Properties

Label 900.2.s.a.49.2
Level 900900
Weight 22
Character 900.49
Analytic conductor 7.1877.187
Analytic rank 00
Dimension 44
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [900,2,Mod(49,900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(900, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("900.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 900=223252 900 = 2^{2} \cdot 3^{2} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 900.s (of order 66, degree 22, 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: 7.186536181927.18653618192
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(ζ12)\Q(\zeta_{12})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 180)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 49.2
Root 0.866025+0.500000i-0.866025 + 0.500000i of defining polynomial
Character χ\chi == 900.49
Dual form 900.2.s.a.349.2

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) == q+(0.8660251.50000i)q3+(0.866025+0.500000i)q7+(1.500002.59808i)q9+(3.464102.00000i)q136.00000iq172.00000q19+1.73205iq21+(2.598081.50000i)q235.19615q27+(1.50000+2.59808i)q29+(5.000008.66025i)q3110.0000iq37+(6.00000+3.46410i)q39+(4.50000+7.79423i)q41+(3.464102.00000i)q43+(7.794234.50000i)q47+(3.00000+5.19615i)q49+(9.000005.19615i)q51+6.00000iq53+(1.73205+3.00000i)q57+(3.00000+5.19615i)q59+(0.500000+0.866025i)q61+(2.59808+1.50000i)q63+(9.526285.50000i)q67+(4.50000+2.59808i)q69+12.0000q71+4.00000iq73+(5.000008.66025i)q79+(4.50000+7.79423i)q81+(7.794234.50000i)q83+5.19615q879.00000q89+4.00000q91+(8.6602515.0000i)q93+(8.66025+5.00000i)q97+O(q100)q+(0.866025 - 1.50000i) q^{3} +(-0.866025 + 0.500000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-3.46410 - 2.00000i) q^{13} -6.00000i q^{17} -2.00000 q^{19} +1.73205i q^{21} +(-2.59808 - 1.50000i) q^{23} -5.19615 q^{27} +(1.50000 + 2.59808i) q^{29} +(5.00000 - 8.66025i) q^{31} -10.0000i q^{37} +(-6.00000 + 3.46410i) q^{39} +(-4.50000 + 7.79423i) q^{41} +(3.46410 - 2.00000i) q^{43} +(7.79423 - 4.50000i) q^{47} +(-3.00000 + 5.19615i) q^{49} +(-9.00000 - 5.19615i) q^{51} +6.00000i q^{53} +(-1.73205 + 3.00000i) q^{57} +(-3.00000 + 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{61} +(2.59808 + 1.50000i) q^{63} +(-9.52628 - 5.50000i) q^{67} +(-4.50000 + 2.59808i) q^{69} +12.0000 q^{71} +4.00000i q^{73} +(-5.00000 - 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(7.79423 - 4.50000i) q^{83} +5.19615 q^{87} -9.00000 q^{89} +4.00000 q^{91} +(-8.66025 - 15.0000i) q^{93} +(-8.66025 + 5.00000i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q6q98q19+6q29+20q3124q3918q4112q4936q5112q59+2q6118q69+48q7120q7918q8136q89+16q91+O(q100) 4 q - 6 q^{9} - 8 q^{19} + 6 q^{29} + 20 q^{31} - 24 q^{39} - 18 q^{41} - 12 q^{49} - 36 q^{51} - 12 q^{59} + 2 q^{61} - 18 q^{69} + 48 q^{71} - 20 q^{79} - 18 q^{81} - 36 q^{89} + 16 q^{91}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/900Z)×\left(\mathbb{Z}/900\mathbb{Z}\right)^\times.

nn 101101 451451 577577
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) 11 1-1

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0.866025 1.50000i 0.500000 0.866025i
44 0 0
55 0 0
66 0 0
77 −0.866025 + 0.500000i −0.327327 + 0.188982i −0.654654 0.755929i 0.727186π-0.727186\pi
0.327327 + 0.944911i 0.393852π0.393852\pi
88 0 0
99 −1.50000 2.59808i −0.500000 0.866025i
1010 0 0
1111 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
1212 0 0
1313 −3.46410 2.00000i −0.960769 0.554700i −0.0643593 0.997927i 0.520500π-0.520500\pi
−0.896410 + 0.443227i 0.853834π0.853834\pi
1414 0 0
1515 0 0
1616 0 0
1717 6.00000i 1.45521i −0.685994 0.727607i 0.740633π-0.740633\pi
0.685994 0.727607i 0.259367π-0.259367\pi
1818 0 0
1919 −2.00000 −0.458831 −0.229416 0.973329i 0.573682π-0.573682\pi
−0.229416 + 0.973329i 0.573682π0.573682\pi
2020 0 0
2121 1.73205i 0.377964i
2222 0 0
2323 −2.59808 1.50000i −0.541736 0.312772i 0.204046 0.978961i 0.434591π-0.434591\pi
−0.745782 + 0.666190i 0.767924π0.767924\pi
2424 0 0
2525 0 0
2626 0 0
2727 −5.19615 −1.00000
2828 0 0
2929 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i 0.0768152π-0.0768152\pi
−0.692480 + 0.721437i 0.743482π0.743482\pi
3030 0 0
3131 5.00000 8.66025i 0.898027 1.55543i 0.0680129 0.997684i 0.478334π-0.478334\pi
0.830014 0.557743i 0.188333π-0.188333\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0 0
3737 10.0000i 1.64399i −0.569495 0.821995i 0.692861π-0.692861\pi
0.569495 0.821995i 0.307139π-0.307139\pi
3838 0 0
3939 −6.00000 + 3.46410i −0.960769 + 0.554700i
4040 0 0
4141 −4.50000 + 7.79423i −0.702782 + 1.21725i 0.264704 + 0.964330i 0.414726π0.414726\pi
−0.967486 + 0.252924i 0.918608π0.918608\pi
4242 0 0
4343 3.46410 2.00000i 0.528271 0.304997i −0.212041 0.977261i 0.568011π-0.568011\pi
0.740312 + 0.672264i 0.234678π0.234678\pi
4444 0 0
4545 0 0
4646 0 0
4747 7.79423 4.50000i 1.13691 0.656392i 0.191243 0.981543i 0.438748π-0.438748\pi
0.945662 + 0.325150i 0.105415π0.105415\pi
4848 0 0
