LMFDB - Embedded newform 2601.2.a.bh.1.4

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:	$1$
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			1.4
Root			$-2.06104$ 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)

$f(q)$	$=$	$q-0.435433 q^{2} -1.81040 q^{4} -4.22078 q^{5} -2.90981 q^{7} +1.65917 q^{8} +O(q^{10})$	$q-0.435433 q^{2} -1.81040 q^{4} -4.22078 q^{5} -2.90981 q^{7} +1.65917 q^{8} +1.83787 q^{10} -0.559187 q^{11} +1.50148 q^{13} +1.26703 q^{14} +2.89834 q^{16} +6.57122 q^{19} +7.64129 q^{20} +0.243489 q^{22} +1.98909 q^{23} +12.8150 q^{25} -0.653794 q^{26} +5.26792 q^{28} +2.24583 q^{29} -2.41539 q^{31} -4.58038 q^{32} +12.2817 q^{35} +4.90481 q^{37} -2.86133 q^{38} -7.00301 q^{40} -7.01952 q^{41} +5.38597 q^{43} +1.01235 q^{44} -0.866117 q^{46} -7.70625 q^{47} +1.46702 q^{49} -5.58008 q^{50} -2.71828 q^{52} -10.2075 q^{53} +2.36021 q^{55} -4.82789 q^{56} -0.977909 q^{58} +0.354076 q^{59} -4.96456 q^{61} +1.05174 q^{62} -3.80222 q^{64} -6.33742 q^{65} -3.56725 q^{67} -5.34786 q^{70} +3.72962 q^{71} +8.61368 q^{73} -2.13572 q^{74} -11.8965 q^{76} +1.62713 q^{77} -2.73403 q^{79} -12.2332 q^{80} +3.05653 q^{82} -9.16257 q^{83} -2.34523 q^{86} -0.927788 q^{88} +17.6099 q^{89} -4.36903 q^{91} -3.60105 q^{92} +3.35556 q^{94} -27.7357 q^{95} +13.8193 q^{97} -0.638789 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.435433	−0.307898	−0.153949	−	0.988079i	$-0.549199\pi$
$2$	−0.435433	−0.307898	−0.153949	+	0.988079i	$0.549199\pi$
$3$	0	0
$3$	0	0
$4$	−1.81040	−0.905199
$5$	−4.22078	−1.88759	−0.943796	−	0.330530i	$-0.892773\pi$
$5$	−4.22078	−1.88759	−0.943796	+	0.330530i	$0.892773\pi$
$6$	0	0
$7$	−2.90981	−1.09981	−0.549903	−	0.835228i	$-0.685335\pi$
$7$	−2.90981	−1.09981	−0.549903	+	0.835228i	$0.685335\pi$
$8$	1.65917	0.586606
$9$	0	0
$10$	1.83787	0.581185
$11$	−0.559187	−0.168601	−0.0843006	−	0.996440i	$-0.526866\pi$
$11$	−0.559187	−0.168601	−0.0843006	+	0.996440i	$0.526866\pi$
$12$	0	0
$13$	1.50148	0.416435	0.208218	−	0.978083i	$-0.433234\pi$
$13$	1.50148	0.416435	0.208218	+	0.978083i	$0.433234\pi$
$14$	1.26703	0.338628
$15$	0	0
$16$	2.89834	0.724584
$17$	0	0
$17$	0	0
$18$	0	0
$19$	6.57122	1.50754	0.753770	−	0.657138i	$-0.228233\pi$
$19$	6.57122	1.50754	0.753770	+	0.657138i	$0.228233\pi$
$20$	7.64129	1.70865
$21$	0	0
$22$	0.243489	0.0519119
$23$	1.98909	0.414755	0.207377	−	0.978261i	$-0.433507\pi$
$23$	1.98909	0.414755	0.207377	+	0.978261i	$0.433507\pi$
$24$	0	0
$25$	12.8150	2.56300
$26$	−0.653794	−0.128220
$27$	0	0
$28$	5.26792	0.995544
$29$	2.24583	0.417040	0.208520	−	0.978018i	$-0.433135\pi$
$29$	2.24583	0.417040	0.208520	+	0.978018i	$0.433135\pi$
$30$	0	0
$31$	−2.41539	−0.433817	−0.216909	−	0.976192i	$-0.569597\pi$
$31$	−2.41539	−0.433817	−0.216909	+	0.976192i	$0.569597\pi$
$32$	−4.58038	−0.809704
$33$	0	0
$34$	0	0
$35$	12.2817	2.07598
$36$	0	0
$37$	4.90481	0.806345	0.403173	−	0.915124i	$-0.367907\pi$
$37$	4.90481	0.806345	0.403173	+	0.915124i	$0.367907\pi$
$38$	−2.86133	−0.464168
$39$	0	0
$40$	−7.00301	−1.10727
$41$	−7.01952	−1.09627	−0.548133	−	0.836391i	$-0.684661\pi$
$41$	−7.01952	−1.09627	−0.548133	+	0.836391i	$0.684661\pi$
$42$	0	0
$43$	5.38597	0.821352	0.410676	−	0.911781i	$-0.365293\pi$
$43$	5.38597	0.821352	0.410676	+	0.911781i	$0.365293\pi$
$44$	1.01235	0.152618
$45$	0	0
$46$	−0.866117	−0.127702
$47$	−7.70625	−1.12407	−0.562036	−	0.827113i	$-0.689982\pi$
$47$	−7.70625	−1.12407	−0.562036	+	0.827113i	$0.689982\pi$
$48$	0	0
$49$	1.46702	0.209574
$50$	−5.58008	−0.789142
$51$	0	0
$52$	−2.71828	−0.376957
$53$	−10.2075	−1.40210	−0.701051	−	0.713111i	$-0.747285\pi$
$53$	−10.2075	−1.40210	−0.701051	+	0.713111i	$0.747285\pi$
$54$	0	0
$55$	2.36021	0.318250
$56$	−4.82789	−0.645154
$57$	0	0
$58$	−0.977909	−0.128406
$59$	0.354076	0.0460968	0.0230484	−	0.999734i	$-0.492663\pi$
$59$	0.354076	0.0460968	0.0230484	+	0.999734i	$0.492663\pi$
$60$	0	0
$61$	−4.96456	−0.635647	−0.317824	−	0.948150i	$-0.602952\pi$
$61$	−4.96456	−0.635647	−0.317824	+	0.948150i	$0.602952\pi$
$62$	1.05174	0.133571
$63$	0	0
$64$	−3.80222	−0.475278
$65$	−6.33742	−0.786060
$66$	0	0
$67$	−3.56725	−0.435809	−0.217904	−	0.975970i	$-0.569922\pi$
$67$	−3.56725	−0.435809	−0.217904	+	0.975970i	$0.569922\pi$
$68$	0	0
$69$	0	0
$70$	−5.34786	−0.639191
$71$	3.72962	0.442625	0.221312	−	0.975203i	$-0.428966\pi$
$71$	3.72962	0.442625	0.221312	+	0.975203i	$0.428966\pi$
$72$	0	0
$73$	8.61368	1.00815	0.504077	−	0.863659i	$-0.331833\pi$
$73$	8.61368	1.00815	0.504077	+	0.863659i	$0.331833\pi$
$74$	−2.13572	−0.248272
$75$	0	0
$76$	−11.8965	−1.36462
$77$	1.62713	0.185429
$78$	0	0
$79$	−2.73403	−0.307603	−0.153801	−	0.988102i	$-0.549152\pi$
$79$	−2.73403	−0.307603	−0.153801	+	0.988102i	$0.549152\pi$
$80$	−12.2332	−1.36772
$81$	0	0
$82$	3.05653	0.337538
$83$	−9.16257	−1.00572	−0.502862	−	0.864367i	$-0.667719\pi$
$83$	−9.16257	−1.00572	−0.502862	+	0.864367i	$0.667719\pi$
