LMFDB - Embedded newform 1035.2.a.p.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			$0.139251$ 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)

$f(q)$	$=$	$q+2.70812 q^{2} +5.33392 q^{4} -1.00000 q^{5} +1.21406 q^{7} +9.02867 q^{8} -2.70812 q^{10} +2.12841 q^{11} -4.32055 q^{13} +3.28783 q^{14} +13.7829 q^{16} -1.98662 q^{17} +5.28783 q^{19} -5.33392 q^{20} +5.76401 q^{22} +1.00000 q^{23} +1.00000 q^{25} -11.7006 q^{26} +6.47571 q^{28} -7.10648 q^{29} -2.33392 q^{31} +19.2684 q^{32} -5.38002 q^{34} -1.21406 q^{35} +5.81865 q^{37} +14.3201 q^{38} -9.02867 q^{40} -11.5822 q^{41} +1.78112 q^{43} +11.3528 q^{44} +2.70812 q^{46} +7.89242 q^{47} -5.52605 q^{49} +2.70812 q^{50} -23.0455 q^{52} -4.89046 q^{53} -2.12841 q^{55} +10.9614 q^{56} -19.2452 q^{58} +0.118364 q^{59} -8.79626 q^{61} -6.32055 q^{62} +24.6154 q^{64} +4.32055 q^{65} -1.16946 q^{67} -10.5965 q^{68} -3.28783 q^{70} -14.3135 q^{71} +8.32055 q^{73} +15.7576 q^{74} +28.2049 q^{76} +2.58403 q^{77} +11.3895 q^{79} -13.7829 q^{80} -31.3660 q^{82} -8.91130 q^{83} +1.98662 q^{85} +4.82348 q^{86} +19.2167 q^{88} +2.07508 q^{89} -5.24541 q^{91} +5.33392 q^{92} +21.3736 q^{94} -5.28783 q^{95} -18.9612 q^{97} -14.9652 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q + 10 q^{4} - 6 q^{5} + 6 q^{7} + 4 q^{11} + 12 q^{13} - 4 q^{14} + 14 q^{16} + 4 q^{17} + 8 q^{19} - 10 q^{20} + 8 q^{22} + 6 q^{23} + 6 q^{25} - 12 q^{26} + 24 q^{28} - 6 q^{29} + 8 q^{31} + 20 q^{32}+ \cdots - 4 q^{98}+O(q^{100})$ 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

)

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

$2$	2.70812	1.91493	0.957466	−	0.288548i	$-0.0931724\pi$
$2$	2.70812	1.91493	0.957466	+	0.288548i	$0.0931724\pi$
$3$	0	0
$3$	0	0
$4$	5.33392	2.66696
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	1.21406	0.458872	0.229436	−	0.973324i	$-0.426312\pi$
$7$	1.21406	0.458872	0.229436	+	0.973324i	$0.426312\pi$
$8$	9.02867	3.19212
$9$	0	0
$10$	−2.70812	−0.856383
$11$	2.12841	0.641741	0.320871	−	0.947123i	$-0.396025\pi$
$11$	2.12841	0.641741	0.320871	+	0.947123i	$0.396025\pi$
$12$	0	0
$13$	−4.32055	−1.19830	−0.599152	−	0.800635i	$-0.704495\pi$
$13$	−4.32055	−1.19830	−0.599152	+	0.800635i	$0.704495\pi$
$14$	3.28783	0.878709
$15$	0	0
$16$	13.7829	3.44572
$17$	−1.98662	−0.481827	−0.240913	−	0.970547i	$-0.577447\pi$
$17$	−1.98662	−0.481827	−0.240913	+	0.970547i	$0.577447\pi$
$18$	0	0
$19$	5.28783	1.21311	0.606556	−	0.795041i	$-0.292551\pi$
$19$	5.28783	1.21311	0.606556	+	0.795041i	$0.292551\pi$
$20$	−5.33392	−1.19270
$21$	0	0
$22$	5.76401	1.22889
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	1.00000	0.200000
$26$	−11.7006	−2.29467
$27$	0	0
$28$	6.47571	1.22379
$29$	−7.10648	−1.31964	−0.659820	−	0.751423i	$-0.729368\pi$
$29$	−7.10648	−1.31964	−0.659820	+	0.751423i	$0.729368\pi$
$30$	0	0
$31$	−2.33392	−0.419185	−0.209592	−	0.977789i	$-0.567214\pi$
$31$	−2.33392	−0.419185	−0.209592	+	0.977789i	$0.567214\pi$
$32$	19.2684	3.40620
$33$	0	0
$34$	−5.38002	−0.922665
$35$	−1.21406	−0.205214
$36$	0	0
$37$	5.81865	0.956581	0.478290	−	0.878202i	$-0.341257\pi$
$37$	5.81865	0.956581	0.478290	+	0.878202i	$0.341257\pi$
$38$	14.3201	2.32302
$39$	0	0
$40$	−9.02867	−1.42756
$41$	−11.5822	−1.80884	−0.904418	−	0.426648i	$-0.859694\pi$
$41$	−11.5822	−1.80884	−0.904418	+	0.426648i	$0.859694\pi$
$42$	0	0
$43$	1.78112	0.271618	0.135809	−	0.990735i	$-0.456637\pi$
$43$	1.78112	0.271618	0.135809	+	0.990735i	$0.456637\pi$
$44$	11.3528	1.71150
$45$	0	0
$46$	2.70812	0.399291
$47$	7.89242	1.15123	0.575614	−	0.817722i	$-0.304763\pi$
$47$	7.89242	1.15123	0.575614	+	0.817722i	$0.304763\pi$
$48$	0	0
$49$	−5.52605	−0.789436
$50$	2.70812	0.382986
$51$	0	0
$52$	−23.0455	−3.19583
$53$	−4.89046	−0.671757	−0.335878	−	0.941905i	$-0.609033\pi$
$53$	−4.89046	−0.671757	−0.335878	+	0.941905i	$0.609033\pi$
$54$	0	0
$55$	−2.12841	−0.286995
$56$	10.9614	1.46477
$57$	0	0
$58$	−19.2452	−2.52702
$59$	0.118364	0.0154097	0.00770486	−	0.999970i	$-0.497547\pi$
$59$	0.118364	0.0154097	0.00770486	+	0.999970i	$0.497547\pi$
$60$	0	0
$61$	−8.79626	−1.12625	−0.563123	−	0.826373i	$-0.690400\pi$
$61$	−8.79626	−1.12625	−0.563123	+	0.826373i	$0.690400\pi$
$62$	−6.32055	−0.802710
$63$	0	0
$64$	24.6154	3.07692
$65$	4.32055	0.535898
$66$	0	0
$67$	−1.16946	−0.142873	−0.0714364	−	0.997445i	$-0.522758\pi$
$67$	−1.16946	−0.142873	−0.0714364	+	0.997445i	$0.522758\pi$
$68$	−10.5965	−1.28501
$69$	0	0
$70$	−3.28783	−0.392971
$71$	−14.3135	−1.69870	−0.849349	−	0.527831i	$-0.823005\pi$
$71$	−14.3135	−1.69870	−0.849349	+	0.527831i	$0.823005\pi$
$72$	0	0
$73$	8.32055	0.973846	0.486923	−	0.873445i	$-0.338119\pi$
