Properties

Label 3150.2.bf.f.1151.7
Level 31503150
Weight 22
Character 3150.1151
Analytic conductor 25.15325.153
Analytic rank 00
Dimension 3232
Inner twists 88

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [3150,2,Mod(1151,3150)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3150, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3150.1151"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 3150=232527 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3150.bf (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [32,0,0,16,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 25.152876636725.1528766367
Analytic rank: 00
Dimension: 3232
Relative dimension: 1616 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 1151.7
Character χ\chi == 3150.1151
Dual form 3150.2.bf.f.1601.7

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.866025+0.500000i)q2+(0.5000000.866025i)q4+(1.29693+2.30608i)q7+1.00000iq8+(1.11120+0.641550i)q11+6.14864iq13+(0.02986662.64558i)q14+(0.5000000.866025i)q16+(3.26128+5.64871i)q17+(5.22868+3.01878i)q191.28310q22+(2.493431.43958i)q23+(3.074325.32488i)q26+(1.34866+2.27621i)q28+1.35052iq29+(7.495584.32758i)q31+(0.866025+0.500000i)q326.52257iq34+(4.766908.25652i)q37+(3.018785.22868i)q38+8.71759q41+5.35859q43+(1.111200.641550i)q44+(1.43958+2.49343i)q46+(0.4030860.698165i)q47+(3.635975.98162i)q49+(5.32488+3.07432i)q52+(5.77488+3.33413i)q53+(2.306081.29693i)q56+(0.6752601.16959i)q58+(0.7981101.38237i)q59+(5.50239+3.17681i)q61+8.65515q621.00000q64+(2.697314.67188i)q67+(3.26128+5.64871i)q6815.6787iq71+(10.75326.20837i)q73+(8.25652+4.76690i)q74+6.03756iq76+(2.92060+1.73046i)q77+(5.59093+9.68377i)q79+(7.54966+4.35880i)q823.74493q83+(4.64067+2.67929i)q86+(0.641550+1.11120i)q88+(1.819713.15183i)q89+(14.17927.97433i)q912.87917iq92+(0.698165+0.403086i)q94+8.76818iq97+(6.13965+3.36225i)q98+O(q100)q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.29693 + 2.30608i) q^{7} +1.00000i q^{8} +(1.11120 + 0.641550i) q^{11} +6.14864i q^{13} +(-0.0298666 - 2.64558i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.26128 + 5.64871i) q^{17} +(-5.22868 + 3.01878i) q^{19} -1.28310 q^{22} +(2.49343 - 1.43958i) q^{23} +(-3.07432 - 5.32488i) q^{26} +(1.34866 + 2.27621i) q^{28} +1.35052i q^{29} +(-7.49558 - 4.32758i) q^{31} +(0.866025 + 0.500000i) q^{32} -6.52257i q^{34} +(-4.76690 - 8.25652i) q^{37} +(3.01878 - 5.22868i) q^{38} +8.71759 q^{41} +5.35859 q^{43} +(1.11120 - 0.641550i) q^{44} +(-1.43958 + 2.49343i) q^{46} +(-0.403086 - 0.698165i) q^{47} +(-3.63597 - 5.98162i) q^{49} +(5.32488 + 3.07432i) q^{52} +(5.77488 + 3.33413i) q^{53} +(-2.30608 - 1.29693i) q^{56} +(-0.675260 - 1.16959i) q^{58} +(0.798110 - 1.38237i) q^{59} +(-5.50239 + 3.17681i) q^{61} +8.65515 q^{62} -1.00000 q^{64} +(2.69731 - 4.67188i) q^{67} +(3.26128 + 5.64871i) q^{68} -15.6787i q^{71} +(-10.7532 - 6.20837i) q^{73} +(8.25652 + 4.76690i) q^{74} +6.03756i q^{76} +(-2.92060 + 1.73046i) q^{77} +(5.59093 + 9.68377i) q^{79} +(-7.54966 + 4.35880i) q^{82} -3.74493 q^{83} +(-4.64067 + 2.67929i) q^{86} +(-0.641550 + 1.11120i) q^{88} +(-1.81971 - 3.15183i) q^{89} +(-14.1792 - 7.97433i) q^{91} -2.87917i q^{92} +(0.698165 + 0.403086i) q^{94} +8.76818i q^{97} +(6.13965 + 3.36225i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+16q416q1648q19+24q3116q46+56q49+48q6132q648q7956q91+120q94+O(q100) 32 q + 16 q^{4} - 16 q^{16} - 48 q^{19} + 24 q^{31} - 16 q^{46} + 56 q^{49} + 48 q^{61} - 32 q^{64} - 8 q^{79} - 56 q^{91} + 120 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3150Z)×\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times.

nn 127127 451451 28012801
χ(n)\chi(n) 11 e(16)e\left(\frac{1}{6}\right) 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.866025 + 0.500000i −0.612372 + 0.353553i
33 0 0
44 0.500000 0.866025i 0.250000 0.433013i
55 0 0
66 0 0
77 −1.29693 + 2.30608i −0.490192 + 0.871614i
88 1.00000i 0.353553i
99 0 0
1010 0 0
1111 1.11120 + 0.641550i 0.335038 + 0.193435i 0.658076 0.752952i 0.271371π-0.271371\pi
−0.323037 + 0.946386i 0.604704π0.604704\pi
1212 0 0
1313 6.14864i 1.70533i 0.522462 + 0.852663i 0.325014π0.325014\pi
−0.522462 + 0.852663i 0.674986π0.674986\pi
1414 −0.0298666 2.64558i −0.00798219 0.707062i
1515 0 0
1616 −0.500000 0.866025i −0.125000 0.216506i
1717 −3.26128 + 5.64871i −0.790977 + 1.37001i 0.134385 + 0.990929i 0.457094π0.457094\pi
−0.925362 + 0.379084i 0.876239π0.876239\pi
1818 0 0
1919 −5.22868 + 3.01878i −1.19954 + 0.692555i −0.960453 0.278443i 0.910182π-0.910182\pi
−0.239088 + 0.970998i 0.576848π0.576848\pi
2020 0 0
2121 0 0
2222 −1.28310 −0.273558
2323 2.49343 1.43958i 0.519917 0.300174i −0.216984 0.976175i 0.569622π-0.569622\pi
0.736901 + 0.676001i 0.236289π0.236289\pi
2424 0 0
2525 0 0
2626 −3.07432 5.32488i −0.602923 1.04429i
2727 0 0
2828 1.34866 + 2.27621i 0.254872 + 0.430163i
2929 1.35052i 0.250785i 0.992107 + 0.125393i 0.0400191π0.0400191\pi
−0.992107 + 0.125393i 0.959981π0.959981\pi
3030 0 0
3131 −7.49558 4.32758i −1.34625 0.777255i −0.358530 0.933518i 0.616722π-0.616722\pi
−0.987716 + 0.156263i 0.950055π0.950055\pi
3232 0.866025 + 0.500000i 0.153093 + 0.0883883i
3333 0 0
3434 6.52257i 1.11861i
3535 0 0
3636 0 0
3737 −4.76690 8.25652i −0.783674 1.35736i −0.929788 0.368095i 0.880010π-0.880010\pi
0.146114 0.989268i 0.453323π-0.453323\pi
3838 3.01878 5.22868i 0.489710 0.848203i
3939 0 0
4040 0 0
4141 8.71759 1.36146 0.680730 0.732535i 0.261663π-0.261663\pi
0.680730 + 0.732535i 0.261663π0.261663\pi
4242 0 0
4343 5.35859 0.817177 0.408588 0.912719i 0.366021π-0.366021\pi
0.408588 + 0.912719i 0.366021π0.366021\pi
4444 1.11120 0.641550i 0.167519 0.0967173i
4545 0 0
4646 −1.43958 + 2.49343i −0.212255 + 0.367637i
4747 −0.403086 0.698165i −0.0587961 0.101838i 0.835129 0.550054i 0.185393π-0.185393\pi
