LMFDB - Embedded newform 1008.2.t.g.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	1008.193
Dual form			1008.2.t.g.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73025 + 0.0789082i) q^{3} -0.460505 q^{5} +(-2.25729 - 1.38008i) q^{7} +(2.98755 - 0.273062i) q^{9} +O(q^{10})$	\(q+(-1.73025 + 0.0789082i) q^{3} -0.460505 q^{5} +(-2.25729 - 1.38008i) q^{7} +(2.98755 - 0.273062i) q^{9} +3.64766 q^{11} +(0.730252 - 1.26483i) q^{13} +(0.796790 - 0.0363376i) q^{15} +(-1.86693 + 3.23361i) q^{17} +(2.02704 + 3.51094i) q^{19} +(4.01459 + 2.20977i) q^{21} -1.13307 q^{23} -4.78794 q^{25} +(-5.14766 + 0.708209i) q^{27} +(-4.48755 - 7.77266i) q^{29} +(-0.257295 - 0.445647i) q^{31} +(-6.31138 + 0.287831i) q^{33} +(1.03950 + 0.635534i) q^{35} +(-4.55408 - 7.88791i) q^{37} +(-1.16372 + 2.24611i) q^{39} +(-0.472958 + 0.819187i) q^{41} +(-4.66372 - 8.07779i) q^{43} +(-1.37578 + 0.125747i) q^{45} +(1.16372 - 2.01561i) q^{47} +(3.19076 + 6.23049i) q^{49} +(2.97509 - 5.74228i) q^{51} +(6.21780 - 10.7695i) q^{53} -1.67977 q^{55} +(-3.78434 - 5.91486i) q^{57} +(-6.44805 - 11.1684i) q^{59} +(-6.04163 + 10.4644i) q^{61} +(-7.12062 - 3.50667i) q^{63} +(-0.336285 + 0.582462i) q^{65} +(-1.16012 - 2.00938i) q^{67} +(1.96050 - 0.0894089i) q^{69} -1.67977 q^{71} +(-6.62062 + 11.4673i) q^{73} +(8.28434 - 0.377808i) q^{75} +(-8.23385 - 5.03407i) q^{77} +(-2.50360 + 4.33636i) q^{79} +(8.85087 - 1.63157i) q^{81} +(-3.32383 - 5.75705i) q^{83} +(0.859728 - 1.48909i) q^{85} +(8.37792 + 13.0946i) q^{87} +(-1.36333 - 2.36135i) q^{89} +(-3.39397 + 1.84730i) q^{91} +(0.480350 + 0.750780i) q^{93} +(-0.933463 - 1.61680i) q^{95} +(-5.59358 - 9.68836i) q^{97} +(10.8976 - 0.996040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) $ 6 * q - 4 * q^3 + 10 * q^5 + 2 * q^7 - 4 * q^9	$ 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} + 4 q^{25} - 7 q^{27} - 5 q^{29} + 14 q^{31} - 4 q^{33} + 19 q^{35} - 9 q^{37} + 3 q^{39} - 12 q^{41} - 18 q^{43} - 31 q^{45} - 3 q^{47} - 26 q^{51} + 9 q^{53} - 14 q^{55} + 2 q^{57} - 4 q^{59} + 4 q^{61} - 28 q^{63} - 12 q^{65} - 5 q^{67} - q^{69} - 14 q^{71} - 25 q^{73} + 25 q^{75} - 35 q^{77} - 7 q^{79} + 32 q^{81} - 8 q^{83} + 14 q^{85} + 20 q^{87} - 9 q^{89} - 4 q^{91} - 3 q^{93} - 2 q^{95} - 28 q^{97} + 41 q^{99}+O(q^{100}) $ 6 * q - 4 * q^3 + 10 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 - 2 * q^13 + 2 * q^15 - 4 * q^17 + 3 * q^19 - 7 * q^21 - 14 * q^23 + 4 * q^25 - 7 * q^27 - 5 * q^29 + 14 * q^31 - 4 * q^33 + 19 * q^35 - 9 * q^37 + 3 * q^39 - 12 * q^41 - 18 * q^43 - 31 * q^45 - 3 * q^47 - 26 * q^51 + 9 * q^53 - 14 * q^55 + 2 * q^57 - 4 * q^59 + 4 * q^61 - 28 * q^63 - 12 * q^65 - 5 * q^67 - q^69 - 14 * q^71 - 25 * q^73 + 25 * q^75 - 35 * q^77 - 7 * q^79 + 32 * q^81 - 8 * q^83 + 14 * q^85 + 20 * q^87 - 9 * q^89 - 4 * q^91 - 3 * q^93 - 2 * q^95 - 28 * q^97 + 41 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.73025	+	0.0789082i	−0.998962	+	0.0455577i
$3$	−1.73025	+	0.0789082i	−0.998962	+	0.0455577i
$4$		0			0
$5$	−0.460505			−0.205944			−0.102972	−	0.994684i	$-0.532835\pi$
$5$	−0.460505			−0.205944			−0.102972	+	0.994684i	$0.532835\pi$
$6$		0			0
$7$	−2.25729	−	1.38008i	−0.853177	−	0.521621i
$7$	−2.25729	−	1.38008i	−0.853177	−	0.521621i
$8$		0			0
$9$	2.98755	−	0.273062i	0.995849	−	0.0910208i
$10$		0			0
$11$	3.64766			1.09981			0.549906	−	0.835227i	$-0.314664\pi$
$11$	3.64766			1.09981			0.549906	+	0.835227i	$0.314664\pi$
$12$		0			0
$13$	0.730252	−	1.26483i	0.202536	−	0.350802i	−0.746809	−	0.665038i	$-0.768415\pi$
$13$	0.730252	−	1.26483i	0.202536	−	0.350802i	0.949345	+	0.314236i	$0.101748\pi$
$14$		0			0
$15$	0.796790	−	0.0363376i	0.205730	−	0.00938234i
$16$		0			0
$17$	−1.86693	+	3.23361i	−0.452796	+	0.784266i	−0.998558	−	0.0536743i	$-0.982907\pi$
$17$	−1.86693	+	3.23361i	−0.452796	+	0.784266i	0.545763	+	0.837940i	$0.316240\pi$
$18$		0			0
$19$	2.02704	+	3.51094i	0.465035	+	0.805465i	0.999203	−	0.0399136i	$-0.0127083\pi$
$19$	2.02704	+	3.51094i	0.465035	+	0.805465i	−0.534168	+	0.845378i	$0.679375\pi$
$20$		0			0
$21$	4.01459	+	2.20977i	0.876055	+	0.482211i
$22$		0			0
$23$	−1.13307			−0.236262			−0.118131	−	0.992998i	$-0.537690\pi$
$23$	−1.13307			−0.236262			−0.118131	+	0.992998i	$0.537690\pi$
$24$		0			0
$25$	−4.78794			−0.957587
$26$		0			0
$27$	−5.14766	+	0.708209i	−0.990668	+	0.136295i
$28$		0			0
$29$	−4.48755	−	7.77266i	−0.833317	−	1.44335i	−0.895394	−	0.445275i	$-0.853106\pi$
$29$	−4.48755	−	7.77266i	−0.833317	−	1.44335i	0.0620772	−	0.998071i	$-0.480228\pi$
$30$		0			0
$31$	−0.257295	−	0.445647i	−0.0462115	−	0.0800406i	0.841994	−	0.539486i	$-0.181381\pi$
$31$	−0.257295	−	0.445647i	−0.0462115	−	0.0800406i	−0.888206	+	0.459446i	$0.848048\pi$
$32$		0			0
$33$	−6.31138	+	0.287831i	−1.09867	+	0.0501049i
$34$		0			0
$35$	1.03950	+	0.635534i	0.175707	+	0.107425i
$36$		0			0
$37$	−4.55408	−	7.88791i	−0.748687	−	1.29676i	−0.948452	−	0.316920i	$-0.897351\pi$
$37$	−4.55408	−	7.88791i	−0.748687	−	1.29676i	0.199765	−	0.979844i	$-0.435982\pi$
$38$		0			0
$39$	−1.16372	+	2.24611i	−0.186344	+	0.359665i
$40$		0			0
$41$	−0.472958	+	0.819187i	−0.0738636	+	0.127936i	−0.900592	−	0.434666i	$-0.856866\pi$
$41$	−0.472958	+	0.819187i	−0.0738636	+	0.127936i	0.826728	+	0.562602i	$0.190200\pi$
$42$		0			0
$43$	−4.66372	−	8.07779i	−0.711210	−	1.23185i	−0.964403	−	0.264436i	$-0.914814\pi$
$43$	−4.66372	−	8.07779i	−0.711210	−	1.23185i	0.253193	−	0.967416i	$-0.418519\pi$
$44$		0			0
$45$	−1.37578	+	0.125747i	−0.205089	+	0.0187452i
$46$		0			0
$47$	1.16372	−	2.01561i	0.169745	−	0.294007i	−0.768585	−	0.639748i	$-0.779039\pi$
$47$	1.16372	−	2.01561i	0.169745	−	0.294007i	0.938330	+	0.345740i	$0.112372\pi$
$48$		0			0
$49$	3.19076	+	6.23049i	0.455822	+	0.890071i
$50$		0			0
$51$	2.97509	−	5.74228i	0.416596	−	0.804080i
$52$		0			0
$53$	6.21780	−	10.7695i	0.854080	−	1.47931i	−0.0234151	−	0.999726i	$-0.507454\pi$
$53$	6.21780	−	10.7695i	0.854080	−	1.47931i	0.877495	−	0.479585i	$-0.159213\pi$
$54$		0			0
$55$	−1.67977			−0.226500
$56$		0			0
$57$	−3.78434	−	5.91486i	−0.501248	−	0.783443i
$58$		0			0
$59$	−6.44805	−	11.1684i	−0.839465	−	1.45400i	−0.890343	−	0.455291i	$-0.849535\pi$
$59$	−6.44805	−	11.1684i	−0.839465	−	1.45400i	0.0508779	−	0.998705i	$-0.483798\pi$
$60$		0			0
$61$	−6.04163	+	10.4644i	−0.773552	+	1.33983i	0.162053	+	0.986782i	$0.448188\pi$
$61$	−6.04163	+	10.4644i	−0.773552	+	1.33983i	−0.935605	+	0.353049i	$0.885145\pi$
$62$		0			0
$63$	−7.12062	−	3.50667i	−0.897114	−	0.441799i
$64$		0			0
$65$	−0.336285	+	0.582462i	−0.0417110	+	0.0722456i
$66$		0			0
$67$	−1.16012	−	2.00938i	−0.141731	−	0.245485i	0.786418	−	0.617695i	$-0.211933\pi$
$67$	−1.16012	−	2.00938i	−0.141731	−	0.245485i	−0.928148	+	0.372210i	$0.878600\pi$
$68$		0			0
$69$	1.96050	−	0.0894089i	0.236017	−	0.0107636i
$70$		0			0
$71$	−1.67977			−0.199352			−0.0996758	−	0.995020i	$-0.531781\pi$
$71$	−1.67977			−0.199352			−0.0996758	+	0.995020i	$0.531781\pi$
$72$		0			0
$73$	−6.62062	+	11.4673i	−0.774885	+	1.34214i	0.159974	+	0.987121i	$0.448859\pi$
