Properties

Label 9196.2.a.s.1.3
Level 91969196
Weight 22
Character 9196.1
Self dual yes
Analytic conductor 73.43073.430
Analytic rank 11
Dimension 1010
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] = [9196,2,Mod(1,9196)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9196, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9196.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 9196=2211219 9196 = 2^{2} \cdot 11^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 9196.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: 73.430429698873.4304296988
Analytic rank: 11
Dimension: 1010
Coefficient field: Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x1016x83x7+84x6+16x5174x416x3+122x29 x^{10} - 16x^{8} - 3x^{7} + 84x^{6} + 16x^{5} - 174x^{4} - 16x^{3} + 122x^{2} - 9 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 836)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 1.439171.43917 of defining polynomial
Character χ\chi == 9196.1

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) == q1.43917q31.46040q5+2.94667q70.928777q9+2.95605q13+2.10178q15+1.11490q17+1.00000q194.24077q21+6.23162q232.86722q25+5.65420q275.44747q294.95247q314.30332q352.84952q374.25427q3912.2615q411.95512q43+1.35639q454.03225q47+1.68285q491.60453q51+0.0749606q531.43917q57+2.93575q590.0740859q612.73680q634.31703q65+3.18622q678.96839q69+11.5779q710.483015q73+4.12643q75+5.27944q795.35104q818.39444q831.62820q85+7.83986q87+7.78559q89+8.71050q91+7.12746q931.46040q95+4.75458q97+O(q100)q-1.43917 q^{3} -1.46040 q^{5} +2.94667 q^{7} -0.928777 q^{9} +2.95605 q^{13} +2.10178 q^{15} +1.11490 q^{17} +1.00000 q^{19} -4.24077 q^{21} +6.23162 q^{23} -2.86722 q^{25} +5.65420 q^{27} -5.44747 q^{29} -4.95247 q^{31} -4.30332 q^{35} -2.84952 q^{37} -4.25427 q^{39} -12.2615 q^{41} -1.95512 q^{43} +1.35639 q^{45} -4.03225 q^{47} +1.68285 q^{49} -1.60453 q^{51} +0.0749606 q^{53} -1.43917 q^{57} +2.93575 q^{59} -0.0740859 q^{61} -2.73680 q^{63} -4.31703 q^{65} +3.18622 q^{67} -8.96839 q^{69} +11.5779 q^{71} -0.483015 q^{73} +4.12643 q^{75} +5.27944 q^{79} -5.35104 q^{81} -8.39444 q^{83} -1.62820 q^{85} +7.83986 q^{87} +7.78559 q^{89} +8.71050 q^{91} +7.12746 q^{93} -1.46040 q^{95} +4.75458 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q+8q55q7+2q9+2q1310q154q17+10q196q218q2310q259q27+3q2912q319q3523q37+18q39+5q41+14q43++22q97+O(q100) 10 q + 8 q^{5} - 5 q^{7} + 2 q^{9} + 2 q^{13} - 10 q^{15} - 4 q^{17} + 10 q^{19} - 6 q^{21} - 8 q^{23} - 10 q^{25} - 9 q^{27} + 3 q^{29} - 12 q^{31} - 9 q^{35} - 23 q^{37} + 18 q^{39} + 5 q^{41} + 14 q^{43}+ \cdots + 22 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 −1.43917 −0.830908 −0.415454 0.909614i 0.636377π-0.636377\pi
−0.415454 + 0.909614i 0.636377π0.636377\pi
44 0 0
55 −1.46040 −0.653112 −0.326556 0.945178i 0.605888π-0.605888\pi
−0.326556 + 0.945178i 0.605888π0.605888\pi
66 0 0
77 2.94667 1.11374 0.556868 0.830601i 0.312003π-0.312003\pi
0.556868 + 0.830601i 0.312003π0.312003\pi
88 0 0
99 −0.928777 −0.309592
1010 0 0
1111 0 0
1212 0 0
1313 2.95605 0.819861 0.409931 0.912117i 0.365553π-0.365553\pi
0.409931 + 0.912117i 0.365553π0.365553\pi
1414 0 0
1515 2.10178 0.542676
1616 0 0
1717 1.11490 0.270402 0.135201 0.990818i 0.456832π-0.456832\pi
0.135201 + 0.990818i 0.456832π0.456832\pi
1818 0 0
1919 1.00000 0.229416
2020 0 0
2121 −4.24077 −0.925411
2222 0 0
2323 6.23162 1.29938 0.649691 0.760198i 0.274898π-0.274898\pi
0.649691 + 0.760198i 0.274898π0.274898\pi
2424 0 0
2525 −2.86722 −0.573444
2626 0 0
2727 5.65420 1.08815
2828 0 0
2929 −5.44747 −1.01157 −0.505785 0.862660i 0.668797π-0.668797\pi
−0.505785 + 0.862660i 0.668797π0.668797\pi
3030 0 0
3131 −4.95247 −0.889489 −0.444745 0.895657i 0.646706π-0.646706\pi
−0.444745 + 0.895657i 0.646706π0.646706\pi
3232 0 0
3333 0 0
3434 0 0
3535 −4.30332 −0.727394
3636 0 0
3737 −2.84952 −0.468458 −0.234229 0.972181i 0.575257π-0.575257\pi
−0.234229 + 0.972181i 0.575257π0.575257\pi
3838 0 0
3939 −4.25427 −0.681229
4040 0 0
4141 −12.2615 −1.91493 −0.957464 0.288551i 0.906826π-0.906826\pi
−0.957464 + 0.288551i 0.906826π0.906826\pi
4242 0 0
4343 −1.95512 −0.298154 −0.149077 0.988826i 0.547630π-0.547630\pi
−0.149077 + 0.988826i 0.547630π0.547630\pi
4444 0 0
4545 1.35639 0.202199
4646 0 0
4747 −4.03225 −0.588164 −0.294082 0.955780i 0.595014π-0.595014\pi
