LMFDB - Embedded newform 672.2.bd.a.431.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(431,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))

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

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

chi := DirichletCharacter("672.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bd (of order $6$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.6
Character	$\chi$	$=$	672.431
Dual form			672.2.bd.a.527.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28463 - 1.16178i) q^{3} +(0.646402 + 1.11960i) q^{5} +(2.42742 - 1.05244i) q^{7} +(0.300539 + 2.98491i) q^{9} +O(q^{10})$	\(q+(-1.28463 - 1.16178i) q^{3} +(0.646402 + 1.11960i) q^{5} +(2.42742 - 1.05244i) q^{7} +(0.300539 + 2.98491i) q^{9} +(-1.60004 - 0.923782i) q^{11} -2.25432i q^{13} +(0.470342 - 2.18925i) q^{15} +(3.89580 + 2.24924i) q^{17} +(2.80851 + 4.86448i) q^{19} +(-4.34104 - 1.46812i) q^{21} +(0.519880 + 0.900459i) q^{23} +(1.66433 - 2.88270i) q^{25} +(3.08172 - 4.18366i) q^{27} +1.32085 q^{29} +(-3.69700 - 2.13446i) q^{31} +(0.982223 + 3.04561i) q^{33} +(2.74740 + 2.03744i) q^{35} +(8.18394 - 4.72500i) q^{37} +(-2.61902 + 2.89596i) q^{39} -1.39634i q^{41} +6.02578 q^{43} +(-3.14763 + 2.26593i) q^{45} +(-5.90249 - 10.2234i) q^{47} +(4.78472 - 5.10944i) q^{49} +(-2.39154 - 7.41551i) q^{51} +(6.02901 - 10.4425i) q^{53} -2.38854i q^{55} +(2.04356 - 9.51192i) q^{57} +(9.57732 + 5.52947i) q^{59} +(-7.65220 + 4.41800i) q^{61} +(3.87098 + 6.92932i) q^{63} +(2.52393 - 1.45719i) q^{65} +(-3.05545 + 5.29219i) q^{67} +(0.378281 - 1.76074i) q^{69} +14.0121 q^{71} +(-4.38664 + 7.59788i) q^{73} +(-5.48711 + 1.76962i) q^{75} +(-4.85619 - 0.558456i) q^{77} +(2.37061 - 1.36867i) q^{79} +(-8.81935 + 1.79416i) q^{81} +4.74366i q^{83} +5.81566i q^{85} +(-1.69681 - 1.53454i) q^{87} +(-8.31219 + 4.79904i) q^{89} +(-2.37254 - 5.47217i) q^{91} +(2.26949 + 7.03709i) q^{93} +(-3.63085 + 6.28882i) q^{95} -8.73466 q^{97} +(2.27653 - 5.05360i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 2 q^{9}+O(q^{10}) $ 56 * q + 2 * q^3 - 2 * q^9	$ 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.28463	−	1.16178i	−0.741680	−	0.670753i
$3$	−1.28463	−	1.16178i	−0.741680	−	0.670753i
$4$		0			0
$5$	0.646402	+	1.11960i	0.289080	+	0.500700i	0.973590	−	0.228302i	$-0.0733175\pi$
$5$	0.646402	+	1.11960i	0.289080	+	0.500700i	−0.684511	+	0.729003i	$0.739984\pi$
$6$		0			0
$7$	2.42742	−	1.05244i	0.917478	−	0.397786i
$7$	2.42742	−	1.05244i	0.917478	−	0.397786i
$8$		0			0
$9$	0.300539	+	2.98491i	0.100180	+	0.994969i
$10$		0			0
$11$	−1.60004	−	0.923782i	−0.482430	−	0.278531i	0.238999	−	0.971020i	$-0.423181\pi$
$11$	−1.60004	−	0.923782i	−0.482430	−	0.278531i	−0.721428	+	0.692489i	$0.756514\pi$
$12$		0			0
$13$		−	2.25432i		−	0.625235i	−0.949879	−	0.312617i	$-0.898794\pi$
$13$		−	2.25432i		−	0.625235i	0.949879	−	0.312617i	$-0.101206\pi$
$14$		0			0
$15$	0.470342	−	2.18925i	0.121442	−	0.565261i
$16$		0			0
$17$	3.89580	+	2.24924i	0.944871	+	0.545522i	0.891484	−	0.453052i	$-0.149665\pi$
$17$	3.89580	+	2.24924i	0.944871	+	0.545522i	0.0533874	+	0.998574i	$0.482998\pi$
$18$		0			0
$19$	2.80851	+	4.86448i	0.644317	+	1.11599i	0.984459	+	0.175615i	$0.0561914\pi$
$19$	2.80851	+	4.86448i	0.644317	+	1.11599i	−0.340142	+	0.940374i	$0.610475\pi$
$20$		0			0
$21$	−4.34104	−	1.46812i	−0.947292	−	0.320371i
$22$		0			0
$23$	0.519880	+	0.900459i	0.108402	+	0.187759i	0.915123	−	0.403174i	$-0.132093\pi$
$23$	0.519880	+	0.900459i	0.108402	+	0.187759i	−0.806721	+	0.590933i	$0.798760\pi$
$24$		0			0
$25$	1.66433	−	2.88270i	0.332866	−	0.576541i
$26$		0			0
$27$	3.08172	−	4.18366i	0.593078	−	0.805145i
$28$		0			0
$29$	1.32085			0.245277			0.122638	−	0.992451i	$-0.460865\pi$
$29$	1.32085			0.245277			0.122638	+	0.992451i	$0.460865\pi$
$30$		0			0
$31$	−3.69700	−	2.13446i	−0.664000	−	0.383361i	0.129799	−	0.991540i	$-0.458567\pi$
$31$	−3.69700	−	2.13446i	−0.664000	−	0.383361i	−0.793800	+	0.608179i	$0.791900\pi$
$32$		0			0
$33$	0.982223	+	3.04561i	0.170983	+	0.530172i
$34$		0			0
$35$	2.74740	+	2.03744i	0.464396	+	0.344390i
$36$		0			0
$37$	8.18394	−	4.72500i	1.34543	−	0.776786i	0.357834	−	0.933785i	$-0.383516\pi$
$37$	8.18394	−	4.72500i	1.34543	−	0.776786i	0.987599	+	0.157000i	$0.0501822\pi$
$38$		0			0
$39$	−2.61902	+	2.89596i	−0.419378	+	0.463724i
$40$		0			0
$41$		−	1.39634i		−	0.218072i	−0.994038	−	0.109036i	$-0.965224\pi$
$41$		−	1.39634i		−	0.218072i	0.994038	−	0.109036i	$-0.0347764\pi$
$42$		0			0
$43$	6.02578			0.918922			0.459461	−	0.888198i	$-0.348043\pi$
$43$	6.02578			0.918922			0.459461	+	0.888198i	$0.348043\pi$
$44$		0			0
$45$	−3.14763	+	2.26593i	−0.469222	+	0.337785i
$46$		0			0
$47$	−5.90249	−	10.2234i	−0.860966	−	1.49124i	−0.870997	−	0.491288i	$-0.836526\pi$
$47$	−5.90249	−	10.2234i	−0.860966	−	1.49124i	0.0100312	−	0.999950i	$-0.496807\pi$
$48$		0			0
$49$	4.78472	−	5.10944i	0.683532	−	0.729921i
$50$		0			0
$51$	−2.39154	−	7.41551i	−0.334882	−	1.03838i
$52$		0			0
$53$	6.02901	−	10.4425i	0.828148	−	1.43439i	−0.0713414	−	0.997452i	$-0.522728\pi$
$53$	6.02901	−	10.4425i	0.828148	−	1.43439i	0.899489	−	0.436943i	$-0.143939\pi$
$54$		0			0
$55$		−	2.38854i		−	0.322070i
$56$		0			0
$57$	2.04356	−	9.51192i	0.270676	−	1.25988i
$58$		0			0
$59$	9.57732	+	5.52947i	1.24686	+	0.719875i	0.970482	−	0.241174i	$-0.0775324\pi$
$59$	9.57732	+	5.52947i	1.24686	+	0.719875i	0.276378	+	0.961049i	$0.410866\pi$
$60$		0			0
$61$	−7.65220	+	4.41800i	−0.979764	+	0.565667i	−0.902199	−	0.431320i	$-0.858048\pi$
$61$	−7.65220	+	4.41800i	−0.979764	+	0.565667i	−0.0775652	+	0.996987i	$0.524715\pi$
$62$		0			0
$63$	3.87098	+	6.92932i	0.487698	+	0.873012i
$64$		0			0
$65$	2.52393	−	1.45719i	0.313055	−	0.180743i
$66$		0			0
$67$	−3.05545	+	5.29219i	−0.373283	+	0.646544i	−0.990068	−	0.140587i	$-0.955101\pi$
$67$	−3.05545	+	5.29219i	−0.373283	+	0.646544i	0.616786	+	0.787131i	$0.288434\pi$
$68$		0			0
$69$	0.378281	−	1.76074i	0.0455397	−	0.211968i
$70$		0			0
$71$	14.0121			1.66293			0.831464	−	0.555578i	$-0.187503\pi$
$71$	14.0121			1.66293			0.831464	+	0.555578i	$0.187503\pi$
$72$		0			0
$73$	−4.38664	+	7.59788i	−0.513417	+	0.889264i	0.486462	+	0.873702i	$0.338287\pi$
$73$	−4.38664	+	7.59788i	−0.513417	+	0.889264i	−0.999879	+	0.0155626i	$0.995046\pi$
$74$		0			0
$75$	−5.48711	+	1.76962i	−0.633597	+	0.204338i
$76$		0			0
$77$	−4.85619	−	0.558456i	−0.553414	−	0.0636420i
$78$		0			0
$79$	2.37061	−	1.36867i	0.266714	−	0.153987i	−0.360679	−	0.932690i	$-0.617455\pi$
$79$	2.37061	−	1.36867i	0.266714	−	0.153987i	0.627393	+	0.778702i	$0.284122\pi$
