LMFDB - Embedded newform 1035.2.a.q.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1035,2,Mod(1,1035)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1035, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1035.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$1035 = 3^{2} \cdot 5 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1035.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,0,0,10,6,0,6,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$8.26451660920$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.98838128.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - x^{5} - 10x^{4} - x^{3} + 16x^{2} + 5x - 1$ x^6 - x^5 - 10x^4 - x^3 + 16x^2 + 5*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{2}$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.36724$ of defining polynomial
Character	$\chi$	$=$	1035.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.11684 q^{2} +2.48100 q^{4} +1.00000 q^{5} -1.01690 q^{7} +1.01820 q^{8} +2.11684 q^{10} +6.38628 q^{11} +0.901360 q^{13} -2.15261 q^{14} -2.80664 q^{16} -0.382359 q^{17} +4.15261 q^{19} +2.48100 q^{20} +13.5187 q^{22} -1.00000 q^{23} +1.00000 q^{25} +1.90803 q^{26} -2.52292 q^{28} +4.11554 q^{29} +0.519001 q^{31} -7.97760 q^{32} -0.809392 q^{34} -1.01690 q^{35} +3.96293 q^{37} +8.79039 q^{38} +1.01820 q^{40} -0.407384 q^{41} -6.24964 q^{43} +15.8444 q^{44} -2.11684 q^{46} -7.13243 q^{47} -5.96592 q^{49} +2.11684 q^{50} +2.23627 q^{52} -10.9391 q^{53} +6.38628 q^{55} -1.03540 q^{56} +8.71192 q^{58} -2.31542 q^{59} +5.42428 q^{61} +1.09864 q^{62} -11.2740 q^{64} +0.901360 q^{65} +2.16281 q^{67} -0.948633 q^{68} -2.15261 q^{70} +14.1653 q^{71} +3.09864 q^{73} +8.38888 q^{74} +10.3026 q^{76} -6.49419 q^{77} -2.99839 q^{79} -2.80664 q^{80} -0.862366 q^{82} -16.1929 q^{83} -0.382359 q^{85} -13.2295 q^{86} +6.50249 q^{88} -14.4251 q^{89} -0.916591 q^{91} -2.48100 q^{92} -15.0982 q^{94} +4.15261 q^{95} +14.5931 q^{97} -12.6289 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q + 10 q^{4} + 6 q^{5} + 6 q^{7} - 4 q^{11} + 12 q^{13} + 4 q^{14} + 14 q^{16} - 4 q^{17} + 8 q^{19} + 10 q^{20} + 8 q^{22} - 6 q^{23} + 6 q^{25} + 12 q^{26} + 24 q^{28} + 6 q^{29} + 8 q^{31} - 20 q^{32}+ \cdots + 4 q^{98}+O(q^{100})$ 6 * q + 10 * q^4 + 6 * q^5 + 6 * q^7 - 4 * q^11 + 12 * q^13 + 4 * q^14 + 14 * q^16 - 4 * q^17 + 8 * q^19 + 10 * q^20 + 8 * q^22 - 6 * q^23 + 6 * q^25 + 12 * q^26 + 24 * q^28 + 6 * q^29 + 8 * q^31 - 20 * q^32 - 12 * q^34 + 6 * q^35 + 22 * q^37 - 36 * q^38 + 18 * q^41 + 8 * q^43 - 4 * q^44 - 12 * q^47 + 18 * q^49 - 4 * q^53 - 4 * q^55 - 4 * q^56 - 16 * q^58 + 6 * q^59 + 14 * q^64 + 12 * q^65 + 10 * q^67 - 28 * q^68 + 4 * q^70 + 22 * q^71 + 12 * q^73 + 20 * q^74 + 16 * q^76 + 4 * q^77 + 4 * q^79 + 14 * q^80 - 12 * q^82 - 24 * q^83 - 4 * q^85 - 20 * q^86 - 8 * q^88 + 8 * q^89 + 4 * q^91 - 10 * q^92 + 20 * q^94 + 8 * q^95 + 12 * q^97 + 4 * q^98

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

)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$\alpha_n$			$\theta_n$
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$\alpha_p$			$\theta_p$

$2$	2.11684	1.49683	0.748415	−	0.663231i	$-0.230815\pi$
$2$	2.11684	1.49683	0.748415	+	0.663231i	$0.230815\pi$
$3$	0	0
$3$	0	0
$4$	2.48100	1.24050
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−1.01690	−0.384351	−0.192176	−	0.981361i	$-0.561554\pi$
$7$	−1.01690	−0.384351	−0.192176	+	0.981361i	$0.561554\pi$
$8$	1.01820	0.359987
$9$	0	0
$10$	2.11684	0.669403
$11$	6.38628	1.92554	0.962768	−	0.270329i	$-0.0871325\pi$
$11$	6.38628	1.92554	0.962768	+	0.270329i	$0.0871325\pi$
$12$	0	0
$13$	0.901360	0.249992	0.124996	−	0.992157i	$-0.460108\pi$
$13$	0.901360	0.249992	0.124996	+	0.992157i	$0.460108\pi$
$14$	−2.15261	−0.575308
$15$	0	0
$16$	−2.80664	−0.701660
$17$	−0.382359	−0.0927358	−0.0463679	−	0.998924i	$-0.514765\pi$
$17$	−0.382359	−0.0927358	−0.0463679	+	0.998924i	$0.514765\pi$
$18$	0	0
$19$	4.15261	0.952673	0.476337	−	0.879263i	$-0.341964\pi$
$19$	4.15261	0.952673	0.476337	+	0.879263i	$0.341964\pi$
$20$	2.48100	0.554768
$21$	0	0
$22$	13.5187	2.88220
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	1.00000	0.200000
$26$	1.90803	0.374196
$27$	0	0
$28$	−2.52292	−0.476787
$29$	4.11554	0.764236	0.382118	−	0.924114i	$-0.375195\pi$
$29$	4.11554	0.764236	0.382118	+	0.924114i	$0.375195\pi$
$30$	0	0
$31$	0.519001	0.0932153	0.0466076	−	0.998913i	$-0.485159\pi$
$31$	0.519001	0.0932153	0.0466076	+	0.998913i	$0.485159\pi$
$32$	−7.97760	−1.41025
$33$	0	0
$34$	−0.809392	−0.138810
$35$	−1.01690	−0.171887
$36$	0	0
$37$	3.96293	0.651502	0.325751	−	0.945456i	$-0.394383\pi$
$37$	3.96293	0.651502	0.325751	+	0.945456i	$0.394383\pi$
$38$	8.79039	1.42599
$39$	0	0
$40$	1.01820	0.160991
$41$	−0.407384	−0.0636228	−0.0318114	−	0.999494i	$-0.510128\pi$
$41$	−0.407384	−0.0636228	−0.0318114	+	0.999494i	$0.510128\pi$
$42$	0	0
