Properties

Label 9196.2.a.t.1.1
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 1.1
Root 3.053483.05348 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) == q3.05348q3+2.08326q5+3.50519q7+6.32373q92.38232q136.36119q15+1.39662q171.00000q1910.7030q210.551290q230.660029q2510.1490q27+8.08217q29+0.0680194q31+7.30222q35+10.0355q37+7.27436q3910.9265q417.50111q43+13.1740q457.59871q47+5.28634q494.26456q518.04102q53+3.05348q570.812498q59+1.73955q61+22.1659q634.96299q6510.9218q67+1.68335q6916.1169q7111.9028q73+2.01538q753.11141q79+12.0184q810.715131q83+2.90953q8524.6787q8713.9144q898.35047q910.207696q932.08326q95+3.53255q97+O(q100)q-3.05348 q^{3} +2.08326 q^{5} +3.50519 q^{7} +6.32373 q^{9} -2.38232 q^{13} -6.36119 q^{15} +1.39662 q^{17} -1.00000 q^{19} -10.7030 q^{21} -0.551290 q^{23} -0.660029 q^{25} -10.1490 q^{27} +8.08217 q^{29} +0.0680194 q^{31} +7.30222 q^{35} +10.0355 q^{37} +7.27436 q^{39} -10.9265 q^{41} -7.50111 q^{43} +13.1740 q^{45} -7.59871 q^{47} +5.28634 q^{49} -4.26456 q^{51} -8.04102 q^{53} +3.05348 q^{57} -0.812498 q^{59} +1.73955 q^{61} +22.1659 q^{63} -4.96299 q^{65} -10.9218 q^{67} +1.68335 q^{69} -16.1169 q^{71} -11.9028 q^{73} +2.01538 q^{75} -3.11141 q^{79} +12.0184 q^{81} -0.715131 q^{83} +2.90953 q^{85} -24.6787 q^{87} -13.9144 q^{89} -8.35047 q^{91} -0.207696 q^{93} -2.08326 q^{95} +3.53255 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q+8q5+5q7+2q92q1310q15+4q1710q19+6q218q2310q259q273q2912q31+9q3523q3718q395q4114q43++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 −3.05348 −1.76293 −0.881463 0.472252i 0.843441π-0.843441\pi
−0.881463 + 0.472252i 0.843441π0.843441\pi
44 0 0
55 2.08326 0.931662 0.465831 0.884874i 0.345755π-0.345755\pi
0.465831 + 0.884874i 0.345755π0.345755\pi
66 0 0
77 3.50519 1.32484 0.662418 0.749134i 0.269530π-0.269530\pi
0.662418 + 0.749134i 0.269530π0.269530\pi
88 0 0
99 6.32373 2.10791
1010 0 0
1111 0 0
1212 0 0
1313 −2.38232 −0.660736 −0.330368 0.943852i 0.607173π-0.607173\pi
−0.330368 + 0.943852i 0.607173π0.607173\pi
1414 0 0
1515 −6.36119 −1.64245
1616 0 0
1717 1.39662 0.338731 0.169366 0.985553i 0.445828π-0.445828\pi
0.169366 + 0.985553i 0.445828π0.445828\pi
1818 0 0
1919 −1.00000 −0.229416
2020 0 0
2121 −10.7030 −2.33559
2222 0 0
2323 −0.551290 −0.114952 −0.0574759 0.998347i 0.518305π-0.518305\pi
−0.0574759 + 0.998347i 0.518305π0.518305\pi
2424 0 0
2525 −0.660029 −0.132006
2626 0 0
2727 −10.1490 −1.95317
2828 0 0
2929 8.08217 1.50082 0.750411 0.660972i 0.229856π-0.229856\pi
0.750411 + 0.660972i 0.229856π0.229856\pi
3030 0 0
3131 0.0680194 0.0122166 0.00610832 0.999981i 0.498056π-0.498056\pi
0.00610832 + 0.999981i 0.498056π0.498056\pi
3232 0 0
3333 0 0
3434 0 0
3535 7.30222 1.23430
3636 0 0
3737 10.0355 1.64982 0.824910 0.565265i 0.191226π-0.191226\pi
0.824910 + 0.565265i 0.191226π0.191226\pi
3838 0 0
3939 7.27436 1.16483
4040 0 0
4141 −10.9265 −1.70643 −0.853215 0.521560i 0.825350π-0.825350\pi
−0.853215 + 0.521560i 0.825350π0.825350\pi
4242 0 0
4343 −7.50111 −1.14391 −0.571955 0.820285i 0.693815π-0.693815\pi
−0.571955 + 0.820285i 0.693815π0.693815\pi
4444 0 0
4545 13.1740 1.96386
4646 0 0
4747 −7.59871 −1.10839 −0.554193 0.832388i 0.686973π-0.686973\pi
−0.554193 + 0.832388i 0.686973π0.686973\pi
4848 0 0
4949 5.28634 0.755192
5050 0 0
5151 −4.26456 −0.597158
5252 0 0
5353 −8.04102 −1.10452 −0.552259 0.833672i 0.686234π-0.686234\pi
−0.552259 + 0.833672i 0.686234π0.686234\pi
5454 0 0
5555 0 0
5656 0 0
5757 3.05348 0.404443
5858 0 0
5959 −0.812498 −0.105778 −0.0528891 0.998600i 0.516843π-0.516843\pi
−0.0528891 + 0.998600i 0.516843π0.516843\pi
6060 0 0
6161 1.73955 0.222726 0.111363 0.993780i 0.464478π-0.464478\pi
0.111363 + 0.993780i 0.464478π0.464478\pi
6262 0 0
6363 22.1659 2.79264
6464 0 0
6565 −4.96299 −0.615583
6666 0 0
6767 −10.9218 −1.33431 −0.667153 0.744921i 0.732487π-0.732487\pi
−0.667153 + 0.744921i 0.732487π0.732487\pi
6868 0 0
6969 1.68335 0.202652
7070 0 0
7171 −16.1169 −1.91273 −0.956365 0.292175i 0.905621π-0.905621\pi
−0.956365 + 0.292175i 0.905621π0.905621\pi
7272 0 0
7373 −11.9028 −1.39312 −0.696560 0.717498i 0.745287π-0.745287\pi
