LMFDB - Embedded newform 5733.2.a.bf.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:	$4$
Coefficient field:	4.4.17428.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 4x + 6 $ x^4 - x^3 - 6x^2 + 4x + 6
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			1.2
Root			$-2.10710$ 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)

$f(q)$	$=$	$q-1.43986 q^{2} +0.0731828 q^{4} +0.926817 q^{5} +2.77434 q^{8} +O(q^{10})$	$q-1.43986 q^{2} +0.0731828 q^{4} +0.926817 q^{5} +2.77434 q^{8} -1.33448 q^{10} -4.21419 q^{11} -1.00000 q^{13} -4.14101 q^{16} -2.87971 q^{17} +1.28738 q^{19} +0.0678271 q^{20} +6.06783 q^{22} +8.02072 q^{23} -4.14101 q^{25} +1.43986 q^{26} -3.28738 q^{29} +7.04680 q^{31} +0.413779 q^{32} +4.14637 q^{34} +8.57475 q^{37} -1.85363 q^{38} +2.57130 q^{40} -12.0678 q^{41} +7.14101 q^{43} -0.308407 q^{44} -11.5487 q^{46} +1.95289 q^{47} +5.96245 q^{50} -0.0731828 q^{52} +5.14101 q^{53} -3.90579 q^{55} +4.73334 q^{58} -7.33448 q^{59} -7.75942 q^{61} -10.1464 q^{62} +7.68624 q^{64} -0.926817 q^{65} +12.0414 q^{67} -0.210745 q^{68} -10.7889 q^{71} +8.32568 q^{73} -12.3464 q^{74} +0.0942138 q^{76} +4.47204 q^{79} -3.83796 q^{80} +17.3759 q^{82} -3.80653 q^{83} -2.66896 q^{85} -10.2820 q^{86} -11.6916 q^{88} -5.64793 q^{89} +0.586979 q^{92} -2.81188 q^{94} +1.19316 q^{95} -6.90043 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 7 q^{4} - 3 q^{5} - 3 q^{8}+O(q^{10}) $ 4 * q - q^2 + 7 * q^4 - 3 * q^5 - 3 * q^8	$ 4 q - q^{2} + 7 q^{4} - 3 q^{5} - 3 q^{8} + 4 q^{10} + 2 q^{11} - 4 q^{13} + 9 q^{16} - 2 q^{17} - 7 q^{19} - 32 q^{20} - 8 q^{22} - 3 q^{23} + 9 q^{25} + q^{26} - q^{29} - 3 q^{31} - 7 q^{32} + 30 q^{34} + 10 q^{37} + 6 q^{38} + 14 q^{40} - 16 q^{41} + 3 q^{43} + 12 q^{44} - 18 q^{46} + 5 q^{47} - 13 q^{50} - 7 q^{52} - 5 q^{53} - 10 q^{55} - 4 q^{58} - 20 q^{59} - 12 q^{61} - 54 q^{62} + 5 q^{64} + 3 q^{65} - 22 q^{67} - 10 q^{68} + 13 q^{73} + 6 q^{74} + 6 q^{76} + 11 q^{79} - 42 q^{80} - 10 q^{82} + q^{83} + 8 q^{85} + 10 q^{86} - 60 q^{88} - 5 q^{89} - 34 q^{92} - 34 q^{94} - 13 q^{95} + 17 q^{97}+O(q^{100}) $ 4 * q - q^2 + 7 * q^4 - 3 * q^5 - 3 * q^8 + 4 * q^10 + 2 * q^11 - 4 * q^13 + 9 * q^16 - 2 * q^17 - 7 * q^19 - 32 * q^20 - 8 * q^22 - 3 * q^23 + 9 * q^25 + q^26 - q^29 - 3 * q^31 - 7 * q^32 + 30 * q^34 + 10 * q^37 + 6 * q^38 + 14 * q^40 - 16 * q^41 + 3 * q^43 + 12 * q^44 - 18 * q^46 + 5 * q^47 - 13 * q^50 - 7 * q^52 - 5 * q^53 - 10 * q^55 - 4 * q^58 - 20 * q^59 - 12 * q^61 - 54 * q^62 + 5 * q^64 + 3 * q^65 - 22 * q^67 - 10 * q^68 + 13 * q^73 + 6 * q^74 + 6 * q^76 + 11 * q^79 - 42 * q^80 - 10 * q^82 + q^83 + 8 * q^85 + 10 * q^86 - 60 * q^88 - 5 * q^89 - 34 * q^92 - 34 * q^94 - 13 * q^95 + 17 * 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 $

$2$	−1.43986	−1.01813	−0.509066	−	0.860728i	$-0.670009\pi$
$2$	−1.43986	−1.01813	−0.509066	+	0.860728i	$0.670009\pi$
$3$	0	0
$3$	0	0
$4$	0.0731828	0.0365914
$5$	0.926817	0.414485	0.207243	−	0.978290i	$-0.433551\pi$
$5$	0.926817	0.414485	0.207243	+	0.978290i	$0.433551\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	2.77434	0.980876
$9$	0	0
$10$	−1.33448	−0.422000
$11$	−4.21419	−1.27063	−0.635313	−	0.772254i	$-0.719129\pi$
$11$	−4.21419	−1.27063	−0.635313	+	0.772254i	$0.719129\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0	0
$16$	−4.14101	−1.03525
$17$	−2.87971	−0.698432	−0.349216	−	0.937042i	$-0.613552\pi$
$17$	−2.87971	−0.698432	−0.349216	+	0.937042i	$0.613552\pi$
$18$	0	0
$19$	1.28738	0.295344	0.147672	−	0.989036i	$-0.452822\pi$
$19$	1.28738	0.295344	0.147672	+	0.989036i	$0.452822\pi$
$20$	0.0678271	0.0151666
$21$	0	0
$22$	6.06783	1.29367
$23$	8.02072	1.67244	0.836218	−	0.548397i	$-0.184762\pi$
$23$	8.02072	1.67244	0.836218	+	0.548397i	$0.184762\pi$
$24$	0	0
$25$	−4.14101	−0.828202
$26$	1.43986	0.282379
$27$	0	0
$28$	0	0
$29$	−3.28738	−0.610450	−0.305225	−	0.952280i	$-0.598732\pi$
$29$	−3.28738	−0.610450	−0.305225	+	0.952280i	$0.598732\pi$
$30$	0	0
$31$	7.04680	1.26564	0.632821	−	0.774298i	$-0.281897\pi$
$31$	7.04680	1.26564	0.632821	+	0.774298i	$0.281897\pi$
$32$	0.413779	0.0731465
$33$	0	0
$34$	4.14637	0.711096
$35$	0	0
$36$	0	0
$37$	8.57475	1.40968	0.704840	−	0.709366i	$-0.251019\pi$
$37$	8.57475	1.40968	0.704840	+	0.709366i	$0.251019\pi$
$38$	−1.85363	−0.300699
$39$	0	0
$40$	2.57130	0.406559
$41$	−12.0678	−1.88468	−0.942339	−	0.334660i	$-0.891379\pi$
$41$	−12.0678	−1.88468	−0.942339	+	0.334660i	$0.891379\pi$
$42$	0	0
$43$	7.14101	1.08899	0.544497	−	0.838763i	$-0.316721\pi$
$43$	7.14101	1.08899	0.544497	+	0.838763i	$0.316721\pi$
$44$	−0.308407	−0.0464940
$45$	0	0
$46$	−11.5487	−1.70276
$47$	1.95289	0.284859	0.142429	−	0.989805i	$-0.454509\pi$
$47$	1.95289	0.284859	0.142429	+	0.989805i	$0.454509\pi$
$48$	0	0
$49$	0	0
$50$	5.96245	0.843218
$51$	0	0
$52$	−0.0731828	−0.0101486
$53$	5.14101	0.706172	0.353086	−	0.935591i	$-0.385132\pi$
$53$	5.14101	0.706172	0.353086	+	0.935591i	$0.385132\pi$
$54$	0	0
$55$	−3.90579	−0.526656
$56$	0	0
$57$	0	0
