LMFDB - Embedded newform 1320.2.ba.a.329.66

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(329,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1320.329");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.ba (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			329.66
Character	$\chi$	$=$	1320.329
Dual form			1320.2.ba.a.329.68

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.72010 - 0.203093i) q^{3} +(0.910442 + 2.04233i) q^{5} +4.06802 q^{7} +(2.91751 - 0.698681i) q^{9} +(-3.04109 - 1.32355i) q^{11} +0.487030 q^{13} +(1.98084 + 3.32811i) q^{15} -6.71182i q^{17} -1.77760i q^{19} +(6.99741 - 0.826186i) q^{21} +4.87073 q^{23} +(-3.34219 + 3.71884i) q^{25} +(4.87651 - 1.79433i) q^{27} -1.32904 q^{29} +6.21817 q^{31} +(-5.49978 - 1.65903i) q^{33} +(3.70370 + 8.30822i) q^{35} +7.96402i q^{37} +(0.837742 - 0.0989123i) q^{39} -5.07398 q^{41} -4.68285 q^{43} +(4.08316 + 5.32239i) q^{45} -10.7188 q^{47} +9.54880 q^{49} +(-1.36312 - 11.5450i) q^{51} -9.51918 q^{53} +(-0.0656055 - 7.41591i) q^{55} +(-0.361018 - 3.05766i) q^{57} +5.13015i q^{59} +2.61817i q^{61} +(11.8685 - 2.84225i) q^{63} +(0.443413 + 0.994674i) q^{65} +8.52433i q^{67} +(8.37816 - 0.989210i) q^{69} +6.00972i q^{71} -0.708858 q^{73} +(-4.99364 + 7.07556i) q^{75} +(-12.3712 - 5.38424i) q^{77} +7.16015i q^{79} +(8.02369 - 4.07681i) q^{81} +13.8902i q^{83} +(13.7077 - 6.11072i) q^{85} +(-2.28609 + 0.269919i) q^{87} -15.9597i q^{89} +1.98125 q^{91} +(10.6959 - 1.26287i) q^{93} +(3.63044 - 1.61840i) q^{95} +0.844397i q^{97} +(-9.79713 - 1.73673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 6 q^{15} - 4 q^{25} + 34 q^{45} + 96 q^{49} - 28 q^{55} + 28 q^{69} + 14 q^{75} + 16 q^{81} - 48 q^{91} - 4 q^{99}+O(q^{100}) $ 72 * q - 6 * q^15 - 4 * q^25 + 34 * q^45 + 96 * q^49 - 28 * q^55 + 28 * q^69 + 14 * q^75 + 16 * q^81 - 48 * q^91 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.72010	−	0.203093i	0.993102	−	0.117256i
$3$	1.72010	−	0.203093i	0.993102	−	0.117256i
$4$		0			0
$5$	0.910442	+	2.04233i	0.407162	+	0.913356i
$5$	0.910442	+	2.04233i	0.407162	+	0.913356i
$6$		0			0
$7$	4.06802			1.53757			0.768784	−	0.639509i	$-0.220862\pi$
$7$	4.06802			1.53757			0.768784	+	0.639509i	$0.220862\pi$
$8$		0			0
$9$	2.91751	−	0.698681i	0.972502	−	0.232894i
$10$		0			0
$11$	−3.04109	−	1.32355i	−0.916922	−	0.399066i
$11$	−3.04109	−	1.32355i	−0.916922	−	0.399066i
$12$		0			0
$13$	0.487030			0.135078			0.0675389	−	0.997717i	$-0.478485\pi$
$13$	0.487030			0.135078			0.0675389	+	0.997717i	$0.478485\pi$
$14$		0			0
$15$	1.98084	+	3.32811i	0.511450	+	0.859313i
$16$		0			0
$17$		−	6.71182i		−	1.62786i	−0.580966	−	0.813928i	$-0.697325\pi$
$17$		−	6.71182i		−	1.62786i	0.580966	−	0.813928i	$-0.302675\pi$
$18$		0			0
$19$		−	1.77760i		−	0.407810i	−0.978991	−	0.203905i	$-0.934637\pi$
$19$		−	1.77760i		−	0.407810i	0.978991	−	0.203905i	$-0.0653633\pi$
$20$		0			0
$21$	6.99741	−	0.826186i	1.52696	−	0.180288i
$22$		0			0
$23$	4.87073			1.01562			0.507809	−	0.861470i	$-0.330456\pi$
$23$	4.87073			1.01562			0.507809	+	0.861470i	$0.330456\pi$
$24$		0			0
$25$	−3.34219	+	3.71884i	−0.668438	+	0.743768i
$26$		0			0
$27$	4.87651	−	1.79433i	0.938486	−	0.345318i
$28$		0			0
$29$	−1.32904			−0.246797			−0.123398	−	0.992357i	$-0.539379\pi$
$29$	−1.32904			−0.246797			−0.123398	+	0.992357i	$0.539379\pi$
$30$		0			0
$31$	6.21817			1.11682			0.558408	−	0.829566i	$-0.311412\pi$
$31$	6.21817			1.11682			0.558408	+	0.829566i	$0.311412\pi$
$32$		0			0
$33$	−5.49978	−	1.65903i	−0.957390	−	0.288799i
$34$		0			0
$35$	3.70370	+	8.30822i	0.626039	+	1.40435i
$36$		0			0
$37$			7.96402i			1.30928i	0.755942	+	0.654638i	$0.227179\pi$
$37$			7.96402i			1.30928i	−0.755942	+	0.654638i	$0.772821\pi$
$38$		0			0
$39$	0.837742	−	0.0989123i	0.134146	−	0.0158386i
$40$		0			0
$41$	−5.07398			−0.792423			−0.396212	−	0.918159i	$-0.629675\pi$
$41$	−5.07398			−0.792423			−0.396212	+	0.918159i	$0.629675\pi$
$42$		0			0
$43$	−4.68285			−0.714128			−0.357064	−	0.934080i	$-0.616222\pi$
$43$	−4.68285			−0.714128			−0.357064	+	0.934080i	$0.616222\pi$
$44$		0			0
$45$	4.08316	+	5.32239i	0.608681	+	0.793415i
$46$		0			0
$47$	−10.7188			−1.56350			−0.781751	−	0.623591i	$-0.785673\pi$
$47$	−10.7188			−1.56350			−0.781751	+	0.623591i	$0.785673\pi$
$48$		0			0
$49$	9.54880			1.36411
$50$		0			0
$51$	−1.36312	−	11.5450i	−0.190875	−	1.61663i
$52$		0			0
$53$	−9.51918			−1.30756			−0.653780	−	0.756685i	$-0.726818\pi$
$53$	−9.51918			−1.30756			−0.653780	+	0.756685i	$0.726818\pi$
$54$		0			0
$55$	−0.0656055	−	7.41591i	−0.00884624	−	0.999961i
$56$		0			0
$57$	−0.361018	−	3.05766i	−0.0478180	−	0.404996i
$58$		0			0
$59$			5.13015i			0.667889i	0.942593	+	0.333944i	$0.108380\pi$
$59$			5.13015i			0.667889i	−0.942593	+	0.333944i	$0.891620\pi$
$60$		0			0
$61$			2.61817i			0.335223i	0.985853	+	0.167611i	$0.0536054\pi$
$61$			2.61817i			0.335223i	−0.985853	+	0.167611i	$0.946395\pi$
$62$		0			0
$63$	11.8685	−	2.84225i	1.49529	−	0.358090i
$64$		0			0
$65$	0.443413	+	0.994674i	0.0549986	+	0.123374i
$66$		0			0
$67$			8.52433i			1.04141i	0.853736	+	0.520706i	$0.174331\pi$
$67$			8.52433i			1.04141i	−0.853736	+	0.520706i	$0.825669\pi$
$68$		0			0
$69$	8.37816	−	0.989210i	1.00861	−	0.119087i
$70$		0			0
$71$			6.00972i			0.713223i	0.934253	+	0.356611i	$0.116068\pi$
$71$			6.00972i			0.713223i	−0.934253	+	0.356611i	$0.883932\pi$
$72$		0			0
$73$	−0.708858			−0.0829655			−0.0414828	−	0.999139i	$-0.513208\pi$
$73$	−0.708858			−0.0829655			−0.0414828	+	0.999139i	$0.513208\pi$
$74$		0			0
$75$	−4.99364	+	7.07556i	−0.576616	+	0.817015i
$76$		0			0
$77$	−12.3712	−	5.38424i	−1.40983	−	0.613592i
$78$		0			0
$79$			7.16015i			0.805580i	0.915292	+	0.402790i	$0.131960\pi$
$79$			7.16015i			0.805580i	−0.915292	+	0.402790i	$0.868040\pi$
$80$		0			0
$81$	8.02369	−	4.07681i	0.891521	−	0.452979i
$82$		0			0
