LMFDB - Embedded newform 5733.2.a.bq.1.5

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:	$5$
Coefficient field:	5.5.375116.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 7x^{2} + 2x - 2 $ x^5 - x^4 - 6x^3 + 7x^2 + 2*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.44025$ 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)

$f(q)$	$=$	$q+2.14957 q^{2} +2.62066 q^{4} +3.73093 q^{5} +1.33415 q^{8} +O(q^{10})$	$q+2.14957 q^{2} +2.62066 q^{4} +3.73093 q^{5} +1.33415 q^{8} +8.01989 q^{10} -0.528912 q^{11} -1.00000 q^{13} -2.37346 q^{16} +3.80524 q^{17} +3.88050 q^{19} +9.77749 q^{20} -1.13693 q^{22} +2.43608 q^{23} +8.91980 q^{25} -2.14957 q^{26} +3.56822 q^{29} -4.99412 q^{31} -7.77023 q^{32} +8.17964 q^{34} +9.45167 q^{37} +8.34141 q^{38} +4.97763 q^{40} -5.21465 q^{41} +10.3457 q^{43} -1.38610 q^{44} +5.23653 q^{46} -11.5477 q^{47} +19.1738 q^{50} -2.62066 q^{52} -7.62994 q^{53} -1.97333 q^{55} +7.67014 q^{58} +13.4643 q^{59} -5.80524 q^{61} -10.7352 q^{62} -11.9558 q^{64} -3.73093 q^{65} +6.15975 q^{67} +9.97225 q^{68} +6.88638 q^{71} +6.45597 q^{73} +20.3171 q^{74} +10.1695 q^{76} -3.70905 q^{79} -8.85520 q^{80} -11.2093 q^{82} -2.16853 q^{83} +14.1971 q^{85} +22.2388 q^{86} -0.705650 q^{88} +1.46383 q^{89} +6.38413 q^{92} -24.8227 q^{94} +14.4778 q^{95} -11.6089 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 6 q^{4} + 3 q^{5} - 3 q^{8}+O(q^{10}) $ 5 * q + 6 * q^4 + 3 * q^5 - 3 * q^8	$ 5 q + 6 q^{4} + 3 q^{5} - 3 q^{8} - 2 q^{10} + q^{11} - 5 q^{13} + 13 q^{17} - 7 q^{19} + 13 q^{20} - 19 q^{22} + 4 q^{23} + 16 q^{25} + 12 q^{29} - 6 q^{31} - 21 q^{32} - 7 q^{34} + 11 q^{37} + 14 q^{38} - 11 q^{40} + 10 q^{41} + 10 q^{43} + 29 q^{44} + q^{46} - 4 q^{47} + 29 q^{50} - 6 q^{52} + 9 q^{53} + 12 q^{55} + 34 q^{58} + 7 q^{59} - 23 q^{61} - 24 q^{62} - 13 q^{64} - 3 q^{65} + 25 q^{67} + 20 q^{68} + 27 q^{71} - 18 q^{73} - 15 q^{74} - 2 q^{76} + 8 q^{79} + 41 q^{80} - 26 q^{82} + 12 q^{83} + 10 q^{85} + 19 q^{86} - 36 q^{88} + 29 q^{89} + 50 q^{92} + 2 q^{94} + 33 q^{95} - 13 q^{97}+O(q^{100}) $ 5 * q + 6 * q^4 + 3 * q^5 - 3 * q^8 - 2 * q^10 + q^11 - 5 * q^13 + 13 * q^17 - 7 * q^19 + 13 * q^20 - 19 * q^22 + 4 * q^23 + 16 * q^25 + 12 * q^29 - 6 * q^31 - 21 * q^32 - 7 * q^34 + 11 * q^37 + 14 * q^38 - 11 * q^40 + 10 * q^41 + 10 * q^43 + 29 * q^44 + q^46 - 4 * q^47 + 29 * q^50 - 6 * q^52 + 9 * q^53 + 12 * q^55 + 34 * q^58 + 7 * q^59 - 23 * q^61 - 24 * q^62 - 13 * q^64 - 3 * q^65 + 25 * q^67 + 20 * q^68 + 27 * q^71 - 18 * q^73 - 15 * q^74 - 2 * q^76 + 8 * q^79 + 41 * q^80 - 26 * q^82 + 12 * q^83 + 10 * q^85 + 19 * q^86 - 36 * q^88 + 29 * q^89 + 50 * q^92 + 2 * q^94 + 33 * q^95 - 13 * 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 $

$2$	2.14957	1.51998	0.759989	−	0.649937i	$-0.225205\pi$
$2$	2.14957	1.51998	0.759989	+	0.649937i	$0.225205\pi$
$3$	0	0
$3$	0	0
$4$	2.62066	1.31033
$5$	3.73093	1.66852	0.834260	−	0.551371i	$-0.185895\pi$
$5$	3.73093	1.66852	0.834260	+	0.551371i	$0.185895\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	1.33415	0.471695
$9$	0	0
$10$	8.01989	2.53611
$11$	−0.528912	−0.159473	−0.0797365	−	0.996816i	$-0.525408\pi$
$11$	−0.528912	−0.159473	−0.0797365	+	0.996816i	$0.525408\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	−2.37346	−0.593365
$17$	3.80524	0.922907	0.461453	−	0.887164i	$-0.347328\pi$
$17$	3.80524	0.922907	0.461453	+	0.887164i	$0.347328\pi$
$18$	0	0
$19$	3.88050	0.890247	0.445124	−	0.895469i	$-0.353160\pi$
$19$	3.88050	0.890247	0.445124	+	0.895469i	$0.353160\pi$
$20$	9.77749	2.18631
$21$	0	0
$22$	−1.13693	−0.242395
$23$	2.43608	0.507957	0.253979	−	0.967210i	$-0.418261\pi$
$23$	2.43608	0.507957	0.253979	+	0.967210i	$0.418261\pi$
$24$	0	0
$25$	8.91980	1.78396
$26$	−2.14957	−0.421566
$27$	0	0
$28$	0	0
$29$	3.56822	0.662602	0.331301	−	0.943525i	$-0.392513\pi$
$29$	3.56822	0.662602	0.331301	+	0.943525i	$0.392513\pi$
$30$	0	0
$31$	−4.99412	−0.896971	−0.448485	−	0.893790i	$-0.648036\pi$
$31$	−4.99412	−0.896971	−0.448485	+	0.893790i	$0.648036\pi$
$32$	−7.77023	−1.37360
$33$	0	0
$34$	8.17964	1.40280
$35$	0	0
$36$	0	0
$37$	9.45167	1.55385	0.776923	−	0.629596i	$-0.216779\pi$
$37$	9.45167	1.55385	0.776923	+	0.629596i	$0.216779\pi$
$38$	8.34141	1.35316
$39$	0	0
$40$	4.97763	0.787032
$41$	−5.21465	−0.814392	−0.407196	−	0.913341i	$-0.633493\pi$
$41$	−5.21465	−0.814392	−0.407196	+	0.913341i	$0.633493\pi$
$42$	0	0
$43$	10.3457	1.57771	0.788853	−	0.614582i	$-0.210675\pi$
$43$	10.3457	1.57771	0.788853	+	0.614582i	$0.210675\pi$
$44$	−1.38610	−0.208962
$45$	0	0
$46$	5.23653	0.772084
$47$	−11.5477	−1.68441	−0.842204	−	0.539159i	$-0.818742\pi$
$47$	−11.5477	−1.68441	−0.842204	+	0.539159i	$0.818742\pi$
$48$	0	0
$49$	0	0
$50$	19.1738	2.71158
$51$	0	0
$52$	−2.62066	−0.363420
$53$	−7.62994	−1.04805	−0.524026	−	0.851702i	$-0.675571\pi$
$53$	−7.62994	−1.04805	−0.524026	+	0.851702i	$0.675571\pi$
$54$	0	0
$55$	−1.97333	−0.266084
$56$	0	0
$57$	0	0
$58$	7.67014	1.00714
