Properties

Label 1035.2.a.n.1.3
Level 10351035
Weight 22
Character 1035.1
Self dual yes
Analytic conductor 8.2658.265
Analytic rank 00
Dimension 33
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1035,2,Mod(1,1035)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1035.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1035, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 1035=32523 1035 = 3^{2} \cdot 5 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1035.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,1,0,3,-3,0,6,3,0,-1,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 8.264516609208.26451660920
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.316.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x3x24x+2 x^{3} - x^{2} - 4x + 2 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 345)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 2.342922.34292 of defining polynomial
Character χ\chi == 1035.1

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+2.34292q2+3.48929q41.00000q5+4.48929q7+3.48929q82.34292q10+1.14637q11+0.853635q13+10.5181q14+1.19656q161.34292q173.83221q193.48929q20+2.68585q221.00000q23+1.00000q25+2.00000q26+15.6644q28+8.02877q29+2.19656q314.17513q323.14637q344.48929q352.48929q378.97858q383.48929q4011.3001q41+10.6858q43+4.00000q442.34292q461.53948q47+13.1537q49+2.34292q50+2.97858q524.02877q531.14637q55+15.6644q56+18.8108q58+15.0073q595.83221q61+5.14637q6212.1751q640.853635q6511.5682q674.68585q6810.5181q704.32150q7113.1035q735.83221q7413.3717q76+5.14637q77+0.585462q791.19656q8026.4752q825.63565q83+1.34292q85+25.0361q86+4.00000q88+0.100384q89+3.83221q913.48929q923.60688q94+3.83221q95+11.5640q97+30.8181q98+O(q100)q+2.34292 q^{2} +3.48929 q^{4} -1.00000 q^{5} +4.48929 q^{7} +3.48929 q^{8} -2.34292 q^{10} +1.14637 q^{11} +0.853635 q^{13} +10.5181 q^{14} +1.19656 q^{16} -1.34292 q^{17} -3.83221 q^{19} -3.48929 q^{20} +2.68585 q^{22} -1.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} +15.6644 q^{28} +8.02877 q^{29} +2.19656 q^{31} -4.17513 q^{32} -3.14637 q^{34} -4.48929 q^{35} -2.48929 q^{37} -8.97858 q^{38} -3.48929 q^{40} -11.3001 q^{41} +10.6858 q^{43} +4.00000 q^{44} -2.34292 q^{46} -1.53948 q^{47} +13.1537 q^{49} +2.34292 q^{50} +2.97858 q^{52} -4.02877 q^{53} -1.14637 q^{55} +15.6644 q^{56} +18.8108 q^{58} +15.0073 q^{59} -5.83221 q^{61} +5.14637 q^{62} -12.1751 q^{64} -0.853635 q^{65} -11.5682 q^{67} -4.68585 q^{68} -10.5181 q^{70} -4.32150 q^{71} -13.1035 q^{73} -5.83221 q^{74} -13.3717 q^{76} +5.14637 q^{77} +0.585462 q^{79} -1.19656 q^{80} -26.4752 q^{82} -5.63565 q^{83} +1.34292 q^{85} +25.0361 q^{86} +4.00000 q^{88} +0.100384 q^{89} +3.83221 q^{91} -3.48929 q^{92} -3.60688 q^{94} +3.83221 q^{95} +11.5640 q^{97} +30.8181 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+q2+3q43q5+6q7+3q8q10+2q11+4q13+6q14q16+2q17+2q193q204q223q23+3q25+6q26+20q28+6q29++31q98+O(q100) 3 q + q^{2} + 3 q^{4} - 3 q^{5} + 6 q^{7} + 3 q^{8} - q^{10} + 2 q^{11} + 4 q^{13} + 6 q^{14} - q^{16} + 2 q^{17} + 2 q^{19} - 3 q^{20} - 4 q^{22} - 3 q^{23} + 3 q^{25} + 6 q^{26} + 20 q^{28} + 6 q^{29}+ \cdots + 31 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 2.34292 1.65670 0.828348 0.560213i 0.189281π-0.189281\pi
0.828348 + 0.560213i 0.189281π0.189281\pi
33 0 0
44 3.48929 1.74464
55 −1.00000 −0.447214
66 0 0
77 4.48929 1.69679 0.848396 0.529362i 0.177569π-0.177569\pi
0.848396 + 0.529362i 0.177569π0.177569\pi
88 3.48929 1.23365
99 0 0
1010 −2.34292 −0.740897
1111 1.14637 0.345642 0.172821 0.984953i 0.444712π-0.444712\pi
0.172821 + 0.984953i 0.444712π0.444712\pi
1212 0 0
1313 0.853635 0.236756 0.118378 0.992969i 0.462231π-0.462231\pi
0.118378 + 0.992969i 0.462231π0.462231\pi
1414 10.5181 2.81107
1515 0 0
1616 1.19656 0.299139
1717 −1.34292 −0.325707 −0.162853 0.986650i 0.552070π-0.552070\pi
−0.162853 + 0.986650i 0.552070π0.552070\pi
1818 0 0
1919 −3.83221 −0.879170 −0.439585 0.898201i 0.644874π-0.644874\pi
−0.439585 + 0.898201i 0.644874π0.644874\pi
2020 −3.48929 −0.780229
2121 0 0
2222 2.68585 0.572624
2323 −1.00000 −0.208514
2424 0 0
2525 1.00000 0.200000
2626 2.00000 0.392232
2727 0 0
2828 15.6644 2.96030
2929 8.02877 1.49091 0.745453 0.666559i 0.232233π-0.232233\pi
0.745453 + 0.666559i 0.232233π0.232233\pi
3030 0 0
3131 2.19656 0.394513 0.197257 0.980352i 0.436797π-0.436797\pi
0.197257 + 0.980352i 0.436797π0.436797\pi
3232 −4.17513 −0.738067
3333 0 0
3434 −3.14637 −0.539597
3535 −4.48929 −0.758828
3636 0 0
3737 −2.48929 −0.409237 −0.204618 0.978842i 0.565595π-0.565595\pi
−0.204618 + 0.978842i 0.565595π0.565595\pi
3838 −8.97858 −1.45652
3939 0 0
4040 −3.48929 −0.551705
4141 −11.3001 −1.76478 −0.882388 0.470523i 0.844065π-0.844065\pi
