Properties

Label 2475.2.c.k.199.2
Level 24752475
Weight 22
Character 2475.199
Analytic conductor 19.76319.763
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2475,2,Mod(199,2475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2475, 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("2475.199");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 2475=325211 2475 = 3^{2} \cdot 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2475.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: 19.762974500319.7629745003
Analytic rank: 00
Dimension: 44
Coefficient field: Q(i,13)\Q(i, \sqrt{13})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+7x2+9 x^{4} + 7x^{2} + 9 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 275)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 199.2
Root 1.30278i-1.30278i of defining polynomial
Character χ\chi == 2475.199
Dual form 2475.2.c.k.199.3

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) == q1.30278iq2+0.302776q40.697224iq73.00000iq8+1.00000q11+5.00000iq130.908327q143.30278q16+6.90833iq17+1.00000q191.30278iq22+7.30278iq23+6.51388q260.211103iq28+0.908327q29+10.2111q311.69722iq32+9.00000q342.39445iq371.30278iq38+5.60555q41+7.21110iq43+0.302776q44+9.51388q463.00000iq47+6.51388q49+1.51388iq52+1.30278iq532.09167q561.18335iq5814.2111q597.90833q6113.3028iq628.81665q64+4.00000iq67+2.09167iq68+2.60555q717.90833iq733.11943q74+0.302776q760.697224iq77+10.9083q797.30278iq82+3.51388iq83+9.39445q863.00000iq88+1.69722q89+3.48612q91+2.21110iq923.90833q9415.3028iq978.48612iq98+O(q100)q-1.30278i q^{2} +0.302776 q^{4} -0.697224i q^{7} -3.00000i q^{8} +1.00000 q^{11} +5.00000i q^{13} -0.908327 q^{14} -3.30278 q^{16} +6.90833i q^{17} +1.00000 q^{19} -1.30278i q^{22} +7.30278i q^{23} +6.51388 q^{26} -0.211103i q^{28} +0.908327 q^{29} +10.2111 q^{31} -1.69722i q^{32} +9.00000 q^{34} -2.39445i q^{37} -1.30278i q^{38} +5.60555 q^{41} +7.21110i q^{43} +0.302776 q^{44} +9.51388 q^{46} -3.00000i q^{47} +6.51388 q^{49} +1.51388i q^{52} +1.30278i q^{53} -2.09167 q^{56} -1.18335i q^{58} -14.2111 q^{59} -7.90833 q^{61} -13.3028i q^{62} -8.81665 q^{64} +4.00000i q^{67} +2.09167i q^{68} +2.60555 q^{71} -7.90833i q^{73} -3.11943 q^{74} +0.302776 q^{76} -0.697224i q^{77} +10.9083 q^{79} -7.30278i q^{82} +3.51388i q^{83} +9.39445 q^{86} -3.00000i q^{88} +1.69722 q^{89} +3.48612 q^{91} +2.21110i q^{92} -3.90833 q^{94} -15.3028i q^{97} -8.48612i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q6q4+4q11+18q146q16+4q1910q2618q29+12q31+36q34+8q416q44+2q4610q4930q5628q5910q61+8q644q71++6q94+O(q100) 4 q - 6 q^{4} + 4 q^{11} + 18 q^{14} - 6 q^{16} + 4 q^{19} - 10 q^{26} - 18 q^{29} + 12 q^{31} + 36 q^{34} + 8 q^{41} - 6 q^{44} + 2 q^{46} - 10 q^{49} - 30 q^{56} - 28 q^{59} - 10 q^{61} + 8 q^{64} - 4 q^{71}+ \cdots + 6 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2475Z)×\left(\mathbb{Z}/2475\mathbb{Z}\right)^\times.

nn 551551 20262026 23772377
χ(n)\chi(n) 11 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 − 1.30278i − 0.921201i −0.887607 0.460601i 0.847634π-0.847634\pi
0.887607 0.460601i 0.152366π-0.152366\pi
33 0 0
44 0.302776 0.151388
55 0 0
66 0 0
77 − 0.697224i − 0.263526i −0.991281 0.131763i 0.957936π-0.957936\pi
0.991281 0.131763i 0.0420638π-0.0420638\pi
88 − 3.00000i − 1.06066i
99 0 0
1010 0 0
1111 1.00000 0.301511
1212 0 0
1313 5.00000i 1.38675i 0.720577 + 0.693375i 0.243877π0.243877\pi
−0.720577 + 0.693375i 0.756123π0.756123\pi
1414 −0.908327 −0.242761
1515 0 0
1616 −3.30278 −0.825694
1717 6.90833i 1.67552i 0.546042 + 0.837758i 0.316134π0.316134\pi
−0.546042 + 0.837758i 0.683866π0.683866\pi
1818 0 0
1919 1.00000 0.229416 0.114708 0.993399i 0.463407π-0.463407\pi
0.114708 + 0.993399i 0.463407π0.463407\pi
2020 0 0
2121 0 0
2222 − 1.30278i − 0.277753i
2323 7.30278i 1.52273i 0.648321 + 0.761367i 0.275471π0.275471\pi
−0.648321 + 0.761367i 0.724529π0.724529\pi
2424 0 0
2525 0 0
2626 6.51388 1.27748
2727 0 0
2828 − 0.211103i − 0.0398946i
2929 0.908327 0.168672 0.0843360 0.996437i 0.473123π-0.473123\pi
0.0843360 + 0.996437i 0.473123π0.473123\pi
3030 0 0
3131 10.2111 1.83397 0.916984 0.398924i 0.130616π-0.130616\pi
0.916984 + 0.398924i 0.130616π0.130616\pi
3232 − 1.69722i − 0.300030i
3333 0 0
3434 9.00000 1.54349
3535 0 0
3636 0 0
3737 − 2.39445i − 0.393645i −0.980439 0.196822i 0.936938π-0.936938\pi
0.980439 0.196822i 0.0630623π-0.0630623\pi
3838 − 1.30278i − 0.211338i
3939 0 0
4040 0 0
4141 5.60555 0.875440 0.437720 0.899111i 0.355786π-0.355786\pi
0.437720 + 0.899111i 0.355786π0.355786\pi
4242 0 0
4343 7.21110i 1.09968i 0.835269 + 0.549841i 0.185312π0.185312\pi