$73$	−6.62062	+	11.4673i	−0.774885	+	1.34214i	−0.934859	+	0.355019i	$0.884474\pi$
$74$		0			0
$75$	8.28434	−	0.377808i	0.956593	−	0.0436255i
$76$		0			0
$77$	−8.23385	−	5.03407i	−0.938334	−	0.573685i
$78$		0			0
$79$	−2.50360	+	4.33636i	−0.281677	+	0.487879i	−0.971798	−	0.235815i	$-0.924224\pi$
$79$	−2.50360	+	4.33636i	−0.281677	+	0.487879i	0.690121	+	0.723694i	$0.257557\pi$
$80$		0			0
$81$	8.85087	−	1.63157i	0.983430	−	0.181286i
$82$		0			0
$83$	−3.32383	−	5.75705i	−0.364838	−	0.631918i	0.623912	−	0.781494i	$-0.285542\pi$
$83$	−3.32383	−	5.75705i	−0.364838	−	0.631918i	−0.988750	+	0.149577i	$0.952209\pi$
$84$		0			0
$85$	0.859728	−	1.48909i	0.0932506	−	0.161515i
$86$		0			0
$87$	8.37792	+	13.0946i	0.898207	+	1.40388i
$88$		0			0
$89$	−1.36333	−	2.36135i	−0.144512	−	0.250303i	0.784679	−	0.619903i	$-0.212828\pi$
$89$	−1.36333	−	2.36135i	−0.144512	−	0.250303i	−0.929191	+	0.369600i	$0.879495\pi$
$90$		0			0
$91$	−3.39397	+	1.84730i	−0.355784	+	0.193649i
$92$		0			0
$93$	0.480350	+	0.750780i	0.0498099	+	0.0778522i
$94$		0			0
$95$	−0.933463	−	1.61680i	−0.0957713	−	0.165881i
$96$		0			0
$97$	−5.59358	−	9.68836i	−0.567942	−	0.983704i	−0.996769	−	0.0803178i	$-0.974406\pi$
$97$	−5.59358	−	9.68836i	−0.567942	−	0.983704i	0.428827	−	0.903386i	$-0.358927\pi$
$98$		0			0
$99$	10.8976	−	0.996040i	1.09525	−	0.100106i
$100$		0			0
$101$	13.7558			1.36876			0.684378	−	0.729127i	$-0.260074\pi$
$101$	13.7558			1.36876			0.684378	+	0.729127i	$0.260074\pi$
$102$		0			0
$103$	−11.1623			−1.09985			−0.549925	−	0.835214i	$-0.685344\pi$
$103$	−11.1623			−1.09985			−0.549925	+	0.835214i	$0.685344\pi$
$104$		0			0
$105$	−1.84874	−	1.01761i	−0.180418	−	0.0993085i
$106$		0			0
$107$	3.89037	+	6.73832i	0.376096	+	0.651418i	0.990490	−	0.137581i	$-0.0439329\pi$
$107$	3.89037	+	6.73832i	0.376096	+	0.651418i	−0.614394	+	0.788999i	$0.710600\pi$
$108$		0			0
$109$	−3.75729	+	6.50783i	−0.359884	+	0.623337i	−0.987941	−	0.154830i	$-0.950517\pi$
$109$	−3.75729	+	6.50783i	−0.359884	+	0.623337i	0.628058	+	0.778167i	$0.283850\pi$
$110$		0			0
$111$	8.50214	+	13.2887i	0.806987	+	1.26131i
$112$		0			0
$113$	3.03064	−	5.24922i	0.285099	−	0.493805i	−0.687534	−	0.726152i	$-0.741307\pi$
$113$	3.03064	−	5.24922i	0.285099	−	0.493805i	0.972633	+	0.232346i	$0.0746403\pi$
$114$		0			0
$115$	0.521786			0.0486568
$116$		0			0
$117$	1.83628	−	3.97816i	0.169765	−	0.367781i
$118$		0			0
$119$	8.67684	−	4.72270i	0.795405	−	0.432929i
$120$		0			0
$121$	2.30545			0.209586
$122$		0			0
$123$	0.753696	−	1.45472i	0.0679585	−	0.131168i
$124$		0			0
$125$	4.50739			0.403153
$126$		0			0
$127$	−8.80992			−0.781754			−0.390877	−	0.920443i	$-0.627828\pi$
$127$	−8.80992			−0.781754			−0.390877	+	0.920443i	$0.627828\pi$
$128$		0			0
$129$	8.70681	+	13.6086i	0.766592	+	1.19817i
$130$		0			0
$131$	−21.1373			−1.84678			−0.923389	−	0.383865i	$-0.874593\pi$
$131$	−21.1373			−1.84678			−0.923389	+	0.383865i	$0.874593\pi$
$132$		0			0
$133$	0.269748	−	10.7227i	0.0233901	−	0.929777i
$134$		0			0
$135$	2.37052	−	0.326134i	0.204022	−	0.0280691i
$136$		0			0
$137$	−4.40642			−0.376466			−0.188233	−	0.982124i	$-0.560276\pi$
$137$	−4.40642			−0.376466			−0.188233	+	0.982124i	$0.560276\pi$
$138$		0			0
$139$	1.01245	−	1.75362i	0.0858751	−	0.148740i	−0.819889	−	0.572523i	$-0.805965\pi$
$139$	1.01245	−	1.75362i	0.0858751	−	0.148740i	0.905764	+	0.423783i	$0.139298\pi$
$140$		0			0
$141$	−1.85447	+	3.57935i	−0.156175	+	0.301435i
$142$		0			0
$143$	2.66372	−	4.61369i	0.222751	−	0.385816i
$144$		0			0
$145$	2.06654	+	3.57935i	0.171617	+	0.297249i
$146$		0			0
$147$	−6.01245	−	10.5286i	−0.495899	−	0.868380i
$148$		0			0
$149$	−9.16225			−0.750601			−0.375300	−	0.926903i	$-0.622460\pi$
$149$	−9.16225			−0.750601			−0.375300	+	0.926903i	$0.622460\pi$
$150$		0			0
$151$	0.103896			0.00845496			0.00422748	−	0.999991i	$-0.498654\pi$
$151$	0.103896			0.00845496			0.00422748	+	0.999991i	$0.498654\pi$
$152$		0			0
$153$	−4.69455	+	10.1703i	−0.379532	+	0.822224i
$154$		0			0
$155$	0.118485	+	0.205223i	0.00951698	+	0.0164839i
$156$		0			0
$157$	−10.4911	−	18.1712i	−0.837285	−	1.45022i	−0.892157	−	0.451726i	$-0.850808\pi$
$157$	−10.4911	−	18.1712i	−0.837285	−	1.45022i	0.0548721	−	0.998493i	$-0.482525\pi$
$158$		0			0
$159$	−9.90856	+	19.1247i	−0.785800	+	1.51668i
$160$		0			0
$161$	2.55768	+	1.56373i	0.201574	+	0.123239i
$162$		0			0
$163$	11.5182	+	19.9501i	0.902174	+	1.56261i	0.824666	+	0.565620i	$0.191363\pi$
$163$	11.5182	+	19.9501i	0.902174	+	1.56261i	0.0775078	+	0.996992i	$0.475304\pi$
$164$		0			0
$165$	2.90642	−	0.132547i	0.226265	−	0.0103188i
$166$		0			0
$167$	5.31498	−	9.20581i	0.411285	−	0.712367i	−0.583745	−	0.811937i	$-0.698413\pi$
$167$	5.31498	−	9.20581i	0.411285	−	0.712367i	0.995031	+	0.0995698i	$0.0317467\pi$
$168$		0			0
$169$	5.43346	+	9.41103i	0.417959	+	0.723926i
$170$		0			0
$171$	7.01459	+	9.93559i	0.536419	+	0.759793i
$172$		0			0
$173$	−1.46936	+	2.54500i	−0.111713	+	0.193493i	−0.916461	−	0.400124i	$-0.868967\pi$
$173$	−1.46936	+	2.54500i	−0.111713	+	0.193493i	0.804748	+	0.593617i	$0.202301\pi$
$174$		0			0
$175$	10.8078	+	6.60773i	0.816991	+	0.499498i
$176$		0			0
$177$	12.0380	+	18.8153i	0.904834	+	1.41424i
$178$		0			0
$179$	4.58113	−	7.93474i	0.342409	−	0.593071i	−0.642470	−	0.766311i	$-0.722090\pi$
$179$	4.58113	−	7.93474i	0.342409	−	0.593071i	0.984880	+	0.173240i	$0.0554237\pi$
$180$		0			0
$181$	22.4284			1.66709			0.833545	−	0.552452i	$-0.186308\pi$
$181$	22.4284			1.66709			0.833545	+	0.552452i	$0.186308\pi$
$182$		0			0
$183$	9.62782	−	18.5828i	0.711709	−	1.37368i
$184$		0			0
$185$	2.09718	+	3.63242i	0.154188	+	0.267061i
$186$		0			0
$187$	−6.80992	+	11.7951i	−0.497990	+	0.862545i
$188$		0			0
$189$	12.5972	+	5.50555i	0.916310	+	0.400470i
$190$		0			0
$191$	1.24484	−	2.15613i	0.0900736	−	0.156012i	−0.817468	−	0.575974i	$-0.804623\pi$
$191$	1.24484	−	2.15613i	0.0900736	−	0.156012i	0.907542	+	0.419962i	$0.137956\pi$
$192$		0			0
$193$	−2.24484	−	3.88818i	−0.161587	−	0.279877i	0.773851	−	0.633368i	$-0.218328\pi$
$193$	−2.24484	−	3.88818i	−0.161587	−	0.279877i	−0.935438	+	0.353491i	$0.884995\pi$
$194$		0			0
$195$	0.535897	−	1.03434i	0.0383763	−	0.0740708i
$196$		0			0
$197$	12.7339			0.907249			0.453625	−	0.891193i	$-0.350131\pi$
$197$	12.7339			0.907249			0.453625	+	0.891193i	$0.350131\pi$
$198$		0			0
$199$	1.47296	−	2.55124i	0.104415	−	0.180852i	−0.809084	−	0.587693i	$-0.800036\pi$
$199$	1.47296	−	2.55124i	0.104415	−	0.180852i	0.913499	+	0.406841i	$0.133370\pi$
$200$		0			0
$201$	2.16585	+	3.38519i	0.152767	+	0.238773i
$202$		0			0
$203$	−0.597178	+	23.7384i	−0.0419137	+	1.66611i
$204$		0			0
$205$	0.217799	−	0.377240i	0.0152118	−	0.0263476i
$206$		0			0
$207$	−3.38511	+	0.309400i	−0.235282	+	0.0215048i
$208$		0			0
$209$	7.39397	+	12.8067i	0.511451	+	0.885860i
$210$		0			0
$211$	0.608168	−	1.05338i	0.0418680	−	0.0725176i	−0.844332	−	0.535820i	$-0.820002\pi$
$211$	0.608168	−	1.05338i	0.0418680	−	0.0725176i	0.886200	+	0.463303i	$0.153336\pi$
