LMFDB - Embedded newform 2832.2.a.t.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2832,2,Mod(1,2832)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2832, 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("2832.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2832 = 2^{4} \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2832.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:	$22.6136338524$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.254102$ of defining polynomial
Character	$\chi$	$=$	2832.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +1.68133 q^{5} -2.74590 q^{7} +1.00000 q^{9} +O(q^{10})$	$q+1.00000 q^{3} +1.68133 q^{5} -2.74590 q^{7} +1.00000 q^{9} -2.18953 q^{11} +4.18953 q^{13} +1.68133 q^{15} -6.29809 q^{17} -4.93543 q^{19} -2.74590 q^{21} -3.44364 q^{23} -2.17313 q^{25} +1.00000 q^{27} -9.12497 q^{29} +0.616763 q^{31} -2.18953 q^{33} -4.61676 q^{35} +1.44364 q^{37} +4.18953 q^{39} +4.10856 q^{41} -8.53579 q^{43} +1.68133 q^{45} +6.48763 q^{47} +0.539958 q^{49} -6.29809 q^{51} -0.664924 q^{53} -3.68133 q^{55} -4.93543 q^{57} -1.00000 q^{59} -10.9958 q^{61} -2.74590 q^{63} +7.04399 q^{65} +9.93126 q^{67} -3.44364 q^{69} -6.82687 q^{71} +13.5040 q^{73} -2.17313 q^{75} +6.01224 q^{77} +1.17313 q^{79} +1.00000 q^{81} +15.3421 q^{83} -10.5892 q^{85} -9.12497 q^{87} +1.97942 q^{89} -11.5040 q^{91} +0.616763 q^{93} -8.29809 q^{95} +3.33508 q^{97} -2.18953 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} - 2 q^{5} - 9 q^{7} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^3 - 2 * q^5 - 9 * q^7 + 3 * q^9	$ 3 q + 3 q^{3} - 2 q^{5} - 9 q^{7} + 3 q^{9} + 2 q^{11} + 4 q^{13} - 2 q^{15} + 3 q^{17} - 7 q^{19} - 9 q^{21} - q^{23} - q^{25} + 3 q^{27} - 11 q^{29} - 13 q^{31} + 2 q^{33} + q^{35} - 5 q^{37} + 4 q^{39} - q^{41} - 6 q^{43} - 2 q^{45} - 11 q^{47} + 14 q^{49} + 3 q^{51} + 2 q^{53} - 4 q^{55} - 7 q^{57} - 3 q^{59} - q^{61} - 9 q^{63} - 10 q^{67} - q^{69} - 26 q^{71} + 7 q^{73} - q^{75} - 17 q^{77} - 2 q^{79} + 3 q^{81} + 3 q^{83} - 35 q^{85} - 11 q^{87} - 23 q^{89} - q^{91} - 13 q^{93} - 3 q^{95} + 14 q^{97} + 2 q^{99}+O(q^{100}) $ 3 * q + 3 * q^3 - 2 * q^5 - 9 * q^7 + 3 * q^9 + 2 * q^11 + 4 * q^13 - 2 * q^15 + 3 * q^17 - 7 * q^19 - 9 * q^21 - q^23 - q^25 + 3 * q^27 - 11 * q^29 - 13 * q^31 + 2 * q^33 + q^35 - 5 * q^37 + 4 * q^39 - q^41 - 6 * q^43 - 2 * q^45 - 11 * q^47 + 14 * q^49 + 3 * q^51 + 2 * q^53 - 4 * q^55 - 7 * q^57 - 3 * q^59 - q^61 - 9 * q^63 - 10 * q^67 - q^69 - 26 * q^71 + 7 * q^73 - q^75 - 17 * q^77 - 2 * q^79 + 3 * q^81 + 3 * q^83 - 35 * q^85 - 11 * q^87 - 23 * q^89 - q^91 - 13 * q^93 - 3 * q^95 + 14 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0	0
$5$	1.68133	0.751914	0.375957	−	0.926637i	$-0.377314\pi$
$5$	1.68133	0.751914	0.375957	+	0.926637i	$0.377314\pi$
$6$	0	0
$7$	−2.74590	−1.03785	−0.518926	−	0.854819i	$-0.673668\pi$
$7$	−2.74590	−1.03785	−0.518926	+	0.854819i	$0.673668\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.18953	−0.660169	−0.330085	−	0.943951i	$-0.607077\pi$
$11$	−2.18953	−0.660169	−0.330085	+	0.943951i	$0.607077\pi$
$12$	0	0
$13$	4.18953	1.16197	0.580984	−	0.813915i	$-0.302668\pi$
$13$	4.18953	1.16197	0.580984	+	0.813915i	$0.302668\pi$
$14$	0	0
$15$	1.68133	0.434118
$16$	0	0
$17$	−6.29809	−1.52751	−0.763756	−	0.645505i	$-0.776647\pi$
$17$	−6.29809	−1.52751	−0.763756	+	0.645505i	$0.776647\pi$
$18$	0	0
$19$	−4.93543	−1.13227	−0.566133	−	0.824314i	$-0.691561\pi$
$19$	−4.93543	−1.13227	−0.566133	+	0.824314i	$0.691561\pi$
$20$	0	0
$21$	−2.74590	−0.599204
$22$	0	0
$23$	−3.44364	−0.718048	−0.359024	−	0.933328i	$-0.616890\pi$
$23$	−3.44364	−0.718048	−0.359024	+	0.933328i	$0.616890\pi$
$24$	0	0
$25$	−2.17313	−0.434625
$26$	0	0
$27$	1.00000	0.192450
$28$	0	0
$29$	−9.12497	−1.69446	−0.847232	−	0.531223i	$-0.821733\pi$
$29$	−9.12497	−1.69446	−0.847232	+	0.531223i	$0.821733\pi$
$30$	0	0
$31$	0.616763	0.110774	0.0553870	−	0.998465i	$-0.482361\pi$
$31$	0.616763	0.110774	0.0553870	+	0.998465i	$0.482361\pi$
$32$	0	0
$33$	−2.18953	−0.381149
$34$	0	0
$35$	−4.61676	−0.780375
$36$	0	0
$37$	1.44364	0.237332	0.118666	−	0.992934i	$-0.462138\pi$
$37$	1.44364	0.237332	0.118666	+	0.992934i	$0.462138\pi$
$38$	0	0
$39$	4.18953	0.670862
$40$	0	0
$41$	4.10856	0.641649	0.320825	−	0.947139i	$-0.396040\pi$
$41$	4.10856	0.641649	0.320825	+	0.947139i	$0.396040\pi$
$42$	0	0
$43$	−8.53579	−1.30170	−0.650848	−	0.759208i	$-0.725586\pi$
$43$	−8.53579	−1.30170	−0.650848	+	0.759208i	$0.725586\pi$
$44$	0	0
$45$	1.68133	0.250638
$46$	0	0
$47$	6.48763	0.946318	0.473159	−	0.880977i	$-0.343114\pi$
$47$	6.48763	0.946318	0.473159	+	0.880977i	$0.343114\pi$
$48$	0	0
$49$	0.539958	0.0771368
$50$	0	0
$51$	−6.29809	−0.881910
$52$	0	0
$53$	−0.664924	−0.0913343	−0.0456672	−	0.998957i	$-0.514541\pi$