−0.835269 + 0.549841i 0.814688π0.814688\pi
4444 0.302776 0.0456451
4545 0 0
4646 9.51388 1.40274
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 6.51388 0.930554
5050 0 0
5151 0 0
5252 1.51388i 0.209937i
5353 1.30278i 0.178950i 0.995989 + 0.0894750i 0.0285189π0.0285189\pi
−0.995989 + 0.0894750i 0.971481π0.971481\pi
5454 0 0
5555 0 0
5656 −2.09167 −0.279512
5757 0 0
5858 − 1.18335i − 0.155381i
5959 −14.2111 −1.85013 −0.925064 0.379811i 0.875989π-0.875989\pi
−0.925064 + 0.379811i 0.875989π0.875989\pi
6060 0 0
6161 −7.90833 −1.01256 −0.506279 0.862370i 0.668979π-0.668979\pi
−0.506279 + 0.862370i 0.668979π0.668979\pi
6262 − 13.3028i − 1.68945i
6363 0 0
6464 −8.81665 −1.10208
6565 0 0
6666 0 0
6767 4.00000i 0.488678i 0.969690 + 0.244339i 0.0785709π0.0785709\pi
−0.969690 + 0.244339i 0.921429π0.921429\pi
6868 2.09167i 0.253653i
6969 0 0
7070 0 0
7171 2.60555 0.309222 0.154611 0.987975i 0.450588π-0.450588\pi
0.154611 + 0.987975i 0.450588π0.450588\pi
7272 0 0
7373 − 7.90833i − 0.925600i −0.886463 0.462800i 0.846845π-0.846845\pi
0.886463 0.462800i 0.153155π-0.153155\pi
7474 −3.11943 −0.362626
7575 0 0
7676 0.302776 0.0347307
7777 − 0.697224i − 0.0794561i
7878 0 0
7979 10.9083 1.22728 0.613641 0.789585i 0.289704π-0.289704\pi
0.613641 + 0.789585i 0.289704π0.289704\pi
8080 0 0
8181 0 0
8282 − 7.30278i − 0.806457i
8383 3.51388i 0.385698i 0.981228 + 0.192849i 0.0617728π0.0617728\pi
−0.981228 + 0.192849i 0.938227π0.938227\pi
8484 0 0
8585 0 0
8686 9.39445 1.01303
8787 0 0
8888 − 3.00000i − 0.319801i
8989 1.69722 0.179905 0.0899527 0.995946i 0.471328π-0.471328\pi
0.0899527 + 0.995946i 0.471328π0.471328\pi
9090 0 0
9191 3.48612 0.365445
9292 2.21110i 0.230523i
9393 0 0
9494 −3.90833 −0.403113
9595 0 0
9696 0 0
9797 − 15.3028i − 1.55376i −0.629648 0.776881i 0.716801π-0.716801\pi
0.629648 0.776881i 0.283199π-0.283199\pi
9898 − 8.48612i − 0.857228i
9999 0 0
100100 0 0
101101 0.513878 0.0511328 0.0255664 0.999673i 0.491861π-0.491861\pi
0.0255664 + 0.999673i 0.491861π0.491861\pi
102102 0 0
103103 2.90833i 0.286566i 0.989682 + 0.143283i 0.0457659π0.0457659\pi
−0.989682 + 0.143283i 0.954234π0.954234\pi
104104 15.0000 1.47087
105105 0 0
106106 1.69722 0.164849
107107 − 3.00000i − 0.290021i −0.989430 0.145010i 0.953678π-0.953678\pi
0.989430 0.145010i 0.0463216π-0.0463216\pi
108108 0 0
109109 −11.5139 −1.10283 −0.551415 0.834231i 0.685912π-0.685912\pi
−0.551415 + 0.834231i 0.685912π0.685912\pi
110110 0 0
111111 0 0
112112 2.30278i 0.217592i
113113 10.8167i 1.01755i 0.860901 + 0.508773i 0.169901π0.169901\pi
−0.860901 + 0.508773i 0.830099π0.830099\pi
114114 0 0
115115 0 0
116116 0.275019 0.0255349
117117 0 0
118118 18.5139i 1.70434i
119119 4.81665 0.441542
120120 0 0
121121 1.00000 0.0909091
122122 10.3028i 0.932769i
123123 0 0
124124 3.09167 0.277640
125125 0 0
126126 0 0
127127 − 8.11943i − 0.720483i −0.932859 0.360241i 0.882694π-0.882694\pi
0.932859 0.360241i 0.117306π-0.117306\pi
128128 8.09167i 0.715210i
129129 0 0
130130 0 0
131131 9.90833 0.865695 0.432847 0.901467i 0.357509π-0.357509\pi
0.432847 + 0.901467i 0.357509π0.357509\pi
132132 0 0
133133 − 0.697224i − 0.0604570i
134134 5.21110 0.450171
135135 0 0
136136 20.7250 1.77715
137137 − 12.9083i − 1.10283i −0.834230 0.551416i 0.814088π-0.814088\pi
0.834230 0.551416i 0.185912π-0.185912\pi
138138 0 0
139139 6.21110 0.526819 0.263409 0.964684i 0.415153π-0.415153\pi
0.263409 + 0.964684i 0.415153π0.415153\pi
140140 0 0
141141 0 0
142142 − 3.39445i − 0.284856i
143143 5.00000i 0.418121i
144144 0 0
145145 0 0
146146 −10.3028 −0.852664
147147 0 0
148148 − 0.724981i − 0.0595930i
149149 17.2111 1.40999 0.704994 0.709213i 0.250950π-0.250950\pi
0.704994 + 0.709213i 0.250950π0.250950\pi
150150 0 0
151151 0.816654 0.0664583 0.0332292 0.999448i 0.489421π-0.489421\pi
0.0332292 + 0.999448i 0.489421π0.489421\pi
152152 − 3.00000i − 0.243332i
153153 0 0
154154 −0.908327 −0.0731951
155155 0 0
156156 0 0
157157 − 19.2111i − 1.53321i −0.642117 0.766606i 0.721944π-0.721944\pi
0.642117 0.766606i 0.278056π-0.278056\pi
158158 − 14.2111i − 1.13057i
159159 0 0
160160 0 0
161161 5.09167 0.401280
162162 0 0
163163 9.30278i 0.728650i 0.931272 + 0.364325i 0.118700π0.118700\pi
−0.931272 + 0.364325i 0.881300π0.881300\pi
164164 1.69722 0.132531
165165 0 0
166166 4.57779 0.355306
167167 13.4222i 1.03864i 0.854579 + 0.519321i 0.173815π0.173815\pi
−0.854579 + 0.519321i 0.826185π0.826185\pi
168168 0 0
169169 −12.0000 −0.923077
170170 0 0
171171 0 0
172172 2.18335i 0.166479i
173173 4.81665i 0.366203i 0.983094 + 0.183102i 0.0586138π0.0586138\pi
−0.983094 + 0.183102i 0.941386π0.941386\pi
174174 0 0
175175 0 0
176176 −3.30278 −0.248956
