LMFDB - Embedded newform 6498.2.a.ca.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6498,2,Mod(1,6498)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6498, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6498.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6498 = 2 \cdot 3^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6498.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:	$51.8867912334$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 722)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.90211$ of defining polynomial
Character	$\chi$	$=$	6498.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +2.34458 q^{5} -1.28408 q^{7} +1.00000 q^{8} +O(q^{10})$	$q+1.00000 q^{2} +1.00000 q^{4} +2.34458 q^{5} -1.28408 q^{7} +1.00000 q^{8} +2.34458 q^{10} -5.75621 q^{11} -0.304282 q^{13} -1.28408 q^{14} +1.00000 q^{16} -4.18619 q^{17} +2.34458 q^{20} -5.75621 q^{22} +6.47684 q^{23} +0.497039 q^{25} -0.304282 q^{26} -1.28408 q^{28} -3.12756 q^{29} -6.44246 q^{31} +1.00000 q^{32} -4.18619 q^{34} -3.01062 q^{35} +3.97980 q^{37} +2.34458 q^{40} -5.01719 q^{41} -0.989378 q^{43} -5.75621 q^{44} +6.47684 q^{46} +4.39445 q^{47} -5.35114 q^{49} +0.497039 q^{50} -0.304282 q^{52} +3.29064 q^{53} -13.4959 q^{55} -1.28408 q^{56} -3.12756 q^{58} +3.31375 q^{59} -10.9615 q^{61} -6.44246 q^{62} +1.00000 q^{64} -0.713414 q^{65} +4.38081 q^{67} -4.18619 q^{68} -3.01062 q^{70} -4.41570 q^{71} -2.26689 q^{73} +3.97980 q^{74} +7.39144 q^{77} -8.57659 q^{79} +2.34458 q^{80} -5.01719 q^{82} +9.76464 q^{83} -9.81485 q^{85} -0.989378 q^{86} -5.75621 q^{88} -15.0765 q^{89} +0.390723 q^{91} +6.47684 q^{92} +4.39445 q^{94} -17.3522 q^{97} -5.35114 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^7 + 4 * q^8	$ 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{8} + 2 q^{10} - 2 q^{11} - 18 q^{13} - 2 q^{14} + 4 q^{16} - 6 q^{17} + 2 q^{20} - 2 q^{22} + 10 q^{23} + 6 q^{25} - 18 q^{26} - 2 q^{28} - 2 q^{29} - 26 q^{31} + 4 q^{32} - 6 q^{34} - 6 q^{35} - 4 q^{37} + 2 q^{40} - 12 q^{41} - 10 q^{43} - 2 q^{44} + 10 q^{46} + 12 q^{47} - 12 q^{49} + 6 q^{50} - 18 q^{52} + 8 q^{53} - 26 q^{55} - 2 q^{56} - 2 q^{58} - 8 q^{59} - 26 q^{62} + 4 q^{64} - 4 q^{65} - 10 q^{67} - 6 q^{68} - 6 q^{70} - 14 q^{73} - 4 q^{74} - 4 q^{77} - 22 q^{79} + 2 q^{80} - 12 q^{82} + 12 q^{83} - 18 q^{85} - 10 q^{86} - 2 q^{88} - 16 q^{89} + 4 q^{91} + 10 q^{92} + 12 q^{94} - 28 q^{97} - 12 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^7 + 4 * q^8 + 2 * q^10 - 2 * q^11 - 18 * q^13 - 2 * q^14 + 4 * q^16 - 6 * q^17 + 2 * q^20 - 2 * q^22 + 10 * q^23 + 6 * q^25 - 18 * q^26 - 2 * q^28 - 2 * q^29 - 26 * q^31 + 4 * q^32 - 6 * q^34 - 6 * q^35 - 4 * q^37 + 2 * q^40 - 12 * q^41 - 10 * q^43 - 2 * q^44 + 10 * q^46 + 12 * q^47 - 12 * q^49 + 6 * q^50 - 18 * q^52 + 8 * q^53 - 26 * q^55 - 2 * q^56 - 2 * q^58 - 8 * q^59 - 26 * q^62 + 4 * q^64 - 4 * q^65 - 10 * q^67 - 6 * q^68 - 6 * q^70 - 14 * q^73 - 4 * q^74 - 4 * q^77 - 22 * q^79 + 2 * q^80 - 12 * q^82 + 12 * q^83 - 18 * q^85 - 10 * q^86 - 2 * q^88 - 16 * q^89 + 4 * q^91 + 10 * q^92 + 12 * q^94 - 28 * q^97 - 12 * q^98

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	2.34458	1.04853	0.524263	−	0.851556i	$-0.324341\pi$
$5$	2.34458	1.04853	0.524263	+	0.851556i	$0.324341\pi$
$6$	0	0
$7$	−1.28408	−0.485336	−0.242668	−	0.970109i	$-0.578023\pi$
$7$	−1.28408	−0.485336	−0.242668	+	0.970109i	$0.578023\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	2.34458	0.741420
$11$	−5.75621	−1.73556	−0.867782	−	0.496945i	$-0.834455\pi$
$11$	−5.75621	−1.73556	−0.867782	+	0.496945i	$0.834455\pi$
$12$	0	0
$13$	−0.304282	−0.0843928	−0.0421964	−	0.999109i	$-0.513436\pi$
$13$	−0.304282	−0.0843928	−0.0421964	+	0.999109i	$0.513436\pi$
$14$	−1.28408	−0.343185
$15$	0	0
$16$	1.00000	0.250000
$17$	−4.18619	−1.01530	−0.507650	−	0.861563i	$-0.669486\pi$
$17$	−4.18619	−1.01530	−0.507650	+	0.861563i	$0.669486\pi$
$18$	0	0
$19$	0	0
$19$	0	0
$20$	2.34458	0.524263
$21$	0	0
$22$	−5.75621	−1.22723
$23$	6.47684	1.35051	0.675257	−	0.737583i	$-0.264033\pi$
$23$	6.47684	1.35051	0.675257	+	0.737583i	$0.264033\pi$
$24$	0	0
$25$	0.497039	0.0994078
$26$	−0.304282	−0.0596747
$27$	0	0
$28$	−1.28408	−0.242668
$29$	−3.12756	−0.580773	−0.290387	−	0.956909i	$-0.593784\pi$
$29$	−3.12756	−0.580773	−0.290387	+	0.956909i	$0.593784\pi$
$30$	0	0
$31$	−6.44246	−1.15710	−0.578550	−	0.815647i	$-0.696381\pi$
$31$	−6.44246	−1.15710	−0.578550	+	0.815647i	$0.696381\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−4.18619	−0.717926
$35$	−3.01062	−0.508888
$36$	0	0
$37$	3.97980	0.654275	0.327137	−	0.944977i	$-0.393916\pi$
$37$	3.97980	0.654275	0.327137	+	0.944977i	$0.393916\pi$
$38$	0	0
$39$	0	0
$40$	2.34458	0.370710
$41$	−5.01719	−0.783553	−0.391776	−	0.920060i	$-0.628139\pi$
$41$	−5.01719	−0.783553	−0.391776	+	0.920060i	$0.628139\pi$
$42$	0	0
$43$	−0.989378	−0.150879	−0.0754394	−	0.997150i	$-0.524036\pi$
$43$	−0.989378	−0.150879	−0.0754394	+	0.997150i	$0.524036\pi$
$44$	−5.75621	−0.867782
$45$	0	0
$46$	6.47684	0.954957
$47$	4.39445	0.640997	0.320498	−	0.947249i	$-0.396150\pi$
$47$	4.39445	0.640997	0.320498	+	0.947249i	$0.396150\pi$
$48$	0	0
$49$	−5.35114	−0.764449
$50$	0.497039	0.0702919
$51$	0	0
$52$	−0.304282	−0.0421964
$53$	3.29064	0.452005	0.226002	−	0.974127i	$-0.427434\pi$
