LMFDB - Embedded newform 1470.2.d.g.1469.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(1469,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1470.1469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.d (of order $2$, degree $1$, 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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1469.15
Character	$\chi$	$=$	1470.1469
Dual form			1470.2.d.g.1469.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.03805 - 1.38652i) q^{3} +1.00000 q^{4} +(-1.98784 + 1.02395i) q^{5} +(-1.03805 + 1.38652i) q^{6} -1.00000 q^{8} +(-0.844897 - 2.87857i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.03805 - 1.38652i) q^{3} +1.00000 q^{4} +(-1.98784 + 1.02395i) q^{5} +(-1.03805 + 1.38652i) q^{6} -1.00000 q^{8} +(-0.844897 - 2.87857i) q^{9} +(1.98784 - 1.02395i) q^{10} -1.27840i q^{11} +(1.03805 - 1.38652i) q^{12} -1.32254 q^{13} +(-0.643753 + 3.81911i) q^{15} +1.00000 q^{16} -5.76944i q^{17} +(0.844897 + 2.87857i) q^{18} +2.44195i q^{19} +(-1.98784 + 1.02395i) q^{20} +1.27840i q^{22} -0.680020 q^{23} +(-1.03805 + 1.38652i) q^{24} +(2.90305 - 4.07091i) q^{25} +1.32254 q^{26} +(-4.86825 - 1.81663i) q^{27} +6.12676i q^{29} +(0.643753 - 3.81911i) q^{30} +6.94293i q^{31} -1.00000 q^{32} +(-1.77253 - 1.32704i) q^{33} +5.76944i q^{34} +(-0.844897 - 2.87857i) q^{36} -4.67531i q^{37} -2.44195i q^{38} +(-1.37286 + 1.83373i) q^{39} +(1.98784 - 1.02395i) q^{40} -12.3285 q^{41} -1.87753i q^{43} -1.27840i q^{44} +(4.62703 + 4.85701i) q^{45} +0.680020 q^{46} +7.97726i q^{47} +(1.03805 - 1.38652i) q^{48} +(-2.90305 + 4.07091i) q^{50} +(-7.99947 - 5.98898i) q^{51} -1.32254 q^{52} -6.98682 q^{53} +(4.86825 + 1.81663i) q^{54} +(1.30902 + 2.54126i) q^{55} +(3.38582 + 2.53487i) q^{57} -6.12676i q^{58} -9.65619 q^{59} +(-0.643753 + 3.81911i) q^{60} -4.22958i q^{61} -6.94293i q^{62} +1.00000 q^{64} +(2.62899 - 1.35421i) q^{65} +(1.77253 + 1.32704i) q^{66} -12.9467i q^{67} -5.76944i q^{68} +(-0.705896 + 0.942863i) q^{69} +5.09896i q^{71} +(0.844897 + 2.87857i) q^{72} -16.4851 q^{73} +4.67531i q^{74} +(-2.63090 - 8.25096i) q^{75} +2.44195i q^{76} +(1.37286 - 1.83373i) q^{78} -15.5370 q^{79} +(-1.98784 + 1.02395i) q^{80} +(-7.57230 + 4.86419i) q^{81} +12.3285 q^{82} -3.33498i q^{83} +(5.90762 + 11.4688i) q^{85} +1.87753i q^{86} +(8.49490 + 6.35990i) q^{87} +1.27840i q^{88} +12.7400 q^{89} +(-4.62703 - 4.85701i) q^{90} -0.680020 q^{92} +(9.62654 + 7.20712i) q^{93} -7.97726i q^{94} +(-2.50043 - 4.85421i) q^{95} +(-1.03805 + 1.38652i) q^{96} -2.90682 q^{97} +(-3.67995 + 1.08011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9	$ 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9} + 24 q^{16} - 8 q^{18} - 16 q^{23} + 8 q^{25} - 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} - 8 q^{50} + 16 q^{51} + 16 q^{53} + 16 q^{57} + 24 q^{64} - 48 q^{65} - 8 q^{72} - 16 q^{78} - 48 q^{79} - 24 q^{81} + 16 q^{85} - 16 q^{92} + 64 q^{93} - 112 q^{95} - 64 q^{99}+O(q^{100}) $ 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9 + 24 * q^16 - 8 * q^18 - 16 * q^23 + 8 * q^25 - 24 * q^32 + 8 * q^36 + 16 * q^39 + 16 * q^46 - 8 * q^50 + 16 * q^51 + 16 * q^53 + 16 * q^57 + 24 * q^64 - 48 * q^65 - 8 * q^72 - 16 * q^78 - 48 * q^79 - 24 * q^81 + 16 * q^85 - 16 * q^92 + 64 * q^93 - 112 * q^95 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.03805	−	1.38652i	0.599319	−	0.800510i
$3$	1.03805	−	1.38652i	0.599319	−	0.800510i
$4$	1.00000			0.500000
$5$	−1.98784	+	1.02395i	−0.888991	+	0.457925i
$5$	−1.98784	+	1.02395i	−0.888991	+	0.457925i
$6$	−1.03805	+	1.38652i	−0.423783	+	0.566046i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.844897	−	2.87857i	−0.281632	−	0.959522i
$10$	1.98784	−	1.02395i	0.628612	−	0.323802i
$11$		−	1.27840i		−	0.385451i	−0.981253	−	0.192726i	$-0.938267\pi$
$11$		−	1.27840i		−	0.385451i	0.981253	−	0.192726i	$-0.0617328\pi$
$12$	1.03805	−	1.38652i	0.299660	−	0.400255i
$13$	−1.32254			−0.366805			−0.183403	−	0.983038i	$-0.558711\pi$
$13$	−1.32254			−0.366805			−0.183403	+	0.983038i	$0.558711\pi$
$14$		0			0
$15$	−0.643753	+	3.81911i	−0.166216	+	0.986089i
$16$	1.00000			0.250000
$17$		−	5.76944i		−	1.39929i	−0.714488	−	0.699647i	$-0.753340\pi$
$17$		−	5.76944i		−	1.39929i	0.714488	−	0.699647i	$-0.246660\pi$
$18$	0.844897	+	2.87857i	0.199144	+	0.678485i
$19$			2.44195i			0.560221i	0.959968	+	0.280111i	$0.0903711\pi$
$19$			2.44195i			0.560221i	−0.959968	+	0.280111i	$0.909629\pi$
$20$	−1.98784	+	1.02395i	−0.444496	+	0.228962i
$21$		0			0
$22$			1.27840i			0.272555i
$23$	−0.680020			−0.141794			−0.0708969	−	0.997484i	$-0.522586\pi$
$23$	−0.680020			−0.141794			−0.0708969	+	0.997484i	$0.522586\pi$
$24$	−1.03805	+	1.38652i	−0.211891	+	0.283023i
$25$	2.90305	−	4.07091i	0.580610	−	0.814182i
$26$	1.32254			0.259371
$27$	−4.86825	−	1.81663i	−0.936895	−	0.349611i
$28$		0			0
$29$			6.12676i			1.13771i	0.822437	+	0.568856i	$0.192614\pi$
$29$			6.12676i			1.13771i	−0.822437	+	0.568856i	$0.807386\pi$
$30$	0.643753	−	3.81911i	0.117533	−	0.697270i
$31$			6.94293i			1.24699i	0.781829	+	0.623493i	$0.214287\pi$
$31$			6.94293i			1.24699i	−0.781829	+	0.623493i	$0.785713\pi$
$32$	−1.00000			−0.176777
$33$	−1.77253	−	1.32704i	−0.308558	−	0.231009i
$34$			5.76944i			0.989451i
$35$		0			0
$36$	−0.844897	−	2.87857i	−0.140816	−	0.479761i
$37$		−	4.67531i		−	0.768616i	−0.923205	−	0.384308i	$-0.874440\pi$
$37$		−	4.67531i		−	0.768616i	0.923205	−	0.384308i	$-0.125560\pi$
$38$		−	2.44195i		−	0.396136i
$39$	−1.37286	+	1.83373i	−0.219834	+	0.293631i
$40$	1.98784	−	1.02395i	0.314306	−	0.161901i
$41$	−12.3285			−1.92538			−0.962691	−	0.270603i	$-0.912777\pi$
$41$	−12.3285			−1.92538			−0.962691	+	0.270603i	$0.912777\pi$
$42$		0			0
$43$		−	1.87753i		−	0.286321i	−0.989700	−	0.143160i	$-0.954274\pi$
$43$		−	1.87753i		−	0.286321i	0.989700	−	0.143160i	$-0.0457265\pi$
$44$		−	1.27840i		−	0.192726i
$45$	4.62703	+	4.85701i	0.689758	+	0.724040i
$46$	0.680020			0.100263
$47$			7.97726i			1.16360i	0.813331	+	0.581802i	$0.197652\pi$
$47$			7.97726i			1.16360i	−0.813331	+	0.581802i	$0.802348\pi$
$48$	1.03805	−	1.38652i	0.149830	−	0.200127i
$49$		0			0
$50$	−2.90305	+	4.07091i	−0.410553	+	0.575713i
$51$	−7.99947	−	5.98898i	−1.12015	−	0.838625i
$52$	−1.32254			−0.183403
$53$	−6.98682			−0.959713			−0.479857	−	0.877347i	$-0.659311\pi$
$53$	−6.98682			−0.959713			−0.479857	+	0.877347i	$0.659311\pi$
$54$	4.86825	+	1.81663i	0.662485	+	0.247212i
$55$	1.30902	+	2.54126i	0.176508	+	0.342663i
$56$		0			0
$57$	3.38582	+	2.53487i	0.448463	+	0.335751i
$58$		−	6.12676i		−	0.804483i
$59$	−9.65619			−1.25713			−0.628564	−	0.777758i	$-0.716357\pi$
$59$	−9.65619			−1.25713			−0.628564	+	0.777758i	$0.716357\pi$
$60$	−0.643753	+	3.81911i	−0.0831082	+	0.493045i
$61$		−	4.22958i		−	0.541542i	−0.962644	−	0.270771i	$-0.912721\pi$
$61$		−	4.22958i		−	0.541542i	0.962644	−	0.270771i	$-0.0872786\pi$