$80$		0			0
$81$	−8.81935	+	1.79416i	−0.979928	+	0.199352i
$82$		0			0
$83$			4.74366i			0.520685i	0.965516	+	0.260342i	$0.0838354\pi$
$83$			4.74366i			0.520685i	−0.965516	+	0.260342i	$0.916165\pi$
$84$		0			0
$85$			5.81566i			0.630797i
$86$		0			0
$87$	−1.69681	−	1.53454i	−0.181917	−	0.164520i
$88$		0			0
$89$	−8.31219	+	4.79904i	−0.881090	+	0.508697i	−0.871018	−	0.491252i	$-0.836539\pi$
$89$	−8.31219	+	4.79904i	−0.881090	+	0.508697i	−0.0100723	+	0.999949i	$0.503206\pi$
$90$		0			0
$91$	−2.37254	−	5.47217i	−0.248710	−	0.573639i
$92$		0			0
$93$	2.26949	+	7.03709i	0.235336	+	0.729712i
$94$		0			0
$95$	−3.63085	+	6.28882i	−0.372517	+	0.645219i
$96$		0			0
$97$	−8.73466			−0.886871			−0.443435	−	0.896306i	$-0.646240\pi$
$97$	−8.73466			−0.886871			−0.443435	+	0.896306i	$0.646240\pi$
$98$		0			0
$99$	2.27653	−	5.05360i	0.228800	−	0.507906i
$100$		0			0
$101$	−3.42033	+	5.92419i	−0.340336	+	0.589479i	−0.984495	−	0.175413i	$-0.943874\pi$
$101$	−3.42033	+	5.92419i	−0.340336	+	0.589479i	0.644159	+	0.764891i	$0.277207\pi$
$102$		0			0
$103$	−3.88733	+	2.24435i	−0.383030	+	0.221143i	−0.679136	−	0.734013i	$-0.737645\pi$
$103$	−3.88733	+	2.24435i	−0.383030	+	0.221143i	0.296106	+	0.955155i	$0.404312\pi$
$104$		0			0
$105$	−1.16234	−	5.80923i	−0.113433	−	0.566922i
$106$		0			0
$107$	−6.27888	+	3.62511i	−0.607002	+	0.350453i	−0.771791	−	0.635876i	$-0.780639\pi$
$107$	−6.27888	+	3.62511i	−0.607002	+	0.350453i	0.164789	+	0.986329i	$0.447306\pi$
$108$		0			0
$109$	−10.6680	−	6.15916i	−1.02181	−	0.589941i	−0.107180	−	0.994240i	$-0.534182\pi$
$109$	−10.6680	−	6.15916i	−1.02181	−	0.589941i	−0.914627	+	0.404299i	$0.867516\pi$
$110$		0			0
$111$	−16.0027	−	3.43806i	−1.51891	−	0.326326i
$112$		0			0
$113$			7.27566i			0.684437i	0.939620	+	0.342218i	$0.111178\pi$
$113$			7.27566i			0.684437i	−0.939620	+	0.342218i	$0.888822\pi$
$114$		0			0
$115$	−0.672102	+	1.16412i	−0.0626739	+	0.108554i
$116$		0			0
$117$	6.72893	−	0.677511i	0.622089	−	0.0626359i
$118$		0			0
$119$	11.8240	+	1.35974i	1.08390	+	0.124647i
$120$		0			0
$121$	−3.79325	−	6.57011i	−0.344841	−	0.597282i
$122$		0			0
$123$	−1.62224	+	1.79378i	−0.146272	+	0.161740i
$124$		0			0
$125$	10.7673			0.963058
$126$		0			0
$127$			21.7722i			1.93197i	0.258595	+	0.965986i	$0.416740\pi$
$127$			21.7722i			1.93197i	−0.258595	+	0.965986i	$0.583260\pi$
$128$		0			0
$129$	−7.74088	−	7.00062i	−0.681547	−	0.616370i
$130$		0			0
$131$	4.65916	−	2.68997i	0.407073	−	0.235024i	−0.282458	−	0.959280i	$-0.591150\pi$
$131$	4.65916	−	2.68997i	0.407073	−	0.235024i	0.689531	+	0.724256i	$0.257817\pi$
$132$		0			0
$133$	11.9370	+	8.85234i	1.03507	+	0.767595i
$134$		0			0
$135$	6.67605	+	0.745974i	0.574583	+	0.0642033i
$136$		0			0
$137$	11.3713	+	6.56523i	0.971517	+	0.560905i	0.899698	−	0.436512i	$-0.143786\pi$
$137$	11.3713	+	6.56523i	0.971517	+	0.560905i	0.0718185	+	0.997418i	$0.477120\pi$
$138$		0			0
$139$	−12.9760			−1.10061			−0.550307	−	0.834963i	$-0.685489\pi$
$139$	−12.9760			−1.10061			−0.550307	+	0.834963i	$0.685489\pi$
$140$		0			0
$141$	−4.29484	+	19.9907i	−0.361691	+	1.68352i
$142$		0			0
$143$	−2.08250	+	3.60699i	−0.174147	+	0.301632i
$144$		0			0
$145$	0.853802	+	1.47883i	0.0709044	+	0.122810i
$146$		0			0
$147$	−12.0826	+	1.00495i	−0.996559	+	0.0828866i
$148$		0			0
$149$	−3.42033	−	5.92419i	−0.280205	−	0.485328i	0.691230	−	0.722634i	$-0.257069\pi$
$149$	−3.42033	−	5.92419i	−0.280205	−	0.485328i	−0.971435	+	0.237306i	$0.923736\pi$
$150$		0			0
$151$	3.16245	+	1.82584i	0.257356	+	0.148585i	0.623128	−	0.782120i	$-0.285862\pi$
$151$	3.16245	+	1.82584i	0.257356	+	0.148585i	−0.365772	+	0.930705i	$0.619195\pi$
$152$		0			0
$153$	−5.54294	+	12.3046i	−0.448120	+	0.994768i
$154$		0			0
$155$		−	5.51888i		−	0.443287i
$156$		0			0
$157$	−2.34584	−	1.35437i	−0.187219	−	0.108091i	0.403461	−	0.914997i	$-0.367807\pi$
$157$	−2.34584	−	1.35437i	−0.187219	−	0.108091i	−0.590680	+	0.806906i	$0.701140\pi$
$158$		0			0
$159$	−19.8770	+	6.41042i	−1.57635	+	0.508379i
$160$		0			0
$161$	2.20965	+	1.63865i	0.174145	+	0.129143i
$162$		0			0
$163$	−4.41842	−	7.65293i	−0.346078	−	0.599424i	0.639471	−	0.768815i	$-0.279153\pi$
$163$	−4.41842	−	7.65293i	−0.346078	−	0.599424i	−0.985549	+	0.169391i	$0.945820\pi$
$164$		0			0
$165$	−2.77495	+	3.06838i	−0.216030	+	0.238873i
$166$		0			0
$167$	11.8815			0.919417			0.459709	−	0.888070i	$-0.347954\pi$
$167$	11.8815			0.919417			0.459709	+	0.888070i	$0.347954\pi$
$168$		0			0
$169$	7.91806			0.609081
$170$		0			0
$171$	−13.6760	+	9.84512i	−1.04583	+	0.752875i
$172$		0			0
$173$	3.12500	+	5.41265i	0.237589	+	0.411516i	0.960022	−	0.279925i	$-0.0903095\pi$
$173$	3.12500	+	5.41265i	0.237589	+	0.411516i	−0.722433	+	0.691441i	$0.756976\pi$
$174$		0			0
$175$	1.00614	−	8.74915i	0.0760571	−	0.661373i
$176$		0			0
$177$	−5.87927	−	18.2300i	−0.441913	−	1.37025i
$178$		0			0
$179$	−1.43978	−	0.831255i	−0.107614	−	0.0621309i	0.445227	−	0.895418i	$-0.353123\pi$
$179$	−1.43978	−	0.831255i	−0.107614	−	0.0621309i	−0.552841	+	0.833287i	$0.686456\pi$
$180$		0			0
$181$			4.46877i			0.332161i	0.986112	+	0.166081i	$0.0531112\pi$
$181$			4.46877i			0.332161i	−0.986112	+	0.166081i	$0.946889\pi$
$182$		0			0
$183$	14.9630	+	3.21468i	1.10609	+	0.237636i
$184$		0			0
$185$	10.5802	+	6.10850i	0.777874	+	0.449106i
$186$		0			0
$187$	−4.15562	−	7.19775i	−0.303889	−	0.526352i
$188$		0			0
$189$	3.07756	−	13.3988i	0.223860	−	0.974621i
$190$		0			0
$191$	−11.2771	−	19.5325i	−0.815982	−	1.41332i	−0.908620	−	0.417623i	$-0.862863\pi$
$191$	−11.2771	−	19.5325i	−0.815982	−	1.41332i	0.0926380	−	0.995700i	$-0.470470\pi$
$192$		0			0
$193$	−2.90298	+	5.02810i	−0.208961	+	0.361931i	−0.951387	−	0.307997i	$-0.900341\pi$
$193$	−2.90298	+	5.02810i	−0.208961	+	0.361931i	0.742427	+	0.669927i	$0.233675\pi$
$194$		0			0
$195$	−4.93525	−	1.06030i	−0.353421	−	0.0759297i
$196$		0			0
$197$	−3.15873			−0.225050			−0.112525	−	0.993649i	$-0.535894\pi$
$197$	−3.15873			−0.225050			−0.112525	+	0.993649i	$0.535894\pi$
$198$		0			0
$199$	−12.2352	−	7.06397i	−0.867327	−	0.500751i	−0.000867851	−	1.00000i	$-0.500276\pi$
$199$	−12.2352	−	7.06397i	−0.867327	−	0.500751i	−0.866459	+	0.499248i	$0.833610\pi$
$200$		0			0
$201$	10.0735	−	3.24874i	0.710528	−	0.229149i
$202$		0			0
$203$	3.20627	−	1.39013i	0.225036	−	0.0975677i
$204$		0			0
$205$	1.56334	−	0.902597i	0.109189	−	0.0630401i
$206$		0			0
$207$	−2.53154	+	1.82242i	−0.175954	+	0.126667i
$208$		0			0
$209$		−	10.3778i		−	0.717848i
$210$		0			0
$211$	−1.95410			−0.134526			−0.0672629	−	0.997735i	$-0.521427\pi$
$211$	−1.95410			−0.134526			−0.0672629	+	0.997735i	$0.521427\pi$
