LMFDB - Embedded newform 2601.2.a.bi.1.3

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			1.3
Root			$-0.857616$ 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)

$f(q)$	$=$	$q-0.907065 q^{2} -1.17723 q^{4} -3.19333 q^{5} +3.56234 q^{7} +2.88196 q^{8} +O(q^{10})$	$q-0.907065 q^{2} -1.17723 q^{4} -3.19333 q^{5} +3.56234 q^{7} +2.88196 q^{8} +2.89656 q^{10} +3.27613 q^{11} +5.58411 q^{13} -3.23128 q^{14} -0.259660 q^{16} -4.23574 q^{19} +3.75929 q^{20} -2.97167 q^{22} +4.60128 q^{23} +5.19735 q^{25} -5.06515 q^{26} -4.19370 q^{28} -2.08430 q^{29} +0.448868 q^{31} -5.52839 q^{32} -11.3757 q^{35} -0.742912 q^{37} +3.84209 q^{38} -9.20304 q^{40} +4.49315 q^{41} +6.10953 q^{43} -3.85677 q^{44} -4.17367 q^{46} +2.26801 q^{47} +5.69028 q^{49} -4.71434 q^{50} -6.57379 q^{52} -7.55680 q^{53} -10.4618 q^{55} +10.2665 q^{56} +1.89059 q^{58} +2.83196 q^{59} -3.91386 q^{61} -0.407152 q^{62} +5.53393 q^{64} -17.8319 q^{65} -14.5019 q^{67} +10.3185 q^{70} +3.64422 q^{71} +11.6532 q^{73} +0.673870 q^{74} +4.98645 q^{76} +11.6707 q^{77} -5.63303 q^{79} +0.829180 q^{80} -4.07558 q^{82} +3.92274 q^{83} -5.54175 q^{86} +9.44167 q^{88} -14.6181 q^{89} +19.8925 q^{91} -5.41678 q^{92} -2.05724 q^{94} +13.5261 q^{95} -0.828387 q^{97} -5.16145 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.907065	−0.641392	−0.320696	−	0.947182i	$-0.603917\pi$
$2$	−0.907065	−0.641392	−0.320696	+	0.947182i	$0.603917\pi$
$3$	0	0
$3$	0	0
$4$	−1.17723	−0.588616
$5$	−3.19333	−1.42810	−0.714050	−	0.700095i	$-0.753141\pi$
$5$	−3.19333	−1.42810	−0.714050	+	0.700095i	$0.753141\pi$
$6$	0	0
$7$	3.56234	1.34644	0.673219	−	0.739443i	$-0.264911\pi$
$7$	3.56234	1.34644	0.673219	+	0.739443i	$0.264911\pi$
$8$	2.88196	1.01893
$9$	0	0
$10$	2.89656	0.915972
$11$	3.27613	0.987791	0.493895	−	0.869521i	$-0.335573\pi$
$11$	3.27613	0.987791	0.493895	+	0.869521i	$0.335573\pi$
$12$	0	0
$13$	5.58411	1.54875	0.774377	−	0.632725i	$-0.218064\pi$
$13$	5.58411	1.54875	0.774377	+	0.632725i	$0.218064\pi$
$14$	−3.23128	−0.863595
$15$	0	0
$16$	−0.259660	−0.0649150
$17$	0	0
$17$	0	0
$18$	0	0
$19$	−4.23574	−0.971745	−0.485872	−	0.874030i	$-0.661498\pi$
$19$	−4.23574	−0.971745	−0.485872	+	0.874030i	$0.661498\pi$
$20$	3.75929	0.840603
$21$	0	0
$22$	−2.97167	−0.633561
$23$	4.60128	0.959434	0.479717	−	0.877423i	$-0.340739\pi$
$23$	4.60128	0.959434	0.479717	+	0.877423i	$0.340739\pi$
$24$	0	0
$25$	5.19735	1.03947
$26$	−5.06515	−0.993358
$27$	0	0
$28$	−4.19370	−0.792535
$29$	−2.08430	−0.387044	−0.193522	−	0.981096i	$-0.561991\pi$
$29$	−2.08430	−0.387044	−0.193522	+	0.981096i	$0.561991\pi$
$30$	0	0
$31$	0.448868	0.0806190	0.0403095	−	0.999187i	$-0.487166\pi$
$31$	0.448868	0.0806190	0.0403095	+	0.999187i	$0.487166\pi$
$32$	−5.52839	−0.977290
$33$	0	0
$34$	0	0
$35$	−11.3757	−1.92285
$36$	0	0
$37$	−0.742912	−0.122134	−0.0610670	−	0.998134i	$-0.519450\pi$
$37$	−0.742912	−0.122134	−0.0610670	+	0.998134i	$0.519450\pi$
$38$	3.84209	0.623270
$39$	0	0
$40$	−9.20304	−1.45513
$41$	4.49315	0.701712	0.350856	−	0.936430i	$-0.385891\pi$
$41$	4.49315	0.701712	0.350856	+	0.936430i	$0.385891\pi$
$42$	0	0
$43$	6.10953	0.931695	0.465848	−	0.884865i	$-0.345750\pi$
$43$	6.10953	0.931695	0.465848	+	0.884865i	$0.345750\pi$
$44$	−3.85677	−0.581429
$45$	0	0
$46$	−4.17367	−0.615374
$47$	2.26801	0.330824	0.165412	−	0.986225i	$-0.447105\pi$
$47$	2.26801	0.330824	0.165412	+	0.986225i	$0.447105\pi$
$48$	0	0
$49$	5.69028	0.812897
$50$	−4.71434	−0.666708
$51$	0	0
$52$	−6.57379	−0.911621
$53$	−7.55680	−1.03801	−0.519003	−	0.854772i	$-0.673697\pi$
$53$	−7.55680	−1.03801	−0.519003	+	0.854772i	$0.673697\pi$
$54$	0	0
$55$	−10.4618	−1.41066
$56$	10.2665	1.37192
$57$	0	0
$58$	1.89059	0.248247
$59$	2.83196	0.368690	0.184345	−	0.982862i	$-0.440984\pi$
$59$	2.83196	0.368690	0.184345	+	0.982862i	$0.440984\pi$
$60$	0	0
$61$	−3.91386	−0.501118	−0.250559	−	0.968101i	$-0.580614\pi$
$61$	−3.91386	−0.501118	−0.250559	+	0.968101i	$0.580614\pi$
$62$	−0.407152	−0.0517084
$63$	0	0
$64$	5.53393	0.691741
$65$	−17.8319	−2.21178
$66$	0	0
$67$	−14.5019	−1.77168	−0.885842	−	0.463986i	$-0.846419\pi$
$67$	−14.5019	−1.77168	−0.885842	+	0.463986i	$0.846419\pi$
$68$	0	0
$69$	0	0
$70$	10.3185	1.23330
$71$	3.64422	0.432489	0.216245	−	0.976339i	$-0.430619\pi$
$71$	3.64422	0.432489	0.216245	+	0.976339i	$0.430619\pi$
$72$	0	0
$73$	11.6532	1.36390	0.681951	−	0.731398i	$-0.261132\pi$
$73$	11.6532	1.36390	0.681951	+	0.731398i	$0.261132\pi$
$74$	0.673870	0.0783358
$75$	0	0
$76$	4.98645	0.571985
$77$	11.6707	1.33000
$78$	0	0
$79$	−5.63303	−0.633766	−0.316883	−	0.948465i	$-0.602636\pi$
$79$	−5.63303	−0.633766	−0.316883	+	0.948465i	$0.602636\pi$
$80$	0.829180	0.0927051
$81$	0	0
$82$	−4.07558	−0.450072
$83$	3.92274	0.430577	0.215288	−	0.976551i	$-0.430931\pi$
$83$	3.92274	0.430577	0.215288	+	0.976551i	$0.430931\pi$
$84$	0	0
$85$	0	0
$86$	−5.54175	−0.597582
