 0.491001i −0.969396 0.245501i 0.921048π-0.921048\pi
0.969396 0.245501i 0.0789524π-0.0789524\pi
444444 0 0
445445 158.723 9917.65i 0.0169083 1.05650i
446446 0 0
447447 3315.45i 0.350817i
448448 0 0
449449 −6875.21 −0.722630 −0.361315 0.932444i 0.617672π-0.617672\pi
−0.361315 + 0.932444i 0.617672π0.617672\pi
450450 0 0
451451 −2663.02 −0.278042
452452 0 0
453453 6868.90i 0.712427i
454454 0 0
455455 −236.202 + 14758.9i −0.0243370 + 1.52067i
456456 0 0
457457 7351.97i 0.752540i −0.926510 0.376270i 0.877207π-0.877207\pi
0.926510 0.376270i 0.122793π-0.122793\pi
458458 0 0
459459 −2586.31 −0.263003
460460 0 0
461461 −15614.5 −1.57752 −0.788762 0.614698i 0.789278π-0.789278\pi
−0.788762 + 0.614698i 0.789278π0.789278\pi
462462 0 0
463463 1684.73i 0.169106i −0.996419 0.0845530i 0.973054π-0.973054\pi
0.996419 0.0845530i 0.0269462π-0.0269462\pi
464464 0 0
465465 6655.05 + 106.508i 0.663700 + 0.0106219i
466466 0 0
467467 10235.2i 1.01420i −0.861888 0.507099i 0.830718π-0.830718\pi
0.861888 0.507099i 0.169282π-0.169282\pi
468468 0 0
469469 −30730.2 −3.02556
470470 0 0
471471 484.542 0.0474024
472472 0 0
473473 2769.36i 0.269207i
474474 0 0
475475 −6354.56 203.450i −0.613826 0.0196525i
476476 0 0
477477 2750.78i 0.264045i
478478 0 0
479479 12247.2 1.16825 0.584123 0.811665i 0.301439π-0.301439\pi
0.584123 + 0.811665i 0.301439π0.301439\pi
480480 0 0
481481 10048.4 0.952532
482482 0 0
483483 11665.0i 1.09891i
484484 0 0
485485 6221.62 + 99.5714i 0.582493 + 0.00932228i
486486 0 0
487487 7895.91i 0.734698i 0.930083 + 0.367349i 0.119735π0.119735\pi
−0.930083 + 0.367349i 0.880265π0.880265\pi
488488 0 0
489489 −4782.44 −0.442269
490490 0 0
491491 7625.48 0.700882 0.350441 0.936585i 0.386032π-0.386032\pi
0.350441 + 0.936585i 0.386032π0.386032\pi
492492 0 0
493493 5220.96i 0.476958i
494494 0 0
495495 −41.2884 + 2579.86i −0.00374904 + 0.234255i
496496 0 0
497497 20538.9i 1.85371i
498498 0 0
499499 −8655.23 −0.776476 −0.388238 0.921559i 0.626916π-0.626916\pi
−0.388238 + 0.921559i 0.626916π0.626916\pi
500500 0 0
501501 3052.18 0.272178
502502 0 0
503503 118.441i 0.0104990i 0.999986 + 0.00524951i 0.00167098π0.00167098\pi
−0.999986 + 0.00524951i 0.998329π0.998329\pi
504504 0 0
505505 −284.660 + 17786.7i −0.0250835 + 1.56732i
506506 0 0
507507 2340.20i 0.204994i
508508 0 0
509509 −5359.43 −0.466704 −0.233352 0.972392i 0.574970π-0.574970\pi
−0.233352 + 0.972392i 0.574970π0.574970\pi
510510 0 0
511511 −39899.5 −3.45411
512512 0 0
513513 1373.29i 0.118191i
514514 0 0
515515 −15102.1 241.695i −1.29219 0.0206803i
516516 0 0
517517 15308.6i 1.30227i
518518 0 0
519519 −7333.47 −0.620238
520520 0 0
521521 −10862.4 −0.913414 −0.456707 0.889617i 0.650971π-0.650971\pi
−0.456707 + 0.889617i 0.650971π0.650971\pi
522522 0 0
523523 9553.39i 0.798740i −0.916790 0.399370i 0.869229π-0.869229\pi
