LMFDB - Embedded newform 5733.2.a.bz.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5733,2,Mod(1,5733)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5733, 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("5733.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5733 = 3^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5733.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:	$45.7782354788$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 18x^{8} + 110x^{6} - 265x^{4} + 243x^{2} - 63 $ x^10 - 18x^8 + 110x^6 - 265x^4 + 243x^2 - 63
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	no (minimal twist has level 819)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$2.55095$ of defining polynomial
Character	$\chi$	$=$	5733.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.55095 q^{2} +4.50732 q^{4} -1.71239 q^{5} +6.39604 q^{8} +O(q^{10})$	$q+2.55095 q^{2} +4.50732 q^{4} -1.71239 q^{5} +6.39604 q^{8} -4.36821 q^{10} +0.945869 q^{11} -1.00000 q^{13} +7.30130 q^{16} +0.170552 q^{17} -2.87466 q^{19} -7.71828 q^{20} +2.41286 q^{22} +5.66479 q^{23} -2.06772 q^{25} -2.55095 q^{26} +9.22485 q^{29} +7.36902 q^{31} +5.83313 q^{32} +0.435068 q^{34} +5.50732 q^{37} -7.33311 q^{38} -10.9525 q^{40} +11.0005 q^{41} +2.58714 q^{43} +4.26333 q^{44} +14.4506 q^{46} -0.418242 q^{47} -5.27465 q^{50} -4.50732 q^{52} -0.626142 q^{53} -1.61970 q^{55} +23.5321 q^{58} +6.73714 q^{59} +8.16219 q^{61} +18.7980 q^{62} +0.277410 q^{64} +1.71239 q^{65} -8.39123 q^{67} +0.768731 q^{68} +0.382966 q^{71} +2.22066 q^{73} +14.0489 q^{74} -12.9570 q^{76} +13.5304 q^{79} -12.5027 q^{80} +28.0616 q^{82} -5.90576 q^{83} -0.292051 q^{85} +6.59965 q^{86} +6.04981 q^{88} -17.7074 q^{89} +25.5330 q^{92} -1.06691 q^{94} +4.92254 q^{95} -7.69624 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 16 q^{4}+O(q^{10}) $ 10 * q + 16 * q^4	$ 10 q + 16 q^{4} + 4 q^{10} - 10 q^{13} + 32 q^{16} - 6 q^{19} + 10 q^{22} + 24 q^{25} - 12 q^{31} - 34 q^{34} + 26 q^{37} + 70 q^{40} + 40 q^{43} - 6 q^{46} - 16 q^{52} + 24 q^{55} + 36 q^{58} + 22 q^{61} + 78 q^{64} + 26 q^{67} - 24 q^{73} - 4 q^{76} + 28 q^{79} + 28 q^{82} - 20 q^{85} + 12 q^{88} - 4 q^{94} - 18 q^{97}+O(q^{100}) $ 10 * q + 16 * q^4 + 4 * q^10 - 10 * q^13 + 32 * q^16 - 6 * q^19 + 10 * q^22 + 24 * q^25 - 12 * q^31 - 34 * q^34 + 26 * q^37 + 70 * q^40 + 40 * q^43 - 6 * q^46 - 16 * q^52 + 24 * q^55 + 36 * q^58 + 22 * q^61 + 78 * q^64 + 26 * q^67 - 24 * q^73 - 4 * q^76 + 28 * q^79 + 28 * q^82 - 20 * q^85 + 12 * q^88 - 4 * q^94 - 18 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.55095	1.80379	0.901895	−	0.431955i	$-0.142176\pi$
$2$	2.55095	1.80379	0.901895	+	0.431955i	$0.142176\pi$
$3$	0	0
$3$	0	0
$4$	4.50732	2.25366
$5$	−1.71239	−0.765804	−0.382902	−	0.923789i	$-0.625075\pi$
$5$	−1.71239	−0.765804	−0.382902	+	0.923789i	$0.625075\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	6.39604	2.26134
$9$	0	0
$10$	−4.36821	−1.38135
$11$	0.945869	0.285190	0.142595	−	0.989781i	$-0.454455\pi$
$11$	0.945869	0.285190	0.142595	+	0.989781i	$0.454455\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	7.30130	1.82532
$17$	0.170552	0.0413648	0.0206824	−	0.999786i	$-0.493416\pi$
$17$	0.170552	0.0413648	0.0206824	+	0.999786i	$0.493416\pi$
$18$	0	0
$19$	−2.87466	−0.659493	−0.329747	−	0.944070i	$-0.606963\pi$
$19$	−2.87466	−0.659493	−0.329747	+	0.944070i	$0.606963\pi$
$20$	−7.71828	−1.72586
$21$	0	0
$22$	2.41286	0.514423
$23$	5.66479	1.18119	0.590595	−	0.806968i	$-0.298893\pi$
$23$	5.66479	1.18119	0.590595	+	0.806968i	$0.298893\pi$
$24$	0	0
$25$	−2.06772	−0.413545
$26$	−2.55095	−0.500281
$27$	0	0
$28$	0	0
$29$	9.22485	1.71301	0.856505	−	0.516138i	$-0.172631\pi$
$29$	9.22485	1.71301	0.856505	+	0.516138i	$0.172631\pi$
$30$	0	0
$31$	7.36902	1.32352	0.661758	−	0.749718i	$-0.269811\pi$
$31$	7.36902	1.32352	0.661758	+	0.749718i	$0.269811\pi$
$32$	5.83313	1.03116
$33$	0	0
$34$	0.435068	0.0746135
$35$	0	0
$36$	0	0
$37$	5.50732	0.905398	0.452699	−	0.891663i	$-0.350461\pi$
$37$	5.50732	0.905398	0.452699	+	0.891663i	$0.350461\pi$
$38$	−7.33311	−1.18959
$39$	0	0
$40$	−10.9525	−1.73174
$41$	11.0005	1.71799	0.858993	−	0.511988i	$-0.171091\pi$
$41$	11.0005	1.71799	0.858993	+	0.511988i	$0.171091\pi$
$42$	0	0
$43$	2.58714	0.394535	0.197268	−	0.980350i	$-0.436793\pi$
$43$	2.58714	0.394535	0.197268	+	0.980350i	$0.436793\pi$
$44$	4.26333	0.642722
$45$	0	0
$46$	14.4506	2.13062
$47$	−0.418242	−0.0610069	−0.0305034	−	0.999535i	$-0.509711\pi$
$47$	−0.418242	−0.0610069	−0.0305034	+	0.999535i	$0.509711\pi$
$48$	0	0
$49$	0	0
$50$	−5.27465	−0.745948
$51$	0	0
$52$	−4.50732	−0.625053
$53$	−0.626142	−0.0860072	−0.0430036	−	0.999075i	$-0.513693\pi$
$53$	−0.626142	−0.0860072	−0.0430036	+	0.999075i	$0.513693\pi$
$54$	0	0
$55$	−1.61970	−0.218400
$56$	0	0
$57$	0	0
$58$	23.5321	3.08991
$59$	6.73714	0.877101	0.438550	−	0.898707i	$-0.355492\pi$