$87$	0	0
$88$	9.44167	1.00649
$89$	−14.6181	−1.54951	−0.774757	−	0.632259i	$-0.782128\pi$
$89$	−14.6181	−1.54951	−0.774757	+	0.632259i	$0.782128\pi$
$90$	0	0
$91$	19.8925	2.08530
$92$	−5.41678	−0.564738
$93$	0	0
$94$	−2.05724	−0.212188
$95$	13.5261	1.38775
$96$	0	0
$97$	−0.828387	−0.0841099	−0.0420550	−	0.999115i	$-0.513390\pi$
$97$	−0.828387	−0.0841099	−0.0420550	+	0.999115i	$0.513390\pi$
$98$	−5.16145	−0.521386
$99$	0	0
$100$	−6.11849	−0.611849
$101$	−4.92944	−0.490497	−0.245249	−	0.969460i	$-0.578870\pi$
$101$	−4.92944	−0.490497	−0.245249	+	0.969460i	$0.578870\pi$
$102$	0	0
$103$	11.4347	1.12669	0.563347	−	0.826221i	$-0.309514\pi$
$103$	11.4347	1.12669	0.563347	+	0.826221i	$0.309514\pi$
$104$	16.0932	1.57807
$105$	0	0
$106$	6.85452	0.665769
$107$	17.5925	1.70073	0.850366	−	0.526192i	$-0.176381\pi$
$107$	17.5925	1.70073	0.850366	+	0.526192i	$0.176381\pi$
$108$	0	0
$109$	−14.1515	−1.35546	−0.677732	−	0.735309i	$-0.737037\pi$
$109$	−14.1515	−1.35546	−0.677732	+	0.735309i	$0.737037\pi$
$110$	9.48951	0.904789
$111$	0	0
$112$	−0.924998	−0.0874041
$113$	20.4015	1.91921	0.959607	−	0.281346i	$-0.0907807\pi$
$113$	20.4015	1.91921	0.959607	+	0.281346i	$0.0907807\pi$
$114$	0	0
$115$	−14.6934	−1.37017
$116$	2.45370	0.227821
$117$	0	0
$118$	−2.56877	−0.236475
$119$	0	0
$120$	0	0
$121$	−0.266966	−0.0242696
$122$	3.55013	0.321413
$123$	0	0
$124$	−0.528421	−0.0474536
$125$	−0.630210	−0.0563677
$126$	0	0
$127$	2.93340	0.260297	0.130148	−	0.991495i	$-0.458455\pi$
$127$	2.93340	0.260297	0.130148	+	0.991495i	$0.458455\pi$
$128$	6.03714	0.533613
$129$	0	0
$130$	16.1747	1.41862
$131$	−6.61671	−0.578104	−0.289052	−	0.957313i	$-0.593340\pi$
$131$	−6.61671	−0.578104	−0.289052	+	0.957313i	$0.593340\pi$
$132$	0	0
$133$	−15.0891	−1.30839
$134$	13.1541	1.13634
$135$	0	0
$136$	0	0
$137$	10.4851	0.895804	0.447902	−	0.894083i	$-0.352171\pi$
$137$	10.4851	0.895804	0.447902	+	0.894083i	$0.352171\pi$
$138$	0	0
$139$	5.28597	0.448350	0.224175	−	0.974549i	$-0.428031\pi$
$139$	5.28597	0.448350	0.224175	+	0.974549i	$0.428031\pi$
$140$	13.3919	1.13182
$141$	0	0
$142$	−3.30555	−0.277395
$143$	18.2943	1.52984
$144$	0	0
$145$	6.65585	0.552738
$146$	−10.5702	−0.874795
$147$	0	0
$148$	0.874580	0.0718901
$149$	22.4592	1.83993	0.919965	−	0.392000i	$-0.128217\pi$
$149$	22.4592	1.83993	0.919965	+	0.392000i	$0.128217\pi$
$150$	0	0
$151$	−9.52717	−0.775310	−0.387655	−	0.921804i	$-0.626715\pi$
$151$	−9.52717	−0.775310	−0.387655	+	0.921804i	$0.626715\pi$
$152$	−12.2072	−0.990136
$153$	0	0
$154$	−10.5861	−0.853051
$155$	−1.43338	−0.115132
$156$	0	0
$157$	14.1185	1.12678	0.563390	−	0.826191i	$-0.309497\pi$
$157$	14.1185	1.12678	0.563390	+	0.826191i	$0.309497\pi$
$158$	5.10953	0.406492
$159$	0	0
$160$	17.6540	1.39567
$161$	16.3913	1.29182
$162$	0	0
$163$	3.53391	0.276797	0.138398	−	0.990377i	$-0.455805\pi$
$163$	3.53391	0.276797	0.138398	+	0.990377i	$0.455805\pi$
$164$	−5.28948	−0.413039
$165$	0	0
$166$	−3.55818	−0.276169
$167$	16.1872	1.25260	0.626300	−	0.779582i	$-0.284568\pi$
$167$	16.1872	1.25260	0.626300	+	0.779582i	$0.284568\pi$
$168$	0	0
$169$	18.1823	1.39864
$170$	0	0
$171$	0	0
$172$	−7.19234	−0.548411
$173$	18.3180	1.39269	0.696346	−	0.717706i	$-0.254808\pi$
$173$	18.3180	1.39269	0.696346	+	0.717706i	$0.254808\pi$
$174$	0	0
$175$	18.5147	1.39958
$176$	−0.850680	−0.0641224
$177$	0	0
$178$	13.2596	0.993846
$179$	−20.7057	−1.54762	−0.773809	−	0.633419i	$-0.781651\pi$
$179$	−20.7057	−1.54762	−0.773809	+	0.633419i	$0.781651\pi$
$180$	0	0
$181$	18.6500	1.38624	0.693122	−	0.720820i	$-0.256235\pi$
$181$	18.6500	1.38624	0.693122	+	0.720820i	$0.256235\pi$
$182$	−18.0438	−1.33750
$183$	0	0
$184$	13.2607	0.977592
$185$	2.37236	0.174420
$186$	0	0
$187$	0	0
$188$	−2.66998	−0.194728
$189$	0	0
$190$	−12.2691	−0.890091
$191$	−2.19374	−0.158734	−0.0793669	−	0.996845i	$-0.525290\pi$
$191$	−2.19374	−0.158734	−0.0793669	+	0.996845i	$0.525290\pi$
$192$	0	0
$193$	3.31205	0.238407	0.119203	−	0.992870i	$-0.461966\pi$
$193$	3.31205	0.238407	0.119203	+	0.992870i	$0.461966\pi$
$194$	0.751401	0.0539474
$195$	0	0
$196$	−6.69878	−0.478484
$197$	18.0182	1.28374	0.641872	−	0.766811i	$-0.278158\pi$
$197$	18.0182	1.28374	0.641872	+	0.766811i	$0.278158\pi$
$198$	0	0
$199$	−3.98156	−0.282245	−0.141123	−	0.989992i	$-0.545071\pi$
$199$	−3.98156	−0.282245	−0.141123	+	0.989992i	$0.545071\pi$
$200$	14.9785	1.05914
$201$	0	0
$202$	4.47132	0.314601
$203$	−7.42498	−0.521131
$204$	0	0
$205$	−14.3481	−1.00211
$206$	−10.3720	−0.722652
$207$	0	0
$208$	−1.44997	−0.100537
$209$	−13.8768	−0.959881
$210$	0	0
$211$	−0.200896	−0.0138303	−0.00691514	−	0.999976i	$-0.502201\pi$
$211$	−0.200896	−0.0138303	−0.00691514	+	0.999976i	$0.502201\pi$
$212$	8.89611	0.610988
$213$	0	0
$214$	−15.9576	−1.09084
$215$	−19.5097	−1.33055
$216$	0	0
$217$	1.59902	0.108549
$218$	12.8363	0.869384
$219$	0	0
$220$	12.3159	0.830340
