Properties

Label 1425.2.c.h.799.1
Level 14251425
Weight 22
Character 1425.799
Analytic conductor 11.37911.379
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1425,2,Mod(799,1425)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1425, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1425.799");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1425=35219 1425 = 3 \cdot 5^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1425.c (of order 22, degree 11, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 11.378682288011.3786822880
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 799.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 1425.799
Dual form 1425.2.c.h.799.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q1.00000iq2+1.00000iq3+1.00000q4+1.00000q63.00000iq81.00000q9+5.00000q11+1.00000iq124.00000iq131.00000q164.00000iq17+1.00000iq18+1.00000q195.00000iq22+9.00000iq23+3.00000q244.00000q261.00000iq277.00000q29+3.00000q315.00000iq32+5.00000iq334.00000q341.00000q3610.0000iq371.00000iq38+4.00000q392.00000q414.00000iq43+5.00000q44+9.00000q46+8.00000iq471.00000iq48+7.00000q49+4.00000q514.00000iq5211.0000iq531.00000q54+1.00000iq57+7.00000iq588.00000q59+13.0000q613.00000iq627.00000q64+5.00000q66+9.00000iq674.00000iq689.00000q69+10.0000q71+3.00000iq72+5.00000iq7310.0000q74+1.00000q764.00000iq78+15.0000q79+1.00000q81+2.00000iq829.00000iq834.00000q867.00000iq8715.0000iq883.00000q89+9.00000iq92+3.00000iq93+8.00000q94+5.00000q9610.0000iq977.00000iq985.00000q99+O(q100)q-1.00000i q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000 q^{6} -3.00000i q^{8} -1.00000 q^{9} +5.00000 q^{11} +1.00000i q^{12} -4.00000i q^{13} -1.00000 q^{16} -4.00000i q^{17} +1.00000i q^{18} +1.00000 q^{19} -5.00000i q^{22} +9.00000i q^{23} +3.00000 q^{24} -4.00000 q^{26} -1.00000i q^{27} -7.00000 q^{29} +3.00000 q^{31} -5.00000i q^{32} +5.00000i q^{33} -4.00000 q^{34} -1.00000 q^{36} -10.0000i q^{37} -1.00000i q^{38} +4.00000 q^{39} -2.00000 q^{41} -4.00000i q^{43} +5.00000 q^{44} +9.00000 q^{46} +8.00000i q^{47} -1.00000i q^{48} +7.00000 q^{49} +4.00000 q^{51} -4.00000i q^{52} -11.0000i q^{53} -1.00000 q^{54} +1.00000i q^{57} +7.00000i q^{58} -8.00000 q^{59} +13.0000 q^{61} -3.00000i q^{62} -7.00000 q^{64} +5.00000 q^{66} +9.00000i q^{67} -4.00000i q^{68} -9.00000 q^{69} +10.0000 q^{71} +3.00000i q^{72} +5.00000i q^{73} -10.0000 q^{74} +1.00000 q^{76} -4.00000i q^{78} +15.0000 q^{79} +1.00000 q^{81} +2.00000i q^{82} -9.00000i q^{83} -4.00000 q^{86} -7.00000i q^{87} -15.0000i q^{88} -3.00000 q^{89} +9.00000i q^{92} +3.00000i q^{93} +8.00000 q^{94} +5.00000 q^{96} -10.0000i q^{97} -7.00000i q^{98} -5.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q4+2q62q9+10q112q16+2q19+6q248q2614q29+6q318q342q36+8q394q41+10q44+18q46+14q49+8q51+10q99+O(q100) 2 q + 2 q^{4} + 2 q^{6} - 2 q^{9} + 10 q^{11} - 2 q^{16} + 2 q^{19} + 6 q^{24} - 8 q^{26} - 14 q^{29} + 6 q^{31} - 8 q^{34} - 2 q^{36} + 8 q^{39} - 4 q^{41} + 10 q^{44} + 18 q^{46} + 14 q^{49} + 8 q^{51}+ \cdots - 10 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1425Z)×\left(\mathbb{Z}/1425\mathbb{Z}\right)^\times.

nn 476476 10271027 13511351
χ(n)\chi(n) 11 1-1 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 −0.935414 0.353553i 0.884973π-0.884973\pi
0.935414 0.353553i 0.115027π-0.115027\pi
33 1.00000i 0.577350i
44 1.00000 0.500000
55 0 0
66 1.00000 0.408248
77 0 0 1.00000 00
−1.00000 π\pi
88 − 3.00000i − 1.06066i
99 −1.00000 −0.333333
1010 0 0
1111 5.00000 1.50756 0.753778 0.657129i 0.228229π-0.228229\pi
0.753778 + 0.657129i 0.228229π0.228229\pi
1212 1.00000i 0.288675i
1313 − 4.00000i − 1.10940i −0.832050 0.554700i 0.812833π-0.812833\pi
0.832050 0.554700i 0.187167π-0.187167\pi
1414 0 0
1515 0 0
1616 −1.00000 −0.250000
1717 − 4.00000i − 0.970143i −0.874475 0.485071i 0.838794π-0.838794\pi
0.874475 0.485071i 0.161206π-0.161206\pi
1818 1.00000i 0.235702i
1919 1.00000 0.229416
2020 0 0
2121 0 0
2222 − 5.00000i − 1.06600i
2323 9.00000i 1.87663i 0.345782 + 0.938315i 0.387614π0.387614\pi
−0.345782 + 0.938315i 0.612386π0.612386\pi
2424 3.00000 0.612372
2525 0 0
2626 −4.00000 −0.784465
2727 − 1.00000i − 0.192450i
2828 0 0
2929 −7.00000 −1.29987 −0.649934 0.759991i 0.725203π-0.725203\pi
−0.649934 + 0.759991i 0.725203π0.725203\pi
3030 0 0
3131 3.00000 0.538816 0.269408 0.963026i 0.413172π-0.413172\pi
0.269408 + 0.963026i 0.413172π0.413172\pi
3232 − 5.00000i − 0.883883i
3333 5.00000i 0.870388i
3434 −4.00000 −0.685994
3535 0 0
3636 −1.00000 −0.166667
3737 − 10.0000i − 1.64399i −0.569495 0.821995i 0.692861π-0.692861\pi
0.569495 0.821995i 0.307139π-0.307139\pi
3838 − 1.00000i − 0.162221i
3939 4.00000 0.640513
4040 0 0
4141 −2.00000 −0.312348 −0.156174 0.987730i 0.549916π-0.549916\pi
−0.156174 + 0.987730i 0.549916π0.549916\pi
4242 0 0
4343 − 4.00000i − 0.609994i −0.952353 0.304997i 0.901344π-0.901344\pi