−0.893925 + 0.448216i 0.852060π0.852060\pi
4848 0 0
4949 −3.63597 5.98162i −0.519424 0.854517i
5050 0 0
5151 0 0
5252 5.32488 + 3.07432i 0.738427 + 0.426331i
5353 5.77488 + 3.33413i 0.793241 + 0.457978i 0.841102 0.540876i 0.181907π-0.181907\pi
−0.0478611 + 0.998854i 0.515240π0.515240\pi
5454 0 0
5555 0 0
5656 −2.30608 1.29693i −0.308162 0.173309i
5757 0 0
5858 −0.675260 1.16959i −0.0886660 0.153574i
5959 0.798110 1.38237i 0.103905 0.179969i −0.809385 0.587278i 0.800200π-0.800200\pi
0.913290 + 0.407309i 0.133533π0.133533\pi
6060 0 0
6161 −5.50239 + 3.17681i −0.704509 + 0.406748i −0.809025 0.587775i 0.800004π-0.800004\pi
0.104516 + 0.994523i 0.466671π0.466671\pi
6262 8.65515 1.09921
6363 0 0
6464 −1.00000 −0.125000
6565 0 0
6666 0 0
6767 2.69731 4.67188i 0.329529 0.570761i −0.652889 0.757453i 0.726443π-0.726443\pi
0.982418 + 0.186692i 0.0597766π0.0597766\pi
6868 3.26128 + 5.64871i 0.395489 + 0.685006i
6969 0 0
7070 0 0
7171 15.6787i 1.86072i −0.366650 0.930359i 0.619495π-0.619495\pi
0.366650 0.930359i 0.380505π-0.380505\pi
7272 0 0
7373 −10.7532 6.20837i −1.25857 0.726635i −0.285772 0.958298i 0.592250π-0.592250\pi
−0.972796 + 0.231663i 0.925583π0.925583\pi
7474 8.25652 + 4.76690i 0.959801 + 0.554141i
7575 0 0
7676 6.03756i 0.692555i
7777 −2.92060 + 1.73046i −0.332834 + 0.197204i
7878 0 0
7979 5.59093 + 9.68377i 0.629028 + 1.08951i 0.987747 + 0.156064i 0.0498805π0.0498805\pi
−0.358719 + 0.933446i 0.616786π0.616786\pi
8080 0 0
8181 0 0
8282 −7.54966 + 4.35880i −0.833720 + 0.481349i
8383 −3.74493 −0.411059 −0.205530 0.978651i 0.565892π-0.565892\pi
−0.205530 + 0.978651i 0.565892π0.565892\pi
8484 0 0
8585 0 0
8686 −4.64067 + 2.67929i −0.500417 + 0.288916i
8787 0 0
8888 −0.641550 + 1.11120i −0.0683894 + 0.118454i
8989 −1.81971 3.15183i −0.192889 0.334093i 0.753318 0.657657i 0.228452π-0.228452\pi
−0.946206 + 0.323564i 0.895119π0.895119\pi
9090 0 0
9191 −14.1792 7.97433i −1.48639 0.835937i
9292 2.87917i 0.300174i
9393 0 0
9494 0.698165 + 0.403086i 0.0720102 + 0.0415751i
9595 0 0
9696 0 0
9797 8.76818i 0.890274i 0.895463 + 0.445137i 0.146845π0.146845\pi
−0.895463 + 0.445137i 0.853155π0.853155\pi
9898 6.13965 + 3.36225i 0.620198 + 0.339639i
9999 0 0
100100 0 0
101101 0.853270 1.47791i 0.0849035 0.147057i −0.820447 0.571723i 0.806275π-0.806275\pi
0.905350 + 0.424666i 0.139608π0.139608\pi
102102 0 0
103103 −8.97583 + 5.18220i −0.884415 + 0.510617i −0.872112 0.489307i 0.837250π-0.837250\pi
−0.0123035 + 0.999924i 0.503916π0.503916\pi
104104 −6.14864 −0.602923
105105 0 0
106106 −6.66826 −0.647679
107107 9.97106 5.75680i 0.963939 0.556531i 0.0665560 0.997783i 0.478799π-0.478799\pi
0.897383 + 0.441252i 0.145466π0.145466\pi
108108 0 0
109109 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i 0.802798π-0.802798\pi
0.909935 + 0.414751i 0.136131π0.136131\pi
110110 0 0
111111 0 0
112112 2.64558 0.0298666i 0.249984 0.00282213i
113113 13.3875i 1.25939i 0.776843 + 0.629695i 0.216820π0.216820\pi
−0.776843 + 0.629695i 0.783180π0.783180\pi
114114 0 0
115115 0 0
116116 1.16959 + 0.675260i 0.108593 + 0.0626963i
117117 0 0
118118 1.59622i 0.146944i
119119 −8.79670 14.8467i −0.806392 1.36100i
120120 0 0
121121 −4.67683 8.10050i −0.425166 0.736409i
122122 3.17681 5.50239i 0.287615 0.498163i
123123 0 0
124124 −7.49558 + 4.32758i −0.673123 + 0.388628i
125125 0 0
126126 0 0
127127 5.65313 0.501634 0.250817 0.968035i 0.419301π-0.419301\pi
0.250817 + 0.968035i 0.419301π0.419301\pi
128128 0.866025 0.500000i 0.0765466 0.0441942i
129129 0 0
130130 0 0
131131 −6.23366 10.7970i −0.544638 0.943340i −0.998630 0.0523344i 0.983334π-0.983334\pi
0.453992 0.891006i 0.349999π-0.349999\pi
132132 0 0
133133 −0.180321 15.9729i −0.0156358 1.38502i
134134 5.39463i 0.466025i
135135 0 0
136136 −5.64871 3.26128i −0.484373 0.279653i
137137 −0.0441401 0.0254843i −0.00377114 0.00217727i 0.498113 0.867112i 0.334026π-0.334026\pi
−0.501884 + 0.864935i 0.667360π0.667360\pi
138138 0 0
139139 1.05069i 0.0891184i −0.999007 0.0445592i 0.985812π-0.985812\pi
0.999007 0.0445592i 0.0141883π-0.0141883\pi
140140 0 0
141141 0 0
142142 7.83934 + 13.5781i 0.657863 + 1.13945i
143143 −3.94466 + 6.83235i −0.329869 + 0.571350i
144144 0 0
145145 0 0
146146 12.4167 1.02762
147147 0 0
148148 −9.53381 −0.783674
149149 7.12137 4.11153i 0.583406 0.336829i −0.179080 0.983835i 0.557312π-0.557312\pi
0.762486 + 0.647005i 0.223979π0.223979\pi
150150 0 0
151151 2.13357 3.69546i 0.173628 0.300732i −0.766058 0.642772i 0.777784π-0.777784\pi
0.939686 + 0.342040i 0.111118π0.111118\pi
152152 −3.01878 5.22868i −0.244855 0.424102i
153153 0 0
154154 1.66409 2.95892i 0.134096 0.238437i
155155 0 0
156156 0 0
157157 −4.18466 2.41601i −0.333972 0.192819i 0.323631 0.946183i 0.395096π-0.395096\pi
−0.657603 + 0.753364i 0.728430π0.728430\pi
158158 −9.68377 5.59093i −0.770399 0.444790i
159159 0 0
160160 0 0
161161 0.0859910 + 7.61708i 0.00677704 + 0.600310i
162162 0 0
163163 5.37661 + 9.31256i 0.421128 + 0.729416i 0.996050 0.0887927i 0.0283009π-0.0283009\pi
−0.574922 + 0.818208i 0.694968π0.694968\pi
164164 4.35880 7.54966i 0.340365 0.589529i
165165 0 0
166166 3.24320 1.87246i 0.251721 0.145331i
167167 −18.9267 −1.46459 −0.732295 0.680988i 0.761551π-0.761551\pi
−0.732295 + 0.680988i 0.761551π0.761551\pi
168168 0 0
169169 −24.8057 −1.90813
170170 0 0
171171 0 0
172172 2.67929 4.64067i 0.204294 0.353848i
173173 −5.92176 10.2568i −0.450223 0.779810i 0.548176 0.836363i 0.315322π-0.315322\pi
−0.998400 + 0.0565531i 0.981989π0.981989\pi
174174 0 0
175175 0 0
176176 1.28310i 0.0967173i
177177 0 0
178178 3.15183 + 1.81971i 0.236239 + 0.136393i
179179 3.27843 + 1.89280i 0.245041 + 0.141475i 0.617492 0.786577i 0.288149π-0.288149\pi
−0.372450 + 0.928052i 0.621482π0.621482\pi
180180 0 0
181181 19.0033i 1.41251i 0.707960 + 0.706253i 0.249616π0.249616\pi