$221$	0	0
$222$	0	0
$223$	−11.5997	−0.776770	−0.388385	−	0.921497i	$-0.626967\pi$
$223$	−11.5997	−0.776770	−0.388385	+	0.921497i	$0.626967\pi$
$224$	−19.6940	−1.31586
$225$	0	0
$226$	−18.5055	−1.23097
$227$	−9.51394	−0.631462	−0.315731	−	0.948849i	$-0.602250\pi$
$227$	−9.51394	−0.631462	−0.315731	+	0.948849i	$0.602250\pi$
$228$	0	0
$229$	−16.7700	−1.10819	−0.554097	−	0.832452i	$-0.686936\pi$
$229$	−16.7700	−1.10819	−0.554097	+	0.832452i	$0.686936\pi$
$230$	13.3279	0.878815
$231$	0	0
$232$	−6.00686	−0.394370
$233$	9.44867	0.619003	0.309501	−	0.950899i	$-0.399838\pi$
$233$	9.44867	0.619003	0.309501	+	0.950899i	$0.399838\pi$
$234$	0	0
$235$	−7.24251	−0.472450
$236$	−3.33387	−0.217017
$237$	0	0
$238$	0	0
$239$	−6.42079	−0.415326	−0.207663	−	0.978200i	$-0.566586\pi$
$239$	−6.42079	−0.415326	−0.207663	+	0.978200i	$0.566586\pi$
$240$	0	0
$241$	15.4831	0.997355	0.498678	−	0.866788i	$-0.333819\pi$
$241$	15.4831	0.997355	0.498678	+	0.866788i	$0.333819\pi$
$242$	0.242155	0.0155663
$243$	0	0
$244$	4.60752	0.294966
$245$	−18.1709	−1.16090
$246$	0	0
$247$	−23.6528	−1.50499
$248$	1.29362	0.0821448
$249$	0	0
$250$	0.571642	0.0361538
$251$	−25.7024	−1.62232	−0.811162	−	0.584821i	$-0.801165\pi$
$251$	−25.7024	−1.62232	−0.811162	+	0.584821i	$0.801165\pi$
$252$	0	0
$253$	15.0744	0.947720
$254$	−2.66078	−0.166952
$255$	0	0
$256$	−16.5439	−1.03400
$257$	−2.50466	−0.156236	−0.0781182	−	0.996944i	$-0.524891\pi$
$257$	−2.50466	−0.156236	−0.0781182	+	0.996944i	$0.524891\pi$
$258$	0	0
$259$	−2.64651	−0.164446
$260$	20.9923	1.30189
$261$	0	0
$262$	6.00179	0.370792
$263$	−6.09867	−0.376060	−0.188030	−	0.982163i	$-0.560210\pi$
$263$	−6.09867	−0.376060	−0.188030	+	0.982163i	$0.560210\pi$
$264$	0	0
$265$	24.1314	1.48238
$266$	13.6868	0.839194
$267$	0	0
$268$	17.0721	1.04284
$269$	4.11451	0.250866	0.125433	−	0.992102i	$-0.459968\pi$
$269$	4.11451	0.250866	0.125433	+	0.992102i	$0.459968\pi$
$270$	0	0
$271$	−11.8548	−0.720128	−0.360064	−	0.932928i	$-0.617245\pi$
$271$	−11.8548	−0.720128	−0.360064	+	0.932928i	$0.617245\pi$
$272$	0	0
$273$	0	0
$274$	−9.51068	−0.574561
$275$	17.0272	1.02678
$276$	0	0
$277$	−16.2756	−0.977908	−0.488954	−	0.872309i	$-0.662621\pi$
$277$	−16.2756	−0.977908	−0.488954	+	0.872309i	$0.662621\pi$
$278$	−4.79472	−0.287568
$279$	0	0
$280$	−32.7844	−1.95924
$281$	−15.2506	−0.909774	−0.454887	−	0.890549i	$-0.650320\pi$
$281$	−15.2506	−0.909774	−0.454887	+	0.890549i	$0.650320\pi$
$282$	0	0
$283$	20.8911	1.24185	0.620924	−	0.783871i	$-0.286758\pi$
$283$	20.8911	1.24185	0.620924	+	0.783871i	$0.286758\pi$
$284$	−4.29009	−0.254570
$285$	0	0
$286$	−16.5941	−0.981230
$287$	16.0061	0.944811
$288$	0	0
$289$	0	0
$290$	−6.03729	−0.354522
$291$	0	0
$292$	−13.7185	−0.802814
$293$	−22.4544	−1.31180	−0.655900	−	0.754848i	$-0.727711\pi$
$293$	−22.4544	−1.31180	−0.655900	+	0.754848i	$0.727711\pi$
$294$	0	0
$295$	−9.04338	−0.526526
$296$	−2.14104	−0.124446
$297$	0	0
$298$	−20.3720	−1.18012
$299$	25.6941	1.48593
$300$	0	0
$301$	21.7642	1.25447
$302$	8.64177	0.497278
$303$	0	0
$304$	1.09985	0.0630808
$305$	12.4982	0.715647
$306$	0	0
$307$	−0.733467	−0.0418611	−0.0209306	−	0.999781i	$-0.506663\pi$
$307$	−0.733467	−0.0418611	−0.0209306	+	0.999781i	$0.506663\pi$
$308$	−13.7391	−0.782859
$309$	0	0
$310$	1.30017	0.0738448
$311$	−24.2195	−1.37336	−0.686681	−	0.726959i	$-0.740933\pi$
$311$	−24.2195	−1.37336	−0.686681	+	0.726959i	$0.740933\pi$
$312$	0	0
$313$	−3.82843	−0.216396	−0.108198	−	0.994129i	$-0.534508\pi$
$313$	−3.82843	−0.216396	−0.108198	+	0.994129i	$0.534508\pi$
$314$	−12.8064	−0.722708
$315$	0	0
$316$	6.63139	0.373045
$317$	3.49283	0.196177	0.0980885	−	0.995178i	$-0.468727\pi$
$317$	3.49283	0.196177	0.0980885	+	0.995178i	$0.468727\pi$
$318$	0	0
$319$	−6.82843	−0.382319
$320$	−17.6717	−0.987876
$321$	0	0
$322$	−14.8680	−0.828563
$323$	0	0
$324$	0	0
$325$	29.0226	1.60988
$326$	−3.20548	−0.177535
$327$	0	0
$328$	12.9491	0.714992
$329$	8.07944	0.445434
$330$	0	0
$331$	5.00357	0.275021	0.137511	−	0.990500i	$-0.456090\pi$
$331$	5.00357	0.275021	0.137511	+	0.990500i	$0.456090\pi$
$332$	−4.61798	−0.253444
$333$	0	0
$334$	−14.6828	−0.803408
$335$	46.3092	2.53014
$336$	0	0
$337$	27.0434	1.47315	0.736573	−	0.676358i	$-0.236443\pi$
$337$	27.0434	1.47315	0.736573	+	0.676358i	$0.236443\pi$
$338$	−16.4925	−0.897075
$339$	0	0
$340$	0	0
$341$	1.47055	0.0796347
$342$	0	0
$343$	−4.66568	−0.251923
$344$	17.6074	0.949328
$345$	0	0
$346$	−16.6156	−0.893262
$347$	−4.31305	−0.231537	−0.115768	−	0.993276i	$-0.536933\pi$
$347$	−4.31305	−0.231537	−0.115768	+	0.993276i	$0.536933\pi$
$348$	0	0
$349$	29.1251	1.55903	0.779516	−	0.626382i	$-0.215465\pi$
$349$	29.1251	1.55903	0.779516	+	0.626382i	$0.215465\pi$
$350$	−16.7941	−0.897682
$351$	0	0
$352$	−18.1117	−0.965358
$353$	11.5730	0.615971	0.307985	−	0.951391i	$-0.400345\pi$
$353$	11.5730	0.615971	0.307985	+	0.951391i	$0.400345\pi$
