Properties

Label 700.5.o.a.649.3
Level 700700
Weight 55
Character 700.649
Analytic conductor 72.35972.359
Analytic rank 00
Dimension 1212
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [700,5,Mod(549,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.549");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: N N == 700=22527 700 = 2^{2} \cdot 5^{2} \cdot 7
Weight: k k == 5 5
Character orbit: [χ][\chi] == 700.o (of order 66, degree 22, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 72.358974158772.3589741587
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: 12.0.32905425960566784.37
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x12+36x10+432x8+2040x6+3780x4+2592x2+576 x^{12} + 36x^{10} + 432x^{8} + 2040x^{6} + 3780x^{4} + 2592x^{2} + 576 Copy content Toggle raw display
Coefficient ring: Z[a1,,a19]\Z[a_1, \ldots, a_{19}]
Coefficient ring index: 263674 2^{6}\cdot 3^{6}\cdot 7^{4}
Twist minimal: no (minimal twist has level 28)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 649.3
Root 0.802567i0.802567i of defining polynomial
Character χ\chi == 700.649
Dual form 700.5.o.a.549.3

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) == q+(0.7846231.35901i)q3+(24.566742.3967i)q7+(39.268768.0154i)q9+(11.755720.3615i)q11+136.269q13+(131.251+227.333i)q17+(387.162+223.528i)q19+(38.3418+66.6517i)q21+(648.800+374.585i)q23250.353q27406.524q29+(584.199+337.287i)q31+(18.4476+31.9521i)q33+(645.476+372.666i)q37+(106.920185.191i)q392476.20iq412636.68iq43+(334.343+579.099i)q47+(1193.96+2083.09i)q49+(205.964356.741i)q51+(1757.36+1014.61i)q53701.541iq57+(1014.22585.561i)q59+(2022.051167.43i)q61+(3848.33+6.04891i)q63+(6546.783779.79i)q671175.63iq69+7575.36q71+(1896.12+3284.18i)q73+(574.460+998.615i)q77+(3897.336750.37i)q79+(2984.335169.02i)q81+2181.41q83+(318.968+552.469i)q87+(8050.384647.89i)q89+(3347.695777.37i)q91+(916.751+529.287i)q93+9981.90q971846.52q99+O(q100)q+(-0.784623 - 1.35901i) q^{3} +(-24.5667 - 42.3967i) q^{7} +(39.2687 - 68.0154i) q^{9} +(-11.7557 - 20.3615i) q^{11} +136.269 q^{13} +(131.251 + 227.333i) q^{17} +(387.162 + 223.528i) q^{19} +(-38.3418 + 66.6517i) q^{21} +(648.800 + 374.585i) q^{23} -250.353 q^{27} -406.524 q^{29} +(-584.199 + 337.287i) q^{31} +(-18.4476 + 31.9521i) q^{33} +(645.476 + 372.666i) q^{37} +(-106.920 - 185.191i) q^{39} -2476.20i q^{41} -2636.68i q^{43} +(-334.343 + 579.099i) q^{47} +(-1193.96 + 2083.09i) q^{49} +(205.964 - 356.741i) q^{51} +(-1757.36 + 1014.61i) q^{53} -701.541i q^{57} +(1014.22 - 585.561i) q^{59} +(-2022.05 - 1167.43i) q^{61} +(-3848.33 + 6.04891i) q^{63} +(6546.78 - 3779.79i) q^{67} -1175.63i q^{69} +7575.36 q^{71} +(1896.12 + 3284.18i) q^{73} +(-574.460 + 998.615i) q^{77} +(3897.33 - 6750.37i) q^{79} +(-2984.33 - 5169.02i) q^{81} +2181.41 q^{83} +(318.968 + 552.469i) q^{87} +(-8050.38 - 4647.89i) q^{89} +(-3347.69 - 5777.37i) q^{91} +(916.751 + 529.287i) q^{93} +9981.90 q^{97} -1846.52 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q180q9+270q11+1494q19+4338q21+1080q2910710q3113176q3916860q491782q51+5886q59+8082q61+4536q71+15546q7914958q81+16200q99+O(q100) 12 q - 180 q^{9} + 270 q^{11} + 1494 q^{19} + 4338 q^{21} + 1080 q^{29} - 10710 q^{31} - 13176 q^{39} - 16860 q^{49} - 1782 q^{51} + 5886 q^{59} + 8082 q^{61} + 4536 q^{71} + 15546 q^{79} - 14958 q^{81}+ \cdots - 16200 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/700Z)×\left(\mathbb{Z}/700\mathbb{Z}\right)^\times.

nn 101101 351351 477477
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) 11 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 −0.784623 1.35901i −0.0871803 0.151001i 0.819138 0.573597i 0.194452π-0.194452\pi
−0.906318 + 0.422596i 0.861119π0.861119\pi
44 0 0
55 0 0
66 0 0
77 −24.5667 42.3967i −0.501361 0.865238i
88 0 0
99 39.2687 68.0154i 0.484799 0.839697i
1010 0 0
1111 −11.7557 20.3615i −0.0971545 0.168276i 0.813351 0.581773i 0.197641π-0.197641\pi
−0.910506 + 0.413496i 0.864307π0.864307\pi
1212 0 0
1313 136.269 0.806328 0.403164 0.915128i 0.367910π-0.367910\pi
0.403164 + 0.915128i 0.367910π0.367910\pi
1414 0 0
1515 0 0
1616 0 0
1717 131.251 + 227.333i 0.454154 + 0.786618i 0.998639 0.0521523i 0.0166081π-0.0166081\pi
−0.544485 + 0.838771i 0.683275π0.683275\pi
1818 0 0
1919 387.162 + 223.528i 1.07247 + 0.619191i 0.928855 0.370442i 0.120794π-0.120794\pi
0.143615 + 0.989634i 0.454127π0.454127\pi
2020 0 0
2121 −38.3418 + 66.6517i −0.0869429 + 0.151138i
2222 0 0
2323 648.800 + 374.585i 1.22646 + 0.708100i 0.966288 0.257462i 0.0828861π-0.0828861\pi
0.260176 + 0.965561i 0.416219π0.416219\pi
2424 0 0
2525 0 0
2626 0 0
2727 −250.353 −0.343420
2828 0 0
2929 −406.524 −0.483382 −0.241691 0.970353i 0.577702π-0.577702\pi
−0.241691 + 0.970353i 0.577702π0.577702\pi
3030 0 0
3131 −584.199 + 337.287i −0.607907 + 0.350975i −0.772146 0.635445i 0.780817π-0.780817\pi
0.164239 + 0.986421i 0.447483π0.447483\pi
3232 0 0
3333 −18.4476 + 31.9521i −0.0169399 + 0.0293408i
3434 0 0
3535 0 0
3636 0 0
3737 645.476 + 372.666i 0.471495 + 0.272218i 0.716865 0.697212i 0.245576π-0.245576\pi
−0.245370 + 0.969429i 0.578910π0.578910\pi
3838 0 0
3939 −106.920 185.191i −0.0702959 0.121756i
4040 0 0
4141 2476.20i 1.47305i −0.676410 0.736526i 0.736465π-0.736465\pi
