LMFDB - Embedded newform 495.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(1,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, 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("495.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.48704.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 6x^{2} + 4x + 6 $ x^4 - 2x^3 - 6x^2 + 4*x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.69696$ of defining polynomial
Character	$\chi$	$=$	495.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69696 q^{2} +5.27358 q^{4} -1.00000 q^{5} -4.13176 q^{7} -8.82872 q^{8} +O(q^{10})$	\(q-2.69696 q^{2} +5.27358 q^{4} -1.00000 q^{5} -4.13176 q^{7} -8.82872 q^{8} +2.69696 q^{10} +1.00000 q^{11} +2.73785 q^{13} +11.1432 q^{14} +13.2635 q^{16} -2.41541 q^{17} -1.15325 q^{19} -5.27358 q^{20} -2.69696 q^{22} +8.54717 q^{23} +1.00000 q^{25} -7.38386 q^{26} -21.7892 q^{28} +1.67756 q^{29} -10.2635 q^{31} -18.1137 q^{32} +6.51425 q^{34} +4.13176 q^{35} +5.71636 q^{37} +3.11028 q^{38} +8.82872 q^{40} +9.11028 q^{41} +8.13176 q^{43} +5.27358 q^{44} -23.0514 q^{46} -1.47569 q^{47} +10.0715 q^{49} -2.69696 q^{50} +14.4383 q^{52} +2.54717 q^{53} -1.00000 q^{55} +36.4782 q^{56} -4.52431 q^{58} +8.24066 q^{59} +3.47569 q^{61} +27.6803 q^{62} +22.3249 q^{64} -2.73785 q^{65} +15.3350 q^{67} -12.7378 q^{68} -11.1432 q^{70} -2.54717 q^{71} +2.73785 q^{73} -15.4168 q^{74} -6.08178 q^{76} -4.13176 q^{77} +5.15325 q^{79} -13.2635 q^{80} -24.5700 q^{82} -9.28502 q^{83} +2.41541 q^{85} -21.9310 q^{86} -8.82872 q^{88} -4.78783 q^{89} -11.3121 q^{91} +45.0742 q^{92} +3.97989 q^{94} +1.15325 q^{95} +4.24066 q^{97} -27.1624 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 8 q^{4} - 4 q^{5} + 4 q^{7} - 6 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 + 8 * q^4 - 4 * q^5 + 4 * q^7 - 6 * q^8	$ 4 q - 2 q^{2} + 8 q^{4} - 4 q^{5} + 4 q^{7} - 6 q^{8} + 2 q^{10} + 4 q^{11} + 8 q^{13} + 8 q^{14} + 12 q^{16} - 4 q^{17} + 4 q^{19} - 8 q^{20} - 2 q^{22} + 8 q^{23} + 4 q^{25} + 16 q^{26} - 8 q^{28} + 4 q^{29} - 14 q^{32} + 4 q^{34} - 4 q^{35} + 8 q^{37} - 20 q^{38} + 6 q^{40} + 4 q^{41} + 12 q^{43} + 8 q^{44} - 16 q^{46} + 20 q^{49} - 2 q^{50} + 20 q^{52} - 16 q^{53} - 4 q^{55} + 48 q^{56} - 24 q^{58} + 24 q^{59} + 8 q^{61} + 20 q^{62} - 8 q^{65} - 48 q^{68} - 8 q^{70} + 16 q^{71} + 8 q^{73} - 12 q^{74} - 36 q^{76} + 4 q^{77} + 12 q^{79} - 12 q^{80} - 40 q^{82} - 8 q^{83} + 4 q^{85} - 16 q^{86} - 6 q^{88} + 16 q^{89} - 16 q^{91} + 72 q^{92} - 40 q^{94} - 4 q^{95} + 8 q^{97} - 62 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 8 * q^4 - 4 * q^5 + 4 * q^7 - 6 * q^8 + 2 * q^10 + 4 * q^11 + 8 * q^13 + 8 * q^14 + 12 * q^16 - 4 * q^17 + 4 * q^19 - 8 * q^20 - 2 * q^22 + 8 * q^23 + 4 * q^25 + 16 * q^26 - 8 * q^28 + 4 * q^29 - 14 * q^32 + 4 * q^34 - 4 * q^35 + 8 * q^37 - 20 * q^38 + 6 * q^40 + 4 * q^41 + 12 * q^43 + 8 * q^44 - 16 * q^46 + 20 * q^49 - 2 * q^50 + 20 * q^52 - 16 * q^53 - 4 * q^55 + 48 * q^56 - 24 * q^58 + 24 * q^59 + 8 * q^61 + 20 * q^62 - 8 * q^65 - 48 * q^68 - 8 * q^70 + 16 * q^71 + 8 * q^73 - 12 * q^74 - 36 * q^76 + 4 * q^77 + 12 * q^79 - 12 * q^80 - 40 * q^82 - 8 * q^83 + 4 * q^85 - 16 * q^86 - 6 * q^88 + 16 * q^89 - 16 * q^91 + 72 * q^92 - 40 * q^94 - 4 * q^95 + 8 * q^97 - 62 * 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 $

$2$	−2.69696	−1.90704	−0.953519	−	0.301334i	$-0.902568\pi$
$2$	−2.69696	−1.90704	−0.953519	+	0.301334i	$0.902568\pi$
$3$	0	0
$3$	0	0
$4$	5.27358	2.63679
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−4.13176	−1.56166	−0.780830	−	0.624744i	$-0.785204\pi$
$7$	−4.13176	−1.56166	−0.780830	+	0.624744i	$0.785204\pi$
$8$	−8.82872	−3.12142
$9$	0	0
$10$	2.69696	0.852853
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	2.73785	0.759342	0.379671	−	0.925122i	$-0.376037\pi$
$13$	2.73785	0.759342	0.379671	+	0.925122i	$0.376037\pi$
$14$	11.1432	2.97814
$15$	0	0
$16$	13.2635	3.31588
$17$	−2.41541	−0.585822	−0.292911	−	0.956140i	$-0.594624\pi$
$17$	−2.41541	−0.585822	−0.292911	+	0.956140i	$0.594624\pi$
$18$	0	0
$19$	−1.15325	−0.264574	−0.132287	−	0.991211i	$-0.542232\pi$
$19$	−1.15325	−0.264574	−0.132287	+	0.991211i	$0.542232\pi$
$20$	−5.27358	−1.17921
$21$	0	0
$22$	−2.69696	−0.574993
$23$	8.54717	1.78221	0.891104	−	0.453799i	$-0.149932\pi$
$23$	8.54717	1.78221	0.891104	+	0.453799i	$0.149932\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	−7.38386	−1.44809
$27$	0	0
$28$	−21.7892	−4.11777
$29$	1.67756	0.311515	0.155757	−	0.987795i	$-0.450218\pi$
$29$	1.67756	0.311515	0.155757	+	0.987795i	$0.450218\pi$
$30$	0	0
$31$	−10.2635	−1.84338	−0.921692	−	0.387922i	$-0.873193\pi$
$31$	−10.2635	−1.84338	−0.921692	+	0.387922i	$0.873193\pi$
$32$	−18.1137	−3.20209
$33$	0	0
$34$	6.51425	1.11718
$35$	4.13176	0.698396
$36$	0	0
$37$	5.71636	0.939764	0.469882	−	0.882729i	$-0.344297\pi$
$37$	5.71636	0.939764	0.469882	+	0.882729i	$0.344297\pi$
$38$	3.11028	0.504553
$39$	0	0
$40$	8.82872	1.39594
$41$	9.11028	1.42279	0.711393	−	0.702794i	$-0.248065\pi$
$41$	9.11028	1.42279	0.711393	+	0.702794i	$0.248065\pi$
$42$	0	0
$43$	8.13176	1.24008	0.620041	−	0.784569i	$-0.287116\pi$
$43$	8.13176	1.24008	0.620041	+	0.784569i	$0.287116\pi$
$44$	5.27358	0.795023
$45$	0	0
$46$	−23.0514	−3.39874
$47$	−1.47569	−0.215252	−0.107626	−	0.994191i	$-0.534325\pi$