$83$			13.8902i			1.52464i	0.647198	+	0.762322i	$0.275941\pi$
$83$			13.8902i			1.52464i	−0.647198	+	0.762322i	$0.724059\pi$
$84$		0			0
$85$	13.7077	−	6.11072i	1.48681	−	0.662801i
$86$		0			0
$87$	−2.28609	+	0.269919i	−0.245095	+	0.0289383i
$88$		0			0
$89$		−	15.9597i		−	1.69172i	−0.533401	−	0.845862i	$-0.679086\pi$
$89$		−	15.9597i		−	1.69172i	0.533401	−	0.845862i	$-0.320914\pi$
$90$		0			0
$91$	1.98125			0.207691
$92$		0			0
$93$	10.6959	−	1.26287i	1.10911	−	0.130953i
$94$		0			0
$95$	3.63044	−	1.61840i	0.372475	−	0.166045i
$96$		0			0
$97$			0.844397i			0.0857356i	0.999081	+	0.0428678i	$0.0136494\pi$
$97$			0.844397i			0.0857356i	−0.999081	+	0.0428678i	$0.986351\pi$
$98$		0			0
$99$	−9.79713	−	1.73673i	−0.984649	−	0.174548i
$100$		0			0
$101$	11.3862			1.13297			0.566487	−	0.824071i	$-0.308302\pi$
$101$	11.3862			1.13297			0.566487	+	0.824071i	$0.308302\pi$
$102$		0			0
$103$		−	15.7776i		−	1.55461i	−0.629122	−	0.777307i	$-0.716585\pi$
$103$		−	15.7776i		−	1.55461i	0.629122	−	0.777307i	$-0.283415\pi$
$104$		0			0
$105$	8.05808	+	13.5388i	0.786388	+	1.32125i
$106$		0			0
$107$			13.8398i			1.33795i	0.743286	+	0.668974i	$0.233266\pi$
$107$			13.8398i			1.33795i	−0.743286	+	0.668974i	$0.766734\pi$
$108$		0			0
$109$		−	14.9906i		−	1.43583i	−0.696129	−	0.717917i	$-0.745096\pi$
$109$		−	14.9906i		−	1.43583i	0.696129	−	0.717917i	$-0.254904\pi$
$110$		0			0
$111$	1.61743	+	13.6989i	0.153520	+	1.30024i
$112$		0			0
$113$	−2.24055			−0.210774			−0.105387	−	0.994431i	$-0.533608\pi$
$113$	−2.24055			−0.210774			−0.105387	+	0.994431i	$0.533608\pi$
$114$		0			0
$115$	4.43452	+	9.94762i	0.413521	+	0.927620i
$116$		0			0
$117$	1.42091	−	0.340279i	0.131364	−	0.0314588i
$118$		0			0
$119$		−	27.3038i		−	2.50294i
$120$		0			0
$121$	7.49641	+	8.05008i	0.681492	+	0.731826i
$122$		0			0
$123$	−8.72777	+	1.03049i	−0.786957	+	0.0929161i
$124$		0			0
$125$	−10.6380	−	3.44005i	−0.951487	−	0.307688i
$126$		0			0
$127$	0.504158			0.0447368			0.0223684	−	0.999750i	$-0.492879\pi$
$127$	0.504158			0.0447368			0.0223684	+	0.999750i	$0.492879\pi$
$128$		0			0
$129$	−8.05498	+	0.951053i	−0.709202	+	0.0837355i
$130$		0			0
$131$	−12.0129			−1.04957			−0.524785	−	0.851235i	$-0.675854\pi$
$131$	−12.0129			−1.04957			−0.524785	+	0.851235i	$0.675854\pi$
$132$		0			0
$133$		−	7.23132i		−	0.627035i
$134$		0			0
$135$	8.10439	+	8.32580i	0.697514	+	0.716571i
$136$		0			0
$137$	6.09143			0.520426			0.260213	−	0.965551i	$-0.416207\pi$
$137$	6.09143			0.520426			0.260213	+	0.965551i	$0.416207\pi$
$138$		0			0
$139$		−	15.5072i		−	1.31531i	−0.753321	−	0.657653i	$-0.771549\pi$
$139$		−	15.5072i		−	1.31531i	0.753321	−	0.657653i	$-0.228451\pi$
$140$		0			0
$141$	−18.4375	+	2.17692i	−1.55272	+	0.183329i
$142$		0			0
$143$	−1.48110	−	0.644611i	−0.123856	−	0.0539050i
$144$		0			0
$145$	−1.21002	−	2.71434i	−0.100486	−	0.225413i
$146$		0			0
$147$	16.4249	−	1.93929i	1.35470	−	0.159950i
$148$		0			0
$149$	−10.9221			−0.894777			−0.447388	−	0.894340i	$-0.647646\pi$
$149$	−10.9221			−0.894777			−0.447388	+	0.894340i	$0.647646\pi$
$150$		0			0
$151$			8.12518i			0.661218i	0.943768	+	0.330609i	$0.107254\pi$
$151$			8.12518i			0.661218i	−0.943768	+	0.330609i	$0.892746\pi$
$152$		0			0
$153$	−4.68942	−	19.5818i	−0.379117	−	1.58309i
$154$		0			0
$155$	5.66129	+	12.6995i	0.454725	+	1.02005i
$156$		0			0
$157$		−	17.1960i		−	1.37239i	−0.727416	−	0.686197i	$-0.759279\pi$
$157$		−	17.1960i		−	1.37239i	0.727416	−	0.686197i	$-0.240721\pi$
$158$		0			0
$159$	−16.3740	+	1.93328i	−1.29854	+	0.153319i
$160$		0			0
$161$	19.8142			1.56158
$162$		0			0
$163$		−	2.94978i		−	0.231045i	−0.993305	−	0.115522i	$-0.963146\pi$
$163$		−	2.94978i		−	0.231045i	0.993305	−	0.115522i	$-0.0368542\pi$
$164$		0			0
$165$	−1.61897	−	12.7428i	−0.126036	−	0.992026i
$166$		0			0
$167$			6.23678i			0.482616i	0.970449	+	0.241308i	$0.0775765\pi$
$167$			6.23678i			0.482616i	−0.970449	+	0.241308i	$0.922424\pi$
$168$		0			0
$169$	−12.7628			−0.981754
$170$		0			0
$171$	−1.24198	−	5.18616i	−0.0949762	−	0.396596i
$172$		0			0
$173$		−	16.4466i		−	1.25042i	−0.780459	−	0.625208i	$-0.785014\pi$
$173$		−	16.4466i		−	1.25042i	0.780459	−	0.625208i	$-0.214986\pi$
$174$		0			0
$175$	−13.5961	+	15.1283i	−1.02777	+	1.14359i
$176$		0			0
$177$	1.04190	+	8.82439i	0.0783137	+	0.663282i
$178$		0			0
$179$		−	21.5926i		−	1.61391i	−0.590615	−	0.806954i	$-0.701115\pi$
$179$		−	21.5926i		−	1.61391i	0.590615	−	0.806954i	$-0.298885\pi$
$180$		0			0
$181$	−6.77626			−0.503676			−0.251838	−	0.967769i	$-0.581035\pi$
$181$	−6.77626			−0.503676			−0.251838	+	0.967769i	$0.581035\pi$
$182$		0			0
$183$	0.531732	+	4.50353i	0.0393068	+	0.332910i
$184$		0			0
$185$	−16.2651	+	7.25078i	−1.19584	+	0.533088i
$186$		0			0
$187$	−8.88345	+	20.4112i	−0.649622	+	1.49262i
$188$		0			0
$189$	19.8378	−	7.29936i	1.44298	−	0.530950i
$190$		0			0
$191$			7.83016i			0.566570i	0.959036	+	0.283285i	$0.0914243\pi$
$191$			7.83016i			0.566570i	−0.959036	+	0.283285i	$0.908576\pi$
$192$		0			0
$193$	−9.86217			−0.709894			−0.354947	−	0.934886i	$-0.615501\pi$
$193$	−9.86217			−0.709894			−0.354947	+	0.934886i	$0.615501\pi$
$194$		0			0
$195$	0.964727	+	1.62089i	0.0690855	+	0.116074i
$196$		0			0
$197$			10.8165i			0.770642i	0.922783	+	0.385321i	$0.125909\pi$
$197$			10.8165i			0.770642i	−0.922783	+	0.385321i	$0.874091\pi$
$198$		0			0
$199$	8.15499			0.578092			0.289046	−	0.957315i	$-0.406662\pi$
$199$	8.15499			0.578092			0.289046	+	0.957315i	$0.406662\pi$
$200$		0			0
$201$	1.73123	+	14.6627i	0.122111	+	1.03423i
$202$		0			0
$203$	−5.40657			−0.379467
$204$		0			0
$205$	−4.61957	−	10.3627i	−0.322645	−	0.723764i
$206$		0			0
$207$	14.2104	−	3.40309i	0.987690	−	0.236531i
$208$		0			0
$209$	−2.35275	+	5.40584i	−0.162743	+	0.373930i
$210$		0			0
$211$			21.9241i			1.50932i	0.656118	+	0.754659i	$0.272198\pi$