0.952353 0.304997i 0.0986555π-0.0986555\pi
4444 5.00000 0.753778
4545 0 0
4646 9.00000 1.32698
4747 8.00000i 1.16692i 0.812142 + 0.583460i 0.198301π0.198301\pi
−0.812142 + 0.583460i 0.801699π0.801699\pi
4848 − 1.00000i − 0.144338i
4949 7.00000 1.00000
5050 0 0
5151 4.00000 0.560112
5252 − 4.00000i − 0.554700i
5353 − 11.0000i − 1.51097i −0.655168 0.755483i 0.727402π-0.727402\pi
0.655168 0.755483i 0.272598π-0.272598\pi
5454 −1.00000 −0.136083
5555 0 0
5656 0 0
5757 1.00000i 0.132453i
5858 7.00000i 0.919145i
5959 −8.00000 −1.04151 −0.520756 0.853706i 0.674350π-0.674350\pi
−0.520756 + 0.853706i 0.674350π0.674350\pi
6060 0 0
6161 13.0000 1.66448 0.832240 0.554416i 0.187058π-0.187058\pi
0.832240 + 0.554416i 0.187058π0.187058\pi
6262 − 3.00000i − 0.381000i
6363 0 0
6464 −7.00000 −0.875000
6565 0 0
6666 5.00000 0.615457
6767 9.00000i 1.09952i 0.835321 + 0.549762i 0.185282π0.185282\pi
−0.835321 + 0.549762i 0.814718π0.814718\pi
6868 − 4.00000i − 0.485071i
6969 −9.00000 −1.08347
7070 0 0
7171 10.0000 1.18678 0.593391 0.804914i 0.297789π-0.297789\pi
0.593391 + 0.804914i 0.297789π0.297789\pi
7272 3.00000i 0.353553i
7373 5.00000i 0.585206i 0.956234 + 0.292603i 0.0945214π0.0945214\pi
−0.956234 + 0.292603i 0.905479π0.905479\pi
7474 −10.0000 −1.16248
7575 0 0
7676 1.00000 0.114708
7777 0 0
7878 − 4.00000i − 0.452911i
7979 15.0000 1.68763 0.843816 0.536633i 0.180304π-0.180304\pi
0.843816 + 0.536633i 0.180304π0.180304\pi
8080 0 0
8181 1.00000 0.111111
8282 2.00000i 0.220863i
8383 − 9.00000i − 0.987878i −0.869496 0.493939i 0.835557π-0.835557\pi
0.869496 0.493939i 0.164443π-0.164443\pi
8484 0 0
8585 0 0
8686 −4.00000 −0.431331
8787 − 7.00000i − 0.750479i
8888 − 15.0000i − 1.59901i
8989 −3.00000 −0.317999 −0.159000 0.987279i 0.550827π-0.550827\pi
−0.159000 + 0.987279i 0.550827π0.550827\pi
9090 0 0
9191 0 0
9292 9.00000i 0.938315i
9393 3.00000i 0.311086i
9494 8.00000 0.825137
9595 0 0
9696 5.00000 0.510310
9797 − 10.0000i − 1.01535i −0.861550 0.507673i 0.830506π-0.830506\pi
0.861550 0.507673i 0.169494π-0.169494\pi
9898 − 7.00000i − 0.707107i
9999 −5.00000 −0.502519
100100 0 0
101101 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
102102 − 4.00000i − 0.396059i
103103 13.0000i 1.28093i 0.767988 + 0.640464i 0.221258π0.221258\pi
−0.767988 + 0.640464i 0.778742π0.778742\pi
104104 −12.0000 −1.17670
105105 0 0
106106 −11.0000 −1.06841
107107 6.00000i 0.580042i 0.957020 + 0.290021i 0.0936623π0.0936623\pi
−0.957020 + 0.290021i 0.906338π0.906338\pi
108108 − 1.00000i − 0.0962250i
109109 10.0000 0.957826 0.478913 0.877862i 0.341031π-0.341031\pi
0.478913 + 0.877862i 0.341031π0.341031\pi
110110 0 0
111111 10.0000 0.949158
112112 0 0
113113 1.00000i 0.0940721i 0.998893 + 0.0470360i 0.0149776π0.0149776\pi
−0.998893 + 0.0470360i 0.985022π0.985022\pi
114114 1.00000 0.0936586
115115 0 0
116116 −7.00000 −0.649934
117117 4.00000i 0.369800i
118118 8.00000i 0.736460i
119119 0 0
120120 0 0
121121 14.0000 1.27273
122122 − 13.0000i − 1.17696i
123123 − 2.00000i − 0.180334i
124124 3.00000 0.269408
125125 0 0
126126 0 0
127127 13.0000i 1.15356i 0.816898 + 0.576782i 0.195692π0.195692\pi
−0.816898 + 0.576782i 0.804308π0.804308\pi
128128 − 3.00000i − 0.265165i
129129 4.00000 0.352180
130130 0 0
131131 3.00000 0.262111 0.131056 0.991375i 0.458163π-0.458163\pi
0.131056 + 0.991375i 0.458163π0.458163\pi
132132 5.00000i 0.435194i
133133 0 0
134134 9.00000 0.777482
135135 0 0
136136 −12.0000 −1.02899
137137 12.0000i 1.02523i 0.858619 + 0.512615i 0.171323π0.171323\pi
−0.858619 + 0.512615i 0.828677π0.828677\pi
138138 9.00000i 0.766131i
139139 −14.0000 −1.18746 −0.593732 0.804663i 0.702346π-0.702346\pi
−0.593732 + 0.804663i 0.702346π0.702346\pi
140140 0 0
141141 −8.00000 −0.673722
142142 − 10.0000i − 0.839181i
143143 − 20.0000i − 1.67248i
144144 1.00000 0.0833333
145145 0 0
146146 5.00000 0.413803
147147 7.00000i 0.577350i
148148 − 10.0000i − 0.821995i
149149 −16.0000 −1.31077 −0.655386 0.755295i 0.727494π-0.727494\pi
−0.655386 + 0.755295i 0.727494π0.727494\pi
150150 0 0
151151 −8.00000 −0.651031 −0.325515 0.945537i 0.605538π-0.605538\pi
−0.325515 + 0.945537i 0.605538π0.605538\pi
152152 − 3.00000i − 0.243332i
153153 4.00000i 0.323381i
154154 0 0
155155 0 0
156156 4.00000 0.320256
157157 2.00000i 0.159617i 0.996810 + 0.0798087i 0.0254309π0.0254309\pi
−0.996810 + 0.0798087i 0.974569π0.974569\pi
158158 − 15.0000i − 1.19334i
159159 11.0000 0.872357
160160 0 0
161161 0 0
162162 − 1.00000i − 0.0785674i
163163 − 14.0000i − 1.09656i −0.836293 0.548282i 0.815282π-0.815282\pi
0.836293 0.548282i 0.184718π-0.184718\pi
164164 −2.00000 −0.156174
165165 0 0
166166 −9.00000 −0.698535
167167 6.00000i 0.464294i 0.972681 + 0.232147i 0.0745750π0.0745750\pi
−0.972681 + 0.232147i 0.925425π0.925425\pi
168168 0 0
169169 −3.00000 −0.230769
170170 0 0
171171 −1.00000 −0.0764719
