LMFDB - Embedded newform 1600.2.j.e.1007.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(143,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("1600.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.j (of order $4$, degree $2$, not 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1007.1
Character	$\chi$	$=$	1600.1007
Dual form			1600.2.j.e.143.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.25766i q^{3} +(-2.54012 - 2.54012i) q^{7} -7.61238 q^{9} +O(q^{10})$	$q-3.25766i q^{3} +(-2.54012 - 2.54012i) q^{7} -7.61238 q^{9} +(0.462406 + 0.462406i) q^{11} +1.33473 q^{13} +(-2.37342 - 2.37342i) q^{17} +(-2.69776 - 2.69776i) q^{19} +(-8.27486 + 8.27486i) q^{21} +(2.10420 - 2.10420i) q^{23} +15.0256i q^{27} +(-1.97767 + 1.97767i) q^{29} +7.03054i q^{31} +(1.50636 - 1.50636i) q^{33} +7.81135 q^{37} -4.34811i q^{39} -2.17459i q^{41} -3.10070 q^{43} +(0.0727309 - 0.0727309i) q^{47} +5.90443i q^{49} +(-7.73182 + 7.73182i) q^{51} +0.719718i q^{53} +(-8.78840 + 8.78840i) q^{57} +(-8.67421 + 8.67421i) q^{59} +(-7.10027 - 7.10027i) q^{61} +(19.3364 + 19.3364i) q^{63} -10.8172 q^{67} +(-6.85476 - 6.85476i) q^{69} +15.3474 q^{71} +(-0.905052 - 0.905052i) q^{73} -2.34913i q^{77} +3.90167 q^{79} +26.1112 q^{81} +6.02206i q^{83} +(6.44260 + 6.44260i) q^{87} +7.46664 q^{89} +(-3.39038 - 3.39038i) q^{91} +22.9031 q^{93} +(-3.74551 - 3.74551i) q^{97} +(-3.52001 - 3.52001i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 40 q^{9}+O(q^{10}) $ 24 * q - 40 * q^9	$ 24 q - 40 q^{9} + 20 q^{11} + 12 q^{19} + 8 q^{29} - 20 q^{51} - 8 q^{59} - 48 q^{61} - 64 q^{69} + 16 q^{71} + 104 q^{79} + 48 q^{81} + 96 q^{89} - 64 q^{91} - 128 q^{99}+O(q^{100}) $ 24 * q - 40 * q^9 + 20 * q^11 + 12 * q^19 + 8 * q^29 - 20 * q^51 - 8 * q^59 - 48 * q^61 - 64 * q^69 + 16 * q^71 + 104 * q^79 + 48 * q^81 + 96 * q^89 - 64 * q^91 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$		−	3.25766i		−	1.88081i	−0.340052	−	0.940407i	$-0.610445\pi$
$3$		−	3.25766i		−	1.88081i	0.340052	−	0.940407i	$-0.389555\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.54012	−	2.54012i	−0.960075	−	0.960075i	0.0391576	−	0.999233i	$-0.487533\pi$
$7$	−2.54012	−	2.54012i	−0.960075	−	0.960075i	−0.999233	+	0.0391576i	$0.987533\pi$
$8$		0			0
$9$	−7.61238			−2.53746
$10$		0			0
$11$	0.462406	+	0.462406i	0.139421	+	0.139421i	0.773372	−	0.633952i	$-0.218568\pi$
$11$	0.462406	+	0.462406i	0.139421	+	0.139421i	−0.633952	+	0.773372i	$0.718568\pi$
$12$		0			0
$13$	1.33473			0.370188			0.185094	−	0.982721i	$-0.440741\pi$
$13$	1.33473			0.370188			0.185094	+	0.982721i	$0.440741\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.37342	−	2.37342i	−0.575640	−	0.575640i	0.358059	−	0.933699i	$-0.383439\pi$
$17$	−2.37342	−	2.37342i	−0.575640	−	0.575640i	−0.933699	+	0.358059i	$0.883439\pi$
$18$		0			0
$19$	−2.69776	−	2.69776i	−0.618909	−	0.618909i	0.326343	−	0.945251i	$-0.394184\pi$
$19$	−2.69776	−	2.69776i	−0.618909	−	0.618909i	−0.945251	+	0.326343i	$0.894184\pi$
$20$		0			0
$21$	−8.27486	+	8.27486i	−1.80572	+	1.80572i
$22$		0			0
$23$	2.10420	−	2.10420i	0.438755	−	0.438755i	−0.452838	−	0.891593i	$-0.649588\pi$
$23$	2.10420	−	2.10420i	0.438755	−	0.438755i	0.891593	+	0.452838i	$0.149588\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			15.0256i			2.89168i
$28$		0			0
$29$	−1.97767	+	1.97767i	−0.367245	+	0.367245i	−0.866471	−	0.499227i	$-0.833618\pi$
$29$	−1.97767	+	1.97767i	−0.367245	+	0.367245i	0.499227	+	0.866471i	$0.333618\pi$
$30$		0			0
$31$			7.03054i			1.26272i	0.775489	+	0.631361i	$0.217503\pi$
$31$			7.03054i			1.26272i	−0.775489	+	0.631361i	$0.782497\pi$
$32$		0			0
$33$	1.50636	−	1.50636i	0.262224	−	0.262224i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	7.81135			1.28418			0.642089	−	0.766630i	$-0.278068\pi$
$37$	7.81135			1.28418			0.642089	+	0.766630i	$0.278068\pi$
$38$		0			0
$39$		−	4.34811i		−	0.696255i
$40$		0			0
$41$		−	2.17459i		−	0.339614i	−0.985477	−	0.169807i	$-0.945686\pi$
$41$		−	2.17459i		−	0.339614i	0.985477	−	0.169807i	$-0.0543144\pi$
$42$		0			0
$43$	−3.10070			−0.472852			−0.236426	−	0.971650i	$-0.575976\pi$
$43$	−3.10070			−0.472852			−0.236426	+	0.971650i	$0.575976\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.0727309	−	0.0727309i	0.0106089	−	0.0106089i	−0.701782	−	0.712391i	$-0.747612\pi$
$47$	0.0727309	−	0.0727309i	0.0106089	−	0.0106089i	0.712391	+	0.701782i	$0.247612\pi$
$48$		0			0
$49$			5.90443i			0.843490i
$50$		0			0
$51$	−7.73182	+	7.73182i	−1.08267	+	1.08267i
$52$		0			0
$53$			0.719718i			0.0988609i	0.998778	+	0.0494304i	$0.0157406\pi$
$53$			0.719718i			0.0988609i	−0.998778	+	0.0494304i	$0.984259\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−8.78840	+	8.78840i	−1.16405	+	1.16405i
$58$		0			0
$59$	−8.67421	+	8.67421i	−1.12929	+	1.12929i	−0.138993	+	0.990293i	$0.544387\pi$
$59$	−8.67421	+	8.67421i	−1.12929	+	1.12929i	−0.990293	+	0.138993i	$0.955613\pi$
$60$		0			0
$61$	−7.10027	−	7.10027i	−0.909097	−	0.909097i	0.0871025	−	0.996199i	$-0.472239\pi$
$61$	−7.10027	−	7.10027i	−0.909097	−	0.909097i	−0.996199	+	0.0871025i	$0.972239\pi$
$62$		0			0
$63$	19.3364	+	19.3364i	2.43615	+	2.43615i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−10.8172			−1.32153			−0.660765	−	0.750593i	$-0.729768\pi$
$67$	−10.8172			−1.32153			−0.660765	+	0.750593i	$0.729768\pi$
$68$		0			0
$69$	−6.85476	−	6.85476i	−0.825217	−	0.825217i
$70$		0			0
$71$	15.3474			1.82140			0.910698	−	0.413072i	$-0.135544\pi$
$71$	15.3474			1.82140			0.910698	+	0.413072i	$0.135544\pi$
$72$		0			0
$73$	−0.905052	−	0.905052i	−0.105928	−	0.105928i	0.652156	−	0.758085i	$-0.273865\pi$
$73$	−0.905052	−	0.905052i	−0.105928	−	0.105928i	−0.758085	+	0.652156i	$0.773865\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	2.34913i		−	0.267709i
$78$		0			0
$79$	3.90167			0.438972			0.219486	−	0.975616i	$-0.429562\pi$