$53$	3.29064	0.452005	0.226002	+	0.974127i	$0.427434\pi$
$54$	0	0
$55$	−13.4959	−1.81978
$56$	−1.28408	−0.171592
$57$	0	0
$58$	−3.12756	−0.410669
$59$	3.31375	0.431414	0.215707	−	0.976458i	$-0.430794\pi$
$59$	3.31375	0.431414	0.215707	+	0.976458i	$0.430794\pi$
$60$	0	0
$61$	−10.9615	−1.40347	−0.701735	−	0.712438i	$-0.747591\pi$
$61$	−10.9615	−1.40347	−0.701735	+	0.712438i	$0.747591\pi$
$62$	−6.44246	−0.818194
$63$	0	0
$64$	1.00000	0.125000
$65$	−0.713414	−0.0884881
$66$	0	0
$67$	4.38081	0.535202	0.267601	−	0.963530i	$-0.413769\pi$
$67$	4.38081	0.535202	0.267601	+	0.963530i	$0.413769\pi$
$68$	−4.18619	−0.507650
$69$	0	0
$70$	−3.01062	−0.359838
$71$	−4.41570	−0.524047	−0.262023	−	0.965062i	$-0.584390\pi$
$71$	−4.41570	−0.524047	−0.262023	+	0.965062i	$0.584390\pi$
$72$	0	0
$73$	−2.26689	−0.265320	−0.132660	−	0.991162i	$-0.542352\pi$
$73$	−2.26689	−0.265320	−0.132660	+	0.991162i	$0.542352\pi$
$74$	3.97980	0.462642
$75$	0	0
$76$	0	0
$77$	7.39144	0.842332
$78$	0	0
$79$	−8.57659	−0.964941	−0.482471	−	0.875912i	$-0.660261\pi$
$79$	−8.57659	−0.964941	−0.482471	+	0.875912i	$0.660261\pi$
$80$	2.34458	0.262132
$81$	0	0
$82$	−5.01719	−0.554056
$83$	9.76464	1.07181	0.535904	−	0.844279i	$-0.319971\pi$
$83$	9.76464	1.07181	0.535904	+	0.844279i	$0.319971\pi$
$84$	0	0
$85$	−9.81485	−1.06457
$86$	−0.989378	−0.106687
$87$	0	0
$88$	−5.75621	−0.613615
$89$	−15.0765	−1.59811	−0.799055	−	0.601259i	$-0.794666\pi$
$89$	−15.0765	−1.59811	−0.799055	+	0.601259i	$0.794666\pi$
$90$	0	0
$91$	0.390723	0.0409589
$92$	6.47684	0.675257
$93$	0	0
$94$	4.39445	0.453253
$95$	0	0
$96$	0	0
$97$	−17.3522	−1.76185	−0.880924	−	0.473259i	$-0.843078\pi$
$97$	−17.3522	−1.76185	−0.880924	+	0.473259i	$0.843078\pi$
$98$	−5.35114	−0.540547
$99$	0	0
$100$	0.497039	0.0497039
$101$	−3.67667	−0.365842	−0.182921	−	0.983128i	$-0.558555\pi$
$101$	−3.67667	−0.365842	−0.182921	+	0.983128i	$0.558555\pi$
$102$	0	0
$103$	−19.0135	−1.87346	−0.936729	−	0.350055i	$-0.886163\pi$
$103$	−19.0135	−1.87346	−0.936729	+	0.350055i	$0.886163\pi$
$104$	−0.304282	−0.0298374
$105$	0	0
$106$	3.29064	0.319616
$107$	10.0373	0.970340	0.485170	−	0.874420i	$-0.338758\pi$
$107$	10.0373	0.970340	0.485170	+	0.874420i	$0.338758\pi$
$108$	0	0
$109$	8.84348	0.847052	0.423526	−	0.905884i	$-0.360792\pi$
$109$	8.84348	0.847052	0.423526	+	0.905884i	$0.360792\pi$
$110$	−13.4959	−1.28678
$111$	0	0
$112$	−1.28408	−0.121334
$113$	−14.2502	−1.34055	−0.670275	−	0.742113i	$-0.733824\pi$
$113$	−14.2502	−1.34055	−0.670275	+	0.742113i	$0.733824\pi$
$114$	0	0
$115$	15.1854	1.41605
$116$	−3.12756	−0.290387
$117$	0	0
$118$	3.31375	0.305056
$119$	5.37540	0.492762
$120$	0	0
$121$	22.1340	2.01218
$122$	−10.9615	−0.992404
$123$	0	0
$124$	−6.44246	−0.578550
$125$	−10.5575	−0.944295
$126$	0	0
$127$	−2.23015	−0.197893	−0.0989467	−	0.995093i	$-0.531547\pi$
$127$	−2.23015	−0.197893	−0.0989467	+	0.995093i	$0.531547\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−0.713414	−0.0625705
$131$	−1.52265	−0.133035	−0.0665175	−	0.997785i	$-0.521189\pi$
$131$	−1.52265	−0.133035	−0.0665175	+	0.997785i	$0.521189\pi$
$132$	0	0
$133$	0	0
$134$	4.38081	0.378445
$135$	0	0
$136$	−4.18619	−0.358963
$137$	−10.7118	−0.915167	−0.457583	−	0.889167i	$-0.651285\pi$
$137$	−10.7118	−0.915167	−0.457583	+	0.889167i	$0.651285\pi$
$138$	0	0
$139$	−10.8143	−0.917260	−0.458630	−	0.888627i	$-0.651660\pi$
$139$	−10.8143	−0.917260	−0.458630	+	0.888627i	$0.651660\pi$
$140$	−3.01062	−0.254444
$141$	0	0
$142$	−4.41570	−0.370557
$143$	1.75152	0.146469
$144$	0	0
$145$	−7.33280	−0.608956
$146$	−2.26689	−0.187609
$147$	0	0
$148$	3.97980	0.327137
$149$	9.33384	0.764658	0.382329	−	0.924026i	$-0.375122\pi$
$149$	9.33384	0.764658	0.382329	+	0.924026i	$0.375122\pi$
$150$	0	0
$151$	−19.8232	−1.61319	−0.806593	−	0.591107i	$-0.798691\pi$
$151$	−19.8232	−1.61319	−0.806593	+	0.591107i	$0.798691\pi$
$152$	0	0
$153$	0	0
$154$	7.39144	0.595619
$155$	−15.1048	−1.21325
$156$	0	0
$157$	13.8676	1.10676	0.553379	−	0.832930i	$-0.313338\pi$
$157$	13.8676	1.10676	0.553379	+	0.832930i	$0.313338\pi$
$158$	−8.57659	−0.682317
$159$	0	0
$160$	2.34458	0.185355
$161$	−8.31677	−0.655453
$162$	0	0
$163$	14.2496	1.11611	0.558057	−	0.829803i	$-0.311547\pi$
$163$	14.2496	1.11611	0.558057	+	0.829803i	$0.311547\pi$
$164$	−5.01719	−0.391776
$165$	0	0
$166$	9.76464	0.757883
$167$	11.5901	0.896870	0.448435	−	0.893815i	$-0.351982\pi$
$167$	11.5901	0.896870	0.448435	+	0.893815i	$0.351982\pi$
$168$	0	0
$169$	−12.9074	−0.992878
$170$	−9.81485	−0.752764
$171$	0	0
$172$	−0.989378	−0.0754394
$173$	3.98353	0.302862	0.151431	−	0.988468i	$-0.451612\pi$
$173$	3.98353	0.302862	0.151431	+	0.988468i	$0.451612\pi$
$174$	0	0
$175$	−0.638237	−0.0482462
$176$	−5.75621	−0.433891
$177$	0	0
$178$	−15.0765	−1.13003
$179$	−8.45089	−0.631649	−0.315825	−	0.948818i	$-0.602281\pi$
$179$	−8.45089	−0.631649	−0.315825	+	0.948818i	$0.602281\pi$
$180$	0	0
$181$	−8.48526	−0.630705	−0.315352	−	0.948975i	$-0.602123\pi$
$181$	−8.48526	−0.630705	−0.315352	+	0.948975i	$0.602123\pi$
$182$	0.390723	0.0289623
$183$	0	0
$184$	6.47684	0.477479
$185$	9.33094	0.686024
$186$	0	0
$187$	24.0966	1.76212
$188$	4.39445	0.320498
$189$	0	0
$190$	0	0
$191$	22.3790	1.61929	0.809644	−	0.586921i	$-0.199660\pi$
$191$	22.3790	1.61929	0.809644	+	0.586921i	$0.199660\pi$
$192$	0	0
