LMFDB - Embedded newform 5733.2.a.bl.1.2

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:	$1$
Dimension:	$5$
Coefficient field:	5.5.746052.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 7x^{3} + 8x + 2 $ x^5 - x^4 - 7x^3 + 8x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.21332$ 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)

$f(q)$	$=$	$q-2.21332 q^{2} +2.89879 q^{4} +2.12280 q^{5} -1.98932 q^{8} +O(q^{10})$	$q-2.21332 q^{2} +2.89879 q^{4} +2.12280 q^{5} -1.98932 q^{8} -4.69843 q^{10} -4.78896 q^{11} +1.00000 q^{13} -1.39458 q^{16} +3.77828 q^{17} -3.56723 q^{19} +6.15355 q^{20} +10.5995 q^{22} -4.47443 q^{23} -0.493740 q^{25} -2.21332 q^{26} +5.90107 q^{29} -3.77116 q^{31} +7.06530 q^{32} -8.36254 q^{34} +5.62570 q^{37} +7.89544 q^{38} -4.22292 q^{40} -10.3948 q^{41} +3.40733 q^{43} -13.8822 q^{44} +9.90335 q^{46} +7.10876 q^{47} +1.09280 q^{50} +2.89879 q^{52} +12.3801 q^{53} -10.1660 q^{55} -13.0610 q^{58} -4.78896 q^{59} +3.20697 q^{61} +8.34680 q^{62} -12.8486 q^{64} +2.12280 q^{65} -2.89955 q^{67} +10.9524 q^{68} +2.53876 q^{71} +7.70071 q^{73} -12.4515 q^{74} -10.3407 q^{76} -5.17850 q^{79} -2.96041 q^{80} +23.0071 q^{82} -3.46731 q^{83} +8.02051 q^{85} -7.54152 q^{86} +9.52677 q^{88} -3.66432 q^{89} -12.9704 q^{92} -15.7340 q^{94} -7.57251 q^{95} -5.40733 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 9 q^{8}+O(q^{10}) $ 5 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 - 9 * q^8	$ 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 9 q^{8} - 5 q^{10} - 11 q^{11} + 5 q^{13} + 10 q^{16} + 5 q^{17} + 9 q^{19} - q^{20} + 8 q^{22} - 10 q^{23} + 9 q^{25} - 4 q^{26} + 3 q^{29} - 6 q^{31} - 22 q^{32} - 22 q^{34} + 4 q^{37} + 10 q^{38} + 28 q^{40} - 14 q^{41} + 2 q^{43} + 3 q^{46} - q^{47} - 9 q^{50} + 8 q^{52} - 17 q^{53} - 27 q^{58} - 11 q^{59} - 11 q^{61} + 23 q^{62} + 9 q^{64} - 2 q^{65} + 13 q^{67} + 32 q^{68} - 15 q^{71} + 33 q^{74} + 8 q^{76} + 2 q^{79} - 55 q^{80} + 34 q^{82} - 6 q^{83} - 22 q^{85} - 28 q^{86} - 3 q^{88} + 4 q^{89} - 21 q^{92} + 20 q^{94} + 12 q^{95} - 12 q^{97}+O(q^{100}) $ 5 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 - 9 * q^8 - 5 * q^10 - 11 * q^11 + 5 * q^13 + 10 * q^16 + 5 * q^17 + 9 * q^19 - q^20 + 8 * q^22 - 10 * q^23 + 9 * q^25 - 4 * q^26 + 3 * q^29 - 6 * q^31 - 22 * q^32 - 22 * q^34 + 4 * q^37 + 10 * q^38 + 28 * q^40 - 14 * q^41 + 2 * q^43 + 3 * q^46 - q^47 - 9 * q^50 + 8 * q^52 - 17 * q^53 - 27 * q^58 - 11 * q^59 - 11 * q^61 + 23 * q^62 + 9 * q^64 - 2 * q^65 + 13 * q^67 + 32 * q^68 - 15 * q^71 + 33 * q^74 + 8 * q^76 + 2 * q^79 - 55 * q^80 + 34 * q^82 - 6 * q^83 - 22 * q^85 - 28 * q^86 - 3 * q^88 + 4 * q^89 - 21 * q^92 + 20 * q^94 + 12 * q^95 - 12 * 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 $

$2$	−2.21332	−1.56505	−0.782527	−	0.622616i	$-0.786070\pi$
$2$	−2.21332	−1.56505	−0.782527	+	0.622616i	$0.786070\pi$
$3$	0	0
$3$	0	0
$4$	2.89879	1.44940
$5$	2.12280	0.949343	0.474671	−	0.880163i	$-0.342567\pi$
$5$	2.12280	0.949343	0.474671	+	0.880163i	$0.342567\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−1.98932	−0.703331
$9$	0	0
$10$	−4.69843	−1.48577
$11$	−4.78896	−1.44392	−0.721962	−	0.691932i	$-0.756760\pi$
$11$	−4.78896	−1.44392	−0.721962	+	0.691932i	$0.756760\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	0	0
$16$	−1.39458	−0.348645
$17$	3.77828	0.916367	0.458183	−	0.888858i	$-0.348500\pi$
$17$	3.77828	0.916367	0.458183	+	0.888858i	$0.348500\pi$
$18$	0	0
$19$	−3.56723	−0.818379	−0.409190	−	0.912449i	$-0.634189\pi$
$19$	−3.56723	−0.818379	−0.409190	+	0.912449i	$0.634189\pi$
$20$	6.15355	1.37597
$21$	0	0
$22$	10.5995	2.25982
$23$	−4.47443	−0.932983	−0.466491	−	0.884526i	$-0.654482\pi$
$23$	−4.47443	−0.932983	−0.466491	+	0.884526i	$0.654482\pi$
$24$	0	0
$25$	−0.493740	−0.0987479
$26$	−2.21332	−0.434068
$27$	0	0
$28$	0	0
$29$	5.90107	1.09580	0.547901	−	0.836543i	$-0.315427\pi$
$29$	5.90107	1.09580	0.547901	+	0.836543i	$0.315427\pi$
$30$	0	0
$31$	−3.77116	−0.677321	−0.338660	−	0.940909i	$-0.609974\pi$
$31$	−3.77116	−0.677321	−0.338660	+	0.940909i	$0.609974\pi$
$32$	7.06530	1.24898
$33$	0	0
$34$	−8.36254	−1.43416
$35$	0	0
$36$	0	0
$37$	5.62570	0.924859	0.462429	−	0.886656i	$-0.346978\pi$
$37$	5.62570	0.924859	0.462429	+	0.886656i	$0.346978\pi$
$38$	7.89544	1.28081
$39$	0	0
$40$	−4.22292	−0.667702
$41$	−10.3948	−1.62340	−0.811698	−	0.584077i	$-0.801457\pi$
$41$	−10.3948	−1.62340	−0.811698	+	0.584077i	$0.801457\pi$
$42$	0	0
$43$	3.40733	0.519613	0.259807	−	0.965661i	$-0.416341\pi$
$43$	3.40733	0.519613	0.259807	+	0.965661i	$0.416341\pi$
$44$	−13.8822	−2.09282
$45$	0	0
$46$	9.90335	1.46017
$47$	7.10876	1.03692	0.518459	−	0.855102i	$-0.326506\pi$
$47$	7.10876	1.03692	0.518459	+	0.855102i	$0.326506\pi$
$48$	0	0
$49$	0	0
$50$	1.09280	0.154546
$51$	0	0
$52$	2.89879	0.401990
$53$	12.3801	1.70053	0.850266	−	0.526354i	$-0.176441\pi$
$53$	12.3801	1.70053	0.850266	+	0.526354i	$0.176441\pi$
$54$	0	0
$55$	−10.1660	−1.37078
$56$	0	0
$57$	0	0
$58$	−13.0610	−1.71499