−0.696560 + 0.717498i 0.745287π0.745287\pi
7474 0 0
7575 2.01538 0.232716
7676 0 0
7777 0 0
7878 0 0
7979 −3.11141 −0.350061 −0.175031 0.984563i 0.556002π-0.556002\pi
−0.175031 + 0.984563i 0.556002π0.556002\pi
8080 0 0
8181 12.0184 1.33538
8282 0 0
8383 −0.715131 −0.0784959 −0.0392479 0.999230i 0.512496π-0.512496\pi
−0.0392479 + 0.999230i 0.512496π0.512496\pi
8484 0 0
8585 2.90953 0.315583
8686 0 0
8787 −24.6787 −2.64584
8888 0 0
8989 −13.9144 −1.47492 −0.737462 0.675389i 0.763976π-0.763976\pi
−0.737462 + 0.675389i 0.763976π0.763976\pi
9090 0 0
9191 −8.35047 −0.875367
9292 0 0
9393 −0.207696 −0.0215370
9494 0 0
9595 −2.08326 −0.213738
9696 0 0
9797 3.53255 0.358676 0.179338 0.983788i 0.442604π-0.442604\pi
0.179338 + 0.983788i 0.442604π0.442604\pi
9898 0 0
9999 0 0
100100 0 0
101101 −0.473952 −0.0471600 −0.0235800 0.999722i 0.507506π-0.507506\pi
−0.0235800 + 0.999722i 0.507506π0.507506\pi
102102 0 0
103103 11.2007 1.10364 0.551818 0.833965i 0.313934π-0.313934\pi
0.551818 + 0.833965i 0.313934π0.313934\pi
104104 0 0
105105 −22.2972 −2.17598
106106 0 0
107107 −7.87157 −0.760973 −0.380487 0.924786i 0.624243π-0.624243\pi
−0.380487 + 0.924786i 0.624243π0.624243\pi
108108 0 0
109109 −7.26224 −0.695596 −0.347798 0.937569i 0.613070π-0.613070\pi
−0.347798 + 0.937569i 0.613070π0.613070\pi
110110 0 0
111111 −30.6431 −2.90851
112112 0 0
113113 4.83686 0.455013 0.227507 0.973777i 0.426943π-0.426943\pi
0.227507 + 0.973777i 0.426943π0.426943\pi
114114 0 0
115115 −1.14848 −0.107096
116116 0 0
117117 −15.0651 −1.39277
118118 0 0
119119 4.89543 0.448763
120120 0 0
121121 0 0
122122 0 0
123123 33.3638 3.00831
124124 0 0
125125 −11.7913 −1.05465
126126 0 0
127127 −17.4610 −1.54941 −0.774706 0.632322i 0.782102π-0.782102\pi
−0.774706 + 0.632322i 0.782102π0.782102\pi
128128 0 0
129129 22.9045 2.01663
130130 0 0
131131 0.966995 0.0844868 0.0422434 0.999107i 0.486550π-0.486550\pi
0.0422434 + 0.999107i 0.486550π0.486550\pi
132132 0 0
133133 −3.50519 −0.303938
134134 0 0
135135 −21.1429 −1.81969
136136 0 0
137137 12.6932 1.08445 0.542226 0.840233i 0.317582π-0.317582\pi
0.542226 + 0.840233i 0.317582π0.317582\pi
138138 0 0
139139 16.9312 1.43609 0.718044 0.695998i 0.245038π-0.245038\pi
0.718044 + 0.695998i 0.245038π0.245038\pi
140140 0 0
141141 23.2025 1.95400
142142 0 0
143143 0 0
144144 0 0
145145 16.8373 1.39826
146146 0 0
147147 −16.1417 −1.33135
148148 0 0
149149 −2.11599 −0.173349 −0.0866743 0.996237i 0.527624π-0.527624\pi
−0.0866743 + 0.996237i 0.527624π0.527624\pi
150150 0 0
151151 −11.8277 −0.962528 −0.481264 0.876576i 0.659822π-0.659822\pi
−0.481264 + 0.876576i 0.659822π0.659822\pi
152152 0 0
153153 8.83188 0.714015
154154 0 0
155155 0.141702 0.0113818
156156 0 0
157157 19.7632 1.57728 0.788639 0.614857i 0.210786π-0.210786\pi
0.788639 + 0.614857i 0.210786π0.210786\pi
158158 0 0
159159 24.5531 1.94719
160160 0 0
161161 −1.93237 −0.152292
162162 0 0
163163 5.75390 0.450680 0.225340 0.974280i 0.427651π-0.427651\pi
0.225340 + 0.974280i 0.427651π0.427651\pi
164164 0 0
165165 0 0
166166 0 0
167167 2.23982 0.173322 0.0866611 0.996238i 0.472380π-0.472380\pi
0.0866611 + 0.996238i 0.472380π0.472380\pi
168168 0 0
169169 −7.32456 −0.563428
170170 0 0
171171 −6.32373 −0.483588
172172 0 0
173173 3.93251 0.298983 0.149492 0.988763i 0.452236π-0.452236\pi
0.149492 + 0.988763i 0.452236π0.452236\pi
174174 0 0
175175 −2.31352 −0.174886
176176 0 0
177177 2.48095 0.186479
178178 0 0
179179 −20.9513 −1.56598 −0.782988 0.622036i 0.786306π-0.786306\pi
−0.782988 + 0.622036i 0.786306π0.786306\pi
180180 0 0
181181 −20.4731 −1.52175 −0.760876 0.648897i 0.775231π-0.775231\pi
−0.760876 + 0.648897i 0.775231π0.775231\pi
182182 0 0
183183 −5.31167 −0.392650
184184 0 0
185185 20.9065 1.53707
186186 0 0
187187 0 0
188188 0 0
189189 −35.5740 −2.58763
190190 0 0
191191 15.5073 1.12207 0.561034 0.827792i 0.310404π-0.310404\pi
0.561034 + 0.827792i 0.310404π0.310404\pi
192192 0 0
193193 −12.3196 −0.886787 −0.443394 0.896327i 0.646226π-0.646226\pi
−0.443394 + 0.896327i 0.646226π0.646226\pi
194194 0 0
195195 15.1544 1.08523
196196 0 0
197197 9.59230 0.683423 0.341712 0.939805i 0.388993π-0.388993\pi