$193$	−7.42811	−0.534687	−0.267344	−	0.963601i	$-0.586146\pi$
$193$	−7.42811	−0.534687	−0.267344	+	0.963601i	$0.586146\pi$
$194$	−17.3522	−1.24581
$195$	0	0
$196$	−5.35114	−0.382224
$197$	−8.53554	−0.608132	−0.304066	−	0.952651i	$-0.598344\pi$
$197$	−8.53554	−0.608132	−0.304066	+	0.952651i	$0.598344\pi$
$198$	0	0
$199$	−6.35926	−0.450796	−0.225398	−	0.974267i	$-0.572368\pi$
$199$	−6.35926	−0.450796	−0.225398	+	0.974267i	$0.572368\pi$
$200$	0.497039	0.0351460
$201$	0	0
$202$	−3.67667	−0.258689
$203$	4.01603	0.281870
$204$	0	0
$205$	−11.7632	−0.821576
$206$	−19.0135	−1.32474
$207$	0	0
$208$	−0.304282	−0.0210982
$209$	0	0
$210$	0	0
$211$	13.9578	0.960894	0.480447	−	0.877024i	$-0.340474\pi$
$211$	13.9578	0.960894	0.480447	+	0.877024i	$0.340474\pi$
$212$	3.29064	0.226002
$213$	0	0
$214$	10.0373	0.686134
$215$	−2.31967	−0.158200
$216$	0	0
$217$	8.27263	0.561583
$218$	8.84348	0.598956
$219$	0	0
$220$	−13.4959	−0.909892
$221$	1.27378	0.0856840
$222$	0	0
$223$	−8.92400	−0.597595	−0.298798	−	0.954317i	$-0.596586\pi$
$223$	−8.92400	−0.597595	−0.298798	+	0.954317i	$0.596586\pi$
$224$	−1.28408	−0.0857961
$225$	0	0
$226$	−14.2502	−0.947912
$227$	−0.659796	−0.0437922	−0.0218961	−	0.999760i	$-0.506970\pi$
$227$	−0.659796	−0.0437922	−0.0218961	+	0.999760i	$0.506970\pi$
$228$	0	0
$229$	−6.97208	−0.460728	−0.230364	−	0.973105i	$-0.573992\pi$
$229$	−6.97208	−0.460728	−0.230364	+	0.973105i	$0.573992\pi$
$230$	15.1854	1.00130
$231$	0	0
$232$	−3.12756	−0.205334
$233$	29.6097	1.93980	0.969898	−	0.243512i	$-0.0782997\pi$
$233$	29.6097	1.93980	0.969898	+	0.243512i	$0.0782997\pi$
$234$	0	0
$235$	10.3031	0.672102
$236$	3.31375	0.215707
$237$	0	0
$238$	5.37540	0.348436
$239$	24.7034	1.59793	0.798965	−	0.601378i	$-0.205381\pi$
$239$	24.7034	1.59793	0.798965	+	0.601378i	$0.205381\pi$
$240$	0	0
$241$	−27.5586	−1.77521	−0.887604	−	0.460607i	$-0.847632\pi$
$241$	−27.5586	−1.77521	−0.887604	+	0.460607i	$0.847632\pi$
$242$	22.1340	1.42283
$243$	0	0
$244$	−10.9615	−0.701735
$245$	−12.5462	−0.801545
$246$	0	0
$247$	0	0
$248$	−6.44246	−0.409097
$249$	0	0
$250$	−10.5575	−0.667717
$251$	2.98855	0.188636	0.0943179	−	0.995542i	$-0.469933\pi$
$251$	2.98855	0.188636	0.0943179	+	0.995542i	$0.469933\pi$
$252$	0	0
$253$	−37.2821	−2.34390
$254$	−2.23015	−0.139932
$255$	0	0
$256$	1.00000	0.0625000
$257$	14.1323	0.881546	0.440773	−	0.897619i	$-0.354704\pi$
$257$	14.1323	0.881546	0.440773	+	0.897619i	$0.354704\pi$
$258$	0	0
$259$	−5.11037	−0.317543
$260$	−0.713414	−0.0442440
$261$	0	0
$262$	−1.52265	−0.0940699
$263$	−7.56887	−0.466717	−0.233358	−	0.972391i	$-0.574971\pi$
$263$	−7.56887	−0.466717	−0.233358	+	0.972391i	$0.574971\pi$
$264$	0	0
$265$	7.71517	0.473939
$266$	0	0
$267$	0	0
$268$	4.38081	0.267601
$269$	−7.67074	−0.467694	−0.233847	−	0.972273i	$-0.575131\pi$
$269$	−7.67074	−0.467694	−0.233847	+	0.972273i	$0.575131\pi$
$270$	0	0
$271$	11.6649	0.708592	0.354296	−	0.935133i	$-0.384721\pi$
$271$	11.6649	0.708592	0.354296	+	0.935133i	$0.384721\pi$
$272$	−4.18619	−0.253825
$273$	0	0
$274$	−10.7118	−0.647121
$275$	−2.86106	−0.172529
$276$	0	0
$277$	27.4405	1.64874	0.824370	−	0.566052i	$-0.191530\pi$
$277$	27.4405	1.64874	0.824370	+	0.566052i	$0.191530\pi$
$278$	−10.8143	−0.648601
$279$	0	0
$280$	−3.01062	−0.179919
$281$	16.2715	0.970675	0.485338	−	0.874327i	$-0.338697\pi$
$281$	16.2715	0.970675	0.485338	+	0.874327i	$0.338697\pi$
$282$	0	0
$283$	3.39374	0.201737	0.100868	−	0.994900i	$-0.467838\pi$
$283$	3.39374	0.201737	0.100868	+	0.994900i	$0.467838\pi$
$284$	−4.41570	−0.262023
$285$	0	0
$286$	1.75152	0.103569
$287$	6.44246	0.380287
$288$	0	0
$289$	0.524204	0.0308355
$290$	−7.33280	−0.430597
$291$	0	0
$292$	−2.26689	−0.132660
$293$	23.3783	1.36578	0.682888	−	0.730523i	$-0.260724\pi$
$293$	23.3783	1.36578	0.682888	+	0.730523i	$0.260724\pi$
$294$	0	0
$295$	7.76934	0.452349
$296$	3.97980	0.231321
$297$	0	0
$298$	9.33384	0.540695
$299$	−1.97079	−0.113974
$300$	0	0
$301$	1.27044	0.0732270
$302$	−19.8232	−1.14069
$303$	0	0
$304$	0	0
$305$	−25.7000	−1.47158
$306$	0	0
$307$	1.38802	0.0792185	0.0396093	−	0.999215i	$-0.487389\pi$
$307$	1.38802	0.0792185	0.0396093	+	0.999215i	$0.487389\pi$
$308$	7.39144	0.421166
$309$	0	0
$310$	−15.1048	−0.857898
$311$	12.1902	0.691246	0.345623	−	0.938374i	$-0.387668\pi$
$311$	12.1902	0.691246	0.345623	+	0.938374i	$0.387668\pi$
$312$	0	0
$313$	16.5314	0.934411	0.467205	−	0.884149i	$-0.345261\pi$
$313$	16.5314	0.934411	0.467205	+	0.884149i	$0.345261\pi$
$314$	13.8676	0.782596
$315$	0	0
$316$	−8.57659	−0.482471
$317$	2.68811	0.150979	0.0754897	−	0.997147i	$-0.475948\pi$
$317$	2.68811	0.150979	0.0754897	+	0.997147i	$0.475948\pi$
$318$	0	0
$319$	18.0029	1.00797
$320$	2.34458	0.131066
$321$	0	0
$322$	−8.31677	−0.463475
$323$	0	0
$324$	0	0
$325$	−0.151240	−0.00838930
$326$	14.2496	0.789212
$327$	0	0
$328$	−5.01719	−0.277028
$329$	−5.64282	−0.311099
$330$	0	0
$331$	−5.21303	−0.286534	−0.143267	−	0.989684i	$-0.545761\pi$
$331$	−5.21303	−0.286534	−0.143267	+	0.989684i	$0.545761\pi$
$332$	9.76464	0.535904
$333$	0	0
$334$	11.5901	0.634183
$335$	10.2712	0.561173
$336$	0	0
$337$	26.7275	1.45594	0.727969	−	0.685610i	$-0.240464\pi$
$337$	26.7275	1.45594	0.727969	+	0.685610i	$0.240464\pi$
$338$	−12.9074	−0.702071
$339$	0	0
$340$	−9.81485	−0.532285
$341$	37.0842	2.00822
$342$	0	0
$343$	15.8598	0.856351