$58$	4.73334	0.621519
$59$	−7.33448	−0.954868	−0.477434	−	0.878668i	$-0.658433\pi$
$59$	−7.33448	−0.954868	−0.477434	+	0.878668i	$0.658433\pi$
$60$	0	0
$61$	−7.75942	−0.993492	−0.496746	−	0.867896i	$-0.665472\pi$
$61$	−7.75942	−0.993492	−0.496746	+	0.867896i	$0.665472\pi$
$62$	−10.1464	−1.28859
$63$	0	0
$64$	7.68624	0.960780
$65$	−0.926817	−0.114958
$66$	0	0
$67$	12.0414	1.47110	0.735548	−	0.677473i	$-0.236925\pi$
$67$	12.0414	1.47110	0.735548	+	0.677473i	$0.236925\pi$
$68$	−0.210745	−0.0255566
$69$	0	0
$70$	0	0
$71$	−10.7889	−1.28041	−0.640206	−	0.768203i	$-0.721151\pi$
$71$	−10.7889	−1.28041	−0.640206	+	0.768203i	$0.721151\pi$
$72$	0	0
$73$	8.32568	0.974447	0.487224	−	0.873277i	$-0.338010\pi$
$73$	8.32568	0.974447	0.487224	+	0.873277i	$0.338010\pi$
$74$	−12.3464	−1.43524
$75$	0	0
$76$	0.0942138	0.0108071
$77$	0	0
$78$	0	0
$79$	4.47204	0.503144	0.251572	−	0.967839i	$-0.419052\pi$
$79$	4.47204	0.503144	0.251572	+	0.967839i	$0.419052\pi$
$80$	−3.83796	−0.429097
$81$	0	0
$82$	17.3759	1.91885
$83$	−3.80653	−0.417821	−0.208910	−	0.977935i	$-0.566992\pi$
$83$	−3.80653	−0.417821	−0.208910	+	0.977935i	$0.566992\pi$
$84$	0	0
$85$	−2.66896	−0.289490
$86$	−10.2820	−1.10874
$87$	0	0
$88$	−11.6916	−1.24633
$89$	−5.64793	−0.598680	−0.299340	−	0.954147i	$-0.596766\pi$
$89$	−5.64793	−0.598680	−0.299340	+	0.954147i	$0.596766\pi$
$90$	0	0
$91$	0	0
$92$	0.586979	0.0611968
$93$	0	0
$94$	−2.81188	−0.290024
$95$	1.19316	0.122416
$96$	0	0
$97$	−6.90043	−0.700633	−0.350316	−	0.936631i	$-0.613926\pi$
$97$	−6.90043	−0.700633	−0.350316	+	0.936631i	$0.613926\pi$
$98$	0	0
$99$	0	0
$100$	−0.303051	−0.0303051
$101$	−10.9739	−1.09195	−0.545973	−	0.837803i	$-0.683840\pi$
$101$	−10.9739	−1.09195	−0.545973	+	0.837803i	$0.683840\pi$
$102$	0	0
$103$	−16.4284	−1.61874	−0.809368	−	0.587301i	$-0.800190\pi$
$103$	−16.4284	−1.61874	−0.809368	+	0.587301i	$0.800190\pi$
$104$	−2.77434	−0.272046
$105$	0	0
$106$	−7.40231	−0.718976
$107$	3.45446	0.333955	0.166978	−	0.985961i	$-0.446599\pi$
$107$	3.45446	0.333955	0.166978	+	0.985961i	$0.446599\pi$
$108$	0	0
$109$	4.66896	0.447206	0.223603	−	0.974680i	$-0.428218\pi$
$109$	4.66896	0.447206	0.223603	+	0.974680i	$0.428218\pi$
$110$	5.62377	0.536205
$111$	0	0
$112$	0	0
$113$	3.28738	0.309250	0.154625	−	0.987973i	$-0.450583\pi$
$113$	3.28738	0.309250	0.154625	+	0.987973i	$0.450583\pi$
$114$	0	0
$115$	7.43374	0.693200
$116$	−0.240579	−0.0223372
$117$	0	0
$118$	10.5606	0.972181
$119$	0	0
$120$	0	0
$121$	6.75942	0.614493
$122$	11.1724	1.01151
$123$	0	0
$124$	0.515704	0.0463116
$125$	−8.47204	−0.757763
$126$	0	0
$127$	−0.428386	−0.0380131	−0.0190065	−	0.999819i	$-0.506050\pi$
$127$	−0.428386	−0.0380131	−0.0190065	+	0.999819i	$0.506050\pi$
$128$	−11.8946	−1.05135
$129$	0	0
$130$	1.33448	0.117042
$131$	14.1878	1.23959	0.619797	−	0.784762i	$-0.287215\pi$
$131$	14.1878	1.23959	0.619797	+	0.784762i	$0.287215\pi$
$132$	0	0
$133$	0	0
$134$	−17.3379	−1.49777
$135$	0	0
$136$	−7.98929	−0.685076
$137$	−14.7070	−1.25650	−0.628250	−	0.778011i	$-0.716229\pi$
$137$	−14.7070	−1.25650	−0.628250	+	0.778011i	$0.716229\pi$
$138$	0	0
$139$	−9.85363	−0.835774	−0.417887	−	0.908499i	$-0.637229\pi$
$139$	−9.85363	−0.835774	−0.417887	+	0.908499i	$0.637229\pi$
$140$	0	0
$141$	0	0
$142$	15.5345	1.30363
$143$	4.21419	0.352409
$144$	0	0
$145$	−3.04680	−0.253023
$146$	−11.9878	−0.992115
$147$	0	0
$148$	0.627525	0.0515822
$149$	3.38663	0.277444	0.138722	−	0.990331i	$-0.455701\pi$
$149$	3.38663	0.277444	0.138722	+	0.990331i	$0.455701\pi$
$150$	0	0
$151$	−21.8951	−1.78180	−0.890898	−	0.454204i	$-0.849924\pi$
$151$	−21.8951	−1.78180	−0.890898	+	0.454204i	$0.849924\pi$
$152$	3.57161	0.289696
$153$	0	0
$154$	0	0
$155$	6.53109	0.524590
$156$	0	0
$157$	0.867482	0.0692326	0.0346163	−	0.999401i	$-0.488979\pi$
$157$	0.867482	0.0692326	0.0346163	+	0.999401i	$0.488979\pi$
$158$	−6.43910	−0.512267
$159$	0	0
$160$	0.383498	0.0303182
$161$	0	0
$162$	0	0
$163$	4.42839	0.346858	0.173429	−	0.984846i	$-0.444515\pi$
$163$	4.42839	0.346858	0.173429	+	0.984846i	$0.444515\pi$
$164$	−0.883158	−0.0689630
$165$	0	0
$166$	5.48085	0.425396
$167$	20.5276	1.58848	0.794238	−	0.607606i	$-0.207870\pi$
$167$	20.5276	1.58848	0.794238	+	0.607606i	$0.207870\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	3.84292	0.294739
$171$	0	0
$172$	0.522599	0.0398478
$173$	15.0154	1.14160	0.570799	−	0.821090i	$-0.306634\pi$
$173$	15.0154	1.14160	0.570799	+	0.821090i	$0.306634\pi$
$174$	0	0
$175$	0	0
$176$	17.4510	1.31542
$177$	0	0
$178$	8.13221	0.609535
$179$	5.35176	0.400009	0.200004	−	0.979795i	$-0.435904\pi$
$179$	5.35176	0.400009	0.200004	+	0.979795i	$0.435904\pi$
$180$	0	0
$181$	−11.4667	−0.852312	−0.426156	−	0.904650i	$-0.640133\pi$
$181$	−11.4667	−0.852312	−0.426156	+	0.904650i	$0.640133\pi$
$182$	0	0
$183$	0	0
$184$	22.2522	1.64045
$185$	7.94723	0.584292
$186$	0	0
$187$	12.1357	0.887447
$188$	0.142918	0.0104234
$189$	0	0
$190$	−1.71798	−0.124635
$191$	−20.1756	−1.45985	−0.729927	−	0.683525i	$-0.760446\pi$