0.676410 0.736526i 0.263535π-0.263535\pi
4242 0 0
4343 2636.68i 1.42601i −0.701161 0.713003i 0.747335π-0.747335\pi
0.701161 0.713003i 0.252665π-0.252665\pi
4444 0 0
4545 0 0
4646 0 0
4747 −334.343 + 579.099i −0.151355 + 0.262154i −0.931726 0.363163i 0.881697π-0.881697\pi
0.780371 + 0.625317i 0.215030π0.215030\pi
4848 0 0
4949 −1193.96 + 2083.09i −0.497275 + 0.867593i
5050 0 0
5151 205.964 356.741i 0.0791866 0.137155i
5252 0 0
5353 −1757.36 + 1014.61i −0.625617 + 0.361200i −0.779053 0.626959i 0.784300π-0.784300\pi
0.153436 + 0.988159i 0.450966π0.450966\pi
5454 0 0
5555 0 0
5656 0 0
5757 701.541i 0.215925i
5858 0 0
5959 1014.22 585.561i 0.291359 0.168216i −0.347195 0.937793i 0.612866π-0.612866\pi
0.638555 + 0.769576i 0.279533π0.279533\pi
6060 0 0
6161 −2022.05 1167.43i −0.543416 0.313741i 0.203047 0.979169i 0.434916π-0.434916\pi
−0.746462 + 0.665428i 0.768249π0.768249\pi
6262 0 0
6363 −3848.33 + 6.04891i −0.969597 + 0.00152404i
6464 0 0
6565 0 0
6666 0 0
6767 6546.78 3779.79i 1.45841 0.842011i 0.459472 0.888192i 0.348039π-0.348039\pi
0.998933 + 0.0461815i 0.0147052π0.0147052\pi
6868 0 0
6969 1175.63i 0.246929i
7070 0 0
7171 7575.36 1.50275 0.751375 0.659876i 0.229391π-0.229391\pi
0.751375 + 0.659876i 0.229391π0.229391\pi
7272 0 0
7373 1896.12 + 3284.18i 0.355812 + 0.616284i 0.987257 0.159137i 0.0508710π-0.0508710\pi
−0.631445 + 0.775421i 0.717538π0.717538\pi
7474 0 0
7575 0 0
7676 0 0
7777 −574.460 + 998.615i −0.0968898 + 0.168429i
7878 0 0
7979 3897.33 6750.37i 0.624472 1.08162i −0.364171 0.931332i 0.618647π-0.618647\pi
0.988643 0.150285i 0.0480192π-0.0480192\pi
8080 0 0
8181 −2984.33 5169.02i −0.454860 0.787840i
8282 0 0
8383 2181.41 0.316651 0.158326 0.987387i 0.449390π-0.449390\pi
0.158326 + 0.987387i 0.449390π0.449390\pi
8484 0 0
8585 0 0
8686 0 0
8787 318.968 + 552.469i 0.0421414 + 0.0729910i
8888 0 0
8989 −8050.38 4647.89i −1.01633 0.586781i −0.103294 0.994651i 0.532938π-0.532938\pi
−0.913040 + 0.407870i 0.866272π0.866272\pi
9090 0 0
9191 −3347.69 5777.37i −0.404261 0.697666i
9292 0 0
9393 916.751 + 529.287i 0.105995 + 0.0611963i
9494 0 0
9595 0 0
9696 0 0
9797 9981.90 1.06089 0.530444 0.847720i 0.322025π-0.322025\pi
0.530444 + 0.847720i 0.322025π0.322025\pi
9898 0 0
9999 −1846.52 −0.188402
100100 0 0
101101 −675.552 + 390.030i −0.0662241 + 0.0382345i −0.532746 0.846275i 0.678840π-0.678840\pi
0.466522 + 0.884509i 0.345507π0.345507\pi
102102 0 0
103103 −1376.35 + 2383.90i −0.129734 + 0.224706i −0.923573 0.383422i 0.874746π-0.874746\pi
0.793840 + 0.608127i 0.208079π0.208079\pi
104104 0 0
105105 0 0
106106 0 0
107107 12868.2 + 7429.46i 1.12396 + 0.648917i 0.942408 0.334464i 0.108555π-0.108555\pi
0.181550 + 0.983382i 0.441889π0.441889\pi
108108 0 0
109109 1378.33 + 2387.33i 0.116011 + 0.200937i 0.918183 0.396155i 0.129656π-0.129656\pi
−0.802172 + 0.597092i 0.796323π0.796323\pi
110110 0 0
111111 1169.61i 0.0949281i
112112 0 0
113113 6264.79i 0.490625i 0.969444 + 0.245312i 0.0788905π0.0788905\pi
−0.969444 + 0.245312i 0.921109π0.921109\pi
114114 0 0
115115 0 0
116116 0 0
117117 5351.13 9268.43i 0.390907 0.677071i
118118 0 0
119119 6413.76 11149.4i 0.452917 0.787331i
120120 0 0
121121 7044.11 12200.8i 0.481122 0.833328i
122122 0 0
123123 −3365.17 + 1942.88i −0.222432 + 0.128421i
124124 0 0
125125 0 0
126126 0 0
127127 12855.0i 0.797010i −0.917166 0.398505i 0.869529π-0.869529\pi
0.917166 0.398505i 0.130471π-0.130471\pi
128128 0 0
129129 −3583.27 + 2068.80i −0.215328 + 0.124320i
130130 0 0
131131 −21412.5 12362.5i −1.24774 0.720383i −0.277082 0.960846i 0.589367π-0.589367\pi
−0.970658 + 0.240464i 0.922701π0.922701\pi
132132 0 0
133133 −34.4320 21905.7i −0.00194652 1.23838i
134134 0 0
135135 0 0
136136 0 0
137137 −1145.02 + 661.078i −0.0610059 + 0.0352218i −0.530193 0.847877i 0.677880π-0.677880\pi
0.469187 + 0.883099i 0.344547π0.344547\pi
138138 0 0
139139 5119.78i 0.264985i 0.991184 + 0.132493i 0.0422981π0.0422981\pi
−0.991184 + 0.132493i 0.957702π0.957702\pi
140140 0 0
141141 1049.33 0.0527807
142142 0 0
143143 −1601.94 2774.64i −0.0783384 0.135686i
144144 0 0
145145 0 0
146146 0 0
147147 3767.74 11.8445i 0.174360 0.000548128i
148148 0 0
149149 5104.93 8842.00i 0.229942 0.398270i −0.727849 0.685737i 0.759480π-0.759480\pi
0.957791 + 0.287467i 0.0928132π0.0928132\pi
150150 0 0
151151 −14672.1 25412.8i −0.643483 1.11455i −0.984650 0.174543i 0.944155π-0.944155\pi
0.341166 0.940003i 0.389178π-0.389178\pi
152152 0 0
153153 20616.2 0.880695
154154 0 0
155155 0 0
156156 0 0
157157 15030.2 + 26033.1i 0.609770 + 1.05615i 0.991278 + 0.131787i 0.0420716π0.0420716\pi
−0.381508 + 0.924366i 0.624595π0.624595\pi
158158 0 0
159159 2757.73 + 1592.17i 0.109083 + 0.0629791i
160160 0 0
161161 −57.7005 36709.3i −0.00222602 1.41620i
162162 0 0
163163 −26742.3 15439.7i −1.00652 0.581115i −0.0963500 0.995348i 0.530717π-0.530717\pi
−0.910171 + 0.414232i 0.864050π0.864050\pi
164164 0 0
165165 0 0
166166 0 0
167167 12858.8 0.461070 0.230535 0.973064i 0.425952π-0.425952\pi
0.230535 + 0.973064i 0.425952π0.425952\pi
168168 0 0
169169 −9991.63 −0.349835
170170 0 0
171171 30406.7 17555.3i 1.03987 0.600367i
172172 0 0
173173 −7845.51 + 13588.8i −0.262137 + 0.454035i −0.966810 0.255498i 0.917761π-0.917761\pi