$53$	−0.664924	−0.0913343	−0.0456672	+	0.998957i	$0.514541\pi$
$54$	0	0
$55$	−3.68133	−0.496391
$56$	0	0
$57$	−4.93543	−0.653714
$58$	0	0
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	0	0
$61$	−10.9958	−1.40787	−0.703936	−	0.710263i	$-0.748576\pi$
$61$	−10.9958	−1.40787	−0.703936	+	0.710263i	$0.748576\pi$
$62$	0	0
$63$	−2.74590	−0.345951
$64$	0	0
$65$	7.04399	0.873700
$66$	0	0
$67$	9.93126	1.21330	0.606648	−	0.794970i	$-0.292514\pi$
$67$	9.93126	1.21330	0.606648	+	0.794970i	$0.292514\pi$
$68$	0	0
$69$	−3.44364	−0.414565
$70$	0	0
$71$	−6.82687	−0.810201	−0.405100	−	0.914272i	$-0.632763\pi$
$71$	−6.82687	−0.810201	−0.405100	+	0.914272i	$0.632763\pi$
$72$	0	0
$73$	13.5040	1.58053	0.790264	−	0.612767i	$-0.209943\pi$
$73$	13.5040	1.58053	0.790264	+	0.612767i	$0.209943\pi$
$74$	0	0
$75$	−2.17313	−0.250931
$76$	0	0
$77$	6.01224	0.685158
$78$	0	0
$79$	1.17313	0.131987	0.0659936	−	0.997820i	$-0.478978\pi$
$79$	1.17313	0.131987	0.0659936	+	0.997820i	$0.478978\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	15.3421	1.68401	0.842006	−	0.539468i	$-0.181374\pi$
$83$	15.3421	1.68401	0.842006	+	0.539468i	$0.181374\pi$
$84$	0	0
$85$	−10.5892	−1.14856
$86$	0	0
$87$	−9.12497	−0.978299
$88$	0	0
$89$	1.97942	0.209819	0.104909	−	0.994482i	$-0.466545\pi$
$89$	1.97942	0.209819	0.104909	+	0.994482i	$0.466545\pi$
$90$	0	0
$91$	−11.5040	−1.20595
$92$	0	0
$93$	0.616763	0.0639553
$94$	0	0
$95$	−8.29809	−0.851366
$96$	0	0
$97$	3.33508	0.338626	0.169313	−	0.985562i	$-0.445845\pi$
$97$	3.33508	0.338626	0.169313	+	0.985562i	$0.445845\pi$
$98$	0	0
$99$	−2.18953	−0.220056
$100$	0	0
$101$	−3.49180	−0.347447	−0.173723	−	0.984794i	$-0.555580\pi$
$101$	−3.49180	−0.347447	−0.173723	+	0.984794i	$0.555580\pi$
$102$	0	0
$103$	−8.21712	−0.809657	−0.404828	−	0.914393i	$-0.632669\pi$
$103$	−8.21712	−0.809657	−0.404828	+	0.914393i	$0.632669\pi$
$104$	0	0
$105$	−4.61676	−0.450550
$106$	0	0
$107$	−17.7899	−1.71981	−0.859907	−	0.510451i	$-0.829478\pi$
$107$	−17.7899	−1.71981	−0.859907	+	0.510451i	$0.829478\pi$
$108$	0	0
$109$	−18.2981	−1.75264	−0.876320	−	0.481730i	$-0.840009\pi$
$109$	−18.2981	−1.75264	−0.876320	+	0.481730i	$0.840009\pi$
$110$	0	0
$111$	1.44364	0.137024
$112$	0	0
$113$	−7.71414	−0.725686	−0.362843	−	0.931850i	$-0.618194\pi$
$113$	−7.71414	−0.725686	−0.362843	+	0.931850i	$0.618194\pi$
$114$	0	0
$115$	−5.78989	−0.539910
$116$	0	0
$117$	4.18953	0.387323
$118$	0	0
$119$	17.2939	1.58533
$120$	0	0
$121$	−6.20594	−0.564176
$122$	0	0
$123$	4.10856	0.370456
$124$	0	0
$125$	−12.0604	−1.07871
$126$	0	0
$127$	−6.18953	−0.549232	−0.274616	−	0.961554i	$-0.588551\pi$
$127$	−6.18953	−0.549232	−0.274616	+	0.961554i	$0.588551\pi$
$128$	0	0
$129$	−8.53579	−0.751534
$130$	0	0
$131$	15.5798	1.36121	0.680606	−	0.732650i	$-0.261717\pi$
$131$	15.5798	1.36121	0.680606	+	0.732650i	$0.261717\pi$
$132$	0	0
$133$	13.5522	1.17512
$134$	0	0
$135$	1.68133	0.144706
$136$	0	0
$137$	0.664924	0.0568083	0.0284041	−	0.999597i	$-0.490957\pi$
$137$	0.664924	0.0568083	0.0284041	+	0.999597i	$0.490957\pi$
$138$	0	0
$139$	18.7857	1.59338	0.796692	−	0.604385i	$-0.206581\pi$
$139$	18.7857	1.59338	0.796692	+	0.604385i	$0.206581\pi$
$140$	0	0
$141$	6.48763	0.546357
$142$	0	0
$143$	−9.17313	−0.767095
$144$	0	0
$145$	−15.3421	−1.27409
$146$	0	0
$147$	0.539958	0.0445349
$148$	0	0
$149$	−8.04816	−0.659331	−0.329666	−	0.944098i	$-0.606936\pi$
$149$	−8.04816	−0.659331	−0.329666	+	0.944098i	$0.606936\pi$
$150$	0	0
$151$	17.8503	1.45264	0.726318	−	0.687359i	$-0.241230\pi$
$151$	17.8503	1.45264	0.726318	+	0.687359i	$0.241230\pi$
$152$	0	0
$153$	−6.29809	−0.509171
$154$	0	0
$155$	1.03698	0.0832924
$156$	0	0
$157$	10.4395	0.833160	0.416580	−	0.909099i	$-0.363229\pi$
$157$	10.4395	0.833160	0.416580	+	0.909099i	$0.363229\pi$
$158$	0	0
$159$	−0.664924	−0.0527319
$160$	0	0
$161$	9.45587	0.745227
$162$	0	0
$163$	3.76231	0.294686	0.147343	−	0.989085i	$-0.452928\pi$
$163$	3.76231	0.294686	0.147343	+	0.989085i	$0.452928\pi$
$164$	0	0
$165$	−3.68133	−0.286591
$166$	0	0
$167$	−18.1086	−1.40128	−0.700641	−	0.713514i	$-0.747103\pi$
$167$	−18.1086	−1.40128	−0.700641	+	0.713514i	$0.747103\pi$
$168$	0	0
$169$	4.55220	0.350169
$170$	0	0
$171$	−4.93543	−0.377422
$172$	0	0
$173$	−9.66598	−0.734891	−0.367446	−	0.930045i	$-0.619768\pi$
$173$	−9.66598	−0.734891	−0.367446	+	0.930045i	$0.619768\pi$
$174$	0	0
$175$	5.96719	0.451077
$176$	0	0
$177$	−1.00000	−0.0751646
$178$	0	0
$179$	8.95601	0.669403	0.334702	−	0.942324i	$-0.391364\pi$
$179$	8.95601	0.669403	0.334702	+	0.942324i	$0.391364\pi$
$180$	0	0
$181$	−0.487628	−0.0362451	−0.0181225	−	0.999836i	$-0.505769\pi$
$181$	−0.487628	−0.0362451	−0.0181225	+	0.999836i	$0.505769\pi$
$182$	0	0
$183$	−10.9958	−0.812835
$184$	0	0
$185$	2.42723	0.178453
$186$	0	0
$187$	13.7899	1.00842
$188$	0	0
$189$	−2.74590	−0.199735
$190$	0	0
