Properties

Label 600.3.u.a.193.2
Level 600600
Weight 33
Character 600.193
Analytic conductor 16.34916.349
Analytic rank 00
Dimension 44
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [600,3,Mod(193,600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(600, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("600.193");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 600=23352 600 = 2^{3} \cdot 3 \cdot 5^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 600.u (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: 16.348815861616.3488158616
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(i)\Q(i)
Coefficient field: Q(i,6)\Q(i, \sqrt{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+9 x^{4} + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 193.2
Root 1.22474+1.22474i1.22474 + 1.22474i of defining polynomial
Character χ\chi == 600.193
Dual form 600.3.u.a.457.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.22474+1.22474i)q3+(6.44949+6.44949i)q7+3.00000iq911.7980q11+(2.44949+2.44949i)q13+(0.8989790.898979i)q1733.5959iq1915.7980q21+(21.798021.7980i)q23+(3.67423+3.67423i)q273.59592iq2925.1918q31+(14.449514.4495i)q33+(9.146439.14643i)q37+6.00000iq3960.7878q41+(22.2020+22.2020i)q43+(4.49490+4.49490i)q4734.1918iq49+2.20204q51+(52.0908+52.0908i)q53+(41.146441.1464i)q5786.9898iq59108.384q61+(19.348519.3485i)q63+(77.8888+77.8888i)q6753.3939iq6966.7878q71+(78.6969+78.6969i)q73+(76.090876.0908i)q77+66.0000iq799.00000q81+(84.090884.0908i)q83+(4.404084.40408i)q879.59592iq8931.5959q91+(30.853630.8536i)q93+(53.080653.0806i)q9735.3939iq99+O(q100)q+(1.22474 + 1.22474i) q^{3} +(-6.44949 + 6.44949i) q^{7} +3.00000i q^{9} -11.7980 q^{11} +(2.44949 + 2.44949i) q^{13} +(0.898979 - 0.898979i) q^{17} -33.5959i q^{19} -15.7980 q^{21} +(-21.7980 - 21.7980i) q^{23} +(-3.67423 + 3.67423i) q^{27} -3.59592i q^{29} -25.1918 q^{31} +(-14.4495 - 14.4495i) q^{33} +(9.14643 - 9.14643i) q^{37} +6.00000i q^{39} -60.7878 q^{41} +(22.2020 + 22.2020i) q^{43} +(-4.49490 + 4.49490i) q^{47} -34.1918i q^{49} +2.20204 q^{51} +(52.0908 + 52.0908i) q^{53} +(41.1464 - 41.1464i) q^{57} -86.9898i q^{59} -108.384 q^{61} +(-19.3485 - 19.3485i) q^{63} +(-77.8888 + 77.8888i) q^{67} -53.3939i q^{69} -66.7878 q^{71} +(78.6969 + 78.6969i) q^{73} +(76.0908 - 76.0908i) q^{77} +66.0000i q^{79} -9.00000 q^{81} +(-84.0908 - 84.0908i) q^{83} +(4.40408 - 4.40408i) q^{87} -9.59592i q^{89} -31.5959 q^{91} +(-30.8536 - 30.8536i) q^{93} +(53.0806 - 53.0806i) q^{97} -35.3939i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q16q78q1116q1724q2148q23+56q3148q3332q378q41+128q43+80q47+48q51+32q53+96q57120q6148q6396q67+160q97+O(q100) 4 q - 16 q^{7} - 8 q^{11} - 16 q^{17} - 24 q^{21} - 48 q^{23} + 56 q^{31} - 48 q^{33} - 32 q^{37} - 8 q^{41} + 128 q^{43} + 80 q^{47} + 48 q^{51} + 32 q^{53} + 96 q^{57} - 120 q^{61} - 48 q^{63} - 96 q^{67}+ \cdots - 160 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/600Z)×\left(\mathbb{Z}/600\mathbb{Z}\right)^\times.

nn 151151 301301 401401 577577
χ(n)\chi(n) 11 11 11 e(34)e\left(\frac{3}{4}\right)

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 1.22474 + 1.22474i 0.408248 + 0.408248i
44 0 0
55 0 0
66 0 0
77 −6.44949 + 6.44949i −0.921356 + 0.921356i −0.997125 0.0757697i 0.975859π-0.975859\pi
0.0757697 + 0.997125i 0.475859π0.475859\pi
88 0 0
99 3.00000i 0.333333i
1010 0 0
1111 −11.7980 −1.07254 −0.536271 0.844046i 0.680167π-0.680167\pi
−0.536271 + 0.844046i 0.680167π0.680167\pi
1212 0 0
1313 2.44949 + 2.44949i 0.188422 + 0.188422i 0.795014 0.606591i 0.207464π-0.207464\pi
−0.606591 + 0.795014i 0.707464π0.707464\pi
1414 0 0
1515 0 0
1616 0 0
1717 0.898979 0.898979i 0.0528811 0.0528811i −0.680172 0.733053i 0.738095π-0.738095\pi
0.733053 + 0.680172i 0.238095π0.238095\pi
1818 0 0
1919 33.5959i 1.76821i −0.467292 0.884103i 0.654770π-0.654770\pi
0.467292 0.884103i 0.345230π-0.345230\pi
2020 0 0
2121 −15.7980 −0.752284
2222 0 0
2323 −21.7980 21.7980i −0.947737 0.947737i 0.0509632 0.998701i 0.483771π-0.483771\pi
−0.998701 + 0.0509632i 0.983771π0.983771\pi
2424 0 0
2525 0 0
2626 0 0
2727 −3.67423 + 3.67423i −0.136083 + 0.136083i
2828 0 0
2929 3.59592i 0.123997i −0.998076 0.0619986i 0.980253π-0.980253\pi
0.998076 0.0619986i 0.0197474π-0.0197474\pi
3030 0 0
3131 −25.1918 −0.812640 −0.406320 0.913731i 0.633188π-0.633188\pi
−0.406320 + 0.913731i 0.633188π0.633188\pi
3232 0 0
3333 −14.4495 14.4495i −0.437863 0.437863i
3434 0 0
3535 0 0
3636 0 0
3737 9.14643 9.14643i 0.247201 0.247201i −0.572620 0.819821i 0.694073π-0.694073\pi
0.819821 + 0.572620i 0.194073π0.194073\pi
3838 0 0
3939 6.00000i 0.153846i
4040 0 0
4141 −60.7878 −1.48263 −0.741314 0.671158i 0.765797π-0.765797\pi
−0.741314 + 0.671158i 0.765797π0.765797\pi
4242 0 0
4343 22.2020 + 22.2020i 0.516327 + 0.516327i 0.916458 0.400131i 0.131035π-0.131035\pi
−0.400131 + 0.916458i 0.631035π0.631035\pi