$43$	−6.24964	−0.953061	−0.476531	−	0.879158i	$-0.658106\pi$
$43$	−6.24964	−0.953061	−0.476531	+	0.879158i	$0.658106\pi$
$44$	15.8444	2.38863
$45$	0	0
$46$	−2.11684	−0.312111
$47$	−7.13243	−1.04037	−0.520186	−	0.854053i	$-0.674137\pi$
$47$	−7.13243	−1.04037	−0.520186	+	0.854053i	$0.674137\pi$
$48$	0	0
$49$	−5.96592	−0.852274
$50$	2.11684	0.299366
$51$	0	0
$52$	2.23627	0.310115
$53$	−10.9391	−1.50260	−0.751299	−	0.659962i	$-0.770572\pi$
$53$	−10.9391	−1.50260	−0.751299	+	0.659962i	$0.770572\pi$
$54$	0	0
$55$	6.38628	0.861126
$56$	−1.03540	−0.138361
$57$	0	0
$58$	8.71192	1.14393
$59$	−2.31542	−0.301442	−0.150721	−	0.988576i	$-0.548159\pi$
$59$	−2.31542	−0.301442	−0.150721	+	0.988576i	$0.548159\pi$
$60$	0	0
$61$	5.42428	0.694508	0.347254	−	0.937771i	$-0.387114\pi$
$61$	5.42428	0.694508	0.347254	+	0.937771i	$0.387114\pi$
$62$	1.09864	0.139527
$63$	0	0
$64$	−11.2740	−1.40925
$65$	0.901360	0.111800
$66$	0	0
$67$	2.16281	0.264229	0.132115	−	0.991234i	$-0.457823\pi$
$67$	2.16281	0.264229	0.132115	+	0.991234i	$0.457823\pi$
$68$	−0.948633	−0.115039
$69$	0	0
$70$	−2.15261	−0.257286
$71$	14.1653	1.68111	0.840556	−	0.541725i	$-0.182229\pi$
$71$	14.1653	1.68111	0.840556	+	0.541725i	$0.182229\pi$
$72$	0	0
$73$	3.09864	0.362668	0.181334	−	0.983422i	$-0.441958\pi$
$73$	3.09864	0.362668	0.181334	+	0.983422i	$0.441958\pi$
$74$	8.38888	0.975187
$75$	0	0
$76$	10.3026	1.18179
$77$	−6.49419	−0.740082
$78$	0	0
$79$	−2.99839	−0.337346	−0.168673	−	0.985672i	$-0.553948\pi$
$79$	−2.99839	−0.337346	−0.168673	+	0.985672i	$0.553948\pi$
$80$	−2.80664	−0.313792
$81$	0	0
$82$	−0.862366	−0.0952324
$83$	−16.1929	−1.77740	−0.888702	−	0.458485i	$-0.848392\pi$
$83$	−16.1929	−1.77740	−0.888702	+	0.458485i	$0.848392\pi$
$84$	0	0
$85$	−0.382359	−0.0414727
$86$	−13.2295	−1.42657
$87$	0	0
$88$	6.50249	0.693168
$89$	−14.4251	−1.52906	−0.764531	−	0.644587i	$-0.777029\pi$
$89$	−14.4251	−1.52906	−0.764531	+	0.644587i	$0.777029\pi$
$90$	0	0
$91$	−0.916591	−0.0960848
$92$	−2.48100	−0.258662
$93$	0	0
$94$	−15.0982	−1.55726
$95$	4.15261	0.426048
$96$	0	0
$97$	14.5931	1.48171	0.740853	−	0.671667i	$-0.234422\pi$
$97$	14.5931	1.48171	0.740853	+	0.671667i	$0.234422\pi$
$98$	−12.6289	−1.27571
$99$	0	0
$100$	2.48100	0.248100
$101$	−12.3652	−1.23038	−0.615191	−	0.788378i	$-0.710921\pi$
$101$	−12.3652	−1.23038	−0.615191	+	0.788378i	$0.710921\pi$
$102$	0	0
$103$	−10.9903	−1.08290	−0.541452	−	0.840732i	$-0.682125\pi$
$103$	−10.9903	−1.08290	−0.541452	+	0.840732i	$0.682125\pi$
$104$	0.917762	0.0899940
$105$	0	0
$106$	−23.1562	−2.24913
$107$	−7.83348	−0.757292	−0.378646	−	0.925542i	$-0.623610\pi$
$107$	−7.83348	−0.757292	−0.378646	+	0.925542i	$0.623610\pi$
$108$	0	0
$109$	−9.12691	−0.874200	−0.437100	−	0.899413i	$-0.643994\pi$
$109$	−9.12691	−0.874200	−0.437100	+	0.899413i	$0.643994\pi$
$110$	13.5187	1.28896
$111$	0	0
$112$	2.85407	0.269684
$113$	−8.83114	−0.830764	−0.415382	−	0.909647i	$-0.636352\pi$
$113$	−8.83114	−0.830764	−0.415382	+	0.909647i	$0.636352\pi$
$114$	0	0
$115$	−1.00000	−0.0932505
$116$	10.2106	0.948035
$117$	0	0
$118$	−4.90136	−0.451207
$119$	0.388820	0.0356431
$120$	0	0
$121$	29.7846	2.70769
$122$	11.4823	1.03956
$123$	0	0
$124$	1.28764	0.115634
$125$	1.00000	0.0894427
$126$	0	0
$127$	14.5618	1.29215	0.646075	−	0.763274i	$-0.276409\pi$
$127$	14.5618	1.29215	0.646075	+	0.763274i	$0.276409\pi$
$128$	−7.91001	−0.699152
$129$	0	0
$130$	1.90803	0.167346
$131$	−15.0081	−1.31126	−0.655632	−	0.755081i	$-0.727598\pi$
$131$	−15.0081	−1.31126	−0.655632	+	0.755081i	$0.727598\pi$
$132$	0	0
$133$	−4.22277	−0.366161
$134$	4.57832	0.395506
$135$	0	0
$136$	−0.389317	−0.0333837
$137$	0.670152	0.0572549	0.0286275	−	0.999590i	$-0.490886\pi$
$137$	0.670152	0.0572549	0.0286275	+	0.999590i	$0.490886\pi$
$138$	0	0
$139$	3.60936	0.306142	0.153071	−	0.988215i	$-0.451084\pi$
$139$	3.60936	0.306142	0.153071	+	0.988215i	$0.451084\pi$
$140$	−2.52292	−0.213226
$141$	0	0
$142$	29.9856	2.51634
$143$	5.75634	0.481369
$144$	0	0
$145$	4.11554	0.341777
$146$	6.55932	0.542853
$147$	0	0
$148$	9.83203	0.808188
$149$	−8.14866	−0.667564	−0.333782	−	0.942650i	$-0.608325\pi$
$149$	−8.14866	−0.667564	−0.333782	+	0.942650i	$0.608325\pi$
$150$	0	0
$151$	14.2093	1.15634	0.578168	−	0.815918i	$-0.303768\pi$
$151$	14.2093	1.15634	0.578168	+	0.815918i	$0.303768\pi$
$152$	4.22817	0.342950
$153$	0	0
$154$	−13.7471	−1.10778
$155$	0.519001	0.0416871
$156$	0	0
$157$	5.41406	0.432089	0.216044	−	0.976384i	$-0.430684\pi$
$157$	5.41406	0.432089	0.216044	+	0.976384i	$0.430684\pi$
$158$	−6.34711	−0.504949
$159$	0	0
$160$	−7.97760	−0.630684
$161$	1.01690	0.0801427
$162$	0	0
$163$	1.15928	0.0908017	0.0454009	−	0.998969i	$-0.485543\pi$
$163$	1.15928	0.0908017	0.0454009	+	0.998969i	$0.485543\pi$
$164$	−1.01072	−0.0789240
$165$	0	0
$166$	−34.2778	−2.66047
$167$	3.97129	0.307308	0.153654	−	0.988125i	$-0.450896\pi$
$167$	3.97129	0.307308	0.153654	+	0.988125i	$0.450896\pi$