$191$	−5.07681	−0.367345	−0.183672	−	0.982988i	$-0.558799\pi$
$191$	−5.07681	−0.367345	−0.183672	+	0.982988i	$0.558799\pi$
$192$	0	0
$193$	9.36266	0.673939	0.336970	−	0.941516i	$-0.390598\pi$
$193$	9.36266	0.673939	0.336970	+	0.941516i	$0.390598\pi$
$194$	0	0
$195$	7.04399	0.504431
$196$	0	0
$197$	−16.2499	−1.15776	−0.578880	−	0.815413i	$-0.696510\pi$
$197$	−16.2499	−1.15776	−0.578880	+	0.815413i	$0.696510\pi$
$198$	0	0
$199$	−6.64958	−0.471376	−0.235688	−	0.971829i	$-0.575734\pi$
$199$	−6.64958	−0.471376	−0.235688	+	0.971829i	$0.575734\pi$
$200$	0	0
$201$	9.93126	0.700497
$202$	0	0
$203$	25.0562	1.75860
$204$	0	0
$205$	6.90785	0.482465
$206$	0	0
$207$	−3.44364	−0.239349
$208$	0	0
$209$	10.8063	0.747487
$210$	0	0
$211$	−13.1526	−0.905459	−0.452729	−	0.891648i	$-0.649550\pi$
$211$	−13.1526	−0.905459	−0.452729	+	0.891648i	$0.649550\pi$
$212$	0	0
$213$	−6.82687	−0.467770
$214$	0	0
$215$	−14.3515	−0.978763
$216$	0	0
$217$	−1.69357	−0.114967
$218$	0	0
$219$	13.5040	0.912518
$220$	0	0
$221$	−26.3861	−1.77492
$222$	0	0
$223$	9.70892	0.650157	0.325079	−	0.945687i	$-0.394609\pi$
$223$	9.70892	0.650157	0.325079	+	0.945687i	$0.394609\pi$
$224$	0	0
$225$	−2.17313	−0.144875
$226$	0	0
$227$	−6.16896	−0.409448	−0.204724	−	0.978820i	$-0.565630\pi$
$227$	−6.16896	−0.409448	−0.204724	+	0.978820i	$0.565630\pi$
$228$	0	0
$229$	25.8175	1.70607	0.853033	−	0.521856i	$-0.174760\pi$
$229$	25.8175	1.70607	0.853033	+	0.521856i	$0.174760\pi$
$230$	0	0
$231$	6.01224	0.395576
$232$	0	0
$233$	12.2499	0.802520	0.401260	−	0.915964i	$-0.368572\pi$
$233$	12.2499	0.802520	0.401260	+	0.915964i	$0.368572\pi$
$234$	0	0
$235$	10.9078	0.711549
$236$	0	0
$237$	1.17313	0.0762028
$238$	0	0
$239$	22.9477	1.48436	0.742181	−	0.670200i	$-0.233792\pi$
$239$	22.9477	1.48436	0.742181	+	0.670200i	$0.233792\pi$
$240$	0	0
$241$	4.67015	0.300831	0.150415	−	0.988623i	$-0.451939\pi$
$241$	4.67015	0.300831	0.150415	+	0.988623i	$0.451939\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	0	0
$245$	0.907847	0.0580002
$246$	0	0
$247$	−20.6772	−1.31566
$248$	0	0
$249$	15.3421	0.972265
$250$	0	0
$251$	−22.4067	−1.41430	−0.707148	−	0.707066i	$-0.750018\pi$
$251$	−22.4067	−1.41430	−0.707148	+	0.707066i	$0.750018\pi$
$252$	0	0
$253$	7.53996	0.474033
$254$	0	0
$255$	−10.5892	−0.663120
$256$	0	0
$257$	31.1372	1.94229	0.971143	−	0.238499i	$-0.0766554\pi$
$257$	31.1372	1.94229	0.971143	+	0.238499i	$0.0766554\pi$
$258$	0	0
$259$	−3.96408	−0.246316
$260$	0	0
$261$	−9.12497	−0.564821
$262$	0	0
$263$	−24.9547	−1.53877	−0.769386	−	0.638784i	$-0.779438\pi$
$263$	−24.9547	−1.53877	−0.769386	+	0.638784i	$0.779438\pi$
$264$	0	0
$265$	−1.11796	−0.0686755
$266$	0	0
$267$	1.97942	0.121139
$268$	0	0
$269$	5.99477	0.365508	0.182754	−	0.983159i	$-0.441499\pi$
$269$	5.99477	0.365508	0.182754	+	0.983159i	$0.441499\pi$
$270$	0	0
$271$	1.97241	0.119816	0.0599078	−	0.998204i	$-0.480919\pi$
$271$	1.97241	0.119816	0.0599078	+	0.998204i	$0.480919\pi$
$272$	0	0
$273$	−11.5040	−0.696256
$274$	0	0
$275$	4.75814	0.286926
$276$	0	0
$277$	−2.53579	−0.152361	−0.0761804	−	0.997094i	$-0.524272\pi$
$277$	−2.53579	−0.152361	−0.0761804	+	0.997094i	$0.524272\pi$
$278$	0	0
$279$	0.616763	0.0369246
$280$	0	0
$281$	−18.8545	−1.12476	−0.562381	−	0.826878i	$-0.690115\pi$
$281$	−18.8545	−1.12476	−0.562381	+	0.826878i	$0.690115\pi$
$282$	0	0
$283$	5.78989	0.344173	0.172087	−	0.985082i	$-0.444949\pi$
$283$	5.78989	0.344173	0.172087	+	0.985082i	$0.444949\pi$
$284$	0	0
$285$	−8.29809	−0.491537
$286$	0	0
$287$	−11.2817	−0.665937
$288$	0	0
$289$	22.6660	1.33329
$290$	0	0
$291$	3.33508	0.195506
$292$	0	0
$293$	7.73472	0.451867	0.225934	−	0.974143i	$-0.427457\pi$
$293$	7.73472	0.451867	0.225934	+	0.974143i	$0.427457\pi$
$294$	0	0
$295$	−1.68133	−0.0978909
$296$	0	0
$297$	−2.18953	−0.127050
$298$	0	0
$299$	−14.4272	−0.834348
$300$	0	0
$301$	23.4384	1.35097
$302$	0	0
$303$	−3.49180	−0.200598
$304$	0	0
$305$	−18.4876	−1.05860
$306$	0	0
$307$	−16.4999	−0.941697	−0.470849	−	0.882214i	$-0.656052\pi$
$307$	−16.4999	−0.941697	−0.470849	+	0.882214i	$0.656052\pi$
$308$	0	0
$309$	−8.21712	−0.467456
$310$	0	0
$311$	−24.9354	−1.41396	−0.706979	−	0.707234i	$-0.749943\pi$
$311$	−24.9354	−1.41396	−0.706979	+	0.707234i	$0.749943\pi$
$312$	0	0
$313$	−24.1690	−1.36611	−0.683055	−	0.730367i	$-0.739349\pi$
$313$	−24.1690	−1.36611	−0.683055	+	0.730367i	$0.739349\pi$
$314$	0	0
$315$	−4.61676	−0.260125
$316$	0	0
$317$	−18.1812	−1.02116	−0.510579	−	0.859831i	$-0.670569\pi$
$317$	−18.1812	−1.02116	−0.510579	+	0.859831i	$0.670569\pi$
$318$	0	0
$319$	19.9794	1.11863
$320$	0	0
$321$	−17.7899	−0.992935
$322$	0	0
$323$	31.0838	1.72955
$324$	0	0
$325$	−9.10439	−0.505021
$326$	0	0
$327$	−18.2981	−1.01189
$328$	0	0
$329$	−17.8144	−0.982138
$330$	0	0
$331$	14.6290	0.804083	0.402041	−	0.915622i	$-0.368301\pi$
$331$	14.6290	0.804083	0.402041	+	0.915622i	$0.368301\pi$