$212$		0			0
$213$	−18.0003	−	16.2789i	−1.23336	−	1.11541i
$214$		0			0
$215$	3.89507	+	6.74646i	0.265642	+	0.460105i
$216$		0			0
$217$	−11.2206	−	1.29035i	−0.761702	−	0.0875948i
$218$		0			0
$219$	14.4623	−	4.66415i	0.977269	−	0.315174i
$220$		0			0
$221$	5.07051	−	8.78238i	0.341079	−	0.590766i
$222$		0			0
$223$			3.59985i			0.241064i	0.992709	+	0.120532i	$0.0384600\pi$
$223$			3.59985i			0.241064i	−0.992709	+	0.120532i	$0.961540\pi$
$224$		0			0
$225$	9.10480	+	4.10151i	0.606987	+	0.273434i
$226$		0			0
$227$	−5.05015	−	2.91571i	−0.335190	−	0.193522i	0.322953	−	0.946415i	$-0.395325\pi$
$227$	−5.05015	−	2.91571i	−0.335190	−	0.193522i	−0.658143	+	0.752893i	$0.728658\pi$
$228$		0			0
$229$	−11.2803	+	6.51269i	−0.745424	+	0.430371i	−0.824038	−	0.566535i	$-0.808284\pi$
$229$	−11.2803	+	6.51269i	−0.745424	+	0.430371i	0.0786144	+	0.996905i	$0.474950\pi$
$230$		0			0
$231$	5.58960	+	6.35923i	0.367768	+	0.418406i
$232$		0			0
$233$	−13.6565	+	7.88458i	−0.894667	+	0.516536i	−0.875466	−	0.483279i	$-0.839446\pi$
$233$	−13.6565	+	7.88458i	−0.894667	+	0.516536i	−0.0192009	+	0.999816i	$0.506112\pi$
$234$		0			0
$235$	7.63075	−	13.2169i	0.497775	−	0.862172i
$236$		0			0
$237$	−4.63544	−	0.995889i	−0.301104	−	0.0646899i
$238$		0			0
$239$	−22.7458			−1.47130			−0.735651	−	0.677361i	$-0.763124\pi$
$239$	−22.7458			−1.47130			−0.735651	+	0.677361i	$0.763124\pi$
$240$		0			0
$241$	−6.82067	+	11.8137i	−0.439358	+	0.760990i	−0.997640	−	0.0686608i	$-0.978127\pi$
$241$	−6.82067	+	11.8137i	−0.439358	+	0.760990i	0.558282	+	0.829651i	$0.311461\pi$
$242$		0			0
$243$	13.4140	+	7.94130i	0.860509	+	0.509435i
$244$		0			0
$245$	8.81339	+	2.05422i	0.563067	+	0.131240i
$246$		0			0
$247$	10.9661	−	6.33127i	0.697755	−	0.402849i
$248$		0			0
$249$	5.51109	−	6.09384i	0.349251	−	0.386182i
$250$		0			0
$251$			5.33090i			0.336484i	0.985746	+	0.168242i	$0.0538089\pi$
$251$			5.33090i			0.336484i	−0.985746	+	0.168242i	$0.946191\pi$
$252$		0			0
$253$		−	1.92102i		−	0.120774i
$254$		0			0
$255$	6.75651	−	7.47096i	0.423109	−	0.467850i
$256$		0			0
$257$	7.26678	−	4.19547i	0.453289	−	0.261707i	−0.255929	−	0.966696i	$-0.582381\pi$
$257$	7.26678	−	4.19547i	0.453289	−	0.261707i	0.709218	+	0.704989i	$0.249048\pi$
$258$		0			0
$259$	14.8931	−	20.0827i	0.925410	−	1.24788i
$260$		0			0
$261$	0.396969	+	3.94263i	0.0245717	+	0.244043i
$262$		0			0
$263$	1.58410	−	2.74375i	0.0976800	−	0.169187i	−0.813044	−	0.582202i	$-0.802191\pi$
$263$	1.58410	−	2.74375i	0.0976800	−	0.169187i	0.910724	+	0.413016i	$0.135525\pi$
$264$		0			0
$265$	15.5886			0.957603
$266$		0			0
$267$	16.2535	+	3.49194i	0.994698	+	0.213703i
$268$		0			0
$269$	−7.81827	+	13.5416i	−0.476689	+	0.825649i	−0.999643	−	0.0267117i	$-0.991496\pi$
$269$	−7.81827	+	13.5416i	−0.476689	+	0.825649i	0.522955	+	0.852361i	$0.324830\pi$
$270$		0			0
$271$	12.4371	−	7.18058i	0.755502	−	0.436189i	−0.0721766	−	0.997392i	$-0.522995\pi$
$271$	12.4371	−	7.18058i	0.755502	−	0.436189i	0.827678	+	0.561203i	$0.189661\pi$
$272$		0			0
$273$	−3.30962	+	9.78607i	−0.200307	+	0.592280i
$274$		0			0
$275$	−5.32598	+	3.07496i	−0.321169	+	0.185427i
$276$		0			0
$277$	3.23202	+	1.86601i	0.194193	+	0.112117i	0.593944	−	0.804506i	$-0.297570\pi$
$277$	3.23202	+	1.86601i	0.194193	+	0.112117i	−0.399751	+	0.916624i	$0.630903\pi$
$278$		0			0
$279$	5.26008	−	11.6767i	0.314913	−	0.699065i
$280$		0			0
$281$		−	18.8375i		−	1.12375i	−0.827223	−	0.561874i	$-0.810080\pi$
$281$		−	18.8375i		−	1.12375i	0.827223	−	0.561874i	$-0.189920\pi$
$282$		0			0
$283$	−10.7726	+	18.6586i	−0.640362	+	1.10914i	0.344989	+	0.938607i	$0.387883\pi$
$283$	−10.7726	+	18.6586i	−0.640362	+	1.10914i	−0.985352	+	0.170534i	$0.945451\pi$
$284$		0			0
$285$	11.9705	−	3.86055i	0.709072	−	0.228679i
$286$		0			0
$287$	−1.46957	−	3.38951i	−0.0867460	−	0.200076i
$288$		0			0
$289$	1.61820	+	2.80280i	0.0951880	+	0.164870i
$290$		0			0
$291$	11.2208	+	10.1477i	0.657775	+	0.594871i
$292$		0			0
$293$	−4.13814			−0.241753			−0.120876	−	0.992668i	$-0.538570\pi$
$293$	−4.13814			−0.241753			−0.120876	+	0.992668i	$0.538570\pi$
$294$		0			0
$295$			14.2970i			0.832405i
$296$		0			0
$297$	−8.79566	+	3.84717i	−0.510376	+	0.223235i
$298$		0			0
$299$	2.02992	−	1.17197i	0.117393	−	0.0677770i
$300$		0			0
$301$	14.6271	−	6.34179i	0.843091	−	0.365535i
$302$		0			0
$303$	11.2765	−	3.63671i	0.647815	−	0.208924i
$304$		0			0
$305$	−9.89279	−	5.71160i	−0.566459	−	0.327046i
$306$		0			0
$307$	4.63154			0.264336			0.132168	−	0.991227i	$-0.457806\pi$
$307$	4.63154			0.264336			0.132168	+	0.991227i	$0.457806\pi$
$308$		0			0
$309$	7.60122	+	1.63306i	0.432418	+	0.0929017i
$310$		0			0
$311$	−7.04878	+	12.2088i	−0.399700	+	0.692300i	−0.993689	−	0.112173i	$-0.964219\pi$
$311$	−7.04878	+	12.2088i	−0.399700	+	0.692300i	0.593989	+	0.804473i	$0.297552\pi$
$312$		0			0
$313$	6.95418	+	12.0450i	0.393074	+	0.680824i	0.992853	−	0.119342i	$-0.0380784\pi$
$313$	6.95418	+	12.0450i	0.393074	+	0.680824i	−0.599780	+	0.800165i	$0.704745\pi$
$314$		0			0
$315$	−5.25586	+	8.81308i	−0.296134	+	0.496561i
$316$		0			0
$317$	−8.34364	−	14.4516i	−0.468625	−	0.811683i	0.530731	−	0.847540i	$-0.321917\pi$
$317$	−8.34364	−	14.4516i	−0.468625	−	0.811683i	−0.999357	+	0.0358569i	$0.988584\pi$
$318$		0			0
$319$	−2.11342	−	1.22018i	−0.118329	−	0.0683171i
$320$		0			0
$321$	12.2776	+	2.63775i	0.685269	+	0.147225i
$322$		0			0
$323$			25.2681i			1.40595i
$324$		0			0
$325$	−6.49853	−	3.75193i	−0.360473	−	0.208119i
$326$		0			0
$327$	6.54881	+	20.3061i	0.362150	+	1.12293i
$328$		0			0
$329$	−25.0874	−	18.6045i	−1.38311	−	1.02570i
$330$		0			0
$331$	4.82148	+	8.35105i	0.265012	+	0.459015i	0.967567	−	0.252615i	$-0.0812906\pi$
$331$	4.82148	+	8.35105i	0.265012	+	0.459015i	−0.702554	+	0.711630i	$0.747957\pi$
$332$		0			0
$333$	16.5633	+	23.0083i	0.907663	+	1.26085i
$334$		0			0
$335$	−7.90019			−0.431633
$336$		0			0
$337$	29.4886			1.60635			0.803173	−	0.595746i	$-0.203144\pi$
$337$	29.4886			1.60635			0.803173	+	0.595746i	$0.203144\pi$
$338$		0			0
$339$	8.45271	−	9.34652i	0.459088	−	0.507633i
$340$		0			0
$341$	3.94356	+	6.83044i	0.213556	+	0.369889i
$342$		0			0
$343$	6.23712	−	17.4384i	0.336773	−	0.941586i
$344$		0			0
$345$	2.21585	−	0.714621i	0.119297	−	0.0384739i
$346$		0			0
$347$	−10.8911	−	6.28800i	−0.584667	−	0.337558i	0.178319	−	0.983973i	$-0.442934\pi$
$347$	−10.8911	−	6.28800i	−0.584667	−	0.337558i	−0.762986	+	0.646415i	$0.776267\pi$
$348$		0			0
$349$		−	34.5012i		−	1.84681i	−0.383830	−	0.923404i	$-0.625395\pi$
$349$		−	34.5012i		−	1.84681i	0.383830	−	0.923404i	$-0.374605\pi$