$59$	13.4643	1.75290	0.876452	−	0.481489i	$-0.159904\pi$
$59$	13.4643	1.75290	0.876452	+	0.481489i	$0.159904\pi$
$60$	0	0
$61$	−5.80524	−0.743285	−0.371643	−	0.928376i	$-0.621205\pi$
$61$	−5.80524	−0.743285	−0.371643	+	0.928376i	$0.621205\pi$
$62$	−10.7352	−1.36337
$63$	0	0
$64$	−11.9558	−1.49447
$65$	−3.73093	−0.462764
$66$	0	0
$67$	6.15975	0.752533	0.376267	−	0.926511i	$-0.377208\pi$
$67$	6.15975	0.752533	0.376267	+	0.926511i	$0.377208\pi$
$68$	9.97225	1.20931
$69$	0	0
$70$	0	0
$71$	6.88638	0.817263	0.408631	−	0.912700i	$-0.366006\pi$
$71$	6.88638	0.817263	0.408631	+	0.912700i	$0.366006\pi$
$72$	0	0
$73$	6.45597	0.755614	0.377807	−	0.925884i	$-0.376678\pi$
$73$	6.45597	0.755614	0.377807	+	0.925884i	$0.376678\pi$
$74$	20.3171	2.36181
$75$	0	0
$76$	10.1695	1.16652
$77$	0	0
$78$	0	0
$79$	−3.70905	−0.417301	−0.208650	−	0.977990i	$-0.566907\pi$
$79$	−3.70905	−0.417301	−0.208650	+	0.977990i	$0.566907\pi$
$80$	−8.85520	−0.990042
$81$	0	0
$82$	−11.2093	−1.23786
$83$	−2.16853	−0.238027	−0.119013	−	0.992893i	$-0.537973\pi$
$83$	−2.16853	−0.238027	−0.119013	+	0.992893i	$0.537973\pi$
$84$	0	0
$85$	14.1971	1.53989
$86$	22.2388	2.39808
$87$	0	0
$88$	−0.705650	−0.0752225
$89$	1.46383	0.155166	0.0775830	−	0.996986i	$-0.475280\pi$
$89$	1.46383	0.155166	0.0775830	+	0.996986i	$0.475280\pi$
$90$	0	0
$91$	0	0
$92$	6.38413	0.665592
$93$	0	0
$94$	−24.8227	−2.56026
$95$	14.4778	1.48540
$96$	0	0
$97$	−11.6089	−1.17871	−0.589353	−	0.807876i	$-0.700617\pi$
$97$	−11.6089	−1.17871	−0.589353	+	0.807876i	$0.700617\pi$
$98$	0	0
$99$	0	0
$100$	23.3758	2.33758
$101$	−12.6410	−1.25783	−0.628913	−	0.777476i	$-0.716500\pi$
$101$	−12.6410	−1.25783	−0.628913	+	0.777476i	$0.716500\pi$
$102$	0	0
$103$	13.8963	1.36925	0.684624	−	0.728897i	$-0.259966\pi$
$103$	13.8963	1.36925	0.684624	+	0.728897i	$0.259966\pi$
$104$	−1.33415	−0.130825
$105$	0	0
$106$	−16.4011	−1.59302
$107$	15.6037	1.50847	0.754234	−	0.656606i	$-0.228009\pi$
$107$	15.6037	1.50847	0.754234	+	0.656606i	$0.228009\pi$
$108$	0	0
$109$	4.85566	0.465088	0.232544	−	0.972586i	$-0.425295\pi$
$109$	4.85566	0.465088	0.232544	+	0.972586i	$0.425295\pi$
$110$	−4.24182	−0.404441
$111$	0	0
$112$	0	0
$113$	4.32152	0.406534	0.203267	−	0.979123i	$-0.434844\pi$
$113$	4.32152	0.406534	0.203267	+	0.979123i	$0.434844\pi$
$114$	0	0
$115$	9.08883	0.847537
$116$	9.35109	0.868227
$117$	0	0
$118$	28.9425	2.66437
$119$	0	0
$120$	0	0
$121$	−10.7203	−0.974568
$122$	−12.4788	−1.12978
$123$	0	0
$124$	−13.0879	−1.17533
$125$	14.6245	1.30805
$126$	0	0
$127$	−17.2976	−1.53491	−0.767457	−	0.641101i	$-0.778478\pi$
$127$	−17.2976	−1.53491	−0.767457	+	0.641101i	$0.778478\pi$
$128$	−10.1593	−0.897963
$129$	0	0
$130$	−8.01989	−0.703391
$131$	12.5511	1.09659	0.548296	−	0.836284i	$-0.315277\pi$
$131$	12.5511	1.09659	0.548296	+	0.836284i	$0.315277\pi$
$132$	0	0
$133$	0	0
$134$	13.2408	1.14383
$135$	0	0
$136$	5.07678	0.435330
$137$	−4.86350	−0.415517	−0.207759	−	0.978180i	$-0.566617\pi$
$137$	−4.86350	−0.415517	−0.207759	+	0.978180i	$0.566617\pi$
$138$	0	0
$139$	−16.4230	−1.39298	−0.696490	−	0.717567i	$-0.745256\pi$
$139$	−16.4230	−1.39298	−0.696490	+	0.717567i	$0.745256\pi$
$140$	0	0
$141$	0	0
$142$	14.8028	1.24222
$143$	0.528912	0.0442298
$144$	0	0
$145$	13.3128	1.10556
$146$	13.8776	1.14852
$147$	0	0
$148$	24.7696	2.03605
$149$	−8.77319	−0.718728	−0.359364	−	0.933198i	$-0.617006\pi$
$149$	−8.77319	−0.718728	−0.359364	+	0.933198i	$0.617006\pi$
$150$	0	0
$151$	15.6060	1.27000	0.634998	−	0.772513i	$-0.281001\pi$
$151$	15.6060	1.27000	0.634998	+	0.772513i	$0.281001\pi$
$152$	5.17718	0.419925
$153$	0	0
$154$	0	0
$155$	−18.6327	−1.49661
$156$	0	0
$157$	−15.0461	−1.20081	−0.600405	−	0.799696i	$-0.704994\pi$
$157$	−15.0461	−1.20081	−0.600405	+	0.799696i	$0.704994\pi$
$158$	−7.97287	−0.634288
$159$	0	0
$160$	−28.9902	−2.29187
$161$	0	0
$162$	0	0
$163$	−6.63561	−0.519741	−0.259871	−	0.965643i	$-0.583680\pi$
$163$	−6.63561	−0.519741	−0.259871	+	0.965643i	$0.583680\pi$
$164$	−13.6658	−1.06712
$165$	0	0
$166$	−4.66140	−0.361795
$167$	−14.1593	−1.09568	−0.547839	−	0.836584i	$-0.684549\pi$
$167$	−14.1593	−1.09568	−0.547839	+	0.836584i	$0.684549\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	30.5176	2.34060
$171$	0	0
$172$	27.1126	2.06731
$173$	−1.05826	−0.0804581	−0.0402290	−	0.999190i	$-0.512809\pi$
$173$	−1.05826	−0.0804581	−0.0402290	+	0.999190i	$0.512809\pi$
$174$	0	0
$175$	0	0
$176$	1.25535	0.0946257
$177$	0	0
$178$	3.14661	0.235849
$179$	16.1559	1.20755	0.603774	−	0.797155i	$-0.293663\pi$
$179$	16.1559	1.20755	0.603774	+	0.797155i	$0.293663\pi$
$180$	0	0
$181$	−8.79784	−0.653938	−0.326969	−	0.945035i	$-0.606027\pi$
$181$	−8.79784	−0.653938	−0.326969	+	0.945035i	$0.606027\pi$
$182$	0	0
$183$	0	0
$184$	3.25010	0.239601
$185$	35.2635	2.59262
$186$	0	0
$187$	−2.01264	−0.147179
$188$	−30.2626	−2.20713
$189$	0	0
$190$	31.1212	2.25777
$191$	−5.19862	−0.376159	−0.188079	−	0.982154i	$-0.560226\pi$
$191$	−5.19862	−0.376159	−0.188079	+	0.982154i	$0.560226\pi$
