LMFDB - Embedded newform 1890.2.bk.a.341.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(341,1890)]

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, 5]))

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

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

chi := DirichletCharacter("1890.341");

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.bk (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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1890.341
Dual form			1890.2.bk.a.521.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} +(4.09808 + 2.36603i) q^{11} +(-3.00000 - 1.73205i) q^{13} +(-0.866025 + 2.50000i) q^{14} +1.00000 q^{16} +(-1.09808 - 0.633975i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(2.36603 - 4.09808i) q^{22} +(-2.19615 + 1.26795i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.73205 + 3.00000i) q^{26} +(2.50000 + 0.866025i) q^{28} +(5.59808 - 3.23205i) q^{29} +8.19615i q^{31} -1.00000i q^{32} +(-0.500000 - 2.59808i) q^{35} +(-3.09808 + 5.36603i) q^{37} +(-0.633975 + 1.09808i) q^{38} +(-0.866025 + 0.500000i) q^{40} +(-4.50000 + 7.79423i) q^{41} +(-1.59808 - 2.76795i) q^{43} +(-4.09808 - 2.36603i) q^{44} +(1.26795 + 2.19615i) q^{46} +9.00000 q^{47} +(5.50000 + 4.33013i) q^{49} +(0.866025 + 0.500000i) q^{50} +(3.00000 + 1.73205i) q^{52} +(-6.29423 + 3.63397i) q^{53} +4.73205i q^{55} +(0.866025 - 2.50000i) q^{56} +(-3.23205 - 5.59808i) q^{58} -2.19615 q^{59} +12.9282i q^{61} +8.19615 q^{62} -1.00000 q^{64} -3.46410i q^{65} -4.00000 q^{67} +(-2.59808 + 0.500000i) q^{70} +4.73205i q^{71} +(6.00000 - 3.46410i) q^{73} +(5.36603 + 3.09808i) q^{74} +(1.09808 + 0.633975i) q^{76} +(-8.19615 - 9.46410i) q^{77} +14.5885 q^{79} +(0.500000 + 0.866025i) q^{80} +(7.79423 + 4.50000i) q^{82} +(5.59808 + 9.69615i) q^{83} +(-2.76795 + 1.59808i) q^{86} +(-2.36603 + 4.09808i) q^{88} +(-2.19615 + 3.80385i) q^{89} +(6.00000 + 6.92820i) q^{91} +(2.19615 - 1.26795i) q^{92} -9.00000i q^{94} -1.26795i q^{95} +(-7.39230 + 4.26795i) q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 2 q^{5} - 10 q^{7}+O(q^{10}) $ 4 * q - 4 * q^4 + 2 * q^5 - 10 * q^7	$ 4 q - 4 q^{4} + 2 q^{5} - 10 q^{7} + 6 q^{11} - 12 q^{13} + 4 q^{16} + 6 q^{19} - 2 q^{20} + 6 q^{22} + 12 q^{23} - 2 q^{25} + 10 q^{28} + 12 q^{29} - 2 q^{35} - 2 q^{37} - 6 q^{38} - 18 q^{41} + 4 q^{43} - 6 q^{44} + 12 q^{46} + 36 q^{47} + 22 q^{49} + 12 q^{52} + 6 q^{53} - 6 q^{58} + 12 q^{59} + 12 q^{62} - 4 q^{64} - 16 q^{67} + 24 q^{73} + 18 q^{74} - 6 q^{76} - 12 q^{77} - 4 q^{79} + 2 q^{80} + 12 q^{83} - 18 q^{86} - 6 q^{88} + 12 q^{89} + 24 q^{91} - 12 q^{92} + 12 q^{97}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^5 - 10 * q^7 + 6 * q^11 - 12 * q^13 + 4 * q^16 + 6 * q^19 - 2 * q^20 + 6 * q^22 + 12 * q^23 - 2 * q^25 + 10 * q^28 + 12 * q^29 - 2 * q^35 - 2 * q^37 - 6 * q^38 - 18 * q^41 + 4 * q^43 - 6 * q^44 + 12 * q^46 + 36 * q^47 + 22 * q^49 + 12 * q^52 + 6 * q^53 - 6 * q^58 + 12 * q^59 + 12 * q^62 - 4 * q^64 - 16 * q^67 + 24 * q^73 + 18 * q^74 - 6 * q^76 - 12 * q^77 - 4 * q^79 + 2 * q^80 + 12 * q^83 - 18 * q^86 - 6 * q^88 + 12 * q^89 + 24 * q^91 - 12 * q^92 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$	4.09808	+	2.36603i	1.23562	+	0.713384i	0.968195	−	0.250196i	$-0.0804951\pi$
$11$	4.09808	+	2.36603i	1.23562	+	0.713384i	0.267421	+	0.963580i	$0.413828\pi$
$12$		0			0
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	0.0225039	−	0.999747i	$-0.492836\pi$
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	−0.854554	+	0.519362i	$0.826170\pi$
$14$	−0.866025	+	2.50000i	−0.231455	+	0.668153i
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	0.368725	−	0.929538i	$-0.379794\pi$
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	−0.620641	+	0.784095i	$0.713128\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		0			0
$22$	2.36603	−	4.09808i	0.504438	−	0.873713i
$23$	−2.19615	+	1.26795i	−0.457929	+	0.264386i	−0.711173	−	0.703017i	$-0.751836\pi$
$23$	−2.19615	+	1.26795i	−0.457929	+	0.264386i	0.253244	+	0.967402i	$0.418503\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.73205	+	3.00000i	−0.339683	+	0.588348i
$27$		0			0
$28$	2.50000	+	0.866025i	0.472456	+	0.163663i
$29$	5.59808	−	3.23205i	1.03954	−	0.600177i	0.119835	−	0.992794i	$-0.461764\pi$
$29$	5.59808	−	3.23205i	1.03954	−	0.600177i	0.919702	+	0.392617i	$0.128430\pi$
$30$		0			0
$31$			8.19615i			1.47207i	0.676942	+	0.736036i	$0.263305\pi$
$31$			8.19615i			1.47207i	−0.676942	+	0.736036i	$0.736695\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$		0			0
$35$	−0.500000	−	2.59808i	−0.0845154	−	0.439155i
$36$		0			0
$37$	−3.09808	+	5.36603i	−0.509321	+	0.882169i	0.490621	+	0.871373i	$0.336770\pi$
$37$	−3.09808	+	5.36603i	−0.509321	+	0.882169i	−0.999942	+	0.0107961i	$0.996563\pi$
$38$	−0.633975	+	1.09808i	−0.102844	+	0.178131i
$39$		0			0
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$		0			0
$43$	−1.59808	−	2.76795i	−0.243704	−	0.422108i	0.718062	−	0.695979i	$-0.245029\pi$
$43$	−1.59808	−	2.76795i	−0.243704	−	0.422108i	−0.961767	+	0.273871i	$0.911696\pi$
$44$	−4.09808	−	2.36603i	−0.617808	−	0.356692i
$45$		0			0
$46$	1.26795	+	2.19615i	0.186949	+	0.323805i
$47$	9.00000			1.31278			0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000			1.31278			0.656392	+	0.754420i	$0.272082\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$	3.00000	+	1.73205i	0.416025	+	0.240192i
$53$	−6.29423	+	3.63397i	−0.864579	+	0.499165i	−0.865543	−	0.500835i	$-0.833026\pi$
$53$	−6.29423	+	3.63397i	−0.864579	+	0.499165i	0.000964138		1.00000i	$0.499693\pi$
$54$		0			0
$55$			4.73205i			0.638070i
$56$	0.866025	−	2.50000i	0.115728	−	0.334077i
$57$		0			0
$58$	−3.23205	−	5.59808i	−0.424389	−	0.735063i
$59$	−2.19615			−0.285915			−0.142957	−	0.989729i	$-0.545661\pi$
$59$	−2.19615			−0.285915			−0.142957	+	0.989729i	$0.545661\pi$
$60$		0			0
$61$			12.9282i			1.65529i	0.561254	+	0.827643i	$0.310319\pi$
$61$			12.9282i			1.65529i	−0.561254	+	0.827643i	$0.689681\pi$
$62$	8.19615			1.04091
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	3.46410i		−	0.429669i
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$		0			0
$70$	−2.59808	+	0.500000i	−0.310530	+	0.0597614i
$71$			4.73205i			0.561591i	0.959768	+	0.280796i	$0.0905983\pi$
$71$			4.73205i			0.561591i	−0.959768	+	0.280796i	$0.909402\pi$
$72$		0			0
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	−0.105937	−	0.994373i	$-0.533784\pi$
$73$	6.00000	−	3.46410i	0.702247	−	0.405442i	0.808184	+	0.588930i	$0.200451\pi$
$74$	5.36603	+	3.09808i	0.623788	+	0.360144i
$75$		0			0
$76$	1.09808	+	0.633975i	0.125958	+	0.0727219i
$77$	−8.19615	−	9.46410i	−0.934038	−	1.07853i
$78$		0			0
$79$	14.5885			1.64133			0.820665	−	0.571410i	$-0.193603\pi$
$79$	14.5885			1.64133			0.820665	+	0.571410i	$0.193603\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$		0			0
$82$	7.79423	+	4.50000i	0.860729	+	0.496942i
