Properties

Label 400.4.n.d.143.3
Level 400400
Weight 44
Character 400.143
Analytic conductor 23.60123.601
Analytic rank 00
Dimension 88
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [400,4,Mod(143,400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(400, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("400.143");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 400=2452 400 = 2^{4} \cdot 5^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 400.n (of order 44, degree 22, 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: 23.600764002323.6007640023
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(i)\Q(i)
Coefficient field: 8.0.1731891456.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x89x6+65x4144x2+256 x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 222 2^{22}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 143.3
Root 1.35234+0.780776i-1.35234 + 0.780776i of defining polynomial
Character χ\chi == 400.143
Dual form 400.4.n.d.207.4

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+(4.123114.12311i)q3+(4.12311+4.12311i)q77.00000iq913.8564iq11+(57.131457.1314i)q13+(57.131457.1314i)q1796.9948q19+34.0000q21+(86.585286.5852i)q23+(82.4621+82.4621i)q27174.000iq29193.990iq31+(57.131457.1314i)q33471.118q39+252.000q41+(202.032+202.032i)q43+(284.494284.494i)q47309.000iq49471.118iq51+(399.920+399.920i)q53+(399.920+399.920i)q57872.954q59+56.0000q61+(28.861728.8617i)q63+(317.479+317.479i)q67714.000iq69387.979iq71+(399.920+399.920i)q73+(57.131457.1314i)q77692.820q79+869.000q81+(482.403+482.403i)q83+(717.420717.420i)q87+42.0000iq89471.118iq91+(799.840799.840i)q93+(742.709742.709i)q9796.9948q99+O(q100)q+(4.12311 - 4.12311i) q^{3} +(4.12311 + 4.12311i) q^{7} -7.00000i q^{9} -13.8564i q^{11} +(-57.1314 - 57.1314i) q^{13} +(57.1314 - 57.1314i) q^{17} -96.9948 q^{19} +34.0000 q^{21} +(86.5852 - 86.5852i) q^{23} +(82.4621 + 82.4621i) q^{27} -174.000i q^{29} -193.990i q^{31} +(-57.1314 - 57.1314i) q^{33} -471.118 q^{39} +252.000 q^{41} +(-202.032 + 202.032i) q^{43} +(-284.494 - 284.494i) q^{47} -309.000i q^{49} -471.118i q^{51} +(399.920 + 399.920i) q^{53} +(-399.920 + 399.920i) q^{57} -872.954 q^{59} +56.0000 q^{61} +(28.8617 - 28.8617i) q^{63} +(317.479 + 317.479i) q^{67} -714.000i q^{69} -387.979i q^{71} +(399.920 + 399.920i) q^{73} +(57.1314 - 57.1314i) q^{77} -692.820 q^{79} +869.000 q^{81} +(-482.403 + 482.403i) q^{83} +(-717.420 - 717.420i) q^{87} +42.0000i q^{89} -471.118i q^{91} +(-799.840 - 799.840i) q^{93} +(742.709 - 742.709i) q^{97} -96.9948 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+272q21+2016q41+448q61+6952q81+O(q100) 8 q + 272 q^{21} + 2016 q^{41} + 448 q^{61} + 6952 q^{81}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/400Z)×\left(\mathbb{Z}/400\mathbb{Z}\right)^\times.

nn 101101 177177 351351
χ(n)\chi(n) 11 e(34)e\left(\frac{3}{4}\right) 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 4.12311 4.12311i 0.793492 0.793492i −0.188568 0.982060i 0.560385π-0.560385\pi
0.982060 + 0.188568i 0.0603846π0.0603846\pi
44 0 0
55 0 0
66 0 0
77 4.12311 + 4.12311i 0.222627 + 0.222627i 0.809604 0.586977i 0.199682π-0.199682\pi
−0.586977 + 0.809604i 0.699682π0.699682\pi
88 0 0
99 7.00000i 0.259259i
1010 0 0
1111 13.8564i 0.379806i −0.981803 0.189903i 0.939183π-0.939183\pi
0.981803 0.189903i 0.0608173π-0.0608173\pi
1212 0 0
1313 −57.1314 57.1314i −1.21888 1.21888i −0.968025 0.250852i 0.919289π-0.919289\pi
−0.250852 0.968025i 0.580711π-0.580711\pi
1414 0 0
1515 0 0
1616 0 0
1717 57.1314 57.1314i 0.815083 0.815083i −0.170308 0.985391i 0.554476π-0.554476\pi
0.985391 + 0.170308i 0.0544763π0.0544763\pi
1818 0 0
1919 −96.9948 −1.17117 −0.585583 0.810613i 0.699134π-0.699134\pi
−0.585583 + 0.810613i 0.699134π0.699134\pi
2020 0 0
2121 34.0000 0.353305
2222 0 0
2323 86.5852 86.5852i 0.784968 0.784968i −0.195696 0.980665i 0.562697π-0.562697\pi
0.980665 + 0.195696i 0.0626967π0.0626967\pi
2424 0 0
2525 0 0
2626 0 0
2727 82.4621 + 82.4621i 0.587772 + 0.587772i
2828 0 0
2929 174.000i 1.11417i −0.830455 0.557086i 0.811919π-0.811919\pi
0.830455 0.557086i 0.188081π-0.188081\pi
3030 0 0
3131 193.990i 1.12392i −0.827164 0.561961i 0.810047π-0.810047\pi
0.827164 0.561961i 0.189953π-0.189953\pi
3232 0 0
3333 −57.1314 57.1314i −0.301373 0.301373i
3434 0 0
3535 0 0
3636 0 0
3737 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
3838 0 0
3939 −471.118 −1.93434
4040 0 0
4141 252.000 0.959897 0.479949 0.877297i 0.340655π-0.340655\pi
0.479949 + 0.877297i 0.340655π0.340655\pi
4242 0 0
4343 −202.032 + 202.032i −0.716503 + 0.716503i −0.967887 0.251385i 0.919114π-0.919114\pi
0.251385 + 0.967887i 0.419114π0.419114\pi
4444 0 0
4545 0 0
4646 0 0
4747 −284.494 284.494i −0.882931 0.882931i 0.110901 0.993832i 0.464627π-0.464627\pi
