Properties

Label 1792.4.a.c.1.1
Level 17921792
Weight 44
Character 1792.1
Self dual yes
Analytic conductor 105.731105.731
Analytic rank 11
Dimension 22
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1792,4,Mod(1,1792)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1792.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 1792=287 1792 = 2^{8} \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 1792.a (trivial)

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: yes
Analytic conductor: 105.731422730105.731422730
Analytic rank: 11
Dimension: 22
Coefficient field: Q(ζ12)+\Q(\zeta_{12})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x23 x^{2} - 3 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 448)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 1.73205-1.73205 of defining polynomial
Character χ\chi == 1792.1

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) == q7.66025q322.1962q57.00000q7+31.6795q940.1051q1114.4833q13+170.028q15111.569q17117.804q19+53.6218q21+119.751q23+367.669q2535.8461q2792.8897q29181.569q31+307.215q33+155.373q35+247.090q37+110.946q3958.1333q41+249.885q43703.163q45+101.913q47+49.0000q49+854.649q51570.697q53+890.179q55+902.407q57+277.391q59+82.9526q61221.756q63+321.474q65+397.969q67917.325q69+6.22055q71+209.769q732816.44q75+280.736q77+271.902q79580.756q81+1010.28q83+2476.41q85+711.559q87+730.420q89+101.383q91+1390.87q93+2614.79q95+707.451q971270.51q99+O(q100)q-7.66025 q^{3} -22.1962 q^{5} -7.00000 q^{7} +31.6795 q^{9} -40.1051 q^{11} -14.4833 q^{13} +170.028 q^{15} -111.569 q^{17} -117.804 q^{19} +53.6218 q^{21} +119.751 q^{23} +367.669 q^{25} -35.8461 q^{27} -92.8897 q^{29} -181.569 q^{31} +307.215 q^{33} +155.373 q^{35} +247.090 q^{37} +110.946 q^{39} -58.1333 q^{41} +249.885 q^{43} -703.163 q^{45} +101.913 q^{47} +49.0000 q^{49} +854.649 q^{51} -570.697 q^{53} +890.179 q^{55} +902.407 q^{57} +277.391 q^{59} +82.9526 q^{61} -221.756 q^{63} +321.474 q^{65} +397.969 q^{67} -917.325 q^{69} +6.22055 q^{71} +209.769 q^{73} -2816.44 q^{75} +280.736 q^{77} +271.902 q^{79} -580.756 q^{81} +1010.28 q^{83} +2476.41 q^{85} +711.559 q^{87} +730.420 q^{89} +101.383 q^{91} +1390.87 q^{93} +2614.79 q^{95} +707.451 q^{97} -1270.51 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q334q514q7+98q94q1174q13+56q15140q17246q1914q21+288q23+382q25+344q2768q29280q31+656q33+238q35++1124q99+O(q100) 2 q + 2 q^{3} - 34 q^{5} - 14 q^{7} + 98 q^{9} - 4 q^{11} - 74 q^{13} + 56 q^{15} - 140 q^{17} - 246 q^{19} - 14 q^{21} + 288 q^{23} + 382 q^{25} + 344 q^{27} - 68 q^{29} - 280 q^{31} + 656 q^{33} + 238 q^{35}+ \cdots + 1124 q^{99}+O(q^{100}) Copy content Toggle raw display

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 −7.66025 −1.47422 −0.737108 0.675775i 0.763809π-0.763809\pi
−0.737108 + 0.675775i 0.763809π0.763809\pi
44 0 0
55 −22.1962 −1.98528 −0.992642 0.121085i 0.961363π-0.961363\pi
−0.992642 + 0.121085i 0.961363π0.961363\pi
66 0 0
77 −7.00000 −0.377964
88 0 0
99 31.6795 1.17331
1010 0 0
1111 −40.1051 −1.09929 −0.549643 0.835400i 0.685236π-0.685236\pi
−0.549643 + 0.835400i 0.685236π0.685236\pi
1212 0 0
1313 −14.4833 −0.308997 −0.154498 0.987993i 0.549376π-0.549376\pi
−0.154498 + 0.987993i 0.549376π0.549376\pi
1414 0 0
1515 170.028 2.92674
1616 0 0
1717 −111.569 −1.59174 −0.795868 0.605470i 0.792985π-0.792985\pi
−0.795868 + 0.605470i 0.792985π0.792985\pi
1818 0 0
1919 −117.804 −1.42242 −0.711212 0.702978i 0.751853π-0.751853\pi
−0.711212 + 0.702978i 0.751853π0.751853\pi
2020 0 0
2121 53.6218 0.557201
2222 0 0
2323 119.751 1.08565 0.542823 0.839847i 0.317355π-0.317355\pi
0.542823 + 0.839847i 0.317355π0.317355\pi
2424 0 0
2525 367.669 2.94135
2626 0 0
2727 −35.8461 −0.255503
2828 0 0
2929 −92.8897 −0.594800 −0.297400 0.954753i 0.596119π-0.596119\pi
−0.297400 + 0.954753i 0.596119π0.596119\pi
3030 0 0
3131 −181.569 −1.05196 −0.525981 0.850497i 0.676302π-0.676302\pi
−0.525981 + 0.850497i 0.676302π0.676302\pi
3232 0 0
3333 307.215 1.62059
3434 0 0
3535 155.373 0.750367
3636 0 0
3737 247.090 1.09787 0.548936 0.835864i 0.315033π-0.315033\pi
0.548936 + 0.835864i 0.315033π0.315033\pi
3838 0 0
3939 110.946 0.455528
4040 0 0
4141 −58.1333 −0.221436 −0.110718 0.993852i 0.535315π-0.535315\pi
−0.110718 + 0.993852i 0.535315π0.535315\pi
4242 0 0
4343 249.885 0.886210 0.443105 0.896470i 0.353877π-0.353877\pi
0.443105 + 0.896470i 0.353877π0.353877\pi