−0.294082 + 0.955780i 0.595014π0.595014\pi
4848 0 0
4949 1.68285 0.240407
5050 0 0
5151 −1.60453 −0.224679
5252 0 0
5353 0.0749606 0.0102966 0.00514832 0.999987i 0.498361π-0.498361\pi
0.00514832 + 0.999987i 0.498361π0.498361\pi
5454 0 0
5555 0 0
5656 0 0
5757 −1.43917 −0.190623
5858 0 0
5959 2.93575 0.382202 0.191101 0.981570i 0.438794π-0.438794\pi
0.191101 + 0.981570i 0.438794π0.438794\pi
6060 0 0
6161 −0.0740859 −0.00948573 −0.00474287 0.999989i 0.501510π-0.501510\pi
−0.00474287 + 0.999989i 0.501510π0.501510\pi
6262 0 0
6363 −2.73680 −0.344804
6464 0 0
6565 −4.31703 −0.535462
6666 0 0
6767 3.18622 0.389259 0.194630 0.980877i 0.437650π-0.437650\pi
0.194630 + 0.980877i 0.437650π0.437650\pi
6868 0 0
6969 −8.96839 −1.07967
7070 0 0
7171 11.5779 1.37405 0.687023 0.726636i 0.258917π-0.258917\pi
0.687023 + 0.726636i 0.258917π0.258917\pi
7272 0 0
7373 −0.483015 −0.0565326 −0.0282663 0.999600i 0.508999π-0.508999\pi
−0.0282663 + 0.999600i 0.508999π0.508999\pi
7474 0 0
7575 4.12643 0.476479
7676 0 0
7777 0 0
7878 0 0
7979 5.27944 0.593983 0.296991 0.954880i 0.404017π-0.404017\pi
0.296991 + 0.954880i 0.404017π0.404017\pi
8080 0 0
8181 −5.35104 −0.594560
8282 0 0
8383 −8.39444 −0.921410 −0.460705 0.887553i 0.652403π-0.652403\pi
−0.460705 + 0.887553i 0.652403π0.652403\pi
8484 0 0
8585 −1.62820 −0.176603
8686 0 0
8787 7.83986 0.840521
8888 0 0
8989 7.78559 0.825271 0.412635 0.910896i 0.364608π-0.364608\pi
0.412635 + 0.910896i 0.364608π0.364608\pi
9090 0 0
9191 8.71050 0.913109
9292 0 0
9393 7.12746 0.739083
9494 0 0
9595 −1.46040 −0.149834
9696 0 0
9797 4.75458 0.482754 0.241377 0.970431i 0.422401π-0.422401\pi
0.241377 + 0.970431i 0.422401π0.422401\pi
9898 0 0
9999 0 0
100100 0 0
101101 −1.87406 −0.186476 −0.0932380 0.995644i 0.529722π-0.529722\pi
−0.0932380 + 0.995644i 0.529722π0.529722\pi
102102 0 0
103103 −2.68834 −0.264890 −0.132445 0.991190i 0.542283π-0.542283\pi
−0.132445 + 0.991190i 0.542283π0.542283\pi
104104 0 0
105105 6.19323 0.604398
106106 0 0
107107 2.65438 0.256609 0.128304 0.991735i 0.459047π-0.459047\pi
0.128304 + 0.991735i 0.459047π0.459047\pi
108108 0 0
109109 8.05431 0.771463 0.385731 0.922611i 0.373949π-0.373949\pi
0.385731 + 0.922611i 0.373949π0.373949\pi
110110 0 0
111111 4.10095 0.389245
112112 0 0
113113 0.257951 0.0242660 0.0121330 0.999926i 0.496138π-0.496138\pi
0.0121330 + 0.999926i 0.496138π0.496138\pi
114114 0 0
115115 −9.10068 −0.848643
116116 0 0
117117 −2.74551 −0.253823
118118 0 0
119119 3.28523 0.301157
120120 0 0
121121 0 0
122122 0 0
123123 17.6465 1.59113
124124 0 0
125125 11.4893 1.02764
126126 0 0
127127 −19.7585 −1.75329 −0.876643 0.481142i 0.840222π-0.840222\pi
−0.876643 + 0.481142i 0.840222π0.840222\pi
128128 0 0
129129 2.81377 0.247738
130130 0 0
131131 4.64754 0.406057 0.203029 0.979173i 0.434922π-0.434922\pi
0.203029 + 0.979173i 0.434922π0.434922\pi
132132 0 0
133133 2.94667 0.255508
134134 0 0
135135 −8.25741 −0.710684
136136 0 0
137137 −11.6941 −0.999096 −0.499548 0.866286i 0.666501π-0.666501\pi
−0.499548 + 0.866286i 0.666501π0.666501\pi
138138 0 0
139139 16.8580 1.42988 0.714938 0.699188i 0.246455π-0.246455\pi
0.714938 + 0.699188i 0.246455π0.246455\pi
140140 0 0
141141 5.80311 0.488710
142142 0 0
143143 0 0
144144 0 0
145145 7.95550 0.660668
146146 0 0
147147 −2.42191 −0.199756
148148 0 0
149149 −14.1985 −1.16318 −0.581592 0.813480i 0.697570π-0.697570\pi
−0.581592 + 0.813480i 0.697570π0.697570\pi
150150 0 0
151151 15.2687 1.24255 0.621273 0.783594i 0.286616π-0.286616\pi
0.621273 + 0.783594i 0.286616π0.286616\pi
152152 0 0
153153 −1.03549 −0.0837145
154154 0 0
155155 7.23260 0.580936
156156 0 0
157157 19.4455 1.55192 0.775959 0.630783i 0.217266π-0.217266\pi
0.775959 + 0.630783i 0.217266π0.217266\pi
158158 0 0
159159 −0.107881 −0.00855555
160160 0 0
161161 18.3625 1.44717
162162 0 0
163163 −19.4845 −1.52615 −0.763074 0.646312i 0.776311π-0.776311\pi
−0.763074 + 0.646312i 0.776311π0.776311\pi
164164 0 0
165165 0 0
166166 0 0
167167 −7.64762 −0.591791 −0.295895 0.955220i 0.595618π-0.595618\pi
−0.295895 + 0.955220i 0.595618π0.595618\pi
168168 0 0
169169 −4.26176 −0.327827
170170 0 0
171171 −0.928777 −0.0710254
172172 0 0
173173 −1.71505 −0.130393 −0.0651963 0.997872i 0.520767π-0.520767\pi
−0.0651963 + 0.997872i 0.520767π0.520767\pi