$191$	−20.1756	−1.45985	−0.729927	+	0.683525i	$0.760446\pi$
$192$	0	0
$193$	−26.3756	−1.89856	−0.949279	−	0.314435i	$-0.898185\pi$
$193$	−26.3756	−1.89856	−0.949279	+	0.314435i	$0.898185\pi$
$194$	9.93562	0.713336
$195$	0	0
$196$	0	0
$197$	20.1322	1.43436	0.717180	−	0.696888i	$-0.245432\pi$
$197$	20.1322	1.43436	0.717180	+	0.696888i	$0.245432\pi$
$198$	0	0
$199$	−1.75942	−0.124722	−0.0623610	−	0.998054i	$-0.519863\pi$
$199$	−1.75942	−0.124722	−0.0623610	+	0.998054i	$0.519863\pi$
$200$	−11.4886	−0.812364
$201$	0	0
$202$	15.8009	1.11174
$203$	0	0
$204$	0	0
$205$	−11.1847	−0.781171
$206$	23.6545	1.64809
$207$	0	0
$208$	4.14101	0.287127
$209$	−5.42525	−0.375272
$210$	0	0
$211$	15.5694	1.07184	0.535921	−	0.844268i	$-0.319965\pi$
$211$	15.5694	1.07184	0.535921	+	0.844268i	$0.319965\pi$
$212$	0.376234	0.0258398
$213$	0	0
$214$	−4.97392	−0.340010
$215$	6.61841	0.451372
$216$	0	0
$217$	0	0
$218$	−6.72263	−0.455314
$219$	0	0
$220$	−0.285836	−0.0192711
$221$	2.87971	0.193710
$222$	0	0
$223$	11.5694	0.774744	0.387372	−	0.921923i	$-0.373383\pi$
$223$	11.5694	0.774744	0.387372	+	0.921923i	$0.373383\pi$
$224$	0	0
$225$	0	0
$226$	−4.73334	−0.314857
$227$	−11.0418	−0.732867	−0.366433	−	0.930444i	$-0.619421\pi$
$227$	−11.0418	−0.732867	−0.366433	+	0.930444i	$0.619421\pi$
$228$	0	0
$229$	13.7073	0.905802	0.452901	−	0.891561i	$-0.350389\pi$
$229$	13.7073	0.905802	0.452901	+	0.891561i	$0.350389\pi$
$230$	−10.7035	−0.705769
$231$	0	0
$232$	−9.12029	−0.598776
$233$	−1.23522	−0.0809222	−0.0404611	−	0.999181i	$-0.512883\pi$
$233$	−1.23522	−0.0809222	−0.0404611	+	0.999181i	$0.512883\pi$
$234$	0	0
$235$	1.80997	0.118070
$236$	−0.536758	−0.0349400
$237$	0	0
$238$	0	0
$239$	−19.1061	−1.23587	−0.617936	−	0.786228i	$-0.712031\pi$
$239$	−19.1061	−1.23587	−0.617936	+	0.786228i	$0.712031\pi$
$240$	0	0
$241$	12.0329	0.775110	0.387555	−	0.921847i	$-0.373320\pi$
$241$	12.0329	0.775110	0.387555	+	0.921847i	$0.373320\pi$
$242$	−9.73259	−0.625634
$243$	0	0
$244$	−0.567856	−0.0363533
$245$	0	0
$246$	0	0
$247$	−1.28738	−0.0819137
$248$	19.5502	1.24144
$249$	0	0
$250$	12.1985	0.771502
$251$	−15.0031	−0.946990	−0.473495	−	0.880797i	$-0.657008\pi$
$251$	−15.0031	−0.946990	−0.473495	+	0.880797i	$0.657008\pi$
$252$	0	0
$253$	−33.8009	−2.12504
$254$	0.616813	0.0387023
$255$	0	0
$256$	1.75406	0.109629
$257$	−13.0261	−0.812544	−0.406272	−	0.913752i	$-0.633172\pi$
$257$	−13.0261	−0.812544	−0.406272	+	0.913752i	$0.633172\pi$
$258$	0	0
$259$	0	0
$260$	−0.0678271	−0.00420646
$261$	0	0
$262$	−20.4284	−1.26207
$263$	2.59547	0.160044	0.0800218	−	0.996793i	$-0.474501\pi$
$263$	2.59547	0.160044	0.0800218	+	0.996793i	$0.474501\pi$
$264$	0	0
$265$	4.76478	0.292698
$266$	0	0
$267$	0	0
$268$	0.881227	0.0538295
$269$	−23.3081	−1.42112	−0.710560	−	0.703637i	$-0.751558\pi$
$269$	−23.3081	−1.42112	−0.710560	+	0.703637i	$0.751558\pi$
$270$	0	0
$271$	6.05215	0.367642	0.183821	−	0.982960i	$-0.441153\pi$
$271$	6.05215	0.367642	0.183821	+	0.982960i	$0.441153\pi$
$272$	11.9249	0.723054
$273$	0	0
$274$	21.1759	1.27928
$275$	17.4510	1.05234
$276$	0	0
$277$	15.1932	0.912869	0.456434	−	0.889757i	$-0.349126\pi$
$277$	15.1932	0.912869	0.456434	+	0.889757i	$0.349126\pi$
$278$	14.1878	0.850928
$279$	0	0
$280$	0	0
$281$	7.57506	0.451890	0.225945	−	0.974140i	$-0.427453\pi$
$281$	7.57506	0.451890	0.225945	+	0.974140i	$0.427453\pi$
$282$	0	0
$283$	−19.0974	−1.13522	−0.567610	−	0.823298i	$-0.692132\pi$
$283$	−19.0974	−1.13522	−0.567610	+	0.823298i	$0.692132\pi$
$284$	−0.789565	−0.0468521
$285$	0	0
$286$	−6.06783	−0.358798
$287$	0	0
$288$	0	0
$289$	−8.70727	−0.512192
$290$	4.38695	0.257610
$291$	0	0
$292$	0.609297	0.0356564
$293$	−3.79430	−0.221665	−0.110833	−	0.993839i	$-0.535352\pi$
$293$	−3.79430	−0.221665	−0.110833	+	0.993839i	$0.535352\pi$
$294$	0	0
$295$	−6.79772	−0.395779
$296$	23.7893	1.38272
$297$	0	0
$298$	−4.87626	−0.282474
$299$	−8.02072	−0.463850
$300$	0	0
$301$	0	0
$302$	31.5257	1.81410
$303$	0	0
$304$	−5.33104	−0.305756
$305$	−7.19156	−0.411788
$306$	0	0
$307$	5.19316	0.296389	0.148195	−	0.988958i	$-0.452654\pi$
$307$	5.19316	0.296389	0.148195	+	0.988958i	$0.452654\pi$
$308$	0	0
$309$	0	0
$310$	−9.40383	−0.534101
$311$	−13.8536	−0.785568	−0.392784	−	0.919631i	$-0.628488\pi$
$311$	−13.8536	−0.785568	−0.392784	+	0.919631i	$0.628488\pi$
$312$	0	0
$313$	32.6162	1.84358	0.921788	−	0.387694i	$-0.126728\pi$
$313$	32.6162	1.84358	0.921788	+	0.387694i	$0.126728\pi$
$314$	−1.24905	−0.0704879
$315$	0	0
$316$	0.327277	0.0184108
$317$	−12.0380	−0.676121	−0.338061	−	0.941124i	$-0.609771\pi$
$317$	−12.0380	−0.676121	−0.338061	+	0.941124i	$0.609771\pi$
$318$	0	0
$319$	13.8536	0.775655
$320$	7.12374	0.398229
$321$	0	0
$322$	0	0
$323$	−3.70727	−0.206278
$324$	0	0
$325$	4.14101	0.229702
$326$	−6.37623	−0.353147
$327$	0	0
$328$	−33.4802	−1.84864
$329$	0	0
$330$	0	0
$331$	−26.2820	−1.44459	−0.722295	−	0.691585i	$-0.756913\pi$
$331$	−26.2820	−1.44459	−0.722295	+	0.691585i	$0.756913\pi$
$332$	−0.278572	−0.0152886
$333$	0	0