$354$	0	0
$355$	−11.6372	−0.617638
$356$	17.2089	0.912069
$357$	0	0
$358$	18.7814	0.992630
$359$	26.1470	1.37998	0.689992	−	0.723817i	$-0.257614\pi$
$359$	26.1470	1.37998	0.689992	+	0.723817i	$0.257614\pi$
$360$	0	0
$361$	−1.05852	−0.0557118
$362$	−16.9168	−0.889126
$363$	0	0
$364$	−23.4181	−1.22744
$365$	−37.2124	−1.94779
$366$	0	0
$367$	21.8427	1.14018	0.570089	−	0.821583i	$-0.306909\pi$
$367$	21.8427	1.14018	0.570089	+	0.821583i	$0.306909\pi$
$368$	−1.19477	−0.0622817
$369$	0	0
$370$	−2.15189	−0.111871
$371$	−26.9199	−1.39761
$372$	0	0
$373$	31.0065	1.60545	0.802727	−	0.596347i	$-0.203382\pi$
$373$	31.0065	1.60545	0.802727	+	0.596347i	$0.203382\pi$
$374$	0	0
$375$	0	0
$376$	6.53632	0.337085
$377$	−11.6389	−0.599436
$378$	0	0
$379$	−11.7686	−0.604513	−0.302256	−	0.953227i	$-0.597740\pi$
$379$	−11.7686	−0.604513	−0.302256	+	0.953227i	$0.597740\pi$
$380$	−15.9234	−0.816852
$381$	0	0
$382$	1.98987	0.101811
$383$	20.0262	1.02329	0.511645	−	0.859197i	$-0.329036\pi$
$383$	20.0262	1.02329	0.511645	+	0.859197i	$0.329036\pi$
$384$	0	0
$385$	−37.2684	−1.89937
$386$	−3.00425	−0.152912
$387$	0	0
$388$	0.975203	0.0495085
$389$	−12.7561	−0.646758	−0.323379	−	0.946270i	$-0.604819\pi$
$389$	−12.7561	−0.646758	−0.323379	+	0.946270i	$0.604819\pi$
$390$	0	0
$391$	0	0
$392$	16.3991	0.828282
$393$	0	0
$394$	−16.3437	−0.823384
$395$	17.9881	0.905081
$396$	0	0
$397$	−27.3141	−1.37086	−0.685428	−	0.728140i	$-0.740385\pi$
$397$	−27.3141	−1.37086	−0.685428	+	0.728140i	$0.740385\pi$
$398$	3.61153	0.181030
$399$	0	0
$400$	−1.34954	−0.0674772
$401$	−31.3594	−1.56601	−0.783007	−	0.622013i	$-0.786315\pi$
$401$	−31.3594	−1.56601	−0.783007	+	0.622013i	$0.786315\pi$
$402$	0	0
$403$	2.50653	0.124859
$404$	5.80309	0.288715
$405$	0	0
$406$	6.73494	0.334250
$407$	−2.43388	−0.120643
$408$	0	0
$409$	17.1030	0.845688	0.422844	−	0.906202i	$-0.361032\pi$
$409$	17.1030	0.845688	0.422844	+	0.906202i	$0.361032\pi$
$410$	13.0147	0.642748
$411$	0	0
$412$	−13.4613	−0.663190
$413$	10.0884	0.496418
$414$	0	0
$415$	−12.5266	−0.614907
$416$	−30.8711	−1.51358
$417$	0	0
$418$	12.5872	0.615660
$419$	−15.2428	−0.744660	−0.372330	−	0.928100i	$-0.621441\pi$
$419$	−15.2428	−0.744660	−0.372330	+	0.928100i	$0.621441\pi$
$420$	0	0
$421$	6.96252	0.339332	0.169666	−	0.985502i	$-0.445731\pi$
$421$	6.96252	0.339332	0.169666	+	0.985502i	$0.445731\pi$
$422$	0.182226	0.00887063
$423$	0	0
$424$	−21.7784	−1.05765
$425$	0	0
$426$	0	0
$427$	−13.9425	−0.674725
$428$	−20.7105	−1.00108
$429$	0	0
$430$	17.6966	0.853407
$431$	21.4684	1.03410	0.517049	−	0.855956i	$-0.327031\pi$
$431$	21.4684	1.03410	0.517049	+	0.855956i	$0.327031\pi$
$432$	0	0
$433$	33.1954	1.59527	0.797635	−	0.603140i	$-0.206084\pi$
$433$	33.1954	1.59527	0.797635	+	0.603140i	$0.206084\pi$
$434$	−1.45042	−0.0696222
$435$	0	0
$436$	16.6596	0.797848
$437$	−19.4898	−0.932325
$438$	0	0
$439$	35.7203	1.70484	0.852418	−	0.522861i	$-0.175135\pi$
$439$	35.7203	1.70484	0.852418	+	0.522861i	$0.175135\pi$
$440$	−30.1504	−1.43736
$441$	0	0
$442$	0	0
$443$	−13.8366	−0.657398	−0.328699	−	0.944435i	$-0.606610\pi$
$443$	−13.8366	−0.657398	−0.328699	+	0.944435i	$0.606610\pi$
$444$	0	0
$445$	46.6803	2.21286
$446$	10.5216	0.498214
$447$	0	0
$448$	19.7137	0.931387
$449$	−4.67471	−0.220613	−0.110307	−	0.993898i	$-0.535183\pi$
$449$	−4.67471	−0.220613	−0.110307	+	0.993898i	$0.535183\pi$
$450$	0	0
$451$	14.7201	0.693144
$452$	−24.0173	−1.12968
$453$	0	0
$454$	8.62977	0.405015
$455$	−63.5233	−2.97802
$456$	0	0
$457$	−5.17186	−0.241930	−0.120965	−	0.992657i	$-0.538599\pi$
$457$	−5.17186	−0.241930	−0.120965	+	0.992657i	$0.538599\pi$
$458$	15.2115	0.710787
$459$	0	0
$460$	17.2976	0.806503
$461$	−22.6450	−1.05468	−0.527341	−	0.849654i	$-0.676811\pi$
$461$	−22.6450	−1.05468	−0.527341	+	0.849654i	$0.676811\pi$
$462$	0	0
$463$	38.8961	1.80766	0.903828	−	0.427897i	$-0.140745\pi$
$463$	38.8961	1.80766	0.903828	+	0.427897i	$0.140745\pi$
$464$	0.541209	0.0251250
$465$	0	0
$466$	−8.57056	−0.397023
$467$	16.7116	0.773322	0.386661	−	0.922222i	$-0.373628\pi$
$467$	16.7116	0.773322	0.386661	+	0.922222i	$0.373628\pi$
$468$	0	0
$469$	−51.6606	−2.38546
$470$	6.56944	0.303025
$471$	0	0
$472$	8.16159	0.375667
$473$	20.0156	0.920320
$474$	0	0
$475$	−22.0146	−1.01010
$476$	0	0
$477$	0	0
$478$	5.82408	0.266387
$479$	−10.5031	−0.479899	−0.239949	−	0.970785i	$-0.577131\pi$
$479$	−10.5031	−0.479899	−0.239949	+	0.970785i	$0.577131\pi$
$480$	0	0
$481$	−4.14851	−0.189156
$482$	−14.0442	−0.639696
$483$	0	0
$484$	0.314280	0.0142855
$485$	2.64531	0.120117
$486$	0	0
$487$	−24.2456	−1.09867	−0.549336	−	0.835601i	$-0.685119\pi$
$487$	−24.2456	−1.09867	−0.549336	+	0.835601i	$0.685119\pi$
$488$	−11.2796	−0.510603
$489$	0	0
$490$	16.4822	0.744591
$491$	14.7261	0.664580	0.332290	−	0.943177i	$-0.392179\pi$
$491$	14.7261	0.664580	0.332290	+	0.943177i	$0.392179\pi$
$492$	0	0