172172 − 4.00000i − 0.304997i
173173 3.00000i 0.228086i 0.993476 + 0.114043i 0.0363801π0.0363801\pi
−0.993476 + 0.114043i 0.963620π0.963620\pi
174174 −7.00000 −0.530669
175175 0 0
176176 −5.00000 −0.376889
177177 − 8.00000i − 0.601317i
178178 3.00000i 0.224860i
179179 4.00000 0.298974 0.149487 0.988764i 0.452238π-0.452238\pi
0.149487 + 0.988764i 0.452238π0.452238\pi
180180 0 0
181181 −16.0000 −1.18927 −0.594635 0.803996i 0.702704π-0.702704\pi
−0.594635 + 0.803996i 0.702704π0.702704\pi
182182 0 0
183183 13.0000i 0.960988i
184184 27.0000 1.99047
185185 0 0
186186 3.00000 0.219971
187187 − 20.0000i − 1.46254i
188188 8.00000i 0.583460i
189189 0 0
190190 0 0
191191 −17.0000 −1.23008 −0.615038 0.788497i 0.710860π-0.710860\pi
−0.615038 + 0.788497i 0.710860π0.710860\pi
192192 − 7.00000i − 0.505181i
193193 − 14.0000i − 1.00774i −0.863779 0.503871i 0.831909π-0.831909\pi
0.863779 0.503871i 0.168091π-0.168091\pi
194194 −10.0000 −0.717958
195195 0 0
196196 7.00000 0.500000
197197 12.0000i 0.854965i 0.904024 + 0.427482i 0.140599π0.140599\pi
−0.904024 + 0.427482i 0.859401π0.859401\pi
198198 5.00000i 0.355335i
199199 −22.0000 −1.55954 −0.779769 0.626067i 0.784664π-0.784664\pi
−0.779769 + 0.626067i 0.784664π0.784664\pi
200200 0 0
201201 −9.00000 −0.634811
202202 0 0
203203 0 0
204204 4.00000 0.280056
205205 0 0
206206 13.0000 0.905753
207207 − 9.00000i − 0.625543i
208208 4.00000i 0.277350i
209209 5.00000 0.345857
210210 0 0
211211 11.0000 0.757271 0.378636 0.925546i 0.376393π-0.376393\pi
0.378636 + 0.925546i 0.376393π0.376393\pi
212212 − 11.0000i − 0.755483i
213213 10.0000i 0.685189i
214214 6.00000 0.410152
215215 0 0
216216 −3.00000 −0.204124
217217 0 0
218218 − 10.0000i − 0.677285i
219219 −5.00000 −0.337869
220220 0 0
221221 −16.0000 −1.07628
222222 − 10.0000i − 0.671156i
223223 1.00000i 0.0669650i 0.999439 + 0.0334825i 0.0106598π0.0106598\pi
−0.999439 + 0.0334825i 0.989340π0.989340\pi
224224 0 0
225225 0 0
226226 1.00000 0.0665190
227227 22.0000i 1.46019i 0.683345 + 0.730096i 0.260525π0.260525\pi
−0.683345 + 0.730096i 0.739475π0.739475\pi
228228 1.00000i 0.0662266i
229229 −21.0000 −1.38772 −0.693860 0.720110i 0.744091π-0.744091\pi
−0.693860 + 0.720110i 0.744091π0.744091\pi
230230 0 0
231231 0 0
232232 21.0000i 1.37872i
233233 0 0 1.00000 00
−1.00000 π\pi
234234 4.00000 0.261488
235235 0 0
236236 −8.00000 −0.520756
237237 15.0000i 0.974355i
238238 0 0
239239 −8.00000 −0.517477 −0.258738 0.965947i 0.583307π-0.583307\pi
−0.258738 + 0.965947i 0.583307π0.583307\pi
240240 0 0
241241 4.00000 0.257663 0.128831 0.991667i 0.458877π-0.458877\pi
0.128831 + 0.991667i 0.458877π0.458877\pi
242242 − 14.0000i − 0.899954i
243243 1.00000i 0.0641500i
244244 13.0000 0.832240
245245 0 0
246246 −2.00000 −0.127515
247247 − 4.00000i − 0.254514i
248248 − 9.00000i − 0.571501i
249249 9.00000 0.570352
250250 0 0
251251 −24.0000 −1.51487 −0.757433 0.652913i 0.773547π-0.773547\pi
−0.757433 + 0.652913i 0.773547π0.773547\pi
252252 0 0
253253 45.0000i 2.82913i
254254 13.0000 0.815693
255255 0 0
256256 −17.0000 −1.06250
257257 21.0000i 1.30994i 0.755653 + 0.654972i 0.227320π0.227320\pi
−0.755653 + 0.654972i 0.772680π0.772680\pi
258258 − 4.00000i − 0.249029i
259259 0 0
260260 0 0
261261 7.00000 0.433289
262262 − 3.00000i − 0.185341i
263263 17.0000i 1.04826i 0.851637 + 0.524132i 0.175610π0.175610\pi
−0.851637 + 0.524132i 0.824390π0.824390\pi
264264 15.0000 0.923186
265265 0 0
266266 0 0
267267 − 3.00000i − 0.183597i
268268 9.00000i 0.549762i
269269 −14.0000 −0.853595 −0.426798 0.904347i 0.640358π-0.640358\pi
−0.426798 + 0.904347i 0.640358π0.640358\pi
270270 0 0
271271 10.0000 0.607457 0.303728 0.952759i 0.401768π-0.401768\pi
0.303728 + 0.952759i 0.401768π0.401768\pi
272272 4.00000i 0.242536i
273273 0 0
274274 12.0000 0.724947
275275 0 0
276276 −9.00000 −0.541736
277277 33.0000i 1.98278i 0.130950 + 0.991389i 0.458197π0.458197\pi
−0.130950 + 0.991389i 0.541803π0.541803\pi
278278 14.0000i 0.839664i
279279 −3.00000 −0.179605
280280 0 0
281281 −15.0000 −0.894825 −0.447412 0.894328i 0.647654π-0.647654\pi
−0.447412 + 0.894328i 0.647654π0.647654\pi
282282 8.00000i 0.476393i
283283 0 0 1.00000 00
−1.00000 π\pi
284284 10.0000 0.593391
285285 0 0
286286 −20.0000 −1.18262
287287 0 0
288288 5.00000i 0.294628i
289289 1.00000 0.0588235
290290 0 0
291291 10.0000 0.586210
292292 5.00000i 0.292603i
293293 − 9.00000i − 0.525786i −0.964825 0.262893i 0.915323π-0.915323\pi
0.964825 0.262893i 0.0846766π-0.0846766\pi
294294 7.00000 0.408248
295295 0 0
296296 −30.0000 −1.74371
297297 − 5.00000i − 0.290129i
298298 16.0000i 0.926855i
299299 36.0000 2.08193
300300 0 0
301301 0 0
302302 8.00000i 0.460348i
303303 0 0
304304 −1.00000 −0.0573539
305305 0 0
306306 4.00000 0.228665
307307 − 23.0000i − 1.31268i −0.754466 0.656340i 0.772104π-0.772104\pi
0.754466 0.656340i 0.227896π-0.227896\pi
308308 0 0
