LMFDB - Embedded newform 2106.2.e.bd.1405.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2106,2,Mod(703,2106)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2106, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2106.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2106 = 2 \cdot 3^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2106.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.8164946657$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1405.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2106.1405
Dual form			2106.2.e.bd.703.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.36603 - 2.36603i) q^{5} +(1.23205 + 2.13397i) q^{7} +1.00000 q^{8} -2.73205 q^{10} +(-2.86603 - 4.96410i) q^{11} +(0.500000 - 0.866025i) q^{13} +(1.23205 - 2.13397i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.92820 q^{17} +1.73205 q^{19} +(1.36603 + 2.36603i) q^{20} +(-2.86603 + 4.96410i) q^{22} +(-2.09808 + 3.63397i) q^{23} +(-1.23205 - 2.13397i) q^{25} -1.00000 q^{26} -2.46410 q^{28} +(-4.86603 - 8.42820i) q^{29} +(-3.73205 + 6.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.46410 + 6.00000i) q^{34} +6.73205 q^{35} -2.53590 q^{37} +(-0.866025 - 1.50000i) q^{38} +(1.36603 - 2.36603i) q^{40} +(-0.633975 + 1.09808i) q^{41} +(-2.46410 - 4.26795i) q^{43} +5.73205 q^{44} +4.19615 q^{46} +(-0.267949 - 0.464102i) q^{47} +(0.464102 - 0.803848i) q^{49} +(-1.23205 + 2.13397i) q^{50} +(0.500000 + 0.866025i) q^{52} +8.66025 q^{53} -15.6603 q^{55} +(1.23205 + 2.13397i) q^{56} +(-4.86603 + 8.42820i) q^{58} +(-7.06218 + 12.2321i) q^{59} +(-1.59808 - 2.76795i) q^{61} +7.46410 q^{62} +1.00000 q^{64} +(-1.36603 - 2.36603i) q^{65} +(6.19615 - 10.7321i) q^{67} +(3.46410 - 6.00000i) q^{68} +(-3.36603 - 5.83013i) q^{70} +10.4641 q^{71} -13.4641 q^{73} +(1.26795 + 2.19615i) q^{74} +(-0.866025 + 1.50000i) q^{76} +(7.06218 - 12.2321i) q^{77} +(-2.90192 - 5.02628i) q^{79} -2.73205 q^{80} +1.26795 q^{82} +(-7.33013 - 12.6962i) q^{83} +(-9.46410 + 16.3923i) q^{85} +(-2.46410 + 4.26795i) q^{86} +(-2.86603 - 4.96410i) q^{88} -14.1962 q^{89} +2.46410 q^{91} +(-2.09808 - 3.63397i) q^{92} +(-0.267949 + 0.464102i) q^{94} +(2.36603 - 4.09808i) q^{95} +(-4.63397 - 8.02628i) q^{97} -0.928203 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{8} - 4 q^{10} - 8 q^{11} + 2 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{20} - 8 q^{22} + 2 q^{23} + 2 q^{25} - 4 q^{26} + 4 q^{28} - 16 q^{29} - 8 q^{31} - 2 q^{32}+ \cdots + 24 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - 2 * q^7 + 4 * q^8 - 4 * q^10 - 8 * q^11 + 2 * q^13 - 2 * q^14 - 2 * q^16 + 2 * q^20 - 8 * q^22 + 2 * q^23 + 2 * q^25 - 4 * q^26 + 4 * q^28 - 16 * q^29 - 8 * q^31 - 2 * q^32 + 20 * q^35 - 24 * q^37 + 2 * q^40 - 6 * q^41 + 4 * q^43 + 16 * q^44 - 4 * q^46 - 8 * q^47 - 12 * q^49 + 2 * q^50 + 2 * q^52 - 28 * q^55 - 2 * q^56 - 16 * q^58 - 4 * q^59 + 4 * q^61 + 16 * q^62 + 4 * q^64 - 2 * q^65 + 4 * q^67 - 10 * q^70 + 28 * q^71 - 40 * q^73 + 12 * q^74 + 4 * q^77 - 22 * q^79 - 4 * q^80 + 12 * q^82 - 12 * q^83 - 24 * q^85 + 4 * q^86 - 8 * q^88 - 36 * q^89 - 4 * q^91 + 2 * q^92 - 8 * q^94 + 6 * q^95 - 22 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2106\mathbb{Z}\right)^\times$.

$n$	$1379$	$1783$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.36603	−	2.36603i	0.610905	−	1.05812i	−0.380183	−	0.924911i	$-0.624139\pi$
$5$	1.36603	−	2.36603i	0.610905	−	1.05812i	0.991088	−	0.133207i	$-0.0425277\pi$
$6$		0			0
$7$	1.23205	+	2.13397i	0.465671	+	0.806567i	0.999232	−	0.0391956i	$-0.0124795\pi$
$7$	1.23205	+	2.13397i	0.465671	+	0.806567i	−0.533560	+	0.845762i	$0.679146\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.73205			−0.863950
$11$	−2.86603	−	4.96410i	−0.864139	−	1.49673i	−0.867899	−	0.496740i	$-0.834530\pi$
$11$	−2.86603	−	4.96410i	−0.864139	−	1.49673i	0.00376022	−	0.999993i	$-0.498803\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	1.23205	−	2.13397i	0.329279	−	0.570329i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.92820			−1.68034			−0.840168	−	0.542326i	$-0.817544\pi$
$17$	−6.92820			−1.68034			−0.840168	+	0.542326i	$0.817544\pi$
$18$		0			0
$19$	1.73205			0.397360			0.198680	−	0.980064i	$-0.436335\pi$
$19$	1.73205			0.397360			0.198680	+	0.980064i	$0.436335\pi$
$20$	1.36603	+	2.36603i	0.305453	+	0.529059i
$21$		0			0
$22$	−2.86603	+	4.96410i	−0.611039	+	1.05835i
$23$	−2.09808	+	3.63397i	−0.437479	+	0.757736i	−0.997494	−	0.0707462i	$-0.977462\pi$
$23$	−2.09808	+	3.63397i	−0.437479	+	0.757736i	0.560015	+	0.828482i	$0.310795\pi$
$24$		0			0
$25$	−1.23205	−	2.13397i	−0.246410	−	0.426795i
$26$	−1.00000			−0.196116
$27$		0			0
$28$	−2.46410			−0.465671
$29$	−4.86603	−	8.42820i	−0.903598	−	1.56508i	−0.822788	−	0.568349i	$-0.807583\pi$
$29$	−4.86603	−	8.42820i	−0.903598	−	1.56508i	−0.0808103	−	0.996729i	$-0.525751\pi$
$30$		0			0
$31$	−3.73205	+	6.46410i	−0.670296	+	1.16099i	0.307524	+	0.951540i	$0.400500\pi$
$31$	−3.73205	+	6.46410i	−0.670296	+	1.16099i	−0.977820	+	0.209447i	$0.932834\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	3.46410	+	6.00000i	0.594089	+	1.02899i
$35$	6.73205			1.13792
$36$		0			0
$37$	−2.53590			−0.416899			−0.208450	−	0.978033i	$-0.566842\pi$
$37$	−2.53590			−0.416899			−0.208450	+	0.978033i	$0.566842\pi$
$38$	−0.866025	−	1.50000i	−0.140488	−	0.243332i
$39$		0			0
$40$	1.36603	−	2.36603i	0.215988	−	0.374101i
$41$	−0.633975	+	1.09808i	−0.0990102	+	0.171491i	−0.911275	−	0.411798i	$-0.864901\pi$
$41$	−0.633975	+	1.09808i	−0.0990102	+	0.171491i	0.812265	+	0.583289i	$0.198234\pi$
$42$		0			0
$43$	−2.46410	−	4.26795i	−0.375772	−	0.650856i	0.614670	−	0.788784i	$-0.289289\pi$
$43$	−2.46410	−	4.26795i	−0.375772	−	0.650856i	−0.990442	+	0.137928i	$0.955956\pi$
$44$	5.73205			0.864139
$45$		0			0
$46$	4.19615			0.618689
$47$	−0.267949	−	0.464102i	−0.0390844	−	0.0676962i	0.845821	−	0.533466i	$-0.179111\pi$
$47$	−0.267949	−	0.464102i	−0.0390844	−	0.0676962i	−0.884906	+	0.465770i	$0.845777\pi$
$48$		0			0
$49$	0.464102	−	0.803848i	0.0663002	−	0.114835i
$50$	−1.23205	+	2.13397i	−0.174238	+	0.301790i
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	8.66025			1.18958			0.594789	−	0.803882i	$-0.297236\pi$
$53$	8.66025			1.18958			0.594789	+	0.803882i	$0.297236\pi$
$54$		0			0
$55$	−15.6603			−2.11163
$56$	1.23205	+	2.13397i	0.164640	+	0.285164i
$57$		0			0
$58$	−4.86603	+	8.42820i	−0.638940	+	1.10668i
$59$	−7.06218	+	12.2321i	−0.919417	+	1.59248i	−0.119115	+	0.992880i	$0.538006\pi$
$59$	−7.06218	+	12.2321i	−0.919417	+	1.59248i	−0.800302	+	0.599597i	$0.795328\pi$
$60$		0			0
$61$	−1.59808	−	2.76795i	−0.204613	−	0.354400i	0.745397	−	0.666621i	$-0.232260\pi$
$61$	−1.59808	−	2.76795i	−0.204613	−	0.354400i	−0.950009	+	0.312222i	$0.898927\pi$
$62$	7.46410			0.947942
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.36603	−	2.36603i	−0.169435	−	0.293469i
$66$		0			0
$67$	6.19615	−	10.7321i	0.756980	−	1.31113i	−0.187403	−	0.982283i	$-0.560007\pi$
$67$	6.19615	−	10.7321i	0.756980	−	1.31113i	0.944384	−	0.328846i	$-0.106660\pi$
