Properties

Label 2200.2.a.y.1.1
Level 22002200
Weight 22
Character 2200.1
Self dual yes
Analytic conductor 17.56717.567
Analytic rank 00
Dimension 44
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [2200,2,Mod(1,2200)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2200, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2200.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 2200=235211 2200 = 2^{3} \cdot 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2200.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,1,0,0,0,1,0,7,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 17.567088444717.5670884447
Analytic rank: 00
Dimension: 44
Coefficient field: 4.4.54764.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4x39x2+3x+2 x^{4} - x^{3} - 9x^{2} + 3x + 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 440)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 2.67673-2.67673 of defining polynomial
Character χ\chi == 2200.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q2.67673q3+4.38559q7+4.16490q9+1.00000q11+4.00000q13+5.87995q170.526486q1911.7391q21+6.15025q233.11812q270.967873q299.60629q312.67673q33+1.76466q3710.7069q39+2.50564q413.85911q434.91208q47+12.2334q4915.7391q515.29767q53+1.40926q572.63841q59+8.96787q61+18.2655q637.97440q6716.4626q69+13.8718q71+12.7712q73+4.38559q7713.2768q794.14832q817.61901q83+2.59074q87+2.83510q89+17.5424q91+25.7135q9310.4800q97+4.16490q99+O(q100)q-2.67673 q^{3} +4.38559 q^{7} +4.16490 q^{9} +1.00000 q^{11} +4.00000 q^{13} +5.87995 q^{17} -0.526486 q^{19} -11.7391 q^{21} +6.15025 q^{23} -3.11812 q^{27} -0.967873 q^{29} -9.60629 q^{31} -2.67673 q^{33} +1.76466 q^{37} -10.7069 q^{39} +2.50564 q^{41} -3.85911 q^{43} -4.91208 q^{47} +12.2334 q^{49} -15.7391 q^{51} -5.29767 q^{53} +1.40926 q^{57} -2.63841 q^{59} +8.96787 q^{61} +18.2655 q^{63} -7.97440 q^{67} -16.4626 q^{69} +13.8718 q^{71} +12.7712 q^{73} +4.38559 q^{77} -13.2768 q^{79} -4.14832 q^{81} -7.61901 q^{83} +2.59074 q^{87} +2.83510 q^{89} +17.5424 q^{91} +25.7135 q^{93} -10.4800 q^{97} +4.16490 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+q3+q7+7q9+4q11+16q13+7q179q197q21+6q23+13q27+3q2915q31+q33+5q37+4q39+10q41+8q4310q47+9q49++7q99+O(q100) 4 q + q^{3} + q^{7} + 7 q^{9} + 4 q^{11} + 16 q^{13} + 7 q^{17} - 9 q^{19} - 7 q^{21} + 6 q^{23} + 13 q^{27} + 3 q^{29} - 15 q^{31} + q^{33} + 5 q^{37} + 4 q^{39} + 10 q^{41} + 8 q^{43} - 10 q^{47} + 9 q^{49}+ \cdots + 7 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 −2.67673 −1.54541 −0.772706 0.634764i 0.781097π-0.781097\pi
−0.772706 + 0.634764i 0.781097π0.781097\pi
44 0 0
55 0 0
66 0 0
77 4.38559 1.65760 0.828799 0.559546i 0.189025π-0.189025\pi
0.828799 + 0.559546i 0.189025π0.189025\pi
88 0 0
99 4.16490 1.38830
1010 0 0
1111 1.00000 0.301511
1212 0 0
1313 4.00000 1.10940 0.554700 0.832050i 0.312833π-0.312833\pi
0.554700 + 0.832050i 0.312833π0.312833\pi
1414 0 0
1515 0 0
1616 0 0
1717 5.87995 1.42610 0.713049 0.701114i 0.247314π-0.247314\pi
0.713049 + 0.701114i 0.247314π0.247314\pi
1818 0 0
1919 −0.526486 −0.120784 −0.0603920 0.998175i 0.519235π-0.519235\pi
−0.0603920 + 0.998175i 0.519235π0.519235\pi
2020 0 0
2121 −11.7391 −2.56167
2222 0 0
2323 6.15025 1.28242 0.641208 0.767367i 0.278434π-0.278434\pi
0.641208 + 0.767367i 0.278434π0.278434\pi
2424 0 0
2525 0 0
2626 0 0
2727 −3.11812 −0.600083
2828 0 0
2929 −0.967873 −0.179730 −0.0898648 0.995954i 0.528643π-0.528643\pi
−0.0898648 + 0.995954i 0.528643π0.528643\pi
3030 0 0
3131 −9.60629 −1.72534 −0.862670 0.505767i 0.831209π-0.831209\pi
−0.862670 + 0.505767i 0.831209π0.831209\pi
3232 0 0
3333 −2.67673 −0.465959
3434 0 0
3535 0 0
3636 0 0
3737 1.76466 0.290108 0.145054 0.989424i 0.453664π-0.453664\pi
0.145054 + 0.989424i 0.453664π0.453664\pi
3838 0 0
3939 −10.7069 −1.71448
4040 0 0
4141 2.50564 0.391315 0.195658 0.980672i 0.437316π-0.437316\pi
0.195658 + 0.980672i 0.437316π0.437316\pi
4242 0 0
4343 −3.85911 −0.588508 −0.294254 0.955727i 0.595071π-0.595071\pi
−0.294254 + 0.955727i 0.595071π0.595071\pi
4444 0 0
4545 0 0
4646 0 0
4747 −4.91208 −0.716500 −0.358250 0.933626i 0.616626π-0.616626\pi
−0.358250 + 0.933626i 0.616626π0.616626\pi
4848 0 0
4949 12.2334 1.74763