$59$	6.73714	0.877101	0.438550	+	0.898707i	$0.355492\pi$
$60$	0	0
$61$	8.16219	1.04506	0.522530	−	0.852621i	$-0.324988\pi$
$61$	8.16219	1.04506	0.522530	+	0.852621i	$0.324988\pi$
$62$	18.7980	2.38734
$63$	0	0
$64$	0.277410	0.0346762
$65$	1.71239	0.212396
$66$	0	0
$67$	−8.39123	−1.02515	−0.512576	−	0.858642i	$-0.671309\pi$
$67$	−8.39123	−1.02515	−0.512576	+	0.858642i	$0.671309\pi$
$68$	0.768731	0.0932223
$69$	0	0
$70$	0	0
$71$	0.382966	0.0454497	0.0227248	−	0.999742i	$-0.492766\pi$
$71$	0.382966	0.0454497	0.0227248	+	0.999742i	$0.492766\pi$
$72$	0	0
$73$	2.22066	0.259909	0.129955	−	0.991520i	$-0.458517\pi$
$73$	2.22066	0.259909	0.129955	+	0.991520i	$0.458517\pi$
$74$	14.0489	1.63315
$75$	0	0
$76$	−12.9570	−1.48627
$77$	0	0
$78$	0	0
$79$	13.5304	1.52229	0.761144	−	0.648583i	$-0.224638\pi$
$79$	13.5304	1.52229	0.761144	+	0.648583i	$0.224638\pi$
$80$	−12.5027	−1.39784
$81$	0	0
$82$	28.0616	3.09889
$83$	−5.90576	−0.648241	−0.324121	−	0.946016i	$-0.605068\pi$
$83$	−5.90576	−0.648241	−0.324121	+	0.946016i	$0.605068\pi$
$84$	0	0
$85$	−0.292051	−0.0316773
$86$	6.59965	0.711659
$87$	0	0
$88$	6.04981	0.644912
$89$	−17.7074	−1.87698	−0.938492	−	0.345300i	$-0.887777\pi$
$89$	−17.7074	−1.87698	−0.938492	+	0.345300i	$0.887777\pi$
$90$	0	0
$91$	0	0
$92$	25.5330	2.66200
$93$	0	0
$94$	−1.06691	−0.110044
$95$	4.92254	0.505042
$96$	0	0
$97$	−7.69624	−0.781435	−0.390718	−	0.920511i	$-0.627773\pi$
$97$	−7.69624	−0.781435	−0.390718	+	0.920511i	$0.627773\pi$
$98$	0	0
$99$	0	0
$100$	−9.31990	−0.931990
$101$	−7.15538	−0.711987	−0.355994	−	0.934488i	$-0.615857\pi$
$101$	−7.15538	−0.711987	−0.355994	+	0.934488i	$0.615857\pi$
$102$	0	0
$103$	6.48058	0.638551	0.319275	−	0.947662i	$-0.396560\pi$
$103$	6.48058	0.638551	0.319275	+	0.947662i	$0.396560\pi$
$104$	−6.39604	−0.627183
$105$	0	0
$106$	−1.59725	−0.155139
$107$	−5.32369	−0.514661	−0.257330	−	0.966324i	$-0.582843\pi$
$107$	−5.32369	−0.514661	−0.257330	+	0.966324i	$0.582843\pi$
$108$	0	0
$109$	14.4367	1.38279	0.691395	−	0.722477i	$-0.256997\pi$
$109$	14.4367	1.38279	0.691395	+	0.722477i	$0.256997\pi$
$110$	−4.13175	−0.393947
$111$	0	0
$112$	0	0
$113$	−8.90291	−0.837515	−0.418758	−	0.908098i	$-0.637534\pi$
$113$	−8.90291	−0.837515	−0.418758	+	0.908098i	$0.637534\pi$
$114$	0	0
$115$	−9.70033	−0.904560
$116$	41.5793	3.86054
$117$	0	0
$118$	17.1861	1.58211
$119$	0	0
$120$	0	0
$121$	−10.1053	−0.918667
$122$	20.8213	1.88507
$123$	0	0
$124$	33.2145	2.98275
$125$	12.1027	1.08250
$126$	0	0
$127$	20.4367	1.81347	0.906734	−	0.421703i	$-0.138568\pi$
$127$	20.4367	1.81347	0.906734	+	0.421703i	$0.138568\pi$
$128$	−10.9586	−0.968614
$129$	0	0
$130$	4.36821	0.383117
$131$	−9.79064	−0.855412	−0.427706	−	0.903918i	$-0.640678\pi$
$131$	−9.79064	−0.855412	−0.427706	+	0.903918i	$0.640678\pi$
$132$	0	0
$133$	0	0
$134$	−21.4056	−1.84916
$135$	0	0
$136$	1.09085	0.0935400
$137$	−14.8880	−1.27197	−0.635985	−	0.771702i	$-0.719406\pi$
$137$	−14.8880	−1.27197	−0.635985	+	0.771702i	$0.719406\pi$
$138$	0	0
$139$	−4.38193	−0.371670	−0.185835	−	0.982581i	$-0.559499\pi$
$139$	−4.38193	−0.371670	−0.185835	+	0.982581i	$0.559499\pi$
$140$	0	0
$141$	0	0
$142$	0.976925	0.0819817
$143$	−0.945869	−0.0790975
$144$	0	0
$145$	−15.7965	−1.31183
$146$	5.66479	0.468822
$147$	0	0
$148$	24.8233	2.04046
$149$	−4.19071	−0.343316	−0.171658	−	0.985157i	$-0.554912\pi$
$149$	−4.19071	−0.343316	−0.171658	+	0.985157i	$0.554912\pi$
$150$	0	0
$151$	−13.5718	−1.10446	−0.552230	−	0.833692i	$-0.686223\pi$
$151$	−13.5718	−1.10446	−0.552230	+	0.833692i	$0.686223\pi$
$152$	−18.3865	−1.49134
$153$	0	0
$154$	0	0
$155$	−12.6186	−1.01355
$156$	0	0
$157$	19.1330	1.52698	0.763489	−	0.645820i	$-0.223485\pi$
$157$	19.1330	1.52698	0.763489	+	0.645820i	$0.223485\pi$
$158$	34.5153	2.74589
$159$	0	0
$160$	−9.98859	−0.789668
$161$	0	0
$162$	0	0
$163$	13.0953	1.02571	0.512853	−	0.858477i	$-0.328589\pi$
$163$	13.0953	1.02571	0.512853	+	0.858477i	$0.328589\pi$
$164$	49.5827	3.87176
$165$	0	0
$166$	−15.0653	−1.16929
$167$	−7.06625	−0.546803	−0.273402	−	0.961900i	$-0.588149\pi$
$167$	−7.06625	−0.546803	−0.273402	+	0.961900i	$0.588149\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−0.745005	−0.0571393
$171$	0	0
$172$	11.6611	0.889148
$173$	−17.9309	−1.36326	−0.681629	−	0.731698i	$-0.738728\pi$
$173$	−17.9309	−1.36326	−0.681629	+	0.731698i	$0.738728\pi$
$174$	0	0
$175$	0	0
$176$	6.90607	0.520565
$177$	0	0
$178$	−45.1707	−3.38569
$179$	−20.9307	−1.56443	−0.782216	−	0.623007i	$-0.785911\pi$
$179$	−20.9307	−1.56443	−0.782216	+	0.623007i	$0.785911\pi$
$180$	0	0
$181$	20.2884	1.50802	0.754012	−	0.656861i	$-0.228116\pi$
$181$	20.2884	1.50802	0.754012	+	0.656861i	$0.228116\pi$
$182$	0	0
$183$	0	0
$184$	36.2322	2.67107
$185$	−9.43067	−0.693357
$186$	0	0
$187$	0.161319	0.0117968
$188$	−1.88515	−0.137489
$189$	0	0
$190$	12.5571	0.910990
$191$	−15.9714	−1.15565	−0.577824	−	0.816161i	$-0.696098\pi$
