Properties

Label 6975.2.a.y.1.2
Level 69756975
Weight 22
Character 6975.1
Self dual yes
Analytic conductor 55.69655.696
Analytic rank 11
Dimension 22
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] = [6975,2,Mod(1,6975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6975, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6975.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 6975=325231 6975 = 3^{2} \cdot 5^{2} \cdot 31
Weight: k k == 2 2
Character orbit: [χ][\chi] == 6975.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,1,0,-1,0,0,4,0,0,0,-4,0,2,-3,0,-3,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 55.695655409855.6956554098
Analytic rank: 11
Dimension: 22
Coefficient field: Q(ζ10)+\Q(\zeta_{10})^+
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2x1 x^{2} - x - 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 31)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.618031.61803 of defining polynomial
Character χ\chi == 6975.1

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+1.61803q2+0.618034q40.236068q72.23607q82.00000q11+3.23607q130.381966q144.85410q16+0.763932q172.23607q193.23607q22+5.70820q23+5.23607q260.145898q282.76393q29+1.00000q313.38197q32+1.23607q34+2.00000q373.61803q387.00000q411.23607q431.23607q44+9.23607q46+2.47214q476.94427q49+2.00000q5210.4721q53+0.527864q564.47214q582.23607q59+8.18034q61+1.61803q62+4.23607q648.00000q67+0.472136q68+9.18034q718.47214q73+3.23607q741.38197q76+0.472136q7711.7082q7911.3262q8214.9443q832.00000q86+4.47214q8811.7082q890.763932q91+3.52786q92+4.00000q94+15.9443q9711.2361q98+O(q100)q+1.61803 q^{2} +0.618034 q^{4} -0.236068 q^{7} -2.23607 q^{8} -2.00000 q^{11} +3.23607 q^{13} -0.381966 q^{14} -4.85410 q^{16} +0.763932 q^{17} -2.23607 q^{19} -3.23607 q^{22} +5.70820 q^{23} +5.23607 q^{26} -0.145898 q^{28} -2.76393 q^{29} +1.00000 q^{31} -3.38197 q^{32} +1.23607 q^{34} +2.00000 q^{37} -3.61803 q^{38} -7.00000 q^{41} -1.23607 q^{43} -1.23607 q^{44} +9.23607 q^{46} +2.47214 q^{47} -6.94427 q^{49} +2.00000 q^{52} -10.4721 q^{53} +0.527864 q^{56} -4.47214 q^{58} -2.23607 q^{59} +8.18034 q^{61} +1.61803 q^{62} +4.23607 q^{64} -8.00000 q^{67} +0.472136 q^{68} +9.18034 q^{71} -8.47214 q^{73} +3.23607 q^{74} -1.38197 q^{76} +0.472136 q^{77} -11.7082 q^{79} -11.3262 q^{82} -14.9443 q^{83} -2.00000 q^{86} +4.47214 q^{88} -11.7082 q^{89} -0.763932 q^{91} +3.52786 q^{92} +4.00000 q^{94} +15.9443 q^{97} -11.2361 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q2q4+4q74q11+2q133q143q16+6q172q222q23+6q267q2810q29+2q319q322q34+4q375q3814q41+18q98+O(q100) 2 q + q^{2} - q^{4} + 4 q^{7} - 4 q^{11} + 2 q^{13} - 3 q^{14} - 3 q^{16} + 6 q^{17} - 2 q^{22} - 2 q^{23} + 6 q^{26} - 7 q^{28} - 10 q^{29} + 2 q^{31} - 9 q^{32} - 2 q^{34} + 4 q^{37} - 5 q^{38} - 14 q^{41}+ \cdots - 18 q^{98}+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 1.61803 1.14412 0.572061 0.820211i 0.306144π-0.306144\pi
0.572061 + 0.820211i 0.306144π0.306144\pi
33 0 0
44 0.618034 0.309017
55 0 0
66 0 0
77 −0.236068 −0.0892253 −0.0446127 0.999004i 0.514205π-0.514205\pi
−0.0446127 + 0.999004i 0.514205π0.514205\pi
88 −2.23607 −0.790569
99 0 0
1010 0 0
1111 −2.00000 −0.603023 −0.301511 0.953463i 0.597491π-0.597491\pi
−0.301511 + 0.953463i 0.597491π0.597491\pi
1212 0 0
1313 3.23607 0.897524 0.448762 0.893651i 0.351865π-0.351865\pi
0.448762 + 0.893651i 0.351865π0.351865\pi
1414 −0.381966 −0.102085
1515 0 0
1616 −4.85410 −1.21353
1717 0.763932 0.185281 0.0926404 0.995700i 0.470469π-0.470469\pi
0.0926404 + 0.995700i 0.470469π0.470469\pi
1818 0 0
1919 −2.23607 −0.512989 −0.256495 0.966546i 0.582568π-0.582568\pi
−0.256495 + 0.966546i 0.582568π0.582568\pi
2020 0 0
2121 0 0
2222 −3.23607 −0.689932
2323 5.70820 1.19024 0.595121 0.803636i 0.297104π-0.297104\pi
0.595121 + 0.803636i 0.297104π0.297104\pi
2424 0 0
2525 0 0
2626 5.23607 1.02688
2727 0 0
2828 −0.145898 −0.0275721
2929 −2.76393 −0.513249 −0.256625 0.966511i 0.582610π-0.582610\pi
−0.256625 + 0.966511i 0.582610π0.582610\pi
3030 0 0
3131 1.00000 0.179605
3232 −3.38197 −0.597853
3333 0 0
3434 1.23607 0.211984
3535 0 0
3636 0 0
3737 2.00000 0.328798 0.164399 0.986394i 0.447432π-0.447432\pi
0.164399 + 0.986394i 0.447432π0.447432\pi
3838 −3.61803 −0.586923
3939 0 0
4040 0 0
4141 −7.00000 −1.09322 −0.546608 0.837389i 0.684081π-0.684081\pi
−0.546608 + 0.837389i 0.684081π0.684081\pi
4242 0 0
4343 −1.23607 −0.188499 −0.0942493 0.995549i 0.530045π-0.530045\pi
−0.0942493 + 0.995549i 0.530045π0.530045\pi
4444 −1.23607 −0.186344
4545 0 0
4646 9.23607 1.36178
4747 2.47214 0.360598 0.180299 0.983612i 0.442293π-0.442293\pi
0.180299 + 0.983612i 0.442293π0.442293\pi
4848 0 0
4949 −6.94427 −0.992039
5050 0 0
5151 0 0
5252 2.00000 0.277350
5353 −10.4721 −1.43846 −0.719229 0.694773i 0.755505π-0.755505\pi