$493$	0	0
$494$	21.4547	0.965291
$495$	0	0
$496$	−0.116553	−0.00523338
$497$	12.9820	0.582320
$498$	0	0
$499$	14.3585	0.642775	0.321388	−	0.946948i	$-0.395851\pi$
$499$	14.3585	0.642775	0.321388	+	0.946948i	$0.395851\pi$
$500$	0.741904	0.0331789
$501$	0	0
$502$	23.3138	1.04055
$503$	−16.5970	−0.740022	−0.370011	−	0.929027i	$-0.620646\pi$
$503$	−16.5970	−0.740022	−0.370011	+	0.929027i	$0.620646\pi$
$504$	0	0
$505$	15.7413	0.700479
$506$	−13.6735	−0.607860
$507$	0	0
$508$	−3.45329	−0.153215
$509$	33.1048	1.46734	0.733672	−	0.679503i	$-0.237805\pi$
$509$	33.1048	1.46734	0.733672	+	0.679503i	$0.237805\pi$
$510$	0	0
$511$	41.5126	1.83641
$512$	2.93216	0.129584
$513$	0	0
$514$	2.27189	0.100209
$515$	−36.5147	−1.60903
$516$	0	0
$517$	7.43031	0.326785
$518$	2.40056	0.105474
$519$	0	0
$520$	−51.3908	−2.25364
$521$	24.2541	1.06259	0.531295	−	0.847187i	$-0.321706\pi$
$521$	24.2541	1.06259	0.531295	+	0.847187i	$0.321706\pi$
$522$	0	0
$523$	−2.14935	−0.0939843	−0.0469922	−	0.998895i	$-0.514964\pi$
$523$	−2.14935	−0.0939843	−0.0469922	+	0.998895i	$0.514964\pi$
$524$	7.78940	0.340282
$525$	0	0
$526$	5.53189	0.241202
$527$	0	0
$528$	0	0
$529$	−1.82818	−0.0794862
$530$	−21.8887	−0.950786
$531$	0	0
$532$	17.7634	0.770142
$533$	25.0902	1.08678
$534$	0	0
$535$	−56.1787	−2.42882
$536$	−41.7938	−1.80522
$537$	0	0
$538$	−3.73213	−0.160904
$539$	18.6421	0.802972
$540$	0	0
$541$	−4.04781	−0.174029	−0.0870145	−	0.996207i	$-0.527733\pi$
$541$	−4.04781	−0.174029	−0.0870145	+	0.996207i	$0.527733\pi$
$542$	10.7531	0.461884
$543$	0	0
$544$	0	0
$545$	45.1903	1.93574
$546$	0	0
$547$	−38.1034	−1.62918	−0.814591	−	0.580036i	$-0.803039\pi$
$547$	−38.1034	−1.62918	−0.814591	+	0.580036i	$0.803039\pi$
$548$	−12.3434	−0.527284
$549$	0	0
$550$	−15.4448	−0.658568
$551$	8.82854	0.376108
$552$	0	0
$553$	−20.0668	−0.853327
$554$	14.7631	0.627223
$555$	0	0
$556$	−6.22282	−0.263906
$557$	−47.0274	−1.99262	−0.996308	−	0.0858461i	$-0.972641\pi$
$557$	−47.0274	−1.99262	−0.996308	+	0.0858461i	$0.972641\pi$
$558$	0	0
$559$	34.1163	1.44297
$560$	2.95382	0.124822
$561$	0	0
$562$	13.8333	0.583522
$563$	−28.7543	−1.21185	−0.605925	−	0.795521i	$-0.707197\pi$
$563$	−28.7543	−1.21185	−0.605925	+	0.795521i	$0.707197\pi$
$564$	0	0
$565$	−65.1488	−2.74083
$566$	−18.9496	−0.796512
$567$	0	0
$568$	10.5025	0.440675
$569$	1.04600	0.0438505	0.0219252	−	0.999760i	$-0.493020\pi$
$569$	1.04600	0.0438505	0.0219252	+	0.999760i	$0.493020\pi$
$570$	0	0
$571$	26.2531	1.09866	0.549330	−	0.835606i	$-0.314883\pi$
$571$	26.2531	1.09866	0.549330	+	0.835606i	$0.314883\pi$
$572$	−21.5366	−0.900491
$573$	0	0
$574$	−14.5186	−0.605995
$575$	23.9145	0.997303
$576$	0	0
$577$	38.7607	1.61363	0.806814	−	0.590806i	$-0.201190\pi$
$577$	38.7607	1.61363	0.806814	+	0.590806i	$0.201190\pi$
$578$	0	0
$579$	0	0
$580$	−7.83548	−0.325351
$581$	13.9741	0.579745
$582$	0	0
$583$	−24.7571	−1.02533
$584$	33.5840	1.38971
$585$	0	0
$586$	20.3676	0.841378
$587$	41.5716	1.71584	0.857921	−	0.513781i	$-0.171756\pi$
$587$	41.5716	1.71584	0.857921	+	0.513781i	$0.171756\pi$
$588$	0	0
$589$	−1.90129	−0.0783411
$590$	8.20294	0.337710
$591$	0	0
$592$	0.192905	0.00792833
$593$	13.7886	0.566230	0.283115	−	0.959086i	$-0.408632\pi$
$593$	13.7886	0.566230	0.283115	+	0.959086i	$0.408632\pi$
$594$	0	0
$595$	0	0
$596$	−26.4397	−1.08301
$597$	0	0
$598$	−23.3062	−0.953062
$599$	−0.372690	−0.0152277	−0.00761386	−	0.999971i	$-0.502424\pi$
$599$	−0.372690	−0.0152277	−0.00761386	+	0.999971i	$0.502424\pi$
$600$	0	0
$601$	23.0325	0.939515	0.469757	−	0.882796i	$-0.344341\pi$
$601$	23.0325	0.939515	0.469757	+	0.882796i	$0.344341\pi$
$602$	−19.7416	−0.804607
$603$	0	0
$604$	11.2157	0.456360
$605$	0.852509	0.0346594
$606$	0	0
$607$	−16.1050	−0.653681	−0.326840	−	0.945080i	$-0.605984\pi$
$607$	−16.1050	−0.653681	−0.326840	+	0.945080i	$0.605984\pi$
$608$	23.4168	0.949677
$609$	0	0
$610$	−11.3367	−0.459011
$611$	12.6648	0.512365
$612$	0	0
$613$	−14.9606	−0.604251	−0.302126	−	0.953268i	$-0.597696\pi$
$613$	−14.9606	−0.604251	−0.302126	+	0.953268i	$0.597696\pi$
$614$	0.665302	0.0268494
$615$	0	0
$616$	33.6345	1.35517
$617$	4.75542	0.191446	0.0957230	−	0.995408i	$-0.469484\pi$
$617$	4.75542	0.191446	0.0957230	+	0.995408i	$0.469484\pi$
$618$	0	0
$619$	43.0995	1.73232	0.866158	−	0.499770i	$-0.166582\pi$
$619$	43.0995	1.73232	0.866158	+	0.499770i	$0.166582\pi$
$620$	1.68742	0.0677686
$621$	0	0
$622$	21.9687	0.880864
$623$	−52.0746	−2.08632
$624$	0	0
$625$	−23.9743	−0.958972
$626$	3.47264	0.138795
$627$	0	0
$628$	−16.6208	−0.663241
$629$	0	0
$630$	0	0
$631$	11.3212	0.450690	0.225345	−	0.974279i	$-0.427649\pi$
$631$	11.3212	0.450690	0.225345	+	0.974279i	$0.427649\pi$
$632$	−16.2342	−0.645760
$633$	0	0
$634$	−3.16823	−0.125826
$635$	−9.36730	−0.371730
$636$	0	0
$637$	31.7751	1.25898
$638$	6.19384	0.245216
$639$	0	0
$640$	−19.2786	−0.762052