$212$		0			0
$213$	2.90642	−	0.132547i	0.199145	−	0.00908200i
$214$		0			0
$215$	2.14766	+	3.71986i	0.146469	+	0.253693i
$216$		0			0
$217$	−0.0342393	+	1.36104i	−0.00232432	+	0.0923937i
$218$		0			0
$219$	10.5505	−	20.3637i	0.712936	−	1.37605i
$220$		0			0
$221$	2.72665	+	4.72270i	0.183415	+	0.317683i
$222$		0			0
$223$	0.445916	+	0.772349i	0.0298607	+	0.0517203i	0.880570	−	0.473917i	$-0.157160\pi$
$223$	0.445916	+	0.772349i	0.0298607	+	0.0517203i	−0.850709	+	0.525637i	$0.823827\pi$
$224$		0			0
$225$	−14.3042	+	1.30740i	−0.953612	+	0.0871603i
$226$		0			0
$227$	14.6519			0.972483			0.486242	−	0.873824i	$-0.338368\pi$
$227$	14.6519			0.972483			0.486242	+	0.873824i	$0.338368\pi$
$228$		0			0
$229$	−9.57587			−0.632791			−0.316396	−	0.948627i	$-0.602473\pi$
$229$	−9.57587			−0.632791			−0.316396	+	0.948627i	$0.602473\pi$
$230$		0			0
$231$	14.6439	+	8.06049i	0.963496	+	0.530341i
$232$		0			0
$233$	7.21420	+	12.4954i	0.472618	+	0.818598i	0.999509	−	0.0313345i	$-0.00997571\pi$
$233$	7.21420	+	12.4954i	0.472618	+	0.818598i	−0.526891	+	0.849933i	$0.676642\pi$
$234$		0			0
$235$	−0.535897	+	0.928200i	−0.0349580	+	0.0605491i
$236$		0			0
$237$	3.98968	−	7.70055i	0.259158	−	0.500205i
$238$		0			0
$239$	9.15486	−	15.8567i	0.592179	−	1.02568i	−0.401760	−	0.915745i	$-0.631601\pi$
$239$	9.15486	−	15.8567i	0.592179	−	1.02568i	0.993938	−	0.109938i	$-0.0350654\pi$
$240$		0			0
$241$	0.0933847			0.00601544			0.00300772	−	0.999995i	$-0.499043\pi$
$241$	0.0933847			0.00601544			0.00300772	+	0.999995i	$0.499043\pi$
$242$		0			0
$243$	−15.1855	+	3.52144i	−0.974150	+	0.225901i
$244$		0			0
$245$	−1.46936	−	2.86917i	−0.0938739	−	0.183305i
$246$		0			0
$247$	5.92101			0.376745
$248$		0			0
$249$	6.20535	+	9.69886i	0.393248	+	0.614641i
$250$		0			0
$251$	18.2733			1.15340			0.576702	−	0.816955i	$-0.304339\pi$
$251$	18.2733			1.15340			0.576702	+	0.816955i	$0.304339\pi$
$252$		0			0
$253$	−4.13307			−0.259844
$254$		0			0
$255$	−1.37005	+	2.64435i	−0.0857956	+	0.165595i
$256$		0			0
$257$	−21.0512			−1.31314			−0.656568	−	0.754267i	$-0.727992\pi$
$257$	−21.0512			−1.31314			−0.656568	+	0.754267i	$0.727992\pi$
$258$		0			0
$259$	−0.606032	+	24.0903i	−0.0376570	+	1.49690i
$260$		0			0
$261$	−15.5292	−	21.9958i	−0.961232	−	1.36151i
$262$		0			0
$263$	5.16518			0.318499			0.159249	−	0.987238i	$-0.449093\pi$
$263$	5.16518			0.318499			0.159249	+	0.987238i	$0.449093\pi$
$264$		0			0
$265$	−2.86333	+	4.95943i	−0.175893	+	0.304655i
$266$		0			0
$267$	2.54523	+	3.97816i	0.155766	+	0.243459i
$268$		0			0
$269$	8.42840	−	14.5984i	0.513889	−	0.890081i	−0.485981	−	0.873969i	$-0.661538\pi$
$269$	8.42840	−	14.5984i	0.513889	−	0.890081i	0.999870	−	0.0161123i	$-0.00512891\pi$
$270$		0			0
$271$	−12.5562	−	21.7480i	−0.762736	−	1.32110i	−0.941435	−	0.337194i	$-0.890522\pi$
$271$	−12.5562	−	21.7480i	−0.762736	−	1.32110i	0.178699	−	0.983904i	$-0.442811\pi$
$272$		0			0
$273$	5.72665	−	3.46410i	0.346593	−	0.209657i
$274$		0			0
$275$	−17.4648			−1.05317
$276$		0			0
$277$	3.38151			0.203176			0.101588	−	0.994827i	$-0.467608\pi$
$277$	3.38151			0.203176			0.101588	+	0.994827i	$0.467608\pi$
$278$		0			0
$279$	−0.890369	−	1.26113i	−0.0533050	−	0.0755022i
$280$		0			0
$281$	−10.1388	−	17.5609i	−0.604831	−	1.04760i	−0.992078	−	0.125622i	$-0.959907\pi$
$281$	−10.1388	−	17.5609i	−0.604831	−	1.04760i	0.387248	−	0.921976i	$-0.373426\pi$
$282$		0			0
$283$	8.67471	+	15.0250i	0.515658	+	0.893145i	0.999835	+	0.0181754i	$0.00578571\pi$
$283$	8.67471	+	15.0250i	0.515658	+	0.893145i	−0.484177	+	0.874970i	$0.660881\pi$
$284$		0			0
$285$	1.74271	+	2.72382i	0.103229	+	0.161345i
$286$		0			0
$287$	2.19815	−	1.19643i	0.129753	−	0.0706228i
$288$		0			0
$289$	1.52918	+	2.64861i	0.0899517	+	0.155801i
$290$		0			0
$291$	10.4428	+	16.3219i	0.612168	+	0.956809i
$292$		0			0
$293$	−4.93560	+	8.54871i	−0.288341	+	0.499421i	−0.973414	−	0.229054i	$-0.926437\pi$
$293$	−4.93560	+	8.54871i	−0.288341	+	0.499421i	0.685073	+	0.728474i	$0.259770\pi$
$294$		0			0
$295$	2.96936	+	5.14308i	0.172883	+	0.299442i
$296$		0			0
$297$	−18.7769	+	2.58331i	−1.08955	+	0.149899i
$298$		0			0
$299$	−0.827430	+	1.43315i	−0.0478515	+	0.0828813i
$300$		0			0
$301$	−0.620621	+	24.6703i	−0.0357720	+	1.42197i
$302$		0			0
$303$	−23.8011	+	1.08545i	−1.36734	+	0.0623574i
$304$		0			0
$305$	2.78220	−	4.81891i	0.159308	−	0.275930i
$306$		0			0
$307$	−7.78794			−0.444481			−0.222240	−	0.974992i	$-0.571337\pi$
$307$	−7.78794			−0.444481			−0.222240	+	0.974992i	$0.571337\pi$
$308$		0			0
$309$	19.3135	−	0.880794i	1.09871	−	0.0501066i
$310$		0			0
$311$	7.70535	+	13.3461i	0.436930	+	0.756785i	0.997451	−	0.0713552i	$-0.0227324\pi$
$311$	7.70535	+	13.3461i	0.436930	+	0.756785i	−0.560521	+	0.828140i	$0.689399\pi$
$312$		0			0
$313$	−4.24844	+	7.35851i	−0.240136	+	0.415928i	−0.960753	−	0.277406i	$-0.910525\pi$
$313$	−4.24844	+	7.35851i	−0.240136	+	0.415928i	0.720617	+	0.693334i	$0.243859\pi$
$314$		0			0
$315$	3.27908	+	1.61484i	0.184755	+	0.0909859i
$316$		0			0
$317$	7.05262	−	12.2155i	0.396115	−	0.686091i	−0.597128	−	0.802146i	$-0.703692\pi$
$317$	7.05262	−	12.2155i	0.396115	−	0.686091i	0.993243	+	0.116055i	$0.0370249\pi$
$318$		0			0
$319$	−16.3691	−	28.3520i	−0.916491	−	1.58741i
$320$		0			0
$321$	−7.26303	−	11.3520i	−0.405383	−	0.633607i
$322$		0			0
$323$	−15.1373			−0.842264
$324$		0			0
$325$	−3.49640	+	6.05594i	−0.193945	+	0.335923i
$326$		0			0
$327$	5.98755	−	11.5567i	0.331112	−	0.639085i
$328$		0			0
$329$	−5.40856	+	2.94381i	−0.298183	+	0.162298i
$330$		0			0
$331$	13.7719	−	23.8536i	0.756971	−	1.31111i	−0.187417	−	0.982280i	$-0.560012\pi$
$331$	13.7719	−	23.8536i	0.756971	−	1.31111i	0.944388	−	0.328832i	$-0.106655\pi$
$332$		0			0
$333$	−15.7594	−	22.3219i	−0.863611	−	1.22323i
$334$		0			0
$335$	0.534239	+	0.925330i	0.0291886	+	0.0505562i
$336$		0			0
$337$	0.748440	−	1.29634i	0.0407701	−	0.0706159i	−0.844920	−	0.534892i	$-0.820352\pi$
$337$	0.748440	−	1.29634i	0.0407701	−	0.0706159i	0.885690	+	0.464276i	$0.153686\pi$
$338$		0			0
$339$	−4.82957	+	9.32162i	−0.262306	+	0.506281i
$340$		0			0
$341$	−0.938524	−	1.62557i	−0.0508239	−	0.0880296i
$342$		0			0
$343$	1.39610	−	18.4676i	0.0753825	−	0.997155i
$344$		0			0
$345$	−0.902822	+	0.0411732i	−0.0486063	+	0.00221669i
$346$		0			0
$347$	−9.14406	−	15.8380i	−0.490879	−	0.850228i	0.509066	−	0.860728i	$-0.329991\pi$
$347$	−9.14406	−	15.8380i	−0.490879	−	0.850228i	−0.999945	+	0.0105001i	$0.996658\pi$
$348$		0			0
$349$	−3.90136	−	6.75735i	−0.208835	−	0.361713i	0.742513	−	0.669832i	$-0.233634\pi$
$349$	−3.90136	−	6.75735i	−0.208835	−	0.361713i	−0.951348	+	0.308119i	$0.900300\pi$
$350$		0			0
$351$	−2.86333	+	7.02811i	−0.152833	+	0.375133i
$352$		0			0
$353$	26.9253			1.43309			0.716544	−	0.697542i	$-0.245723\pi$
$353$	26.9253			1.43309			0.716544	+	0.697542i	$0.245723\pi$
$354$		0			0
$355$	0.773541			0.0410553
$356$		0			0
$357$	−14.6405	+	8.85614i	−0.774856	+	0.468717i
$358$		0			0
$359$	3.13161	+	5.42411i	0.165280	+	0.286274i	0.936755	−	0.349987i	$-0.113814\pi$