−0.993832 + 0.110901i 0.964627π0.964627\pi
4848 0 0
4949 309.000i 0.900875i
5050 0 0
5151 471.118i 1.29352i
5252 0 0
5353 399.920 + 399.920i 1.03648 + 1.03648i 0.999309 + 0.0371671i 0.0118334π0.0118334\pi
0.0371671 + 0.999309i 0.488167π0.488167\pi
5454 0 0
5555 0 0
5656 0 0
5757 −399.920 + 399.920i −0.929310 + 0.929310i
5858 0 0
5959 −872.954 −1.92625 −0.963126 0.269050i 0.913290π-0.913290\pi
−0.963126 + 0.269050i 0.913290π0.913290\pi
6060 0 0
6161 56.0000 0.117542 0.0587710 0.998271i 0.481282π-0.481282\pi
0.0587710 + 0.998271i 0.481282π0.481282\pi
6262 0 0
6363 28.8617 28.8617i 0.0577181 0.0577181i
6464 0 0
6565 0 0
6666 0 0
6767 317.479 + 317.479i 0.578899 + 0.578899i 0.934600 0.355701i 0.115758π-0.115758\pi
−0.355701 + 0.934600i 0.615758π0.615758\pi
6868 0 0
6969 714.000i 1.24573i
7070 0 0
7171 387.979i 0.648517i −0.945969 0.324258i 0.894885π-0.894885\pi
0.945969 0.324258i 0.105115π-0.105115\pi
7272 0 0
7373 399.920 + 399.920i 0.641193 + 0.641193i 0.950849 0.309656i 0.100214π-0.100214\pi
−0.309656 + 0.950849i 0.600214π0.600214\pi
7474 0 0
7575 0 0
7676 0 0
7777 57.1314 57.1314i 0.0845549 0.0845549i
7878 0 0
7979 −692.820 −0.986688 −0.493344 0.869834i 0.664226π-0.664226\pi
−0.493344 + 0.869834i 0.664226π0.664226\pi
8080 0 0
8181 869.000 1.19204
8282 0 0
8383 −482.403 + 482.403i −0.637960 + 0.637960i −0.950052 0.312092i 0.898970π-0.898970\pi
0.312092 + 0.950052i 0.398970π0.398970\pi
8484 0 0
8585 0 0
8686 0 0
8787 −717.420 717.420i −0.884087 0.884087i
8888 0 0
8989 42.0000i 0.0500224i 0.999687 + 0.0250112i 0.00796214π0.00796214\pi
−0.999687 + 0.0250112i 0.992038π0.992038\pi
9090 0 0
9191 471.118i 0.542710i
9292 0 0
9393 −799.840 799.840i −0.891823 0.891823i
9494 0 0
9595 0 0
9696 0 0
9797 742.709 742.709i 0.777429 0.777429i −0.201964 0.979393i 0.564732π-0.564732\pi
0.979393 + 0.201964i 0.0647323π0.0647323\pi
9898 0 0
9999 −96.9948 −0.0984682
100100 0 0
101101 −1050.00 −1.03444 −0.517222 0.855851i 0.673034π-0.673034\pi
−0.517222 + 0.855851i 0.673034π0.673034\pi
102102 0 0
103103 869.975 869.975i 0.832245 0.832245i −0.155579 0.987823i 0.549724π-0.549724\pi
0.987823 + 0.155579i 0.0497242π0.0497242\pi
104104 0 0
105105 0 0
106106 0 0
107107 1298.78 + 1298.78i 1.17344 + 1.17344i 0.981385 + 0.192051i 0.0615139π0.0615139\pi
0.192051 + 0.981385i 0.438486π0.438486\pi
108108 0 0
109109 272.000i 0.239017i −0.992833 0.119509i 0.961868π-0.961868\pi
0.992833 0.119509i 0.0381319π-0.0381319\pi
110110 0 0
111111 0 0
112112 0 0
113113 −799.840 799.840i −0.665864 0.665864i 0.290892 0.956756i 0.406048π-0.406048\pi
−0.956756 + 0.290892i 0.906048π0.906048\pi
114114 0 0
115115 0 0
116116 0 0
117117 −399.920 + 399.920i −0.316005 + 0.316005i
118118 0 0
119119 471.118 0.362918
120120 0 0
121121 1139.00 0.855748
122122 0 0
123123 1039.02 1039.02i 0.761671 0.761671i
124124 0 0
125125 0 0
126126 0 0
127127 −28.8617 28.8617i −0.0201659 0.0201659i 0.696952 0.717118i 0.254539π-0.254539\pi
−0.717118 + 0.696952i 0.754539π0.754539\pi
128128 0 0
129129 1666.00i 1.13708i
130130 0 0
131131 1842.90i 1.22912i 0.788869 + 0.614561i 0.210667π0.210667\pi
−0.788869 + 0.614561i 0.789333π0.789333\pi
132132 0 0
133133 −399.920 399.920i −0.260733 0.260733i
134134 0 0
135135 0 0
136136 0 0
137137 799.840 799.840i 0.498795 0.498795i −0.412268 0.911063i 0.635263π-0.635263\pi
0.911063 + 0.412268i 0.135263π0.135263\pi
138138 0 0
139139 2036.89 1.24293 0.621464 0.783443i 0.286538π-0.286538\pi
0.621464 + 0.783443i 0.286538π0.286538\pi
140140 0 0
141141 −2346.00 −1.40120
142142 0 0
143143 −791.636 + 791.636i −0.462937 + 0.462937i
144144 0 0
145145 0 0
146146 0 0
147147 −1274.04 1274.04i −0.714837 0.714837i
148148 0 0
149149 744.000i 0.409066i −0.978860 0.204533i 0.934432π-0.934432\pi
0.978860 0.204533i 0.0655676π-0.0655676\pi
150150 0 0
151151 859.097i 0.462996i 0.972835 + 0.231498i 0.0743626π0.0743626\pi
−0.972835 + 0.231498i 0.925637π0.925637\pi
152152 0 0
153153 −399.920 399.920i −0.211318 0.211318i
154154 0 0
155155 0 0
156156 0 0
157157 799.840 799.840i 0.406587 0.406587i −0.473960 0.880547i 0.657176π-0.657176\pi
0.880547 + 0.473960i 0.157176π0.157176\pi
158158 0 0
159159 3297.82 1.64487
160160 0 0
161161 714.000 0.349510
162162 0 0
163163 −1356.50 + 1356.50i −0.651837 + 0.651837i −0.953435 0.301598i 0.902480π-0.902480\pi
0.301598 + 0.953435i 0.402480π0.402480\pi
164164 0 0
165165 0 0
166166 0 0
167167 1274.04 + 1274.04i 0.590348 + 0.590348i 0.937725 0.347377i 0.112928π-0.112928\pi
−0.347377 + 0.937725i 0.612928π0.612928\pi
168168 0 0
169169 4331.00i 1.97132i
170170 0 0
171171 678.964i 0.303635i
172172 0 0
173173 2856.57 + 2856.57i 1.25538 + 1.25538i 0.953274 + 0.302109i 0.0976905π0.0976905\pi
0.302109 + 0.953274i 0.402309π0.402309\pi
174174 0 0
175175 0 0
176176 0 0
177177 −3599.28 + 3599.28i −1.52847 + 1.52847i