5050 0 0
5151 −15.7391 −2.20391
5252 0 0
5353 −5.29767 −0.727691 −0.363845 0.931459i 0.618536π-0.618536\pi
−0.363845 + 0.931459i 0.618536π0.618536\pi
5454 0 0
5555 0 0
5656 0 0
5757 1.40926 0.186661
5858 0 0
5959 −2.63841 −0.343492 −0.171746 0.985141i 0.554941π-0.554941\pi
−0.171746 + 0.985141i 0.554941π0.554941\pi
6060 0 0
6161 8.96787 1.14822 0.574109 0.818779i 0.305348π-0.305348\pi
0.574109 + 0.818779i 0.305348π0.305348\pi
6262 0 0
6363 18.2655 2.30124
6464 0 0
6565 0 0
6666 0 0
6767 −7.97440 −0.974228 −0.487114 0.873338i 0.661950π-0.661950\pi
−0.487114 + 0.873338i 0.661950π0.661950\pi
6868 0 0
6969 −16.4626 −1.98186
7070 0 0
7171 13.8718 1.64628 0.823142 0.567836i 0.192219π-0.192219\pi
0.823142 + 0.567836i 0.192219π0.192219\pi
7272 0 0
7373 12.7712 1.49475 0.747377 0.664400i 0.231313π-0.231313\pi
0.747377 + 0.664400i 0.231313π0.231313\pi
7474 0 0
7575 0 0
7676 0 0
7777 4.38559 0.499785
7878 0 0
7979 −13.2768 −1.49376 −0.746880 0.664959i 0.768449π-0.768449\pi
−0.746880 + 0.664959i 0.768449π0.768449\pi
8080 0 0
8181 −4.14832 −0.460924
8282 0 0
8383 −7.61901 −0.836295 −0.418147 0.908379i 0.637320π-0.637320\pi
−0.418147 + 0.908379i 0.637320π0.637320\pi
8484 0 0
8585 0 0
8686 0 0
8787 2.59074 0.277756
8888 0 0
8989 2.83510 0.300520 0.150260 0.988646i 0.451989π-0.451989\pi
0.150260 + 0.988646i 0.451989π0.451989\pi
9090 0 0
9191 17.5424 1.83894
9292 0 0
9393 25.7135 2.66636
9494 0 0
9595 0 0
9696 0 0
9797 −10.4800 −1.06409 −0.532044 0.846717i 0.678576π-0.678576\pi
−0.532044 + 0.846717i 0.678576π0.678576\pi
9898 0 0
9999 4.16490 0.418588
100100 0 0
101101 8.70693 0.866372 0.433186 0.901305i 0.357389π-0.357389\pi
0.433186 + 0.901305i 0.357389π0.357389\pi
102102 0 0
103103 15.6190 1.53899 0.769493 0.638655i 0.220509π-0.220509\pi
0.769493 + 0.638655i 0.220509π0.220509\pi
104104 0 0
105105 0 0
106106 0 0
107107 7.08792 0.685215 0.342608 0.939479i 0.388690π-0.388690\pi
0.342608 + 0.939479i 0.388690π0.388690\pi
108108 0 0
109109 −15.5424 −1.48869 −0.744344 0.667796i 0.767238π-0.767238\pi
−0.744344 + 0.667796i 0.767238π0.767238\pi
110110 0 0
111111 −4.72351 −0.448336
112112 0 0
113113 8.11530 0.763423 0.381711 0.924282i 0.375335π-0.375335\pi
0.381711 + 0.924282i 0.375335π0.375335\pi
114114 0 0
115115 0 0
116116 0 0
117117 16.6596 1.54018
118118 0 0
119119 25.7871 2.36390
120120 0 0
121121 1.00000 0.0909091
122122 0 0
123123 −6.70693 −0.604744
124124 0 0
125125 0 0
126126 0 0
127127 4.32980 0.384207 0.192104 0.981375i 0.438469π-0.438469\pi
0.192104 + 0.981375i 0.438469π0.438469\pi
128128 0 0
129129 10.3298 0.909488
130130 0 0
131131 −17.6748 −1.54425 −0.772127 0.635468i 0.780807π-0.780807\pi
−0.772127 + 0.635468i 0.780807π0.780807\pi
132132 0 0
133133 −2.30895 −0.200211
134134 0 0
135135 0 0
136136 0 0
137137 18.4800 1.57886 0.789428 0.613843i 0.210377π-0.210377\pi
0.789428 + 0.613843i 0.210377π0.210377\pi
138138 0 0
139139 −5.55861 −0.471475 −0.235738 0.971817i 0.575751π-0.575751\pi
−0.235738 + 0.971817i 0.575751π0.575751\pi
140140 0 0
141141 13.1483 1.10729
142142 0 0
143143 4.00000 0.334497
144144 0 0
145145 0 0
146146 0 0
147147 −32.7456 −2.70081
148148 0 0
149149 20.9516 1.71642 0.858212 0.513295i 0.171575π-0.171575\pi
0.858212 + 0.513295i 0.171575π0.171575\pi
150150 0 0
151151 −1.67020 −0.135919 −0.0679596 0.997688i 0.521649π-0.521649\pi
−0.0679596 + 0.997688i 0.521649π0.521649\pi
152152 0 0
153153 24.4894 1.97985
154154 0 0
155155 0 0
156156 0 0
157157 −8.94228 −0.713671 −0.356836 0.934167i 0.616144π-0.616144\pi
−0.356836 + 0.934167i 0.616144π0.616144\pi
158158 0 0
159159 14.1804 1.12458
160160 0 0
161161 26.9725 2.12573
162162 0 0
163163 −9.43856 −0.739285 −0.369643 0.929174i 0.620520π-0.620520\pi
−0.369643 + 0.929174i 0.620520π0.620520\pi
164164 0 0
165165 0 0
166166 0 0
167167 8.96787 0.693955 0.346977 0.937873i 0.387208π-0.387208\pi
0.346977 + 0.937873i 0.387208π0.387208\pi
168168 0 0
169169 3.00000 0.230769
170170 0 0
171171 −2.19276 −0.167684
172172 0 0
173173 2.64653 0.201212 0.100606 0.994926i 0.467922π-0.467922\pi
0.100606 + 0.994926i 0.467922π0.467922\pi
174174 0 0
175175 0 0
176176 0 0
177177 7.06232 0.530837
178178 0 0
179179 20.2225 1.51150 0.755749 0.654861i 0.227273π-0.227273\pi