174174 0 0
175175 −8.44875 −0.638665
176176 0 0
177177 −4.22505 −0.317574
178178 0 0
179179 −8.39932 −0.627795 −0.313897 0.949457i 0.601635π-0.601635\pi
−0.313897 + 0.949457i 0.601635π0.601635\pi
180180 0 0
181181 −20.0508 −1.49037 −0.745183 0.666860i 0.767638π-0.767638\pi
−0.745183 + 0.666860i 0.767638π0.767638\pi
182182 0 0
183183 0.106623 0.00788177
184184 0 0
185185 4.16145 0.305956
186186 0 0
187187 0 0
188188 0 0
189189 16.6610 1.21191
190190 0 0
191191 −13.4448 −0.972832 −0.486416 0.873727i 0.661696π-0.661696\pi
−0.486416 + 0.873727i 0.661696π0.661696\pi
192192 0 0
193193 −11.9698 −0.861608 −0.430804 0.902445i 0.641770π-0.641770\pi
−0.430804 + 0.902445i 0.641770π0.641770\pi
194194 0 0
195195 6.21296 0.444919
196196 0 0
197197 −18.0316 −1.28469 −0.642347 0.766414i 0.722039π-0.722039\pi
−0.642347 + 0.766414i 0.722039π0.722039\pi
198198 0 0
199199 21.3508 1.51352 0.756760 0.653693i 0.226781π-0.226781\pi
0.756760 + 0.653693i 0.226781π0.226781\pi
200200 0 0
201201 −4.58553 −0.323438
202202 0 0
203203 −16.0519 −1.12662
204204 0 0
205205 17.9068 1.25066
206206 0 0
207207 −5.78778 −0.402279
208208 0 0
209209 0 0
210210 0 0
211211 27.8923 1.92018 0.960092 0.279684i 0.0902297π-0.0902297\pi
0.960092 + 0.279684i 0.0902297π0.0902297\pi
212212 0 0
213213 −16.6626 −1.14171
214214 0 0
215215 2.85527 0.194728
216216 0 0
217217 −14.5933 −0.990656
218218 0 0
219219 0.695143 0.0469734
220220 0 0
221221 3.29570 0.221692
222222 0 0
223223 7.46194 0.499689 0.249844 0.968286i 0.419621π-0.419621\pi
0.249844 + 0.968286i 0.419621π0.419621\pi
224224 0 0
225225 2.66301 0.177534
226226 0 0
227227 −27.6861 −1.83759 −0.918796 0.394733i 0.870837π-0.870837\pi
−0.918796 + 0.394733i 0.870837π0.870837\pi
228228 0 0
229229 −21.0639 −1.39194 −0.695970 0.718071i 0.745025π-0.745025\pi
−0.695970 + 0.718071i 0.745025π0.745025\pi
230230 0 0
231231 0 0
232232 0 0
233233 24.8659 1.62902 0.814509 0.580151i 0.197006π-0.197006\pi
0.814509 + 0.580151i 0.197006π0.197006\pi
234234 0 0
235235 5.88871 0.384137
236236 0 0
237237 −7.59803 −0.493545
238238 0 0
239239 −15.7089 −1.01613 −0.508063 0.861320i 0.669638π-0.669638\pi
−0.508063 + 0.861320i 0.669638π0.669638\pi
240240 0 0
241241 −14.3016 −0.921249 −0.460624 0.887595i 0.652374π-0.652374\pi
−0.460624 + 0.887595i 0.652374π0.652374\pi
242242 0 0
243243 −9.26150 −0.594126
244244 0 0
245245 −2.45764 −0.157013
246246 0 0
247247 2.95605 0.188089
248248 0 0
249249 12.0811 0.765607
250250 0 0
251251 0.351776 0.0222039 0.0111019 0.999938i 0.496466π-0.496466\pi
0.0111019 + 0.999938i 0.496466π0.496466\pi
252252 0 0
253253 0 0
254254 0 0
255255 2.34326 0.146741
256256 0 0
257257 1.17252 0.0731401 0.0365700 0.999331i 0.488357π-0.488357\pi
0.0365700 + 0.999331i 0.488357π0.488357\pi
258258 0 0
259259 −8.39658 −0.521738
260260 0 0
261261 5.05948 0.313174
262262 0 0
263263 −11.5816 −0.714154 −0.357077 0.934075i 0.616227π-0.616227\pi
−0.357077 + 0.934075i 0.616227π0.616227\pi
264264 0 0
265265 −0.109473 −0.00672486
266266 0 0
267267 −11.2048 −0.685724
268268 0 0
269269 0.822788 0.0501662 0.0250831 0.999685i 0.492015π-0.492015\pi
0.0250831 + 0.999685i 0.492015π0.492015\pi
270270 0 0
271271 11.6980 0.710602 0.355301 0.934752i 0.384378π-0.384378\pi
0.355301 + 0.934752i 0.384378π0.384378\pi
272272 0 0
273273 −12.5359 −0.758709
274274 0 0
275275 0 0
276276 0 0
277277 1.53225 0.0920643 0.0460321 0.998940i 0.485342π-0.485342\pi
0.0460321 + 0.998940i 0.485342π0.485342\pi
278278 0 0
279279 4.59974 0.275379
280280 0 0
281281 15.2564 0.910121 0.455060 0.890461i 0.349618π-0.349618\pi
0.455060 + 0.890461i 0.349618π0.349618\pi
282282 0 0
283283 8.96708 0.533038 0.266519 0.963830i 0.414127π-0.414127\pi
0.266519 + 0.963830i 0.414127π0.414127\pi
284284 0 0
285285 2.10178 0.124498
286286 0 0
287287 −36.1306 −2.13272
288288 0 0
289289 −15.7570 −0.926883
290290 0 0
291291 −6.84267 −0.401124
292292 0 0
293293 −14.7384 −0.861026 −0.430513 0.902584i 0.641667π-0.641667\pi
−0.430513 + 0.902584i 0.641667π0.641667\pi
294294 0 0
295295 −4.28738 −0.249621
296296 0 0
297297 0 0
298298 0 0
299299 18.4210 1.06531
300300 0 0
301301 −5.76110 −0.332064
302302 0 0
303303 2.69710 0.154944
304304 0 0
305305 0.108195 0.00619525
306306 0 0
307307 5.58452 0.318726 0.159363 0.987220i 0.449056π-0.449056\pi
0.159363 + 0.987220i 0.449056π0.449056\pi