$350$		0			0
$351$	−9.43129	−	6.94718i	−0.503405	−	0.370813i
$352$		0			0
$353$	−9.10737	−	5.25815i	−0.484737	−	0.279863i	0.237652	−	0.971350i	$-0.423622\pi$
$353$	−9.10737	−	5.25815i	−0.484737	−	0.279863i	−0.722388	+	0.691488i	$0.756956\pi$
$354$		0			0
$355$	9.05743	+	15.6879i	0.480719	+	0.832629i
$356$		0			0
$357$	−13.6097	−	15.4836i	−0.720300	−	0.819478i
$358$		0			0
$359$	8.02903	+	13.9067i	0.423756	+	0.733967i	0.996303	−	0.0859047i	$-0.0273780\pi$
$359$	8.02903	+	13.9067i	0.423756	+	0.733967i	−0.572547	+	0.819872i	$0.694045\pi$
$360$		0			0
$361$	−6.27547	+	10.8694i	−0.330288	+	0.572075i
$362$		0			0
$363$	−2.76009	+	12.8471i	−0.144867	+	0.674296i
$364$		0			0
$365$	−11.3421			−0.593673
$366$		0			0
$367$	−20.8250	−	12.0233i	−1.08706	−	0.627613i	−0.154266	−	0.988029i	$-0.549301\pi$
$367$	−20.8250	−	12.0233i	−1.08706	−	0.627613i	−0.932791	+	0.360417i	$0.882634\pi$
$368$		0			0
$369$	4.16795	−	0.419655i	0.216975	−	0.0218464i
$370$		0			0
$371$	3.64473	−	31.6936i	0.189225	−	1.64545i
$372$		0			0
$373$	12.5120	−	7.22381i	0.647847	−	0.374035i	−0.139784	−	0.990182i	$-0.544641\pi$
$373$	12.5120	−	7.22381i	0.647847	−	0.374035i	0.787631	+	0.616147i	$0.211307\pi$
$374$		0			0
$375$	−13.8320	−	12.5092i	−0.714281	−	0.645975i
$376$		0			0
$377$		−	2.97762i		−	0.153355i
$378$		0			0
$379$	29.8048			1.53097			0.765485	−	0.643453i	$-0.222499\pi$
$379$	29.8048			1.53097			0.765485	+	0.643453i	$0.222499\pi$
$380$		0			0
$381$	25.2945	−	27.9692i	1.29588	−	1.43291i
$382$		0			0
$383$	5.62806	+	9.74809i	0.287581	+	0.498104i	0.973232	−	0.229826i	$-0.0738158\pi$
$383$	5.62806	+	9.74809i	0.287581	+	0.498104i	−0.685651	+	0.727930i	$0.740482\pi$
$384$		0			0
$385$	−2.51380	−	5.79798i	−0.128115	−	0.295492i
$386$		0			0
$387$	1.81098	+	17.9864i	0.0920574	+	0.914300i
$388$		0			0
$389$	−13.4807	+	23.3492i	−0.683498	+	1.18385i	0.290408	+	0.956903i	$0.406209\pi$
$389$	−13.4807	+	23.3492i	−0.683498	+	1.18385i	−0.973906	+	0.226950i	$0.927124\pi$
$390$		0			0
$391$			4.67735i			0.236544i
$392$		0			0
$393$	−9.11045	−	1.95731i	−0.459561	−	0.0987331i
$394$		0			0
$395$	3.06473	+	1.76942i	0.154203	+	0.0890293i
$396$		0			0
$397$	−6.75185	+	3.89818i	−0.338866	+	0.195644i	−0.659770	−	0.751467i	$-0.729346\pi$
$397$	−6.75185	+	3.89818i	−0.338866	+	0.195644i	0.320905	+	0.947111i	$0.396013\pi$
$398$		0			0
$399$	−5.05018	−	25.2402i	−0.252825	−	1.26359i
$400$		0			0
$401$	−2.98430	+	1.72299i	−0.149029	+	0.0860420i	−0.572660	−	0.819793i	$-0.694089\pi$
$401$	−2.98430	+	1.72299i	−0.149029	+	0.0860420i	0.423631	+	0.905835i	$0.360755\pi$
$402$		0			0
$403$	−4.81175	+	8.33420i	−0.239691	+	0.415156i
$404$		0			0
$405$	−7.70959	−	8.71440i	−0.383093	−	0.433022i
$406$		0			0
$407$	−17.4595			−0.865435
$408$		0			0
$409$	9.79039	−	16.9575i	0.484104	−	0.838492i	−0.515729	−	0.856752i	$-0.672479\pi$
$409$	9.79039	−	16.9575i	0.484104	−	0.838492i	0.999833	+	0.0182590i	$0.00581236\pi$
$410$		0			0
$411$	−6.98056	−	21.6448i	−0.344326	−	1.06766i
$412$		0			0
$413$	29.0676	+	3.34274i	1.43032	+	0.164485i
$414$		0			0
$415$	−5.31101	+	3.06631i	−0.260707	+	0.150519i
$416$		0			0
$417$	16.6694	+	15.0753i	0.816303	+	0.738240i
$418$		0			0
$419$		−	27.6189i		−	1.34927i	−0.738150	−	0.674637i	$-0.764300\pi$
$419$		−	27.6189i		−	1.34927i	0.738150	−	0.674637i	$-0.235700\pi$
$420$		0			0
$421$			9.36226i			0.456289i	0.973627	+	0.228144i	$0.0732658\pi$
$421$			9.36226i			0.456289i	−0.973627	+	0.228144i	$0.926734\pi$
$422$		0			0
$423$	28.7420	−	20.6909i	1.39748	−	1.00603i
$424$		0			0
$425$	12.9678	−	7.48697i	0.629031	−	0.363171i
$426$		0			0
$427$	−13.9254	+	18.7779i	−0.673897	+	0.908724i
$428$		0			0
$429$	6.86576	−	2.21424i	0.331482	−	0.106905i
$430$		0			0
$431$	4.22951	−	7.32573i	0.203729	−	0.352868i	−0.745998	−	0.665948i	$-0.768027\pi$
$431$	4.22951	−	7.32573i	0.203729	−	0.352868i	0.949727	+	0.313080i	$0.101361\pi$
$432$		0			0
$433$	−10.9191			−0.524737			−0.262369	−	0.964968i	$-0.584504\pi$
$433$	−10.9191			−0.524737			−0.262369	+	0.964968i	$0.584504\pi$
$434$		0			0
$435$	0.621254	−	2.89168i	0.0297868	−	0.138645i
$436$		0			0
$437$	−2.92018	+	5.05790i	−0.139691	+	0.241952i
$438$		0			0
$439$	20.2600	−	11.6971i	0.966959	−	0.558274i	0.0686510	−	0.997641i	$-0.478131\pi$
$439$	20.2600	−	11.6971i	0.966959	−	0.558274i	0.898308	+	0.439367i	$0.144797\pi$
$440$		0			0
$441$	16.6892	+	12.7464i	0.794725	+	0.606970i
$442$		0			0
$443$	−5.31199	+	3.06688i	−0.252380	+	0.145712i	−0.620854	−	0.783926i	$-0.713214\pi$
$443$	−5.31199	+	3.06688i	−0.252380	+	0.145712i	0.368473	+	0.929638i	$0.379881\pi$
$444$		0			0
$445$	−10.7460	−	6.20422i	−0.509410	−	0.294108i
$446$		0			0
$447$	−2.48874	+	11.5840i	−0.117713	+	0.547907i
$448$		0			0
$449$			35.8658i			1.69261i	0.532696	+	0.846307i	$0.321179\pi$
$449$			35.8658i			1.69261i	−0.532696	+	0.846307i	$0.678821\pi$
$450$		0			0
$451$	−1.28992	+	2.23420i	−0.0607397	+	0.105204i
$452$		0			0
$453$	−1.94135	−	6.01959i	−0.0912124	−	0.282825i
$454$		0			0
$455$	4.59303	−	6.19352i	0.215324	−	0.290357i
$456$		0			0
$457$	−1.51987	−	2.63249i	−0.0710964	−	0.123143i	0.828286	−	0.560306i	$-0.189316\pi$
$457$	−1.51987	−	2.63249i	−0.0710964	−	0.123143i	−0.899382	+	0.437163i	$0.855983\pi$
$458$		0			0
$459$	21.4159	−	9.36717i	0.999606	−	0.437222i
$460$		0			0
$461$	−30.7564			−1.43247			−0.716233	−	0.697861i	$-0.754135\pi$
$461$	−30.7564			−1.43247			−0.716233	+	0.697861i	$0.754135\pi$
$462$		0			0
$463$			9.54146i			0.443429i	0.975112	+	0.221715i	$0.0711653\pi$
$463$			9.54146i			0.443429i	−0.975112	+	0.221715i	$0.928835\pi$
$464$		0			0
$465$	−6.41172	+	7.08971i	−0.297336	+	0.328777i
$466$		0			0
$467$	−4.36437	+	2.51977i	−0.201959	+	0.116601i	−0.597569	−	0.801818i	$-0.703867\pi$
$467$	−4.36437	+	2.51977i	−0.201959	+	0.116601i	0.395610	+	0.918419i	$0.370533\pi$
$468$		0			0
$469$	−1.84712	+	16.0621i	−0.0852920	+	0.741677i
$470$		0			0
$471$	1.44005	+	4.46522i	0.0663542	+	0.205746i
$472$		0			0
$473$	−9.64147	−	5.56650i	−0.443315	−	0.255948i
$474$		0			0
$475$	18.6972			0.857884
$476$		0			0
$477$	32.9820	+	14.8576i	1.51014	+	0.680285i
$478$		0			0
$479$	−13.6307	+	23.6091i	−0.622804	+	1.07873i	0.366157	+	0.930553i	$0.380673\pi$
$479$	−13.6307	+	23.6091i	−0.622804	+	1.07873i	−0.988961	+	0.148175i	$0.952660\pi$
$480$		0			0
$481$	−10.6516	−	18.4492i	−0.485673	−	0.841211i
$482$		0			0
$483$	−0.934833	−	4.67217i	−0.0425364	−	0.212591i
$484$		0			0
$485$	−5.64610	−	9.77933i	−0.256376	−	0.444057i
$486$		0			0
$487$	0.905513	+	0.522798i	0.0410327	+	0.0236902i	0.520376	−	0.853937i	$-0.325792\pi$