−0.707960 + 0.706253i 0.750384π0.750384\pi
182182 16.2667 0.183639i 1.20577 0.0136122i
183183 0 0
184184 1.43958 + 2.49343i 0.106128 + 0.183818i
185185 0 0
186186 0 0
187187 −7.24785 + 4.18455i −0.530016 + 0.306005i
188188 −0.806172 −0.0587961
189189 0 0
190190 0 0
191191 −2.44949 + 1.41421i −0.177239 + 0.102329i −0.585995 0.810315i 0.699296π-0.699296\pi
0.408756 + 0.912644i 0.365963π0.365963\pi
192192 0 0
193193 −1.76946 + 3.06479i −0.127368 + 0.220608i −0.922656 0.385623i 0.873986π-0.873986\pi
0.795288 + 0.606232i 0.207320π0.207320\pi
194194 −4.38409 7.59347i −0.314759 0.545179i
195195 0 0
196196 −6.99822 + 0.158029i −0.499873 + 0.0112878i
197197 2.36728i 0.168662i 0.996438 + 0.0843308i 0.0268752π0.0268752\pi
−0.996438 + 0.0843308i 0.973125π0.973125\pi
198198 0 0
199199 3.00000 + 1.73205i 0.212664 + 0.122782i 0.602549 0.798082i 0.294152π-0.294152\pi
−0.389885 + 0.920864i 0.627485π0.627485\pi
200200 0 0
201201 0 0
202202 1.70654i 0.120072i
203203 −3.11440 1.75153i −0.218588 0.122933i
204204 0 0
205205 0 0
206206 5.18220 8.97583i 0.361061 0.625376i
207207 0 0
208208 5.32488 3.07432i 0.369214 0.213166i
209209 −7.74679 −0.535856
210210 0 0
211211 −14.3620 −0.988721 −0.494361 0.869257i 0.664598π-0.664598\pi
−0.494361 + 0.869257i 0.664598π0.664598\pi
212212 5.77488 3.33413i 0.396621 0.228989i
213213 0 0
214214 −5.75680 + 9.97106i −0.393527 + 0.681608i
215215 0 0
216216 0 0
217217 19.7009 11.6728i 1.33739 0.792403i
218218 2.00000i 0.135457i
219219 0 0
220220 0 0
221221 −34.7319 20.0524i −2.33632 1.34887i
222222 0 0
223223 13.5975i 0.910557i −0.890349 0.455279i 0.849540π-0.849540\pi
0.890349 0.455279i 0.150460π-0.150460\pi
224224 −2.27621 + 1.34866i −0.152086 + 0.0901109i
225225 0 0
226226 −6.69375 11.5939i −0.445261 0.771215i
227227 −6.17797 + 10.7006i −0.410046 + 0.710221i −0.994894 0.100922i 0.967821π-0.967821\pi
0.584848 + 0.811143i 0.301154π0.301154\pi
228228 0 0
229229 2.09008 1.20671i 0.138116 0.0797414i −0.429350 0.903138i 0.641257π-0.641257\pi
0.567466 + 0.823397i 0.307924π0.307924\pi
230230 0 0
231231 0 0
232232 −1.35052 −0.0886660
233233 −11.1506 + 6.43780i −0.730500 + 0.421754i −0.818605 0.574357i 0.805252π-0.805252\pi
0.0881051 + 0.996111i 0.471919π0.471919\pi
234234 0 0
235235 0 0
236236 −0.798110 1.38237i −0.0519525 0.0899844i
237237 0 0
238238 15.0415 + 8.45929i 0.974997 + 0.548334i
239239 27.2546i 1.76296i 0.472226 + 0.881478i 0.343451π0.343451\pi
−0.472226 + 0.881478i 0.656549π0.656549\pi
240240 0 0
241241 2.26690 + 1.30880i 0.146024 + 0.0843070i 0.571232 0.820789i 0.306466π-0.306466\pi
−0.425208 + 0.905096i 0.639799π0.639799\pi
242242 8.10050 + 4.67683i 0.520720 + 0.300638i
243243 0 0
244244 6.35361i 0.406748i
245245 0 0
246246 0 0
247247 −18.5614 32.1492i −1.18103 2.04561i
248248 4.32758 7.49558i 0.274801 0.475970i
249249 0 0
250250 0 0
251251 26.7173 1.68638 0.843190 0.537615i 0.180675π-0.180675\pi
0.843190 + 0.537615i 0.180675π0.180675\pi
252252 0 0
253253 3.69426 0.232256
254254 −4.89575 + 2.82656i −0.307187 + 0.177354i
255255 0 0
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 −5.28063 9.14632i −0.329397 0.570532i 0.652996 0.757362i 0.273512π-0.273512\pi
−0.982392 + 0.186830i 0.940179π0.940179\pi
258258 0 0
259259 25.2225 0.284743i 1.56725 0.0176930i
260260 0 0
261261 0 0
262262 10.7970 + 6.23366i 0.667042 + 0.385117i
263263 7.21550 + 4.16587i 0.444927 + 0.256879i 0.705685 0.708526i 0.250639π-0.250639\pi
−0.260759 + 0.965404i 0.583973π0.583973\pi
264264 0 0
265265 0 0
266266 8.14259 + 13.7427i 0.499254 + 0.842621i
267267 0 0
268268 −2.69731 4.67188i −0.164765 0.285381i
269269 7.14171 12.3698i 0.435438 0.754201i −0.561893 0.827210i 0.689927π-0.689927\pi
0.997331 + 0.0730091i 0.0232602π0.0232602\pi
270270 0 0
271271 −6.58566 + 3.80223i −0.400050 + 0.230969i −0.686506 0.727125i 0.740856π-0.740856\pi
0.286456 + 0.958094i 0.407523π0.407523\pi
272272 6.52257 0.395489
273273 0 0
274274 0.0509686 0.00307912
275275 0 0
276276 0 0
277277 −6.02002 + 10.4270i −0.361708 + 0.626497i −0.988242 0.152897i 0.951140π-0.951140\pi
0.626534 + 0.779394i 0.284473π0.284473\pi
278278 0.525345 + 0.909924i 0.0315081 + 0.0545736i
279279 0 0
280280 0 0
281281 12.7879i 0.762861i 0.924397 + 0.381431i 0.124569π0.124569\pi
−0.924397 + 0.381431i 0.875431π0.875431\pi
282282 0 0
283283 13.4685 + 7.77607i 0.800622 + 0.462239i 0.843689 0.536833i 0.180379π-0.180379\pi
−0.0430666 + 0.999072i 0.513713π0.513713\pi
284284 −13.5781 7.83934i −0.805715 0.465180i
285285 0 0
286286 7.88931i 0.466505i
287287 −11.3061 + 20.1034i −0.667376 + 1.18667i
288288 0 0
289289 −12.7719 22.1216i −0.751290 1.30127i
290290 0 0
291291 0 0
292292 −10.7532 + 6.20837i −0.629284 + 0.363317i
293293 −11.5536 −0.674967 −0.337483 0.941331i 0.609576π-0.609576\pi
−0.337483 + 0.941331i 0.609576π0.609576\pi
294294 0 0
295295 0 0
296296 8.25652 4.76690i 0.479900 0.277071i
297297 0 0
298298 −4.11153 + 7.12137i −0.238174 + 0.412530i
299299 8.85148 + 15.3312i 0.511894 + 0.886627i
300300 0 0
301301 −6.94969 + 12.3573i −0.400573 + 0.712263i
302302 4.26715i 0.245547i
303303 0 0
304304 5.22868 + 3.01878i 0.299885 + 0.173139i
305305 0 0
306306 0 0
307307 2.57617i 0.147030i 0.997294 + 0.0735150i 0.0234217π0.0234217\pi
−0.997294 + 0.0735150i 0.976578π0.976578\pi
308308 0.0383219 + 3.39455i 0.00218359 + 0.193422i
309309 0 0
310310 0 0
311311 12.3570 21.4030i 0.700702 1.21365i −0.267519 0.963553i 0.586204π-0.586204\pi
0.968220 0.250098i 0.0804629π-0.0804629\pi
312312 0 0
313313 −7.79573 + 4.50087i −0.440641 + 0.254404i −0.703869 0.710329i 0.748546π-0.748546\pi
0.263229 + 0.964733i 0.415213π0.415213\pi
314314 4.83203 0.272687
315315 0 0
316316 11.1819 0.629028
317317 −20.7031 + 11.9529i −1.16280 + 0.671344i −0.951974 0.306180i 0.900949π-0.900949\pi
−0.210828 + 0.977523i 0.567616π0.567616\pi