$334$	−29.5568	−1.61728
$335$	11.1602	0.609748
$336$	0	0
$337$	26.2905	1.43214	0.716068	−	0.698031i	$-0.245940\pi$
$337$	26.2905	1.43214	0.716068	+	0.698031i	$0.245940\pi$
$338$	−1.43986	−0.0783178
$339$	0	0
$340$	−0.195322	−0.0105928
$341$	−29.6966	−1.60816
$342$	0	0
$343$	0	0
$344$	19.8116	1.06817
$345$	0	0
$346$	−21.6199	−1.16230
$347$	−16.4928	−0.885378	−0.442689	−	0.896675i	$-0.645975\pi$
$347$	−16.4928	−0.885378	−0.442689	+	0.896675i	$0.645975\pi$
$348$	0	0
$349$	−14.1793	−0.759001	−0.379501	−	0.925191i	$-0.623904\pi$
$349$	−14.1793	−0.759001	−0.379501	+	0.925191i	$0.623904\pi$
$350$	0	0
$351$	0	0
$352$	−1.74375	−0.0929419
$353$	−29.8272	−1.58754	−0.793772	−	0.608215i	$-0.791886\pi$
$353$	−29.8272	−1.58754	−0.793772	+	0.608215i	$0.791886\pi$
$354$	0	0
$355$	−9.99938	−0.530712
$356$	−0.413332	−0.0219065
$357$	0	0
$358$	−7.70575	−0.407262
$359$	−1.34671	−0.0710767	−0.0355383	−	0.999368i	$-0.511315\pi$
$359$	−1.34671	−0.0710767	−0.0355383	+	0.999368i	$0.511315\pi$
$360$	0	0
$361$	−17.3427	−0.912772
$362$	16.5104	0.867766
$363$	0	0
$364$	0	0
$365$	7.71638	0.403894
$366$	0	0
$367$	−36.1771	−1.88843	−0.944214	−	0.329331i	$-0.893177\pi$
$367$	−36.1771	−1.88843	−0.944214	+	0.329331i	$0.893177\pi$
$368$	−33.2139	−1.73139
$369$	0	0
$370$	−11.4429	−0.594886
$371$	0	0
$372$	0	0
$373$	−16.9089	−0.875511	−0.437755	−	0.899094i	$-0.644226\pi$
$373$	−16.9089	−0.875511	−0.437755	+	0.899094i	$0.644226\pi$
$374$	−17.4736	−0.903538
$375$	0	0
$376$	5.41798	0.279411
$377$	3.28738	0.169308
$378$	0	0
$379$	−11.6131	−0.596523	−0.298261	−	0.954484i	$-0.596407\pi$
$379$	−11.6131	−0.596523	−0.298261	+	0.954484i	$0.596407\pi$
$380$	0.0873190	0.00447937
$381$	0	0
$382$	29.0499	1.48632
$383$	14.6134	0.746708	0.373354	−	0.927689i	$-0.378208\pi$
$383$	14.6134	0.746708	0.373354	+	0.927689i	$0.378208\pi$
$384$	0	0
$385$	0	0
$386$	37.9771	1.93298
$387$	0	0
$388$	−0.504993	−0.0256371
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	−23.0974	−1.16808
$392$	0	0
$393$	0	0
$394$	−28.9875	−1.46037
$395$	4.14477	0.208546
$396$	0	0
$397$	−25.6982	−1.28975	−0.644877	−	0.764287i	$-0.723091\pi$
$397$	−25.6982	−1.28975	−0.644877	+	0.764287i	$0.723091\pi$
$398$	2.53331	0.126983
$399$	0	0
$400$	17.1480	0.857398
$401$	19.5637	0.976966	0.488483	−	0.872573i	$-0.337550\pi$
$401$	19.5637	0.976966	0.488483	+	0.872573i	$0.337550\pi$
$402$	0	0
$403$	−7.04680	−0.351026
$404$	−0.803103	−0.0399559
$405$	0	0
$406$	0	0
$407$	−36.1357	−1.79118
$408$	0	0
$409$	−3.19316	−0.157892	−0.0789458	−	0.996879i	$-0.525155\pi$
$409$	−3.19316	−0.157892	−0.0789458	+	0.996879i	$0.525155\pi$
$410$	16.1043	0.795335
$411$	0	0
$412$	−1.20228	−0.0592319
$413$	0	0
$414$	0	0
$415$	−3.52796	−0.173181
$416$	−0.413779	−0.0202872
$417$	0	0
$418$	7.81157	0.382076
$419$	30.2292	1.47680	0.738398	−	0.674366i	$-0.235583\pi$
$419$	30.2292	1.47680	0.738398	+	0.674366i	$0.235583\pi$
$420$	0	0
$421$	26.9510	1.31351	0.656755	−	0.754104i	$-0.271928\pi$
$421$	26.9510	1.31351	0.656755	+	0.754104i	$0.271928\pi$
$422$	−22.4177	−1.09128
$423$	0	0
$424$	14.2629	0.692668
$425$	11.9249	0.578443
$426$	0	0
$427$	0	0
$428$	0.252807	0.0122199
$429$	0	0
$430$	−9.52955	−0.459556
$431$	−16.7713	−0.807847	−0.403923	−	0.914793i	$-0.632354\pi$
$431$	−16.7713	−0.807847	−0.403923	+	0.914793i	$0.632354\pi$
$432$	0	0
$433$	−25.8530	−1.24242	−0.621208	−	0.783646i	$-0.713358\pi$
$433$	−25.8530	−1.24242	−0.621208	+	0.783646i	$0.713358\pi$
$434$	0	0
$435$	0	0
$436$	0.341688	0.0163639
$437$	10.3257	0.493944
$438$	0	0
$439$	−25.0553	−1.19582	−0.597912	−	0.801562i	$-0.704003\pi$
$439$	−25.0553	−1.19582	−0.597912	+	0.801562i	$0.704003\pi$
$440$	−10.8360	−0.516585
$441$	0	0
$442$	−4.14637	−0.197223
$443$	−4.64762	−0.220815	−0.110408	−	0.993886i	$-0.535216\pi$
$443$	−4.64762	−0.220815	−0.110408	+	0.993886i	$0.535216\pi$
$444$	0	0
$445$	−5.23460	−0.248144
$446$	−16.6583	−0.788791
$447$	0	0
$448$	0	0
$449$	−0.494696	−0.0233462	−0.0116731	−	0.999932i	$-0.503716\pi$
$449$	−0.494696	−0.0233462	−0.0116731	+	0.999932i	$0.503716\pi$
$450$	0	0
$451$	50.8561	2.39472
$452$	0.240579	0.0113159
$453$	0	0
$454$	15.8985	0.746155
$455$	0	0
$456$	0	0
$457$	26.4698	1.23821	0.619103	−	0.785310i	$-0.287496\pi$
$457$	26.4698	1.23821	0.619103	+	0.785310i	$0.287496\pi$
$458$	−19.7365	−0.922225
$459$	0	0
$460$	0.544022	0.0253652
$461$	−1.08168	−0.0503786	−0.0251893	−	0.999683i	$-0.508019\pi$
$461$	−1.08168	−0.0503786	−0.0251893	+	0.999683i	$0.508019\pi$
$462$	0	0
$463$	−32.7098	−1.52015	−0.760076	−	0.649834i	$-0.774838\pi$
$463$	−32.7098	−1.52015	−0.760076	+	0.649834i	$0.774838\pi$
$464$	13.6131	0.631970
$465$	0	0
$466$	1.77854	0.0823894
$467$	−17.0797	−0.790356	−0.395178	−	0.918605i	$-0.629317\pi$
$467$	−17.0797	−0.790356	−0.395178	+	0.918605i	$0.629317\pi$
$468$	0	0
$469$	0	0
$470$	−2.60610	−0.120211
$471$	0	0
$472$	−20.3483	−0.936608
$473$	−30.0936	−1.38370
$474$	0	0
$475$	−5.33104	−0.244605
$476$	0	0
$477$	0	0
$478$	27.5101	1.25828
$479$	−17.1790	−0.784929	−0.392464	−	0.919767i	$-0.628377\pi$
