LMFDB - Embedded newform 5733.2.a.bw.1.1

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 10x^{8} + 52x^{7} + 16x^{6} - 212x^{5} + 64x^{4} + 300x^{3} - 159x^{2} - 80x + 46 $ x^10 - 4x^9 - 10x^8 + 52x^7 + 16x^6 - 212x^5 + 64x^4 + 300x^3 - 159x^2 - 80*x + 46
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1911)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.76760$ 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)

$f(q)$	$=$	$q-2.76760 q^{2} +5.65960 q^{4} -0.300737 q^{5} -10.1283 q^{8} +O(q^{10})$	$q-2.76760 q^{2} +5.65960 q^{4} -0.300737 q^{5} -10.1283 q^{8} +0.832320 q^{10} -1.37125 q^{11} +1.00000 q^{13} +16.7118 q^{16} -4.90389 q^{17} -1.43566 q^{19} -1.70205 q^{20} +3.79508 q^{22} +5.39075 q^{23} -4.90956 q^{25} -2.76760 q^{26} +6.32791 q^{29} -6.83785 q^{31} -25.9951 q^{32} +13.5720 q^{34} +11.1663 q^{37} +3.97333 q^{38} +3.04595 q^{40} -0.336828 q^{41} +1.87883 q^{43} -7.76074 q^{44} -14.9194 q^{46} -12.0801 q^{47} +13.5877 q^{50} +5.65960 q^{52} +3.80614 q^{53} +0.412387 q^{55} -17.5131 q^{58} +6.17696 q^{59} +14.7631 q^{61} +18.9244 q^{62} +38.5202 q^{64} -0.300737 q^{65} -13.8548 q^{67} -27.7540 q^{68} -8.26783 q^{71} +7.40347 q^{73} -30.9039 q^{74} -8.12526 q^{76} +7.32993 q^{79} -5.02587 q^{80} +0.932206 q^{82} +11.7977 q^{83} +1.47478 q^{85} -5.19984 q^{86} +13.8884 q^{88} +12.9614 q^{89} +30.5095 q^{92} +33.4329 q^{94} +0.431757 q^{95} -10.3451 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + 16 q^{4} - 6 q^{5} - 12 q^{8}+O(q^{10}) $ 10 * q - 4 * q^2 + 16 * q^4 - 6 * q^5 - 12 * q^8	$ 10 q - 4 q^{2} + 16 q^{4} - 6 q^{5} - 12 q^{8} - 8 q^{10} - 12 q^{11} + 10 q^{13} + 24 q^{16} - 10 q^{19} - 16 q^{20} + 8 q^{22} - 14 q^{23} + 32 q^{25} - 4 q^{26} - 18 q^{29} - 14 q^{31} - 28 q^{32} - 4 q^{34} + 24 q^{37} - 4 q^{38} - 16 q^{40} - 24 q^{41} + 2 q^{43} - 48 q^{44} + 20 q^{46} - 18 q^{47} + 28 q^{50} + 16 q^{52} - 10 q^{53} - 12 q^{55} + 12 q^{58} - 12 q^{59} + 4 q^{61} + 4 q^{62} + 32 q^{64} - 6 q^{65} - 12 q^{67} - 40 q^{68} - 32 q^{71} + 18 q^{73} - 24 q^{74} - 32 q^{76} + 34 q^{79} - 32 q^{80} - 48 q^{82} - 30 q^{83} - 40 q^{86} + 32 q^{88} - 10 q^{89} + 40 q^{92} + 24 q^{94} + 30 q^{95} + 2 q^{97}+O(q^{100}) $ 10 * q - 4 * q^2 + 16 * q^4 - 6 * q^5 - 12 * q^8 - 8 * q^10 - 12 * q^11 + 10 * q^13 + 24 * q^16 - 10 * q^19 - 16 * q^20 + 8 * q^22 - 14 * q^23 + 32 * q^25 - 4 * q^26 - 18 * q^29 - 14 * q^31 - 28 * q^32 - 4 * q^34 + 24 * q^37 - 4 * q^38 - 16 * q^40 - 24 * q^41 + 2 * q^43 - 48 * q^44 + 20 * q^46 - 18 * q^47 + 28 * q^50 + 16 * q^52 - 10 * q^53 - 12 * q^55 + 12 * q^58 - 12 * q^59 + 4 * q^61 + 4 * q^62 + 32 * q^64 - 6 * q^65 - 12 * q^67 - 40 * q^68 - 32 * q^71 + 18 * q^73 - 24 * q^74 - 32 * q^76 + 34 * q^79 - 32 * q^80 - 48 * q^82 - 30 * q^83 - 40 * q^86 + 32 * q^88 - 10 * q^89 + 40 * q^92 + 24 * q^94 + 30 * q^95 + 2 * 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 $

$2$	−2.76760	−1.95699	−0.978493	−	0.206278i	$-0.933865\pi$
$2$	−2.76760	−1.95699	−0.978493	+	0.206278i	$0.933865\pi$
$3$	0	0
$3$	0	0
$4$	5.65960	2.82980
$5$	−0.300737	−0.134494	−0.0672469	−	0.997736i	$-0.521422\pi$
$5$	−0.300737	−0.134494	−0.0672469	+	0.997736i	$0.521422\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	−10.1283	−3.58089
$9$	0	0
$10$	0.832320	0.263203
$11$	−1.37125	−0.413448	−0.206724	−	0.978399i	$-0.566280\pi$
$11$	−1.37125	−0.413448	−0.206724	+	0.978399i	$0.566280\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	0	0
$16$	16.7118	4.17796
$17$	−4.90389	−1.18937	−0.594684	−	0.803959i	$-0.702723\pi$
$17$	−4.90389	−1.18937	−0.594684	+	0.803959i	$0.702723\pi$
$18$	0	0
$19$	−1.43566	−0.329363	−0.164682	−	0.986347i	$-0.552660\pi$
$19$	−1.43566	−0.329363	−0.164682	+	0.986347i	$0.552660\pi$
$20$	−1.70205	−0.380590
$21$	0	0
$22$	3.79508	0.809113
$23$	5.39075	1.12405	0.562025	−	0.827120i	$-0.310023\pi$
$23$	5.39075	1.12405	0.562025	+	0.827120i	$0.310023\pi$
$24$	0	0
$25$	−4.90956	−0.981911
$26$	−2.76760	−0.542771
$27$	0	0
$28$	0	0
$29$	6.32791	1.17506	0.587532	−	0.809201i	$-0.300100\pi$
$29$	6.32791	1.17506	0.587532	+	0.809201i	$0.300100\pi$
$30$	0	0
$31$	−6.83785	−1.22811	−0.614057	−	0.789262i	$-0.710464\pi$
$31$	−6.83785	−1.22811	−0.614057	+	0.789262i	$0.710464\pi$
$32$	−25.9951	−4.59532
$33$	0	0
$34$	13.5720	2.32758
$35$	0	0
$36$	0	0
$37$	11.1663	1.83573	0.917865	−	0.396892i	$-0.129911\pi$
$37$	11.1663	1.83573	0.917865	+	0.396892i	$0.129911\pi$
$38$	3.97333	0.644560
$39$	0	0
$40$	3.04595	0.481608
$41$	−0.336828	−0.0526038	−0.0263019	−	0.999654i	$-0.508373\pi$
$41$	−0.336828	−0.0526038	−0.0263019	+	0.999654i	$0.508373\pi$
$42$	0	0
$43$	1.87883	0.286519	0.143259	−	0.989685i	$-0.454242\pi$
$43$	1.87883	0.286519	0.143259	+	0.989685i	$0.454242\pi$
$44$	−7.76074	−1.16998
$45$	0	0
$46$	−14.9194	−2.19975
$47$	−12.0801	−1.76207	−0.881033	−	0.473055i	$-0.843151\pi$
$47$	−12.0801	−1.76207	−0.881033	+	0.473055i	$0.843151\pi$
$48$	0	0
$49$	0	0
$50$	13.5877	1.92159
$51$	0	0
$52$	5.65960	0.784845
$53$	3.80614	0.522814	0.261407	−	0.965229i	$-0.415814\pi$
