LMFDB - Embedded newform 1035.2.a.q.1.6

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			1.6
Root			$-1.44541$ 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)

$f(q)$	$=$	$q+2.50089 q^{2} +4.25445 q^{4} +1.00000 q^{5} +3.78907 q^{7} +5.63815 q^{8} +2.50089 q^{10} -4.47428 q^{11} +5.13725 q^{13} +9.47606 q^{14} +5.59148 q^{16} -6.39171 q^{17} -7.47606 q^{19} +4.25445 q^{20} -11.1897 q^{22} -1.00000 q^{23} +1.00000 q^{25} +12.8477 q^{26} +16.1204 q^{28} -4.92633 q^{29} -1.25445 q^{31} +2.70738 q^{32} -15.9850 q^{34} +3.78907 q^{35} +6.54973 q^{37} -18.6968 q^{38} +5.63815 q^{40} +9.19411 q^{41} -3.17189 q^{43} -19.0356 q^{44} -2.50089 q^{46} +6.71540 q^{47} +7.35708 q^{49} +2.50089 q^{50} +21.8562 q^{52} +11.3069 q^{53} -4.47428 q^{55} +21.3633 q^{56} -12.3202 q^{58} -3.65360 q^{59} -8.98319 q^{61} -3.13725 q^{62} -4.41209 q^{64} +5.13725 q^{65} +15.1297 q^{67} -27.1932 q^{68} +9.47606 q^{70} -8.33437 q^{71} -1.13725 q^{73} +16.3802 q^{74} -31.8066 q^{76} -16.9534 q^{77} -15.7852 q^{79} +5.59148 q^{80} +22.9935 q^{82} +3.06575 q^{83} -6.39171 q^{85} -7.93254 q^{86} -25.2266 q^{88} -13.4432 q^{89} +19.4654 q^{91} -4.25445 q^{92} +16.7945 q^{94} -7.47606 q^{95} -4.42230 q^{97} +18.3992 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q + 10 q^{4} + 6 q^{5} + 6 q^{7} - 4 q^{11} + 12 q^{13} + 4 q^{14} + 14 q^{16} - 4 q^{17} + 8 q^{19} + 10 q^{20} + 8 q^{22} - 6 q^{23} + 6 q^{25} + 12 q^{26} + 24 q^{28} + 6 q^{29} + 8 q^{31} - 20 q^{32}+ \cdots + 4 q^{98}+O(q^{100})$ 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

)

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

$2$	2.50089	1.76840	0.884198	−	0.467111i	$-0.154705\pi$
$2$	2.50089	1.76840	0.884198	+	0.467111i	$0.154705\pi$
$3$	0	0
$3$	0	0
$4$	4.25445	2.12723
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	3.78907	1.43214	0.716068	−	0.698031i	$-0.245940\pi$
$7$	3.78907	1.43214	0.716068	+	0.698031i	$0.245940\pi$
$8$	5.63815	1.99339
$9$	0	0
$10$	2.50089	0.790851
$11$	−4.47428	−1.34905	−0.674523	−	0.738254i	$-0.735651\pi$
$11$	−4.47428	−1.34905	−0.674523	+	0.738254i	$0.735651\pi$
$12$	0	0
$13$	5.13725	1.42482	0.712409	−	0.701764i	$-0.247604\pi$
$13$	5.13725	1.42482	0.712409	+	0.701764i	$0.247604\pi$
$14$	9.47606	2.53258
$15$	0	0
$16$	5.59148	1.39787
$17$	−6.39171	−1.55022	−0.775109	−	0.631828i	$-0.782305\pi$
$17$	−6.39171	−1.55022	−0.775109	+	0.631828i	$0.782305\pi$
$18$	0	0
$19$	−7.47606	−1.71513	−0.857563	−	0.514379i	$-0.828022\pi$
$19$	−7.47606	−1.71513	−0.857563	+	0.514379i	$0.828022\pi$
$20$	4.25445	0.951325
$21$	0	0
$22$	−11.1897	−2.38565
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	1.00000	0.200000
$26$	12.8477	2.51964
$27$	0	0
$28$	16.1204	3.04648
$29$	−4.92633	−0.914796	−0.457398	−	0.889262i	$-0.651219\pi$
$29$	−4.92633	−0.914796	−0.457398	+	0.889262i	$0.651219\pi$
$30$	0	0
$31$	−1.25445	−0.225307	−0.112653	−	0.993634i	$-0.535935\pi$
$31$	−1.25445	−0.225307	−0.112653	+	0.993634i	$0.535935\pi$
$32$	2.70738	0.478602
$33$	0	0
$34$	−15.9850	−2.74140
$35$	3.78907	0.640470
$36$	0	0
$37$	6.54973	1.07677	0.538385	−	0.842699i	$-0.319035\pi$
$37$	6.54973	1.07677	0.538385	+	0.842699i	$0.319035\pi$
$38$	−18.6968	−3.03302
$39$	0	0
$40$	5.63815	0.891469
$41$	9.19411	1.43588	0.717940	−	0.696105i	$-0.245085\pi$
$41$	9.19411	1.43588	0.717940	+	0.696105i	$0.245085\pi$
$42$	0	0
$43$	−3.17189	−0.483708	−0.241854	−	0.970313i	$-0.577756\pi$
$43$	−3.17189	−0.483708	−0.241854	+	0.970313i	$0.577756\pi$
$44$	−19.0356	−2.86973
$45$	0	0
$46$	−2.50089	−0.368736
$47$	6.71540	0.979542	0.489771	−	0.871851i	$-0.337080\pi$
$47$	6.71540	0.979542	0.489771	+	0.871851i	$0.337080\pi$
$48$	0	0
$49$	7.35708	1.05101
$50$	2.50089	0.353679
$51$	0	0
$52$	21.8562	3.03091
$53$	11.3069	1.55312	0.776560	−	0.630044i	$-0.216963\pi$
$53$	11.3069	1.55312	0.776560	+	0.630044i	$0.216963\pi$
$54$	0	0
$55$	−4.47428	−0.603311
$56$	21.3633	2.85480
$57$	0	0
$58$	−12.3202	−1.61772
$59$	−3.65360	−0.475658	−0.237829	−	0.971307i	$-0.576436\pi$
$59$	−3.65360	−0.475658	−0.237829	+	0.971307i	$0.576436\pi$
$60$	0	0
$61$	−8.98319	−1.15018	−0.575090	−	0.818090i	$-0.695033\pi$
$61$	−8.98319	−1.15018	−0.575090	+	0.818090i	$0.695033\pi$
$62$	−3.13725	−0.398432
$63$	0	0
$64$	−4.41209	−0.551511
$65$	5.13725	0.637198
$66$	0	0
$67$	15.1297	1.84838	0.924191	−	0.381931i	$-0.124741\pi$
$67$	15.1297	1.84838	0.924191	+	0.381931i	$0.124741\pi$
$68$	−27.1932	−3.29767
$69$	0	0
$70$	9.47606	1.13261
$71$	−8.33437	−0.989108	−0.494554	−	0.869147i	$-0.664669\pi$
$71$	−8.33437	−0.989108	−0.494554	+	0.869147i	$0.664669\pi$
$72$	0	0
$73$	−1.13725	−0.133106	−0.0665528	−	0.997783i	$-0.521200\pi$
$73$	−1.13725	−0.133106	−0.0665528	+	0.997783i	$0.521200\pi$
