Properties

Label 1530.2.d.f.919.3
Level 15301530
Weight 22
Character 1530.919
Analytic conductor 12.21712.217
Analytic rank 00
Dimension 44
Inner twists 22

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] = [1530,2,Mod(919,1530)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1530, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 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("1530.919"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1530=232517 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1530.d (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,-4,0,0,0,0,0,0,-8] 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: no
Analytic conductor: 12.217111509312.2171115093
Analytic rank: 00
Dimension: 44
Coefficient field: Q(i,5)\Q(i, \sqrt{5})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4+3x2+1 x^{4} + 3x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 510)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 919.3
Root 0.618034i0.618034i of defining polynomial
Character χ\chi == 1530.919
Dual form 1530.2.d.f.919.2

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+1.00000iq21.00000q42.23607iq5+1.23607iq71.00000iq8+2.23607q102.00000q11+5.23607iq131.23607q14+1.00000q16+1.00000iq17+6.47214q19+2.23607iq202.00000iq224.00000iq235.00000q255.23607q261.23607iq284.00000q29+2.47214q31+1.00000iq321.00000q34+2.76393q352.00000iq37+6.47214iq382.23607q40+7.70820q41+12.1803iq43+2.00000q44+4.00000q46+10.4721iq47+5.47214q495.00000iq505.23607iq52+10.9443iq53+4.47214iq55+1.23607q564.00000iq58+11.7082q59+4.47214q61+2.47214iq621.00000q64+11.7082q65+1.70820iq671.00000iq68+2.76393iq7011.2361q71+8.76393iq73+2.00000q746.47214q762.47214iq770.944272q792.23607iq80+7.70820iq8210.4721iq83+2.23607q8512.1803q86+2.00000iq88+12.4721q896.47214q91+4.00000iq9210.4721q9414.4721iq95+1.70820iq97+5.47214iq98+O(q100)q+1.00000i q^{2} -1.00000 q^{4} -2.23607i q^{5} +1.23607i q^{7} -1.00000i q^{8} +2.23607 q^{10} -2.00000 q^{11} +5.23607i q^{13} -1.23607 q^{14} +1.00000 q^{16} +1.00000i q^{17} +6.47214 q^{19} +2.23607i q^{20} -2.00000i q^{22} -4.00000i q^{23} -5.00000 q^{25} -5.23607 q^{26} -1.23607i q^{28} -4.00000 q^{29} +2.47214 q^{31} +1.00000i q^{32} -1.00000 q^{34} +2.76393 q^{35} -2.00000i q^{37} +6.47214i q^{38} -2.23607 q^{40} +7.70820 q^{41} +12.1803i q^{43} +2.00000 q^{44} +4.00000 q^{46} +10.4721i q^{47} +5.47214 q^{49} -5.00000i q^{50} -5.23607i q^{52} +10.9443i q^{53} +4.47214i q^{55} +1.23607 q^{56} -4.00000i q^{58} +11.7082 q^{59} +4.47214 q^{61} +2.47214i q^{62} -1.00000 q^{64} +11.7082 q^{65} +1.70820i q^{67} -1.00000i q^{68} +2.76393i q^{70} -11.2361 q^{71} +8.76393i q^{73} +2.00000 q^{74} -6.47214 q^{76} -2.47214i q^{77} -0.944272 q^{79} -2.23607i q^{80} +7.70820i q^{82} -10.4721i q^{83} +2.23607 q^{85} -12.1803 q^{86} +2.00000i q^{88} +12.4721 q^{89} -6.47214 q^{91} +4.00000i q^{92} -10.4721 q^{94} -14.4721i q^{95} +1.70820i q^{97} +5.47214i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q48q11+4q14+4q16+8q1920q2512q2616q298q314q34+20q35+4q41+8q44+16q46+4q494q56+20q594q64+24q94+O(q100) 4 q - 4 q^{4} - 8 q^{11} + 4 q^{14} + 4 q^{16} + 8 q^{19} - 20 q^{25} - 12 q^{26} - 16 q^{29} - 8 q^{31} - 4 q^{34} + 20 q^{35} + 4 q^{41} + 8 q^{44} + 16 q^{46} + 4 q^{49} - 4 q^{56} + 20 q^{59} - 4 q^{64}+ \cdots - 24 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1530Z)×\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times.

nn 307307 12611261 13611361
χ(n)\chi(n) 1-1 11 11

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 1.00000i 0.707107i
33 0 0
44 −1.00000 −0.500000
55 − 2.23607i − 1.00000i
66 0 0
77 1.23607i 0.467190i 0.972334 + 0.233595i 0.0750489π0.0750489\pi
−0.972334 + 0.233595i 0.924951π0.924951\pi
88 − 1.00000i − 0.353553i
99 0 0
1010 2.23607 0.707107
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 5.23607i 1.45222i 0.687576 + 0.726112i 0.258675π0.258675\pi
−0.687576 + 0.726112i 0.741325π0.741325\pi
1414 −1.23607 −0.330353
1515 0 0
1616 1.00000 0.250000
1717 1.00000i 0.242536i
1818 0 0
1919 6.47214 1.48481 0.742405 0.669951i 0.233685π-0.233685\pi
0.742405 + 0.669951i 0.233685π0.233685\pi
2020 2.23607i 0.500000i
2121 0 0
2222 − 2.00000i − 0.426401i
2323 − 4.00000i − 0.834058i −0.908893 0.417029i 0.863071π-0.863071\pi
0.908893 0.417029i 0.136929π-0.136929\pi
2424 0 0
2525 −5.00000 −1.00000
2626 −5.23607 −1.02688
2727 0 0
2828 − 1.23607i − 0.233595i
2929 −4.00000 −0.742781 −0.371391 0.928477i 0.621119π-0.621119\pi
−0.371391 + 0.928477i 0.621119π0.621119\pi
3030 0 0
3131 2.47214 0.444009 0.222004 0.975046i 0.428740π-0.428740\pi
0.222004 + 0.975046i 0.428740π0.428740\pi
3232 1.00000i 0.176777i
3333 0 0
3434 −1.00000 −0.171499
3535 2.76393 0.467190
3636 0 0
3737 − 2.00000i − 0.328798i −0.986394 0.164399i 0.947432π-0.947432\pi
0.986394 0.164399i 0.0525685π-0.0525685\pi
3838 6.47214i 1.04992i
3939 0 0
4040 −2.23607 −0.353553