$59$	−4.78896	−0.623469	−0.311734	−	0.950169i	$-0.600910\pi$
$59$	−4.78896	−0.623469	−0.311734	+	0.950169i	$0.600910\pi$
$60$	0	0
$61$	3.20697	0.410610	0.205305	−	0.978698i	$-0.434181\pi$
$61$	3.20697	0.410610	0.205305	+	0.978698i	$0.434181\pi$
$62$	8.34680	1.06004
$63$	0	0
$64$	−12.8486	−1.60608
$65$	2.12280	0.263300
$66$	0	0
$67$	−2.89955	−0.354237	−0.177118	−	0.984190i	$-0.556678\pi$
$67$	−2.89955	−0.354237	−0.177118	+	0.984190i	$0.556678\pi$
$68$	10.9524	1.32818
$69$	0	0
$70$	0	0
$71$	2.53876	0.301295	0.150648	−	0.988588i	$-0.451864\pi$
$71$	2.53876	0.301295	0.150648	+	0.988588i	$0.451864\pi$
$72$	0	0
$73$	7.70071	0.901300	0.450650	−	0.892701i	$-0.351192\pi$
$73$	7.70071	0.901300	0.450650	+	0.892701i	$0.351192\pi$
$74$	−12.4515	−1.44745
$75$	0	0
$76$	−10.3407	−1.18616
$77$	0	0
$78$	0	0
$79$	−5.17850	−0.582626	−0.291313	−	0.956628i	$-0.594092\pi$
$79$	−5.17850	−0.582626	−0.291313	+	0.956628i	$0.594092\pi$
$80$	−2.96041	−0.330984
$81$	0	0
$82$	23.0071	2.54071
$83$	−3.46731	−0.380587	−0.190294	−	0.981727i	$-0.560944\pi$
$83$	−3.46731	−0.380587	−0.190294	+	0.981727i	$0.560944\pi$
$84$	0	0
$85$	8.02051	0.869946
$86$	−7.54152	−0.813223
$87$	0	0
$88$	9.52677	1.01556
$89$	−3.66432	−0.388417	−0.194209	−	0.980960i	$-0.562214\pi$
$89$	−3.66432	−0.388417	−0.194209	+	0.980960i	$0.562214\pi$
$90$	0	0
$91$	0	0
$92$	−12.9704	−1.35226
$93$	0	0
$94$	−15.7340	−1.62283
$95$	−7.57251	−0.776923
$96$	0	0
$97$	−5.40733	−0.549031	−0.274516	−	0.961583i	$-0.588518\pi$
$97$	−5.40733	−0.549031	−0.274516	+	0.961583i	$0.588518\pi$
$98$	0	0
$99$	0	0
$100$	−1.43125	−0.143125
$101$	−9.31724	−0.927100	−0.463550	−	0.886071i	$-0.653425\pi$
$101$	−9.31724	−0.927100	−0.463550	+	0.886071i	$0.653425\pi$
$102$	0	0
$103$	7.30636	0.719917	0.359958	−	0.932968i	$-0.382791\pi$
$103$	7.30636	0.719917	0.359958	+	0.932968i	$0.382791\pi$
$104$	−1.98932	−0.195069
$105$	0	0
$106$	−27.4011	−2.66143
$107$	−6.74729	−0.652286	−0.326143	−	0.945321i	$-0.605749\pi$
$107$	−6.74729	−0.652286	−0.326143	+	0.945321i	$0.605749\pi$
$108$	0	0
$109$	4.17645	0.400031	0.200016	−	0.979793i	$-0.435901\pi$
$109$	4.17645	0.400031	0.200016	+	0.979793i	$0.435901\pi$
$110$	22.5006	2.14535
$111$	0	0
$112$	0	0
$113$	−5.90107	−0.555126	−0.277563	−	0.960707i	$-0.589527\pi$
$113$	−5.90107	−0.555126	−0.277563	+	0.960707i	$0.589527\pi$
$114$	0	0
$115$	−9.49830	−0.885721
$116$	17.1060	1.58825
$117$	0	0
$118$	10.5995	0.975763
$119$	0	0
$120$	0	0
$121$	11.9341	1.08492
$122$	−7.09805	−0.642628
$123$	0	0
$124$	−10.9318	−0.981707
$125$	−11.6621	−1.04309
$126$	0	0
$127$	−10.5268	−0.934100	−0.467050	−	0.884231i	$-0.654683\pi$
$127$	−10.5268	−0.934100	−0.467050	+	0.884231i	$0.654683\pi$
$128$	14.3075	1.26462
$129$	0	0
$130$	−4.69843	−0.412080
$131$	−5.42409	−0.473905	−0.236952	−	0.971521i	$-0.576149\pi$
$131$	−5.42409	−0.473905	−0.236952	+	0.971521i	$0.576149\pi$
$132$	0	0
$133$	0	0
$134$	6.41765	0.554400
$135$	0	0
$136$	−7.51620	−0.644509
$137$	−22.2447	−1.90050	−0.950248	−	0.311494i	$-0.899171\pi$
$137$	−22.2447	−1.90050	−0.950248	+	0.311494i	$0.899171\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	0	0
$142$	−5.61909	−0.471544
$143$	−4.78896	−0.400473
$144$	0	0
$145$	12.5268	1.04029
$146$	−17.0441	−1.41058
$147$	0	0
$148$	16.3077	1.34049
$149$	−2.95472	−0.242060	−0.121030	−	0.992649i	$-0.538620\pi$
$149$	−2.95472	−0.242060	−0.121030	+	0.992649i	$0.538620\pi$
$150$	0	0
$151$	−18.5547	−1.50996	−0.754981	−	0.655747i	$-0.772354\pi$
$151$	−18.5547	−1.50996	−0.754981	+	0.655747i	$0.772354\pi$
$152$	7.09637	0.575592
$153$	0	0
$154$	0	0
$155$	−8.00541	−0.643010
$156$	0	0
$157$	−9.79964	−0.782096	−0.391048	−	0.920370i	$-0.627887\pi$
$157$	−9.79964	−0.782096	−0.391048	+	0.920370i	$0.627887\pi$
$158$	11.4617	0.911842
$159$	0	0
$160$	14.9982	1.18571
$161$	0	0
$162$	0	0
$163$	13.8342	1.08358	0.541788	−	0.840515i	$-0.317747\pi$
$163$	13.8342	1.08358	0.541788	+	0.840515i	$0.317747\pi$
$164$	−30.1324	−2.35295
$165$	0	0
$166$	7.67428	0.595640
$167$	−17.3534	−1.34285	−0.671424	−	0.741073i	$-0.734317\pi$
$167$	−17.3534	−1.34285	−0.671424	+	0.741073i	$0.734317\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−17.7520	−1.36151
$171$	0	0
$172$	9.87716	0.753126
$173$	2.96138	0.225149	0.112575	−	0.993643i	$-0.464090\pi$
$173$	2.96138	0.225149	0.112575	+	0.993643i	$0.464090\pi$
$174$	0	0
$175$	0	0
$176$	6.67859	0.503418
$177$	0	0
$178$	8.11032	0.607894
$179$	5.66888	0.423712	0.211856	−	0.977301i	$-0.432049\pi$
$179$	5.66888	0.423712	0.211856	+	0.977301i	$0.432049\pi$
$180$	0	0
$181$	7.17645	0.533421	0.266711	−	0.963777i	$-0.414063\pi$
$181$	7.17645	0.533421	0.266711	+	0.963777i	$0.414063\pi$
$182$	0	0
$183$	0	0
$184$	8.90107	0.656196
$185$	11.9422	0.878008
$186$	0	0
$187$	−18.0940	−1.32316
$188$	20.6068	1.50291
$189$	0	0
$190$	16.7604	1.21593
$191$	−11.8818	−0.859734	−0.429867	−	0.902892i	$-0.641440\pi$
$191$	−11.8818	−0.859734	−0.429867	+	0.902892i	$0.641440\pi$
$192$	0	0
$193$	22.9702	1.65343	0.826714	−	0.562622i	$-0.190207\pi$
$193$	22.9702	1.65343	0.826714	+	0.562622i	$0.190207\pi$