$641$	15.8764	0.627081	0.313541	−	0.949575i	$-0.398485\pi$
$641$	15.8764	0.627081	0.313541	+	0.949575i	$0.398485\pi$
$642$	0	0
$643$	−25.7352	−1.01490	−0.507448	−	0.861682i	$-0.669411\pi$
$643$	−25.7352	−1.01490	−0.507448	+	0.861682i	$0.669411\pi$
$644$	−19.2964	−0.760386
$645$	0	0
$646$	0	0
$647$	26.9015	1.05761	0.528804	−	0.848744i	$-0.322641\pi$
$647$	26.9015	1.05761	0.528804	+	0.848744i	$0.322641\pi$
$648$	0	0
$649$	9.27787	0.364188
$650$	−26.3254	−1.03257
$651$	0	0
$652$	−4.16023	−0.162927
$653$	−20.6599	−0.808484	−0.404242	−	0.914652i	$-0.632465\pi$
$653$	−20.6599	−0.808484	−0.404242	+	0.914652i	$0.632465\pi$
$654$	0	0
$655$	21.1293	0.825591
$656$	−1.16669	−0.0455516
$657$	0	0
$658$	−7.32858	−0.285698
$659$	25.5651	0.995875	0.497937	−	0.867213i	$-0.334091\pi$
$659$	25.5651	0.995875	0.497937	+	0.867213i	$0.334091\pi$
$660$	0	0
$661$	27.9387	1.08669	0.543345	−	0.839510i	$-0.317158\pi$
$661$	27.9387	1.08669	0.543345	+	0.839510i	$0.317158\pi$
$662$	−4.53857	−0.176396
$663$	0	0
$664$	11.3052	0.438726
$665$	48.1846	1.86852
$666$	0	0
$667$	−9.59045	−0.371344
$668$	−19.0561	−0.737301
$669$	0	0
$670$	−42.0055	−1.62281
$671$	−12.8223	−0.495000
$672$	0	0
$673$	2.58625	0.0996927	0.0498464	−	0.998757i	$-0.484127\pi$
$673$	2.58625	0.0996927	0.0498464	+	0.998757i	$0.484127\pi$
$674$	−24.5301	−0.944865
$675$	0	0
$676$	−21.4048	−0.823261
$677$	−0.886837	−0.0340839	−0.0170420	−	0.999855i	$-0.505425\pi$
$677$	−0.886837	−0.0340839	−0.0170420	+	0.999855i	$0.505425\pi$
$678$	0	0
$679$	−2.95100	−0.113249
$680$	0	0
$681$	0	0
$682$	−1.33388	−0.0510771
$683$	26.9328	1.03055	0.515277	−	0.857024i	$-0.327689\pi$
$683$	26.9328	1.03055	0.515277	+	0.857024i	$0.327689\pi$
$684$	0	0
$685$	−33.4824	−1.27930
$686$	4.23208	0.161581
$687$	0	0
$688$	−1.58640	−0.0604810
$689$	−42.1980	−1.60762
$690$	0	0
$691$	−10.3832	−0.394994	−0.197497	−	0.980303i	$-0.563281\pi$
$691$	−10.3832	−0.394994	−0.197497	+	0.980303i	$0.563281\pi$
$692$	−21.5646	−0.819761
$693$	0	0
$694$	3.91222	0.148506
$695$	−16.8798	−0.640289
$696$	0	0
$697$	0	0
$698$	−26.4184	−0.999951
$699$	0	0
$700$	−21.7962	−0.823817
$701$	−49.5351	−1.87091	−0.935457	−	0.353440i	$-0.885012\pi$
$701$	−49.5351	−1.87091	−0.935457	+	0.353440i	$0.885012\pi$
$702$	0	0
$703$	3.14678	0.118683
$704$	18.1299	0.683295
$705$	0	0
$706$	−10.4975	−0.395079
$707$	−17.5603	−0.660424
$708$	0	0
$709$	−36.3527	−1.36526	−0.682628	−	0.730766i	$-0.739163\pi$
$709$	−36.3527	−1.36526	−0.682628	+	0.730766i	$0.739163\pi$
$710$	10.5557	0.396148
$711$	0	0
$712$	−42.1287	−1.57884
$713$	2.06537	0.0773486
$714$	0	0
$715$	−58.4197	−2.18477
$716$	24.3754	0.910953
$717$	0	0
$718$	−23.7170	−0.885112
$719$	−18.0506	−0.673175	−0.336588	−	0.941652i	$-0.609273\pi$
$719$	−18.0506	−0.673175	−0.336588	+	0.941652i	$0.609273\pi$
$720$	0	0
$721$	40.7343	1.51702
$722$	0.960151	0.0357331
$723$	0	0
$724$	−21.9554	−0.815966
$725$	−10.8328	−0.402321
$726$	0	0
$727$	25.6114	0.949873	0.474936	−	0.880020i	$-0.342471\pi$
$727$	25.6114	0.949873	0.474936	+	0.880020i	$0.342471\pi$
$728$	57.3294	2.12477
$729$	0	0
$730$	33.7541	1.24930
$731$	0	0
$732$	0	0
$733$	31.6733	1.16988	0.584941	−	0.811076i	$-0.301118\pi$
$733$	31.6733	1.16988	0.584941	+	0.811076i	$0.301118\pi$
$734$	−19.8127	−0.731301
$735$	0	0
$736$	−25.4377	−0.937645
$737$	−47.5100	−1.75005
$738$	0	0
$739$	−31.3462	−1.15309	−0.576543	−	0.817066i	$-0.695599\pi$
$739$	−31.3462	−1.15309	−0.576543	+	0.817066i	$0.695599\pi$
$740$	−2.79282	−0.102666
$741$	0	0
$742$	24.4181	0.896418
$743$	−3.20001	−0.117397	−0.0586984	−	0.998276i	$-0.518695\pi$
$743$	−3.20001	−0.117397	−0.0586984	+	0.998276i	$0.518695\pi$
$744$	0	0
$745$	−71.7196	−2.62760
$746$	−28.1249	−1.02973
$747$	0	0
$748$	0	0
$749$	62.6705	2.28993
$750$	0	0
$751$	−27.5933	−1.00689	−0.503446	−	0.864026i	$-0.667935\pi$
$751$	−27.5933	−1.00689	−0.503446	+	0.864026i	$0.667935\pi$
$752$	−0.588913	−0.0214754
$753$	0	0
$754$	10.5573	0.384474
$755$	30.4234	1.10722
$756$	0	0
$757$	−10.1597	−0.369259	−0.184629	−	0.982808i	$-0.559108\pi$
$757$	−10.1597	−0.369259	−0.184629	+	0.982808i	$0.559108\pi$
$758$	10.6749	0.387730
$759$	0	0
$760$	38.9817	1.41401
$761$	−8.12911	−0.294680	−0.147340	−	0.989086i	$-0.547071\pi$
$761$	−8.12911	−0.294680	−0.147340	+	0.989086i	$0.547071\pi$
$762$	0	0
$763$	−50.4124	−1.82505
$764$	2.58255	0.0934333
$765$	0	0
$766$	−18.1650	−0.656330
$767$	15.8140	0.571009
$768$	0	0
$769$	16.6656	0.600978	0.300489	−	0.953785i	$-0.402850\pi$
$769$	16.6656	0.600978	0.300489	+	0.953785i	$0.402850\pi$
$770$	33.8049	1.21824
$771$	0	0
$772$	−3.89906	−0.140330
$773$	−42.9077	−1.54328	−0.771641	−	0.636058i	$-0.780564\pi$
$773$	−42.9077	−1.54328	−0.771641	+	0.636058i	$0.780564\pi$
$774$	0	0
$775$	2.33292	0.0838011
$776$	−2.38738	−0.0857018
$777$	0	0
$778$	11.5706	0.414826
$779$	−19.0318	−0.681885
$780$	0	0
$781$	11.9389	0.427209
$782$	0	0
$783$	0	0
$784$	−1.47754	−0.0527692