0.341712 + 0.939805i 0.388993π0.388993\pi
198198 0 0
199199 5.07345 0.359648 0.179824 0.983699i 0.442447π-0.442447\pi
0.179824 + 0.983699i 0.442447π0.442447\pi
200200 0 0
201201 33.3494 2.35228
202202 0 0
203203 28.3295 1.98834
204204 0 0
205205 −22.7627 −1.58982
206206 0 0
207207 −3.48621 −0.242308
208208 0 0
209209 0 0
210210 0 0
211211 −16.8848 −1.16240 −0.581198 0.813762i 0.697416π-0.697416\pi
−0.581198 + 0.813762i 0.697416π0.697416\pi
212212 0 0
213213 49.2128 3.37200
214214 0 0
215215 −15.6268 −1.06574
216216 0 0
217217 0.238421 0.0161851
218218 0 0
219219 36.3450 2.45597
220220 0 0
221221 −3.32720 −0.223812
222222 0 0
223223 4.10825 0.275109 0.137554 0.990494i 0.456076π-0.456076\pi
0.137554 + 0.990494i 0.456076π0.456076\pi
224224 0 0
225225 −4.17385 −0.278256
226226 0 0
227227 1.41894 0.0941786 0.0470893 0.998891i 0.485005π-0.485005\pi
0.0470893 + 0.998891i 0.485005π0.485005\pi
228228 0 0
229229 −10.4598 −0.691200 −0.345600 0.938382i 0.612325π-0.612325\pi
−0.345600 + 0.938382i 0.612325π0.612325\pi
230230 0 0
231231 0 0
232232 0 0
233233 27.4052 1.79537 0.897686 0.440637i 0.145247π-0.145247\pi
0.897686 + 0.440637i 0.145247π0.145247\pi
234234 0 0
235235 −15.8301 −1.03264
236236 0 0
237237 9.50063 0.617132
238238 0 0
239239 10.5793 0.684321 0.342160 0.939642i 0.388841π-0.388841\pi
0.342160 + 0.939642i 0.388841π0.388841\pi
240240 0 0
241241 26.2304 1.68965 0.844824 0.535045i 0.179705π-0.179705\pi
0.844824 + 0.535045i 0.179705π0.179705\pi
242242 0 0
243243 −6.25110 −0.401008
244244 0 0
245245 11.0128 0.703583
246246 0 0
247247 2.38232 0.151583
248248 0 0
249249 2.18364 0.138382
250250 0 0
251251 −14.7375 −0.930225 −0.465113 0.885252i 0.653986π-0.653986\pi
−0.465113 + 0.885252i 0.653986π0.653986\pi
252252 0 0
253253 0 0
254254 0 0
255255 −8.88419 −0.556350
256256 0 0
257257 25.5264 1.59229 0.796146 0.605104i 0.206869π-0.206869\pi
0.796146 + 0.605104i 0.206869π0.206869\pi
258258 0 0
259259 35.1762 2.18574
260260 0 0
261261 51.1095 3.16360
262262 0 0
263263 −11.7944 −0.727276 −0.363638 0.931540i 0.618465π-0.618465\pi
−0.363638 + 0.931540i 0.618465π0.618465\pi
264264 0 0
265265 −16.7515 −1.02904
266266 0 0
267267 42.4873 2.60018
268268 0 0
269269 19.2620 1.17443 0.587214 0.809432i 0.300225π-0.300225\pi
0.587214 + 0.809432i 0.300225π0.300225\pi
270270 0 0
271271 14.1232 0.857925 0.428962 0.903322i 0.358879π-0.358879\pi
0.428962 + 0.903322i 0.358879π0.358879\pi
272272 0 0
273273 25.4980 1.54321
274274 0 0
275275 0 0
276276 0 0
277277 −28.8578 −1.73390 −0.866948 0.498399i 0.833921π-0.833921\pi
−0.866948 + 0.498399i 0.833921π0.833921\pi
278278 0 0
279279 0.430137 0.0257516
280280 0 0
281281 −22.0345 −1.31447 −0.657235 0.753686i 0.728274π-0.728274\pi
−0.657235 + 0.753686i 0.728274π0.728274\pi
282282 0 0
283283 12.8574 0.764291 0.382145 0.924102i 0.375185π-0.375185\pi
0.382145 + 0.924102i 0.375185π0.375185\pi
284284 0 0
285285 6.36119 0.376804
286286 0 0
287287 −38.2994 −2.26074
288288 0 0
289289 −15.0494 −0.885261
290290 0 0
291291 −10.7866 −0.632319
292292 0 0
293293 24.9253 1.45615 0.728077 0.685496i 0.240414π-0.240414\pi
0.728077 + 0.685496i 0.240414π0.240414\pi
294294 0 0
295295 −1.69265 −0.0985496
296296 0 0
297297 0 0
298298 0 0
299299 1.31335 0.0759528
300300 0 0
301301 −26.2928 −1.51549
302302 0 0
303303 1.44720 0.0831396
304304 0 0
305305 3.62393 0.207505
306306 0 0
307307 −18.7523 −1.07025 −0.535125 0.844773i 0.679736π-0.679736\pi
−0.535125 + 0.844773i 0.679736π0.679736\pi
308308 0 0
309309 −34.2010 −1.94563
310310 0 0
311311 −33.7192 −1.91204 −0.956020 0.293301i 0.905246π-0.905246\pi
−0.956020 + 0.293301i 0.905246π0.905246\pi
312312 0 0
313313 0.808485 0.0456983 0.0228491 0.999739i 0.492726π-0.492726\pi
0.0228491 + 0.999739i 0.492726π0.492726\pi
314314 0 0
315315 46.1773 2.60179
316316 0 0
317317 8.10995 0.455500 0.227750 0.973720i 0.426863π-0.426863\pi
0.227750 + 0.973720i 0.426863π0.426863\pi
318318 0 0
319319 0 0
320320 0 0
321321 24.0357 1.34154
322322 0 0
323323 −1.39662 −0.0777103
324324 0 0
325325 1.57240 0.0872209
326326 0 0
327327 22.1751 1.22628
328328 0 0
329329 −26.6349 −1.46843
330330 0 0