0.916790 0.399370i 0.130771π-0.130771\pi
524524 0 0
525525 13145.8 + 420.881i 1.09282 + 0.0349881i
526526 0 0
527527 19008.5i 1.57120i
528528 0 0
529529 −123.501 −0.0101505
530530 0 0
531531 2011.80 0.164415
532532 0 0
533533 3909.26i 0.317690i
534534 0 0
535535 14907.1 + 238.575i 1.20466 + 0.0192795i
536536 0 0
537537 668.339i 0.0537076i
538538 0 0
539539 22748.4 1.81789
540540 0 0
541541 −6132.47 −0.487348 −0.243674 0.969857i 0.578353π-0.578353\pi
−0.243674 + 0.969857i 0.578353π0.578353\pi
542542 0 0
543543 300.101i 0.0237174i
544544 0 0
545545 −109.118 + 6818.12i −0.00857633 + 0.535883i
546546 0 0
547547 2853.85i 0.223075i 0.993760 + 0.111537i 0.0355775π0.0355775\pi
−0.993760 + 0.111537i 0.964422π0.964422\pi
548548 0 0
549549 −4369.05 −0.339648
550550 0 0
551551 2772.25 0.214341
552552 0 0
553553 24025.6i 1.84751i
554554 0 0
555555 143.276 8952.48i 0.0109581 0.684705i
556556 0 0
557557 5192.60i 0.395005i 0.980302 + 0.197502i 0.0632830π0.0632830\pi
−0.980302 + 0.197502i 0.936717π0.936717\pi
558558 0 0
559559 4065.36 0.307596
560560 0 0
561561 −7368.72 −0.554559
562562 0 0
563563 10907.2i 0.816492i −0.912872 0.408246i 0.866141π-0.866141\pi
0.912872 0.408246i 0.133859π-0.133859\pi
564564 0 0
565565 2703.15 + 43.2615i 0.201278 + 0.00322128i
566566 0 0
567567 2840.95i 0.210421i
568568 0 0
569569 155.257 0.0114389 0.00571945 0.999984i 0.498179π-0.498179\pi
0.00571945 + 0.999984i 0.498179π0.498179\pi
570570 0 0
571571 4925.15 0.360965 0.180483 0.983578i 0.442234π-0.442234\pi
0.180483 + 0.983578i 0.442234π0.442234\pi
572572 0 0
573573 2107.21i 0.153630i
574574 0 0
575575 443.450 13850.7i 0.0321620 1.00455i
576576 0 0
577577 5292.05i 0.381822i 0.981607 + 0.190911i 0.0611441π0.0611441\pi
−0.981607 + 0.190911i 0.938856π0.938856\pi
578578 0 0
579579 −12379.9 −0.888585
580580 0 0
581581 −10722.8 −0.765677
582582 0 0
583583 7837.33i 0.556757i
584584 0 0
585585 −3787.19 60.6105i −0.267660 0.00428365i
586586 0 0
587587 19658.5i 1.38227i −0.722727 0.691134i 0.757112π-0.757112\pi
0.722727 0.691134i 0.242888π-0.242888\pi
588588 0 0
589589 −10093.2 −0.706083
590590 0 0
591591 −9313.36 −0.648224
592592 0 0
593593 6578.08i 0.455530i 0.973716 + 0.227765i 0.0731418π0.0731418\pi
−0.973716 + 0.227765i 0.926858π0.926858\pi
594594 0 0
595595 −601.070 + 37557.3i −0.0414142 + 2.58773i
596596 0 0
597597 1102.85i 0.0756056i
598598 0 0
599599 16915.9 1.15386 0.576931 0.816793i 0.304250π-0.304250\pi
0.576931 + 0.816793i 0.304250π0.304250\pi
600600 0 0
601601 19801.4 1.34395 0.671977 0.740572i 0.265445π-0.265445\pi
0.671977 + 0.740572i 0.265445π0.265445\pi
602602 0 0
603603 7885.49i 0.532541i
604604 0 0
605605 120.491 7528.75i 0.00809695 0.505930i
606606 0 0
607607 22498.4i 1.50442i −0.658926 0.752208i 0.728989π-0.728989\pi
0.658926 0.752208i 0.271011π-0.271011\pi
