LMFDB - Embedded newform 2601.2.a.bi.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2601,2,Mod(1,2601)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2601, 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("2601.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2601 = 3^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2601.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:	$20.7690895657$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.3418281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} - 4x^{3} + 18x^{2} + 12x - 1 $ x^6 - 9x^4 - 4x^3 + 18x^2 + 12x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 867)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.71374$ of defining polynomial
Character	$\chi$	$=$	2601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44395 q^{2} +3.97290 q^{4} -2.87349 q^{5} -1.56252 q^{7} -4.82168 q^{8} +O(q^{10})$	$q-2.44395 q^{2} +3.97290 q^{4} -2.87349 q^{5} -1.56252 q^{7} -4.82168 q^{8} +7.02266 q^{10} +6.34249 q^{11} +0.803928 q^{13} +3.81872 q^{14} +3.83815 q^{16} +3.25173 q^{19} -11.4161 q^{20} -15.5007 q^{22} +6.17389 q^{23} +3.25692 q^{25} -1.96476 q^{26} -6.20773 q^{28} +1.52895 q^{29} +2.17313 q^{31} +0.263112 q^{32} +4.48987 q^{35} +0.636236 q^{37} -7.94707 q^{38} +13.8550 q^{40} -5.61579 q^{41} -11.0241 q^{43} +25.1981 q^{44} -15.0887 q^{46} -7.46399 q^{47} -4.55854 q^{49} -7.95975 q^{50} +3.19393 q^{52} -1.34692 q^{53} -18.2250 q^{55} +7.53396 q^{56} -3.73668 q^{58} -4.03412 q^{59} +8.36818 q^{61} -5.31104 q^{62} -8.31932 q^{64} -2.31008 q^{65} +7.75709 q^{67} -10.9730 q^{70} +4.51749 q^{71} +8.28093 q^{73} -1.55493 q^{74} +12.9188 q^{76} -9.91025 q^{77} +1.50720 q^{79} -11.0289 q^{80} +13.7247 q^{82} -7.52521 q^{83} +26.9424 q^{86} -30.5814 q^{88} +6.12748 q^{89} -1.25615 q^{91} +24.5282 q^{92} +18.2416 q^{94} -9.34380 q^{95} +4.84158 q^{97} +11.1408 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 9 q^{4} + 3 q^{5} + 3 q^{7} - 12 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 + 9 * q^4 + 3 * q^5 + 3 * q^7 - 12 * q^8	$ 6 q - 3 q^{2} + 9 q^{4} + 3 q^{5} + 3 q^{7} - 12 q^{8} + 12 q^{10} + 9 q^{11} + 9 q^{13} + 6 q^{14} + 15 q^{16} + 9 q^{19} - 6 q^{20} - 18 q^{22} + 9 q^{23} + 15 q^{25} + 12 q^{26} - 15 q^{28} + 6 q^{29} + 24 q^{31} - 42 q^{32} - 3 q^{37} + 6 q^{38} - 3 q^{40} + 18 q^{41} + 3 q^{44} + 15 q^{46} - 24 q^{47} + 21 q^{49} - 12 q^{50} - 18 q^{52} - 24 q^{53} - 24 q^{55} + 54 q^{56} + 3 q^{58} + 9 q^{59} + 21 q^{61} + 30 q^{62} + 24 q^{64} - 9 q^{65} - 6 q^{67} - 3 q^{70} + 27 q^{71} + 18 q^{73} + 36 q^{74} - 3 q^{76} - 33 q^{77} + 24 q^{79} + 3 q^{80} - 15 q^{82} - 6 q^{83} - 6 q^{86} - 24 q^{88} + 39 q^{91} - 15 q^{94} + 42 q^{95} - 33 q^{97} + 57 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + 9 * q^4 + 3 * q^5 + 3 * q^7 - 12 * q^8 + 12 * q^10 + 9 * q^11 + 9 * q^13 + 6 * q^14 + 15 * q^16 + 9 * q^19 - 6 * q^20 - 18 * q^22 + 9 * q^23 + 15 * q^25 + 12 * q^26 - 15 * q^28 + 6 * q^29 + 24 * q^31 - 42 * q^32 - 3 * q^37 + 6 * q^38 - 3 * q^40 + 18 * q^41 + 3 * q^44 + 15 * q^46 - 24 * q^47 + 21 * q^49 - 12 * q^50 - 18 * q^52 - 24 * q^53 - 24 * q^55 + 54 * q^56 + 3 * q^58 + 9 * q^59 + 21 * q^61 + 30 * q^62 + 24 * q^64 - 9 * q^65 - 6 * q^67 - 3 * q^70 + 27 * q^71 + 18 * q^73 + 36 * q^74 - 3 * q^76 - 33 * q^77 + 24 * q^79 + 3 * q^80 - 15 * q^82 - 6 * q^83 - 6 * q^86 - 24 * q^88 + 39 * q^91 - 15 * q^94 + 42 * q^95 - 33 * q^97 + 57 * 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 $

$2$	−2.44395	−1.72814	−0.864068	−	0.503376i	$-0.832091\pi$
$2$	−2.44395	−1.72814	−0.864068	+	0.503376i	$0.832091\pi$
$3$	0	0
$3$	0	0
$4$	3.97290	1.98645
$5$	−2.87349	−1.28506	−0.642531	−	0.766260i	$-0.722116\pi$
$5$	−2.87349	−1.28506	−0.642531	+	0.766260i	$0.722116\pi$
$6$	0	0
$7$	−1.56252	−0.590576	−0.295288	−	0.955408i	$-0.595416\pi$
$7$	−1.56252	−0.590576	−0.295288	+	0.955408i	$0.595416\pi$
$8$	−4.82168	−1.70472
$9$	0	0
$10$	7.02266	2.22076
$11$	6.34249	1.91233	0.956166	−	0.292826i	$-0.0945955\pi$
$11$	6.34249	1.91233	0.956166	+	0.292826i	$0.0945955\pi$
$12$	0	0
$13$	0.803928	0.222970	0.111485	−	0.993766i	$-0.464439\pi$
$13$	0.803928	0.222970	0.111485	+	0.993766i	$0.464439\pi$
$14$	3.81872	1.02060
$15$	0	0
$16$	3.83815	0.959536
$17$	0	0
$17$	0	0
$18$	0	0
$19$	3.25173	0.745998	0.372999	−	0.927832i	$-0.378329\pi$
$19$	3.25173	0.745998	0.372999	+	0.927832i	$0.378329\pi$
$20$	−11.4161	−2.55271
$21$	0	0
$22$	−15.5007	−3.30477
$23$	6.17389	1.28734	0.643672	−	0.765301i	$-0.277410\pi$
$23$	6.17389	1.28734	0.643672	+	0.765301i	$0.277410\pi$
$24$	0	0
$25$	3.25692	0.651384
$26$	−1.96476	−0.385321
$27$	0	0
$28$	−6.20773	−1.17315
$29$	1.52895	0.283919	0.141959	−	0.989872i	$-0.454660\pi$
$29$	1.52895	0.283919	0.141959	+	0.989872i	$0.454660\pi$
$30$	0	0
$31$	2.17313	0.390306	0.195153	−	0.980773i	$-0.437480\pi$
$31$	2.17313	0.390306	0.195153	+	0.980773i	$0.437480\pi$
$32$	0.263112	0.0465121
$33$	0	0
$34$	0	0
$35$	4.48987	0.758927
$36$	0	0
$37$	0.636236	0.104597	0.0522983	−	0.998632i	$-0.483345\pi$
$37$	0.636236	0.104597	0.0522983	+	0.998632i	$0.483345\pi$
$38$	−7.94707	−1.28919
$39$	0	0
$40$	13.8550	2.19067
$41$	−5.61579	−0.877039	−0.438519	−	0.898722i	$-0.644497\pi$
$41$	−5.61579	−0.877039	−0.438519	+	0.898722i	$0.644497\pi$
$42$	0	0