$73$	8.32055	0.973846	0.486923	+	0.873445i	$0.338119\pi$
$74$	15.7576	1.83179
$75$	0	0
$76$	28.2049	3.23532
$77$	2.58403	0.294477
$78$	0	0
$79$	11.3895	1.28142	0.640709	−	0.767784i	$-0.278641\pi$
$79$	11.3895	1.28142	0.640709	+	0.767784i	$0.278641\pi$
$80$	−13.7829	−1.54097
$81$	0	0
$82$	−31.3660	−3.46379
$83$	−8.91130	−0.978142	−0.489071	−	0.872244i	$-0.662664\pi$
$83$	−8.91130	−0.978142	−0.489071	+	0.872244i	$0.662664\pi$
$84$	0	0
$85$	1.98662	0.215480
$86$	4.82348	0.520129
$87$	0	0
$88$	19.2167	2.04851
$89$	2.07508	0.219958	0.109979	−	0.993934i	$-0.464922\pi$
$89$	2.07508	0.219958	0.109979	+	0.993934i	$0.464922\pi$
$90$	0	0
$91$	−5.24541	−0.549868
$92$	5.33392	0.556100
$93$	0	0
$94$	21.3736	2.20452
$95$	−5.28783	−0.542520
$96$	0	0
$97$	−18.9612	−1.92522	−0.962608	−	0.270899i	$-0.912679\pi$
$97$	−18.9612	−1.92522	−0.962608	+	0.270899i	$0.912679\pi$
$98$	−14.9652	−1.51172
$99$	0	0
$100$	5.33392	0.533392
$101$	7.32537	0.728901	0.364451	−	0.931223i	$-0.381257\pi$
$101$	7.32537	0.728901	0.364451	+	0.931223i	$0.381257\pi$
$102$	0	0
$103$	17.3082	1.70543	0.852714	−	0.522378i	$-0.174955\pi$
$103$	17.3082	1.70543	0.852714	+	0.522378i	$0.174955\pi$
$104$	−39.0088	−3.82512
$105$	0	0
$106$	−13.2440	−1.28637
$107$	6.63363	0.641297	0.320649	−	0.947198i	$-0.396099\pi$
$107$	6.63363	0.641297	0.320649	+	0.947198i	$0.396099\pi$
$108$	0	0
$109$	19.6555	1.88266	0.941328	−	0.337494i	$-0.109579\pi$
$109$	19.6555	1.88266	0.941328	+	0.337494i	$0.109579\pi$
$110$	−5.76401	−0.549576
$111$	0	0
$112$	16.7333	1.58115
$113$	1.17497	0.110532	0.0552660	−	0.998472i	$-0.482399\pi$
$113$	1.17497	0.110532	0.0552660	+	0.998472i	$0.482399\pi$
$114$	0	0
$115$	−1.00000	−0.0932505
$116$	−37.9054	−3.51943
$117$	0	0
$118$	0.320545	0.0295086
$119$	−2.41188	−0.221097
$120$	0	0
$121$	−6.46985	−0.588168
$122$	−23.8213	−2.15668
$123$	0	0
$124$	−12.4490	−1.11795
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	1.72778	0.153316	0.0766578	−	0.997057i	$-0.475575\pi$
$127$	1.72778	0.153316	0.0766578	+	0.997057i	$0.475575\pi$
$128$	28.1246	2.48589
$129$	0	0
$130$	11.7006	1.02621
$131$	−19.3715	−1.69249	−0.846246	−	0.532793i	$-0.821143\pi$
$131$	−19.3715	−1.69249	−0.846246	+	0.532793i	$0.821143\pi$
$132$	0	0
$133$	6.41975	0.556663
$134$	−3.16705	−0.273592
$135$	0	0
$136$	−17.9366	−1.53805
$137$	−21.3565	−1.82461	−0.912305	−	0.409510i	$-0.865700\pi$
$137$	−21.3565	−1.82461	−0.912305	+	0.409510i	$0.865700\pi$
$138$	0	0
$139$	−23.4240	−1.98680	−0.993398	−	0.114721i	$-0.963402\pi$
$139$	−23.4240	−1.98680	−0.993398	+	0.114721i	$0.963402\pi$
$140$	−6.47571	−0.547298
$141$	0	0
$142$	−38.7627	−3.25289
$143$	−9.19591	−0.769001
$144$	0	0
$145$	7.10648	0.590161
$146$	22.5330	1.86485
$147$	0	0
$148$	31.0363	2.55116
$149$	−11.5603	−0.947058	−0.473529	−	0.880778i	$-0.657020\pi$
$149$	−11.5603	−0.947058	−0.473529	+	0.880778i	$0.657020\pi$
$150$	0	0
$151$	5.42807	0.441730	0.220865	−	0.975304i	$-0.429112\pi$
$151$	5.42807	0.441730	0.220865	+	0.975304i	$0.429112\pi$
$152$	47.7420	3.87239
$153$	0	0
$154$	6.99786	0.563904
$155$	2.33392	0.187465
$156$	0	0
$157$	8.43891	0.673498	0.336749	−	0.941594i	$-0.390673\pi$
$157$	8.43891	0.673498	0.336749	+	0.941594i	$0.390673\pi$
$158$	30.8441	2.45383
$159$	0	0
$160$	−19.2684	−1.52330
$161$	1.21406	0.0956815
$162$	0	0
$163$	17.3089	1.35574	0.677870	−	0.735182i	$-0.262903\pi$
$163$	17.3089	1.35574	0.677870	+	0.735182i	$0.262903\pi$
$164$	−61.7785	−4.82409
$165$	0	0
$166$	−24.1329	−1.87307
$167$	3.71813	0.287718	0.143859	−	0.989598i	$-0.454049\pi$
$167$	3.71813	0.287718	0.143859	+	0.989598i	$0.454049\pi$
$168$	0	0
$169$	5.66711	0.435932
$170$	5.38002	0.412628
$171$	0	0
$172$	9.50033	0.724393
$173$	−4.82348	−0.366722	−0.183361	−	0.983046i	$-0.558698\pi$
$173$	−4.82348	−0.366722	−0.183361	+	0.983046i	$0.558698\pi$
$174$	0	0
$175$	1.21406	0.0917745
$176$	29.3357	2.21126
$177$	0	0
$178$	5.61956	0.421204
$179$	16.7043	1.24854	0.624271	−	0.781208i	$-0.285396\pi$
$179$	16.7043	1.24854	0.624271	+	0.781208i	$0.285396\pi$
$180$	0	0
$181$	12.4764	0.927367	0.463684	−	0.886001i	$-0.346527\pi$
$181$	12.4764	0.927367	0.463684	+	0.886001i	$0.346527\pi$
$182$	−14.2052	−1.05296
$183$	0	0
$184$	9.02867	0.665602
$185$	−5.81865	−0.427796
$186$	0	0
$187$	−4.22836	−0.309208
$188$	42.0976	3.07028
$189$	0	0
$190$	−14.3201	−1.03889
$191$	21.6287	1.56500	0.782501	−	0.622650i	$-0.213944\pi$
$191$	21.6287	1.56500	0.782501	+	0.622650i	$0.213944\pi$
$192$	0	0
$193$	10.6678	0.767888	0.383944	−	0.923356i	$-0.374566\pi$
$193$	10.6678	0.767888	0.383944	+	0.923356i	$0.374566\pi$
$194$	−51.3492	−3.68665
$195$	0	0
$196$	−29.4755	−2.10540
$197$	−1.49132	−0.106252	−0.0531261	−	0.998588i	$-0.516919\pi$