178178 0 0
179179 1842.90 0.769525 0.384762 0.923016i 0.374283π-0.374283\pi
0.384762 + 0.923016i 0.374283π0.374283\pi
180180 0 0
181181 −3094.00 −1.27058 −0.635291 0.772273i 0.719120π-0.719120\pi
−0.635291 + 0.772273i 0.719120π0.719120\pi
182182 0 0
183183 230.894 230.894i 0.0932687 0.0932687i
184184 0 0
185185 0 0
186186 0 0
187187 −791.636 791.636i −0.309573 0.309573i
188188 0 0
189189 680.000i 0.261708i
190190 0 0
191191 3990.65i 1.51180i 0.654690 + 0.755898i 0.272799π0.272799\pi
−0.654690 + 0.755898i 0.727201π0.727201\pi
192192 0 0
193193 2799.44 + 2799.44i 1.04408 + 1.04408i 0.998982 + 0.0451010i 0.0143610π0.0143610\pi
0.0451010 + 0.998982i 0.485639π0.485639\pi
194194 0 0
195195 0 0
196196 0 0
197197 399.920 399.920i 0.144635 0.144635i −0.631081 0.775717i 0.717389π-0.717389\pi
0.775717 + 0.631081i 0.217389π0.217389\pi
198198 0 0
199199 3103.84 1.10565 0.552827 0.833296i 0.313549π-0.313549\pi
0.552827 + 0.833296i 0.313549π0.313549\pi
200200 0 0
201201 2618.00 0.918704
202202 0 0
203203 717.420 717.420i 0.248045 0.248045i
204204 0 0
205205 0 0
206206 0 0
207207 −606.097 606.097i −0.203510 0.203510i
208208 0 0
209209 1344.00i 0.444815i
210210 0 0
211211 180.133i 0.0587720i 0.999568 + 0.0293860i 0.00935520π0.00935520\pi
−0.999568 + 0.0293860i 0.990645π0.990645\pi
212212 0 0
213213 −1599.68 1599.68i −0.514593 0.514593i
214214 0 0
215215 0 0
216216 0 0
217217 799.840 799.840i 0.250215 0.250215i
218218 0 0
219219 3297.82 1.01756
220220 0 0
221221 −6528.00 −1.98697
222222 0 0
223223 −3756.15 + 3756.15i −1.12794 + 1.12794i −0.137427 + 0.990512i 0.543883π0.543883\pi
−0.990512 + 0.137427i 0.956117π0.956117\pi
224224 0 0
225225 0 0
226226 0 0
227227 −3401.56 3401.56i −0.994580 0.994580i 0.00540561 0.999985i 0.498279π-0.498279\pi
−0.999985 + 0.00540561i 0.998279π0.998279\pi
228228 0 0
229229 2170.00i 0.626191i −0.949722 0.313095i 0.898634π-0.898634\pi
0.949722 0.313095i 0.101366π-0.101366\pi
230230 0 0
231231 471.118i 0.134187i
232232 0 0
233233 −1199.76 1199.76i −0.337334 0.337334i 0.518029 0.855363i 0.326666π-0.326666\pi
−0.855363 + 0.518029i 0.826666π0.826666\pi
234234 0 0
235235 0 0
236236 0 0
237237 −2856.57 + 2856.57i −0.782929 + 0.782929i
238238 0 0
239239 −2798.99 −0.757539 −0.378770 0.925491i 0.623653π-0.623653\pi
−0.378770 + 0.925491i 0.623653π0.623653\pi
240240 0 0
241241 5908.00 1.57912 0.789560 0.613674i 0.210309π-0.210309\pi
0.789560 + 0.613674i 0.210309π0.210309\pi
242242 0 0
243243 1356.50 1356.50i 0.358105 0.358105i
244244 0 0
245245 0 0
246246 0 0
247247 5541.45 + 5541.45i 1.42751 + 1.42751i
248248 0 0
249249 3978.00i 1.01243i
250250 0 0
251251 3588.81i 0.902485i 0.892401 + 0.451242i 0.149019π0.149019\pi
−0.892401 + 0.451242i 0.850981π0.850981\pi
252252 0 0
253253 −1199.76 1199.76i −0.298135 0.298135i
254254 0 0
255255 0 0
256256 0 0
257257 4799.04 4799.04i 1.16481 1.16481i 0.181399 0.983410i 0.441937π-0.441937\pi
0.983410 0.181399i 0.0580627π-0.0580627\pi
258258 0 0
259259 0 0
260260 0 0
261261 −1218.00 −0.288859
262262 0 0
263263 3723.16 3723.16i 0.872928 0.872928i −0.119862 0.992791i 0.538245π-0.538245\pi
0.992791 + 0.119862i 0.0382453π0.0382453\pi
264264 0 0
265265 0 0
266266 0 0
267267 173.170 + 173.170i 0.0396924 + 0.0396924i
268268 0 0
269269 2856.00i 0.647336i −0.946171 0.323668i 0.895084π-0.895084\pi
0.946171 0.323668i 0.104916π-0.104916\pi
270270 0 0
271271 6013.68i 1.34799i −0.738736 0.673995i 0.764577π-0.764577\pi
0.738736 0.673995i 0.235423π-0.235423\pi
272272 0 0
273273 −1942.47 1942.47i −0.430636 0.430636i
274274 0 0
275275 0 0
276276 0 0
277277 1599.68 1599.68i 0.346987 0.346987i −0.511999 0.858986i 0.671095π-0.671095\pi
0.858986 + 0.511999i 0.171095π0.171095\pi
278278 0 0
279279 −1357.93 −0.291387
280280 0 0
281281 636.000 0.135020 0.0675099 0.997719i 0.478495π-0.478495\pi
0.0675099 + 0.997719i 0.478495π0.478495\pi
282282 0 0
283283 5661.02 5661.02i 1.18909 1.18909i 0.211773 0.977319i 0.432076π-0.432076\pi
0.977319 0.211773i 0.0679237π-0.0679237\pi
284284 0 0
285285 0 0
286286 0 0
287287 1039.02 + 1039.02i 0.213699 + 0.213699i
288288 0 0
289289 1615.00i 0.328720i
290290 0 0
291291 6124.53i 1.23377i
292292 0 0
293293 −1942.47 1942.47i −0.387305 0.387305i 0.486420 0.873725i 0.338302π-0.338302\pi
−0.873725 + 0.486420i 0.838302π0.838302\pi
294294 0 0
295295 0 0
296296 0 0
297297 1142.63 1142.63i 0.223239 0.223239i
298298 0 0
299299 −9893.47 −1.91356
300300 0 0
301301 −1666.00 −0.319025
302302 0 0
303303 −4329.26 + 4329.26i −0.820824 + 0.820824i
304304 0 0
305305 0 0
306306 0 0
307307 −1331.76 1331.76i −0.247582 0.247582i 0.572395 0.819978i 0.306014π-0.306014\pi
−0.819978 + 0.572395i 0.806014π0.806014\pi
308308 0 0
309309 7174.00i 1.32076i
310310 0 0
311311 4849.74i 0.884256i 0.896952 + 0.442128i 0.145776π0.145776\pi