$43$	−11.0241	−1.68116	−0.840582	−	0.541685i	$-0.817787\pi$
$43$	−11.0241	−1.68116	−0.840582	+	0.541685i	$0.817787\pi$
$44$	25.1981	3.79875
$45$	0	0
$46$	−15.0887	−2.22470
$47$	−7.46399	−1.08874	−0.544368	−	0.838847i	$-0.683230\pi$
$47$	−7.46399	−1.08874	−0.544368	+	0.838847i	$0.683230\pi$
$48$	0	0
$49$	−4.55854	−0.651220
$50$	−7.95975	−1.12568
$51$	0	0
$52$	3.19393	0.442918
$53$	−1.34692	−0.185014	−0.0925071	−	0.995712i	$-0.529488\pi$
$53$	−1.34692	−0.185014	−0.0925071	+	0.995712i	$0.529488\pi$
$54$	0	0
$55$	−18.2250	−2.45746
$56$	7.53396	1.00677
$57$	0	0
$58$	−3.73668	−0.490650
$59$	−4.03412	−0.525198	−0.262599	−	0.964905i	$-0.584580\pi$
$59$	−4.03412	−0.525198	−0.262599	+	0.964905i	$0.584580\pi$
$60$	0	0
$61$	8.36818	1.07144	0.535718	−	0.844397i	$-0.320041\pi$
$61$	8.36818	1.07144	0.535718	+	0.844397i	$0.320041\pi$
$62$	−5.31104	−0.674502
$63$	0	0
$64$	−8.31932	−1.03992
$65$	−2.31008	−0.286530
$66$	0	0
$67$	7.75709	0.947680	0.473840	−	0.880611i	$-0.342868\pi$
$67$	7.75709	0.947680	0.473840	+	0.880611i	$0.342868\pi$
$68$	0	0
$69$	0	0
$70$	−10.9730	−1.31153
$71$	4.51749	0.536127	0.268064	−	0.963401i	$-0.413616\pi$
$71$	4.51749	0.536127	0.268064	+	0.963401i	$0.413616\pi$
$72$	0	0
$73$	8.28093	0.969209	0.484605	−	0.874733i	$-0.338963\pi$
$73$	8.28093	0.969209	0.484605	+	0.874733i	$0.338963\pi$
$74$	−1.55493	−0.180757
$75$	0	0
$76$	12.9188	1.48189
$77$	−9.91025	−1.12938
$78$	0	0
$79$	1.50720	0.169573	0.0847865	−	0.996399i	$-0.472979\pi$
$79$	1.50720	0.169573	0.0847865	+	0.996399i	$0.472979\pi$
$80$	−11.0289	−1.23306
$81$	0	0
$82$	13.7247	1.51564
$83$	−7.52521	−0.825999	−0.413000	−	0.910731i	$-0.635519\pi$
$83$	−7.52521	−0.825999	−0.413000	+	0.910731i	$0.635519\pi$
$84$	0	0
$85$	0	0
$86$	26.9424	2.90528
$87$	0	0
$88$	−30.5814	−3.25999
$89$	6.12748	0.649511	0.324756	−	0.945798i	$-0.394718\pi$
$89$	6.12748	0.649511	0.324756	+	0.945798i	$0.394718\pi$
$90$	0	0
$91$	−1.25615	−0.131680
$92$	24.5282	2.55725
$93$	0	0
$94$	18.2416	1.88148
$95$	−9.34380	−0.958654
$96$	0	0
$97$	4.84158	0.491588	0.245794	−	0.969322i	$-0.420951\pi$
$97$	4.84158	0.491588	0.245794	+	0.969322i	$0.420951\pi$
$98$	11.1408	1.12540
$99$	0	0
$100$	12.9394	1.29394
$101$	15.8161	1.57376	0.786882	−	0.617104i	$-0.211694\pi$
$101$	15.8161	1.57376	0.786882	+	0.617104i	$0.211694\pi$
$102$	0	0
$103$	−7.19272	−0.708720	−0.354360	−	0.935109i	$-0.615301\pi$
$103$	−7.19272	−0.708720	−0.354360	+	0.935109i	$0.615301\pi$
$104$	−3.87628	−0.380101
$105$	0	0
$106$	3.29182	0.319730
$107$	−3.67769	−0.355535	−0.177768	−	0.984072i	$-0.556888\pi$
$107$	−3.67769	−0.355535	−0.177768	+	0.984072i	$0.556888\pi$
$108$	0	0
$109$	10.2836	0.984992	0.492496	−	0.870315i	$-0.336085\pi$
$109$	10.2836	0.984992	0.492496	+	0.870315i	$0.336085\pi$
$110$	44.5411	4.24683
$111$	0	0
$112$	−5.99717	−0.566679
$113$	−13.9303	−1.31045	−0.655226	−	0.755433i	$-0.727427\pi$
$113$	−13.9303	−1.31045	−0.655226	+	0.755433i	$0.727427\pi$
$114$	0	0
$115$	−17.7406	−1.65432
$116$	6.07437	0.563991
$117$	0	0
$118$	9.85920	0.907613
$119$	0	0
$120$	0	0
$121$	29.2271	2.65701
$122$	−20.4514	−1.85159
$123$	0	0
$124$	8.63365	0.775325
$125$	5.00872	0.447993
$126$	0	0
$127$	2.17742	0.193215	0.0966076	−	0.995323i	$-0.469201\pi$
$127$	2.17742	0.193215	0.0966076	+	0.995323i	$0.469201\pi$
$128$	19.8058	1.75060
$129$	0	0
$130$	5.64571	0.495162
$131$	4.40863	0.385184	0.192592	−	0.981279i	$-0.438311\pi$
$131$	4.40863	0.385184	0.192592	+	0.981279i	$0.438311\pi$
$132$	0	0
$133$	−5.08089	−0.440569
$134$	−18.9580	−1.63772
$135$	0	0
$136$	0	0
$137$	−0.311499	−0.0266131	−0.0133066	−	0.999911i	$-0.504236\pi$
$137$	−0.311499	−0.0266131	−0.0133066	+	0.999911i	$0.504236\pi$
$138$	0	0
$139$	−10.8097	−0.916871	−0.458435	−	0.888728i	$-0.651590\pi$
$139$	−10.8097	−0.916871	−0.458435	+	0.888728i	$0.651590\pi$
$140$	17.8378	1.50757
$141$	0	0
$142$	−11.0405	−0.926501
$143$	5.09890	0.426392
$144$	0	0
$145$	−4.39341	−0.364853
$146$	−20.2382	−1.67492
$147$	0	0
$148$	2.52770	0.207776
$149$	−17.7269	−1.45225	−0.726123	−	0.687565i	$-0.758680\pi$
$149$	−17.7269	−1.45225	−0.726123	+	0.687565i	$0.758680\pi$
$150$	0	0
$151$	−16.1244	−1.31219	−0.656093	−	0.754680i	$-0.727792\pi$
$151$	−16.1244	−1.31219	−0.656093	+	0.754680i	$0.727792\pi$
$152$	−15.6788	−1.27172
$153$	0	0
$154$	24.2202	1.95172
$155$	−6.24447	−0.501568
$156$	0	0
$157$	19.6347	1.56702	0.783510	−	0.621380i	$-0.213428\pi$
$157$	19.6347	1.56702	0.783510	+	0.621380i	$0.213428\pi$
$158$	−3.68352	−0.293045
$159$	0	0
$160$	−0.756049	−0.0597709
$161$	−9.64681	−0.760275
$162$	0	0
$163$	−10.8776	−0.852002	−0.426001	−	0.904723i	$-0.640078\pi$
$163$	−10.8776	−0.852002	−0.426001	+	0.904723i	$0.640078\pi$
$164$	−22.3110	−1.74219
$165$	0	0
$166$	18.3913	1.42744
$167$	10.5141	0.813603	0.406802	−	0.913517i	$-0.366644\pi$
$167$	10.5141	0.813603	0.406802	+	0.913517i	$0.366644\pi$
$168$	0	0
$169$	−12.3537	−0.950285
$170$	0	0
$171$	0	0
$172$	−43.7978	−3.33955
$173$	7.74845	0.589104	0.294552	−	0.955635i	$-0.404830\pi$
$173$	7.74845	0.589104	0.294552	+	0.955635i	$0.404830\pi$
$174$	0	0
$175$	−5.08899	−0.384692
$176$	24.3434	1.83495
$177$	0	0
$178$	−14.9753	−1.12244
$179$	11.9475	0.893001	0.446501	−	0.894783i	$-0.352670\pi$
$179$	11.9475	0.893001	0.446501	+	0.894783i	$0.352670\pi$
$180$	0	0
$181$	−1.75313	−0.130309	−0.0651544	−	0.997875i	$-0.520754\pi$
