Properties

Label 693.4.a.t.1.2
Level 693693
Weight 44
Character 693.1
Self dual yes
Analytic conductor 40.88840.888
Analytic rank 00
Dimension 88
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [693,4,Mod(1,693)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(693, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("693.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 693=32711 693 = 3^{2} \cdot 7 \cdot 11
Weight: k k == 4 4
Character orbit: [χ][\chi] == 693.a (trivial)

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: yes
Analytic conductor: 40.888323634040.8883236340
Analytic rank: 00
Dimension: 88
Coefficient field: Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x82x745x6+77x5+540x4915x31452x2+2660x672 x^{8} - 2x^{7} - 45x^{6} + 77x^{5} + 540x^{4} - 915x^{3} - 1452x^{2} + 2660x - 672 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 23 2^{3}
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 3.85529-3.85529 of defining polynomial
Character χ\chi == 693.1

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) == q3.85529q2+6.86327q45.82801q57.00000q7+4.38244q8+22.4687q1011.0000q1187.1386q13+26.9870q1471.8017q16+119.043q17+23.9715q1939.9992q20+42.4082q22119.203q2391.0343q25+335.945q2648.0429q28+53.7711q2969.0226q31+241.757q32458.946q34+40.7961q35+28.6224q3792.4171q3825.5409q40419.188q4140.0463q4375.4959q44+459.562q4674.1512q47+49.0000q49+350.964q50598.055q52+244.861q53+64.1081q5530.6770q56207.303q58+365.224q59456.885q61+266.102q62357.630q64+507.844q65470.272q67+817.025q68157.281q70359.954q71902.375q73110.348q74+164.523q76+77.0000q77+707.463q79+418.461q80+1616.09q82541.450q83693.784q85+154.390q8648.2068q88+559.797q89+609.970q91818.122q92+285.875q94139.706q95+1524.76q97188.909q98+O(q100)q-3.85529 q^{2} +6.86327 q^{4} -5.82801 q^{5} -7.00000 q^{7} +4.38244 q^{8} +22.4687 q^{10} -11.0000 q^{11} -87.1386 q^{13} +26.9870 q^{14} -71.8017 q^{16} +119.043 q^{17} +23.9715 q^{19} -39.9992 q^{20} +42.4082 q^{22} -119.203 q^{23} -91.0343 q^{25} +335.945 q^{26} -48.0429 q^{28} +53.7711 q^{29} -69.0226 q^{31} +241.757 q^{32} -458.946 q^{34} +40.7961 q^{35} +28.6224 q^{37} -92.4171 q^{38} -25.5409 q^{40} -419.188 q^{41} -40.0463 q^{43} -75.4959 q^{44} +459.562 q^{46} -74.1512 q^{47} +49.0000 q^{49} +350.964 q^{50} -598.055 q^{52} +244.861 q^{53} +64.1081 q^{55} -30.6770 q^{56} -207.303 q^{58} +365.224 q^{59} -456.885 q^{61} +266.102 q^{62} -357.630 q^{64} +507.844 q^{65} -470.272 q^{67} +817.025 q^{68} -157.281 q^{70} -359.954 q^{71} -902.375 q^{73} -110.348 q^{74} +164.523 q^{76} +77.0000 q^{77} +707.463 q^{79} +418.461 q^{80} +1616.09 q^{82} -541.450 q^{83} -693.784 q^{85} +154.390 q^{86} -48.2068 q^{88} +559.797 q^{89} +609.970 q^{91} -818.122 q^{92} +285.875 q^{94} -139.706 q^{95} +1524.76 q^{97} -188.909 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+2q2+30q4+10q556q7+15q813q1088q11148q1314q14+266q16+114q17+58q19+291q2022q22+246q23+244q25+305q26++98q98+O(q100) 8 q + 2 q^{2} + 30 q^{4} + 10 q^{5} - 56 q^{7} + 15 q^{8} - 13 q^{10} - 88 q^{11} - 148 q^{13} - 14 q^{14} + 266 q^{16} + 114 q^{17} + 58 q^{19} + 291 q^{20} - 22 q^{22} + 246 q^{23} + 244 q^{25} + 305 q^{26}+ \cdots + 98 q^{98}+O(q^{100}) Copy content Toggle raw display

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 −3.85529 −1.36305 −0.681526 0.731794i 0.738683π-0.738683\pi
−0.681526 + 0.731794i 0.738683π0.738683\pi
33 0 0
44 6.86327 0.857908
55 −5.82801 −0.521273 −0.260636 0.965437i 0.583932π-0.583932\pi
−0.260636 + 0.965437i 0.583932π0.583932\pi
66 0 0
77 −7.00000 −0.377964
88 4.38244 0.193678
99 0 0
1010 22.4687 0.710522
1111 −11.0000 −0.301511
1212 0 0
1313 −87.1386 −1.85907 −0.929535 0.368735i 0.879791π-0.879791\pi
−0.929535 + 0.368735i 0.879791π0.879791\pi
1414 26.9870 0.515185
1515 0 0
1616 −71.8017 −1.12190
1717 119.043 1.69836 0.849182 0.528100i 0.177095π-0.177095\pi
0.849182 + 0.528100i 0.177095π0.177095\pi
1818 0 0
1919 23.9715 0.289444 0.144722 0.989472i 0.453771π-0.453771\pi
0.144722 + 0.989472i 0.453771π0.453771\pi
2020 −39.9992 −0.447204
2121 0 0
2222 42.4082 0.410975
2323 −119.203 −1.08068 −0.540338 0.841448i 0.681704π-0.681704\pi
−0.540338 + 0.841448i 0.681704π0.681704\pi
2424 0 0
2525 −91.0343 −0.728275
2626 335.945 2.53401
2727 0 0
2828 −48.0429 −0.324259
2929 53.7711 0.344312 0.172156 0.985070i 0.444927π-0.444927\pi
0.172156 + 0.985070i 0.444927π0.444927\pi
3030 0 0
3131 −69.0226 −0.399898 −0.199949 0.979806i 0.564078π-0.564078\pi
−0.199949 + 0.979806i 0.564078π0.564078\pi
3232 241.757 1.33553
3333 0 0
3434 −458.946 −2.31496
3535 40.7961 0.197023
3636 0 0
3737 28.6224 0.127176 0.0635878 0.997976i 0.479746π-0.479746\pi
0.0635878 + 0.997976i 0.479746π0.479746\pi