318318 0 0
319319 −0.866426 + 1.50069i −0.0485106 + 0.0840227i
320320 0 0
321321 0 0
322322 −3.88301 6.55359i −0.216392 0.365217i
323323 39.3804i 2.19118i
324324 0 0
325325 0 0
326326 −9.31256 5.37661i −0.515775 0.297783i
327327 0 0
328328 8.71759i 0.481349i
329329 2.13279 0.0240776i 0.117585 0.00132744i
330330 0 0
331331 −2.18364 3.78217i −0.120024 0.207887i 0.799753 0.600329i 0.204964π-0.204964\pi
−0.919777 + 0.392442i 0.871630π0.871630\pi
332332 −1.87246 + 3.24320i −0.102765 + 0.177994i
333333 0 0
334334 16.3910 9.46334i 0.896874 0.517811i
335335 0 0
336336 0 0
337337 −19.5159 −1.06310 −0.531549 0.847028i 0.678390π-0.678390\pi
−0.531549 + 0.847028i 0.678390π0.678390\pi
338338 21.4824 12.4029i 1.16849 0.674627i
339339 0 0
340340 0 0
341341 −5.55271 9.61758i −0.300696 0.520821i
342342 0 0
343343 18.5096 0.627092i 0.999427 0.0338598i
344344 5.35859i 0.288916i
345345 0 0
346346 10.2568 + 5.92176i 0.551409 + 0.318356i
347347 −23.3088 13.4574i −1.25128 0.722429i −0.279919 0.960024i 0.590308π-0.590308\pi
−0.971364 + 0.237595i 0.923641π0.923641\pi
348348 0 0
349349 10.3821i 0.555741i −0.960619 0.277870i 0.910371π-0.910371\pi
0.960619 0.277870i 0.0896286π-0.0896286\pi
350350 0 0
351351 0 0
352352 0.641550 + 1.11120i 0.0341947 + 0.0592270i
353353 0.0844756 0.146316i 0.00449618 0.00778761i −0.863769 0.503889i 0.831902π-0.831902\pi
0.868265 + 0.496101i 0.165235π0.165235\pi
354354 0 0
355355 0 0
356356 −3.63941 −0.192889
357357 0 0
358358 −3.78561 −0.200075
359359 32.6198 18.8330i 1.72161 0.993970i 0.805975 0.591949i 0.201641π-0.201641\pi
0.915631 0.402021i 0.131692π-0.131692\pi
360360 0 0
361361 8.72604 15.1139i 0.459265 0.795471i
362362 −9.50166 16.4574i −0.499396 0.864979i
363363 0 0
364364 −13.9956 + 8.29240i −0.733568 + 0.434640i
365365 0 0
366366 0 0
367367 13.1253 + 7.57787i 0.685133 + 0.395562i 0.801786 0.597611i 0.203883π-0.203883\pi
−0.116653 + 0.993173i 0.537217π0.537217\pi
368368 −2.49343 1.43958i −0.129979 0.0750435i
369369 0 0
370370 0 0
371371 −15.1784 + 8.99319i −0.788021 + 0.466903i
372372 0 0
373373 −6.02002 10.4270i −0.311705 0.539889i 0.667027 0.745034i 0.267567π-0.267567\pi
−0.978732 + 0.205145i 0.934233π0.934233\pi
374374 4.18455 7.24785i 0.216378 0.374778i
375375 0 0
376376 0.698165 0.403086i 0.0360051 0.0207876i
377377 −8.30386 −0.427671
378378 0 0
379379 −18.0918 −0.929312 −0.464656 0.885491i 0.653822π-0.653822\pi
−0.464656 + 0.885491i 0.653822π0.653822\pi
380380 0 0
381381 0 0
382382 1.41421 2.44949i 0.0723575 0.125327i
383383 −14.5769 25.2480i −0.744846 1.29011i −0.950267 0.311437i 0.899190π-0.899190\pi
0.205421 0.978674i 0.434144π-0.434144\pi
384384 0 0
385385 0 0
386386 3.53892i 0.180126i
387387 0 0
388388 7.59347 + 4.38409i 0.385500 + 0.222568i
389389 −17.0297 9.83207i −0.863438 0.498506i 0.00172432 0.999999i 0.499451π-0.499451\pi
−0.865162 + 0.501493i 0.832784π0.832784\pi
390390 0 0
391391 18.7796i 0.949723i
392392 5.98162 3.63597i 0.302117 0.183644i
393393 0 0
394394 −1.18364 2.05012i −0.0596309 0.103284i
395395 0 0
396396 0 0
397397 4.92295 2.84227i 0.247076 0.142649i −0.371349 0.928493i 0.621105π-0.621105\pi
0.618425 + 0.785844i 0.287771π0.287771\pi
398398 −3.46410 −0.173640
399399 0 0
400400 0 0
401401 −8.84787 + 5.10832i −0.441842 + 0.255097i −0.704378 0.709825i 0.748774π-0.748774\pi
0.262537 + 0.964922i 0.415441π0.415441\pi
402402 0 0
403403 26.6087 46.0876i 1.32547 2.29579i
404404 −0.853270 1.47791i −0.0424518 0.0735286i
405405 0 0
406406 3.57291 0.0403355i 0.177321 0.00200182i
407407 12.2328i 0.606359i
408408 0 0
409409 −12.0969 6.98414i −0.598153 0.345344i 0.170162 0.985416i 0.445571π-0.445571\pi
−0.768314 + 0.640073i 0.778904π0.778904\pi
410410 0 0
411411 0 0
412412 10.3644i 0.510617i
413413 2.15275 + 3.63333i 0.105930 + 0.178784i
414414 0 0
415415 0 0
416416 −3.07432 + 5.32488i −0.150731 + 0.261074i
417417 0 0
418418 6.70891 3.87339i 0.328144 0.189454i
419419 −11.3181 −0.552924 −0.276462 0.961025i 0.589162π-0.589162\pi
−0.276462 + 0.961025i 0.589162π0.589162\pi
420420 0 0
421421 −13.9099 −0.677928 −0.338964 0.940799i 0.610077π-0.610077\pi
−0.338964 + 0.940799i 0.610077π0.610077\pi
422422 12.4379 7.18100i 0.605466 0.349566i
423423 0 0
424424 −3.33413 + 5.77488i −0.161920 + 0.280453i
425425 0 0
426426 0 0
427427 −0.189761 16.8090i −0.00918318 0.813445i
428428 11.5136i 0.556531i
429429 0 0
430430 0 0
431431 22.5947 + 13.0451i 1.08835 + 0.628359i 0.933137 0.359522i 0.117060π-0.117060\pi
0.155213 + 0.987881i 0.450394π0.450394\pi
432432 0 0
433433 8.42614i 0.404935i 0.979289 + 0.202467i 0.0648960π0.0648960\pi
−0.979289 + 0.202467i 0.935104π0.935104\pi
434434 −11.2251 + 19.9594i −0.538822 + 0.958083i
435435 0 0
436436 −1.00000 1.73205i −0.0478913 0.0829502i
437437 −8.69157 + 15.0542i −0.415774 + 0.720142i
438438 0 0
439439 23.9529 13.8292i 1.14321 0.660033i 0.195987 0.980606i 0.437209π-0.437209\pi
0.947224 + 0.320573i 0.103875π0.103875\pi
440440 0 0
441441 0 0
442442 40.1049 1.90759
443443 2.04142 1.17861i 0.0969906 0.0559975i −0.450720 0.892665i 0.648833π-0.648833\pi
0.547711 + 0.836668i 0.315499π0.315499\pi
444444 0 0
445445 0 0
446446 6.79876 + 11.7758i 0.321931 + 0.557600i
447447 0 0
448448 1.29693 2.30608i 0.0612740 0.108952i
449449 12.8021i 0.604169i −0.953281 0.302084i 0.902318π-0.902318\pi
0.953281 0.302084i 0.0976824π-0.0976824\pi
450450 0 0
451451 9.68696 + 5.59277i 0.456141 + 0.263353i
452452 11.5939 + 6.69375i 0.545332 + 0.314847i
453453 0 0
454454 12.3559i 0.579893i
455455 0 0
456456 0 0
457457 −17.2621 29.8989i −0.807488 1.39861i −0.914599 0.404363i 0.867493π-0.867493\pi
0.107111 0.994247i 0.465840π-0.465840\pi
458458 −1.20671 + 2.09008i −0.0563857 + 0.0976628i
459459 0 0
460460 0 0
461461 20.2692 0.944032 0.472016 0.881590i 0.343526π-0.343526\pi
0.472016 + 0.881590i 0.343526π0.343526\pi