4141 7.70820 1.20382 0.601910 0.798564i 0.294407π-0.294407\pi
0.601910 + 0.798564i 0.294407π0.294407\pi
4242 0 0
4343 12.1803i 1.85748i 0.370726 + 0.928742i 0.379109π0.379109\pi
−0.370726 + 0.928742i 0.620891π0.620891\pi
4444 2.00000 0.301511
4545 0 0
4646 4.00000 0.589768
4747 10.4721i 1.52752i 0.645501 + 0.763759i 0.276648π0.276648\pi
−0.645501 + 0.763759i 0.723352π0.723352\pi
4848 0 0
4949 5.47214 0.781734
5050 − 5.00000i − 0.707107i
5151 0 0
5252 − 5.23607i − 0.726112i
5353 10.9443i 1.50331i 0.659556 + 0.751656i 0.270744π0.270744\pi
−0.659556 + 0.751656i 0.729256π0.729256\pi
5454 0 0
5555 4.47214i 0.603023i
5656 1.23607 0.165177
5757 0 0
5858 − 4.00000i − 0.525226i
5959 11.7082 1.52428 0.762139 0.647413i 0.224149π-0.224149\pi
0.762139 + 0.647413i 0.224149π0.224149\pi
6060 0 0
6161 4.47214 0.572598 0.286299 0.958140i 0.407575π-0.407575\pi
0.286299 + 0.958140i 0.407575π0.407575\pi
6262 2.47214i 0.313962i
6363 0 0
6464 −1.00000 −0.125000
6565 11.7082 1.45222
6666 0 0
6767 1.70820i 0.208690i 0.994541 + 0.104345i 0.0332747π0.0332747\pi
−0.994541 + 0.104345i 0.966725π0.966725\pi
6868 − 1.00000i − 0.121268i
6969 0 0
7070 2.76393i 0.330353i
7171 −11.2361 −1.33348 −0.666738 0.745292i 0.732310π-0.732310\pi
−0.666738 + 0.745292i 0.732310π0.732310\pi
7272 0 0
7373 8.76393i 1.02574i 0.858466 + 0.512870i 0.171418π0.171418\pi
−0.858466 + 0.512870i 0.828582π0.828582\pi
7474 2.00000 0.232495
7575 0 0
7676 −6.47214 −0.742405
7777 − 2.47214i − 0.281726i
7878 0 0
7979 −0.944272 −0.106239 −0.0531194 0.998588i 0.516916π-0.516916\pi
−0.0531194 + 0.998588i 0.516916π0.516916\pi
8080 − 2.23607i − 0.250000i
8181 0 0
8282 7.70820i 0.851229i
8383 − 10.4721i − 1.14947i −0.818341 0.574733i 0.805106π-0.805106\pi
0.818341 0.574733i 0.194894π-0.194894\pi
8484 0 0
8585 2.23607 0.242536
8686 −12.1803 −1.31344
8787 0 0
8888 2.00000i 0.213201i
8989 12.4721 1.32204 0.661022 0.750367i 0.270123π-0.270123\pi
0.661022 + 0.750367i 0.270123π0.270123\pi
9090 0 0
9191 −6.47214 −0.678464
9292 4.00000i 0.417029i
9393 0 0
9494 −10.4721 −1.08012
9595 − 14.4721i − 1.48481i
9696 0 0
9797 1.70820i 0.173442i 0.996233 + 0.0867209i 0.0276388π0.0276388\pi
−0.996233 + 0.0867209i 0.972361π0.972361\pi
9898 5.47214i 0.552769i
9999 0 0
100100 5.00000 0.500000
101101 1.70820 0.169973 0.0849863 0.996382i 0.472915π-0.472915\pi
0.0849863 + 0.996382i 0.472915π0.472915\pi
102102 0 0
103103 10.9443i 1.07837i 0.842187 + 0.539186i 0.181268π0.181268\pi
−0.842187 + 0.539186i 0.818732π0.818732\pi
104104 5.23607 0.513439
105105 0 0
106106 −10.9443 −1.06300
107107 8.00000i 0.773389i 0.922208 + 0.386695i 0.126383π0.126383\pi
−0.922208 + 0.386695i 0.873617π0.873617\pi
108108 0 0
109109 7.52786 0.721039 0.360519 0.932752i 0.382599π-0.382599\pi
0.360519 + 0.932752i 0.382599π0.382599\pi
110110 −4.47214 −0.426401
111111 0 0
112112 1.23607i 0.116797i
113113 10.0000i 0.940721i 0.882474 + 0.470360i 0.155876π0.155876\pi
−0.882474 + 0.470360i 0.844124π0.844124\pi
114114 0 0
115115 −8.94427 −0.834058
116116 4.00000 0.371391
117117 0 0
118118 11.7082i 1.07783i
119119 −1.23607 −0.113310
120120 0 0
121121 −7.00000 −0.636364
122122 4.47214i 0.404888i
123123 0 0
124124 −2.47214 −0.222004
125125 11.1803i 1.00000i
126126 0 0
127127 − 14.0000i − 1.24230i −0.783692 0.621150i 0.786666π-0.786666\pi
0.783692 0.621150i 0.213334π-0.213334\pi
128128 − 1.00000i − 0.0883883i
129129 0 0
130130 11.7082i 1.02688i
131131 −12.4721 −1.08970 −0.544848 0.838535i 0.683413π-0.683413\pi
−0.544848 + 0.838535i 0.683413π0.683413\pi
132132 0 0
133133 8.00000i 0.693688i
134134 −1.70820 −0.147566
135135 0 0
136136 1.00000 0.0857493
137137 − 2.00000i − 0.170872i −0.996344 0.0854358i 0.972772π-0.972772\pi
0.996344 0.0854358i 0.0272282π-0.0272282\pi
138138 0 0
139139 −1.52786 −0.129592 −0.0647959 0.997899i 0.520640π-0.520640\pi
−0.0647959 + 0.997899i 0.520640π0.520640\pi
140140 −2.76393 −0.233595
141141 0 0
142142 − 11.2361i − 0.942910i
143143 − 10.4721i − 0.875724i
144144 0 0
145145 8.94427i 0.742781i
146146 −8.76393 −0.725308
147147 0 0
148148 2.00000i 0.164399i
149149 12.1803 0.997852 0.498926 0.866644i 0.333728π-0.333728\pi
0.498926 + 0.866644i 0.333728π0.333728\pi
150150 0 0
151151 −4.00000 −0.325515 −0.162758 0.986666i 0.552039π-0.552039\pi
−0.162758 + 0.986666i 0.552039π0.552039\pi
152152 − 6.47214i − 0.524960i
153153 0 0
154154 2.47214 0.199210
155155 − 5.52786i − 0.444009i
156156 0 0
157157 − 10.1803i − 0.812480i −0.913767 0.406240i 0.866840π-0.866840\pi
0.913767 0.406240i 0.133160π-0.133160\pi
158158 − 0.944272i − 0.0751222i
159159 0 0
160160 2.23607 0.176777
161161 4.94427 0.389663
162162 0 0
163163 − 22.4721i − 1.76015i −0.474831 0.880077i 0.657491π-0.657491\pi
0.474831 0.880077i 0.342509π-0.342509\pi
164164 −7.70820 −0.601910
165165 0 0
166166 10.4721 0.812795
167167 − 13.8885i − 1.07473i −0.843350 0.537364i 0.819420π-0.819420\pi
0.843350 0.537364i 0.180580π-0.180580\pi
168168 0 0
169169 −14.4164 −1.10895