$83$	5.59808	+	9.69615i	0.614469	+	1.06429i	0.990477	+	0.137675i	$0.0439629\pi$
$83$	5.59808	+	9.69615i	0.614469	+	1.06429i	−0.376009	+	0.926616i	$0.622704\pi$
$84$		0			0
$85$		0			0
$86$	−2.76795	+	1.59808i	−0.298476	+	0.172325i
$87$		0			0
$88$	−2.36603	+	4.09808i	−0.252219	+	0.436856i
$89$	−2.19615	+	3.80385i	−0.232792	+	0.403207i	−0.958629	−	0.284660i	$-0.908119\pi$
$89$	−2.19615	+	3.80385i	−0.232792	+	0.403207i	0.725837	+	0.687867i	$0.241453\pi$
$90$		0			0
$91$	6.00000	+	6.92820i	0.628971	+	0.726273i
$92$	2.19615	−	1.26795i	0.228965	−	0.132193i
$93$		0			0
$94$		−	9.00000i		−	0.928279i
$95$		−	1.26795i		−	0.130089i
$96$		0			0
$97$	−7.39230	+	4.26795i	−0.750575	+	0.433345i	−0.825902	−	0.563814i	$-0.809333\pi$
$97$	−7.39230	+	4.26795i	−0.750575	+	0.433345i	0.0753267	+	0.997159i	$0.476000\pi$
$98$	4.33013	−	5.50000i	0.437409	−	0.555584i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	5.59808	−	9.69615i	0.557029	−	0.964803i	−0.440713	−	0.897648i	$-0.645274\pi$
$101$	5.59808	−	9.69615i	0.557029	−	0.964803i	0.997743	−	0.0671552i	$-0.0213923\pi$
$102$		0			0
$103$	−10.5000	+	6.06218i	−1.03460	+	0.597324i	−0.918298	−	0.395890i	$-0.870436\pi$
$103$	−10.5000	+	6.06218i	−1.03460	+	0.597324i	−0.116298	+	0.993214i	$0.537103\pi$
$104$	1.73205	−	3.00000i	0.169842	−	0.294174i
$105$		0			0
$106$	3.63397	+	6.29423i	0.352963	+	0.611350i
$107$	13.7942	+	7.96410i	1.33354	+	0.769919i	0.985840	−	0.167688i	$-0.0536300\pi$
$107$	13.7942	+	7.96410i	1.33354	+	0.769919i	0.347698	+	0.937606i	$0.386963\pi$
$108$		0			0
$109$	3.59808	+	6.23205i	0.344633	+	0.596922i	0.985287	−	0.170908i	$-0.0546700\pi$
$109$	3.59808	+	6.23205i	0.344633	+	0.596922i	−0.640654	+	0.767830i	$0.721337\pi$
$110$	4.73205			0.451183
$111$		0			0
$112$	−2.50000	−	0.866025i	−0.236228	−	0.0818317i
$113$	10.9019	+	6.29423i	1.02557	+	0.592111i	0.915711	−	0.401836i	$-0.131628\pi$
$113$	10.9019	+	6.29423i	1.02557	+	0.592111i	0.109855	+	0.993948i	$0.464961\pi$
$114$		0			0
$115$	−2.19615	−	1.26795i	−0.204792	−	0.118237i
$116$	−5.59808	+	3.23205i	−0.519768	+	0.300088i
$117$		0			0
$118$			2.19615i			0.202172i
$119$		0			0
$120$		0			0
$121$	5.69615	+	9.86603i	0.517832	+	0.896911i
$122$	12.9282			1.17046
$123$		0			0
$124$		−	8.19615i		−	0.736036i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−11.3923			−1.01090			−0.505452	−	0.862855i	$-0.668674\pi$
$127$	−11.3923			−1.01090			−0.505452	+	0.862855i	$0.668674\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−3.46410			−0.303822
$131$	−2.19615	−	3.80385i	−0.191879	−	0.332344i	0.753994	−	0.656881i	$-0.228125\pi$
$131$	−2.19615	−	3.80385i	−0.191879	−	0.332344i	−0.945873	+	0.324537i	$0.894791\pi$
$132$		0			0
$133$	2.19615	+	2.53590i	0.190431	+	0.219890i
$134$			4.00000i			0.345547i
$135$		0			0
$136$		0			0
$137$	−6.29423	−	3.63397i	−0.537752	−	0.310471i	0.206415	−	0.978464i	$-0.433820\pi$
$137$	−6.29423	−	3.63397i	−0.537752	−	0.310471i	−0.744167	+	0.667993i	$0.767154\pi$
$138$		0			0
$139$	−19.0981	−	11.0263i	−1.61988	−	0.935237i	−0.986950	−	0.161026i	$-0.948520\pi$
$139$	−19.0981	−	11.0263i	−1.61988	−	0.935237i	−0.632927	−	0.774211i	$-0.718147\pi$
$140$	0.500000	+	2.59808i	0.0422577	+	0.219578i
$141$		0			0
$142$	4.73205			0.397105
$143$	−8.19615	−	14.1962i	−0.685397	−	1.18714i
$144$		0			0
$145$	5.59808	+	3.23205i	0.464895	+	0.268407i
$146$	−3.46410	−	6.00000i	−0.286691	−	0.496564i
$147$		0			0
$148$	3.09808	−	5.36603i	0.254660	−	0.441085i
$149$	−10.3923	+	6.00000i	−0.851371	+	0.491539i	−0.861113	−	0.508413i	$-0.830232\pi$
$149$	−10.3923	+	6.00000i	−0.851371	+	0.491539i	0.00974235	+	0.999953i	$0.496899\pi$
$150$		0			0
$151$	2.09808	−	3.63397i	0.170739	−	0.295729i	−0.767939	−	0.640522i	$-0.778718\pi$
$151$	2.09808	−	3.63397i	0.170739	−	0.295729i	0.938678	+	0.344794i	$0.112051\pi$
$152$	0.633975	−	1.09808i	0.0514221	−	0.0890657i
$153$		0			0
$154$	−9.46410	+	8.19615i	−0.762639	+	0.660465i
$155$	−7.09808	+	4.09808i	−0.570131	+	0.329165i
$156$		0			0
$157$			17.6603i			1.40944i	0.709485	+	0.704721i	$0.248928\pi$
$157$			17.6603i			1.40944i	−0.709485	+	0.704721i	$0.751072\pi$
$158$		−	14.5885i		−	1.16060i
$159$		0			0
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	6.58846	−	1.26795i	0.519243	−	0.0999284i
$162$		0			0
$163$	4.19615	−	7.26795i	0.328668	−	0.569270i	−0.653580	−	0.756858i	$-0.726734\pi$
$163$	4.19615	−	7.26795i	0.328668	−	0.569270i	0.982248	+	0.187588i	$0.0600669\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$	9.69615	−	5.59808i	0.752567	−	0.434495i
$167$	5.19615	−	9.00000i	0.402090	−	0.696441i	−0.591888	−	0.806020i	$-0.701617\pi$
$167$	5.19615	−	9.00000i	0.402090	−	0.696441i	0.993978	+	0.109580i	$0.0349504\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$		0			0
$172$	1.59808	+	2.76795i	0.121852	+	0.211054i
$173$	−8.19615			−0.623142			−0.311571	−	0.950223i	$-0.600855\pi$
$173$	−8.19615			−0.623142			−0.311571	+	0.950223i	$0.600855\pi$
$174$		0			0
$175$	2.00000	−	1.73205i	0.151186	−	0.130931i
$176$	4.09808	+	2.36603i	0.308904	+	0.178346i
$177$		0			0
$178$	3.80385	+	2.19615i	0.285110	+	0.164609i
$179$	21.2942	−	12.2942i	1.59161	−	0.918914i	0.598573	−	0.801068i	$-0.295734\pi$
$179$	21.2942	−	12.2942i	1.59161	−	0.918914i	0.993032	−	0.117846i	$-0.0375989\pi$
$180$		0			0
$181$			13.3923i			0.995442i	0.867337	+	0.497721i	$0.165830\pi$
$181$			13.3923i			0.995442i	−0.867337	+	0.497721i	$0.834170\pi$
$182$	6.92820	−	6.00000i	0.513553	−	0.444750i
$183$		0			0
$184$	−1.26795	−	2.19615i	−0.0934745	−	0.161903i
$185$	−6.19615			−0.455550
$186$		0			0
$187$		0			0
$188$	−9.00000			−0.656392
$189$		0			0
$190$	−1.26795			−0.0919867
$191$			3.46410i			0.250654i	0.992116	+	0.125327i	$0.0399979\pi$
$191$			3.46410i			0.250654i	−0.992116	+	0.125327i	$0.960002\pi$
$192$		0			0
$193$	13.8038			0.993623			0.496811	−	0.867859i	$-0.334504\pi$
$193$	13.8038			0.993623			0.496811	+	0.867859i	$0.334504\pi$
$194$	4.26795	+	7.39230i	0.306421	+	0.530737i
$195$		0			0
$196$	−5.50000	−	4.33013i	−0.392857	−	0.309295i
$197$			23.6603i			1.68572i	0.538130	+	0.842862i	$0.319131\pi$
$197$			23.6603i			1.68572i	−0.538130	+	0.842862i	$0.680869\pi$
$198$		0			0
$199$	6.00000	−	3.46410i	0.425329	−	0.245564i	−0.272026	−	0.962290i	$-0.587694\pi$
$199$	6.00000	−	3.46410i	0.425329	−	0.245564i	0.697355	+	0.716726i	$0.254360\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$		0			0
$202$	−9.69615	−	5.59808i	−0.682219	−	0.393879i
$203$	−16.7942	+	3.23205i	−1.17872	+	0.226845i
$204$		0			0
$205$	−9.00000			−0.628587
$206$	6.06218	+	10.5000i	0.422372	+	0.731570i
$207$		0			0
$208$	−3.00000	−	1.73205i	−0.208013	−	0.120096i
$209$	−3.00000	−	5.19615i	−0.207514	−	0.359425i
$210$		0			0
$211$	10.2942	−	17.8301i	0.708684	−	1.22748i	−0.256662	−	0.966501i	$-0.582623\pi$
$211$	10.2942	−	17.8301i	0.708684	−	1.22748i	0.965345	−	0.260975i	$-0.0840441\pi$
$212$	6.29423	−	3.63397i	0.432289	−	0.249582i
$213$		0			0
$214$	7.96410	−	13.7942i	0.544415	−	0.942954i