608608 0 0
609609 −5735.01 −0.381600
610610 0 0
611611 −22472.7 −1.48797
612612 0 0
613613 23829.3i 1.57008i −0.619446 0.785039i 0.712643π-0.712643\pi
0.619446 0.785039i 0.287357π-0.287357\pi
614614 0 0
615615 −3482.89 55.7406i −0.228364 0.00365476i
616616 0 0
617617 4277.52i 0.279103i 0.990215 + 0.139551i 0.0445660π0.0445660\pi
−0.990215 + 0.139551i 0.955434π0.955434\pi
618618 0 0
619619 4995.99 0.324404 0.162202 0.986758i 0.448140π-0.448140\pi
0.162202 + 0.986758i 0.448140π0.448140\pi
620620 0 0
621621 2993.29 0.193424
622622 0 0
623623 31116.3i 2.00104i
624624 0 0
625625 15593.0 + 999.488i 0.997952 + 0.0639672i
626626 0 0
627627 3912.68i 0.249214i
628628 0 0
629629 25570.5 1.62092
630630 0 0
631631 11328.0 0.714675 0.357337 0.933975i 0.383685π-0.383685\pi
0.357337 + 0.933975i 0.383685π0.383685\pi
632632 0 0
633633 7784.54i 0.488796i
634634 0 0
635635 −11692.4 187.127i −0.730708 0.0116943i
636636 0 0
637637 33394.1i 2.07712i
638638 0 0
639639 5270.37 0.326280
640640 0 0
641641 5955.35 0.366961 0.183481 0.983023i 0.441264π-0.441264\pi
0.183481 + 0.983023i 0.441264π0.441264\pi
642642 0 0
643643 15727.7i 0.964605i 0.876005 + 0.482302i 0.160199π0.160199\pi
−0.876005 + 0.482302i 0.839801π0.839801\pi
644644 0 0
645645 57.9663 3621.97i 0.00353864 0.221108i
646646 0 0
647647 9582.24i 0.582252i 0.956685 + 0.291126i 0.0940298π0.0940298\pi
−0.956685 + 0.291126i 0.905970π0.905970\pi
648648 0 0
649649 5731.87 0.346681
650650 0 0
651651 20880.0 1.25707
652652 0 0
653653 8313.70i 0.498224i −0.968475 0.249112i 0.919861π-0.919861\pi
0.968475 0.249112i 0.0801388π-0.0801388\pi
654654 0 0
655655 −158.606 + 9910.37i −0.00946148 + 0.591191i
656656 0 0
657657 10238.4i 0.607971i
658658 0 0
659659 15095.5 0.892317 0.446158 0.894954i 0.352792π-0.352792\pi
0.446158 + 0.894954i 0.352792π0.352792\pi
660660 0 0
661661 8266.98 0.486457 0.243229 0.969969i 0.421793π-0.421793\pi
0.243229 + 0.969969i 0.421793π0.421793\pi
662662 0 0
663663 10817.1i 0.633639i
664664 0 0
665665 −19942.3 319.159i −1.16290 0.0186112i
666666 0 0
667667 6042.53i 0.350776i
668668 0 0
669669 5503.23 0.318038
670670 0 0
671671 −12448.0 −0.716170
672672 0 0
673673 11186.7i 0.640735i −0.947293 0.320367i 0.896194π-0.896194\pi
0.947293 0.320367i 0.103806π-0.103806\pi
674674 0 0
675675 −108.000 + 3373.27i −0.00615840 + 0.192352i
676676 0 0
677677 7675.84i 0.435756i 0.975976 + 0.217878i 0.0699134π0.0699134\pi
−0.975976 + 0.217878i 0.930087π0.930087\pi
678678 0 0
679679 19520.1 1.10326
680680 0 0
681681 527.434 0.0296789
682682 0 0
683683 10550.9i 0.591099i 0.955327 + 0.295549i 0.0955027π0.0955027\pi
−0.955327 + 0.295549i 0.904497π0.904497\pi
684684 0 0
685685 1796.71 + 28.7547i 0.100217 + 0.00160388i
686686 0 0
687687 4867.06i 0.270291i
688688 0 0
689689 11505.0 0.636150
690690 0 0
