LMFDB - Embedded newform 1400.2.a.t.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(1,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1400.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.76156$ of defining polynomial
Character	$\chi$	$=$	1400.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.76156 q^{3} -1.00000 q^{7} +0.103084 q^{9} +O(q^{10})$	$q-1.76156 q^{3} -1.00000 q^{7} +0.103084 q^{9} -0.626198 q^{11} -5.49084 q^{13} -0.896916 q^{17} +6.38776 q^{19} +1.76156 q^{21} +3.72928 q^{23} +5.10308 q^{27} -7.87859 q^{29} +7.52311 q^{31} +1.10308 q^{33} -6.00000 q^{37} +9.67243 q^{39} +7.72928 q^{41} -1.72928 q^{43} -5.87859 q^{47} +1.00000 q^{49} +1.57997 q^{51} +6.77551 q^{53} -11.2524 q^{57} -0.593923 q^{59} +7.13536 q^{61} -0.103084 q^{63} +5.79383 q^{67} -6.56934 q^{69} +5.52311 q^{71} +3.72928 q^{73} +0.626198 q^{77} -5.67243 q^{79} -9.29862 q^{81} +17.4340 q^{83} +13.8786 q^{87} +14.2986 q^{89} +5.49084 q^{91} -13.2524 q^{93} +10.1493 q^{97} -0.0645508 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{3} - 3 q^{7} + 4 q^{9}+O(q^{10}) $ 3 * q + q^3 - 3 * q^7 + 4 * q^9	$ 3 q + q^{3} - 3 q^{7} + 4 q^{9} + 7 q^{11} - 5 q^{13} + q^{17} + 4 q^{19} - q^{21} + 6 q^{23} + 19 q^{27} + 3 q^{29} + 10 q^{31} + 7 q^{33} - 18 q^{37} - 5 q^{39} + 18 q^{41} + 9 q^{47} + 3 q^{49} + 21 q^{51} - 10 q^{53} - 16 q^{57} + 6 q^{59} + 24 q^{61} - 4 q^{63} + 10 q^{67} + 18 q^{69} + 4 q^{71} + 6 q^{73} - 7 q^{77} + 17 q^{79} + 15 q^{81} + 12 q^{83} + 15 q^{87} + 5 q^{91} - 22 q^{93} + 9 q^{97} + 2 q^{99}+O(q^{100}) $ 3 * q + q^3 - 3 * q^7 + 4 * q^9 + 7 * q^11 - 5 * q^13 + q^17 + 4 * q^19 - q^21 + 6 * q^23 + 19 * q^27 + 3 * q^29 + 10 * q^31 + 7 * q^33 - 18 * q^37 - 5 * q^39 + 18 * q^41 + 9 * q^47 + 3 * q^49 + 21 * q^51 - 10 * q^53 - 16 * q^57 + 6 * q^59 + 24 * q^61 - 4 * q^63 + 10 * q^67 + 18 * q^69 + 4 * q^71 + 6 * q^73 - 7 * q^77 + 17 * q^79 + 15 * q^81 + 12 * q^83 + 15 * q^87 + 5 * q^91 - 22 * q^93 + 9 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0	0
$2$	0	0
$3$	−1.76156	−1.01704	−0.508518	−	0.861052i	$-0.669806\pi$
$3$	−1.76156	−1.01704	−0.508518	+	0.861052i	$0.669806\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	0.103084	0.0343612
$10$	0	0
$11$	−0.626198	−0.188806	−0.0944029	−	0.995534i	$-0.530094\pi$
$11$	−0.626198	−0.188806	−0.0944029	+	0.995534i	$0.530094\pi$
$12$	0	0
$13$	−5.49084	−1.52288	−0.761442	−	0.648233i	$-0.775508\pi$
$13$	−5.49084	−1.52288	−0.761442	+	0.648233i	$0.775508\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−0.896916	−0.217534	−0.108767	−	0.994067i	$-0.534690\pi$
$17$	−0.896916	−0.217534	−0.108767	+	0.994067i	$0.534690\pi$
$18$	0	0
$19$	6.38776	1.46545	0.732726	−	0.680524i	$-0.238248\pi$
$19$	6.38776	1.46545	0.732726	+	0.680524i	$0.238248\pi$
$20$	0	0
$21$	1.76156	0.384403
$22$	0	0
$23$	3.72928	0.777609	0.388805	−	0.921320i	$-0.372888\pi$
$23$	3.72928	0.777609	0.388805	+	0.921320i	$0.372888\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	5.10308	0.982089
$28$	0	0
$29$	−7.87859	−1.46302	−0.731509	−	0.681832i	$-0.761184\pi$
$29$	−7.87859	−1.46302	−0.731509	+	0.681832i	$0.761184\pi$
$30$	0	0
$31$	7.52311	1.35119	0.675596	−	0.737272i	$-0.263887\pi$
$31$	7.52311	1.35119	0.675596	+	0.737272i	$0.263887\pi$
$32$	0	0
$33$	1.10308	0.192022
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	0	0
$39$	9.67243	1.54883
$40$	0	0
$41$	7.72928	1.20711	0.603556	−	0.797321i	$-0.293750\pi$
$41$	7.72928	1.20711	0.603556	+	0.797321i	$0.293750\pi$
$42$	0	0
$43$	−1.72928	−0.263713	−0.131856	−	0.991269i	$-0.542094\pi$
$43$	−1.72928	−0.263713	−0.131856	+	0.991269i	$0.542094\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−5.87859	−0.857481	−0.428741	−	0.903428i	$-0.641043\pi$
$47$	−5.87859	−0.857481	−0.428741	+	0.903428i	$0.641043\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	1.57997	0.221240
$52$	0	0
$53$	6.77551	0.930688	0.465344	−	0.885130i	$-0.345931\pi$
$53$	6.77551	0.930688	0.465344	+	0.885130i	$0.345931\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−11.2524	−1.49042
$58$	0	0
$59$	−0.593923	−0.0773221	−0.0386611	−	0.999252i	$-0.512309\pi$
$59$	−0.593923	−0.0773221	−0.0386611	+	0.999252i	$0.512309\pi$
$60$	0	0
$61$	7.13536	0.913589	0.456795	−	0.889572i	$-0.348997\pi$
$61$	7.13536	0.913589	0.456795	+	0.889572i	$0.348997\pi$
$62$	0	0
$63$	−0.103084	−0.0129873
$64$	0	0
$65$	0	0
$66$	0	0
$67$	5.79383	0.707829	0.353915	−	0.935278i	$-0.384850\pi$
$67$	5.79383	0.707829	0.353915	+	0.935278i	$0.384850\pi$
$68$	0	0
$69$	−6.56934	−0.790856
$70$	0	0
$71$	5.52311	0.655473	0.327737	−	0.944769i	$-0.393714\pi$
$71$	5.52311	0.655473	0.327737	+	0.944769i	$0.393714\pi$
$72$	0	0
$73$	3.72928	0.436479	0.218240	−	0.975895i	$-0.429969\pi$