$62$		−	6.94293i		−	0.881753i
$63$		0			0
$64$	1.00000			0.125000
$65$	2.62899	−	1.35421i	0.326087	−	0.167969i
$66$	1.77253	+	1.32704i	0.218183	+	0.163348i
$67$		−	12.9467i		−	1.58169i	−0.612014	−	0.790847i	$-0.709641\pi$
$67$		−	12.9467i		−	1.58169i	0.612014	−	0.790847i	$-0.290359\pi$
$68$		−	5.76944i		−	0.699647i
$69$	−0.705896	+	0.942863i	−0.0849798	+	0.113507i
$70$		0			0
$71$			5.09896i			0.605135i	0.953128	+	0.302567i	$0.0978437\pi$
$71$			5.09896i			0.605135i	−0.953128	+	0.302567i	$0.902156\pi$
$72$	0.844897	+	2.87857i	0.0995721	+	0.339242i
$73$	−16.4851			−1.92944			−0.964720	−	0.263277i	$-0.915197\pi$
$73$	−16.4851			−1.92944			−0.964720	+	0.263277i	$0.915197\pi$
$74$			4.67531i			0.543493i
$75$	−2.63090	−	8.25096i	−0.303790	−	0.952739i
$76$			2.44195i			0.280111i
$77$		0			0
$78$	1.37286	−	1.83373i	0.155446	−	0.207629i
$79$	−15.5370			−1.74805			−0.874027	−	0.485877i	$-0.838500\pi$
$79$	−15.5370			−1.74805			−0.874027	+	0.485877i	$0.838500\pi$
$80$	−1.98784	+	1.02395i	−0.222248	+	0.114481i
$81$	−7.57230	+	4.86419i	−0.841366	+	0.540465i
$82$	12.3285			1.36145
$83$		−	3.33498i		−	0.366061i	−0.983107	−	0.183031i	$-0.941409\pi$
$83$		−	3.33498i		−	0.366061i	0.983107	−	0.183031i	$-0.0585907\pi$
$84$		0			0
$85$	5.90762	+	11.4688i	0.640772	+	1.24396i
$86$			1.87753i			0.202459i
$87$	8.49490	+	6.35990i	0.910749	+	0.681852i
$88$			1.27840i			0.136278i
$89$	12.7400			1.35043			0.675217	−	0.737619i	$-0.264050\pi$
$89$	12.7400			1.35043			0.675217	+	0.737619i	$0.264050\pi$
$90$	−4.62703	−	4.85701i	−0.487732	−	0.511974i
$91$		0			0
$92$	−0.680020			−0.0708969
$93$	9.62654	+	7.20712i	0.998225	+	0.747343i
$94$		−	7.97726i		−	0.822792i
$95$	−2.50043	−	4.85421i	−0.256539	−	0.498031i
$96$	−1.03805	+	1.38652i	−0.105946	+	0.141512i
$97$	−2.90682			−0.295142			−0.147571	−	0.989051i	$-0.547146\pi$
$97$	−2.90682			−0.295142			−0.147571	+	0.989051i	$0.547146\pi$
$98$		0			0
$99$	−3.67995	+	1.08011i	−0.369849	+	0.108556i
$100$	2.90305	−	4.07091i	0.290305	−	0.407091i
$101$	−9.02428			−0.897949			−0.448975	−	0.893544i	$-0.648211\pi$
$101$	−9.02428			−0.897949			−0.448975	+	0.893544i	$0.648211\pi$
$102$	7.99947	+	5.98898i	0.792065	+	0.592997i
$103$	−17.4764			−1.72200			−0.861002	−	0.508602i	$-0.830162\pi$
$103$	−17.4764			−1.72200			−0.861002	+	0.508602i	$0.830162\pi$
$104$	1.32254			0.129685
$105$		0			0
$106$	6.98682			0.678620
$107$	12.1115			1.17087			0.585433	−	0.810721i	$-0.300925\pi$
$107$	12.1115			1.17087			0.585433	+	0.810721i	$0.300925\pi$
$108$	−4.86825	−	1.81663i	−0.468448	−	0.174805i
$109$	11.1753			1.07040			0.535199	−	0.844726i	$-0.320237\pi$
$109$	11.1753			1.07040			0.535199	+	0.844726i	$0.320237\pi$
$110$	−1.30902	−	2.54126i	−0.124810	−	0.242299i
$111$	−6.48242	−	4.85321i	−0.615284	−	0.460646i
$112$		0			0
$113$	0.00477454			0.000449151			0.000224575	−	1.00000i	$-0.499929\pi$
$113$	0.00477454			0.000449151			0.000224575		1.00000i	$0.499929\pi$
$114$	−3.38582	−	2.53487i	−0.317111	−	0.237412i
$115$	1.35177	−	0.696306i	0.126053	−	0.0649309i
$116$			6.12676i			0.568856i
$117$	1.11741	+	3.80701i	0.103304	+	0.351958i
$118$	9.65619			0.888924
$119$		0			0
$120$	0.643753	−	3.81911i	0.0587664	−	0.348635i
$121$	9.36570			0.851427
$122$			4.22958i			0.382928i
$123$	−12.7976	+	17.0937i	−1.15392	+	1.54129i
$124$			6.94293i			0.623493i
$125$	−1.60240	+	11.0649i	−0.143323	+	0.989676i
$126$		0			0
$127$		−	7.34269i		−	0.651558i	−0.945446	−	0.325779i	$-0.894373\pi$
$127$		−	7.34269i		−	0.651558i	0.945446	−	0.325779i	$-0.105627\pi$
$128$	−1.00000			−0.0883883
$129$	−2.60324	−	1.94897i	−0.229203	−	0.171598i
$130$	−2.62899	+	1.35421i	−0.230578	+	0.118772i
$131$	−0.0771448			−0.00674018			−0.00337009	−	0.999994i	$-0.501073\pi$
$131$	−0.0771448			−0.00674018			−0.00337009	+	0.999994i	$0.501073\pi$
$132$	−1.77253	−	1.32704i	−0.154279	−	0.115504i
$133$		0			0
$134$			12.9467i			1.11843i
$135$	11.5375	−	1.37367i	0.992987	−	0.118226i
$136$			5.76944i			0.494725i
$137$	11.7831			1.00670			0.503351	−	0.864082i	$-0.332100\pi$
$137$	11.7831			1.00670			0.503351	+	0.864082i	$0.332100\pi$
$138$	0.705896	−	0.942863i	0.0600898	−	0.0802619i
$139$			15.9840i			1.35574i	0.735181	+	0.677871i	$0.237097\pi$
$139$			15.9840i			1.35574i	−0.735181	+	0.677871i	$0.762903\pi$
$140$		0			0
$141$	11.0607	+	8.28081i	0.931476	+	0.697370i
$142$		−	5.09896i		−	0.427895i
$143$			1.69073i			0.141386i
$144$	−0.844897	−	2.87857i	−0.0704081	−	0.239881i
$145$	−6.27350	−	12.1790i	−0.520986	−	1.01141i
$146$	16.4851			1.36432
$147$		0			0
$148$		−	4.67531i		−	0.384308i
$149$			20.2680i			1.66042i	0.557449	+	0.830211i	$0.311780\pi$
$149$			20.2680i			1.66042i	−0.557449	+	0.830211i	$0.688220\pi$
$150$	2.63090	+	8.25096i	0.214812	+	0.673688i
$151$	10.0657			0.819135			0.409568	−	0.912280i	$-0.365680\pi$
$151$	10.0657			0.819135			0.409568	+	0.912280i	$0.365680\pi$
$152$		−	2.44195i		−	0.198068i
$153$	−16.6077	+	4.87459i	−1.34265	+	0.394087i
$154$		0			0
$155$	−7.10922	−	13.8015i	−0.571026	−	1.10856i
$156$	−1.37286	+	1.83373i	−0.109917	+	0.146816i
$157$	−9.84780			−0.785940			−0.392970	−	0.919551i	$-0.628552\pi$
$157$	−9.84780			−0.785940			−0.392970	+	0.919551i	$0.628552\pi$
$158$	15.5370			1.23606
$159$	−7.25268	+	9.68739i	−0.575175	+	0.768260i
$160$	1.98784	−	1.02395i	0.157153	−	0.0809504i
$161$		0			0
$162$	7.57230	−	4.86419i	0.594936	−	0.382167i
$163$			11.4412i			0.896147i	0.893997	+	0.448073i	$0.147890\pi$
$163$			11.4412i			0.896147i	−0.893997	+	0.448073i	$0.852110\pi$
$164$	−12.3285			−0.962691
$165$	4.88234	+	0.822973i	0.380089	+	0.0640683i
$166$			3.33498i			0.258844i
$167$		−	14.1922i		−	1.09823i	−0.835748	−	0.549114i	$-0.814965\pi$
$167$		−	14.1922i		−	1.09823i	0.835748	−	0.549114i	$-0.185035\pi$
$168$		0			0
$169$	−11.2509			−0.865454
$170$	−5.90762	−	11.4688i	−0.453094	−	0.879613i
$171$	7.02931	−	2.06319i	0.537545	−	0.157776i
$172$		−	1.87753i		−	0.143160i
$173$			0.985415i			0.0749197i	0.999298	+	0.0374599i	$0.0119266\pi$
$173$			0.985415i			0.0749197i	−0.999298	+	0.0374599i	$0.988073\pi$
$174$	−8.49490	−	6.35990i	−0.643997	−	0.482142i
$175$		0			0
$176$		−	1.27840i		−	0.0963628i
$177$	−10.0236	+	13.3885i	−0.753422	+	1.00634i
$178$	−12.7400			−0.954901
$179$		−	10.2949i		−	0.769478i	−0.923025	−	0.384739i	$-0.874291\pi$
$179$		−	10.2949i		−	0.769478i	0.923025	−	0.384739i	$-0.125709\pi$
$180$	4.62703	+	4.85701i	0.344879	+	0.362020i
$181$		−	5.05282i		−	0.375573i	−0.982210	−	0.187787i	$-0.939869\pi$
$181$		−	5.05282i		−	0.375573i	0.982210	−	0.187787i	$-0.0601313\pi$
$182$		0			0
$183$	−5.86441	−	4.39052i	−0.433510	−	0.324557i
$184$	0.680020			0.0501317
$185$	4.78728	+	9.29378i	0.351968	+	0.683292i
$186$	−9.62654	−	7.20712i	−0.705852	−	0.528452i
$187$	−7.37564			−0.539360
$188$			7.97726i			0.581802i
$189$		0			0
$190$	2.50043	+	4.85421i	0.181400	+	0.352161i
$191$		−	9.31528i		−	0.674030i	−0.941499	−	0.337015i	$-0.890583\pi$