0.704672 + 0.709533i 0.251094π0.251094\pi
174174 0 0
175175 0 0
176176 0 0
177177 −1591.56 918.890i −0.0508016 0.0293303i
178178 0 0
179179 −15993.2 27701.0i −0.499148 0.864550i 0.500851 0.865533i 0.333020π-0.333020\pi
−1.00000 0.000983488i 0.999687π0.999687\pi
180180 0 0
181181 47967.6i 1.46417i −0.681215 0.732083i 0.738548π-0.738548\pi
0.681215 0.732083i 0.261452π-0.261452\pi
182182 0 0
183183 3663.97i 0.109408i
184184 0 0
185185 0 0
186186 0 0
187187 3085.88 5344.91i 0.0882462 0.152847i
188188 0 0
189189 6150.35 + 10614.2i 0.172177 + 0.297141i
190190 0 0
191191 −2227.93 + 3858.88i −0.0610709 + 0.105778i −0.894944 0.446178i 0.852785π-0.852785\pi
0.833873 + 0.551956i 0.186118π0.186118\pi
192192 0 0
193193 −25460.9 + 14699.9i −0.683533 + 0.394638i −0.801185 0.598417i 0.795797π-0.795797\pi
0.117652 + 0.993055i 0.462463π0.462463\pi
194194 0 0
195195 0 0
196196 0 0
197197 23816.0i 0.613671i −0.951763 0.306836i 0.900730π-0.900730\pi
0.951763 0.306836i 0.0992701π-0.0992701\pi
198198 0 0
199199 42280.9 24410.9i 1.06767 0.616421i 0.140128 0.990133i 0.455249π-0.455249\pi
0.927545 + 0.373713i 0.121915π0.121915\pi
200200 0 0
201201 −10273.5 5931.41i −0.254288 0.146813i
202202 0 0
203203 9986.94 + 17235.3i 0.242349 + 0.418241i
204204 0 0
205205 0 0
206206 0 0
207207 50955.1 29418.9i 1.18918 0.686572i
208208 0 0
209209 10510.9i 0.240629i
210210 0 0
211211 −9582.07 −0.215226 −0.107613 0.994193i 0.534321π-0.534321\pi
−0.107613 + 0.994193i 0.534321π0.534321\pi
212212 0 0
213213 −5943.80 10295.0i −0.131010 0.226916i
214214 0 0
215215 0 0
216216 0 0
217217 28651.7 + 16482.1i 0.608458 + 0.350019i
218218 0 0
219219 2975.48 5153.68i 0.0620396 0.107456i
220220 0 0
221221 17885.5 + 30978.5i 0.366197 + 0.634273i
222222 0 0
223223 54978.9 1.10557 0.552785 0.833324i 0.313565π-0.313565\pi
0.552785 + 0.833324i 0.313565π0.313565\pi
224224 0 0
225225 0 0
226226 0 0
227227 4340.66 + 7518.24i 0.0842372 + 0.145903i 0.905066 0.425271i 0.139821π-0.139821\pi
−0.820829 + 0.571174i 0.806488π0.806488\pi
228228 0 0
229229 6262.86 + 3615.86i 0.119427 + 0.0689511i 0.558523 0.829489i 0.311368π-0.311368\pi
−0.439097 + 0.898440i 0.644701π0.644701\pi
230230 0 0
231231 1807.86 2.84164i 0.0338798 5.32531e-5i
232232 0 0
233233 −7660.79 4422.96i −0.141111 0.0814707i 0.427782 0.903882i 0.359295π-0.359295\pi
−0.568894 + 0.822411i 0.692628π0.692628\pi
234234 0 0
235235 0 0
236236 0 0
237237 −12231.7 −0.217767
238238 0 0
239239 −88491.7 −1.54920 −0.774599 0.632453i 0.782048π-0.782048\pi
−0.774599 + 0.632453i 0.782048π0.782048\pi
240240 0 0
241241 −53365.8 + 30810.7i −0.918816 + 0.530479i −0.883257 0.468889i 0.844654π-0.844654\pi
−0.0355589 + 0.999368i 0.511321π0.511321\pi
242242 0 0
243243 −14822.5 + 25673.3i −0.251020 + 0.434779i
244244 0 0
245245 0 0
246246 0 0
247247 52758.4 + 30460.0i 0.864763 + 0.499271i
248248 0 0
249249 −1711.59 2964.55i −0.0276058 0.0478146i
250250 0 0
251251 57796.3i 0.917386i −0.888595 0.458693i 0.848318π-0.848318\pi
0.888595 0.458693i 0.151682π-0.151682\pi
252252 0 0
253253 17614.0i 0.275180i
254254 0 0
255255 0 0
256256 0 0
257257 35065.0 60734.3i 0.530893 0.919534i −0.468457 0.883486i 0.655190π-0.655190\pi
0.999350 0.0360479i 0.0114769π-0.0114769\pi
258258 0 0
259259 −57.4050 36521.2i −0.000855756 0.544435i
260260 0 0
261261 −15963.7 + 27649.9i −0.234343 + 0.405894i
262262 0 0
263263 19262.0 11120.9i 0.278477 0.160779i −0.354257 0.935148i 0.615266π-0.615266\pi
0.632734 + 0.774369i 0.281933π0.281933\pi
264264 0 0
265265 0 0
266266 0 0
267267 14587.4i 0.204623i
268268 0 0
269269 −40332.3 + 23285.9i −0.557376 + 0.321801i −0.752092 0.659058i 0.770955π-0.770955\pi
0.194715 + 0.980860i 0.437622π0.437622\pi
270270 0 0
271271 71958.3 + 41545.1i 0.979811 + 0.565694i 0.902213 0.431291i 0.141942π-0.141942\pi
0.0775980 + 0.996985i 0.475275π0.475275\pi
272272 0 0
273273 −5224.82 + 9082.59i −0.0701045 + 0.121866i
274274 0 0
275275 0 0
276276 0 0
277277 7818.59 4514.06i 0.101899 0.0588313i −0.448185 0.893941i 0.647929π-0.647929\pi
0.550083 + 0.835110i 0.314596π0.314596\pi
278278 0 0
279279 52979.4i 0.680610i
280280 0 0
281281 64188.4 0.812912 0.406456 0.913670i 0.366764π-0.366764\pi
0.406456 + 0.913670i 0.366764π0.366764\pi
282282 0 0
283283 11295.1 + 19563.7i 0.141032 + 0.244274i 0.927885 0.372865i 0.121625π-0.121625\pi
−0.786854 + 0.617140i 0.788291π0.788291\pi
284284 0 0
285285 0 0
286286 0 0
287287 −104983. + 60832.0i −1.27454 + 0.738530i
288288 0 0
289289 7307.06 12656.2i 0.0874877 0.151533i
290290 0 0
291291 −7832.02 13565.5i −0.0924885 0.160195i
292292 0 0
293293 −130473. −1.51980 −0.759900 0.650040i 0.774752π-0.774752\pi
−0.759900 + 0.650040i 0.774752π0.774752\pi
294294 0 0
295295 0 0
296296 0 0
297297 2943.08 + 5097.56i 0.0333648 + 0.0577896i
298298 0 0
299299 88411.6 + 51044.5i 0.988933 + 0.570961i
300300 0 0
301301 −111787. + 64774.5i −1.23383 + 0.714943i
302302 0 0
303303 1060.11 + 612.053i 0.0115469 + 0.00666659i
304304 0 0
305305 0 0
306306 0 0
307307 −56173.9 −0.596015 −0.298008 0.954563i 0.596322π-0.596322\pi
−0.298008 + 0.954563i 0.596322π0.596322\pi
308308 0 0
309309 4319.65 0.0452410
310310 0 0
311311 40087.2 23144.4i 0.414462 0.239290i −0.278243 0.960511i 0.589752π-0.589752\pi