$192$	0	0
$193$	−14.1552	−1.01892	−0.509458	−	0.860495i	$-0.670154\pi$
$193$	−14.1552	−1.01892	−0.509458	+	0.860495i	$0.670154\pi$
$194$	−24.9542	−1.79161
$195$	0	0
$196$	0	0
$197$	−20.4646	−1.45804	−0.729020	−	0.684492i	$-0.760024\pi$
$197$	−20.4646	−1.45804	−0.729020	+	0.684492i	$0.760024\pi$
$198$	0	0
$199$	20.7931	1.47398	0.736991	−	0.675902i	$-0.236246\pi$
$199$	20.7931	1.47398	0.736991	+	0.675902i	$0.236246\pi$
$200$	11.9004	0.841485
$201$	0	0
$202$	−27.1727	−1.91187
$203$	0	0
$204$	0	0
$205$	−19.4555	−1.35883
$206$	29.8712	2.08123
$207$	0	0
$208$	2.37346	0.164570
$209$	−2.05244	−0.141970
$210$	0	0
$211$	1.47513	0.101552	0.0507761	−	0.998710i	$-0.483831\pi$
$211$	1.47513	0.101552	0.0507761	+	0.998710i	$0.483831\pi$
$212$	−19.9955	−1.37330
$213$	0	0
$214$	33.5413	2.29284
$215$	38.5991	2.63243
$216$	0	0
$217$	0	0
$218$	10.4376	0.706924
$219$	0	0
$220$	−5.17143	−0.348658
$221$	−3.80524	−0.255968
$222$	0	0
$223$	−18.9314	−1.26774	−0.633869	−	0.773441i	$-0.718534\pi$
$223$	−18.9314	−1.26774	−0.633869	+	0.773441i	$0.718534\pi$
$224$	0	0
$225$	0	0
$226$	9.28941	0.617922
$227$	6.43602	0.427174	0.213587	−	0.976924i	$-0.431485\pi$
$227$	6.43602	0.427174	0.213587	+	0.976924i	$0.431485\pi$
$228$	0	0
$229$	−18.4074	−1.21640	−0.608199	−	0.793785i	$-0.708108\pi$
$229$	−18.4074	−1.21640	−0.608199	+	0.793785i	$0.708108\pi$
$230$	19.5371	1.28824
$231$	0	0
$232$	4.76055	0.312546
$233$	14.8076	0.970075	0.485038	−	0.874493i	$-0.338806\pi$
$233$	14.8076	0.970075	0.485038	+	0.874493i	$0.338806\pi$
$234$	0	0
$235$	−43.0837	−2.81047
$236$	35.2854	2.29688
$237$	0	0
$238$	0	0
$239$	−1.48600	−0.0961213	−0.0480606	−	0.998844i	$-0.515304\pi$
$239$	−1.48600	−0.0961213	−0.0480606	+	0.998844i	$0.515304\pi$
$240$	0	0
$241$	−27.1228	−1.74713	−0.873565	−	0.486707i	$-0.838198\pi$
$241$	−27.1228	−1.74713	−0.873565	+	0.486707i	$0.838198\pi$
$242$	−23.0440	−1.48132
$243$	0	0
$244$	−15.2136	−0.973949
$245$	0	0
$246$	0	0
$247$	−3.88050	−0.246910
$248$	−6.66293	−0.423096
$249$	0	0
$250$	31.4364	1.98821
$251$	3.04811	0.192395	0.0961974	−	0.995362i	$-0.469332\pi$
$251$	3.04811	0.192395	0.0961974	+	0.995362i	$0.469332\pi$
$252$	0	0
$253$	−1.28847	−0.0810055
$254$	−37.1824	−2.33303
$255$	0	0
$256$	2.07338	0.129586
$257$	20.1383	1.25619	0.628096	−	0.778136i	$-0.283834\pi$
$257$	20.1383	1.25619	0.628096	+	0.778136i	$0.283834\pi$
$258$	0	0
$259$	0	0
$260$	−9.77749	−0.606374
$261$	0	0
$262$	26.9794	1.66680
$263$	20.0617	1.23706	0.618529	−	0.785762i	$-0.287729\pi$
$263$	20.0617	1.23706	0.618529	+	0.785762i	$0.287729\pi$
$264$	0	0
$265$	−28.4667	−1.74870
$266$	0	0
$267$	0	0
$268$	16.1426	0.986067
$269$	−19.0100	−1.15906	−0.579530	−	0.814951i	$-0.696764\pi$
$269$	−19.0100	−1.15906	−0.579530	+	0.814951i	$0.696764\pi$
$270$	0	0
$271$	−16.8274	−1.02219	−0.511096	−	0.859524i	$-0.670760\pi$
$271$	−16.8274	−1.02219	−0.511096	+	0.859524i	$0.670760\pi$
$272$	−9.03159	−0.547621
$273$	0	0
$274$	−10.4544	−0.631576
$275$	−4.71779	−0.284493
$276$	0	0
$277$	−23.0432	−1.38453	−0.692267	−	0.721641i	$-0.743388\pi$
$277$	−23.0432	−1.38453	−0.692267	+	0.721641i	$0.743388\pi$
$278$	−35.3024	−2.11730
$279$	0	0
$280$	0	0
$281$	17.7086	1.05641	0.528203	−	0.849118i	$-0.322866\pi$
$281$	17.7086	1.05641	0.528203	+	0.849118i	$0.322866\pi$
$282$	0	0
$283$	−17.3781	−1.03302	−0.516510	−	0.856281i	$-0.672769\pi$
$283$	−17.3781	−1.03302	−0.516510	+	0.856281i	$0.672769\pi$
$284$	18.0469	1.07088
$285$	0	0
$286$	1.13693	0.0672283
$287$	0	0
$288$	0	0
$289$	−2.52013	−0.148243
$290$	28.6167	1.68043
$291$	0	0
$292$	16.9189	0.990104
$293$	−31.0543	−1.81421	−0.907105	−	0.420905i	$-0.861712\pi$
$293$	−31.0543	−1.81421	−0.907105	+	0.420905i	$0.861712\pi$
$294$	0	0
$295$	50.2343	2.92476
$296$	12.6100	0.732941
$297$	0	0
$298$	−18.8586	−1.09245
$299$	−2.43608	−0.140882
$300$	0	0
$301$	0	0
$302$	33.5462	1.93037
$303$	0	0
$304$	−9.21021	−0.528242
$305$	−21.6589	−1.24019
$306$	0	0
$307$	15.7951	0.901474	0.450737	−	0.892657i	$-0.351161\pi$
$307$	15.7951	0.901474	0.450737	+	0.892657i	$0.351161\pi$
$308$	0	0
$309$	0	0
$310$	−40.0523	−2.27482
$311$	6.58699	0.373514	0.186757	−	0.982406i	$-0.440202\pi$
$311$	6.58699	0.373514	0.186757	+	0.982406i	$0.440202\pi$
$312$	0	0
$313$	12.9625	0.732682	0.366341	−	0.930481i	$-0.380610\pi$
$313$	12.9625	0.732682	0.366341	+	0.930481i	$0.380610\pi$
$314$	−32.3427	−1.82520
$315$	0	0
$316$	−9.72016	−0.546802
$317$	−24.9452	−1.40106	−0.700532	−	0.713621i	$-0.747054\pi$
$317$	−24.9452	−1.40106	−0.700532	+	0.713621i	$0.747054\pi$
$318$	0	0
$319$	−1.88727	−0.105667
$320$	−44.6060	−2.49355
$321$	0	0
$322$	0	0
$323$	14.7662	0.821615
$324$	0	0
$325$	−8.91980	−0.494782
$326$	−14.2637	−0.789995
$327$	0	0
$328$	−6.95715	−0.384144
$329$	0	0
$330$	0	0
$331$	4.37115	0.240260	0.120130	−	0.992758i	$-0.461669\pi$
$331$	4.37115	0.240260	0.120130	+	0.992758i	$0.461669\pi$
$332$	−5.68297	−0.311893
$333$	0	0
$334$	−30.4364	−1.66541
$335$	22.9816	1.25562
$336$	0	0