4949 −3.00000 + 5.19615i −0.428571 + 0.742307i
5050 0 0
5151 −9.00000 5.19615i −1.26025 0.727607i
5252 0 0
5353 6.00000i 0.824163i 0.911147 + 0.412082i 0.135198π0.135198\pi
−0.911147 + 0.412082i 0.864802π0.864802\pi
5454 0 0
5555 0 0
5656 0 0
5757 −1.73205 + 3.00000i −0.229416 + 0.397360i
5858 0 0
5959 −3.00000 + 5.19615i −0.390567 + 0.676481i −0.992524 0.122047i 0.961054π-0.961054\pi
0.601958 + 0.798528i 0.294388π0.294388\pi
6060 0 0
6161 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i 0.146275π-0.146275\pi
−0.832240 + 0.554416i 0.812942π0.812942\pi
6262 0 0
6363 2.59808 + 1.50000i 0.327327 + 0.188982i
6464 0 0
6565 0 0
6666 0 0
6767 −9.52628 5.50000i −1.16382 0.671932i −0.211604 0.977356i 0.567869π-0.567869\pi
−0.952217 + 0.305424i 0.901202π0.901202\pi
6868 0 0
6969 −4.50000 + 2.59808i −0.541736 + 0.312772i
7070 0 0
7171 12.0000 1.42414 0.712069 0.702109i 0.247758π-0.247758\pi
0.712069 + 0.702109i 0.247758π0.247758\pi
7272 0 0
7373 4.00000i 0.468165i 0.972217 + 0.234082i 0.0752085π0.0752085\pi
−0.972217 + 0.234082i 0.924791π0.924791\pi
7474 0 0
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i 0.976489π-0.976489\pi
0.434730 0.900561i 0.356844π-0.356844\pi
8080 0 0
8181 −4.50000 + 7.79423i −0.500000 + 0.866025i
8282 0 0
8383 7.79423 4.50000i 0.855528 0.493939i −0.00698436 0.999976i 0.502223π-0.502223\pi
0.862512 + 0.506036i 0.168890π0.168890\pi
8484 0 0
8585 0 0
8686 0 0
8787 5.19615 0.557086
8888 0 0
8989 −9.00000 −0.953998 −0.476999 0.878904i 0.658275π-0.658275\pi
−0.476999 + 0.878904i 0.658275π0.658275\pi
9090 0 0
9191 4.00000 0.419314
9292 0 0
9393 −8.66025 15.0000i −0.898027 1.55543i
9494 0 0
9595 0 0
9696 0 0
9797 −8.66025 + 5.00000i −0.879316 + 0.507673i −0.870433 0.492287i 0.836161π-0.836161\pi
−0.00888289 + 0.999961i 0.502828π0.502828\pi
9898 0 0
9999 0 0
100100 0 0
101101 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i 0.186539π0.186539\pi
0.0623905 + 0.998052i 0.480128π0.480128\pi
102102 0 0
103103 6.92820 + 4.00000i 0.682656 + 0.394132i 0.800855 0.598858i 0.204379π-0.204379\pi
−0.118199 + 0.992990i 0.537712π0.537712\pi
104104 0 0
105105 0 0
106106 0 0
107107 9.00000i 0.870063i 0.900415 + 0.435031i 0.143263π0.143263\pi
−0.900415 + 0.435031i 0.856737π0.856737\pi
108108 0 0
109109 19.0000 1.81987 0.909935 0.414751i 0.136131π-0.136131\pi
0.909935 + 0.414751i 0.136131π0.136131\pi
110110 0 0
111111 −15.0000 8.66025i −1.42374 0.821995i
112112 0 0
113113 −10.3923 6.00000i −0.977626 0.564433i −0.0760733 0.997102i 0.524238π-0.524238\pi
−0.901553 + 0.432670i 0.857572π0.857572\pi
114114 0 0
115115 0 0
116116 0 0
117117 12.0000i 1.10940i
118118 0 0
119119 3.00000 + 5.19615i 0.275010 + 0.476331i
120120 0 0
121121 5.50000 9.52628i 0.500000 0.866025i
122122 0 0
123123 7.79423 + 13.5000i 0.702782 + 1.21725i
124124 0 0
125125 0 0
126126 0 0
127127 7.00000i 0.621150i −0.950549 0.310575i 0.899478π-0.899478\pi
0.950549 0.310575i 0.100522π-0.100522\pi
128128 0 0
129129 6.92820i 0.609994i
130130 0 0
131131 −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i 0.917752π-0.917752\pi
0.704692 + 0.709514i 0.251085π0.251085\pi
132132 0 0
133133 1.73205 1.00000i 0.150188 0.0867110i
134134 0 0
135135 0 0
136136 0 0
137137 10.3923 6.00000i 0.887875 0.512615i 0.0146279 0.999893i 0.495344π-0.495344\pi
0.873247 + 0.487278i 0.162010π0.162010\pi
138138 0 0
139139 10.0000 17.3205i 0.848189 1.46911i −0.0346338 0.999400i 0.511026π-0.511026\pi
0.882823 0.469706i 0.155640π-0.155640\pi
140140 0 0
141141 15.5885i 1.31278i
142142 0 0
143143 0 0
144144 0 0
145145 0 0
146146 0 0
147147 5.19615 + 9.00000i 0.428571 + 0.742307i
148148 0 0
149149 4.50000 7.79423i 0.368654 0.638528i −0.620701 0.784047i 0.713152π-0.713152\pi
0.989355 + 0.145519i 0.0464853π0.0464853\pi
150150 0 0
151151 −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i 0.272204π-0.272204\pi
−0.981617 + 0.190864i 0.938871π0.938871\pi
152152 0 0
153153 −15.5885 + 9.00000i −1.26025 + 0.727607i
154154 0 0
155155 0 0
156156 0 0
157157 −1.73205 1.00000i −0.138233 0.0798087i 0.429289 0.903167i 0.358764π-0.358764\pi
−0.567521 + 0.823359i 0.692098π0.692098\pi
158158 0 0
159159 9.00000 + 5.19615i 0.713746 + 0.412082i
160160 0 0
161161 3.00000 0.236433
162162 0 0
163163 4.00000i 0.313304i 0.987654 + 0.156652i 0.0500701π0.0500701\pi
−0.987654 + 0.156652i 0.949930π0.949930\pi
164164 0 0
165165 0 0
166166 0 0
167167 12.9904 + 7.50000i 1.00523 + 0.580367i 0.909790 0.415068i 0.136242π-0.136242\pi
0.0954356 + 0.995436i 0.469576π0.469576\pi
168168 0 0
169169 1.50000 + 2.59808i 0.115385 + 0.199852i
170170 0 0
171171 3.00000 + 5.19615i 0.229416 + 0.397360i
172172 0 0
173173 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
174174 0 0
175175 0 0
176176 0 0
177177 5.19615 + 9.00000i 0.390567 + 0.676481i
178178 0 0
179179 24.0000 1.79384 0.896922 0.442189i 0.145798π-0.145798\pi
0.896922 + 0.442189i 0.145798π0.145798\pi
180180 0 0
181181 5.00000 0.371647 0.185824 0.982583i 0.440505π-0.440505\pi
0.185824 + 0.982583i 0.440505π0.440505\pi