$194$	11.9682	0.859264
$195$	0	0
$196$	0	0
$197$	−16.9216	−1.20561	−0.602806	−	0.797888i	$-0.705951\pi$
$197$	−16.9216	−1.20561	−0.602806	+	0.797888i	$0.705951\pi$
$198$	0	0
$199$	10.0591	0.713068	0.356534	−	0.934282i	$-0.383958\pi$
$199$	10.0591	0.713068	0.356534	+	0.934282i	$0.383958\pi$
$200$	0.982206	0.0694525
$201$	0	0
$202$	20.6221	1.45096
$203$	0	0
$204$	0	0
$205$	−22.0661	−1.54116
$206$	−16.1713	−1.12671
$207$	0	0
$208$	−1.39458	−0.0966968
$209$	17.0833	1.18168
$210$	0	0
$211$	−24.4609	−1.68396	−0.841978	−	0.539512i	$-0.818609\pi$
$211$	−24.4609	−1.68396	−0.841978	+	0.539512i	$0.818609\pi$
$212$	35.8872	2.46475
$213$	0	0
$214$	14.9339	1.02086
$215$	7.23307	0.493291
$216$	0	0
$217$	0	0
$218$	−9.24382	−0.626071
$219$	0	0
$220$	−29.4691	−1.98680
$221$	3.77828	0.254154
$222$	0	0
$223$	−29.2625	−1.95956	−0.979780	−	0.200076i	$-0.935881\pi$
$223$	−29.2625	−1.95956	−0.979780	+	0.200076i	$0.935881\pi$
$224$	0	0
$225$	0	0
$226$	13.0610	0.868803
$227$	10.0737	0.668615	0.334307	−	0.942464i	$-0.391498\pi$
$227$	10.0737	0.668615	0.334307	+	0.942464i	$0.391498\pi$
$228$	0	0
$229$	−11.1399	−0.736148	−0.368074	−	0.929796i	$-0.619983\pi$
$229$	−11.1399	−0.736148	−0.368074	+	0.929796i	$0.619983\pi$
$230$	21.0228	1.38620
$231$	0	0
$232$	−11.7391	−0.770711
$233$	17.0833	1.11917	0.559583	−	0.828774i	$-0.310961\pi$
$233$	17.0833	1.11917	0.559583	+	0.828774i	$0.310961\pi$
$234$	0	0
$235$	15.0904	0.984392
$236$	−13.8822	−0.903654
$237$	0	0
$238$	0	0
$239$	−6.92142	−0.447710	−0.223855	−	0.974622i	$-0.571864\pi$
$239$	−6.92142	−0.447710	−0.223855	+	0.974622i	$0.571864\pi$
$240$	0	0
$241$	6.49625	0.418460	0.209230	−	0.977866i	$-0.432904\pi$
$241$	6.49625	0.418460	0.209230	+	0.977866i	$0.432904\pi$
$242$	−26.4140	−1.69796
$243$	0	0
$244$	9.29634	0.595137
$245$	0	0
$246$	0	0
$247$	−3.56723	−0.226978
$248$	7.50205	0.476381
$249$	0	0
$250$	25.8119	1.63249
$251$	9.86804	0.622865	0.311433	−	0.950268i	$-0.399191\pi$
$251$	9.86804	0.622865	0.311433	+	0.950268i	$0.399191\pi$
$252$	0	0
$253$	21.4278	1.34716
$254$	23.2991	1.46192
$255$	0	0
$256$	−5.96994	−0.373121
$257$	−6.86468	−0.428207	−0.214104	−	0.976811i	$-0.568683\pi$
$257$	−6.86468	−0.428207	−0.214104	+	0.976811i	$0.568683\pi$
$258$	0	0
$259$	0	0
$260$	6.15355	0.381627
$261$	0	0
$262$	12.0052	0.741687
$263$	0.126551	0.00780345	0.00390172	−	0.999992i	$-0.498758\pi$
$263$	0.126551	0.00780345	0.00390172	+	0.999992i	$0.498758\pi$
$264$	0	0
$265$	26.2803	1.61439
$266$	0	0
$267$	0	0
$268$	−8.40521	−0.513430
$269$	4.24308	0.258705	0.129353	−	0.991599i	$-0.458710\pi$
$269$	4.24308	0.258705	0.129353	+	0.991599i	$0.458710\pi$
$270$	0	0
$271$	1.56723	0.0952026	0.0476013	−	0.998866i	$-0.484842\pi$
$271$	1.56723	0.0952026	0.0476013	+	0.998866i	$0.484842\pi$
$272$	−5.26911	−0.319487
$273$	0	0
$274$	49.2348	2.97438
$275$	2.36450	0.142585
$276$	0	0
$277$	−12.7452	−0.765785	−0.382892	−	0.923793i	$-0.625072\pi$
$277$	−12.7452	−0.765785	−0.382892	+	0.923793i	$0.625072\pi$
$278$	8.85329	0.530985
$279$	0	0
$280$	0	0
$281$	−4.62986	−0.276194	−0.138097	−	0.990419i	$-0.544099\pi$
$281$	−4.62986	−0.276194	−0.138097	+	0.990419i	$0.544099\pi$
$282$	0	0
$283$	3.64832	0.216870	0.108435	−	0.994104i	$-0.465416\pi$
$283$	3.64832	0.216870	0.108435	+	0.994104i	$0.465416\pi$
$284$	7.35934	0.436697
$285$	0	0
$286$	10.5995	0.626762
$287$	0	0
$288$	0	0
$289$	−2.72462	−0.160272
$290$	−27.7258	−1.62811
$291$	0	0
$292$	22.3228	1.30634
$293$	21.0415	1.22926	0.614630	−	0.788816i	$-0.289305\pi$
$293$	21.0415	1.22926	0.614630	+	0.788816i	$0.289305\pi$
$294$	0	0
$295$	−10.1660	−0.591886
$296$	−11.1913	−0.650482
$297$	0	0
$298$	6.53976	0.378838
$299$	−4.47443	−0.258763
$300$	0	0
$301$	0	0
$302$	41.0676	2.36317
$303$	0	0
$304$	4.97480	0.285324
$305$	6.80774	0.389810
$306$	0	0
$307$	−4.95861	−0.283003	−0.141502	−	0.989938i	$-0.545193\pi$
$307$	−4.95861	−0.283003	−0.141502	+	0.989938i	$0.545193\pi$
$308$	0	0
$309$	0	0
$310$	17.7185	1.00635
$311$	2.42158	0.137315	0.0686575	−	0.997640i	$-0.478128\pi$
$311$	2.42158	0.137315	0.0686575	+	0.997640i	$0.478128\pi$
$312$	0	0
$313$	13.9605	0.789096	0.394548	−	0.918875i	$-0.370901\pi$
$313$	13.9605	0.789096	0.394548	+	0.918875i	$0.370901\pi$
$314$	21.6897	1.22402
$315$	0	0
$316$	−15.0114	−0.844457
$317$	−3.06862	−0.172351	−0.0861753	−	0.996280i	$-0.527465\pi$
$317$	−3.06862	−0.172351	−0.0861753	+	0.996280i	$0.527465\pi$
$318$	0	0
$319$	−28.2600	−1.58225
$320$	−27.2750	−1.52472
$321$	0	0
$322$	0	0
$323$	−13.4780	−0.749936
$324$	0	0
$325$	−0.493740	−0.0273877
$326$	−30.6195	−1.69586
$327$	0	0
$328$	20.6786	1.14179
$329$	0	0
$330$	0	0
$331$	13.6052	0.747810	0.373905	−	0.927467i	$-0.378019\pi$
$331$	13.6052	0.747810	0.373905	+	0.927467i	$0.378019\pi$
$332$	−10.0510	−0.551622
$333$	0	0
$334$	38.4087	2.10163
$335$	−6.15516	−0.336292
$336$	0	0
$337$	−35.1646	−1.91554	−0.957769	−	0.287538i	$-0.907163\pi$
$337$	−35.1646	−1.91554	−0.957769	+	0.287538i	$0.907163\pi$
$338$	−2.21332	−0.120389
$339$	0	0
$340$	23.2498	1.26090
$341$	18.0599	0.978000
$342$	0	0