$68$	3.46410	−	6.00000i	0.420084	−	0.727607i
$69$		0			0
$70$	−3.36603	−	5.83013i	−0.402317	−	0.696833i
$71$	10.4641			1.24186			0.620930	−	0.783866i	$-0.286755\pi$
$71$	10.4641			1.24186			0.620930	+	0.783866i	$0.286755\pi$
$72$		0			0
$73$	−13.4641			−1.57585			−0.787927	−	0.615769i	$-0.788846\pi$
$73$	−13.4641			−1.57585			−0.787927	+	0.615769i	$0.788846\pi$
$74$	1.26795	+	2.19615i	0.147396	+	0.255298i
$75$		0			0
$76$	−0.866025	+	1.50000i	−0.0993399	+	0.172062i
$77$	7.06218	−	12.2321i	0.804810	−	1.39397i
$78$		0			0
$79$	−2.90192	−	5.02628i	−0.326492	−	0.565501i	0.655321	−	0.755350i	$-0.272533\pi$
$79$	−2.90192	−	5.02628i	−0.326492	−	0.565501i	−0.981813	+	0.189850i	$0.939200\pi$
$80$	−2.73205			−0.305453
$81$		0			0
$82$	1.26795			0.140022
$83$	−7.33013	−	12.6962i	−0.804586	−	1.39358i	−0.916570	−	0.399874i	$-0.869054\pi$
$83$	−7.33013	−	12.6962i	−0.804586	−	1.39358i	0.111984	−	0.993710i	$-0.464279\pi$
$84$		0			0
$85$	−9.46410	+	16.3923i	−1.02653	+	1.77800i
$86$	−2.46410	+	4.26795i	−0.265711	+	0.460225i
$87$		0			0
$88$	−2.86603	−	4.96410i	−0.305519	−	0.529175i
$89$	−14.1962			−1.50479			−0.752395	−	0.658713i	$-0.771101\pi$
$89$	−14.1962			−1.50479			−0.752395	+	0.658713i	$0.771101\pi$
$90$		0			0
$91$	2.46410			0.258308
$92$	−2.09808	−	3.63397i	−0.218740	−	0.378868i
$93$		0			0
$94$	−0.267949	+	0.464102i	−0.0276368	+	0.0478684i
$95$	2.36603	−	4.09808i	0.242749	−	0.420454i
$96$		0			0
$97$	−4.63397	−	8.02628i	−0.470509	−	0.814945i	0.528922	−	0.848670i	$-0.322596\pi$
$97$	−4.63397	−	8.02628i	−0.470509	−	0.814945i	−0.999431	+	0.0337250i	$0.989263\pi$
$98$	−0.928203			−0.0937627
$99$		0			0
$100$	2.46410			0.246410
$101$	4.06218	+	7.03590i	0.404202	+	0.700098i	0.994228	−	0.107286i	$-0.0342160\pi$
$101$	4.06218	+	7.03590i	0.404202	+	0.700098i	−0.590026	+	0.807384i	$0.700883\pi$
$102$		0			0
$103$	−3.73205	+	6.46410i	−0.367730	+	0.636927i	−0.989210	−	0.146503i	$-0.953198\pi$
$103$	−3.73205	+	6.46410i	−0.367730	+	0.636927i	0.621480	+	0.783430i	$0.286532\pi$
$104$	0.500000	−	0.866025i	0.0490290	−	0.0849208i
$105$		0			0
$106$	−4.33013	−	7.50000i	−0.420579	−	0.728464i
$107$	6.73205			0.650812			0.325406	−	0.945574i	$-0.394499\pi$
$107$	6.73205			0.650812			0.325406	+	0.945574i	$0.394499\pi$
$108$		0			0
$109$	10.5885			1.01419			0.507095	−	0.861890i	$-0.330719\pi$
$109$	10.5885			1.01419			0.507095	+	0.861890i	$0.330719\pi$
$110$	7.83013	+	13.5622i	0.746573	+	1.29310i
$111$		0			0
$112$	1.23205	−	2.13397i	0.116418	−	0.201642i
$113$	3.96410	−	6.86603i	0.372911	−	0.645901i	−0.617101	−	0.786884i	$-0.711693\pi$
$113$	3.96410	−	6.86603i	0.372911	−	0.645901i	0.990012	+	0.140983i	$0.0450262\pi$
$114$		0			0
$115$	5.73205	+	9.92820i	0.534516	+	0.925810i
$116$	9.73205			0.903598
$117$		0			0
$118$	14.1244			1.30025
$119$	−8.53590	−	14.7846i	−0.782485	−	1.35530i
$120$		0			0
$121$	−10.9282	+	18.9282i	−0.993473	+	1.72075i
$122$	−1.59808	+	2.76795i	−0.144683	+	0.250598i
$123$		0			0
$124$	−3.73205	−	6.46410i	−0.335148	−	0.580493i
$125$	6.92820			0.619677
$126$		0			0
$127$	−4.53590			−0.402496			−0.201248	−	0.979540i	$-0.564500\pi$
$127$	−4.53590			−0.402496			−0.201248	+	0.979540i	$0.564500\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.36603	+	2.36603i	−0.119808	+	0.207514i
$131$	−4.46410	+	7.73205i	−0.390030	+	0.675552i	−0.992453	−	0.122625i	$-0.960869\pi$
$131$	−4.46410	+	7.73205i	−0.390030	+	0.675552i	0.602423	+	0.798177i	$0.294202\pi$
$132$		0			0
$133$	2.13397	+	3.69615i	0.185039	+	0.320497i
$134$	−12.3923			−1.07053
$135$		0			0
$136$	−6.92820			−0.594089
$137$	−0.464102	−	0.803848i	−0.0396509	−	0.0686773i	0.845519	−	0.533945i	$-0.179291\pi$
$137$	−0.464102	−	0.803848i	−0.0396509	−	0.0686773i	−0.885170	+	0.465268i	$0.845958\pi$
$138$		0			0
$139$	5.09808	−	8.83013i	0.432413	−	0.748962i	−0.564667	−	0.825319i	$-0.690996\pi$
$139$	5.09808	−	8.83013i	0.432413	−	0.748962i	0.997081	+	0.0763570i	$0.0243289\pi$
$140$	−3.36603	+	5.83013i	−0.284481	+	0.492736i
$141$		0			0
$142$	−5.23205	−	9.06218i	−0.439064	−	0.760481i
$143$	−5.73205			−0.479338
$144$		0			0
$145$	−26.5885			−2.20805
$146$	6.73205	+	11.6603i	0.557148	+	0.965009i
$147$		0			0
$148$	1.26795	−	2.19615i	0.104225	−	0.180523i
$149$	−11.3660	+	19.6865i	−0.931141	+	1.61278i	−0.149766	+	0.988721i	$0.547852\pi$
$149$	−11.3660	+	19.6865i	−0.931141	+	1.61278i	−0.781375	+	0.624062i	$0.785481\pi$
$150$		0			0
$151$	6.69615	+	11.5981i	0.544925	+	0.943838i	0.998612	+	0.0526767i	$0.0167753\pi$
$151$	6.69615	+	11.5981i	0.544925	+	0.943838i	−0.453686	+	0.891161i	$0.649891\pi$
$152$	1.73205			0.140488
$153$		0			0
$154$	−14.1244			−1.13817
$155$	10.1962	+	17.6603i	0.818975	+	1.41851i
$156$		0			0
$157$	2.86603	−	4.96410i	0.228734	−	0.396178i	−0.728699	−	0.684834i	$-0.759875\pi$
$157$	2.86603	−	4.96410i	0.228734	−	0.396178i	0.957433	+	0.288655i	$0.0932082\pi$
$158$	−2.90192	+	5.02628i	−0.230865	+	0.399869i
$159$		0			0
$160$	1.36603	+	2.36603i	0.107994	+	0.187051i
$161$	−10.3397			−0.814886
$162$		0			0
$163$	−6.53590			−0.511931			−0.255966	−	0.966686i	$-0.582393\pi$
$163$	−6.53590			−0.511931			−0.255966	+	0.966686i	$0.582393\pi$
$164$	−0.633975	−	1.09808i	−0.0495051	−	0.0857453i
$165$		0			0
$166$	−7.33013	+	12.6962i	−0.568928	+	0.985413i
$167$	3.69615	−	6.40192i	0.286017	−	0.495396i	−0.686838	−	0.726810i	$-0.741002\pi$
$167$	3.69615	−	6.40192i	0.286017	−	0.495396i	0.972855	+	0.231414i	$0.0743353\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	18.9282			1.45173
$171$		0			0
$172$	4.92820			0.375772
$173$	−3.59808	−	6.23205i	−0.273557	−	0.473814i	0.696213	−	0.717835i	$-0.254867\pi$
$173$	−3.59808	−	6.23205i	−0.273557	−	0.473814i	−0.969770	+	0.244021i	$0.921533\pi$
$174$		0			0
$175$	3.03590	−	5.25833i	0.229492	−	0.397492i
$176$	−2.86603	+	4.96410i	−0.216035	+	0.374183i
$177$		0			0
$178$	7.09808	+	12.2942i	0.532023	+	0.921491i
$179$	2.53590			0.189542			0.0947710	−	0.995499i	$-0.469788\pi$
$179$	2.53590			0.189542			0.0947710	+	0.995499i	$0.469788\pi$
$180$		0			0
$181$	−9.58846			−0.712704			−0.356352	−	0.934352i	$-0.615980\pi$
$181$	−9.58846			−0.712704			−0.356352	+	0.934352i	$0.615980\pi$
$182$	−1.23205	−	2.13397i	−0.0913257	−	0.158181i
$183$		0			0
$184$	−2.09808	+	3.63397i	−0.154672	+	0.267900i
$185$	−3.46410	+	6.00000i	−0.254686	+	0.441129i
$186$		0			0
$187$	19.8564	+	34.3923i	1.45204	+	2.51501i
$188$	0.535898			0.0390844
$189$		0			0
$190$	−4.73205			−0.343299
$191$	4.46410	+	7.73205i	0.323011	+	0.559472i	0.981108	−	0.193462i	$-0.0619716\pi$
$191$	4.46410	+	7.73205i	0.323011	+	0.559472i	−0.658097	+	0.752933i	$0.728638\pi$
$192$		0			0
$193$	−2.09808	+	3.63397i	−0.151023	+	0.261579i	−0.931604	−	0.363476i	$-0.881590\pi$
$193$	−2.09808	+	3.63397i	−0.151023	+	0.261579i	0.780581	+	0.625055i	$0.214923\pi$
$194$	−4.63397	+	8.02628i	−0.332700	+	0.576253i
$195$		0			0
$196$	0.464102	+	0.803848i	0.0331501	+	0.0574177i
$197$	−26.7846			−1.90832			−0.954162	−	0.299290i	$-0.903250\pi$
$197$	−26.7846			−1.90832			−0.954162	+	0.299290i	$0.903250\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$	−1.23205	−	2.13397i	−0.0871191	−	0.150895i