−0.719229 + 0.694773i 0.755505π0.755505\pi
5454 0 0
5555 0 0
5656 0.527864 0.0705388
5757 0 0
5858 −4.47214 −0.587220
5959 −2.23607 −0.291111 −0.145556 0.989350i 0.546497π-0.546497\pi
−0.145556 + 0.989350i 0.546497π0.546497\pi
6060 0 0
6161 8.18034 1.04739 0.523693 0.851907i 0.324554π-0.324554\pi
0.523693 + 0.851907i 0.324554π0.324554\pi
6262 1.61803 0.205491
6363 0 0
6464 4.23607 0.529508
6565 0 0
6666 0 0
6767 −8.00000 −0.977356 −0.488678 0.872464i 0.662521π-0.662521\pi
−0.488678 + 0.872464i 0.662521π0.662521\pi
6868 0.472136 0.0572549
6969 0 0
7070 0 0
7171 9.18034 1.08951 0.544753 0.838597i 0.316623π-0.316623\pi
0.544753 + 0.838597i 0.316623π0.316623\pi
7272 0 0
7373 −8.47214 −0.991589 −0.495794 0.868440i 0.665123π-0.665123\pi
−0.495794 + 0.868440i 0.665123π0.665123\pi
7474 3.23607 0.376185
7575 0 0
7676 −1.38197 −0.158522
7777 0.472136 0.0538049
7878 0 0
7979 −11.7082 −1.31728 −0.658638 0.752460i 0.728867π-0.728867\pi
−0.658638 + 0.752460i 0.728867π0.728867\pi
8080 0 0
8181 0 0
8282 −11.3262 −1.25077
8383 −14.9443 −1.64035 −0.820173 0.572115i 0.806123π-0.806123\pi
−0.820173 + 0.572115i 0.806123π0.806123\pi
8484 0 0
8585 0 0
8686 −2.00000 −0.215666
8787 0 0
8888 4.47214 0.476731
8989 −11.7082 −1.24107 −0.620534 0.784180i 0.713084π-0.713084\pi
−0.620534 + 0.784180i 0.713084π0.713084\pi
9090 0 0
9191 −0.763932 −0.0800818
9292 3.52786 0.367805
9393 0 0
9494 4.00000 0.412568
9595 0 0
9696 0 0
9797 15.9443 1.61890 0.809448 0.587192i 0.199767π-0.199767\pi
0.809448 + 0.587192i 0.199767π0.199767\pi
9898 −11.2361 −1.13501
9999 0 0
100100 0 0
101101 3.00000 0.298511 0.149256 0.988799i 0.452312π-0.452312\pi
0.149256 + 0.988799i 0.452312π0.452312\pi
102102 0 0
103103 −6.23607 −0.614458 −0.307229 0.951636i 0.599402π-0.599402\pi
−0.307229 + 0.951636i 0.599402π0.599402\pi
104104 −7.23607 −0.709555
105105 0 0
106106 −16.9443 −1.64577
107107 5.76393 0.557220 0.278610 0.960404i 0.410126π-0.410126\pi
0.278610 + 0.960404i 0.410126π0.410126\pi
108108 0 0
109109 −13.9443 −1.33562 −0.667810 0.744332i 0.732768π-0.732768\pi
−0.667810 + 0.744332i 0.732768π0.732768\pi
110110 0 0
111111 0 0
112112 1.14590 0.108277
113113 3.47214 0.326631 0.163316 0.986574i 0.447781π-0.447781\pi
0.163316 + 0.986574i 0.447781π0.447781\pi
114114 0 0
115115 0 0
116116 −1.70820 −0.158603
117117 0 0
118118 −3.61803 −0.333067
119119 −0.180340 −0.0165317
120120 0 0
121121 −7.00000 −0.636364
122122 13.2361 1.19834
123123 0 0
124124 0.618034 0.0555011
125125 0 0
126126 0 0
127127 −12.4721 −1.10672 −0.553362 0.832941i 0.686655π-0.686655\pi
−0.553362 + 0.832941i 0.686655π0.686655\pi
128128 13.6180 1.20368
129129 0 0
130130 0 0
131131 −12.0000 −1.04844 −0.524222 0.851581i 0.675644π-0.675644\pi
−0.524222 + 0.851581i 0.675644π0.675644\pi
132132 0 0
133133 0.527864 0.0457716
134134 −12.9443 −1.11821
135135 0 0
136136 −1.70820 −0.146477
137137 6.29180 0.537544 0.268772 0.963204i 0.413382π-0.413382\pi
0.268772 + 0.963204i 0.413382π0.413382\pi
138138 0 0
139139 13.4164 1.13796 0.568982 0.822350i 0.307337π-0.307337\pi
0.568982 + 0.822350i 0.307337π0.307337\pi
140140 0 0
141141 0 0
142142 14.8541 1.24653
143143 −6.47214 −0.541227
144144 0 0
145145 0 0
146146 −13.7082 −1.13450
147147 0 0
148148 1.23607 0.101604
149149 −10.0000 −0.819232 −0.409616 0.912258i 0.634337π-0.634337\pi
−0.409616 + 0.912258i 0.634337π0.634337\pi
150150 0 0
151151 −14.1803 −1.15398 −0.576990 0.816751i 0.695773π-0.695773\pi
−0.576990 + 0.816751i 0.695773π0.695773\pi
152152 5.00000 0.405554
153153 0 0
154154 0.763932 0.0615594
155155 0 0
156156 0 0
157157 −20.8885 −1.66709 −0.833544 0.552454i 0.813692π-0.813692\pi
−0.833544 + 0.552454i 0.813692π0.813692\pi
158158 −18.9443 −1.50713
159159 0 0
160160 0 0
161161 −1.34752 −0.106200
162162 0 0
163163 −10.7082 −0.838731 −0.419366 0.907817i 0.637747π-0.637747\pi
−0.419366 + 0.907817i 0.637747π0.637747\pi
164164 −4.32624 −0.337822
165165 0 0
166166 −24.1803 −1.87676
167167 −6.47214 −0.500829 −0.250414 0.968139i 0.580567π-0.580567\pi
−0.250414 + 0.968139i 0.580567π0.580567\pi
168168 0 0
169169 −2.52786 −0.194451
170170 0 0
171171 0 0
172172 −0.763932 −0.0582493
173173 2.94427 0.223849 0.111924 0.993717i 0.464299π-0.464299\pi
0.111924 + 0.993717i 0.464299π0.464299\pi
174174 0 0
175175 0 0
176176 9.70820 0.731783
177177 0 0
178178 −18.9443 −1.41993
179179 −1.70820 −0.127677 −0.0638386 0.997960i 0.520334π-0.520334\pi
−0.0638386 + 0.997960i 0.520334π0.520334\pi
180180 0 0
181181 −4.18034 −0.310722 −0.155361 0.987858i 0.549654π-0.549654\pi
−0.155361 + 0.987858i 0.549654π0.549654\pi
182182 −1.23607 −0.0916235
183183 0 0
184184 −12.7639 −0.940970
185185 0 0
186186 0 0
187187 −1.52786 −0.111728
188188 1.52786 0.111431
189189 0 0
190190 0 0
191191 19.1803 1.38784 0.693920 0.720052i 0.255882π-0.255882\pi