182182 0 0
183183 1.73205 0.128037
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 0 0
189189 4.50000 2.59808i 0.327327 0.188982i
190190 0 0
191191 −3.00000 5.19615i −0.217072 0.375980i 0.736839 0.676068i 0.236317π-0.236317\pi
−0.953912 + 0.300088i 0.902984π0.902984\pi
192192 0 0
193193 −3.46410 2.00000i −0.249351 0.143963i 0.370116 0.928986i 0.379318π-0.379318\pi
−0.619467 + 0.785022i 0.712651π0.712651\pi
194194 0 0
195195 0 0
196196 0 0
197197 12.0000i 0.854965i 0.904024 + 0.427482i 0.140599π0.140599\pi
−0.904024 + 0.427482i 0.859401π0.859401\pi
198198 0 0
199199 −2.00000 −0.141776 −0.0708881 0.997484i 0.522583π-0.522583\pi
−0.0708881 + 0.997484i 0.522583π0.522583\pi
200200 0 0
201201 −16.5000 + 9.52628i −1.16382 + 0.671932i
202202 0 0
203203 −2.59808 1.50000i −0.182349 0.105279i
204204 0 0
205205 0 0
206206 0 0
207207 9.00000i 0.625543i
208208 0 0
209209 0 0
210210 0 0
211211 2.00000 3.46410i 0.137686 0.238479i −0.788935 0.614477i 0.789367π-0.789367\pi
0.926620 + 0.375999i 0.122700π0.122700\pi
212212 0 0
213213 10.3923 18.0000i 0.712069 1.23334i
214214 0 0
215215 0 0
216216 0 0
217217 10.0000i 0.678844i
218218 0 0
219219 6.00000 + 3.46410i 0.405442 + 0.234082i
220220 0 0
221221 −12.0000 + 20.7846i −0.807207 + 1.39812i
222222 0 0
223223 −9.52628 + 5.50000i −0.637927 + 0.368307i −0.783815 0.620994i 0.786729π-0.786729\pi
0.145889 + 0.989301i 0.453396π0.453396\pi
224224 0 0
225225 0 0
226226 0 0
227227 10.3923 6.00000i 0.689761 0.398234i −0.113761 0.993508i 0.536290π-0.536290\pi
0.803523 + 0.595274i 0.202957π0.202957\pi
228228 0 0
229229 −0.500000 + 0.866025i −0.0330409 + 0.0572286i −0.882073 0.471113i 0.843853π-0.843853\pi
0.849032 + 0.528341i 0.177186π0.177186\pi
230230 0 0
231231 0 0
232232 0 0
233233 30.0000i 1.96537i 0.185296 + 0.982683i 0.440675π0.440675\pi
−0.185296 + 0.982683i 0.559325π0.559325\pi
234234 0 0
235235 0 0
236236 0 0
237237 −17.3205 −1.12509
238238 0 0
239239 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
240240 0 0
241241 3.50000 + 6.06218i 0.225455 + 0.390499i 0.956456 0.291877i 0.0942799π-0.0942799\pi
−0.731001 + 0.682376i 0.760947π0.760947\pi
242242 0 0
243243 7.79423 + 13.5000i 0.500000 + 0.866025i
244244 0 0
245245 0 0
246246 0 0
247247 6.92820 + 4.00000i 0.440831 + 0.254514i
248248 0 0
249249 15.5885i 0.987878i
250250 0 0
251251 18.0000 1.13615 0.568075 0.822977i 0.307688π-0.307688\pi
0.568075 + 0.822977i 0.307688π0.307688\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0 0
257257 −5.19615 3.00000i −0.324127 0.187135i 0.329104 0.944294i 0.393253π-0.393253\pi
−0.653231 + 0.757159i 0.726587π0.726587\pi
258258 0 0
259259 5.00000 + 8.66025i 0.310685 + 0.538122i
260260 0 0
261261 4.50000 7.79423i 0.278543 0.482451i
262262 0 0
263263 20.7846 12.0000i 1.28163 0.739952i 0.304487 0.952517i 0.401515π-0.401515\pi
0.977147 + 0.212565i 0.0681817π0.0681817\pi
264264 0 0
265265 0 0
266266 0 0
267267 −7.79423 + 13.5000i −0.476999 + 0.826187i
268268 0 0
269269 −9.00000 −0.548740 −0.274370 0.961624i 0.588469π-0.588469\pi
−0.274370 + 0.961624i 0.588469π0.588469\pi
270270 0 0
271271 14.0000 0.850439 0.425220 0.905090i 0.360197π-0.360197\pi
0.425220 + 0.905090i 0.360197π0.360197\pi
272272 0 0
273273 3.46410 6.00000i 0.209657 0.363137i
274274 0 0
275275 0 0
276276 0 0
277277 1.73205 1.00000i 0.104069 0.0600842i −0.447062 0.894503i 0.647530π-0.647530\pi
0.551131 + 0.834419i 0.314196π0.314196\pi
278278 0 0
279279 −30.0000 −1.79605
280280 0 0
281281 −16.5000 28.5788i −0.984307 1.70487i −0.644974 0.764204i 0.723132π-0.723132\pi
−0.339333 0.940666i 0.610201π-0.610201\pi
282282 0 0
283283 −0.866025 0.500000i −0.0514799 0.0297219i 0.474039 0.880504i 0.342796π-0.342796\pi
−0.525519 + 0.850782i 0.676129π0.676129\pi
284284 0 0
285285 0 0
286286 0 0
287287 9.00000i 0.531253i
288288 0 0
289289 −19.0000 −1.11765
290290 0 0
291291 17.3205i 1.01535i
292292 0 0
293293 −5.19615 3.00000i −0.303562 0.175262i 0.340480 0.940252i 0.389411π-0.389411\pi
−0.644042 + 0.764990i 0.722744π0.722744\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 6.00000 + 10.3923i 0.346989 + 0.601003i
300300 0 0
301301 −2.00000 + 3.46410i −0.115278 + 0.199667i
302302 0 0
303303 31.1769 1.79107
304304 0 0
305305 0 0
306306 0 0
307307 29.0000i 1.65512i 0.561379 + 0.827559i 0.310271π0.310271\pi
−0.561379 + 0.827559i 0.689729π0.689729\pi
308308 0 0
309309 12.0000 6.92820i 0.682656 0.394132i
310310 0 0
311311 −9.00000 + 15.5885i −0.510343 + 0.883940i 0.489585 + 0.871956i 0.337148π0.337148\pi
−0.999928 + 0.0119847i 0.996185π0.996185\pi
312312 0 0
313313 13.8564 8.00000i 0.783210 0.452187i −0.0543564 0.998522i 0.517311π-0.517311\pi
0.837567 + 0.546335i 0.183977π0.183977\pi
314314 0 0
315315 0 0
316316 0 0
317317 −10.3923 + 6.00000i −0.583690 + 0.336994i −0.762598 0.646872i 0.776077π-0.776077\pi
0.178908 + 0.983866i 0.442743π0.442743\pi
318318 0 0
319319 0 0
320320 0 0
321321 13.5000 + 7.79423i 0.753497 + 0.435031i
322322 0 0
323323 12.0000i 0.667698i