331331 8.07134 0.443641 0.221820 0.975088i 0.428800π-0.428800\pi
0.221820 + 0.975088i 0.428800π0.428800\pi
332332 0 0
333333 63.4616 3.47767
334334 0 0
335335 −22.7529 −1.24312
336336 0 0
337337 −15.2995 −0.833419 −0.416710 0.909040i 0.636817π-0.636817\pi
−0.416710 + 0.909040i 0.636817π0.636817\pi
338338 0 0
339339 −14.7692 −0.802155
340340 0 0
341341 0 0
342342 0 0
343343 −6.00670 −0.324331
344344 0 0
345345 3.50686 0.188803
346346 0 0
347347 14.1828 0.761374 0.380687 0.924704i 0.375687π-0.375687\pi
0.380687 + 0.924704i 0.375687π0.375687\pi
348348 0 0
349349 28.9302 1.54860 0.774299 0.632820i 0.218103π-0.218103\pi
0.774299 + 0.632820i 0.218103π0.218103\pi
350350 0 0
351351 24.1780 1.29053
352352 0 0
353353 −24.1841 −1.28719 −0.643594 0.765367i 0.722558π-0.722558\pi
−0.643594 + 0.765367i 0.722558π0.722558\pi
354354 0 0
355355 −33.5758 −1.78202
356356 0 0
357357 −14.9481 −0.791137
358358 0 0
359359 −12.9054 −0.681122 −0.340561 0.940222i 0.610617π-0.610617\pi
−0.340561 + 0.940222i 0.610617π0.610617\pi
360360 0 0
361361 1.00000 0.0526316
362362 0 0
363363 0 0
364364 0 0
365365 −24.7967 −1.29792
366366 0 0
367367 −20.0813 −1.04824 −0.524118 0.851646i 0.675605π-0.675605\pi
−0.524118 + 0.851646i 0.675605π0.675605\pi
368368 0 0
369369 −69.0961 −3.59700
370370 0 0
371371 −28.1853 −1.46331
372372 0 0
373373 18.9551 0.981459 0.490730 0.871312i 0.336730π-0.336730\pi
0.490730 + 0.871312i 0.336730π0.336730\pi
374374 0 0
375375 36.0045 1.85927
376376 0 0
377377 −19.2543 −0.991647
378378 0 0
379379 −17.2133 −0.884186 −0.442093 0.896969i 0.645764π-0.645764\pi
−0.442093 + 0.896969i 0.645764π0.645764\pi
380380 0 0
381381 53.3168 2.73150
382382 0 0
383383 −21.0603 −1.07613 −0.538064 0.842904i 0.680844π-0.680844\pi
−0.538064 + 0.842904i 0.680844π0.680844\pi
384384 0 0
385385 0 0
386386 0 0
387387 −47.4350 −2.41126
388388 0 0
389389 8.89827 0.451160 0.225580 0.974225i 0.427572π-0.427572\pi
0.225580 + 0.974225i 0.427572π0.427572\pi
390390 0 0
391391 −0.769945 −0.0389378
392392 0 0
393393 −2.95270 −0.148944
394394 0 0
395395 −6.48188 −0.326139
396396 0 0
397397 26.3146 1.32069 0.660345 0.750963i 0.270410π-0.270410\pi
0.660345 + 0.750963i 0.270410π0.270410\pi
398398 0 0
399399 10.7030 0.535821
400400 0 0
401401 11.0752 0.553070 0.276535 0.961004i 0.410814π-0.410814\pi
0.276535 + 0.961004i 0.410814π0.410814\pi
402402 0 0
403403 −0.162044 −0.00807198
404404 0 0
405405 25.0375 1.24412
406406 0 0
407407 0 0
408408 0 0
409409 3.20897 0.158673 0.0793367 0.996848i 0.474720π-0.474720\pi
0.0793367 + 0.996848i 0.474720π0.474720\pi
410410 0 0
411411 −38.7584 −1.91181
412412 0 0
413413 −2.84796 −0.140139
414414 0 0
415415 −1.48980 −0.0731316
416416 0 0
417417 −51.6991 −2.53172
418418 0 0
419419 36.2166 1.76930 0.884648 0.466260i 0.154399π-0.154399\pi
0.884648 + 0.466260i 0.154399π0.154399\pi
420420 0 0
421421 13.3904 0.652607 0.326304 0.945265i 0.394197π-0.394197\pi
0.326304 + 0.945265i 0.394197π0.394197\pi
422422 0 0
423423 −48.0522 −2.33638
424424 0 0
425425 −0.921812 −0.0447145
426426 0 0
427427 6.09743 0.295076
428428 0 0
429429 0 0
430430 0 0
431431 −1.73872 −0.0837513 −0.0418757 0.999123i 0.513333π-0.513333\pi
−0.0418757 + 0.999123i 0.513333π0.513333\pi
432432 0 0
433433 −11.2285 −0.539605 −0.269803 0.962916i 0.586958π-0.586958\pi
−0.269803 + 0.962916i 0.586958π0.586958\pi
434434 0 0
435435 −51.4122 −2.46503
436436 0 0
437437 0.551290 0.0263718
438438 0 0
439439 8.47555 0.404516 0.202258 0.979332i 0.435172π-0.435172\pi
0.202258 + 0.979332i 0.435172π0.435172\pi
440440 0 0
441441 33.4294 1.59188
442442 0 0
443443 −8.64275 −0.410630 −0.205315 0.978696i 0.565822π-0.565822\pi
−0.205315 + 0.978696i 0.565822π0.565822\pi
444444 0 0
445445 −28.9873 −1.37413
446446 0 0
447447 6.46113 0.305601
448448 0 0
449449 −24.9761 −1.17870 −0.589348 0.807880i 0.700615π-0.700615\pi
−0.589348 + 0.807880i 0.700615π0.700615\pi
450450 0 0
451451 0 0
452452 0 0
453453 36.1158 1.69687
454454 0 0
455455 −17.3962 −0.815546
456456 0 0
457457 19.0076 0.889139 0.444570 0.895744i 0.353357π-0.353357\pi
0.444570 + 0.895744i 0.353357π0.353357\pi
458458 0 0
459459 −14.1743 −0.661598
460460 0 0