$479$	−17.1790	−0.784929	−0.392464	+	0.919767i	$0.628377\pi$
$480$	0	0
$481$	−8.57475	−0.390975
$482$	−17.3257	−0.789164
$483$	0	0
$484$	0.494674	0.0224852
$485$	−6.39544	−0.290402
$486$	0	0
$487$	−4.28264	−0.194065	−0.0970325	−	0.995281i	$-0.530935\pi$
$487$	−4.28264	−0.194065	−0.0970325	+	0.995281i	$0.530935\pi$
$488$	−21.5273	−0.974493
$489$	0	0
$490$	0	0
$491$	−27.4545	−1.23900	−0.619501	−	0.784996i	$-0.712665\pi$
$491$	−27.4545	−1.23900	−0.619501	+	0.784996i	$0.712665\pi$
$492$	0	0
$493$	9.46669	0.426358
$494$	1.85363	0.0833990
$495$	0	0
$496$	−29.1809	−1.31026
$497$	0	0
$498$	0	0
$499$	−37.0452	−1.65837	−0.829185	−	0.558974i	$-0.811195\pi$
$499$	−37.0452	−1.65837	−0.829185	+	0.558974i	$0.811195\pi$
$500$	−0.620008	−0.0277276
$501$	0	0
$502$	21.6023	0.964160
$503$	3.23744	0.144350	0.0721752	−	0.997392i	$-0.477006\pi$
$503$	3.23744	0.144350	0.0721752	+	0.997392i	$0.477006\pi$
$504$	0	0
$505$	−10.1708	−0.452596
$506$	48.6683	2.16357
$507$	0	0
$508$	−0.0313505	−0.00139095
$509$	−30.4877	−1.35134	−0.675672	−	0.737202i	$-0.736147\pi$
$509$	−30.4877	−1.35134	−0.675672	+	0.737202i	$0.736147\pi$
$510$	0	0
$511$	0	0
$512$	21.2637	0.939730
$513$	0	0
$514$	18.7557	0.827277
$515$	−15.2261	−0.670943
$516$	0	0
$517$	−8.22987	−0.361949
$518$	0	0
$519$	0	0
$520$	−2.57130	−0.112759
$521$	−25.3602	−1.11105	−0.555526	−	0.831499i	$-0.687483\pi$
$521$	−25.3602	−1.11105	−0.555526	+	0.831499i	$0.687483\pi$
$522$	0	0
$523$	7.00314	0.306226	0.153113	−	0.988209i	$-0.451070\pi$
$523$	7.00314	0.306226	0.153113	+	0.988209i	$0.451070\pi$
$524$	1.03830	0.0453585
$525$	0	0
$526$	−3.73710	−0.162945
$527$	−20.2927	−0.883965
$528$	0	0
$529$	41.3320	1.79704
$530$	−6.86059	−0.298005
$531$	0	0
$532$	0	0
$533$	12.0678	0.522716
$534$	0	0
$535$	3.20165	0.138420
$536$	33.4070	1.44296
$537$	0	0
$538$	33.5603	1.44689
$539$	0	0
$540$	0	0
$541$	−1.42463	−0.0612495	−0.0306248	−	0.999531i	$-0.509750\pi$
$541$	−1.42463	−0.0612495	−0.0306248	+	0.999531i	$0.509750\pi$
$542$	−8.71422	−0.374308
$543$	0	0
$544$	−1.19156	−0.0510879
$545$	4.32728	0.185360
$546$	0	0
$547$	−22.0499	−0.942787	−0.471394	−	0.881923i	$-0.656249\pi$
$547$	−22.0499	−0.942787	−0.471394	+	0.881923i	$0.656249\pi$
$548$	−1.07630	−0.0459771
$549$	0	0
$550$	−25.1269	−1.07142
$551$	−4.23209	−0.180293
$552$	0	0
$553$	0	0
$554$	−21.8760	−0.929420
$555$	0	0
$556$	−0.721117	−0.0305822
$557$	9.08319	0.384867	0.192434	−	0.981310i	$-0.438362\pi$
$557$	9.08319	0.384867	0.192434	+	0.981310i	$0.438362\pi$
$558$	0	0
$559$	−7.14101	−0.302033
$560$	0	0
$561$	0	0
$562$	−10.9070	−0.460084
$563$	34.1350	1.43862	0.719310	−	0.694689i	$-0.244458\pi$
$563$	34.1350	1.43862	0.719310	+	0.694689i	$0.244458\pi$
$564$	0	0
$565$	3.04680	0.128180
$566$	27.4974	1.15580
$567$	0	0
$568$	−29.9322	−1.25593
$569$	−1.23522	−0.0517833	−0.0258916	−	0.999665i	$-0.508242\pi$
$569$	−1.23522	−0.0517833	−0.0258916	+	0.999665i	$0.508242\pi$
$570$	0	0
$571$	−26.4613	−1.10737	−0.553686	−	0.832725i	$-0.686779\pi$
$571$	−26.4613	−1.10737	−0.553686	+	0.832725i	$0.686779\pi$
$572$	0.308407	0.0128951
$573$	0	0
$574$	0	0
$575$	−33.2139	−1.38511
$576$	0	0
$577$	23.2852	0.969374	0.484687	−	0.874688i	$-0.338934\pi$
$577$	23.2852	0.969374	0.484687	+	0.874688i	$0.338934\pi$
$578$	12.5372	0.521479
$579$	0	0
$580$	−0.222973	−0.00925846
$581$	0	0
$582$	0	0
$583$	−21.6652	−0.897281
$584$	23.0982	0.955812
$585$	0	0
$586$	5.46324	0.225684
$587$	−10.7155	−0.442274	−0.221137	−	0.975243i	$-0.570977\pi$
$587$	−10.7155	−0.442274	−0.221137	+	0.975243i	$0.570977\pi$
$588$	0	0
$589$	9.07187	0.373800
$590$	9.78774	0.402955
$591$	0	0
$592$	−35.5081	−1.45938
$593$	14.1008	0.579049	0.289525	−	0.957171i	$-0.406503\pi$
$593$	14.1008	0.579049	0.289525	+	0.957171i	$0.406503\pi$
$594$	0	0
$595$	0	0
$596$	0.247843	0.0101521
$597$	0	0
$598$	11.5487	0.472260
$599$	38.9296	1.59062	0.795311	−	0.606202i	$-0.207308\pi$
$599$	38.9296	1.59062	0.795311	+	0.606202i	$0.207308\pi$
$600$	0	0
$601$	32.6162	1.33044	0.665221	−	0.746646i	$-0.268337\pi$
$601$	32.6162	1.33044	0.665221	+	0.746646i	$0.268337\pi$
$602$	0	0
$603$	0	0
$604$	−1.60234	−0.0651984
$605$	6.26475	0.254698
$606$	0	0
$607$	−19.3203	−0.784188	−0.392094	−	0.919925i	$-0.628249\pi$
$607$	−19.3203	−0.784188	−0.392094	+	0.919925i	$0.628249\pi$
$608$	0.532689	0.0216034
$609$	0	0
$610$	10.3548	0.419254
$611$	−1.95289	−0.0790056
$612$	0	0
$613$	35.3197	1.42655	0.713275	−	0.700885i	$-0.247211\pi$
$613$	35.3197	1.42655	0.713275	+	0.700885i	$0.247211\pi$
$614$	−7.47740	−0.301763
$615$	0	0
$616$	0	0
$617$	24.4318	0.983589	0.491794	−	0.870711i	$-0.336341\pi$
$617$	24.4318	0.983589	0.491794	+	0.870711i	$0.336341\pi$
$618$	0	0
$619$	−2.90892	−0.116919	−0.0584597	−	0.998290i	$-0.518619\pi$
$619$	−2.90892	−0.116919	−0.0584597	+	0.998290i	$0.518619\pi$
$620$	0.477964	0.0191955
$621$	0	0
$622$	19.9472	0.799811
$623$	0	0
$624$	0	0
$625$	12.8530	0.514121
$626$	−46.9626	−1.87700
$627$	0	0
$628$	0.0634848	0.00253332
$629$	−24.6928	−0.984566
$630$	0	0