$74$	16.3802	1.90416
$75$	0	0
$76$	−31.8066	−3.64846
$77$	−16.9534	−1.93202
$78$	0	0
$79$	−15.7852	−1.77597	−0.887987	−	0.459869i	$-0.847897\pi$
$79$	−15.7852	−1.77597	−0.887987	+	0.459869i	$0.847897\pi$
$80$	5.59148	0.625146
$81$	0	0
$82$	22.9935	2.53920
$83$	3.06575	0.336510	0.168255	−	0.985743i	$-0.446187\pi$
$83$	3.06575	0.336510	0.168255	+	0.985743i	$0.446187\pi$
$84$	0	0
$85$	−6.39171	−0.693278
$86$	−7.93254	−0.855388
$87$	0	0
$88$	−25.2266	−2.68917
$89$	−13.4432	−1.42498	−0.712490	−	0.701682i	$-0.752433\pi$
$89$	−13.4432	−1.42498	−0.712490	+	0.701682i	$0.752433\pi$
$90$	0	0
$91$	19.4654	2.04053
$92$	−4.25445	−0.443558
$93$	0	0
$94$	16.7945	1.73222
$95$	−7.47606	−0.767027
$96$	0	0
$97$	−4.42230	−0.449016	−0.224508	−	0.974472i	$-0.572078\pi$
$97$	−4.42230	−0.449016	−0.224508	+	0.974472i	$0.572078\pi$
$98$	18.3992	1.85860
$99$	0	0
$100$	4.25445	0.425445
$101$	−0.245559	−0.0244341	−0.0122170	−	0.999925i	$-0.503889\pi$
$101$	−0.245559	−0.0244341	−0.0122170	+	0.999925i	$0.503889\pi$
$102$	0	0
$103$	6.11688	0.602714	0.301357	−	0.953511i	$-0.402560\pi$
$103$	6.11688	0.602714	0.301357	+	0.953511i	$0.402560\pi$
$104$	28.9646	2.84021
$105$	0	0
$106$	28.2773	2.74653
$107$	−8.35832	−0.808030	−0.404015	−	0.914752i	$-0.632386\pi$
$107$	−8.35832	−0.808030	−0.404015	+	0.914752i	$0.632386\pi$
$108$	0	0
$109$	15.7630	1.50983	0.754913	−	0.655825i	$-0.227679\pi$
$109$	15.7630	1.50983	0.754913	+	0.655825i	$0.227679\pi$
$110$	−11.1897	−1.06689
$111$	0	0
$112$	21.1865	2.00194
$113$	−1.37073	−0.128947	−0.0644737	−	0.997919i	$-0.520537\pi$
$113$	−1.37073	−0.128947	−0.0644737	+	0.997919i	$0.520537\pi$
$114$	0	0
$115$	−1.00000	−0.0932505
$116$	−20.9588	−1.94598
$117$	0	0
$118$	−9.13725	−0.841153
$119$	−24.2187	−2.22012
$120$	0	0
$121$	9.01916	0.819923
$122$	−22.4660	−2.03397
$123$	0	0
$124$	−5.33702	−0.479279
$125$	1.00000	0.0894427
$126$	0	0
$127$	5.79707	0.514407	0.257203	−	0.966357i	$-0.417199\pi$
$127$	5.79707	0.514407	0.257203	+	0.966357i	$0.417199\pi$
$128$	−16.4489	−1.45389
$129$	0	0
$130$	12.8477	1.12682
$131$	7.86513	0.687180	0.343590	−	0.939120i	$-0.388357\pi$
$131$	7.86513	0.687180	0.343590	+	0.939120i	$0.388357\pi$
$132$	0	0
$133$	−28.3273	−2.45629
$134$	37.8376	3.26867
$135$	0	0
$136$	−36.0374	−3.09018
$137$	4.77670	0.408101	0.204050	−	0.978960i	$-0.434589\pi$
$137$	4.77670	0.408101	0.204050	+	0.978960i	$0.434589\pi$
$138$	0	0
$139$	3.68303	0.312391	0.156195	−	0.987726i	$-0.450077\pi$
$139$	3.68303	0.312391	0.156195	+	0.987726i	$0.450077\pi$
$140$	16.1204	1.36243
$141$	0	0
$142$	−20.8433	−1.74913
$143$	−22.9855	−1.92214
$144$	0	0
$145$	−4.92633	−0.409109
$146$	−2.84415	−0.235384
$147$	0	0
$148$	27.8655	2.29053
$149$	−1.32155	−0.108265	−0.0541327	−	0.998534i	$-0.517239\pi$
$149$	−1.32155	−0.108265	−0.0541327	+	0.998534i	$0.517239\pi$
$150$	0	0
$151$	6.69320	0.544685	0.272343	−	0.962200i	$-0.412202\pi$
$151$	6.69320	0.544685	0.272343	+	0.962200i	$0.412202\pi$
$152$	−42.1511	−3.41891
$153$	0	0
$154$	−42.3985	−3.41657
$155$	−1.25445	−0.100760
$156$	0	0
$157$	2.51635	0.200826	0.100413	−	0.994946i	$-0.467984\pi$
$157$	2.51635	0.200826	0.100413	+	0.994946i	$0.467984\pi$
$158$	−39.4771	−3.14063
$159$	0	0
$160$	2.70738	0.214037
$161$	−3.78907	−0.298621
$162$	0	0
$163$	−3.76560	−0.294945	−0.147472	−	0.989066i	$-0.547114\pi$
$163$	−3.76560	−0.294945	−0.147472	+	0.989066i	$0.547114\pi$
$164$	39.1159	3.05444
$165$	0	0
$166$	7.66712	0.595084
$167$	−3.03144	−0.234580	−0.117290	−	0.993098i	$-0.537421\pi$
$167$	−3.03144	−0.234580	−0.117290	+	0.993098i	$0.537421\pi$
$168$	0	0
$169$	13.3914	1.03011
$170$	−15.9850	−1.22599
$171$	0	0
$172$	−13.4947	−1.02896
$173$	7.93254	0.603100	0.301550	−	0.953450i	$-0.402496\pi$
$173$	7.93254	0.603100	0.301550	+	0.953450i	$0.402496\pi$
$174$	0	0
$175$	3.78907	0.286427
$176$	−25.0178	−1.88579
$177$	0	0
$178$	−33.6201	−2.51993
$179$	2.52626	0.188821	0.0944107	−	0.995533i	$-0.469903\pi$
$179$	2.52626	0.188821	0.0944107	+	0.995533i	$0.469903\pi$
$180$	0	0
$181$	12.2380	0.909641	0.454820	−	0.890583i	$-0.349703\pi$
$181$	12.2380	0.909641	0.454820	+	0.890583i	$0.349703\pi$
$182$	48.6809	3.60847
$183$	0	0
$184$	−5.63815	−0.415650
$185$	6.54973	0.481546
$186$	0	0
$187$	28.5983	2.09131
$188$	28.5704	2.08371
$189$	0	0
$190$	−18.6968	−1.35641
$191$	−0.979624	−0.0708831	−0.0354415	−	0.999372i	$-0.511284\pi$
$191$	−0.979624	−0.0708831	−0.0354415	+	0.999372i	$0.511284\pi$
$192$	0	0
$193$	8.50891	0.612485	0.306242	−	0.951954i	$-0.400928\pi$
$193$	8.50891	0.612485	0.306242	+	0.951954i	$0.400928\pi$
$194$	−11.0597	−0.794039
$195$	0	0
$196$	31.3004	2.23574
$197$	2.44145	0.173946	0.0869732	−	0.996211i	$-0.472281\pi$