324324 0 0
325325 0 0
326326 0 0
327327 16.4545 28.5000i 0.909935 1.57605i
328328 0 0
329329 −4.50000 + 7.79423i −0.248093 + 0.429710i
330330 0 0
331331 −13.0000 22.5167i −0.714545 1.23763i −0.963135 0.269019i 0.913301π-0.913301\pi
0.248590 0.968609i 0.420033π-0.420033\pi
332332 0 0
333333 −25.9808 + 15.0000i −1.42374 + 0.821995i
334334 0 0
335335 0 0
336336 0 0
337337 −6.92820 4.00000i −0.377403 0.217894i 0.299285 0.954164i 0.403252π-0.403252\pi
−0.676688 + 0.736270i 0.736585π0.736585\pi
338338 0 0
339339 −18.0000 + 10.3923i −0.977626 + 0.564433i
340340 0 0
341341 0 0
342342 0 0
343343 13.0000i 0.701934i
344344 0 0
345345 0 0
346346 0 0
347347 −20.7846 12.0000i −1.11578 0.644194i −0.175457 0.984487i 0.556140π-0.556140\pi
−0.940319 + 0.340293i 0.889474π0.889474\pi
348348 0 0
349349 11.5000 + 19.9186i 0.615581 + 1.06622i 0.990282 + 0.139072i 0.0444119π0.0444119\pi
−0.374701 + 0.927146i 0.622255π0.622255\pi
350350 0 0
351351 18.0000 + 10.3923i 0.960769 + 0.554700i
352352 0 0
353353 −10.3923 + 6.00000i −0.553127 + 0.319348i −0.750382 0.661004i 0.770130π-0.770130\pi
0.197256 + 0.980352i 0.436797π0.436797\pi
354354 0 0
355355 0 0
356356 0 0
357357 10.3923 0.550019
358358 0 0
359359 6.00000 0.316668 0.158334 0.987386i 0.449388π-0.449388\pi
0.158334 + 0.987386i 0.449388π0.449388\pi
360360 0 0
361361 −15.0000 −0.789474
362362 0 0
363363 −9.52628 16.5000i −0.500000 0.866025i
364364 0 0
365365 0 0
366366 0 0
367367 27.7128 16.0000i 1.44660 0.835193i 0.448320 0.893873i 0.352022π-0.352022\pi
0.998277 + 0.0586798i 0.0186891π0.0186891\pi
368368 0 0
369369 27.0000 1.40556
370370 0 0
371371 −3.00000 5.19615i −0.155752 0.269771i
372372 0 0
373373 12.1244 + 7.00000i 0.627775 + 0.362446i 0.779890 0.625917i 0.215275π-0.215275\pi
−0.152115 + 0.988363i 0.548608π0.548608\pi
374374 0 0
375375 0 0
376376 0 0
377377 12.0000i 0.618031i
378378 0 0
379379 −14.0000 −0.719132 −0.359566 0.933120i 0.617075π-0.617075\pi
−0.359566 + 0.933120i 0.617075π0.617075\pi
380380 0 0
381381 −10.5000 6.06218i −0.537931 0.310575i
382382 0 0
383383 −20.7846 12.0000i −1.06204 0.613171i −0.136047 0.990702i 0.543440π-0.543440\pi
−0.925997 + 0.377531i 0.876773π0.876773\pi
384384 0 0
385385 0 0
386386 0 0
387387 −10.3923 6.00000i −0.528271 0.304997i
388388 0 0
389389 −7.50000 12.9904i −0.380265 0.658638i 0.610835 0.791758i 0.290834π-0.290834\pi
−0.991100 + 0.133120i 0.957501π0.957501\pi
390390 0 0
391391 −9.00000 + 15.5885i −0.455150 + 0.788342i
392392 0 0
393393 5.19615 + 9.00000i 0.262111 + 0.453990i
394394 0 0
395395 0 0
396396 0 0
397397 22.0000i 1.10415i −0.833795 0.552074i 0.813837π-0.813837\pi
0.833795 0.552074i 0.186163π-0.186163\pi
398398 0 0
399399 3.46410i 0.173422i
400400 0 0
401401 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i 0.684957π-0.684957\pi
0.998350 + 0.0574304i 0.0182907π0.0182907\pi
402402 0 0
403403 −34.6410 + 20.0000i −1.72559 + 0.996271i
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i 0.912855π-0.912855\pi
0.715523 + 0.698589i 0.246188π0.246188\pi
410410 0 0
411411 20.7846i 1.02523i
412412 0 0
413413 6.00000i 0.295241i
414414 0 0
415415 0 0
416416 0 0
417417 −17.3205 30.0000i −0.848189 1.46911i
418418 0 0
419419 6.00000 10.3923i 0.293119 0.507697i −0.681426 0.731887i 0.738640π-0.738640\pi
0.974546 + 0.224189i 0.0719734π0.0719734\pi
420420 0 0
421421 11.0000 + 19.0526i 0.536107 + 0.928565i 0.999109 + 0.0422075i 0.0134391π0.0134391\pi
−0.463002 + 0.886357i 0.653228π0.653228\pi
422422 0 0
423423 −23.3827 13.5000i −1.13691 0.656392i
424424 0 0
425425 0 0
426426 0 0
427427 −0.866025 0.500000i −0.0419099 0.0241967i
428428 0 0
429429 0 0
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 0 0
433433 26.0000i 1.24948i −0.780833 0.624740i 0.785205π-0.785205\pi
0.780833 0.624740i 0.214795π-0.214795\pi
434434 0 0
435435 0 0
436436 0 0
437437 5.19615 + 3.00000i 0.248566 + 0.143509i
438438 0 0
439439 −14.0000 24.2487i −0.668184 1.15733i −0.978412 0.206666i 0.933739π-0.933739\pi
0.310228 0.950662i 0.399595π-0.399595\pi
440440 0 0
441441 18.0000 0.857143
442442 0 0
443443 23.3827 13.5000i 1.11094 0.641404i 0.171871 0.985119i 0.445019π-0.445019\pi
0.939074 + 0.343715i 0.111685π0.111685\pi
444444 0 0
445445 0 0
446446 0 0
447447 −7.79423 13.5000i −0.368654 0.638528i
448448 0 0
449449 −30.0000 −1.41579 −0.707894 0.706319i 0.750354π-0.750354\pi
−0.707894 + 0.706319i 0.750354π0.750354\pi
450450 0 0
451451 0 0
452452 0 0
453453 −13.8564 −0.651031
454454 0 0
455455 0 0
456456 0 0
457457 −8.66025 + 5.00000i −0.405110 + 0.233890i −0.688686 0.725059i 0.741812π-0.741812\pi
0.283577 + 0.958950i 0.408479π0.408479\pi
458458 0 0
459459 31.1769i 1.45521i
460460 0 0
461461 −16.5000 28.5788i −0.768482 1.33105i −0.938386 0.345589i 0.887679π-0.887679\pi
0.169904 0.985461i 0.445654π-0.445654\pi
462462 0 0
463463 −3.46410 2.00000i −0.160990 0.0929479i 0.417340 0.908750i 0.362962π-0.362962\pi
−0.578331 + 0.815802i 0.696296π0.696296\pi
464464 0 0
465465 0 0
466466 0 0