308308 0 0
309309 3.86899 0.220099
310310 0 0
311311 −28.5036 −1.61629 −0.808145 0.588984i 0.799528π-0.799528\pi
−0.808145 + 0.588984i 0.799528π0.799528\pi
312312 0 0
313313 −16.5910 −0.937781 −0.468890 0.883256i 0.655346π-0.655346\pi
−0.468890 + 0.883256i 0.655346π0.655346\pi
314314 0 0
315315 3.99683 0.225196
316316 0 0
317317 22.1448 1.24378 0.621888 0.783106i 0.286366π-0.286366\pi
0.621888 + 0.783106i 0.286366π0.286366\pi
318318 0 0
319319 0 0
320320 0 0
321321 −3.82011 −0.213218
322322 0 0
323323 1.11490 0.0620346
324324 0 0
325325 −8.47566 −0.470145
326326 0 0
327327 −11.5916 −0.641014
328328 0 0
329329 −11.8817 −0.655059
330330 0 0
331331 23.4297 1.28781 0.643907 0.765104i 0.277312π-0.277312\pi
0.643907 + 0.765104i 0.277312π0.277312\pi
332332 0 0
333333 2.64657 0.145031
334334 0 0
335335 −4.65317 −0.254230
336336 0 0
337337 −16.0969 −0.876854 −0.438427 0.898767i 0.644464π-0.644464\pi
−0.438427 + 0.898767i 0.644464π0.644464\pi
338338 0 0
339339 −0.371237 −0.0201628
340340 0 0
341341 0 0
342342 0 0
343343 −15.6679 −0.845986
344344 0 0
345345 13.0975 0.705144
346346 0 0
347347 −3.83321 −0.205778 −0.102889 0.994693i 0.532809π-0.532809\pi
−0.102889 + 0.994693i 0.532809π0.532809\pi
348348 0 0
349349 −4.53771 −0.242898 −0.121449 0.992598i 0.538754π-0.538754\pi
−0.121449 + 0.992598i 0.538754π0.538754\pi
350350 0 0
351351 16.7141 0.892132
352352 0 0
353353 27.3402 1.45517 0.727586 0.686017i 0.240642π-0.240642\pi
0.727586 + 0.686017i 0.240642π0.240642\pi
354354 0 0
355355 −16.9084 −0.897406
356356 0 0
357357 −4.72802 −0.250233
358358 0 0
359359 24.9406 1.31631 0.658157 0.752881i 0.271336π-0.271336\pi
0.658157 + 0.752881i 0.271336π0.271336\pi
360360 0 0
361361 1.00000 0.0526316
362362 0 0
363363 0 0
364364 0 0
365365 0.705397 0.0369221
366366 0 0
367367 −17.7477 −0.926422 −0.463211 0.886248i 0.653303π-0.653303\pi
−0.463211 + 0.886248i 0.653303π0.653303\pi
368368 0 0
369369 11.3882 0.592847
370370 0 0
371371 0.220884 0.0114677
372372 0 0
373373 21.7030 1.12374 0.561870 0.827225i 0.310082π-0.310082\pi
0.561870 + 0.827225i 0.310082π0.310082\pi
374374 0 0
375375 −16.5351 −0.853871
376376 0 0
377377 −16.1030 −0.829347
378378 0 0
379379 −1.58372 −0.0813504 −0.0406752 0.999172i 0.512951π-0.512951\pi
−0.0406752 + 0.999172i 0.512951π0.512951\pi
380380 0 0
381381 28.4360 1.45682
382382 0 0
383383 −33.2985 −1.70147 −0.850736 0.525593i 0.823844π-0.823844\pi
−0.850736 + 0.525593i 0.823844π0.823844\pi
384384 0 0
385385 0 0
386386 0 0
387387 1.81588 0.0923061
388388 0 0
389389 29.9928 1.52070 0.760349 0.649515i 0.225028π-0.225028\pi
0.760349 + 0.649515i 0.225028π0.225028\pi
390390 0 0
391391 6.94762 0.351356
392392 0 0
393393 −6.68862 −0.337396
394394 0 0
395395 −7.71011 −0.387938
396396 0 0
397397 3.94977 0.198234 0.0991168 0.995076i 0.468398π-0.468398\pi
0.0991168 + 0.995076i 0.468398π0.468398\pi
398398 0 0
399399 −4.24077 −0.212304
400400 0 0
401401 −34.8660 −1.74112 −0.870561 0.492060i 0.836244π-0.836244\pi
−0.870561 + 0.492060i 0.836244π0.836244\pi
402402 0 0
403403 −14.6397 −0.729258
404404 0 0
405405 7.81468 0.388315
406406 0 0
407407 0 0
408408 0 0
409409 3.93351 0.194500 0.0972498 0.995260i 0.468995π-0.468995\pi
0.0972498 + 0.995260i 0.468995π0.468995\pi
410410 0 0
411411 16.8299 0.830157
412412 0 0
413413 8.65067 0.425672
414414 0 0
415415 12.2593 0.601784
416416 0 0
417417 −24.2616 −1.18810
418418 0 0
419419 −22.8214 −1.11490 −0.557449 0.830211i 0.688220π-0.688220\pi
−0.557449 + 0.830211i 0.688220π0.688220\pi
420420 0 0
421421 27.3763 1.33424 0.667119 0.744951i 0.267527π-0.267527\pi
0.667119 + 0.744951i 0.267527π0.267527\pi
422422 0 0
423423 3.74506 0.182091
424424 0 0
425425 −3.19666 −0.155061
426426 0 0
427427 −0.218307 −0.0105646
428428 0 0
429429 0 0
430430 0 0
431431 −15.6547 −0.754062 −0.377031 0.926201i 0.623055π-0.623055\pi
−0.377031 + 0.926201i 0.623055π0.623055\pi
432432 0 0
433433 21.0192 1.01012 0.505060 0.863085i 0.331471π-0.331471\pi
0.505060 + 0.863085i 0.331471π0.331471\pi
434434 0 0
435435 −11.4494 −0.548955
436436 0 0
437437 6.23162 0.298099
438438 0 0
439439 −12.7001 −0.606144 −0.303072 0.952968i 0.598012π-0.598012\pi
−0.303072 + 0.952968i 0.598012π0.598012\pi
440440 0 0
441441 −1.56299 −0.0744281
442442 0 0
443443 −16.0928 −0.764593 −0.382296 0.924040i 0.624867π-0.624867\pi