$201$		0			0
$202$	4.06218	−	7.03590i	0.285814	−	0.495044i
$203$	11.9904	−	20.7679i	0.841560	−	1.45762i
$204$		0			0
$205$	1.73205	+	3.00000i	0.120972	+	0.209529i
$206$	7.46410			0.520049
$207$		0			0
$208$	−1.00000			−0.0693375
$209$	−4.96410	−	8.59808i	−0.343374	−	0.594741i
$210$		0			0
$211$	9.56218	−	16.5622i	0.658287	−	1.14019i	−0.322771	−	0.946477i	$-0.604614\pi$
$211$	9.56218	−	16.5622i	0.658287	−	1.14019i	0.981059	−	0.193710i	$-0.0620522\pi$
$212$	−4.33013	+	7.50000i	−0.297394	+	0.515102i
$213$		0			0
$214$	−3.36603	−	5.83013i	−0.230097	−	0.398539i
$215$	−13.4641			−0.918244
$216$		0			0
$217$	−18.3923			−1.24855
$218$	−5.29423	−	9.16987i	−0.358570	−	0.621062i
$219$		0			0
$220$	7.83013	−	13.5622i	0.527907	−	0.914362i
$221$	−3.46410	+	6.00000i	−0.233021	+	0.403604i
$222$		0			0
$223$	−5.89230	−	10.2058i	−0.394578	−	0.683429i	0.598469	−	0.801146i	$-0.295776\pi$
$223$	−5.89230	−	10.2058i	−0.394578	−	0.683429i	−0.993047	+	0.117717i	$0.962443\pi$
$224$	−2.46410			−0.164640
$225$		0			0
$226$	−7.92820			−0.527376
$227$	−7.33013	−	12.6962i	−0.486518	−	0.842673i	0.513362	−	0.858172i	$-0.328400\pi$
$227$	−7.33013	−	12.6962i	−0.486518	−	0.842673i	−0.999880	+	0.0154988i	$0.995066\pi$
$228$		0			0
$229$	6.46410	−	11.1962i	0.427160	−	0.739863i	−0.569460	−	0.822019i	$-0.692847\pi$
$229$	6.46410	−	11.1962i	0.427160	−	0.739863i	0.996619	+	0.0821568i	$0.0261808\pi$
$230$	5.73205	−	9.92820i	0.377960	−	0.654646i
$231$		0			0
$232$	−4.86603	−	8.42820i	−0.319470	−	0.553339i
$233$	−3.39230			−0.222237			−0.111119	−	0.993807i	$-0.535443\pi$
$233$	−3.39230			−0.222237			−0.111119	+	0.993807i	$0.535443\pi$
$234$		0			0
$235$	−1.46410			−0.0955075
$236$	−7.06218	−	12.2321i	−0.459709	−	0.796239i
$237$		0			0
$238$	−8.53590	+	14.7846i	−0.553300	+	0.958344i
$239$	1.03590	−	1.79423i	0.0670067	−	0.116059i	−0.830576	−	0.556906i	$-0.811988\pi$
$239$	1.03590	−	1.79423i	0.0670067	−	0.116059i	0.897582	+	0.440847i	$0.145322\pi$
$240$		0			0
$241$	3.63397	+	6.29423i	0.234085	+	0.405447i	0.959006	−	0.283385i	$-0.0914573\pi$
$241$	3.63397	+	6.29423i	0.234085	+	0.405447i	−0.724921	+	0.688832i	$0.758124\pi$
$242$	21.8564			1.40498
$243$		0			0
$244$	3.19615			0.204613
$245$	−1.26795	−	2.19615i	−0.0810063	−	0.140307i
$246$		0			0
$247$	0.866025	−	1.50000i	0.0551039	−	0.0954427i
$248$	−3.73205	+	6.46410i	−0.236985	+	0.410471i
$249$		0			0
$250$	−3.46410	−	6.00000i	−0.219089	−	0.379473i
$251$	2.19615			0.138620			0.0693100	−	0.997595i	$-0.477920\pi$
$251$	2.19615			0.138620			0.0693100	+	0.997595i	$0.477920\pi$
$252$		0			0
$253$	24.0526			1.51217
$254$	2.26795	+	3.92820i	0.142304	+	0.246477i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.232051	+	0.401924i	−0.0144749	+	0.0250713i	−0.873172	−	0.487412i	$-0.837941\pi$
$257$	−0.232051	+	0.401924i	−0.0144749	+	0.0250713i	0.858697	+	0.512483i	$0.171274\pi$
$258$		0			0
$259$	−3.12436	−	5.41154i	−0.194138	−	0.336257i
$260$	2.73205			0.169435
$261$		0			0
$262$	8.92820			0.551586
$263$	9.63397	+	16.6865i	0.594056	+	1.02894i	0.993679	+	0.112256i	$0.0358077\pi$
$263$	9.63397	+	16.6865i	0.594056	+	1.02894i	−0.399623	+	0.916680i	$0.630859\pi$
$264$		0			0
$265$	11.8301	−	20.4904i	0.726719	−	1.25871i
$266$	2.13397	−	3.69615i	0.130842	−	0.226626i
$267$		0			0
$268$	6.19615	+	10.7321i	0.378490	+	0.655564i
$269$	−11.0718			−0.675059			−0.337530	−	0.941315i	$-0.609591\pi$
$269$	−11.0718			−0.675059			−0.337530	+	0.941315i	$0.609591\pi$
$270$		0			0
$271$	5.39230			0.327559			0.163780	−	0.986497i	$-0.447631\pi$
$271$	5.39230			0.327559			0.163780	+	0.986497i	$0.447631\pi$
$272$	3.46410	+	6.00000i	0.210042	+	0.363803i
$273$		0			0
$274$	−0.464102	+	0.803848i	−0.0280374	+	0.0485622i
$275$	−7.06218	+	12.2321i	−0.425865	+	0.737620i
$276$		0			0
$277$	−7.79423	−	13.5000i	−0.468310	−	0.811136i	0.531034	−	0.847350i	$-0.321804\pi$
$277$	−7.79423	−	13.5000i	−0.468310	−	0.811136i	−0.999344	+	0.0362140i	$0.988470\pi$
$278$	−10.1962			−0.611525
$279$		0			0
$280$	6.73205			0.402317
$281$	−15.3923	−	26.6603i	−0.918228	−	1.59042i	−0.802105	−	0.597183i	$-0.796287\pi$
$281$	−15.3923	−	26.6603i	−0.918228	−	1.59042i	−0.116123	−	0.993235i	$-0.537047\pi$
$282$		0			0
$283$	−3.73205	+	6.46410i	−0.221847	+	0.384251i	−0.955369	−	0.295415i	$-0.904542\pi$
$283$	−3.73205	+	6.46410i	−0.221847	+	0.384251i	0.733522	+	0.679666i	$0.237875\pi$
$284$	−5.23205	+	9.06218i	−0.310465	+	0.537741i
$285$		0			0
$286$	2.86603	+	4.96410i	0.169472	+	0.293533i
$287$	−3.12436			−0.184425
$288$		0			0
$289$	31.0000			1.82353
$290$	13.2942	+	23.0263i	0.780664	+	1.35215i
$291$		0			0
$292$	6.73205	−	11.6603i	0.393963	−	0.682365i
$293$	−2.00000	+	3.46410i	−0.116841	+	0.202375i	−0.918514	−	0.395388i	$-0.870610\pi$
$293$	−2.00000	+	3.46410i	−0.116841	+	0.202375i	0.801673	+	0.597763i	$0.203944\pi$
$294$		0			0
$295$	19.2942	+	33.4186i	1.12335	+	1.94571i
$296$	−2.53590			−0.147396
$297$		0			0
$298$	22.7321			1.31683
$299$	2.09808	+	3.63397i	0.121335	+	0.210158i
$300$		0			0
$301$	6.07180	−	10.5167i	0.349973	−	0.606170i
$302$	6.69615	−	11.5981i	0.385320	−	0.667394i
$303$		0			0
$304$	−0.866025	−	1.50000i	−0.0496700	−	0.0860309i
$305$	−8.73205			−0.499996
$306$		0			0
$307$	−9.07180			−0.517755			−0.258877	−	0.965910i	$-0.583353\pi$
$307$	−9.07180			−0.517755			−0.258877	+	0.965910i	$0.583353\pi$
$308$	7.06218	+	12.2321i	0.402405	+	0.696986i
$309$		0			0
$310$	10.1962	−	17.6603i	0.579103	−	1.00304i
$311$	2.07180	−	3.58846i	0.117481	−	0.203483i	−0.801288	−	0.598279i	$-0.795851\pi$
$311$	2.07180	−	3.58846i	0.117481	−	0.203483i	0.918769	+	0.394796i	$0.129185\pi$
$312$		0			0
$313$	−11.5000	−	19.9186i	−0.650018	−	1.12586i	−0.983118	−	0.182973i	$-0.941428\pi$
$313$	−11.5000	−	19.9186i	−0.650018	−	1.12586i	0.333099	−	0.942892i	$-0.391906\pi$
$314$	−5.73205			−0.323478
$315$		0			0
$316$	5.80385			0.326492
$317$	4.56218	+	7.90192i	0.256237	+	0.443816i	0.965231	−	0.261399i	$-0.0841838\pi$
$317$	4.56218	+	7.90192i	0.256237	+	0.443816i	−0.708993	+	0.705215i	$0.750850\pi$
$318$		0			0
$319$	−27.8923	+	48.3109i	−1.56167	+	2.70489i
$320$	1.36603	−	2.36603i	0.0763631	−	0.132265i
$321$		0			0
$322$	5.16987	+	8.95448i	0.288106	+	0.499014i
$323$	−12.0000			−0.667698
$324$		0			0
$325$	−2.46410			−0.136684
$326$	3.26795	+	5.66025i	0.180995	+	0.313492i
$327$		0			0
$328$	−0.633975	+	1.09808i	−0.0350054	+	0.0606311i
$329$	0.660254	−	1.14359i	0.0364010	−	0.0630484i
$330$		0			0
$331$	−2.73205	−	4.73205i	−0.150167	−	0.260097i	0.781122	−	0.624379i	$-0.214648\pi$
$331$	−2.73205	−	4.73205i	−0.150167	−	0.260097i	−0.931289	+	0.364282i	$0.881314\pi$
$332$	14.6603			0.804586
$333$		0			0
$334$	−7.39230			−0.404489
$335$	−16.9282	−	29.3205i	−0.924887	−	1.60195i
$336$		0			0
$337$	8.92820	−	15.4641i	0.486350	−	0.842383i	−0.513527	−	0.858074i	$-0.671661\pi$
$337$	8.92820	−	15.4641i	0.486350	−	0.842383i	0.999877	+	0.0156903i	$0.00499459\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$		0			0
$340$	−9.46410	−	16.3923i	−0.513263	−	0.888998i
$341$	42.7846			2.31692
$342$		0			0