$487$	0.905513	+	0.522798i	0.0410327	+	0.0236902i	−0.479343	+	0.877627i	$0.659125\pi$
$488$		0			0
$489$	−3.21499	+	14.9644i	−0.145387	+	0.676714i
$490$		0			0
$491$		−	29.3101i		−	1.32275i	−0.750057	−	0.661373i	$-0.769974\pi$
$491$		−	29.3101i		−	1.32275i	0.750057	−	0.661373i	$-0.230026\pi$
$492$		0			0
$493$	5.14579	+	2.97092i	0.231755	+	0.133804i
$494$		0			0
$495$	7.12956	−	0.717849i	0.320450	−	0.0322649i
$496$		0			0
$497$	34.0132	−	14.7469i	1.52570	−	0.661490i
$498$		0			0
$499$	−14.3749	−	24.8981i	−0.643510	−	1.11459i	−0.984643	−	0.174578i	$-0.944144\pi$
$499$	−14.3749	−	24.8981i	−0.643510	−	1.11459i	0.341133	−	0.940015i	$-0.389189\pi$
$500$		0			0
$501$	−15.2633	−	13.8037i	−0.681914	−	0.616702i
$502$		0			0
$503$	19.8016			0.882910			0.441455	−	0.897283i	$-0.354462\pi$
$503$	19.8016			0.882910			0.441455	+	0.897283i	$0.354462\pi$
$504$		0			0
$505$	−8.84363			−0.393536
$506$		0			0
$507$	−10.1718	−	9.19903i	−0.451744	−	0.408543i
$508$		0			0
$509$	−14.1795	−	24.5596i	−0.628494	−	1.08858i	−0.987854	−	0.155385i	$-0.950338\pi$
$509$	−14.1795	−	24.5596i	−0.628494	−	1.08858i	0.359360	−	0.933199i	$-0.382995\pi$
$510$		0			0
$511$	−2.65186	+	23.0599i	−0.117312	+	1.02011i
$512$		0			0
$513$	29.0064	+	3.24114i	1.28066	+	0.143100i
$514$		0			0
$515$	−5.02555	−	2.90151i	−0.221452	−	0.127856i
$516$		0			0
$517$			21.8104i			0.959222i
$518$		0			0
$519$	2.27385	−	10.5838i	0.0998108	−	0.464577i
$520$		0			0
$521$	27.4943	+	15.8738i	1.20455	+	0.695445i	0.961563	−	0.274585i	$-0.0885404\pi$
$521$	27.4943	+	15.8738i	1.20455	+	0.695445i	0.242984	+	0.970030i	$0.421874\pi$
$522$		0			0
$523$	−3.11470	−	5.39482i	−0.136196	−	0.235899i	0.789858	−	0.613290i	$-0.210154\pi$
$523$	−3.11470	−	5.39482i	−0.136196	−	0.235899i	−0.926054	+	0.377392i	$0.876821\pi$
$524$		0			0
$525$	−11.4571	+	10.0705i	−0.500028	+	0.439512i
$526$		0			0
$527$	−9.60185	−	16.6309i	−0.418263	−	0.724453i
$528$		0			0
$529$	10.9594	−	18.9823i	0.476498	−	0.825318i
$530$		0			0
$531$	−13.6266	+	30.2492i	−0.591344	+	1.31270i
$532$		0			0
$533$	−3.14780			−0.136346
$534$		0			0
$535$	−8.11735	−	4.68656i	−0.350944	−	0.202618i
$536$		0			0
$537$	0.883842	+	2.74056i	0.0381406	+	0.118264i
$538$		0			0
$539$	−12.3758	+	3.75526i	−0.533061	+	0.161751i
$540$		0			0
$541$	−1.99979	+	1.15458i	−0.0859776	+	0.0496392i	−0.542372	−	0.840138i	$-0.682474\pi$
$541$	−1.99979	+	1.15458i	−0.0859776	+	0.0496392i	0.456395	+	0.889777i	$0.349140\pi$
$542$		0			0
$543$	5.19172	−	5.74071i	0.222798	−	0.246357i
$544$		0			0
$545$		−	15.9252i		−	0.682159i
$546$		0			0
$547$	−32.5136			−1.39018			−0.695090	−	0.718922i	$-0.744636\pi$
$547$	−32.5136			−1.39018			−0.695090	+	0.718922i	$0.744636\pi$
$548$		0			0
$549$	−15.4871	−	21.5133i	−0.660974	−	0.918167i
$550$		0			0
$551$	3.70963	+	6.42528i	0.158036	+	0.273726i
$552$		0			0
$553$	4.31401	−	5.81727i	0.183450	−	0.247375i
$554$		0			0
$555$	−6.49494	−	20.1390i	−0.275695	−	0.854854i
$556$		0			0
$557$	−16.5711	+	28.7020i	−0.702140	+	1.21614i	0.265574	+	0.964091i	$0.414439\pi$
$557$	−16.5711	+	28.7020i	−0.702140	+	1.21614i	−0.967714	+	0.252052i	$0.918895\pi$
$558$		0			0
$559$		−	13.5840i		−	0.574542i
$560$		0			0
$561$	−3.02376	+	14.0743i	−0.127663	+	0.594219i
$562$		0			0
$563$	13.6362	+	7.87286i	0.574697	+	0.331801i	0.759023	−	0.651064i	$-0.225677\pi$
$563$	13.6362	+	7.87286i	0.574697	+	0.331801i	−0.184326	+	0.982865i	$0.559010\pi$
$564$		0			0
$565$	−8.14583	+	4.70300i	−0.342698	+	0.197857i
$566$		0			0
$567$	−19.5200	+	13.6371i	−0.819763	+	0.572703i
$568$		0			0
$569$	−20.1971	+	11.6608i	−0.846706	+	0.488846i	−0.859538	−	0.511072i	$-0.829249\pi$
$569$	−20.1971	+	11.6608i	−0.846706	+	0.488846i	0.0128319	+	0.999918i	$0.495915\pi$
$570$		0			0
$571$	−12.0030	+	20.7898i	−0.502311	+	0.870027i	0.497686	+	0.867357i	$0.334183\pi$
$571$	−12.0030	+	20.7898i	−0.502311	+	0.870027i	−0.999996	+	0.00267009i	$0.999150\pi$
$572$		0			0
$573$	−8.20558	+	38.1935i	−0.342793	+	1.59556i
$574$		0			0
$575$	3.46101			0.144334
$576$		0			0
$577$	−2.69246	+	4.66349i	−0.112089	+	0.194143i	−0.916612	−	0.399777i	$-0.869087\pi$
$577$	−2.69246	+	4.66349i	−0.112089	+	0.194143i	0.804523	+	0.593921i	$0.202421\pi$
$578$		0			0
$579$	9.57079	−	3.08663i	0.397749	−	0.128276i
$580$		0			0
$581$	4.99244	+	11.5149i	0.207121	+	0.477717i
$582$		0			0
$583$	−19.2933	+	11.1390i	−0.799046	+	0.461329i
$584$		0			0
$585$	5.10813	+	7.09576i	0.211195	+	0.293374i
$586$		0			0
$587$		−	20.8871i		−	0.862104i	−0.902327	−	0.431052i	$-0.858143\pi$
$587$		−	20.8871i		−	0.862104i	0.902327	−	0.431052i	$-0.141857\pi$
$588$		0			0
$589$		−	23.9786i		−	0.988023i
$590$		0			0
$591$	4.05780	+	3.66975i	0.166915	+	0.150953i
$592$		0			0
$593$	−31.7953	+	18.3570i	−1.30567	+	0.753832i	−0.981371	−	0.192122i	$-0.938463\pi$
$593$	−31.7953	+	18.3570i	−1.30567	+	0.753832i	−0.324303	+	0.945953i	$0.605130\pi$
$594$		0			0
$595$	6.12065	+	14.1170i	0.250922	+	0.578742i
$596$		0			0
$597$	7.51085	+	23.2891i	0.307399	+	0.953160i
$598$		0			0
$599$	12.0639	−	20.8953i	0.492918	−	0.853760i	−0.507048	−	0.861918i	$-0.669263\pi$
$599$	12.0639	−	20.8953i	0.492918	−	0.853760i	0.999967	+	0.00815783i	$0.00259675\pi$
$600$		0			0
$601$	−30.7421			−1.25399			−0.626997	−	0.779021i	$-0.715716\pi$
$601$	−30.7421			−1.25399			−0.626997	+	0.779021i	$0.715716\pi$
$602$		0			0
$603$	−16.7150	−	7.52972i	−0.680687	−	0.306634i
$604$		0			0
$605$	4.90393	−	8.49385i	0.199373	−	0.345324i
$606$		0			0
$607$	−3.75552	+	2.16825i	−0.152432	+	0.0880066i	−0.574276	−	0.818662i	$-0.694716\pi$
$607$	−3.75552	+	2.16825i	−0.152432	+	0.0880066i	0.421844	+	0.906668i	$0.361383\pi$
$608$		0			0
$609$	−5.73388	−	1.93918i	−0.232349	−	0.0785795i
$610$		0			0
$611$	−23.0468	+	13.3061i	−0.932373	+	0.538306i
$612$		0			0
$613$	26.2945	+	15.1812i	1.06203	+	0.613161i	0.925992	−	0.377543i	$-0.123231\pi$
$613$	26.2945	+	15.1812i	1.06203	+	0.613161i	0.136034	+	0.990704i	$0.456564\pi$
$614$		0			0
$615$	−3.05693	−	0.656759i	−0.123268	−	0.0264831i
$616$		0			0
$617$		−	11.5709i		−	0.465827i	−0.972497	−	0.232913i	$-0.925174\pi$
$617$		−	11.5709i		−	0.465827i	0.972497	−	0.232913i	$-0.0748259\pi$
$618$		0			0
$619$	8.62076	−	14.9316i	0.346497	−	0.600151i	−0.639127	−	0.769101i	$-0.720704\pi$
$619$	8.62076	−	14.9316i	0.346497	−	0.600151i	0.985625	+	0.168950i	$0.0540376\pi$
$620$		0			0
$621$	5.36934	+	0.599963i	0.215464	+	0.0240757i
$622$		0			0
$623$	−15.1264	+	20.3974i	−0.606028	+	0.817204i
$624$		0			0
$625$	−1.36164	−	2.35843i	−0.0544656	−	0.0943372i
$626$		0			0
$627$	−12.0567	+	13.3316i	−0.481499	+	0.532414i
$628$		0			0
$629$	42.5107			1.69501
$630$		0			0