$337$	2.61680	0.142546	0.0712731	−	0.997457i	$-0.477294\pi$
$337$	2.61680	0.142546	0.0712731	+	0.997457i	$0.477294\pi$
$338$	2.14957	0.116921
$339$	0	0
$340$	37.2057	2.01776
$341$	2.64145	0.143043
$342$	0	0
$343$	0	0
$344$	13.8028	0.744195
$345$	0	0
$346$	−2.27481	−0.122294
$347$	17.0188	0.913617	0.456809	−	0.889565i	$-0.348992\pi$
$347$	17.0188	0.913617	0.456809	+	0.889565i	$0.348992\pi$
$348$	0	0
$349$	−11.1055	−0.594464	−0.297232	−	0.954805i	$-0.596064\pi$
$349$	−11.1055	−0.594464	−0.297232	+	0.954805i	$0.596064\pi$
$350$	0	0
$351$	0	0
$352$	4.10977	0.219051
$353$	15.7257	0.836996	0.418498	−	0.908218i	$-0.362557\pi$
$353$	15.7257	0.836996	0.418498	+	0.908218i	$0.362557\pi$
$354$	0	0
$355$	25.6926	1.36362
$356$	3.83621	0.203319
$357$	0	0
$358$	34.7283	1.83545
$359$	2.66357	0.140578	0.0702890	−	0.997527i	$-0.477608\pi$
$359$	2.66357	0.140578	0.0702890	+	0.997527i	$0.477608\pi$
$360$	0	0
$361$	−3.94174	−0.207460
$362$	−18.9116	−0.993971
$363$	0	0
$364$	0	0
$365$	24.0867	1.26076
$366$	0	0
$367$	13.8145	0.721109	0.360555	−	0.932738i	$-0.382587\pi$
$367$	13.8145	0.721109	0.360555	+	0.932738i	$0.382587\pi$
$368$	−5.78194	−0.301404
$369$	0	0
$370$	75.8014	3.94073
$371$	0	0
$372$	0	0
$373$	1.40620	0.0728101	0.0364051	−	0.999337i	$-0.488409\pi$
$373$	1.40620	0.0728101	0.0364051	+	0.999337i	$0.488409\pi$
$374$	−4.32631	−0.223708
$375$	0	0
$376$	−15.4064	−0.794526
$377$	−3.56822	−0.183773
$378$	0	0
$379$	10.4746	0.538046	0.269023	−	0.963134i	$-0.413299\pi$
$379$	10.4746	0.538046	0.269023	+	0.963134i	$0.413299\pi$
$380$	37.9415	1.94636
$381$	0	0
$382$	−11.1748	−0.571753
$383$	−3.63078	−0.185524	−0.0927620	−	0.995688i	$-0.529570\pi$
$383$	−3.63078	−0.185524	−0.0927620	+	0.995688i	$0.529570\pi$
$384$	0	0
$385$	0	0
$386$	−30.4277	−1.54873
$387$	0	0
$388$	−30.4230	−1.54449
$389$	−11.6835	−0.592378	−0.296189	−	0.955129i	$-0.595716\pi$
$389$	−11.6835	−0.592378	−0.296189	+	0.955129i	$0.595716\pi$
$390$	0	0
$391$	9.26987	0.468797
$392$	0	0
$393$	0	0
$394$	−43.9901	−2.21619
$395$	−13.8382	−0.696275
$396$	0	0
$397$	6.67982	0.335250	0.167625	−	0.985851i	$-0.446390\pi$
$397$	6.67982	0.335250	0.167625	+	0.985851i	$0.446390\pi$
$398$	44.6962	2.24042
$399$	0	0
$400$	−21.1708	−1.05854
$401$	25.6428	1.28054	0.640271	−	0.768149i	$-0.278822\pi$
$401$	25.6428	1.28054	0.640271	+	0.768149i	$0.278822\pi$
$402$	0	0
$403$	4.99412	0.248775
$404$	−33.1277	−1.64817
$405$	0	0
$406$	0	0
$407$	−4.99910	−0.247796
$408$	0	0
$409$	22.5418	1.11462	0.557311	−	0.830304i	$-0.311833\pi$
$409$	22.5418	1.11462	0.557311	+	0.830304i	$0.311833\pi$
$410$	−41.8209	−2.06539
$411$	0	0
$412$	36.4176	1.79417
$413$	0	0
$414$	0	0
$415$	−8.09061	−0.397152
$416$	7.77023	0.380967
$417$	0	0
$418$	−4.41187	−0.215792
$419$	−10.1169	−0.494242	−0.247121	−	0.968985i	$-0.579484\pi$
$419$	−10.1169	−0.494242	−0.247121	+	0.968985i	$0.579484\pi$
$420$	0	0
$421$	26.8426	1.30823	0.654113	−	0.756396i	$-0.273042\pi$
$421$	26.8426	1.30823	0.654113	+	0.756396i	$0.273042\pi$
$422$	3.17090	0.154357
$423$	0	0
$424$	−10.1795	−0.494361
$425$	33.9420	1.64643
$426$	0	0
$427$	0	0
$428$	40.8920	1.97659
$429$	0	0
$430$	82.9715	4.00124
$431$	−5.32813	−0.256647	−0.128323	−	0.991732i	$-0.540960\pi$
$431$	−5.32813	−0.256647	−0.128323	+	0.991732i	$0.540960\pi$
$432$	0	0
$433$	−2.75478	−0.132386	−0.0661932	−	0.997807i	$-0.521085\pi$
$433$	−2.75478	−0.132386	−0.0661932	+	0.997807i	$0.521085\pi$
$434$	0	0
$435$	0	0
$436$	12.7250	0.609419
$437$	9.45320	0.452208
$438$	0	0
$439$	23.9811	1.14455	0.572277	−	0.820060i	$-0.306060\pi$
$439$	23.9811	1.14455	0.572277	+	0.820060i	$0.306060\pi$
$440$	−2.63273	−0.125510
$441$	0	0
$442$	−8.17964	−0.389066
$443$	−19.6584	−0.933999	−0.466999	−	0.884258i	$-0.654665\pi$
$443$	−19.6584	−0.933999	−0.466999	+	0.884258i	$0.654665\pi$
$444$	0	0
$445$	5.46145	0.258898
$446$	−40.6943	−1.92693
$447$	0	0
$448$	0	0
$449$	18.5726	0.876493	0.438246	−	0.898855i	$-0.355600\pi$
$449$	18.5726	0.876493	0.438246	+	0.898855i	$0.355600\pi$
$450$	0	0
$451$	2.75809	0.129873
$452$	11.3252	0.532694
$453$	0	0
$454$	13.8347	0.649294
$455$	0	0
$456$	0	0
$457$	8.39115	0.392521	0.196261	−	0.980552i	$-0.437120\pi$
$457$	8.39115	0.392521	0.196261	+	0.980552i	$0.437120\pi$
$458$	−39.5681	−1.84890
$459$	0	0
$460$	23.8187	1.11055
$461$	−1.50338	−0.0700195	−0.0350097	−	0.999387i	$-0.511146\pi$
$461$	−1.50338	−0.0700195	−0.0350097	+	0.999387i	$0.511146\pi$
$462$	0	0
$463$	−30.3510	−1.41053	−0.705265	−	0.708944i	$-0.749172\pi$
$463$	−30.3510	−1.41053	−0.705265	+	0.708944i	$0.749172\pi$
$464$	−8.46903	−0.393165
$465$	0	0
$466$	31.8299	1.47449
$467$	−27.0373	−1.25114	−0.625569	−	0.780169i	$-0.715133\pi$
$467$	−27.0373	−1.25114	−0.625569	+	0.780169i	$0.715133\pi$
$468$	0	0
$469$	0	0
$470$	−92.6115	−4.27185
$471$	0	0
$472$	17.9635	0.826835
$473$	−5.47197	−0.251601
$474$	0	0
$475$	34.6133	1.58817
$476$	0	0
$477$	0	0
$478$	−3.19426	−0.146102
$479$	−19.2791	−0.880885	−0.440442	−	0.897781i	$-0.645178\pi$