$168$	0	0
$169$	−12.1876	−0.937504
$170$	−0.809392	−0.0620776
$171$	0	0
$172$	−15.5053	−1.18227
$173$	13.2295	1.00582	0.502909	−	0.864339i	$-0.332263\pi$
$173$	13.2295	1.00582	0.502909	+	0.864339i	$0.332263\pi$
$174$	0	0
$175$	−1.01690	−0.0768702
$176$	−17.9240	−1.35107
$177$	0	0
$178$	−30.5357	−2.28875
$179$	−0.179450	−0.0134127	−0.00670636	−	0.999978i	$-0.502135\pi$
$179$	−0.179450	−0.0134127	−0.00670636	+	0.999978i	$0.502135\pi$
$180$	0	0
$181$	15.6266	1.16152	0.580759	−	0.814076i	$-0.302756\pi$
$181$	15.6266	1.16152	0.580759	+	0.814076i	$0.302756\pi$
$182$	−1.94027	−0.143823
$183$	0	0
$184$	−1.01820	−0.0750625
$185$	3.96293	0.291360
$186$	0	0
$187$	−2.44185	−0.178566
$188$	−17.6956	−1.29058
$189$	0	0
$190$	8.79039	0.637722
$191$	11.8916	0.860448	0.430224	−	0.902722i	$-0.358435\pi$
$191$	11.8916	0.860448	0.430224	+	0.902722i	$0.358435\pi$
$192$	0	0
$193$	4.96200	0.357172	0.178586	−	0.983924i	$-0.442848\pi$
$193$	4.96200	0.357172	0.178586	+	0.983924i	$0.442848\pi$
$194$	30.8912	2.21786
$195$	0	0
$196$	−14.8014	−1.05725
$197$	4.19147	0.298630	0.149315	−	0.988790i	$-0.452293\pi$
$197$	4.19147	0.298630	0.149315	+	0.988790i	$0.452293\pi$
$198$	0	0
$199$	−1.46111	−0.103576	−0.0517878	−	0.998658i	$-0.516492\pi$
$199$	−1.46111	−0.103576	−0.0517878	+	0.998658i	$0.516492\pi$
$200$	1.01820	0.0719974
$201$	0	0
$202$	−26.1751	−1.84167
$203$	−4.18508	−0.293735
$204$	0	0
$205$	−0.407384	−0.0284530
$206$	−23.2646	−1.62092
$207$	0	0
$208$	−2.52979	−0.175410
$209$	26.5197	1.83441
$210$	0	0
$211$	−24.1034	−1.65935	−0.829675	−	0.558247i	$-0.811474\pi$
$211$	−24.1034	−1.65935	−0.829675	+	0.558247i	$0.811474\pi$
$212$	−27.1398	−1.86397
$213$	0	0
$214$	−16.5822	−1.13354
$215$	−6.24964	−0.426222
$216$	0	0
$217$	−0.527770	−0.0358274
$218$	−19.3202	−1.30853
$219$	0	0
$220$	15.8444	1.06823
$221$	−0.344643	−0.0231832
$222$	0	0
$223$	−26.0940	−1.74738	−0.873691	−	0.486481i	$-0.838280\pi$
$223$	−26.0940	−1.74738	−0.873691	+	0.486481i	$0.838280\pi$
$224$	8.11240	0.542032
$225$	0	0
$226$	−18.6941	−1.24351
$227$	−20.0995	−1.33405	−0.667026	−	0.745034i	$-0.732433\pi$
$227$	−20.0995	−1.33405	−0.667026	+	0.745034i	$0.732433\pi$
$228$	0	0
$229$	26.0754	1.72311	0.861557	−	0.507662i	$-0.169490\pi$
$229$	26.0754	1.72311	0.861557	+	0.507662i	$0.169490\pi$
$230$	−2.11684	−0.139580
$231$	0	0
$232$	4.19043	0.275115
$233$	22.8409	1.49636	0.748178	−	0.663498i	$-0.230929\pi$
$233$	22.8409	1.49636	0.748178	+	0.663498i	$0.230929\pi$
$234$	0	0
$235$	−7.13243	−0.465269
$236$	−5.74455	−0.373938
$237$	0	0
$238$	0.823069	0.0533516
$239$	0.335846	0.0217241	0.0108620	−	0.999941i	$-0.496542\pi$
$239$	0.335846	0.0217241	0.0108620	+	0.999941i	$0.496542\pi$
$240$	0	0
$241$	−12.8536	−0.827975	−0.413988	−	0.910283i	$-0.635864\pi$
$241$	−12.8536	−0.827975	−0.413988	+	0.910283i	$0.635864\pi$
$242$	63.0491	4.05295
$243$	0	0
$244$	13.4576	0.861537
$245$	−5.96592	−0.381149
$246$	0	0
$247$	3.74299	0.238161
$248$	0.528445	0.0335563
$249$	0	0
$250$	2.11684	0.133881
$251$	−15.7346	−0.993157	−0.496578	−	0.867992i	$-0.665410\pi$
$251$	−15.7346	−0.993157	−0.496578	+	0.867992i	$0.665410\pi$
$252$	0	0
$253$	−6.38628	−0.401502
$254$	30.8249	1.93413
$255$	0	0
$256$	5.80378	0.362736
$257$	6.67553	0.416408	0.208204	−	0.978085i	$-0.433238\pi$
$257$	6.67553	0.416408	0.208204	+	0.978085i	$0.433238\pi$
$258$	0	0
$259$	−4.02989	−0.250405
$260$	2.23627	0.138688
$261$	0	0
$262$	−31.7697	−1.96274
$263$	25.2544	1.55725	0.778627	−	0.627487i	$-0.215916\pi$
$263$	25.2544	1.55725	0.778627	+	0.627487i	$0.215916\pi$
$264$	0	0
$265$	−10.9391	−0.671982
$266$	−8.93893	−0.548081
$267$	0	0
$268$	5.36593	0.327776
$269$	12.5829	0.767192	0.383596	−	0.923501i	$-0.374686\pi$
$269$	12.5829	0.767192	0.383596	+	0.923501i	$0.374686\pi$
$270$	0	0
$271$	−12.4037	−0.753470	−0.376735	−	0.926321i	$-0.622953\pi$
$271$	−12.4037	−0.753470	−0.376735	+	0.926321i	$0.622953\pi$
$272$	1.07315	0.0650690
$273$	0	0
$274$	1.41860	0.0857009
$275$	6.38628	0.385107
$276$	0	0
$277$	18.5886	1.11688	0.558441	−	0.829544i	$-0.311400\pi$
$277$	18.5886	1.11688	0.558441	+	0.829544i	$0.311400\pi$
$278$	7.64043	0.458243
$279$	0	0
$280$	−1.03540	−0.0618771
$281$	4.33390	0.258539	0.129269	−	0.991610i	$-0.458737\pi$
$281$	4.33390	0.258539	0.129269	+	0.991610i	$0.458737\pi$
$282$	0	0
$283$	−24.4541	−1.45364	−0.726822	−	0.686826i	$-0.759004\pi$
$283$	−24.4541	−1.45364	−0.726822	+	0.686826i	$0.759004\pi$
$284$	35.1441	2.08542
$285$	0	0
$286$	12.1852	0.720528
$287$	0.414268	0.0244535
$288$	0	0
$289$	−16.8538	−0.991400
$290$	8.71192	0.511582
$291$	0	0
$292$	7.68772	0.449890
$293$	−19.8436	−1.15928	−0.579639	−	0.814874i	$-0.696806\pi$
$293$	−19.8436	−1.15928	−0.579639	+	0.814874i	$0.696806\pi$
$294$	0	0
$295$	−2.31542	−0.134809
$296$	4.03505	0.234532
$297$	0	0
$298$	−17.2494	−0.999230
$299$	−0.901360	−0.0521270
$300$	0	0
$301$	6.35524	0.366310
$302$	30.0788	1.73084
$303$	0	0
