LMFDB - Embedded newform 1890.2.t.c.1151.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1151,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("1890.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.t (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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.9
Character	$\chi$	$=$	1890.1151
Dual form			1890.2.t.c.1601.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-2.63727 - 0.211686i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-2.63727 - 0.211686i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} -4.91498i q^{11} +(3.91899 + 2.26263i) q^{13} +(-2.17810 - 1.50196i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.06626 + 3.57887i) q^{17} +(6.89368 - 3.98007i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(2.45749 - 4.25650i) q^{22} +5.03744i q^{23} +1.00000 q^{25} +(2.26263 + 3.91899i) q^{26} +(-1.13531 - 2.38979i) q^{28} +(2.46914 - 1.42556i) q^{29} +(1.36826 - 0.789963i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.57887 + 2.06626i) q^{34} +(2.63727 + 0.211686i) q^{35} +(5.05807 + 8.76083i) q^{37} +7.96013 q^{38} -1.00000i q^{40} +(4.31484 - 7.47352i) q^{41} +(-2.88672 - 4.99995i) q^{43} +(4.25650 - 2.45749i) q^{44} +(-2.51872 + 4.36255i) q^{46} +(-0.227083 + 0.393319i) q^{47} +(6.91038 + 1.11655i) q^{49} +(0.866025 + 0.500000i) q^{50} +4.52526i q^{52} +(10.7712 + 6.21874i) q^{53} +4.91498i q^{55} +(0.211686 - 2.63727i) q^{56} +2.85112 q^{58} +(5.48237 + 9.49575i) q^{59} +(3.66392 + 2.11537i) q^{61} +1.57993 q^{62} -1.00000 q^{64} +(-3.91899 - 2.26263i) q^{65} +(-1.96604 - 3.40527i) q^{67} -4.13252 q^{68} +(2.17810 + 1.50196i) q^{70} -8.14278i q^{71} +(2.06838 + 1.19418i) q^{73} +10.1161i q^{74} +(6.89368 + 3.98007i) q^{76} +(-1.04044 + 12.9621i) q^{77} +(-4.86467 + 8.42586i) q^{79} +(0.500000 - 0.866025i) q^{80} +(7.47352 - 4.31484i) q^{82} +(1.42589 + 2.46971i) q^{83} +(2.06626 - 3.57887i) q^{85} -5.77345i q^{86} +4.91498 q^{88} +(-2.95275 - 5.11432i) q^{89} +(-9.85647 - 6.79677i) q^{91} +(-4.36255 + 2.51872i) q^{92} +(-0.393319 + 0.227083i) q^{94} +(-6.89368 + 3.98007i) q^{95} +(1.74470 - 1.00730i) q^{97} +(5.42629 + 4.42215i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7}+O(q^{10}) $ 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7	$ 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7} - 16 q^{16} - 6 q^{17} - 16 q^{20} + 32 q^{25} - 12 q^{26} + 2 q^{28} - 6 q^{29} + 18 q^{31} + 2 q^{35} + 2 q^{37} + 6 q^{41} - 28 q^{43} + 6 q^{44} - 24 q^{47} + 32 q^{49} + 36 q^{53} + 6 q^{56} + 30 q^{59} + 54 q^{61} - 32 q^{64} + 4 q^{67} - 12 q^{68} - 30 q^{73} + 6 q^{77} + 4 q^{79} + 16 q^{80} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 12 q^{89} - 66 q^{91} + 18 q^{92} - 42 q^{94} + 96 q^{97} + 24 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7 - 16 * q^16 - 6 * q^17 - 16 * q^20 + 32 * q^25 - 12 * q^26 + 2 * q^28 - 6 * q^29 + 18 * q^31 + 2 * q^35 + 2 * q^37 + 6 * q^41 - 28 * q^43 + 6 * q^44 - 24 * q^47 + 32 * q^49 + 36 * q^53 + 6 * q^56 + 30 * q^59 + 54 * q^61 - 32 * q^64 + 4 * q^67 - 12 * q^68 - 30 * q^73 + 6 * q^77 + 4 * q^79 + 16 * q^80 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 12 * q^89 - 66 * q^91 + 18 * q^92 - 42 * q^94 + 96 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−2.63727	−	0.211686i	−0.996794	−	0.0800100i
$7$	−2.63727	−	0.211686i	−0.996794	−	0.0800100i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$		−	4.91498i		−	1.48192i	−0.671548	−	0.740961i	$-0.734370\pi$
$11$		−	4.91498i		−	1.48192i	0.671548	−	0.740961i	$-0.265630\pi$
$12$		0			0
$13$	3.91899	+	2.26263i	1.08693	+	0.627541i	0.932758	−	0.360502i	$-0.117395\pi$
$13$	3.91899	+	2.26263i	1.08693	+	0.627541i	0.154175	+	0.988044i	$0.450728\pi$
$14$	−2.17810	−	1.50196i	−0.582121	−	0.401416i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.06626	+	3.57887i	−0.501142	+	0.868003i	0.498857	+	0.866684i	$0.333753\pi$
$17$	−2.06626	+	3.57887i	−0.501142	+	0.868003i	−0.999999	+	0.00131881i	$0.999580\pi$
$18$		0			0
$19$	6.89368	−	3.98007i	1.58152	−	0.913090i	0.586880	−	0.809674i	$-0.300356\pi$
$19$	6.89368	−	3.98007i	1.58152	−	0.913090i	0.994638	−	0.103416i	$-0.0329772\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	2.45749	−	4.25650i	0.523939	−	0.907489i
$23$			5.03744i			1.05038i	0.850986	+	0.525189i	$0.176005\pi$
$23$			5.03744i			1.05038i	−0.850986	+	0.525189i	$0.823995\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	2.26263	+	3.91899i	0.443739	+	0.768578i
$27$		0			0
$28$	−1.13531	−	2.38979i	−0.214553	−	0.451627i
$29$	2.46914	−	1.42556i	0.458508	−	0.264720i	−0.252909	−	0.967490i	$-0.581387\pi$
$29$	2.46914	−	1.42556i	0.458508	−	0.264720i	0.711417	+	0.702770i	$0.248054\pi$
$30$		0			0
$31$	1.36826	−	0.789963i	0.245746	−	0.141882i	−0.372069	−	0.928205i	$-0.621351\pi$
$31$	1.36826	−	0.789963i	0.245746	−	0.141882i	0.617815	+	0.786324i	$0.288018\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−3.57887	+	2.06626i	−0.613771	+	0.354361i
$35$	2.63727	+	0.211686i	0.445780	+	0.0357815i
$36$		0			0
$37$	5.05807	+	8.76083i	0.831541	+	1.44027i	0.896816	+	0.442404i	$0.145874\pi$
$37$	5.05807	+	8.76083i	0.831541	+	1.44027i	−0.0652749	+	0.997867i	$0.520792\pi$
$38$	7.96013			1.29130
$39$		0			0
$40$		−	1.00000i		−	0.158114i
$41$	4.31484	−	7.47352i	0.673865	−	1.16717i	−0.302935	−	0.953011i	$-0.597966\pi$
$41$	4.31484	−	7.47352i	0.673865	−	1.16717i	0.976799	−	0.214156i	$-0.0687002\pi$
$42$		0			0
$43$	−2.88672	−	4.99995i	−0.440221	−	0.762486i	0.557484	−	0.830187i	$-0.311767\pi$
$43$	−2.88672	−	4.99995i	−0.440221	−	0.762486i	−0.997706	+	0.0677018i	$0.978433\pi$
$44$	4.25650	−	2.45749i	0.641691	−	0.370481i
$45$		0			0
$46$	−2.51872	+	4.36255i	−0.371365	+	0.643223i
$47$	−0.227083	+	0.393319i	−0.0331234	+	0.0573714i	−0.882112	−	0.471040i	$-0.843879\pi$
$47$	−0.227083	+	0.393319i	−0.0331234	+	0.0573714i	0.848988	+	0.528411i	$0.177212\pi$
$48$		0			0
$49$	6.91038	+	1.11655i	0.987197	+	0.159507i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$			4.52526i			0.627541i
$53$	10.7712	+	6.21874i	1.47953	+	0.854209i	0.999732	−	0.0231676i	$-0.00737512\pi$
$53$	10.7712	+	6.21874i	1.47953	+	0.854209i	0.479802	+	0.877377i	$0.340708\pi$
$54$		0			0
$55$			4.91498i			0.662736i
$56$	0.211686	−	2.63727i	0.0282878	−	0.352420i
$57$		0			0
$58$	2.85112			0.374370
$59$	5.48237	+	9.49575i	0.713744	+	1.23624i	0.963442	+	0.267917i	$0.0863353\pi$
$59$	5.48237	+	9.49575i	0.713744	+	1.23624i	−0.249698	+	0.968324i	$0.580331\pi$
$60$		0			0
$61$	3.66392	+	2.11537i	0.469117	+	0.270845i	0.715870	−	0.698233i	$-0.246030\pi$
$61$	3.66392	+	2.11537i	0.469117	+	0.270845i	−0.246753	+	0.969078i	$0.579364\pi$
$62$	1.57993			0.200651
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.91899	−	2.26263i	−0.486091	−	0.280645i
$66$		0			0
$67$	−1.96604	−	3.40527i	−0.240189	−	0.416020i	0.720579	−	0.693373i	$-0.243876\pi$
$67$	−1.96604	−	3.40527i	−0.240189	−	0.416020i	−0.960768	+	0.277353i	$0.910543\pi$
$68$	−4.13252			−0.501142
$69$		0			0
$70$	2.17810	+	1.50196i	0.260333	+	0.179519i
$71$		−	8.14278i		−	0.966371i	−0.875518	−	0.483185i	$-0.839480\pi$
$71$		−	8.14278i		−	0.966371i	0.875518	−	0.483185i	$-0.160520\pi$
$72$		0			0