$47$	−1.47569	−0.215252	−0.107626	+	0.994191i	$0.534325\pi$
$48$	0	0
$49$	10.0715	1.43878
$50$	−2.69696	−0.381408
$51$	0	0
$52$	14.4383	2.00223
$53$	2.54717	0.349881	0.174940	−	0.984579i	$-0.444027\pi$
$53$	2.54717	0.349881	0.174940	+	0.984579i	$0.444027\pi$
$54$	0	0
$55$	−1.00000	−0.134840
$56$	36.4782	4.87460
$57$	0	0
$58$	−4.52431	−0.594070
$59$	8.24066	1.07284	0.536422	−	0.843950i	$-0.319776\pi$
$59$	8.24066	1.07284	0.536422	+	0.843950i	$0.319776\pi$
$60$	0	0
$61$	3.47569	0.445017	0.222509	−	0.974931i	$-0.428575\pi$
$61$	3.47569	0.445017	0.222509	+	0.974931i	$0.428575\pi$
$62$	27.6803	3.51540
$63$	0	0
$64$	22.3249	2.79062
$65$	−2.73785	−0.339588
$66$	0	0
$67$	15.3350	1.87347	0.936734	−	0.350041i	$-0.113832\pi$
$67$	15.3350	1.87347	0.936734	+	0.350041i	$0.113832\pi$
$68$	−12.7378	−1.54469
$69$	0	0
$70$	−11.1432	−1.33187
$71$	−2.54717	−0.302293	−0.151147	−	0.988511i	$-0.548297\pi$
$71$	−2.54717	−0.302293	−0.151147	+	0.988511i	$0.548297\pi$
$72$	0	0
$73$	2.73785	0.320441	0.160220	−	0.987081i	$-0.448780\pi$
$73$	2.73785	0.320441	0.160220	+	0.987081i	$0.448780\pi$
$74$	−15.4168	−1.79216
$75$	0	0
$76$	−6.08178	−0.697628
$77$	−4.13176	−0.470858
$78$	0	0
$79$	5.15325	0.579786	0.289893	−	0.957059i	$-0.406380\pi$
$79$	5.15325	0.579786	0.289893	+	0.957059i	$0.406380\pi$
$80$	−13.2635	−1.48291
$81$	0	0
$82$	−24.5700	−2.71331
$83$	−9.28502	−1.01916	−0.509582	−	0.860422i	$-0.670200\pi$
$83$	−9.28502	−1.01916	−0.509582	+	0.860422i	$0.670200\pi$
$84$	0	0
$85$	2.41541	0.261988
$86$	−21.9310	−2.36488
$87$	0	0
$88$	−8.82872	−0.941145
$89$	−4.78783	−0.507509	−0.253755	−	0.967269i	$-0.581666\pi$
$89$	−4.78783	−0.507509	−0.253755	+	0.967269i	$0.581666\pi$
$90$	0	0
$91$	−11.3121	−1.18583
$92$	45.0742	4.69931
$93$	0	0
$94$	3.97989	0.410494
$95$	1.15325	0.118321
$96$	0	0
$97$	4.24066	0.430574	0.215287	−	0.976551i	$-0.430931\pi$
$97$	4.24066	0.430574	0.215287	+	0.976551i	$0.430931\pi$
$98$	−27.1624	−2.74381
$99$	0	0
$100$	5.27358	0.527358
$101$	13.9411	1.38719	0.693595	−	0.720365i	$-0.256026\pi$
$101$	13.9411	1.38719	0.693595	+	0.720365i	$0.256026\pi$
$102$	0	0
$103$	−18.5042	−1.82327	−0.911636	−	0.410998i	$-0.865180\pi$
$103$	−18.5042	−1.82327	−0.911636	+	0.410998i	$0.865180\pi$
$104$	−24.1717	−2.37023
$105$	0	0
$106$	−6.86961	−0.667236
$107$	−13.7663	−1.33084	−0.665421	−	0.746468i	$-0.731748\pi$
$107$	−13.7663	−1.33084	−0.665421	+	0.746468i	$0.731748\pi$
$108$	0	0
$109$	12.7878	1.22485	0.612426	−	0.790528i	$-0.290194\pi$
$109$	12.7878	1.22485	0.612426	+	0.790528i	$0.290194\pi$
$110$	2.69696	0.257145
$111$	0	0
$112$	−54.8018	−5.17828
$113$	14.8107	1.39327	0.696637	−	0.717424i	$-0.254679\pi$
$113$	14.8107	1.39327	0.696637	+	0.717424i	$0.254679\pi$
$114$	0	0
$115$	−8.54717	−0.797028
$116$	8.84675	0.821400
$117$	0	0
$118$	−22.2247	−2.04595
$119$	9.97989	0.914855
$120$	0	0
$121$	1.00000	0.0909091
$122$	−9.37380	−0.848664
$123$	0	0
$124$	−54.1256	−4.86062
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	12.9626	1.15024	0.575121	−	0.818068i	$-0.304955\pi$
$127$	12.9626	1.15024	0.575121	+	0.818068i	$0.304955\pi$
$128$	−23.9820	−2.11973
$129$	0	0
$130$	7.38386	0.647607
$131$	1.47569	0.128932	0.0644660	−	0.997920i	$-0.479466\pi$
$131$	1.47569	0.128932	0.0644660	+	0.997920i	$0.479466\pi$
$132$	0	0
$133$	4.76497	0.413175
$134$	−41.3579	−3.57278
$135$	0	0
$136$	21.3249	1.82860
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	−0.889725	−0.0754655	−0.0377327	−	0.999288i	$-0.512014\pi$
$139$	−0.889725	−0.0754655	−0.0377327	+	0.999288i	$0.512014\pi$
$140$	21.7892	1.84152
$141$	0	0
$142$	6.86961	0.576485
$143$	2.73785	0.228950
$144$	0	0
$145$	−1.67756	−0.139314
$146$	−7.38386	−0.611093
$147$	0	0
$148$	30.1457	2.47796
$149$	−12.7289	−1.04279	−0.521397	−	0.853314i	$-0.674589\pi$
$149$	−12.7289	−1.04279	−0.521397	+	0.853314i	$0.674589\pi$
$150$	0	0
$151$	−1.15325	−0.0938504	−0.0469252	−	0.998898i	$-0.514942\pi$
$151$	−1.15325	−0.0938504	−0.0469252	+	0.998898i	$0.514942\pi$
$152$	10.1818	0.825849
$153$	0	0
$154$	11.1432	0.897944
$155$	10.2635	0.824386
$156$	0	0
$157$	−3.95702	−0.315805	−0.157902	−	0.987455i	$-0.550473\pi$
$157$	−3.95702	−0.315805	−0.157902	+	0.987455i	$0.550473\pi$
$158$	−13.8981	−1.10567
$159$	0	0
$160$	18.1137	1.43202
$161$	−35.3149	−2.78320
$162$	0	0
$163$	3.07148	0.240577	0.120288	−	0.992739i	$-0.461618\pi$
$163$	3.07148	0.240577	0.120288	+	0.992739i	$0.461618\pi$
$164$	48.0438	3.75159
$165$	0	0
$166$	25.0413	1.94358
$167$	−2.71498	−0.210092	−0.105046	−	0.994467i	$-0.533499\pi$
$167$	−2.71498	−0.210092	−0.105046	+	0.994467i	$0.533499\pi$
$168$	0	0
$169$	−5.50419	−0.423399
$170$	−6.51425	−0.499620
$171$	0	0
$172$	42.8835	3.26984
$173$	−14.4154	−1.09598	−0.547992	−	0.836484i	$-0.684607\pi$
$173$	−14.4154	−1.09598	−0.547992	+	0.836484i	$0.684607\pi$
$174$	0	0
$175$	−4.13176	−0.312332
$176$	13.2635	0.999776
$177$	0	0
$178$	12.9126	0.967839
$179$	−10.7878	−0.806321	−0.403160	−	0.915129i	$-0.632088\pi$
$179$	−10.7878	−0.806321	−0.403160	+	0.915129i	$0.632088\pi$
$180$	0	0
$181$	−6.50419	−0.483453	−0.241726	−	0.970344i	$-0.577714\pi$
$181$	−6.50419	−0.483453	−0.241726	+	0.970344i	$0.577714\pi$
$182$	30.5084	2.26143
$183$	0	0
$184$	−75.4606	−5.56303
$185$	−5.71636	−0.420275
$186$	0	0
$187$	−2.41541	−0.176632
$188$	−7.78220	−0.567575
