Properties

Label 2368.2.a.bg.1.2
Level 23682368
Weight 22
Character 2368.1
Self dual yes
Analytic conductor 18.90918.909
Analytic rank 11
Dimension 44
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2368,2,Mod(1,2368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2368, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2368.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 2368=2637 2368 = 2^{6} \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2368.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: 18.908575198618.9085751986
Analytic rank: 11
Dimension: 44
Coefficient field: 4.4.48389.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x42x38x2+3x+10 x^{4} - 2x^{3} - 8x^{2} + 3x + 10 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 296)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.26726-1.26726 of defining polynomial
Character χ\chi == 2368.1

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) == q2.26726q3+2.21602q5+3.07555q7+2.14048q91.14048q112.80828q135.02431q15+2.00000q173.89752q196.97307q217.62376q230.0892395q25+1.94876q27+3.34281q2910.3671q31+2.58576q33+6.81548q351.00000q37+6.36711q39+2.54822q418.43205q43+4.74335q457.17802q47+2.45898q494.53452q515.61007q532.52733q55+8.83671q57+6.17848q59+10.6481q61+6.58314q636.22322q65+0.318501q67+17.2851q69+6.42555q71+16.0046q73+0.202329q753.50759q778.69281q7910.8398q81+9.76116q83+4.43205q857.57902q878.25357q898.63700q91+23.5050q938.63700q9513.2201q972.44117q99+O(q100)q-2.26726 q^{3} +2.21602 q^{5} +3.07555 q^{7} +2.14048 q^{9} -1.14048 q^{11} -2.80828 q^{13} -5.02431 q^{15} +2.00000 q^{17} -3.89752 q^{19} -6.97307 q^{21} -7.62376 q^{23} -0.0892395 q^{25} +1.94876 q^{27} +3.34281 q^{29} -10.3671 q^{31} +2.58576 q^{33} +6.81548 q^{35} -1.00000 q^{37} +6.36711 q^{39} +2.54822 q^{41} -8.43205 q^{43} +4.74335 q^{45} -7.17802 q^{47} +2.45898 q^{49} -4.53452 q^{51} -5.61007 q^{53} -2.52733 q^{55} +8.83671 q^{57} +6.17848 q^{59} +10.6481 q^{61} +6.58314 q^{63} -6.22322 q^{65} +0.318501 q^{67} +17.2851 q^{69} +6.42555 q^{71} +16.0046 q^{73} +0.202329 q^{75} -3.50759 q^{77} -8.69281 q^{79} -10.8398 q^{81} +9.76116 q^{83} +4.43205 q^{85} -7.57902 q^{87} -8.25357 q^{89} -8.63700 q^{91} +23.5050 q^{93} -8.63700 q^{95} -13.2201 q^{97} -2.44117 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q2q35q5q7+8q94q115q13+8q172q19q219q23+7q25+q277q29q31+3q33+12q354q3715q39+2q41+44q99+O(q100) 4 q - 2 q^{3} - 5 q^{5} - q^{7} + 8 q^{9} - 4 q^{11} - 5 q^{13} + 8 q^{17} - 2 q^{19} - q^{21} - 9 q^{23} + 7 q^{25} + q^{27} - 7 q^{29} - q^{31} + 3 q^{33} + 12 q^{35} - 4 q^{37} - 15 q^{39} + 2 q^{41}+ \cdots - 44 q^{99}+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 0 0
33 −2.26726 −1.30900 −0.654502 0.756060i 0.727122π-0.727122\pi
−0.654502 + 0.756060i 0.727122π0.727122\pi
44 0 0
55 2.21602 0.991036 0.495518 0.868598i 0.334978π-0.334978\pi
0.495518 + 0.868598i 0.334978π0.334978\pi
66 0 0
77 3.07555 1.16245 0.581223 0.813744i 0.302574π-0.302574\pi
0.581223 + 0.813744i 0.302574π0.302574\pi
88 0 0
99 2.14048 0.713493
1010 0 0
1111 −1.14048 −0.343867 −0.171934 0.985109i 0.555001π-0.555001\pi
−0.171934 + 0.985109i 0.555001π0.555001\pi
1212 0 0
1313 −2.80828 −0.778878 −0.389439 0.921052i 0.627331π-0.627331\pi
−0.389439 + 0.921052i 0.627331π0.627331\pi
1414 0 0
1515 −5.02431 −1.29727
1616 0 0
1717 2.00000 0.485071 0.242536 0.970143i 0.422021π-0.422021\pi
0.242536 + 0.970143i 0.422021π0.422021\pi
1818 0 0
1919 −3.89752 −0.894153 −0.447077 0.894496i 0.647535π-0.647535\pi
−0.447077 + 0.894496i 0.647535π0.647535\pi
2020 0 0
2121 −6.97307 −1.52165
2222 0 0
2323 −7.62376 −1.58966 −0.794832 0.606829i 0.792441π-0.792441\pi
−0.794832 + 0.606829i 0.792441π0.792441\pi
2424 0 0
2525 −0.0892395 −0.0178479
2626 0 0
2727 1.94876 0.375039
2828 0 0
2929 3.34281 0.620744 0.310372 0.950615i 0.399546π-0.399546\pi
0.310372 + 0.950615i 0.399546π0.399546\pi
3030 0 0
3131 −10.3671 −1.86199 −0.930994 0.365034i 0.881057π-0.881057\pi
−0.930994 + 0.365034i 0.881057π0.881057\pi
3232 0 0
3333 2.58576 0.450124
3434 0 0
3535 6.81548 1.15203
3636 0 0
3737 −1.00000 −0.164399
3838 0 0
3939 6.36711 1.01955
4040 0 0
4141 2.54822 0.397965 0.198982 0.980003i 0.436236π-0.436236\pi
0.198982 + 0.980003i 0.436236π0.436236\pi
4242 0 0
4343 −8.43205 −1.28588 −0.642938 0.765919i 0.722285π-0.722285\pi
−0.642938 + 0.765919i 0.722285π0.722285\pi
4444 0 0
