LMFDB - Embedded newform 3249.2.a.t.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3249,2,Mod(1,3249)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3249, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3249.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3249 = 3^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3249.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:	$25.9433956167$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.564.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 3 $ x^3 - x^2 - 5*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.08613$ of defining polynomial
Character	$\chi$	$=$	3249.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.08613 q^{2} +2.35194 q^{4} -1.35194 q^{5} +0.351939 q^{7} +0.734191 q^{8} +O(q^{10})$	$q+2.08613 q^{2} +2.35194 q^{4} -1.35194 q^{5} +0.351939 q^{7} +0.734191 q^{8} -2.82032 q^{10} -5.52420 q^{11} +5.17226 q^{13} +0.734191 q^{14} -3.17226 q^{16} -3.17968 q^{20} -11.5242 q^{22} -8.82032 q^{23} -3.17226 q^{25} +10.7900 q^{26} +0.827740 q^{28} +2.70388 q^{29} +0.524200 q^{31} -8.08613 q^{32} -0.475800 q^{35} +1.00000 q^{37} -0.992582 q^{40} -2.70388 q^{41} -6.52420 q^{43} -12.9926 q^{44} -18.4003 q^{46} +6.00000 q^{47} -6.87614 q^{49} -6.61775 q^{50} +12.1648 q^{52} -4.05582 q^{53} +7.46838 q^{55} +0.258391 q^{56} +5.64064 q^{58} -5.52420 q^{59} -1.87614 q^{61} +1.09355 q^{62} -10.5242 q^{64} -6.99258 q^{65} -11.9926 q^{67} -0.992582 q^{70} +5.04840 q^{71} +7.70388 q^{73} +2.08613 q^{74} -1.94418 q^{77} -7.82032 q^{79} +4.28870 q^{80} -5.64064 q^{82} -8.34452 q^{83} -13.6103 q^{86} -4.05582 q^{88} -4.64806 q^{89} +1.82032 q^{91} -20.7449 q^{92} +12.5168 q^{94} +13.8129 q^{97} -14.3445 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 5 q^{4} - 2 q^{5} - q^{7} - 3 q^{8}+O(q^{10}) $ 3 * q - q^2 + 5 * q^4 - 2 * q^5 - q^7 - 3 * q^8	$ 3 q - q^{2} + 5 q^{4} - 2 q^{5} - q^{7} - 3 q^{8} + 4 q^{10} + q^{13} - 3 q^{14} + 5 q^{16} - 22 q^{20} - 18 q^{22} - 14 q^{23} + 5 q^{25} + 21 q^{26} + 17 q^{28} + 4 q^{29} - 15 q^{31} - 17 q^{32} - 18 q^{35} + 3 q^{37} + 24 q^{40} - 4 q^{41} - 3 q^{43} - 12 q^{44} - 20 q^{46} + 18 q^{47} - 2 q^{49} - 23 q^{50} - 5 q^{52} - 6 q^{53} + 12 q^{55} - 21 q^{56} - 8 q^{58} + 13 q^{61} + 23 q^{62} - 15 q^{64} + 6 q^{65} - 9 q^{67} + 24 q^{70} - 18 q^{71} + 19 q^{73} - q^{74} - 12 q^{77} - 11 q^{79} - 10 q^{80} + 8 q^{82} + 4 q^{83} - 17 q^{86} - 6 q^{88} - 16 q^{89} - 7 q^{91} + 2 q^{92} - 6 q^{94} + 2 q^{97} - 14 q^{98}+O(q^{100}) $ 3 * q - q^2 + 5 * q^4 - 2 * q^5 - q^7 - 3 * q^8 + 4 * q^10 + q^13 - 3 * q^14 + 5 * q^16 - 22 * q^20 - 18 * q^22 - 14 * q^23 + 5 * q^25 + 21 * q^26 + 17 * q^28 + 4 * q^29 - 15 * q^31 - 17 * q^32 - 18 * q^35 + 3 * q^37 + 24 * q^40 - 4 * q^41 - 3 * q^43 - 12 * q^44 - 20 * q^46 + 18 * q^47 - 2 * q^49 - 23 * q^50 - 5 * q^52 - 6 * q^53 + 12 * q^55 - 21 * q^56 - 8 * q^58 + 13 * q^61 + 23 * q^62 - 15 * q^64 + 6 * q^65 - 9 * q^67 + 24 * q^70 - 18 * q^71 + 19 * q^73 - q^74 - 12 * q^77 - 11 * q^79 - 10 * q^80 + 8 * q^82 + 4 * q^83 - 17 * q^86 - 6 * q^88 - 16 * q^89 - 7 * q^91 + 2 * q^92 - 6 * q^94 + 2 * q^97 - 14 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.08613	1.47512	0.737558	−	0.675283i	$-0.235979\pi$
$2$	2.08613	1.47512	0.737558	+	0.675283i	$0.235979\pi$
$3$	0	0
$3$	0	0
$4$	2.35194	1.17597
$5$	−1.35194	−0.604606	−0.302303	−	0.953212i	$-0.597755\pi$
$5$	−1.35194	−0.604606	−0.302303	+	0.953212i	$0.597755\pi$
$6$	0	0
$7$	0.351939	0.133021	0.0665103	−	0.997786i	$-0.478813\pi$
$7$	0.351939	0.133021	0.0665103	+	0.997786i	$0.478813\pi$
$8$	0.734191	0.259576
$9$	0	0
$10$	−2.82032	−0.891864
$11$	−5.52420	−1.66561	−0.832804	−	0.553567i	$-0.813266\pi$
$11$	−5.52420	−1.66561	−0.832804	+	0.553567i	$0.813266\pi$
$12$	0	0
$13$	5.17226	1.43453	0.717263	−	0.696802i	$-0.245394\pi$
$13$	5.17226	1.43453	0.717263	+	0.696802i	$0.245394\pi$
$14$	0.734191	0.196221
$15$	0	0
$16$	−3.17226	−0.793065
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	0	0
$19$	0	0
$20$	−3.17968	−0.710998
$21$	0	0
$22$	−11.5242	−2.45697
$23$	−8.82032	−1.83916	−0.919582	−	0.392898i	$-0.871473\pi$
$23$	−8.82032	−1.83916	−0.919582	+	0.392898i	$0.871473\pi$
$24$	0	0
$25$	−3.17226	−0.634452
$26$	10.7900	2.11609
$27$	0	0
$28$	0.827740	0.156428
$29$	2.70388	0.502098	0.251049	−	0.967974i	$-0.419225\pi$
$29$	2.70388	0.502098	0.251049	+	0.967974i	$0.419225\pi$
$30$	0	0
$31$	0.524200	0.0941490	0.0470745	−	0.998891i	$-0.485010\pi$
$31$	0.524200	0.0941490	0.0470745	+	0.998891i	$0.485010\pi$
$32$	−8.08613	−1.42944
$33$	0	0
$34$	0	0
$35$	−0.475800	−0.0804249
$36$	0	0
$37$	1.00000	0.164399	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	1.00000	0.164399	0.0821995	+	0.996616i	$0.473806\pi$
$38$	0	0
$39$	0	0
$40$	−0.992582	−0.156941
$41$	−2.70388	−0.422275	−0.211137	−	0.977456i	$-0.567717\pi$
$41$	−2.70388	−0.422275	−0.211137	+	0.977456i	$0.567717\pi$
$42$	0	0
$43$	−6.52420	−0.994931	−0.497466	−	0.867484i	$-0.665736\pi$
$43$	−6.52420	−0.994931	−0.497466	+	0.867484i	$0.665736\pi$
$44$	−12.9926	−1.95871
$45$	0	0
$46$	−18.4003	−2.71298
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	0	0