$359$	3.13161	+	5.42411i	0.165280	+	0.286274i	−0.771475	+	0.636260i	$0.780481\pi$
$360$		0			0
$361$	1.28220	−	2.22084i	0.0674842	−	0.116886i
$362$		0			0
$363$	−3.98901	+	0.181919i	−0.209369	+	0.00954827i
$364$		0			0
$365$	3.04883	−	5.28073i	0.159583	−	0.276406i
$366$		0			0
$367$	−29.2733			−1.52806			−0.764028	−	0.645183i	$-0.776781\pi$
$367$	−29.2733			−1.52806			−0.764028	+	0.645183i	$0.776781\pi$
$368$		0			0
$369$	−1.18929	+	2.57651i	−0.0619122	+	0.134128i
$370$		0			0
$371$	−28.8982	+	15.7290i	−1.50032	+	0.816608i
$372$		0			0
$373$	17.8597			0.924742			0.462371	−	0.886687i	$-0.346999\pi$
$373$	17.8597			0.924742			0.462371	+	0.886687i	$0.346999\pi$
$374$		0			0
$375$	−7.79893	+	0.355670i	−0.402735	+	0.0183667i
$376$		0			0
$377$	−13.1082			−0.675105
$378$		0			0
$379$	22.4255			1.15192			0.575960	−	0.817478i	$-0.304629\pi$
$379$	22.4255			1.15192			0.575960	+	0.817478i	$0.304629\pi$
$380$		0			0
$381$	15.2434	−	0.695175i	0.780942	−	0.0356149i
$382$		0			0
$383$	14.1403			0.722534			0.361267	−	0.932462i	$-0.382344\pi$
$383$	14.1403			0.722534			0.361267	+	0.932462i	$0.382344\pi$
$384$		0			0
$385$	3.79173	+	2.31821i	0.193244	+	0.118147i
$386$		0			0
$387$	−16.1388	−	22.8593i	−0.820382	−	1.16200i
$388$		0			0
$389$	−23.1301			−1.17275			−0.586373	−	0.810041i	$-0.699445\pi$
$389$	−23.1301			−1.17275			−0.586373	+	0.810041i	$0.699445\pi$
$390$		0			0
$391$	2.11537	−	3.66392i	0.106979	−	0.185292i
$392$		0			0
$393$	36.5729	−	1.66791i	1.84486	−	0.0841350i
$394$		0			0
$395$	1.15292	−	1.99691i	0.0580097	−	0.100476i
$396$		0			0
$397$	−5.13307	−	8.89075i	−0.257622	−	0.446214i	0.707983	−	0.706230i	$-0.249605\pi$
$397$	−5.13307	−	8.89075i	−0.257622	−	0.446214i	−0.965604	+	0.260016i	$0.916272\pi$
$398$		0			0
$399$	0.379379	+	18.5743i	0.0189927	+	0.929877i
$400$		0			0
$401$	34.0335			1.69955			0.849775	−	0.527146i	$-0.176738\pi$
$401$	34.0335			1.69955			0.849775	+	0.527146i	$0.176738\pi$
$402$		0			0
$403$	−0.751560			−0.0374379
$404$		0			0
$405$	−4.07587	+	0.751347i	−0.202532	+	0.0373348i
$406$		0			0
$407$	−16.6118	−	28.7724i	−0.823415	−	1.42620i
$408$		0			0
$409$	1.74484	+	3.02215i	0.0862769	+	0.149436i	0.905935	−	0.423418i	$-0.139170\pi$
$409$	1.74484	+	3.02215i	0.0862769	+	0.149436i	−0.819658	+	0.572854i	$0.805836\pi$
$410$		0			0
$411$	7.62422	−	0.347703i	0.376075	−	0.0171509i
$412$		0			0
$413$	−0.858071	+	34.1091i	−0.0422229	+	1.67840i
$414$		0			0
$415$	1.53064	+	2.65115i	0.0751362	+	0.130140i
$416$		0			0
$417$	−1.61342	+	3.11410i	−0.0790097	+	0.152498i
$418$		0			0
$419$	−14.4897	+	25.0969i	−0.707867	+	1.22606i	0.257779	+	0.966204i	$0.417009\pi$
$419$	−14.4897	+	25.0969i	−0.707867	+	1.22606i	−0.965647	+	0.259858i	$0.916324\pi$
$420$		0			0
$421$	−1.06128	−	1.83819i	−0.0517237	−	0.0895881i	0.839004	−	0.544125i	$-0.183138\pi$
$421$	−1.06128	−	1.83819i	−0.0517237	−	0.0895881i	−0.890728	+	0.454537i	$0.849805\pi$
$422$		0			0
$423$	2.92627	−	6.33951i	0.142280	−	0.308237i
$424$		0			0
$425$	8.93872	−	15.4823i	0.433592	−	0.751003i
$426$		0			0
$427$	28.0795	−	15.2833i	1.35886	−	0.739612i
$428$		0			0
$429$	−4.24484	+	8.19304i	−0.204943	+	0.395564i
$430$		0			0
$431$	−10.9356	+	18.9410i	−0.526749	+	0.912356i	0.472765	+	0.881189i	$0.343256\pi$
$431$	−10.9356	+	18.9410i	−0.526749	+	0.912356i	−0.999514	+	0.0311679i	$0.990077\pi$
$432$		0			0
$433$	−13.0512			−0.627199			−0.313599	−	0.949555i	$-0.601535\pi$
$433$	−13.0512			−0.627199			−0.313599	+	0.949555i	$0.601535\pi$
$434$		0			0
$435$	−3.85807	−	6.03011i	−0.184980	−	0.289122i
$436$		0			0
$437$	−2.29679	−	3.97816i	−0.109870	−	0.190301i
$438$		0			0
$439$	2.43200	−	4.21235i	0.116073	−	0.201044i	−0.802135	−	0.597143i	$-0.796303\pi$
$439$	2.43200	−	4.21235i	0.116073	−	0.201044i	0.918208	+	0.396098i	$0.129636\pi$
$440$		0			0
$441$	11.2339	+	17.7426i	0.534945	+	0.844887i
$442$		0			0
$443$	−5.76975	+	9.99350i	−0.274129	+	0.474805i	−0.969915	−	0.243444i	$-0.921723\pi$
$443$	−5.76975	+	9.99350i	−0.274129	+	0.474805i	0.695786	+	0.718249i	$0.255056\pi$
$444$		0			0
$445$	0.627819	+	1.08741i	0.0297615	+	0.0515484i
$446$		0			0
$447$	15.8530	−	0.722977i	0.749822	−	0.0341957i
$448$		0			0
$449$	−26.4251			−1.24708			−0.623538	−	0.781793i	$-0.714306\pi$
$449$	−26.4251			−1.24708			−0.623538	+	0.781793i	$0.714306\pi$
$450$		0			0
$451$	−1.72519	+	2.98812i	−0.0812361	+	0.140705i
$452$		0			0
$453$	−0.179767	+	0.00819828i	−0.00844618	+	0.000385189i
$454$		0			0
$455$	1.56294	−	0.850689i	0.0732717	−	0.0398809i
$456$		0			0
$457$	1.86906	−	3.23731i	0.0874310	−	0.151435i	−0.818994	−	0.573803i	$-0.805468\pi$
$457$	1.86906	−	3.23731i	0.0874310	−	0.151435i	0.906425	+	0.422368i	$0.138801\pi$
$458$		0			0
$459$	7.32023	−	17.9677i	0.341679	−	0.838661i
$460$		0			0
$461$	−7.90496	−	13.6918i	−0.368171	−	0.637690i	0.621109	−	0.783724i	$-0.286682\pi$
$461$	−7.90496	−	13.6918i	−0.368171	−	0.637690i	−0.989280	+	0.146034i	$0.953349\pi$
$462$		0			0
$463$	−19.1965	+	33.2493i	−0.892137	+	1.54523i	−0.0548278	+	0.998496i	$0.517461\pi$
$463$	−19.1965	+	33.2493i	−0.892137	+	1.54523i	−0.837309	+	0.546730i	$0.815872\pi$
$464$		0			0
$465$	−0.221203	−	0.345738i	−0.0102581	−	0.0160332i
$466$		0			0
$467$	−3.15652	−	5.46725i	−0.146066	−	0.252994i	0.783704	−	0.621134i	$-0.213328\pi$
$467$	−3.15652	−	5.46725i	−0.146066	−	0.252994i	−0.929770	+	0.368140i	$0.879995\pi$
$468$		0			0
$469$	−0.154382	+	6.13682i	−0.00712869	+	0.283372i
$470$		0			0
$471$	19.5862	+	30.6129i	0.902484	+	1.41057i
$472$		0			0
$473$	−17.0117	−	29.4651i	−0.782197	−	1.35481i
$474$		0			0
$475$	−9.70535	−	16.8102i	−0.445312	−	0.771303i
$476$		0			0
$477$	15.6352	−	33.8724i	0.715887	−	1.55091i
$478$		0			0
$479$	20.4136			0.932722			0.466361	−	0.884594i	$-0.345565\pi$
$479$	20.4136			0.932722			0.466361	+	0.884594i	$0.345565\pi$
$480$		0			0
$481$	−13.3025			−0.606543
$482$		0			0
$483$	−4.54883	−	2.50383i	−0.206979	−	0.113928i
$484$		0			0
$485$	2.57587	+	4.46154i	0.116964	+	0.202588i
$486$		0			0
$487$	−6.18190	+	10.7074i	−0.280129	+	0.485197i	−0.971416	−	0.237383i	$-0.923710\pi$
$487$	−6.18190	+	10.7074i	−0.280129	+	0.485197i	0.691287	+	0.722580i	$0.257044\pi$
$488$		0			0
$489$	−21.5036	−	33.6098i	−0.972426	−	1.51989i
$490$		0			0
$491$	−0.207004	+	0.358541i	−0.00934194	+	0.0161807i	−0.870659	−	0.491888i	$-0.836307\pi$
$491$	−0.207004	+	0.358541i	−0.00934194	+	0.0161807i	0.861317	+	0.508069i	$0.169640\pi$
$492$		0			0
$493$	33.5117			1.50929
$494$		0			0
$495$	−5.01838	+	0.458681i	−0.225560	+	0.0206162i
$496$		0			0
$497$	3.79173	+	2.31821i	0.170082	+	0.103986i
$498$		0			0
$499$	0.923935			0.0413610			0.0206805	−	0.999786i	$-0.493417\pi$
$499$	0.923935			0.0413610			0.0206805	+	0.999786i	$0.493417\pi$
$500$		0			0
$501$	−8.46984	+	16.3478i	−0.378404	+	0.730365i
$502$		0			0
$503$	23.8142			1.06182			0.530911	−	0.847428i	$-0.321850\pi$
$503$	23.8142			1.06182			0.530911	+	0.847428i	$0.321850\pi$
$504$		0			0
$505$	−6.33463			−0.281887
$506$		0			0
$507$	−10.1439	−	15.8547i	−0.450505	−	0.704133i