4545 4.74335 0.707097
4646 0 0
4747 −7.17802 −1.04702 −0.523511 0.852019i 0.675378π-0.675378\pi
−0.523511 + 0.852019i 0.675378π0.675378\pi
4848 0 0
4949 2.45898 0.351283
5050 0 0
5151 −4.53452 −0.634960
5252 0 0
5353 −5.61007 −0.770602 −0.385301 0.922791i 0.625902π-0.625902\pi
−0.385301 + 0.922791i 0.625902π0.625902\pi
5454 0 0
5555 −2.52733 −0.340785
5656 0 0
5757 8.83671 1.17045
5858 0 0
5959 6.17848 0.804369 0.402185 0.915559i 0.368251π-0.368251\pi
0.402185 + 0.915559i 0.368251π0.368251\pi
6060 0 0
6161 10.6481 1.36335 0.681673 0.731657i 0.261253π-0.261253\pi
0.681673 + 0.731657i 0.261253π0.261253\pi
6262 0 0
6363 6.58314 0.829397
6464 0 0
6565 −6.22322 −0.771896
6666 0 0
6767 0.318501 0.0389111 0.0194555 0.999811i 0.493807π-0.493807\pi
0.0194555 + 0.999811i 0.493807π0.493807\pi
6868 0 0
6969 17.2851 2.08088
7070 0 0
7171 6.42555 0.762573 0.381286 0.924457i 0.375481π-0.375481\pi
0.381286 + 0.924457i 0.375481π0.375481\pi
7272 0 0
7373 16.0046 1.87319 0.936597 0.350409i 0.113957π-0.113957\pi
0.936597 + 0.350409i 0.113957π0.113957\pi
7474 0 0
7575 0.202329 0.0233630
7676 0 0
7777 −3.50759 −0.399727
7878 0 0
7979 −8.69281 −0.978018 −0.489009 0.872279i 0.662641π-0.662641\pi
−0.489009 + 0.872279i 0.662641π0.662641\pi
8080 0 0
8181 −10.8398 −1.20442
8282 0 0
8383 9.76116 1.07143 0.535713 0.844400i 0.320043π-0.320043\pi
0.535713 + 0.844400i 0.320043π0.320043\pi
8484 0 0
8585 4.43205 0.480723
8686 0 0
8787 −7.57902 −0.812556
8888 0 0
8989 −8.25357 −0.874876 −0.437438 0.899248i 0.644114π-0.644114\pi
−0.437438 + 0.899248i 0.644114π0.644114\pi
9090 0 0
9191 −8.63700 −0.905404
9292 0 0
9393 23.5050 2.43735
9494 0 0
9595 −8.63700 −0.886138
9696 0 0
9797 −13.2201 −1.34230 −0.671151 0.741321i 0.734200π-0.734200\pi
−0.671151 + 0.741321i 0.734200π0.734200\pi
9898 0 0
9999 −2.44117 −0.245347
100100 0 0
101101 −16.3231 −1.62421 −0.812103 0.583514i 0.801677π-0.801677\pi
−0.812103 + 0.583514i 0.801677π0.801677\pi
102102 0 0
103103 9.93507 0.978931 0.489466 0.872023i 0.337192π-0.337192\pi
0.489466 + 0.872023i 0.337192π0.337192\pi
104104 0 0
105105 −15.4525 −1.50801
106106 0 0
107107 −5.34281 −0.516509 −0.258254 0.966077i 0.583147π-0.583147\pi
−0.258254 + 0.966077i 0.583147π0.583147\pi
108108 0 0
109109 −5.79505 −0.555065 −0.277532 0.960716i 0.589517π-0.589517\pi
−0.277532 + 0.960716i 0.589517π0.589517\pi
110110 0 0
111111 2.26726 0.215199
112112 0 0
113113 11.0690 1.04129 0.520644 0.853774i 0.325692π-0.325692\pi
0.520644 + 0.853774i 0.325692π0.325692\pi
114114 0 0
115115 −16.8944 −1.57541
116116 0 0
117117 −6.01107 −0.555724
118118 0 0
119119 6.15109 0.563870
120120 0 0
121121 −9.69931 −0.881755
122122 0 0
123123 −5.77748 −0.520938
124124 0 0
125125 −11.2779 −1.00872
126126 0 0
127127 −2.43854 −0.216386 −0.108193 0.994130i 0.534506π-0.534506\pi
−0.108193 + 0.994130i 0.534506π0.534506\pi
128128 0 0
129129 19.1177 1.68322
130130 0 0
131131 −12.3296 −1.07724 −0.538620 0.842549i 0.681054π-0.681054\pi
−0.538620 + 0.842549i 0.681054π0.681054\pi
132132 0 0
133133 −11.9870 −1.03941
134134 0 0
135135 4.31850 0.371677
136136 0 0
137137 −13.5516 −1.15779 −0.578897 0.815401i 0.696517π-0.696517\pi
−0.578897 + 0.815401i 0.696517π0.696517\pi
138138 0 0
139139 6.20690 0.526463 0.263231 0.964733i 0.415212π-0.415212\pi
0.263231 + 0.964733i 0.415212π0.415212\pi
140140 0 0
141141 16.2745 1.37056
142142 0 0
143143 3.20279 0.267830
144144 0 0
145145 7.40774 0.615179
146146 0 0
147147 −5.57515 −0.459831
148148 0 0
149149 −2.26006 −0.185152 −0.0925758 0.995706i 0.529510π-0.529510\pi
−0.0925758 + 0.995706i 0.529510π0.529510\pi
150150 0 0
151151 17.5011 1.42422 0.712110 0.702068i 0.247740π-0.247740\pi
0.712110 + 0.702068i 0.247740π0.247740\pi
152152 0 0
153153 4.28096 0.346095
154154 0 0
155155 −22.9738 −1.84530
156156 0 0
157157 −11.9661 −0.955000 −0.477500 0.878632i 0.658457π-0.658457\pi
−0.477500 + 0.878632i 0.658457π0.658457\pi
158158 0 0
159159 12.7195 1.00872
160160 0 0
161161 −23.4472 −1.84790
162162 0 0
163163 −1.18452 −0.0927787 −0.0463893 0.998923i 0.514771π-0.514771\pi
−0.0463893 + 0.998923i 0.514771π0.514771\pi
164164 0 0
165165 5.73011 0.446089
166166 0 0
167167 −20.2160 −1.56436 −0.782181 0.623051i 0.785893π-0.785893\pi
−0.782181 + 0.623051i 0.785893π0.785893\pi
168168 0 0
169169 −5.11355 −0.393350
170170 0 0
171171 −8.34256 −0.637972
172172 0 0
173173 −22.6791 −1.72426 −0.862131 0.506686i 0.830870π-0.830870\pi