$211$			21.9241i			1.50932i	−0.656118	+	0.754659i	$0.727802\pi$
$212$		0			0
$213$	1.22053	+	10.3373i	0.0836294	+	0.708303i
$214$		0			0
$215$	−4.26346	−	9.56391i	−0.290766	−	0.652253i
$216$		0			0
$217$	25.2956			1.71718
$218$		0			0
$219$	−1.21931	+	0.143964i	−0.0823932	+	0.00972818i
$220$		0			0
$221$		−	3.26886i		−	0.219887i
$222$		0			0
$223$			1.87033i			0.125247i	0.998037	+	0.0626234i	$0.0199467\pi$
$223$			1.87033i			0.125247i	−0.998037	+	0.0626234i	$0.980053\pi$
$224$		0			0
$225$	−7.15258	+	13.1849i	−0.476839	+	0.878991i
$226$		0			0
$227$			7.79604i			0.517442i	0.965952	+	0.258721i	$0.0833010\pi$
$227$			7.79604i			0.517442i	−0.965952	+	0.258721i	$0.916699\pi$
$228$		0			0
$229$	2.31997			0.153308			0.0766541	−	0.997058i	$-0.475576\pi$
$229$	2.31997			0.153308			0.0766541	+	0.997058i	$0.475576\pi$
$230$		0			0
$231$	−22.3732	−	6.74895i	−1.47205	−	0.444048i
$232$		0			0
$233$			13.4363i			0.880242i	0.897938	+	0.440121i	$0.145064\pi$
$233$			13.4363i			0.880242i	−0.897938	+	0.440121i	$0.854936\pi$
$234$		0			0
$235$	−9.75888	−	21.8913i	−0.636599	−	1.42803i
$236$		0			0
$237$	1.45418	+	12.3162i	0.0944588	+	0.800023i
$238$		0			0
$239$	−27.3786			−1.77097			−0.885486	−	0.464667i	$-0.846174\pi$
$239$	−27.3786			−1.77097			−0.885486	+	0.464667i	$0.846174\pi$
$240$		0			0
$241$		−	21.4071i		−	1.37895i	−0.724309	−	0.689476i	$-0.757841\pi$
$241$		−	21.4071i		−	1.37895i	0.724309	−	0.689476i	$-0.242159\pi$
$242$		0			0
$243$	12.9736	−	8.64209i	0.832257	−	0.554390i
$244$		0			0
$245$	8.69363	+	19.5018i	0.555415	+	1.24592i
$246$		0			0
$247$		−	0.865745i		−	0.0550860i
$248$		0			0
$249$	2.82099	+	23.8925i	0.178773	+	1.51413i
$250$		0			0
$251$			13.5309i			0.854065i	0.904236	+	0.427033i	$0.140441\pi$
$251$			13.5309i			0.854065i	−0.904236	+	0.427033i	$0.859559\pi$
$252$		0			0
$253$	−14.8123	−	6.44667i	−0.931242	−	0.405299i
$254$		0			0
$255$	22.3376	−	13.2950i	1.39884	−	0.832566i
$256$		0			0
$257$	1.12756			0.0703354			0.0351677	−	0.999381i	$-0.488803\pi$
$257$	1.12756			0.0703354			0.0351677	+	0.999381i	$0.488803\pi$
$258$		0			0
$259$			32.3978i			2.01310i
$260$		0			0
$261$	−3.87749	+	0.928576i	−0.240011	+	0.0574774i
$262$		0			0
$263$		−	5.30436i		−	0.327081i	−0.986537	−	0.163540i	$-0.947709\pi$
$263$		−	5.30436i		−	0.327081i	0.986537	−	0.163540i	$-0.0522914\pi$
$264$		0			0
$265$	−8.66666	−	19.4413i	−0.532389	−	1.19427i
$266$		0			0
$267$	−3.24130	−	27.4523i	−0.198364	−	1.68005i
$268$		0			0
$269$		−	20.3758i		−	1.24234i	−0.783677	−	0.621168i	$-0.786658\pi$
$269$		−	20.3758i		−	1.24234i	0.783677	−	0.621168i	$-0.213342\pi$
$270$		0			0
$271$			10.9132i			0.662928i	0.943468	+	0.331464i	$0.107543\pi$
$271$			10.9132i			0.662928i	−0.943468	+	0.331464i	$0.892457\pi$
$272$		0			0
$273$	3.40795	−	0.402377i	0.206259	−	0.0243530i
$274$		0			0
$275$	15.0860	−	6.88574i	0.909718	−	0.415226i
$276$		0			0
$277$	11.4973			0.690803			0.345402	−	0.938455i	$-0.387743\pi$
$277$	11.4973			0.690803			0.345402	+	0.938455i	$0.387743\pi$
$278$		0			0
$279$	18.1416	−	4.34452i	1.08611	−	0.260099i
$280$		0			0
$281$	26.2511			1.56601			0.783006	−	0.622015i	$-0.213686\pi$
$281$	26.2511			1.56601			0.783006	+	0.622015i	$0.213686\pi$
$282$		0			0
$283$	29.8807			1.77623			0.888113	−	0.459626i	$-0.152017\pi$
$283$	29.8807			1.77623			0.888113	+	0.459626i	$0.152017\pi$
$284$		0			0
$285$	5.91604	−	3.52113i	0.350436	−	0.208574i
$286$		0			0
$287$	−20.6411			−1.21840
$288$		0			0
$289$	−28.0485			−1.64991
$290$		0			0
$291$	0.171491	+	1.45245i	0.0100530	+	0.0851441i
$292$		0			0
$293$		−	9.36390i		−	0.547045i	−0.961866	−	0.273522i	$-0.911811\pi$
$293$		−	9.36390i		−	0.547045i	0.961866	−	0.273522i	$-0.0881888\pi$
$294$		0			0
$295$	−10.4774	+	4.67071i	−0.610020	+	0.271939i
$296$		0			0
$297$	−17.2048	−	0.997624i	−0.998323	−	0.0578880i
$298$		0			0
$299$	2.37219			0.137187
$300$		0			0
$301$	−19.0499			−1.09802
$302$		0			0
$303$	19.5855	−	2.31246i	1.12516	−	0.132848i
$304$		0			0
$305$	−5.34717	+	2.38370i	−0.306178	+	0.136490i
$306$		0			0
$307$	−21.2866			−1.21489			−0.607446	−	0.794361i	$-0.707806\pi$
$307$	−21.2866			−1.21489			−0.607446	+	0.794361i	$0.707806\pi$
$308$		0			0
$309$	−3.20432	−	27.1391i	−0.182287	−	1.54389i
$310$		0			0
$311$		−	9.11702i		−	0.516979i	−0.966014	−	0.258490i	$-0.916775\pi$
$311$		−	9.11702i		−	0.516979i	0.966014	−	0.258490i	$-0.0832247\pi$
$312$		0			0
$313$			4.00507i			0.226380i	0.993573	+	0.113190i	$0.0361068\pi$
$313$			4.00507i			0.226380i	−0.993573	+	0.113190i	$0.963893\pi$
$314$		0			0
$315$	16.6104	+	21.6516i	0.935888	+	1.21993i
$316$		0			0
$317$	23.6367			1.32757			0.663785	−	0.747924i	$-0.268949\pi$
$317$	23.6367			1.32757			0.663785	+	0.747924i	$0.268949\pi$
$318$		0			0
$319$	4.04173	+	1.75906i	0.226294	+	0.0984884i
$320$		0			0
$321$	2.81077	+	23.8059i	0.156882	+	1.32872i
$322$		0			0
$323$	−11.9309			−0.663855
$324$		0			0
$325$	−1.62775	+	1.81119i	−0.0902912	+	0.100467i
$326$		0			0
$327$	−3.04447	−	25.7853i	−0.168360	−	1.42593i
$328$		0			0
$329$	−43.6044			−2.40399
$330$		0			0
$331$	−29.8074			−1.63837			−0.819183	−	0.573533i	$-0.805573\pi$
$331$	−29.8074			−1.63837			−0.819183	+	0.573533i	$0.805573\pi$
$332$		0			0
$333$	5.56431	+	23.2351i	0.304922	+	1.27327i
$334$		0			0
$335$	−17.4095	+	7.76091i	−0.951180	+	0.424024i
$336$		0			0
$337$	−16.3537			−0.890842			−0.445421	−	0.895321i	$-0.646946\pi$
$337$	−16.3537			−0.890842			−0.445421	+	0.895321i	$0.646946\pi$
$338$		0			0
$339$	−3.85398	+	0.455040i	−0.209320	+	0.0247144i
$340$		0			0
$341$	−18.9100	−	8.23008i	−1.02403	−	0.445684i
$342$		0			0
$343$	10.3686			0.559849
$344$		0			0
$345$	9.64812	+	16.2103i	0.519437	+	0.872734i
$346$		0			0
$347$			4.73694i			0.254292i	0.991884	+	0.127146i	$0.0405817\pi$
$347$			4.73694i			0.254292i	−0.991884	+	0.127146i	$0.959418\pi$
$348$		0			0
$349$			13.2603i			0.709808i	0.934903	+	0.354904i	$0.115486\pi$