$508$		0			0
$509$	−30.6342			−1.35784			−0.678919	−	0.734213i	$-0.737551\pi$
$509$	−30.6342			−1.35784			−0.678919	+	0.734213i	$0.737551\pi$
$510$		0			0
$511$	30.7704	−	16.7480i	1.36120	−	0.740887i
$512$		0			0
$513$	−12.9210	−	16.6376i	−0.570477	−	0.734567i
$514$		0			0
$515$	5.14027			0.226507
$516$		0			0
$517$	4.24484	−	7.35228i	0.186688	−	0.323353i
$518$		0			0
$519$	2.34154	−	4.51945i	0.102782	−	0.198382i
$520$		0			0
$521$	−13.4518	+	23.2993i	−0.589336	+	1.02076i	0.404984	+	0.914324i	$0.367277\pi$
$521$	−13.4518	+	23.2993i	−0.589336	+	1.02076i	−0.994320	+	0.106436i	$0.966056\pi$
$522$		0			0
$523$	7.85301	+	13.6018i	0.343388	+	0.594766i	0.985060	−	0.172214i	$-0.0550920\pi$
$523$	7.85301	+	13.6018i	0.343388	+	0.594766i	−0.641671	+	0.766980i	$0.721759\pi$
$524$		0			0
$525$	−19.2216	−	10.5802i	−0.838899	−	0.461759i
$526$		0			0
$527$	1.92140			0.0836975
$528$		0			0
$529$	−21.7161			−0.944180
$530$		0			0
$531$	−22.3135	−	31.6053i	−0.968324	−	1.37155i
$532$		0			0
$533$	0.690757	+	1.19643i	0.0299200	+	0.0518230i
$534$		0			0
$535$	−1.79153	−	3.10303i	−0.0774548	−	0.134156i
$536$		0			0
$537$	−7.30039	+	14.0906i	−0.315035	+	0.608054i
$538$		0			0
$539$	11.6388	+	22.7267i	0.501319	+	0.978910i
$540$		0			0
$541$	−2.05934	−	3.56688i	−0.0885379	−	0.153352i	0.818355	−	0.574713i	$-0.194886\pi$
$541$	−2.05934	−	3.56688i	−0.0885379	−	0.153352i	−0.906893	+	0.421360i	$0.861553\pi$
$542$		0			0
$543$	−38.8068	+	1.76979i	−1.66536	+	0.0759488i
$544$		0			0
$545$	1.73025	−	2.99689i	0.0741159	−	0.128372i
$546$		0			0
$547$	11.8602	+	20.5425i	0.507106	+	0.878333i	0.999966	+	0.00822465i	$0.00261802\pi$
$547$	11.8602	+	20.5425i	0.507106	+	0.878333i	−0.492860	+	0.870108i	$0.664049\pi$
$548$		0			0
$549$	−15.1922	+	32.9127i	−0.648388	+	1.40468i
$550$		0			0
$551$	18.1929	−	31.5110i	0.775043	−	1.34241i
$552$		0			0
$553$	11.6359	−	6.33327i	0.494808	−	0.269318i
$554$		0			0
$555$	−3.91528	−	6.11952i	−0.166194	−	0.259759i
$556$		0			0
$557$	−21.0313	+	36.4273i	−0.891125	+	1.54347i	−0.0525975	+	0.998616i	$0.516750\pi$
$557$	−21.0313	+	36.4273i	−0.891125	+	1.54347i	−0.838528	+	0.544859i	$0.816583\pi$
$558$		0			0
$559$	−13.6228			−0.576181
$560$		0			0
$561$	10.8521	−	20.9459i	0.458178	−	0.884336i
$562$		0			0
$563$	5.91216	+	10.2402i	0.249168	+	0.431571i	0.963295	−	0.268445i	$-0.0865097\pi$
$563$	5.91216	+	10.2402i	0.249168	+	0.431571i	−0.714127	+	0.700016i	$0.753176\pi$
$564$		0			0
$565$	−1.39562	+	2.41729i	−0.0587144	+	0.101696i
$566$		0			0
$567$	−22.2307	−	8.53197i	−0.933603	−	0.358309i
$568$		0			0
$569$	−7.10078	+	12.2989i	−0.297680	+	0.515597i	−0.975605	−	0.219534i	$-0.929546\pi$
$569$	−7.10078	+	12.2989i	−0.297680	+	0.515597i	0.677925	+	0.735131i	$0.262880\pi$
$570$		0			0
$571$	5.97869	+	10.3554i	0.250200	+	0.433360i	0.963581	−	0.267417i	$-0.0861701\pi$
$571$	5.97869	+	10.3554i	0.250200	+	0.433360i	−0.713380	+	0.700777i	$0.752837\pi$
$572$		0			0
$573$	−1.98375	+	3.82888i	−0.0828725	+	0.159954i
$574$		0			0
$575$	5.42509			0.226242
$576$		0			0
$577$	21.3135	−	36.9161i	0.887293	−	1.53684i	0.0442307	−	0.999021i	$-0.485916\pi$
$577$	21.3135	−	36.9161i	0.887293	−	1.53684i	0.843062	−	0.537816i	$-0.180750\pi$
$578$		0			0
$579$	4.19095	+	6.55040i	0.174170	+	0.272225i
$580$		0			0
$581$	−0.442317	+	17.5825i	−0.0183504	+	0.729445i
$582$		0			0
$583$	22.6804	−	39.2837i	0.939328	−	1.62696i
$584$		0			0
$585$	−0.845618	+	1.83196i	−0.0349620	+	0.0757422i
$586$		0			0
$587$	−20.5328	−	35.5638i	−0.847478	−	1.46788i	−0.883451	−	0.468523i	$-0.844786\pi$
$587$	−20.5328	−	35.5638i	−0.847478	−	1.46788i	0.0359730	−	0.999353i	$-0.488547\pi$
$588$		0			0
$589$	1.04309	−	1.80669i	0.0429799	−	0.0744434i
$590$		0			0
$591$	−22.0328	+	1.00481i	−0.906307	+	0.0413322i
$592$		0			0
$593$	16.1008	+	27.8874i	0.661180	+	1.14520i	0.980306	+	0.197485i	$0.0632772\pi$
$593$	16.1008	+	27.8874i	0.661180	+	1.14520i	−0.319126	+	0.947712i	$0.603389\pi$
$594$		0			0
$595$	−3.99573	+	2.17483i	−0.163809	+	0.0891592i
$596$		0			0
$597$	−2.34728	+	4.53051i	−0.0960676	+	0.185422i
$598$		0			0
$599$	9.53590	+	16.5167i	0.389626	+	0.674852i	0.992399	−	0.123060i	$-0.0392709\pi$
$599$	9.53590	+	16.5167i	0.389626	+	0.674852i	−0.602773	+	0.797913i	$0.705938\pi$
$600$		0			0
$601$	4.27188	+	7.39912i	0.174254	+	0.301816i	0.939903	−	0.341442i	$-0.110915\pi$
$601$	4.27188	+	7.39912i	0.174254	+	0.301816i	−0.765649	+	0.643259i	$0.777582\pi$
$602$		0			0
$603$	−4.01459	−	5.68634i	−0.163487	−	0.231565i
$604$		0			0
$605$	−1.06167			−0.0431631
$606$		0			0
$607$	−38.0115			−1.54284			−0.771419	−	0.636328i	$-0.780453\pi$
$607$	−38.0115			−1.54284			−0.771419	+	0.636328i	$0.780453\pi$
$608$		0			0
$609$	−0.839883	−	41.1205i	−0.0340338	−	1.66629i
$610$		0			0
$611$	−1.69961	−	2.94381i	−0.0687589	−	0.119094i
$612$		0			0
$613$	11.3296	−	19.6234i	0.457597	−	0.792581i	−0.541237	−	0.840870i	$-0.682044\pi$
$613$	11.3296	−	19.6234i	0.457597	−	0.792581i	0.998833	+	0.0482894i	$0.0153770\pi$
$614$		0			0
$615$	−0.347081	+	0.669906i	−0.0139956	+	0.0270132i
$616$		0			0
$617$	−10.1388	+	17.5609i	−0.408173	+	0.706977i	−0.994685	−	0.102964i	$-0.967167\pi$
$617$	−10.1388	+	17.5609i	−0.408173	+	0.706977i	0.586512	+	0.809941i	$0.300501\pi$
$618$		0			0
$619$	−2.06128			−0.0828499			−0.0414249	−	0.999142i	$-0.513190\pi$
$619$	−2.06128			−0.0828499			−0.0414249	+	0.999142i	$0.513190\pi$
$620$		0			0
$621$	5.83269	−	0.802453i	0.234058	−	0.0322013i
$622$		0			0
$623$	−0.181424	+	7.21177i	−0.00726860	+	0.288933i
$624$		0			0
$625$	21.8640			0.874560
$626$		0			0
$627$	−13.8040	−	21.5754i	−0.551278	−	0.861640i
$628$		0			0
$629$	34.0085			1.35601
$630$		0			0
$631$	−1.63715			−0.0651740			−0.0325870	−	0.999469i	$-0.510375\pi$
$631$	−1.63715			−0.0651740			−0.0325870	+	0.999469i	$0.510375\pi$
$632$		0			0
$633$	−0.969165	+	1.87060i	−0.0385208	+	0.0743497i
$634$		0			0
$635$	4.05701			0.160998
$636$		0			0
$637$	10.2106	+	0.514055i	0.404559	+	0.0203676i
$638$		0			0
$639$	−5.01838	+	0.458681i	−0.198524	+	0.0181451i
$640$		0			0
$641$	21.9325			0.866281			0.433140	−	0.901326i	$-0.357405\pi$
$641$	21.9325			0.866281			0.433140	+	0.901326i	$0.357405\pi$
$642$		0			0
$643$	14.1819	−	24.5638i	0.559280	−	0.968701i	−0.438277	−	0.898840i	$-0.644411\pi$
$643$	14.1819	−	24.5638i	0.559280	−	0.968701i	0.997557	−	0.0698609i	$-0.0222555\pi$
$644$		0			0
$645$	−4.00953	−	6.26683i	−0.157875	−	0.246756i
$646$		0			0
$647$	−17.3904	+	30.1210i	−0.683686	+	1.18418i	0.290162	+	0.956978i	$0.406291\pi$
$647$	−17.3904	+	30.1210i	−0.683686	+	1.18418i	−0.973848	+	0.227201i	$0.927042\pi$
$648$		0			0
$649$	−23.5203	−	40.7384i	−0.923253	−	1.59912i
$650$		0			0
$651$	−0.0481549	−	2.35765i	−0.00188734	−	0.0924037i
$652$		0			0
$653$	−3.19863			−0.125172			−0.0625860	−	0.998040i	$-0.519935\pi$
$653$	−3.19863			−0.125172			−0.0625860	+	0.998040i	$0.519935\pi$
$654$		0			0
$655$	9.73385			0.380333
$656$		0			0
$657$	−16.6481	+	36.0668i	−0.649506	+	1.40710i
$658$		0			0
$659$	−5.30418	−	9.18711i	−0.206622	−	0.357879i	0.744027	−	0.668150i	$-0.232914\pi$