$344$	−0.989378	−0.0533437
$345$	0	0
$346$	3.98353	0.214156
$347$	32.6682	1.75372	0.876860	−	0.480745i	$-0.159634\pi$
$347$	32.6682	1.75372	0.876860	+	0.480745i	$0.159634\pi$
$348$	0	0
$349$	−29.1058	−1.55800	−0.778998	−	0.627026i	$-0.784272\pi$
$349$	−29.1058	−1.55800	−0.778998	+	0.627026i	$0.784272\pi$
$350$	−0.638237	−0.0341152
$351$	0	0
$352$	−5.75621	−0.306807
$353$	14.3049	0.761372	0.380686	−	0.924704i	$-0.375688\pi$
$353$	14.3049	0.761372	0.380686	+	0.924704i	$0.375688\pi$
$354$	0	0
$355$	−10.3529	−0.549477
$356$	−15.0765	−0.799055
$357$	0	0
$358$	−8.45089	−0.446644
$359$	−19.6707	−1.03818	−0.519090	−	0.854720i	$-0.673729\pi$
$359$	−19.6707	−1.03818	−0.519090	+	0.854720i	$0.673729\pi$
$360$	0	0
$361$	0	0
$362$	−8.48526	−0.445976
$363$	0	0
$364$	0.390723	0.0204794
$365$	−5.31490	−0.278195
$366$	0	0
$367$	9.55053	0.498534	0.249267	−	0.968435i	$-0.419810\pi$
$367$	9.55053	0.498534	0.249267	+	0.968435i	$0.419810\pi$
$368$	6.47684	0.337628
$369$	0	0
$370$	9.33094	0.485092
$371$	−4.22545	−0.219374
$372$	0	0
$373$	−3.64010	−0.188477	−0.0942387	−	0.995550i	$-0.530042\pi$
$373$	−3.64010	−0.188477	−0.0942387	+	0.995550i	$0.530042\pi$
$374$	24.0966	1.24601
$375$	0	0
$376$	4.39445	0.226627
$377$	0.951662	0.0490131
$378$	0	0
$379$	−8.34741	−0.428778	−0.214389	−	0.976748i	$-0.568776\pi$
$379$	−8.34741	−0.428778	−0.214389	+	0.976748i	$0.568776\pi$
$380$	0	0
$381$	0	0
$382$	22.3790	1.14501
$383$	−9.48566	−0.484695	−0.242347	−	0.970190i	$-0.577917\pi$
$383$	−9.48566	−0.484695	−0.242347	+	0.970190i	$0.577917\pi$
$384$	0	0
$385$	17.3298	0.883208
$386$	−7.42811	−0.378081
$387$	0	0
$388$	−17.3522	−0.880924
$389$	−36.0480	−1.82770	−0.913852	−	0.406047i	$-0.866907\pi$
$389$	−36.0480	−1.82770	−0.913852	+	0.406047i	$0.866907\pi$
$390$	0	0
$391$	−27.1133	−1.37118
$392$	−5.35114	−0.270273
$393$	0	0
$394$	−8.53554	−0.430014
$395$	−20.1085	−1.01177
$396$	0	0
$397$	−6.40906	−0.321662	−0.160831	−	0.986982i	$-0.551417\pi$
$397$	−6.40906	−0.321662	−0.160831	+	0.986982i	$0.551417\pi$
$398$	−6.35926	−0.318761
$399$	0	0
$400$	0.497039	0.0248520
$401$	0.187660	0.00937128	0.00468564	−	0.999989i	$-0.498509\pi$
$401$	0.187660	0.00937128	0.00468564	+	0.999989i	$0.498509\pi$
$402$	0	0
$403$	1.96033	0.0976509
$404$	−3.67667	−0.182921
$405$	0	0
$406$	4.01603	0.199312
$407$	−22.9086	−1.13554
$408$	0	0
$409$	−17.2663	−0.853762	−0.426881	−	0.904308i	$-0.640388\pi$
$409$	−17.2663	−0.853762	−0.426881	+	0.904308i	$0.640388\pi$
$410$	−11.7632	−0.580942
$411$	0	0
$412$	−19.0135	−0.936729
$413$	−4.25512	−0.209381
$414$	0	0
$415$	22.8940	1.12382
$416$	−0.304282	−0.0149187
$417$	0	0
$418$	0	0
$419$	1.72572	0.0843068	0.0421534	−	0.999111i	$-0.486578\pi$
$419$	1.72572	0.0843068	0.0421534	+	0.999111i	$0.486578\pi$
$420$	0	0
$421$	−32.7546	−1.59636	−0.798180	−	0.602420i	$-0.794203\pi$
$421$	−32.7546	−1.59636	−0.798180	+	0.602420i	$0.794203\pi$
$422$	13.9578	0.679455
$423$	0	0
$424$	3.29064	0.159808
$425$	−2.08070	−0.100929
$426$	0	0
$427$	14.0754	0.681155
$428$	10.0373	0.485170
$429$	0	0
$430$	−2.31967	−0.111865
$431$	−25.5119	−1.22887	−0.614433	−	0.788969i	$-0.710615\pi$
$431$	−25.5119	−1.22887	−0.614433	+	0.788969i	$0.710615\pi$
$432$	0	0
$433$	−24.4834	−1.17660	−0.588299	−	0.808644i	$-0.700202\pi$
$433$	−24.4834	−1.17660	−0.588299	+	0.808644i	$0.700202\pi$
$434$	8.27263	0.397099
$435$	0	0
$436$	8.84348	0.423526
$437$	0	0
$438$	0	0
$439$	30.8388	1.47186	0.735928	−	0.677060i	$-0.236746\pi$
$439$	30.8388	1.47186	0.735928	+	0.677060i	$0.236746\pi$
$440$	−13.4959	−0.643391
$441$	0	0
$442$	1.27378	0.0605878
$443$	−10.7047	−0.508595	−0.254297	−	0.967126i	$-0.581844\pi$
$443$	−10.7047	−0.508595	−0.254297	+	0.967126i	$0.581844\pi$
$444$	0	0
$445$	−35.3481	−1.67566
$446$	−8.92400	−0.422564
$447$	0	0
$448$	−1.28408	−0.0606670
$449$	2.31562	0.109281	0.0546403	−	0.998506i	$-0.482599\pi$
$449$	2.31562	0.109281	0.0546403	+	0.998506i	$0.482599\pi$
$450$	0	0
$451$	28.8800	1.35991
$452$	−14.2502	−0.670275
$453$	0	0
$454$	−0.659796	−0.0309657
$455$	0.916079	0.0429465
$456$	0	0
$457$	−0.0521810	−0.00244092	−0.00122046	−	0.999999i	$-0.500388\pi$
$457$	−0.0521810	−0.00244092	−0.00122046	+	0.999999i	$0.500388\pi$
$458$	−6.97208	−0.325784
$459$	0	0
$460$	15.1854	0.708025
$461$	−39.4720	−1.83840	−0.919198	−	0.393796i	$-0.871162\pi$
$461$	−39.4720	−1.83840	−0.919198	+	0.393796i	$0.871162\pi$
$462$	0	0
$463$	−6.19056	−0.287700	−0.143850	−	0.989600i	$-0.545948\pi$
$463$	−6.19056	−0.287700	−0.143850	+	0.989600i	$0.545948\pi$
$464$	−3.12756	−0.145193
$465$	0	0
$466$	29.6097	1.37164
$467$	20.9962	0.971586	0.485793	−	0.874074i	$-0.338531\pi$
$467$	20.9962	0.971586	0.485793	+	0.874074i	$0.338531\pi$
$468$	0	0
$469$	−5.62531	−0.259753
$470$	10.3031	0.475248
$471$	0	0
$472$	3.31375	0.152528
$473$	5.69507	0.261860
$474$	0	0
$475$	0	0
$476$	5.37540	0.246381
$477$	0	0
$478$	24.7034	1.12991
$479$	−15.5229	−0.709261	−0.354631	−	0.935006i	$-0.615393\pi$
$479$	−15.5229	−0.709261	−0.354631	+	0.935006i	$0.615393\pi$
$480$	0	0
$481$	−1.21098	−0.0552160
$482$	−27.5586	−1.25526
$483$	0	0
$484$	22.1340	1.00609
$485$	−40.6835	−1.84734
$486$	0	0
$487$	28.6065	1.29629	0.648143	−	0.761519i	$-0.275546\pi$
$487$	28.6065	1.29629	0.648143	+	0.761519i	$0.275546\pi$
$488$	−10.9615	−0.496202
$489$	0	0
$490$	−12.5462	−0.566778