$197$	2.44145	0.173946	0.0869732	+	0.996211i	$0.472281\pi$
$198$	0	0
$199$	−23.9503	−1.69779	−0.848897	−	0.528558i	$-0.822733\pi$
$199$	−23.9503	−1.69779	−0.848897	+	0.528558i	$0.822733\pi$
$200$	5.63815	0.398677
$201$	0	0
$202$	−0.614117	−0.0432091
$203$	−18.6662	−1.31011
$204$	0	0
$205$	9.19411	0.642145
$206$	15.2976	1.06584
$207$	0	0
$208$	28.7248	1.99171
$209$	33.4500	2.31378
$210$	0	0
$211$	19.6821	1.35497	0.677485	−	0.735537i	$-0.263070\pi$
$211$	19.6821	1.35497	0.677485	+	0.735537i	$0.263070\pi$
$212$	48.1046	3.30384
$213$	0	0
$214$	−20.9033	−1.42892
$215$	−3.17189	−0.216321
$216$	0	0
$217$	−4.75322	−0.322670
$218$	39.4217	2.66997
$219$	0	0
$220$	−19.0356	−1.28338
$221$	−32.8358	−2.20878
$222$	0	0
$223$	−24.2415	−1.62333	−0.811666	−	0.584121i	$-0.801439\pi$
$223$	−24.2415	−1.62333	−0.811666	+	0.584121i	$0.801439\pi$
$224$	10.2585	0.685423
$225$	0	0
$226$	−3.42804	−0.228030
$227$	6.81608	0.452399	0.226200	−	0.974081i	$-0.427370\pi$
$227$	6.81608	0.452399	0.226200	+	0.974081i	$0.427370\pi$
$228$	0	0
$229$	−26.8883	−1.77683	−0.888413	−	0.459044i	$-0.848192\pi$
$229$	−26.8883	−1.77683	−0.888413	+	0.459044i	$0.848192\pi$
$230$	−2.50089	−0.164904
$231$	0	0
$232$	−27.7754	−1.82354
$233$	2.66795	0.174783	0.0873916	−	0.996174i	$-0.472147\pi$
$233$	2.66795	0.174783	0.0873916	+	0.996174i	$0.472147\pi$
$234$	0	0
$235$	6.71540	0.438065
$236$	−15.5441	−1.01183
$237$	0	0
$238$	−60.5682	−3.92605
$239$	14.7598	0.954731	0.477366	−	0.878705i	$-0.341592\pi$
$239$	14.7598	0.954731	0.477366	+	0.878705i	$0.341592\pi$
$240$	0	0
$241$	−3.52929	−0.227341	−0.113671	−	0.993518i	$-0.536261\pi$
$241$	−3.52929	−0.227341	−0.113671	+	0.993518i	$0.536261\pi$
$242$	22.5559	1.44995
$243$	0	0
$244$	−38.2186	−2.44669
$245$	7.35708	0.470026
$246$	0	0
$247$	−38.4064	−2.44374
$248$	−7.07280	−0.449123
$249$	0	0
$250$	2.50089	0.158170
$251$	2.43964	0.153989	0.0769945	−	0.997032i	$-0.475468\pi$
$251$	2.43964	0.153989	0.0769945	+	0.997032i	$0.475468\pi$
$252$	0	0
$253$	4.47428	0.281295
$254$	14.4978	0.909676
$255$	0	0
$256$	−32.3128	−2.01955
$257$	−23.5965	−1.47191	−0.735955	−	0.677031i	$-0.763266\pi$
$257$	−23.5965	−1.47191	−0.735955	+	0.677031i	$0.763266\pi$
$258$	0	0
$259$	24.8174	1.54208
$260$	21.8562	1.35547
$261$	0	0
$262$	19.6698	1.21521
$263$	18.7323	1.15508	0.577542	−	0.816361i	$-0.304012\pi$
$263$	18.7323	1.15508	0.577542	+	0.816361i	$0.304012\pi$
$264$	0	0
$265$	11.3069	0.694576
$266$	−70.8436	−4.34370
$267$	0	0
$268$	64.3685	3.93193
$269$	5.07723	0.309564	0.154782	−	0.987949i	$-0.450532\pi$
$269$	5.07723	0.309564	0.154782	+	0.987949i	$0.450532\pi$
$270$	0	0
$271$	−16.2939	−0.989782	−0.494891	−	0.868955i	$-0.664792\pi$
$271$	−16.2939	−0.989782	−0.494891	+	0.868955i	$0.664792\pi$
$272$	−35.7391	−2.16700
$273$	0	0
$274$	11.9460	0.721684
$275$	−4.47428	−0.269809
$276$	0	0
$277$	18.7469	1.12639	0.563195	−	0.826324i	$-0.309572\pi$
$277$	18.7469	1.12639	0.563195	+	0.826324i	$0.309572\pi$
$278$	9.21086	0.552431
$279$	0	0
$280$	21.3633	1.27670
$281$	24.1846	1.44273	0.721365	−	0.692555i	$-0.243515\pi$
$281$	24.1846	1.44273	0.721365	+	0.692555i	$0.243515\pi$
$282$	0	0
$283$	9.00857	0.535504	0.267752	−	0.963488i	$-0.413719\pi$
$283$	9.00857	0.535504	0.267752	+	0.963488i	$0.413719\pi$
$284$	−35.4582	−2.10406
$285$	0	0
$286$	−57.4842	−3.39911
$287$	34.8372	2.05637
$288$	0	0
$289$	23.8540	1.40317
$290$	−12.3202	−0.723468
$291$	0	0
$292$	−4.83840	−0.283146
$293$	−23.2444	−1.35795	−0.678976	−	0.734160i	$-0.737576\pi$
$293$	−23.2444	−1.35795	−0.678976	+	0.734160i	$0.737576\pi$
$294$	0	0
$295$	−3.65360	−0.212721
$296$	36.9283	2.14642
$297$	0	0
$298$	−3.30504	−0.191456
$299$	−5.13725	−0.297095
$300$	0	0
$301$	−12.0185	−0.692736
$302$	16.7390	0.963219
$303$	0	0
$304$	−41.8022	−2.39752
$305$	−8.98319	−0.514376
$306$	0	0
$307$	7.52192	0.429299	0.214649	−	0.976691i	$-0.431139\pi$
$307$	7.52192	0.429299	0.214649	+	0.976691i	$0.431139\pi$
$308$	−72.1273	−4.10984
$309$	0	0
$310$	−3.13725	−0.178184
$311$	3.83306	0.217353	0.108676	−	0.994077i	$-0.465339\pi$
$311$	3.83306	0.217353	0.108676	+	0.994077i	$0.465339\pi$
$312$	0	0
$313$	−12.0622	−0.681794	−0.340897	−	0.940101i	$-0.610731\pi$
$313$	−12.0622	−0.681794	−0.340897	+	0.940101i	$0.610731\pi$
$314$	6.29310	0.355140
$315$	0	0
$316$	−67.1574	−3.77790
$317$	−6.17993	−0.347099	−0.173550	−	0.984825i	$-0.555524\pi$
$317$	−6.17993	−0.347099	−0.173550	+	0.984825i	$0.555524\pi$
$318$	0	0
$319$	22.0418	1.23410
$320$	−4.41209	−0.246643
$321$	0	0
$322$	−9.47606	−0.528080
$323$	47.7848	2.65882
$324$	0	0
$325$	5.13725	0.284964
$326$	−9.41735	−0.521579
$327$	0	0
$328$	51.8378	2.86226
$329$	25.4452	1.40284
$330$	0	0
$331$	−2.97930	−0.163757	−0.0818786	−	0.996642i	$-0.526092\pi$