462462 0 0
463463 −13.1246 −0.609952 −0.304976 0.952360i 0.598648π-0.598648\pi
−0.304976 + 0.952360i 0.598648π0.598648\pi
464464 1.16959 0.675260i 0.0542966 0.0313482i
465465 0 0
466466 6.43780 11.1506i 0.298225 0.516541i
467467 −0.765836 1.32647i −0.0354387 0.0613816i 0.847762 0.530377i 0.177950π-0.177950\pi
−0.883201 + 0.468995i 0.844616π0.844616\pi
468468 0 0
469469 7.27550 + 12.2793i 0.335951 + 0.567005i
470470 0 0
471471 0 0
472472 1.38237 + 0.798110i 0.0636286 + 0.0367360i
473473 5.95444 + 3.43780i 0.273786 + 0.158070i
474474 0 0
475475 0 0
476476 −17.2560 + 0.194807i −0.790927 + 0.00892896i
477477 0 0
478478 −13.6273 23.6032i −0.623299 1.07959i
479479 −14.6585 + 25.3893i −0.669764 + 1.16007i 0.308205 + 0.951320i 0.400272π0.400272\pi
−0.977970 + 0.208746i 0.933062π0.933062\pi
480480 0 0
481481 50.7663 29.3100i 2.31475 1.33642i
482482 −2.61759 −0.119228
483483 0 0
484484 −9.35366 −0.425166
485485 0 0
486486 0 0
487487 −4.09770 + 7.09743i −0.185685 + 0.321615i −0.943807 0.330497i 0.892784π-0.892784\pi
0.758122 + 0.652112i 0.226117π0.226117\pi
488488 −3.17681 5.50239i −0.143807 0.249082i
489489 0 0
490490 0 0
491491 40.4383i 1.82495i 0.409129 + 0.912477i 0.365833π0.365833\pi
−0.409129 + 0.912477i 0.634167π0.634167\pi
492492 0 0
493493 −7.62869 4.40443i −0.343579 0.198366i
494494 32.1492 + 18.5614i 1.44646 + 0.835116i
495495 0 0
496496 8.65515i 0.388628i
497497 36.1562 + 20.3341i 1.62183 + 0.912109i
498498 0 0
499499 8.72450 + 15.1113i 0.390562 + 0.676474i 0.992524 0.122051i 0.0389473π-0.0389473\pi
−0.601961 + 0.798525i 0.705614π0.705614\pi
500500 0 0
501501 0 0
502502 −23.1379 + 13.3586i −1.03269 + 0.596226i
503503 −1.91949 −0.0855860 −0.0427930 0.999084i 0.513626π-0.513626\pi
−0.0427930 + 0.999084i 0.513626π0.513626\pi
504504 0 0
505505 0 0
506506 −3.19932 + 1.84713i −0.142227 + 0.0821149i
507507 0 0
508508 2.82656 4.89575i 0.125408 0.217214i
509509 5.54549 + 9.60508i 0.245800 + 0.425737i 0.962356 0.271792i 0.0876161π-0.0876161\pi
−0.716556 + 0.697529i 0.754283π0.754283\pi
510510 0 0
511511 28.2631 16.7459i 1.25029 0.740796i
512512 1.00000i 0.0441942i
513513 0 0
514514 9.14632 + 5.28063i 0.403427 + 0.232919i
515515 0 0
516516 0 0
517517 1.03440i 0.0454928i
518518 −21.7009 + 12.8578i −0.953484 + 0.564941i
519519 0 0
520520 0 0
521521 −19.8706 + 34.4168i −0.870546 + 1.50783i −0.00911254 + 0.999958i 0.502901π0.502901\pi
−0.861433 + 0.507871i 0.830433π0.830433\pi
522522 0 0
523523 −27.0900 + 15.6404i −1.18456 + 0.683907i −0.957065 0.289872i 0.906387π-0.906387\pi
−0.227496 + 0.973779i 0.573054π0.573054\pi
524524 −12.4673 −0.544638
525525 0 0
526526 −8.33174 −0.363281
527527 48.8904 28.2269i 2.12970 1.22958i
528528 0 0
529529 −7.35519 + 12.7396i −0.319791 + 0.553894i
530530 0 0
531531 0 0
532532 −13.9231 7.83026i −0.603641 0.339485i
533533 53.6013i 2.32173i
534534 0 0
535535 0 0
536536 4.67188 + 2.69731i 0.201795 + 0.116506i
537537 0 0
538538 14.2834i 0.615802i
539539 −0.202767 8.97941i −0.00873380 0.386771i
540540 0 0
541541 12.3987 + 21.4752i 0.533061 + 0.923290i 0.999254 + 0.0386065i 0.0122919π0.0122919\pi
−0.466193 + 0.884683i 0.654375π0.654375\pi
542542 3.80223 6.58566i 0.163320 0.282878i
543543 0 0
544544 −5.64871 + 3.26128i −0.242186 + 0.139826i
545545 0 0
546546 0 0
547547 40.5380 1.73328 0.866640 0.498934i 0.166275π-0.166275\pi
0.866640 + 0.498934i 0.166275π0.166275\pi
548548 −0.0441401 + 0.0254843i −0.00188557 + 0.00108863i
549549 0 0
550550 0 0
551551 −4.07692 7.06144i −0.173683 0.300827i
552552 0 0
553553 −29.5825 + 0.333964i −1.25798 + 0.0142016i
554554 12.0400i 0.511532i
555555 0 0
556556 −0.909924 0.525345i −0.0385894 0.0222796i
557557 −20.5650 11.8732i −0.871367 0.503084i −0.00356477 0.999994i 0.501135π-0.501135\pi
−0.867802 + 0.496910i 0.834468π0.834468\pi
558558 0 0
559559 32.9480i 1.39355i
560560 0 0
561561 0 0
562562 −6.39394 11.0746i −0.269712 0.467155i
563563 −4.21434 + 7.29944i −0.177613 + 0.307635i −0.941062 0.338233i 0.890171π-0.890171\pi
0.763449 + 0.645868i 0.223504π0.223504\pi
564564 0 0
565565 0 0
566566 −15.5521 −0.653705
567567 0 0
568568 15.6787 0.657863
569569 −20.3139 + 11.7283i −0.851605 + 0.491674i −0.861192 0.508280i 0.830282π-0.830282\pi
0.00958727 + 0.999954i 0.496948π0.496948\pi
570570 0 0
571571 −7.67946 + 13.3012i −0.321376 + 0.556639i −0.980772 0.195157i 0.937479π-0.937479\pi
0.659397 + 0.751795i 0.270812π0.270812\pi
572572 3.94466 + 6.83235i 0.164934 + 0.285675i
573573 0 0
574574 −0.260365 23.0631i −0.0108674 0.962636i
575575 0 0
576576 0 0
577577 12.3329 + 7.12041i 0.513426 + 0.296426i 0.734241 0.678889i 0.237538π-0.237538\pi
−0.220815 + 0.975316i 0.570872π0.570872\pi
578578 22.1216 + 12.7719i 0.920139 + 0.531242i
579579 0 0
580580 0 0
581581 4.85690 8.63609i 0.201498 0.358285i
582582 0 0
583583 4.27802 + 7.40975i 0.177178 + 0.306881i
584584 6.20837 10.7532i 0.256904 0.444971i
585585 0 0
586586 10.0057 5.77679i 0.413331 0.238637i
587587 −12.5249 −0.516958 −0.258479 0.966017i 0.583221π-0.583221\pi
−0.258479 + 0.966017i 0.583221π0.583221\pi
588588 0 0
589589 52.2560 2.15317
590590 0 0
591591 0 0
592592 −4.76690 + 8.25652i −0.195919 + 0.339341i
593593 7.35750 + 12.7436i 0.302136 + 0.523316i 0.976620 0.214975i 0.0689669π-0.0689669\pi
−0.674483 + 0.738290i 0.735634π0.735634\pi
594594 0 0
595595 0 0
596596 8.22305i 0.336829i
597597 0 0
598598 −15.3312 8.85148i −0.626940 0.361964i
599599 −23.9304 13.8162i −0.977769 0.564515i −0.0761732 0.997095i 0.524270π-0.524270\pi
−0.901596 + 0.432579i 0.857604π0.857604\pi
600600 0 0
601601 8.82137i 0.359831i 0.983682 + 0.179916i 0.0575825π0.0575825\pi
−0.983682 + 0.179916i 0.942418π0.942418\pi
602602 −0.160043 14.1766i −0.00652286 0.577794i
603603 0 0
604604 −2.13357 3.69546i −0.0868139 0.150366i
605605 0 0
606606 0 0