$191$	−15.9714	−1.15565	−0.577824	+	0.816161i	$0.696098\pi$
$192$	0	0
$193$	−0.579628	−0.0417225	−0.0208613	−	0.999782i	$-0.506641\pi$
$193$	−0.579628	−0.0417225	−0.0208613	+	0.999782i	$0.506641\pi$
$194$	−19.6327	−1.40955
$195$	0	0
$196$	0	0
$197$	3.18381	0.226837	0.113419	−	0.993547i	$-0.463820\pi$
$197$	3.18381	0.226837	0.113419	+	0.993547i	$0.463820\pi$
$198$	0	0
$199$	19.4381	1.37793	0.688964	−	0.724796i	$-0.258066\pi$
$199$	19.4381	1.37793	0.688964	+	0.724796i	$0.258066\pi$
$200$	−13.2252	−0.935166
$201$	0	0
$202$	−18.2530	−1.28428
$203$	0	0
$204$	0	0
$205$	−18.8371	−1.31564
$206$	16.5316	1.15181
$207$	0	0
$208$	−7.30130	−0.506254
$209$	−2.71905	−0.188081
$210$	0	0
$211$	−17.6859	−1.21755	−0.608773	−	0.793344i	$-0.708338\pi$
$211$	−17.6859	−1.21755	−0.608773	+	0.793344i	$0.708338\pi$
$212$	−2.82222	−0.193831
$213$	0	0
$214$	−13.5804	−0.928340
$215$	−4.43019	−0.302136
$216$	0	0
$217$	0	0
$218$	36.8273	2.49426
$219$	0	0
$220$	−7.30048	−0.492199
$221$	−0.170552	−0.0114725
$222$	0	0
$223$	4.74846	0.317980	0.158990	−	0.987280i	$-0.449176\pi$
$223$	4.74846	0.317980	0.158990	+	0.987280i	$0.449176\pi$
$224$	0	0
$225$	0	0
$226$	−22.7108	−1.51070
$227$	12.0779	0.801640	0.400820	−	0.916157i	$-0.368725\pi$
$227$	12.0779	0.801640	0.400820	+	0.916157i	$0.368725\pi$
$228$	0	0
$229$	−14.9478	−0.987781	−0.493890	−	0.869524i	$-0.664426\pi$
$229$	−14.9478	−0.987781	−0.493890	+	0.869524i	$0.664426\pi$
$230$	−24.7450	−1.63164
$231$	0	0
$232$	59.0025	3.87370
$233$	−22.6812	−1.48590	−0.742948	−	0.669349i	$-0.766573\pi$
$233$	−22.6812	−1.48590	−0.742948	+	0.669349i	$0.766573\pi$
$234$	0	0
$235$	0.716193	0.0467193
$236$	30.3664	1.97669
$237$	0	0
$238$	0	0
$239$	12.9840	0.839865	0.419933	−	0.907555i	$-0.362054\pi$
$239$	12.9840	0.839865	0.419933	+	0.907555i	$0.362054\pi$
$240$	0	0
$241$	−7.02215	−0.452337	−0.226168	−	0.974088i	$-0.572620\pi$
$241$	−7.02215	−0.452337	−0.226168	+	0.974088i	$0.572620\pi$
$242$	−25.7781	−1.65708
$243$	0	0
$244$	36.7896	2.35521
$245$	0	0
$246$	0	0
$247$	2.87466	0.182910
$248$	47.1325	2.99292
$249$	0	0
$250$	30.8733	1.95260
$251$	12.9538	0.817638	0.408819	−	0.912615i	$-0.365941\pi$
$251$	12.9538	0.817638	0.408819	+	0.912615i	$0.365941\pi$
$252$	0	0
$253$	5.35815	0.336864
$254$	52.1330	3.27112
$255$	0	0
$256$	−28.5096	−1.78185
$257$	30.3685	1.89434	0.947168	−	0.320737i	$-0.103931\pi$
$257$	30.3685	1.89434	0.947168	+	0.320737i	$0.103931\pi$
$258$	0	0
$259$	0	0
$260$	7.71828	0.478668
$261$	0	0
$262$	−24.9754	−1.54298
$263$	14.7986	0.912521	0.456260	−	0.889846i	$-0.349189\pi$
$263$	14.7986	0.912521	0.456260	+	0.889846i	$0.349189\pi$
$264$	0	0
$265$	1.07220	0.0658646
$266$	0	0
$267$	0	0
$268$	−37.8220	−2.31034
$269$	−11.5959	−0.707012	−0.353506	−	0.935432i	$-0.615011\pi$
$269$	−11.5959	−0.707012	−0.353506	+	0.935432i	$0.615011\pi$
$270$	0	0
$271$	−30.3093	−1.84116	−0.920579	−	0.390556i	$-0.872283\pi$
$271$	−30.3093	−1.84116	−0.920579	+	0.390556i	$0.872283\pi$
$272$	1.24525	0.0755042
$273$	0	0
$274$	−37.9785	−2.29437
$275$	−1.95580	−0.117939
$276$	0	0
$277$	5.34980	0.321438	0.160719	−	0.987000i	$-0.448619\pi$
$277$	5.34980	0.321438	0.160719	+	0.987000i	$0.448619\pi$
$278$	−11.1781	−0.670416
$279$	0	0
$280$	0	0
$281$	22.1624	1.32210	0.661049	−	0.750343i	$-0.270112\pi$
$281$	22.1624	1.32210	0.661049	+	0.750343i	$0.270112\pi$
$282$	0	0
$283$	−14.1677	−0.842182	−0.421091	−	0.907018i	$-0.638353\pi$
$283$	−14.1677	−0.842182	−0.421091	+	0.907018i	$0.638353\pi$
$284$	1.72615	0.102428
$285$	0	0
$286$	−2.41286	−0.142675
$287$	0	0
$288$	0	0
$289$	−16.9709	−0.998289
$290$	−40.2961	−2.36627
$291$	0	0
$292$	10.0092	0.585747
$293$	29.8938	1.74641	0.873206	−	0.487351i	$-0.162037\pi$
$293$	29.8938	1.74641	0.873206	+	0.487351i	$0.162037\pi$
$294$	0	0
$295$	−11.5366	−0.671687
$296$	35.2250	2.04741
$297$	0	0
$298$	−10.6903	−0.619271
$299$	−5.66479	−0.327603
$300$	0	0
$301$	0	0
$302$	−34.6210	−1.99221
$303$	0	0
$304$	−20.9888	−1.20379
$305$	−13.9768	−0.800311
$306$	0	0
$307$	12.5659	0.717171	0.358586	−	0.933497i	$-0.383259\pi$
$307$	12.5659	0.717171	0.358586	+	0.933497i	$0.383259\pi$
$308$	0	0
$309$	0	0
$310$	−32.1894	−1.82824
$311$	−24.3379	−1.38007	−0.690037	−	0.723774i	$-0.742406\pi$
$311$	−24.3379	−1.38007	−0.690037	+	0.723774i	$0.742406\pi$
$312$	0	0
$313$	26.7536	1.51220	0.756102	−	0.654454i	$-0.227102\pi$
$313$	26.7536	1.51220	0.756102	+	0.654454i	$0.227102\pi$
$314$	48.8072	2.75435
$315$	0	0
$316$	60.9858	3.43072
$317$	−14.7383	−0.827783	−0.413891	−	0.910326i	$-0.635831\pi$
$317$	−14.7383	−0.827783	−0.413891	+	0.910326i	$0.635831\pi$
$318$	0	0
$319$	8.72549	0.488534
$320$	−0.475033	−0.0265552
$321$	0	0
$322$	0	0
$323$	−0.490278	−0.0272798
$324$	0	0
$325$	2.06772	0.114697
$326$	33.4055	1.85016
$327$	0	0
$328$	70.3594	3.88495
$329$	0	0
$330$	0	0
$331$	−2.71497	−0.149228	−0.0746141	−	0.997212i	$-0.523772\pi$
$331$	−2.71497	−0.149228	−0.0746141	+	0.997212i	$0.523772\pi$