3838 −92.4171 −0.394527
3939 0 0
4040 −25.5409 −0.100959
4141 −419.188 −1.59674 −0.798369 0.602169i 0.794303π-0.794303\pi
−0.798369 + 0.602169i 0.794303π0.794303\pi
4242 0 0
4343 −40.0463 −0.142023 −0.0710117 0.997475i 0.522623π-0.522623\pi
−0.0710117 + 0.997475i 0.522623π0.522623\pi
4444 −75.4959 −0.258669
4545 0 0
4646 459.562 1.47302
4747 −74.1512 −0.230129 −0.115065 0.993358i 0.536707π-0.536707\pi
−0.115065 + 0.993358i 0.536707π0.536707\pi
4848 0 0
4949 49.0000 0.142857
5050 350.964 0.992676
5151 0 0
5252 −598.055 −1.59491
5353 244.861 0.634608 0.317304 0.948324i 0.397223π-0.397223\pi
0.317304 + 0.948324i 0.397223π0.397223\pi
5454 0 0
5555 64.1081 0.157170
5656 −30.6770 −0.0732034
5757 0 0
5858 −207.303 −0.469315
5959 365.224 0.805900 0.402950 0.915222i 0.367985π-0.367985\pi
0.402950 + 0.915222i 0.367985π0.367985\pi
6060 0 0
6161 −456.885 −0.958986 −0.479493 0.877546i 0.659179π-0.659179\pi
−0.479493 + 0.877546i 0.659179π0.659179\pi
6262 266.102 0.545081
6363 0 0
6464 −357.630 −0.698496
6565 507.844 0.969082
6666 0 0
6767 −470.272 −0.857506 −0.428753 0.903422i 0.641047π-0.641047\pi
−0.428753 + 0.903422i 0.641047π0.641047\pi
6868 817.025 1.45704
6969 0 0
7070 −157.281 −0.268552
7171 −359.954 −0.601671 −0.300835 0.953676i 0.597266π-0.597266\pi
−0.300835 + 0.953676i 0.597266π0.597266\pi
7272 0 0
7373 −902.375 −1.44678 −0.723391 0.690439i 0.757417π-0.757417\pi
−0.723391 + 0.690439i 0.757417π0.757417\pi
7474 −110.348 −0.173347
7575 0 0
7676 164.523 0.248317
7777 77.0000 0.113961
7878 0 0
7979 707.463 1.00754 0.503771 0.863837i 0.331945π-0.331945\pi
0.503771 + 0.863837i 0.331945π0.331945\pi
8080 418.461 0.584817
8181 0 0
8282 1616.09 2.17643
8383 −541.450 −0.716047 −0.358024 0.933713i 0.616549π-0.616549\pi
−0.358024 + 0.933713i 0.616549π0.616549\pi
8484 0 0
8585 −693.784 −0.885311
8686 154.390 0.193585
8787 0 0
8888 −48.2068 −0.0583961
8989 559.797 0.666723 0.333362 0.942799i 0.391817π-0.391817\pi
0.333362 + 0.942799i 0.391817π0.391817\pi
9090 0 0
9191 609.970 0.702662
9292 −818.122 −0.927121
9393 0 0
9494 285.875 0.313678
9595 −139.706 −0.150879
9696 0 0
9797 1524.76 1.59604 0.798021 0.602629i 0.205880π-0.205880\pi
0.798021 + 0.602629i 0.205880π0.205880\pi
9898 −188.909 −0.194722
9999 0 0
100100 −624.793 −0.624793
101101 1053.14 1.03754 0.518768 0.854915i 0.326391π-0.326391\pi
0.518768 + 0.854915i 0.326391π0.326391\pi
102102 0 0
103103 43.8955 0.0419917 0.0209959 0.999780i 0.493316π-0.493316\pi
0.0209959 + 0.999780i 0.493316π0.493316\pi
104104 −381.879 −0.360061
105105 0 0
106106 −944.009 −0.865003
107107 449.939 0.406516 0.203258 0.979125i 0.434847π-0.434847\pi
0.203258 + 0.979125i 0.434847π0.434847\pi
108108 0 0
109109 −1315.63 −1.15610 −0.578048 0.816003i 0.696185π-0.696185\pi
−0.578048 + 0.816003i 0.696185π0.696185\pi
110110 −247.155 −0.214230
111111 0 0
112112 502.612 0.424039
113113 −725.136 −0.603673 −0.301837 0.953360i 0.597600π-0.597600\pi
−0.301837 + 0.953360i 0.597600π0.597600\pi
114114 0 0
115115 694.716 0.563327
116116 369.046 0.295388
117117 0 0
118118 −1408.04 −1.09848
119119 −833.302 −0.641921
120120 0 0
121121 121.000 0.0909091
122122 1761.42 1.30715
123123 0 0
124124 −473.720 −0.343075
125125 1259.05 0.900903
126126 0 0
127127 2440.43 1.70514 0.852572 0.522610i 0.175042π-0.175042\pi
0.852572 + 0.522610i 0.175042π0.175042\pi
128128 −555.289 −0.383446
129129 0 0
130130 −1957.89 −1.32091
131131 1258.33 0.839242 0.419621 0.907699i 0.362163π-0.362163\pi
0.419621 + 0.907699i 0.362163π0.362163\pi
132132 0 0
133133 −167.801 −0.109400
134134 1813.04 1.16882
135135 0 0
136136 521.699 0.328936
137137 2790.08 1.73995 0.869974 0.493097i 0.164135π-0.164135\pi
0.869974 + 0.493097i 0.164135π0.164135\pi
138138 0 0
139139 539.573 0.329251 0.164626 0.986356i 0.447358π-0.447358\pi
0.164626 + 0.986356i 0.447358π0.447358\pi
140140 279.994 0.169027
141141 0 0
142142 1387.73 0.820108
143143 958.525 0.560530
144144 0 0
145145 −313.379 −0.179481
146146 3478.92 1.97204
147147 0 0
148148 196.443 0.109105
149149 873.101 0.480049 0.240024 0.970767i 0.422845π-0.422845\pi
0.240024 + 0.970767i 0.422845π0.422845\pi
150150 0 0
151151 1116.95 0.601963 0.300981 0.953630i 0.402686π-0.402686\pi
0.300981 + 0.953630i 0.402686π0.402686\pi
152152 105.054 0.0560590
153153 0 0
154154 −296.857 −0.155334
155155 402.264 0.208456
156156 0 0
157157 3064.79 1.55794 0.778970 0.627061i 0.215742π-0.215742\pi
0.778970 + 0.627061i 0.215742π0.215742\pi
158158 −2727.48 −1.37333
159159 0 0
160160 −1408.96 −0.696176
161161 834.421 0.408457
162162 0 0
163163 4051.58 1.94690 0.973449 0.228902i 0.0735136π-0.0735136\pi
0.973449 + 0.228902i 0.0735136π0.0735136\pi
164164 −2877.00 −1.36985
165165 0 0
166166 2087.45 0.976009