−0.882388 + 0.470523i 0.844065π0.844065\pi
4242 0 0
4343 10.6858 1.62958 0.814788 0.579759i 0.196853π-0.196853\pi
0.814788 + 0.579759i 0.196853π0.196853\pi
4444 4.00000 0.603023
4545 0 0
4646 −2.34292 −0.345445
4747 −1.53948 −0.224556 −0.112278 0.993677i 0.535815π-0.535815\pi
−0.112278 + 0.993677i 0.535815π0.535815\pi
4848 0 0
4949 13.1537 1.87910
5050 2.34292 0.331339
5151 0 0
5252 2.97858 0.413054
5353 −4.02877 −0.553394 −0.276697 0.960957i 0.589240π-0.589240\pi
−0.276697 + 0.960957i 0.589240π0.589240\pi
5454 0 0
5555 −1.14637 −0.154576
5656 15.6644 2.09325
5757 0 0
5858 18.8108 2.46998
5959 15.0073 1.95379 0.976895 0.213720i 0.0685579π-0.0685579\pi
0.976895 + 0.213720i 0.0685579π0.0685579\pi
6060 0 0
6161 −5.83221 −0.746738 −0.373369 0.927683i 0.621797π-0.621797\pi
−0.373369 + 0.927683i 0.621797π0.621797\pi
6262 5.14637 0.653589
6363 0 0
6464 −12.1751 −1.52189
6565 −0.853635 −0.105880
6666 0 0
6767 −11.5682 −1.41329 −0.706643 0.707570i 0.749791π-0.749791\pi
−0.706643 + 0.707570i 0.749791π0.749791\pi
6868 −4.68585 −0.568242
6969 0 0
7070 −10.5181 −1.25715
7171 −4.32150 −0.512868 −0.256434 0.966562i 0.582548π-0.582548\pi
−0.256434 + 0.966562i 0.582548π0.582548\pi
7272 0 0
7373 −13.1035 −1.53365 −0.766825 0.641856i 0.778165π-0.778165\pi
−0.766825 + 0.641856i 0.778165π0.778165\pi
7474 −5.83221 −0.677981
7575 0 0
7676 −13.3717 −1.53384
7777 5.14637 0.586483
7878 0 0
7979 0.585462 0.0658696 0.0329348 0.999458i 0.489515π-0.489515\pi
0.0329348 + 0.999458i 0.489515π0.489515\pi
8080 −1.19656 −0.133779
8181 0 0
8282 −26.4752 −2.92370
8383 −5.63565 −0.618593 −0.309297 0.950966i 0.600094π-0.600094\pi
−0.309297 + 0.950966i 0.600094π0.600094\pi
8484 0 0
8585 1.34292 0.145660
8686 25.0361 2.69971
8787 0 0
8888 4.00000 0.426401
8989 0.100384 0.0106407 0.00532035 0.999986i 0.498306π-0.498306\pi
0.00532035 + 0.999986i 0.498306π0.498306\pi
9090 0 0
9191 3.83221 0.401725
9292 −3.48929 −0.363783
9393 0 0
9494 −3.60688 −0.372022
9595 3.83221 0.393177
9696 0 0
9797 11.5640 1.17415 0.587075 0.809532i 0.300279π-0.300279\pi
0.587075 + 0.809532i 0.300279π0.300279\pi
9898 30.8181 3.11310
9999 0 0
100100 3.48929 0.348929
101101 −11.6932 −1.16352 −0.581758 0.813362i 0.697635π-0.697635\pi
−0.581758 + 0.813362i 0.697635π0.697635\pi
102102 0 0
103103 −19.7220 −1.94326 −0.971631 0.236501i 0.923999π-0.923999\pi
−0.971631 + 0.236501i 0.923999π0.923999\pi
104104 2.97858 0.292074
105105 0 0
106106 −9.43910 −0.916806
107107 −5.44331 −0.526224 −0.263112 0.964765i 0.584749π-0.584749\pi
−0.263112 + 0.964765i 0.584749π0.584749\pi
108108 0 0
109109 −12.5181 −1.19901 −0.599506 0.800370i 0.704636π-0.704636\pi
−0.599506 + 0.800370i 0.704636π0.704636\pi
110110 −2.68585 −0.256085
111111 0 0
112112 5.37169 0.507577
113113 14.1292 1.32916 0.664579 0.747218i 0.268611π-0.268611\pi
0.664579 + 0.747218i 0.268611π0.268611\pi
114114 0 0
115115 1.00000 0.0932505
116116 28.0147 2.60110
117117 0 0
118118 35.1611 3.23684
119119 −6.02877 −0.552656
120120 0 0
121121 −9.68585 −0.880531
122122 −13.6644 −1.23712
123123 0 0
124124 7.66442 0.688286
125125 −1.00000 −0.0894427
126126 0 0
127127 5.48194 0.486444 0.243222 0.969971i 0.421796π-0.421796\pi
0.243222 + 0.969971i 0.421796π0.421796\pi
128128 −20.1751 −1.78325
129129 0 0
130130 −2.00000 −0.175412
131131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
132132 0 0
133133 −17.2039 −1.49177
134134 −27.1035 −2.34139
135135 0 0
136136 −4.68585 −0.401808
137137 −11.7648 −1.00514 −0.502568 0.864538i 0.667611π-0.667611\pi
−0.502568 + 0.864538i 0.667611π0.667611\pi
138138 0 0
139139 8.15371 0.691589 0.345794 0.938310i 0.387609π-0.387609\pi
0.345794 + 0.938310i 0.387609π0.387609\pi
140140 −15.6644 −1.32389
141141 0 0
142142 −10.1249 −0.849666
143143 0.978577 0.0818327
144144 0 0
145145 −8.02877 −0.666753
146146 −30.7005 −2.54079
147147 0 0
148148 −8.68585 −0.713972
149149 3.73183 0.305723 0.152862 0.988248i 0.451151π-0.451151\pi
0.152862 + 0.988248i 0.451151π0.451151\pi
150150 0 0
151151 16.6430 1.35439 0.677194 0.735804i 0.263196π-0.263196\pi
0.677194 + 0.735804i 0.263196π0.263196\pi
152152 −13.3717 −1.08459
153153 0 0
154154 12.0575 0.971624
155155 −2.19656 −0.176432
156156 0 0
157157 −13.2327 −1.05608 −0.528041 0.849219i 0.677073π-0.677073\pi
−0.528041 + 0.849219i 0.677073π0.677073\pi
158158 1.37169 0.109126
159159 0 0
160160 4.17513 0.330073
161161 −4.48929 −0.353806
162162 0 0
163163 16.3931 1.28401 0.642004 0.766701i 0.278103π-0.278103\pi
0.642004 + 0.766701i 0.278103π0.278103\pi
164164 −39.4292 −3.07891
165165 0 0
166166 −13.2039 −1.02482
167167 −3.04598 −0.235705 −0.117853 0.993031i 0.537601π-0.537601\pi
−0.117853 + 0.993031i 0.537601π0.537601\pi
168168 0 0
169169 −12.2713 −0.943947
170170 3.14637 0.241315
171171 0 0