$343$	19.5359			1.05484
$344$	−2.46410	−	4.26795i	−0.132855	−	0.230112i
$345$		0			0
$346$	−3.59808	+	6.23205i	−0.193434	+	0.335037i
$347$	9.63397	−	16.6865i	0.517179	−	0.895780i	−0.482622	−	0.875829i	$-0.660316\pi$
$347$	9.63397	−	16.6865i	0.517179	−	0.895780i	0.999801	−	0.0199514i	$-0.00635113\pi$
$348$		0			0
$349$	11.7321	+	20.3205i	0.628002	+	1.08773i	0.987952	+	0.154760i	$0.0494605\pi$
$349$	11.7321	+	20.3205i	0.628002	+	1.08773i	−0.359950	+	0.932972i	$0.617206\pi$
$350$	−6.07180			−0.324551
$351$		0			0
$352$	5.73205			0.305519
$353$	10.2942	+	17.8301i	0.547907	+	0.949002i	0.998418	+	0.0562312i	$0.0179084\pi$
$353$	10.2942	+	17.8301i	0.547907	+	0.949002i	−0.450511	+	0.892771i	$0.648758\pi$
$354$		0			0
$355$	14.2942	−	24.7583i	0.758659	−	1.31404i
$356$	7.09808	−	12.2942i	0.376197	−	0.651593i
$357$		0			0
$358$	−1.26795	−	2.19615i	−0.0670132	−	0.116070i
$359$	19.8564			1.04798			0.523991	−	0.851724i	$-0.324443\pi$
$359$	19.8564			1.04798			0.523991	+	0.851724i	$0.324443\pi$
$360$		0			0
$361$	−16.0000			−0.842105
$362$	4.79423	+	8.30385i	0.251979	+	0.436441i
$363$		0			0
$364$	−1.23205	+	2.13397i	−0.0645770	+	0.111851i
$365$	−18.3923	+	31.8564i	−0.962697	+	1.66744i
$366$		0			0
$367$	2.29423	+	3.97372i	0.119758	+	0.207427i	0.919672	−	0.392688i	$-0.128455\pi$
$367$	2.29423	+	3.97372i	0.119758	+	0.207427i	−0.799914	+	0.600115i	$0.795122\pi$
$368$	4.19615			0.218740
$369$		0			0
$370$	6.92820			0.360180
$371$	10.6699	+	18.4808i	0.553952	+	0.959473i
$372$		0			0
$373$	−0.937822	+	1.62436i	−0.0485586	+	0.0841059i	−0.889283	−	0.457357i	$-0.848796\pi$
$373$	−0.937822	+	1.62436i	−0.0485586	+	0.0841059i	0.840724	+	0.541463i	$0.182129\pi$
$374$	19.8564	−	34.3923i	1.02675	−	1.77838i
$375$		0			0
$376$	−0.267949	−	0.464102i	−0.0138184	−	0.0239342i
$377$	−9.73205			−0.501226
$378$		0			0
$379$	35.0526			1.80053			0.900265	−	0.435343i	$-0.143373\pi$
$379$	35.0526			1.80053			0.900265	+	0.435343i	$0.143373\pi$
$380$	2.36603	+	4.09808i	0.121375	+	0.210227i
$381$		0			0
$382$	4.46410	−	7.73205i	0.228403	−	0.395606i
$383$	−3.69615	+	6.40192i	−0.188865	+	0.327123i	−0.944872	−	0.327440i	$-0.893814\pi$
$383$	−3.69615	+	6.40192i	−0.188865	+	0.327123i	0.756007	+	0.654563i	$0.227147\pi$
$384$		0			0
$385$	−19.2942	−	33.4186i	−0.983325	−	1.70317i
$386$	4.19615			0.213579
$387$		0			0
$388$	9.26795			0.470509
$389$	6.92820	+	12.0000i	0.351274	+	0.608424i	0.986473	−	0.163924i	$-0.0524153\pi$
$389$	6.92820	+	12.0000i	0.351274	+	0.608424i	−0.635199	+	0.772348i	$0.719082\pi$
$390$		0			0
$391$	14.5359	−	25.1769i	0.735112	−	1.27325i
$392$	0.464102	−	0.803848i	0.0234407	−	0.0406004i
$393$		0			0
$394$	13.3923	+	23.1962i	0.674695	+	1.16861i
$395$	−15.8564			−0.797822
$396$		0			0
$397$	33.8564			1.69920			0.849602	−	0.527424i	$-0.176842\pi$
$397$	33.8564			1.69920			0.849602	+	0.527424i	$0.176842\pi$
$398$	2.00000	+	3.46410i	0.100251	+	0.173640i
$399$		0			0
$400$	−1.23205	+	2.13397i	−0.0616025	+	0.106699i
$401$	7.09808	−	12.2942i	0.354461	−	0.613944i	−0.632565	−	0.774508i	$-0.717998\pi$
$401$	7.09808	−	12.2942i	0.354461	−	0.613944i	0.987026	+	0.160563i	$0.0513310\pi$
$402$		0			0
$403$	3.73205	+	6.46410i	0.185907	+	0.322000i
$404$	−8.12436			−0.404202
$405$		0			0
$406$	−23.9808			−1.19015
$407$	7.26795	+	12.5885i	0.360259	+	0.623987i
$408$		0			0
$409$	11.7321	−	20.3205i	0.580113	−	1.00478i	−0.415353	−	0.909660i	$-0.636342\pi$
$409$	11.7321	−	20.3205i	0.580113	−	1.00478i	0.995465	−	0.0951241i	$-0.0303248\pi$
$410$	1.73205	−	3.00000i	0.0855399	−	0.148159i
$411$		0			0
$412$	−3.73205	−	6.46410i	−0.183865	−	0.318463i
$413$	−34.8038			−1.71259
$414$		0			0
$415$	−40.0526			−1.96610
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$		0			0
$418$	−4.96410	+	8.59808i	−0.242802	+	0.420546i
$419$	8.83013	−	15.2942i	0.431380	−	0.747172i	−0.565612	−	0.824671i	$-0.691360\pi$
$419$	8.83013	−	15.2942i	0.431380	−	0.747172i	0.996992	+	0.0774992i	$0.0246935\pi$
$420$		0			0
$421$	−17.7583	−	30.7583i	−0.865488	−	1.49907i	−0.866562	−	0.499070i	$-0.833675\pi$
$421$	−17.7583	−	30.7583i	−0.865488	−	1.49907i	0.00107369	−	0.999999i	$-0.499658\pi$
$422$	−19.1244			−0.930959
$423$		0			0
$424$	8.66025			0.420579
$425$	8.53590	+	14.7846i	0.414052	+	0.717159i
$426$		0			0
$427$	3.93782	−	6.82051i	0.190565	−	0.330068i
$428$	−3.36603	+	5.83013i	−0.162703	+	0.281810i
$429$		0			0
$430$	6.73205	+	11.6603i	0.324648	+	0.562307i
$431$	36.4641			1.75641			0.878207	−	0.478281i	$-0.158740\pi$
$431$	36.4641			1.75641			0.878207	+	0.478281i	$0.158740\pi$
$432$		0			0
$433$	2.60770			0.125318			0.0626589	−	0.998035i	$-0.480042\pi$
$433$	2.60770			0.125318			0.0626589	+	0.998035i	$0.480042\pi$
$434$	9.19615	+	15.9282i	0.441429	+	0.764578i
$435$		0			0
$436$	−5.29423	+	9.16987i	−0.253548	+	0.439157i
$437$	−3.63397	+	6.29423i	−0.173837	+	0.301094i
$438$		0			0
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$	−15.6603			−0.746573
$441$		0			0
$442$	6.92820			0.329541
$443$	13.8564	+	24.0000i	0.658338	+	1.14027i	0.981046	+	0.193776i	$0.0620735\pi$
$443$	13.8564	+	24.0000i	0.658338	+	1.14027i	−0.322708	+	0.946499i	$0.604593\pi$
$444$		0			0
$445$	−19.3923	+	33.5885i	−0.919283	+	1.59225i
$446$	−5.89230	+	10.2058i	−0.279009	+	0.483257i
$447$		0			0
$448$	1.23205	+	2.13397i	0.0582089	+	0.100821i
$449$	−8.00000			−0.377543			−0.188772	−	0.982021i	$-0.560451\pi$
$449$	−8.00000			−0.377543			−0.188772	+	0.982021i	$0.560451\pi$
$450$		0			0
$451$	7.26795			0.342234
$452$	3.96410	+	6.86603i	0.186456	+	0.322951i
$453$		0			0
$454$	−7.33013	+	12.6962i	−0.344020	+	0.595860i
$455$	3.36603	−	5.83013i	0.157802	−	0.273321i
$456$		0			0
$457$	−11.1699	−	19.3468i	−0.522505	−	0.905005i	−0.999657	−	0.0261840i	$-0.991664\pi$
$457$	−11.1699	−	19.3468i	−0.522505	−	0.905005i	0.477153	−	0.878821i	$-0.341669\pi$
$458$	−12.9282			−0.604095
$459$		0			0
$460$	−11.4641			−0.534516
$461$	−19.0981	−	33.0788i	−0.889486	−	1.54064i	−0.840484	−	0.541836i	$-0.817729\pi$
$461$	−19.0981	−	33.0788i	−0.889486	−	1.54064i	−0.0490021	−	0.998799i	$-0.515604\pi$
$462$		0			0
$463$	−0.160254	+	0.277568i	−0.00744764	+	0.0128997i	−0.869725	−	0.493536i	$-0.835704\pi$
$463$	−0.160254	+	0.277568i	−0.00744764	+	0.0128997i	0.862278	+	0.506436i	$0.169037\pi$
$464$	−4.86603	+	8.42820i	−0.225900	+	0.391270i
$465$		0			0
$466$	1.69615	+	2.93782i	0.0785727	+	0.136092i
$467$	−0.875644			−0.0405200			−0.0202600	−	0.999795i	$-0.506449\pi$
$467$	−0.875644			−0.0405200			−0.0202600	+	0.999795i	$0.506449\pi$
$468$		0			0
$469$	30.5359			1.41002
$470$	0.732051	+	1.26795i	0.0337670	+	0.0584861i
$471$		0			0
$472$	−7.06218	+	12.2321i	−0.325063	+	0.563026i
$473$	−14.1244	+	24.4641i	−0.649439	+	1.12486i
$474$		0			0
$475$	−2.13397	−	3.69615i	−0.0979135	−	0.169591i
$476$	17.0718			0.782485
$477$		0			0
$478$	−2.07180			−0.0947618
$479$	−13.6244	−	23.5981i	−0.622513	−	1.07822i	−0.989016	−	0.147807i	$-0.952779\pi$
$479$	−13.6244	−	23.5981i	−0.622513	−	1.07822i	0.366504	−	0.930417i	$-0.380555\pi$
$480$		0			0
$481$	−1.26795	+	2.19615i	−0.0578135	+	0.100136i