$332$	−26.6191	−1.46092
$333$	0	0
$334$	−18.0256	−0.986318
$335$	14.3690	0.785065
$336$	0	0
$337$	14.2245	0.774859	0.387429	−	0.921899i	$-0.373363\pi$
$337$	14.2245	0.774859	0.387429	+	0.921899i	$0.373363\pi$
$338$	2.55095	0.138753
$339$	0	0
$340$	−1.31637	−0.0713900
$341$	6.97013	0.377454
$342$	0	0
$343$	0	0
$344$	16.5474	0.892179
$345$	0	0
$346$	−45.7406	−2.45903
$347$	12.7508	0.684499	0.342249	−	0.939609i	$-0.388811\pi$
$347$	12.7508	0.684499	0.342249	+	0.939609i	$0.388811\pi$
$348$	0	0
$349$	−12.9040	−0.690735	−0.345368	−	0.938467i	$-0.612246\pi$
$349$	−12.9040	−0.690735	−0.345368	+	0.938467i	$0.612246\pi$
$350$	0	0
$351$	0	0
$352$	5.51738	0.294077
$353$	−10.0199	−0.533306	−0.266653	−	0.963793i	$-0.585918\pi$
$353$	−10.0199	−0.533306	−0.266653	+	0.963793i	$0.585918\pi$
$354$	0	0
$355$	−0.655786	−0.0348055
$356$	−79.8131	−4.23009
$357$	0	0
$358$	−53.3930	−2.82191
$359$	−32.0182	−1.68986	−0.844928	−	0.534880i	$-0.820357\pi$
$359$	−32.0182	−1.68986	−0.844928	+	0.534880i	$0.820357\pi$
$360$	0	0
$361$	−10.7363	−0.565069
$362$	51.7546	2.72016
$363$	0	0
$364$	0	0
$365$	−3.80264	−0.199039
$366$	0	0
$367$	21.4376	1.11903	0.559516	−	0.828820i	$-0.310987\pi$
$367$	21.4376	1.11903	0.559516	+	0.828820i	$0.310987\pi$
$368$	41.3603	2.15606
$369$	0	0
$370$	−24.0571	−1.25067
$371$	0	0
$372$	0	0
$373$	8.85712	0.458604	0.229302	−	0.973355i	$-0.426356\pi$
$373$	8.85712	0.458604	0.229302	+	0.973355i	$0.426356\pi$
$374$	0.411517	0.0212790
$375$	0	0
$376$	−2.67509	−0.137957
$377$	−9.22485	−0.475104
$378$	0	0
$379$	6.14238	0.315513	0.157757	−	0.987478i	$-0.449574\pi$
$379$	6.14238	0.315513	0.157757	+	0.987478i	$0.449574\pi$
$380$	22.1875	1.13819
$381$	0	0
$382$	−40.7421	−2.08455
$383$	3.09085	0.157935	0.0789675	−	0.996877i	$-0.474838\pi$
$383$	3.09085	0.157935	0.0789675	+	0.996877i	$0.474838\pi$
$384$	0	0
$385$	0	0
$386$	−1.47860	−0.0752587
$387$	0	0
$388$	−34.6894	−1.76109
$389$	19.7251	1.00010	0.500052	−	0.865996i	$-0.333314\pi$
$389$	19.7251	1.00010	0.500052	+	0.865996i	$0.333314\pi$
$390$	0	0
$391$	0.966139	0.0488598
$392$	0	0
$393$	0	0
$394$	8.12173	0.409167
$395$	−23.1693	−1.16577
$396$	0	0
$397$	12.2724	0.615936	0.307968	−	0.951397i	$-0.400351\pi$
$397$	12.2724	0.615936	0.307968	+	0.951397i	$0.400351\pi$
$398$	49.5854	2.48549
$399$	0	0
$400$	−15.0971	−0.754854
$401$	1.67260	0.0835256	0.0417628	−	0.999128i	$-0.486703\pi$
$401$	1.67260	0.0835256	0.0417628	+	0.999128i	$0.486703\pi$
$402$	0	0
$403$	−7.36902	−0.367077
$404$	−32.2516	−1.60458
$405$	0	0
$406$	0	0
$407$	5.20920	0.258211
$408$	0	0
$409$	−31.3713	−1.55121	−0.775606	−	0.631217i	$-0.782556\pi$
$409$	−31.3713	−1.55121	−0.775606	+	0.631217i	$0.782556\pi$
$410$	−48.0524	−2.37314
$411$	0	0
$412$	29.2101	1.43908
$413$	0	0
$414$	0	0
$415$	10.1130	0.496425
$416$	−5.83313	−0.285993
$417$	0	0
$418$	−6.93616	−0.339259
$419$	4.81220	0.235091	0.117546	−	0.993067i	$-0.462497\pi$
$419$	4.81220	0.235091	0.117546	+	0.993067i	$0.462497\pi$
$420$	0	0
$421$	−2.96460	−0.144486	−0.0722428	−	0.997387i	$-0.523016\pi$
$421$	−2.96460	−0.144486	−0.0722428	+	0.997387i	$0.523016\pi$
$422$	−45.1157	−2.19620
$423$	0	0
$424$	−4.00483	−0.194492
$425$	−0.352654	−0.0171062
$426$	0	0
$427$	0	0
$428$	−23.9956	−1.15987
$429$	0	0
$430$	−11.3012	−0.544991
$431$	−22.4741	−1.08254	−0.541270	−	0.840849i	$-0.682056\pi$
$431$	−22.4741	−1.08254	−0.541270	+	0.840849i	$0.682056\pi$
$432$	0	0
$433$	−3.29895	−0.158537	−0.0792686	−	0.996853i	$-0.525258\pi$
$433$	−3.29895	−0.158537	−0.0792686	+	0.996853i	$0.525258\pi$
$434$	0	0
$435$	0	0
$436$	65.0710	3.11634
$437$	−16.2844	−0.778987
$438$	0	0
$439$	−37.2693	−1.77876	−0.889382	−	0.457164i	$-0.848865\pi$
$439$	−37.2693	−1.77876	−0.889382	+	0.457164i	$0.848865\pi$
$440$	−10.3596	−0.493876
$441$	0	0
$442$	−0.435068	−0.0206941
$443$	−33.5072	−1.59198	−0.795988	−	0.605312i	$-0.793048\pi$
$443$	−33.5072	−1.59198	−0.795988	+	0.605312i	$0.793048\pi$
$444$	0	0
$445$	30.3220	1.43740
$446$	12.1131	0.573570
$447$	0	0
$448$	0	0
$449$	5.41038	0.255331	0.127666	−	0.991817i	$-0.459252\pi$
$449$	5.41038	0.255331	0.127666	+	0.991817i	$0.459252\pi$
$450$	0	0
$451$	10.4050	0.489953
$452$	−40.1283	−1.88747
$453$	0	0
$454$	30.8101	1.44599
$455$	0	0
$456$	0	0
$457$	−9.05154	−0.423413	−0.211707	−	0.977333i	$-0.567902\pi$
$457$	−9.05154	−0.423413	−0.211707	+	0.977333i	$0.567902\pi$
$458$	−38.1311	−1.78175
$459$	0	0
$460$	−43.7225	−2.03857
$461$	20.8560	0.971360	0.485680	−	0.874137i	$-0.338572\pi$
$461$	20.8560	0.971360	0.485680	+	0.874137i	$0.338572\pi$
$462$	0	0
$463$	16.3606	0.760341	0.380170	−	0.924916i	$-0.375865\pi$
$463$	16.3606	0.760341	0.380170	+	0.924916i	$0.375865\pi$
$464$	67.3533	3.12680
$465$	0	0
$466$	−57.8586	−2.68025
$467$	18.9701	0.877834	0.438917	−	0.898528i	$-0.355362\pi$
$467$	18.9701	0.877834	0.438917	+	0.898528i	$0.355362\pi$
$468$	0	0
$469$	0	0
$470$	1.82697	0.0842718