172172 37.2860 2.84303
173173 24.9357 1.89583 0.947914 0.318526i 0.103188π-0.103188\pi
0.947914 + 0.318526i 0.103188π0.103188\pi
174174 0 0
175175 4.48929 0.339358
176176 1.37169 0.103395
177177 0 0
178178 0.235192 0.0176284
179179 6.68585 0.499724 0.249862 0.968282i 0.419615π-0.419615\pi
0.249862 + 0.968282i 0.419615π0.419615\pi
180180 0 0
181181 −20.6002 −1.53120 −0.765599 0.643318i 0.777557π-0.777557\pi
−0.765599 + 0.643318i 0.777557π0.777557\pi
182182 8.97858 0.665536
183183 0 0
184184 −3.48929 −0.257234
185185 2.48929 0.183016
186186 0 0
187187 −1.53948 −0.112578
188188 −5.37169 −0.391771
189189 0 0
190190 8.97858 0.651374
191191 −4.95402 −0.358460 −0.179230 0.983807i 0.557361π-0.557361\pi
−0.179230 + 0.983807i 0.557361π0.557361\pi
192192 0 0
193193 6.05754 0.436031 0.218016 0.975945i 0.430042π-0.430042\pi
0.218016 + 0.975945i 0.430042π0.430042\pi
194194 27.0937 1.94521
195195 0 0
196196 45.8971 3.27836
197197 24.4078 1.73898 0.869492 0.493947i 0.164446π-0.164446\pi
0.869492 + 0.493947i 0.164446π0.164446\pi
198198 0 0
199199 −3.85677 −0.273399 −0.136700 0.990613i 0.543650π-0.543650\pi
−0.136700 + 0.990613i 0.543650π0.543650\pi
200200 3.48929 0.246730
201201 0 0
202202 −27.3963 −1.92759
203203 36.0435 2.52976
204204 0 0
205205 11.3001 0.789232
206206 −46.2070 −3.21940
207207 0 0
208208 1.02142 0.0708229
209209 −4.39312 −0.303878
210210 0 0
211211 −0.824865 −0.0567861 −0.0283930 0.999597i 0.509039π-0.509039\pi
−0.0283930 + 0.999597i 0.509039π0.509039\pi
212212 −14.0575 −0.965476
213213 0 0
214214 −12.7533 −0.871794
215215 −10.6858 −0.728769
216216 0 0
217217 9.86098 0.669407
218218 −29.3288 −1.98640
219219 0 0
220220 −4.00000 −0.269680
221221 −1.14637 −0.0771129
222222 0 0
223223 5.56404 0.372596 0.186298 0.982493i 0.440351π-0.440351\pi
0.186298 + 0.982493i 0.440351π0.440351\pi
224224 −18.7434 −1.25235
225225 0 0
226226 33.1035 2.20201
227227 −16.5855 −1.10082 −0.550408 0.834896i 0.685528π-0.685528\pi
−0.550408 + 0.834896i 0.685528π0.685528\pi
228228 0 0
229229 6.64300 0.438982 0.219491 0.975615i 0.429560π-0.429560\pi
0.219491 + 0.975615i 0.429560π0.429560\pi
230230 2.34292 0.154488
231231 0 0
232232 28.0147 1.83925
233233 14.3931 0.942924 0.471462 0.881886i 0.343726π-0.343726\pi
0.471462 + 0.881886i 0.343726π0.343726\pi
234234 0 0
235235 1.53948 0.100425
236236 52.3650 3.40867
237237 0 0
238238 −14.1249 −0.915584
239239 13.1077 0.847869 0.423934 0.905693i 0.360649π-0.360649\pi
0.423934 + 0.905693i 0.360649π0.360649\pi
240240 0 0
241241 12.5181 0.806359 0.403179 0.915121i 0.367905π-0.367905\pi
0.403179 + 0.915121i 0.367905π0.367905\pi
242242 −22.6932 −1.45877
243243 0 0
244244 −20.3503 −1.30279
245245 −13.1537 −0.840360
246246 0 0
247247 −3.27131 −0.208148
248248 7.66442 0.486691
249249 0 0
250250 −2.34292 −0.148179
251251 26.3503 1.66321 0.831607 0.555364i 0.187421π-0.187421\pi
0.831607 + 0.555364i 0.187421π0.187421\pi
252252 0 0
253253 −1.14637 −0.0720714
254254 12.8438 0.805890
255255 0 0
256256 −22.9185 −1.43241
257257 27.0116 1.68493 0.842467 0.538747i 0.181102π-0.181102\pi
0.842467 + 0.538747i 0.181102π0.181102\pi
258258 0 0
259259 −11.1751 −0.694389
260260 −2.97858 −0.184724
261261 0 0
262262 0 0
263263 −21.8855 −1.34952 −0.674760 0.738037i 0.735753π-0.735753\pi
−0.674760 + 0.738037i 0.735753π0.735753\pi
264264 0 0
265265 4.02877 0.247485
266266 −40.3074 −2.47141
267267 0 0
268268 −40.3650 −2.46568
269269 −3.69319 −0.225178 −0.112589 0.993642i 0.535914π-0.535914\pi
−0.112589 + 0.993642i 0.535914π0.535914\pi
270270 0 0
271271 0.288520 0.0175264 0.00876318 0.999962i 0.497211π-0.497211\pi
0.00876318 + 0.999962i 0.497211π0.497211\pi
272272 −1.60688 −0.0974317
273273 0 0
274274 −27.5640 −1.66520
275275 1.14637 0.0691284
276276 0 0
277277 21.3288 1.28153 0.640763 0.767739i 0.278618π-0.278618\pi
0.640763 + 0.767739i 0.278618π0.278618\pi
278278 19.1035 1.14575
279279 0 0
280280 −15.6644 −0.936128
281281 26.6676 1.59085 0.795427 0.606050i 0.207247π-0.207247\pi
0.795427 + 0.606050i 0.207247π0.207247\pi
282282 0 0
283283 25.9185 1.54070 0.770348 0.637624i 0.220082π-0.220082\pi
0.770348 + 0.637624i 0.220082π0.220082\pi
284284 −15.0790 −0.894772
285285 0 0
286286 2.29273 0.135572
287287 −50.7293 −2.99446
288288 0 0
289289 −15.1966 −0.893915
290290 −18.8108 −1.10461
291291 0 0
292292 −45.7220 −2.67568
293293 −13.6503 −0.797462 −0.398731 0.917068i 0.630549π-0.630549\pi
−0.398731 + 0.917068i 0.630549π0.630549\pi
294294 0 0
295295 −15.0073 −0.873761
296296 −8.68585 −0.504855
297297 0 0
298298 8.74338 0.506491
299299 −0.853635 −0.0493670
300300 0 0
301301 47.9718 2.76505
302302 38.9933 2.24381
303303 0 0
304304 −4.58546 −0.262994
305305 5.83221 0.333951
306306 0 0
307307 −9.78937 −0.558709 −0.279354 0.960188i 0.590120π-0.590120\pi
