LMFDB - Embedded newform 1050.2.u.g.299.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1050,2,Mod(299,1050)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1050, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1050.299"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,6,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 11x^10 - 32x^9 + 64x^8 - 120x^7 + 237x^6 - 360x^5 + 576x^4 - 864x^3 + 891x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.4
Root			$-0.111613 - 1.72845i$ of defining polynomial
Character	$\chi$	$=$	1050.299
Dual form			1050.2.u.g.899.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.111613 + 1.72845i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.55269 + 0.767566i) q^{6} +(-1.82168 - 1.91871i) q^{7} -1.00000 q^{8} +(-2.97509 + 0.385834i) q^{9} +(-1.99775 + 1.15340i) q^{11} +(1.44108 - 0.960885i) q^{12} +5.00084 q^{13} +(-2.57250 + 0.618268i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.45795 + 3.15115i) q^{17} +(-1.15340 + 2.76942i) q^{18} +(-6.54470 - 3.77859i) q^{19} +(3.11308 - 3.36285i) q^{21} +2.30680i q^{22} +(-3.18628 + 5.51880i) q^{23} +(-0.111613 - 1.72845i) q^{24} +(2.50042 - 4.33086i) q^{26} +(-0.998953 - 5.09922i) q^{27} +(-0.750813 + 2.53698i) q^{28} -3.83533i q^{29} +(-3.79452 + 2.19077i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.21657 - 3.32428i) q^{33} +6.30230i q^{34} +(1.82168 + 2.38358i) q^{36} +(5.98363 + 3.45465i) q^{37} +(-6.54470 + 3.77859i) q^{38} +(0.558158 + 8.64371i) q^{39} -9.79371 q^{41} +(-1.35577 - 4.37743i) q^{42} -2.55278i q^{43} +(1.99775 + 1.15340i) q^{44} +(3.18628 + 5.51880i) q^{46} +(1.43486 + 0.828416i) q^{47} +(-1.55269 - 0.767566i) q^{48} +(-0.362928 + 6.99059i) q^{49} +(-6.05578 - 9.08209i) q^{51} +(-2.50042 - 4.33086i) q^{52} +(-1.62639 - 2.81699i) q^{53} +(-4.91553 - 1.68449i) q^{54} +(1.82168 + 1.91871i) q^{56} +(5.80063 - 11.7339i) q^{57} +(-3.32150 - 1.91767i) q^{58} +(-4.96573 - 8.60089i) q^{59} +(-5.18202 - 2.99184i) q^{61} +4.38153i q^{62} +(6.15997 + 5.00547i) q^{63} +1.00000 q^{64} +(-3.98719 + 0.257468i) q^{66} +(-2.39643 + 1.38358i) q^{67} +(5.45795 + 3.15115i) q^{68} +(-9.89460 - 4.89136i) q^{69} -2.85910i q^{71} +(2.97509 - 0.385834i) q^{72} +(1.84089 + 3.18851i) q^{73} +(5.98363 - 3.45465i) q^{74} +7.55717i q^{76} +(5.85231 + 1.73198i) q^{77} +(7.76475 + 3.83848i) q^{78} +(1.27945 - 2.21607i) q^{79} +(8.70226 - 2.29578i) q^{81} +(-4.89686 + 8.48160i) q^{82} -1.83743i q^{83} +(-4.46885 - 1.01458i) q^{84} +(-2.21077 - 1.27639i) q^{86} +(6.62919 - 0.428072i) q^{87} +(1.99775 - 1.15340i) q^{88} +(-2.94387 + 5.09894i) q^{89} +(-9.10996 - 9.59518i) q^{91} +6.37256 q^{92} +(-4.21015 - 6.31412i) q^{93} +(1.43486 - 0.828416i) q^{94} +(-1.44108 + 0.960885i) q^{96} +4.61723 q^{97} +(5.87256 + 3.80960i) q^{98} +(5.49845 - 4.20226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 2 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} - 12 q^{11} + 2 q^{12} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 12 q^{17} - 18 q^{21} - 2 q^{23} + 4 q^{24} - 4 q^{26} - 28 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 2 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 - 12 * q^11 + 2 * q^12 - 8 * q^13 - 12 * q^14 - 6 * q^16 - 12 * q^17 - 18 * q^21 - 2 * q^23 + 4 * q^24 - 4 * q^26 - 28 * q^27 - 6 * q^28 + 12 * q^31 + 6 * q^32 - 14 * q^33 + 6 * q^36 - 30 * q^39 - 4 * q^41 - 6 * q^42 + 12 * q^44 + 2 * q^46 - 24 * q^47 + 2 * q^48 + 14 * q^49 + 4 * q^51 + 4 * q^52 - 8 * q^53 + 4 * q^54 + 6 * q^56 + 20 * q^57 + 18 * q^58 - 12 * q^59 - 30 * q^61 + 38 * q^63 + 12 * q^64 - 34 * q^66 - 6 * q^67 + 12 * q^68 - 50 * q^69 + 6 * q^72 + 20 * q^77 + 12 * q^78 + 4 * q^79 + 50 * q^81 - 2 * q^82 + 12 * q^84 - 54 * q^86 + 34 * q^87 + 12 * q^88 - 26 * q^89 + 28 * q^91 + 4 * q^92 - 60 * q^93 - 24 * q^94 - 2 * q^96 + 72 * q^97 - 2 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.111613	+	1.72845i	0.0644396	+	0.997922i
$3$	0.111613	+	1.72845i	0.0644396	+	0.997922i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	1.55269	+	0.767566i	0.633883	+	0.313358i
$7$	−1.82168	−	1.91871i	−0.688532	−	0.725206i
$7$	−1.82168	−	1.91871i	−0.688532	−	0.725206i
$8$	−1.00000			−0.353553
$9$	−2.97509	+	0.385834i	−0.991695	+	0.128611i
$10$		0			0
$11$	−1.99775	+	1.15340i	−0.602344	+	0.347763i	−0.769963	−	0.638089i	$-0.779725\pi$
$11$	−1.99775	+	1.15340i	−0.602344	+	0.347763i	0.167619	+	0.985852i	$0.446392\pi$
$12$	1.44108	−	0.960885i	0.416003	−	0.277384i
$13$	5.00084			1.38698			0.693492	−	0.720464i	$-0.256071\pi$
$13$	5.00084			1.38698			0.693492	+	0.720464i	$0.256071\pi$
$14$	−2.57250	+	0.618268i	−0.687529	+	0.165239i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.45795	+	3.15115i	−1.32375	+	0.764266i	−0.984324	−	0.176368i	$-0.943565\pi$
$17$	−5.45795	+	3.15115i	−1.32375	+	0.764266i	−0.339423	+	0.940634i	$0.610232\pi$
$18$	−1.15340	+	2.76942i	−0.271859	+	0.652758i
$19$	−6.54470	−	3.77859i	−1.50146	−	0.866867i	−0.999999	−	0.00168616i	$-0.999463\pi$
$19$	−6.54470	−	3.77859i	−1.50146	−	0.866867i	−0.501460	−	0.865181i	$-0.667203\pi$
$20$		0			0
$21$	3.11308	−	3.36285i	0.679330	−	0.733833i
$22$			2.30680i			0.491812i
$23$	−3.18628	+	5.51880i	−0.664385	+	1.15075i	0.315066	+	0.949070i	$0.397973\pi$
$23$	−3.18628	+	5.51880i	−0.664385	+	1.15075i	−0.979452	+	0.201679i	$0.935360\pi$
$24$	−0.111613	−	1.72845i	−0.0227829	−	0.352819i
$25$		0			0
$26$	2.50042	−	4.33086i	0.490373	−	0.849351i
$27$	−0.998953	−	5.09922i	−0.192249	−	0.981346i
$28$	−0.750813	+	2.53698i	−0.141890	+	0.479445i
$29$		−	3.83533i		−	0.712204i	−0.934447	−	0.356102i	$-0.884106\pi$
$29$		−	3.83533i		−	0.712204i	0.934447	−	0.356102i	$-0.115894\pi$
$30$		0			0
$31$	−3.79452	+	2.19077i	−0.681516	+	0.393473i	−0.800426	−	0.599432i	$-0.795393\pi$
$31$	−3.79452	+	2.19077i	−0.681516	+	0.393473i	0.118910	+	0.992905i	$0.462060\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.21657	−	3.32428i	−0.385855	−	0.578682i
$34$			6.30230i			1.08083i
$35$		0			0
$36$	1.82168	+	2.38358i	0.303614	+	0.397264i
$37$	5.98363	+	3.45465i	0.983703	+	0.567941i	0.903386	−	0.428828i	$-0.141074\pi$
$37$	5.98363	+	3.45465i	0.983703	+	0.567941i	0.0803166	+	0.996769i	$0.474407\pi$
$38$	−6.54470	+	3.77859i	−1.06169	+	0.612968i
$39$	0.558158	+	8.64371i	0.0893767	+	1.38410i
$40$		0			0
$41$	−9.79371			−1.52952			−0.764760	−	0.644315i	$-0.777143\pi$
$41$	−9.79371			−1.52952			−0.764760	+	0.644315i	$0.777143\pi$
$42$	−1.35577	−	4.37743i	−0.209200	−	0.675452i
$43$		−	2.55278i		−	0.389296i	−0.980873	−	0.194648i	$-0.937644\pi$
$43$		−	2.55278i		−	0.389296i	0.980873	−	0.194648i	$-0.0623564\pi$
$44$	1.99775	+	1.15340i	0.301172	+	0.173882i
$45$		0			0
$46$	3.18628	+	5.51880i	0.469791	+	0.813703i
$47$	1.43486	+	0.828416i	0.209296	+	0.120837i	0.600984	−	0.799261i	$-0.294776\pi$
$47$	1.43486	+	0.828416i	0.209296	+	0.120837i	−0.391688	+	0.920098i	$0.628109\pi$
$48$	−1.55269	−	0.767566i	−0.224111	−	0.110789i
$49$	−0.362928	+	6.99059i	−0.0518469	+	0.998655i
$50$		0			0
$51$	−6.05578	−	9.08209i	−0.847979	−	1.27175i
$52$	−2.50042	−	4.33086i	−0.346746	−	0.600582i
$53$	−1.62639	−	2.81699i	−0.223402	−	0.386944i	0.732437	−	0.680835i	$-0.238383\pi$
$53$	−1.62639	−	2.81699i	−0.223402	−	0.386944i	−0.955839	+	0.293891i	$0.905050\pi$
$54$	−4.91553	−	1.68449i	−0.668920	−	0.229231i
$55$		0			0
$56$	1.82168	+	1.91871i	0.243433	+	0.256399i
$57$	5.80063	−	11.7339i	0.768312	−	1.55420i
$58$	−3.32150	−	1.91767i	−0.436134	−	0.251802i
$59$	−4.96573	−	8.60089i	−0.646483	−	1.11974i	−0.983957	−	0.178406i	$-0.942906\pi$
$59$	−4.96573	−	8.60089i	−0.646483	−	1.11974i	0.337474	−	0.941335i	$-0.390427\pi$
$60$		0			0
$61$	−5.18202	−	2.99184i	−0.663489	−	0.383066i	0.130116	−	0.991499i	$-0.458465\pi$
$61$	−5.18202	−	2.99184i	−0.663489	−	0.383066i	−0.793605	+	0.608433i	$0.791798\pi$
$62$			4.38153i			0.556455i
$63$	6.15997	+	5.00547i	0.776084	+	0.630630i
$64$	1.00000			0.125000
$65$		0			0
$66$	−3.98719	+	0.257468i	−0.490789	+	0.0316922i
$67$	−2.39643	+	1.38358i	−0.292771	+	0.169031i	−0.639191	−	0.769048i	$-0.720731\pi$
$67$	−2.39643	+	1.38358i	−0.292771	+	0.169031i	0.346420	+	0.938080i	$0.387397\pi$
$68$	5.45795	+	3.15115i	0.661874	+	0.382133i