$215$	1.59808	−	2.76795i	0.108988	−	0.188773i
$216$		0			0
$217$	7.09808	−	20.4904i	0.481849	−	1.39098i
$218$	6.23205	−	3.59808i	0.422088	−	0.243692i
$219$		0			0
$220$		−	4.73205i		−	0.319035i
$221$		0			0
$222$		0			0
$223$	−11.8923	+	6.86603i	−0.796368	+	0.459783i	−0.842199	−	0.539166i	$-0.818740\pi$
$223$	−11.8923	+	6.86603i	−0.796368	+	0.459783i	0.0458318	+	0.998949i	$0.485406\pi$
$224$	−0.866025	+	2.50000i	−0.0578638	+	0.167038i
$225$		0			0
$226$	6.29423	−	10.9019i	0.418686	−	0.725185i
$227$	8.19615	−	14.1962i	0.543998	−	0.942232i	−0.454672	−	0.890659i	$-0.650243\pi$
$227$	8.19615	−	14.1962i	0.543998	−	0.942232i	0.998669	−	0.0515725i	$-0.0164233\pi$
$228$		0			0
$229$	−12.1865	+	7.03590i	−0.805309	+	0.464945i	−0.845324	−	0.534254i	$-0.820593\pi$
$229$	−12.1865	+	7.03590i	−0.805309	+	0.464945i	0.0400153	+	0.999199i	$0.487259\pi$
$230$	−1.26795	+	2.19615i	−0.0836061	+	0.144810i
$231$		0			0
$232$	3.23205	+	5.59808i	0.212195	+	0.367532i
$233$	1.09808	+	0.633975i	0.0719374	+	0.0415331i	0.535537	−	0.844512i	$-0.320109\pi$
$233$	1.09808	+	0.633975i	0.0719374	+	0.0415331i	−0.463600	+	0.886045i	$0.653442\pi$
$234$		0			0
$235$	4.50000	+	7.79423i	0.293548	+	0.508439i
$236$	2.19615			0.142957
$237$		0			0
$238$		0			0
$239$	−2.70577	−	1.56218i	−0.175022	−	0.101049i	0.409930	−	0.912117i	$-0.365553\pi$
$239$	−2.70577	−	1.56218i	−0.175022	−	0.101049i	−0.584952	+	0.811068i	$0.698887\pi$
$240$		0			0
$241$	2.89230	+	1.66987i	0.186310	+	0.107566i	0.590254	−	0.807218i	$-0.299028\pi$
$241$	2.89230	+	1.66987i	0.186310	+	0.107566i	−0.403944	+	0.914784i	$0.632361\pi$
$242$	9.86603	−	5.69615i	0.634212	−	0.366163i
$243$		0			0
$244$		−	12.9282i		−	0.827643i
$245$	−1.00000	+	6.92820i	−0.0638877	+	0.442627i
$246$		0			0
$247$	2.19615	+	3.80385i	0.139738	+	0.242033i
$248$	−8.19615			−0.520456
$249$		0			0
$250$			1.00000i			0.0632456i
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$			11.3923i			0.714817i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−14.1962	−	24.5885i	−0.885532	−	1.53379i	−0.845103	−	0.534603i	$-0.820461\pi$
$257$	−14.1962	−	24.5885i	−0.885532	−	1.53379i	−0.0404286	−	0.999182i	$-0.512872\pi$
$258$		0			0
$259$	12.3923	−	10.7321i	0.770020	−	0.666857i
$260$			3.46410i			0.214834i
$261$		0			0
$262$	−3.80385	+	2.19615i	−0.235002	+	0.135679i
$263$	11.8923	+	6.86603i	0.733311	+	0.423377i	0.819632	−	0.572890i	$-0.194178\pi$
$263$	11.8923	+	6.86603i	0.733311	+	0.423377i	−0.0863213	+	0.996267i	$0.527511\pi$
$264$		0			0
$265$	−6.29423	−	3.63397i	−0.386651	−	0.223233i
$266$	2.53590	−	2.19615i	0.155486	−	0.134655i
$267$		0			0
$268$	4.00000			0.244339
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$		0			0
$271$	5.70577	+	3.29423i	0.346601	+	0.200110i	0.663187	−	0.748454i	$-0.269203\pi$
$271$	5.70577	+	3.29423i	0.346601	+	0.200110i	−0.316586	+	0.948564i	$0.602537\pi$
$272$		0			0
$273$		0			0
$274$	−3.63397	+	6.29423i	−0.219536	+	0.380248i
$275$	−4.09808	+	2.36603i	−0.247123	+	0.142677i
$276$		0			0
$277$	12.0981	−	20.9545i	0.726903	−	1.25903i	−0.231283	−	0.972887i	$-0.574292\pi$
$277$	12.0981	−	20.9545i	0.726903	−	1.25903i	0.958186	−	0.286146i	$-0.0923743\pi$
$278$	−11.0263	+	19.0981i	−0.661312	+	1.14543i
$279$		0			0
$280$	2.59808	−	0.500000i	0.155265	−	0.0298807i
$281$	−12.6962	+	7.33013i	−0.757389	+	0.437279i	−0.828357	−	0.560200i	$-0.810724\pi$
$281$	−12.6962	+	7.33013i	−0.757389	+	0.437279i	0.0709685	+	0.997479i	$0.477391\pi$
$282$		0			0
$283$			16.8564i			1.00201i	0.865445	+	0.501005i	$0.167036\pi$
$283$			16.8564i			1.00201i	−0.865445	+	0.501005i	$0.832964\pi$
$284$		−	4.73205i		−	0.280796i
$285$		0			0
$286$	−14.1962	+	8.19615i	−0.839436	+	0.484649i
$287$	18.0000	−	15.5885i	1.06251	−	0.920158i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	3.23205	−	5.59808i	0.189793	−	0.328730i
$291$		0			0
$292$	−6.00000	+	3.46410i	−0.351123	+	0.202721i
$293$	−8.19615	+	14.1962i	−0.478824	+	0.829348i	−0.999705	−	0.0242813i	$-0.992270\pi$
$293$	−8.19615	+	14.1962i	−0.478824	+	0.829348i	0.520881	+	0.853629i	$0.325604\pi$
$294$		0			0
$295$	−1.09808	−	1.90192i	−0.0639325	−	0.110734i
$296$	−5.36603	−	3.09808i	−0.311894	−	0.180072i
$297$		0			0
$298$	6.00000	+	10.3923i	0.347571	+	0.602010i
$299$	8.78461			0.508027
$300$		0			0
$301$	1.59808	+	8.30385i	0.0921116	+	0.478626i
$302$	−3.63397	−	2.09808i	−0.209112	−	0.120731i
$303$		0			0
$304$	−1.09808	−	0.633975i	−0.0629790	−	0.0363609i
$305$	−11.1962	+	6.46410i	−0.641090	+	0.370133i
$306$		0			0
$307$		−	23.7846i		−	1.35746i	−0.734388	−	0.678730i	$-0.762531\pi$
$307$		−	23.7846i		−	1.35746i	0.734388	−	0.678730i	$-0.237469\pi$
$308$	8.19615	+	9.46410i	0.467019	+	0.539267i
$309$		0			0
$310$	4.09808	+	7.09808i	0.232755	+	0.403144i
$311$	15.8038			0.896154			0.448077	−	0.893995i	$-0.352109\pi$
$311$	15.8038			0.896154			0.448077	+	0.893995i	$0.352109\pi$
$312$		0			0
$313$		−	20.1962i		−	1.14155i	−0.821105	−	0.570777i	$-0.806642\pi$
$313$		−	20.1962i		−	1.14155i	0.821105	−	0.570777i	$-0.193358\pi$
$314$	17.6603			0.996626
$315$		0			0
$316$	−14.5885			−0.820665
$317$			20.5359i			1.15341i	0.816952	+	0.576705i	$0.195662\pi$
$317$			20.5359i			1.15341i	−0.816952	+	0.576705i	$0.804338\pi$
$318$		0			0
$319$	30.5885			1.71262
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	−1.26795	−	6.58846i	−0.0706600	−	0.367160i
$323$		0			0
$324$		0			0
$325$	3.00000	−	1.73205i	0.166410	−	0.0960769i
$326$	−7.26795	−	4.19615i	−0.402534	−	0.232403i
$327$		0			0
$328$	−7.79423	−	4.50000i	−0.430364	−	0.248471i
$329$	−22.5000	−	7.79423i	−1.24047	−	0.429710i
$330$		0			0
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$	−5.59808	−	9.69615i	−0.307234	−	0.532145i
$333$		0			0
$334$	−9.00000	−	5.19615i	−0.492458	−	0.284321i
$335$	−2.00000	−	3.46410i	−0.109272	−	0.189264i
$336$		0			0
$337$	−5.00000	+	8.66025i	−0.272367	+	0.471754i	−0.969468	−	0.245220i	$-0.921140\pi$
$337$	−5.00000	+	8.66025i	−0.272367	+	0.471754i	0.697100	+	0.716974i	$0.254473\pi$
$338$	−0.866025	+	0.500000i	−0.0471056	+	0.0271964i
$339$		0			0
$340$		0			0
$341$	−19.3923	+	33.5885i	−1.05015	+	1.81892i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	2.76795	−	1.59808i	0.149238	−	0.0861625i
$345$		0			0
$346$			8.19615i			0.440628i
$347$		−	21.2487i		−	1.14069i	−0.821405	−	0.570345i	$-0.806809\pi$
$347$		−	21.2487i		−	1.14069i	0.821405	−	0.570345i	$-0.193191\pi$
$348$		0			0
$349$	−14.1962	+	8.19615i	−0.759903	+	0.438730i	−0.829261	−	0.558862i	$-0.811238\pi$
$349$	−14.1962	+	8.19615i	−0.759903	+	0.438730i	0.0693582	+	0.997592i	$0.477905\pi$
$350$	−1.73205	−	2.00000i	−0.0925820	−	0.106904i
$351$		0			0
$352$	2.36603	−	4.09808i	0.126110	−	0.218428i
$353$	0.294229	−	0.509619i	0.0156602	−	0.0271243i	−0.858089	−	0.513501i	$-0.828348\pi$
$353$	0.294229	−	0.509619i	0.0156602	−	0.0271243i	0.873749	+	0.486377i	$0.161682\pi$
$354$		0			0
$355$	−4.09808	+	2.36603i	−0.217503	+	0.125576i
$356$	2.19615	−	3.80385i	0.116396	−	0.201604i
$357$		0			0