177177 0 0
178178 − 2.21110i − 0.165729i
179179 12.5139 0.935331 0.467666 0.883905i 0.345095π-0.345095\pi
0.467666 + 0.883905i 0.345095π0.345095\pi
180180 0 0
181181 −19.9083 −1.47977 −0.739887 0.672731i 0.765121π-0.765121\pi
−0.739887 + 0.672731i 0.765121π0.765121\pi
182182 − 4.54163i − 0.336648i
183183 0 0
184184 21.9083 1.61510
185185 0 0
186186 0 0
187187 6.90833i 0.505187i
188188 − 0.908327i − 0.0662465i
189189 0 0
190190 0 0
191191 −10.3028 −0.745483 −0.372741 0.927935i 0.621582π-0.621582\pi
−0.372741 + 0.927935i 0.621582π0.621582\pi
192192 0 0
193193 13.2111i 0.950956i 0.879728 + 0.475478i 0.157725π0.157725\pi
−0.879728 + 0.475478i 0.842275π0.842275\pi
194194 −19.9361 −1.43133
195195 0 0
196196 1.97224 0.140875
197197 13.3028i 0.947784i 0.880583 + 0.473892i 0.157151π0.157151\pi
−0.880583 + 0.473892i 0.842849π0.842849\pi
198198 0 0
199199 6.48612 0.459789 0.229894 0.973216i 0.426162π-0.426162\pi
0.229894 + 0.973216i 0.426162π0.426162\pi
200200 0 0
201201 0 0
202202 − 0.669468i − 0.0471036i
203203 − 0.633308i − 0.0444495i
204204 0 0
205205 0 0
206206 3.78890 0.263985
207207 0 0
208208 − 16.5139i − 1.14503i
209209 1.00000 0.0691714
210210 0 0
211211 −25.2389 −1.73751 −0.868757 0.495238i 0.835081π-0.835081\pi
−0.868757 + 0.495238i 0.835081π0.835081\pi
212212 0.394449i 0.0270908i
213213 0 0
214214 −3.90833 −0.267168
215215 0 0
216216 0 0
217217 − 7.11943i − 0.483298i
218218 15.0000i 1.01593i
219219 0 0
220220 0 0
221221 −34.5416 −2.32352
222222 0 0
223223 − 22.6333i − 1.51564i −0.652465 0.757819i 0.726265π-0.726265\pi
0.652465 0.757819i 0.273735π-0.273735\pi
224224 −1.18335 −0.0790656
225225 0 0
226226 14.0917 0.937364
227227 1.69722i 0.112649i 0.998413 + 0.0563244i 0.0179381π0.0179381\pi
−0.998413 + 0.0563244i 0.982062π0.982062\pi
228228 0 0
229229 18.7250 1.23738 0.618691 0.785635i 0.287663π-0.287663\pi
0.618691 + 0.785635i 0.287663π0.287663\pi
230230 0 0
231231 0 0
232232 − 2.72498i − 0.178904i
233233 − 15.9083i − 1.04219i −0.853499 0.521095i 0.825524π-0.825524\pi
0.853499 0.521095i 0.174476π-0.174476\pi
234234 0 0
235235 0 0
236236 −4.30278 −0.280087
237237 0 0
238238 − 6.27502i − 0.406749i
239239 21.1194 1.36610 0.683051 0.730371i 0.260653π-0.260653\pi
0.683051 + 0.730371i 0.260653π0.260653\pi
240240 0 0
241241 21.9361 1.41303 0.706514 0.707699i 0.250267π-0.250267\pi
0.706514 + 0.707699i 0.250267π0.250267\pi
242242 − 1.30278i − 0.0837456i
243243 0 0
244244 −2.39445 −0.153289
245245 0 0
246246 0 0
247247 5.00000i 0.318142i
248248 − 30.6333i − 1.94522i
249249 0 0
250250 0 0
251251 −6.90833 −0.436050 −0.218025 0.975943i 0.569961π-0.569961\pi
−0.218025 + 0.975943i 0.569961π0.569961\pi
252252 0 0
253253 7.30278i 0.459122i
254254 −10.5778 −0.663710
255255 0 0
256256 −7.09167 −0.443230
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 −1.66947 −0.103736
260260 0 0
261261 0 0
262262 − 12.9083i − 0.797479i
263263 22.8167i 1.40694i 0.710727 + 0.703468i 0.248366π0.248366\pi
−0.710727 + 0.703468i 0.751634π0.751634\pi
264264 0 0
265265 0 0
266266 −0.908327 −0.0556931
267267 0 0
268268 1.21110i 0.0739799i
269269 8.72498 0.531971 0.265986 0.963977i 0.414303π-0.414303\pi
0.265986 + 0.963977i 0.414303π0.414303\pi
270270 0 0
271271 −0.211103 −0.0128236 −0.00641178 0.999979i 0.502041π-0.502041\pi
−0.00641178 + 0.999979i 0.502041π0.502041\pi
272272 − 22.8167i − 1.38346i
273273 0 0
274274 −16.8167 −1.01593
275275 0 0
276276 0 0
277277 − 14.3944i − 0.864879i −0.901663 0.432439i 0.857653π-0.857653\pi
0.901663 0.432439i 0.142347π-0.142347\pi
278278 − 8.09167i − 0.485306i
279279 0 0
280280 0 0
281281 1.18335 0.0705925 0.0352963 0.999377i 0.488763π-0.488763\pi
0.0352963 + 0.999377i 0.488763π0.488763\pi
282282 0 0
283283 6.30278i 0.374661i 0.982297 + 0.187331i 0.0599836π0.0599836\pi
−0.982297 + 0.187331i 0.940016π0.940016\pi
284284 0.788897 0.0468125
285285 0 0
286286 6.51388 0.385174
287287 − 3.90833i − 0.230701i
288288 0 0
289289 −30.7250 −1.80735
290290 0 0
291291 0 0
292292 − 2.39445i − 0.140125i
293293 − 0.788897i − 0.0460879i −0.999734 0.0230439i 0.992664π-0.992664\pi
0.999734 0.0230439i 0.00733576π-0.00733576\pi
294294 0 0
295295 0 0
296296 −7.18335 −0.417524
297297 0 0
298298 − 22.4222i − 1.29888i
299299 −36.5139 −2.11165
300300 0 0
301301 5.02776 0.289795
302302 − 1.06392i − 0.0612215i
303303 0 0
304304 −3.30278 −0.189427
305305 0 0
306306 0 0
307307 16.9083i 0.965009i 0.875893 + 0.482505i 0.160273π0.160273\pi
−0.875893 + 0.482505i 0.839727π0.839727\pi
308308 − 0.211103i − 0.0120287i
309309 0 0
310310 0 0
311311 −4.81665 −0.273127 −0.136564 0.990631i 0.543606π-0.543606\pi
−0.136564 + 0.990631i 0.543606π0.543606\pi
312312 0 0