$53$	3.80614	0.522814	0.261407	+	0.965229i	$0.415814\pi$
$54$	0	0
$55$	0.412387	0.0556063
$56$	0	0
$57$	0	0
$58$	−17.5131	−2.29959
$59$	6.17696	0.804171	0.402086	−	0.915602i	$-0.368285\pi$
$59$	6.17696	0.804171	0.402086	+	0.915602i	$0.368285\pi$
$60$	0	0
$61$	14.7631	1.89022	0.945110	−	0.326751i	$-0.105954\pi$
$61$	14.7631	1.89022	0.945110	+	0.326751i	$0.105954\pi$
$62$	18.9244	2.40340
$63$	0	0
$64$	38.5202	4.81502
$65$	−0.300737	−0.0373019
$66$	0	0
$67$	−13.8548	−1.69264	−0.846319	−	0.532677i	$-0.821186\pi$
$67$	−13.8548	−1.69264	−0.846319	+	0.532677i	$0.821186\pi$
$68$	−27.7540	−3.36567
$69$	0	0
$70$	0	0
$71$	−8.26783	−0.981211	−0.490606	−	0.871382i	$-0.663224\pi$
$71$	−8.26783	−0.981211	−0.490606	+	0.871382i	$0.663224\pi$
$72$	0	0
$73$	7.40347	0.866511	0.433256	−	0.901271i	$-0.357365\pi$
$73$	7.40347	0.866511	0.433256	+	0.901271i	$0.357365\pi$
$74$	−30.9039	−3.59250
$75$	0	0
$76$	−8.12526	−0.932032
$77$	0	0
$78$	0	0
$79$	7.32993	0.824682	0.412341	−	0.911030i	$-0.364711\pi$
$79$	7.32993	0.824682	0.412341	+	0.911030i	$0.364711\pi$
$80$	−5.02587	−0.561910
$81$	0	0
$82$	0.932206	0.102945
$83$	11.7977	1.29497	0.647484	−	0.762079i	$-0.275821\pi$
$83$	11.7977	1.29497	0.647484	+	0.762079i	$0.275821\pi$
$84$	0	0
$85$	1.47478	0.159963
$86$	−5.19984	−0.560713
$87$	0	0
$88$	13.8884	1.48051
$89$	12.9614	1.37390	0.686951	−	0.726704i	$-0.258949\pi$
$89$	12.9614	1.37390	0.686951	+	0.726704i	$0.258949\pi$
$90$	0	0
$91$	0	0
$92$	30.5095	3.18083
$93$	0	0
$94$	33.4329	3.44834
$95$	0.431757	0.0442973
$96$	0	0
$97$	−10.3451	−1.05039	−0.525195	−	0.850982i	$-0.676008\pi$
$97$	−10.3451	−1.05039	−0.525195	+	0.850982i	$0.676008\pi$
$98$	0	0
$99$	0	0
$100$	−27.7861	−2.77861
$101$	−1.80416	−0.179521	−0.0897605	−	0.995963i	$-0.528610\pi$
$101$	−1.80416	−0.179521	−0.0897605	+	0.995963i	$0.528610\pi$
$102$	0	0
$103$	−7.86222	−0.774688	−0.387344	−	0.921935i	$-0.626607\pi$
$103$	−7.86222	−0.774688	−0.387344	+	0.921935i	$0.626607\pi$
$104$	−10.1283	−0.993160
$105$	0	0
$106$	−10.5339	−1.02314
$107$	0.289723	0.0280085	0.0140043	−	0.999902i	$-0.495542\pi$
$107$	0.289723	0.0280085	0.0140043	+	0.999902i	$0.495542\pi$
$108$	0	0
$109$	−5.17079	−0.495272	−0.247636	−	0.968853i	$-0.579654\pi$
$109$	−5.17079	−0.495272	−0.247636	+	0.968853i	$0.579654\pi$
$110$	−1.14132	−0.108821
$111$	0	0
$112$	0	0
$113$	3.51191	0.330373	0.165186	−	0.986262i	$-0.447177\pi$
$113$	3.51191	0.330373	0.165186	+	0.986262i	$0.447177\pi$
$114$	0	0
$115$	−1.62120	−0.151178
$116$	35.8134	3.32519
$117$	0	0
$118$	−17.0953	−1.57375
$119$	0	0
$120$	0	0
$121$	−9.11966	−0.829060
$122$	−40.8583	−3.69914
$123$	0	0
$124$	−38.6995	−3.47532
$125$	2.98017	0.266555
$126$	0	0
$127$	−7.60799	−0.675100	−0.337550	−	0.941308i	$-0.609598\pi$
$127$	−7.60799	−0.675100	−0.337550	+	0.941308i	$0.609598\pi$
$128$	−54.6182	−4.82761
$129$	0	0
$130$	0.832320	0.0729993
$131$	−3.40667	−0.297642	−0.148821	−	0.988864i	$-0.547548\pi$
$131$	−3.40667	−0.297642	−0.148821	+	0.988864i	$0.547548\pi$
$132$	0	0
$133$	0	0
$134$	38.3446	3.31247
$135$	0	0
$136$	49.6680	4.25900
$137$	6.10766	0.521813	0.260906	−	0.965364i	$-0.415979\pi$
$137$	6.10766	0.521813	0.260906	+	0.965364i	$0.415979\pi$
$138$	0	0
$139$	−18.3821	−1.55915	−0.779575	−	0.626309i	$-0.784565\pi$
$139$	−18.3821	−1.55915	−0.779575	+	0.626309i	$0.784565\pi$
$140$	0	0
$141$	0	0
$142$	22.8820	1.92022
$143$	−1.37125	−0.114670
$144$	0	0
$145$	−1.90304	−0.158039
$146$	−20.4898	−1.69575
$147$	0	0
$148$	63.1968	5.19475
$149$	13.3818	1.09628	0.548141	−	0.836386i	$-0.315336\pi$
$149$	13.3818	1.09628	0.548141	+	0.836386i	$0.315336\pi$
$150$	0	0
$151$	−13.7737	−1.12089	−0.560446	−	0.828191i	$-0.689370\pi$
$151$	−13.7737	−1.12089	−0.560446	+	0.828191i	$0.689370\pi$
$152$	14.5408	1.17941
$153$	0	0
$154$	0	0
$155$	2.05640	0.165174
$156$	0	0
$157$	−17.0296	−1.35911	−0.679554	−	0.733625i	$-0.737827\pi$
$157$	−17.0296	−1.35911	−0.679554	+	0.733625i	$0.737827\pi$
$158$	−20.2863	−1.61389
$159$	0	0
$160$	7.81768	0.618042
$161$	0	0
$162$	0	0
$163$	−3.49771	−0.273962	−0.136981	−	0.990574i	$-0.543740\pi$
$163$	−3.49771	−0.273962	−0.136981	+	0.990574i	$0.543740\pi$
$164$	−1.90631	−0.148858
$165$	0	0
$166$	−32.6513	−2.53424
$167$	0.346591	0.0268200	0.0134100	−	0.999910i	$-0.495731\pi$
$167$	0.346591	0.0268200	0.0134100	+	0.999910i	$0.495731\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−4.08161	−0.313045
$171$	0	0
$172$	10.6334	0.810789
$173$	−25.6175	−1.94766	−0.973831	−	0.227275i	$-0.927018\pi$
$173$	−25.6175	−1.94766	−0.973831	+	0.227275i	$0.927018\pi$
$174$	0	0
$175$	0	0
$176$	−22.9162	−1.72737
$177$	0	0
$178$	−35.8718	−2.68871
$179$	5.94537	0.444377	0.222189	−	0.975004i	$-0.428680\pi$
$179$	5.94537	0.444377	0.222189	+	0.975004i	$0.428680\pi$
$180$	0	0
$181$	0.0315154	0.00234252	0.00117126	−	0.999999i	$-0.499627\pi$
$181$	0.0315154	0.00234252	0.00117126	+	0.999999i	$0.499627\pi$
$182$	0	0
$183$	0	0
$184$	−54.5991	−4.02510
$185$	−3.35813	−0.246894
$186$	0	0
$187$	6.72448	0.491742