$73$	2.06838	+	1.19418i	0.242086	+	0.139768i	0.616135	−	0.787641i	$-0.288698\pi$
$73$	2.06838	+	1.19418i	0.242086	+	0.139768i	−0.374049	+	0.927409i	$0.622031\pi$
$74$			10.1161i			1.17598i
$75$		0			0
$76$	6.89368	+	3.98007i	0.790759	+	0.456545i
$77$	−1.04044	+	12.9621i	−0.118569	+	1.47717i
$78$		0			0
$79$	−4.86467	+	8.42586i	−0.547318	+	0.947983i	0.451139	+	0.892454i	$0.351018\pi$
$79$	−4.86467	+	8.42586i	−0.547318	+	0.947983i	−0.998457	+	0.0555291i	$0.982315\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	7.47352	−	4.31484i	0.825312	−	0.476494i
$83$	1.42589	+	2.46971i	0.156512	+	0.271086i	0.933608	−	0.358295i	$-0.116642\pi$
$83$	1.42589	+	2.46971i	0.156512	+	0.271086i	−0.777097	+	0.629381i	$0.783309\pi$
$84$		0			0
$85$	2.06626	−	3.57887i	0.224117	−	0.388183i
$86$		−	5.77345i		−	0.622567i
$87$		0			0
$88$	4.91498			0.523939
$89$	−2.95275	−	5.11432i	−0.312991	−	0.542117i	0.666017	−	0.745936i	$-0.267998\pi$
$89$	−2.95275	−	5.11432i	−0.312991	−	0.542117i	−0.979008	+	0.203820i	$0.934664\pi$
$90$		0			0
$91$	−9.85647	−	6.79677i	−1.03324	−	0.712495i
$92$	−4.36255	+	2.51872i	−0.454827	+	0.262595i
$93$		0			0
$94$	−0.393319	+	0.227083i	−0.0405677	+	0.0234218i
$95$	−6.89368	+	3.98007i	−0.707276	+	0.408346i
$96$		0			0
$97$	1.74470	−	1.00730i	0.177147	−	0.102276i	−0.408805	−	0.912622i	$-0.634054\pi$
$97$	1.74470	−	1.00730i	0.177147	−	0.102276i	0.585952	+	0.810346i	$0.300721\pi$
$98$	5.42629	+	4.42215i	0.548138	+	0.446704i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	6.47106			0.643895			0.321947	−	0.946758i	$-0.395663\pi$
$101$	6.47106			0.643895			0.321947	+	0.946758i	$0.395663\pi$
$102$		0			0
$103$		−	4.11259i		−	0.405226i	−0.979259	−	0.202613i	$-0.935057\pi$
$103$		−	4.11259i		−	0.405226i	0.979259	−	0.202613i	$-0.0649433\pi$
$104$	−2.26263	+	3.91899i	−0.221869	+	0.384289i
$105$		0			0
$106$	6.21874	+	10.7712i	0.604017	+	1.04619i
$107$	10.8227	−	6.24846i	1.04627	−	0.604061i	0.124664	−	0.992199i	$-0.460215\pi$
$107$	10.8227	−	6.24846i	1.04627	−	0.604061i	0.921601	+	0.388138i	$0.126881\pi$
$108$		0			0
$109$	−6.80795	+	11.7917i	−0.652083	+	1.12944i	0.330533	+	0.943794i	$0.392771\pi$
$109$	−6.80795	+	11.7917i	−0.652083	+	1.12944i	−0.982617	+	0.185647i	$0.940562\pi$
$110$	−2.45749	+	4.25650i	−0.234313	+	0.405841i
$111$		0			0
$112$	1.50196	−	2.17810i	0.141922	−	0.205811i
$113$	−14.5943	−	8.42603i	−1.37292	−	0.792655i	−0.381623	−	0.924318i	$-0.624635\pi$
$113$	−14.5943	−	8.42603i	−1.37292	−	0.792655i	−0.991294	+	0.131663i	$0.957968\pi$
$114$		0			0
$115$		−	5.03744i		−	0.469743i
$116$	2.46914	+	1.42556i	0.229254	+	0.132360i
$117$		0			0
$118$			10.9647i			1.00939i
$119$	6.20688	−	9.00104i	0.568984	−	0.825124i
$120$		0			0
$121$	−13.1570			−1.19610
$122$	2.11537	+	3.66392i	0.191516	+	0.331716i
$123$		0			0
$124$	1.36826	+	0.789963i	0.122873	+	0.0709408i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	10.8636			0.963991			0.481996	−	0.876174i	$-0.339912\pi$
$127$	10.8636			0.963991			0.481996	+	0.876174i	$0.339912\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−2.26263	−	3.91899i	−0.198446	−	0.343719i
$131$	4.65956			0.407108			0.203554	−	0.979064i	$-0.434751\pi$
$131$	4.65956			0.407108			0.203554	+	0.979064i	$0.434751\pi$
$132$		0			0
$133$	−19.0230	+	9.03721i	−1.64950	+	0.783625i
$134$		−	3.93207i		−	0.339679i
$135$		0			0
$136$	−3.57887	−	2.06626i	−0.306885	−	0.177180i
$137$			9.91164i			0.846808i	0.905941	+	0.423404i	$0.139165\pi$
$137$			9.91164i			0.846808i	−0.905941	+	0.423404i	$0.860835\pi$
$138$		0			0
$139$	0.175478	+	0.101312i	0.0148838	+	0.00859319i	0.507423	−	0.861697i	$-0.330598\pi$
$139$	0.175478	+	0.101312i	0.0148838	+	0.00859319i	−0.492540	+	0.870290i	$0.663931\pi$
$140$	1.13531	+	2.38979i	0.0959511	+	0.201974i
$141$		0			0
$142$	4.07139	−	7.05186i	0.341664	−	0.591779i
$143$	11.1208	−	19.2618i	0.929968	−	1.61075i
$144$		0			0
$145$	−2.46914	+	1.42556i	−0.205051	+	0.118386i
$146$	1.19418	+	2.06838i	0.0988311	+	0.171181i
$147$		0			0
$148$	−5.05807	+	8.76083i	−0.415770	+	0.720136i
$149$			3.00122i			0.245869i	0.992415	+	0.122935i	$0.0392305\pi$
$149$			3.00122i			0.245869i	−0.992415	+	0.122935i	$0.960769\pi$
$150$		0			0
$151$	−19.7332			−1.60587			−0.802935	−	0.596067i	$-0.796729\pi$
$151$	−19.7332			−1.60587			−0.802935	+	0.596067i	$0.796729\pi$
$152$	3.98007	+	6.89368i	0.322826	+	0.559151i
$153$		0			0
$154$	−7.38211	+	10.7053i	−0.594867	+	0.862659i
$155$	−1.36826	+	0.789963i	−0.109901	+	0.0634514i
$156$		0			0
$157$	7.30661	−	4.21847i	0.583131	−	0.336671i	−0.179246	−	0.983804i	$-0.557366\pi$
$157$	7.30661	−	4.21847i	0.583131	−	0.336671i	0.762377	+	0.647134i	$0.224032\pi$
$158$	−8.42586	+	4.86467i	−0.670325	+	0.387012i
$159$		0			0
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	1.06636	−	13.2851i	0.0840407	−	1.04701i
$162$		0			0
$163$	−6.64195	−	11.5042i	−0.520238	−	0.901079i	−0.999723	−	0.0235286i	$-0.992510\pi$
$163$	−6.64195	−	11.5042i	−0.520238	−	0.901079i	0.479485	−	0.877550i	$-0.340823\pi$
$164$	8.62968			0.673865
$165$		0			0
$166$			2.85178i			0.221341i
$167$	8.15100	−	14.1179i	0.630743	−	1.09248i	−0.356657	−	0.934235i	$-0.616084\pi$
$167$	8.15100	−	14.1179i	0.630743	−	1.09248i	0.987400	−	0.158243i	$-0.0505831\pi$
$168$		0			0
$169$	3.73901	+	6.47616i	0.287616	+	0.498166i
$170$	3.57887	−	2.06626i	0.274487	−	0.158475i
$171$		0			0
$172$	2.88672	−	4.99995i	0.220111	−	0.381243i
$173$	10.6052	−	18.3687i	0.806295	−	1.39654i	−0.109119	−	0.994029i	$-0.534803\pi$
$173$	10.6052	−	18.3687i	0.806295	−	1.39654i	0.915413	−	0.402515i	$-0.131864\pi$
$174$		0			0
$175$	−2.63727	−	0.211686i	−0.199359	−	0.0160020i
$176$	4.25650	+	2.45749i	0.320846	+	0.185240i
$177$		0			0
$178$		−	5.90551i		−	0.442636i
$179$	−2.93274	−	1.69322i	−0.219203	−	0.126557i	0.386378	−	0.922341i	$-0.373726\pi$
$179$	−2.93274	−	1.69322i	−0.219203	−	0.126557i	−0.605581	+	0.795783i	$0.707059\pi$
$180$		0			0
$181$		−	4.99826i		−	0.371517i	−0.982595	−	0.185759i	$-0.940526\pi$
$181$		−	4.99826i		−	0.371517i	0.982595	−	0.185759i	$-0.0594743\pi$
$182$	−5.13757	−	10.8144i	−0.380822	−	0.801617i
$183$		0			0
$184$	−5.03744			−0.371365
$185$	−5.05807	−	8.76083i	−0.371876	−	0.644109i
$186$		0			0
$187$	17.5901	+	10.1556i	1.28631	+	0.742653i
$188$	−0.454165			−0.0331234
$189$		0			0
$190$	−7.96013			−0.577489
$191$	−4.95729	−	2.86209i	−0.358697	−	0.207094i	0.309812	−	0.950798i	$-0.399734\pi$
$191$	−4.95729	−	2.86209i	−0.358697	−	0.207094i	−0.668509	+	0.743704i	$0.733067\pi$
$192$		0			0
$193$	−2.70156	−	4.67925i	−0.194463	−	0.336820i	0.752261	−	0.658865i	$-0.228963\pi$
$193$	−2.70156	−	4.67925i	−0.194463	−	0.336820i	−0.946724	+	0.322045i	$0.895630\pi$
$194$	2.01460			0.144640
$195$		0			0
$196$	2.48823	+	6.54284i	0.177731	+	0.467345i
$197$			12.5138i			0.891571i	0.895140	+	0.445786i	$0.147076\pi$
$197$			12.5138i			0.891571i	−0.895140	+	0.445786i	$0.852924\pi$
$198$		0			0
$199$	−15.4969	−	8.94715i	−1.09855	−	0.634247i	−0.162708	−	0.986674i	$-0.552023\pi$
$199$	−15.4969	−	8.94715i	−1.09855	−	0.634247i	−0.935839	+	0.352428i	$0.885356\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	5.60410	+	3.23553i	0.394303	+	0.227651i
$203$	−6.81356	+	3.23690i	−0.478218	+	0.227186i
$204$		0			0
$205$	−4.31484	+	7.47352i	−0.301361	+	0.521973i