$197$	−1.49132	−0.106252	−0.0531261	+	0.998588i	$0.516919\pi$
$198$	0	0
$199$	−8.84059	−0.626693	−0.313346	−	0.949639i	$-0.601450\pi$
$199$	−8.84059	−0.626693	−0.313346	+	0.949639i	$0.601450\pi$
$200$	9.02867	0.638423
$201$	0	0
$202$	19.8380	1.39580
$203$	−8.62771	−0.605547
$204$	0	0
$205$	11.5822	0.808936
$206$	46.8727	3.26578
$207$	0	0
$208$	−59.5496	−4.12902
$209$	11.2547	0.778503
$210$	0	0
$211$	−12.2722	−0.844854	−0.422427	−	0.906397i	$-0.638822\pi$
$211$	−12.2722	−0.844854	−0.422427	+	0.906397i	$0.638822\pi$
$212$	−26.0853	−1.79155
$213$	0	0
$214$	17.9647	1.22804
$215$	−1.78112	−0.121471
$216$	0	0
$217$	−2.83353	−0.192352
$218$	53.2295	3.60516
$219$	0	0
$220$	−11.3528	−0.765406
$221$	8.58329	0.577375
$222$	0	0
$223$	−3.64396	−0.244018	−0.122009	−	0.992529i	$-0.538934\pi$
$223$	−3.64396	−0.244018	−0.122009	+	0.992529i	$0.538934\pi$
$224$	23.3930	1.56301
$225$	0	0
$226$	3.18197	0.211661
$227$	14.4140	0.956691	0.478346	−	0.878172i	$-0.341237\pi$
$227$	14.4140	0.956691	0.478346	+	0.878172i	$0.341237\pi$
$228$	0	0
$229$	4.86017	0.321169	0.160584	−	0.987022i	$-0.448662\pi$
$229$	4.86017	0.321169	0.160584	+	0.987022i	$0.448662\pi$
$230$	−2.70812	−0.178568
$231$	0	0
$232$	−64.1621	−4.21245
$233$	11.0439	0.723510	0.361755	−	0.932273i	$-0.382178\pi$
$233$	11.0439	0.723510	0.361755	+	0.932273i	$0.382178\pi$
$234$	0	0
$235$	−7.89242	−0.514845
$236$	0.631346	0.0410971
$237$	0	0
$238$	−6.53167	−0.423386
$239$	23.5741	1.52488	0.762441	−	0.647058i	$-0.224001\pi$
$239$	23.5741	1.52488	0.762441	+	0.647058i	$0.224001\pi$
$240$	0	0
$241$	14.9609	0.963716	0.481858	−	0.876249i	$-0.339962\pi$
$241$	14.9609	0.963716	0.481858	+	0.876249i	$0.339962\pi$
$242$	−17.5211	−1.12630
$243$	0	0
$244$	−46.9186	−3.00365
$245$	5.52605	0.353047
$246$	0	0
$247$	−22.8463	−1.45368
$248$	−21.0722	−1.33809
$249$	0	0
$250$	−2.70812	−0.171277
$251$	4.41102	0.278421	0.139210	−	0.990263i	$-0.455544\pi$
$251$	4.41102	0.278421	0.139210	+	0.990263i	$0.455544\pi$
$252$	0	0
$253$	2.12841	0.133812
$254$	4.67903	0.293589
$255$	0	0
$256$	26.9342	1.68339
$257$	1.18789	0.0740983	0.0370491	−	0.999313i	$-0.488204\pi$
$257$	1.18789	0.0740983	0.0370491	+	0.999313i	$0.488204\pi$
$258$	0	0
$259$	7.06421	0.438949
$260$	23.0455	1.42922
$261$	0	0
$262$	−52.4602	−3.24100
$263$	−12.9484	−0.798434	−0.399217	−	0.916856i	$-0.630718\pi$
$263$	−12.9484	−0.798434	−0.399217	+	0.916856i	$0.630718\pi$
$264$	0	0
$265$	4.89046	0.300419
$266$	17.3855	1.06597
$267$	0	0
$268$	−6.23783	−0.381036
$269$	3.72600	0.227178	0.113589	−	0.993528i	$-0.463765\pi$
$269$	3.72600	0.227178	0.113589	+	0.993528i	$0.463765\pi$
$270$	0	0
$271$	4.11803	0.250152	0.125076	−	0.992147i	$-0.460082\pi$
$271$	4.11803	0.250152	0.125076	+	0.992147i	$0.460082\pi$
$272$	−27.3814	−1.66024
$273$	0	0
$274$	−57.8361	−3.49400
$275$	2.12841	0.128348
$276$	0	0
$277$	21.1443	1.27044	0.635219	−	0.772332i	$-0.280910\pi$
$277$	21.1443	1.27044	0.635219	+	0.772332i	$0.280910\pi$
$278$	−63.4350	−3.80458
$279$	0	0
$280$	−10.9614	−0.655067
$281$	−27.0717	−1.61496	−0.807480	−	0.589895i	$-0.799169\pi$
$281$	−27.0717	−1.61496	−0.807480	+	0.589895i	$0.799169\pi$
$282$	0	0
$283$	3.66229	0.217700	0.108850	−	0.994058i	$-0.465283\pi$
$283$	3.66229	0.217700	0.108850	+	0.994058i	$0.465283\pi$
$284$	−76.3470	−4.53036
$285$	0	0
$286$	−24.9036	−1.47258
$287$	−14.0615	−0.830025
$288$	0	0
$289$	−13.0533	−0.767843
$290$	19.2452	1.13012
$291$	0	0
$292$	44.3811	2.59721
$293$	7.11899	0.415896	0.207948	−	0.978140i	$-0.433322\pi$
$293$	7.11899	0.415896	0.207948	+	0.978140i	$0.433322\pi$
$294$	0	0
$295$	−0.118364	−0.00689144
$296$	52.5347	3.05352
$297$	0	0
$298$	−31.3068	−1.81355
$299$	−4.32055	−0.249864
$300$	0	0
$301$	2.16239	0.124638
$302$	14.6999	0.845882
$303$	0	0
$304$	72.8815	4.18004
$305$	8.79626	0.503672
$306$	0	0
$307$	23.6763	1.35128	0.675640	−	0.737232i	$-0.263867\pi$
$307$	23.6763	1.35128	0.675640	+	0.737232i	$0.263867\pi$
$308$	13.7830	0.785360
$309$	0	0
$310$	6.32055	0.358983
$311$	14.1324	0.801376	0.400688	−	0.916215i	$-0.368771\pi$
$311$	14.1324	0.801376	0.400688	+	0.916215i	$0.368771\pi$
$312$	0	0
$313$	23.6646	1.33760	0.668800	−	0.743442i	$-0.266808\pi$
$313$	23.6646	1.33760	0.668800	+	0.743442i	$0.266808\pi$
$314$	22.8536	1.28970
$315$	0	0
$316$	60.7506	3.41749
$317$	21.8223	1.22566	0.612832	−	0.790213i	$-0.290030\pi$
$317$	21.8223	1.22566	0.612832	+	0.790213i	$0.290030\pi$
$318$	0	0
$319$	−15.1255	−0.846868
$320$	−24.6154	−1.37604
$321$	0	0
$322$	3.28783	0.183224
$323$	−10.5049	−0.584509
$324$	0	0
$325$	−4.32055	−0.239661
$326$	46.8747	2.59615
$327$	0	0
$328$	−104.572	−5.77401
$329$	9.58189	0.528267
$330$	0	0
$331$	−24.2825	−1.33469	−0.667343	−	0.744751i	$-0.732568\pi$