691691 26950.9 1.48373 0.741867 0.670547i 0.233940π-0.233940\pi
0.741867 + 0.670547i 0.233940π0.233940\pi
692692 0 0
693693 8094.24i 0.443686i
694694 0 0
695695 10.2453 640.166i 0.000559173 0.0349394i
696696 0 0
697697 9947.99i 0.540613i
698698 0 0
699699 11897.0 0.643754
700700 0 0
701701 12791.6 0.689204 0.344602 0.938749i 0.388014π-0.388014\pi
0.344602 + 0.938749i 0.388014π0.388014\pi
702702 0 0
703703 13577.5i 0.728429i
704704 0 0
705705 −320.430 + 20021.7i −0.0171179 + 1.06959i
706706 0 0
707707 55805.1i 2.96855i
708708 0 0
709709 16238.3 0.860142 0.430071 0.902795i 0.358489π-0.358489\pi
0.430071 + 0.902795i 0.358489π0.358489\pi
710710 0 0
711711 −6165.08 −0.325188
712712 0 0
713713 21999.6i 1.15553i
714714 0 0
715715 −10790.2 172.687i −0.564378 0.00903236i
716716 0 0
717717 18969.8i 0.988060i
718718 0 0
719719 −24285.8 −1.25968 −0.629839 0.776726i 0.716879π-0.716879\pi
−0.629839 + 0.776726i 0.716879π0.716879\pi
720720 0 0
721721 −47382.3 −2.44745
722722 0 0
723723 10222.5i 0.525836i
724724 0 0
725725 −6809.60 218.019i −0.348831 0.0111683i
726726 0 0
727727 4466.82i 0.227875i −0.993488 0.113937i 0.963654π-0.963654\pi
0.993488 0.113937i 0.0363464π-0.0363464\pi
728728 0 0
729729 −729.000 −0.0370370
730730 0 0
731731 10345.2 0.523436
732732 0 0
733733 30802.1i 1.55212i 0.630661 + 0.776059i 0.282784π0.282784\pi
−0.630661 + 0.776059i 0.717216π0.717216\pi
734734 0 0
735735 29752.0 + 476.154i 1.49309 + 0.0238955i
736736 0 0
737737 22466.8i 1.12290i
738738 0 0
739739 −12920.5 −0.643151 −0.321576 0.946884i 0.604212π-0.604212\pi
−0.321576 + 0.946884i 0.604212π0.604212\pi
740740 0 0
741741 5743.73 0.284752
742742 0 0
743743 2571.29i 0.126960i 0.997983 + 0.0634802i 0.0202200π0.0202200\pi
−0.997983 + 0.0634802i 0.979780π0.979780\pi
744744 0 0
745745 −197.720 + 12354.4i −0.00972337 + 0.607555i
746746 0 0
747747 2751.53i 0.134770i
748748 0 0
749749 46770.7 2.28166
750750 0 0
751751 13427.4 0.652426 0.326213 0.945296i 0.394227π-0.394227\pi
0.326213 + 0.945296i 0.394227π0.394227\pi
752752 0 0
753753 4037.42i 0.195394i
754754 0 0
755755 409.635 25595.6i 0.0197459 1.23380i
756756 0 0
757757 7103.66i 0.341066i 0.985352 + 0.170533i 0.0545489π0.0545489\pi
−0.985352 + 0.170533i 0.945451π0.945451\pi
758758 0 0
759759 8528.27 0.407848
760760 0 0
761761 19205.2 0.914831 0.457416 0.889253i 0.348775π-0.348775\pi
0.457416 + 0.889253i 0.348775π0.348775\pi
762762 0 0
763763 21391.6i 1.01498i
764764 0 0
765765 −9637.36 154.237i −0.455476 0.00728949i
766766 0 0
767767 8414.27i 0.396117i
768768 0 0
769769 −19508.1 −0.914799 −0.457399 0.889261i 0.651219π-0.651219\pi
−0.457399 + 0.889261i 0.651219π0.651219\pi
770770 0 0
771771 −14091.6 −0.658230
772772 0 0
773773 38852.5i 1.80780i −0.427746 0.903899i 0.640692π-0.640692\pi
0.427746 0.903899i 0.359308π-0.359308\pi
774774 0 0