$304$	−11.6549	−0.668453
$305$	5.42428	0.310593
$306$	0	0
$307$	−14.3808	−0.820753	−0.410377	−	0.911916i	$-0.634603\pi$
$307$	−14.3808	−0.820753	−0.410377	+	0.911916i	$0.634603\pi$
$308$	−16.1121	−0.918071
$309$	0	0
$310$	1.09864	0.0623986
$311$	−6.38875	−0.362273	−0.181136	−	0.983458i	$-0.557978\pi$
$311$	−6.38875	−0.362273	−0.181136	+	0.983458i	$0.557978\pi$
$312$	0	0
$313$	16.3001	0.921335	0.460667	−	0.887573i	$-0.347610\pi$
$313$	16.3001	0.921335	0.460667	+	0.887573i	$0.347610\pi$
$314$	11.4607	0.646763
$315$	0	0
$316$	−7.43901	−0.418477
$317$	22.6464	1.27195	0.635973	−	0.771711i	$-0.280599\pi$
$317$	22.6464	1.27195	0.635973	+	0.771711i	$0.280599\pi$
$318$	0	0
$319$	26.2830	1.47156
$320$	−11.2740	−0.630235
$321$	0	0
$322$	2.15261	0.119960
$323$	−1.58779	−0.0883469
$324$	0	0
$325$	0.901360	0.0499985
$326$	2.45400	0.135915
$327$	0	0
$328$	−0.414798	−0.0229034
$329$	7.25295	0.399868
$330$	0	0
$331$	29.4615	1.61935	0.809676	−	0.586877i	$-0.199643\pi$
$331$	29.4615	1.61935	0.809676	+	0.586877i	$0.199643\pi$
$332$	−40.1746	−2.20487
$333$	0	0
$334$	8.40658	0.459987
$335$	2.16281	0.118167
$336$	0	0
$337$	−15.7710	−0.859099	−0.429549	−	0.903043i	$-0.641328\pi$
$337$	−15.7710	−0.859099	−0.429549	+	0.903043i	$0.641328\pi$
$338$	−25.7991	−1.40328
$339$	0	0
$340$	−0.948633	−0.0514469
$341$	3.31448	0.179489
$342$	0	0
$343$	13.1850	0.711924
$344$	−6.36336	−0.343090
$345$	0	0
$346$	28.0046	1.50554
$347$	1.42472	0.0764829	0.0382415	−	0.999269i	$-0.487824\pi$
$347$	1.42472	0.0764829	0.0382415	+	0.999269i	$0.487824\pi$
$348$	0	0
$349$	24.8176	1.32846	0.664229	−	0.747529i	$-0.268760\pi$
$349$	24.8176	1.32846	0.664229	+	0.747529i	$0.268760\pi$
$350$	−2.15261	−0.115062
$351$	0	0
$352$	−50.9472	−2.71549
$353$	4.86362	0.258864	0.129432	−	0.991588i	$-0.458685\pi$
$353$	4.86362	0.258864	0.129432	+	0.991588i	$0.458685\pi$
$354$	0	0
$355$	14.1653	0.751816
$356$	−35.7888	−1.89680
$357$	0	0
$358$	−0.379866	−0.0200766
$359$	−27.3223	−1.44202	−0.721009	−	0.692926i	$-0.756321\pi$
$359$	−27.3223	−1.44202	−0.721009	+	0.692926i	$0.756321\pi$
$360$	0	0
$361$	−1.75586	−0.0924138
$362$	33.0790	1.73859
$363$	0	0
$364$	−2.27406	−0.119193
$365$	3.09864	0.162190
$366$	0	0
$367$	20.4583	1.06791	0.533956	−	0.845512i	$-0.320705\pi$
$367$	20.4583	1.06791	0.533956	+	0.845512i	$0.320705\pi$
$368$	2.80664	0.146306
$369$	0	0
$370$	8.38888	0.436117
$371$	11.1239	0.577525
$372$	0	0
$373$	28.3550	1.46816	0.734082	−	0.679060i	$-0.237613\pi$
$373$	28.3550	1.46816	0.734082	+	0.679060i	$0.237613\pi$
$374$	−5.16901	−0.267283
$375$	0	0
$376$	−7.26222	−0.374521
$377$	3.70958	0.191053
$378$	0	0
$379$	−24.3276	−1.24963	−0.624814	−	0.780774i	$-0.714825\pi$
$379$	−24.3276	−1.24963	−0.624814	+	0.780774i	$0.714825\pi$
$380$	10.3026	0.528513
$381$	0	0
$382$	25.1726	1.28794
$383$	−30.5843	−1.56278	−0.781392	−	0.624041i	$-0.785490\pi$
$383$	−30.5843	−1.56278	−0.781392	+	0.624041i	$0.785490\pi$
$384$	0	0
$385$	−6.49419	−0.330975
$386$	10.5037	0.534626
$387$	0	0
$388$	36.2055	1.83806
$389$	4.59704	0.233079	0.116540	−	0.993186i	$-0.462820\pi$
$389$	4.59704	0.233079	0.116540	+	0.993186i	$0.462820\pi$
$390$	0	0
$391$	0.382359	0.0193367
$392$	−6.07448	−0.306808
$393$	0	0
$394$	8.87265	0.446998
$395$	−2.99839	−0.150866
$396$	0	0
$397$	8.67118	0.435194	0.217597	−	0.976039i	$-0.430178\pi$
$397$	8.67118	0.435194	0.217597	+	0.976039i	$0.430178\pi$
$398$	−3.09294	−0.155035
$399$	0	0
$400$	−2.80664	−0.140332
$401$	4.52523	0.225979	0.112990	−	0.993596i	$-0.463957\pi$
$401$	4.52523	0.225979	0.112990	+	0.993596i	$0.463957\pi$
$402$	0	0
$403$	0.467807	0.0233031
$404$	−30.6780	−1.52629
$405$	0	0
$406$	−8.85913	−0.439671
$407$	25.3084	1.25449
$408$	0	0
$409$	−3.22295	−0.159364	−0.0796822	−	0.996820i	$-0.525391\pi$
$409$	−3.22295	−0.159364	−0.0796822	+	0.996820i	$0.525391\pi$
$410$	−0.862366	−0.0425892
$411$	0	0
$412$	−27.2669	−1.34334
$413$	2.35454	0.115859
$414$	0	0
$415$	−16.1929	−0.794879
$416$	−7.19069	−0.352552
$417$	0	0
$418$	56.1379	2.74579
$419$	24.2885	1.18657	0.593286	−	0.804992i	$-0.297830\pi$
$419$	24.2885	1.18657	0.593286	+	0.804992i	$0.297830\pi$
$420$	0	0
$421$	6.99593	0.340961	0.170480	−	0.985361i	$-0.445468\pi$
$421$	6.99593	0.340961	0.170480	+	0.985361i	$0.445468\pi$
$422$	−51.0231	−2.48376
$423$	0	0
$424$	−11.1381	−0.540916
$425$	−0.382359	−0.0185472
$426$	0	0
$427$	−5.51594	−0.266935
$428$	−19.4349	−0.939420
$429$	0	0
$430$	−13.2295	−0.637982
$431$	4.98566	0.240151	0.120075	−	0.992765i	$-0.461686\pi$
$431$	4.98566	0.240151	0.120075	+	0.992765i	$0.461686\pi$
$432$	0	0
$433$	−2.70722	−0.130101	−0.0650504	−	0.997882i	$-0.520721\pi$
$433$	−2.70722	−0.130101	−0.0650504	+	0.997882i	$0.520721\pi$
$434$	−1.11720	−0.0536275
$435$	0	0
$436$	−22.6439	−1.08444
$437$	−4.15261	−0.198646
$438$	0	0
$439$	37.5571	1.79250	0.896252	−	0.443545i	$-0.146279\pi$
$439$	37.5571	1.79250	0.896252	+	0.443545i	$0.146279\pi$
$440$	6.50249	0.309994