$331$	−24.2825	−1.33469	−0.667343	+	0.744751i	$0.732568\pi$
$332$	−47.5322	−2.60867
$333$	0	0
$334$	10.0692	0.550960
$335$	1.16946	0.0638946
$336$	0	0
$337$	15.6463	0.852309	0.426155	−	0.904650i	$-0.359868\pi$
$337$	15.6463	0.852309	0.426155	+	0.904650i	$0.359868\pi$
$338$	15.3472	0.834779
$339$	0	0
$340$	10.5965	0.574675
$341$	−4.96755	−0.269008
$342$	0	0
$343$	−15.2074	−0.821123
$344$	16.0811	0.867035
$345$	0	0
$346$	−13.0626	−0.702248
$347$	−28.8979	−1.55132	−0.775661	−	0.631150i	$-0.782583\pi$
$347$	−28.8979	−1.55132	−0.775661	+	0.631150i	$0.782583\pi$
$348$	0	0
$349$	31.8007	1.70225	0.851125	−	0.524962i	$-0.175921\pi$
$349$	31.8007	1.70225	0.851125	+	0.524962i	$0.175921\pi$
$350$	3.28783	0.175742
$351$	0	0
$352$	41.0111	2.18590
$353$	16.7406	0.891011	0.445505	−	0.895279i	$-0.353024\pi$
$353$	16.7406	0.891011	0.445505	+	0.895279i	$0.353024\pi$
$354$	0	0
$355$	14.3135	0.759681
$356$	11.0683	0.586619
$357$	0	0
$358$	45.2374	2.39087
$359$	16.6840	0.880546	0.440273	−	0.897864i	$-0.354882\pi$
$359$	16.6840	0.880546	0.440273	+	0.897864i	$0.354882\pi$
$360$	0	0
$361$	8.96113	0.471638
$362$	33.7877	1.77584
$363$	0	0
$364$	−27.9786	−1.46648
$365$	−8.32055	−0.435517
$366$	0	0
$367$	−14.5917	−0.761682	−0.380841	−	0.924641i	$-0.624365\pi$
$367$	−14.5917	−0.761682	−0.380841	+	0.924641i	$0.624365\pi$
$368$	13.7829	0.718482
$369$	0	0
$370$	−15.7576	−0.819200
$371$	−5.93733	−0.308251
$372$	0	0
$373$	27.7827	1.43853	0.719266	−	0.694735i	$-0.244478\pi$
$373$	27.7827	1.43853	0.719266	+	0.694735i	$0.244478\pi$
$374$	−11.4509	−0.592112
$375$	0	0
$376$	71.2580	3.67485
$377$	30.7039	1.58133
$378$	0	0
$379$	7.77228	0.399235	0.199618	−	0.979874i	$-0.436030\pi$
$379$	7.77228	0.399235	0.199618	+	0.979874i	$0.436030\pi$
$380$	−28.2049	−1.44688
$381$	0	0
$382$	58.5733	2.99687
$383$	−2.40809	−0.123048	−0.0615239	−	0.998106i	$-0.519596\pi$
$383$	−2.40809	−0.123048	−0.0615239	+	0.998106i	$0.519596\pi$
$384$	0	0
$385$	−2.58403	−0.131694
$386$	28.8898	1.47045
$387$	0	0
$388$	−101.137	−5.13447
$389$	−4.66485	−0.236517	−0.118259	−	0.992983i	$-0.537731\pi$
$389$	−4.66485	−0.236517	−0.118259	+	0.992983i	$0.537731\pi$
$390$	0	0
$391$	−1.98662	−0.100468
$392$	−49.8929	−2.51997
$393$	0	0
$394$	−4.03868	−0.203466
$395$	−11.3895	−0.573067
$396$	0	0
$397$	5.02754	0.252325	0.126163	−	0.992010i	$-0.459734\pi$
$397$	5.02754	0.252325	0.126163	+	0.992010i	$0.459734\pi$
$398$	−23.9414	−1.20007
$399$	0	0
$400$	13.7829	0.689144
$401$	3.70677	0.185107	0.0925537	−	0.995708i	$-0.470497\pi$
$401$	3.70677	0.185107	0.0925537	+	0.995708i	$0.470497\pi$
$402$	0	0
$403$	10.0838	0.502311
$404$	39.0729	1.94395
$405$	0	0
$406$	−23.3649	−1.15958
$407$	12.3845	0.613877
$408$	0	0
$409$	−16.5945	−0.820544	−0.410272	−	0.911963i	$-0.634566\pi$
$409$	−16.5945	−0.820544	−0.410272	+	0.911963i	$0.634566\pi$
$410$	31.3660	1.54906
$411$	0	0
$412$	92.3206	4.54831
$413$	0.143702	0.00707110
$414$	0	0
$415$	8.91130	0.437438
$416$	−83.2499	−4.08166
$417$	0	0
$418$	30.4791	1.49078
$419$	0.355499	0.0173673	0.00868363	−	0.999962i	$-0.497236\pi$
$419$	0.355499	0.0173673	0.00868363	+	0.999962i	$0.497236\pi$
$420$	0	0
$421$	−23.6503	−1.15265	−0.576323	−	0.817222i	$-0.695513\pi$
$421$	−23.6503	−1.15265	−0.576323	+	0.817222i	$0.695513\pi$
$422$	−33.2346	−1.61784
$423$	0	0
$424$	−44.1543	−2.14432
$425$	−1.98662	−0.0963654
$426$	0	0
$427$	−10.6792	−0.516803
$428$	35.3833	1.71032
$429$	0	0
$430$	−4.82348	−0.232609
$431$	−4.97648	−0.239709	−0.119854	−	0.992791i	$-0.538243\pi$
$431$	−4.97648	−0.239709	−0.119854	+	0.992791i	$0.538243\pi$
$432$	0	0
$433$	−21.5379	−1.03504	−0.517522	−	0.855670i	$-0.673145\pi$
$433$	−21.5379	−1.03504	−0.517522	+	0.855670i	$0.673145\pi$
$434$	−7.67354	−0.368342
$435$	0	0
$436$	104.841	5.02097
$437$	5.28783	0.252951
$438$	0	0
$439$	−15.7267	−0.750593	−0.375297	−	0.926905i	$-0.622459\pi$
$439$	−15.7267	−0.750593	−0.375297	+	0.926905i	$0.622459\pi$
$440$	−19.2167	−0.916122
$441$	0	0
$442$	23.2446	1.10563
$443$	30.5028	1.44923	0.724617	−	0.689152i	$-0.242017\pi$
$443$	30.5028	1.44923	0.724617	+	0.689152i	$0.242017\pi$
$444$	0	0
$445$	−2.07508	−0.0983681
$446$	−9.86829	−0.467277
$447$	0	0
$448$	29.8846	1.41191
$449$	−25.4811	−1.20253	−0.601264	−	0.799051i	$-0.705336\pi$
$449$	−25.4811	−1.20253	−0.601264	+	0.799051i	$0.705336\pi$
$450$	0	0
$451$	−24.6517	−1.16080
$452$	6.26721	0.294785
$453$	0	0
$454$	39.0349	1.83200
$455$	5.24541	0.245909
$456$	0	0
$457$	−28.3815	−1.32763	−0.663816	−	0.747896i	$-0.731064\pi$
$457$	−28.3815	−1.32763	−0.663816	+	0.747896i	$0.731064\pi$
$458$	13.1619	0.615016
$459$	0	0
$460$	−5.33392	−0.248695
$461$	18.8017	0.875683	0.437841	−	0.899052i	$-0.355743\pi$