$349$			13.2603i			0.709808i	−0.934903	+	0.354904i	$0.884514\pi$
$350$		0			0
$351$	2.37501	−	0.873891i	0.126769	−	0.0466449i
$352$		0			0
$353$	−25.1335			−1.33772			−0.668860	−	0.743388i	$-0.733218\pi$
$353$	−25.1335			−1.33772			−0.668860	+	0.743388i	$0.733218\pi$
$354$		0			0
$355$	−12.2738	+	5.47151i	−0.651426	+	0.290397i
$356$		0			0
$357$	−5.54521	−	46.9654i	−0.293484	−	2.48567i
$358$		0			0
$359$	32.4183			1.71097			0.855487	−	0.517824i	$-0.173258\pi$
$359$	32.4183			1.71097			0.855487	+	0.517824i	$0.173258\pi$
$360$		0			0
$361$	15.8401			0.833691
$362$		0			0
$363$	14.5295	+	12.3245i	0.762602	+	0.646869i
$364$		0			0
$365$	−0.645374	−	1.44772i	−0.0337804	−	0.0757771i
$366$		0			0
$367$			14.6914i			0.766886i	0.923565	+	0.383443i	$0.125262\pi$
$367$			14.6914i			0.766886i	−0.923565	+	0.383443i	$0.874738\pi$
$368$		0			0
$369$	−14.8034	+	3.54509i	−0.770633	+	0.184550i
$370$		0			0
$371$	−38.7242			−2.01046
$372$		0			0
$373$	−22.3850			−1.15905			−0.579526	−	0.814954i	$-0.696762\pi$
$373$	−22.3850			−1.15905			−0.579526	+	0.814954i	$0.696762\pi$
$374$		0			0
$375$	−18.9970	−	3.75675i	−0.981002	−	0.193998i
$376$		0			0
$377$	−0.647284			−0.0333368
$378$		0			0
$379$	5.14877			0.264475			0.132237	−	0.991218i	$-0.457784\pi$
$379$	5.14877			0.264475			0.132237	+	0.991218i	$0.457784\pi$
$380$		0			0
$381$	0.867204	−	0.102391i	0.0444282	−	0.00524564i
$382$		0			0
$383$	0.856386			0.0437593			0.0218796	−	0.999761i	$-0.493035\pi$
$383$	0.856386			0.0437593			0.0218796	+	0.999761i	$0.493035\pi$
$384$		0			0
$385$	−0.266884	−	30.1681i	−0.0136017	−	1.53751i
$386$		0			0
$387$	−13.6622	+	3.27182i	−0.694491	+	0.166316i
$388$		0			0
$389$		−	34.4192i		−	1.74512i	−0.488506	−	0.872560i	$-0.662458\pi$
$389$		−	34.4192i		−	1.74512i	0.488506	−	0.872560i	$-0.337542\pi$
$390$		0			0
$391$		−	32.6915i		−	1.65328i
$392$		0			0
$393$	−20.6634	+	2.43973i	−1.04233	+	0.123068i
$394$		0			0
$395$	−14.6234	+	6.51890i	−0.735781	+	0.328002i
$396$		0			0
$397$			35.3725i			1.77529i	0.460526	+	0.887646i	$0.347661\pi$
$397$			35.3725i			1.77529i	−0.460526	+	0.887646i	$0.652339\pi$
$398$		0			0
$399$	−1.46863	−	12.4386i	−0.0735234	−	0.622709i
$400$		0			0
$401$		−	10.6690i		−	0.532786i	−0.963865	−	0.266393i	$-0.914168\pi$
$401$		−	10.6690i		−	0.532786i	0.963865	−	0.266393i	$-0.0858318\pi$
$402$		0			0
$403$	3.02844			0.150857
$404$		0			0
$405$	15.6313	+	12.6753i	0.776725	+	0.629840i
$406$		0			0
$407$	10.5408	−	24.2193i	0.522488	−	1.20050i
$408$		0			0
$409$		−	28.4363i		−	1.40608i	−0.711148	−	0.703042i	$-0.751825\pi$
$409$		−	28.4363i		−	1.40608i	0.711148	−	0.703042i	$-0.248175\pi$
$410$		0			0
$411$	10.4779	−	1.23713i	0.516836	−	0.0610229i
$412$		0			0
$413$			20.8696i			1.02692i
$414$		0			0
$415$	−28.3682	+	12.6462i	−1.39254	+	0.620777i
$416$		0			0
$417$	−3.14941	−	26.6740i	−0.154227	−	1.30623i
$418$		0			0
$419$		−	2.94511i		−	0.143878i	−0.997409	−	0.0719391i	$-0.977081\pi$
$419$		−	2.94511i		−	0.143878i	0.997409	−	0.0719391i	$-0.0229187\pi$
$420$		0			0
$421$	−13.1762			−0.642170			−0.321085	−	0.947050i	$-0.604048\pi$
$421$	−13.1762			−0.642170			−0.321085	+	0.947050i	$0.604048\pi$
$422$		0			0
$423$	−31.2723	+	7.48904i	−1.52051	+	0.364130i
$424$		0			0
$425$	24.9602	+	22.4322i	1.21075	+	1.08812i
$426$		0			0
$427$			10.6508i			0.515428i
$428$		0			0
$429$	−2.67856	−	0.807996i	−0.129322	−	0.0390104i
$430$		0			0
$431$	18.4389			0.888171			0.444086	−	0.895984i	$-0.353529\pi$
$431$	18.4389			0.888171			0.444086	+	0.895984i	$0.353529\pi$
$432$		0			0
$433$			16.6376i			0.799553i	0.916613	+	0.399776i	$0.130912\pi$
$433$			16.6376i			0.799553i	−0.916613	+	0.399776i	$0.869088\pi$
$434$		0			0
$435$	−2.63261	−	4.42319i	−0.126224	−	0.212076i
$436$		0			0
$437$		−	8.65821i		−	0.414179i
$438$		0			0
$439$		−	17.3196i		−	0.826619i	−0.910591	−	0.413310i	$-0.864373\pi$
$439$		−	17.3196i		−	0.826619i	0.910591	−	0.413310i	$-0.135627\pi$
$440$		0			0
$441$	27.8587	−	6.67156i	1.32660	−	0.317693i
$442$		0			0
$443$	11.0984			0.527299			0.263650	−	0.964619i	$-0.415074\pi$
$443$	11.0984			0.527299			0.263650	+	0.964619i	$0.415074\pi$
$444$		0			0
$445$	32.5949	−	14.5304i	1.54515	−	0.688806i
$446$		0			0
$447$	−18.7872	+	2.21821i	−0.888604	+	0.104918i
$448$		0			0
$449$			10.7509i			0.507366i	0.967287	+	0.253683i	$0.0816420\pi$
$449$			10.7509i			0.507366i	−0.967287	+	0.253683i	$0.918358\pi$
$450$		0			0
$451$	15.4304	+	6.71569i	0.726590	+	0.316229i
$452$		0			0
$453$	1.65017	+	13.9762i	0.0775316	+	0.656657i
$454$		0			0
$455$	1.80381	+	4.04636i	0.0845640	+	0.189696i
$456$		0			0
$457$	18.0288			0.843349			0.421675	−	0.906747i	$-0.361442\pi$
$457$	18.0288			0.843349			0.421675	+	0.906747i	$0.361442\pi$
$458$		0			0
$459$	−12.0432	−	32.7303i	−0.562128	−	1.52772i
$460$		0			0
$461$	−11.4037			−0.531121			−0.265561	−	0.964094i	$-0.585557\pi$
$461$	−11.4037			−0.531121			−0.265561	+	0.964094i	$0.585557\pi$
$462$		0			0
$463$		−	15.0077i		−	0.697465i	−0.937222	−	0.348733i	$-0.886612\pi$
$463$		−	15.0077i		−	0.697465i	0.937222	−	0.348733i	$-0.113388\pi$
$464$		0			0
$465$	12.3172	+	20.6947i	0.571195	+	0.959695i
$466$		0			0
$467$	−23.8630			−1.10425			−0.552123	−	0.833762i	$-0.686182\pi$
$467$	−23.8630			−1.10425			−0.552123	+	0.833762i	$0.686182\pi$
$468$		0			0
$469$			34.6771i			1.60124i
$470$		0			0
$471$	−3.49239	−	29.5790i	−0.160921	−	1.36293i
$472$		0			0
$473$	14.2410	+	6.19800i	0.654800	+	0.284985i
$474$		0			0
$475$	6.61061	+	5.94108i	0.303316	+	0.272595i
$476$		0			0
$477$	−27.7723	+	6.65087i	−1.27161	+	0.304522i
$478$		0			0
$479$	32.6508			1.49185			0.745927	−	0.666027i	$-0.232007\pi$
$479$	32.6508			1.49185			0.745927	+	0.666027i	$0.232007\pi$
$480$		0			0
$481$			3.87872i			0.176854i
$482$		0			0
$483$	34.0825	−	4.02413i	1.55081	−	0.183104i
$484$		0			0
$485$	−1.72453	+	0.768775i	−0.0783071	+	0.0349083i