$84$	0	0
$85$	0	0
$86$	−2.34523	−0.252893
$87$	0	0
$88$	−0.927788	−0.0989026
$89$	17.6099	1.86665	0.933325	−	0.359033i	$-0.116893\pi$
$89$	17.6099	1.86665	0.933325	+	0.359033i	$0.116893\pi$
$90$	0	0
$91$	−4.36903	−0.457998
$92$	−3.60105	−0.375435
$93$	0	0
$94$	3.35556	0.346099
$95$	−27.7357	−2.84562
$96$	0	0
$97$	13.8193	1.40314	0.701568	−	0.712602i	$-0.252484\pi$
$97$	13.8193	1.40314	0.701568	+	0.712602i	$0.252484\pi$
$98$	−0.638789	−0.0645274
$99$	0	0
$100$	−23.2002	−2.32002
$101$	−11.0077	−1.09531	−0.547655	−	0.836704i	$-0.684479\pi$
$101$	−11.0077	−1.09531	−0.547655	+	0.836704i	$0.684479\pi$
$102$	0	0
$103$	6.83769	0.673737	0.336869	−	0.941552i	$-0.390632\pi$
$103$	6.83769	0.673737	0.336869	+	0.941552i	$0.390632\pi$
$104$	2.49121	0.244284
$105$	0	0
$106$	4.44466	0.431704
$107$	11.8699	1.14751	0.573753	−	0.819029i	$-0.305487\pi$
$107$	11.8699	1.14751	0.573753	+	0.819029i	$0.305487\pi$
$108$	0	0
$109$	−1.58122	−0.151453	−0.0757265	−	0.997129i	$-0.524128\pi$
$109$	−1.58122	−0.151453	−0.0757265	+	0.997129i	$0.524128\pi$
$110$	−1.02771	−0.0979885
$111$	0	0
$112$	−8.43362	−0.796902
$113$	1.21085	0.113907	0.0569537	−	0.998377i	$-0.481861\pi$
$113$	1.21085	0.113907	0.0569537	+	0.998377i	$0.481861\pi$
$114$	0	0
$115$	−8.39553	−0.782887
$116$	−4.06585	−0.377505
$117$	0	0
$118$	−0.154177	−0.0141931
$119$	0	0
$120$	0	0
$121$	−10.6873	−0.971574
$122$	2.16174	0.195714
$123$	0	0
$124$	4.37282	0.392691
$125$	−32.9854	−2.95030
$126$	0	0
$127$	−6.68311	−0.593030	−0.296515	−	0.955028i	$-0.595824\pi$
$127$	−6.68311	−0.593030	−0.296515	+	0.955028i	$0.595824\pi$
$128$	10.8164	0.956041
$129$	0	0
$130$	2.75952	0.242026
$131$	20.8620	1.82272	0.911360	−	0.411609i	$-0.135033\pi$
$131$	20.8620	1.82272	0.911360	+	0.411609i	$0.135033\pi$
$132$	0	0
$133$	−19.1210	−1.65800
$134$	1.55330	0.134185
$135$	0	0
$136$	0	0
$137$	6.62465	0.565982	0.282991	−	0.959123i	$-0.408673\pi$
$137$	6.62465	0.565982	0.282991	+	0.959123i	$0.408673\pi$
$138$	0	0
$139$	−6.78241	−0.575276	−0.287638	−	0.957739i	$-0.592870\pi$
$139$	−6.78241	−0.575276	−0.287638	+	0.957739i	$0.592870\pi$
$140$	−22.2347	−1.87918
$141$	0	0
$142$	−1.62400	−0.136283
$143$	−0.839608	−0.0702115
$144$	0	0
$145$	−9.47916	−0.787202
$146$	−3.75068	−0.310409
$147$	0	0
$148$	−8.87965	−0.729903
$149$	4.79286	0.392646	0.196323	−	0.980539i	$-0.437100\pi$
$149$	4.79286	0.392646	0.196323	+	0.980539i	$0.437100\pi$
$150$	0	0
$151$	10.4572	0.850992	0.425496	−	0.904960i	$-0.360100\pi$
$151$	10.4572	0.850992	0.425496	+	0.904960i	$0.360100\pi$
$152$	10.9028	0.884333
$153$	0	0
$154$	−0.708507	−0.0570931
$155$	10.1948	0.818869
$156$	0	0
$157$	−3.74076	−0.298545	−0.149273	−	0.988796i	$-0.547693\pi$
$157$	−3.74076	−0.298545	−0.149273	+	0.988796i	$0.547693\pi$
$158$	1.19049	0.0947101
$159$	0	0
$160$	19.3328	1.52839
$161$	−5.78789	−0.456150
$162$	0	0
$163$	−13.0820	−1.02466	−0.512332	−	0.858788i	$-0.671218\pi$
$163$	−13.0820	−1.02466	−0.512332	+	0.858788i	$0.671218\pi$
$164$	12.7081	0.992338
$165$	0	0
$166$	3.98969	0.309660
$167$	−6.33891	−0.490519	−0.245260	−	0.969457i	$-0.578873\pi$
$167$	−6.33891	−0.490519	−0.245260	+	0.969457i	$0.578873\pi$
$168$	0	0
$169$	−10.7456	−0.826582
$170$	0	0
$171$	0	0
$172$	−9.75074	−0.743487
$173$	−9.59885	−0.729787	−0.364893	−	0.931049i	$-0.618895\pi$
$173$	−9.59885	−0.729787	−0.364893	+	0.931049i	$0.618895\pi$
$174$	0	0
$175$	−37.2893	−2.81880
$176$	−1.62071	−0.122166
$177$	0	0
$178$	−7.66795	−0.574737
$179$	16.7361	1.25092	0.625458	−	0.780258i	$-0.284912\pi$
$179$	16.7361	1.25092	0.625458	+	0.780258i	$0.284912\pi$
$180$	0	0
$181$	−17.5761	−1.30642	−0.653210	−	0.757177i	$-0.726578\pi$
$181$	−17.5761	−1.30642	−0.653210	+	0.757177i	$0.726578\pi$
$182$	1.90242	0.141017
$183$	0	0
$184$	3.30025	0.243298
$185$	−20.7021	−1.52205
$186$	0	0
$187$	0	0
$188$	13.9514	1.01751
$189$	0	0
$190$	12.0770	0.876160
$191$	4.81522	0.348417	0.174209	−	0.984709i	$-0.444263\pi$
$191$	4.81522	0.348417	0.174209	+	0.984709i	$0.444263\pi$
$192$	0	0
$193$	6.67034	0.480142	0.240071	−	0.970755i	$-0.422829\pi$
$193$	6.67034	0.480142	0.240071	+	0.970755i	$0.422829\pi$
$194$	−6.01738	−0.432022
$195$	0	0
$196$	−2.65589	−0.189706
$197$	19.5257	1.39115	0.695574	−	0.718454i	$-0.255150\pi$
$197$	19.5257	1.39115	0.695574	+	0.718454i	$0.255150\pi$
$198$	0	0
$199$	−18.1817	−1.28887	−0.644433	−	0.764660i	$-0.722907\pi$
$199$	−18.1817	−1.28887	−0.644433	+	0.764660i	$0.722907\pi$
$200$	21.2623	1.50347
$201$	0	0
$202$	4.79313	0.337243
$203$	−6.53495	−0.458664
$204$	0	0
$205$	29.6279	2.06930
$206$	−2.97736	−0.207442
$207$	0	0
$208$	4.35179	0.301743
$209$	−3.67454	−0.254173
$210$	0	0
$211$	−25.3182	−1.74298	−0.871490	−	0.490414i	$-0.836846\pi$
$211$	−25.3182	−1.74298	−0.871490	+	0.490414i	$0.836846\pi$
$212$	18.4796	1.26918
$213$	0	0
$214$	−5.16854	−0.353314
$215$	−22.7330	−1.55038
$216$	0	0
$217$	7.02834	0.477115