$479$	−19.2791	−0.880885	−0.440442	+	0.897781i	$0.645178\pi$
$480$	0	0
$481$	−9.45167	−0.430959
$482$	−58.3023	−2.65560
$483$	0	0
$484$	−28.0941	−1.27701
$485$	−43.3119	−1.96669
$486$	0	0
$487$	−14.5719	−0.660316	−0.330158	−	0.943926i	$-0.607102\pi$
$487$	−14.5719	−0.660316	−0.330158	+	0.943926i	$0.607102\pi$
$488$	−7.74509	−0.350604
$489$	0	0
$490$	0	0
$491$	−16.7357	−0.755271	−0.377636	−	0.925954i	$-0.623263\pi$
$491$	−16.7357	−0.755271	−0.377636	+	0.925954i	$0.623263\pi$
$492$	0	0
$493$	13.5779	0.611519
$494$	−8.34141	−0.375298
$495$	0	0
$496$	11.8533	0.532231
$497$	0	0
$498$	0	0
$499$	−2.72382	−0.121935	−0.0609674	−	0.998140i	$-0.519419\pi$
$499$	−2.72382	−0.121935	−0.0609674	+	0.998140i	$0.519419\pi$
$500$	38.3258	1.71398
$501$	0	0
$502$	6.55213	0.292436
$503$	−6.96312	−0.310470	−0.155235	−	0.987878i	$-0.549613\pi$
$503$	−6.96312	−0.310470	−0.155235	+	0.987878i	$0.549613\pi$
$504$	0	0
$505$	−47.1626	−2.09871
$506$	−2.76966	−0.123126
$507$	0	0
$508$	−45.3311	−2.01124
$509$	−13.6370	−0.604449	−0.302224	−	0.953237i	$-0.597729\pi$
$509$	−13.6370	−0.604449	−0.302224	+	0.953237i	$0.597729\pi$
$510$	0	0
$511$	0	0
$512$	24.7755	1.09493
$513$	0	0
$514$	43.2887	1.90938
$515$	51.8462	2.28462
$516$	0	0
$517$	6.10773	0.268618
$518$	0	0
$519$	0	0
$520$	−4.97763	−0.218283
$521$	42.1653	1.84730	0.923648	−	0.383242i	$-0.125192\pi$
$521$	42.1653	1.84730	0.923648	+	0.383242i	$0.125192\pi$
$522$	0	0
$523$	9.87664	0.431875	0.215938	−	0.976407i	$-0.430719\pi$
$523$	9.87664	0.431875	0.215938	+	0.976407i	$0.430719\pi$
$524$	32.8921	1.43690
$525$	0	0
$526$	43.1241	1.88030
$527$	−19.0038	−0.827820
$528$	0	0
$529$	−17.0655	−0.741979
$530$	−61.1913	−2.65798
$531$	0	0
$532$	0	0
$533$	5.21465	0.225872
$534$	0	0
$535$	58.2163	2.51691
$536$	8.21805	0.354966
$537$	0	0
$538$	−40.8634	−1.76175
$539$	0	0
$540$	0	0
$541$	−12.6880	−0.545500	−0.272750	−	0.962085i	$-0.587933\pi$
$541$	−12.6880	−0.545500	−0.272750	+	0.962085i	$0.587933\pi$
$542$	−36.1717	−1.55371
$543$	0	0
$544$	−29.5676	−1.26770
$545$	18.1161	0.776009
$546$	0	0
$547$	−32.9907	−1.41058	−0.705291	−	0.708918i	$-0.749184\pi$
$547$	−32.9907	−1.41058	−0.705291	+	0.708918i	$0.749184\pi$
$548$	−12.7456	−0.544465
$549$	0	0
$550$	−10.1412	−0.432424
$551$	13.8465	0.589879
$552$	0	0
$553$	0	0
$554$	−49.5331	−2.10446
$555$	0	0
$556$	−43.0391	−1.82526
$557$	18.7978	0.796489	0.398245	−	0.917279i	$-0.369620\pi$
$557$	18.7978	0.796489	0.398245	+	0.917279i	$0.369620\pi$
$558$	0	0
$559$	−10.3457	−0.437577
$560$	0	0
$561$	0	0
$562$	38.0659	1.60571
$563$	−25.8645	−1.09006	−0.545030	−	0.838416i	$-0.683482\pi$
$563$	−25.8645	−1.09006	−0.545030	+	0.838416i	$0.683482\pi$
$564$	0	0
$565$	16.1233	0.678310
$566$	−37.3555	−1.57017
$567$	0	0
$568$	9.18749	0.385498
$569$	44.0629	1.84721	0.923607	−	0.383341i	$-0.125226\pi$
$569$	44.0629	1.84721	0.923607	+	0.383341i	$0.125226\pi$
$570$	0	0
$571$	6.08341	0.254583	0.127291	−	0.991865i	$-0.459372\pi$
$571$	6.08341	0.254583	0.127291	+	0.991865i	$0.459372\pi$
$572$	1.38610	0.0579557
$573$	0	0
$574$	0	0
$575$	21.7293	0.906176
$576$	0	0
$577$	−1.20699	−0.0502477	−0.0251238	−	0.999684i	$-0.507998\pi$
$577$	−1.20699	−0.0502477	−0.0251238	+	0.999684i	$0.507998\pi$
$578$	−5.41721	−0.225326
$579$	0	0
$580$	34.8882	1.44865
$581$	0	0
$582$	0	0
$583$	4.03557	0.167136
$584$	8.61326	0.356419
$585$	0	0
$586$	−66.7534	−2.75756
$587$	29.7974	1.22987	0.614935	−	0.788578i	$-0.289182\pi$
$587$	29.7974	1.22987	0.614935	+	0.788578i	$0.289182\pi$
$588$	0	0
$589$	−19.3797	−0.798526
$590$	107.982	4.44556
$591$	0	0
$592$	−22.4332	−0.921998
$593$	1.33274	0.0547291	0.0273646	−	0.999626i	$-0.491289\pi$
$593$	1.33274	0.0547291	0.0273646	+	0.999626i	$0.491289\pi$
$594$	0	0
$595$	0	0
$596$	−22.9916	−0.941771
$597$	0	0
$598$	−5.23653	−0.214137
$599$	−15.6611	−0.639897	−0.319948	−	0.947435i	$-0.603666\pi$
$599$	−15.6611	−0.639897	−0.319948	+	0.947435i	$0.603666\pi$
$600$	0	0
$601$	−9.62304	−0.392532	−0.196266	−	0.980551i	$-0.562882\pi$
$601$	−9.62304	−0.392532	−0.196266	+	0.980551i	$0.562882\pi$
$602$	0	0
$603$	0	0
$604$	40.8980	1.66411
$605$	−39.9965	−1.62609
$606$	0	0
$607$	−39.8297	−1.61664	−0.808318	−	0.588746i	$-0.799622\pi$
$607$	−39.8297	−1.61664	−0.808318	+	0.588746i	$0.799622\pi$
$608$	−30.1524	−1.22284
$609$	0	0
$610$	−46.5574	−1.88505
$611$	11.5477	0.467171
$612$	0	0
$613$	−24.6932	−0.997350	−0.498675	−	0.866789i	$-0.666180\pi$
$613$	−24.6932	−0.997350	−0.498675	+	0.866789i	$0.666180\pi$
$614$	33.9527	1.37022
$615$	0	0
$616$	0	0
$617$	−24.3968	−0.982178	−0.491089	−	0.871109i	$-0.663401\pi$
$617$	−24.3968	−0.982178	−0.491089	+	0.871109i	$0.663401\pi$
$618$	0	0
$619$	17.1583	0.689649	0.344825	−	0.938667i	$-0.387938\pi$
$619$	17.1583	0.689649	0.344825	+	0.938667i	$0.387938\pi$
$620$	−48.8300	−1.96106
$621$	0	0
$622$	14.1592	0.567733
$623$	0	0
$624$	0	0
$625$	9.96389	0.398556
$626$	27.8638	1.11366
$627$	0	0
$628$	−39.4307	−1.57346
$629$	35.9659	1.43405
$630$	0	0
$631$	−4.49651	−0.179003	−0.0895016	−	0.995987i	$-0.528527\pi$