$332$	0	0
$333$	1.44364	0.0791107
$334$	0	0
$335$	16.6977	0.912295
$336$	0	0
$337$	−19.1526	−1.04331	−0.521653	−	0.853158i	$-0.674684\pi$
$337$	−19.1526	−1.04331	−0.521653	+	0.853158i	$0.674684\pi$
$338$	0	0
$339$	−7.71414	−0.418975
$340$	0	0
$341$	−1.35042	−0.0731295
$342$	0	0
$343$	17.7386	0.957795
$344$	0	0
$345$	−5.78989	−0.311717
$346$	0	0
$347$	−29.4301	−1.57989	−0.789944	−	0.613178i	$-0.789891\pi$
$347$	−29.4301	−1.57989	−0.789944	+	0.613178i	$0.789891\pi$
$348$	0	0
$349$	28.9065	1.54733	0.773665	−	0.633595i	$-0.218421\pi$
$349$	28.9065	1.54733	0.773665	+	0.633595i	$0.218421\pi$
$350$	0	0
$351$	4.18953	0.223621
$352$	0	0
$353$	0.0481609	0.00256335	0.00128167	−	0.999999i	$-0.499592\pi$
$353$	0.0481609	0.00256335	0.00128167	+	0.999999i	$0.499592\pi$
$354$	0	0
$355$	−11.4782	−0.609201
$356$	0	0
$357$	17.2939	0.915292
$358$	0	0
$359$	−11.7417	−0.619705	−0.309852	−	0.950785i	$-0.600280\pi$
$359$	−11.7417	−0.619705	−0.309852	+	0.950785i	$0.600280\pi$
$360$	0	0
$361$	5.35849	0.282026
$362$	0	0
$363$	−6.20594	−0.325727
$364$	0	0
$365$	22.7047	1.18842
$366$	0	0
$367$	7.04399	0.367693	0.183847	−	0.982955i	$-0.441145\pi$
$367$	7.04399	0.367693	0.183847	+	0.982955i	$0.441145\pi$
$368$	0	0
$369$	4.10856	0.213883
$370$	0	0
$371$	1.82581	0.0947915
$372$	0	0
$373$	31.5316	1.63265	0.816323	−	0.577596i	$-0.196009\pi$
$373$	31.5316	1.63265	0.816323	+	0.577596i	$0.196009\pi$
$374$	0	0
$375$	−12.0604	−0.622796
$376$	0	0
$377$	−38.2294	−1.96891
$378$	0	0
$379$	10.5030	0.539502	0.269751	−	0.962930i	$-0.413059\pi$
$379$	10.5030	0.539502	0.269751	+	0.962930i	$0.413059\pi$
$380$	0	0
$381$	−6.18953	−0.317099
$382$	0	0
$383$	−23.3023	−1.19069	−0.595345	−	0.803470i	$-0.702985\pi$
$383$	−23.3023	−1.19069	−0.595345	+	0.803470i	$0.702985\pi$
$384$	0	0
$385$	10.1086	0.515180
$386$	0	0
$387$	−8.53579	−0.433899
$388$	0	0
$389$	−33.4835	−1.69768	−0.848839	−	0.528651i	$-0.822698\pi$
$389$	−33.4835	−1.69768	−0.848839	+	0.528651i	$0.822698\pi$
$390$	0	0
$391$	21.6883	1.09683
$392$	0	0
$393$	15.5798	0.785896
$394$	0	0
$395$	1.97241	0.0992430
$396$	0	0
$397$	−10.6977	−0.536904	−0.268452	−	0.963293i	$-0.586512\pi$
$397$	−10.6977	−0.536904	−0.268452	+	0.963293i	$0.586512\pi$
$398$	0	0
$399$	13.5522	0.678458
$400$	0	0
$401$	−23.3145	−1.16427	−0.582135	−	0.813092i	$-0.697783\pi$
$401$	−23.3145	−1.16427	−0.582135	+	0.813092i	$0.697783\pi$
$402$	0	0
$403$	2.58395	0.128716
$404$	0	0
$405$	1.68133	0.0835460
$406$	0	0
$407$	−3.16089	−0.156679
$408$	0	0
$409$	−8.65970	−0.428194	−0.214097	−	0.976812i	$-0.568681\pi$
$409$	−8.65970	−0.428194	−0.214097	+	0.976812i	$0.568681\pi$
$410$	0	0
$411$	0.664924	0.0327983
$412$	0	0
$413$	2.74590	0.135117
$414$	0	0
$415$	25.7951	1.26623
$416$	0	0
$417$	18.7857	0.919941
$418$	0	0
$419$	−4.63734	−0.226549	−0.113274	−	0.993564i	$-0.536134\pi$
$419$	−4.63734	−0.226549	−0.113274	+	0.993564i	$0.536134\pi$
$420$	0	0
$421$	1.68133	0.0819430	0.0409715	−	0.999160i	$-0.486955\pi$
$421$	1.68133	0.0819430	0.0409715	+	0.999160i	$0.486955\pi$
$422$	0	0
$423$	6.48763	0.315439
$424$	0	0
$425$	13.6866	0.663896
$426$	0	0
$427$	30.1934	1.46116
$428$	0	0
$429$	−9.17313	−0.442883
$430$	0	0
$431$	−11.5040	−0.554130	−0.277065	−	0.960851i	$-0.589362\pi$
$431$	−11.5040	−0.554130	−0.277065	+	0.960851i	$0.589362\pi$
$432$	0	0
$433$	24.5069	1.17773	0.588863	−	0.808233i	$-0.299576\pi$
$433$	24.5069	1.17773	0.588863	+	0.808233i	$0.299576\pi$
$434$	0	0
$435$	−15.3421	−0.735597
$436$	0	0
$437$	16.9958	0.813021
$438$	0	0
$439$	5.63840	0.269106	0.134553	−	0.990906i	$-0.457040\pi$
$439$	5.63840	0.269106	0.134553	+	0.990906i	$0.457040\pi$
$440$	0	0
$441$	0.539958	0.0257123
$442$	0	0
$443$	38.0070	1.80577	0.902884	−	0.429885i	$-0.141446\pi$
$443$	38.0070	1.80577	0.902884	+	0.429885i	$0.141446\pi$
$444$	0	0
$445$	3.32807	0.157765
$446$	0	0
$447$	−8.04816	−0.380665
$448$	0	0
$449$	−11.0357	−0.520805	−0.260402	−	0.965500i	$-0.583855\pi$
$449$	−11.0357	−0.520805	−0.260402	+	0.965500i	$0.583855\pi$
$450$	0	0
$451$	−8.99583	−0.423597
$452$	0	0
$453$	17.8503	0.838680
$454$	0	0
$455$	−19.3421	−0.906771
$456$	0	0
$457$	−32.3913	−1.51520	−0.757601	−	0.652718i	$-0.773629\pi$
$457$	−32.3913	−1.51520	−0.757601	+	0.652718i	$0.773629\pi$
$458$	0	0
$459$	−6.29809	−0.293970
$460$	0	0
$461$	34.9599	1.62825	0.814123	−	0.580693i	$-0.197218\pi$
$461$	34.9599	1.62825	0.814123	+	0.580693i	$0.197218\pi$
$462$	0	0
$463$	22.8063	1.05990	0.529949	−	0.848029i	$-0.322211\pi$
$463$	22.8063	1.05990	0.529949	+	0.848029i	$0.322211\pi$
$464$	0	0
$465$	1.03698	0.0480889
$466$	0	0
$467$	36.2416	1.67706	0.838530	−	0.544855i	$-0.183415\pi$
$467$	36.2416	1.67706	0.838530	+	0.544855i	$0.183415\pi$
$468$	0	0
$469$	−27.2702	−1.25922
$470$	0	0
$471$	10.4395	0.481025
$472$	0	0
$473$	18.6894	0.859340
$474$	0	0
$475$	10.7253	0.492112
$476$	0	0