$181$	−1.75313	−0.130309	−0.0651544	+	0.997875i	$0.520754\pi$
$182$	3.06997	0.227562
$183$	0	0
$184$	−29.7685	−2.19456
$185$	−1.82822	−0.134413
$186$	0	0
$187$	0	0
$188$	−29.6537	−2.16272
$189$	0	0
$190$	22.8358	1.65668
$191$	22.3232	1.61525	0.807627	−	0.589694i	$-0.200752\pi$
$191$	22.3232	1.61525	0.807627	+	0.589694i	$0.200752\pi$
$192$	0	0
$193$	−26.1577	−1.88287	−0.941435	−	0.337195i	$-0.890522\pi$
$193$	−26.1577	−1.88287	−0.941435	+	0.337195i	$0.890522\pi$
$194$	−11.8326	−0.849530
$195$	0	0
$196$	−18.1106	−1.29362
$197$	17.7960	1.26791	0.633957	−	0.773368i	$-0.281429\pi$
$197$	17.7960	1.26791	0.633957	+	0.773368i	$0.281429\pi$
$198$	0	0
$199$	22.6540	1.60590	0.802951	−	0.596045i	$-0.203262\pi$
$199$	22.6540	1.60590	0.802951	+	0.596045i	$0.203262\pi$
$200$	−15.7038	−1.11043
$201$	0	0
$202$	−38.6538	−2.71968
$203$	−2.38901	−0.167676
$204$	0	0
$205$	16.1369	1.12705
$206$	17.5787	1.22476
$207$	0	0
$208$	3.08559	0.213947
$209$	20.6241	1.42660
$210$	0	0
$211$	22.7255	1.56449	0.782245	−	0.622971i	$-0.214075\pi$
$211$	22.7255	1.56449	0.782245	+	0.622971i	$0.214075\pi$
$212$	−5.35120	−0.367522
$213$	0	0
$214$	8.98809	0.614413
$215$	31.6777	2.16040
$216$	0	0
$217$	−3.39556	−0.230506
$218$	−25.1327	−1.70220
$219$	0	0
$220$	−72.4063	−4.88163
$221$	0	0
$222$	0	0
$223$	0.594738	0.0398266	0.0199133	−	0.999802i	$-0.493661\pi$
$223$	0.594738	0.0398266	0.0199133	+	0.999802i	$0.493661\pi$
$224$	−0.411118	−0.0274690
$225$	0	0
$226$	34.0450	2.26464
$227$	−20.0429	−1.33030	−0.665148	−	0.746711i	$-0.731632\pi$
$227$	−20.0429	−1.33030	−0.665148	+	0.746711i	$0.731632\pi$
$228$	0	0
$229$	1.93974	0.128182	0.0640909	−	0.997944i	$-0.479585\pi$
$229$	1.93974	0.128182	0.0640909	+	0.997944i	$0.479585\pi$
$230$	43.3571	2.85888
$231$	0	0
$232$	−7.37210	−0.484002
$233$	−8.44275	−0.553103	−0.276551	−	0.960999i	$-0.589192\pi$
$233$	−8.44275	−0.553103	−0.276551	+	0.960999i	$0.589192\pi$
$234$	0	0
$235$	21.4477	1.39909
$236$	−16.0272	−1.04328
$237$	0	0
$238$	0	0
$239$	−15.5030	−1.00281	−0.501403	−	0.865214i	$-0.667183\pi$
$239$	−15.5030	−1.00281	−0.501403	+	0.865214i	$0.667183\pi$
$240$	0	0
$241$	29.7917	1.91906	0.959528	−	0.281615i	$-0.0908701\pi$
$241$	29.7917	1.91906	0.959528	+	0.281615i	$0.0908701\pi$
$242$	−71.4297	−4.59168
$243$	0	0
$244$	33.2460	2.12836
$245$	13.0989	0.836858
$246$	0	0
$247$	2.61416	0.166335
$248$	−10.4782	−0.665363
$249$	0	0
$250$	−12.2411	−0.774193
$251$	4.59133	0.289802	0.144901	−	0.989446i	$-0.453714\pi$
$251$	4.59133	0.289802	0.144901	+	0.989446i	$0.453714\pi$
$252$	0	0
$253$	39.1578	2.46183
$254$	−5.32152	−0.333902
$255$	0	0
$256$	−31.7658	−1.98536
$257$	29.0731	1.81353	0.906765	−	0.421637i	$-0.138544\pi$
$257$	29.0731	1.81353	0.906765	+	0.421637i	$0.138544\pi$
$258$	0	0
$259$	−0.994130	−0.0617722
$260$	−9.17770	−0.569177
$261$	0	0
$262$	−10.7745	−0.665649
$263$	1.07458	0.0662617	0.0331308	−	0.999451i	$-0.489452\pi$
$263$	1.07458	0.0662617	0.0331308	+	0.999451i	$0.489452\pi$
$264$	0	0
$265$	3.87037	0.237755
$266$	12.4174	0.761362
$267$	0	0
$268$	30.8182	1.88252
$269$	25.3189	1.54372	0.771860	−	0.635793i	$-0.219327\pi$
$269$	25.3189	1.54372	0.771860	+	0.635793i	$0.219327\pi$
$270$	0	0
$271$	19.4812	1.18340	0.591699	−	0.806159i	$-0.298458\pi$
$271$	19.4812	1.18340	0.591699	+	0.806159i	$0.298458\pi$
$272$	0	0
$273$	0	0
$274$	0.761288	0.0459911
$275$	20.6570	1.24566
$276$	0	0
$277$	−9.50313	−0.570988	−0.285494	−	0.958381i	$-0.592158\pi$
$277$	−9.50313	−0.570988	−0.285494	+	0.958381i	$0.592158\pi$
$278$	26.4185	1.58448
$279$	0	0
$280$	−21.6487	−1.29376
$281$	−14.4217	−0.860329	−0.430164	−	0.902751i	$-0.641544\pi$
$281$	−14.4217	−0.860329	−0.430164	+	0.902751i	$0.641544\pi$
$282$	0	0
$283$	19.4109	1.15386	0.576928	−	0.816795i	$-0.304251\pi$
$283$	19.4109	1.15386	0.576928	+	0.816795i	$0.304251\pi$
$284$	17.9475	1.06499
$285$	0	0
$286$	−12.4615	−0.736862
$287$	8.77477	0.517958
$288$	0	0
$289$	0	0
$290$	10.7373	0.630516
$291$	0	0
$292$	32.8993	1.92529
$293$	1.07338	0.0627076	0.0313538	−	0.999508i	$-0.490018\pi$
$293$	1.07338	0.0627076	0.0313538	+	0.999508i	$0.490018\pi$
$294$	0	0
$295$	11.5920	0.674912
$296$	−3.06772	−0.178308
$297$	0	0
$298$	43.3238	2.50968
$299$	4.96336	0.287038
$300$	0	0
$301$	17.2254	0.992855
$302$	39.4073	2.26764
$303$	0	0
$304$	12.4806	0.715812
$305$	−24.0459	−1.37686
$306$	0	0
$307$	14.5796	0.832104	0.416052	−	0.909341i	$-0.363413\pi$
$307$	14.5796	0.832104	0.416052	+	0.909341i	$0.363413\pi$
$308$	−39.3724	−2.24345
$309$	0	0
$310$	15.2612	0.866777
$311$	−14.3449	−0.813427	−0.406714	−	0.913556i	$-0.633325\pi$
$311$	−14.3449	−0.813427	−0.406714	+	0.913556i	$0.633325\pi$
$312$	0	0
$313$	−11.3185	−0.639757	−0.319879	−	0.947458i	$-0.603642\pi$
$313$	−11.3185	−0.639757	−0.319879	+	0.947458i	$0.603642\pi$
$314$	−47.9863	−2.70802
$315$	0	0
$316$	5.98795	0.336849
$317$	−11.7623	−0.660635	−0.330317	−	0.943870i	$-0.607156\pi$
$317$	−11.7623	−0.660635	−0.330317	+	0.943870i	$0.607156\pi$
$318$	0	0
$319$	9.69734	0.542947
$320$	23.9055	1.33636
$321$	0	0
$322$	23.5763	1.31386
$323$	0	0
$324$	0	0
$325$	2.61833	0.145239
$326$	26.5844	1.47237
$327$	0	0
$328$	27.0775	1.49511
$329$	11.6626	0.642981
$330$	0	0
$331$	−20.2084	−1.11075	−0.555376	−	0.831600i	$-0.687426\pi$
$331$	−20.2084	−1.11075	−0.555376	+	0.831600i	$0.687426\pi$