−0.896952 + 0.442128i 0.854224π0.854224\pi
312312 0 0
313313 −2742.31 2742.31i −0.495222 0.495222i 0.414725 0.909947i 0.363878π-0.363878\pi
−0.909947 + 0.414725i 0.863878π0.863878\pi
314314 0 0
315315 0 0
316316 0 0
317317 1199.76 1199.76i 0.212572 0.212572i −0.592787 0.805359i 0.701973π-0.701973\pi
0.805359 + 0.592787i 0.201973π0.201973\pi
318318 0 0
319319 −2411.01 −0.423169
320320 0 0
321321 10710.0 1.86222
322322 0 0
323323 −5541.45 + 5541.45i −0.954597 + 0.954597i
324324 0 0
325325 0 0
326326 0 0
327327 −1121.48 1121.48i −0.189658 0.189658i
328328 0 0
329329 2346.00i 0.393128i
330330 0 0
331331 5722.70i 0.950296i −0.879906 0.475148i 0.842395π-0.842395\pi
0.879906 0.475148i 0.157605π-0.157605\pi
332332 0 0
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 −4799.04 + 4799.04i −0.775728 + 0.775728i −0.979101 0.203373i 0.934810π-0.934810\pi
0.203373 + 0.979101i 0.434810π0.434810\pi
338338 0 0
339339 −6595.65 −1.05672
340340 0 0
341341 −2688.00 −0.426872
342342 0 0
343343 2688.26 2688.26i 0.423186 0.423186i
344344 0 0
345345 0 0
346346 0 0
347347 3203.65 + 3203.65i 0.495623 + 0.495623i 0.910072 0.414450i 0.136026π-0.136026\pi
−0.414450 + 0.910072i 0.636026π0.636026\pi
348348 0 0
349349 1778.00i 0.272705i −0.990660 0.136353i 0.956462π-0.956462\pi
0.990660 0.136353i 0.0435380π-0.0435380\pi
350350 0 0
351351 9422.36i 1.43284i
352352 0 0
353353 3656.41 + 3656.41i 0.551306 + 0.551306i 0.926818 0.375511i 0.122533π-0.122533\pi
−0.375511 + 0.926818i 0.622533π0.622533\pi
354354 0 0
355355 0 0
356356 0 0
357357 1942.47 1942.47i 0.287973 0.287973i
358358 0 0
359359 −11445.4 −1.68263 −0.841316 0.540544i 0.818218π-0.818218\pi
−0.841316 + 0.540544i 0.818218π0.818218\pi
360360 0 0
361361 2549.00 0.371629
362362 0 0
363363 4696.22 4696.22i 0.679029 0.679029i
364364 0 0
365365 0 0
366366 0 0
367367 −6930.94 6930.94i −0.985810 0.985810i 0.0140910 0.999901i 0.495515π-0.495515\pi
−0.999901 + 0.0140910i 0.995515π0.995515\pi
368368 0 0
369369 1764.00i 0.248862i
370370 0 0
371371 3297.82i 0.461495i
372372 0 0
373373 8798.24 + 8798.24i 1.22133 + 1.22133i 0.967160 + 0.254169i 0.0818019π0.0818019\pi
0.254169 + 0.967160i 0.418198π0.418198\pi
374374 0 0
375375 0 0
376376 0 0
377377 −9940.87 + 9940.87i −1.35804 + 1.35804i
378378 0 0
379379 −872.954 −0.118313 −0.0591565 0.998249i 0.518841π-0.518841\pi
−0.0591565 + 0.998249i 0.518841π0.518841\pi
380380 0 0
381381 −238.000 −0.0320029
382382 0 0
383383 −1941.98 + 1941.98i −0.259088 + 0.259088i −0.824683 0.565595i 0.808647π-0.808647\pi
0.565595 + 0.824683i 0.308647π0.308647\pi
384384 0 0
385385 0 0
386386 0 0
387387 1414.23 + 1414.23i 0.185760 + 0.185760i
388388 0 0
389389 11880.0i 1.54843i −0.632922 0.774216i 0.718144π-0.718144\pi
0.632922 0.774216i 0.281856π-0.281856\pi
390390 0 0
391391 9893.47i 1.27963i
392392 0 0
393393 7598.48 + 7598.48i 0.975299 + 0.975299i
394394 0 0
395395 0 0
396396 0 0
397397 −57.1314 + 57.1314i −0.00722253 + 0.00722253i −0.710709 0.703486i 0.751626π-0.751626\pi
0.703486 + 0.710709i 0.251626π0.251626\pi
398398 0 0
399399 −3297.82 −0.413779
400400 0 0
401401 −498.000 −0.0620173 −0.0310086 0.999519i 0.509872π-0.509872\pi
−0.0310086 + 0.999519i 0.509872π0.509872\pi
402402 0 0
403403 −11082.9 + 11082.9i −1.36992 + 1.36992i
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 7700.00i 0.930906i 0.885073 + 0.465453i 0.154109π0.154109\pi
−0.885073 + 0.465453i 0.845891π0.845891\pi
410410 0 0
411411 6595.65i 0.791580i
412412 0 0
413413 −3599.28 3599.28i −0.428835 0.428835i
414414 0 0
415415 0 0
416416 0 0
417417 8398.32 8398.32i 0.986253 0.986253i
418418 0 0
419419 −3976.79 −0.463673 −0.231836 0.972755i 0.574473π-0.574473\pi
−0.231836 + 0.972755i 0.574473π0.574473\pi
420420 0 0
421421 11768.0 1.36232 0.681161 0.732134i 0.261476π-0.261476\pi
0.681161 + 0.732134i 0.261476π0.261476\pi
422422 0 0
423423 −1991.46 + 1991.46i −0.228908 + 0.228908i
424424 0 0
425425 0 0
426426 0 0
427427 230.894 + 230.894i 0.0261680 + 0.0261680i
428428 0 0
429429 6528.00i 0.734673i
430430 0 0
431431 17542.2i 1.96051i 0.197745 + 0.980254i 0.436638π0.436638\pi
−0.197745 + 0.980254i 0.563362π0.563362\pi
432432 0 0
433433 −7598.48 7598.48i −0.843325 0.843325i 0.145965 0.989290i 0.453371π-0.453371\pi
−0.989290 + 0.145965i 0.953371π0.953371\pi
434434 0 0
435435 0 0
436436 0 0
437437 −8398.32 + 8398.32i −0.919328 + 0.919328i
438438 0 0
439439 1745.91 0.189812 0.0949062 0.995486i 0.469745π-0.469745\pi
0.0949062 + 0.995486i 0.469745π0.469745\pi
440440 0 0
441441 −2163.00 −0.233560
442442 0 0
443443 −1471.95 + 1471.95i −0.157865 + 0.157865i −0.781620 0.623755i 0.785606π-0.785606\pi
0.623755 + 0.781620i 0.285606π0.285606\pi
444444 0 0
445445 0 0
446446 0 0
447447 −3067.59 3067.59i −0.324591 0.324591i
448448 0 0
