Properties

Label 968.4.a.n.1.7
Level 968968
Weight 44
Character 968.1
Self dual yes
Analytic conductor 57.11457.114
Analytic rank 11
Dimension 88
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] = [968,4,Mod(1,968)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("968.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(968, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")
 
Level: N N == 968=23112 968 = 2^{3} \cdot 11^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 968.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,-8,0,-13,0,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 57.113848885657.1138488856
Analytic rank: 11
Dimension: 88
Coefficient field: Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x82x787x6+12x5+2157x4+2939x35906x23030x+45 x^{8} - 2x^{7} - 87x^{6} + 12x^{5} + 2157x^{4} + 2939x^{3} - 5906x^{2} - 3030x + 45 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 2611 2^{6}\cdot 11
Twist minimal: no (minimal twist has level 88)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.7
Root 7.889047.88904 of defining polynomial
Character χ\chi == 968.1

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) == q+5.54031q36.21683q510.0967q7+3.69499q9+19.8412q1334.4431q15+0.0283422q17+72.4162q1955.9390q21+92.3700q2386.3511q25129.117q27+83.3142q29172.056q31+62.7697q35+178.367q37+109.926q39235.671q4169.3945q4322.9711q45433.018q47241.056q49+0.157025q51599.884q53+401.208q57365.211q59685.581q6137.3073q63123.349q65+224.941q67+511.758q69254.652q71882.320q73478.411q75+386.959q79815.112q81+1214.30q830.176199q85+461.586q871236.77q89200.332q91953.241q93450.199q95891.507q97+O(q100)q+5.54031 q^{3} -6.21683 q^{5} -10.0967 q^{7} +3.69499 q^{9} +19.8412 q^{13} -34.4431 q^{15} +0.0283422 q^{17} +72.4162 q^{19} -55.9390 q^{21} +92.3700 q^{23} -86.3511 q^{25} -129.117 q^{27} +83.3142 q^{29} -172.056 q^{31} +62.7697 q^{35} +178.367 q^{37} +109.926 q^{39} -235.671 q^{41} -69.3945 q^{43} -22.9711 q^{45} -433.018 q^{47} -241.056 q^{49} +0.157025 q^{51} -599.884 q^{53} +401.208 q^{57} -365.211 q^{59} -685.581 q^{61} -37.3073 q^{63} -123.349 q^{65} +224.941 q^{67} +511.758 q^{69} -254.652 q^{71} -882.320 q^{73} -478.411 q^{75} +386.959 q^{79} -815.112 q^{81} +1214.30 q^{83} -0.176199 q^{85} +461.586 q^{87} -1236.77 q^{89} -200.332 q^{91} -953.241 q^{93} -450.199 q^{95} -891.507 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q8q313q59q7+36q9+7q1366q15+94q1792q19+17q2146q23+101q25+124q27+241q29265q31664q35469q37+788q39+4702q97+O(q100) 8 q - 8 q^{3} - 13 q^{5} - 9 q^{7} + 36 q^{9} + 7 q^{13} - 66 q^{15} + 94 q^{17} - 92 q^{19} + 17 q^{21} - 46 q^{23} + 101 q^{25} + 124 q^{27} + 241 q^{29} - 265 q^{31} - 664 q^{35} - 469 q^{37} + 788 q^{39}+ \cdots - 4702 q^{97}+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 5.54031 1.06623 0.533116 0.846042i 0.321021π-0.321021\pi
0.533116 + 0.846042i 0.321021π0.321021\pi
44 0 0
55 −6.21683 −0.556050 −0.278025 0.960574i 0.589680π-0.589680\pi
−0.278025 + 0.960574i 0.589680π0.589680\pi
66 0 0
77 −10.0967 −0.545173 −0.272586 0.962131i 0.587879π-0.587879\pi
−0.272586 + 0.962131i 0.587879π0.587879\pi
88 0 0
99 3.69499 0.136851
1010 0 0
1111 0 0
1212 0 0
1313 19.8412 0.423305 0.211652 0.977345i 0.432115π-0.432115\pi
0.211652 + 0.977345i 0.432115π0.432115\pi
1414 0 0
1515 −34.4431 −0.592878
1616 0 0
1717 0.0283422 0.000404353 0 0.000202176 1.00000i 0.499936π-0.499936\pi
0.000202176 1.00000i 0.499936π0.499936\pi
1818 0 0
1919 72.4162 0.874391 0.437195 0.899367i 0.355972π-0.355972\pi
0.437195 + 0.899367i 0.355972π0.355972\pi
2020 0 0
2121 −55.9390 −0.581281
2222 0 0
2323 92.3700 0.837412 0.418706 0.908122i 0.362484π-0.362484\pi
0.418706 + 0.908122i 0.362484π0.362484\pi
2424 0 0
2525 −86.3511 −0.690808
2626 0 0
2727 −129.117 −0.920317
2828 0 0
2929 83.3142 0.533485 0.266742 0.963768i 0.414053π-0.414053\pi
0.266742 + 0.963768i 0.414053π0.414053\pi
3030 0 0
3131 −172.056 −0.996842 −0.498421 0.866935i 0.666087π-0.666087\pi
−0.498421 + 0.866935i 0.666087π0.666087\pi
3232 0 0
3333 0 0
3434 0 0
3535 62.7697 0.303143
3636 0 0
3737 178.367 0.792521 0.396260 0.918138i 0.370308π-0.370308\pi
0.396260 + 0.918138i 0.370308π0.370308\pi
3838 0 0
3939 109.926 0.451341
4040 0 0
4141 −235.671 −0.897697 −0.448849 0.893608i 0.648166π-0.648166\pi
−0.448849 + 0.893608i 0.648166π0.648166\pi
4242 0 0