309309 −13.0000 −0.739544
310310 0 0
311311 24.0000 1.36092 0.680458 0.732787i 0.261781π-0.261781\pi
0.680458 + 0.732787i 0.261781π0.261781\pi
312312 − 12.0000i − 0.679366i
313313 13.0000i 0.734803i 0.930062 + 0.367402i 0.119753π0.119753\pi
−0.930062 + 0.367402i 0.880247π0.880247\pi
314314 2.00000 0.112867
315315 0 0
316316 15.0000 0.843816
317317 1.00000i 0.0561656i 0.999606 + 0.0280828i 0.00894021π0.00894021\pi
−0.999606 + 0.0280828i 0.991060π0.991060\pi
318318 − 11.0000i − 0.616849i
319319 −35.0000 −1.95962
320320 0 0
321321 −6.00000 −0.334887
322322 0 0
323323 − 4.00000i − 0.222566i
324324 1.00000 0.0555556
325325 0 0
326326 −14.0000 −0.775388
327327 10.0000i 0.553001i
328328 6.00000i 0.331295i
329329 0 0
330330 0 0
331331 −3.00000 −0.164895 −0.0824475 0.996595i 0.526274π-0.526274\pi
−0.0824475 + 0.996595i 0.526274π0.526274\pi
332332 − 9.00000i − 0.493939i
333333 10.0000i 0.547997i
334334 6.00000 0.328305
335335 0 0
336336 0 0
337337 − 8.00000i − 0.435788i −0.975972 0.217894i 0.930081π-0.930081\pi
0.975972 0.217894i 0.0699187π-0.0699187\pi
338338 3.00000i 0.163178i
339339 −1.00000 −0.0543125
340340 0 0
341341 15.0000 0.812296
342342 1.00000i 0.0540738i
343343 0 0
344344 −12.0000 −0.646997
345345 0 0
346346 3.00000 0.161281
347347 20.0000i 1.07366i 0.843692 + 0.536828i 0.180378π0.180378\pi
−0.843692 + 0.536828i 0.819622π0.819622\pi
348348 − 7.00000i − 0.375239i
349349 17.0000 0.909989 0.454995 0.890494i 0.349641π-0.349641\pi
0.454995 + 0.890494i 0.349641π0.349641\pi
350350 0 0
351351 −4.00000 −0.213504
352352 − 25.0000i − 1.33250i
353353 − 12.0000i − 0.638696i −0.947638 0.319348i 0.896536π-0.896536\pi
0.947638 0.319348i 0.103464π-0.103464\pi
354354 −8.00000 −0.425195
355355 0 0
356356 −3.00000 −0.159000
357357 0 0
358358 − 4.00000i − 0.211407i
359359 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
360360 0 0
361361 1.00000 0.0526316
362362 16.0000i 0.840941i
363363 14.0000i 0.734809i
364364 0 0
365365 0 0
366366 13.0000 0.679521
367367 18.0000i 0.939592i 0.882775 + 0.469796i 0.155673π0.155673\pi
−0.882775 + 0.469796i 0.844327π0.844327\pi
368368 − 9.00000i − 0.469157i
369369 2.00000 0.104116
370370 0 0
371371 0 0
372372 3.00000i 0.155543i
373373 20.0000i 1.03556i 0.855514 + 0.517780i 0.173242π0.173242\pi
−0.855514 + 0.517780i 0.826758π0.826758\pi
374374 −20.0000 −1.03418
375375 0 0
376376 24.0000 1.23771
377377 28.0000i 1.44207i
378378 0 0
379379 8.00000 0.410932 0.205466 0.978664i 0.434129π-0.434129\pi
0.205466 + 0.978664i 0.434129π0.434129\pi
380380 0 0
381381 −13.0000 −0.666010
382382 17.0000i 0.869796i
383383 18.0000i 0.919757i 0.887982 + 0.459879i 0.152107π0.152107\pi
−0.887982 + 0.459879i 0.847893π0.847893\pi
384384 3.00000 0.153093
385385 0 0
386386 −14.0000 −0.712581
387387 4.00000i 0.203331i
388388 − 10.0000i − 0.507673i
389389 30.0000 1.52106 0.760530 0.649303i 0.224939π-0.224939\pi
0.760530 + 0.649303i 0.224939π0.224939\pi
390390 0 0
391391 36.0000 1.82060
392392 − 21.0000i − 1.06066i
393393 3.00000i 0.151330i
394394 12.0000 0.604551
395395 0 0
396396 −5.00000 −0.251259
397397 − 29.0000i − 1.45547i −0.685859 0.727734i 0.740573π-0.740573\pi
0.685859 0.727734i 0.259427π-0.259427\pi
398398 22.0000i 1.10276i
399399 0 0
400400 0 0
401401 3.00000 0.149813 0.0749064 0.997191i 0.476134π-0.476134\pi
0.0749064 + 0.997191i 0.476134π0.476134\pi
402402 9.00000i 0.448879i
403403 − 12.0000i − 0.597763i
404404 0 0
405405 0 0
406406 0 0
407407 − 50.0000i − 2.47841i
408408 − 12.0000i − 0.594089i
409409 34.0000 1.68119 0.840596 0.541663i 0.182205π-0.182205\pi
0.840596 + 0.541663i 0.182205π0.182205\pi
410410 0 0
411411 −12.0000 −0.591916
412412 13.0000i 0.640464i
413413 0 0
414414 −9.00000 −0.442326
415415 0 0
416416 −20.0000 −0.980581
417417 − 14.0000i − 0.685583i
418418 − 5.00000i − 0.244558i
419419 −28.0000 −1.36789 −0.683945 0.729534i 0.739737π-0.739737\pi
−0.683945 + 0.729534i 0.739737π0.739737\pi
420420 0 0
421421 −26.0000 −1.26716 −0.633581 0.773676i 0.718416π-0.718416\pi
−0.633581 + 0.773676i 0.718416π0.718416\pi
422422 − 11.0000i − 0.535472i
423423 − 8.00000i − 0.388973i
424424 −33.0000 −1.60262
425425 0 0
426426 10.0000 0.484502
427427 0 0
428428 6.00000i 0.290021i
429429 20.0000 0.965609
430430 0 0
431431 6.00000 0.289010 0.144505 0.989504i 0.453841π-0.453841\pi
0.144505 + 0.989504i 0.453841π0.453841\pi
432432 1.00000i 0.0481125i
433433 26.0000i 1.24948i 0.780833 + 0.624740i 0.214795π0.214795\pi
−0.780833 + 0.624740i 0.785205π0.785205\pi
434434 0 0
435435 0 0
436436 10.0000 0.478913
437437 9.00000i 0.430528i
438438 5.00000i 0.238909i
439439 −37.0000 −1.76591 −0.882957 0.469454i 0.844451π-0.844451\pi
−0.882957 + 0.469454i 0.844451π0.844451\pi
440440 0 0
441441 −7.00000 −0.333333
442442 16.0000i 0.761042i
443443 15.0000i 0.712672i 0.934358 + 0.356336i 0.115974π0.115974\pi
−0.934358 + 0.356336i 0.884026π0.884026\pi