$69$	−9.89460	−	4.89136i	−1.19117	−	0.588851i
$70$		0			0
$71$		−	2.85910i		−	0.339312i	−0.985503	−	0.169656i	$-0.945734\pi$
$71$		−	2.85910i		−	0.339312i	0.985503	−	0.169656i	$-0.0542657\pi$
$72$	2.97509	−	0.385834i	0.350617	−	0.0454710i
$73$	1.84089	+	3.18851i	0.215459	+	0.373187i	0.953415	−	0.301663i	$-0.0975418\pi$
$73$	1.84089	+	3.18851i	0.215459	+	0.373187i	−0.737955	+	0.674850i	$0.764208\pi$
$74$	5.98363	−	3.45465i	0.695583	−	0.401595i
$75$		0			0
$76$			7.55717i			0.866867i
$77$	5.85231	+	1.73198i	0.666933	+	0.197377i
$78$	7.76475	+	3.83848i	0.879185	+	0.434622i
$79$	1.27945	−	2.21607i	0.143949	−	0.249327i	−0.785031	−	0.619456i	$-0.787353\pi$
$79$	1.27945	−	2.21607i	0.143949	−	0.249327i	0.928980	+	0.370129i	$0.120687\pi$
$80$		0			0
$81$	8.70226	−	2.29578i	0.966918	−	0.255087i
$82$	−4.89686	+	8.48160i	−0.540767	+	0.936636i
$83$		−	1.83743i		−	0.201684i	−0.994902	−	0.100842i	$-0.967846\pi$
$83$		−	1.83743i		−	0.201684i	0.994902	−	0.100842i	$-0.0321537\pi$
$84$	−4.46885	−	1.01458i	−0.487592	−	0.110700i
$85$		0			0
$86$	−2.21077	−	1.27639i	−0.238394	−	0.137637i
$87$	6.62919	−	0.428072i	0.710723	−	0.0458942i
$88$	1.99775	−	1.15340i	0.212961	−	0.122953i
$89$	−2.94387	+	5.09894i	−0.312050	+	0.540486i	−0.978806	−	0.204790i	$-0.934349\pi$
$89$	−2.94387	+	5.09894i	−0.312050	+	0.540486i	0.666756	+	0.745276i	$0.267682\pi$
$90$		0			0
$91$	−9.10996	−	9.59518i	−0.954983	−	1.00585i
$92$	6.37256			0.664385
$93$	−4.21015	−	6.31412i	−0.436572	−	0.654744i
$94$	1.43486	−	0.828416i	0.147994	−	0.0854446i
$95$		0			0
$96$	−1.44108	+	0.960885i	−0.147079	+	0.0980699i
$97$	4.61723			0.468808			0.234404	−	0.972139i	$-0.424686\pi$
$97$	4.61723			0.468808			0.234404	+	0.972139i	$0.424686\pi$
$98$	5.87256	+	3.80960i	0.593218	+	0.384827i
$99$	5.49845	−	4.20226i	0.552615	−	0.422343i
$100$		0			0
$101$	5.65702	+	9.79825i	0.562894	+	0.974962i	0.997242	+	0.0742165i	$0.0236456\pi$
$101$	5.65702	+	9.79825i	0.562894	+	0.974962i	−0.434348	+	0.900745i	$0.643021\pi$
$102$	−10.8932	+	0.703417i	−1.07859	+	0.0696486i
$103$	3.68203	−	6.37747i	0.362802	−	0.628391i	−0.625619	−	0.780129i	$-0.715154\pi$
$103$	3.68203	−	6.37747i	0.362802	−	0.628391i	0.988421	+	0.151738i	$0.0484869\pi$
$104$	−5.00084			−0.490373
$105$		0			0
$106$	−3.25278			−0.315938
$107$	−4.20937	+	7.29084i	−0.406935	+	0.704832i	−0.994545	−	0.104312i	$-0.966736\pi$
$107$	−4.20937	+	7.29084i	−0.406935	+	0.704832i	0.587609	+	0.809145i	$0.300069\pi$
$108$	−3.91658	+	3.41473i	−0.376873	+	0.328583i
$109$	−3.33156	−	5.77043i	−0.319105	−	0.552707i	0.661196	−	0.750213i	$-0.270049\pi$
$109$	−3.33156	−	5.77043i	−0.319105	−	0.552707i	−0.980302	+	0.197506i	$0.936716\pi$
$110$		0			0
$111$	−5.30334	+	10.7280i	−0.503371	+	1.01826i
$112$	2.57250	−	0.618268i	0.243078	−	0.0584209i
$113$	4.45505			0.419096			0.209548	−	0.977798i	$-0.432801\pi$
$113$	4.45505			0.419096			0.209548	+	0.977798i	$0.432801\pi$
$114$	−7.26157	−	10.8905i	−0.680109	−	1.01999i
$115$		0			0
$116$	−3.32150	+	1.91767i	−0.308393	+	0.178051i
$117$	−14.8779	+	1.92950i	−1.37546	+	0.178382i
$118$	−9.93145			−0.914264
$119$	15.9888	+	4.73184i	1.46569	+	0.433767i
$120$		0			0
$121$	−2.83934	+	4.91787i	−0.258121	+	0.447079i
$122$	−5.18202	+	2.99184i	−0.469158	+	0.270868i
$123$	−1.09310	−	16.9279i	−0.0985618	−	1.52634i
$124$	3.79452	+	2.19077i	0.340758	+	0.196737i
$125$		0			0
$126$	7.41485	−	2.83196i	0.660567	−	0.252291i
$127$		−	1.83694i		−	0.163002i	−0.996673	−	0.0815011i	$-0.974029\pi$
$127$		−	1.83694i		−	0.163002i	0.996673	−	0.0815011i	$-0.0259714\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	4.41236	−	0.284923i	0.388487	−	0.0250861i
$130$		0			0
$131$	2.76942	−	4.79677i	0.241965	−	0.419096i	−0.719309	−	0.694690i	$-0.755541\pi$
$131$	2.76942	−	4.79677i	0.241965	−	0.419096i	0.961274	+	0.275595i	$0.0888747\pi$
$132$	−1.77062	+	3.58174i	−0.154113	+	0.311751i
$133$	4.67236	+	19.4408i	0.405145	+	1.68573i
$134$			2.76716i			0.239047i
$135$		0			0
$136$	5.45795	−	3.15115i	0.468015	−	0.270209i
$137$	−0.620520	−	1.07477i	−0.0530146	−	0.0918240i	0.838300	−	0.545209i	$-0.183550\pi$
$137$	−0.620520	−	1.07477i	−0.0530146	−	0.0918240i	−0.891315	+	0.453385i	$0.850216\pi$
$138$	−9.18334	+	6.12330i	−0.781738	+	0.521250i
$139$			12.5344i			1.06315i	0.847011	+	0.531576i	$0.178400\pi$
$139$			12.5344i			1.06315i	−0.847011	+	0.531576i	$0.821600\pi$
$140$		0			0
$141$	−1.27173	+	2.57255i	−0.107099	+	0.216647i
$142$	−2.47605	−	1.42955i	−0.207786	−	0.119965i
$143$	−9.99042	+	5.76797i	−0.835441	+	0.482342i
$144$	1.15340	−	2.76942i	0.0961167	−	0.230785i
$145$		0			0
$146$	3.68177			0.304706
$147$	−12.1234	+	0.152935i	−0.999920	+	0.0126138i
$148$		−	6.90930i		−	0.567941i
$149$	13.5058	+	7.79757i	1.10644	+	0.638802i	0.937904	−	0.346894i	$-0.112764\pi$
$149$	13.5058	+	7.79757i	1.10644	+	0.638802i	0.168533	+	0.985696i	$0.446097\pi$
$150$		0			0
$151$	−1.51958	−	2.63198i	−0.123661	−	0.214188i	0.797548	−	0.603256i	$-0.206130\pi$
$151$	−1.51958	−	2.63198i	−0.123661	−	0.214188i	−0.921209	+	0.389068i	$0.872797\pi$
$152$	6.54470	+	3.77859i	0.530846	+	0.306484i
$153$	15.0220	−	11.4808i	1.21446	−	0.928168i
$154$	4.42609	−	4.20226i	0.356665	−	0.338628i
$155$		0			0
$156$	7.20659	−	4.80523i	0.576989	−	0.384727i
$157$	7.91260	+	13.7050i	0.631494	+	1.09378i	0.987246	+	0.159200i	$0.0508913\pi$
$157$	7.91260	+	13.7050i	0.631494	+	1.09378i	−0.355752	+	0.934580i	$0.615775\pi$
$158$	−1.27945	−	2.21607i	−0.101787	−	0.176301i
$159$	4.68751	−	3.12555i	0.371744	−	0.247872i
$160$		0			0
$161$	16.3934	−	3.93995i	1.29198	−	0.310512i
$162$	2.36293	−	8.68427i	0.185649	−	0.682301i
$163$	−7.46238	−	4.30841i	−0.584499	−	0.337461i	0.178420	−	0.983954i	$-0.442901\pi$
$163$	−7.46238	−	4.30841i	−0.584499	−	0.337461i	−0.762919	+	0.646494i	$0.776235\pi$
$164$	4.89686	+	8.48160i	0.382380	+	0.662302i
$165$		0			0
$166$	−1.59126	−	0.918714i	−0.123506	−	0.0713060i
$167$			8.64948i			0.669317i	0.942339	+	0.334658i	$0.108621\pi$
$167$			8.64948i			0.669317i	−0.942339	+	0.334658i	$0.891379\pi$
$168$	−3.11308	+	3.36285i	−0.240179	+	0.259449i
$169$	12.0084			0.923724
$170$		0			0
$171$	20.9290	+	8.71645i	1.60048	+	0.666563i
$172$	−2.21077	+	1.27639i	−0.168570	+	0.0973239i
$173$	15.5291	+	8.96573i	1.18066	+	0.681652i	0.956166	−	0.292825i	$-0.0945954\pi$
$173$	15.5291	+	8.96573i	1.18066	+	0.681652i	0.224489	+	0.974477i	$0.427929\pi$
$174$	2.94387	−	5.95508i	0.223174	−	0.451454i
$175$		0			0
$176$		−	2.30680i		−	0.173882i
$177$	14.3120	−	9.54298i	1.07575	−	0.717295i
$178$	2.94387	+	5.09894i	0.220653	+	0.382181i
$179$	10.4070	−	6.00848i	0.777855	−	0.449095i	−0.0578145	−	0.998327i	$-0.518413\pi$
$179$	10.4070	−	6.00848i	0.777855	−	0.449095i	0.835670	+	0.549233i	$0.185080\pi$
$180$		0			0
$181$		−	9.52612i		−	0.708071i	−0.935232	−	0.354036i	$-0.884809\pi$
$181$		−	9.52612i		−	0.708071i	0.935232	−	0.354036i	$-0.115191\pi$
$182$	−12.8647	+	3.09186i	−0.953591	+	0.229184i
$183$	4.59287	−	9.29079i	0.339514	−	0.686795i
$184$	3.18628	−	5.51880i	0.234896	−	0.406851i
$185$		0			0
$186$	−7.57326	+	0.489035i	−0.555299	+	0.0358578i
$187$	7.26907	−	12.5904i	0.531567	−	0.920701i
$188$		−	1.65683i		−	0.120837i
$189$	−7.96418	+	11.2059i	−0.579309	+	0.815108i
$190$		0			0
$191$	−4.30564	−	2.48586i	−0.311545	−	0.179871i	0.336073	−	0.941836i	$-0.390901\pi$
$191$	−4.30564	−	2.48586i	−0.311545	−	0.179871i	−0.647618	+	0.761965i	$0.724235\pi$
$192$	0.111613	+	1.72845i	0.00805496	+	0.124740i
$193$	−5.22491	+	3.01660i	−0.376097	+	0.217140i	−0.676119	−	0.736793i	$-0.736339\pi$
$193$	−5.22491	+	3.01660i	−0.376097	+	0.217140i	0.300022	+	0.953932i	$0.403006\pi$
$194$	2.30861	−	3.99864i	0.165749	−	0.287085i
$195$		0			0
$196$	6.23549	−	3.18099i	0.445392	−	0.227213i
$197$	14.2144			1.01273			0.506366	−	0.862318i	$-0.330988\pi$
$197$	14.2144			1.01273			0.506366	+	0.862318i	$0.330988\pi$
$198$	−0.890043	−	6.86293i	−0.0632526	−	0.487727i
$199$	−1.94932	+	1.12544i	−0.138183	+	0.0797802i	−0.567498	−	0.823375i	$-0.692089\pi$
$199$	−1.94932	+	1.12544i	−0.138183	+	0.0797802i	0.429315	+	0.903155i	$0.358755\pi$
$200$		0			0
$201$	−2.65893	−	3.98769i	−0.187546	−	0.281270i
$202$	11.3140			0.796053
$203$	−7.35891	+	6.98677i	−0.516494	+	0.490375i