−0.862131 + 0.506686i 0.830870π0.830870\pi
174174 0 0
175175 −0.274460 −0.0207472
176176 0 0
177177 −14.0082 −1.05292
178178 0 0
179179 14.5831 1.08999 0.544997 0.838438i 0.316531π-0.316531\pi
0.544997 + 0.838438i 0.316531π0.316531\pi
180180 0 0
181181 −24.7277 −1.83800 −0.918999 0.394260i 0.871001π-0.871001\pi
−0.918999 + 0.394260i 0.871001π0.871001\pi
182182 0 0
183183 −24.1420 −1.78463
184184 0 0
185185 −2.21602 −0.162925
186186 0 0
187187 −2.28096 −0.166800
188188 0 0
189189 5.99350 0.435963
190190 0 0
191191 −14.7241 −1.06540 −0.532698 0.846305i 0.678822π-0.678822\pi
−0.532698 + 0.846305i 0.678822π0.678822\pi
192192 0 0
193193 18.1997 1.31004 0.655022 0.755610i 0.272659π-0.272659\pi
0.655022 + 0.755610i 0.272659π0.272659\pi
194194 0 0
195195 14.1097 1.01041
196196 0 0
197197 −8.52803 −0.607597 −0.303798 0.952736i 0.598255π-0.598255\pi
−0.303798 + 0.952736i 0.598255π0.598255\pi
198198 0 0
199199 22.7130 1.61008 0.805041 0.593219i 0.202143π-0.202143\pi
0.805041 + 0.593219i 0.202143π0.202143\pi
200200 0 0
201201 −0.722125 −0.0509348
202202 0 0
203203 10.2810 0.721582
204204 0 0
205205 5.64691 0.394397
206206 0 0
207207 −16.3185 −1.13421
208208 0 0
209209 4.44504 0.307470
210210 0 0
211211 6.22252 0.428376 0.214188 0.976792i 0.431289π-0.431289\pi
0.214188 + 0.976792i 0.431289π0.431289\pi
212212 0 0
213213 −14.5684 −0.998211
214214 0 0
215215 −18.6856 −1.27435
216216 0 0
217217 −31.8845 −2.16446
218218 0 0
219219 −36.2866 −2.45202
220220 0 0
221221 −5.61657 −0.377811
222222 0 0
223223 −12.6040 −0.844028 −0.422014 0.906589i 0.638677π-0.638677\pi
−0.422014 + 0.906589i 0.638677π0.638677\pi
224224 0 0
225225 −0.191015 −0.0127344
226226 0 0
227227 26.3652 1.74992 0.874960 0.484196i 0.160888π-0.160888\pi
0.874960 + 0.484196i 0.160888π0.160888\pi
228228 0 0
229229 12.2957 0.812522 0.406261 0.913757i 0.366832π-0.366832\pi
0.406261 + 0.913757i 0.366832π0.366832\pi
230230 0 0
231231 7.95263 0.523245
232232 0 0
233233 14.1439 0.926597 0.463299 0.886202i 0.346666π-0.346666\pi
0.463299 + 0.886202i 0.346666π0.346666\pi
234234 0 0
235235 −15.9067 −1.03764
236236 0 0
237237 19.7089 1.28023
238238 0 0
239239 13.7171 0.887287 0.443643 0.896203i 0.353686π-0.353686\pi
0.443643 + 0.896203i 0.353686π0.353686\pi
240240 0 0
241241 28.9127 1.86243 0.931216 0.364469i 0.118749π-0.118749\pi
0.931216 + 0.364469i 0.118749π0.118749\pi
242242 0 0
243243 18.7304 1.20155
244244 0 0
245245 5.44916 0.348134
246246 0 0
247247 10.9453 0.696436
248248 0 0
249249 −22.1311 −1.40250
250250 0 0
251251 −21.3712 −1.34894 −0.674470 0.738302i 0.735628π-0.735628\pi
−0.674470 + 0.738302i 0.735628π0.735628\pi
252252 0 0
253253 8.69474 0.546633
254254 0 0
255255 −10.0486 −0.629269
256256 0 0
257257 3.64395 0.227304 0.113652 0.993521i 0.463745π-0.463745\pi
0.113652 + 0.993521i 0.463745π0.463745\pi
258258 0 0
259259 −3.07555 −0.191105
260260 0 0
261261 7.15521 0.442896
262262 0 0
263263 −18.2062 −1.12264 −0.561321 0.827598i 0.689707π-0.689707\pi
−0.561321 + 0.827598i 0.689707π0.689707\pi
264264 0 0
265265 −12.4320 −0.763695
266266 0 0
267267 18.7130 1.14522
268268 0 0
269269 −8.04861 −0.490733 −0.245366 0.969430i 0.578908π-0.578908\pi
−0.245366 + 0.969430i 0.578908π0.578908\pi
270270 0 0
271271 −13.8159 −0.839258 −0.419629 0.907696i 0.637840π-0.637840\pi
−0.419629 + 0.907696i 0.637840π0.637840\pi
272272 0 0
273273 19.5823 1.18518
274274 0 0
275275 0.101776 0.00613731
276276 0 0
277277 2.21602 0.133148 0.0665740 0.997781i 0.478793π-0.478793\pi
0.0665740 + 0.997781i 0.478793π0.478793\pi
278278 0 0
279279 −22.1906 −1.32852
280280 0 0
281281 −2.10248 −0.125423 −0.0627116 0.998032i 0.519975π-0.519975\pi
−0.0627116 + 0.998032i 0.519975π0.519975\pi
282282 0 0
283283 −6.26796 −0.372592 −0.186296 0.982494i 0.559648π-0.559648\pi
−0.186296 + 0.982494i 0.559648π0.559648\pi
284284 0 0
285285 19.5823 1.15996
286286 0 0
287287 7.83716 0.462613
288288 0 0
289289 −13.0000 −0.764706
290290 0 0
291291 29.9735 1.75708
292292 0 0
293293 10.3166 0.602701 0.301350 0.953513i 0.402563π-0.402563\pi
0.301350 + 0.953513i 0.402563π0.402563\pi
294294 0 0
295295 13.6917 0.797159
296296 0 0
297297 −2.22252 −0.128964
298298 0 0
299299 21.4097 1.23815
300300 0 0
301301 −25.9331 −1.49476
302302 0 0
303303 37.0087 2.12609
304304 0 0
305305 23.5964 1.35112
306306 0 0
307307 −11.1040 −0.633737 −0.316868 0.948469i 0.602631π-0.602631\pi