$218$	0.688513	0.0466320
$219$	0	0
$220$	−4.27291	−0.288080
$221$	0	0
$222$	0	0
$223$	13.0170	0.871683	0.435842	−	0.900023i	$-0.356451\pi$
$223$	13.0170	0.871683	0.435842	+	0.900023i	$0.356451\pi$
$224$	13.3281	0.890518
$225$	0	0
$226$	−0.527245	−0.0350718
$227$	−9.85814	−0.654308	−0.327154	−	0.944971i	$-0.606090\pi$
$227$	−9.85814	−0.654308	−0.327154	+	0.944971i	$0.606090\pi$
$228$	0	0
$229$	4.93284	0.325971	0.162985	−	0.986628i	$-0.447888\pi$
$229$	4.93284	0.325971	0.162985	+	0.986628i	$0.447888\pi$
$230$	3.65569	0.241049
$231$	0	0
$232$	3.72622	0.244639
$233$	−21.2161	−1.38991	−0.694955	−	0.719053i	$-0.744576\pi$
$233$	−21.2161	−1.38991	−0.694955	+	0.719053i	$0.744576\pi$
$234$	0	0
$235$	32.5264	2.12179
$236$	−0.641019	−0.0417268
$237$	0	0
$238$	0	0
$239$	−24.8188	−1.60540	−0.802698	−	0.596386i	$-0.796603\pi$
$239$	−24.8188	−1.60540	−0.802698	+	0.596386i	$0.796603\pi$
$240$	0	0
$241$	21.3921	1.37799	0.688994	−	0.724767i	$-0.258053\pi$
$241$	21.3921	1.37799	0.688994	+	0.724767i	$0.258053\pi$
$242$	4.65361	0.299145
$243$	0	0
$244$	8.98784	0.575387
$245$	−6.19197	−0.395590
$246$	0	0
$247$	9.86655	0.627793
$248$	−4.00755	−0.254480
$249$	0	0
$250$	14.3629	0.908392
$251$	−13.8822	−0.876236	−0.438118	−	0.898917i	$-0.644355\pi$
$251$	−13.8822	−0.876236	−0.438118	+	0.898917i	$0.644355\pi$
$252$	0	0
$253$	−1.11227	−0.0699281
$254$	2.91005	0.182593
$255$	0	0
$256$	2.89464	0.180915
$257$	20.0544	1.25096	0.625481	−	0.780240i	$-0.284903\pi$
$257$	20.0544	1.25096	0.625481	+	0.780240i	$0.284903\pi$
$258$	0	0
$259$	−14.2721	−0.886824
$260$	11.4732	0.711541
$261$	0	0
$262$	−9.08400	−0.561212
$263$	21.1753	1.30573	0.652863	−	0.757476i	$-0.273568\pi$
$263$	21.1753	1.30573	0.652863	+	0.757476i	$0.273568\pi$
$264$	0	0
$265$	43.0834	2.64659
$266$	8.32593	0.510495
$267$	0	0
$268$	6.45814	0.394494
$269$	−15.1182	−0.921771	−0.460886	−	0.887460i	$-0.652468\pi$
$269$	−15.1182	−0.921771	−0.460886	+	0.887460i	$0.652468\pi$
$270$	0	0
$271$	3.15522	0.191666	0.0958331	−	0.995397i	$-0.469449\pi$
$271$	3.15522	0.191666	0.0958331	+	0.995397i	$0.469449\pi$
$272$	0	0
$273$	0	0
$274$	−2.88459	−0.174265
$275$	−7.16598	−0.432125
$276$	0	0
$277$	15.7417	0.945828	0.472914	−	0.881108i	$-0.343202\pi$
$277$	15.7417	0.945828	0.472914	+	0.881108i	$0.343202\pi$
$278$	2.95329	0.177126
$279$	0	0
$280$	20.3775	1.21779
$281$	−20.0917	−1.19857	−0.599285	−	0.800536i	$-0.704548\pi$
$281$	−20.0917	−1.19857	−0.599285	+	0.800536i	$0.704548\pi$
$282$	0	0
$283$	8.11052	0.482120	0.241060	−	0.970510i	$-0.422505\pi$
$283$	8.11052	0.482120	0.241060	+	0.970510i	$0.422505\pi$
$284$	−6.75210	−0.400664
$285$	0	0
$286$	0.365593	0.0216180
$287$	20.4255	1.20568
$288$	0	0
$289$	0	0
$290$	4.12754	0.242378
$291$	0	0
$292$	−15.5942	−0.912581
$293$	−6.47618	−0.378343	−0.189171	−	0.981944i	$-0.560580\pi$
$293$	−6.47618	−0.378343	−0.189171	+	0.981944i	$0.560580\pi$
$294$	0	0
$295$	−1.49448	−0.0870119
$296$	8.13793	0.473007
$297$	0	0
$298$	−2.08697	−0.120895
$299$	2.98658	0.172718
$300$	0	0
$301$	−15.6722	−0.903329
$302$	−4.55340	−0.262019
$303$	0	0
$304$	19.0456	1.09234
$305$	20.9543	1.19984
$306$	0	0
$307$	−25.5479	−1.45809	−0.729046	−	0.684464i	$-0.760036\pi$
$307$	−25.5479	−1.45809	−0.729046	+	0.684464i	$0.760036\pi$
$308$	−2.94575	−0.167850
$309$	0	0
$310$	−4.43917	−0.252128
$311$	−27.8203	−1.57754	−0.788772	−	0.614686i	$-0.789283\pi$
$311$	−27.8203	−1.57754	−0.788772	+	0.614686i	$0.789283\pi$
$312$	0	0
$313$	−17.8009	−1.00617	−0.503084	−	0.864238i	$-0.667801\pi$
$313$	−17.8009	−1.00617	−0.503084	+	0.864238i	$0.667801\pi$
$314$	1.62885	0.0919214
$315$	0	0
$316$	4.94968	0.278441
$317$	16.5610	0.930158	0.465079	−	0.885269i	$-0.346026\pi$
$317$	16.5610	0.930158	0.465079	+	0.885269i	$0.346026\pi$
$318$	0	0
$319$	−1.25584	−0.0703135
$320$	16.0484	0.897131
$321$	0	0
$322$	2.52024	0.140447
$323$	0	0
$324$	0	0
$325$	19.2415	1.06732
$326$	5.69635	0.315491
$327$	0	0
$328$	−11.6466	−0.643076
$329$	22.4238	1.23626
$330$	0	0
$331$	5.59155	0.307339	0.153670	−	0.988122i	$-0.450891\pi$
$331$	5.59155	0.307339	0.153670	+	0.988122i	$0.450891\pi$
$332$	16.5879	0.910379
$333$	0	0
$334$	2.76017	0.151030
$335$	15.0566	0.822629
$336$	0	0
$337$	−16.5055	−0.899113	−0.449557	−	0.893252i	$-0.648418\pi$
$337$	−16.5055	−0.899113	−0.449557	+	0.893252i	$0.648418\pi$
$338$	4.67897	0.254503
$339$	0	0
$340$	0	0
$341$	1.35066	0.0731421
$342$	0	0
$343$	16.0999	0.869315
$344$	8.93626	0.481811
$345$	0	0
$346$	4.17966	0.224700
$347$	−17.0571	−0.915671	−0.457835	−	0.889037i	$-0.651375\pi$
$347$	−17.0571	−0.915671	−0.457835	+	0.889037i	$0.651375\pi$
$348$	0	0
$349$	−22.2811	−1.19268	−0.596340	−	0.802732i	$-0.703379\pi$
$349$	−22.2811	−1.19268	−0.596340	+	0.802732i	$0.703379\pi$
$350$	16.2370	0.867903
$351$	0	0
$352$	2.56129	0.136517
$353$	−34.8725	−1.85608	−0.928038	−	0.372485i	$-0.878506\pi$
$353$	−34.8725	−1.85608	−0.928038	+	0.372485i	$0.878506\pi$