$206$	2.05630	−	3.56161i	0.143269	−	0.248149i
$207$		0			0
$208$	−3.91899	+	2.26263i	−0.271733	+	0.156885i
$209$	−19.5620	−	33.8823i	−1.35313	−	2.34369i
$210$		0			0
$211$	−8.73086	+	15.1223i	−0.601057	+	1.04106i	0.391604	+	0.920134i	$0.371920\pi$
$211$	−8.73086	+	15.1223i	−0.601057	+	1.04106i	−0.992661	+	0.120928i	$0.961413\pi$
$212$			12.4375i			0.854209i
$213$		0			0
$214$	12.4969			0.854272
$215$	2.88672	+	4.99995i	0.196873	+	0.340994i
$216$		0			0
$217$	−3.77568	+	1.79370i	−0.256310	+	0.121765i
$218$	−11.7917	+	6.80795i	−0.798636	+	0.461092i
$219$		0			0
$220$	−4.25650	+	2.45749i	−0.286973	+	0.165684i
$221$	−16.1953	+	9.35037i	−1.08942	+	0.628974i
$222$		0			0
$223$	9.84741	−	5.68541i	0.659431	−	0.380723i	−0.132629	−	0.991166i	$-0.542342\pi$
$223$	9.84741	−	5.68541i	0.659431	−	0.380723i	0.792060	+	0.610443i	$0.209008\pi$
$224$	2.38979	−	1.13531i	0.159674	−	0.0758560i
$225$		0			0
$226$	−8.42603	−	14.5943i	−0.560491	−	0.970800i
$227$	7.08592			0.470309			0.235155	−	0.971958i	$-0.424440\pi$
$227$	7.08592			0.470309			0.235155	+	0.971958i	$0.424440\pi$
$228$		0			0
$229$			3.05403i			0.201816i	0.994896	+	0.100908i	$0.0321748\pi$
$229$			3.05403i			0.201816i	−0.994896	+	0.100908i	$0.967825\pi$
$230$	2.51872	−	4.36255i	0.166079	−	0.287658i
$231$		0			0
$232$	1.42556	+	2.46914i	0.0935925	+	0.162107i
$233$	−18.5443	+	10.7066i	−1.21488	+	0.701410i	−0.963818	−	0.266562i	$-0.914112\pi$
$233$	−18.5443	+	10.7066i	−1.21488	+	0.701410i	−0.251060	+	0.967972i	$0.580779\pi$
$234$		0			0
$235$	0.227083	−	0.393319i	0.0148132	−	0.0256573i
$236$	−5.48237	+	9.49575i	−0.356872	+	0.618120i
$237$		0			0
$238$	9.87584	−	4.69169i	0.640155	−	0.304117i
$239$	15.7328	+	9.08336i	1.01767	+	0.587554i	0.913429	−	0.406998i	$-0.133424\pi$
$239$	15.7328	+	9.08336i	1.01767	+	0.587554i	0.104244	+	0.994552i	$0.466758\pi$
$240$		0			0
$241$			20.8546i			1.34336i	0.740840	+	0.671681i	$0.234428\pi$
$241$			20.8546i			1.34336i	−0.740840	+	0.671681i	$0.765572\pi$
$242$	−11.3943	−	6.57852i	−0.732456	−	0.422883i
$243$		0			0
$244$			4.23073i			0.270845i
$245$	−6.91038	−	1.11655i	−0.441488	−	0.0713337i
$246$		0			0
$247$	36.0217			2.29201
$248$	0.789963	+	1.36826i	0.0501627	+	0.0868844i
$249$		0			0
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	27.8633			1.75872			0.879359	−	0.476159i	$-0.157971\pi$
$251$	27.8633			1.75872			0.879359	+	0.476159i	$0.157971\pi$
$252$		0			0
$253$	24.7589			1.55658
$254$	9.40818	+	5.43182i	0.590322	+	0.340822i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	17.0070			1.06087			0.530433	−	0.847727i	$-0.322029\pi$
$257$	17.0070			1.06087			0.530433	+	0.847727i	$0.322029\pi$
$258$		0			0
$259$	−11.4849	−	24.1754i	−0.713639	−	1.50219i
$260$		−	4.52526i		−	0.280645i
$261$		0			0
$262$	4.03530	+	2.32978i	0.249302	+	0.143934i
$263$			3.06763i			0.189158i	0.995517	+	0.0945791i	$0.0301505\pi$
$263$			3.06763i			0.189158i	−0.995517	+	0.0945791i	$0.969849\pi$
$264$		0			0
$265$	−10.7712	−	6.21874i	−0.661668	−	0.382014i
$266$	−20.9930	−	1.68505i	−1.28716	−	0.103317i
$267$		0			0
$268$	1.96604	−	3.40527i	0.120095	−	0.208010i
$269$	3.48949	−	6.04397i	0.212758	−	0.368507i	−0.739819	−	0.672806i	$-0.765089\pi$
$269$	3.48949	−	6.04397i	0.212758	−	0.368507i	0.952577	+	0.304299i	$0.0984222\pi$
$270$		0			0
$271$	1.95182	−	1.12689i	0.118565	−	0.0684534i	−0.439545	−	0.898221i	$-0.644860\pi$
$271$	1.95182	−	1.12689i	0.118565	−	0.0684534i	0.558110	+	0.829767i	$0.311527\pi$
$272$	−2.06626	−	3.57887i	−0.125285	−	0.217001i
$273$		0			0
$274$	−4.95582	+	8.58373i	−0.299392	+	0.518562i
$275$		−	4.91498i		−	0.296385i
$276$		0			0
$277$	−28.3005			−1.70042			−0.850208	−	0.526448i	$-0.823524\pi$
$277$	−28.3005			−1.70042			−0.850208	+	0.526448i	$0.823524\pi$
$278$	0.101312	+	0.175478i	0.00607631	+	0.0105245i
$279$		0			0
$280$	−0.211686	+	2.63727i	−0.0126507	+	0.157607i
$281$	−10.7190	+	6.18859i	−0.639439	+	0.369180i	−0.784399	−	0.620257i	$-0.787028\pi$
$281$	−10.7190	+	6.18859i	−0.639439	+	0.369180i	0.144959	+	0.989438i	$0.453695\pi$
$282$		0			0
$283$	−18.7596	+	10.8309i	−1.11514	+	0.643827i	−0.940156	−	0.340744i	$-0.889321\pi$
$283$	−18.7596	+	10.8309i	−1.11514	+	0.643827i	−0.174985	+	0.984571i	$0.555988\pi$
$284$	7.05186	−	4.07139i	0.418451	−	0.241593i
$285$		0			0
$286$	19.2618	−	11.1208i	1.13897	−	0.657586i
$287$	−12.9614	+	18.7963i	−0.765089	+	1.10951i
$288$		0			0
$289$	−0.0388616	−	0.0673103i	−0.00228598	−	0.00395943i
$290$	−2.85112			−0.167423
$291$		0			0
$292$			2.38836i			0.139768i
$293$	1.38901	−	2.40584i	0.0811469	−	0.140551i	−0.822596	−	0.568626i	$-0.807475\pi$
$293$	1.38901	−	2.40584i	0.0811469	−	0.140551i	0.903743	+	0.428076i	$0.140808\pi$
$294$		0			0
$295$	−5.48237	−	9.49575i	−0.319196	−	0.552864i
$296$	−8.76083	+	5.05807i	−0.509213	+	0.293994i
$297$		0			0
$298$	−1.50061	+	2.59913i	−0.0869279	+	0.150564i
$299$	−11.3979	+	19.7417i	−0.659156	+	1.14169i
$300$		0			0
$301$	6.55465	+	13.7973i	0.377804	+	0.795263i
$302$	−17.0895	−	9.86662i	−0.983390	−	0.567760i
$303$		0			0
$304$			7.96013i			0.456545i
$305$	−3.66392	−	2.11537i	−0.209796	−	0.121126i
$306$		0			0
$307$			3.67227i			0.209588i	0.994494	+	0.104794i	$0.0334183\pi$
$307$			3.67227i			0.209588i	−0.994494	+	0.104794i	$0.966582\pi$
$308$	−11.7458	+	5.58002i	−0.669276	+	0.317951i
$309$		0			0
$310$	−1.57993			−0.0897338
$311$	−3.66692	−	6.35130i	−0.207932	−	0.360149i	0.743131	−	0.669146i	$-0.233340\pi$
$311$	−3.66692	−	6.35130i	−0.207932	−	0.360149i	−0.951063	+	0.308997i	$0.900007\pi$
$312$		0			0
$313$	−24.7521	−	14.2906i	−1.39907	−	0.807753i	−0.404775	−	0.914417i	$-0.632650\pi$
$313$	−24.7521	−	14.2906i	−1.39907	−	0.807753i	−0.994295	+	0.106663i	$0.965983\pi$
$314$	8.43694			0.476124
$315$		0			0
$316$	−9.72934			−0.547318
$317$	−5.83771	−	3.37041i	−0.327879	−	0.189301i	0.327020	−	0.945017i	$-0.393955\pi$
$317$	−5.83771	−	3.37041i	−0.327879	−	0.189301i	−0.654899	+	0.755717i	$0.727289\pi$
$318$		0			0
$319$	−7.00660	−	12.1358i	−0.392294	−	0.679473i
$320$	1.00000			0.0559017
$321$		0			0
$322$	7.56603	−	10.9720i	0.421638	−	0.611448i
$323$			32.8954i			1.83035i
$324$		0			0
$325$	3.91899	+	2.26263i	0.217387	+	0.125508i
$326$		−	13.2839i		−	0.735728i
$327$		0			0
$328$	7.47352	+	4.31484i	0.412656	+	0.238247i
$329$	0.682138	−	0.989217i	0.0376075	−	0.0545373i
$330$		0			0
$331$	14.4113	−	24.9612i	0.792119	−	1.37199i	−0.132534	−	0.991178i	$-0.542311\pi$
$331$	14.4113	−	24.9612i	0.792119	−	1.37199i	0.924653	−	0.380811i	$-0.124355\pi$
$332$	−1.42589	+	2.46971i	−0.0782558	+	0.135543i
$333$		0			0
$334$	14.1179	−	8.15100i	0.772499	−	0.446003i
$335$	1.96604	+	3.40527i	0.107416	+	0.186050i
$336$		0			0
$337$	12.0913	−	20.9427i	0.658652	−	1.14082i	−0.322312	−	0.946633i	$-0.604460\pi$
$337$	12.0913	−	20.9427i	0.658652	−	1.14082i	0.980965	−	0.194186i	$-0.0622065\pi$
$338$			7.47802i			0.406751i
$339$		0			0
$340$	4.13252			0.224117
$341$	−3.88265	−	6.72496i	−0.210258	−	0.364177i
$342$		0			0
$343$	−17.9882	−	4.40747i	−0.971270	−	0.237981i
$344$	4.99995	−	2.88672i	0.269579	−	0.155642i
$345$		0			0
$346$	18.3687	−	10.6052i	0.987505	−	0.570137i
$347$	−15.0958	+	8.71559i	−0.810387	+	0.467877i	−0.847090	−	0.531449i	$-0.821648\pi$
$347$	−15.0958	+	8.71559i	−0.810387	+	0.467877i	0.0367033	+	0.999326i	$0.488314\pi$