4444 0 0
4545 0 0
4646 0 0
4747 −4.49490 + 4.49490i −0.0956361 + 0.0956361i −0.753306 0.657670i 0.771542π-0.771542\pi
0.657670 + 0.753306i 0.271542π0.271542\pi
4848 0 0
4949 34.1918i 0.697793i
5050 0 0
5151 2.20204 0.0431773
5252 0 0
5353 52.0908 + 52.0908i 0.982846 + 0.982846i 0.999855 0.0170098i 0.00541463π-0.00541463\pi
−0.0170098 + 0.999855i 0.505415π0.505415\pi
5454 0 0
5555 0 0
5656 0 0
5757 41.1464 41.1464i 0.721867 0.721867i
5858 0 0
5959 86.9898i 1.47440i −0.675673 0.737202i 0.736147π-0.736147\pi
0.675673 0.737202i 0.263853π-0.263853\pi
6060 0 0
6161 −108.384 −1.77678 −0.888391 0.459088i 0.848176π-0.848176\pi
−0.888391 + 0.459088i 0.848176π0.848176\pi
6262 0 0
6363 −19.3485 19.3485i −0.307119 0.307119i
6464 0 0
6565 0 0
6666 0 0
6767 −77.8888 + 77.8888i −1.16252 + 1.16252i −0.178597 + 0.983922i 0.557156π0.557156\pi
−0.983922 + 0.178597i 0.942844π0.942844\pi
6868 0 0
6969 53.3939i 0.773824i
7070 0 0
7171 −66.7878 −0.940673 −0.470336 0.882487i 0.655867π-0.655867\pi
−0.470336 + 0.882487i 0.655867π0.655867\pi
7272 0 0
7373 78.6969 + 78.6969i 1.07804 + 1.07804i 0.996685 + 0.0813551i 0.0259248π0.0259248\pi
0.0813551 + 0.996685i 0.474075π0.474075\pi
7474 0 0
7575 0 0
7676 0 0
7777 76.0908 76.0908i 0.988192 0.988192i
7878 0 0
7979 66.0000i 0.835443i 0.908575 + 0.417722i 0.137171π0.137171\pi
−0.908575 + 0.417722i 0.862829π0.862829\pi
8080 0 0
8181 −9.00000 −0.111111
8282 0 0
8383 −84.0908 84.0908i −1.01314 1.01314i −0.999912 0.0132299i 0.995789π-0.995789\pi
−0.0132299 0.999912i 0.504211π-0.504211\pi
8484 0 0
8585 0 0
8686 0 0
8787 4.40408 4.40408i 0.0506216 0.0506216i
8888 0 0
8989 9.59592i 0.107819i −0.998546 0.0539097i 0.982832π-0.982832\pi
0.998546 0.0539097i 0.0171683π-0.0171683\pi
9090 0 0
9191 −31.5959 −0.347208
9292 0 0
9393 −30.8536 30.8536i −0.331759 0.331759i
9494 0 0
9595 0 0
9696 0 0
9797 53.0806 53.0806i 0.547223 0.547223i −0.378414 0.925637i 0.623530π-0.623530\pi
0.925637 + 0.378414i 0.123530π0.123530\pi
9898 0 0
9999 35.3939i 0.357514i
100100 0 0
101101 155.192 1.53655 0.768276 0.640118i 0.221115π-0.221115\pi
0.768276 + 0.640118i 0.221115π0.221115\pi
102102 0 0
103103 42.3587 + 42.3587i 0.411249 + 0.411249i 0.882174 0.470924i 0.156080π-0.156080\pi
−0.470924 + 0.882174i 0.656080π0.656080\pi
104104 0 0
105105 0 0
106106 0 0
107107 −29.8888 + 29.8888i −0.279334 + 0.279334i −0.832843 0.553509i 0.813288π-0.813288\pi
0.553509 + 0.832843i 0.313288π0.313288\pi
108108 0 0
109109 17.1918i 0.157723i 0.996886 + 0.0788616i 0.0251285π0.0251285\pi
−0.996886 + 0.0788616i 0.974871π0.974871\pi
110110 0 0
111111 22.4041 0.201839
112112 0 0
113113 −134.293 134.293i −1.18843 1.18843i −0.977501 0.210932i 0.932350π-0.932350\pi
−0.210932 0.977501i 0.567650π-0.567650\pi
114114 0 0
115115 0 0
116116 0 0
117117 −7.34847 + 7.34847i −0.0628074 + 0.0628074i
118118 0 0
119119 11.5959i 0.0974447i
120120 0 0
121121 18.1918 0.150346
122122 0 0
123123 −74.4495 74.4495i −0.605280 0.605280i
124124 0 0
125125 0 0
126126 0 0
127127 −153.237 + 153.237i −1.20659 + 1.20659i −0.234469 + 0.972124i 0.575335π0.575335\pi
−0.972124 + 0.234469i 0.924665π0.924665\pi
128128 0 0
129129 54.3837i 0.421579i
130130 0 0
131131 −196.606 −1.50081 −0.750405 0.660978i 0.770142π-0.770142\pi
−0.750405 + 0.660978i 0.770142π0.770142\pi
132132 0 0
133133 216.677 + 216.677i 1.62915 + 1.62915i
134134 0 0
135135 0 0
136136 0 0
137137 81.0806 81.0806i 0.591829 0.591829i −0.346296 0.938125i 0.612561π-0.612561\pi
0.938125 + 0.346296i 0.112561π0.112561\pi
138138 0 0
139139 37.1918i 0.267567i 0.991011 + 0.133784i 0.0427127π0.0427127\pi
−0.991011 + 0.133784i 0.957287π0.957287\pi
140140 0 0
141141 −11.0102 −0.0780866
142142 0 0
143143 −28.8990 28.8990i −0.202091 0.202091i
144144 0 0
145145 0 0
146146 0 0
147147 41.8763 41.8763i 0.284873 0.284873i
148148 0 0
149149 86.7878i 0.582468i 0.956652 + 0.291234i 0.0940658π0.0940658\pi
−0.956652 + 0.291234i 0.905934π0.905934\pi
150150 0 0
151151 266.767 1.76667 0.883336 0.468741i 0.155292π-0.155292\pi
0.883336 + 0.468741i 0.155292π0.155292\pi
152152 0 0
153153 2.69694 + 2.69694i 0.0176270 + 0.0176270i
154154 0 0
155155 0 0
156156 0 0
157157 −203.439 + 203.439i −1.29579 + 1.29579i −0.364645 + 0.931147i 0.618810π0.618810\pi
−0.931147 + 0.364645i 0.881190π0.881190\pi
158158 0 0
159159 127.596i 0.802490i
160160 0 0
161161 281.171 1.74641
162162 0 0
163163 29.2122 + 29.2122i 0.179216 + 0.179216i 0.791014 0.611798i 0.209553π-0.209553\pi
−0.611798 + 0.791014i 0.709553π0.709553\pi
164164 0 0
165165 0 0
166166 0 0
167167 −116.182 + 116.182i −0.695698 + 0.695698i −0.963480 0.267781i 0.913710π-0.913710\pi
0.267781 + 0.963480i 0.413710π0.413710\pi
168168 0 0
169169 157.000i 0.928994i
170170 0 0
171171 100.788 0.589402
172172 0 0
173173 60.2724 + 60.2724i 0.348396 + 0.348396i 0.859512 0.511116i 0.170768π-0.170768\pi
−0.511116 + 0.859512i 0.670768π0.670768\pi
174174 0 0