$79$	3.90167			0.438972			0.219486	+	0.975616i	$0.429562\pi$
$80$		0			0
$81$	26.1112			2.90124
$82$		0			0
$83$			6.02206i			0.661007i	0.943805	+	0.330503i	$0.107218\pi$
$83$			6.02206i			0.661007i	−0.943805	+	0.330503i	$0.892782\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.44260	+	6.44260i	0.690719	+	0.690719i
$88$		0			0
$89$	7.46664			0.791462			0.395731	−	0.918366i	$-0.370491\pi$
$89$	7.46664			0.791462			0.395731	+	0.918366i	$0.370491\pi$
$90$		0			0
$91$	−3.39038	−	3.39038i	−0.355408	−	0.355408i
$92$		0			0
$93$	22.9031			2.37494
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.74551	−	3.74551i	−0.380299	−	0.380299i	0.490911	−	0.871210i	$-0.336664\pi$
$97$	−3.74551	−	3.74551i	−0.380299	−	0.380299i	−0.871210	+	0.490911i	$0.836664\pi$
$98$		0			0
$99$	−3.52001	−	3.52001i	−0.353774	−	0.353774i
$100$		0			0
$101$	4.39232	−	4.39232i	0.437052	−	0.437052i	−0.453966	−	0.891019i	$-0.649991\pi$
$101$	4.39232	−	4.39232i	0.437052	−	0.437052i	0.891019	+	0.453966i	$0.149991\pi$
$102$		0			0
$103$	6.36518	−	6.36518i	0.627179	−	0.627179i	−0.320178	−	0.947357i	$-0.603743\pi$
$103$	6.36518	−	6.36518i	0.627179	−	0.627179i	0.947357	+	0.320178i	$0.103743\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	10.8172i		−	1.04574i	−0.852413	−	0.522869i	$-0.824862\pi$
$107$		−	10.8172i		−	1.04574i	0.852413	−	0.522869i	$-0.175138\pi$
$108$		0			0
$109$	−7.56691	+	7.56691i	−0.724779	+	0.724779i	−0.969575	−	0.244796i	$-0.921279\pi$
$109$	−7.56691	+	7.56691i	−0.724779	+	0.724779i	0.244796	+	0.969575i	$0.421279\pi$
$110$		0			0
$111$		−	25.4468i		−	2.41530i
$112$		0			0
$113$	−12.2142	+	12.2142i	−1.14902	+	1.14902i	−0.162270	+	0.986746i	$0.551882\pi$
$113$	−12.2142	+	12.2142i	−1.14902	+	1.14902i	−0.986746	+	0.162270i	$0.948118\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−10.1605			−0.939337
$118$		0			0
$119$			12.0576i			1.10532i
$120$		0			0
$121$		−	10.5724i		−	0.961124i
$122$		0			0
$123$	−7.08408			−0.638750
$124$		0			0
$125$		0			0
$126$		0			0
$127$	8.98272	−	8.98272i	0.797087	−	0.797087i	−0.185548	−	0.982635i	$-0.559406\pi$
$127$	8.98272	−	8.98272i	0.797087	−	0.797087i	0.982635	+	0.185548i	$0.0594059\pi$
$128$		0			0
$129$			10.1010i			0.889346i
$130$		0			0
$131$	5.01718	−	5.01718i	0.438353	−	0.438353i	−0.453104	−	0.891458i	$-0.649683\pi$
$131$	5.01718	−	5.01718i	0.438353	−	0.438353i	0.891458	+	0.453104i	$0.149683\pi$
$132$		0			0
$133$			13.7053i			1.18840i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.21068	−	3.21068i	0.274307	−	0.274307i	−0.556524	−	0.830831i	$-0.687865\pi$
$137$	3.21068	−	3.21068i	0.274307	−	0.274307i	0.830831	+	0.556524i	$0.187865\pi$
$138$		0			0
$139$	−0.102562	+	0.102562i	−0.00869923	+	0.00869923i	−0.711443	−	0.702744i	$-0.751958\pi$
$139$	−0.102562	+	0.102562i	−0.00869923	+	0.00869923i	0.702744	+	0.711443i	$0.251958\pi$
$140$		0			0
$141$	−0.236933	−	0.236933i	−0.0199533	−	0.0199533i
$142$		0			0
$143$	0.617188	+	0.617188i	0.0516118	+	0.0516118i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	19.2346			1.58645
$148$		0			0
$149$	−2.12805	−	2.12805i	−0.174337	−	0.174337i	0.614545	−	0.788882i	$-0.289340\pi$
$149$	−2.12805	−	2.12805i	−0.174337	−	0.174337i	−0.788882	+	0.614545i	$0.789340\pi$
$150$		0			0
$151$	−21.6723			−1.76366			−0.881832	−	0.471564i	$-0.843690\pi$
$151$	−21.6723			−1.76366			−0.881832	+	0.471564i	$0.843690\pi$
$152$		0			0
$153$	18.0674	+	18.0674i	1.46066	+	1.46066i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			17.3539i			1.38499i	0.721421	+	0.692496i	$0.243489\pi$
$157$			17.3539i			1.38499i	−0.721421	+	0.692496i	$0.756511\pi$
$158$		0			0
$159$	2.34460			0.185939
$160$		0			0
$161$	−10.6898			−0.842476
$162$		0			0
$163$		−	6.29032i		−	0.492696i	−0.969181	−	0.246348i	$-0.920769\pi$
$163$		−	6.29032i		−	0.492696i	0.969181	−	0.246348i	$-0.0792306\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.61495	−	6.61495i	−0.511880	−	0.511880i	0.403222	−	0.915102i	$-0.367890\pi$
$167$	−6.61495	−	6.61495i	−0.511880	−	0.511880i	−0.915102	+	0.403222i	$0.867890\pi$
$168$		0			0
$169$	−11.2185			−0.862961
$170$		0			0
$171$	20.5364	+	20.5364i	1.57046	+	1.57046i
$172$		0			0
$173$	−0.857921			−0.0652265			−0.0326133	−	0.999468i	$-0.510383\pi$
$173$	−0.857921			−0.0652265			−0.0326133	+	0.999468i	$0.510383\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	28.2577	+	28.2577i	2.12398	+	2.12398i
$178$		0			0
$179$	−0.571652	−	0.571652i	−0.0427273	−	0.0427273i	0.685420	−	0.728148i	$-0.259618\pi$
$179$	−0.571652	−	0.571652i	−0.0427273	−	0.0427273i	−0.728148	+	0.685420i	$0.759618\pi$
$180$		0			0
$181$	−10.3879	+	10.3879i	−0.772130	+	0.772130i	−0.978478	−	0.206349i	$-0.933842\pi$
$181$	−10.3879	+	10.3879i	−0.772130	+	0.772130i	0.206349	+	0.978478i	$0.433842\pi$
$182$		0			0
$183$	−23.1303	+	23.1303i	−1.70984	+	1.70984i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		−	2.19497i		−	0.160512i
$188$		0			0
$189$	38.1668	−	38.1668i	2.77623	−	2.77623i
$190$		0			0
$191$		−	22.5293i		−	1.63017i	−0.579344	−	0.815083i	$-0.696691\pi$
$191$		−	22.5293i		−	1.63017i	0.579344	−	0.815083i	$-0.303309\pi$
$192$		0			0
$193$	−7.95941	+	7.95941i	−0.572931	+	0.572931i	−0.932946	−	0.360015i	$-0.882771\pi$
$193$	−7.95941	+	7.95941i	−0.572931	+	0.572931i	0.360015	+	0.932946i	$0.382771\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−17.5546			−1.25071			−0.625357	−	0.780338i	$-0.715047\pi$
$197$	−17.5546			−1.25071			−0.625357	+	0.780338i	$0.715047\pi$
$198$		0			0
$199$			18.7910i			1.33206i	0.745924	+	0.666031i	$0.232008\pi$
$199$			18.7910i			1.33206i	−0.745924	+	0.666031i	$0.767992\pi$
$200$		0			0
$201$			35.2388i			2.48555i
$202$		0			0
$203$	10.0471			0.705165
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−16.0179	+	16.0179i	−1.11332	+	1.11332i
$208$		0			0
$209$		−	2.49492i		−	0.172577i
$210$		0			0