461461 3.03082 0.141159 0.0705796 0.997506i 0.477515π-0.477515\pi
0.0705796 + 0.997506i 0.477515π0.477515\pi
462462 0 0
463463 −3.52642 −0.163887 −0.0819433 0.996637i 0.526113π-0.526113\pi
−0.0819433 + 0.996637i 0.526113π0.526113\pi
464464 0 0
465465 −0.432684 −0.0200653
466466 0 0
467467 1.37161 0.0634707 0.0317353 0.999496i 0.489897π-0.489897\pi
0.0317353 + 0.999496i 0.489897π0.489897\pi
468468 0 0
469469 −38.2828 −1.76774
470470 0 0
471471 −60.3466 −2.78062
472472 0 0
473473 0 0
474474 0 0
475475 0.660029 0.0302842
476476 0 0
477477 −50.8492 −2.32823
478478 0 0
479479 −22.7631 −1.04007 −0.520037 0.854143i 0.674082π-0.674082\pi
−0.520037 + 0.854143i 0.674082π0.674082\pi
480480 0 0
481481 −23.9076 −1.09009
482482 0 0
483483 5.90046 0.268480
484484 0 0
485485 7.35921 0.334165
486486 0 0
487487 −27.6490 −1.25290 −0.626448 0.779463i 0.715492π-0.715492\pi
−0.626448 + 0.779463i 0.715492π0.715492\pi
488488 0 0
489489 −17.5694 −0.794517
490490 0 0
491491 19.6440 0.886520 0.443260 0.896393i 0.353822π-0.353822\pi
0.443260 + 0.896393i 0.353822π0.353822\pi
492492 0 0
493493 11.2878 0.508375
494494 0 0
495495 0 0
496496 0 0
497497 −56.4929 −2.53405
498498 0 0
499499 −33.9361 −1.51919 −0.759595 0.650396i 0.774603π-0.774603\pi
−0.759595 + 0.650396i 0.774603π0.774603\pi
500500 0 0
501501 −6.83923 −0.305554
502502 0 0
503503 1.83967 0.0820269 0.0410134 0.999159i 0.486941π-0.486941\pi
0.0410134 + 0.999159i 0.486941π0.486941\pi
504504 0 0
505505 −0.987365 −0.0439372
506506 0 0
507507 22.3654 0.993282
508508 0 0
509509 5.25743 0.233031 0.116516 0.993189i 0.462827π-0.462827\pi
0.116516 + 0.993189i 0.462827π0.462827\pi
510510 0 0
511511 −41.7216 −1.84566
512512 0 0
513513 10.1490 0.448087
514514 0 0
515515 23.3339 1.02822
516516 0 0
517517 0 0
518518 0 0
519519 −12.0078 −0.527086
520520 0 0
521521 −6.37350 −0.279228 −0.139614 0.990206i 0.544586π-0.544586\pi
−0.139614 + 0.990206i 0.544586π0.544586\pi
522522 0 0
523523 4.61267 0.201698 0.100849 0.994902i 0.467844π-0.467844\pi
0.100849 + 0.994902i 0.467844π0.467844\pi
524524 0 0
525525 7.06430 0.308311
526526 0 0
527527 0.0949976 0.00413816
528528 0 0
529529 −22.6961 −0.986786
530530 0 0
531531 −5.13802 −0.222971
532532 0 0
533533 26.0303 1.12750
534534 0 0
535535 −16.3985 −0.708970
536536 0 0
537537 63.9745 2.76070
538538 0 0
539539 0 0
540540 0 0
541541 16.2770 0.699801 0.349901 0.936787i 0.386215π-0.386215\pi
0.349901 + 0.936787i 0.386215π0.386215\pi
542542 0 0
543543 62.5141 2.68274
544544 0 0
545545 −15.1291 −0.648060
546546 0 0
547547 −23.0109 −0.983874 −0.491937 0.870631i 0.663711π-0.663711\pi
−0.491937 + 0.870631i 0.663711π0.663711\pi
548548 0 0
549549 11.0004 0.469487
550550 0 0
551551 −8.08217 −0.344312
552552 0 0
553553 −10.9061 −0.463774
554554 0 0
555555 −63.8375 −2.70975
556556 0 0
557557 −16.1595 −0.684701 −0.342351 0.939572i 0.611223π-0.611223\pi
−0.342351 + 0.939572i 0.611223π0.611223\pi
558558 0 0
559559 17.8700 0.755822
560560 0 0
561561 0 0
562562 0 0
563563 17.0059 0.716712 0.358356 0.933585i 0.383337π-0.383337\pi
0.358356 + 0.933585i 0.383337π0.383337\pi
564564 0 0
565565 10.0764 0.423919
566566 0 0
567567 42.1268 1.76916
568568 0 0
569569 28.0037 1.17398 0.586989 0.809595i 0.300313π-0.300313\pi
0.586989 + 0.809595i 0.300313π0.300313\pi
570570 0 0
571571 43.2441 1.80971 0.904855 0.425721i 0.139979π-0.139979\pi
0.904855 + 0.425721i 0.139979π0.139979\pi
572572 0 0
573573 −47.3512 −1.97813
574574 0 0
575575 0.363867 0.0151743
576576 0 0
577577 −30.5136 −1.27030 −0.635149 0.772390i 0.719061π-0.719061\pi
−0.635149 + 0.772390i 0.719061π0.719061\pi
578578 0 0
579579 37.6178 1.56334
580580 0 0
581581 −2.50667 −0.103994
582582 0 0
583583 0 0
584584 0 0
585585 −31.3846 −1.29759
586586 0 0
587587 −26.0375 −1.07468 −0.537341 0.843365i 0.680571π-0.680571\pi
−0.537341 + 0.843365i 0.680571π0.680571\pi
588588 0 0
589589 −0.0680194 −0.00280269
590590 0 0
591591 −29.2899 −1.20483
592592 0 0
593593 31.5922 1.29734 0.648668 0.761072i 0.275327π-0.275327\pi
0.648668 + 0.761072i 0.275327π0.275327\pi
594594 0 0
595595 10.1985 0.418096
596596 0 0
597597 −15.4917 −0.634032
598598 0 0