0.693920 + 0.720052i 0.255882π0.255882\pi
192192 0 0
193193 −3.47214 −0.249930 −0.124965 0.992161i 0.539882π-0.539882\pi
−0.124965 + 0.992161i 0.539882π0.539882\pi
194194 25.7984 1.85222
195195 0 0
196196 −4.29180 −0.306557
197197 11.4164 0.813385 0.406693 0.913565i 0.366682π-0.366682\pi
0.406693 + 0.913565i 0.366682π0.366682\pi
198198 0 0
199199 −18.9443 −1.34292 −0.671462 0.741039i 0.734333π-0.734333\pi
−0.671462 + 0.741039i 0.734333π0.734333\pi
200200 0 0
201201 0 0
202202 4.85410 0.341533
203203 0.652476 0.0457948
204204 0 0
205205 0 0
206206 −10.0902 −0.703015
207207 0 0
208208 −15.7082 −1.08917
209209 4.47214 0.309344
210210 0 0
211211 23.1803 1.59580 0.797900 0.602790i 0.205944π-0.205944\pi
0.797900 + 0.602790i 0.205944π0.205944\pi
212212 −6.47214 −0.444508
213213 0 0
214214 9.32624 0.637528
215215 0 0
216216 0 0
217217 −0.236068 −0.0160253
218218 −22.5623 −1.52811
219219 0 0
220220 0 0
221221 2.47214 0.166294
222222 0 0
223223 −4.00000 −0.267860 −0.133930 0.990991i 0.542760π-0.542760\pi
−0.133930 + 0.990991i 0.542760π0.542760\pi
224224 0.798374 0.0533436
225225 0 0
226226 5.61803 0.373706
227227 −6.47214 −0.429571 −0.214785 0.976661i 0.568905π-0.568905\pi
−0.214785 + 0.976661i 0.568905π0.568905\pi
228228 0 0
229229 −13.4164 −0.886581 −0.443291 0.896378i 0.646189π-0.646189\pi
−0.443291 + 0.896378i 0.646189π0.646189\pi
230230 0 0
231231 0 0
232232 6.18034 0.405759
233233 17.9443 1.17557 0.587784 0.809018i 0.300000π-0.300000\pi
0.587784 + 0.809018i 0.300000π0.300000\pi
234234 0 0
235235 0 0
236236 −1.38197 −0.0899583
237237 0 0
238238 −0.291796 −0.0189143
239239 11.7082 0.757341 0.378670 0.925532i 0.376381π-0.376381\pi
0.378670 + 0.925532i 0.376381π0.376381\pi
240240 0 0
241241 14.3607 0.925053 0.462526 0.886606i 0.346943π-0.346943\pi
0.462526 + 0.886606i 0.346943π0.346943\pi
242242 −11.3262 −0.728078
243243 0 0
244244 5.05573 0.323660
245245 0 0
246246 0 0
247247 −7.23607 −0.460420
248248 −2.23607 −0.141990
249249 0 0
250250 0 0
251251 1.81966 0.114856 0.0574280 0.998350i 0.481710π-0.481710\pi
0.0574280 + 0.998350i 0.481710π0.481710\pi
252252 0 0
253253 −11.4164 −0.717743
254254 −20.1803 −1.26623
255255 0 0
256256 13.5623 0.847644
257257 1.94427 0.121280 0.0606402 0.998160i 0.480686π-0.480686\pi
0.0606402 + 0.998160i 0.480686π0.480686\pi
258258 0 0
259259 −0.472136 −0.0293371
260260 0 0
261261 0 0
262262 −19.4164 −1.19955
263263 −23.2361 −1.43280 −0.716399 0.697691i 0.754211π-0.754211\pi
−0.716399 + 0.697691i 0.754211π0.754211\pi
264264 0 0
265265 0 0
266266 0.854102 0.0523684
267267 0 0
268268 −4.94427 −0.302019
269269 11.0557 0.674080 0.337040 0.941490i 0.390574π-0.390574\pi
0.337040 + 0.941490i 0.390574π0.390574\pi
270270 0 0
271271 −14.1803 −0.861394 −0.430697 0.902497i 0.641732π-0.641732\pi
−0.430697 + 0.902497i 0.641732π0.641732\pi
272272 −3.70820 −0.224843
273273 0 0
274274 10.1803 0.615017
275275 0 0
276276 0 0
277277 12.6525 0.760214 0.380107 0.924943i 0.375887π-0.375887\pi
0.380107 + 0.924943i 0.375887π0.375887\pi
278278 21.7082 1.30197
279279 0 0
280280 0 0
281281 −17.0000 −1.01413 −0.507067 0.861906i 0.669271π-0.669271\pi
−0.507067 + 0.861906i 0.669271π0.669271\pi
282282 0 0
283283 13.8885 0.825588 0.412794 0.910824i 0.364553π-0.364553\pi
0.412794 + 0.910824i 0.364553π0.364553\pi
284284 5.67376 0.336676
285285 0 0
286286 −10.4721 −0.619230
287287 1.65248 0.0975426
288288 0 0
289289 −16.4164 −0.965671
290290 0 0
291291 0 0
292292 −5.23607 −0.306418
293293 −0.472136 −0.0275825 −0.0137912 0.999905i 0.504390π-0.504390\pi
−0.0137912 + 0.999905i 0.504390π0.504390\pi
294294 0 0
295295 0 0
296296 −4.47214 −0.259938
297297 0 0
298298 −16.1803 −0.937302
299299 18.4721 1.06827
300300 0 0
301301 0.291796 0.0168188
302302 −22.9443 −1.32029
303303 0 0
304304 10.8541 0.622525
305305 0 0
306306 0 0
307307 28.7082 1.63846 0.819232 0.573462i 0.194400π-0.194400\pi
0.819232 + 0.573462i 0.194400π0.194400\pi
308308 0.291796 0.0166266
309309 0 0
310310 0 0
311311 29.1803 1.65467 0.827333 0.561712i 0.189857π-0.189857\pi
0.827333 + 0.561712i 0.189857π0.189857\pi
312312 0 0
313313 −16.7639 −0.947553 −0.473777 0.880645i 0.657110π-0.657110\pi
−0.473777 + 0.880645i 0.657110π0.657110\pi
314314 −33.7984 −1.90735
315315 0 0
316316 −7.23607 −0.407061
317317 4.05573 0.227792 0.113896 0.993493i 0.463667π-0.463667\pi
0.113896 + 0.993493i 0.463667π0.463667\pi
318318 0 0
319319 5.52786 0.309501
320320 0 0
321321 0 0
322322 −2.18034 −0.121506
323323 −1.70820 −0.0950470
324324 0 0
325325 0 0
326326 −17.3262 −0.959612
327327 0 0
328328 15.6525 0.864263
329329 −0.583592 −0.0321745
330330 0 0
331331 2.00000 0.109930 0.0549650 0.998488i 0.482495π-0.482495\pi
0.0549650 + 0.998488i 0.482495π0.482495\pi
332332 −9.23607 −0.506895
333333 0 0
334334 −10.4721 −0.573010
335335 0 0