$188$	−68.3685	−4.98629
$189$	0	0
$190$	−1.19493	−0.0866893
$191$	−8.37564	−0.606040	−0.303020	−	0.952984i	$-0.597995\pi$
$191$	−8.37564	−0.606040	−0.303020	+	0.952984i	$0.597995\pi$
$192$	0	0
$193$	−9.19011	−0.661518	−0.330759	−	0.943715i	$-0.607305\pi$
$193$	−9.19011	−0.661518	−0.330759	+	0.943715i	$0.607305\pi$
$194$	28.6312	2.05560
$195$	0	0
$196$	0	0
$197$	−20.4735	−1.45868	−0.729338	−	0.684154i	$-0.760172\pi$
$197$	−20.4735	−1.45868	−0.729338	+	0.684154i	$0.760172\pi$
$198$	0	0
$199$	3.32236	0.235516	0.117758	−	0.993042i	$-0.462429\pi$
$199$	3.32236	0.235516	0.117758	+	0.993042i	$0.462429\pi$
$200$	49.7254	3.51612
$201$	0	0
$202$	4.99320	0.351320
$203$	0	0
$204$	0	0
$205$	0.101297	0.00707488
$206$	21.7595	1.51605
$207$	0	0
$208$	16.7118	1.15876
$209$	1.96866	0.136175
$210$	0	0
$211$	15.6311	1.07609	0.538044	−	0.842917i	$-0.319163\pi$
$211$	15.6311	1.07609	0.538044	+	0.842917i	$0.319163\pi$
$212$	21.5412	1.47946
$213$	0	0
$214$	−0.801835	−0.0548123
$215$	−0.565033	−0.0385350
$216$	0	0
$217$	0	0
$218$	14.3107	0.969241
$219$	0	0
$220$	2.33394	0.157354
$221$	−4.90389	−0.329871
$222$	0	0
$223$	−8.94068	−0.598712	−0.299356	−	0.954141i	$-0.596772\pi$
$223$	−8.94068	−0.598712	−0.299356	+	0.954141i	$0.596772\pi$
$224$	0	0
$225$	0	0
$226$	−9.71955	−0.646535
$227$	−17.2200	−1.14293	−0.571466	−	0.820626i	$-0.693625\pi$
$227$	−17.2200	−1.14293	−0.571466	+	0.820626i	$0.693625\pi$
$228$	0	0
$229$	−17.0260	−1.12511	−0.562555	−	0.826760i	$-0.690182\pi$
$229$	−17.0260	−1.12511	−0.562555	+	0.826760i	$0.690182\pi$
$230$	4.48683	0.295853
$231$	0	0
$232$	−64.0909	−4.20778
$233$	−5.13198	−0.336207	−0.168104	−	0.985769i	$-0.553764\pi$
$233$	−5.13198	−0.336207	−0.168104	+	0.985769i	$0.553764\pi$
$234$	0	0
$235$	3.63294	0.236987
$236$	34.9591	2.27564
$237$	0	0
$238$	0	0
$239$	14.0571	0.909281	0.454641	−	0.890675i	$-0.349768\pi$
$239$	14.0571	0.909281	0.454641	+	0.890675i	$0.349768\pi$
$240$	0	0
$241$	17.0408	1.09770	0.548848	−	0.835922i	$-0.315066\pi$
$241$	17.0408	1.09770	0.548848	+	0.835922i	$0.315066\pi$
$242$	25.2396	1.62246
$243$	0	0
$244$	83.5532	5.34894
$245$	0	0
$246$	0	0
$247$	−1.43566	−0.0913489
$248$	69.2557	4.39774
$249$	0	0
$250$	−8.24792	−0.521644
$251$	24.0873	1.52038	0.760190	−	0.649701i	$-0.225106\pi$
$251$	24.0873	1.52038	0.760190	+	0.649701i	$0.225106\pi$
$252$	0	0
$253$	−7.39209	−0.464736
$254$	21.0558	1.32116
$255$	0	0
$256$	74.1209	4.63256
$257$	−17.4806	−1.09041	−0.545204	−	0.838303i	$-0.683548\pi$
$257$	−17.4806	−1.09041	−0.545204	+	0.838303i	$0.683548\pi$
$258$	0	0
$259$	0	0
$260$	−1.70205	−0.105557
$261$	0	0
$262$	9.42829	0.582482
$263$	6.48774	0.400051	0.200026	−	0.979791i	$-0.435897\pi$
$263$	6.48774	0.400051	0.200026	+	0.979791i	$0.435897\pi$
$264$	0	0
$265$	−1.14465	−0.0703152
$266$	0	0
$267$	0	0
$268$	−78.4128	−4.78982
$269$	20.6124	1.25676	0.628381	−	0.777905i	$-0.283718\pi$
$269$	20.6124	1.25676	0.628381	+	0.777905i	$0.283718\pi$
$270$	0	0
$271$	0.716088	0.0434993	0.0217496	−	0.999763i	$-0.493076\pi$
$271$	0.716088	0.0434993	0.0217496	+	0.999763i	$0.493076\pi$
$272$	−81.9530	−4.96913
$273$	0	0
$274$	−16.9036	−1.02118
$275$	6.73225	0.405970
$276$	0	0
$277$	17.8574	1.07295	0.536473	−	0.843917i	$-0.319756\pi$
$277$	17.8574	1.07295	0.536473	+	0.843917i	$0.319756\pi$
$278$	50.8743	3.05124
$279$	0	0
$280$	0	0
$281$	−26.5571	−1.58426	−0.792132	−	0.610350i	$-0.791029\pi$
$281$	−26.5571	−1.58426	−0.792132	+	0.610350i	$0.791029\pi$
$282$	0	0
$283$	0.809120	0.0480972	0.0240486	−	0.999711i	$-0.492344\pi$
$283$	0.809120	0.0480972	0.0240486	+	0.999711i	$0.492344\pi$
$284$	−46.7926	−2.77663
$285$	0	0
$286$	3.79508	0.224408
$287$	0	0
$288$	0	0
$289$	7.04814	0.414597
$290$	5.26685	0.309280
$291$	0	0
$292$	41.9007	2.45205
$293$	−7.99747	−0.467217	−0.233609	−	0.972331i	$-0.575053\pi$
$293$	−7.99747	−0.467217	−0.233609	+	0.972331i	$0.575053\pi$
$294$	0	0
$295$	−1.85764	−0.108156
$296$	−113.096	−6.57355
$297$	0	0
$298$	−37.0355	−2.14541
$299$	5.39075	0.311755
$300$	0	0
$301$	0	0
$302$	38.1202	2.19357
$303$	0	0
$304$	−23.9925	−1.37607
$305$	−4.43981	−0.254223
$306$	0	0
$307$	11.4417	0.653011	0.326505	−	0.945195i	$-0.394129\pi$
$307$	11.4417	0.653011	0.326505	+	0.945195i	$0.394129\pi$
$308$	0	0
$309$	0	0
$310$	−5.69128	−0.323243
$311$	−22.7406	−1.28950	−0.644752	−	0.764392i	$-0.723039\pi$
$311$	−22.7406	−1.28950	−0.644752	+	0.764392i	$0.723039\pi$
$312$	0	0
$313$	7.11425	0.402121	0.201060	−	0.979579i	$-0.435561\pi$
$313$	7.11425	0.402121	0.201060	+	0.979579i	$0.435561\pi$
$314$	47.1310	2.65976
$315$	0	0
$316$	41.4844	2.33368
$317$	13.8772	0.779420	0.389710	−	0.920938i	$-0.372575\pi$
$317$	13.8772	0.779420	0.389710	+	0.920938i	$0.372575\pi$
$318$	0	0
$319$	−8.67717	−0.485828
$320$	−11.5845	−0.647591
$321$	0	0
$322$	0	0
$323$	7.04033	0.391734
$324$	0	0
$325$	−4.90956	−0.272333
$326$	9.68024	0.536139
$327$	0	0
$328$	3.41150	0.188368
$329$	0	0
$330$	0	0
$331$	34.0955	1.87406	0.937030	−	0.349250i	$-0.113563\pi$
$331$	34.0955	1.87406	0.937030	+	0.349250i	$0.113563\pi$