175175 0 0
176176 0 0
177177 106.540 106.540i 0.601923 0.601923i
178178 0 0
179179 176.161i 0.984141i 0.870555 + 0.492070i 0.163760π0.163760\pi
−0.870555 + 0.492070i 0.836240π0.836240\pi
180180 0 0
181181 161.959 0.894802 0.447401 0.894333i 0.352350π-0.352350\pi
0.447401 + 0.894333i 0.352350π0.352350\pi
182182 0 0
183183 −132.742 132.742i −0.725368 0.725368i
184184 0 0
185185 0 0
186186 0 0
187187 −10.6061 + 10.6061i −0.0567172 + 0.0567172i
188188 0 0
189189 47.3939i 0.250761i
190190 0 0
191191 250.747 1.31281 0.656406 0.754408i 0.272076π-0.272076\pi
0.656406 + 0.754408i 0.272076π0.272076\pi
192192 0 0
193193 8.62653 + 8.62653i 0.0446971 + 0.0446971i 0.729102 0.684405i 0.239938π-0.239938\pi
−0.684405 + 0.729102i 0.739938π0.739938\pi
194194 0 0
195195 0 0
196196 0 0
197197 182.202 182.202i 0.924883 0.924883i −0.0724860 0.997369i 0.523093π-0.523093\pi
0.997369 + 0.0724860i 0.0230933π0.0230933\pi
198198 0 0
199199 81.1918i 0.407999i 0.978971 + 0.204000i 0.0653941π0.0653941\pi
−0.978971 + 0.204000i 0.934606π0.934606\pi
200200 0 0
201201 −190.788 −0.949193
202202 0 0
203203 23.1918 + 23.1918i 0.114245 + 0.114245i
204204 0 0
205205 0 0
206206 0 0
207207 65.3939 65.3939i 0.315912 0.315912i
208208 0 0
209209 396.363i 1.89647i
210210 0 0
211211 199.576 0.945855 0.472928 0.881101i 0.343197π-0.343197\pi
0.472928 + 0.881101i 0.343197π0.343197\pi
212212 0 0
213213 −81.7980 81.7980i −0.384028 0.384028i
214214 0 0
215215 0 0
216216 0 0
217217 162.474 162.474i 0.748730 0.748730i
218218 0 0
219219 192.767i 0.880216i
220220 0 0
221221 4.40408 0.0199280
222222 0 0
223223 134.944 + 134.944i 0.605132 + 0.605132i 0.941670 0.336538i 0.109256π-0.109256\pi
−0.336538 + 0.941670i 0.609256π0.609256\pi
224224 0 0
225225 0 0
226226 0 0
227227 60.8990 60.8990i 0.268277 0.268277i −0.560128 0.828406i 0.689248π-0.689248\pi
0.828406 + 0.560128i 0.189248π0.189248\pi
228228 0 0
229229 138.767i 0.605971i 0.952995 + 0.302985i 0.0979834π0.0979834\pi
−0.952995 + 0.302985i 0.902017π0.902017\pi
230230 0 0
231231 186.384 0.806856
232232 0 0
233233 −254.656 254.656i −1.09294 1.09294i −0.995213 0.0977319i 0.968841π-0.968841\pi
−0.0977319 0.995213i 0.531159π-0.531159\pi
234234 0 0
235235 0 0
236236 0 0
237237 −80.8332 + 80.8332i −0.341068 + 0.341068i
238238 0 0
239239 422.788i 1.76899i −0.466553 0.884493i 0.654504π-0.654504\pi
0.466553 0.884493i 0.345496π-0.345496\pi
240240 0 0
241241 10.7673 0.0446778 0.0223389 0.999750i 0.492889π-0.492889\pi
0.0223389 + 0.999750i 0.492889π0.492889\pi
242242 0 0
243243 −11.0227 11.0227i −0.0453609 0.0453609i
244244 0 0
245245 0 0
246246 0 0
247247 82.2929 82.2929i 0.333169 0.333169i
248248 0 0
249249 205.980i 0.827227i
250250 0 0
251251 −177.818 −0.708440 −0.354220 0.935162i 0.615254π-0.615254\pi
−0.354220 + 0.935162i 0.615254π0.615254\pi
252252 0 0
253253 257.171 + 257.171i 1.01649 + 1.01649i
254254 0 0
255255 0 0
256256 0 0
257257 −142.293 + 142.293i −0.553669 + 0.553669i −0.927498 0.373829i 0.878045π-0.878045\pi
0.373829 + 0.927498i 0.378045π0.378045\pi
258258 0 0
259259 117.980i 0.455520i
260260 0 0
261261 10.7878 0.0413324
262262 0 0
263263 −36.0000 36.0000i −0.136882 0.136882i 0.635346 0.772228i 0.280858π-0.280858\pi
−0.772228 + 0.635346i 0.780858π0.780858\pi
264264 0 0
265265 0 0
266266 0 0
267267 11.7526 11.7526i 0.0440170 0.0440170i
268268 0 0
269269 38.8286i 0.144344i 0.997392 + 0.0721721i 0.0229931π0.0229931\pi
−0.997392 + 0.0721721i 0.977007π0.977007\pi
270270 0 0
271271 −11.5755 −0.0427141 −0.0213570 0.999772i 0.506799π-0.506799\pi
−0.0213570 + 0.999772i 0.506799π0.506799\pi
272272 0 0
273273 −38.6969 38.6969i −0.141747 0.141747i
274274 0 0
275275 0 0
276276 0 0
277277 −282.499 + 282.499i −1.01985 + 1.01985i −0.0200549 + 0.999799i 0.506384π0.506384\pi
−0.999799 + 0.0200549i 0.993616π0.993616\pi
278278 0 0
279279 75.5755i 0.270880i
280280 0 0
281281 432.384 1.53873 0.769366 0.638808i 0.220572π-0.220572\pi
0.769366 + 0.638808i 0.220572π0.220572\pi
282282 0 0
283283 223.868 + 223.868i 0.791054 + 0.791054i 0.981666 0.190611i 0.0610470π-0.0610470\pi
−0.190611 + 0.981666i 0.561047π0.561047\pi
284284 0 0
285285 0 0
286286 0 0
287287 392.050 392.050i 1.36603 1.36603i
288288 0 0
289289 287.384i 0.994407i
290290 0 0
291291 130.020 0.446806
292292 0 0
293293 196.767 + 196.767i 0.671561 + 0.671561i 0.958076 0.286515i 0.0924968π-0.0924968\pi
−0.286515 + 0.958076i 0.592497π0.592497\pi
294294 0 0
295295 0 0
296296 0 0
297297 43.3485 43.3485i 0.145954 0.145954i
298298 0 0
299299 106.788i 0.357150i
300300 0 0
301301 −286.384 −0.951441
302302 0 0
303303 190.070 + 190.070i 0.627295 + 0.627295i
304304 0 0
305305 0 0
306306 0 0
307307 −141.707 + 141.707i −0.461587 + 0.461587i −0.899175 0.437589i 0.855833π-0.855833\pi
0.437589 + 0.899175i 0.355833π0.355833\pi
308308 0 0
309309 103.757i 0.335784i
310310 0 0
311311 −411.555 −1.32333 −0.661664 0.749800i 0.730150π-0.730150\pi