$191$		−	9.31528i		−	0.674030i	0.941499	−	0.337015i	$-0.109417\pi$
$192$	1.03805	−	1.38652i	0.0749149	−	0.100064i
$193$			2.53974i			0.182814i	0.995814	+	0.0914072i	$0.0291365\pi$
$193$			2.53974i			0.182814i	−0.995814	+	0.0914072i	$0.970864\pi$
$194$	2.90682			0.208697
$195$	0.851387	−	5.05091i	0.0609691	−	0.361703i
$196$		0			0
$197$	8.65660			0.616757			0.308379	−	0.951264i	$-0.400214\pi$
$197$	8.65660			0.616757			0.308379	+	0.951264i	$0.400214\pi$
$198$	3.67995	−	1.08011i	0.261523	−	0.0767604i
$199$		−	27.9233i		−	1.97943i	−0.143062	−	0.989714i	$-0.545695\pi$
$199$		−	27.9233i		−	1.97943i	0.143062	−	0.989714i	$-0.454305\pi$
$200$	−2.90305	+	4.07091i	−0.205277	+	0.287857i
$201$	−17.9509	−	13.4394i	−1.26616	−	0.947939i
$202$	9.02428			0.634946
$203$		0			0
$204$	−7.99947	−	5.98898i	−0.560075	−	0.419312i
$205$	24.5071	−	12.6237i	1.71165	−	0.881680i
$206$	17.4764			1.21764
$207$	0.574547	+	1.95748i	0.0399338	+	0.136054i
$208$	−1.32254			−0.0917013
$209$	3.12178			0.215938
$210$		0			0
$211$	−12.5665			−0.865116			−0.432558	−	0.901606i	$-0.642389\pi$
$211$	−12.5665			−0.865116			−0.432558	+	0.901606i	$0.642389\pi$
$212$	−6.98682			−0.479857
$213$	7.06983	+	5.29298i	0.484416	+	0.362669i
$214$	−12.1115			−0.827927
$215$	1.92250	+	3.73224i	0.131113	+	0.254537i
$216$	4.86825	+	1.81663i	0.331242	+	0.123606i
$217$		0			0
$218$	−11.1753			−0.756886
$219$	−17.1124	+	22.8570i	−1.15635	+	1.54454i
$220$	1.30902	+	2.54126i	0.0882538	+	0.171331i
$221$			7.63029i			0.513269i
$222$	6.48242	+	4.85321i	0.435072	+	0.325726i
$223$	13.1623			0.881415			0.440708	−	0.897651i	$-0.354728\pi$
$223$	13.1623			0.881415			0.440708	+	0.897651i	$0.354728\pi$
$224$		0			0
$225$	−14.1712	−	4.91713i	−0.944744	−	0.327808i
$226$	−0.00477454			−0.000317598
$227$		−	15.5346i		−	1.03107i	−0.856870	−	0.515533i	$-0.827594\pi$
$227$		−	15.5346i		−	1.03107i	0.856870	−	0.515533i	$-0.172406\pi$
$228$	3.38582	+	2.53487i	0.224231	+	0.167876i
$229$		−	4.02816i		−	0.266188i	−0.991103	−	0.133094i	$-0.957509\pi$
$229$		−	4.02816i		−	0.266188i	0.991103	−	0.133094i	$-0.0424912\pi$
$230$	−1.35177	+	0.696306i	−0.0891333	+	0.0459131i
$231$		0			0
$232$		−	6.12676i		−	0.402242i
$233$	−28.2529			−1.85091			−0.925454	−	0.378861i	$-0.876316\pi$
$233$	−28.2529			−1.85091			−0.925454	+	0.378861i	$0.876316\pi$
$234$	−1.11741	−	3.80701i	−0.0730472	−	0.248872i
$235$	−8.16832	−	15.8576i	−0.532843	−	1.03443i
$236$	−9.65619			−0.628564
$237$	−16.1283	+	21.5425i	−1.04764	+	1.39933i
$238$		0			0
$239$		−	10.6358i		−	0.687973i	−0.938975	−	0.343987i	$-0.888223\pi$
$239$		−	10.6358i		−	0.687973i	0.938975	−	0.343987i	$-0.111777\pi$
$240$	−0.643753	+	3.81911i	−0.0415541	+	0.246522i
$241$		−	3.42344i		−	0.220523i	−0.993903	−	0.110262i	$-0.964831\pi$
$241$		−	3.42344i		−	0.220523i	0.993903	−	0.110262i	$-0.0351688\pi$
$242$	−9.36570			−0.602050
$243$	−1.11612	+	15.5484i	−0.0715994	+	0.997433i
$244$		−	4.22958i		−	0.270771i
$245$		0			0
$246$	12.7976	−	17.0937i	0.815944	−	1.08985i
$247$		−	3.22956i		−	0.205492i
$248$		−	6.94293i		−	0.440876i
$249$	−4.62402	−	3.46188i	−0.293036	−	0.219388i
$250$	1.60240	−	11.0649i	0.101345	−	0.699807i
$251$	1.41048			0.0890287			0.0445143	−	0.999009i	$-0.485826\pi$
$251$	1.41048			0.0890287			0.0445143	+	0.999009i	$0.485826\pi$
$252$		0			0
$253$			0.869335i			0.0546547i
$254$			7.34269i			0.460721i
$255$	22.0341	+	3.71410i	1.37983	+	0.232586i
$256$	1.00000			0.0625000
$257$			17.8668i			1.11450i	0.830345	+	0.557249i	$0.188143\pi$
$257$			17.8668i			1.11450i	−0.830345	+	0.557249i	$0.811857\pi$
$258$	2.60324	+	1.94897i	0.162071	+	0.121338i
$259$		0			0
$260$	2.62899	−	1.35421i	0.163043	−	0.0839846i
$261$	17.6363	−	5.17648i	1.09166	−	0.320416i
$262$	0.0771448			0.00476602
$263$	−1.07247			−0.0661314			−0.0330657	−	0.999453i	$-0.510527\pi$
$263$	−1.07247			−0.0661314			−0.0330657	+	0.999453i	$0.510527\pi$
$264$	1.77253	+	1.32704i	0.109092	+	0.0816738i
$265$	13.8887	−	7.15416i	0.853176	−	0.439476i
$266$		0			0
$267$	13.2247	−	17.6643i	0.809341	−	1.08104i
$268$		−	12.9467i		−	0.790847i
$269$	10.3792			0.632832			0.316416	−	0.948621i	$-0.397520\pi$
$269$	10.3792			0.632832			0.316416	+	0.948621i	$0.397520\pi$
$270$	−11.5375	+	1.37367i	−0.702148	+	0.0835987i
$271$			9.90724i			0.601822i	0.953652	+	0.300911i	$0.0972907\pi$
$271$			9.90724i			0.601822i	−0.953652	+	0.300911i	$0.902709\pi$
$272$		−	5.76944i		−	0.349824i
$273$		0			0
$274$	−11.7831			−0.711846
$275$	−5.20424	−	3.71125i	−0.313827	−	0.223797i
$276$	−0.705896	+	0.942863i	−0.0424899	+	0.0567537i
$277$		−	18.3865i		−	1.10474i	−0.833600	−	0.552368i	$-0.813724\pi$
$277$		−	18.3865i		−	1.10474i	0.833600	−	0.552368i	$-0.186276\pi$
$278$		−	15.9840i		−	0.958655i
$279$	19.9857	−	5.86606i	1.19651	−	0.351192i
$280$		0			0
$281$		−	19.0144i		−	1.13431i	−0.823612	−	0.567153i	$-0.808045\pi$
$281$		−	19.0144i		−	1.13431i	0.823612	−	0.567153i	$-0.191955\pi$
$282$	−11.0607	−	8.28081i	−0.658653	−	0.493115i
$283$	18.6645			1.10949			0.554744	−	0.832021i	$-0.312816\pi$
$283$	18.6645			1.10949			0.554744	+	0.832021i	$0.312816\pi$
$284$			5.09896i			0.302567i
$285$	−9.32606	−	1.57201i	−0.552428	−	0.0931179i
$286$		−	1.69073i		−	0.0999747i
$287$		0			0
$288$	0.844897	+	2.87857i	0.0497861	+	0.169621i
$289$	−16.2864			−0.958026
$290$	6.27350	+	12.1790i	0.368393	+	0.715178i
$291$	−3.01743	+	4.03037i	−0.176885	+	0.236264i
$292$	−16.4851			−0.964720
$293$			3.41725i			0.199638i	0.995006	+	0.0998189i	$0.0318264\pi$
$293$			3.41725i			0.199638i	−0.995006	+	0.0998189i	$0.968174\pi$
$294$		0			0
$295$	19.1950	−	9.88746i	1.11758	−	0.575670i
$296$			4.67531i			0.271747i
$297$	−2.32238	+	6.22356i	−0.134758	+	0.361127i
$298$		−	20.2680i		−	1.17410i
$299$	0.899350			0.0520108
$300$	−2.63090	−	8.25096i	−0.151895	−	0.476370i
$301$		0			0
$302$	−10.0657			−0.579216
$303$	−9.36767	+	12.5124i	−0.538158	+	0.718817i
$304$			2.44195i			0.140055i
$305$	4.33088	+	8.40775i	0.247985	+	0.481426i
$306$	16.6077	−	4.87459i	0.949400	−	0.278661i
$307$	13.3096			0.759620			0.379810	−	0.925064i	$-0.375989\pi$
$307$	13.3096			0.759620			0.379810	+	0.925064i	$0.375989\pi$
$308$		0			0
$309$	−18.1414	+	24.2315i	−1.03203	+	1.37848i
$310$	7.10922	+	13.8015i	0.403776	+	0.783870i
$311$	11.7713			0.667487			0.333743	−	0.942664i	$-0.391688\pi$
$311$	11.7713			0.667487			0.333743	+	0.942664i	$0.391688\pi$
$312$	1.37286	−	1.83373i	0.0777229	−	0.103814i
$313$	11.2347			0.635022			0.317511	−	0.948255i	$-0.397153\pi$
$313$	11.2347			0.635022			0.317511	+	0.948255i	$0.397153\pi$
$314$	9.84780			0.555743
$315$		0			0
$316$	−15.5370			−0.874027
$317$	4.68621			0.263204			0.131602	−	0.991303i	$-0.457988\pi$
$317$	4.68621			0.263204			0.131602	+	0.991303i	$0.457988\pi$
$318$	7.25268	−	9.68739i	0.406710	−	0.543242i
$319$	7.83244			0.438532
$320$	−1.98784	+	1.02395i	−0.111124	+	0.0572406i
$321$	12.5724	−	16.7929i	0.701723	−	0.937290i