0.755749 + 0.654861i 0.227273π0.227273\pi
180180 0 0
181181 15.3453 1.14061 0.570305 0.821433i 0.306825π-0.306825\pi
0.570305 + 0.821433i 0.306825π0.306825\pi
182182 0 0
183183 −24.0046 −1.77447
184184 0 0
185185 0 0
186186 0 0
187187 5.87995 0.429985
188188 0 0
189189 −13.6748 −0.994696
190190 0 0
191191 −5.62713 −0.407165 −0.203582 0.979058i 0.565258π-0.565258\pi
−0.203582 + 0.979058i 0.565258π0.565258\pi
192192 0 0
193193 −7.23342 −0.520673 −0.260336 0.965518i 0.583833π-0.583833\pi
−0.260336 + 0.965518i 0.583833π0.583833\pi
194194 0 0
195195 0 0
196196 0 0
197197 5.35347 0.381419 0.190709 0.981647i 0.438921π-0.438921\pi
0.190709 + 0.981647i 0.438921π0.438921\pi
198198 0 0
199199 7.23342 0.512763 0.256382 0.966576i 0.417470π-0.417470\pi
0.256382 + 0.966576i 0.417470π0.417470\pi
200200 0 0
201201 21.3453 1.50558
202202 0 0
203203 −4.24470 −0.297919
204204 0 0
205205 0 0
206206 0 0
207207 25.6152 1.78038
208208 0 0
209209 −0.526486 −0.0364178
210210 0 0
211211 −12.2447 −0.842960 −0.421480 0.906838i 0.638489π-0.638489\pi
−0.421480 + 0.906838i 0.638489π0.638489\pi
212212 0 0
213213 −37.1312 −2.54419
214214 0 0
215215 0 0
216216 0 0
217217 −42.1292 −2.85992
218218 0 0
219219 −34.1850 −2.31001
220220 0 0
221221 23.5198 1.58211
222222 0 0
223223 19.4525 1.30264 0.651318 0.758805i 0.274216π-0.274216\pi
0.651318 + 0.758805i 0.274216π0.274216\pi
224224 0 0
225225 0 0
226226 0 0
227227 3.90080 0.258905 0.129452 0.991586i 0.458678π-0.458678\pi
0.129452 + 0.991586i 0.458678π0.458678\pi
228228 0 0
229229 13.4096 0.886131 0.443066 0.896489i 0.353891π-0.353891\pi
0.443066 + 0.896489i 0.353891π0.353891\pi
230230 0 0
231231 −11.7391 −0.772373
232232 0 0
233233 −3.36192 −0.220247 −0.110123 0.993918i 0.535125π-0.535125\pi
−0.110123 + 0.993918i 0.535125π0.535125\pi
234234 0 0
235235 0 0
236236 0 0
237237 35.5385 2.30847
238238 0 0
239239 −13.2768 −0.858806 −0.429403 0.903113i 0.641276π-0.641276\pi
−0.429403 + 0.903113i 0.641276π0.641276\pi
240240 0 0
241241 −17.7437 −1.14297 −0.571485 0.820613i 0.693632π-0.693632\pi
−0.571485 + 0.820613i 0.693632π0.693632\pi
242242 0 0
243243 20.4583 1.31240
244244 0 0
245245 0 0
246246 0 0
247247 −2.10594 −0.133998
248248 0 0
249249 20.3940 1.29242
250250 0 0
251251 8.57416 0.541196 0.270598 0.962692i 0.412779π-0.412779\pi
0.270598 + 0.962692i 0.412779π0.412779\pi
252252 0 0
253253 6.15025 0.386663
254254 0 0
255255 0 0
256256 0 0
257257 −2.70693 −0.168854 −0.0844269 0.996430i 0.526906π-0.526906\pi
−0.0844269 + 0.996430i 0.526906π0.526906\pi
258258 0 0
259259 7.73906 0.480882
260260 0 0
261261 −4.03109 −0.249518
262262 0 0
263263 14.3213 0.883092 0.441546 0.897239i 0.354430π-0.354430\pi
0.441546 + 0.897239i 0.354430π0.354430\pi
264264 0 0
265265 0 0
266266 0 0
267267 −7.58881 −0.464428
268268 0 0
269269 −11.9357 −0.727735 −0.363868 0.931451i 0.618544π-0.618544\pi
−0.363868 + 0.931451i 0.618544π0.618544\pi
270270 0 0
271271 −24.4195 −1.48338 −0.741689 0.670744i 0.765975π-0.765975\pi
−0.741689 + 0.670744i 0.765975π0.765975\pi
272272 0 0
273273 −46.9562 −2.84192
274274 0 0
275275 0 0
276276 0 0
277277 −23.0074 −1.38238 −0.691191 0.722672i 0.742914π-0.742914\pi
−0.691191 + 0.722672i 0.742914π0.742914\pi
278278 0 0
279279 −40.0092 −2.39529
280280 0 0
281281 −10.6596 −0.635898 −0.317949 0.948108i 0.602994π-0.602994\pi
−0.317949 + 0.948108i 0.602994π0.602994\pi
282282 0 0
283283 10.3771 0.616857 0.308428 0.951248i 0.400197π-0.400197\pi
0.308428 + 0.951248i 0.400197π0.400197\pi
284284 0 0
285285 0 0
286286 0 0
287287 10.9887 0.648644
288288 0 0
289289 17.5738 1.03375
290290 0 0
291291 28.0523 1.64445
292292 0 0
293293 −22.7069 −1.32655 −0.663277 0.748374i 0.730835π-0.730835\pi
−0.663277 + 0.748374i 0.730835π0.730835\pi
294294 0 0
295295 0 0
296296 0 0
297297 −3.11812 −0.180932
298298 0 0
299299 24.6010 1.42271
300300 0 0
301301 −16.9245 −0.975510
302302 0 0
303303 −23.3061 −1.33890
304304 0 0
305305 0 0
306306 0 0
307307 −5.49436 −0.313580 −0.156790 0.987632i 0.550115π-0.550115\pi
−0.156790 + 0.987632i 0.550115π0.550115\pi
308308 0 0
309309 −41.8079 −2.37837
310310 0 0
311311 −24.2447 −1.37479 −0.687395 0.726283i 0.741246π-0.741246\pi
−0.687395 + 0.726283i 0.741246π0.741246\pi
