Properties

Label 2100.2.f.c.1049.3
Level 21002100
Weight 22
Character 2100.1049
Analytic conductor 16.76916.769
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] = [2100,2,Mod(1049,2100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2100, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2100.1049");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 2100=223527 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2100.f (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: 16.768584424516.7685844245
Analytic rank: 00
Dimension: 44
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 420)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1049.3
Root 0.8660250.500000i-0.866025 - 0.500000i of defining polynomial
Character χ\chi == 2100.1049
Dual form 2100.2.f.c.1049.4

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+(1.732052.00000i)q7+(1.500002.59808i)q95.19615iq11+1.73205q133.00000iq17+3.46410iq19+(1.500004.33013i)q215.19615q27+5.19615iq2910.3923iq31+(7.794234.50000i)q33+8.00000iq37+(1.500002.59808i)q39+6.00000q41+10.0000iq433.00000iq47+(1.000006.92820i)q49+(4.500002.59808i)q5110.3923q53+(5.19615+3.00000i)q576.00000q59+6.92820iq61+(7.794231.50000i)q632.00000iq6710.3923iq716.92820q73+(10.39239.00000i)q77+13.0000q79+(4.50000+7.79423i)q8112.0000iq83+(7.79423+4.50000i)q87+(3.000003.46410i)q91+(15.58859.00000i)q931.73205q97+(13.5000+7.79423i)q99+O(q100)q+(0.866025 - 1.50000i) q^{3} +(1.73205 - 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} -5.19615i q^{11} +1.73205 q^{13} -3.00000i q^{17} +3.46410i q^{19} +(-1.50000 - 4.33013i) q^{21} -5.19615 q^{27} +5.19615i q^{29} -10.3923i q^{31} +(-7.79423 - 4.50000i) q^{33} +8.00000i q^{37} +(1.50000 - 2.59808i) q^{39} +6.00000 q^{41} +10.0000i q^{43} -3.00000i q^{47} +(-1.00000 - 6.92820i) q^{49} +(-4.50000 - 2.59808i) q^{51} -10.3923 q^{53} +(5.19615 + 3.00000i) q^{57} -6.00000 q^{59} +6.92820i q^{61} +(-7.79423 - 1.50000i) q^{63} -2.00000i q^{67} -10.3923i q^{71} -6.92820 q^{73} +(-10.3923 - 9.00000i) q^{77} +13.0000 q^{79} +(-4.50000 + 7.79423i) q^{81} -12.0000i q^{83} +(7.79423 + 4.50000i) q^{87} +(3.00000 - 3.46410i) q^{91} +(-15.5885 - 9.00000i) q^{93} -1.73205 q^{97} +(-13.5000 + 7.79423i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q6q96q21+6q39+24q414q4918q5124q59+52q7918q81+12q9154q99+O(q100) 4 q - 6 q^{9} - 6 q^{21} + 6 q^{39} + 24 q^{41} - 4 q^{49} - 18 q^{51} - 24 q^{59} + 52 q^{79} - 18 q^{81} + 12 q^{91} - 54 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2100Z)×\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times.

nn 701701 10511051 11771177 15011501
χ(n)\chi(n) 1-1 11 1-1 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 1.73205 2.00000i 0.654654 0.755929i
88 0 0
99 −1.50000 2.59808i −0.500000 0.866025i
1010 0 0
1111 5.19615i 1.56670i −0.621582 0.783349i 0.713510π-0.713510\pi
0.621582 0.783349i 0.286490π-0.286490\pi
1212 0 0
1313 1.73205 0.480384 0.240192 0.970725i 0.422790π-0.422790\pi
0.240192 + 0.970725i 0.422790π0.422790\pi
1414 0 0
1515 0 0
1616 0 0
1717 3.00000i 0.727607i −0.931476 0.363803i 0.881478π-0.881478\pi
0.931476 0.363803i 0.118522π-0.118522\pi
1818 0 0
1919 3.46410i 0.794719i 0.917663 + 0.397360i 0.130073π0.130073\pi
−0.917663 + 0.397360i 0.869927π0.869927\pi
2020 0 0
2121 −1.50000 4.33013i −0.327327 0.944911i
2222 0 0
2323 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2424 0 0
2525 0 0
2626 0 0
2727 −5.19615 −1.00000
2828 0 0
2929 5.19615i 0.964901i 0.875923 + 0.482451i 0.160253π0.160253\pi
−0.875923 + 0.482451i 0.839747π0.839747\pi
3030 0 0
3131 10.3923i 1.86651i −0.359211 0.933257i 0.616954π-0.616954\pi
0.359211 0.933257i 0.383046π-0.383046\pi
3232 0 0
3333 −7.79423 4.50000i −1.35680 0.783349i
3434 0 0
3535 0 0
3636 0 0
3737 8.00000i 1.31519i 0.753371 + 0.657596i 0.228427π0.228427\pi
−0.753371 + 0.657596i 0.771573π0.771573\pi
3838 0 0
3939 1.50000 2.59808i 0.240192 0.416025i
4040 0 0
4141 6.00000 0.937043 0.468521 0.883452i 0.344787π-0.344787\pi
0.468521 + 0.883452i 0.344787π0.344787\pi
4242 0 0
4343 10.0000i 1.52499i 0.646997 + 0.762493i 0.276025π0.276025\pi
−0.646997 + 0.762493i 0.723975π0.723975\pi
4444 0 0
4545 0 0
4646 0 0
4747 3.00000i 0.437595i −0.975770 0.218797i 0.929787π-0.929787\pi
0.975770 0.218797i 0.0702134π-0.0702134\pi
4848 0 0
4949 −1.00000 6.92820i −0.142857 0.989743i
5050 0 0
5151 −4.50000 2.59808i −0.630126 0.363803i
5252 0 0
5353 −10.3923 −1.42749 −0.713746 0.700404i 0.753003π-0.753003\pi
−0.713746 + 0.700404i 0.753003π0.753003\pi
5454 0 0
5555 0 0