775775 24792.4 + 793.763i 1.14912 + 0.0367907i
776776 0 0
777777 28088.1i 1.29685i
778778 0 0
779779 5282.23 0.242947
780780 0 0
781781 15016.0 0.687982
782782 0 0
783783 1471.63i 0.0671669i
784784 0 0
785785 1805.55 + 28.8962i 0.0820929 + 0.00131382i
786786 0 0
787787 24851.1i 1.12560i −0.826594 0.562799i 0.809725π-0.809725\pi
0.826594 0.562799i 0.190275π-0.190275\pi
788788 0 0
789789 −14102.0 −0.636304
790790 0 0
791791 8481.04 0.381228
792792 0 0
793793 18273.4i 0.818295i
794794 0 0
795795 164.046 10250.2i 0.00731837 0.457281i
796796 0 0
797797 33040.1i 1.46843i 0.678916 + 0.734216i 0.262450π0.262450\pi
−0.678916 + 0.734216i 0.737550π0.737550\pi
798798 0 0
799799 −57187.0 −2.53208
800800 0 0
801801 7984.58 0.352211
802802 0 0
803803 29170.5i 1.28195i
804804 0 0
805805 695.655 43467.3i 0.0304579 1.90313i
806806 0 0
807807 23888.0i 1.04200i
808808 0 0
809809 −10756.6 −0.467467 −0.233734 0.972301i 0.575094π-0.575094\pi
−0.233734 + 0.972301i 0.575094π0.575094\pi
810810 0 0
811811 5985.48 0.259160 0.129580 0.991569i 0.458637π-0.458637\pi
0.129580 + 0.991569i 0.458637π0.458637\pi
812812 0 0
813813 18368.2i 0.792375i
814814 0 0
815815 −17820.8 285.206i −0.765934 0.0122581i
816816 0 0
817817 5493.15i 0.235228i
818818 0 0
819819 −11882.2 −0.506956
820820 0 0
821821 16426.4 0.698276 0.349138 0.937071i 0.386474π-0.386474\pi
0.349138 + 0.937071i 0.386474π0.386474\pi
822822 0 0
823823 27124.3i 1.14884i 0.818561 + 0.574419i 0.194772π0.194772\pi
−0.818561 + 0.574419i 0.805228π0.805228\pi
824824 0 0
825825 −307.706 + 9610.89i −0.0129854 + 0.405586i
826826 0 0
827827 32759.9i 1.37748i −0.725011 0.688738i 0.758165π-0.758165\pi
0.725011 0.688738i 0.241835π-0.241835\pi
828828 0 0
829829 18211.8 0.762995 0.381498 0.924370i 0.375408π-0.375408\pi
0.381498 + 0.924370i 0.375408π0.375408\pi
830830 0 0
831831 25252.7 1.05416
832832 0 0
833833 84979.0i 3.53463i
834834 0 0
835835 11373.3 + 182.020i 0.471366 + 0.00754379i
836836 0 0
837837 5357.90i 0.221262i
838838 0 0
839839 −37500.6 −1.54310 −0.771552 0.636166i 0.780519π-0.780519\pi
−0.771552 + 0.636166i 0.780519π0.780519\pi
840840 0 0
841841 −21418.2 −0.878192
842842 0 0
843843 9092.98i 0.371505i
844844 0 0
845845 −139.560 + 8720.29i −0.00568168 + 0.355014i
846846 0 0
847847 23621.2i 0.958246i
848848 0 0
849849 −8672.43 −0.350574
850850 0 0
851851 −29594.2 −1.19210
852852 0 0
853853 2421.81i 0.0972112i 0.998818 + 0.0486056i 0.0154777π0.0154777\pi
−0.998818 + 0.0486056i 0.984522π0.984522\pi
854854 0 0
855855 81.8976 5117.29i 0.00327583 0.204687i
856856 0 0
857857 37700.0i 1.50269i −0.659908 0.751346i 0.729405π-0.729405\pi
0.659908 0.751346i 0.270595π-0.270595\pi
858858 0 0
859859 −14709.0 −0.584242 −0.292121 0.956381i 0.594361π-0.594361\pi
−0.292121 + 0.956381i 0.594361π0.594361\pi
860860 0 0
861861 −10927.5 −0.432528