336336 0 0
337337 14.7639 0.804243 0.402121 0.915586i 0.368273π-0.368273\pi
0.402121 + 0.915586i 0.368273π0.368273\pi
338338 −4.09017 −0.222476
339339 0 0
340340 0 0
341341 −2.00000 −0.108306
342342 0 0
343343 3.29180 0.177740
344344 2.76393 0.149021
345345 0 0
346346 4.76393 0.256111
347347 24.1803 1.29807 0.649034 0.760759i 0.275173π-0.275173\pi
0.649034 + 0.760759i 0.275173π0.275173\pi
348348 0 0
349349 −7.88854 −0.422264 −0.211132 0.977458i 0.567715π-0.567715\pi
−0.211132 + 0.977458i 0.567715π0.567715\pi
350350 0 0
351351 0 0
352352 6.76393 0.360519
353353 7.41641 0.394736 0.197368 0.980330i 0.436761π-0.436761\pi
0.197368 + 0.980330i 0.436761π0.436761\pi
354354 0 0
355355 0 0
356356 −7.23607 −0.383511
357357 0 0
358358 −2.76393 −0.146078
359359 −22.2361 −1.17357 −0.586787 0.809741i 0.699608π-0.699608\pi
−0.586787 + 0.809741i 0.699608π0.699608\pi
360360 0 0
361361 −14.0000 −0.736842
362362 −6.76393 −0.355504
363363 0 0
364364 −0.472136 −0.0247466
365365 0 0
366366 0 0
367367 −18.0000 −0.939592 −0.469796 0.882775i 0.655673π-0.655673\pi
−0.469796 + 0.882775i 0.655673π0.655673\pi
368368 −27.7082 −1.44439
369369 0 0
370370 0 0
371371 2.47214 0.128347
372372 0 0
373373 −19.0000 −0.983783 −0.491891 0.870657i 0.663694π-0.663694\pi
−0.491891 + 0.870657i 0.663694π0.663694\pi
374374 −2.47214 −0.127831
375375 0 0
376376 −5.52786 −0.285078
377377 −8.94427 −0.460653
378378 0 0
379379 −2.11146 −0.108458 −0.0542291 0.998529i 0.517270π-0.517270\pi
−0.0542291 + 0.998529i 0.517270π0.517270\pi
380380 0 0
381381 0 0
382382 31.0344 1.58786
383383 −23.8885 −1.22065 −0.610324 0.792152i 0.708961π-0.708961\pi
−0.610324 + 0.792152i 0.708961π0.708961\pi
384384 0 0
385385 0 0
386386 −5.61803 −0.285950
387387 0 0
388388 9.85410 0.500266
389389 17.8885 0.906985 0.453493 0.891260i 0.350178π-0.350178\pi
0.453493 + 0.891260i 0.350178π0.350178\pi
390390 0 0
391391 4.36068 0.220529
392392 15.5279 0.784276
393393 0 0
394394 18.4721 0.930613
395395 0 0
396396 0 0
397397 7.00000 0.351320 0.175660 0.984451i 0.443794π-0.443794\pi
0.175660 + 0.984451i 0.443794π0.443794\pi
398398 −30.6525 −1.53647
399399 0 0
400400 0 0
401401 −38.1803 −1.90664 −0.953318 0.301969i 0.902356π-0.902356\pi
−0.953318 + 0.301969i 0.902356π0.902356\pi
402402 0 0
403403 3.23607 0.161200
404404 1.85410 0.0922450
405405 0 0
406406 1.05573 0.0523949
407407 −4.00000 −0.198273
408408 0 0
409409 −3.81966 −0.188870 −0.0944350 0.995531i 0.530104π-0.530104\pi
−0.0944350 + 0.995531i 0.530104π0.530104\pi
410410 0 0
411411 0 0
412412 −3.85410 −0.189878
413413 0.527864 0.0259745
414414 0 0
415415 0 0
416416 −10.9443 −0.536587
417417 0 0
418418 7.23607 0.353928
419419 10.1246 0.494620 0.247310 0.968936i 0.420453π-0.420453\pi
0.247310 + 0.968936i 0.420453π0.420453\pi
420420 0 0
421421 29.3607 1.43095 0.715476 0.698637i 0.246210π-0.246210\pi
0.715476 + 0.698637i 0.246210π0.246210\pi
422422 37.5066 1.82579
423423 0 0
424424 23.4164 1.13720
425425 0 0
426426 0 0
427427 −1.93112 −0.0934533
428428 3.56231 0.172191
429429 0 0
430430 0 0
431431 −12.0000 −0.578020 −0.289010 0.957326i 0.593326π-0.593326\pi
−0.289010 + 0.957326i 0.593326π0.593326\pi
432432 0 0
433433 −10.1803 −0.489236 −0.244618 0.969620i 0.578663π-0.578663\pi
−0.244618 + 0.969620i 0.578663π0.578663\pi
434434 −0.381966 −0.0183350
435435 0 0
436436 −8.61803 −0.412729
437437 −12.7639 −0.610582
438438 0 0
439439 −1.18034 −0.0563345 −0.0281673 0.999603i 0.508967π-0.508967\pi
−0.0281673 + 0.999603i 0.508967π0.508967\pi
440440 0 0
441441 0 0
442442 4.00000 0.190261
443443 30.7082 1.45899 0.729495 0.683986i 0.239755π-0.239755\pi
0.729495 + 0.683986i 0.239755π0.239755\pi
444444 0 0
445445 0 0
446446 −6.47214 −0.306465
447447 0 0
448448 −1.00000 −0.0472456
449449 31.3050 1.47737 0.738686 0.674050i 0.235447π-0.235447\pi
0.738686 + 0.674050i 0.235447π0.235447\pi
450450 0 0
451451 14.0000 0.659234
452452 2.14590 0.100935
453453 0 0
454454 −10.4721 −0.491482
455455 0 0
456456 0 0
457457 3.05573 0.142941 0.0714705 0.997443i 0.477231π-0.477231\pi
0.0714705 + 0.997443i 0.477231π0.477231\pi
458458 −21.7082 −1.01436
459459 0 0
460460 0 0
461461 −34.3607 −1.60034 −0.800168 0.599776i 0.795256π-0.795256\pi
−0.800168 + 0.599776i 0.795256π0.795256\pi
462462 0 0
463463 2.58359 0.120070 0.0600349 0.998196i 0.480879π-0.480879\pi
0.0600349 + 0.998196i 0.480879π0.480879\pi
464464 13.4164 0.622841
465465 0 0
466466 29.0344 1.34499
467467 4.70820 0.217870 0.108935 0.994049i 0.465256π-0.465256\pi
0.108935 + 0.994049i 0.465256π0.465256\pi
468468 0 0
469469 1.88854 0.0872049
470470 0 0
471471 0 0
472472 5.00000 0.230144
473473 2.47214 0.113669
474474 0 0
475475 0 0
476476 −0.111456 −0.00510859
477477 0 0
478478 18.9443 0.866491
479479 −23.2918 −1.06423 −0.532115 0.846672i 0.678602π-0.678602\pi