$211$	−9.00592	+	9.00592i	−0.619993	+	0.619993i	−0.945530	−	0.325536i	$-0.894455\pi$
$211$	−9.00592	+	9.00592i	−0.619993	+	0.619993i	0.325536	+	0.945530i	$0.394455\pi$
$212$		0			0
$213$		−	49.9965i		−	3.42571i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	17.8584	−	17.8584i	1.21231	−	1.21231i
$218$		0			0
$219$	−2.94836	+	2.94836i	−0.199232	+	0.199232i
$220$		0			0
$221$	−3.16788	−	3.16788i	−0.213095	−	0.213095i
$222$		0			0
$223$	−9.16630	−	9.16630i	−0.613821	−	0.613821i	0.330119	−	0.943939i	$-0.392911\pi$
$223$	−9.16630	−	9.16630i	−0.613821	−	0.613821i	−0.943939	+	0.330119i	$0.892911\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−21.2474			−1.41024			−0.705120	−	0.709088i	$-0.749107\pi$
$227$	−21.2474			−1.41024			−0.705120	+	0.709088i	$0.749107\pi$
$228$		0			0
$229$	14.0502	+	14.0502i	0.928461	+	0.928461i	0.997607	−	0.0691452i	$-0.0220272\pi$
$229$	14.0502	+	14.0502i	0.928461	+	0.928461i	−0.0691452	+	0.997607i	$0.522027\pi$
$230$		0			0
$231$	−7.65269			−0.503510
$232$		0			0
$233$	−19.7571	−	19.7571i	−1.29433	−	1.29433i	−0.932083	−	0.362244i	$-0.882011\pi$
$233$	−19.7571	−	19.7571i	−1.29433	−	1.29433i	−0.362244	−	0.932083i	$-0.617989\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	12.7103i		−	0.825625i
$238$		0			0
$239$	−1.51630			−0.0980814			−0.0490407	−	0.998797i	$-0.515616\pi$
$239$	−1.51630			−0.0980814			−0.0490407	+	0.998797i	$0.515616\pi$
$240$		0			0
$241$	5.91616			0.381094			0.190547	−	0.981678i	$-0.438974\pi$
$241$	5.91616			0.381094			0.190547	+	0.981678i	$0.438974\pi$
$242$		0			0
$243$		−	39.9847i		−	2.56502i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.60079	−	3.60079i	−0.229112	−	0.229112i
$248$		0			0
$249$	19.6178			1.24323
$250$		0			0
$251$	11.8723	+	11.8723i	0.749376	+	0.749376i	0.974362	−	0.224986i	$-0.0722336\pi$
$251$	11.8723	+	11.8723i	0.749376	+	0.749376i	−0.224986	+	0.974362i	$0.572234\pi$
$252$		0			0
$253$	1.94598			0.122343
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.39452	−	8.39452i	−0.523636	−	0.523636i	0.395032	−	0.918667i	$-0.370734\pi$
$257$	−8.39452	−	8.39452i	−0.523636	−	0.523636i	−0.918667	+	0.395032i	$0.870734\pi$
$258$		0			0
$259$	−19.8418	−	19.8418i	−1.23291	−	1.23291i
$260$		0			0
$261$	15.0548	−	15.0548i	0.931869	−	0.931869i
$262$		0			0
$263$	10.8623	−	10.8623i	0.669798	−	0.669798i	−0.287871	−	0.957669i	$-0.592947\pi$
$263$	10.8623	−	10.8623i	0.669798	−	0.669798i	0.957669	+	0.287871i	$0.0929474\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	24.3238i		−	1.48859i
$268$		0			0
$269$	−12.9373	+	12.9373i	−0.788804	+	0.788804i	−0.981298	−	0.192494i	$-0.938342\pi$
$269$	−12.9373	+	12.9373i	−0.788804	+	0.788804i	0.192494	+	0.981298i	$0.438342\pi$
$270$		0			0
$271$		−	1.44017i		−	0.0874842i	−0.999043	−	0.0437421i	$-0.986072\pi$
$271$		−	1.44017i		−	0.0874842i	0.999043	−	0.0437421i	$-0.0139280\pi$
$272$		0			0
$273$	−11.0447	+	11.0447i	−0.668457	+	0.668457i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−13.0758			−0.785647			−0.392823	−	0.919614i	$-0.628502\pi$
$277$	−13.0758			−0.785647			−0.392823	+	0.919614i	$0.628502\pi$
$278$		0			0
$279$		−	53.5191i		−	3.20411i
$280$		0			0
$281$			6.00639i			0.358311i	0.983821	+	0.179156i	$0.0573366\pi$
$281$			6.00639i			0.358311i	−0.983821	+	0.179156i	$0.942663\pi$
$282$		0			0
$283$	0.542533			0.0322502			0.0161251	−	0.999870i	$-0.494867\pi$
$283$	0.542533			0.0322502			0.0161251	+	0.999870i	$0.494867\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.52372	+	5.52372i	−0.326055	+	0.326055i
$288$		0			0
$289$		−	5.73372i		−	0.337278i
$290$		0			0
$291$	−12.2016	+	12.2016i	−0.715271	+	0.715271i
$292$		0			0
$293$		−	26.6018i		−	1.55409i	−0.629443	−	0.777046i	$-0.716717\pi$
$293$		−	26.6018i		−	1.55409i	0.629443	−	0.777046i	$-0.283283\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−6.94792	+	6.94792i	−0.403159	+	0.403159i
$298$		0			0
$299$	2.80854	−	2.80854i	0.162422	−	0.162422i
$300$		0			0
$301$	7.87615	+	7.87615i	0.453973	+	0.453973i
$302$		0			0
$303$	−14.3087	−	14.3087i	−0.822014	−	0.822014i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	6.72156			0.383619			0.191810	−	0.981432i	$-0.438564\pi$
$307$	6.72156			0.383619			0.191810	+	0.981432i	$0.438564\pi$
$308$		0			0
$309$	−20.7356	−	20.7356i	−1.17961	−	1.17961i
$310$		0			0
$311$	−0.636143			−0.0360723			−0.0180362	−	0.999837i	$-0.505741\pi$
$311$	−0.636143			−0.0360723			−0.0180362	+	0.999837i	$0.505741\pi$
$312$		0			0
$313$	0.109268	+	0.109268i	0.00617619	+	0.00617619i	0.710188	−	0.704012i	$-0.248610\pi$
$313$	0.109268	+	0.109268i	0.00617619	+	0.00617619i	−0.704012	+	0.710188i	$0.748610\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	34.6913i		−	1.94846i	−0.225566	−	0.974228i	$-0.572423\pi$
$317$		−	34.6913i		−	1.94846i	0.225566	−	0.974228i	$-0.427577\pi$
$318$		0			0
$319$	−1.82898			−0.102403
$320$		0			0
$321$	−35.2388			−1.96684
$322$		0			0
$323$			12.8059i			0.712537i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	24.6505	+	24.6505i	1.36317	+	1.36317i
$328$		0			0
$329$	−0.369490			−0.0203707
$330$		0			0
$331$	−7.51089	−	7.51089i	−0.412836	−	0.412836i	0.469890	−	0.882725i	$-0.344294\pi$
$331$	−7.51089	−	7.51089i	−0.412836	−	0.412836i	−0.882725	+	0.469890i	$0.844294\pi$
$332$		0			0
$333$	−59.4630			−3.25855
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−6.00053	−	6.00053i	−0.326870	−	0.326870i	0.524525	−	0.851395i	$-0.324243\pi$
$337$	−6.00053	−	6.00053i	−0.326870	−	0.326870i	−0.851395	+	0.524525i	$0.824243\pi$
$338$		0			0
$339$	39.7898	+	39.7898i	2.16109	+	2.16109i
$340$		0			0
$341$	−3.25096	+	3.25096i	−0.176049	+	0.176049i
$342$		0			0
$343$	−2.78289	+	2.78289i	−0.150262	+	0.150262i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	23.5337i		−	1.26336i	−0.775231	−	0.631678i	$-0.782366\pi$
$347$		−	23.5337i		−	1.26336i	0.775231	−	0.631678i	$-0.217634\pi$