312312 0 0
313313 −11.7562 −0.664500 −0.332250 0.943191i 0.607808π-0.607808\pi
−0.332250 + 0.943191i 0.607808π0.607808\pi
314314 0 0
315315 0 0
316316 0 0
317317 −9.05387 −0.508516 −0.254258 0.967136i 0.581831π-0.581831\pi
−0.254258 + 0.967136i 0.581831π0.581831\pi
318318 0 0
319319 −0.967873 −0.0541905
320320 0 0
321321 −18.9725 −1.05894
322322 0 0
323323 −3.09571 −0.172250
324324 0 0
325325 0 0
326326 0 0
327327 41.6028 2.30064
328328 0 0
329329 −21.5424 −1.18767
330330 0 0
331331 −3.29733 −0.181238 −0.0906190 0.995886i 0.528885π-0.528885\pi
−0.0906190 + 0.995886i 0.528885π0.528885\pi
332332 0 0
333333 7.34961 0.402756
334334 0 0
335335 0 0
336336 0 0
337337 −3.17302 −0.172845 −0.0864227 0.996259i 0.527544π-0.527544\pi
−0.0864227 + 0.996259i 0.527544π0.527544\pi
338338 0 0
339339 −21.7225 −1.17980
340340 0 0
341341 −9.60629 −0.520210
342342 0 0
343343 22.9516 1.23927
344344 0 0
345345 0 0
346346 0 0
347347 −4.44139 −0.238426 −0.119213 0.992869i 0.538037π-0.538037\pi
−0.119213 + 0.992869i 0.538037π0.538037\pi
348348 0 0
349349 29.2380 1.56508 0.782538 0.622603i 0.213925π-0.213925\pi
0.782538 + 0.622603i 0.213925π0.213925\pi
350350 0 0
351351 −12.4725 −0.665732
352352 0 0
353353 1.04927 0.0558469 0.0279234 0.999610i 0.491111π-0.491111\pi
0.0279234 + 0.999610i 0.491111π0.491111\pi
354354 0 0
355355 0 0
356356 0 0
357357 −69.0251 −3.65319
358358 0 0
359359 9.69565 0.511717 0.255858 0.966714i 0.417642π-0.417642\pi
0.255858 + 0.966714i 0.417642π0.417642\pi
360360 0 0
361361 −18.7228 −0.985411
362362 0 0
363363 −2.67673 −0.140492
364364 0 0
365365 0 0
366366 0 0
367367 11.3921 0.594664 0.297332 0.954774i 0.403903π-0.403903\pi
0.297332 + 0.954774i 0.403903π0.403903\pi
368368 0 0
369369 10.4357 0.543263
370370 0 0
371371 −23.2334 −1.20622
372372 0 0
373373 −6.47634 −0.335332 −0.167666 0.985844i 0.553623π-0.553623\pi
−0.167666 + 0.985844i 0.553623π0.553623\pi
374374 0 0
375375 0 0
376376 0 0
377377 −3.87149 −0.199392
378378 0 0
379379 −33.4993 −1.72074 −0.860372 0.509667i 0.829768π-0.829768\pi
−0.860372 + 0.509667i 0.829768π0.829768\pi
380380 0 0
381381 −11.5897 −0.593759
382382 0 0
383383 30.8702 1.57740 0.788698 0.614781i 0.210756π-0.210756\pi
0.788698 + 0.614781i 0.210756π0.210756\pi
384384 0 0
385385 0 0
386386 0 0
387387 −16.0728 −0.817026
388388 0 0
389389 −23.3453 −1.18366 −0.591828 0.806064i 0.701594π-0.701594\pi
−0.591828 + 0.806064i 0.701594π0.701594\pi
390390 0 0
391391 36.1632 1.82885
392392 0 0
393393 47.3107 2.38651
394394 0 0
395395 0 0
396396 0 0
397397 19.4781 0.977579 0.488789 0.872402i 0.337439π-0.337439\pi
0.488789 + 0.872402i 0.337439π0.337439\pi
398398 0 0
399399 6.18045 0.309409
400400 0 0
401401 2.24470 0.112095 0.0560474 0.998428i 0.482150π-0.482150\pi
0.0560474 + 0.998428i 0.482150π0.482150\pi
402402 0 0
403403 −38.4251 −1.91409
404404 0 0
405405 0 0
406406 0 0
407407 1.76466 0.0874707
408408 0 0
409409 29.4781 1.45760 0.728799 0.684727i 0.240079π-0.240079\pi
0.728799 + 0.684727i 0.240079π0.240079\pi
410410 0 0
411411 −49.4661 −2.43998
412412 0 0
413413 −11.5710 −0.569372
414414 0 0
415415 0 0
416416 0 0
417417 14.8789 0.728624
418418 0 0
419419 7.64831 0.373644 0.186822 0.982394i 0.440181π-0.440181\pi
0.186822 + 0.982394i 0.440181π0.440181\pi
420420 0 0
421421 29.4781 1.43668 0.718338 0.695695i 0.244903π-0.244903\pi
0.718338 + 0.695695i 0.244903π0.244903\pi
422422 0 0
423423 −20.4583 −0.994717
424424 0 0
425425 0 0
426426 0 0
427427 39.3294 1.90328
428428 0 0
429429 −10.7069 −0.516935
430430 0 0
431431 −2.08970 −0.100657 −0.0503286 0.998733i 0.516027π-0.516027\pi
−0.0503286 + 0.998733i 0.516027π0.516027\pi
432432 0 0
433433 −5.17777 −0.248828 −0.124414 0.992230i 0.539705π-0.539705\pi
−0.124414 + 0.992230i 0.539705π0.539705\pi
434434 0 0
435435 0 0
436436 0 0
437437 −3.23802 −0.154895
438438 0 0
439439 27.6066 1.31759 0.658796 0.752322i 0.271066π-0.271066\pi
0.658796 + 0.752322i 0.271066π0.271066\pi
440440 0 0
441441 50.9509 2.42623
442442 0 0
443443 −14.1502 −0.672299 −0.336149 0.941809i 0.609125π-0.609125\pi
−0.336149 + 0.941809i 0.609125π0.609125\pi
444444 0 0
445445 0 0
446446 0 0
447447 −56.0819 −2.65258
448448 0 0
449449 −6.46257 −0.304987 −0.152494 0.988304i 0.548730π-0.548730\pi