−0.316868 + 0.948469i 0.602631π0.602631\pi
308308 0 0
309309 −22.5254 −1.28143
310310 0 0
311311 10.3094 0.584591 0.292296 0.956328i 0.405581π-0.405581\pi
0.292296 + 0.956328i 0.405581π0.405581\pi
312312 0 0
313313 2.95218 0.166867 0.0834334 0.996513i 0.473411π-0.473411\pi
0.0834334 + 0.996513i 0.473411π0.473411\pi
314314 0 0
315315 14.5884 0.821963
316316 0 0
317317 14.1867 0.796805 0.398403 0.917211i 0.369565π-0.369565\pi
0.398403 + 0.917211i 0.369565π0.369565\pi
318318 0 0
319319 −3.81240 −0.213453
320320 0 0
321321 12.1135 0.676112
322322 0 0
323323 −7.79505 −0.433728
324324 0 0
325325 0.250610 0.0139013
326326 0 0
327327 13.1389 0.726582
328328 0 0
329329 −22.0763 −1.21711
330330 0 0
331331 26.4533 1.45400 0.727002 0.686636i 0.240913π-0.240913\pi
0.727002 + 0.686636i 0.240913π0.240913\pi
332332 0 0
333333 −2.14048 −0.117297
334334 0 0
335335 0.705806 0.0385623
336336 0 0
337337 2.57857 0.140463 0.0702317 0.997531i 0.477626π-0.477626\pi
0.0702317 + 0.997531i 0.477626π0.477626\pi
338338 0 0
339339 −25.0964 −1.36305
340340 0 0
341341 11.8235 0.640277
342342 0 0
343343 −13.9661 −0.754099
344344 0 0
345345 38.3041 2.06222
346346 0 0
347347 10.2810 0.551911 0.275955 0.961170i 0.411006π-0.411006\pi
0.275955 + 0.961170i 0.411006π0.411006\pi
348348 0 0
349349 23.9187 1.28034 0.640171 0.768233i 0.278864π-0.278864\pi
0.640171 + 0.768233i 0.278864π0.278864\pi
350350 0 0
351351 −5.47267 −0.292110
352352 0 0
353353 21.9596 1.16879 0.584396 0.811468i 0.301331π-0.301331\pi
0.584396 + 0.811468i 0.301331π0.301331\pi
354354 0 0
355355 14.2392 0.755737
356356 0 0
357357 −13.9461 −0.738108
358358 0 0
359359 −2.64350 −0.139518 −0.0697592 0.997564i 0.522223π-0.522223\pi
−0.0697592 + 0.997564i 0.522223π0.522223\pi
360360 0 0
361361 −3.80932 −0.200490
362362 0 0
363363 21.9909 1.15422
364364 0 0
365365 35.4665 1.85640
366366 0 0
367367 −13.9187 −0.726553 −0.363276 0.931681i 0.618342π-0.618342\pi
−0.363276 + 0.931681i 0.618342π0.618342\pi
368368 0 0
369369 5.45441 0.283945
370370 0 0
371371 −17.2540 −0.895784
372372 0 0
373373 15.2136 0.787733 0.393866 0.919168i 0.371137π-0.371137\pi
0.393866 + 0.919168i 0.371137π0.371137\pi
374374 0 0
375375 25.5699 1.32042
376376 0 0
377377 −9.38755 −0.483483
378378 0 0
379379 −1.17082 −0.0601412 −0.0300706 0.999548i 0.509573π-0.509573\pi
−0.0300706 + 0.999548i 0.509573π0.509573\pi
380380 0 0
381381 5.52882 0.283250
382382 0 0
383383 −17.6310 −0.900900 −0.450450 0.892802i 0.648736π-0.648736\pi
−0.450450 + 0.892802i 0.648736π0.648736\pi
384384 0 0
385385 −7.77291 −0.396144
386386 0 0
387387 −18.0486 −0.917463
388388 0 0
389389 −27.6176 −1.40027 −0.700134 0.714012i 0.746876π-0.746876\pi
−0.700134 + 0.714012i 0.746876π0.746876\pi
390390 0 0
391391 −15.2475 −0.771101
392392 0 0
393393 27.9544 1.41011
394394 0 0
395395 −19.2635 −0.969251
396396 0 0
397397 5.85541 0.293874 0.146937 0.989146i 0.453058π-0.453058\pi
0.146937 + 0.989146i 0.453058π0.453058\pi
398398 0 0
399399 27.1777 1.36059
400400 0 0
401401 −0.485911 −0.0242653 −0.0121326 0.999926i 0.503862π-0.503862\pi
−0.0121326 + 0.999926i 0.503862π0.503862\pi
402402 0 0
403403 29.1138 1.45026
404404 0 0
405405 −24.0212 −1.19362
406406 0 0
407407 1.14048 0.0565314
408408 0 0
409409 27.0417 1.33712 0.668562 0.743656i 0.266910π-0.266910\pi
0.668562 + 0.743656i 0.266910π0.266910\pi
410410 0 0
411411 30.7251 1.51556
412412 0 0
413413 19.0022 0.935037
414414 0 0
415415 21.6310 1.06182
416416 0 0
417417 −14.0727 −0.689142
418418 0 0
419419 −20.5704 −1.00493 −0.502464 0.864598i 0.667573π-0.667573\pi
−0.502464 + 0.864598i 0.667573π0.667573\pi
420420 0 0
421421 11.6594 0.568244 0.284122 0.958788i 0.408298π-0.408298\pi
0.284122 + 0.958788i 0.408298π0.408298\pi
422422 0 0
423423 −15.3644 −0.747043
424424 0 0
425425 −0.178479 −0.00865751
426426 0 0
427427 32.7486 1.58482
428428 0 0
429429 −7.26156 −0.350591
430430 0 0
431431 13.0690 0.629514 0.314757 0.949172i 0.398077π-0.398077\pi
0.314757 + 0.949172i 0.398077π0.398077\pi
432432 0 0
433433 −26.6454 −1.28050 −0.640249 0.768167i 0.721169π-0.721169\pi
−0.640249 + 0.768167i 0.721169π0.721169\pi
434434 0 0
435435 −16.7953 −0.805273
436436 0 0
437437 29.7138 1.42140
438438 0 0
439439 15.5964 0.744374 0.372187 0.928158i 0.378608π-0.378608\pi
0.372187 + 0.928158i 0.378608π0.378608\pi
440440 0 0
441441 5.26339 0.250638
442442 0 0
443443 −30.6546 −1.45644 −0.728221 0.685342i 0.759653π-0.759653\pi
