LMFDB - Embedded newform 1050.2.s.f.101.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1050,2,Mod(101,1050)] 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, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1050.101"); 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.s (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-2,6,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == 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:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Root			$-0.111613 + 1.72845i$ of defining polynomial
Character	$\chi$	$=$	1050.101
Dual form			1050.2.s.f.551.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.960885 + 1.44108i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.55269 - 0.767566i) q^{6} +(1.91871 + 1.82168i) q^{7} +1.00000i q^{8} +(-1.15340 + 2.76942i) q^{9} +(1.99775 + 1.15340i) q^{11} +(1.72845 - 0.111613i) q^{12} +5.00084i q^{13} +(-2.57250 - 0.618268i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.15115 - 5.45795i) q^{17} +(-0.385834 - 2.97509i) q^{18} +(6.54470 - 3.77859i) q^{19} +(-0.781523 + 4.51544i) q^{21} -2.30680 q^{22} +(-5.51880 + 3.18628i) q^{23} +(-1.44108 + 0.960885i) q^{24} +(-2.50042 - 4.33086i) q^{26} +(-5.09922 + 0.998953i) q^{27} +(2.53698 - 0.750813i) q^{28} +3.83533i q^{29} +(-3.79452 - 2.19077i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.257468 + 3.98719i) q^{33} +6.30230i q^{34} +(1.82168 + 2.38358i) q^{36} +(-3.45465 - 5.98363i) q^{37} +(-3.77859 + 6.54470i) q^{38} +(-7.20659 + 4.80523i) q^{39} +9.79371 q^{41} +(-1.58090 - 4.30125i) q^{42} -2.55278 q^{43} +(1.99775 - 1.15340i) q^{44} +(3.18628 - 5.51880i) q^{46} +(0.828416 + 1.43486i) q^{47} +(0.767566 - 1.55269i) q^{48} +(0.362928 + 6.99059i) q^{49} +(10.8932 - 0.703417i) q^{51} +(4.33086 + 2.50042i) q^{52} +(2.81699 + 1.62639i) q^{53} +(3.91658 - 3.41473i) q^{54} +(-1.82168 + 1.91871i) q^{56} +(11.7339 + 5.80063i) q^{57} +(-1.91767 - 3.32150i) q^{58} +(-4.96573 + 8.60089i) q^{59} +(-5.18202 + 2.99184i) q^{61} +4.38153 q^{62} +(-7.25805 + 3.21259i) q^{63} -1.00000 q^{64} +(-2.21657 - 3.32428i) q^{66} +(-1.38358 + 2.39643i) q^{67} +(-3.15115 - 5.45795i) q^{68} +(-9.89460 - 4.89136i) q^{69} -2.85910i q^{71} +(-2.76942 - 1.15340i) q^{72} +(3.18851 + 1.84089i) q^{73} +(5.98363 + 3.45465i) q^{74} -7.55717i q^{76} +(1.73198 + 5.85231i) q^{77} +(3.83848 - 7.76475i) q^{78} +(-1.27945 - 2.21607i) q^{79} +(-6.33934 - 6.38849i) q^{81} +(-8.48160 + 4.89686i) q^{82} +1.83743 q^{83} +(3.51973 + 2.93454i) q^{84} +(2.21077 - 1.27639i) q^{86} +(-5.52701 + 3.68532i) q^{87} +(-1.15340 + 1.99775i) q^{88} +(-2.94387 - 5.09894i) q^{89} +(-9.10996 + 9.59518i) q^{91} +6.37256i q^{92} +(-0.489035 - 7.57326i) q^{93} +(-1.43486 - 0.828416i) q^{94} +(0.111613 + 1.72845i) q^{96} -4.61723i q^{97} +(-3.80960 - 5.87256i) q^{98} +(-5.49845 + 4.20226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 6 q^{4} + 2 q^{6} - 8 q^{7} + 12 q^{11} + 2 q^{12} - 12 q^{14} - 6 q^{16} + 12 q^{17} + 4 q^{18} + 4 q^{21} - 24 q^{23} - 2 q^{24} + 4 q^{26} - 8 q^{27} - 4 q^{28} + 12 q^{31} + 2 q^{33}+ \cdots + 48 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 6 * q^4 + 2 * q^6 - 8 * q^7 + 12 * q^11 + 2 * q^12 - 12 * q^14 - 6 * q^16 + 12 * q^17 + 4 * q^18 + 4 * q^21 - 24 * q^23 - 2 * q^24 + 4 * q^26 - 8 * q^27 - 4 * q^28 + 12 * q^31 + 2 * q^33 + 6 * q^36 + 8 * q^37 + 8 * q^38 - 42 * q^39 + 4 * q^41 - 24 * q^42 + 12 * q^44 + 2 * q^46 + 16 * q^47 + 4 * q^48 - 14 * q^49 - 8 * q^51 + 12 * q^52 - 48 * q^53 - 32 * q^54 - 6 * q^56 + 36 * q^57 - 8 * q^58 - 12 * q^59 - 30 * q^61 + 8 * q^62 - 20 * q^63 - 12 * q^64 - 14 * q^66 + 4 * q^67 - 12 * q^68 - 50 * q^69 - 4 * q^72 + 20 * q^77 - 32 * q^78 - 4 * q^79 - 40 * q^81 - 40 * q^83 + 20 * q^84 + 54 * q^86 - 64 * q^87 - 26 * q^89 + 28 * q^91 - 4 * q^93 + 24 * q^94 - 4 * q^96 + 16 * q^98 + 48 * q^99

Character values

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

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

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.960885	+	1.44108i	0.554767	+	0.832006i
$3$	0.960885	+	1.44108i	0.554767	+	0.832006i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.55269	−	0.767566i	−0.633883	−	0.313358i
$7$	1.91871	+	1.82168i	0.725206	+	0.688532i
$7$	1.91871	+	1.82168i	0.725206	+	0.688532i
$8$			1.00000i			0.353553i
$9$	−1.15340	+	2.76942i	−0.384467	+	0.923139i
$10$		0			0
$11$	1.99775	+	1.15340i	0.602344	+	0.347763i	0.769963	−	0.638089i	$-0.220275\pi$
$11$	1.99775	+	1.15340i	0.602344	+	0.347763i	−0.167619	+	0.985852i	$0.553608\pi$
$12$	1.72845	−	0.111613i	0.498961	−	0.0322198i
$13$			5.00084i			1.38698i	0.720464	+	0.693492i	$0.243929\pi$
$13$			5.00084i			1.38698i	−0.720464	+	0.693492i	$0.756071\pi$
$14$	−2.57250	−	0.618268i	−0.687529	−	0.165239i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.15115	−	5.45795i	0.764266	−	1.32375i	−0.176368	−	0.984324i	$-0.556435\pi$
$17$	3.15115	−	5.45795i	0.764266	−	1.32375i	0.940634	−	0.339423i	$-0.110232\pi$
$18$	−0.385834	−	2.97509i	−0.0909420	−	0.701234i
$19$	6.54470	−	3.77859i	1.50146	−	0.866867i	0.501460	−	0.865181i	$-0.332797\pi$
$19$	6.54470	−	3.77859i	1.50146	−	0.866867i	0.999999	−	0.00168616i	$-0.000536721\pi$
$20$		0			0
$21$	−0.781523	+	4.51544i	−0.170542	+	0.985350i
$22$	−2.30680			−0.491812
$23$	−5.51880	+	3.18628i	−1.15075	+	0.664385i	−0.949070	−	0.315066i	$-0.897973\pi$
$23$	−5.51880	+	3.18628i	−1.15075	+	0.664385i	−0.201679	+	0.979452i	$0.564640\pi$
$24$	−1.44108	+	0.960885i	−0.294158	+	0.196140i
$25$		0			0
$26$	−2.50042	−	4.33086i	−0.490373	−	0.849351i
$27$	−5.09922	+	0.998953i	−0.981346	+	0.192249i
$28$	2.53698	−	0.750813i	0.479445	−	0.141890i
$29$			3.83533i			0.712204i	0.934447	+	0.356102i	$0.115894\pi$
$29$			3.83533i			0.712204i	−0.934447	+	0.356102i	$0.884106\pi$
$30$		0			0
$31$	−3.79452	−	2.19077i	−0.681516	−	0.393473i	0.118910	−	0.992905i	$-0.462060\pi$
$31$	−3.79452	−	2.19077i	−0.681516	−	0.393473i	−0.800426	+	0.599432i	$0.795393\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.257468	+	3.98719i	0.0448195	+	0.694081i
$34$			6.30230i			1.08083i
$35$		0			0
$36$	1.82168	+	2.38358i	0.303614	+	0.397264i
$37$	−3.45465	−	5.98363i	−0.567941	−	0.983703i	−0.996769	−	0.0803166i	$-0.974407\pi$
$37$	−3.45465	−	5.98363i	−0.567941	−	0.983703i	0.428828	−	0.903386i	$-0.358926\pi$
$38$	−3.77859	+	6.54470i	−0.612968	+	1.06169i
$39$	−7.20659	+	4.80523i	−1.15398	+	0.769453i
$40$		0			0
$41$	9.79371			1.52952			0.764760	−	0.644315i	$-0.222857\pi$
$41$	9.79371			1.52952			0.764760	+	0.644315i	$0.222857\pi$
$42$	−1.58090	−	4.30125i	−0.243939	−	0.663697i
$43$	−2.55278			−0.389296			−0.194648	−	0.980873i	$-0.562356\pi$
$43$	−2.55278			−0.389296			−0.194648	+	0.980873i	$0.562356\pi$
$44$	1.99775	−	1.15340i	0.301172	−	0.173882i
$45$		0			0
$46$	3.18628	−	5.51880i	0.469791	−	0.813703i
$47$	0.828416	+	1.43486i	0.120837	+	0.209296i	0.920098	−	0.391688i	$-0.128109\pi$
$47$	0.828416	+	1.43486i	0.120837	+	0.209296i	−0.799261	+	0.600984i	$0.794776\pi$
$48$	0.767566	−	1.55269i	0.110789	−	0.224111i
$49$	0.362928	+	6.99059i	0.0518469	+	0.998655i
$50$		0			0
$51$	10.8932	−	0.703417i	1.52535	−	0.0984980i
$52$	4.33086	+	2.50042i	0.600582	+	0.346746i
$53$	2.81699	+	1.62639i	0.386944	+	0.223402i	0.680835	−	0.732437i	$-0.261617\pi$
$53$	2.81699	+	1.62639i	0.386944	+	0.223402i	−0.293891	+	0.955839i	$0.594950\pi$
$54$	3.91658	−	3.41473i	0.532979	−	0.464686i
$55$		0			0
$56$	−1.82168	+	1.91871i	−0.243433	+	0.256399i
$57$	11.7339	+	5.80063i	1.55420	+	0.768312i
$58$	−1.91767	−	3.32150i	−0.251802	−	0.436134i
$59$	−4.96573	+	8.60089i	−0.646483	+	1.11974i	0.337474	+	0.941335i	$0.390427\pi$
$59$	−4.96573	+	8.60089i	−0.646483	+	1.11974i	−0.983957	+	0.178406i	$0.942906\pi$
$60$		0			0
$61$	−5.18202	+	2.99184i	−0.663489	+	0.383066i	−0.793605	−	0.608433i	$-0.791798\pi$
$61$	−5.18202	+	2.99184i	−0.663489	+	0.383066i	0.130116	+	0.991499i	$0.458465\pi$