$477$	−0.664924	−0.0304448
$478$	0	0
$479$	−17.0562	−0.779319	−0.389660	−	0.920959i	$-0.627407\pi$
$479$	−17.0562	−0.779319	−0.389660	+	0.920959i	$0.627407\pi$
$480$	0	0
$481$	6.04816	0.275772
$482$	0	0
$483$	9.45587	0.430257
$484$	0	0
$485$	5.60737	0.254617
$486$	0	0
$487$	−15.3473	−0.695453	−0.347727	−	0.937596i	$-0.613046\pi$
$487$	−15.3473	−0.695453	−0.347727	+	0.937596i	$0.613046\pi$
$488$	0	0
$489$	3.76231	0.170137
$490$	0	0
$491$	−18.0122	−0.812881	−0.406440	−	0.913677i	$-0.633230\pi$
$491$	−18.0122	−0.812881	−0.406440	+	0.913677i	$0.633230\pi$
$492$	0	0
$493$	57.4699	2.58831
$494$	0	0
$495$	−3.68133	−0.165464
$496$	0	0
$497$	18.7459	0.840868
$498$	0	0
$499$	21.6074	0.967279	0.483639	−	0.875267i	$-0.339315\pi$
$499$	21.6074	0.967279	0.483639	+	0.875267i	$0.339315\pi$
$500$	0	0
$501$	−18.1086	−0.809031
$502$	0	0
$503$	−7.76231	−0.346104	−0.173052	−	0.984913i	$-0.555363\pi$
$503$	−7.76231	−0.346104	−0.173052	+	0.984913i	$0.555363\pi$
$504$	0	0
$505$	−5.87086	−0.261250
$506$	0	0
$507$	4.55220	0.202170
$508$	0	0
$509$	40.7704	1.80712	0.903558	−	0.428467i	$-0.140946\pi$
$509$	40.7704	1.80712	0.903558	+	0.428467i	$0.140946\pi$
$510$	0	0
$511$	−37.0807	−1.64035
$512$	0	0
$513$	−4.93543	−0.217905
$514$	0	0
$515$	−13.8157	−0.608792
$516$	0	0
$517$	−14.2049	−0.624730
$518$	0	0
$519$	−9.66598	−0.424290
$520$	0	0
$521$	41.0427	1.79811	0.899056	−	0.437834i	$-0.144254\pi$
$521$	41.0427	1.79811	0.899056	+	0.437834i	$0.144254\pi$
$522$	0	0
$523$	22.5686	0.986856	0.493428	−	0.869787i	$-0.335744\pi$
$523$	22.5686	0.986856	0.493428	+	0.869787i	$0.335744\pi$
$524$	0	0
$525$	5.96719	0.260429
$526$	0	0
$527$	−3.88443	−0.169208
$528$	0	0
$529$	−11.1414	−0.484408
$530$	0	0
$531$	−1.00000	−0.0433963
$532$	0	0
$533$	17.2130	0.745576
$534$	0	0
$535$	−29.9107	−1.29315
$536$	0	0
$537$	8.95601	0.386480
$538$	0	0
$539$	−1.18226	−0.0509233
$540$	0	0
$541$	35.0357	1.50630	0.753150	−	0.657849i	$-0.228533\pi$
$541$	35.0357	1.50630	0.753150	+	0.657849i	$0.228533\pi$
$542$	0	0
$543$	−0.487628	−0.0209261
$544$	0	0
$545$	−30.7651	−1.31783
$546$	0	0
$547$	−3.70191	−0.158282	−0.0791410	−	0.996863i	$-0.525218\pi$
$547$	−3.70191	−0.158282	−0.0791410	+	0.996863i	$0.525218\pi$
$548$	0	0
$549$	−10.9958	−0.469291
$550$	0	0
$551$	45.0357	1.91858
$552$	0	0
$553$	−3.22129	−0.136983
$554$	0	0
$555$	2.42723	0.103030
$556$	0	0
$557$	−16.7253	−0.708675	−0.354337	−	0.935118i	$-0.615294\pi$
$557$	−16.7253	−0.708675	−0.354337	+	0.935118i	$0.615294\pi$
$558$	0	0
$559$	−35.7610	−1.51253
$560$	0	0
$561$	13.7899	0.582210
$562$	0	0
$563$	−24.9149	−1.05004	−0.525018	−	0.851091i	$-0.675941\pi$
$563$	−24.9149	−1.05004	−0.525018	+	0.851091i	$0.675941\pi$
$564$	0	0
$565$	−12.9700	−0.545653
$566$	0	0
$567$	−2.74590	−0.115317
$568$	0	0
$569$	42.4548	1.77980	0.889899	−	0.456157i	$-0.150775\pi$
$569$	42.4548	1.77980	0.889899	+	0.456157i	$0.150775\pi$
$570$	0	0
$571$	32.6977	1.36836	0.684179	−	0.729314i	$-0.260161\pi$
$571$	32.6977	1.36836	0.684179	+	0.729314i	$0.260161\pi$
$572$	0	0
$573$	−5.07681	−0.212087
$574$	0	0
$575$	7.48346	0.312082
$576$	0	0
$577$	−13.2716	−0.552503	−0.276251	−	0.961085i	$-0.589092\pi$
$577$	−13.2716	−0.552503	−0.276251	+	0.961085i	$0.589092\pi$
$578$	0	0
$579$	9.36266	0.389099
$580$	0	0
$581$	−42.1278	−1.74776
$582$	0	0
$583$	1.45587	0.0602961
$584$	0	0
$585$	7.04399	0.291233
$586$	0	0
$587$	14.4067	0.594626	0.297313	−	0.954780i	$-0.403909\pi$
$587$	14.4067	0.594626	0.297313	+	0.954780i	$0.403909\pi$
$588$	0	0
$589$	−3.04399	−0.125426
$590$	0	0
$591$	−16.2499	−0.668433
$592$	0	0
$593$	−1.85863	−0.0763247	−0.0381623	−	0.999272i	$-0.512150\pi$
$593$	−1.85863	−0.0763247	−0.0381623	+	0.999272i	$0.512150\pi$
$594$	0	0
$595$	29.0768	1.19203
$596$	0	0
$597$	−6.64958	−0.272149
$598$	0	0
$599$	20.2171	0.826049	0.413025	−	0.910720i	$-0.364472\pi$
$599$	20.2171	0.826049	0.413025	+	0.910720i	$0.364472\pi$
$600$	0	0
$601$	−29.6608	−1.20989	−0.604944	−	0.796268i	$-0.706804\pi$
$601$	−29.6608	−1.20989	−0.604944	+	0.796268i	$0.706804\pi$
$602$	0	0
$603$	9.93126	0.404432
$604$	0	0
$605$	−10.4342	−0.424212
$606$	0	0
$607$	−8.06040	−0.327161	−0.163581	−	0.986530i	$-0.552304\pi$
$607$	−8.06040	−0.327161	−0.163581	+	0.986530i	$0.552304\pi$
$608$	0	0
$609$	25.0562	1.01533
$610$	0	0
$611$	27.1801	1.09959
$612$	0	0
$613$	−35.7886	−1.44549	−0.722743	−	0.691117i	$-0.757119\pi$
$613$	−35.7886	−1.44549	−0.722743	+	0.691117i	$0.757119\pi$
$614$	0	0
$615$	6.90785	0.278551
$616$	0	0
$617$	21.7159	0.874250	0.437125	−	0.899401i	$-0.355997\pi$
$617$	21.7159	0.874250	0.437125	+	0.899401i	$0.355997\pi$
$618$	0	0
$619$	15.3679	0.617688	0.308844	−	0.951113i	$-0.400058\pi$
$619$	15.3679	0.617688	0.308844	+	0.951113i	$0.400058\pi$
$620$	0	0
$621$	−3.44364	−0.138188
$622$	0	0
$623$	−5.43530	−0.217761
$624$	0	0
$625$	−9.41188	−0.376475
$626$	0	0