599599 −27.6041 −1.12787 −0.563936 0.825818i 0.690714π-0.690714\pi
−0.563936 + 0.825818i 0.690714π0.690714\pi
600600 0 0
601601 34.0255 1.38793 0.693964 0.720009i 0.255863π-0.255863\pi
0.693964 + 0.720009i 0.255863π0.255863\pi
602602 0 0
603603 −69.0663 −2.81260
604604 0 0
605605 0 0
606606 0 0
607607 −13.0663 −0.530346 −0.265173 0.964201i 0.585429π-0.585429\pi
−0.265173 + 0.964201i 0.585429π0.585429\pi
608608 0 0
609609 −86.5036 −3.50530
610610 0 0
611611 18.1025 0.732350
612612 0 0
613613 30.6984 1.23990 0.619948 0.784643i 0.287154π-0.287154\pi
0.619948 + 0.784643i 0.287154π0.287154\pi
614614 0 0
615615 69.5054 2.80273
616616 0 0
617617 −28.3062 −1.13956 −0.569782 0.821796i 0.692972π-0.692972\pi
−0.569782 + 0.821796i 0.692972π0.692972\pi
618618 0 0
619619 11.0167 0.442799 0.221399 0.975183i 0.428938π-0.428938\pi
0.221399 + 0.975183i 0.428938π0.428938\pi
620620 0 0
621621 5.59501 0.224520
622622 0 0
623623 −48.7726 −1.95403
624624 0 0
625625 −21.2642 −0.850569
626626 0 0
627627 0 0
628628 0 0
629629 14.0158 0.558845
630630 0 0
631631 −23.7546 −0.945657 −0.472828 0.881155i 0.656767π-0.656767\pi
−0.472828 + 0.881155i 0.656767π0.656767\pi
632632 0 0
633633 51.5573 2.04922
634634 0 0
635635 −36.3758 −1.44353
636636 0 0
637637 −12.5937 −0.498982
638638 0 0
639639 −101.919 −4.03186
640640 0 0
641641 −36.4978 −1.44158 −0.720789 0.693154i 0.756220π-0.756220\pi
−0.720789 + 0.693154i 0.756220π0.756220\pi
642642 0 0
643643 −5.89653 −0.232536 −0.116268 0.993218i 0.537093π-0.537093\pi
−0.116268 + 0.993218i 0.537093π0.537093\pi
644644 0 0
645645 47.7160 1.87882
646646 0 0
647647 16.8028 0.660586 0.330293 0.943879i 0.392852π-0.392852\pi
0.330293 + 0.943879i 0.392852π0.392852\pi
648648 0 0
649649 0 0
650650 0 0
651651 −0.728013 −0.0285331
652652 0 0
653653 −22.1959 −0.868591 −0.434295 0.900771i 0.643003π-0.643003\pi
−0.434295 + 0.900771i 0.643003π0.643003\pi
654654 0 0
655655 2.01450 0.0787131
656656 0 0
657657 −75.2703 −2.93657
658658 0 0
659659 −1.41754 −0.0552197 −0.0276098 0.999619i 0.508790π-0.508790\pi
−0.0276098 + 0.999619i 0.508790π0.508790\pi
660660 0 0
661661 36.4936 1.41943 0.709717 0.704486i 0.248823π-0.248823\pi
0.709717 + 0.704486i 0.248823π0.248823\pi
662662 0 0
663663 10.1595 0.394564
664664 0 0
665665 −7.30222 −0.283168
666666 0 0
667667 −4.45562 −0.172522
668668 0 0
669669 −12.5444 −0.484996
670670 0 0
671671 0 0
672672 0 0
673673 27.2994 1.05231 0.526157 0.850388i 0.323633π-0.323633\pi
0.526157 + 0.850388i 0.323633π0.323633\pi
674674 0 0
675675 6.69860 0.257829
676676 0 0
677677 −19.8920 −0.764512 −0.382256 0.924056i 0.624853π-0.624853\pi
−0.382256 + 0.924056i 0.624853π0.624853\pi
678678 0 0
679679 12.3822 0.475187
680680 0 0
681681 −4.33271 −0.166030
682682 0 0
683683 −6.64803 −0.254380 −0.127190 0.991878i 0.540596π-0.540596\pi
−0.127190 + 0.991878i 0.540596π0.540596\pi
684684 0 0
685685 26.4432 1.01034
686686 0 0
687687 31.9386 1.21854
688688 0 0
689689 19.1563 0.729795
690690 0 0
691691 3.48030 0.132397 0.0661985 0.997806i 0.478913π-0.478913\pi
0.0661985 + 0.997806i 0.478913π0.478913\pi
692692 0 0
693693 0 0
694694 0 0
695695 35.2721 1.33795
696696 0 0
697697 −15.2602 −0.578021
698698 0 0
699699 −83.6810 −3.16511
700700 0 0
701701 24.0929 0.909977 0.454988 0.890497i 0.349643π-0.349643\pi
0.454988 + 0.890497i 0.349643π0.349643\pi
702702 0 0
703703 −10.0355 −0.378494
704704 0 0
705705 48.3368 1.82047
706706 0 0
707707 −1.66129 −0.0624792
708708 0 0
709709 17.0675 0.640985 0.320492 0.947251i 0.396152π-0.396152\pi
0.320492 + 0.947251i 0.396152π0.396152\pi
710710 0 0
711711 −19.6757 −0.737898
712712 0 0
713713 −0.0374984 −0.00140433
714714 0 0
715715 0 0
716716 0 0
717717 −32.3038 −1.20641
718718 0 0
719719 4.55560 0.169895 0.0849477 0.996385i 0.472928π-0.472928\pi
0.0849477 + 0.996385i 0.472928π0.472928\pi
720720 0 0
721721 39.2605 1.46214
722722 0 0
723723 −80.0939 −2.97872
724724 0 0
725725 −5.33446 −0.198117
726726 0 0
727727 −2.54229 −0.0942882 −0.0471441 0.998888i 0.515012π-0.515012\pi
−0.0471441 + 0.998888i 0.515012π0.515012\pi
728728 0 0
729729 −16.9676 −0.628430
730730 0 0
731731 −10.4762 −0.387478
732732 0 0