$73$	3.72928	0.436479	0.218240	+	0.975895i	$0.429969\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0.626198	0.0713619
$78$	0	0
$79$	−5.67243	−0.638198	−0.319099	−	0.947721i	$-0.603380\pi$
$79$	−5.67243	−0.638198	−0.319099	+	0.947721i	$0.603380\pi$
$80$	0	0
$81$	−9.29862	−1.03318
$82$	0	0
$83$	17.4340	1.91363	0.956814	−	0.290700i	$-0.0938882\pi$
$83$	17.4340	1.91363	0.956814	+	0.290700i	$0.0938882\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	13.8786	1.48794
$88$	0	0
$89$	14.2986	1.51565	0.757826	−	0.652457i	$-0.226262\pi$
$89$	14.2986	1.51565	0.757826	+	0.652457i	$0.226262\pi$
$90$	0	0
$91$	5.49084	0.575596
$92$	0	0
$93$	−13.2524	−1.37421
$94$	0	0
$95$	0	0
$96$	0	0
$97$	10.1493	1.03051	0.515253	−	0.857038i	$-0.327698\pi$
$97$	10.1493	1.03051	0.515253	+	0.857038i	$0.327698\pi$
$98$	0	0
$99$	−0.0645508	−0.00648760
$100$	0	0
$101$	9.64015	0.959231	0.479615	−	0.877479i	$-0.340776\pi$
$101$	9.64015	0.959231	0.479615	+	0.877479i	$0.340776\pi$
$102$	0	0
$103$	0.626198	0.0617011	0.0308506	−	0.999524i	$-0.490178\pi$
$103$	0.626198	0.0617011	0.0308506	+	0.999524i	$0.490178\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	18.9248	1.81267	0.906335	−	0.422561i	$-0.138869\pi$
$109$	18.9248	1.81267	0.906335	+	0.422561i	$0.138869\pi$
$110$	0	0
$111$	10.5693	1.00320
$112$	0	0
$113$	1.04623	0.0984209	0.0492105	−	0.998788i	$-0.484329\pi$
$113$	1.04623	0.0984209	0.0492105	+	0.998788i	$0.484329\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−0.566016	−0.0523282
$118$	0	0
$119$	0.896916	0.0822202
$120$	0	0
$121$	−10.6079	−0.964352
$122$	0	0
$123$	−13.6156	−1.22767
$124$	0	0
$125$	0	0
$126$	0	0
$127$	21.2803	1.88832	0.944161	−	0.329485i	$-0.106875\pi$
$127$	21.2803	1.88832	0.944161	+	0.329485i	$0.106875\pi$
$128$	0	0
$129$	3.04623	0.268205
$130$	0	0
$131$	−9.91087	−0.865917	−0.432958	−	0.901414i	$-0.642530\pi$
$131$	−9.91087	−0.865917	−0.432958	+	0.901414i	$0.642530\pi$
$132$	0	0
$133$	−6.38776	−0.553889
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−3.45856	−0.295485	−0.147743	−	0.989026i	$-0.547201\pi$
$137$	−3.45856	−0.295485	−0.147743	+	0.989026i	$0.547201\pi$
$138$	0	0
$139$	−20.4157	−1.73163	−0.865817	−	0.500361i	$-0.833201\pi$
$139$	−20.4157	−1.73163	−0.865817	+	0.500361i	$0.833201\pi$
$140$	0	0
$141$	10.3555	0.872089
$142$	0	0
$143$	3.43835	0.287530
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−1.76156	−0.145291
$148$	0	0
$149$	−17.0462	−1.39648	−0.698241	−	0.715863i	$-0.746033\pi$
$149$	−17.0462	−1.39648	−0.698241	+	0.715863i	$0.746033\pi$
$150$	0	0
$151$	2.89692	0.235748	0.117874	−	0.993029i	$-0.462392\pi$
$151$	2.89692	0.235748	0.117874	+	0.993029i	$0.462392\pi$
$152$	0	0
$153$	−0.0924575	−0.00747474
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−10.1170	−0.807427	−0.403714	−	0.914885i	$-0.632281\pi$
$157$	−10.1170	−0.807427	−0.403714	+	0.914885i	$0.632281\pi$
$158$	0	0
$159$	−11.9354	−0.946543
$160$	0	0
$161$	−3.72928	−0.293909
$162$	0	0
$163$	−0.476886	−0.0373526	−0.0186763	−	0.999826i	$-0.505945\pi$
$163$	−0.476886	−0.0373526	−0.0186763	+	0.999826i	$0.505945\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	13.1676	1.01894	0.509471	−	0.860488i	$-0.329841\pi$
$167$	13.1676	1.01894	0.509471	+	0.860488i	$0.329841\pi$
$168$	0	0
$169$	17.1493	1.31918
$170$	0	0
$171$	0.658473	0.0503547
$172$	0	0
$173$	−13.9677	−1.06195	−0.530973	−	0.847389i	$-0.678174\pi$
$173$	−13.9677	−1.06195	−0.530973	+	0.847389i	$0.678174\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	1.04623	0.0786394
$178$	0	0
$179$	7.45856	0.557479	0.278740	−	0.960367i	$-0.410083\pi$
$179$	7.45856	0.557479	0.278740	+	0.960367i	$0.410083\pi$
$180$	0	0
$181$	−14.1170	−1.04931	−0.524656	−	0.851315i	$-0.675806\pi$
$181$	−14.1170	−1.04931	−0.524656	+	0.851315i	$0.675806\pi$
$182$	0	0
$183$	−12.5693	−0.929153
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0.561647	0.0410717
$188$	0	0
$189$	−5.10308	−0.371195
$190$	0	0
$191$	−8.42003	−0.609252	−0.304626	−	0.952472i	$-0.598531\pi$
$191$	−8.42003	−0.609252	−0.304626	+	0.952472i	$0.598531\pi$
$192$	0	0
$193$	22.2986	1.60509	0.802545	−	0.596591i	$-0.203479\pi$
$193$	22.2986	1.60509	0.802545	+	0.596591i	$0.203479\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−26.3632	−1.87830	−0.939149	−	0.343509i	$-0.888384\pi$
$197$	−26.3632	−1.87830	−0.939149	+	0.343509i	$0.888384\pi$
$198$	0	0
$199$	22.4402	1.59075	0.795373	−	0.606120i	$-0.207275\pi$
$199$	22.4402	1.59075	0.795373	+	0.606120i	$0.207275\pi$
$200$	0	0
$201$	−10.2062	−0.719888
$202$	0	0
$203$	7.87859	0.552969
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0.384428	0.0267196
$208$	0	0
$209$	−4.00000	−0.276686
$210$	0	0
$211$	−15.1955	−1.04610	−0.523052	−	0.852301i	$-0.675207\pi$