$471$	0	0
$472$	43.0910	1.98342
$473$	2.44710	0.112518
$474$	0	0
$475$	5.94401	0.272730
$476$	0	0
$477$	0	0
$478$	33.1215	1.51494
$479$	−16.0811	−0.734765	−0.367383	−	0.930070i	$-0.619746\pi$
$479$	−16.0811	−0.734765	−0.367383	+	0.930070i	$0.619746\pi$
$480$	0	0
$481$	−5.50732	−0.251112
$482$	−17.9131	−0.815921
$483$	0	0
$484$	−45.5480	−2.07036
$485$	13.1790	0.598426
$486$	0	0
$487$	23.7280	1.07522	0.537610	−	0.843194i	$-0.319327\pi$
$487$	23.7280	1.07522	0.537610	+	0.843194i	$0.319327\pi$
$488$	52.2056	2.36324
$489$	0	0
$490$	0	0
$491$	−25.2613	−1.14003	−0.570013	−	0.821635i	$-0.693062\pi$
$491$	−25.2613	−1.14003	−0.570013	+	0.821635i	$0.693062\pi$
$492$	0	0
$493$	1.57331	0.0708584
$494$	7.33311	0.329932
$495$	0	0
$496$	53.8034	2.41584
$497$	0	0
$498$	0	0
$499$	−11.4025	−0.510446	−0.255223	−	0.966882i	$-0.582149\pi$
$499$	−11.4025	−0.510446	−0.255223	+	0.966882i	$0.582149\pi$
$500$	54.5507	2.43958
$501$	0	0
$502$	33.0445	1.47485
$503$	−32.2176	−1.43651	−0.718256	−	0.695779i	$-0.755059\pi$
$503$	−32.2176	−1.43651	−0.718256	+	0.695779i	$0.755059\pi$
$504$	0	0
$505$	12.2528	0.545242
$506$	13.6683	0.607632
$507$	0	0
$508$	92.1150	4.08694
$509$	−14.5352	−0.644262	−0.322131	−	0.946695i	$-0.604399\pi$
$509$	−14.5352	−0.644262	−0.322131	+	0.946695i	$0.604399\pi$
$510$	0	0
$511$	0	0
$512$	−50.8093	−2.24547
$513$	0	0
$514$	77.4684	3.41699
$515$	−11.0973	−0.489005
$516$	0	0
$517$	−0.395602	−0.0173986
$518$	0	0
$519$	0	0
$520$	10.9525	0.480299
$521$	41.4253	1.81487	0.907437	−	0.420187i	$-0.138036\pi$
$521$	41.4253	1.81487	0.907437	+	0.420187i	$0.138036\pi$
$522$	0	0
$523$	−5.74016	−0.251000	−0.125500	−	0.992094i	$-0.540053\pi$
$523$	−5.74016	−0.251000	−0.125500	+	0.992094i	$0.540053\pi$
$524$	−44.1296	−1.92781
$525$	0	0
$526$	37.7504	1.64600
$527$	1.25680	0.0547470
$528$	0	0
$529$	9.08988	0.395212
$530$	2.73512	0.118806
$531$	0	0
$532$	0	0
$533$	−11.0005	−0.476483
$534$	0	0
$535$	9.11623	0.394129
$536$	−53.6706	−2.31822
$537$	0	0
$538$	−29.5804	−1.27530
$539$	0	0
$540$	0	0
$541$	−28.2743	−1.21561	−0.607804	−	0.794087i	$-0.707949\pi$
$541$	−28.2743	−1.21561	−0.607804	+	0.794087i	$0.707949\pi$
$542$	−77.3173	−3.32106
$543$	0	0
$544$	0.994850	0.0426539
$545$	−24.7213	−1.05895
$546$	0	0
$547$	−7.27163	−0.310912	−0.155456	−	0.987843i	$-0.549685\pi$
$547$	−7.27163	−0.310912	−0.155456	+	0.987843i	$0.549685\pi$
$548$	−67.1051	−2.86659
$549$	0	0
$550$	−4.98913	−0.212737
$551$	−26.5183	−1.12972
$552$	0	0
$553$	0	0
$554$	13.6470	0.579807
$555$	0	0
$556$	−19.7508	−0.837619
$557$	−21.9639	−0.930640	−0.465320	−	0.885143i	$-0.654061\pi$
$557$	−21.9639	−0.930640	−0.465320	+	0.885143i	$0.654061\pi$
$558$	0	0
$559$	−2.58714	−0.109424
$560$	0	0
$561$	0	0
$562$	56.5351	2.38479
$563$	−0.925026	−0.0389852	−0.0194926	−	0.999810i	$-0.506205\pi$
$563$	−0.925026	−0.0389852	−0.0194926	+	0.999810i	$0.506205\pi$
$564$	0	0
$565$	15.2452	0.641372
$566$	−36.1410	−1.51912
$567$	0	0
$568$	2.44946	0.102777
$569$	25.4286	1.06602	0.533012	−	0.846108i	$-0.321060\pi$
$569$	25.4286	1.06602	0.533012	+	0.846108i	$0.321060\pi$
$570$	0	0
$571$	27.4393	1.14830	0.574149	−	0.818751i	$-0.305333\pi$
$571$	27.4393	1.14830	0.574149	+	0.818751i	$0.305333\pi$
$572$	−4.26333	−0.178259
$573$	0	0
$574$	0	0
$575$	−11.7132	−0.488476
$576$	0	0
$577$	−28.1653	−1.17254	−0.586269	−	0.810117i	$-0.699404\pi$
$577$	−28.1653	−1.17254	−0.586269	+	0.810117i	$0.699404\pi$
$578$	−43.2919	−1.80070
$579$	0	0
$580$	−71.2000	−2.95642
$581$	0	0
$582$	0	0
$583$	−0.592248	−0.0245284
$584$	14.2035	0.587743
$585$	0	0
$586$	76.2574	3.15016
$587$	12.9149	0.533055	0.266528	−	0.963827i	$-0.414124\pi$
$587$	12.9149	0.533055	0.266528	+	0.963827i	$0.414124\pi$
$588$	0	0
$589$	−21.1835	−0.872849
$590$	−29.4292	−1.21158
$591$	0	0
$592$	40.2106	1.65264
$593$	43.2007	1.77404	0.887020	−	0.461731i	$-0.152772\pi$
$593$	43.2007	1.77404	0.887020	+	0.461731i	$0.152772\pi$
$594$	0	0
$595$	0	0
$596$	−18.8889	−0.773718
$597$	0	0
$598$	−14.4506	−0.590928
$599$	−1.40835	−0.0575435	−0.0287718	−	0.999586i	$-0.509160\pi$
$599$	−1.40835	−0.0575435	−0.0287718	+	0.999586i	$0.509160\pi$
$600$	0	0
$601$	12.3321	0.503038	0.251519	−	0.967852i	$-0.419070\pi$
$601$	12.3321	0.503038	0.251519	+	0.967852i	$0.419070\pi$
$602$	0	0
$603$	0	0
$604$	−61.1726	−2.48908
$605$	17.3043	0.703518
$606$	0	0
$607$	−19.0729	−0.774145	−0.387072	−	0.922049i	$-0.626514\pi$
$607$	−19.0729	−0.774145	−0.387072	+	0.922049i	$0.626514\pi$
$608$	−16.7683	−0.680044
$609$	0	0
$610$	−35.6541	−1.44359
$611$	0.418242	0.0169203
$612$	0	0
$613$	25.5970	1.03385	0.516926	−	0.856030i	$-0.327076\pi$
$613$	25.5970	1.03385	0.516926	+	0.856030i	$0.327076\pi$
$614$	32.0548	1.29363
$615$	0	0
$616$	0	0
$617$	−26.3910	−1.06246	−0.531232	−	0.847227i	$-0.678271\pi$
$617$	−26.3910	−1.06246	−0.531232	+	0.847227i	$0.678271\pi$
$618$	0	0
$619$	23.6491	0.950537	0.475269	−	0.879841i	$-0.342351\pi$