170170 2.23607i 0.171499i
171171 0 0
172172 − 12.1803i − 0.928742i
173173 15.8885i 1.20798i 0.796991 + 0.603992i 0.206424π0.206424\pi
−0.796991 + 0.603992i 0.793576π0.793576\pi
174174 0 0
175175 − 6.18034i − 0.467190i
176176 −2.00000 −0.150756
177177 0 0
178178 12.4721i 0.934826i
179179 −7.70820 −0.576138 −0.288069 0.957610i 0.593013π-0.593013\pi
−0.288069 + 0.957610i 0.593013π0.593013\pi
180180 0 0
181181 0.472136 0.0350936 0.0175468 0.999846i 0.494414π-0.494414\pi
0.0175468 + 0.999846i 0.494414π0.494414\pi
182182 − 6.47214i − 0.479747i
183183 0 0
184184 −4.00000 −0.294884
185185 −4.47214 −0.328798
186186 0 0
187187 − 2.00000i − 0.146254i
188188 − 10.4721i − 0.763759i
189189 0 0
190190 14.4721 1.04992
191191 −5.52786 −0.399982 −0.199991 0.979798i 0.564091π-0.564091\pi
−0.199991 + 0.979798i 0.564091π0.564091\pi
192192 0 0
193193 − 23.5967i − 1.69853i −0.527966 0.849266i 0.677045π-0.677045\pi
0.527966 0.849266i 0.322955π-0.322955\pi
194194 −1.70820 −0.122642
195195 0 0
196196 −5.47214 −0.390867
197197 15.8885i 1.13201i 0.824401 + 0.566006i 0.191512π0.191512\pi
−0.824401 + 0.566006i 0.808488π0.808488\pi
198198 0 0
199199 8.94427 0.634043 0.317021 0.948418i 0.397317π-0.397317\pi
0.317021 + 0.948418i 0.397317π0.397317\pi
200200 5.00000i 0.353553i
201201 0 0
202202 1.70820i 0.120189i
203203 − 4.94427i − 0.347020i
204204 0 0
205205 − 17.2361i − 1.20382i
206206 −10.9443 −0.762524
207207 0 0
208208 5.23607i 0.363056i
209209 −12.9443 −0.895374
210210 0 0
211211 −24.9443 −1.71723 −0.858617 0.512617i 0.828676π-0.828676\pi
−0.858617 + 0.512617i 0.828676π0.828676\pi
212212 − 10.9443i − 0.751656i
213213 0 0
214214 −8.00000 −0.546869
215215 27.2361 1.85748
216216 0 0
217217 3.05573i 0.207436i
218218 7.52786i 0.509851i
219219 0 0
220220 − 4.47214i − 0.301511i
221221 −5.23607 −0.352216
222222 0 0
223223 9.05573i 0.606416i 0.952924 + 0.303208i 0.0980578π0.0980578\pi
−0.952924 + 0.303208i 0.901942π0.901942\pi
224224 −1.23607 −0.0825883
225225 0 0
226226 −10.0000 −0.665190
227227 9.88854i 0.656326i 0.944621 + 0.328163i 0.106429π0.106429\pi
−0.944621 + 0.328163i 0.893571π0.893571\pi
228228 0 0
229229 21.4164 1.41524 0.707618 0.706595i 0.249770π-0.249770\pi
0.707618 + 0.706595i 0.249770π0.249770\pi
230230 − 8.94427i − 0.589768i
231231 0 0
232232 4.00000i 0.262613i
233233 − 5.41641i − 0.354841i −0.984135 0.177420i 0.943225π-0.943225\pi
0.984135 0.177420i 0.0567752π-0.0567752\pi
234234 0 0
235235 23.4164 1.52752
236236 −11.7082 −0.762139
237237 0 0
238238 − 1.23607i − 0.0801224i
239239 −21.8885 −1.41585 −0.707926 0.706287i 0.750369π-0.750369\pi
−0.707926 + 0.706287i 0.750369π0.750369\pi
240240 0 0
241241 9.41641 0.606564 0.303282 0.952901i 0.401918π-0.401918\pi
0.303282 + 0.952901i 0.401918π0.401918\pi
242242 − 7.00000i − 0.449977i
243243 0 0
244244 −4.47214 −0.286299
245245 − 12.2361i − 0.781734i
246246 0 0
247247 33.8885i 2.15628i
248248 − 2.47214i − 0.156981i
249249 0 0
250250 −11.1803 −0.707107
251251 10.1803 0.642577 0.321289 0.946981i 0.395884π-0.395884\pi
0.321289 + 0.946981i 0.395884π0.395884\pi
252252 0 0
253253 8.00000i 0.502956i
254254 14.0000 0.878438
255255 0 0
256256 1.00000 0.0625000
257257 18.0000i 1.12281i 0.827541 + 0.561405i 0.189739π0.189739\pi
−0.827541 + 0.561405i 0.810261π0.810261\pi
258258 0 0
259259 2.47214 0.153611
260260 −11.7082 −0.726112
261261 0 0
262262 − 12.4721i − 0.770531i
263263 4.00000i 0.246651i 0.992366 + 0.123325i 0.0393559π0.0393559\pi
−0.992366 + 0.123325i 0.960644π0.960644\pi
264264 0 0
265265 24.4721 1.50331
266266 −8.00000 −0.490511
267267 0 0
268268 − 1.70820i − 0.104345i
269269 −7.05573 −0.430195 −0.215098 0.976593i 0.569007π-0.569007\pi
−0.215098 + 0.976593i 0.569007π0.569007\pi
270270 0 0
271271 4.00000 0.242983 0.121491 0.992592i 0.461232π-0.461232\pi
0.121491 + 0.992592i 0.461232π0.461232\pi
272272 1.00000i 0.0606339i
273273 0 0
274274 2.00000 0.120824
275275 10.0000 0.603023
276276 0 0
277277 − 26.3607i − 1.58386i −0.610612 0.791930i 0.709077π-0.709077\pi
0.610612 0.791930i 0.290923π-0.290923\pi
278278 − 1.52786i − 0.0916352i
279279 0 0
280280 − 2.76393i − 0.165177i
281281 −1.41641 −0.0844958 −0.0422479 0.999107i 0.513452π-0.513452\pi
−0.0422479 + 0.999107i 0.513452π0.513452\pi
282282 0 0
283283 − 25.8885i − 1.53891i −0.638699 0.769457i 0.720527π-0.720527\pi
0.638699 0.769457i 0.279473π-0.279473\pi
284284 11.2361 0.666738
285285 0 0
286286 10.4721 0.619230
287287 9.52786i 0.562412i
288288 0 0
289289 −1.00000 −0.0588235
290290 −8.94427 −0.525226
291291 0 0
292292 − 8.76393i − 0.512870i
293293 − 29.4164i − 1.71852i −0.511535 0.859262i 0.670923π-0.670923\pi
0.511535 0.859262i 0.329077π-0.329077\pi
294294 0 0
295295 − 26.1803i − 1.52428i
296296 −2.00000 −0.116248
297297 0 0
298298 12.1803i 0.705588i
299299 20.9443 1.21124
300300 0 0
301301 −15.0557 −0.867798
302302 − 4.00000i − 0.230174i
303303 0 0
304304 6.47214 0.371202
305305 − 10.0000i − 0.572598i
306306 0 0