$204$	−4.83743	+	9.78550i	−0.338688	+	0.685122i
$205$		0			0
$206$	−3.68203	−	6.37747i	−0.256540	−	0.444339i
$207$	7.35011	−	17.6483i	0.510868	−	1.22664i
$208$	−2.50042	+	4.33086i	−0.173373	+	0.300291i
$209$	17.4329			1.20586
$210$		0			0
$211$	27.6034			1.90029			0.950147	−	0.311804i	$-0.100933\pi$
$211$	27.6034			1.90029			0.950147	+	0.311804i	$0.100933\pi$
$212$	−1.62639	+	2.81699i	−0.111701	+	0.193472i
$213$	4.94181	−	0.319112i	0.338607	−	0.0218652i
$214$	4.20937	+	7.29084i	0.287747	+	0.498392i
$215$		0			0
$216$	0.998953	+	5.09922i	0.0679701	+	0.346958i
$217$	11.1159	+	3.28971i	0.754594	+	0.223320i
$218$	−6.66311			−0.451283
$219$	−5.30571	+	3.53776i	−0.358527	+	0.239060i
$220$		0			0
$221$	−27.2943	+	15.7584i	−1.83602	+	1.06002i
$222$	6.63904	+	9.95683i	0.445583	+	0.668258i
$223$	−23.0777			−1.54539			−0.772697	−	0.634775i	$-0.781093\pi$
$223$	−23.0777			−1.54539			−0.772697	+	0.634775i	$0.781093\pi$
$224$	0.750813	−	2.53698i	0.0501658	−	0.169509i
$225$		0			0
$226$	2.22752	−	3.85818i	0.148173	−	0.256643i
$227$	−17.3509	+	10.0175i	−1.15162	+	0.664887i	−0.949281	−	0.314429i	$-0.898187\pi$
$227$	−17.3509	+	10.0175i	−1.15162	+	0.664887i	−0.202337	+	0.979316i	$0.564854\pi$
$228$	−13.0622	+	0.843477i	−0.865066	+	0.0558606i
$229$	−24.9111	−	14.3824i	−1.64617	−	0.950417i	−0.978575	−	0.205892i	$-0.933990\pi$
$229$	−24.9111	−	14.3824i	−1.64617	−	0.950417i	−0.667595	−	0.744524i	$-0.732676\pi$
$230$		0			0
$231$	−2.34044	+	10.3087i	−0.153990	+	0.678266i
$232$			3.83533i			0.251802i
$233$	12.8558	−	22.2668i	0.842209	−	1.45875i	−0.0458133	−	0.998950i	$-0.514588\pi$
$233$	12.8558	−	22.2668i	0.842209	−	1.45875i	0.888023	−	0.459799i	$-0.152079\pi$
$234$	−5.76797	+	13.8494i	−0.377064	+	0.905364i
$235$		0			0
$236$	−4.96573	+	8.60089i	−0.323241	+	0.559870i
$237$	3.97317	+	1.96412i	0.258085	+	0.127583i
$238$	12.0923	−	11.4808i	0.783828	−	0.744190i
$239$			10.7220i			0.693551i	0.937948	+	0.346776i	$0.112723\pi$
$239$			10.7220i			0.693551i	−0.937948	+	0.346776i	$0.887277\pi$
$240$		0			0
$241$	1.02594	−	0.592325i	0.0660864	−	0.0381550i	−0.466593	−	0.884472i	$-0.654519\pi$
$241$	1.02594	−	0.592325i	0.0660864	−	0.0381550i	0.532679	+	0.846317i	$0.321185\pi$
$242$	2.83934	+	4.91787i	0.182519	+	0.316133i
$243$	4.93943	+	14.7852i	0.316864	+	0.948471i
$244$			5.98368i			0.383066i
$245$		0			0
$246$	−15.2066	−	7.51732i	−0.969536	−	0.479287i
$247$	−32.7290	−	18.8961i	−2.08250	−	1.20233i
$248$	3.79452	−	2.19077i	0.240952	−	0.139114i
$249$	3.17590	−	0.205080i	0.201265	−	0.0129964i
$250$		0			0
$251$	14.3689			0.906958			0.453479	−	0.891267i	$-0.350183\pi$
$251$	14.3689			0.906958			0.453479	+	0.891267i	$0.350183\pi$
$252$	1.25488	−	7.83743i	0.0790498	−	0.493712i
$253$		−	14.7002i		−	0.924195i
$254$	−1.59084	−	0.918471i	−0.0998181	−	0.0576300i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.3206	−	8.26802i	−0.893297	−	0.515745i	−0.0182774	−	0.999833i	$-0.505818\pi$
$257$	−14.3206	−	8.26802i	−0.893297	−	0.515745i	−0.875019	+	0.484088i	$0.839152\pi$
$258$	1.95943	−	3.96368i	0.121989	−	0.246768i
$259$	−4.27180	−	17.7742i	−0.265437	−	1.10443i
$260$		0			0
$261$	1.47980	+	11.4104i	0.0915975	+	0.706289i
$262$	−2.76942	−	4.79677i	−0.171095	−	0.296345i
$263$	−15.4700	−	26.7948i	−0.953920	−	1.65224i	−0.736820	−	0.676089i	$-0.763673\pi$
$263$	−15.4700	−	26.7948i	−0.953920	−	1.65224i	−0.217100	−	0.976149i	$-0.569660\pi$
$264$	2.21657	+	3.32428i	0.136420	+	0.204595i
$265$		0			0
$266$	19.1724	+	5.67402i	1.17554	+	0.347897i
$267$	−9.14184	−	4.51923i	−0.559471	−	0.276573i
$268$	2.39643	+	1.38358i	0.146386	+	0.0845157i
$269$	−2.05211	−	3.55436i	−0.125119	−	0.216713i	0.796660	−	0.604427i	$-0.206598\pi$
$269$	−2.05211	−	3.55436i	−0.125119	−	0.216713i	−0.921780	+	0.387714i	$0.873265\pi$
$270$		0			0
$271$	−7.86071	−	4.53838i	−0.477504	−	0.275687i	0.241872	−	0.970308i	$-0.422239\pi$
$271$	−7.86071	−	4.53838i	−0.477504	−	0.275687i	−0.719376	+	0.694621i	$0.755572\pi$
$272$		−	6.30230i		−	0.382133i
$273$	15.5680	−	16.8171i	0.942219	−	1.01781i
$274$	−1.24104			−0.0749740
$275$		0			0
$276$	0.711259	+	11.0147i	0.0428128	+	0.663004i
$277$	0.187473	−	0.108238i	0.0112642	−	0.00650338i	−0.494357	−	0.869259i	$-0.664597\pi$
$277$	0.187473	−	0.108238i	0.0112642	−	0.00650338i	0.505622	+	0.862755i	$0.331263\pi$
$278$	10.8551	+	6.26718i	0.651044	+	0.375881i
$279$	10.4437	−	7.98177i	0.625250	−	0.477856i
$280$		0			0
$281$		−	18.8498i		−	1.12448i	−0.826973	−	0.562241i	$-0.809939\pi$
$281$		−	18.8498i		−	1.12448i	0.826973	−	0.562241i	$-0.190061\pi$
$282$	1.59203	+	2.38762i	0.0948037	+	0.142181i
$283$	0.999159	+	1.73059i	0.0593939	+	0.102873i	0.894193	−	0.447681i	$-0.147750\pi$
$283$	0.999159	+	1.73059i	0.0593939	+	0.102873i	−0.834800	+	0.550554i	$0.814417\pi$
$284$	−2.47605	+	1.42955i	−0.146927	+	0.0848281i
$285$		0			0
$286$			11.5359i			0.682135i
$287$	17.8411	+	18.7913i	1.05312	+	1.10922i
$288$	−1.82168	−	2.38358i	−0.107344	−	0.140454i
$289$	11.3595	−	19.6752i	0.668204	−	1.15736i
$290$		0			0
$291$	0.515341	+	7.98065i	0.0302099	+	0.467834i
$292$	1.84089	−	3.18851i	0.107730	−	0.186593i
$293$			9.28117i			0.542212i	0.962550	+	0.271106i	$0.0873894\pi$
$293$			9.28117i			0.542212i	−0.962550	+	0.271106i	$0.912611\pi$
$294$	−5.92925	+	10.5756i	−0.345801	+	0.616783i
$295$		0			0
$296$	−5.98363	−	3.45465i	−0.347791	−	0.200797i
$297$	7.87710	+	9.03477i	0.457076	+	0.524251i
$298$	13.5058	−	7.79757i	0.782370	−	0.451701i
$299$	−15.9341	+	27.5986i	−0.921492	+	1.59607i
$300$		0			0
$301$	−4.89806	+	4.65037i	−0.282319	+	0.268043i
$302$	−3.03915			−0.174883
$303$	−16.3044	+	10.8715i	−0.936663	+	0.624551i
$304$	6.54470	−	3.77859i	0.375365	−	0.216717i
$305$		0			0
$306$	−2.43164	−	18.7499i	−0.139008	−	1.07186i
$307$	−26.9282			−1.53687			−0.768436	−	0.639927i	$-0.778965\pi$
$307$	−26.9282			−1.53687			−0.768436	+	0.639927i	$0.778965\pi$
$308$	−1.42622	−	5.93424i	−0.0812665	−	0.338135i
$309$	11.4341	+	5.65241i	0.650464	+	0.321554i
$310$		0			0
$311$	−1.41065	−	2.44331i	−0.0799905	−	0.138548i	0.823255	−	0.567672i	$-0.192156\pi$
$311$	−1.41065	−	2.44331i	−0.0799905	−	0.138548i	−0.903246	+	0.429124i	$0.858822\pi$
$312$	−0.558158	−	8.64371i	−0.0315994	−	0.489354i
$313$	−5.72135	+	9.90967i	−0.323390	+	0.560128i	−0.981185	−	0.193069i	$-0.938156\pi$
$313$	−5.72135	+	9.90967i	−0.323390	+	0.560128i	0.657795	+	0.753197i	$0.271489\pi$
$314$	15.8252			0.893068
$315$		0			0
$316$	−2.55889			−0.143949
$317$	−4.65491	+	8.06254i	−0.261446	+	0.452837i	−0.966626	−	0.256190i	$-0.917533\pi$
$317$	−4.65491	+	8.06254i	−0.261446	+	0.452837i	0.705181	+	0.709028i	$0.250866\pi$
$318$	−0.363052	−	5.62228i	−0.0203589	−	0.315282i
$319$	4.42368	+	7.66203i	0.247678	+	0.428991i
$320$		0			0
$321$	−13.0717	−	6.46194i	−0.729590	−	0.360670i
$322$	4.78460	−	16.1671i	0.266635	−	0.900956i
$323$	47.6275			2.65007
$324$	−6.33934	−	6.38849i	−0.352185	−	0.354916i
$325$		0			0
$326$	−7.46238	+	4.30841i	−0.413303	+	0.238621i
$327$	9.60205	−	6.40249i	0.530995	−	0.354058i
$328$	9.79371			0.540767
$329$	−1.02437	−	4.26220i	−0.0564752	−	0.234983i
$330$		0			0
$331$	−9.14801	+	15.8448i	−0.502820	+	0.870910i	0.497175	+	0.867650i	$0.334371\pi$
$331$	−9.14801	+	15.8448i	−0.502820	+	0.870910i	−0.999995	+	0.00325921i	$0.998963\pi$
$332$	−1.59126	+	0.918714i	−0.0873317	+	0.0504210i
$333$	−19.1347	−	7.96919i	−1.04858	−	0.436709i
$334$	7.49067	+	4.32474i	0.409871	+	0.236639i
$335$		0			0
$336$	1.35577	+	4.37743i	0.0739633	+	0.238808i
$337$			7.84516i			0.427353i	0.976904	+	0.213676i	$0.0685438\pi$
$337$			7.84516i			0.427353i	−0.976904	+	0.213676i	$0.931456\pi$
$338$	6.00420	−	10.3996i	0.326586	−	0.565663i
$339$	0.497240	+	7.70033i	0.0270064	+	0.418225i
$340$		0			0
$341$	5.05366	−	8.75320i	0.273671	−	0.474012i
$342$	18.0131	−	13.7668i	0.974039	−	0.744423i
$343$	14.0741	−	12.0383i	0.759929	−	0.650006i
$344$			2.55278i			0.137637i
$345$		0			0
$346$	15.5291	−	8.96573i	0.834849	−	0.482000i
$347$	0.116147	+	0.201172i	0.00623509	+	0.0107995i	0.869126	−	0.494591i	$-0.164682\pi$
$347$	0.116147	+	0.201172i	0.00623509	+	0.0107995i	−0.862891	+	0.505390i	$0.831349\pi$
$348$	−3.68532	−	5.52701i	−0.197554	−	0.296279i
$349$		−	11.5685i		−	0.619249i	−0.950859	−	0.309624i	$-0.899797\pi$