−0.728221 + 0.685342i 0.759653π0.759653\pi
444444 0 0
445445 −18.2901 −0.867034
446446 0 0
447447 5.12416 0.242364
448448 0 0
449449 18.8641 0.890252 0.445126 0.895468i 0.353159π-0.353159\pi
0.445126 + 0.895468i 0.353159π0.353159\pi
450450 0 0
451451 −2.90619 −0.136847
452452 0 0
453453 −39.6796 −1.86431
454454 0 0
455455 −19.1398 −0.897288
456456 0 0
457457 −29.8571 −1.39666 −0.698329 0.715777i 0.746073π-0.746073\pi
−0.698329 + 0.715777i 0.746073π0.746073\pi
458458 0 0
459459 3.89752 0.181921
460460 0 0
461461 −30.1390 −1.40371 −0.701857 0.712318i 0.747645π-0.747645\pi
−0.701857 + 0.712318i 0.747645π0.747645\pi
462462 0 0
463463 −20.1857 −0.938108 −0.469054 0.883169i 0.655405π-0.655405\pi
−0.469054 + 0.883169i 0.655405π0.655405\pi
464464 0 0
465465 52.0876 2.41550
466466 0 0
467467 −31.2201 −1.44470 −0.722348 0.691530i 0.756937π-0.756937\pi
−0.722348 + 0.691530i 0.756937π0.756937\pi
468468 0 0
469469 0.979564 0.0452321
470470 0 0
471471 27.1303 1.25010
472472 0 0
473473 9.61657 0.442170
474474 0 0
475475 0.347813 0.0159588
476476 0 0
477477 −12.0082 −0.549819
478478 0 0
479479 36.7900 1.68098 0.840490 0.541827i 0.182267π-0.182267\pi
0.840490 + 0.541827i 0.182267π0.182267\pi
480480 0 0
481481 2.80828 0.128047
482482 0 0
483483 53.1610 2.41891
484484 0 0
485485 −29.2961 −1.33027
486486 0 0
487487 17.9461 0.813217 0.406609 0.913602i 0.366711π-0.366711\pi
0.406609 + 0.913602i 0.366711π0.366711\pi
488488 0 0
489489 2.68562 0.121448
490490 0 0
491491 29.3428 1.32422 0.662111 0.749406i 0.269661π-0.269661\pi
0.662111 + 0.749406i 0.269661π0.269661\pi
492492 0 0
493493 6.68562 0.301105
494494 0 0
495495 −5.40969 −0.243147
496496 0 0
497497 19.7621 0.886450
498498 0 0
499499 6.17848 0.276587 0.138293 0.990391i 0.455838π-0.455838\pi
0.138293 + 0.990391i 0.455838π0.455838\pi
500500 0 0
501501 45.8350 2.04776
502502 0 0
503503 6.14917 0.274178 0.137089 0.990559i 0.456225π-0.456225\pi
0.137089 + 0.990559i 0.456225π0.456225\pi
504504 0 0
505505 −36.1723 −1.60965
506506 0 0
507507 11.5938 0.514897
508508 0 0
509509 −27.6183 −1.22416 −0.612080 0.790796i 0.709667π-0.709667\pi
−0.612080 + 0.790796i 0.709667π0.709667\pi
510510 0 0
511511 49.2228 2.17749
512512 0 0
513513 −7.59534 −0.335343
514514 0 0
515515 22.0163 0.970156
516516 0 0
517517 8.18638 0.360037
518518 0 0
519519 51.4195 2.25707
520520 0 0
521521 −10.1720 −0.445643 −0.222821 0.974859i 0.571527π-0.571527\pi
−0.222821 + 0.974859i 0.571527π0.571527\pi
522522 0 0
523523 −9.41161 −0.411541 −0.205771 0.978600i 0.565970π-0.565970\pi
−0.205771 + 0.978600i 0.565970π0.565970\pi
524524 0 0
525525 0.622273 0.0271582
526526 0 0
527527 −20.7342 −0.903197
528528 0 0
529529 35.1218 1.52703
530530 0 0
531531 13.2249 0.573912
532532 0 0
533533 −7.15612 −0.309966
534534 0 0
535535 −11.8398 −0.511879
536536 0 0
537537 −33.0638 −1.42681
538538 0 0
539539 −2.80441 −0.120795
540540 0 0
541541 2.04371 0.0878659 0.0439329 0.999034i 0.486011π-0.486011\pi
0.0439329 + 0.999034i 0.486011π0.486011\pi
542542 0 0
543543 56.0643 2.40595
544544 0 0
545545 −12.8420 −0.550089
546546 0 0
547547 −22.9271 −0.980292 −0.490146 0.871640i 0.663057π-0.663057\pi
−0.490146 + 0.871640i 0.663057π0.663057\pi
548548 0 0
549549 22.7920 0.972737
550550 0 0
551551 −13.0287 −0.555040
552552 0 0
553553 −26.7351 −1.13689
554554 0 0
555555 5.02431 0.213270
556556 0 0
557557 33.6633 1.42636 0.713179 0.700982i 0.247255π-0.247255\pi
0.713179 + 0.700982i 0.247255π0.247255\pi
558558 0 0
559559 23.6796 1.00154
560560 0 0
561561 5.17153 0.218342
562562 0 0
563563 10.0486 0.423499 0.211749 0.977324i 0.432084π-0.432084\pi
0.211749 + 0.977324i 0.432084π0.432084\pi
564564 0 0
565565 24.5293 1.03195
566566 0 0
567567 −33.3383 −1.40008
568568 0 0
569569 33.9947 1.42513 0.712567 0.701604i 0.247532π-0.247532\pi
0.712567 + 0.701604i 0.247532π0.247532\pi
570570 0 0
571571 6.71755 0.281121 0.140560 0.990072i 0.455110π-0.455110\pi
0.140560 + 0.990072i 0.455110π0.455110\pi
572572 0 0
573573 33.3833 1.39461
574574 0 0
575575 0.680341 0.0283722
576576 0 0
577577 −32.5701 −1.35591 −0.677956 0.735102i 0.737134π-0.737134\pi
−0.677956 + 0.735102i 0.737134π0.737134\pi
578578 0 0
579579 −41.2635 −1.71485
580580 0 0
581581 30.0209 1.24548
582582 0 0
583583 6.39816 0.264985
584584 0 0
585585 −13.3207 −0.550742
586586 0 0
587587 −30.6948 −1.26691 −0.633454 0.773780i 0.718363π-0.718363\pi
−0.633454 + 0.773780i 0.718363π0.718363\pi