307307 − 4.18034i − 0.238585i −0.992859 0.119292i 0.961937π-0.961937\pi
0.992859 0.119292i 0.0380626π-0.0380626\pi
308308 2.47214i 0.140863i
309309 0 0
310310 5.52786 0.313962
311311 −19.5967 −1.11123 −0.555615 0.831440i 0.687517π-0.687517\pi
−0.555615 + 0.831440i 0.687517π0.687517\pi
312312 0 0
313313 − 21.7082i − 1.22702i −0.789687 0.613510i 0.789757π-0.789757\pi
0.789687 0.613510i 0.210243π-0.210243\pi
314314 10.1803 0.574510
315315 0 0
316316 0.944272 0.0531194
317317 11.8885i 0.667727i 0.942621 + 0.333864i 0.108352π0.108352\pi
−0.942621 + 0.333864i 0.891648π0.891648\pi
318318 0 0
319319 8.00000 0.447914
320320 2.23607i 0.125000i
321321 0 0
322322 4.94427i 0.275534i
323323 6.47214i 0.360119i
324324 0 0
325325 − 26.1803i − 1.45222i
326326 22.4721 1.24462
327327 0 0
328328 − 7.70820i − 0.425614i
329329 −12.9443 −0.713641
330330 0 0
331331 −3.41641 −0.187783 −0.0938914 0.995582i 0.529931π-0.529931\pi
−0.0938914 + 0.995582i 0.529931π0.529931\pi
332332 10.4721i 0.574733i
333333 0 0
334334 13.8885 0.759947
335335 3.81966 0.208690
336336 0 0
337337 20.1803i 1.09929i 0.835397 + 0.549647i 0.185238π0.185238\pi
−0.835397 + 0.549647i 0.814762π0.814762\pi
338338 − 14.4164i − 0.784149i
339339 0 0
340340 −2.23607 −0.121268
341341 −4.94427 −0.267747
342342 0 0
343343 15.4164i 0.832408i
344344 12.1803 0.656720
345345 0 0
346346 −15.8885 −0.854173
347347 − 22.8328i − 1.22573i −0.790188 0.612865i 0.790017π-0.790017\pi
0.790188 0.612865i 0.209983π-0.209983\pi
348348 0 0
349349 28.4721 1.52408 0.762039 0.647531i 0.224198π-0.224198\pi
0.762039 + 0.647531i 0.224198π0.224198\pi
350350 6.18034 0.330353
351351 0 0
352352 − 2.00000i − 0.106600i
353353 14.9443i 0.795403i 0.917515 + 0.397702i 0.130192π0.130192\pi
−0.917515 + 0.397702i 0.869808π0.869808\pi
354354 0 0
355355 25.1246i 1.33348i
356356 −12.4721 −0.661022
357357 0 0
358358 − 7.70820i − 0.407391i
359359 −9.52786 −0.502861 −0.251431 0.967875i 0.580901π-0.580901\pi
−0.251431 + 0.967875i 0.580901π0.580901\pi
360360 0 0
361361 22.8885 1.20466
362362 0.472136i 0.0248149i
363363 0 0
364364 6.47214 0.339232
365365 19.5967 1.02574
366366 0 0
367367 5.81966i 0.303784i 0.988397 + 0.151892i 0.0485366π0.0485366\pi
−0.988397 + 0.151892i 0.951463π0.951463\pi
368368 − 4.00000i − 0.208514i
369369 0 0
370370 − 4.47214i − 0.232495i
371371 −13.5279 −0.702332
372372 0 0
373373 − 1.23607i − 0.0640012i −0.999488 0.0320006i 0.989812π-0.989812\pi
0.999488 0.0320006i 0.0101878π-0.0101878\pi
374374 2.00000 0.103418
375375 0 0
376376 10.4721 0.540059
377377 − 20.9443i − 1.07868i
378378 0 0
379379 1.52786 0.0784811 0.0392406 0.999230i 0.487506π-0.487506\pi
0.0392406 + 0.999230i 0.487506π0.487506\pi
380380 14.4721i 0.742405i
381381 0 0
382382 − 5.52786i − 0.282830i
383383 − 17.8885i − 0.914062i −0.889451 0.457031i 0.848913π-0.848913\pi
0.889451 0.457031i 0.151087π-0.151087\pi
384384 0 0
385385 −5.52786 −0.281726
386386 23.5967 1.20104
387387 0 0
388388 − 1.70820i − 0.0867209i
389389 20.1803 1.02318 0.511592 0.859229i 0.329056π-0.329056\pi
0.511592 + 0.859229i 0.329056π0.329056\pi
390390 0 0
391391 4.00000 0.202289
392392 − 5.47214i − 0.276385i
393393 0 0
394394 −15.8885 −0.800453
395395 2.11146i 0.106239i
396396 0 0
397397 − 3.88854i − 0.195160i −0.995228 0.0975802i 0.968890π-0.968890\pi
0.995228 0.0975802i 0.0311103π-0.0311103\pi
398398 8.94427i 0.448336i
399399 0 0
400400 −5.00000 −0.250000
401401 36.0689 1.80119 0.900597 0.434655i 0.143130π-0.143130\pi
0.900597 + 0.434655i 0.143130π0.143130\pi
402402 0 0
403403 12.9443i 0.644800i
404404 −1.70820 −0.0849863
405405 0 0
406406 4.94427 0.245380
407407 4.00000i 0.198273i
408408 0 0
409409 −26.3607 −1.30345 −0.651726 0.758455i 0.725955π-0.725955\pi
−0.651726 + 0.758455i 0.725955π0.725955\pi
410410 17.2361 0.851229
411411 0 0
412412 − 10.9443i − 0.539186i
413413 14.4721i 0.712127i
414414 0 0
415415 −23.4164 −1.14947
416416 −5.23607 −0.256719
417417 0 0
418418 − 12.9443i − 0.633125i
419419 6.36068 0.310740 0.155370 0.987856i 0.450343π-0.450343\pi
0.155370 + 0.987856i 0.450343π0.450343\pi
420420 0 0
421421 −37.4164 −1.82356 −0.911782 0.410674i 0.865293π-0.865293\pi
−0.911782 + 0.410674i 0.865293π0.865293\pi
422422 − 24.9443i − 1.21427i
423423 0 0
424424 10.9443 0.531501
425425 − 5.00000i − 0.242536i
426426 0 0
427427 5.52786i 0.267512i
428428 − 8.00000i − 0.386695i
429429 0 0
430430 27.2361i 1.31344i
431431 −31.5967 −1.52196 −0.760981 0.648774i 0.775282π-0.775282\pi
−0.760981 + 0.648774i 0.775282π0.775282\pi
432432 0 0
433433 28.3607i 1.36293i 0.731852 + 0.681464i 0.238656π0.238656\pi
−0.731852 + 0.681464i 0.761344π0.761344\pi
434434 −3.05573 −0.146680
435435 0 0
436436 −7.52786 −0.360519
437437 − 25.8885i − 1.23842i
438438 0 0
439439 −13.5279 −0.645650 −0.322825 0.946459i 0.604632π-0.604632\pi
−0.322825 + 0.946459i 0.604632π0.604632\pi
440440 4.47214 0.213201
441441 0 0
442442 − 5.23607i − 0.249054i
443443 − 4.00000i − 0.190046i −0.995475 0.0950229i 0.969708π-0.969708\pi