$348$		0			0
$349$	31.4274	−	18.1446i	1.68227	−	0.971259i	0.722122	−	0.691766i	$-0.243167\pi$
$349$	31.4274	−	18.1446i	1.68227	−	0.971259i	0.960148	−	0.279493i	$-0.0901665\pi$
$350$	−2.17810	−	1.50196i	−0.116424	−	0.0802832i
$351$		0			0
$352$	2.45749	+	4.25650i	0.130985	+	0.226872i
$353$	−21.7513			−1.15770			−0.578852	−	0.815432i	$-0.696499\pi$
$353$	−21.7513			−1.15770			−0.578852	+	0.815432i	$0.696499\pi$
$354$		0			0
$355$			8.14278i			0.432174i
$356$	2.95275	−	5.11432i	0.156496	−	0.271058i
$357$		0			0
$358$	−1.69322	−	2.93274i	−0.0894894	−	0.155000i
$359$	−19.5772	+	11.3029i	−1.03325	+	0.596544i	−0.917913	−	0.396783i	$-0.870127\pi$
$359$	−19.5772	+	11.3029i	−1.03325	+	0.596544i	−0.115333	+	0.993327i	$0.536793\pi$
$360$		0			0
$361$	22.1819	−	38.4201i	1.16747	−	2.02211i
$362$	2.49913	−	4.32862i	0.131351	−	0.227507i
$363$		0			0
$364$	0.957937	−	11.9343i	0.0502096	−	0.625529i
$365$	−2.06838	−	1.19418i	−0.108264	−	0.0625063i
$366$		0			0
$367$			12.1778i			0.635676i	0.948145	+	0.317838i	$0.102957\pi$
$367$			12.1778i			0.635676i	−0.948145	+	0.317838i	$0.897043\pi$
$368$	−4.36255	−	2.51872i	−0.227414	−	0.131297i
$369$		0			0
$370$		−	10.1161i		−	0.525913i
$371$	−27.0900	−	18.6806i	−1.40645	−	0.969848i
$372$		0			0
$373$	−29.4797			−1.52640			−0.763199	−	0.646163i	$-0.776373\pi$
$373$	−29.4797			−1.52640			−0.763199	+	0.646163i	$0.776373\pi$
$374$	10.1556	+	17.5901i	0.525135	+	0.909561i
$375$		0			0
$376$	−0.393319	−	0.227083i	−0.0202839	−	0.0117109i
$377$	12.9021			0.664490
$378$		0			0
$379$	27.9939			1.43795			0.718974	−	0.695037i	$-0.244612\pi$
$379$	27.9939			1.43795			0.718974	+	0.695037i	$0.244612\pi$
$380$	−6.89368	−	3.98007i	−0.353638	−	0.204173i
$381$		0			0
$382$	−2.86209	−	4.95729i	−0.146437	−	0.253637i
$383$	13.6842			0.699229			0.349615	−	0.936894i	$-0.386313\pi$
$383$	13.6842			0.699229			0.349615	+	0.936894i	$0.386313\pi$
$384$		0			0
$385$	1.04044	−	12.9621i	0.0530255	−	0.660611i
$386$		−	5.40313i		−	0.275012i
$387$		0			0
$388$	1.74470	+	1.00730i	0.0885735	+	0.0511379i
$389$			6.87117i			0.348382i	0.984712	+	0.174191i	$0.0557310\pi$
$389$			6.87117i			0.348382i	−0.984712	+	0.174191i	$0.944269\pi$
$390$		0			0
$391$	−18.0283	−	10.4087i	−0.911731	−	0.526388i
$392$	−1.11655	+	6.91038i	−0.0563942	+	0.349027i
$393$		0			0
$394$	−6.25690	+	10.8373i	−0.315218	+	0.545974i
$395$	4.86467	−	8.42586i	0.244768	−	0.423951i
$396$		0			0
$397$	−4.44511	+	2.56639i	−0.223094	+	0.128803i	−0.607382	−	0.794410i	$-0.707780\pi$
$397$	−4.44511	+	2.56639i	−0.223094	+	0.128803i	0.384288	+	0.923213i	$0.374447\pi$
$398$	−8.94715	−	15.4969i	−0.448480	−	0.776790i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	8.86214i		−	0.442554i	−0.975211	−	0.221277i	$-0.928978\pi$
$401$		−	8.86214i		−	0.442554i	0.975211	−	0.221277i	$-0.0710225\pi$
$402$		0			0
$403$	7.14959			0.356146
$404$	3.23553	+	5.60410i	0.160974	+	0.278815i
$405$		0			0
$406$	−7.51917	−	0.603543i	−0.373170	−	0.0299533i
$407$	43.0593	−	24.8603i	2.13437	−	1.23228i
$408$		0			0
$409$	−2.25993	+	1.30477i	−0.111746	+	0.0645167i	−0.554831	−	0.831963i	$-0.687217\pi$
$409$	−2.25993	+	1.30477i	−0.111746	+	0.0645167i	0.443085	+	0.896480i	$0.353884\pi$
$410$	−7.47352	+	4.31484i	−0.369091	+	0.213095i
$411$		0			0
$412$	3.56161	−	2.05630i	0.175468	−	0.101306i
$413$	−12.4484	−	26.2034i	−0.612544	−	1.28938i
$414$		0			0
$415$	−1.42589	−	2.46971i	−0.0699941	−	0.121233i
$416$	−4.52526			−0.221869
$417$		0			0
$418$		−	39.1239i		−	1.91361i
$419$	−8.15665	+	14.1277i	−0.398478	+	0.690185i	−0.993538	−	0.113496i	$-0.963795\pi$
$419$	−8.15665	+	14.1277i	−0.398478	+	0.690185i	0.595060	+	0.803681i	$0.297128\pi$
$420$		0			0
$421$	1.59756	+	2.76706i	0.0778603	+	0.134858i	0.902327	−	0.431053i	$-0.141858\pi$
$421$	1.59756	+	2.76706i	0.0778603	+	0.134858i	−0.824466	+	0.565911i	$0.808525\pi$
$422$	−15.1223	+	8.73086i	−0.736142	+	0.425012i
$423$		0			0
$424$	−6.21874	+	10.7712i	−0.302009	+	0.523094i
$425$	−2.06626	+	3.57887i	−0.100228	+	0.173601i
$426$		0			0
$427$	−9.21496	−	6.35440i	−0.445943	−	0.307511i
$428$	10.8227	+	6.24846i	0.523133	+	0.302031i
$429$		0			0
$430$			5.77345i			0.278420i
$431$	17.7856	+	10.2685i	0.856701	+	0.494616i	0.862906	−	0.505364i	$-0.168642\pi$
$431$	17.7856	+	10.2685i	0.856701	+	0.494616i	−0.00620540	+	0.999981i	$0.501975\pi$
$432$		0			0
$433$			5.62555i			0.270347i	0.990822	+	0.135173i	$0.0431591\pi$
$433$			5.62555i			0.270347i	−0.990822	+	0.135173i	$0.956841\pi$
$434$	−4.16669	−	0.334449i	−0.200008	−	0.0160541i
$435$		0			0
$436$	−13.6159			−0.652083
$437$	20.0493	+	34.7265i	0.959090	+	1.66119i
$438$		0			0
$439$	2.11031	+	1.21839i	0.100720	+	0.0581506i	0.549514	−	0.835485i	$-0.314813\pi$
$439$	2.11031	+	1.21839i	0.100720	+	0.0581506i	−0.448794	+	0.893635i	$0.648146\pi$
$440$	−4.91498			−0.234313
$441$		0			0
$442$	−18.7007			−0.889504
$443$	1.07735	+	0.622006i	0.0511862	+	0.0295524i	0.525375	−	0.850871i	$-0.323925\pi$
$443$	1.07735	+	0.622006i	0.0511862	+	0.0295524i	−0.474189	+	0.880423i	$0.657258\pi$
$444$		0			0
$445$	2.95275	+	5.11432i	0.139974	+	0.242442i
$446$	11.3708			0.538424
$447$		0			0
$448$	2.63727	+	0.211686i	0.124599	+	0.0100012i
$449$			17.5222i			0.826924i	0.910521	+	0.413462i	$0.135681\pi$
$449$			17.5222i			0.826924i	−0.910521	+	0.413462i	$0.864319\pi$
$450$		0			0
$451$	−36.7322	−	21.2074i	−1.72965	−	0.998615i
$452$		−	16.8521i		−	0.792655i
$453$		0			0
$454$	6.13659	+	3.54296i	0.288004	+	0.166279i
$455$	9.85647	+	6.79677i	0.462079	+	0.318637i
$456$		0			0
$457$	−14.3903	+	24.9247i	−0.673150	+	1.16593i	0.303856	+	0.952718i	$0.401726\pi$
$457$	−14.3903	+	24.9247i	−0.673150	+	1.16593i	−0.977006	+	0.213212i	$0.931607\pi$
$458$	−1.52702	+	2.64487i	−0.0713528	+	0.123587i
$459$		0			0
$460$	4.36255	−	2.51872i	0.203405	−	0.117436i
$461$	−17.0159	−	29.4723i	−0.792508	−	1.37266i	−0.924410	−	0.381401i	$-0.875442\pi$
$461$	−17.0159	−	29.4723i	−0.792508	−	1.37266i	0.131902	−	0.991263i	$-0.457891\pi$
$462$		0			0
$463$	−4.73816	+	8.20674i	−0.220201	+	0.381399i	−0.954869	−	0.297028i	$-0.904005\pi$
$463$	−4.73816	+	8.20674i	−0.220201	+	0.381399i	0.734668	+	0.678427i	$0.237338\pi$
$464$			2.85112i			0.132360i
$465$		0			0
$466$	−21.4131			−0.991943
$467$	−8.13248	−	14.0859i	−0.376326	−	0.651816i	0.614198	−	0.789152i	$-0.289479\pi$
$467$	−8.13248	−	14.0859i	−0.376326	−	0.651816i	−0.990525	+	0.137336i	$0.956146\pi$
$468$		0			0
$469$	4.46411	+	9.39680i	0.206134	+	0.433904i
$470$	0.393319	−	0.227083i	0.0181424	−	0.0104745i
$471$		0			0
$472$	−9.49575	+	5.48237i	−0.437077	+	0.252347i
$473$	−24.5747	+	14.1882i	−1.12994	+	0.652374i
$474$		0			0
$475$	6.89368	−	3.98007i	0.316304	−	0.182618i
$476$	10.8986	+	0.874799i	0.499535	+	0.0400963i
$477$		0			0
$478$	9.08336	+	15.7328i	0.415463	+	0.719603i
$479$	−5.87379			−0.268380			−0.134190	−	0.990956i	$-0.542843\pi$
$479$	−5.87379			−0.268380			−0.134190	+	0.990956i	$0.542843\pi$
$480$		0			0
$481$			45.7782i			2.08731i
$482$	−10.4273	+	18.0606i	−0.474950	+	0.822638i
$483$		0			0
$484$	−6.57852	−	11.3943i	−0.299024	−	0.517924i
$485$	−1.74470	+	1.00730i	−0.0792225	+	0.0457392i
$486$		0			0
$487$	−4.11305	+	7.12401i	−0.186380	+	0.322820i	−0.944041	−	0.329829i	$-0.893009\pi$