$461$	18.8017	0.875683	0.437841	+	0.899052i	$0.355743\pi$
$462$	0	0
$463$	−0.281866	−0.0130994	−0.00654971	−	0.999979i	$-0.502085\pi$
$463$	−0.281866	−0.0130994	−0.00654971	+	0.999979i	$0.502085\pi$
$464$	−97.9478	−4.54711
$465$	0	0
$466$	29.9082	1.38547
$467$	−4.12950	−0.191091	−0.0955453	−	0.995425i	$-0.530459\pi$
$467$	−4.12950	−0.191091	−0.0955453	+	0.995425i	$0.530459\pi$
$468$	0	0
$469$	−1.41980	−0.0655604
$470$	−21.3736	−0.985892
$471$	0	0
$472$	1.06867	0.0491896
$473$	3.79095	0.174308
$474$	0	0
$475$	5.28783	0.242622
$476$	−12.8648	−0.589657
$477$	0	0
$478$	63.8415	2.92004
$479$	32.8864	1.50262	0.751308	−	0.659952i	$-0.229423\pi$
$479$	32.8864	1.50262	0.751308	+	0.659952i	$0.229423\pi$
$480$	0	0
$481$	−25.1398	−1.14627
$482$	40.5159	1.84545
$483$	0	0
$484$	−34.5097	−1.56862
$485$	18.9612	0.860982
$486$	0	0
$487$	−30.4470	−1.37969	−0.689844	−	0.723958i	$-0.742321\pi$
$487$	−30.4470	−1.37969	−0.689844	+	0.723958i	$0.742321\pi$
$488$	−79.4185	−3.59511
$489$	0	0
$490$	14.9652	0.676060
$491$	12.4504	0.561881	0.280940	−	0.959725i	$-0.409354\pi$
$491$	12.4504	0.561881	0.280940	+	0.959725i	$0.409354\pi$
$492$	0	0
$493$	14.1179	0.635838
$494$	−61.8706	−2.78369
$495$	0	0
$496$	−32.1682	−1.44439
$497$	−17.3775	−0.779486
$498$	0	0
$499$	14.5298	0.650442	0.325221	−	0.945638i	$-0.394561\pi$
$499$	14.5298	0.650442	0.325221	+	0.945638i	$0.394561\pi$
$500$	−5.33392	−0.238540
$501$	0	0
$502$	11.9456	0.533157
$503$	1.76847	0.0788523	0.0394261	−	0.999222i	$-0.487447\pi$
$503$	1.76847	0.0788523	0.0394261	+	0.999222i	$0.487447\pi$
$504$	0	0
$505$	−7.32537	−0.325975
$506$	5.76401	0.256241
$507$	0	0
$508$	9.21584	0.408887
$509$	−26.3984	−1.17009	−0.585045	−	0.811001i	$-0.698923\pi$
$509$	−26.3984	−1.17009	−0.585045	+	0.811001i	$0.698923\pi$
$510$	0	0
$511$	10.1017	0.446871
$512$	16.6918	0.737680
$513$	0	0
$514$	3.21694	0.141893
$515$	−17.3082	−0.762690
$516$	0	0
$517$	16.7983	0.738790
$518$	19.1307	0.840556
$519$	0	0
$520$	39.0088	1.71065
$521$	−41.9476	−1.83776	−0.918878	−	0.394541i	$-0.870904\pi$
$521$	−41.9476	−1.83776	−0.918878	+	0.394541i	$0.870904\pi$
$522$	0	0
$523$	31.4020	1.37311	0.686557	−	0.727076i	$-0.259121\pi$
$523$	31.4020	1.37311	0.686557	+	0.727076i	$0.259121\pi$
$524$	−103.326	−4.51381
$525$	0	0
$526$	−35.0659	−1.52895
$527$	4.63662	0.201974
$528$	0	0
$529$	1.00000	0.0434783
$530$	13.2440	0.575281
$531$	0	0
$532$	34.2425	1.48460
$533$	50.0414	2.16753
$534$	0	0
$535$	−6.63363	−0.286797
$536$	−10.5587	−0.456066
$537$	0	0
$538$	10.0905	0.435031
$539$	−11.7617	−0.506614
$540$	0	0
$541$	−10.1302	−0.435533	−0.217766	−	0.976001i	$-0.569877\pi$
$541$	−10.1302	−0.435533	−0.217766	+	0.976001i	$0.569877\pi$
$542$	11.1521	0.479025
$543$	0	0
$544$	−38.2790	−1.64120
$545$	−19.6555	−0.841949
$546$	0	0
$547$	−7.92182	−0.338713	−0.169356	−	0.985555i	$-0.554169\pi$
$547$	−7.92182	−0.338713	−0.169356	+	0.985555i	$0.554169\pi$
$548$	−113.914	−4.86617
$549$	0	0
$550$	5.76401	0.245778
$551$	−37.5779	−1.60087
$552$	0	0
$553$	13.8275	0.588007
$554$	57.2613	2.43280
$555$	0	0
$556$	−124.942	−5.29871
$557$	10.1854	0.431570	0.215785	−	0.976441i	$-0.430769\pi$
$557$	10.1854	0.431570	0.215785	+	0.976441i	$0.430769\pi$
$558$	0	0
$559$	−7.69539	−0.325480
$560$	−16.7333	−0.707110
$561$	0	0
$562$	−73.3134	−3.09254
$563$	35.1935	1.48323	0.741615	−	0.670825i	$-0.234060\pi$
$563$	35.1935	1.48323	0.741615	+	0.670825i	$0.234060\pi$
$564$	0	0
$565$	−1.17497	−0.0494314
$566$	9.91792	0.416881
$567$	0	0
$568$	−129.232	−5.42244
$569$	36.0976	1.51329	0.756644	−	0.653827i	$-0.226838\pi$
$569$	36.0976	1.51329	0.756644	+	0.653827i	$0.226838\pi$
$570$	0	0
$571$	−39.9923	−1.67362	−0.836812	−	0.547490i	$-0.815583\pi$
$571$	−39.9923	−1.67362	−0.836812	+	0.547490i	$0.815583\pi$
$572$	−49.0503	−2.05090
$573$	0	0
$574$	−38.0803	−1.58944
$575$	1.00000	0.0417029
$576$	0	0
$577$	−30.1288	−1.25428	−0.627139	−	0.778907i	$-0.715774\pi$
$577$	−30.1288	−1.25428	−0.627139	+	0.778907i	$0.715774\pi$
$578$	−35.3500	−1.47037
$579$	0	0
$580$	37.9054	1.57394
$581$	−10.8189	−0.448842
$582$	0	0
$583$	−10.4089	−0.431094
$584$	75.1234	3.10863
$585$	0	0
$586$	19.2791	0.796412
$587$	29.8608	1.23249	0.616244	−	0.787555i	$-0.288653\pi$
$587$	29.8608	1.23249	0.616244	+	0.787555i	$0.288653\pi$
$588$	0	0
$589$	−12.3414	−0.508518
$590$	−0.320545	−0.0131966
$591$	0	0
$592$	80.1978	3.29611
$593$	1.62566	0.0667577	0.0333788	−	0.999443i	$-0.489373\pi$
$593$	1.62566	0.0667577	0.0333788	+	0.999443i	$0.489373\pi$
$594$	0	0
$595$	2.41188	0.0988776
$596$	−61.6619	−2.52577
$597$	0	0
$598$	−11.7006	−0.478472
$599$	23.8860	0.975957	0.487979	−	0.872856i	$-0.337734\pi$