$348$		0			0
$349$	−14.4715	+	14.4715i	−0.774643	+	0.774643i	−0.978914	−	0.204271i	$-0.934518\pi$
$349$	−14.4715	+	14.4715i	−0.774643	+	0.774643i	0.204271	+	0.978914i	$0.434518\pi$
$350$		0			0
$351$			20.0551i			1.07046i
$352$		0			0
$353$	20.4898	−	20.4898i	1.09056	−	1.09056i	0.0950957	−	0.995468i	$-0.469684\pi$
$353$	20.4898	−	20.4898i	1.09056	−	1.09056i	0.995468	−	0.0950957i	$-0.0303157\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	39.2795			2.07889
$358$		0			0
$359$			9.83355i			0.518995i	0.965744	+	0.259498i	$0.0835570\pi$
$359$			9.83355i			0.518995i	−0.965744	+	0.259498i	$0.916443\pi$
$360$		0			0
$361$		−	4.44419i		−	0.233905i
$362$		0			0
$363$	−34.4412			−1.80769
$364$		0			0
$365$		0			0
$366$		0			0
$367$	25.2123	−	25.2123i	1.31607	−	1.31607i	0.399214	−	0.916858i	$-0.369283\pi$
$367$	25.2123	−	25.2123i	1.31607	−	1.31607i	0.916858	−	0.399214i	$-0.130717\pi$
$368$		0			0
$369$			16.5538i			0.861756i
$370$		0			0
$371$	1.82817	−	1.82817i	0.0949139	−	0.0949139i
$372$		0			0
$373$			15.6020i			0.807839i	0.914794	+	0.403920i	$0.132352\pi$
$373$			15.6020i			0.807839i	−0.914794	+	0.403920i	$0.867648\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.63966	+	2.63966i	−0.135950	+	0.135950i
$378$		0			0
$379$	11.1868	−	11.1868i	0.574627	−	0.574627i	−0.358791	−	0.933418i	$-0.616811\pi$
$379$	11.1868	−	11.1868i	0.574627	−	0.574627i	0.933418	+	0.358791i	$0.116811\pi$
$380$		0			0
$381$	−29.2627	−	29.2627i	−1.49917	−	1.49917i
$382$		0			0
$383$	−11.3975	−	11.3975i	−0.582386	−	0.582386i	0.353172	−	0.935558i	$-0.385103\pi$
$383$	−11.3975	−	11.3975i	−0.582386	−	0.582386i	−0.935558	+	0.353172i	$0.885103\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	23.6037			1.19984
$388$		0			0
$389$	−11.8767	−	11.8767i	−0.602170	−	0.602170i	0.338718	−	0.940888i	$-0.390007\pi$
$389$	−11.8767	−	11.8767i	−0.602170	−	0.602170i	−0.940888	+	0.338718i	$0.890007\pi$
$390$		0			0
$391$	−9.98829			−0.505130
$392$		0			0
$393$	−16.3443	−	16.3443i	−0.824461	−	0.824461i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			16.0768i			0.806870i	0.915008	+	0.403435i	$0.132184\pi$
$397$			16.0768i			0.806870i	−0.915008	+	0.403435i	$0.867816\pi$
$398$		0			0
$399$	44.6472			2.23515
$400$		0			0
$401$	21.8966			1.09346			0.546731	−	0.837308i	$-0.315872\pi$
$401$	21.8966			1.09346			0.546731	+	0.837308i	$0.315872\pi$
$402$		0			0
$403$			9.38388i			0.467444i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.61201	+	3.61201i	0.179041	+	0.179041i
$408$		0			0
$409$	20.1426			0.995987			0.497993	−	0.867181i	$-0.334070\pi$
$409$	20.1426			0.995987			0.497993	+	0.867181i	$0.334070\pi$
$410$		0			0
$411$	−10.4593	−	10.4593i	−0.515921	−	0.515921i
$412$		0			0
$413$	44.0671			2.16840
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.334114	+	0.334114i	0.0163616	+	0.0163616i
$418$		0			0
$419$	−2.87077	−	2.87077i	−0.140246	−	0.140246i	0.633498	−	0.773744i	$-0.281619\pi$
$419$	−2.87077	−	2.87077i	−0.140246	−	0.140246i	−0.773744	+	0.633498i	$0.781619\pi$
$420$		0			0
$421$	12.9834	−	12.9834i	0.632774	−	0.632774i	−0.315989	−	0.948763i	$-0.602336\pi$
$421$	12.9834	−	12.9834i	0.632774	−	0.632774i	0.948763	+	0.315989i	$0.102336\pi$
$422$		0			0
$423$	−0.553655	+	0.553655i	−0.0269196	+	0.0269196i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			36.0711i			1.74560i
$428$		0			0
$429$	2.01059	−	2.01059i	0.0970722	−	0.0970722i
$430$		0			0
$431$			11.2042i			0.539686i	0.962904	+	0.269843i	$0.0869719\pi$
$431$			11.2042i			0.539686i	−0.962904	+	0.269843i	$0.913028\pi$
$432$		0			0
$433$	−20.8634	+	20.8634i	−1.00263	+	1.00263i	−0.00263391	+	0.999997i	$0.500838\pi$
$433$	−20.8634	+	20.8634i	−1.00263	+	1.00263i	−0.999997	+	0.00263391i	$0.999162\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−11.3532			−0.543099
$438$		0			0
$439$			26.6495i			1.27191i	0.771726	+	0.635956i	$0.219394\pi$
$439$			26.6495i			1.27191i	−0.771726	+	0.635956i	$0.780606\pi$
$440$		0			0
$441$		−	44.9467i		−	2.14032i
$442$		0			0
$443$	5.97706			0.283979			0.141989	−	0.989868i	$-0.454650\pi$
$443$	5.97706			0.283979			0.141989	+	0.989868i	$0.454650\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−6.93247	+	6.93247i	−0.327895	+	0.327895i
$448$		0			0
$449$		−	29.5495i		−	1.39453i	−0.716814	−	0.697264i	$-0.754400\pi$
$449$		−	29.5495i		−	1.39453i	0.716814	−	0.697264i	$-0.245600\pi$
$450$		0			0
$451$	1.00554	−	1.00554i	0.0473492	−	0.0473492i
$452$		0			0
$453$			70.6010i			3.31712i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	19.1813	−	19.1813i	0.897262	−	0.897262i	−0.0979311	−	0.995193i	$-0.531222\pi$
$457$	19.1813	−	19.1813i	0.897262	−	0.897262i	0.995193	+	0.0979311i	$0.0312225\pi$
$458$		0			0
$459$	35.6621	−	35.6621i	1.66456	−	1.66456i
$460$		0			0
$461$	18.3016	+	18.3016i	0.852390	+	0.852390i	0.990427	−	0.138037i	$-0.0440794\pi$
$461$	18.3016	+	18.3016i	0.852390	+	0.852390i	−0.138037	+	0.990427i	$0.544079\pi$
$462$		0			0
$463$	2.71513	+	2.71513i	0.126183	+	0.126183i	0.767378	−	0.641195i	$-0.221561\pi$
$463$	2.71513	+	2.71513i	0.126183	+	0.126183i	−0.641195	+	0.767378i	$0.721561\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−27.1096			−1.25448			−0.627241	−	0.778826i	$-0.715816\pi$
$467$	−27.1096			−1.25448			−0.627241	+	0.778826i	$0.715816\pi$
$468$		0			0
$469$	27.4770	+	27.4770i	1.26877	+	1.26877i
$470$		0			0
$471$	56.5332			2.60491
$472$		0			0
$473$	−1.43378	−	1.43378i	−0.0659253	−	0.0659253i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	5.47877i		−	0.250855i
$478$		0			0
$479$	8.86610			0.405102			0.202551	−	0.979272i	$-0.435077\pi$
$479$	8.86610			0.405102			0.202551	+	0.979272i	$0.435077\pi$
$480$		0			0
$481$	10.4261			0.475387
$482$		0			0
$483$			34.8239i			1.58454i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−8.24646	−	8.24646i	−0.373683	−	0.373683i	0.495134	−	0.868817i	$-0.335119\pi$