467467 36.0000i 1.66588i 0.553362 + 0.832941i 0.313345π0.313345\pi
−0.553362 + 0.832941i 0.686655π0.686655\pi
468468 0 0
469469 11.0000 0.507933
470470 0 0
471471 −3.00000 + 1.73205i −0.138233 + 0.0798087i
472472 0 0
473473 0 0
474474 0 0
475475 0 0
476476 0 0
477477 15.5885 9.00000i 0.713746 0.412082i
478478 0 0
479479 −15.0000 25.9808i −0.685367 1.18709i −0.973321 0.229447i 0.926308π-0.926308\pi
0.287954 0.957644i 0.407025π-0.407025\pi
480480 0 0
481481 −20.0000 + 34.6410i −0.911922 + 1.57949i
482482 0 0
483483 2.59808 4.50000i 0.118217 0.204757i
484484 0 0
485485 0 0
486486 0 0
487487 16.0000i 0.725029i −0.931978 0.362515i 0.881918π-0.881918\pi
0.931978 0.362515i 0.118082π-0.118082\pi
488488 0 0
489489 6.00000 + 3.46410i 0.271329 + 0.156652i
490490 0 0
491491 12.0000 20.7846i 0.541552 0.937996i −0.457263 0.889332i 0.651170π-0.651170\pi
0.998815 0.0486647i 0.0154966π-0.0154966\pi
492492 0 0
493493 15.5885 9.00000i 0.702069 0.405340i
494494 0 0
495495 0 0
496496 0 0
497497 −10.3923 + 6.00000i −0.466159 + 0.269137i
498498 0 0
499499 −2.00000 + 3.46410i −0.0895323 + 0.155074i −0.907314 0.420455i 0.861871π-0.861871\pi
0.817781 + 0.575529i 0.195204π0.195204\pi
500500 0 0
501501 22.5000 12.9904i 1.00523 0.580367i
502502 0 0
503503 3.00000i 0.133763i −0.997761 0.0668817i 0.978695π-0.978695\pi
0.997761 0.0668817i 0.0213050π-0.0213050\pi
504504 0 0
505505 0 0
506506 0 0
507507 5.19615 0.230769
508508 0 0
509509 −4.50000 + 7.79423i −0.199459 + 0.345473i −0.948353 0.317217i 0.897252π-0.897252\pi
0.748894 + 0.662690i 0.230585π0.230585\pi
510510 0 0
511511 −2.00000 3.46410i −0.0884748 0.153243i
512512 0 0
513513 10.3923 0.458831
514514 0 0
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 27.0000 1.18289 0.591446 0.806345i 0.298557π-0.298557\pi
0.591446 + 0.806345i 0.298557π0.298557\pi
522522 0 0
523523 7.00000i 0.306089i 0.988219 + 0.153044i 0.0489077π0.0489077\pi
−0.988219 + 0.153044i 0.951092π0.951092\pi
524524 0 0
525525 0 0
526526 0 0
527527 −51.9615 30.0000i −2.26348 1.30682i
528528 0 0
529529 −7.00000 12.1244i −0.304348 0.527146i
530530 0 0
531531 18.0000 0.781133
532532 0 0
533533 31.1769 18.0000i 1.35042 0.779667i
534534 0 0
535535 0 0
536536 0 0
537537 20.7846 36.0000i 0.896922 1.55351i
538538 0 0
539539 0 0
540540 0 0
541541 −7.00000 −0.300954 −0.150477 0.988614i 0.548081π-0.548081\pi
−0.150477 + 0.988614i 0.548081π0.548081\pi
542542 0 0
543543 4.33013 7.50000i 0.185824 0.321856i
544544 0 0
545545 0 0
546546 0 0
547547 −6.06218 + 3.50000i −0.259200 + 0.149649i −0.623970 0.781449i 0.714481π-0.714481\pi
0.364770 + 0.931098i 0.381148π0.381148\pi
548548 0 0
549549 1.50000 2.59808i 0.0640184 0.110883i
550550 0 0
551551 −3.00000 5.19615i −0.127804 0.221364i
552552 0 0
553553 8.66025 + 5.00000i 0.368271 + 0.212622i
554554 0 0
555555 0 0
556556 0 0
557557 6.00000i 0.254228i −0.991888 0.127114i 0.959429π-0.959429\pi
0.991888 0.127114i 0.0405714π-0.0405714\pi
558558 0 0
559559 −16.0000 −0.676728
560560 0 0
561561 0 0
562562 0 0
563563 −33.7750 19.5000i −1.42345 0.821827i −0.426855 0.904320i 0.640378π-0.640378\pi
−0.996592 + 0.0824933i 0.973712π0.973712\pi
564564 0 0
565565 0 0
566566 0 0
567567 9.00000i 0.377964i
568568 0 0
569569 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i 0.126528π-0.126528\pi
−0.796266 + 0.604947i 0.793194π0.793194\pi
570570 0 0
571571 −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i 0.400192π0.400192\pi
−0.978022 + 0.208502i 0.933141π0.933141\pi
572572 0 0
573573 −10.3923 −0.434145
574574 0 0
575575 0 0
576576 0 0
577577 38.0000i 1.58196i 0.611842 + 0.790980i 0.290429π0.290429\pi
−0.611842 + 0.790980i 0.709571π0.709571\pi
578578 0 0
579579 −6.00000 + 3.46410i −0.249351 + 0.143963i
580580 0 0
581581 −4.50000 + 7.79423i −0.186691 + 0.323359i
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 −23.3827 + 13.5000i −0.965107 + 0.557205i −0.897741 0.440524i 0.854793π-0.854793\pi
−0.0673658 + 0.997728i 0.521459π0.521459\pi
588588 0 0
589589 −10.0000 + 17.3205i −0.412043 + 0.713679i
590590 0 0
591591 18.0000 + 10.3923i 0.740421 + 0.427482i
592592 0 0
593593 6.00000i 0.246390i 0.992382 + 0.123195i 0.0393141π0.0393141\pi
−0.992382 + 0.123195i 0.960686π0.960686\pi
594594 0 0
595595 0 0
596596 0 0
597597 −1.73205 + 3.00000i −0.0708881 + 0.122782i
598598 0 0
599599 3.00000 5.19615i 0.122577 0.212309i −0.798206 0.602384i 0.794218π-0.794218\pi
0.920783 + 0.390075i 0.127551π0.127551\pi
600600 0 0
601601 11.0000 + 19.0526i 0.448699 + 0.777170i 0.998302 0.0582563i 0.0185541π-0.0185541\pi
−0.549602 + 0.835426i 0.685221π0.685221\pi
602602 0 0
603603 33.0000i 1.34386i
604604 0 0
605605 0 0
606606 0 0
607607 6.06218 + 3.50000i 0.246056 + 0.142061i 0.617957 0.786212i 0.287961π-0.287961\pi
−0.371901 + 0.928272i 0.621294π0.621294\pi
608608 0 0
609609 −4.50000 + 2.59808i −0.182349 + 0.105279i
610610 0 0
611611 −36.0000 −1.45640
612612 0 0
613613 22.0000i 0.888572i 0.895885 + 0.444286i 0.146543π0.146543\pi
−0.895885 + 0.444286i 0.853457π0.853457\pi