167167 1148.16 0.532021 0.266011 0.963970i 0.414294π-0.414294\pi
0.266011 + 0.963970i 0.414294π0.414294\pi
168168 0 0
169169 5396.14 2.45614
170170 2674.74 1.20672
171171 0 0
172172 −274.848 −0.121843
173173 2605.86 1.14520 0.572601 0.819834i 0.305934π-0.305934\pi
0.572601 + 0.819834i 0.305934π0.305934\pi
174174 0 0
175175 637.240 0.275262
176176 789.819 0.338266
177177 0 0
178178 −2158.18 −0.908778
179179 −3411.18 −1.42438 −0.712188 0.701988i 0.752296π-0.752296\pi
−0.712188 + 0.701988i 0.752296π0.752296\pi
180180 0 0
181181 −641.028 −0.263244 −0.131622 0.991300i 0.542019π-0.542019\pi
−0.131622 + 0.991300i 0.542019π0.542019\pi
182182 −2351.61 −0.957764
183183 0 0
184184 −522.399 −0.209303
185185 −166.812 −0.0662932
186186 0 0
187187 −1309.47 −0.512076
188188 −508.920 −0.197430
189189 0 0
190190 538.608 0.205656
191191 3007.51 1.13935 0.569676 0.821870i 0.307069π-0.307069\pi
0.569676 + 0.821870i 0.307069π0.307069\pi
192192 0 0
193193 294.968 0.110012 0.0550058 0.998486i 0.482482π-0.482482\pi
0.0550058 + 0.998486i 0.482482π0.482482\pi
194194 −5878.40 −2.17549
195195 0 0
196196 336.300 0.122558
197197 −2299.84 −0.831761 −0.415880 0.909419i 0.636527π-0.636527\pi
−0.415880 + 0.909419i 0.636527π0.636527\pi
198198 0 0
199199 −2375.19 −0.846095 −0.423048 0.906107i 0.639040π-0.639040\pi
−0.423048 + 0.906107i 0.639040π0.639040\pi
200200 −398.952 −0.141051
201201 0 0
202202 −4060.15 −1.41422
203203 −376.398 −0.130138
204204 0 0
205205 2443.03 0.832336
206206 −169.230 −0.0572369
207207 0 0
208208 6256.70 2.08569
209209 −263.687 −0.0872707
210210 0 0
211211 −2712.37 −0.884964 −0.442482 0.896777i 0.645902π-0.645902\pi
−0.442482 + 0.896777i 0.645902π0.645902\pi
212212 1680.54 0.544435
213213 0 0
214214 −1734.64 −0.554102
215215 233.390 0.0740329
216216 0 0
217217 483.158 0.151147
218218 5072.13 1.57582
219219 0 0
220220 439.991 0.134837
221221 −10373.3 −3.15738
222222 0 0
223223 −4334.42 −1.30159 −0.650794 0.759255i 0.725564π-0.725564\pi
−0.650794 + 0.759255i 0.725564π0.725564\pi
224224 −1692.30 −0.504783
225225 0 0
226226 2795.61 0.822837
227227 3140.12 0.918138 0.459069 0.888401i 0.348183π-0.348183\pi
0.459069 + 0.888401i 0.348183π0.348183\pi
228228 0 0
229229 5091.07 1.46912 0.734558 0.678546i 0.237390π-0.237390\pi
0.734558 + 0.678546i 0.237390π0.237390\pi
230230 −2678.33 −0.767843
231231 0 0
232232 235.649 0.0666857
233233 −1892.55 −0.532125 −0.266062 0.963956i 0.585723π-0.585723\pi
−0.266062 + 0.963956i 0.585723π0.585723\pi
234234 0 0
235235 432.154 0.119960
236236 2506.63 0.691389
237237 0 0
238238 3212.62 0.874972
239239 −5139.77 −1.39106 −0.695531 0.718496i 0.744831π-0.744831\pi
−0.695531 + 0.718496i 0.744831π0.744831\pi
240240 0 0
241241 −1898.64 −0.507477 −0.253738 0.967273i 0.581660π-0.581660\pi
−0.253738 + 0.967273i 0.581660π0.581660\pi
242242 −466.490 −0.123914
243243 0 0
244244 −3135.72 −0.822722
245245 −285.572 −0.0744675
246246 0 0
247247 −2088.84 −0.538097
248248 −302.487 −0.0774514
249249 0 0
250250 −4854.00 −1.22798
251251 −306.680 −0.0771215 −0.0385607 0.999256i 0.512277π-0.512277\pi
−0.0385607 + 0.999256i 0.512277π0.512277\pi
252252 0 0
253253 1311.23 0.325836
254254 −9408.57 −2.32420
255255 0 0
256256 5001.84 1.22115
257257 3742.75 0.908428 0.454214 0.890893i 0.349920π-0.349920\pi
0.454214 + 0.890893i 0.349920π0.349920\pi
258258 0 0
259259 −200.357 −0.0480679
260260 3485.47 0.831384
261261 0 0
262262 −4851.23 −1.14393
263263 3529.68 0.827564 0.413782 0.910376i 0.364208π-0.364208\pi
0.413782 + 0.910376i 0.364208π0.364208\pi
264264 0 0
265265 −1427.05 −0.330804
266266 646.920 0.149117
267267 0 0
268268 −3227.60 −0.735662
269269 1625.18 0.368361 0.184181 0.982892i 0.441037π-0.441037\pi
0.184181 + 0.982892i 0.441037π0.441037\pi
270270 0 0
271271 2770.60 0.621041 0.310521 0.950567i 0.399497π-0.399497\pi
0.310521 + 0.950567i 0.399497π0.399497\pi
272272 −8547.50 −1.90540
273273 0 0
274274 −10756.6 −2.37164
275275 1001.38 0.219583
276276 0 0
277277 −6395.47 −1.38724 −0.693622 0.720339i 0.743986π-0.743986\pi
−0.693622 + 0.720339i 0.743986π0.743986\pi
278278 −2080.21 −0.448787
279279 0 0
280280 178.786 0.0381590
281281 −5580.81 −1.18478 −0.592390 0.805652i 0.701815π-0.701815\pi
−0.592390 + 0.805652i 0.701815π0.701815\pi
282282 0 0
283283 −3176.32 −0.667182 −0.333591 0.942718i 0.608261π-0.608261\pi
−0.333591 + 0.942718i 0.608261π0.608261\pi
284284 −2470.46 −0.516179
285285 0 0
286286 −3695.39 −0.764032
287287 2934.32 0.603510
288288 0 0
289289 9258.26 1.88444
290290 1208.17 0.244641
291291 0 0
292292 −6193.24 −1.24121
293293 3683.92 0.734528 0.367264 0.930117i 0.380295π-0.380295\pi
0.367264 + 0.930117i 0.380295π0.380295\pi
294294 0 0
295295 −2128.53 −0.420094
296296 125.436 0.0246311
297297 0 0