−0.532115 + 0.846672i 0.678602π0.678602\pi
480480 0 0
481481 6.47214 0.295104
482482 23.2361 1.05837
483483 0 0
484484 −4.32624 −0.196647
485485 0 0
486486 0 0
487487 19.2361 0.871669 0.435835 0.900027i 0.356453π-0.356453\pi
0.435835 + 0.900027i 0.356453π0.356453\pi
488488 −18.2918 −0.828031
489489 0 0
490490 0 0
491491 −4.36068 −0.196795 −0.0983974 0.995147i 0.531372π-0.531372\pi
−0.0983974 + 0.995147i 0.531372π0.531372\pi
492492 0 0
493493 −2.11146 −0.0950952
494494 −11.7082 −0.526777
495495 0 0
496496 −4.85410 −0.217956
497497 −2.16718 −0.0972115
498498 0 0
499499 −6.58359 −0.294722 −0.147361 0.989083i 0.547078π-0.547078\pi
−0.147361 + 0.989083i 0.547078π0.547078\pi
500500 0 0
501501 0 0
502502 2.94427 0.131409
503503 29.6525 1.32214 0.661069 0.750325i 0.270103π-0.270103\pi
0.661069 + 0.750325i 0.270103π0.270103\pi
504504 0 0
505505 0 0
506506 −18.4721 −0.821187
507507 0 0
508508 −7.70820 −0.341996
509509 −29.5967 −1.31185 −0.655926 0.754825i 0.727722π-0.727722\pi
−0.655926 + 0.754825i 0.727722π0.727722\pi
510510 0 0
511511 2.00000 0.0884748
512512 −5.29180 −0.233867
513513 0 0
514514 3.14590 0.138760
515515 0 0
516516 0 0
517517 −4.94427 −0.217449
518518 −0.763932 −0.0335652
519519 0 0
520520 0 0
521521 −2.00000 −0.0876216 −0.0438108 0.999040i 0.513950π-0.513950\pi
−0.0438108 + 0.999040i 0.513950π0.513950\pi
522522 0 0
523523 17.7082 0.774326 0.387163 0.922011i 0.373455π-0.373455\pi
0.387163 + 0.922011i 0.373455π0.373455\pi
524524 −7.41641 −0.323987
525525 0 0
526526 −37.5967 −1.63930
527527 0.763932 0.0332774
528528 0 0
529529 9.58359 0.416678
530530 0 0
531531 0 0
532532 0.326238 0.0141442
533533 −22.6525 −0.981188
534534 0 0
535535 0 0
536536 17.8885 0.772667
537537 0 0
538538 17.8885 0.771230
539539 13.8885 0.598222
540540 0 0
541541 −25.3607 −1.09034 −0.545170 0.838325i 0.683535π-0.683535\pi
−0.545170 + 0.838325i 0.683535π0.683535\pi
542542 −22.9443 −0.985541
543543 0 0
544544 −2.58359 −0.110771
545545 0 0
546546 0 0
547547 12.1246 0.518411 0.259205 0.965822i 0.416539π-0.416539\pi
0.259205 + 0.965822i 0.416539π0.416539\pi
548548 3.88854 0.166110
549549 0 0
550550 0 0
551551 6.18034 0.263291
552552 0 0
553553 2.76393 0.117534
554554 20.4721 0.869778
555555 0 0
556556 8.29180 0.351650
557557 −12.0000 −0.508456 −0.254228 0.967144i 0.581821π-0.581821\pi
−0.254228 + 0.967144i 0.581821π0.581821\pi
558558 0 0
559559 −4.00000 −0.169182
560560 0 0
561561 0 0
562562 −27.5066 −1.16029
563563 27.5410 1.16072 0.580358 0.814362i 0.302913π-0.302913\pi
0.580358 + 0.814362i 0.302913π0.302913\pi
564564 0 0
565565 0 0
566566 22.4721 0.944574
567567 0 0
568568 −20.5279 −0.861330
569569 −5.52786 −0.231740 −0.115870 0.993264i 0.536966π-0.536966\pi
−0.115870 + 0.993264i 0.536966π0.536966\pi
570570 0 0
571571 28.1803 1.17931 0.589655 0.807655i 0.299264π-0.299264\pi
0.589655 + 0.807655i 0.299264π0.299264\pi
572572 −4.00000 −0.167248
573573 0 0
574574 2.67376 0.111601
575575 0 0
576576 0 0
577577 28.8328 1.20033 0.600163 0.799878i 0.295102π-0.295102\pi
0.600163 + 0.799878i 0.295102π0.295102\pi
578578 −26.5623 −1.10485
579579 0 0
580580 0 0
581581 3.52786 0.146360
582582 0 0
583583 20.9443 0.867423
584584 18.9443 0.783920
585585 0 0
586586 −0.763932 −0.0315577
587587 −6.47214 −0.267134 −0.133567 0.991040i 0.542643π-0.542643\pi
−0.133567 + 0.991040i 0.542643π0.542643\pi
588588 0 0
589589 −2.23607 −0.0921356
590590 0 0
591591 0 0
592592 −9.70820 −0.399005
593593 −6.52786 −0.268067 −0.134034 0.990977i 0.542793π-0.542793\pi
−0.134034 + 0.990977i 0.542793π0.542793\pi
594594 0 0
595595 0 0
596596 −6.18034 −0.253157
597597 0 0
598598 29.8885 1.22223
599599 14.5967 0.596407 0.298203 0.954502i 0.403613π-0.403613\pi
0.298203 + 0.954502i 0.403613π0.403613\pi
600600 0 0
601601 30.5410 1.24579 0.622897 0.782304i 0.285956π-0.285956\pi
0.622897 + 0.782304i 0.285956π0.285956\pi
602602 0.472136 0.0192428
603603 0 0
604604 −8.76393 −0.356599
605605 0 0
606606 0 0
607607 −22.4721 −0.912116 −0.456058 0.889950i 0.650739π-0.650739\pi
−0.456058 + 0.889950i 0.650739π0.650739\pi
608608 7.56231 0.306692
609609 0 0
610610 0 0
611611 8.00000 0.323645
612612 0 0
613613 43.8885 1.77264 0.886321 0.463072i 0.153253π-0.153253\pi
0.886321 + 0.463072i 0.153253π0.153253\pi
614614 46.4508 1.87460
615615 0 0
616616 −1.05573 −0.0425365
617617 32.4721 1.30728 0.653639 0.756806i 0.273241π-0.273241\pi
0.653639 + 0.756806i 0.273241π0.273241\pi
618618 0 0
619619 6.18034 0.248409 0.124204 0.992257i 0.460362π-0.460362\pi
0.124204 + 0.992257i 0.460362π0.460362\pi
620620 0 0
621621 0 0
622622 47.2148 1.89314
623623 2.76393 0.110735
624624 0 0
625625 0 0
626626 −27.1246 −1.08412
627627 0 0
628628 −12.9098 −0.515158
629629 1.52786 0.0609199
630630 0 0
631631 34.3607 1.36788 0.683939 0.729540i 0.260266π-0.260266\pi