$491$	30.3488	1.36962	0.684812	−	0.728720i	$-0.259884\pi$
$491$	30.3488	1.36962	0.684812	+	0.728720i	$0.259884\pi$
$492$	0	0
$493$	13.0926	0.589659
$494$	0	0
$495$	0	0
$496$	−6.44246	−0.289275
$497$	5.67010	0.254339
$498$	0	0
$499$	8.77624	0.392878	0.196439	−	0.980516i	$-0.437062\pi$
$499$	8.77624	0.392878	0.196439	+	0.980516i	$0.437062\pi$
$500$	−10.5575	−0.472147
$501$	0	0
$502$	2.98855	0.133386
$503$	21.1043	0.940996	0.470498	−	0.882401i	$-0.344074\pi$
$503$	21.1043	0.940996	0.470498	+	0.882401i	$0.344074\pi$
$504$	0	0
$505$	−8.62023	−0.383595
$506$	−37.2821	−1.65739
$507$	0	0
$508$	−2.23015	−0.0989467
$509$	22.2212	0.984936	0.492468	−	0.870331i	$-0.336095\pi$
$509$	22.2212	0.984936	0.492468	+	0.870331i	$0.336095\pi$
$510$	0	0
$511$	2.91087	0.128769
$512$	1.00000	0.0441942
$513$	0	0
$514$	14.1323	0.623347
$515$	−44.5787	−1.96437
$516$	0	0
$517$	−25.2954	−1.11249
$518$	−5.11037	−0.224537
$519$	0	0
$520$	−0.713414	−0.0312853
$521$	10.0332	0.439563	0.219782	−	0.975549i	$-0.429466\pi$
$521$	10.0332	0.439563	0.219782	+	0.975549i	$0.429466\pi$
$522$	0	0
$523$	−29.2823	−1.28042	−0.640212	−	0.768198i	$-0.721154\pi$
$523$	−29.2823	−1.28042	−0.640212	+	0.768198i	$0.721154\pi$
$524$	−1.52265	−0.0665175
$525$	0	0
$526$	−7.56887	−0.330018
$527$	26.9694	1.17481
$528$	0	0
$529$	18.9494	0.823887
$530$	7.71517	0.335125
$531$	0	0
$532$	0	0
$533$	1.52664	0.0661262
$534$	0	0
$535$	23.5332	1.01743
$536$	4.38081	0.189222
$537$	0	0
$538$	−7.67074	−0.330709
$539$	30.8023	1.32675
$540$	0	0
$541$	−37.8404	−1.62688	−0.813442	−	0.581646i	$-0.802409\pi$
$541$	−37.8404	−1.62688	−0.813442	+	0.581646i	$0.802409\pi$
$542$	11.6649	0.501050
$543$	0	0
$544$	−4.18619	−0.179482
$545$	20.7342	0.888156
$546$	0	0
$547$	14.4976	0.619871	0.309936	−	0.950758i	$-0.399692\pi$
$547$	14.4976	0.619871	0.309936	+	0.950758i	$0.399692\pi$
$548$	−10.7118	−0.457583
$549$	0	0
$550$	−2.86106	−0.121996
$551$	0	0
$552$	0	0
$553$	11.0130	0.468321
$554$	27.4405	1.16583
$555$	0	0
$556$	−10.8143	−0.458630
$557$	4.33801	0.183807	0.0919037	−	0.995768i	$-0.470705\pi$
$557$	4.33801	0.183807	0.0919037	+	0.995768i	$0.470705\pi$
$558$	0	0
$559$	0.301051	0.0127331
$560$	−3.01062	−0.127222
$561$	0	0
$562$	16.2715	0.686371
$563$	−27.2936	−1.15029	−0.575144	−	0.818052i	$-0.695054\pi$
$563$	−27.2936	−1.15029	−0.575144	+	0.818052i	$0.695054\pi$
$564$	0	0
$565$	−33.4108	−1.40560
$566$	3.39374	0.142650
$567$	0	0
$568$	−4.41570	−0.185278
$569$	−7.19043	−0.301439	−0.150719	−	0.988577i	$-0.548159\pi$
$569$	−7.19043	−0.301439	−0.150719	+	0.988577i	$0.548159\pi$
$570$	0	0
$571$	42.0134	1.75821	0.879103	−	0.476631i	$-0.158142\pi$
$571$	42.0134	1.75821	0.879103	+	0.476631i	$0.158142\pi$
$572$	1.75152	0.0732345
$573$	0	0
$574$	6.44246	0.268903
$575$	3.21924	0.134252
$576$	0	0
$577$	21.6713	0.902190	0.451095	−	0.892476i	$-0.351034\pi$
$577$	21.6713	0.902190	0.451095	+	0.892476i	$0.351034\pi$
$578$	0.524204	0.0218040
$579$	0	0
$580$	−7.33280	−0.304478
$581$	−12.5386	−0.520188
$582$	0	0
$583$	−18.9417	−0.784483
$584$	−2.26689	−0.0938047
$585$	0	0
$586$	23.3783	0.965749
$587$	1.26864	0.0523626	0.0261813	−	0.999657i	$-0.491665\pi$
$587$	1.26864	0.0523626	0.0261813	+	0.999657i	$0.491665\pi$
$588$	0	0
$589$	0	0
$590$	7.76934	0.319859
$591$	0	0
$592$	3.97980	0.163569
$593$	−21.5600	−0.885363	−0.442682	−	0.896679i	$-0.645973\pi$
$593$	−21.5600	−0.885363	−0.442682	+	0.896679i	$0.645973\pi$
$594$	0	0
$595$	12.6030	0.516674
$596$	9.33384	0.382329
$597$	0	0
$598$	−1.97079	−0.0805915
$599$	−28.6417	−1.17027	−0.585135	−	0.810936i	$-0.698958\pi$
$599$	−28.6417	−1.17027	−0.585135	+	0.810936i	$0.698958\pi$
$600$	0	0
$601$	−7.55865	−0.308324	−0.154162	−	0.988046i	$-0.549268\pi$
$601$	−7.55865	−0.308324	−0.154162	+	0.988046i	$0.549268\pi$
$602$	1.27044	0.0517793
$603$	0	0
$604$	−19.8232	−0.806593
$605$	51.8949	2.10983
$606$	0	0
$607$	−1.72737	−0.0701117	−0.0350558	−	0.999385i	$-0.511161\pi$
$607$	−1.72737	−0.0701117	−0.0350558	+	0.999385i	$0.511161\pi$
$608$	0	0
$609$	0	0
$610$	−25.7000	−1.04056
$611$	−1.33715	−0.0540955
$612$	0	0
$613$	−27.4169	−1.10736	−0.553680	−	0.832730i	$-0.686777\pi$
$613$	−27.4169	−1.10736	−0.553680	+	0.832730i	$0.686777\pi$
$614$	1.38802	0.0560160
$615$	0	0
$616$	7.39144	0.297809
$617$	−10.6275	−0.427847	−0.213924	−	0.976850i	$-0.568624\pi$
$617$	−10.6275	−0.427847	−0.213924	+	0.976850i	$0.568624\pi$
$618$	0	0
$619$	8.36008	0.336020	0.168010	−	0.985785i	$-0.446266\pi$
$619$	8.36008	0.336020	0.168010	+	0.985785i	$0.446266\pi$
$620$	−15.1048	−0.606625
$621$	0	0
$622$	12.1902	0.488784
$623$	19.3595	0.775620
$624$	0	0
$625$	−27.2381	−1.08953
$626$	16.5314	0.660728
$627$	0	0
$628$	13.8676	0.553379
$629$	−16.6602	−0.664285
$630$	0	0
$631$	24.5301	0.976530	0.488265	−	0.872696i	$-0.337630\pi$
$631$	24.5301	0.976530	0.488265	+	0.872696i	$0.337630\pi$
$632$	−8.57659	−0.341158
$633$	0	0
$634$	2.68811	0.106759
$635$	−5.22875	−0.207497
$636$	0	0
$637$	1.62826	0.0645139
$638$	18.0029	0.712742
$639$	0	0
$640$	2.34458	0.0926775
$641$	−6.97270	−0.275405	−0.137703	−	0.990474i	$-0.543972\pi$
$641$	−6.97270	−0.275405	−0.137703	+	0.990474i	$0.543972\pi$
$642$	0	0
$643$	−9.09024	−0.358484	−0.179242	−	0.983805i	$-0.557365\pi$
$643$	−9.09024	−0.358484	−0.179242	+	0.983805i	$0.557365\pi$
$644$	−8.31677	−0.327727
$645$	0	0
$646$	0	0