313313 0.183346i 0.0103633i 0.999987 + 0.00518167i 0.00164938π0.00164938\pi
−0.999987 + 0.00518167i 0.998351π0.998351\pi
314314 −25.0278 −1.41240
315315 0 0
316316 3.30278 0.185796
317317 − 0.908327i − 0.0510167i −0.999675 0.0255084i 0.991880π-0.991880\pi
0.999675 0.0255084i 0.00812044π-0.00812044\pi
318318 0 0
319319 0.908327 0.0508565
320320 0 0
321321 0 0
322322 − 6.63331i − 0.369660i
323323 6.90833i 0.384390i
324324 0 0
325325 0 0
326326 12.1194 0.671233
327327 0 0
328328 − 16.8167i − 0.928544i
329329 −2.09167 −0.115318
330330 0 0
331331 −21.6056 −1.18755 −0.593774 0.804632i 0.702363π-0.702363\pi
−0.593774 + 0.804632i 0.702363π0.702363\pi
332332 1.06392i 0.0583900i
333333 0 0
334334 17.4861 0.956798
335335 0 0
336336 0 0
337337 30.8444i 1.68020i 0.542430 + 0.840101i 0.317504π0.317504\pi
−0.542430 + 0.840101i 0.682496π0.682496\pi
338338 15.6333i 0.850340i
339339 0 0
340340 0 0
341341 10.2111 0.552962
342342 0 0
343343 − 9.42221i − 0.508751i
344344 21.6333 1.16639
345345 0 0
346346 6.27502 0.337347
347347 − 12.5139i − 0.671780i −0.941901 0.335890i 0.890963π-0.890963\pi
0.941901 0.335890i 0.109037π-0.109037\pi
348348 0 0
349349 5.18335 0.277458 0.138729 0.990330i 0.455698π-0.455698\pi
0.138729 + 0.990330i 0.455698π0.455698\pi
350350 0 0
351351 0 0
352352 − 1.69722i − 0.0904624i
353353 − 18.6333i − 0.991751i −0.868394 0.495875i 0.834847π-0.834847\pi
0.868394 0.495875i 0.165153π-0.165153\pi
354354 0 0
355355 0 0
356356 0.513878 0.0272355
357357 0 0
358358 − 16.3028i − 0.861628i
359359 0.788897 0.0416364 0.0208182 0.999783i 0.493373π-0.493373\pi
0.0208182 + 0.999783i 0.493373π0.493373\pi
360360 0 0
361361 −18.0000 −0.947368
362362 25.9361i 1.36317i
363363 0 0
364364 1.05551 0.0553239
365365 0 0
366366 0 0
367367 20.6972i 1.08039i 0.841541 + 0.540193i 0.181649π0.181649\pi
−0.841541 + 0.540193i 0.818351π0.818351\pi
368368 − 24.1194i − 1.25731i
369369 0 0
370370 0 0
371371 0.908327 0.0471580
372372 0 0
373373 27.4222i 1.41987i 0.704268 + 0.709934i 0.251275π0.251275\pi
−0.704268 + 0.709934i 0.748725π0.748725\pi
374374 9.00000 0.465379
375375 0 0
376376 −9.00000 −0.464140
377377 4.54163i 0.233906i
378378 0 0
379379 −3.18335 −0.163518 −0.0817588 0.996652i 0.526054π-0.526054\pi
−0.0817588 + 0.996652i 0.526054π0.526054\pi
380380 0 0
381381 0 0
382382 13.4222i 0.686740i
383383 − 21.6333i − 1.10541i −0.833377 0.552705i 0.813596π-0.813596\pi
0.833377 0.552705i 0.186404π-0.186404\pi
384384 0 0
385385 0 0
386386 17.2111 0.876022
387387 0 0
388388 − 4.63331i − 0.235221i
389389 12.0000 0.608424 0.304212 0.952604i 0.401607π-0.401607\pi
0.304212 + 0.952604i 0.401607π0.401607\pi
390390 0 0
391391 −50.4500 −2.55136
392392 − 19.5416i − 0.987002i
393393 0 0
394394 17.3305 0.873100
395395 0 0
396396 0 0
397397 − 21.6972i − 1.08895i −0.838776 0.544476i 0.816728π-0.816728\pi
0.838776 0.544476i 0.183272π-0.183272\pi
398398 − 8.44996i − 0.423558i
399399 0 0
400400 0 0
401401 12.7889 0.638647 0.319324 0.947646i 0.396544π-0.396544\pi
0.319324 + 0.947646i 0.396544π0.396544\pi
402402 0 0
403403 51.0555i 2.54326i
404404 0.155590 0.00774088
405405 0 0
406406 −0.825058 −0.0409469
407407 − 2.39445i − 0.118688i
408408 0 0
409409 6.21110 0.307119 0.153560 0.988139i 0.450926π-0.450926\pi
0.153560 + 0.988139i 0.450926π0.450926\pi
410410 0 0
411411 0 0
412412 0.880571i 0.0433826i
413413 9.90833i 0.487557i
414414 0 0
415415 0 0
416416 8.48612 0.416066
417417 0 0
418418 − 1.30278i − 0.0637208i
419419 6.39445 0.312389 0.156195 0.987726i 0.450077π-0.450077\pi
0.156195 + 0.987726i 0.450077π0.450077\pi
420420 0 0
421421 0.697224 0.0339806 0.0169903 0.999856i 0.494592π-0.494592\pi
0.0169903 + 0.999856i 0.494592π0.494592\pi
422422 32.8806i 1.60060i
423423 0 0
424424 3.90833 0.189805
425425 0 0
426426 0 0
427427 5.51388i 0.266835i
428428 − 0.908327i − 0.0439056i
429429 0 0
430430 0 0
431431 −33.0000 −1.58955 −0.794777 0.606902i 0.792412π-0.792412\pi
−0.794777 + 0.606902i 0.792412π0.792412\pi
432432 0 0
433433 5.00000i 0.240285i 0.992757 + 0.120142i 0.0383351π0.0383351\pi
−0.992757 + 0.120142i 0.961665π0.961665\pi
434434 −9.27502 −0.445215
435435 0 0
436436 −3.48612 −0.166955
437437 7.30278i 0.349339i
438438 0 0
439439 −24.3028 −1.15991 −0.579954 0.814649i 0.696930π-0.696930\pi
−0.579954 + 0.814649i 0.696930π0.696930\pi
440440 0 0
441441 0 0
442442 45.0000i 2.14043i
443443 8.60555i 0.408862i 0.978881 + 0.204431i 0.0655344π0.0655344\pi
−0.978881 + 0.204431i 0.934466π0.934466\pi
444444 0 0
445445 0 0
446446 −29.4861 −1.39621
447447 0 0
448448 6.14719i 0.290427i
449449 23.4861 1.10838 0.554189 0.832391i 0.313028π-0.313028\pi
0.554189 + 0.832391i 0.313028π0.313028\pi