0.692705 + 0.721221i 0.256419π0.256419\pi
312312 0 0
313313 69174.4 119814.i 0.706085 1.22298i −0.260213 0.965551i 0.583793π-0.583793\pi
0.966299 0.257424i 0.0828737π-0.0828737\pi
314314 0 0
315315 0 0
316316 0 0
317317 −50493.9 29152.7i −0.502482 0.290108i 0.227256 0.973835i 0.427025π-0.427025\pi
−0.729738 + 0.683727i 0.760358π0.760358\pi
318318 0 0
319319 4778.97 + 8277.42i 0.0469627 + 0.0813418i
320320 0 0
321321 23317.3i 0.226291i
322322 0 0
323323 117353.i 1.12483i
324324 0 0
325325 0 0
326326 0 0
327327 2162.93 3746.31i 0.0202278 0.0350355i
328328 0 0
329329 32765.6 51.5018i 0.302709 0.000475806i
330330 0 0
331331 −494.602 + 856.675i −0.00451440 + 0.00781916i −0.868274 0.496085i 0.834770π-0.834770\pi
0.863759 + 0.503904i 0.168104π0.168104\pi
332332 0 0
333333 50694.1 29268.2i 0.457161 0.263942i
334334 0 0
335335 0 0
336336 0 0
337337 55958.7i 0.492728i 0.969177 + 0.246364i 0.0792359π0.0792359\pi
−0.969177 + 0.246364i 0.920764π0.920764\pi
338338 0 0
339339 8513.89 4915.49i 0.0740847 0.0427728i
340340 0 0
341341 13735.3 + 7930.09i 0.118122 + 0.0681976i
342342 0 0
343343 117648. 554.769i 0.999989 0.00471546i
344344 0 0
345345 0 0
346346 0 0
347347 −113141. + 65322.2i −0.939641 + 0.542502i −0.889848 0.456257i 0.849190π-0.849190\pi
−0.0497936 + 0.998760i 0.515856π0.515856\pi
348348 0 0
349349 110948.i 0.910899i 0.890262 + 0.455450i 0.150522π0.150522\pi
−0.890262 + 0.455450i 0.849478π0.849478\pi
350350 0 0
351351 −34115.5 −0.276910
352352 0 0
353353 8503.18 + 14727.9i 0.0682389 + 0.118193i 0.898126 0.439738i 0.144929π-0.144929\pi
−0.829887 + 0.557931i 0.811595π0.811595\pi
354354 0 0
355355 0 0
356356 0 0
357357 −20184.5 + 31.7265i −0.158373 + 0.000248935i
358358 0 0
359359 35732.4 61890.3i 0.277251 0.480212i −0.693450 0.720505i 0.743910π-0.743910\pi
0.970701 + 0.240293i 0.0772434π0.0772434\pi
360360 0 0
361361 34769.0 + 60221.8i 0.266795 + 0.462103i
362362 0 0
363363 −22107.9 −0.167777
364364 0 0
365365 0 0
366366 0 0
367367 −85183.8 147543.i −0.632448 1.09543i −0.987050 0.160415i 0.948717π-0.948717\pi
0.354602 0.935017i 0.384617π-0.384617\pi
368368 0 0
369369 −168420. 97237.2i −1.23692 0.714134i
370370 0 0
371371 86188.6 + 49580.5i 0.626184 + 0.360216i
372372 0 0
373373 −130503. 75346.0i −0.938001 0.541555i −0.0486680 0.998815i 0.515498π-0.515498\pi
−0.889333 + 0.457260i 0.848831π0.848831\pi
374374 0 0
375375 0 0
376376 0 0
377377 −55396.8 −0.389764
378378 0 0
379379 211477. 1.47226 0.736129 0.676841i 0.236652π-0.236652\pi
0.736129 + 0.676841i 0.236652π0.236652\pi
380380 0 0
381381 −17470.0 + 10086.3i −0.120349 + 0.0694836i
382382 0 0
383383 59333.6 102769.i 0.404486 0.700590i −0.589776 0.807567i 0.700784π-0.700784\pi
0.994261 + 0.106977i 0.0341172π0.0341172\pi
384384 0 0
385385 0 0
386386 0 0
387387 −179335. 103539.i −1.19741 0.691326i
388388 0 0
389389 107858. + 186816.i 0.712778 + 1.23457i 0.963810 + 0.266588i 0.0858964π0.0858964\pi
−0.251033 + 0.967979i 0.580770π0.580770\pi
390390 0 0
391391 196658.i 1.28635i
392392 0 0
393393 38799.6i 0.251213i
394394 0 0
395395 0 0
396396 0 0
397397 −77371.1 + 134011.i −0.490905 + 0.850273i −0.999945 0.0104699i 0.996667π-0.996667\pi
0.509040 + 0.860743i 0.330001π0.330001\pi
398398 0 0
399399 −29743.0 + 17234.5i −0.186827 + 0.108256i
400400 0 0
401401 −100029. + 173255.i −0.622067 + 1.07745i 0.367033 + 0.930208i 0.380374π0.380374\pi
−0.989100 + 0.147244i 0.952960π0.952960\pi
402402 0 0
403403 −79608.5 + 45962.0i −0.490173 + 0.283001i
404404 0 0
405405 0 0
406406 0 0
407407 17523.8i 0.105789i
408408 0 0
409409 −190382. + 109917.i −1.13810 + 0.657080i −0.945958 0.324288i 0.894875π-0.894875\pi
−0.192137 + 0.981368i 0.561542π0.561542\pi
410410 0 0
411411 1796.82 + 1037.39i 0.0106370 + 0.00614129i
412412 0 0
413413 −49741.9 28614.4i −0.291623 0.167758i
414414 0 0
415415 0 0
416416 0 0
417417 6957.81 4017.10i 0.0400130 0.0231015i
418418 0 0
419419 31359.8i 0.178626i 0.996004 + 0.0893132i 0.0284672π0.0284672\pi
−0.996004 + 0.0893132i 0.971533π0.971533\pi
420420 0 0
421421 −73690.7 −0.415766 −0.207883 0.978154i 0.566657π-0.566657\pi
−0.207883 + 0.978154i 0.566657π0.566657\pi
422422 0 0
423423 26258.5 + 45481.0i 0.146753 + 0.254184i
424424 0 0
425425 0 0
426426 0 0
427427 179.830 + 114408.i 0.000986291 + 0.627481i
428428 0 0
429429 −2513.84 + 4354.10i −0.0136591 + 0.0236583i
430430 0 0
431431 132586. + 229646.i 0.713746 + 1.23624i 0.963441 + 0.267920i 0.0863364π0.0863364\pi
−0.249695 + 0.968325i 0.580330π0.580330\pi
432432 0 0
433433 124873. 0.666027 0.333014 0.942922i 0.391934π-0.391934\pi
0.333014 + 0.942922i 0.391934π0.391934\pi
434434 0 0
435435 0 0
436436 0 0
437437 167460. + 290050.i 0.876898 + 1.51883i
438438 0 0
439439 120989. + 69852.8i 0.627792 + 0.362456i 0.779896 0.625909i 0.215272π-0.215272\pi
−0.152105 + 0.988364i 0.548605π0.548605\pi
440440 0 0
441441 94797.1 + 163008.i 0.487437 + 0.838169i
442442 0 0
443443 191556. + 110595.i 0.976087 + 0.563544i 0.901087 0.433639i 0.142771π-0.142771\pi
0.0750005 + 0.997183i 0.476104π0.476104\pi
444444 0 0
445445 0 0
446446 0 0
447447 −16021.8 −0.0801855
448448 0 0
449449 −255878. −1.26923 −0.634615 0.772828i 0.718841π-0.718841\pi
−0.634615 + 0.772828i 0.718841π0.718841\pi