−0.279354 + 0.960188i 0.590120π0.590120\pi
308308 17.9572 1.02320
309309 0 0
310310 −5.14637 −0.292294
311311 3.32885 0.188762 0.0943808 0.995536i 0.469913π-0.469913\pi
0.0943808 + 0.995536i 0.469913π0.469913\pi
312312 0 0
313313 −18.8824 −1.06730 −0.533648 0.845707i 0.679179π-0.679179\pi
−0.533648 + 0.845707i 0.679179π0.679179\pi
314314 −31.0031 −1.74961
315315 0 0
316316 2.04285 0.114919
317317 8.06740 0.453111 0.226555 0.973998i 0.427254π-0.427254\pi
0.226555 + 0.973998i 0.427254π0.427254\pi
318318 0 0
319319 9.20390 0.515320
320320 12.1751 0.680611
321321 0 0
322322 −10.5181 −0.586148
323323 5.14637 0.286351
324324 0 0
325325 0.853635 0.0473511
326326 38.4078 2.12721
327327 0 0
328328 −39.4292 −2.17712
329329 −6.91117 −0.381025
330330 0 0
331331 −26.6388 −1.46420 −0.732100 0.681197i 0.761460π-0.761460\pi
−0.732100 + 0.681197i 0.761460π0.761460\pi
332332 −19.6644 −1.07923
333333 0 0
334334 −7.13650 −0.390492
335335 11.5682 0.632041
336336 0 0
337337 −8.54262 −0.465346 −0.232673 0.972555i 0.574747π-0.574747\pi
−0.232673 + 0.972555i 0.574747π0.574747\pi
338338 −28.7507 −1.56383
339339 0 0
340340 4.68585 0.254126
341341 2.51806 0.136360
342342 0 0
343343 27.6258 1.49165
344344 37.2860 2.01033
345345 0 0
346346 58.4225 3.14081
347347 16.2499 0.872340 0.436170 0.899864i 0.356335π-0.356335\pi
0.436170 + 0.899864i 0.356335π0.356335\pi
348348 0 0
349349 23.1898 1.24132 0.620662 0.784079i 0.286864π-0.286864\pi
0.620662 + 0.784079i 0.286864π0.286864\pi
350350 10.5181 0.562214
351351 0 0
352352 −4.78623 −0.255107
353353 7.48194 0.398224 0.199112 0.979977i 0.436194π-0.436194\pi
0.199112 + 0.979977i 0.436194π0.436194\pi
354354 0 0
355355 4.32150 0.229361
356356 0.350269 0.0185642
357357 0 0
358358 15.6644 0.827890
359359 −1.87506 −0.0989617 −0.0494809 0.998775i 0.515757π-0.515757\pi
−0.0494809 + 0.998775i 0.515757π0.515757\pi
360360 0 0
361361 −4.31415 −0.227061
362362 −48.2646 −2.53673
363363 0 0
364364 13.3717 0.700867
365365 13.1035 0.685870
366366 0 0
367367 −4.68164 −0.244379 −0.122190 0.992507i 0.538992π-0.538992\pi
−0.122190 + 0.992507i 0.538992π0.538992\pi
368368 −1.19656 −0.0623749
369369 0 0
370370 5.83221 0.303202
371371 −18.0863 −0.938994
372372 0 0
373373 18.6430 0.965298 0.482649 0.875814i 0.339675π-0.339675\pi
0.482649 + 0.875814i 0.339675π0.339675\pi
374374 −3.60688 −0.186508
375375 0 0
376376 −5.37169 −0.277024
377377 6.85363 0.352980
378378 0 0
379379 29.8715 1.53439 0.767197 0.641412i 0.221651π-0.221651\pi
0.767197 + 0.641412i 0.221651π0.221651\pi
380380 13.3717 0.685953
381381 0 0
382382 −11.6069 −0.593860
383383 −20.5714 −1.05115 −0.525574 0.850748i 0.676150π-0.676150\pi
−0.525574 + 0.850748i 0.676150π0.676150\pi
384384 0 0
385385 −5.14637 −0.262283
386386 14.1923 0.722371
387387 0 0
388388 40.3503 2.04847
389389 2.33558 0.118418 0.0592092 0.998246i 0.481142π-0.481142\pi
0.0592092 + 0.998246i 0.481142π0.481142\pi
390390 0 0
391391 1.34292 0.0679145
392392 45.8971 2.31815
393393 0 0
394394 57.1856 2.88097
395395 −0.585462 −0.0294578
396396 0 0
397397 29.1365 1.46232 0.731160 0.682207i 0.238980π-0.238980\pi
0.731160 + 0.682207i 0.238980π0.238980\pi
398398 −9.03612 −0.452940
399399 0 0
400400 1.19656 0.0598279
401401 14.8353 0.740842 0.370421 0.928864i 0.379213π-0.379213\pi
0.370421 + 0.928864i 0.379213π0.379213\pi
402402 0 0
403403 1.87506 0.0934033
404404 −40.8009 −2.02992
405405 0 0
406406 84.4471 4.19104
407407 −2.85363 −0.141449
408408 0 0
409409 −38.0189 −1.87991 −0.939957 0.341293i 0.889135π-0.889135\pi
−0.939957 + 0.341293i 0.889135π0.889135\pi
410410 26.4752 1.30752
411411 0 0
412412 −68.8156 −3.39030
413413 67.3723 3.31517
414414 0 0
415415 5.63565 0.276643
416416 −3.56404 −0.174741
417417 0 0
418418 −10.2927 −0.503434
419419 −21.8469 −1.06729 −0.533646 0.845708i 0.679178π-0.679178\pi
−0.533646 + 0.845708i 0.679178π0.679178\pi
420420 0 0
421421 21.4391 1.04488 0.522439 0.852677i 0.325022π-0.325022\pi
0.522439 + 0.852677i 0.325022π0.325022\pi
422422 −1.93260 −0.0940773
423423 0 0
424424 −14.0575 −0.682694
425425 −1.34292 −0.0651413
426426 0 0
427427 −26.1825 −1.26706
428428 −18.9933 −0.918074
429429 0 0
430430 −25.0361 −1.20735
431431 −29.8223 −1.43649 −0.718246 0.695789i 0.755055π-0.755055\pi
−0.718246 + 0.695789i 0.755055π0.755055\pi
432432 0 0
433433 −0.925249 −0.0444647 −0.0222323 0.999753i 0.507077π-0.507077\pi
−0.0222323 + 0.999753i 0.507077π0.507077\pi
434434 23.1035 1.10900
435435 0 0
436436 −43.6791 −2.09185
437437 3.83221 0.183320
438438 0 0
439439 −21.6791 −1.03469 −0.517344 0.855778i 0.673079π-0.673079\pi
−0.517344 + 0.855778i 0.673079π0.673079\pi
440440 −4.00000 −0.190693
441441 0 0
442442 −2.68585 −0.127753
443443 −5.20390 −0.247245 −0.123622 0.992329i 0.539451π-0.539451\pi