$332$	66.7703	3.66450
$333$	0	0
$334$	−0.959224	−0.0524864
$335$	4.16667	0.227649
$336$	0	0
$337$	9.29553	0.506360	0.253180	−	0.967419i	$-0.418524\pi$
$337$	9.29553	0.506360	0.253180	+	0.967419i	$0.418524\pi$
$338$	−2.76760	−0.150537
$339$	0	0
$340$	8.34667	0.452662
$341$	9.37643	0.507762
$342$	0	0
$343$	0	0
$344$	−19.0293	−1.02599
$345$	0	0
$346$	70.8989	3.81155
$347$	−12.5628	−0.674406	−0.337203	−	0.941432i	$-0.609481\pi$
$347$	−12.5628	−0.674406	−0.337203	+	0.941432i	$0.609481\pi$
$348$	0	0
$349$	−9.47575	−0.507225	−0.253613	−	0.967306i	$-0.581619\pi$
$349$	−9.47575	−0.507225	−0.253613	+	0.967306i	$0.581619\pi$
$350$	0	0
$351$	0	0
$352$	35.6458	1.89993
$353$	−8.10619	−0.431449	−0.215724	−	0.976454i	$-0.569211\pi$
$353$	−8.10619	−0.431449	−0.215724	+	0.976454i	$0.569211\pi$
$354$	0	0
$355$	2.48645	0.131967
$356$	73.3561	3.88786
$357$	0	0
$358$	−16.4544	−0.869641
$359$	21.0782	1.11246	0.556232	−	0.831027i	$-0.312247\pi$
$359$	21.0782	1.11246	0.556232	+	0.831027i	$0.312247\pi$
$360$	0	0
$361$	−16.9389	−0.891520
$362$	−0.0872218	−0.00458428
$363$	0	0
$364$	0	0
$365$	−2.22650	−0.116540
$366$	0	0
$367$	−28.2036	−1.47221	−0.736107	−	0.676865i	$-0.763338\pi$
$367$	−28.2036	−1.47221	−0.736107	+	0.676865i	$0.763338\pi$
$368$	90.0893	4.69623
$369$	0	0
$370$	9.29394	0.483169
$371$	0	0
$372$	0	0
$373$	35.6733	1.84709	0.923546	−	0.383488i	$-0.125277\pi$
$373$	35.6733	1.84709	0.923546	+	0.383488i	$0.125277\pi$
$374$	−18.6106	−0.962333
$375$	0	0
$376$	122.351	6.30976
$377$	6.32791	0.325904
$378$	0	0
$379$	13.7416	0.705861	0.352930	−	0.935650i	$-0.385185\pi$
$379$	13.7416	0.705861	0.352930	+	0.935650i	$0.385185\pi$
$380$	2.44357	0.125352
$381$	0	0
$382$	23.1804	1.18601
$383$	−12.5163	−0.639555	−0.319777	−	0.947493i	$-0.603608\pi$
$383$	−12.5163	−0.639555	−0.319777	+	0.947493i	$0.603608\pi$
$384$	0	0
$385$	0	0
$386$	25.4345	1.29458
$387$	0	0
$388$	−58.5493	−2.97239
$389$	8.67596	0.439889	0.219944	−	0.975512i	$-0.429412\pi$
$389$	8.67596	0.439889	0.219944	+	0.975512i	$0.429412\pi$
$390$	0	0
$391$	−26.4357	−1.33691
$392$	0	0
$393$	0	0
$394$	56.6624	2.85461
$395$	−2.20438	−0.110915
$396$	0	0
$397$	−32.3282	−1.62251	−0.811253	−	0.584696i	$-0.801214\pi$
$397$	−32.3282	−1.62251	−0.811253	+	0.584696i	$0.801214\pi$
$398$	−9.19495	−0.460901
$399$	0	0
$400$	−82.0477	−4.10238
$401$	−32.3111	−1.61354	−0.806769	−	0.590867i	$-0.798786\pi$
$401$	−32.3111	−1.61354	−0.806769	+	0.590867i	$0.798786\pi$
$402$	0	0
$403$	−6.83785	−0.340618
$404$	−10.2108	−0.508008
$405$	0	0
$406$	0	0
$407$	−15.3118	−0.758980
$408$	0	0
$409$	−7.13464	−0.352785	−0.176393	−	0.984320i	$-0.556443\pi$
$409$	−7.13464	−0.352785	−0.176393	+	0.984320i	$0.556443\pi$
$410$	−0.280349	−0.0138455
$411$	0	0
$412$	−44.4970	−2.19221
$413$	0	0
$414$	0	0
$415$	−3.54801	−0.174165
$416$	−25.9951	−1.27451
$417$	0	0
$418$	−5.44845	−0.266492
$419$	19.2416	0.940014	0.470007	−	0.882663i	$-0.344251\pi$
$419$	19.2416	0.940014	0.470007	+	0.882663i	$0.344251\pi$
$420$	0	0
$421$	−2.32354	−0.113242	−0.0566212	−	0.998396i	$-0.518033\pi$
$421$	−2.32354	−0.113242	−0.0566212	+	0.998396i	$0.518033\pi$
$422$	−43.2605	−2.10589
$423$	0	0
$424$	−38.5497	−1.87214
$425$	24.0759	1.16785
$426$	0	0
$427$	0	0
$428$	1.63971	0.0792585
$429$	0	0
$430$	1.56379	0.0754124
$431$	−3.10556	−0.149590	−0.0747949	−	0.997199i	$-0.523830\pi$
$431$	−3.10556	−0.149590	−0.0747949	+	0.997199i	$0.523830\pi$
$432$	0	0
$433$	−9.44212	−0.453759	−0.226880	−	0.973923i	$-0.572852\pi$
$433$	−9.44212	−0.453759	−0.226880	+	0.973923i	$0.572852\pi$
$434$	0	0
$435$	0	0
$436$	−29.2646	−1.40152
$437$	−7.73929	−0.370221
$438$	0	0
$439$	−1.57016	−0.0749396	−0.0374698	−	0.999298i	$-0.511930\pi$
$439$	−1.57016	−0.0749396	−0.0374698	+	0.999298i	$0.511930\pi$
$440$	−4.17677	−0.199120
$441$	0	0
$442$	13.5720	0.645554
$443$	14.7632	0.701423	0.350712	−	0.936484i	$-0.385940\pi$
$443$	14.7632	0.701423	0.350712	+	0.936484i	$0.385940\pi$
$444$	0	0
$445$	−3.89797	−0.184781
$446$	24.7442	1.17167
$447$	0	0
$448$	0	0
$449$	−4.40580	−0.207923	−0.103961	−	0.994581i	$-0.533152\pi$
$449$	−4.40580	−0.207923	−0.103961	+	0.994581i	$0.533152\pi$
$450$	0	0
$451$	0.461877	0.0217489
$452$	19.8760	0.934888
$453$	0	0
$454$	47.6580	2.23670
$455$	0	0
$456$	0	0
$457$	−13.9992	−0.654855	−0.327427	−	0.944876i	$-0.606182\pi$
$457$	−13.9992	−0.654855	−0.327427	+	0.944876i	$0.606182\pi$
$458$	47.1212	2.20183
$459$	0	0
$460$	−9.17534	−0.427802
$461$	−7.09480	−0.330438	−0.165219	−	0.986257i	$-0.552833\pi$
$461$	−7.09480	−0.330438	−0.165219	+	0.986257i	$0.552833\pi$
$462$	0	0
$463$	−8.31974	−0.386651	−0.193325	−	0.981135i	$-0.561927\pi$
$463$	−8.31974	−0.386651	−0.193325	+	0.981135i	$0.561927\pi$
$464$	105.751	4.90937
$465$	0	0
$466$	14.2033	0.657953
$467$	−21.5945	−0.999273	−0.499637	−	0.866235i	$-0.666533\pi$
$467$	−21.5945	−0.999273	−0.499637	+	0.866235i	$0.666533\pi$
$468$	0	0
$469$	0	0
$470$	−10.0545	−0.463780
$471$	0	0
$472$	−62.5620	−2.87965
$473$	−2.57635	−0.118461
$474$	0	0
$475$	7.04846	0.323406