607607 −22.9803 + 13.2677i −0.932743 + 0.538519i −0.887678 0.460465i 0.847683π-0.847683\pi
−0.0450649 + 0.998984i 0.514349π0.514349\pi
608608 −6.03756 −0.244855
609609 0 0
610610 0 0
611611 4.29276 2.47843i 0.173667 0.100266i
612612 0 0
613613 −0.456842 + 0.791273i −0.0184517 + 0.0319592i −0.875104 0.483935i 0.839207π-0.839207\pi
0.856652 + 0.515894i 0.172540π0.172540\pi
614614 −1.28809 2.23103i −0.0519830 0.0900371i
615615 0 0
616616 −1.73046 2.92060i −0.0697223 0.117674i
617617 35.0558i 1.41129i 0.708565 + 0.705646i 0.249343π0.249343\pi
−0.708565 + 0.705646i 0.750657π0.750657\pi
618618 0 0
619619 −16.5382 9.54835i −0.664727 0.383781i 0.129348 0.991599i 0.458711π-0.458711\pi
−0.794076 + 0.607819i 0.792045π0.792045\pi
620620 0 0
621621 0 0
622622 24.7140i 0.990942i
623623 9.62837 0.108697i 0.385753 0.00435485i
624624 0 0
625625 0 0
626626 4.50087 7.79573i 0.179891 0.311580i
627627 0 0
628628 −4.18466 + 2.41601i −0.166986 + 0.0964095i
629629 62.1849 2.47947
630630 0 0
631631 21.5350 0.857296 0.428648 0.903472i 0.358990π-0.358990\pi
0.428648 + 0.903472i 0.358990π0.358990\pi
632632 −9.68377 + 5.59093i −0.385200 + 0.222395i
633633 0 0
634634 11.9529 20.7031i 0.474712 0.822225i
635635 0 0
636636 0 0
637637 36.7788 22.3562i 1.45723 0.885786i
638638 1.73285i 0.0686043i
639639 0 0
640640 0 0
641641 28.6767 + 16.5565i 1.13266 + 0.653943i 0.944603 0.328214i 0.106447π-0.106447\pi
0.188060 + 0.982158i 0.439780π0.439780\pi
642642 0 0
643643 3.31191i 0.130609i −0.997865 0.0653044i 0.979198π-0.979198\pi
0.997865 0.0653044i 0.0208018π-0.0208018\pi
644644 6.63958 + 3.73407i 0.261636 + 0.147143i
645645 0 0
646646 19.6902 + 34.1044i 0.774700 + 1.34182i
647647 11.6669 20.2077i 0.458674 0.794447i −0.540217 0.841526i 0.681658π-0.681658\pi
0.998891 + 0.0470789i 0.0149912π0.0149912\pi
648648 0 0
649649 1.77371 1.02405i 0.0696244 0.0401977i
650650 0 0
651651 0 0
652652 10.7532 0.421128
653653 −15.1211 + 8.73019i −0.591735 + 0.341639i −0.765783 0.643099i 0.777649π-0.777649\pi
0.174048 + 0.984737i 0.444315π0.444315\pi
654654 0 0
655655 0 0
656656 −4.35880 7.54966i −0.170182 0.294765i
657657 0 0
658658 −1.83501 + 1.08725i −0.0715363 + 0.0423854i
659659 1.29864i 0.0505877i 0.999680 + 0.0252939i 0.00805215π0.00805215\pi
−0.999680 + 0.0252939i 0.991948π0.991948\pi
660660 0 0
661661 4.39869 + 2.53959i 0.171089 + 0.0987785i 0.583099 0.812401i 0.301840π-0.301840\pi
−0.412010 + 0.911179i 0.635173π0.635173\pi
662662 3.78217 + 2.18364i 0.146998 + 0.0848695i
663663 0 0
664664 3.74493i 0.145331i
665665 0 0
666666 0 0
667667 1.94419 + 3.36743i 0.0752793 + 0.130387i
668668 −9.46334 + 16.3910i −0.366147 + 0.634186i
669669 0 0
670670 0 0
671671 −8.15232 −0.314717
672672 0 0
673673 18.4124 0.709747 0.354873 0.934914i 0.384524π-0.384524\pi
0.354873 + 0.934914i 0.384524π0.384524\pi
674674 16.9012 9.75794i 0.651012 0.375862i
675675 0 0
676676 −12.4029 + 21.4824i −0.477033 + 0.826246i
677677 −20.6397 35.7491i −0.793250 1.37395i −0.923945 0.382526i 0.875054π-0.875054\pi
0.130695 0.991423i 0.458279π-0.458279\pi
678678 0 0
679679 −20.2201 11.3717i −0.775976 0.436405i
680680 0 0
681681 0 0
682682 9.61758 + 5.55271i 0.368276 + 0.212624i
683683 −19.9007 11.4896i −0.761477 0.439639i 0.0683485 0.997662i 0.478227π-0.478227\pi
−0.829826 + 0.558022i 0.811560π0.811560\pi
684684 0 0
685685 0 0
686686 −15.7163 + 9.79790i −0.600050 + 0.374085i
687687 0 0
688688 −2.67929 4.64067i −0.102147 0.176924i
689689 −20.5004 + 35.5077i −0.781001 + 1.35273i
690690 0 0
691691 11.0048 6.35361i 0.418642 0.241703i −0.275854 0.961199i 0.588961π-0.588961\pi
0.694496 + 0.719497i 0.255627π0.255627\pi
692692 −11.8435 −0.450223
693693 0 0
694694 26.9147 1.02167
695695 0 0
696696 0 0
697697 −28.4305 + 49.2431i −1.07688 + 1.86522i
698698 5.19105 + 8.99116i 0.196484 + 0.340320i
699699 0 0
700700 0 0
701701 26.5441i 1.00256i 0.865286 + 0.501279i 0.167137π0.167137\pi
−0.865286 + 0.501279i 0.832863π0.832863\pi
702702 0 0
703703 49.8492 + 28.7804i 1.88010 + 1.08548i
704704 −1.11120 0.641550i −0.0418798 0.0241793i
705705 0 0
706706 0.168951i 0.00635856i
707707 2.30154 + 3.88444i 0.0865582 + 0.146089i
708708 0 0
709709 21.1766 + 36.6789i 0.795303 + 1.37751i 0.922646 + 0.385647i 0.126022π0.126022\pi
−0.127343 + 0.991859i 0.540645π0.540645\pi
710710 0 0
711711 0 0
712712 3.15183 1.81971i 0.118120 0.0681964i
713713 −24.9196 −0.933248
714714 0 0
715715 0 0
716716 3.27843 1.89280i 0.122521 0.0707374i
717717 0 0
718718 −18.8330 + 32.6198i −0.702843 + 1.21736i
719719 −11.9507 20.6992i −0.445686 0.771951i 0.552413 0.833570i 0.313707π-0.313707\pi
−0.998100 + 0.0616189i 0.980374π0.980374\pi
720720 0 0
721721 −0.309550 27.4199i −0.0115282 1.02117i
722722 17.4521i 0.649499i
723723 0 0
724724 16.4574 + 9.50166i 0.611633 + 0.353126i
725725 0 0
726726 0 0
727727 22.4529i 0.832731i 0.909197 + 0.416365i 0.136696π0.136696\pi
−0.909197 + 0.416365i 0.863304π0.863304\pi
728728 7.97433 14.1792i 0.295548 0.525517i
729729 0 0
730730 0 0
731731 −17.4759 + 30.2691i −0.646368 + 1.11954i
732732 0 0
733733 −23.8547 + 13.7725i −0.881094 + 0.508700i −0.871019 0.491249i 0.836540π-0.836540\pi
−0.0100750 + 0.999949i 0.503207π0.503207\pi
734734 −15.1557 −0.559409
735735 0 0
736736 2.87917 0.106128
737737 5.99449 3.46092i 0.220810 0.127485i
738738 0 0
739739 15.5456 26.9258i 0.571856 0.990483i −0.424520 0.905419i 0.639557π-0.639557\pi
0.996375 0.0850646i 0.0271097π-0.0271097\pi
740740 0 0
741741 0 0
742742 8.64824 15.3775i 0.317487 0.564526i
743743 1.12610i 0.0413127i 0.999787 + 0.0206564i 0.00657559π0.00657559\pi
−0.999787 + 0.0206564i 0.993424π0.993424\pi
744744 0 0
745745 0 0
746746 10.4270 + 6.02002i 0.381759 + 0.220409i
747747 0 0
748748 8.36910i 0.306005i
749749 0.343872 + 30.4602i 0.0125648 + 1.11299i
750750 0 0
751751 4.77108 + 8.26375i 0.174099 + 0.301549i 0.939849 0.341590i 0.110965π-0.110965\pi