$659$	−5.30418	−	9.18711i	−0.206622	−	0.357879i	−0.950648	+	0.310271i	$0.899580\pi$
$660$		0			0
$661$	−5.06507	−	8.77297i	−0.197009	−	0.341229i	0.750549	−	0.660815i	$-0.229789\pi$
$661$	−5.06507	−	8.77297i	−0.197009	−	0.341229i	−0.947557	+	0.319586i	$0.896456\pi$
$662$		0			0
$663$	−5.09046	−	7.95631i	−0.197697	−	0.308998i
$664$		0			0
$665$	−0.124220	+	4.93786i	−0.00481705	+	0.191482i
$666$		0			0
$667$	5.08472	+	8.80700i	0.196881	+	0.341008i
$668$		0			0
$669$	−0.832492	−	1.30117i	−0.0321860	−	0.0503062i
$670$		0			0
$671$	−22.0378	+	38.1707i	−0.850761	+	1.47356i
$672$		0			0
$673$	1.60817	+	2.78543i	0.0619903	+	0.107370i	0.895355	−	0.445353i	$-0.146922\pi$
$673$	1.60817	+	2.78543i	0.0619903	+	0.107370i	−0.833365	+	0.552724i	$0.813589\pi$
$674$		0			0
$675$	24.6467	−	3.39086i	0.948651	−	0.130514i
$676$		0			0
$677$	14.6819	−	25.4298i	0.564271	−	0.977347i	−0.432846	−	0.901468i	$-0.642491\pi$
$677$	14.6819	−	25.4298i	0.564271	−	0.977347i	0.997117	−	0.0758786i	$-0.0241762\pi$
$678$		0			0
$679$	−0.744363	+	29.5891i	−0.0285660	+	1.13552i
$680$		0			0
$681$	−25.3515	+	1.15616i	−0.971473	+	0.0443041i
$682$		0			0
$683$	−12.6278	+	21.8720i	−0.483190	+	0.836910i	−0.999814	−	0.0193029i	$-0.993855\pi$
$683$	−12.6278	+	21.8720i	−0.483190	+	0.836910i	0.516624	+	0.856213i	$0.327189\pi$
$684$		0			0
$685$	2.02918			0.0775309
$686$		0			0
$687$	16.5687	−	0.755615i	0.632134	−	0.0288285i
$688$		0			0
$689$	−9.08113	−	15.7290i	−0.345963	−	0.599226i
$690$		0			0
$691$	−7.68190	+	13.3054i	−0.292233	+	0.506163i	−0.974338	−	0.225092i	$-0.927732\pi$
$691$	−7.68190	+	13.3054i	−0.292233	+	0.506163i	0.682104	+	0.731255i	$0.261065\pi$
$692$		0			0
$693$	−25.9736	−	12.7912i	−0.986657	−	0.485896i
$694$		0			0
$695$	−0.466240	+	0.807551i	−0.0176855	+	0.0306321i
$696$		0			0
$697$	−1.76595	−	3.05872i	−0.0668903	−	0.115857i
$698$		0			0
$699$	−13.4684	−	21.0509i	−0.509421	−	0.796217i
$700$		0			0
$701$	−13.3700			−0.504980			−0.252490	−	0.967600i	$-0.581249\pi$
$701$	−13.3700			−0.504980			−0.252490	+	0.967600i	$0.581249\pi$
$702$		0			0
$703$	18.4626	−	31.9782i	0.696332	−	1.20608i
$704$		0			0
$705$	0.853994	−	1.64831i	0.0321633	−	0.0620788i
$706$		0			0
$707$	−31.0510	−	18.9842i	−1.16779	−	0.713972i
$708$		0			0
$709$	0.562939	−	0.975038i	0.0211416	−	0.0366183i	−0.855261	−	0.518197i	$-0.826603\pi$
$709$	0.562939	−	0.975038i	0.0211416	−	0.0366183i	0.876403	+	0.481579i	$0.159937\pi$
$710$		0			0
$711$	−6.29552	+	13.6387i	−0.236101	+	0.511492i
$712$		0			0
$713$	0.291534	+	0.504951i	0.0109180	+	0.0189106i
$714$		0			0
$715$	−1.22665	+	2.12463i	−0.0458743	+	0.0794565i
$716$		0			0
$717$	−14.5890	+	28.1585i	−0.544836	+	1.05160i
$718$		0			0
$719$	−9.13667	−	15.8252i	−0.340740	−	0.590180i	0.643830	−	0.765169i	$-0.277344\pi$
$719$	−9.13667	−	15.8252i	−0.340740	−	0.590180i	−0.984570	+	0.174989i	$0.944011\pi$
$720$		0			0
$721$	25.1965	+	15.4048i	0.938366	+	0.573705i
$722$		0			0
$723$	−0.161579	+	0.00736882i	−0.00600919	+	0.000274050i
$724$		0			0
$725$	21.4861	+	37.2150i	0.797973	+	1.38213i
$726$		0			0
$727$	14.8478	+	25.7171i	0.550673	+	0.953793i	0.998226	+	0.0595359i	$0.0189621\pi$
$727$	14.8478	+	25.7171i	0.550673	+	0.953793i	−0.447553	+	0.894257i	$0.647705\pi$
$728$		0			0
$729$	25.9969	−	7.29124i	0.962847	−	0.270046i
$730$		0			0
$731$	34.8272			1.28813
$732$		0			0
$733$	19.2278			0.710195			0.355098	−	0.934829i	$-0.384448\pi$
$733$	19.2278			0.710195			0.355098	+	0.934829i	$0.384448\pi$
$734$		0			0
$735$	2.76876	+	4.84845i	0.102127	+	0.178838i
$736$		0			0
$737$	−4.23171	−	7.32955i	−0.155877	−	0.269987i
$738$		0			0
$739$	15.1336	−	26.2121i	0.556697	−	0.964227i	−0.441073	−	0.897471i	$-0.645402\pi$
$739$	15.1336	−	26.2121i	0.556697	−	0.964227i	0.997769	−	0.0667556i	$-0.0212648\pi$
$740$		0			0
$741$	−10.2448	+	0.467216i	−0.376354	+	0.0171636i
$742$		0			0
$743$	11.8815	−	20.5794i	0.435890	−	0.754984i	−0.561477	−	0.827492i	$-0.689767\pi$
$743$	11.8815	−	20.5794i	0.435890	−	0.754984i	0.997368	+	0.0725076i	$0.0231002\pi$
$744$		0			0
$745$	4.21926			0.154582
$746$		0			0
$747$	−11.5021	−	16.2918i	−0.420841	−	0.596087i
$748$		0			0
$749$	0.517709	−	20.5794i	0.0189167	−	0.751954i
$750$		0			0
$751$	−12.6683			−0.462273			−0.231136	−	0.972921i	$-0.574244\pi$
$751$	−12.6683			−0.462273			−0.231136	+	0.972921i	$0.574244\pi$
$752$		0			0
$753$	−31.6175	+	1.44192i	−1.15221	+	0.0525464i
$754$		0			0
$755$	−0.0478448			−0.00174125
$756$		0			0
$757$	−29.0799			−1.05693			−0.528464	−	0.848955i	$-0.677232\pi$
$757$	−29.0799			−1.05693			−0.528464	+	0.848955i	$0.677232\pi$
$758$		0			0
$759$	7.15126	−	0.326134i	0.259574	−	0.0118379i
$760$		0			0
$761$	29.2029			1.05860			0.529302	−	0.848433i	$-0.322454\pi$
$761$	29.2029			1.05860			0.529302	+	0.848433i	$0.322454\pi$
$762$		0			0
$763$	17.4626	−	9.50471i	0.632190	−	0.344094i
$764$		0			0
$765$	2.16186	−	4.68350i	0.0781623	−	0.169332i
$766$		0			0
$767$	−18.8348			−0.680086
$768$		0			0
$769$	12.5869	−	21.8011i	0.453894	−	0.786167i	−0.544730	−	0.838611i	$-0.683368\pi$
$769$	12.5869	−	21.8011i	0.453894	−	0.786167i	0.998624	+	0.0524443i	$0.0167012\pi$
$770$		0			0
$771$	36.4238	−	1.66111i	1.31177	−	0.0598234i
$772$		0			0
$773$	−0.752039	+	1.30257i	−0.0270490	+	0.0468502i	−0.879233	−	0.476392i	$-0.841944\pi$
$773$	−0.752039	+	1.30257i	−0.0270490	+	0.0468502i	0.852184	+	0.523242i	$0.175278\pi$
$774$		0			0
$775$	1.23191	+	2.13373i	0.0442515	+	0.0766458i
$776$		0			0
$777$	−0.852336	−	41.7302i	−0.0305774	−	1.49706i
$778$		0			0
$779$	−3.83482			−0.137397
$780$		0			0
$781$	−6.12722			−0.219249
$782$		0			0
$783$	28.6050	+	36.8329i	1.02226	+	1.31630i
$784$		0			0
$785$	4.83122	+	8.36792i	0.172434	+	0.298664i
$786$		0			0
$787$	−7.47656	−	12.9498i	−0.266510	−	0.461610i	0.701448	−	0.712721i	$-0.252537\pi$
$787$	−7.47656	−	12.9498i	−0.266510	−	0.461610i	−0.967958	+	0.251111i	$0.919204\pi$
$788$		0			0
$789$	−8.93706	+	0.407575i	−0.318168	+	0.0145101i
$790$		0			0
$791$	−14.0854	+	7.66652i	−0.500819	+	0.272590i
$792$		0			0
$793$	8.82383	+	15.2833i	0.313343	+	0.542727i
$794$		0			0
$795$	4.56294	−	8.80700i	0.161831	−	0.312352i
$796$		0			0
$797$	−4.56294	+	7.90324i	−0.161628	+	0.279947i	−0.935453	−	0.353452i	$-0.885008\pi$
$797$	−4.56294	+	7.90324i	−0.161628	+	0.279947i	0.773825	+	0.633400i	$0.218341\pi$
$798$		0			0
$799$	4.34514	+	7.52600i	0.153720	+	0.266251i
$800$		0			0
$801$	−4.71780	−	6.68238i	−0.166695	−	0.236110i
$802$		0			0
$803$	−24.1498	+	41.8287i	−0.852228	+	1.47610i
$804$		0			0
$805$	−1.17783	−	0.720107i	−0.0415129	−	0.0253804i
$806$		0			0
$807$	−13.4313	+	25.9240i	−0.472805	+	0.912569i
$808$		0			0
$809$	17.7755	−	30.7880i	0.624953	−	1.08245i	−0.363597	−	0.931556i	$-0.618452\pi$
$809$	17.7755	−	30.7880i	0.624953	−	1.08245i	0.988550	−	0.150894i	$-0.0482151\pi$
$810$		0			0
$811$	13.5070			0.474295			0.237148	−	0.971474i	$-0.423788\pi$
$811$	13.5070			0.474295			0.237148	+	0.971474i	$0.423788\pi$
$812$		0			0
$813$	23.4415	+	36.6388i	0.822130	+	1.28498i