0.995475 0.0950229i 0.0302924π-0.0302924\pi
444444 0 0
445445 − 27.8885i − 1.32204i
446446 −9.05573 −0.428801
447447 0 0
448448 − 1.23607i − 0.0583987i
449449 17.5967 0.830442 0.415221 0.909721i 0.363704π-0.363704\pi
0.415221 + 0.909721i 0.363704π0.363704\pi
450450 0 0
451451 −15.4164 −0.725930
452452 − 10.0000i − 0.470360i
453453 0 0
454454 −9.88854 −0.464092
455455 14.4721i 0.678464i
456456 0 0
457457 16.3607i 0.765320i 0.923889 + 0.382660i 0.124992π0.124992\pi
−0.923889 + 0.382660i 0.875008π0.875008\pi
458458 21.4164i 1.00072i
459459 0 0
460460 8.94427 0.417029
461461 30.0689 1.40045 0.700224 0.713923i 0.253084π-0.253084\pi
0.700224 + 0.713923i 0.253084π0.253084\pi
462462 0 0
463463 − 18.9443i − 0.880415i −0.897896 0.440207i 0.854905π-0.854905\pi
0.897896 0.440207i 0.145095π-0.145095\pi
464464 −4.00000 −0.185695
465465 0 0
466466 5.41641 0.250910
467467 0.944272i 0.0436957i 0.999761 + 0.0218478i 0.00695494π0.00695494\pi
−0.999761 + 0.0218478i 0.993045π0.993045\pi
468468 0 0
469469 −2.11146 −0.0974980
470470 23.4164i 1.08012i
471471 0 0
472472 − 11.7082i − 0.538914i
473473 − 24.3607i − 1.12011i
474474 0 0
475475 −32.3607 −1.48481
476476 1.23607 0.0566551
477477 0 0
478478 − 21.8885i − 1.00116i
479479 −35.5967 −1.62646 −0.813228 0.581945i 0.802292π-0.802292\pi
−0.813228 + 0.581945i 0.802292π0.802292\pi
480480 0 0
481481 10.4721 0.477488
482482 9.41641i 0.428906i
483483 0 0
484484 7.00000 0.318182
485485 3.81966 0.173442
486486 0 0
487487 16.2918i 0.738252i 0.929379 + 0.369126i 0.120343π0.120343\pi
−0.929379 + 0.369126i 0.879657π0.879657\pi
488488 − 4.47214i − 0.202444i
489489 0 0
490490 12.2361 0.552769
491491 −12.2918 −0.554721 −0.277360 0.960766i 0.589460π-0.589460\pi
−0.277360 + 0.960766i 0.589460π0.589460\pi
492492 0 0
493493 − 4.00000i − 0.180151i
494494 −33.8885 −1.52472
495495 0 0
496496 2.47214 0.111002
497497 − 13.8885i − 0.622986i
498498 0 0
499499 16.0000 0.716258 0.358129 0.933672i 0.383415π-0.383415\pi
0.358129 + 0.933672i 0.383415π0.383415\pi
500500 − 11.1803i − 0.500000i
501501 0 0
502502 10.1803i 0.454371i
503503 27.4164i 1.22244i 0.791462 + 0.611219i 0.209320π0.209320\pi
−0.791462 + 0.611219i 0.790680π0.790680\pi
504504 0 0
505505 − 3.81966i − 0.169973i
506506 −8.00000 −0.355643
507507 0 0
508508 14.0000i 0.621150i
509509 1.34752 0.0597280 0.0298640 0.999554i 0.490493π-0.490493\pi
0.0298640 + 0.999554i 0.490493π0.490493\pi
510510 0 0
511511 −10.8328 −0.479216
512512 1.00000i 0.0441942i
513513 0 0
514514 −18.0000 −0.793946
515515 24.4721 1.07837
516516 0 0
517517 − 20.9443i − 0.921128i
518518 2.47214i 0.108619i
519519 0 0
520520 − 11.7082i − 0.513439i
521521 −5.81966 −0.254964 −0.127482 0.991841i 0.540689π-0.540689\pi
−0.127482 + 0.991841i 0.540689π0.540689\pi
522522 0 0
523523 − 14.2918i − 0.624937i −0.949928 0.312468i 0.898844π-0.898844\pi
0.949928 0.312468i 0.101156π-0.101156\pi
524524 12.4721 0.544848
525525 0 0
526526 −4.00000 −0.174408
527527 2.47214i 0.107688i
528528 0 0
529529 7.00000 0.304348
530530 24.4721i 1.06300i
531531 0 0
532532 − 8.00000i − 0.346844i
533533 40.3607i 1.74822i
534534 0 0
535535 17.8885 0.773389
536536 1.70820 0.0737832
537537 0 0
538538 − 7.05573i − 0.304194i
539539 −10.9443 −0.471403
540540 0 0
541541 −31.3050 −1.34590 −0.672952 0.739686i 0.734974π-0.734974\pi
−0.672952 + 0.739686i 0.734974π0.734974\pi
542542 4.00000i 0.171815i
543543 0 0
544544 −1.00000 −0.0428746
545545 − 16.8328i − 0.721039i
546546 0 0
547547 − 0.944272i − 0.0403742i −0.999796 0.0201871i 0.993574π-0.993574\pi
0.999796 0.0201871i 0.00642618π-0.00642618\pi
548548 2.00000i 0.0854358i
549549 0 0
550550 10.0000i 0.426401i
551551 −25.8885 −1.10289
552552 0 0
553553 − 1.16718i − 0.0496337i
554554 26.3607 1.11996
555555 0 0
556556 1.52786 0.0647959
557557 − 25.0557i − 1.06165i −0.847483 0.530823i 0.821883π-0.821883\pi
0.847483 0.530823i 0.178117π-0.178117\pi
558558 0 0
559559 −63.7771 −2.69748
560560 2.76393 0.116797
561561 0 0
562562 − 1.41641i − 0.0597476i
563563 − 2.11146i − 0.0889873i −0.999010 0.0444936i 0.985833π-0.985833\pi
0.999010 0.0444936i 0.0141674π-0.0141674\pi
564564 0 0
565565 22.3607 0.940721
566566 25.8885 1.08818
567567 0 0
568568 11.2361i 0.471455i
569569 6.00000 0.251533 0.125767 0.992060i 0.459861π-0.459861\pi
0.125767 + 0.992060i 0.459861π0.459861\pi
570570 0 0
571571 36.3607 1.52165 0.760824 0.648959i 0.224795π-0.224795\pi
0.760824 + 0.648959i 0.224795π0.224795\pi
572572 10.4721i 0.437862i
573573 0 0
574574 −9.52786 −0.397685
575575 20.0000i 0.834058i
576576 0 0
577577 35.4164i 1.47440i 0.675672 + 0.737202i 0.263853π0.263853\pi
−0.675672 + 0.737202i 0.736147π0.736147\pi
578578 − 1.00000i − 0.0415945i
579579 0 0
580580 − 8.94427i − 0.371391i
581581 12.9443 0.537019
582582 0 0
583583 − 21.8885i − 0.906531i
584584 8.76393 0.362654
585585 0 0
586586 29.4164 1.21518
587587 − 5.52786i − 0.228159i −0.993472 0.114080i 0.963608π-0.963608\pi