$487$	−4.11305	+	7.12401i	−0.186380	+	0.322820i	0.757661	+	0.652649i	$0.226342\pi$
$488$	−2.11537	+	3.66392i	−0.0957582	+	0.165858i
$489$		0			0
$490$	−5.42629	−	4.42215i	−0.245135	−	0.199772i
$491$	−23.2893	−	13.4461i	−1.05103	−	0.606814i	−0.128094	−	0.991762i	$-0.540886\pi$
$491$	−23.2893	−	13.4461i	−1.05103	−	0.606814i	−0.922938	+	0.384948i	$0.874219\pi$
$492$		0			0
$493$			11.7823i			0.530648i
$494$	31.1957	+	18.0109i	1.40356	+	0.810347i
$495$		0			0
$496$			1.57993i			0.0709408i
$497$	−1.72372	+	21.4747i	−0.0773193	+	0.963273i
$498$		0			0
$499$	31.1031			1.39237			0.696183	−	0.717865i	$-0.254880\pi$
$499$	31.1031			1.39237			0.696183	+	0.717865i	$0.254880\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	24.1304	+	13.9317i	1.07699	+	0.621801i
$503$	3.49948			0.156034			0.0780170	−	0.996952i	$-0.475141\pi$
$503$	3.49948			0.156034			0.0780170	+	0.996952i	$0.475141\pi$
$504$		0			0
$505$	−6.47106			−0.287958
$506$	21.4418	+	12.3795i	0.953206	+	0.550334i
$507$		0			0
$508$	5.43182	+	9.40818i	0.240998	+	0.417421i
$509$	−6.83469			−0.302942			−0.151471	−	0.988462i	$-0.548401\pi$
$509$	−6.83469			−0.302942			−0.151471	+	0.988462i	$0.548401\pi$
$510$		0			0
$511$	−5.20209	−	3.58723i	−0.230127	−	0.158689i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	14.7285	+	8.50350i	0.649646	+	0.375073i
$515$			4.11259i			0.181223i
$516$		0			0
$517$	1.93315	+	1.11611i	0.0850200	+	0.0490863i
$518$	2.14145	−	26.6790i	0.0940898	−	1.17221i
$519$		0			0
$520$	2.26263	−	3.91899i	0.0992230	−	0.171859i
$521$	−8.40753	+	14.5623i	−0.368341	+	0.637985i	−0.989306	−	0.145853i	$-0.953407\pi$
$521$	−8.40753	+	14.5623i	−0.368341	+	0.637985i	0.620966	+	0.783838i	$0.286741\pi$
$522$		0			0
$523$	−5.55234	+	3.20565i	−0.242787	+	0.140173i	−0.616457	−	0.787389i	$-0.711433\pi$
$523$	−5.55234	+	3.20565i	−0.242787	+	0.140173i	0.373670	+	0.927562i	$0.378099\pi$
$524$	2.32978	+	4.03530i	0.101777	+	0.176283i
$525$		0			0
$526$	−1.53381	+	2.65664i	−0.0668775	+	0.115835i
$527$			6.52908i			0.284411i
$528$		0			0
$529$	−2.37577			−0.103294
$530$	−6.21874	−	10.7712i	−0.270125	−	0.467870i
$531$		0			0
$532$	−17.3380	−	11.9558i	−0.751696	−	0.518350i
$533$	33.8197	−	19.5258i	1.46489	−	0.845756i
$534$		0			0
$535$	−10.8227	+	6.24846i	−0.467904	+	0.270144i
$536$	3.40527	−	1.96604i	0.147085	−	0.0849198i
$537$		0			0
$538$	6.04397	−	3.48949i	0.260574	−	0.150442i
$539$	5.48781	−	33.9644i	0.236377	−	1.46295i
$540$		0			0
$541$	−8.20896	−	14.2183i	−0.352931	−	0.611294i	0.633831	−	0.773472i	$-0.281482\pi$
$541$	−8.20896	−	14.2183i	−0.352931	−	0.611294i	−0.986762	+	0.162178i	$0.948148\pi$
$542$	2.25377			0.0968078
$543$		0			0
$544$		−	4.13252i		−	0.177180i
$545$	6.80795	−	11.7917i	0.291620	−	0.505101i
$546$		0			0
$547$	−16.7310	−	28.9790i	−0.715366	−	1.23905i	−0.962818	−	0.270150i	$-0.912927\pi$
$547$	−16.7310	−	28.9790i	−0.715366	−	1.23905i	0.247452	−	0.968900i	$-0.420407\pi$
$548$	−8.58373	+	4.95582i	−0.366679	+	0.211702i
$549$		0			0
$550$	2.45749	−	4.25650i	0.104788	−	0.181498i
$551$	11.3476	−	19.6547i	0.483426	−	0.837318i
$552$		0			0
$553$	14.6131	−	21.1915i	0.621412	−	0.901153i
$554$	−24.5090	−	14.1503i	−1.04129	−	0.601188i
$555$		0			0
$556$			0.202625i			0.00859319i
$557$	13.5808	+	7.84087i	0.575436	+	0.332228i	0.759318	−	0.650720i	$-0.225533\pi$
$557$	13.5808	+	7.84087i	0.575436	+	0.332228i	−0.183881	+	0.982948i	$0.558866\pi$
$558$		0			0
$559$		−	26.1264i		−	1.10503i
$560$	−1.50196	+	2.17810i	−0.0634694	+	0.0920415i
$561$		0			0
$562$	−12.3772			−0.522100
$563$	3.73368	+	6.46693i	0.157356	+	0.272548i	0.933914	−	0.357497i	$-0.116370\pi$
$563$	3.73368	+	6.46693i	0.157356	+	0.272548i	−0.776558	+	0.630045i	$0.783036\pi$
$564$		0			0
$565$	14.5943	+	8.42603i	0.613988	+	0.354486i
$566$	−21.6617			−0.910509
$567$		0			0
$568$	8.14278			0.341664
$569$	−20.1857	−	11.6542i	−0.846229	−	0.488571i	0.0131477	−	0.999914i	$-0.495815\pi$
$569$	−20.1857	−	11.6542i	−0.846229	−	0.488571i	−0.859377	+	0.511343i	$0.829148\pi$
$570$		0			0
$571$	−1.21978	−	2.11273i	−0.0510463	−	0.0884148i	0.839373	−	0.543556i	$-0.182922\pi$
$571$	−1.21978	−	2.11273i	−0.0510463	−	0.0884148i	−0.890420	+	0.455141i	$0.849589\pi$
$572$	22.2416			0.929968
$573$		0			0
$574$	−20.6231	+	9.79735i	−0.860791	+	0.408933i
$575$			5.03744i			0.210076i
$576$		0			0
$577$	30.7749	+	17.7679i	1.28118	+	0.739688i	0.977064	−	0.212948i	$-0.0683063\pi$
$577$	30.7749	+	17.7679i	1.28118	+	0.739688i	0.304114	+	0.952636i	$0.401640\pi$
$578$		−	0.0777233i		−	0.00323286i
$579$		0			0
$580$	−2.46914	−	1.42556i	−0.102525	−	0.0591931i
$581$	−3.23765	−	6.81513i	−0.134320	−	0.282739i
$582$		0			0
$583$	30.5650	−	52.9401i	1.26587	−	2.19255i
$584$	−1.19418	+	2.06838i	−0.0494156	+	0.0855903i
$585$		0			0
$586$	2.40584	−	1.38901i	0.0993842	−	0.0573795i
$587$	−6.06540	−	10.5056i	−0.250346	−	0.433612i	0.713275	−	0.700884i	$-0.247211\pi$
$587$	−6.06540	−	10.5056i	−0.250346	−	0.433612i	−0.963621	+	0.267272i	$0.913878\pi$
$588$		0			0
$589$	6.28821	−	10.8915i	0.259101	−	0.448777i
$590$		−	10.9647i		−	0.451411i
$591$		0			0
$592$	−10.1161			−0.415770
$593$	15.5440	+	26.9230i	0.638315	+	1.10559i	0.985802	+	0.167910i	$0.0537017\pi$
$593$	15.5440	+	26.9230i	0.638315	+	1.10559i	−0.347487	+	0.937685i	$0.612965\pi$
$594$		0			0
$595$	−6.20688	+	9.00104i	−0.254457	+	0.369007i
$596$	−2.59913	+	1.50061i	−0.106465	+	0.0614673i
$597$		0			0
$598$	−19.7417	+	11.3979i	−0.807298	+	0.466093i
$599$	−1.31153	+	0.757213i	−0.0535877	+	0.0309389i	−0.526554	−	0.850141i	$-0.676516\pi$
$599$	−1.31153	+	0.757213i	−0.0535877	+	0.0309389i	0.472967	+	0.881080i	$0.343183\pi$
$600$		0			0
$601$	−28.7908	+	16.6224i	−1.17440	+	0.678040i	−0.954712	−	0.297530i	$-0.903837\pi$
$601$	−28.7908	+	16.6224i	−1.17440	+	0.678040i	−0.219688	+	0.975570i	$0.570504\pi$
$602$	−1.22216	+	15.2261i	−0.0498116	+	0.620571i
$603$		0			0
$604$	−9.86662	−	17.0895i	−0.401467	−	0.695362i
$605$	13.1570			0.534910
$606$		0			0
$607$			16.4368i			0.667150i	0.942724	+	0.333575i	$0.108255\pi$
$607$			16.4368i			0.667150i	−0.942724	+	0.333575i	$0.891745\pi$
$608$	−3.98007	+	6.89368i	−0.161413	+	0.279576i
$609$		0			0
$610$	−2.11537	−	3.66392i	−0.0856487	−	0.148348i
$611$	−1.77987	+	1.02761i	−0.0720058	+	0.0415726i
$612$		0			0
$613$	−6.16764	+	10.6827i	−0.249109	+	0.431469i	−0.963279	−	0.268503i	$-0.913471\pi$
$613$	−6.16764	+	10.6827i	−0.249109	+	0.431469i	0.714170	+	0.699972i	$0.246804\pi$
$614$	−1.83614	+	3.18028i	−0.0741004	+	0.128346i
$615$		0			0
$616$	−12.9621	−	1.04044i	−0.522259	−	0.0419203i
$617$	14.9813	+	8.64945i	0.603124	+	0.348214i	0.770270	−	0.637718i	$-0.220122\pi$
$617$	14.9813	+	8.64945i	0.603124	+	0.348214i	−0.167146	+	0.985932i	$0.553455\pi$
$618$		0			0
$619$			6.35168i			0.255295i	0.991820	+	0.127648i	$0.0407427\pi$
$619$			6.35168i			0.255295i	−0.991820	+	0.127648i	$0.959257\pi$
$620$	−1.36826	−	0.789963i	−0.0549505	−	0.0317257i
$621$		0			0
$622$		−	7.33384i		−	0.294060i
$623$	6.70457	+	14.1129i	0.268613	+	0.565421i
$624$		0			0
$625$	1.00000			0.0400000
$626$	−14.2906	−	24.7521i	−0.571168	−	0.989292i
$627$		0			0
$628$	7.30661	+	4.21847i	0.291565	+	0.168335i
$629$	−41.8051			−1.66688
$630$		0			0
$631$	0.419169			0.0166869			0.00834343	−	0.999965i	$-0.497344\pi$