$599$	23.8860	0.975957	0.487979	+	0.872856i	$0.337734\pi$
$600$	0	0
$601$	−24.0286	−0.980149	−0.490074	−	0.871681i	$-0.663030\pi$
$601$	−24.0286	−0.980149	−0.490074	+	0.871681i	$0.663030\pi$
$602$	5.85600	0.238673
$603$	0	0
$604$	28.9529	1.17808
$605$	6.46985	0.263037
$606$	0	0
$607$	13.1188	0.532476	0.266238	−	0.963907i	$-0.414219\pi$
$607$	13.1188	0.532476	0.266238	+	0.963907i	$0.414219\pi$
$608$	101.888	4.13210
$609$	0	0
$610$	23.8213	0.964498
$611$	−34.0996	−1.37952
$612$	0	0
$613$	45.8575	1.85217	0.926084	−	0.377316i	$-0.123153\pi$
$613$	45.8575	1.85217	0.926084	+	0.377316i	$0.123153\pi$
$614$	64.1184	2.58761
$615$	0	0
$616$	23.3303	0.940006
$617$	28.9724	1.16638	0.583192	−	0.812334i	$-0.301804\pi$
$617$	28.9724	1.16638	0.583192	+	0.812334i	$0.301804\pi$
$618$	0	0
$619$	−24.7720	−0.995672	−0.497836	−	0.867271i	$-0.665872\pi$
$619$	−24.7720	−0.995672	−0.497836	+	0.867271i	$0.665872\pi$
$620$	12.4490	0.499962
$621$	0	0
$622$	38.2723	1.53458
$623$	2.51927	0.100933
$624$	0	0
$625$	1.00000	0.0400000
$626$	64.0865	2.56141
$627$	0	0
$628$	45.0125	1.79619
$629$	−11.5595	−0.460906
$630$	0	0
$631$	−35.5321	−1.41451	−0.707256	−	0.706958i	$-0.750067\pi$
$631$	−35.5321	−1.41451	−0.707256	+	0.706958i	$0.750067\pi$
$632$	102.832	4.09043
$633$	0	0
$634$	59.0975	2.34706
$635$	−1.72778	−0.0685648
$636$	0	0
$637$	23.8756	0.945984
$638$	−40.9618	−1.62169
$639$	0	0
$640$	−28.1246	−1.11172
$641$	28.4375	1.12321	0.561606	−	0.827405i	$-0.310184\pi$
$641$	28.4375	1.12321	0.561606	+	0.827405i	$0.310184\pi$
$642$	0	0
$643$	−41.4662	−1.63527	−0.817634	−	0.575738i	$-0.804715\pi$
$643$	−41.4662	−1.63527	−0.817634	+	0.575738i	$0.804715\pi$
$644$	6.47571	0.255179
$645$	0	0
$646$	−28.4486	−1.11930
$647$	−2.93696	−0.115464	−0.0577320	−	0.998332i	$-0.518387\pi$
$647$	−2.93696	−0.115464	−0.0577320	+	0.998332i	$0.518387\pi$
$648$	0	0
$649$	0.251928	0.00988906
$650$	−11.7006	−0.458934
$651$	0	0
$652$	92.3245	3.61571
$653$	−24.4006	−0.954869	−0.477435	−	0.878667i	$-0.658433\pi$
$653$	−24.4006	−0.954869	−0.477435	+	0.878667i	$0.658433\pi$
$654$	0	0
$655$	19.3715	0.756905
$656$	−159.636	−6.23274
$657$	0	0
$658$	25.9489	1.01159
$659$	40.5705	1.58040	0.790202	−	0.612847i	$-0.209976\pi$
$659$	40.5705	1.58040	0.790202	+	0.612847i	$0.209976\pi$
$660$	0	0
$661$	18.8622	0.733656	0.366828	−	0.930289i	$-0.380444\pi$
$661$	18.8622	0.733656	0.366828	+	0.930289i	$0.380444\pi$
$662$	−65.7599	−2.55583
$663$	0	0
$664$	−80.4571	−3.12234
$665$	−6.41975	−0.248947
$666$	0	0
$667$	−7.10648	−0.275164
$668$	19.8322	0.767332
$669$	0	0
$670$	3.16705	0.122354
$671$	−18.7221	−0.722758
$672$	0	0
$673$	17.4011	0.670765	0.335382	−	0.942082i	$-0.391134\pi$
$673$	17.4011	0.670765	0.335382	+	0.942082i	$0.391134\pi$
$674$	42.3721	1.63211
$675$	0	0
$676$	30.2279	1.16261
$677$	31.6827	1.21767	0.608833	−	0.793298i	$-0.291638\pi$
$677$	31.6827	1.21767	0.608833	+	0.793298i	$0.291638\pi$
$678$	0	0
$679$	−23.0200	−0.883428
$680$	17.9366	0.687836
$681$	0	0
$682$	−13.4527	−0.515132
$683$	−18.8558	−0.721496	−0.360748	−	0.932663i	$-0.617479\pi$
$683$	−18.8558	−0.721496	−0.360748	+	0.932663i	$0.617479\pi$
$684$	0	0
$685$	21.3565	0.815991
$686$	−41.1835	−1.57239
$687$	0	0
$688$	24.5489	0.935918
$689$	21.1295	0.804968
$690$	0	0
$691$	47.2210	1.79637	0.898186	−	0.439616i	$-0.144885\pi$
$691$	47.2210	1.79637	0.898186	+	0.439616i	$0.144885\pi$
$692$	−25.7281	−0.978034
$693$	0	0
$694$	−78.2591	−2.97067
$695$	23.4240	0.888522
$696$	0	0
$697$	23.0095	0.871545
$698$	86.1201	3.25969
$699$	0	0
$700$	6.47571	0.244759
$701$	−14.4222	−0.544718	−0.272359	−	0.962196i	$-0.587804\pi$
$701$	−14.4222	−0.544718	−0.272359	+	0.962196i	$0.587804\pi$
$702$	0	0
$703$	30.7680	1.16044
$704$	52.3917	1.97459
$705$	0	0
$706$	45.3355	1.70622
$707$	8.89345	0.334473
$708$	0	0
$709$	26.4996	0.995213	0.497607	−	0.867403i	$-0.334212\pi$
$709$	26.4996	0.995213	0.497607	+	0.867403i	$0.334212\pi$
$710$	38.7627	1.45474
$711$	0	0
$712$	18.7352	0.702131
$713$	−2.33392	−0.0874061
$714$	0	0
$715$	9.19591	0.343908
$716$	89.0997	3.32981
$717$	0	0
$718$	45.1822	1.68619
$719$	1.39174	0.0519031	0.0259516	−	0.999663i	$-0.491738\pi$
$719$	1.39174	0.0519031	0.0259516	+	0.999663i	$0.491738\pi$
$720$	0	0
$721$	21.0132	0.782574
$722$	24.2678	0.903155
$723$	0	0
$724$	66.5484	2.47325
$725$	−7.10648	−0.263928
$726$	0	0
$727$	−33.8951	−1.25710	−0.628550	−	0.777770i	$-0.716351\pi$
$727$	−33.8951	−1.25710	−0.628550	+	0.777770i	$0.716351\pi$
$728$	−47.3591	−1.75524
$729$	0	0
$730$	−22.5330	−0.833986
$731$	−3.53840	−0.130873
$732$	0	0
$733$	−31.7370	−1.17223	−0.586117	−	0.810227i	$-0.699344\pi$
$733$	−31.7370	−1.17223	−0.586117	+	0.810227i	$0.699344\pi$
$734$	−39.5162	−1.45857
$735$	0	0