444444 10.0000 0.474579
445445 0 0
446446 1.00000 0.0473514
447447 − 16.0000i − 0.756774i
448448 0 0
449449 7.00000 0.330350 0.165175 0.986264i 0.447181π-0.447181\pi
0.165175 + 0.986264i 0.447181π0.447181\pi
450450 0 0
451451 −10.0000 −0.470882
452452 1.00000i 0.0470360i
453453 − 8.00000i − 0.375873i
454454 22.0000 1.03251
455455 0 0
456456 3.00000 0.140488
457457 − 14.0000i − 0.654892i −0.944870 0.327446i 0.893812π-0.893812\pi
0.944870 0.327446i 0.106188π-0.106188\pi
458458 21.0000i 0.981266i
459459 −4.00000 −0.186704
460460 0 0
461461 12.0000 0.558896 0.279448 0.960161i 0.409849π-0.409849\pi
0.279448 + 0.960161i 0.409849π0.409849\pi
462462 0 0
463463 12.0000i 0.557687i 0.960337 + 0.278844i 0.0899511π0.0899511\pi
−0.960337 + 0.278844i 0.910049π0.910049\pi
464464 7.00000 0.324967
465465 0 0
466466 0 0
467467 7.00000i 0.323921i 0.986797 + 0.161961i 0.0517818π0.0517818\pi
−0.986797 + 0.161961i 0.948218π0.948218\pi
468468 4.00000i 0.184900i
469469 0 0
470470 0 0
471471 −2.00000 −0.0921551
472472 24.0000i 1.10469i
473473 − 20.0000i − 0.919601i
474474 15.0000 0.688973
475475 0 0
476476 0 0
477477 11.0000i 0.503655i
478478 8.00000i 0.365911i
479479 −15.0000 −0.685367 −0.342684 0.939451i 0.611336π-0.611336\pi
−0.342684 + 0.939451i 0.611336π0.611336\pi
480480 0 0
481481 −40.0000 −1.82384
482482 − 4.00000i − 0.182195i
483483 0 0
484484 14.0000 0.636364
485485 0 0
486486 1.00000 0.0453609
487487 8.00000i 0.362515i 0.983436 + 0.181257i 0.0580167π0.0580167\pi
−0.983436 + 0.181257i 0.941983π0.941983\pi
488488 − 39.0000i − 1.76545i
489489 14.0000 0.633102
490490 0 0
491491 28.0000 1.26362 0.631811 0.775122i 0.282312π-0.282312\pi
0.631811 + 0.775122i 0.282312π0.282312\pi
492492 − 2.00000i − 0.0901670i
493493 28.0000i 1.26106i
494494 −4.00000 −0.179969
495495 0 0
496496 −3.00000 −0.134704
497497 0 0
498498 − 9.00000i − 0.403300i
499499 32.0000 1.43252 0.716258 0.697835i 0.245853π-0.245853\pi
0.716258 + 0.697835i 0.245853π0.245853\pi
500500 0 0
501501 −6.00000 −0.268060
502502 24.0000i 1.07117i
503503 − 28.0000i − 1.24846i −0.781241 0.624229i 0.785413π-0.785413\pi
0.781241 0.624229i 0.214587π-0.214587\pi
504504 0 0
505505 0 0
506506 45.0000 2.00049
507507 − 3.00000i − 0.133235i
508508 13.0000i 0.576782i
509509 7.00000 0.310270 0.155135 0.987893i 0.450419π-0.450419\pi
0.155135 + 0.987893i 0.450419π0.450419\pi
510510 0 0
511511 0 0
512512 11.0000i 0.486136i
513513 − 1.00000i − 0.0441511i
514514 21.0000 0.926270
515515 0 0
516516 4.00000 0.176090
517517 40.0000i 1.75920i
518518 0 0
519519 −3.00000 −0.131685
520520 0 0
521521 −41.0000 −1.79624 −0.898121 0.439748i 0.855068π-0.855068\pi
−0.898121 + 0.439748i 0.855068π0.855068\pi
522522 − 7.00000i − 0.306382i
523523 − 28.0000i − 1.22435i −0.790721 0.612177i 0.790294π-0.790294\pi
0.790721 0.612177i 0.209706π-0.209706\pi
524524 3.00000 0.131056
525525 0 0
526526 17.0000 0.741235
527527 − 12.0000i − 0.522728i
528528 − 5.00000i − 0.217597i
529529 −58.0000 −2.52174
530530 0 0
531531 8.00000 0.347170
532532 0 0
533533 8.00000i 0.346518i
534534 −3.00000 −0.129823
535535 0 0
536536 27.0000 1.16622
537537 4.00000i 0.172613i
538538 14.0000i 0.603583i
539539 35.0000 1.50756
540540 0 0
541541 −21.0000 −0.902861 −0.451430 0.892306i 0.649086π-0.649086\pi
−0.451430 + 0.892306i 0.649086π0.649086\pi
542542 − 10.0000i − 0.429537i
543543 − 16.0000i − 0.686626i
544544 −20.0000 −0.857493
545545 0 0
546546 0 0
547547 31.0000i 1.32546i 0.748857 + 0.662732i 0.230603π0.230603\pi
−0.748857 + 0.662732i 0.769397π0.769397\pi
548548 12.0000i 0.512615i
549549 −13.0000 −0.554826
550550 0 0
551551 −7.00000 −0.298210
552552 27.0000i 1.14920i
553553 0 0
554554 33.0000 1.40204
555555 0 0
556556 −14.0000 −0.593732
557557 0 0 1.00000 00
−1.00000 π\pi
558558 3.00000i 0.127000i
559559 −16.0000 −0.676728
560560 0 0
561561 20.0000 0.844401
562562 15.0000i 0.632737i
563563 − 30.0000i − 1.26435i −0.774826 0.632175i 0.782163π-0.782163\pi
0.774826 0.632175i 0.217837π-0.217837\pi
564564 −8.00000 −0.336861
565565 0 0
566566 0 0
567567 0 0
568568 − 30.0000i − 1.25877i
569569 −6.00000 −0.251533 −0.125767 0.992060i 0.540139π-0.540139\pi
−0.125767 + 0.992060i 0.540139π0.540139\pi
570570 0 0
571571 14.0000 0.585882 0.292941 0.956131i 0.405366π-0.405366\pi
0.292941 + 0.956131i 0.405366π0.405366\pi
572572 − 20.0000i − 0.836242i
573573 − 17.0000i − 0.710185i
574574 0 0
575575 0 0
576576 7.00000 0.291667
577577 − 13.0000i − 0.541197i −0.962692 0.270599i 0.912778π-0.912778\pi
0.962692 0.270599i 0.0872216π-0.0872216\pi
578578 − 1.00000i − 0.0415945i
579579 14.0000 0.581820
580580 0 0
581581 0 0
582582 − 10.0000i − 0.414513i
583583 − 55.0000i − 2.27787i
584584 15.0000 0.620704
585585 0 0
586586 −9.00000 −0.371787
587587 − 3.00000i − 0.123823i −0.998082 0.0619116i 0.980280π-0.980280\pi
0.998082 0.0619116i 0.0197197π-0.0197197\pi