$211$	−15.1955	−1.04610	−0.523052	+	0.852301i	$0.675207\pi$
$212$	0	0
$213$	−9.72928	−0.666639
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−7.52311	−0.510702
$218$	0	0
$219$	−6.56934	−0.443915
$220$	0	0
$221$	4.92482	0.331279
$222$	0	0
$223$	6.89692	0.461852	0.230926	−	0.972971i	$-0.425825\pi$
$223$	6.89692	0.461852	0.230926	+	0.972971i	$0.425825\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	2.77988	0.184507	0.0922535	−	0.995736i	$-0.470593\pi$
$227$	2.77988	0.184507	0.0922535	+	0.995736i	$0.470593\pi$
$228$	0	0
$229$	18.6585	1.23299	0.616493	−	0.787360i	$-0.288553\pi$
$229$	18.6585	1.23299	0.616493	+	0.787360i	$0.288553\pi$
$230$	0	0
$231$	−1.10308	−0.0725776
$232$	0	0
$233$	11.0462	0.723663	0.361831	−	0.932244i	$-0.382152\pi$
$233$	11.0462	0.723663	0.361831	+	0.932244i	$0.382152\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	9.99230	0.649070
$238$	0	0
$239$	−20.1493	−1.30335	−0.651675	−	0.758498i	$-0.725934\pi$
$239$	−20.1493	−1.30335	−0.651675	+	0.758498i	$0.725934\pi$
$240$	0	0
$241$	3.72928	0.240224	0.120112	−	0.992760i	$-0.461675\pi$
$241$	3.72928	0.240224	0.120112	+	0.992760i	$0.461675\pi$
$242$	0	0
$243$	1.07081	0.0686924
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−35.0741	−2.23171
$248$	0	0
$249$	−30.7110	−1.94623
$250$	0	0
$251$	−21.4985	−1.35698	−0.678488	−	0.734612i	$-0.737364\pi$
$251$	−21.4985	−1.35698	−0.678488	+	0.734612i	$0.737364\pi$
$252$	0	0
$253$	−2.33527	−0.146817
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−4.27072	−0.266400	−0.133200	−	0.991089i	$-0.542525\pi$
$257$	−4.27072	−0.266400	−0.133200	+	0.991089i	$0.542525\pi$
$258$	0	0
$259$	6.00000	0.372822
$260$	0	0
$261$	−0.812155	−0.0502711
$262$	0	0
$263$	11.4586	0.706565	0.353283	−	0.935517i	$-0.385065\pi$
$263$	11.4586	0.706565	0.353283	+	0.935517i	$0.385065\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−25.1878	−1.54147
$268$	0	0
$269$	−7.07081	−0.431115	−0.215557	−	0.976491i	$-0.569157\pi$
$269$	−7.07081	−0.431115	−0.215557	+	0.976491i	$0.569157\pi$
$270$	0	0
$271$	17.0096	1.03326	0.516629	−	0.856209i	$-0.327187\pi$
$271$	17.0096	1.03326	0.516629	+	0.856209i	$0.327187\pi$
$272$	0	0
$273$	−9.67243	−0.585402
$274$	0	0
$275$	0	0
$276$	0	0
$277$	18.7755	1.12811	0.564056	−	0.825737i	$-0.309240\pi$
$277$	18.7755	1.12811	0.564056	+	0.825737i	$0.309240\pi$
$278$	0	0
$279$	0.775511	0.0464286
$280$	0	0
$281$	−4.59829	−0.274311	−0.137156	−	0.990550i	$-0.543796\pi$
$281$	−4.59829	−0.274311	−0.137156	+	0.990550i	$0.543796\pi$
$282$	0	0
$283$	13.5833	0.807443	0.403722	−	0.914882i	$-0.367716\pi$
$283$	13.5833	0.807443	0.403722	+	0.914882i	$0.367716\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−7.72928	−0.456245
$288$	0	0
$289$	−16.1955	−0.952679
$290$	0	0
$291$	−17.8786	−1.04806
$292$	0	0
$293$	−11.8261	−0.690889	−0.345444	−	0.938439i	$-0.612272\pi$
$293$	−11.8261	−0.690889	−0.345444	+	0.938439i	$0.612272\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−3.19554	−0.185424
$298$	0	0
$299$	−20.4769	−1.18421
$300$	0	0
$301$	1.72928	0.0996741
$302$	0	0
$303$	−16.9817	−0.975572
$304$	0	0
$305$	0	0
$306$	0	0
$307$	20.9860	1.19774	0.598868	−	0.800847i	$-0.295617\pi$
$307$	20.9860	1.19774	0.598868	+	0.800847i	$0.295617\pi$
$308$	0	0
$309$	−1.10308	−0.0627522
$310$	0	0
$311$	−22.5048	−1.27613	−0.638065	−	0.769983i	$-0.720265\pi$
$311$	−22.5048	−1.27613	−0.638065	+	0.769983i	$0.720265\pi$
$312$	0	0
$313$	12.4846	0.705670	0.352835	−	0.935686i	$-0.385218\pi$
$313$	12.4846	0.705670	0.352835	+	0.935686i	$0.385218\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−25.5231	−1.43352	−0.716760	−	0.697319i	$-0.754376\pi$
$317$	−25.5231	−1.43352	−0.716760	+	0.697319i	$0.754376\pi$
$318$	0	0
$319$	4.93356	0.276226
$320$	0	0
$321$	0	0
$322$	0	0
$323$	−5.72928	−0.318786
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−33.3372	−1.84355
$328$	0	0
$329$	5.87859	0.324097
$330$	0	0
$331$	−2.68305	−0.147474	−0.0737370	−	0.997278i	$-0.523493\pi$
$331$	−2.68305	−0.147474	−0.0737370	+	0.997278i	$0.523493\pi$
$332$	0	0
$333$	−0.618502	−0.0338937
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−12.5048	−0.681179	−0.340590	−	0.940212i	$-0.610627\pi$
$337$	−12.5048	−0.681179	−0.340590	+	0.940212i	$0.610627\pi$
$338$	0	0
$339$	−1.84299	−0.100098
$340$	0	0
$341$	−4.71096	−0.255113
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	0	0
$346$	0	0
$347$	28.9450	1.55385	0.776925	−	0.629593i	$-0.216778\pi$
$347$	28.9450	1.55385	0.776925	+	0.629593i	$0.216778\pi$
$348$	0	0
$349$	32.1449	1.72068	0.860340	−	0.509721i	$-0.170251\pi$
$349$	32.1449	1.72068	0.860340	+	0.509721i	$0.170251\pi$
$350$	0	0
$351$	−28.0202	−1.49561
$352$	0	0