−0.152494 + 0.988304i 0.548730π0.548730\pi
450450 0 0
451451 2.50564 0.117986
452452 0 0
453453 4.47069 0.210051
454454 0 0
455455 0 0
456456 0 0
457457 −38.5582 −1.80368 −0.901839 0.432071i 0.857783π-0.857783\pi
−0.901839 + 0.432071i 0.857783π0.857783\pi
458458 0 0
459459 −18.3344 −0.855776
460460 0 0
461461 −18.4234 −0.858064 −0.429032 0.903289i 0.641145π-0.641145\pi
−0.429032 + 0.903289i 0.641145π0.641145\pi
462462 0 0
463463 7.09163 0.329576 0.164788 0.986329i 0.447306π-0.447306\pi
0.164788 + 0.986329i 0.447306π0.447306\pi
464464 0 0
465465 0 0
466466 0 0
467467 40.4328 1.87101 0.935503 0.353319i 0.114947π-0.114947\pi
0.935503 + 0.353319i 0.114947π0.114947\pi
468468 0 0
469469 −34.9725 −1.61488
470470 0 0
471471 23.9361 1.10292
472472 0 0
473473 −3.85911 −0.177442
474474 0 0
475475 0 0
476476 0 0
477477 −22.0643 −1.01025
478478 0 0
479479 −10.7486 −0.491117 −0.245559 0.969382i 0.578971π-0.578971\pi
−0.245559 + 0.969382i 0.578971π0.578971\pi
480480 0 0
481481 7.05862 0.321845
482482 0 0
483483 −72.1981 −3.28513
484484 0 0
485485 0 0
486486 0 0
487487 −38.6396 −1.75093 −0.875465 0.483282i 0.839445π-0.839445\pi
−0.875465 + 0.483282i 0.839445π0.839445\pi
488488 0 0
489489 25.2645 1.14250
490490 0 0
491491 32.9460 1.48683 0.743416 0.668830i 0.233204π-0.233204\pi
0.743416 + 0.668830i 0.233204π0.233204\pi
492492 0 0
493493 −5.69105 −0.256312
494494 0 0
495495 0 0
496496 0 0
497497 60.8362 2.72888
498498 0 0
499499 26.9562 1.20673 0.603363 0.797466i 0.293827π-0.293827\pi
0.603363 + 0.797466i 0.293827π0.293827\pi
500500 0 0
501501 −24.0046 −1.07245
502502 0 0
503503 14.0766 0.627646 0.313823 0.949481i 0.398390π-0.398390\pi
0.313823 + 0.949481i 0.398390π0.398390\pi
504504 0 0
505505 0 0
506506 0 0
507507 −8.03020 −0.356634
508508 0 0
509509 1.28109 0.0567833 0.0283917 0.999597i 0.490961π-0.490961\pi
0.0283917 + 0.999597i 0.490961π0.490961\pi
510510 0 0
511511 56.0092 2.47770
512512 0 0
513513 1.64165 0.0724804
514514 0 0
515515 0 0
516516 0 0
517517 −4.91208 −0.216033
518518 0 0
519519 −7.08407 −0.310956
520520 0 0
521521 −29.2394 −1.28100 −0.640501 0.767958i 0.721273π-0.721273\pi
−0.640501 + 0.767958i 0.721273π0.721273\pi
522522 0 0
523523 −2.50564 −0.109564 −0.0547820 0.998498i 0.517446π-0.517446\pi
−0.0547820 + 0.998498i 0.517446π0.517446\pi
524524 0 0
525525 0 0
526526 0 0
527527 −56.4845 −2.46050
528528 0 0
529529 14.8255 0.644589
530530 0 0
531531 −10.9887 −0.476870
532532 0 0
533533 10.0226 0.434125
534534 0 0
535535 0 0
536536 0 0
537537 −54.1301 −2.33589
538538 0 0
539539 12.2334 0.526931
540540 0 0
541541 −3.27222 −0.140684 −0.0703420 0.997523i 0.522409π-0.522409\pi
−0.0703420 + 0.997523i 0.522409π0.522409\pi
542542 0 0
543543 −41.0754 −1.76271
544544 0 0
545545 0 0
546546 0 0
547547 3.03673 0.129841 0.0649205 0.997890i 0.479321π-0.479321\pi
0.0649205 + 0.997890i 0.479321π0.479321\pi
548548 0 0
549549 37.3503 1.59407
550550 0 0
551551 0.509572 0.0217085
552552 0 0
553553 −58.2267 −2.47605
554554 0 0
555555 0 0
556556 0 0
557557 −1.52366 −0.0645596 −0.0322798 0.999479i 0.510277π-0.510277\pi
−0.0322798 + 0.999479i 0.510277π0.510277\pi
558558 0 0
559559 −15.4364 −0.652891
560560 0 0
561561 −15.7391 −0.664504
562562 0 0
563563 27.9195 1.17667 0.588333 0.808618i 0.299784π-0.299784\pi
0.588333 + 0.808618i 0.299784π0.299784\pi
564564 0 0
565565 0 0
566566 0 0
567567 −18.1928 −0.764027
568568 0 0
569569 −13.7437 −0.576164 −0.288082 0.957606i 0.593018π-0.593018\pi
−0.288082 + 0.957606i 0.593018π0.593018\pi
570570 0 0
571571 −1.42618 −0.0596836 −0.0298418 0.999555i 0.509500π-0.509500\pi
−0.0298418 + 0.999555i 0.509500π0.509500\pi
572572 0 0
573573 15.0623 0.629238
574574 0 0
575575 0 0
576576 0 0
577577 6.35154 0.264418 0.132209 0.991222i 0.457793π-0.457793\pi
0.132209 + 0.991222i 0.457793π0.457793\pi
578578 0 0
579579 19.3619 0.804654
580580 0 0
581581 −33.4139 −1.38624
582582 0 0
583583 −5.29767 −0.219407
584584 0 0
585585 0 0
586586 0 0
587587 22.1681 0.914974 0.457487 0.889216i 0.348750π-0.348750\pi
0.457487 + 0.889216i 0.348750π0.348750\pi
588588 0 0
589589 5.05757 0.208394
590590 0 0
591591 −14.3298 −0.589449
592592 0 0
593593 1.05297 0.0432403 0.0216202 0.999766i 0.493118π-0.493118\pi