$62$	4.38153			0.556455
$63$	−7.25805	+	3.21259i	−0.914428	+	0.404748i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−2.21657	−	3.32428i	−0.272841	−	0.409190i
$67$	−1.38358	+	2.39643i	−0.169031	+	0.292771i	−0.938080	−	0.346420i	$-0.887397\pi$
$67$	−1.38358	+	2.39643i	−0.169031	+	0.292771i	0.769048	+	0.639191i	$0.220731\pi$
$68$	−3.15115	−	5.45795i	−0.382133	−	0.661874i
$69$	−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	$-0.0542657\pi$
$72$	−2.76942	−	1.15340i	−0.326379	−	0.135930i
$73$	3.18851	+	1.84089i	0.373187	+	0.215459i	0.674850	−	0.737955i	$-0.264208\pi$
$73$	3.18851	+	1.84089i	0.373187	+	0.215459i	−0.301663	+	0.953415i	$0.597542\pi$
$74$	5.98363	+	3.45465i	0.695583	+	0.401595i
$75$		0			0
$76$		−	7.55717i		−	0.866867i
$77$	1.73198	+	5.85231i	0.197377	+	0.666933i
$78$	3.83848	−	7.76475i	0.434622	−	0.879185i
$79$	−1.27945	−	2.21607i	−0.143949	−	0.249327i	0.785031	−	0.619456i	$-0.212647\pi$
$79$	−1.27945	−	2.21607i	−0.143949	−	0.249327i	−0.928980	+	0.370129i	$0.879313\pi$
$80$		0			0
$81$	−6.33934	−	6.38849i	−0.704371	−	0.709832i
$82$	−8.48160	+	4.89686i	−0.936636	+	0.540767i
$83$	1.83743			0.201684			0.100842	−	0.994902i	$-0.467846\pi$
$83$	1.83743			0.201684			0.100842	+	0.994902i	$0.467846\pi$
$84$	3.51973	+	2.93454i	0.384034	+	0.320185i
$85$		0			0
$86$	2.21077	−	1.27639i	0.238394	−	0.137637i
$87$	−5.52701	+	3.68532i	−0.592558	+	0.395107i
$88$	−1.15340	+	1.99775i	−0.122953	+	0.212961i
$89$	−2.94387	−	5.09894i	−0.312050	−	0.540486i	0.666756	−	0.745276i	$-0.267682\pi$
$89$	−2.94387	−	5.09894i	−0.312050	−	0.540486i	−0.978806	+	0.204790i	$0.934349\pi$
$90$		0			0
$91$	−9.10996	+	9.59518i	−0.954983	+	1.00585i
$92$			6.37256i			0.664385i
$93$	−0.489035	−	7.57326i	−0.0507105	−	0.785311i
$94$	−1.43486	−	0.828416i	−0.147994	−	0.0854446i
$95$		0			0
$96$	0.111613	+	1.72845i	0.0113914	+	0.176409i
$97$		−	4.61723i		−	0.468808i	−0.972139	−	0.234404i	$-0.924686\pi$
$97$		−	4.61723i		−	0.468808i	0.972139	−	0.234404i	$-0.0753139\pi$
$98$	−3.80960	−	5.87256i	−0.384827	−	0.593218i
$99$	−5.49845	+	4.20226i	−0.552615	+	0.422343i
$100$		0			0
$101$	−5.65702	+	9.79825i	−0.562894	+	0.974962i	0.434348	+	0.900745i	$0.356979\pi$
$101$	−5.65702	+	9.79825i	−0.562894	+	0.974962i	−0.997242	+	0.0742165i	$0.976354\pi$
$102$	−9.08209	+	6.05578i	−0.899261	+	0.599612i
$103$	−6.37747	+	3.68203i	−0.628391	+	0.362802i	−0.780129	−	0.625619i	$-0.784846\pi$
$103$	−6.37747	+	3.68203i	−0.628391	+	0.362802i	0.151738	+	0.988421i	$0.451513\pi$
$104$	−5.00084			−0.490373
$105$		0			0
$106$	−3.25278			−0.315938
$107$	7.29084	−	4.20937i	0.704832	−	0.406935i	−0.104312	−	0.994545i	$-0.533264\pi$
$107$	7.29084	−	4.20937i	0.704832	−	0.406935i	0.809145	+	0.587609i	$0.199931\pi$
$108$	−1.68449	+	4.91553i	−0.162090	+	0.472998i
$109$	3.33156	−	5.77043i	0.319105	−	0.552707i	−0.661196	−	0.750213i	$-0.729951\pi$
$109$	3.33156	−	5.77043i	0.319105	−	0.552707i	0.980302	+	0.197506i	$0.0632843\pi$
$110$		0			0
$111$	5.30334	−	10.7280i	0.503371	−	1.01826i
$112$	0.618268	−	2.57250i	0.0584209	−	0.243078i
$113$		−	4.45505i		−	0.419096i	−0.977798	−	0.209548i	$-0.932801\pi$
$113$		−	4.45505i		−	0.419096i	0.977798	−	0.209548i	$-0.0671992\pi$
$114$	−13.0622	+	0.843477i	−1.22339	+	0.0789988i
$115$		0			0
$116$	3.32150	+	1.91767i	0.308393	+	0.178051i
$117$	−13.8494	−	5.76797i	−1.28038	−	0.533249i
$118$		−	9.93145i		−	0.914264i
$119$	15.9888	−	4.73184i	1.46569	−	0.433767i
$120$		0			0
$121$	−2.83934	−	4.91787i	−0.258121	−	0.447079i
$122$	2.99184	−	5.18202i	0.270868	−	0.469158i
$123$	9.41063	+	14.1135i	0.848528	+	1.27257i
$124$	−3.79452	+	2.19077i	−0.340758	+	0.196737i
$125$		0			0
$126$	4.67936	−	6.41121i	0.416871	−	0.571156i
$127$	1.83694			0.163002			0.0815011	−	0.996673i	$-0.474029\pi$
$127$	1.83694			0.163002			0.0815011	+	0.996673i	$0.474029\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.45293	−	3.67875i	−0.215968	−	0.323896i
$130$		0			0
$131$	−2.76942	−	4.79677i	−0.241965	−	0.419096i	0.719309	−	0.694690i	$-0.244459\pi$
$131$	−2.76942	−	4.79677i	−0.241965	−	0.419096i	−0.961274	+	0.275595i	$0.911125\pi$
$132$	3.58174	+	1.77062i	0.311751	+	0.154113i
$133$	19.4408	+	4.67236i	1.68573	+	0.405145i
$134$		−	2.76716i		−	0.239047i
$135$		0			0
$136$	5.45795	+	3.15115i	0.468015	+	0.270209i
$137$	−1.07477	−	0.620520i	−0.0918240	−	0.0530146i	0.453385	−	0.891315i	$-0.350216\pi$
$137$	−1.07477	−	0.620520i	−0.0918240	−	0.0530146i	−0.545209	+	0.838300i	$0.683550\pi$
$138$	11.0147	−	0.711259i	0.937630	−	0.0605464i
$139$			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
$142$	1.42955	+	2.47605i	0.119965	+	0.207786i
$143$	−5.76797	+	9.99042i	−0.482342	+	0.835441i
$144$	2.97509	−	0.385834i	0.247924	−	0.0321529i
$145$		0			0
$146$	−3.68177			−0.304706
$147$	−9.72523	+	7.24016i	−0.802124	+	0.597158i
$148$	−6.90930			−0.567941
$149$	13.5058	−	7.79757i	1.10644	−	0.638802i	0.168533	−	0.985696i	$-0.446097\pi$
$149$	13.5058	−	7.79757i	1.10644	−	0.638802i	0.937904	+	0.346894i	$0.112764\pi$
$150$		0			0
$151$	−1.51958	+	2.63198i	−0.123661	+	0.214188i	−0.921209	−	0.389068i	$-0.872797\pi$
$151$	−1.51958	+	2.63198i	−0.123661	+	0.214188i	0.797548	+	0.603256i	$0.206130\pi$
$152$	3.77859	+	6.54470i	0.306484	+	0.530846i
$153$	11.4808	+	15.0220i	0.928168	+	1.21446i
$154$	−4.42609	−	4.20226i	−0.356665	−	0.338628i
$155$		0			0
$156$	0.558158	+	8.64371i	0.0446884	+	0.692050i
$157$	−13.7050	−	7.91260i	−1.09378	−	0.631494i	−0.159200	−	0.987246i	$-0.550891\pi$
$157$	−13.7050	−	7.91260i	−1.09378	−	0.631494i	−0.934580	+	0.355752i	$0.884225\pi$
$158$	2.21607	+	1.27945i	0.176301	+	0.101787i
$159$	0.363052	+	5.62228i	0.0287919	+	0.445876i
$160$		0			0
$161$	−16.3934	−	3.93995i	−1.29198	−	0.310512i
$162$	8.68427	+	2.36293i	0.682301	+	0.185649i
$163$	−4.30841	−	7.46238i	−0.337461	−	0.584499i	0.646494	−	0.762919i	$-0.276235\pi$
$163$	−4.30841	−	7.46238i	−0.337461	−	0.584499i	−0.983954	+	0.178420i	$0.942901\pi$
$164$	4.89686	−	8.48160i	0.382380	−	0.662302i
$165$		0			0
$166$	−1.59126	+	0.918714i	−0.123506	+	0.0713060i
$167$	8.64948			0.669317			0.334658	−	0.942339i	$-0.391379\pi$
$167$	8.64948			0.669317			0.334658	+	0.942339i	$0.391379\pi$
$168$	−4.51544	−	0.781523i	−0.348374	−	0.0602958i
$169$	−12.0084			−0.923724
$170$		0			0
$171$	2.91582	+	22.4832i	0.222978	+	1.71934i
$172$	−1.27639	+	2.21077i	−0.0973239	+	0.168570i
$173$	−8.96573	−	15.5291i	−0.681652	−	1.18066i	−0.974477	−	0.224489i	$-0.927929\pi$
$173$	−8.96573	−	15.5291i	−0.681652	−	1.18066i	0.292825	−	0.956166i	$-0.405405\pi$
$174$	2.94387	−	5.95508i	0.223174	−	0.451454i
$175$		0			0
$176$		−	2.30680i		−	0.173882i
$177$	−17.1660	+	1.10848i	−1.29028	+	0.0833182i
$178$	5.09894	+	2.94387i	0.382181	+	0.220653i
$179$	10.4070	+	6.00848i	0.777855	+	0.449095i	0.835670	−	0.549233i	$-0.185080\pi$
$179$	10.4070	+	6.00848i	0.777855	+	0.449095i	−0.0578145	+	0.998327i	$0.518413\pi$
$180$		0			0
$181$			9.52612i			0.708071i	0.935232	+	0.354036i	$0.115191\pi$
$181$			9.52612i			0.708071i	−0.935232	+	0.354036i	$0.884809\pi$
$182$	3.09186	−	12.8647i	0.229184	−	0.953591i
$183$	−9.29079	−	4.59287i	−0.686795	−	0.339514i
$184$	−3.18628	−	5.51880i	−0.234896	−	0.406851i
$185$		0			0
$186$	4.21015	+	6.31412i	0.308703	+	0.462974i
$187$	12.5904	−	7.26907i	0.920701	−	0.531567i
$188$	1.65683			0.120837
$189$	−11.6037	−	7.37248i	−0.844047	−	0.536269i
$190$		0			0
$191$	4.30564	−	2.48586i	0.311545	−	0.179871i	−0.336073	−	0.941836i	$-0.609099\pi$
$191$	4.30564	−	2.48586i	0.311545	−	0.179871i	0.647618	+	0.761965i	$0.275765\pi$
$192$	−0.960885	−	1.44108i	−0.0693459	−	0.104001i
$193$	3.01660	−	5.22491i	0.217140	−	0.376097i	−0.736793	−	0.676119i	$-0.763661\pi$
$193$	3.01660	−	5.22491i	0.217140	−	0.376097i	0.953932	+	0.300022i	$0.0969939\pi$
$194$	2.30861	+	3.99864i	0.165749	+	0.287085i
$195$		0			0
$196$	6.23549	+	3.18099i	0.445392	+	0.227213i
$197$			14.2144i			1.01273i	0.862318	+	0.506366i	$0.169012\pi$