298298 −3366.06 −0.654331
299299 10387.2 2.00905
300300 0 0
301301 280.324 0.0536798
302302 −4306.18 −0.820506
303303 0 0
304304 −1721.20 −0.324728
305305 2662.73 0.499893
306306 0 0
307307 −6180.56 −1.14900 −0.574501 0.818504i 0.694804π-0.694804\pi
−0.574501 + 0.818504i 0.694804π0.694804\pi
308308 528.472 0.0977677
309309 0 0
310310 −1550.85 −0.284136
311311 −5980.82 −1.09049 −0.545243 0.838278i 0.683563π-0.683563\pi
−0.545243 + 0.838278i 0.683563π0.683563\pi
312312 0 0
313313 4757.98 0.859224 0.429612 0.903014i 0.358650π-0.358650\pi
0.429612 + 0.903014i 0.358650π0.358650\pi
314314 −11815.6 −2.12355
315315 0 0
316316 4855.51 0.864379
317317 −4391.93 −0.778155 −0.389078 0.921205i 0.627206π-0.627206\pi
−0.389078 + 0.921205i 0.627206π0.627206\pi
318318 0 0
319319 −591.483 −0.103814
320320 2084.27 0.364107
321321 0 0
322322 −3216.93 −0.556748
323323 2853.64 0.491582
324324 0 0
325325 7932.60 1.35391
326326 −15620.0 −2.65372
327327 0 0
328328 −1837.07 −0.309253
329329 519.059 0.0869806
330330 0 0
331331 8105.82 1.34603 0.673015 0.739628i 0.264999π-0.264999\pi
0.673015 + 0.739628i 0.264999π0.264999\pi
332332 −3716.12 −0.614303
333333 0 0
334334 −4426.50 −0.725172
335335 2740.75 0.446995
336336 0 0
337337 4039.57 0.652965 0.326482 0.945203i 0.394137π-0.394137\pi
0.326482 + 0.945203i 0.394137π0.394137\pi
338338 −20803.7 −3.34784
339339 0 0
340340 −4761.63 −0.759516
341341 759.248 0.120574
342342 0 0
343343 −343.000 −0.0539949
344344 −175.500 −0.0275068
345345 0 0
346346 −10046.4 −1.56097
347347 8412.95 1.30153 0.650765 0.759279i 0.274448π-0.274448\pi
0.650765 + 0.759279i 0.274448π0.274448\pi
348348 0 0
349349 −7559.52 −1.15946 −0.579730 0.814808i 0.696842π-0.696842\pi
−0.579730 + 0.814808i 0.696842π0.696842\pi
350350 −2456.75 −0.375196
351351 0 0
352352 −2659.33 −0.402678
353353 7724.92 1.16475 0.582374 0.812921i 0.302124π-0.302124\pi
0.582374 + 0.812921i 0.302124π0.302124\pi
354354 0 0
355355 2097.81 0.313635
356356 3842.04 0.571987
357357 0 0
358358 13151.1 1.94150
359359 −920.274 −0.135293 −0.0676465 0.997709i 0.521549π-0.521549\pi
−0.0676465 + 0.997709i 0.521549π0.521549\pi
360360 0 0
361361 −6284.37 −0.916222
362362 2471.35 0.358816
363363 0 0
364364 4186.39 0.602820
365365 5259.05 0.754168
366366 0 0
367367 −2615.68 −0.372037 −0.186018 0.982546i 0.559558π-0.559558\pi
−0.186018 + 0.982546i 0.559558π0.559558\pi
368368 8558.98 1.21241
369369 0 0
370370 643.108 0.0903610
371371 −1714.02 −0.239859
372372 0 0
373373 −4037.37 −0.560449 −0.280224 0.959935i 0.590409π-0.590409\pi
−0.280224 + 0.959935i 0.590409π0.590409\pi
374374 5048.40 0.697986
375375 0 0
376376 −324.963 −0.0445710
377377 −4685.54 −0.640100
378378 0 0
379379 4939.84 0.669506 0.334753 0.942306i 0.391347π-0.391347\pi
0.334753 + 0.942306i 0.391347π0.391347\pi
380380 −958.840 −0.129441
381381 0 0
382382 −11594.8 −1.55299
383383 245.085 0.0326978 0.0163489 0.999866i 0.494796π-0.494796\pi
0.0163489 + 0.999866i 0.494796π0.494796\pi
384384 0 0
385385 −448.757 −0.0594046
386386 −1137.19 −0.149951
387387 0 0
388388 10464.9 1.36926
389389 −9961.20 −1.29834 −0.649168 0.760645i 0.724883π-0.724883\pi
−0.649168 + 0.760645i 0.724883π0.724883\pi
390390 0 0
391391 −14190.3 −1.83538
392392 214.739 0.0276683
393393 0 0
394394 8866.56 1.13373
395395 −4123.10 −0.525204
396396 0 0
397397 −4848.35 −0.612926 −0.306463 0.951883i 0.599146π-0.599146\pi
−0.306463 + 0.951883i 0.599146π0.599146\pi
398398 9157.06 1.15327
399399 0 0
400400 6536.42 0.817052
401401 954.553 0.118873 0.0594365 0.998232i 0.481070π-0.481070\pi
0.0594365 + 0.998232i 0.481070π0.481070\pi
402402 0 0
403403 6014.53 0.743437
404404 7227.97 0.890111
405405 0 0
406406 1451.12 0.177384
407407 −314.847 −0.0383449
408408 0 0
409409 −199.139 −0.0240753 −0.0120376 0.999928i 0.503832π-0.503832\pi
−0.0120376 + 0.999928i 0.503832π0.503832\pi
410410 −9418.60 −1.13452
411411 0 0
412412 301.266 0.0360251
413413 −2556.57 −0.304602
414414 0 0
415415 3155.58 0.373256
416416 −21066.4 −2.48284
417417 0 0
418418 1016.59 0.118954
419419 16428.4 1.91547 0.957734 0.287654i 0.0928752π-0.0928752\pi
0.957734 + 0.287654i 0.0928752π0.0928752\pi
420420 0 0
421421 11222.8 1.29920 0.649602 0.760274i 0.274936π-0.274936\pi
0.649602 + 0.760274i 0.274936π0.274936\pi
422422 10457.0 1.20625
423423 0 0
424424 1073.09 0.122910
425425 −10837.0 −1.23688
426426 0 0
427427 3198.19 0.362463
428428 3088.05 0.348753
429429 0 0
430430 −899.787 −0.100911
431431 16786.0 1.87599 0.937996 0.346645i 0.112679π-0.112679\pi
0.937996 + 0.346645i 0.112679π0.112679\pi
432432 0 0
433433 −1619.31 −0.179721 −0.0898604 0.995954i 0.528642π-0.528642\pi
−0.0898604 + 0.995954i 0.528642π0.528642\pi
434434 −1862.72 −0.206021
435435 0 0
436436 −9029.52 −0.991824