$441$	0	0
$442$	−0.729554	−0.0347013
$443$	15.5780	0.740134	0.370067	−	0.929005i	$-0.379335\pi$
$443$	15.5780	0.740134	0.370067	+	0.929005i	$0.379335\pi$
$444$	0	0
$445$	−14.4251	−0.683817
$446$	−55.2367	−2.61553
$447$	0	0
$448$	11.4645	0.541646
$449$	8.55231	0.403608	0.201804	−	0.979426i	$-0.435320\pi$
$449$	8.55231	0.403608	0.201804	+	0.979426i	$0.435320\pi$
$450$	0	0
$451$	−2.60167	−0.122508
$452$	−21.9101	−1.03056
$453$	0	0
$454$	−42.5474	−1.99685
$455$	−0.916591	−0.0429704
$456$	0	0
$457$	39.5470	1.84993	0.924966	−	0.380049i	$-0.124093\pi$
$457$	39.5470	1.84993	0.924966	+	0.380049i	$0.124093\pi$
$458$	55.1974	2.57921
$459$	0	0
$460$	−2.48100	−0.115677
$461$	8.88891	0.413998	0.206999	−	0.978341i	$-0.433630\pi$
$461$	8.88891	0.413998	0.206999	+	0.978341i	$0.433630\pi$
$462$	0	0
$463$	−7.97129	−0.370457	−0.185229	−	0.982695i	$-0.559303\pi$
$463$	−7.97129	−0.370457	−0.185229	+	0.982695i	$0.559303\pi$
$464$	−11.5508	−0.536234
$465$	0	0
$466$	48.3504	2.23979
$467$	−38.3359	−1.77397	−0.886987	−	0.461794i	$-0.847206\pi$
$467$	−38.3359	−1.77397	−0.886987	+	0.461794i	$0.847206\pi$
$468$	0	0
$469$	−2.19936	−0.101557
$470$	−15.0982	−0.696428
$471$	0	0
$472$	−2.35755	−0.108515
$473$	−39.9119	−1.83515
$474$	0	0
$475$	4.15261	0.190535
$476$	0.964663	0.0442152
$477$	0	0
$478$	0.710932	0.0325173
$479$	18.7577	0.857063	0.428531	−	0.903527i	$-0.359031\pi$
$479$	18.7577	0.857063	0.428531	+	0.903527i	$0.359031\pi$
$480$	0	0
$481$	3.57203	0.162870
$482$	−27.2090	−1.23934
$483$	0	0
$484$	73.8955	3.35889
$485$	14.5931	0.662639
$486$	0	0
$487$	−13.0630	−0.591940	−0.295970	−	0.955197i	$-0.595643\pi$
$487$	−13.0630	−0.591940	−0.295970	+	0.955197i	$0.595643\pi$
$488$	5.52299	0.250014
$489$	0	0
$490$	−12.6289	−0.570515
$491$	41.8068	1.88672	0.943358	−	0.331777i	$-0.107648\pi$
$491$	41.8068	1.88672	0.943358	+	0.331777i	$0.107648\pi$
$492$	0	0
$493$	−1.57361	−0.0708720
$494$	7.92331	0.356486
$495$	0	0
$496$	−1.45665	−0.0654055
$497$	−14.4047	−0.646137
$498$	0	0
$499$	21.4804	0.961596	0.480798	−	0.876831i	$-0.340347\pi$
$499$	21.4804	0.961596	0.480798	+	0.876831i	$0.340347\pi$
$500$	2.48100	0.110954
$501$	0	0
$502$	−33.3075	−1.48659
$503$	−3.51755	−0.156840	−0.0784199	−	0.996920i	$-0.524987\pi$
$503$	−3.51755	−0.156840	−0.0784199	+	0.996920i	$0.524987\pi$
$504$	0	0
$505$	−12.3652	−0.550243
$506$	−13.5187	−0.600980
$507$	0	0
$508$	36.1278	1.60291
$509$	−2.45212	−0.108688	−0.0543441	−	0.998522i	$-0.517307\pi$
$509$	−2.45212	−0.108688	−0.0543441	+	0.998522i	$0.517307\pi$
$510$	0	0
$511$	−3.15100	−0.139392
$512$	28.1057	1.24211
$513$	0	0
$514$	14.1310	0.623292
$515$	−10.9903	−0.484289
$516$	0	0
$517$	−45.5497	−2.00327
$518$	−8.53063	−0.374814
$519$	0	0
$520$	0.917762	0.0402465
$521$	23.1861	1.01580	0.507902	−	0.861415i	$-0.330421\pi$
$521$	23.1861	1.01580	0.507902	+	0.861415i	$0.330421\pi$
$522$	0	0
$523$	−27.8092	−1.21601	−0.608006	−	0.793932i	$-0.708030\pi$
$523$	−27.8092	−1.21601	−0.608006	+	0.793932i	$0.708030\pi$
$524$	−37.2351	−1.62662
$525$	0	0
$526$	53.4595	2.33094
$527$	−0.198445	−0.00864439
$528$	0	0
$529$	1.00000	0.0434783
$530$	−23.1562	−1.00584
$531$	0	0
$532$	−10.4767	−0.454223
$533$	−0.367200	−0.0159052
$534$	0	0
$535$	−7.83348	−0.338671
$536$	2.20217	0.0951191
$537$	0	0
$538$	26.6359	1.14836
$539$	−38.1000	−1.64108
$540$	0	0
$541$	−4.47885	−0.192561	−0.0962804	−	0.995354i	$-0.530695\pi$
$541$	−4.47885	−0.192561	−0.0962804	+	0.995354i	$0.530695\pi$
$542$	−26.2566	−1.12782
$543$	0	0
$544$	3.05031	0.130781
$545$	−9.12691	−0.390954
$546$	0	0
$547$	−27.6961	−1.18420	−0.592099	−	0.805865i	$-0.701701\pi$
$547$	−27.6961	−1.18420	−0.592099	+	0.805865i	$0.701701\pi$
$548$	1.66265	0.0710247
$549$	0	0
$550$	13.5187	0.576440
$551$	17.0902	0.728067
$552$	0	0
$553$	3.04906	0.129659
$554$	39.3491	1.67178
$555$	0	0
$556$	8.95482	0.379769
$557$	−37.2707	−1.57921	−0.789605	−	0.613616i	$-0.789714\pi$
$557$	−37.2707	−1.57921	−0.789605	+	0.613616i	$0.789714\pi$
$558$	0	0
$559$	−5.63317	−0.238258
$560$	2.85407	0.120606
$561$	0	0
$562$	9.17416	0.386989
$563$	24.0415	1.01323	0.506613	−	0.862173i	$-0.330897\pi$
$563$	24.0415	1.01323	0.506613	+	0.862173i	$0.330897\pi$
$564$	0	0
$565$	−8.83114	−0.371529
$566$	−51.7653	−2.17586
$567$	0	0
$568$	14.4231	0.605178
$569$	−11.6956	−0.490304	−0.245152	−	0.969485i	$-0.578838\pi$
$569$	−11.6956	−0.490304	−0.245152	+	0.969485i	$0.578838\pi$
$570$	0	0
$571$	13.7483	0.575348	0.287674	−	0.957728i	$-0.407118\pi$
$571$	13.7483	0.575348	0.287674	+	0.957728i	$0.407118\pi$
$572$	14.2815	0.597138
$573$	0	0
$574$	0.876938	0.0366027
$575$	−1.00000	−0.0417029
$576$	0	0
$577$	20.2061	0.841191	0.420596	−	0.907248i	$-0.361821\pi$
$577$	20.2061	0.841191	0.420596	+	0.907248i	$0.361821\pi$
$578$	−35.6768	−1.48396
$579$	0	0
$580$	10.2106	0.423974
$581$	16.4665	0.683147
$582$	0	0
$583$	−69.8600	−2.89331
$584$	3.15503	0.130556
$585$	0	0
$586$	−42.0057	−1.73524