$197$			14.2144i			1.01273i	−0.862318	+	0.506366i	$0.830988\pi$
$198$	2.66066	−	6.38849i	0.189085	−	0.454010i
$199$	1.94932	+	1.12544i	0.138183	+	0.0797802i	0.567498	−	0.823375i	$-0.307911\pi$
$199$	1.94932	+	1.12544i	0.138183	+	0.0797802i	−0.429315	+	0.903155i	$0.641245\pi$
$200$		0			0
$201$	−4.78291	+	0.308851i	−0.337360	+	0.0217847i
$202$		−	11.3140i		−	0.796053i
$203$	−6.98677	+	7.35891i	−0.490375	+	0.516494i
$204$	4.83743	−	9.78550i	0.338688	−	0.685122i
$205$		0			0
$206$	3.68203	−	6.37747i	0.256540	−	0.444339i
$207$	−2.45875	−	18.9589i	−0.170895	−	1.31774i
$208$	4.33086	−	2.50042i	0.300291	−	0.173373i
$209$	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	$0.100933\pi$
$212$	2.81699	−	1.62639i	0.193472	−	0.111701i
$213$	4.12018	−	2.74726i	0.282310	−	0.188239i
$214$	−4.20937	+	7.29084i	−0.287747	+	0.498392i
$215$		0			0
$216$	−0.998953	−	5.09922i	−0.0679701	−	0.346958i
$217$	−3.28971	−	11.1159i	−0.223320	−	0.754594i
$218$			6.66311i			0.451283i
$219$	0.410933	+	6.36376i	0.0277683	+	0.430023i
$220$		0			0
$221$	27.2943	+	15.7584i	1.83602	+	1.06002i
$222$	0.771166	+	11.9424i	0.0517573	+	0.801520i
$223$		−	23.0777i		−	1.54539i	−0.634775	−	0.772697i	$-0.718907\pi$
$223$		−	23.0777i		−	1.54539i	0.634775	−	0.772697i	$-0.281093\pi$
$224$	0.750813	+	2.53698i	0.0501658	+	0.169509i
$225$		0			0
$226$	2.22752	+	3.85818i	0.148173	+	0.256643i
$227$	10.0175	−	17.3509i	0.664887	−	1.15162i	−0.314429	−	0.949281i	$-0.601813\pi$
$227$	10.0175	−	17.3509i	0.664887	−	1.15162i	0.979316	−	0.202337i	$-0.0648538\pi$
$228$	10.8905	−	7.26157i	0.721238	−	0.480909i
$229$	24.9111	−	14.3824i	1.64617	−	0.950417i	0.667595	−	0.744524i	$-0.267324\pi$
$229$	24.9111	−	14.3824i	1.64617	−	0.950417i	0.978575	−	0.205892i	$-0.0660097\pi$
$230$		0			0
$231$	−6.76940	+	8.11931i	−0.445394	+	0.534211i
$232$	−3.83533			−0.251802
$233$	22.2668	−	12.8558i	1.45875	−	0.842209i	0.459799	−	0.888023i	$-0.347921\pi$
$233$	22.2668	−	12.8558i	1.45875	−	0.842209i	0.998950	+	0.0458133i	$0.0145879\pi$
$234$	14.8779	−	1.92950i	0.972601	−	0.126135i
$235$		0			0
$236$	4.96573	+	8.60089i	0.323241	+	0.559870i
$237$	1.96412	−	3.97317i	0.127583	−	0.258085i
$238$	−11.4808	+	12.0923i	−0.744190	+	0.783828i
$239$		−	10.7220i		−	0.693551i	−0.937948	−	0.346776i	$-0.887277\pi$
$239$		−	10.7220i		−	0.693551i	0.937948	−	0.346776i	$-0.112723\pi$
$240$		0			0
$241$	1.02594	+	0.592325i	0.0660864	+	0.0381550i	0.532679	−	0.846317i	$-0.321185\pi$
$241$	1.02594	+	0.592325i	0.0660864	+	0.0381550i	−0.466593	+	0.884472i	$0.654519\pi$
$242$	4.91787	+	2.83934i	0.316133	+	0.182519i
$243$	3.11493	−	15.2741i	0.199823	−	0.979832i
$244$			5.98368i			0.383066i
$245$		0			0
$246$	−15.2066	−	7.51732i	−0.969536	−	0.479287i
$247$	18.8961	+	32.7290i	1.20233	+	2.08250i
$248$	2.19077	−	3.79452i	0.139114	−	0.240952i
$249$	1.76556	+	2.64787i	0.111888	+	0.167802i
$250$		0			0
$251$	−14.3689			−0.906958			−0.453479	−	0.891267i	$-0.649817\pi$
$251$	−14.3689			−0.906958			−0.453479	+	0.891267i	$0.649817\pi$
$252$	−0.846843	+	7.89195i	−0.0533461	+	0.497146i
$253$	−14.7002			−0.924195
$254$	−1.59084	+	0.918471i	−0.0998181	+	0.0576300i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.26802	−	14.3206i	−0.515745	−	0.893297i	−0.999833	−	0.0182774i	$-0.994182\pi$
$257$	−8.26802	−	14.3206i	−0.515745	−	0.893297i	0.484088	−	0.875019i	$-0.339152\pi$
$258$	3.96368	+	1.95943i	0.246768	+	0.121989i
$259$	4.27180	−	17.7742i	0.265437	−	1.10443i
$260$		0			0
$261$	−10.6216	−	4.42368i	−0.657463	−	0.273819i
$262$	4.79677	+	2.76942i	0.296345	+	0.171095i
$263$	26.7948	+	15.4700i	1.65224	+	0.953920i	0.976149	+	0.217100i	$0.0696599\pi$
$263$	26.7948	+	15.4700i	1.65224	+	0.953920i	0.676089	+	0.736820i	$0.263673\pi$
$264$	−3.98719	+	0.257468i	−0.245395	+	0.0158461i
$265$		0			0
$266$	−19.1724	+	5.67402i	−1.17554	+	0.347897i
$267$	4.51923	−	9.14184i	0.276573	−	0.559471i
$268$	1.38358	+	2.39643i	0.0845157	+	0.146386i
$269$	−2.05211	+	3.55436i	−0.125119	+	0.216713i	−0.921780	−	0.387714i	$-0.873265\pi$
$269$	−2.05211	+	3.55436i	−0.125119	+	0.216713i	0.796660	+	0.604427i	$0.206598\pi$
$270$		0			0
$271$	−7.86071	+	4.53838i	−0.477504	+	0.275687i	−0.719376	−	0.694621i	$-0.755572\pi$
$271$	−7.86071	+	4.53838i	−0.477504	+	0.275687i	0.241872	+	0.970308i	$0.422239\pi$
$272$	−6.30230			−0.382133
$273$	−22.5810	−	3.90827i	−1.36666	−	0.236539i
$274$	1.24104			0.0749740
$275$		0			0
$276$	−9.18334	+	6.12330i	−0.552772	+	0.368579i
$277$	0.108238	−	0.187473i	0.00650338	−	0.0112642i	−0.862755	−	0.505622i	$-0.831263\pi$
$277$	0.108238	−	0.187473i	0.00650338	−	0.0112642i	0.869259	+	0.494357i	$0.164597\pi$
$278$	−6.26718	−	10.8551i	−0.375881	−	0.651044i
$279$	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	$-0.190061\pi$
$282$	−0.184924	−	2.86375i	−0.0110120	−	0.170534i
$283$	1.73059	+	0.999159i	0.102873	+	0.0593939i	0.550554	−	0.834800i	$-0.314417\pi$
$283$	1.73059	+	0.999159i	0.102873	+	0.0593939i	−0.447681	+	0.894193i	$0.647750\pi$
$284$	−2.47605	−	1.42955i	−0.146927	−	0.0848281i
$285$		0			0
$286$		−	11.5359i		−	0.682135i
$287$	18.7913	+	17.8411i	1.10922	+	1.05312i
$288$	−2.38358	+	1.82168i	−0.140454	+	0.107344i
$289$	−11.3595	−	19.6752i	−0.668204	−	1.15736i
$290$		0			0
$291$	6.65378	−	4.43662i	0.390051	−	0.260080i
$292$	3.18851	−	1.84089i	0.186593	−	0.107730i
$293$	−9.28117			−0.542212			−0.271106	−	0.962550i	$-0.587389\pi$
$293$	−9.28117			−0.542212			−0.271106	+	0.962550i	$0.587389\pi$
$294$	4.80222	−	11.1328i	0.280071	−	0.649277i
$295$		0			0
$296$	5.98363	−	3.45465i	0.347791	−	0.200797i
$297$	−11.3392	−	3.88579i	−0.657965	−	0.225476i
$298$	−7.79757	+	13.5058i	−0.451701	+	0.782370i
$299$	−15.9341	−	27.5986i	−0.921492	−	1.59607i
$300$		0			0
$301$	−4.89806	−	4.65037i	−0.282319	−	0.268043i
$302$		−	3.03915i		−	0.174883i
$303$	−19.5558	+	1.26279i	−1.12345	+	0.0725454i
$304$	−6.54470	−	3.77859i	−0.375365	−	0.216717i
$305$		0			0
$306$	−17.4537	−	7.26907i	−0.997761	−	0.415545i
$307$			26.9282i			1.53687i	0.639927	+	0.768436i	$0.278965\pi$
$307$			26.9282i			1.53687i	−0.639927	+	0.768436i	$0.721035\pi$
$308$	5.93424	+	1.42622i	0.338135	+	0.0812665i
$309$	−11.4341	−	5.65241i	−0.650464	−	0.321554i
$310$		0			0
$311$	1.41065	−	2.44331i	0.0799905	−	0.138548i	−0.823255	−	0.567672i	$-0.807844\pi$
$311$	1.41065	−	2.44331i	0.0799905	−	0.138548i	0.903246	+	0.429124i	$0.141178\pi$
$312$	−4.80523	−	7.20659i	−0.272043	−	0.407993i
$313$	9.90967	−	5.72135i	0.560128	−	0.323390i	−0.193069	−	0.981185i	$-0.561844\pi$
$313$	9.90967	−	5.72135i	0.560128	−	0.323390i	0.753197	+	0.657795i	$0.228511\pi$
$314$	15.8252			0.893068
$315$		0			0
$316$	−2.55889			−0.143949
$317$	8.06254	−	4.65491i	0.452837	−	0.261446i	−0.256190	−	0.966626i	$-0.582467\pi$
$317$	8.06254	−	4.65491i	0.452837	−	0.261446i	0.709028	+	0.705181i	$0.249134\pi$
$318$	−3.12555	−	4.68751i	−0.175272	−	0.262862i
$319$	−4.42368	+	7.66203i	−0.247678	+	0.428991i
$320$		0			0
$321$	13.0717	+	6.46194i	0.729590	+	0.360670i
$322$	16.1671	−	4.78460i	0.900956	−	0.266635i
$323$		−	47.6275i		−	2.65007i
$324$	−8.70226	+	2.29578i	−0.483459	+	0.127543i
$325$		0			0
$326$	7.46238	+	4.30841i	0.413303	+	0.238621i
$327$	11.5169	−	0.743688i	0.636884	−	0.0411261i
$328$			9.79371i			0.540767i
$329$	−1.02437	+	4.26220i	−0.0564752	+	0.234983i
$330$		0			0
$331$	−9.14801	−	15.8448i	−0.502820	−	0.870910i	−0.999995	−	0.00325921i	$-0.998963\pi$
$331$	−9.14801	−	15.8448i	−0.502820	−	0.870910i	0.497175	−	0.867650i	$-0.334371\pi$
$332$	0.918714	−	1.59126i	0.0504210	−	0.0873317i
$333$	20.5558	−	2.66584i	1.12645	−	0.146087i
$334$	−7.49067	+	4.32474i	−0.409871	+	0.236639i
$335$		0			0
$336$	4.30125	−	1.58090i	0.234652	−	0.0862453i
$337$	−7.84516			−0.427353			−0.213676	−	0.976904i	$-0.568544\pi$
$337$	−7.84516			−0.427353			−0.213676	+	0.976904i	$0.568544\pi$
$338$	10.3996	−	6.00420i	0.565663	−	0.326586i
$339$	6.42006	−	4.28079i	0.348690	−	0.232500i
$340$		0			0
$341$	−5.05366	−	8.75320i	−0.273671	−	0.474012i