0.683939 + 0.729540i 0.260266π0.260266\pi
632632 26.1803 1.04140
633633 0 0
634634 6.56231 0.260622
635635 0 0
636636 0 0
637637 −22.4721 −0.890378
638638 8.94427 0.354107
639639 0 0
640640 0 0
641641 −12.0000 −0.473972 −0.236986 0.971513i 0.576159π-0.576159\pi
−0.236986 + 0.971513i 0.576159π0.576159\pi
642642 0 0
643643 −19.5279 −0.770104 −0.385052 0.922895i 0.625816π-0.625816\pi
−0.385052 + 0.922895i 0.625816π0.625816\pi
644644 −0.832816 −0.0328175
645645 0 0
646646 −2.76393 −0.108745
647647 −0.944272 −0.0371232 −0.0185616 0.999828i 0.505909π-0.505909\pi
−0.0185616 + 0.999828i 0.505909π0.505909\pi
648648 0 0
649649 4.47214 0.175547
650650 0 0
651651 0 0
652652 −6.61803 −0.259182
653653 −47.3050 −1.85119 −0.925593 0.378521i 0.876433π-0.876433\pi
−0.925593 + 0.378521i 0.876433π0.876433\pi
654654 0 0
655655 0 0
656656 33.9787 1.32665
657657 0 0
658658 −0.944272 −0.0368116
659659 −25.6525 −0.999279 −0.499639 0.866234i 0.666534π-0.666534\pi
−0.499639 + 0.866234i 0.666534π0.666534\pi
660660 0 0
661661 −0.639320 −0.0248667 −0.0124333 0.999923i 0.503958π-0.503958\pi
−0.0124333 + 0.999923i 0.503958π0.503958\pi
662662 3.23607 0.125773
663663 0 0
664664 33.4164 1.29681
665665 0 0
666666 0 0
667667 −15.7771 −0.610891
668668 −4.00000 −0.154765
669669 0 0
670670 0 0
671671 −16.3607 −0.631597
672672 0 0
673673 29.0132 1.11837 0.559187 0.829041i 0.311113π-0.311113\pi
0.559187 + 0.829041i 0.311113π0.311113\pi
674674 23.8885 0.920152
675675 0 0
676676 −1.56231 −0.0600887
677677 −46.7214 −1.79565 −0.897824 0.440355i 0.854853π-0.854853\pi
−0.897824 + 0.440355i 0.854853π0.854853\pi
678678 0 0
679679 −3.76393 −0.144446
680680 0 0
681681 0 0
682682 −3.23607 −0.123915
683683 5.18034 0.198220 0.0991101 0.995076i 0.468400π-0.468400\pi
0.0991101 + 0.995076i 0.468400π0.468400\pi
684684 0 0
685685 0 0
686686 5.32624 0.203357
687687 0 0
688688 6.00000 0.228748
689689 −33.8885 −1.29105
690690 0 0
691691 3.18034 0.120986 0.0604929 0.998169i 0.480733π-0.480733\pi
0.0604929 + 0.998169i 0.480733π0.480733\pi
692692 1.81966 0.0691731
693693 0 0
694694 39.1246 1.48515
695695 0 0
696696 0 0
697697 −5.34752 −0.202552
698698 −12.7639 −0.483122
699699 0 0
700700 0 0
701701 −7.00000 −0.264386 −0.132193 0.991224i 0.542202π-0.542202\pi
−0.132193 + 0.991224i 0.542202π0.542202\pi
702702 0 0
703703 −4.47214 −0.168670
704704 −8.47214 −0.319306
705705 0 0
706706 12.0000 0.451626
707707 −0.708204 −0.0266348
708708 0 0
709709 25.5279 0.958719 0.479360 0.877619i 0.340869π-0.340869\pi
0.479360 + 0.877619i 0.340869π0.340869\pi
710710 0 0
711711 0 0
712712 26.1803 0.981150
713713 5.70820 0.213774
714714 0 0
715715 0 0
716716 −1.05573 −0.0394544
717717 0 0
718718 −35.9787 −1.34271
719719 13.8197 0.515386 0.257693 0.966227i 0.417038π-0.417038\pi
0.257693 + 0.966227i 0.417038π0.417038\pi
720720 0 0
721721 1.47214 0.0548252
722722 −22.6525 −0.843038
723723 0 0
724724 −2.58359 −0.0960184
725725 0 0
726726 0 0
727727 44.2361 1.64062 0.820312 0.571916i 0.193800π-0.193800\pi
0.820312 + 0.571916i 0.193800π0.193800\pi
728728 1.70820 0.0633102
729729 0 0
730730 0 0
731731 −0.944272 −0.0349252
732732 0 0
733733 −3.47214 −0.128246 −0.0641231 0.997942i 0.520425π-0.520425\pi
−0.0641231 + 0.997942i 0.520425π0.520425\pi
734734 −29.1246 −1.07501
735735 0 0
736736 −19.3050 −0.711590
737737 16.0000 0.589368
738738 0 0
739739 6.18034 0.227347 0.113674 0.993518i 0.463738π-0.463738\pi
0.113674 + 0.993518i 0.463738π0.463738\pi
740740 0 0
741741 0 0
742742 4.00000 0.146845
743743 50.1803 1.84094 0.920469 0.390815i 0.127807π-0.127807\pi
0.920469 + 0.390815i 0.127807π0.127807\pi
744744 0 0
745745 0 0
746746 −30.7426 −1.12557
747747 0 0
748748 −0.944272 −0.0345260
749749 −1.36068 −0.0497182
750750 0 0
751751 −21.5410 −0.786043 −0.393021 0.919529i 0.628570π-0.628570\pi
−0.393021 + 0.919529i 0.628570π0.628570\pi
752752 −12.0000 −0.437595
753753 0 0
754754 −14.4721 −0.527044
755755 0 0
756756 0 0
757757 −8.65248 −0.314480 −0.157240 0.987560i 0.550260π-0.550260\pi
−0.157240 + 0.987560i 0.550260π0.550260\pi
758758 −3.41641 −0.124090
759759 0 0
760760 0 0
761761 −2.00000 −0.0724999 −0.0362500 0.999343i 0.511541π-0.511541\pi
−0.0362500 + 0.999343i 0.511541π0.511541\pi
762762 0 0
763763 3.29180 0.119171
764764 11.8541 0.428866
765765 0 0
766766 −38.6525 −1.39657
767767 −7.23607 −0.261279
768768 0 0
769769 −47.3607 −1.70787 −0.853935 0.520380i 0.825790π-0.825790\pi
−0.853935 + 0.520380i 0.825790π0.825790\pi
770770 0 0
771771 0 0
772772 −2.14590 −0.0772326
773773 −11.1246 −0.400124 −0.200062 0.979783i 0.564114π-0.564114\pi
−0.200062 + 0.979783i 0.564114π0.564114\pi
774774 0 0
775775 0 0
776776 −35.6525 −1.27985
777777 0 0
778778 28.9443 1.03770
779779 15.6525 0.560808
780780 0 0
781781 −18.3607 −0.656997
782782 7.05573 0.252312
783783 0 0
784784 33.7082 1.20386