862862 0 0
863863 28950.4i 1.14193i 0.820975 + 0.570963i 0.193430π0.193430\pi
−0.820975 + 0.570963i 0.806570π0.806570\pi
864864 0 0
865865 −27326.7 437.340i −1.07415 0.0171907i
866866 0 0
867867 12787.6i 0.500913i
868868 0 0
869869 −17565.1 −0.685681
870870 0 0
871871 32980.8 1.28302
872872 0 0
873873 5008.95i 0.194189i
874874 0 0
875875 48960.2 + 2352.30i 1.89161 + 0.0908824i
876876 0 0
877877 17501.3i 0.673860i 0.941530 + 0.336930i 0.109389π0.109389\pi
−0.941530 + 0.336930i 0.890611π0.890611\pi
878878 0 0
879879 −26900.2 −1.03222
880880 0 0
881881 −45136.0 −1.72607 −0.863037 0.505140i 0.831441π-0.831441\pi
−0.863037 + 0.505140i 0.831441π0.831441\pi
882882 0 0
883883 51564.8i 1.96522i −0.185673 0.982612i 0.559446π-0.559446\pi
0.185673 0.982612i 0.440554π-0.440554\pi
884884 0 0
885885 7496.57 + 119.976i 0.284739 + 0.00455700i
886886 0 0
887887 19226.4i 0.727800i −0.931438 0.363900i 0.881445π-0.881445\pi
0.931438 0.363900i 0.118555π-0.118555\pi
888888 0 0
889889 −36684.6 −1.38398
890890 0 0
891891 −2077.02 −0.0780950
892892 0 0
893893 30365.4i 1.13789i
894894 0 0
895895 −39.8571 + 2490.43i −0.00148858 + 0.0930123i
896896 0 0
897897 12519.3i 0.466007i
898898 0 0
899899 −10816.0 −0.401259
900900 0 0
901901 29277.2 1.08254
902902 0 0
903903 11363.8i 0.418786i
904904 0 0
905905 17.8969 1118.27i 0.000657361 0.0410746i
906906 0 0
907907 32050.1i 1.17333i −0.809831 0.586663i 0.800441π-0.800441\pi
0.809831 0.586663i 0.199559π-0.199559\pi
908908 0 0
909909 −14319.8 −0.522507
910910 0 0
911911 29674.6 1.07921 0.539606 0.841918i 0.318573π-0.318573\pi
0.539606 + 0.841918i 0.318573π0.318573\pi
912912 0 0
913913 7839.46i 0.284171i
914914 0 0
915915 −16280.4 260.553i −0.588212 0.00941380i
916916 0 0
917917 31093.4i 1.11973i
918918 0 0
919919 −6029.99 −0.216443 −0.108221 0.994127i 0.534516π-0.534516\pi
−0.108221 + 0.994127i 0.534516π0.534516\pi
920920 0 0
921921 −9895.25 −0.354028
922922 0 0
923923 22043.2i 0.786088i
924924 0 0
925925 1067.78 33351.1i 0.0379551 1.18549i
926926 0 0
927927 12158.5i 0.430785i
928928 0 0
929929 35365.2 1.24897 0.624485 0.781037i 0.285309π-0.285309\pi
0.624485 + 0.781037i 0.285309π0.285309\pi
930930 0 0
931931 −45122.5 −1.58843
932932 0 0
933933 10184.8i 0.357379i
934934 0 0
935935 −27458.1 439.442i −0.960402 0.0153704i
936936 0 0
937937 35637.0i 1.24249i 0.783618 + 0.621243i 0.213372π0.213372\pi
−0.783618 + 0.621243i 0.786628π0.786628\pi
938938 0 0
939939 −17840.9 −0.620037
940940 0 0
941941 −6609.70 −0.228980 −0.114490 0.993424i 0.536523π-0.536523\pi
−0.114490 + 0.993424i 0.536523π0.536523\pi
942942 0 0
943943 11513.4i 0.397591i
944944 0 0
945945 −169.423 + 10586.2i −0.00583210 + 0.364413i
946946 0 0
947947 42650.9i 1.46354i 0.681553 + 0.731768i 0.261305π0.261305\pi
−0.681553 + 0.731768i 0.738695π0.738695\pi
948948 0 0