$814$		0			0
$815$	−5.30418	−	9.18711i	−0.185797	−	0.321810i
$816$		0			0
$817$	18.9071	−	32.7480i	0.661475	−	1.14571i
$818$		0			0
$819$	−9.63521	+	6.44565i	−0.336682	+	0.225229i
$820$		0			0
$821$	−10.8114	+	18.7259i	−0.377320	+	0.653537i	−0.990671	−	0.136273i	$-0.956488\pi$
$821$	−10.8114	+	18.7259i	−0.377320	+	0.653537i	0.613352	+	0.789810i	$0.289821\pi$
$822$		0			0
$823$	−0.753501	−	1.30510i	−0.0262654	−	0.0454930i	0.852594	−	0.522574i	$-0.175028\pi$
$823$	−0.753501	−	1.30510i	−0.0262654	−	0.0454930i	−0.878859	+	0.477081i	$0.841695\pi$
$824$		0			0
$825$	30.2185	−	1.37811i	1.05207	−	0.0479798i
$826$		0			0
$827$	−23.3786			−0.812953			−0.406477	−	0.913661i	$-0.633243\pi$
$827$	−23.3786			−0.812953			−0.406477	+	0.913661i	$0.633243\pi$
$828$		0			0
$829$	−11.0095	+	19.0691i	−0.382377	+	0.662296i	−0.991401	−	0.130855i	$-0.958228\pi$
$829$	−11.0095	+	19.0691i	−0.382377	+	0.662296i	0.609025	+	0.793151i	$0.291561\pi$
$830$		0			0
$831$	−5.85087	+	0.266829i	−0.202965	+	0.00925621i
$832$		0			0
$833$	−26.1039	−	1.31421i	−0.904446	−	0.0455345i
$834$		0			0
$835$	−2.44757	+	4.23932i	−0.0847018	+	0.146708i
$836$		0			0
$837$	1.64008	+	2.11182i	0.0566894	+	0.0729953i
$838$		0			0
$839$	1.06507	+	1.84476i	0.0367705	+	0.0636883i	0.883825	−	0.467818i	$-0.154960\pi$
$839$	1.06507	+	1.84476i	0.0367705	+	0.0636883i	−0.847055	+	0.531506i	$0.821626\pi$
$840$		0			0
$841$	−25.7762	+	44.6456i	−0.888833	+	1.53950i
$842$		0			0
$843$	18.9284	+	29.5848i	0.651929	+	1.01896i
$844$		0			0
$845$	−2.50214	−	4.33383i	−0.0860761	−	0.149088i
$846$		0			0
$847$	−5.20408	−	3.18171i	−0.178814	−	0.109325i
$848$		0			0
$849$	−16.1950	−	25.3126i	−0.555812	−	0.868726i
$850$		0			0
$851$	5.16012	+	8.93758i	0.176887	+	0.306376i
$852$		0			0
$853$	−3.50146	−	6.06471i	−0.119888	−	0.207652i	0.799835	−	0.600220i	$-0.204920\pi$
$853$	−3.50146	−	6.06471i	−0.119888	−	0.207652i	−0.919723	+	0.392568i	$0.871587\pi$
$854$		0			0
$855$	−3.23025	−	4.57539i	−0.110472	−	0.156475i
$856$		0			0
$857$	10.9282			0.373300			0.186650	−	0.982426i	$-0.440237\pi$
$857$	10.9282			0.373300			0.186650	+	0.982426i	$0.440237\pi$
$858$		0			0
$859$	13.9076			0.474520			0.237260	−	0.971446i	$-0.423751\pi$
$859$	13.9076			0.474520			0.237260	+	0.971446i	$0.423751\pi$
$860$		0			0
$861$	−3.70895	+	2.24357i	−0.126401	+	0.0764607i
$862$		0			0
$863$	18.4231	+	31.9098i	0.627131	+	1.08622i	0.988125	+	0.153655i	$0.0491043\pi$
$863$	18.4231	+	31.9098i	0.627131	+	1.08622i	−0.360993	+	0.932568i	$0.617562\pi$
$864$		0			0
$865$	0.676647	−	1.17199i	0.0230067	−	0.0398488i
$866$		0			0
$867$	−2.85486	−	4.46211i	−0.0969562	−	0.151541i
$868$		0			0
$869$	−9.13229	+	15.8176i	−0.309792	+	0.536575i
$870$		0			0
$871$	−3.38871			−0.114822
$872$		0			0
$873$	−19.3566	−	27.4170i	−0.655122	−	0.927926i
$874$		0			0
$875$	−10.1745	−	6.22056i	−0.343961	−	0.210293i
$876$		0			0
$877$	−10.3595			−0.349817			−0.174908	−	0.984585i	$-0.555963\pi$
$877$	−10.3595			−0.349817			−0.174908	+	0.984585i	$0.555963\pi$
$878$		0			0
$879$	7.86527	−	15.1809i	0.265289	−	0.512038i
$880$		0			0
$881$	9.34806			0.314944			0.157472	−	0.987523i	$-0.449666\pi$
$881$	9.34806			0.314944			0.157472	+	0.987523i	$0.449666\pi$
$882$		0			0
$883$	−2.29494			−0.0772308			−0.0386154	−	0.999254i	$-0.512295\pi$
$883$	−2.29494			−0.0772308			−0.0386154	+	0.999254i	$0.512295\pi$
$884$		0			0
$885$	−5.54357	−	8.66452i	−0.186345	−	0.291255i
$886$		0			0
$887$	27.6726			0.929154			0.464577	−	0.885533i	$-0.346206\pi$
$887$	27.6726			0.929154			0.464577	+	0.885533i	$0.346206\pi$
$888$		0			0
$889$	19.8866	+	12.1584i	0.666974	+	0.407779i
$890$		0			0
$891$	32.2850	−	5.95143i	1.08159	−	0.199380i
$892$		0			0
$893$	9.43560			0.315750
$894$		0			0
$895$	−2.10963	+	3.65399i	−0.0705172	+	0.122139i
$896$		0			0
$897$	1.31858	−	2.54500i	0.0440260	−	0.0849752i
$898$		0			0
$899$	−2.30924	+	3.99973i	−0.0770176	+	0.133398i
$900$		0			0
$901$	23.2163	+	40.2119i	0.773448	+	1.33965i
$902$		0			0
$903$	−0.872855	−	42.7347i	−0.0290468	−	1.42212i
$904$		0			0
$905$	−10.3284			−0.343327
$906$		0			0
$907$	2.93152			0.0973396			0.0486698	−	0.998815i	$-0.484502\pi$
$907$	2.93152			0.0973396			0.0486698	+	0.998815i	$0.484502\pi$
$908$		0			0
$909$	41.0962	−	3.75620i	1.36307	−	0.124585i
$910$		0			0
$911$	−15.3171	−	26.5300i	−0.507479	−	0.878979i	−0.999963	−	0.00865719i	$-0.997244\pi$
$911$	−15.3171	−	26.5300i	−0.507479	−	0.878979i	0.492484	−	0.870322i	$-0.336089\pi$
$912$		0			0
$913$	−12.1242	−	20.9998i	−0.401253	−	0.694991i
$914$		0			0
$915$	−4.43366	+	8.55747i	−0.146572	+	0.282901i
$916$		0			0
$917$	47.7132	+	29.1712i	1.57563	+	0.963319i
$918$		0			0
$919$	−13.1857	−	22.8383i	−0.434956	−	0.753366i	0.562336	−	0.826909i	$-0.309903\pi$
$919$	−13.1857	−	22.8383i	−0.434956	−	0.753366i	−0.997292	+	0.0735429i	$0.976569\pi$
$920$		0			0
$921$	13.4751	−	0.614532i	0.444019	−	0.0202495i
$922$		0			0
$923$	−1.22665	+	2.12463i	−0.0403758	+	0.0699329i
$924$		0			0
$925$	21.8047	+	37.7668i	0.716933	+	1.24176i
$926$		0			0
$927$	−33.3478	+	3.04799i	−1.09528	+	0.100109i
$928$		0			0
$929$	−8.93706	+	15.4794i	−0.293215	+	0.507864i	−0.974568	−	0.224091i	$-0.928059\pi$
$929$	−8.93706	+	15.4794i	−0.293215	+	0.507864i	0.681353	+	0.731955i	$0.261392\pi$
$930$		0			0
$931$	−15.4071	+	23.8320i	−0.504947	+	0.781063i
$932$		0			0
$933$	−14.3853	−	22.4840i	−0.470954	−	0.736094i
$934$		0			0
$935$	3.13600	−	5.43171i	0.102558	−	0.177636i
$936$		0			0
$937$	15.9134			0.519869			0.259934	−	0.965626i	$-0.416299\pi$
$937$	15.9134			0.519869			0.259934	+	0.965626i	$0.416299\pi$
$938$		0			0
$939$	6.77023	−	13.0673i	0.220938	−	0.426436i
$940$		0			0
$941$	8.14027	+	14.0994i	0.265365	+	0.459626i	0.967659	−	0.252261i	$-0.0811741\pi$
$941$	8.14027	+	14.0994i	0.265365	+	0.459626i	−0.702294	+	0.711887i	$0.747841\pi$
$942$		0			0
$943$	0.535897	−	0.928200i	0.0174512	−	0.0302264i
$944$		0			0
$945$	−5.80106	−	2.53533i	−0.188709	−	0.0824744i
$946$		0			0
$947$	−14.2951	+	24.7599i	−0.464529	+	0.804589i	−0.999180	−	0.0404846i	$-0.987110\pi$
$947$	−14.2951	+	24.7599i	−0.464529	+	0.804589i	0.534651	+	0.845073i	$0.320443\pi$
$948$		0			0
$949$	9.66945	+	16.7480i	0.313884	+	0.543662i
$950$		0			0
$951$	−11.2389	+	21.6924i	−0.364447	+	0.703424i
$952$		0			0
$953$	−29.3537			−0.950859			−0.475430	−	0.879754i	$-0.657707\pi$
$953$	−29.3537			−0.950859			−0.475430	+	0.879754i	$0.657707\pi$
$954$		0			0
$955$	−0.573256	+	0.992908i	−0.0185501	+	0.0321297i
$956$		0			0
$957$	30.5598	+	47.7645i	0.987859	+	1.54401i
$958$		0			0
$959$	9.94659	+	6.08121i	0.321192	+	0.196373i
$960$		0			0
$961$	15.3676	−	26.6175i	0.495729	−	0.858628i
$962$		0			0
$963$	13.4626	+	19.0687i	0.433828	+	0.614481i
$964$		0			0
$965$	1.03376	+	1.79053i	0.0332779	+	0.0576391i
$966$		0			0
$967$	4.69815	−	8.13743i	0.151082	−	0.261682i	−0.780543	−	0.625102i	$-0.785057\pi$
$967$	4.69815	−	8.13743i	0.151082	−	0.261682i	0.931626	+	0.363419i	$0.118391\pi$
$968$		0			0
$969$	26.1914	−	1.19446i	0.841390	−	0.0383716i
$970$		0			0