$358$	−12.2942	−	21.2942i	−0.649770	−	1.12543i
$359$	−13.6865	−	7.90192i	−0.722348	−	0.417048i	0.0932685	−	0.995641i	$-0.470268\pi$
$359$	−13.6865	−	7.90192i	−0.722348	−	0.417048i	−0.815616	+	0.578593i	$0.803602\pi$
$360$		0			0
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$	13.3923			0.703884
$363$		0			0
$364$	−6.00000	−	6.92820i	−0.314485	−	0.363137i
$365$	6.00000	+	3.46410i	0.314054	+	0.181319i
$366$		0			0
$367$	−25.2846	−	14.5981i	−1.31985	−	0.762013i	−0.336142	−	0.941811i	$-0.609122\pi$
$367$	−25.2846	−	14.5981i	−1.31985	−	0.762013i	−0.983704	+	0.179798i	$0.942456\pi$
$368$	−2.19615	+	1.26795i	−0.114482	+	0.0660964i
$369$		0			0
$370$			6.19615i			0.322123i
$371$	18.8827	−	3.63397i	0.980340	−	0.188667i
$372$		0			0
$373$	−5.09808	−	8.83013i	−0.263968	−	0.457207i	0.703324	−	0.710869i	$-0.251698\pi$
$373$	−5.09808	−	8.83013i	−0.263968	−	0.457207i	−0.967293	+	0.253662i	$0.918365\pi$
$374$		0			0
$375$		0			0
$376$			9.00000i			0.464140i
$377$	−22.3923			−1.15326
$378$		0			0
$379$	−9.60770			−0.493514			−0.246757	−	0.969077i	$-0.579365\pi$
$379$	−9.60770			−0.493514			−0.246757	+	0.969077i	$0.579365\pi$
$380$			1.26795i			0.0650444i
$381$		0			0
$382$	3.46410			0.177239
$383$	−9.69615	−	16.7942i	−0.495450	−	0.858145i	0.504536	−	0.863391i	$-0.331664\pi$
$383$	−9.69615	−	16.7942i	−0.495450	−	0.858145i	−0.999986	+	0.00524566i	$0.998330\pi$
$384$		0			0
$385$	4.09808	−	11.8301i	0.208857	−	0.602919i
$386$		−	13.8038i		−	0.702597i
$387$		0			0
$388$	7.39230	−	4.26795i	0.375287	−	0.216672i
$389$	−21.4019	−	12.3564i	−1.08512	−	0.626495i	−0.152847	−	0.988250i	$-0.548844\pi$
$389$	−21.4019	−	12.3564i	−1.08512	−	0.626495i	−0.932273	+	0.361755i	$0.882178\pi$
$390$		0			0
$391$		0			0
$392$	−4.33013	+	5.50000i	−0.218704	+	0.277792i
$393$		0			0
$394$	23.6603			1.19199
$395$	7.29423	+	12.6340i	0.367012	+	0.635684i
$396$		0			0
$397$	−26.4904	−	15.2942i	−1.32951	−	0.767595i	−0.344290	−	0.938863i	$-0.611880\pi$
$397$	−26.4904	−	15.2942i	−1.32951	−	0.767595i	−0.985224	+	0.171268i	$0.945214\pi$
$398$	−3.46410	−	6.00000i	−0.173640	−	0.300753i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−3.10770	+	1.79423i	−0.155191	+	0.0895995i	−0.575584	−	0.817742i	$-0.695225\pi$
$401$	−3.10770	+	1.79423i	−0.155191	+	0.0895995i	0.420393	+	0.907342i	$0.361892\pi$
$402$		0			0
$403$	14.1962	−	24.5885i	0.707161	−	1.22484i
$404$	−5.59808	+	9.69615i	−0.278515	+	0.482402i
$405$		0			0
$406$	3.23205	+	16.7942i	0.160404	+	0.833484i
$407$	−25.3923	+	14.6603i	−1.25865	+	0.726682i
$408$		0			0
$409$			10.5167i			0.520015i	0.965607	+	0.260008i	$0.0837251\pi$
$409$			10.5167i			0.520015i	−0.965607	+	0.260008i	$0.916275\pi$
$410$			9.00000i			0.444478i
$411$		0			0
$412$	10.5000	−	6.06218i	0.517298	−	0.298662i
$413$	5.49038	+	1.90192i	0.270164	+	0.0935876i
$414$		0			0
$415$	−5.59808	+	9.69615i	−0.274799	+	0.475965i
$416$	−1.73205	+	3.00000i	−0.0849208	+	0.147087i
$417$		0			0
$418$	−5.19615	+	3.00000i	−0.254152	+	0.146735i
$419$	5.19615	−	9.00000i	0.253849	−	0.439679i	−0.710734	−	0.703461i	$-0.751637\pi$
$419$	5.19615	−	9.00000i	0.253849	−	0.439679i	0.964582	+	0.263783i	$0.0849701\pi$
$420$		0			0
$421$	14.9904	+	25.9641i	0.730586	+	1.26541i	0.956633	+	0.291296i	$0.0940866\pi$
$421$	14.9904	+	25.9641i	0.730586	+	1.26541i	−0.226046	+	0.974117i	$0.572580\pi$
$422$	−17.8301	−	10.2942i	−0.867957	−	0.501115i
$423$		0			0
$424$	−3.63397	−	6.29423i	−0.176481	−	0.305675i
$425$		0			0
$426$		0			0
$427$	11.1962	−	32.3205i	0.541820	−	1.56410i
$428$	−13.7942	−	7.96410i	−0.666769	−	0.384959i
$429$		0			0
$430$	−2.76795	−	1.59808i	−0.133482	−	0.0770661i
$431$	−33.5885	+	19.3923i	−1.61790	+	0.934094i	−0.630437	+	0.776241i	$0.717124\pi$
$431$	−33.5885	+	19.3923i	−1.61790	+	0.934094i	−0.987463	+	0.157854i	$0.949543\pi$
$432$		0			0
$433$			18.0000i			0.865025i	0.901628	+	0.432512i	$0.142373\pi$
$433$			18.0000i			0.865025i	−0.901628	+	0.432512i	$0.857627\pi$
$434$	−20.4904	−	7.09808i	−0.983570	−	0.340719i
$435$		0			0
$436$	−3.59808	−	6.23205i	−0.172317	−	0.298461i
$437$	3.21539			0.153813
$438$		0			0
$439$			29.6603i			1.41561i	0.706410	+	0.707803i	$0.250314\pi$
$439$			29.6603i			1.41561i	−0.706410	+	0.707803i	$0.749686\pi$
$440$	−4.73205			−0.225592
$441$		0			0
$442$		0			0
$443$			9.00000i			0.427603i	0.976877	+	0.213801i	$0.0685846\pi$
$443$			9.00000i			0.427603i	−0.976877	+	0.213801i	$0.931415\pi$
$444$		0			0
$445$	−4.39230			−0.208215
$446$	6.86603	+	11.8923i	0.325116	+	0.563117i
$447$		0			0
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$		−	9.58846i		−	0.452507i	−0.974068	−	0.226254i	$-0.927352\pi$
$449$		−	9.58846i		−	0.452507i	0.974068	−	0.226254i	$-0.0726478\pi$
$450$		0			0
$451$	−36.8827	+	21.2942i	−1.73674	+	1.00271i
$452$	−10.9019	−	6.29423i	−0.512783	−	0.296056i
$453$		0			0
$454$	−14.1962	−	8.19615i	−0.666258	−	0.384664i
$455$	−3.00000	+	8.66025i	−0.140642	+	0.405999i
$456$		0			0
$457$	2.39230			0.111907			0.0559537	−	0.998433i	$-0.482180\pi$
$457$	2.39230			0.111907			0.0559537	+	0.998433i	$0.482180\pi$
$458$	7.03590	+	12.1865i	0.328766	+	0.569439i
$459$		0			0
$460$	2.19615	+	1.26795i	0.102396	+	0.0591184i
$461$	−2.59808	−	4.50000i	−0.121004	−	0.209586i	0.799160	−	0.601119i	$-0.205278\pi$
$461$	−2.59808	−	4.50000i	−0.121004	−	0.209586i	−0.920164	+	0.391533i	$0.871945\pi$
$462$		0			0
$463$	1.30385	−	2.25833i	0.0605949	−	0.104954i	−0.834137	−	0.551558i	$-0.814034\pi$
$463$	1.30385	−	2.25833i	0.0605949	−	0.104954i	0.894731	+	0.446604i	$0.147367\pi$
$464$	5.59808	−	3.23205i	0.259884	−	0.150044i
$465$		0			0
$466$	0.633975	−	1.09808i	0.0293683	−	0.0508674i
$467$	3.40192	−	5.89230i	0.157422	−	0.272663i	−0.776516	−	0.630097i	$-0.783015\pi$
$467$	3.40192	−	5.89230i	0.157422	−	0.272663i	0.933938	+	0.357434i	$0.116348\pi$
$468$		0			0
$469$	10.0000	+	3.46410i	0.461757	+	0.159957i
$470$	7.79423	−	4.50000i	0.359521	−	0.207570i
$471$		0			0
$472$		−	2.19615i		−	0.101086i
$473$		−	15.1244i		−	0.695419i
$474$		0			0
$475$	1.09808	−	0.633975i	0.0503832	−	0.0290887i
$476$		0			0
$477$		0			0
$478$	−1.56218	+	2.70577i	−0.0714524	+	0.123759i
$479$	5.19615	−	9.00000i	0.237418	−	0.411220i	−0.722554	−	0.691314i	$-0.757032\pi$
$479$	5.19615	−	9.00000i	0.237418	−	0.411220i	0.959973	+	0.280094i	$0.0903655\pi$
$480$		0			0
$481$	18.5885	−	10.7321i	0.847561	−	0.489339i
$482$	1.66987	−	2.89230i	0.0760606	−	0.131741i
$483$		0			0
$484$	−5.69615	−	9.86603i	−0.258916	−	0.448456i
$485$	−7.39230	−	4.26795i	−0.335667	−	0.193798i
$486$		0			0
$487$	−17.0000	−	29.4449i	−0.770344	−	1.33427i	−0.937375	−	0.348323i	$-0.886751\pi$
$487$	−17.0000	−	29.4449i	−0.770344	−	1.33427i	0.167031	−	0.985952i	$-0.446582\pi$
$488$	−12.9282			−0.585232
$489$		0			0
$490$	6.92820	+	1.00000i	0.312984	+	0.0451754i
$491$	23.4904	+	13.5622i	1.06011	+	0.612053i	0.925462	−	0.378841i	$-0.123677\pi$
$491$	23.4904	+	13.5622i	1.06011	+	0.612053i	0.134644	+	0.990894i	$0.457011\pi$
$492$		0			0
$493$		0			0