733733 17.2073 0.635566 0.317783 0.948164i 0.397062π-0.397062\pi
0.317783 + 0.948164i 0.397062π0.397062\pi
734734 0 0
735735 −33.6274 −1.24037
736736 0 0
737737 0 0
738738 0 0
739739 −24.8269 −0.913271 −0.456635 0.889654i 0.650946π-0.650946\pi
−0.456635 + 0.889654i 0.650946π0.650946\pi
740740 0 0
741741 −7.27436 −0.267230
742742 0 0
743743 10.6452 0.390536 0.195268 0.980750i 0.437442π-0.437442\pi
0.195268 + 0.980750i 0.437442π0.437442\pi
744744 0 0
745745 −4.40816 −0.161502
746746 0 0
747747 −4.52230 −0.165462
748748 0 0
749749 −27.5913 −1.00817
750750 0 0
751751 −43.9781 −1.60478 −0.802392 0.596797i 0.796440π-0.796440\pi
−0.802392 + 0.596797i 0.796440π0.796440\pi
752752 0 0
753753 45.0008 1.63992
754754 0 0
755755 −24.6403 −0.896751
756756 0 0
757757 −27.6806 −1.00607 −0.503034 0.864266i 0.667783π-0.667783\pi
−0.503034 + 0.864266i 0.667783π0.667783\pi
758758 0 0
759759 0 0
760760 0 0
761761 −43.6445 −1.58211 −0.791057 0.611743i 0.790469π-0.790469\pi
−0.791057 + 0.611743i 0.790469π0.790469\pi
762762 0 0
763763 −25.4555 −0.921551
764764 0 0
765765 18.3991 0.665221
766766 0 0
767767 1.93563 0.0698915
768768 0 0
769769 49.5413 1.78650 0.893252 0.449556i 0.148418π-0.148418\pi
0.893252 + 0.449556i 0.148418π0.148418\pi
770770 0 0
771771 −77.9443 −2.80710
772772 0 0
773773 −37.6221 −1.35317 −0.676587 0.736362i 0.736542π-0.736542\pi
−0.676587 + 0.736362i 0.736542π0.736542\pi
774774 0 0
775775 −0.0448947 −0.00161267
776776 0 0
777777 −107.410 −3.85330
778778 0 0
779779 10.9265 0.391482
780780 0 0
781781 0 0
782782 0 0
783783 −82.0255 −2.93135
784784 0 0
785785 41.1719 1.46949
786786 0 0
787787 24.8221 0.884814 0.442407 0.896814i 0.354125π-0.354125\pi
0.442407 + 0.896814i 0.354125π0.354125\pi
788788 0 0
789789 36.0140 1.28213
790790 0 0
791791 16.9541 0.602818
792792 0 0
793793 −4.14415 −0.147163
794794 0 0
795795 51.1504 1.81412
796796 0 0
797797 −6.60415 −0.233931 −0.116966 0.993136i 0.537317π-0.537317\pi
−0.116966 + 0.993136i 0.537317π0.537317\pi
798798 0 0
799799 −10.6125 −0.375445
800800 0 0
801801 −87.9910 −3.10901
802802 0 0
803803 0 0
804804 0 0
805805 −4.02564 −0.141885
806806 0 0
807807 −58.8162 −2.07043
808808 0 0
809809 −10.1926 −0.358353 −0.179177 0.983817i 0.557343π-0.557343\pi
−0.179177 + 0.983817i 0.557343π0.557343\pi
810810 0 0
811811 −25.3847 −0.891378 −0.445689 0.895188i 0.647041π-0.647041\pi
−0.445689 + 0.895188i 0.647041π0.647041\pi
812812 0 0
813813 −43.1250 −1.51246
814814 0 0
815815 11.9869 0.419882
816816 0 0
817817 7.50111 0.262431
818818 0 0
819819 −52.8062 −1.84520
820820 0 0
821821 −42.6490 −1.48846 −0.744231 0.667922i 0.767184π-0.767184\pi
−0.744231 + 0.667922i 0.767184π0.767184\pi
822822 0 0
823823 49.9772 1.74210 0.871048 0.491199i 0.163441π-0.163441\pi
0.871048 + 0.491199i 0.163441π0.163441\pi
824824 0 0
825825 0 0
826826 0 0
827827 38.1252 1.32574 0.662872 0.748733i 0.269337π-0.269337\pi
0.662872 + 0.748733i 0.269337π0.269337\pi
828828 0 0
829829 50.6945 1.76069 0.880347 0.474330i 0.157310π-0.157310\pi
0.880347 + 0.474330i 0.157310π0.157310\pi
830830 0 0
831831 88.1166 3.05673
832832 0 0
833833 7.38303 0.255807
834834 0 0
835835 4.66612 0.161478
836836 0 0
837837 −0.690325 −0.0238611
838838 0 0
839839 1.66069 0.0573334 0.0286667 0.999589i 0.490874π-0.490874\pi
0.0286667 + 0.999589i 0.490874π0.490874\pi
840840 0 0
841841 36.3215 1.25246
842842 0 0
843843 67.2820 2.31731
844844 0 0
845845 −15.2590 −0.524924
846846 0 0
847847 0 0
848848 0 0
849849 −39.2597 −1.34739
850850 0 0
851851 −5.53244 −0.189650
852852 0 0
853853 −41.4654 −1.41975 −0.709875 0.704328i 0.751249π-0.751249\pi
−0.709875 + 0.704328i 0.751249π0.751249\pi
854854 0 0
855855 −13.1740 −0.450541
856856 0 0
857857 15.9836 0.545990 0.272995 0.962015i 0.411986π-0.411986\pi
0.272995 + 0.962015i 0.411986π0.411986\pi
858858 0 0
859859 16.5496 0.564665 0.282332 0.959317i 0.408892π-0.408892\pi
0.282332 + 0.959317i 0.408892π0.408892\pi
860860 0 0
861861 116.946 3.98552
862862 0 0
863863 9.96667 0.339269 0.169635 0.985507i 0.445741π-0.445741\pi
0.169635 + 0.985507i 0.445741π0.445741\pi
864864 0 0
865865 8.19245 0.278552
866866 0 0
867867 45.9531 1.56065
868868 0 0
869869 0 0