450450 0 0
451451 5.60555 0.263955
452452 3.27502i 0.154044i
453453 0 0
454454 2.21110 0.103772
455455 0 0
456456 0 0
457457 20.6972i 0.968175i 0.875020 + 0.484088i 0.160848π0.160848\pi
−0.875020 + 0.484088i 0.839152π0.839152\pi
458458 − 24.3944i − 1.13988i
459459 0 0
460460 0 0
461461 −32.2111 −1.50022 −0.750110 0.661313i 0.770000π-0.770000\pi
−0.750110 + 0.661313i 0.770000π0.770000\pi
462462 0 0
463463 11.7889i 0.547877i 0.961747 + 0.273938i 0.0883264π0.0883264\pi
−0.961747 + 0.273938i 0.911674π0.911674\pi
464464 −3.00000 −0.139272
465465 0 0
466466 −20.7250 −0.960066
467467 − 18.6333i − 0.862247i −0.902293 0.431123i 0.858117π-0.858117\pi
0.902293 0.431123i 0.141883π-0.141883\pi
468468 0 0
469469 2.78890 0.128779
470470 0 0
471471 0 0
472472 42.6333i 1.96236i
473473 7.21110i 0.331567i
474474 0 0
475475 0 0
476476 1.45837 0.0668441
477477 0 0
478478 − 27.5139i − 1.25846i
479479 −34.8167 −1.59081 −0.795407 0.606076i 0.792743π-0.792743\pi
−0.795407 + 0.606076i 0.792743π0.792743\pi
480480 0 0
481481 11.9722 0.545887
482482 − 28.5778i − 1.30168i
483483 0 0
484484 0.302776 0.0137625
485485 0 0
486486 0 0
487487 − 4.21110i − 0.190823i −0.995438 0.0954116i 0.969583π-0.969583\pi
0.995438 0.0954116i 0.0304167π-0.0304167\pi
488488 23.7250i 1.07398i
489489 0 0
490490 0 0
491491 9.78890 0.441767 0.220883 0.975300i 0.429106π-0.429106\pi
0.220883 + 0.975300i 0.429106π0.429106\pi
492492 0 0
493493 6.27502i 0.282613i
494494 6.51388 0.293073
495495 0 0
496496 −33.7250 −1.51430
497497 − 1.81665i − 0.0814881i
498498 0 0
499499 3.48612 0.156060 0.0780301 0.996951i 0.475137π-0.475137\pi
0.0780301 + 0.996951i 0.475137π0.475137\pi
500500 0 0
501501 0 0
502502 9.00000i 0.401690i
503503 − 9.39445i − 0.418878i −0.977822 0.209439i 0.932836π-0.932836\pi
0.977822 0.209439i 0.0671637π-0.0671637\pi
504504 0 0
505505 0 0
506506 9.51388 0.422943
507507 0 0
508508 − 2.45837i − 0.109072i
509509 −22.6972 −1.00604 −0.503018 0.864276i 0.667777π-0.667777\pi
−0.503018 + 0.864276i 0.667777π0.667777\pi
510510 0 0
511511 −5.51388 −0.243920
512512 25.4222i 1.12351i
513513 0 0
514514 −23.4500 −1.03433
515515 0 0
516516 0 0
517517 − 3.00000i − 0.131940i
518518 2.17494i 0.0955615i
519519 0 0
520520 0 0
521521 41.4500 1.81596 0.907978 0.419018i 0.137626π-0.137626\pi
0.907978 + 0.419018i 0.137626π0.137626\pi
522522 0 0
523523 − 32.4222i − 1.41772i −0.705347 0.708862i 0.749209π-0.749209\pi
0.705347 0.708862i 0.250791π-0.250791\pi
524524 3.00000 0.131056
525525 0 0
526526 29.7250 1.29607
527527 70.5416i 3.07284i
528528 0 0
529529 −30.3305 −1.31872
530530 0 0
531531 0 0
532532 − 0.211103i − 0.00915246i
533533 28.0278i 1.21402i
534534 0 0
535535 0 0
536536 12.0000 0.518321
537537 0 0
538538 − 11.3667i − 0.490053i
539539 6.51388 0.280573
540540 0 0
541541 25.7250 1.10600 0.553002 0.833180i 0.313482π-0.313482\pi
0.553002 + 0.833180i 0.313482π0.313482\pi
542542 0.275019i 0.0118131i
543543 0 0
544544 11.7250 0.502704
545545 0 0
546546 0 0
547547 7.11943i 0.304405i 0.988349 + 0.152202i 0.0486366π0.0486366\pi
−0.988349 + 0.152202i 0.951363π0.951363\pi
548548 − 3.90833i − 0.166955i
549549 0 0
550550 0 0
551551 0.908327 0.0386960
552552 0 0
553553 − 7.60555i − 0.323421i
554554 −18.7527 −0.796727
555555 0 0
556556 1.88057 0.0797540
557557 19.4222i 0.822945i 0.911422 + 0.411473i 0.134985π0.134985\pi
−0.911422 + 0.411473i 0.865015π0.865015\pi
558558 0 0
559559 −36.0555 −1.52499
560560 0 0
561561 0 0
562562 − 1.54163i − 0.0650299i
563563 − 8.09167i − 0.341023i −0.985356 0.170512i 0.945458π-0.945458\pi
0.985356 0.170512i 0.0545421π-0.0545421\pi
564564 0 0
565565 0 0
566566 8.21110 0.345138
567567 0 0
568568 − 7.81665i − 0.327980i
569569 −46.1472 −1.93459 −0.967295 0.253653i 0.918368π-0.918368\pi
−0.967295 + 0.253653i 0.918368π0.918368\pi
570570 0 0
571571 22.3305 0.934504 0.467252 0.884124i 0.345244π-0.345244\pi
0.467252 + 0.884124i 0.345244π0.345244\pi
572572 1.51388i 0.0632984i
573573 0 0
574574 −5.09167 −0.212522
575575 0 0
576576 0 0
577577 − 44.3583i − 1.84666i −0.384008 0.923330i 0.625456π-0.625456\pi
0.384008 0.923330i 0.374544π-0.374544\pi
578578 40.0278i 1.66494i
579579 0 0
580580 0 0
581581 2.44996 0.101642
582582 0 0
583583 1.30278i 0.0539555i
584584 −23.7250 −0.981747
585585 0 0
586586 −1.02776 −0.0424562
587587 16.5416i 0.682746i 0.939928 + 0.341373i 0.110892π0.110892\pi
−0.939928 + 0.341373i 0.889108π0.889108\pi
588588 0 0
589589 10.2111 0.420741
590590 0 0
591591 0 0
592592 7.90833i 0.325030i
593593 6.39445i 0.262589i 0.991343 + 0.131294i 0.0419133π0.0419133\pi
−0.991343 + 0.131294i 0.958087π0.958087\pi
594594 0 0
595595 0 0
596596 5.21110 0.213455
597597 0 0