$322$		0			0
$323$	14.0887			0.783914
$324$	−7.57230	+	4.86419i	−0.420683	+	0.270233i
$325$	−3.83939	+	5.38392i	−0.212971	+	0.298646i
$326$		−	11.4412i		−	0.633672i
$327$	11.6005	−	15.4948i	0.641510	−	0.856864i
$328$	12.3285			0.680725
$329$		0			0
$330$	−4.88234	−	0.822973i	−0.268764	−	0.0453032i
$331$	26.6248			1.46343			0.731717	−	0.681609i	$-0.238719\pi$
$331$	26.6248			1.46343			0.731717	+	0.681609i	$0.238719\pi$
$332$		−	3.33498i		−	0.183031i
$333$	−13.4582	+	3.95015i	−0.737504	+	0.216467i
$334$			14.1922i			0.776564i
$335$	13.2568	+	25.7361i	0.724296	+	1.40611i
$336$		0			0
$337$			18.2212i			0.992570i	0.868160	+	0.496285i	$0.165303\pi$
$337$			18.2212i			0.992570i	−0.868160	+	0.496285i	$0.834697\pi$
$338$	11.2509			0.611968
$339$	0.00495622	−	0.00662001i	0.000269185	−	0.000359550i
$340$	5.90762	+	11.4688i	0.320386	+	0.621980i
$341$	8.87582			0.480653
$342$	−7.02931	+	2.06319i	−0.380101	+	0.111565i
$343$		0			0
$344$			1.87753i			0.101230i
$345$	0.437765	−	2.59707i	0.0235685	−	0.139821i
$346$		−	0.985415i		−	0.0529762i
$347$	−2.17760			−0.116900			−0.0584498	−	0.998290i	$-0.518616\pi$
$347$	−2.17760			−0.116900			−0.0584498	+	0.998290i	$0.518616\pi$
$348$	8.49490	+	6.35990i	0.455375	+	0.340926i
$349$		−	21.1821i		−	1.13385i	−0.823769	−	0.566925i	$-0.808133\pi$
$349$		−	21.1821i		−	1.13385i	0.823769	−	0.566925i	$-0.191867\pi$
$350$		0			0
$351$	6.43843	+	2.40256i	0.343658	+	0.128239i
$352$			1.27840i			0.0681388i
$353$			27.1933i			1.44735i	0.690140	+	0.723676i	$0.257549\pi$
$353$			27.1933i			1.44735i	−0.690140	+	0.723676i	$0.742451\pi$
$354$	10.0236	−	13.3885i	0.532749	−	0.711593i
$355$	−5.22108	−	10.1359i	−0.277106	−	0.537959i
$356$	12.7400			0.675217
$357$		0			0
$358$			10.2949i			0.544103i
$359$			29.0266i			1.53197i	0.642860	+	0.765984i	$0.277748\pi$
$359$			29.0266i			1.53197i	−0.642860	+	0.765984i	$0.722252\pi$
$360$	−4.62703	−	4.85701i	−0.243866	−	0.255987i
$361$	13.0369			0.686152
$362$			5.05282i			0.265570i
$363$	9.72208	−	12.9858i	0.510277	−	0.681576i
$364$		0			0
$365$	32.7699	−	16.8800i	1.71526	−	0.883538i
$366$	5.86441	+	4.39052i	0.306538	+	0.229496i
$367$	1.78381			0.0931141			0.0465570	−	0.998916i	$-0.485175\pi$
$367$	1.78381			0.0931141			0.0465570	+	0.998916i	$0.485175\pi$
$368$	−0.680020			−0.0354485
$369$	10.4163	+	35.4883i	0.542250	+	1.84745i
$370$	−4.78728	−	9.29378i	−0.248879	−	0.483161i
$371$		0			0
$372$	9.62654	+	7.20712i	0.499113	+	0.373672i
$373$		−	19.6625i		−	1.01809i	−0.860741	−	0.509044i	$-0.829999\pi$
$373$		−	19.6625i		−	1.01809i	0.860741	−	0.509044i	$-0.170001\pi$
$374$	7.37564			0.381385
$375$	13.6784	+	13.7077i	0.706349	+	0.707864i
$376$		−	7.97726i		−	0.411396i
$377$		−	8.10286i		−	0.417319i
$378$		0			0
$379$	−16.7309			−0.859408			−0.429704	−	0.902970i	$-0.641382\pi$
$379$	−16.7309			−0.859408			−0.429704	+	0.902970i	$0.641382\pi$
$380$	−2.50043	−	4.85421i	−0.128269	−	0.249016i
$381$	−10.1808	−	7.62209i	−0.521579	−	0.390491i
$382$			9.31528i			0.476611i
$383$		−	8.48194i		−	0.433407i	−0.976237	−	0.216704i	$-0.930470\pi$
$383$		−	8.48194i		−	0.433407i	0.976237	−	0.216704i	$-0.0695305\pi$
$384$	−1.03805	+	1.38652i	−0.0529729	+	0.0707558i
$385$		0			0
$386$		−	2.53974i		−	0.129269i
$387$	−5.40460	+	1.58632i	−0.274731	+	0.0806372i
$388$	−2.90682			−0.147571
$389$		−	22.1622i		−	1.12367i	−0.827249	−	0.561835i	$-0.810096\pi$
$389$		−	22.1622i		−	1.12367i	0.827249	−	0.561835i	$-0.189904\pi$
$390$	−0.851387	+	5.05091i	−0.0431116	+	0.255763i
$391$			3.92333i			0.198411i
$392$		0			0
$393$	−0.0800803	+	0.106963i	−0.00403952	+	0.00539558i
$394$	−8.65660			−0.436113
$395$	30.8852	−	15.9092i	1.55400	−	0.800477i
$396$	−3.67995	+	1.08011i	−0.184925	+	0.0542778i
$397$	21.7809			1.09315			0.546577	−	0.837409i	$-0.315931\pi$
$397$	21.7809			1.09315			0.546577	+	0.837409i	$0.315931\pi$
$398$			27.9233i			1.39967i
$399$		0			0
$400$	2.90305	−	4.07091i	0.145153	−	0.203545i
$401$		−	14.1195i		−	0.705094i	−0.935794	−	0.352547i	$-0.885316\pi$
$401$		−	14.1195i		−	0.705094i	0.935794	−	0.352547i	$-0.114684\pi$
$402$	17.9509	+	13.4394i	0.895311	+	0.670294i
$403$		−	9.18227i		−	0.457402i
$404$	−9.02428			−0.448975
$405$	10.0719	−	17.4229i	0.500475	−	0.865751i
$406$		0			0
$407$	−5.97690			−0.296264
$408$	7.99947	+	5.98898i	0.396033	+	0.296499i
$409$		−	23.7751i		−	1.17560i	−0.809005	−	0.587801i	$-0.799994\pi$
$409$		−	23.7751i		−	1.17560i	0.809005	−	0.587801i	$-0.200006\pi$
$410$	−24.5071	+	12.6237i	−1.21032	+	0.623442i
$411$	12.2315	−	16.3376i	0.603336	−	0.805875i
$412$	−17.4764			−0.861002
$413$		0			0
$414$	−0.574547	−	1.95748i	−0.0282374	−	0.0962050i
$415$	3.41485	+	6.62941i	0.167628	+	0.325425i
$416$	1.32254			0.0648426
$417$	22.1622	+	16.5922i	1.08529	+	0.812523i
$418$	−3.12178			−0.152691
$419$	7.09712			0.346717			0.173359	−	0.984859i	$-0.444538\pi$
$419$	7.09712			0.346717			0.173359	+	0.984859i	$0.444538\pi$
$420$		0			0
$421$	−10.5901			−0.516128			−0.258064	−	0.966128i	$-0.583085\pi$
$421$	−10.5901			−0.516128			−0.258064	+	0.966128i	$0.583085\pi$
$422$	12.5665			0.611729
$423$	22.9631	−	6.73997i	1.11650	−	0.327708i
$424$	6.98682			0.339310
$425$	−23.4869	−	16.7490i	−1.13928	−	0.812445i
$426$	−7.06983	−	5.29298i	−0.342534	−	0.256446i
$427$		0			0
$428$	12.1115			0.585433
$429$	2.34423	+	1.75506i	0.113181	+	0.0847352i
$430$	−1.92250	−	3.73224i	−0.0927111	−	0.179985i
$431$		−	30.8160i		−	1.48435i	−0.670205	−	0.742176i	$-0.733794\pi$
$431$		−	30.8160i		−	1.48435i	0.670205	−	0.742176i	$-0.266206\pi$
$432$	−4.86825	−	1.81663i	−0.234224	−	0.0874027i
$433$	−24.3465			−1.17002			−0.585010	−	0.811026i	$-0.698909\pi$
$433$	−24.3465			−1.17002			−0.585010	+	0.811026i	$0.698909\pi$
$434$		0			0
$435$	−23.3988	−	3.94412i	−1.12188	−	0.189106i
$436$	11.1753			0.535199
$437$		−	1.66057i		−	0.0794359i
$438$	17.1124	−	22.8570i	0.817664	−	1.09215i
$439$			12.6887i			0.605598i	0.953054	+	0.302799i	$0.0979211\pi$
$439$			12.6887i			0.605598i	−0.953054	+	0.302799i	$0.902079\pi$
$440$	−1.30902	−	2.54126i	−0.0624049	−	0.121150i
$441$		0			0
$442$		−	7.63029i		−	0.362936i
$443$	9.71974			0.461799			0.230899	−	0.972978i	$-0.425833\pi$
$443$	9.71974			0.461799			0.230899	+	0.972978i	$0.425833\pi$
$444$	−6.48242	−	4.85321i	−0.307642	−	0.230323i
$445$	−25.3251	+	13.0451i	−1.20052	+	0.618397i
$446$	−13.1623			−0.623255
$447$	28.1021	+	21.0393i	1.32918	+	0.995123i
$448$		0			0
$449$			6.90138i			0.325696i	0.986651	+	0.162848i	$0.0520680\pi$
$449$			6.90138i			0.325696i	−0.986651	+	0.162848i	$0.947932\pi$
$450$	14.1712	+	4.91713i	0.668035	+	0.231796i
$451$			15.7607i			0.742141i
$452$	0.00477454			0.000224575
$453$	10.4487	−	13.9563i	0.490924	−	0.655726i
$454$			15.5346i			0.729074i
$455$		0			0
$456$	−3.38582	−	2.53487i	−0.158555	−	0.118706i
$457$			4.52428i			0.211637i	0.994385	+	0.105818i	$0.0337462\pi$
$457$			4.52428i			0.211637i	−0.994385	+	0.105818i	$0.966254\pi$