$631$	−4.49651	−0.179003	−0.0895016	+	0.995987i	$0.528527\pi$
$632$	−4.94844	−0.196839
$633$	0	0
$634$	−53.6216	−2.12958
$635$	−64.5361	−2.56104
$636$	0	0
$637$	0	0
$638$	−4.05683	−0.160611
$639$	0	0
$640$	−37.9035	−1.49827
$641$	−21.6506	−0.855146	−0.427573	−	0.903981i	$-0.640631\pi$
$641$	−21.6506	−0.855146	−0.427573	+	0.903981i	$0.640631\pi$
$642$	0	0
$643$	3.00336	0.118441	0.0592204	−	0.998245i	$-0.481139\pi$
$643$	3.00336	0.118441	0.0592204	+	0.998245i	$0.481139\pi$
$644$	0	0
$645$	0	0
$646$	31.7411	1.24884
$647$	−31.8567	−1.25242	−0.626208	−	0.779656i	$-0.715394\pi$
$647$	−31.8567	−1.25242	−0.626208	+	0.779656i	$0.715394\pi$
$648$	0	0
$649$	−7.12144	−0.279541
$650$	−19.1738	−0.752057
$651$	0	0
$652$	−17.3897	−0.681033
$653$	23.9761	0.938257	0.469128	−	0.883130i	$-0.344568\pi$
$653$	23.9761	0.938257	0.469128	+	0.883130i	$0.344568\pi$
$654$	0	0
$655$	46.8271	1.82969
$656$	12.3768	0.483232
$657$	0	0
$658$	0	0
$659$	−23.5364	−0.916849	−0.458425	−	0.888733i	$-0.651586\pi$
$659$	−23.5364	−0.916849	−0.458425	+	0.888733i	$0.651586\pi$
$660$	0	0
$661$	−38.6096	−1.50174	−0.750870	−	0.660450i	$-0.770366\pi$
$661$	−38.6096	−1.50174	−0.750870	+	0.660450i	$0.770366\pi$
$662$	9.39609	0.365189
$663$	0	0
$664$	−2.89315	−0.112276
$665$	0	0
$666$	0	0
$667$	8.69246	0.336573
$668$	−37.1067	−1.43570
$669$	0	0
$670$	49.4005	1.90851
$671$	3.07046	0.118534
$672$	0	0
$673$	16.6618	0.642266	0.321133	−	0.947034i	$-0.395936\pi$
$673$	16.6618	0.642266	0.321133	+	0.947034i	$0.395936\pi$
$674$	5.62500	0.216667
$675$	0	0
$676$	2.62066	0.100795
$677$	7.62777	0.293159	0.146579	−	0.989199i	$-0.453174\pi$
$677$	7.62777	0.293159	0.146579	+	0.989199i	$0.453174\pi$
$678$	0	0
$679$	0	0
$680$	18.9411	0.726357
$681$	0	0
$682$	5.67799	0.217421
$683$	−1.09427	−0.0418711	−0.0209355	−	0.999781i	$-0.506664\pi$
$683$	−1.09427	−0.0418711	−0.0209355	+	0.999781i	$0.506664\pi$
$684$	0	0
$685$	−18.1454	−0.693299
$686$	0	0
$687$	0	0
$688$	−24.5551	−0.936155
$689$	7.62994	0.290678
$690$	0	0
$691$	5.87856	0.223631	0.111815	−	0.993729i	$-0.464333\pi$
$691$	5.87856	0.223631	0.111815	+	0.993729i	$0.464333\pi$
$692$	−2.77334	−0.105427
$693$	0	0
$694$	36.5832	1.38868
$695$	−61.2729	−2.32421
$696$	0	0
$697$	−19.8430	−0.751608
$698$	−23.8721	−0.903572
$699$	0	0
$700$	0	0
$701$	8.84963	0.334246	0.167123	−	0.985936i	$-0.446552\pi$
$701$	8.84963	0.334246	0.167123	+	0.985936i	$0.446552\pi$
$702$	0	0
$703$	36.6772	1.38331
$704$	6.32354	0.238327
$705$	0	0
$706$	33.8036	1.27222
$707$	0	0
$708$	0	0
$709$	−14.2588	−0.535502	−0.267751	−	0.963488i	$-0.586280\pi$
$709$	−14.2588	−0.535502	−0.267751	+	0.963488i	$0.586280\pi$
$710$	55.2280	2.07267
$711$	0	0
$712$	1.95298	0.0731909
$713$	−12.1661	−0.455623
$714$	0	0
$715$	1.97333	0.0737984
$716$	42.3391	1.58229
$717$	0	0
$718$	5.72554	0.213675
$719$	25.8818	0.965227	0.482614	−	0.875833i	$-0.339688\pi$
$719$	25.8818	0.965227	0.482614	+	0.875833i	$0.339688\pi$
$720$	0	0
$721$	0	0
$722$	−8.47305	−0.315334
$723$	0	0
$724$	−23.0562	−0.856875
$725$	31.8278	1.18206
$726$	0	0
$727$	29.9940	1.11242	0.556209	−	0.831043i	$-0.312256\pi$
$727$	29.9940	1.11242	0.556209	+	0.831043i	$0.312256\pi$
$728$	0	0
$729$	0	0
$730$	51.7762	1.91632
$731$	39.3679	1.45607
$732$	0	0
$733$	−16.6763	−0.615951	−0.307976	−	0.951394i	$-0.599652\pi$
$733$	−16.6763	−0.615951	−0.307976	+	0.951394i	$0.599652\pi$
$734$	29.6952	1.09607
$735$	0	0
$736$	−18.9289	−0.697728
$737$	−3.25796	−0.120009
$738$	0	0
$739$	18.1001	0.665823	0.332911	−	0.942958i	$-0.391969\pi$
$739$	18.1001	0.665823	0.332911	+	0.942958i	$0.391969\pi$
$740$	92.4136	3.39719
$741$	0	0
$742$	0	0
$743$	15.3219	0.562107	0.281054	−	0.959692i	$-0.409316\pi$
$743$	15.3219	0.562107	0.281054	+	0.959692i	$0.409316\pi$
$744$	0	0
$745$	−32.7321	−1.19921
$746$	3.02272	0.110670
$747$	0	0
$748$	−5.27444	−0.192853
$749$	0	0
$750$	0	0
$751$	−32.6153	−1.19015	−0.595075	−	0.803670i	$-0.702878\pi$
$751$	−32.6153	−1.19015	−0.595075	+	0.803670i	$0.702878\pi$
$752$	27.4081	0.999469
$753$	0	0
$754$	−7.67014	−0.279330
$755$	58.2247	2.11902
$756$	0	0
$757$	32.2037	1.17046	0.585232	−	0.810866i	$-0.301003\pi$
$757$	32.2037	1.17046	0.585232	+	0.810866i	$0.301003\pi$
$758$	22.5160	0.817817
$759$	0	0
$760$	19.3157	0.700653
$761$	25.1610	0.912086	0.456043	−	0.889958i	$-0.349266\pi$
$761$	25.1610	0.912086	0.456043	+	0.889958i	$0.349266\pi$
$762$	0	0
$763$	0	0
$764$	−13.6238	−0.492892
$765$	0	0
$766$	−7.80462	−0.281992
$767$	−13.4643	−0.486168
$768$	0	0
$769$	−20.3041	−0.732186	−0.366093	−	0.930578i	$-0.619305\pi$
$769$	−20.3041	−0.732186	−0.366093	+	0.930578i	$0.619305\pi$
$770$	0	0
$771$	0	0
$772$	−37.0961	−1.33512
$773$	−5.54678	−0.199504	−0.0997519	−	0.995012i	$-0.531805\pi$
$773$	−5.54678	−0.199504	−0.0997519	+	0.995012i	$0.531805\pi$
$774$	0	0
$775$	−44.5466	−1.60016
$776$	−15.4881	−0.555989
$777$	0	0
$778$	−25.1146	−0.900400
$779$	−20.2354	−0.725010
$780$	0	0
$781$	−3.64229	−0.130331
$782$	19.9262	0.712561
$783$	0	0
$784$	0	0