450450 0 0
451451 −50419.0 + 29109.4i −0.247880 + 0.143114i
452452 0 0
453453 −23024.1 + 39878.9i −0.112198 + 0.194333i
454454 0 0
455455 0 0
456456 0 0
457457 −277065. 159964.i −1.32663 0.765929i −0.341852 0.939754i 0.611054π-0.611054\pi
−0.984777 + 0.173825i 0.944387π0.944387\pi
458458 0 0
459459 −32859.0 56913.5i −0.155966 0.270141i
460460 0 0
461461 369557.i 1.73892i 0.494002 + 0.869461i 0.335534π0.335534\pi
−0.494002 + 0.869461i 0.664466π0.664466\pi
462462 0 0
463463 32715.0i 0.152611i 0.997084 + 0.0763053i 0.0243124π0.0243124\pi
−0.997084 + 0.0763053i 0.975688π0.975688\pi
464464 0 0
465465 0 0
466466 0 0
467467 153186. 265325.i 0.702400 1.21659i −0.265222 0.964187i 0.585445π-0.585445\pi
0.967622 0.252405i 0.0812214π-0.0812214\pi
468468 0 0
469469 −321083. 184705.i −1.45973 0.839717i
470470 0 0
471471 23586.1 40852.3i 0.106320 0.184151i
472472 0 0
473473 −53686.7 + 30996.0i −0.239963 + 0.138543i
474474 0 0
475475 0 0
476476 0 0
477477 159370.i 0.700438i
478478 0 0
479479 226801. 130944.i 0.988493 0.570707i 0.0836697 0.996494i 0.473336π-0.473336\pi
0.904824 + 0.425787i 0.140003π0.140003\pi
480480 0 0
481481 87958.7 + 50783.0i 0.380180 + 0.219497i
482482 0 0
483483 −49842.8 + 28881.3i −0.213653 + 0.123801i
484484 0 0
485485 0 0
486486 0 0
487487 −71235.3 + 41127.7i −0.300357 + 0.173411i −0.642603 0.766199i 0.722146π-0.722146\pi
0.342246 + 0.939610i 0.388812π0.388812\pi
488488 0 0
489489 48457.2i 0.202647i
490490 0 0
491491 −102923. −0.426924 −0.213462 0.976951i 0.568474π-0.568474\pi
−0.213462 + 0.976951i 0.568474π0.568474\pi
492492 0 0
493493 −53356.5 92416.2i −0.219530 0.380237i
494494 0 0
495495 0 0
496496 0 0
497497 −186101. 321170.i −0.753420 1.30024i
498498 0 0
499499 75028.2 129953.i 0.301317 0.521896i −0.675118 0.737710i 0.735907π-0.735907\pi
0.976434 + 0.215814i 0.0692405π0.0692405\pi
500500 0 0
501501 −10089.3 17475.2i −0.0401962 0.0696219i
502502 0 0
503503 91806.6 0.362859 0.181430 0.983404i 0.441928π-0.441928\pi
0.181430 + 0.983404i 0.441928π0.441928\pi
504504 0 0
505505 0 0
506506 0 0
507507 7839.66 + 13578.7i 0.0304987 + 0.0528253i
508508 0 0
509509 412600. + 238215.i 1.59255 + 0.919460i 0.992867 + 0.119224i 0.0380405π0.0380405\pi
0.599684 + 0.800237i 0.295293π0.295293\pi
510510 0 0
511511 92656.9 161071.i 0.354843 0.616843i
512512 0 0
513513 −96927.3 55961.0i −0.368308 0.212643i
514514 0 0
515515 0 0
516516 0 0
517517 15721.7 0.0588192
518518 0 0
519519 24623.1 0.0914128
520520 0 0
521521 147768. 85314.0i 0.544384 0.314300i −0.202470 0.979289i 0.564897π-0.564897\pi
0.746854 + 0.664988i 0.231563π0.231563\pi
522522 0 0
523523 −49098.2 + 85040.5i −0.179499 + 0.310901i −0.941709 0.336428i 0.890781π-0.890781\pi
0.762210 + 0.647330i 0.224114π0.224114\pi
524524 0 0
525525 0 0
526526 0 0
527527 −153353. 88538.3i −0.552167 0.318794i
528528 0 0
529529 140707. + 243711.i 0.502810 + 0.870892i
530530 0 0
531531 91977.0i 0.326205i
532532 0 0
533533 337430.i 1.18776i
534534 0 0
535535 0 0
536536 0 0
537537 −25097.3 + 43469.7i −0.0870318 + 0.150743i
538538 0 0
539539 56450.5 177.461i 0.194308 0.000610838i
540540 0 0
541541 52833.7 91510.6i 0.180516 0.312663i −0.761540 0.648118i 0.775557π-0.775557\pi
0.942056 + 0.335454i 0.108890π0.108890\pi
542542 0 0
543543 −65188.2 + 37636.4i −0.221090 + 0.127646i
544544 0 0
545545 0 0
546546 0 0
547547 127121.i 0.424855i 0.977177 + 0.212428i 0.0681370π0.0681370\pi
−0.977177 + 0.212428i 0.931863π0.931863\pi
548548 0 0
549549 −158807. + 91687.0i −0.526895 + 0.304203i
550550 0 0
551551 −157391. 90869.5i −0.518413 0.299306i
552552 0 0
553553 −381938. + 600.340i −1.24894 + 0.00196312i
554554 0 0
555555 0 0
556556 0 0
557557 −26407.6 + 15246.5i −0.0851176 + 0.0491427i −0.541955 0.840408i 0.682316π-0.682316\pi
0.456837 + 0.889550i 0.348982π0.348982\pi
558558 0 0
559559 359300.i 1.14983i
560560 0 0
561561 −9685.01 −0.0307733
562562 0 0
563563 265237. + 459404.i 0.836791 + 1.44936i 0.892564 + 0.450921i 0.148905π0.148905\pi
−0.0557725 + 0.998444i 0.517762π0.517762\pi
564564 0 0
565565 0 0
566566 0 0
567567 −145834. + 253511.i −0.453621 + 0.788554i
568568 0 0
569569 −169366. + 293351.i −0.523121 + 0.906072i 0.476517 + 0.879165i 0.341899π0.341899\pi
−0.999638 + 0.0269067i 0.991434π0.991434\pi
570570 0 0
571571 53455.6 + 92587.8i 0.163954 + 0.283976i 0.936283 0.351246i 0.114242π-0.114242\pi
−0.772330 + 0.635222i 0.780909π0.780909\pi
572572 0 0
573573 6992.33 0.0212967
574574 0 0
575575 0 0
576576 0 0
577577 60238.8 + 104337.i 0.180936 + 0.313390i 0.942200 0.335052i 0.108754π-0.108754\pi
−0.761264 + 0.648443i 0.775421π0.775421\pi
578578 0 0
579579 39954.4 + 23067.7i 0.119181 + 0.0688093i
580580 0 0
581581 −53590.0 92484.6i −0.158757 0.273979i
582582 0 0
583583 41317.9 + 23854.9i 0.121563 + 0.0701844i
584584 0 0
585585 0 0
586586 0 0
587587 525818. 1.52602 0.763008 0.646389i 0.223722π-0.223722\pi
0.763008 + 0.646389i 0.223722π0.223722\pi
588588 0 0
589589 −301573. −0.869283
590590 0 0
591591 −32366.0 + 18686.5i −0.0926648 + 0.0535000i
592592 0 0
593593 37113.8 64283.0i 0.105542 0.182804i −0.808417 0.588610i 0.799676π-0.799676\pi
0.913960 + 0.405805i 0.133009π0.133009\pi
594594 0 0
595595 0 0
596596 0 0
597597 −66349.1 38306.7i −0.186160 0.107480i