4444 0 0
4545 −703.163 −2.32936
4646 0 0
4747 101.913 0.316287 0.158144 0.987416i 0.449449π-0.449449\pi
0.158144 + 0.987416i 0.449449π0.449449\pi
4848 0 0
4949 49.0000 0.142857
5050 0 0
5151 854.649 2.34656
5252 0 0
5353 −570.697 −1.47908 −0.739541 0.673112i 0.764957π-0.764957\pi
−0.739541 + 0.673112i 0.764957π0.764957\pi
5454 0 0
5555 890.179 2.18240
5656 0 0
5757 902.407 2.09696
5858 0 0
5959 277.391 0.612089 0.306044 0.952017i 0.400994π-0.400994\pi
0.306044 + 0.952017i 0.400994π0.400994\pi
6060 0 0
6161 82.9526 0.174115 0.0870573 0.996203i 0.472254π-0.472254\pi
0.0870573 + 0.996203i 0.472254π0.472254\pi
6262 0 0
6363 −221.756 −0.443471
6464 0 0
6565 321.474 0.613446
6666 0 0
6767 397.969 0.725667 0.362833 0.931854i 0.381809π-0.381809\pi
0.362833 + 0.931854i 0.381809π0.381809\pi
6868 0 0
6969 −917.325 −1.60048
7070 0 0
7171 6.22055 0.0103978 0.00519889 0.999986i 0.498345π-0.498345\pi
0.00519889 + 0.999986i 0.498345π0.498345\pi
7272 0 0
7373 209.769 0.336324 0.168162 0.985759i 0.446217π-0.446217\pi
0.168162 + 0.985759i 0.446217π0.446217\pi
7474 0 0
7575 −2816.44 −4.33619
7676 0 0
7777 280.736 0.415491
7878 0 0
7979 271.902 0.387233 0.193617 0.981077i 0.437978π-0.437978\pi
0.193617 + 0.981077i 0.437978π0.437978\pi
8080 0 0
8181 −580.756 −0.796648
8282 0 0
8383 1010.28 1.33606 0.668028 0.744136i 0.267138π-0.267138\pi
0.668028 + 0.744136i 0.267138π0.267138\pi
8484 0 0
8585 2476.41 3.16005
8686 0 0
8787 711.559 0.876863
8888 0 0
8989 730.420 0.869937 0.434969 0.900446i 0.356759π-0.356759\pi
0.434969 + 0.900446i 0.356759π0.356759\pi
9090 0 0
9191 101.383 0.116790
9292 0 0
9393 1390.87 1.55082
9494 0 0
9595 2614.79 2.82392
9696 0 0
9797 707.451 0.740523 0.370262 0.928927i 0.379268π-0.379268\pi
0.370262 + 0.928927i 0.379268π0.379268\pi
9898 0 0
9999 −1270.51 −1.28981
100100 0 0
101101 −596.558 −0.587720 −0.293860 0.955849i 0.594940π-0.594940\pi
−0.293860 + 0.955849i 0.594940π0.594940\pi
102102 0 0
103103 539.959 0.516541 0.258270 0.966073i 0.416847π-0.416847\pi
0.258270 + 0.966073i 0.416847π0.416847\pi
104104 0 0
105105 −1190.20 −1.10620
106106 0 0
107107 660.497 0.596754 0.298377 0.954448i 0.403555π-0.403555\pi
0.298377 + 0.954448i 0.403555π0.403555\pi
108108 0 0
109109 234.157 0.205763 0.102881 0.994694i 0.467194π-0.467194\pi
0.102881 + 0.994694i 0.467194π0.467194\pi
110110 0 0
111111 −1892.77 −1.61850
112112 0 0
113113 −1740.74 −1.44916 −0.724578 0.689193i 0.757965π-0.757965\pi
−0.724578 + 0.689193i 0.757965π0.757965\pi
114114 0 0
115115 −2658.02 −2.15532
116116 0 0
117117 −458.825 −0.362550
118118 0 0
119119 780.985 0.601620
120120 0 0
121121 277.420 0.208430
122122 0 0
123123 445.316 0.326445
124124 0 0
125125 −5386.32 −3.85414
126126 0 0
127127 341.377 0.238522 0.119261 0.992863i 0.461947π-0.461947\pi
0.119261 + 0.992863i 0.461947π0.461947\pi
128128 0 0
129129 −1914.18 −1.30647
130130 0 0
131131 405.014 0.270124 0.135062 0.990837i 0.456877π-0.456877\pi
0.135062 + 0.990837i 0.456877π0.456877\pi
132132 0 0
133133 824.627 0.537626
134134 0 0
135135 795.645 0.507246
136136 0 0
137137 1590.40 0.991803 0.495902 0.868379i 0.334838π-0.334838\pi
0.495902 + 0.868379i 0.334838π0.334838\pi
138138 0 0
139139 605.609 0.369547 0.184774 0.982781i 0.440845π-0.440845\pi
0.184774 + 0.982781i 0.440845π0.440845\pi
140140 0 0
141141 −780.677 −0.466276
142142 0 0
143143 580.856 0.339676
144144 0 0
145145 2061.79 1.18085
146146 0 0
147147 −375.352 −0.210602
148148 0 0
149149 −1986.22 −1.09206 −0.546032 0.837764i 0.683862π-0.683862\pi
−0.546032 + 0.837764i 0.683862π0.683862\pi
150150 0 0
151151 678.905 0.365884 0.182942 0.983124i 0.441438π-0.441438\pi
0.182942 + 0.983124i 0.441438π0.441438\pi
152152 0 0
153153 −3534.46 −1.86761
154154 0 0
155155 4030.14 2.08844
156156 0 0
157157 −3202.21 −1.62780 −0.813899 0.581006i 0.802659π-0.802659\pi
−0.813899 + 0.581006i 0.802659π0.802659\pi
158158 0 0
159159 4371.69 2.18049
160160 0 0
161161 −838.259 −0.410336
162162 0 0
163163 340.941 0.163831 0.0819157 0.996639i 0.473896π-0.473896\pi
0.0819157 + 0.996639i 0.473896π0.473896\pi
164164 0 0
165165 −6819.00 −3.21732
166166 0 0
167167 −3038.90 −1.40812 −0.704062 0.710138i 0.748633π-0.748633\pi
−0.704062 + 0.710138i 0.748633π0.748633\pi
168168 0 0
169169 −1987.23 −0.904521
170170 0 0
171171 −3731.97 −1.66895
172172 0 0
173173 2611.06 1.14749 0.573743 0.819035i 0.305491π-0.305491\pi
0.573743 + 0.819035i 0.305491π0.305491\pi