437437 −2857.48 −0.312795
438438 0 0
439439 −581.616 −0.0632324 −0.0316162 0.999500i 0.510065π-0.510065\pi
−0.0316162 + 0.999500i 0.510065π0.510065\pi
440440 280.950 0.0304403
441441 0 0
442442 39991.9 4.30367
443443 −1171.84 −0.125679 −0.0628397 0.998024i 0.520016π-0.520016\pi
−0.0628397 + 0.998024i 0.520016π0.520016\pi
444444 0 0
445445 −3262.50 −0.347545
446446 16710.4 1.77413
447447 0 0
448448 2503.41 0.264007
449449 11428.6 1.20122 0.600609 0.799543i 0.294925π-0.294925\pi
0.600609 + 0.799543i 0.294925π0.294925\pi
450450 0 0
451451 4611.07 0.481434
452452 −4976.80 −0.517896
453453 0 0
454454 −12106.1 −1.25147
455455 −3554.91 −0.366279
456456 0 0
457457 −10643.0 −1.08940 −0.544701 0.838630i 0.683357π-0.683357\pi
−0.544701 + 0.838630i 0.683357π0.683357\pi
458458 −19627.6 −2.00248
459459 0 0
460460 4768.02 0.483283
461461 −2911.16 −0.294114 −0.147057 0.989128i 0.546980π-0.546980\pi
−0.147057 + 0.989128i 0.546980π0.546980\pi
462462 0 0
463463 −15206.9 −1.52640 −0.763202 0.646160i 0.776374π-0.776374\pi
−0.763202 + 0.646160i 0.776374π0.776374\pi
464464 −3860.86 −0.386284
465465 0 0
466466 7296.33 0.725313
467467 14031.2 1.39034 0.695169 0.718847i 0.255330π-0.255330\pi
0.695169 + 0.718847i 0.255330π0.255330\pi
468468 0 0
469469 3291.91 0.324107
470470 −1666.08 −0.163512
471471 0 0
472472 1600.57 0.156085
473473 440.509 0.0428216
474474 0 0
475475 −2182.23 −0.210795
476476 −5719.17 −0.550710
477477 0 0
478478 19815.3 1.89609
479479 −14647.2 −1.39718 −0.698590 0.715523i 0.746189π-0.746189\pi
−0.698590 + 0.715523i 0.746189π0.746189\pi
480480 0 0
481481 −2494.12 −0.236428
482482 7319.79 0.691716
483483 0 0
484484 830.455 0.0779917
485485 −8886.33 −0.831974
486486 0 0
487487 −11869.8 −1.10446 −0.552230 0.833692i 0.686223π-0.686223\pi
−0.552230 + 0.833692i 0.686223π0.686223\pi
488488 −2002.27 −0.185735
489489 0 0
490490 1100.96 0.101503
491491 −959.814 −0.0882195 −0.0441098 0.999027i 0.514045π-0.514045\pi
−0.0441098 + 0.999027i 0.514045π0.514045\pi
492492 0 0
493493 6401.08 0.584767
494494 8053.10 0.733454
495495 0 0
496496 4955.94 0.448646
497497 2519.68 0.227410
498498 0 0
499499 18146.9 1.62799 0.813997 0.580869i 0.197287π-0.197287\pi
0.813997 + 0.580869i 0.197287π0.197287\pi
500500 8641.19 0.772892
501501 0 0
502502 1182.34 0.105121
503503 −10934.7 −0.969294 −0.484647 0.874710i 0.661052π-0.661052\pi
−0.484647 + 0.874710i 0.661052π0.661052\pi
504504 0 0
505505 −6137.70 −0.540840
506506 −5055.18 −0.444131
507507 0 0
508508 16749.3 1.46286
509509 −3876.11 −0.337535 −0.168768 0.985656i 0.553979π-0.553979\pi
−0.168768 + 0.985656i 0.553979π0.553979\pi
510510 0 0
511511 6316.63 0.546832
512512 −14841.2 −1.28105
513513 0 0
514514 −14429.4 −1.23823
515515 −255.823 −0.0218892
516516 0 0
517517 815.664 0.0693865
518518 772.435 0.0655190
519519 0 0
520520 2225.60 0.187690
521521 −2971.13 −0.249842 −0.124921 0.992167i 0.539868π-0.539868\pi
−0.124921 + 0.992167i 0.539868π0.539868\pi
522522 0 0
523523 20391.8 1.70491 0.852457 0.522797i 0.175112π-0.175112\pi
0.852457 + 0.522797i 0.175112π0.175112\pi
524524 8636.25 0.719993
525525 0 0
526526 −13607.9 −1.12801
527527 −8216.66 −0.679172
528528 0 0
529529 2042.35 0.167860
530530 5501.69 0.450902
531531 0 0
532532 −1151.66 −0.0938549
533533 36527.5 2.96844
534534 0 0
535535 −2622.25 −0.211906
536536 −2060.94 −0.166080
537537 0 0
538538 −6265.55 −0.502095
539539 −539.000 −0.0430730
540540 0 0
541541 −13628.9 −1.08309 −0.541544 0.840672i 0.682160π-0.682160\pi
−0.541544 + 0.840672i 0.682160π0.682160\pi
542542 −10681.5 −0.846511
543543 0 0
544544 28779.5 2.26822
545545 7667.50 0.602641
546546 0 0
547547 −4077.34 −0.318710 −0.159355 0.987221i 0.550941π-0.550941\pi
−0.159355 + 0.987221i 0.550941π0.550941\pi
548548 19149.1 1.49272
549549 0 0
550550 −3860.60 −0.299303
551551 1288.98 0.0996591
552552 0 0
553553 −4952.24 −0.380815
554554 24656.4 1.89088
555555 0 0
556556 3703.23 0.282468
557557 −7792.93 −0.592813 −0.296407 0.955062i 0.595788π-0.595788\pi
−0.296407 + 0.955062i 0.595788π0.595788\pi
558558 0 0
559559 3489.58 0.264031
560560 −2929.23 −0.221040
561561 0 0
562562 21515.6 1.61491
563563 18076.2 1.35315 0.676575 0.736374i 0.263464π-0.263464\pi
0.676575 + 0.736374i 0.263464π0.263464\pi
564564 0 0
565565 4226.10 0.314678
566566 12245.6 0.909404
567567 0 0
568568 −1577.47 −0.116530
569569 −23137.8 −1.70472 −0.852362 0.522951i 0.824831π-0.824831\pi
−0.852362 + 0.522951i 0.824831π0.824831\pi
570570 0 0
571571 −25202.6 −1.84711 −0.923553 0.383470i 0.874729π-0.874729\pi
−0.923553 + 0.383470i 0.874729π0.874729\pi
572572 6578.61 0.480884
573573 0 0
574574 −11312.7 −0.822615
575575 10851.6 0.787029
576576 0 0
577577 18777.6 1.35480 0.677402 0.735613i 0.263106π-0.263106\pi