−0.123622 + 0.992329i 0.539451π0.539451\pi
444444 0 0
445445 −0.100384 −0.00475867
446446 13.0361 0.617278
447447 0 0
448448 −54.6577 −2.58233
449449 10.8578 0.512413 0.256207 0.966622i 0.417527π-0.417527\pi
0.256207 + 0.966622i 0.417527π0.417527\pi
450450 0 0
451451 −12.9540 −0.609981
452452 49.3007 2.31891
453453 0 0
454454 −38.8585 −1.82372
455455 −3.83221 −0.179657
456456 0 0
457457 27.2755 1.27589 0.637947 0.770080i 0.279784π-0.279784\pi
0.637947 + 0.770080i 0.279784π0.279784\pi
458458 15.5640 0.727260
459459 0 0
460460 3.48929 0.162689
461461 −20.2070 −0.941136 −0.470568 0.882364i 0.655951π-0.655951\pi
−0.470568 + 0.882364i 0.655951π0.655951\pi
462462 0 0
463463 8.03298 0.373324 0.186662 0.982424i 0.440233π-0.440233\pi
0.186662 + 0.982424i 0.440233π0.440233\pi
464464 9.60688 0.445988
465465 0 0
466466 33.7220 1.56214
467467 19.4580 0.900409 0.450204 0.892926i 0.351351π-0.351351\pi
0.450204 + 0.892926i 0.351351π0.351351\pi
468468 0 0
469469 −51.9332 −2.39805
470470 3.60688 0.166373
471471 0 0
472472 52.3650 2.41029
473473 12.2499 0.563250
474474 0 0
475475 −3.83221 −0.175834
476476 −21.0361 −0.964189
477477 0 0
478478 30.7104 1.40466
479479 −28.9540 −1.32294 −0.661471 0.749970i 0.730068π-0.730068\pi
−0.661471 + 0.749970i 0.730068π0.730068\pi
480480 0 0
481481 −2.12494 −0.0968890
482482 29.3288 1.33589
483483 0 0
484484 −33.7967 −1.53621
485485 −11.5640 −0.525096
486486 0 0
487487 20.8108 0.943027 0.471513 0.881859i 0.343708π-0.343708\pi
0.471513 + 0.881859i 0.343708π0.343708\pi
488488 −20.3503 −0.921213
489489 0 0
490490 −30.8181 −1.39222
491491 −35.1140 −1.58467 −0.792336 0.610084i 0.791135π-0.791135\pi
−0.792336 + 0.610084i 0.791135π0.791135\pi
492492 0 0
493493 −10.7820 −0.485598
494494 −7.66442 −0.344839
495495 0 0
496496 2.62831 0.118014
497497 −19.4005 −0.870230
498498 0 0
499499 −7.31836 −0.327615 −0.163807 0.986492i 0.552378π-0.552378\pi
−0.163807 + 0.986492i 0.552378π0.552378\pi
500500 −3.48929 −0.156046
501501 0 0
502502 61.7367 2.75544
503503 22.0006 0.980959 0.490479 0.871453i 0.336822π-0.336822\pi
0.490479 + 0.871453i 0.336822π0.336822\pi
504504 0 0
505505 11.6932 0.520340
506506 −2.68585 −0.119400
507507 0 0
508508 19.1281 0.848671
509509 35.4783 1.57255 0.786275 0.617877i 0.212007π-0.212007\pi
0.786275 + 0.617877i 0.212007π0.212007\pi
510510 0 0
511511 −58.8255 −2.60229
512512 −13.3461 −0.589818
513513 0 0
514514 63.2860 2.79143
515515 19.7220 0.869053
516516 0 0
517517 −1.76481 −0.0776161
518518 −26.1825 −1.15039
519519 0 0
520520 −2.97858 −0.130619
521521 −21.4966 −0.941785 −0.470892 0.882191i 0.656068π-0.656068\pi
−0.470892 + 0.882191i 0.656068π0.656068\pi
522522 0 0
523523 −11.3288 −0.495376 −0.247688 0.968840i 0.579671π-0.579671\pi
−0.247688 + 0.968840i 0.579671π0.579671\pi
524524 0 0
525525 0 0
526526 −51.2761 −2.23575
527527 −2.94981 −0.128496
528528 0 0
529529 1.00000 0.0434783
530530 9.43910 0.410008
531531 0 0
532532 −60.0294 −2.60260
533533 −9.64614 −0.417821
534534 0 0
535535 5.44331 0.235335
536536 −40.3650 −1.74350
537537 0 0
538538 −8.65287 −0.373052
539539 15.0790 0.649497
540540 0 0
541541 −7.67912 −0.330151 −0.165075 0.986281i 0.552787π-0.552787\pi
−0.165075 + 0.986281i 0.552787π0.552787\pi
542542 0.675981 0.0290358
543543 0 0
544544 5.60688 0.240393
545545 12.5181 0.536215
546546 0 0
547547 31.5296 1.34811 0.674054 0.738682i 0.264551π-0.264551\pi
0.674054 + 0.738682i 0.264551π0.264551\pi
548548 −41.0508 −1.75360
549549 0 0
550550 2.68585 0.114525
551551 −30.7679 −1.31076
552552 0 0
553553 2.62831 0.111767
554554 49.9718 2.12310
555555 0 0
556556 28.4507 1.20658
557557 10.1292 0.429186 0.214593 0.976704i 0.431157π-0.431157\pi
0.214593 + 0.976704i 0.431157π0.431157\pi
558558 0 0
559559 9.12181 0.385811
560560 −5.37169 −0.226995
561561 0 0
562562 62.4800 2.63556
563563 −40.7146 −1.71592 −0.857958 0.513719i 0.828267π-0.828267\pi
−0.857958 + 0.513719i 0.828267π0.828267\pi
564564 0 0
565565 −14.1292 −0.594418
566566 60.7251 2.55247
567567 0 0
568568 −15.0790 −0.632699
569569 −1.66442 −0.0697763 −0.0348881 0.999391i 0.511107π-0.511107\pi
−0.0348881 + 0.999391i 0.511107π0.511107\pi
570570 0 0
571571 −41.8469 −1.75124 −0.875619 0.483002i 0.839546π-0.839546\pi
−0.875619 + 0.483002i 0.839546π0.839546\pi
572572 3.41454 0.142769
573573 0 0
574574 −118.855 −4.96091
575575 −1.00000 −0.0417029
576576 0 0
577577 21.6069 0.899506 0.449753 0.893153i 0.351512π-0.351512\pi
0.449753 + 0.893153i 0.351512π0.351512\pi
578578 −35.6044 −1.48095
579579 0 0
580580 −28.0147 −1.16325
581581 −25.3001 −1.04962
582582 0 0
583583 −4.61844 −0.191276
584584 −45.7220 −1.89199
585585 0 0
586586 −31.9817 −1.32115
587587 −0.393115 −0.0162256 −0.00811280 0.999967i 0.502582π-0.502582\pi