$587$	−1.06473	−0.0439462	−0.0219731	−	0.999759i	$-0.506995\pi$
$587$	−1.06473	−0.0439462	−0.0219731	+	0.999759i	$0.506995\pi$
$588$	0	0
$589$	2.15521	0.0888037
$590$	−4.90136	−0.201786
$591$	0	0
$592$	−11.1225	−0.457133
$593$	−9.82375	−0.403413	−0.201707	−	0.979446i	$-0.564649\pi$
$593$	−9.82375	−0.403413	−0.201707	+	0.979446i	$0.564649\pi$
$594$	0	0
$595$	0.388820	0.0159401
$596$	−20.2168	−0.828113
$597$	0	0
$598$	−1.90803	−0.0780252
$599$	8.77516	0.358543	0.179272	−	0.983800i	$-0.442626\pi$
$599$	8.77516	0.358543	0.179272	+	0.983800i	$0.442626\pi$
$600$	0	0
$601$	18.3240	0.747452	0.373726	−	0.927539i	$-0.378080\pi$
$601$	18.3240	0.747452	0.373726	+	0.927539i	$0.378080\pi$
$602$	13.4530	0.548304
$603$	0	0
$604$	35.2533	1.43443
$605$	29.7846	1.21092
$606$	0	0
$607$	20.1680	0.818594	0.409297	−	0.912401i	$-0.365774\pi$
$607$	20.1680	0.818594	0.409297	+	0.912401i	$0.365774\pi$
$608$	−33.1278	−1.34351
$609$	0	0
$610$	11.4823	0.464906
$611$	−6.42889	−0.260085
$612$	0	0
$613$	35.1516	1.41976	0.709880	−	0.704323i	$-0.248749\pi$
$613$	35.1516	1.41976	0.709880	+	0.704323i	$0.248749\pi$
$614$	−30.4417	−1.22853
$615$	0	0
$616$	−6.61237	−0.266420
$617$	0.120649	0.00485715	0.00242858	−	0.999997i	$-0.499227\pi$
$617$	0.120649	0.00485715	0.00242858	+	0.999997i	$0.499227\pi$
$618$	0	0
$619$	17.7131	0.711948	0.355974	−	0.934496i	$-0.384149\pi$
$619$	17.7131	0.711948	0.355974	+	0.934496i	$0.384149\pi$
$620$	1.28764	0.0517129
$621$	0	0
$622$	−13.5239	−0.542260
$623$	14.6689	0.587697
$624$	0	0
$625$	1.00000	0.0400000
$626$	34.5046	1.37908
$627$	0	0
$628$	13.4323	0.536006
$629$	−1.51526	−0.0604175
$630$	0	0
$631$	−25.3263	−1.00822	−0.504112	−	0.863639i	$-0.668180\pi$
$631$	−25.3263	−1.00822	−0.504112	+	0.863639i	$0.668180\pi$
$632$	−3.05295	−0.121440
$633$	0	0
$634$	47.9387	1.90389
$635$	14.5618	0.577867
$636$	0	0
$637$	−5.37744	−0.213062
$638$	55.6368	2.20268
$639$	0	0
$640$	−7.91001	−0.312670
$641$	34.7587	1.37289	0.686444	−	0.727183i	$-0.259171\pi$
$641$	34.7587	1.37289	0.686444	+	0.727183i	$0.259171\pi$
$642$	0	0
$643$	−29.2484	−1.15344	−0.576722	−	0.816940i	$-0.695669\pi$
$643$	−29.2484	−1.15344	−0.576722	+	0.816940i	$0.695669\pi$
$644$	2.52292	0.0994170
$645$	0	0
$646$	−3.36109	−0.132240
$647$	16.5214	0.649525	0.324762	−	0.945796i	$-0.394716\pi$
$647$	16.5214	0.649525	0.324762	+	0.945796i	$0.394716\pi$
$648$	0	0
$649$	−14.7869	−0.580437
$650$	1.90803	0.0748392
$651$	0	0
$652$	2.87617	0.112639
$653$	0.170125	0.00665751	0.00332875	−	0.999994i	$-0.498940\pi$
$653$	0.170125	0.00665751	0.00332875	+	0.999994i	$0.498940\pi$
$654$	0	0
$655$	−15.0081	−0.586415
$656$	1.14338	0.0446416
$657$	0	0
$658$	15.3533	0.598535
$659$	31.4705	1.22592	0.612959	−	0.790115i	$-0.289979\pi$
$659$	31.4705	1.22592	0.612959	+	0.790115i	$0.289979\pi$
$660$	0	0
$661$	−1.33767	−0.0520293	−0.0260147	−	0.999662i	$-0.508282\pi$
$661$	−1.33767	−0.0520293	−0.0260147	+	0.999662i	$0.508282\pi$
$662$	62.3653	2.42390
$663$	0	0
$664$	−16.4876	−0.639842
$665$	−4.22277	−0.163752
$666$	0	0
$667$	−4.11554	−0.159354
$668$	9.85277	0.381215
$669$	0	0
$670$	4.57832	0.176876
$671$	34.6410	1.33730
$672$	0	0
$673$	−8.89628	−0.342926	−0.171463	−	0.985191i	$-0.554849\pi$
$673$	−8.89628	−0.342926	−0.171463	+	0.985191i	$0.554849\pi$
$674$	−33.3845	−1.28592
$675$	0	0
$676$	−30.2373	−1.16297
$677$	−39.4004	−1.51428	−0.757140	−	0.653253i	$-0.773404\pi$
$677$	−39.4004	−1.51428	−0.757140	+	0.653253i	$0.773404\pi$
$678$	0	0
$679$	−14.8397	−0.569495
$680$	−0.389317	−0.0149296
$681$	0	0
$682$	7.01622	0.268665
$683$	−17.5508	−0.671562	−0.335781	−	0.941940i	$-0.609000\pi$
$683$	−17.5508	−0.671562	−0.335781	+	0.941940i	$0.609000\pi$
$684$	0	0
$685$	0.670152	0.0256052
$686$	27.9105	1.06563
$687$	0	0
$688$	17.5405	0.668725
$689$	−9.86005	−0.375638
$690$	0	0
$691$	29.5380	1.12368	0.561840	−	0.827246i	$-0.310094\pi$
$691$	29.5380	1.12368	0.561840	+	0.827246i	$0.310094\pi$
$692$	32.8223	1.24772
$693$	0	0
$694$	3.01590	0.114482
$695$	3.60936	0.136911
$696$	0	0
$697$	0.155767	0.00590010
$698$	52.5349	1.98848
$699$	0	0
$700$	−2.52292	−0.0953575
$701$	2.65999	0.100466	0.0502331	−	0.998738i	$-0.484004\pi$
$701$	2.65999	0.100466	0.0502331	+	0.998738i	$0.484004\pi$
$702$	0	0
$703$	16.4565	0.620668
$704$	−71.9989	−2.71356
$705$	0	0
$706$	10.2955	0.387476
$707$	12.5741	0.472898
$708$	0	0
$709$	44.0088	1.65278	0.826392	−	0.563096i	$-0.190390\pi$
$709$	44.0088	1.65278	0.826392	+	0.563096i	$0.190390\pi$
$710$	29.9856	1.12534
$711$	0	0
$712$	−14.6876	−0.550442
$713$	−0.519001	−0.0194367
$714$	0	0
$715$	5.75634	0.215275
$716$	−0.445215	−0.0166385
$717$	0	0
$718$	−57.8369	−2.15845
$719$	−43.6295	−1.62710	−0.813552	−	0.581492i	$-0.802469\pi$
$719$	−43.6295	−1.62710	−0.813552	+	0.581492i	$0.802469\pi$
$720$	0	0
$721$	11.1760	0.416215
$722$	−3.71687	−0.138328
$723$	0	0
$724$	38.7697	1.44086
$725$	4.11554	0.152847
$726$	0	0