$486$		0			0
$487$		−	29.7269i		−	1.34706i	−0.739162	−	0.673528i	$-0.764778\pi$
$487$		−	29.7269i		−	1.34706i	0.739162	−	0.673528i	$-0.235222\pi$
$488$		0			0
$489$	−0.599079	−	5.07392i	−0.0270913	−	0.229451i
$490$		0			0
$491$	41.1627			1.85765			0.928823	−	0.370524i	$-0.120822\pi$
$491$	41.1627			1.85765			0.928823	+	0.370524i	$0.120822\pi$
$492$		0			0
$493$			8.92029i			0.401750i
$494$		0			0
$495$	−5.37276	−	21.5901i	−0.241487	−	0.970404i
$496$		0			0
$497$			24.4477i			1.09663i
$498$		0			0
$499$	−3.18648			−0.142646			−0.0713232	−	0.997453i	$-0.522722\pi$
$499$	−3.18648			−0.142646			−0.0713232	+	0.997453i	$0.522722\pi$
$500$		0			0
$501$	1.26664	+	10.7279i	0.0565895	+	0.479287i
$502$		0			0
$503$		−	19.8089i		−	0.883234i	−0.897204	−	0.441617i	$-0.854405\pi$
$503$		−	19.8089i		−	0.883234i	0.897204	−	0.441617i	$-0.145595\pi$
$504$		0			0
$505$	10.3665	+	23.2544i	0.461304	+	1.03481i
$506$		0			0
$507$	−21.9533	+	2.59203i	−0.974982	+	0.115116i
$508$		0			0
$509$			13.4429i			0.595845i	0.954590	+	0.297922i	$0.0962937\pi$
$509$			13.4429i			0.595845i	−0.954590	+	0.297922i	$0.903706\pi$
$510$		0			0
$511$	−2.88365			−0.127565
$512$		0			0
$513$	−3.18960	−	8.66849i	−0.140824	−	0.382723i
$514$		0			0
$515$	32.2230	−	14.3646i	1.41992	−	0.632980i
$516$		0			0
$517$	32.5969	+	14.1869i	1.43361	+	0.623941i
$518$		0			0
$519$	−3.34019	−	28.2899i	−0.146618	−	1.24179i
$520$		0			0
$521$			10.9273i			0.478732i	0.970929	+	0.239366i	$0.0769395\pi$
$521$			10.9273i			0.478732i	−0.970929	+	0.239366i	$0.923060\pi$
$522$		0			0
$523$	−3.81921			−0.167003			−0.0835013	−	0.996508i	$-0.526610\pi$
$523$	−3.81921			−0.167003			−0.0835013	+	0.996508i	$0.526610\pi$
$524$		0			0
$525$	−20.3142	+	28.7835i	−0.886586	+	1.25622i
$526$		0			0
$527$		−	41.7352i		−	1.81802i
$528$		0			0
$529$	0.724020			0.0314791
$530$		0			0
$531$	3.58434	+	14.9673i	0.155547	+	0.649523i
$532$		0			0
$533$	−2.47118			−0.107039
$534$		0			0
$535$	−28.2655	+	12.6004i	−1.22202	+	0.544761i
$536$		0			0
$537$	−4.38530	−	37.1415i	−0.189240	−	1.60277i
$538$		0			0
$539$	−29.0387	−	12.6383i	−1.25079	−	0.544372i
$540$		0			0
$541$			11.5067i			0.494710i	0.968925	+	0.247355i	$0.0795613\pi$
$541$			11.5067i			0.494710i	−0.968925	+	0.247355i	$0.920439\pi$
$542$		0			0
$543$	−11.6559	+	1.37621i	−0.500201	+	0.0590588i
$544$		0			0
$545$	30.6156	−	13.6480i	1.31143	−	0.584617i
$546$		0			0
$547$	6.69674			0.286332			0.143166	−	0.989699i	$-0.454272\pi$
$547$	6.69674			0.286332			0.143166	+	0.989699i	$0.454272\pi$
$548$		0			0
$549$	1.82927	+	7.63854i	0.0780713	+	0.326005i
$550$		0			0
$551$			2.36251i			0.100646i
$552$		0			0
$553$			29.1277i			1.23863i
$554$		0			0
$555$	−26.5051	+	15.7754i	−1.12508	+	0.669629i
$556$		0			0
$557$			24.3328i			1.03102i	0.856885	+	0.515508i	$0.172397\pi$
$557$			24.3328i			1.03102i	−0.856885	+	0.515508i	$0.827603\pi$
$558$		0			0
$559$	−2.28069			−0.0964629
$560$		0			0
$561$	−11.1351	+	36.9136i	−0.470123	+	1.55849i
$562$		0			0
$563$			42.6342i			1.79682i	0.439160	+	0.898409i	$0.355276\pi$
$563$			42.6342i			1.79682i	−0.439160	+	0.898409i	$0.644724\pi$
$564$		0			0
$565$	−2.03990	−	4.57594i	−0.0858191	−	0.192511i
$566$		0			0
$567$	32.6405	−	16.5846i	1.37077	−	0.696486i
$568$		0			0
$569$	−22.9670			−0.962825			−0.481413	−	0.876494i	$-0.659876\pi$
$569$	−22.9670			−0.962825			−0.481413	+	0.876494i	$0.659876\pi$
$570$		0			0
$571$		−	8.36110i		−	0.349901i	−0.984577	−	0.174951i	$-0.944023\pi$
$571$		−	8.36110i		−	0.349901i	0.984577	−	0.174951i	$-0.0559766\pi$
$572$		0			0
$573$	1.59025	+	13.4687i	0.0664336	+	0.562662i
$574$		0			0
$575$	−16.2789	+	18.1135i	−0.678877	+	0.755384i
$576$		0			0
$577$		−	15.7206i		−	0.654456i	−0.944945	−	0.327228i	$-0.893885\pi$
$577$		−	15.7206i		−	0.654456i	0.944945	−	0.327228i	$-0.106115\pi$
$578$		0			0
$579$	−16.9639	+	2.00293i	−0.704997	+	0.0832391i
$580$		0			0
$581$			56.5055i			2.34424i
$582$		0			0
$583$	28.9487	+	12.5991i	1.19893	+	0.521803i
$584$		0			0
$585$	1.98862	+	2.59216i	0.0822193	+	0.107173i
$586$		0			0
$587$	12.3947			0.511583			0.255792	−	0.966732i	$-0.417664\pi$
$587$	12.3947			0.511583			0.255792	+	0.966732i	$0.417664\pi$
$588$		0			0
$589$		−	11.0534i		−	0.455448i
$590$		0			0
$591$	2.19675	+	18.6055i	0.0903622	+	0.765326i
$592$		0			0
$593$			22.7756i			0.935282i	0.883918	+	0.467641i	$0.154896\pi$
$593$			22.7756i			0.935282i	−0.883918	+	0.467641i	$0.845104\pi$
$594$		0			0
$595$	55.7633	−	24.8586i	2.28607	−	1.01910i
$596$		0			0
$597$	14.0274	−	1.65622i	0.574104	−	0.0677845i
$598$		0			0
$599$		−	16.3904i		−	0.669694i	−0.942273	−	0.334847i	$-0.891315\pi$
$599$		−	16.3904i		−	0.669694i	0.942273	−	0.334847i	$-0.108685\pi$
$600$		0			0
$601$		−	32.1587i		−	1.31178i	−0.754855	−	0.655891i	$-0.772293\pi$
$601$		−	32.1587i		−	1.31178i	0.754855	−	0.655891i	$-0.227707\pi$
$602$		0			0
$603$	5.95578	+	24.8698i	0.242538	+	1.01278i
$604$		0			0
$605$	−9.61584	+	22.6392i	−0.390940	+	0.920416i
$606$		0			0
$607$	19.8544			0.805863			0.402932	−	0.915230i	$-0.367991\pi$
$607$	19.8544			0.805863			0.402932	+	0.915230i	$0.367991\pi$
$608$		0			0
$609$	−9.29986	+	1.09804i	−0.376849	+	0.0444947i
$610$		0			0
$611$	−5.22039			−0.211195
$612$		0			0
$613$	−9.51906			−0.384471			−0.192236	−	0.981349i	$-0.561574\pi$
$613$	−9.51906			−0.384471			−0.192236	+	0.981349i	$0.561574\pi$
$614$		0			0
$615$	−10.0507	−	16.8868i	−0.405284	−	0.680940i
$616$		0			0
$617$	20.0214			0.806031			0.403015	−	0.915193i	$-0.367962\pi$
$617$	20.0214			0.806031			0.403015	+	0.915193i	$0.367962\pi$
$618$		0			0
$619$	44.4802			1.78781			0.893905	−	0.448257i	$-0.147955\pi$
$619$	44.4802			1.78781			0.893905	+	0.448257i	$0.147955\pi$
$620$		0			0
$621$	23.7522	−	8.73968i	0.953142	−	0.350711i
$622$		0			0
$623$		−	64.9244i		−	2.60114i
$624$		0			0
$625$	−2.65953	−	24.8581i	−0.106381	−	0.994325i
$626$		0			0