$785$	−56.1359	−2.00358
$786$	0	0
$787$	−0.466851	−0.0166414	−0.00832071	−	0.999965i	$-0.502649\pi$
$787$	−0.466851	−0.0166414	−0.00832071	+	0.999965i	$0.502649\pi$
$788$	−53.6307	−1.91051
$789$	0	0
$790$	−29.7462	−1.05832
$791$	0	0
$792$	0	0
$793$	5.80524	0.206150
$794$	14.3587	0.509573
$795$	0	0
$796$	54.4916	1.93140
$797$	−12.2437	−0.433694	−0.216847	−	0.976206i	$-0.569577\pi$
$797$	−12.2437	−0.433694	−0.216847	+	0.976206i	$0.569577\pi$
$798$	0	0
$799$	−43.9419	−1.55455
$800$	−69.3090	−2.45044
$801$	0	0
$802$	55.1211	1.94639
$803$	−3.41464	−0.120500
$804$	0	0
$805$	0	0
$806$	10.7352	0.378132
$807$	0	0
$808$	−16.8650	−0.593309
$809$	43.8846	1.54290	0.771451	−	0.636289i	$-0.219531\pi$
$809$	43.8846	1.54290	0.771451	+	0.636289i	$0.219531\pi$
$810$	0	0
$811$	−30.2691	−1.06289	−0.531446	−	0.847092i	$-0.678351\pi$
$811$	−30.2691	−1.06289	−0.531446	+	0.847092i	$0.678351\pi$
$812$	0	0
$813$	0	0
$814$	−10.7459	−0.376645
$815$	−24.7570	−0.867199
$816$	0	0
$817$	40.1465	1.40455
$818$	48.4553	1.69420
$819$	0	0
$820$	−50.9862	−1.78051
$821$	35.0880	1.22458	0.612290	−	0.790633i	$-0.290248\pi$
$821$	35.0880	1.22458	0.612290	+	0.790633i	$0.290248\pi$
$822$	0	0
$823$	−40.3528	−1.40661	−0.703305	−	0.710889i	$-0.748293\pi$
$823$	−40.3528	−1.40661	−0.703305	+	0.710889i	$0.748293\pi$
$824$	18.5399	0.645867
$825$	0	0
$826$	0	0
$827$	26.5847	0.924439	0.462220	−	0.886766i	$-0.347053\pi$
$827$	26.5847	0.924439	0.462220	+	0.886766i	$0.347053\pi$
$828$	0	0
$829$	−14.4672	−0.502468	−0.251234	−	0.967926i	$-0.580836\pi$
$829$	−14.4672	−0.502468	−0.251234	+	0.967926i	$0.580836\pi$
$830$	−17.3913	−0.603662
$831$	0	0
$832$	11.9558	0.414491
$833$	0	0
$834$	0	0
$835$	−52.8272	−1.82816
$836$	−5.37875	−0.186028
$837$	0	0
$838$	−21.7470	−0.751236
$839$	32.7480	1.13059	0.565294	−	0.824890i	$-0.308763\pi$
$839$	32.7480	1.13059	0.565294	+	0.824890i	$0.308763\pi$
$840$	0	0
$841$	−16.2678	−0.560959
$842$	57.7000	1.98847
$843$	0	0
$844$	3.86582	0.133067
$845$	3.73093	0.128348
$846$	0	0
$847$	0	0
$848$	18.1094	0.621878
$849$	0	0
$850$	72.9608	2.50253
$851$	23.0250	0.789288
$852$	0	0
$853$	−4.69850	−0.160873	−0.0804367	−	0.996760i	$-0.525631\pi$
$853$	−4.69850	−0.160873	−0.0804367	+	0.996760i	$0.525631\pi$
$854$	0	0
$855$	0	0
$856$	20.8177	0.711536
$857$	−17.1751	−0.586690	−0.293345	−	0.956007i	$-0.594768\pi$
$857$	−17.1751	−0.586690	−0.293345	+	0.956007i	$0.594768\pi$
$858$	0	0
$859$	38.2619	1.30548	0.652739	−	0.757583i	$-0.273620\pi$
$859$	38.2619	1.30548	0.652739	+	0.757583i	$0.273620\pi$
$860$	101.155	3.44936
$861$	0	0
$862$	−11.4532	−0.390097
$863$	7.68202	0.261499	0.130750	−	0.991415i	$-0.458262\pi$
$863$	7.68202	0.261499	0.130750	+	0.991415i	$0.458262\pi$
$864$	0	0
$865$	−3.94829	−0.134246
$866$	−5.92160	−0.201224
$867$	0	0
$868$	0	0
$869$	1.96176	0.0665482
$870$	0	0
$871$	−6.15975	−0.208715
$872$	6.47820	0.219380
$873$	0	0
$874$	20.3203	0.687345
$875$	0	0
$876$	0	0
$877$	44.3178	1.49650	0.748252	−	0.663415i	$-0.230893\pi$
$877$	44.3178	1.49650	0.748252	+	0.663415i	$0.230893\pi$
$878$	51.5490	1.73970
$879$	0	0
$880$	4.68362	0.157885
$881$	−25.8704	−0.871598	−0.435799	−	0.900044i	$-0.643534\pi$
$881$	−25.8704	−0.871598	−0.435799	+	0.900044i	$0.643534\pi$
$882$	0	0
$883$	11.3880	0.383236	0.191618	−	0.981470i	$-0.438627\pi$
$883$	11.3880	0.383236	0.191618	+	0.981470i	$0.438627\pi$
$884$	−9.97225	−0.335403
$885$	0	0
$886$	−42.2572	−1.41966
$887$	19.8155	0.665338	0.332669	−	0.943044i	$-0.392051\pi$
$887$	19.8155	0.665338	0.332669	+	0.943044i	$0.392051\pi$
$888$	0	0
$889$	0	0
$890$	11.7398	0.393518
$891$	0	0
$892$	−49.6127	−1.66115
$893$	−44.8109	−1.49954
$894$	0	0
$895$	60.2764	2.01482
$896$	0	0
$897$	0	0
$898$	39.9230	1.33225
$899$	−17.8201	−0.594334
$900$	0	0
$901$	−29.0338	−0.967255
$902$	5.92872	0.197405
$903$	0	0
$904$	5.76557	0.191760
$905$	−32.8241	−1.09111
$906$	0	0
$907$	27.1502	0.901508	0.450754	−	0.892648i	$-0.351155\pi$
$907$	27.1502	0.901508	0.450754	+	0.892648i	$0.351155\pi$
$908$	16.8666	0.559738
$909$	0	0
$910$	0	0
$911$	−22.2728	−0.737932	−0.368966	−	0.929443i	$-0.620288\pi$
$911$	−22.2728	−0.737932	−0.368966	+	0.929443i	$0.620288\pi$
$912$	0	0
$913$	1.14696	0.0379588
$914$	18.0374	0.596623
$915$	0	0
$916$	−48.2396	−1.59388
$917$	0	0
$918$	0	0
$919$	−10.7030	−0.353060	−0.176530	−	0.984295i	$-0.556487\pi$
$919$	−10.7030	−0.353060	−0.176530	+	0.984295i	$0.556487\pi$
$920$	12.1259	0.399779
$921$	0	0
$922$	−3.23163	−0.106428
$923$	−6.88638	−0.226668
$924$	0	0
$925$	84.3071	2.77200
$926$	−65.2416	−2.14397
$927$	0	0
$928$	−27.7259	−0.910147
$929$	23.5275	0.771911	0.385956	−	0.922517i	$-0.373872\pi$
$929$	23.5275	0.771911	0.385956	+	0.922517i	$0.373872\pi$
$930$	0	0
$931$	0	0
$932$	38.8056	1.27112
$933$	0	0
$934$	−58.1186	−1.90170
$935$	−7.50900	−0.245571
$936$	0	0
$937$	−7.08326	−0.231400	−0.115700	−	0.993284i	$-0.536911\pi$
$937$	−7.08326	−0.231400	−0.115700	+	0.993284i	$0.536911\pi$
$938$	0	0
$939$	0	0
$940$	−112.908	−3.68264