$785$	−45.0851	−1.60916
$786$	0	0
$787$	−10.6447	−0.379444	−0.189722	−	0.981838i	$-0.560759\pi$
$787$	−10.6447	−0.379444	−0.189722	+	0.981838i	$0.560759\pi$
$788$	−21.2116	−0.755633
$789$	0	0
$790$	−16.3164	−0.580512
$791$	72.6772	2.58410
$792$	0	0
$793$	−21.8554	−0.776109
$794$	24.7757	0.879257
$795$	0	0
$796$	4.68722	0.166134
$797$	29.6872	1.05157	0.525787	−	0.850617i	$-0.323771\pi$
$797$	29.6872	1.05157	0.525787	+	0.850617i	$0.323771\pi$
$798$	0	0
$799$	0	0
$800$	−28.7330	−1.01586
$801$	0	0
$802$	28.4450	1.00443
$803$	38.1773	1.34725
$804$	0	0
$805$	−52.3430	−1.84485
$806$	−2.27358	−0.0800836
$807$	0	0
$808$	−14.2064	−0.499780
$809$	22.8310	0.802694	0.401347	−	0.915926i	$-0.368542\pi$
$809$	22.8310	0.802694	0.401347	+	0.915926i	$0.368542\pi$
$810$	0	0
$811$	37.2506	1.30805	0.654023	−	0.756475i	$-0.273080\pi$
$811$	37.2506	1.30805	0.654023	+	0.756475i	$0.273080\pi$
$812$	8.74093	0.306746
$813$	0	0
$814$	2.20769	0.0773794
$815$	−11.2849	−0.395294
$816$	0	0
$817$	−25.8784	−0.905370
$818$	−15.5135	−0.542418
$819$	0	0
$820$	16.8910	0.589861
$821$	3.29267	0.114915	0.0574574	−	0.998348i	$-0.481701\pi$
$821$	3.29267	0.114915	0.0574574	+	0.998348i	$0.481701\pi$
$822$	0	0
$823$	−12.7887	−0.445786	−0.222893	−	0.974843i	$-0.571550\pi$
$823$	−12.7887	−0.445786	−0.222893	+	0.974843i	$0.571550\pi$
$824$	32.9543	1.14802
$825$	0	0
$826$	−9.15084	−0.318399
$827$	36.4922	1.26896	0.634480	−	0.772939i	$-0.281214\pi$
$827$	36.4922	1.26896	0.634480	+	0.772939i	$0.281214\pi$
$828$	0	0
$829$	−0.425058	−0.0147629	−0.00738144	−	0.999973i	$-0.502350\pi$
$829$	−0.425058	−0.0147629	−0.00738144	+	0.999973i	$0.502350\pi$
$830$	11.3624	0.394396
$831$	0	0
$832$	30.9021	1.07134
$833$	0	0
$834$	0	0
$835$	−51.6909	−1.78884
$836$	16.3363	0.565001
$837$	0	0
$838$	13.8262	0.477619
$839$	−31.6812	−1.09376	−0.546879	−	0.837212i	$-0.684184\pi$
$839$	−31.6812	−1.09376	−0.546879	+	0.837212i	$0.684184\pi$
$840$	0	0
$841$	−24.6557	−0.850197
$842$	−6.31546	−0.217645
$843$	0	0
$844$	0.236502	0.00814072
$845$	−58.0620	−1.99740
$846$	0	0
$847$	−0.951023	−0.0326775
$848$	1.96220	0.0673822
$849$	0	0
$850$	0	0
$851$	−3.41835	−0.117180
$852$	0	0
$853$	−15.3947	−0.527104	−0.263552	−	0.964645i	$-0.584894\pi$
$853$	−15.3947	−0.527104	−0.263552	+	0.964645i	$0.584894\pi$
$854$	12.6468	0.432763
$855$	0	0
$856$	50.7009	1.73292
$857$	−40.7518	−1.39205	−0.696027	−	0.718016i	$-0.745051\pi$
$857$	−40.7518	−1.39205	−0.696027	+	0.718016i	$0.745051\pi$
$858$	0	0
$859$	−46.4431	−1.58462	−0.792310	−	0.610119i	$-0.791122\pi$
$859$	−46.4431	−1.58462	−0.792310	+	0.610119i	$0.791122\pi$
$860$	22.9675	0.783185
$861$	0	0
$862$	−19.4733	−0.663262
$863$	47.2341	1.60787	0.803934	−	0.594719i	$-0.202737\pi$
$863$	47.2341	1.60787	0.803934	+	0.594719i	$0.202737\pi$
$864$	0	0
$865$	−58.4954	−1.98890
$866$	−30.1104	−1.02319
$867$	0	0
$868$	−1.88242	−0.0638934
$869$	−18.4546	−0.626028
$870$	0	0
$871$	−80.9800	−2.74390
$872$	−40.7839	−1.38112
$873$	0	0
$874$	17.6786	0.597986
$875$	−2.24502	−0.0758957
$876$	0	0
$877$	−0.316438	−0.0106854	−0.00534268	−	0.999986i	$-0.501701\pi$
$877$	−0.316438	−0.0106854	−0.00534268	+	0.999986i	$0.501701\pi$
$878$	−32.4006	−1.09347
$879$	0	0
$880$	2.71650	0.0915733
$881$	−36.1357	−1.21744	−0.608721	−	0.793385i	$-0.708317\pi$
$881$	−36.1357	−1.21744	−0.608721	+	0.793385i	$0.708317\pi$
$882$	0	0
$883$	0.156899	0.00528008	0.00264004	−	0.999997i	$-0.499160\pi$
$883$	0.156899	0.00528008	0.00264004	+	0.999997i	$0.499160\pi$
$884$	0	0
$885$	0	0
$886$	12.5507	0.421650
$887$	−30.1071	−1.01090	−0.505448	−	0.862857i	$-0.668673\pi$
$887$	−30.1071	−1.01090	−0.505448	+	0.862857i	$0.668673\pi$
$888$	0	0
$889$	10.4498	0.350474
$890$	−42.3421	−1.41931
$891$	0	0
$892$	13.6555	0.457219
$893$	−9.60671	−0.321476
$894$	0	0
$895$	66.1202	2.21015
$896$	21.5063	0.718477
$897$	0	0
$898$	4.24027	0.141500
$899$	−0.935574	−0.0312031
$900$	0	0
$901$	0	0
$902$	−13.3521	−0.444577
$903$	0	0
$904$	58.7963	1.95554
$905$	−59.5556	−1.97970
$906$	0	0
$907$	38.4765	1.27759	0.638795	−	0.769377i	$-0.279433\pi$
$907$	38.4765	1.27759	0.638795	+	0.769377i	$0.279433\pi$
$908$	11.2001	0.371689
$909$	0	0
$910$	57.6198	1.91008
$911$	1.87182	0.0620162	0.0310081	−	0.999519i	$-0.490128\pi$
$911$	1.87182	0.0620162	0.0310081	+	0.999519i	$0.490128\pi$
$912$	0	0
$913$	12.8514	0.425320
$914$	4.69122	0.155172
$915$	0	0
$916$	19.7422	0.652301
$917$	−23.5710	−0.778382
$918$	0	0
$919$	6.41003	0.211447	0.105724	−	0.994396i	$-0.466284\pi$
$919$	6.41003	0.211447	0.105724	+	0.994396i	$0.466284\pi$
$920$	−42.3458	−1.39610
$921$	0	0
$922$	20.5405	0.676464
$923$	20.3497	0.669819
$924$	0	0
$925$	−3.86118	−0.126955
$926$	−35.2813	−1.15942
$927$	0	0
$928$	11.5228	0.378255
$929$	−5.74229	−0.188398	−0.0941992	−	0.995553i	$-0.530029\pi$
$929$	−5.74229	−0.188398	−0.0941992	+	0.995553i	$0.530029\pi$
$930$	0	0
$931$	−24.1025	−0.789928