$627$	10.8063	0.431562
$628$	0	0
$629$	−9.09215	−0.362528
$630$	0	0
$631$	24.5358	0.976754	0.488377	−	0.872633i	$-0.337589\pi$
$631$	24.5358	0.976754	0.488377	+	0.872633i	$0.337589\pi$
$632$	0	0
$633$	−13.1526	−0.522767
$634$	0	0
$635$	−10.4067	−0.412975
$636$	0	0
$637$	2.26217	0.0896305
$638$	0	0
$639$	−6.82687	−0.270067
$640$	0	0
$641$	−16.0521	−0.634018	−0.317009	−	0.948422i	$-0.602679\pi$
$641$	−16.0521	−0.634018	−0.317009	+	0.948422i	$0.602679\pi$
$642$	0	0
$643$	9.47645	0.373715	0.186857	−	0.982387i	$-0.440170\pi$
$643$	9.47645	0.373715	0.186857	+	0.982387i	$0.440170\pi$
$644$	0	0
$645$	−14.3515	−0.565089
$646$	0	0
$647$	−41.1924	−1.61944	−0.809720	−	0.586817i	$-0.800381\pi$
$647$	−41.1924	−1.61944	−0.809720	+	0.586817i	$0.800381\pi$
$648$	0	0
$649$	2.18953	0.0859467
$650$	0	0
$651$	−1.69357	−0.0663762
$652$	0	0
$653$	14.0757	0.550827	0.275413	−	0.961326i	$-0.411185\pi$
$653$	14.0757	0.550827	0.275413	+	0.961326i	$0.411185\pi$
$654$	0	0
$655$	26.1948	1.02351
$656$	0	0
$657$	13.5040	0.526843
$658$	0	0
$659$	20.6220	0.803319	0.401659	−	0.915789i	$-0.368434\pi$
$659$	20.6220	0.803319	0.401659	+	0.915789i	$0.368434\pi$
$660$	0	0
$661$	−30.1414	−1.17236	−0.586182	−	0.810180i	$-0.699370\pi$
$661$	−30.1414	−1.17236	−0.586182	+	0.810180i	$0.699370\pi$
$662$	0	0
$663$	−26.3861	−1.02475
$664$	0	0
$665$	22.7857	0.883592
$666$	0	0
$667$	31.4231	1.21671
$668$	0	0
$669$	9.70892	0.375368
$670$	0	0
$671$	24.0757	0.929434
$672$	0	0
$673$	3.27468	0.126230	0.0631148	−	0.998006i	$-0.479897\pi$
$673$	3.27468	0.126230	0.0631148	+	0.998006i	$0.479897\pi$
$674$	0	0
$675$	−2.17313	−0.0836437
$676$	0	0
$677$	19.6126	0.753773	0.376887	−	0.926259i	$-0.376995\pi$
$677$	19.6126	0.753773	0.376887	+	0.926259i	$0.376995\pi$
$678$	0	0
$679$	−9.15778	−0.351443
$680$	0	0
$681$	−6.16896	−0.236395
$682$	0	0
$683$	−12.1812	−0.466101	−0.233050	−	0.972465i	$-0.574871\pi$
$683$	−12.1812	−0.466101	−0.233050	+	0.972465i	$0.574871\pi$
$684$	0	0
$685$	1.11796	0.0427149
$686$	0	0
$687$	25.8175	0.984998
$688$	0	0
$689$	−2.78572	−0.106128
$690$	0	0
$691$	13.8052	0.525176	0.262588	−	0.964908i	$-0.415424\pi$
$691$	13.8052	0.525176	0.262588	+	0.964908i	$0.415424\pi$
$692$	0	0
$693$	6.01224	0.228386
$694$	0	0
$695$	31.5850	1.19809
$696$	0	0
$697$	−25.8761	−0.980127
$698$	0	0
$699$	12.2499	0.463335
$700$	0	0
$701$	−9.06980	−0.342561	−0.171281	−	0.985222i	$-0.554791\pi$
$701$	−9.06980	−0.342561	−0.171281	+	0.985222i	$0.554791\pi$
$702$	0	0
$703$	−7.12497	−0.268723
$704$	0	0
$705$	10.9078	0.410813
$706$	0	0
$707$	9.58812	0.360598
$708$	0	0
$709$	26.2171	0.984605	0.492302	−	0.870424i	$-0.336155\pi$
$709$	26.2171	0.984605	0.492302	+	0.870424i	$0.336155\pi$
$710$	0	0
$711$	1.17313	0.0439957
$712$	0	0
$713$	−2.12391	−0.0795409
$714$	0	0
$715$	−15.4231	−0.576790
$716$	0	0
$717$	22.9477	0.856996
$718$	0	0
$719$	37.5972	1.40214	0.701070	−	0.713092i	$-0.252706\pi$
$719$	37.5972	1.40214	0.701070	+	0.713092i	$0.252706\pi$
$720$	0	0
$721$	22.5634	0.840304
$722$	0	0
$723$	4.67015	0.173685
$724$	0	0
$725$	19.8297	0.736457
$726$	0	0
$727$	−42.3463	−1.57054	−0.785268	−	0.619156i	$-0.787475\pi$
$727$	−42.3463	−1.57054	−0.785268	+	0.619156i	$0.787475\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	53.7592	1.98836
$732$	0	0
$733$	−5.96408	−0.220288	−0.110144	−	0.993916i	$-0.535131\pi$
$733$	−5.96408	−0.220288	−0.110144	+	0.993916i	$0.535131\pi$
$734$	0	0
$735$	0.907847	0.0334864
$736$	0	0
$737$	−21.7448	−0.800981
$738$	0	0
$739$	−39.9435	−1.46935	−0.734673	−	0.678422i	$-0.762664\pi$
$739$	−39.9435	−1.46935	−0.734673	+	0.678422i	$0.762664\pi$
$740$	0	0
$741$	−20.6772	−0.759595
$742$	0	0
$743$	−22.7407	−0.834274	−0.417137	−	0.908844i	$-0.636967\pi$
$743$	−22.7407	−0.834274	−0.417137	+	0.908844i	$0.636967\pi$
$744$	0	0
$745$	−13.5316	−0.495760
$746$	0	0
$747$	15.3421	0.561338
$748$	0	0
$749$	48.8492	1.78491
$750$	0	0
$751$	−17.8052	−0.649722	−0.324861	−	0.945762i	$-0.605318\pi$
$751$	−17.8052	−0.649722	−0.324861	+	0.945762i	$0.605318\pi$
$752$	0	0
$753$	−22.4067	−0.816544
$754$	0	0
$755$	30.0122	1.09226
$756$	0	0
$757$	27.4353	0.997153	0.498576	−	0.866846i	$-0.333856\pi$
$757$	27.4353	0.997153	0.498576	+	0.866846i	$0.333856\pi$
$758$	0	0
$759$	7.53996	0.273683
$760$	0	0
$761$	10.1812	0.369068	0.184534	−	0.982826i	$-0.440922\pi$
$761$	10.1812	0.369068	0.184534	+	0.982826i	$0.440922\pi$
$762$	0	0
$763$	50.2447	1.81898
$764$	0	0
$765$	−10.5892	−0.382853
$766$	0	0
$767$	−4.18953	−0.151275
$768$	0	0
$769$	38.0398	1.37175	0.685876	−	0.727719i	$-0.259419\pi$
$769$	38.0398	1.37175	0.685876	+	0.727719i	$0.259419\pi$
$770$	0	0
$771$	31.1372	1.12138
$772$	0	0
$773$	−44.1676	−1.58860	−0.794300	−	0.607526i	$-0.792162\pi$
$773$	−44.1676	−1.58860	−0.794300	+	0.607526i	$0.792162\pi$
$774$	0	0
$775$	−1.34030	−0.0481452
$776$	0	0
$777$	−3.96408	−0.142210