$458$			4.02816i			0.188223i
$459$	−10.4809	+	28.0871i	−0.489209	+	1.31099i
$460$	1.35177	−	0.696306i	0.0630267	−	0.0324655i
$461$	−13.8000			−0.642732			−0.321366	−	0.946955i	$-0.604142\pi$
$461$	−13.8000			−0.642732			−0.321366	+	0.946955i	$0.604142\pi$
$462$		0			0
$463$			22.5955i			1.05010i	0.851071	+	0.525051i	$0.175954\pi$
$463$			22.5955i			1.05010i	−0.851071	+	0.525051i	$0.824046\pi$
$464$			6.12676i			0.284428i
$465$	−26.5158	−	4.46953i	−1.22964	−	0.207270i
$466$	28.2529			1.30879
$467$		−	22.7817i		−	1.05421i	−0.849799	−	0.527107i	$-0.823277\pi$
$467$		−	22.7817i		−	1.05421i	0.849799	−	0.527107i	$-0.176723\pi$
$468$	1.11741	+	3.80701i	0.0516521	+	0.175979i
$469$		0			0
$470$	8.16832	+	15.8576i	0.376777	+	0.731455i
$471$	−10.2225	+	13.6542i	−0.471029	+	0.629153i
$472$	9.65619			0.444462
$473$	−2.40023			−0.110363
$474$	16.1283	−	21.5425i	0.740795	−	0.989479i
$475$	9.94094	+	7.08910i	0.456122	+	0.325270i
$476$		0			0
$477$	5.90314	+	20.1120i	0.270286	+	0.920866i
$478$			10.6358i			0.486470i
$479$	−31.9484			−1.45976			−0.729880	−	0.683575i	$-0.760424\pi$
$479$	−31.9484			−1.45976			−0.729880	+	0.683575i	$0.760424\pi$
$480$	0.643753	−	3.81911i	0.0293832	−	0.174318i
$481$			6.18326i			0.281932i
$482$			3.42344i			0.155933i
$483$		0			0
$484$	9.36570			0.425714
$485$	5.77830	−	2.97644i	0.262379	−	0.135153i
$486$	1.11612	−	15.5484i	0.0506284	−	0.705292i
$487$		−	6.93234i		−	0.314135i	−0.987588	−	0.157067i	$-0.949796\pi$
$487$		−	6.93234i		−	0.314135i	0.987588	−	0.157067i	$-0.0502039\pi$
$488$			4.22958i			0.191464i
$489$	15.8635	+	11.8766i	0.717374	+	0.537078i
$490$		0			0
$491$		−	24.3178i		−	1.09745i	−0.836004	−	0.548723i	$-0.815114\pi$
$491$		−	24.3178i		−	1.09745i	0.836004	−	0.548723i	$-0.184886\pi$
$492$	−12.7976	+	17.0937i	−0.576959	+	0.770644i
$493$	35.3480			1.59199
$494$			3.22956i			0.145305i
$495$	6.20919	−	5.91519i	0.279082	−	0.265868i
$496$			6.94293i			0.311747i
$497$		0			0
$498$	4.62402	+	3.46188i	0.207207	+	0.155130i
$499$	−22.5999			−1.01171			−0.505854	−	0.862619i	$-0.668823\pi$
$499$	−22.5999			−1.01171			−0.505854	+	0.862619i	$0.668823\pi$
$500$	−1.60240	+	11.0649i	−0.0716617	+	0.494838i
$501$	−19.6779	−	14.7323i	−0.879142	−	0.658189i
$502$	−1.41048			−0.0629528
$503$		−	28.1932i		−	1.25707i	−0.777781	−	0.628535i	$-0.783655\pi$
$503$		−	28.1932i		−	1.25707i	0.777781	−	0.628535i	$-0.216345\pi$
$504$		0			0
$505$	17.9389	−	9.24042i	0.798269	−	0.411193i
$506$		−	0.869335i		−	0.0386467i
$507$	−11.6790	+	15.5996i	−0.518683	+	0.692804i
$508$		−	7.34269i		−	0.325779i
$509$	29.2730			1.29750			0.648752	−	0.761000i	$-0.275291\pi$
$509$	29.2730			1.29750			0.648752	+	0.761000i	$0.275291\pi$
$510$	−22.0341	−	3.71410i	−0.975687	−	0.164463i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	4.43612	−	11.8880i	0.195859	−	0.524868i
$514$		−	17.8668i		−	0.788069i
$515$	34.7404	−	17.8950i	1.53085	−	0.788548i
$516$	−2.60324	−	1.94897i	−0.114601	−	0.0857988i
$517$	10.1981			0.448513
$518$		0			0
$519$	1.36630	+	1.02291i	0.0599740	+	0.0449008i
$520$	−2.62899	+	1.35421i	−0.115289	+	0.0593861i
$521$	−1.10870			−0.0485729			−0.0242865	−	0.999705i	$-0.507731\pi$
$521$	−1.10870			−0.0485729			−0.0242865	+	0.999705i	$0.507731\pi$
$522$	−17.6363	+	5.17648i	−0.771920	+	0.226569i
$523$	38.3222			1.67571			0.837857	−	0.545890i	$-0.183808\pi$
$523$	38.3222			1.67571			0.837857	+	0.545890i	$0.183808\pi$
$524$	−0.0771448			−0.00337009
$525$		0			0
$526$	1.07247			0.0467620
$527$	40.0568			1.74490
$528$	−1.77253	−	1.32704i	−0.0771394	−	0.0577521i
$529$	−22.5376			−0.979894
$530$	−13.8887	+	7.15416i	−0.603287	+	0.310757i
$531$	8.15849	+	27.7960i	0.354048	+	1.20624i
$532$		0			0
$533$	16.3048			0.706240
$534$	−13.2247	+	17.6643i	−0.572291	+	0.764408i
$535$	−24.0758	+	12.4016i	−1.04089	+	0.536168i
$536$			12.9467i			0.559213i
$537$	−14.2741	−	10.6867i	−0.615975	−	0.461163i
$538$	−10.3792			−0.447480
$539$		0			0
$540$	11.5375	−	1.37367i	0.496493	−	0.0591132i
$541$	4.97661			0.213961			0.106981	−	0.994261i	$-0.465882\pi$
$541$	4.97661			0.213961			0.106981	+	0.994261i	$0.465882\pi$
$542$		−	9.90724i		−	0.425552i
$543$	−7.00586	−	5.24509i	−0.300650	−	0.225088i
$544$			5.76944i			0.247363i
$545$	−22.2147	+	11.4429i	−0.951574	+	0.490162i
$546$		0			0
$547$		−	28.0840i		−	1.20079i	−0.799705	−	0.600393i	$-0.795011\pi$
$547$		−	28.0840i		−	1.20079i	0.799705	−	0.600393i	$-0.204989\pi$
$548$	11.7831			0.503351
$549$	−12.1751	+	3.57356i	−0.519622	+	0.152516i
$550$	5.20424	+	3.71125i	0.221910	+	0.158248i
$551$	−14.9612			−0.637370
$552$	0.705896	−	0.942863i	0.0300449	−	0.0401309i
$553$		0			0
$554$			18.3865i			0.781166i
$555$	17.8555	+	3.00974i	0.757924	+	0.127757i
$556$			15.9840i			0.677871i
$557$	−23.5775			−0.999009			−0.499504	−	0.866311i	$-0.666485\pi$
$557$	−23.5775			−0.999009			−0.499504	+	0.866311i	$0.666485\pi$
$558$	−19.9857	+	5.86606i	−0.846062	+	0.248330i
$559$			2.48310i			0.105024i
$560$		0			0
$561$	−7.65630	+	10.2265i	−0.323249	+	0.431763i
$562$			19.0144i			0.802075i
$563$			18.4990i			0.779639i	0.920891	+	0.389819i	$0.127463\pi$
$563$			18.4990i			0.779639i	−0.920891	+	0.389819i	$0.872537\pi$
$564$	11.0607	+	8.28081i	0.465738	+	0.348685i
$565$	−0.00949104	+	0.00488889i	−0.000399291	+	0.000205677i
$566$	−18.6645			−0.784526
$567$		0			0
$568$		−	5.09896i		−	0.213947i
$569$		−	19.5845i		−	0.821026i	−0.911855	−	0.410513i	$-0.865350\pi$
$569$		−	19.5845i		−	0.821026i	0.911855	−	0.410513i	$-0.134650\pi$
$570$	9.32606	+	1.57201i	0.390626	+	0.0658443i
$571$	−15.4720			−0.647481			−0.323741	−	0.946146i	$-0.604941\pi$
$571$	−15.4720			−0.647481			−0.323741	+	0.946146i	$0.604941\pi$
$572$			1.69073i			0.0706928i
$573$	−12.9159	−	9.66974i	−0.539568	−	0.403959i
$574$		0			0
$575$	−1.97413	+	2.76830i	−0.0823270	+	0.115446i
$576$	−0.844897	−	2.87857i	−0.0352041	−	0.119940i
$577$	−31.3327			−1.30440			−0.652199	−	0.758048i	$-0.726153\pi$
$577$	−31.3327			−1.30440			−0.652199	+	0.758048i	$0.726153\pi$
$578$	16.2864			0.677427
$579$	3.52141	+	2.63638i	0.146345	+	0.109564i
$580$	−6.27350	−	12.1790i	−0.260493	−	0.505707i
$581$		0			0
$582$	3.01743	−	4.03037i	0.125076	−	0.167064i
$583$			8.93193i			0.369923i
$584$	16.4851			0.682160
$585$	−6.11942	−	6.42357i	−0.253007	−	0.265582i
$586$		−	3.41725i		−	0.141165i
$587$		−	34.0806i		−	1.40666i	−0.710865	−	0.703329i	$-0.751696\pi$
$587$		−	34.0806i		−	1.40666i	0.710865	−	0.703329i	$-0.248304\pi$
$588$		0			0
$589$	−16.9543			−0.698588
$590$	−19.1950	+	9.88746i	−0.790246	+	0.407060i
$591$	8.98600	−	12.0026i	0.369635	−	0.493720i
$592$		−	4.67531i		−	0.192154i
$593$			17.1989i			0.706274i	0.935572	+	0.353137i	$0.114885\pi$
$593$			17.1989i			0.706274i	−0.935572	+	0.353137i	$0.885115\pi$
$594$	2.32238	−	6.22356i	0.0952883	−	0.255356i
$595$		0			0
$596$			20.2680i			0.830211i
$597$	−38.7163	−	28.9858i	−1.58455	−	1.18631i
$598$	−0.899350			−0.0367772