$631$	5.66521	0.225528	0.112764	−	0.993622i	$-0.464030\pi$
$631$	5.66521	0.225528	0.112764	+	0.993622i	$0.464030\pi$
$632$	12.4070	0.493522
$633$	0	0
$634$	17.3330	0.688380
$635$	−0.397035	−0.0157559
$636$	0	0
$637$	0	0
$638$	−19.9472	−0.789718
$639$	0	0
$640$	−11.0241	−0.435768
$641$	−12.2842	−0.485198	−0.242599	−	0.970127i	$-0.578000\pi$
$641$	−12.2842	−0.485198	−0.242599	+	0.970127i	$0.578000\pi$
$642$	0	0
$643$	−9.14950	−0.360821	−0.180411	−	0.983591i	$-0.557743\pi$
$643$	−9.14950	−0.360821	−0.180411	+	0.983591i	$0.557743\pi$
$644$	0	0
$645$	0	0
$646$	5.33793	0.210018
$647$	38.4108	1.51008	0.755042	−	0.655677i	$-0.227617\pi$
$647$	38.4108	1.51008	0.755042	+	0.655677i	$0.227617\pi$
$648$	0	0
$649$	30.9089	1.21328
$650$	−5.96245	−0.233867
$651$	0	0
$652$	0.324082	0.0126920
$653$	−28.4805	−1.11453	−0.557265	−	0.830335i	$-0.688149\pi$
$653$	−28.4805	−1.11453	−0.557265	+	0.830335i	$0.688149\pi$
$654$	0	0
$655$	13.1495	0.513794
$656$	49.9730	1.95112
$657$	0	0
$658$	0	0
$659$	30.4384	1.18571	0.592856	−	0.805309i	$-0.298000\pi$
$659$	30.4384	1.18571	0.592856	+	0.805309i	$0.298000\pi$
$660$	0	0
$661$	−36.7710	−1.43023	−0.715114	−	0.699008i	$-0.753625\pi$
$661$	−36.7710	−1.43023	−0.715114	+	0.699008i	$0.753625\pi$
$662$	37.8423	1.47078
$663$	0	0
$664$	−10.5606	−0.409830
$665$	0	0
$666$	0	0
$667$	−26.3671	−1.02094
$668$	1.50227	0.0581246
$669$	0	0
$670$	−16.0691	−0.620803
$671$	32.6997	1.26236
$672$	0	0
$673$	26.7961	1.03291	0.516457	−	0.856313i	$-0.327250\pi$
$673$	26.7961	1.03291	0.516457	+	0.856313i	$0.327250\pi$
$674$	−37.8545	−1.45810
$675$	0	0
$676$	0.0731828	0.00281472
$677$	−20.3050	−0.780383	−0.390191	−	0.920734i	$-0.627591\pi$
$677$	−20.3050	−0.780383	−0.390191	+	0.920734i	$0.627591\pi$
$678$	0	0
$679$	0	0
$680$	−7.40461	−0.283954
$681$	0	0
$682$	42.7587	1.63732
$683$	−44.9240	−1.71897	−0.859484	−	0.511162i	$-0.829215\pi$
$683$	−44.9240	−1.71897	−0.859484	+	0.511162i	$0.829215\pi$
$684$	0	0
$685$	−13.6307	−0.520801
$686$	0	0
$687$	0	0
$688$	−29.5710	−1.12738
$689$	−5.14101	−0.195857
$690$	0	0
$691$	−22.0085	−0.837243	−0.418621	−	0.908161i	$-0.637487\pi$
$691$	−22.0085	−0.837243	−0.418621	+	0.908161i	$0.637487\pi$
$692$	1.09887	0.0417726
$693$	0	0
$694$	23.7472	0.901431
$695$	−9.13252	−0.346416
$696$	0	0
$697$	34.7518	1.31632
$698$	20.4162	0.772763
$699$	0	0
$700$	0	0
$701$	−31.4645	−1.18840	−0.594198	−	0.804319i	$-0.702531\pi$
$701$	−31.4645	−1.18840	−0.594198	+	0.804319i	$0.702531\pi$
$702$	0	0
$703$	11.0389	0.416341
$704$	−32.3913	−1.22079
$705$	0	0
$706$	42.9469	1.61633
$707$	0	0
$708$	0	0
$709$	−25.3373	−0.951563	−0.475781	−	0.879564i	$-0.657835\pi$
$709$	−25.3373	−0.951563	−0.475781	+	0.879564i	$0.657835\pi$
$710$	14.3977	0.540334
$711$	0	0
$712$	−15.6693	−0.587231
$713$	56.5204	2.11670
$714$	0	0
$715$	3.90579	0.146068
$716$	0.391657	0.0146369
$717$	0	0
$718$	1.93907	0.0723654
$719$	−43.8002	−1.63347	−0.816737	−	0.577011i	$-0.804219\pi$
$719$	−43.8002	−1.63347	−0.816737	+	0.577011i	$0.804219\pi$
$720$	0	0
$721$	0	0
$722$	24.9709	0.929322
$723$	0	0
$724$	−0.839165	−0.0311873
$725$	13.6131	0.505576
$726$	0	0
$727$	−0.944090	−0.0350144	−0.0175072	−	0.999847i	$-0.505573\pi$
$727$	−0.944090	−0.0350144	−0.0175072	+	0.999847i	$0.505573\pi$
$728$	0	0
$729$	0	0
$730$	−11.1105	−0.411217
$731$	−20.5640	−0.760588
$732$	0	0
$733$	5.09957	0.188357	0.0941784	−	0.995555i	$-0.469978\pi$
$733$	5.09957	0.188357	0.0941784	+	0.995555i	$0.469978\pi$
$734$	52.0898	1.92267
$735$	0	0
$736$	3.31881	0.122333
$737$	−50.7450	−1.86921
$738$	0	0
$739$	−8.25129	−0.303529	−0.151764	−	0.988417i	$-0.548495\pi$
$739$	−8.25129	−0.303529	−0.151764	+	0.988417i	$0.548495\pi$
$740$	0.581601	0.0213801
$741$	0	0
$742$	0	0
$743$	−38.4962	−1.41229	−0.706145	−	0.708068i	$-0.749567\pi$
$743$	−38.4962	−1.41229	−0.706145	+	0.708068i	$0.749567\pi$
$744$	0	0
$745$	3.13879	0.114996
$746$	24.3464	0.891385
$747$	0	0
$748$	0.888121	0.0324729
$749$	0	0
$750$	0	0
$751$	−41.3175	−1.50770	−0.753848	−	0.657049i	$-0.771805\pi$
$751$	−41.3175	−1.50770	−0.753848	+	0.657049i	$0.771805\pi$
$752$	−8.08695	−0.294901
$753$	0	0
$754$	−4.73334	−0.172378
$755$	−20.2927	−0.738528
$756$	0	0
$757$	−39.7158	−1.44349	−0.721747	−	0.692157i	$-0.756661\pi$
$757$	−39.7158	−1.44349	−0.721747	+	0.692157i	$0.756661\pi$
$758$	16.7211	0.607338
$759$	0	0
$760$	3.31023	0.120075
$761$	10.7390	0.389289	0.194644	−	0.980874i	$-0.437645\pi$
$761$	10.7390	0.389289	0.194644	+	0.980874i	$0.437645\pi$
$762$	0	0
$763$	0	0
$764$	−1.47651	−0.0534181
$765$	0	0
$766$	−21.0411	−0.760247
$767$	7.33448	0.264833
$768$	0	0
$769$	50.5549	1.82306	0.911529	−	0.411237i	$-0.134903\pi$
$769$	50.5549	1.82306	0.911529	+	0.411237i	$0.134903\pi$
$770$	0	0
$771$	0	0
$772$	−1.93024	−0.0694709
$773$	8.91770	0.320747	0.160374	−	0.987056i	$-0.448730\pi$
$773$	8.91770	0.320747	0.160374	+	0.987056i	$0.448730\pi$
$774$	0	0
$775$	−29.1809	−1.04821
$776$	−19.1441	−0.687234
$777$	0	0
$778$	8.63913	0.309728
$779$	−15.5358	−0.556629
$780$	0	0