$354$	0	0
$355$	−15.7419	−0.835495
$356$	−31.8810	−1.68969
$357$	0	0
$358$	−7.28746	−0.385154
$359$	−11.7621	−0.620780	−0.310390	−	0.950609i	$-0.600460\pi$
$359$	−11.7621	−0.620780	−0.310390	+	0.950609i	$0.600460\pi$
$360$	0	0
$361$	24.1809	1.27268
$362$	7.65321	0.402244
$363$	0	0
$364$	7.90968	0.414580
$365$	−36.3565	−1.90298
$366$	0	0
$367$	−13.3052	−0.694526	−0.347263	−	0.937768i	$-0.612889\pi$
$367$	−13.3052	−0.694526	−0.347263	+	0.937768i	$0.612889\pi$
$368$	5.76506	0.300525
$369$	0	0
$370$	9.01439	0.468636
$371$	29.7018	1.54204
$372$	0	0
$373$	−9.53711	−0.493813	−0.246907	−	0.969039i	$-0.579414\pi$
$373$	−9.53711	−0.493813	−0.246907	+	0.969039i	$0.579414\pi$
$374$	0	0
$375$	0	0
$376$	−12.7860	−0.659388
$377$	3.37207	0.173670
$378$	0	0
$379$	11.5286	0.592186	0.296093	−	0.955159i	$-0.404316\pi$
$379$	11.5286	0.592186	0.296093	+	0.955159i	$0.404316\pi$
$380$	50.2126	2.57585
$381$	0	0
$382$	−2.09671	−0.107277
$383$	−18.0993	−0.924833	−0.462416	−	0.886663i	$-0.653017\pi$
$383$	−18.0993	−0.924833	−0.462416	+	0.886663i	$0.653017\pi$
$384$	0	0
$385$	−6.86776	−0.350014
$386$	−2.90449	−0.147835
$387$	0	0
$388$	−25.0184	−1.27012
$389$	0.621547	0.0315137	0.0157568	−	0.999876i	$-0.494984\pi$
$389$	0.621547	0.0315137	0.0157568	+	0.999876i	$0.494984\pi$
$390$	0	0
$391$	0	0
$392$	2.43404	0.122938
$393$	0	0
$394$	−8.50214	−0.428332
$395$	11.5397	0.580628
$396$	0	0
$397$	−3.15802	−0.158497	−0.0792483	−	0.996855i	$-0.525252\pi$
$397$	−3.15802	−0.158497	−0.0792483	+	0.996855i	$0.525252\pi$
$398$	7.91692	0.396839
$399$	0	0
$400$	37.1422	1.85711
$401$	15.5021	0.774136	0.387068	−	0.922051i	$-0.373488\pi$
$401$	15.5021	0.774136	0.387068	+	0.922051i	$0.373488\pi$
$402$	0	0
$403$	−3.62666	−0.180657
$404$	19.9284	0.991473
$405$	0	0
$406$	2.84553	0.141222
$407$	−2.74270	−0.135951
$408$	0	0
$409$	−34.2765	−1.69486	−0.847432	−	0.530904i	$-0.821852\pi$
$409$	−34.2765	−1.69486	−0.847432	+	0.530904i	$0.821852\pi$
$410$	−12.9010	−0.637133
$411$	0	0
$412$	−12.3789	−0.609866
$413$	−1.03030	−0.0506975
$414$	0	0
$415$	38.6732	1.89839
$416$	−6.87734	−0.337190
$417$	0	0
$418$	1.60002	0.0782594
$419$	−13.2521	−0.647409	−0.323704	−	0.946158i	$-0.604928\pi$
$419$	−13.2521	−0.647409	−0.323704	+	0.946158i	$0.604928\pi$
$420$	0	0
$421$	−21.7307	−1.05909	−0.529544	−	0.848283i	$-0.677637\pi$
$421$	−21.7307	−1.05909	−0.529544	+	0.848283i	$0.677637\pi$
$422$	11.0244	0.536659
$423$	0	0
$424$	−16.9359	−0.822482
$425$	0	0
$426$	0	0
$427$	14.4460	0.699089
$428$	−21.4892	−1.03872
$429$	0	0
$430$	9.89870	0.477358
$431$	12.7657	0.614900	0.307450	−	0.951564i	$-0.400524\pi$
$431$	12.7657	0.614900	0.307450	+	0.951564i	$0.400524\pi$
$432$	0	0
$433$	−15.5294	−0.746295	−0.373148	−	0.927772i	$-0.621721\pi$
$433$	−15.5294	−0.746295	−0.373148	+	0.927772i	$0.621721\pi$
$434$	−3.06037	−0.146903
$435$	0	0
$436$	2.86263	0.137095
$437$	13.0708	0.625259
$438$	0	0
$439$	22.4530	1.07162	0.535812	−	0.844337i	$-0.320006\pi$
$439$	22.4530	1.07162	0.535812	+	0.844337i	$0.320006\pi$
$440$	3.91599	0.186688
$441$	0	0
$442$	0	0
$443$	−25.1062	−1.19283	−0.596415	−	0.802676i	$-0.703409\pi$
$443$	−25.1062	−1.19283	−0.596415	+	0.802676i	$0.703409\pi$
$444$	0	0
$445$	−74.3277	−3.52347
$446$	−5.66804	−0.268389
$447$	0	0
$448$	11.0638	0.522714
$449$	11.1081	0.524224	0.262112	−	0.965037i	$-0.415581\pi$
$449$	11.1081	0.524224	0.262112	+	0.965037i	$0.415581\pi$
$450$	0	0
$451$	3.92523	0.184832
$452$	−2.19212	−0.103109
$453$	0	0
$454$	4.29256	0.201460
$455$	18.4407	0.864514
$456$	0	0
$457$	−16.4256	−0.768358	−0.384179	−	0.923259i	$-0.625515\pi$
$457$	−16.4256	−0.768358	−0.384179	+	0.923259i	$0.625515\pi$
$458$	−2.14792	−0.100366
$459$	0	0
$460$	15.1992	0.708668
$461$	−23.9357	−1.11480	−0.557398	−	0.830246i	$-0.688200\pi$
$461$	−23.9357	−1.11480	−0.557398	+	0.830246i	$0.688200\pi$
$462$	0	0
$463$	16.0152	0.744291	0.372145	−	0.928174i	$-0.378622\pi$
$463$	16.0152	0.744291	0.372145	+	0.928174i	$0.378622\pi$
$464$	6.50917	0.302181
$465$	0	0
$466$	9.23818	0.427950
$467$	−16.9602	−0.784827	−0.392413	−	0.919789i	$-0.628360\pi$
$467$	−16.9602	−0.784827	−0.392413	+	0.919789i	$0.628360\pi$
$468$	0	0
$469$	10.3800	0.479305
$470$	−14.1631	−0.653294
$471$	0	0
$472$	0.587474	0.0270407
$473$	−3.01176	−0.138481
$474$	0	0
$475$	84.2101	3.86383
$476$	0	0
$477$	0	0
$478$	10.8069	0.494298
$479$	−16.3362	−0.746421	−0.373210	−	0.927747i	$-0.621743\pi$
$479$	−16.3362	−0.746421	−0.373210	+	0.927747i	$0.621743\pi$
$480$	0	0
$481$	7.36447	0.335791
$482$	−9.31484	−0.424279
$483$	0	0
$484$	19.3483	0.879467
$485$	−58.3282	−2.64855
$486$	0	0
$487$	25.7634	1.16745	0.583726	−	0.811951i	$-0.301594\pi$
$487$	25.7634	1.16745	0.583726	+	0.811951i	$0.301594\pi$
$488$	−8.23707	−0.372875
$489$	0	0
$490$	2.69619	0.121801
$491$	29.8841	1.34865	0.674325	−	0.738435i	$-0.264435\pi$
$491$	29.8841	1.34865	0.674325	+	0.738435i	$0.264435\pi$