4343 −69.3945 −0.246106 −0.123053 0.992400i 0.539269π-0.539269\pi
−0.123053 + 0.992400i 0.539269π0.539269\pi
4444 0 0
4545 −22.9711 −0.0760962
4646 0 0
4747 −433.018 −1.34388 −0.671938 0.740607i 0.734538π-0.734538\pi
−0.671938 + 0.740607i 0.734538π0.734538\pi
4848 0 0
4949 −241.056 −0.702787
5050 0 0
5151 0.157025 0.000431134 0
5252 0 0
5353 −599.884 −1.55472 −0.777362 0.629054i 0.783443π-0.783443\pi
−0.777362 + 0.629054i 0.783443π0.783443\pi
5454 0 0
5555 0 0
5656 0 0
5757 401.208 0.932303
5858 0 0
5959 −365.211 −0.805871 −0.402935 0.915228i 0.632010π-0.632010\pi
−0.402935 + 0.915228i 0.632010π0.632010\pi
6060 0 0
6161 −685.581 −1.43901 −0.719506 0.694487i 0.755632π-0.755632\pi
−0.719506 + 0.694487i 0.755632π0.755632\pi
6262 0 0
6363 −37.3073 −0.0746076
6464 0 0
6565 −123.349 −0.235379
6666 0 0
6767 224.941 0.410164 0.205082 0.978745i 0.434254π-0.434254\pi
0.205082 + 0.978745i 0.434254π0.434254\pi
6868 0 0
6969 511.758 0.892876
7070 0 0
7171 −254.652 −0.425657 −0.212828 0.977090i 0.568268π-0.568268\pi
−0.212828 + 0.977090i 0.568268π0.568268\pi
7272 0 0
7373 −882.320 −1.41463 −0.707313 0.706900i 0.750093π-0.750093\pi
−0.707313 + 0.706900i 0.750093π0.750093\pi
7474 0 0
7575 −478.411 −0.736562
7676 0 0
7777 0 0
7878 0 0
7979 386.959 0.551092 0.275546 0.961288i 0.411141π-0.411141\pi
0.275546 + 0.961288i 0.411141π0.411141\pi
8080 0 0
8181 −815.112 −1.11812
8282 0 0
8383 1214.30 1.60587 0.802935 0.596067i 0.203271π-0.203271\pi
0.802935 + 0.596067i 0.203271π0.203271\pi
8484 0 0
8585 −0.176199 −0.000224840 0
8686 0 0
8787 461.586 0.568819
8888 0 0
8989 −1236.77 −1.47300 −0.736500 0.676438i 0.763523π-0.763523\pi
−0.736500 + 0.676438i 0.763523π0.763523\pi
9090 0 0
9191 −200.332 −0.230774
9292 0 0
9393 −953.241 −1.06287
9494 0 0
9595 −450.199 −0.486205
9696 0 0
9797 −891.507 −0.933184 −0.466592 0.884473i 0.654518π-0.654518\pi
−0.466592 + 0.884473i 0.654518π0.654518\pi
9898 0 0
9999 0 0
100100 0 0
101101 −308.007 −0.303444 −0.151722 0.988423i 0.548482π-0.548482\pi
−0.151722 + 0.988423i 0.548482π0.548482\pi
102102 0 0
103103 −1112.92 −1.06465 −0.532325 0.846540i 0.678682π-0.678682\pi
−0.532325 + 0.846540i 0.678682π0.678682\pi
104104 0 0
105105 347.763 0.323221
106106 0 0
107107 −1733.86 −1.56653 −0.783266 0.621687i 0.786448π-0.786448\pi
−0.783266 + 0.621687i 0.786448π0.786448\pi
108108 0 0
109109 1565.32 1.37550 0.687752 0.725946i 0.258598π-0.258598\pi
0.687752 + 0.725946i 0.258598π0.258598\pi
110110 0 0
111111 988.205 0.845011
112112 0 0
113113 656.139 0.546233 0.273117 0.961981i 0.411945π-0.411945\pi
0.273117 + 0.961981i 0.411945π0.411945\pi
114114 0 0
115115 −574.249 −0.465643
116116 0 0
117117 73.3130 0.0579298
118118 0 0
119119 −0.286164 −0.000220442 0
120120 0 0
121121 0 0
122122 0 0
123123 −1305.69 −0.957154
124124 0 0
125125 1313.93 0.940174
126126 0 0
127127 2668.84 1.86474 0.932368 0.361510i 0.117739π-0.117739\pi
0.932368 + 0.361510i 0.117739π0.117739\pi
128128 0 0
129129 −384.467 −0.262406
130130 0 0
131131 694.820 0.463410 0.231705 0.972786i 0.425570π-0.425570\pi
0.231705 + 0.972786i 0.425570π0.425570\pi
132132 0 0
133133 −731.168 −0.476694
134134 0 0
135135 802.697 0.511742
136136 0 0
137137 2477.03 1.54472 0.772361 0.635184i 0.219076π-0.219076\pi
0.772361 + 0.635184i 0.219076π0.219076\pi
138138 0 0
139139 −2196.35 −1.34023 −0.670115 0.742257i 0.733755π-0.733755\pi
−0.670115 + 0.742257i 0.733755π0.733755\pi
140140 0 0
141141 −2399.05 −1.43288
142142 0 0
143143 0 0
144144 0 0
145145 −517.950 −0.296644
146146 0 0
147147 −1335.52 −0.749334
148148 0 0
149149 3340.74 1.83681 0.918403 0.395645i 0.129479π-0.129479\pi
0.918403 + 0.395645i 0.129479π0.129479\pi
150150 0 0
151151 −728.502 −0.392613 −0.196307 0.980543i 0.562895π-0.562895\pi
−0.196307 + 0.980543i 0.562895π0.562895\pi
152152 0 0
153153 0.104724 5.53362e−5 0
154154 0 0
155155 1069.64 0.554294
156156 0 0
157157 2954.83 1.50204 0.751022 0.660277i 0.229561π-0.229561\pi
0.751022 + 0.660277i 0.229561π0.229561\pi
158158 0 0
159159 −3323.54 −1.65770
160160 0 0
161161 −932.636 −0.456534
162162 0 0
163163 −6.35358 −0.00305307 −0.00152654 0.999999i 0.500486π-0.500486\pi
−0.00152654 + 0.999999i 0.500486π0.500486\pi
164164 0 0
165165 0 0
166166 0 0
167167 −733.870 −0.340051 −0.170026 0.985440i 0.554385π-0.554385\pi
−0.170026 + 0.985440i 0.554385π0.554385\pi
168168 0 0
169169 −1803.33 −0.820813
170170 0 0