$781$	45.4667	1.62693
$782$	33.2568	1.18926
$783$	0	0
$784$	0	0
$785$	0.803998	0.0286959
$786$	0	0
$787$	−22.3671	−0.797302	−0.398651	−	0.917103i	$-0.630521\pi$
$787$	−22.3671	−0.797302	−0.398651	+	0.917103i	$0.630521\pi$
$788$	1.47333	0.0524853
$789$	0	0
$790$	−5.96787	−0.212327
$791$	0	0
$792$	0	0
$793$	7.75942	0.275545
$794$	37.0016	1.31314
$795$	0	0
$796$	−0.128759	−0.00456375
$797$	20.5518	0.727983	0.363991	−	0.931402i	$-0.381414\pi$
$797$	20.5518	0.727983	0.363991	+	0.931402i	$0.381414\pi$
$798$	0	0
$799$	−5.62377	−0.198955
$800$	−1.71346	−0.0605801
$801$	0	0
$802$	−28.1689	−0.994680
$803$	−35.0860	−1.23816
$804$	0	0
$805$	0	0
$806$	10.1464	0.357390
$807$	0	0
$808$	−30.4454	−1.07106
$809$	−7.83443	−0.275444	−0.137722	−	0.990471i	$-0.543978\pi$
$809$	−7.83443	−0.275444	−0.137722	+	0.990471i	$0.543978\pi$
$810$	0	0
$811$	47.5502	1.66971	0.834857	−	0.550468i	$-0.185551\pi$
$811$	47.5502	1.66971	0.834857	+	0.550468i	$0.185551\pi$
$812$	0	0
$813$	0	0
$814$	52.0301	1.82365
$815$	4.10430	0.143767
$816$	0	0
$817$	9.19316	0.321628
$818$	4.59769	0.160754
$819$	0	0
$820$	−0.818526	−0.0285842
$821$	−4.42494	−0.154431	−0.0772157	−	0.997014i	$-0.524603\pi$
$821$	−4.42494	−0.154431	−0.0772157	+	0.997014i	$0.524603\pi$
$822$	0	0
$823$	−28.7525	−1.00225	−0.501124	−	0.865375i	$-0.667080\pi$
$823$	−28.7525	−1.00225	−0.501124	+	0.865375i	$0.667080\pi$
$824$	−45.5779	−1.58778
$825$	0	0
$826$	0	0
$827$	5.58667	0.194267	0.0971337	−	0.995271i	$-0.469033\pi$
$827$	5.58667	0.194267	0.0971337	+	0.995271i	$0.469033\pi$
$828$	0	0
$829$	−53.4974	−1.85804	−0.929021	−	0.370027i	$-0.879348\pi$
$829$	−53.4974	−1.85804	−0.929021	+	0.370027i	$0.879348\pi$
$830$	5.07974	0.176320
$831$	0	0
$832$	−7.68624	−0.266472
$833$	0	0
$834$	0	0
$835$	19.0254	0.658400
$836$	−0.397035	−0.0137317
$837$	0	0
$838$	−43.5257	−1.50357
$839$	−43.0405	−1.48592	−0.742962	−	0.669334i	$-0.766580\pi$
$839$	−43.0405	−1.48592	−0.742962	+	0.669334i	$0.766580\pi$
$840$	0	0
$841$	−18.1932	−0.627350
$842$	−38.8055	−1.33733
$843$	0	0
$844$	1.13941	0.0392202
$845$	0.926817	0.0318835
$846$	0	0
$847$	0	0
$848$	−21.2890	−0.731066
$849$	0	0
$850$	−17.1701	−0.588931
$851$	68.7757	2.35760
$852$	0	0
$853$	30.7434	1.05263	0.526316	−	0.850289i	$-0.323573\pi$
$853$	30.7434	1.05263	0.526316	+	0.850289i	$0.323573\pi$
$854$	0	0
$855$	0	0
$856$	9.58384	0.327569
$857$	−24.5449	−0.838438	−0.419219	−	0.907885i	$-0.637696\pi$
$857$	−24.5449	−0.838438	−0.419219	+	0.907885i	$0.637696\pi$
$858$	0	0
$859$	52.1243	1.77846	0.889229	−	0.457461i	$-0.151241\pi$
$859$	52.1243	1.77846	0.889229	+	0.457461i	$0.151241\pi$
$860$	0.484354	0.0165163
$861$	0	0
$862$	24.1483	0.822494
$863$	−22.2563	−0.757612	−0.378806	−	0.925476i	$-0.623665\pi$
$863$	−22.2563	−0.757612	−0.378806	+	0.925476i	$0.623665\pi$
$864$	0	0
$865$	13.9165	0.473175
$866$	37.2246	1.26494
$867$	0	0
$868$	0	0
$869$	−18.8461	−0.639309
$870$	0	0
$871$	−12.0414	−0.408009
$872$	12.9533	0.438654
$873$	0	0
$874$	−14.8675	−0.502900
$875$	0	0
$876$	0	0
$877$	41.0547	1.38632	0.693159	−	0.720785i	$-0.256218\pi$
$877$	41.0547	1.38632	0.693159	+	0.720785i	$0.256218\pi$
$878$	36.0760	1.21751
$879$	0	0
$880$	16.1739	0.545222
$881$	−31.0568	−1.04633	−0.523165	−	0.852231i	$-0.675249\pi$
$881$	−31.0568	−1.04633	−0.523165	+	0.852231i	$0.675249\pi$
$882$	0	0
$883$	−56.5357	−1.90258	−0.951289	−	0.308300i	$-0.900240\pi$
$883$	−56.5357	−1.90258	−0.951289	+	0.308300i	$0.900240\pi$
$884$	0.210745	0.00708813
$885$	0	0
$886$	6.69190	0.224819
$887$	9.94785	0.334016	0.167008	−	0.985956i	$-0.446589\pi$
$887$	9.94785	0.334016	0.167008	+	0.985956i	$0.446589\pi$
$888$	0	0
$889$	0	0
$890$	7.53707	0.252643
$891$	0	0
$892$	0.846681	0.0283490
$893$	2.51411	0.0841314
$894$	0	0
$895$	4.96010	0.165798
$896$	0	0
$897$	0	0
$898$	0.712291	0.0237695
$899$	−23.1655	−0.772612
$900$	0	0
$901$	−14.8046	−0.493213
$902$	−73.2255	−2.43814
$903$	0	0
$904$	9.12029	0.303336
$905$	−10.6275	−0.353271
$906$	0	0
$907$	−31.2936	−1.03909	−0.519544	−	0.854444i	$-0.673898\pi$
$907$	−31.2936	−1.03909	−0.519544	+	0.854444i	$0.673898\pi$
$908$	−0.808067	−0.0268166
$909$	0	0
$910$	0	0
$911$	9.39320	0.311210	0.155605	−	0.987819i	$-0.450267\pi$
$911$	9.39320	0.311210	0.155605	+	0.987819i	$0.450267\pi$
$912$	0	0
$913$	16.0414	0.530894
$914$	−38.1127	−1.26066
$915$	0	0
$916$	1.00314	0.0331446
$917$	0	0
$918$	0	0
$919$	21.7066	0.716036	0.358018	−	0.933715i	$-0.383453\pi$
$919$	21.7066	0.716036	0.358018	+	0.933715i	$0.383453\pi$
$920$	20.6237	0.679944
$921$	0	0
$922$	1.55746	0.0512921
$923$	10.7889	0.355122
$924$	0	0
$925$	−35.5081	−1.16750
$926$	47.0974	1.54771
$927$	0	0
$928$	−1.36025	−0.0446523
$929$	35.6787	1.17058	0.585289	−	0.810824i	$-0.300981\pi$
$929$	35.6787	1.17058	0.585289	+	0.810824i	$0.300981\pi$
$930$	0	0
$931$	0	0
$932$	−0.0903972	−0.00296106
$933$	0	0
$934$	24.5924	0.804687
$935$	11.2475	0.367834
$936$	0	0
$937$	47.0866	1.53825	0.769127	−	0.639096i	$-0.220691\pi$
$937$	47.0866	1.53825	0.769127	+	0.639096i	$0.220691\pi$