174174 0 0
175175 −2573.68 −1.11173
176176 0 0
177177 −2124.88 −0.902351
178178 0 0
179179 2055.56 0.858325 0.429162 0.903227i 0.358809π-0.358809\pi
0.429162 + 0.903227i 0.358809π0.358809\pi
180180 0 0
181181 −1986.95 −0.815961 −0.407981 0.912991i 0.633767π-0.633767\pi
−0.407981 + 0.912991i 0.633767π0.633767\pi
182182 0 0
183183 −635.438 −0.256683
184184 0 0
185185 −5484.44 −2.17959
186186 0 0
187187 4474.50 1.74977
188188 0 0
189189 250.923 0.0965711
190190 0 0
191191 −441.866 −0.167394 −0.0836971 0.996491i 0.526673π-0.526673\pi
−0.0836971 + 0.996491i 0.526673π0.526673\pi
192192 0 0
193193 −5059.63 −1.88705 −0.943524 0.331304i 0.892511π-0.892511\pi
−0.943524 + 0.331304i 0.892511π0.892511\pi
194194 0 0
195195 −2462.58 −0.904352
196196 0 0
197197 −3150.30 −1.13934 −0.569669 0.821875i 0.692928π-0.692928\pi
−0.569669 + 0.821875i 0.692928π0.692928\pi
198198 0 0
199199 −539.846 −0.192305 −0.0961525 0.995367i 0.530654π-0.530654\pi
−0.0961525 + 0.995367i 0.530654π0.530654\pi
200200 0 0
201201 −3048.54 −1.06979
202202 0 0
203203 650.228 0.224813
204204 0 0
205205 1290.34 0.439614
206206 0 0
207207 3793.66 1.27380
208208 0 0
209209 4724.54 1.56365
210210 0 0
211211 5413.14 1.76614 0.883071 0.469239i 0.155472π-0.155472\pi
0.883071 + 0.469239i 0.155472π0.155472\pi
212212 0 0
213213 −47.6510 −0.0153286
214214 0 0
215215 −5546.48 −1.75938
216216 0 0
217217 1270.98 0.397604
218218 0 0
219219 −1606.88 −0.495814
220220 0 0
221221 1615.89 0.491841
222222 0 0
223223 −2289.18 −0.687422 −0.343711 0.939075i 0.611684π-0.611684\pi
−0.343711 + 0.939075i 0.611684π0.611684\pi
224224 0 0
225225 11647.6 3.45113
226226 0 0
227227 −6742.24 −1.97136 −0.985679 0.168634i 0.946064π-0.946064\pi
−0.985679 + 0.168634i 0.946064π0.946064\pi
228228 0 0
229229 1536.97 0.443520 0.221760 0.975101i 0.428820π-0.428820\pi
0.221760 + 0.975101i 0.428820π0.428820\pi
230230 0 0
231231 −2150.51 −0.612524
232232 0 0
233233 1568.19 0.440926 0.220463 0.975395i 0.429243π-0.429243\pi
0.220463 + 0.975395i 0.429243π0.429243\pi
234234 0 0
235235 −2262.07 −0.627920
236236 0 0
237237 −2082.84 −0.570865
238238 0 0
239239 −4907.22 −1.32812 −0.664062 0.747677i 0.731169π-0.731169\pi
−0.664062 + 0.747677i 0.731169π0.731169\pi
240240 0 0
241241 1403.57 0.375154 0.187577 0.982250i 0.439937π-0.439937\pi
0.187577 + 0.982250i 0.439937π0.439937\pi
242242 0 0
243243 5416.58 1.42993
244244 0 0
245245 −1087.61 −0.283612
246246 0 0
247247 1706.19 0.439524
248248 0 0
249249 −7739.01 −1.96964
250250 0 0
251251 3774.48 0.949175 0.474588 0.880208i 0.342597π-0.342597\pi
0.474588 + 0.880208i 0.342597π0.342597\pi
252252 0 0
253253 −4802.64 −1.19344
254254 0 0
255255 −18969.9 −4.65860
256256 0 0
257257 −3233.01 −0.784708 −0.392354 0.919814i 0.628339π-0.628339\pi
−0.392354 + 0.919814i 0.628339π0.628339\pi
258258 0 0
259259 −1729.63 −0.414957
260260 0 0
261261 −2942.70 −0.697887
262262 0 0
263263 3259.84 0.764298 0.382149 0.924101i 0.375184π-0.375184\pi
0.382149 + 0.924101i 0.375184π0.375184\pi
264264 0 0
265265 12667.3 2.93640
266266 0 0
267267 −5595.21 −1.28248
268268 0 0
269269 7328.77 1.66113 0.830563 0.556925i 0.188019π-0.188019\pi
0.830563 + 0.556925i 0.188019π0.188019\pi
270270 0 0
271271 7009.29 1.57116 0.785579 0.618761i 0.212365π-0.212365\pi
0.785579 + 0.618761i 0.212365π0.212365\pi
272272 0 0
273273 −776.622 −0.172173
274274 0 0
275275 −14745.4 −3.23339
276276 0 0
277277 −3753.77 −0.814233 −0.407116 0.913376i 0.633466π-0.633466\pi
−0.407116 + 0.913376i 0.633466π0.633466\pi
278278 0 0
279279 −5752.02 −1.23428
280280 0 0
281281 36.9750 0.00784961 0.00392481 0.999992i 0.498751π-0.498751\pi
0.00392481 + 0.999992i 0.498751π0.498751\pi
282282 0 0
283283 3236.79 0.679884 0.339942 0.940446i 0.389593π-0.389593\pi
0.339942 + 0.940446i 0.389593π0.389593\pi
284284 0 0
285285 −20030.0 −4.16306
286286 0 0
287287 406.933 0.0836951
288288 0 0
289289 7534.69 1.53362
290290 0 0
291291 −5419.25 −1.09169
292292 0 0
293293 4412.89 0.879876 0.439938 0.898028i 0.355000π-0.355000\pi
0.439938 + 0.898028i 0.355000π0.355000\pi
294294 0 0
295295 −6157.01 −1.21517
296296 0 0
297297 1437.61 0.280871
298298 0 0
299299 −1734.40 −0.335461
300300 0 0
301301 −1749.19 −0.334956
302302 0 0
303303 4569.78 0.866426
304304 0 0
305305 −1841.23 −0.345667
306306 0 0
307307 588.428 0.109392 0.0546961 0.998503i 0.482581π-0.482581\pi
0.0546961 + 0.998503i 0.482581π0.482581\pi
308308 0 0