$49$	−6.87614	−0.982306
$50$	−6.61775	−0.935891
$51$	0	0
$52$	12.1648	1.68696
$53$	−4.05582	−0.557109	−0.278555	−	0.960420i	$-0.589855\pi$
$53$	−4.05582	−0.557109	−0.278555	+	0.960420i	$0.589855\pi$
$54$	0	0
$55$	7.46838	1.00704
$56$	0.258391	0.0345289
$57$	0	0
$58$	5.64064	0.740653
$59$	−5.52420	−0.719190	−0.359595	−	0.933109i	$-0.617085\pi$
$59$	−5.52420	−0.719190	−0.359595	+	0.933109i	$0.617085\pi$
$60$	0	0
$61$	−1.87614	−0.240215	−0.120107	−	0.992761i	$-0.538324\pi$
$61$	−1.87614	−0.240215	−0.120107	+	0.992761i	$0.538324\pi$
$62$	1.09355	0.138881
$63$	0	0
$64$	−10.5242	−1.31552
$65$	−6.99258	−0.867323
$66$	0	0
$67$	−11.9926	−1.46513	−0.732564	−	0.680699i	$-0.761676\pi$
$67$	−11.9926	−1.46513	−0.732564	+	0.680699i	$0.761676\pi$
$68$	0	0
$69$	0	0
$70$	−0.992582	−0.118636
$71$	5.04840	0.599135	0.299567	−	0.954075i	$-0.403158\pi$
$71$	5.04840	0.599135	0.299567	+	0.954075i	$0.403158\pi$
$72$	0	0
$73$	7.70388	0.901671	0.450835	−	0.892607i	$-0.351126\pi$
$73$	7.70388	0.901671	0.450835	+	0.892607i	$0.351126\pi$
$74$	2.08613	0.242508
$75$	0	0
$76$	0	0
$77$	−1.94418	−0.221560
$78$	0	0
$79$	−7.82032	−0.879855	−0.439927	−	0.898033i	$-0.644996\pi$
$79$	−7.82032	−0.879855	−0.439927	+	0.898033i	$0.644996\pi$
$80$	4.28870	0.479492
$81$	0	0
$82$	−5.64064	−0.622905
$83$	−8.34452	−0.915930	−0.457965	−	0.888970i	$-0.651422\pi$
$83$	−8.34452	−0.915930	−0.457965	+	0.888970i	$0.651422\pi$
$84$	0	0
$85$	0	0
$86$	−13.6103	−1.46764
$87$	0	0
$88$	−4.05582	−0.432352
$89$	−4.64806	−0.492693	−0.246347	−	0.969182i	$-0.579230\pi$
$89$	−4.64806	−0.492693	−0.246347	+	0.969182i	$0.579230\pi$
$90$	0	0
$91$	1.82032	0.190822
$92$	−20.7449	−2.16280
$93$	0	0
$94$	12.5168	1.29101
$95$	0	0
$96$	0	0
$97$	13.8129	1.40249	0.701244	−	0.712921i	$-0.252628\pi$
$97$	13.8129	1.40249	0.701244	+	0.712921i	$0.252628\pi$
$98$	−14.3445	−1.44902
$99$	0	0
$100$	−7.46096	−0.746096
$101$	2.34452	0.233289	0.116644	−	0.993174i	$-0.462786\pi$
$101$	2.34452	0.233289	0.116644	+	0.993174i	$0.462786\pi$
$102$	0	0
$103$	16.1042	1.58680	0.793398	−	0.608703i	$-0.208310\pi$
$103$	16.1042	1.58680	0.793398	+	0.608703i	$0.208310\pi$
$104$	3.79743	0.372368
$105$	0	0
$106$	−8.46096	−0.821801
$107$	−0.592243	−0.0572543	−0.0286272	−	0.999590i	$-0.509114\pi$
$107$	−0.592243	−0.0572543	−0.0286272	+	0.999590i	$0.509114\pi$
$108$	0	0
$109$	13.5800	1.30073	0.650365	−	0.759622i	$-0.274616\pi$
$109$	13.5800	1.30073	0.650365	+	0.759622i	$0.274616\pi$
$110$	15.5800	1.48550
$111$	0	0
$112$	−1.11644	−0.105494
$113$	−12.9926	−1.22224	−0.611120	−	0.791538i	$-0.709281\pi$
$113$	−12.9926	−1.22224	−0.611120	+	0.791538i	$0.709281\pi$
$114$	0	0
$115$	11.9245	1.11197
$116$	6.35936	0.590452
$117$	0	0
$118$	−11.5242	−1.06089
$119$	0	0
$120$	0	0
$121$	19.5168	1.77425
$122$	−3.91387	−0.354345
$123$	0	0
$124$	1.23289	0.110716
$125$	11.0484	0.988199
$126$	0	0
$127$	−10.7039	−0.949816	−0.474908	−	0.880036i	$-0.657519\pi$
$127$	−10.7039	−0.949816	−0.474908	+	0.880036i	$0.657519\pi$
$128$	−5.78259	−0.511114
$129$	0	0
$130$	−14.5874	−1.27940
$131$	3.29612	0.287983	0.143992	−	0.989579i	$-0.454006\pi$
$131$	3.29612	0.287983	0.143992	+	0.989579i	$0.454006\pi$
$132$	0	0
$133$	0	0
$134$	−25.0181	−2.16123
$135$	0	0
$136$	0	0
$137$	−17.0484	−1.45654	−0.728272	−	0.685289i	$-0.759676\pi$
$137$	−17.0484	−1.45654	−0.728272	+	0.685289i	$0.759676\pi$
$138$	0	0
$139$	−17.9320	−1.52097	−0.760484	−	0.649356i	$-0.775038\pi$
$139$	−17.9320	−1.52097	−0.760484	+	0.649356i	$0.775038\pi$
$140$	−1.11905	−0.0945773
$141$	0	0
$142$	10.5316	0.883794
$143$	−28.5726	−2.38936
$144$	0	0
$145$	−3.65548	−0.303571
$146$	16.0713	1.33007
$147$	0	0
$148$	2.35194	0.193328
$149$	−1.94418	−0.159274	−0.0796368	−	0.996824i	$-0.525376\pi$
$149$	−1.94418	−0.159274	−0.0796368	+	0.996824i	$0.525376\pi$
$150$	0	0
$151$	−13.6406	−1.11006	−0.555030	−	0.831830i	$-0.687293\pi$
$151$	−13.6406	−1.11006	−0.555030	+	0.831830i	$0.687293\pi$
$152$	0	0
$153$	0	0
$154$	−4.05582	−0.326827
$155$	−0.708686	−0.0569230
$156$	0	0
$157$	16.6406	1.32807	0.664034	−	0.747702i	$-0.268843\pi$
$157$	16.6406	1.32807	0.664034	+	0.747702i	$0.268843\pi$
$158$	−16.3142	−1.29789
$159$	0	0
$160$	10.9320	0.864247
$161$	−3.10422	−0.244647
$162$	0	0
$163$	−1.99258	−0.156071	−0.0780355	−	0.996951i	$-0.524865\pi$
$163$	−1.99258	−0.156071	−0.0780355	+	0.996951i	$0.524865\pi$
$164$	−6.35936	−0.496582
$165$	0	0
$166$	−17.4078	−1.35110
$167$	2.58744	0.200222	0.100111	−	0.994976i	$-0.468080\pi$
$167$	2.58744	0.200222	0.100111	+	0.994976i	$0.468080\pi$
$168$	0	0
$169$	13.7523	1.05787
$170$	0	0
$171$	0	0
$172$	−15.3445	−1.17001
$173$	17.6406	1.34119	0.670597	−	0.741822i	$-0.266038\pi$
$173$	17.6406	1.34119	0.670597	+	0.741822i	$0.266038\pi$
$174$	0	0
$175$	−1.11644	−0.0843951
$176$	17.5242	1.32094
$177$	0	0
$178$	−9.69646	−0.726780
$179$	2.22808	0.166534	0.0832672	−	0.996527i	$-0.473465\pi$
$179$	2.22808	0.166534	0.0832672	+	0.996527i	$0.473465\pi$
$180$	0	0
$181$	−9.46838	−0.703779	−0.351890	−	0.936041i	$-0.614461\pi$
$181$	−9.46838	−0.703779	−0.351890	+	0.936041i	$0.614461\pi$
$182$	3.79743	0.281484
$183$	0	0
$184$	−6.47580	−0.477402
$185$	−1.35194	−0.0993965