$343$	0	0
$344$	−6.77828	−0.365460
$345$	0	0
$346$	−6.55448	−0.352371
$347$	5.47102	0.293700	0.146850	−	0.989159i	$-0.453087\pi$
$347$	5.47102	0.293700	0.146850	+	0.989159i	$0.453087\pi$
$348$	0	0
$349$	4.34196	0.232420	0.116210	−	0.993225i	$-0.462925\pi$
$349$	4.34196	0.232420	0.116210	+	0.993225i	$0.462925\pi$
$350$	0	0
$351$	0	0
$352$	−33.8354	−1.80343
$353$	−27.5992	−1.46896	−0.734479	−	0.678631i	$-0.762573\pi$
$353$	−27.5992	−1.46896	−0.734479	+	0.678631i	$0.762573\pi$
$354$	0	0
$355$	5.38927	0.286033
$356$	−10.6221	−0.562971
$357$	0	0
$358$	−12.5470	−0.663132
$359$	−6.62855	−0.349841	−0.174921	−	0.984583i	$-0.555967\pi$
$359$	−6.62855	−0.349841	−0.174921	+	0.984583i	$0.555967\pi$
$360$	0	0
$361$	−6.27485	−0.330255
$362$	−15.8838	−0.834833
$363$	0	0
$364$	0	0
$365$	16.3470	0.855643
$366$	0	0
$367$	31.2074	1.62901	0.814506	−	0.580156i	$-0.197008\pi$
$367$	31.2074	1.62901	0.814506	+	0.580156i	$0.197008\pi$
$368$	6.23995	0.325280
$369$	0	0
$370$	−26.4319	−1.37413
$371$	0	0
$372$	0	0
$373$	−15.7746	−0.816778	−0.408389	−	0.912808i	$-0.633909\pi$
$373$	−15.7746	−0.816778	−0.408389	+	0.912808i	$0.633909\pi$
$374$	40.0479	2.07083
$375$	0	0
$376$	−14.1416	−0.729297
$377$	5.90107	0.303921
$378$	0	0
$379$	31.6512	1.62581	0.812907	−	0.582393i	$-0.197884\pi$
$379$	31.6512	1.62581	0.812907	+	0.582393i	$0.197884\pi$
$380$	−21.9511	−1.12607
$381$	0	0
$382$	26.2982	1.34553
$383$	−12.3935	−0.633278	−0.316639	−	0.948546i	$-0.602554\pi$
$383$	−12.3935	−0.633278	−0.316639	+	0.948546i	$0.602554\pi$
$384$	0	0
$385$	0	0
$386$	−50.8404	−2.58771
$387$	0	0
$388$	−15.6747	−0.795765
$389$	14.0741	0.713585	0.356792	−	0.934184i	$-0.383870\pi$
$389$	14.0741	0.713585	0.356792	+	0.934184i	$0.383870\pi$
$390$	0	0
$391$	−16.9056	−0.854954
$392$	0	0
$393$	0	0
$394$	37.4529	1.88685
$395$	−10.9929	−0.553112
$396$	0	0
$397$	−6.97305	−0.349967	−0.174984	−	0.984571i	$-0.555987\pi$
$397$	−6.97305	−0.349967	−0.174984	+	0.984571i	$0.555987\pi$
$398$	−22.2639	−1.11599
$399$	0	0
$400$	0.688560	0.0344280
$401$	−2.73682	−0.136670	−0.0683352	−	0.997662i	$-0.521769\pi$
$401$	−2.73682	−0.136670	−0.0683352	+	0.997662i	$0.521769\pi$
$402$	0	0
$403$	−3.77116	−0.187855
$404$	−27.0088	−1.34374
$405$	0	0
$406$	0	0
$407$	−26.9412	−1.33543
$408$	0	0
$409$	−24.5154	−1.21221	−0.606104	−	0.795386i	$-0.707268\pi$
$409$	−24.5154	−1.21221	−0.606104	+	0.795386i	$0.707268\pi$
$410$	48.8393	2.41200
$411$	0	0
$412$	21.1796	1.04345
$413$	0	0
$414$	0	0
$415$	−7.36040	−0.361308
$416$	7.06530	0.346405
$417$	0	0
$418$	−37.8109	−1.84939
$419$	3.01252	0.147171	0.0735856	−	0.997289i	$-0.476556\pi$
$419$	3.01252	0.147171	0.0735856	+	0.997289i	$0.476556\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	54.1398	2.63548
$423$	0	0
$424$	−24.6279	−1.19604
$425$	−1.86548	−0.0904893
$426$	0	0
$427$	0	0
$428$	−19.5590	−0.945421
$429$	0	0
$430$	−16.0091	−0.772028
$431$	18.7942	0.905286	0.452643	−	0.891692i	$-0.350481\pi$
$431$	18.7942	0.905286	0.452643	+	0.891692i	$0.350481\pi$
$432$	0	0
$433$	−7.76911	−0.373360	−0.186680	−	0.982421i	$-0.559773\pi$
$433$	−7.76911	−0.373360	−0.186680	+	0.982421i	$0.559773\pi$
$434$	0	0
$435$	0	0
$436$	12.1067	0.579804
$437$	15.9613	0.763534
$438$	0	0
$439$	−37.9681	−1.81212	−0.906060	−	0.423150i	$-0.860924\pi$
$439$	−37.9681	−1.81212	−0.906060	+	0.423150i	$0.860924\pi$
$440$	20.2234	0.964112
$441$	0	0
$442$	−8.36254	−0.397766
$443$	−35.6270	−1.69269	−0.846344	−	0.532637i	$-0.821201\pi$
$443$	−35.6270	−1.69269	−0.846344	+	0.532637i	$0.821201\pi$
$444$	0	0
$445$	−7.77860	−0.368741
$446$	64.7673	3.06682
$447$	0	0
$448$	0	0
$449$	8.05285	0.380038	0.190019	−	0.981780i	$-0.439145\pi$
$449$	8.05285	0.380038	0.190019	+	0.981780i	$0.439145\pi$
$450$	0	0
$451$	49.7803	2.34406
$452$	−17.1060	−0.804598
$453$	0	0
$454$	−22.2963	−1.04642
$455$	0	0
$456$	0	0
$457$	15.5976	0.729626	0.364813	−	0.931081i	$-0.381133\pi$
$457$	15.5976	0.729626	0.364813	+	0.931081i	$0.381133\pi$
$458$	24.6563	1.15211
$459$	0	0
$460$	−27.5336	−1.28376
$461$	25.6991	1.19692	0.598462	−	0.801151i	$-0.295779\pi$
$461$	25.6991	1.19692	0.598462	+	0.801151i	$0.295779\pi$
$462$	0	0
$463$	−20.5209	−0.953685	−0.476842	−	0.878989i	$-0.658219\pi$
$463$	−20.5209	−0.953685	−0.476842	+	0.878989i	$0.658219\pi$
$464$	−8.22952	−0.382046
$465$	0	0
$466$	−37.8109	−1.75156
$467$	−11.8248	−0.547187	−0.273594	−	0.961845i	$-0.588212\pi$
$467$	−11.8248	−0.547187	−0.273594	+	0.961845i	$0.588212\pi$
$468$	0	0
$469$	0	0
$470$	−33.4000	−1.54063
$471$	0	0
$472$	9.52677	0.438505
$473$	−16.3176	−0.750283
$474$	0	0
$475$	1.76128	0.0808133
$476$	0	0
$477$	0	0
$478$	15.3193	0.700690
$479$	−22.6552	−1.03514	−0.517571	−	0.855640i	$-0.673164\pi$
$479$	−22.6552	−1.03514	−0.517571	+	0.855640i	$0.673164\pi$
$480$	0	0
$481$	5.62570	0.256510
$482$	−14.3783	−0.654913
$483$	0	0
$484$	34.5945	1.57248
$485$	−11.4787	−0.521219
$486$	0	0
$487$	−32.7167	−1.48254	−0.741268	−	0.671209i	$-0.765775\pi$
$487$	−32.7167	−1.48254	−0.741268	+	0.671209i	$0.765775\pi$
$488$	−6.37969	−0.288795
$489$	0	0
$490$	0	0