$331$	−2.97930	−0.163757	−0.0818786	+	0.996642i	$0.526092\pi$
$332$	13.0431	0.715834
$333$	0	0
$334$	−7.58131	−0.414831
$335$	15.1297	0.826622
$336$	0	0
$337$	−6.83665	−0.372416	−0.186208	−	0.982510i	$-0.559620\pi$
$337$	−6.83665	−0.372416	−0.186208	+	0.982510i	$0.559620\pi$
$338$	33.4904	1.82164
$339$	0	0
$340$	−27.1932	−1.47476
$341$	5.61278	0.303949
$342$	0	0
$343$	1.35299	0.0730547
$344$	−17.8836	−0.964217
$345$	0	0
$346$	19.8384	1.06652
$347$	14.6740	0.787744	0.393872	−	0.919165i	$-0.371135\pi$
$347$	14.6740	0.787744	0.393872	+	0.919165i	$0.371135\pi$
$348$	0	0
$349$	21.8418	1.16917	0.584584	−	0.811333i	$-0.301258\pi$
$349$	21.8418	1.16917	0.584584	+	0.811333i	$0.301258\pi$
$350$	9.47606	0.506517
$351$	0	0
$352$	−12.1136	−0.645656
$353$	23.5130	1.25147	0.625736	−	0.780035i	$-0.284799\pi$
$353$	23.5130	1.25147	0.625736	+	0.780035i	$0.284799\pi$
$354$	0	0
$355$	−8.33437	−0.442342
$356$	−57.1936	−3.03126
$357$	0	0
$358$	6.31789	0.333911
$359$	4.11920	0.217403	0.108701	−	0.994074i	$-0.465331\pi$
$359$	4.11920	0.217403	0.108701	+	0.994074i	$0.465331\pi$
$360$	0	0
$361$	36.8915	1.94166
$362$	30.6058	1.60861
$363$	0	0
$364$	82.8148	4.34068
$365$	−1.13725	−0.0595266
$366$	0	0
$367$	21.6911	1.13227	0.566133	−	0.824314i	$-0.308439\pi$
$367$	21.6911	1.13227	0.566133	+	0.824314i	$0.308439\pi$
$368$	−5.59148	−0.291476
$369$	0	0
$370$	16.3802	0.851564
$371$	42.8426	2.22428
$372$	0	0
$373$	−8.36016	−0.432873	−0.216436	−	0.976297i	$-0.569443\pi$
$373$	−8.36016	−0.432873	−0.216436	+	0.976297i	$0.569443\pi$
$374$	71.5212	3.69827
$375$	0	0
$376$	37.8624	1.95260
$377$	−25.3078	−1.30342
$378$	0	0
$379$	−23.2433	−1.19393	−0.596964	−	0.802268i	$-0.703627\pi$
$379$	−23.2433	−1.19393	−0.596964	+	0.802268i	$0.703627\pi$
$380$	−31.8066	−1.63164
$381$	0	0
$382$	−2.44993	−0.125349
$383$	−19.9556	−1.01968	−0.509842	−	0.860268i	$-0.670296\pi$
$383$	−19.9556	−1.01968	−0.509842	+	0.860268i	$0.670296\pi$
$384$	0	0
$385$	−16.9534	−0.864023
$386$	21.2799	1.08312
$387$	0	0
$388$	−18.8145	−0.955160
$389$	16.8853	0.856121	0.428061	−	0.903750i	$-0.359197\pi$
$389$	16.8853	0.856121	0.428061	+	0.903750i	$0.359197\pi$
$390$	0	0
$391$	6.39171	0.323243
$392$	41.4803	2.09507
$393$	0	0
$394$	6.10581	0.307606
$395$	−15.7852	−0.794240
$396$	0	0
$397$	15.7859	0.792271	0.396135	−	0.918192i	$-0.370351\pi$
$397$	15.7859	0.792271	0.396135	+	0.918192i	$0.370351\pi$
$398$	−59.8972	−3.00237
$399$	0	0
$400$	5.59148	0.279574
$401$	22.4976	1.12348	0.561738	−	0.827315i	$-0.310133\pi$
$401$	22.4976	1.12348	0.561738	+	0.827315i	$0.310133\pi$
$402$	0	0
$403$	−6.44446	−0.321021
$404$	−1.04472	−0.0519768
$405$	0	0
$406$	−46.6822	−2.31680
$407$	−29.3053	−1.45261
$408$	0	0
$409$	4.05591	0.200552	0.100276	−	0.994960i	$-0.468027\pi$
$409$	4.05591	0.200552	0.100276	+	0.994960i	$0.468027\pi$
$410$	22.9935	1.13557
$411$	0	0
$412$	26.0240	1.28211
$413$	−13.8438	−0.681207
$414$	0	0
$415$	3.06575	0.150492
$416$	13.9085	0.681921
$417$	0	0
$418$	83.6547	4.09169
$419$	−5.01585	−0.245040	−0.122520	−	0.992466i	$-0.539098\pi$
$419$	−5.01585	−0.245040	−0.122520	+	0.992466i	$0.539098\pi$
$420$	0	0
$421$	19.1440	0.933020	0.466510	−	0.884516i	$-0.345511\pi$
$421$	19.1440	0.933020	0.466510	+	0.884516i	$0.345511\pi$
$422$	49.2227	2.39612
$423$	0	0
$424$	63.7498	3.09597
$425$	−6.39171	−0.310043
$426$	0	0
$427$	−34.0380	−1.64721
$428$	−35.5601	−1.71886
$429$	0	0
$430$	−7.93254	−0.382541
$431$	−40.0606	−1.92965	−0.964825	−	0.262894i	$-0.915323\pi$
$431$	−40.0606	−1.92965	−0.964825	+	0.262894i	$0.915323\pi$
$432$	0	0
$433$	−4.22696	−0.203135	−0.101567	−	0.994829i	$-0.532386\pi$
$433$	−4.22696	−0.203135	−0.101567	+	0.994829i	$0.532386\pi$
$434$	−11.8873	−0.570608
$435$	0	0
$436$	67.0632	3.21174
$437$	7.47606	0.357628
$438$	0	0
$439$	−4.92940	−0.235267	−0.117634	−	0.993057i	$-0.537531\pi$
$439$	−4.92940	−0.235267	−0.117634	+	0.993057i	$0.537531\pi$
$440$	−25.2266	−1.20263
$441$	0	0
$442$	−82.1189	−3.90600
$443$	−22.2712	−1.05814	−0.529069	−	0.848579i	$-0.677459\pi$
$443$	−22.2712	−1.05814	−0.529069	+	0.848579i	$0.677459\pi$
$444$	0	0
$445$	−13.4432	−0.637271
$446$	−60.6254	−2.87070
$447$	0	0
$448$	−16.7177	−0.789838
$449$	−14.9150	−0.703883	−0.351942	−	0.936022i	$-0.614478\pi$
$449$	−14.9150	−0.703883	−0.351942	+	0.936022i	$0.614478\pi$
$450$	0	0
$451$	−41.1370	−1.93707
$452$	−5.83170	−0.274300
$453$	0	0
$454$	17.0463	0.800021
$455$	19.4654	0.912554
$456$	0	0
$457$	26.7834	1.25287	0.626436	−	0.779473i	$-0.284513\pi$
$457$	26.7834	1.25287	0.626436	+	0.779473i	$0.284513\pi$
$458$	−67.2446	−3.14213
$459$	0	0
$460$	−4.25445	−0.198365
$461$	−15.4877	−0.721334	−0.360667	−	0.932695i	$-0.617451\pi$