$932$	−11.1233	−0.364355
$933$	0	0
$934$	−15.1585	−0.496003
$935$	0	0
$936$	0	0
$937$	−35.7264	−1.16713	−0.583566	−	0.812066i	$-0.698343\pi$
$937$	−35.7264	−1.16713	−0.583566	+	0.812066i	$0.698343\pi$
$938$	46.8595	1.53002
$939$	0	0
$940$	8.52612	0.278091
$941$	10.9669	0.357511	0.178756	−	0.983893i	$-0.442793\pi$
$941$	10.9669	0.357511	0.178756	+	0.983893i	$0.442793\pi$
$942$	0	0
$943$	20.6742	0.673246
$944$	−0.735347	−0.0239335
$945$	0	0
$946$	−18.1555	−0.590286
$947$	39.7162	1.29060	0.645301	−	0.763928i	$-0.276732\pi$
$947$	39.7162	1.29060	0.645301	+	0.763928i	$0.276732\pi$
$948$	0	0
$949$	65.0726	2.11235
$950$	19.9687	0.647870
$951$	0	0
$952$	0	0
$953$	5.33601	0.172850	0.0864252	−	0.996258i	$-0.472456\pi$
$953$	5.33601	0.172850	0.0864252	+	0.996258i	$0.472456\pi$
$954$	0	0
$955$	7.00535	0.226688
$956$	7.55876	0.244468
$957$	0	0
$958$	9.52700	0.307803
$959$	37.3516	1.20614
$960$	0	0
$961$	−30.7985	−0.993501
$962$	3.76297	0.121323
$963$	0	0
$964$	−18.2272	−0.587059
$965$	−10.5765	−0.340469
$966$	0	0
$967$	49.3477	1.58692	0.793458	−	0.608625i	$-0.208279\pi$
$967$	49.3477	1.58692	0.793458	+	0.608625i	$0.208279\pi$
$968$	−0.769384	−0.0247289
$969$	0	0
$970$	−2.39947	−0.0770424
$971$	15.7566	0.505654	0.252827	−	0.967512i	$-0.418640\pi$
$971$	15.7566	0.505654	0.252827	+	0.967512i	$0.418640\pi$
$972$	0	0
$973$	18.8304	0.603676
$974$	21.9923	0.704680
$975$	0	0
$976$	1.01627	0.0325301
$977$	37.9092	1.21282	0.606411	−	0.795151i	$-0.292609\pi$
$977$	37.9092	1.21282	0.606411	+	0.795151i	$0.292609\pi$
$978$	0	0
$979$	−47.8908	−1.53060
$980$	21.3914	0.683323
$981$	0	0
$982$	−13.3575	−0.426257
$983$	1.08178	0.0345035	0.0172518	−	0.999851i	$-0.494508\pi$
$983$	1.08178	0.0345035	0.0172518	+	0.999851i	$0.494508\pi$
$984$	0	0
$985$	−57.5381	−1.83332
$986$	0	0
$987$	0	0
$988$	27.8449	0.885863
$989$	28.1117	0.893900
$990$	0	0
$991$	−9.64197	−0.306287	−0.153144	−	0.988204i	$-0.548940\pi$
$991$	−9.64197	−0.306287	−0.153144	+	0.988204i	$0.548940\pi$
$992$	−2.48151	−0.0787882
$993$	0	0
$994$	−11.7755	−0.373496
$995$	12.7144	0.403074
$996$	0	0
$997$	6.84545	0.216798	0.108399	−	0.994107i	$-0.465428\pi$
$997$	6.84545	0.216798	0.108399	+	0.994107i	$0.465428\pi$
$998$	−13.0241	−0.412271
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.bi.1.3		6
3.2	odd	2		867.2.a.p.1.4	yes	6
17.16	even	2		2601.2.a.bh.1.3		6
51.2	odd	8		867.2.e.k.616.8		24
51.5	even	16		867.2.h.m.688.5		48
51.8	odd	8		867.2.e.k.829.5		24
51.11	even	16		867.2.h.m.733.7		48
51.14	even	16		867.2.h.m.757.7		48
51.20	even	16		867.2.h.m.757.8		48
51.23	even	16		867.2.h.m.733.8		48
51.26	odd	8		867.2.e.k.829.6		24
51.29	even	16		867.2.h.m.688.6		48
51.32	odd	8		867.2.e.k.616.7		24
51.38	odd	4		867.2.d.g.577.5		12
51.41	even	16		867.2.h.m.712.5		48
51.44	even	16		867.2.h.m.712.6		48
51.47	odd	4		867.2.d.g.577.6		12
51.50	odd	2		867.2.a.o.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.o.1.4	✓	6	51.50	odd	2
867.2.a.p.1.4	yes	6	3.2	odd	2
867.2.d.g.577.5		12	51.38	odd	4
867.2.d.g.577.6		12	51.47	odd	4
867.2.e.k.616.7		24	51.32	odd	8
867.2.e.k.616.8		24	51.2	odd	8
867.2.e.k.829.5		24	51.8	odd	8
867.2.e.k.829.6		24	51.26	odd	8
867.2.h.m.688.5		48	51.5	even	16
867.2.h.m.688.6		48	51.29	even	16
867.2.h.m.712.5		48	51.41	even	16
867.2.h.m.712.6		48	51.44	even	16
867.2.h.m.733.7		48	51.11	even	16
867.2.h.m.733.8		48	51.23	even	16
867.2.h.m.757.7		48	51.14	even	16
867.2.h.m.757.8		48	51.20	even	16
2601.2.a.bh.1.3		6	17.16	even	2
2601.2.a.bi.1.3		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)

\(f(q)\)	\(=\)	\(q-0.907065 q^{2} -1.17723 q^{4} -3.19333 q^{5} +3.56234 q^{7} +2.88196 q^{8} +O(q^{10})\)	\(q-0.907065 q^{2} -1.17723 q^{4} -3.19333 q^{5} +3.56234 q^{7} +2.88196 q^{8} +2.89656 q^{10} +3.27613 q^{11} +5.58411 q^{13} -3.23128 q^{14} -0.259660 q^{16} -4.23574 q^{19} +3.75929 q^{20} -2.97167 q^{22} +4.60128 q^{23} +5.19735 q^{25} -5.06515 q^{26} -4.19370 q^{28} -2.08430 q^{29} +0.448868 q^{31} -5.52839 q^{32} -11.3757 q^{35} -0.742912 q^{37} +3.84209 q^{38} -9.20304 q^{40} +4.49315 q^{41} +6.10953 q^{43} -3.85677 q^{44} -4.17367 q^{46} +2.26801 q^{47} +5.69028 q^{49} -4.71434 q^{50} -6.57379 q^{52} -7.55680 q^{53} -10.4618 q^{55} +10.2665 q^{56} +1.89059 q^{58} +2.83196 q^{59} -3.91386 q^{61} -0.407152 q^{62} +5.53393 q^{64} -17.8319 q^{65} -14.5019 q^{67} +10.3185 q^{70} +3.64422 q^{71} +11.6532 q^{73} +0.673870 q^{74} +4.98645 q^{76} +11.6707 q^{77} -5.63303 q^{79} +0.829180 q^{80} -4.07558 q^{82} +3.92274 q^{83} -5.54175 q^{86} +9.44167 q^{88} -14.6181 q^{89} +19.8925 q^{91} -5.41678 q^{92} -2.05724 q^{94} +13.5261 q^{95} -0.828387 q^{97} -5.16145 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 9 q^{4} + 3 q^{5} + 3 q^{7} - 12 q^{8}+O(q^{10}) \) 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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