$627$	−2.94908	+	9.77642i	−0.117775	+	0.390433i
$628$		0			0
$629$	53.4530			2.13131
$630$		0			0
$631$	1.35237			0.0538370			0.0269185	−	0.999638i	$-0.491431\pi$
$631$	1.35237			0.0538370			0.0269185	+	0.999638i	$0.491431\pi$
$632$		0			0
$633$	4.45263	+	37.7117i	0.176976	+	1.49891i
$634$		0			0
$635$	0.459007	+	1.02965i	0.0182151	+	0.0408606i
$636$		0			0
$637$	4.65055			0.184262
$638$		0			0
$639$	4.19888	+	17.5334i	0.166105	+	0.693611i
$640$		0			0
$641$		−	8.72758i		−	0.344719i	−0.985034	−	0.172359i	$-0.944861\pi$
$641$		−	8.72758i		−	0.344719i	0.985034	−	0.172359i	$-0.0551391\pi$
$642$		0			0
$643$			31.9235i			1.25894i	0.777024	+	0.629471i	$0.216728\pi$
$643$			31.9235i			1.25894i	−0.777024	+	0.629471i	$0.783272\pi$
$644$		0			0
$645$	−9.27596	−	15.5850i	−0.365240	−	0.613660i
$646$		0			0
$647$	−16.5851			−0.652026			−0.326013	−	0.945365i	$-0.605705\pi$
$647$	−16.5851			−0.652026			−0.326013	+	0.945365i	$0.605705\pi$
$648$		0			0
$649$	6.79003	−	15.6012i	0.266532	−	0.612402i
$650$		0			0
$651$	43.5111	−	5.13736i	1.70534	−	0.201349i
$652$		0			0
$653$	30.0000			1.17399			0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000			1.17399			0.586995	+	0.809590i	$0.300311\pi$
$654$		0			0
$655$	−10.9370	−	24.5342i	−0.427345	−	0.958630i
$656$		0			0
$657$	−2.06810	+	0.495265i	−0.0806842	+	0.0193221i
$658$		0			0
$659$	19.8443			0.773025			0.386512	−	0.922284i	$-0.373680\pi$
$659$	19.8443			0.773025			0.386512	+	0.922284i	$0.373680\pi$
$660$		0			0
$661$	7.27040			0.282786			0.141393	−	0.989954i	$-0.454842\pi$
$661$	7.27040			0.282786			0.141393	+	0.989954i	$0.454842\pi$
$662$		0			0
$663$	−0.663881	−	5.62277i	−0.0257830	−	0.218370i
$664$		0			0
$665$	14.7687	−	6.58370i	0.572706	−	0.255305i
$666$		0			0
$667$	−6.47341			−0.250651
$668$		0			0
$669$	0.379851	+	3.21716i	0.0146859	+	0.124383i
$670$		0			0
$671$	3.46529	−	7.96210i	0.133776	−	0.307373i
$672$		0			0
$673$	−4.18041			−0.161143			−0.0805716	−	0.996749i	$-0.525675\pi$
$673$	−4.18041			−0.161143			−0.0805716	+	0.996749i	$0.525675\pi$
$674$		0			0
$675$	−9.62542	+	24.1320i	−0.370483	+	0.928839i
$676$		0			0
$677$		−	32.1263i		−	1.23471i	−0.786683	−	0.617357i	$-0.788203\pi$
$677$		−	32.1263i		−	1.23471i	0.786683	−	0.617357i	$-0.211797\pi$
$678$		0			0
$679$			3.43503i			0.131824i
$680$		0			0
$681$	1.58332	+	13.4100i	0.0606730	+	0.513872i
$682$		0			0
$683$	4.24883			0.162577			0.0812884	−	0.996691i	$-0.474097\pi$
$683$	4.24883			0.162577			0.0812884	+	0.996691i	$0.474097\pi$
$684$		0			0
$685$	5.54590	+	12.4407i	0.211898	+	0.475334i
$686$		0			0
$687$	3.99059	−	0.471170i	0.152251	−	0.0179762i
$688$		0			0
$689$	−4.63613			−0.176622
$690$		0			0
$691$	5.59047			0.212671			0.106336	−	0.994330i	$-0.466088\pi$
$691$	5.59047			0.212671			0.106336	+	0.994330i	$0.466088\pi$
$692$		0			0
$693$	−39.8549	−	7.06505i	−1.51396	−	0.268379i
$694$		0			0
$695$	31.6708	−	14.1184i	1.20134	−	0.535543i
$696$		0			0
$697$			34.0557i			1.28995i
$698$		0			0
$699$	2.72882	+	23.1118i	0.103213	+	0.874170i
$700$		0			0
$701$	−36.5121			−1.37904			−0.689521	−	0.724266i	$-0.742179\pi$
$701$	−36.5121			−1.37904			−0.689521	+	0.724266i	$0.742179\pi$
$702$		0			0
$703$	14.1568			0.533935
$704$		0			0
$705$	−21.2322	−	35.6734i	−0.799653	−	1.34354i
$706$		0			0
$707$	46.3195			1.74202
$708$		0			0
$709$	28.7632			1.08023			0.540113	−	0.841592i	$-0.318381\pi$
$709$	28.7632			1.08023			0.540113	+	0.841592i	$0.318381\pi$
$710$		0			0
$711$	5.00266	+	20.8898i	0.187614	+	0.783428i
$712$		0			0
$713$	30.2870			1.13426
$714$		0			0
$715$	−0.0319518	−	3.61177i	−0.00119493	−	0.135073i
$716$		0			0
$717$	−47.0939	+	5.56039i	−1.75875	+	0.207656i
$718$		0			0
$719$		−	24.9024i		−	0.928702i	−0.885651	−	0.464351i	$-0.846288\pi$
$719$		−	24.9024i		−	0.928702i	0.885651	−	0.464351i	$-0.153712\pi$
$720$		0			0
$721$		−	64.1836i		−	2.39032i
$722$		0			0
$723$	−4.34762	−	36.8224i	−0.161690	−	1.36944i
$724$		0			0
$725$	4.44191	−	4.94250i	0.164968	−	0.183560i
$726$		0			0
$727$			33.0847i			1.22704i	0.789678	+	0.613522i	$0.210248\pi$
$727$			33.0847i			1.22704i	−0.789678	+	0.613522i	$0.789752\pi$
$728$		0			0
$729$	20.5608	−	17.5001i	0.761510	−	0.648153i
$730$		0			0
$731$			31.4304i			1.16250i
$732$		0			0
$733$	−10.3268			−0.381431			−0.190715	−	0.981645i	$-0.561081\pi$
$733$	−10.3268			−0.381431			−0.190715	+	0.981645i	$0.561081\pi$
$734$		0			0
$735$	18.9146	+	31.7794i	0.697675	+	1.17220i
$736$		0			0
$737$	11.2824	−	25.9232i	0.415593	−	0.954894i
$738$		0			0
$739$		−	16.7742i		−	0.617047i	−0.951217	−	0.308524i	$-0.900165\pi$
$739$		−	16.7742i		−	0.617047i	0.951217	−	0.308524i	$-0.0998349\pi$
$740$		0			0
$741$	−0.175827	−	1.48917i	−0.00645915	−	0.0547060i
$742$		0			0
$743$			11.9919i			0.439940i	0.975507	+	0.219970i	$0.0705960\pi$
$743$			11.9919i			0.439940i	−0.975507	+	0.219970i	$0.929404\pi$
$744$		0			0
$745$	−9.94398	−	22.3066i	−0.364319	−	0.817250i
$746$		0			0
$747$	9.70479	+	40.5246i	0.355080	+	1.48272i
$748$		0			0
$749$			56.3007i			2.05718i
$750$		0			0
$751$	43.0821			1.57209			0.786043	−	0.618172i	$-0.212126\pi$
$751$	43.0821			1.57209			0.786043	+	0.618172i	$0.212126\pi$
$752$		0			0
$753$	2.74804	+	23.2746i	0.100144	+	0.848174i
$754$		0			0
$755$	−16.5943	+	7.39751i	−0.603927	+	0.269223i
$756$		0			0
$757$			17.0338i			0.619105i	0.950882	+	0.309553i	$0.100179\pi$
$757$			17.0338i			0.619105i	−0.950882	+	0.309553i	$0.899821\pi$
$758$		0			0
$759$	−26.7880	−	8.08067i	−0.972342	−	0.293310i
$760$		0			0
$761$	7.99473			0.289809			0.144904	−	0.989446i	$-0.453713\pi$
$761$	7.99473			0.289809			0.144904	+	0.989446i	$0.453713\pi$
$762$		0			0
$763$		−	60.9819i		−	2.20769i
$764$		0			0
$765$	35.7229	−	27.4054i	1.29156	−	0.990844i
$766$		0			0
$767$			2.49854i			0.0902170i
$768$		0			0
$769$		−	32.3828i		−	1.16775i	−0.811842	−	0.583877i	$-0.801535\pi$