−0.765750 + 0.643138i 0.777632π0.777632\pi
752752 −0.403086 + 0.698165i −0.0146990 + 0.0254595i
753753 0 0
754754 7.19135 4.15193i 0.261894 0.151204i
755755 0 0
756756 0 0
757757 −33.1687 −1.20554 −0.602768 0.797917i 0.705935π-0.705935\pi
−0.602768 + 0.797917i 0.705935π0.705935\pi
758758 15.6679 9.04589i 0.569085 0.328562i
759759 0 0
760760 0 0
761761 −2.17122 3.76067i −0.0787068 0.136324i 0.823985 0.566611i 0.191746π-0.191746\pi
−0.902692 + 0.430287i 0.858412π0.858412\pi
762762 0 0
763763 2.69731 + 4.55242i 0.0976493 + 0.164809i
764764 2.82843i 0.102329i
765765 0 0
766766 25.2480 + 14.5769i 0.912246 + 0.526685i
767767 8.49967 + 4.90729i 0.306905 + 0.177192i
768768 0 0
769769 46.1795i 1.66528i 0.553818 + 0.832638i 0.313170π0.313170\pi
−0.553818 + 0.832638i 0.686830π0.686830\pi
770770 0 0
771771 0 0
772772 1.76946 + 3.06479i 0.0636842 + 0.110304i
773773 −8.98723 + 15.5663i −0.323248 + 0.559883i −0.981156 0.193216i 0.938108π-0.938108\pi
0.657908 + 0.753098i 0.271442π0.271442\pi
774774 0 0
775775 0 0
776776 −8.76818 −0.314759
777777 0 0
778778 19.6641 0.704994
779779 −45.5815 + 26.3165i −1.63313 + 0.942886i
780780 0 0
781781 10.0587 17.4221i 0.359927 0.623412i
782782 −9.38978 16.2636i −0.335778 0.581584i
783783 0 0
784784 −3.36225 + 6.13965i −0.120080 + 0.219273i
785785 0 0
786786 0 0
787787 11.9873 + 6.92087i 0.427301 + 0.246702i 0.698196 0.715907i 0.253986π-0.253986\pi
−0.270895 + 0.962609i 0.587320π0.587320\pi
788788 2.05012 + 1.18364i 0.0730326 + 0.0421654i
789789 0 0
790790 0 0
791791 −30.8726 17.3626i −1.09770 0.617342i
792792 0 0
793793 −19.5330 33.8322i −0.693638 1.20142i
794794 −2.84227 + 4.92295i −0.100868 + 0.174709i
795795 0 0
796796 3.00000 1.73205i 0.106332 0.0613909i
797797 7.46138 0.264296 0.132148 0.991230i 0.457813π-0.457813\pi
0.132148 + 0.991230i 0.457813π0.457813\pi
798798 0 0
799799 5.25831 0.186026
800800 0 0
801801 0 0
802802 5.10832 8.84787i 0.180381 0.312429i
803803 −7.96596 13.7974i −0.281113 0.486901i
804804 0 0
805805 0 0
806806 53.2174i 1.87450i
807807 0 0
808808 1.47791 + 0.853270i 0.0519926 + 0.0300179i
809809 −1.28750 0.743340i −0.0452662 0.0261344i 0.477196 0.878797i 0.341653π-0.341653\pi
−0.522462 + 0.852662i 0.674986π0.674986\pi
810810 0 0
811811 31.5494i 1.10785i −0.832567 0.553925i 0.813129π-0.813129\pi
0.832567 0.553925i 0.186871π-0.186871\pi
812812 −3.07407 + 1.82139i −0.107879 + 0.0639182i
813813 0 0
814814 6.11641 + 10.5939i 0.214380 + 0.371317i
815815 0 0
816816 0 0
817817 −28.0183 + 16.1764i −0.980237 + 0.565940i
818818 13.9683 0.488390
819819 0 0
820820 0 0
821821 27.5430 15.9020i 0.961257 0.554982i 0.0646976 0.997905i 0.479392π-0.479392\pi
0.896560 + 0.442923i 0.146058π0.146058\pi
822822 0 0
823823 −18.3186 + 31.7287i −0.638545 + 1.10599i 0.347207 + 0.937788i 0.387130π0.387130\pi
−0.985752 + 0.168204i 0.946203π0.946203\pi
824824 −5.18220 8.97583i −0.180530 0.312688i
825825 0 0
826826 −3.68100 2.07018i −0.128078 0.0720308i
827827 21.9864i 0.764541i 0.924050 + 0.382271i 0.124858π0.124858\pi
−0.924050 + 0.382271i 0.875142π0.875142\pi
828828 0 0
829829 21.0498 + 12.1531i 0.731090 + 0.422095i 0.818821 0.574049i 0.194628π-0.194628\pi
−0.0877305 + 0.996144i 0.527961π0.527961\pi
830830 0 0
831831 0 0
832832 6.14864i 0.213166i
833833 45.6463 1.03076i 1.58155 0.0357136i
834834 0 0
835835 0 0
836836 −3.87339 + 6.70891i −0.133964 + 0.232033i
837837 0 0
838838 9.80175 5.65904i 0.338596 0.195488i
839839 27.3914 0.945655 0.472827 0.881155i 0.343233π-0.343233\pi
0.472827 + 0.881155i 0.343233π0.343233\pi
840840 0 0
841841 27.1761 0.937107
842842 12.0463 6.95496i 0.415145 0.239684i
843843 0 0
844844 −7.18100 + 12.4379i −0.247180 + 0.428129i
845845 0 0
846846 0 0
847847 24.7459 0.279362i 0.850278 0.00959899i
848848 6.66826i 0.228989i
849849 0 0
850850 0 0
851851 −23.7719 13.7247i −0.814890 0.470477i
852852 0 0
853853 22.6073i 0.774060i 0.922067 + 0.387030i 0.126499π0.126499\pi
−0.922067 + 0.387030i 0.873501π0.873501\pi
854854 8.56884 + 14.4622i 0.293220 + 0.494885i
855855 0 0
856856 5.75680 + 9.97106i 0.196763 + 0.340804i
857857 −23.9289 + 41.4461i −0.817396 + 1.41577i 0.0901984 + 0.995924i 0.471250π0.471250\pi
−0.907595 + 0.419848i 0.862083π0.862083\pi
858858 0 0
859859 −41.5770 + 24.0045i −1.41859 + 0.819022i −0.996175 0.0873810i 0.972150π-0.972150\pi
−0.422413 + 0.906403i 0.638817π0.638817\pi
860860 0 0
861861 0 0
862862 −26.0901 −0.888634
863863 41.1855 23.7785i 1.40197 0.809428i 0.407376 0.913260i 0.366444π-0.366444\pi
0.994595 + 0.103832i 0.0331104π0.0331104\pi
864864 0 0
865865 0 0
866866 −4.21307 7.29726i −0.143166 0.247971i
867867 0 0
868868 −0.258500 22.8979i −0.00877406 0.777206i
869869 14.3474i 0.486703i
870870 0 0
871871 28.7257 + 16.5848i 0.973334 + 0.561955i
872872 1.73205 + 1.00000i 0.0586546 + 0.0338643i
873873 0 0
874874 17.3831i 0.587993i
875875 0 0
876876 0 0
877877 −18.5002 32.0433i −0.624707 1.08202i −0.988597 0.150583i 0.951885π-0.951885\pi
0.363890 0.931442i 0.381448π-0.381448\pi
878878 −13.8292 + 23.9529i −0.466714 + 0.808372i
879879 0 0
880880 0 0
881881 5.97213 0.201206 0.100603 0.994927i 0.467923π-0.467923\pi
0.100603 + 0.994927i 0.467923π0.467923\pi
882882 0 0
883883 −11.0589 −0.372163 −0.186081 0.982534i 0.559579π-0.559579\pi
−0.186081 + 0.982534i 0.559579π0.559579\pi
884884 −34.7319 + 20.0524i −1.16816 + 0.674437i
885885 0 0
886886 −1.17861 + 2.04142i −0.0395962 + 0.0685827i
887887 2.97535 + 5.15346i 0.0999026 + 0.173036i 0.911644 0.410980i 0.134814π-0.134814\pi
−0.811742 + 0.584017i 0.801480π0.801480\pi
888888 0 0
889889 −7.33169 + 13.0365i −0.245897 + 0.437231i
890890 0 0
891891 0 0
892892 −11.7758 6.79876i −0.394283 0.227639i
893893 4.21521 + 2.43365i 0.141057 + 0.0814391i
894894 0 0
895895 0 0
896896 0.0298666 + 2.64558i 0.000997774 + 0.0883827i
897897 0 0