$491$	−6.17281	−0.278575	−0.139288	−	0.990252i	$-0.544481\pi$
$491$	−6.17281	−0.278575	−0.139288	+	0.990252i	$0.544481\pi$
$492$	0	0
$493$	22.2959	1.00416
$494$	7.89544	0.355232
$495$	0	0
$496$	5.25919	0.236145
$497$	0	0
$498$	0	0
$499$	−14.6387	−0.655317	−0.327659	−	0.944796i	$-0.606260\pi$
$499$	−14.6387	−0.655317	−0.327659	+	0.944796i	$0.606260\pi$
$500$	−33.8060	−1.51185
$501$	0	0
$502$	−21.8412	−0.974818
$503$	−12.7787	−0.569774	−0.284887	−	0.958561i	$-0.591956\pi$
$503$	−12.7787	−0.569774	−0.284887	+	0.958561i	$0.591956\pi$
$504$	0	0
$505$	−19.7786	−0.880136
$506$	−47.4267	−2.10837
$507$	0	0
$508$	−30.5149	−1.35388
$509$	−11.6853	−0.517940	−0.258970	−	0.965885i	$-0.583383\pi$
$509$	−11.6853	−0.517940	−0.258970	+	0.965885i	$0.583383\pi$
$510$	0	0
$511$	0	0
$512$	−15.4017	−0.680664
$513$	0	0
$514$	15.1938	0.670168
$515$	15.5099	0.683448
$516$	0	0
$517$	−34.0435	−1.49723
$518$	0	0
$519$	0	0
$520$	−4.22292	−0.185187
$521$	−8.47675	−0.371373	−0.185687	−	0.982609i	$-0.559451\pi$
$521$	−8.47675	−0.371373	−0.185687	+	0.982609i	$0.559451\pi$
$522$	0	0
$523$	32.7108	1.43034	0.715172	−	0.698949i	$-0.246348\pi$
$523$	32.7108	1.43034	0.715172	+	0.698949i	$0.246348\pi$
$524$	−15.7233	−0.686876
$525$	0	0
$526$	−0.280097	−0.0122128
$527$	−14.2485	−0.620674
$528$	0	0
$529$	−2.97949	−0.129543
$530$	−58.1668	−2.52661
$531$	0	0
$532$	0	0
$533$	−10.3948	−0.450249
$534$	0	0
$535$	−14.3231	−0.619243
$536$	5.76814	0.249146
$537$	0	0
$538$	−9.39131	−0.404888
$539$	0	0
$540$	0	0
$541$	−28.1705	−1.21115	−0.605573	−	0.795790i	$-0.707056\pi$
$541$	−28.1705	−1.21115	−0.605573	+	0.795790i	$0.707056\pi$
$542$	−3.46879	−0.148997
$543$	0	0
$544$	26.6947	1.14452
$545$	8.86574	0.379767
$546$	0	0
$547$	−18.5377	−0.792615	−0.396307	−	0.918118i	$-0.629709\pi$
$547$	−18.5377	−0.792615	−0.396307	+	0.918118i	$0.629709\pi$
$548$	−64.4829	−2.75457
$549$	0	0
$550$	−5.23339	−0.223153
$551$	−21.0505	−0.896781
$552$	0	0
$553$	0	0
$554$	28.2092	1.19850
$555$	0	0
$556$	−11.5952	−0.491745
$557$	−4.00283	−0.169605	−0.0848027	−	0.996398i	$-0.527026\pi$
$557$	−4.00283	−0.169605	−0.0848027	+	0.996398i	$0.527026\pi$
$558$	0	0
$559$	3.40733	0.144115
$560$	0	0
$561$	0	0
$562$	10.2474	0.432259
$563$	17.8620	0.752794	0.376397	−	0.926459i	$-0.377163\pi$
$563$	17.8620	0.752794	0.376397	+	0.926459i	$0.377163\pi$
$564$	0	0
$565$	−12.5268	−0.527005
$566$	−8.07490	−0.339413
$567$	0	0
$568$	−5.05041	−0.211910
$569$	37.4672	1.57071	0.785353	−	0.619048i	$-0.212481\pi$
$569$	37.4672	1.57071	0.785353	+	0.619048i	$0.212481\pi$
$570$	0	0
$571$	17.5703	0.735293	0.367646	−	0.929966i	$-0.380164\pi$
$571$	17.5703	0.735293	0.367646	+	0.929966i	$0.380164\pi$
$572$	−13.8822	−0.580444
$573$	0	0
$574$	0	0
$575$	2.20920	0.0921301
$576$	0	0
$577$	−34.2494	−1.42582	−0.712910	−	0.701256i	$-0.752623\pi$
$577$	−34.2494	−1.42582	−0.712910	+	0.701256i	$0.752623\pi$
$578$	6.03047	0.250835
$579$	0	0
$580$	36.3125	1.50780
$581$	0	0
$582$	0	0
$583$	−59.2876	−2.45544
$584$	−15.3192	−0.633912
$585$	0	0
$586$	−46.5717	−1.92386
$587$	29.4494	1.21551	0.607754	−	0.794126i	$-0.292071\pi$
$587$	29.4494	1.21551	0.607754	+	0.794126i	$0.292071\pi$
$588$	0	0
$589$	13.4526	0.554305
$590$	22.5006	0.926334
$591$	0	0
$592$	−7.84549	−0.322448
$593$	34.0001	1.39622	0.698109	−	0.715992i	$-0.254025\pi$
$593$	34.0001	1.39622	0.698109	+	0.715992i	$0.254025\pi$
$594$	0	0
$595$	0	0
$596$	−8.56514	−0.350842
$597$	0	0
$598$	9.90335	0.404978
$599$	−21.4418	−0.876087	−0.438043	−	0.898954i	$-0.644328\pi$
$599$	−21.4418	−0.876087	−0.438043	+	0.898954i	$0.644328\pi$
$600$	0	0
$601$	40.4039	1.64811	0.824054	−	0.566511i	$-0.191707\pi$
$601$	40.4039	1.64811	0.824054	+	0.566511i	$0.191707\pi$
$602$	0	0
$603$	0	0
$604$	−53.7863	−2.18853
$605$	25.3337	1.02996
$606$	0	0
$607$	−43.8913	−1.78149	−0.890746	−	0.454501i	$-0.849818\pi$
$607$	−43.8913	−1.78149	−0.890746	+	0.454501i	$0.849818\pi$
$608$	−25.2036	−1.02214
$609$	0	0
$610$	−15.0677	−0.610074
$611$	7.10876	0.287590
$612$	0	0
$613$	−14.3155	−0.578199	−0.289100	−	0.957299i	$-0.593356\pi$
$613$	−14.3155	−0.578199	−0.289100	+	0.957299i	$0.593356\pi$
$614$	10.9750	0.442915
$615$	0	0
$616$	0	0
$617$	36.9097	1.48593	0.742965	−	0.669330i	$-0.233419\pi$
$617$	36.9097	1.48593	0.742965	+	0.669330i	$0.233419\pi$
$618$	0	0
$619$	14.2929	0.574481	0.287240	−	0.957859i	$-0.407262\pi$
$619$	14.2929	0.574481	0.287240	+	0.957859i	$0.407262\pi$
$620$	−23.2060	−0.931976
$621$	0	0
$622$	−5.35973	−0.214906
$623$	0	0
$624$	0	0
$625$	−22.2875	−0.891501
$626$	−30.8991	−1.23498
$627$	0	0
$628$	−28.4071	−1.13357
$629$	21.2554	0.847510
$630$	0	0
$631$	−0.0431064	−0.00171604	−0.000858019	−	1.00000i	$-0.500273\pi$
$631$	−0.0431064	−0.00171604	−0.000858019		1.00000i	$0.500273\pi$
$632$	10.3017	0.409779
$633$	0	0
$634$	6.79184	0.269738
$635$	−22.3462	−0.886781
$636$	0	0
$637$	0	0
$638$	62.5484	2.47632
$639$	0	0
$640$	30.3720	1.20056
$641$	−42.6655	−1.68519	−0.842594	−	0.538550i	$-0.818972\pi$
$641$	−42.6655	−1.68519	−0.842594	+	0.538550i	$0.818972\pi$
$642$	0	0