$476$	0	0
$477$	0	0
$478$	−38.9045	−1.77945
$479$	−27.9605	−1.27755	−0.638774	−	0.769394i	$-0.720558\pi$
$479$	−27.9605	−1.27755	−0.638774	+	0.769394i	$0.720558\pi$
$480$	0	0
$481$	11.1663	0.509140
$482$	−47.1622	−2.14818
$483$	0	0
$484$	−51.6136	−2.34607
$485$	3.11117	0.141271
$486$	0	0
$487$	−29.8107	−1.35085	−0.675426	−	0.737428i	$-0.736040\pi$
$487$	−29.8107	−1.35085	−0.675426	+	0.737428i	$0.736040\pi$
$488$	−149.525	−6.76867
$489$	0	0
$490$	0	0
$491$	−14.1885	−0.640317	−0.320158	−	0.947364i	$-0.603736\pi$
$491$	−14.1885	−0.640317	−0.320158	+	0.947364i	$0.603736\pi$
$492$	0	0
$493$	−31.0314	−1.39758
$494$	3.97333	0.178769
$495$	0	0
$496$	−114.273	−5.13101
$497$	0	0
$498$	0	0
$499$	13.9590	0.624890	0.312445	−	0.949936i	$-0.398852\pi$
$499$	13.9590	0.624890	0.312445	+	0.949936i	$0.398852\pi$
$500$	16.8666	0.754296
$501$	0	0
$502$	−66.6641	−2.97536
$503$	12.8280	0.571970	0.285985	−	0.958234i	$-0.407679\pi$
$503$	12.8280	0.571970	0.285985	+	0.958234i	$0.407679\pi$
$504$	0	0
$505$	0.542579	0.0241445
$506$	20.4583	0.909483
$507$	0	0
$508$	−43.0581	−1.91040
$509$	−17.8726	−0.792188	−0.396094	−	0.918210i	$-0.629635\pi$
$509$	−17.8726	−0.792188	−0.396094	+	0.918210i	$0.629635\pi$
$510$	0	0
$511$	0	0
$512$	−95.9004	−4.23824
$513$	0	0
$514$	48.3792	2.13391
$515$	2.36446	0.104191
$516$	0	0
$517$	16.5649	0.728523
$518$	0	0
$519$	0	0
$520$	3.04595	0.133574
$521$	−7.43448	−0.325710	−0.162855	−	0.986650i	$-0.552070\pi$
$521$	−7.43448	−0.325710	−0.162855	+	0.986650i	$0.552070\pi$
$522$	0	0
$523$	17.7032	0.774105	0.387052	−	0.922058i	$-0.373493\pi$
$523$	17.7032	0.774105	0.387052	+	0.922058i	$0.373493\pi$
$524$	−19.2804	−0.842267
$525$	0	0
$526$	−17.9554	−0.782895
$527$	33.5321	1.46068
$528$	0	0
$529$	6.06020	0.263487
$530$	3.16793	0.137606
$531$	0	0
$532$	0	0
$533$	−0.336828	−0.0145897
$534$	0	0
$535$	−0.0871304	−0.00376697
$536$	140.326	6.06115
$537$	0	0
$538$	−57.0469	−2.45947
$539$	0	0
$540$	0	0
$541$	−5.50862	−0.236834	−0.118417	−	0.992964i	$-0.537782\pi$
$541$	−5.50862	−0.236834	−0.118417	+	0.992964i	$0.537782\pi$
$542$	−1.98184	−0.0851275
$543$	0	0
$544$	127.477	5.46553
$545$	1.55505	0.0666110
$546$	0	0
$547$	−21.7824	−0.931350	−0.465675	−	0.884956i	$-0.654188\pi$
$547$	−21.7824	−0.931350	−0.465675	+	0.884956i	$0.654188\pi$
$548$	34.5669	1.47663
$549$	0	0
$550$	−18.6321	−0.794478
$551$	−9.08474	−0.387023
$552$	0	0
$553$	0	0
$554$	−49.4220	−2.09974
$555$	0	0
$556$	−104.035	−4.41208
$557$	−24.4012	−1.03391	−0.516957	−	0.856012i	$-0.672935\pi$
$557$	−24.4012	−1.03391	−0.516957	+	0.856012i	$0.672935\pi$
$558$	0	0
$559$	1.87883	0.0794659
$560$	0	0
$561$	0	0
$562$	73.4994	3.10038
$563$	43.9719	1.85320	0.926598	−	0.376054i	$-0.122719\pi$
$563$	43.9719	1.85320	0.926598	+	0.376054i	$0.122719\pi$
$564$	0	0
$565$	−1.05616	−0.0444331
$566$	−2.23932	−0.0941256
$567$	0	0
$568$	83.7390	3.51361
$569$	−38.5378	−1.61559	−0.807794	−	0.589465i	$-0.799338\pi$
$569$	−38.5378	−1.61559	−0.807794	+	0.589465i	$0.799338\pi$
$570$	0	0
$571$	39.4963	1.65287	0.826434	−	0.563034i	$-0.190366\pi$
$571$	39.4963	1.65287	0.826434	+	0.563034i	$0.190366\pi$
$572$	−7.76074	−0.324493
$573$	0	0
$574$	0	0
$575$	−26.4662	−1.10372
$576$	0	0
$577$	−6.83588	−0.284581	−0.142291	−	0.989825i	$-0.545447\pi$
$577$	−6.83588	−0.284581	−0.142291	+	0.989825i	$0.545447\pi$
$578$	−19.5064	−0.811360
$579$	0	0
$580$	−10.7704	−0.447218
$581$	0	0
$582$	0	0
$583$	−5.21919	−0.216157
$584$	−74.9845	−3.10288
$585$	0	0
$586$	22.1338	0.914338
$587$	−28.7848	−1.18807	−0.594037	−	0.804438i	$-0.702467\pi$
$587$	−28.7848	−1.18807	−0.594037	+	0.804438i	$0.702467\pi$
$588$	0	0
$589$	9.81684	0.404496
$590$	5.14120	0.211660
$591$	0	0
$592$	186.610	7.66960
$593$	−31.8353	−1.30732	−0.653661	−	0.756788i	$-0.726768\pi$
$593$	−31.8353	−1.30732	−0.653661	+	0.756788i	$0.726768\pi$
$594$	0	0
$595$	0	0
$596$	75.7358	3.10226
$597$	0	0
$598$	−14.9194	−0.610101
$599$	−35.5556	−1.45276	−0.726381	−	0.687292i	$-0.758799\pi$
$599$	−35.5556	−1.45276	−0.726381	+	0.687292i	$0.758799\pi$
$600$	0	0
$601$	24.7299	1.00875	0.504376	−	0.863484i	$-0.331723\pi$
$601$	24.7299	1.00875	0.504376	+	0.863484i	$0.331723\pi$
$602$	0	0
$603$	0	0
$604$	−77.9538	−3.17190
$605$	2.74262	0.111503
$606$	0	0
$607$	−40.0051	−1.62376	−0.811878	−	0.583827i	$-0.801555\pi$
$607$	−40.0051	−1.62376	−0.811878	+	0.583827i	$0.801555\pi$
$608$	37.3201	1.51353
$609$	0	0
$610$	12.2876	0.497511
$611$	−12.0801	−0.488709
$612$	0	0
$613$	−1.35914	−0.0548951	−0.0274475	−	0.999623i	$-0.508738\pi$
$613$	−1.35914	−0.0548951	−0.0274475	+	0.999623i	$0.508738\pi$
$614$	−31.6659	−1.27793
$615$	0	0
$616$	0	0
$617$	−30.7080	−1.23626	−0.618129	−	0.786076i	$-0.712109\pi$
$617$	−30.7080	−1.23626	−0.618129	+	0.786076i	$0.712109\pi$
$618$	0	0
$619$	−9.38209	−0.377098	−0.188549	−	0.982064i	$-0.560378\pi$
$619$	−9.38209	−0.377098	−0.188549	+	0.982064i	$0.560378\pi$
$620$	11.6384	0.467408
$621$	0	0
$622$	62.9369	2.52354
$623$	0	0
$624$	0	0
$625$	23.6515	0.946061
$626$	−19.6894	−0.786945
$627$	0	0