$189$	0	0
$190$	−3.11028	−0.225643
$191$	−15.8822	−1.14919	−0.574597	−	0.818437i	$-0.694841\pi$
$191$	−15.8822	−1.14919	−0.574597	+	0.818437i	$0.694841\pi$
$192$	0	0
$193$	−3.83219	−0.275847	−0.137923	−	0.990443i	$-0.544043\pi$
$193$	−3.83219	−0.275847	−0.137923	+	0.990443i	$0.544043\pi$
$194$	−11.4369	−0.821121
$195$	0	0
$196$	53.1128	3.79377
$197$	2.67893	0.190866	0.0954331	−	0.995436i	$-0.469576\pi$
$197$	2.67893	0.190866	0.0954331	+	0.995436i	$0.469576\pi$
$198$	0	0
$199$	6.78783	0.481177	0.240588	−	0.970627i	$-0.422660\pi$
$199$	6.78783	0.481177	0.240588	+	0.970627i	$0.422660\pi$
$200$	−8.82872	−0.624285
$201$	0	0
$202$	−37.5985	−2.64542
$203$	−6.93128	−0.486480
$204$	0	0
$205$	−9.11028	−0.636289
$206$	49.9050	3.47705
$207$	0	0
$208$	36.3135	2.51789
$209$	−1.15325	−0.0797722
$210$	0	0
$211$	17.6803	1.21716	0.608581	−	0.793491i	$-0.291739\pi$
$211$	17.6803	1.21716	0.608581	+	0.793491i	$0.291739\pi$
$212$	13.4327	0.922563
$213$	0	0
$214$	37.1273	2.53797
$215$	−8.13176	−0.554582
$216$	0	0
$217$	42.4065	2.87874
$218$	−34.4883	−2.33584
$219$	0	0
$220$	−5.27358	−0.355545
$221$	−6.61301	−0.444839
$222$	0	0
$223$	−8.83081	−0.591355	−0.295677	−	0.955288i	$-0.595545\pi$
$223$	−8.83081	−0.591355	−0.295677	+	0.955288i	$0.595545\pi$
$224$	74.8417	5.00057
$225$	0	0
$226$	−39.9438	−2.65702
$227$	−10.4972	−0.696723	−0.348361	−	0.937360i	$-0.613262\pi$
$227$	−10.4972	−0.696723	−0.348361	+	0.937360i	$0.613262\pi$
$228$	0	0
$229$	4.95139	0.327197	0.163598	−	0.986527i	$-0.447690\pi$
$229$	4.95139	0.327197	0.163598	+	0.986527i	$0.447690\pi$
$230$	23.0514	1.51996
$231$	0	0
$232$	−14.8107	−0.972370
$233$	3.89110	0.254914	0.127457	−	0.991844i	$-0.459318\pi$
$233$	3.89110	0.254914	0.127457	+	0.991844i	$0.459318\pi$
$234$	0	0
$235$	1.47569	0.0962637
$236$	43.4578	2.82886
$237$	0	0
$238$	−26.9153	−1.74466
$239$	15.6186	1.01029	0.505143	−	0.863036i	$-0.331440\pi$
$239$	15.6186	1.01029	0.505143	+	0.863036i	$0.331440\pi$
$240$	0	0
$241$	−10.2635	−0.661132	−0.330566	−	0.943783i	$-0.607240\pi$
$241$	−10.2635	−0.661132	−0.330566	+	0.943783i	$0.607240\pi$
$242$	−2.69696	−0.173367
$243$	0	0
$244$	18.3294	1.17342
$245$	−10.0715	−0.643443
$246$	0	0
$247$	−3.15743	−0.200902
$248$	90.6138	5.75398
$249$	0	0
$250$	2.69696	0.170571
$251$	19.6415	1.23976	0.619881	−	0.784696i	$-0.287181\pi$
$251$	19.6415	1.23976	0.619881	+	0.784696i	$0.287181\pi$
$252$	0	0
$253$	8.54717	0.537356
$254$	−34.9595	−2.19356
$255$	0	0
$256$	20.0285	1.25178
$257$	1.16919	0.0729320	0.0364660	−	0.999335i	$-0.488390\pi$
$257$	1.16919	0.0729320	0.0364660	+	0.999335i	$0.488390\pi$
$258$	0	0
$259$	−23.6186	−1.46759
$260$	−14.4383	−0.895424
$261$	0	0
$262$	−3.97989	−0.245878
$263$	−8.93553	−0.550989	−0.275494	−	0.961303i	$-0.588842\pi$
$263$	−8.93553	−0.550989	−0.275494	+	0.961303i	$0.588842\pi$
$264$	0	0
$265$	−2.54717	−0.156471
$266$	−12.8509	−0.787941
$267$	0	0
$268$	80.8704	4.93995
$269$	14.9514	0.911602	0.455801	−	0.890082i	$-0.349353\pi$
$269$	14.9514	0.911602	0.455801	+	0.890082i	$0.349353\pi$
$270$	0	0
$271$	−22.7289	−1.38068	−0.690342	−	0.723483i	$-0.742540\pi$
$271$	−22.7289	−1.38068	−0.690342	+	0.723483i	$0.742540\pi$
$272$	−32.0368	−1.94252
$273$	0	0
$274$	−16.1818	−0.977575
$275$	1.00000	0.0603023
$276$	0	0
$277$	−22.1387	−1.33019	−0.665093	−	0.746761i	$-0.731608\pi$
$277$	−22.1387	−1.33019	−0.665093	+	0.746761i	$0.731608\pi$
$278$	2.39955	0.143915
$279$	0	0
$280$	−36.4782	−2.17999
$281$	19.9841	1.19215	0.596075	−	0.802929i	$-0.296726\pi$
$281$	19.9841	1.19215	0.596075	+	0.802929i	$0.296726\pi$
$282$	0	0
$283$	24.2775	1.44315	0.721573	−	0.692339i	$-0.243420\pi$
$283$	24.2775	1.44315	0.721573	+	0.692339i	$0.243420\pi$
$284$	−13.4327	−0.797085
$285$	0	0
$286$	−7.38386	−0.436617
$287$	−37.6415	−2.22191
$288$	0	0
$289$	−11.1658	−0.656813
$290$	4.52431	0.265676
$291$	0	0
$292$	14.4383	0.844936
$293$	16.4182	0.959159	0.479579	−	0.877498i	$-0.340789\pi$
$293$	16.4182	0.959159	0.479579	+	0.877498i	$0.340789\pi$
$294$	0	0
$295$	−8.24066	−0.479790
$296$	−50.4681	−2.93340
$297$	0	0
$298$	34.3294	1.98865
$299$	23.4008	1.35331
$300$	0	0
$301$	−33.5985	−1.93659
$302$	3.11028	0.178976
$303$	0	0
$304$	−15.2962	−0.877297
$305$	−3.47569	−0.199018
$306$	0	0
$307$	5.44390	0.310700	0.155350	−	0.987859i	$-0.450349\pi$
$307$	5.44390	0.310700	0.155350	+	0.987859i	$0.450349\pi$
$308$	−21.7892	−1.24156
$309$	0	0
$310$	−27.6803	−1.57214
$311$	−28.2864	−1.60397	−0.801987	−	0.597341i	$-0.796224\pi$
$311$	−28.2864	−1.60397	−0.801987	+	0.597341i	$0.796224\pi$
$312$	0	0
$313$	22.8107	1.28934	0.644668	−	0.764462i	$-0.276995\pi$
$313$	22.8107	1.28934	0.644668	+	0.764462i	$0.276995\pi$
$314$	10.6719	0.602252
$315$	0	0
$316$	27.1761	1.52878
$317$	−23.8593	−1.34007	−0.670036	−	0.742328i	$-0.733721\pi$
$317$	−23.8593	−1.34007	−0.670036	+	0.742328i	$0.733721\pi$
$318$	0	0
$319$	1.67756	0.0939252
$320$	−22.3249	−1.24800
$321$	0	0
$322$	95.2428	5.30767
$323$	2.78557	0.154993
$324$	0	0
$325$	2.73785	0.151868
$326$	−8.28364	−0.458788
$327$	0	0
$328$	−80.4321	−4.44112
$329$	6.09722	0.336151
$330$	0	0
$331$	−18.9084	−1.03930	−0.519650	−	0.854379i	$-0.673938\pi$
$331$	−18.9084	−1.03930	−0.519650	+	0.854379i	$0.673938\pi$
$332$	−48.9653	−2.68732
$333$	0	0
$334$	7.32220	0.400653
$335$	−15.3350	−0.837841
$336$	0	0