309309 −4136.22 −0.761493
310310 0 0
311311 −7495.29 −1.36662 −0.683310 0.730128i 0.739460π-0.739460\pi
−0.683310 + 0.730128i 0.739460π0.739460\pi
312312 0 0
313313 6652.87 1.20141 0.600707 0.799469i 0.294886π-0.294886\pi
0.600707 + 0.799469i 0.294886π0.294886\pi
314314 0 0
315315 4922.14 0.880416
316316 0 0
317317 −7215.06 −1.27835 −0.639177 0.769060i 0.720725π-0.720725\pi
−0.639177 + 0.769060i 0.720725π0.720725\pi
318318 0 0
319319 3725.35 0.653855
320320 0 0
321321 −5059.58 −0.879745
322322 0 0
323323 13143.3 2.26412
324324 0 0
325325 −5325.08 −0.908868
326326 0 0
327327 −1793.70 −0.303339
328328 0 0
329329 −713.389 −0.119545
330330 0 0
331331 −1123.85 −0.186623 −0.0933116 0.995637i 0.529745π-0.529745\pi
−0.0933116 + 0.995637i 0.529745π0.529745\pi
332332 0 0
333333 7827.67 1.28815
334334 0 0
335335 −8833.38 −1.44065
336336 0 0
337337 −735.459 −0.118881 −0.0594407 0.998232i 0.518932π-0.518932\pi
−0.0594407 + 0.998232i 0.518932π0.518932\pi
338338 0 0
339339 13334.5 2.13637
340340 0 0
341341 7281.85 1.15641
342342 0 0
343343 −343.000 −0.0539949
344344 0 0
345345 20361.1 3.17740
346346 0 0
347347 8412.83 1.30151 0.650756 0.759287i 0.274452π-0.274452\pi
0.650756 + 0.759287i 0.274452π0.274452\pi
348348 0 0
349349 8577.90 1.31566 0.657829 0.753167i 0.271475π-0.271475\pi
0.657829 + 0.753167i 0.271475π0.271475\pi
350350 0 0
351351 519.171 0.0789496
352352 0 0
353353 −34.2817 −0.00516892 −0.00258446 0.999997i 0.500823π-0.500823\pi
−0.00258446 + 0.999997i 0.500823π0.500823\pi
354354 0 0
355355 −138.072 −0.0206426
356356 0 0
357357 −5982.54 −0.886918
358358 0 0
359359 1007.89 0.148174 0.0740872 0.997252i 0.476396π-0.476396\pi
0.0740872 + 0.997252i 0.476396π0.476396\pi
360360 0 0
361361 7018.75 1.02329
362362 0 0
363363 −2125.11 −0.307271
364364 0 0
365365 −4656.07 −0.667698
366366 0 0
367367 13076.7 1.85994 0.929969 0.367638i 0.119834π-0.119834\pi
0.929969 + 0.367638i 0.119834π0.119834\pi
368368 0 0
369369 −1841.63 −0.259815
370370 0 0
371371 3994.88 0.559040
372372 0 0
373373 −8552.62 −1.18723 −0.593616 0.804748i 0.702300π-0.702300\pi
−0.593616 + 0.804748i 0.702300π0.702300\pi
374374 0 0
375375 41260.6 5.68183
376376 0 0
377377 1345.35 0.183791
378378 0 0
379379 −9753.81 −1.32195 −0.660975 0.750408i 0.729857π-0.729857\pi
−0.660975 + 0.750408i 0.729857π0.729857\pi
380380 0 0
381381 −2615.03 −0.351633
382382 0 0
383383 7141.71 0.952805 0.476402 0.879227i 0.341941π-0.341941\pi
0.476402 + 0.879227i 0.341941π0.341941\pi
384384 0 0
385385 −6231.26 −0.824868
386386 0 0
387387 7916.22 1.03980
388388 0 0
389389 4854.81 0.632773 0.316386 0.948630i 0.397530π-0.397530\pi
0.316386 + 0.948630i 0.397530π0.397530\pi
390390 0 0
391391 −13360.6 −1.72806
392392 0 0
393393 −3102.51 −0.398221
394394 0 0
395395 −6035.19 −0.768768
396396 0 0
397397 −10401.6 −1.31496 −0.657481 0.753471i 0.728378π-0.728378\pi
−0.657481 + 0.753471i 0.728378π0.728378\pi
398398 0 0
399399 −6316.85 −0.792577
400400 0 0
401401 4386.56 0.546271 0.273135 0.961976i 0.411939π-0.411939\pi
0.273135 + 0.961976i 0.411939π0.411939\pi
402402 0 0
403403 2629.73 0.325052
404404 0 0
405405 12890.6 1.58157
406406 0 0
407407 −9909.56 −1.20688
408408 0 0
409409 6474.49 0.782746 0.391373 0.920232i 0.372000π-0.372000\pi
0.391373 + 0.920232i 0.372000π0.372000\pi
410410 0 0
411411 −12182.9 −1.46213
412412 0 0
413413 −1941.74 −0.231348
414414 0 0
415415 −22424.3 −2.65245
416416 0 0
417417 −4639.12 −0.544793
418418 0 0
419419 −4781.90 −0.557544 −0.278772 0.960357i 0.589927π-0.589927\pi
−0.278772 + 0.960357i 0.589927π0.589927\pi
420420 0 0
421421 271.468 0.0314265 0.0157133 0.999877i 0.494998π-0.494998\pi
0.0157133 + 0.999877i 0.494998π0.494998\pi
422422 0 0
423423 3228.54 0.371104
424424 0 0
425425 −41020.6 −4.68186
426426 0 0
427427 −580.668 −0.0658091
428428 0 0
429429 −4449.50 −0.500756
430430 0 0
431431 −10024.3 −1.12031 −0.560153 0.828389i 0.689258π-0.689258\pi
−0.560153 + 0.828389i 0.689258π0.689258\pi
432432 0 0
433433 14997.2 1.66448 0.832242 0.554413i 0.187057π-0.187057\pi
0.832242 + 0.554413i 0.187057π0.187057\pi
434434 0 0
435435 −15793.9 −1.74082
436436 0 0
437437 −14107.2 −1.54425
438438 0 0
439439 7619.62 0.828393 0.414196 0.910188i 0.364063π-0.364063\pi
0.414196 + 0.910188i 0.364063π0.364063\pi
440440 0 0
441441 1552.30 0.167616
442442 0 0
443443 3188.70 0.341985 0.170993 0.985272i 0.445303π-0.445303\pi
0.170993 + 0.985272i 0.445303π0.445303\pi