−0.661664 + 0.749800i 0.730150π0.730150\pi
312312 0 0
313313 −365.939 365.939i −1.16913 1.16913i −0.982413 0.186720i 0.940214π-0.940214\pi
−0.186720 0.982413i 0.559786π-0.559786\pi
314314 0 0
315315 0 0
316316 0 0
317317 −338.343 + 338.343i −1.06733 + 1.06733i −0.0697641 + 0.997564i 0.522225π0.522225\pi
−0.997564 + 0.0697641i 0.977775π0.977775\pi
318318 0 0
319319 42.4245i 0.132992i
320320 0 0
321321 −73.2122 −0.228076
322322 0 0
323323 −30.2020 30.2020i −0.0935048 0.0935048i
324324 0 0
325325 0 0
326326 0 0
327327 −21.0556 + 21.0556i −0.0643903 + 0.0643903i
328328 0 0
329329 57.9796i 0.176230i
330330 0 0
331331 −97.5551 −0.294728 −0.147364 0.989082i 0.547079π-0.547079\pi
−0.147364 + 0.989082i 0.547079π0.547079\pi
332332 0 0
333333 27.4393 + 27.4393i 0.0824003 + 0.0824003i
334334 0 0
335335 0 0
336336 0 0
337337 −72.4949 + 72.4949i −0.215118 + 0.215118i −0.806438 0.591319i 0.798607π-0.798607\pi
0.591319 + 0.806438i 0.298607π0.298607\pi
338338 0 0
339339 328.949i 0.970351i
340340 0 0
341341 297.212 0.871590
342342 0 0
343343 −95.5051 95.5051i −0.278441 0.278441i
344344 0 0
345345 0 0
346346 0 0
347347 40.8582 40.8582i 0.117747 0.117747i −0.645778 0.763525i 0.723467π-0.723467\pi
0.763525 + 0.645778i 0.223467π0.223467\pi
348348 0 0
349349 332.343i 0.952272i −0.879372 0.476136i 0.842037π-0.842037\pi
0.879372 0.476136i 0.157963π-0.157963\pi
350350 0 0
351351 −18.0000 −0.0512821
352352 0 0
353353 −260.232 260.232i −0.737200 0.737200i 0.234835 0.972035i 0.424545π-0.424545\pi
−0.972035 + 0.234835i 0.924545π0.924545\pi
354354 0 0
355355 0 0
356356 0 0
357357 −14.2020 + 14.2020i −0.0397816 + 0.0397816i
358358 0 0
359359 332.000i 0.924791i −0.886674 0.462396i 0.846990π-0.846990\pi
0.886674 0.462396i 0.153010π-0.153010\pi
360360 0 0
361361 −767.686 −2.12655
362362 0 0
363363 22.2804 + 22.2804i 0.0613784 + 0.0613784i
364364 0 0
365365 0 0
366366 0 0
367367 210.409 210.409i 0.573321 0.573321i −0.359734 0.933055i 0.617133π-0.617133\pi
0.933055 + 0.359734i 0.117133π0.117133\pi
368368 0 0
369369 182.363i 0.494209i
370370 0 0
371371 −671.918 −1.81110
372372 0 0
373373 −222.672 222.672i −0.596976 0.596976i 0.342531 0.939507i 0.388716π-0.388716\pi
−0.939507 + 0.342531i 0.888716π0.888716\pi
374374 0 0
375375 0 0
376376 0 0
377377 8.80816 8.80816i 0.0233638 0.0233638i
378378 0 0
379379 222.767i 0.587777i −0.955840 0.293888i 0.905051π-0.905051\pi
0.955840 0.293888i 0.0949494π-0.0949494\pi
380380 0 0
381381 −375.353 −0.985179
382382 0 0
383383 −120.717 120.717i −0.315189 0.315189i 0.531727 0.846916i 0.321543π-0.321543\pi
−0.846916 + 0.531727i 0.821543π0.821543\pi
384384 0 0
385385 0 0
386386 0 0
387387 −66.6061 + 66.6061i −0.172109 + 0.172109i
388388 0 0
389389 80.8082i 0.207733i 0.994591 + 0.103867i 0.0331215π0.0331215\pi
−0.994591 + 0.103867i 0.966879π0.966879\pi
390390 0 0
391391 −39.1918 −0.100235
392392 0 0
393393 −240.792 240.792i −0.612703 0.612703i
394394 0 0
395395 0 0
396396 0 0
397397 21.9954 21.9954i 0.0554041 0.0554041i −0.678862 0.734266i 0.737527π-0.737527\pi
0.734266 + 0.678862i 0.237527π0.237527\pi
398398 0 0
399399 530.747i 1.33019i
400400 0 0
401401 −267.131 −0.666161 −0.333081 0.942898i 0.608088π-0.608088\pi
−0.333081 + 0.942898i 0.608088π0.608088\pi
402402 0 0
403403 −61.7071 61.7071i −0.153119 0.153119i
404404 0 0
405405 0 0
406406 0 0
407407 −107.909 + 107.909i −0.265133 + 0.265133i
408408 0 0
409409 510.767i 1.24882i −0.781097 0.624410i 0.785339π-0.785339\pi
0.781097 0.624410i 0.214661π-0.214661\pi
410410 0 0
411411 198.606 0.483227
412412 0 0
413413 561.040 + 561.040i 1.35845 + 1.35845i
414414 0 0
415415 0 0
416416 0 0
417417 −45.5505 + 45.5505i −0.109234 + 0.109234i
418418 0 0
419419 40.1204i 0.0957527i −0.998853 0.0478764i 0.984755π-0.984755\pi
0.998853 0.0478764i 0.0152454π-0.0152454\pi
420420 0 0
421421 −132.343 −0.314354 −0.157177 0.987570i 0.550239π-0.550239\pi
−0.157177 + 0.987570i 0.550239π0.550239\pi
422422 0 0
423423 −13.4847 13.4847i −0.0318787 0.0318787i
424424 0 0
425425 0 0
426426 0 0
427427 699.019 699.019i 1.63705 1.63705i
428428 0 0
429429 70.7878i 0.165006i
430430 0 0
431431 −510.343 −1.18409 −0.592045 0.805905i 0.701679π-0.701679\pi
−0.592045 + 0.805905i 0.701679π0.701679\pi
432432 0 0
433433 −443.828 443.828i −1.02501 1.02501i −0.999679 0.0253266i 0.991937π-0.991937\pi
−0.0253266 0.999679i 0.508063π-0.508063\pi
434434 0 0
435435 0 0
436436 0 0
437437 −732.322 + 732.322i −1.67580 + 1.67580i
438438 0 0
439439 306.808i 0.698880i 0.936959 + 0.349440i 0.113628π0.113628\pi
−0.936959 + 0.349440i 0.886372π0.886372\pi
440440 0 0
441441 102.576 0.232598
442442 0 0
443443 443.646 + 443.646i 1.00146 + 1.00146i 0.999999 + 0.00145911i 0.000464448π0.000464448\pi
0.00145911 + 0.999999i 0.499536π0.499536\pi
444444 0 0
445445 0 0
446446 0 0
447447 −106.293 + 106.293i −0.237792 + 0.237792i
448448 0 0