−0.00811280 + 0.999967i 0.502582π0.502582\pi
588588 0 0
589589 −8.41767 −0.346844
590590 −35.1611 −1.44756
591591 0 0
592592 −2.97858 −0.122419
593593 8.31729 0.341550 0.170775 0.985310i 0.445373π-0.445373\pi
0.170775 + 0.985310i 0.445373π0.445373\pi
594594 0 0
595595 6.02877 0.247155
596596 13.0214 0.533378
597597 0 0
598598 −2.00000 −0.0817861
599599 −9.03612 −0.369206 −0.184603 0.982813i 0.559100π-0.559100\pi
−0.184603 + 0.982813i 0.559100π0.559100\pi
600600 0 0
601601 −27.6602 −1.12828 −0.564142 0.825678i 0.690793π-0.690793\pi
−0.564142 + 0.825678i 0.690793π0.690793\pi
602602 112.394 4.58085
603603 0 0
604604 58.0722 2.36293
605605 9.68585 0.393786
606606 0 0
607607 29.6461 1.20330 0.601650 0.798760i 0.294510π-0.294510\pi
0.601650 + 0.798760i 0.294510π0.294510\pi
608608 16.0000 0.648886
609609 0 0
610610 13.6644 0.553256
611611 −1.31415 −0.0531650
612612 0 0
613613 39.4868 1.59486 0.797428 0.603414i 0.206193π-0.206193\pi
0.797428 + 0.603414i 0.206193π0.206193\pi
614614 −22.9357 −0.925611
615615 0 0
616616 17.9572 0.723514
617617 −16.8641 −0.678924 −0.339462 0.940620i 0.610245π-0.610245\pi
−0.339462 + 0.940620i 0.610245π0.610245\pi
618618 0 0
619619 2.74338 0.110266 0.0551330 0.998479i 0.482442π-0.482442\pi
0.0551330 + 0.998479i 0.482442π0.482442\pi
620620 −7.66442 −0.307811
621621 0 0
622622 7.79923 0.312721
623623 0.450654 0.0180551
624624 0 0
625625 1.00000 0.0400000
626626 −44.2400 −1.76819
627627 0 0
628628 −46.1726 −1.84249
629629 3.34292 0.133291
630630 0 0
631631 −9.93260 −0.395410 −0.197705 0.980262i 0.563349π-0.563349\pi
−0.197705 + 0.980262i 0.563349π0.563349\pi
632632 2.04285 0.0812600
633633 0 0
634634 18.9013 0.750667
635635 −5.48194 −0.217544
636636 0 0
637637 11.2285 0.444888
638638 21.5640 0.853728
639639 0 0
640640 20.1751 0.797492
641641 10.6184 0.419403 0.209702 0.977765i 0.432751π-0.432751\pi
0.209702 + 0.977765i 0.432751π0.432751\pi
642642 0 0
643643 20.5959 0.812225 0.406112 0.913823i 0.366884π-0.366884\pi
0.406112 + 0.913823i 0.366884π0.366884\pi
644644 −15.6644 −0.617265
645645 0 0
646646 12.0575 0.474398
647647 6.71883 0.264144 0.132072 0.991240i 0.457837π-0.457837\pi
0.132072 + 0.991240i 0.457837π0.457837\pi
648648 0 0
649649 17.2039 0.675312
650650 2.00000 0.0784465
651651 0 0
652652 57.2003 2.24014
653653 4.07583 0.159499 0.0797497 0.996815i 0.474588π-0.474588\pi
0.0797497 + 0.996815i 0.474588π0.474588\pi
654654 0 0
655655 0 0
656656 −13.5212 −0.527914
657657 0 0
658658 −16.1923 −0.631243
659659 29.0607 1.13204 0.566022 0.824390i 0.308482π-0.308482\pi
0.566022 + 0.824390i 0.308482π0.308482\pi
660660 0 0
661661 31.2369 1.21497 0.607487 0.794330i 0.292178π-0.292178\pi
0.607487 + 0.794330i 0.292178π0.292178\pi
662662 −62.4126 −2.42574
663663 0 0
664664 −19.6644 −0.763128
665665 17.2039 0.667139
666666 0 0
667667 −8.02877 −0.310875
668668 −10.6283 −0.411222
669669 0 0
670670 27.1035 1.04710
671671 −6.68585 −0.258104
672672 0 0
673673 9.74652 0.375701 0.187850 0.982198i 0.439848π-0.439848\pi
0.187850 + 0.982198i 0.439848π0.439848\pi
674674 −20.0147 −0.770937
675675 0 0
676676 −42.8181 −1.64685
677677 −6.80031 −0.261357 −0.130679 0.991425i 0.541716π-0.541716\pi
−0.130679 + 0.991425i 0.541716π0.541716\pi
678678 0 0
679679 51.9143 1.99229
680680 4.68585 0.179694
681681 0 0
682682 5.89962 0.225908
683683 41.5029 1.58806 0.794032 0.607876i 0.207978π-0.207978\pi
0.794032 + 0.607876i 0.207978π0.207978\pi
684684 0 0
685685 11.7648 0.449510
686686 64.7251 2.47122
687687 0 0
688688 12.7862 0.487470
689689 −3.43910 −0.131019
690690 0 0
691691 −31.2713 −1.18962 −0.594808 0.803868i 0.702772π-0.702772\pi
−0.594808 + 0.803868i 0.702772π0.702772\pi
692692 87.0080 3.30755
693693 0 0
694694 38.0722 1.44520
695695 −8.15371 −0.309288
696696 0 0
697697 15.1751 0.574799
698698 54.3320 2.05650
699699 0 0
700700 15.6644 0.592060
701701 6.02456 0.227544 0.113772 0.993507i 0.463707π-0.463707\pi
0.113772 + 0.993507i 0.463707π0.463707\pi
702702 0 0
703703 9.53948 0.359788
704704 −13.9572 −0.526030
705705 0 0
706706 17.5296 0.659736
707707 −52.4941 −1.97424
708708 0 0
709709 37.6974 1.41576 0.707878 0.706335i 0.249653π-0.249653\pi
0.707878 + 0.706335i 0.249653π0.249653\pi
710710 10.1249 0.379982
711711 0 0
712712 0.350269 0.0131269
713713 −2.19656 −0.0822617
714714 0 0
715715 −0.978577 −0.0365967
716716 23.3288 0.871840
717717 0 0
718718 −4.39312 −0.163950
719719 −19.8708 −0.741058 −0.370529 0.928821i 0.620824π-0.620824\pi
−0.370529 + 0.928821i 0.620824π0.620824\pi
720720 0 0
721721 −88.5376 −3.29731
722722 −10.1077 −0.376171
723723 0 0
724724 −71.8799 −2.67139
725725 8.02877 0.298181
726726 0 0
727727 15.8757 0.588796 0.294398 0.955683i 0.404881π-0.404881\pi
0.294398 + 0.955683i 0.404881π0.404881\pi