444444 0 0
445445 −16212.5 −1.72707
446446 0 0
447447 15215.0 1.60994
448448 0 0
449449 3446.04 0.362202 0.181101 0.983464i 0.442034π-0.442034\pi
0.181101 + 0.983464i 0.442034π0.442034\pi
450450 0 0
451451 2331.44 0.243422
452452 0 0
453453 −5200.58 −0.539392
454454 0 0
455455 −2250.32 −0.231861
456456 0 0
457457 7559.50 0.773782 0.386891 0.922126i 0.373549π-0.373549\pi
0.386891 + 0.922126i 0.373549π0.373549\pi
458458 0 0
459459 3999.32 0.406694
460460 0 0
461461 10358.3 1.04650 0.523249 0.852180i 0.324720π-0.324720\pi
0.523249 + 0.852180i 0.324720π0.324720\pi
462462 0 0
463463 −5546.46 −0.556730 −0.278365 0.960475i 0.589792π-0.589792\pi
−0.278365 + 0.960475i 0.589792π0.589792\pi
464464 0 0
465465 −30871.9 −3.07882
466466 0 0
467467 −7296.87 −0.723038 −0.361519 0.932365i 0.617742π-0.617742\pi
−0.361519 + 0.932365i 0.617742π0.617742\pi
468468 0 0
469469 −2785.78 −0.274276
470470 0 0
471471 24529.8 2.39973
472472 0 0
473473 −10021.7 −0.974199
474474 0 0
475475 −43312.8 −4.18385
476476 0 0
477477 −18079.4 −1.73543
478478 0 0
479479 −19437.2 −1.85409 −0.927046 0.374946i 0.877661π-0.877661\pi
−0.927046 + 0.374946i 0.877661π0.877661\pi
480480 0 0
481481 −3578.68 −0.339239
482482 0 0
483483 6421.28 0.604924
484484 0 0
485485 −15702.7 −1.47015
486486 0 0
487487 6540.19 0.608551 0.304276 0.952584i 0.401586π-0.401586\pi
0.304276 + 0.952584i 0.401586π0.401586\pi
488488 0 0
489489 −2611.69 −0.241523
490490 0 0
491491 8542.59 0.785176 0.392588 0.919714i 0.371580π-0.371580\pi
0.392588 + 0.919714i 0.371580π0.371580\pi
492492 0 0
493493 10363.6 0.946764
494494 0 0
495495 28200.4 2.56064
496496 0 0
497497 −43.5438 −0.00392999
498498 0 0
499499 17254.6 1.54794 0.773968 0.633224i 0.218269π-0.218269\pi
0.773968 + 0.633224i 0.218269π0.218269\pi
500500 0 0
501501 23278.7 2.07588
502502 0 0
503503 −5597.51 −0.496184 −0.248092 0.968736i 0.579804π-0.579804\pi
−0.248092 + 0.968736i 0.579804π0.579804\pi
504504 0 0
505505 13241.3 1.16679
506506 0 0
507507 15222.7 1.33346
508508 0 0
509509 −5232.92 −0.455688 −0.227844 0.973698i 0.573168π-0.573168\pi
−0.227844 + 0.973698i 0.573168π0.573168\pi
510510 0 0
511511 −1468.38 −0.127118
512512 0 0
513513 4222.81 0.363434
514514 0 0
515515 −11985.0 −1.02548
516516 0 0
517517 −4087.22 −0.347690
518518 0 0
519519 −20001.4 −1.69164
520520 0 0
521521 −7429.89 −0.624778 −0.312389 0.949954i 0.601129π-0.601129\pi
−0.312389 + 0.949954i 0.601129π0.601129\pi
522522 0 0
523523 −2963.01 −0.247732 −0.123866 0.992299i 0.539529π-0.539529\pi
−0.123866 + 0.992299i 0.539529π0.539529\pi
524524 0 0
525525 19715.1 1.63893
526526 0 0
527527 20257.5 1.67444
528528 0 0
529529 2173.37 0.178628
530530 0 0
531531 8787.60 0.718172
532532 0 0
533533 841.964 0.0684231
534534 0 0
535535 −14660.5 −1.18473
536536 0 0
537537 −15746.1 −1.26536
538538 0 0
539539 −1965.15 −0.157041
540540 0 0
541541 19355.9 1.53822 0.769109 0.639118i 0.220701π-0.220701\pi
0.769109 + 0.639118i 0.220701π0.220701\pi
542542 0 0
543543 15220.6 1.20290
544544 0 0
545545 −5197.38 −0.408498
546546 0 0
547547 −7653.95 −0.598280 −0.299140 0.954209i 0.596700π-0.596700\pi
−0.299140 + 0.954209i 0.596700π0.596700\pi
548548 0 0
549549 2627.90 0.204291
550550 0 0
551551 10942.8 0.846057
552552 0 0
553553 −1903.32 −0.146360
554554 0 0
555555 42012.2 3.21319
556556 0 0
557557 10896.0 0.828864 0.414432 0.910080i 0.363980π-0.363980\pi
0.414432 + 0.910080i 0.363980π0.363980\pi
558558 0 0
559559 −3619.16 −0.273836
560560 0 0
561561 −34275.8 −2.57954
562562 0 0
563563 −15441.8 −1.15594 −0.577972 0.816057i 0.696156π-0.696156\pi
−0.577972 + 0.816057i 0.696156π0.696156\pi
564564 0 0
565565 38637.6 2.87699
566566 0 0
567567 4065.29 0.301104
568568 0 0
569569 5615.59 0.413739 0.206870 0.978369i 0.433672π-0.433672\pi
0.206870 + 0.978369i 0.433672π0.433672\pi
570570 0 0
571571 14371.0 1.05325 0.526626 0.850097i 0.323457π-0.323457\pi
0.526626 + 0.850097i 0.323457π0.323457\pi
572572 0 0
573573 3384.81 0.246775
574574 0 0
575575 44028.9 3.19327
576576 0 0
577577 −18933.5 −1.36605 −0.683027 0.730393i 0.739337π-0.739337\pi
−0.683027 + 0.730393i 0.739337π0.739337\pi
578578 0 0
579579 38758.1 2.78192
580580 0 0
581581 −7071.96 −0.504982
582582 0 0
583583 22887.9 1.62593
584584 0 0
585585 10184.1 0.719765
586586 0 0
587587 17871.6 1.25663 0.628315 0.777959i 0.283745π-0.283745\pi
0.628315 + 0.777959i 0.283745π0.283745\pi
588588 0 0