$492$	0	0
$493$	0	0
$494$	−4.29622	−0.193296
$495$	0	0
$496$	−7.00062	−0.314337
$497$	−10.8525	−0.486802
$498$	0	0
$499$	−40.5340	−1.81455	−0.907275	−	0.420538i	$-0.861841\pi$
$499$	−40.5340	−1.81455	−0.907275	+	0.420538i	$0.861841\pi$
$500$	59.7167	2.67061
$501$	0	0
$502$	6.04477	0.269791
$503$	−16.3128	−0.727351	−0.363676	−	0.931526i	$-0.618478\pi$
$503$	−16.3128	−0.727351	−0.363676	+	0.931526i	$0.618478\pi$
$504$	0	0
$505$	46.4612	2.06750
$506$	0.484321	0.0215307
$507$	0	0
$508$	12.0991	0.536810
$509$	34.4184	1.52557	0.762784	−	0.646654i	$-0.223832\pi$
$509$	34.4184	1.52557	0.762784	+	0.646654i	$0.223832\pi$
$510$	0	0
$511$	−25.0642	−1.10877
$512$	−22.8932	−1.01174
$513$	0	0
$514$	−8.73237	−0.385168
$515$	−28.8604	−1.27174
$516$	0	0
$517$	4.30924	0.189520
$518$	6.21454	0.273051
$519$	0	0
$520$	−10.5149	−0.461108
$521$	−8.28427	−0.362940	−0.181470	−	0.983396i	$-0.558086\pi$
$521$	−8.28427	−0.362940	−0.181470	+	0.983396i	$0.558086\pi$
$522$	0	0
$523$	−15.9133	−0.695840	−0.347920	−	0.937524i	$-0.613112\pi$
$523$	−15.9133	−0.695840	−0.347920	+	0.937524i	$0.613112\pi$
$524$	−37.7685	−1.64992
$525$	0	0
$526$	−9.22044	−0.402030
$527$	0	0
$528$	0	0
$529$	−19.0435	−0.827979
$530$	−18.7600	−0.814880
$531$	0	0
$532$	34.6167	1.50082
$533$	−10.5397	−0.456524
$534$	0	0
$535$	−50.1002	−2.16602
$536$	−5.91869	−0.255648
$537$	0	0
$538$	6.58295	0.283811
$539$	−0.820338	−0.0353345
$540$	0	0
$541$	−10.5686	−0.454378	−0.227189	−	0.973851i	$-0.572953\pi$
$541$	−10.5686	−0.454378	−0.227189	+	0.973851i	$0.572953\pi$
$542$	−1.37389	−0.0590136
$543$	0	0
$544$	0	0
$545$	6.67396	0.285881
$546$	0	0
$547$	5.17102	0.221097	0.110549	−	0.993871i	$-0.464739\pi$
$547$	5.17102	0.221097	0.110549	+	0.993871i	$0.464739\pi$
$548$	−11.9932	−0.512326
$549$	0	0
$550$	3.12031	0.133050
$551$	14.7578	0.628705
$552$	0	0
$553$	7.95552	0.338303
$554$	−6.85447	−0.291218
$555$	0	0
$556$	12.2789	0.520740
$557$	26.0577	1.10410	0.552051	−	0.833810i	$-0.313845\pi$
$557$	26.0577	1.10410	0.552051	+	0.833810i	$0.313845\pi$
$558$	0	0
$559$	8.08692	0.342040
$560$	35.5965	1.50423
$561$	0	0
$562$	8.74859	0.369037
$563$	26.9192	1.13451	0.567255	−	0.823542i	$-0.308005\pi$
$563$	26.9192	1.13451	0.567255	+	0.823542i	$0.308005\pi$
$564$	0	0
$565$	−5.11074	−0.215011
$566$	−3.53159	−0.148444
$567$	0	0
$568$	6.18809	0.259647
$569$	−20.9535	−0.878417	−0.439208	−	0.898385i	$-0.644741\pi$
$569$	−20.9535	−0.878417	−0.439208	+	0.898385i	$0.644741\pi$
$570$	0	0
$571$	−7.08769	−0.296610	−0.148305	−	0.988942i	$-0.547382\pi$
$571$	−7.08769	−0.296610	−0.148305	+	0.988942i	$0.547382\pi$
$572$	1.52002	0.0635554
$573$	0	0
$574$	−8.89394	−0.371226
$575$	25.4902	1.06302
$576$	0	0
$577$	−6.75914	−0.281386	−0.140693	−	0.990053i	$-0.544933\pi$
$577$	−6.75914	−0.281386	−0.140693	+	0.990053i	$0.544933\pi$
$578$	0	0
$579$	0	0
$580$	17.1611	0.712574
$581$	26.6614	1.10610
$582$	0	0
$583$	5.70788	0.236396
$584$	14.2916	0.591390
$585$	0	0
$586$	2.81994	0.116491
$587$	13.1684	0.543518	0.271759	−	0.962365i	$-0.412395\pi$
$587$	13.1684	0.543518	0.271759	+	0.962365i	$0.412395\pi$
$588$	0	0
$589$	−15.8721	−0.653997
$590$	0.650745	0.0267908
$591$	0	0
$592$	14.2158	0.584265
$593$	7.03629	0.288946	0.144473	−	0.989509i	$-0.453851\pi$
$593$	7.03629	0.288946	0.144473	+	0.989509i	$0.453851\pi$
$594$	0	0
$595$	0	0
$596$	−8.67698	−0.355423
$597$	0	0
$598$	−1.30046	−0.0531796
$599$	31.7436	1.29701	0.648505	−	0.761210i	$-0.275395\pi$
$599$	31.7436	1.29701	0.648505	+	0.761210i	$0.275395\pi$
$600$	0	0
$601$	2.02247	0.0824984	0.0412492	−	0.999149i	$-0.486866\pi$
$601$	2.02247	0.0824984	0.0412492	+	0.999149i	$0.486866\pi$
$602$	6.82418	0.278133
$603$	0	0
$604$	−18.9316	−0.770317
$605$	45.1088	1.83393
$606$	0	0
$607$	−27.8731	−1.13133	−0.565667	−	0.824634i	$-0.691381\pi$
$607$	−27.8731	−1.13133	−0.565667	+	0.824634i	$0.691381\pi$
$608$	−30.0987	−1.22066
$609$	0	0
$610$	−9.12421	−0.369429
$611$	−11.5708	−0.468103
$612$	0	0
$613$	7.61689	0.307643	0.153822	−	0.988099i	$-0.450842\pi$
$613$	7.61689	0.307643	0.153822	+	0.988099i	$0.450842\pi$
$614$	11.1244	0.448944
$615$	0	0
$616$	2.69969	0.108774
$617$	43.6126	1.75578	0.877889	−	0.478864i	$-0.158951\pi$
$617$	43.6126	1.75578	0.877889	+	0.478864i	$0.158951\pi$
$618$	0	0
$619$	29.3070	1.17795	0.588974	−	0.808152i	$-0.299532\pi$
$619$	29.3070	1.17795	0.588974	+	0.808152i	$0.299532\pi$
$620$	−18.4567	−0.741240
$621$	0	0
$622$	12.1139	0.485722
$623$	−51.2417	−2.05295
$624$	0	0
$625$	75.1492	3.00597
$626$	7.75111	0.309797
$627$	0	0
$628$	6.77227	0.270243
$629$	0	0
$630$	0	0
$631$	−21.3551	−0.850132	−0.425066	−	0.905162i	$-0.639749\pi$
$631$	−21.3551	−0.850132	−0.425066	+	0.905162i	$0.639749\pi$
$632$	−4.53623	−0.180442
$633$	0	0
$634$	−7.21120	−0.286393
$635$	28.2079	1.11940
$636$	0	0
$637$	2.20270	0.0872741
$638$	0.546834	0.0216494
$639$	0	0
$640$	−45.6536	−1.80462