5656 0 0
5757 5.19615 + 3.00000i 0.688247 + 0.397360i
5858 0 0
5959 −6.00000 −0.781133 −0.390567 0.920575i 0.627721π-0.627721\pi
−0.390567 + 0.920575i 0.627721π0.627721\pi
6060 0 0
6161 6.92820i 0.887066i 0.896258 + 0.443533i 0.146275π0.146275\pi
−0.896258 + 0.443533i 0.853725π0.853725\pi
6262 0 0
6363 −7.79423 1.50000i −0.981981 0.188982i
6464 0 0
6565 0 0
6666 0 0
6767 2.00000i 0.244339i −0.992509 0.122169i 0.961015π-0.961015\pi
0.992509 0.122169i 0.0389851π-0.0389851\pi
6868 0 0
6969 0 0
7070 0 0
7171 10.3923i 1.23334i −0.787222 0.616670i 0.788481π-0.788481\pi
0.787222 0.616670i 0.211519π-0.211519\pi
7272 0 0
7373 −6.92820 −0.810885 −0.405442 0.914121i 0.632883π-0.632883\pi
−0.405442 + 0.914121i 0.632883π0.632883\pi
7474 0 0
7575 0 0
7676 0 0
7777 −10.3923 9.00000i −1.18431 1.02565i
7878 0 0
7979 13.0000 1.46261 0.731307 0.682048i 0.238911π-0.238911\pi
0.731307 + 0.682048i 0.238911π0.238911\pi
8080 0 0
8181 −4.50000 + 7.79423i −0.500000 + 0.866025i
8282 0 0
8383 12.0000i 1.31717i −0.752506 0.658586i 0.771155π-0.771155\pi
0.752506 0.658586i 0.228845π-0.228845\pi
8484 0 0
8585 0 0
8686 0 0
8787 7.79423 + 4.50000i 0.835629 + 0.482451i
8888 0 0
8989 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
9090 0 0
9191 3.00000 3.46410i 0.314485 0.363137i
9292 0 0
9393 −15.5885 9.00000i −1.61645 0.933257i
9494 0 0
9595 0 0
9696 0 0
9797 −1.73205 −0.175863 −0.0879316 0.996127i 0.528026π-0.528026\pi
−0.0879316 + 0.996127i 0.528026π0.528026\pi
9898 0 0
9999 −13.5000 + 7.79423i −1.35680 + 0.783349i
100100 0 0
101101 18.0000 1.79107 0.895533 0.444994i 0.146794π-0.146794\pi
0.895533 + 0.444994i 0.146794π0.146794\pi
102102 0 0
103103 −1.73205 −0.170664 −0.0853320 0.996353i 0.527195π-0.527195\pi
−0.0853320 + 0.996353i 0.527195π0.527195\pi
104104 0 0
105105 0 0
106106 0 0
107107 10.3923 1.00466 0.502331 0.864675i 0.332476π-0.332476\pi
0.502331 + 0.864675i 0.332476π0.332476\pi
108108 0 0
109109 11.0000 1.05361 0.526804 0.849987i 0.323390π-0.323390\pi
0.526804 + 0.849987i 0.323390π0.323390\pi
110110 0 0
111111 12.0000 + 6.92820i 1.13899 + 0.657596i
112112 0 0
113113 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
114114 0 0
115115 0 0
116116 0 0
117117 −2.59808 4.50000i −0.240192 0.416025i
118118 0 0
119119 −6.00000 5.19615i −0.550019 0.476331i
120120 0 0
121121 −16.0000 −1.45455
122122 0 0
123123 5.19615 9.00000i 0.468521 0.811503i
124124 0 0
125125 0 0
126126 0 0
127127 2.00000i 0.177471i −0.996055 0.0887357i 0.971717π-0.971717\pi
0.996055 0.0887357i 0.0282826π-0.0282826\pi
128128 0 0
129129 15.0000 + 8.66025i 1.32068 + 0.762493i
130130 0 0
131131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
132132 0 0
133133 6.92820 + 6.00000i 0.600751 + 0.520266i
134134 0 0
135135 0 0
136136 0 0
137137 −20.7846 −1.77575 −0.887875 0.460086i 0.847819π-0.847819\pi
−0.887875 + 0.460086i 0.847819π0.847819\pi
138138 0 0
139139 6.92820i 0.587643i −0.955860 0.293821i 0.905073π-0.905073\pi
0.955860 0.293821i 0.0949270π-0.0949270\pi
140140 0 0
141141 −4.50000 2.59808i −0.378968 0.218797i
142142 0 0
143143 9.00000i 0.752618i
144144 0 0
145145 0 0
146146 0 0
147147 −11.2583 4.50000i −0.928571 0.371154i
148148 0 0
149149 0 0 1.00000 00
−1.00000 π\pi
150150 0 0
151151 −5.00000 −0.406894 −0.203447 0.979086i 0.565214π-0.565214\pi
−0.203447 + 0.979086i 0.565214π0.565214\pi
152152 0 0
153153 −7.79423 + 4.50000i −0.630126 + 0.363803i
154154 0 0
155155 0 0
156156 0 0
157157 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
158158 0 0
159159 −9.00000 + 15.5885i −0.713746 + 1.23625i
160160 0 0
161161 0 0
162162 0 0
163163 8.00000i 0.626608i 0.949653 + 0.313304i 0.101436π0.101436\pi
−0.949653 + 0.313304i 0.898564π0.898564\pi
164164 0 0
165165 0 0
166166 0 0
167167 15.0000i 1.16073i 0.814355 + 0.580367i 0.197091π0.197091\pi
−0.814355 + 0.580367i 0.802909π0.802909\pi
168168 0 0
169169 −10.0000 −0.769231
170170 0 0
171171 9.00000 5.19615i 0.688247 0.397360i
172172 0 0
173173 9.00000i 0.684257i −0.939653 0.342129i 0.888852π-0.888852\pi
0.939653 0.342129i 0.111148π-0.111148\pi
174174 0 0
175175 0 0
176176 0 0
177177 −5.19615 + 9.00000i −0.390567 + 0.676481i
178178 0 0
179179 10.3923i 0.776757i −0.921500 0.388379i 0.873035π-0.873035\pi
0.921500 0.388379i 0.126965π-0.126965\pi
180180 0 0
181181 17.3205i 1.28742i −0.765268 0.643712i 0.777394π-0.777394\pi
0.765268 0.643712i 0.222606π-0.222606\pi
182182 0 0
183183 10.3923 + 6.00000i 0.768221 + 0.443533i
184184 0 0
185185 0 0
186186 0 0
187187 −15.5885 −1.13994
188188 0 0