449449 230.727i 0.513868i −0.966429 0.256934i 0.917288π-0.917288\pi
0.966429 0.256934i 0.0827122π-0.0827122\pi
450450 0 0
451451 717.171 1.59018
452452 0 0
453453 326.722 + 326.722i 0.721240 + 0.721240i
454454 0 0
455455 0 0
456456 0 0
457457 −27.2827 + 27.2827i −0.0596995 + 0.0596995i −0.736326 0.676627i 0.763441π-0.763441\pi
0.676627 + 0.736326i 0.263441π0.263441\pi
458458 0 0
459459 6.60612i 0.0143924i
460460 0 0
461461 −256.322 −0.556014 −0.278007 0.960579i 0.589674π-0.589674\pi
−0.278007 + 0.960579i 0.589674π0.589674\pi
462462 0 0
463463 173.196 + 173.196i 0.374074 + 0.374074i 0.868959 0.494884i 0.164790π-0.164790\pi
−0.494884 + 0.868959i 0.664790π0.664790\pi
464464 0 0
465465 0 0
466466 0 0
467467 285.707 285.707i 0.611793 0.611793i −0.331620 0.943413i 0.607595π-0.607595\pi
0.943413 + 0.331620i 0.107595π0.107595\pi
468468 0 0
469469 1004.69i 2.14219i
470470 0 0
471471 −498.322 −1.05801
472472 0 0
473473 −261.939 261.939i −0.553782 0.553782i
474474 0 0
475475 0 0
476476 0 0
477477 −156.272 + 156.272i −0.327615 + 0.327615i
478478 0 0
479479 356.404i 0.744059i −0.928221 0.372029i 0.878662π-0.878662\pi
0.928221 0.372029i 0.121338π-0.121338\pi
480480 0 0
481481 44.8082 0.0931563
482482 0 0
483483 344.363 + 344.363i 0.712967 + 0.712967i
484484 0 0
485485 0 0
486486 0 0
487487 −55.6209 + 55.6209i −0.114211 + 0.114211i −0.761903 0.647691i 0.775735π-0.775735\pi
0.647691 + 0.761903i 0.275735π0.275735\pi
488488 0 0
489489 71.5551i 0.146329i
490490 0 0
491491 106.141 0.216173 0.108086 0.994142i 0.465528π-0.465528\pi
0.108086 + 0.994142i 0.465528π0.465528\pi
492492 0 0
493493 −3.23266 3.23266i −0.00655711 0.00655711i
494494 0 0
495495 0 0
496496 0 0
497497 430.747 430.747i 0.866694 0.866694i
498498 0 0
499499 298.363i 0.597922i −0.954265 0.298961i 0.903360π-0.903360\pi
0.954265 0.298961i 0.0966401π-0.0966401\pi
500500 0 0
501501 −284.586 −0.568035
502502 0 0
503503 655.101 + 655.101i 1.30239 + 1.30239i 0.926778 + 0.375610i 0.122567π0.122567\pi
0.375610 + 0.926778i 0.377433π0.377433\pi
504504 0 0
505505 0 0
506506 0 0
507507 192.285 192.285i 0.379260 0.379260i
508508 0 0
509509 683.110i 1.34206i 0.741429 + 0.671032i 0.234149π0.234149\pi
−0.741429 + 0.671032i 0.765851π0.765851\pi
510510 0 0
511511 −1015.11 −1.98652
512512 0 0
513513 123.439 + 123.439i 0.240622 + 0.240622i
514514 0 0
515515 0 0
516516 0 0
517517 53.0306 53.0306i 0.102574 0.102574i
518518 0 0
519519 147.637i 0.284464i
520520 0 0
521521 −6.76734 −0.0129891 −0.00649457 0.999979i 0.502067π-0.502067\pi
−0.00649457 + 0.999979i 0.502067π0.502067\pi
522522 0 0
523523 −600.990 600.990i −1.14912 1.14912i −0.986726 0.162394i 0.948078π-0.948078\pi
−0.162394 0.986726i 0.551922π-0.551922\pi
524524 0 0
525525 0 0
526526 0 0
527527 −22.6469 + 22.6469i −0.0429733 + 0.0429733i
528528 0 0
529529 421.302i 0.796412i
530530 0 0
531531 260.969 0.491468
532532 0 0
533533 −148.899 148.899i −0.279360 0.279360i
534534 0 0
535535 0 0
536536 0 0
537537 −215.753 + 215.753i −0.401774 + 0.401774i
538538 0 0
539539 403.394i 0.748412i
540540 0 0
541541 177.110 0.327376 0.163688 0.986512i 0.447661π-0.447661\pi
0.163688 + 0.986512i 0.447661π0.447661\pi
542542 0 0
543543 198.359 + 198.359i 0.365301 + 0.365301i
544544 0 0
545545 0 0
546546 0 0
547547 −35.3326 + 35.3326i −0.0645935 + 0.0645935i −0.738666 0.674072i 0.764544π-0.764544\pi
0.674072 + 0.738666i 0.264544π0.264544\pi
548548 0 0
549549 325.151i 0.592261i
550550 0 0
551551 −120.808 −0.219253
552552 0 0
553553 −425.666 425.666i −0.769740 0.769740i
554554 0 0
555555 0 0
556556 0 0
557557 121.930 121.930i 0.218904 0.218904i −0.589132 0.808037i 0.700530π-0.700530\pi
0.808037 + 0.589132i 0.200530π0.200530\pi
558558 0 0
559559 108.767i 0.194575i
560560 0 0
561561 −25.9796 −0.0463094
562562 0 0
563563 −436.636 436.636i −0.775552 0.775552i 0.203519 0.979071i 0.434762π-0.434762\pi
−0.979071 + 0.203519i 0.934762π0.934762\pi
564564 0 0
565565 0 0
566566 0 0
567567 58.0454 58.0454i 0.102373 0.102373i
568568 0 0
569569 394.363i 0.693081i −0.938035 0.346541i 0.887356π-0.887356\pi
0.938035 0.346541i 0.112644π-0.112644\pi
570570 0 0
571571 32.0612 0.0561493 0.0280746 0.999606i 0.491062π-0.491062\pi
0.0280746 + 0.999606i 0.491062π0.491062\pi
572572 0 0
573573 307.101 + 307.101i 0.535953 + 0.535953i
574574 0 0
575575 0 0
576576 0 0
577577 545.848 545.848i 0.946010 0.946010i −0.0526051 0.998615i 0.516752π-0.516752\pi
0.998615 + 0.0526051i 0.0167524π0.0167524\pi
578578 0 0
579579 21.1306i 0.0364950i
580580 0 0
581581 1084.69 1.86693
582582 0 0
583583 −614.565 614.565i −1.05414 1.05414i
584584 0 0
585585 0 0
586586 0 0
587587 −307.728 + 307.728i −0.524238 + 0.524238i −0.918848 0.394611i 0.870879π-0.870879\pi
0.394611 + 0.918848i 0.370879π0.370879\pi
588588 0 0
589589 846.343i 1.43691i
590590 0 0
591591 446.302 0.755164
592592 0 0
593593 228.940 + 228.940i 0.386070 + 0.386070i 0.873283 0.487213i 0.161986π-0.161986\pi