$631$	0.419169			0.0166869			0.00834343	+	0.999965i	$0.497344\pi$
$632$	−8.42586	−	4.86467i	−0.335163	−	0.193506i
$633$		0			0
$634$	−3.37041	−	5.83771i	−0.133856	−	0.231845i
$635$	−10.8636			−0.431110
$636$		0			0
$637$	24.5554	+	20.0114i	0.972920	+	0.792880i
$638$		−	14.0132i		−	0.554788i
$639$		0			0
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$			15.8516i			0.626100i	0.949737	+	0.313050i	$0.101351\pi$
$641$			15.8516i			0.626100i	−0.949737	+	0.313050i	$0.898649\pi$
$642$		0			0
$643$	−21.8689	−	12.6260i	−0.862427	−	0.497923i	0.00239717	−	0.999997i	$-0.499237\pi$
$643$	−21.8689	−	12.6260i	−0.862427	−	0.497923i	−0.864824	+	0.502075i	$0.832570\pi$
$644$	12.0384	−	5.71905i	0.474379	−	0.225362i
$645$		0			0
$646$	−16.4477	+	28.4883i	−0.647126	+	1.12086i
$647$	5.47945	−	9.49068i	0.215419	−	0.373117i	−0.737983	−	0.674819i	$-0.764222\pi$
$647$	5.47945	−	9.49068i	0.215419	−	0.373117i	0.953402	+	0.301702i	$0.0975548\pi$
$648$		0			0
$649$	46.6714	−	26.9458i	1.83201	−	1.05771i
$650$	2.26263	+	3.91899i	0.0887477	+	0.153716i
$651$		0			0
$652$	6.64195	−	11.5042i	0.260119	−	0.450539i
$653$		−	20.7019i		−	0.810128i	−0.914288	−	0.405064i	$-0.867249\pi$
$653$		−	20.7019i		−	0.810128i	0.914288	−	0.405064i	$-0.132751\pi$
$654$		0			0
$655$	−4.65956			−0.182064
$656$	4.31484	+	7.47352i	0.168466	+	0.291792i
$657$		0			0
$658$	1.08536	−	0.515618i	0.0423116	−	0.0201009i
$659$	−18.2719	+	10.5493i	−0.711774	+	0.410943i	−0.811718	−	0.584050i	$-0.801467\pi$
$659$	−18.2719	+	10.5493i	−0.711774	+	0.410943i	0.0999436	+	0.994993i	$0.468134\pi$
$660$		0			0
$661$	3.90709	−	2.25576i	0.151968	−	0.0877389i	−0.422088	−	0.906555i	$-0.638703\pi$
$661$	3.90709	−	2.25576i	0.151968	−	0.0877389i	0.574056	+	0.818816i	$0.305369\pi$
$662$	24.9612	−	14.4113i	0.970143	−	0.560112i
$663$		0			0
$664$	−2.46971	+	1.42589i	−0.0958433	+	0.0553352i
$665$	19.0230	−	9.03721i	0.737681	−	0.350448i
$666$		0			0
$667$	7.18116	+	12.4381i	0.278056	+	0.481607i
$668$	16.3020			0.630743
$669$		0			0
$670$			3.93207i			0.151909i
$671$	10.3970	−	18.0081i	0.401371	−	0.695196i
$672$		0			0
$673$	0.596334	+	1.03288i	0.0229870	+	0.0398147i	0.877290	−	0.479961i	$-0.159349\pi$
$673$	0.596334	+	1.03288i	0.0229870	+	0.0398147i	−0.854303	+	0.519775i	$0.826016\pi$
$674$	20.9427	−	12.0913i	0.806681	−	0.465738i
$675$		0			0
$676$	−3.73901	+	6.47616i	−0.143808	+	0.249083i
$677$	−11.6201	+	20.1267i	−0.446598	+	0.773530i	−0.998162	−	0.0606024i	$-0.980698\pi$
$677$	−11.6201	+	20.1267i	−0.446598	+	0.773530i	0.551564	+	0.834132i	$0.314031\pi$
$678$		0			0
$679$	−4.81446	+	2.28719i	−0.184762	+	0.0877745i
$680$	3.57887	+	2.06626i	0.137243	+	0.0792375i
$681$		0			0
$682$		−	7.76531i		−	0.297349i
$683$	−6.84887	−	3.95420i	−0.262065	−	0.151303i	0.363211	−	0.931707i	$-0.381680\pi$
$683$	−6.84887	−	3.95420i	−0.262065	−	0.151303i	−0.625276	+	0.780404i	$0.715014\pi$
$684$		0			0
$685$		−	9.91164i		−	0.378704i
$686$	−13.3745	−	12.8111i	−0.510640	−	0.489129i
$687$		0			0
$688$	5.77345			0.220111
$689$	28.1414	+	48.7424i	1.07210	+	1.85694i
$690$		0			0
$691$	11.1512	+	6.43817i	0.424213	+	0.244920i	0.696878	−	0.717189i	$-0.254572\pi$
$691$	11.1512	+	6.43817i	0.424213	+	0.244920i	−0.272665	+	0.962109i	$0.587905\pi$
$692$	21.2103			0.806295
$693$		0			0
$694$	−17.4312			−0.661678
$695$	−0.175478	−	0.101312i	−0.00665626	−	0.00384299i
$696$		0			0
$697$	17.8312	+	30.8845i	0.675403	+	1.16983i
$698$	36.2892			1.37357
$699$		0			0
$700$	−1.13531	−	2.38979i	−0.0429106	−	0.0903254i
$701$		−	1.81441i		−	0.0685292i	−0.999413	−	0.0342646i	$-0.989091\pi$
$701$		−	1.81441i		−	0.0685292i	0.999413	−	0.0342646i	$-0.0109089\pi$
$702$		0			0
$703$	69.7373	+	40.2629i	2.63019	+	1.51854i
$704$			4.91498i			0.185240i
$705$		0			0
$706$	−18.8372	−	10.8756i	−0.708946	−	0.409310i
$707$	−17.0659	−	1.36984i	−0.641830	−	0.0515180i
$708$		0			0
$709$	−2.21427	+	3.83523i	−0.0831587	+	0.144035i	−0.904605	−	0.426251i	$-0.859834\pi$
$709$	−2.21427	+	3.83523i	−0.0831587	+	0.144035i	0.821446	+	0.570286i	$0.193168\pi$
$710$	−4.07139	+	7.05186i	−0.152797	+	0.264652i
$711$		0			0
$712$	5.11432	−	2.95275i	0.191667	−	0.110659i
$713$	3.97939	+	6.89251i	0.149029	+	0.258126i
$714$		0			0
$715$	−11.1208	+	19.2618i	−0.415894	+	0.720350i
$716$		−	3.38644i		−	0.126557i
$717$		0			0
$718$	−22.6058			−0.843641
$719$	−8.23556	−	14.2644i	−0.307134	−	0.531973i	0.670600	−	0.741819i	$-0.266037\pi$
$719$	−8.23556	−	14.2644i	−0.307134	−	0.531973i	−0.977734	+	0.209847i	$0.932703\pi$
$720$		0			0
$721$	−0.870581	+	10.8460i	−0.0324221	+	0.403927i
$722$	38.4201	−	22.1819i	1.42985	−	0.825523i
$723$		0			0
$724$	4.32862	−	2.49913i	0.160872	−	0.0928793i
$725$	2.46914	−	1.42556i	0.0917016	−	0.0529439i
$726$		0			0
$727$	40.8484	−	23.5838i	1.51498	−	0.874676i	0.515138	−	0.857107i	$-0.327740\pi$
$727$	40.8484	−	23.5838i	1.51498	−	0.874676i	0.999846	−	0.0175695i	$-0.00559284\pi$
$728$	6.79677	−	9.85647i	0.251905	−	0.365305i
$729$		0			0
$730$	−1.19418	−	2.06838i	−0.0441986	−	0.0765543i
$731$	23.8589			0.882453
$732$		0			0
$733$			48.2222i			1.78113i	0.454858	+	0.890564i	$0.349690\pi$
$733$			48.2222i			1.78113i	−0.454858	+	0.890564i	$0.650310\pi$
$734$	−6.08890	+	10.5463i	−0.224745	+	0.389270i
$735$		0			0
$736$	−2.51872	−	4.36255i	−0.0928412	−	0.160806i
$737$	−16.7369	+	9.66303i	−0.616510	+	0.355942i
$738$		0			0
$739$	18.2730	−	31.6498i	0.672184	−	1.16426i	−0.305099	−	0.952320i	$-0.598690\pi$
$739$	18.2730	−	31.6498i	0.672184	−	1.16426i	0.977283	−	0.211936i	$-0.0679769\pi$
$740$	5.05807	−	8.76083i	0.185938	−	0.322054i
$741$		0			0
$742$	−14.1204	−	29.7229i	−0.518375	−	1.09116i
$743$	−18.6193	−	10.7498i	−0.683075	−	0.394373i	0.117938	−	0.993021i	$-0.462372\pi$
$743$	−18.6193	−	10.7498i	−0.683075	−	0.394373i	−0.801013	+	0.598648i	$0.795705\pi$
$744$		0			0
$745$		−	3.00122i		−	0.109956i
$746$	−25.5301	−	14.7398i	−0.934724	−	0.539663i
$747$		0			0
$748$			20.3113i			0.742653i
$749$	−29.8650	+	14.1879i	−1.09124	+	0.518413i
$750$		0			0
$751$	16.7351			0.610672			0.305336	−	0.952245i	$-0.401231\pi$
$751$	16.7351			0.610672			0.305336	+	0.952245i	$0.401231\pi$
$752$	−0.227083	−	0.393319i	−0.00828085	−	0.0143429i
$753$		0			0
$754$	11.1735	+	6.45103i	0.406915	+	0.234933i
$755$	19.7332			0.718166
$756$		0			0
$757$	−33.5973			−1.22112			−0.610558	−	0.791972i	$-0.709055\pi$
$757$	−33.5973			−1.22112			−0.610558	+	0.791972i	$0.709055\pi$
$758$	24.2434	+	13.9969i	0.880560	+	0.508392i
$759$		0			0
$760$	−3.98007	−	6.89368i	−0.144372	−	0.250060i
$761$	−28.5379			−1.03450			−0.517249	−	0.855835i	$-0.673044\pi$
$761$	−28.5379			−1.03450			−0.517249	+	0.855835i	$0.673044\pi$
$762$		0			0
$763$	20.4505	−	29.6568i	0.740359	−	1.07365i
$764$		−	5.72419i		−	0.207094i
$765$		0			0
$766$	11.8509	+	6.84209i	0.428189	+	0.247215i
$767$			49.6184i			1.79162i
$768$		0			0
$769$	4.36339	+	2.51920i	0.157348	+	0.0908448i	0.576606	−	0.817022i	$-0.304377\pi$
$769$	4.36339	+	2.51920i	0.157348	+	0.0908448i	−0.419259	+	0.907867i	$0.637710\pi$
$770$	7.38211	−	10.7053i	0.266033	−	0.385793i
$771$		0			0
$772$	2.70156	−	4.67925i	0.0972314	−	0.168410i
$773$	−9.36638	+	16.2231i	−0.336885	+	0.583503i	−0.983845	−	0.179022i	$-0.942707\pi$
$773$	−9.36638	+	16.2231i	−0.336885	+	0.583503i	0.646960	+	0.762524i	$0.276040\pi$
$774$		0			0