$619$	23.6491	0.950537	0.475269	+	0.879841i	$0.342351\pi$
$620$	−56.8762	−2.28420
$621$	0	0
$622$	−62.0845	−2.48936
$623$	0	0
$624$	0	0
$625$	−10.3859	−0.415436
$626$	68.2470	2.72770
$627$	0	0
$628$	86.2385	3.44129
$629$	0.939282	0.0374516
$630$	0	0
$631$	−27.3253	−1.08780	−0.543901	−	0.839149i	$-0.683053\pi$
$631$	−27.3253	−1.08780	−0.543901	+	0.839149i	$0.683053\pi$
$632$	86.5409	3.44241
$633$	0	0
$634$	−37.5965	−1.49315
$635$	−34.9957	−1.38876
$636$	0	0
$637$	0	0
$638$	22.2583	0.881213
$639$	0	0
$640$	18.7654	0.741768
$641$	−32.0621	−1.26638	−0.633189	−	0.773997i	$-0.718254\pi$
$641$	−32.0621	−1.26638	−0.633189	+	0.773997i	$0.718254\pi$
$642$	0	0
$643$	13.9492	0.550102	0.275051	−	0.961430i	$-0.411305\pi$
$643$	13.9492	0.550102	0.275051	+	0.961430i	$0.411305\pi$
$644$	0	0
$645$	0	0
$646$	−1.25067	−0.0492071
$647$	−9.05163	−0.355856	−0.177928	−	0.984043i	$-0.556939\pi$
$647$	−9.05163	−0.355856	−0.177928	+	0.984043i	$0.556939\pi$
$648$	0	0
$649$	6.37245	0.250141
$650$	5.27465	0.206889
$651$	0	0
$652$	59.0248	2.31159
$653$	−48.6482	−1.90375	−0.951875	−	0.306485i	$-0.900847\pi$
$653$	−48.6482	−1.90375	−0.951875	+	0.306485i	$0.900847\pi$
$654$	0	0
$655$	16.7654	0.655078
$656$	80.3177	3.13588
$657$	0	0
$658$	0	0
$659$	−0.495381	−0.0192973	−0.00964865	−	0.999953i	$-0.503071\pi$
$659$	−0.495381	−0.0192973	−0.00964865	+	0.999953i	$0.503071\pi$
$660$	0	0
$661$	−20.4339	−0.794787	−0.397393	−	0.917648i	$-0.630085\pi$
$661$	−20.4339	−0.794787	−0.397393	+	0.917648i	$0.630085\pi$
$662$	−6.92574	−0.269176
$663$	0	0
$664$	−37.7734	−1.46589
$665$	0	0
$666$	0	0
$667$	52.2568	2.02339
$668$	−31.8499	−1.23231
$669$	0	0
$670$	36.6547	1.41609
$671$	7.72036	0.298041
$672$	0	0
$673$	27.7119	1.06822	0.534108	−	0.845416i	$-0.320648\pi$
$673$	27.7119	1.06822	0.534108	+	0.845416i	$0.320648\pi$
$674$	36.2860	1.39768
$675$	0	0
$676$	4.50732	0.173358
$677$	31.4521	1.20880	0.604401	−	0.796680i	$-0.293412\pi$
$677$	31.4521	1.20880	0.604401	+	0.796680i	$0.293412\pi$
$678$	0	0
$679$	0	0
$680$	−1.86797	−0.0716332
$681$	0	0
$682$	17.7804	0.680847
$683$	−43.6581	−1.67053	−0.835266	−	0.549846i	$-0.814686\pi$
$683$	−43.6581	−1.67053	−0.835266	+	0.549846i	$0.814686\pi$
$684$	0	0
$685$	25.4941	0.974078
$686$	0	0
$687$	0	0
$688$	18.8895	0.720155
$689$	0.626142	0.0238541
$690$	0	0
$691$	6.80736	0.258964	0.129482	−	0.991582i	$-0.458669\pi$
$691$	6.80736	0.258964	0.129482	+	0.991582i	$0.458669\pi$
$692$	−80.8201	−3.07232
$693$	0	0
$694$	32.5266	1.23469
$695$	7.50357	0.284627
$696$	0	0
$697$	1.87615	0.0710642
$698$	−32.9174	−1.24594
$699$	0	0
$700$	0	0
$701$	−6.52605	−0.246485	−0.123243	−	0.992377i	$-0.539329\pi$
$701$	−6.52605	−0.246485	−0.123243	+	0.992377i	$0.539329\pi$
$702$	0	0
$703$	−15.8317	−0.597104
$704$	0.262393	0.00988931
$705$	0	0
$706$	−25.5603	−0.961973
$707$	0	0
$708$	0	0
$709$	12.0610	0.452961	0.226481	−	0.974016i	$-0.427278\pi$
$709$	12.0610	0.452961	0.226481	+	0.974016i	$0.427278\pi$
$710$	−1.67288	−0.0627819
$711$	0	0
$712$	−113.257	−4.24450
$713$	41.7440	1.56332
$714$	0	0
$715$	1.61970	0.0605732
$716$	−94.3412	−3.52570
$717$	0	0
$718$	−81.6767	−3.04815
$719$	−40.4591	−1.50887	−0.754435	−	0.656375i	$-0.772089\pi$
$719$	−40.4591	−1.50887	−0.754435	+	0.656375i	$0.772089\pi$
$720$	0	0
$721$	0	0
$722$	−27.3877	−1.01927
$723$	0	0
$724$	91.4463	3.39857
$725$	−19.0744	−0.708407
$726$	0	0
$727$	−50.2601	−1.86404	−0.932022	−	0.362402i	$-0.881957\pi$
$727$	−50.2601	−1.86404	−0.932022	+	0.362402i	$0.881957\pi$
$728$	0	0
$729$	0	0
$730$	−9.70033	−0.359025
$731$	0.441241	0.0163199
$732$	0	0
$733$	−38.9127	−1.43728	−0.718638	−	0.695385i	$-0.755234\pi$
$733$	−38.9127	−1.43728	−0.718638	+	0.695385i	$0.755234\pi$
$734$	54.6860	2.01850
$735$	0	0
$736$	33.0435	1.21800
$737$	−7.93700	−0.292363
$738$	0	0
$739$	12.7456	0.468853	0.234426	−	0.972134i	$-0.424679\pi$
$739$	12.7456	0.468853	0.234426	+	0.972134i	$0.424679\pi$
$740$	−42.5071	−1.56259
$741$	0	0
$742$	0	0
$743$	−32.9198	−1.20771	−0.603856	−	0.797094i	$-0.706370\pi$
$743$	−32.9198	−1.20771	−0.603856	+	0.797094i	$0.706370\pi$
$744$	0	0
$745$	7.17612	0.262913
$746$	22.5940	0.827226
$747$	0	0
$748$	0.727118	0.0265861
$749$	0	0
$750$	0	0
$751$	24.8325	0.906151	0.453075	−	0.891472i	$-0.350327\pi$
$751$	24.8325	0.906151	0.453075	+	0.891472i	$0.350327\pi$
$752$	−3.05371	−0.111357
$753$	0	0
$754$	−23.5321	−0.856988
$755$	23.2402	0.845799
$756$	0	0
$757$	−50.3919	−1.83153	−0.915763	−	0.401718i	$-0.868413\pi$
$757$	−50.3919	−1.83153	−0.915763	+	0.401718i	$0.868413\pi$
$758$	15.6689	0.569119
$759$	0	0
$760$	31.4848	1.14207
$761$	−23.4517	−0.850125	−0.425063	−	0.905164i	$-0.639748\pi$
$761$	−23.4517	−0.850125	−0.425063	+	0.905164i	$0.639748\pi$
$762$	0	0
$763$	0	0
$764$	−71.9881	−2.60444
$765$	0	0
$766$	7.88459	0.284882
$767$	−6.73714	−0.243264
$768$	0	0
$769$	−30.0016	−1.08188	−0.540942	−	0.841060i	$-0.681932\pi$
$769$	−30.0016	−1.08188	−0.540942	+	0.841060i	$0.681932\pi$