0.993472 0.114080i 0.0363919π-0.0363919\pi
588588 0 0
589589 16.0000 0.659269
590590 26.1803 1.07783
591591 0 0
592592 − 2.00000i − 0.0821995i
593593 − 30.9443i − 1.27073i −0.772212 0.635364i 0.780850π-0.780850\pi
0.772212 0.635364i 0.219150π-0.219150\pi
594594 0 0
595595 2.76393i 0.113310i
596596 −12.1803 −0.498926
597597 0 0
598598 20.9443i 0.856475i
599599 25.5279 1.04304 0.521520 0.853239i 0.325365π-0.325365\pi
0.521520 + 0.853239i 0.325365π0.325365\pi
600600 0 0
601601 −28.4721 −1.16140 −0.580701 0.814117i 0.697222π-0.697222\pi
−0.580701 + 0.814117i 0.697222π0.697222\pi
602602 − 15.0557i − 0.613626i
603603 0 0
604604 4.00000 0.162758
605605 15.6525i 0.636364i
606606 0 0
607607 31.1246i 1.26331i 0.775250 + 0.631655i 0.217624π0.217624\pi
−0.775250 + 0.631655i 0.782376π0.782376\pi
608608 6.47214i 0.262480i
609609 0 0
610610 10.0000 0.404888
611611 −54.8328 −2.21830
612612 0 0
613613 − 42.1803i − 1.70365i −0.523828 0.851824i 0.675497π-0.675497\pi
0.523828 0.851824i 0.324503π-0.324503\pi
614614 4.18034 0.168705
615615 0 0
616616 −2.47214 −0.0996052
617617 − 20.4721i − 0.824177i −0.911144 0.412089i 0.864799π-0.864799\pi
0.911144 0.412089i 0.135201π-0.135201\pi
618618 0 0
619619 48.9443 1.96724 0.983618 0.180264i 0.0576953π-0.0576953\pi
0.983618 + 0.180264i 0.0576953π0.0576953\pi
620620 5.52786i 0.222004i
621621 0 0
622622 − 19.5967i − 0.785758i
623623 15.4164i 0.617645i
624624 0 0
625625 25.0000 1.00000
626626 21.7082 0.867634
627627 0 0
628628 10.1803i 0.406240i
629629 2.00000 0.0797452
630630 0 0
631631 −9.88854 −0.393657 −0.196828 0.980438i 0.563064π-0.563064\pi
−0.196828 + 0.980438i 0.563064π0.563064\pi
632632 0.944272i 0.0375611i
633633 0 0
634634 −11.8885 −0.472154
635635 −31.3050 −1.24230
636636 0 0
637637 28.6525i 1.13525i
638638 8.00000i 0.316723i
639639 0 0
640640 −2.23607 −0.0883883
641641 −11.7082 −0.462446 −0.231223 0.972901i 0.574273π-0.574273\pi
−0.231223 + 0.972901i 0.574273π0.574273\pi
642642 0 0
643643 − 27.4164i − 1.08120i −0.841281 0.540599i 0.818198π-0.818198\pi
0.841281 0.540599i 0.181802π-0.181802\pi
644644 −4.94427 −0.194832
645645 0 0
646646 −6.47214 −0.254643
647647 − 20.9443i − 0.823404i −0.911318 0.411702i 0.864934π-0.864934\pi
0.911318 0.411702i 0.135066π-0.135066\pi
648648 0 0
649649 −23.4164 −0.919174
650650 26.1803 1.02688
651651 0 0
652652 22.4721i 0.880077i
653653 3.52786i 0.138056i 0.997615 + 0.0690280i 0.0219898π0.0219898\pi
−0.997615 + 0.0690280i 0.978010π0.978010\pi
654654 0 0
655655 27.8885i 1.08970i
656656 7.70820 0.300955
657657 0 0
658658 − 12.9443i − 0.504620i
659659 28.2918 1.10209 0.551046 0.834475i 0.314229π-0.314229\pi
0.551046 + 0.834475i 0.314229π0.314229\pi
660660 0 0
661661 13.4164 0.521838 0.260919 0.965361i 0.415974π-0.415974\pi
0.260919 + 0.965361i 0.415974π0.415974\pi
662662 − 3.41641i − 0.132782i
663663 0 0
664664 −10.4721 −0.406398
665665 17.8885 0.693688
666666 0 0
667667 16.0000i 0.619522i
668668 13.8885i 0.537364i
669669 0 0
670670 3.81966i 0.147566i
671671 −8.94427 −0.345290
672672 0 0
673673 4.18034i 0.161140i 0.996749 + 0.0805701i 0.0256741π0.0256741\pi
−0.996749 + 0.0805701i 0.974326π0.974326\pi
674674 −20.1803 −0.777318
675675 0 0
676676 14.4164 0.554477
677677 − 9.05573i − 0.348040i −0.984742 0.174020i 0.944324π-0.944324\pi
0.984742 0.174020i 0.0556757π-0.0556757\pi
678678 0 0
679679 −2.11146 −0.0810303
680680 − 2.23607i − 0.0857493i
681681 0 0
682682 − 4.94427i − 0.189326i
683683 32.9443i 1.26058i 0.776361 + 0.630289i 0.217064π0.217064\pi
−0.776361 + 0.630289i 0.782936π0.782936\pi
684684 0 0
685685 −4.47214 −0.170872
686686 −15.4164 −0.588601
687687 0 0
688688 12.1803i 0.464371i
689689 −57.3050 −2.18314
690690 0 0
691691 −4.94427 −0.188089 −0.0940445 0.995568i 0.529980π-0.529980\pi
−0.0940445 + 0.995568i 0.529980π0.529980\pi
692692 − 15.8885i − 0.603992i
693693 0 0
694694 22.8328 0.866722
695695 3.41641i 0.129592i
696696 0 0
697697 7.70820i 0.291969i
698698 28.4721i 1.07769i
699699 0 0
700700 6.18034i 0.233595i
701701 −11.5967 −0.438003 −0.219002 0.975725i 0.570280π-0.570280\pi
−0.219002 + 0.975725i 0.570280π0.570280\pi
702702 0 0
703703 − 12.9443i − 0.488202i
704704 2.00000 0.0753778
705705 0 0
706706 −14.9443 −0.562435
707707 2.11146i 0.0794095i
708708 0 0
709709 39.5279 1.48450 0.742250 0.670123i 0.233759π-0.233759\pi
0.742250 + 0.670123i 0.233759π0.233759\pi
710710 −25.1246 −0.942910
711711 0 0
712712 − 12.4721i − 0.467413i
713713 − 9.88854i − 0.370329i
714714 0 0
715715 −23.4164 −0.875724
716716 7.70820 0.288069
717717 0 0
718718 − 9.52786i − 0.355577i
719719 −36.5410 −1.36275 −0.681375 0.731934i 0.738618π-0.738618\pi
−0.681375 + 0.731934i 0.738618π0.738618\pi
720720 0 0
721721 −13.5279 −0.503804
722722 22.8885i 0.851823i
723723 0 0
724724 −0.472136 −0.0175468
725725 20.0000 0.742781
726726 0 0
727727 23.8885i 0.885977i 0.896527 + 0.442989i 0.146082π0.146082\pi
−0.896527 + 0.442989i 0.853918π0.853918\pi
728728 6.47214i 0.239873i