$332$	−29.8969	−1.64081
$333$	0	0
$334$	−25.6959	−1.40602
$335$	−22.2899	−1.21783
$336$	0	0
$337$	6.40801	0.349067	0.174533	−	0.984651i	$-0.444158\pi$
$337$	6.40801	0.349067	0.174533	+	0.984651i	$0.444158\pi$
$338$	30.1919	1.64222
$339$	0	0
$340$	0	0
$341$	13.7831	0.746395
$342$	0	0
$343$	18.0604	0.975171
$344$	53.1548	2.86591
$345$	0	0
$346$	−18.9368	−1.01805
$347$	11.7291	0.629649	0.314824	−	0.949150i	$-0.398054\pi$
$347$	11.7291	0.629649	0.314824	+	0.949150i	$0.398054\pi$
$348$	0	0
$349$	25.7808	1.38001	0.690007	−	0.723803i	$-0.257607\pi$
$349$	25.7808	1.38001	0.690007	+	0.723803i	$0.257607\pi$
$350$	12.4373	0.664799
$351$	0	0
$352$	1.66879	0.0889466
$353$	3.96309	0.210934	0.105467	−	0.994423i	$-0.466366\pi$
$353$	3.96309	0.210934	0.105467	+	0.994423i	$0.466366\pi$
$354$	0	0
$355$	−12.9809	−0.688957
$356$	24.3439	1.29022
$357$	0	0
$358$	−29.1992	−1.54323
$359$	11.2422	0.593340	0.296670	−	0.954980i	$-0.404124\pi$
$359$	11.2422	0.593340	0.296670	+	0.954980i	$0.404124\pi$
$360$	0	0
$361$	−8.42625	−0.443487
$362$	4.28455	0.225191
$363$	0	0
$364$	−4.99057	−0.261577
$365$	−23.7951	−1.24549
$366$	0	0
$367$	−15.4532	−0.806649	−0.403324	−	0.915057i	$-0.632145\pi$
$367$	−15.4532	−0.806649	−0.403324	+	0.915057i	$0.632145\pi$
$368$	23.6963	1.23525
$369$	0	0
$370$	4.46807	0.232284
$371$	2.10459	0.109265
$372$	0	0
$373$	−5.14892	−0.266601	−0.133300	−	0.991076i	$-0.542558\pi$
$373$	−5.14892	−0.266601	−0.133300	+	0.991076i	$0.542558\pi$
$374$	0	0
$375$	0	0
$376$	35.9890	1.85599
$377$	1.22917	0.0633052
$378$	0	0
$379$	11.8468	0.608531	0.304265	−	0.952587i	$-0.401589\pi$
$379$	11.8468	0.608531	0.304265	+	0.952587i	$0.401589\pi$
$380$	−37.1220	−1.90432
$381$	0	0
$382$	−54.5569	−2.79138
$383$	−30.7346	−1.57047	−0.785234	−	0.619200i	$-0.787457\pi$
$383$	−30.7346	−1.57047	−0.785234	+	0.619200i	$0.787457\pi$
$384$	0	0
$385$	28.4770	1.45132
$386$	63.9281	3.25385
$387$	0	0
$388$	19.2351	0.976515
$389$	−19.3503	−0.981099	−0.490549	−	0.871413i	$-0.663204\pi$
$389$	−19.3503	−0.981099	−0.490549	+	0.871413i	$0.663204\pi$
$390$	0	0
$391$	0	0
$392$	21.9798	1.11015
$393$	0	0
$394$	−43.4926	−2.19113
$395$	−4.33091	−0.217912
$396$	0	0
$397$	13.5426	0.679681	0.339841	−	0.940483i	$-0.389627\pi$
$397$	13.5426	0.679681	0.339841	+	0.940483i	$0.389627\pi$
$398$	−55.3654	−2.77522
$399$	0	0
$400$	12.5005	0.625026
$401$	8.65508	0.432214	0.216107	−	0.976370i	$-0.430664\pi$
$401$	8.65508	0.432214	0.216107	+	0.976370i	$0.430664\pi$
$402$	0	0
$403$	1.74704	0.0870264
$404$	62.8359	3.12620
$405$	0	0
$406$	5.83863	0.289766
$407$	4.03532	0.200023
$408$	0	0
$409$	20.2269	1.00015	0.500077	−	0.865981i	$-0.333305\pi$
$409$	20.2269	1.00015	0.500077	+	0.865981i	$0.333305\pi$
$410$	−39.4378	−1.94769
$411$	0	0
$412$	−28.5760	−1.40784
$413$	6.30339	0.310169
$414$	0	0
$415$	21.6236	1.06146
$416$	0.211523	0.0103708
$417$	0	0
$418$	−50.4042	−2.46535
$419$	27.8667	1.36138	0.680690	−	0.732572i	$-0.261680\pi$
$419$	27.8667	1.36138	0.680690	+	0.732572i	$0.261680\pi$
$420$	0	0
$421$	−30.5071	−1.48682	−0.743411	−	0.668834i	$-0.766794\pi$
$421$	−30.5071	−1.48682	−0.743411	+	0.668834i	$0.766794\pi$
$422$	−55.5401	−2.70365
$423$	0	0
$424$	6.49443	0.315398
$425$	0	0
$426$	0	0
$427$	−13.0754	−0.632765
$428$	−14.6111	−0.706254
$429$	0	0
$430$	−77.4187	−3.73346
$431$	11.8366	0.570151	0.285075	−	0.958505i	$-0.407981\pi$
$431$	11.8366	0.570151	0.285075	+	0.958505i	$0.407981\pi$
$432$	0	0
$433$	24.9436	1.19871	0.599355	−	0.800483i	$-0.295424\pi$
$433$	24.9436	1.19871	0.599355	+	0.800483i	$0.295424\pi$
$434$	8.29859	0.398345
$435$	0	0
$436$	40.8558	1.95664
$437$	20.0758	0.960356
$438$	0	0
$439$	14.2845	0.681763	0.340882	−	0.940106i	$-0.389274\pi$
$439$	14.2845	0.681763	0.340882	+	0.940106i	$0.389274\pi$
$440$	87.8753	4.18929
$441$	0	0
$442$	0	0
$443$	−3.36806	−0.160021	−0.0800107	−	0.996794i	$-0.525495\pi$
$443$	−3.36806	−0.160021	−0.0800107	+	0.996794i	$0.525495\pi$
$444$	0	0
$445$	−17.6072	−0.834662
$446$	−1.45351	−0.0688257
$447$	0	0
$448$	12.9991	0.614149
$449$	3.93610	0.185756	0.0928781	−	0.995677i	$-0.470393\pi$
$449$	3.93610	0.185756	0.0928781	+	0.995677i	$0.470393\pi$
$450$	0	0
$451$	−35.6181	−1.67719
$452$	−55.3437	−2.60315
$453$	0	0
$454$	48.9840	2.29893
$455$	3.60953	0.169218
$456$	0	0
$457$	−14.8175	−0.693132	−0.346566	−	0.938026i	$-0.612652\pi$
$457$	−14.8175	−0.693132	−0.346566	+	0.938026i	$0.612652\pi$
$458$	−4.74064	−0.221515
$459$	0	0
$460$	−70.4815	−3.28622
$461$	33.2839	1.55019	0.775093	−	0.631847i	$-0.217703\pi$
$461$	33.2839	1.55019	0.775093	+	0.631847i	$0.217703\pi$
$462$	0	0
$463$	19.1509	0.890018	0.445009	−	0.895526i	$-0.353201\pi$
$463$	19.1509	0.890018	0.445009	+	0.895526i	$0.353201\pi$
$464$	5.86833	0.272430
$465$	0	0
$466$	20.6337	0.955837
$467$	37.8301	1.75057	0.875285	−	0.483607i	$-0.160674\pi$
$467$	37.8301	1.75057	0.875285	+	0.483607i	$0.160674\pi$
$468$	0	0
$469$	−12.1206	−0.559677
$470$	−52.4171	−2.41782
$471$	0	0
$472$	19.4512	0.895315
$473$	−69.9204	−3.21494
$474$	0	0
$475$	10.5906	0.485931
$476$	0	0
$477$	0	0
$478$	37.8886	1.73298
$479$	−0.429488	−0.0196238	−0.00981191	−	0.999952i	$-0.503123\pi$
$479$	−0.429488	−0.0196238	−0.00981191	+	0.999952i	$0.503123\pi$
$480$	0	0
$481$	0.511488	0.0233218
$482$	−72.8096	−3.31639
$483$	0	0
$484$	116.117	5.27803
$485$	−13.9122	−0.631721
$486$	0	0