$631$			4.91146i			0.195522i	0.995210	+	0.0977611i	$0.0311681\pi$
$631$			4.91146i			0.195522i	−0.995210	+	0.0977611i	$0.968832\pi$
$632$		0			0
$633$	2.51029	+	2.27023i	0.0997752	+	0.0902336i
$634$		0			0
$635$	−24.3762	+	14.0736i	−0.967339	+	0.558493i
$636$		0			0
$637$	−11.5183	−	10.7863i	−0.456372	−	0.427368i
$638$		0			0
$639$	4.21118	+	41.8248i	0.166592	+	1.65456i
$640$		0			0
$641$	−34.7916	−	20.0870i	−1.37419	−	0.793387i	−0.382735	−	0.923858i	$-0.625018\pi$
$641$	−34.7916	−	20.0870i	−1.37419	−	0.793387i	−0.991452	+	0.130471i	$0.958351\pi$
$642$		0			0
$643$	−12.5997			−0.496884			−0.248442	−	0.968647i	$-0.579919\pi$
$643$	−12.5997			−0.496884			−0.248442	+	0.968647i	$0.579919\pi$
$644$		0			0
$645$	2.83418	−	13.1919i	0.111596	−	0.519431i
$646$		0			0
$647$	−9.55483	+	16.5495i	−0.375639	+	0.650626i	−0.990422	−	0.138070i	$-0.955910\pi$
$647$	−9.55483	+	16.5495i	−0.375639	+	0.650626i	0.614783	+	0.788696i	$0.289243\pi$
$648$		0			0
$649$	−10.2160	−	17.6947i	−0.401015	−	0.694578i
$650$		0			0
$651$	12.9152	+	14.6934i	0.506185	+	0.575881i
$652$		0			0
$653$	4.01546	+	6.95497i	0.157137	+	0.272169i	0.933835	−	0.357704i	$-0.116440\pi$
$653$	4.01546	+	6.95497i	0.157137	+	0.272169i	−0.776698	+	0.629873i	$0.783107\pi$
$654$		0			0
$655$	6.02338	+	3.47760i	0.235353	+	0.135881i
$656$		0			0
$657$	−23.9973	−	10.8102i	−0.936225	−	0.421748i
$658$		0			0
$659$			5.21061i			0.202977i	0.994837	+	0.101488i	$0.0323604\pi$
$659$			5.21061i			0.202977i	−0.994837	+	0.101488i	$0.967640\pi$
$660$		0			0
$661$	33.5498	+	19.3700i	1.30494	+	0.753406i	0.981246	−	0.192757i	$-0.0617431\pi$
$661$	33.5498	+	19.3700i	1.30494	+	0.753406i	0.323690	+	0.946163i	$0.395076\pi$
$662$		0			0
$663$	−16.7169	+	5.39128i	−0.649230	+	0.209380i
$664$		0			0
$665$	−2.19497	+	19.0869i	−0.0851171	+	0.740157i
$666$		0			0
$667$	0.686686	+	1.18937i	0.0265886	+	0.0460528i
$668$		0			0
$669$	4.18223	−	4.62447i	0.161694	−	0.178792i
$670$		0			0
$671$	16.3251			0.630223
$672$		0			0
$673$	−33.1783			−1.27893			−0.639465	−	0.768821i	$-0.720844\pi$
$673$	−33.1783			−1.27893			−0.639465	+	0.768821i	$0.720844\pi$
$674$		0			0
$675$	−6.93124	−	15.8467i	−0.266784	−	0.609939i
$676$		0			0
$677$	−15.7573	−	27.2925i	−0.605602	−	1.04893i	−0.991956	−	0.126583i	$-0.959599\pi$
$677$	−15.7573	−	27.2925i	−0.605602	−	1.04893i	0.386354	−	0.922351i	$-0.373734\pi$
$678$		0			0
$679$	−21.2027	+	9.19274i	−0.813684	+	0.352785i
$680$		0			0
$681$	3.10016	+	9.61276i	0.118798	+	0.368362i
$682$		0			0
$683$	19.4038	+	11.2028i	0.742465	+	0.428663i	0.822965	−	0.568092i	$-0.192318\pi$
$683$	19.4038	+	11.2028i	0.742465	+	0.428663i	−0.0804996	+	0.996755i	$0.525652\pi$
$684$		0			0
$685$			16.9751i			0.648585i
$686$		0			0
$687$	22.0573	+	4.73884i	0.841539	+	0.180798i
$688$		0			0
$689$	−23.5408	−	13.5913i	−0.896833	−	0.517787i
$690$		0			0
$691$	7.24483	+	12.5484i	0.275606	+	0.477364i	0.970288	−	0.241953i	$-0.0777880\pi$
$691$	7.24483	+	12.5484i	0.275606	+	0.477364i	−0.694682	+	0.719317i	$0.744455\pi$
$692$		0			0
$693$	0.207464	−	14.6631i	0.00788090	−	0.557006i
$694$		0			0
$695$	−8.38773	−	14.5280i	−0.318165	−	0.551077i
$696$		0			0
$697$	3.14071	−	5.43987i	0.118963	−	0.206050i
$698$		0			0
$699$	26.7037	+	5.73708i	1.01003	+	0.216996i
$700$		0			0
$701$	21.9950			0.830738			0.415369	−	0.909653i	$-0.363652\pi$
$701$	21.9950			0.830738			0.415369	+	0.909653i	$0.363652\pi$
$702$		0			0
$703$	45.9694	+	26.5404i	1.73377	+	1.00099i
$704$		0			0
$705$	−25.1577	+	8.11349i	−0.947495	+	0.305572i
$706$		0			0
$707$	−2.06770	+	17.9802i	−0.0777639	+	0.676215i
$708$		0			0
$709$	−17.2122	+	9.93745i	−0.646416	+	0.373209i	−0.787082	−	0.616849i	$-0.788409\pi$
$709$	−17.2122	+	9.93745i	−0.646416	+	0.373209i	0.140666	+	0.990057i	$0.455076\pi$
$710$		0			0
$711$	4.79782	+	6.66471i	0.179932	+	0.249946i
$712$		0			0
$713$		−	4.43866i		−	0.166229i
$714$		0			0
$715$	−5.38452			−0.201370
$716$		0			0
$717$	29.2199	+	26.4256i	1.09124	+	0.986881i
$718$		0			0
$719$	4.05138	+	7.01719i	0.151091	+	0.261697i	0.931629	−	0.363411i	$-0.118388\pi$
$719$	4.05138	+	7.01719i	0.151091	+	0.261697i	−0.780538	+	0.625108i	$0.785055\pi$
$720$		0			0
$721$	−7.07413	+	9.53918i	−0.263454	+	0.355258i
$722$		0			0
$723$	22.4870	−	7.25216i	0.836300	−	0.269711i
$724$		0			0
$725$	2.19834	−	3.80763i	0.0816442	−	0.141412i
$726$		0			0
$727$		−	1.56460i		−	0.0580278i	−0.999579	−	0.0290139i	$-0.990763\pi$
$727$		−	1.56460i		−	0.0580278i	0.999579	−	0.0290139i	$-0.00923671\pi$
$728$		0			0
$729$	−8.00598	−	25.7857i	−0.296518	−	0.955027i
$730$		0			0
$731$	23.4752	+	13.5534i	0.868263	+	0.501292i
$732$		0			0
$733$	−10.2679	+	5.92818i	−0.379254	+	0.218962i	−0.677493	−	0.735529i	$-0.736934\pi$
$733$	−10.2679	+	5.92818i	−0.379254	+	0.218962i	0.298240	+	0.954491i	$0.403600\pi$
$734$		0			0
$735$	−8.93537	−	12.8781i	−0.329586	−	0.475017i
$736$		0			0
$737$	9.77767	−	5.64514i	0.360165	−	0.207941i
$738$		0			0
$739$	6.94639	−	12.0315i	0.255527	−	0.442586i	−0.709511	−	0.704694i	$-0.751084\pi$
$739$	6.94639	−	12.0315i	0.255527	−	0.442586i	0.965039	+	0.262108i	$0.0844176\pi$
$740$		0			0
$741$	−21.4429	−	4.60684i	−0.787724	−	0.169236i
$742$		0			0
$743$	−25.3287			−0.929221			−0.464611	−	0.885515i	$-0.653806\pi$
$743$	−25.3287			−0.929221			−0.464611	+	0.885515i	$0.653806\pi$
$744$		0			0
$745$	4.42182	−	7.65881i	0.162003	−	0.280597i
$746$		0			0
$747$	−14.1594	+	1.42566i	−0.518065	+	0.0521621i
$748$		0			0
$749$	−11.4262	+	15.4078i	−0.417506	+	0.562990i
$750$		0			0
$751$	−10.4902	+	6.05653i	−0.382793	+	0.221006i	−0.679033	−	0.734108i	$-0.737601\pi$
$751$	−10.4902	+	6.05653i	−0.382793	+	0.221006i	0.296240	+	0.955114i	$0.404267\pi$
$752$		0			0
$753$	6.19333	−	6.84823i	0.225698	−	0.249563i
$754$		0			0
$755$			4.72090i			0.171811i
$756$		0			0
$757$		−	21.6528i		−	0.786983i	−0.919328	−	0.393491i	$-0.871267\pi$
$757$		−	21.6528i		−	0.786983i	0.919328	−	0.393491i	$-0.128733\pi$
$758$		0			0
$759$	−2.23180	+	2.46780i	−0.0810094	+	0.0895755i
$760$		0			0
$761$	33.4532	−	19.3142i	1.21268	−	0.700141i	0.249337	−	0.968417i	$-0.419787\pi$
$761$	33.4532	−	19.3142i	1.21268	−	0.700141i	0.963342	+	0.268276i	$0.0864539\pi$
$762$		0			0
$763$	−32.3778	−	3.72341i	−1.17216	−	0.134797i
$764$		0			0
$765$	−17.3592	+	1.74783i	−0.627623	+	0.0631931i
$766$		0			0
$767$	12.4652	−	21.5903i	0.450091	−	0.779580i
$768$		0			0
$769$	32.8604			1.18498			0.592489	−	0.805579i	$-0.298145\pi$
$769$	32.8604			1.18498			0.592489	+	0.805579i	$0.298145\pi$
$770$		0			0
$771$	−14.2093	−	3.05276i	−0.511736	−	0.109943i
$772$		0			0