171171 267.577 0.119661
172172 0 0
173173 329.366 0.144747 0.0723736 0.997378i 0.476943π-0.476943\pi
0.0723736 + 0.997378i 0.476943π0.476943\pi
174174 0 0
175175 871.864 0.376610
176176 0 0
177177 −2023.38 −0.859245
178178 0 0
179179 2671.42 1.11548 0.557741 0.830015i 0.311668π-0.311668\pi
0.557741 + 0.830015i 0.311668π0.311668\pi
180180 0 0
181181 −1545.63 −0.634727 −0.317364 0.948304i 0.602798π-0.602798\pi
−0.317364 + 0.948304i 0.602798π0.602798\pi
182182 0 0
183183 −3798.33 −1.53432
184184 0 0
185185 −1108.87 −0.440681
186186 0 0
187187 0 0
188188 0 0
189189 1303.66 0.501732
190190 0 0
191191 1185.87 0.449248 0.224624 0.974445i 0.427885π-0.427885\pi
0.224624 + 0.974445i 0.427885π0.427885\pi
192192 0 0
193193 −1340.94 −0.500117 −0.250059 0.968231i 0.580450π-0.580450\pi
−0.250059 + 0.968231i 0.580450π0.580450\pi
194194 0 0
195195 −683.394 −0.250968
196196 0 0
197197 797.183 0.288309 0.144155 0.989555i 0.453954π-0.453954\pi
0.144155 + 0.989555i 0.453954π0.453954\pi
198198 0 0
199199 119.756 0.0426597 0.0213299 0.999772i 0.493210π-0.493210\pi
0.0213299 + 0.999772i 0.493210π0.493210\pi
200200 0 0
201201 1246.24 0.437330
202202 0 0
203203 −841.202 −0.290841
204204 0 0
205205 1465.12 0.499164
206206 0 0
207207 341.306 0.114601
208208 0 0
209209 0 0
210210 0 0
211211 1059.12 0.345559 0.172780 0.984961i 0.444725π-0.444725\pi
0.172780 + 0.984961i 0.444725π0.444725\pi
212212 0 0
213213 −1410.85 −0.453849
214214 0 0
215215 431.414 0.136847
216216 0 0
217217 1737.20 0.543451
218218 0 0
219219 −4888.32 −1.50832
220220 0 0
221221 0.562344 0.000171165 0
222222 0 0
223223 −6175.28 −1.85438 −0.927192 0.374587i 0.877785π-0.877785\pi
−0.927192 + 0.374587i 0.877785π0.877785\pi
224224 0 0
225225 −319.066 −0.0945380
226226 0 0
227227 −4220.64 −1.23407 −0.617034 0.786936i 0.711666π-0.711666\pi
−0.617034 + 0.786936i 0.711666π0.711666\pi
228228 0 0
229229 −2459.73 −0.709798 −0.354899 0.934905i 0.615485π-0.615485\pi
−0.354899 + 0.934905i 0.615485π0.615485\pi
230230 0 0
231231 0 0
232232 0 0
233233 −1244.39 −0.349884 −0.174942 0.984579i 0.555974π-0.555974\pi
−0.174942 + 0.984579i 0.555974π0.555974\pi
234234 0 0
235235 2692.00 0.747263
236236 0 0
237237 2143.87 0.587592
238238 0 0
239239 −3484.12 −0.942967 −0.471483 0.881875i 0.656281π-0.656281\pi
−0.471483 + 0.881875i 0.656281π0.656281\pi
240240 0 0
241241 6857.39 1.83288 0.916439 0.400174i 0.131050π-0.131050\pi
0.916439 + 0.400174i 0.131050π0.131050\pi
242242 0 0
243243 −1029.81 −0.271862
244244 0 0
245245 1498.60 0.390784
246246 0 0
247247 1436.83 0.370134
248248 0 0
249249 6727.61 1.71223
250250 0 0
251251 −5654.75 −1.42201 −0.711005 0.703187i 0.751760π-0.751760\pi
−0.711005 + 0.703187i 0.751760π0.751760\pi
252252 0 0
253253 0 0
254254 0 0
255255 −0.976195 −0.000239732 0
256256 0 0
257257 −3870.41 −0.939416 −0.469708 0.882822i 0.655641π-0.655641\pi
−0.469708 + 0.882822i 0.655641π0.655641\pi
258258 0 0
259259 −1800.92 −0.432061
260260 0 0
261261 307.845 0.0730081
262262 0 0
263263 −1016.12 −0.238239 −0.119119 0.992880i 0.538007π-0.538007\pi
−0.119119 + 0.992880i 0.538007π0.538007\pi
264264 0 0
265265 3729.37 0.864504
266266 0 0
267267 −6852.06 −1.57056
268268 0 0
269269 452.110 0.102474 0.0512372 0.998687i 0.483684π-0.483684\pi
0.0512372 + 0.998687i 0.483684π0.483684\pi
270270 0 0
271271 444.082 0.0995428 0.0497714 0.998761i 0.484151π-0.484151\pi
0.0497714 + 0.998761i 0.484151π0.484151\pi
272272 0 0
273273 −1109.90 −0.246059
274274 0 0
275275 0 0
276276 0 0
277277 7800.35 1.69198 0.845988 0.533202i 0.179011π-0.179011\pi
0.845988 + 0.533202i 0.179011π0.179011\pi
278278 0 0
279279 −635.743 −0.136419
280280 0 0
281281 −4754.72 −1.00941 −0.504703 0.863293i 0.668398π-0.668398\pi
−0.504703 + 0.863293i 0.668398π0.668398\pi
282282 0 0
283283 −5405.83 −1.13549 −0.567744 0.823205i 0.692184π-0.692184\pi
−0.567744 + 0.823205i 0.692184π0.692184\pi
284284 0 0
285285 −2494.24 −0.518407
286286 0 0
287287 2379.51 0.489400
288288 0 0
289289 −4913.00 −1.00000
290290 0 0
291291 −4939.22 −0.994991
292292 0 0
293293 5578.19 1.11222 0.556112 0.831107i 0.312293π-0.312293\pi
0.556112 + 0.831107i 0.312293π0.312293\pi
294294 0 0
295295 2270.45 0.448104
296296 0 0
297297 0 0
298298 0 0
299299 1832.73 0.354481
300300 0 0
301301 700.658 0.134170
302302 0 0
303303 −1706.45 −0.323541
304304 0 0
305305 4262.14 0.800162
306306 0 0