−0.487213 + 0.873283i 0.661986π0.661986\pi
594594 0 0
595595 0 0
596596 0 0
597597 −99.4393 + 99.4393i −0.166565 + 0.166565i
598598 0 0
599599 345.657i 0.577057i −0.957471 0.288529i 0.906834π-0.906834\pi
0.957471 0.288529i 0.0931660π-0.0931660\pi
600600 0 0
601601 893.069 1.48597 0.742986 0.669307i 0.233409π-0.233409\pi
0.742986 + 0.669307i 0.233409π0.233409\pi
602602 0 0
603603 −233.666 233.666i −0.387506 0.387506i
604604 0 0
605605 0 0
606606 0 0
607607 560.974 560.974i 0.924175 0.924175i −0.0731466 0.997321i 0.523304π-0.523304\pi
0.997321 + 0.0731466i 0.0233041π0.0233041\pi
608608 0 0
609609 56.8082i 0.0932811i
610610 0 0
611611 −22.0204 −0.0360400
612612 0 0
613613 439.448 + 439.448i 0.716882 + 0.716882i 0.967965 0.251084i 0.0807869π-0.0807869\pi
−0.251084 + 0.967965i 0.580787π0.580787\pi
614614 0 0
615615 0 0
616616 0 0
617617 199.201 199.201i 0.322854 0.322854i −0.527007 0.849861i 0.676686π-0.676686\pi
0.849861 + 0.527007i 0.176686π0.176686\pi
618618 0 0
619619 121.151i 0.195721i −0.995200 0.0978603i 0.968800π-0.968800\pi
0.995200 0.0978603i 0.0311998π-0.0311998\pi
620620 0 0
621621 160.182 0.257941
622622 0 0
623623 61.8888 + 61.8888i 0.0993399 + 0.0993399i
624624 0 0
625625 0 0
626626 0 0
627627 −485.444 + 485.444i −0.774233 + 0.774233i
628628 0 0
629629 16.4449i 0.0261445i
630630 0 0
631631 247.494 0.392225 0.196112 0.980581i 0.437168π-0.437168\pi
0.196112 + 0.980581i 0.437168π0.437168\pi
632632 0 0
633633 244.429 + 244.429i 0.386144 + 0.386144i
634634 0 0
635635 0 0
636636 0 0
637637 83.7526 83.7526i 0.131480 0.131480i
638638 0 0
639639 200.363i 0.313558i
640640 0 0
641641 70.6857 0.110274 0.0551371 0.998479i 0.482440π-0.482440\pi
0.0551371 + 0.998479i 0.482440π0.482440\pi
642642 0 0
643643 −231.373 231.373i −0.359834 0.359834i 0.503917 0.863752i 0.331892π-0.331892\pi
−0.863752 + 0.503917i 0.831892π0.831892\pi
644644 0 0
645645 0 0
646646 0 0
647647 −500.958 + 500.958i −0.774278 + 0.774278i −0.978851 0.204573i 0.934419π-0.934419\pi
0.204573 + 0.978851i 0.434419π0.434419\pi
648648 0 0
649649 1026.30i 1.58136i
650650 0 0
651651 397.980 0.611336
652652 0 0
653653 −261.031 261.031i −0.399741 0.399741i 0.478401 0.878142i 0.341217π-0.341217\pi
−0.878142 + 0.478401i 0.841217π0.841217\pi
654654 0 0
655655 0 0
656656 0 0
657657 −236.091 + 236.091i −0.359347 + 0.359347i
658658 0 0
659659 800.524i 1.21476i 0.794413 + 0.607378i 0.207779π0.207779\pi
−0.794413 + 0.607378i 0.792221π0.792221\pi
660660 0 0
661661 −313.192 −0.473815 −0.236908 0.971532i 0.576134π-0.576134\pi
−0.236908 + 0.971532i 0.576134π0.576134\pi
662662 0 0
663663 5.39388 + 5.39388i 0.00813556 + 0.00813556i
664664 0 0
665665 0 0
666666 0 0
667667 −78.3837 + 78.3837i −0.117517 + 0.117517i
668668 0 0
669669 330.545i 0.494088i
670670 0 0
671671 1278.71 1.90567
672672 0 0
673673 −688.677 688.677i −1.02329 1.02329i −0.999722 0.0235713i 0.992496π-0.992496\pi
−0.0235713 0.999722i 0.507504π-0.507504\pi
674674 0 0
675675 0 0
676676 0 0
677677 −660.767 + 660.767i −0.976023 + 0.976023i −0.999719 0.0236965i 0.992456π-0.992456\pi
0.0236965 + 0.999719i 0.492456π0.492456\pi
678678 0 0
679679 684.686i 1.00837i
680680 0 0
681681 149.171 0.219048
682682 0 0
683683 952.232 + 952.232i 1.39419 + 1.39419i 0.815664 + 0.578525i 0.196372π0.196372\pi
0.578525 + 0.815664i 0.303628π0.303628\pi
684684 0 0
685685 0 0
686686 0 0
687687 −169.955 + 169.955i −0.247387 + 0.247387i
688688 0 0
689689 255.192i 0.370380i
690690 0 0
691691 568.665 0.822960 0.411480 0.911419i 0.365012π-0.365012\pi
0.411480 + 0.911419i 0.365012π0.365012\pi
692692 0 0
693693 228.272 + 228.272i 0.329397 + 0.329397i
694694 0 0
695695 0 0
696696 0 0
697697 −54.6469 + 54.6469i −0.0784031 + 0.0784031i
698698 0 0
699699 623.778i 0.892386i
700700 0 0
701701 −125.698 −0.179312 −0.0896562 0.995973i 0.528577π-0.528577\pi
−0.0896562 + 0.995973i 0.528577π0.528577\pi
702702 0 0
703703 −307.283 307.283i −0.437102 0.437102i
704704 0 0
705705 0 0
706706 0 0
707707 −1000.91 + 1000.91i −1.41571 + 1.41571i
708708 0 0
709709 201.069i 0.283596i 0.989896 + 0.141798i 0.0452883π0.0452883\pi
−0.989896 + 0.141798i 0.954712π0.954712\pi
710710 0 0
711711 −198.000 −0.278481
712712 0 0
713713 549.131 + 549.131i 0.770169 + 0.770169i
714714 0 0
715715 0 0
716716 0 0
717717 517.807 517.807i 0.722186 0.722186i
718718 0 0
719719 785.576i 1.09259i −0.837591 0.546297i 0.816037π-0.816037\pi
0.837591 0.546297i 0.183963π-0.183963\pi
720720 0 0
721721 −546.384 −0.757814
722722 0 0
723723 13.1872 + 13.1872i 0.0182396 + 0.0182396i
724724 0 0
725725 0 0
726726 0 0
727727 −282.459 + 282.459i −0.388526 + 0.388526i −0.874162 0.485635i 0.838588π-0.838588\pi
0.485635 + 0.874162i 0.338588π0.338588\pi
728728 0 0
729729 27.0000i 0.0370370i
730730 0 0
731731 39.9184 0.0546079
732732 0 0
733733 54.9036 + 54.9036i 0.0749025 + 0.0749025i 0.743566 0.668663i 0.233133π-0.233133\pi