$353$	−8.17722	−0.435229	−0.217615	−	0.976035i	$-0.569828\pi$
$353$	−8.17722	−0.435229	−0.217615	+	0.976035i	$0.569828\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−1.57997	−0.0836208
$358$	0	0
$359$	18.5048	0.976646	0.488323	−	0.872663i	$-0.337609\pi$
$359$	18.5048	0.976646	0.488323	+	0.872663i	$0.337609\pi$
$360$	0	0
$361$	21.8034	1.14755
$362$	0	0
$363$	18.6864	0.980781
$364$	0	0
$365$	0	0
$366$	0	0
$367$	27.4942	1.43518	0.717592	−	0.696464i	$-0.245244\pi$
$367$	27.4942	1.43518	0.717592	+	0.696464i	$0.245244\pi$
$368$	0	0
$369$	0.796763	0.0414778
$370$	0	0
$371$	−6.77551	−0.351767
$372$	0	0
$373$	−6.06455	−0.314011	−0.157005	−	0.987598i	$-0.550184\pi$
$373$	−6.06455	−0.314011	−0.157005	+	0.987598i	$0.550184\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	43.2601	2.22801
$378$	0	0
$379$	−5.72928	−0.294293	−0.147147	−	0.989115i	$-0.547009\pi$
$379$	−5.72928	−0.294293	−0.147147	+	0.989115i	$0.547009\pi$
$380$	0	0
$381$	−37.4865	−1.92049
$382$	0	0
$383$	1.72928	0.0883622	0.0441811	−	0.999024i	$-0.485932\pi$
$383$	1.72928	0.0883622	0.0441811	+	0.999024i	$0.485932\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−0.178261	−0.00906150
$388$	0	0
$389$	−36.7187	−1.86171	−0.930855	−	0.365389i	$-0.880936\pi$
$389$	−36.7187	−1.86171	−0.930855	+	0.365389i	$0.880936\pi$
$390$	0	0
$391$	−3.34485	−0.169157
$392$	0	0
$393$	17.4586	0.880668
$394$	0	0
$395$	0	0
$396$	0	0
$397$	2.03228	0.101997	0.0509985	−	0.998699i	$-0.483760\pi$
$397$	2.03228	0.101997	0.0509985	+	0.998699i	$0.483760\pi$
$398$	0	0
$399$	11.2524	0.563324
$400$	0	0
$401$	−1.64452	−0.0821234	−0.0410617	−	0.999157i	$-0.513074\pi$
$401$	−1.64452	−0.0821234	−0.0410617	+	0.999157i	$0.513074\pi$
$402$	0	0
$403$	−41.3082	−2.05771
$404$	0	0
$405$	0	0
$406$	0	0
$407$	3.75719	0.186237
$408$	0	0
$409$	−4.98168	−0.246328	−0.123164	−	0.992386i	$-0.539304\pi$
$409$	−4.98168	−0.246328	−0.123164	+	0.992386i	$0.539304\pi$
$410$	0	0
$411$	6.09246	0.300519
$412$	0	0
$413$	0.593923	0.0292250
$414$	0	0
$415$	0	0
$416$	0	0
$417$	35.9634	1.76113
$418$	0	0
$419$	22.9205	1.11974	0.559869	−	0.828581i	$-0.310852\pi$
$419$	22.9205	1.11974	0.559869	+	0.828581i	$0.310852\pi$
$420$	0	0
$421$	−20.9527	−1.02117	−0.510587	−	0.859826i	$-0.670572\pi$
$421$	−20.9527	−1.02117	−0.510587	+	0.859826i	$0.670572\pi$
$422$	0	0
$423$	−0.605987	−0.0294641
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−7.13536	−0.345304
$428$	0	0
$429$	−6.05685	−0.292428
$430$	0	0
$431$	33.1589	1.59721	0.798604	−	0.601857i	$-0.205572\pi$
$431$	33.1589	1.59721	0.798604	+	0.601857i	$0.205572\pi$
$432$	0	0
$433$	18.5414	0.891045	0.445522	−	0.895271i	$-0.353018\pi$
$433$	18.5414	0.891045	0.445522	+	0.895271i	$0.353018\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	23.8217	1.13955
$438$	0	0
$439$	−20.8401	−0.994642	−0.497321	−	0.867567i	$-0.665683\pi$
$439$	−20.8401	−0.994642	−0.497321	+	0.867567i	$0.665683\pi$
$440$	0	0
$441$	0.103084	0.00490875
$442$	0	0
$443$	−17.5510	−0.833874	−0.416937	−	0.908935i	$-0.636896\pi$
$443$	−17.5510	−0.833874	−0.416937	+	0.908935i	$0.636896\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	30.0279	1.42027
$448$	0	0
$449$	−13.1955	−0.622736	−0.311368	−	0.950289i	$-0.600787\pi$
$449$	−13.1955	−0.622736	−0.311368	+	0.950289i	$0.600787\pi$
$450$	0	0
$451$	−4.84006	−0.227910
$452$	0	0
$453$	−5.10308	−0.239764
$454$	0	0
$455$	0	0
$456$	0	0
$457$	29.1020	1.36134	0.680668	−	0.732592i	$-0.261690\pi$
$457$	29.1020	1.36134	0.680668	+	0.732592i	$0.261690\pi$
$458$	0	0
$459$	−4.57704	−0.213638
$460$	0	0
$461$	−18.8280	−0.876907	−0.438454	−	0.898754i	$-0.644474\pi$
$461$	−18.8280	−0.876907	−0.438454	+	0.898754i	$0.644474\pi$
$462$	0	0
$463$	14.0925	0.654932	0.327466	−	0.944863i	$-0.393805\pi$
$463$	14.0925	0.654932	0.327466	+	0.944863i	$0.393805\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	12.2663	0.567619	0.283809	−	0.958881i	$-0.408402\pi$
$467$	12.2663	0.567619	0.283809	+	0.958881i	$0.408402\pi$
$468$	0	0
$469$	−5.79383	−0.267534
$470$	0	0
$471$	17.8217	0.821182
$472$	0	0
$473$	1.08287	0.0497905
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0.698445	0.0319796
$478$	0	0
$479$	−14.1570	−0.646850	−0.323425	−	0.946254i	$-0.604834\pi$
$479$	−14.1570	−0.646850	−0.323425	+	0.946254i	$0.604834\pi$
$480$	0	0
$481$	32.9450	1.50216
$482$	0	0
$483$	6.56934	0.298915
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−30.2341	−1.37004	−0.685018	−	0.728526i	$-0.740206\pi$
$487$	−30.2341	−1.37004	−0.685018	+	0.728526i	$0.740206\pi$
$488$	0	0
$489$	0.840061	0.0379889
$490$	0	0
$491$	39.9065	1.80096	0.900478	−	0.434902i	$-0.143217\pi$
$491$	39.9065	1.80096	0.900478	+	0.434902i	$0.143217\pi$
$492$	0	0
$493$	7.06644	0.318256
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−5.52311	−0.247746