189189 −9.00000 + 10.3923i −0.654654 + 0.755929i
190190 0 0
191191 15.5885i 1.12794i 0.825795 + 0.563971i 0.190727π0.190727\pi
−0.825795 + 0.563971i 0.809273π0.809273\pi
192192 0 0
193193 16.0000i 1.15171i 0.817554 + 0.575853i 0.195330π0.195330\pi
−0.817554 + 0.575853i 0.804670π0.804670\pi
194194 0 0
195195 0 0
196196 0 0
197197 10.3923 0.740421 0.370211 0.928948i 0.379286π-0.379286\pi
0.370211 + 0.928948i 0.379286π0.379286\pi
198198 0 0
199199 24.2487i 1.71895i −0.511182 0.859473i 0.670792π-0.670792\pi
0.511182 0.859473i 0.329208π-0.329208\pi
200200 0 0
201201 −3.00000 1.73205i −0.211604 0.122169i
202202 0 0
203203 10.3923 + 9.00000i 0.729397 + 0.631676i
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 18.0000 1.24509
210210 0 0
211211 25.0000 1.72107 0.860535 0.509390i 0.170129π-0.170129\pi
0.860535 + 0.509390i 0.170129π0.170129\pi
212212 0 0
213213 −15.5885 9.00000i −1.06810 0.616670i
214214 0 0
215215 0 0
216216 0 0
217217 −20.7846 18.0000i −1.41095 1.22192i
218218 0 0
219219 −6.00000 + 10.3923i −0.405442 + 0.702247i
220220 0 0
221221 5.19615i 0.349531i
222222 0 0
223223 5.19615 0.347960 0.173980 0.984749i 0.444337π-0.444337\pi
0.173980 + 0.984749i 0.444337π0.444337\pi
224224 0 0
225225 0 0
226226 0 0
227227 27.0000i 1.79205i 0.444001 + 0.896026i 0.353559π0.353559\pi
−0.444001 + 0.896026i 0.646441π0.646441\pi
228228 0 0
229229 10.3923i 0.686743i −0.939200 0.343371i 0.888431π-0.888431\pi
0.939200 0.343371i 0.111569π-0.111569\pi
230230 0 0
231231 −22.5000 + 7.79423i −1.48039 + 0.512823i
232232 0 0
233233 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
234234 0 0
235235 0 0
236236 0 0
237237 11.2583 19.5000i 0.731307 1.26666i
238238 0 0
239239 25.9808i 1.68056i 0.542156 + 0.840278i 0.317608π0.317608\pi
−0.542156 + 0.840278i 0.682392π0.682392\pi
240240 0 0
241241 6.92820i 0.446285i 0.974786 + 0.223142i 0.0716315π0.0716315\pi
−0.974786 + 0.223142i 0.928369π0.928369\pi
242242 0 0
243243 7.79423 + 13.5000i 0.500000 + 0.866025i
244244 0 0
245245 0 0
246246 0 0
247247 6.00000i 0.381771i
248248 0 0
249249 −18.0000 10.3923i −1.14070 0.658586i
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 0 0
254254 0 0
255255 0 0
256256 0 0
257257 18.0000i 1.12281i −0.827541 0.561405i 0.810261π-0.810261\pi
0.827541 0.561405i 0.189739π-0.189739\pi
258258 0 0
259259 16.0000 + 13.8564i 0.994192 + 0.860995i
260260 0 0
261261 13.5000 7.79423i 0.835629 0.482451i
262262 0 0
263263 −31.1769 −1.92245 −0.961225 0.275764i 0.911069π-0.911069\pi
−0.961225 + 0.275764i 0.911069π0.911069\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 0 0
269269 12.0000 0.731653 0.365826 0.930683i 0.380786π-0.380786\pi
0.365826 + 0.930683i 0.380786π0.380786\pi
270270 0 0
271271 6.92820i 0.420858i −0.977609 0.210429i 0.932514π-0.932514\pi
0.977609 0.210429i 0.0674861π-0.0674861\pi
272272 0 0
273273 −2.59808 7.50000i −0.157243 0.453921i
274274 0 0
275275 0 0
276276 0 0
277277 8.00000i 0.480673i −0.970690 0.240337i 0.922742π-0.922742\pi
0.970690 0.240337i 0.0772579π-0.0772579\pi
278278 0 0
279279 −27.0000 + 15.5885i −1.61645 + 0.933257i
280280 0 0
281281 5.19615i 0.309976i 0.987916 + 0.154988i 0.0495340π0.0495340\pi
−0.987916 + 0.154988i 0.950466π0.950466\pi
282282 0 0
283283 25.9808 1.54440 0.772198 0.635382i 0.219157π-0.219157\pi
0.772198 + 0.635382i 0.219157π0.219157\pi
284284 0 0
285285 0 0
286286 0 0
287287 10.3923 12.0000i 0.613438 0.708338i
288288 0 0
289289 8.00000 0.470588
290290 0 0
291291 −1.50000 + 2.59808i −0.0879316 + 0.152302i
292292 0 0
293293 3.00000i 0.175262i −0.996153 0.0876309i 0.972070π-0.972070\pi
0.996153 0.0876309i 0.0279296π-0.0279296\pi
294294 0 0
295295 0 0
296296 0 0
297297 27.0000i 1.56670i
298298 0 0
299299 0 0
300300 0 0
301301 20.0000 + 17.3205i 1.15278 + 0.998337i
302302 0 0
303303 15.5885 27.0000i 0.895533 1.55111i
304304 0 0
305305 0 0
306306 0 0
307307 25.9808 1.48280 0.741400 0.671063i 0.234162π-0.234162\pi
0.741400 + 0.671063i 0.234162π0.234162\pi
308308 0 0
309309 −1.50000 + 2.59808i −0.0853320 + 0.147799i
310310 0 0
311311 30.0000 1.70114 0.850572 0.525859i 0.176256π-0.176256\pi
0.850572 + 0.525859i 0.176256π0.176256\pi
312312 0 0
313313 22.5167 1.27272 0.636358 0.771393i 0.280440π-0.280440\pi
0.636358 + 0.771393i 0.280440π0.280440\pi
314314 0 0
315315 0 0
316316 0 0
317317 10.3923 0.583690 0.291845 0.956466i 0.405731π-0.405731\pi
0.291845 + 0.956466i 0.405731π0.405731\pi
318318 0 0
319319 27.0000 1.51171
320320 0 0
321321 9.00000 15.5885i 0.502331 0.870063i
322322 0 0
323323 10.3923 0.578243
324324 0 0
325325 0 0
326326 0 0