$349$		−	11.5685i		−	0.619249i	0.950859	−	0.309624i	$-0.100203\pi$
$350$		0			0
$351$	−4.99561	−	25.5004i	−0.266646	−	1.36111i
$352$	−1.99775	−	1.15340i	−0.106480	−	0.0614764i
$353$	−30.0575	+	17.3537i	−1.59980	+	0.923646i	−0.608277	+	0.793725i	$0.708139\pi$
$353$	−30.0575	+	17.3537i	−1.59980	+	0.923646i	−0.991524	+	0.129921i	$0.958528\pi$
$354$	−1.10848	−	17.1660i	−0.0589149	−	0.912364i
$355$		0			0
$356$	5.88774			0.312050
$357$	−6.39421	+	28.1640i	−0.338417	+	1.49060i
$358$		−	12.0170i		−	0.635116i
$359$	15.1834	+	8.76612i	0.801347	+	0.462658i	0.843942	−	0.536434i	$-0.180229\pi$
$359$	15.1834	+	8.76612i	0.801347	+	0.462658i	−0.0425949	+	0.999092i	$0.513562\pi$
$360$		0			0
$361$	19.0554	+	33.0050i	1.00292	+	1.73710i
$362$	−8.24987	−	4.76306i	−0.433603	−	0.250341i
$363$	−8.81721	−	4.35875i	−0.462783	−	0.228775i
$364$	−3.75470	+	12.6870i	−0.196799	+	0.664982i
$365$		0			0
$366$	−5.74962	−	8.62293i	−0.300538	−	0.450728i
$367$	−5.02009	−	8.69505i	−0.262047	−	0.453878i	0.704739	−	0.709467i	$-0.251064\pi$
$367$	−5.02009	−	8.69505i	−0.262047	−	0.453878i	−0.966786	+	0.255589i	$0.917731\pi$
$368$	−3.18628	−	5.51880i	−0.166096	−	0.287687i
$369$	29.1371	−	3.77875i	1.51682	−	0.196714i
$370$		0			0
$371$	−2.44223	+	8.25225i	−0.126794	+	0.428436i
$372$	−3.36311	+	6.80316i	−0.174369	+	0.352727i
$373$	−0.00417483	−	0.00241034i	−0.000216164	−	0.000124803i	0.499892	−	0.866088i	$-0.333373\pi$
$373$	−0.00417483	−	0.00241034i	−0.000216164	−	0.000124803i	−0.500108	+	0.865963i	$0.666706\pi$
$374$	−7.26907	−	12.5904i	−0.375875	−	0.651034i
$375$		0			0
$376$	−1.43486	−	0.828416i	−0.0739972	−	0.0427223i
$377$		−	19.1799i		−	0.987815i
$378$	5.72249	+	12.5001i	0.294333	+	0.642937i
$379$	−18.6572			−0.958356			−0.479178	−	0.877718i	$-0.659065\pi$
$379$	−18.6572			−0.958356			−0.479178	+	0.877718i	$0.659065\pi$
$380$		0			0
$381$	3.17506	−	0.205026i	0.162663	−	0.0105038i
$382$	−4.30564	+	2.48586i	−0.220296	+	0.127188i
$383$	−16.3214	−	9.42316i	−0.833984	−	0.481501i	0.0212308	−	0.999775i	$-0.493242\pi$
$383$	−16.3214	−	9.42316i	−0.833984	−	0.481501i	−0.855215	+	0.518274i	$0.826575\pi$
$384$	1.55269	+	0.767566i	0.0792353	+	0.0391697i
$385$		0			0
$386$			6.03321i			0.307082i
$387$	0.984951	+	7.59475i	0.0500679	+	0.386063i
$388$	−2.30861	−	3.99864i	−0.117202	−	0.203000i
$389$	−9.40510	+	5.43003i	−0.476857	+	0.275314i	−0.719106	−	0.694901i	$-0.755448\pi$
$389$	−9.40510	+	5.43003i	−0.476857	+	0.275314i	0.242249	+	0.970214i	$0.422115\pi$
$390$		0			0
$391$		−	40.1618i		−	2.03107i
$392$	0.362928	−	6.99059i	0.0183306	−	0.353078i
$393$	8.60008	+	4.25142i	0.433817	+	0.214456i
$394$	7.10719	−	12.3100i	0.358055	−	0.620170i
$395$		0			0
$396$	−6.38849	−	2.66066i	−0.321034	−	0.133703i
$397$	13.5204	−	23.4180i	0.678570	−	1.17532i	−0.296841	−	0.954927i	$-0.595933\pi$
$397$	13.5204	−	23.4180i	0.678570	−	1.17532i	0.975412	−	0.220391i	$-0.0707334\pi$
$398$			2.25088i			0.112826i
$399$	−33.0810	+	10.2458i	−1.65612	+	0.512931i
$400$		0			0
$401$	21.2396	+	12.2627i	1.06066	+	0.612371i	0.925614	−	0.378469i	$-0.123549\pi$
$401$	21.2396	+	12.2627i	1.06066	+	0.612371i	0.135043	+	0.990840i	$0.456883\pi$
$402$	−4.78291	+	0.308851i	−0.238550	+	0.0154041i
$403$	−18.9758	+	10.9557i	−0.945251	+	0.545741i
$404$	5.65702	−	9.79825i	0.281447	−	0.487481i
$405$		0			0
$406$	2.37127	+	9.86639i	0.117684	+	0.489661i
$407$	−15.9384			−0.790036
$408$	6.05578	+	9.08209i	0.299806	+	0.449630i
$409$	−4.67954	+	2.70173i	−0.231388	+	0.133592i	−0.611212	−	0.791467i	$-0.709318\pi$
$409$	−4.67954	+	2.70173i	−0.231388	+	0.133592i	0.379824	+	0.925059i	$0.375985\pi$
$410$		0			0
$411$	1.78843	−	1.19250i	0.0882170	−	0.0588216i
$412$	−7.36407			−0.362802
$413$	−7.45666	+	25.1959i	−0.366918	+	1.23981i
$414$	−11.6088	−	15.1895i	−0.570541	−	0.746524i
$415$		0			0
$416$	2.50042	+	4.33086i	0.122593	+	0.212338i
$417$	−21.6650	+	1.39899i	−1.06094	+	0.0685091i
$418$	8.71645	−	15.0973i	0.426335	−	0.738434i
$419$	−28.2930			−1.38220			−0.691101	−	0.722758i	$-0.742874\pi$
$419$	−28.2930			−1.38220			−0.691101	+	0.722758i	$0.742874\pi$
$420$		0			0
$421$	−25.1687			−1.22665			−0.613323	−	0.789832i	$-0.710168\pi$
$421$	−25.1687			−1.22665			−0.613323	+	0.789832i	$0.710168\pi$
$422$	13.8017	−	23.9052i	0.671855	−	1.16369i
$423$	−4.58846	−	1.91099i	−0.223099	−	0.0929156i
$424$	1.62639	+	2.81699i	0.0789846	+	0.136805i
$425$		0			0
$426$	2.19455	−	4.43929i	0.106326	−	0.215084i
$427$	3.69952	+	15.3930i	0.179032	+	0.744919i
$428$	8.41874			0.406935
$429$	−11.0847	−	16.6242i	−0.535175	−	0.802622i
$430$		0			0
$431$	9.71524	−	5.60910i	0.467967	−	0.270181i	−0.247421	−	0.968908i	$-0.579583\pi$
$431$	9.71524	−	5.60910i	0.467967	−	0.270181i	0.715388	+	0.698727i	$0.246250\pi$
$432$	4.91553	+	1.68449i	0.236499	+	0.0810452i
$433$	−0.639592			−0.0307368			−0.0153684	−	0.999882i	$-0.504892\pi$
$433$	−0.639592			−0.0307368			−0.0153684	+	0.999882i	$0.504892\pi$
$434$	8.40691	−	7.98177i	0.403544	−	0.383137i
$435$		0			0
$436$	−3.33156	+	5.77043i	−0.159553	+	0.276353i
$437$	41.7065	−	24.0793i	1.99509	−	1.15187i
$438$	0.410933	+	6.36376i	0.0196351	+	0.304072i
$439$	11.3999	+	6.58174i	0.544088	+	0.314129i	0.746734	−	0.665123i	$-0.231621\pi$
$439$	11.3999	+	6.58174i	0.544088	+	0.314129i	−0.202646	+	0.979252i	$0.564954\pi$
$440$		0			0
$441$	−1.61747	−	20.9376i	−0.0770221	−	0.997029i
$442$			31.5168i			1.49910i
$443$	12.9223	−	22.3821i	0.613957	−	1.06341i	−0.376609	−	0.926372i	$-0.622910\pi$
$443$	12.9223	−	22.3821i	0.613957	−	1.06341i	0.990566	−	0.137033i	$-0.0437567\pi$
$444$	11.9424	−	0.771166i	0.566761	−	0.0365979i
$445$		0			0
$446$	−11.5388	+	19.9858i	−0.546380	+	0.946357i
$447$	−11.9703	+	24.2144i	−0.566176	+	1.14530i
$448$	−1.82168	−	1.91871i	−0.0860665	−	0.0906507i
$449$		−	28.3586i		−	1.33833i	−0.743116	−	0.669163i	$-0.766653\pi$
$449$		−	28.3586i		−	1.33833i	0.743116	−	0.669163i	$-0.233347\pi$
$450$		0			0
$451$	19.5654	−	11.2961i	0.921297	−	0.531911i
$452$	−2.22752	−	3.85818i	−0.104774	−	0.181474i
$453$	4.37965	−	2.92027i	0.205774	−	0.137206i
$454$			20.0351i			0.940293i
$455$		0			0
$456$	−5.80063	+	11.7339i	−0.271639	+	0.549492i
$457$	25.2797	+	14.5953i	1.18254	+	0.682737i	0.956600	−	0.291405i	$-0.0941226\pi$
$457$	25.2797	+	14.5953i	1.18254	+	0.682737i	0.225936	+	0.974142i	$0.427456\pi$
$458$	−24.9111	+	14.3824i	−1.16402	+	0.672046i
$459$	21.5206	+	24.6835i	1.00450	+	1.15213i
$460$		0			0
$461$	−31.0968			−1.44832			−0.724162	−	0.689630i	$-0.757773\pi$
$461$	−31.0968			−1.44832			−0.724162	+	0.689630i	$0.757773\pi$
$462$	7.75741	+	7.18125i	0.360908	+	0.334102i
$463$			33.4915i			1.55648i	0.627967	+	0.778240i	$0.283887\pi$
$463$			33.4915i			1.55648i	−0.627967	+	0.778240i	$0.716113\pi$
$464$	3.32150	+	1.91767i	0.154197	+	0.0890255i
$465$		0			0
$466$	−12.8558	−	22.2668i	−0.595532	−	1.03149i
$467$	12.8389	+	7.41254i	0.594113	+	0.343012i	0.766722	−	0.641979i	$-0.221886\pi$
$467$	12.8389	+	7.41254i	0.594113	+	0.343012i	−0.172609	+	0.984990i	$0.555220\pi$
$468$	9.10996	+	11.9199i	0.421108	+	0.550998i
$469$	7.02025	+	2.07762i	0.324165	+	0.0959357i
$470$		0			0
$471$	−22.8053	+	15.2062i	−1.05081	+	0.700664i
$472$	4.96573	+	8.60089i	0.228566	+	0.395888i
$473$	2.94438	+	5.09982i	0.135383	+	0.234490i
$474$	3.68756	−	2.45880i	0.169375	−	0.112937i
$475$		0			0
$476$	−3.89651	−	16.2126i	−0.178596	−	0.743105i
$477$	5.92555	+	7.75328i	0.271312	+	0.354998i
$478$	9.28556	+	5.36102i	0.424712	+	0.245207i
$479$	−11.5223	−	19.9573i	−0.526469	−	0.911871i	−0.999524	−	0.0308386i	$-0.990182\pi$
$479$	−11.5223	−	19.9573i	−0.526469	−	0.911871i	0.473055	−	0.881033i	$-0.343151\pi$
$480$		0			0
$481$	29.9232	+	17.2762i	1.36438	+	0.787725i
$482$		−	1.18465i		−	0.0539593i
$483$	8.63973	+	27.8954i	0.393121	+	1.26929i
$484$	5.67867			0.258121
$485$		0			0
$486$	15.2741	+	3.11493i	0.692846	+	0.141296i
$487$	−9.20383	+	5.31384i	−0.417066	+	0.240793i	−0.693821	−	0.720147i	$-0.744074\pi$
$487$	−9.20383	+	5.31384i	−0.417066	+	0.240793i	0.276756	+	0.960940i	$0.410741\pi$
$488$	5.18202	+	2.99184i	0.234579	+	0.135434i
$489$	6.61397	−	13.3792i	0.299094	−	0.605030i
$490$		0			0
$491$		−	22.4687i		−	1.01400i	−0.861947	−	0.506998i	$-0.830755\pi$