598598 0 0
599599 10990.7 + 19036.5i 0.0306318 + 0.0530558i 0.880935 0.473237i 0.156915π-0.156915\pi
−0.850303 + 0.526293i 0.823581π0.823581\pi
600600 0 0
601601 77418.2i 0.214336i −0.994241 0.107168i 0.965822π-0.965822\pi
0.994241 0.107168i 0.0341782π-0.0341782\pi
602602 0 0
603603 593710.i 1.63282i
604604 0 0
605605 0 0
606606 0 0
607607 89931.2 155765.i 0.244081 0.422760i −0.717792 0.696257i 0.754847π-0.754847\pi
0.961873 + 0.273498i 0.0881805π0.0881805\pi
608608 0 0
609609 15586.9 27095.5i 0.0420266 0.0730572i
610610 0 0
611611 −45560.7 + 78913.5i −0.122042 + 0.211382i
612612 0 0
613613 544968. 314637.i 1.45027 0.837316i 0.451777 0.892131i 0.350790π-0.350790\pi
0.998497 + 0.0548147i 0.0174568π0.0174568\pi
614614 0 0
615615 0 0
616616 0 0
617617 52877.1i 0.138899i 0.997585 + 0.0694493i 0.0221242π0.0221242\pi
−0.997585 + 0.0694493i 0.977876π0.977876\pi
618618 0 0
619619 −447040. + 258099.i −1.16672 + 0.673603i −0.952904 0.303271i 0.901921π-0.901921\pi
−0.213811 + 0.976875i 0.568588π0.568588\pi
620620 0 0
621621 −162429. 93778.6i −0.421193 0.243176i
622622 0 0
623623 715.955 + 455493.i 0.00184463 + 1.17356i
624624 0 0
625625 0 0
626626 0 0
627627 −14284.4 + 8247.09i −0.0363351 + 0.0209781i
628628 0 0
629629 195651.i 0.494515i
630630 0 0
631631 193439. 0.485831 0.242915 0.970047i 0.421896π-0.421896\pi
0.242915 + 0.970047i 0.421896π0.421896\pi
632632 0 0
633633 7518.31 + 13022.1i 0.0187635 + 0.0324993i
634634 0 0
635635 0 0
636636 0 0
637637 −162700. + 283862.i −0.400967 + 0.699565i
638638 0 0
639639 297475. 515242.i 0.728532 1.26185i
640640 0 0
641641 −376563. 652226.i −0.916477 1.58738i −0.804725 0.593648i 0.797687π-0.797687\pi
−0.111751 0.993736i 0.535646π-0.535646\pi
642642 0 0
643643 −7110.23 −0.0171974 −0.00859868 0.999963i 0.502737π-0.502737\pi
−0.00859868 + 0.999963i 0.502737π0.502737\pi
644644 0 0
645645 0 0
646646 0 0
647647 197343. + 341808.i 0.471426 + 0.816534i 0.999466 0.0326859i 0.0104061π-0.0104061\pi
−0.528040 + 0.849220i 0.677073π0.677073\pi
648648 0 0
649649 −23845.8 13767.4i −0.0566137 0.0326860i
650650 0 0
651651 −81.5306 51870.0i −0.000192380 0.122392i
652652 0 0
653653 −200186. 115578.i −0.469470 0.271049i 0.246548 0.969131i 0.420704π-0.420704\pi
−0.716018 + 0.698082i 0.754037π0.754037\pi
654654 0 0
655655 0 0
656656 0 0
657657 297833. 0.689989
658658 0 0
659659 772498. 1.77880 0.889399 0.457131i 0.151123π-0.151123\pi
0.889399 + 0.457131i 0.151123π0.151123\pi
660660 0 0
661661 −195287. + 112749.i −0.446962 + 0.258053i −0.706546 0.707667i 0.749748π-0.749748\pi
0.259584 + 0.965720i 0.416414π0.416414\pi
662662 0 0
663663 28066.7 48612.9i 0.0638504 0.110592i
664664 0 0
665665 0 0
666666 0 0
667667 −263753. 152278.i −0.592851 0.342282i
668668 0 0
669669 −43137.7 74716.6i −0.0963839 0.166942i
670670 0 0
671671 54895.8i 0.121925i
672672 0 0
673673 59564.6i 0.131510i 0.997836 + 0.0657549i 0.0209455π0.0209455\pi
−0.997836 + 0.0657549i 0.979054π0.979054\pi
674674 0 0
675675 0 0
676676 0 0
677677 396715. 687131.i 0.865569 1.49921i −0.000912440 1.00000i 0.500290π-0.500290\pi
0.866481 0.499210i 0.166376π-0.166376\pi
678678 0 0
679679 −245222. 423199.i −0.531888 0.917921i
680680 0 0
681681 6811.56 11798.0i 0.0146876 0.0254397i
682682 0 0
683683 −80201.3 + 46304.3i −0.171925 + 0.0992612i −0.583493 0.812118i 0.698315π-0.698315\pi
0.411568 + 0.911379i 0.364981π0.364981\pi
684684 0 0
685685 0 0
686686 0 0
687687 11348.4i 0.0240447i
688688 0 0
689689 −239474. + 138261.i −0.504453 + 0.291246i
690690 0 0
691691 −162273. 93688.2i −0.339852 0.196213i 0.320355 0.947298i 0.396198π-0.396198\pi
−0.660206 + 0.751084i 0.729531π0.729531\pi
692692 0 0
693693 45362.9 + 78286.5i 0.0944571 + 0.163012i
694694 0 0
695695 0 0
696696 0 0
697697 562921. 325003.i 1.15873 0.668993i
698698 0 0
699699 13881.4i 0.0284105i
700700 0 0
701701 326056. 0.663522 0.331761 0.943363i 0.392357π-0.392357\pi
0.331761 + 0.943363i 0.392357π0.392357\pi
702702 0 0
703703 166603. + 288564.i 0.337110 + 0.583891i
704704 0 0
705705 0 0
706706 0 0
707707 33132.0 + 19059.4i 0.0662841 + 0.0381303i
708708 0 0
709709 32372.6 56070.9i 0.0643998 0.111544i −0.832028 0.554734i 0.812820π-0.812820\pi
0.896428 + 0.443190i 0.146153π0.146153\pi
710710 0 0
711711 −306086. 530157.i −0.605487 1.04873i
712712 0 0
713713 −505371. −0.994102
714714 0 0
715715 0 0
716716 0 0
717717 69432.6 + 120261.i 0.135060 + 0.233930i
718718 0 0
719719 616355. + 355853.i 1.19227 + 0.688355i 0.958820 0.284014i 0.0916664π-0.0916664\pi
0.233446 + 0.972370i 0.425000π0.425000\pi
720720 0 0
721721 134882. 212.011i 0.259468 0.000407838i
722722 0 0
723723 83744.0 + 48349.6i 0.160205 + 0.0924946i
724724 0 0
725725 0 0
726726 0 0
727727 763134. 1.44388 0.721941 0.691954i 0.243250π-0.243250\pi
0.721941 + 0.691954i 0.243250π0.243250\pi
728728 0 0
729729 −436942. −0.822183
730730 0 0
731731 599404. 346066.i 1.12172 0.647626i
732732 0 0
733733 10304.6 17848.0i 0.0191788 0.0332187i −0.856277 0.516517i 0.827228π-0.827228\pi
0.875456 + 0.483299i 0.160561π0.160561\pi
734734 0 0
735735 0 0
736736 0 0
737737 −153924. 88868.0i −0.283381 0.163610i
738738 0 0
739739 −393194. 681032.i −0.719976 1.24703i −0.961009 0.276518i 0.910819π-0.910819\pi