449449 15252.0i 1.60309i −0.597936 0.801544i 0.704012π-0.704012\pi
0.597936 0.801544i 0.295988π-0.295988\pi
450450 0 0
451451 3491.81i 0.364575i
452452 0 0
453453 3542.15 + 3542.15i 0.367383 + 0.367383i
454454 0 0
455455 0 0
456456 0 0
457457 6398.72 6398.72i 0.654966 0.654966i −0.299219 0.954185i 0.596726π-0.596726\pi
0.954185 + 0.299219i 0.0967260π0.0967260\pi
458458 0 0
459459 9422.36 0.958165
460460 0 0
461461 −15582.0 −1.57424 −0.787122 0.616798i 0.788430π-0.788430\pi
−0.787122 + 0.616798i 0.788430π0.788430\pi
462462 0 0
463463 11919.9 11919.9i 1.19647 1.19647i 0.221251 0.975217i 0.428986π-0.428986\pi
0.975217 0.221251i 0.0710140π-0.0710140\pi
464464 0 0
465465 0 0
466466 0 0
467467 3005.74 + 3005.74i 0.297836 + 0.297836i 0.840166 0.542330i 0.182458π-0.182458\pi
−0.542330 + 0.840166i 0.682458π0.682458\pi
468468 0 0
469469 2618.00i 0.257757i
470470 0 0
471471 6595.65i 0.645247i
472472 0 0
473473 2799.44 + 2799.44i 0.272132 + 0.272132i
474474 0 0
475475 0 0
476476 0 0
477477 2799.44 2799.44i 0.268716 0.268716i
478478 0 0
479479 −387.979 −0.0370088 −0.0185044 0.999829i 0.505890π-0.505890\pi
−0.0185044 + 0.999829i 0.505890π0.505890\pi
480480 0 0
481481 0 0
482482 0 0
483483 2943.90 2943.90i 0.277333 0.277333i
484484 0 0
485485 0 0
486486 0 0
487487 −1356.50 1356.50i −0.126220 0.126220i 0.641175 0.767395i 0.278447π-0.278447\pi
−0.767395 + 0.641175i 0.778447π0.778447\pi
488488 0 0
489489 11186.0i 1.03445i
490490 0 0
491491 14369.1i 1.32071i 0.750954 + 0.660354i 0.229594π0.229594\pi
−0.750954 + 0.660354i 0.770406π0.770406\pi
492492 0 0
493493 −9940.87 9940.87i −0.908142 0.908142i
494494 0 0
495495 0 0
496496 0 0
497497 1599.68 1599.68i 0.144377 0.144377i
498498 0 0
499499 7357.75 0.660077 0.330038 0.943968i 0.392938π-0.392938\pi
0.330038 + 0.943968i 0.392938π0.392938\pi
500500 0 0
501501 10506.0 0.936873
502502 0 0
503503 12579.6 12579.6i 1.11510 1.11510i 0.122653 0.992450i 0.460860π-0.460860\pi
0.992450 0.122653i 0.0391401π-0.0391401\pi
504504 0 0
505505 0 0
506506 0 0
507507 17857.2 + 17857.2i 1.56423 + 1.56423i
508508 0 0
509509 20370.0i 1.77384i 0.461923 + 0.886920i 0.347159π0.347159\pi
−0.461923 + 0.886920i 0.652841π0.652841\pi
510510 0 0
511511 3297.82i 0.285493i
512512 0 0
513513 −7998.40 7998.40i −0.688378 0.688378i
514514 0 0
515515 0 0
516516 0 0
517517 −3942.07 + 3942.07i −0.335342 + 0.335342i
518518 0 0
519519 23555.9 1.99227
520520 0 0
521521 −18438.0 −1.55045 −0.775224 0.631686i 0.782363π-0.782363\pi
−0.775224 + 0.631686i 0.782363π0.782363\pi
522522 0 0
523523 −3904.58 + 3904.58i −0.326454 + 0.326454i −0.851236 0.524782i 0.824147π-0.824147\pi
0.524782 + 0.851236i 0.324147π0.324147\pi
524524 0 0
525525 0 0
526526 0 0
527527 −11082.9 11082.9i −0.916089 0.916089i
528528 0 0
529529 2827.00i 0.232350i
530530 0 0
531531 6110.68i 0.499399i
532532 0 0
533533 −14397.1 14397.1i −1.17000 1.17000i
534534 0 0
535535 0 0
536536 0 0
537537 7598.48 7598.48i 0.610612 0.610612i
538538 0 0
539539 −4281.63 −0.342157
540540 0 0
541541 6322.00 0.502410 0.251205 0.967934i 0.419173π-0.419173\pi
0.251205 + 0.967934i 0.419173π0.419173\pi
542542 0 0
543543 −12756.9 + 12756.9i −1.00820 + 1.00820i
544544 0 0
545545 0 0
546546 0 0
547547 −1587.40 1587.40i −0.124081 0.124081i 0.642340 0.766420i 0.277964π-0.277964\pi
−0.766420 + 0.642340i 0.777964π0.777964\pi
548548 0 0
549549 392.000i 0.0304739i
550550 0 0
551551 16877.1i 1.30488i
552552 0 0
553553 −2856.57 2856.57i −0.219663 0.219663i
554554 0 0
555555 0 0
556556 0 0
557557 12797.4 12797.4i 0.973510 0.973510i −0.0261483 0.999658i 0.508324π-0.508324\pi
0.999658 + 0.0261483i 0.00832422π0.00832422\pi
558558 0 0
559559 23084.8 1.74666
560560 0 0
561561 −6528.00 −0.491288
562562 0 0
563563 729.790 729.790i 0.0546305 0.0546305i −0.679264 0.733894i 0.737701π-0.737701\pi
0.733894 + 0.679264i 0.237701π0.237701\pi
564564 0 0
565565 0 0
566566 0 0
567567 3582.98 + 3582.98i 0.265381 + 0.265381i
568568 0 0
569569 5196.00i 0.382825i 0.981510 + 0.191413i 0.0613069π0.0613069\pi
−0.981510 + 0.191413i 0.938693π0.938693\pi
570570 0 0
571571 5528.71i 0.405200i −0.979262 0.202600i 0.935061π-0.935061\pi
0.979262 0.202600i 0.0649391π-0.0649391\pi
572572 0 0
573573 16453.9 + 16453.9i 1.19960 + 1.19960i
574574 0 0
575575 0 0
576576 0 0
577577 −17253.7 + 17253.7i −1.24485 + 1.24485i −0.286890 + 0.957963i 0.592621π0.592621\pi
−0.957963 + 0.286890i 0.907379π0.907379\pi
578578 0 0
579579 23084.8 1.65694
580580 0 0
581581 −3978.00 −0.284054
582582 0 0
583583 5541.45 5541.45i 0.393660 0.393660i
584584 0 0
585585 0 0
586586 0 0
587587 −13989.7 13989.7i −0.983674 0.983674i 0.0161949 0.999869i 0.494845π-0.494845\pi
−0.999869 + 0.0161949i 0.994845π0.994845\pi
588588 0 0
589589 18816.0i 1.31630i
590590 0 0
591591 3297.82i 0.229534i
592592 0 0