728728 13.3717 0.495588
729729 0 0
730730 30.7005 1.13628
731731 −14.3503 −0.530764
732732 0 0
733733 37.1751 1.37309 0.686547 0.727085i 0.259125π-0.259125\pi
0.686547 + 0.727085i 0.259125π0.259125\pi
734734 −10.9687 −0.404863
735735 0 0
736736 4.17513 0.153898
737737 −13.2614 −0.488492
738738 0 0
739739 44.0189 1.61926 0.809631 0.586940i 0.199667π-0.199667\pi
0.809631 + 0.586940i 0.199667π0.199667\pi
740740 8.68585 0.319298
741741 0 0
742742 −42.3748 −1.55563
743743 −51.5296 −1.89044 −0.945219 0.326437i 0.894152π-0.894152\pi
−0.945219 + 0.326437i 0.894152π0.894152\pi
744744 0 0
745745 −3.73183 −0.136724
746746 43.6791 1.59921
747747 0 0
748748 −5.37169 −0.196409
749749 −24.4366 −0.892893
750750 0 0
751751 −3.91790 −0.142966 −0.0714832 0.997442i 0.522773π-0.522773\pi
−0.0714832 + 0.997442i 0.522773π0.522773\pi
752752 −1.84208 −0.0671736
753753 0 0
754754 16.0575 0.584781
755755 −16.6430 −0.605701
756756 0 0
757757 25.7606 0.936285 0.468142 0.883653i 0.344923π-0.344923\pi
0.468142 + 0.883653i 0.344923π0.344923\pi
758758 69.9865 2.54203
759759 0 0
760760 13.3717 0.485042
761761 15.7507 0.570964 0.285482 0.958384i 0.407846π-0.407846\pi
0.285482 + 0.958384i 0.407846π0.407846\pi
762762 0 0
763763 −56.1972 −2.03447
764764 −17.2860 −0.625386
765765 0 0
766766 −48.1972 −1.74143
767767 12.8108 0.462571
768768 0 0
769769 −19.0031 −0.685271 −0.342635 0.939468i 0.611320π-0.611320\pi
−0.342635 + 0.939468i 0.611320π0.611320\pi
770770 −12.0575 −0.434524
771771 0 0
772772 21.1365 0.760719
773773 41.7795 1.50270 0.751352 0.659902i 0.229402π-0.229402\pi
0.751352 + 0.659902i 0.229402π0.229402\pi
774774 0 0
775775 2.19656 0.0789027
776776 40.3503 1.44849
777777 0 0
778778 5.47208 0.196183
779779 43.3043 1.55154
780780 0 0
781781 −4.95402 −0.177269
782782 3.14637 0.112514
783783 0 0
784784 15.7392 0.562113
785785 13.2327 0.472294
786786 0 0
787787 −21.8610 −0.779260 −0.389630 0.920972i 0.627397π-0.627397\pi
−0.389630 + 0.920972i 0.627397π0.627397\pi
788788 85.1659 3.03391
789789 0 0
790790 −1.37169 −0.0488026
791791 63.4298 2.25531
792792 0 0
793793 −4.97858 −0.176794
794794 68.2646 2.42262
795795 0 0
796796 −13.4574 −0.476984
797797 27.8280 0.985718 0.492859 0.870109i 0.335952π-0.335952\pi
0.492859 + 0.870109i 0.335952π0.335952\pi
798798 0 0
799799 2.06740 0.0731395
800800 −4.17513 −0.147613
801801 0 0
802802 34.7581 1.22735
803803 −15.0214 −0.530095
804804 0 0
805805 4.48929 0.158227
806806 4.39312 0.154741
807807 0 0
808808 −40.8009 −1.43537
809809 21.0565 0.740306 0.370153 0.928971i 0.379305π-0.379305\pi
0.370153 + 0.928971i 0.379305π0.379305\pi
810810 0 0
811811 −16.8249 −0.590801 −0.295400 0.955374i 0.595453π-0.595453\pi
−0.295400 + 0.955374i 0.595453π0.595453\pi
812812 125.766 4.41352
813813 0 0
814814 −6.68585 −0.234339
815815 −16.3931 −0.574226
816816 0 0
817817 −40.9504 −1.43267
818818 −89.0754 −3.11445
819819 0 0
820820 39.4292 1.37693
821821 2.59388 0.0905272 0.0452636 0.998975i 0.485587π-0.485587\pi
0.0452636 + 0.998975i 0.485587π0.485587\pi
822822 0 0
823823 0.786230 0.0274063 0.0137031 0.999906i 0.495638π-0.495638\pi
0.0137031 + 0.999906i 0.495638π0.495638\pi
824824 −68.8156 −2.39731
825825 0 0
826826 157.848 5.49224
827827 −10.2211 −0.355423 −0.177712 0.984083i 0.556869π-0.556869\pi
−0.177712 + 0.984083i 0.556869π0.556869\pi
828828 0 0
829829 −8.97437 −0.311693 −0.155846 0.987781i 0.549810π-0.549810\pi
−0.155846 + 0.987781i 0.549810π0.549810\pi
830830 13.2039 0.458314
831831 0 0
832832 −10.3931 −0.360316
833833 −17.6644 −0.612036
834834 0 0
835835 3.04598 0.105411
836836 −15.3288 −0.530159
837837 0 0
838838 −51.1856 −1.76818
839839 −19.6069 −0.676905 −0.338452 0.940984i 0.609903π-0.609903\pi
−0.338452 + 0.940984i 0.609903π0.609903\pi
840840 0 0
841841 35.4611 1.22280
842842 50.2302 1.73105
843843 0 0
844844 −2.87819 −0.0990715
845845 12.2713 0.422146
846846 0 0
847847 −43.4826 −1.49408
848848 −4.82065 −0.165542
849849 0 0
850850 −3.14637 −0.107919
851851 2.48929 0.0853317
852852 0 0
853853 −14.3650 −0.491847 −0.245923 0.969289i 0.579091π-0.579091\pi
−0.245923 + 0.969289i 0.579091π0.579091\pi
854854 −61.3435 −2.09913
855855 0 0
856856 −18.9933 −0.649177
857857 −22.0000 −0.751506 −0.375753 0.926720i 0.622616π-0.622616\pi
−0.375753 + 0.926720i 0.622616π0.622616\pi
858858 0 0
859859 −4.85425 −0.165625 −0.0828125 0.996565i 0.526390π-0.526390\pi
−0.0828125 + 0.996565i 0.526390π0.526390\pi
860860 −37.2860 −1.27144
861861 0 0
862862 −69.8715 −2.37983
863863 −41.8139 −1.42336 −0.711681 0.702503i 0.752066π-0.752066\pi
−0.711681 + 0.702503i 0.752066π0.752066\pi
864864 0 0
865865 −24.9357 −0.847840
866866 −2.16779 −0.0736644
867867 0 0
868868 34.4078 1.16788
869869 0.671153 0.0227673
870870 0 0