−0.382296 + 0.924040i 0.624867π0.624867\pi
444444 0 0
445445 −11.3701 −0.538995
446446 0 0
447447 20.4341 0.966499
448448 0 0
449449 −0.908087 −0.0428553 −0.0214276 0.999770i 0.506821π-0.506821\pi
−0.0214276 + 0.999770i 0.506821π0.506821\pi
450450 0 0
451451 0 0
452452 0 0
453453 −21.9743 −1.03244
454454 0 0
455455 −12.7208 −0.596363
456456 0 0
457457 −21.1577 −0.989718 −0.494859 0.868973i 0.664780π-0.664780\pi
−0.494859 + 0.868973i 0.664780π0.664780\pi
458458 0 0
459459 6.30385 0.294238
460460 0 0
461461 −27.9700 −1.30269 −0.651347 0.758780i 0.725796π-0.725796\pi
−0.651347 + 0.758780i 0.725796π0.725796\pi
462462 0 0
463463 −29.9663 −1.39265 −0.696325 0.717726i 0.745183π-0.745183\pi
−0.696325 + 0.717726i 0.745183π0.745183\pi
464464 0 0
465465 −10.4090 −0.482704
466466 0 0
467467 −2.78850 −0.129036 −0.0645181 0.997917i 0.520551π-0.520551\pi
−0.0645181 + 0.997917i 0.520551π0.520551\pi
468468 0 0
469469 9.38874 0.433532
470470 0 0
471471 −27.9854 −1.28950
472472 0 0
473473 0 0
474474 0 0
475475 −2.86722 −0.131557
476476 0 0
477477 −0.0696217 −0.00318776
478478 0 0
479479 15.7397 0.719167 0.359583 0.933113i 0.382919π-0.382919\pi
0.359583 + 0.933113i 0.382919π0.382919\pi
480480 0 0
481481 −8.42333 −0.384071
482482 0 0
483483 −26.4268 −1.20246
484484 0 0
485485 −6.94360 −0.315293
486486 0 0
487487 −28.9843 −1.31340 −0.656702 0.754151i 0.728049π-0.728049\pi
−0.656702 + 0.754151i 0.728049π0.728049\pi
488488 0 0
489489 28.0417 1.26809
490490 0 0
491491 5.29830 0.239109 0.119554 0.992828i 0.461853π-0.461853\pi
0.119554 + 0.992828i 0.461853π0.461853\pi
492492 0 0
493493 −6.07337 −0.273531
494494 0 0
495495 0 0
496496 0 0
497497 34.1163 1.53032
498498 0 0
499499 −27.4614 −1.22934 −0.614670 0.788784i 0.710711π-0.710711\pi
−0.614670 + 0.788784i 0.710711π0.710711\pi
500500 0 0
501501 11.0063 0.491723
502502 0 0
503503 −24.7566 −1.10384 −0.551920 0.833897i 0.686105π-0.686105\pi
−0.551920 + 0.833897i 0.686105π0.686105\pi
504504 0 0
505505 2.73688 0.121790
506506 0 0
507507 6.13341 0.272394
508508 0 0
509509 −31.0388 −1.37577 −0.687886 0.725819i 0.741461π-0.741461\pi
−0.687886 + 0.725819i 0.741461π0.741461\pi
510510 0 0
511511 −1.42328 −0.0629624
512512 0 0
513513 5.65420 0.249639
514514 0 0
515515 3.92606 0.173003
516516 0 0
517517 0 0
518518 0 0
519519 2.46825 0.108344
520520 0 0
521521 −5.95793 −0.261021 −0.130511 0.991447i 0.541662π-0.541662\pi
−0.130511 + 0.991447i 0.541662π0.541662\pi
522522 0 0
523523 7.62722 0.333515 0.166758 0.985998i 0.446670π-0.446670\pi
0.166758 + 0.985998i 0.446670π0.446670\pi
524524 0 0
525525 12.1592 0.530672
526526 0 0
527527 −5.52149 −0.240520
528528 0 0
529529 15.8331 0.688394
530530 0 0
531531 −2.72666 −0.118327
532532 0 0
533533 −36.2457 −1.56998
534534 0 0
535535 −3.87647 −0.167594
536536 0 0
537537 12.0881 0.521639
538538 0 0
539539 0 0
540540 0 0
541541 −17.8559 −0.767687 −0.383844 0.923398i 0.625400π-0.625400\pi
−0.383844 + 0.923398i 0.625400π0.625400\pi
542542 0 0
543543 28.8566 1.23836
544544 0 0
545545 −11.7625 −0.503852
546546 0 0
547547 19.8352 0.848092 0.424046 0.905641i 0.360610π-0.360610\pi
0.424046 + 0.905641i 0.360610π0.360610\pi
548548 0 0
549549 0.0688093 0.00293671
550550 0 0
551551 −5.44747 −0.232070
552552 0 0
553553 15.5567 0.661540
554554 0 0
555555 −5.98905 −0.254221
556556 0 0
557557 −3.04144 −0.128870 −0.0644350 0.997922i 0.520525π-0.520525\pi
−0.0644350 + 0.997922i 0.520525π0.520525\pi
558558 0 0
559559 −5.77945 −0.244445
560560 0 0
561561 0 0
562562 0 0
563563 −14.5682 −0.613975 −0.306988 0.951713i 0.599321π-0.599321\pi
−0.306988 + 0.951713i 0.599321π0.599321\pi
564564 0 0
565565 −0.376713 −0.0158484
566566 0 0
567567 −15.7677 −0.662183
568568 0 0
569569 −15.0474 −0.630819 −0.315409 0.948956i 0.602142π-0.602142\pi
−0.315409 + 0.948956i 0.602142π0.602142\pi
570570 0 0
571571 9.64735 0.403729 0.201864 0.979413i 0.435300π-0.435300\pi
0.201864 + 0.979413i 0.435300π0.435300\pi
572572 0 0
573573 19.3494 0.808334
574574 0 0
575575 −17.8674 −0.745123
576576 0 0
577577 2.58272 0.107520 0.0537600 0.998554i 0.482879π-0.482879\pi
0.0537600 + 0.998554i 0.482879π0.482879\pi
578578 0 0
579579 17.2267 0.715917
580580 0 0
581581 −24.7356 −1.02621
582582 0 0
583583 0 0
584584 0 0
585585 4.00956 0.165775
586586 0 0