$337$	24.6630	1.34348	0.671740	−	0.740787i	$-0.265547\pi$
$337$	24.6630	1.34348	0.671740	+	0.740787i	$0.265547\pi$
$338$	14.8446	0.807439
$339$	0	0
$340$	12.7378	0.690807
$341$	−10.2635	−0.555801
$342$	0	0
$343$	−12.6906	−0.685229
$344$	−71.7931	−3.87082
$345$	0	0
$346$	38.8778	2.09008
$347$	15.5056	0.832383	0.416191	−	0.909277i	$-0.363365\pi$
$347$	15.5056	0.832383	0.416191	+	0.909277i	$0.363365\pi$
$348$	0	0
$349$	20.4841	1.09649	0.548244	−	0.836319i	$-0.315297\pi$
$349$	20.4841	1.09649	0.548244	+	0.836319i	$0.315297\pi$
$350$	11.1432	0.595629
$351$	0	0
$352$	−18.1137	−0.965466
$353$	21.9799	1.16987	0.584936	−	0.811080i	$-0.301120\pi$
$353$	21.9799	1.16987	0.584936	+	0.811080i	$0.301120\pi$
$354$	0	0
$355$	2.54717	0.135190
$356$	−25.2490	−1.33820
$357$	0	0
$358$	29.0943	1.53768
$359$	19.6962	1.03953	0.519764	−	0.854310i	$-0.326020\pi$
$359$	19.6962	1.03953	0.519764	+	0.854310i	$0.326020\pi$
$360$	0	0
$361$	−17.6700	−0.930000
$362$	17.5415	0.921963
$363$	0	0
$364$	−59.6555	−3.12680
$365$	−2.73785	−0.143305
$366$	0	0
$367$	−28.2635	−1.47534	−0.737672	−	0.675159i	$-0.764075\pi$
$367$	−28.2635	−1.47534	−0.737672	+	0.675159i	$0.764075\pi$
$368$	113.366	5.90959
$369$	0	0
$370$	15.4168	0.801480
$371$	−10.5243	−0.546395
$372$	0	0
$373$	−9.78921	−0.506866	−0.253433	−	0.967353i	$-0.581560\pi$
$373$	−9.78921	−0.506866	−0.253433	+	0.967353i	$0.581560\pi$
$374$	6.51425	0.336844
$375$	0	0
$376$	13.0285	0.671893
$377$	4.59290	0.236546
$378$	0	0
$379$	5.66162	0.290818	0.145409	−	0.989372i	$-0.453550\pi$
$379$	5.66162	0.290818	0.145409	+	0.989372i	$0.453550\pi$
$380$	6.08178	0.311989
$381$	0	0
$382$	42.8336	2.19156
$383$	26.5042	1.35430	0.677150	−	0.735845i	$-0.263215\pi$
$383$	26.5042	1.35430	0.677150	+	0.735845i	$0.263215\pi$
$384$	0	0
$385$	4.13176	0.210574
$386$	10.3352	0.526050
$387$	0	0
$388$	22.3635	1.13533
$389$	15.3551	0.778535	0.389268	−	0.921125i	$-0.372728\pi$
$389$	15.3551	0.778535	0.389268	+	0.921125i	$0.372728\pi$
$390$	0	0
$391$	−20.6449	−1.04406
$392$	−88.9183	−4.49105
$393$	0	0
$394$	−7.22497	−0.363989
$395$	−5.15325	−0.259288
$396$	0	0
$397$	16.7677	0.841548	0.420774	−	0.907166i	$-0.361759\pi$
$397$	16.7677	0.841548	0.420774	+	0.907166i	$0.361759\pi$
$398$	−18.3065	−0.917622
$399$	0	0
$400$	13.2635	0.663176
$401$	26.0457	1.30066	0.650331	−	0.759651i	$-0.274630\pi$
$401$	26.0457	1.30066	0.650331	+	0.759651i	$0.274630\pi$
$402$	0	0
$403$	−28.1000	−1.39976
$404$	73.5195	3.65773
$405$	0	0
$406$	18.6934	0.927736
$407$	5.71636	0.283349
$408$	0	0
$409$	22.4495	1.11005	0.555027	−	0.831832i	$-0.312708\pi$
$409$	22.4495	1.11005	0.555027	+	0.831832i	$0.312708\pi$
$410$	24.5700	1.21343
$411$	0	0
$412$	−97.5834	−4.80759
$413$	−34.0485	−1.67542
$414$	0	0
$415$	9.28502	0.455784
$416$	−49.5927	−2.43148
$417$	0	0
$418$	3.11028	0.152129
$419$	−27.8822	−1.36213	−0.681067	−	0.732221i	$-0.738484\pi$
$419$	−27.8822	−1.36213	−0.681067	+	0.732221i	$0.738484\pi$
$420$	0	0
$421$	15.5985	0.760226	0.380113	−	0.924940i	$-0.375885\pi$
$421$	15.5985	0.760226	0.380113	+	0.924940i	$0.375885\pi$
$422$	−47.6831	−2.32118
$423$	0	0
$424$	−22.4883	−1.09213
$425$	−2.41541	−0.117164
$426$	0	0
$427$	−14.3608	−0.694965
$428$	−72.5980	−3.50916
$429$	0	0
$430$	21.9310	1.05761
$431$	−2.95139	−0.142163	−0.0710817	−	0.997470i	$-0.522645\pi$
$431$	−2.95139	−0.142163	−0.0710817	+	0.997470i	$0.522645\pi$
$432$	0	0
$433$	24.2864	1.16713	0.583565	−	0.812067i	$-0.301657\pi$
$433$	24.2864	1.16713	0.583565	+	0.812067i	$0.301657\pi$
$434$	−114.369	−5.48986
$435$	0	0
$436$	67.4377	3.22968
$437$	−9.85705	−0.471527
$438$	0	0
$439$	−19.1103	−0.912084	−0.456042	−	0.889958i	$-0.650733\pi$
$439$	−19.1103	−0.912084	−0.456042	+	0.889958i	$0.650733\pi$
$440$	8.82872	0.420893
$441$	0	0
$442$	17.8350	0.848325
$443$	1.97714	0.0939365	0.0469683	−	0.998896i	$-0.485044\pi$
$443$	1.97714	0.0939365	0.0469683	+	0.998896i	$0.485044\pi$
$444$	0	0
$445$	4.78783	0.226965
$446$	23.8163	1.12774
$447$	0	0
$448$	−92.2414	−4.35800
$449$	−15.1719	−0.716008	−0.358004	−	0.933720i	$-0.616543\pi$
$449$	−15.1719	−0.716008	−0.358004	+	0.933720i	$0.616543\pi$
$450$	0	0
$451$	9.11028	0.428986
$452$	78.1055	3.67377
$453$	0	0
$454$	28.3105	1.32868
$455$	11.3121	0.530321
$456$	0	0
$457$	−6.17056	−0.288647	−0.144323	−	0.989531i	$-0.546101\pi$
$457$	−6.17056	−0.288647	−0.144323	+	0.989531i	$0.546101\pi$
$458$	−13.3537	−0.623977
$459$	0	0
$460$	−45.0742	−2.10160
$461$	23.1990	1.08048	0.540242	−	0.841510i	$-0.318333\pi$
$461$	23.1990	1.08048	0.540242	+	0.841510i	$0.318333\pi$
$462$	0	0
$463$	−1.39809	−0.0649750	−0.0324875	−	0.999472i	$-0.510343\pi$
$463$	−1.39809	−0.0649750	−0.0324875	+	0.999472i	$0.510343\pi$
$464$	22.2503	1.03295
$465$	0	0
$466$	−10.4941	−0.486131
$467$	22.6901	1.04997	0.524987	−	0.851110i	$-0.324070\pi$
$467$	22.6901	1.04997	0.524987	+	0.851110i	$0.324070\pi$
$468$	0	0
$469$	−63.3606	−2.92572
$470$	−3.97989	−0.183578
$471$	0	0
$472$	−72.7545	−3.34880
$473$	8.13176	0.373899
$474$	0	0
$475$	−1.15325	−0.0529149
$476$	52.6298	2.41228
$477$	0	0
$478$	−42.1228	−1.92665
$479$	24.7906	1.13271	0.566355	−	0.824161i	$-0.308353\pi$
$479$	24.7906	1.13271	0.566355	+	0.824161i	$0.308353\pi$
$480$	0	0
$481$	15.6505	0.713602
$482$	27.6803	1.26080
$483$	0	0
$484$	5.27358	0.239708
$485$	−4.24066	−0.192559
$486$	0	0