614614 0 0
615615 0 0
616616 0 0
617617 10.3923 + 6.00000i 0.418378 + 0.241551i 0.694383 0.719605i 0.255677π-0.255677\pi
−0.276005 + 0.961156i 0.589011π0.589011\pi
618618 0 0
619619 13.0000 + 22.5167i 0.522514 + 0.905021i 0.999657 + 0.0261952i 0.00833914π0.00833914\pi
−0.477143 + 0.878826i 0.658328π0.658328\pi
620620 0 0
621621 13.5000 + 7.79423i 0.541736 + 0.312772i
622622 0 0
623623 7.79423 4.50000i 0.312269 0.180289i
624624 0 0
625625 0 0
626626 0 0
627627 0 0
628628 0 0
629629 −60.0000 −2.39236
630630 0 0
631631 −40.0000 −1.59237 −0.796187 0.605050i 0.793153π-0.793153\pi
−0.796187 + 0.605050i 0.793153π0.793153\pi
632632 0 0
633633 −3.46410 6.00000i −0.137686 0.238479i
634634 0 0
635635 0 0
636636 0 0
637637 20.7846 12.0000i 0.823516 0.475457i
638638 0 0
639639 −18.0000 31.1769i −0.712069 1.23334i
640640 0 0
641641 −10.5000 18.1865i −0.414725 0.718325i 0.580674 0.814136i 0.302789π-0.302789\pi
−0.995400 + 0.0958109i 0.969456π0.969456\pi
642642 0 0
643643 −26.8468 15.5000i −1.05873 0.611260i −0.133652 0.991028i 0.542670π-0.542670\pi
−0.925082 + 0.379768i 0.876004π0.876004\pi
644644 0 0
645645 0 0
646646 0 0
647647 9.00000i 0.353827i 0.984226 + 0.176913i 0.0566112π0.0566112\pi
−0.984226 + 0.176913i 0.943389π0.943389\pi
648648 0 0
649649 0 0
650650 0 0
651651 15.0000 + 8.66025i 0.587896 + 0.339422i
652652 0 0
653653 5.19615 + 3.00000i 0.203341 + 0.117399i 0.598213 0.801337i 0.295878π-0.295878\pi
−0.394872 + 0.918736i 0.629211π0.629211\pi
654654 0 0
655655 0 0
656656 0 0
657657 10.3923 6.00000i 0.405442 0.234082i
658658 0 0
659659 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i 0.0806766π0.0806766\pi
−0.266872 + 0.963732i 0.585990π0.585990\pi
660660 0 0
661661 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i 0.771032π-0.771032\pi
0.946729 + 0.322031i 0.104366π0.104366\pi
662662 0 0
663663 20.7846 + 36.0000i 0.807207 + 1.39812i
664664 0 0
665665 0 0
666666 0 0
667667 9.00000i 0.348481i
668668 0 0
669669 19.0526i 0.736614i
670670 0 0
671671 0 0
672672 0 0
673673 24.2487 14.0000i 0.934719 0.539660i 0.0464181 0.998922i 0.485219π-0.485219\pi
0.888301 + 0.459262i 0.151886π0.151886\pi
674674 0 0
675675 0 0
676676 0 0
677677 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
678678 0 0
679679 5.00000 8.66025i 0.191882 0.332350i
680680 0 0
681681 20.7846i 0.796468i
682682 0 0
683683 12.0000i 0.459167i 0.973289 + 0.229584i 0.0737364π0.0737364\pi
−0.973289 + 0.229584i 0.926264π0.926264\pi
684684 0 0
685685 0 0
686686 0 0
687687 0.866025 + 1.50000i 0.0330409 + 0.0572286i
688688 0 0
689689 12.0000 20.7846i 0.457164 0.791831i
690690 0 0
691691 5.00000 + 8.66025i 0.190209 + 0.329452i 0.945319 0.326146i 0.105750π-0.105750\pi
−0.755110 + 0.655598i 0.772417π0.772417\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 46.7654 + 27.0000i 1.77136 + 1.02270i
698698 0 0
699699 45.0000 + 25.9808i 1.70206 + 0.982683i
700700 0 0
701701 −21.0000 −0.793159 −0.396580 0.918000i 0.629803π-0.629803\pi
−0.396580 + 0.918000i 0.629803π0.629803\pi
702702 0 0
703703 20.0000i 0.754314i
704704 0 0
705705 0 0
706706 0 0
707707 −15.5885 9.00000i −0.586264 0.338480i
708708 0 0
709709 17.5000 + 30.3109i 0.657226 + 1.13835i 0.981331 + 0.192328i 0.0616038π0.0616038\pi
−0.324104 + 0.946021i 0.605063π0.605063\pi
710710 0 0
711711 −15.0000 + 25.9808i −0.562544 + 0.974355i
712712 0 0
713713 −25.9808 + 15.0000i −0.972987 + 0.561754i
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 42.0000 1.56634 0.783168 0.621810i 0.213603π-0.213603\pi
0.783168 + 0.621810i 0.213603π0.213603\pi
720720 0 0
721721 −8.00000 −0.297936
722722 0 0
723723 12.1244 0.450910
724724 0 0
725725 0 0
726726 0 0
727727 −16.4545 + 9.50000i −0.610263 + 0.352335i −0.773068 0.634323i 0.781279π-0.781279\pi
0.162805 + 0.986658i 0.447946π0.447946\pi
728728 0 0
729729 27.0000 1.00000
730730 0 0
731731 −12.0000 20.7846i −0.443836 0.768747i
732732 0 0
733733 12.1244 + 7.00000i 0.447823 + 0.258551i 0.706910 0.707303i 0.250088π-0.250088\pi
−0.259087 + 0.965854i 0.583422π0.583422\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 −2.00000 −0.0735712 −0.0367856 0.999323i 0.511712π-0.511712\pi
−0.0367856 + 0.999323i 0.511712π0.511712\pi
740740 0 0
741741 12.0000 6.92820i 0.440831 0.254514i
742742 0 0
743743 28.5788 + 16.5000i 1.04846 + 0.605326i 0.922217 0.386674i 0.126376π-0.126376\pi
0.126239 + 0.992000i 0.459709π0.459709\pi
744744 0 0
745745 0 0
746746 0 0
747747 −23.3827 13.5000i −0.855528 0.493939i
748748 0 0
749749 −4.50000 7.79423i −0.164426 0.284795i
750750 0 0
751751 8.00000 13.8564i 0.291924 0.505627i −0.682341 0.731034i 0.739038π-0.739038\pi
0.974265 + 0.225407i 0.0723712π0.0723712\pi
752752 0 0
753753 15.5885 27.0000i 0.568075 0.983935i
754754 0 0
755755 0 0
756756 0 0
757757 20.0000i 0.726912i 0.931611 + 0.363456i 0.118403π0.118403\pi
−0.931611 + 0.363456i 0.881597π0.881597\pi
758758 0 0
759759 0 0
760760 0 0
761761 22.5000 38.9711i 0.815624 1.41270i −0.0932544 0.995642i 0.529727π-0.529727\pi