$770$	0	0
$771$	0	0
$772$	−2.61257	−0.0940284
$773$	20.1710	0.725501	0.362751	−	0.931886i	$-0.381838\pi$
$773$	20.1710	0.725501	0.362751	+	0.931886i	$0.381838\pi$
$774$	0	0
$775$	−15.2371	−0.547333
$776$	−49.2255	−1.76709
$777$	0	0
$778$	50.3177	1.80398
$779$	−31.6227	−1.13300
$780$	0	0
$781$	0.362235	0.0129618
$782$	2.46457	0.0881328
$783$	0	0
$784$	0	0
$785$	−32.7631	−1.16937
$786$	0	0
$787$	43.0122	1.53322	0.766610	−	0.642113i	$-0.221942\pi$
$787$	43.0122	1.53322	0.766610	+	0.642113i	$0.221942\pi$
$788$	14.3505	0.511214
$789$	0	0
$790$	−59.1036	−2.10281
$791$	0	0
$792$	0	0
$793$	−8.16219	−0.289848
$794$	31.3063	1.11102
$795$	0	0
$796$	87.6136	3.10538
$797$	−25.9842	−0.920408	−0.460204	−	0.887813i	$-0.652224\pi$
$797$	−25.9842	−0.920408	−0.460204	+	0.887813i	$0.652224\pi$
$798$	0	0
$799$	−0.0713318	−0.00252354
$800$	−12.0613	−0.426432
$801$	0	0
$802$	4.26671	0.150663
$803$	2.10046	0.0741235
$804$	0	0
$805$	0	0
$806$	−18.7980	−0.662130
$807$	0	0
$808$	−45.7661	−1.61005
$809$	−11.1651	−0.392545	−0.196272	−	0.980549i	$-0.562884\pi$
$809$	−11.1651	−0.392545	−0.196272	+	0.980549i	$0.562884\pi$
$810$	0	0
$811$	−1.42780	−0.0501370	−0.0250685	−	0.999686i	$-0.507980\pi$
$811$	−1.42780	−0.0501370	−0.0250685	+	0.999686i	$0.507980\pi$
$812$	0	0
$813$	0	0
$814$	13.2884	0.465758
$815$	−22.4243	−0.785489
$816$	0	0
$817$	−7.43716	−0.260193
$818$	−80.0265	−2.79806
$819$	0	0
$820$	−84.9048	−2.96500
$821$	13.5993	0.474618	0.237309	−	0.971434i	$-0.423735\pi$
$821$	13.5993	0.474618	0.237309	+	0.971434i	$0.423735\pi$
$822$	0	0
$823$	1.71358	0.0597315	0.0298658	−	0.999554i	$-0.490492\pi$
$823$	1.71358	0.0597315	0.0298658	+	0.999554i	$0.490492\pi$
$824$	41.4501	1.44398
$825$	0	0
$826$	0	0
$827$	26.1056	0.907779	0.453890	−	0.891058i	$-0.350036\pi$
$827$	26.1056	0.907779	0.453890	+	0.891058i	$0.350036\pi$
$828$	0	0
$829$	−42.3246	−1.46999	−0.734996	−	0.678071i	$-0.762816\pi$
$829$	−42.3246	−1.46999	−0.734996	+	0.678071i	$0.762816\pi$
$830$	25.7976	0.895447
$831$	0	0
$832$	−0.277410	−0.00961745
$833$	0	0
$834$	0	0
$835$	12.1002	0.418744
$836$	−12.2556	−0.423870
$837$	0	0
$838$	12.2757	0.424055
$839$	9.93079	0.342849	0.171424	−	0.985197i	$-0.445163\pi$
$839$	9.93079	0.342849	0.171424	+	0.985197i	$0.445163\pi$
$840$	0	0
$841$	56.0978	1.93441
$842$	−7.56252	−0.260622
$843$	0	0
$844$	−79.7159	−2.74394
$845$	−1.71239	−0.0589080
$846$	0	0
$847$	0	0
$848$	−4.57165	−0.156991
$849$	0	0
$850$	−0.899600	−0.0308560
$851$	31.1978	1.06945
$852$	0	0
$853$	12.7011	0.434879	0.217439	−	0.976074i	$-0.430230\pi$
$853$	12.7011	0.434879	0.217439	+	0.976074i	$0.430230\pi$
$854$	0	0
$855$	0	0
$856$	−34.0505	−1.16382
$857$	7.43718	0.254049	0.127025	−	0.991900i	$-0.459457\pi$
$857$	7.43718	0.254049	0.127025	+	0.991900i	$0.459457\pi$
$858$	0	0
$859$	−19.9696	−0.681354	−0.340677	−	0.940180i	$-0.610656\pi$
$859$	−19.9696	−0.681354	−0.340677	+	0.940180i	$0.610656\pi$
$860$	−19.9683	−0.680913
$861$	0	0
$862$	−57.3303	−1.95268
$863$	24.8553	0.846083	0.423042	−	0.906110i	$-0.360962\pi$
$863$	24.8553	0.846083	0.423042	+	0.906110i	$0.360962\pi$
$864$	0	0
$865$	30.7046	1.04399
$866$	−8.41543	−0.285968
$867$	0	0
$868$	0	0
$869$	12.7980	0.434142
$870$	0	0
$871$	8.39123	0.284326
$872$	92.3380	3.12696
$873$	0	0
$874$	−41.5405	−1.40513
$875$	0	0
$876$	0	0
$877$	6.50366	0.219613	0.109806	−	0.993953i	$-0.464977\pi$
$877$	6.50366	0.219613	0.109806	+	0.993953i	$0.464977\pi$
$878$	−95.0718	−3.20852
$879$	0	0
$880$	−11.8259	−0.398650
$881$	23.2792	0.784295	0.392148	−	0.919902i	$-0.371732\pi$
$881$	23.2792	0.784295	0.392148	+	0.919902i	$0.371732\pi$
$882$	0	0
$883$	58.0834	1.95466	0.977331	−	0.211719i	$-0.0679062\pi$
$883$	58.0834	1.95466	0.977331	+	0.211719i	$0.0679062\pi$
$884$	−0.768731	−0.0258552
$885$	0	0
$886$	−85.4751	−2.87159
$887$	30.4508	1.02244	0.511218	−	0.859451i	$-0.329194\pi$
$887$	30.4508	1.02244	0.511218	+	0.859451i	$0.329194\pi$
$888$	0	0
$889$	0	0
$890$	77.3498	2.59277
$891$	0	0
$892$	21.4028	0.716620
$893$	1.20231	0.0402336
$894$	0	0
$895$	35.8414	1.19805
$896$	0	0
$897$	0	0
$898$	13.8016	0.460565
$899$	67.9781	2.26720
$900$	0	0
$901$	−0.106790	−0.00355767
$902$	26.5426	0.883772
$903$	0	0
$904$	−56.9433	−1.89391
$905$	−34.7416	−1.15485
$906$	0	0
$907$	20.2830	0.673486	0.336743	−	0.941597i	$-0.390675\pi$
$907$	20.2830	0.673486	0.336743	+	0.941597i	$0.390675\pi$
$908$	54.4391	1.80662
$909$	0	0
$910$	0	0
$911$	−5.25462	−0.174093	−0.0870466	−	0.996204i	$-0.527743\pi$
$911$	−5.25462	−0.174093	−0.0870466	+	0.996204i	$0.527743\pi$
$912$	0	0
$913$	−5.58607	−0.184872
$914$	−23.0900	−0.763749
$915$	0	0
$916$	−67.3747	−2.22612
$917$	0	0
$918$	0	0
$919$	1.58055	0.0521375	0.0260687	−	0.999660i	$-0.491701\pi$
$919$	1.58055	0.0521375	0.0260687	+	0.999660i	$0.491701\pi$
$920$	−62.0437	−2.04552
$921$	0	0
$922$	53.2024	1.75213
$923$	−0.382966	−0.0126055
$924$	0	0
$925$	−11.3876	−0.374423