588588 0 0
589589 40.4061 1.66490
590590 0 0
591591 19.3353 0.795347
592592 0 0
593593 −44.7258 −1.83667 −0.918334 0.395805i 0.870465π-0.870465\pi
−0.918334 + 0.395805i 0.870465π0.870465\pi
594594 0 0
595595 13.6310 0.558815
596596 0 0
597597 −51.4963 −2.10760
598598 0 0
599599 4.23268 0.172942 0.0864712 0.996254i 0.472441π-0.472441\pi
0.0864712 + 0.996254i 0.472441π0.472441\pi
600600 0 0
601601 7.01028 0.285955 0.142978 0.989726i 0.454332π-0.454332\pi
0.142978 + 0.989726i 0.454332π0.454332\pi
602602 0 0
603603 0.681744 0.0277628
604604 0 0
605605 −21.4939 −0.873851
606606 0 0
607607 23.4188 0.950540 0.475270 0.879840i 0.342350π-0.342350\pi
0.475270 + 0.879840i 0.342350π0.342350\pi
608608 0 0
609609 −23.3096 −0.944554
610610 0 0
611611 20.1579 0.815502
612612 0 0
613613 7.78855 0.314577 0.157288 0.987553i 0.449725π-0.449725\pi
0.157288 + 0.987553i 0.449725π0.449725\pi
614614 0 0
615615 −12.8030 −0.516268
616616 0 0
617617 −25.4388 −1.02413 −0.512064 0.858948i 0.671119π-0.671119\pi
−0.512064 + 0.858948i 0.671119π0.671119\pi
618618 0 0
619619 21.0948 0.847873 0.423937 0.905692i 0.360648π-0.360648\pi
0.423937 + 0.905692i 0.360648π0.360648\pi
620620 0 0
621621 −14.8569 −0.596187
622622 0 0
623623 −25.3842 −1.01700
624624 0 0
625625 −24.5458 −0.981834
626626 0 0
627627 −10.0781 −0.402479
628628 0 0
629629 −2.00000 −0.0797452
630630 0 0
631631 3.60937 0.143687 0.0718433 0.997416i 0.477112π-0.477112\pi
0.0718433 + 0.997416i 0.477112π0.477112\pi
632632 0 0
633633 −14.1081 −0.560746
634634 0 0
635635 −5.40387 −0.214446
636636 0 0
637637 −6.90551 −0.273606
638638 0 0
639639 13.7538 0.544090
640640 0 0
641641 −36.8109 −1.45394 −0.726972 0.686667i 0.759073π-0.759073\pi
−0.726972 + 0.686667i 0.759073π0.759073\pi
642642 0 0
643643 28.3296 1.11721 0.558605 0.829434i 0.311337π-0.311337\pi
0.558605 + 0.829434i 0.311337π0.311337\pi
644644 0 0
645645 42.3652 1.66813
646646 0 0
647647 −0.581191 −0.0228490 −0.0114245 0.999935i 0.503637π-0.503637\pi
−0.0114245 + 0.999935i 0.503637π0.503637\pi
648648 0 0
649649 −7.04642 −0.276596
650650 0 0
651651 72.2906 2.83329
652652 0 0
653653 3.71276 0.145291 0.0726457 0.997358i 0.476856π-0.476856\pi
0.0726457 + 0.997358i 0.476856π0.476856\pi
654654 0 0
655655 −27.3226 −1.06758
656656 0 0
657657 34.2574 1.33651
658658 0 0
659659 −15.5269 −0.604841 −0.302420 0.953175i 0.597795π-0.597795\pi
−0.302420 + 0.953175i 0.597795π0.597795\pi
660660 0 0
661661 −17.2760 −0.671957 −0.335978 0.941870i 0.609067π-0.609067\pi
−0.335978 + 0.941870i 0.609067π0.609067\pi
662662 0 0
663663 12.7342 0.494556
664664 0 0
665665 −26.5635 −1.03009
666666 0 0
667667 −25.4848 −0.986774
668668 0 0
669669 28.5766 1.10484
670670 0 0
671671 −12.1439 −0.468810
672672 0 0
673673 −8.68491 −0.334779 −0.167389 0.985891i 0.553534π-0.553534\pi
−0.167389 + 0.985891i 0.553534π0.553534\pi
674674 0 0
675675 −0.173907 −0.00669367
676676 0 0
677677 −35.7279 −1.37313 −0.686567 0.727067i 0.740883π-0.740883\pi
−0.686567 + 0.727067i 0.740883π0.740883\pi
678678 0 0
679679 −40.6591 −1.56035
680680 0 0
681681 −59.7768 −2.29065
682682 0 0
683683 8.80932 0.337079 0.168540 0.985695i 0.446095π-0.446095\pi
0.168540 + 0.985695i 0.446095π0.446095\pi
684684 0 0
685685 −30.0307 −1.14742
686686 0 0
687687 −27.8775 −1.06359
688688 0 0
689689 15.7547 0.600205
690690 0 0
691691 −6.36904 −0.242290 −0.121145 0.992635i 0.538657π-0.538657\pi
−0.121145 + 0.992635i 0.538657π0.538657\pi
692692 0 0
693693 −7.50793 −0.285203
694694 0 0
695695 13.7546 0.521743
696696 0 0
697697 5.09644 0.193041
698698 0 0
699699 −32.0679 −1.21292
700700 0 0
701701 −11.6199 −0.438877 −0.219439 0.975626i 0.570423π-0.570423\pi
−0.219439 + 0.975626i 0.570423π0.570423\pi
702702 0 0
703703 3.89752 0.146998
704704 0 0
705705 36.0646 1.35827
706706 0 0
707707 −50.2024 −1.88805
708708 0 0
709709 20.2372 0.760026 0.380013 0.924981i 0.375920π-0.375920\pi
0.380013 + 0.924981i 0.375920π0.375920\pi
710710 0 0
711711 −18.6068 −0.697809
712712 0 0
713713 79.0364 2.95994
714714 0 0
715715 7.09745 0.265430
716716 0 0
717717 −31.1003 −1.16146
718718 0 0
719719 −10.8432 −0.404383 −0.202192 0.979346i 0.564806π-0.564806\pi
−0.202192 + 0.979346i 0.564806π0.564806\pi
720720 0 0
721721 30.5557 1.13796
722722 0 0
723723 −65.5527 −2.43793
724724 0 0
725725 −0.298311 −0.0110790
726726 0 0
727727 −35.3481 −1.31099 −0.655494 0.755200i 0.727540π-0.727540\pi