$491$		−	22.4687i		−	1.01400i	0.861947	−	0.506998i	$-0.169245\pi$
$492$	−14.1135	+	9.41063i	−0.636285	+	0.424264i
$493$	12.0857	+	20.9331i	0.544313	+	0.942778i
$494$	−32.7290	+	18.8961i	−1.47255	+	0.850176i
$495$		0			0
$496$		−	4.38153i		−	0.196737i
$497$	−5.48579	+	5.20837i	−0.246071	+	0.233627i
$498$	1.41035	−	2.85295i	0.0631992	−	0.127844i
$499$	−19.8794	+	34.4322i	−0.889925	+	1.54140i	−0.0499622	+	0.998751i	$0.515910\pi$
$499$	−19.8794	+	34.4322i	−0.889925	+	1.54140i	−0.839963	+	0.542644i	$0.817423\pi$
$500$		0			0
$501$	−14.9502	+	0.965392i	−0.667926	+	0.0431305i
$502$	7.18445	−	12.4438i	0.320658	−	0.555396i
$503$			18.6717i			0.832530i	0.909243	+	0.416265i	$0.136661\pi$
$503$			18.6717i			0.832530i	−0.909243	+	0.416265i	$0.863339\pi$
$504$	−6.15997	−	5.00547i	−0.274387	−	0.222961i
$505$		0			0
$506$	−12.7308	−	7.35011i	−0.565952	−	0.326752i
$507$	1.34029	+	20.7559i	0.0595244	+	0.921804i
$508$	−1.59084	+	0.918471i	−0.0705820	+	0.0407506i
$509$	2.01643	−	3.49256i	0.0893768	−	0.154805i	−0.817871	−	0.575402i	$-0.804846\pi$
$509$	2.01643	−	3.49256i	0.0893768	−	0.154805i	0.907248	+	0.420596i	$0.138179\pi$
$510$		0			0
$511$	2.76432	−	9.34059i	0.122286	−	0.413203i
$512$	−1.00000			−0.0441942
$513$	−12.7300	+	37.1475i	−0.562044	+	1.64010i
$514$	−14.3206	+	8.26802i	−0.631656	+	0.364687i
$515$		0			0
$516$	−2.45293	−	3.67875i	−0.107984	−	0.161948i
$517$	−3.82198			−0.168091
$518$	−17.5288	−	5.18759i	−0.770170	−	0.227930i
$519$	−13.7636	+	27.8420i	−0.604154	+	1.22213i
$520$		0			0
$521$	5.27733	+	9.14060i	0.231204	+	0.400457i	0.958163	−	0.286224i	$-0.0924002\pi$
$521$	5.27733	+	9.14060i	0.231204	+	0.400457i	−0.726959	+	0.686681i	$0.759067\pi$
$522$	10.6216	+	4.42368i	0.464896	+	0.193619i
$523$	−10.2661	+	17.7815i	−0.448907	+	0.777529i	−0.998315	−	0.0580246i	$-0.981520\pi$
$523$	−10.2661	+	17.7815i	−0.448907	+	0.777529i	0.549408	+	0.835554i	$0.314853\pi$
$524$	−5.53883			−0.241965
$525$		0			0
$526$	−30.9400			−1.34905
$527$	13.8069	−	23.9142i	0.601436	−	1.04172i
$528$	3.98719	−	0.257468i	0.173520	−	0.0112049i
$529$	−8.80476	−	15.2503i	−0.382816	−	0.663056i
$530$		0			0
$531$	18.0920	+	23.6724i	0.785125	+	1.02730i
$532$	14.5001	−	13.7668i	0.628657	−	0.596866i
$533$	−48.9768			−2.12142
$534$	−8.48469	+	5.65745i	−0.367168	+	0.244822i
$535$		0			0
$536$	2.39643	−	1.38358i	0.103510	−	0.0597616i
$537$	11.5469	+	17.3174i	0.498286	+	0.747299i
$538$	−4.10422			−0.176946
$539$	−7.33790	−	14.3840i	−0.316066	−	0.619564i
$540$		0			0
$541$	4.59255	−	7.95454i	0.197449	−	0.341992i	−0.750251	−	0.661153i	$-0.770068\pi$
$541$	4.59255	−	7.95454i	0.197449	−	0.341992i	0.947701	+	0.319160i	$0.103401\pi$
$542$	−7.86071	+	4.53838i	−0.337646	+	0.194940i
$543$	16.4654	−	1.06324i	0.706600	−	0.0456279i
$544$	−5.45795	−	3.15115i	−0.234008	−	0.135104i
$545$		0			0
$546$	−6.77999	−	21.8908i	−0.290157	−	0.936841i
$547$		−	5.21319i		−	0.222900i	−0.993770	−	0.111450i	$-0.964450\pi$
$547$		−	5.21319i		−	0.222900i	0.993770	−	0.111450i	$-0.0355495\pi$
$548$	−0.620520	+	1.07477i	−0.0265073	+	0.0459120i
$549$	16.5713	+	6.90157i	0.707246	+	0.294552i
$550$		0			0
$551$	−14.4921	+	25.1011i	−0.617386	+	1.06934i
$552$	9.89460	+	4.89136i	0.421142	+	0.208190i
$553$	−6.58275	+	1.58208i	−0.279927	+	0.0672770i
$554$		−	0.216476i		−	0.00919717i
$555$		0			0
$556$	10.8551	−	6.26718i	0.460358	−	0.265788i
$557$	−12.9066	−	22.3550i	−0.546872	−	0.947210i	−0.998487	−	0.0549970i	$-0.982485\pi$
$557$	−12.9066	−	22.3550i	−0.546872	−	0.947210i	0.451614	−	0.892213i	$-0.350848\pi$
$558$	−1.69055	−	13.0354i	−0.0715665	−	0.551834i
$559$		−	12.7661i		−	0.539947i
$560$		0			0
$561$	22.5732	+	11.1590i	0.953042	+	0.471133i
$562$	−16.3244	−	9.42488i	−0.688602	−	0.397565i
$563$	−32.4704	+	18.7468i	−1.36847	+	0.790084i	−0.990732	−	0.135831i	$-0.956630\pi$
$563$	−32.4704	+	18.7468i	−1.36847	+	0.790084i	−0.377733	+	0.925914i	$0.623296\pi$
$564$	2.86375	−	0.184924i	0.120586	−	0.00778669i
$565$		0			0
$566$	1.99832			0.0839956
$567$	−20.2577	−	12.5150i	−0.850745	−	0.525579i
$568$			2.85910i			0.119965i
$569$	−35.0352	−	20.2276i	−1.46875	−	0.847985i	−0.469367	−	0.883003i	$-0.655518\pi$
$569$	−35.0352	−	20.2276i	−1.46875	−	0.847985i	−0.999387	+	0.0350177i	$0.988851\pi$
$570$		0			0
$571$	14.5551	+	25.2101i	0.609111	+	1.05501i	0.991387	+	0.130963i	$0.0418070\pi$
$571$	14.5551	+	25.2101i	0.609111	+	1.05501i	−0.382276	+	0.924048i	$0.624860\pi$
$572$	9.99042	+	5.76797i	0.417720	+	0.241171i
$573$	3.81613	−	7.71954i	0.159421	−	0.322488i
$574$	25.1943	−	6.05514i	1.05159	−	0.252737i
$575$		0			0
$576$	−2.97509	+	0.385834i	−0.123962	+	0.0160764i
$577$	−7.58769	−	13.1423i	−0.315880	−	0.547120i	0.663744	−	0.747959i	$-0.268966\pi$
$577$	−7.58769	−	13.1423i	−0.315880	−	0.547120i	−0.979624	+	0.200840i	$0.935633\pi$
$578$	−11.3595	−	19.6752i	−0.472492	−	0.818380i
$579$	−5.79722	−	8.69431i	−0.240924	−	0.361323i
$580$		0			0
$581$	−3.52550	+	3.34722i	−0.146262	+	0.138866i
$582$	7.16912	+	3.54403i	0.297169	+	0.146905i
$583$	6.49824	+	3.75176i	0.269130	+	0.155382i
$584$	−1.84089	−	3.18851i	−0.0761764	−	0.131941i
$585$		0			0
$586$	8.03773	+	4.64059i	0.332036	+	0.191701i
$587$			3.22807i			0.133237i	0.997779	+	0.0666183i	$0.0212210\pi$
$587$			3.22807i			0.133237i	−0.997779	+	0.0666183i	$0.978779\pi$
$588$	6.19414	+	10.4227i	0.255442	+	0.429825i
$589$	33.1120			1.36436
$590$		0			0
$591$	1.58651	+	24.5689i	0.0652601	+	1.01063i
$592$	−5.98363	+	3.45465i	−0.245926	+	0.141985i
$593$	37.8717	+	21.8653i	1.55521	+	0.897899i	0.997704	+	0.0677234i	$0.0215735\pi$
$593$	37.8717	+	21.8653i	1.55521	+	0.897899i	0.557502	+	0.830175i	$0.311760\pi$
$594$	11.7629	−	2.30439i	0.482637	−	0.0945501i
$595$		0			0
$596$		−	15.5951i		−	0.638802i
$597$	−2.16283	−	3.24369i	−0.0885189	−	0.132755i
$598$	15.9341	+	27.5986i	0.651593	+	1.12859i
$599$	6.96777	−	4.02284i	0.284695	−	0.164369i	−0.350852	−	0.936431i	$-0.614108\pi$
$599$	6.96777	−	4.02284i	0.284695	−	0.164369i	0.635547	+	0.772062i	$0.280775\pi$
$600$		0			0
$601$			8.38546i			0.342050i	0.985267	+	0.171025i	$0.0547079\pi$
$601$			8.38546i			0.342050i	−0.985267	+	0.171025i	$0.945292\pi$
$602$	1.57830	+	6.56703i	0.0643269	+	0.267652i
$603$	6.59576	−	5.04090i	0.268600	−	0.205281i
$604$	−1.51958	+	2.63198i	−0.0618306	+	0.107094i
$605$		0			0
$606$	1.26279	+	19.5558i	0.0512974	+	0.794398i
$607$	−8.46682	+	14.6650i	−0.343658	+	0.595232i	−0.985109	−	0.171931i	$-0.944999\pi$
$607$	−8.46682	+	14.6650i	−0.343658	+	0.595232i	0.641451	+	0.767164i	$0.278333\pi$
$608$		−	7.55717i		−	0.306484i
$609$	−12.8976	−	11.9397i	−0.522639	−	0.483821i
$610$		0			0
$611$	7.17550	+	4.14278i	0.290290	+	0.167599i
$612$	−17.4537	−	7.26907i	−0.705523	−	0.293835i
$613$	−29.3464	+	16.9432i	−1.18529	+	0.684328i	−0.957233	−	0.289319i	$-0.906571\pi$
$613$	−29.3464	+	16.9432i	−1.18529	+	0.684328i	−0.228058	+	0.973647i	$0.573238\pi$
$614$	−13.4641	+	23.3205i	−0.543366	+	0.941138i
$615$		0			0
$616$	−5.85231	−	1.73198i	−0.235796	−	0.0697833i
$617$	−37.5359			−1.51114			−0.755570	−	0.655068i	$-0.772640\pi$
$617$	−37.5359			−1.51114			−0.755570	+	0.655068i	$0.772640\pi$
$618$	10.6122	−	7.07602i	0.426885	−	0.284639i
$619$	−14.6497	+	8.45802i	−0.588822	+	0.339957i	−0.764632	−	0.644468i	$-0.777079\pi$
$619$	−14.6497	+	8.45802i	−0.588822	+	0.339957i	0.175809	+	0.984424i	$0.443746\pi$
$620$		0			0
$621$	31.3245	+	10.7345i	1.25701	+	0.430762i
$622$	−2.82130			−0.113124
$623$	15.1462	−	3.64021i	0.606820	−	0.145842i
$624$	−7.76475	−	3.83848i	−0.310839	−	0.153662i
$625$		0			0
$626$	5.72135	+	9.90967i	0.228671	+	0.396070i
$627$	1.94573	+	30.1319i	0.0777051	+	1.20335i
$628$	7.91260	−	13.7050i	0.315747	−	0.546890i
$629$	−43.5445			−1.73623
$630$		0			0
$631$	−29.1879			−1.16195			−0.580977	−	0.813920i	$-0.697329\pi$
$631$	−29.1879			−1.16195			−0.580977	+	0.813920i	$0.697329\pi$
$632$	−1.27945	+	2.21607i	−0.0508937	+	0.0881504i
$633$	3.08089	+	47.7110i	0.122454	+	1.89634i
$634$	4.65491	+	8.06254i	0.184870	+	0.320204i
$635$		0			0
$636$	−5.05056	−	2.49673i	−0.200268	−	0.0990016i
$637$	−1.81495	+	34.9588i	−0.0719108	+	1.38512i
$638$	8.84735			0.350270
$639$	1.10314	+	8.50606i	0.0436394	+	0.336494i
$640$		0			0
$641$	3.95871	−	2.28556i	0.156360	−	0.0902743i	−0.419779	−	0.907627i	$-0.637892\pi$