589589 21389.6 1.49633
590590 0 0
591591 24132.1 1.67963
592592 0 0
593593 45.4735 0.00314902 0.00157451 0.999999i 0.499499π-0.499499\pi
0.00157451 + 0.999999i 0.499499π0.499499\pi
594594 0 0
595595 −17334.9 −1.19439
596596 0 0
597597 4135.36 0.283499
598598 0 0
599599 10336.6 0.705078 0.352539 0.935797i 0.385318π-0.385318\pi
0.352539 + 0.935797i 0.385318π0.385318\pi
600600 0 0
601601 −4844.95 −0.328835 −0.164417 0.986391i 0.552574π-0.552574\pi
−0.164417 + 0.986391i 0.552574π0.552574\pi
602602 0 0
603603 12607.5 0.851435
604604 0 0
605605 −6157.67 −0.413793
606606 0 0
607607 −15710.1 −1.05050 −0.525249 0.850949i 0.676028π-0.676028\pi
−0.525249 + 0.850949i 0.676028π0.676028\pi
608608 0 0
609609 −4980.91 −0.331423
610610 0 0
611611 −1476.04 −0.0977317
612612 0 0
613613 −23320.2 −1.53653 −0.768267 0.640130i 0.778881π-0.778881\pi
−0.768267 + 0.640130i 0.778881π0.778881\pi
614614 0 0
615615 −9884.30 −0.648087
616616 0 0
617617 10540.0 0.687720 0.343860 0.939021i 0.388266π-0.388266\pi
0.343860 + 0.939021i 0.388266π0.388266\pi
618618 0 0
619619 17788.6 1.15507 0.577533 0.816367i 0.304016π-0.304016\pi
0.577533 + 0.816367i 0.304016π0.304016\pi
620620 0 0
621621 −4292.62 −0.277386
622622 0 0
623623 −5112.94 −0.328805
624624 0 0
625625 73597.0 4.71021
626626 0 0
627627 −36191.2 −2.30516
628628 0 0
629629 −27567.6 −1.74752
630630 0 0
631631 12278.6 0.774648 0.387324 0.921944i 0.373399π-0.373399\pi
0.387324 + 0.921944i 0.373399π0.373399\pi
632632 0 0
633633 −41466.1 −2.60368
634634 0 0
635635 −7577.25 −0.473534
636636 0 0
637637 −709.684 −0.0441424
638638 0 0
639639 197.064 0.0121999
640640 0 0
641641 15729.2 0.969216 0.484608 0.874732i 0.338962π-0.338962\pi
0.484608 + 0.874732i 0.338962π0.338962\pi
642642 0 0
643643 −7527.17 −0.461652 −0.230826 0.972995i 0.574143π-0.574143\pi
−0.230826 + 0.972995i 0.574143π0.574143\pi
644644 0 0
645645 42487.4 2.59371
646646 0 0
647647 −4431.02 −0.269245 −0.134622 0.990897i 0.542982π-0.542982\pi
−0.134622 + 0.990897i 0.542982π0.542982\pi
648648 0 0
649649 −11124.8 −0.672860
650650 0 0
651651 −9736.06 −0.586154
652652 0 0
653653 −4155.52 −0.249032 −0.124516 0.992218i 0.539738π-0.539738\pi
−0.124516 + 0.992218i 0.539738π0.539738\pi
654654 0 0
655655 −8989.75 −0.536272
656656 0 0
657657 6645.38 0.394613
658658 0 0
659659 10380.1 0.613583 0.306791 0.951777i 0.400745π-0.400745\pi
0.306791 + 0.951777i 0.400745π0.400745\pi
660660 0 0
661661 17788.9 1.04676 0.523381 0.852099i 0.324671π-0.324671\pi
0.523381 + 0.852099i 0.324671π0.324671\pi
662662 0 0
663663 −12378.2 −0.725080
664664 0 0
665665 −18303.5 −1.06734
666666 0 0
667667 −11123.7 −0.645742
668668 0 0
669669 17535.7 1.01341
670670 0 0
671671 −3326.82 −0.191402
672672 0 0
673673 13619.4 0.780074 0.390037 0.920799i 0.372462π-0.372462\pi
0.390037 + 0.920799i 0.372462π0.372462\pi
674674 0 0
675675 −13179.5 −0.751525
676676 0 0
677677 10454.1 0.593478 0.296739 0.954959i 0.404101π-0.404101\pi
0.296739 + 0.954959i 0.404101π0.404101\pi
678678 0 0
679679 −4952.16 −0.279892
680680 0 0
681681 51647.3 2.90621
682682 0 0
683683 −11405.9 −0.638996 −0.319498 0.947587i 0.603514π-0.603514\pi
−0.319498 + 0.947587i 0.603514π0.603514\pi
684684 0 0
685685 −35300.8 −1.96901
686686 0 0
687687 −11773.6 −0.653844
688688 0 0
689689 8265.60 0.457031
690690 0 0
691691 5921.64 0.326006 0.163003 0.986626i 0.447882π-0.447882\pi
0.163003 + 0.986626i 0.447882π0.447882\pi
692692 0 0
693693 8893.57 0.487502
694694 0 0
695695 −13442.2 −0.733656
696696 0 0
697697 6485.89 0.352468
698698 0 0
699699 −12012.8 −0.650021
700700 0 0
701701 24236.4 1.30584 0.652921 0.757426i 0.273543π-0.273543\pi
0.652921 + 0.757426i 0.273543π0.273543\pi
702702 0 0
703703 −29108.1 −1.56164
704704 0 0
705705 17328.0 0.925690
706706 0 0
707707 4175.90 0.222137
708708 0 0
709709 30145.3 1.59680 0.798400 0.602128i 0.205680π-0.205680\pi
0.798400 + 0.602128i 0.205680π0.205680\pi
710710 0 0
711711 8613.73 0.454346
712712 0 0
713713 −21743.1 −1.14206
714714 0 0
715715 −12892.8 −0.674353
716716 0 0
717717 37590.6 1.95794
718718 0 0
719719 5159.52 0.267619 0.133809 0.991007i 0.457279π-0.457279\pi
0.133809 + 0.991007i 0.457279π0.457279\pi
720720 0 0
721721 −3779.71 −0.195234
722722 0 0
723723 −10751.7 −0.553059
724724 0 0
725725 −34152.7 −1.74952
726726 0 0
727727 22475.2 1.14657 0.573286 0.819355i 0.305668π-0.305668\pi
0.573286 + 0.819355i 0.305668π0.305668\pi
728728 0 0