−0.655494 + 0.755200i 0.727540π0.727540\pi
728728 0 0
729729 −9.94727 −0.368417
730730 0 0
731731 −16.8641 −0.623741
732732 0 0
733733 −27.3253 −1.00928 −0.504641 0.863329i 0.668375π-0.668375\pi
−0.504641 + 0.863329i 0.668375π0.668375\pi
734734 0 0
735735 −12.3547 −0.455709
736736 0 0
737737 −0.363243 −0.0133802
738738 0 0
739739 27.8208 1.02341 0.511703 0.859162i 0.329015π-0.329015\pi
0.511703 + 0.859162i 0.329015π0.329015\pi
740740 0 0
741741 −24.8160 −0.911638
742742 0 0
743743 −37.9335 −1.39164 −0.695822 0.718214i 0.744960π-0.744960\pi
−0.695822 + 0.718214i 0.744960π0.744960\pi
744744 0 0
745745 −5.00836 −0.183492
746746 0 0
747747 20.8936 0.764455
748748 0 0
749749 −16.4320 −0.600414
750750 0 0
751751 47.0299 1.71615 0.858073 0.513528i 0.171662π-0.171662\pi
0.858073 + 0.513528i 0.171662π0.171662\pi
752752 0 0
753753 48.4542 1.76577
754754 0 0
755755 38.7828 1.41145
756756 0 0
757757 −13.0041 −0.472643 −0.236321 0.971675i 0.575942π-0.575942\pi
−0.236321 + 0.971675i 0.575942π0.575942\pi
758758 0 0
759759 −19.7132 −0.715546
760760 0 0
761761 48.7562 1.76741 0.883705 0.468045i 0.155041π-0.155041\pi
0.883705 + 0.468045i 0.155041π0.155041\pi
762762 0 0
763763 −17.8229 −0.645233
764764 0 0
765765 9.48670 0.342992
766766 0 0
767767 −17.3509 −0.626505
768768 0 0
769769 25.5641 0.921865 0.460933 0.887435i 0.347515π-0.347515\pi
0.460933 + 0.887435i 0.347515π0.347515\pi
770770 0 0
771771 −8.26180 −0.297541
772772 0 0
773773 −10.6026 −0.381350 −0.190675 0.981653i 0.561068π-0.561068\pi
−0.190675 + 0.981653i 0.561068π0.561068\pi
774774 0 0
775775 0.925156 0.0332326
776776 0 0
777777 6.97307 0.250157
778778 0 0
779779 −9.93174 −0.355842
780780 0 0
781781 −7.32820 −0.262224
782782 0 0
783783 6.51433 0.232803
784784 0 0
785785 −26.5172 −0.946439
786786 0 0
787787 40.9813 1.46083 0.730413 0.683006i 0.239328π-0.239328\pi
0.730413 + 0.683006i 0.239328π0.239328\pi
788788 0 0
789789 41.2782 1.46954
790790 0 0
791791 34.0434 1.21044
792792 0 0
793793 −29.9028 −1.06188
794794 0 0
795795 28.1867 0.999680
796796 0 0
797797 45.0984 1.59747 0.798733 0.601685i 0.205504π-0.205504\pi
0.798733 + 0.601685i 0.205504π0.205504\pi
798798 0 0
799799 −14.3560 −0.507880
800800 0 0
801801 −17.6666 −0.624218
802802 0 0
803803 −18.2529 −0.644130
804804 0 0
805805 −51.9596 −1.83134
806806 0 0
807807 18.2483 0.642371
808808 0 0
809809 13.4342 0.472323 0.236161 0.971714i 0.424111π-0.424111\pi
0.236161 + 0.971714i 0.424111π0.424111\pi
810810 0 0
811811 33.6020 1.17993 0.589963 0.807431i 0.299142π-0.299142\pi
0.589963 + 0.807431i 0.299142π0.299142\pi
812812 0 0
813813 31.3244 1.09859
814814 0 0
815815 −2.62492 −0.0919470
816816 0 0
817817 32.8641 1.14977
818818 0 0
819819 −18.4873 −0.645999
820820 0 0
821821 7.15680 0.249774 0.124887 0.992171i 0.460143π-0.460143\pi
0.124887 + 0.992171i 0.460143π0.460143\pi
822822 0 0
823823 17.7282 0.617966 0.308983 0.951068i 0.400011π-0.400011\pi
0.308983 + 0.951068i 0.400011π0.400011\pi
824824 0 0
825825 −0.230752 −0.00803376
826826 0 0
827827 30.4129 1.05756 0.528780 0.848759i 0.322650π-0.322650\pi
0.528780 + 0.848759i 0.322650π0.322650\pi
828828 0 0
829829 32.3315 1.12292 0.561460 0.827504i 0.310240π-0.310240\pi
0.561460 + 0.827504i 0.310240π0.310240\pi
830830 0 0
831831 −5.02431 −0.174291
832832 0 0
833833 4.91796 0.170397
834834 0 0
835835 −44.7992 −1.55034
836836 0 0
837837 −20.2030 −0.698319
838838 0 0
839839 3.00604 0.103780 0.0518900 0.998653i 0.483475π-0.483475\pi
0.0518900 + 0.998653i 0.483475π0.483475\pi
840840 0 0
841841 −17.8256 −0.614677
842842 0 0
843843 4.76687 0.164180
844844 0 0
845845 −11.3317 −0.389824
846846 0 0
847847 −29.8307 −1.02499
848848 0 0
849849 14.2111 0.487724
850850 0 0
851851 7.62376 0.261339
852852 0 0
853853 −32.2920 −1.10566 −0.552829 0.833295i 0.686452π-0.686452\pi
−0.552829 + 0.833295i 0.686452π0.686452\pi
854854 0 0
855855 −18.4873 −0.632253
856856 0 0
857857 42.8093 1.46234 0.731169 0.682196i 0.238975π-0.238975\pi
0.731169 + 0.682196i 0.238975π0.238975\pi
858858 0 0
859859 20.5567 0.701384 0.350692 0.936491i 0.385946π-0.385946\pi
0.350692 + 0.936491i 0.385946π0.385946\pi
860860 0 0
861861 −17.7689 −0.605563
862862 0 0
863863 −30.2353 −1.02922 −0.514611 0.857424i 0.672064π-0.672064\pi
−0.514611 + 0.857424i 0.672064π0.672064\pi
864864 0 0
865865 −50.2575 −1.70880
866866 0 0
867867 29.4744 1.00100
868868 0 0
869869 9.91396 0.336308
870870 0 0