327327 9.52628 16.5000i 0.526804 0.912452i
328328 0 0
329329 −6.00000 5.19615i −0.330791 0.286473i
330330 0 0
331331 4.00000 0.219860 0.109930 0.993939i 0.464937π-0.464937\pi
0.109930 + 0.993939i 0.464937π0.464937\pi
332332 0 0
333333 20.7846 12.0000i 1.13899 0.657596i
334334 0 0
335335 0 0
336336 0 0
337337 20.0000i 1.08947i 0.838608 + 0.544735i 0.183370π0.183370\pi
−0.838608 + 0.544735i 0.816630π0.816630\pi
338338 0 0
339339 0 0
340340 0 0
341341 −54.0000 −2.92426
342342 0 0
343343 −15.5885 10.0000i −0.841698 0.539949i
344344 0 0
345345 0 0
346346 0 0
347347 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
348348 0 0
349349 17.3205i 0.927146i −0.886059 0.463573i 0.846567π-0.846567\pi
0.886059 0.463573i 0.153433π-0.153433\pi
350350 0 0
351351 −9.00000 −0.480384
352352 0 0
353353 21.0000i 1.11772i 0.829263 + 0.558859i 0.188761π0.188761\pi
−0.829263 + 0.558859i 0.811239π0.811239\pi
354354 0 0
355355 0 0
356356 0 0
357357 −12.9904 + 4.50000i −0.687524 + 0.238165i
358358 0 0
359359 10.3923i 0.548485i −0.961661 0.274242i 0.911573π-0.911573\pi
0.961661 0.274242i 0.0884271π-0.0884271\pi
360360 0 0
361361 7.00000 0.368421
362362 0 0
363363 −13.8564 + 24.0000i −0.727273 + 1.25967i
364364 0 0
365365 0 0
366366 0 0
367367 29.4449 1.53701 0.768505 0.639844i 0.221001π-0.221001\pi
0.768505 + 0.639844i 0.221001π0.221001\pi
368368 0 0
369369 −9.00000 15.5885i −0.468521 0.811503i
370370 0 0
371371 −18.0000 + 20.7846i −0.934513 + 1.07908i
372372 0 0
373373 20.0000i 1.03556i 0.855514 + 0.517780i 0.173242π0.173242\pi
−0.855514 + 0.517780i 0.826758π0.826758\pi
374374 0 0
375375 0 0
376376 0 0
377377 9.00000i 0.463524i
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 −3.00000 1.73205i −0.153695 0.0887357i
382382 0 0
383383 24.0000i 1.22634i 0.789950 + 0.613171i 0.210106π0.210106\pi
−0.789950 + 0.613171i 0.789894π0.789894\pi
384384 0 0
385385 0 0
386386 0 0
387387 25.9808 15.0000i 1.32068 0.762493i
388388 0 0
389389 15.5885i 0.790366i −0.918602 0.395183i 0.870681π-0.870681\pi
0.918602 0.395183i 0.129319π-0.129319\pi
390390 0 0
391391 0 0
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 −5.19615 −0.260787 −0.130394 0.991462i 0.541624π-0.541624\pi
−0.130394 + 0.991462i 0.541624π0.541624\pi
398398 0 0
399399 15.0000 5.19615i 0.750939 0.260133i
400400 0 0
401401 5.19615i 0.259483i −0.991548 0.129742i 0.958585π-0.958585\pi
0.991548 0.129742i 0.0414148π-0.0414148\pi
402402 0 0
403403 18.0000i 0.896644i
404404 0 0
405405 0 0
406406 0 0
407407 41.5692 2.06051
408408 0 0
409409 3.46410i 0.171289i 0.996326 + 0.0856444i 0.0272949π0.0272949\pi
−0.996326 + 0.0856444i 0.972705π0.972705\pi
410410 0 0
411411 −18.0000 + 31.1769i −0.887875 + 1.53784i
412412 0 0
413413 −10.3923 + 12.0000i −0.511372 + 0.590481i
414414 0 0
415415 0 0
416416 0 0
417417 −10.3923 6.00000i −0.508913 0.293821i
418418 0 0
419419 6.00000 0.293119 0.146560 0.989202i 0.453180π-0.453180\pi
0.146560 + 0.989202i 0.453180π0.453180\pi
420420 0 0
421421 −13.0000 −0.633581 −0.316791 0.948495i 0.602605π-0.602605\pi
−0.316791 + 0.948495i 0.602605π0.602605\pi
422422 0 0
423423 −7.79423 + 4.50000i −0.378968 + 0.218797i
424424 0 0
425425 0 0
426426 0 0
427427 13.8564 + 12.0000i 0.670559 + 0.580721i
428428 0 0
429429 −13.5000 7.79423i −0.651786 0.376309i
430430 0 0
431431 5.19615i 0.250290i 0.992138 + 0.125145i 0.0399396π0.0399396\pi
−0.992138 + 0.125145i 0.960060π0.960060\pi
432432 0 0
433433 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
434434 0 0
435435 0 0
436436 0 0
437437 0 0
438438 0 0
439439 20.7846i 0.991995i −0.868324 0.495998i 0.834802π-0.834802\pi
0.868324 0.495998i 0.165198π-0.165198\pi
440440 0 0
441441 −16.5000 + 12.9904i −0.785714 + 0.618590i
442442 0 0
443443 31.1769 1.48126 0.740630 0.671913i 0.234527π-0.234527\pi
0.740630 + 0.671913i 0.234527π0.234527\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 25.9808i 1.22611i −0.790041 0.613054i 0.789941π-0.789941\pi
0.790041 0.613054i 0.210059π-0.210059\pi
450450 0 0
451451 31.1769i 1.46806i
452452 0 0
453453 −4.33013 + 7.50000i −0.203447 + 0.352381i
454454 0 0
455455 0 0
456456 0 0
457457 10.0000i 0.467780i −0.972263 0.233890i 0.924854π-0.924854\pi
0.972263 0.233890i 0.0751456π-0.0751456\pi
458458 0 0
459459 15.5885i 0.727607i
460460 0 0
461461 −12.0000 −0.558896 −0.279448 0.960161i 0.590151π-0.590151\pi
−0.279448 + 0.960161i 0.590151π0.590151\pi
462462 0 0
463463 16.0000i 0.743583i −0.928316 0.371792i 0.878744π-0.878744\pi
0.928316 0.371792i 0.121256π-0.121256\pi
464464 0 0
465465 0 0