$736$	19.2684	0.710242
$737$	−2.48910	−0.0916873
$738$	0	0
$739$	−29.3281	−1.07885	−0.539425	−	0.842034i	$-0.681358\pi$
$739$	−29.3281	−1.07885	−0.539425	+	0.842034i	$0.681358\pi$
$740$	−31.0363	−1.14092
$741$	0	0
$742$	−16.0790	−0.590279
$743$	−34.3962	−1.26187	−0.630937	−	0.775834i	$-0.717329\pi$
$743$	−34.3962	−1.26187	−0.630937	+	0.775834i	$0.717329\pi$
$744$	0	0
$745$	11.5603	0.423537
$746$	75.2388	2.75469
$747$	0	0
$748$	−22.5537	−0.824646
$749$	8.05364	0.294274
$750$	0	0
$751$	−10.8039	−0.394240	−0.197120	−	0.980379i	$-0.563159\pi$
$751$	−10.8039	−0.394240	−0.197120	+	0.980379i	$0.563159\pi$
$752$	108.780	3.96681
$753$	0	0
$754$	83.1498	3.02814
$755$	−5.42807	−0.197548
$756$	0	0
$757$	−46.6785	−1.69656	−0.848279	−	0.529549i	$-0.822361\pi$
$757$	−46.6785	−1.69656	−0.848279	+	0.529549i	$0.822361\pi$
$758$	21.0483	0.764508
$759$	0	0
$760$	−47.7420	−1.73179
$761$	4.95595	0.179653	0.0898264	−	0.995957i	$-0.471369\pi$
$761$	4.95595	0.179653	0.0898264	+	0.995957i	$0.471369\pi$
$762$	0	0
$763$	23.8630	0.863899
$764$	115.366	4.17380
$765$	0	0
$766$	−6.52141	−0.235628
$767$	−0.511399	−0.0184655
$768$	0	0
$769$	−17.8075	−0.642155	−0.321078	−	0.947053i	$-0.604045\pi$
$769$	−17.8075	−0.642155	−0.321078	+	0.947053i	$0.604045\pi$
$770$	−6.99786	−0.252185
$771$	0	0
$772$	56.9015	2.04793
$773$	−45.9947	−1.65431	−0.827157	−	0.561971i	$-0.810043\pi$
$773$	−45.9947	−1.65431	−0.827157	+	0.561971i	$0.810043\pi$
$774$	0	0
$775$	−2.33392	−0.0838370
$776$	−171.194	−6.14551
$777$	0	0
$778$	−12.6330	−0.452915
$779$	−61.2447	−2.19432
$780$	0	0
$781$	−30.4650	−1.09012
$782$	−5.38002	−0.192389
$783$	0	0
$784$	−76.1649	−2.72018
$785$	−8.43891	−0.301198
$786$	0	0
$787$	−14.1742	−0.505255	−0.252627	−	0.967564i	$-0.581295\pi$
$787$	−14.1742	−0.505255	−0.252627	+	0.967564i	$0.581295\pi$
$788$	−7.95459	−0.283371
$789$	0	0
$790$	−30.8441	−1.09738
$791$	1.42649	0.0507201
$792$	0	0
$793$	38.0046	1.34958
$794$	13.6152	0.483185
$795$	0	0
$796$	−47.1550	−1.67136
$797$	35.4453	1.25554	0.627769	−	0.778399i	$-0.283968\pi$
$797$	35.4453	1.25554	0.627769	+	0.778399i	$0.283968\pi$
$798$	0	0
$799$	−15.6793	−0.554692
$800$	19.2684	0.681240
$801$	0	0
$802$	10.0384	0.354468
$803$	17.7096	0.624957
$804$	0	0
$805$	−1.21406	−0.0427901
$806$	27.3082	0.961890
$807$	0	0
$808$	66.1383	2.32674
$809$	−38.0117	−1.33642	−0.668210	−	0.743973i	$-0.732939\pi$
$809$	−38.0117	−1.33642	−0.668210	+	0.743973i	$0.732939\pi$
$810$	0	0
$811$	8.96681	0.314867	0.157434	−	0.987530i	$-0.449678\pi$
$811$	8.96681	0.314867	0.157434	+	0.987530i	$0.449678\pi$
$812$	−46.0196	−1.61497
$813$	0	0
$814$	33.5388	1.17553
$815$	−17.3089	−0.606306
$816$	0	0
$817$	9.41823	0.329502
$818$	−44.9399	−1.57129
$819$	0	0
$820$	61.7785	2.15740
$821$	−23.6910	−0.826821	−0.413411	−	0.910545i	$-0.635663\pi$
$821$	−23.6910	−0.826821	−0.413411	+	0.910545i	$0.635663\pi$
$822$	0	0
$823$	−26.9890	−0.940776	−0.470388	−	0.882460i	$-0.655886\pi$
$823$	−26.9890	−0.940776	−0.470388	+	0.882460i	$0.655886\pi$
$824$	156.270	5.44392
$825$	0	0
$826$	0.389162	0.0135407
$827$	17.1055	0.594817	0.297408	−	0.954750i	$-0.403878\pi$
$827$	17.1055	0.594817	0.297408	+	0.954750i	$0.403878\pi$
$828$	0	0
$829$	35.7258	1.24081	0.620404	−	0.784283i	$-0.286969\pi$
$829$	35.7258	1.24081	0.620404	+	0.784283i	$0.286969\pi$
$830$	24.1329	0.837664
$831$	0	0
$832$	−106.352	−3.68709
$833$	10.9782	0.380371
$834$	0	0
$835$	−3.71813	−0.128671
$836$	60.0317	2.07624
$837$	0	0
$838$	0.962734	0.0332571
$839$	−35.0696	−1.21074	−0.605369	−	0.795945i	$-0.706974\pi$
$839$	−35.0696	−1.21074	−0.605369	+	0.795945i	$0.706974\pi$
$840$	0	0
$841$	21.5021	0.741452
$842$	−64.0479	−2.20724
$843$	0	0
$844$	−65.4590	−2.25319
$845$	−5.66711	−0.194955
$846$	0	0
$847$	−7.85480	−0.269894
$848$	−67.4047	−2.31469
$849$	0	0
$850$	−5.38002	−0.184533
$851$	5.81865	0.199461
$852$	0	0
$853$	−37.2116	−1.27410	−0.637050	−	0.770823i	$-0.719845\pi$
$853$	−37.2116	−1.27410	−0.637050	+	0.770823i	$0.719845\pi$
$854$	−28.9206	−0.989642
$855$	0	0
$856$	59.8929	2.04710
$857$	−2.47751	−0.0846302	−0.0423151	−	0.999104i	$-0.513473\pi$
$857$	−2.47751	−0.0846302	−0.0423151	+	0.999104i	$0.513473\pi$
$858$	0	0
$859$	13.2049	0.450545	0.225273	−	0.974296i	$-0.427673\pi$
$859$	13.2049	0.450545	0.225273	+	0.974296i	$0.427673\pi$
$860$	−9.50033	−0.323959
$861$	0	0
$862$	−13.4769	−0.459026
$863$	−30.1713	−1.02704	−0.513521	−	0.858077i	$-0.671659\pi$
$863$	−30.1713	−1.02704	−0.513521	+	0.858077i	$0.671659\pi$
$864$	0	0
$865$	4.82348	0.164003
$866$	−58.3272	−1.98204
$867$	0	0
$868$	−15.1138	−0.512996
$869$	24.2416	0.822338
$870$	0	0
$871$	5.05272	0.171205
$872$	177.463	6.00965
$873$	0	0
$874$	14.3201	0.484384