−0.668663 + 0.743566i 0.733133π0.733133\pi
734734 0 0
735735 0 0
736736 0 0
737737 918.929 918.929i 1.24685 1.24685i
738738 0 0
739739 276.624i 0.374323i 0.982329 + 0.187161i 0.0599287π0.0599287\pi
−0.982329 + 0.187161i 0.940071π0.940071\pi
740740 0 0
741741 201.576 0.272032
742742 0 0
743743 −143.101 143.101i −0.192599 0.192599i 0.604219 0.796818i 0.293485π-0.293485\pi
−0.796818 + 0.604219i 0.793485π0.793485\pi
744744 0 0
745745 0 0
746746 0 0
747747 252.272 252.272i 0.337714 0.337714i
748748 0 0
749749 385.535i 0.514733i
750750 0 0
751751 871.453 1.16039 0.580195 0.814478i 0.302976π-0.302976\pi
0.580195 + 0.814478i 0.302976π0.302976\pi
752752 0 0
753753 −217.782 217.782i −0.289219 0.289219i
754754 0 0
755755 0 0
756756 0 0
757757 304.702 304.702i 0.402512 0.402512i −0.476605 0.879117i 0.658133π-0.658133\pi
0.879117 + 0.476605i 0.158133π0.158133\pi
758758 0 0
759759 629.939i 0.829959i
760760 0 0
761761 613.959 0.806779 0.403390 0.915028i 0.367832π-0.367832\pi
0.403390 + 0.915028i 0.367832π0.367832\pi
762762 0 0
763763 −110.879 110.879i −0.145319 0.145319i
764764 0 0
765765 0 0
766766 0 0
767767 213.081 213.081i 0.277810 0.277810i
768768 0 0
769769 887.412i 1.15398i −0.816750 0.576991i 0.804227π-0.804227\pi
0.816750 0.576991i 0.195773π-0.195773\pi
770770 0 0
771771 −348.545 −0.452069
772772 0 0
773773 605.757 + 605.757i 0.783644 + 0.783644i 0.980444 0.196799i 0.0630548π-0.0630548\pi
−0.196799 + 0.980444i 0.563055π0.563055\pi
774774 0 0
775775 0 0
776776 0 0
777777 −144.495 + 144.495i −0.185965 + 0.185965i
778778 0 0
779779 2042.22i 2.62159i
780780 0 0
781781 787.959 1.00891
782782 0 0
783783 13.2122 + 13.2122i 0.0168739 + 0.0168739i
784784 0 0
785785 0 0
786786 0 0
787787 −616.463 + 616.463i −0.783308 + 0.783308i −0.980387 0.197080i 0.936854π-0.936854\pi
0.197080 + 0.980387i 0.436854π0.436854\pi
788788 0 0
789789 88.1816i 0.111764i
790790 0 0
791791 1732.24 2.18994
792792 0 0
793793 −265.485 265.485i −0.334785 0.334785i
794794 0 0
795795 0 0
796796 0 0
797797 −247.768 + 247.768i −0.310876 + 0.310876i −0.845249 0.534373i 0.820548π-0.820548\pi
0.534373 + 0.845249i 0.320548π0.320548\pi
798798 0 0
799799 8.08164i 0.0101147i
800800 0 0
801801 28.7878 0.0359398
802802 0 0
803803 −928.463 928.463i −1.15624 1.15624i
804804 0 0
805805 0 0
806806 0 0
807807 −47.5551 + 47.5551i −0.0589282 + 0.0589282i
808808 0 0
809809 1556.10i 1.92348i 0.273958 + 0.961742i 0.411667π0.411667\pi
−0.273958 + 0.961742i 0.588333π0.588333\pi
810810 0 0
811811 277.192 0.341790 0.170895 0.985289i 0.445334π-0.445334\pi
0.170895 + 0.985289i 0.445334π0.445334\pi
812812 0 0
813813 −14.1770 14.1770i −0.0174379 0.0174379i
814814 0 0
815815 0 0
816816 0 0
817817 745.898 745.898i 0.912972 0.912972i
818818 0 0
819819 94.7878i 0.115736i
820820 0 0
821821 −1485.86 −1.80981 −0.904907 0.425610i 0.860060π-0.860060\pi
−0.904907 + 0.425610i 0.860060π0.860060\pi
822822 0 0
823823 −809.519 809.519i −0.983620 0.983620i 0.0162485 0.999868i 0.494828π-0.494828\pi
−0.999868 + 0.0162485i 0.994828π0.994828\pi
824824 0 0
825825 0 0
826826 0 0
827827 1122.66 1122.66i 1.35750 1.35750i 0.480521 0.876983i 0.340447π-0.340447\pi
0.876983 0.480521i 0.159553π-0.159553\pi
828828 0 0
829829 849.151i 1.02431i 0.858894 + 0.512154i 0.171152π0.171152\pi
−0.858894 + 0.512154i 0.828848π0.828848\pi
830830 0 0
831831 −691.980 −0.832707
832832 0 0
833833 −30.7378 30.7378i −0.0369001 0.0369001i
834834 0 0
835835 0 0
836836 0 0
837837 92.5607 92.5607i 0.110586 0.110586i
838838 0 0
839839 1606.26i 1.91449i −0.289270 0.957247i 0.593413π-0.593413\pi
0.289270 0.957247i 0.406587π-0.406587\pi
840840 0 0
841841 828.069 0.984625
842842 0 0
843843 529.560 + 529.560i 0.628185 + 0.628185i
844844 0 0
845845 0 0
846846 0 0
847847 −117.328 + 117.328i −0.138522 + 0.138522i
848848 0 0
849849 548.363i 0.645893i
850850 0 0
851851 −398.747 −0.468563
852852 0 0
853853 632.702 + 632.702i 0.741737 + 0.741737i 0.972912 0.231175i 0.0742571π-0.0742571\pi
−0.231175 + 0.972912i 0.574257π0.574257\pi
854854 0 0
855855 0 0
856856 0 0
857857 258.879 258.879i 0.302075 0.302075i −0.539750 0.841825i 0.681481π-0.681481\pi
0.841825 + 0.539750i 0.181481π0.181481\pi
858858 0 0
859859 534.082i 0.621748i −0.950451 0.310874i 0.899378π-0.899378\pi
0.950451 0.310874i 0.100622π-0.100622\pi
860860 0 0
861861 960.322 1.11536
862862 0 0
863863 −711.878 711.878i −0.824887 0.824887i 0.161917 0.986804i 0.448232π-0.448232\pi
−0.986804 + 0.161917i 0.948232π0.948232\pi
864864 0 0
865865 0 0
866866 0 0
867867 −351.972 + 351.972i −0.405965 + 0.405965i
868868 0 0
869869 778.665i 0.896048i
870870 0 0
871871 −381.576 −0.438089
872872 0 0
873873 159.242 + 159.242i 0.182408 + 0.182408i
874874 0 0
875875 0 0
876876 0 0
877877 742.590 742.590i 0.846739 0.846739i −0.142986 0.989725i 0.545670π-0.545670\pi
0.989725 + 0.142986i 0.0456702π0.0456702\pi
878878 0 0
879879 481.980i 0.548327i