$498$	0	0
$499$	27.3246	1.22322	0.611610	−	0.791160i	$-0.290522\pi$
$499$	27.3246	1.22322	0.611610	+	0.791160i	$0.290522\pi$
$500$	0	0
$501$	−23.1955	−1.03630
$502$	0	0
$503$	−1.40171	−0.0624991	−0.0312495	−	0.999512i	$-0.509949\pi$
$503$	−1.40171	−0.0624991	−0.0312495	+	0.999512i	$0.509949\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−30.2095	−1.34165
$508$	0	0
$509$	18.6585	0.827022	0.413511	−	0.910499i	$-0.364302\pi$
$509$	18.6585	0.827022	0.413511	+	0.910499i	$0.364302\pi$
$510$	0	0
$511$	−3.72928	−0.164974
$512$	0	0
$513$	32.5972	1.43920
$514$	0	0
$515$	0	0
$516$	0	0
$517$	3.68116	0.161897
$518$	0	0
$519$	24.6049	1.08004
$520$	0	0
$521$	−4.02791	−0.176466	−0.0882329	−	0.996100i	$-0.528122\pi$
$521$	−4.02791	−0.176466	−0.0882329	+	0.996100i	$0.528122\pi$
$522$	0	0
$523$	−38.4436	−1.68102	−0.840510	−	0.541796i	$-0.817744\pi$
$523$	−38.4436	−1.68102	−0.840510	+	0.541796i	$0.817744\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−6.74760	−0.293930
$528$	0	0
$529$	−9.09246	−0.395324
$530$	0	0
$531$	−0.0612237	−0.00265688
$532$	0	0
$533$	−42.4402	−1.83829
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−13.1387	−0.566976
$538$	0	0
$539$	−0.626198	−0.0269723
$540$	0	0
$541$	12.4846	0.536754	0.268377	−	0.963314i	$-0.413513\pi$
$541$	12.4846	0.536754	0.268377	+	0.963314i	$0.413513\pi$
$542$	0	0
$543$	24.8680	1.06719
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−37.7851	−1.61557	−0.807787	−	0.589474i	$-0.799335\pi$
$547$	−37.7851	−1.61557	−0.807787	+	0.589474i	$0.799335\pi$
$548$	0	0
$549$	0.735539	0.0313921
$550$	0	0
$551$	−50.3265	−2.14398
$552$	0	0
$553$	5.67243	0.241216
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−1.93545	−0.0820076	−0.0410038	−	0.999159i	$-0.513056\pi$
$557$	−1.93545	−0.0820076	−0.0410038	+	0.999159i	$0.513056\pi$
$558$	0	0
$559$	9.49521	0.401604
$560$	0	0
$561$	−0.989374	−0.0417714
$562$	0	0
$563$	29.8463	1.25787	0.628936	−	0.777457i	$-0.283491\pi$
$563$	29.8463	1.25787	0.628936	+	0.777457i	$0.283491\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	9.29862	0.390506
$568$	0	0
$569$	15.3449	0.643290	0.321645	−	0.946860i	$-0.395764\pi$
$569$	15.3449	0.643290	0.321645	+	0.946860i	$0.395764\pi$
$570$	0	0
$571$	35.8217	1.49909	0.749547	−	0.661952i	$-0.230272\pi$
$571$	35.8217	1.49909	0.749547	+	0.661952i	$0.230272\pi$
$572$	0	0
$573$	14.8324	0.619631
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−2.92482	−0.121762	−0.0608810	−	0.998145i	$-0.519391\pi$
$577$	−2.92482	−0.121762	−0.0608810	+	0.998145i	$0.519391\pi$
$578$	0	0
$579$	−39.2803	−1.63243
$580$	0	0
$581$	−17.4340	−0.723284
$582$	0	0
$583$	−4.24281	−0.175719
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−19.5756	−0.807972	−0.403986	−	0.914765i	$-0.632375\pi$
$587$	−19.5756	−0.807972	−0.403986	+	0.914765i	$0.632375\pi$
$588$	0	0
$589$	48.0558	1.98011
$590$	0	0
$591$	46.4402	1.91030
$592$	0	0
$593$	−8.00770	−0.328837	−0.164418	−	0.986391i	$-0.552575\pi$
$593$	−8.00770	−0.328837	−0.164418	+	0.986391i	$0.552575\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−39.5298	−1.61785
$598$	0	0
$599$	−29.3005	−1.19719	−0.598593	−	0.801053i	$-0.704273\pi$
$599$	−29.3005	−1.19719	−0.598593	+	0.801053i	$0.704273\pi$
$600$	0	0
$601$	21.3449	0.870675	0.435337	−	0.900267i	$-0.356629\pi$
$601$	21.3449	0.870675	0.435337	+	0.900267i	$0.356629\pi$
$602$	0	0
$603$	0.597250	0.0243219
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−9.53081	−0.386844	−0.193422	−	0.981116i	$-0.561959\pi$
$607$	−9.53081	−0.386844	−0.193422	+	0.981116i	$0.561959\pi$
$608$	0	0
$609$	−13.8786	−0.562389
$610$	0	0
$611$	32.2784	1.30584
$612$	0	0
$613$	9.75719	0.394089	0.197045	−	0.980395i	$-0.436866\pi$
$613$	9.75719	0.394089	0.197045	+	0.980395i	$0.436866\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	37.9267	1.52687	0.763436	−	0.645884i	$-0.223511\pi$
$617$	37.9267	1.52687	0.763436	+	0.645884i	$0.223511\pi$
$618$	0	0
$619$	41.9109	1.68454	0.842270	−	0.539056i	$-0.181219\pi$
$619$	41.9109	1.68454	0.842270	+	0.539056i	$0.181219\pi$
$620$	0	0
$621$	19.0308	0.763681
$622$	0	0
$623$	−14.2986	−0.572862
$624$	0	0
$625$	0	0
$626$	0	0
$627$	7.04623	0.281399
$628$	0	0
$629$	5.38150	0.214574
$630$	0	0
$631$	−8.42003	−0.335196	−0.167598	−	0.985855i	$-0.553601\pi$
$631$	−8.42003	−0.335196	−0.167598	+	0.985855i	$0.553601\pi$
$632$	0	0
$633$	26.7678	1.06393
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−5.49084	−0.217555
$638$	0	0
$639$	0.569343	0.0225229
$640$	0	0
$641$	−2.07707	−0.0820392	−0.0410196	−	0.999158i	$-0.513061\pi$
$641$	−2.07707	−0.0820392	−0.0410196	+	0.999158i	$0.513061\pi$
$642$	0	0
$643$	27.2480	1.07456	0.537279	−	0.843405i	$-0.319452\pi$