$342$	−13.7668	−	18.0131i	−0.744423	−	0.974039i
$343$	−12.0383	+	14.0741i	−0.650006	+	0.759929i
$344$		−	2.55278i		−	0.137637i
$345$		0			0
$346$	15.5291	+	8.96573i	0.834849	+	0.482000i
$347$	0.201172	+	0.116147i	0.0107995	+	0.00623509i	0.505390	−	0.862891i	$-0.331349\pi$
$347$	0.201172	+	0.116147i	0.0107995	+	0.00623509i	−0.494591	+	0.869126i	$0.664682\pi$
$348$	0.428072	+	6.62919i	0.0229471	+	0.355362i
$349$		−	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
$352$	1.15340	+	1.99775i	0.0614764	+	0.106480i
$353$	−17.3537	+	30.0575i	−0.923646	+	1.59980i	−0.129921	+	0.991524i	$0.541472\pi$
$353$	−17.3537	+	30.0575i	−0.923646	+	1.59980i	−0.793725	+	0.608277i	$0.791861\pi$
$354$	14.3120	−	9.54298i	0.760673	−	0.507204i
$355$		0			0
$356$	−5.88774			−0.312050
$357$	22.1824	+	18.4943i	1.17401	+	0.978824i
$358$	−12.0170			−0.635116
$359$	15.1834	−	8.76612i	0.801347	−	0.462658i	−0.0425949	−	0.999092i	$-0.513562\pi$
$359$	15.1834	−	8.76612i	0.801347	−	0.462658i	0.843942	+	0.536434i	$0.180229\pi$
$360$		0			0
$361$	19.0554	−	33.0050i	1.00292	−	1.73710i
$362$	−4.76306	−	8.24987i	−0.250341	−	0.433603i
$363$	4.35875	−	8.81721i	0.228775	−	0.462783i
$364$	3.75470	+	12.6870i	0.196799	+	0.664982i
$365$		0			0
$366$	10.3425	−	0.667855i	0.540611	−	0.0349093i
$367$	8.69505	+	5.02009i	0.453878	+	0.262047i	0.709467	−	0.704739i	$-0.248936\pi$
$367$	8.69505	+	5.02009i	0.453878	+	0.262047i	−0.255589	+	0.966786i	$0.582269\pi$
$368$	5.51880	+	3.18628i	0.287687	+	0.166096i
$369$	−11.2961	+	27.1229i	−0.588050	+	1.41196i
$370$		0			0
$371$	2.44223	+	8.25225i	0.126794	+	0.428436i
$372$	−6.80316	−	3.36311i	−0.352727	−	0.174369i
$373$	−0.00241034	−	0.00417483i	−0.000124803	−	0.000216164i	0.865963	−	0.500108i	$-0.166706\pi$
$373$	−0.00241034	−	0.00417483i	−0.000124803	−	0.000216164i	−0.866088	+	0.499892i	$0.833373\pi$
$374$	−7.26907	+	12.5904i	−0.375875	+	0.651034i
$375$		0			0
$376$	−1.43486	+	0.828416i	−0.0739972	+	0.0427223i
$377$	−19.1799			−0.987815
$378$	13.7354	+	0.582885i	0.706471	+	0.0299803i
$379$	18.6572			0.958356			0.479178	−	0.877718i	$-0.340935\pi$
$379$	18.6572			0.958356			0.479178	+	0.877718i	$0.340935\pi$
$380$		0			0
$381$	1.76509	+	2.64717i	0.0904283	+	0.135619i
$382$	−2.48586	+	4.30564i	−0.127188	+	0.220296i
$383$	9.42316	+	16.3214i	0.481501	+	0.833984i	0.999775	−	0.0212308i	$-0.00675849\pi$
$383$	9.42316	+	16.3214i	0.481501	+	0.833984i	−0.518274	+	0.855215i	$0.673425\pi$
$384$	1.55269	+	0.767566i	0.0792353	+	0.0391697i
$385$		0			0
$386$			6.03321i			0.307082i
$387$	2.94438	−	7.06972i	0.149671	−	0.359374i
$388$	−3.99864	−	2.30861i	−0.203000	−	0.117202i
$389$	−9.40510	−	5.43003i	−0.476857	−	0.275314i	0.242249	−	0.970214i	$-0.422115\pi$
$389$	−9.40510	−	5.43003i	−0.476857	−	0.275314i	−0.719106	+	0.694901i	$0.755448\pi$
$390$		0			0
$391$			40.1618i			2.03107i
$392$	−6.99059	+	0.362928i	−0.353078	+	0.0183306i
$393$	4.25142	−	8.60008i	0.214456	−	0.433817i
$394$	−7.10719	−	12.3100i	−0.358055	−	0.620170i
$395$		0			0
$396$	0.890043	+	6.86293i	0.0447263	+	0.344875i
$397$	23.4180	−	13.5204i	1.17532	−	0.678570i	0.220391	−	0.975412i	$-0.429267\pi$
$397$	23.4180	−	13.5204i	1.17532	−	0.678570i	0.954927	+	0.296841i	$0.0959332\pi$
$398$	−2.25088			−0.112826
$399$	11.9472	+	32.5053i	0.598106	+	1.62730i
$400$		0			0
$401$	−21.2396	+	12.2627i	−1.06066	+	0.612371i	−0.925614	−	0.378469i	$-0.876451\pi$
$401$	−21.2396	+	12.2627i	−1.06066	+	0.612371i	−0.135043	+	0.990840i	$0.543117\pi$
$402$	3.98769	−	2.65893i	0.198888	−	0.132615i
$403$	10.9557	−	18.9758i	0.545741	−	0.945251i
$404$	5.65702	+	9.79825i	0.281447	+	0.487481i
$405$		0			0
$406$	2.37127	−	9.86639i	0.117684	−	0.489661i
$407$		−	15.9384i		−	0.790036i
$408$	0.703417	+	10.8932i	0.0348243	+	0.539294i
$409$	4.67954	+	2.70173i	0.231388	+	0.133592i	0.611212	−	0.791467i	$-0.290682\pi$
$409$	4.67954	+	2.70173i	0.231388	+	0.133592i	−0.379824	+	0.925059i	$0.624015\pi$
$410$		0			0
$411$	−0.138516	−	2.14508i	−0.00683249	−	0.105809i
$412$			7.36407i			0.362802i
$413$	−25.1959	+	7.45666i	−1.23981	+	0.366918i
$414$	11.6088	+	15.1895i	0.570541	+	0.746524i
$415$		0			0
$416$	−2.50042	+	4.33086i	−0.122593	+	0.212338i
$417$	−18.0630	+	12.0441i	−0.884548	+	0.589801i
$418$	−15.0973	+	8.71645i	−0.738434	+	0.426335i
$419$	−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	$0.710168\pi$
$422$	−23.9052	+	13.8017i	−1.16369	+	0.671855i
$423$	−4.92922	+	0.639263i	−0.239667	+	0.0310820i
$424$	−1.62639	+	2.81699i	−0.0789846	+	0.136805i
$425$		0			0
$426$	−2.19455	+	4.43929i	−0.106326	+	0.215084i
$427$	−15.3930	−	3.69952i	−0.744919	−	0.179032i
$428$		−	8.41874i		−	0.406935i
$429$	−19.9393	+	1.28756i	−0.962679	+	0.0621639i
$430$		0			0
$431$	−9.71524	−	5.60910i	−0.467967	−	0.270181i	0.247421	−	0.968908i	$-0.420417\pi$
$431$	−9.71524	−	5.60910i	−0.467967	−	0.270181i	−0.715388	+	0.698727i	$0.753750\pi$
$432$	3.41473	+	3.91658i	0.164291	+	0.188437i
$433$		−	0.639592i		−	0.0307368i	−0.999882	−	0.0153684i	$-0.995108\pi$
$433$		−	0.639592i		−	0.0307368i	0.999882	−	0.0153684i	$-0.00489211\pi$
$434$	8.40691	+	7.98177i	0.403544	+	0.383137i
$435$		0			0
$436$	−3.33156	−	5.77043i	−0.159553	−	0.276353i
$437$	−24.0793	+	41.7065i	−1.15187	+	1.99509i
$438$	−3.53776	−	5.30571i	−0.169041	−	0.253517i
$439$	−11.3999	+	6.58174i	−0.544088	+	0.314129i	−0.746734	−	0.665123i	$-0.768379\pi$
$439$	−11.3999	+	6.58174i	−0.544088	+	0.314129i	0.202646	+	0.979252i	$0.435046\pi$
$440$		0			0
$441$	−19.7784	−	7.05784i	−0.941831	−	0.336088i
$442$	−31.5168			−1.49910
$443$	22.3821	−	12.9223i	1.06341	−	0.613957i	0.137033	−	0.990566i	$-0.456243\pi$
$443$	22.3821	−	12.9223i	1.06341	−	0.613957i	0.926372	+	0.376609i	$0.122910\pi$
$444$	−6.63904	−	9.95683i	−0.315075	−	0.472530i
$445$		0			0
$446$	11.5388	+	19.9858i	0.546380	+	0.946357i
$447$	24.2144	+	11.9703i	1.14530	+	0.566176i
$448$	−1.91871	−	1.82168i	−0.0906507	−	0.0860665i
$449$			28.3586i			1.33833i	0.743116	+	0.669163i	$0.233347\pi$
$449$			28.3586i			1.33833i	−0.743116	+	0.669163i	$0.766653\pi$
$450$		0			0
$451$	19.5654	+	11.2961i	0.921297	+	0.531911i
$452$	−3.85818	−	2.22752i	−0.181474	−	0.104774i
$453$	−5.25302	+	0.339208i	−0.246809	+	0.0159374i
$454$			20.0351i			0.940293i
$455$		0			0
$456$	−5.80063	+	11.7339i	−0.271639	+	0.549492i
$457$	−14.5953	−	25.2797i	−0.682737	−	1.18254i	−0.974142	−	0.225936i	$-0.927456\pi$
$457$	−14.5953	−	25.2797i	−0.682737	−	1.18254i	0.291405	−	0.956600i	$-0.405877\pi$
$458$	−14.3824	+	24.9111i	−0.672046	+	1.16402i
$459$	−10.6162	+	30.9792i	−0.495521	+	1.44598i
$460$		0			0
$461$	31.0968			1.44832			0.724162	−	0.689630i	$-0.242227\pi$
$461$	31.0968			1.44832			0.724162	+	0.689630i	$0.242227\pi$
$462$	1.80282	−	10.4162i	0.0838747	−	0.484607i
$463$	33.4915			1.55648			0.778240	−	0.627967i	$-0.216113\pi$
$463$	33.4915			1.55648			0.778240	+	0.627967i	$0.216113\pi$
$464$	3.32150	−	1.91767i	0.154197	−	0.0890255i
$465$		0			0
$466$	−12.8558	+	22.2668i	−0.595532	+	1.03149i
$467$	7.41254	+	12.8389i	0.343012	+	0.594113i	0.984990	−	0.172609i	$-0.0552197\pi$
$467$	7.41254	+	12.8389i	0.343012	+	0.594113i	−0.641979	+	0.766722i	$0.721886\pi$
$468$	−11.9199	+	9.10996i	−0.550998	+	0.421108i
$469$	−7.02025	+	2.07762i	−0.324165	+	0.0959357i
$470$		0			0
$471$	−1.76629	−	27.3531i	−0.0813865	−	1.26036i
$472$	−8.60089	−	4.96573i	−0.395888	−	0.228566i
$473$	−5.09982	−	2.94438i	−0.234490	−	0.135383i
$474$	0.285605	+	4.42292i	0.0131183	+	0.203152i
$475$		0			0
$476$	3.89651	−	16.2126i	0.178596	−	0.743105i
$477$	−7.75328	+	5.92555i	−0.354998	+	0.271312i
$478$	5.36102	+	9.28556i	0.245207	+	0.424712i
$479$	−11.5223	+	19.9573i	−0.526469	+	0.911871i	0.473055	+	0.881033i	$0.343151\pi$
$479$	−11.5223	+	19.9573i	−0.526469	+	0.911871i	−0.999524	+	0.0308386i	$0.990182\pi$
$480$		0			0
$481$	29.9232	−	17.2762i	1.36438	−	0.787725i
$482$	−1.18465			−0.0539593
$483$	−10.0744	−	27.4100i	−0.458401	−	1.24720i
$484$	−5.67867			−0.258121
$485$		0			0