$643$	−5.49737	−0.216795	−0.108398	−	0.994108i	$-0.534572\pi$
$643$	−5.49737	−0.216795	−0.108398	+	0.994108i	$0.534572\pi$
$644$	0	0
$645$	0	0
$646$	29.8311	1.17369
$647$	38.1867	1.50127	0.750637	−	0.660715i	$-0.229747\pi$
$647$	38.1867	1.50127	0.750637	+	0.660715i	$0.229747\pi$
$648$	0	0
$649$	22.9341	0.900242
$650$	1.09280	0.0428633
$651$	0	0
$652$	40.1024	1.57053
$653$	−38.5019	−1.50670	−0.753349	−	0.657621i	$-0.771563\pi$
$653$	−38.5019	−1.50670	−0.753349	+	0.657621i	$0.771563\pi$
$654$	0	0
$655$	−11.5142	−0.449898
$656$	14.4964	0.565990
$657$	0	0
$658$	0	0
$659$	−19.4843	−0.759002	−0.379501	−	0.925191i	$-0.623904\pi$
$659$	−19.4843	−0.759002	−0.379501	+	0.925191i	$0.623904\pi$
$660$	0	0
$661$	−41.6667	−1.62065	−0.810324	−	0.585983i	$-0.800709\pi$
$661$	−41.6667	−1.62065	−0.810324	+	0.585983i	$0.800709\pi$
$662$	−30.1127	−1.17036
$663$	0	0
$664$	6.89760	0.267679
$665$	0	0
$666$	0	0
$667$	−26.4039	−1.02236
$668$	−50.3040	−1.94632
$669$	0	0
$670$	13.6234	0.526316
$671$	−15.3580	−0.592890
$672$	0	0
$673$	−14.3157	−0.551830	−0.275915	−	0.961182i	$-0.588981\pi$
$673$	−14.3157	−0.551830	−0.275915	+	0.961182i	$0.588981\pi$
$674$	77.8306	2.99792
$675$	0	0
$676$	2.89879	0.111492
$677$	29.5281	1.13486	0.567429	−	0.823423i	$-0.307938\pi$
$677$	29.5281	1.13486	0.567429	+	0.823423i	$0.307938\pi$
$678$	0	0
$679$	0	0
$680$	−15.9554	−0.611860
$681$	0	0
$682$	−39.9724	−1.53062
$683$	−47.0699	−1.80108	−0.900539	−	0.434774i	$-0.856828\pi$
$683$	−47.0699	−1.80108	−0.900539	+	0.434774i	$0.856828\pi$
$684$	0	0
$685$	−47.2210	−1.80422
$686$	0	0
$687$	0	0
$688$	−4.75180	−0.181161
$689$	12.3801	0.471643
$690$	0	0
$691$	−30.8668	−1.17423	−0.587113	−	0.809505i	$-0.699736\pi$
$691$	−30.8668	−1.17423	−0.587113	+	0.809505i	$0.699736\pi$
$692$	8.58442	0.326331
$693$	0	0
$694$	−12.1091	−0.459656
$695$	−8.49118	−0.322089
$696$	0	0
$697$	−39.2745	−1.48763
$698$	−9.61016	−0.363750
$699$	0	0
$700$	0	0
$701$	−6.48958	−0.245108	−0.122554	−	0.992462i	$-0.539108\pi$
$701$	−6.48958	−0.245108	−0.122554	+	0.992462i	$0.539108\pi$
$702$	0	0
$703$	−20.0682	−0.756885
$704$	61.5315	2.31905
$705$	0	0
$706$	61.0860	2.29900
$707$	0	0
$708$	0	0
$709$	−13.3738	−0.502263	−0.251131	−	0.967953i	$-0.580803\pi$
$709$	−13.3738	−0.502263	−0.251131	+	0.967953i	$0.580803\pi$
$710$	−11.9282	−0.447657
$711$	0	0
$712$	7.28951	0.273186
$713$	16.8738	0.631929
$714$	0	0
$715$	−10.1660	−0.380186
$716$	16.4329	0.614126
$717$	0	0
$718$	14.6711	0.547521
$719$	16.7410	0.624333	0.312166	−	0.950027i	$-0.398945\pi$
$719$	16.7410	0.624333	0.312166	+	0.950027i	$0.398945\pi$
$720$	0	0
$721$	0	0
$722$	13.8883	0.516868
$723$	0	0
$724$	20.8030	0.773139
$725$	−2.91359	−0.108208
$726$	0	0
$727$	38.8138	1.43952	0.719761	−	0.694221i	$-0.244251\pi$
$727$	38.8138	1.43952	0.719761	+	0.694221i	$0.244251\pi$
$728$	0	0
$729$	0	0
$730$	−36.1812	−1.33913
$731$	12.8738	0.476156
$732$	0	0
$733$	37.7279	1.39351	0.696756	−	0.717309i	$-0.254626\pi$
$733$	37.7279	1.39351	0.696756	+	0.717309i	$0.254626\pi$
$734$	−69.0719	−2.54949
$735$	0	0
$736$	−31.6132	−1.16528
$737$	13.8858	0.511491
$738$	0	0
$739$	−9.22952	−0.339514	−0.169757	−	0.985486i	$-0.554298\pi$
$739$	−9.22952	−0.339514	−0.169757	+	0.985486i	$0.554298\pi$
$740$	34.6180	1.27258
$741$	0	0
$742$	0	0
$743$	3.56327	0.130724	0.0653619	−	0.997862i	$-0.479180\pi$
$743$	3.56327	0.130724	0.0653619	+	0.997862i	$0.479180\pi$
$744$	0	0
$745$	−6.27228	−0.229798
$746$	34.9143	1.27830
$747$	0	0
$748$	−52.4508	−1.91779
$749$	0	0
$750$	0	0
$751$	51.2106	1.86870	0.934350	−	0.356357i	$-0.115981\pi$
$751$	51.2106	1.86870	0.934350	+	0.356357i	$0.115981\pi$
$752$	−9.91374	−0.361517
$753$	0	0
$754$	−13.0610	−0.475653
$755$	−39.3879	−1.43347
$756$	0	0
$757$	25.2305	0.917019	0.458509	−	0.888690i	$-0.348384\pi$
$757$	25.2305	0.917019	0.458509	+	0.888690i	$0.348384\pi$
$758$	−70.0543	−2.54449
$759$	0	0
$760$	15.0641	0.546434
$761$	−3.64744	−0.132220	−0.0661099	−	0.997812i	$-0.521059\pi$
$761$	−3.64744	−0.132220	−0.0661099	+	0.997812i	$0.521059\pi$
$762$	0	0
$763$	0	0
$764$	−34.4428	−1.24610
$765$	0	0
$766$	27.4308	0.991115
$767$	−4.78896	−0.172919
$768$	0	0
$769$	21.9882	0.792914	0.396457	−	0.918053i	$-0.370240\pi$
$769$	21.9882	0.792914	0.396457	+	0.918053i	$0.370240\pi$
$770$	0	0
$771$	0	0
$772$	66.5858	2.39647
$773$	−21.8590	−0.786215	−0.393108	−	0.919493i	$-0.628600\pi$
$773$	−21.8590	−0.786215	−0.393108	+	0.919493i	$0.628600\pi$
$774$	0	0
$775$	1.86197	0.0668840
$776$	10.7569	0.386151
$777$	0	0
$778$	−31.1505	−1.11680
$779$	37.0807	1.32855
$780$	0	0
$781$	−12.1580	−0.435048
$782$	37.4176	1.33805
$783$	0	0
$784$	0	0
$785$	−20.8026	−0.742477
$786$	0	0
$787$	39.8673	1.42111	0.710557	−	0.703639i	$-0.248443\pi$
$787$	39.8673	1.42111	0.710557	+	0.703639i	$0.248443\pi$
$788$	−49.0522	−1.74741
$789$	0	0
$790$	24.3308	0.865651
$791$	0	0
$792$	0	0
$793$	3.20697	0.113883
$794$	15.4336	0.547718
$795$	0	0
$796$	29.1591	1.03352
$797$	40.1971	1.42385	0.711927	−	0.702253i	$-0.247822\pi$
$797$	40.1971	1.42385	0.711927	+	0.702253i	$0.247822\pi$
$798$	0	0