$641$	3.95871	−	2.28556i	0.156360	−	0.0902743i	0.576138	+	0.817352i	$0.304559\pi$
$642$	−12.1320	+	8.08944i	−0.478814	+	0.319265i
$643$	24.0758			0.949457			0.474728	−	0.880132i	$-0.342546\pi$
$643$	24.0758			0.949457			0.474728	+	0.880132i	$0.342546\pi$
$644$	−11.6088	−	12.2271i	−0.457451	−	0.481816i
$645$		0			0
$646$	23.8138	−	41.2467i	0.936940	−	1.62283i
$647$	−15.0897	+	8.71205i	−0.593238	+	0.342506i	−0.766377	−	0.642391i	$-0.777942\pi$
$647$	−15.0897	+	8.71205i	−0.593238	+	0.342506i	0.173139	+	0.984897i	$0.444609\pi$
$648$	−8.70226	+	2.29578i	−0.341857	+	0.0901867i
$649$	19.8405	+	11.4549i	0.778809	+	0.449646i
$650$		0			0
$651$	−4.44543	+	19.5804i	−0.174230	+	0.767417i
$652$			8.61682i			0.337461i
$653$	18.9455	−	32.8146i	0.741396	−	1.28414i	−0.210464	−	0.977602i	$-0.567497\pi$
$653$	18.9455	−	32.8146i	0.741396	−	1.28414i	0.951860	−	0.306534i	$-0.0991693\pi$
$654$	−0.743688	−	11.5169i	−0.0290805	−	0.450345i
$655$		0			0
$656$	4.89686	−	8.48160i	0.191190	−	0.331151i
$657$	−6.70703	−	8.77580i	−0.261666	−	0.342377i
$658$	−4.20336	−	1.24397i	−0.163864	−	0.0484950i
$659$		−	24.7262i		−	0.963197i	−0.876392	−	0.481599i	$-0.840056\pi$
$659$		−	24.7262i		−	0.963197i	0.876392	−	0.481599i	$-0.159944\pi$
$660$		0			0
$661$	−37.8348	+	21.8439i	−1.47160	+	0.849631i	−0.999491	−	0.0319070i	$-0.989842\pi$
$661$	−37.8348	+	21.8439i	−1.47160	+	0.849631i	−0.472113	+	0.881538i	$0.656509\pi$
$662$	9.14801	+	15.8448i	0.355547	+	0.615826i
$663$	−30.2840	−	45.4181i	−1.17613	−	1.76389i
$664$			1.83743i			0.0713060i
$665$		0			0
$666$	−16.4689	+	12.5866i	−0.638156	+	0.487720i
$667$	21.1664	+	12.2205i	0.819568	+	0.473178i
$668$	7.49067	−	4.32474i	0.289823	−	0.167329i
$669$	−2.57576	−	39.8886i	−0.0995847	−	1.54218i
$670$		0			0
$671$	13.8031			0.532865
$672$	4.46885	+	1.01458i	0.172390	+	0.0391384i
$673$		−	34.1588i		−	1.31673i	−0.752701	−	0.658363i	$-0.771249\pi$
$673$		−	34.1588i		−	1.31673i	0.752701	−	0.658363i	$-0.228751\pi$
$674$	6.79410	+	3.92258i	0.261699	+	0.151092i
$675$		0			0
$676$	−6.00420	−	10.3996i	−0.230931	−	0.399984i
$677$	11.3732	+	6.56630i	0.437106	+	0.252364i	0.702369	−	0.711813i	$-0.252125\pi$
$677$	11.3732	+	6.56630i	0.437106	+	0.252364i	−0.265263	+	0.964176i	$0.585459\pi$
$678$	6.91730	+	3.41954i	0.265657	+	0.131327i
$679$	−8.41113	−	8.85914i	−0.322790	−	0.339983i
$680$		0			0
$681$	−19.2514	−	28.8721i	−0.737715	−	1.10638i
$682$	−5.05366	−	8.75320i	−0.193515	−	0.335177i
$683$	22.9411	+	39.7352i	0.877818	+	1.52043i	0.853730	+	0.520716i	$0.174335\pi$
$683$	22.9411	+	39.7352i	0.877818	+	1.52043i	0.0240882	+	0.999710i	$0.492332\pi$
$684$	−2.91582	−	22.4832i	−0.111489	−	0.859668i
$685$		0			0
$686$	−3.38843	−	18.2077i	−0.129371	−	0.695171i
$687$	22.0789	−	44.6628i	0.842363	−	1.70399i
$688$	2.21077	+	1.27639i	0.0842850	+	0.0486620i
$689$	−8.13333	−	14.0873i	−0.309855	−	0.536685i
$690$		0			0
$691$	−15.2114	−	8.78233i	−0.578671	−	0.334096i	0.181934	−	0.983311i	$-0.441764\pi$
$691$	−15.2114	−	8.78233i	−0.578671	−	0.334096i	−0.760605	+	0.649215i	$0.775098\pi$
$692$		−	17.9315i		−	0.681652i
$693$	−18.0794	−	2.89475i	−0.686779	−	0.109963i
$694$	0.232294			0.00881775
$695$		0			0
$696$	−6.62919	+	0.428072i	−0.251279	+	0.0162260i
$697$	53.4536	−	30.8614i	2.02470	−	1.16896i
$698$	−10.0186	−	5.78426i	−0.379211	−	0.218938i
$699$	39.9220	+	19.7353i	1.50999	+	0.746458i
$700$		0			0
$701$		−	39.2501i		−	1.48246i	−0.671253	−	0.741228i	$-0.734244\pi$
$701$		−	39.2501i		−	1.48246i	0.671253	−	0.741228i	$-0.265756\pi$
$702$	−24.5818	−	8.42388i	−0.927780	−	0.317939i
$703$	−26.1074	−	45.2193i	−0.984659	−	1.70548i
$704$	−1.99775	+	1.15340i	−0.0752930	+	0.0434704i
$705$		0			0
$706$			34.7075i			1.30623i
$707$	8.49472	−	28.7035i	0.319477	−	1.07951i
$708$	−15.4205	−	7.62305i	−0.579536	−	0.286492i
$709$	−23.8340	+	41.2817i	−0.895105	+	1.55037i	−0.0614314	+	0.998111i	$0.519567\pi$
$709$	−23.8340	+	41.2817i	−0.895105	+	1.55037i	−0.833674	+	0.552257i	$0.813767\pi$
$710$		0			0
$711$	−2.95143	+	7.08664i	−0.110687	+	0.265770i
$712$	2.94387	−	5.09894i	0.110326	−	0.191091i
$713$		−	27.9216i		−	1.04567i
$714$	21.1937	+	19.6196i	0.793152	+	0.734243i
$715$		0			0
$716$	−10.4070	−	6.00848i	−0.388928	−	0.224547i
$717$	−18.5325	+	1.19672i	−0.692110	+	0.0446922i
$718$	15.1834	−	8.76612i	0.566638	−	0.327149i
$719$	−16.7107	+	28.9438i	−0.623205	+	1.07942i	0.365680	+	0.930740i	$0.380836\pi$
$719$	−16.7107	+	28.9438i	−0.623205	+	1.07942i	−0.988885	+	0.148682i	$0.952497\pi$
$720$		0			0
$721$	−18.9441	+	4.55297i	−0.705513	+	0.169561i
$722$	38.1109			1.41834
$723$	1.13831	+	1.70717i	0.0423343	+	0.0634904i
$724$	−8.24987	+	4.76306i	−0.306604	+	0.177018i
$725$		0			0
$726$	−8.18340	+	5.45655i	−0.303714	+	0.202512i
$727$	−31.9845			−1.18624			−0.593119	−	0.805115i	$-0.702104\pi$
$727$	−31.9845			−1.18624			−0.593119	+	0.805115i	$0.702104\pi$
$728$	9.10996	+	9.59518i	0.337637	+	0.355621i
$729$	−25.0042	+	10.1878i	−0.926081	+	0.377325i
$730$		0			0
$731$	8.04420	+	13.9330i	0.297525	+	0.515329i
$732$	−10.3425	+	0.667855i	−0.382269	+	0.0246846i
$733$	19.6001	−	33.9483i	0.723945	−	1.25391i	−0.235461	−	0.971884i	$-0.575660\pi$
$733$	19.6001	−	33.9483i	0.723945	−	1.25391i	0.959407	−	0.282026i	$-0.0910066\pi$
$734$	−10.0402			−0.370590
$735$		0			0
$736$	−6.37256			−0.234896
$737$	3.19165	−	5.52810i	0.117566	−	0.203630i
$738$	11.2961	−	27.1229i	0.415814	−	0.998406i
$739$	−16.8814	−	29.2394i	−0.620992	−	1.07559i	−0.989301	−	0.145886i	$-0.953397\pi$
$739$	−16.8814	−	29.2394i	−0.620992	−	1.07559i	0.368310	−	0.929703i	$-0.379937\pi$
$740$		0			0
$741$	29.0080	−	58.6796i	1.06564	−	2.15565i
$742$	5.92555	+	6.24116i	0.217534	+	0.229120i
$743$	14.3933			0.528038			0.264019	−	0.964517i	$-0.414952\pi$
$743$	14.3933			0.528038			0.264019	+	0.964517i	$0.414952\pi$
$744$	4.21015	+	6.31412i	0.154352	+	0.231487i
$745$		0			0
$746$	−0.00417483	+	0.00241034i	−0.000152851	+	8.82487e-5i
$747$	0.708943	+	5.46651i	0.0259389	+	0.200009i
$748$	−14.5381			−0.531567
$749$	21.6572	−	5.20504i	0.791336	−	0.190188i
$750$		0			0
$751$	−8.92040	+	15.4506i	−0.325510	+	0.563800i	−0.981615	−	0.190869i	$-0.938869\pi$
$751$	−8.92040	+	15.4506i	−0.325510	+	0.563800i	0.656105	+	0.754669i	$0.272203\pi$
$752$	−1.43486	+	0.828416i	−0.0523239	+	0.0302092i
$753$	1.60375	+	24.8360i	0.0584440	+	0.905073i
$754$	−16.6103	−	9.58995i	−0.604911	−	0.349245i
$755$		0			0
$756$	13.6867	+	1.29424i	0.497779	+	0.0470709i
$757$		−	1.90604i		−	0.0692760i	−0.999400	−	0.0346380i	$-0.988972\pi$
$757$		−	1.90604i		−	0.0692760i	0.999400	−	0.0346380i	$-0.0110278\pi$
$758$	−9.32860	+	16.1576i	−0.338830	+	0.586871i
$759$	25.4086	−	1.64073i	0.922274	−	0.0595548i
$760$		0			0
$761$	14.1364	−	24.4850i	0.512445	−	0.887581i	−0.487451	−	0.873150i	$-0.662073\pi$
$761$	14.1364	−	24.4850i	0.512445	−	0.887581i	0.999896	−	0.0144304i	$-0.00459350\pi$
$762$	1.40997	−	2.85220i	0.0510780	−	0.103324i
$763$	−5.00275	+	16.9042i	−0.181112	+	0.611973i
$764$			4.97173i			0.179871i
$765$		0			0
$766$	−16.3214	+	9.42316i	−0.589716	+	0.340473i
$767$	−24.8328	−	43.0117i	−0.896661	−	1.55306i
$768$	1.44108	−	0.960885i	0.0520004	−	0.0346729i
$769$			1.43146i			0.0516197i	0.999667	+	0.0258098i	$0.00821644\pi$
$769$			1.43146i			0.0516197i	−0.999667	+	0.0258098i	$0.991784\pi$
$770$		0			0
$771$	12.6925	−	25.6753i	0.457109	−	0.924675i
$772$	5.22491	+	3.01660i	0.188049	+	0.108570i
$773$	30.1528	−	17.4088i	1.08452	−	0.626149i	0.152410	−	0.988317i	$-0.451297\pi$
$773$	30.1528	−	17.4088i	1.08452	−	0.626149i	0.932113	+	0.362168i	$0.117963\pi$
$774$	7.06972	+	2.94438i	0.254116	+	0.105834i
$775$		0			0
$776$	−4.61723			−0.165749
$777$	30.2450	−	9.36742i	1.08503	−	0.336054i
$778$			10.8601i			0.389352i
$779$	64.0969	+	37.0064i	2.29651	+	1.32589i
$780$		0			0
$781$	3.29768	+	5.71175i	0.118000	+	0.204383i
$782$	−34.7811	−	20.0809i	−1.24377	−	0.718091i
$783$	−19.5572	+	3.83132i	−0.698918	+	0.136920i
$784$	−5.87256	−	3.80960i	−0.209734	−	0.136057i
$785$		0			0
$786$	7.98188	−	5.32218i	0.284704	−	0.189836i
$787$	−24.8541	−	43.0486i	−0.885953	−	1.53452i	−0.844617	−	0.535370i	$-0.820172\pi$
$787$	−24.8541	−	43.0486i	−0.885953	−	1.53452i	−0.0413355	−	0.999145i	$-0.513161\pi$