0.908879 0.417061i 0.136940π-0.136940\pi
762762 0 0
763763 −16.4545 + 9.50000i −0.595692 + 0.343923i
764764 0 0
765765 0 0
766766 0 0
767767 20.7846 12.0000i 0.750489 0.433295i
768768 0 0
769769 −15.5000 + 26.8468i −0.558944 + 0.968120i 0.438641 + 0.898663i 0.355460π0.355460\pi
−0.997585 + 0.0694574i 0.977873π0.977873\pi
770770 0 0
771771 −9.00000 + 5.19615i −0.324127 + 0.187135i
772772 0 0
773773 36.0000i 1.29483i 0.762138 + 0.647415i 0.224150π0.224150\pi
−0.762138 + 0.647415i 0.775850π0.775850\pi
774774 0 0
775775 0 0
776776 0 0
777777 17.3205 0.621370
778778 0 0
779779 9.00000 15.5885i 0.322458 0.558514i
780780 0 0
781781 0 0
782782 0 0
783783 −7.79423 13.5000i −0.278543 0.482451i
784784 0 0
785785 0 0
786786 0 0
787787 34.6410 + 20.0000i 1.23482 + 0.712923i 0.968031 0.250832i 0.0807042π-0.0807042\pi
0.266788 + 0.963755i 0.414038π0.414038\pi
788788 0 0
789789 41.5692i 1.47990i
790790 0 0
791791 12.0000 0.426671
792792 0 0
793793 4.00000i 0.142044i
794794 0 0
795795 0 0
796796 0 0
797797 20.7846 + 12.0000i 0.736229 + 0.425062i 0.820696 0.571364i 0.193586π-0.193586\pi
−0.0844678 + 0.996426i 0.526919π0.526919\pi
798798 0 0
799799 −27.0000 46.7654i −0.955191 1.65444i
800800 0 0
801801 13.5000 + 23.3827i 0.476999 + 0.826187i
802802 0 0
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 −7.79423 + 13.5000i −0.274370 + 0.475223i
808808 0 0
809809 54.0000 1.89854 0.949269 0.314464i 0.101825π-0.101825\pi
0.949269 + 0.314464i 0.101825π0.101825\pi
810810 0 0
811811 −22.0000 −0.772524 −0.386262 0.922389i 0.626234π-0.626234\pi
−0.386262 + 0.922389i 0.626234π0.626234\pi
812812 0 0
813813 12.1244 21.0000i 0.425220 0.736502i
814814 0 0
815815 0 0
816816 0 0
817817 −6.92820 + 4.00000i −0.242387 + 0.139942i
818818 0 0
819819 −6.00000 10.3923i −0.209657 0.363137i
820820 0 0
821821 −1.50000 2.59808i −0.0523504 0.0906735i 0.838663 0.544651i 0.183338π-0.183338\pi
−0.891013 + 0.453978i 0.850005π0.850005\pi
822822 0 0
823823 −42.4352 24.5000i −1.47920 0.854016i −0.479477 0.877555i 0.659174π-0.659174\pi
−0.999723 + 0.0235383i 0.992507π0.992507\pi
824824 0 0
825825 0 0
826826 0 0
827827 27.0000i 0.938882i 0.882964 + 0.469441i 0.155545π0.155545\pi
−0.882964 + 0.469441i 0.844455π0.844455\pi
828828 0 0
829829 7.00000 0.243120 0.121560 0.992584i 0.461210π-0.461210\pi
0.121560 + 0.992584i 0.461210π0.461210\pi
830830 0 0
831831 3.46410i 0.120168i
832832 0 0
833833 31.1769 + 18.0000i 1.08022 + 0.623663i
834834 0 0
835835 0 0
836836 0 0
837837 −25.9808 + 45.0000i −0.898027 + 1.55543i
838838 0 0
839839 −15.0000 25.9808i −0.517858 0.896956i −0.999785 0.0207443i 0.993396π-0.993396\pi
0.481927 0.876211i 0.339937π-0.339937\pi
840840 0 0
841841 10.0000 17.3205i 0.344828 0.597259i
842842 0 0
843843 −57.1577 −1.96861
844844 0 0
845845 0 0
846846 0 0
847847 11.0000i 0.377964i
848848 0 0
849849 −1.50000 + 0.866025i −0.0514799 + 0.0297219i
850850 0 0
851851 −15.0000 + 25.9808i −0.514193 + 0.890609i
852852 0 0
853853 3.46410 2.00000i 0.118609 0.0684787i −0.439522 0.898232i 0.644852π-0.644852\pi
0.558131 + 0.829753i 0.311519π0.311519\pi
854854 0 0
855855 0 0
856856 0 0
857857 −41.5692 + 24.0000i −1.41998 + 0.819824i −0.996296 0.0859870i 0.972596π-0.972596\pi
−0.423681 + 0.905811i 0.639262π0.639262\pi
858858 0 0
859859 10.0000 17.3205i 0.341196 0.590968i −0.643459 0.765480i 0.722501π-0.722501\pi
0.984655 + 0.174512i 0.0558348π0.0558348\pi
860860 0 0
861861 −13.5000 7.79423i −0.460079 0.265627i
862862 0 0
863863 15.0000i 0.510606i −0.966861 0.255303i 0.917825π-0.917825\pi
0.966861 0.255303i 0.0821752π-0.0821752\pi
864864 0 0
865865 0 0
866866 0 0
867867 −16.4545 + 28.5000i −0.558824 + 0.967911i
868868 0 0
869869 0 0
870870 0 0
871871 22.0000 + 38.1051i 0.745442 + 1.29114i
872872 0 0
873873 25.9808 + 15.0000i 0.879316 + 0.507673i
874874 0 0
875875 0 0
876876 0 0
877877 3.46410 + 2.00000i 0.116974 + 0.0675352i 0.557346 0.830281i 0.311820π-0.311820\pi
−0.440371 + 0.897816i 0.645153π0.645153\pi
878878 0 0
879879 −9.00000 + 5.19615i −0.303562 + 0.175262i
880880 0 0
881881 −15.0000 −0.505363 −0.252681 0.967550i 0.581312π-0.581312\pi
−0.252681 + 0.967550i 0.581312π0.581312\pi
882882 0 0
883883 29.0000i 0.975928i −0.872864 0.487964i 0.837740π-0.837740\pi
0.872864 0.487964i 0.162260π-0.162260\pi
884884 0 0
885885 0 0
886886 0 0
887887 41.5692 + 24.0000i 1.39576 + 0.805841i 0.993945 0.109881i 0.0350469π-0.0350469\pi
0.401813 + 0.915722i 0.368380π0.368380\pi
888888 0 0
889889 3.50000 + 6.06218i 0.117386 + 0.203319i
890890 0 0
891891 0 0
892892 0 0
893893 −15.5885 + 9.00000i −0.521648 + 0.301174i
894894 0 0
895895 0 0
896896 0 0
897897 20.7846 0.693978
898898 0 0
899899 30.0000 1.00056
900900 0 0
901901 36.0000 1.19933
902902 0 0
903903 3.46410 + 6.00000i 0.115278 + 0.199667i
904904 0 0
905905 0 0
906906 0 0
907907 −0.866025 + 0.500000i −0.0287559 + 0.0166022i −0.514309 0.857605i 0.671952π-0.671952\pi
0.485553 + 0.874207i 0.338618π0.338618\pi
908908 0 0
909909 27.0000 46.7654i 0.895533 1.55111i