$487$	−8.24646	−	8.24646i	−0.373683	−	0.373683i	−0.868817	+	0.495134i	$0.835119\pi$
$488$		0			0
$489$	−20.4918			−0.926670
$490$		0			0
$491$	−23.4901	−	23.4901i	−1.06010	−	1.06010i	−0.998075	−	0.0620205i	$-0.980246\pi$
$491$	−23.4901	−	23.4901i	−1.06010	−	1.06010i	−0.0620205	−	0.998075i	$-0.519754\pi$
$492$		0			0
$493$	9.38771			0.422801
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−38.9841	−	38.9841i	−1.74868	−	1.74868i
$498$		0			0
$499$	−15.8371	−	15.8371i	−0.708965	−	0.708965i	0.257353	−	0.966317i	$-0.417150\pi$
$499$	−15.8371	−	15.8371i	−0.708965	−	0.708965i	−0.966317	+	0.257353i	$0.917150\pi$
$500$		0			0
$501$	−21.5493	+	21.5493i	−0.962751	+	0.962751i
$502$		0			0
$503$	16.4080	−	16.4080i	0.731597	−	0.731597i	−0.239339	−	0.970936i	$-0.576931\pi$
$503$	16.4080	−	16.4080i	0.731597	−	0.731597i	0.970936	+	0.239339i	$0.0769307\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			36.5461i			1.62307i
$508$		0			0
$509$	0.698178	−	0.698178i	0.0309462	−	0.0309462i	−0.691464	−	0.722411i	$-0.743034\pi$
$509$	0.698178	−	0.698178i	0.0309462	−	0.0309462i	0.722411	+	0.691464i	$0.243034\pi$
$510$		0			0
$511$			4.59789i			0.203398i
$512$		0			0
$513$	40.5354	−	40.5354i	1.78968	−	1.78968i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.0672624			0.00295819
$518$		0			0
$519$			2.79482i			0.122679i
$520$		0			0
$521$		−	24.0336i		−	1.05293i	−0.850196	−	0.526466i	$-0.823517\pi$
$521$		−	24.0336i		−	1.05293i	0.850196	−	0.526466i	$-0.176483\pi$
$522$		0			0
$523$	−21.7876			−0.952705			−0.476353	−	0.879254i	$-0.658041\pi$
$523$	−21.7876			−0.952705			−0.476353	+	0.879254i	$0.658041\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	16.6864	−	16.6864i	0.726873	−	0.726873i
$528$		0			0
$529$			14.1447i			0.614988i
$530$		0			0
$531$	66.0314	−	66.0314i	2.86552	−	2.86552i
$532$		0			0
$533$		−	2.90249i		−	0.125721i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.86225	+	1.86225i	−0.0803620	+	0.0803620i
$538$		0			0
$539$	−2.73024	+	2.73024i	−0.117600	+	0.117600i
$540$		0			0
$541$	12.1010	+	12.1010i	0.520264	+	0.520264i	0.917651	−	0.397387i	$-0.130083\pi$
$541$	12.1010	+	12.1010i	0.520264	+	0.520264i	−0.397387	+	0.917651i	$0.630083\pi$
$542$		0			0
$543$	33.8404	+	33.8404i	1.45223	+	1.45223i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	27.3827			1.17080			0.585399	−	0.810745i	$-0.300938\pi$
$547$	27.3827			1.17080			0.585399	+	0.810745i	$0.300938\pi$
$548$		0			0
$549$	54.0500	+	54.0500i	2.30680	+	2.30680i
$550$		0			0
$551$	10.6706			0.454582
$552$		0			0
$553$	−9.91071	−	9.91071i	−0.421446	−	0.421446i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			18.8103i			0.797018i	0.917164	+	0.398509i	$0.130472\pi$
$557$			18.8103i			0.797018i	−0.917164	+	0.398509i	$0.869528\pi$
$558$		0			0
$559$	−4.13860			−0.175044
$560$		0			0
$561$	−7.15048			−0.301893
$562$		0			0
$563$		−	4.43590i		−	0.186951i	−0.995622	−	0.0934755i	$-0.970202\pi$
$563$		−	4.43590i		−	0.186951i	0.995622	−	0.0934755i	$-0.0297977\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−66.3256	−	66.3256i	−2.78541	−	2.78541i
$568$		0			0
$569$	8.76043			0.367256			0.183628	−	0.982996i	$-0.441216\pi$
$569$	8.76043			0.367256			0.183628	+	0.982996i	$0.441216\pi$
$570$		0			0
$571$	4.44131	+	4.44131i	0.185863	+	0.185863i	0.793905	−	0.608042i	$-0.208045\pi$
$571$	4.44131	+	4.44131i	0.185863	+	0.185863i	−0.608042	+	0.793905i	$0.708045\pi$
$572$		0			0
$573$	−73.3930			−3.06604
$574$		0			0
$575$		0			0
$576$		0			0
$577$	9.25383	+	9.25383i	0.385242	+	0.385242i	0.872986	−	0.487745i	$-0.162180\pi$
$577$	9.25383	+	9.25383i	0.385242	+	0.385242i	−0.487745	+	0.872986i	$0.662180\pi$
$578$		0			0
$579$	25.9291	+	25.9291i	1.07758	+	1.07758i
$580$		0			0
$581$	15.2968	−	15.2968i	0.634616	−	0.634616i
$582$		0			0
$583$	−0.332802	+	0.332802i	−0.0137832	+	0.0137832i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			21.9676i			0.906700i	0.891333	+	0.453350i	$0.149771\pi$
$587$			21.9676i			0.906700i	−0.891333	+	0.453350i	$0.850229\pi$
$588$		0			0
$589$	18.9667	−	18.9667i	0.781509	−	0.781509i
$590$		0			0
$591$			57.1871i			2.35236i
$592$		0			0
$593$	9.10461	−	9.10461i	0.373881	−	0.373881i	−0.495007	−	0.868889i	$-0.664835\pi$
$593$	9.10461	−	9.10461i	0.373881	−	0.373881i	0.868889	+	0.495007i	$0.164835\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	61.2149			2.50536
$598$		0			0
$599$		−	28.3551i		−	1.15856i	−0.815130	−	0.579279i	$-0.803334\pi$
$599$		−	28.3551i		−	1.15856i	0.815130	−	0.579279i	$-0.196666\pi$
$600$		0			0
$601$		−	40.3072i		−	1.64417i	−0.569368	−	0.822083i	$-0.692812\pi$
$601$		−	40.3072i		−	1.64417i	0.569368	−	0.822083i	$-0.307188\pi$
$602$		0			0
$603$	82.3446			3.35333
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−33.3427	+	33.3427i	−1.35334	+	1.35334i	−0.471442	+	0.881897i	$0.656266\pi$
$607$	−33.3427	+	33.3427i	−1.35334	+	1.35334i	−0.881897	+	0.471442i	$0.843734\pi$
$608$		0			0
$609$		−	32.7300i		−	1.32628i
$610$		0			0
$611$	0.0970762	−	0.0970762i	0.00392728	−	0.00392728i
$612$		0			0
$613$			22.1895i			0.896227i	0.893977	+	0.448113i	$0.147904\pi$
$613$			22.1895i			0.896227i	−0.893977	+	0.448113i	$0.852096\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.7719	+	15.7719i	−0.634954	+	0.634954i	−0.949306	−	0.314353i	$-0.898213\pi$
$617$	−15.7719	+	15.7719i	−0.634954	+	0.634954i	0.314353	+	0.949306i	$0.398213\pi$
$618$		0			0
$619$	−5.07600	+	5.07600i	−0.204022	+	0.204022i	−0.801721	−	0.597699i	$-0.796082\pi$
$619$	−5.07600	+	5.07600i	−0.204022	+	0.204022i	0.597699	+	0.801721i	$0.296082\pi$
$620$		0			0
$621$	31.6168	+	31.6168i	1.26874	+	1.26874i
$622$		0			0
$623$	−18.9662	−	18.9662i	−0.759863	−	0.759863i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−8.12761			−0.324586
$628$		0			0
$629$	−18.5396	−	18.5396i	−0.739224	−	0.739224i