587587 −22.2977 −0.920325 −0.460163 0.887835i 0.652209π-0.652209\pi
−0.460163 + 0.887835i 0.652209π0.652209\pi
588588 0 0
589589 −4.95247 −0.204063
590590 0 0
591591 25.9505 1.06746
592592 0 0
593593 −15.2005 −0.624208 −0.312104 0.950048i 0.601034π-0.601034\pi
−0.312104 + 0.950048i 0.601034π0.601034\pi
594594 0 0
595595 −4.79777 −0.196689
596596 0 0
597597 −30.7276 −1.25759
598598 0 0
599599 −22.0761 −0.902006 −0.451003 0.892523i 0.648934π-0.648934\pi
−0.451003 + 0.892523i 0.648934π0.648934\pi
600600 0 0
601601 −16.5255 −0.674088 −0.337044 0.941489i 0.609427π-0.609427\pi
−0.337044 + 0.941489i 0.609427π0.609427\pi
602602 0 0
603603 −2.95929 −0.120512
604604 0 0
605605 0 0
606606 0 0
607607 7.92037 0.321478 0.160739 0.986997i 0.448612π-0.448612\pi
0.160739 + 0.986997i 0.448612π0.448612\pi
608608 0 0
609609 23.1014 0.936118
610610 0 0
611611 −11.9195 −0.482213
612612 0 0
613613 18.8271 0.760419 0.380209 0.924900i 0.375852π-0.375852\pi
0.380209 + 0.924900i 0.375852π0.375852\pi
614614 0 0
615615 −25.7710 −1.03919
616616 0 0
617617 −13.2885 −0.534975 −0.267487 0.963561i 0.586193π-0.586193\pi
−0.267487 + 0.963561i 0.586193π0.586193\pi
618618 0 0
619619 −39.1318 −1.57284 −0.786420 0.617692i 0.788068π-0.788068\pi
−0.786420 + 0.617692i 0.788068π0.788068\pi
620620 0 0
621621 35.2348 1.41392
622622 0 0
623623 22.9415 0.919134
624624 0 0
625625 −2.44294 −0.0977174
626626 0 0
627627 0 0
628628 0 0
629629 −3.17692 −0.126672
630630 0 0
631631 −22.1395 −0.881361 −0.440680 0.897664i 0.645263π-0.645263\pi
−0.440680 + 0.897664i 0.645263π0.645263\pi
632632 0 0
633633 −40.1419 −1.59550
634634 0 0
635635 28.8554 1.14509
636636 0 0
637637 4.97458 0.197100
638638 0 0
639639 −10.7533 −0.425394
640640 0 0
641641 −7.71948 −0.304901 −0.152451 0.988311i 0.548717π-0.548717\pi
−0.152451 + 0.988311i 0.548717π0.548717\pi
642642 0 0
643643 42.6046 1.68016 0.840081 0.542461i 0.182508π-0.182508\pi
0.840081 + 0.542461i 0.182508π0.182508\pi
644644 0 0
645645 −4.10923 −0.161801
646646 0 0
647647 −10.6127 −0.417228 −0.208614 0.977998i 0.566895π-0.566895\pi
−0.208614 + 0.977998i 0.566895π0.566895\pi
648648 0 0
649649 0 0
650650 0 0
651651 21.0023 0.823143
652652 0 0
653653 −48.3078 −1.89043 −0.945215 0.326448i 0.894148π-0.894148\pi
−0.945215 + 0.326448i 0.894148π0.894148\pi
654654 0 0
655655 −6.78728 −0.265201
656656 0 0
657657 0.448613 0.0175021
658658 0 0
659659 1.71267 0.0667161 0.0333581 0.999443i 0.489380π-0.489380\pi
0.0333581 + 0.999443i 0.489380π0.489380\pi
660660 0 0
661661 48.7587 1.89649 0.948246 0.317536i 0.102855π-0.102855\pi
0.948246 + 0.317536i 0.102855π0.102855\pi
662662 0 0
663663 −4.74308 −0.184206
664664 0 0
665665 −4.30332 −0.166876
666666 0 0
667667 −33.9465 −1.31442
668668 0 0
669669 −10.7390 −0.415195
670670 0 0
671671 0 0
672672 0 0
673673 16.2999 0.628313 0.314157 0.949371i 0.398278π-0.398278\pi
0.314157 + 0.949371i 0.398278π0.398278\pi
674674 0 0
675675 −16.2118 −0.623994
676676 0 0
677677 −0.534093 −0.0205268 −0.0102634 0.999947i 0.503267π-0.503267\pi
−0.0102634 + 0.999947i 0.503267π0.503267\pi
678678 0 0
679679 14.0102 0.537661
680680 0 0
681681 39.8451 1.52687
682682 0 0
683683 −22.9689 −0.878882 −0.439441 0.898271i 0.644823π-0.644823\pi
−0.439441 + 0.898271i 0.644823π0.644823\pi
684684 0 0
685685 17.0781 0.652522
686686 0 0
687687 30.3146 1.15657
688688 0 0
689689 0.221588 0.00844181
690690 0 0
691691 48.6707 1.85152 0.925760 0.378111i 0.123426π-0.123426\pi
0.925760 + 0.378111i 0.123426π0.123426\pi
692692 0 0
693693 0 0
694694 0 0
695695 −24.6195 −0.933870
696696 0 0
697697 −13.6703 −0.517801
698698 0 0
699699 −35.7863 −1.35356
700700 0 0
701701 23.9477 0.904493 0.452247 0.891893i 0.350623π-0.350623\pi
0.452247 + 0.891893i 0.350623π0.350623\pi
702702 0 0
703703 −2.84952 −0.107472
704704 0 0
705705 −8.47488 −0.319182
706706 0 0
707707 −5.52223 −0.207685
708708 0 0
709709 −25.5406 −0.959199 −0.479600 0.877487i 0.659218π-0.659218\pi
−0.479600 + 0.877487i 0.659218π0.659218\pi
710710 0 0
711711 −4.90342 −0.183893
712712 0 0
713713 −30.8619 −1.15579
714714 0 0
715715 0 0
716716 0 0
717717 22.6079 0.844307
718718 0 0
719719 30.3372 1.13139 0.565693 0.824616i 0.308609π-0.308609\pi
0.565693 + 0.824616i 0.308609π0.308609\pi
720720 0 0
721721 −7.92164 −0.295017
722722 0 0
723723 20.5825 0.765473
724724 0 0
725725 15.6191 0.580079