$487$	−0.195626	−0.00886466	−0.00443233	−	0.999990i	$-0.501411\pi$
$487$	−0.195626	−0.00886466	−0.00443233	+	0.999990i	$0.501411\pi$
$488$	−40.3487	−1.82650
$489$	0	0
$490$	−32.0131	−1.44620
$491$	9.32805	0.420969	0.210485	−	0.977597i	$-0.432496\pi$
$491$	9.32805	0.420969	0.210485	+	0.977597i	$0.432496\pi$
$492$	0	0
$493$	0	0
$494$	−6.38888	−0.287449
$495$	0	0
$496$	8.34081	0.374513
$497$	−7.05866	−0.316624
$498$	0	0
$499$	8.21386	0.367703	0.183851	−	0.982954i	$-0.441143\pi$
$499$	8.21386	0.367703	0.183851	+	0.982954i	$0.441143\pi$
$500$	19.8991	0.889917
$501$	0	0
$502$	−11.2210	−0.500818
$503$	29.9327	1.33463	0.667316	−	0.744775i	$-0.267443\pi$
$503$	29.9327	1.33463	0.667316	+	0.744775i	$0.267443\pi$
$504$	0	0
$505$	−45.4474	−2.02238
$506$	−95.6998	−4.25437
$507$	0	0
$508$	8.65069	0.383812
$509$	−2.71603	−0.120386	−0.0601929	−	0.998187i	$-0.519172\pi$
$509$	−2.71603	−0.120386	−0.0601929	+	0.998187i	$0.519172\pi$
$510$	0	0
$511$	−12.9391	−0.572392
$512$	38.0225	1.68037
$513$	0	0
$514$	−71.0532	−3.13402
$515$	20.6682	0.910749
$516$	0	0
$517$	−47.3403	−2.08202
$518$	2.42961	0.106751
$519$	0	0
$520$	11.1384	0.488453
$521$	2.07489	0.0909026	0.0454513	−	0.998967i	$-0.485527\pi$
$521$	2.07489	0.0909026	0.0454513	+	0.998967i	$0.485527\pi$
$522$	0	0
$523$	17.2333	0.753558	0.376779	−	0.926303i	$-0.377032\pi$
$523$	17.2333	0.753558	0.376779	+	0.926303i	$0.377032\pi$
$524$	17.5150	0.765148
$525$	0	0
$526$	−2.62623	−0.114509
$527$	0	0
$528$	0	0
$529$	15.1169	0.657255
$530$	−9.45899	−0.410872
$531$	0	0
$532$	−20.1859	−0.875168
$533$	−4.51469	−0.195553
$534$	0	0
$535$	10.5678	0.456885
$536$	−37.4022	−1.61553
$537$	0	0
$538$	−61.8782	−2.66776
$539$	−28.9125	−1.24535
$540$	0	0
$541$	−3.53584	−0.152018	−0.0760088	−	0.997107i	$-0.524218\pi$
$541$	−3.53584	−0.152018	−0.0760088	+	0.997107i	$0.524218\pi$
$542$	−47.6111	−2.04507
$543$	0	0
$544$	0	0
$545$	−29.5498	−1.26578
$546$	0	0
$547$	19.5703	0.836766	0.418383	−	0.908271i	$-0.362597\pi$
$547$	19.5703	0.836766	0.418383	+	0.908271i	$0.362597\pi$
$548$	−1.23755	−0.0528657
$549$	0	0
$550$	−50.4846	−2.15267
$551$	4.97173	0.211803
$552$	0	0
$553$	−2.35502	−0.100146
$554$	23.2252	0.986744
$555$	0	0
$556$	−42.9461	−1.82132
$557$	−15.0835	−0.639110	−0.319555	−	0.947568i	$-0.603533\pi$
$557$	−15.0835	−0.639110	−0.319555	+	0.947568i	$0.603533\pi$
$558$	0	0
$559$	−8.86260	−0.374848
$560$	17.2328	0.728218
$561$	0	0
$562$	35.2460	1.48676
$563$	−38.6507	−1.62893	−0.814466	−	0.580212i	$-0.802970\pi$
$563$	−38.6507	−1.62893	−0.814466	+	0.580212i	$0.802970\pi$
$564$	0	0
$565$	40.0285	1.68401
$566$	−47.4392	−1.99402
$567$	0	0
$568$	−21.7819	−0.913947
$569$	3.19348	0.133878	0.0669389	−	0.997757i	$-0.478677\pi$
$569$	3.19348	0.133878	0.0669389	+	0.997757i	$0.478677\pi$
$570$	0	0
$571$	5.32142	0.222695	0.111347	−	0.993782i	$-0.464483\pi$
$571$	5.32142	0.222695	0.111347	+	0.993782i	$0.464483\pi$
$572$	20.2574	0.847006
$573$	0	0
$574$	−21.4451	−0.895102
$575$	20.1078	0.838555
$576$	0	0
$577$	−10.4307	−0.434236	−0.217118	−	0.976145i	$-0.569666\pi$
$577$	−10.4307	−0.434236	−0.217118	+	0.976145i	$0.569666\pi$
$578$	0	0
$579$	0	0
$580$	−17.4546	−0.724763
$581$	11.7583	0.487816
$582$	0	0
$583$	−8.54285	−0.353809
$584$	−39.9280	−1.65223
$585$	0	0
$586$	−2.62329	−0.108367
$587$	18.7387	0.773427	0.386714	−	0.922200i	$-0.373610\pi$
$587$	18.7387	0.773427	0.386714	+	0.922200i	$0.373610\pi$
$588$	0	0
$589$	7.06645	0.291168
$590$	−28.3303	−1.16634
$591$	0	0
$592$	2.44197	0.100364
$593$	7.29409	0.299533	0.149766	−	0.988721i	$-0.452148\pi$
$593$	7.29409	0.299533	0.149766	+	0.988721i	$0.452148\pi$
$594$	0	0
$595$	0	0
$596$	−70.4273	−2.88482
$597$	0	0
$598$	−12.1302	−0.496041
$599$	−31.8625	−1.30187	−0.650933	−	0.759135i	$-0.725622\pi$
$599$	−31.8625	−1.30187	−0.650933	+	0.759135i	$0.725622\pi$
$600$	0	0
$601$	−0.524164	−0.0213811	−0.0106905	−	0.999943i	$-0.503403\pi$
$601$	−0.524164	−0.0213811	−0.0106905	+	0.999943i	$0.503403\pi$
$602$	−42.0980	−1.71579
$603$	0	0
$604$	−64.0607	−2.60659
$605$	−83.9838	−3.41443
$606$	0	0
$607$	−0.949127	−0.0385239	−0.0192619	−	0.999814i	$-0.506132\pi$
$607$	−0.949127	−0.0385239	−0.0192619	+	0.999814i	$0.506132\pi$
$608$	0.855570	0.0346980
$609$	0	0
$610$	58.7669	2.37940
$611$	−6.00051	−0.242755
$612$	0	0
$613$	3.89703	0.157399	0.0786997	−	0.996898i	$-0.474923\pi$
$613$	3.89703	0.157399	0.0786997	+	0.996898i	$0.474923\pi$
$614$	−35.6319	−1.43799
$615$	0	0
$616$	47.7840	1.92527
$617$	19.3509	0.779037	0.389518	−	0.921019i	$-0.372641\pi$
$617$	19.3509	0.779037	0.389518	+	0.921019i	$0.372641\pi$
$618$	0	0
$619$	−19.6749	−0.790803	−0.395401	−	0.918508i	$-0.629394\pi$
$619$	−19.6749	−0.790803	−0.395401	+	0.918508i	$0.629394\pi$
$620$	−24.8087	−0.996340
$621$	0	0
$622$	35.0584	1.40571
$623$	−9.57429	−0.383586
$624$	0	0
$625$	−30.6771	−1.22708
$626$	27.6618	1.10559
$627$	0	0
$628$	78.0067	3.11281
$629$	0	0
$630$	0	0
$631$	−2.77834	−0.110604	−0.0553019	−	0.998470i	$-0.517612\pi$
$631$	−2.77834	−0.110604	−0.0553019	+	0.998470i	$0.517612\pi$
$632$	−7.26722	−0.289075
$633$	0	0
$634$	28.7464	1.14167
$635$	−6.25680	−0.248293
$636$	0	0
$637$	−3.66474	−0.145202
$638$	−23.6998	−0.938286
$639$	0	0
$640$	−56.9117	−2.24963
$641$	−21.5166	−0.849855	−0.424928	−	0.905227i	$-0.639700\pi$
$641$	−21.5166	−0.849855	−0.424928	+	0.905227i	$0.639700\pi$