0.0216202 + 0.999766i 0.493118π0.493118\pi
594594 0 0
595595 0 0
596596 0 0
597597 −19.3619 −0.792431
598598 0 0
599599 −5.12747 −0.209503 −0.104751 0.994498i 0.533405π-0.533405\pi
−0.104751 + 0.994498i 0.533405π0.533405\pi
600600 0 0
601601 −1.71821 −0.0700874 −0.0350437 0.999386i 0.511157π-0.511157\pi
−0.0350437 + 0.999386i 0.511157π0.511157\pi
602602 0 0
603603 −33.2126 −1.35252
604604 0 0
605605 0 0
606606 0 0
607607 4.42728 0.179698 0.0898489 0.995955i 0.471362π-0.471362\pi
0.0898489 + 0.995955i 0.471362π0.471362\pi
608608 0 0
609609 11.3619 0.460408
610610 0 0
611611 −19.6483 −0.794886
612612 0 0
613613 −33.8334 −1.36652 −0.683258 0.730177i 0.739438π-0.739438\pi
−0.683258 + 0.730177i 0.739438π0.739438\pi
614614 0 0
615615 0 0
616616 0 0
617617 40.3778 1.62555 0.812775 0.582578i 0.197956π-0.197956\pi
0.812775 + 0.582578i 0.197956π0.197956\pi
618618 0 0
619619 −1.62713 −0.0653999 −0.0327000 0.999465i 0.510411π-0.510411\pi
−0.0327000 + 0.999465i 0.510411π0.510411\pi
620620 0 0
621621 −19.1772 −0.769555
622622 0 0
623623 12.4336 0.498142
624624 0 0
625625 0 0
626626 0 0
627627 1.40926 0.0562805
628628 0 0
629629 10.3761 0.413722
630630 0 0
631631 3.71223 0.147781 0.0738907 0.997266i 0.476458π-0.476458\pi
0.0738907 + 0.997266i 0.476458π0.476458\pi
632632 0 0
633633 32.7758 1.30272
634634 0 0
635635 0 0
636636 0 0
637637 48.9337 1.93882
638638 0 0
639639 57.7748 2.28553
640640 0 0
641641 32.5562 1.28589 0.642946 0.765911i 0.277712π-0.277712\pi
0.642946 + 0.765911i 0.277712π0.277712\pi
642642 0 0
643643 27.9017 1.10034 0.550168 0.835054i 0.314564π-0.314564\pi
0.550168 + 0.835054i 0.314564π0.314564\pi
644644 0 0
645645 0 0
646646 0 0
647647 28.7873 1.13174 0.565872 0.824493i 0.308540π-0.308540\pi
0.565872 + 0.824493i 0.308540π0.308540\pi
648648 0 0
649649 −2.63841 −0.103567
650650 0 0
651651 112.769 4.41976
652652 0 0
653653 34.7152 1.35851 0.679256 0.733901i 0.262303π-0.262303\pi
0.679256 + 0.733901i 0.262303π0.262303\pi
654654 0 0
655655 0 0
656656 0 0
657657 53.1907 2.07517
658658 0 0
659659 −25.5632 −0.995801 −0.497901 0.867234i 0.665896π-0.665896\pi
−0.497901 + 0.867234i 0.665896π0.665896\pi
660660 0 0
661661 1.40960 0.0548269 0.0274135 0.999624i 0.491273π-0.491273\pi
0.0274135 + 0.999624i 0.491273π0.491273\pi
662662 0 0
663663 −62.9562 −2.44502
664664 0 0
665665 0 0
666666 0 0
667667 −5.95266 −0.230488
668668 0 0
669669 −52.0692 −2.01311
670670 0 0
671671 8.96787 0.346201
672672 0 0
673673 0.0557959 0.00215078 0.00107539 0.999999i 0.499658π-0.499658\pi
0.00107539 + 0.999999i 0.499658π0.499658\pi
674674 0 0
675675 0 0
676676 0 0
677677 20.8316 0.800623 0.400311 0.916379i 0.368902π-0.368902\pi
0.400311 + 0.916379i 0.368902π0.368902\pi
678678 0 0
679679 −45.9612 −1.76383
680680 0 0
681681 −10.4414 −0.400115
682682 0 0
683683 21.5085 0.822999 0.411499 0.911410i 0.365005π-0.365005\pi
0.411499 + 0.911410i 0.365005π0.365005\pi
684684 0 0
685685 0 0
686686 0 0
687687 −35.8939 −1.36944
688688 0 0
689689 −21.1907 −0.807301
690690 0 0
691691 5.49862 0.209178 0.104589 0.994516i 0.466647π-0.466647\pi
0.104589 + 0.994516i 0.466647π0.466647\pi
692692 0 0
693693 18.2655 0.693851
694694 0 0
695695 0 0
696696 0 0
697697 14.7330 0.558054
698698 0 0
699699 8.99897 0.340372
700700 0 0
701701 −6.00460 −0.226791 −0.113395 0.993550i 0.536173π-0.536173\pi
−0.113395 + 0.993550i 0.536173π0.536173\pi
702702 0 0
703703 −0.929066 −0.0350404
704704 0 0
705705 0 0
706706 0 0
707707 38.1850 1.43610
708708 0 0
709709 17.7168 0.665369 0.332685 0.943038i 0.392046π-0.392046\pi
0.332685 + 0.943038i 0.392046π0.392046\pi
710710 0 0
711711 −55.2966 −2.07379
712712 0 0
713713 −59.0810 −2.21260
714714 0 0
715715 0 0
716716 0 0
717717 35.5385 1.32721
718718 0 0
719719 30.5308 1.13860 0.569302 0.822128i 0.307213π-0.307213\pi
0.569302 + 0.822128i 0.307213π0.307213\pi
720720 0 0
721721 68.4986 2.55102
722722 0 0
723723 47.4950 1.76636
724724 0 0
725725 0 0
726726 0 0
727727 −43.9063 −1.62839 −0.814197 0.580589i 0.802823π-0.802823\pi
−0.814197 + 0.580589i 0.802823π0.802823\pi
728728 0 0
729729 −42.3165 −1.56728
730730 0 0
731731 −22.6914 −0.839270
732732 0 0
733733 −20.6427 −0.762455 −0.381227 0.924481i 0.624498π-0.624498\pi