$778$	0	0
$779$	−20.2775	−0.726517
$780$	0	0
$781$	14.9477	0.534870
$782$	0	0
$783$	−9.12497	−0.326100
$784$	0	0
$785$	17.5522	0.626465
$786$	0	0
$787$	16.3379	0.582384	0.291192	−	0.956665i	$-0.405948\pi$
$787$	16.3379	0.582384	0.291192	+	0.956665i	$0.405948\pi$
$788$	0	0
$789$	−24.9547	−0.888410
$790$	0	0
$791$	21.1823	0.753154
$792$	0	0
$793$	−46.0674	−1.63590
$794$	0	0
$795$	−1.11796	−0.0396498
$796$	0	0
$797$	−32.9424	−1.16688	−0.583441	−	0.812156i	$-0.698294\pi$
$797$	−32.9424	−1.16688	−0.583441	+	0.812156i	$0.698294\pi$
$798$	0	0
$799$	−40.8597	−1.44551
$800$	0	0
$801$	1.97942	0.0699395
$802$	0	0
$803$	−29.5675	−1.04342
$804$	0	0
$805$	15.8984	0.560347
$806$	0	0
$807$	5.99477	0.211026
$808$	0	0
$809$	−51.9659	−1.82702	−0.913511	−	0.406814i	$-0.866640\pi$
$809$	−51.9659	−1.82702	−0.913511	+	0.406814i	$0.866640\pi$
$810$	0	0
$811$	−26.9424	−0.946077	−0.473039	−	0.881042i	$-0.656843\pi$
$811$	−26.9424	−0.946077	−0.473039	+	0.881042i	$0.656843\pi$
$812$	0	0
$813$	1.97241	0.0691756
$814$	0	0
$815$	6.32568	0.221579
$816$	0	0
$817$	42.1278	1.47387
$818$	0	0
$819$	−11.5040	−0.401983
$820$	0	0
$821$	−27.8914	−0.973418	−0.486709	−	0.873564i	$-0.661803\pi$
$821$	−27.8914	−0.973418	−0.486709	+	0.873564i	$0.661803\pi$
$822$	0	0
$823$	−18.3103	−0.638258	−0.319129	−	0.947711i	$-0.603390\pi$
$823$	−18.3103	−0.638258	−0.319129	+	0.947711i	$0.603390\pi$
$824$	0	0
$825$	4.75814	0.165657
$826$	0	0
$827$	4.37384	0.152093	0.0760467	−	0.997104i	$-0.475770\pi$
$827$	4.37384	0.152093	0.0760467	+	0.997104i	$0.475770\pi$
$828$	0	0
$829$	30.5204	1.06002	0.530009	−	0.847992i	$-0.322188\pi$
$829$	30.5204	1.06002	0.530009	+	0.847992i	$0.322188\pi$
$830$	0	0
$831$	−2.53579	−0.0879655
$832$	0	0
$833$	−3.40070	−0.117827
$834$	0	0
$835$	−30.4465	−1.05364
$836$	0	0
$837$	0.616763	0.0213184
$838$	0	0
$839$	0.859686	0.0296797	0.0148398	−	0.999890i	$-0.495276\pi$
$839$	0.859686	0.0296797	0.0148398	+	0.999890i	$0.495276\pi$
$840$	0	0
$841$	54.2650	1.87121
$842$	0	0
$843$	−18.8545	−0.649382
$844$	0	0
$845$	7.65375	0.263297
$846$	0	0
$847$	17.0409	0.585532
$848$	0	0
$849$	5.78989	0.198709
$850$	0	0
$851$	−4.97136	−0.170416
$852$	0	0
$853$	50.4741	1.72820	0.864099	−	0.503321i	$-0.167889\pi$
$853$	50.4741	1.72820	0.864099	+	0.503321i	$0.167889\pi$
$854$	0	0
$855$	−8.29809	−0.283789
$856$	0	0
$857$	38.4946	1.31495	0.657476	−	0.753476i	$-0.271624\pi$
$857$	38.4946	1.31495	0.657476	+	0.753476i	$0.271624\pi$
$858$	0	0
$859$	27.1044	0.924790	0.462395	−	0.886674i	$-0.346990\pi$
$859$	27.1044	0.924790	0.462395	+	0.886674i	$0.346990\pi$
$860$	0	0
$861$	−11.2817	−0.384479
$862$	0	0
$863$	−10.6443	−0.362338	−0.181169	−	0.983452i	$-0.557988\pi$
$863$	−10.6443	−0.362338	−0.181169	+	0.983452i	$0.557988\pi$
$864$	0	0
$865$	−16.2517	−0.552575
$866$	0	0
$867$	22.6660	0.769777
$868$	0	0
$869$	−2.56860	−0.0871339
$870$	0	0
$871$	41.6074	1.40981
$872$	0	0
$873$	3.33508	0.112875
$874$	0	0
$875$	33.1166	1.11955
$876$	0	0
$877$	40.0328	1.35181	0.675906	−	0.736988i	$-0.263753\pi$
$877$	40.0328	1.35181	0.675906	+	0.736988i	$0.263753\pi$
$878$	0	0
$879$	7.73472	0.260886
$880$	0	0
$881$	29.9588	1.00934	0.504670	−	0.863313i	$-0.331614\pi$
$881$	29.9588	1.00934	0.504670	+	0.863313i	$0.331614\pi$
$882$	0	0
$883$	12.3239	0.414732	0.207366	−	0.978263i	$-0.433511\pi$
$883$	12.3239	0.414732	0.207366	+	0.978263i	$0.433511\pi$
$884$	0	0
$885$	−1.68133	−0.0565173
$886$	0	0
$887$	−25.4559	−0.854725	−0.427362	−	0.904080i	$-0.640557\pi$
$887$	−25.4559	−0.854725	−0.427362	+	0.904080i	$0.640557\pi$
$888$	0	0
$889$	16.9958	0.570022
$890$	0	0
$891$	−2.18953	−0.0733521
$892$	0	0
$893$	−32.0192	−1.07148
$894$	0	0
$895$	15.0580	0.503334
$896$	0	0
$897$	−14.4272	−0.481711
$898$	0	0
$899$	−5.62794	−0.187702
$900$	0	0
$901$	4.18775	0.139514
$902$	0	0
$903$	23.4384	0.779981
$904$	0	0
$905$	−0.819863	−0.0272532
$906$	0	0
$907$	−38.4863	−1.27792	−0.638958	−	0.769241i	$-0.720634\pi$
$907$	−38.4863	−1.27792	−0.638958	+	0.769241i	$0.720634\pi$
$908$	0	0
$909$	−3.49180	−0.115816
$910$	0	0
$911$	−21.2234	−0.703163	−0.351581	−	0.936157i	$-0.614356\pi$
$911$	−21.2234	−0.703163	−0.351581	+	0.936157i	$0.614356\pi$
$912$	0	0
$913$	−33.5920	−1.11173
$914$	0	0
$915$	−18.4876	−0.611182
$916$	0	0
$917$	−42.7805	−1.41274
$918$	0	0
$919$	−46.3051	−1.52746	−0.763732	−	0.645533i	$-0.776635\pi$
$919$	−46.3051	−1.52746	−0.763732	+	0.645533i	$0.776635\pi$
$920$	0	0
$921$	−16.4999	−0.543689
$922$	0	0
$923$	−28.6014	−0.941427
$924$	0	0
$925$	−3.13720	−0.103151
$926$	0	0
$927$	−8.21712	−0.269886
$928$	0	0
$929$	31.9313	1.04763	0.523815	−	0.851832i	$-0.324508\pi$
$929$	31.9313	1.04763	0.523815	+	0.851832i	$0.324508\pi$
$930$	0	0
$931$	−2.66492	−0.0873394
$932$	0	0
$933$	−24.9354	−0.816349
$934$	0	0
$935$	23.1854	0.758243
$936$	0	0
$937$	−33.6813	−1.10032	−0.550161	−	0.835059i	$-0.685433\pi$