$642$	0	0
$643$	−44.4358	−1.75238	−0.876188	−	0.481970i	$-0.839922\pi$
$643$	−44.4358	−1.75238	−0.876188	+	0.481970i	$0.839922\pi$
$644$	−38.3258	−1.51025
$645$	0	0
$646$	0	0
$647$	43.8840	1.72526	0.862629	−	0.505838i	$-0.168817\pi$
$647$	43.8840	1.72526	0.862629	+	0.505838i	$0.168817\pi$
$648$	0	0
$649$	−25.5864	−1.00435
$650$	−6.39907	−0.250992
$651$	0	0
$652$	−43.2158	−1.69246
$653$	−8.54832	−0.334522	−0.167261	−	0.985913i	$-0.553492\pi$
$653$	−8.54832	−0.334522	−0.167261	+	0.985913i	$0.553492\pi$
$654$	0	0
$655$	−12.6681	−0.494985
$656$	−21.5542	−0.841551
$657$	0	0
$658$	−28.5029	−1.11116
$659$	−36.1408	−1.40785	−0.703924	−	0.710276i	$-0.748570\pi$
$659$	−36.1408	−1.40785	−0.703924	+	0.710276i	$0.748570\pi$
$660$	0	0
$661$	46.4203	1.80554	0.902771	−	0.430122i	$-0.141529\pi$
$661$	46.4203	1.80554	0.902771	+	0.430122i	$0.141529\pi$
$662$	49.3882	1.91953
$663$	0	0
$664$	36.2841	1.40810
$665$	14.5999	0.566158
$666$	0	0
$667$	9.43956	0.365501
$668$	41.7714	1.61618
$669$	0	0
$670$	54.4754	2.10457
$671$	53.0751	2.04894
$672$	0	0
$673$	45.1306	1.73966	0.869829	−	0.493353i	$-0.164229\pi$
$673$	45.1306	1.73966	0.869829	+	0.493353i	$0.164229\pi$
$674$	−15.6609	−0.603234
$675$	0	0
$676$	−49.0800	−1.88769
$677$	36.2356	1.39265	0.696324	−	0.717727i	$-0.254818\pi$
$677$	36.2356	1.39265	0.696324	+	0.717727i	$0.254818\pi$
$678$	0	0
$679$	−7.56505	−0.290320
$680$	0	0
$681$	0	0
$682$	−33.6852	−1.28987
$683$	−24.3296	−0.930947	−0.465474	−	0.885062i	$-0.654116\pi$
$683$	−24.3296	−0.930947	−0.465474	+	0.885062i	$0.654116\pi$
$684$	0	0
$685$	0.895087	0.0341995
$686$	−44.1388	−1.68523
$687$	0	0
$688$	−42.3122	−1.61314
$689$	−1.08283	−0.0412525
$690$	0	0
$691$	−21.3887	−0.813666	−0.406833	−	0.913503i	$-0.633367\pi$
$691$	−21.3887	−0.813666	−0.406833	+	0.913503i	$0.633367\pi$
$692$	30.7838	1.17023
$693$	0	0
$694$	−28.6652	−1.08812
$695$	31.0617	1.17824
$696$	0	0
$697$	0	0
$698$	−63.0070	−2.38485
$699$	0	0
$700$	−20.2181	−0.764171
$701$	15.3315	0.579063	0.289532	−	0.957168i	$-0.406500\pi$
$701$	15.3315	0.579063	0.289532	+	0.957168i	$0.406500\pi$
$702$	0	0
$703$	2.06887	0.0780288
$704$	−52.7652	−1.98866
$705$	0	0
$706$	−9.68560	−0.364522
$707$	−24.7130	−0.929427
$708$	0	0
$709$	−38.5013	−1.44595	−0.722974	−	0.690875i	$-0.757225\pi$
$709$	−38.5013	−1.44595	−0.722974	+	0.690875i	$0.757225\pi$
$710$	31.7248	1.19061
$711$	0	0
$712$	−29.5447	−1.10723
$713$	13.4167	0.502459
$714$	0	0
$715$	−14.6516	−0.547940
$716$	47.4664	1.77390
$717$	0	0
$718$	−27.4754	−1.02537
$719$	−15.2312	−0.568028	−0.284014	−	0.958820i	$-0.591666\pi$
$719$	−15.2312	−0.568028	−0.284014	+	0.958820i	$0.591666\pi$
$720$	0	0
$721$	11.2388	0.418553
$722$	20.5933	0.766405
$723$	0	0
$724$	−6.96499	−0.258852
$725$	4.97967	0.184940
$726$	0	0
$727$	11.2839	0.418495	0.209248	−	0.977863i	$-0.432899\pi$
$727$	11.2839	0.418495	0.209248	+	0.977863i	$0.432899\pi$
$728$	6.05676	0.224478
$729$	0	0
$730$	58.1542	2.15238
$731$	0	0
$732$	0	0
$733$	−26.5213	−0.979585	−0.489793	−	0.871839i	$-0.662927\pi$
$733$	−26.5213	−0.979585	−0.489793	+	0.871839i	$0.662927\pi$
$734$	37.7668	1.39400
$735$	0	0
$736$	1.62443	0.0598771
$737$	49.1993	1.81228
$738$	0	0
$739$	0.861682	0.0316975	0.0158487	−	0.999874i	$-0.494955\pi$
$739$	0.861682	0.0316975	0.0158487	+	0.999874i	$0.494955\pi$
$740$	−7.26332	−0.267005
$741$	0	0
$742$	−5.14352	−0.188825
$743$	−4.33692	−0.159106	−0.0795531	−	0.996831i	$-0.525349\pi$
$743$	−4.33692	−0.159106	−0.0795531	+	0.996831i	$0.525349\pi$
$744$	0	0
$745$	50.9381	1.86623
$746$	12.5837	0.460722
$747$	0	0
$748$	0	0
$749$	5.74645	0.209971
$750$	0	0
$751$	34.0949	1.24414	0.622071	−	0.782961i	$-0.286291\pi$
$751$	34.0949	1.24414	0.622071	+	0.782961i	$0.286291\pi$
$752$	−28.6479	−1.04468
$753$	0	0
$754$	−3.00402	−0.109400
$755$	46.3333	1.68624
$756$	0	0
$757$	35.7904	1.30082	0.650412	−	0.759581i	$-0.274596\pi$
$757$	35.7904	1.30082	0.650412	+	0.759581i	$0.274596\pi$
$758$	−28.9531	−1.05162
$759$	0	0
$760$	45.0528	1.63424
$761$	−24.8283	−0.900025	−0.450013	−	0.893022i	$-0.648580\pi$
$761$	−24.8283	−0.900025	−0.450013	+	0.893022i	$0.648580\pi$
$762$	0	0
$763$	−16.0683	−0.581713
$764$	88.6880	3.20862
$765$	0	0
$766$	75.1140	2.71398
$767$	−3.24314	−0.117103
$768$	0	0
$769$	−47.0234	−1.69571	−0.847854	−	0.530230i	$-0.822106\pi$
$769$	−47.0234	−1.69571	−0.847854	+	0.530230i	$0.822106\pi$
$770$	−69.5963	−2.50808
$771$	0	0
$772$	−103.922	−3.74023
$773$	−41.7490	−1.50161	−0.750804	−	0.660525i	$-0.770334\pi$
$773$	−41.7490	−1.50161	−0.750804	+	0.660525i	$0.770334\pi$
$774$	0	0
$775$	7.07772	0.254239
$776$	−23.3445	−0.838020
$777$	0	0
$778$	47.2912	1.69547
$779$	−18.2610	−0.654269
$780$	0	0
$781$	28.6521	1.02525
$782$	0	0
$783$	0	0
$784$	−17.4963	−0.624869
$785$	−56.4200	−2.01372
$786$	0	0
$787$	2.38063	0.0848604	0.0424302	−	0.999099i	$-0.486490\pi$
$787$	2.38063	0.0848604	0.0424302	+	0.999099i	$0.486490\pi$
$788$	70.7019	2.51865
$789$	0	0
$790$	10.5845	0.376581
$791$	21.7663	0.773922
$792$	0	0
$793$	6.72742	0.238898
$794$	−33.0974	−1.17458
$795$	0	0
$796$	90.0023	3.19005
$797$	38.4308	1.36129	0.680645	−	0.732614i	$-0.261700\pi$
$797$	38.4308	1.36129	0.680645	+	0.732614i	$0.261700\pi$
$798$	0	0
$799$	0	0
$800$	0.856935	0.0302972
$801$	0	0
$802$	−21.1526	−0.746924
$803$	52.5217	1.85345