870870 0 0
871871 26.0191 0.881624
872872 0 0
873873 22.3389 0.756057
874874 0 0
875875 −41.3308 −1.39723
876876 0 0
877877 49.8742 1.68413 0.842065 0.539376i 0.181340π-0.181340\pi
0.842065 + 0.539376i 0.181340π0.181340\pi
878878 0 0
879879 −76.1090 −2.56709
880880 0 0
881881 −8.44750 −0.284604 −0.142302 0.989823i 0.545450π-0.545450\pi
−0.142302 + 0.989823i 0.545450π0.545450\pi
882882 0 0
883883 12.2373 0.411817 0.205909 0.978571i 0.433985π-0.433985\pi
0.205909 + 0.978571i 0.433985π0.433985\pi
884884 0 0
885885 5.16846 0.173736
886886 0 0
887887 −2.60472 −0.0874580 −0.0437290 0.999043i 0.513924π-0.513924\pi
−0.0437290 + 0.999043i 0.513924π0.513924\pi
888888 0 0
889889 −61.2040 −2.05272
890890 0 0
891891 0 0
892892 0 0
893893 7.59871 0.254281
894894 0 0
895895 −43.6471 −1.45896
896896 0 0
897897 −4.01028 −0.133899
898898 0 0
899899 0.549744 0.0183350
900900 0 0
901901 −11.2303 −0.374135
902902 0 0
903903 80.2845 2.67170
904904 0 0
905905 −42.6507 −1.41776
906906 0 0
907907 −43.0986 −1.43106 −0.715532 0.698580i 0.753816π-0.753816\pi
−0.715532 + 0.698580i 0.753816π0.753816\pi
908908 0 0
909909 −2.99714 −0.0994090
910910 0 0
911911 −24.0874 −0.798050 −0.399025 0.916940i 0.630651π-0.630651\pi
−0.399025 + 0.916940i 0.630651π0.630651\pi
912912 0 0
913913 0 0
914914 0 0
915915 −11.0656 −0.365817
916916 0 0
917917 3.38950 0.111931
918918 0 0
919919 27.4929 0.906907 0.453453 0.891280i 0.350192π-0.350192\pi
0.453453 + 0.891280i 0.350192π0.350192\pi
920920 0 0
921921 57.2598 1.88677
922922 0 0
923923 38.3957 1.26381
924924 0 0
925925 −6.62369 −0.217786
926926 0 0
927927 70.8301 2.32637
928928 0 0
929929 −43.6254 −1.43130 −0.715652 0.698457i 0.753870π-0.753870\pi
−0.715652 + 0.698457i 0.753870π0.753870\pi
930930 0 0
931931 −5.28634 −0.173253
932932 0 0
933933 102.961 3.37079
934934 0 0
935935 0 0
936936 0 0
937937 29.0810 0.950034 0.475017 0.879977i 0.342442π-0.342442\pi
0.475017 + 0.879977i 0.342442π0.342442\pi
938938 0 0
939939 −2.46869 −0.0805627
940940 0 0
941941 −34.6526 −1.12964 −0.564822 0.825213i 0.691055π-0.691055\pi
−0.564822 + 0.825213i 0.691055π0.691055\pi
942942 0 0
943943 6.02365 0.196157
944944 0 0
945945 −74.1098 −2.41079
946946 0 0
947947 −10.7999 −0.350949 −0.175475 0.984484i 0.556146π-0.556146\pi
−0.175475 + 0.984484i 0.556146π0.556146\pi
948948 0 0
949949 28.3563 0.920485
950950 0 0
951951 −24.7636 −0.803014
952952 0 0
953953 −52.3488 −1.69574 −0.847872 0.530201i 0.822117π-0.822117\pi
−0.847872 + 0.530201i 0.822117π0.822117\pi
954954 0 0
955955 32.3057 1.04539
956956 0 0
957957 0 0
958958 0 0
959959 44.4920 1.43672
960960 0 0
961961 −30.9954 −0.999851
962962 0 0
963963 −49.7777 −1.60406
964964 0 0
965965 −25.6650 −0.826186
966966 0 0
967967 11.1964 0.360053 0.180026 0.983662i 0.442382π-0.442382\pi
0.180026 + 0.983662i 0.442382π0.442382\pi
968968 0 0
969969 4.26456 0.136998
970970 0 0
971971 44.6433 1.43267 0.716336 0.697756i 0.245818π-0.245818\pi
0.716336 + 0.697756i 0.245818π0.245818\pi
972972 0 0
973973 59.3471 1.90258
974974 0 0
975975 −4.80128 −0.153764
976976 0 0
977977 6.05033 0.193567 0.0967836 0.995305i 0.469145π-0.469145\pi
0.0967836 + 0.995305i 0.469145π0.469145\pi
978978 0 0
979979 0 0
980980 0 0
981981 −45.9244 −1.46625
982982 0 0
983983 44.3592 1.41484 0.707420 0.706794i 0.249859π-0.249859\pi
0.707420 + 0.706794i 0.249859π0.249859\pi
984984 0 0
985985 19.9833 0.636720
986986 0 0
987987 81.3291 2.58873
988988 0 0
989989 4.13529 0.131494
990990 0 0
991991 54.2098 1.72203 0.861016 0.508578i 0.169829π-0.169829\pi
0.861016 + 0.508578i 0.169829π0.169829\pi
992992 0 0
993993 −24.6457 −0.782107
994994 0 0
995995 10.5693 0.335070
996996 0 0
997997 22.7327 0.719952 0.359976 0.932962i 0.382785π-0.382785\pi
0.359976 + 0.932962i 0.382785π0.382785\pi
998998 0 0
999999 −101.849 −3.22237
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.t.1.1 10
11.7 odd 10 836.2.j.b.533.5 yes 20
11.8 odd 10 836.2.j.b.229.5 20
11.10 odd 2 9196.2.a.s.1.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
836.2.j.b.229.5 20 11.8 odd 10
836.2.j.b.533.5 yes 20 11.7 odd 10
9196.2.a.s.1.1 10 11.10 odd 2
9196.2.a.t.1.1 10 1.1 even 1 trivial