$641$	−8.72100	−0.344459	−0.172229	−	0.985057i	$-0.555097\pi$
$641$	−8.72100	−0.344459	−0.172229	+	0.985057i	$0.555097\pi$
$642$	0	0
$643$	−0.493963	−0.0194800	−0.00974001	−	0.999953i	$-0.503100\pi$
$643$	−0.493963	−0.0194800	−0.00974001	+	0.999953i	$0.503100\pi$
$644$	10.4784	0.412906
$645$	0	0
$646$	0	0
$647$	−9.67958	−0.380544	−0.190272	−	0.981731i	$-0.560937\pi$
$647$	−9.67958	−0.380544	−0.190272	+	0.981731i	$0.560937\pi$
$648$	0	0
$649$	−0.197995	−0.00777198
$650$	−8.37837	−0.328627
$651$	0	0
$652$	23.6837	0.927524
$653$	0.672371	0.0263119	0.0131560	−	0.999913i	$-0.495812\pi$
$653$	0.672371	0.0263119	0.0131560	+	0.999913i	$0.495812\pi$
$654$	0	0
$655$	−88.0539	−3.44055
$656$	−20.3449	−0.794336
$657$	0	0
$658$	−9.76405	−0.380642
$659$	6.20820	0.241837	0.120919	−	0.992662i	$-0.461416\pi$
$659$	6.20820	0.241837	0.120919	+	0.992662i	$0.461416\pi$
$660$	0	0
$661$	25.3899	0.987554	0.493777	−	0.869589i	$-0.335616\pi$
$661$	25.3899	0.987554	0.493777	+	0.869589i	$0.335616\pi$
$662$	−2.43475	−0.0946291
$663$	0	0
$664$	−15.2023	−0.589964
$665$	80.7057	3.12963
$666$	0	0
$667$	4.46717	0.172969
$668$	11.4759	0.444018
$669$	0	0
$670$	−6.55613	−0.253286
$671$	2.77612	0.107171
$672$	0	0
$673$	−8.33820	−0.321414	−0.160707	−	0.987002i	$-0.551377\pi$
$673$	−8.33820	−0.321414	−0.160707	+	0.987002i	$0.551377\pi$
$674$	7.18705	0.276835
$675$	0	0
$676$	19.4537	0.748221
$677$	43.8355	1.68474	0.842368	−	0.538903i	$-0.181161\pi$
$677$	43.8355	1.68474	0.842368	+	0.538903i	$0.181161\pi$
$678$	0	0
$679$	−40.2116	−1.54318
$680$	0	0
$681$	0	0
$682$	−0.588120	−0.0225203
$683$	−41.1425	−1.57427	−0.787136	−	0.616779i	$-0.788437\pi$
$683$	−41.1425	−1.57427	−0.787136	+	0.616779i	$0.788437\pi$
$684$	0	0
$685$	−27.9612	−1.06834
$686$	−7.01045	−0.267660
$687$	0	0
$688$	15.6103	0.595139
$689$	−15.3263	−0.583885
$690$	0	0
$691$	30.1651	1.14754	0.573768	−	0.819018i	$-0.305481\pi$
$691$	30.1651	1.14754	0.573768	+	0.819018i	$0.305481\pi$
$692$	17.3777	0.660602
$693$	0	0
$694$	7.42721	0.281933
$695$	28.6271	1.08589
$696$	0	0
$697$	0	0
$698$	9.70193	0.367223
$699$	0	0
$700$	67.5084	2.55158
$701$	−36.5308	−1.37975	−0.689876	−	0.723928i	$-0.742335\pi$
$701$	−36.5308	−1.37975	−0.689876	+	0.723928i	$0.742335\pi$
$702$	0	0
$703$	32.2306	1.21560
$704$	2.12615	0.0801325
$705$	0	0
$706$	15.1846	0.571482
$707$	32.0304	1.20463
$708$	0	0
$709$	0.408071	0.0153254	0.00766272	−	0.999971i	$-0.497561\pi$
$709$	0.408071	0.0153254	0.00766272	+	0.999971i	$0.497561\pi$
$710$	6.85456	0.257247
$711$	0	0
$712$	29.2179	1.09499
$713$	−4.80444	−0.179928
$714$	0	0
$715$	3.54380	0.132531
$716$	−30.2990	−1.13233
$717$	0	0
$718$	5.12161	0.191137
$719$	18.0214	0.672085	0.336042	−	0.941847i	$-0.390911\pi$
$719$	18.0214	0.672085	0.336042	+	0.941847i	$0.390911\pi$
$720$	0	0
$721$	−19.8964	−0.740981
$722$	−10.5292	−0.391855
$723$	0	0
$724$	31.8197	1.18257
$725$	28.7803	1.06887
$726$	0	0
$727$	−37.5943	−1.39430	−0.697148	−	0.716927i	$-0.745548\pi$
$727$	−37.5943	−1.39430	−0.697148	+	0.716927i	$0.745548\pi$
$728$	−7.24897	−0.268665
$729$	0	0
$730$	15.8308	0.585924
$731$	0	0
$732$	0	0
$733$	3.00866	0.111127	0.0555636	−	0.998455i	$-0.482304\pi$
$733$	3.00866	0.111127	0.0555636	+	0.998455i	$0.482304\pi$
$734$	5.79353	0.213843
$735$	0	0
$736$	−9.11080	−0.335829
$737$	1.99476	0.0734779
$738$	0	0
$739$	43.6797	1.60678	0.803392	−	0.595451i	$-0.203027\pi$
$739$	43.6797	1.60678	0.803392	+	0.595451i	$0.203027\pi$
$740$	37.4791	1.37776
$741$	0	0
$742$	−12.9331	−0.474791
$743$	−34.3405	−1.25983	−0.629916	−	0.776663i	$-0.716911\pi$
$743$	−34.3405	−1.25983	−0.629916	+	0.776663i	$0.716911\pi$
$744$	0	0
$745$	−20.2296	−0.741155
$746$	4.15278	0.152044
$747$	0	0
$748$	0	0
$749$	−34.5392	−1.26203
$750$	0	0
$751$	5.69060	0.207653	0.103827	−	0.994595i	$-0.466891\pi$
$751$	5.69060	0.207653	0.103827	+	0.994595i	$0.466891\pi$
$752$	−22.3353	−0.814485
$753$	0	0
$754$	−1.46831	−0.0534727
$755$	−44.1374	−1.60633
$756$	0	0
$757$	19.7067	0.716253	0.358126	−	0.933673i	$-0.383416\pi$
$757$	19.7067	0.716253	0.358126	+	0.933673i	$0.383416\pi$
$758$	−5.01995	−0.182333
$759$	0	0
$760$	−46.0183	−1.66926
$761$	22.8678	0.828958	0.414479	−	0.910059i	$-0.363964\pi$
$761$	22.8678	0.828958	0.414479	+	0.910059i	$0.363964\pi$
$762$	0	0
$763$	4.60104	0.166569
$764$	−8.71746	−0.315387
$765$	0	0
$766$	7.88105	0.284754
$767$	0.531638	0.0191963
$768$	0	0
$769$	−11.5521	−0.416579	−0.208290	−	0.978067i	$-0.566790\pi$
$769$	−11.5521	−0.416579	−0.208290	+	0.978067i	$0.566790\pi$
$770$	2.99045	0.107768
$771$	0	0
$772$	−12.0760	−0.434624
$773$	43.9216	1.57975	0.789875	−	0.613267i	$-0.210145\pi$
$773$	43.9216	1.57975	0.789875	+	0.613267i	$0.210145\pi$
$774$	0	0
$775$	−30.9532	−1.11187
$776$	22.9286	0.823089
$777$	0	0
$778$	−0.270642	−0.00970299
$779$	−46.1268	−1.65266
$780$	0	0
$781$	−2.08556	−0.0746271
$782$	0	0
$783$	0	0
$784$	4.25191	0.151854
$785$	15.7889	0.563531