$630$		0			0
$631$	−31.2617			−1.24451			−0.622254	−	0.782816i	$-0.713783\pi$
$631$	−31.2617			−1.24451			−0.622254	+	0.782816i	$0.713783\pi$
$632$		0			0
$633$	29.3383	+	29.3383i	1.16609	+	1.16609i
$634$		0			0
$635$		0			0
$636$		0			0
$637$			7.88083i			0.312250i
$638$		0			0
$639$	−116.830			−4.62172
$640$		0			0
$641$	−4.38681			−0.173269			−0.0866343	−	0.996240i	$-0.527611\pi$
$641$	−4.38681			−0.173269			−0.0866343	+	0.996240i	$0.527611\pi$
$642$		0			0
$643$			28.1726i			1.11102i	0.831511	+	0.555509i	$0.187476\pi$
$643$			28.1726i			1.11102i	−0.831511	+	0.555509i	$0.812524\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.3260	+	13.3260i	0.523900	+	0.523900i	0.918747	−	0.394847i	$-0.129202\pi$
$647$	13.3260	+	13.3260i	0.523900	+	0.523900i	−0.394847	+	0.918747i	$0.629202\pi$
$648$		0			0
$649$	−8.02201			−0.314892
$650$		0			0
$651$	−58.1767	−	58.1767i	−2.28013	−	2.28013i
$652$		0			0
$653$	3.61001			0.141271			0.0706354	−	0.997502i	$-0.477497\pi$
$653$	3.61001			0.141271			0.0706354	+	0.997502i	$0.477497\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	6.88960	+	6.88960i	0.268789	+	0.268789i
$658$		0			0
$659$	−10.6066	−	10.6066i	−0.413173	−	0.413173i	0.469669	−	0.882842i	$-0.344373\pi$
$659$	−10.6066	−	10.6066i	−0.413173	−	0.413173i	−0.882842	+	0.469669i	$0.844373\pi$
$660$		0			0
$661$	−14.7397	+	14.7397i	−0.573307	+	0.573307i	−0.933051	−	0.359744i	$-0.882864\pi$
$661$	−14.7397	+	14.7397i	−0.573307	+	0.573307i	0.359744	+	0.933051i	$0.382864\pi$
$662$		0			0
$663$	−10.3199	+	10.3199i	−0.400792	+	0.400792i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			8.32282i			0.322261i
$668$		0			0
$669$	−29.8607	+	29.8607i	−1.15448	+	1.15448i
$670$		0			0
$671$		−	6.56642i		−	0.253494i
$672$		0			0
$673$	−1.21655	+	1.21655i	−0.0468946	+	0.0468946i	−0.730165	−	0.683271i	$-0.760557\pi$
$673$	−1.21655	+	1.21655i	−0.0468946	+	0.0468946i	0.683271	+	0.730165i	$0.260557\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	29.4713			1.13267			0.566337	−	0.824174i	$-0.308360\pi$
$677$	29.4713			1.13267			0.566337	+	0.824174i	$0.308360\pi$
$678$		0			0
$679$			19.0281i			0.730231i
$680$		0			0
$681$			69.2169i			2.65240i
$682$		0			0
$683$	−45.5003			−1.74102			−0.870510	−	0.492151i	$-0.836211\pi$
$683$	−45.5003			−1.74102			−0.870510	+	0.492151i	$0.836211\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	45.7707	−	45.7707i	1.74626	−	1.74626i
$688$		0			0
$689$			0.960630i			0.0365971i
$690$		0			0
$691$	−21.4526	+	21.4526i	−0.816096	+	0.816096i	−0.985540	−	0.169444i	$-0.945803\pi$
$691$	−21.4526	+	21.4526i	−0.816096	+	0.816096i	0.169444	+	0.985540i	$0.445803\pi$
$692$		0			0
$693$			17.8825i			0.679300i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−5.16122	+	5.16122i	−0.195495	+	0.195495i
$698$		0			0
$699$	−64.3618	+	64.3618i	−2.43439	+	2.43439i
$700$		0			0
$701$	−17.4263	−	17.4263i	−0.658183	−	0.658183i	0.296767	−	0.954950i	$-0.404091\pi$
$701$	−17.4263	−	17.4263i	−0.658183	−	0.658183i	−0.954950	+	0.296767i	$0.904091\pi$
$702$		0			0
$703$	−21.0731	−	21.0731i	−0.794789	−	0.794789i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−22.3141			−0.839207
$708$		0			0
$709$	−14.0431	−	14.0431i	−0.527401	−	0.527401i	0.392396	−	0.919796i	$-0.371646\pi$
$709$	−14.0431	−	14.0431i	−0.527401	−	0.527401i	−0.919796	+	0.392396i	$0.871646\pi$
$710$		0			0
$711$	−29.7010			−1.11387
$712$		0			0
$713$	14.7936	+	14.7936i	0.554025	+	0.554025i
$714$		0			0
$715$		0			0
$716$		0			0
$717$			4.93960i			0.184473i
$718$		0			0
$719$	36.8139			1.37293			0.686463	−	0.727165i	$-0.259162\pi$
$719$	36.8139			1.37293			0.686463	+	0.727165i	$0.259162\pi$
$720$		0			0
$721$	−32.3366			−1.20428
$722$		0			0
$723$		−	19.2729i		−	0.716766i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	21.9475	+	21.9475i	0.813989	+	0.813989i	0.985229	−	0.171240i	$-0.0547775\pi$
$727$	21.9475	+	21.9475i	0.813989	+	0.813989i	−0.171240	+	0.985229i	$0.554778\pi$
$728$		0			0
$729$	−51.9233			−1.92308
$730$		0			0
$731$	7.35927	+	7.35927i	0.272192	+	0.272192i
$732$		0			0
$733$	34.2145			1.26374			0.631870	−	0.775074i	$-0.282288\pi$
$733$	34.2145			1.26374			0.631870	+	0.775074i	$0.282288\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.00193	−	5.00193i	−0.184249	−	0.184249i
$738$		0			0
$739$	−5.64086	−	5.64086i	−0.207502	−	0.207502i	0.595703	−	0.803205i	$-0.296874\pi$
$739$	−5.64086	−	5.64086i	−0.207502	−	0.207502i	−0.803205	+	0.595703i	$0.796874\pi$
$740$		0			0
$741$	−11.7302	+	11.7302i	−0.430918	+	0.430918i
$742$		0			0
$743$	0.765980	−	0.765980i	0.0281011	−	0.0281011i	−0.692917	−	0.721018i	$-0.743675\pi$
$743$	0.765980	−	0.765980i	0.0281011	−	0.0281011i	0.721018	+	0.692917i	$0.243675\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	45.8422i		−	1.67728i
$748$		0			0
$749$	−27.4770	+	27.4770i	−1.00399	+	1.00399i
$750$		0			0
$751$			9.66983i			0.352857i	0.984313	+	0.176429i	$0.0564544\pi$
$751$			9.66983i			0.352857i	−0.984313	+	0.176429i	$0.943546\pi$
$752$		0			0
$753$	38.6761	−	38.6761i	1.40944	−	1.40944i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−4.33702			−0.157632			−0.0788158	−	0.996889i	$-0.525114\pi$
$757$	−4.33702			−0.157632			−0.0788158	+	0.996889i	$0.525114\pi$
$758$		0			0
$759$		−	6.33937i		−	0.230104i
$760$		0			0
$761$			49.2936i			1.78689i	0.449170	+	0.893446i	$0.351720\pi$
$761$			49.2936i			1.78689i	−0.449170	+	0.893446i	$0.648280\pi$
$762$		0			0
$763$	38.4417			1.39168
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.5777	+	11.5777i	−0.418048	+	0.418048i
$768$		0			0
$769$		−	30.9736i		−	1.11694i	−0.829526	−	0.558468i	$-0.811389\pi$
$769$		−	30.9736i		−	1.11694i	0.829526	−	0.558468i	$-0.188611\pi$
$770$		0			0
$771$	−27.3465	+	27.3465i	−0.984861	+	0.984861i
$772$		0			0
$773$		−	15.1058i		−	0.543319i	−0.962393	−	0.271660i	$-0.912427\pi$