$461$	−15.4877	−0.721334	−0.360667	+	0.932695i	$0.617451\pi$
$462$	0	0
$463$	−0.968557	−0.0450127	−0.0225063	−	0.999747i	$-0.507165\pi$
$463$	−0.968557	−0.0450127	−0.0225063	+	0.999747i	$0.507165\pi$
$464$	−27.5455	−1.27877
$465$	0	0
$466$	6.67225	0.309086
$467$	17.0051	0.786901	0.393450	−	0.919346i	$-0.371281\pi$
$467$	17.0051	0.786901	0.393450	+	0.919346i	$0.371281\pi$
$468$	0	0
$469$	57.3274	2.64713
$470$	16.7945	0.774672
$471$	0	0
$472$	−20.5995	−0.948170
$473$	14.1919	0.652544
$474$	0	0
$475$	−7.47606	−0.343025
$476$	−103.037	−4.72270
$477$	0	0
$478$	36.9126	1.68834
$479$	−10.9306	−0.499434	−0.249717	−	0.968319i	$-0.580338\pi$
$479$	−10.9306	−0.499434	−0.249717	+	0.968319i	$0.580338\pi$
$480$	0	0
$481$	33.6476	1.53420
$482$	−8.82636	−0.402030
$483$	0	0
$484$	38.3716	1.74416
$485$	−4.42230	−0.200806
$486$	0	0
$487$	−20.3593	−0.922566	−0.461283	−	0.887253i	$-0.652611\pi$
$487$	−20.3593	−0.922566	−0.461283	+	0.887253i	$0.652611\pi$
$488$	−50.6485	−2.29275
$489$	0	0
$490$	18.3992	0.831193
$491$	17.9621	0.810620	0.405310	−	0.914179i	$-0.367164\pi$
$491$	17.9621	0.810620	0.405310	+	0.914179i	$0.367164\pi$
$492$	0	0
$493$	31.4877	1.41813
$494$	−96.0503	−4.32151
$495$	0	0
$496$	−7.01426	−0.314949
$497$	−31.5795	−1.41654
$498$	0	0
$499$	−22.6160	−1.01243	−0.506215	−	0.862407i	$-0.668956\pi$
$499$	−22.6160	−1.01243	−0.506215	+	0.862407i	$0.668956\pi$
$500$	4.25445	0.190265
$501$	0	0
$502$	6.10128	0.272314
$503$	21.4461	0.956233	0.478117	−	0.878296i	$-0.341320\pi$
$503$	21.4461	0.956233	0.478117	+	0.878296i	$0.341320\pi$
$504$	0	0
$505$	−0.245559	−0.0109272
$506$	11.1897	0.497442
$507$	0	0
$508$	24.6634	1.09426
$509$	−28.6063	−1.26795	−0.633975	−	0.773354i	$-0.718578\pi$
$509$	−28.6063	−1.26795	−0.633975	+	0.773354i	$0.718578\pi$
$510$	0	0
$511$	−4.30914	−0.190625
$512$	−47.9129	−2.11747
$513$	0	0
$514$	−59.0123	−2.60292
$515$	6.11688	0.269542
$516$	0	0
$517$	−30.0466	−1.32145
$518$	62.0656	2.72701
$519$	0	0
$520$	28.9646	1.27018
$521$	−8.92105	−0.390838	−0.195419	−	0.980720i	$-0.562607\pi$
$521$	−8.92105	−0.390838	−0.195419	+	0.980720i	$0.562607\pi$
$522$	0	0
$523$	−26.1946	−1.14541	−0.572705	−	0.819762i	$-0.694106\pi$
$523$	−26.1946	−1.14541	−0.572705	+	0.819762i	$0.694106\pi$
$524$	33.4618	1.46179
$525$	0	0
$526$	46.8475	2.04265
$527$	8.01811	0.349274
$528$	0	0
$529$	1.00000	0.0434783
$530$	28.2773	1.22829
$531$	0	0
$532$	−120.517	−5.22509
$533$	47.2325	2.04587
$534$	0	0
$535$	−8.35832	−0.361362
$536$	85.3032	3.68454
$537$	0	0
$538$	12.6976	0.547433
$539$	−32.9176	−1.41786
$540$	0	0
$541$	14.7624	0.634686	0.317343	−	0.948311i	$-0.397209\pi$
$541$	14.7624	0.634686	0.317343	+	0.948311i	$0.397209\pi$
$542$	−40.7492	−1.75033
$543$	0	0
$544$	−17.3048	−0.741937
$545$	15.7630	0.675215
$546$	0	0
$547$	−3.16331	−0.135253	−0.0676267	−	0.997711i	$-0.521543\pi$
$547$	−3.16331	−0.135253	−0.0676267	+	0.997711i	$0.521543\pi$
$548$	20.3222	0.868123
$549$	0	0
$550$	−11.1897	−0.477130
$551$	36.8295	1.56899
$552$	0	0
$553$	−59.8113	−2.54343
$554$	46.8839	1.99191
$555$	0	0
$556$	15.6693	0.664526
$557$	−9.13882	−0.387224	−0.193612	−	0.981078i	$-0.562020\pi$
$557$	−9.13882	−0.387224	−0.193612	+	0.981078i	$0.562020\pi$
$558$	0	0
$559$	−16.2948	−0.689196
$560$	21.1865	0.895294
$561$	0	0
$562$	60.4830	2.55132
$563$	4.59832	0.193796	0.0968981	−	0.995294i	$-0.469108\pi$
$563$	4.59832	0.193796	0.0968981	+	0.995294i	$0.469108\pi$
$564$	0	0
$565$	−1.37073	−0.0576670
$566$	22.5295	0.946984
$567$	0	0
$568$	−46.9904	−1.97167
$569$	34.5704	1.44927	0.724633	−	0.689135i	$-0.242009\pi$
$569$	34.5704	1.44927	0.724633	+	0.689135i	$0.242009\pi$
$570$	0	0
$571$	30.5865	1.28001	0.640003	−	0.768372i	$-0.278933\pi$
$571$	30.5865	1.28001	0.640003	+	0.768372i	$0.278933\pi$
$572$	−97.7908	−4.08884
$573$	0	0
$574$	87.1240	3.63648
$575$	−1.00000	−0.0417029
$576$	0	0
$577$	2.15835	0.0898535	0.0449267	−	0.998990i	$-0.485695\pi$
$577$	2.15835	0.0898535	0.0449267	+	0.998990i	$0.485695\pi$
$578$	59.6561	2.48137
$579$	0	0
$580$	−20.9588	−0.870269
$581$	11.6164	0.481928
$582$	0	0
$583$	−50.5901	−2.09523
$584$	−6.41201	−0.265331
$585$	0	0
$586$	−58.1317	−2.40140
$587$	47.8776	1.97612	0.988060	−	0.154073i	$-0.0492390\pi$
$587$	47.8776	1.97612	0.988060	+	0.154073i	$0.0492390\pi$
$588$	0	0
$589$	9.37838	0.386429
$590$	−9.13725	−0.376175
$591$	0	0
$592$	36.6227	1.50518
$593$	−33.9403	−1.39376	−0.696880	−	0.717188i	$-0.745429\pi$
$593$	−33.9403	−1.39376	−0.696880	+	0.717188i	$0.745429\pi$
$594$	0	0
$595$	−24.2187	−0.992868
$596$	−5.62246	−0.230305
$597$	0	0
$598$	−12.8477	−0.525382
$599$	5.90588	0.241308	0.120654	−	0.992695i	$-0.461501\pi$
$599$	5.90588	0.241308	0.120654	+	0.992695i	$0.461501\pi$