$482$	3.63397	−	6.29423i	0.165523	−	0.286694i
$483$		0			0
$484$	−10.9282	−	18.9282i	−0.496737	−	0.860373i
$485$	−25.3205			−1.14975
$486$		0			0
$487$	0.607695			0.0275373			0.0137686	−	0.999905i	$-0.495617\pi$
$487$	0.607695			0.0275373			0.0137686	+	0.999905i	$0.495617\pi$
$488$	−1.59808	−	2.76795i	−0.0723415	−	0.125299i
$489$		0			0
$490$	−1.26795	+	2.19615i	−0.0572801	+	0.0992121i
$491$	15.6603	−	27.1244i	0.706737	−	1.22411i	−0.259324	−	0.965791i	$-0.583500\pi$
$491$	15.6603	−	27.1244i	0.706737	−	1.22411i	0.966061	−	0.258315i	$-0.0831671\pi$
$492$		0			0
$493$	33.7128	+	58.3923i	1.51835	+	2.62986i
$494$	−1.73205			−0.0779287
$495$		0			0
$496$	7.46410			0.335148
$497$	12.8923	+	22.3301i	0.578299	+	1.00164i
$498$		0			0
$499$	−1.59808	+	2.76795i	−0.0715397	+	0.123910i	−0.899576	−	0.436764i	$-0.856125\pi$
$499$	−1.59808	+	2.76795i	−0.0715397	+	0.123910i	0.828037	+	0.560674i	$0.189458\pi$
$500$	−3.46410	+	6.00000i	−0.154919	+	0.268328i
$501$		0			0
$502$	−1.09808	−	1.90192i	−0.0490095	−	0.0848870i
$503$	20.9808			0.935486			0.467743	−	0.883865i	$-0.345067\pi$
$503$	20.9808			0.935486			0.467743	+	0.883865i	$0.345067\pi$
$504$		0			0
$505$	22.1962			0.987716
$506$	−12.0263	−	20.8301i	−0.534633	−	0.926012i
$507$		0			0
$508$	2.26795	−	3.92820i	0.100624	−	0.174286i
$509$	5.26795	−	9.12436i	0.233498	−	0.404430i	−0.725337	−	0.688394i	$-0.758316\pi$
$509$	5.26795	−	9.12436i	0.233498	−	0.404430i	0.958835	+	0.283964i	$0.0916495\pi$
$510$		0			0
$511$	−16.5885	−	28.7321i	−0.733830	−	1.27103i
$512$	1.00000			0.0441942
$513$		0			0
$514$	0.464102			0.0204706
$515$	10.1962	+	17.6603i	0.449296	+	0.778204i
$516$		0			0
$517$	−1.53590	+	2.66025i	−0.0675487	+	0.116998i
$518$	−3.12436	+	5.41154i	−0.137276	+	0.237770i
$519$		0			0
$520$	−1.36603	−	2.36603i	−0.0599042	−	0.103757i
$521$	−21.2487			−0.930923			−0.465461	−	0.885068i	$-0.654112\pi$
$521$	−21.2487			−0.930923			−0.465461	+	0.885068i	$0.654112\pi$
$522$		0			0
$523$	19.5167			0.853404			0.426702	−	0.904392i	$-0.359675\pi$
$523$	19.5167			0.853404			0.426702	+	0.904392i	$0.359675\pi$
$524$	−4.46410	−	7.73205i	−0.195015	−	0.337776i
$525$		0			0
$526$	9.63397	−	16.6865i	0.420061	−	0.727567i
$527$	25.8564	−	44.7846i	1.12632	−	1.95085i
$528$		0			0
$529$	2.69615	+	4.66987i	0.117224	+	0.203038i
$530$	−23.6603			−1.02774
$531$		0			0
$532$	−4.26795			−0.185039
$533$	0.633975	+	1.09808i	0.0274605	+	0.0475630i
$534$		0			0
$535$	9.19615	−	15.9282i	0.397584	−	0.688636i
$536$	6.19615	−	10.7321i	0.267633	−	0.463554i
$537$		0			0
$538$	5.53590	+	9.58846i	0.238670	+	0.413388i
$539$	−5.32051			−0.229171
$540$		0			0
$541$	10.8756			0.467580			0.233790	−	0.972287i	$-0.424887\pi$
$541$	10.8756			0.467580			0.233790	+	0.972287i	$0.424887\pi$
$542$	−2.69615	−	4.66987i	−0.115810	−	0.200588i
$543$		0			0
$544$	3.46410	−	6.00000i	0.148522	−	0.257248i
$545$	14.4641	−	25.0526i	0.619574	−	1.07313i
$546$		0			0
$547$	−20.4641	−	35.4449i	−0.874982	−	1.51551i	−0.856782	−	0.515679i	$-0.827540\pi$
$547$	−20.4641	−	35.4449i	−0.874982	−	1.51551i	−0.0181997	−	0.999834i	$-0.505793\pi$
$548$	0.928203			0.0396509
$549$		0			0
$550$	14.1244			0.602265
$551$	−8.42820	−	14.5981i	−0.359054	−	0.621899i
$552$		0			0
$553$	7.15064	−	12.3853i	0.304076	−	0.526675i
$554$	−7.79423	+	13.5000i	−0.331145	+	0.573560i
$555$		0			0
$556$	5.09808	+	8.83013i	0.216207	+	0.374481i
$557$	18.2487			0.773223			0.386611	−	0.922243i	$-0.373645\pi$
$557$	18.2487			0.773223			0.386611	+	0.922243i	$0.373645\pi$
$558$		0			0
$559$	−4.92820			−0.208441
$560$	−3.36603	−	5.83013i	−0.142241	−	0.246368i
$561$		0			0
$562$	−15.3923	+	26.6603i	−0.649285	+	1.12459i
$563$	21.0981	−	36.5429i	0.889178	−	1.54010i	0.0483289	−	0.998831i	$-0.484610\pi$
$563$	21.0981	−	36.5429i	0.889178	−	1.54010i	0.840849	−	0.541270i	$-0.182056\pi$
$564$		0			0
$565$	−10.8301	−	18.7583i	−0.455627	−	0.789169i
$566$	7.46410			0.313740
$567$		0			0
$568$	10.4641			0.439064
$569$	−14.0000	−	24.2487i	−0.586911	−	1.01656i	−0.994634	−	0.103454i	$-0.967011\pi$
$569$	−14.0000	−	24.2487i	−0.586911	−	1.01656i	0.407724	−	0.913105i	$-0.366323\pi$
$570$		0			0
$571$	17.3660	−	30.0788i	0.726746	−	1.25876i	−0.231506	−	0.972833i	$-0.574365\pi$
$571$	17.3660	−	30.0788i	0.726746	−	1.25876i	0.958251	−	0.285927i	$-0.0923014\pi$
$572$	2.86603	−	4.96410i	0.119835	−	0.207560i
$573$		0			0
$574$	1.56218	+	2.70577i	0.0652040	+	0.112937i
$575$	10.3397			0.431197
$576$		0			0
$577$	2.53590			0.105571			0.0527854	−	0.998606i	$-0.483190\pi$
$577$	2.53590			0.105571			0.0527854	+	0.998606i	$0.483190\pi$
$578$	−15.5000	−	26.8468i	−0.644715	−	1.11668i
$579$		0			0
$580$	13.2942	−	23.0263i	0.552013	−	0.956114i
$581$	18.0622	−	31.2846i	0.749345	−	1.29790i
$582$		0			0
$583$	−24.8205	−	42.9904i	−1.02796	−	1.78048i
$584$	−13.4641			−0.557148
$585$		0			0
$586$	4.00000			0.165238
$587$	−3.19615	−	5.53590i	−0.131919	−	0.228491i	0.792497	−	0.609876i	$-0.208781\pi$
$587$	−3.19615	−	5.53590i	−0.131919	−	0.228491i	−0.924416	+	0.381385i	$0.875447\pi$
$588$		0			0
$589$	−6.46410	+	11.1962i	−0.266349	+	0.461329i
$590$	19.2942	−	33.4186i	0.794331	−	1.37582i
$591$		0			0
$592$	1.26795	+	2.19615i	0.0521124	+	0.0902613i
$593$	−9.66025			−0.396699			−0.198350	−	0.980131i	$-0.563558\pi$
$593$	−9.66025			−0.396699			−0.198350	+	0.980131i	$0.563558\pi$
$594$		0			0
$595$	−46.6410			−1.91210
$596$	−11.3660	−	19.6865i	−0.465571	−	0.806392i
$597$		0			0
$598$	2.09808	−	3.63397i	0.0857967	−	0.148604i
$599$	11.2224	−	19.4378i	0.458536	−	0.794208i	−0.540348	−	0.841442i	$-0.681707\pi$
$599$	11.2224	−	19.4378i	0.458536	−	0.794208i	0.998884	+	0.0472339i	$0.0150406\pi$
$600$		0			0
$601$	21.0885	+	36.5263i	0.860216	+	1.48994i	0.871720	+	0.490004i	$0.163005\pi$
$601$	21.0885	+	36.5263i	0.860216	+	1.48994i	−0.0115040	+	0.999934i	$0.503662\pi$
$602$	−12.1436			−0.494936
$603$		0			0
$604$	−13.3923			−0.544925
$605$	29.8564	+	51.7128i	1.21384	+	2.10242i
$606$		0			0
$607$	−14.1962	+	24.5885i	−0.576204	+	0.998015i	0.419706	+	0.907660i	$0.362133\pi$
$607$	−14.1962	+	24.5885i	−0.576204	+	0.998015i	−0.995910	+	0.0903544i	$0.971200\pi$
$608$	−0.866025	+	1.50000i	−0.0351220	+	0.0608330i
$609$		0			0
$610$	4.36603	+	7.56218i	0.176775	+	0.306184i
$611$	−0.535898			−0.0216801
$612$		0			0
$613$	−10.9282			−0.441386			−0.220693	−	0.975343i	$-0.570832\pi$
$613$	−10.9282			−0.441386			−0.220693	+	0.975343i	$0.570832\pi$
$614$	4.53590	+	7.85641i	0.183054	+	0.317059i
$615$		0			0
$616$	7.06218	−	12.2321i	0.284543	−	0.492843i
$617$	−4.36603	+	7.56218i	−0.175770	+	0.304442i	−0.940427	−	0.339995i	$-0.889575\pi$
$617$	−4.36603	+	7.56218i	−0.175770	+	0.304442i	0.764658	+	0.644437i	$0.222908\pi$
$618$		0			0
$619$	−13.7224	−	23.7679i	−0.551551	−	0.955315i	−0.998163	−	0.0605867i	$-0.980703\pi$
$619$	−13.7224	−	23.7679i	−0.551551	−	0.955315i	0.446612	−	0.894728i	$-0.352631\pi$
$620$	−20.3923			−0.818975
$621$		0			0
$622$	−4.14359			−0.166143
$623$	−17.4904	−	30.2942i	−0.700737	−	1.21371i
$624$		0			0
$625$	15.6244	−	27.0622i	0.624974	−	1.08249i
$626$	−11.5000	+	19.9186i	−0.459632	+	0.796107i
$627$		0			0