0.677402 + 0.735613i 0.263106π0.263106\pi
578578 −35693.3 −2.56859
579579 0 0
580580 −2150.80 −0.153978
581581 3790.15 0.270640
582582 0 0
583583 −2693.47 −0.191341
584584 −3954.60 −0.280210
585585 0 0
586586 −14202.6 −1.00120
587587 17123.4 1.20402 0.602008 0.798490i 0.294367π-0.294367\pi
0.602008 + 0.798490i 0.294367π0.294367\pi
588588 0 0
589589 −1654.58 −0.115748
590590 8206.09 0.572609
591591 0 0
592592 −2055.14 −0.142679
593593 22319.3 1.54561 0.772803 0.634647i 0.218854π-0.218854\pi
0.772803 + 0.634647i 0.218854π0.218854\pi
594594 0 0
595595 4856.49 0.334616
596596 5992.33 0.411838
597597 0 0
598598 −40045.6 −2.73844
599599 5844.36 0.398655 0.199327 0.979933i 0.436124π-0.436124\pi
0.199327 + 0.979933i 0.436124π0.436124\pi
600600 0 0
601601 −27815.8 −1.88791 −0.943953 0.330081i 0.892924π-0.892924\pi
−0.943953 + 0.330081i 0.892924π0.892924\pi
602602 −1080.73 −0.0731683
603603 0 0
604604 7665.95 0.516429
605605 −705.189 −0.0473884
606606 0 0
607607 −15980.5 −1.06858 −0.534290 0.845301i 0.679421π-0.679421\pi
−0.534290 + 0.845301i 0.679421π0.679421\pi
608608 5795.28 0.386562
609609 0 0
610610 −10265.6 −0.681380
611611 6461.43 0.427826
612612 0 0
613613 22639.1 1.49166 0.745829 0.666138i 0.232054π-0.232054\pi
0.745829 + 0.666138i 0.232054π0.232054\pi
614614 23827.9 1.56615
615615 0 0
616616 337.448 0.0220717
617617 6134.28 0.400254 0.200127 0.979770i 0.435864π-0.435864\pi
0.200127 + 0.979770i 0.435864π0.435864\pi
618618 0 0
619619 13953.0 0.906005 0.453003 0.891509i 0.350353π-0.350353\pi
0.453003 + 0.891509i 0.350353π0.350353\pi
620620 2760.85 0.178836
621621 0 0
622622 23057.8 1.48639
623623 −3918.58 −0.251998
624624 0 0
625625 4041.54 0.258659
626626 −18343.4 −1.17117
627627 0 0
628628 21034.4 1.33657
629629 3407.30 0.215991
630630 0 0
631631 −15765.0 −0.994602 −0.497301 0.867578i 0.665676π-0.665676\pi
−0.497301 + 0.867578i 0.665676π0.665676\pi
632632 3100.41 0.195139
633633 0 0
634634 16932.2 1.06067
635635 −14222.9 −0.888845
636636 0 0
637637 −4269.79 −0.265581
638638 2280.34 0.141504
639639 0 0
640640 3236.23 0.199880
641641 1189.73 0.0733097 0.0366549 0.999328i 0.488330π-0.488330\pi
0.0366549 + 0.999328i 0.488330π0.488330\pi
642642 0 0
643643 13633.3 0.836149 0.418075 0.908413i 0.362705π-0.362705\pi
0.418075 + 0.908413i 0.362705π0.362705\pi
644644 5726.85 0.350419
645645 0 0
646646 −11001.6 −0.670051
647647 11326.2 0.688221 0.344110 0.938929i 0.388181π-0.388181\pi
0.344110 + 0.938929i 0.388181π0.388181\pi
648648 0 0
649649 −4017.46 −0.242988
650650 −30582.5 −1.84545
651651 0 0
652652 27807.1 1.67026
653653 28224.5 1.69144 0.845719 0.533629i 0.179172π-0.179172\pi
0.845719 + 0.533629i 0.179172π0.179172\pi
654654 0 0
655655 −7333.55 −0.437474
656656 30098.4 1.79138
657657 0 0
658658 −2001.12 −0.118559
659659 5538.71 0.327402 0.163701 0.986510i 0.447657π-0.447657\pi
0.163701 + 0.986510i 0.447657π0.447657\pi
660660 0 0
661661 3176.03 0.186888 0.0934441 0.995625i 0.470212π-0.470212\pi
0.0934441 + 0.995625i 0.470212π0.470212\pi
662662 −31250.3 −1.83471
663663 0 0
664664 −2372.87 −0.138683
665665 977.943 0.0570271
666666 0 0
667667 −6409.68 −0.372090
668668 7880.15 0.456425
669669 0 0
670670 −10566.4 −0.609277
671671 5025.73 0.289145
672672 0 0
673673 32576.2 1.86586 0.932928 0.360062i 0.117245π-0.117245\pi
0.932928 + 0.360062i 0.117245π0.117245\pi
674674 −15573.7 −0.890025
675675 0 0
676676 37035.1 2.10714
677677 −18529.8 −1.05193 −0.525967 0.850505i 0.676296π-0.676296\pi
−0.525967 + 0.850505i 0.676296π0.676296\pi
678678 0 0
679679 −10673.3 −0.603248
680680 −3040.46 −0.171465
681681 0 0
682682 −2927.12 −0.164348
683683 34880.4 1.95412 0.977058 0.212972i 0.0683143π-0.0683143\pi
0.977058 + 0.212972i 0.0683143π0.0683143\pi
684684 0 0
685685 −16260.6 −0.906988
686686 1322.36 0.0735978
687687 0 0
688688 2875.39 0.159336
689689 −21336.8 −1.17978
690690 0 0
691691 −21942.1 −1.20798 −0.603992 0.796991i 0.706424π-0.706424\pi
−0.603992 + 0.796991i 0.706424π0.706424\pi
692692 17884.7 0.982479
693693 0 0
694694 −32434.4 −1.77405
695695 −3144.63 −0.171630
696696 0 0
697697 −49901.5 −2.71184
698698 29144.1 1.58040
699699 0 0
700700 4373.55 0.236150
701701 8513.96 0.458727 0.229364 0.973341i 0.426335π-0.426335\pi
0.229364 + 0.973341i 0.426335π0.426335\pi
702702 0 0
703703 686.123 0.0368103
704704 3933.93 0.210604
705705 0 0
706706 −29781.8 −1.58761
707707 −7371.97 −0.392152
708708 0 0
709709 −27813.5 −1.47329 −0.736643 0.676282i 0.763590π-0.763590\pi
−0.736643 + 0.676282i 0.763590π0.763590\pi
710710 −8087.68 −0.427500
711711 0 0
712712 2453.27 0.129130
713713 8227.70 0.432159
714714 0 0
715715 −5586.29 −0.292189
716716 −23411.8 −1.22198
717717 0 0
718718 3547.92 0.184411