598598 47.5694i 1.94526i
599599 −24.9083 −1.01773 −0.508863 0.860847i 0.669934π-0.669934\pi
−0.508863 + 0.860847i 0.669934π0.669934\pi
600600 0 0
601601 −1.90833 −0.0778423 −0.0389211 0.999242i 0.512392π-0.512392\pi
−0.0389211 + 0.999242i 0.512392π0.512392\pi
602602 − 6.55004i − 0.266960i
603603 0 0
604604 0.247263 0.0100610
605605 0 0
606606 0 0
607607 − 7.21110i − 0.292690i −0.989234 0.146345i 0.953249π-0.953249\pi
0.989234 0.146345i 0.0467509π-0.0467509\pi
608608 − 1.69722i − 0.0688315i
609609 0 0
610610 0 0
611611 15.0000 0.606835
612612 0 0
613613 − 15.8806i − 0.641410i −0.947179 0.320705i 0.896080π-0.896080\pi
0.947179 0.320705i 0.103920π-0.103920\pi
614614 22.0278 0.888968
615615 0 0
616616 −2.09167 −0.0842759
617617 3.39445i 0.136655i 0.997663 + 0.0683277i 0.0217663π0.0217663\pi
−0.997663 + 0.0683277i 0.978234π0.978234\pi
618618 0 0
619619 11.4222 0.459097 0.229549 0.973297i 0.426275π-0.426275\pi
0.229549 + 0.973297i 0.426275π0.426275\pi
620620 0 0
621621 0 0
622622 6.27502i 0.251605i
623623 − 1.18335i − 0.0474098i
624624 0 0
625625 0 0
626626 0.238859 0.00954672
627627 0 0
628628 − 5.81665i − 0.232110i
629629 16.5416 0.659558
630630 0 0
631631 6.93608 0.276121 0.138061 0.990424i 0.455913π-0.455913\pi
0.138061 + 0.990424i 0.455913π0.455913\pi
632632 − 32.7250i − 1.30173i
633633 0 0
634634 −1.18335 −0.0469967
635635 0 0
636636 0 0
637637 32.5694i 1.29045i
638638 − 1.18335i − 0.0468491i
639639 0 0
640640 0 0
641641 −27.7889 −1.09760 −0.548798 0.835955i 0.684914π-0.684914\pi
−0.548798 + 0.835955i 0.684914π0.684914\pi
642642 0 0
643643 − 22.0000i − 0.867595i −0.901010 0.433798i 0.857173π-0.857173\pi
0.901010 0.433798i 0.142827π-0.142827\pi
644644 1.54163 0.0607489
645645 0 0
646646 9.00000 0.354100
647647 − 33.2389i − 1.30675i −0.757033 0.653377i 0.773352π-0.773352\pi
0.757033 0.653377i 0.226648π-0.226648\pi
648648 0 0
649649 −14.2111 −0.557835
650650 0 0
651651 0 0
652652 2.81665i 0.110309i
653653 − 6.11943i − 0.239472i −0.992806 0.119736i 0.961795π-0.961795\pi
0.992806 0.119736i 0.0382048π-0.0382048\pi
654654 0 0
655655 0 0
656656 −18.5139 −0.722846
657657 0 0
658658 2.72498i 0.106231i
659659 −30.9083 −1.20402 −0.602009 0.798489i 0.705633π-0.705633\pi
−0.602009 + 0.798489i 0.705633π0.705633\pi
660660 0 0
661661 −8.81665 −0.342928 −0.171464 0.985190i 0.554850π-0.554850\pi
−0.171464 + 0.985190i 0.554850π0.554850\pi
662662 28.1472i 1.09397i
663663 0 0
664664 10.5416 0.409095
665665 0 0
666666 0 0
667667 6.63331i 0.256843i
668668 4.06392i 0.157238i
669669 0 0
670670 0 0
671671 −7.90833 −0.305298
672672 0 0
673673 30.0278i 1.15748i 0.815510 + 0.578742i 0.196456π0.196456\pi
−0.815510 + 0.578742i 0.803544π0.803544\pi
674674 40.1833 1.54780
675675 0 0
676676 −3.63331 −0.139743
677677 24.2389i 0.931575i 0.884897 + 0.465788i 0.154229π0.154229\pi
−0.884897 + 0.465788i 0.845771π0.845771\pi
678678 0 0
679679 −10.6695 −0.409457
680680 0 0
681681 0 0
682682 − 13.3028i − 0.509390i
683683 − 47.8444i − 1.83072i −0.402642 0.915358i 0.631908π-0.631908\pi
0.402642 0.915358i 0.368092π-0.368092\pi
684684 0 0
685685 0 0
686686 −12.2750 −0.468662
687687 0 0
688688 − 23.8167i − 0.908001i
689689 −6.51388 −0.248159
690690 0 0
691691 27.5416 1.04773 0.523867 0.851800i 0.324489π-0.324489\pi
0.523867 + 0.851800i 0.324489π0.324489\pi
692692 1.45837i 0.0554387i
693693 0 0
694694 −16.3028 −0.618845
695695 0 0
696696 0 0
697697 38.7250i 1.46681i
698698 − 6.75274i − 0.255595i
699699 0 0
700700 0 0
701701 41.2111 1.55652 0.778261 0.627941i 0.216102π-0.216102\pi
0.778261 + 0.627941i 0.216102π0.216102\pi
702702 0 0
703703 − 2.39445i − 0.0903083i
704704 −8.81665 −0.332290
705705 0 0
706706 −24.2750 −0.913602
707707 − 0.358288i − 0.0134748i
708708 0 0
709709 31.6333 1.18801 0.594007 0.804460i 0.297545π-0.297545\pi
0.594007 + 0.804460i 0.297545π0.297545\pi
710710 0 0
711711 0 0
712712 − 5.09167i − 0.190819i
713713 74.5694i 2.79265i
714714 0 0
715715 0 0
716716 3.78890 0.141598
717717 0 0
718718 − 1.02776i − 0.0383555i
719719 7.18335 0.267894 0.133947 0.990989i 0.457235π-0.457235\pi
0.133947 + 0.990989i 0.457235π0.457235\pi
720720 0 0
721721 2.02776 0.0755176
722722 23.4500i 0.872717i
723723 0 0
724724 −6.02776 −0.224020
725725 0 0
726726 0 0
727727 39.3305i 1.45869i 0.684147 + 0.729344i 0.260175π0.260175\pi
−0.684147 + 0.729344i 0.739825π0.739825\pi
728728 − 10.4584i − 0.387613i
729729 0 0
730730 0 0
731731 −49.8167 −1.84254
732732 0 0
733733 19.6056i 0.724148i 0.932149 + 0.362074i 0.117931π0.117931\pi
−0.932149 + 0.362074i 0.882069π0.882069\pi
734734 26.9638 0.995253
735735 0 0
736736 12.3944 0.456865
737737 4.00000i 0.147342i
738738 0 0