588588 7.00000i 0.288675i
589589 3.00000 0.123613
590590 0 0
591591 −12.0000 −0.493614
592592 10.0000i 0.410997i
593593 20.0000i 0.821302i 0.911793 + 0.410651i 0.134698π0.134698\pi
−0.911793 + 0.410651i 0.865302π0.865302\pi
594594 −5.00000 −0.205152
595595 0 0
596596 −16.0000 −0.655386
597597 − 22.0000i − 0.900400i
598598 − 36.0000i − 1.47215i
599599 44.0000 1.79779 0.898896 0.438163i 0.144371π-0.144371\pi
0.898896 + 0.438163i 0.144371π0.144371\pi
600600 0 0
601601 −10.0000 −0.407909 −0.203954 0.978980i 0.565379π-0.565379\pi
−0.203954 + 0.978980i 0.565379π0.565379\pi
602602 0 0
603603 − 9.00000i − 0.366508i
604604 −8.00000 −0.325515
605605 0 0
606606 0 0
607607 1.00000i 0.0405887i 0.999794 + 0.0202944i 0.00646034π0.00646034\pi
−0.999794 + 0.0202944i 0.993540π0.993540\pi
608608 − 5.00000i − 0.202777i
609609 0 0
610610 0 0
611611 32.0000 1.29458
612612 4.00000i 0.161690i
613613 26.0000i 1.05013i 0.851062 + 0.525065i 0.175959π0.175959\pi
−0.851062 + 0.525065i 0.824041π0.824041\pi
614614 −23.0000 −0.928204
615615 0 0
616616 0 0
617617 − 42.0000i − 1.69086i −0.534089 0.845428i 0.679345π-0.679345\pi
0.534089 0.845428i 0.320655π-0.320655\pi
618618 13.0000i 0.522937i
619619 −32.0000 −1.28619 −0.643094 0.765787i 0.722350π-0.722350\pi
−0.643094 + 0.765787i 0.722350π0.722350\pi
620620 0 0
621621 9.00000 0.361158
622622 − 24.0000i − 0.962312i
623623 0 0
624624 −4.00000 −0.160128
625625 0 0
626626 13.0000 0.519584
627627 5.00000i 0.199681i
628628 2.00000i 0.0798087i
629629 −40.0000 −1.59490
630630 0 0
631631 28.0000 1.11466 0.557331 0.830290i 0.311825π-0.311825\pi
0.557331 + 0.830290i 0.311825π0.311825\pi
632632 − 45.0000i − 1.79000i
633633 11.0000i 0.437211i
634634 1.00000 0.0397151
635635 0 0
636636 11.0000 0.436178
637637 − 28.0000i − 1.10940i
638638 35.0000i 1.38566i
639639 −10.0000 −0.395594
640640 0 0
641641 −42.0000 −1.65890 −0.829450 0.558581i 0.811346π-0.811346\pi
−0.829450 + 0.558581i 0.811346π0.811346\pi
642642 6.00000i 0.236801i
643643 − 30.0000i − 1.18308i −0.806274 0.591542i 0.798519π-0.798519\pi
0.806274 0.591542i 0.201481π-0.201481\pi
644644 0 0
645645 0 0
646646 −4.00000 −0.157378
647647 − 31.0000i − 1.21874i −0.792888 0.609368i 0.791423π-0.791423\pi
0.792888 0.609368i 0.208577π-0.208577\pi
648648 − 3.00000i − 0.117851i
649649 −40.0000 −1.57014
650650 0 0
651651 0 0
652652 − 14.0000i − 0.548282i
653653 − 16.0000i − 0.626128i −0.949732 0.313064i 0.898644π-0.898644\pi
0.949732 0.313064i 0.101356π-0.101356\pi
654654 10.0000 0.391031
655655 0 0
656656 2.00000 0.0780869
657657 − 5.00000i − 0.195069i
658658 0 0
659659 4.00000 0.155818 0.0779089 0.996960i 0.475176π-0.475176\pi
0.0779089 + 0.996960i 0.475176π0.475176\pi
660660 0 0
661661 16.0000 0.622328 0.311164 0.950356i 0.399281π-0.399281\pi
0.311164 + 0.950356i 0.399281π0.399281\pi
662662 3.00000i 0.116598i
663663 − 16.0000i − 0.621389i
664664 −27.0000 −1.04780
665665 0 0
666666 10.0000 0.387492
667667 − 63.0000i − 2.43937i
668668 6.00000i 0.232147i
669669 −1.00000 −0.0386622
670670 0 0
671671 65.0000 2.50930
672672 0 0
673673 − 36.0000i − 1.38770i −0.720121 0.693849i 0.755914π-0.755914\pi
0.720121 0.693849i 0.244086π-0.244086\pi
674674 −8.00000 −0.308148
675675 0 0
676676 −3.00000 −0.115385
677677 27.0000i 1.03769i 0.854867 + 0.518847i 0.173639π0.173639\pi
−0.854867 + 0.518847i 0.826361π0.826361\pi
678678 1.00000i 0.0384048i
679679 0 0
680680 0 0
681681 −22.0000 −0.843042
682682 − 15.0000i − 0.574380i
683683 6.00000i 0.229584i 0.993390 + 0.114792i 0.0366201π0.0366201\pi
−0.993390 + 0.114792i 0.963380π0.963380\pi
684684 −1.00000 −0.0382360
685685 0 0
686686 0 0
687687 − 21.0000i − 0.801200i
688688 4.00000i 0.152499i
689689 −44.0000 −1.67627
690690 0 0
691691 10.0000 0.380418 0.190209 0.981744i 0.439083π-0.439083\pi
0.190209 + 0.981744i 0.439083π0.439083\pi
692692 3.00000i 0.114043i
693693 0 0
694694 20.0000 0.759190
695695 0 0
696696 −21.0000 −0.796003
697697 8.00000i 0.303022i
698698 − 17.0000i − 0.643459i
699699 0 0
700700 0 0
701701 −8.00000 −0.302156 −0.151078 0.988522i 0.548274π-0.548274\pi
−0.151078 + 0.988522i 0.548274π0.548274\pi
702702 4.00000i 0.150970i
703703 − 10.0000i − 0.377157i
704704 −35.0000 −1.31911
705705 0 0
706706 −12.0000 −0.451626
707707 0 0
708708 − 8.00000i − 0.300658i
709709 −13.0000 −0.488225 −0.244113 0.969747i 0.578497π-0.578497\pi
−0.244113 + 0.969747i 0.578497π0.578497\pi
710710 0 0
711711 −15.0000 −0.562544
712712 9.00000i 0.337289i
713713 27.0000i 1.01116i
714714 0 0
715715 0 0
716716 4.00000 0.149487
717717 − 8.00000i − 0.298765i
718718 0 0
719719 −15.0000 −0.559406 −0.279703 0.960087i 0.590236π-0.590236\pi
−0.279703 + 0.960087i 0.590236π0.590236\pi
720720 0 0
721721 0 0
722722 − 1.00000i − 0.0372161i
723723 4.00000i 0.148762i
724724 −16.0000 −0.594635
725725 0 0
726726 14.0000 0.519589
727727 2.00000i 0.0741759i 0.999312 + 0.0370879i 0.0118082π0.0118082\pi