$599$			28.4544i			1.16262i	0.813684	+	0.581308i	$0.197459\pi$
$599$			28.4544i			1.16262i	−0.813684	+	0.581308i	$0.802541\pi$
$600$	2.63090	+	8.25096i	0.107406	+	0.336844i
$601$		−	2.32232i		−	0.0947295i	−0.998878	−	0.0473647i	$-0.984918\pi$
$601$		−	2.32232i		−	0.0947295i	0.998878	−	0.0473647i	$-0.0150823\pi$
$602$		0			0
$603$	−37.2680	+	10.9386i	−1.51767	+	0.445456i
$604$	10.0657			0.409568
$605$	−18.6176	+	9.59001i	−0.756911	+	0.389889i
$606$	9.36767	−	12.5124i	0.380536	−	0.508281i
$607$	−32.2377			−1.30849			−0.654244	−	0.756283i	$-0.727013\pi$
$607$	−32.2377			−1.30849			−0.654244	+	0.756283i	$0.727013\pi$
$608$		−	2.44195i		−	0.0990340i
$609$		0			0
$610$	−4.33088	−	8.40775i	−0.175352	−	0.340420i
$611$		−	10.5502i		−	0.426816i
$612$	−16.6077	+	4.87459i	−0.671327	+	0.197043i
$613$			14.4301i			0.582825i	0.956597	+	0.291413i	$0.0941252\pi$
$613$			14.4301i			0.582825i	−0.956597	+	0.291413i	$0.905875\pi$
$614$	−13.3096			−0.537133
$615$	7.93649	−	47.0837i	0.320030	−	1.89860i
$616$		0			0
$617$	−41.6916			−1.67844			−0.839219	−	0.543793i	$-0.816988\pi$
$617$	−41.6916			−1.67844			−0.839219	+	0.543793i	$0.816988\pi$
$618$	18.1414	−	24.2315i	0.729755	−	0.974733i
$619$			7.38411i			0.296792i	0.988928	+	0.148396i	$0.0474111\pi$
$619$			7.38411i			0.296792i	−0.988928	+	0.148396i	$0.952589\pi$
$620$	−7.10922	−	13.8015i	−0.285513	−	0.554280i
$621$	3.31050	+	1.23534i	0.132846	+	0.0495727i
$622$	−11.7713			−0.471984
$623$		0			0
$624$	−1.37286	+	1.83373i	−0.0549584	+	0.0734078i
$625$	−8.14459	−	23.6361i	−0.325784	−	0.945444i
$626$	−11.2347			−0.449029
$627$	3.24057	−	4.32842i	0.129416	−	0.172860i
$628$	−9.84780			−0.392970
$629$	−26.9739			−1.07552
$630$		0			0
$631$	43.8396			1.74523			0.872613	−	0.488412i	$-0.162423\pi$
$631$	43.8396			1.74523			0.872613	+	0.488412i	$0.162423\pi$
$632$	15.5370			0.618031
$633$	−13.0447	+	17.4238i	−0.518481	+	0.692534i
$634$	−4.68621			−0.186113
$635$	7.51855	+	14.5961i	0.298364	+	0.579229i
$636$	−7.25268	+	9.68739i	−0.287587	+	0.384130i
$637$		0			0
$638$	−7.83244			−0.310089
$639$	14.6777	−	4.30809i	0.580640	−	0.170426i
$640$	1.98784	−	1.02395i	0.0785764	−	0.0404752i
$641$			15.9563i			0.630236i	0.949052	+	0.315118i	$0.102044\pi$
$641$			15.9563i			0.630236i	−0.949052	+	0.315118i	$0.897956\pi$
$642$	−12.5724	+	16.7929i	−0.496193	+	0.662764i
$643$	3.11117			0.122692			0.0613462	−	0.998117i	$-0.480461\pi$
$643$	3.11117			0.122692			0.0613462	+	0.998117i	$0.480461\pi$
$644$		0			0
$645$	7.17049	+	1.20867i	0.282338	+	0.0475912i
$646$	−14.0887			−0.554311
$647$		−	28.0993i		−	1.10470i	−0.833613	−	0.552350i	$-0.813731\pi$
$647$		−	28.0993i		−	1.10470i	0.833613	−	0.552350i	$-0.186269\pi$
$648$	7.57230	−	4.86419i	0.297468	−	0.191083i
$649$			12.3444i			0.484562i
$650$	3.83939	−	5.38392i	0.150593	−	0.211175i
$651$		0			0
$652$			11.4412i			0.448073i
$653$	−37.3861			−1.46303			−0.731515	−	0.681825i	$-0.761186\pi$
$653$	−37.3861			−1.46303			−0.731515	+	0.681825i	$0.761186\pi$
$654$	−11.6005	+	15.4948i	−0.453616	+	0.605895i
$655$	0.153352	−	0.0789925i	0.00599196	−	0.00308649i
$656$	−12.3285			−0.481345
$657$	13.9283	+	47.4536i	0.543393	+	1.85134i
$658$		0			0
$659$		−	15.3543i		−	0.598119i	−0.954234	−	0.299059i	$-0.903327\pi$
$659$		−	15.3543i		−	0.598119i	0.954234	−	0.299059i	$-0.0966729\pi$
$660$	4.88234	+	0.822973i	0.190045	+	0.0320342i
$661$			40.0450i			1.55757i	0.627291	+	0.778785i	$0.284164\pi$
$661$			40.0450i			1.55757i	−0.627291	+	0.778785i	$0.715836\pi$
$662$	−26.6248			−1.03480
$663$	10.5796	+	7.92064i	0.410877	+	0.307612i
$664$			3.33498i			0.129422i
$665$		0			0
$666$	13.4582	−	3.95015i	0.521494	−	0.153065i
$667$		−	4.16632i		−	0.161320i
$668$		−	14.1922i		−	0.549114i
$669$	13.6632	−	18.2499i	0.528249	−	0.705582i
$670$	−13.2568	−	25.7361i	−0.512155	−	0.994271i
$671$	−5.40708			−0.208738
$672$		0			0
$673$		−	18.2669i		−	0.704137i	−0.935974	−	0.352069i	$-0.885478\pi$
$673$		−	18.2669i		−	0.704137i	0.935974	−	0.352069i	$-0.114522\pi$
$674$		−	18.2212i		−	0.701853i
$675$	−21.5281	+	14.5444i	−0.828617	+	0.559815i
$676$	−11.2509			−0.432727
$677$		−	18.1380i		−	0.697098i	−0.937291	−	0.348549i	$-0.886674\pi$
$677$		−	18.1380i		−	0.697098i	0.937291	−	0.348549i	$-0.113326\pi$
$678$	−0.00495622	+	0.00662001i	−0.000190342	+	0.000254240i
$679$		0			0
$680$	−5.90762	−	11.4688i	−0.226547	−	0.439807i
$681$	−21.5391	−	16.1257i	−0.825379	−	0.617938i
$682$	−8.87582			−0.339873
$683$	6.08580			0.232867			0.116433	−	0.993199i	$-0.462854\pi$
$683$	6.08580			0.232867			0.116433	+	0.993199i	$0.462854\pi$
$684$	7.02931	−	2.06319i	0.268772	−	0.0788882i
$685$	−23.4231	+	12.0654i	−0.894949	+	0.460994i
$686$		0			0
$687$	−5.58514	−	4.18144i	−0.213086	−	0.159532i
$688$		−	1.87753i		−	0.0715802i
$689$	9.24031			0.352028
$690$	−0.437765	+	2.59707i	−0.0166654	+	0.0988687i
$691$			3.60562i			0.137164i	0.997645	+	0.0685820i	$0.0218475\pi$
$691$			3.60562i			0.137164i	−0.997645	+	0.0685820i	$0.978153\pi$
$692$			0.985415i			0.0374599i
$693$		0			0
$694$	2.17760			0.0826605
$695$	−16.3668	−	31.7736i	−0.620828	−	1.20524i
$696$	−8.49490	−	6.35990i	−0.321998	−	0.241071i
$697$			71.1283i			2.69418i
$698$			21.1821i			0.801753i
$699$	−29.3279	+	39.1733i	−1.10928	+	1.48167i
$700$		0			0
$701$			17.6543i			0.666794i	0.942786	+	0.333397i	$0.108195\pi$
$701$			17.6543i			0.666794i	−0.942786	+	0.333397i	$0.891805\pi$
$702$	−6.43843	−	2.40256i	−0.243003	−	0.0906788i
$703$	11.4168			0.430595
$704$		−	1.27840i		−	0.0481814i
$705$	−30.4660	−	5.13539i	−1.14742	−	0.193410i
$706$		−	27.1933i		−	1.02343i
$707$		0			0
$708$	−10.0236	+	13.3885i	−0.376711	+	0.503172i
$709$	−28.6814			−1.07715			−0.538575	−	0.842577i	$-0.681037\pi$
$709$	−28.6814			−1.07715			−0.538575	+	0.842577i	$0.681037\pi$
$710$	5.22108	+	10.1359i	0.195944	+	0.380395i
$711$	13.1272	+	44.7244i	0.492309	+	1.67730i
$712$	−12.7400			−0.477451
$713$		−	4.72133i		−	0.176815i
$714$		0			0
$715$	−1.73122	−	3.36090i	−0.0647440	−	0.125691i
$716$		−	10.2949i		−	0.384739i
$717$	−14.7468	−	11.0405i	−0.550729	−	0.412316i
$718$		−	29.0266i		−	1.08326i
$719$	12.4782			0.465359			0.232680	−	0.972553i	$-0.425251\pi$
$719$	12.4782			0.465359			0.232680	+	0.972553i	$0.425251\pi$
$720$	4.62703	+	4.85701i	0.172439	+	0.181010i
$721$		0			0
$722$	−13.0369			−0.485183
$723$	−4.74668	−	3.55371i	−0.176531	−	0.132164i
$724$		−	5.05282i		−	0.187787i
$725$	24.9415	+	17.7863i	0.926304	+	0.660567i
$726$	−9.72208	+	12.9858i	−0.360820	+	0.481947i
$727$	7.85466			0.291313			0.145657	−	0.989335i	$-0.453471\pi$
$727$	7.85466			0.291313			0.145657	+	0.989335i	$0.453471\pi$
$728$		0			0
$729$	20.3997	+	17.6876i	0.755545	+	0.655097i
$730$	−32.7699	+	16.8800i	−1.21287	+	0.624756i
$731$	−10.8323			−0.400647
$732$	−5.86441	−	4.39052i	−0.216755	−	0.162278i
$733$	15.3864			0.568308			0.284154	−	0.958779i	$-0.408287\pi$
$733$	15.3864			0.568308			0.284154	+	0.958779i	$0.408287\pi$