$486$	4.93943	+	14.7852i	0.224057	+	0.670670i
$487$	−5.31384	+	9.20383i	−0.240793	+	0.417066i	−0.960940	−	0.276756i	$-0.910741\pi$
$487$	−5.31384	+	9.20383i	−0.240793	+	0.417066i	0.720147	+	0.693821i	$0.244074\pi$
$488$	−2.99184	−	5.18202i	−0.135434	−	0.234579i
$489$	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	$-0.169245\pi$
$492$	16.9279	−	1.09310i	0.763171	−	0.0492809i
$493$	20.9331	+	12.0857i	0.942778	+	0.544313i
$494$	−32.7290	−	18.8961i	−1.47255	−	0.850176i
$495$		0			0
$496$			4.38153i			0.196737i
$497$	5.20837	−	5.48579i	0.233627	−	0.246071i
$498$	−2.85295	−	1.41035i	−0.127844	−	0.0631992i
$499$	19.8794	+	34.4322i	0.889925	+	1.54140i	0.839963	+	0.542644i	$0.182577\pi$
$499$	19.8794	+	34.4322i	0.889925	+	1.54140i	0.0499622	+	0.998751i	$0.484090\pi$
$500$		0			0
$501$	8.31116	+	12.4646i	0.371315	+	0.556875i
$502$	12.4438	−	7.18445i	0.555396	−	0.320658i
$503$	−18.6717			−0.832530			−0.416265	−	0.909243i	$-0.636661\pi$
$503$	−18.6717			−0.832530			−0.416265	+	0.909243i	$0.636661\pi$
$504$	−3.21259	−	7.25805i	−0.143100	−	0.323299i
$505$		0			0
$506$	12.7308	−	7.35011i	0.565952	−	0.326752i
$507$	−11.5387	−	17.3050i	−0.512452	−	0.768543i
$508$	0.918471	−	1.59084i	0.0407506	−	0.0705820i
$509$	2.01643	+	3.49256i	0.0893768	+	0.154805i	0.907248	−	0.420596i	$-0.138179\pi$
$509$	2.01643	+	3.49256i	0.0893768	+	0.154805i	−0.817871	+	0.575402i	$0.804846\pi$
$510$		0			0
$511$	2.76432	+	9.34059i	0.122286	+	0.413203i
$512$		−	1.00000i		−	0.0441942i
$513$	−29.5983	+	25.8057i	−1.30680	+	1.13935i
$514$	14.3206	+	8.26802i	0.631656	+	0.364687i
$515$		0			0
$516$	−4.41236	+	0.284923i	−0.194243	+	0.0125430i
$517$			3.82198i			0.168091i
$518$	5.18759	+	17.5288i	0.227930	+	0.770170i
$519$	13.7636	−	27.8420i	0.604154	−	1.22213i
$520$		0			0
$521$	−5.27733	+	9.14060i	−0.231204	+	0.400457i	−0.958163	−	0.286224i	$-0.907600\pi$
$521$	−5.27733	+	9.14060i	−0.231204	+	0.400457i	0.726959	+	0.686681i	$0.240933\pi$
$522$	11.4104	−	1.47980i	0.499422	−	0.0647692i
$523$	17.7815	−	10.2661i	0.777529	−	0.448907i	−0.0580246	−	0.998315i	$-0.518480\pi$
$523$	17.7815	−	10.2661i	0.777529	−	0.448907i	0.835554	+	0.549408i	$0.185147\pi$
$524$	−5.53883			−0.241965
$525$		0			0
$526$	−30.9400			−1.34905
$527$	−23.9142	+	13.8069i	−1.04172	+	0.601436i
$528$	3.32428	−	2.21657i	0.144671	−	0.0964638i
$529$	8.80476	−	15.2503i	0.382816	−	0.663056i
$530$		0			0
$531$	−18.0920	−	23.6724i	−0.785125	−	1.02730i
$532$	13.7668	−	14.5001i	0.596866	−	0.628657i
$533$			48.9768i			2.12142i
$534$	0.657147	+	10.1767i	0.0284375	+	0.440388i
$535$		0			0
$536$	−2.39643	−	1.38358i	−0.103510	−	0.0597616i
$537$	1.34125	+	20.7707i	0.0578790	+	0.896323i
$538$		−	4.10422i		−	0.176946i
$539$	−7.33790	+	14.3840i	−0.316066	+	0.619564i
$540$		0			0
$541$	4.59255	+	7.95454i	0.197449	+	0.341992i	0.947701	−	0.319160i	$-0.103401\pi$
$541$	4.59255	+	7.95454i	0.197449	+	0.341992i	−0.750251	+	0.661153i	$0.770068\pi$
$542$	4.53838	−	7.86071i	0.194940	−	0.337646i
$543$	−13.7279	+	9.15351i	−0.589119	+	0.392815i
$544$	5.45795	−	3.15115i	0.234008	−	0.135104i
$545$		0			0
$546$	21.5099	−	7.90584i	0.920537	−	0.338339i
$547$	5.21319			0.222900			0.111450	−	0.993770i	$-0.464450\pi$
$547$	5.21319			0.222900			0.111450	+	0.993770i	$0.464450\pi$
$548$	−1.07477	+	0.620520i	−0.0459120	+	0.0265073i
$549$	−2.30871	−	17.8019i	−0.0985332	−	0.759769i
$550$		0			0
$551$	14.4921	+	25.1011i	0.617386	+	1.06934i
$552$	4.89136	−	9.89460i	0.208190	−	0.421142i
$553$	1.58208	−	6.58275i	0.0672770	−	0.279927i
$554$			0.216476i			0.00919717i
$555$		0			0
$556$	10.8551	+	6.26718i	0.460358	+	0.265788i
$557$	−22.3550	−	12.9066i	−0.947210	−	0.546872i	−0.0549970	−	0.998487i	$-0.517515\pi$
$557$	−22.3550	−	12.9066i	−0.947210	−	0.546872i	−0.892213	+	0.451614i	$0.850848\pi$
$558$	−5.05366	+	12.1343i	−0.213938	+	0.513685i
$559$		−	12.7661i		−	0.539947i
$560$		0			0
$561$	22.5732	+	11.1590i	0.953042	+	0.471133i
$562$	9.42488	+	16.3244i	0.397565	+	0.688602i
$563$	−18.7468	+	32.4704i	−0.790084	+	1.36847i	0.135831	+	0.990732i	$0.456630\pi$
$563$	−18.7468	+	32.4704i	−0.790084	+	1.36847i	−0.925914	+	0.377733i	$0.876704\pi$
$564$	1.59203	+	2.38762i	0.0670364	+	0.100537i
$565$		0			0
$566$	−1.99832			−0.0839956
$567$	−0.525554	−	23.8060i	−0.0220712	−	0.999756i
$568$	2.85910			0.119965
$569$	−35.0352	+	20.2276i	−1.46875	+	0.847985i	−0.999387	−	0.0350177i	$-0.988851\pi$
$569$	−35.0352	+	20.2276i	−1.46875	+	0.847985i	−0.469367	+	0.883003i	$0.655518\pi$
$570$		0			0
$571$	14.5551	−	25.2101i	0.609111	−	1.05501i	−0.382276	−	0.924048i	$-0.624860\pi$
$571$	14.5551	−	25.2101i	0.609111	−	1.05501i	0.991387	−	0.130963i	$-0.0418070\pi$
$572$	5.76797	+	9.99042i	0.241171	+	0.417720i
$573$	7.71954	+	3.81613i	0.322488	+	0.159421i
$574$	−25.1943	−	6.05514i	−1.05159	−	0.252737i
$575$		0			0
$576$	1.15340	−	2.76942i	0.0480583	−	0.115392i
$577$	13.1423	+	7.58769i	0.547120	+	0.315880i	0.747959	−	0.663744i	$-0.231034\pi$
$577$	13.1423	+	7.58769i	0.547120	+	0.315880i	−0.200840	+	0.979624i	$0.564367\pi$
$578$	19.6752	+	11.3595i	0.818380	+	0.472492i
$579$	10.4281	−	0.673383i	0.433377	−	0.0279848i
$580$		0			0
$581$	3.52550	+	3.34722i	0.146262	+	0.138866i
$582$	−3.54403	+	7.16912i	−0.146905	+	0.297169i
$583$	3.75176	+	6.49824i	0.155382	+	0.269130i
$584$	−1.84089	+	3.18851i	−0.0761764	+	0.131941i
$585$		0			0
$586$	8.03773	−	4.64059i	0.332036	−	0.191701i
$587$	3.22807			0.133237			0.0666183	−	0.997779i	$-0.478779\pi$
$587$	3.22807			0.133237			0.0666183	+	0.997779i	$0.478779\pi$
$588$	1.40754	+	12.0424i	0.0580461	+	0.496619i
$589$	−33.1120			−1.36436
$590$		0			0
$591$	−20.4840	+	13.6584i	−0.842599	+	0.561831i
$592$	−3.45465	+	5.98363i	−0.141985	+	0.245926i
$593$	−21.8653	−	37.8717i	−0.897899	−	1.55521i	−0.830175	−	0.557502i	$-0.811760\pi$
$593$	−21.8653	−	37.8717i	−0.897899	−	1.55521i	−0.0677234	−	0.997704i	$-0.521574\pi$
$594$	11.7629	−	2.30439i	0.482637	−	0.0945501i
$595$		0			0
$596$		−	15.5951i		−	0.638802i
$597$	0.251227	+	3.89053i	0.0102820	+	0.159229i
$598$	27.5986	+	15.9341i	1.12859	+	0.651593i
$599$	6.96777	+	4.02284i	0.284695	+	0.164369i	0.635547	−	0.772062i	$-0.280775\pi$
$599$	6.96777	+	4.02284i	0.284695	+	0.164369i	−0.350852	+	0.936431i	$0.614108\pi$
$600$		0			0
$601$		−	8.38546i		−	0.342050i	−0.985267	−	0.171025i	$-0.945292\pi$
$601$		−	8.38546i		−	0.342050i	0.985267	−	0.171025i	$-0.0547079\pi$
$602$	6.56703	+	1.57830i	0.267652	+	0.0643269i
$603$	−5.04090	−	6.59576i	−0.205281	−	0.268600i
$604$	1.51958	+	2.63198i	0.0618306	+	0.107094i
$605$		0			0
$606$	16.3044	−	10.8715i	0.662321	−	0.441624i
$607$	−14.6650	+	8.46682i	−0.595232	+	0.343658i	−0.767164	−	0.641451i	$-0.778333\pi$
$607$	−14.6650	+	8.46682i	−0.595232	+	0.343658i	0.171931	+	0.985109i	$0.444999\pi$
$608$	7.55717			0.306484
$609$	−17.3182	−	2.99740i	−0.701770	−	0.121461i
$610$		0			0
$611$	−7.17550	+	4.14278i	−0.290290	+	0.167599i
$612$	18.7499	−	2.43164i	0.757919	−	0.0982933i
$613$	16.9432	−	29.3464i	0.684328	−	1.18529i	−0.289319	−	0.957233i	$-0.593429\pi$
$613$	16.9432	−	29.3464i	0.684328	−	1.18529i	0.973647	−	0.228058i	$-0.0732377\pi$
$614$	−13.4641	−	23.3205i	−0.543366	−	0.941138i
$615$		0			0
$616$	−5.85231	+	1.73198i	−0.235796	+	0.0697833i
$617$		−	37.5359i		−	1.51114i	−0.655068	−	0.755570i	$-0.727360\pi$
$617$		−	37.5359i		−	1.51114i	0.655068	−	0.755570i	$-0.272640\pi$
$618$	12.7284	−	0.821924i	0.512013	−	0.0330626i
$619$	14.6497	+	8.45802i	0.588822	+	0.339957i	0.764632	−	0.644468i	$-0.222921\pi$
$619$	14.6497	+	8.45802i	0.588822	+	0.339957i	−0.175809	+	0.984424i	$0.556254\pi$
$620$		0			0
$621$	24.9587	−	21.7606i	1.00156	−	0.873222i
$622$			2.82130i			0.113124i
$623$	3.64021	−	15.1462i	0.145842	−	0.606820i
$624$	7.76475	+	3.83848i	0.310839	+	0.153662i
$625$		0			0
$626$	−5.72135	+	9.90967i	−0.228671	+	0.396070i
$627$	16.7510	+	25.1221i	0.668971	+	1.00328i
$628$	−13.7050	+	7.91260i	−0.546890	+	0.315747i
$629$	−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	$0.697329\pi$