$788$	−7.10719	−	12.3100i	−0.253183	−	0.438526i
$789$	44.5869	−	29.7298i	1.58733	−	1.05841i
$790$		0			0
$791$	−8.11569	−	8.54796i	−0.288561	−	0.303931i
$792$	−5.49845	+	4.20226i	−0.195379	+	0.149321i
$793$	−25.9144	−	14.9617i	−0.920249	−	0.531306i
$794$	−13.5204	−	23.4180i	−0.479822	−	0.831075i
$795$		0			0
$796$	1.94932	+	1.12544i	0.0690917	+	0.0398901i
$797$		−	8.43295i		−	0.298710i	−0.988784	−	0.149355i	$-0.952280\pi$
$797$		−	8.43295i		−	0.298710i	0.988784	−	0.149355i	$-0.0477198\pi$
$798$	−7.66738	+	33.7719i	−0.271422	+	1.19551i
$799$	−10.4419			−0.369406
$800$		0			0
$801$	6.79093	−	16.3056i	0.239946	−	0.576131i
$802$	21.2396	−	12.2627i	0.749998	−	0.433012i
$803$	−7.35525	−	4.24656i	−0.259561	−	0.149858i
$804$	−2.12398	+	4.29655i	−0.0749070	+	0.151527i
$805$		0			0
$806$			21.9113i			0.771794i
$807$	5.91449	−	3.94368i	0.208200	−	0.138824i
$808$	−5.65702	−	9.79825i	−0.199013	−	0.344701i
$809$	−33.7531	+	19.4873i	−1.18669	+	0.685138i	−0.957554	−	0.288255i	$-0.906925\pi$
$809$	−33.7531	+	19.4873i	−1.18669	+	0.685138i	−0.229141	+	0.973393i	$0.573592\pi$
$810$		0			0
$811$		−	29.5668i		−	1.03823i	−0.854704	−	0.519116i	$-0.826261\pi$
$811$		−	29.5668i		−	1.03823i	0.854704	−	0.519116i	$-0.173739\pi$
$812$	9.73018	+	2.87962i	0.341462	+	0.101055i
$813$	6.96702	−	14.0934i	0.244344	−	0.494277i
$814$	−7.96919	+	13.8030i	−0.279320	+	0.483796i
$815$		0			0
$816$	10.8932	−	0.703417i	0.381339	−	0.0246245i
$817$	−9.64591	+	16.7072i	−0.337468	+	0.584511i
$818$			5.40347i			0.188928i
$819$	30.8050	+	25.0316i	1.07642	+	0.874673i
$820$		0			0
$821$	29.1479	+	16.8285i	1.01727	+	0.587320i	0.913311	−	0.407262i	$-0.133516\pi$
$821$	29.1479	+	16.8285i	1.01727	+	0.587320i	0.103956	+	0.994582i	$0.466850\pi$
$822$	−0.138516	−	2.14508i	−0.00483130	−	0.0748182i
$823$	10.8604	−	6.27024i	0.378569	−	0.218567i	−0.298627	−	0.954370i	$-0.596528\pi$
$823$	10.8604	−	6.27024i	0.378569	−	0.218567i	0.677195	+	0.735803i	$0.263195\pi$
$824$	−3.68203	+	6.37747i	−0.128270	+	0.222170i
$825$		0			0
$826$	18.0920	+	19.0556i	0.629501	+	0.663030i
$827$	15.6875			0.545506			0.272753	−	0.962084i	$-0.412066\pi$
$827$	15.6875			0.545506			0.272753	+	0.962084i	$0.412066\pi$
$828$	−18.9589	+	2.45875i	−0.658868	+	0.0854476i
$829$	4.91198	−	2.83593i	0.170600	−	0.0984959i	−0.412269	−	0.911062i	$-0.635264\pi$
$829$	4.91198	−	2.83593i	0.170600	−	0.0984959i	0.582869	+	0.812566i	$0.301930\pi$
$830$		0			0
$831$	0.208008	+	0.311958i	0.00721572	+	0.0108217i
$832$	5.00084			0.173373
$833$	−20.0475	−	39.2979i	−0.694606	−	1.36159i
$834$	−9.62095	+	19.4620i	−0.333146	+	0.673913i
$835$		0			0
$836$	−8.71645	−	15.0973i	−0.301465	−	0.522152i
$837$	14.9618	+	17.1606i	0.517154	+	0.593158i
$838$	−14.1465	+	24.5024i	−0.488682	+	0.846422i
$839$	−14.5217			−0.501346			−0.250673	−	0.968072i	$-0.580652\pi$
$839$	−14.5217			−0.501346			−0.250673	+	0.968072i	$0.580652\pi$
$840$		0			0
$841$	14.2902			0.492766
$842$	−12.5843	+	21.7967i	−0.433685	+	0.751165i
$843$	32.5809	−	2.10387i	1.12215	−	0.0724613i
$844$	−13.8017	−	23.9052i	−0.475073	−	0.822851i
$845$		0			0
$846$	−3.94920	+	3.01823i	−0.135776	+	0.103769i
$847$	14.6084	−	3.51094i	0.501949	−	0.120637i
$848$	3.25278			0.111701
$849$	−2.87973	+	1.92015i	−0.0988320	+	0.0658995i
$850$		0			0
$851$	−38.1310	+	22.0150i	−1.30712	+	0.754663i
$852$	−2.74726	−	4.12018i	−0.0941197	−	0.141155i
$853$	3.66698			0.125555			0.0627775	−	0.998028i	$-0.480004\pi$
$853$	3.66698			0.125555			0.0627775	+	0.998028i	$0.480004\pi$
$854$	15.1805	+	4.49262i	0.519465	+	0.153734i
$855$		0			0
$856$	4.20937	−	7.29084i	0.143873	−	0.249196i
$857$	10.0138	−	5.78149i	0.342066	−	0.197492i	−0.319119	−	0.947715i	$-0.603387\pi$
$857$	10.0138	−	5.78149i	0.342066	−	0.197492i	0.661185	+	0.750223i	$0.270054\pi$
$858$	−19.9393	+	1.28756i	−0.680717	+	0.0439565i
$859$	12.9614	+	7.48325i	0.442236	+	0.255325i	0.704546	−	0.709659i	$-0.251151\pi$
$859$	12.9614	+	7.48325i	0.442236	+	0.255325i	−0.262310	+	0.964984i	$0.584484\pi$
$860$		0			0
$861$	−30.4886	+	32.9347i	−1.03905	+	1.12241i
$862$		−	11.2182i		−	0.382093i
$863$	−4.68639	+	8.11706i	−0.159526	+	0.276308i	−0.934698	−	0.355443i	$-0.884330\pi$
$863$	−4.68639	+	8.11706i	−0.159526	+	0.276308i	0.775172	+	0.631751i	$0.217663\pi$
$864$	3.91658	−	3.41473i	0.133245	−	0.116172i
$865$		0			0
$866$	−0.319796	+	0.553903i	−0.0108671	+	0.0188224i
$867$	35.2754	+	17.4383i	1.19802	+	0.592235i
$868$	−2.70896	−	11.2715i	−0.0919482	−	0.382579i
$869$			5.90286i			0.200241i
$870$		0			0
$871$	−11.9842	+	6.91907i	−0.406069	+	0.234444i
$872$	3.33156	+	5.77043i	0.112821	+	0.195411i
$873$	−13.7366	+	1.78148i	−0.464915	+	0.0602941i
$874$		−	48.1585i		−	1.62899i
$875$		0			0
$876$	5.71664	+	2.82600i	0.193148	+	0.0954818i
$877$	13.5293	+	7.81117i	0.456853	+	0.263764i	0.710720	−	0.703475i	$-0.248369\pi$
$877$	13.5293	+	7.81117i	0.456853	+	0.263764i	−0.253867	+	0.967239i	$0.581703\pi$
$878$	11.3999	−	6.58174i	0.384728	−	0.222123i
$879$	−16.0420	+	1.03590i	−0.541085	+	0.0349399i
$880$		0			0
$881$	−4.54709			−0.153195			−0.0765977	−	0.997062i	$-0.524406\pi$
$881$	−4.54709			−0.153195			−0.0765977	+	0.997062i	$0.524406\pi$
$882$	−18.9412	−	9.06804i	−0.637785	−	0.305337i
$883$			48.8190i			1.64289i	0.570288	+	0.821445i	$0.306831\pi$
$883$			48.8190i			1.64289i	−0.570288	+	0.821445i	$0.693169\pi$
$884$	27.2943	+	15.7584i	0.918008	+	0.530012i
$885$		0			0
$886$	−12.9223	−	22.3821i	−0.434133	−	0.751941i
$887$	−6.30758	−	3.64168i	−0.211788	−	0.122276i	0.390354	−	0.920665i	$-0.372353\pi$
$887$	−6.30758	−	3.64168i	−0.211788	−	0.122276i	−0.602142	+	0.798389i	$0.705686\pi$
$888$	5.30334	−	10.7280i	0.177969	−	0.360008i
$889$	−3.52457	+	3.34633i	−0.118210	+	0.112232i
$890$		0			0
$891$	−14.7370	+	14.6236i	−0.493707	+	0.489908i
$892$	11.5388	+	19.9858i	0.386349	+	0.669176i
$893$	−6.26049	−	10.8435i	−0.209499	−	0.362863i
$894$	14.9851	+	22.4738i	0.501178	+	0.751636i
$895$		0			0
$896$	−2.57250	+	0.618268i	−0.0859411	+	0.0206549i
$897$	−49.4813	−	24.4609i	−1.65213	−	0.816726i
$898$	−24.5593	−	14.1793i	−0.819554	−	0.473170i
$899$	8.40232	+	14.5532i	0.280233	+	0.485378i
$900$		0			0
$901$	17.7535	+	10.2500i	0.591456	+	0.341477i
$902$		−	22.5921i		−	0.752236i
$903$	−8.58461	−	7.94702i	−0.285678	−	0.264460i
$904$	−4.45505			−0.148173
$905$		0			0
$906$	−0.339208	−	5.25302i	−0.0112694	−	0.174520i
$907$	−23.2928	+	13.4481i	−0.773425	+	0.446537i	−0.834095	−	0.551621i	$-0.814010\pi$
$907$	−23.2928	+	13.4481i	−0.773425	+	0.446537i	0.0606703	+	0.998158i	$0.480676\pi$
$908$	17.3509	+	10.0175i	0.575809	+	0.332444i
$909$	−20.6106	−	26.9679i	−0.683611	−	0.894470i
$910$		0			0
$911$			46.4059i			1.53750i	0.639552	+	0.768748i	$0.279120\pi$
$911$			46.4059i			1.53750i	−0.639552	+	0.768748i	$0.720880\pi$
$912$	7.26157	+	10.8905i	0.240455	+	0.360619i
$913$	2.11929	+	3.67072i	0.0701383	+	0.121483i
$914$	25.2797	−	14.5953i	0.836179	−	0.482768i
$915$		0			0
$916$			28.7648i			0.950417i
$917$	−14.2486	+	3.42448i	−0.470531	+	0.113086i
$918$	32.1368	−	6.29570i	1.06067	−	0.207789i
$919$	−2.26073	+	3.91570i	−0.0745746	+	0.129167i	−0.900901	−	0.434024i	$-0.857093\pi$
$919$	−2.26073	+	3.91570i	−0.0745746	+	0.129167i	0.826327	+	0.563191i	$0.190427\pi$
$920$		0			0
$921$	−3.00553	−	46.5440i	−0.0990355	−	1.53368i
$922$	−15.5484	+	26.9306i	−0.512060	+	0.886913i
$923$		−	14.2979i		−	0.470621i
$924$	10.0979	−	3.12749i	0.332195	−	0.102887i
$925$		0			0
$926$	29.0045	+	16.7457i	0.953146	+	0.550299i
$927$	−8.49372	+	20.3942i	−0.278970	+	0.669833i
$928$	3.32150	−	1.91767i	0.109033	−	0.0629505i
$929$	−8.30472	+	14.3842i	−0.272469	+	0.471930i	−0.969493	−	0.245117i	$-0.921174\pi$
$929$	−8.30472	+	14.3842i	−0.272469	+	0.471930i	0.697025	+	0.717047i	$0.254507\pi$
$930$		0			0
$931$	28.7898	−	44.3800i	0.943547	−	1.45449i
$932$	−25.7115			−0.842209
$933$	4.06570	−	2.71094i	0.133105	−	0.0887522i
$934$	12.8389	−	7.41254i	0.420102	−	0.242546i
$935$		0			0
$936$	14.8779	−	1.92950i	0.486300	−	0.0630675i
$937$	−20.5347			−0.670839			−0.335419	−	0.942069i	$-0.608878\pi$
$937$	−20.5347			−0.670839			−0.335419	+	0.942069i	$0.608878\pi$
$938$	5.30940	−	5.04090i	0.173358	−	0.164591i
$939$	−17.7670	−	8.78303i	−0.579803	−	0.286623i