871871 −9.87506 −0.334604
872872 −43.6791 −1.47916
873873 0 0
874874 8.97858 0.303705
875875 −4.48929 −0.151766
876876 0 0
877877 −1.27973 −0.0432134 −0.0216067 0.999767i 0.506878π-0.506878\pi
−0.0216067 + 0.999767i 0.506878π0.506878\pi
878878 −50.7925 −1.71416
879879 0 0
880880 −1.37169 −0.0462397
881881 −52.9687 −1.78456 −0.892281 0.451481i 0.850896π-0.850896\pi
−0.892281 + 0.451481i 0.850896π0.850896\pi
882882 0 0
883883 −17.5479 −0.590534 −0.295267 0.955415i 0.595409π-0.595409\pi
−0.295267 + 0.955415i 0.595409π0.595409\pi
884884 −4.00000 −0.134535
885885 0 0
886886 −12.1923 −0.409610
887887 11.2713 0.378453 0.189227 0.981933i 0.439402π-0.439402\pi
0.189227 + 0.981933i 0.439402π0.439402\pi
888888 0 0
889889 24.6100 0.825394
890890 −0.235192 −0.00788367
891891 0 0
892892 19.4145 0.650047
893893 5.89962 0.197423
894894 0 0
895895 −6.68585 −0.223483
896896 −90.5720 −3.02580
897897 0 0
898898 25.4391 0.848914
899899 17.6357 0.588182
900900 0 0
901901 5.41033 0.180244
902902 −30.3503 −1.01055
903903 0 0
904904 49.3007 1.63972
905905 20.6002 0.684772
906906 0 0
907907 27.2045 0.903311 0.451656 0.892192i 0.350834π-0.350834\pi
0.451656 + 0.892192i 0.350834π0.350834\pi
908908 −57.8715 −1.92053
909909 0 0
910910 −8.97858 −0.297637
911911 3.41454 0.113129 0.0565643 0.998399i 0.481985π-0.481985\pi
0.0565643 + 0.998399i 0.481985π0.481985\pi
912912 0 0
913913 −6.46052 −0.213812
914914 63.9044 2.11377
915915 0 0
916916 23.1793 0.765867
917917 0 0
918918 0 0
919919 20.4998 0.676225 0.338113 0.941106i 0.390212π-0.390212\pi
0.338113 + 0.941106i 0.390212π0.390212\pi
920920 3.48929 0.115038
921921 0 0
922922 −47.3435 −1.55918
923923 −3.68898 −0.121424
924924 0 0
925925 −2.48929 −0.0818473
926926 18.8207 0.618485
927927 0 0
928928 −33.5212 −1.10039
929929 −38.2640 −1.25540 −0.627700 0.778455i 0.716004π-0.716004\pi
−0.627700 + 0.778455i 0.716004π0.716004\pi
930930 0 0
931931 −50.4078 −1.65205
932932 50.2217 1.64507
933933 0 0
934934 45.5886 1.49170
935935 1.53948 0.0503464
936936 0 0
937937 35.6791 1.16559 0.582793 0.812621i 0.301960π-0.301960\pi
0.582793 + 0.812621i 0.301960π0.301960\pi
938938 −121.676 −3.97285
939939 0 0
940940 5.37169 0.175205
941941 −15.2321 −0.496551 −0.248275 0.968689i 0.579864π-0.579864\pi
−0.248275 + 0.968689i 0.579864π0.579864\pi
942942 0 0
943943 11.3001 0.367981
944944 17.9572 0.584456
945945 0 0
946946 28.7005 0.933135
947947 −6.29273 −0.204486 −0.102243 0.994759i 0.532602π-0.532602\pi
−0.102243 + 0.994759i 0.532602π0.532602\pi
948948 0 0
949949 −11.1856 −0.363100
950950 −8.97858 −0.291304
951951 0 0
952952 −21.0361 −0.681784
953953 −20.3418 −0.658937 −0.329469 0.944167i 0.606870π-0.606870\pi
−0.329469 + 0.944167i 0.606870π0.606870\pi
954954 0 0
955955 4.95402 0.160308
956956 45.7367 1.47923
957957 0 0
958958 −67.8370 −2.19172
959959 −52.8156 −1.70551
960960 0 0
961961 −26.1751 −0.844359
962962 −4.97858 −0.160516
963963 0 0
964964 43.6791 1.40681
965965 −6.05754 −0.194999
966966 0 0
967967 −37.6461 −1.21062 −0.605309 0.795991i 0.706950π-0.706950\pi
−0.605309 + 0.795991i 0.706950π0.706950\pi
968968 −33.7967 −1.08627
969969 0 0
970970 −27.0937 −0.869925
971971 29.6216 0.950602 0.475301 0.879823i 0.342339π-0.342339\pi
0.475301 + 0.879823i 0.342339π0.342339\pi
972972 0 0
973973 36.6044 1.17348
974974 48.7581 1.56231
975975 0 0
976976 −6.97858 −0.223379
977977 −21.0158 −0.672354 −0.336177 0.941799i 0.609134π-0.609134\pi
−0.336177 + 0.941799i 0.609134π0.609134\pi
978978 0 0
979979 0.115077 0.00367788
980980 −45.8971 −1.46613
981981 0 0
982982 −82.2694 −2.62532
983983 27.5647 0.879176 0.439588 0.898200i 0.355124π-0.355124\pi
0.439588 + 0.898200i 0.355124π0.355124\pi
984984 0 0
985985 −24.4078 −0.777697
986986 −25.2614 −0.804488
987987 0 0
988988 −11.4145 −0.363145
989989 −10.6858 −0.339790
990990 0 0
991991 −20.1537 −0.640204 −0.320102 0.947383i 0.603717π-0.603717\pi
−0.320102 + 0.947383i 0.603717π0.603717\pi
992992 −9.17092 −0.291177
993993 0 0
994994 −45.4538 −1.44171
995995 3.85677 0.122268
996996 0 0
997997 14.9295 0.472821 0.236410 0.971653i 0.424029π-0.424029\pi
0.236410 + 0.971653i 0.424029π0.424029\pi
998998 −17.1464 −0.542759
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 1035.2.a.n.1.3 3
3.2 odd 2 345.2.a.j.1.1 3
5.4 even 2 5175.2.a.br.1.1 3
12.11 even 2 5520.2.a.by.1.1 3
15.2 even 4 1725.2.b.u.1174.1 6
15.8 even 4 1725.2.b.u.1174.6 6
15.14 odd 2 1725.2.a.bi.1.3 3
69.68 even 2 7935.2.a.u.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
345.2.a.j.1.1 3 3.2 odd 2
1035.2.a.n.1.3 3 1.1 even 1 trivial
1725.2.a.bi.1.3 3 15.14 odd 2
1725.2.b.u.1174.1 6 15.2 even 4
1725.2.b.u.1174.6 6 15.8 even 4
5175.2.a.br.1.1 3 5.4 even 2
5520.2.a.by.1.1 3 12.11 even 2
7935.2.a.u.1.1 3 69.68 even 2