729729 0 0
730730 19.5967i 0.725308i
731731 −12.1803 −0.450506
732732 0 0
733733 38.5410i 1.42355i 0.702410 + 0.711773i 0.252107π0.252107\pi
−0.702410 + 0.711773i 0.747893π0.747893\pi
734734 −5.81966 −0.214808
735735 0 0
736736 4.00000 0.147442
737737 − 3.41641i − 0.125845i
738738 0 0
739739 −33.5279 −1.23334 −0.616671 0.787221i 0.711519π-0.711519\pi
−0.616671 + 0.787221i 0.711519π0.711519\pi
740740 4.47214 0.164399
741741 0 0
742742 − 13.5279i − 0.496624i
743743 − 33.5279i − 1.23002i −0.788520 0.615009i 0.789152π-0.789152\pi
0.788520 0.615009i 0.210848π-0.210848\pi
744744 0 0
745745 − 27.2361i − 0.997852i
746746 1.23607 0.0452557
747747 0 0
748748 2.00000i 0.0731272i
749749 −9.88854 −0.361320
750750 0 0
751751 29.8885 1.09065 0.545324 0.838225i 0.316407π-0.316407\pi
0.545324 + 0.838225i 0.316407π0.316407\pi
752752 10.4721i 0.381880i
753753 0 0
754754 20.9443 0.762745
755755 8.94427i 0.325515i
756756 0 0
757757 37.5967i 1.36648i 0.730195 + 0.683239i 0.239429π0.239429\pi
−0.730195 + 0.683239i 0.760571π0.760571\pi
758758 1.52786i 0.0554945i
759759 0 0
760760 −14.4721 −0.524960
761761 −52.8328 −1.91519 −0.957594 0.288121i 0.906969π-0.906969\pi
−0.957594 + 0.288121i 0.906969π0.906969\pi
762762 0 0
763763 9.30495i 0.336862i
764764 5.52786 0.199991
765765 0 0
766766 17.8885 0.646339
767767 61.3050i 2.21359i
768768 0 0
769769 34.3607 1.23908 0.619539 0.784966i 0.287320π-0.287320\pi
0.619539 + 0.784966i 0.287320π0.287320\pi
770770 − 5.52786i − 0.199210i
771771 0 0
772772 23.5967i 0.849266i
773773 − 33.4164i − 1.20190i −0.799285 0.600952i 0.794788π-0.794788\pi
0.799285 0.600952i 0.205212π-0.205212\pi
774774 0 0
775775 −12.3607 −0.444009
776776 1.70820 0.0613209
777777 0 0
778778 20.1803i 0.723500i
779779 49.8885 1.78744
780780 0 0
781781 22.4721 0.804116
782782 4.00000i 0.143040i
783783 0 0
784784 5.47214 0.195433
785785 −22.7639 −0.812480
786786 0 0
787787 − 46.4721i − 1.65655i −0.560320 0.828276i 0.689322π-0.689322\pi
0.560320 0.828276i 0.310678π-0.310678\pi
788788 − 15.8885i − 0.566006i
789789 0 0
790790 −2.11146 −0.0751222
791791 −12.3607 −0.439495
792792 0 0
793793 23.4164i 0.831541i
794794 3.88854 0.137999
795795 0 0
796796 −8.94427 −0.317021
797797 46.0000i 1.62940i 0.579880 + 0.814702i 0.303099π0.303099\pi
−0.579880 + 0.814702i 0.696901π0.696901\pi
798798 0 0
799799 −10.4721 −0.370478
800800 − 5.00000i − 0.176777i
801801 0 0
802802 36.0689i 1.27364i
803803 − 17.5279i − 0.618545i
804804 0 0
805805 − 11.0557i − 0.389663i
806806 −12.9443 −0.455943
807807 0 0
808808 − 1.70820i − 0.0600944i
809809 47.1246 1.65681 0.828407 0.560127i 0.189248π-0.189248\pi
0.828407 + 0.560127i 0.189248π0.189248\pi
810810 0 0
811811 42.2492 1.48357 0.741785 0.670637i 0.233979π-0.233979\pi
0.741785 + 0.670637i 0.233979π0.233979\pi
812812 4.94427i 0.173510i
813813 0 0
814814 −4.00000 −0.140200
815815 −50.2492 −1.76015
816816 0 0
817817 78.8328i 2.75801i
818818 − 26.3607i − 0.921680i
819819 0 0
820820 17.2361i 0.601910i
821821 −15.4164 −0.538036 −0.269018 0.963135i 0.586699π-0.586699\pi
−0.269018 + 0.963135i 0.586699π0.586699\pi
822822 0 0
823823 38.1803i 1.33088i 0.746450 + 0.665441i 0.231757π0.231757\pi
−0.746450 + 0.665441i 0.768243π0.768243\pi
824824 10.9443 0.381262
825825 0 0
826826 −14.4721 −0.503550
827827 − 23.0557i − 0.801726i −0.916138 0.400863i 0.868710π-0.868710\pi
0.916138 0.400863i 0.131290π-0.131290\pi
828828 0 0
829829 −34.0000 −1.18087 −0.590434 0.807086i 0.701044π-0.701044\pi
−0.590434 + 0.807086i 0.701044π0.701044\pi
830830 − 23.4164i − 0.812795i
831831 0 0
832832 − 5.23607i − 0.181528i
833833 5.47214i 0.189598i
834834 0 0
835835 −31.0557 −1.07473
836836 12.9443 0.447687
837837 0 0
838838 6.36068i 0.219726i
839839 −22.0689 −0.761902 −0.380951 0.924595i 0.624403π-0.624403\pi
−0.380951 + 0.924595i 0.624403π0.624403\pi
840840 0 0
841841 −13.0000 −0.448276
842842 − 37.4164i − 1.28945i
843843 0 0
844844 24.9443 0.858617
845845 32.2361i 1.10895i
846846 0 0
847847 − 8.65248i − 0.297303i
848848 10.9443i 0.375828i
849849 0 0
850850 5.00000 0.171499
851851 −8.00000 −0.274236
852852 0 0
853853 − 6.36068i − 0.217786i −0.994054 0.108893i 0.965269π-0.965269\pi
0.994054 0.108893i 0.0347305π-0.0347305\pi
854854 −5.52786 −0.189160
855855 0 0
856856 8.00000 0.273434
857857 50.3607i 1.72029i 0.510051 + 0.860144i 0.329626π0.329626\pi
−0.510051 + 0.860144i 0.670374π0.670374\pi
858858 0 0
859859 −7.05573 −0.240738 −0.120369 0.992729i 0.538408π-0.538408\pi
−0.120369 + 0.992729i 0.538408π0.538408\pi
860860 −27.2361 −0.928742
861861 0 0
862862 − 31.5967i − 1.07619i
863863 21.3050i 0.725229i 0.931939 + 0.362614i 0.118116π0.118116\pi
−0.931939 + 0.362614i 0.881884π0.881884\pi
864864 0 0
865865 35.5279 1.20798
866866 −28.3607 −0.963735
867867 0 0
868868 − 3.05573i − 0.103718i
869869 1.88854 0.0640645
870870 0 0
871871 −8.94427 −0.303065
872872 − 7.52786i − 0.254926i
873873 0 0
874874 25.8885 0.875693
875875 −13.8197 −0.467190