739739 −35.1194 −1.29189 −0.645945 0.763384i 0.723536π-0.723536\pi
−0.645945 + 0.763384i 0.723536π0.723536\pi
740740 0 0
741741 0 0
742742 − 1.18335i − 0.0434420i
743743 − 40.6972i − 1.49304i −0.665365 0.746518i 0.731724π-0.731724\pi
0.665365 0.746518i 0.268276π-0.268276\pi
744744 0 0
745745 0 0
746746 35.7250 1.30798
747747 0 0
748748 2.09167i 0.0764791i
749749 −2.09167 −0.0764281
750750 0 0
751751 −45.3305 −1.65413 −0.827067 0.562103i 0.809992π-0.809992\pi
−0.827067 + 0.562103i 0.809992π0.809992\pi
752752 9.90833i 0.361320i
753753 0 0
754754 5.91673 0.215475
755755 0 0
756756 0 0
757757 − 49.0555i − 1.78295i −0.453067 0.891476i 0.649670π-0.649670\pi
0.453067 0.891476i 0.350330π-0.350330\pi
758758 4.14719i 0.150633i
759759 0 0
760760 0 0
761761 13.5778 0.492195 0.246097 0.969245i 0.420852π-0.420852\pi
0.246097 + 0.969245i 0.420852π0.420852\pi
762762 0 0
763763 8.02776i 0.290624i
764764 −3.11943 −0.112857
765765 0 0
766766 −28.1833 −1.01831
767767 − 71.0555i − 2.56567i
768768 0 0
769769 5.18335 0.186916 0.0934581 0.995623i 0.470208π-0.470208\pi
0.0934581 + 0.995623i 0.470208π0.470208\pi
770770 0 0
771771 0 0
772772 4.00000i 0.143963i
773773 − 3.11943i − 0.112198i −0.998425 0.0560990i 0.982134π-0.982134\pi
0.998425 0.0560990i 0.0178663π-0.0178663\pi
774774 0 0
775775 0 0
776776 −45.9083 −1.64801
777777 0 0
778778 − 15.6333i − 0.560481i
779779 5.60555 0.200840
780780 0 0
781781 2.60555 0.0932340
782782 65.7250i 2.35032i
783783 0 0
784784 −21.5139 −0.768353
785785 0 0
786786 0 0
787787 − 10.2111i − 0.363986i −0.983300 0.181993i 0.941745π-0.941745\pi
0.983300 0.181993i 0.0582549π-0.0582549\pi
788788 4.02776i 0.143483i
789789 0 0
790790 0 0
791791 7.54163 0.268150
792792 0 0
793793 − 39.5416i − 1.40416i
794794 −28.2666 −1.00314
795795 0 0
796796 1.96384 0.0696065
797797 3.51388i 0.124468i 0.998062 + 0.0622340i 0.0198225π0.0198225\pi
−0.998062 + 0.0622340i 0.980178π0.980178\pi
798798 0 0
799799 20.7250 0.733197
800800 0 0
801801 0 0
802802 − 16.6611i − 0.588323i
803803 − 7.90833i − 0.279079i
804804 0 0
805805 0 0
806806 66.5139 2.34285
807807 0 0
808808 − 1.54163i − 0.0542345i
809809 39.6333 1.39343 0.696716 0.717347i 0.254644π-0.254644\pi
0.696716 + 0.717347i 0.254644π0.254644\pi
810810 0 0
811811 38.8722 1.36499 0.682493 0.730892i 0.260896π-0.260896\pi
0.682493 + 0.730892i 0.260896π0.260896\pi
812812 − 0.191750i − 0.00672911i
813813 0 0
814814 −3.11943 −0.109336
815815 0 0
816816 0 0
817817 7.21110i 0.252285i
818818 − 8.09167i − 0.282919i
819819 0 0
820820 0 0
821821 −12.0000 −0.418803 −0.209401 0.977830i 0.567152π-0.567152\pi
−0.209401 + 0.977830i 0.567152π0.567152\pi
822822 0 0
823823 18.4222i 0.642158i 0.947052 + 0.321079i 0.104045π0.104045\pi
−0.947052 + 0.321079i 0.895955π0.895955\pi
824824 8.72498 0.303949
825825 0 0
826826 12.9083 0.449138
827827 13.8167i 0.480452i 0.970717 + 0.240226i 0.0772216π0.0772216\pi
−0.970717 + 0.240226i 0.922778π0.922778\pi
828828 0 0
829829 −29.7527 −1.03336 −0.516678 0.856180i 0.672831π-0.672831\pi
−0.516678 + 0.856180i 0.672831π0.672831\pi
830830 0 0
831831 0 0
832832 − 44.0833i − 1.52831i
833833 45.0000i 1.55916i
834834 0 0
835835 0 0
836836 0.302776 0.0104717
837837 0 0
838838 − 8.33053i − 0.287773i
839839 −9.11943 −0.314838 −0.157419 0.987532i 0.550317π-0.550317\pi
−0.157419 + 0.987532i 0.550317π0.550317\pi
840840 0 0
841841 −28.1749 −0.971550
842842 − 0.908327i − 0.0313030i
843843 0 0
844844 −7.64171 −0.263039
845845 0 0
846846 0 0
847847 − 0.697224i − 0.0239569i
848848 − 4.30278i − 0.147758i
849849 0 0
850850 0 0
851851 17.4861 0.599417
852852 0 0
853853 − 12.7250i − 0.435695i −0.975983 0.217848i 0.930096π-0.930096\pi
0.975983 0.217848i 0.0699035π-0.0699035\pi
854854 7.18335 0.245809
855855 0 0
856856 −9.00000 −0.307614
857857 − 3.00000i − 0.102478i −0.998686 0.0512390i 0.983683π-0.983683\pi
0.998686 0.0512390i 0.0163170π-0.0163170\pi
858858 0 0
859859 −41.3944 −1.41236 −0.706180 0.708032i 0.749583π-0.749583\pi
−0.706180 + 0.708032i 0.749583π0.749583\pi
860860 0 0
861861 0 0
862862 42.9916i 1.46430i
863863 12.3944i 0.421912i 0.977496 + 0.210956i 0.0676577π0.0676577\pi
−0.977496 + 0.210956i 0.932342π0.932342\pi
864864 0 0
865865 0 0
866866 6.51388 0.221351
867867 0 0
868868 − 2.15559i − 0.0731655i
869869 10.9083 0.370040
870870 0 0
871871 −20.0000 −0.677674
872872 34.5416i 1.16973i
873873 0 0
874874 9.51388 0.321812
875875 0 0
876876 0 0
877877 − 20.0000i − 0.675352i −0.941262 0.337676i 0.890359π-0.890359\pi
0.941262 0.337676i 0.109641π-0.109641\pi
878878 31.6611i 1.06851i
879879 0 0
880880 0 0
881881 −19.5416 −0.658374 −0.329187 0.944265i 0.606775π-0.606775\pi