719719 65.2658 0.00338526 0.00169263 0.999999i 0.499461π-0.499461\pi
0.00169263 + 0.999999i 0.499461π0.499461\pi
720720 0 0
721721 −307.268 −0.0158714
722722 24228.1 1.24886
723723 0 0
724724 −4399.55 −0.225840
725725 −4895.02 −0.250754
726726 0 0
727727 24711.7 1.26067 0.630334 0.776324i 0.282918π-0.282918\pi
0.630334 + 0.776324i 0.282918π0.282918\pi
728728 2673.16 0.136090
729729 0 0
730730 −20275.2 −1.02797
731731 −4767.24 −0.241207
732732 0 0
733733 −27286.3 −1.37496 −0.687478 0.726205i 0.741282π-0.741282\pi
−0.687478 + 0.726205i 0.741282π0.741282\pi
734734 10084.2 0.507105
735735 0 0
736736 −28818.1 −1.44328
737737 5173.00 0.258548
738738 0 0
739739 1330.19 0.0662138 0.0331069 0.999452i 0.489460π-0.489460\pi
0.0331069 + 0.999452i 0.489460π0.489460\pi
740740 −1144.87 −0.0568735
741741 0 0
742742 6608.06 0.326940
743743 14905.2 0.735963 0.367982 0.929833i 0.380049π-0.380049\pi
0.367982 + 0.929833i 0.380049π0.380049\pi
744744 0 0
745745 −5088.44 −0.250236
746746 15565.3 0.763920
747747 0 0
748748 −8987.27 −0.439314
749749 −3149.57 −0.153649
750750 0 0
751751 −21448.2 −1.04215 −0.521076 0.853510i 0.674469π-0.674469\pi
−0.521076 + 0.853510i 0.674469π0.674469\pi
752752 5324.18 0.258182
753753 0 0
754754 18064.1 0.872489
755755 −6509.61 −0.313787
756756 0 0
757757 5266.07 0.252838 0.126419 0.991977i 0.459652π-0.459652\pi
0.126419 + 0.991977i 0.459652π0.459652\pi
758758 −19044.5 −0.912571
759759 0 0
760760 −612.253 −0.0292220
761761 24314.9 1.15823 0.579117 0.815244i 0.303397π-0.303397\pi
0.579117 + 0.815244i 0.303397π0.303397\pi
762762 0 0
763763 9209.41 0.436963
764764 20641.4 0.977459
765765 0 0
766766 −944.873 −0.0445687
767767 −31825.1 −1.49822
768768 0 0
769769 −6799.74 −0.318862 −0.159431 0.987209i 0.550966π-0.550966\pi
−0.159431 + 0.987209i 0.550966π0.550966\pi
770770 1730.09 0.0809714
771771 0 0
772772 2024.44 0.0943798
773773 −2665.83 −0.124040 −0.0620202 0.998075i 0.519754π-0.519754\pi
−0.0620202 + 0.998075i 0.519754π0.519754\pi
774774 0 0
775775 6283.43 0.291235
776776 6682.17 0.309119
777777 0 0
778778 38403.3 1.76970
779779 −10048.6 −0.462166
780780 0 0
781781 3959.49 0.181411
782782 54707.7 2.50172
783783 0 0
784784 −3518.28 −0.160272
785785 −17861.6 −0.812112
786786 0 0
787787 −19896.6 −0.901191 −0.450596 0.892728i 0.648788π-0.648788\pi
−0.450596 + 0.892728i 0.648788π0.648788\pi
788788 −15784.4 −0.713575
789789 0 0
790790 15895.8 0.715880
791791 5075.95 0.228167
792792 0 0
793793 39812.3 1.78282
794794 18691.8 0.835449
795795 0 0
796796 −16301.6 −0.725872
797797 30665.5 1.36289 0.681447 0.731868i 0.261351π-0.261351\pi
0.681447 + 0.731868i 0.261351π0.261351\pi
798798 0 0
799799 −8827.19 −0.390843
800800 −22008.2 −0.972633
801801 0 0
802802 −3680.08 −0.162030
803803 9926.13 0.436221
804804 0 0
805805 −4863.01 −0.212918
806806 −23187.8 −1.01334
807807 0 0
808808 4615.31 0.200948
809809 −26189.0 −1.13814 −0.569071 0.822289i 0.692697π-0.692697\pi
−0.569071 + 0.822289i 0.692697π0.692697\pi
810810 0 0
811811 19230.2 0.832631 0.416315 0.909220i 0.363321π-0.363321\pi
0.416315 + 0.909220i 0.363321π0.363321\pi
812812 −2583.32 −0.111646
813813 0 0
814814 1213.83 0.0522661
815815 −23612.7 −1.01487
816816 0 0
817817 −959.970 −0.0411078
818818 767.739 0.0328158
819819 0 0
820820 16767.2 0.714068
821821 −42674.2 −1.81406 −0.907028 0.421070i 0.861655π-0.861655\pi
−0.907028 + 0.421070i 0.861655π0.861655\pi
822822 0 0
823823 −21127.7 −0.894856 −0.447428 0.894320i 0.647660π-0.647660\pi
−0.447428 + 0.894320i 0.647660π0.647660\pi
824824 192.369 0.00813288
825825 0 0
826826 9856.31 0.415188
827827 −3011.35 −0.126620 −0.0633101 0.997994i 0.520166π-0.520166\pi
−0.0633101 + 0.997994i 0.520166π0.520166\pi
828828 0 0
829829 −5221.80 −0.218770 −0.109385 0.993999i 0.534888π-0.534888\pi
−0.109385 + 0.993999i 0.534888π0.534888\pi
830830 −12165.7 −0.508767
831831 0 0
832832 31163.4 1.29855
833833 5833.11 0.242623
834834 0 0
835835 −6691.50 −0.277328
836836 −1809.75 −0.0748703
837837 0 0
838838 −63336.4 −2.61088
839839 −46130.3 −1.89821 −0.949104 0.314963i 0.898008π-0.898008\pi
−0.949104 + 0.314963i 0.898008π0.898008\pi
840840 0 0
841841 −21497.7 −0.881449
842842 −43267.1 −1.77088
843843 0 0
844844 −18615.7 −0.759218
845845 −31448.7 −1.28032
846846 0 0
847847 −847.000 −0.0343604
848848 −17581.4 −0.711967
849849 0 0
850850 41779.8 1.68592
851851 −3411.88 −0.137436
852852 0 0
853853 15030.9 0.603338 0.301669 0.953413i 0.402456π-0.402456\pi
0.301669 + 0.953413i 0.402456π0.402456\pi
854854 −12330.0 −0.494055
855855 0 0
856856 1971.83 0.0787332
857857 33506.6 1.33555 0.667773 0.744365i 0.267248π-0.267248\pi
0.667773 + 0.744365i 0.267248π0.267248\pi
858858 0 0
859859 18085.0 0.718338 0.359169 0.933273i 0.383060π-0.383060\pi