466466 0 0
467467 9.00000i 0.416470i 0.978079 + 0.208235i 0.0667719π0.0667719\pi
−0.978079 + 0.208235i 0.933228π0.933228\pi
468468 0 0
469469 −4.00000 3.46410i −0.184703 0.159957i
470470 0 0
471471 0 0
472472 0 0
473473 51.9615 2.38919
474474 0 0
475475 0 0
476476 0 0
477477 15.5885 + 27.0000i 0.713746 + 1.23625i
478478 0 0
479479 12.0000 0.548294 0.274147 0.961688i 0.411605π-0.411605\pi
0.274147 + 0.961688i 0.411605π0.411605\pi
480480 0 0
481481 13.8564i 0.631798i
482482 0 0
483483 0 0
484484 0 0
485485 0 0
486486 0 0
487487 8.00000i 0.362515i 0.983436 + 0.181257i 0.0580167π0.0580167\pi
−0.983436 + 0.181257i 0.941983π0.941983\pi
488488 0 0
489489 12.0000 + 6.92820i 0.542659 + 0.313304i
490490 0 0
491491 5.19615i 0.234499i 0.993102 + 0.117250i 0.0374077π0.0374077\pi
−0.993102 + 0.117250i 0.962592π0.962592\pi
492492 0 0
493493 15.5885 0.702069
494494 0 0
495495 0 0
496496 0 0
497497 −20.7846 18.0000i −0.932317 0.807410i
498498 0 0
499499 −13.0000 −0.581960 −0.290980 0.956729i 0.593981π-0.593981\pi
−0.290980 + 0.956729i 0.593981π0.593981\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 −8.66025 + 15.0000i −0.384615 + 0.666173i
508508 0 0
509509 −24.0000 −1.06378 −0.531891 0.846813i 0.678518π-0.678518\pi
−0.531891 + 0.846813i 0.678518π0.678518\pi
510510 0 0
511511 −12.0000 + 13.8564i −0.530849 + 0.612971i
512512 0 0
513513 18.0000i 0.794719i
514514 0 0
515515 0 0
516516 0 0
517517 −15.5885 −0.685580
518518 0 0
519519 −13.5000 7.79423i −0.592584 0.342129i
520520 0 0
521521 42.0000 1.84005 0.920027 0.391856i 0.128167π-0.128167\pi
0.920027 + 0.391856i 0.128167π0.128167\pi
522522 0 0
523523 17.3205 0.757373 0.378686 0.925525i 0.376376π-0.376376\pi
0.378686 + 0.925525i 0.376376π0.376376\pi
524524 0 0
525525 0 0
526526 0 0
527527 −31.1769 −1.35809
528528 0 0
529529 −23.0000 −1.00000
530530 0 0
531531 9.00000 + 15.5885i 0.390567 + 0.676481i
532532 0 0
533533 10.3923 0.450141
534534 0 0
535535 0 0
536536 0 0
537537 −15.5885 9.00000i −0.672692 0.388379i
538538 0 0
539539 −36.0000 + 5.19615i −1.55063 + 0.223814i
540540 0 0
541541 17.0000 0.730887 0.365444 0.930834i 0.380917π-0.380917\pi
0.365444 + 0.930834i 0.380917π0.380917\pi
542542 0 0
543543 −25.9808 15.0000i −1.11494 0.643712i
544544 0 0
545545 0 0
546546 0 0
547547 32.0000i 1.36822i −0.729378 0.684111i 0.760191π-0.760191\pi
0.729378 0.684111i 0.239809π-0.239809\pi
548548 0 0
549549 18.0000 10.3923i 0.768221 0.443533i
550550 0 0
551551 −18.0000 −0.766826
552552 0 0
553553 22.5167 26.0000i 0.957506 1.10563i
554554 0 0
555555 0 0
556556 0 0
557557 20.7846 0.880672 0.440336 0.897833i 0.354859π-0.354859\pi
0.440336 + 0.897833i 0.354859π0.354859\pi
558558 0 0
559559 17.3205i 0.732579i
560560 0 0
561561 −13.5000 + 23.3827i −0.569970 + 0.987218i
562562 0 0
563563 36.0000i 1.51722i 0.651546 + 0.758610i 0.274121π0.274121\pi
−0.651546 + 0.758610i 0.725879π0.725879\pi
564564 0 0
565565 0 0
566566 0 0
567567 7.79423 + 22.5000i 0.327327 + 0.944911i
568568 0 0
569569 20.7846i 0.871336i 0.900107 + 0.435668i 0.143488π0.143488\pi
−0.900107 + 0.435668i 0.856512π0.856512\pi
570570 0 0
571571 20.0000 0.836974 0.418487 0.908223i 0.362561π-0.362561\pi
0.418487 + 0.908223i 0.362561π0.362561\pi
572572 0 0
573573 23.3827 + 13.5000i 0.976826 + 0.563971i
574574 0 0
575575 0 0
576576 0 0
577577 1.73205 0.0721062 0.0360531 0.999350i 0.488521π-0.488521\pi
0.0360531 + 0.999350i 0.488521π0.488521\pi
578578 0 0
579579 24.0000 + 13.8564i 0.997406 + 0.575853i
580580 0 0
581581 −24.0000 20.7846i −0.995688 0.862291i
582582 0 0
583583 54.0000i 2.23645i
584584 0 0
585585 0 0
586586 0 0
587587 36.0000i 1.48588i 0.669359 + 0.742940i 0.266569π0.266569\pi
−0.669359 + 0.742940i 0.733431π0.733431\pi
588588 0 0
589589 36.0000 1.48335
590590 0 0
591591 9.00000 15.5885i 0.370211 0.641223i
592592 0 0
593593 21.0000i 0.862367i −0.902264 0.431183i 0.858096π-0.858096\pi
0.902264 0.431183i 0.141904π-0.141904\pi
594594 0 0
595595 0 0
596596 0 0
597597 −36.3731 21.0000i −1.48865 0.859473i
598598 0 0
599599 25.9808i 1.06155i 0.847514 + 0.530773i 0.178098π0.178098\pi
−0.847514 + 0.530773i 0.821902π0.821902\pi
600600 0 0
601601 31.1769i 1.27173i 0.771799 + 0.635866i 0.219357π0.219357\pi
−0.771799 + 0.635866i 0.780643π0.780643\pi
602602 0 0
603603 −5.19615 + 3.00000i −0.211604 + 0.122169i
604604 0 0
605605 0 0
606606 0 0
607607 8.66025 0.351509 0.175754 0.984434i 0.443764π-0.443764\pi
0.175754 + 0.984434i 0.443764π0.443764\pi
608608 0 0
609609 22.5000 7.79423i 0.911746 0.315838i
610610 0 0
611611 5.19615i 0.210214i