$940$		0			0
$941$	−12.1992	−	21.1296i	−0.397682	−	0.688805i	0.595758	−	0.803164i	$-0.296852\pi$
$941$	−12.1992	−	21.1296i	−0.397682	−	0.688805i	−0.993439	+	0.114359i	$0.963519\pi$
$942$	1.76629	+	27.3531i	0.0575490	+	0.891211i
$943$	31.2055	−	54.0495i	1.01619	−	1.76009i
$944$	9.93145			0.323241
$945$		0			0
$946$	5.88876			0.191460
$947$	9.55667	−	16.5526i	0.310550	−	0.537888i	−0.667932	−	0.744223i	$-0.732820\pi$
$947$	9.55667	−	16.5526i	0.310550	−	0.537888i	0.978482	+	0.206334i	$0.0661534\pi$
$948$	−0.285605	−	4.42292i	−0.00927602	−	0.143650i
$949$	9.20598	+	15.9452i	0.298839	+	0.517604i
$950$		0			0
$951$	−14.4553	−	7.14590i	−0.468744	−	0.231722i
$952$	−15.9888	−	4.73184i	−0.518200	−	0.153360i
$953$	−7.20297			−0.233327			−0.116664	−	0.993171i	$-0.537220\pi$
$953$	−7.20297			−0.233327			−0.116664	+	0.993171i	$0.537220\pi$
$954$	9.67731	−	1.25504i	0.313314	−	0.0406333i
$955$		0			0
$956$	9.28556	−	5.36102i	0.300317	−	0.173388i
$957$	−12.7497	+	8.50129i	−0.412139	+	0.274808i
$958$	−23.0447			−0.744540
$959$	−0.931789	+	3.14850i	−0.0300890	+	0.101670i
$960$		0			0
$961$	−5.90109	+	10.2210i	−0.190358	+	0.329709i
$962$	29.9232	−	17.2762i	0.964762	−	0.557006i
$963$	9.71018	−	23.3150i	0.312906	−	0.751315i
$964$	−1.02594	−	0.592325i	−0.0330432	−	0.0190775i
$965$		0			0
$966$	28.4780	+	6.46549i	0.916265	+	0.208024i
$967$		−	12.2448i		−	0.393765i	−0.980427	−	0.196883i	$-0.936918\pi$
$967$		−	12.2448i		−	0.393765i	0.980427	−	0.196883i	$-0.0630818\pi$
$968$	2.83934	−	4.91787i	0.0912597	−	0.158066i
$969$	5.31584	+	82.3219i	0.170769	+	2.64456i
$970$		0			0
$971$	13.4388	−	23.2768i	0.431273	−	0.746987i	−0.565710	−	0.824604i	$-0.691398\pi$
$971$	13.4388	−	23.2768i	0.431273	−	0.746987i	0.996983	+	0.0776173i	$0.0247312\pi$
$972$	10.3346	−	11.6703i	0.331484	−	0.374324i
$973$	24.0499	−	22.8337i	0.771003	−	0.732014i
$974$			10.6277i			0.340533i
$975$		0			0
$976$	5.18202	−	2.99184i	0.165872	−	0.0957664i
$977$	18.3770	+	31.8298i	0.587931	+	1.01833i	0.994503	+	0.104707i	$0.0333906\pi$
$977$	18.3770	+	31.8298i	0.587931	+	1.01833i	−0.406572	+	0.913619i	$0.633276\pi$
$978$	−8.27977	−	12.4175i	−0.264758	−	0.397067i
$979$		−	13.5819i		−	0.434078i
$980$		0			0
$981$	12.1381	+	15.8821i	0.387540	+	0.507076i
$982$	−19.4584	−	11.2343i	−0.620943	−	0.358502i
$983$	−11.5791	+	6.68519i	−0.369315	+	0.213224i	−0.673159	−	0.739498i	$-0.735063\pi$
$983$	−11.5791	+	6.68519i	−0.369315	+	0.213224i	0.303844	+	0.952722i	$0.401730\pi$
$984$	1.09310	+	16.9279i	0.0348468	+	0.539643i
$985$		0			0
$986$	24.1714			0.769775
$987$	7.25267	−	2.24628i	0.230855	−	0.0715000i
$988$			37.7922i			1.20233i
$989$	14.0883	+	8.13388i	0.447982	+	0.258642i
$990$		0			0
$991$	−8.34843	−	14.4599i	−0.265197	−	0.459334i	0.702419	−	0.711764i	$-0.252104\pi$
$991$	−8.34843	−	14.4599i	−0.265197	−	0.459334i	−0.967615	+	0.252430i	$0.918770\pi$
$992$	−3.79452	−	2.19077i	−0.120476	−	0.0695569i
$993$	−28.4080	−	14.0434i	−0.901501	−	0.445654i
$994$	1.76769	+	7.35502i	0.0560677	+	0.233287i
$995$		0			0
$996$	−1.76556	−	2.64787i	−0.0559438	−	0.0839011i
$997$	24.5927	+	42.5957i	0.778857	+	1.34902i	0.932601	+	0.360910i	$0.117534\pi$
$997$	24.5927	+	42.5957i	0.778857	+	1.34902i	−0.153743	+	0.988111i	$0.549133\pi$
$998$	19.8794	+	34.4322i	0.629272	+	1.08993i
$999$	11.6387	−	33.9629i	0.368231	−	1.07454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.u.g.299.4		12
3.2	odd	2		1050.2.u.e.299.6		12
5.2	odd	4		1050.2.s.g.551.6		12
5.3	odd	4		210.2.r.a.131.1	yes	12
5.4	even	2		1050.2.u.f.299.3		12
7.3	odd	6		1050.2.u.h.899.1		12
15.2	even	4		1050.2.s.f.551.3		12
15.8	even	4		210.2.r.b.131.4	yes	12
15.14	odd	2		1050.2.u.h.299.1		12
21.17	even	6		1050.2.u.f.899.3		12
35.3	even	12		210.2.r.b.101.4	yes	12
35.17	even	12		1050.2.s.f.101.3		12
35.23	odd	12		1470.2.b.b.881.10		12
35.24	odd	6		1050.2.u.e.899.6		12
35.33	even	12		1470.2.b.a.881.9		12
105.17	odd	12		1050.2.s.g.101.6		12
105.23	even	12		1470.2.b.a.881.3		12
105.38	odd	12		210.2.r.a.101.1	✓	12
105.59	even	6	inner	1050.2.u.g.899.4		12
105.68	odd	12		1470.2.b.b.881.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.1	✓	12	105.38	odd	12
210.2.r.a.131.1	yes	12	5.3	odd	4
210.2.r.b.101.4	yes	12	35.3	even	12
210.2.r.b.131.4	yes	12	15.8	even	4
1050.2.s.f.101.3		12	35.17	even	12
1050.2.s.f.551.3		12	15.2	even	4
1050.2.s.g.101.6		12	105.17	odd	12
1050.2.s.g.551.6		12	5.2	odd	4
1050.2.u.e.299.6		12	3.2	odd	2
1050.2.u.e.899.6		12	35.24	odd	6
1050.2.u.f.299.3		12	5.4	even	2
1050.2.u.f.899.3		12	21.17	even	6
1050.2.u.g.299.4		12	1.1	even	1	trivial
1050.2.u.g.899.4		12	105.59	even	6	inner
1050.2.u.h.299.1		12	15.14	odd	2
1050.2.u.h.899.1		12	7.3	odd	6
1470.2.b.a.881.3		12	105.23	even	12
1470.2.b.a.881.9		12	35.33	even	12
1470.2.b.b.881.4		12	105.68	odd	12
1470.2.b.b.881.10		12	35.23	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.111613 + 1.72845i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.55269 + 0.767566i) q^{6} +(-1.82168 - 1.91871i) q^{7} -1.00000 q^{8} +(-2.97509 + 0.385834i) q^{9} +(-1.99775 + 1.15340i) q^{11} +(1.44108 - 0.960885i) q^{12} +5.00084 q^{13} +(-2.57250 + 0.618268i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.45795 + 3.15115i) q^{17} +(-1.15340 + 2.76942i) q^{18} +(-6.54470 - 3.77859i) q^{19} +(3.11308 - 3.36285i) q^{21} +2.30680i q^{22} +(-3.18628 + 5.51880i) q^{23} +(-0.111613 - 1.72845i) q^{24} +(2.50042 - 4.33086i) q^{26} +(-0.998953 - 5.09922i) q^{27} +(-0.750813 + 2.53698i) q^{28} -3.83533i q^{29} +(-3.79452 + 2.19077i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.21657 - 3.32428i) q^{33} +6.30230i q^{34} +(1.82168 + 2.38358i) q^{36} +(5.98363 + 3.45465i) q^{37} +(-6.54470 + 3.77859i) q^{38} +(0.558158 + 8.64371i) q^{39} -9.79371 q^{41} +(-1.35577 - 4.37743i) q^{42} -2.55278i q^{43} +(1.99775 + 1.15340i) q^{44} +(3.18628 + 5.51880i) q^{46} +(1.43486 + 0.828416i) q^{47} +(-1.55269 - 0.767566i) q^{48} +(-0.362928 + 6.99059i) q^{49} +(-6.05578 - 9.08209i) q^{51} +(-2.50042 - 4.33086i) q^{52} +(-1.62639 - 2.81699i) q^{53} +(-4.91553 - 1.68449i) q^{54} +(1.82168 + 1.91871i) q^{56} +(5.80063 - 11.7339i) q^{57} +(-3.32150 - 1.91767i) q^{58} +(-4.96573 - 8.60089i) q^{59} +(-5.18202 - 2.99184i) q^{61} +4.38153i q^{62} +(6.15997 + 5.00547i) q^{63} +1.00000 q^{64} +(-3.98719 + 0.257468i) q^{66} +(-2.39643 + 1.38358i) q^{67} +(5.45795 + 3.15115i) q^{68} +(-9.89460 - 4.89136i) q^{69} -2.85910i q^{71} +(2.97509 - 0.385834i) q^{72} +(1.84089 + 3.18851i) q^{73} +(5.98363 - 3.45465i) q^{74} +7.55717i q^{76} +(5.85231 + 1.73198i) q^{77} +(7.76475 + 3.83848i) q^{78} +(1.27945 - 2.21607i) q^{79} +(8.70226 - 2.29578i) q^{81} +(-4.89686 + 8.48160i) q^{82} -1.83743i q^{83} +(-4.46885 - 1.01458i) q^{84} +(-2.21077 - 1.27639i) q^{86} +(6.62919 - 0.428072i) q^{87} +(1.99775 - 1.15340i) q^{88} +(-2.94387 + 5.09894i) q^{89} +(-9.10996 - 9.59518i) q^{91} +6.37256 q^{92} +(-4.21015 - 6.31412i) q^{93} +(1.43486 - 0.828416i) q^{94} +(-1.44108 + 0.960885i) q^{96} +4.61723 q^{97} +(5.87256 + 3.80960i) q^{98} +(5.49845 - 4.20226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 2 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} - 12 q^{11} + 2 q^{12} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 12 q^{17} - 18 q^{21} - 2 q^{23} + 4 q^{24} - 4 q^{26} - 28 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 2 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 - 12 * q^11 + 2 * q^12 - 8 * q^13 - 12 * q^14 - 6 * q^16 - 12 * q^17 - 18 * q^21 - 2 * q^23 + 4 * q^24 - 4 * q^26 - 28 * q^27 - 6 * q^28 + 12 * q^31 + 6 * q^32 - 14 * q^33 + 6 * q^36 - 30 * q^39 - 4 * q^41 - 6 * q^42 + 12 * q^44 + 2 * q^46 - 24 * q^47 + 2 * q^48 + 14 * q^49 + 4 * q^51 + 4 * q^52 - 8 * q^53 + 4 * q^54 + 6 * q^56 + 20 * q^57 + 18 * q^58 - 12 * q^59 - 30 * q^61 + 38 * q^63 + 12 * q^64 - 34 * q^66 - 6 * q^67 + 12 * q^68 - 50 * q^69 + 6 * q^72 + 20 * q^77 + 12 * q^78 + 4 * q^79 + 50 * q^81 - 2 * q^82 + 12 * q^84 - 54 * q^86 + 34 * q^87 + 12 * q^88 - 26 * q^89 + 28 * q^91 + 4 * q^92 - 60 * q^93 - 24 * q^94 - 2 * q^96 + 72 * q^97 - 2 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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