−0.999312 + 0.0370879i 0.988192π0.988192\pi
728728 0 0
729729 −1.00000 −0.0370370
730730 0 0
731731 −16.0000 −0.591781
732732 13.0000i 0.480494i
733733 1.00000i 0.0369358i 0.999829 + 0.0184679i 0.00587886π0.00587886\pi
−0.999829 + 0.0184679i 0.994121π0.994121\pi
734734 18.0000 0.664392
735735 0 0
736736 45.0000 1.65872
737737 45.0000i 1.65760i
738738 − 2.00000i − 0.0736210i
739739 −4.00000 −0.147142 −0.0735712 0.997290i 0.523440π-0.523440\pi
−0.0735712 + 0.997290i 0.523440π0.523440\pi
740740 0 0
741741 4.00000 0.146944
742742 0 0
743743 40.0000i 1.46746i 0.679442 + 0.733729i 0.262222π0.262222\pi
−0.679442 + 0.733729i 0.737778π0.737778\pi
744744 9.00000 0.329956
745745 0 0
746746 20.0000 0.732252
747747 9.00000i 0.329293i
748748 − 20.0000i − 0.731272i
749749 0 0
750750 0 0
751751 16.0000 0.583848 0.291924 0.956441i 0.405705π-0.405705\pi
0.291924 + 0.956441i 0.405705π0.405705\pi
752752 − 8.00000i − 0.291730i
753753 − 24.0000i − 0.874609i
754754 28.0000 1.01970
755755 0 0
756756 0 0
757757 7.00000i 0.254419i 0.991876 + 0.127210i 0.0406021π0.0406021\pi
−0.991876 + 0.127210i 0.959398π0.959398\pi
758758 − 8.00000i − 0.290573i
759759 −45.0000 −1.63340
760760 0 0
761761 −30.0000 −1.08750 −0.543750 0.839248i 0.682996π-0.682996\pi
−0.543750 + 0.839248i 0.682996π0.682996\pi
762762 13.0000i 0.470940i
763763 0 0
764764 −17.0000 −0.615038
765765 0 0
766766 18.0000 0.650366
767767 32.0000i 1.15545i
768768 − 17.0000i − 0.613435i
769769 37.0000 1.33425 0.667127 0.744944i 0.267524π-0.267524\pi
0.667127 + 0.744944i 0.267524π0.267524\pi
770770 0 0
771771 −21.0000 −0.756297
772772 − 14.0000i − 0.503871i
773773 18.0000i 0.647415i 0.946157 + 0.323708i 0.104929π0.104929\pi
−0.946157 + 0.323708i 0.895071π0.895071\pi
774774 4.00000 0.143777
775775 0 0
776776 −30.0000 −1.07694
777777 0 0
778778 − 30.0000i − 1.07555i
779779 −2.00000 −0.0716574
780780 0 0
781781 50.0000 1.78914
782782 − 36.0000i − 1.28736i
783783 7.00000i 0.250160i
784784 −7.00000 −0.250000
785785 0 0
786786 3.00000 0.107006
787787 − 29.0000i − 1.03374i −0.856064 0.516869i 0.827097π-0.827097\pi
0.856064 0.516869i 0.172903π-0.172903\pi
788788 12.0000i 0.427482i
789789 −17.0000 −0.605216
790790 0 0
791791 0 0
792792 15.0000i 0.533002i
793793 − 52.0000i − 1.84657i
794794 −29.0000 −1.02917
795795 0 0
796796 −22.0000 −0.779769
797797 − 14.0000i − 0.495905i −0.968772 0.247953i 0.920242π-0.920242\pi
0.968772 0.247953i 0.0797578π-0.0797578\pi
798798 0 0
799799 32.0000 1.13208
800800 0 0
801801 3.00000 0.106000
802802 − 3.00000i − 0.105934i
803803 25.0000i 0.882231i
804804 −9.00000 −0.317406
805805 0 0
806806 −12.0000 −0.422682
807807 − 14.0000i − 0.492823i
808808 0 0
809809 44.0000 1.54696 0.773479 0.633822i 0.218515π-0.218515\pi
0.773479 + 0.633822i 0.218515π0.218515\pi
810810 0 0
811811 −51.0000 −1.79085 −0.895426 0.445210i 0.853129π-0.853129\pi
−0.895426 + 0.445210i 0.853129π0.853129\pi
812812 0 0
813813 10.0000i 0.350715i
814814 −50.0000 −1.75250
815815 0 0
816816 −4.00000 −0.140028
817817 − 4.00000i − 0.139942i
818818 − 34.0000i − 1.18878i
819819 0 0
820820 0 0
821821 18.0000 0.628204 0.314102 0.949389i 0.398297π-0.398297\pi
0.314102 + 0.949389i 0.398297π0.398297\pi
822822 12.0000i 0.418548i
823823 − 2.00000i − 0.0697156i −0.999392 0.0348578i 0.988902π-0.988902\pi
0.999392 0.0348578i 0.0110978π-0.0110978\pi
824824 39.0000 1.35863
825825 0 0
826826 0 0
827827 8.00000i 0.278187i 0.990279 + 0.139094i 0.0444189π0.0444189\pi
−0.990279 + 0.139094i 0.955581π0.955581\pi
828828 − 9.00000i − 0.312772i
829829 −30.0000 −1.04194 −0.520972 0.853574i 0.674430π-0.674430\pi
−0.520972 + 0.853574i 0.674430π0.674430\pi
830830 0 0
831831 −33.0000 −1.14476
832832 28.0000i 0.970725i
833833 − 28.0000i − 0.970143i
834834 −14.0000 −0.484780
835835 0 0
836836 5.00000 0.172929
837837 − 3.00000i − 0.103695i
838838 28.0000i 0.967244i
839839 20.0000 0.690477 0.345238 0.938515i 0.387798π-0.387798\pi
0.345238 + 0.938515i 0.387798π0.387798\pi
840840 0 0
841841 20.0000 0.689655
842842 26.0000i 0.896019i
843843 − 15.0000i − 0.516627i
844844 11.0000 0.378636
845845 0 0
846846 −8.00000 −0.275046
847847 0 0
848848 11.0000i 0.377742i
849849 0 0
850850 0 0
851851 90.0000 3.08516
852852 10.0000i 0.342594i
853853 42.0000i 1.43805i 0.694983 + 0.719026i 0.255412π0.255412\pi
−0.694983 + 0.719026i 0.744588π0.744588\pi
854854 0 0
855855 0 0
856856 18.0000 0.615227
857857 − 10.0000i − 0.341593i −0.985306 0.170797i 0.945366π-0.945366\pi
0.985306 0.170797i 0.0546341π-0.0546341\pi
858858 − 20.0000i − 0.682789i
859859 −22.0000 −0.750630 −0.375315 0.926897i 0.622466π-0.622466\pi
−0.375315 + 0.926897i 0.622466π0.622466\pi
860860 0 0
861861 0 0
862862 − 6.00000i − 0.204361i
863863 20.0000i 0.680808i 0.940279 + 0.340404i 0.110564π0.110564\pi
−0.940279 + 0.340404i 0.889436π0.889436\pi
864864 −5.00000 −0.170103
865865 0 0