$632$	2.21607	−	1.27945i	0.0881504	−	0.0508937i
$633$	26.5236	+	39.7785i	1.05422	+	1.58105i
$634$	−4.65491	+	8.06254i	−0.184870	+	0.320204i
$635$		0			0
$636$	5.05056	+	2.49673i	0.200268	+	0.0990016i
$637$	−34.9588	+	1.81495i	−1.38512	+	0.0719108i
$638$		−	8.84735i		−	0.350270i
$639$	7.91803	+	3.29768i	0.313232	+	0.130454i
$640$		0			0
$641$	−3.95871	−	2.28556i	−0.156360	−	0.0902743i	0.419779	−	0.907627i	$-0.362108\pi$
$641$	−3.95871	−	2.28556i	−0.156360	−	0.0902743i	−0.576138	+	0.817352i	$0.695441\pi$
$642$	−14.5514	+	0.939639i	−0.574297	+	0.0370846i
$643$			24.0758i			0.949457i	0.880132	+	0.474728i	$0.157454\pi$
$643$			24.0758i			0.949457i	−0.880132	+	0.474728i	$0.842546\pi$
$644$	−11.6088	+	12.2271i	−0.457451	+	0.481816i
$645$		0			0
$646$	23.8138	+	41.2467i	0.936940	+	1.62283i
$647$	8.71205	−	15.0897i	0.342506	−	0.593238i	−0.642391	−	0.766377i	$-0.722058\pi$
$647$	8.71205	−	15.0897i	0.342506	−	0.593238i	0.984897	+	0.173139i	$0.0553909\pi$
$648$	6.38849	−	6.33934i	0.250964	−	0.249033i
$649$	−19.8405	+	11.4549i	−0.778809	+	0.449646i
$650$		0			0
$651$	12.8578	−	15.4218i	0.503936	−	0.604428i
$652$	−8.61682			−0.337461
$653$	32.8146	−	18.9455i	1.28414	−	0.741396i	0.306534	−	0.951860i	$-0.400831\pi$
$653$	32.8146	−	18.9455i	1.28414	−	0.741396i	0.977602	+	0.210464i	$0.0674973\pi$
$654$	−9.60205	+	6.40249i	−0.375470	+	0.250357i
$655$		0			0
$656$	−4.89686	−	8.48160i	−0.191190	−	0.331151i
$657$	−8.77580	+	6.70703i	−0.342377	+	0.261666i
$658$	−1.24397	−	4.20336i	−0.0484950	−	0.163864i
$659$			24.7262i			0.963197i	0.876392	+	0.481599i	$0.159944\pi$
$659$			24.7262i			0.963197i	−0.876392	+	0.481599i	$0.840056\pi$
$660$		0			0
$661$	−37.8348	−	21.8439i	−1.47160	−	0.849631i	−0.472113	−	0.881538i	$-0.656509\pi$
$661$	−37.8348	−	21.8439i	−1.47160	−	0.849631i	−0.999491	+	0.0319070i	$0.989842\pi$
$662$	15.8448	+	9.14801i	0.615826	+	0.355547i
$663$	3.51767	+	54.4752i	0.136615	+	2.11564i
$664$			1.83743i			0.0713060i
$665$		0			0
$666$	−16.4689	+	12.5866i	−0.638156	+	0.487720i
$667$	−12.2205	−	21.1664i	−0.473178	−	0.819568i
$668$	4.32474	−	7.49067i	0.167329	−	0.289823i
$669$	33.2567	−	22.1750i	1.28578	−	0.857334i
$670$		0			0
$671$	−13.8031			−0.532865
$672$	−2.93454	+	3.51973i	−0.113202	+	0.135776i
$673$	−34.1588			−1.31673			−0.658363	−	0.752701i	$-0.728751\pi$
$673$	−34.1588			−1.31673			−0.658363	+	0.752701i	$0.728751\pi$
$674$	6.79410	−	3.92258i	0.261699	−	0.151092i
$675$		0			0
$676$	−6.00420	+	10.3996i	−0.230931	+	0.399984i
$677$	6.56630	+	11.3732i	0.252364	+	0.437106i	0.964176	−	0.265263i	$-0.0854588\pi$
$677$	6.56630	+	11.3732i	0.252364	+	0.437106i	−0.711813	+	0.702369i	$0.752125\pi$
$678$	−3.41954	+	6.91730i	−0.131327	+	0.265657i
$679$	8.41113	−	8.85914i	0.322790	−	0.339983i
$680$		0			0
$681$	34.6296	−	2.23617i	1.32701	−	0.0856902i
$682$	8.75320	+	5.05366i	0.335177	+	0.193515i
$683$	−39.7352	−	22.9411i	−1.52043	−	0.877818i	−0.999710	−	0.0240882i	$-0.992332\pi$
$683$	−39.7352	−	22.9411i	−1.52043	−	0.877818i	−0.520716	−	0.853730i	$-0.674335\pi$
$684$	20.9290	+	8.71645i	0.800239	+	0.333282i
$685$		0			0
$686$	3.38843	−	18.2077i	0.129371	−	0.695171i
$687$	44.6628	+	22.0789i	1.70399	+	0.842363i
$688$	1.27639	+	2.21077i	0.0486620	+	0.0842850i
$689$	−8.13333	+	14.0873i	−0.309855	+	0.536685i
$690$		0			0
$691$	−15.2114	+	8.78233i	−0.578671	+	0.334096i	−0.760605	−	0.649215i	$-0.775098\pi$
$691$	−15.2114	+	8.78233i	−0.578671	+	0.334096i	0.181934	+	0.983311i	$0.441764\pi$
$692$	−17.9315			−0.681652
$693$	−18.2052	−	1.95350i	−0.691557	−	0.0742073i
$694$	−0.232294			−0.00881775
$695$		0			0
$696$	−3.68532	−	5.52701i	−0.139692	−	0.209501i
$697$	30.8614	−	53.4536i	1.16896	−	2.02470i
$698$	5.78426	+	10.0186i	0.218938	+	0.379211i
$699$	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	$-0.265756\pi$
$702$	17.0765	+	19.5862i	0.644512	+	0.739234i
$703$	−45.2193	−	26.1074i	−1.70548	−	0.984659i
$704$	−1.99775	−	1.15340i	−0.0752930	−	0.0434704i
$705$		0			0
$706$		−	34.7075i		−	1.30623i
$707$	−28.7035	+	8.49472i	−1.07951	+	0.319477i
$708$	−7.62305	+	15.4205i	−0.286492	+	0.579536i
$709$	23.8340	+	41.2817i	0.895105	+	1.55037i	0.833674	+	0.552257i	$0.186233\pi$
$709$	23.8340	+	41.2817i	0.895105	+	1.55037i	0.0614314	+	0.998111i	$0.480433\pi$
$710$		0			0
$711$	7.61293	−	0.987309i	0.285507	−	0.0370270i
$712$	5.09894	−	2.94387i	0.191091	−	0.110326i
$713$	27.9216			1.04567
$714$	−28.4577	−	4.92539i	−1.06500	−	0.184328i
$715$		0			0
$716$	10.4070	−	6.00848i	0.388928	−	0.224547i
$717$	15.4513	−	10.3026i	0.577039	−	0.384759i
$718$	−8.76612	+	15.1834i	−0.327149	+	0.566638i
$719$	−16.7107	−	28.9438i	−0.623205	−	1.07942i	−0.988885	−	0.148682i	$-0.952497\pi$
$719$	−16.7107	−	28.9438i	−0.623205	−	1.07942i	0.365680	−	0.930740i	$-0.380836\pi$
$720$		0			0
$721$	−18.9441	−	4.55297i	−0.705513	−	0.169561i
$722$			38.1109i			1.41834i
$723$	0.132222	+	2.04761i	0.00491739	+	0.0761514i
$724$	8.24987	+	4.76306i	0.306604	+	0.177018i
$725$		0			0
$726$	0.633812	+	9.81530i	0.0235230	+	0.364280i
$727$			31.9845i			1.18624i	0.805115	+	0.593119i	$0.202104\pi$
$727$			31.9845i			1.18624i	−0.805115	+	0.593119i	$0.797896\pi$
$728$	−9.59518	−	9.10996i	−0.355621	−	0.337637i
$729$	25.0042	−	10.1878i	0.926081	−	0.377325i
$730$		0			0
$731$	−8.04420	+	13.9330i	−0.297525	+	0.515329i
$732$	−8.62293	+	5.74962i	−0.318713	+	0.212512i
$733$	−33.9483	+	19.6001i	−1.25391	+	0.723945i	−0.971884	−	0.235461i	$-0.924340\pi$
$733$	−33.9483	+	19.6001i	−1.25391	+	0.723945i	−0.282026	+	0.959407i	$0.591007\pi$
$734$	−10.0402			−0.370590
$735$		0			0
$736$	−6.37256			−0.234896
$737$	−5.52810	+	3.19165i	−0.203630	+	0.117566i
$738$	−3.77875	−	29.1371i	−0.139098	−	1.07255i
$739$	16.8814	−	29.2394i	0.620992	−	1.07559i	−0.368310	−	0.929703i	$-0.620063\pi$
$739$	16.8814	−	29.2394i	0.620992	−	1.07559i	0.989301	−	0.145886i	$-0.0466033\pi$
$740$		0			0
$741$	−29.0080	+	58.6796i	−1.06564	+	2.15565i
$742$	−6.24116	−	5.92555i	−0.229120	−	0.217534i
$743$		−	14.3933i		−	0.528038i	−0.964517	−	0.264019i	$-0.914952\pi$
$743$		−	14.3933i		−	0.528038i	0.964517	−	0.264019i	$-0.0850482\pi$
$744$	7.57326	−	0.489035i	0.277649	−	0.0179289i
$745$		0			0
$746$	0.00417483	+	0.00241034i	0.000152851	+	8.82487e-5i
$747$	−2.11929	+	5.08860i	−0.0775408	+	0.186182i
$748$		−	14.5381i		−	0.531567i
$749$	21.6572	+	5.20504i	0.791336	+	0.190188i
$750$		0			0
$751$	−8.92040	−	15.4506i	−0.325510	−	0.563800i	0.656105	−	0.754669i	$-0.272203\pi$
$751$	−8.92040	−	15.4506i	−0.325510	−	0.563800i	−0.981615	+	0.190869i	$0.938869\pi$
$752$	0.828416	−	1.43486i	0.0302092	−	0.0523239i
$753$	−13.8069	−	20.7067i	−0.503150	−	0.754594i
$754$	16.6103	−	9.58995i	0.604911	−	0.349245i
$755$		0			0
$756$	−12.1866	+	6.36289i	−0.443223	+	0.231416i
$757$	1.90604			0.0692760			0.0346380	−	0.999400i	$-0.488972\pi$
$757$	1.90604			0.0692760			0.0346380	+	0.999400i	$0.488972\pi$
$758$	−16.1576	+	9.32860i	−0.586871	+	0.338830i
$759$	−14.1252	−	21.1841i	−0.512713	−	0.768936i
$760$		0			0
$761$	−14.1364	−	24.4850i	−0.512445	−	0.887581i	−0.999896	−	0.0144304i	$-0.995407\pi$
$761$	−14.1364	−	24.4850i	−0.512445	−	0.887581i	0.487451	−	0.873150i	$-0.337927\pi$
$762$	−2.85220	−	1.40997i	−0.103324	−	0.0510780i
$763$	16.9042	−	5.00275i	0.611973	−	0.181112i
$764$		−	4.97173i		−	0.179871i
$765$		0			0
$766$	−16.3214	−	9.42316i	−0.589716	−	0.340473i
$767$	−43.0117	−	24.8328i	−1.55306	−	0.896661i
$768$	−1.72845	+	0.111613i	−0.0623701	+	0.00402748i
$769$			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
$772$	−3.01660	−	5.22491i	−0.108570	−	0.188049i
$773$	17.4088	−	30.1528i	0.626149	−	1.08452i	−0.362168	−	0.932113i	$-0.617963\pi$
$773$	17.4088	−	30.1528i	0.626149	−	1.08452i	0.988317	−	0.152410i	$-0.0487033\pi$
$774$	0.984951	+	7.59475i	0.0354033	+	0.272987i
$775$		0			0
$776$	4.61723			0.165749
$777$	29.7186	−	10.9229i	1.06615	−	0.391858i
$778$	10.8601			0.389352
$779$	64.0969	−	37.0064i	2.29651	−	1.32589i