949949 42821.6 1.46475
950950 0 0
951951 −7562.48 −0.257866
952952 0 0
953953 38382.4i 1.30465i 0.757941 + 0.652323i 0.226205π0.226205\pi
−0.757941 + 0.652323i 0.773795π0.773795\pi
954954 0 0
955955 125.666 7852.10i 0.00425806 0.266061i
956956 0 0
957957 4192.86i 0.141626i
958958 0 0
959959 5637.11 0.189814
960960 0 0
961961 9587.71 0.321832
962962 0 0
963963 12001.6i 0.401604i
964964 0 0
965965 −46131.2 738.288i −1.53888 0.0246283i
966966 0 0
967967 2611.76i 0.0868549i −0.999057 0.0434275i 0.986172π-0.986172\pi
0.999057 0.0434275i 0.0138277π-0.0138277\pi
968968 0 0
969969 14616.2 0.484562
970970 0 0
971971 −7846.09 −0.259313 −0.129657 0.991559i 0.541387π-0.541387\pi
−0.129657 + 0.991559i 0.541387π0.541387\pi
972972 0 0
973973 2008.50i 0.0661763i
974974 0 0
975975 −14108.6 451.706i −0.463422 0.0148371i
976976 0 0
977977 35667.2i 1.16796i −0.811769 0.583979i 0.801495π-0.801495\pi
0.811769 0.583979i 0.198505π-0.198505\pi
978978 0 0
979979 22749.1 0.742661
980980 0 0
981981 −5489.19 −0.178651
982982 0 0
983983 13421.6i 0.435485i −0.976006 0.217742i 0.930131π-0.930131\pi
0.976006 0.217742i 0.0698693π-0.0698693\pi
984984 0 0
985985 −34704.4 555.412i −1.12261 0.0179664i
986986 0 0
987987 62817.5i 2.02584i
988988 0 0
989989 −11973.2 −0.384959
990990 0 0
991991 −40673.7 −1.30378 −0.651888 0.758315i 0.726023π-0.726023\pi
−0.651888 + 0.758315i 0.726023π0.726023\pi
992992 0 0
993993 13760.6i 0.439757i
994994 0 0
995995 65.7696 4109.54i 0.00209551 0.130936i
996996 0 0
997997 29558.8i 0.938954i −0.882945 0.469477i 0.844442π-0.844442\pi
0.882945 0.469477i 0.155558π-0.155558\pi
998998 0 0
999999 7207.53 0.228264
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 240.4.f.g.49.3 4
3.2 odd 2 720.4.f.i.289.3 4
4.3 odd 2 120.4.f.d.49.1 4
5.2 odd 4 1200.4.a.bq.1.1 2
5.3 odd 4 1200.4.a.bo.1.2 2
5.4 even 2 inner 240.4.f.g.49.1 4
8.3 odd 2 960.4.f.n.769.4 4
8.5 even 2 960.4.f.o.769.2 4
12.11 even 2 360.4.f.d.289.3 4
15.14 odd 2 720.4.f.i.289.4 4
20.3 even 4 600.4.a.v.1.1 2
20.7 even 4 600.4.a.t.1.2 2
20.19 odd 2 120.4.f.d.49.3 yes 4
40.19 odd 2 960.4.f.n.769.2 4
40.29 even 2 960.4.f.o.769.4 4
60.23 odd 4 1800.4.a.bl.1.1 2
60.47 odd 4 1800.4.a.bn.1.2 2
60.59 even 2 360.4.f.d.289.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.f.d.49.1 4 4.3 odd 2
120.4.f.d.49.3 yes 4 20.19 odd 2
240.4.f.g.49.1 4 5.4 even 2 inner
240.4.f.g.49.3 4 1.1 even 1 trivial
360.4.f.d.289.3 4 12.11 even 2
360.4.f.d.289.4 4 60.59 even 2
600.4.a.t.1.2 2 20.7 even 4
600.4.a.v.1.1 2 20.3 even 4
720.4.f.i.289.3 4 3.2 odd 2
720.4.f.i.289.4 4 15.14 odd 2
960.4.f.n.769.2 4 40.19 odd 2
960.4.f.n.769.4 4 8.3 odd 2
960.4.f.o.769.2 4 8.5 even 2
960.4.f.o.769.4 4 40.29 even 2
1200.4.a.bo.1.2 2 5.3 odd 4
1200.4.a.bq.1.1 2 5.2 odd 4
1800.4.a.bl.1.1 2 60.23 odd 4
1800.4.a.bn.1.2 2 60.47 odd 4