$494$	3.80385	−	2.19615i	0.171143	−	0.0988096i
$495$		0			0
$496$			8.19615i			0.368018i
$497$	4.09808	−	11.8301i	0.183824	−	0.530654i
$498$		0			0
$499$	8.09808	+	14.0263i	0.362520	+	0.627903i	0.988375	−	0.152037i	$-0.0485832\pi$
$499$	8.09808	+	14.0263i	0.362520	+	0.627903i	−0.625855	+	0.779939i	$0.715250\pi$
$500$	1.00000			0.0447214
$501$		0			0
$502$			18.0000i			0.803379i
$503$	−7.39230			−0.329607			−0.164803	−	0.986326i	$-0.552699\pi$
$503$	−7.39230			−0.329607			−0.164803	+	0.986326i	$0.552699\pi$
$504$		0			0
$505$	11.1962			0.498222
$506$			12.0000i			0.533465i
$507$		0			0
$508$	11.3923			0.505452
$509$	−4.79423	−	8.30385i	−0.212500	−	0.368062i	0.739996	−	0.672611i	$-0.234827\pi$
$509$	−4.79423	−	8.30385i	−0.212500	−	0.368062i	−0.952496	+	0.304550i	$0.901494\pi$
$510$		0			0
$511$	−18.0000	+	3.46410i	−0.796273	+	0.153243i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−24.5885	+	14.1962i	−1.08455	+	0.626165i
$515$	−10.5000	−	6.06218i	−0.462685	−	0.267131i
$516$		0			0
$517$	36.8827	+	21.2942i	1.62210	+	0.936519i
$518$	−10.7321	−	12.3923i	−0.471539	−	0.544487i
$519$		0			0
$520$	3.46410			0.151911
$521$	10.5000	+	18.1865i	0.460013	+	0.796766i	0.998961	−	0.0455727i	$-0.0145113\pi$
$521$	10.5000	+	18.1865i	0.460013	+	0.796766i	−0.538948	+	0.842339i	$0.681178\pi$
$522$		0			0
$523$	28.5788	+	16.5000i	1.24967	+	0.721495i	0.971043	−	0.238906i	$-0.0767888\pi$
$523$	28.5788	+	16.5000i	1.24967	+	0.721495i	0.278623	+	0.960401i	$0.410122\pi$
$524$	2.19615	+	3.80385i	0.0959394	+	0.166172i
$525$		0			0
$526$	6.86603	−	11.8923i	0.299373	−	0.518529i
$527$		0			0
$528$		0			0
$529$	−8.28461	+	14.3494i	−0.360200	+	0.623885i
$530$	−3.63397	+	6.29423i	−0.157850	+	0.273404i
$531$		0			0
$532$	−2.19615	−	2.53590i	−0.0952153	−	0.109945i
$533$	27.0000	−	15.5885i	1.16950	−	0.675211i
$534$		0			0
$535$			15.9282i			0.688636i
$536$		−	4.00000i		−	0.172774i
$537$		0			0
$538$	15.5885	−	9.00000i	0.672066	−	0.388018i
$539$	12.2942	+	30.7583i	0.529550	+	1.32486i
$540$		0			0
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$	3.29423	−	5.70577i	0.141499	−	0.245084i
$543$		0			0
$544$		0			0
$545$	−3.59808	+	6.23205i	−0.154125	+	0.266952i
$546$		0			0
$547$	−2.79423	−	4.83975i	−0.119473	−	0.206933i	0.800086	−	0.599885i	$-0.204787\pi$
$547$	−2.79423	−	4.83975i	−0.119473	−	0.206933i	−0.919559	+	0.392952i	$0.871454\pi$
$548$	6.29423	+	3.63397i	0.268876	+	0.155236i
$549$		0			0
$550$	2.36603	+	4.09808i	0.100888	+	0.174743i
$551$	−8.19615			−0.349168
$552$		0			0
$553$	−36.4711	−	12.6340i	−1.55091	−	0.537251i
$554$	−20.9545	−	12.0981i	−0.890271	−	0.513998i
$555$		0			0
$556$	19.0981	+	11.0263i	0.809939	+	0.467618i
$557$	28.3923	−	16.3923i	1.20302	−	0.694564i	0.241795	−	0.970327i	$-0.422264\pi$
$557$	28.3923	−	16.3923i	1.20302	−	0.694564i	0.961226	+	0.275763i	$0.0889305\pi$
$558$		0			0
$559$			11.0718i			0.468287i
$560$	−0.500000	−	2.59808i	−0.0211289	−	0.109789i
$561$		0			0
$562$	7.33013	+	12.6962i	0.309203	+	0.535555i
$563$	13.6077			0.573496			0.286748	−	0.958006i	$-0.407426\pi$
$563$	13.6077			0.573496			0.286748	+	0.958006i	$0.407426\pi$
$564$		0			0
$565$			12.5885i			0.529600i
$566$	16.8564			0.708528
$567$		0			0
$568$	−4.73205			−0.198552
$569$		−	6.00000i		−	0.251533i	−0.992060	−	0.125767i	$-0.959861\pi$
$569$		−	6.00000i		−	0.251533i	0.992060	−	0.125767i	$-0.0401390\pi$
$570$		0			0
$571$	21.6077			0.904254			0.452127	−	0.891954i	$-0.350665\pi$
$571$	21.6077			0.904254			0.452127	+	0.891954i	$0.350665\pi$
$572$	8.19615	+	14.1962i	0.342698	+	0.593571i
$573$		0			0
$574$	−15.5885	−	18.0000i	−0.650650	−	0.751305i
$575$		−	2.53590i		−	0.105754i
$576$		0			0
$577$	20.7846	−	12.0000i	0.865275	−	0.499567i	−0.000500448	−	1.00000i	$-0.500159\pi$
$577$	20.7846	−	12.0000i	0.865275	−	0.499567i	0.865775	+	0.500433i	$0.166826\pi$
$578$	−14.7224	−	8.50000i	−0.612372	−	0.353553i
$579$		0			0
$580$	−5.59808	−	3.23205i	−0.232447	−	0.134204i
$581$	−5.59808	−	29.0885i	−0.232247	−	1.20679i
$582$		0			0
$583$	−34.3923			−1.42438
$584$	3.46410	+	6.00000i	0.143346	+	0.248282i
$585$		0			0
$586$	14.1962	+	8.19615i	0.586438	+	0.338580i
$587$	15.4019	+	26.6769i	0.635705	+	1.10107i	0.986365	+	0.164571i	$0.0526240\pi$
$587$	15.4019	+	26.6769i	0.635705	+	1.10107i	−0.350660	+	0.936503i	$0.614043\pi$
$588$		0			0
$589$	5.19615	−	9.00000i	0.214104	−	0.370839i
$590$	−1.90192	+	1.09808i	−0.0783010	+	0.0452071i
$591$		0			0
$592$	−3.09808	+	5.36603i	−0.127330	+	0.220542i
$593$	−13.3923	+	23.1962i	−0.549956	+	0.952552i	0.448321	+	0.893873i	$0.352022\pi$
$593$	−13.3923	+	23.1962i	−0.549956	+	0.952552i	−0.998277	+	0.0586791i	$0.981311\pi$
$594$		0			0
$595$		0			0
$596$	10.3923	−	6.00000i	0.425685	−	0.245770i
$597$		0			0
$598$		−	8.78461i		−	0.359229i
$599$		−	4.39230i		−	0.179465i	−0.995966	−	0.0897324i	$-0.971399\pi$
$599$		−	4.39230i		−	0.179465i	0.995966	−	0.0897324i	$-0.0286012\pi$
$600$		0			0
$601$	−27.5885	+	15.9282i	−1.12536	+	0.649725i	−0.942763	−	0.333464i	$-0.891783\pi$
$601$	−27.5885	+	15.9282i	−1.12536	+	0.649725i	−0.182594	+	0.983188i	$0.558449\pi$
$602$	8.30385	−	1.59808i	0.338440	−	0.0651327i
$603$		0			0
$604$	−2.09808	+	3.63397i	−0.0853695	+	0.147864i
$605$	−5.69615	+	9.86603i	−0.231582	+	0.401111i
$606$		0			0
$607$	−5.30385	+	3.06218i	−0.215277	+	0.124290i	−0.603761	−	0.797165i	$-0.706332\pi$
$607$	−5.30385	+	3.06218i	−0.215277	+	0.124290i	0.388485	+	0.921455i	$0.372999\pi$
$608$	−0.633975	+	1.09808i	−0.0257111	+	0.0445329i
$609$		0			0
$610$	6.46410	+	11.1962i	0.261724	+	0.453319i
$611$	−27.0000	−	15.5885i	−1.09230	−	0.630641i
$612$		0			0
$613$	3.39230	+	5.87564i	0.137014	+	0.237315i	0.926365	−	0.376627i	$-0.122916\pi$
$613$	3.39230	+	5.87564i	0.137014	+	0.237315i	−0.789351	+	0.613942i	$0.789583\pi$
$614$	−23.7846			−0.959869
$615$		0			0
$616$	9.46410	−	8.19615i	0.381320	−	0.330232i
$617$	−15.8038	−	9.12436i	−0.636239	−	0.367333i	0.146925	−	0.989148i	$-0.453062\pi$
$617$	−15.8038	−	9.12436i	−0.636239	−	0.367333i	−0.783164	+	0.621815i	$0.786396\pi$
$618$		0			0
$619$	14.1962	+	8.19615i	0.570592	+	0.329431i	0.757386	−	0.652968i	$-0.226476\pi$
$619$	14.1962	+	8.19615i	0.570592	+	0.329431i	−0.186794	+	0.982399i	$0.559810\pi$
$620$	7.09808	−	4.09808i	0.285066	−	0.164583i
$621$		0			0
$622$		−	15.8038i		−	0.633677i
$623$	8.78461	−	7.60770i	0.351948	−	0.304796i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−20.1962			−0.807201
$627$		0			0
$628$		−	17.6603i		−	0.704721i
$629$		0			0
$630$		0			0
$631$	12.3923			0.493330			0.246665	−	0.969101i	$-0.420665\pi$
$631$	12.3923			0.493330			0.246665	+	0.969101i	$0.420665\pi$
$632$			14.5885i			0.580298i
$633$		0			0
$634$	20.5359			0.815585
$635$	−5.69615	−	9.86603i	−0.226045	−	0.391521i
$636$		0			0
$637$	−9.00000	−	22.5167i	−0.356593	−	0.892143i
$638$		−	30.5885i		−	1.21101i
$639$		0			0
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$	−2.78461	−	1.60770i	−0.109985	−	0.0635001i	0.443998	−	0.896028i	$-0.353560\pi$