$186$	0	0
$187$	0	0
$188$	14.1116	1.02920
$189$	0	0
$190$	0	0
$191$	22.5726	1.63330	0.816648	−	0.577136i	$-0.195830\pi$
$191$	22.5726	1.63330	0.816648	+	0.577136i	$0.195830\pi$
$192$	0	0
$193$	13.8761	0.998826	0.499413	−	0.866364i	$-0.333549\pi$
$193$	13.8761	0.998826	0.499413	+	0.866364i	$0.333549\pi$
$194$	28.8155	2.06883
$195$	0	0
$196$	−16.1723	−1.15516
$197$	−8.30354	−0.591603	−0.295801	−	0.955249i	$-0.595587\pi$
$197$	−8.30354	−0.591603	−0.295801	+	0.955249i	$0.595587\pi$
$198$	0	0
$199$	−6.88356	−0.487962	−0.243981	−	0.969780i	$-0.578454\pi$
$199$	−6.88356	−0.487962	−0.243981	+	0.969780i	$0.578454\pi$
$200$	−2.32905	−0.164688
$201$	0	0
$202$	4.89098	0.344128
$203$	0.951601	0.0667893
$204$	0	0
$205$	3.65548	0.255310
$206$	33.5955	2.34071
$207$	0	0
$208$	−16.4078	−1.13767
$209$	0	0
$210$	0	0
$211$	8.63583	0.594515	0.297258	−	0.954797i	$-0.403928\pi$
$211$	8.63583	0.594515	0.297258	+	0.954797i	$0.403928\pi$
$212$	−9.53904	−0.655144
$213$	0	0
$214$	−1.23550	−0.0844568
$215$	8.82032	0.601541
$216$	0	0
$217$	0.184486	0.0125238
$218$	28.3297	1.91873
$219$	0	0
$220$	17.5652	1.18424
$221$	0	0
$222$	0	0
$223$	−12.2765	−0.822094	−0.411047	−	0.911614i	$-0.634837\pi$
$223$	−12.2765	−0.822094	−0.411047	+	0.911614i	$0.634837\pi$
$224$	−2.84583	−0.190145
$225$	0	0
$226$	−27.1042	−1.80295
$227$	0.475800	0.0315800	0.0157900	−	0.999875i	$-0.494974\pi$
$227$	0.475800	0.0315800	0.0157900	+	0.999875i	$0.494974\pi$
$228$	0	0
$229$	−5.17226	−0.341793	−0.170896	−	0.985289i	$-0.554666\pi$
$229$	−5.17226	−0.341793	−0.170896	+	0.985289i	$0.554666\pi$
$230$	24.8761	1.64028
$231$	0	0
$232$	1.98516	0.130332
$233$	10.6890	0.700262	0.350131	−	0.936701i	$-0.386137\pi$
$233$	10.6890	0.700262	0.350131	+	0.936701i	$0.386137\pi$
$234$	0	0
$235$	−8.11164	−0.529145
$236$	−12.9926	−0.845745
$237$	0	0
$238$	0	0
$239$	0.475800	0.0307770	0.0153885	−	0.999882i	$-0.495101\pi$
$239$	0.475800	0.0307770	0.0153885	+	0.999882i	$0.495101\pi$
$240$	0	0
$241$	0.640642	0.0412674	0.0206337	−	0.999787i	$-0.493432\pi$
$241$	0.640642	0.0412674	0.0206337	+	0.999787i	$0.493432\pi$
$242$	40.7145	2.61723
$243$	0	0
$244$	−4.41256	−0.282485
$245$	9.29612	0.593907
$246$	0	0
$247$	0	0
$248$	0.384863	0.0244388
$249$	0	0
$250$	23.0484	1.45771
$251$	5.04840	0.318652	0.159326	−	0.987226i	$-0.449068\pi$
$251$	5.04840	0.318652	0.159326	+	0.987226i	$0.449068\pi$
$252$	0	0
$253$	48.7252	3.06333
$254$	−22.3297	−1.40109
$255$	0	0
$256$	8.98516	0.561573
$257$	20.7449	1.29403	0.647014	−	0.762478i	$-0.276017\pi$
$257$	20.7449	1.29403	0.647014	+	0.762478i	$0.276017\pi$
$258$	0	0
$259$	0.351939	0.0218684
$260$	−16.4461	−1.01995
$261$	0	0
$262$	6.87614	0.424809
$263$	−17.0484	−1.05125	−0.525625	−	0.850717i	$-0.676168\pi$
$263$	−17.0484	−1.05125	−0.525625	+	0.850717i	$0.676168\pi$
$264$	0	0
$265$	5.48322	0.336831
$266$	0	0
$267$	0	0
$268$	−28.2058	−1.72294
$269$	9.10422	0.555094	0.277547	−	0.960712i	$-0.410479\pi$
$269$	9.10422	0.555094	0.277547	+	0.960712i	$0.410479\pi$
$270$	0	0
$271$	26.4413	1.60620	0.803098	−	0.595847i	$-0.203184\pi$
$271$	26.4413	1.60620	0.803098	+	0.595847i	$0.203184\pi$
$272$	0	0
$273$	0	0
$274$	−35.5652	−2.14857
$275$	17.5242	1.05675
$276$	0	0
$277$	26.1574	1.57165	0.785824	−	0.618451i	$-0.212239\pi$
$277$	26.1574	1.57165	0.785824	+	0.618451i	$0.212239\pi$
$278$	−37.4084	−2.24361
$279$	0	0
$280$	−0.349328	−0.0208764
$281$	−24.4003	−1.45560	−0.727801	−	0.685788i	$-0.759458\pi$
$281$	−24.4003	−1.45560	−0.727801	+	0.685788i	$0.759458\pi$
$282$	0	0
$283$	−0.344521	−0.0204796	−0.0102398	−	0.999948i	$-0.503259\pi$
$283$	−0.344521	−0.0204796	−0.0102398	+	0.999948i	$0.503259\pi$
$284$	11.8735	0.704564
$285$	0	0
$286$	−59.6062	−3.52459
$287$	−0.951601	−0.0561712
$288$	0	0
$289$	−17.0000	−1.00000
$290$	−7.62581	−0.447803
$291$	0	0
$292$	18.1191	1.06034
$293$	17.2813	1.00958	0.504792	−	0.863241i	$-0.331569\pi$
$293$	17.2813	1.00958	0.504792	+	0.863241i	$0.331569\pi$
$294$	0	0
$295$	7.46838	0.434826
$296$	0.734191	0.0426740
$297$	0	0
$298$	−4.05582	−0.234947
$299$	−45.6210	−2.63833
$300$	0	0
$301$	−2.29612	−0.132346
$302$	−28.4562	−1.63747
$303$	0	0
$304$	0	0
$305$	2.53643	0.145235
$306$	0	0
$307$	−8.87614	−0.506588	−0.253294	−	0.967389i	$-0.581514\pi$
$307$	−8.87614	−0.506588	−0.253294	+	0.967389i	$0.581514\pi$
$308$	−4.57260	−0.260548
$309$	0	0
$310$	−1.47841	−0.0839681
$311$	11.1648	0.633100	0.316550	−	0.948576i	$-0.397475\pi$
$311$	11.1648	0.633100	0.316550	+	0.948576i	$0.397475\pi$
$312$	0	0
$313$	−4.51678	−0.255304	−0.127652	−	0.991819i	$-0.540744\pi$
$313$	−4.51678	−0.255304	−0.127652	+	0.991819i	$0.540744\pi$
$314$	34.7145	1.95906
$315$	0	0
$316$	−18.3929	−1.03468
$317$	−5.00742	−0.281245	−0.140622	−	0.990063i	$-0.544910\pi$
$317$	−5.00742	−0.281245	−0.140622	+	0.990063i	$0.544910\pi$
$318$	0	0
$319$	−14.9368	−0.836298
$320$	14.2281	0.795374
$321$	0	0
$322$	−6.47580	−0.360882
$323$	0	0
$324$	0	0
$325$	−16.4078	−0.910139
$326$	−4.15678	−0.230223
$327$	0	0
$328$	−1.98516	−0.109612
$329$	2.11164	0.116418
$330$	0	0
$331$	10.1797	0.559526	0.279763	−	0.960069i	$-0.409744\pi$
$331$	10.1797	0.559526	0.279763	+	0.960069i	$0.409744\pi$
$332$	−19.6258	−1.07711