$938$	0	0
$939$	0	0
$940$	0.132459	0.00432034
$941$	45.2923	1.47649	0.738244	−	0.674534i	$-0.235655\pi$
$941$	45.2923	1.47649	0.738244	+	0.674534i	$0.235655\pi$
$942$	0	0
$943$	−96.7927	−3.15200
$944$	30.3722	0.988530
$945$	0	0
$946$	43.3304	1.40879
$947$	−4.77134	−0.155048	−0.0775238	−	0.996991i	$-0.524701\pi$
$947$	−4.77134	−0.155048	−0.0775238	+	0.996991i	$0.524701\pi$
$948$	0	0
$949$	−8.32568	−0.270263
$950$	7.67592	0.249040
$951$	0	0
$952$	0	0
$953$	3.95572	0.128138	0.0640692	−	0.997945i	$-0.479592\pi$
$953$	3.95572	0.128138	0.0640692	+	0.997945i	$0.479592\pi$
$954$	0	0
$955$	−18.6991	−0.605088
$956$	−1.39824	−0.0452223
$957$	0	0
$958$	24.7353	0.799160
$959$	0	0
$960$	0	0
$961$	18.6573	0.601850
$962$	12.3464	0.398064
$963$	0	0
$964$	0.880605	0.0283624
$965$	−24.4454	−0.786924
$966$	0	0
$967$	50.2292	1.61526	0.807632	−	0.589687i	$-0.200749\pi$
$967$	50.2292	1.61526	0.807632	+	0.589687i	$0.200749\pi$
$968$	18.7529	0.602742
$969$	0	0
$970$	9.20850	0.295667
$971$	38.6576	1.24058	0.620291	−	0.784372i	$-0.287014\pi$
$971$	38.6576	1.24058	0.620291	+	0.784372i	$0.287014\pi$
$972$	0	0
$973$	0	0
$974$	6.16638	0.197584
$975$	0	0
$976$	32.1318	1.02852
$977$	20.6134	0.659480	0.329740	−	0.944072i	$-0.393039\pi$
$977$	20.6134	0.659480	0.329740	+	0.944072i	$0.393039\pi$
$978$	0	0
$979$	23.8015	0.760699
$980$	0	0
$981$	0	0
$982$	39.5304	1.26147
$983$	−4.48620	−0.143088	−0.0715438	−	0.997437i	$-0.522793\pi$
$983$	−4.48620	−0.143088	−0.0715438	+	0.997437i	$0.522793\pi$
$984$	0	0
$985$	18.6589	0.594521
$986$	−13.6307	−0.434089
$987$	0	0
$988$	−0.0942138	−0.00299734
$989$	57.2760	1.82127
$990$	0	0
$991$	−32.7971	−1.04183	−0.520917	−	0.853607i	$-0.674410\pi$
$991$	−32.7971	−1.04183	−0.520917	+	0.853607i	$0.674410\pi$
$992$	2.91582	0.0925773
$993$	0	0
$994$	0	0
$995$	−1.63066	−0.0516954
$996$	0	0
$997$	−0.491870	−0.0155777	−0.00778884	−	0.999970i	$-0.502479\pi$
$997$	−0.491870	−0.0155777	−0.00778884	+	0.999970i	$0.502479\pi$
$998$	53.3397	1.68844
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bf.1.2		4
3.2	odd	2		1911.2.a.s.1.3		4
7.6	odd	2		819.2.a.k.1.2		4
21.20	even	2		273.2.a.e.1.3	✓	4
84.83	odd	2		4368.2.a.br.1.3		4
105.104	even	2		6825.2.a.bg.1.2		4
273.272	even	2		3549.2.a.w.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.a.e.1.3	✓	4	21.20	even	2
819.2.a.k.1.2		4	7.6	odd	2
1911.2.a.s.1.3		4	3.2	odd	2
3549.2.a.w.1.2		4	273.272	even	2
4368.2.a.br.1.3		4	84.83	odd	2
5733.2.a.bf.1.2		4	1.1	even	1	trivial
6825.2.a.bg.1.2		4	105.104	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)

\(f(q)\)	\(=\)	\(q-1.43986 q^{2} +0.0731828 q^{4} +0.926817 q^{5} +2.77434 q^{8} +O(q^{10})\)	\(q-1.43986 q^{2} +0.0731828 q^{4} +0.926817 q^{5} +2.77434 q^{8} -1.33448 q^{10} -4.21419 q^{11} -1.00000 q^{13} -4.14101 q^{16} -2.87971 q^{17} +1.28738 q^{19} +0.0678271 q^{20} +6.06783 q^{22} +8.02072 q^{23} -4.14101 q^{25} +1.43986 q^{26} -3.28738 q^{29} +7.04680 q^{31} +0.413779 q^{32} +4.14637 q^{34} +8.57475 q^{37} -1.85363 q^{38} +2.57130 q^{40} -12.0678 q^{41} +7.14101 q^{43} -0.308407 q^{44} -11.5487 q^{46} +1.95289 q^{47} +5.96245 q^{50} -0.0731828 q^{52} +5.14101 q^{53} -3.90579 q^{55} +4.73334 q^{58} -7.33448 q^{59} -7.75942 q^{61} -10.1464 q^{62} +7.68624 q^{64} -0.926817 q^{65} +12.0414 q^{67} -0.210745 q^{68} -10.7889 q^{71} +8.32568 q^{73} -12.3464 q^{74} +0.0942138 q^{76} +4.47204 q^{79} -3.83796 q^{80} +17.3759 q^{82} -3.80653 q^{83} -2.66896 q^{85} -10.2820 q^{86} -11.6916 q^{88} -5.64793 q^{89} +0.586979 q^{92} -2.81188 q^{94} +1.19316 q^{95} -6.90043 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 7 q^{4} - 3 q^{5} - 3 q^{8}+O(q^{10}) \) 4 * q - q^2 + 7 * q^4 - 3 * q^5 - 3 * q^8	\( 4 q - q^{2} + 7 q^{4} - 3 q^{5} - 3 q^{8} + 4 q^{10} + 2 q^{11} - 4 q^{13} + 9 q^{16} - 2 q^{17} - 7 q^{19} - 32 q^{20} - 8 q^{22} - 3 q^{23} + 9 q^{25} + q^{26} - q^{29} - 3 q^{31} - 7 q^{32} + 30 q^{34} + 10 q^{37} + 6 q^{38} + 14 q^{40} - 16 q^{41} + 3 q^{43} + 12 q^{44} - 18 q^{46} + 5 q^{47} - 13 q^{50} - 7 q^{52} - 5 q^{53} - 10 q^{55} - 4 q^{58} - 20 q^{59} - 12 q^{61} - 54 q^{62} + 5 q^{64} + 3 q^{65} - 22 q^{67} - 10 q^{68} + 13 q^{73} + 6 q^{74} + 6 q^{76} + 11 q^{79} - 42 q^{80} - 10 q^{82} + q^{83} + 8 q^{85} + 10 q^{86} - 60 q^{88} - 5 q^{89} - 34 q^{92} - 34 q^{94} - 13 q^{95} + 17 q^{97}+O(q^{100}) \) 4 * q - q^2 + 7 * q^4 - 3 * q^5 - 3 * q^8 + 4 * q^10 + 2 * q^11 - 4 * q^13 + 9 * q^16 - 2 * q^17 - 7 * q^19 - 32 * q^20 - 8 * q^22 - 3 * q^23 + 9 * q^25 + q^26 - q^29 - 3 * q^31 - 7 * q^32 + 30 * q^34 + 10 * q^37 + 6 * q^38 + 14 * q^40 - 16 * q^41 + 3 * q^43 + 12 * q^44 - 18 * q^46 + 5 * q^47 - 13 * q^50 - 7 * q^52 - 5 * q^53 - 10 * q^55 - 4 * q^58 - 20 * q^59 - 12 * q^61 - 54 * q^62 + 5 * q^64 + 3 * q^65 - 22 * q^67 - 10 * q^68 + 13 * q^73 + 6 * q^74 + 6 * q^76 + 11 * q^79 - 42 * q^80 - 10 * q^82 + q^83 + 8 * q^85 + 10 * q^86 - 60 * q^88 - 5 * q^89 - 34 * q^92 - 34 * q^94 - 13 * q^95 + 17 * q^97

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