$734$	−1.78381			−0.0658416
$735$		0			0
$736$	0.680020			0.0250659
$737$	−16.5511			−0.609666
$738$	−10.4163	−	35.4883i	−0.383429	−	1.30634i
$739$	2.33784			0.0859990			0.0429995	−	0.999075i	$-0.486309\pi$
$739$	2.33784			0.0859990			0.0429995	+	0.999075i	$0.486309\pi$
$740$	4.78728	+	9.29378i	0.175984	+	0.341646i
$741$	−4.47786	−	3.35245i	−0.164498	−	0.123155i
$742$		0			0
$743$	−18.4896			−0.678318			−0.339159	−	0.940729i	$-0.610142\pi$
$743$	−18.4896			−0.678318			−0.339159	+	0.940729i	$0.610142\pi$
$744$	−9.62654	−	7.20712i	−0.352926	−	0.264226i
$745$	−20.7535	−	40.2897i	−0.760348	−	1.47610i
$746$			19.6625i			0.719897i
$747$	−9.59995	+	2.81771i	−0.351244	+	0.103095i
$748$	−7.37564			−0.269680
$749$		0			0
$750$	−13.6784	−	13.7077i	−0.499464	−	0.500535i
$751$	−1.91013			−0.0697016			−0.0348508	−	0.999393i	$-0.511096\pi$
$751$	−1.91013			−0.0697016			−0.0348508	+	0.999393i	$0.511096\pi$
$752$			7.97726i			0.290901i
$753$	1.46415	−	1.95566i	0.0533566	−	0.0712683i
$754$			8.10286i			0.295089i
$755$	−20.0090	+	10.3068i	−0.728204	+	0.375102i
$756$		0			0
$757$			13.3724i			0.486026i	0.970023	+	0.243013i	$0.0781358\pi$
$757$			13.3724i			0.486026i	−0.970023	+	0.243013i	$0.921864\pi$
$758$	16.7309			0.607693
$759$	1.20535	+	0.902415i	0.0437516	+	0.0327556i
$760$	2.50043	+	4.85421i	0.0907002	+	0.176081i
$761$	−3.76731			−0.136565			−0.0682824	−	0.997666i	$-0.521752\pi$
$761$	−3.76731			−0.136565			−0.0682824	+	0.997666i	$0.521752\pi$
$762$	10.1808	+	7.62209i	0.368812	+	0.276119i
$763$		0			0
$764$		−	9.31528i		−	0.337015i
$765$	28.0222	−	26.6954i	1.01315	−	0.965174i
$766$			8.48194i			0.306465i
$767$	12.7707			0.461121
$768$	1.03805	−	1.38652i	0.0374575	−	0.0500319i
$769$			11.2974i			0.407393i	0.979034	+	0.203696i	$0.0652956\pi$
$769$			11.2974i			0.407393i	−0.979034	+	0.203696i	$0.934704\pi$
$770$		0			0
$771$	24.7727	+	18.5466i	0.892167	+	0.667941i
$772$			2.53974i			0.0914072i
$773$			16.3617i			0.588490i	0.955730	+	0.294245i	$0.0950682\pi$
$773$			16.3617i			0.588490i	−0.955730	+	0.294245i	$0.904932\pi$
$774$	5.40460	−	1.58632i	0.194264	−	0.0570191i
$775$	28.2640	+	20.1557i	1.01527	+	0.724013i
$776$	2.90682			0.104349
$777$		0			0
$778$			22.1622i			0.794554i
$779$		−	30.1054i		−	1.07864i
$780$	0.851387	−	5.05091i	0.0304845	−	0.180851i
$781$	6.51849			0.233250
$782$		−	3.92333i		−	0.140298i
$783$	11.1301	−	29.8266i	0.397756	−	1.06592i
$784$		0			0
$785$	19.5759	−	10.0837i	0.698693	−	0.359901i
$786$	0.0800803	−	0.106963i	0.00285637	−	0.00381525i
$787$	40.2948			1.43636			0.718178	−	0.695859i	$-0.244976\pi$
$787$	40.2948			1.43636			0.718178	+	0.695859i	$0.244976\pi$
$788$	8.65660			0.308379
$789$	−1.11328	+	1.48701i	−0.0396338	+	0.0529389i
$790$	−30.8852	+	15.9092i	−1.09885	+	0.566023i
$791$		0			0
$792$	3.67995	−	1.08011i	0.130761	−	0.0383802i
$793$			5.59377i			0.198641i
$794$	−21.7809			−0.772976
$795$	4.49779	−	26.6834i	0.159520	−	0.946363i
$796$		−	27.9233i		−	0.989714i
$797$		−	30.0110i		−	1.06304i	−0.847044	−	0.531522i	$-0.821620\pi$
$797$		−	30.0110i		−	1.06304i	0.847044	−	0.531522i	$-0.178380\pi$
$798$		0			0
$799$	46.0244			1.62822
$800$	−2.90305	+	4.07091i	−0.102638	+	0.143928i
$801$	−10.7640	−	36.6729i	−0.380326	−	1.29577i
$802$			14.1195i			0.498577i
$803$			21.0746i			0.743705i
$804$	−17.9509	−	13.4394i	−0.633081	−	0.473970i
$805$		0			0
$806$			9.18227i			0.323432i
$807$	10.7742	−	14.3910i	0.379269	−	0.506588i
$808$	9.02428			0.317473
$809$			27.1711i			0.955286i	0.878554	+	0.477643i	$0.158509\pi$
$809$			27.1711i			0.955286i	−0.878554	+	0.477643i	$0.841491\pi$
$810$	−10.0719	+	17.4229i	−0.353889	+	0.612178i
$811$			6.57732i			0.230961i	0.993310	+	0.115480i	$0.0368407\pi$
$811$			6.57732i			0.230961i	−0.993310	+	0.115480i	$0.963159\pi$
$812$		0			0
$813$	13.7366	+	10.2842i	0.481764	+	0.360683i
$814$	5.97690			0.209490
$815$	−11.7153	−	22.7434i	−0.410368	−	0.796667i
$816$	−7.99947	−	5.98898i	−0.280037	−	0.209656i
$817$	4.58483			0.160403
$818$			23.7751i			0.831277i
$819$		0			0
$820$	24.5071	−	12.6237i	0.855824	−	0.440840i
$821$			0.162186i			0.00566035i	0.999996	+	0.00283017i	$0.000900873\pi$
$821$			0.162186i			0.00566035i	−0.999996	+	0.00283017i	$0.999099\pi$
$822$	−12.2315	+	16.3376i	−0.426623	+	0.569840i
$823$			53.1286i			1.85195i	0.377588	+	0.925974i	$0.376753\pi$
$823$			53.1286i			1.85195i	−0.377588	+	0.925974i	$0.623247\pi$
$824$	17.4764			0.608820
$825$	−10.5480	+	3.36333i	−0.367235	+	0.117096i
$826$		0			0
$827$	−47.5055			−1.65193			−0.825964	−	0.563723i	$-0.809369\pi$
$827$	−47.5055			−1.65193			−0.825964	+	0.563723i	$0.809369\pi$
$828$	0.574547	+	1.95748i	0.0199669	+	0.0680272i
$829$			6.47482i			0.224880i	0.993659	+	0.112440i	$0.0358666\pi$
$829$			6.47482i			0.224880i	−0.993659	+	0.112440i	$0.964133\pi$
$830$	−3.41485	−	6.62941i	−0.118531	−	0.230110i
$831$	−25.4933	−	19.0861i	−0.884352	−	0.662090i
$832$	−1.32254			−0.0458507
$833$		0			0
$834$	−22.1622	−	16.5922i	−0.767413	−	0.574540i
$835$	14.5321	+	28.2119i	0.502905	+	0.976314i
$836$	3.12178			0.107969
$837$	12.6127	−	33.7999i	0.435960	−	1.16830i
$838$	−7.09712			−0.245166
$839$	28.7089			0.991142			0.495571	−	0.868567i	$-0.334959\pi$
$839$	28.7089			0.991142			0.495571	+	0.868567i	$0.334959\pi$
$840$		0			0
$841$	−8.53721			−0.294386
$842$	10.5901			0.364958
$843$	−26.3640	−	19.7380i	−0.908023	−	0.679812i
$844$	−12.5665			−0.432558
$845$	22.3650	−	11.5204i	0.769381	−	0.396313i
$846$	−22.9631	+	6.73997i	−0.789487	+	0.231725i
$847$		0			0
$848$	−6.98682			−0.239928
$849$	19.3747	−	25.8787i	0.664937	−	0.888156i
$850$	23.4869	+	16.7490i	0.805593	+	0.574485i
$851$			3.17930i			0.108985i
$852$	7.06983	+	5.29298i	0.242208	+	0.181335i
$853$	−41.9863			−1.43758			−0.718792	−	0.695225i	$-0.755305\pi$
$853$	−41.9863			−1.43758			−0.718792	+	0.695225i	$0.755305\pi$
$854$		0			0
$855$	−11.8606	+	11.2990i	−0.405623	+	0.386417i
$856$	−12.1115			−0.413964
$857$		−	26.7333i		−	0.913193i	−0.889674	−	0.456596i	$-0.849068\pi$
$857$		−	26.7333i		−	0.913193i	0.889674	−	0.456596i	$-0.150932\pi$
$858$	−2.34423	−	1.75506i	−0.0800308	−	0.0599168i
$859$		−	55.5429i		−	1.89510i	−0.319610	−	0.947549i	$-0.603552\pi$
$859$		−	55.5429i		−	1.89510i	0.319610	−	0.947549i	$-0.396448\pi$
$860$	1.92250	+	3.73224i	0.0655567	+	0.127268i
$861$		0			0
$862$			30.8160i			1.04960i
$863$	−21.2657			−0.723892			−0.361946	−	0.932199i	$-0.617888\pi$
$863$	−21.2657			−0.723892			−0.361946	+	0.932199i	$0.617888\pi$
$864$	4.86825	+	1.81663i	0.165621	+	0.0618030i
$865$	−1.00902	−	1.95885i	−0.0343076	−	0.0666030i
$866$	24.3465			0.827329
$867$	−16.9062	+	22.5816i	−0.574164	+	0.766910i
$868$		0			0
$869$			19.8625i			0.673790i
$870$	23.3988	+	3.94412i	0.793292	+	0.133718i
$871$			17.1225i			0.580174i
$872$	−11.1753			−0.378443
$873$	2.45596	+	8.36747i	0.0831217	+	0.283196i
$874$			1.66057i			0.0561697i
$875$		0			0