910910 0 0
911911 3.00000 + 5.19615i 0.0993944 + 0.172156i 0.911434 0.411446i 0.134976π-0.134976\pi
−0.812040 + 0.583602i 0.801643π0.801643\pi
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 0 0
917917 6.00000i 0.198137i
918918 0 0
919919 34.0000 1.12156 0.560778 0.827966i 0.310502π-0.310502\pi
0.560778 + 0.827966i 0.310502π0.310502\pi
920920 0 0
921921 43.5000 + 25.1147i 1.43337 + 0.827559i
922922 0 0
923923 −41.5692 24.0000i −1.36827 0.789970i
924924 0 0
925925 0 0
926926 0 0
927927 24.0000i 0.788263i
928928 0 0
929929 3.00000 + 5.19615i 0.0984268 + 0.170480i 0.911034 0.412332i 0.135286π-0.135286\pi
−0.812607 + 0.582812i 0.801952π0.801952\pi
930930 0 0
931931 6.00000 10.3923i 0.196642 0.340594i
932932 0 0
933933 15.5885 + 27.0000i 0.510343 + 0.883940i
934934 0 0
935935 0 0
936936 0 0
937937 16.0000i 0.522697i −0.965244 0.261349i 0.915833π-0.915833\pi
0.965244 0.261349i 0.0841672π-0.0841672\pi
938938 0 0
939939 27.7128i 0.904373i
940940 0 0
941941 −22.5000 + 38.9711i −0.733479 + 1.27042i 0.221908 + 0.975068i 0.428771π0.428771\pi
−0.955387 + 0.295355i 0.904562π0.904562\pi
942942 0 0
943943 23.3827 13.5000i 0.761445 0.439620i
944944 0 0
945945 0 0
946946 0 0
947947 12.9904 7.50000i 0.422131 0.243717i −0.273858 0.961770i 0.588300π-0.588300\pi
0.695988 + 0.718053i 0.254966π0.254966\pi
948948 0 0
949949 8.00000 13.8564i 0.259691 0.449798i
950950 0 0
951951 20.7846i 0.673987i
952952 0 0
953953 24.0000i 0.777436i −0.921357 0.388718i 0.872918π-0.872918\pi
0.921357 0.388718i 0.127082π-0.127082\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 −6.00000 + 10.3923i −0.193750 + 0.335585i
960960 0 0
961961 −34.5000 59.7558i −1.11290 1.92760i
962962 0 0
963963 23.3827 13.5000i 0.753497 0.435031i
964964 0 0
965965 0 0
966966 0 0
967967 0.866025 + 0.500000i 0.0278495 + 0.0160789i 0.513860 0.857874i 0.328215π-0.328215\pi
−0.486011 + 0.873953i 0.661548π0.661548\pi
968968 0 0
969969 18.0000 + 10.3923i 0.578243 + 0.333849i
970970 0 0
971971 42.0000 1.34784 0.673922 0.738802i 0.264608π-0.264608\pi
0.673922 + 0.738802i 0.264608π0.264608\pi
972972 0 0
973973 20.0000i 0.641171i
974974 0 0
975975 0 0
976976 0 0
977977 −20.7846 12.0000i −0.664959 0.383914i 0.129205 0.991618i 0.458757π-0.458757\pi
−0.794164 + 0.607704i 0.792091π0.792091\pi
978978 0 0
979979 0 0
980980 0 0
981981 −28.5000 49.3634i −0.909935 1.57605i
982982 0 0
983983 −7.79423 + 4.50000i −0.248597 + 0.143528i −0.619122 0.785295i 0.712511π-0.712511\pi
0.370525 + 0.928823i 0.379178π0.379178\pi
984984 0 0
985985 0 0
986986 0 0
987987 7.79423 + 13.5000i 0.248093 + 0.429710i
988988 0 0
989989 −12.0000 −0.381578
990990 0 0
991991 2.00000 0.0635321 0.0317660 0.999495i 0.489887π-0.489887\pi
0.0317660 + 0.999495i 0.489887π0.489887\pi
992992 0 0
993993 −45.0333 −1.42909
994994 0 0
995995 0 0
996996 0 0
997997 −8.66025 + 5.00000i −0.274273 + 0.158352i −0.630828 0.775923i 0.717285π-0.717285\pi
0.356555 + 0.934274i 0.383951π0.383951\pi
998998 0 0
999999 51.9615i 1.64399i
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 900.2.s.a.49.2 4
3.2 odd 2 2700.2.s.a.1549.1 4
5.2 odd 4 900.2.i.a.301.1 2
5.3 odd 4 180.2.i.a.121.1 yes 2
5.4 even 2 inner 900.2.s.a.49.1 4
9.2 odd 6 2700.2.s.a.2449.2 4
9.4 even 3 8100.2.d.e.649.1 2
9.5 odd 6 8100.2.d.f.649.1 2
9.7 even 3 inner 900.2.s.a.349.1 4
15.2 even 4 2700.2.i.a.901.1 2
15.8 even 4 540.2.i.a.361.1 2
15.14 odd 2 2700.2.s.a.1549.2 4
20.3 even 4 720.2.q.a.481.1 2
45.2 even 12 2700.2.i.a.1801.1 2
45.4 even 6 8100.2.d.e.649.2 2
45.7 odd 12 900.2.i.a.601.1 2
45.13 odd 12 1620.2.a.e.1.1 1
45.14 odd 6 8100.2.d.f.649.2 2
45.22 odd 12 8100.2.a.i.1.1 1
45.23 even 12 1620.2.a.b.1.1 1
45.29 odd 6 2700.2.s.a.2449.1 4
45.32 even 12 8100.2.a.h.1.1 1
45.34 even 6 inner 900.2.s.a.349.2 4
45.38 even 12 540.2.i.a.181.1 2
45.43 odd 12 180.2.i.a.61.1 2
60.23 odd 4 2160.2.q.e.1441.1 2
180.23 odd 12 6480.2.a.h.1.1 1
180.43 even 12 720.2.q.a.241.1 2
180.83 odd 12 2160.2.q.e.721.1 2
180.103 even 12 6480.2.a.t.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
180.2.i.a.61.1 2 45.43 odd 12
180.2.i.a.121.1 yes 2 5.3 odd 4
540.2.i.a.181.1 2 45.38 even 12
540.2.i.a.361.1 2 15.8 even 4
720.2.q.a.241.1 2 180.43 even 12
720.2.q.a.481.1 2 20.3 even 4
900.2.i.a.301.1 2 5.2 odd 4
900.2.i.a.601.1 2 45.7 odd 12
900.2.s.a.49.1 4 5.4 even 2 inner
900.2.s.a.49.2 4 1.1 even 1 trivial
900.2.s.a.349.1 4 9.7 even 3 inner
900.2.s.a.349.2 4 45.34 even 6 inner
1620.2.a.b.1.1 1 45.23 even 12
1620.2.a.e.1.1 1 45.13 odd 12
2160.2.q.e.721.1 2 180.83 odd 12
2160.2.q.e.1441.1 2 60.23 odd 4
2700.2.i.a.901.1 2 15.2 even 4
2700.2.i.a.1801.1 2 45.2 even 12
2700.2.s.a.1549.1 4 3.2 odd 2
2700.2.s.a.1549.2 4 15.14 odd 2
2700.2.s.a.2449.1 4 45.29 odd 6
2700.2.s.a.2449.2 4 9.2 odd 6
6480.2.a.h.1.1 1 180.23 odd 12
6480.2.a.t.1.1 1 180.103 even 12
8100.2.a.h.1.1 1 45.32 even 12
8100.2.a.i.1.1 1 45.22 odd 12
8100.2.d.e.649.1 2 9.4 even 3
8100.2.d.e.649.2 2 45.4 even 6
8100.2.d.f.649.1 2 9.5 odd 6
8100.2.d.f.649.2 2 45.14 odd 6