−0.329187 + 0.944265i 0.606775π0.606775\pi
882882 0 0
883883 52.4500i 1.76508i 0.470236 + 0.882541i 0.344169π0.344169\pi
−0.470236 + 0.882541i 0.655831π0.655831\pi
884884 −10.4584 −0.351753
885885 0 0
886886 11.2111 0.376644
887887 − 3.23886i − 0.108750i −0.998521 0.0543751i 0.982683π-0.982683\pi
0.998521 0.0543751i 0.0173167π-0.0173167\pi
888888 0 0
889889 −5.66106 −0.189866
890890 0 0
891891 0 0
892892 − 6.85281i − 0.229449i
893893 − 3.00000i − 0.100391i
894894 0 0
895895 0 0
896896 5.64171 0.188476
897897 0 0
898898 − 30.5971i − 1.02104i
899899 9.27502 0.309339
900900 0 0
901901 −9.00000 −0.299833
902902 − 7.30278i − 0.243156i
903903 0 0
904904 32.4500 1.07927
905905 0 0
906906 0 0
907907 4.00000i 0.132818i 0.997792 + 0.0664089i 0.0211542π0.0211542\pi
−0.997792 + 0.0664089i 0.978846π0.978846\pi
908908 0.513878i 0.0170536i
909909 0 0
910910 0 0
911911 24.7889 0.821293 0.410646 0.911795i 0.365303π-0.365303\pi
0.410646 + 0.911795i 0.365303π0.365303\pi
912912 0 0
913913 3.51388i 0.116292i
914914 26.9638 0.891885
915915 0 0
916916 5.66947 0.187324
917917 − 6.90833i − 0.228133i
918918 0 0
919919 −26.7889 −0.883684 −0.441842 0.897093i 0.645675π-0.645675\pi
−0.441842 + 0.897093i 0.645675π0.645675\pi
920920 0 0
921921 0 0
922922 41.9638i 1.38201i
923923 13.0278i 0.428814i
924924 0 0
925925 0 0
926926 15.3583 0.504705
927927 0 0
928928 − 1.54163i − 0.0506066i
929929 53.6056 1.75874 0.879371 0.476138i 0.157964π-0.157964\pi
0.879371 + 0.476138i 0.157964π0.157964\pi
930930 0 0
931931 6.51388 0.213484
932932 − 4.81665i − 0.157775i
933933 0 0
934934 −24.2750 −0.794303
935935 0 0
936936 0 0
937937 9.21110i 0.300914i 0.988617 + 0.150457i 0.0480744π0.0480744\pi
−0.988617 + 0.150457i 0.951926π0.951926\pi
938938 − 3.63331i − 0.118632i
939939 0 0
940940 0 0
941941 −59.6056 −1.94309 −0.971543 0.236864i 0.923880π-0.923880\pi
−0.971543 + 0.236864i 0.923880π0.923880\pi
942942 0 0
943943 40.9361i 1.33306i
944944 46.9361 1.52764
945945 0 0
946946 9.39445 0.305440
947947 6.63331i 0.215554i 0.994175 + 0.107777i 0.0343732π0.0343732\pi
−0.994175 + 0.107777i 0.965627π0.965627\pi
948948 0 0
949949 39.5416 1.28358
950950 0 0
951951 0 0
952952 − 14.4500i − 0.468326i
953953 − 37.2666i − 1.20718i −0.797293 0.603592i 0.793736π-0.793736\pi
0.797293 0.603592i 0.206264π-0.206264\pi
954954 0 0
955955 0 0
956956 6.39445 0.206811
957957 0 0
958958 45.3583i 1.46546i
959959 −9.00000 −0.290625
960960 0 0
961961 73.2666 2.36344
962962 − 15.5971i − 0.502872i
963963 0 0
964964 6.64171 0.213915
965965 0 0
966966 0 0
967967 − 14.9083i − 0.479419i −0.970845 0.239710i 0.922948π-0.922948\pi
0.970845 0.239710i 0.0770523π-0.0770523\pi
968968 − 3.00000i − 0.0964237i
969969 0 0
970970 0 0
971971 −45.3583 −1.45562 −0.727808 0.685781i 0.759461π-0.759461\pi
−0.727808 + 0.685781i 0.759461π0.759461\pi
972972 0 0
973973 − 4.33053i − 0.138830i
974974 −5.48612 −0.175787
975975 0 0
976976 26.1194 0.836063
977977 − 52.0278i − 1.66452i −0.554389 0.832258i 0.687048π-0.687048\pi
0.554389 0.832258i 0.312952π-0.312952\pi
978978 0 0
979979 1.69722 0.0542435
980980 0 0
981981 0 0
982982 − 12.7527i − 0.406956i
983983 − 8.84441i − 0.282093i −0.990003 0.141046i 0.954953π-0.954953\pi
0.990003 0.141046i 0.0450467π-0.0450467\pi
984984 0 0
985985 0 0
986986 8.17494 0.260343
987987 0 0
988988 1.51388i 0.0481629i
989989 −52.6611 −1.67452
990990 0 0
991991 −16.9083 −0.537111 −0.268555 0.963264i 0.586546π-0.586546\pi
−0.268555 + 0.963264i 0.586546π0.586546\pi
992992 − 17.3305i − 0.550245i
993993 0 0
994994 −2.36669 −0.0750669
995995 0 0
996996 0 0
997997 − 46.7250i − 1.47979i −0.672720 0.739897i 0.734874π-0.734874\pi
0.672720 0.739897i 0.265126π-0.265126\pi
998998 − 4.54163i − 0.143763i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2475.2.c.k.199.2 4
3.2 odd 2 275.2.b.c.199.3 4
5.2 odd 4 2475.2.a.o.1.2 2
5.3 odd 4 2475.2.a.t.1.1 2
5.4 even 2 inner 2475.2.c.k.199.3 4
12.11 even 2 4400.2.b.y.4049.1 4
15.2 even 4 275.2.a.f.1.1 yes 2
15.8 even 4 275.2.a.e.1.2 2
15.14 odd 2 275.2.b.c.199.2 4
60.23 odd 4 4400.2.a.bs.1.2 2
60.47 odd 4 4400.2.a.bh.1.1 2
60.59 even 2 4400.2.b.y.4049.4 4
165.32 odd 4 3025.2.a.h.1.2 2
165.98 odd 4 3025.2.a.n.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
275.2.a.e.1.2 2 15.8 even 4
275.2.a.f.1.1 yes 2 15.2 even 4
275.2.b.c.199.2 4 15.14 odd 2
275.2.b.c.199.3 4 3.2 odd 2
2475.2.a.o.1.2 2 5.2 odd 4
2475.2.a.t.1.1 2 5.3 odd 4
2475.2.c.k.199.2 4 1.1 even 1 trivial
2475.2.c.k.199.3 4 5.4 even 2 inner
3025.2.a.h.1.2 2 165.32 odd 4
3025.2.a.n.1.1 2 165.98 odd 4
4400.2.a.bh.1.1 2 60.47 odd 4
4400.2.a.bs.1.2 2 60.23 odd 4
4400.2.b.y.4049.1 4 12.11 even 2
4400.2.b.y.4049.4 4 60.59 even 2