$773$	−14.2511	+	24.6836i	−0.512576	+	0.887808i	0.487318	+	0.873225i	$0.337975\pi$
$773$	−14.2511	+	24.6836i	−0.512576	+	0.887808i	−0.999894	+	0.0145830i	$0.995358\pi$
$774$		0			0
$775$	−12.3061	+	7.10490i	−0.442046	+	0.255216i
$776$		0			0
$777$	−42.4637	+	8.49636i	−1.52338	+	0.304805i
$778$		0			0
$779$	6.79248	−	3.92164i	0.243366	−	0.140507i
$780$		0			0
$781$	−22.4199	−	12.9441i	−0.802246	−	0.463177i
$782$		0			0
$783$	4.07051	−	5.52600i	0.145468	−	0.197483i
$784$		0			0
$785$		−	3.50188i		−	0.124987i
$786$		0			0
$787$	18.8558	−	32.6593i	0.672138	−	1.16418i	−0.305159	−	0.952301i	$-0.598710\pi$
$787$	18.8558	−	32.6593i	0.672138	−	1.16418i	0.977297	−	0.211875i	$-0.0679571\pi$
$788$		0			0
$789$	−5.22261	+	1.68432i	−0.185930	+	0.0599633i
$790$		0			0
$791$	7.65723	+	17.6611i	0.272260	+	0.627956i
$792$		0			0
$793$	9.95957	+	17.2505i	0.353675	+	0.612583i
$794$		0			0
$795$	−20.0256	−	18.1106i	−0.710235	−	0.642315i
$796$		0			0
$797$	46.8382			1.65910			0.829548	−	0.558436i	$-0.188598\pi$
$797$	46.8382			1.65910			0.829548	+	0.558436i	$0.188598\pi$
$798$		0			0
$799$		−	53.1045i		−	1.87870i
$800$		0			0
$801$	−16.8228	−	23.3688i	−0.594406	−	0.825696i
$802$		0			0
$803$	14.0376	−	8.10460i	0.495375	−	0.286005i
$804$		0			0
$805$	−0.406308	+	3.53315i	−0.0143205	+	0.124527i
$806$		0			0
$807$	25.7760	−	8.31288i	0.907357	−	0.292627i
$808$		0			0
$809$	0.943718	+	0.544856i	0.0331794	+	0.0191561i	0.516498	−	0.856288i	$-0.327235\pi$
$809$	0.943718	+	0.544856i	0.0331794	+	0.0191561i	−0.483319	+	0.875445i	$0.660569\pi$
$810$		0			0
$811$	10.7828			0.378634			0.189317	−	0.981916i	$-0.439373\pi$
$811$	10.7828			0.378634			0.189317	+	0.981916i	$0.439373\pi$
$812$		0			0
$813$	−24.3193	−	5.22482i	−0.852916	−	0.183242i
$814$		0			0
$815$	5.71215	−	9.89373i	0.200088	−	0.346562i
$816$		0			0
$817$	16.9235	+	29.3123i	0.592077	+	1.02551i
$818$		0			0
$819$	15.6209	−	8.72642i	0.545838	−	0.304926i
$820$		0			0
$821$	−8.63020	−	14.9479i	−0.301196	−	0.521687i	0.675211	−	0.737625i	$-0.264053\pi$
$821$	−8.63020	−	14.9479i	−0.301196	−	0.521687i	−0.976407	+	0.215938i	$0.930719\pi$
$822$		0			0
$823$	31.7271	+	18.3176i	1.10594	+	0.638513i	0.937774	−	0.347246i	$-0.112883\pi$
$823$	31.7271	+	18.3176i	1.10594	+	0.638513i	0.168163	+	0.985759i	$0.446217\pi$
$824$		0			0
$825$	10.4143	+	2.23744i	0.362580	+	0.0778976i
$826$		0			0
$827$			46.5193i			1.61764i	0.588060	+	0.808818i	$0.299892\pi$
$827$			46.5193i			1.61764i	−0.588060	+	0.808818i	$0.700108\pi$
$828$		0			0
$829$	−29.9474	−	17.2901i	−1.04011	−	0.600511i	−0.120249	−	0.992744i	$-0.538369\pi$
$829$	−29.9474	−	17.2901i	−1.04011	−	0.600511i	−0.919866	+	0.392233i	$0.871703\pi$
$830$		0			0
$831$	−1.98405	−	6.15201i	−0.0688260	−	0.213411i
$832$		0			0
$833$	30.1327	−	9.14339i	1.04404	−	0.316800i
$834$		0			0
$835$	7.68021	+	13.3025i	0.265785	+	0.460353i
$836$		0			0
$837$	−20.3230	+	8.88915i	−0.702465	+	0.307254i
$838$		0			0
$839$	−39.6383			−1.36847			−0.684233	−	0.729264i	$-0.739863\pi$
$839$	−39.6383			−1.36847			−0.684233	+	0.729264i	$0.739863\pi$
$840$		0			0
$841$	−27.2553			−0.939839
$842$		0			0
$843$	−21.8850	+	24.1991i	−0.753758	+	0.833462i
$844$		0			0
$845$	5.11825	+	8.86506i	0.176073	+	0.304967i
$846$		0			0
$847$	−16.1225	−	11.9562i	−0.553975	−	0.410820i
$848$		0			0
$849$	35.5159	−	11.4541i	1.21890	−	0.393102i
$850$		0			0
$851$	8.50934	+	4.91287i	0.291696	+	0.168411i
$852$		0			0
$853$			10.8810i			0.372557i	0.982497	+	0.186279i	$0.0596427\pi$
$853$			10.8810i			0.372557i	−0.982497	+	0.186279i	$0.940357\pi$
$854$		0			0
$855$	−19.8628	−	8.94772i	−0.679292	−	0.306006i
$856$		0			0
$857$	39.8564	+	23.0111i	1.36147	+	0.786045i	0.989820	−	0.142328i	$-0.0454588\pi$
$857$	39.8564	+	23.0111i	1.36147	+	0.786045i	0.371650	+	0.928373i	$0.378792\pi$
$858$		0			0
$859$	−11.4205	−	19.7808i	−0.389661	−	0.674912i	0.602743	−	0.797935i	$-0.294074\pi$
$859$	−11.4205	−	19.7808i	−0.389661	−	0.674912i	−0.992404	+	0.123023i	$0.960741\pi$
$860$		0			0
$861$	−2.05000	+	6.06157i	−0.0698639	+	0.206578i
$862$		0			0
$863$	2.49061	+	4.31386i	0.0847813	+	0.146846i	0.905298	−	0.424777i	$-0.139647\pi$
$863$	2.49061	+	4.31386i	0.0847813	+	0.146846i	−0.820517	+	0.571623i	$0.806314\pi$
$864$		0			0
$865$	−4.04001	+	6.99750i	−0.137364	+	0.237922i
$866$		0			0
$867$	1.17745	−	5.48054i	0.0399883	−	0.186129i
$868$		0			0
$869$	−5.05741			−0.171561
$870$		0			0
$871$	11.9303	+	6.88795i	0.404242	+	0.233389i
$872$		0			0
$873$	−2.62511	−	26.0722i	−0.0888465	−	0.882409i
$874$		0			0
$875$	26.1368	−	11.3320i	0.883585	−	0.383091i
$876$		0			0
$877$	−25.7564	+	14.8705i	−0.869731	+	0.502139i	−0.867259	−	0.497857i	$-0.834120\pi$
$877$	−25.7564	+	14.8705i	−0.869731	+	0.502139i	−0.00247223	+	0.999997i	$0.500787\pi$
$878$		0			0
$879$	5.31597	+	4.80761i	0.179303	+	0.162157i
$880$		0			0
$881$			34.5022i			1.16241i	0.813757	+	0.581205i	$0.197419\pi$
$881$			34.5022i			1.16241i	−0.813757	+	0.581205i	$0.802581\pi$
$882$		0			0
$883$	−34.9022			−1.17455			−0.587276	−	0.809387i	$-0.699800\pi$
$883$	−34.9022			−1.17455			−0.587276	+	0.809387i	$0.699800\pi$
$884$		0			0
$885$	16.6100	−	18.3664i	0.558338	−	0.617378i
$886$		0			0
$887$	−20.1225	−	34.8531i	−0.675646	−	1.17025i	−0.976280	−	0.216513i	$-0.930532\pi$
$887$	−20.1225	−	34.8531i	−0.675646	−	1.17025i	0.300634	−	0.953740i	$-0.402802\pi$
$888$		0			0
$889$	22.9140	+	52.8503i	0.768512	+	1.77254i
$890$		0			0
$891$	15.7687	+	5.27643i	0.528272	+	0.176767i
$892$		0			0
$893$	33.1544	−	57.4251i	1.10947	−	1.92166i
$894$		0			0
$895$		−	2.14930i		−	0.0718431i
$896$		0			0
$897$	−3.96926	−	0.852766i	−0.132530	−	0.0284730i
$898$		0			0
$899$	−4.88320	−	2.81931i	−0.162864	−	0.0940294i
$900$		0			0
$901$	46.9757	−	27.1214i	1.56499	−	0.903546i
$902$		0			0
$903$	−26.1581	−	8.84659i	−0.870488	−	0.294396i
$904$		0			0
$905$	−5.00324	+	2.88862i	−0.166313	+	0.0960210i
$906$		0			0
$907$	3.79336	−	6.57028i	0.125956	−	0.218163i	−0.796150	−	0.605099i	$-0.793133\pi$
$907$	3.79336	−	6.57028i	0.125956	−	0.218163i	0.922106	+	0.386937i	$0.126467\pi$
$908$		0			0
$909$	−18.7111	−	8.42892i	−0.620608	−	0.279570i
$910$		0			0
$911$	34.9091			1.15659			0.578294	−	0.815828i	$-0.303719\pi$
$911$	34.9091			1.15659			0.578294	+	0.815828i	$0.303719\pi$
$912$		0			0
$913$	4.38211	−	7.59004i	0.145027	−	0.251194i
$914$		0			0
$915$	6.07293	+	18.8305i	0.200765	+	0.622518i
$916$		0			0
$917$	8.47870	−	11.4332i	0.279991	−	0.377557i
$918$		0			0
$919$	−14.5134	+	8.37933i	−0.478754	+	0.276409i	−0.719897	−	0.694081i	$-0.755811\pi$
$919$	−14.5134	+	8.37933i	−0.478754	+	0.276409i	0.241143	+	0.970490i	$0.422478\pi$
$920$		0			0