$804$	0	0
$805$	27.7200	0.977000
$806$	−4.26969	−0.150393
$807$	0	0
$808$	−76.2602	−2.68283
$809$	14.5807	0.512630	0.256315	−	0.966593i	$-0.417492\pi$
$809$	14.5807	0.512630	0.256315	+	0.966593i	$0.417492\pi$
$810$	0	0
$811$	0.278172	0.00976792	0.00488396	−	0.999988i	$-0.498445\pi$
$811$	0.278172	0.00976792	0.00488396	+	0.999988i	$0.498445\pi$
$812$	−9.49131	−0.333080
$813$	0	0
$814$	−9.86213	−0.345667
$815$	31.2567	1.09487
$816$	0	0
$817$	−35.8475	−1.25414
$818$	−49.4335	−1.72840
$819$	0	0
$820$	64.1103	2.23883
$821$	−12.4495	−0.434492	−0.217246	−	0.976117i	$-0.569707\pi$
$821$	−12.4495	−0.434492	−0.217246	+	0.976117i	$0.569707\pi$
$822$	0	0
$823$	20.9324	0.729659	0.364829	−	0.931074i	$-0.381127\pi$
$823$	20.9324	0.729659	0.364829	+	0.931074i	$0.381127\pi$
$824$	34.6810	1.20817
$825$	0	0
$826$	−15.4052	−0.536015
$827$	30.9351	1.07572	0.537859	−	0.843035i	$-0.319233\pi$
$827$	30.9351	1.07572	0.537859	+	0.843035i	$0.319233\pi$
$828$	0	0
$829$	5.04799	0.175324	0.0876620	−	0.996150i	$-0.472060\pi$
$829$	5.04799	0.175324	0.0876620	+	0.996150i	$0.472060\pi$
$830$	−52.8470	−1.83435
$831$	0	0
$832$	−6.68814	−0.231869
$833$	0	0
$834$	0	0
$835$	−30.2120	−1.04553
$836$	81.9374	2.83386
$837$	0	0
$838$	−68.1050	−2.35265
$839$	−10.9660	−0.378589	−0.189294	−	0.981920i	$-0.560620\pi$
$839$	−10.9660	−0.378589	−0.189294	+	0.981920i	$0.560620\pi$
$840$	0	0
$841$	−26.6623	−0.919390
$842$	74.5578	2.56943
$843$	0	0
$844$	90.2863	3.10778
$845$	35.4982	1.22117
$846$	0	0
$847$	−45.6679	−1.56917
$848$	−5.16969	−0.177528
$849$	0	0
$850$	0	0
$851$	3.92805	0.134652
$852$	0	0
$853$	−26.6307	−0.911819	−0.455910	−	0.890026i	$-0.650686\pi$
$853$	−26.6307	−0.911819	−0.455910	+	0.890026i	$0.650686\pi$
$854$	31.9557	1.09350
$855$	0	0
$856$	17.7326	0.606088
$857$	−1.33422	−0.0455762	−0.0227881	−	0.999740i	$-0.507254\pi$
$857$	−1.33422	−0.0455762	−0.0227881	+	0.999740i	$0.507254\pi$
$858$	0	0
$859$	−24.4857	−0.835441	−0.417721	−	0.908575i	$-0.637171\pi$
$859$	−24.4857	−0.835441	−0.417721	+	0.908575i	$0.637171\pi$
$860$	125.852	4.29153
$861$	0	0
$862$	−28.9282	−0.985297
$863$	39.3336	1.33893	0.669465	−	0.742843i	$-0.266523\pi$
$863$	39.3336	1.33893	0.669465	+	0.742843i	$0.266523\pi$
$864$	0	0
$865$	−22.2651	−0.757035
$866$	−60.9609	−2.07153
$867$	0	0
$868$	−13.4902	−0.457888
$869$	9.55939	0.324280
$870$	0	0
$871$	6.23614	0.211304
$872$	−49.5843	−1.67914
$873$	0	0
$874$	−49.0643	−1.65963
$875$	−7.82621	−0.264574
$876$	0	0
$877$	−3.86722	−0.130587	−0.0652934	−	0.997866i	$-0.520798\pi$
$877$	−3.86722	−0.130587	−0.0652934	+	0.997866i	$0.520798\pi$
$878$	−34.9107	−1.17818
$879$	0	0
$880$	−69.9504	−2.35803
$881$	16.3448	0.550670	0.275335	−	0.961348i	$-0.411211\pi$
$881$	16.3448	0.550670	0.275335	+	0.961348i	$0.411211\pi$
$882$	0	0
$883$	−33.5409	−1.12874	−0.564370	−	0.825522i	$-0.690881\pi$
$883$	−33.5409	−1.12874	−0.564370	+	0.825522i	$0.690881\pi$
$884$	0	0
$885$	0	0
$886$	8.23138	0.276539
$887$	25.1866	0.845683	0.422841	−	0.906204i	$-0.361033\pi$
$887$	25.1866	0.845683	0.422841	+	0.906204i	$0.361033\pi$
$888$	0	0
$889$	−3.40226	−0.114108
$890$	43.0312	1.44241
$891$	0	0
$892$	2.36283	0.0791135
$893$	−24.2709	−0.812195
$894$	0	0
$895$	−34.3311	−1.14756
$896$	−30.9469	−1.03386
$897$	0	0
$898$	−9.61965	−0.321012
$899$	3.32261	0.110815
$900$	0	0
$901$	0	0
$902$	87.0488	2.89841
$903$	0	0
$904$	67.1674	2.23395
$905$	5.03758	0.167455
$906$	0	0
$907$	−45.0671	−1.49643	−0.748214	−	0.663457i	$-0.769089\pi$
$907$	−45.0671	−1.49643	−0.748214	+	0.663457i	$0.769089\pi$
$908$	−79.6286	−2.64257
$909$	0	0
$910$	−8.82153	−0.292431
$911$	45.0324	1.49199	0.745995	−	0.665952i	$-0.231974\pi$
$911$	45.0324	1.49199	0.745995	+	0.665952i	$0.231974\pi$
$912$	0	0
$913$	−47.7286	−1.57958
$914$	36.2132	1.19783
$915$	0	0
$916$	7.70640	0.254627
$917$	−6.88856	−0.227480
$918$	0	0
$919$	−56.5601	−1.86574	−0.932872	−	0.360208i	$-0.882706\pi$
$919$	−56.5601	−1.86574	−0.932872	+	0.360208i	$0.882706\pi$
$920$	85.5393	2.82015
$921$	0	0
$922$	−81.3443	−2.67893
$923$	3.63174	0.119540
$924$	0	0
$925$	2.07217	0.0681325
$926$	−46.8039	−1.53807
$927$	0	0
$928$	0.402285	0.0132057
$929$	−33.6201	−1.10304	−0.551520	−	0.834161i	$-0.685952\pi$
$929$	−33.6201	−1.10304	−0.551520	+	0.834161i	$0.685952\pi$
$930$	0	0
$931$	−14.8231	−0.485809
$932$	−33.5422	−1.09871
$933$	0	0
$934$	−92.4550	−3.02522
$935$	0	0
$936$	0	0
$937$	−2.08118	−0.0679891	−0.0339946	−	0.999422i	$-0.510823\pi$
$937$	−2.08118	−0.0679891	−0.0339946	+	0.999422i	$0.510823\pi$
$938$	29.6222	0.967198
$939$	0	0
$940$	85.2095	2.77923
$941$	5.76562	0.187954	0.0939769	−	0.995574i	$-0.470042\pi$
$941$	5.76562	0.187954	0.0939769	+	0.995574i	$0.470042\pi$
$942$	0	0
$943$	−34.6712	−1.12905
$944$	−15.4835	−0.503946
$945$	0	0
$946$	170.882	5.55585
$947$	24.5255	0.796971	0.398486	−	0.917175i	$-0.369536\pi$
$947$	24.5255	0.796971	0.398486	+	0.917175i	$0.369536\pi$
$948$	0	0
$949$	6.65727	0.216104
$950$	−25.8830	−0.839755
$951$	0	0
$952$	0	0
$953$	−13.3063	−0.431033	−0.215517	−	0.976500i	$-0.569144\pi$
$953$	−13.3063	−0.431033	−0.215517	+	0.976500i	$0.569144\pi$
$954$	0	0
$955$	−64.1455	−2.07570
$956$	−61.5919	−1.99202
$957$	0	0
$958$	1.04965	0.0339126
$959$	0.486722	0.0157171
$960$	0	0
$961$	−26.2775	−0.847661
$962$	−1.25005	−0.0403033
$963$	0	0
$964$	118.360	3.81211