785785 0 0
786786 0 0
787787 −7.34752 −0.261911 −0.130955 0.991388i 0.541804π-0.541804\pi
−0.130955 + 0.991388i 0.541804π0.541804\pi
788788 7.05573 0.251350
789789 0 0
790790 0 0
791791 −0.819660 −0.0291438
792792 0 0
793793 26.4721 0.940053
794794 11.3262 0.401953
795795 0 0
796796 −11.7082 −0.414986
797797 −55.4164 −1.96295 −0.981475 0.191591i 0.938635π-0.938635\pi
−0.981475 + 0.191591i 0.938635π0.938635\pi
798798 0 0
799799 1.88854 0.0668119
800800 0 0
801801 0 0
802802 −61.7771 −2.18142
803803 16.9443 0.597950
804804 0 0
805805 0 0
806806 5.23607 0.184433
807807 0 0
808808 −6.70820 −0.235994
809809 −23.4164 −0.823277 −0.411639 0.911347i 0.635043π-0.635043\pi
−0.411639 + 0.911347i 0.635043π0.635043\pi
810810 0 0
811811 −28.0000 −0.983213 −0.491606 0.870817i 0.663590π-0.663590\pi
−0.491606 + 0.870817i 0.663590π0.663590\pi
812812 0.403252 0.0141514
813813 0 0
814814 −6.47214 −0.226848
815815 0 0
816816 0 0
817817 2.76393 0.0966977
818818 −6.18034 −0.216091
819819 0 0
820820 0 0
821821 −30.5410 −1.06589 −0.532944 0.846150i 0.678915π-0.678915\pi
−0.532944 + 0.846150i 0.678915π0.678915\pi
822822 0 0
823823 14.2918 0.498181 0.249090 0.968480i 0.419868π-0.419868\pi
0.249090 + 0.968480i 0.419868π0.419868\pi
824824 13.9443 0.485772
825825 0 0
826826 0.854102 0.0297180
827827 17.3475 0.603233 0.301616 0.953429i 0.402474π-0.402474\pi
0.301616 + 0.953429i 0.402474π0.402474\pi
828828 0 0
829829 16.8328 0.584628 0.292314 0.956322i 0.405575π-0.405575\pi
0.292314 + 0.956322i 0.405575π0.405575\pi
830830 0 0
831831 0 0
832832 13.7082 0.475246
833833 −5.30495 −0.183806
834834 0 0
835835 0 0
836836 2.76393 0.0955926
837837 0 0
838838 16.3820 0.565906
839839 −28.9443 −0.999267 −0.499634 0.866237i 0.666532π-0.666532\pi
−0.499634 + 0.866237i 0.666532π0.666532\pi
840840 0 0
841841 −21.3607 −0.736575
842842 47.5066 1.63718
843843 0 0
844844 14.3262 0.493129
845845 0 0
846846 0 0
847847 1.65248 0.0567797
848848 50.8328 1.74561
849849 0 0
850850 0 0
851851 11.4164 0.391349
852852 0 0
853853 −10.5836 −0.362375 −0.181188 0.983449i 0.557994π-0.557994\pi
−0.181188 + 0.983449i 0.557994π0.557994\pi
854854 −3.12461 −0.106922
855855 0 0
856856 −12.8885 −0.440521
857857 −55.6656 −1.90150 −0.950751 0.309956i 0.899686π-0.899686\pi
−0.950751 + 0.309956i 0.899686π0.899686\pi
858858 0 0
859859 2.11146 0.0720420 0.0360210 0.999351i 0.488532π-0.488532\pi
0.0360210 + 0.999351i 0.488532π0.488532\pi
860860 0 0
861861 0 0
862862 −19.4164 −0.661325
863863 −9.81966 −0.334265 −0.167133 0.985934i 0.553451π-0.553451\pi
−0.167133 + 0.985934i 0.553451π0.553451\pi
864864 0 0
865865 0 0
866866 −16.4721 −0.559746
867867 0 0
868868 −0.145898 −0.00495210
869869 23.4164 0.794347
870870 0 0
871871 −25.8885 −0.877200
872872 31.1803 1.05590
873873 0 0
874874 −20.6525 −0.698580
875875 0 0
876876 0 0
877877 18.0557 0.609699 0.304849 0.952401i 0.401394π-0.401394\pi
0.304849 + 0.952401i 0.401394π0.401394\pi
878878 −1.90983 −0.0644536
879879 0 0
880880 0 0
881881 20.3607 0.685969 0.342984 0.939341i 0.388562π-0.388562\pi
0.342984 + 0.939341i 0.388562π0.388562\pi
882882 0 0
883883 31.7771 1.06938 0.534692 0.845047i 0.320428π-0.320428\pi
0.534692 + 0.845047i 0.320428π0.320428\pi
884884 1.52786 0.0513876
885885 0 0
886886 49.6869 1.66926
887887 27.0689 0.908884 0.454442 0.890776i 0.349839π-0.349839\pi
0.454442 + 0.890776i 0.349839π0.349839\pi
888888 0 0
889889 2.94427 0.0987477
890890 0 0
891891 0 0
892892 −2.47214 −0.0827732
893893 −5.52786 −0.184983
894894 0 0
895895 0 0
896896 −3.21478 −0.107398
897897 0 0
898898 50.6525 1.69030
899899 −2.76393 −0.0921823
900900 0 0
901901 −8.00000 −0.266519
902902 22.6525 0.754245
903903 0 0
904904 −7.76393 −0.258225
905905 0 0
906906 0 0
907907 24.2361 0.804745 0.402373 0.915476i 0.368186π-0.368186\pi
0.402373 + 0.915476i 0.368186π0.368186\pi
908908 −4.00000 −0.132745
909909 0 0
910910 0 0
911911 −18.1803 −0.602342 −0.301171 0.953570i 0.597377π-0.597377\pi
−0.301171 + 0.953570i 0.597377π0.597377\pi
912912 0 0
913913 29.8885 0.989166
914914 4.94427 0.163542
915915 0 0
916916 −8.29180 −0.273969
917917 2.83282 0.0935478
918918 0 0
919919 −14.4721 −0.477392 −0.238696 0.971094i 0.576720π-0.576720\pi
−0.238696 + 0.971094i 0.576720π0.576720\pi
920920 0 0
921921 0 0
922922 −55.5967 −1.83098
923923 29.7082 0.977857
924924 0 0
925925 0 0
926926 4.18034 0.137374
927927 0 0
928928 9.34752 0.306848
929929 20.0000 0.656179 0.328089 0.944647i 0.393595π-0.393595\pi
0.328089 + 0.944647i 0.393595π0.393595\pi
930930 0 0
931931 15.5279 0.508905
932932 11.0902 0.363271
933933 0 0
934934 7.61803 0.249270
935935 0 0
936936 0 0
937937 −9.05573 −0.295838 −0.147919 0.988999i 0.547257π-0.547257\pi
−0.147919 + 0.988999i 0.547257π0.547257\pi
938938 3.05573 0.0997731
939939 0 0
940940 0 0