$971$	−7.77335	−	13.4638i	−0.249459	−	0.432075i	0.713917	−	0.700230i	$-0.246919\pi$
$971$	−7.77335	−	13.4638i	−0.249459	−	0.432075i	−0.963376	+	0.268155i	$0.913586\pi$
$972$		0			0
$973$	−4.70554	+	2.56117i	−0.150853	+	0.0821074i
$974$		0			0
$975$	5.57179	−	10.7542i	0.178440	−	0.344410i
$976$		0			0
$977$	4.79893	+	8.31198i	0.153531	+	0.265924i	0.932523	−	0.361110i	$-0.117602\pi$
$977$	4.79893	+	8.31198i	0.153531	+	0.265924i	−0.778992	+	0.627034i	$0.784269\pi$
$978$		0			0
$979$	−4.97296	−	8.61342i	−0.158936	−	0.275286i
$980$		0			0
$981$	−9.44805	+	20.4684i	−0.301653	+	0.653506i
$982$		0			0
$983$	46.8535			1.49439			0.747197	−	0.664603i	$-0.231399\pi$
$983$	46.8535			1.49439			0.747197	+	0.664603i	$0.231399\pi$
$984$		0			0
$985$	−5.86400			−0.186843
$986$		0			0
$987$	9.12588	−	5.52032i	0.290480	−	0.175714i
$988$		0			0
$989$	5.28434	+	9.15274i	0.168032	+	0.291040i
$990$		0			0
$991$	−10.8260	+	18.7511i	−0.343898	+	0.595649i	−0.985153	−	0.171679i	$-0.945081\pi$
$991$	−10.8260	+	18.7511i	−0.343898	+	0.595649i	0.641255	+	0.767328i	$0.278414\pi$
$992$		0			0
$993$	−21.9466	+	42.3595i	−0.696454	+	1.34424i
$994$		0			0
$995$	−0.678304	+	1.17486i	−0.0215037	+	0.0372455i
$996$		0			0
$997$	−57.2379			−1.81274			−0.906372	−	0.422481i	$-0.861159\pi$
$997$	−57.2379			−1.81274			−0.906372	+	0.422481i	$0.861159\pi$
$998$		0			0
$999$	29.0292	+	37.3790i	0.918443	+	1.18262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.g.193.1		6
3.2	odd	2		3024.2.t.g.1873.3		6
4.3	odd	2		126.2.h.c.67.3	yes	6
7.2	even	3		1008.2.q.h.625.2		6
9.2	odd	6		3024.2.q.h.2881.1		6
9.7	even	3		1008.2.q.h.529.2		6
12.11	even	2		378.2.h.d.361.3		6
21.2	odd	6		3024.2.q.h.2305.1		6
28.3	even	6		882.2.f.m.589.2		6
28.11	odd	6		882.2.f.l.589.2		6
28.19	even	6		882.2.e.p.373.2		6
28.23	odd	6		126.2.e.d.121.2	yes	6
28.27	even	2		882.2.h.o.67.1		6
36.7	odd	6		126.2.e.d.25.2	✓	6
36.11	even	6		378.2.e.c.235.1		6
36.23	even	6		1134.2.g.n.487.1		6
36.31	odd	6		1134.2.g.k.487.3		6
63.2	odd	6		3024.2.t.g.289.3		6
63.16	even	3	inner	1008.2.t.g.961.1		6
84.11	even	6		2646.2.f.o.1765.1		6
84.23	even	6		378.2.e.c.37.1		6
84.47	odd	6		2646.2.e.o.1549.3		6
84.59	odd	6		2646.2.f.n.1765.3		6
84.83	odd	2		2646.2.h.p.361.1		6
252.11	even	6		2646.2.f.o.883.1		6
252.23	even	6		1134.2.g.n.163.1		6
252.31	even	6		7938.2.a.by.1.3		3
252.47	odd	6		2646.2.h.p.667.1		6
252.59	odd	6		7938.2.a.bx.1.1		3
252.67	odd	6		7938.2.a.cb.1.1		3
252.79	odd	6		126.2.h.c.79.3	yes	6
252.83	odd	6		2646.2.e.o.2125.3		6
252.95	even	6		7938.2.a.bu.1.3		3
252.115	even	6		882.2.f.m.295.2		6
252.151	odd	6		882.2.f.l.295.2		6
252.187	even	6		882.2.h.o.79.1		6
252.191	even	6		378.2.h.d.289.3		6
252.223	even	6		882.2.e.p.655.2		6
252.227	odd	6		2646.2.f.n.883.3		6
252.247	odd	6		1134.2.g.k.163.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.2	✓	6	36.7	odd	6
126.2.e.d.121.2	yes	6	28.23	odd	6
126.2.h.c.67.3	yes	6	4.3	odd	2
126.2.h.c.79.3	yes	6	252.79	odd	6
378.2.e.c.37.1		6	84.23	even	6
378.2.e.c.235.1		6	36.11	even	6
378.2.h.d.289.3		6	252.191	even	6
378.2.h.d.361.3		6	12.11	even	2
882.2.e.p.373.2		6	28.19	even	6
882.2.e.p.655.2		6	252.223	even	6
882.2.f.l.295.2		6	252.151	odd	6
882.2.f.l.589.2		6	28.11	odd	6
882.2.f.m.295.2		6	252.115	even	6
882.2.f.m.589.2		6	28.3	even	6
882.2.h.o.67.1		6	28.27	even	2
882.2.h.o.79.1		6	252.187	even	6
1008.2.q.h.529.2		6	9.7	even	3
1008.2.q.h.625.2		6	7.2	even	3
1008.2.t.g.193.1		6	1.1	even	1	trivial
1008.2.t.g.961.1		6	63.16	even	3	inner
1134.2.g.k.163.3		6	252.247	odd	6
1134.2.g.k.487.3		6	36.31	odd	6
1134.2.g.n.163.1		6	252.23	even	6
1134.2.g.n.487.1		6	36.23	even	6
2646.2.e.o.1549.3		6	84.47	odd	6
2646.2.e.o.2125.3		6	252.83	odd	6
2646.2.f.n.883.3		6	252.227	odd	6
2646.2.f.n.1765.3		6	84.59	odd	6
2646.2.f.o.883.1		6	252.11	even	6
2646.2.f.o.1765.1		6	84.11	even	6
2646.2.h.p.361.1		6	84.83	odd	2
2646.2.h.p.667.1		6	252.47	odd	6
3024.2.q.h.2305.1		6	21.2	odd	6
3024.2.q.h.2881.1		6	9.2	odd	6
3024.2.t.g.289.3		6	63.2	odd	6
3024.2.t.g.1873.3		6	3.2	odd	2
7938.2.a.bu.1.3		3	252.95	even	6
7938.2.a.bx.1.1		3	252.59	odd	6
7938.2.a.by.1.3		3	252.31	even	6
7938.2.a.cb.1.1		3	252.67	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73025 + 0.0789082i) q^{3} -0.460505 q^{5} +(-2.25729 - 1.38008i) q^{7} +(2.98755 - 0.273062i) q^{9} +O(q^{10})\)	\(q+(-1.73025 + 0.0789082i) q^{3} -0.460505 q^{5} +(-2.25729 - 1.38008i) q^{7} +(2.98755 - 0.273062i) q^{9} +3.64766 q^{11} +(0.730252 - 1.26483i) q^{13} +(0.796790 - 0.0363376i) q^{15} +(-1.86693 + 3.23361i) q^{17} +(2.02704 + 3.51094i) q^{19} +(4.01459 + 2.20977i) q^{21} -1.13307 q^{23} -4.78794 q^{25} +(-5.14766 + 0.708209i) q^{27} +(-4.48755 - 7.77266i) q^{29} +(-0.257295 - 0.445647i) q^{31} +(-6.31138 + 0.287831i) q^{33} +(1.03950 + 0.635534i) q^{35} +(-4.55408 - 7.88791i) q^{37} +(-1.16372 + 2.24611i) q^{39} +(-0.472958 + 0.819187i) q^{41} +(-4.66372 - 8.07779i) q^{43} +(-1.37578 + 0.125747i) q^{45} +(1.16372 - 2.01561i) q^{47} +(3.19076 + 6.23049i) q^{49} +(2.97509 - 5.74228i) q^{51} +(6.21780 - 10.7695i) q^{53} -1.67977 q^{55} +(-3.78434 - 5.91486i) q^{57} +(-6.44805 - 11.1684i) q^{59} +(-6.04163 + 10.4644i) q^{61} +(-7.12062 - 3.50667i) q^{63} +(-0.336285 + 0.582462i) q^{65} +(-1.16012 - 2.00938i) q^{67} +(1.96050 - 0.0894089i) q^{69} -1.67977 q^{71} +(-6.62062 + 11.4673i) q^{73} +(8.28434 - 0.377808i) q^{75} +(-8.23385 - 5.03407i) q^{77} +(-2.50360 + 4.33636i) q^{79} +(8.85087 - 1.63157i) q^{81} +(-3.32383 - 5.75705i) q^{83} +(0.859728 - 1.48909i) q^{85} +(8.37792 + 13.0946i) q^{87} +(-1.36333 - 2.36135i) q^{89} +(-3.39397 + 1.84730i) q^{91} +(0.480350 + 0.750780i) q^{93} +(-0.933463 - 1.61680i) q^{95} +(-5.59358 - 9.68836i) q^{97} +(10.8976 - 0.996040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 6 * q - 4 * q^3 + 10 * q^5 + 2 * q^7 - 4 * q^9	\( 6 q - 4 q^{3} + 10 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 3 q^{19} - 7 q^{21} - 14 q^{23} + 4 q^{25} - 7 q^{27} - 5 q^{29} + 14 q^{31} - 4 q^{33} + 19 q^{35} - 9 q^{37} + 3 q^{39} - 12 q^{41} - 18 q^{43} - 31 q^{45} - 3 q^{47} - 26 q^{51} + 9 q^{53} - 14 q^{55} + 2 q^{57} - 4 q^{59} + 4 q^{61} - 28 q^{63} - 12 q^{65} - 5 q^{67} - q^{69} - 14 q^{71} - 25 q^{73} + 25 q^{75} - 35 q^{77} - 7 q^{79} + 32 q^{81} - 8 q^{83} + 14 q^{85} + 20 q^{87} - 9 q^{89} - 4 q^{91} - 3 q^{93} - 2 q^{95} - 28 q^{97} + 41 q^{99}+O(q^{100}) \) 6 * q - 4 * q^3 + 10 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 - 2 * q^13 + 2 * q^15 - 4 * q^17 + 3 * q^19 - 7 * q^21 - 14 * q^23 + 4 * q^25 - 7 * q^27 - 5 * q^29 + 14 * q^31 - 4 * q^33 + 19 * q^35 - 9 * q^37 + 3 * q^39 - 12 * q^41 - 18 * q^43 - 31 * q^45 - 3 * q^47 - 26 * q^51 + 9 * q^53 - 14 * q^55 + 2 * q^57 - 4 * q^59 + 4 * q^61 - 28 * q^63 - 12 * q^65 - 5 * q^67 - q^69 - 14 * q^71 - 25 * q^73 + 25 * q^75 - 35 * q^77 - 7 * q^79 + 32 * q^81 - 8 * q^83 + 14 * q^85 + 20 * q^87 - 9 * q^89 - 4 * q^91 - 3 * q^93 - 2 * q^95 - 28 * q^97 + 41 * q^99

Introduction

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