$786$	0	0
$787$	−5.44232	−0.193998	−0.0969988	−	0.995284i	$-0.530924\pi$
$787$	−5.44232	−0.193998	−0.0969988	+	0.995284i	$0.530924\pi$
$788$	−35.3493	−1.25927
$789$	0	0
$790$	−5.02479	−0.178774
$791$	−3.52335	−0.125276
$792$	0	0
$793$	−7.45419	−0.264706
$794$	1.37511	0.0488007
$795$	0	0
$796$	32.9161	1.16668
$797$	32.9602	1.16751	0.583756	−	0.811929i	$-0.301583\pi$
$797$	32.9602	1.16751	0.583756	+	0.811929i	$0.301583\pi$
$798$	0	0
$799$	0	0
$800$	−58.6976	−2.07527
$801$	0	0
$802$	−6.75011	−0.238355
$803$	−4.81666	−0.169976
$804$	0	0
$805$	24.4294	0.861024
$806$	1.57917	0.0556238
$807$	0	0
$808$	−18.2637	−0.642516
$809$	−34.8891	−1.22663	−0.613317	−	0.789837i	$-0.710165\pi$
$809$	−34.8891	−1.22663	−0.613317	+	0.789837i	$0.710165\pi$
$810$	0	0
$811$	26.6041	0.934197	0.467098	−	0.884205i	$-0.345299\pi$
$811$	26.6041	0.934197	0.467098	+	0.884205i	$0.345299\pi$
$812$	11.8309	0.415182
$813$	0	0
$814$	1.19426	0.0418590
$815$	55.2164	1.93414
$816$	0	0
$817$	35.3924	1.23822
$818$	14.9251	0.521845
$819$	0	0
$820$	−53.6382	−1.87313
$821$	25.9507	0.905685	0.452842	−	0.891591i	$-0.350410\pi$
$821$	25.9507	0.905685	0.452842	+	0.891591i	$0.350410\pi$
$822$	0	0
$823$	−49.8042	−1.73606	−0.868032	−	0.496508i	$-0.834615\pi$
$823$	−49.8042	−1.73606	−0.868032	+	0.496508i	$0.834615\pi$
$824$	11.3449	0.395219
$825$	0	0
$826$	0.448625	0.0156097
$827$	13.2577	0.461016	0.230508	−	0.973070i	$-0.425961\pi$
$827$	13.2577	0.461016	0.230508	+	0.973070i	$0.425961\pi$
$828$	0	0
$829$	−52.2456	−1.81456	−0.907282	−	0.420523i	$-0.861847\pi$
$829$	−52.2456	−1.81456	−0.907282	+	0.420523i	$0.861847\pi$
$830$	−16.8396	−0.584511
$831$	0	0
$832$	−5.70896	−0.197923
$833$	0	0
$834$	0	0
$835$	26.7552	0.925900
$836$	6.65238	0.230077
$837$	0	0
$838$	5.77041	0.199336
$839$	5.07950	0.175364	0.0876819	−	0.996149i	$-0.472054\pi$
$839$	5.07950	0.175364	0.0876819	+	0.996149i	$0.472054\pi$
$840$	0	0
$841$	−23.9562	−0.826077
$842$	9.46225	0.326091
$843$	0	0
$844$	45.8361	1.57774
$845$	45.3547	1.56025
$846$	0	0
$847$	31.0981	1.06854
$848$	−29.5846	−1.01594
$849$	0	0
$850$	0	0
$851$	9.75612	0.334435
$852$	0	0
$853$	39.0339	1.33650	0.668248	−	0.743938i	$-0.267044\pi$
$853$	39.0339	1.33650	0.668248	+	0.743938i	$0.267044\pi$
$854$	−6.29025	−0.215248
$855$	0	0
$856$	19.6942	0.673134
$857$	−11.5433	−0.394313	−0.197157	−	0.980372i	$-0.563171\pi$
$857$	−11.5433	−0.394313	−0.197157	+	0.980372i	$0.563171\pi$
$858$	0	0
$859$	18.1539	0.619403	0.309701	−	0.950834i	$-0.399771\pi$
$859$	18.1539	0.619403	0.309701	+	0.950834i	$0.399771\pi$
$860$	41.1558	1.40340
$861$	0	0
$862$	−5.55859	−0.189326
$863$	−22.7778	−0.775365	−0.387682	−	0.921793i	$-0.626724\pi$
$863$	−22.7778	−0.775365	−0.387682	+	0.921793i	$0.626724\pi$
$864$	0	0
$865$	40.5146	1.37754
$866$	6.76201	0.229783
$867$	0	0
$868$	−12.7241	−0.431884
$869$	1.52883	0.0518622
$870$	0	0
$871$	−5.35615	−0.181486
$872$	−2.62351	−0.0888433
$873$	0	0
$874$	−5.69144	−0.192516
$875$	95.9814	3.24476
$876$	0	0
$877$	31.8147	1.07431	0.537153	−	0.843485i	$-0.319500\pi$
$877$	31.8147	1.07431	0.537153	+	0.843485i	$0.319500\pi$
$878$	−9.77679	−0.329951
$879$	0	0
$880$	6.84067	0.230599
$881$	−4.35753	−0.146809	−0.0734045	−	0.997302i	$-0.523386\pi$
$881$	−4.35753	−0.146809	−0.0734045	+	0.997302i	$0.523386\pi$
$882$	0	0
$883$	29.8332	1.00397	0.501983	−	0.864878i	$-0.332604\pi$
$883$	29.8332	1.00397	0.501983	+	0.864878i	$0.332604\pi$
$884$	0	0
$885$	0	0
$886$	10.9321	0.367270
$887$	−5.28874	−0.177579	−0.0887893	−	0.996050i	$-0.528300\pi$
$887$	−5.28874	−0.177579	−0.0887893	+	0.996050i	$0.528300\pi$
$888$	0	0
$889$	19.4466	0.652218
$890$	32.3648	1.08487
$891$	0	0
$892$	−23.5660	−0.789047
$893$	−50.6394	−1.69458
$894$	0	0
$895$	−70.6395	−2.36122
$896$	−31.4736	−1.05146
$897$	0	0
$898$	−4.83684	−0.161407
$899$	−5.42456	−0.180919
$900$	0	0
$901$	0	0
$902$	−1.70917	−0.0569093
$903$	0	0
$904$	2.00901	0.0668188
$905$	74.1848	2.46599
$906$	0	0
$907$	15.1953	0.504550	0.252275	−	0.967656i	$-0.418821\pi$
$907$	15.1953	0.504550	0.252275	+	0.967656i	$0.418821\pi$
$908$	17.8472	0.592279
$909$	0	0
$910$	−8.02969	−0.266182
$911$	14.6408	0.485073	0.242536	−	0.970142i	$-0.422021\pi$
$911$	14.6408	0.485073	0.242536	+	0.970142i	$0.422021\pi$
$912$	0	0
$913$	5.12359	0.169566
$914$	7.15226	0.236576
$915$	0	0
$916$	−8.93040	−0.295069
$917$	−60.7045	−2.00464
$918$	0	0
$919$	22.4973	0.742118	0.371059	−	0.928609i	$-0.378995\pi$
$919$	22.4973	0.742118	0.371059	+	0.928609i	$0.378995\pi$
$920$	−13.9296	−0.459247
$921$	0	0
$922$	10.4224	0.343243
$923$	5.59995	0.184325
$924$	0	0
$925$	62.8551	2.06666
$926$	−6.97356	−0.229165
$927$	0	0
$928$	−10.2868	−0.337679
$929$	52.2124	1.71303	0.856517	−	0.516119i	$-0.172624\pi$
$929$	52.2124	1.71303	0.856517	+	0.516119i	$0.172624\pi$
$930$	0	0
$931$	9.64010	0.315942
$932$	38.4095	1.25815
$933$	0	0
$934$	7.38505	0.241646
$935$	0	0
$936$	0	0