$773$		−	15.1058i		−	0.543319i	0.962393	−	0.271660i	$-0.0875725\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−64.6378	+	64.6378i	−2.31887	+	2.31887i
$778$		0			0
$779$	−5.86652	+	5.86652i	−0.210190	+	0.210190i
$780$		0			0
$781$	7.09671	+	7.09671i	0.253940	+	0.253940i
$782$		0			0
$783$	−29.7157	−	29.7157i	−1.06195	−	1.06195i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	30.2095			1.07685			0.538426	−	0.842673i	$-0.319019\pi$
$787$	30.2095			1.07685			0.538426	+	0.842673i	$0.319019\pi$
$788$		0			0
$789$	−35.3857	−	35.3857i	−1.25977	−	1.25977i
$790$		0			0
$791$	62.0512			2.20629
$792$		0			0
$793$	−9.47696	−	9.47696i	−0.336537	−	0.336537i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			9.39226i			0.332691i	0.986068	+	0.166346i	$0.0531967\pi$
$797$			9.39226i			0.332691i	−0.986068	+	0.166346i	$0.946803\pi$
$798$		0			0
$799$	−0.345242			−0.0122138
$800$		0			0
$801$	−56.8389			−2.00830
$802$		0			0
$803$		−	0.837003i		−	0.0295372i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	42.1455	+	42.1455i	1.48359	+	1.48359i
$808$		0			0
$809$	49.0307			1.72383			0.861914	−	0.507054i	$-0.169266\pi$
$809$	49.0307			1.72383			0.861914	+	0.507054i	$0.169266\pi$
$810$		0			0
$811$	20.4561	+	20.4561i	0.718311	+	0.718311i	0.968259	−	0.249948i	$-0.0804137\pi$
$811$	20.4561	+	20.4561i	0.718311	+	0.718311i	−0.249948	+	0.968259i	$0.580414\pi$
$812$		0			0
$813$	−4.69160			−0.164541
$814$		0			0
$815$		0			0
$816$		0			0
$817$	8.36494	+	8.36494i	0.292652	+	0.292652i
$818$		0			0
$819$	25.8089	+	25.8089i	0.901834	+	0.901834i
$820$		0			0
$821$	34.8437	−	34.8437i	1.21605	−	1.21605i	0.247050	−	0.969003i	$-0.420539\pi$
$821$	34.8437	−	34.8437i	1.21605	−	1.21605i	0.969003	−	0.247050i	$-0.0794610\pi$
$822$		0			0
$823$	8.05406	−	8.05406i	0.280747	−	0.280747i	−0.552660	−	0.833407i	$-0.686387\pi$
$823$	8.05406	−	8.05406i	0.280747	−	0.280747i	0.833407	+	0.552660i	$0.186387\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	39.7148i		−	1.38102i	−0.723323	−	0.690510i	$-0.757386\pi$
$827$		−	39.7148i		−	1.38102i	0.723323	−	0.690510i	$-0.242614\pi$
$828$		0			0
$829$	20.7529	−	20.7529i	0.720778	−	0.720778i	−0.247985	−	0.968764i	$-0.579769\pi$
$829$	20.7529	−	20.7529i	0.720778	−	0.720778i	0.968764	+	0.247985i	$0.0797685\pi$
$830$		0			0
$831$			42.5965i			1.47765i
$832$		0			0
$833$	14.0137	−	14.0137i	0.485546	−	0.485546i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−105.638			−3.65138
$838$		0			0
$839$		−	44.3056i		−	1.52960i	−0.644267	−	0.764800i	$-0.722838\pi$
$839$		−	44.3056i		−	1.52960i	0.644267	−	0.764800i	$-0.277162\pi$
$840$		0			0
$841$			21.1776i			0.730262i
$842$		0			0
$843$	19.5668			0.673917
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−26.8551	+	26.8551i	−0.922751	+	0.922751i
$848$		0			0
$849$		−	1.76739i		−	0.0606567i
$850$		0			0
$851$	16.4366	−	16.4366i	0.563440	−	0.563440i
$852$		0			0
$853$		−	29.5903i		−	1.01315i	−0.862195	−	0.506577i	$-0.830911\pi$
$853$		−	29.5903i		−	1.01315i	0.862195	−	0.506577i	$-0.169089\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.9315	+	22.9315i	−0.783326	+	0.783326i	−0.980391	−	0.197064i	$-0.936859\pi$
$857$	−22.9315	+	22.9315i	−0.783326	+	0.783326i	0.197064	+	0.980391i	$0.436859\pi$
$858$		0			0
$859$	23.1388	−	23.1388i	0.789486	−	0.789486i	−0.191924	−	0.981410i	$-0.561473\pi$
$859$	23.1388	−	23.1388i	0.789486	−	0.789486i	0.981410	+	0.191924i	$0.0614727\pi$
$860$		0			0
$861$	17.9944	+	17.9944i	0.613248	+	0.613248i
$862$		0			0
$863$	10.8789	+	10.8789i	0.370322	+	0.370322i	0.867594	−	0.497273i	$-0.165665\pi$
$863$	10.8789	+	10.8789i	0.370322	+	0.370322i	−0.497273	+	0.867594i	$0.665665\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−18.6786			−0.634357
$868$		0			0
$869$	1.80415	+	1.80415i	0.0612018	+	0.0612018i
$870$		0			0
$871$	−14.4381			−0.489215
$872$		0			0
$873$	28.5122	+	28.5122i	0.964993	+	0.964993i
$874$		0			0
$875$		0			0
$876$		0			0
$877$			21.3146i			0.719742i	0.933002	+	0.359871i	$0.117179\pi$
$877$			21.3146i			0.719742i	−0.933002	+	0.359871i	$0.882821\pi$
$878$		0			0
$879$	−86.6597			−2.92296
$880$		0			0
$881$	43.6540			1.47074			0.735370	−	0.677666i	$-0.237009\pi$
$881$	43.6540			1.47074			0.735370	+	0.677666i	$0.237009\pi$
$882$		0			0
$883$		−	12.9408i		−	0.435492i	−0.976006	−	0.217746i	$-0.930130\pi$
$883$		−	12.9408i		−	0.435492i	0.976006	−	0.217746i	$-0.0698704\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−28.9454	−	28.9454i	−0.971892	−	0.971892i	0.0277234	−	0.999616i	$-0.491174\pi$
$887$	−28.9454	−	28.9454i	−0.971892	−	0.971892i	−0.999616	+	0.0277234i	$0.991174\pi$
$888$		0			0
$889$	−45.6344			−1.53053
$890$		0			0
$891$	12.0740	+	12.0740i	0.404493	+	0.404493i
$892$		0			0
$893$	−0.392421			−0.0131319
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−9.14927	−	9.14927i	−0.305485	−	0.305485i
$898$		0			0
$899$	−13.9041	−	13.9041i	−0.463728	−	0.463728i
$900$		0			0
$901$	1.70820	−	1.70820i	0.0569082	−	0.0569082i
$902$		0			0
$903$	25.6578	−	25.6578i	0.853840	−	0.853840i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	6.83334i		−	0.226897i	−0.993544	−	0.113449i	$-0.963810\pi$
$907$		−	6.83334i		−	0.226897i	0.993544	−	0.113449i	$-0.0361898\pi$
$908$		0			0
$909$	−33.4360	+	33.4360i	−1.10900	+	1.10900i
$910$		0			0
$911$			25.5381i			0.846114i	0.906103	+	0.423057i	$0.139043\pi$
$911$			25.5381i			0.846114i	−0.906103	+	0.423057i	$0.860957\pi$
$912$		0			0
$913$	−2.78463	+	2.78463i	−0.0921579	+	0.0921579i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−25.4885			−0.841704
$918$		0			0
$919$			2.49036i			0.0821493i	0.999156	+	0.0410746i	$0.0130781\pi$
$919$			2.49036i			0.0821493i	−0.999156	+	0.0410746i	$0.986922\pi$
$920$		0			0
$921$		−	21.8966i		−	0.721517i
$922$		0			0
$923$	20.4846			0.674259
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−48.4541	+	48.4541i	−1.59144	+	1.59144i