$487$	−33.7191	−1.52796	−0.763979	−	0.645241i	$-0.776757\pi$
$487$	−33.7191	−1.52796	−0.763979	+	0.645241i	$0.776757\pi$
$488$	−30.6859	−1.38909
$489$	0	0
$490$	27.1624	1.22707
$491$	−6.90566	−0.311648	−0.155824	−	0.987785i	$-0.549803\pi$
$491$	−6.90566	−0.311648	−0.155824	+	0.987785i	$0.549803\pi$
$492$	0	0
$493$	−4.05198	−0.182492
$494$	8.51546	0.383129
$495$	0	0
$496$	−136.131	−6.11244
$497$	10.5243	0.472080
$498$	0	0
$499$	−2.26078	−0.101206	−0.0506031	−	0.998719i	$-0.516114\pi$
$499$	−2.26078	−0.101206	−0.0506031	+	0.998719i	$0.516114\pi$
$500$	−5.27358	−0.235842
$501$	0	0
$502$	−52.9723	−2.36427
$503$	−20.5999	−0.918504	−0.459252	−	0.888306i	$-0.651883\pi$
$503$	−20.5999	−0.918504	−0.459252	+	0.888306i	$0.651883\pi$
$504$	0	0
$505$	−13.9411	−0.620370
$506$	−23.0514	−1.02476
$507$	0	0
$508$	68.3592	3.03295
$509$	7.43272	0.329449	0.164725	−	0.986340i	$-0.447326\pi$
$509$	7.43272	0.329449	0.164725	+	0.986340i	$0.447326\pi$
$510$	0	0
$511$	−11.3121	−0.500420
$512$	−6.05208	−0.267466
$513$	0	0
$514$	−3.15325	−0.139084
$515$	18.5042	0.815392
$516$	0	0
$517$	−1.47569	−0.0649010
$518$	63.6985	2.79875
$519$	0	0
$520$	24.1717	1.06000
$521$	35.0084	1.53375	0.766873	−	0.641799i	$-0.221812\pi$
$521$	35.0084	1.53375	0.766873	+	0.641799i	$0.221812\pi$
$522$	0	0
$523$	−1.52986	−0.0668960	−0.0334480	−	0.999440i	$-0.510649\pi$
$523$	−1.52986	−0.0668960	−0.0334480	+	0.999440i	$0.510649\pi$
$524$	7.78220	0.339967
$525$	0	0
$526$	24.0988	1.05076
$527$	24.7906	1.07989
$528$	0	0
$529$	50.0541	2.17627
$530$	6.86961	0.298397
$531$	0	0
$532$	25.1285	1.08946
$533$	24.9425	1.08038
$534$	0	0
$535$	13.7663	0.595171
$536$	−135.388	−5.84789
$537$	0	0
$538$	−40.3233	−1.73846
$539$	10.0715	0.433809
$540$	0	0
$541$	16.6700	0.716700	0.358350	−	0.933587i	$-0.383340\pi$
$541$	16.6700	0.716700	0.358350	+	0.933587i	$0.383340\pi$
$542$	61.2990	2.63302
$543$	0	0
$544$	43.7520	1.87585
$545$	−12.7878	−0.547771
$546$	0	0
$547$	−2.25234	−0.0963032	−0.0481516	−	0.998840i	$-0.515333\pi$
$547$	−2.25234	−0.0963032	−0.0481516	+	0.998840i	$0.515333\pi$
$548$	31.6415	1.35166
$549$	0	0
$550$	−2.69696	−0.114999
$551$	−1.93465	−0.0824188
$552$	0	0
$553$	−21.2920	−0.905429
$554$	59.7071	2.53671
$555$	0	0
$556$	−4.69204	−0.198987
$557$	11.9911	0.508078	0.254039	−	0.967194i	$-0.418241\pi$
$557$	11.9911	0.508078	0.254039	+	0.967194i	$0.418241\pi$
$558$	0	0
$559$	22.2635	0.941647
$560$	54.8018	2.31580
$561$	0	0
$562$	−53.8962	−2.27347
$563$	19.4598	0.820134	0.410067	−	0.912055i	$-0.365505\pi$
$563$	19.4598	0.820134	0.410067	+	0.912055i	$0.365505\pi$
$564$	0	0
$565$	−14.8107	−0.623091
$566$	−65.4753	−2.75213
$567$	0	0
$568$	22.4883	0.943586
$569$	−19.7205	−0.826728	−0.413364	−	0.910566i	$-0.635646\pi$
$569$	−19.7205	−0.826728	−0.413364	+	0.910566i	$0.635646\pi$
$570$	0	0
$571$	5.41678	0.226685	0.113343	−	0.993556i	$-0.463844\pi$
$571$	5.41678	0.226685	0.113343	+	0.993556i	$0.463844\pi$
$572$	14.4383	0.603694
$573$	0	0
$574$	101.518	4.23726
$575$	8.54717	0.356442
$576$	0	0
$577$	6.42708	0.267563	0.133781	−	0.991011i	$-0.457288\pi$
$577$	6.42708	0.267563	0.133781	+	0.991011i	$0.457288\pi$
$578$	30.1137	1.25257
$579$	0	0
$580$	−8.84675	−0.367341
$581$	38.3635	1.59159
$582$	0	0
$583$	2.54717	0.105493
$584$	−24.1717	−1.00023
$585$	0	0
$586$	−44.2791	−1.82915
$587$	−44.9883	−1.85686	−0.928432	−	0.371502i	$-0.878843\pi$
$587$	−44.9883	−1.85686	−0.928432	+	0.371502i	$0.878843\pi$
$588$	0	0
$589$	11.8364	0.487712
$590$	22.2247	0.914978
$591$	0	0
$592$	75.8191	3.11615
$593$	−21.3892	−0.878348	−0.439174	−	0.898402i	$-0.644729\pi$
$593$	−21.3892	−0.878348	−0.439174	+	0.898402i	$0.644729\pi$
$594$	0	0
$595$	−9.97989	−0.409135
$596$	−67.1270	−2.74963
$597$	0	0
$598$	−63.1111	−2.58081
$599$	26.9514	1.10120	0.550602	−	0.834768i	$-0.314398\pi$
$599$	26.9514	1.10120	0.550602	+	0.834768i	$0.314398\pi$
$600$	0	0
$601$	6.42708	0.262166	0.131083	−	0.991371i	$-0.458155\pi$
$601$	6.42708	0.262166	0.131083	+	0.991371i	$0.458155\pi$
$602$	90.6138	3.69314
$603$	0	0
$604$	−6.08178	−0.247464
$605$	−1.00000	−0.0406558
$606$	0	0
$607$	12.9626	0.526135	0.263067	−	0.964777i	$-0.415266\pi$
$607$	12.9626	0.526135	0.263067	+	0.964777i	$0.415266\pi$
$608$	20.8897	0.847190
$609$	0	0
$610$	9.37380	0.379534
$611$	−4.04023	−0.163450
$612$	0	0
$613$	−24.4771	−0.988620	−0.494310	−	0.869286i	$-0.664579\pi$
$613$	−24.4771	−0.988620	−0.494310	+	0.869286i	$0.664579\pi$
$614$	−14.6820	−0.592517
$615$	0	0
$616$	36.4782	1.46975
$617$	11.9453	0.480898	0.240449	−	0.970662i	$-0.422705\pi$
$617$	11.9453	0.480898	0.240449	+	0.970662i	$0.422705\pi$
$618$	0	0
$619$	−18.9084	−0.759993	−0.379997	−	0.924988i	$-0.624075\pi$
$619$	−18.9084	−0.759993	−0.379997	+	0.924988i	$0.624075\pi$
$620$	54.1256	2.17374
$621$	0	0
$622$	76.2872	3.05884
$623$	19.7822	0.792557
$624$	0	0
$625$	1.00000	0.0400000
$626$	−61.5195	−2.45881
$627$	0	0
$628$	−20.8677	−0.832712
$629$	−13.8073	−0.550534
$630$	0	0
$631$	−11.8364	−0.471201	−0.235601	−	0.971850i	$-0.575706\pi$
$631$	−11.8364	−0.471201	−0.235601	+	0.971850i	$0.575706\pi$
$632$	−45.4966	−1.80976
$633$	0	0
$634$	64.3476	2.55557
$635$	−12.9626	−0.514404
$636$	0	0
$637$	27.5742	1.09253
$638$	−4.52431	−0.179119
$639$	0	0
$640$	23.9820	0.947971
$641$	12.2206	0.482683	0.241341	−	0.970440i	$-0.422413\pi$