307307 −7248.81 −1.34759 −0.673797 0.738916i 0.735338π-0.735338\pi
−0.673797 + 0.738916i 0.735338π0.735338\pi
308308 0 0
309309 −6165.90 −1.13517
310310 0 0
311311 953.186 0.173795 0.0868975 0.996217i 0.472305π-0.472305\pi
0.0868975 + 0.996217i 0.472305π0.472305\pi
312312 0 0
313313 3365.71 0.607800 0.303900 0.952704i 0.401711π-0.401711\pi
0.303900 + 0.952704i 0.401711π0.401711\pi
314314 0 0
315315 231.933 0.0414856
316316 0 0
317317 8802.93 1.55969 0.779845 0.625972i 0.215298π-0.215298\pi
0.779845 + 0.625972i 0.215298π0.215298\pi
318318 0 0
319319 0 0
320320 0 0
321321 −9606.13 −1.67029
322322 0 0
323323 2.05244 0.000353562 0
324324 0 0
325325 −1713.31 −0.292423
326326 0 0
327327 8672.32 1.46661
328328 0 0
329329 4372.07 0.732645
330330 0 0
331331 1884.62 0.312955 0.156478 0.987682i 0.449986π-0.449986\pi
0.156478 + 0.987682i 0.449986π0.449986\pi
332332 0 0
333333 659.062 0.108458
334334 0 0
335335 −1398.42 −0.228071
336336 0 0
337337 1979.74 0.320009 0.160005 0.987116i 0.448849π-0.448849\pi
0.160005 + 0.987116i 0.448849π0.448849\pi
338338 0 0
339339 3635.21 0.582412
340340 0 0
341341 0 0
342342 0 0
343343 5897.06 0.928313
344344 0 0
345345 −3181.51 −0.496484
346346 0 0
347347 −8538.82 −1.32100 −0.660502 0.750825i 0.729656π-0.729656\pi
−0.660502 + 0.750825i 0.729656π0.729656\pi
348348 0 0
349349 −944.572 −0.144876 −0.0724381 0.997373i 0.523078π-0.523078\pi
−0.0724381 + 0.997373i 0.523078π0.523078\pi
350350 0 0
351351 −2561.84 −0.389575
352352 0 0
353353 3709.02 0.559239 0.279619 0.960111i 0.409792π-0.409792\pi
0.279619 + 0.960111i 0.409792π0.409792\pi
354354 0 0
355355 1583.13 0.236687
356356 0 0
357357 −1.58544 −0.000235043 0
358358 0 0
359359 −9466.81 −1.39175 −0.695876 0.718162i 0.744984π-0.744984\pi
−0.695876 + 0.718162i 0.744984π0.744984\pi
360360 0 0
361361 −1614.89 −0.235441
362362 0 0
363363 0 0
364364 0 0
365365 5485.23 0.786603
366366 0 0
367367 2353.26 0.334712 0.167356 0.985897i 0.446477π-0.446477\pi
0.167356 + 0.985897i 0.446477π0.446477\pi
368368 0 0
369369 −870.800 −0.122851
370370 0 0
371371 6056.87 0.847593
372372 0 0
373373 1447.21 0.200894 0.100447 0.994942i 0.467973π-0.467973\pi
0.100447 + 0.994942i 0.467973π0.467973\pi
374374 0 0
375375 7279.59 1.00244
376376 0 0
377377 1653.06 0.225827
378378 0 0
379379 8402.10 1.13875 0.569376 0.822078i 0.307185π-0.307185\pi
0.569376 + 0.822078i 0.307185π0.307185\pi
380380 0 0
381381 14786.2 1.98824
382382 0 0
383383 7136.19 0.952069 0.476035 0.879427i 0.342074π-0.342074\pi
0.476035 + 0.879427i 0.342074π0.342074\pi
384384 0 0
385385 0 0
386386 0 0
387387 −256.412 −0.0336799
388388 0 0
389389 11712.7 1.52663 0.763316 0.646025i 0.223570π-0.223570\pi
0.763316 + 0.646025i 0.223570π0.223570\pi
390390 0 0
391391 2.61797 0.000338610 0
392392 0 0
393393 3849.52 0.494103
394394 0 0
395395 −2405.66 −0.306435
396396 0 0
397397 −13000.5 −1.64352 −0.821759 0.569835i 0.807007π-0.807007\pi
−0.821759 + 0.569835i 0.807007π0.807007\pi
398398 0 0
399399 −4050.89 −0.508267
400400 0 0
401401 11061.4 1.37750 0.688750 0.724999i 0.258160π-0.258160\pi
0.688750 + 0.724999i 0.258160π0.258160\pi
402402 0 0
403403 −3413.79 −0.421968
404404 0 0
405405 5067.41 0.621732
406406 0 0
407407 0 0
408408 0 0
409409 −9340.89 −1.12928 −0.564642 0.825336i 0.690986π-0.690986\pi
−0.564642 + 0.825336i 0.690986π0.690986\pi
410410 0 0
411411 13723.5 1.64703
412412 0 0
413413 3687.44 0.439339
414414 0 0
415415 −7549.12 −0.892944
416416 0 0
417417 −12168.5 −1.42900
418418 0 0
419419 2181.92 0.254400 0.127200 0.991877i 0.459401π-0.459401\pi
0.127200 + 0.991877i 0.459401π0.459401\pi
420420 0 0
421421 3508.41 0.406151 0.203076 0.979163i 0.434906π-0.434906\pi
0.203076 + 0.979163i 0.434906π0.434906\pi
422422 0 0
423423 −1600.00 −0.183911
424424 0 0
425425 −2.44738 −0.000279330 0
426426 0 0
427427 6922.14 0.784510
428428 0 0
429429 0 0
430430 0 0
431431 −12861.8 −1.43742 −0.718712 0.695308i 0.755268π-0.755268\pi
−0.718712 + 0.695308i 0.755268π0.755268\pi
432432 0 0
433433 8152.45 0.904808 0.452404 0.891813i 0.350567π-0.350567\pi
0.452404 + 0.891813i 0.350567π0.350567\pi
434434 0 0
435435 −2869.60 −0.316292
436436 0 0
437437 6689.09 0.732225
438438 0 0
439439 1617.22 0.175821 0.0879107 0.996128i 0.471981π-0.471981\pi
0.0879107 + 0.996128i 0.471981π0.471981\pi
440440 0 0
441441 −890.698 −0.0961773
442442 0 0
443443 4746.12 0.509018 0.254509 0.967070i 0.418086π-0.418086\pi