$928$		0			0
$929$			8.45665i			0.277454i	0.990331	+	0.138727i	$0.0443010\pi$
$929$			8.45665i			0.277454i	−0.990331	+	0.138727i	$0.955699\pi$
$930$		0			0
$931$	15.9287	−	15.9287i	0.522043	−	0.522043i
$932$		0			0
$933$			2.07234i			0.0678453i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	40.1339	−	40.1339i	1.31112	−	1.31112i	0.390523	−	0.920593i	$-0.372294\pi$
$937$	40.1339	−	40.1339i	1.31112	−	1.31112i	0.920593	−	0.390523i	$-0.127706\pi$
$938$		0			0
$939$	0.355959	−	0.355959i	0.0116163	−	0.0116163i
$940$		0			0
$941$	35.3857	+	35.3857i	1.15354	+	1.15354i	0.985837	+	0.167704i	$0.0536354\pi$
$941$	35.3857	+	35.3857i	1.15354	+	1.15354i	0.167704	+	0.985837i	$0.446365\pi$
$942$		0			0
$943$	−4.57576	−	4.57576i	−0.149007	−	0.149007i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−10.4999			−0.341200			−0.170600	−	0.985340i	$-0.554571\pi$
$947$	−10.4999			−0.341200			−0.170600	+	0.985340i	$0.554571\pi$
$948$		0			0
$949$	−1.20800	−	1.20800i	−0.0392134	−	0.0392134i
$950$		0			0
$951$	−113.013			−3.66468
$952$		0			0
$953$	−4.72367	−	4.72367i	−0.153015	−	0.153015i	0.626448	−	0.779463i	$-0.284508\pi$
$953$	−4.72367	−	4.72367i	−0.153015	−	0.153015i	−0.779463	+	0.626448i	$0.784508\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			5.95819i			0.192601i
$958$		0			0
$959$	−16.3111			−0.526711
$960$		0			0
$961$	−18.4284			−0.594466
$962$		0			0
$963$			82.3446i			2.65352i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−4.08577	−	4.08577i	−0.131390	−	0.131390i	0.638354	−	0.769743i	$-0.279616\pi$
$967$	−4.08577	−	4.08577i	−0.131390	−	0.131390i	−0.769743	+	0.638354i	$0.779616\pi$
$968$		0			0
$969$	41.7172			1.34015
$970$		0			0
$971$	13.5569	+	13.5569i	0.435062	+	0.435062i	0.890346	−	0.455284i	$-0.150462\pi$
$971$	13.5569	+	13.5569i	0.435062	+	0.435062i	−0.455284	+	0.890346i	$0.650462\pi$
$972$		0			0
$973$	0.521042			0.0167038
$974$		0			0
$975$		0			0
$976$		0			0
$977$	24.7102	+	24.7102i	0.790550	+	0.790550i	0.981584	−	0.191034i	$-0.0611839\pi$
$977$	24.7102	+	24.7102i	0.790550	+	0.790550i	−0.191034	+	0.981584i	$0.561184\pi$
$978$		0			0
$979$	3.45262	+	3.45262i	0.110346	+	0.110346i
$980$		0			0
$981$	57.6022	−	57.6022i	1.83910	−	1.83910i
$982$		0			0
$983$	−15.4292	+	15.4292i	−0.492115	+	0.492115i	−0.908972	−	0.416857i	$-0.863132\pi$
$983$	−15.4292	+	15.4292i	−0.492115	+	0.492115i	0.416857	+	0.908972i	$0.363132\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			1.20368i			0.0383134i
$988$		0			0
$989$	−6.52447	+	6.52447i	−0.207466	+	0.207466i
$990$		0			0
$991$		−	29.6537i		−	0.941981i	−0.882138	−	0.470990i	$-0.843897\pi$
$991$		−	29.6537i		−	0.941981i	0.882138	−	0.470990i	$-0.156103\pi$
$992$		0			0
$993$	−24.4680	+	24.4680i	−0.776467	+	0.776467i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−36.4336			−1.15386			−0.576932	−	0.816792i	$-0.695750\pi$
$997$	−36.4336			−1.15386			−0.576932	+	0.816792i	$0.695750\pi$
$998$		0			0
$999$			117.370i			3.71343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.j.e.1007.1		24
4.3	odd	2		400.2.j.e.307.11	yes	24
5.2	odd	4		1600.2.s.e.943.1		24
5.3	odd	4		1600.2.s.e.943.12		24
5.4	even	2	inner	1600.2.j.e.1007.12		24
16.5	even	4		400.2.s.e.107.5	yes	24
16.11	odd	4		1600.2.s.e.207.12		24
20.3	even	4		400.2.s.e.243.5	yes	24
20.7	even	4		400.2.s.e.243.8	yes	24
20.19	odd	2		400.2.j.e.307.2	yes	24
80.27	even	4	inner	1600.2.j.e.143.1		24
80.37	odd	4		400.2.j.e.43.2	✓	24
80.43	even	4	inner	1600.2.j.e.143.12		24
80.53	odd	4		400.2.j.e.43.11	yes	24
80.59	odd	4		1600.2.s.e.207.1		24
80.69	even	4		400.2.s.e.107.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.e.43.2	✓	24	80.37	odd	4
400.2.j.e.43.11	yes	24	80.53	odd	4
400.2.j.e.307.2	yes	24	20.19	odd	2
400.2.j.e.307.11	yes	24	4.3	odd	2
400.2.s.e.107.5	yes	24	16.5	even	4
400.2.s.e.107.8	yes	24	80.69	even	4
400.2.s.e.243.5	yes	24	20.3	even	4
400.2.s.e.243.8	yes	24	20.7	even	4
1600.2.j.e.143.1		24	80.27	even	4	inner
1600.2.j.e.143.12		24	80.43	even	4	inner
1600.2.j.e.1007.1		24	1.1	even	1	trivial
1600.2.j.e.1007.12		24	5.4	even	2	inner
1600.2.s.e.207.1		24	80.59	odd	4
1600.2.s.e.207.12		24	16.11	odd	4
1600.2.s.e.943.1		24	5.2	odd	4
1600.2.s.e.943.12		24	5.3	odd	4

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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.25766i q^{3} +(-2.54012 - 2.54012i) q^{7} -7.61238 q^{9} +O(q^{10})\)	\(q-3.25766i q^{3} +(-2.54012 - 2.54012i) q^{7} -7.61238 q^{9} +(0.462406 + 0.462406i) q^{11} +1.33473 q^{13} +(-2.37342 - 2.37342i) q^{17} +(-2.69776 - 2.69776i) q^{19} +(-8.27486 + 8.27486i) q^{21} +(2.10420 - 2.10420i) q^{23} +15.0256i q^{27} +(-1.97767 + 1.97767i) q^{29} +7.03054i q^{31} +(1.50636 - 1.50636i) q^{33} +7.81135 q^{37} -4.34811i q^{39} -2.17459i q^{41} -3.10070 q^{43} +(0.0727309 - 0.0727309i) q^{47} +5.90443i q^{49} +(-7.73182 + 7.73182i) q^{51} +0.719718i q^{53} +(-8.78840 + 8.78840i) q^{57} +(-8.67421 + 8.67421i) q^{59} +(-7.10027 - 7.10027i) q^{61} +(19.3364 + 19.3364i) q^{63} -10.8172 q^{67} +(-6.85476 - 6.85476i) q^{69} +15.3474 q^{71} +(-0.905052 - 0.905052i) q^{73} -2.34913i q^{77} +3.90167 q^{79} +26.1112 q^{81} +6.02206i q^{83} +(6.44260 + 6.44260i) q^{87} +7.46664 q^{89} +(-3.39038 - 3.39038i) q^{91} +22.9031 q^{93} +(-3.74551 - 3.74551i) q^{97} +(-3.52001 - 3.52001i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 40 q^{9}+O(q^{10}) \) 24 * q - 40 * q^9	\( 24 q - 40 q^{9} + 20 q^{11} + 12 q^{19} + 8 q^{29} - 20 q^{51} - 8 q^{59} - 48 q^{61} - 64 q^{69} + 16 q^{71} + 104 q^{79} + 48 q^{81} + 96 q^{89} - 64 q^{91} - 128 q^{99}+O(q^{100}) \) 24 * q - 40 * q^9 + 20 * q^11 + 12 * q^19 + 8 * q^29 - 20 * q^51 - 8 * q^59 - 48 * q^61 - 64 * q^69 + 16 * q^71 + 104 * q^79 + 48 * q^81 + 96 * q^89 - 64 * q^91 - 128 * q^99

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