$628$	−96.3805	−3.84600
$629$	−54.7584	−2.18336
$630$	0	0
$631$	24.0739	0.958365	0.479183	−	0.877715i	$-0.340933\pi$
$631$	24.0739	0.958365	0.479183	+	0.877715i	$0.340933\pi$
$632$	−74.2397	−2.95310
$633$	0	0
$634$	−38.4064	−1.52531
$635$	2.28801	0.0907967
$636$	0	0
$637$	0	0
$638$	24.0149	0.950760
$639$	0	0
$640$	16.4257	0.649284
$641$	−14.5716	−0.575545	−0.287772	−	0.957699i	$-0.592915\pi$
$641$	−14.5716	−0.575545	−0.287772	+	0.957699i	$0.592915\pi$
$642$	0	0
$643$	−3.38618	−0.133538	−0.0667689	−	0.997768i	$-0.521269\pi$
$643$	−3.38618	−0.133538	−0.0667689	+	0.997768i	$0.521269\pi$
$644$	0	0
$645$	0	0
$646$	−19.4848	−0.766619
$647$	−38.7553	−1.52363	−0.761814	−	0.647796i	$-0.775691\pi$
$647$	−38.7553	−1.52363	−0.761814	+	0.647796i	$0.775691\pi$
$648$	0	0
$649$	−8.47017	−0.332483
$650$	13.5877	0.532953
$651$	0	0
$652$	−19.7956	−0.775256
$653$	14.4416	0.565143	0.282572	−	0.959246i	$-0.408812\pi$
$653$	14.4416	0.565143	0.282572	+	0.959246i	$0.408812\pi$
$654$	0	0
$655$	1.02451	0.0400310
$656$	−5.62902	−0.219776
$657$	0	0
$658$	0	0
$659$	6.41732	0.249983	0.124992	−	0.992158i	$-0.460110\pi$
$659$	6.41732	0.249983	0.124992	+	0.992158i	$0.460110\pi$
$660$	0	0
$661$	−13.5934	−0.528724	−0.264362	−	0.964424i	$-0.585161\pi$
$661$	−13.5934	−0.528724	−0.264362	+	0.964424i	$0.585161\pi$
$662$	−94.3627	−3.66751
$663$	0	0
$664$	−119.491	−4.63714
$665$	0	0
$666$	0	0
$667$	34.1122	1.32083
$668$	1.96156	0.0758952
$669$	0	0
$670$	−11.5317	−0.445507
$671$	−20.2439	−0.781509
$672$	0	0
$673$	26.2209	1.01074	0.505370	−	0.862903i	$-0.331356\pi$
$673$	26.2209	1.01074	0.505370	+	0.862903i	$0.331356\pi$
$674$	−25.7263	−0.990940
$675$	0	0
$676$	5.65960	0.217677
$677$	6.21306	0.238787	0.119394	−	0.992847i	$-0.461905\pi$
$677$	6.21306	0.238787	0.119394	+	0.992847i	$0.461905\pi$
$678$	0	0
$679$	0	0
$680$	−14.9370	−0.572809
$681$	0	0
$682$	−25.9502	−0.993684
$683$	0.442054	0.0169147	0.00845737	−	0.999964i	$-0.497308\pi$
$683$	0.442054	0.0169147	0.00845737	+	0.999964i	$0.497308\pi$
$684$	0	0
$685$	−1.83680	−0.0701806
$686$	0	0
$687$	0	0
$688$	31.3987	1.19706
$689$	3.80614	0.145002
$690$	0	0
$691$	−42.9959	−1.63564	−0.817820	−	0.575473i	$-0.804818\pi$
$691$	−42.9959	−1.63564	−0.817820	+	0.575473i	$0.804818\pi$
$692$	−144.985	−5.51149
$693$	0	0
$694$	34.7687	1.31980
$695$	5.52819	0.209696
$696$	0	0
$697$	1.65177	0.0625652
$698$	26.2250	0.992633
$699$	0	0
$700$	0	0
$701$	48.5342	1.83311	0.916556	−	0.399907i	$-0.130958\pi$
$701$	48.5342	1.83311	0.916556	+	0.399907i	$0.130958\pi$
$702$	0	0
$703$	−16.0310	−0.604622
$704$	−52.8209	−1.99076
$705$	0	0
$706$	22.4347	0.844340
$707$	0	0
$708$	0	0
$709$	−0.877116	−0.0329408	−0.0164704	−	0.999864i	$-0.505243\pi$
$709$	−0.877116	−0.0329408	−0.0164704	+	0.999864i	$0.505243\pi$
$710$	−6.88148	−0.258257
$711$	0	0
$712$	−131.276	−4.91979
$713$	−36.8612	−1.38046
$714$	0	0
$715$	0.412387	0.0154224
$716$	33.6484	1.25750
$717$	0	0
$718$	−58.3359	−2.17708
$719$	−3.44345	−0.128419	−0.0642096	−	0.997936i	$-0.520453\pi$
$719$	−3.44345	−0.128419	−0.0642096	+	0.997936i	$0.520453\pi$
$720$	0	0
$721$	0	0
$722$	46.8800	1.74469
$723$	0	0
$724$	0.178364	0.00662885
$725$	−31.0673	−1.15381
$726$	0	0
$727$	−41.4681	−1.53797	−0.768983	−	0.639270i	$-0.779237\pi$
$727$	−41.4681	−1.53797	−0.768983	+	0.639270i	$0.779237\pi$
$728$	0	0
$729$	0	0
$730$	6.16206	0.228068
$731$	−9.21356	−0.340776
$732$	0	0
$733$	12.7537	0.471068	0.235534	−	0.971866i	$-0.424316\pi$
$733$	12.7537	0.471068	0.235534	+	0.971866i	$0.424316\pi$
$734$	78.0561	2.88110
$735$	0	0
$736$	−140.133	−5.16537
$737$	18.9985	0.699818
$738$	0	0
$739$	−5.20836	−0.191593	−0.0957963	−	0.995401i	$-0.530540\pi$
$739$	−5.20836	−0.191593	−0.0957963	+	0.995401i	$0.530540\pi$
$740$	−19.0056	−0.698661
$741$	0	0
$742$	0	0
$743$	0.428948	0.0157366	0.00786829	−	0.999969i	$-0.497495\pi$
$743$	0.428948	0.0157366	0.00786829	+	0.999969i	$0.497495\pi$
$744$	0	0
$745$	−4.02442	−0.147443
$746$	−98.7292	−3.61473
$747$	0	0
$748$	38.0578	1.39153
$749$	0	0
$750$	0	0
$751$	−28.9132	−1.05506	−0.527528	−	0.849537i	$-0.676881\pi$
$751$	−28.9132	−1.05506	−0.527528	+	0.849537i	$0.676881\pi$
$752$	−201.881	−7.36184
$753$	0	0
$754$	−17.5131	−0.637790
$755$	4.14228	0.150753
$756$	0	0
$757$	14.2735	0.518779	0.259390	−	0.965773i	$-0.416479\pi$
$757$	14.2735	0.518779	0.259390	+	0.965773i	$0.416479\pi$
$758$	−38.0313	−1.38136
$759$	0	0
$760$	−4.37296	−0.158624
$761$	−0.825567	−0.0299268	−0.0149634	−	0.999888i	$-0.504763\pi$
$761$	−0.825567	−0.0299268	−0.0149634	+	0.999888i	$0.504763\pi$
$762$	0	0
$763$	0	0
$764$	−47.4028	−1.71497
$765$	0	0
$766$	34.6402	1.25160
$767$	6.17696	0.223037
$768$	0	0
$769$	22.1934	0.800315	0.400157	−	0.916446i	$-0.368955\pi$
$769$	22.1934	0.800315	0.400157	+	0.916446i	$0.368955\pi$
$770$	0	0
$771$	0	0
$772$	−52.0123	−1.87196
$773$	19.1972	0.690475	0.345237	−	0.938515i	$-0.387798\pi$
$773$	19.1972	0.690475	0.345237	+	0.938515i	$0.387798\pi$
$774$	0	0
$775$	33.5708	1.20590
$776$	104.779	3.76133
$777$	0	0
$778$	−24.0116	−0.860856