$799$	26.8589	0.950198
$800$	−3.48842	−0.123334
$801$	0	0
$802$	6.05747	0.213897
$803$	−36.8784	−1.30141
$804$	0	0
$805$	0	0
$806$	8.34680	0.294003
$807$	0	0
$808$	18.5350	0.652058
$809$	−2.53849	−0.0892485	−0.0446243	−	0.999004i	$-0.514209\pi$
$809$	−2.53849	−0.0892485	−0.0446243	+	0.999004i	$0.514209\pi$
$810$	0	0
$811$	−41.7062	−1.46450	−0.732251	−	0.681035i	$-0.761530\pi$
$811$	−41.7062	−1.46450	−0.732251	+	0.681035i	$0.761530\pi$
$812$	0	0
$813$	0	0
$814$	59.6296	2.09002
$815$	29.3671	1.02869
$816$	0	0
$817$	−12.1547	−0.425241
$818$	54.2604	1.89717
$819$	0	0
$820$	−63.9650	−2.23375
$821$	−31.9304	−1.11438	−0.557189	−	0.830386i	$-0.688120\pi$
$821$	−31.9304	−1.11438	−0.557189	+	0.830386i	$0.688120\pi$
$822$	0	0
$823$	−34.2531	−1.19399	−0.596995	−	0.802245i	$-0.703639\pi$
$823$	−34.2531	−1.19399	−0.596995	+	0.802245i	$0.703639\pi$
$824$	−14.5347	−0.506340
$825$	0	0
$826$	0	0
$827$	−36.9755	−1.28576	−0.642882	−	0.765965i	$-0.722261\pi$
$827$	−36.9755	−1.28576	−0.642882	+	0.765965i	$0.722261\pi$
$828$	0	0
$829$	−19.9895	−0.694263	−0.347131	−	0.937817i	$-0.612844\pi$
$829$	−19.9895	−0.694263	−0.347131	+	0.937817i	$0.612844\pi$
$830$	16.2909	0.565466
$831$	0	0
$832$	−12.8486	−0.445446
$833$	0	0
$834$	0	0
$835$	−36.8378	−1.27482
$836$	49.5210	1.71272
$837$	0	0
$838$	−6.66768	−0.230331
$839$	−12.8147	−0.442411	−0.221206	−	0.975227i	$-0.570999\pi$
$839$	−12.8147	−0.442411	−0.221206	+	0.975227i	$0.570999\pi$
$840$	0	0
$841$	5.82265	0.200781
$842$	22.1332	0.762761
$843$	0	0
$844$	−70.9070	−2.44072
$845$	2.12280	0.0730264
$846$	0	0
$847$	0	0
$848$	−17.2650	−0.592882
$849$	0	0
$850$	4.12892	0.141621
$851$	−25.1718	−0.862877
$852$	0	0
$853$	−30.1839	−1.03348	−0.516739	−	0.856143i	$-0.672854\pi$
$853$	−30.1839	−1.03348	−0.516739	+	0.856143i	$0.672854\pi$
$854$	0	0
$855$	0	0
$856$	13.4225	0.458773
$857$	53.2327	1.81839	0.909197	−	0.416366i	$-0.136696\pi$
$857$	53.2327	1.81839	0.909197	+	0.416366i	$0.136696\pi$
$858$	0	0
$859$	−12.2719	−0.418713	−0.209357	−	0.977839i	$-0.567137\pi$
$859$	−12.2719	−0.418713	−0.209357	+	0.977839i	$0.567137\pi$
$860$	20.9672	0.714975
$861$	0	0
$862$	−41.5977	−1.41682
$863$	−24.4453	−0.832127	−0.416064	−	0.909335i	$-0.636591\pi$
$863$	−24.4453	−0.832127	−0.416064	+	0.909335i	$0.636591\pi$
$864$	0	0
$865$	6.28640	0.213744
$866$	17.1956	0.584329
$867$	0	0
$868$	0	0
$869$	24.7996	0.841268
$870$	0	0
$871$	−2.89955	−0.0982477
$872$	−8.30829	−0.281354
$873$	0	0
$874$	−35.3276	−1.19497
$875$	0	0
$876$	0	0
$877$	−52.8753	−1.78547	−0.892736	−	0.450580i	$-0.851217\pi$
$877$	−52.8753	−1.78547	−0.892736	+	0.450580i	$0.851217\pi$
$878$	84.0357	2.83607
$879$	0	0
$880$	14.1773	0.477916
$881$	−55.0118	−1.85339	−0.926697	−	0.375809i	$-0.877365\pi$
$881$	−55.0118	−1.85339	−0.926697	+	0.375809i	$0.877365\pi$
$882$	0	0
$883$	44.1730	1.48654	0.743269	−	0.668992i	$-0.233274\pi$
$883$	44.1730	1.48654	0.743269	+	0.668992i	$0.233274\pi$
$884$	10.9524	0.368371
$885$	0	0
$886$	78.8539	2.64915
$887$	5.08659	0.170791	0.0853955	−	0.996347i	$-0.472785\pi$
$887$	5.08659	0.170791	0.0853955	+	0.996347i	$0.472785\pi$
$888$	0	0
$889$	0	0
$890$	17.2165	0.577100
$891$	0	0
$892$	−84.8259	−2.84018
$893$	−25.3586	−0.848593
$894$	0	0
$895$	12.0339	0.402248
$896$	0	0
$897$	0	0
$898$	−17.8236	−0.594780
$899$	−22.2539	−0.742209
$900$	0	0
$901$	46.7753	1.55831
$902$	−110.180	−3.66859
$903$	0	0
$904$	11.7391	0.390437
$905$	15.2341	0.506400
$906$	0	0
$907$	−18.1253	−0.601840	−0.300920	−	0.953649i	$-0.597294\pi$
$907$	−18.1253	−0.601840	−0.300920	+	0.953649i	$0.597294\pi$
$908$	29.2016	0.969088
$909$	0	0
$910$	0	0
$911$	9.65804	0.319985	0.159993	−	0.987118i	$-0.448853\pi$
$911$	9.65804	0.319985	0.159993	+	0.987118i	$0.448853\pi$
$912$	0	0
$913$	16.6048	0.549539
$914$	−34.5226	−1.14190
$915$	0	0
$916$	−32.2924	−1.06697
$917$	0	0
$918$	0	0
$919$	47.7603	1.57547	0.787733	−	0.616017i	$-0.211255\pi$
$919$	47.7603	1.57547	0.787733	+	0.616017i	$0.211255\pi$
$920$	18.8952	0.622955
$921$	0	0
$922$	−56.8803	−1.87325
$923$	2.53876	0.0835643
$924$	0	0
$925$	−2.77763	−0.0913279
$926$	45.4193	1.49257
$927$	0	0
$928$	41.6928	1.36863
$929$	−33.9811	−1.11488	−0.557442	−	0.830216i	$-0.688217\pi$
$929$	−33.9811	−1.11488	−0.557442	+	0.830216i	$0.688217\pi$
$930$	0	0
$931$	0	0
$932$	49.5210	1.62212
$933$	0	0
$934$	26.1721	0.856378
$935$	−38.4099	−1.25614
$936$	0	0
$937$	−24.7948	−0.810012	−0.405006	−	0.914314i	$-0.632731\pi$
$937$	−24.7948	−0.810012	−0.405006	+	0.914314i	$0.632731\pi$
$938$	0	0
$939$	0	0
$940$	43.7441	1.42677
$941$	8.24196	0.268680	0.134340	−	0.990935i	$-0.457109\pi$
$941$	8.24196	0.268680	0.134340	+	0.990935i	$0.457109\pi$
$942$	0	0
$943$	46.5108	1.51460
$944$	6.67859	0.217370
$945$	0	0
$946$	36.1160	1.17423
$947$	−19.9729	−0.649031	−0.324515	−	0.945880i	$-0.605201\pi$
$947$	−19.9729	−0.649031	−0.324515	+	0.945880i	$0.605201\pi$
$948$	0	0
$949$	7.70071	0.249976
$950$	−3.89829	−0.126477
$951$	0	0
$952$	0	0
$953$	21.5341	0.697557	0.348778	−	0.937205i	$-0.386597\pi$
$953$	21.5341	0.697557	0.348778	+	0.937205i	$0.386597\pi$