$875$	−1.21406	−0.0410428
$876$	0	0
$877$	15.2627	0.515385	0.257692	−	0.966227i	$-0.417038\pi$
$877$	15.2627	0.515385	0.257692	+	0.966227i	$0.417038\pi$
$878$	−42.5898	−1.43733
$879$	0	0
$880$	−29.3357	−0.988906
$881$	−9.62761	−0.324362	−0.162181	−	0.986761i	$-0.551853\pi$
$881$	−9.62761	−0.324362	−0.162181	+	0.986761i	$0.551853\pi$
$882$	0	0
$883$	−43.9311	−1.47840	−0.739199	−	0.673487i	$-0.764796\pi$
$883$	−43.9311	−1.47840	−0.739199	+	0.673487i	$0.764796\pi$
$884$	45.7826	1.53984
$885$	0	0
$886$	82.6054	2.77518
$887$	35.4705	1.19098	0.595491	−	0.803362i	$-0.296958\pi$
$887$	35.4705	1.19098	0.595491	+	0.803362i	$0.296958\pi$
$888$	0	0
$889$	2.09763	0.0703523
$890$	−5.61956	−0.188368
$891$	0	0
$892$	−19.4366	−0.650786
$893$	41.7338	1.39657
$894$	0	0
$895$	−16.7043	−0.558365
$896$	34.1451	1.14071
$897$	0	0
$898$	−69.0059	−2.30276
$899$	16.5860	0.553173
$900$	0	0
$901$	9.71550	0.323670
$902$	−66.7598	−2.22286
$903$	0	0
$904$	10.6084	0.352831
$905$	−12.4764	−0.414731
$906$	0	0
$907$	15.5274	0.515579	0.257790	−	0.966201i	$-0.417006\pi$
$907$	15.5274	0.515579	0.257790	+	0.966201i	$0.417006\pi$
$908$	76.8832	2.55146
$909$	0	0
$910$	14.2052	0.470898
$911$	6.70505	0.222148	0.111074	−	0.993812i	$-0.464571\pi$
$911$	6.70505	0.222148	0.111074	+	0.993812i	$0.464571\pi$
$912$	0	0
$913$	−18.9669	−0.627714
$914$	−76.8607	−2.54233
$915$	0	0
$916$	25.9238	0.856545
$917$	−23.5182	−0.776638
$918$	0	0
$919$	−0.198341	−0.00654266	−0.00327133	−	0.999995i	$-0.501041\pi$
$919$	−0.198341	−0.00654266	−0.00327133	+	0.999995i	$0.501041\pi$
$920$	−9.02867	−0.297666
$921$	0	0
$922$	50.9173	1.67687
$923$	61.8421	2.03556
$924$	0	0
$925$	5.81865	0.191316
$926$	−0.763327	−0.0250845
$927$	0	0
$928$	−136.930	−4.49496
$929$	−36.5756	−1.20001	−0.600003	−	0.799998i	$-0.704834\pi$
$929$	−36.5756	−1.20001	−0.600003	+	0.799998i	$0.704834\pi$
$930$	0	0
$931$	−29.2208	−0.957674
$932$	58.9073	1.92957
$933$	0	0
$934$	−11.1832	−0.365925
$935$	4.22836	0.138282
$936$	0	0
$937$	34.5234	1.12783	0.563915	−	0.825833i	$-0.309294\pi$
$937$	34.5234	1.12783	0.563915	+	0.825833i	$0.309294\pi$
$938$	−3.84500	−0.125544
$939$	0	0
$940$	−42.0976	−1.37307
$941$	−16.3274	−0.532257	−0.266129	−	0.963938i	$-0.585745\pi$
$941$	−16.3274	−0.532257	−0.266129	+	0.963938i	$0.585745\pi$
$942$	0	0
$943$	−11.5822	−0.377168
$944$	1.63140	0.0530976
$945$	0	0
$946$	10.2664	0.333788
$947$	−23.1333	−0.751731	−0.375865	−	0.926674i	$-0.622654\pi$
$947$	−23.1333	−0.751731	−0.375865	+	0.926674i	$0.622654\pi$
$948$	0	0
$949$	−35.9493	−1.16696
$950$	14.3201	0.464605
$951$	0	0
$952$	−21.7761	−0.705767
$953$	45.7304	1.48135	0.740677	−	0.671862i	$-0.234505\pi$
$953$	45.7304	1.48135	0.740677	+	0.671862i	$0.234505\pi$
$954$	0	0
$955$	−21.6287	−0.699890
$956$	125.742	4.06680
$957$	0	0
$958$	89.0603	2.87741
$959$	−25.9282	−0.837264
$960$	0	0
$961$	−25.5528	−0.824284
$962$	−68.0815	−2.19504
$963$	0	0
$964$	79.8003	2.57019
$965$	−10.6678	−0.343410
$966$	0	0
$967$	0.302509	0.00972803	0.00486402	−	0.999988i	$-0.498452\pi$
$967$	0.302509	0.00972803	0.00486402	+	0.999988i	$0.498452\pi$
$968$	−58.4141	−1.87750
$969$	0	0
$970$	51.3492	1.64872
$971$	9.02535	0.289637	0.144819	−	0.989458i	$-0.453740\pi$
$971$	9.02535	0.289637	0.144819	+	0.989458i	$0.453740\pi$
$972$	0	0
$973$	−28.4382	−0.911686
$974$	−82.4543	−2.64201
$975$	0	0
$976$	−121.238	−3.88073
$977$	−3.64104	−0.116487	−0.0582436	−	0.998302i	$-0.518550\pi$
$977$	−3.64104	−0.116487	−0.0582436	+	0.998302i	$0.518550\pi$
$978$	0	0
$979$	4.41663	0.141156
$980$	29.4755	0.941561
$981$	0	0
$982$	33.7173	1.07596
$983$	−21.0997	−0.672976	−0.336488	−	0.941688i	$-0.609239\pi$
$983$	−21.0997	−0.672976	−0.336488	+	0.941688i	$0.609239\pi$
$984$	0	0
$985$	1.49132	0.0475174
$986$	38.2330	1.21759
$987$	0	0
$988$	−121.860	−3.87690
$989$	1.78112	0.0566362
$990$	0	0
$991$	−48.9360	−1.55450	−0.777252	−	0.629189i	$-0.783387\pi$
$991$	−48.9360	−1.55450	−0.777252	+	0.629189i	$0.783387\pi$
$992$	−44.9709	−1.42783
$993$	0	0
$994$	−47.0603	−1.49266
$995$	8.84059	0.280265
$996$	0	0
$997$	−9.67207	−0.306318	−0.153159	−	0.988202i	$-0.548945\pi$
$997$	−9.67207	−0.306318	−0.153159	+	0.988202i	$0.548945\pi$
$998$	39.3484	1.24555
$999$	0	0

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a_n

instead) (See

a_n

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a_n

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Twists

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

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

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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.p.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	$1$