$780$		0			0
$781$	3.29768	−	5.71175i	0.118000	−	0.204383i
$782$	−20.0809	−	34.7811i	−0.718091	−	1.24377i
$783$	−3.83132	−	19.5572i	−0.136920	−	0.698918i
$784$	5.87256	−	3.80960i	0.209734	−	0.136057i
$785$		0			0
$786$	0.618204	+	9.57360i	0.0220506	+	0.341479i
$787$	43.0486	+	24.8541i	1.53452	+	0.885953i	0.999145	+	0.0413355i	$0.0131612\pi$
$787$	43.0486	+	24.8541i	1.53452	+	0.885953i	0.535370	+	0.844617i	$0.320172\pi$
$788$	12.3100	+	7.10719i	0.438526	+	0.253183i
$789$	3.45330	+	53.4782i	0.122941	+	1.90388i
$790$		0			0
$791$	8.11569	−	8.54796i	0.288561	−	0.303931i
$792$	−4.20226	−	5.49845i	−0.149321	−	0.195379i
$793$	−14.9617	−	25.9144i	−0.531306	−	0.920249i
$794$	−13.5204	+	23.4180i	−0.479822	+	0.831075i
$795$		0			0
$796$	1.94932	−	1.12544i	0.0690917	−	0.0398901i
$797$	−8.43295			−0.298710			−0.149355	−	0.988784i	$-0.547720\pi$
$797$	−8.43295			−0.298710			−0.149355	+	0.988784i	$0.547720\pi$
$798$	−26.5992	−	22.1768i	−0.941601	−	0.785051i
$799$	10.4419			0.369406
$800$		0			0
$801$	17.5165	−	2.27169i	0.618917	−	0.0802664i
$802$	12.2627	−	21.2396i	0.433012	−	0.749998i
$803$	4.24656	+	7.35525i	0.149858	+	0.259561i
$804$	−2.12398	+	4.29655i	−0.0749070	+	0.151527i
$805$		0			0
$806$			21.9113i			0.771794i
$807$	−7.09394	+	0.458083i	−0.249719	+	0.0161253i
$808$	−9.79825	−	5.65702i	−0.344701	−	0.199013i
$809$	−33.7531	−	19.4873i	−1.18669	−	0.685138i	−0.229141	−	0.973393i	$-0.573592\pi$
$809$	−33.7531	−	19.4873i	−1.18669	−	0.685138i	−0.957554	+	0.288255i	$0.906925\pi$
$810$		0			0
$811$			29.5668i			1.03823i	0.854704	+	0.519116i	$0.173739\pi$
$811$			29.5668i			1.03823i	−0.854704	+	0.519116i	$0.826261\pi$
$812$	2.87962	+	9.73018i	0.101055	+	0.341462i
$813$	−14.0934	−	6.96702i	−0.494277	−	0.244344i
$814$	7.96919	+	13.8030i	0.279320	+	0.483796i
$815$		0			0
$816$	−6.05578	−	9.08209i	−0.211995	−	0.317937i
$817$	−16.7072	+	9.64591i	−0.584511	+	0.337468i
$818$	−5.40347			−0.188928
$819$	−16.0656	−	36.2964i	−0.561379	−	1.26830i
$820$		0			0
$821$	−29.1479	+	16.8285i	−1.01727	+	0.587320i	−0.913311	−	0.407262i	$-0.866484\pi$
$821$	−29.1479	+	16.8285i	−1.01727	+	0.587320i	−0.103956	+	0.994582i	$0.533150\pi$
$822$	1.19250	+	1.78843i	0.0415931	+	0.0623788i
$823$	−6.27024	+	10.8604i	−0.218567	+	0.378569i	−0.954370	−	0.298627i	$-0.903472\pi$
$823$	−6.27024	+	10.8604i	−0.218567	+	0.378569i	0.735803	+	0.677195i	$0.236805\pi$
$824$	−3.68203	−	6.37747i	−0.128270	−	0.222170i
$825$		0			0
$826$	18.0920	−	19.0556i	0.629501	−	0.663030i
$827$			15.6875i			0.545506i	0.962084	+	0.272753i	$0.0879342\pi$
$827$			15.6875i			0.545506i	−0.962084	+	0.272753i	$0.912066\pi$
$828$	−17.6483	−	7.35011i	−0.613320	−	0.255434i
$829$	−4.91198	−	2.83593i	−0.170600	−	0.0984959i	0.412269	−	0.911062i	$-0.364736\pi$
$829$	−4.91198	−	2.83593i	−0.170600	−	0.0984959i	−0.582869	+	0.812566i	$0.698070\pi$
$830$		0			0
$831$	0.374168	−	0.0241614i	0.0129797	−	0.000838151i
$832$		−	5.00084i		−	0.173373i
$833$	39.2979	+	20.0475i	1.36159	+	0.694606i
$834$	9.62095	−	19.4620i	0.333146	−	0.673913i
$835$		0			0
$836$	8.71645	−	15.0973i	0.301465	−	0.522152i
$837$	21.5376	+	7.38066i	0.744447	+	0.255113i
$838$	24.5024	−	14.1465i	0.846422	−	0.488682i
$839$	−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
$842$	21.7967	−	12.5843i	0.751165	−	0.433685i
$843$	27.1639	−	18.1125i	0.935576	−	0.623826i
$844$	13.8017	−	23.9052i	0.475073	−	0.822851i
$845$		0			0
$846$	3.94920	−	3.01823i	0.135776	−	0.103769i
$847$	3.51094	−	14.6084i	0.120637	−	0.501949i
$848$		−	3.25278i		−	0.111701i
$849$	0.223038	+	3.45400i	0.00765464	+	0.118541i
$850$		0			0
$851$	38.1310	+	22.0150i	1.30712	+	0.754663i
$852$	−0.319112	−	4.94181i	−0.0109326	−	0.169304i
$853$			3.66698i			0.125555i	0.998028	+	0.0627775i	$0.0199958\pi$
$853$			3.66698i			0.125555i	−0.998028	+	0.0627775i	$0.980004\pi$
$854$	15.1805	−	4.49262i	0.519465	−	0.153734i
$855$		0			0
$856$	4.20937	+	7.29084i	0.143873	+	0.249196i
$857$	−5.78149	+	10.0138i	−0.197492	+	0.342066i	−0.947715	−	0.319119i	$-0.896613\pi$
$857$	−5.78149	+	10.0138i	−0.197492	+	0.342066i	0.750223	+	0.661185i	$0.229946\pi$
$858$	16.6242	−	11.0847i	0.567540	−	0.378426i
$859$	−12.9614	+	7.48325i	−0.442236	+	0.255325i	−0.704546	−	0.709659i	$-0.748849\pi$
$859$	−12.9614	+	7.48325i	−0.442236	+	0.255325i	0.262310	+	0.964984i	$0.415516\pi$
$860$		0			0
$861$	−7.65401	+	44.2229i	−0.260848	+	1.50711i
$862$	11.2182			0.382093
$863$	−8.11706	+	4.68639i	−0.276308	+	0.159526i	−0.631751	−	0.775172i	$-0.717663\pi$
$863$	−8.11706	+	4.68639i	−0.276308	+	0.159526i	0.355443	+	0.934698i	$0.384330\pi$
$864$	−4.91553	−	1.68449i	−0.167230	−	0.0573076i
$865$		0			0
$866$	0.319796	+	0.553903i	0.0108671	+	0.0188224i
$867$	17.4383	−	35.2754i	0.592235	−	1.19802i
$868$	−11.2715	−	2.70896i	−0.382579	−	0.0919482i
$869$		−	5.90286i		−	0.200241i
$870$		0			0
$871$	−11.9842	−	6.91907i	−0.406069	−	0.234444i
$872$	5.77043	+	3.33156i	0.195411	+	0.112821i
$873$	12.7870	+	5.32551i	0.432775	+	0.180241i
$874$		−	48.1585i		−	1.62899i
$875$		0			0
$876$	5.71664	+	2.82600i	0.193148	+	0.0954818i
$877$	−7.81117	−	13.5293i	−0.263764	−	0.456853i	0.703475	−	0.710720i	$-0.251631\pi$
$877$	−7.81117	−	13.5293i	−0.263764	−	0.456853i	−0.967239	+	0.253867i	$0.918297\pi$
$878$	6.58174	−	11.3999i	0.222123	−	0.384728i
$879$	−8.91814	−	13.3749i	−0.300801	−	0.451123i
$880$		0			0
$881$	4.54709			0.153195			0.0765977	−	0.997062i	$-0.475594\pi$
$881$	4.54709			0.153195			0.0765977	+	0.997062i	$0.475594\pi$
$882$	20.6576	−	3.77695i	0.695576	−	0.127177i
$883$	48.8190			1.64289			0.821445	−	0.570288i	$-0.193169\pi$
$883$	48.8190			1.64289			0.821445	+	0.570288i	$0.193169\pi$
$884$	27.2943	−	15.7584i	0.918008	−	0.530012i
$885$		0			0
$886$	−12.9223	+	22.3821i	−0.434133	+	0.751941i
$887$	−3.64168	−	6.30758i	−0.122276	−	0.211788i	0.798389	−	0.602142i	$-0.205686\pi$
$887$	−3.64168	−	6.30758i	−0.122276	−	0.211788i	−0.920665	+	0.390354i	$0.872353\pi$
$888$	10.7280	+	5.30334i	0.360008	+	0.177969i
$889$	3.52457	+	3.34633i	0.118210	+	0.112232i
$890$		0			0
$891$	−5.29591	−	20.0744i	−0.177420	−	0.672517i
$892$	−19.9858	−	11.5388i	−0.669176	−	0.386349i
$893$	10.8435	+	6.26049i	0.362863	+	0.209499i
$894$	−26.9554	+	1.74062i	−0.901525	+	0.0582149i
$895$		0			0
$896$	2.57250	+	0.618268i	0.0859411	+	0.0206549i
$897$	24.4609	−	49.4813i	0.816726	−	1.65213i
$898$	−14.1793	−	24.5593i	−0.473170	−	0.819554i
$899$	8.40232	−	14.5532i	0.280233	−	0.485378i
$900$		0			0
$901$	17.7535	−	10.2500i	0.591456	−	0.341477i
$902$	−22.5921			−0.752236
$903$	1.99506	−	11.5269i	0.0663914	−	0.383593i
$904$	4.45505			0.148173
$905$		0			0
$906$	4.37965	−	2.92027i	0.145504	−	0.0970196i
$907$	−13.4481	+	23.2928i	−0.446537	+	0.773425i	−0.998158	−	0.0606703i	$-0.980676\pi$
$907$	−13.4481	+	23.2928i	−0.446537	+	0.773425i	0.551621	+	0.834095i	$0.314010\pi$
$908$	−10.0175	−	17.3509i	−0.332444	−	0.575809i
$909$	−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	$0.720880\pi$
$912$	−0.843477	−	13.0622i	−0.0279303	−	0.432533i
$913$	3.67072	+	2.11929i	0.121483	+	0.0701383i
$914$	25.2797	+	14.5953i	0.836179	+	0.482768i
$915$		0			0
$916$		−	28.7648i		−	0.950417i
$917$	3.42448	−	14.2486i	0.113086	−	0.470531i
$918$	−6.29570	−	32.1368i	−0.207789	−	1.06067i
$919$	2.26073	+	3.91570i	0.0745746	+	0.129167i	0.900901	−	0.434024i	$-0.142907\pi$
$919$	2.26073	+	3.91570i	0.0745746	+	0.129167i	−0.826327	+	0.563191i	$0.809573\pi$
$920$		0			0
$921$	−38.8055	+	25.8749i	−1.27869	+	0.852606i
$922$	−26.9306	+	15.5484i	−0.886913	+	0.512060i
$923$	14.2979			0.470621
$924$	3.64683	+	9.92212i	0.119972	+	0.326414i
$925$		0			0
$926$	−29.0045	+	16.7457i	−0.953146	+	0.550299i
$927$	−2.84131	−	21.9087i	−0.0933209	−	0.719577i
$928$	−1.91767	+	3.32150i	−0.0629505	+	0.109033i
$929$	−8.30472	−	14.3842i	−0.272469	−	0.471930i	0.697025	−	0.717047i	$-0.254507\pi$
$929$	−8.30472	−	14.3842i	−0.272469	−	0.471930i	−0.969493	+	0.245117i	$0.921174\pi$