$954$	0	0
$955$	−25.2225	−0.816182
$956$	−20.0638	−0.648909
$957$	0	0
$958$	50.1432	1.62005
$959$	0	0
$960$	0	0
$961$	−16.7783	−0.541237
$962$	−12.4515	−0.401452
$963$	0	0
$964$	18.8313	0.606515
$965$	48.7610	1.56967
$966$	0	0
$967$	43.2887	1.39207	0.696036	−	0.718007i	$-0.254945\pi$
$967$	43.2887	1.39207	0.696036	+	0.718007i	$0.254945\pi$
$968$	−23.7408	−0.763057
$969$	0	0
$970$	25.4060	0.815737
$971$	52.6713	1.69030	0.845151	−	0.534528i	$-0.179510\pi$
$971$	52.6713	1.69030	0.845151	+	0.534528i	$0.179510\pi$
$972$	0	0
$973$	0	0
$974$	72.4127	2.32025
$975$	0	0
$976$	−4.47238	−0.143157
$977$	−15.4061	−0.492885	−0.246442	−	0.969157i	$-0.579262\pi$
$977$	−15.4061	−0.492885	−0.246442	+	0.969157i	$0.579262\pi$
$978$	0	0
$979$	17.5483	0.560845
$980$	0	0
$981$	0	0
$982$	13.6624	0.435985
$983$	−7.58146	−0.241811	−0.120906	−	0.992664i	$-0.538580\pi$
$983$	−7.58146	−0.241811	−0.120906	+	0.992664i	$0.538580\pi$
$984$	0	0
$985$	−35.9211	−1.14454
$986$	−49.3480	−1.57156
$987$	0	0
$988$	−10.3407	−0.328981
$989$	−15.2459	−0.484790
$990$	0	0
$991$	−19.0185	−0.604141	−0.302071	−	0.953286i	$-0.597678\pi$
$991$	−19.0185	−0.604141	−0.302071	+	0.953286i	$0.597678\pi$
$992$	−26.6444	−0.845960
$993$	0	0
$994$	0	0
$995$	21.3533	0.676946
$996$	0	0
$997$	46.0998	1.46000	0.729998	−	0.683449i	$-0.239521\pi$
$997$	46.0998	1.46000	0.729998	+	0.683449i	$0.239521\pi$
$998$	32.4001	1.02561
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bl.1.2		5
3.2	odd	2		637.2.a.l.1.4		5
7.2	even	3		819.2.j.h.235.4		10
7.4	even	3		819.2.j.h.352.4		10
7.6	odd	2		5733.2.a.bm.1.2		5
21.2	odd	6		91.2.e.c.53.2	✓	10
21.5	even	6		637.2.e.m.508.2		10
21.11	odd	6		91.2.e.c.79.2	yes	10
21.17	even	6		637.2.e.m.79.2		10
21.20	even	2		637.2.a.k.1.4		5
39.38	odd	2		8281.2.a.bw.1.2		5
84.11	even	6		1456.2.r.p.625.5		10
84.23	even	6		1456.2.r.p.417.5		10
273.116	odd	6		1183.2.e.f.170.4		10
273.233	odd	6		1183.2.e.f.508.4		10
273.272	even	2		8281.2.a.bx.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.2	✓	10	21.2	odd	6
91.2.e.c.79.2	yes	10	21.11	odd	6
637.2.a.k.1.4		5	21.20	even	2
637.2.a.l.1.4		5	3.2	odd	2
637.2.e.m.79.2		10	21.17	even	6
637.2.e.m.508.2		10	21.5	even	6
819.2.j.h.235.4		10	7.2	even	3
819.2.j.h.352.4		10	7.4	even	3
1183.2.e.f.170.4		10	273.116	odd	6
1183.2.e.f.508.4		10	273.233	odd	6
1456.2.r.p.417.5		10	84.23	even	6
1456.2.r.p.625.5		10	84.11	even	6
5733.2.a.bl.1.2		5	1.1	even	1	trivial
5733.2.a.bm.1.2		5	7.6	odd	2
8281.2.a.bw.1.2		5	39.38	odd	2
8281.2.a.bx.1.2		5	273.272	even	2

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)

\(f(q)\)	\(=\)	\(q-2.21332 q^{2} +2.89879 q^{4} +2.12280 q^{5} -1.98932 q^{8} +O(q^{10})\)	\(q-2.21332 q^{2} +2.89879 q^{4} +2.12280 q^{5} -1.98932 q^{8} -4.69843 q^{10} -4.78896 q^{11} +1.00000 q^{13} -1.39458 q^{16} +3.77828 q^{17} -3.56723 q^{19} +6.15355 q^{20} +10.5995 q^{22} -4.47443 q^{23} -0.493740 q^{25} -2.21332 q^{26} +5.90107 q^{29} -3.77116 q^{31} +7.06530 q^{32} -8.36254 q^{34} +5.62570 q^{37} +7.89544 q^{38} -4.22292 q^{40} -10.3948 q^{41} +3.40733 q^{43} -13.8822 q^{44} +9.90335 q^{46} +7.10876 q^{47} +1.09280 q^{50} +2.89879 q^{52} +12.3801 q^{53} -10.1660 q^{55} -13.0610 q^{58} -4.78896 q^{59} +3.20697 q^{61} +8.34680 q^{62} -12.8486 q^{64} +2.12280 q^{65} -2.89955 q^{67} +10.9524 q^{68} +2.53876 q^{71} +7.70071 q^{73} -12.4515 q^{74} -10.3407 q^{76} -5.17850 q^{79} -2.96041 q^{80} +23.0071 q^{82} -3.46731 q^{83} +8.02051 q^{85} -7.54152 q^{86} +9.52677 q^{88} -3.66432 q^{89} -12.9704 q^{92} -15.7340 q^{94} -7.57251 q^{95} -5.40733 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 9 q^{8}+O(q^{10}) \) 5 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 - 9 * q^8	\( 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 9 q^{8} - 5 q^{10} - 11 q^{11} + 5 q^{13} + 10 q^{16} + 5 q^{17} + 9 q^{19} - q^{20} + 8 q^{22} - 10 q^{23} + 9 q^{25} - 4 q^{26} + 3 q^{29} - 6 q^{31} - 22 q^{32} - 22 q^{34} + 4 q^{37} + 10 q^{38} + 28 q^{40} - 14 q^{41} + 2 q^{43} + 3 q^{46} - q^{47} - 9 q^{50} + 8 q^{52} - 17 q^{53} - 27 q^{58} - 11 q^{59} - 11 q^{61} + 23 q^{62} + 9 q^{64} - 2 q^{65} + 13 q^{67} + 32 q^{68} - 15 q^{71} + 33 q^{74} + 8 q^{76} + 2 q^{79} - 55 q^{80} + 34 q^{82} - 6 q^{83} - 22 q^{85} - 28 q^{86} - 3 q^{88} + 4 q^{89} - 21 q^{92} + 20 q^{94} + 12 q^{95} - 12 q^{97}+O(q^{100}) \) 5 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 - 9 * q^8 - 5 * q^10 - 11 * q^11 + 5 * q^13 + 10 * q^16 + 5 * q^17 + 9 * q^19 - q^20 + 8 * q^22 - 10 * q^23 + 9 * q^25 - 4 * q^26 + 3 * q^29 - 6 * q^31 - 22 * q^32 - 22 * q^34 + 4 * q^37 + 10 * q^38 + 28 * q^40 - 14 * q^41 + 2 * q^43 + 3 * q^46 - q^47 - 9 * q^50 + 8 * q^52 - 17 * q^53 - 27 * q^58 - 11 * q^59 - 11 * q^61 + 23 * q^62 + 9 * q^64 - 2 * q^65 + 13 * q^67 + 32 * q^68 - 15 * q^71 + 33 * q^74 + 8 * q^76 + 2 * q^79 - 55 * q^80 + 34 * q^82 - 6 * q^83 - 22 * q^85 - 28 * q^86 - 3 * q^88 + 4 * q^89 - 21 * q^92 + 20 * q^94 + 12 * q^95 - 12 * q^97

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