$600$	0	0
$601$	16.3457	0.666755	0.333377	−	0.942794i	$-0.391812\pi$
$601$	16.3457	0.666755	0.333377	+	0.942794i	$0.391812\pi$
$602$	−30.0570	−1.22503
$603$	0	0
$604$	28.4759	1.15867
$605$	9.01916	0.366681
$606$	0	0
$607$	−41.1764	−1.67130	−0.835649	−	0.549263i	$-0.814908\pi$
$607$	−41.1764	−1.67130	−0.835649	+	0.549263i	$0.814908\pi$
$608$	−20.2406	−0.820863
$609$	0	0
$610$	−22.4660	−0.909621
$611$	34.4987	1.39567
$612$	0	0
$613$	38.8687	1.56989	0.784946	−	0.619564i	$-0.212690\pi$
$613$	38.8687	1.56989	0.784946	+	0.619564i	$0.212690\pi$
$614$	18.8115	0.759170
$615$	0	0
$616$	−95.5855	−3.85125
$617$	−15.8847	−0.639492	−0.319746	−	0.947503i	$-0.603598\pi$
$617$	−15.8847	−0.639492	−0.319746	+	0.947503i	$0.603598\pi$
$618$	0	0
$619$	−7.65739	−0.307777	−0.153888	−	0.988088i	$-0.549180\pi$
$619$	−7.65739	−0.307777	−0.153888	+	0.988088i	$0.549180\pi$
$620$	−5.33702	−0.214340
$621$	0	0
$622$	9.58605	0.384366
$623$	−50.9374	−2.04076
$624$	0	0
$625$	1.00000	0.0400000
$626$	−30.1662	−1.20568
$627$	0	0
$628$	10.7057	0.427203
$629$	−41.8640	−1.66923
$630$	0	0
$631$	10.9168	0.434591	0.217295	−	0.976106i	$-0.430276\pi$
$631$	10.9168	0.434591	0.217295	+	0.976106i	$0.430276\pi$
$632$	−88.9993	−3.54020
$633$	0	0
$634$	−15.4553	−0.613809
$635$	5.79707	0.230050
$636$	0	0
$637$	37.7952	1.49750
$638$	55.1240	2.18238
$639$	0	0
$640$	−16.4489	−0.650200
$641$	44.1838	1.74516	0.872578	−	0.488476i	$-0.162447\pi$
$641$	44.1838	1.74516	0.872578	+	0.488476i	$0.162447\pi$
$642$	0	0
$643$	−44.8947	−1.77047	−0.885237	−	0.465141i	$-0.846004\pi$
$643$	−44.8947	−1.77047	−0.885237	+	0.465141i	$0.846004\pi$
$644$	−16.1204	−0.635234
$645$	0	0
$646$	119.505	4.70184
$647$	3.31839	0.130459	0.0652296	−	0.997870i	$-0.479222\pi$
$647$	3.31839	0.130459	0.0652296	+	0.997870i	$0.479222\pi$
$648$	0	0
$649$	16.3472	0.641685
$650$	12.8477	0.503929
$651$	0	0
$652$	−16.0206	−0.627414
$653$	36.6445	1.43401	0.717006	−	0.697067i	$-0.245512\pi$
$653$	36.6445	1.43401	0.717006	+	0.697067i	$0.245512\pi$
$654$	0	0
$655$	7.86513	0.307316
$656$	51.4087	2.00717
$657$	0	0
$658$	63.6355	2.48077
$659$	−34.4549	−1.34217	−0.671086	−	0.741380i	$-0.734172\pi$
$659$	−34.4549	−1.34217	−0.671086	+	0.741380i	$0.734172\pi$
$660$	0	0
$661$	0.403420	0.0156912	0.00784560	−	0.999969i	$-0.497503\pi$
$661$	0.403420	0.0156912	0.00784560	+	0.999969i	$0.497503\pi$
$662$	−7.45091	−0.289588
$663$	0	0
$664$	17.2852	0.670795
$665$	−28.3273	−1.09849
$666$	0	0
$667$	4.92633	0.190748
$668$	−12.8971	−0.499005
$669$	0	0
$670$	37.8376	1.46180
$671$	40.1933	1.55164
$672$	0	0
$673$	−40.6260	−1.56602	−0.783009	−	0.622010i	$-0.786316\pi$
$673$	−40.6260	−1.56602	−0.783009	+	0.622010i	$0.786316\pi$
$674$	−17.0977	−0.658579
$675$	0	0
$676$	56.9731	2.19127
$677$	−22.0206	−0.846321	−0.423160	−	0.906055i	$-0.639079\pi$
$677$	−22.0206	−0.846321	−0.423160	+	0.906055i	$0.639079\pi$
$678$	0	0
$679$	−16.7564	−0.643052
$680$	−36.0374	−1.38197
$681$	0	0
$682$	14.0369	0.537503
$683$	−3.36375	−0.128710	−0.0643551	−	0.997927i	$-0.520499\pi$
$683$	−3.36375	−0.128710	−0.0643551	+	0.997927i	$0.520499\pi$
$684$	0	0
$685$	4.77670	0.182508
$686$	3.38369	0.129190
$687$	0	0
$688$	−17.7355	−0.676161
$689$	58.0863	2.21291
$690$	0	0
$691$	−13.5824	−0.516698	−0.258349	−	0.966052i	$-0.583178\pi$
$691$	−13.5824	−0.516698	−0.258349	+	0.966052i	$0.583178\pi$
$692$	33.7487	1.28293
$693$	0	0
$694$	36.6982	1.39304
$695$	3.68303	0.139705
$696$	0	0
$697$	−58.7661	−2.22593
$698$	54.6241	2.06755
$699$	0	0
$700$	16.1204	0.609295
$701$	50.8750	1.92152	0.960762	−	0.277374i	$-0.0894641\pi$
$701$	50.8750	1.92152	0.960762	+	0.277374i	$0.0894641\pi$
$702$	0	0
$703$	−48.9662	−1.84679
$704$	19.7409	0.744013
$705$	0	0
$706$	58.8035	2.21310
$707$	−0.930442	−0.0349929
$708$	0	0
$709$	−41.0413	−1.54134	−0.770668	−	0.637237i	$-0.780077\pi$
$709$	−41.0413	−1.54134	−0.770668	+	0.637237i	$0.780077\pi$
$710$	−20.8433	−0.782237
$711$	0	0
$712$	−75.7949	−2.84054
$713$	1.25445	0.0469797
$714$	0	0
$715$	−22.9855	−0.859609
$716$	10.7478	0.401666
$717$	0	0
$718$	10.3017	0.384454
$719$	−19.6091	−0.731298	−0.365649	−	0.930753i	$-0.619153\pi$
$719$	−19.6091	−0.731298	−0.365649	+	0.930753i	$0.619153\pi$
$720$	0	0
$721$	23.1773	0.863168
$722$	92.2615	3.43362
$723$	0	0
$724$	52.0659	1.93501
$725$	−4.92633	−0.182959
$726$	0	0
$727$	−32.5903	−1.20871	−0.604354	−	0.796716i	$-0.706569\pi$
$727$	−32.5903	−1.20871	−0.604354	+	0.796716i	$0.706569\pi$
$728$	109.749	4.06757
$729$	0	0
$730$	−2.84415	−0.105267
$731$	20.2738	0.749853
$732$	0	0
$733$	46.0357	1.70037	0.850183	−	0.526487i	$-0.176491\pi$
$733$	46.0357	1.70037	0.850183	+	0.526487i	$0.176491\pi$
$734$	54.2471	2.00230
$735$	0	0
$736$	−2.70738	−0.0997954