593593 9255.29 + 9255.29i 0.640926 + 0.640926i 0.950783 0.309857i 0.100281π-0.100281\pi
−0.309857 + 0.950783i 0.600281π0.600281\pi
594594 0 0
595595 0 0
596596 0 0
597597 12797.4 12797.4i 0.877327 0.877327i
598598 0 0
599599 −10586.3 −0.722111 −0.361055 0.932544i 0.617583π-0.617583\pi
−0.361055 + 0.932544i 0.617583π0.617583\pi
600600 0 0
601601 −17612.0 −1.19536 −0.597678 0.801737i 0.703910π-0.703910\pi
−0.597678 + 0.801737i 0.703910π0.703910\pi
602602 0 0
603603 2222.35 2222.35i 0.150085 0.150085i
604604 0 0
605605 0 0
606606 0 0
607607 13338.2 + 13338.2i 0.891899 + 0.891899i 0.994702 0.102803i 0.0327810π-0.0327810\pi
−0.102803 + 0.994702i 0.532781π0.532781\pi
608608 0 0
609609 5916.00i 0.393643i
610610 0 0
611611 32507.1i 2.15237i
612612 0 0
613613 5198.96 + 5198.96i 0.342551 + 0.342551i 0.857326 0.514774i 0.172124π-0.172124\pi
−0.514774 + 0.857326i 0.672124π0.672124\pi
614614 0 0
615615 0 0
616616 0 0
617617 −12397.5 + 12397.5i −0.808923 + 0.808923i −0.984471 0.175548i 0.943830π-0.943830\pi
0.175548 + 0.984471i 0.443830π0.443830\pi
618618 0 0
619619 19108.0 1.24073 0.620367 0.784311i 0.286984π-0.286984\pi
0.620367 + 0.784311i 0.286984π0.286984\pi
620620 0 0
621621 14280.0 0.922764
622622 0 0
623623 −173.170 + 173.170i −0.0111363 + 0.0111363i
624624 0 0
625625 0 0
626626 0 0
627627 5541.45 + 5541.45i 0.352958 + 0.352958i
628628 0 0
629629 0 0
630630 0 0
631631 4572.61i 0.288483i 0.989543 + 0.144242i 0.0460742π0.0460742\pi
−0.989543 + 0.144242i 0.953926π0.953926\pi
632632 0 0
633633 742.709 + 742.709i 0.0466351 + 0.0466351i
634634 0 0
635635 0 0
636636 0 0
637637 −17653.6 + 17653.6i −1.09806 + 1.09806i
638638 0 0
639639 −2715.86 −0.168134
640640 0 0
641641 −10404.0 −0.641082 −0.320541 0.947235i 0.603865π-0.603865\pi
−0.320541 + 0.947235i 0.603865π0.603865\pi
642642 0 0
643643 −1034.90 + 1034.90i −0.0634719 + 0.0634719i −0.738130 0.674658i 0.764291π-0.764291\pi
0.674658 + 0.738130i 0.264291π0.264291\pi
644644 0 0
645645 0 0
646646 0 0
647647 −3500.52 3500.52i −0.212704 0.212704i 0.592711 0.805415i 0.298058π-0.298058\pi
−0.805415 + 0.592711i 0.798058π0.798058\pi
648648 0 0
649649 12096.0i 0.731602i
650650 0 0
651651 6595.65i 0.397087i
652652 0 0
653653 11597.7 + 11597.7i 0.695026 + 0.695026i 0.963333 0.268307i 0.0864642π-0.0864642\pi
−0.268307 + 0.963333i 0.586464π0.586464\pi
654654 0 0
655655 0 0
656656 0 0
657657 2799.44 2799.44i 0.166235 0.166235i
658658 0 0
659659 −762.102 −0.0450490 −0.0225245 0.999746i 0.507170π-0.507170\pi
−0.0225245 + 0.999746i 0.507170π0.507170\pi
660660 0 0
661661 18592.0 1.09402 0.547008 0.837127i 0.315767π-0.315767\pi
0.547008 + 0.837127i 0.315767π0.315767\pi
662662 0 0
663663 −26915.6 + 26915.6i −1.57665 + 1.57665i
664664 0 0
665665 0 0
666666 0 0
667667 −15065.8 15065.8i −0.874589 0.874589i
668668 0 0
669669 30974.0i 1.79002i
670670 0 0
671671 775.959i 0.0446432i
672672 0 0
673673 9998.00 + 9998.00i 0.572652 + 0.572652i 0.932869 0.360217i 0.117297π-0.117297\pi
−0.360217 + 0.932869i 0.617297π0.617297\pi
674674 0 0
675675 0 0
676676 0 0
677677 −7141.43 + 7141.43i −0.405417 + 0.405417i −0.880137 0.474720i 0.842549π-0.842549\pi
0.474720 + 0.880137i 0.342549π0.342549\pi
678678 0 0
679679 6124.53 0.346153
680680 0 0
681681 −28050.0 −1.57838
682682 0 0
683683 −5974.38 + 5974.38i −0.334705 + 0.334705i −0.854370 0.519665i 0.826057π-0.826057\pi
0.519665 + 0.854370i 0.326057π0.326057\pi
684684 0 0
685685 0 0
686686 0 0
687687 −8947.14 8947.14i −0.496877 0.496877i
688688 0 0
689689 45696.0i 2.52667i
690690 0 0
691691 29001.5i 1.59662i −0.602244 0.798312i 0.705726π-0.705726\pi
0.602244 0.798312i 0.294274π-0.294274\pi
692692 0 0
693693 −399.920 399.920i −0.0219217 0.0219217i
694694 0 0
695695 0 0
696696 0 0
697697 14397.1 14397.1i 0.782396 0.782396i
698698 0 0
699699 −9893.47 −0.535344
700700 0 0
701701 3408.00 0.183621 0.0918105 0.995776i 0.470735π-0.470735\pi
0.0918105 + 0.995776i 0.470735π0.470735\pi
702702 0 0
703703 0 0
704704 0 0
705705 0 0
706706 0 0
707707 −4329.26 4329.26i −0.230295 0.230295i
708708 0 0
709709 16486.0i 0.873265i −0.899640 0.436632i 0.856171π-0.856171\pi
0.899640 0.436632i 0.143829π-0.143829\pi
710710 0 0
711711 4849.74i 0.255808i
712712 0 0
713713 −16796.6 16796.6i −0.882243 0.882243i
714714 0 0
715715 0 0
716716 0 0
717717 −11540.5 + 11540.5i −0.601101 + 0.601101i
718718 0 0
719719 2521.87 0.130806 0.0654032 0.997859i 0.479167π-0.479167\pi
0.0654032 + 0.997859i 0.479167π0.479167\pi
720720 0 0
721721 7174.00 0.370560
722722 0 0
723723 24359.3 24359.3i 1.25302 1.25302i
724724 0 0
725725 0 0
726726 0 0
727727 1653.37 + 1653.37i 0.0843465 + 0.0843465i 0.748021 0.663675i 0.231004π-0.231004\pi
−0.663675 + 0.748021i 0.731004π0.731004\pi
728728 0 0
729729 12277.0i 0.623736i
730730 0 0
731731 23084.8i 1.16802i
732732 0 0