726726 0 0
727727 −21.9102 −0.812605 −0.406302 0.913739i 0.633182π-0.633182\pi
−0.406302 + 0.913739i 0.633182π0.633182\pi
728728 0 0
729729 29.3820 1.08822
730730 0 0
731731 −2.17976 −0.0806215
732732 0 0
733733 −33.6541 −1.24304 −0.621522 0.783397i 0.713485π-0.713485\pi
−0.621522 + 0.783397i 0.713485π0.713485\pi
734734 0 0
735735 3.53697 0.130463
736736 0 0
737737 0 0
738738 0 0
739739 23.0890 0.849341 0.424671 0.905348i 0.360390π-0.360390\pi
0.424671 + 0.905348i 0.360390π0.360390\pi
740740 0 0
741741 −4.25427 −0.156285
742742 0 0
743743 42.0685 1.54334 0.771671 0.636021i 0.219421π-0.219421\pi
0.771671 + 0.636021i 0.219421π0.219421\pi
744744 0 0
745745 20.7355 0.759690
746746 0 0
747747 7.79657 0.285261
748748 0 0
749749 7.82157 0.285794
750750 0 0
751751 −32.2661 −1.17741 −0.588703 0.808349i 0.700361π-0.700361\pi
−0.588703 + 0.808349i 0.700361π0.700361\pi
752752 0 0
753753 −0.506267 −0.0184494
754754 0 0
755755 −22.2984 −0.811522
756756 0 0
757757 −39.0348 −1.41874 −0.709372 0.704834i 0.751021π-0.751021\pi
−0.709372 + 0.704834i 0.751021π0.751021\pi
758758 0 0
759759 0 0
760760 0 0
761761 −53.7651 −1.94898 −0.974492 0.224424i 0.927950π-0.927950\pi
−0.974492 + 0.224424i 0.927950π0.927950\pi
762762 0 0
763763 23.7334 0.859206
764764 0 0
765765 1.51224 0.0546750
766766 0 0
767767 8.67822 0.313353
768768 0 0
769769 37.2325 1.34264 0.671319 0.741168i 0.265728π-0.265728\pi
0.671319 + 0.741168i 0.265728π0.265728\pi
770770 0 0
771771 −1.68747 −0.0607727
772772 0 0
773773 9.16819 0.329757 0.164878 0.986314i 0.447277π-0.447277\pi
0.164878 + 0.986314i 0.447277π0.447277\pi
774774 0 0
775775 14.1998 0.510072
776776 0 0
777777 12.0841 0.433516
778778 0 0
779779 −12.2615 −0.439315
780780 0 0
781781 0 0
782782 0 0
783783 −30.8010 −1.10074
784784 0 0
785785 −28.3982 −1.01358
786786 0 0
787787 2.26024 0.0805688 0.0402844 0.999188i 0.487174π-0.487174\pi
0.0402844 + 0.999188i 0.487174π0.487174\pi
788788 0 0
789789 16.6680 0.593396
790790 0 0
791791 0.760097 0.0270259
792792 0 0
793793 −0.219002 −0.00777699
794794 0 0
795795 0.157550 0.00558774
796796 0 0
797797 29.5147 1.04546 0.522732 0.852497i 0.324913π-0.324913\pi
0.522732 + 0.852497i 0.324913π0.324913\pi
798798 0 0
799799 −4.49554 −0.159041
800800 0 0
801801 −7.23108 −0.255498
802802 0 0
803803 0 0
804804 0 0
805805 −26.8167 −0.945163
806806 0 0
807807 −1.18413 −0.0416835
808808 0 0
809809 −45.6411 −1.60466 −0.802328 0.596883i 0.796406π-0.796406\pi
−0.802328 + 0.596883i 0.796406π0.796406\pi
810810 0 0
811811 −26.8997 −0.944577 −0.472288 0.881444i 0.656572π-0.656572\pi
−0.472288 + 0.881444i 0.656572π0.656572\pi
812812 0 0
813813 −16.8354 −0.590445
814814 0 0
815815 28.4553 0.996746
816816 0 0
817817 −1.95512 −0.0684012
818818 0 0
819819 −8.09011 −0.282691
820820 0 0
821821 −27.7319 −0.967850 −0.483925 0.875110i 0.660789π-0.660789\pi
−0.483925 + 0.875110i 0.660789π0.660789\pi
822822 0 0
823823 −0.507131 −0.0176775 −0.00883873 0.999961i 0.502813π-0.502813\pi
−0.00883873 + 0.999961i 0.502813π0.502813\pi
824824 0 0
825825 0 0
826826 0 0
827827 1.86838 0.0649699 0.0324850 0.999472i 0.489658π-0.489658\pi
0.0324850 + 0.999472i 0.489658π0.489658\pi
828828 0 0
829829 43.1546 1.49882 0.749410 0.662106i 0.230337π-0.230337\pi
0.749410 + 0.662106i 0.230337π0.230337\pi
830830 0 0
831831 −2.20518 −0.0764969
832832 0 0
833833 1.87620 0.0650066
834834 0 0
835835 11.1686 0.386506
836836 0 0
837837 −28.0022 −0.967898
838838 0 0
839839 −16.9808 −0.586243 −0.293121 0.956075i 0.594694π-0.594694\pi
−0.293121 + 0.956075i 0.594694π0.594694\pi
840840 0 0
841841 0.674908 0.0232727
842842 0 0
843843 −21.9566 −0.756226
844844 0 0
845845 6.22388 0.214108
846846 0 0
847847 0 0
848848 0 0
849849 −12.9052 −0.442905
850850 0 0
851851 −17.7571 −0.608706
852852 0 0
853853 20.4011 0.698519 0.349260 0.937026i 0.386433π-0.386433\pi
0.349260 + 0.937026i 0.386433π0.386433\pi
854854 0 0
855855 1.35639 0.0463875
856856 0 0
857857 −24.6779 −0.842981 −0.421490 0.906833i 0.638493π-0.638493\pi
−0.421490 + 0.906833i 0.638493π0.638493\pi
858858 0 0
859859 −3.52545 −0.120287 −0.0601433 0.998190i 0.519156π-0.519156\pi
−0.0601433 + 0.998190i 0.519156π0.519156\pi
860860 0 0
861861 51.9983 1.77210
862862 0 0
863863 −39.3399 −1.33915 −0.669573 0.742746i 0.733523π-0.733523\pi