$737$	−67.6943	−2.49355
$738$	0	0
$739$	−3.11486	−0.114582	−0.0572909	−	0.998358i	$-0.518246\pi$
$739$	−3.11486	−0.114582	−0.0572909	+	0.998358i	$0.518246\pi$
$740$	27.8655	1.02436
$741$	0	0
$742$	107.145	3.93340
$743$	−16.1123	−0.591103	−0.295551	−	0.955327i	$-0.595503\pi$
$743$	−16.1123	−0.591103	−0.295551	+	0.955327i	$0.595503\pi$
$744$	0	0
$745$	−1.32155	−0.0484177
$746$	−20.9078	−0.765491
$747$	0	0
$748$	121.670	4.44870
$749$	−31.6703	−1.15721
$750$	0	0
$751$	8.96619	0.327181	0.163590	−	0.986528i	$-0.447692\pi$
$751$	8.96619	0.327181	0.163590	+	0.986528i	$0.447692\pi$
$752$	37.5490	1.36927
$753$	0	0
$754$	−63.2921	−2.30496
$755$	6.69320	0.243591
$756$	0	0
$757$	6.54466	0.237870	0.118935	−	0.992902i	$-0.462052\pi$
$757$	6.54466	0.237870	0.118935	+	0.992902i	$0.462052\pi$
$758$	−58.1290	−2.11134
$759$	0	0
$760$	−42.1511	−1.52898
$761$	17.7896	0.644873	0.322437	−	0.946591i	$-0.395498\pi$
$761$	17.7896	0.644873	0.322437	+	0.946591i	$0.395498\pi$
$762$	0	0
$763$	59.7273	2.16227
$764$	−4.16777	−0.150784
$765$	0	0
$766$	−49.9068	−1.80321
$767$	−18.7695	−0.677726
$768$	0	0
$769$	−4.86138	−0.175306	−0.0876529	−	0.996151i	$-0.527937\pi$
$769$	−4.86138	−0.175306	−0.0876529	+	0.996151i	$0.527937\pi$
$770$	−42.3985	−1.52794
$771$	0	0
$772$	36.2008	1.30289
$773$	−32.8988	−1.18329	−0.591644	−	0.806200i	$-0.701521\pi$
$773$	−32.8988	−1.18329	−0.591644	+	0.806200i	$0.701521\pi$
$774$	0	0
$775$	−1.25445	−0.0450614
$776$	−24.9336	−0.895063
$777$	0	0
$778$	42.2284	1.51396
$779$	−68.7357	−2.46271
$780$	0	0
$781$	37.2903	1.33435
$782$	15.9850	0.571621
$783$	0	0
$784$	41.1369	1.46918
$785$	2.51635	0.0898122
$786$	0	0
$787$	50.1718	1.78843	0.894215	−	0.447638i	$-0.147735\pi$
$787$	50.1718	1.78843	0.894215	+	0.447638i	$0.147735\pi$
$788$	10.3871	0.370024
$789$	0	0
$790$	−39.4771	−1.40453
$791$	−5.19379	−0.184670
$792$	0	0
$793$	−46.1489	−1.63880
$794$	39.4788	1.40105
$795$	0	0
$796$	−101.896	−3.61159
$797$	29.1815	1.03366	0.516831	−	0.856087i	$-0.327111\pi$
$797$	29.1815	1.03366	0.516831	+	0.856087i	$0.327111\pi$
$798$	0	0
$799$	−42.9229	−1.51850
$800$	2.70738	0.0957204
$801$	0	0
$802$	56.2640	1.98675
$803$	5.08839	0.179566
$804$	0	0
$805$	−3.78907	−0.133547
$806$	−16.1169	−0.567693
$807$	0	0
$808$	−1.38450	−0.0487065
$809$	36.7855	1.29331	0.646655	−	0.762783i	$-0.276167\pi$
$809$	36.7855	1.29331	0.646655	+	0.762783i	$0.276167\pi$
$810$	0	0
$811$	−8.38974	−0.294604	−0.147302	−	0.989092i	$-0.547059\pi$
$811$	−8.38974	−0.294604	−0.147302	+	0.989092i	$0.547059\pi$
$812$	−79.4146	−2.78691
$813$	0	0
$814$	−73.2894	−2.56879
$815$	−3.76560	−0.131903
$816$	0	0
$817$	23.7132	0.829621
$818$	10.1434	0.354655
$819$	0	0
$820$	39.1159	1.36599
$821$	8.65877	0.302193	0.151097	−	0.988519i	$-0.451720\pi$
$821$	8.65877	0.302193	0.151097	+	0.988519i	$0.451720\pi$
$822$	0	0
$823$	37.0466	1.29136	0.645682	−	0.763606i	$-0.276573\pi$
$823$	37.0466	1.29136	0.645682	+	0.763606i	$0.276573\pi$
$824$	34.4879	1.20144
$825$	0	0
$826$	−34.6217	−1.20464
$827$	−44.9678	−1.56368	−0.781842	−	0.623477i	$-0.785719\pi$
$827$	−44.9678	−1.56368	−0.781842	+	0.623477i	$0.785719\pi$
$828$	0	0
$829$	−35.6089	−1.23675	−0.618374	−	0.785884i	$-0.712208\pi$
$829$	−35.6089	−1.23675	−0.618374	+	0.785884i	$0.712208\pi$
$830$	7.66712	0.266130
$831$	0	0
$832$	−22.6660	−0.785803
$833$	−47.0243	−1.62930
$834$	0	0
$835$	−3.03144	−0.104907
$836$	142.311	4.92194
$837$	0	0
$838$	−12.5441	−0.433328
$839$	−10.7850	−0.372338	−0.186169	−	0.982518i	$-0.559607\pi$
$839$	−10.7850	−0.372338	−0.186169	+	0.982518i	$0.559607\pi$
$840$	0	0
$841$	−4.73129	−0.163148
$842$	47.8770	1.64995
$843$	0	0
$844$	83.7365	2.88233
$845$	13.3914	0.460678
$846$	0	0
$847$	34.1742	1.17424
$848$	63.2222	2.17106
$849$	0	0
$850$	−15.9850	−0.548280
$851$	−6.54973	−0.224522
$852$	0	0
$853$	46.1337	1.57959	0.789793	−	0.613373i	$-0.210188\pi$
$853$	46.1337	1.57959	0.789793	+	0.613373i	$0.210188\pi$
$854$	−85.1252	−2.91292
$855$	0	0
$856$	−47.1255	−1.61071
$857$	54.6211	1.86582	0.932910	−	0.360108i	$-0.117260\pi$
$857$	54.6211	1.86582	0.932910	+	0.360108i	$0.117260\pi$
$858$	0	0
$859$	−1.06927	−0.0364832	−0.0182416	−	0.999834i	$-0.505807\pi$
$859$	−1.06927	−0.0364832	−0.0182416	+	0.999834i	$0.505807\pi$
$860$	−13.4947	−0.460164
$861$	0	0
$862$	−100.187	−3.41239
$863$	30.6296	1.04264	0.521322	−	0.853360i	$-0.325439\pi$
$863$	30.6296	1.04264	0.521322	+	0.853360i	$0.325439\pi$
$864$	0	0
$865$	7.93254	0.269715
$866$	−10.5712	−0.359223
$867$	0	0
$868$	−20.2224	−0.686392
$869$	70.6274	2.39587
$870$	0	0
$871$	77.7249	2.63361
$872$	88.8743	3.00966
$873$	0	0
$874$	18.6968	0.632429
$875$	3.78907	0.128094
$876$	0	0
$877$	45.0882	1.52252	0.761259	−	0.648447i	$-0.224581\pi$