$647$	−30.0074	−1.17971	−0.589856	−	0.807509i	$-0.700815\pi$
$647$	−30.0074	−1.17971	−0.589856	+	0.807509i	$0.700815\pi$
$648$	0	0
$649$	−19.0747	−0.748746
$650$	−0.151240	−0.00593213
$651$	0	0
$652$	14.2496	0.558057
$653$	−10.4191	−0.407732	−0.203866	−	0.978999i	$-0.565351\pi$
$653$	−10.4191	−0.407732	−0.203866	+	0.978999i	$0.565351\pi$
$654$	0	0
$655$	−3.56998	−0.139491
$656$	−5.01719	−0.195888
$657$	0	0
$658$	−5.64282	−0.219980
$659$	−26.3756	−1.02745	−0.513724	−	0.857956i	$-0.671734\pi$
$659$	−26.3756	−1.02745	−0.513724	+	0.857956i	$0.671734\pi$
$660$	0	0
$661$	24.6939	0.960483	0.480242	−	0.877136i	$-0.340549\pi$
$661$	24.6939	0.960483	0.480242	+	0.877136i	$0.340549\pi$
$662$	−5.21303	−0.202610
$663$	0	0
$664$	9.76464	0.378942
$665$	0	0
$666$	0	0
$667$	−20.2567	−0.784342
$668$	11.5901	0.448435
$669$	0	0
$670$	10.2712	0.396809
$671$	63.0965	2.43581
$672$	0	0
$673$	9.77380	0.376752	0.188376	−	0.982097i	$-0.439678\pi$
$673$	9.77380	0.376752	0.188376	+	0.982097i	$0.439678\pi$
$674$	26.7275	1.02950
$675$	0	0
$676$	−12.9074	−0.496439
$677$	−21.5747	−0.829184	−0.414592	−	0.910007i	$-0.636076\pi$
$677$	−21.5747	−0.829184	−0.414592	+	0.910007i	$0.636076\pi$
$678$	0	0
$679$	22.2816	0.855088
$680$	−9.81485	−0.376382
$681$	0	0
$682$	37.0842	1.42003
$683$	33.2509	1.27231	0.636155	−	0.771561i	$-0.280524\pi$
$683$	33.2509	1.27231	0.636155	+	0.771561i	$0.280524\pi$
$684$	0	0
$685$	−25.1145	−0.959576
$686$	15.8598	0.605532
$687$	0	0
$688$	−0.989378	−0.0377197
$689$	−1.00129	−0.0381459
$690$	0	0
$691$	4.80932	0.182955	0.0914776	−	0.995807i	$-0.470841\pi$
$691$	4.80932	0.182955	0.0914776	+	0.995807i	$0.470841\pi$
$692$	3.98353	0.151431
$693$	0	0
$694$	32.6682	1.24007
$695$	−25.3550	−0.961772
$696$	0	0
$697$	21.0029	0.795542
$698$	−29.1058	−1.10167
$699$	0	0
$700$	−0.638237	−0.0241231
$701$	−3.46466	−0.130859	−0.0654293	−	0.997857i	$-0.520842\pi$
$701$	−3.46466	−0.130859	−0.0654293	+	0.997857i	$0.520842\pi$
$702$	0	0
$703$	0	0
$704$	−5.75621	−0.216946
$705$	0	0
$706$	14.3049	0.538371
$707$	4.72113	0.177556
$708$	0	0
$709$	20.5743	0.772684	0.386342	−	0.922356i	$-0.373738\pi$
$709$	20.5743	0.772684	0.386342	+	0.922356i	$0.373738\pi$
$710$	−10.3529	−0.388539
$711$	0	0
$712$	−15.0765	−0.565017
$713$	−41.7268	−1.56268
$714$	0	0
$715$	4.10656	0.153577
$716$	−8.45089	−0.315825
$717$	0	0
$718$	−19.6707	−0.734104
$719$	−24.1885	−0.902080	−0.451040	−	0.892504i	$-0.648947\pi$
$719$	−24.1885	−0.902080	−0.451040	+	0.892504i	$0.648947\pi$
$720$	0	0
$721$	24.4149	0.909257
$722$	0	0
$723$	0	0
$724$	−8.48526	−0.315352
$725$	−1.55452	−0.0577334
$726$	0	0
$727$	18.1276	0.672317	0.336158	−	0.941806i	$-0.390872\pi$
$727$	18.1276	0.672317	0.336158	+	0.941806i	$0.390872\pi$
$728$	0.390723	0.0144811
$729$	0	0
$730$	−5.31490	−0.196713
$731$	4.14173	0.153187
$732$	0	0
$733$	22.7363	0.839785	0.419893	−	0.907574i	$-0.362068\pi$
$733$	22.7363	0.839785	0.419893	+	0.907574i	$0.362068\pi$
$734$	9.55053	0.352517
$735$	0	0
$736$	6.47684	0.238739
$737$	−25.2169	−0.928877
$738$	0	0
$739$	15.1787	0.558356	0.279178	−	0.960239i	$-0.409938\pi$
$739$	15.1787	0.558356	0.279178	+	0.960239i	$0.409938\pi$
$740$	9.33094	0.343012
$741$	0	0
$742$	−4.22545	−0.155121
$743$	−3.27625	−0.120194	−0.0600970	−	0.998193i	$-0.519141\pi$
$743$	−3.27625	−0.120194	−0.0600970	+	0.998193i	$0.519141\pi$
$744$	0	0
$745$	21.8839	0.801764
$746$	−3.64010	−0.133274
$747$	0	0
$748$	24.0966	0.881060
$749$	−12.8887	−0.470941
$750$	0	0
$751$	−52.2323	−1.90598	−0.952992	−	0.302995i	$-0.902013\pi$
$751$	−52.2323	−1.90598	−0.952992	+	0.302995i	$0.902013\pi$
$752$	4.39445	0.160249
$753$	0	0
$754$	0.951662	0.0346575
$755$	−46.4769	−1.69147
$756$	0	0
$757$	−24.2342	−0.880807	−0.440404	−	0.897800i	$-0.645165\pi$
$757$	−24.2342	−0.880807	−0.440404	+	0.897800i	$0.645165\pi$
$758$	−8.34741	−0.303192
$759$	0	0
$760$	0	0
$761$	24.8054	0.899195	0.449597	−	0.893231i	$-0.351567\pi$
$761$	24.8054	0.899195	0.449597	+	0.893231i	$0.351567\pi$
$762$	0	0
$763$	−11.3557	−0.411105
$764$	22.3790	0.809644
$765$	0	0
$766$	−9.48566	−0.342731
$767$	−1.00832	−0.0364082
$768$	0	0
$769$	9.64289	0.347732	0.173866	−	0.984769i	$-0.444374\pi$
$769$	9.64289	0.347732	0.173866	+	0.984769i	$0.444374\pi$
$770$	17.3298	0.624522
$771$	0	0
$772$	−7.42811	−0.267344
$773$	1.28731	0.0463014	0.0231507	−	0.999732i	$-0.492630\pi$
$773$	1.28731	0.0463014	0.0231507	+	0.999732i	$0.492630\pi$
$774$	0	0
$775$	−3.20216	−0.115025
$776$	−17.3522	−0.622907
$777$	0	0
$778$	−36.0480	−1.29238
$779$	0	0
$780$	0	0
$781$	25.4177	0.909517
$782$	−27.1133	−0.969569
$783$	0	0
$784$	−5.35114	−0.191112
$785$	32.5137	1.16046
$786$	0	0
$787$	16.3446	0.582624	0.291312	−	0.956628i	$-0.405908\pi$
$787$	16.3446	0.582624	0.291312	+	0.956628i	$0.405908\pi$
$788$	−8.53554	−0.304066
$789$	0	0
$790$	−20.1085	−0.715427
$791$	18.2984	0.650617
$792$	0	0
$793$	3.33538	0.118443
$794$	−6.40906	−0.227449
$795$	0	0
$796$	−6.35926	−0.225398
$797$	−15.6884	−0.555712	−0.277856	−	0.960623i	$-0.589624\pi$
$797$	−15.6884	−0.555712	−0.277856	+	0.960623i	$0.589624\pi$
$798$	0	0
$799$	−18.3960	−0.650804
$800$	0.497039	0.0175730
$801$	0	0
$802$	0.187660	0.00662650
$803$	13.0487	0.460479
$804$	0	0
$805$	−19.4993	−0.687260
$806$	1.96033	0.0690496
$807$	0	0
$808$	−3.67667	−0.129345
$809$	11.5248	0.405192	0.202596	−	0.979262i	$-0.435062\pi$