612612 0 0
613613 26.0000i 1.05013i 0.851062 + 0.525065i 0.175959π0.175959\pi
−0.851062 + 0.525065i 0.824041π0.824041\pi
614614 0 0
615615 0 0
616616 0 0
617617 −41.5692 −1.67351 −0.836757 0.547575i 0.815551π-0.815551\pi
−0.836757 + 0.547575i 0.815551π0.815551\pi
618618 0 0
619619 6.92820i 0.278468i 0.990260 + 0.139234i 0.0444640π0.0444640\pi
−0.990260 + 0.139234i 0.955536π0.955536\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 0 0
626626 0 0
627627 15.5885 27.0000i 0.622543 1.07828i
628628 0 0
629629 24.0000 0.956943
630630 0 0
631631 17.0000 0.676759 0.338380 0.941010i 0.390121π-0.390121\pi
0.338380 + 0.941010i 0.390121π0.390121\pi
632632 0 0
633633 21.6506 37.5000i 0.860535 1.49049i
634634 0 0
635635 0 0
636636 0 0
637637 −1.73205 12.0000i −0.0686264 0.475457i
638638 0 0
639639 −27.0000 + 15.5885i −1.06810 + 0.616670i
640640 0 0
641641 20.7846i 0.820943i 0.911873 + 0.410471i 0.134636π0.134636\pi
−0.911873 + 0.410471i 0.865364π0.865364\pi
642642 0 0
643643 15.5885 0.614749 0.307374 0.951589i 0.400550π-0.400550\pi
0.307374 + 0.951589i 0.400550π0.400550\pi
644644 0 0
645645 0 0
646646 0 0
647647 36.0000i 1.41531i 0.706560 + 0.707653i 0.250246π0.250246\pi
−0.706560 + 0.707653i 0.749754π0.749754\pi
648648 0 0
649649 31.1769i 1.22380i
650650 0 0
651651 −45.0000 + 15.5885i −1.76369 + 0.610960i
652652 0 0
653653 −10.3923 −0.406682 −0.203341 0.979108i 0.565180π-0.565180\pi
−0.203341 + 0.979108i 0.565180π0.565180\pi
654654 0 0
655655 0 0
656656 0 0
657657 10.3923 + 18.0000i 0.405442 + 0.702247i
658658 0 0
659659 15.5885i 0.607240i 0.952793 + 0.303620i 0.0981953π0.0981953\pi
−0.952793 + 0.303620i 0.901805π0.901805\pi
660660 0 0
661661 48.4974i 1.88633i −0.332323 0.943166i 0.607832π-0.607832\pi
0.332323 0.943166i 0.392168π-0.392168\pi
662662 0 0
663663 −7.79423 4.50000i −0.302703 0.174766i
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 4.50000 7.79423i 0.173980 0.301342i
670670 0 0
671671 36.0000 1.38976
672672 0 0
673673 32.0000i 1.23351i −0.787155 0.616755i 0.788447π-0.788447\pi
0.787155 0.616755i 0.211553π-0.211553\pi
674674 0 0
675675 0 0
676676 0 0
677677 27.0000i 1.03769i −0.854867 0.518847i 0.826361π-0.826361\pi
0.854867 0.518847i 0.173639π-0.173639\pi
678678 0 0
679679 −3.00000 + 3.46410i −0.115129 + 0.132940i
680680 0 0
681681 40.5000 + 23.3827i 1.55196 + 0.896026i
682682 0 0
683683 20.7846 0.795301 0.397650 0.917537i 0.369826π-0.369826\pi
0.397650 + 0.917537i 0.369826π0.369826\pi
684684 0 0
685685 0 0
686686 0 0
687687 −15.5885 9.00000i −0.594737 0.343371i
688688 0 0
689689 −18.0000 −0.685745
690690 0 0
691691 41.5692i 1.58137i 0.612225 + 0.790684i 0.290275π0.290275\pi
−0.612225 + 0.790684i 0.709725π0.709725\pi
692692 0 0
693693 −7.79423 + 40.5000i −0.296078 + 1.53847i
694694 0 0
695695 0 0
696696 0 0
697697 18.0000i 0.681799i
698698 0 0
699699 0 0
700700 0 0
701701 36.3731i 1.37379i 0.726756 + 0.686896i 0.241027π0.241027\pi
−0.726756 + 0.686896i 0.758973π0.758973\pi
702702 0 0
703703 −27.7128 −1.04521
704704 0 0
705705 0 0
706706 0 0
707707 31.1769 36.0000i 1.17253 1.35392i
708708 0 0
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 −19.5000 33.7750i −0.731307 1.26666i
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 38.9711 + 22.5000i 1.45540 + 0.840278i
718718 0 0
719719 12.0000 0.447524 0.223762 0.974644i 0.428166π-0.428166\pi
0.223762 + 0.974644i 0.428166π0.428166\pi
720720 0 0
721721 −3.00000 + 3.46410i −0.111726 + 0.129010i
722722 0 0
723723 10.3923 + 6.00000i 0.386494 + 0.223142i
724724 0 0
725725 0 0
726726 0 0
727727 −51.9615 −1.92715 −0.963573 0.267445i 0.913821π-0.913821\pi
−0.963573 + 0.267445i 0.913821π0.913821\pi
728728 0 0
729729 27.0000 1.00000
730730 0 0
731731 30.0000 1.10959
732732 0 0
733733 −36.3731 −1.34347 −0.671735 0.740792i 0.734451π-0.734451\pi
−0.671735 + 0.740792i 0.734451π0.734451\pi
734734 0 0
735735 0 0
736736 0 0
737737 −10.3923 −0.382805
738738 0 0
739739 −11.0000 −0.404642 −0.202321 0.979319i 0.564848π-0.564848\pi
−0.202321 + 0.979319i 0.564848π0.564848\pi
740740 0 0
741741 9.00000 + 5.19615i 0.330623 + 0.190885i
742742 0 0
743743 −10.3923 −0.381257 −0.190628 0.981662i 0.561053π-0.561053\pi
−0.190628 + 0.981662i 0.561053π0.561053\pi
744744 0 0
745745 0 0
746746 0 0
747747 −31.1769 + 18.0000i −1.14070 + 0.658586i
748748 0 0
749749 18.0000 20.7846i 0.657706 0.759453i
750750 0 0
751751 −11.0000 −0.401396 −0.200698 0.979653i 0.564321π-0.564321\pi
−0.200698 + 0.979653i 0.564321π0.564321\pi
752752 0 0
753753 −20.7846 + 36.0000i −0.757433 + 1.31191i