729729 −25812.0 −1.31139
730730 0 0
731731 −27879.4 −1.41061
732732 0 0
733733 15258.4 0.768871 0.384436 0.923152i 0.374396π-0.374396\pi
0.384436 + 0.923152i 0.374396π0.374396\pi
734734 0 0
735735 8331.38 0.418106
736736 0 0
737737 −15960.6 −0.797715
738738 0 0
739739 −27519.3 −1.36984 −0.684922 0.728616i 0.740164π-0.740164\pi
−0.684922 + 0.728616i 0.740164π0.740164\pi
740740 0 0
741741 −13069.9 −0.647954
742742 0 0
743743 −38497.6 −1.90086 −0.950431 0.310937i 0.899357π-0.899357\pi
−0.950431 + 0.310937i 0.899357π0.899357\pi
744744 0 0
745745 44086.5 2.16806
746746 0 0
747747 32005.2 1.56761
748748 0 0
749749 −4623.48 −0.225552
750750 0 0
751751 −25060.1 −1.21765 −0.608827 0.793303i 0.708359π-0.708359\pi
−0.608827 + 0.793303i 0.708359π0.708359\pi
752752 0 0
753753 −28913.5 −1.39929
754754 0 0
755755 −15069.1 −0.726384
756756 0 0
757757 7440.21 0.357225 0.178612 0.983920i 0.442839π-0.442839\pi
0.178612 + 0.983920i 0.442839π0.442839\pi
758758 0 0
759759 36789.4 1.75938
760760 0 0
761761 −11058.6 −0.526773 −0.263386 0.964690i 0.584839π-0.584839\pi
−0.263386 + 0.964690i 0.584839π0.584839\pi
762762 0 0
763763 −1639.10 −0.0777710
764764 0 0
765765 78451.3 3.70773
766766 0 0
767767 −4017.55 −0.189133
768768 0 0
769769 39340.3 1.84479 0.922397 0.386243i 0.126227π-0.126227\pi
0.922397 + 0.386243i 0.126227π0.126227\pi
770770 0 0
771771 24765.7 1.15683
772772 0 0
773773 −28953.3 −1.34719 −0.673595 0.739100i 0.735251π-0.735251\pi
−0.673595 + 0.739100i 0.735251π0.735251\pi
774774 0 0
775775 −66757.4 −3.09419
776776 0 0
777777 13249.4 0.611736
778778 0 0
779779 6848.32 0.314976
780780 0 0
781781 −249.476 −0.0114301
782782 0 0
783783 3329.73 0.151973
784784 0 0
785785 71076.8 3.23164
786786 0 0
787787 15424.4 0.698627 0.349313 0.937006i 0.386415π-0.386415\pi
0.349313 + 0.937006i 0.386415π0.386415\pi
788788 0 0
789789 −24971.2 −1.12674
790790 0 0
791791 12185.2 0.547730
792792 0 0
793793 −1201.43 −0.0538008
794794 0 0
795795 −97034.6 −4.32888
796796 0 0
797797 −13348.5 −0.593258 −0.296629 0.954993i 0.595862π-0.595862\pi
−0.296629 + 0.954993i 0.595862π0.595862\pi
798798 0 0
799799 −11370.3 −0.503446
800800 0 0
801801 23139.3 1.02071
802802 0 0
803803 −8412.82 −0.369716
804804 0 0
805805 18606.1 0.814633
806806 0 0
807807 −56140.2 −2.44886
808808 0 0
809809 −18871.7 −0.820139 −0.410070 0.912054i 0.634496π-0.634496\pi
−0.410070 + 0.912054i 0.634496π0.634496\pi
810810 0 0
811811 8113.79 0.351312 0.175656 0.984452i 0.443795π-0.443795\pi
0.175656 + 0.984452i 0.443795π0.443795\pi
812812 0 0
813813 −53692.9 −2.31623
814814 0 0
815815 −7567.57 −0.325252
816816 0 0
817817 −29437.4 −1.26057
818818 0 0
819819 3211.77 0.137031
820820 0 0
821821 16368.2 0.695804 0.347902 0.937531i 0.386894π-0.386894\pi
0.347902 + 0.937531i 0.386894π0.386894\pi
822822 0 0
823823 −34575.7 −1.46444 −0.732220 0.681069i 0.761516π-0.761516\pi
−0.732220 + 0.681069i 0.761516π0.761516\pi
824824 0 0
825825 112954. 4.76672
826826 0 0
827827 43222.0 1.81739 0.908693 0.417466i 0.137082π-0.137082\pi
0.908693 + 0.417466i 0.137082π0.137082\pi
828828 0 0
829829 −29288.6 −1.22706 −0.613532 0.789670i 0.710252π-0.710252\pi
−0.613532 + 0.789670i 0.710252π0.710252\pi
830830 0 0
831831 28754.9 1.20036
832832 0 0
833833 −5466.89 −0.227391
834834 0 0
835835 67451.8 2.79553
836836 0 0
837837 6508.55 0.268779
838838 0 0
839839 −16518.3 −0.679708 −0.339854 0.940478i 0.610378π-0.610378\pi
−0.339854 + 0.940478i 0.610378π0.610378\pi
840840 0 0
841841 −15760.5 −0.646213
842842 0 0
843843 −283.238 −0.0115720
844844 0 0
845845 44108.9 1.79573
846846 0 0
847847 −1941.94 −0.0787792
848848 0 0
849849 −24794.6 −1.00230
850850 0 0
851851 29589.3 1.19190
852852 0 0
853853 8649.24 0.347180 0.173590 0.984818i 0.444463π-0.444463\pi
0.173590 + 0.984818i 0.444463π0.444463\pi
854854 0 0
855855 82835.3 3.31334
856856 0 0
857857 −16342.9 −0.651413 −0.325707 0.945471i 0.605602π-0.605602\pi
−0.325707 + 0.945471i 0.605602π0.605602\pi
858858 0 0
859859 29613.4 1.17625 0.588123 0.808772i 0.299867π-0.299867\pi
0.588123 + 0.808772i 0.299867π0.299867\pi
860860 0 0
861861 −3117.21 −0.123385
862862 0 0
863863 −20366.7 −0.803348 −0.401674 0.915783i 0.631571π-0.631571\pi
−0.401674 + 0.915783i 0.631571π0.631571\pi
864864 0 0
865865 −57955.5 −2.27809
866866 0 0
867867 −57717.6 −2.26089
868868 0 0
869869 −10904.7 −0.425680
870870 0 0
871871 −5763.92 −0.224228
872872 0 0
873873 22411.7 0.868867