$643$	27.2480	1.07456	0.537279	+	0.843405i	$0.319452\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−12.3632	−0.486047	−0.243023	−	0.970020i	$-0.578139\pi$
$647$	−12.3632	−0.486047	−0.243023	+	0.970020i	$0.578139\pi$
$648$	0	0
$649$	0.371913	0.0145989
$650$	0	0
$651$	13.2524	0.519402
$652$	0	0
$653$	−37.3449	−1.46142	−0.730709	−	0.682690i	$-0.760810\pi$
$653$	−37.3449	−1.46142	−0.730709	+	0.682690i	$0.760810\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0.384428	0.0149980
$658$	0	0
$659$	−14.1772	−0.552266	−0.276133	−	0.961119i	$-0.589053\pi$
$659$	−14.1772	−0.552266	−0.276133	+	0.961119i	$0.589053\pi$
$660$	0	0
$661$	−1.76925	−0.0688160	−0.0344080	−	0.999408i	$-0.510955\pi$
$661$	−1.76925	−0.0688160	−0.0344080	+	0.999408i	$0.510955\pi$
$662$	0	0
$663$	−8.67536	−0.336923
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−29.3815	−1.13766
$668$	0	0
$669$	−12.1493	−0.469720
$670$	0	0
$671$	−4.46815	−0.172491
$672$	0	0
$673$	−4.05581	−0.156340	−0.0781701	−	0.996940i	$-0.524908\pi$
$673$	−4.05581	−0.156340	−0.0781701	+	0.996940i	$0.524908\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	9.37713	0.360392	0.180196	−	0.983631i	$-0.442327\pi$
$677$	9.37713	0.360392	0.180196	+	0.983631i	$0.442327\pi$
$678$	0	0
$679$	−10.1493	−0.389495
$680$	0	0
$681$	−4.89692	−0.187650
$682$	0	0
$683$	5.49521	0.210268	0.105134	−	0.994458i	$-0.466473\pi$
$683$	5.49521	0.210268	0.105134	+	0.994458i	$0.466473\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−32.8680	−1.25399
$688$	0	0
$689$	−37.2032	−1.41733
$690$	0	0
$691$	−3.03416	−0.115425	−0.0577125	−	0.998333i	$-0.518381\pi$
$691$	−3.03416	−0.115425	−0.0577125	+	0.998333i	$0.518381\pi$
$692$	0	0
$693$	0.0645508	0.00245208
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−6.93252	−0.262588
$698$	0	0
$699$	−19.4586	−0.735990
$700$	0	0
$701$	35.2234	1.33037	0.665186	−	0.746678i	$-0.268352\pi$
$701$	35.2234	1.33037	0.665186	+	0.746678i	$0.268352\pi$
$702$	0	0
$703$	−38.3265	−1.44551
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−9.64015	−0.362555
$708$	0	0
$709$	28.7187	1.07855	0.539276	−	0.842129i	$-0.318698\pi$
$709$	28.7187	1.07855	0.539276	+	0.842129i	$0.318698\pi$
$710$	0	0
$711$	−0.584735	−0.0219293
$712$	0	0
$713$	28.0558	1.05070
$714$	0	0
$715$	0	0
$716$	0	0
$717$	35.4942	1.32555
$718$	0	0
$719$	−8.60599	−0.320949	−0.160475	−	0.987040i	$-0.551302\pi$
$719$	−8.60599	−0.320949	−0.160475	+	0.987040i	$0.551302\pi$
$720$	0	0
$721$	−0.626198	−0.0233208
$722$	0	0
$723$	−6.56934	−0.244316
$724$	0	0
$725$	0	0
$726$	0	0
$727$	15.2803	0.566715	0.283358	−	0.959014i	$-0.408552\pi$
$727$	15.2803	0.566715	0.283358	+	0.959014i	$0.408552\pi$
$728$	0	0
$729$	26.0096	0.963318
$730$	0	0
$731$	1.55102	0.0573666
$732$	0	0
$733$	46.0235	1.69992	0.849959	−	0.526849i	$-0.176627\pi$
$733$	46.0235	1.69992	0.849959	+	0.526849i	$0.176627\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−3.62809	−0.133642
$738$	0	0
$739$	46.3467	1.70489	0.852446	−	0.522815i	$-0.175118\pi$
$739$	46.3467	1.70489	0.852446	+	0.522815i	$0.175118\pi$
$740$	0	0
$741$	61.7851	2.26973
$742$	0	0
$743$	−10.7755	−0.395315	−0.197658	−	0.980271i	$-0.563333\pi$
$743$	−10.7755	−0.395315	−0.197658	+	0.980271i	$0.563333\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	1.79716	0.0657546
$748$	0	0
$749$	0	0
$750$	0	0
$751$	2.76781	0.100999	0.0504995	−	0.998724i	$-0.483919\pi$
$751$	2.76781	0.100999	0.0504995	+	0.998724i	$0.483919\pi$
$752$	0	0
$753$	37.8709	1.38009
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−14.8401	−0.539371	−0.269686	−	0.962948i	$-0.586920\pi$
$757$	−14.8401	−0.539371	−0.269686	+	0.962948i	$0.586920\pi$
$758$	0	0
$759$	4.11371	0.149318
$760$	0	0
$761$	31.3169	1.13524	0.567619	−	0.823291i	$-0.307865\pi$
$761$	31.3169	1.13524	0.567619	+	0.823291i	$0.307865\pi$
$762$	0	0
$763$	−18.9248	−0.685125
$764$	0	0
$765$	0	0
$766$	0	0
$767$	3.26113	0.117753
$768$	0	0
$769$	8.92586	0.321875	0.160937	−	0.986965i	$-0.448548\pi$
$769$	8.92586	0.321875	0.160937	+	0.986965i	$0.448548\pi$
$770$	0	0
$771$	7.52311	0.270938
$772$	0	0
$773$	−36.7711	−1.32257	−0.661283	−	0.750136i	$-0.729988\pi$
$773$	−36.7711	−1.32257	−0.661283	+	0.750136i	$0.729988\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−10.5693	−0.379173
$778$	0	0
$779$	49.3728	1.76896
$780$	0	0
$781$	−3.45856	−0.123757
$782$	0	0
$783$	−40.2051	−1.43681
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−6.53707	−0.233021	−0.116511	−	0.993189i	$-0.537171\pi$
$787$	−6.53707	−0.233021	−0.116511	+	0.993189i	$0.537171\pi$
$788$	0	0
$789$	−20.1849	−0.718602
$790$	0	0
$791$	−1.04623	−0.0371996
$792$	0	0
$793$	−39.1791	−1.39129
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−7.82611	−0.277215	−0.138607	−	0.990347i	$-0.544263\pi$