$333$	0	0
$334$	5.39773	0.295351
$335$	16.2132	0.885824
$336$	0	0
$337$	−23.5168	−1.28104	−0.640520	−	0.767941i	$-0.721281\pi$
$337$	−23.5168	−1.28104	−0.640520	+	0.767941i	$0.721281\pi$
$338$	28.6890	1.56048
$339$	0	0
$340$	0	0
$341$	−2.89578	−0.156815
$342$	0	0
$343$	−4.88356	−0.263687
$344$	−4.79001	−0.258260
$345$	0	0
$346$	36.8007	1.97842
$347$	−12.4758	−0.669736	−0.334868	−	0.942265i	$-0.608692\pi$
$347$	−12.4758	−0.669736	−0.334868	+	0.942265i	$0.608692\pi$
$348$	0	0
$349$	6.23550	0.333778	0.166889	−	0.985976i	$-0.446628\pi$
$349$	6.23550	0.333778	0.166889	+	0.985976i	$0.446628\pi$
$350$	−2.32905	−0.124493
$351$	0	0
$352$	44.6694	2.38089
$353$	−29.8081	−1.58652	−0.793262	−	0.608880i	$-0.791619\pi$
$353$	−29.8081	−1.58652	−0.793262	+	0.608880i	$0.791619\pi$
$354$	0	0
$355$	−6.82513	−0.362240
$356$	−10.9320	−0.579393
$357$	0	0
$358$	4.64806	0.245658
$359$	13.7523	0.725817	0.362909	−	0.931825i	$-0.381784\pi$
$359$	13.7523	0.725817	0.362909	+	0.931825i	$0.381784\pi$
$360$	0	0
$361$	0	0
$362$	−19.7523	−1.03816
$363$	0	0
$364$	4.28128	0.224400
$365$	−10.4152	−0.545155
$366$	0	0
$367$	18.5094	0.966181	0.483090	−	0.875570i	$-0.339514\pi$
$367$	18.5094	0.966181	0.483090	+	0.875570i	$0.339514\pi$
$368$	27.9804	1.45858
$369$	0	0
$370$	−2.82032	−0.146622
$371$	−1.42740	−0.0741070
$372$	0	0
$373$	−6.53162	−0.338194	−0.169097	−	0.985599i	$-0.554085\pi$
$373$	−6.53162	−0.338194	−0.169097	+	0.985599i	$0.554085\pi$
$374$	0	0
$375$	0	0
$376$	4.40515	0.227178
$377$	13.9852	0.720273
$378$	0	0
$379$	−24.8687	−1.27742	−0.638710	−	0.769447i	$-0.720532\pi$
$379$	−24.8687	−1.27742	−0.638710	+	0.769447i	$0.720532\pi$
$380$	0	0
$381$	0	0
$382$	47.0894	2.40930
$383$	−9.98036	−0.509972	−0.254986	−	0.966945i	$-0.582071\pi$
$383$	−9.98036	−0.509972	−0.254986	+	0.966945i	$0.582071\pi$
$384$	0	0
$385$	2.62842	0.133957
$386$	28.9474	1.47339
$387$	0	0
$388$	32.4871	1.64928
$389$	17.0894	0.866466	0.433233	−	0.901282i	$-0.357373\pi$
$389$	17.0894	0.866466	0.433233	+	0.901282i	$0.357373\pi$
$390$	0	0
$391$	0	0
$392$	−5.04840	−0.254983
$393$	0	0
$394$	−17.3223	−0.872683
$395$	10.5726	0.531965
$396$	0	0
$397$	−1.64325	−0.0824725	−0.0412363	−	0.999149i	$-0.513130\pi$
$397$	−1.64325	−0.0824725	−0.0412363	+	0.999149i	$0.513130\pi$
$398$	−14.3600	−0.719802
$399$	0	0
$400$	10.0632	0.503162
$401$	−7.35194	−0.367138	−0.183569	−	0.983007i	$-0.558765\pi$
$401$	−7.35194	−0.367138	−0.183569	+	0.983007i	$0.558765\pi$
$402$	0	0
$403$	2.71130	0.135059
$404$	5.51417	0.274340
$405$	0	0
$406$	1.98516	0.0985220
$407$	−5.52420	−0.273824
$408$	0	0
$409$	−2.07546	−0.102625	−0.0513125	−	0.998683i	$-0.516340\pi$
$409$	−2.07546	−0.102625	−0.0513125	+	0.998683i	$0.516340\pi$
$410$	7.62581	0.376612
$411$	0	0
$412$	37.8761	1.86602
$413$	−1.94418	−0.0956670
$414$	0	0
$415$	11.2813	0.553776
$416$	−41.8236	−2.05057
$417$	0	0
$418$	0	0
$419$	−8.22808	−0.401968	−0.200984	−	0.979595i	$-0.564414\pi$
$419$	−8.22808	−0.401968	−0.200984	+	0.979595i	$0.564414\pi$
$420$	0	0
$421$	−5.58002	−0.271953	−0.135977	−	0.990712i	$-0.543417\pi$
$421$	−5.58002	−0.271953	−0.135977	+	0.990712i	$0.543417\pi$
$422$	18.0155	0.876980
$423$	0	0
$424$	−2.97774	−0.144612
$425$	0	0
$426$	0	0
$427$	−0.660287	−0.0319535
$428$	−1.39292	−0.0673293
$429$	0	0
$430$	18.4003	0.887343
$431$	28.0968	1.35338	0.676688	−	0.736270i	$-0.263415\pi$
$431$	28.0968	1.35338	0.676688	+	0.736270i	$0.263415\pi$
$432$	0	0
$433$	−28.3323	−1.36156	−0.680782	−	0.732486i	$-0.738360\pi$
$433$	−28.3323	−1.36156	−0.680782	+	0.732486i	$0.738360\pi$
$434$	0.384863	0.0184740
$435$	0	0
$436$	31.9394	1.52962
$437$	0	0
$438$	0	0
$439$	10.3371	0.493363	0.246681	−	0.969097i	$-0.420660\pi$
$439$	10.3371	0.493363	0.246681	+	0.969097i	$0.420660\pi$
$440$	5.48322	0.261402
$441$	0	0
$442$	0	0
$443$	0.951601	0.0452119	0.0226060	−	0.999744i	$-0.492804\pi$
$443$	0.951601	0.0452119	0.0226060	+	0.999744i	$0.492804\pi$
$444$	0	0
$445$	6.28390	0.297885
$446$	−25.6103	−1.21268
$447$	0	0
$448$	−3.70388	−0.174992
$449$	−21.8639	−1.03182	−0.515911	−	0.856642i	$-0.672546\pi$
$449$	−21.8639	−1.03182	−0.515911	+	0.856642i	$0.672546\pi$
$450$	0	0
$451$	14.9368	0.703345
$452$	−30.5578	−1.43732
$453$	0	0
$454$	0.992582	0.0465842
$455$	−2.46096	−0.115372
$456$	0	0
$457$	21.7645	1.01810	0.509050	−	0.860737i	$-0.329997\pi$
$457$	21.7645	1.01810	0.509050	+	0.860737i	$0.329997\pi$
$458$	−10.7900	−0.504184
$459$	0	0
$460$	28.0458	1.30764
$461$	−21.1042	−0.982921	−0.491461	−	0.870900i	$-0.663537\pi$
$461$	−21.1042	−0.982921	−0.491461	+	0.870900i	$0.663537\pi$
$462$	0	0
$463$	5.16745	0.240152	0.120076	−	0.992765i	$-0.461686\pi$
$463$	5.16745	0.240152	0.120076	+	0.992765i	$0.461686\pi$
$464$	−8.57741	−0.398196
$465$	0	0
$466$	22.2987	1.03297
$467$	36.8007	1.70293	0.851466	−	0.524410i	$-0.175714\pi$
$467$	36.8007	1.70293	0.851466	+	0.524410i	$0.175714\pi$
$468$	0	0
$469$	−4.22066	−0.194892
$470$	−16.9219	−0.780550
$471$	0	0
$472$	−4.05582	−0.186684
$473$	36.0410	1.65717
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	0.992582	0.0453996
$479$	−14.5774	−0.666059	−0.333029	−	0.942916i	$-0.608071\pi$