0.241033 0.970517i 0.422514π-0.422514\pi
740740 0 0
741741 95598.6i 0.174107i
742742 0 0
743743 740479.i 1.34133i 0.741761 + 0.670664i 0.233991π0.233991\pi
−0.741761 + 0.670664i 0.766009π0.766009\pi
744744 0 0
745745 0 0
746746 0 0
747747 85661.3 148370.i 0.153512 0.265891i
748748 0 0
749749 −1144.42 728086.i −0.00203997 1.29783i
750750 0 0
751751 247292. 428322.i 0.438460 0.759436i −0.559111 0.829093i 0.688857π-0.688857\pi
0.997571 + 0.0696574i 0.0221906π0.0221906\pi
752752 0 0
753753 −78545.5 + 45348.3i −0.138526 + 0.0799780i
754754 0 0
755755 0 0
756756 0 0
757757 139399.i 0.243258i 0.992576 + 0.121629i 0.0388118π0.0388118\pi
−0.992576 + 0.121629i 0.961188π0.961188\pi
758758 0 0
759759 −23937.5 + 13820.3i −0.0415524 + 0.0239903i
760760 0 0
761761 −207340. 119708.i −0.358025 0.206706i 0.310189 0.950675i 0.399608π-0.399608\pi
−0.668214 + 0.743969i 0.732941π0.732941\pi
762762 0 0
763763 67354.1 117085.i 0.115695 0.201119i
764764 0 0
765765 0 0
766766 0 0
767767 138208. 79794.1i 0.234931 0.135638i
768768 0 0
769769 98701.5i 0.166906i −0.996512 0.0834528i 0.973405π-0.973405\pi
0.996512 0.0834528i 0.0265948π-0.0265948\pi
770770 0 0
771771 −110051. −0.185134
772772 0 0
773773 −293248. 507921.i −0.490769 0.850036i 0.509175 0.860663i 0.329951π-0.329951\pi
−0.999944 + 0.0106268i 0.996617π0.996617\pi
774774 0 0
775775 0 0
776776 0 0
777777 −49587.5 + 28733.4i −0.0821354 + 0.0475932i
778778 0 0
779779 553500. 958690.i 0.912100 1.57980i
780780 0 0
781781 −89053.6 154245.i −0.145999 0.252877i
782782 0 0
783783 101775. 0.166003
784784 0 0
785785 0 0
786786 0 0
787787 74787.4 + 129536.i 0.120748 + 0.209141i 0.920063 0.391771i 0.128137π-0.128137\pi
−0.799315 + 0.600912i 0.794804π0.794804\pi
788788 0 0
789789 −30226.8 17451.4i −0.0485554 0.0280335i
790790 0 0
791791 265606. 153905.i 0.424507 0.245980i
792792 0 0
793793 −275544. 159085.i −0.438171 0.252978i
794794 0 0
795795 0 0
796796 0 0
797797 241092. 0.379547 0.189774 0.981828i 0.439225π-0.439225\pi
0.189774 + 0.981828i 0.439225π0.439225\pi
798798 0 0
799799 −175531. −0.274954
800800 0 0
801801 −632256. + 365033.i −0.985436 + 0.568941i
802802 0 0
803803 44580.4 77215.6i 0.0691374 0.119750i
804804 0 0
805805 0 0
806806 0 0
807807 63291.3 + 36541.3i 0.0971845 + 0.0561095i
808808 0 0
809809 100933. + 174820.i 0.154218 + 0.267113i 0.932774 0.360462i 0.117381π-0.117381\pi
−0.778556 + 0.627575i 0.784048π0.784048\pi
810810 0 0
811811 1.16747e6i 1.77503i −0.460779 0.887515i 0.652430π-0.652430\pi
0.460779 0.887515i 0.347570π-0.347570\pi
812812 0 0
813813 130389.i 0.197270i
814814 0 0
815815 0 0
816816 0 0
817817 589373. 1.02082e6i 0.882970 1.52935i
818818 0 0
819819 −524410. + 824.281i −0.781814 + 0.00122887i
820820 0 0
821821 324585. 562198.i 0.481551 0.834071i −0.518225 0.855245i 0.673407π-0.673407\pi
0.999776 + 0.0211734i 0.00674022π0.00674022\pi
822822 0 0
823823 −425193. + 245486.i −0.627750 + 0.362432i −0.779880 0.625929i 0.784720π-0.784720\pi
0.152130 + 0.988360i 0.451387π0.451387\pi
824824 0 0
825825 0 0
826826 0 0
827827 709017.i 1.03668i 0.855174 + 0.518341i 0.173450π0.173450\pi
−0.855174 + 0.518341i 0.826550π0.826550\pi
828828 0 0
829829 −534645. + 308677.i −0.777958 + 0.449154i −0.835706 0.549177i 0.814941π-0.814941\pi
0.0577480 + 0.998331i 0.481608π0.481608\pi
830830 0 0
831831 −12269.3 7083.68i −0.0177671 0.0102579i
832832 0 0
833833 −630262. + 1981.33i −0.908304 + 0.00285540i
834834 0 0
835835 0 0
836836 0 0
837837 146256. 84441.0i 0.208768 0.120532i
838838 0 0
839839 493961.i 0.701728i 0.936426 + 0.350864i 0.114112π0.114112\pi
−0.936426 + 0.350864i 0.885888π0.885888\pi
840840 0 0
841841 −542019. −0.766342
842842 0 0
843843 −50363.7 87232.4i −0.0708699 0.122750i
844844 0 0
845845 0 0
846846 0 0
847847 −690322. + 1085.07i −0.962243 + 0.00151248i
848848 0 0
849849 17724.8 30700.2i 0.0245904 0.0425918i
850850 0 0
851851 279190. + 483571.i 0.385514 + 0.667730i
852852 0 0
853853 505142. 0.694249 0.347124 0.937819i 0.387158π-0.387158\pi
0.347124 + 0.937819i 0.387158π0.387158\pi
854854 0 0
855855 0 0
856856 0 0
857857 560018. + 969980.i 0.762501 + 1.32069i 0.941557 + 0.336852i 0.109362π0.109362\pi
−0.179056 + 0.983839i 0.557304π0.557304\pi
858858 0 0
859859 605141. + 349379.i 0.820107 + 0.473489i 0.850453 0.526050i 0.176328π-0.176328\pi
−0.0303463 + 0.999539i 0.509661π0.509661\pi
860860 0 0
861861 165043. + 94941.9i 0.222633 + 0.128071i
862862 0 0
863863 −830576. 479533.i −1.11521 0.643868i −0.175038 0.984562i 0.556005π-0.556005\pi
−0.940175 + 0.340693i 0.889338π0.889338\pi
864864 0 0
865865 0 0
866866 0 0
867867 −22933.1 −0.0305088
868868 0 0
869869 −183263. −0.242681
870870 0 0
871871 892127. 515069.i 1.17595 0.678937i
872872 0 0
873873 391976. 678923.i 0.514318 0.890824i
874874 0 0
875875 0 0
876876 0 0
877877 −863326. 498442.i −1.12247 0.648060i −0.180442 0.983586i 0.557753π-0.557753\pi
−0.942031 + 0.335526i 0.891086π0.891086\pi
878878 0 0
879879 102372. + 177314.i 0.132497 + 0.229491i
880880 0 0
881881 494568.i 0.637198i −0.947890 0.318599i 0.896788π-0.896788\pi
0.947890 0.318599i 0.103212π-0.103212\pi
882882 0 0
883883 887278.i 1.13799i 0.822341 + 0.568995i 0.192667π0.192667\pi
−0.822341 + 0.568995i 0.807333π0.807333\pi