$965$	75.1637	2.41960
$966$	0	0
$967$	−18.0996	−0.582044	−0.291022	−	0.956716i	$-0.593995\pi$
$967$	−18.0996	−0.582044	−0.291022	+	0.956716i	$0.593995\pi$
$968$	−140.924	−4.52946
$969$	0	0
$970$	34.0008	1.09170
$971$	−2.40360	−0.0771352	−0.0385676	−	0.999256i	$-0.512279\pi$
$971$	−2.40360	−0.0771352	−0.0385676	+	0.999256i	$0.512279\pi$
$972$	0	0
$973$	16.8904	0.541482
$974$	0.478101	0.0153193
$975$	0	0
$976$	32.1183	1.02808
$977$	−41.4410	−1.32581	−0.662907	−	0.748701i	$-0.730678\pi$
$977$	−41.4410	−1.32581	−0.662907	+	0.748701i	$0.730678\pi$
$978$	0	0
$979$	38.8634	1.24208
$980$	52.0406	1.66238
$981$	0	0
$982$	−22.7973	−0.727491
$983$	−37.8963	−1.20870	−0.604352	−	0.796718i	$-0.706568\pi$
$983$	−37.8963	−1.20870	−0.604352	+	0.796718i	$0.706568\pi$
$984$	0	0
$985$	−51.1366	−1.62935
$986$	0	0
$987$	0	0
$988$	10.3858	0.330416
$989$	−68.0617	−2.16424
$990$	0	0
$991$	−25.3455	−0.805127	−0.402563	−	0.915392i	$-0.631881\pi$
$991$	−25.3455	−0.805127	−0.402563	+	0.915392i	$0.631881\pi$
$992$	0.571778	0.0181540
$993$	0	0
$994$	17.2510	0.547169
$995$	−65.0960	−2.06368
$996$	0	0
$997$	−33.7990	−1.07043	−0.535213	−	0.844717i	$-0.679769\pi$
$997$	−33.7990	−1.07043	−0.535213	+	0.844717i	$0.679769\pi$
$998$	−20.0743	−0.635440
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.bi.1.2		6
3.2	odd	2		867.2.a.p.1.5	yes	6
17.16	even	2		2601.2.a.bh.1.2		6
51.2	odd	8		867.2.e.k.616.10		24
51.5	even	16		867.2.h.m.688.3		48
51.8	odd	8		867.2.e.k.829.3		24
51.11	even	16		867.2.h.m.733.9		48
51.14	even	16		867.2.h.m.757.9		48
51.20	even	16		867.2.h.m.757.10		48
51.23	even	16		867.2.h.m.733.10		48
51.26	odd	8		867.2.e.k.829.4		24
51.29	even	16		867.2.h.m.688.4		48
51.32	odd	8		867.2.e.k.616.9		24
51.38	odd	4		867.2.d.g.577.3		12
51.41	even	16		867.2.h.m.712.3		48
51.44	even	16		867.2.h.m.712.4		48
51.47	odd	4		867.2.d.g.577.4		12
51.50	odd	2		867.2.a.o.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.o.1.5	✓	6	51.50	odd	2
867.2.a.p.1.5	yes	6	3.2	odd	2
867.2.d.g.577.3		12	51.38	odd	4
867.2.d.g.577.4		12	51.47	odd	4
867.2.e.k.616.9		24	51.32	odd	8
867.2.e.k.616.10		24	51.2	odd	8
867.2.e.k.829.3		24	51.8	odd	8
867.2.e.k.829.4		24	51.26	odd	8
867.2.h.m.688.3		48	51.5	even	16
867.2.h.m.688.4		48	51.29	even	16
867.2.h.m.712.3		48	51.41	even	16
867.2.h.m.712.4		48	51.44	even	16
867.2.h.m.733.9		48	51.11	even	16
867.2.h.m.733.10		48	51.23	even	16
867.2.h.m.757.9		48	51.14	even	16
867.2.h.m.757.10		48	51.20	even	16
2601.2.a.bh.1.2		6	17.16	even	2
2601.2.a.bi.1.2		6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2601.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44395 q^{2} +3.97290 q^{4} -2.87349 q^{5} -1.56252 q^{7} -4.82168 q^{8} +O(q^{10})\)	\(q-2.44395 q^{2} +3.97290 q^{4} -2.87349 q^{5} -1.56252 q^{7} -4.82168 q^{8} +7.02266 q^{10} +6.34249 q^{11} +0.803928 q^{13} +3.81872 q^{14} +3.83815 q^{16} +3.25173 q^{19} -11.4161 q^{20} -15.5007 q^{22} +6.17389 q^{23} +3.25692 q^{25} -1.96476 q^{26} -6.20773 q^{28} +1.52895 q^{29} +2.17313 q^{31} +0.263112 q^{32} +4.48987 q^{35} +0.636236 q^{37} -7.94707 q^{38} +13.8550 q^{40} -5.61579 q^{41} -11.0241 q^{43} +25.1981 q^{44} -15.0887 q^{46} -7.46399 q^{47} -4.55854 q^{49} -7.95975 q^{50} +3.19393 q^{52} -1.34692 q^{53} -18.2250 q^{55} +7.53396 q^{56} -3.73668 q^{58} -4.03412 q^{59} +8.36818 q^{61} -5.31104 q^{62} -8.31932 q^{64} -2.31008 q^{65} +7.75709 q^{67} -10.9730 q^{70} +4.51749 q^{71} +8.28093 q^{73} -1.55493 q^{74} +12.9188 q^{76} -9.91025 q^{77} +1.50720 q^{79} -11.0289 q^{80} +13.7247 q^{82} -7.52521 q^{83} +26.9424 q^{86} -30.5814 q^{88} +6.12748 q^{89} -1.25615 q^{91} +24.5282 q^{92} +18.2416 q^{94} -9.34380 q^{95} +4.84158 q^{97} +11.1408 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 9 q^{4} + 3 q^{5} + 3 q^{7} - 12 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 + 9 * q^4 + 3 * q^5 + 3 * q^7 - 12 * q^8	\( 6 q - 3 q^{2} + 9 q^{4} + 3 q^{5} + 3 q^{7} - 12 q^{8} + 12 q^{10} + 9 q^{11} + 9 q^{13} + 6 q^{14} + 15 q^{16} + 9 q^{19} - 6 q^{20} - 18 q^{22} + 9 q^{23} + 15 q^{25} + 12 q^{26} - 15 q^{28} + 6 q^{29} + 24 q^{31} - 42 q^{32} - 3 q^{37} + 6 q^{38} - 3 q^{40} + 18 q^{41} + 3 q^{44} + 15 q^{46} - 24 q^{47} + 21 q^{49} - 12 q^{50} - 18 q^{52} - 24 q^{53} - 24 q^{55} + 54 q^{56} + 3 q^{58} + 9 q^{59} + 21 q^{61} + 30 q^{62} + 24 q^{64} - 9 q^{65} - 6 q^{67} - 3 q^{70} + 27 q^{71} + 18 q^{73} + 36 q^{74} - 3 q^{76} - 33 q^{77} + 24 q^{79} + 3 q^{80} - 15 q^{82} - 6 q^{83} - 6 q^{86} - 24 q^{88} + 39 q^{91} - 15 q^{94} + 42 q^{95} - 33 q^{97} + 57 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + 9 * q^4 + 3 * q^5 + 3 * q^7 - 12 * q^8 + 12 * q^10 + 9 * q^11 + 9 * q^13 + 6 * q^14 + 15 * q^16 + 9 * q^19 - 6 * q^20 - 18 * q^22 + 9 * q^23 + 15 * q^25 + 12 * q^26 - 15 * q^28 + 6 * q^29 + 24 * q^31 - 42 * q^32 - 3 * q^37 + 6 * q^38 - 3 * q^40 + 18 * q^41 + 3 * q^44 + 15 * q^46 - 24 * q^47 + 21 * q^49 - 12 * q^50 - 18 * q^52 - 24 * q^53 - 24 * q^55 + 54 * q^56 + 3 * q^58 + 9 * q^59 + 21 * q^61 + 30 * q^62 + 24 * q^64 - 9 * q^65 - 6 * q^67 - 3 * q^70 + 27 * q^71 + 18 * q^73 + 36 * q^74 - 3 * q^76 - 33 * q^77 + 24 * q^79 + 3 * q^80 - 15 * q^82 - 6 * q^83 - 6 * q^86 - 24 * q^88 + 39 * q^91 - 15 * q^94 + 42 * q^95 - 33 * q^97 + 57 * q^98

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