$921$	−5.94981	−	5.38083i	−0.196053	−	0.177304i
$922$		0			0
$923$		−	31.5877i		−	1.03972i
$924$		0			0
$925$		−	31.4559i		−	1.03426i
$926$		0			0
$927$	−7.86748	−	10.9288i	−0.258402	−	0.358949i
$928$		0			0
$929$	−18.0406	+	10.4157i	−0.591892	+	0.341729i	−0.765845	−	0.643025i	$-0.777679\pi$
$929$	−18.0406	+	10.4157i	−0.591892	+	0.341729i	0.173953	+	0.984754i	$0.444346\pi$
$930$		0			0
$931$	38.2928	+	8.92528i	1.25499	+	0.292514i
$932$		0			0
$933$	23.2390	−	7.49470i	0.760812	−	0.245366i
$934$		0			0
$935$	5.37240	−	9.30527i	0.175696	−	0.304315i
$936$		0			0
$937$	43.8738			1.43329			0.716647	−	0.697437i	$-0.245676\pi$
$937$	43.8738			1.43329			0.716647	+	0.697437i	$0.245676\pi$
$938$		0			0
$939$	5.06009	−	23.5526i	0.165130	−	0.768609i
$940$		0			0
$941$	−25.3064	+	43.8320i	−0.824966	+	1.42888i	0.0769795	+	0.997033i	$0.475472\pi$
$941$	−25.3064	+	43.8320i	−0.824966	+	1.42888i	−0.901945	+	0.431850i	$0.857861\pi$
$942$		0			0
$943$	1.25735	−	0.725930i	0.0409449	−	0.0236395i
$944$		0			0
$945$	16.9907	−	5.21538i	0.552707	−	0.169656i
$946$		0			0
$947$	31.6220	−	18.2569i	1.02758	−	0.593271i	0.111286	−	0.993788i	$-0.464503\pi$
$947$	31.6220	−	18.2569i	1.02758	−	0.593271i	0.916289	+	0.400517i	$0.131170\pi$
$948$		0			0
$949$	17.1280	+	9.88887i	0.555999	+	0.321006i
$950$		0			0
$951$	−6.07110	+	28.2584i	−0.196869	+	0.916342i
$952$		0			0
$953$		−	19.5458i		−	0.633151i	−0.948567	−	0.316576i	$-0.897467\pi$
$953$		−	19.5458i		−	0.633151i	0.948567	−	0.316576i	$-0.102533\pi$
$954$		0			0
$955$	14.5791	−	25.2517i	0.471768	−	0.817125i
$956$		0			0
$957$	1.29737	+	4.02280i	0.0419381	+	0.130039i
$958$		0			0
$959$	34.5125	+	3.96889i	1.11447	+	0.128162i
$960$		0			0
$961$	−6.38814	−	11.0646i	−0.206069	−	0.356922i
$962$		0			0
$963$	−12.7077	−	17.6524i	−0.409499	−	0.568840i
$964$		0			0
$965$	−7.50596			−0.241625
$966$		0			0
$967$		−	43.0521i		−	1.38446i	−0.721675	−	0.692232i	$-0.756628\pi$
$967$		−	43.0521i		−	1.38446i	0.721675	−	0.692232i	$-0.243372\pi$
$968$		0			0
$969$	29.3560	−	32.4601i	0.943049	−	1.04277i
$970$		0			0
$971$	−27.2617	+	15.7395i	−0.874868	+	0.505105i	−0.868963	−	0.494877i	$-0.835213\pi$
$971$	−27.2617	+	15.7395i	−0.874868	+	0.505105i	−0.00590513	+	0.999983i	$0.501880\pi$
$972$		0			0
$973$	−31.4983	+	13.6566i	−1.00979	+	0.437809i
$974$		0			0
$975$	3.98928	+	12.3697i	0.127759	+	0.396147i
$976$		0			0
$977$	35.4465	+	20.4650i	1.13403	+	0.654734i	0.944946	−	0.327226i	$-0.106114\pi$
$977$	35.4465	+	20.4650i	1.13403	+	0.654734i	0.189087	+	0.981960i	$0.439447\pi$
$978$		0			0
$979$	17.7331			0.566752
$980$		0			0
$981$	15.1784	−	33.6940i	0.484609	−	1.07577i
$982$		0			0
$983$	−4.13945	+	7.16974i	−0.132028	+	0.228679i	−0.924458	−	0.381283i	$-0.875482\pi$
$983$	−4.13945	+	7.16974i	−0.132028	+	0.228679i	0.792430	+	0.609963i	$0.208816\pi$
$984$		0			0
$985$	−2.04181	−	3.53652i	−0.0650574	−	0.112683i
$986$		0			0
$987$	10.6137	+	53.0458i	0.337837	+	1.68847i
$988$		0			0
$989$	3.13268	+	5.42596i	0.0996135	+	0.172536i
$990$		0			0
$991$	−27.2946	−	15.7586i	−0.867043	−	0.500587i	−0.000678305	−	1.00000i	$-0.500216\pi$
$991$	−27.2946	−	15.7586i	−0.867043	−	0.500587i	−0.866364	+	0.499412i	$0.833549\pi$
$992$		0			0
$993$	3.50826	−	16.3295i	0.111331	−	0.518201i
$994$		0			0
$995$		−	18.2646i		−	0.579028i
$996$		0			0
$997$	46.6045	+	26.9071i	1.47598	+	0.852157i	0.999633	−	0.0271004i	$-0.00862738\pi$
$997$	46.6045	+	26.9071i	1.47598	+	0.852157i	0.476347	+	0.879258i	$0.341961\pi$
$998$		0			0
$999$	5.45285	−	48.8000i	0.172521	−	1.54396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bd.a.431.6		56
3.2	odd	2	inner	672.2.bd.a.431.25		56
4.3	odd	2		168.2.v.a.11.13	yes	56
7.2	even	3	inner	672.2.bd.a.527.26		56
8.3	odd	2	inner	672.2.bd.a.431.5		56
8.5	even	2		168.2.v.a.11.4	✓	56
12.11	even	2		168.2.v.a.11.16	yes	56
21.2	odd	6	inner	672.2.bd.a.527.5		56
24.5	odd	2		168.2.v.a.11.25	yes	56
24.11	even	2	inner	672.2.bd.a.431.26		56
28.23	odd	6		168.2.v.a.107.25	yes	56
56.37	even	6		168.2.v.a.107.16	yes	56
56.51	odd	6	inner	672.2.bd.a.527.25		56
84.23	even	6		168.2.v.a.107.4	yes	56
168.107	even	6	inner	672.2.bd.a.527.6		56
168.149	odd	6		168.2.v.a.107.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.4	✓	56	8.5	even	2
168.2.v.a.11.13	yes	56	4.3	odd	2
168.2.v.a.11.16	yes	56	12.11	even	2
168.2.v.a.11.25	yes	56	24.5	odd	2
168.2.v.a.107.4	yes	56	84.23	even	6
168.2.v.a.107.13	yes	56	168.149	odd	6
168.2.v.a.107.16	yes	56	56.37	even	6
168.2.v.a.107.25	yes	56	28.23	odd	6
672.2.bd.a.431.5		56	8.3	odd	2	inner
672.2.bd.a.431.6		56	1.1	even	1	trivial
672.2.bd.a.431.25		56	3.2	odd	2	inner
672.2.bd.a.431.26		56	24.11	even	2	inner
672.2.bd.a.527.5		56	21.2	odd	6	inner
672.2.bd.a.527.6		56	168.107	even	6	inner
672.2.bd.a.527.25		56	56.51	odd	6	inner
672.2.bd.a.527.26		56	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bd (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28463 - 1.16178i) q^{3} +(0.646402 + 1.11960i) q^{5} +(2.42742 - 1.05244i) q^{7} +(0.300539 + 2.98491i) q^{9} +O(q^{10})\)	\(q+(-1.28463 - 1.16178i) q^{3} +(0.646402 + 1.11960i) q^{5} +(2.42742 - 1.05244i) q^{7} +(0.300539 + 2.98491i) q^{9} +(-1.60004 - 0.923782i) q^{11} -2.25432i q^{13} +(0.470342 - 2.18925i) q^{15} +(3.89580 + 2.24924i) q^{17} +(2.80851 + 4.86448i) q^{19} +(-4.34104 - 1.46812i) q^{21} +(0.519880 + 0.900459i) q^{23} +(1.66433 - 2.88270i) q^{25} +(3.08172 - 4.18366i) q^{27} +1.32085 q^{29} +(-3.69700 - 2.13446i) q^{31} +(0.982223 + 3.04561i) q^{33} +(2.74740 + 2.03744i) q^{35} +(8.18394 - 4.72500i) q^{37} +(-2.61902 + 2.89596i) q^{39} -1.39634i q^{41} +6.02578 q^{43} +(-3.14763 + 2.26593i) q^{45} +(-5.90249 - 10.2234i) q^{47} +(4.78472 - 5.10944i) q^{49} +(-2.39154 - 7.41551i) q^{51} +(6.02901 - 10.4425i) q^{53} -2.38854i q^{55} +(2.04356 - 9.51192i) q^{57} +(9.57732 + 5.52947i) q^{59} +(-7.65220 + 4.41800i) q^{61} +(3.87098 + 6.92932i) q^{63} +(2.52393 - 1.45719i) q^{65} +(-3.05545 + 5.29219i) q^{67} +(0.378281 - 1.76074i) q^{69} +14.0121 q^{71} +(-4.38664 + 7.59788i) q^{73} +(-5.48711 + 1.76962i) q^{75} +(-4.85619 - 0.558456i) q^{77} +(2.37061 - 1.36867i) q^{79} +(-8.81935 + 1.79416i) q^{81} +4.74366i q^{83} +5.81566i q^{85} +(-1.69681 - 1.53454i) q^{87} +(-8.31219 + 4.79904i) q^{89} +(-2.37254 - 5.47217i) q^{91} +(2.26949 + 7.03709i) q^{93} +(-3.63085 + 6.28882i) q^{95} -8.73466 q^{97} +(2.27653 - 5.05360i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 2 q^{9}+O(q^{10}) \) 56 * q + 2 * q^3 - 2 * q^9	\( 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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