$809$	11.5248	0.405192	0.202596	+	0.979262i	$0.435062\pi$
$810$	0	0
$811$	8.30102	0.291488	0.145744	−	0.989322i	$-0.453442\pi$
$811$	8.30102	0.291488	0.145744	+	0.989322i	$0.453442\pi$
$812$	4.01603	0.140935
$813$	0	0
$814$	−22.9086	−0.802945
$815$	33.4093	1.17028
$816$	0	0
$817$	0	0
$818$	−17.2663	−0.603701
$819$	0	0
$820$	−11.7632	−0.410788
$821$	33.7112	1.17653	0.588265	−	0.808668i	$-0.299811\pi$
$821$	33.7112	1.17653	0.588265	+	0.808668i	$0.299811\pi$
$822$	0	0
$823$	21.8678	0.762262	0.381131	−	0.924521i	$-0.375535\pi$
$823$	21.8678	0.762262	0.381131	+	0.924521i	$0.375535\pi$
$824$	−19.0135	−0.662368
$825$	0	0
$826$	−4.25512	−0.148055
$827$	39.1695	1.36206	0.681028	−	0.732257i	$-0.261533\pi$
$827$	39.1695	1.36206	0.681028	+	0.732257i	$0.261533\pi$
$828$	0	0
$829$	14.4176	0.500743	0.250371	−	0.968150i	$-0.419447\pi$
$829$	14.4176	0.500743	0.250371	+	0.968150i	$0.419447\pi$
$830$	22.8940	0.794661
$831$	0	0
$832$	−0.304282	−0.0105491
$833$	22.4009	0.776145
$834$	0	0
$835$	27.1739	0.940392
$836$	0	0
$837$	0	0
$838$	1.72572	0.0596139
$839$	20.9532	0.723385	0.361693	−	0.932297i	$-0.382199\pi$
$839$	20.9532	0.723385	0.361693	+	0.932297i	$0.382199\pi$
$840$	0	0
$841$	−19.2184	−0.662702
$842$	−32.7546	−1.12880
$843$	0	0
$844$	13.9578	0.480447
$845$	−30.2624	−1.04106
$846$	0	0
$847$	−28.4218	−0.976585
$848$	3.29064	0.113001
$849$	0	0
$850$	−2.08070	−0.0713675
$851$	25.7765	0.883607
$852$	0	0
$853$	51.9553	1.77892	0.889458	−	0.457017i	$-0.151082\pi$
$853$	51.9553	1.77892	0.889458	+	0.457017i	$0.151082\pi$
$854$	14.0754	0.481650
$855$	0	0
$856$	10.0373	0.343067
$857$	29.1835	0.996888	0.498444	−	0.866922i	$-0.333905\pi$
$857$	29.1835	0.996888	0.498444	+	0.866922i	$0.333905\pi$
$858$	0	0
$859$	21.9913	0.750335	0.375168	−	0.926957i	$-0.377585\pi$
$859$	21.9913	0.750335	0.375168	+	0.926957i	$0.377585\pi$
$860$	−2.31967	−0.0791002
$861$	0	0
$862$	−25.5119	−0.868939
$863$	−35.8157	−1.21918	−0.609590	−	0.792717i	$-0.708666\pi$
$863$	−35.8157	−1.21918	−0.609590	+	0.792717i	$0.708666\pi$
$864$	0	0
$865$	9.33968	0.317559
$866$	−24.4834	−0.831980
$867$	0	0
$868$	8.27263	0.280791
$869$	49.3687	1.67472
$870$	0	0
$871$	−1.33300	−0.0451671
$872$	8.84348	0.299478
$873$	0	0
$874$	0	0
$875$	13.5567	0.458300
$876$	0	0
$877$	−7.82483	−0.264226	−0.132113	−	0.991235i	$-0.542176\pi$
$877$	−7.82483	−0.264226	−0.132113	+	0.991235i	$0.542176\pi$
$878$	30.8388	1.04076
$879$	0	0
$880$	−13.4959	−0.454946
$881$	14.4829	0.487941	0.243970	−	0.969783i	$-0.421550\pi$
$881$	14.4829	0.487941	0.243970	+	0.969783i	$0.421550\pi$
$882$	0	0
$883$	−23.5529	−0.792619	−0.396310	−	0.918117i	$-0.629709\pi$
$883$	−23.5529	−0.792619	−0.396310	+	0.918117i	$0.629709\pi$
$884$	1.27378	0.0428420
$885$	0	0
$886$	−10.7047	−0.359631
$887$	−15.8736	−0.532982	−0.266491	−	0.963837i	$-0.585864\pi$
$887$	−15.8736	−0.532982	−0.266491	+	0.963837i	$0.585864\pi$
$888$	0	0
$889$	2.86368	0.0960449
$890$	−35.3481	−1.18487
$891$	0	0
$892$	−8.92400	−0.298798
$893$	0	0
$894$	0	0
$895$	−19.8138	−0.662301
$896$	−1.28408	−0.0428981
$897$	0	0
$898$	2.31562	0.0772731
$899$	20.1492	0.672013
$900$	0	0
$901$	−13.7753	−0.458921
$902$	28.8800	0.961599
$903$	0	0
$904$	−14.2502	−0.473956
$905$	−19.8944	−0.661311
$906$	0	0
$907$	−45.0127	−1.49462	−0.747311	−	0.664474i	$-0.768656\pi$
$907$	−45.0127	−1.49462	−0.747311	+	0.664474i	$0.768656\pi$
$908$	−0.659796	−0.0218961
$909$	0	0
$910$	0.916079	0.0303677
$911$	−2.75901	−0.0914100	−0.0457050	−	0.998955i	$-0.514553\pi$
$911$	−2.75901	−0.0914100	−0.0457050	+	0.998955i	$0.514553\pi$
$912$	0	0
$913$	−56.2074	−1.86019
$914$	−0.0521810	−0.00172599
$915$	0	0
$916$	−6.97208	−0.230364
$917$	1.95521	0.0645667
$918$	0	0
$919$	−39.3083	−1.29666	−0.648331	−	0.761359i	$-0.724533\pi$
$919$	−39.3083	−1.29666	−0.648331	+	0.761359i	$0.724533\pi$
$920$	15.1854	0.500649
$921$	0	0
$922$	−39.4720	−1.29994
$923$	1.34362	0.0442258
$924$	0	0
$925$	1.97811	0.0650400
$926$	−6.19056	−0.203435
$927$	0	0
$928$	−3.12756	−0.102667
$929$	29.7417	0.975795	0.487897	−	0.872901i	$-0.337764\pi$
$929$	29.7417	0.975795	0.487897	+	0.872901i	$0.337764\pi$
$930$	0	0
$931$	0	0
$932$	29.6097	0.969898
$933$	0	0
$934$	20.9962	0.687015
$935$	56.4964	1.84763
$936$	0	0
$937$	37.7211	1.23229	0.616147	−	0.787631i	$-0.288693\pi$
$937$	37.7211	1.23229	0.616147	+	0.787631i	$0.288693\pi$
$938$	−5.62531	−0.183673
$939$	0	0
$940$	10.3031	0.336051
$941$	−6.47652	−0.211129	−0.105564	−	0.994412i	$-0.533665\pi$
$941$	−6.47652	−0.211129	−0.105564	+	0.994412i	$0.533665\pi$
$942$	0	0
$943$	−32.4955	−1.05820
$944$	3.31375	0.107853
$945$	0	0
$946$	5.69507	0.185163
$947$	−16.2913	−0.529396	−0.264698	−	0.964331i	$-0.585272\pi$
$947$	−16.2913	−0.529396	−0.264698	+	0.964331i	$0.585272\pi$
$948$	0	0
$949$	0.689776	0.0223911
$950$	0	0
$951$	0	0
$952$	5.37540	0.174218
$953$	−34.6213	−1.12150	−0.560748	−	0.827987i	$-0.689486\pi$
$953$	−34.6213	−1.12150	−0.560748	+	0.827987i	$0.689486\pi$
$954$	0	0
$955$	52.4693	1.69787
$956$	24.7034	0.798965
$957$	0	0
$958$	−15.5229	−0.501523
$959$	13.7547	0.444164
$960$	0	0
$961$	10.5053	0.338882
$962$	−1.21098	−0.0390436
$963$	0	0
$964$	−27.5586	−0.887604
$965$	−17.4158	−0.560634
$966$	0	0
$967$	−48.9105	−1.57286	−0.786428	−	0.617682i	$-0.788072\pi$
$967$	−48.9105	−1.57286	−0.786428	+	0.617682i	$0.788072\pi$
$968$	22.1340	0.711414