$641$	12.2206	0.482683	0.241341	+	0.970440i	$0.422413\pi$
$642$	0	0
$643$	−8.84257	−0.348717	−0.174358	−	0.984682i	$-0.555785\pi$
$643$	−8.84257	−0.348717	−0.174358	+	0.984682i	$0.555785\pi$
$644$	−186.236	−7.33873
$645$	0	0
$646$	−7.51258	−0.295578
$647$	−9.40985	−0.369939	−0.184970	−	0.982744i	$-0.559219\pi$
$647$	−9.40985	−0.369939	−0.184970	+	0.982744i	$0.559219\pi$
$648$	0	0
$649$	8.24066	0.323474
$650$	−7.38386	−0.289619
$651$	0	0
$652$	16.1977	0.634350
$653$	−22.7449	−0.890075	−0.445038	−	0.895512i	$-0.646810\pi$
$653$	−22.7449	−0.890075	−0.445038	+	0.895512i	$0.646810\pi$
$654$	0	0
$655$	−1.47569	−0.0576602
$656$	120.834	4.71779
$657$	0	0
$658$	−16.4440	−0.641052
$659$	20.3635	0.793249	0.396625	−	0.917981i	$-0.370181\pi$
$659$	20.3635	0.793249	0.396625	+	0.917981i	$0.370181\pi$
$660$	0	0
$661$	11.6616	0.453585	0.226792	−	0.973943i	$-0.427176\pi$
$661$	11.6616	0.453585	0.226792	+	0.973943i	$0.427176\pi$
$662$	50.9952	1.98198
$663$	0	0
$664$	81.9748	3.18124
$665$	−4.76497	−0.184778
$666$	0	0
$667$	14.3384	0.555184
$668$	−14.3177	−0.553968
$669$	0	0
$670$	41.3579	1.59779
$671$	3.47569	0.134178
$672$	0	0
$673$	30.0070	1.15669	0.578343	−	0.815794i	$-0.303700\pi$
$673$	30.0070	1.15669	0.578343	+	0.815794i	$0.303700\pi$
$674$	−66.5151	−2.56207
$675$	0	0
$676$	−29.0268	−1.11642
$677$	−51.4695	−1.97813	−0.989067	−	0.147466i	$-0.952888\pi$
$677$	−51.4695	−1.97813	−0.989067	+	0.147466i	$0.952888\pi$
$678$	0	0
$679$	−17.5214	−0.672411
$680$	−21.3249	−0.817774
$681$	0	0
$682$	27.6803	1.05993
$683$	27.6186	1.05680	0.528399	−	0.848996i	$-0.322793\pi$
$683$	27.6186	1.05680	0.528399	+	0.848996i	$0.322793\pi$
$684$	0	0
$685$	−6.00000	−0.229248
$686$	34.2261	1.30676
$687$	0	0
$688$	107.856	4.11197
$689$	6.97376	0.265679
$690$	0	0
$691$	−34.2344	−1.30234	−0.651169	−	0.758933i	$-0.725721\pi$
$691$	−34.2344	−1.30234	−0.651169	+	0.758933i	$0.725721\pi$
$692$	−76.0209	−2.88988
$693$	0	0
$694$	−41.8179	−1.58738
$695$	0.889725	0.0337492
$696$	0	0
$697$	−22.0050	−0.833499
$698$	−55.2447	−2.09104
$699$	0	0
$700$	−21.7892	−0.823555
$701$	−11.8524	−0.447658	−0.223829	−	0.974628i	$-0.571856\pi$
$701$	−11.8524	−0.447658	−0.223829	+	0.974628i	$0.571856\pi$
$702$	0	0
$703$	−6.59241	−0.248637
$704$	22.3249	0.841403
$705$	0	0
$706$	−59.2788	−2.23099
$707$	−57.6013	−2.16632
$708$	0	0
$709$	−28.1658	−1.05779	−0.528895	−	0.848687i	$-0.677393\pi$
$709$	−28.1658	−1.05779	−0.528895	+	0.848687i	$0.677393\pi$
$710$	−6.86961	−0.257812
$711$	0	0
$712$	42.2705	1.58415
$713$	−87.7241	−3.28529
$714$	0	0
$715$	−2.73785	−0.102390
$716$	−56.8906	−2.12610
$717$	0	0
$718$	−53.1200	−1.98242
$719$	−26.2663	−0.979567	−0.489783	−	0.871844i	$-0.662924\pi$
$719$	−26.2663	−0.979567	−0.489783	+	0.871844i	$0.662924\pi$
$720$	0	0
$721$	76.4550	2.84733
$722$	47.6553	1.77355
$723$	0	0
$724$	−34.3004	−1.27476
$725$	1.67756	0.0623030
$726$	0	0
$727$	21.1401	0.784042	0.392021	−	0.919956i	$-0.371776\pi$
$727$	21.1401	0.784042	0.392021	+	0.919956i	$0.371776\pi$
$728$	99.8717	3.70149
$729$	0	0
$730$	7.38386	0.273289
$731$	−19.6415	−0.726467
$732$	0	0
$733$	3.86406	0.142722	0.0713611	−	0.997451i	$-0.477266\pi$
$733$	3.86406	0.142722	0.0713611	+	0.997451i	$0.477266\pi$
$734$	76.2256	2.81354
$735$	0	0
$736$	−154.821	−5.70679
$737$	15.3350	0.564872
$738$	0	0
$739$	−14.0298	−0.516094	−0.258047	−	0.966132i	$-0.583079\pi$
$739$	−14.0298	−0.516094	−0.258047	+	0.966132i	$0.583079\pi$
$740$	−30.1457	−1.10818
$741$	0	0
$742$	28.3836	1.04200
$743$	26.2934	0.964611	0.482306	−	0.876003i	$-0.339799\pi$
$743$	26.2934	0.964611	0.482306	+	0.876003i	$0.339799\pi$
$744$	0	0
$745$	12.7289	0.466352
$746$	26.4011	0.966613
$747$	0	0
$748$	−12.7378	−0.465742
$749$	56.8793	2.07832
$750$	0	0
$751$	38.2206	1.39469	0.697344	−	0.716737i	$-0.254365\pi$
$751$	38.2206	1.39469	0.697344	+	0.716737i	$0.254365\pi$
$752$	−19.5729	−0.713751
$753$	0	0
$754$	−12.3869	−0.451103
$755$	1.15325	0.0419712
$756$	0	0
$757$	−36.6158	−1.33082	−0.665411	−	0.746477i	$-0.731744\pi$
$757$	−36.6158	−1.33082	−0.665411	+	0.746477i	$0.731744\pi$
$758$	−15.2692	−0.554601
$759$	0	0
$760$	−10.1818	−0.369331
$761$	51.6803	1.87341	0.936705	−	0.350120i	$-0.113859\pi$
$761$	51.6803	1.87341	0.936705	+	0.350120i	$0.113859\pi$
$762$	0	0
$763$	−52.8363	−1.91280
$764$	−83.7560	−3.03019
$765$	0	0
$766$	−71.4807	−2.58270
$767$	22.5617	0.814655
$768$	0	0
$769$	44.4841	1.60414	0.802068	−	0.597232i	$-0.203733\pi$
$769$	44.4841	1.60414	0.802068	+	0.597232i	$0.203733\pi$
$770$	−11.1432	−0.401573
$771$	0	0
$772$	−20.2094	−0.727351
$773$	0.973762	0.0350238	0.0175119	−	0.999847i	$-0.494426\pi$
$773$	0.973762	0.0350238	0.0175119	+	0.999847i	$0.494426\pi$
$774$	0	0
$775$	−10.2635	−0.368677
$776$	−37.4396	−1.34400
$777$	0	0
$778$	−41.4121	−1.48470
$779$	−10.5065	−0.376433
$780$	0	0
$781$	−2.54717	−0.0911449
$782$	55.6784	1.99106
$783$	0	0
$784$	133.583	4.77083
$785$	3.95702	0.141232
$786$	0	0
$787$	−30.5382	−1.08857	−0.544285	−	0.838900i	$-0.683199\pi$
$787$	−30.5382	−1.08857	−0.544285	+	0.838900i	$0.683199\pi$
$788$	14.1276	0.503274
$789$	0	0
$790$	13.8981	0.494473
$791$	−61.1943	−2.17582
$792$	0	0
$793$	9.51592	0.337920
$794$	−45.2218	−1.60486
$795$	0	0
$796$	35.7962	1.26876
$797$	26.7247	0.946639	0.473319	−	0.880891i	$-0.343056\pi$
$797$	26.7247	0.946639	0.473319	+	0.880891i	$0.343056\pi$