$479$	−14.5774	−0.666059	−0.333029	+	0.942916i	$0.608071\pi$
$480$	0	0
$481$	5.17226	0.235835
$482$	1.33646	0.0608742
$483$	0	0
$484$	45.9023	2.08647
$485$	−18.6742	−0.847952
$486$	0	0
$487$	−7.04840	−0.319393	−0.159697	−	0.987166i	$-0.551052\pi$
$487$	−7.04840	−0.319393	−0.159697	+	0.987166i	$0.551052\pi$
$488$	−1.37744	−0.0623540
$489$	0	0
$490$	19.3929	0.876083
$491$	−10.4562	−0.471880	−0.235940	−	0.971768i	$-0.575817\pi$
$491$	−10.4562	−0.471880	−0.235940	+	0.971768i	$0.575817\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	−1.66290	−0.0746663
$497$	1.77673	0.0796972
$498$	0	0
$499$	4.47319	0.200247	0.100124	−	0.994975i	$-0.468076\pi$
$499$	4.47319	0.200247	0.100124	+	0.994975i	$0.468076\pi$
$500$	25.9852	1.16209
$501$	0	0
$502$	10.5316	0.470049
$503$	−23.0484	−1.02768	−0.513839	−	0.857887i	$-0.671777\pi$
$503$	−23.0484	−1.02768	−0.513839	+	0.857887i	$0.671777\pi$
$504$	0	0
$505$	−3.16965	−0.141048
$506$	101.647	4.51877
$507$	0	0
$508$	−25.1749	−1.11695
$509$	−26.3445	−1.16770	−0.583850	−	0.811861i	$-0.698454\pi$
$509$	−26.3445	−1.16770	−0.583850	+	0.811861i	$0.698454\pi$
$510$	0	0
$511$	2.71130	0.119941
$512$	30.3094	1.33950
$513$	0	0
$514$	43.2765	1.90884
$515$	−21.7719	−0.959386
$516$	0	0
$517$	−33.1452	−1.45772
$518$	0.734191	0.0322585
$519$	0	0
$520$	−5.13389	−0.225136
$521$	42.6332	1.86780	0.933898	−	0.357540i	$-0.116385\pi$
$521$	42.6332	1.86780	0.933898	+	0.357540i	$0.116385\pi$
$522$	0	0
$523$	11.8809	0.519518	0.259759	−	0.965674i	$-0.416357\pi$
$523$	11.8809	0.519518	0.259759	+	0.965674i	$0.416357\pi$
$524$	7.75228	0.338660
$525$	0	0
$526$	−35.5652	−1.55072
$527$	0	0
$528$	0	0
$529$	54.7981	2.38252
$530$	11.4387	0.496866
$531$	0	0
$532$	0	0
$533$	−13.9852	−0.605765
$534$	0	0
$535$	0.800677	0.0346163
$536$	−8.80485	−0.380311
$537$	0	0
$538$	18.9926	0.818828
$539$	37.9852	1.63614
$540$	0	0
$541$	33.9219	1.45842	0.729209	−	0.684291i	$-0.239888\pi$
$541$	33.9219	1.45842	0.729209	+	0.684291i	$0.239888\pi$
$542$	55.1600	2.36933
$543$	0	0
$544$	0	0
$545$	−18.3594	−0.786428
$546$	0	0
$547$	8.99519	0.384607	0.192303	−	0.981336i	$-0.438404\pi$
$547$	8.99519	0.384607	0.192303	+	0.981336i	$0.438404\pi$
$548$	−40.0968	−1.71285
$549$	0	0
$550$	36.5578	1.55883
$551$	0	0
$552$	0	0
$553$	−2.75228	−0.117039
$554$	54.5678	2.31836
$555$	0	0
$556$	−42.1749	−1.78861
$557$	−9.88836	−0.418983	−0.209492	−	0.977810i	$-0.567181\pi$
$557$	−9.88836	−0.418983	−0.209492	+	0.977810i	$0.567181\pi$
$558$	0	0
$559$	−33.7449	−1.42726
$560$	1.50936	0.0637822
$561$	0	0
$562$	−50.9023	−2.14718
$563$	−36.4413	−1.53582	−0.767909	−	0.640559i	$-0.778703\pi$
$563$	−36.4413	−1.53582	−0.767909	+	0.640559i	$0.778703\pi$
$564$	0	0
$565$	17.5652	0.738973
$566$	−0.718715	−0.0302099
$567$	0	0
$568$	3.70649	0.155521
$569$	−27.2717	−1.14329	−0.571644	−	0.820502i	$-0.693694\pi$
$569$	−27.2717	−1.14329	−0.571644	+	0.820502i	$0.693694\pi$
$570$	0	0
$571$	−16.1042	−0.673940	−0.336970	−	0.941515i	$-0.609402\pi$
$571$	−16.1042	−0.673940	−0.336970	+	0.941515i	$0.609402\pi$
$572$	−67.2010	−2.80982
$573$	0	0
$574$	−1.98516	−0.0828591
$575$	27.9804	1.16686
$576$	0	0
$577$	−27.3323	−1.13786	−0.568929	−	0.822387i	$-0.692642\pi$
$577$	−27.3323	−1.13786	−0.568929	+	0.822387i	$0.692642\pi$
$578$	−35.4642	−1.47512
$579$	0	0
$580$	−8.59746	−0.356990
$581$	−2.93676	−0.121838
$582$	0	0
$583$	22.4051	0.927926
$584$	5.65612	0.234052
$585$	0	0
$586$	36.0510	1.48925
$587$	−26.1016	−1.07733	−0.538664	−	0.842520i	$-0.681071\pi$
$587$	−26.1016	−1.07733	−0.538664	+	0.842520i	$0.681071\pi$
$588$	0	0
$589$	0	0
$590$	15.5800	0.641419
$591$	0	0
$592$	−3.17226	−0.130379
$593$	9.10422	0.373865	0.186933	−	0.982373i	$-0.440145\pi$
$593$	9.10422	0.373865	0.186933	+	0.982373i	$0.440145\pi$
$594$	0	0
$595$	0	0
$596$	−4.57260	−0.187301
$597$	0	0
$598$	−95.1713	−3.89185
$599$	−26.5874	−1.08633	−0.543167	−	0.839625i	$-0.682775\pi$
$599$	−26.5874	−1.08633	−0.543167	+	0.839625i	$0.682775\pi$
$600$	0	0
$601$	−31.2691	−1.27549	−0.637746	−	0.770247i	$-0.720133\pi$
$601$	−31.2691	−1.27549	−0.637746	+	0.770247i	$0.720133\pi$
$602$	−4.79001	−0.195226
$603$	0	0
$604$	−32.0820	−1.30540
$605$	−26.3855	−1.07272
$606$	0	0
$607$	−18.8687	−0.765858	−0.382929	−	0.923778i	$-0.625085\pi$
$607$	−18.8687	−0.765858	−0.382929	+	0.923778i	$0.625085\pi$
$608$	0	0
$609$	0	0
$610$	5.29131	0.214239
$611$	31.0336	1.25548
$612$	0	0
$613$	−19.2207	−0.776315	−0.388158	−	0.921593i	$-0.626888\pi$
$613$	−19.2207	−0.776315	−0.388158	+	0.921593i	$0.626888\pi$
$614$	−18.5168	−0.747276
$615$	0	0
$616$	−1.42740	−0.0575116
$617$	−22.5216	−0.906685	−0.453343	−	0.891336i	$-0.649769\pi$
$617$	−22.5216	−0.906685	−0.453343	+	0.891336i	$0.649769\pi$
$618$	0	0
$619$	5.99258	0.240862	0.120431	−	0.992722i	$-0.461572\pi$
$619$	5.99258	0.240862	0.120431	+	0.992722i	$0.461572\pi$
$620$	−1.66679	−0.0669398
$621$	0	0
$622$	23.2913	0.933897
$623$	−1.63583	−0.0655383
$624$	0	0
$625$	0.924538	0.0369815
$626$	−9.42259	−0.376603
$627$	0	0
$628$	39.1378	1.56177
$629$	0	0
$630$	0	0
$631$	−1.40034	−0.0557466	−0.0278733	−	0.999611i	$-0.508873\pi$
$631$	−1.40034	−0.0557466	−0.0278733	+	0.999611i	$0.508873\pi$
$632$	−5.74161	−0.228389
$633$	0	0