$769$		−	32.3828i		−	1.16775i	0.811842	−	0.583877i	$-0.198465\pi$
$770$		0			0
$771$	1.93952	−	0.229000i	0.0698502	−	0.00824722i
$772$		0			0
$773$	−28.6633			−1.03095			−0.515474	−	0.856905i	$-0.672384\pi$
$773$	−28.6633			−1.03095			−0.515474	+	0.856905i	$0.672384\pi$
$774$		0			0
$775$	−20.7823	+	23.1244i	−0.746523	+	0.830652i
$776$		0			0
$777$	6.57976	+	55.7275i	0.236047	+	1.99921i
$778$		0			0
$779$			9.01952i			0.323158i
$780$		0			0
$781$	7.95419	−	18.2761i	0.284623	−	0.653970i
$782$		0			0
$783$	−6.48109	+	2.38474i	−0.231615	+	0.0852235i
$784$		0			0
$785$	35.1199	−	15.6560i	1.25348	−	0.558787i
$786$		0			0
$787$	−54.3410			−1.93705			−0.968523	−	0.248924i	$-0.919923\pi$
$787$	−54.3410			−1.93705			−0.968523	+	0.248924i	$0.919923\pi$
$788$		0			0
$789$	−1.07728	−	9.12404i	−0.0383521	−	0.324825i
$790$		0			0
$791$	−9.11462			−0.324079
$792$		0			0
$793$			1.27513i			0.0452812i
$794$		0			0
$795$	−18.8559	−	31.6808i	−0.668751	−	1.12360i
$796$		0			0
$797$	23.3137			0.825815			0.412907	−	0.910773i	$-0.364513\pi$
$797$	23.3137			0.825815			0.412907	+	0.910773i	$0.364513\pi$
$798$		0			0
$799$			71.9429i			2.54516i
$800$		0			0
$801$	−11.1507	−	46.5625i	−0.393992	−	1.64521i
$802$		0			0
$803$	2.15570	+	0.938211i	0.0760729	+	0.0331088i
$804$		0			0
$805$	18.0397	+	40.4671i	0.635816	+	1.42628i
$806$		0			0
$807$	−4.13818	−	35.0485i	−0.145671	−	1.23377i
$808$		0			0
$809$	−47.8598			−1.68266			−0.841330	−	0.540522i	$-0.818227\pi$
$809$	−47.8598			−1.68266			−0.841330	+	0.540522i	$0.818227\pi$
$810$		0			0
$811$		−	11.5757i		−	0.406479i	−0.979129	−	0.203240i	$-0.934853\pi$
$811$		−	11.5757i		−	0.406479i	0.979129	−	0.203240i	$-0.0651471\pi$
$812$		0			0
$813$	2.21639	+	18.7718i	0.0777321	+	0.658355i
$814$		0			0
$815$	6.02441	−	2.68560i	0.211026	−	0.0940726i
$816$		0			0
$817$			8.32424i			0.291228i
$818$		0			0
$819$	5.78031	−	1.38426i	0.201980	−	0.0483700i
$820$		0			0
$821$	4.39090			0.153243			0.0766217	−	0.997060i	$-0.475587\pi$
$821$	4.39090			0.153243			0.0766217	+	0.997060i	$0.475587\pi$
$822$		0			0
$823$			4.48004i			0.156164i	0.996947	+	0.0780822i	$0.0248797\pi$
$823$			4.48004i			0.156164i	−0.996947	+	0.0780822i	$0.975120\pi$
$824$		0			0
$825$	24.5510	−	14.9080i	0.854755	−	0.519031i
$826$		0			0
$827$		−	11.5880i		−	0.402954i	−0.979493	−	0.201477i	$-0.935426\pi$
$827$		−	11.5880i		−	0.402954i	0.979493	−	0.201477i	$-0.0645742\pi$
$828$		0			0
$829$	35.9085			1.24715			0.623577	−	0.781762i	$-0.285679\pi$
$829$	35.9085			1.24715			0.623577	+	0.781762i	$0.285679\pi$
$830$		0			0
$831$	19.7765	−	2.33501i	0.686038	−	0.0810006i
$832$		0			0
$833$		−	64.0898i		−	2.22058i
$834$		0			0
$835$	−12.7375	+	5.67823i	−0.440800	+	0.196503i
$836$		0			0
$837$	30.3230	−	11.1574i	1.04812	−	0.385657i
$838$		0			0
$839$			47.7992i			1.65021i	0.564978	+	0.825106i	$0.308885\pi$
$839$			47.7992i			1.65021i	−0.564978	+	0.825106i	$0.691115\pi$
$840$		0			0
$841$	−27.2336			−0.939091
$842$		0			0
$843$	45.1546	−	5.33141i	1.55521	−	0.183624i
$844$		0			0
$845$	−11.6198	−	26.0658i	−0.399733	−	0.896691i
$846$		0			0
$847$	30.4956	+	32.7479i	1.04784	+	1.12523i
$848$		0			0
$849$	51.3979	−	6.06856i	1.76397	−	0.208272i
$850$		0			0
$851$			38.7906i			1.32972i
$852$		0			0
$853$	−38.5491			−1.31989			−0.659947	−	0.751312i	$-0.729421\pi$
$853$	−38.5491			−1.31989			−0.659947	+	0.751312i	$0.729421\pi$
$854$		0			0
$855$	9.46108	−	7.25822i	0.323562	−	0.248226i
$856$		0			0
$857$			34.4805i			1.17783i	0.808194	+	0.588916i	$0.200445\pi$
$857$			34.4805i			1.17783i	−0.808194	+	0.588916i	$0.799555\pi$
$858$		0			0
$859$	−19.3752			−0.661074			−0.330537	−	0.943793i	$-0.607230\pi$
$859$	−19.3752			−0.661074			−0.330537	+	0.943793i	$0.607230\pi$
$860$		0			0
$861$	−35.5048	+	4.19205i	−1.21000	+	0.142865i
$862$		0			0
$863$	24.5481			0.835628			0.417814	−	0.908533i	$-0.362796\pi$
$863$	24.5481			0.835628			0.417814	+	0.908533i	$0.362796\pi$
$864$		0			0
$865$	33.5894	−	14.9737i	1.14207	−	0.509122i
$866$		0			0
$867$	−48.2463	+	5.69645i	−1.63853	+	0.193462i
$868$		0			0
$869$	9.47685	−	21.7746i	0.321480	−	0.738654i
$870$		0			0
$871$			4.15160i			0.140672i
$872$		0			0
$873$	0.589964	+	2.46353i	0.0199673	+	0.0833780i
$874$		0			0
$875$	−43.2754	−	13.9942i	−1.46298	−	0.473091i
$876$		0			0
$877$	−50.5199			−1.70594			−0.852969	−	0.521962i	$-0.825200\pi$
$877$	−50.5199			−1.70594			−0.852969	+	0.521962i	$0.825200\pi$
$878$		0			0
$879$	−1.90174	−	16.1069i	−0.0641441	−	0.543271i
$880$		0			0
$881$		−	11.6713i		−	0.393217i	−0.980482	−	0.196609i	$-0.937007\pi$
$881$		−	11.6713i		−	0.393217i	0.980482	−	0.196609i	$-0.0629929\pi$
$882$		0			0
$883$		−	34.6469i		−	1.16596i	−0.812486	−	0.582980i	$-0.801887\pi$
$883$		−	34.6469i		−	1.16596i	0.812486	−	0.582980i	$-0.198113\pi$
$884$		0			0
$885$	−17.0737	+	10.1620i	−0.573926	+	0.341591i
$886$		0			0
$887$			39.7308i			1.33403i	0.745044	+	0.667015i	$0.232428\pi$
$887$			39.7308i			1.33403i	−0.745044	+	0.667015i	$0.767572\pi$
$888$		0			0
$889$	2.05093			0.0687858
$890$		0			0
$891$	−29.7966	+	1.77815i	−0.998224	+	0.0595703i
$892$		0			0
$893$			19.0538i			0.637611i
$894$		0			0
$895$	44.0991	−	19.6588i	1.47407	−	0.657122i
$896$		0			0
$897$	4.08042	−	0.481775i	0.136241	−	0.0160860i
$898$		0			0
$899$	−8.26421			−0.275627
$900$		0			0
$901$			63.8910i			2.12852i
$902$		0			0
$903$	−32.7678	+	3.86890i	−1.09045	+	0.128749i
$904$		0			0
$905$	−6.16940	−	13.8393i	−0.205078	−	0.460035i
$906$		0			0
$907$			31.0066i			1.02956i	0.857323	+	0.514778i	$0.172126\pi$
$907$			31.0066i			1.02956i	−0.857323	+	0.514778i	$0.827874\pi$
$908$		0			0
$909$	33.2194	−	7.95535i	1.10182	−	0.263862i
$910$		0			0
$911$		−	22.9078i		−	0.758968i	−0.925198	−	0.379484i	$-0.876102\pi$
$911$		−	22.9078i		−	0.758968i	0.925198	−	0.379484i	$-0.123898\pi$
$912$		0			0
$913$	18.3844	−	42.2412i	0.608434	−	1.39798i
$914$		0			0