$775$	1.36826	−	0.789963i	0.0491492	−	0.0283763i
$776$	1.00730	+	1.74470i	0.0361600	+	0.0626309i
$777$		0			0
$778$	−3.43558	+	5.95061i	−0.123172	+	0.213340i
$779$		−	68.6934i		−	2.46120i
$780$		0			0
$781$	−40.0216			−1.43209
$782$	−10.4087	−	18.0283i	−0.372213	−	0.644691i
$783$		0			0
$784$	−4.42215	+	5.42629i	−0.157934	+	0.193796i
$785$	−7.30661	+	4.21847i	−0.260784	+	0.150564i
$786$		0			0
$787$	−46.4644	+	26.8262i	−1.65628	+	0.956251i	−0.681864	+	0.731479i	$0.738830\pi$
$787$	−46.4644	+	26.8262i	−1.65628	+	0.956251i	−0.974411	+	0.224772i	$0.927836\pi$
$788$	−10.8373	+	6.25690i	−0.386062	+	0.222893i
$789$		0			0
$790$	8.42586	−	4.86467i	0.299779	−	0.173077i
$791$	36.7055	+	25.3111i	1.30510	+	0.899960i
$792$		0			0
$793$	9.57260	+	16.5802i	0.339933	+	0.588781i
$794$	−5.13278			−0.182155
$795$		0			0
$796$		−	17.8943i		−	0.634247i
$797$	−1.34947	+	2.33735i	−0.0478007	+	0.0827933i	−0.888936	−	0.458032i	$-0.848555\pi$
$797$	−1.34947	+	2.33735i	−0.0478007	+	0.0827933i	0.841135	+	0.540825i	$0.181888\pi$
$798$		0			0
$799$	−0.938423	−	1.62540i	−0.0331990	−	0.0575024i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	4.43107	−	7.67483i	0.156466	−	0.271008i
$803$	5.86938	−	10.1661i	0.207126	−	0.358752i
$804$		0			0
$805$	−1.06636	+	13.2851i	−0.0375842	+	0.468237i
$806$	6.19172	+	3.57479i	0.218094	+	0.125917i
$807$		0			0
$808$			6.47106i			0.227651i
$809$	10.1449	+	5.85717i	0.356676	+	0.205927i	0.667622	−	0.744501i	$-0.267312\pi$
$809$	10.1449	+	5.85717i	0.356676	+	0.205927i	−0.310946	+	0.950428i	$0.600646\pi$
$810$		0			0
$811$		−	1.79458i		−	0.0630161i	−0.999503	−	0.0315081i	$-0.989969\pi$
$811$		−	1.79458i		−	0.0630161i	0.999503	−	0.0315081i	$-0.0100310\pi$
$812$	−6.21002	−	4.28227i	−0.217929	−	0.150278i
$813$		0			0
$814$	49.7206			1.74271
$815$	6.64195	+	11.5042i	0.232657	+	0.402975i
$816$		0			0
$817$	−39.8003	−	22.9787i	−1.39244	−	0.803923i
$818$	−2.60954			−0.0912404
$819$		0			0
$820$	−8.62968			−0.301361
$821$	24.5051	+	14.1480i	0.855234	+	0.493769i	0.862413	−	0.506205i	$-0.168952\pi$
$821$	24.5051	+	14.1480i	0.855234	+	0.493769i	−0.00717960	+	0.999974i	$0.502285\pi$
$822$		0			0
$823$	−1.12364	−	1.94620i	−0.0391676	−	0.0678403i	0.845777	−	0.533536i	$-0.179137\pi$
$823$	−1.12364	−	1.94620i	−0.0391676	−	0.0678403i	−0.884945	+	0.465696i	$0.845804\pi$
$824$	4.11259			0.143269
$825$		0			0
$826$	2.32109	−	28.9170i	0.0807610	−	1.00615i
$827$		−	43.4893i		−	1.51227i	−0.654415	−	0.756136i	$-0.727085\pi$
$827$		−	43.4893i		−	1.51227i	0.654415	−	0.756136i	$-0.272915\pi$
$828$		0			0
$829$	−45.1357	−	26.0591i	−1.56763	−	0.905069i	−0.996445	−	0.0842454i	$-0.973152\pi$
$829$	−45.1357	−	26.0591i	−1.56763	−	0.905069i	−0.571181	−	0.820824i	$-0.693515\pi$
$830$		−	2.85178i		−	0.0989866i
$831$		0			0
$832$	−3.91899	−	2.26263i	−0.135867	−	0.0784427i
$833$	−18.2746	+	22.4242i	−0.633178	+	0.776954i
$834$		0			0
$835$	−8.15100	+	14.1179i	−0.282077	+	0.488571i
$836$	19.5620	−	33.8823i	0.676564	−	1.17184i
$837$		0			0
$838$	−14.1277	+	8.15665i	−0.488034	+	0.281767i
$839$	21.4923	+	37.2258i	0.741998	+	1.28518i	0.951584	+	0.307388i	$0.0994550\pi$
$839$	21.4923	+	37.2258i	0.741998	+	1.28518i	−0.209586	+	0.977790i	$0.567212\pi$
$840$		0			0
$841$	−10.4356	+	18.0749i	−0.359847	+	0.623273i
$842$			3.19512i			0.110111i
$843$		0			0
$844$	−17.4617			−0.601057
$845$	−3.73901	−	6.47616i	−0.128626	−	0.222787i
$846$		0			0
$847$	34.6987	+	2.78517i	1.19226	+	0.0956995i
$848$	−10.7712	+	6.21874i	−0.369883	+	0.213552i
$849$		0			0
$850$	−3.57887	+	2.06626i	−0.122754	+	0.0708721i
$851$	−44.1321	+	25.4797i	−1.51283	+	0.873433i
$852$		0			0
$853$	36.9943	−	21.3587i	1.26666	−	0.731306i	0.292305	−	0.956325i	$-0.405578\pi$
$853$	36.9943	−	21.3587i	1.26666	−	0.731306i	0.974354	+	0.225019i	$0.0722443\pi$
$854$	−4.80319	−	10.1105i	−0.164362	−	0.345976i
$855$		0			0
$856$	6.24846	+	10.8227i	0.213568	+	0.369911i
$857$	39.8521			1.36132			0.680661	−	0.732599i	$-0.261693\pi$
$857$	39.8521			1.36132			0.680661	+	0.732599i	$0.261693\pi$
$858$		0			0
$859$			26.3979i			0.900684i	0.892856	+	0.450342i	$0.148698\pi$
$859$			26.3979i			0.900684i	−0.892856	+	0.450342i	$0.851302\pi$
$860$	−2.88672	+	4.99995i	−0.0984365	+	0.170497i
$861$		0			0
$862$	10.2685	+	17.7856i	0.349747	+	0.605779i
$863$	−22.4654	+	12.9704i	−0.764731	+	0.441517i	−0.830992	−	0.556285i	$-0.812226\pi$
$863$	−22.4654	+	12.9704i	−0.764731	+	0.441517i	0.0662611	+	0.997802i	$0.478893\pi$
$864$		0			0
$865$	−10.6052	+	18.3687i	−0.360586	+	0.624553i
$866$	−2.81278	+	4.87187i	−0.0955820	+	0.165553i
$867$		0			0
$868$	−3.44124	−	2.37299i	−0.116803	−	0.0805444i
$869$	41.4129	+	23.9098i	1.40484	+	0.811083i
$870$		0			0
$871$		−	17.7937i		−	0.602915i
$872$	−11.7917	−	6.80795i	−0.399318	−	0.230546i
$873$		0			0
$874$			40.0987i			1.35636i
$875$	2.63727	+	0.211686i	0.0891560	+	0.00715631i
$876$		0			0
$877$	25.0969			0.847462			0.423731	−	0.905788i	$-0.360720\pi$
$877$	25.0969			0.847462			0.423731	+	0.905788i	$0.360720\pi$
$878$	1.21839	+	2.11031i	0.0411187	+	0.0712196i
$879$		0			0
$880$	−4.25650	−	2.45749i	−0.143487	−	0.0828420i
$881$	−45.7419			−1.54108			−0.770541	−	0.637390i	$-0.780014\pi$
$881$	−45.7419			−1.54108			−0.770541	+	0.637390i	$0.780014\pi$
$882$		0			0
$883$	21.2954			0.716648			0.358324	−	0.933597i	$-0.383348\pi$
$883$	21.2954			0.716648			0.358324	+	0.933597i	$0.383348\pi$
$884$	−16.1953	−	9.35037i	−0.544708	−	0.314487i
$885$		0			0
$886$	0.622006	+	1.07735i	0.0208967	+	0.0361941i
$887$	−15.3159			−0.514259			−0.257130	−	0.966377i	$-0.582777\pi$
$887$	−15.3159			−0.514259			−0.257130	+	0.966377i	$0.582777\pi$
$888$		0			0
$889$	−28.6503	−	2.29968i	−0.960901	−	0.0771289i
$890$			5.90551i			0.197953i
$891$		0			0
$892$	9.84741	+	5.68541i	0.329716	+	0.190361i
$893$			3.61521i			0.120979i
$894$		0			0
$895$	2.93274	+	1.69322i	0.0980308	+	0.0565981i
$896$	2.17810	+	1.50196i	0.0727652	+	0.0501770i
$897$		0			0
$898$	−8.76110	+	15.1747i	−0.292362	+	0.506386i
$899$	2.25228	−	3.90106i	0.0751177	−	0.130108i
$900$		0			0
$901$	−44.5121	+	25.6991i	−1.48291	+	0.856160i
$902$	−21.2074	−	36.7322i	−0.706128	−	1.22305i
$903$		0			0
$904$	8.42603	−	14.5943i	0.280246	−	0.485400i
$905$			4.99826i			0.166148i
$906$		0			0
$907$	−9.70644			−0.322297			−0.161149	−	0.986930i	$-0.551520\pi$
$907$	−9.70644			−0.322297			−0.161149	+	0.986930i	$0.551520\pi$
$908$	3.54296	+	6.13659i	0.117577	+	0.203650i
$909$		0			0
$910$	5.13757	+	10.8144i	0.170309	+	0.358494i
$911$	5.26323	−	3.03873i	0.174379	−	0.100677i	−0.410270	−	0.911964i	$-0.634566\pi$
$911$	5.26323	−	3.03873i	0.174379	−	0.100677i	0.584649	+	0.811286i	$0.301232\pi$
$912$		0			0
$913$	12.1386	−	7.00821i	0.401728	−	0.231938i
$914$	−24.9247	+	14.3903i	−0.824437	+	0.475989i
$915$		0			0
$916$	−2.64487	+	1.52702i	−0.0873889	+	0.0504540i
$917$	−12.2885	−	0.986366i	−0.405803	−	0.0325727i
$918$		0			0
$919$	18.7340	+	32.4483i	0.617979	+	1.07037i	0.989854	+	0.142088i	$0.0453817\pi$
$919$	18.7340	+	32.4483i	0.617979	+	1.07037i	−0.371875	+	0.928283i	$0.621285\pi$
$920$	5.03744			0.166079
$921$		0			0
$922$		−	34.0317i		−	1.12077i
$923$	18.4241	−	31.9115i	0.606438	−	1.05038i
$924$		0			0
$925$	5.05807	+	8.76083i	0.166308	+	0.288054i
$926$	−8.20674	+	4.73816i	−0.269690	+	0.155706i