$727$	−29.3642	−1.08906	−0.544528	−	0.838742i	$-0.683291\pi$
$727$	−29.3642	−1.08906	−0.544528	+	0.838742i	$0.683291\pi$
$728$	−0.933270	−0.0345893
$729$	0	0
$730$	6.55932	0.242771
$731$	2.38961	0.0883828
$732$	0	0
$733$	−14.2139	−0.525004	−0.262502	−	0.964931i	$-0.584548\pi$
$733$	−14.2139	−0.525004	−0.262502	+	0.964931i	$0.584548\pi$
$734$	43.3068	1.59848
$735$	0	0
$736$	7.97760	0.294058
$737$	13.8123	0.508783
$738$	0	0
$739$	0.780656	0.0287169	0.0143584	−	0.999897i	$-0.495429\pi$
$739$	0.780656	0.0287169	0.0143584	+	0.999897i	$0.495429\pi$
$740$	9.83203	0.361433
$741$	0	0
$742$	23.5475	0.864457
$743$	23.3325	0.855985	0.427993	−	0.903782i	$-0.359221\pi$
$743$	23.3325	0.855985	0.427993	+	0.903782i	$0.359221\pi$
$744$	0	0
$745$	−8.14866	−0.298544
$746$	60.0229	2.19759
$747$	0	0
$748$	−6.05824	−0.221511
$749$	7.96585	0.291066
$750$	0	0
$751$	−42.8274	−1.56279	−0.781397	−	0.624034i	$-0.785493\pi$
$751$	−42.8274	−1.56279	−0.781397	+	0.624034i	$0.785493\pi$
$752$	20.0182	0.729988
$753$	0	0
$754$	7.85258	0.285974
$755$	14.2093	0.517129
$756$	0	0
$757$	6.50731	0.236512	0.118256	−	0.992983i	$-0.462270\pi$
$757$	6.50731	0.236512	0.118256	+	0.992983i	$0.462270\pi$
$758$	−51.4977	−1.87048
$759$	0	0
$760$	4.22817	0.153372
$761$	−54.7420	−1.98440	−0.992198	−	0.124670i	$-0.960213\pi$
$761$	−54.7420	−1.98440	−0.992198	+	0.124670i	$0.960213\pi$
$762$	0	0
$763$	9.28113	0.336000
$764$	29.5031	1.06739
$765$	0	0
$766$	−64.7419	−2.33922
$767$	−2.08702	−0.0753581
$768$	0	0
$769$	39.4543	1.42276	0.711379	−	0.702809i	$-0.248071\pi$
$769$	39.4543	1.42276	0.711379	+	0.702809i	$0.248071\pi$
$770$	−13.7471	−0.495413
$771$	0	0
$772$	12.3107	0.443072
$773$	−4.78617	−0.172147	−0.0860733	−	0.996289i	$-0.527432\pi$
$773$	−4.78617	−0.172147	−0.0860733	+	0.996289i	$0.527432\pi$
$774$	0	0
$775$	0.519001	0.0186431
$776$	14.8587	0.533395
$777$	0	0
$778$	9.73118	0.348880
$779$	−1.69171	−0.0606117
$780$	0	0
$781$	90.4636	3.23704
$782$	0.809392	0.0289438
$783$	0	0
$784$	16.7442	0.598007
$785$	5.41406	0.193236
$786$	0	0
$787$	−39.8867	−1.42181	−0.710903	−	0.703290i	$-0.751714\pi$
$787$	−39.8867	−1.42181	−0.710903	+	0.703290i	$0.751714\pi$
$788$	10.3990	0.370450
$789$	0	0
$790$	−6.34711	−0.225820
$791$	8.98037	0.319305
$792$	0	0
$793$	4.88923	0.173622
$794$	18.3555	0.651411
$795$	0	0
$796$	−3.62502	−0.128485
$797$	−1.33134	−0.0471584	−0.0235792	−	0.999722i	$-0.507506\pi$
$797$	−1.33134	−0.0471584	−0.0235792	+	0.999722i	$0.507506\pi$
$798$	0	0
$799$	2.72715	0.0964797
$800$	−7.97760	−0.282051
$801$	0	0
$802$	9.57918	0.338252
$803$	19.7888	0.698331
$804$	0	0
$805$	1.01690	0.0358409
$806$	0.990270	0.0348808
$807$	0	0
$808$	−12.5902	−0.442921
$809$	−52.3897	−1.84192	−0.920962	−	0.389653i	$-0.872595\pi$
$809$	−52.3897	−1.84192	−0.920962	+	0.389653i	$0.872595\pi$
$810$	0	0
$811$	19.8302	0.696331	0.348166	−	0.937433i	$-0.386805\pi$
$811$	19.8302	0.696331	0.348166	+	0.937433i	$0.386805\pi$
$812$	−10.3832	−0.364378
$813$	0	0
$814$	53.5737	1.87776
$815$	1.15928	0.0406078
$816$	0	0
$817$	−25.9523	−0.907956
$818$	−6.82245	−0.238542
$819$	0	0
$820$	−1.01072	−0.0352959
$821$	−22.3195	−0.778957	−0.389478	−	0.921036i	$-0.627345\pi$
$821$	−22.3195	−0.778957	−0.389478	+	0.921036i	$0.627345\pi$
$822$	0	0
$823$	2.13067	0.0742705	0.0371353	−	0.999310i	$-0.488177\pi$
$823$	2.13067	0.0742705	0.0371353	+	0.999310i	$0.488177\pi$
$824$	−11.1903	−0.389831
$825$	0	0
$826$	4.98418	0.173422
$827$	−29.2822	−1.01824	−0.509122	−	0.860695i	$-0.670030\pi$
$827$	−29.2822	−1.01824	−0.509122	+	0.860695i	$0.670030\pi$
$828$	0	0
$829$	−35.3823	−1.22888	−0.614439	−	0.788964i	$-0.710618\pi$
$829$	−35.3823	−1.22888	−0.614439	+	0.788964i	$0.710618\pi$
$830$	−34.2778	−1.18980
$831$	0	0
$832$	−10.1619	−0.352301
$833$	2.28112	0.0790363
$834$	0	0
$835$	3.97129	0.137432
$836$	65.7954	2.27558
$837$	0	0
$838$	51.4148	1.77610
$839$	−40.2326	−1.38898	−0.694492	−	0.719500i	$-0.744371\pi$
$839$	−40.2326	−1.38898	−0.694492	+	0.719500i	$0.744371\pi$
$840$	0	0
$841$	−12.0624	−0.415943
$842$	14.8092	0.510360
$843$	0	0
$844$	−59.8006	−2.05842
$845$	−12.1876	−0.419264
$846$	0	0
$847$	−30.2879	−1.04070
$848$	30.7021	1.05431
$849$	0	0
$850$	−0.809392	−0.0277619
$851$	−3.96293	−0.135848
$852$	0	0
$853$	−22.6335	−0.774955	−0.387478	−	0.921879i	$-0.626654\pi$
$853$	−22.6335	−0.774955	−0.387478	+	0.921879i	$0.626654\pi$
$854$	−11.6763	−0.399556
$855$	0	0
$856$	−7.97603	−0.272615
$857$	−55.8700	−1.90848	−0.954242	−	0.299035i	$-0.903335\pi$
$857$	−55.8700	−1.90848	−0.954242	+	0.299035i	$0.903335\pi$
$858$	0	0
$859$	−45.4875	−1.55201	−0.776007	−	0.630724i	$-0.782758\pi$
$859$	−45.4875	−1.55201	−0.776007	+	0.630724i	$0.782758\pi$
$860$	−15.5053	−0.528728
$861$	0	0
$862$	10.5538	0.359465
$863$	42.7388	1.45484	0.727422	−	0.686190i	$-0.240718\pi$
$863$	42.7388	1.45484	0.727422	+	0.686190i	$0.240718\pi$
$864$	0	0
$865$	13.2295	0.449815
$866$	−5.73074	−0.194739
$867$	0	0