$641$	−2.78461	−	1.60770i	−0.109985	−	0.0635001i	−0.553984	+	0.832528i	$0.686893\pi$
$642$		0			0
$643$	−16.2058	−	9.35641i	−0.639093	−	0.368981i	0.145172	−	0.989406i	$-0.453626\pi$
$643$	−16.2058	−	9.35641i	−0.639093	−	0.368981i	−0.784265	+	0.620426i	$0.786960\pi$
$644$	−6.58846	+	1.26795i	−0.259622	+	0.0499642i
$645$		0			0
$646$		0			0
$647$	2.30385	+	3.99038i	0.0905736	+	0.156878i	0.907753	−	0.419506i	$-0.137797\pi$
$647$	2.30385	+	3.99038i	0.0905736	+	0.156878i	−0.817179	+	0.576384i	$0.804463\pi$
$648$		0			0
$649$	−9.00000	−	5.19615i	−0.353281	−	0.203967i
$650$	−1.73205	−	3.00000i	−0.0679366	−	0.117670i
$651$		0			0
$652$	−4.19615	+	7.26795i	−0.164334	+	0.284635i
$653$	43.1769	−	24.9282i	1.68964	−	0.975516i	0.734857	−	0.678222i	$-0.237249\pi$
$653$	43.1769	−	24.9282i	1.68964	−	0.975516i	0.954786	−	0.297294i	$-0.0960842\pi$
$654$		0			0
$655$	2.19615	−	3.80385i	0.0858108	−	0.148629i
$656$	−4.50000	+	7.79423i	−0.175695	+	0.304314i
$657$		0			0
$658$	−7.79423	+	22.5000i	−0.303851	+	0.877141i
$659$	33.2942	−	19.2224i	1.29696	−	0.748800i	0.317081	−	0.948398i	$-0.397297\pi$
$659$	33.2942	−	19.2224i	1.29696	−	0.748800i	0.979878	+	0.199599i	$0.0639639\pi$
$660$		0			0
$661$		−	13.1436i		−	0.511227i	−0.966779	−	0.255613i	$-0.917723\pi$
$661$		−	13.1436i		−	0.511227i	0.966779	−	0.255613i	$-0.0822774\pi$
$662$			8.00000i			0.310929i
$663$		0			0
$664$	−9.69615	+	5.59808i	−0.376284	+	0.217247i
$665$	−1.09808	+	3.16987i	−0.0425816	+	0.122922i
$666$		0			0
$667$	−8.19615	+	14.1962i	−0.317356	+	0.549677i
$668$	−5.19615	+	9.00000i	−0.201045	+	0.348220i
$669$		0			0
$670$	−3.46410	+	2.00000i	−0.133830	+	0.0772667i
$671$	−30.5885	+	52.9808i	−1.18085	+	2.04530i
$672$		0			0
$673$	12.4904	+	21.6340i	0.481469	+	0.833928i	0.999774	−	0.0212674i	$-0.00677013\pi$
$673$	12.4904	+	21.6340i	0.481469	+	0.833928i	−0.518305	+	0.855196i	$0.673437\pi$
$674$	8.66025	+	5.00000i	0.333581	+	0.192593i
$675$		0			0
$676$	0.500000	+	0.866025i	0.0192308	+	0.0333087i
$677$	−22.9808			−0.883222			−0.441611	−	0.897207i	$-0.645593\pi$
$677$	−22.9808			−0.883222			−0.441611	+	0.897207i	$0.645593\pi$
$678$		0			0
$679$	22.1769	−	4.26795i	0.851072	−	0.163789i
$680$		0			0
$681$		0			0
$682$	33.5885	+	19.3923i	1.28617	+	0.742570i
$683$	30.7750	−	17.7679i	1.17757	−	0.679872i	0.222121	−	0.975019i	$-0.428702\pi$
$683$	30.7750	−	17.7679i	1.17757	−	0.679872i	0.955452	+	0.295148i	$0.0953688\pi$
$684$		0			0
$685$		−	7.26795i		−	0.277694i
$686$	−15.5885	+	10.0000i	−0.595170	+	0.381802i
$687$		0			0
$688$	−1.59808	−	2.76795i	−0.0609261	−	0.105527i
$689$	25.1769			0.959164
$690$		0			0
$691$		−	5.07180i		−	0.192940i	−0.995336	−	0.0964701i	$-0.969245\pi$
$691$		−	5.07180i		−	0.192940i	0.995336	−	0.0964701i	$-0.0307552\pi$
$692$	8.19615			0.311571
$693$		0			0
$694$	−21.2487			−0.806590
$695$		−	22.0526i		−	0.836501i
$696$		0			0
$697$		0			0
$698$	8.19615	+	14.1962i	0.310229	+	0.537332i
$699$		0			0
$700$	−2.00000	+	1.73205i	−0.0755929	+	0.0654654i
$701$		−	44.3205i		−	1.67396i	−0.547232	−	0.836981i	$-0.684318\pi$
$701$		−	44.3205i		−	1.67396i	0.547232	−	0.836981i	$-0.315682\pi$
$702$		0			0
$703$	6.80385	−	3.92820i	0.256612	−	0.148155i
$704$	−4.09808	−	2.36603i	−0.154452	−	0.0891729i
$705$		0			0
$706$	−0.509619	−	0.294229i	−0.0191798	−	0.0110734i
$707$	−22.3923	+	19.3923i	−0.842149	+	0.729323i
$708$		0			0
$709$	−46.7846			−1.75703			−0.878516	−	0.477712i	$-0.841466\pi$
$709$	−46.7846			−1.75703			−0.878516	+	0.477712i	$0.841466\pi$
$710$	2.36603	+	4.09808i	0.0887954	+	0.153798i
$711$		0			0
$712$	−3.80385	−	2.19615i	−0.142555	−	0.0823043i
$713$	−10.3923	−	18.0000i	−0.389195	−	0.674105i
$714$		0			0
$715$	8.19615	−	14.1962i	0.306519	−	0.530906i
$716$	−21.2942	+	12.2942i	−0.795803	+	0.459457i
$717$		0			0
$718$	−7.90192	+	13.6865i	−0.294897	+	0.510777i
$719$	20.7846	−	36.0000i	0.775135	−	1.34257i	−0.159583	−	0.987184i	$-0.551015\pi$
$719$	20.7846	−	36.0000i	0.775135	−	1.34257i	0.934718	−	0.355389i	$-0.115652\pi$
$720$		0			0
$721$	31.5000	−	6.06218i	1.17312	−	0.225767i
$722$	−15.0622	+	8.69615i	−0.560556	+	0.323637i
$723$		0			0
$724$		−	13.3923i		−	0.497721i
$725$			6.46410i			0.240071i
$726$		0			0
$727$	41.7846	−	24.1244i	1.54971	−	0.894723i	0.551542	−	0.834147i	$-0.314040\pi$
$727$	41.7846	−	24.1244i	1.54971	−	0.894723i	0.998164	−	0.0605756i	$-0.0192936\pi$
$728$	−6.92820	+	6.00000i	−0.256776	+	0.222375i
$729$		0			0
$730$	3.46410	−	6.00000i	0.128212	−	0.222070i
$731$		0			0
$732$		0			0
$733$	−29.4904	+	17.0263i	−1.08925	+	0.628880i	−0.933377	−	0.358897i	$-0.883153\pi$
$733$	−29.4904	+	17.0263i	−1.08925	+	0.628880i	−0.155875	+	0.987777i	$0.549820\pi$
$734$	−14.5981	+	25.2846i	−0.538825	+	0.933272i
$735$		0			0
$736$	1.26795	+	2.19615i	0.0467372	+	0.0809513i
$737$	−16.3923	−	9.46410i	−0.603818	−	0.348615i
$738$		0			0
$739$	−16.5885	−	28.7321i	−0.610216	−	1.05693i	−0.991204	−	0.132345i	$-0.957749\pi$
$739$	−16.5885	−	28.7321i	−0.610216	−	1.05693i	0.380987	−	0.924580i	$-0.375584\pi$
$740$	6.19615			0.227775
$741$		0			0
$742$	−3.63397	−	18.8827i	−0.133407	−	0.693205i
$743$	23.6769	+	13.6699i	0.868622	+	0.501499i	0.866890	−	0.498499i	$-0.166115\pi$
$743$	23.6769	+	13.6699i	0.868622	+	0.501499i	0.00173176	+	0.999999i	$0.499449\pi$
$744$		0			0
$745$	−10.3923	−	6.00000i	−0.380745	−	0.219823i
$746$	−8.83013	+	5.09808i	−0.323294	+	0.186654i
$747$		0			0
$748$		0			0
$749$	−27.5885	−	31.8564i	−1.00806	−	1.16401i
$750$		0			0
$751$	10.8038	+	18.7128i	0.394238	+	0.682840i	0.993004	−	0.118084i	$-0.0376752\pi$
$751$	10.8038	+	18.7128i	0.394238	+	0.682840i	−0.598766	+	0.800924i	$0.704342\pi$
$752$	9.00000			0.328196
$753$		0			0
$754$			22.3923i			0.815480i
$755$	4.19615			0.152714
$756$		0			0
$757$	−8.58846			−0.312153			−0.156076	−	0.987745i	$-0.549885\pi$
$757$	−8.58846			−0.312153			−0.156076	+	0.987745i	$0.549885\pi$
$758$			9.60770i			0.348967i
$759$		0			0
$760$	1.26795			0.0459934
$761$	16.5000	+	28.5788i	0.598125	+	1.03598i	0.993098	+	0.117289i	$0.0374205\pi$
$761$	16.5000	+	28.5788i	0.598125	+	1.03598i	−0.394973	+	0.918693i	$0.629246\pi$
$762$		0			0
$763$	−3.59808	−	18.6962i	−0.130259	−	0.676846i
$764$		−	3.46410i		−	0.125327i
$765$		0			0
$766$	−16.7942	+	9.69615i	−0.606800	+	0.350336i
$767$	6.58846	+	3.80385i	0.237895	+	0.137349i
$768$		0			0
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	0.236433	−	0.971648i	$-0.424022\pi$
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	−0.723255	+	0.690581i	$0.757355\pi$
$770$	−11.8301	−	4.09808i	−0.426328	−	0.147684i
$771$		0			0
$772$	−13.8038			−0.496811
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	0.657542	−	0.753418i	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$		0			0
$775$	−7.09808	−	4.09808i	−0.254970	−	0.147207i
$776$	−4.26795	−	7.39230i	−0.153210	−	0.265368i
$777$		0			0
$778$	−12.3564	+	21.4019i	−0.442999	+	0.767296i
$779$	9.88269	−	5.70577i	0.354084	−	0.204430i
$780$		0			0