0.254509 + 0.967070i 0.418086π0.418086\pi
444444 0 0
445445 7688.76 0.819061
446446 0 0
447447 18508.7 1.95846
448448 0 0
449449 6696.84 0.703883 0.351941 0.936022i 0.385522π-0.385522\pi
0.351941 + 0.936022i 0.385522π0.385522\pi
450450 0 0
451451 0 0
452452 0 0
453453 −4036.12 −0.418617
454454 0 0
455455 1245.43 0.128322
456456 0 0
457457 −10921.4 −1.11790 −0.558952 0.829200i 0.688796π-0.688796\pi
−0.558952 + 0.829200i 0.688796π0.688796\pi
458458 0 0
459459 −3.65946 −0.000372133 0
460460 0 0
461461 10627.0 1.07365 0.536823 0.843695i 0.319624π-0.319624\pi
0.536823 + 0.843695i 0.319624π0.319624\pi
462462 0 0
463463 3046.02 0.305746 0.152873 0.988246i 0.451147π-0.451147\pi
0.152873 + 0.988246i 0.451147π0.451147\pi
464464 0 0
465465 5926.13 0.591006
466466 0 0
467467 7881.07 0.780926 0.390463 0.920619i 0.372315π-0.372315\pi
0.390463 + 0.920619i 0.372315π0.372315\pi
468468 0 0
469469 −2271.18 −0.223610
470470 0 0
471471 16370.6 1.60153
472472 0 0
473473 0 0
474474 0 0
475475 −6253.22 −0.604036
476476 0 0
477477 −2216.56 −0.212766
478478 0 0
479479 12763.1 1.21746 0.608730 0.793378i 0.291679π-0.291679\pi
0.608730 + 0.793378i 0.291679π0.291679\pi
480480 0 0
481481 3539.01 0.335478
482482 0 0
483483 −5167.09 −0.486772
484484 0 0
485485 5542.35 0.518897
486486 0 0
487487 −4287.14 −0.398909 −0.199455 0.979907i 0.563917π-0.563917\pi
−0.199455 + 0.979907i 0.563917π0.563917\pi
488488 0 0
489489 −35.2008 −0.00325528
490490 0 0
491491 −1729.93 −0.159003 −0.0795016 0.996835i 0.525333π-0.525333\pi
−0.0795016 + 0.996835i 0.525333π0.525333\pi
492492 0 0
493493 2.36131 0.000215716 0
494494 0 0
495495 0 0
496496 0 0
497497 2571.16 0.232057
498498 0 0
499499 −13257.4 −1.18934 −0.594670 0.803970i 0.702717π-0.702717\pi
−0.594670 + 0.803970i 0.702717π0.702717\pi
500500 0 0
501501 −4065.87 −0.362574
502502 0 0
503503 131.981 0.0116993 0.00584964 0.999983i 0.498138π-0.498138\pi
0.00584964 + 0.999983i 0.498138π0.498138\pi
504504 0 0
505505 1914.82 0.168730
506506 0 0
507507 −9990.98 −0.875177
508508 0 0
509509 8169.00 0.711365 0.355682 0.934607i 0.384249π-0.384249\pi
0.355682 + 0.934607i 0.384249π0.384249\pi
510510 0 0
511511 8908.56 0.771216
512512 0 0
513513 −9350.16 −0.804717
514514 0 0
515515 6918.82 0.591999
516516 0 0
517517 0 0
518518 0 0
519519 1824.79 0.154334
520520 0 0
521521 2530.99 0.212831 0.106415 0.994322i 0.466063π-0.466063\pi
0.106415 + 0.994322i 0.466063π0.466063\pi
522522 0 0
523523 −1559.52 −0.130388 −0.0651940 0.997873i 0.520767π-0.520767\pi
−0.0651940 + 0.997873i 0.520767π0.520767\pi
524524 0 0
525525 4830.39 0.401554
526526 0 0
527527 −4.87644 −0.000403076 0
528528 0 0
529529 −3634.78 −0.298741
530530 0 0
531531 −1349.45 −0.110284
532532 0 0
533533 −4675.99 −0.380000
534534 0 0
535535 10779.1 0.871070
536536 0 0
537537 14800.5 1.18936
538538 0 0
539539 0 0
540540 0 0
541541 14840.8 1.17940 0.589700 0.807622i 0.299246π-0.299246\pi
0.589700 + 0.807622i 0.299246π0.299246\pi
542542 0 0
543543 −8563.25 −0.676767
544544 0 0
545545 −9731.29 −0.764849
546546 0 0
547547 4484.16 0.350510 0.175255 0.984523i 0.443925π-0.443925\pi
0.175255 + 0.984523i 0.443925π0.443925\pi
548548 0 0
549549 −2533.21 −0.196931
550550 0 0
551551 6033.30 0.466474
552552 0 0
553553 −3907.02 −0.300440
554554 0 0
555555 −6143.50 −0.469869
556556 0 0
557557 5315.84 0.404379 0.202190 0.979346i 0.435194π-0.435194\pi
0.202190 + 0.979346i 0.435194π0.435194\pi
558558 0 0
559559 −1376.87 −0.104178
560560 0 0
561561 0 0
562562 0 0
563563 4602.65 0.344544 0.172272 0.985049i 0.444889π-0.444889\pi
0.172272 + 0.985049i 0.444889π0.444889\pi
564564 0 0
565565 −4079.10 −0.303733
566566 0 0
567567 8229.97 0.609570
568568 0 0
569569 7732.30 0.569692 0.284846 0.958573i 0.408058π-0.408058\pi
0.284846 + 0.958573i 0.408058π0.408058\pi
570570 0 0
571571 18830.2 1.38007 0.690033 0.723778i 0.257596π-0.257596\pi
0.690033 + 0.723778i 0.257596π0.257596\pi
572572 0 0
573573 6570.07 0.479003
574574 0 0
575575 −7976.25 −0.578491
576576 0 0
577577 13904.5 1.00321 0.501605 0.865097i 0.332743π-0.332743\pi
0.501605 + 0.865097i 0.332743π0.332743\pi
578578 0 0
579579 −7429.19 −0.533241
580580 0 0
581581 −12260.5 −0.875476
582582 0 0
583583 0 0
584584 0 0
585585 −455.774 −0.0322119
586586 0 0
587587 25593.2 1.79956 0.899782 0.436340i 0.143726π-0.143726\pi
0.899782 + 0.436340i 0.143726π0.143726\pi