$634$	−10.4461	−0.414869
$635$	14.4710	0.574264
$636$	0	0
$637$	−35.5652	−1.40914
$638$	−31.1600	−1.23364
$639$	0	0
$640$	7.81771	0.309022
$641$	10.6071	0.418954	0.209477	−	0.977814i	$-0.432824\pi$
$641$	10.6071	0.418954	0.209477	+	0.977814i	$0.432824\pi$
$642$	0	0
$643$	−43.9926	−1.73490	−0.867449	−	0.497526i	$-0.834242\pi$
$643$	−43.9926	−1.73490	−0.867449	+	0.497526i	$0.834242\pi$
$644$	−7.30093	−0.287697
$645$	0	0
$646$	0	0
$647$	8.11164	0.318901	0.159451	−	0.987206i	$-0.449028\pi$
$647$	8.11164	0.318901	0.159451	+	0.987206i	$0.449028\pi$
$648$	0	0
$649$	30.5168	1.19789
$650$	−34.2287	−1.34256
$651$	0	0
$652$	−4.68643	−0.183535
$653$	−34.6890	−1.35749	−0.678744	−	0.734375i	$-0.737475\pi$
$653$	−34.6890	−1.35749	−0.678744	+	0.734375i	$0.737475\pi$
$654$	0	0
$655$	−4.45616	−0.174116
$656$	8.57741	0.334891
$657$	0	0
$658$	4.40515	0.171730
$659$	31.0436	1.20929	0.604643	−	0.796496i	$-0.293316\pi$
$659$	31.0436	1.20929	0.604643	+	0.796496i	$0.293316\pi$
$660$	0	0
$661$	14.6890	0.571338	0.285669	−	0.958328i	$-0.407784\pi$
$661$	14.6890	0.571338	0.285669	+	0.958328i	$0.407784\pi$
$662$	21.2361	0.825366
$663$	0	0
$664$	−6.12647	−0.237753
$665$	0	0
$666$	0	0
$667$	−23.8491	−0.923440
$668$	6.08549	0.235455
$669$	0	0
$670$	33.8229	1.30669
$671$	10.3642	0.400104
$672$	0	0
$673$	12.3567	0.476318	0.238159	−	0.971226i	$-0.423456\pi$
$673$	12.3567	0.476318	0.238159	+	0.971226i	$0.423456\pi$
$674$	−49.0591	−1.88968
$675$	0	0
$676$	32.3445	1.24402
$677$	32.7858	1.26006	0.630031	−	0.776570i	$-0.283042\pi$
$677$	32.7858	1.26006	0.630031	+	0.776570i	$0.283042\pi$
$678$	0	0
$679$	4.86130	0.186560
$680$	0	0
$681$	0	0
$682$	−6.04098	−0.231321
$683$	41.3977	1.58404	0.792020	−	0.610495i	$-0.209030\pi$
$683$	41.3977	1.58404	0.792020	+	0.610495i	$0.209030\pi$
$684$	0	0
$685$	23.0484	0.880634
$686$	−10.1877	−0.388970
$687$	0	0
$688$	20.6965	0.789045
$689$	−20.9777	−0.799188
$690$	0	0
$691$	−42.9368	−1.63339	−0.816696	−	0.577069i	$-0.804197\pi$
$691$	−42.9368	−1.63339	−0.816696	+	0.577069i	$0.804197\pi$
$692$	41.4897	1.57720
$693$	0	0
$694$	−26.0261	−0.987939
$695$	24.2429	0.919586
$696$	0	0
$697$	0	0
$698$	13.0081	0.492362
$699$	0	0
$700$	−2.62581	−0.0992461
$701$	2.07065	0.0782075	0.0391038	−	0.999235i	$-0.487550\pi$
$701$	2.07065	0.0782075	0.0391038	+	0.999235i	$0.487550\pi$
$702$	0	0
$703$	0	0
$704$	58.1378	2.19115
$705$	0	0
$706$	−62.1836	−2.34031
$707$	0.825129	0.0310322
$708$	0	0
$709$	−12.5652	−0.471895	−0.235948	−	0.971766i	$-0.575819\pi$
$709$	−12.5652	−0.471895	−0.235948	+	0.971766i	$0.575819\pi$
$710$	−14.2381	−0.534347
$711$	0	0
$712$	−3.41256	−0.127891
$713$	−4.62361	−0.173156
$714$	0	0
$715$	38.6284	1.44462
$716$	5.24030	0.195839
$717$	0	0
$718$	28.6890	1.07067
$719$	50.3100	1.87625	0.938124	−	0.346300i	$-0.112562\pi$
$719$	50.3100	1.87625	0.938124	+	0.346300i	$0.112562\pi$
$720$	0	0
$721$	5.66771	0.211076
$722$	0	0
$723$	0	0
$724$	−22.2691	−0.827623
$725$	−8.57741	−0.318557
$726$	0	0
$727$	−33.3345	−1.23631	−0.618154	−	0.786057i	$-0.712119\pi$
$727$	−33.3345	−1.23631	−0.618154	+	0.786057i	$0.712119\pi$
$728$	1.33646	0.0495326
$729$	0	0
$730$	−21.7274	−0.804168
$731$	0	0
$732$	0	0
$733$	−25.8129	−0.953421	−0.476711	−	0.879060i	$-0.658171\pi$
$733$	−25.8129	−0.953421	−0.476711	+	0.879060i	$0.658171\pi$
$734$	38.6129	1.42523
$735$	0	0
$736$	71.3223	2.62897
$737$	66.2494	2.44033
$738$	0	0
$739$	48.5604	1.78632	0.893161	−	0.449737i	$-0.148482\pi$
$739$	48.5604	1.78632	0.893161	+	0.449737i	$0.148482\pi$
$740$	−3.17968	−0.116887
$741$	0	0
$742$	−2.97774	−0.109316
$743$	14.6694	0.538168	0.269084	−	0.963117i	$-0.413279\pi$
$743$	14.6694	0.538168	0.269084	+	0.963117i	$0.413279\pi$
$744$	0	0
$745$	2.62842	0.0962977
$746$	−13.6258	−0.498876
$747$	0	0
$748$	0	0
$749$	−0.208434	−0.00761600
$750$	0	0
$751$	−7.74486	−0.282614	−0.141307	−	0.989966i	$-0.545130\pi$
$751$	−7.74486	−0.282614	−0.141307	+	0.989966i	$0.545130\pi$
$752$	−19.0336	−0.694083
$753$	0	0
$754$	29.1749	1.06249
$755$	18.4413	0.671148
$756$	0	0
$757$	−31.7252	−1.15307	−0.576536	−	0.817072i	$-0.695596\pi$
$757$	−31.7252	−1.15307	−0.576536	+	0.817072i	$0.695596\pi$
$758$	−51.8794	−1.88434
$759$	0	0
$760$	0	0
$761$	37.2255	1.34942	0.674711	−	0.738082i	$-0.264268\pi$
$761$	37.2255	1.34942	0.674711	+	0.738082i	$0.264268\pi$
$762$	0	0
$763$	4.77934	0.173024
$764$	53.0894	1.92071
$765$	0	0
$766$	−20.8203	−0.752269
$767$	−28.5726	−1.03170
$768$	0	0
$769$	−22.5290	−0.812417	−0.406208	−	0.913780i	$-0.633149\pi$
$769$	−22.5290	−0.812417	−0.406208	+	0.913780i	$0.633149\pi$
$770$	5.48322	0.197601
$771$	0	0
$772$	32.6358	1.17459
$773$	−51.1452	−1.83956	−0.919782	−	0.392429i	$-0.871635\pi$
$773$	−51.1452	−1.83956	−0.919782	+	0.392429i	$0.871635\pi$
$774$	0	0
$775$	−1.66290	−0.0597330
$776$	10.1413	0.364052
$777$	0	0
$778$	35.6507	1.27814
$779$	0	0
$780$	0	0
$781$	−27.8884	−0.997924
$782$	0	0
$783$	0	0
$784$	21.8129	0.779032
$785$	−22.4971	−0.802957
$786$	0	0
$787$	1.16745	0.0416152	0.0208076	−	0.999783i	$-0.493376\pi$
$787$	1.16745	0.0416152	0.0208076	+	0.999783i	$0.493376\pi$
$788$	−19.5294	−0.695707
$789$	0	0
$790$	22.0558	0.784711
$791$	−4.57260	−0.162583