$781$	−11.1962	+	19.3923i	−0.400630	+	0.693911i
$782$		0			0
$783$		0			0
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	−15.2942	+	8.83013i	−0.545874	+	0.315161i
$786$		0			0
$787$			9.24871i			0.329681i	0.986320	+	0.164840i	$0.0527109\pi$
$787$			9.24871i			0.329681i	−0.986320	+	0.164840i	$0.947289\pi$
$788$		−	23.6603i		−	0.842862i
$789$		0			0
$790$	12.6340	−	7.29423i	0.449497	−	0.259517i
$791$	−21.8038	−	25.1769i	−0.775256	−	0.895188i
$792$		0			0
$793$	22.3923	−	38.7846i	0.795174	−	1.37728i
$794$	−15.2942	+	26.4904i	−0.542772	+	0.940108i
$795$		0			0
$796$	−6.00000	+	3.46410i	−0.212664	+	0.122782i
$797$	−9.58846	+	16.6077i	−0.339641	+	0.588275i	−0.984365	−	0.176140i	$-0.943639\pi$
$797$	−9.58846	+	16.6077i	−0.339641	+	0.588275i	0.644724	+	0.764415i	$0.276972\pi$
$798$		0			0
$799$		0			0
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	1.79423	+	3.10770i	0.0633564	+	0.109737i
$803$	32.7846			1.15694
$804$		0			0
$805$	4.39230	+	5.07180i	0.154808	+	0.178757i
$806$	−24.5885	−	14.1962i	−0.866091	−	0.500038i
$807$		0			0
$808$	9.69615	+	5.59808i	0.341109	+	0.196940i
$809$	45.4808	−	26.2583i	1.59902	−	0.923194i	0.607342	−	0.794441i	$-0.292236\pi$
$809$	45.4808	−	26.2583i	1.59902	−	0.923194i	0.991677	−	0.128753i	$-0.0410975\pi$
$810$		0			0
$811$		−	44.5359i		−	1.56387i	−0.623362	−	0.781933i	$-0.714234\pi$
$811$		−	44.5359i		−	1.56387i	0.623362	−	0.781933i	$-0.285766\pi$
$812$	16.7942	−	3.23205i	0.589362	−	0.113423i
$813$		0			0
$814$	14.6603	+	25.3923i	0.513842	+	0.890000i
$815$	8.39230			0.293970
$816$		0			0
$817$			4.05256i			0.141781i
$818$	10.5167			0.367706
$819$		0			0
$820$	9.00000			0.314294
$821$			36.7128i			1.28129i	0.767839	+	0.640643i	$0.221332\pi$
$821$			36.7128i			1.28129i	−0.767839	+	0.640643i	$0.778668\pi$
$822$		0			0
$823$	30.6077			1.06692			0.533459	−	0.845826i	$-0.320892\pi$
$823$	30.6077			1.06692			0.533459	+	0.845826i	$0.320892\pi$
$824$	−6.06218	−	10.5000i	−0.211186	−	0.365785i
$825$		0			0
$826$	1.90192	−	5.49038i	0.0661764	−	0.191035i
$827$			31.6410i			1.10027i	0.835077	+	0.550133i	$0.185423\pi$
$827$			31.6410i			1.10027i	−0.835077	+	0.550133i	$0.814577\pi$
$828$		0			0
$829$	30.1865	−	17.4282i	1.04842	−	0.605307i	0.126215	−	0.992003i	$-0.459717\pi$
$829$	30.1865	−	17.4282i	1.04842	−	0.605307i	0.922207	+	0.386696i	$0.126384\pi$
$830$	9.69615	+	5.59808i	0.336558	+	0.194312i
$831$		0			0
$832$	3.00000	+	1.73205i	0.104006	+	0.0600481i
$833$		0			0
$834$		0			0
$835$	10.3923			0.359641
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$		0			0
$838$	−9.00000	−	5.19615i	−0.310900	−	0.179498i
$839$	1.90192	+	3.29423i	0.0656617	+	0.113729i	0.896987	−	0.442056i	$-0.145751\pi$
$839$	1.90192	+	3.29423i	0.0656617	+	0.113729i	−0.831326	+	0.555786i	$0.812418\pi$
$840$		0			0
$841$	6.39230	−	11.0718i	0.220424	−	0.381786i
$842$	25.9641	−	14.9904i	0.894782	−	0.516603i
$843$		0			0
$844$	−10.2942	+	17.8301i	−0.354342	+	0.613738i
$845$	0.500000	−	0.866025i	0.0172005	−	0.0297922i
$846$		0			0
$847$	−5.69615	−	29.5981i	−0.195722	−	1.01700i
$848$	−6.29423	+	3.63397i	−0.216145	+	0.124791i
$849$		0			0
$850$		0			0
$851$		−	15.7128i		−	0.538628i
$852$		0			0
$853$	2.78461	−	1.60770i	0.0953432	−	0.0550464i	−0.451570	−	0.892236i	$-0.649136\pi$
$853$	2.78461	−	1.60770i	0.0953432	−	0.0550464i	0.546914	+	0.837189i	$0.315803\pi$
$854$	−32.3205	−	11.1962i	−1.10599	−	0.383124i
$855$		0			0
$856$	−7.96410	+	13.7942i	−0.272207	+	0.471477i
$857$	8.70577	−	15.0788i	0.297383	−	0.515083i	−0.678153	−	0.734921i	$-0.737219\pi$
$857$	8.70577	−	15.0788i	0.297383	−	0.515083i	0.975537	+	0.219837i	$0.0705527\pi$
$858$		0			0
$859$	−13.6865	+	7.90192i	−0.466978	+	0.269610i	−0.714974	−	0.699151i	$-0.753562\pi$
$859$	−13.6865	+	7.90192i	−0.466978	+	0.269610i	0.247996	+	0.968761i	$0.420228\pi$
$860$	−1.59808	+	2.76795i	−0.0544939	+	0.0943863i
$861$		0			0
$862$	19.3923	+	33.5885i	0.660505	+	1.14403i
$863$	25.3923	+	14.6603i	0.864364	+	0.499041i	0.865471	−	0.500959i	$-0.167019\pi$
$863$	25.3923	+	14.6603i	0.864364	+	0.499041i	−0.00110718	+	0.999999i	$0.500352\pi$
$864$		0			0
$865$	−4.09808	−	7.09808i	−0.139339	−	0.241342i
$866$	18.0000			0.611665
$867$		0			0
$868$	−7.09808	+	20.4904i	−0.240924	+	0.695489i
$869$	59.7846	+	34.5167i	2.02805	+	1.17090i
$870$		0			0
$871$	12.0000	+	6.92820i	0.406604	+	0.234753i
$872$	−6.23205	+	3.59808i	−0.211044	+	0.121846i
$873$		0			0
$874$		−	3.21539i		−	0.108762i
$875$	2.50000	+	0.866025i	0.0845154	+	0.0292770i
$876$		0			0
$877$	−25.8827	−	44.8301i	−0.873996	−	1.51381i	−0.857828	−	0.513937i	$-0.828187\pi$
$877$	−25.8827	−	44.8301i	−0.873996	−	1.51381i	−0.0161680	−	0.999869i	$-0.505147\pi$
$878$	29.6603			1.00099
$879$		0			0
$880$			4.73205i			0.159517i
$881$	−16.3923			−0.552271			−0.276135	−	0.961119i	$-0.589054\pi$
$881$	−16.3923			−0.552271			−0.276135	+	0.961119i	$0.589054\pi$
$882$		0			0
$883$	28.3731			0.954830			0.477415	−	0.878678i	$-0.341574\pi$
$883$	28.3731			0.954830			0.477415	+	0.878678i	$0.341574\pi$
$884$		0			0
$885$		0			0
$886$	9.00000			0.302361
$887$	24.6962	+	42.7750i	0.829216	+	1.43624i	0.898654	+	0.438657i	$0.144546\pi$
$887$	24.6962	+	42.7750i	0.829216	+	1.43624i	−0.0694387	+	0.997586i	$0.522121\pi$
$888$		0			0
$889$	28.4808	+	9.86603i	0.955214	+	0.330896i
$890$			4.39230i			0.147230i
$891$		0			0
$892$	11.8923	−	6.86603i	0.398184	−	0.229892i
$893$	−9.88269	−	5.70577i	−0.330711	−	0.190936i
$894$		0			0
$895$	21.2942	+	12.2942i	0.711788	+	0.410951i
$896$	0.866025	−	2.50000i	0.0289319	−	0.0835191i
$897$		0			0
$898$	−9.58846			−0.319971
$899$	26.4904	+	45.8827i	0.883504	+	1.53027i
$900$		0			0
$901$		0			0
$902$	21.2942	+	36.8827i	0.709020	+	1.22806i
$903$		0			0
$904$	−6.29423	+	10.9019i	−0.209343	+	0.362593i
$905$	−11.5981	+	6.69615i	−0.385533	+	0.222588i
$906$		0			0
$907$	−11.4019	+	19.7487i	−0.378595	+	0.655745i	−0.990858	−	0.134909i	$-0.956926\pi$
$907$	−11.4019	+	19.7487i	−0.378595	+	0.655745i	0.612263	+	0.790654i	$0.290259\pi$
$908$	−8.19615	+	14.1962i	−0.271999	+	0.471116i
$909$		0			0
$910$	8.66025	+	3.00000i	0.287085	+	0.0994490i
$911$	−10.0981	+	5.83013i	−0.334564	+	0.193161i	−0.657866	−	0.753135i	$-0.728541\pi$
$911$	−10.0981	+	5.83013i	−0.334564	+	0.193161i	0.323301	+	0.946296i	$0.395207\pi$
$912$		0			0
$913$			52.9808i			1.75341i
$914$		−	2.39230i		−	0.0791304i
$915$		0			0
$916$	12.1865	−	7.03590i	0.402654	−	0.232473i
$917$	2.19615	+	11.4115i	0.0725233	+	0.376842i
$918$		0			0
$919$	−2.29423	+	3.97372i	−0.0756796	+	0.131081i	−0.901382	−	0.433026i	$-0.857446\pi$
$919$	−2.29423	+	3.97372i	−0.0756796	+	0.131081i	0.825702	+	0.564107i	$0.190779\pi$
$920$	1.26795	−	2.19615i	0.0418030	−	0.0724050i
$921$		0			0
$922$	−4.50000	+	2.59808i	−0.148200	+	0.0855631i
$923$	8.19615	−	14.1962i	0.269780	−	0.467272i
$924$		0			0
$925$	−3.09808	−	5.36603i	−0.101864	−	0.176434i
$926$	−2.25833	−	1.30385i	−0.0742133	−	0.0428471i
$927$		0			0
$928$	−3.23205	−	5.59808i	−0.106097	−	0.183766i