588588 0 0
589589 −12459.6 −0.871629
590590 0 0
591591 4416.64 0.307405
592592 0 0
593593 −14766.2 −1.02256 −0.511279 0.859415i 0.670828π-0.670828\pi
−0.511279 + 0.859415i 0.670828π0.670828\pi
594594 0 0
595595 1.77903 0.000122577 0
596596 0 0
597597 663.485 0.0454852
598598 0 0
599599 −1873.15 −0.127771 −0.0638856 0.997957i 0.520349π-0.520349\pi
−0.0638856 + 0.997957i 0.520349π0.520349\pi
600600 0 0
601601 −1711.60 −0.116169 −0.0580845 0.998312i 0.518499π-0.518499\pi
−0.0580845 + 0.998312i 0.518499π0.518499\pi
602602 0 0
603603 831.155 0.0561314
604604 0 0
605605 0 0
606606 0 0
607607 −13265.7 −0.887046 −0.443523 0.896263i 0.646272π-0.646272\pi
−0.443523 + 0.896263i 0.646272π0.646272\pi
608608 0 0
609609 −4660.52 −0.310105
610610 0 0
611611 −8591.61 −0.568870
612612 0 0
613613 −25182.4 −1.65923 −0.829615 0.558336i 0.811440π-0.811440\pi
−0.829615 + 0.558336i 0.811440π0.811440\pi
614614 0 0
615615 8117.23 0.532225
616616 0 0
617617 −4896.84 −0.319513 −0.159756 0.987156i 0.551071π-0.551071\pi
−0.159756 + 0.987156i 0.551071π0.551071\pi
618618 0 0
619619 −2943.21 −0.191111 −0.0955554 0.995424i 0.530463π-0.530463\pi
−0.0955554 + 0.995424i 0.530463π0.530463\pi
620620 0 0
621621 −11926.5 −0.770685
622622 0 0
623623 12487.3 0.803039
624624 0 0
625625 2625.39 0.168025
626626 0 0
627627 0 0
628628 0 0
629629 5.05530 0.000320458 0
630630 0 0
631631 −30497.6 −1.92408 −0.962038 0.272916i 0.912012π-0.912012\pi
−0.962038 + 0.272916i 0.912012π0.912012\pi
632632 0 0
633633 5867.86 0.368446
634634 0 0
635635 −16591.7 −1.03689
636636 0 0
637637 −4782.84 −0.297493
638638 0 0
639639 −940.936 −0.0582517
640640 0 0
641641 −25166.2 −1.55071 −0.775354 0.631527i 0.782429π-0.782429\pi
−0.775354 + 0.631527i 0.782429π0.782429\pi
642642 0 0
643643 −6165.04 −0.378111 −0.189056 0.981966i 0.560543π-0.560543\pi
−0.189056 + 0.981966i 0.560543π0.560543\pi
644644 0 0
645645 2390.16 0.145911
646646 0 0
647647 −13006.1 −0.790295 −0.395148 0.918618i 0.629307π-0.629307\pi
−0.395148 + 0.918618i 0.629307π0.629307\pi
648648 0 0
649649 0 0
650650 0 0
651651 9624.63 0.579445
652652 0 0
653653 18408.0 1.10316 0.551579 0.834123i 0.314026π-0.314026\pi
0.551579 + 0.834123i 0.314026π0.314026\pi
654654 0 0
655655 −4319.58 −0.257679
656656 0 0
657657 −3260.16 −0.193593
658658 0 0
659659 −13817.0 −0.816745 −0.408372 0.912815i 0.633904π-0.633904\pi
−0.408372 + 0.912815i 0.633904π0.633904\pi
660660 0 0
661661 −4130.31 −0.243042 −0.121521 0.992589i 0.538777π-0.538777\pi
−0.121521 + 0.992589i 0.538777π0.538777\pi
662662 0 0
663663 3.11556 0.000182501 0
664664 0 0
665665 4545.54 0.265066
666666 0 0
667667 7695.74 0.446747
668668 0 0
669669 −34213.0 −1.97720
670670 0 0
671671 0 0
672672 0 0
673673 9193.43 0.526569 0.263284 0.964718i 0.415194π-0.415194\pi
0.263284 + 0.964718i 0.415194π0.415194\pi
674674 0 0
675675 11149.4 0.635763
676676 0 0
677677 4453.79 0.252841 0.126420 0.991977i 0.459651π-0.459651\pi
0.126420 + 0.991977i 0.459651π0.459651\pi
678678 0 0
679679 9001.32 0.508747
680680 0 0
681681 −23383.6 −1.31580
682682 0 0
683683 −12898.6 −0.722620 −0.361310 0.932446i 0.617670π-0.617670\pi
−0.361310 + 0.932446i 0.617670π0.617670\pi
684684 0 0
685685 −15399.3 −0.858942
686686 0 0
687687 −13627.7 −0.756810
688688 0 0
689689 −11902.4 −0.658122
690690 0 0
691691 −29150.8 −1.60485 −0.802424 0.596754i 0.796457π-0.796457\pi
−0.802424 + 0.596754i 0.796457π0.796457\pi
692692 0 0
693693 0 0
694694 0 0
695695 13654.3 0.745235
696696 0 0
697697 −6.67943 −0.000362986 0
698698 0 0
699699 −6894.32 −0.373058
700700 0 0
701701 −154.490 −0.00832382 −0.00416191 0.999991i 0.501325π-0.501325\pi
−0.00416191 + 0.999991i 0.501325π0.501325\pi
702702 0 0
703703 12916.6 0.692973
704704 0 0
705705 14914.5 0.796755
706706 0 0
707707 3109.86 0.165429
708708 0 0
709709 −18780.0 −0.994780 −0.497390 0.867527i 0.665708π-0.665708\pi
−0.497390 + 0.867527i 0.665708π0.665708\pi
710710 0 0
711711 1429.81 0.0754176
712712 0 0
713713 −15892.8 −0.834768
714714 0 0
715715 0 0
716716 0 0
717717 −19303.1 −1.00542
718718 0 0
719719 −10916.4 −0.566222 −0.283111 0.959087i 0.591366π-0.591366\pi
−0.283111 + 0.959087i 0.591366π0.591366\pi
720720 0 0
721721 11236.8 0.580419
722722 0 0
723723 37992.1 1.95427
724724 0 0
725725 −7194.27 −0.368536
726726 0 0
727727 19277.1 0.983424 0.491712 0.870758i 0.336371π-0.336371\pi