$941$	−10.9218	−0.356040	−0.178020	−	0.984027i	$-0.556969\pi$
$941$	−10.9218	−0.356040	−0.178020	+	0.984027i	$0.556969\pi$
$942$	0	0
$943$	−12.7033	−0.413676
$944$	−31.9570	−1.04011
$945$	0	0
$946$	−11.7624	−0.382428
$947$	−32.4458	−1.05435	−0.527173	−	0.849758i	$-0.676748\pi$
$947$	−32.4458	−1.05435	−0.527173	+	0.849758i	$0.676748\pi$
$948$	0	0
$949$	−6.45597	−0.209570
$950$	74.4037	2.41398
$951$	0	0
$952$	0	0
$953$	36.7070	1.18906	0.594528	−	0.804075i	$-0.297339\pi$
$953$	36.7070	1.18906	0.594528	+	0.804075i	$0.297339\pi$
$954$	0	0
$955$	−19.3957	−0.627629
$956$	−3.89430	−0.125951
$957$	0	0
$958$	−41.4418	−1.33892
$959$	0	0
$960$	0	0
$961$	−6.05876	−0.195444
$962$	−20.3171	−0.655048
$963$	0	0
$964$	−71.0795	−2.28932
$965$	−52.8122	−1.70008
$966$	0	0
$967$	−56.6977	−1.82328	−0.911638	−	0.410993i	$-0.865182\pi$
$967$	−56.6977	−1.82328	−0.911638	+	0.410993i	$0.865182\pi$
$968$	−14.3025	−0.459699
$969$	0	0
$970$	−93.1022	−2.98933
$971$	−28.2100	−0.905302	−0.452651	−	0.891688i	$-0.649522\pi$
$971$	−28.2100	−0.905302	−0.452651	+	0.891688i	$0.649522\pi$
$972$	0	0
$973$	0	0
$974$	−31.3234	−1.00367
$975$	0	0
$976$	13.7785	0.441039
$977$	26.0183	0.832400	0.416200	−	0.909273i	$-0.363362\pi$
$977$	26.0183	0.832400	0.416200	+	0.909273i	$0.363362\pi$
$978$	0	0
$979$	−0.774239	−0.0247448
$980$	0	0
$981$	0	0
$982$	−35.9746	−1.14800
$983$	−17.4230	−0.555708	−0.277854	−	0.960623i	$-0.589623\pi$
$983$	−17.4230	−0.555708	−0.277854	+	0.960623i	$0.589623\pi$
$984$	0	0
$985$	−76.3518	−2.43277
$986$	29.1868	0.929496
$987$	0	0
$988$	−10.1695	−0.323534
$989$	25.2030	0.801407
$990$	0	0
$991$	17.1434	0.544577	0.272288	−	0.962216i	$-0.412220\pi$
$991$	17.1434	0.544577	0.272288	+	0.962216i	$0.412220\pi$
$992$	38.8055	1.23208
$993$	0	0
$994$	0	0
$995$	77.5774	2.45937
$996$	0	0
$997$	19.1655	0.606977	0.303489	−	0.952835i	$-0.401849\pi$
$997$	19.1655	0.606977	0.303489	+	0.952835i	$0.401849\pi$
$998$	−5.85504	−0.185338
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bq.1.5		5
3.2	odd	2		1911.2.a.t.1.1		5
7.2	even	3		819.2.j.g.235.1		10
7.4	even	3		819.2.j.g.352.1		10
7.6	odd	2		5733.2.a.bp.1.5		5
21.2	odd	6		273.2.i.e.235.5	yes	10
21.11	odd	6		273.2.i.e.79.5	✓	10
21.20	even	2		1911.2.a.u.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.e.79.5	✓	10	21.11	odd	6
273.2.i.e.235.5	yes	10	21.2	odd	6
819.2.j.g.235.1		10	7.2	even	3
819.2.j.g.352.1		10	7.4	even	3
1911.2.a.t.1.1		5	3.2	odd	2
1911.2.a.u.1.1		5	21.20	even	2
5733.2.a.bp.1.5		5	7.6	odd	2
5733.2.a.bq.1.5		5	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)

\(f(q)\)	\(=\)	\(q+2.14957 q^{2} +2.62066 q^{4} +3.73093 q^{5} +1.33415 q^{8} +O(q^{10})\)	\(q+2.14957 q^{2} +2.62066 q^{4} +3.73093 q^{5} +1.33415 q^{8} +8.01989 q^{10} -0.528912 q^{11} -1.00000 q^{13} -2.37346 q^{16} +3.80524 q^{17} +3.88050 q^{19} +9.77749 q^{20} -1.13693 q^{22} +2.43608 q^{23} +8.91980 q^{25} -2.14957 q^{26} +3.56822 q^{29} -4.99412 q^{31} -7.77023 q^{32} +8.17964 q^{34} +9.45167 q^{37} +8.34141 q^{38} +4.97763 q^{40} -5.21465 q^{41} +10.3457 q^{43} -1.38610 q^{44} +5.23653 q^{46} -11.5477 q^{47} +19.1738 q^{50} -2.62066 q^{52} -7.62994 q^{53} -1.97333 q^{55} +7.67014 q^{58} +13.4643 q^{59} -5.80524 q^{61} -10.7352 q^{62} -11.9558 q^{64} -3.73093 q^{65} +6.15975 q^{67} +9.97225 q^{68} +6.88638 q^{71} +6.45597 q^{73} +20.3171 q^{74} +10.1695 q^{76} -3.70905 q^{79} -8.85520 q^{80} -11.2093 q^{82} -2.16853 q^{83} +14.1971 q^{85} +22.2388 q^{86} -0.705650 q^{88} +1.46383 q^{89} +6.38413 q^{92} -24.8227 q^{94} +14.4778 q^{95} -11.6089 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 6 q^{4} + 3 q^{5} - 3 q^{8}+O(q^{10}) \) 5 * q + 6 * q^4 + 3 * q^5 - 3 * q^8	\( 5 q + 6 q^{4} + 3 q^{5} - 3 q^{8} - 2 q^{10} + q^{11} - 5 q^{13} + 13 q^{17} - 7 q^{19} + 13 q^{20} - 19 q^{22} + 4 q^{23} + 16 q^{25} + 12 q^{29} - 6 q^{31} - 21 q^{32} - 7 q^{34} + 11 q^{37} + 14 q^{38} - 11 q^{40} + 10 q^{41} + 10 q^{43} + 29 q^{44} + q^{46} - 4 q^{47} + 29 q^{50} - 6 q^{52} + 9 q^{53} + 12 q^{55} + 34 q^{58} + 7 q^{59} - 23 q^{61} - 24 q^{62} - 13 q^{64} - 3 q^{65} + 25 q^{67} + 20 q^{68} + 27 q^{71} - 18 q^{73} - 15 q^{74} - 2 q^{76} + 8 q^{79} + 41 q^{80} - 26 q^{82} + 12 q^{83} + 10 q^{85} + 19 q^{86} - 36 q^{88} + 29 q^{89} + 50 q^{92} + 2 q^{94} + 33 q^{95} - 13 q^{97}+O(q^{100}) \) 5 * q + 6 * q^4 + 3 * q^5 - 3 * q^8 - 2 * q^10 + q^11 - 5 * q^13 + 13 * q^17 - 7 * q^19 + 13 * q^20 - 19 * q^22 + 4 * q^23 + 16 * q^25 + 12 * q^29 - 6 * q^31 - 21 * q^32 - 7 * q^34 + 11 * q^37 + 14 * q^38 - 11 * q^40 + 10 * q^41 + 10 * q^43 + 29 * q^44 + q^46 - 4 * q^47 + 29 * q^50 - 6 * q^52 + 9 * q^53 + 12 * q^55 + 34 * q^58 + 7 * q^59 - 23 * q^61 - 24 * q^62 - 13 * q^64 - 3 * q^65 + 25 * q^67 + 20 * q^68 + 27 * q^71 - 18 * q^73 - 15 * q^74 - 2 * q^76 + 8 * q^79 + 41 * q^80 - 26 * q^82 + 12 * q^83 + 10 * q^85 + 19 * q^86 - 36 * q^88 + 29 * q^89 + 50 * q^92 + 2 * q^94 + 33 * q^95 - 13 * q^97

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