$798$	0	0
$799$	3.56440	0.126099
$800$	−18.1137	−0.640417
$801$	0	0
$802$	−70.2442	−2.48041
$803$	2.73785	0.0966165
$804$	0	0
$805$	35.3149	1.24469
$806$	75.7845	2.66939
$807$	0	0
$808$	−123.082	−4.33001
$809$	−17.0327	−0.598837	−0.299418	−	0.954122i	$-0.596793\pi$
$809$	−17.0327	−0.598837	−0.299418	+	0.954122i	$0.596793\pi$
$810$	0	0
$811$	23.1103	0.811512	0.405756	−	0.913982i	$-0.367008\pi$
$811$	23.1103	0.811512	0.405756	+	0.913982i	$0.367008\pi$
$812$	−36.5527	−1.28275
$813$	0	0
$814$	−15.4168	−0.540358
$815$	−3.07148	−0.107589
$816$	0	0
$817$	−9.37798	−0.328094
$818$	−60.5453	−2.11692
$819$	0	0
$820$	−48.0438	−1.67776
$821$	−28.3476	−0.989337	−0.494668	−	0.869082i	$-0.664710\pi$
$821$	−28.3476	−0.989337	−0.494668	+	0.869082i	$0.664710\pi$
$822$	0	0
$823$	−10.4585	−0.364559	−0.182280	−	0.983247i	$-0.558348\pi$
$823$	−10.4585	−0.364559	−0.182280	+	0.983247i	$0.558348\pi$
$824$	163.368	5.69121
$825$	0	0
$826$	91.8273	3.19508
$827$	−45.2672	−1.57409	−0.787047	−	0.616893i	$-0.788391\pi$
$827$	−45.2672	−1.57409	−0.787047	+	0.616893i	$0.788391\pi$
$828$	0	0
$829$	−22.9855	−0.798320	−0.399160	−	0.916881i	$-0.630698\pi$
$829$	−22.9855	−0.798320	−0.399160	+	0.916881i	$0.630698\pi$
$830$	−25.0413	−0.869196
$831$	0	0
$832$	61.1223	2.11903
$833$	−24.3267	−0.842870
$834$	0	0
$835$	2.71498	0.0939559
$836$	−6.08178	−0.210343
$837$	0	0
$838$	75.1971	2.59764
$839$	−20.1547	−0.695818	−0.347909	−	0.937528i	$-0.613108\pi$
$839$	−20.1547	−0.695818	−0.347909	+	0.937528i	$0.613108\pi$
$840$	0	0
$841$	−26.1858	−0.902959
$842$	−42.0686	−1.44978
$843$	0	0
$844$	93.2386	3.20941
$845$	5.50419	0.189350
$846$	0	0
$847$	−4.13176	−0.141969
$848$	33.7845	1.16016
$849$	0	0
$850$	6.51425	0.223437
$851$	48.8587	1.67485
$852$	0	0
$853$	−38.2705	−1.31036	−0.655179	−	0.755474i	$-0.727407\pi$
$853$	−38.2705	−1.31036	−0.655179	+	0.755474i	$0.727407\pi$
$854$	38.7303	1.32533
$855$	0	0
$856$	121.539	4.15413
$857$	−9.51250	−0.324941	−0.162470	−	0.986713i	$-0.551946\pi$
$857$	−9.51250	−0.324941	−0.162470	+	0.986713i	$0.551946\pi$
$858$	0	0
$859$	−1.61865	−0.0552275	−0.0276137	−	0.999619i	$-0.508791\pi$
$859$	−1.61865	−0.0552275	−0.0276137	+	0.999619i	$0.508791\pi$
$860$	−42.8835	−1.46232
$861$	0	0
$862$	7.95977	0.271111
$863$	46.0229	1.56664	0.783318	−	0.621621i	$-0.213526\pi$
$863$	46.0229	1.56664	0.783318	+	0.621621i	$0.213526\pi$
$864$	0	0
$865$	14.4154	0.490138
$866$	−65.4994	−2.22576
$867$	0	0
$868$	223.634	7.59064
$869$	5.15325	0.174812
$870$	0	0
$871$	41.9849	1.42260
$872$	−112.900	−3.82328
$873$	0	0
$874$	26.5841	0.899219
$875$	4.13176	0.139679
$876$	0	0
$877$	−28.7630	−0.971257	−0.485628	−	0.874165i	$-0.661409\pi$
$877$	−28.7630	−0.971257	−0.485628	+	0.874165i	$0.661409\pi$
$878$	51.5396	1.73938
$879$	0	0
$880$	−13.2635	−0.447113
$881$	−23.3149	−0.785499	−0.392749	−	0.919646i	$-0.628476\pi$
$881$	−23.3149	−0.785499	−0.392749	+	0.919646i	$0.628476\pi$
$882$	0	0
$883$	29.6616	0.998193	0.499097	−	0.866546i	$-0.333665\pi$
$883$	29.6616	0.998193	0.499097	+	0.866546i	$0.333665\pi$
$884$	−34.8743	−1.17295
$885$	0	0
$886$	−5.33225	−0.179141
$887$	20.3364	0.682829	0.341414	−	0.939913i	$-0.389094\pi$
$887$	20.3364	0.682829	0.341414	+	0.939913i	$0.389094\pi$
$888$	0	0
$889$	−53.5583	−1.79629
$890$	−12.9126	−0.432831
$891$	0	0
$892$	−46.5700	−1.55928
$893$	1.70185	0.0569502
$894$	0	0
$895$	10.7878	0.360598
$896$	99.0879	3.31029
$897$	0	0
$898$	40.9181	1.36545
$899$	−17.2177	−0.574241
$900$	0	0
$901$	−6.15245	−0.204968
$902$	−24.5700	−0.818093
$903$	0	0
$904$	−130.760	−4.34900
$905$	6.50419	0.216207
$906$	0	0
$907$	9.87942	0.328041	0.164020	−	0.986457i	$-0.447554\pi$
$907$	9.87942	0.328041	0.164020	+	0.986457i	$0.447554\pi$
$908$	−55.3578	−1.83711
$909$	0	0
$910$	−30.5084	−1.01134
$911$	7.22343	0.239323	0.119662	−	0.992815i	$-0.461819\pi$
$911$	7.22343	0.239323	0.119662	+	0.992815i	$0.461819\pi$
$912$	0	0
$913$	−9.28502	−0.307289
$914$	16.6418	0.550460
$915$	0	0
$916$	26.1116	0.862751
$917$	−6.09722	−0.201348
$918$	0	0
$919$	35.7233	1.17840	0.589201	−	0.807986i	$-0.299443\pi$
$919$	35.7233	1.17840	0.589201	+	0.807986i	$0.299443\pi$
$920$	75.4606	2.48786
$921$	0	0
$922$	−62.5667	−2.06052
$923$	−6.97376	−0.229544
$924$	0	0
$925$	5.71636	0.187953
$926$	3.77060	0.123910
$927$	0	0
$928$	−30.3869	−0.997497
$929$	−1.12621	−0.0369498	−0.0184749	−	0.999829i	$-0.505881\pi$
$929$	−1.12621	−0.0369498	−0.0184749	+	0.999829i	$0.505881\pi$
$930$	0	0
$931$	−11.6150	−0.380665
$932$	20.5200	0.672157
$933$	0	0
$934$	−61.1943	−2.00234
$935$	2.41541	0.0789922
$936$	0	0
$937$	−0.127587	−0.00416807	−0.00208404	−	0.999998i	$-0.500663\pi$
$937$	−0.127587	−0.00416807	−0.00208404	+	0.999998i	$0.500663\pi$
$938$	170.881	5.57946
$939$	0	0
$940$	7.78220	0.253827
$941$	1.41403	0.0460961	0.0230480	−	0.999734i	$-0.492663\pi$
$941$	1.41403	0.0460961	0.0230480	+	0.999734i	$0.492663\pi$
$942$	0	0
$943$	77.8671	2.53570
$944$	109.300	3.55742
$945$	0	0
$946$	−21.9310	−0.713039
$947$	−37.1943	−1.20865	−0.604326	−	0.796737i	$-0.706558\pi$
$947$	−37.1943	−1.20865	−0.604326	+	0.796737i	$0.706558\pi$
$948$	0	0
$949$	7.49581	0.243324
$950$	3.11028	0.100911
$951$	0	0
$952$	−88.1097	−2.85565
$953$	−16.5041	−0.534621	−0.267310	−	0.963610i	$-0.586135\pi$
$953$	−16.5041	−0.534621	−0.267310	+	0.963610i	$0.586135\pi$