$628$	2.86603	+	4.96410i	0.114367	+	0.198089i
$629$	17.5692			0.700531
$630$		0			0
$631$	4.21539			0.167812			0.0839060	−	0.996474i	$-0.473260\pi$
$631$	4.21539			0.167812			0.0839060	+	0.996474i	$0.473260\pi$
$632$	−2.90192	−	5.02628i	−0.115432	−	0.199935i
$633$		0			0
$634$	4.56218	−	7.90192i	0.181187	−	0.313825i
$635$	−6.19615	+	10.7321i	−0.245887	+	0.425888i
$636$		0			0
$637$	−0.464102	−	0.803848i	−0.0183884	−	0.0318496i
$638$	55.7846			2.20853
$639$		0			0
$640$	−2.73205			−0.107994
$641$	11.0359	+	19.1147i	0.435892	+	0.754987i	0.997368	−	0.0725062i	$-0.0230997\pi$
$641$	11.0359	+	19.1147i	0.435892	+	0.754987i	−0.561476	+	0.827493i	$0.689766\pi$
$642$		0			0
$643$	17.8660	−	30.9449i	0.704567	−	1.22035i	−0.262280	−	0.964992i	$-0.584474\pi$
$643$	17.8660	−	30.9449i	0.704567	−	1.22035i	0.966847	−	0.255355i	$-0.0821922\pi$
$644$	5.16987	−	8.95448i	0.203722	−	0.352856i
$645$		0			0
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	−20.3397			−0.799638			−0.399819	−	0.916594i	$-0.630927\pi$
$647$	−20.3397			−0.799638			−0.399819	+	0.916594i	$0.630927\pi$
$648$		0			0
$649$	80.9615			3.17802
$650$	1.23205	+	2.13397i	0.0483250	+	0.0837014i
$651$		0			0
$652$	3.26795	−	5.66025i	0.127983	−	0.221673i
$653$	−18.1244	+	31.3923i	−0.709261	+	1.22848i	0.255871	+	0.966711i	$0.417638\pi$
$653$	−18.1244	+	31.3923i	−0.709261	+	1.22848i	−0.965132	+	0.261765i	$0.915696\pi$
$654$		0			0
$655$	12.1962	+	21.1244i	0.476543	+	0.825397i
$656$	1.26795			0.0495051
$657$		0			0
$658$	−1.32051			−0.0514788
$659$	−1.26795	−	2.19615i	−0.0493923	−	0.0855500i	0.840272	−	0.542165i	$-0.182395\pi$
$659$	−1.26795	−	2.19615i	−0.0493923	−	0.0855500i	−0.889665	+	0.456615i	$0.849062\pi$
$660$		0			0
$661$	0.732051	−	1.26795i	0.0284735	−	0.0493175i	−0.851438	−	0.524456i	$-0.824269\pi$
$661$	0.732051	−	1.26795i	0.0284735	−	0.0493175i	0.879911	+	0.475139i	$0.157602\pi$
$662$	−2.73205	+	4.73205i	−0.106184	+	0.183916i
$663$		0			0
$664$	−7.33013	−	12.6962i	−0.284464	−	0.492706i
$665$	11.6603			0.452165
$666$		0			0
$667$	40.8372			1.58122
$668$	3.69615	+	6.40192i	0.143008	+	0.247698i
$669$		0			0
$670$	−16.9282	+	29.3205i	−0.653994	+	1.13275i
$671$	−9.16025	+	15.8660i	−0.353628	+	0.612501i
$672$		0			0
$673$	23.1603	+	40.1147i	0.892762	+	1.54631i	0.836550	+	0.547891i	$0.184569\pi$
$673$	23.1603	+	40.1147i	0.892762	+	1.54631i	0.0562122	+	0.998419i	$0.482098\pi$
$674$	−17.8564			−0.687803
$675$		0			0
$676$	1.00000			0.0384615
$677$	−4.33013	−	7.50000i	−0.166420	−	0.288248i	0.770738	−	0.637152i	$-0.219888\pi$
$677$	−4.33013	−	7.50000i	−0.166420	−	0.288248i	−0.937159	+	0.348903i	$0.886554\pi$
$678$		0			0
$679$	11.4186	−	19.7776i	0.438205	−	0.758993i
$680$	−9.46410	+	16.3923i	−0.362932	+	0.628616i
$681$		0			0
$682$	−21.3923	−	37.0526i	−0.819154	−	1.41882i
$683$	10.6795			0.408639			0.204320	−	0.978904i	$-0.434502\pi$
$683$	10.6795			0.408639			0.204320	+	0.978904i	$0.434502\pi$
$684$		0			0
$685$	−2.53590			−0.0968917
$686$	−9.76795	−	16.9186i	−0.372942	−	0.645955i
$687$		0			0
$688$	−2.46410	+	4.26795i	−0.0939430	+	0.162714i
$689$	4.33013	−	7.50000i	0.164965	−	0.285727i
$690$		0			0
$691$	22.1865	+	38.4282i	0.844016	+	1.46188i	0.886473	+	0.462779i	$0.153148\pi$
$691$	22.1865	+	38.4282i	0.844016	+	1.46188i	−0.0424579	+	0.999098i	$0.513519\pi$
$692$	7.19615			0.273557
$693$		0			0
$694$	−19.2679			−0.731401
$695$	−13.9282	−	24.1244i	−0.528327	−	0.915089i
$696$		0			0
$697$	4.39230	−	7.60770i	0.166370	−	0.288162i
$698$	11.7321	−	20.3205i	0.444065	−	0.769143i
$699$		0			0
$700$	3.03590	+	5.25833i	0.114746	+	0.198746i
$701$	−25.0526			−0.946222			−0.473111	−	0.881003i	$-0.656869\pi$
$701$	−25.0526			−0.946222			−0.473111	+	0.881003i	$0.656869\pi$
$702$		0			0
$703$	−4.39230			−0.165659
$704$	−2.86603	−	4.96410i	−0.108017	−	0.187092i
$705$		0			0
$706$	10.2942	−	17.8301i	0.387428	−	0.671046i
$707$	−10.0096	+	17.3372i	−0.376450	+	0.652031i
$708$		0			0
$709$	3.26795	+	5.66025i	0.122730	+	0.212575i	0.920843	−	0.389932i	$-0.127502\pi$
$709$	3.26795	+	5.66025i	0.122730	+	0.212575i	−0.798113	+	0.602508i	$0.794168\pi$
$710$	−28.5885			−1.07291
$711$		0			0
$712$	−14.1962			−0.532023
$713$	−15.6603	−	27.1244i	−0.586481	−	1.01582i
$714$		0			0
$715$	−7.83013	+	13.5622i	−0.292830	+	0.507197i
$716$	−1.26795	+	2.19615i	−0.0473855	+	0.0820741i
$717$		0			0
$718$	−9.92820	−	17.1962i	−0.370517	−	0.641755i
$719$	33.2679			1.24069			0.620343	−	0.784331i	$-0.286994\pi$
$719$	33.2679			1.24069			0.620343	+	0.784331i	$0.286994\pi$
$720$		0			0
$721$	−18.3923			−0.684965
$722$	8.00000	+	13.8564i	0.297729	+	0.515682i
$723$		0			0
$724$	4.79423	−	8.30385i	0.178176	−	0.308610i
$725$	−11.9904	+	20.7679i	−0.445312	+	0.771302i
$726$		0			0
$727$	−23.4641	−	40.6410i	−0.870235	−	1.50729i	−0.861753	−	0.507328i	$-0.830633\pi$
$727$	−23.4641	−	40.6410i	−0.870235	−	1.50729i	−0.00848222	−	0.999964i	$-0.502700\pi$
$728$	2.46410			0.0913257
$729$		0			0
$730$	36.7846			1.36146
$731$	17.0718	+	29.5692i	0.631423	+	1.09366i
$732$		0			0
$733$	−23.2224	+	40.2224i	−0.857740	+	1.48565i	0.0163394	+	0.999867i	$0.494799\pi$
$733$	−23.2224	+	40.2224i	−0.857740	+	1.48565i	−0.874079	+	0.485783i	$0.838535\pi$
$734$	2.29423	−	3.97372i	0.0846815	−	0.146673i
$735$		0			0
$736$	−2.09808	−	3.63397i	−0.0773361	−	0.133950i
$737$	−71.0333			−2.61655
$738$		0			0
$739$	−43.0526			−1.58371			−0.791857	−	0.610707i	$-0.790886\pi$
$739$	−43.0526			−1.58371			−0.791857	+	0.610707i	$0.790886\pi$
$740$	−3.46410	−	6.00000i	−0.127343	−	0.220564i
$741$		0			0
$742$	10.6699	−	18.4808i	0.391703	−	0.678450i
$743$	−3.16025	+	5.47372i	−0.115938	+	0.200811i	−0.918155	−	0.396223i	$-0.870321\pi$
$743$	−3.16025	+	5.47372i	−0.115938	+	0.200811i	0.802216	+	0.597034i	$0.203654\pi$
$744$		0			0
$745$	31.0526	+	53.7846i	1.13768	+	1.97052i
$746$	1.87564			0.0686722
$747$		0			0
$748$	−39.7128			−1.45204
$749$	8.29423	+	14.3660i	0.303065	+	0.524923i
$750$		0			0
$751$	3.00000	−	5.19615i	0.109472	−	0.189610i	−0.806085	−	0.591800i	$-0.798417\pi$
$751$	3.00000	−	5.19615i	0.109472	−	0.189610i	0.915556	+	0.402190i	$0.131751\pi$
$752$	−0.267949	+	0.464102i	−0.00977110	+	0.0169240i
$753$		0			0
$754$	4.86603	+	8.42820i	0.177210	+	0.306937i
$755$	36.5885			1.33159
$756$		0			0
$757$	14.6603			0.532836			0.266418	−	0.963858i	$-0.414160\pi$
$757$	14.6603			0.532836			0.266418	+	0.963858i	$0.414160\pi$
$758$	−17.5263	−	30.3564i	−0.636583	−	1.10259i
$759$		0			0
$760$	2.36603	−	4.09808i	0.0858248	−	0.148653i
$761$	−22.3923	+	38.7846i	−0.811720	+	1.40594i	0.0999386	+	0.994994i	$0.468135\pi$
$761$	−22.3923	+	38.7846i	−0.811720	+	1.40594i	−0.911659	+	0.410947i	$0.865198\pi$
$762$		0			0
$763$	13.0455	+	22.5955i	0.472279	+	0.818012i
$764$	−8.92820			−0.323011
$765$		0			0
$766$	7.39230			0.267095
$767$	7.06218	+	12.2321i	0.255000	+	0.441674i
$768$		0			0
$769$	−7.85641	+	13.6077i	−0.283309	+	0.490706i	−0.972198	−	0.234161i	$-0.924766\pi$
$769$	−7.85641	+	13.6077i	−0.283309	+	0.490706i	0.688889	+	0.724867i	$0.258099\pi$
$770$	−19.2942	+	33.4186i	−0.695316	+	1.20432i
$771$		0			0