876876 0 0
877877 40.4721i 1.36665i 0.730116 + 0.683323i 0.239466π0.239466\pi
−0.730116 + 0.683323i 0.760534π0.760534\pi
878878 − 13.5279i − 0.456543i
879879 0 0
880880 4.47214i 0.150756i
881881 7.12461 0.240034 0.120017 0.992772i 0.461705π-0.461705\pi
0.120017 + 0.992772i 0.461705π0.461705\pi
882882 0 0
883883 − 27.2361i − 0.916567i −0.888806 0.458283i 0.848465π-0.848465\pi
0.888806 0.458283i 0.151535π-0.151535\pi
884884 5.23607 0.176108
885885 0 0
886886 4.00000 0.134383
887887 8.94427i 0.300319i 0.988662 + 0.150160i 0.0479788π0.0479788\pi
−0.988662 + 0.150160i 0.952021π0.952021\pi
888888 0 0
889889 17.3050 0.580389
890890 27.8885 0.934826
891891 0 0
892892 − 9.05573i − 0.303208i
893893 67.7771i 2.26807i
894894 0 0
895895 17.2361i 0.576138i
896896 1.23607 0.0412941
897897 0 0
898898 17.5967i 0.587211i
899899 −9.88854 −0.329801
900900 0 0
901901 −10.9443 −0.364607
902902 − 15.4164i − 0.513310i
903903 0 0
904904 10.0000 0.332595
905905 − 1.05573i − 0.0350936i
906906 0 0
907907 − 4.36068i − 0.144794i −0.997376 0.0723970i 0.976935π-0.976935\pi
0.997376 0.0723970i 0.0230649π-0.0230649\pi
908908 − 9.88854i − 0.328163i
909909 0 0
910910 −14.4721 −0.479747
911911 12.5410 0.415503 0.207751 0.978182i 0.433386π-0.433386\pi
0.207751 + 0.978182i 0.433386π0.433386\pi
912912 0 0
913913 20.9443i 0.693154i
914914 −16.3607 −0.541163
915915 0 0
916916 −21.4164 −0.707618
917917 − 15.4164i − 0.509095i
918918 0 0
919919 −52.7214 −1.73912 −0.869559 0.493830i 0.835597π-0.835597\pi
−0.869559 + 0.493830i 0.835597π0.835597\pi
920920 8.94427i 0.294884i
921921 0 0
922922 30.0689i 0.990266i
923923 − 58.8328i − 1.93651i
924924 0 0
925925 10.0000i 0.328798i
926926 18.9443 0.622547
927927 0 0
928928 − 4.00000i − 0.131306i
929929 24.0689 0.789674 0.394837 0.918751i 0.370801π-0.370801\pi
0.394837 + 0.918751i 0.370801π0.370801\pi
930930 0 0
931931 35.4164 1.16073
932932 5.41641i 0.177420i
933933 0 0
934934 −0.944272 −0.0308975
935935 −4.47214 −0.146254
936936 0 0
937937 − 17.5279i − 0.572610i −0.958138 0.286305i 0.907573π-0.907573\pi
0.958138 0.286305i 0.0924271π-0.0924271\pi
938938 − 2.11146i − 0.0689415i
939939 0 0
940940 −23.4164 −0.763759
941941 −13.3050 −0.433729 −0.216865 0.976202i 0.569583π-0.569583\pi
−0.216865 + 0.976202i 0.569583π0.569583\pi
942942 0 0
943943 − 30.8328i − 1.00405i
944944 11.7082 0.381070
945945 0 0
946946 24.3607 0.792034
947947 48.7214i 1.58323i 0.611019 + 0.791616i 0.290760π0.290760\pi
−0.611019 + 0.791616i 0.709240π0.709240\pi
948948 0 0
949949 −45.8885 −1.48961
950950 − 32.3607i − 1.04992i
951951 0 0
952952 1.23607i 0.0400612i
953953 − 26.9443i − 0.872811i −0.899750 0.436405i 0.856251π-0.856251\pi
0.899750 0.436405i 0.143749π-0.143749\pi
954954 0 0
955955 12.3607i 0.399982i
956956 21.8885 0.707926
957957 0 0
958958 − 35.5967i − 1.15008i
959959 2.47214 0.0798294
960960 0 0
961961 −24.8885 −0.802856
962962 10.4721i 0.337635i
963963 0 0
964964 −9.41641 −0.303282
965965 −52.7639 −1.69853
966966 0 0
967967 0.472136i 0.0151829i 0.999971 + 0.00759143i 0.00241645π0.00241645\pi
−0.999971 + 0.00759143i 0.997584π0.997584\pi
968968 7.00000i 0.224989i
969969 0 0
970970 3.81966i 0.122642i
971971 22.7639 0.730529 0.365265 0.930904i 0.380978π-0.380978\pi
0.365265 + 0.930904i 0.380978π0.380978\pi
972972 0 0
973973 − 1.88854i − 0.0605439i
974974 −16.2918 −0.522023
975975 0 0
976976 4.47214 0.143150
977977 26.9443i 0.862024i 0.902346 + 0.431012i 0.141843π0.141843\pi
−0.902346 + 0.431012i 0.858157π0.858157\pi
978978 0 0
979979 −24.9443 −0.797222
980980 12.2361i 0.390867i
981981 0 0
982982 − 12.2918i − 0.392247i
983983 − 11.4164i − 0.364127i −0.983287 0.182063i 0.941722π-0.941722\pi
0.983287 0.182063i 0.0582776π-0.0582776\pi
984984 0 0
985985 35.5279 1.13201
986986 4.00000 0.127386
987987 0 0
988988 − 33.8885i − 1.07814i
989989 48.7214 1.54925
990990 0 0
991991 −10.8328 −0.344116 −0.172058 0.985087i 0.555042π-0.555042\pi
−0.172058 + 0.985087i 0.555042π0.555042\pi
992992 2.47214i 0.0784904i
993993 0 0
994994 13.8885 0.440518
995995 − 20.0000i − 0.634043i
996996 0 0
997997 − 41.0557i − 1.30025i −0.759828 0.650124i 0.774717π-0.774717\pi
0.759828 0.650124i 0.225283π-0.225283\pi
998998 16.0000i 0.506471i
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 1530.2.d.f.919.3 4
3.2 odd 2 510.2.d.b.409.2 4
5.2 odd 4 7650.2.a.cx.1.1 2
5.3 odd 4 7650.2.a.da.1.2 2
5.4 even 2 inner 1530.2.d.f.919.2 4
12.11 even 2 4080.2.m.m.2449.4 4
15.2 even 4 2550.2.a.bk.1.1 2
15.8 even 4 2550.2.a.bh.1.2 2
15.14 odd 2 510.2.d.b.409.3 yes 4
60.59 even 2 4080.2.m.m.2449.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
510.2.d.b.409.2 4 3.2 odd 2
510.2.d.b.409.3 yes 4 15.14 odd 2
1530.2.d.f.919.2 4 5.4 even 2 inner
1530.2.d.f.919.3 4 1.1 even 1 trivial
2550.2.a.bh.1.2 2 15.8 even 4
2550.2.a.bk.1.1 2 15.2 even 4
4080.2.m.m.2449.1 4 60.59 even 2
4080.2.m.m.2449.4 4 12.11 even 2
7650.2.a.cx.1.1 2 5.2 odd 4
7650.2.a.da.1.2 2 5.3 odd 4