$954$	0	0
$955$	15.8822	0.513935
$956$	82.3663	2.66391
$957$	0	0
$958$	−66.8592	−2.16012
$959$	−24.7906	−0.800530
$960$	0	0
$961$	74.3400	2.39807
$962$	−42.2088	−1.36087
$963$	0	0
$964$	−54.1256	−1.74327
$965$	3.83219	0.123362
$966$	0	0
$967$	−3.60471	−0.115920	−0.0579598	−	0.998319i	$-0.518460\pi$
$967$	−3.60471	−0.115920	−0.0579598	+	0.998319i	$0.518460\pi$
$968$	−8.82872	−0.283766
$969$	0	0
$970$	11.4369	0.367217
$971$	29.6214	0.950596	0.475298	−	0.879825i	$-0.342340\pi$
$971$	29.6214	0.950596	0.475298	+	0.879825i	$0.342340\pi$
$972$	0	0
$973$	3.67613	0.117851
$974$	90.9390	2.91387
$975$	0	0
$976$	46.1000	1.47562
$977$	−52.7157	−1.68653	−0.843263	−	0.537501i	$-0.819368\pi$
$977$	−52.7157	−1.68653	−0.843263	+	0.537501i	$0.819368\pi$
$978$	0	0
$979$	−4.78783	−0.153020
$980$	−53.1128	−1.69663
$981$	0	0
$982$	18.6243	0.594325
$983$	29.2602	0.933254	0.466627	−	0.884454i	$-0.345469\pi$
$983$	29.2602	0.933254	0.466627	+	0.884454i	$0.345469\pi$
$984$	0	0
$985$	−2.67893	−0.0853579
$986$	10.9280	0.348019
$987$	0	0
$988$	−16.6510	−0.529738
$989$	69.5036	2.21008
$990$	0	0
$991$	38.1776	1.21275	0.606375	−	0.795179i	$-0.292623\pi$
$991$	38.1776	1.21275	0.606375	+	0.795179i	$0.292623\pi$
$992$	185.911	5.90268
$993$	0	0
$994$	−28.3836	−0.900274
$995$	−6.78783	−0.215189
$996$	0	0
$997$	−40.1500	−1.27156	−0.635781	−	0.771870i	$-0.719322\pi$
$997$	−40.1500	−1.27156	−0.635781	+	0.771870i	$0.719322\pi$
$998$	6.09722	0.193004
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.a.f.1.1	✓	4
3.2	odd	2		495.2.a.g.1.4	yes	4
4.3	odd	2		7920.2.a.cm.1.4		4
5.2	odd	4		2475.2.c.t.199.1		8
5.3	odd	4		2475.2.c.t.199.8		8
5.4	even	2		2475.2.a.bj.1.4		4
11.10	odd	2		5445.2.a.bs.1.4		4
12.11	even	2		7920.2.a.cn.1.4		4
15.2	even	4		2475.2.c.s.199.8		8
15.8	even	4		2475.2.c.s.199.1		8
15.14	odd	2		2475.2.a.bf.1.1		4
33.32	even	2		5445.2.a.bh.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.a.f.1.1	✓	4	1.1	even	1	trivial
495.2.a.g.1.4	yes	4	3.2	odd	2
2475.2.a.bf.1.1		4	15.14	odd	2
2475.2.a.bj.1.4		4	5.4	even	2
2475.2.c.s.199.1		8	15.8	even	4
2475.2.c.s.199.8		8	15.2	even	4
2475.2.c.t.199.1		8	5.2	odd	4
2475.2.c.t.199.8		8	5.3	odd	4
5445.2.a.bh.1.1		4	33.32	even	2
5445.2.a.bs.1.4		4	11.10	odd	2
7920.2.a.cm.1.4		4	4.3	odd	2
7920.2.a.cn.1.4		4	12.11	even	2

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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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69696 q^{2} +5.27358 q^{4} -1.00000 q^{5} -4.13176 q^{7} -8.82872 q^{8} +O(q^{10})\)	\(q-2.69696 q^{2} +5.27358 q^{4} -1.00000 q^{5} -4.13176 q^{7} -8.82872 q^{8} +2.69696 q^{10} +1.00000 q^{11} +2.73785 q^{13} +11.1432 q^{14} +13.2635 q^{16} -2.41541 q^{17} -1.15325 q^{19} -5.27358 q^{20} -2.69696 q^{22} +8.54717 q^{23} +1.00000 q^{25} -7.38386 q^{26} -21.7892 q^{28} +1.67756 q^{29} -10.2635 q^{31} -18.1137 q^{32} +6.51425 q^{34} +4.13176 q^{35} +5.71636 q^{37} +3.11028 q^{38} +8.82872 q^{40} +9.11028 q^{41} +8.13176 q^{43} +5.27358 q^{44} -23.0514 q^{46} -1.47569 q^{47} +10.0715 q^{49} -2.69696 q^{50} +14.4383 q^{52} +2.54717 q^{53} -1.00000 q^{55} +36.4782 q^{56} -4.52431 q^{58} +8.24066 q^{59} +3.47569 q^{61} +27.6803 q^{62} +22.3249 q^{64} -2.73785 q^{65} +15.3350 q^{67} -12.7378 q^{68} -11.1432 q^{70} -2.54717 q^{71} +2.73785 q^{73} -15.4168 q^{74} -6.08178 q^{76} -4.13176 q^{77} +5.15325 q^{79} -13.2635 q^{80} -24.5700 q^{82} -9.28502 q^{83} +2.41541 q^{85} -21.9310 q^{86} -8.82872 q^{88} -4.78783 q^{89} -11.3121 q^{91} +45.0742 q^{92} +3.97989 q^{94} +1.15325 q^{95} +4.24066 q^{97} -27.1624 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 8 q^{4} - 4 q^{5} + 4 q^{7} - 6 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 + 8 * q^4 - 4 * q^5 + 4 * q^7 - 6 * q^8	\( 4 q - 2 q^{2} + 8 q^{4} - 4 q^{5} + 4 q^{7} - 6 q^{8} + 2 q^{10} + 4 q^{11} + 8 q^{13} + 8 q^{14} + 12 q^{16} - 4 q^{17} + 4 q^{19} - 8 q^{20} - 2 q^{22} + 8 q^{23} + 4 q^{25} + 16 q^{26} - 8 q^{28} + 4 q^{29} - 14 q^{32} + 4 q^{34} - 4 q^{35} + 8 q^{37} - 20 q^{38} + 6 q^{40} + 4 q^{41} + 12 q^{43} + 8 q^{44} - 16 q^{46} + 20 q^{49} - 2 q^{50} + 20 q^{52} - 16 q^{53} - 4 q^{55} + 48 q^{56} - 24 q^{58} + 24 q^{59} + 8 q^{61} + 20 q^{62} - 8 q^{65} - 48 q^{68} - 8 q^{70} + 16 q^{71} + 8 q^{73} - 12 q^{74} - 36 q^{76} + 4 q^{77} + 12 q^{79} - 12 q^{80} - 40 q^{82} - 8 q^{83} + 4 q^{85} - 16 q^{86} - 6 q^{88} + 16 q^{89} - 16 q^{91} + 72 q^{92} - 40 q^{94} - 4 q^{95} + 8 q^{97} - 62 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 8 * q^4 - 4 * q^5 + 4 * q^7 - 6 * q^8 + 2 * q^10 + 4 * q^11 + 8 * q^13 + 8 * q^14 + 12 * q^16 - 4 * q^17 + 4 * q^19 - 8 * q^20 - 2 * q^22 + 8 * q^23 + 4 * q^25 + 16 * q^26 - 8 * q^28 + 4 * q^29 - 14 * q^32 + 4 * q^34 - 4 * q^35 + 8 * q^37 - 20 * q^38 + 6 * q^40 + 4 * q^41 + 12 * q^43 + 8 * q^44 - 16 * q^46 + 20 * q^49 - 2 * q^50 + 20 * q^52 - 16 * q^53 - 4 * q^55 + 48 * q^56 - 24 * q^58 + 24 * q^59 + 8 * q^61 + 20 * q^62 - 8 * q^65 - 48 * q^68 - 8 * q^70 + 16 * q^71 + 8 * q^73 - 12 * q^74 - 36 * q^76 + 4 * q^77 + 12 * q^79 - 12 * q^80 - 40 * q^82 - 8 * q^83 + 4 * q^85 - 16 * q^86 - 6 * q^88 + 16 * q^89 - 16 * q^91 + 72 * q^92 - 40 * q^94 - 4 * q^95 + 8 * q^97 - 62 * q^98

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