$927$		0			0
$928$	−1.42556	+	2.46914i	−0.0467963	+	0.0810535i
$929$	−6.21064	+	10.7572i	−0.203765	+	0.352931i	−0.949738	−	0.313045i	$-0.898651\pi$
$929$	−6.21064	+	10.7572i	−0.203765	+	0.352931i	0.745974	+	0.665975i	$0.231984\pi$
$930$		0			0
$931$	52.0818	−	19.8066i	1.70691	−	0.649136i
$932$	−18.5443	−	10.7066i	−0.607439	−	0.350705i
$933$		0			0
$934$		−	16.2650i		−	0.532206i
$935$	−17.5901	−	10.1556i	−0.575257	−	0.332125i
$936$		0			0
$937$		−	13.8664i		−	0.452994i	−0.974012	−	0.226497i	$-0.927273\pi$
$937$		−	13.8664i		−	0.452994i	0.974012	−	0.226497i	$-0.0727274\pi$
$938$	−0.832366	+	10.3699i	−0.0271777	+	0.338590i
$939$		0			0
$940$	0.454165			0.0148132
$941$	−28.9912	−	50.2143i	−0.945087	−	1.63694i	−0.755576	−	0.655061i	$-0.772643\pi$
$941$	−28.9912	−	50.2143i	−0.945087	−	1.63694i	−0.189512	−	0.981878i	$-0.560690\pi$
$942$		0			0
$943$	37.6474	+	21.7357i	1.22597	+	0.707813i
$944$	−10.9647			−0.356872
$945$		0			0
$946$	−28.3764			−0.922596
$947$	12.2744	+	7.08663i	0.398864	+	0.230284i	0.685994	−	0.727607i	$-0.259368\pi$
$947$	12.2744	+	7.08663i	0.398864	+	0.230284i	−0.287130	+	0.957892i	$0.592701\pi$
$948$		0			0
$949$	5.40398	+	9.35998i	0.175421	+	0.303838i
$950$	7.96013			0.258261
$951$		0			0
$952$	9.00104	+	6.20688i	0.291725	+	0.201166i
$953$			10.6995i			0.346590i	0.984870	+	0.173295i	$0.0554414\pi$
$953$			10.6995i			0.346590i	−0.984870	+	0.173295i	$0.944559\pi$
$954$		0			0
$955$	4.95729	+	2.86209i	0.160414	+	0.0926151i
$956$			18.1667i			0.587554i
$957$		0			0
$958$	−5.08685	−	2.93690i	−0.164349	−	0.0948868i
$959$	2.09816	−	26.1397i	0.0677531	−	0.844093i
$960$		0			0
$961$	−14.2519	+	24.6850i	−0.459739	+	0.796292i
$962$	−22.8891	+	39.6451i	−0.737974	+	1.27821i
$963$		0			0
$964$	−18.0606	+	10.4273i	−0.581693	+	0.335841i
$965$	2.70156	+	4.67925i	0.0869664	+	0.150630i
$966$		0			0
$967$	2.27153	−	3.93440i	0.0730474	−	0.126522i	−0.827188	−	0.561925i	$-0.810061\pi$
$967$	2.27153	−	3.93440i	0.0730474	−	0.126522i	0.900235	+	0.435403i	$0.143394\pi$
$968$		−	13.1570i		−	0.422883i
$969$		0			0
$970$	−2.01460			−0.0646849
$971$	12.9286	+	22.3930i	0.414899	+	0.718627i	0.995418	−	0.0956201i	$-0.0304834\pi$
$971$	12.9286	+	22.3930i	0.414899	+	0.718627i	−0.580518	+	0.814247i	$0.697150\pi$
$972$		0			0
$973$	−0.441336	−	0.304334i	−0.0141486	−	0.00975650i
$974$	−7.12401	+	4.11305i	−0.228268	+	0.131791i
$975$		0			0
$976$	−3.66392	+	2.11537i	−0.117279	+	0.0677113i
$977$	8.82069	−	5.09263i	0.282199	−	0.162928i	−0.352220	−	0.935917i	$-0.614573\pi$
$977$	8.82069	−	5.09263i	0.282199	−	0.162928i	0.634419	+	0.772990i	$0.281240\pi$
$978$		0			0
$979$	−25.1368	+	14.5127i	−0.803375	+	0.463829i
$980$	−2.48823	−	6.54284i	−0.0794836	−	0.209003i
$981$		0			0
$982$	−13.4461	−	23.2893i	−0.429082	−	0.743192i
$983$	−25.7089			−0.819987			−0.409993	−	0.912088i	$-0.634469\pi$
$983$	−25.7089			−0.819987			−0.409993	+	0.912088i	$0.634469\pi$
$984$		0			0
$985$		−	12.5138i		−	0.398723i
$986$	−5.89115	+	10.2038i	−0.187613	+	0.324954i
$987$		0			0
$988$	18.0109	+	31.1957i	0.573002	+	0.992468i
$989$	25.1869	−	14.5417i	0.800898	−	0.462399i
$990$		0			0
$991$	−6.19103	+	10.7232i	−0.196665	+	0.340633i	−0.947445	−	0.319919i	$-0.896344\pi$
$991$	−6.19103	+	10.7232i	−0.196665	+	0.340633i	0.750780	+	0.660552i	$0.229678\pi$
$992$	−0.789963	+	1.36826i	−0.0250814	+	0.0434422i
$993$		0			0
$994$	−12.2301	+	17.7358i	−0.387917	+	0.562545i
$995$	15.4969	+	8.94715i	0.491285	+	0.283644i
$996$		0			0
$997$			14.7326i			0.466585i	0.972407	+	0.233293i	$0.0749500\pi$
$997$			14.7326i			0.466585i	−0.972407	+	0.233293i	$0.925050\pi$
$998$	26.9361	+	15.5515i	0.852646	+	0.492276i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.c.1151.9		32
3.2	odd	2		630.2.t.c.311.7	✓	32
7.5	odd	6		1890.2.bk.c.341.3		32
9.2	odd	6		1890.2.bk.c.521.3		32
9.7	even	3		630.2.bk.c.101.5	yes	32
21.5	even	6		630.2.bk.c.131.13	yes	32
63.47	even	6	inner	1890.2.t.c.1601.9		32
63.61	odd	6		630.2.t.c.551.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.7	✓	32	3.2	odd	2
630.2.t.c.551.7	yes	32	63.61	odd	6
630.2.bk.c.101.5	yes	32	9.7	even	3
630.2.bk.c.131.13	yes	32	21.5	even	6
1890.2.t.c.1151.9		32	1.1	even	1	trivial
1890.2.t.c.1601.9		32	63.47	even	6	inner
1890.2.bk.c.341.3		32	7.5	odd	6
1890.2.bk.c.521.3		32	9.2	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-2.63727 - 0.211686i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-2.63727 - 0.211686i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} -4.91498i q^{11} +(3.91899 + 2.26263i) q^{13} +(-2.17810 - 1.50196i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.06626 + 3.57887i) q^{17} +(6.89368 - 3.98007i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(2.45749 - 4.25650i) q^{22} +5.03744i q^{23} +1.00000 q^{25} +(2.26263 + 3.91899i) q^{26} +(-1.13531 - 2.38979i) q^{28} +(2.46914 - 1.42556i) q^{29} +(1.36826 - 0.789963i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.57887 + 2.06626i) q^{34} +(2.63727 + 0.211686i) q^{35} +(5.05807 + 8.76083i) q^{37} +7.96013 q^{38} -1.00000i q^{40} +(4.31484 - 7.47352i) q^{41} +(-2.88672 - 4.99995i) q^{43} +(4.25650 - 2.45749i) q^{44} +(-2.51872 + 4.36255i) q^{46} +(-0.227083 + 0.393319i) q^{47} +(6.91038 + 1.11655i) q^{49} +(0.866025 + 0.500000i) q^{50} +4.52526i q^{52} +(10.7712 + 6.21874i) q^{53} +4.91498i q^{55} +(0.211686 - 2.63727i) q^{56} +2.85112 q^{58} +(5.48237 + 9.49575i) q^{59} +(3.66392 + 2.11537i) q^{61} +1.57993 q^{62} -1.00000 q^{64} +(-3.91899 - 2.26263i) q^{65} +(-1.96604 - 3.40527i) q^{67} -4.13252 q^{68} +(2.17810 + 1.50196i) q^{70} -8.14278i q^{71} +(2.06838 + 1.19418i) q^{73} +10.1161i q^{74} +(6.89368 + 3.98007i) q^{76} +(-1.04044 + 12.9621i) q^{77} +(-4.86467 + 8.42586i) q^{79} +(0.500000 - 0.866025i) q^{80} +(7.47352 - 4.31484i) q^{82} +(1.42589 + 2.46971i) q^{83} +(2.06626 - 3.57887i) q^{85} -5.77345i q^{86} +4.91498 q^{88} +(-2.95275 - 5.11432i) q^{89} +(-9.85647 - 6.79677i) q^{91} +(-4.36255 + 2.51872i) q^{92} +(-0.393319 + 0.227083i) q^{94} +(-6.89368 + 3.98007i) q^{95} +(1.74470 - 1.00730i) q^{97} +(5.42629 + 4.42215i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7}+O(q^{10}) \) 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7	\( 32 q + 16 q^{4} - 32 q^{5} - 2 q^{7} - 16 q^{16} - 6 q^{17} - 16 q^{20} + 32 q^{25} - 12 q^{26} + 2 q^{28} - 6 q^{29} + 18 q^{31} + 2 q^{35} + 2 q^{37} + 6 q^{41} - 28 q^{43} + 6 q^{44} - 24 q^{47} + 32 q^{49} + 36 q^{53} + 6 q^{56} + 30 q^{59} + 54 q^{61} - 32 q^{64} + 4 q^{67} - 12 q^{68} - 30 q^{73} + 6 q^{77} + 4 q^{79} + 16 q^{80} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 12 q^{89} - 66 q^{91} + 18 q^{92} - 42 q^{94} + 96 q^{97} + 24 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 - 32 * q^5 - 2 * q^7 - 16 * q^16 - 6 * q^17 - 16 * q^20 + 32 * q^25 - 12 * q^26 + 2 * q^28 - 6 * q^29 + 18 * q^31 + 2 * q^35 + 2 * q^37 + 6 * q^41 - 28 * q^43 + 6 * q^44 - 24 * q^47 + 32 * q^49 + 36 * q^53 + 6 * q^56 + 30 * q^59 + 54 * q^61 - 32 * q^64 + 4 * q^67 - 12 * q^68 - 30 * q^73 + 6 * q^77 + 4 * q^79 + 16 * q^80 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 12 * q^89 - 66 * q^91 + 18 * q^92 - 42 * q^94 + 96 * q^97 + 24 * q^98

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