$868$	−1.30940	−0.0444439
$869$	−19.1486	−0.649571
$870$	0	0
$871$	1.94947	0.0660553
$872$	−9.29300	−0.314701
$873$	0	0
$874$	−8.79039	−0.297339
$875$	−1.01690	−0.0343774
$876$	0	0
$877$	25.4891	0.860706	0.430353	−	0.902661i	$-0.358389\pi$
$877$	25.4891	0.860706	0.430353	+	0.902661i	$0.358389\pi$
$878$	79.5023	2.68307
$879$	0	0
$880$	−17.9240	−0.604218
$881$	53.2995	1.79571	0.897853	−	0.440294i	$-0.145126\pi$
$881$	53.2995	1.79571	0.897853	+	0.440294i	$0.145126\pi$
$882$	0	0
$883$	45.1436	1.51920	0.759601	−	0.650390i	$-0.225394\pi$
$883$	45.1436	1.51920	0.759601	+	0.650390i	$0.225394\pi$
$884$	−0.855060	−0.0287588
$885$	0	0
$886$	32.9761	1.10786
$887$	−37.8512	−1.27092	−0.635459	−	0.772135i	$-0.719189\pi$
$887$	−37.8512	−1.27092	−0.635459	+	0.772135i	$0.719189\pi$
$888$	0	0
$889$	−14.8078	−0.496639
$890$	−30.5357	−1.02356
$891$	0	0
$892$	−64.7391	−2.16763
$893$	−29.6182	−0.991135
$894$	0	0
$895$	−0.179450	−0.00599835
$896$	8.04367	0.268720
$897$	0	0
$898$	18.1038	0.604133
$899$	2.13597	0.0712385
$900$	0	0
$901$	4.18266	0.139345
$902$	−5.50731	−0.183373
$903$	0	0
$904$	−8.99184	−0.299064
$905$	15.6266	0.519447
$906$	0	0
$907$	−20.2809	−0.673417	−0.336708	−	0.941609i	$-0.609314\pi$
$907$	−20.2809	−0.673417	−0.336708	+	0.941609i	$0.609314\pi$
$908$	−49.8669	−1.65489
$909$	0	0
$910$	−1.94027	−0.0643194
$911$	36.2097	1.19968	0.599841	−	0.800119i	$-0.295230\pi$
$911$	36.2097	1.19968	0.599841	+	0.800119i	$0.295230\pi$
$912$	0	0
$913$	−103.413	−3.42246
$914$	83.7147	2.76903
$915$	0	0
$916$	64.6931	2.13752
$917$	15.2617	0.503986
$918$	0	0
$919$	−5.05166	−0.166639	−0.0833194	−	0.996523i	$-0.526552\pi$
$919$	−5.05166	−0.166639	−0.0833194	+	0.996523i	$0.526552\pi$
$920$	−1.01820	−0.0335690
$921$	0	0
$922$	18.8164	0.619684
$923$	12.7680	0.420265
$924$	0	0
$925$	3.96293	0.130300
$926$	−16.8739	−0.554512
$927$	0	0
$928$	−32.8321	−1.07777
$929$	34.5119	1.13230	0.566149	−	0.824303i	$-0.308433\pi$
$929$	34.5119	1.13230	0.566149	+	0.824303i	$0.308433\pi$
$930$	0	0
$931$	−24.7741	−0.811939
$932$	56.6682	1.85623
$933$	0	0
$934$	−81.1509	−2.65534
$935$	−2.44185	−0.0798572
$936$	0	0
$937$	−15.0924	−0.493047	−0.246523	−	0.969137i	$-0.579288\pi$
$937$	−15.0924	−0.493047	−0.246523	+	0.969137i	$0.579288\pi$
$938$	−4.65568	−0.152013
$939$	0	0
$940$	−17.6956	−0.577166
$941$	−14.5081	−0.472950	−0.236475	−	0.971638i	$-0.575992\pi$
$941$	−14.5081	−0.472950	−0.236475	+	0.971638i	$0.575992\pi$
$942$	0	0
$943$	0.407384	0.0132663
$944$	6.49854	0.211510
$945$	0	0
$946$	−84.4871	−2.74691
$947$	−1.39928	−0.0454706	−0.0227353	−	0.999742i	$-0.507237\pi$
$947$	−1.39928	−0.0454706	−0.0227353	+	0.999742i	$0.507237\pi$
$948$	0	0
$949$	2.79299	0.0906643
$950$	8.79039	0.285198
$951$	0	0
$952$	0.395896	0.0128311
$953$	1.04263	0.0337741	0.0168870	−	0.999857i	$-0.494624\pi$
$953$	1.04263	0.0337741	0.0168870	+	0.999857i	$0.494624\pi$
$954$	0	0
$955$	11.8916	0.384804
$956$	0.833234	0.0269487
$957$	0	0
$958$	39.7071	1.28288
$959$	−0.681475	−0.0220060
$960$	0	0
$961$	−30.7306	−0.991311
$962$	7.56140	0.243789
$963$	0	0
$964$	−31.8898	−1.02710
$965$	4.96200	0.159732
$966$	0	0
$967$	−24.9111	−0.801086	−0.400543	−	0.916278i	$-0.631178\pi$
$967$	−24.9111	−0.801086	−0.400543	+	0.916278i	$0.631178\pi$
$968$	30.3266	0.974733
$969$	0	0
$970$	30.8912	0.991858
$971$	−5.16712	−0.165821	−0.0829104	−	0.996557i	$-0.526422\pi$
$971$	−5.16712	−0.165821	−0.0829104	+	0.996557i	$0.526422\pi$
$972$	0	0
$973$	−3.67035	−0.117666
$974$	−27.6522	−0.886034
$975$	0	0
$976$	−15.2240	−0.487309
$977$	−18.2249	−0.583065	−0.291532	−	0.956561i	$-0.594165\pi$
$977$	−18.2249	−0.583065	−0.291532	+	0.956561i	$0.594165\pi$
$978$	0	0
$979$	−92.1230	−2.94426
$980$	−14.8014	−0.472815
$981$	0	0
$982$	88.4982	2.82409
$983$	−7.22251	−0.230362	−0.115181	−	0.993345i	$-0.536745\pi$
$983$	−7.22251	−0.230362	−0.115181	+	0.993345i	$0.536745\pi$
$984$	0	0
$985$	4.19147	0.133551
$986$	−3.33108	−0.106083
$987$	0	0
$988$	9.28636	0.295439
$989$	6.24964	0.198727
$990$	0	0
$991$	−51.4086	−1.63305	−0.816524	−	0.577312i	$-0.804102\pi$
$991$	−51.4086	−1.63305	−0.816524	+	0.577312i	$0.804102\pi$
$992$	−4.14038	−0.131457
$993$	0	0
$994$	−30.4923	−0.967157
$995$	−1.46111	−0.0463204
$996$	0	0
$997$	37.0898	1.17465	0.587323	−	0.809353i	$-0.300182\pi$
$997$	37.0898	1.17465	0.587323	+	0.809353i	$0.300182\pi$
$998$	45.4706	1.43935
$999$	0	0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1035.2.a.q.1.5	yes	6
3.2	odd	2		1035.2.a.p.1.2	✓	6
5.4	even	2		5175.2.a.by.1.2		6
15.14	odd	2		5175.2.a.bz.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1035.2.a.p.1.2	✓	6	3.2	odd	2
1035.2.a.q.1.5	yes	6	1.1	even	1	trivial
5175.2.a.by.1.2		6	5.4	even	2
5175.2.a.bz.1.5		6	15.14	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1035.2.a.q.1.5

Level	$1035$
Weight	$2$
Character	1035.1
Self dual	yes
Analytic conductor	$8.265$
Analytic rank	$0$
Dimension	$6$
CM	no
Inner twists	$1$