0.359169 + 0.933273i 0.383060π0.383060\pi
860860 1601.82 0.0635135
861861 0 0
862862 −64714.9 −2.55707
863863 −23344.1 −0.920791 −0.460396 0.887714i 0.652292π-0.652292\pi
−0.460396 + 0.887714i 0.652292π0.652292\pi
864864 0 0
865865 −15187.0 −0.596963
866866 6242.91 0.244969
867867 0 0
868868 3316.04 0.129670
869869 −7782.10 −0.303785
870870 0 0
871871 40978.9 1.59416
872872 −5765.66 −0.223910
873873 0 0
874874 11016.4 0.426356
875875 −8813.35 −0.340509
876876 0 0
877877 −16403.0 −0.631573 −0.315786 0.948830i 0.602268π-0.602268\pi
−0.315786 + 0.948830i 0.602268π0.602268\pi
878878 2242.30 0.0861890
879879 0 0
880880 −4603.07 −0.176329
881881 −19795.6 −0.757017 −0.378509 0.925598i 0.623563π-0.623563\pi
−0.378509 + 0.925598i 0.623563π0.623563\pi
882882 0 0
883883 −26755.7 −1.01971 −0.509854 0.860261i 0.670301π-0.670301\pi
−0.509854 + 0.860261i 0.670301π0.670301\pi
884884 −71194.4 −2.70874
885885 0 0
886886 4517.80 0.171307
887887 26296.7 0.995442 0.497721 0.867337i 0.334170π-0.334170\pi
0.497721 + 0.867337i 0.334170π0.334170\pi
888888 0 0
889889 −17083.0 −0.644484
890890 12577.9 0.473721
891891 0 0
892892 −29748.3 −1.11664
893893 −1777.52 −0.0666096
894894 0 0
895895 19880.4 0.742489
896896 3887.02 0.144929
897897 0 0
898898 −44060.4 −1.63732
899899 −3711.42 −0.137690
900900 0 0
901901 29149.0 1.07780
902902 −17777.0 −0.656220
903903 0 0
904904 −3177.86 −0.116918
905905 3735.92 0.137222
906906 0 0
907907 −41082.5 −1.50399 −0.751996 0.659167i 0.770909π-0.770909\pi
−0.751996 + 0.659167i 0.770909π0.770909\pi
908908 21551.5 0.787679
909909 0 0
910910 13705.2 0.499257
911911 −34300.4 −1.24745 −0.623723 0.781645i 0.714381π-0.714381\pi
−0.623723 + 0.781645i 0.714381π0.714381\pi
912912 0 0
913913 5955.95 0.215896
914914 41031.7 1.48491
915915 0 0
916916 34941.4 1.26037
917917 −8808.31 −0.317204
918918 0 0
919919 40816.1 1.46507 0.732535 0.680730i 0.238337π-0.238337\pi
0.732535 + 0.680730i 0.238337π0.238337\pi
920920 3044.55 0.109104
921921 0 0
922922 11223.4 0.400892
923923 31365.9 1.11855
924924 0 0
925925 −2605.62 −0.0926188
926926 58627.0 2.08057
927927 0 0
928928 12999.5 0.459839
929929 −11293.8 −0.398857 −0.199429 0.979912i 0.563909π-0.563909\pi
−0.199429 + 0.979912i 0.563909π0.563909\pi
930930 0 0
931931 1174.60 0.0413492
932932 −12989.1 −0.456514
933933 0 0
934934 −54094.5 −1.89510
935935 7631.63 0.266931
936936 0 0
937937 27145.4 0.946428 0.473214 0.880948i 0.343094π-0.343094\pi
0.473214 + 0.880948i 0.343094π0.343094\pi
938938 −12691.3 −0.441774
939939 0 0
940940 2965.99 0.102915
941941 17834.4 0.617838 0.308919 0.951088i 0.400033π-0.400033\pi
0.308919 + 0.951088i 0.400033π0.400033\pi
942942 0 0
943943 49968.5 1.72555
944944 −26223.7 −0.904141
945945 0 0
946946 −1698.29 −0.0583681
947947 36957.3 1.26817 0.634083 0.773265i 0.281378π-0.281378\pi
0.634083 + 0.773265i 0.281378π0.281378\pi
948948 0 0
949949 78631.7 2.68967
950950 8413.13 0.287324
951951 0 0
952952 −3651.89 −0.124326
953953 −42725.6 −1.45227 −0.726137 0.687550i 0.758686π-0.758686\pi
−0.726137 + 0.687550i 0.758686π0.758686\pi
954954 0 0
955955 −17527.8 −0.593913
956956 −35275.6 −1.19340
957957 0 0
958958 56469.3 1.90443
959959 −19530.6 −0.657639
960960 0 0
961961 −25026.9 −0.840082
962962 9615.55 0.322264
963963 0 0
964964 −13030.8 −0.435368
965965 −1719.07 −0.0573460
966966 0 0
967967 −18274.2 −0.607713 −0.303856 0.952718i 0.598274π-0.598274\pi
−0.303856 + 0.952718i 0.598274π0.598274\pi
968968 530.275 0.0176071
969969 0 0
970970 34259.4 1.13402
971971 39923.1 1.31946 0.659729 0.751503i 0.270671π-0.270671\pi
0.659729 + 0.751503i 0.270671π0.270671\pi
972972 0 0
973973 −3777.01 −0.124445
974974 45761.5 1.50543
975975 0 0
976976 32805.1 1.07589
977977 −26746.2 −0.875832 −0.437916 0.899016i 0.644283π-0.644283\pi
−0.437916 + 0.899016i 0.644283π0.644283\pi
978978 0 0
979979 −6157.77 −0.201025
980980 −1959.96 −0.0638863
981981 0 0
982982 3700.36 0.120248
983983 −38975.0 −1.26461 −0.632303 0.774721i 0.717890π-0.717890\pi
−0.632303 + 0.774721i 0.717890π0.717890\pi
984984 0 0
985985 13403.5 0.433574
986986 −24678.0 −0.797068
987987 0 0
988988 −14336.3 −0.461638
989989 4773.64 0.153481
990990 0 0
991991 59856.3 1.91866 0.959332 0.282279i 0.0910903π-0.0910903\pi
0.959332 + 0.282279i 0.0910903π0.0910903\pi
992992 −16686.7 −0.534076
993993 0 0
994994 −9714.08 −0.309972
995995 13842.6 0.441047
996996 0 0
997997 42609.3 1.35351 0.676755 0.736208i 0.263386π-0.263386\pi
0.676755 + 0.736208i 0.263386π0.263386\pi
998998 −69961.8 −2.21904
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 693.4.a.t.1.2 yes 8
3.2 odd 2 693.4.a.s.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
693.4.a.s.1.7 8 3.2 odd 2
693.4.a.t.1.2 yes 8 1.1 even 1 trivial