898898 6.40105 + 11.0869i 0.213606 + 0.369976i
899899 5.84448 10.1229i 0.194924 0.337619i
900900 0 0
901901 −37.6671 + 21.7471i −1.25487 + 0.724500i
902902 −11.1855 −0.372438
903903 0 0
904904 −13.3875 −0.445261
905905 0 0
906906 0 0
907907 27.6572 47.9037i 0.918343 1.59062i 0.116411 0.993201i 0.462861π-0.462861\pi
0.801932 0.597415i 0.203805π-0.203805\pi
908908 6.17797 + 10.7006i 0.205023 + 0.355110i
909909 0 0
910910 0 0
911911 35.2080i 1.16649i 0.812295 + 0.583246i 0.198218π0.198218\pi
−0.812295 + 0.583246i 0.801782π0.801782\pi
912912 0 0
913913 −4.16135 2.40256i −0.137721 0.0795131i
914914 29.8989 + 17.2621i 0.988966 + 0.570980i
915915 0 0
916916 2.41341i 0.0797414i
917917 32.9833 0.372357i 1.08921 0.0122963i
918918 0 0
919919 −25.4437 44.0698i −0.839311 1.45373i −0.890471 0.455039i 0.849625π-0.849625\pi
0.0511601 0.998690i 0.483708π-0.483708\pi
920920 0 0
921921 0 0
922922 −17.5537 + 10.1346i −0.578099 + 0.333766i
923923 96.4026 3.17313
924924 0 0
925925 0 0
926926 11.3662 6.56230i 0.373518 0.215651i
927927 0 0
928928 −0.675260 + 1.16959i −0.0221665 + 0.0383935i
929929 −29.8405 51.6853i −0.979036 1.69574i −0.665918 0.746025i 0.731960π-0.731960\pi
−0.313118 0.949714i 0.601373π-0.601373\pi
930930 0 0
931931 37.0685 + 20.2998i 1.21487 + 0.665298i
932932 12.8756i 0.421754i
933933 0 0
934934 1.32647 + 0.765836i 0.0434033 + 0.0250589i
935935 0 0
936936 0 0
937937 24.2579i 0.792471i −0.918149 0.396235i 0.870316π-0.870316\pi
0.918149 0.396235i 0.129684π-0.129684\pi
938938 −12.4404 6.99643i −0.406194 0.228442i
939939 0 0
940940 0 0
941941 15.0539 26.0742i 0.490744 0.849994i −0.509199 0.860649i 0.670058π-0.670058\pi
0.999943 + 0.0106549i 0.00339164π0.00339164\pi
942942 0 0
943943 21.7367 12.5497i 0.707845 0.408675i
944944 −1.59622 −0.0519525
945945 0 0
946946 −6.87560 −0.223545
947947 39.9779 23.0812i 1.29911 0.750039i 0.318857 0.947803i 0.396701π-0.396701\pi
0.980250 + 0.197764i 0.0633678π0.0633678\pi
948948 0 0
949949 38.1730 66.1176i 1.23915 2.14627i
950950 0 0
951951 0 0
952952 14.8467 8.79670i 0.481185 0.285103i
953953 23.7121i 0.768110i 0.923310 + 0.384055i 0.125473π0.125473\pi
−0.923310 + 0.384055i 0.874527π0.874527\pi
954954 0 0
955955 0 0
956956 23.6032 + 13.6273i 0.763382 + 0.440739i
957957 0 0
958958 29.3170i 0.947190i
959959 0.116015 0.0687391i 0.00374632 0.00221970i
960960 0 0
961961 21.9558 + 38.0286i 0.708252 + 1.22673i
962962 −29.3100 + 50.7663i −0.944991 + 1.63677i
963963 0 0
964964 2.26690 1.30880i 0.0730120 0.0421535i
965965 0 0
966966 0 0
967967 −0.0922780 −0.00296746 −0.00148373 0.999999i 0.500472π-0.500472\pi
−0.00148373 + 0.999999i 0.500472π0.500472\pi
968968 8.10050 4.67683i 0.260360 0.150319i
969969 0 0
970970 0 0
971971 19.8502 + 34.3816i 0.637024 + 1.10336i 0.986082 + 0.166257i 0.0531683π0.0531683\pi
−0.349058 + 0.937101i 0.613498π0.613498\pi
972972 0 0
973973 2.42297 + 1.36267i 0.0776769 + 0.0436851i
974974 8.19540i 0.262598i
975975 0 0
976976 5.50239 + 3.17681i 0.176127 + 0.101687i
977977 31.8758 + 18.4035i 1.01980 + 0.588779i 0.914045 0.405613i 0.132942π-0.132942\pi
0.105751 + 0.994393i 0.466275π0.466275\pi
978978 0 0
979979 4.66973i 0.149245i
980980 0 0
981981 0 0
982982 −20.2191 35.0206i −0.645218 1.11755i
983983 31.2865 54.1899i 0.997885 1.72839i 0.442650 0.896694i 0.354038π-0.354038\pi
0.555235 0.831693i 0.312628π-0.312628\pi
984984 0 0
985985 0 0
986986 8.80886 0.280531
987987 0 0
988988 −37.1227 −1.18103
989989 13.3613 7.71414i 0.424864 0.245295i
990990 0 0
991991 17.4019 30.1410i 0.552791 0.957462i −0.445281 0.895391i 0.646896π-0.646896\pi
0.998072 0.0620708i 0.0197704π-0.0197704\pi
992992 −4.32758 7.49558i −0.137401 0.237985i
993993 0 0
994994 −41.4793 + 0.468269i −1.31564 + 0.0148526i
995995 0 0
996996 0 0
997997 42.3167 + 24.4316i 1.34018 + 0.773755i 0.986834 0.161736i 0.0517094π-0.0517094\pi
0.353349 + 0.935492i 0.385043π0.385043\pi
998998 −15.1113 8.72450i −0.478339 0.276169i
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 3150.2.bf.f.1151.7 32
3.2 odd 2 inner 3150.2.bf.f.1151.9 32
5.2 odd 4 630.2.bo.a.269.3 yes 16
5.3 odd 4 630.2.bo.b.269.8 yes 16
5.4 even 2 inner 3150.2.bf.f.1151.10 32
7.5 odd 6 inner 3150.2.bf.f.1601.9 32
15.2 even 4 630.2.bo.b.269.6 yes 16
15.8 even 4 630.2.bo.a.269.1 yes 16
15.14 odd 2 inner 3150.2.bf.f.1151.8 32
21.5 even 6 inner 3150.2.bf.f.1601.7 32
35.3 even 12 4410.2.d.a.4409.9 16
35.12 even 12 630.2.bo.a.89.1 16
35.17 even 12 4410.2.d.b.4409.10 16
35.18 odd 12 4410.2.d.a.4409.8 16
35.19 odd 6 inner 3150.2.bf.f.1601.8 32
35.32 odd 12 4410.2.d.b.4409.7 16
35.33 even 12 630.2.bo.b.89.6 yes 16
105.17 odd 12 4410.2.d.a.4409.7 16
105.32 even 12 4410.2.d.a.4409.10 16
105.38 odd 12 4410.2.d.b.4409.8 16
105.47 odd 12 630.2.bo.b.89.8 yes 16
105.53 even 12 4410.2.d.b.4409.9 16
105.68 odd 12 630.2.bo.a.89.3 yes 16
105.89 even 6 inner 3150.2.bf.f.1601.10 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.bo.a.89.1 16 35.12 even 12
630.2.bo.a.89.3 yes 16 105.68 odd 12
630.2.bo.a.269.1 yes 16 15.8 even 4
630.2.bo.a.269.3 yes 16 5.2 odd 4
630.2.bo.b.89.6 yes 16 35.33 even 12
630.2.bo.b.89.8 yes 16 105.47 odd 12
630.2.bo.b.269.6 yes 16 15.2 even 4
630.2.bo.b.269.8 yes 16 5.3 odd 4
3150.2.bf.f.1151.7 32 1.1 even 1 trivial
3150.2.bf.f.1151.8 32 15.14 odd 2 inner
3150.2.bf.f.1151.9 32 3.2 odd 2 inner
3150.2.bf.f.1151.10 32 5.4 even 2 inner
3150.2.bf.f.1601.7 32 21.5 even 6 inner
3150.2.bf.f.1601.8 32 35.19 odd 6 inner
3150.2.bf.f.1601.9 32 7.5 odd 6 inner
3150.2.bf.f.1601.10 32 105.89 even 6 inner
4410.2.d.a.4409.7 16 105.17 odd 12
4410.2.d.a.4409.8 16 35.18 odd 12
4410.2.d.a.4409.9 16 35.3 even 12
4410.2.d.a.4409.10 16 105.32 even 12
4410.2.d.b.4409.7 16 35.32 odd 12
4410.2.d.b.4409.8 16 105.38 odd 12
4410.2.d.b.4409.9 16 105.53 even 12
4410.2.d.b.4409.10 16 35.17 even 12