$797$	−7.82611	−0.277215	−0.138607	+	0.990347i	$0.544263\pi$
$798$	0	0
$799$	5.27261	0.186531
$800$	0	0
$801$	1.47396	0.0520796
$802$	0	0
$803$	−2.33527	−0.0824099
$804$	0	0
$805$	0	0
$806$	0	0
$807$	12.4556	0.438459
$808$	0	0
$809$	38.4113	1.35047	0.675235	−	0.737603i	$-0.264042\pi$
$809$	38.4113	1.35047	0.675235	+	0.737603i	$0.264042\pi$
$810$	0	0
$811$	7.64015	0.268282	0.134141	−	0.990962i	$-0.457172\pi$
$811$	7.64015	0.268282	0.134141	+	0.990962i	$0.457172\pi$
$812$	0	0
$813$	−29.9634	−1.05086
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−11.0462	−0.386459
$818$	0	0
$819$	0.566016	0.0197782
$820$	0	0
$821$	2.56165	0.0894021	0.0447011	−	0.999000i	$-0.485766\pi$
$821$	2.56165	0.0894021	0.0447011	+	0.999000i	$0.485766\pi$
$822$	0	0
$823$	−0.784248	−0.0273372	−0.0136686	−	0.999907i	$-0.504351\pi$
$823$	−0.784248	−0.0273372	−0.0136686	+	0.999907i	$0.504351\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−7.28904	−0.253465	−0.126732	−	0.991937i	$-0.540449\pi$
$827$	−7.28904	−0.253465	−0.126732	+	0.991937i	$0.540449\pi$
$828$	0	0
$829$	−11.0708	−0.384505	−0.192253	−	0.981345i	$-0.561579\pi$
$829$	−11.0708	−0.384505	−0.192253	+	0.981345i	$0.561579\pi$
$830$	0	0
$831$	−33.0741	−1.14733
$832$	0	0
$833$	−0.896916	−0.0310763
$834$	0	0
$835$	0	0
$836$	0	0
$837$	38.3911	1.32699
$838$	0	0
$839$	−5.55976	−0.191944	−0.0959721	−	0.995384i	$-0.530596\pi$
$839$	−5.55976	−0.191944	−0.0959721	+	0.995384i	$0.530596\pi$
$840$	0	0
$841$	33.0722	1.14042
$842$	0	0
$843$	8.10015	0.278984
$844$	0	0
$845$	0	0
$846$	0	0
$847$	10.6079	0.364491
$848$	0	0
$849$	−23.9278	−0.821198
$850$	0	0
$851$	−22.3757	−0.767029
$852$	0	0
$853$	−16.0804	−0.550582	−0.275291	−	0.961361i	$-0.588774\pi$
$853$	−16.0804	−0.550582	−0.275291	+	0.961361i	$0.588774\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−1.58767	−0.0542336	−0.0271168	−	0.999632i	$-0.508633\pi$
$857$	−1.58767	−0.0542336	−0.0271168	+	0.999632i	$0.508633\pi$
$858$	0	0
$859$	4.94171	0.168609	0.0843044	−	0.996440i	$-0.473133\pi$
$859$	4.94171	0.168609	0.0843044	+	0.996440i	$0.473133\pi$
$860$	0	0
$861$	13.6156	0.464017
$862$	0	0
$863$	37.6647	1.28212	0.641061	−	0.767490i	$-0.278494\pi$
$863$	37.6647	1.28212	0.641061	+	0.767490i	$0.278494\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	28.5294	0.968908
$868$	0	0
$869$	3.55206	0.120495
$870$	0	0
$871$	−31.8130	−1.07794
$872$	0	0
$873$	1.04623	0.0354095
$874$	0	0
$875$	0	0
$876$	0	0
$877$	3.66473	0.123749	0.0618746	−	0.998084i	$-0.480292\pi$
$877$	3.66473	0.123749	0.0618746	+	0.998084i	$0.480292\pi$
$878$	0	0
$879$	20.8324	0.702658
$880$	0	0
$881$	−43.4373	−1.46344	−0.731720	−	0.681605i	$-0.761282\pi$
$881$	−43.4373	−1.46344	−0.731720	+	0.681605i	$0.761282\pi$
$882$	0	0
$883$	47.3853	1.59464	0.797321	−	0.603556i	$-0.206250\pi$
$883$	47.3853	1.59464	0.797321	+	0.603556i	$0.206250\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−21.3169	−0.715753	−0.357877	−	0.933769i	$-0.616499\pi$
$887$	−21.3169	−0.715753	−0.357877	+	0.933769i	$0.616499\pi$
$888$	0	0
$889$	−21.2803	−0.713718
$890$	0	0
$891$	5.82278	0.195071
$892$	0	0
$893$	−37.5510	−1.25660
$894$	0	0
$895$	0	0
$896$	0	0
$897$	36.0712	1.20438
$898$	0	0
$899$	−59.2716	−1.97682
$900$	0	0
$901$	−6.07707	−0.202456
$902$	0	0
$903$	−3.04623	−0.101372
$904$	0	0
$905$	0	0
$906$	0	0
$907$	18.9325	0.628644	0.314322	−	0.949316i	$-0.398223\pi$
$907$	18.9325	0.628644	0.314322	+	0.949316i	$0.398223\pi$
$908$	0	0
$909$	0.993743	0.0329604
$910$	0	0
$911$	−12.6705	−0.419794	−0.209897	−	0.977724i	$-0.567313\pi$
$911$	−12.6705	−0.419794	−0.209897	+	0.977724i	$0.567313\pi$
$912$	0	0
$913$	−10.9171	−0.361304
$914$	0	0
$915$	0	0
$916$	0	0
$917$	9.91087	0.327286
$918$	0	0
$919$	22.8690	0.754379	0.377190	−	0.926136i	$-0.376891\pi$
$919$	22.8690	0.754379	0.377190	+	0.926136i	$0.376891\pi$
$920$	0	0
$921$	−36.9681	−1.21814
$922$	0	0
$923$	−30.3265	−0.998210
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0.0645508	0.00212013
$928$	0	0
$929$	50.4190	1.65419	0.827097	−	0.562060i	$-0.189991\pi$
$929$	50.4190	1.65419	0.827097	+	0.562060i	$0.189991\pi$
$930$	0	0
$931$	6.38776	0.209350
$932$	0	0
$933$	39.6435	1.29787
$934$	0	0
$935$	0	0
$936$	0	0
$937$	47.9344	1.56595	0.782974	−	0.622054i	$-0.213702\pi$
$937$	47.9344	1.56595	0.782974	+	0.622054i	$0.213702\pi$
$938$	0	0
$939$	−21.9923	−0.717692
$940$	0	0
$941$	59.9667	1.95486	0.977429	−	0.211264i	$-0.0677580\pi$
$941$	59.9667	1.95486	0.977429	+	0.211264i	$0.0677580\pi$
$942$	0	0
$943$	28.8247	0.938660
$944$	0	0
$945$	0	0
$946$	0	0
$947$	27.5231	0.894381	0.447191	−	0.894439i	$-0.352425\pi$
$947$	27.5231	0.894381	0.447191	+	0.894439i	$0.352425\pi$
$948$	0	0
$949$	−20.4769	−0.664708