−0.669573 + 0.742746i 0.733523π0.733523\pi
864864 0 0
865865 2.50466 0.0851610
866866 0 0
867867 22.6771 0.770154
868868 0 0
869869 0 0
870870 0 0
871871 9.41864 0.319139
872872 0 0
873873 −4.41594 −0.149457
874874 0 0
875875 33.8552 1.14451
876876 0 0
877877 −50.9812 −1.72151 −0.860756 0.509018i 0.830009π-0.830009\pi
−0.860756 + 0.509018i 0.830009π0.830009\pi
878878 0 0
879879 21.2111 0.715433
880880 0 0
881881 −11.9057 −0.401112 −0.200556 0.979682i 0.564275π-0.564275\pi
−0.200556 + 0.979682i 0.564275π0.564275\pi
882882 0 0
883883 51.5914 1.73619 0.868094 0.496400i 0.165345π-0.165345\pi
0.868094 + 0.496400i 0.165345π0.165345\pi
884884 0 0
885885 6.17028 0.207412
886886 0 0
887887 −12.0095 −0.403238 −0.201619 0.979464i 0.564620π-0.564620\pi
−0.201619 + 0.979464i 0.564620π0.564620\pi
888888 0 0
889889 −58.2218 −1.95270
890890 0 0
891891 0 0
892892 0 0
893893 −4.03225 −0.134934
894894 0 0
895895 12.2664 0.410020
896896 0 0
897897 −26.5110 −0.885177
898898 0 0
899899 26.9784 0.899780
900900 0 0
901901 0.0835735 0.00278424
902902 0 0
903903 8.29123 0.275915
904904 0 0
905905 29.2823 0.973377
906906 0 0
907907 32.4551 1.07765 0.538826 0.842417i 0.318868π-0.318868\pi
0.538826 + 0.842417i 0.318868π0.318868\pi
908908 0 0
909909 1.74058 0.0577315
910910 0 0
911911 2.82752 0.0936799 0.0468399 0.998902i 0.485085π-0.485085\pi
0.0468399 + 0.998902i 0.485085π0.485085\pi
912912 0 0
913913 0 0
914914 0 0
915915 −0.155712 −0.00514768
916916 0 0
917917 13.6947 0.452240
918918 0 0
919919 −34.3216 −1.13217 −0.566083 0.824348i 0.691542π-0.691542\pi
−0.566083 + 0.824348i 0.691542π0.691542\pi
920920 0 0
921921 −8.03710 −0.264832
922922 0 0
923923 34.2249 1.12653
924924 0 0
925925 8.17020 0.268635
926926 0 0
927927 2.49687 0.0820078
928928 0 0
929929 −43.1300 −1.41505 −0.707524 0.706689i 0.750188π-0.750188\pi
−0.707524 + 0.706689i 0.750188π0.750188\pi
930930 0 0
931931 1.68285 0.0551531
932932 0 0
933933 41.0216 1.34299
934934 0 0
935935 0 0
936936 0 0
937937 55.2852 1.80609 0.903045 0.429547i 0.141327π-0.141327\pi
0.903045 + 0.429547i 0.141327π0.141327\pi
938938 0 0
939939 23.8774 0.779209
940940 0 0
941941 12.8579 0.419155 0.209578 0.977792i 0.432791π-0.432791\pi
0.209578 + 0.977792i 0.432791π0.432791\pi
942942 0 0
943943 −76.4092 −2.48822
944944 0 0
945945 −24.3318 −0.791515
946946 0 0
947947 −5.74390 −0.186652 −0.0933258 0.995636i 0.529750π-0.529750\pi
−0.0933258 + 0.995636i 0.529750π0.529750\pi
948948 0 0
949949 −1.42782 −0.0463489
950950 0 0
951951 −31.8702 −1.03346
952952 0 0
953953 −3.54118 −0.114710 −0.0573551 0.998354i 0.518267π-0.518267\pi
−0.0573551 + 0.998354i 0.518267π0.518267\pi
954954 0 0
955955 19.6348 0.635369
956956 0 0
957957 0 0
958958 0 0
959959 −34.4587 −1.11273
960960 0 0
961961 −6.47308 −0.208809
962962 0 0
963963 −2.46533 −0.0794440
964964 0 0
965965 17.4808 0.562727
966966 0 0
967967 −48.5614 −1.56163 −0.780815 0.624762i 0.785196π-0.785196\pi
−0.780815 + 0.624762i 0.785196π0.785196\pi
968968 0 0
969969 −1.60453 −0.0515450
970970 0 0
971971 −17.7863 −0.570789 −0.285394 0.958410i 0.592125π-0.592125\pi
−0.285394 + 0.958410i 0.592125π0.592125\pi
972972 0 0
973973 49.6749 1.59250
974974 0 0
975975 12.1979 0.390647
976976 0 0
977977 21.2604 0.680181 0.340090 0.940393i 0.389542π-0.389542\pi
0.340090 + 0.940393i 0.389542π0.389542\pi
978978 0 0
979979 0 0
980980 0 0
981981 −7.48066 −0.238839
982982 0 0
983983 −54.3152 −1.73238 −0.866192 0.499711i 0.833440π-0.833440\pi
−0.866192 + 0.499711i 0.833440π0.833440\pi
984984 0 0
985985 26.3333 0.839050
986986 0 0
987987 17.0998 0.544293
988988 0 0
989989 −12.1836 −0.387416
990990 0 0
991991 −15.7311 −0.499714 −0.249857 0.968283i 0.580384π-0.580384\pi
−0.249857 + 0.968283i 0.580384π0.580384\pi
992992 0 0
993993 −33.7194 −1.07005
994994 0 0
995995 −31.1808 −0.988498
996996 0 0
997997 27.8370 0.881605 0.440803 0.897604i 0.354694π-0.354694\pi
0.440803 + 0.897604i 0.354694π0.354694\pi
998998 0 0
999999 −16.1117 −0.509753
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 9196.2.a.s.1.3 10
11.5 even 5 836.2.j.b.685.2 yes 20
11.9 even 5 836.2.j.b.609.2 20
11.10 odd 2 9196.2.a.t.1.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
836.2.j.b.609.2 20 11.9 even 5
836.2.j.b.685.2 yes 20 11.5 even 5
9196.2.a.s.1.3 10 1.1 even 1 trivial
9196.2.a.t.1.3 10 11.10 odd 2