$969$	0	0
$970$	−40.6835	−1.30627
$971$	6.07592	0.194986	0.0974928	−	0.995236i	$-0.468918\pi$
$971$	6.07592	0.194986	0.0974928	+	0.995236i	$0.468918\pi$
$972$	0	0
$973$	13.8865	0.445180
$974$	28.6065	0.916613
$975$	0	0
$976$	−10.9615	−0.350868
$977$	57.0477	1.82512	0.912559	−	0.408944i	$-0.134103\pi$
$977$	57.0477	1.82512	0.912559	+	0.408944i	$0.134103\pi$
$978$	0	0
$979$	86.7838	2.77362
$980$	−12.5462	−0.400772
$981$	0	0
$982$	30.3488	0.968470
$983$	0.186519	0.00594905	0.00297452	−	0.999996i	$-0.499053\pi$
$983$	0.186519	0.00594905	0.00297452	+	0.999996i	$0.499053\pi$
$984$	0	0
$985$	−20.0122	−0.637642
$986$	13.0926	0.416952
$987$	0	0
$988$	0	0
$989$	−6.40804	−0.203764
$990$	0	0
$991$	46.2398	1.46886	0.734428	−	0.678686i	$-0.237450\pi$
$991$	46.2398	1.46886	0.734428	+	0.678686i	$0.237450\pi$
$992$	−6.44246	−0.204548
$993$	0	0
$994$	5.67010	0.179845
$995$	−14.9098	−0.472671
$996$	0	0
$997$	−20.8490	−0.660295	−0.330147	−	0.943929i	$-0.607098\pi$
$997$	−20.8490	−0.660295	−0.330147	+	0.943929i	$0.607098\pi$
$998$	8.77624	0.277807
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6498.2.a.ca.1.3		4
3.2	odd	2		722.2.a.m.1.1	✓	4
12.11	even	2		5776.2.a.bv.1.4		4
19.18	odd	2		6498.2.a.bx.1.3		4
57.2	even	18		722.2.e.r.99.4		24
57.5	odd	18		722.2.e.s.595.4		24
57.8	even	6		722.2.c.m.653.1		8
57.11	odd	6		722.2.c.n.653.4		8
57.14	even	18		722.2.e.r.595.1		24
57.17	odd	18		722.2.e.s.99.1		24
57.23	odd	18		722.2.e.s.415.4		24
57.26	odd	6		722.2.c.n.429.4		8
57.29	even	18		722.2.e.r.423.4		24
57.32	even	18		722.2.e.r.245.4		24
57.35	odd	18		722.2.e.s.389.1		24
57.41	even	18		722.2.e.r.389.4		24
57.44	odd	18		722.2.e.s.245.1		24
57.47	odd	18		722.2.e.s.423.1		24
57.50	even	6		722.2.c.m.429.1		8
57.53	even	18		722.2.e.r.415.1		24
57.56	even	2		722.2.a.n.1.4	yes	4
228.227	odd	2		5776.2.a.bt.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.1	✓	4	3.2	odd	2
722.2.a.n.1.4	yes	4	57.56	even	2
722.2.c.m.429.1		8	57.50	even	6
722.2.c.m.653.1		8	57.8	even	6
722.2.c.n.429.4		8	57.26	odd	6
722.2.c.n.653.4		8	57.11	odd	6
722.2.e.r.99.4		24	57.2	even	18
722.2.e.r.245.4		24	57.32	even	18
722.2.e.r.389.4		24	57.41	even	18
722.2.e.r.415.1		24	57.53	even	18
722.2.e.r.423.4		24	57.29	even	18
722.2.e.r.595.1		24	57.14	even	18
722.2.e.s.99.1		24	57.17	odd	18
722.2.e.s.245.1		24	57.44	odd	18
722.2.e.s.389.1		24	57.35	odd	18
722.2.e.s.415.4		24	57.23	odd	18
722.2.e.s.423.1		24	57.47	odd	18
722.2.e.s.595.4		24	57.5	odd	18
5776.2.a.bt.1.1		4	228.227	odd	2
5776.2.a.bv.1.4		4	12.11	even	2
6498.2.a.bx.1.3		4	19.18	odd	2
6498.2.a.ca.1.3		4	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:	\( N \)	\(=\)	\( 6498 = 2 \cdot 3^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6498.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +2.34458 q^{5} -1.28408 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +2.34458 q^{5} -1.28408 q^{7} +1.00000 q^{8} +2.34458 q^{10} -5.75621 q^{11} -0.304282 q^{13} -1.28408 q^{14} +1.00000 q^{16} -4.18619 q^{17} +2.34458 q^{20} -5.75621 q^{22} +6.47684 q^{23} +0.497039 q^{25} -0.304282 q^{26} -1.28408 q^{28} -3.12756 q^{29} -6.44246 q^{31} +1.00000 q^{32} -4.18619 q^{34} -3.01062 q^{35} +3.97980 q^{37} +2.34458 q^{40} -5.01719 q^{41} -0.989378 q^{43} -5.75621 q^{44} +6.47684 q^{46} +4.39445 q^{47} -5.35114 q^{49} +0.497039 q^{50} -0.304282 q^{52} +3.29064 q^{53} -13.4959 q^{55} -1.28408 q^{56} -3.12756 q^{58} +3.31375 q^{59} -10.9615 q^{61} -6.44246 q^{62} +1.00000 q^{64} -0.713414 q^{65} +4.38081 q^{67} -4.18619 q^{68} -3.01062 q^{70} -4.41570 q^{71} -2.26689 q^{73} +3.97980 q^{74} +7.39144 q^{77} -8.57659 q^{79} +2.34458 q^{80} -5.01719 q^{82} +9.76464 q^{83} -9.81485 q^{85} -0.989378 q^{86} -5.75621 q^{88} -15.0765 q^{89} +0.390723 q^{91} +6.47684 q^{92} +4.39445 q^{94} -17.3522 q^{97} -5.35114 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^7 + 4 * q^8	\( 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{8} + 2 q^{10} - 2 q^{11} - 18 q^{13} - 2 q^{14} + 4 q^{16} - 6 q^{17} + 2 q^{20} - 2 q^{22} + 10 q^{23} + 6 q^{25} - 18 q^{26} - 2 q^{28} - 2 q^{29} - 26 q^{31} + 4 q^{32} - 6 q^{34} - 6 q^{35} - 4 q^{37} + 2 q^{40} - 12 q^{41} - 10 q^{43} - 2 q^{44} + 10 q^{46} + 12 q^{47} - 12 q^{49} + 6 q^{50} - 18 q^{52} + 8 q^{53} - 26 q^{55} - 2 q^{56} - 2 q^{58} - 8 q^{59} - 26 q^{62} + 4 q^{64} - 4 q^{65} - 10 q^{67} - 6 q^{68} - 6 q^{70} - 14 q^{73} - 4 q^{74} - 4 q^{77} - 22 q^{79} + 2 q^{80} - 12 q^{82} + 12 q^{83} - 18 q^{85} - 10 q^{86} - 2 q^{88} - 16 q^{89} + 4 q^{91} + 10 q^{92} + 12 q^{94} - 28 q^{97} - 12 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^7 + 4 * q^8 + 2 * q^10 - 2 * q^11 - 18 * q^13 - 2 * q^14 + 4 * q^16 - 6 * q^17 + 2 * q^20 - 2 * q^22 + 10 * q^23 + 6 * q^25 - 18 * q^26 - 2 * q^28 - 2 * q^29 - 26 * q^31 + 4 * q^32 - 6 * q^34 - 6 * q^35 - 4 * q^37 + 2 * q^40 - 12 * q^41 - 10 * q^43 - 2 * q^44 + 10 * q^46 + 12 * q^47 - 12 * q^49 + 6 * q^50 - 18 * q^52 + 8 * q^53 - 26 * q^55 - 2 * q^56 - 2 * q^58 - 8 * q^59 - 26 * q^62 + 4 * q^64 - 4 * q^65 - 10 * q^67 - 6 * q^68 - 6 * q^70 - 14 * q^73 - 4 * q^74 - 4 * q^77 - 22 * q^79 + 2 * q^80 - 12 * q^82 + 12 * q^83 - 18 * q^85 - 10 * q^86 - 2 * q^88 - 16 * q^89 + 4 * q^91 + 10 * q^92 + 12 * q^94 - 28 * q^97 - 12 * q^98

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