733733 −6055.93 6055.93i −0.305158 0.305158i 0.537870 0.843028i 0.319229π-0.319229\pi
−0.843028 + 0.537870i 0.819229π0.819229\pi
734734 0 0
735735 0 0
736736 0 0
737737 4399.12 4399.12i 0.219869 0.219869i
738738 0 0
739739 −25204.8 −1.25463 −0.627316 0.778764i 0.715847π-0.715847\pi
−0.627316 + 0.778764i 0.715847π0.715847\pi
740740 0 0
741741 45696.0 2.26543
742742 0 0
743743 1125.61 1125.61i 0.0555781 0.0555781i −0.678771 0.734350i 0.737487π-0.737487\pi
0.734350 + 0.678771i 0.237487π0.237487\pi
744744 0 0
745745 0 0
746746 0 0
747747 3376.82 + 3376.82i 0.165397 + 0.165397i
748748 0 0
749749 10710.0i 0.522476i
750750 0 0
751751 11140.6i 0.541311i −0.962676 0.270655i 0.912760π-0.912760\pi
0.962676 0.270655i 0.0872404π-0.0872404\pi
752752 0 0
753753 14797.0 + 14797.0i 0.716114 + 0.716114i
754754 0 0
755755 0 0
756756 0 0
757757 8798.24 8798.24i 0.422427 0.422427i −0.463611 0.886039i 0.653447π-0.653447\pi
0.886039 + 0.463611i 0.153447π0.153447\pi
758758 0 0
759759 −9893.47 −0.473136
760760 0 0
761761 −19110.0 −0.910298 −0.455149 0.890415i 0.650414π-0.650414\pi
−0.455149 + 0.890415i 0.650414π0.650414\pi
762762 0 0
763763 1121.48 1121.48i 0.0532116 0.0532116i
764764 0 0
765765 0 0
766766 0 0
767767 49873.1 + 49873.1i 2.34787 + 2.34787i
768768 0 0
769769 17458.0i 0.818663i −0.912386 0.409331i 0.865762π-0.865762\pi
0.912386 0.409331i 0.134238π-0.134238\pi
770770 0 0
771771 39573.9i 1.84853i
772772 0 0
773773 −12054.7 12054.7i −0.560904 0.560904i 0.368660 0.929564i 0.379817π-0.379817\pi
−0.929564 + 0.368660i 0.879817π0.879817\pi
774774 0 0
775775 0 0
776776 0 0
777777 0 0
778778 0 0
779779 −24442.7 −1.12420
780780 0 0
781781 −5376.00 −0.246310
782782 0 0
783783 14348.4 14348.4i 0.654879 0.654879i
784784 0 0
785785 0 0
786786 0 0
787787 −10443.8 10443.8i −0.473040 0.473040i 0.429857 0.902897i 0.358564π-0.358564\pi
−0.902897 + 0.429857i 0.858564π0.858564\pi
788788 0 0
789789 30702.0i 1.38532i
790790 0 0
791791 6595.65i 0.296478i
792792 0 0
793793 −3199.36 3199.36i −0.143269 0.143269i
794794 0 0
795795 0 0
796796 0 0
797797 3256.49 3256.49i 0.144731 0.144731i −0.631028 0.775760i 0.717367π-0.717367\pi
0.775760 + 0.631028i 0.217367π0.217367\pi
798798 0 0
799799 −32507.1 −1.43932
800800 0 0
801801 294.000 0.0129688
802802 0 0
803803 5541.45 5541.45i 0.243529 0.243529i
804804 0 0
805805 0 0
806806 0 0
807807 −11775.6 11775.6i −0.513656 0.513656i
808808 0 0
809809 12762.0i 0.554621i −0.960780 0.277310i 0.910557π-0.910557\pi
0.960780 0.277310i 0.0894430π-0.0894430\pi
810810 0 0
811811 1842.90i 0.0797941i −0.999204 0.0398971i 0.987297π-0.987297\pi
0.999204 0.0398971i 0.0127030π-0.0127030\pi
812812 0 0
813813 −24795.0 24795.0i −1.06962 1.06962i
814814 0 0
815815 0 0
816816 0 0
817817 19596.1 19596.1i 0.839143 0.839143i
818818 0 0
819819 −3297.82 −0.140702
820820 0 0
821821 18768.0 0.797817 0.398908 0.916991i 0.369389π-0.369389\pi
0.398908 + 0.916991i 0.369389π0.369389\pi
822822 0 0
823823 −16306.9 + 16306.9i −0.690671 + 0.690671i −0.962380 0.271709i 0.912411π-0.912411\pi
0.271709 + 0.962380i 0.412411π0.412411\pi
824824 0 0
825825 0 0
826826 0 0
827827 −14113.4 14113.4i −0.593435 0.593435i 0.345123 0.938558i 0.387837π-0.387837\pi
−0.938558 + 0.345123i 0.887837π0.887837\pi
828828 0 0
829829 19208.0i 0.804730i 0.915479 + 0.402365i 0.131812π0.131812\pi
−0.915479 + 0.402365i 0.868188π0.868188\pi
830830 0 0
831831 13191.3i 0.550663i
832832 0 0
833833 −17653.6 17653.6i −0.734287 0.734287i
834834 0 0
835835 0 0
836836 0 0
837837 15996.8 15996.8i 0.660610 0.660610i
838838 0 0
839839 −38216.0 −1.57254 −0.786270 0.617883i 0.787991π-0.787991\pi
−0.786270 + 0.617883i 0.787991π0.787991\pi
840840 0 0
841841 −5887.00 −0.241379
842842 0 0
843843 2622.30 2622.30i 0.107137 0.107137i
844844 0 0
845845 0 0
846846 0 0
847847 4696.22 + 4696.22i 0.190512 + 0.190512i
848848 0 0
849849 46682.0i 1.88707i
850850 0 0
851851 0 0
852852 0 0
853853 −5198.96 5198.96i −0.208686 0.208686i 0.595023 0.803709i 0.297143π-0.297143\pi
−0.803709 + 0.595023i 0.797143π0.797143\pi
854854 0 0
855855 0 0
856856 0 0
857857 −3999.20 + 3999.20i −0.159405 + 0.159405i −0.782303 0.622898i 0.785955π-0.785955\pi
0.622898 + 0.782303i 0.285955π0.285955\pi
858858 0 0
859859 4946.74 0.196485 0.0982424 0.995163i 0.468678π-0.468678\pi
0.0982424 + 0.995163i 0.468678π0.468678\pi
860860 0 0
861861 8568.00 0.339137
862862 0 0
863863 7013.40 7013.40i 0.276638 0.276638i −0.555127 0.831766i 0.687330π-0.687330\pi
0.831766 + 0.555127i 0.187330π0.187330\pi
864864 0 0
865865 0 0
866866 0 0
867867 −6658.82 6658.82i −0.260836 0.260836i
868868 0 0
869869 9600.00i 0.374750i
870870 0 0
871871 36276.1i 1.41121i
872872 0 0
873873 −5198.96 5198.96i −0.201556 0.201556i
874874 0 0
875875 0 0
876876 0 0
877877 11997.6 11997.6i 0.461950 0.461950i −0.437344 0.899294i 0.644081π-0.644081\pi