874874 0 0
875875 37704.3 1.45673
876876 0 0
877877 −35210.6 −1.35573 −0.677866 0.735186i 0.737095π-0.737095\pi
−0.677866 + 0.735186i 0.737095π0.737095\pi
878878 0 0
879879 −33803.8 −1.29713
880880 0 0
881881 −7354.03 −0.281230 −0.140615 0.990064i 0.544908π-0.544908\pi
−0.140615 + 0.990064i 0.544908π0.544908\pi
882882 0 0
883883 28837.9 1.09906 0.549531 0.835473i 0.314806π-0.314806\pi
0.549531 + 0.835473i 0.314806π0.314806\pi
884884 0 0
885885 47164.3 1.79142
886886 0 0
887887 10861.0 0.411136 0.205568 0.978643i 0.434096π-0.434096\pi
0.205568 + 0.978643i 0.434096π0.434096\pi
888888 0 0
889889 −2389.64 −0.0901528
890890 0 0
891891 23291.3 0.875744
892892 0 0
893893 −12005.7 −0.449895
894894 0 0
895895 −45625.6 −1.70402
896896 0 0
897897 13285.9 0.494542
898898 0 0
899899 16865.9 0.625706
900900 0 0
901901 63672.3 2.35431
902902 0 0
903903 13399.3 0.493798
904904 0 0
905905 44102.7 1.61992
906906 0 0
907907 18682.8 0.683961 0.341980 0.939707i 0.388902π-0.388902\pi
0.341980 + 0.939707i 0.388902π0.388902\pi
908908 0 0
909909 −18898.6 −0.689580
910910 0 0
911911 −34392.2 −1.25078 −0.625392 0.780311i 0.715061π-0.715061\pi
−0.625392 + 0.780311i 0.715061π0.715061\pi
912912 0 0
913913 −40517.4 −1.46871
914914 0 0
915915 14104.3 0.509588
916916 0 0
917917 −2835.10 −0.102097
918918 0 0
919919 −14715.8 −0.528216 −0.264108 0.964493i 0.585078π-0.585078\pi
−0.264108 + 0.964493i 0.585078π0.585078\pi
920920 0 0
921921 −4507.51 −0.161268
922922 0 0
923923 −90.0943 −0.00321288
924924 0 0
925925 90847.3 3.22923
926926 0 0
927927 17105.6 0.606065
928928 0 0
929929 −36204.2 −1.27860 −0.639300 0.768957i 0.720776π-0.720776\pi
−0.639300 + 0.768957i 0.720776π0.720776\pi
930930 0 0
931931 −5772.39 −0.203203
932932 0 0
933933 57415.8 2.01469
934934 0 0
935935 −99316.6 −3.47380
936936 0 0
937937 −43636.5 −1.52139 −0.760694 0.649110i 0.775141π-0.775141\pi
−0.760694 + 0.649110i 0.775141π0.775141\pi
938938 0 0
939939 −50962.7 −1.77114
940940 0 0
941941 −4751.54 −0.164608 −0.0823038 0.996607i 0.526228π-0.526228\pi
−0.0823038 + 0.996607i 0.526228π0.526228\pi
942942 0 0
943943 −6961.54 −0.240402
944944 0 0
945945 −5569.52 −0.191721
946946 0 0
947947 −49387.3 −1.69469 −0.847344 0.531044i 0.821800π-0.821800\pi
−0.847344 + 0.531044i 0.821800π0.821800\pi
948948 0 0
949949 −3038.16 −0.103923
950950 0 0
951951 55269.2 1.88457
952952 0 0
953953 46336.1 1.57500 0.787499 0.616316i 0.211375π-0.211375\pi
0.787499 + 0.616316i 0.211375π0.211375\pi
954954 0 0
955955 9807.72 0.332325
956956 0 0
957957 −28537.2 −0.963924
958958 0 0
959959 −11132.8 −0.374866
960960 0 0
961961 3176.38 0.106622
962962 0 0
963963 20924.2 0.700180
964964 0 0
965965 112304. 3.74633
966966 0 0
967967 21078.1 0.700957 0.350479 0.936571i 0.386019π-0.386019\pi
0.350479 + 0.936571i 0.386019π0.386019\pi
968968 0 0
969969 −100681. −3.33781
970970 0 0
971971 −27225.5 −0.899802 −0.449901 0.893079i 0.648541π-0.648541\pi
−0.449901 + 0.893079i 0.648541π0.648541\pi
972972 0 0
973973 −4239.26 −0.139676
974974 0 0
975975 40791.4 1.33987
976976 0 0
977977 4699.41 0.153887 0.0769434 0.997035i 0.475484π-0.475484\pi
0.0769434 + 0.997035i 0.475484π0.475484\pi
978978 0 0
979979 −29293.6 −0.956310
980980 0 0
981981 7417.96 0.241424
982982 0 0
983983 48128.7 1.56161 0.780807 0.624773i 0.214808π-0.214808\pi
0.780807 + 0.624773i 0.214808π0.214808\pi
984984 0 0
985985 69924.5 2.26191
986986 0 0
987987 5464.74 0.176236
988988 0 0
989989 29924.0 0.962111
990990 0 0
991991 −214.168 −0.00686506 −0.00343253 0.999994i 0.501093π-0.501093\pi
−0.00343253 + 0.999994i 0.501093π0.501093\pi
992992 0 0
993993 8608.96 0.275123
994994 0 0
995995 11982.5 0.381780
996996 0 0
997997 12678.3 0.402735 0.201368 0.979516i 0.435461π-0.435461\pi
0.201368 + 0.979516i 0.435461π0.435461\pi
998998 0 0
999999 −8857.20 −0.280510
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 1792.4.a.c.1.1 2
4.3 odd 2 1792.4.a.a.1.2 2
8.3 odd 2 1792.4.a.d.1.1 2
8.5 even 2 1792.4.a.b.1.2 2
16.3 odd 4 448.4.b.a.225.3 yes 4
16.5 even 4 448.4.b.b.225.3 yes 4
16.11 odd 4 448.4.b.a.225.2 4
16.13 even 4 448.4.b.b.225.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
448.4.b.a.225.2 4 16.11 odd 4
448.4.b.a.225.3 yes 4 16.3 odd 4
448.4.b.b.225.2 yes 4 16.13 even 4
448.4.b.b.225.3 yes 4 16.5 even 4
1792.4.a.a.1.2 2 4.3 odd 2
1792.4.a.b.1.2 2 8.5 even 2
1792.4.a.c.1.1 2 1.1 even 1 trivial
1792.4.a.d.1.1 2 8.3 odd 2