754754 0 0
755755 0 0
756756 0 0
757757 8.00000i 0.290765i 0.989376 + 0.145382i 0.0464413π0.0464413\pi
−0.989376 + 0.145382i 0.953559π0.953559\pi
758758 0 0
759759 0 0
760760 0 0
761761 −12.0000 −0.435000 −0.217500 0.976060i 0.569790π-0.569790\pi
−0.217500 + 0.976060i 0.569790π0.569790\pi
762762 0 0
763763 19.0526 22.0000i 0.689749 0.796453i
764764 0 0
765765 0 0
766766 0 0
767767 −10.3923 −0.375244
768768 0 0
769769 17.3205i 0.624593i −0.949985 0.312297i 0.898902π-0.898902\pi
0.949985 0.312297i 0.101098π-0.101098\pi
770770 0 0
771771 −27.0000 15.5885i −0.972381 0.561405i
772772 0 0
773773 15.0000i 0.539513i −0.962929 0.269756i 0.913057π-0.913057\pi
0.962929 0.269756i 0.0869431π-0.0869431\pi
774774 0 0
775775 0 0
776776 0 0
777777 34.6410 12.0000i 1.24274 0.430498i
778778 0 0
779779 20.7846i 0.744686i
780780 0 0
781781 −54.0000 −1.93227
782782 0 0
783783 27.0000i 0.964901i
784784 0 0
785785 0 0
786786 0 0
787787 50.2295 1.79049 0.895244 0.445577i 0.147001π-0.147001\pi
0.895244 + 0.445577i 0.147001π0.147001\pi
788788 0 0
789789 −27.0000 + 46.7654i −0.961225 + 1.66489i
790790 0 0
791791 0 0
792792 0 0
793793 12.0000i 0.426132i
794794 0 0
795795 0 0
796796 0 0
797797 9.00000i 0.318796i 0.987214 + 0.159398i 0.0509554π0.0509554\pi
−0.987214 + 0.159398i 0.949045π0.949045\pi
798798 0 0
799799 −9.00000 −0.318397
800800 0 0
801801 0 0
802802 0 0
803803 36.0000i 1.27041i
804804 0 0
805805 0 0
806806 0 0
807807 10.3923 18.0000i 0.365826 0.633630i
808808 0 0
809809 36.3731i 1.27881i 0.768871 + 0.639404i 0.220819π0.220819\pi
−0.768871 + 0.639404i 0.779181π0.779181\pi
810810 0 0
811811 20.7846i 0.729846i −0.931038 0.364923i 0.881095π-0.881095\pi
0.931038 0.364923i 0.118905π-0.118905\pi
812812 0 0
813813 −10.3923 6.00000i −0.364474 0.210429i
814814 0 0
815815 0 0
816816 0 0
817817 −34.6410 −1.21194
818818 0 0
819819 −13.5000 2.59808i −0.471728 0.0907841i
820820 0 0
821821 36.3731i 1.26943i −0.772747 0.634714i 0.781118π-0.781118\pi
0.772747 0.634714i 0.218882π-0.218882\pi
822822 0 0
823823 2.00000i 0.0697156i 0.999392 + 0.0348578i 0.0110978π0.0110978\pi
−0.999392 + 0.0348578i 0.988902π0.988902\pi
824824 0 0
825825 0 0
826826 0 0
827827 −41.5692 −1.44550 −0.722752 0.691108i 0.757123π-0.757123\pi
−0.722752 + 0.691108i 0.757123π0.757123\pi
828828 0 0
829829 45.0333i 1.56407i −0.623233 0.782036i 0.714181π-0.714181\pi
0.623233 0.782036i 0.285819π-0.285819\pi
830830 0 0
831831 −12.0000 6.92820i −0.416275 0.240337i
832832 0 0
833833 −20.7846 + 3.00000i −0.720144 + 0.103944i
834834 0 0
835835 0 0
836836 0 0
837837 54.0000i 1.86651i
838838 0 0
839839 −12.0000 −0.414286 −0.207143 0.978311i 0.566417π-0.566417\pi
−0.207143 + 0.978311i 0.566417π0.566417\pi
840840 0 0
841841 2.00000 0.0689655
842842 0 0
843843 7.79423 + 4.50000i 0.268447 + 0.154988i
844844 0 0
845845 0 0
846846 0 0
847847 −27.7128 + 32.0000i −0.952224 + 1.09953i
848848 0 0
849849 22.5000 38.9711i 0.772198 1.33749i
850850 0 0
851851 0 0
852852 0 0
853853 −13.8564 −0.474434 −0.237217 0.971457i 0.576235π-0.576235\pi
−0.237217 + 0.971457i 0.576235π0.576235\pi
854854 0 0
855855 0 0
856856 0 0
857857 6.00000i 0.204956i 0.994735 + 0.102478i 0.0326771π0.0326771\pi
−0.994735 + 0.102478i 0.967323π0.967323\pi
858858 0 0
859859 6.92820i 0.236387i 0.992991 + 0.118194i 0.0377103π0.0377103\pi
−0.992991 + 0.118194i 0.962290π0.962290\pi
860860 0 0
861861 −9.00000 25.9808i −0.306719 0.885422i
862862 0 0
863863 −31.1769 −1.06127 −0.530637 0.847599i 0.678047π-0.678047\pi
−0.530637 + 0.847599i 0.678047π0.678047\pi
864864 0 0
865865 0 0
866866 0 0
867867 6.92820 12.0000i 0.235294 0.407541i
868868 0 0
869869 67.5500i 2.29148i
870870 0 0
871871 3.46410i 0.117377i
872872 0 0
873873 2.59808 + 4.50000i 0.0879316 + 0.152302i
874874 0 0
875875 0 0
876876 0 0
877877 2.00000i 0.0675352i −0.999430 0.0337676i 0.989249π-0.989249\pi
0.999430 0.0337676i 0.0107506π-0.0107506\pi
878878 0 0
879879 −4.50000 2.59808i −0.151781 0.0876309i
880880 0 0
881881 36.0000 1.21287 0.606435 0.795133i 0.292599π-0.292599\pi
0.606435 + 0.795133i 0.292599π0.292599\pi
882882 0 0
883883 44.0000i 1.48072i −0.672212 0.740359i 0.734656π-0.734656\pi
0.672212 0.740359i 0.265344π-0.265344\pi
884884 0 0
885885 0 0
886886 0 0
887887 48.0000i 1.61168i −0.592132 0.805841i 0.701714π-0.701714\pi
0.592132 0.805841i 0.298286π-0.298286\pi
888888 0 0
889889 −4.00000 3.46410i −0.134156 0.116182i
890890 0 0
891891 40.5000 + 23.3827i 1.35680 + 0.783349i
892892 0 0
893893 10.3923 0.347765
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 54.0000 1.80100