871871 −0.894441 −0.0303070
872872 0 0
873873 −28.2974 −0.957723
874874 0 0
875875 −34.6856 −1.17259
876876 0 0
877877 −31.7830 −1.07323 −0.536617 0.843826i 0.680298π-0.680298\pi
−0.536617 + 0.843826i 0.680298π0.680298\pi
878878 0 0
879879 −23.3904 −0.788938
880880 0 0
881881 −9.27159 −0.312368 −0.156184 0.987728i 0.549919π-0.549919\pi
−0.156184 + 0.987728i 0.549919π0.549919\pi
882882 0 0
883883 8.00000 0.269221 0.134611 0.990899i 0.457022π-0.457022\pi
0.134611 + 0.990899i 0.457022π0.457022\pi
884884 0 0
885885 −31.0426 −1.04348
886886 0 0
887887 30.8250 1.03500 0.517500 0.855683i 0.326863π-0.326863\pi
0.517500 + 0.855683i 0.326863π0.326863\pi
888888 0 0
889889 −7.49985 −0.251537
890890 0 0
891891 12.3625 0.414161
892892 0 0
893893 27.9765 0.936198
894894 0 0
895895 32.3166 1.08022
896896 0 0
897897 −48.5414 −1.62075
898898 0 0
899899 −34.6553 −1.15582
900900 0 0
901901 −11.2201 −0.373797
902902 0 0
903903 58.7972 1.95665
904904 0 0
905905 −54.7972 −1.82152
906906 0 0
907907 55.9288 1.85709 0.928543 0.371225i 0.121062π-0.121062\pi
0.928543 + 0.371225i 0.121062π0.121062\pi
908908 0 0
909909 −34.9392 −1.15886
910910 0 0
911911 18.4663 0.611815 0.305907 0.952061i 0.401040π-0.401040\pi
0.305907 + 0.952061i 0.401040π0.401040\pi
912912 0 0
913913 −11.1324 −0.368428
914914 0 0
915915 −53.4992 −1.76863
916916 0 0
917917 −37.9202 −1.25223
918918 0 0
919919 5.12383 0.169019 0.0845097 0.996423i 0.473068π-0.473068\pi
0.0845097 + 0.996423i 0.473068π0.473068\pi
920920 0 0
921921 25.1756 0.829564
922922 0 0
923923 −18.0448 −0.593951
924924 0 0
925925 0.0892395 0.00293418
926926 0 0
927927 21.2658 0.698460
928928 0 0
929929 −0.612450 −0.0200938 −0.0100469 0.999950i 0.503198π-0.503198\pi
−0.0100469 + 0.999950i 0.503198π0.503198\pi
930930 0 0
931931 −9.58393 −0.314101
932932 0 0
933933 −23.3741 −0.765233
934934 0 0
935935 −5.05465 −0.165305
936936 0 0
937937 −3.83662 −0.125337 −0.0626684 0.998034i 0.519961π-0.519961\pi
−0.0626684 + 0.998034i 0.519961π0.519961\pi
938938 0 0
939939 −6.69336 −0.218429
940940 0 0
941941 −3.05465 −0.0995789 −0.0497894 0.998760i 0.515855π-0.515855\pi
−0.0497894 + 0.998760i 0.515855π0.515855\pi
942942 0 0
943943 −19.4270 −0.632631
944944 0 0
945945 13.2817 0.432055
946946 0 0
947947 −38.9604 −1.26604 −0.633022 0.774134i 0.718186π-0.718186\pi
−0.633022 + 0.774134i 0.718186π0.718186\pi
948948 0 0
949949 −44.9454 −1.45899
950950 0 0
951951 −32.1650 −1.04302
952952 0 0
953953 42.2529 1.36871 0.684353 0.729151i 0.260085π-0.260085\pi
0.684353 + 0.729151i 0.260085π0.260085\pi
954954 0 0
955955 −32.6289 −1.05585
956956 0 0
957957 8.64371 0.279411
958958 0 0
959959 −41.6787 −1.34587
960960 0 0
961961 76.4771 2.46700
962962 0 0
963963 −11.4362 −0.368525
964964 0 0
965965 40.3310 1.29830
966966 0 0
967967 36.2122 1.16451 0.582253 0.813008i 0.302171π-0.302171\pi
0.582253 + 0.813008i 0.302171π0.302171\pi
968968 0 0
969969 17.6734 0.567752
970970 0 0
971971 −11.9615 −0.383864 −0.191932 0.981408i 0.561475π-0.561475\pi
−0.191932 + 0.981408i 0.561475π0.561475\pi
972972 0 0
973973 19.0896 0.611985
974974 0 0
975975 −0.568198 −0.0181969
976976 0 0
977977 −38.3440 −1.22673 −0.613366 0.789799i 0.710185π-0.710185\pi
−0.613366 + 0.789799i 0.710185π0.710185\pi
978978 0 0
979979 9.41301 0.300841
980980 0 0
981981 −12.4042 −0.396035
982982 0 0
983983 31.1742 0.994302 0.497151 0.867664i 0.334380π-0.334380\pi
0.497151 + 0.867664i 0.334380π0.334380\pi
984984 0 0
985985 −18.8983 −0.602150
986986 0 0
987987 50.0528 1.59320
988988 0 0
989989 64.2839 2.04411
990990 0 0
991991 −39.2981 −1.24834 −0.624172 0.781287i 0.714564π-0.714564\pi
−0.624172 + 0.781287i 0.714564π0.714564\pi
992992 0 0
993993 −59.9765 −1.90330
994994 0 0
995995 50.3326 1.59565
996996 0 0
997997 −34.3022 −1.08636 −0.543180 0.839616i 0.682780π-0.682780\pi
−0.543180 + 0.839616i 0.682780π0.682780\pi
998998 0 0
999999 −1.94876 −0.0616561
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 2368.2.a.bg.1.2 4
4.3 odd 2 2368.2.a.bh.1.3 4
8.3 odd 2 592.2.a.j.1.2 4
8.5 even 2 296.2.a.d.1.3 4
24.5 odd 2 2664.2.a.r.1.4 4
24.11 even 2 5328.2.a.bp.1.4 4
40.29 even 2 7400.2.a.n.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
296.2.a.d.1.3 4 8.5 even 2
592.2.a.j.1.2 4 8.3 odd 2
2368.2.a.bg.1.2 4 1.1 even 1 trivial
2368.2.a.bh.1.3 4 4.3 odd 2
2664.2.a.r.1.4 4 24.5 odd 2
5328.2.a.bp.1.4 4 24.11 even 2
7400.2.a.n.1.2 4 40.29 even 2