884884 0 0
885885 0 0
886886 0 0
887887 312960. 542062.i 0.397779 0.688973i −0.595673 0.803227i 0.703115π-0.703115\pi
0.993452 + 0.114254i 0.0364479π0.0364479\pi
888888 0 0
889889 −545008. + 315804.i −0.689604 + 0.399589i
890890 0 0
891891 −70165.8 + 121531.i −0.0883833 + 0.153084i
892892 0 0
893893 −258890. + 149470.i −0.324647 + 0.187435i
894894 0 0
895895 0 0
896896 0 0
897897 160203.i 0.199106i
898898 0 0
899899 237491. 137115.i 0.293851 0.169655i
900900 0 0
901901 −461309. 266337.i −0.568253 0.328081i
902902 0 0
903903 175739. + 101095.i 0.215523 + 0.123981i
904904 0 0
905905 0 0
906906 0 0
907907 1.09835e6 634131.i 1.33513 0.770840i 0.349052 0.937103i 0.386504π-0.386504\pi
0.986081 + 0.166263i 0.0531702π0.0531702\pi
908908 0 0
909909 61263.9i 0.0741442i
910910 0 0
911911 −1.09985e6 −1.32525 −0.662625 0.748951i 0.730558π-0.730558\pi
−0.662625 + 0.748951i 0.730558π0.730558\pi
912912 0 0
913913 −25644.0 44416.7i −0.0307641 0.0532850i
914914 0 0
915915 0 0
916916 0 0
917917 1904.30 + 1.21152e6i 0.00226463 + 1.44076i
918918 0 0
919919 430660. 745925.i 0.509922 0.883211i −0.490012 0.871716i 0.663008π-0.663008\pi
0.999934 0.0114950i 0.00365905π-0.00365905\pi
920920 0 0
921921 44075.3 + 76340.6i 0.0519608 + 0.0899987i
922922 0 0
923923 1.03229e6 1.21171
924924 0 0
925925 0 0
926926 0 0
927927 108095. + 187226.i 0.125790 + 0.217874i
928928 0 0
929929 326247. + 188359.i 0.378021 + 0.218250i 0.676957 0.736023i 0.263298π-0.263298\pi
−0.298936 + 0.954273i 0.596632π0.596632\pi
930930 0 0
931931 −927884. + 539610.i −1.07052 + 0.622560i
932932 0 0
933933 −62906.7 36319.2i −0.0722659 0.0417227i
934934 0 0
935935 0 0
936936 0 0
937937 417813. 0.475885 0.237943 0.971279i 0.423527π-0.423527\pi
0.237943 + 0.971279i 0.423527π0.423527\pi
938938 0 0
939939 −217103. −0.246227
940940 0 0
941941 213031. 122994.i 0.240582 0.138900i −0.374862 0.927081i 0.622310π-0.622310\pi
0.615444 + 0.788180i 0.288977π0.288977\pi
942942 0 0
943943 927546. 1.60656e6i 1.04307 1.80665i
944944 0 0
945945 0 0
946946 0 0
947947 −1.25221e6 722964.i −1.39630 0.806152i −0.402294 0.915511i 0.631787π-0.631787\pi
−0.994002 + 0.109359i 0.965120π0.965120\pi
948948 0 0
949949 258384. + 447533.i 0.286901 + 0.496928i
950950 0 0
951951 91495.4i 0.101167i
952952 0 0
953953 907377.i 0.999084i 0.866290 + 0.499542i 0.166498π0.166498\pi
−0.866290 + 0.499542i 0.833502π0.833502\pi
954954 0 0
955955 0 0
956956 0 0
957957 7499.38 12989.3i 0.00818845 0.0141828i
958958 0 0
959959 56156.9 + 32304.6i 0.0610612 + 0.0351259i
960960 0 0
961961 −234235. + 405707.i −0.253633 + 0.439305i
962962 0 0
963963 1.01064e6 583491.i 1.08979 0.629189i
964964 0 0
965965 0 0
966966 0 0
967967 50286.2i 0.0537770i 0.999638 + 0.0268885i 0.00855990π0.00855990\pi
−0.999638 + 0.0268885i 0.991440π0.991440\pi
968968 0 0
969969 159483. 92077.6i 0.169851 0.0980633i
970970 0 0
971971 677500. + 391155.i 0.718573 + 0.414868i 0.814227 0.580546i 0.197161π-0.197161\pi
−0.0956544 + 0.995415i 0.530494π0.530494\pi
972972 0 0
973973 217062. 125776.i 0.229275 0.132853i
974974 0 0
975975 0 0
976976 0 0
977977 −1.10629e6 + 638714.i −1.15899 + 0.669141i −0.951061 0.309004i 0.900004π-0.900004\pi
−0.207925 + 0.978145i 0.566671π0.566671\pi
978978 0 0
979979 218557.i 0.228033i
980980 0 0
981981 216501. 0.224968
982982 0 0
983983 786638. + 1.36250e6i 0.814081 + 1.41003i 0.909986 + 0.414639i 0.136092π0.136092\pi
−0.0959049 + 0.995391i 0.530574π0.530574\pi
984984 0 0
985985 0 0
986986 0 0
987987 −25778.6 44488.2i −0.0264621 0.0456679i
988988 0 0
989989 987661. 1.71068e6i 1.00975 1.74894i
990990 0 0
991991 −162173. 280892.i −0.165132 0.286017i 0.771570 0.636144i 0.219472π-0.219472\pi
−0.936702 + 0.350127i 0.886138π0.886138\pi
992992 0 0
993993 1552.30 0.00157427
994994 0 0
995995 0 0
996996 0 0
997997 907185. + 1.57129e6i 0.912652 + 1.58076i 0.810303 + 0.586012i 0.199303π0.199303\pi
0.102350 + 0.994748i 0.467364π0.467364\pi
998998 0 0
999999 −161597. 93298.2i −0.161921 0.0934851i
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 700.5.o.a.649.3 12
5.2 odd 4 28.5.h.a.5.2 6
5.3 odd 4 700.5.s.a.201.2 6
5.4 even 2 inner 700.5.o.a.649.4 12
7.3 odd 6 inner 700.5.o.a.549.4 12
15.2 even 4 252.5.z.f.145.1 6
20.7 even 4 112.5.s.c.33.2 6
35.2 odd 12 196.5.b.a.97.3 6
35.3 even 12 700.5.s.a.101.2 6
35.12 even 12 196.5.b.a.97.4 6
35.17 even 12 28.5.h.a.17.2 yes 6
35.24 odd 6 inner 700.5.o.a.549.3 12
35.27 even 4 196.5.h.c.117.2 6
35.32 odd 12 196.5.h.c.129.2 6
105.17 odd 12 252.5.z.f.73.1 6
140.47 odd 12 784.5.c.e.97.3 6
140.87 odd 12 112.5.s.c.17.2 6
140.107 even 12 784.5.c.e.97.4 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.5.h.a.5.2 6 5.2 odd 4
28.5.h.a.17.2 yes 6 35.17 even 12
112.5.s.c.17.2 6 140.87 odd 12
112.5.s.c.33.2 6 20.7 even 4
196.5.b.a.97.3 6 35.2 odd 12
196.5.b.a.97.4 6 35.12 even 12
196.5.h.c.117.2 6 35.27 even 4
196.5.h.c.129.2 6 35.32 odd 12
252.5.z.f.73.1 6 105.17 odd 12
252.5.z.f.145.1 6 15.2 even 4
700.5.o.a.549.3 12 35.24 odd 6 inner
700.5.o.a.549.4 12 7.3 odd 6 inner
700.5.o.a.649.3 12 1.1 even 1 trivial
700.5.o.a.649.4 12 5.4 even 2 inner
700.5.s.a.101.2 6 35.3 even 12
700.5.s.a.201.2 6 5.3 odd 4
784.5.c.e.97.3 6 140.47 odd 12
784.5.c.e.97.4 6 140.107 even 12