$915$	−8.71356	+	5.18617i	−0.288062	+	0.171450i
$916$		0			0
$917$	−48.8686			−1.61378
$918$		0			0
$919$		−	12.6635i		−	0.417729i	−0.977945	−	0.208865i	$-0.933023\pi$
$919$		−	12.6635i		−	0.417729i	0.977945	−	0.208865i	$-0.0669768\pi$
$920$		0			0
$921$	−36.6152	+	4.32316i	−1.20651	+	0.142453i
$922$		0			0
$923$			2.92692i			0.0963406i
$924$		0			0
$925$	−29.6169	−	26.6173i	−0.973798	−	0.875170i
$926$		0			0
$927$	−11.0235	−	46.0313i	−0.362059	−	1.51186i
$928$		0			0
$929$			18.3172i			0.600966i	0.953787	+	0.300483i	$0.0971479\pi$
$929$			18.3172i			0.600966i	−0.953787	+	0.300483i	$0.902852\pi$
$930$		0			0
$931$		−	16.9739i		−	0.556299i
$932$		0			0
$933$	−1.85160	−	15.6822i	−0.0606187	−	0.513413i
$934$		0			0
$935$	−49.7742	+	0.440332i	−1.62779	+	0.0144004i
$936$		0			0
$937$	50.9580			1.66472			0.832362	−	0.554232i	$-0.186988\pi$
$937$	50.9580			1.66472			0.832362	+	0.554232i	$0.186988\pi$
$938$		0			0
$939$	0.813400	+	6.88912i	0.0265443	+	0.224818i
$940$		0			0
$941$	1.10936			0.0361640			0.0180820	−	0.999837i	$-0.494244\pi$
$941$	1.10936			0.0361640			0.0180820	+	0.999837i	$0.494244\pi$
$942$		0			0
$943$	−24.7140			−0.804799
$944$		0			0
$945$	32.9688	+	33.8695i	1.07248	+	1.10178i
$946$		0			0
$947$	27.1440			0.882061			0.441030	−	0.897492i	$-0.354613\pi$
$947$	27.1440			0.882061			0.441030	+	0.897492i	$0.354613\pi$
$948$		0			0
$949$	−0.345235			−0.0112068
$950$		0			0
$951$	40.6576	−	4.80044i	1.31841	−	0.155665i
$952$		0			0
$953$		−	23.7432i		−	0.769118i	−0.923100	−	0.384559i	$-0.874353\pi$
$953$		−	23.7432i		−	0.769118i	0.923100	−	0.384559i	$-0.125647\pi$
$954$		0			0
$955$	−15.9917	+	7.12891i	−0.517480	+	0.230686i
$956$		0			0
$957$	7.30945	+	2.20492i	0.236281	+	0.0712748i
$958$		0			0
$959$	24.7801			0.800190
$960$		0			0
$961$	7.66565			0.247279
$962$		0			0
$963$	9.66963	+	40.3778i	0.311599	+	1.30116i
$964$		0			0
$965$	−8.97893	−	20.1418i	−0.289042	−	0.648386i
$966$		0			0
$967$	43.8957			1.41159			0.705796	−	0.708415i	$-0.250590\pi$
$967$	43.8957			1.41159			0.705796	+	0.708415i	$0.250590\pi$
$968$		0			0
$969$	−20.5224	+	2.42309i	−0.659275	+	0.0778407i
$970$		0			0
$971$		−	49.2284i		−	1.57981i	−0.613226	−	0.789907i	$-0.710129\pi$
$971$		−	49.2284i		−	1.57981i	0.613226	−	0.789907i	$-0.289871\pi$
$972$		0			0
$973$		−	63.0838i		−	2.02237i
$974$		0			0
$975$	−2.43205	+	3.44601i	−0.0778880	+	0.110361i
$976$		0			0
$977$	−54.2159			−1.73452			−0.867261	−	0.497854i	$-0.834122\pi$
$977$	−54.2159			−1.73452			−0.867261	+	0.497854i	$0.834122\pi$
$978$		0			0
$979$	−21.1235	+	48.5348i	−0.675111	+	1.55118i
$980$		0			0
$981$	−10.4736	−	43.7350i	−0.334397	−	1.39635i
$982$		0			0
$983$	17.2245			0.549377			0.274689	−	0.961533i	$-0.411425\pi$
$983$	17.2245			0.549377			0.274689	+	0.961533i	$0.411425\pi$
$984$		0			0
$985$	−22.0908	+	9.84778i	−0.703871	+	0.313776i
$986$		0			0
$987$	−75.0041	+	8.85574i	−2.38741	+	0.281881i
$988$		0			0
$989$	−22.8089			−0.725281
$990$		0			0
$991$	7.18071			0.228103			0.114051	−	0.993475i	$-0.463617\pi$
$991$	7.18071			0.228103			0.114051	+	0.993475i	$0.463617\pi$
$992$		0			0
$993$	−51.2719	+	6.05368i	−1.62706	+	0.192108i
$994$		0			0
$995$	7.42464	+	16.6551i	0.235377	+	0.528003i
$996$		0			0
$997$	27.2644			0.863471			0.431736	−	0.902000i	$-0.357901\pi$
$997$	27.2644			0.863471			0.431736	+	0.902000i	$0.357901\pi$
$998$		0			0
$999$	14.2901	+	38.8366i	0.452117	+	1.22874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.ba.a.329.66	yes	72
3.2	odd	2	inner	1320.2.ba.a.329.6	yes	72
5.4	even	2	inner	1320.2.ba.a.329.7	yes	72
11.10	odd	2	inner	1320.2.ba.a.329.65	yes	72
15.14	odd	2	inner	1320.2.ba.a.329.67	yes	72
33.32	even	2	inner	1320.2.ba.a.329.5	✓	72
55.54	odd	2	inner	1320.2.ba.a.329.8	yes	72
165.164	even	2	inner	1320.2.ba.a.329.68	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.ba.a.329.5	✓	72	33.32	even	2	inner
1320.2.ba.a.329.6	yes	72	3.2	odd	2	inner
1320.2.ba.a.329.7	yes	72	5.4	even	2	inner
1320.2.ba.a.329.8	yes	72	55.54	odd	2	inner
1320.2.ba.a.329.65	yes	72	11.10	odd	2	inner
1320.2.ba.a.329.66	yes	72	1.1	even	1	trivial
1320.2.ba.a.329.67	yes	72	15.14	odd	2	inner
1320.2.ba.a.329.68	yes	72	165.164	even	2	inner

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:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.ba (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72010 - 0.203093i) q^{3} +(0.910442 + 2.04233i) q^{5} +4.06802 q^{7} +(2.91751 - 0.698681i) q^{9} +(-3.04109 - 1.32355i) q^{11} +0.487030 q^{13} +(1.98084 + 3.32811i) q^{15} -6.71182i q^{17} -1.77760i q^{19} +(6.99741 - 0.826186i) q^{21} +4.87073 q^{23} +(-3.34219 + 3.71884i) q^{25} +(4.87651 - 1.79433i) q^{27} -1.32904 q^{29} +6.21817 q^{31} +(-5.49978 - 1.65903i) q^{33} +(3.70370 + 8.30822i) q^{35} +7.96402i q^{37} +(0.837742 - 0.0989123i) q^{39} -5.07398 q^{41} -4.68285 q^{43} +(4.08316 + 5.32239i) q^{45} -10.7188 q^{47} +9.54880 q^{49} +(-1.36312 - 11.5450i) q^{51} -9.51918 q^{53} +(-0.0656055 - 7.41591i) q^{55} +(-0.361018 - 3.05766i) q^{57} +5.13015i q^{59} +2.61817i q^{61} +(11.8685 - 2.84225i) q^{63} +(0.443413 + 0.994674i) q^{65} +8.52433i q^{67} +(8.37816 - 0.989210i) q^{69} +6.00972i q^{71} -0.708858 q^{73} +(-4.99364 + 7.07556i) q^{75} +(-12.3712 - 5.38424i) q^{77} +7.16015i q^{79} +(8.02369 - 4.07681i) q^{81} +13.8902i q^{83} +(13.7077 - 6.11072i) q^{85} +(-2.28609 + 0.269919i) q^{87} -15.9597i q^{89} +1.98125 q^{91} +(10.6959 - 1.26287i) q^{93} +(3.63044 - 1.61840i) q^{95} +0.844397i q^{97} +(-9.79713 - 1.73673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 6 q^{15} - 4 q^{25} + 34 q^{45} + 96 q^{49} - 28 q^{55} + 28 q^{69} + 14 q^{75} + 16 q^{81} - 48 q^{91} - 4 q^{99}+O(q^{100}) \) 72 * q - 6 * q^15 - 4 * q^25 + 34 * q^45 + 96 * q^49 - 28 * q^55 + 28 * q^69 + 14 * q^75 + 16 * q^81 - 48 * q^91 - 4 * q^99

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