$930$		0			0
$931$	28.7898	+	44.3800i	0.943547	+	1.45449i
$932$		−	25.7115i		−	0.842209i
$933$	4.87647	−	0.314892i	0.159648	−	0.0103091i
$934$	−12.8389	−	7.41254i	−0.420102	−	0.242546i
$935$		0			0
$936$	5.76797	−	13.8494i	0.188532	−	0.452682i
$937$			20.5347i			0.670839i	0.942069	+	0.335419i	$0.108878\pi$
$937$			20.5347i			0.670839i	−0.942069	+	0.335419i	$0.891122\pi$
$938$	5.04090	−	5.30940i	0.164591	−	0.173358i
$939$	17.7670	+	8.78303i	0.579803	+	0.286623i
$940$		0			0
$941$	12.1992	−	21.1296i	0.397682	−	0.688805i	−0.595758	−	0.803164i	$-0.703148\pi$
$941$	12.1992	−	21.1296i	0.397682	−	0.688805i	0.993439	+	0.114359i	$0.0364814\pi$
$942$	15.2062	+	22.8053i	0.495445	+	0.743037i
$943$	−54.0495	+	31.2055i	−1.76009	+	1.01619i
$944$	9.93145			0.323241
$945$		0			0
$946$	5.88876			0.191460
$947$	−16.5526	+	9.55667i	−0.537888	+	0.310550i	−0.744223	−	0.667932i	$-0.767180\pi$
$947$	−16.5526	+	9.55667i	−0.537888	+	0.310550i	0.206334	+	0.978482i	$0.433847\pi$
$948$	−2.45880	−	3.68756i	−0.0798582	−	0.119766i
$949$	−9.20598	+	15.9452i	−0.298839	+	0.517604i
$950$		0			0
$951$	14.4553	+	7.14590i	0.468744	+	0.231722i
$952$	4.73184	+	15.9888i	0.153360	+	0.518200i
$953$			7.20297i			0.233327i	0.993171	+	0.116664i	$0.0372199\pi$
$953$			7.20297i			0.233327i	−0.993171	+	0.116664i	$0.962780\pi$
$954$	3.75176	−	9.00831i	0.121468	−	0.291655i
$955$		0			0
$956$	−9.28556	−	5.36102i	−0.300317	−	0.173388i
$957$	−15.2922	+	0.987477i	−0.494327	+	0.0319206i
$958$		−	23.0447i		−	0.744540i
$959$	−0.931789	−	3.14850i	−0.0300890	−	0.101670i
$960$		0			0
$961$	−5.90109	−	10.2210i	−0.190358	−	0.329709i
$962$	−17.2762	+	29.9232i	−0.557006	+	0.964762i
$963$	3.24824	+	25.0465i	0.104673	+	0.807111i
$964$	1.02594	−	0.592325i	0.0330432	−	0.0190775i
$965$		0			0
$966$	22.4297	+	18.7005i	0.721663	+	0.601680i
$967$	12.2448			0.393765			0.196883	−	0.980427i	$-0.436918\pi$
$967$	12.2448			0.393765			0.196883	+	0.980427i	$0.436918\pi$
$968$	4.91787	−	2.83934i	0.158066	−	0.0912597i
$969$	68.6349	−	45.7646i	2.20487	−	1.47017i
$970$		0			0
$971$	−13.4388	−	23.2768i	−0.431273	−	0.746987i	0.565710	−	0.824604i	$-0.308602\pi$
$971$	−13.4388	−	23.2768i	−0.431273	−	0.746987i	−0.996983	+	0.0776173i	$0.975269\pi$
$972$	−11.6703	−	10.3346i	−0.374324	−	0.331484i
$973$	−22.8337	+	24.0499i	−0.732014	+	0.771003i
$974$		−	10.6277i		−	0.340533i
$975$		0			0
$976$	5.18202	+	2.99184i	0.165872	+	0.0957664i
$977$	31.8298	+	18.3770i	1.01833	+	0.587931i	0.913619	−	0.406572i	$-0.133276\pi$
$977$	31.8298	+	18.3770i	1.01833	+	0.587931i	0.104707	+	0.994503i	$0.466609\pi$
$978$	0.961746	+	14.8937i	0.0307533	+	0.476249i
$979$		−	13.5819i		−	0.434078i
$980$		0			0
$981$	12.1381	+	15.8821i	0.387540	+	0.507076i
$982$	11.2343	+	19.4584i	0.358502	+	0.620943i
$983$	−6.68519	+	11.5791i	−0.213224	+	0.369315i	−0.952722	−	0.303844i	$-0.901730\pi$
$983$	−6.68519	+	11.5791i	−0.213224	+	0.369315i	0.739498	+	0.673159i	$0.235063\pi$
$984$	−14.1135	+	9.41063i	−0.449921	+	0.300000i
$985$		0			0
$986$	−24.1714			−0.769775
$987$	−7.12645	+	2.61929i	−0.226837	+	0.0833730i
$988$	37.7922			1.20233
$989$	14.0883	−	8.13388i	0.447982	−	0.258642i
$990$		0			0
$991$	−8.34843	+	14.4599i	−0.265197	+	0.459334i	−0.967615	−	0.252430i	$-0.918770\pi$
$991$	−8.34843	+	14.4599i	−0.265197	+	0.459334i	0.702419	+	0.711764i	$0.252104\pi$
$992$	−2.19077	−	3.79452i	−0.0695569	−	0.120476i
$993$	14.0434	−	28.4080i	0.445654	−	0.901501i
$994$	−1.76769	+	7.35502i	−0.0560677	+	0.233287i
$995$		0			0
$996$	3.17590	−	0.205080i	0.100632	−	0.00649822i
$997$	−42.5957	−	24.5927i	−1.34902	−	0.778857i	−0.360910	−	0.932601i	$-0.617534\pi$
$997$	−42.5957	−	24.5927i	−1.34902	−	0.778857i	−0.988111	+	0.153743i	$0.950867\pi$
$998$	−34.4322	−	19.8794i	−1.08993	−	0.629272i
$999$	23.5934	+	27.0608i	0.746462	+	0.856167i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.1	✓	12	15.14	odd	2
210.2.r.a.131.1	yes	12	35.19	odd	6
210.2.r.b.101.4	yes	12	5.4	even	2
210.2.r.b.131.4	yes	12	105.89	even	6
1050.2.s.f.101.3		12	1.1	even	1	trivial
1050.2.s.f.551.3		12	21.5	even	6	inner
1050.2.s.g.101.6		12	3.2	odd	2
1050.2.s.g.551.6		12	7.5	odd	6
1050.2.u.e.299.6		12	105.68	odd	12
1050.2.u.e.899.6		12	5.2	odd	4
1050.2.u.f.299.3		12	35.12	even	12
1050.2.u.f.899.3		12	15.8	even	4
1050.2.u.g.299.4		12	35.33	even	12
1050.2.u.g.899.4		12	15.2	even	4
1050.2.u.h.299.1		12	105.47	odd	12
1050.2.u.h.899.1		12	5.3	odd	4
1470.2.b.a.881.3		12	105.59	even	6
1470.2.b.a.881.9		12	35.4	even	6
1470.2.b.b.881.4		12	105.74	odd	6
1470.2.b.b.881.10		12	35.24	odd	6

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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.960885 + 1.44108i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.55269 - 0.767566i) q^{6} +(1.91871 + 1.82168i) q^{7} +1.00000i q^{8} +(-1.15340 + 2.76942i) q^{9} +(1.99775 + 1.15340i) q^{11} +(1.72845 - 0.111613i) q^{12} +5.00084i q^{13} +(-2.57250 - 0.618268i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.15115 - 5.45795i) q^{17} +(-0.385834 - 2.97509i) q^{18} +(6.54470 - 3.77859i) q^{19} +(-0.781523 + 4.51544i) q^{21} -2.30680 q^{22} +(-5.51880 + 3.18628i) q^{23} +(-1.44108 + 0.960885i) q^{24} +(-2.50042 - 4.33086i) q^{26} +(-5.09922 + 0.998953i) q^{27} +(2.53698 - 0.750813i) q^{28} +3.83533i q^{29} +(-3.79452 - 2.19077i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.257468 + 3.98719i) q^{33} +6.30230i q^{34} +(1.82168 + 2.38358i) q^{36} +(-3.45465 - 5.98363i) q^{37} +(-3.77859 + 6.54470i) q^{38} +(-7.20659 + 4.80523i) q^{39} +9.79371 q^{41} +(-1.58090 - 4.30125i) q^{42} -2.55278 q^{43} +(1.99775 - 1.15340i) q^{44} +(3.18628 - 5.51880i) q^{46} +(0.828416 + 1.43486i) q^{47} +(0.767566 - 1.55269i) q^{48} +(0.362928 + 6.99059i) q^{49} +(10.8932 - 0.703417i) q^{51} +(4.33086 + 2.50042i) q^{52} +(2.81699 + 1.62639i) q^{53} +(3.91658 - 3.41473i) q^{54} +(-1.82168 + 1.91871i) q^{56} +(11.7339 + 5.80063i) q^{57} +(-1.91767 - 3.32150i) q^{58} +(-4.96573 + 8.60089i) q^{59} +(-5.18202 + 2.99184i) q^{61} +4.38153 q^{62} +(-7.25805 + 3.21259i) q^{63} -1.00000 q^{64} +(-2.21657 - 3.32428i) q^{66} +(-1.38358 + 2.39643i) q^{67} +(-3.15115 - 5.45795i) q^{68} +(-9.89460 - 4.89136i) q^{69} -2.85910i q^{71} +(-2.76942 - 1.15340i) q^{72} +(3.18851 + 1.84089i) q^{73} +(5.98363 + 3.45465i) q^{74} -7.55717i q^{76} +(1.73198 + 5.85231i) q^{77} +(3.83848 - 7.76475i) q^{78} +(-1.27945 - 2.21607i) q^{79} +(-6.33934 - 6.38849i) q^{81} +(-8.48160 + 4.89686i) q^{82} +1.83743 q^{83} +(3.51973 + 2.93454i) q^{84} +(2.21077 - 1.27639i) q^{86} +(-5.52701 + 3.68532i) q^{87} +(-1.15340 + 1.99775i) q^{88} +(-2.94387 - 5.09894i) q^{89} +(-9.10996 + 9.59518i) q^{91} +6.37256i q^{92} +(-0.489035 - 7.57326i) q^{93} +(-1.43486 - 0.828416i) q^{94} +(0.111613 + 1.72845i) q^{96} -4.61723i q^{97} +(-3.80960 - 5.87256i) q^{98} +(-5.49845 + 4.20226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 6 q^{4} + 2 q^{6} - 8 q^{7} + 12 q^{11} + 2 q^{12} - 12 q^{14} - 6 q^{16} + 12 q^{17} + 4 q^{18} + 4 q^{21} - 24 q^{23} - 2 q^{24} + 4 q^{26} - 8 q^{27} - 4 q^{28} + 12 q^{31} + 2 q^{33}+ \cdots + 48 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 6 * q^4 + 2 * q^6 - 8 * q^7 + 12 * q^11 + 2 * q^12 - 12 * q^14 - 6 * q^16 + 12 * q^17 + 4 * q^18 + 4 * q^21 - 24 * q^23 - 2 * q^24 + 4 * q^26 - 8 * q^27 - 4 * q^28 + 12 * q^31 + 2 * q^33 + 6 * q^36 + 8 * q^37 + 8 * q^38 - 42 * q^39 + 4 * q^41 - 24 * q^42 + 12 * q^44 + 2 * q^46 + 16 * q^47 + 4 * q^48 - 14 * q^49 - 8 * q^51 + 12 * q^52 - 48 * q^53 - 32 * q^54 - 6 * q^56 + 36 * q^57 - 8 * q^58 - 12 * q^59 - 30 * q^61 + 8 * q^62 - 20 * q^63 - 12 * q^64 - 14 * q^66 + 4 * q^67 - 12 * q^68 - 50 * q^69 - 4 * q^72 + 20 * q^77 - 32 * q^78 - 4 * q^79 - 40 * q^81 - 40 * q^83 + 20 * q^84 + 54 * q^86 - 64 * q^87 - 26 * q^89 + 28 * q^91 - 4 * q^93 + 24 * q^94 - 4 * q^96 + 16 * 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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