0.899294 + 0.437344i 0.144081π0.144081\pi
878878 0 0
879879 −16018.0 −0.614646
880880 0 0
881881 13020.0 0.497906 0.248953 0.968516i 0.419914π-0.419914\pi
0.248953 + 0.968516i 0.419914π0.419914\pi
882882 0 0
883883 9668.68 9668.68i 0.368490 0.368490i −0.498436 0.866926i 0.666092π-0.666092\pi
0.866926 + 0.498436i 0.166092π0.166092\pi
884884 0 0
885885 0 0
886886 0 0
887887 13297.0 + 13297.0i 0.503348 + 0.503348i 0.912477 0.409128i 0.134167π-0.134167\pi
−0.409128 + 0.912477i 0.634167π0.634167\pi
888888 0 0
889889 238.000i 0.00897892i
890890 0 0
891891 12041.2i 0.452745i
892892 0 0
893893 27594.5 + 27594.5i 1.03406 + 1.03406i
894894 0 0
895895 0 0
896896 0 0
897897 −40791.8 + 40791.8i −1.51839 + 1.51839i
898898 0 0
899899 −33754.2 −1.25224
900900 0 0
901901 45696.0 1.68963
902902 0 0
903903 −6869.09 + 6869.09i −0.253144 + 0.253144i
904904 0 0
905905 0 0
906906 0 0
907907 9322.34 + 9322.34i 0.341283 + 0.341283i 0.856849 0.515567i 0.172419π-0.172419\pi
−0.515567 + 0.856849i 0.672419π0.672419\pi
908908 0 0
909909 7350.00i 0.268189i
910910 0 0
911911 2133.89i 0.0776057i 0.999247 + 0.0388029i 0.0123544π0.0123544\pi
−0.999247 + 0.0388029i 0.987646π0.987646\pi
912912 0 0
913913 6684.38 + 6684.38i 0.242301 + 0.242301i
914914 0 0
915915 0 0
916916 0 0
917917 −7598.48 + 7598.48i −0.273636 + 0.273636i
918918 0 0
919919 22613.7 0.811704 0.405852 0.913939i 0.366975π-0.366975\pi
0.405852 + 0.913939i 0.366975π0.366975\pi
920920 0 0
921921 −10982.0 −0.392909
922922 0 0
923923 −22165.8 + 22165.8i −0.790462 + 0.790462i
924924 0 0
925925 0 0
926926 0 0
927927 −6089.83 6089.83i −0.215767 0.215767i
928928 0 0
929929 33684.0i 1.18960i −0.803875 0.594799i 0.797232π-0.797232\pi
0.803875 0.594799i 0.202768π-0.202768\pi
930930 0 0
931931 29971.4i 1.05507i
932932 0 0
933933 19996.0 + 19996.0i 0.701650 + 0.701650i
934934 0 0
935935 0 0
936936 0 0
937937 −20738.7 + 20738.7i −0.723057 + 0.723057i −0.969227 0.246170i 0.920828π-0.920828\pi
0.246170 + 0.969227i 0.420828π0.420828\pi
938938 0 0
939939 −22613.7 −0.785909
940940 0 0
941941 −33054.0 −1.14509 −0.572545 0.819873i 0.694044π-0.694044\pi
−0.572545 + 0.819873i 0.694044π0.694044\pi
942942 0 0
943943 21819.5 21819.5i 0.753489 0.753489i
944944 0 0
945945 0 0
946946 0 0
947947 8398.77 + 8398.77i 0.288198 + 0.288198i 0.836367 0.548170i 0.184675π-0.184675\pi
−0.548170 + 0.836367i 0.684675π0.684675\pi
948948 0 0
949949 45696.0i 1.56307i
950950 0 0
951951 9893.47i 0.337348i
952952 0 0
953953 15197.0 + 15197.0i 0.516556 + 0.516556i 0.916528 0.399972i 0.130980π-0.130980\pi
−0.399972 + 0.916528i 0.630980π0.630980\pi
954954 0 0
955955 0 0
956956 0 0
957957 −9940.87 + 9940.87i −0.335781 + 0.335781i
958958 0 0
959959 6595.65 0.222090
960960 0 0
961961 −7841.00 −0.263200
962962 0 0
963963 9091.45 9091.45i 0.304224 0.304224i
964964 0 0
965965 0 0
966966 0 0
967967 −25484.9 25484.9i −0.847507 0.847507i 0.142314 0.989822i 0.454546π-0.454546\pi
−0.989822 + 0.142314i 0.954546π0.954546\pi
968968 0 0
969969 45696.0i 1.51493i
970970 0 0
971971 52668.2i 1.74068i −0.492449 0.870341i 0.663898π-0.663898\pi
0.492449 0.870341i 0.336102π-0.336102\pi
972972 0 0
973973 8398.32 + 8398.32i 0.276709 + 0.276709i
974974 0 0
975975 0 0
976976 0 0
977977 40391.9 40391.9i 1.32267 1.32267i 0.411069 0.911604i 0.365155π-0.365155\pi
0.911604 0.411069i 0.134845π-0.134845\pi
978978 0 0
979979 581.969 0.0189988
980980 0 0
981981 −1904.00 −0.0619674
982982 0 0
983983 −22104.0 + 22104.0i −0.717200 + 0.717200i −0.968031 0.250831i 0.919296π-0.919296\pi
0.250831 + 0.968031i 0.419296π0.419296\pi
984984 0 0
985985 0 0
986986 0 0
987987 −9672.81 9672.81i −0.311944 0.311944i
988988 0 0
989989 34986.0i 1.12486i
990990 0 0
991991 18235.0i 0.584515i 0.956340 + 0.292258i 0.0944065π0.0944065\pi
−0.956340 + 0.292258i 0.905593π0.905593\pi
992992 0 0
993993 −23595.3 23595.3i −0.754052 0.754052i
994994 0 0
995995 0 0
996996 0 0
997997 −12854.6 + 12854.6i −0.408333 + 0.408333i −0.881157 0.472824i 0.843235π-0.843235\pi
0.472824 + 0.881157i 0.343235π0.343235\pi
998998 0 0
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 400.4.n.d.143.3 yes 8
4.3 odd 2 inner 400.4.n.d.143.2 yes 8
5.2 odd 4 inner 400.4.n.d.207.1 yes 8
5.3 odd 4 inner 400.4.n.d.207.3 yes 8
5.4 even 2 inner 400.4.n.d.143.1 8
20.3 even 4 inner 400.4.n.d.207.2 yes 8
20.7 even 4 inner 400.4.n.d.207.4 yes 8
20.19 odd 2 inner 400.4.n.d.143.4 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
400.4.n.d.143.1 8 5.4 even 2 inner
400.4.n.d.143.2 yes 8 4.3 odd 2 inner
400.4.n.d.143.3 yes 8 1.1 even 1 trivial
400.4.n.d.143.4 yes 8 20.19 odd 2 inner
400.4.n.d.207.1 yes 8 5.2 odd 4 inner
400.4.n.d.207.2 yes 8 20.3 even 4 inner
400.4.n.d.207.3 yes 8 5.3 odd 4 inner
400.4.n.d.207.4 yes 8 20.7 even 4 inner