0.491712 + 0.870758i 0.336371π0.336371\pi
728728 0 0
729729 16302.5 0.828255
730730 0 0
731731 −1.96679 −9.95137e−5 0
732732 0 0
733733 −34562.4 −1.74160 −0.870798 0.491641i 0.836397π-0.836397\pi
−0.870798 + 0.491641i 0.836397π0.836397\pi
734734 0 0
735735 8302.71 0.416667
736736 0 0
737737 0 0
738738 0 0
739739 19140.3 0.952757 0.476378 0.879240i 0.341949π-0.341949\pi
0.476378 + 0.879240i 0.341949π0.341949\pi
740740 0 0
741741 7960.46 0.394649
742742 0 0
743743 18198.4 0.898564 0.449282 0.893390i 0.351680π-0.351680\pi
0.449282 + 0.893390i 0.351680π0.351680\pi
744744 0 0
745745 −20768.8 −1.02136
746746 0 0
747747 4486.84 0.219765
748748 0 0
749749 17506.4 0.854031
750750 0 0
751751 25102.0 1.21969 0.609845 0.792521i 0.291232π-0.291232\pi
0.609845 + 0.792521i 0.291232π0.291232\pi
752752 0 0
753753 −31329.0 −1.51619
754754 0 0
755755 4528.97 0.218313
756756 0 0
757757 30787.1 1.47817 0.739086 0.673611i 0.235258π-0.235258\pi
0.739086 + 0.673611i 0.235258π0.235258\pi
758758 0 0
759759 0 0
760760 0 0
761761 22966.0 1.09398 0.546990 0.837139i 0.315774π-0.315774\pi
0.546990 + 0.837139i 0.315774π0.315774\pi
762762 0 0
763763 −15804.6 −0.749888
764764 0 0
765765 −0.651052 −3.07697e−5 0
766766 0 0
767767 −7246.22 −0.341129
768768 0 0
769769 28729.3 1.34721 0.673605 0.739091i 0.264745π-0.264745\pi
0.673605 + 0.739091i 0.264745π0.264745\pi
770770 0 0
771771 −21443.3 −1.00164
772772 0 0
773773 −19244.6 −0.895446 −0.447723 0.894172i 0.647765π-0.647765\pi
−0.447723 + 0.894172i 0.647765π0.647765\pi
774774 0 0
775775 14857.2 0.688627
776776 0 0
777777 −9977.65 −0.460677
778778 0 0
779779 −17066.4 −0.784938
780780 0 0
781781 0 0
782782 0 0
783783 −10757.3 −0.490975
784784 0 0
785785 −18369.6 −0.835211
786786 0 0
787787 −29271.2 −1.32580 −0.662901 0.748707i 0.730675π-0.730675\pi
−0.662901 + 0.748707i 0.730675π0.730675\pi
788788 0 0
789789 −5629.63 −0.254018
790790 0 0
791791 −6624.87 −0.297792
792792 0 0
793793 −13602.8 −0.609141
794794 0 0
795795 20661.9 0.921762
796796 0 0
797797 −12532.5 −0.556994 −0.278497 0.960437i 0.589836π-0.589836\pi
−0.278497 + 0.960437i 0.589836π0.589836\pi
798798 0 0
799799 −12.2727 −0.000543400 0
800800 0 0
801801 −4569.83 −0.201582
802802 0 0
803803 0 0
804804 0 0
805805 5798.04 0.253856
806806 0 0
807807 2504.83 0.109262
808808 0 0
809809 35942.4 1.56201 0.781006 0.624523i 0.214707π-0.214707\pi
0.781006 + 0.624523i 0.214707π0.214707\pi
810810 0 0
811811 −21630.0 −0.936537 −0.468269 0.883586i 0.655122π-0.655122\pi
−0.468269 + 0.883586i 0.655122π0.655122\pi
812812 0 0
813813 2460.35 0.106136
814814 0 0
815815 39.4991 0.00169766
816816 0 0
817817 −5025.29 −0.215193
818818 0 0
819819 −740.223 −0.0315818
820820 0 0
821821 −31467.1 −1.33765 −0.668824 0.743421i 0.733202π-0.733202\pi
−0.668824 + 0.743421i 0.733202π0.733202\pi
822822 0 0
823823 −35233.1 −1.49228 −0.746142 0.665787i 0.768096π-0.768096\pi
−0.746142 + 0.665787i 0.768096π0.768096\pi
824824 0 0
825825 0 0
826826 0 0
827827 −9490.61 −0.399058 −0.199529 0.979892i 0.563941π-0.563941\pi
−0.199529 + 0.979892i 0.563941π0.563941\pi
828828 0 0
829829 −38433.6 −1.61020 −0.805099 0.593140i 0.797888π-0.797888\pi
−0.805099 + 0.593140i 0.797888π0.797888\pi
830830 0 0
831831 43216.3 1.80404
832832 0 0
833833 −6.83206 −0.000284174 0
834834 0 0
835835 4562.34 0.189086
836836 0 0
837837 22215.3 0.917411
838838 0 0
839839 9689.22 0.398700 0.199350 0.979928i 0.436117π-0.436117\pi
0.199350 + 0.979928i 0.436117π0.436117\pi
840840 0 0
841841 −17447.7 −0.715394
842842 0 0
843843 −26342.6 −1.07626
844844 0 0
845845 11211.0 0.456413
846846 0 0
847847 0 0
848848 0 0
849849 −29950.0 −1.21069
850850 0 0
851851 16475.7 0.663667
852852 0 0
853853 24698.1 0.991380 0.495690 0.868499i 0.334915π-0.334915\pi
0.495690 + 0.868499i 0.334915π0.334915\pi
854854 0 0
855855 −1663.48 −0.0665378
856856 0 0
857857 15732.3 0.627079 0.313539 0.949575i 0.398485π-0.398485\pi
0.313539 + 0.949575i 0.398485π0.398485\pi
858858 0 0
859859 −34609.5 −1.37469 −0.687347 0.726329i 0.741225π-0.741225\pi
−0.687347 + 0.726329i 0.741225π0.741225\pi
860860 0 0
861861 13183.2 0.521814
862862 0 0
863863 −2726.72 −0.107553 −0.0537767 0.998553i 0.517126π-0.517126\pi
−0.0537767 + 0.998553i 0.517126π0.517126\pi
864864 0 0
865865 −2047.61 −0.0804867
866866 0 0
867867 −27219.5 −1.06623
868868 0 0
869869 0 0
870870 0 0
871871 4463.11 0.173624
872872 0 0