$937$	−33.6813	−1.10032	−0.550161	+	0.835059i	$0.685433\pi$
$938$	0	0
$939$	−24.1690	−0.788724
$940$	0	0
$941$	−22.6977	−0.739925	−0.369963	−	0.929047i	$-0.620629\pi$
$941$	−22.6977	−0.739925	−0.369963	+	0.929047i	$0.620629\pi$
$942$	0	0
$943$	−14.1484	−0.460735
$944$	0	0
$945$	−4.61676	−0.150183
$946$	0	0
$947$	−22.5533	−0.732882	−0.366441	−	0.930441i	$-0.619424\pi$
$947$	−22.5533	−0.732882	−0.366441	+	0.930441i	$0.619424\pi$
$948$	0	0
$949$	56.5756	1.83652
$950$	0	0
$951$	−18.1812	−0.589566
$952$	0	0
$953$	−10.3791	−0.336211	−0.168105	−	0.985769i	$-0.553765\pi$
$953$	−10.3791	−0.336211	−0.168105	+	0.985769i	$0.553765\pi$
$954$	0	0
$955$	−8.53579	−0.276212
$956$	0	0
$957$	19.9794	0.645843
$958$	0	0
$959$	−1.82581	−0.0589586
$960$	0	0
$961$	−30.6196	−0.987729
$962$	0	0
$963$	−17.7899	−0.573271
$964$	0	0
$965$	15.7417	0.506744
$966$	0	0
$967$	−32.1913	−1.03520	−0.517601	−	0.855622i	$-0.673175\pi$
$967$	−32.1913	−1.03520	−0.517601	+	0.855622i	$0.673175\pi$
$968$	0	0
$969$	31.0838	0.998556
$970$	0	0
$971$	33.1114	1.06260	0.531298	−	0.847185i	$-0.321705\pi$
$971$	33.1114	1.06260	0.531298	+	0.847185i	$0.321705\pi$
$972$	0	0
$973$	−51.5837	−1.65370
$974$	0	0
$975$	−9.10439	−0.291574
$976$	0	0
$977$	12.2307	0.391294	0.195647	−	0.980674i	$-0.437319\pi$
$977$	12.2307	0.391294	0.195647	+	0.980674i	$0.437319\pi$
$978$	0	0
$979$	−4.33402	−0.138516
$980$	0	0
$981$	−18.2981	−0.584213
$982$	0	0
$983$	7.26111	0.231593	0.115797	−	0.993273i	$-0.463058\pi$
$983$	7.26111	0.231593	0.115797	+	0.993273i	$0.463058\pi$
$984$	0	0
$985$	−27.3215	−0.870536
$986$	0	0
$987$	−17.8144	−0.567038
$988$	0	0
$989$	29.3941	0.934679
$990$	0	0
$991$	20.1054	0.638671	0.319335	−	0.947642i	$-0.396540\pi$
$991$	20.1054	0.638671	0.319335	+	0.947642i	$0.396540\pi$
$992$	0	0
$993$	14.6290	0.464237
$994$	0	0
$995$	−11.1801	−0.354434
$996$	0	0
$997$	−42.3173	−1.34020	−0.670102	−	0.742269i	$-0.733750\pi$
$997$	−42.3173	−1.34020	−0.670102	+	0.742269i	$0.733750\pi$
$998$	0	0
$999$	1.44364	0.0456746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2832.2.a.t.1.3		3
3.2	odd	2		8496.2.a.bl.1.1		3
4.3	odd	2		177.2.a.d.1.2	✓	3
12.11	even	2		531.2.a.d.1.2		3
20.19	odd	2		4425.2.a.w.1.2		3
28.27	even	2		8673.2.a.s.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.a.d.1.2	✓	3	4.3	odd	2
531.2.a.d.1.2		3	12.11	even	2
2832.2.a.t.1.3		3	1.1	even	1	trivial
4425.2.a.w.1.2		3	20.19	odd	2
8496.2.a.bl.1.1		3	3.2	odd	2
8673.2.a.s.1.2		3	28.27	even	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:	\( N \)	\(=\)	\( 2832 = 2^{4} \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2832.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +1.68133 q^{5} -2.74590 q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +1.68133 q^{5} -2.74590 q^{7} +1.00000 q^{9} -2.18953 q^{11} +4.18953 q^{13} +1.68133 q^{15} -6.29809 q^{17} -4.93543 q^{19} -2.74590 q^{21} -3.44364 q^{23} -2.17313 q^{25} +1.00000 q^{27} -9.12497 q^{29} +0.616763 q^{31} -2.18953 q^{33} -4.61676 q^{35} +1.44364 q^{37} +4.18953 q^{39} +4.10856 q^{41} -8.53579 q^{43} +1.68133 q^{45} +6.48763 q^{47} +0.539958 q^{49} -6.29809 q^{51} -0.664924 q^{53} -3.68133 q^{55} -4.93543 q^{57} -1.00000 q^{59} -10.9958 q^{61} -2.74590 q^{63} +7.04399 q^{65} +9.93126 q^{67} -3.44364 q^{69} -6.82687 q^{71} +13.5040 q^{73} -2.17313 q^{75} +6.01224 q^{77} +1.17313 q^{79} +1.00000 q^{81} +15.3421 q^{83} -10.5892 q^{85} -9.12497 q^{87} +1.97942 q^{89} -11.5040 q^{91} +0.616763 q^{93} -8.29809 q^{95} +3.33508 q^{97} -2.18953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} - 2 q^{5} - 9 q^{7} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^3 - 2 * q^5 - 9 * q^7 + 3 * q^9	\( 3 q + 3 q^{3} - 2 q^{5} - 9 q^{7} + 3 q^{9} + 2 q^{11} + 4 q^{13} - 2 q^{15} + 3 q^{17} - 7 q^{19} - 9 q^{21} - q^{23} - q^{25} + 3 q^{27} - 11 q^{29} - 13 q^{31} + 2 q^{33} + q^{35} - 5 q^{37} + 4 q^{39} - q^{41} - 6 q^{43} - 2 q^{45} - 11 q^{47} + 14 q^{49} + 3 q^{51} + 2 q^{53} - 4 q^{55} - 7 q^{57} - 3 q^{59} - q^{61} - 9 q^{63} - 10 q^{67} - q^{69} - 26 q^{71} + 7 q^{73} - q^{75} - 17 q^{77} - 2 q^{79} + 3 q^{81} + 3 q^{83} - 35 q^{85} - 11 q^{87} - 23 q^{89} - q^{91} - 13 q^{93} - 3 q^{95} + 14 q^{97} + 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^3 - 2 * q^5 - 9 * q^7 + 3 * q^9 + 2 * q^11 + 4 * q^13 - 2 * q^15 + 3 * q^17 - 7 * q^19 - 9 * q^21 - q^23 - q^25 + 3 * q^27 - 11 * q^29 - 13 * q^31 + 2 * q^33 + q^35 - 5 * q^37 + 4 * q^39 - q^41 - 6 * q^43 - 2 * q^45 - 11 * q^47 + 14 * q^49 + 3 * q^51 + 2 * q^53 - 4 * q^55 - 7 * q^57 - 3 * q^59 - q^61 - 9 * q^63 - 10 * q^67 - q^69 - 26 * q^71 + 7 * q^73 - q^75 - 17 * q^77 - 2 * q^79 + 3 * q^81 + 3 * q^83 - 35 * q^85 - 11 * q^87 - 23 * q^89 - q^91 - 13 * q^93 - 3 * q^95 + 14 * q^97 + 2 * q^99

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