880880 0 0
881881 −1000.75 −1.13592 −0.567961 0.823056i 0.692267π-0.692267\pi
−0.567961 + 0.823056i 0.692267π0.692267\pi
882882 0 0
883883 546.788 + 546.788i 0.619239 + 0.619239i 0.945336 0.326097i 0.105734π-0.105734\pi
−0.326097 + 0.945336i 0.605734π0.605734\pi
884884 0 0
885885 0 0
886886 0 0
887887 −1138.48 + 1138.48i −1.28352 + 1.28352i −0.344872 + 0.938650i 0.612078π0.612078\pi
−0.938650 + 0.344872i 0.887922π0.887922\pi
888888 0 0
889889 1976.60i 2.22340i
890890 0 0
891891 106.182 0.119171
892892 0 0
893893 151.010 + 151.010i 0.169104 + 0.169104i
894894 0 0
895895 0 0
896896 0 0
897897 130.788 130.788i 0.145806 0.145806i
898898 0 0
899899 90.5878i 0.100765i
900900 0 0
901901 93.6571 0.103948
902902 0 0
903903 −350.747 350.747i −0.388424 0.388424i
904904 0 0
905905 0 0
906906 0 0
907907 162.706 162.706i 0.179389 0.179389i −0.611700 0.791090i 0.709514π-0.709514\pi
0.791090 + 0.611700i 0.209514π0.209514\pi
908908 0 0
909909 465.576i 0.512184i
910910 0 0
911911 −386.988 −0.424794 −0.212397 0.977183i 0.568127π-0.568127\pi
−0.212397 + 0.977183i 0.568127π0.568127\pi
912912 0 0
913913 992.100 + 992.100i 1.08664 + 1.08664i
914914 0 0
915915 0 0
916916 0 0
917917 1268.01 1268.01i 1.38278 1.38278i
918918 0 0
919919 1101.80i 1.19891i −0.800409 0.599454i 0.795385π-0.795385\pi
0.800409 0.599454i 0.204615π-0.204615\pi
920920 0 0
921921 −347.110 −0.376884
922922 0 0
923923 −163.596 163.596i −0.177244 0.177244i
924924 0 0
925925 0 0
926926 0 0
927927 −127.076 + 127.076i −0.137083 + 0.137083i
928928 0 0
929929 261.273i 0.281242i −0.990064 0.140621i 0.955090π-0.955090\pi
0.990064 0.140621i 0.0449098π-0.0449098\pi
930930 0 0
931931 −1148.71 −1.23384
932932 0 0
933933 −504.050 504.050i −0.540247 0.540247i
934934 0 0
935935 0 0
936936 0 0
937937 −57.7980 + 57.7980i −0.0616841 + 0.0616841i −0.737276 0.675592i 0.763888π-0.763888\pi
0.675592 + 0.737276i 0.263888π0.263888\pi
938938 0 0
939939 896.363i 0.954593i
940940 0 0
941941 399.837 0.424906 0.212453 0.977171i 0.431855π-0.431855\pi
0.212453 + 0.977171i 0.431855π0.431855\pi
942942 0 0
943943 1325.05 + 1325.05i 1.40514 + 1.40514i
944944 0 0
945945 0 0
946946 0 0
947947 −464.958 + 464.958i −0.490980 + 0.490980i −0.908615 0.417635i 0.862859π-0.862859\pi
0.417635 + 0.908615i 0.362859π0.362859\pi
948948 0 0
949949 385.535i 0.406254i
950950 0 0
951951 −828.767 −0.871469
952952 0 0
953953 627.242 + 627.242i 0.658176 + 0.658176i 0.954948 0.296772i 0.0959102π-0.0959102\pi
−0.296772 + 0.954948i 0.595910π0.595910\pi
954954 0 0
955955 0 0
956956 0 0
957957 −51.9592 + 51.9592i −0.0542938 + 0.0542938i
958958 0 0
959959 1045.86i 1.09057i
960960 0 0
961961 −326.371 −0.339616
962962 0 0
963963 −89.6663 89.6663i −0.0931114 0.0931114i
964964 0 0
965965 0 0
966966 0 0
967967 −1334.02 + 1334.02i −1.37955 + 1.37955i −0.534173 + 0.845375i 0.679377π0.679377\pi
−0.845375 + 0.534173i 0.820623π0.820623\pi
968968 0 0
969969 73.9796i 0.0763463i
970970 0 0
971971 −1489.17 −1.53365 −0.766823 0.641859i 0.778163π-0.778163\pi
−0.766823 + 0.641859i 0.778163π0.778163\pi
972972 0 0
973973 −239.868 239.868i −0.246525 0.246525i
974974 0 0
975975 0 0
976976 0 0
977977 −1134.66 + 1134.66i −1.16137 + 1.16137i −0.177191 + 0.984176i 0.556701π0.556701\pi
−0.984176 + 0.177191i 0.943299π0.943299\pi
978978 0 0
979979 113.212i 0.115641i
980980 0 0
981981 −51.5755 −0.0525744
982982 0 0
983983 −261.485 261.485i −0.266007 0.266007i 0.561482 0.827489i 0.310231π-0.310231\pi
−0.827489 + 0.561482i 0.810231π0.810231\pi
984984 0 0
985985 0 0
986986 0 0
987987 71.0102 71.0102i 0.0719455 0.0719455i
988988 0 0
989989 967.918i 0.978684i
990990 0 0
991991 −950.645 −0.959278 −0.479639 0.877466i 0.659232π-0.659232\pi
−0.479639 + 0.877466i 0.659232π0.659232\pi
992992 0 0
993993 −119.480 119.480i −0.120322 0.120322i
994994 0 0
995995 0 0
996996 0 0
997997 −96.0566 + 96.0566i −0.0963457 + 0.0963457i −0.753637 0.657291i 0.771702π-0.771702\pi
0.657291 + 0.753637i 0.271702π0.271702\pi
998998 0 0
999999 67.2122i 0.0672795i
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 600.3.u.a.193.2 4
3.2 odd 2 1800.3.v.j.793.1 4
4.3 odd 2 1200.3.bg.m.193.1 4
5.2 odd 4 inner 600.3.u.a.457.2 yes 4
5.3 odd 4 600.3.u.f.457.1 yes 4
5.4 even 2 600.3.u.f.193.1 yes 4
15.2 even 4 1800.3.v.j.1657.1 4
15.8 even 4 1800.3.v.q.1657.2 4
15.14 odd 2 1800.3.v.q.793.2 4
20.3 even 4 1200.3.bg.b.1057.2 4
20.7 even 4 1200.3.bg.m.1057.1 4
20.19 odd 2 1200.3.bg.b.193.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
600.3.u.a.193.2 4 1.1 even 1 trivial
600.3.u.a.457.2 yes 4 5.2 odd 4 inner
600.3.u.f.193.1 yes 4 5.4 even 2
600.3.u.f.457.1 yes 4 5.3 odd 4
1200.3.bg.b.193.2 4 20.19 odd 2
1200.3.bg.b.1057.2 4 20.3 even 4
1200.3.bg.m.193.1 4 4.3 odd 2
1200.3.bg.m.1057.1 4 20.7 even 4
1800.3.v.j.793.1 4 3.2 odd 2
1800.3.v.j.1657.1 4 15.2 even 4
1800.3.v.q.793.2 4 15.14 odd 2
1800.3.v.q.1657.2 4 15.8 even 4