866866 26.0000 0.883516
867867 1.00000i 0.0339618i
868868 0 0
869869 75.0000 2.54420
870870 0 0
871871 36.0000 1.21981
872872 − 30.0000i − 1.01593i
873873 10.0000i 0.338449i
874874 9.00000 0.304430
875875 0 0
876876 −5.00000 −0.168934
877877 − 6.00000i − 0.202606i −0.994856 0.101303i 0.967699π-0.967699\pi
0.994856 0.101303i 0.0323011π-0.0323011\pi
878878 37.0000i 1.24869i
879879 9.00000 0.303562
880880 0 0
881881 32.0000 1.07811 0.539054 0.842271i 0.318782π-0.318782\pi
0.539054 + 0.842271i 0.318782π0.318782\pi
882882 7.00000i 0.235702i
883883 34.0000i 1.14419i 0.820187 + 0.572096i 0.193869π0.193869\pi
−0.820187 + 0.572096i 0.806131π0.806131\pi
884884 −16.0000 −0.538138
885885 0 0
886886 15.0000 0.503935
887887 0 0 1.00000 00
−1.00000 π\pi
888888 − 30.0000i − 1.00673i
889889 0 0
890890 0 0
891891 5.00000 0.167506
892892 1.00000i 0.0334825i
893893 8.00000i 0.267710i
894894 −16.0000 −0.535120
895895 0 0
896896 0 0
897897 36.0000i 1.20201i
898898 − 7.00000i − 0.233593i
899899 −21.0000 −0.700389
900900 0 0
901901 −44.0000 −1.46585
902902 10.0000i 0.332964i
903903 0 0
904904 3.00000 0.0997785
905905 0 0
906906 −8.00000 −0.265782
907907 − 24.0000i − 0.796907i −0.917189 0.398453i 0.869547π-0.869547\pi
0.917189 0.398453i 0.130453π-0.130453\pi
908908 22.0000i 0.730096i
909909 0 0
910910 0 0
911911 14.0000 0.463841 0.231920 0.972735i 0.425499π-0.425499\pi
0.231920 + 0.972735i 0.425499π0.425499\pi
912912 − 1.00000i − 0.0331133i
913913 − 45.0000i − 1.48928i
914914 −14.0000 −0.463079
915915 0 0
916916 −21.0000 −0.693860
917917 0 0
918918 4.00000i 0.132020i
919919 26.0000 0.857661 0.428830 0.903385i 0.358926π-0.358926\pi
0.428830 + 0.903385i 0.358926π0.358926\pi
920920 0 0
921921 23.0000 0.757876
922922 − 12.0000i − 0.395199i
923923 − 40.0000i − 1.31662i
924924 0 0
925925 0 0
926926 12.0000 0.394344
927927 − 13.0000i − 0.426976i
928928 35.0000i 1.14893i
929929 −4.00000 −0.131236 −0.0656179 0.997845i 0.520902π-0.520902\pi
−0.0656179 + 0.997845i 0.520902π0.520902\pi
930930 0 0
931931 7.00000 0.229416
932932 0 0
933933 24.0000i 0.785725i
934934 7.00000 0.229047
935935 0 0
936936 12.0000 0.392232
937937 42.0000i 1.37208i 0.727564 + 0.686040i 0.240653π0.240653\pi
−0.727564 + 0.686040i 0.759347π0.759347\pi
938938 0 0
939939 −13.0000 −0.424239
940940 0 0
941941 13.0000 0.423788 0.211894 0.977293i 0.432037π-0.432037\pi
0.211894 + 0.977293i 0.432037π0.432037\pi
942942 2.00000i 0.0651635i
943943 − 18.0000i − 0.586161i
944944 8.00000 0.260378
945945 0 0
946946 −20.0000 −0.650256
947947 − 12.0000i − 0.389948i −0.980808 0.194974i 0.937538π-0.937538\pi
0.980808 0.194974i 0.0624622π-0.0624622\pi
948948 15.0000i 0.487177i
949949 20.0000 0.649227
950950 0 0
951951 −1.00000 −0.0324272
952952 0 0
953953 − 17.0000i − 0.550684i −0.961346 0.275342i 0.911209π-0.911209\pi
0.961346 0.275342i 0.0887911π-0.0887911\pi
954954 11.0000 0.356138
955955 0 0
956956 −8.00000 −0.258738
957957 − 35.0000i − 1.13139i
958958 15.0000i 0.484628i
959959 0 0
960960 0 0
961961 −22.0000 −0.709677
962962 40.0000i 1.28965i
963963 − 6.00000i − 0.193347i
964964 4.00000 0.128831
965965 0 0
966966 0 0
967967 2.00000i 0.0643157i 0.999483 + 0.0321578i 0.0102379π0.0102379\pi
−0.999483 + 0.0321578i 0.989762π0.989762\pi
968968 − 42.0000i − 1.34993i
969969 4.00000 0.128499
970970 0 0
971971 −36.0000 −1.15529 −0.577647 0.816286i 0.696029π-0.696029\pi
−0.577647 + 0.816286i 0.696029π0.696029\pi
972972 1.00000i 0.0320750i
973973 0 0
974974 8.00000 0.256337
975975 0 0
976976 −13.0000 −0.416120
977977 2.00000i 0.0639857i 0.999488 + 0.0319928i 0.0101854π0.0101854\pi
−0.999488 + 0.0319928i 0.989815π0.989815\pi
978978 − 14.0000i − 0.447671i
979979 −15.0000 −0.479402
980980 0 0
981981 −10.0000 −0.319275
982982 − 28.0000i − 0.893516i
983983 42.0000i 1.33959i 0.742545 + 0.669796i 0.233618π0.233618\pi
−0.742545 + 0.669796i 0.766382π0.766382\pi
984984 −6.00000 −0.191273
985985 0 0
986986 28.0000 0.891702
987987 0 0
988988 − 4.00000i − 0.127257i
989989 36.0000 1.14473
990990 0 0
991991 5.00000 0.158830 0.0794151 0.996842i 0.474695π-0.474695\pi
0.0794151 + 0.996842i 0.474695π0.474695\pi
992992 − 15.0000i − 0.476250i
993993 − 3.00000i − 0.0952021i
994994 0 0
995995 0 0
996996 9.00000 0.285176
997997 3.00000i 0.0950110i 0.998871 + 0.0475055i 0.0151272π0.0151272\pi
−0.998871 + 0.0475055i 0.984873π0.984873\pi
998998 − 32.0000i − 1.01294i
999999 −10.0000 −0.316386
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 1425.2.c.h.799.1 2
5.2 odd 4 1425.2.a.h.1.1 yes 1
5.3 odd 4 1425.2.a.b.1.1 1
5.4 even 2 inner 1425.2.c.h.799.2 2
15.2 even 4 4275.2.a.f.1.1 1
15.8 even 4 4275.2.a.l.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1425.2.a.b.1.1 1 5.3 odd 4
1425.2.a.h.1.1 yes 1 5.2 odd 4
1425.2.c.h.799.1 2 1.1 even 1 trivial
1425.2.c.h.799.2 2 5.4 even 2 inner
4275.2.a.f.1.1 1 15.2 even 4
4275.2.a.l.1.1 1 15.8 even 4