$929$	50.5692			1.65912			0.829561	−	0.558416i	$-0.188591\pi$
$929$	50.5692			1.65912			0.829561	+	0.558416i	$0.188591\pi$
$930$		0			0
$931$	−3.29423	−	8.24167i	−0.107964	−	0.270110i
$932$	−1.09808	−	0.633975i	−0.0359687	−	0.0207665i
$933$		0			0
$934$	−5.89230	−	3.40192i	−0.192802	−	0.111314i
$935$		0			0
$936$		0			0
$937$			42.5885i			1.39130i	0.718379	+	0.695652i	$0.244884\pi$
$937$			42.5885i			1.39130i	−0.718379	+	0.695652i	$0.755116\pi$
$938$	3.46410	−	10.0000i	0.113107	−	0.326512i
$939$		0			0
$940$	−4.50000	−	7.79423i	−0.146774	−	0.254220i
$941$	25.9808			0.846949			0.423474	−	0.905908i	$-0.360810\pi$
$941$	25.9808			0.846949			0.423474	+	0.905908i	$0.360810\pi$
$942$		0			0
$943$		−	22.8231i		−	0.743222i
$944$	−2.19615			−0.0714787
$945$		0			0
$946$	−15.1244			−0.491735
$947$		−	23.5692i		−	0.765897i	−0.923770	−	0.382948i	$-0.874909\pi$
$947$		−	23.5692i		−	0.765897i	0.923770	−	0.382948i	$-0.125091\pi$
$948$		0			0
$949$	−24.0000			−0.779073
$950$	−0.633975	−	1.09808i	−0.0205689	−	0.0356263i
$951$		0			0
$952$		0			0
$953$			1.26795i			0.0410729i	0.999789	+	0.0205365i	$0.00653742\pi$
$953$			1.26795i			0.0410729i	−0.999789	+	0.0205365i	$0.993463\pi$
$954$		0			0
$955$	−3.00000	+	1.73205i	−0.0970777	+	0.0560478i
$956$	2.70577	+	1.56218i	0.0875109	+	0.0505244i
$957$		0			0
$958$	−9.00000	−	5.19615i	−0.290777	−	0.167880i
$959$	12.5885	+	14.5359i	0.406502	+	0.469389i
$960$		0			0
$961$	−36.1769			−1.16700
$962$	−10.7321	−	18.5885i	−0.346015	−	0.599316i
$963$		0			0
$964$	−2.89230	−	1.66987i	−0.0931549	−	0.0537830i
$965$	6.90192	+	11.9545i	0.222181	+	0.384828i
$966$		0			0
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	−0.708245	−	0.705967i	$-0.750513\pi$
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	0.965508	+	0.260375i	$0.0838461\pi$
$968$	−9.86603	+	5.69615i	−0.317106	+	0.183081i
$969$		0			0
$970$	−4.26795	+	7.39230i	−0.137036	+	0.237353i
$971$	7.39230	−	12.8038i	0.237230	−	0.410895i	−0.722688	−	0.691174i	$-0.757094\pi$
$971$	7.39230	−	12.8038i	0.237230	−	0.410895i	0.959919	+	0.280279i	$0.0904271\pi$
$972$		0			0
$973$	38.1962	+	44.1051i	1.22451	+	1.41395i
$974$	−29.4449	+	17.0000i	−0.943474	+	0.544715i
$975$		0			0
$976$			12.9282i			0.413822i
$977$		−	5.07180i		−	0.162261i	−0.996703	−	0.0811306i	$-0.974147\pi$
$977$		−	5.07180i		−	0.162261i	0.996703	−	0.0811306i	$-0.0258531\pi$
$978$		0			0
$979$	−18.0000	+	10.3923i	−0.575282	+	0.332140i
$980$	1.00000	−	6.92820i	0.0319438	−	0.221313i
$981$		0			0
$982$	13.5622	−	23.4904i	0.432786	−	0.749608i
$983$	15.6962	−	27.1865i	0.500630	−	0.867116i	−0.499370	−	0.866389i	$-0.666435\pi$
$983$	15.6962	−	27.1865i	0.500630	−	0.867116i	1.00000		0.000727052i	$-0.000231428\pi$
$984$		0			0
$985$	−20.4904	+	11.8301i	−0.652878	+	0.376939i
$986$		0			0
$987$		0			0
$988$	−2.19615	−	3.80385i	−0.0698689	−	0.121017i
$989$	7.01924	+	4.05256i	0.223199	+	0.128864i
$990$		0			0
$991$	6.70577	+	11.6147i	0.213016	+	0.368954i	0.952657	−	0.304047i	$-0.0983381\pi$
$991$	6.70577	+	11.6147i	0.213016	+	0.368954i	−0.739641	+	0.673002i	$0.765005\pi$
$992$	8.19615			0.260228
$993$		0			0
$994$	−11.8301	−	4.09808i	−0.375229	−	0.129983i
$995$	6.00000	+	3.46410i	0.190213	+	0.109819i
$996$		0			0
$997$	−27.2942	−	15.7583i	−0.864417	−	0.499071i	0.00107201	−	0.999999i	$-0.499659\pi$
$997$	−27.2942	−	15.7583i	−0.864417	−	0.499071i	−0.865489	+	0.500928i	$0.832992\pi$
$998$	14.0263	−	8.09808i	0.443994	−	0.256340i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bk.a.341.1		4
3.2	odd	2		630.2.bk.a.131.2	yes	4
7.3	odd	6		1890.2.t.a.1151.2		4
9.2	odd	6		1890.2.t.a.1601.2		4
9.7	even	3		630.2.t.a.551.1	yes	4
21.17	even	6		630.2.t.a.311.1	✓	4
63.38	even	6	inner	1890.2.bk.a.521.2		4
63.52	odd	6		630.2.bk.a.101.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.a.311.1	✓	4	21.17	even	6
630.2.t.a.551.1	yes	4	9.7	even	3
630.2.bk.a.101.1	yes	4	63.52	odd	6
630.2.bk.a.131.2	yes	4	3.2	odd	2
1890.2.t.a.1151.2		4	7.3	odd	6
1890.2.t.a.1601.2		4	9.2	odd	6
1890.2.bk.a.341.1		4	1.1	even	1	trivial
1890.2.bk.a.521.2		4	63.38	even	6	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bk (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} +(4.09808 + 2.36603i) q^{11} +(-3.00000 - 1.73205i) q^{13} +(-0.866025 + 2.50000i) q^{14} +1.00000 q^{16} +(-1.09808 - 0.633975i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(2.36603 - 4.09808i) q^{22} +(-2.19615 + 1.26795i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.73205 + 3.00000i) q^{26} +(2.50000 + 0.866025i) q^{28} +(5.59808 - 3.23205i) q^{29} +8.19615i q^{31} -1.00000i q^{32} +(-0.500000 - 2.59808i) q^{35} +(-3.09808 + 5.36603i) q^{37} +(-0.633975 + 1.09808i) q^{38} +(-0.866025 + 0.500000i) q^{40} +(-4.50000 + 7.79423i) q^{41} +(-1.59808 - 2.76795i) q^{43} +(-4.09808 - 2.36603i) q^{44} +(1.26795 + 2.19615i) q^{46} +9.00000 q^{47} +(5.50000 + 4.33013i) q^{49} +(0.866025 + 0.500000i) q^{50} +(3.00000 + 1.73205i) q^{52} +(-6.29423 + 3.63397i) q^{53} +4.73205i q^{55} +(0.866025 - 2.50000i) q^{56} +(-3.23205 - 5.59808i) q^{58} -2.19615 q^{59} +12.9282i q^{61} +8.19615 q^{62} -1.00000 q^{64} -3.46410i q^{65} -4.00000 q^{67} +(-2.59808 + 0.500000i) q^{70} +4.73205i q^{71} +(6.00000 - 3.46410i) q^{73} +(5.36603 + 3.09808i) q^{74} +(1.09808 + 0.633975i) q^{76} +(-8.19615 - 9.46410i) q^{77} +14.5885 q^{79} +(0.500000 + 0.866025i) q^{80} +(7.79423 + 4.50000i) q^{82} +(5.59808 + 9.69615i) q^{83} +(-2.76795 + 1.59808i) q^{86} +(-2.36603 + 4.09808i) q^{88} +(-2.19615 + 3.80385i) q^{89} +(6.00000 + 6.92820i) q^{91} +(2.19615 - 1.26795i) q^{92} -9.00000i q^{94} -1.26795i q^{95} +(-7.39230 + 4.26795i) q^{97} +(4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 2 q^{5} - 10 q^{7}+O(q^{10}) \) 4 * q - 4 * q^4 + 2 * q^5 - 10 * q^7	\( 4 q - 4 q^{4} + 2 q^{5} - 10 q^{7} + 6 q^{11} - 12 q^{13} + 4 q^{16} + 6 q^{19} - 2 q^{20} + 6 q^{22} + 12 q^{23} - 2 q^{25} + 10 q^{28} + 12 q^{29} - 2 q^{35} - 2 q^{37} - 6 q^{38} - 18 q^{41} + 4 q^{43} - 6 q^{44} + 12 q^{46} + 36 q^{47} + 22 q^{49} + 12 q^{52} + 6 q^{53} - 6 q^{58} + 12 q^{59} + 12 q^{62} - 4 q^{64} - 16 q^{67} + 24 q^{73} + 18 q^{74} - 6 q^{76} - 12 q^{77} - 4 q^{79} + 2 q^{80} + 12 q^{83} - 18 q^{86} - 6 q^{88} + 12 q^{89} + 24 q^{91} - 12 q^{92} + 12 q^{97}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^5 - 10 * q^7 + 6 * q^11 - 12 * q^13 + 4 * q^16 + 6 * q^19 - 2 * q^20 + 6 * q^22 + 12 * q^23 - 2 * q^25 + 10 * q^28 + 12 * q^29 - 2 * q^35 - 2 * q^37 - 6 * q^38 - 18 * q^41 + 4 * q^43 - 6 * q^44 + 12 * q^46 + 36 * q^47 + 22 * q^49 + 12 * q^52 + 6 * q^53 - 6 * q^58 + 12 * q^59 + 12 * q^62 - 4 * q^64 - 16 * q^67 + 24 * q^73 + 18 * q^74 - 6 * q^76 - 12 * q^77 - 4 * q^79 + 2 * q^80 + 12 * q^83 - 18 * q^86 - 6 * q^88 + 12 * q^89 + 24 * q^91 - 12 * q^92 + 12 * q^97

Introduction

L-functions

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Database

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