941941 38.0000 1.23876 0.619382 0.785090i 0.287383π-0.287383\pi
0.619382 + 0.785090i 0.287383π0.287383\pi
942942 0 0
943943 −39.9574 −1.30119
944944 10.8541 0.353271
945945 0 0
946946 4.00000 0.130051
947947 −13.0557 −0.424254 −0.212127 0.977242i 0.568039π-0.568039\pi
−0.212127 + 0.977242i 0.568039π0.568039\pi
948948 0 0
949949 −27.4164 −0.889974
950950 0 0
951951 0 0
952952 0.403252 0.0130695
953953 45.7082 1.48063 0.740317 0.672258i 0.234675π-0.234675\pi
0.740317 + 0.672258i 0.234675π0.234675\pi
954954 0 0
955955 0 0
956956 7.23607 0.234031
957957 0 0
958958 −37.6869 −1.21761
959959 −1.48529 −0.0479626
960960 0 0
961961 1.00000 0.0322581
962962 10.4721 0.337635
963963 0 0
964964 8.87539 0.285857
965965 0 0
966966 0 0
967967 −60.3607 −1.94107 −0.970534 0.240963i 0.922537π-0.922537\pi
−0.970534 + 0.240963i 0.922537π0.922537\pi
968968 15.6525 0.503090
969969 0 0
970970 0 0
971971 28.0000 0.898563 0.449281 0.893390i 0.351680π-0.351680\pi
0.449281 + 0.893390i 0.351680π0.351680\pi
972972 0 0
973973 −3.16718 −0.101535
974974 31.1246 0.997297
975975 0 0
976976 −39.7082 −1.27103
977977 −47.2492 −1.51164 −0.755818 0.654781i 0.772761π-0.772761\pi
−0.755818 + 0.654781i 0.772761π0.772761\pi
978978 0 0
979979 23.4164 0.748392
980980 0 0
981981 0 0
982982 −7.05573 −0.225157
983983 39.5279 1.26074 0.630372 0.776294i 0.282903π-0.282903\pi
0.630372 + 0.776294i 0.282903π0.282903\pi
984984 0 0
985985 0 0
986986 −3.41641 −0.108801
987987 0 0
988988 −4.47214 −0.142278
989989 −7.05573 −0.224359
990990 0 0
991991 −16.5410 −0.525443 −0.262721 0.964872i 0.584620π-0.584620\pi
−0.262721 + 0.964872i 0.584620π0.584620\pi
992992 −3.38197 −0.107378
993993 0 0
994994 −3.50658 −0.111222
995995 0 0
996996 0 0
997997 29.3607 0.929862 0.464931 0.885347i 0.346079π-0.346079\pi
0.464931 + 0.885347i 0.346079π0.346079\pi
998998 −10.6525 −0.337198
999999 0 0
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 6975.2.a.y.1.2 2
3.2 odd 2 775.2.a.d.1.1 2
5.4 even 2 279.2.a.a.1.1 2
15.2 even 4 775.2.b.d.249.1 4
15.8 even 4 775.2.b.d.249.4 4
15.14 odd 2 31.2.a.a.1.2 2
20.19 odd 2 4464.2.a.bf.1.1 2
60.59 even 2 496.2.a.i.1.2 2
105.104 even 2 1519.2.a.a.1.2 2
120.29 odd 2 1984.2.a.r.1.2 2
120.59 even 2 1984.2.a.n.1.1 2
155.154 odd 2 8649.2.a.c.1.1 2
165.164 even 2 3751.2.a.b.1.1 2
195.194 odd 2 5239.2.a.f.1.1 2
255.254 odd 2 8959.2.a.b.1.2 2
465.14 odd 30 961.2.g.a.816.1 8
465.29 even 10 961.2.d.g.531.1 4
465.44 even 30 961.2.g.e.448.1 8
465.59 odd 30 961.2.g.h.846.1 8
465.74 even 30 961.2.g.e.547.1 8
465.89 even 10 961.2.d.a.388.1 4
465.104 even 30 961.2.g.d.338.1 8
465.119 even 6 961.2.c.c.521.2 4
465.134 odd 30 961.2.g.h.844.1 8
465.149 odd 6 961.2.c.e.439.2 4
465.164 odd 30 961.2.g.a.732.1 8
465.179 even 30 961.2.g.d.235.1 8
465.194 odd 10 961.2.d.c.374.1 4
465.209 even 10 961.2.d.a.374.1 4
465.224 odd 30 961.2.g.a.235.1 8
465.239 even 30 961.2.g.d.732.1 8
465.254 even 6 961.2.c.c.439.2 4
465.269 even 30 961.2.g.e.844.1 8
465.284 odd 6 961.2.c.e.521.2 4
465.299 odd 30 961.2.g.a.338.1 8
465.314 odd 10 961.2.d.c.388.1 4
465.329 odd 30 961.2.g.h.547.1 8
465.344 even 30 961.2.g.e.846.1 8
465.359 odd 30 961.2.g.h.448.1 8
465.374 odd 10 961.2.d.d.531.1 4
465.389 even 30 961.2.g.d.816.1 8
465.419 odd 10 961.2.d.d.628.1 4
465.449 even 10 961.2.d.g.628.1 4
465.464 even 2 961.2.a.f.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
31.2.a.a.1.2 2 15.14 odd 2
279.2.a.a.1.1 2 5.4 even 2
496.2.a.i.1.2 2 60.59 even 2
775.2.a.d.1.1 2 3.2 odd 2
775.2.b.d.249.1 4 15.2 even 4
775.2.b.d.249.4 4 15.8 even 4
961.2.a.f.1.2 2 465.464 even 2
961.2.c.c.439.2 4 465.254 even 6
961.2.c.c.521.2 4 465.119 even 6
961.2.c.e.439.2 4 465.149 odd 6
961.2.c.e.521.2 4 465.284 odd 6
961.2.d.a.374.1 4 465.209 even 10
961.2.d.a.388.1 4 465.89 even 10
961.2.d.c.374.1 4 465.194 odd 10
961.2.d.c.388.1 4 465.314 odd 10
961.2.d.d.531.1 4 465.374 odd 10
961.2.d.d.628.1 4 465.419 odd 10
961.2.d.g.531.1 4 465.29 even 10
961.2.d.g.628.1 4 465.449 even 10
961.2.g.a.235.1 8 465.224 odd 30
961.2.g.a.338.1 8 465.299 odd 30
961.2.g.a.732.1 8 465.164 odd 30
961.2.g.a.816.1 8 465.14 odd 30
961.2.g.d.235.1 8 465.179 even 30
961.2.g.d.338.1 8 465.104 even 30
961.2.g.d.732.1 8 465.239 even 30
961.2.g.d.816.1 8 465.389 even 30
961.2.g.e.448.1 8 465.44 even 30
961.2.g.e.547.1 8 465.74 even 30
961.2.g.e.844.1 8 465.269 even 30
961.2.g.e.846.1 8 465.344 even 30
961.2.g.h.448.1 8 465.359 odd 30
961.2.g.h.547.1 8 465.329 odd 30
961.2.g.h.844.1 8 465.134 odd 30
961.2.g.h.846.1 8 465.59 odd 30
1519.2.a.a.1.2 2 105.104 even 2
1984.2.a.n.1.1 2 120.59 even 2
1984.2.a.r.1.2 2 120.29 odd 2
3751.2.a.b.1.1 2 165.164 even 2
4464.2.a.bf.1.1 2 20.19 odd 2
5239.2.a.f.1.1 2 195.194 odd 2
6975.2.a.y.1.2 2 1.1 even 1 trivial
8649.2.a.c.1.1 2 155.154 odd 2
8959.2.a.b.1.2 2 255.254 odd 2