−0.381227 + 0.924481i 0.624498π0.624498\pi
734734 0 0
735735 0 0
736736 0 0
737737 −7.97440 −0.293741
738738 0 0
739739 −7.73446 −0.284517 −0.142258 0.989830i 0.545436π-0.545436\pi
−0.142258 + 0.989830i 0.545436π0.545436\pi
740740 0 0
741741 5.63705 0.207082
742742 0 0
743743 −29.1755 −1.07034 −0.535172 0.844743i 0.679753π-0.679753\pi
−0.535172 + 0.844743i 0.679753π0.679753\pi
744744 0 0
745745 0 0
746746 0 0
747747 −31.7324 −1.16103
748748 0 0
749749 31.0847 1.13581
750750 0 0
751751 −9.38310 −0.342394 −0.171197 0.985237i 0.554763π-0.554763\pi
−0.171197 + 0.985237i 0.554763π0.554763\pi
752752 0 0
753753 −22.9507 −0.836371
754754 0 0
755755 0 0
756756 0 0
757757 12.8997 0.468847 0.234424 0.972135i 0.424680π-0.424680\pi
0.234424 + 0.972135i 0.424680π0.424680\pi
758758 0 0
759759 −16.4626 −0.597553
760760 0 0
761761 15.6963 0.568991 0.284496 0.958677i 0.408174π-0.408174\pi
0.284496 + 0.958677i 0.408174π0.408174\pi
762762 0 0
763763 −68.1625 −2.46765
764764 0 0
765765 0 0
766766 0 0
767767 −10.5536 −0.381070
768768 0 0
769769 34.1123 1.23012 0.615060 0.788480i 0.289132π-0.289132\pi
0.615060 + 0.788480i 0.289132π0.289132\pi
770770 0 0
771771 7.24573 0.260949
772772 0 0
773773 −52.2539 −1.87944 −0.939721 0.341942i 0.888915π-0.888915\pi
−0.939721 + 0.341942i 0.888915π0.888915\pi
774774 0 0
775775 0 0
776776 0 0
777777 −20.7154 −0.743160
778778 0 0
779779 −1.31918 −0.0472647
780780 0 0
781781 13.8718 0.496373
782782 0 0
783783 3.01795 0.107853
784784 0 0
785785 0 0
786786 0 0
787787 6.89902 0.245924 0.122962 0.992411i 0.460761π-0.460761\pi
0.122962 + 0.992411i 0.460761π0.460761\pi
788788 0 0
789789 −38.3344 −1.36474
790790 0 0
791791 35.5904 1.26545
792792 0 0
793793 35.8715 1.27383
794794 0 0
795795 0 0
796796 0 0
797797 −0.544296 −0.0192800 −0.00963998 0.999954i 0.503069π-0.503069\pi
−0.00963998 + 0.999954i 0.503069π0.503069\pi
798798 0 0
799799 −28.8828 −1.02180
800800 0 0
801801 11.8079 0.417212
802802 0 0
803803 12.7712 0.450685
804804 0 0
805805 0 0
806806 0 0
807807 31.9488 1.12465
808808 0 0
809809 26.3354 0.925905 0.462952 0.886383i 0.346790π-0.346790\pi
0.462952 + 0.886383i 0.346790π0.346790\pi
810810 0 0
811811 −24.4686 −0.859207 −0.429604 0.903018i 0.641347π-0.641347\pi
−0.429604 + 0.903018i 0.641347π0.641347\pi
812812 0 0
813813 65.3645 2.29243
814814 0 0
815815 0 0
816816 0 0
817817 2.03176 0.0710824
818818 0 0
819819 73.0622 2.55300
820820 0 0
821821 42.8503 1.49549 0.747743 0.663989i 0.231138π-0.231138\pi
0.747743 + 0.663989i 0.231138π0.231138\pi
822822 0 0
823823 18.7417 0.653296 0.326648 0.945146i 0.394081π-0.394081\pi
0.326648 + 0.945146i 0.394081π0.394081\pi
824824 0 0
825825 0 0
826826 0 0
827827 −30.6681 −1.06644 −0.533218 0.845978i 0.679017π-0.679017\pi
−0.533218 + 0.845978i 0.679017π0.679017\pi
828828 0 0
829829 −19.8758 −0.690314 −0.345157 0.938545i 0.612174π-0.612174\pi
−0.345157 + 0.938545i 0.612174π0.612174\pi
830830 0 0
831831 61.5847 2.13635
832832 0 0
833833 71.9319 2.49229
834834 0 0
835835 0 0
836836 0 0
837837 29.9536 1.03535
838838 0 0
839839 −48.3178 −1.66812 −0.834058 0.551677i 0.813988π-0.813988\pi
−0.834058 + 0.551677i 0.813988π0.813988\pi
840840 0 0
841841 −28.0632 −0.967697
842842 0 0
843843 28.5329 0.982725
844844 0 0
845845 0 0
846846 0 0
847847 4.38559 0.150691
848848 0 0
849849 −27.7768 −0.953298
850850 0 0
851851 10.8531 0.372038
852852 0 0
853853 39.4686 1.35138 0.675690 0.737186i 0.263846π-0.263846\pi
0.675690 + 0.737186i 0.263846π0.263846\pi
854854 0 0
855855 0 0
856856 0 0
857857 16.7666 0.572736 0.286368 0.958120i 0.407552π-0.407552\pi
0.286368 + 0.958120i 0.407552π0.407552\pi
858858 0 0
859859 0.350976 0.0119751 0.00598757 0.999982i 0.498094π-0.498094\pi
0.00598757 + 0.999982i 0.498094π0.498094\pi
860860 0 0
861861 −29.4139 −1.00242
862862 0 0
863863 −35.2087 −1.19852 −0.599259 0.800555i 0.704538π-0.704538\pi
−0.599259 + 0.800555i 0.704538π0.704538\pi
864864 0 0
865865 0 0
866866 0 0
867867 −47.0404 −1.59758
868868 0 0
869869 −13.2768 −0.450385
870870 0 0
871871 −31.8976 −1.08081
872872 0 0
873873 −43.6483 −1.47727
874874 0 0
875875 0 0
876876 0 0
877877 −8.61790 −0.291006 −0.145503 0.989358i 0.546480π-0.546480\pi