873873 −3294.11 −0.127707
874874 0 0
875875 −13266.4 −0.512557
876876 0 0
877877 2460.98 0.0947564 0.0473782 0.998877i 0.484913π-0.484913\pi
0.0473782 + 0.998877i 0.484913π0.484913\pi
878878 0 0
879879 30904.9 1.18589
880880 0 0
881881 25163.9 0.962307 0.481153 0.876636i 0.340218π-0.340218\pi
0.481153 + 0.876636i 0.340218π0.340218\pi
882882 0 0
883883 8621.41 0.328577 0.164289 0.986412i 0.447467π-0.447467\pi
0.164289 + 0.986412i 0.447467π0.447467\pi
884884 0 0
885885 12579.0 0.477783
886886 0 0
887887 42583.1 1.61195 0.805975 0.591950i 0.201642π-0.201642\pi
0.805975 + 0.591950i 0.201642π0.201642\pi
888888 0 0
889889 −26946.6 −1.01660
890890 0 0
891891 0 0
892892 0 0
893893 −31357.5 −1.17507
894894 0 0
895895 −16607.8 −0.620264
896896 0 0
897897 10153.9 0.377959
898898 0 0
899899 −14334.7 −0.531800
900900 0 0
901901 −17.0020 −0.000628657 0
902902 0 0
903903 3881.86 0.143057
904904 0 0
905905 9608.90 0.352940
906906 0 0
907907 9507.78 0.348071 0.174036 0.984739i 0.444319π-0.444319\pi
0.174036 + 0.984739i 0.444319π0.444319\pi
908908 0 0
909909 −1138.08 −0.0415267
910910 0 0
911911 11475.1 0.417330 0.208665 0.977987i 0.433088π-0.433088\pi
0.208665 + 0.977987i 0.433088π0.433088\pi
912912 0 0
913913 0 0
914914 0 0
915915 23613.6 0.853159
916916 0 0
917917 −7015.42 −0.252639
918918 0 0
919919 42341.9 1.51984 0.759918 0.650019i 0.225239π-0.225239\pi
0.759918 + 0.650019i 0.225239π0.225239\pi
920920 0 0
921921 −40160.6 −1.43685
922922 0 0
923923 −5052.61 −0.180183
924924 0 0
925925 −15402.1 −0.547480
926926 0 0
927927 −4112.21 −0.145699
928928 0 0
929929 −42583.6 −1.50390 −0.751950 0.659221i 0.770886π-0.770886\pi
−0.751950 + 0.659221i 0.770886π0.770886\pi
930930 0 0
931931 −17456.4 −0.614510
932932 0 0
933933 5280.94 0.185306
934934 0 0
935935 0 0
936936 0 0
937937 −8318.19 −0.290014 −0.145007 0.989431i 0.546320π-0.546320\pi
−0.145007 + 0.989431i 0.546320π0.546320\pi
938938 0 0
939939 18647.1 0.648056
940940 0 0
941941 32022.6 1.10936 0.554679 0.832064i 0.312841π-0.312841\pi
0.554679 + 0.832064i 0.312841π0.312841\pi
942942 0 0
943943 −21768.9 −0.751743
944944 0 0
945945 −8104.63 −0.278988
946946 0 0
947947 −28430.6 −0.975575 −0.487788 0.872962i 0.662196π-0.662196\pi
−0.487788 + 0.872962i 0.662196π0.662196\pi
948948 0 0
949949 −17506.3 −0.598818
950950 0 0
951951 48770.9 1.66299
952952 0 0
953953 −6805.74 −0.231332 −0.115666 0.993288i 0.536900π-0.536900\pi
−0.115666 + 0.993288i 0.536900π0.536900\pi
954954 0 0
955955 −7372.34 −0.249804
956956 0 0
957957 0 0
958958 0 0
959959 −25009.9 −0.842140
960960 0 0
961961 −187.857 −0.00630584
962962 0 0
963963 −6406.60 −0.214382
964964 0 0
965965 8336.36 0.278090
966966 0 0
967967 41912.2 1.39380 0.696901 0.717167i 0.254562π-0.254562\pi
0.696901 + 0.717167i 0.254562π0.254562\pi
968968 0 0
969969 11.3711 0.000376980 0
970970 0 0
971971 50663.6 1.67443 0.837216 0.546873i 0.184182π-0.184182\pi
0.837216 + 0.546873i 0.184182π0.184182\pi
972972 0 0
973973 22176.0 0.730657
974974 0 0
975975 −9492.26 −0.311790
976976 0 0
977977 8475.61 0.277542 0.138771 0.990324i 0.455685π-0.455685\pi
0.138771 + 0.990324i 0.455685π0.455685\pi
978978 0 0
979979 0 0
980980 0 0
981981 5783.82 0.188240
982982 0 0
983983 −25920.5 −0.841034 −0.420517 0.907285i 0.638151π-0.638151\pi
−0.420517 + 0.907285i 0.638151π0.638151\pi
984984 0 0
985985 −4955.95 −0.160314
986986 0 0
987987 24222.6 0.781170
988988 0 0
989989 −6409.97 −0.206092
990990 0 0
991991 −52359.2 −1.67835 −0.839174 0.543863i 0.816961π-0.816961\pi
−0.839174 + 0.543863i 0.816961π0.816961\pi
992992 0 0
993993 10441.4 0.333683
994994 0 0
995995 −744.503 −0.0237209
996996 0 0
997997 −15452.3 −0.490852 −0.245426 0.969415i 0.578928π-0.578928\pi
−0.245426 + 0.969415i 0.578928π0.578928\pi
998998 0 0
999999 −23030.1 −0.729370
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 968.4.a.n.1.7 8
4.3 odd 2 1936.4.a.bw.1.2 8
11.5 even 5 88.4.i.a.25.4 16
11.9 even 5 88.4.i.a.81.4 yes 16
11.10 odd 2 968.4.a.o.1.7 8
44.27 odd 10 176.4.m.e.113.1 16
44.31 odd 10 176.4.m.e.81.1 16
44.43 even 2 1936.4.a.bv.1.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
88.4.i.a.25.4 16 11.5 even 5
88.4.i.a.81.4 yes 16 11.9 even 5
176.4.m.e.81.1 16 44.31 odd 10
176.4.m.e.113.1 16 44.27 odd 10
968.4.a.n.1.7 8 1.1 even 1 trivial
968.4.a.o.1.7 8 11.10 odd 2
1936.4.a.bv.1.2 8 44.43 even 2
1936.4.a.bw.1.2 8 4.3 odd 2