$779$	0.483572	0.0173258
$780$	0	0
$781$	11.3373	0.405680
$782$	73.1632	2.61631
$783$	0	0
$784$	0	0
$785$	5.12143	0.182792
$786$	0	0
$787$	−3.24209	−0.115568	−0.0577839	−	0.998329i	$-0.518403\pi$
$787$	−3.24209	−0.115568	−0.0577839	+	0.998329i	$0.518403\pi$
$788$	−115.872	−4.12776
$789$	0	0
$790$	6.10085	0.217058
$791$	0	0
$792$	0	0
$793$	14.7631	0.524253
$794$	89.4714	3.17522
$795$	0	0
$796$	18.8032	0.666462
$797$	−34.4401	−1.21993	−0.609966	−	0.792427i	$-0.708817\pi$
$797$	−34.4401	−1.21993	−0.609966	+	0.792427i	$0.708817\pi$
$798$	0	0
$799$	59.2395	2.09574
$800$	127.624	4.51220
$801$	0	0
$802$	89.4241	3.15767
$803$	−10.1520	−0.358258
$804$	0	0
$805$	0	0
$806$	18.9244	0.666584
$807$	0	0
$808$	18.2731	0.642845
$809$	−21.4461	−0.754003	−0.377002	−	0.926213i	$-0.623045\pi$
$809$	−21.4461	−0.754003	−0.377002	+	0.926213i	$0.623045\pi$
$810$	0	0
$811$	−18.0094	−0.632395	−0.316197	−	0.948693i	$-0.602406\pi$
$811$	−18.0094	−0.632395	−0.316197	+	0.948693i	$0.602406\pi$
$812$	0	0
$813$	0	0
$814$	42.3770	1.48531
$815$	1.05189	0.0368461
$816$	0	0
$817$	−2.69736	−0.0943687
$818$	19.7458	0.690396
$819$	0	0
$820$	0.573299	0.0200205
$821$	−37.3332	−1.30294	−0.651468	−	0.758676i	$-0.725847\pi$
$821$	−37.3332	−1.30294	−0.651468	+	0.758676i	$0.725847\pi$
$822$	0	0
$823$	−21.7988	−0.759860	−0.379930	−	0.925015i	$-0.624052\pi$
$823$	−21.7988	−0.759860	−0.379930	+	0.925015i	$0.624052\pi$
$824$	79.6309	2.77407
$825$	0	0
$826$	0	0
$827$	15.0268	0.522532	0.261266	−	0.965267i	$-0.415860\pi$
$827$	15.0268	0.522532	0.261266	+	0.965267i	$0.415860\pi$
$828$	0	0
$829$	37.3946	1.29877	0.649384	−	0.760461i	$-0.275027\pi$
$829$	37.3946	1.29877	0.649384	+	0.760461i	$0.275027\pi$
$830$	9.81948	0.340839
$831$	0	0
$832$	38.5202	1.33545
$833$	0	0
$834$	0	0
$835$	−0.104233	−0.00360712
$836$	11.1418	0.385347
$837$	0	0
$838$	−53.2530	−1.83960
$839$	−12.0547	−0.416173	−0.208087	−	0.978110i	$-0.566724\pi$
$839$	−12.0547	−0.416173	−0.208087	+	0.978110i	$0.566724\pi$
$840$	0	0
$841$	11.0425	0.380776
$842$	6.43062	0.221614
$843$	0	0
$844$	88.4656	3.04511
$845$	−0.300737	−0.0103457
$846$	0	0
$847$	0	0
$848$	63.6076	2.18429
$849$	0	0
$850$	−66.6325	−2.28548
$851$	60.1948	2.06345
$852$	0	0
$853$	21.4727	0.735210	0.367605	−	0.929982i	$-0.380178\pi$
$853$	21.4727	0.735210	0.367605	+	0.929982i	$0.380178\pi$
$854$	0	0
$855$	0	0
$856$	−2.93439	−0.100295
$857$	41.3842	1.41366	0.706829	−	0.707384i	$-0.250125\pi$
$857$	41.3842	1.41366	0.706829	+	0.707384i	$0.250125\pi$
$858$	0	0
$859$	−21.1788	−0.722613	−0.361306	−	0.932447i	$-0.617669\pi$
$859$	−21.1788	−0.722613	−0.361306	+	0.932447i	$0.617669\pi$
$860$	−3.19786	−0.109046
$861$	0	0
$862$	8.59495	0.292745
$863$	−13.5164	−0.460102	−0.230051	−	0.973179i	$-0.573889\pi$
$863$	−13.5164	−0.460102	−0.230051	+	0.973179i	$0.573889\pi$
$864$	0	0
$865$	7.70413	0.261948
$866$	26.1320	0.888001
$867$	0	0
$868$	0	0
$869$	−10.0512	−0.340963
$870$	0	0
$871$	−13.8548	−0.469453
$872$	52.3713	1.77352
$873$	0	0
$874$	21.4192	0.724517
$875$	0	0
$876$	0	0
$877$	4.17386	0.140941	0.0704707	−	0.997514i	$-0.477550\pi$
$877$	4.17386	0.140941	0.0704707	+	0.997514i	$0.477550\pi$
$878$	4.34557	0.146656
$879$	0	0
$880$	6.89174	0.232321
$881$	−27.0339	−0.910796	−0.455398	−	0.890288i	$-0.650503\pi$
$881$	−27.0339	−0.910796	−0.455398	+	0.890288i	$0.650503\pi$
$882$	0	0
$883$	−38.7597	−1.30437	−0.652184	−	0.758061i	$-0.726147\pi$
$883$	−38.7597	−1.30437	−0.652184	+	0.758061i	$0.726147\pi$
$884$	−27.7540	−0.933469
$885$	0	0
$886$	−40.8587	−1.37268
$887$	−38.3146	−1.28648	−0.643239	−	0.765665i	$-0.722410\pi$
$887$	−38.3146	−1.28648	−0.643239	+	0.765665i	$0.722410\pi$
$888$	0	0
$889$	0	0
$890$	10.7880	0.361615
$891$	0	0
$892$	−50.6007	−1.69424
$893$	17.3429	0.580360
$894$	0	0
$895$	−1.78799	−0.0597660
$896$	0	0
$897$	0	0
$898$	12.1935	0.406902
$899$	−43.2693	−1.44311
$900$	0	0
$901$	−18.6649	−0.621818
$902$	−1.27829	−0.0425624
$903$	0	0
$904$	−35.5696	−1.18303
$905$	−0.00947784	−0.000315054 0
$906$	0	0
$907$	−13.6069	−0.451810	−0.225905	−	0.974149i	$-0.572534\pi$
$907$	−13.6069	−0.451810	−0.225905	+	0.974149i	$0.572534\pi$
$908$	−97.4583	−3.23427
$909$	0	0
$910$	0	0
$911$	−42.2522	−1.39988	−0.699938	−	0.714203i	$-0.746789\pi$
$911$	−42.2522	−1.39988	−0.699938	+	0.714203i	$0.746789\pi$
$912$	0	0
$913$	−16.1777	−0.535403
$914$	38.7441	1.28154
$915$	0	0
$916$	−96.3604	−3.18384
$917$	0	0
$918$	0	0
$919$	−18.3335	−0.604766	−0.302383	−	0.953187i	$-0.597782\pi$
$919$	−18.3335	−0.604766	−0.302383	+	0.953187i	$0.597782\pi$
$920$	16.4200	0.541351
$921$	0	0
$922$	19.6355	0.646662
$923$	−8.26783	−0.272139
$924$	0	0
$925$	−54.8216	−1.80252
$926$	23.0257	0.756671
$927$	0	0
$928$	−164.494	−5.39979
$929$	27.3739	0.898108	0.449054	−	0.893505i	$-0.351761\pi$
$929$	27.3739	0.898108	0.449054	+	0.893505i	$0.351761\pi$
$930$	0	0
$931$	0	0
$932$	−29.0449	−0.951398
$933$	0	0
$934$	59.7648	1.95556
$935$	−2.02230	−0.0661363
$936$	0	0
$937$	30.1225	0.984061	0.492030	−	0.870578i	$-0.336255\pi$