$792$	0	0
$793$	−9.70388	−0.344595
$794$	−3.42804	−0.121657
$795$	0	0
$796$	−16.1897	−0.573829
$797$	37.1600	1.31628	0.658138	−	0.752897i	$-0.271344\pi$
$797$	37.1600	1.31628	0.658138	+	0.752897i	$0.271344\pi$
$798$	0	0
$799$	0	0
$800$	25.6513	0.906911
$801$	0	0
$802$	−15.3371	−0.541572
$803$	−42.5578	−1.50183
$804$	0	0
$805$	4.19671	0.147915
$806$	5.65612	0.199228
$807$	0	0
$808$	1.72133	0.0605560
$809$	−30.7597	−1.08145	−0.540727	−	0.841198i	$-0.681851\pi$
$809$	−30.7597	−1.08145	−0.540727	+	0.841198i	$0.681851\pi$
$810$	0	0
$811$	34.2084	1.20122	0.600610	−	0.799542i	$-0.294924\pi$
$811$	34.2084	1.20122	0.600610	+	0.799542i	$0.294924\pi$
$812$	2.23811	0.0785422
$813$	0	0
$814$	−11.5242	−0.403923
$815$	2.69385	0.0943614
$816$	0	0
$817$	0	0
$818$	−4.32968	−0.151384
$819$	0	0
$820$	8.59746	0.300236
$821$	−28.9219	−1.00938	−0.504691	−	0.863300i	$-0.668394\pi$
$821$	−28.9219	−1.00938	−0.504691	+	0.863300i	$0.668394\pi$
$822$	0	0
$823$	6.48061	0.225900	0.112950	−	0.993601i	$-0.463970\pi$
$823$	6.48061	0.225900	0.112950	+	0.993601i	$0.463970\pi$
$824$	11.8236	0.411894
$825$	0	0
$826$	−4.05582	−0.141120
$827$	−40.4562	−1.40680	−0.703399	−	0.710795i	$-0.748335\pi$
$827$	−40.4562	−1.40680	−0.703399	+	0.710795i	$0.748335\pi$
$828$	0	0
$829$	51.5019	1.78874	0.894368	−	0.447331i	$-0.147626\pi$
$829$	51.5019	1.78874	0.894368	+	0.447331i	$0.147626\pi$
$830$	23.5342	0.816885
$831$	0	0
$832$	−54.4339	−1.88716
$833$	0	0
$834$	0	0
$835$	−3.49806	−0.121055
$836$	0	0
$837$	0	0
$838$	−17.1648	−0.592950
$839$	33.6210	1.16073	0.580363	−	0.814358i	$-0.302911\pi$
$839$	33.6210	1.16073	0.580363	+	0.814358i	$0.302911\pi$
$840$	0	0
$841$	−21.6890	−0.747898
$842$	−11.6406	−0.401163
$843$	0	0
$844$	20.3110	0.699132
$845$	−18.5922	−0.639593
$846$	0	0
$847$	6.86872	0.236012
$848$	12.8661	0.441824
$849$	0	0
$850$	0	0
$851$	−8.82032	−0.302357
$852$	0	0
$853$	−50.6014	−1.73256	−0.866279	−	0.499561i	$-0.833495\pi$
$853$	−50.6014	−1.73256	−0.866279	+	0.499561i	$0.833495\pi$
$854$	−1.37744	−0.0471352
$855$	0	0
$856$	−0.434820	−0.0148618
$857$	−6.00000	−0.204956	−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000	−0.204956	−0.102478	+	0.994735i	$0.532677\pi$
$858$	0	0
$859$	22.0894	0.753680	0.376840	−	0.926278i	$-0.377011\pi$
$859$	22.0894	0.753680	0.376840	+	0.926278i	$0.377011\pi$
$860$	20.7449	0.707394
$861$	0	0
$862$	58.6136	1.99639
$863$	10.6890	0.363859	0.181930	−	0.983312i	$-0.441766\pi$
$863$	10.6890	0.363859	0.181930	+	0.983312i	$0.441766\pi$
$864$	0	0
$865$	−23.8491	−0.810893
$866$	−59.1049	−2.00846
$867$	0	0
$868$	0.433901	0.0147276
$869$	43.2010	1.46549
$870$	0	0
$871$	−62.0288	−2.10176
$872$	9.97033	0.337638
$873$	0	0
$874$	0	0
$875$	3.88836	0.131451
$876$	0	0
$877$	−31.1936	−1.05333	−0.526666	−	0.850072i	$-0.676558\pi$
$877$	−31.1936	−1.05333	−0.526666	+	0.850072i	$0.676558\pi$
$878$	21.5645	0.727768
$879$	0	0
$880$	−23.6917	−0.798645
$881$	9.69646	0.326682	0.163341	−	0.986570i	$-0.447773\pi$
$881$	9.69646	0.326682	0.163341	+	0.986570i	$0.447773\pi$
$882$	0	0
$883$	−38.1500	−1.28385	−0.641925	−	0.766767i	$-0.721864\pi$
$883$	−38.1500	−1.28385	−0.641925	+	0.766767i	$0.721864\pi$
$884$	0	0
$885$	0	0
$886$	1.98516	0.0666929
$887$	−9.98036	−0.335108	−0.167554	−	0.985863i	$-0.553587\pi$
$887$	−9.98036	−0.335108	−0.167554	+	0.985863i	$0.553587\pi$
$888$	0	0
$889$	−3.76711	−0.126345
$890$	13.1090	0.439415
$891$	0	0
$892$	−28.8735	−0.966757
$893$	0	0
$894$	0	0
$895$	−3.01223	−0.100688
$896$	−2.03512	−0.0679886
$897$	0	0
$898$	−45.6110	−1.52206
$899$	1.41737	0.0472720
$900$	0	0
$901$	0	0
$902$	31.1600	1.03752
$903$	0	0
$904$	−9.53904	−0.317264
$905$	12.8007	0.425509
$906$	0	0
$907$	−20.4658	−0.679555	−0.339777	−	0.940506i	$-0.610352\pi$
$907$	−20.4658	−0.679555	−0.339777	+	0.940506i	$0.610352\pi$
$908$	1.11905	0.0371371
$909$	0	0
$910$	−5.13389	−0.170187
$911$	−27.1696	−0.900171	−0.450085	−	0.892986i	$-0.648606\pi$
$911$	−27.1696	−0.900171	−0.450085	+	0.892986i	$0.648606\pi$
$912$	0	0
$913$	46.0968	1.52558
$914$	45.4036	1.50182
$915$	0	0
$916$	−12.1648	−0.401938
$917$	1.16003	0.0383077
$918$	0	0
$919$	33.1378	1.09311	0.546557	−	0.837422i	$-0.315938\pi$
$919$	33.1378	1.09311	0.546557	+	0.837422i	$0.315938\pi$
$920$	8.75489	0.288640
$921$	0	0
$922$	−44.0261	−1.44992
$923$	26.1116	0.859475
$924$	0	0
$925$	−3.17226	−0.104303
$926$	10.7800	0.354252
$927$	0	0
$928$	−21.8639	−0.717718
$929$	48.6332	1.59560	0.797802	−	0.602919i	$-0.205996\pi$
$929$	48.6332	1.59560	0.797802	+	0.602919i	$0.205996\pi$
$930$	0	0
$931$	0	0
$932$	25.1400	0.823487
$933$	0	0
$934$	76.7710	2.51202
$935$	0	0
$936$	0	0
$937$	−49.7252	−1.62445	−0.812226	−	0.583343i	$-0.801744\pi$
$937$	−49.7252	−1.62445	−0.812226	+	0.583343i	$0.801744\pi$
$938$	−8.80485	−0.287488
$939$	0	0
$940$	−19.0781	−0.622258
$941$	47.8491	1.55984	0.779918	−	0.625882i	$-0.215261\pi$
$941$	47.8491	1.55984	0.779918	+	0.625882i	$0.215261\pi$
$942$	0	0
$943$	23.8491	0.776633
$944$	17.5242	0.570364
$945$	0	0
$946$	75.1862	2.44451
$947$	−13.3929	−0.435211	−0.217606	−	0.976037i	$-0.569825\pi$
$947$	−13.3929	−0.435211	−0.217606	+	0.976037i	$0.569825\pi$
$948$	0	0