$772$	−2.09808	−	3.63397i	−0.0755114	−	0.130790i
$773$	33.8564			1.21773			0.608865	−	0.793274i	$-0.291625\pi$
$773$	33.8564			1.21773			0.608865	+	0.793274i	$0.291625\pi$
$774$		0			0
$775$	18.3923			0.660671
$776$	−4.63397	−	8.02628i	−0.166350	−	0.288127i
$777$		0			0
$778$	6.92820	−	12.0000i	0.248388	−	0.430221i
$779$	−1.09808	+	1.90192i	−0.0393427	+	0.0681435i
$780$		0			0
$781$	−29.9904	−	51.9449i	−1.07314	−	1.85873i
$782$	−29.0718			−1.03961
$783$		0			0
$784$	−0.928203			−0.0331501
$785$	−7.83013	−	13.5622i	−0.279469	−	0.484055i
$786$		0			0
$787$	−24.5981	+	42.6051i	−0.876827	+	1.51871i	−0.0220227	+	0.999757i	$0.507011\pi$
$787$	−24.5981	+	42.6051i	−0.876827	+	1.51871i	−0.854804	+	0.518951i	$0.826323\pi$
$788$	13.3923	−	23.1962i	0.477081	−	0.826329i
$789$		0			0
$790$	7.92820	+	13.7321i	0.282073	+	0.488564i
$791$	19.5359			0.694617
$792$		0			0
$793$	−3.19615			−0.113499
$794$	−16.9282	−	29.3205i	−0.600759	−	1.04055i
$795$		0			0
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	−9.99038	+	17.3038i	−0.353877	+	0.612934i	−0.986925	−	0.161179i	$-0.948470\pi$
$797$	−9.99038	+	17.3038i	−0.353877	+	0.612934i	0.633048	+	0.774113i	$0.281804\pi$
$798$		0			0
$799$	1.85641	+	3.21539i	0.0656749	+	0.113752i
$800$	2.46410			0.0871191
$801$		0			0
$802$	−14.1962			−0.501284
$803$	38.5885	+	66.8372i	1.36176	+	2.35863i
$804$		0			0
$805$	−14.1244	+	24.4641i	−0.497818	+	0.862246i
$806$	3.73205	−	6.46410i	0.131456	−	0.227688i
$807$		0			0
$808$	4.06218	+	7.03590i	0.142907	+	0.247522i
$809$	29.7846			1.04717			0.523586	−	0.851973i	$-0.324594\pi$
$809$	29.7846			1.04717			0.523586	+	0.851973i	$0.324594\pi$
$810$		0			0
$811$	−18.6603			−0.655250			−0.327625	−	0.944808i	$-0.606248\pi$
$811$	−18.6603			−0.655250			−0.327625	+	0.944808i	$0.606248\pi$
$812$	11.9904	+	20.7679i	0.420780	+	0.728812i
$813$		0			0
$814$	7.26795	−	12.5885i	0.254741	−	0.441225i
$815$	−8.92820	+	15.4641i	−0.312741	+	0.541684i
$816$		0			0
$817$	−4.26795	−	7.39230i	−0.149317	−	0.258624i
$818$	−23.4641			−0.820403
$819$		0			0
$820$	−3.46410			−0.120972
$821$	−18.1962	−	31.5167i	−0.635050	−	1.09994i	−0.986505	−	0.163734i	$-0.947646\pi$
$821$	−18.1962	−	31.5167i	−0.635050	−	1.09994i	0.351454	−	0.936205i	$-0.385687\pi$
$822$		0			0
$823$	−16.2679	+	28.1769i	−0.567065	+	0.982185i	0.429789	+	0.902929i	$0.358588\pi$
$823$	−16.2679	+	28.1769i	−0.567065	+	0.982185i	−0.996854	+	0.0792562i	$0.974745\pi$
$824$	−3.73205	+	6.46410i	−0.130012	+	0.225188i
$825$		0			0
$826$	17.4019	+	30.1410i	0.605490	+	1.04874i
$827$	−20.7846			−0.722752			−0.361376	−	0.932420i	$-0.617693\pi$
$827$	−20.7846			−0.722752			−0.361376	+	0.932420i	$0.617693\pi$
$828$		0			0
$829$	8.26795			0.287158			0.143579	−	0.989639i	$-0.454139\pi$
$829$	8.26795			0.287158			0.143579	+	0.989639i	$0.454139\pi$
$830$	20.0263	+	34.6865i	0.695122	+	1.20399i
$831$		0			0
$832$	0.500000	−	0.866025i	0.0173344	−	0.0300240i
$833$	−3.21539	+	5.56922i	−0.111407	+	0.192962i
$834$		0			0
$835$	−10.0981	−	17.4904i	−0.349458	−	0.605280i
$836$	9.92820			0.343374
$837$		0			0
$838$	−17.6603			−0.610063
$839$	11.5885	+	20.0718i	0.400078	+	0.692955i	0.993735	−	0.111763i	$-0.0356497\pi$
$839$	11.5885	+	20.0718i	0.400078	+	0.692955i	−0.593657	+	0.804718i	$0.702316\pi$
$840$		0			0
$841$	−32.8564	+	56.9090i	−1.13298	+	1.96238i
$842$	−17.7583	+	30.7583i	−0.611992	+	1.06000i
$843$		0			0
$844$	9.56218	+	16.5622i	0.329144	+	0.570094i
$845$	−2.73205			−0.0939854
$846$		0			0
$847$	−53.8564			−1.85053
$848$	−4.33013	−	7.50000i	−0.148697	−	0.257551i
$849$		0			0
$850$	8.53590	−	14.7846i	0.292779	−	0.507108i
$851$	5.32051	−	9.21539i	0.182385	−	0.315900i
$852$		0			0
$853$	−8.97372	−	15.5429i	−0.307254	−	0.532180i	0.670506	−	0.741904i	$-0.266077\pi$
$853$	−8.97372	−	15.5429i	−0.307254	−	0.532180i	−0.977761	+	0.209724i	$0.932744\pi$
$854$	−7.87564			−0.269499
$855$		0			0
$856$	6.73205			0.230097
$857$	−1.89230	−	3.27757i	−0.0646399	−	0.111960i	0.831894	−	0.554934i	$-0.187257\pi$
$857$	−1.89230	−	3.27757i	−0.0646399	−	0.111960i	−0.896534	+	0.442975i	$0.853923\pi$
$858$		0			0
$859$	−4.75833	+	8.24167i	−0.162352	+	0.281202i	−0.935712	−	0.352765i	$-0.885241\pi$
$859$	−4.75833	+	8.24167i	−0.162352	+	0.281202i	0.773360	+	0.633968i	$0.218575\pi$
$860$	6.73205	−	11.6603i	0.229561	−	0.397611i
$861$		0			0
$862$	−18.2321	−	31.5788i	−0.620986	−	1.07558i
$863$	−41.4974			−1.41259			−0.706294	−	0.707918i	$-0.749634\pi$
$863$	−41.4974			−1.41259			−0.706294	+	0.707918i	$0.749634\pi$
$864$		0			0
$865$	−19.6603			−0.668469
$866$	−1.30385	−	2.25833i	−0.0443065	−	0.0767412i
$867$		0			0
$868$	9.19615	−	15.9282i	0.312138	−	0.540638i
$869$	−16.6340	+	28.8109i	−0.564269	+	0.977342i
$870$		0			0
$871$	−6.19615	−	10.7321i	−0.209949	−	0.363642i
$872$	10.5885			0.358570
$873$		0			0
$874$	7.26795			0.245842
$875$	8.53590	+	14.7846i	0.288566	+	0.499811i
$876$		0			0
$877$	−0.294229	+	0.509619i	−0.00993540	+	0.0172086i	−0.870950	−	0.491371i	$-0.836496\pi$
$877$	−0.294229	+	0.509619i	−0.00993540	+	0.0172086i	0.861015	+	0.508580i	$0.169829\pi$
$878$	14.0000	−	24.2487i	0.472477	−	0.818354i
$879$		0			0
$880$	7.83013	+	13.5622i	0.263954	+	0.457181i
$881$	−6.24871			−0.210524			−0.105262	−	0.994445i	$-0.533568\pi$
$881$	−6.24871			−0.210524			−0.105262	+	0.994445i	$0.533568\pi$
$882$		0			0
$883$	−34.1962			−1.15079			−0.575396	−	0.817875i	$-0.695152\pi$
$883$	−34.1962			−1.15079			−0.575396	+	0.817875i	$0.695152\pi$
$884$	−3.46410	−	6.00000i	−0.116510	−	0.201802i
$885$		0			0
$886$	13.8564	−	24.0000i	0.465515	−	0.806296i
$887$	14.0981	−	24.4186i	0.473367	−	0.819896i	−0.526168	−	0.850381i	$-0.676372\pi$
$887$	14.0981	−	24.4186i	0.473367	−	0.819896i	0.999535	+	0.0304847i	$0.00970509\pi$
$888$		0			0
$889$	−5.58846	−	9.67949i	−0.187431	−	0.324640i
$890$	38.7846			1.30006
$891$		0			0
$892$	11.7846			0.394578
$893$	−0.464102	−	0.803848i	−0.0155306	−	0.0268997i
$894$		0			0
$895$	3.46410	−	6.00000i	0.115792	−	0.200558i
$896$	1.23205	−	2.13397i	0.0411599	−	0.0712911i
$897$		0			0
$898$	4.00000	+	6.92820i	0.133482	+	0.231197i
$899$	72.6410			2.42271
$900$		0			0
$901$	−60.0000			−1.99889
$902$	−3.63397	−	6.29423i	−0.120998	−	0.209575i
$903$		0			0
$904$	3.96410	−	6.86603i	0.131844	−	0.228361i
$905$	−13.0981	+	22.6865i	−0.435395	+	0.754126i
$906$		0			0
$907$	6.46410	+	11.1962i	0.214637	+	0.371762i	0.953160	−	0.302466i	$-0.0978098\pi$
$907$	6.46410	+	11.1962i	0.214637	+	0.371762i	−0.738523	+	0.674228i	$0.764476\pi$
$908$	14.6603			0.486518
$909$		0			0
$910$	−6.73205			−0.223165
$911$	17.3205	+	30.0000i	0.573854	+	0.993944i	0.996165	+	0.0874934i	$0.0278857\pi$
$911$	17.3205	+	30.0000i	0.573854	+	0.993944i	−0.422311	+	0.906451i	$0.638781\pi$
$912$		0			0
$913$	−42.0167	+	72.7750i	−1.39055	+	2.40850i
$914$	−11.1699	+	19.3468i	−0.369467	+	0.639935i
$915$		0			0
$916$	6.46410	+	11.1962i	0.213580	+	0.369931i
$917$	−22.0000			−0.726504
$918$		0			0
$919$	32.1051			1.05905			0.529525	−	0.848294i	$-0.322370\pi$
$919$	32.1051			1.05905			0.529525	+	0.848294i	$0.322370\pi$
$920$	5.73205	+	9.92820i	0.188980	+	0.327323i