$937$	30.1225	0.984061	0.492030	+	0.870578i	$0.336255\pi$
$938$	0	0
$939$	0	0
$940$	20.5610	0.670625
$941$	6.30741	0.205616	0.102808	−	0.994701i	$-0.467217\pi$
$941$	6.30741	0.205616	0.102808	+	0.994701i	$0.467217\pi$
$942$	0	0
$943$	−1.81576	−0.0591292
$944$	103.228	3.35979
$945$	0	0
$946$	7.13030	0.231826
$947$	23.0271	0.748280	0.374140	−	0.927372i	$-0.377938\pi$
$947$	23.0271	0.748280	0.374140	+	0.927372i	$0.377938\pi$
$948$	0	0
$949$	7.40347	0.240327
$950$	−19.5073	−0.632900
$951$	0	0
$952$	0	0
$953$	−7.97764	−0.258421	−0.129211	−	0.991617i	$-0.541244\pi$
$953$	−7.97764	−0.258421	−0.129211	+	0.991617i	$0.541244\pi$
$954$	0	0
$955$	2.51887	0.0815087
$956$	79.5578	2.57308
$957$	0	0
$958$	77.3835	2.50015
$959$	0	0
$960$	0	0
$961$	15.7562	0.508265
$962$	−30.9039	−0.996380
$963$	0	0
$964$	96.4443	3.10626
$965$	2.76381	0.0889701
$966$	0	0
$967$	−45.5748	−1.46559	−0.732793	−	0.680452i	$-0.761783\pi$
$967$	−45.5748	−1.46559	−0.732793	+	0.680452i	$0.761783\pi$
$968$	92.3666	2.96877
$969$	0	0
$970$	−8.61047	−0.276465
$971$	−39.0087	−1.25185	−0.625925	−	0.779883i	$-0.715278\pi$
$971$	−39.0087	−1.25185	−0.625925	+	0.779883i	$0.715278\pi$
$972$	0	0
$973$	0	0
$974$	82.5041	2.64360
$975$	0	0
$976$	246.718	7.89726
$977$	−17.5695	−0.562097	−0.281049	−	0.959694i	$-0.590682\pi$
$977$	−17.5695	−0.562097	−0.281049	+	0.959694i	$0.590682\pi$
$978$	0	0
$979$	−17.7733	−0.568038
$980$	0	0
$981$	0	0
$982$	39.2680	1.25309
$983$	−59.5144	−1.89821	−0.949107	−	0.314953i	$-0.898011\pi$
$983$	−59.5144	−1.89821	−0.949107	+	0.314953i	$0.898011\pi$
$984$	0	0
$985$	6.15714	0.196183
$986$	85.8824	2.73505
$987$	0	0
$988$	−8.12526	−0.258499
$989$	10.1283	0.322061
$990$	0	0
$991$	20.5485	0.652744	0.326372	−	0.945241i	$-0.394174\pi$
$991$	20.5485	0.652744	0.326372	+	0.945241i	$0.394174\pi$
$992$	177.750	5.64358
$993$	0	0
$994$	0	0
$995$	−0.999157	−0.0316754
$996$	0	0
$997$	−50.2127	−1.59025	−0.795125	−	0.606445i	$-0.792595\pi$
$997$	−50.2127	−1.59025	−0.795125	+	0.606445i	$0.792595\pi$
$998$	−38.6329	−1.22290
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5733.2.a.bw.1.1		10
3.2	odd	2		1911.2.a.x.1.10	✓	10
7.6	odd	2		5733.2.a.bx.1.1		10
21.20	even	2		1911.2.a.y.1.10	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.2.a.x.1.10	✓	10	3.2	odd	2
1911.2.a.y.1.10	yes	10	21.20	even	2
5733.2.a.bw.1.1		10	1.1	even	1	trivial
5733.2.a.bx.1.1		10	7.6	odd	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)

\(f(q)\)	\(=\)	\(q-2.76760 q^{2} +5.65960 q^{4} -0.300737 q^{5} -10.1283 q^{8} +O(q^{10})\)	\(q-2.76760 q^{2} +5.65960 q^{4} -0.300737 q^{5} -10.1283 q^{8} +0.832320 q^{10} -1.37125 q^{11} +1.00000 q^{13} +16.7118 q^{16} -4.90389 q^{17} -1.43566 q^{19} -1.70205 q^{20} +3.79508 q^{22} +5.39075 q^{23} -4.90956 q^{25} -2.76760 q^{26} +6.32791 q^{29} -6.83785 q^{31} -25.9951 q^{32} +13.5720 q^{34} +11.1663 q^{37} +3.97333 q^{38} +3.04595 q^{40} -0.336828 q^{41} +1.87883 q^{43} -7.76074 q^{44} -14.9194 q^{46} -12.0801 q^{47} +13.5877 q^{50} +5.65960 q^{52} +3.80614 q^{53} +0.412387 q^{55} -17.5131 q^{58} +6.17696 q^{59} +14.7631 q^{61} +18.9244 q^{62} +38.5202 q^{64} -0.300737 q^{65} -13.8548 q^{67} -27.7540 q^{68} -8.26783 q^{71} +7.40347 q^{73} -30.9039 q^{74} -8.12526 q^{76} +7.32993 q^{79} -5.02587 q^{80} +0.932206 q^{82} +11.7977 q^{83} +1.47478 q^{85} -5.19984 q^{86} +13.8884 q^{88} +12.9614 q^{89} +30.5095 q^{92} +33.4329 q^{94} +0.431757 q^{95} -10.3451 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + 16 q^{4} - 6 q^{5} - 12 q^{8}+O(q^{10}) \) 10 * q - 4 * q^2 + 16 * q^4 - 6 * q^5 - 12 * q^8	\( 10 q - 4 q^{2} + 16 q^{4} - 6 q^{5} - 12 q^{8} - 8 q^{10} - 12 q^{11} + 10 q^{13} + 24 q^{16} - 10 q^{19} - 16 q^{20} + 8 q^{22} - 14 q^{23} + 32 q^{25} - 4 q^{26} - 18 q^{29} - 14 q^{31} - 28 q^{32} - 4 q^{34} + 24 q^{37} - 4 q^{38} - 16 q^{40} - 24 q^{41} + 2 q^{43} - 48 q^{44} + 20 q^{46} - 18 q^{47} + 28 q^{50} + 16 q^{52} - 10 q^{53} - 12 q^{55} + 12 q^{58} - 12 q^{59} + 4 q^{61} + 4 q^{62} + 32 q^{64} - 6 q^{65} - 12 q^{67} - 40 q^{68} - 32 q^{71} + 18 q^{73} - 24 q^{74} - 32 q^{76} + 34 q^{79} - 32 q^{80} - 48 q^{82} - 30 q^{83} - 40 q^{86} + 32 q^{88} - 10 q^{89} + 40 q^{92} + 24 q^{94} + 30 q^{95} + 2 q^{97}+O(q^{100}) \) 10 * q - 4 * q^2 + 16 * q^4 - 6 * q^5 - 12 * q^8 - 8 * q^10 - 12 * q^11 + 10 * q^13 + 24 * q^16 - 10 * q^19 - 16 * q^20 + 8 * q^22 - 14 * q^23 + 32 * q^25 - 4 * q^26 - 18 * q^29 - 14 * q^31 - 28 * q^32 - 4 * q^34 + 24 * q^37 - 4 * q^38 - 16 * q^40 - 24 * q^41 + 2 * q^43 - 48 * q^44 + 20 * q^46 - 18 * q^47 + 28 * q^50 + 16 * q^52 - 10 * q^53 - 12 * q^55 + 12 * q^58 - 12 * q^59 + 4 * q^61 + 4 * q^62 + 32 * q^64 - 6 * q^65 - 12 * q^67 - 40 * q^68 - 32 * q^71 + 18 * q^73 - 24 * q^74 - 32 * q^76 + 34 * q^79 - 32 * q^80 - 48 * q^82 - 30 * q^83 - 40 * q^86 + 32 * q^88 - 10 * q^89 + 40 * q^92 + 24 * q^94 + 30 * q^95 + 2 * q^97

Introduction

L-functions

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Database

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