900900 0 0
901901 31.1769i 1.03865i
902902 0 0
903903 43.3013 15.0000i 1.44098 0.499169i
904904 0 0
905905 0 0
906906 0 0
907907 32.0000i 1.06254i 0.847202 + 0.531271i 0.178286π0.178286\pi
−0.847202 + 0.531271i 0.821714π0.821714\pi
908908 0 0
909909 −27.0000 46.7654i −0.895533 1.55111i
910910 0 0
911911 31.1769i 1.03294i −0.856306 0.516469i 0.827246π-0.827246\pi
0.856306 0.516469i 0.172754π-0.172754\pi
912912 0 0
913913 −62.3538 −2.06361
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 11.0000 0.362857 0.181428 0.983404i 0.441928π-0.441928\pi
0.181428 + 0.983404i 0.441928π0.441928\pi
920920 0 0
921921 22.5000 38.9711i 0.741400 1.28414i
922922 0 0
923923 18.0000i 0.592477i
924924 0 0
925925 0 0
926926 0 0
927927 2.59808 + 4.50000i 0.0853320 + 0.147799i
928928 0 0
929929 −30.0000 −0.984268 −0.492134 0.870519i 0.663783π-0.663783\pi
−0.492134 + 0.870519i 0.663783π0.663783\pi
930930 0 0
931931 24.0000 3.46410i 0.786568 0.113531i
932932 0 0
933933 25.9808 45.0000i 0.850572 1.47323i
934934 0 0
935935 0 0
936936 0 0
937937 22.5167 0.735587 0.367794 0.929907i 0.380113π-0.380113\pi
0.367794 + 0.929907i 0.380113π0.380113\pi
938938 0 0
939939 19.5000 33.7750i 0.636358 1.10221i
940940 0 0
941941 24.0000 0.782378 0.391189 0.920310i 0.372064π-0.372064\pi
0.391189 + 0.920310i 0.372064π0.372064\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 10.3923 0.337705 0.168852 0.985641i 0.445994π-0.445994\pi
0.168852 + 0.985641i 0.445994π0.445994\pi
948948 0 0
949949 −12.0000 −0.389536
950950 0 0
951951 9.00000 15.5885i 0.291845 0.505490i
952952 0 0
953953 −51.9615 −1.68320 −0.841599 0.540102i 0.818386π-0.818386\pi
−0.841599 + 0.540102i 0.818386π0.818386\pi
954954 0 0
955955 0 0
956956 0 0
957957 23.3827 40.5000i 0.755855 1.30918i
958958 0 0
959959 −36.0000 + 41.5692i −1.16250 + 1.34234i
960960 0 0
961961 −77.0000 −2.48387
962962 0 0
963963 −15.5885 27.0000i −0.502331 0.870063i
964964 0 0
965965 0 0
966966 0 0
967967 2.00000i 0.0643157i −0.999483 0.0321578i 0.989762π-0.989762\pi
0.999483 0.0321578i 0.0102379π-0.0102379\pi
968968 0 0
969969 9.00000 15.5885i 0.289122 0.500773i
970970 0 0
971971 6.00000 0.192549 0.0962746 0.995355i 0.469307π-0.469307\pi
0.0962746 + 0.995355i 0.469307π0.469307\pi
972972 0 0
973973 −13.8564 12.0000i −0.444216 0.384702i
974974 0 0
975975 0 0
976976 0 0
977977 51.9615 1.66240 0.831198 0.555976i 0.187655π-0.187655\pi
0.831198 + 0.555976i 0.187655π0.187655\pi
978978 0 0
979979 0 0
980980 0 0
981981 −16.5000 28.5788i −0.526804 0.912452i
982982 0 0
983983 57.0000i 1.81802i −0.416777 0.909009i 0.636840π-0.636840\pi
0.416777 0.909009i 0.363160π-0.363160\pi
984984 0 0
985985 0 0
986986 0 0
987987 −12.9904 + 4.50000i −0.413488 + 0.143237i
988988 0 0
989989 0 0
990990 0 0
991991 28.0000 0.889449 0.444725 0.895667i 0.353302π-0.353302\pi
0.444725 + 0.895667i 0.353302π0.353302\pi
992992 0 0
993993 3.46410 6.00000i 0.109930 0.190404i
994994 0 0
995995 0 0
996996 0 0
997997 −15.5885 −0.493691 −0.246846 0.969055i 0.579394π-0.579394\pi
−0.246846 + 0.969055i 0.579394π0.579394\pi
998998 0 0
999999 41.5692i 1.31519i
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 2100.2.f.c.1049.3 4
3.2 odd 2 2100.2.f.d.1049.4 4
5.2 odd 4 420.2.d.a.41.1 2
5.3 odd 4 2100.2.d.e.1301.2 2
5.4 even 2 inner 2100.2.f.c.1049.2 4
7.6 odd 2 2100.2.f.d.1049.2 4
15.2 even 4 420.2.d.b.41.1 yes 2
15.8 even 4 2100.2.d.a.1301.2 2
15.14 odd 2 2100.2.f.d.1049.1 4
20.7 even 4 1680.2.f.d.881.2 2
21.20 even 2 inner 2100.2.f.c.1049.1 4
35.13 even 4 2100.2.d.a.1301.1 2
35.27 even 4 420.2.d.b.41.2 yes 2
35.34 odd 2 2100.2.f.d.1049.3 4
60.47 odd 4 1680.2.f.a.881.2 2
105.62 odd 4 420.2.d.a.41.2 yes 2
105.83 odd 4 2100.2.d.e.1301.1 2
105.104 even 2 inner 2100.2.f.c.1049.4 4
140.27 odd 4 1680.2.f.a.881.1 2
420.167 even 4 1680.2.f.d.881.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
420.2.d.a.41.1 2 5.2 odd 4
420.2.d.a.41.2 yes 2 105.62 odd 4
420.2.d.b.41.1 yes 2 15.2 even 4
420.2.d.b.41.2 yes 2 35.27 even 4
1680.2.f.a.881.1 2 140.27 odd 4
1680.2.f.a.881.2 2 60.47 odd 4
1680.2.f.d.881.1 2 420.167 even 4
1680.2.f.d.881.2 2 20.7 even 4
2100.2.d.a.1301.1 2 35.13 even 4
2100.2.d.a.1301.2 2 15.8 even 4
2100.2.d.e.1301.1 2 105.83 odd 4
2100.2.d.e.1301.2 2 5.3 odd 4
2100.2.f.c.1049.1 4 21.20 even 2 inner
2100.2.f.c.1049.2 4 5.4 even 2 inner
2100.2.f.c.1049.3 4 1.1 even 1 trivial
2100.2.f.c.1049.4 4 105.104 even 2 inner
2100.2.f.d.1049.1 4 15.14 odd 2
2100.2.f.d.1049.2 4 7.6 odd 2
2100.2.f.d.1049.3 4 35.34 odd 2
2100.2.f.d.1049.4 4 3.2 odd 2