$950$	0	0
$951$	44.9604	1.45794
$952$	0	0
$953$	−0.840061	−0.0272123	−0.0136061	−	0.999907i	$-0.504331\pi$
$953$	−0.840061	−0.0272123	−0.0136061	+	0.999907i	$0.504331\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−8.69075	−0.280932
$958$	0	0
$959$	3.45856	0.111683
$960$	0	0
$961$	25.5972	0.825718
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−31.8988	−1.02580	−0.512898	−	0.858449i	$-0.671428\pi$
$967$	−31.8988	−1.02580	−0.512898	+	0.858449i	$0.671428\pi$
$968$	0	0
$969$	10.0925	0.324216
$970$	0	0
$971$	28.4157	0.911902	0.455951	−	0.890005i	$-0.349299\pi$
$971$	28.4157	0.911902	0.455951	+	0.890005i	$0.349299\pi$
$972$	0	0
$973$	20.4157	0.654496
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−9.55102	−0.305564	−0.152782	−	0.988260i	$-0.548823\pi$
$977$	−9.55102	−0.305564	−0.152782	+	0.988260i	$0.548823\pi$
$978$	0	0
$979$	−8.95377	−0.286164
$980$	0	0
$981$	1.95084	0.0622856
$982$	0	0
$983$	0.0443400	0.00141423	0.000707113	−	1.00000i	$-0.499775\pi$
$983$	0.0443400	0.00141423	0.000707113		1.00000i	$0.499775\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−10.3555	−0.329619
$988$	0	0
$989$	−6.44898	−0.205066
$990$	0	0
$991$	−13.9913	−0.444447	−0.222224	−	0.974996i	$-0.571331\pi$
$991$	−13.9913	−0.444447	−0.222224	+	0.974996i	$0.571331\pi$
$992$	0	0
$993$	4.72635	0.149986
$994$	0	0
$995$	0	0
$996$	0	0
$997$	19.0419	0.603062	0.301531	−	0.953456i	$-0.402502\pi$
$997$	19.0419	0.603062	0.301531	+	0.953456i	$0.402502\pi$
$998$	0	0
$999$	−30.6185	−0.968727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.a.t.1.1		3
4.3	odd	2		2800.2.a.bq.1.3		3
5.2	odd	4		280.2.g.b.169.5	yes	6
5.3	odd	4		280.2.g.b.169.2	✓	6
5.4	even	2		1400.2.a.s.1.3		3
7.6	odd	2		9800.2.a.cd.1.3		3
15.2	even	4		2520.2.t.g.1009.3		6
15.8	even	4		2520.2.t.g.1009.4		6
20.3	even	4		560.2.g.f.449.5		6
20.7	even	4		560.2.g.f.449.2		6
20.19	odd	2		2800.2.a.br.1.1		3
35.13	even	4		1960.2.g.c.1569.5		6
35.27	even	4		1960.2.g.c.1569.2		6
35.34	odd	2		9800.2.a.cg.1.1		3
40.3	even	4		2240.2.g.m.449.2		6
40.13	odd	4		2240.2.g.l.449.5		6
40.27	even	4		2240.2.g.m.449.5		6
40.37	odd	4		2240.2.g.l.449.2		6
60.23	odd	4		5040.2.t.y.1009.4		6
60.47	odd	4		5040.2.t.y.1009.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.g.b.169.2	✓	6	5.3	odd	4
280.2.g.b.169.5	yes	6	5.2	odd	4
560.2.g.f.449.2		6	20.7	even	4
560.2.g.f.449.5		6	20.3	even	4
1400.2.a.s.1.3		3	5.4	even	2
1400.2.a.t.1.1		3	1.1	even	1	trivial
1960.2.g.c.1569.2		6	35.27	even	4
1960.2.g.c.1569.5		6	35.13	even	4
2240.2.g.l.449.2		6	40.37	odd	4
2240.2.g.l.449.5		6	40.13	odd	4
2240.2.g.m.449.2		6	40.3	even	4
2240.2.g.m.449.5		6	40.27	even	4
2520.2.t.g.1009.3		6	15.2	even	4
2520.2.t.g.1009.4		6	15.8	even	4
2800.2.a.bq.1.3		3	4.3	odd	2
2800.2.a.br.1.1		3	20.19	odd	2
5040.2.t.y.1009.3		6	60.47	odd	4
5040.2.t.y.1009.4		6	60.23	odd	4
9800.2.a.cd.1.3		3	7.6	odd	2
9800.2.a.cg.1.1		3	35.34	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.a (trivial)

\(f(q)\)	\(=\)	\(q-1.76156 q^{3} -1.00000 q^{7} +0.103084 q^{9} +O(q^{10})\)	\(q-1.76156 q^{3} -1.00000 q^{7} +0.103084 q^{9} -0.626198 q^{11} -5.49084 q^{13} -0.896916 q^{17} +6.38776 q^{19} +1.76156 q^{21} +3.72928 q^{23} +5.10308 q^{27} -7.87859 q^{29} +7.52311 q^{31} +1.10308 q^{33} -6.00000 q^{37} +9.67243 q^{39} +7.72928 q^{41} -1.72928 q^{43} -5.87859 q^{47} +1.00000 q^{49} +1.57997 q^{51} +6.77551 q^{53} -11.2524 q^{57} -0.593923 q^{59} +7.13536 q^{61} -0.103084 q^{63} +5.79383 q^{67} -6.56934 q^{69} +5.52311 q^{71} +3.72928 q^{73} +0.626198 q^{77} -5.67243 q^{79} -9.29862 q^{81} +17.4340 q^{83} +13.8786 q^{87} +14.2986 q^{89} +5.49084 q^{91} -13.2524 q^{93} +10.1493 q^{97} -0.0645508 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{3} - 3 q^{7} + 4 q^{9}+O(q^{10}) \) 3 * q + q^3 - 3 * q^7 + 4 * q^9	\( 3 q + q^{3} - 3 q^{7} + 4 q^{9} + 7 q^{11} - 5 q^{13} + q^{17} + 4 q^{19} - q^{21} + 6 q^{23} + 19 q^{27} + 3 q^{29} + 10 q^{31} + 7 q^{33} - 18 q^{37} - 5 q^{39} + 18 q^{41} + 9 q^{47} + 3 q^{49} + 21 q^{51} - 10 q^{53} - 16 q^{57} + 6 q^{59} + 24 q^{61} - 4 q^{63} + 10 q^{67} + 18 q^{69} + 4 q^{71} + 6 q^{73} - 7 q^{77} + 17 q^{79} + 15 q^{81} + 12 q^{83} + 15 q^{87} + 5 q^{91} - 22 q^{93} + 9 q^{97} + 2 q^{99}+O(q^{100}) \) 3 * q + q^3 - 3 * q^7 + 4 * q^9 + 7 * q^11 - 5 * q^13 + q^17 + 4 * q^19 - q^21 + 6 * q^23 + 19 * q^27 + 3 * q^29 + 10 * q^31 + 7 * q^33 - 18 * q^37 - 5 * q^39 + 18 * q^41 + 9 * q^47 + 3 * q^49 + 21 * q^51 - 10 * q^53 - 16 * q^57 + 6 * q^59 + 24 * q^61 - 4 * q^63 + 10 * q^67 + 18 * q^69 + 4 * q^71 + 6 * q^73 - 7 * q^77 + 17 * q^79 + 15 * q^81 + 12 * q^83 + 15 * q^87 + 5 * q^91 - 22 * q^93 + 9 * q^97 + 2 * q^99

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