$926$	41.7350	1.37150
$927$	0	0
$928$	53.8098	1.76639
$929$	−26.9760	−0.885053	−0.442527	−	0.896755i	$-0.645918\pi$
$929$	−26.9760	−0.885053	−0.442527	+	0.896755i	$0.645918\pi$
$930$	0	0
$931$	0	0
$932$	−102.232	−3.34871
$933$	0	0
$934$	48.3918	1.58343
$935$	−0.276242	−0.00903406
$936$	0	0
$937$	−14.3690	−0.469415	−0.234708	−	0.972066i	$-0.575413\pi$
$937$	−14.3690	−0.469415	−0.234708	+	0.972066i	$0.575413\pi$
$938$	0	0
$939$	0	0
$940$	3.22811	0.105289
$941$	−6.42582	−0.209476	−0.104738	−	0.994500i	$-0.533400\pi$
$941$	−6.42582	−0.209476	−0.104738	+	0.994500i	$0.533400\pi$
$942$	0	0
$943$	62.3154	2.02927
$944$	49.1899	1.60099
$945$	0	0
$946$	6.24241	0.202958
$947$	−22.7979	−0.740833	−0.370417	−	0.928866i	$-0.620785\pi$
$947$	−22.7979	−0.740833	−0.370417	+	0.928866i	$0.620785\pi$
$948$	0	0
$949$	−2.22066	−0.0720858
$950$	15.1628	0.491948
$951$	0	0
$952$	0	0
$953$	31.3962	1.01702	0.508511	−	0.861055i	$-0.330196\pi$
$953$	31.3962	1.01702	0.508511	+	0.861055i	$0.330196\pi$
$954$	0	0
$955$	27.3492	0.884999
$956$	58.5231	1.89277
$957$	0	0
$958$	−41.0221	−1.32536
$959$	0	0
$960$	0	0
$961$	23.3025	0.751693
$962$	−14.0489	−0.452954
$963$	0	0
$964$	−31.6511	−1.01941
$965$	0.992548	0.0319512
$966$	0	0
$967$	23.3937	0.752290	0.376145	−	0.926561i	$-0.377249\pi$
$967$	23.3937	0.752290	0.376145	+	0.926561i	$0.377249\pi$
$968$	−64.6341	−2.07742
$969$	0	0
$970$	33.6188	1.07943
$971$	48.2200	1.54745	0.773727	−	0.633519i	$-0.218390\pi$
$971$	48.2200	1.54745	0.773727	+	0.633519i	$0.218390\pi$
$972$	0	0
$973$	0	0
$974$	60.5289	1.93947
$975$	0	0
$976$	59.5945	1.90757
$977$	−39.6682	−1.26910	−0.634549	−	0.772883i	$-0.718814\pi$
$977$	−39.6682	−1.26910	−0.634549	+	0.772883i	$0.718814\pi$
$978$	0	0
$979$	−16.7489	−0.535298
$980$	0	0
$981$	0	0
$982$	−64.4402	−2.05637
$983$	−53.7093	−1.71306	−0.856530	−	0.516096i	$-0.827385\pi$
$983$	−53.7093	−1.71306	−0.856530	+	0.516096i	$0.827385\pi$
$984$	0	0
$985$	−5.45192	−0.173713
$986$	4.01343	0.127814
$987$	0	0
$988$	12.9570	0.412218
$989$	14.6556	0.466021
$990$	0	0
$991$	45.1025	1.43273	0.716364	−	0.697727i	$-0.245805\pi$
$991$	45.1025	1.43273	0.716364	+	0.697727i	$0.245805\pi$
$992$	42.9845	1.36476
$993$	0	0
$994$	0	0
$995$	−33.2855	−1.05522
$996$	0	0
$997$	−6.94418	−0.219924	−0.109962	−	0.993936i	$-0.535073\pi$
$997$	−6.94418	−0.219924	−0.109962	+	0.993936i	$0.535073\pi$
$998$	−29.0871	−0.920737
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bz.1.9		10
3.2	odd	2	inner	5733.2.a.bz.1.2		10
7.3	odd	6		819.2.j.j.352.2	yes	20
7.5	odd	6		819.2.j.j.235.2	✓	20
7.6	odd	2		5733.2.a.by.1.9		10
21.5	even	6		819.2.j.j.235.9	yes	20
21.17	even	6		819.2.j.j.352.9	yes	20
21.20	even	2		5733.2.a.by.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.j.j.235.2	✓	20	7.5	odd	6
819.2.j.j.235.9	yes	20	21.5	even	6
819.2.j.j.352.2	yes	20	7.3	odd	6
819.2.j.j.352.9	yes	20	21.17	even	6
5733.2.a.by.1.2		10	21.20	even	2
5733.2.a.by.1.9		10	7.6	odd	2
5733.2.a.bz.1.2		10	3.2	odd	2	inner
5733.2.a.bz.1.9		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5733.a (trivial)

\(f(q)\)	\(=\)	\(q+2.55095 q^{2} +4.50732 q^{4} -1.71239 q^{5} +6.39604 q^{8} +O(q^{10})\)	\(q+2.55095 q^{2} +4.50732 q^{4} -1.71239 q^{5} +6.39604 q^{8} -4.36821 q^{10} +0.945869 q^{11} -1.00000 q^{13} +7.30130 q^{16} +0.170552 q^{17} -2.87466 q^{19} -7.71828 q^{20} +2.41286 q^{22} +5.66479 q^{23} -2.06772 q^{25} -2.55095 q^{26} +9.22485 q^{29} +7.36902 q^{31} +5.83313 q^{32} +0.435068 q^{34} +5.50732 q^{37} -7.33311 q^{38} -10.9525 q^{40} +11.0005 q^{41} +2.58714 q^{43} +4.26333 q^{44} +14.4506 q^{46} -0.418242 q^{47} -5.27465 q^{50} -4.50732 q^{52} -0.626142 q^{53} -1.61970 q^{55} +23.5321 q^{58} +6.73714 q^{59} +8.16219 q^{61} +18.7980 q^{62} +0.277410 q^{64} +1.71239 q^{65} -8.39123 q^{67} +0.768731 q^{68} +0.382966 q^{71} +2.22066 q^{73} +14.0489 q^{74} -12.9570 q^{76} +13.5304 q^{79} -12.5027 q^{80} +28.0616 q^{82} -5.90576 q^{83} -0.292051 q^{85} +6.59965 q^{86} +6.04981 q^{88} -17.7074 q^{89} +25.5330 q^{92} -1.06691 q^{94} +4.92254 q^{95} -7.69624 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 16 q^{4}+O(q^{10}) \) 10 * q + 16 * q^4	\( 10 q + 16 q^{4} + 4 q^{10} - 10 q^{13} + 32 q^{16} - 6 q^{19} + 10 q^{22} + 24 q^{25} - 12 q^{31} - 34 q^{34} + 26 q^{37} + 70 q^{40} + 40 q^{43} - 6 q^{46} - 16 q^{52} + 24 q^{55} + 36 q^{58} + 22 q^{61} + 78 q^{64} + 26 q^{67} - 24 q^{73} - 4 q^{76} + 28 q^{79} + 28 q^{82} - 20 q^{85} + 12 q^{88} - 4 q^{94} - 18 q^{97}+O(q^{100}) \) 10 * q + 16 * q^4 + 4 * q^10 - 10 * q^13 + 32 * q^16 - 6 * q^19 + 10 * q^22 + 24 * q^25 - 12 * q^31 - 34 * q^34 + 26 * q^37 + 70 * q^40 + 40 * q^43 - 6 * q^46 - 16 * q^52 + 24 * q^55 + 36 * q^58 + 22 * q^61 + 78 * q^64 + 26 * q^67 - 24 * q^73 - 4 * q^76 + 28 * q^79 + 28 * q^82 - 20 * q^85 + 12 * q^88 - 4 * q^94 - 18 * q^97

Introduction

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