$877$	45.0882	1.52252	0.761259	+	0.648447i	$0.224581\pi$
$878$	−12.3279	−0.416046
$879$	0	0
$880$	−25.0178	−0.843351
$881$	−51.9802	−1.75126	−0.875629	−	0.482985i	$-0.839552\pi$
$881$	−51.9802	−1.75126	−0.875629	+	0.482985i	$0.839552\pi$
$882$	0	0
$883$	13.0431	0.438935	0.219468	−	0.975620i	$-0.429568\pi$
$883$	13.0431	0.438935	0.219468	+	0.975620i	$0.429568\pi$
$884$	−139.699	−4.69857
$885$	0	0
$886$	−55.6979	−1.87121
$887$	−2.32847	−0.0781825	−0.0390913	−	0.999236i	$-0.512446\pi$
$887$	−2.32847	−0.0781825	−0.0390913	+	0.999236i	$0.512446\pi$
$888$	0	0
$889$	21.9655	0.736700
$890$	−33.6201	−1.12695
$891$	0	0
$892$	−103.134	−3.45320
$893$	−50.2047	−1.68004
$894$	0	0
$895$	2.52626	0.0844435
$896$	−62.3261	−2.08217
$897$	0	0
$898$	−37.3008	−1.24475
$899$	6.17986	0.206110
$900$	0	0
$901$	−72.2703	−2.40767
$902$	−102.879	−3.42550
$903$	0	0
$904$	−7.72837	−0.257042
$905$	12.2380	0.406804
$906$	0	0
$907$	14.7671	0.490334	0.245167	−	0.969481i	$-0.421157\pi$
$907$	14.7671	0.490334	0.245167	+	0.969481i	$0.421157\pi$
$908$	28.9987	0.962356
$909$	0	0
$910$	48.6809	1.61376
$911$	−14.1681	−0.469409	−0.234704	−	0.972067i	$-0.575412\pi$
$911$	−14.1681	−0.469409	−0.234704	+	0.972067i	$0.575412\pi$
$912$	0	0
$913$	−13.7170	−0.453968
$914$	66.9822	2.21558
$915$	0	0
$916$	−114.395	−3.77971
$917$	29.8016	0.984134
$918$	0	0
$919$	38.9568	1.28507	0.642534	−	0.766257i	$-0.277883\pi$
$919$	38.9568	1.28507	0.642534	+	0.766257i	$0.277883\pi$
$920$	−5.63815	−0.185884
$921$	0	0
$922$	−38.7330	−1.27560
$923$	−42.8158	−1.40930
$924$	0	0
$925$	6.54973	0.215354
$926$	−2.42226	−0.0796003
$927$	0	0
$928$	−13.3375	−0.437823
$929$	−36.8330	−1.20845	−0.604226	−	0.796813i	$-0.706518\pi$
$929$	−36.8330	−1.20845	−0.604226	+	0.796813i	$0.706518\pi$
$930$	0	0
$931$	−55.0019	−1.80262
$932$	11.3507	0.371804
$933$	0	0
$934$	42.5278	1.39155
$935$	28.5983	0.935264
$936$	0	0
$937$	10.0785	0.329251	0.164625	−	0.986356i	$-0.447358\pi$
$937$	10.0785	0.329251	0.164625	+	0.986356i	$0.447358\pi$
$938$	143.370	4.68118
$939$	0	0
$940$	28.5704	0.931863
$941$	−24.0027	−0.782466	−0.391233	−	0.920292i	$-0.627951\pi$
$941$	−24.0027	−0.782466	−0.391233	+	0.920292i	$0.627951\pi$
$942$	0	0
$943$	−9.19411	−0.299402
$944$	−20.4290	−0.664908
$945$	0	0
$946$	35.4924	1.15396
$947$	−12.2539	−0.398198	−0.199099	−	0.979979i	$-0.563802\pi$
$947$	−12.2539	−0.398198	−0.199099	+	0.979979i	$0.563802\pi$
$948$	0	0
$949$	−5.84237	−0.189651
$950$	−18.6968	−0.606605
$951$	0	0
$952$	−136.548	−4.42556
$953$	−10.6705	−0.345651	−0.172825	−	0.984952i	$-0.555290\pi$
$953$	−10.6705	−0.345651	−0.172825	+	0.984952i	$0.555290\pi$
$954$	0	0
$955$	−0.979624	−0.0316999
$956$	62.7948	2.03093
$957$	0	0
$958$	−27.3363	−0.883197
$959$	18.0992	0.584455
$960$	0	0
$961$	−29.4263	−0.949237
$962$	84.1491	2.71307
$963$	0	0
$964$	−15.0152	−0.483607
$965$	8.50891	0.273912
$966$	0	0
$967$	6.51308	0.209446	0.104723	−	0.994501i	$-0.466604\pi$
$967$	6.51308	0.209446	0.104723	+	0.994501i	$0.466604\pi$
$968$	50.8513	1.63442
$969$	0	0
$970$	−11.0597	−0.355105
$971$	33.4976	1.07499	0.537494	−	0.843267i	$-0.319371\pi$
$971$	33.4976	1.07499	0.537494	+	0.843267i	$0.319371\pi$
$972$	0	0
$973$	13.9553	0.447386
$974$	−50.9163	−1.63146
$975$	0	0
$976$	−50.2293	−1.60780
$977$	8.72554	0.279155	0.139577	−	0.990211i	$-0.455426\pi$
$977$	8.72554	0.279155	0.139577	+	0.990211i	$0.455426\pi$
$978$	0	0
$979$	60.1488	1.92236
$980$	31.3004	0.999853
$981$	0	0
$982$	44.9213	1.43350
$983$	27.7131	0.883912	0.441956	−	0.897037i	$-0.354285\pi$
$983$	27.7131	0.883912	0.441956	+	0.897037i	$0.354285\pi$
$984$	0	0
$985$	2.44145	0.0777912
$986$	78.7472	2.50782
$987$	0	0
$988$	−163.398	−5.19840
$989$	3.17189	0.100860
$990$	0	0
$991$	−49.1015	−1.55976	−0.779880	−	0.625928i	$-0.784720\pi$
$991$	−49.1015	−1.55976	−0.779880	+	0.625928i	$0.784720\pi$
$992$	−3.39629	−0.107832
$993$	0	0
$994$	−78.9770	−2.50500
$995$	−23.9503	−0.759277
$996$	0	0
$997$	−43.0382	−1.36303	−0.681517	−	0.731802i	$-0.738679\pi$
$997$	−43.0382	−1.36303	−0.681517	+	0.731802i	$0.738679\pi$
$998$	−56.5601	−1.79038
$999$	0	0

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1035.2.a.q.1.6	yes	6
3.2	odd	2		1035.2.a.p.1.1	✓	6
5.4	even	2		5175.2.a.by.1.1		6
15.14	odd	2		5175.2.a.bz.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1035.2.a.p.1.1	✓	6	3.2	odd	2
1035.2.a.q.1.6	yes	6	1.1	even	1	trivial
5175.2.a.by.1.1		6	5.4	even	2
5175.2.a.bz.1.6		6	15.14	odd	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 $\F_{q}$
Belyi maps

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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.1.6

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