$921$		0			0
$922$	−19.0981	+	33.0788i	−0.628962	+	1.08939i
$923$	5.23205	−	9.06218i	0.172215	−	0.298285i
$924$		0			0
$925$	3.12436	+	5.41154i	0.102728	+	0.177930i
$926$	0.320508			0.0105325
$927$		0			0
$928$	9.73205			0.319470
$929$	6.12436	+	10.6077i	0.200934	+	0.348027i	0.948829	−	0.315789i	$-0.102269\pi$
$929$	6.12436	+	10.6077i	0.200934	+	0.348027i	−0.747896	+	0.663816i	$0.768936\pi$
$930$		0			0
$931$	0.803848	−	1.39230i	0.0263450	−	0.0456309i
$932$	1.69615	−	2.93782i	0.0555593	−	0.0962316i
$933$		0			0
$934$	0.437822	+	0.758330i	0.0143260	+	0.0248133i
$935$	108.497			3.54825
$936$		0			0
$937$	19.6077			0.640555			0.320278	−	0.947324i	$-0.396224\pi$
$937$	19.6077			0.640555			0.320278	+	0.947324i	$0.396224\pi$
$938$	−15.2679	−	26.4449i	−0.498516	−	0.863455i
$939$		0			0
$940$	0.732051	−	1.26795i	0.0238769	−	0.0413559i
$941$	17.0526	−	29.5359i	0.555898	−	0.962843i	−0.441936	−	0.897047i	$-0.645708\pi$
$941$	17.0526	−	29.5359i	0.555898	−	0.962843i	0.997833	−	0.0657960i	$-0.0209586\pi$
$942$		0			0
$943$	−2.66025	−	4.60770i	−0.0866298	−	0.150047i
$944$	14.1244			0.459709
$945$		0			0
$946$	28.2487			0.918445
$947$	6.58846	+	11.4115i	0.214096	+	0.370825i	0.952993	−	0.302994i	$-0.0979861\pi$
$947$	6.58846	+	11.4115i	0.214096	+	0.370825i	−0.738896	+	0.673819i	$0.764653\pi$
$948$		0			0
$949$	−6.73205	+	11.6603i	−0.218532	+	0.378508i
$950$	−2.13397	+	3.69615i	−0.0692353	+	0.119919i
$951$		0			0
$952$	−8.53590	−	14.7846i	−0.276650	−	0.479172i
$953$	57.4256			1.86020			0.930099	−	0.367308i	$-0.119721\pi$
$953$	57.4256			1.86020			0.930099	+	0.367308i	$0.119721\pi$
$954$		0			0
$955$	24.3923			0.789316
$956$	1.03590	+	1.79423i	0.0335033	+	0.0580295i
$957$		0			0
$958$	−13.6244	+	23.5981i	−0.440183	+	0.762419i
$959$	1.14359	−	1.98076i	0.0369286	−	0.0639621i
$960$		0			0
$961$	−12.3564	−	21.4019i	−0.398594	−	0.690385i
$962$	2.53590			0.0817606
$963$		0			0
$964$	−7.26795			−0.234085
$965$	5.73205	+	9.92820i	0.184521	+	0.319600i
$966$		0			0
$967$	−0.303848	+	0.526279i	−0.00977108	+	0.0169240i	−0.870870	−	0.491514i	$-0.836444\pi$
$967$	−0.303848	+	0.526279i	−0.00977108	+	0.0169240i	0.861099	+	0.508438i	$0.169777\pi$
$968$	−10.9282	+	18.9282i	−0.351246	+	0.608375i
$969$		0			0
$970$	12.6603	+	21.9282i	0.406496	+	0.704072i
$971$	−25.5167			−0.818869			−0.409434	−	0.912340i	$-0.634274\pi$
$971$	−25.5167			−0.818869			−0.409434	+	0.912340i	$0.634274\pi$
$972$		0			0
$973$	25.1244			0.805450
$974$	−0.303848	−	0.526279i	−0.00973590	−	0.0168631i
$975$		0			0
$976$	−1.59808	+	2.76795i	−0.0511532	+	0.0885999i
$977$	−12.6340	+	21.8827i	−0.404197	+	0.700089i	−0.994228	−	0.107291i	$-0.965782\pi$
$977$	−12.6340	+	21.8827i	−0.404197	+	0.700089i	0.590031	+	0.807381i	$0.299116\pi$
$978$		0			0
$979$	40.6865	+	70.4711i	1.30035	+	2.25227i
$980$	2.53590			0.0810063
$981$		0			0
$982$	−31.3205			−0.999478
$983$	4.08846	+	7.08142i	0.130402	+	0.225862i	0.923831	−	0.382800i	$-0.125040\pi$
$983$	4.08846	+	7.08142i	0.130402	+	0.225862i	−0.793430	+	0.608662i	$0.791707\pi$
$984$		0			0
$985$	−36.5885	+	63.3731i	−1.16581	+	2.01923i
$986$	33.7128	−	58.3923i	1.07363	−	1.85959i
$987$		0			0
$988$	0.866025	+	1.50000i	0.0275519	+	0.0477214i
$989$	20.6795			0.657570
$990$		0			0
$991$	12.5885			0.399886			0.199943	−	0.979808i	$-0.435924\pi$
$991$	12.5885			0.399886			0.199943	+	0.979808i	$0.435924\pi$
$992$	−3.73205	−	6.46410i	−0.118493	−	0.205235i
$993$		0			0
$994$	12.8923	−	22.3301i	0.408919	−	0.708269i
$995$	−5.46410	+	9.46410i	−0.173224	+	0.300032i
$996$		0			0
$997$	−19.5263	−	33.8205i	−0.618403	−	1.07111i	−0.989777	−	0.142623i	$-0.954446\pi$
$997$	−19.5263	−	33.8205i	−0.618403	−	1.07111i	0.371374	−	0.928484i	$-0.378887\pi$
$998$	3.19615			0.101172
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2106.2.e.bd.1405.2		4
3.2	odd	2		2106.2.e.bf.1405.1		4
9.2	odd	6		2106.2.e.bf.703.1		4
9.4	even	3		2106.2.a.n.1.1	yes	2
9.5	odd	6		2106.2.a.k.1.2	✓	2
9.7	even	3	inner	2106.2.e.bd.703.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2106.2.a.k.1.2	✓	2	9.5	odd	6
2106.2.a.n.1.1	yes	2	9.4	even	3
2106.2.e.bd.703.2		4	9.7	even	3	inner
2106.2.e.bd.1405.2		4	1.1	even	1	trivial
2106.2.e.bf.703.1		4	9.2	odd	6
2106.2.e.bf.1405.1		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 2106 = 2 \cdot 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2106.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.36603 - 2.36603i) q^{5} +(1.23205 + 2.13397i) q^{7} +1.00000 q^{8} -2.73205 q^{10} +(-2.86603 - 4.96410i) q^{11} +(0.500000 - 0.866025i) q^{13} +(1.23205 - 2.13397i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.92820 q^{17} +1.73205 q^{19} +(1.36603 + 2.36603i) q^{20} +(-2.86603 + 4.96410i) q^{22} +(-2.09808 + 3.63397i) q^{23} +(-1.23205 - 2.13397i) q^{25} -1.00000 q^{26} -2.46410 q^{28} +(-4.86603 - 8.42820i) q^{29} +(-3.73205 + 6.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.46410 + 6.00000i) q^{34} +6.73205 q^{35} -2.53590 q^{37} +(-0.866025 - 1.50000i) q^{38} +(1.36603 - 2.36603i) q^{40} +(-0.633975 + 1.09808i) q^{41} +(-2.46410 - 4.26795i) q^{43} +5.73205 q^{44} +4.19615 q^{46} +(-0.267949 - 0.464102i) q^{47} +(0.464102 - 0.803848i) q^{49} +(-1.23205 + 2.13397i) q^{50} +(0.500000 + 0.866025i) q^{52} +8.66025 q^{53} -15.6603 q^{55} +(1.23205 + 2.13397i) q^{56} +(-4.86603 + 8.42820i) q^{58} +(-7.06218 + 12.2321i) q^{59} +(-1.59808 - 2.76795i) q^{61} +7.46410 q^{62} +1.00000 q^{64} +(-1.36603 - 2.36603i) q^{65} +(6.19615 - 10.7321i) q^{67} +(3.46410 - 6.00000i) q^{68} +(-3.36603 - 5.83013i) q^{70} +10.4641 q^{71} -13.4641 q^{73} +(1.26795 + 2.19615i) q^{74} +(-0.866025 + 1.50000i) q^{76} +(7.06218 - 12.2321i) q^{77} +(-2.90192 - 5.02628i) q^{79} -2.73205 q^{80} +1.26795 q^{82} +(-7.33013 - 12.6962i) q^{83} +(-9.46410 + 16.3923i) q^{85} +(-2.46410 + 4.26795i) q^{86} +(-2.86603 - 4.96410i) q^{88} -14.1962 q^{89} +2.46410 q^{91} +(-2.09808 - 3.63397i) q^{92} +(-0.267949 + 0.464102i) q^{94} +(2.36603 - 4.09808i) q^{95} +(-4.63397 - 8.02628i) q^{97} -0.928203 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{8} - 4 q^{10} - 8 q^{11} + 2 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{20} - 8 q^{22} + 2 q^{23} + 2 q^{25} - 4 q^{26} + 4 q^{28} - 16 q^{29} - 8 q^{31} - 2 q^{32}+ \cdots + 24 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 - 2 * q^7 + 4 * q^8 - 4 * q^10 - 8 * q^11 + 2 * q^13 - 2 * q^14 - 2 * q^16 + 2 * q^20 - 8 * q^22 + 2 * q^23 + 2 * q^25 - 4 * q^26 + 4 * q^28 - 16 * q^29 - 8 * q^31 - 2 * q^32 + 20 * q^35 - 24 * q^37 + 2 * q^40 - 6 * q^41 + 4 * q^43 + 16 * q^44 - 4 * q^46 - 8 * q^47 - 12 * q^49 + 2 * q^50 + 2 * q^52 - 28 * q^55 - 2 * q^56 - 16 * q^58 - 4 * q^59 + 4 * q^61 + 16 * q^62 + 4 * q^64 - 2 * q^65 + 4 * q^67 - 10 * q^70 + 28 * q^71 - 40 * q^73 + 12 * q^74 + 4 * q^77 - 22 * q^79 - 4 * q^80 + 12 * q^82 - 12 * q^83 - 24 * q^85 + 4 * q^86 - 8 * q^88 - 36 * q^89 - 4 * q^91 + 2 * q^92 - 8 * q^94 + 6 * q^95 - 22 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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