$937$	−41.1400	−1.34398	−0.671992	−	0.740559i	$-0.734561\pi$
$937$	−41.1400	−1.34398	−0.671992	+	0.740559i	$0.734561\pi$
$938$	−4.51981	−0.147577
$939$	0	0
$940$	−58.8857	−1.92064
$941$	−49.1970	−1.60378	−0.801889	−	0.597473i	$-0.796171\pi$
$941$	−49.1970	−1.60378	−0.801889	+	0.597473i	$0.796171\pi$
$942$	0	0
$943$	−13.9625	−0.454681
$944$	1.02623	0.0334010
$945$	0	0
$946$	1.31142	0.0426380
$947$	9.40817	0.305724	0.152862	−	0.988248i	$-0.451151\pi$
$947$	9.40817	0.305724	0.152862	+	0.988248i	$0.451151\pi$
$948$	0	0
$949$	12.9333	0.419831
$950$	−36.6679	−1.18966
$951$	0	0
$952$	0	0
$953$	−5.39098	−0.174631	−0.0873155	−	0.996181i	$-0.527829\pi$
$953$	−5.39098	−0.174631	−0.0873155	+	0.996181i	$0.527829\pi$
$954$	0	0
$955$	−20.3240	−0.657669
$956$	44.9319	1.45320
$957$	0	0
$958$	7.11333	0.229821
$959$	−19.2765	−0.622470
$960$	0	0
$961$	−25.1659	−0.811803
$962$	−3.20673	−0.103389
$963$	0	0
$964$	−38.7283	−1.24735
$965$	−28.1541	−0.906311
$966$	0	0
$967$	−51.7755	−1.66499	−0.832493	−	0.554035i	$-0.813087\pi$
$967$	−51.7755	−1.66499	−0.832493	+	0.554035i	$0.813087\pi$
$968$	−17.7321	−0.569931
$969$	0	0
$970$	25.3980	0.815482
$971$	−24.8977	−0.799005	−0.399502	−	0.916732i	$-0.630817\pi$
$971$	−24.8977	−0.799005	−0.399502	+	0.916732i	$0.630817\pi$
$972$	0	0
$973$	19.7355	0.632693
$974$	−11.2182	−0.359456
$975$	0	0
$976$	−14.3890	−0.460580
$977$	−34.2178	−1.09472	−0.547362	−	0.836896i	$-0.684368\pi$
$977$	−34.2178	−1.09472	−0.547362	+	0.836896i	$0.684368\pi$
$978$	0	0
$979$	−9.84725	−0.314720
$980$	11.2099	0.358088
$981$	0	0
$982$	−13.0125	−0.415246
$983$	5.58630	0.178175	0.0890876	−	0.996024i	$-0.471605\pi$
$983$	5.58630	0.178175	0.0890876	+	0.996024i	$0.471605\pi$
$984$	0	0
$985$	−82.4137	−2.62592
$986$	0	0
$987$	0	0
$988$	−17.8624	−0.568278
$989$	10.7132	0.340660
$990$	0	0
$991$	−22.4192	−0.712169	−0.356085	−	0.934454i	$-0.615888\pi$
$991$	−22.4192	−0.712169	−0.356085	+	0.934454i	$0.615888\pi$
$992$	11.0634	0.351264
$993$	0	0
$994$	4.72554	0.149885
$995$	76.7410	2.43285
$996$	0	0
$997$	9.99751	0.316624	0.158312	−	0.987389i	$-0.449395\pi$
$997$	9.99751	0.316624	0.158312	+	0.987389i	$0.449395\pi$
$998$	17.6498	0.558696
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.bh.1.4		6
3.2	odd	2		867.2.a.o.1.3	✓	6
17.16	even	2		2601.2.a.bi.1.4		6
51.2	odd	8		867.2.e.k.616.5		24
51.5	even	16		867.2.h.m.688.8		48
51.8	odd	8		867.2.e.k.829.8		24
51.11	even	16		867.2.h.m.733.6		48
51.14	even	16		867.2.h.m.757.6		48
51.20	even	16		867.2.h.m.757.5		48
51.23	even	16		867.2.h.m.733.5		48
51.26	odd	8		867.2.e.k.829.7		24
51.29	even	16		867.2.h.m.688.7		48
51.32	odd	8		867.2.e.k.616.6		24
51.38	odd	4		867.2.d.g.577.8		12
51.41	even	16		867.2.h.m.712.8		48
51.44	even	16		867.2.h.m.712.7		48
51.47	odd	4		867.2.d.g.577.7		12
51.50	odd	2		867.2.a.p.1.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.o.1.3	✓	6	3.2	odd	2
867.2.a.p.1.3	yes	6	51.50	odd	2
867.2.d.g.577.7		12	51.47	odd	4
867.2.d.g.577.8		12	51.38	odd	4
867.2.e.k.616.5		24	51.2	odd	8
867.2.e.k.616.6		24	51.32	odd	8
867.2.e.k.829.7		24	51.26	odd	8
867.2.e.k.829.8		24	51.8	odd	8
867.2.h.m.688.7		48	51.29	even	16
867.2.h.m.688.8		48	51.5	even	16
867.2.h.m.712.7		48	51.44	even	16
867.2.h.m.712.8		48	51.41	even	16
867.2.h.m.733.5		48	51.23	even	16
867.2.h.m.733.6		48	51.11	even	16
867.2.h.m.757.5		48	51.20	even	16
867.2.h.m.757.6		48	51.14	even	16
2601.2.a.bh.1.4		6	1.1	even	1	trivial
2601.2.a.bi.1.4		6	17.16	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:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2601.a (trivial)

\(f(q)\)	\(=\)	\(q-0.435433 q^{2} -1.81040 q^{4} -4.22078 q^{5} -2.90981 q^{7} +1.65917 q^{8} +O(q^{10})\)	\(q-0.435433 q^{2} -1.81040 q^{4} -4.22078 q^{5} -2.90981 q^{7} +1.65917 q^{8} +1.83787 q^{10} -0.559187 q^{11} +1.50148 q^{13} +1.26703 q^{14} +2.89834 q^{16} +6.57122 q^{19} +7.64129 q^{20} +0.243489 q^{22} +1.98909 q^{23} +12.8150 q^{25} -0.653794 q^{26} +5.26792 q^{28} +2.24583 q^{29} -2.41539 q^{31} -4.58038 q^{32} +12.2817 q^{35} +4.90481 q^{37} -2.86133 q^{38} -7.00301 q^{40} -7.01952 q^{41} +5.38597 q^{43} +1.01235 q^{44} -0.866117 q^{46} -7.70625 q^{47} +1.46702 q^{49} -5.58008 q^{50} -2.71828 q^{52} -10.2075 q^{53} +2.36021 q^{55} -4.82789 q^{56} -0.977909 q^{58} +0.354076 q^{59} -4.96456 q^{61} +1.05174 q^{62} -3.80222 q^{64} -6.33742 q^{65} -3.56725 q^{67} -5.34786 q^{70} +3.72962 q^{71} +8.61368 q^{73} -2.13572 q^{74} -11.8965 q^{76} +1.62713 q^{77} -2.73403 q^{79} -12.2332 q^{80} +3.05653 q^{82} -9.16257 q^{83} -2.34523 q^{86} -0.927788 q^{88} +17.6099 q^{89} -4.36903 q^{91} -3.60105 q^{92} +3.35556 q^{94} -27.7357 q^{95} +13.8193 q^{97} -0.638789 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 9 q^{4} - 3 q^{5} - 3 q^{7} - 12 q^{8}+O(q^{10}) \) 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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