$949$	39.8465	1.29347
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−5.44874	−0.176502	−0.0882510	−	0.996098i	$-0.528128\pi$
$953$	−5.44874	−0.176502	−0.0882510	+	0.996098i	$0.528128\pi$
$954$	0	0
$955$	−30.5168	−0.987500
$956$	1.11905	0.0361928
$957$	0	0
$958$	−30.4104	−0.982514
$959$	−6.00000	−0.193750
$960$	0	0
$961$	−30.7252	−0.991136
$962$	10.7900	0.347884
$963$	0	0
$964$	1.50675	0.0485292
$965$	−18.7597	−0.603896
$966$	0	0
$967$	33.2132	1.06807	0.534033	−	0.845464i	$-0.320676\pi$
$967$	33.2132	1.06807	0.534033	+	0.845464i	$0.320676\pi$
$968$	14.3290	0.460553
$969$	0	0
$970$	−38.9568	−1.25083
$971$	−53.1304	−1.70503	−0.852517	−	0.522699i	$-0.824925\pi$
$971$	−53.1304	−1.70503	−0.852517	+	0.522699i	$0.824925\pi$
$972$	0	0
$973$	−6.31096	−0.202320
$974$	−14.7039	−0.471143
$975$	0	0
$976$	5.95160	0.190506
$977$	−10.9219	−0.349423	−0.174712	−	0.984620i	$-0.555899\pi$
$977$	−10.9219	−0.349423	−0.174712	+	0.984620i	$0.555899\pi$
$978$	0	0
$979$	25.6768	0.820635
$980$	21.8639	0.698417
$981$	0	0
$982$	−21.8129	−0.696078
$983$	−39.3881	−1.25629	−0.628143	−	0.778098i	$-0.716185\pi$
$983$	−39.3881	−1.25629	−0.628143	+	0.778098i	$0.716185\pi$
$984$	0	0
$985$	11.2259	0.357686
$986$	0	0
$987$	0	0
$988$	0	0
$989$	57.5455	1.82984
$990$	0	0
$991$	−14.3881	−0.457053	−0.228527	−	0.973538i	$-0.573391\pi$
$991$	−14.3881	−0.457053	−0.228527	+	0.973538i	$0.573391\pi$
$992$	−4.23875	−0.134580
$993$	0	0
$994$	3.70649	0.117563
$995$	9.30615	0.295025
$996$	0	0
$997$	35.9516	1.13860	0.569299	−	0.822130i	$-0.307215\pi$
$997$	35.9516	1.13860	0.569299	+	0.822130i	$0.307215\pi$
$998$	9.33166	0.295388
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3249.2.a.t.1.3		3
3.2	odd	2		1083.2.a.o.1.1		3
19.8	odd	6		171.2.f.b.64.3		6
19.12	odd	6		171.2.f.b.163.3		6
19.18	odd	2		3249.2.a.y.1.1		3
57.8	even	6		57.2.e.b.7.1	✓	6
57.50	even	6		57.2.e.b.49.1	yes	6
57.56	even	2		1083.2.a.l.1.3		3
76.27	even	6		2736.2.s.z.577.2		6
76.31	even	6		2736.2.s.z.1873.2		6
228.107	odd	6		912.2.q.l.49.2		6
228.179	odd	6		912.2.q.l.577.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.e.b.7.1	✓	6	57.8	even	6
57.2.e.b.49.1	yes	6	57.50	even	6
171.2.f.b.64.3		6	19.8	odd	6
171.2.f.b.163.3		6	19.12	odd	6
912.2.q.l.49.2		6	228.107	odd	6
912.2.q.l.577.2		6	228.179	odd	6
1083.2.a.l.1.3		3	57.56	even	2
1083.2.a.o.1.1		3	3.2	odd	2
2736.2.s.z.577.2		6	76.27	even	6
2736.2.s.z.1873.2		6	76.31	even	6
3249.2.a.t.1.3		3	1.1	even	1	trivial
3249.2.a.y.1.1		3	19.18	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:	\( N \)	\(=\)	\( 3249 = 3^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3249.a (trivial)

\(f(q)\)	\(=\)	\(q+2.08613 q^{2} +2.35194 q^{4} -1.35194 q^{5} +0.351939 q^{7} +0.734191 q^{8} +O(q^{10})\)	\(q+2.08613 q^{2} +2.35194 q^{4} -1.35194 q^{5} +0.351939 q^{7} +0.734191 q^{8} -2.82032 q^{10} -5.52420 q^{11} +5.17226 q^{13} +0.734191 q^{14} -3.17226 q^{16} -3.17968 q^{20} -11.5242 q^{22} -8.82032 q^{23} -3.17226 q^{25} +10.7900 q^{26} +0.827740 q^{28} +2.70388 q^{29} +0.524200 q^{31} -8.08613 q^{32} -0.475800 q^{35} +1.00000 q^{37} -0.992582 q^{40} -2.70388 q^{41} -6.52420 q^{43} -12.9926 q^{44} -18.4003 q^{46} +6.00000 q^{47} -6.87614 q^{49} -6.61775 q^{50} +12.1648 q^{52} -4.05582 q^{53} +7.46838 q^{55} +0.258391 q^{56} +5.64064 q^{58} -5.52420 q^{59} -1.87614 q^{61} +1.09355 q^{62} -10.5242 q^{64} -6.99258 q^{65} -11.9926 q^{67} -0.992582 q^{70} +5.04840 q^{71} +7.70388 q^{73} +2.08613 q^{74} -1.94418 q^{77} -7.82032 q^{79} +4.28870 q^{80} -5.64064 q^{82} -8.34452 q^{83} -13.6103 q^{86} -4.05582 q^{88} -4.64806 q^{89} +1.82032 q^{91} -20.7449 q^{92} +12.5168 q^{94} +13.8129 q^{97} -14.3445 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 5 q^{4} - 2 q^{5} - q^{7} - 3 q^{8}+O(q^{10}) \) 3 * q - q^2 + 5 * q^4 - 2 * q^5 - q^7 - 3 * q^8	\( 3 q - q^{2} + 5 q^{4} - 2 q^{5} - q^{7} - 3 q^{8} + 4 q^{10} + q^{13} - 3 q^{14} + 5 q^{16} - 22 q^{20} - 18 q^{22} - 14 q^{23} + 5 q^{25} + 21 q^{26} + 17 q^{28} + 4 q^{29} - 15 q^{31} - 17 q^{32} - 18 q^{35} + 3 q^{37} + 24 q^{40} - 4 q^{41} - 3 q^{43} - 12 q^{44} - 20 q^{46} + 18 q^{47} - 2 q^{49} - 23 q^{50} - 5 q^{52} - 6 q^{53} + 12 q^{55} - 21 q^{56} - 8 q^{58} + 13 q^{61} + 23 q^{62} - 15 q^{64} + 6 q^{65} - 9 q^{67} + 24 q^{70} - 18 q^{71} + 19 q^{73} - q^{74} - 12 q^{77} - 11 q^{79} - 10 q^{80} + 8 q^{82} + 4 q^{83} - 17 q^{86} - 6 q^{88} - 16 q^{89} - 7 q^{91} + 2 q^{92} - 6 q^{94} + 2 q^{97} - 14 q^{98}+O(q^{100}) \) 3 * q - q^2 + 5 * q^4 - 2 * q^5 - q^7 - 3 * q^8 + 4 * q^10 + q^13 - 3 * q^14 + 5 * q^16 - 22 * q^20 - 18 * q^22 - 14 * q^23 + 5 * q^25 + 21 * q^26 + 17 * q^28 + 4 * q^29 - 15 * q^31 - 17 * q^32 - 18 * q^35 + 3 * q^37 + 24 * q^40 - 4 * q^41 - 3 * q^43 - 12 * q^44 - 20 * q^46 + 18 * q^47 - 2 * q^49 - 23 * q^50 - 5 * q^52 - 6 * q^53 + 12 * q^55 - 21 * q^56 - 8 * q^58 + 13 * q^61 + 23 * q^62 - 15 * q^64 + 6 * q^65 - 9 * q^67 + 24 * q^70 - 18 * q^71 + 19 * q^73 - q^74 - 12 * q^77 - 11 * q^79 - 10 * q^80 + 8 * q^82 + 4 * q^83 - 17 * q^86 - 6 * q^88 - 16 * q^89 - 7 * q^91 + 2 * q^92 - 6 * q^94 + 2 * q^97 - 14 * q^98

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