−0.145503 + 0.989358i 0.546480π0.546480\pi
878878 0 0
879879 60.7804 2.05007
880880 0 0
881881 −42.5162 −1.43241 −0.716204 0.697891i 0.754122π-0.754122\pi
−0.716204 + 0.697891i 0.754122π0.754122\pi
882882 0 0
883883 25.1568 0.846593 0.423296 0.905991i 0.360873π-0.360873\pi
0.423296 + 0.905991i 0.360873π0.360873\pi
884884 0 0
885885 0 0
886886 0 0
887887 6.27505 0.210696 0.105348 0.994435i 0.466404π-0.466404\pi
0.105348 + 0.994435i 0.466404π0.466404\pi
888888 0 0
889889 18.9887 0.636861
890890 0 0
891891 −4.14832 −0.138974
892892 0 0
893893 2.58614 0.0865418
894894 0 0
895895 0 0
896896 0 0
897897 −65.8503 −2.19868
898898 0 0
899899 9.29767 0.310095
900900 0 0
901901 −31.1500 −1.03776
902902 0 0
903903 45.3023 1.50757
904904 0 0
905905 0 0
906906 0 0
907907 11.0925 0.368321 0.184161 0.982896i 0.441043π-0.441043\pi
0.184161 + 0.982896i 0.441043π0.441043\pi
908908 0 0
909909 36.2635 1.20278
910910 0 0
911911 −32.8175 −1.08729 −0.543646 0.839315i 0.682956π-0.682956\pi
−0.543646 + 0.839315i 0.682956π0.682956\pi
912912 0 0
913913 −7.61901 −0.252152
914914 0 0
915915 0 0
916916 0 0
917917 −77.5145 −2.55975
918918 0 0
919919 0.658922 0.0217358 0.0108679 0.999941i 0.496541π-0.496541\pi
0.0108679 + 0.999941i 0.496541π0.496541\pi
920920 0 0
921921 14.7069 0.484610
922922 0 0
923923 55.4873 1.82639
924924 0 0
925925 0 0
926926 0 0
927927 65.0516 2.13657
928928 0 0
929929 −28.0519 −0.920354 −0.460177 0.887827i 0.652214π-0.652214\pi
−0.460177 + 0.887827i 0.652214π0.652214\pi
930930 0 0
931931 −6.44072 −0.211086
932932 0 0
933933 64.8966 2.12462
934934 0 0
935935 0 0
936936 0 0
937937 26.6652 0.871115 0.435558 0.900161i 0.356551π-0.356551\pi
0.435558 + 0.900161i 0.356551π0.356551\pi
938938 0 0
939939 31.4682 1.02693
940940 0 0
941941 −0.222135 −0.00724139 −0.00362069 0.999993i 0.501153π-0.501153\pi
−0.00362069 + 0.999993i 0.501153π0.501153\pi
942942 0 0
943943 15.4103 0.501829
944944 0 0
945945 0 0
946946 0 0
947947 −4.99028 −0.162162 −0.0810812 0.996707i 0.525837π-0.525837\pi
−0.0810812 + 0.996707i 0.525837π0.525837\pi
948948 0 0
949949 51.0847 1.65828
950950 0 0
951951 24.2348 0.785867
952952 0 0
953953 −9.66807 −0.313179 −0.156590 0.987664i 0.550050π-0.550050\pi
−0.156590 + 0.987664i 0.550050π0.550050\pi
954954 0 0
955955 0 0
956956 0 0
957957 2.59074 0.0837467
958958 0 0
959959 81.0459 2.61711
960960 0 0
961961 61.2807 1.97680
962962 0 0
963963 29.5205 0.951284
964964 0 0
965965 0 0
966966 0 0
967967 −19.8033 −0.636832 −0.318416 0.947951i 0.603151π-0.603151\pi
−0.318416 + 0.947951i 0.603151π0.603151\pi
968968 0 0
969969 8.28639 0.266197
970970 0 0
971971 39.0410 1.25289 0.626443 0.779468i 0.284510π-0.284510\pi
0.626443 + 0.779468i 0.284510π0.284510\pi
972972 0 0
973973 −24.3778 −0.781517
974974 0 0
975975 0 0
976976 0 0
977977 −50.8314 −1.62624 −0.813121 0.582095i 0.802233π-0.802233\pi
−0.813121 + 0.582095i 0.802233π0.802233\pi
978978 0 0
979979 2.83510 0.0906103
980980 0 0
981981 −64.7324 −2.06675
982982 0 0
983983 −21.7569 −0.693936 −0.346968 0.937877i 0.612789π-0.612789\pi
−0.346968 + 0.937877i 0.612789π0.612789\pi
984984 0 0
985985 0 0
986986 0 0
987987 57.6632 1.83544
988988 0 0
989989 −23.7345 −0.754712
990990 0 0
991991 −33.0622 −1.05025 −0.525127 0.851024i 0.675982π-0.675982\pi
−0.525127 + 0.851024i 0.675982π0.675982\pi
992992 0 0
993993 8.82608 0.280087
994994 0 0
995995 0 0
996996 0 0
997997 −19.4008 −0.614430 −0.307215 0.951640i 0.599397π-0.599397\pi
−0.307215 + 0.951640i 0.599397π0.599397\pi
998998 0 0
999999 −5.50241 −0.174088
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 2200.2.a.y.1.1 4
4.3 odd 2 4400.2.a.cb.1.4 4
5.2 odd 4 440.2.b.d.89.7 yes 8
5.3 odd 4 440.2.b.d.89.2 8
5.4 even 2 2200.2.a.x.1.4 4
15.2 even 4 3960.2.d.f.3169.2 8
15.8 even 4 3960.2.d.f.3169.1 8
20.3 even 4 880.2.b.j.529.7 8
20.7 even 4 880.2.b.j.529.2 8
20.19 odd 2 4400.2.a.ce.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
440.2.b.d.89.2 8 5.3 odd 4
440.2.b.d.89.7 yes 8 5.2 odd 4
880.2.b.j.529.2 8 20.7 even 4
880.2.b.j.529.7 8 20.3 even 4
2200.2.a.x.1.4 4 5.4 even 2
2200.2.a.y.1.1 4 1.1 even 1 trivial
3960.2.d.f.3169.1 8 15.8 even 4
3960.2.d.f.3169.2 8 15.2 even 4
4400.2.a.cb.1.4 4 4.3 odd 2
4400.2.a.ce.1.1 4 20.19 odd 2