$876$	−17.1124	+	22.8570i	−0.578176	+	0.772268i
$877$		−	22.3340i		−	0.754166i	−0.926180	−	0.377083i	$-0.876927\pi$
$877$		−	22.3340i		−	0.754166i	0.926180	−	0.377083i	$-0.123073\pi$
$878$		−	12.6887i		−	0.428222i
$879$	4.73810	+	3.54728i	0.159812	+	0.119647i
$880$	1.30902	+	2.54126i	0.0441269	+	0.0856657i
$881$	4.42739			0.149162			0.0745812	−	0.997215i	$-0.476238\pi$
$881$	4.42739			0.149162			0.0745812	+	0.997215i	$0.476238\pi$
$882$		0			0
$883$		−	45.9417i		−	1.54606i	−0.634368	−	0.773031i	$-0.718740\pi$
$883$		−	45.9417i		−	1.54606i	0.634368	−	0.773031i	$-0.281260\pi$
$884$			7.63029i			0.256634i
$885$	6.21620	−	36.8780i	0.208955	−	1.23964i
$886$	−9.71974			−0.326541
$887$		−	10.0111i		−	0.336139i	−0.985775	−	0.168070i	$-0.946247\pi$
$887$		−	10.0111i		−	0.336139i	0.985775	−	0.168070i	$-0.0537533\pi$
$888$	6.48242	+	4.85321i	0.217536	+	0.162863i
$889$		0			0
$890$	25.3251	−	13.0451i	0.848899	−	0.437273i
$891$	6.21837	+	9.68041i	0.208323	+	0.324306i
$892$	13.1623			0.440708
$893$	−19.4801			−0.651875
$894$	−28.1021	−	21.0393i	−0.939875	−	0.703658i
$895$	10.5415	+	20.4647i	0.352363	+	0.684059i
$896$		0			0
$897$	0.933572	−	1.24697i	0.0311711	−	0.0416351i
$898$		−	6.90138i		−	0.230302i
$899$	−42.5377			−1.41871
$900$	−14.1712	−	4.91713i	−0.472372	−	0.163904i
$901$			40.3100i			1.34292i
$902$		−	15.7607i		−	0.524773i
$903$		0			0
$904$	−0.00477454			−0.000158799
$905$	5.17384	+	10.0442i	0.171984	+	0.333881i
$906$	−10.4487	+	13.9563i	−0.347135	+	0.463668i
$907$			35.1538i			1.16726i	0.812019	+	0.583631i	$0.198369\pi$
$907$			35.1538i			1.16726i	−0.812019	+	0.583631i	$0.801631\pi$
$908$		−	15.5346i		−	0.515533i
$909$	7.62459	+	25.9770i	0.252892	+	0.861602i
$910$		0			0
$911$			17.4530i			0.578243i	0.957292	+	0.289122i	$0.0933632\pi$
$911$			17.4530i			0.578243i	−0.957292	+	0.289122i	$0.906637\pi$
$912$	3.38582	+	2.53487i	0.112116	+	0.0839378i
$913$	−4.26342			−0.141099
$914$		−	4.52428i		−	0.149650i
$915$	16.1532	+	2.72281i	0.534009	+	0.0900132i
$916$		−	4.02816i		−	0.133094i
$917$		0			0
$918$	10.4809	−	28.0871i	0.345923	−	0.927012i
$919$	3.80826			0.125623			0.0628114	−	0.998025i	$-0.479993\pi$
$919$	3.80826			0.125623			0.0628114	+	0.998025i	$0.479993\pi$
$920$	−1.35177	+	0.696306i	−0.0445666	+	0.0229565i
$921$	13.8161	−	18.4541i	0.455255	−	0.608083i
$922$	13.8000			0.454480
$923$		−	6.74355i		−	0.221967i
$924$		0			0
$925$	−19.0327	−	13.5726i	−0.625793	−	0.446266i
$926$		−	22.5955i		−	0.742534i
$927$	14.7658	+	50.3071i	0.484972	+	1.65230i
$928$		−	6.12676i		−	0.201121i
$929$	−4.83763			−0.158717			−0.0793587	−	0.996846i	$-0.525287\pi$
$929$	−4.83763			−0.158717			−0.0793587	+	0.996846i	$0.525287\pi$
$930$	26.5158	+	4.46953i	0.869487	+	0.146562i
$931$		0			0
$932$	−28.2529			−0.925454
$933$	12.2192	−	16.3211i	0.400038	−	0.534330i
$934$			22.7817i			0.745441i
$935$	14.6616	−	7.55229i	0.479486	−	0.246986i
$936$	−1.11741	−	3.80701i	−0.0365236	−	0.124436i
$937$	−43.3679			−1.41677			−0.708384	−	0.705827i	$-0.750576\pi$
$937$	−43.3679			−1.41677			−0.708384	+	0.705827i	$0.750576\pi$
$938$		0			0
$939$	11.6622	−	15.5772i	0.380581	−	0.508342i
$940$	−8.16832	−	15.8576i	−0.266421	−	0.517217i
$941$	34.0613			1.11037			0.555183	−	0.831728i	$-0.312648\pi$
$941$	34.0613			1.11037			0.555183	+	0.831728i	$0.312648\pi$
$942$	10.2225	−	13.6542i	0.333068	−	0.444878i
$943$	8.38359			0.273007
$944$	−9.65619			−0.314282
$945$		0			0
$946$	2.40023			0.0780382
$947$	52.0955			1.69288			0.846438	−	0.532487i	$-0.178743\pi$
$947$	52.0955			1.69288			0.846438	+	0.532487i	$0.178743\pi$
$948$	−16.1283	+	21.5425i	−0.523821	+	0.699667i
$949$	21.8022			0.707729
$950$	−9.94094	−	7.08910i	−0.322527	−	0.230001i
$951$	4.86452	−	6.49754i	0.157743	−	0.210697i
$952$		0			0
$953$	29.8965			0.968443			0.484222	−	0.874945i	$-0.339103\pi$
$953$	29.8965			0.968443			0.484222	+	0.874945i	$0.339103\pi$
$954$	−5.90314	−	20.1120i	−0.191121	−	0.651151i
$955$	9.53839	+	18.5173i	0.308655	+	0.599207i
$956$		−	10.6358i		−	0.343987i
$957$	8.13047	−	10.8599i	0.262821	−	0.351049i
$958$	31.9484			1.03221
$959$		0			0
$960$	−0.643753	+	3.81911i	−0.0207770	+	0.123261i
$961$	−17.2043			−0.554976
$962$		−	6.18326i		−	0.199356i
$963$	−10.2330	−	34.8639i	−0.329754	−	1.12347i
$964$		−	3.42344i		−	0.110262i
$965$	−2.60057	−	5.04860i	−0.0837152	−	0.162520i
$966$		0			0
$967$			40.6051i			1.30577i	0.757456	+	0.652887i	$0.226442\pi$
$967$			40.6051i			1.30577i	−0.757456	+	0.652887i	$0.773558\pi$
$968$	−9.36570			−0.301025
$969$	14.6248	−	19.5343i	0.469815	−	0.627531i
$970$	−5.77830	+	2.97644i	−0.185530	+	0.0955676i
$971$	40.9311			1.31354			0.656772	−	0.754090i	$-0.271922\pi$
$971$	40.9311			1.31354			0.656772	+	0.754090i	$0.271922\pi$
$972$	−1.11612	+	15.5484i	−0.0357997	+	0.498717i
$973$		0			0
$974$			6.93234i			0.222127i
$975$	3.47945	+	10.9122i	0.111432	+	0.349470i
$976$		−	4.22958i		−	0.135386i
$977$	−5.94472			−0.190188			−0.0950942	−	0.995468i	$-0.530315\pi$
$977$	−5.94472			−0.190188			−0.0950942	+	0.995468i	$0.530315\pi$
$978$	−15.8635	−	11.8766i	−0.507260	−	0.379772i
$979$		−	16.2867i		−	0.520527i
$980$		0			0
$981$	−9.44197	−	32.1688i	−0.301459	−	1.02707i
$982$			24.3178i			0.776012i
$983$		−	23.5901i		−	0.752408i	−0.926537	−	0.376204i	$-0.877229\pi$
$983$		−	23.5901i		−	0.752408i	0.926537	−	0.376204i	$-0.122771\pi$
$984$	12.7976	−	17.0937i	0.407972	−	0.544927i
$985$	−17.2080	+	8.86393i	−0.548292	+	0.282428i
$986$	−35.3480			−1.12571
$987$		0			0
$988$		−	3.22956i		−	0.102746i
$989$			1.27676i			0.0405985i
$990$	−6.20919	+	5.91519i	−0.197341	+	0.187997i
$991$	0.0743262			0.00236105			0.00118053	−	0.999999i	$-0.499624\pi$
$991$	0.0743262			0.00236105			0.00118053	+	0.999999i	$0.499624\pi$
$992$		−	6.94293i		−	0.220438i
$993$	27.6380	−	36.9160i	0.877064	−	1.17149i
$994$		0			0
$995$	28.5920	+	55.5071i	0.906429	+	1.75969i
$996$	−4.62402	−	3.46188i	−0.146518	−	0.109694i
$997$	11.0516			0.350007			0.175003	−	0.984568i	$-0.444006\pi$
$997$	11.0516			0.350007			0.175003	+	0.984568i	$0.444006\pi$
$998$	22.5999			0.715386
$999$	−8.49331	+	22.7606i	−0.268716	+	0.720112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.d.g.1469.15	yes	24
3.2	odd	2		1470.2.d.h.1469.16	yes	24
5.4	even	2		1470.2.d.h.1469.10	yes	24
7.6	odd	2	inner	1470.2.d.g.1469.10	yes	24
15.14	odd	2	inner	1470.2.d.g.1469.9	✓	24
21.20	even	2		1470.2.d.h.1469.9	yes	24
35.34	odd	2		1470.2.d.h.1469.15	yes	24
105.104	even	2	inner	1470.2.d.g.1469.16	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.d.g.1469.9	✓	24	15.14	odd	2	inner
1470.2.d.g.1469.10	yes	24	7.6	odd	2	inner
1470.2.d.g.1469.15	yes	24	1.1	even	1	trivial
1470.2.d.g.1469.16	yes	24	105.104	even	2	inner
1470.2.d.h.1469.9	yes	24	21.20	even	2
1470.2.d.h.1469.10	yes	24	5.4	even	2
1470.2.d.h.1469.15	yes	24	35.34	odd	2
1470.2.d.h.1469.16	yes	24	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.03805 - 1.38652i) q^{3} +1.00000 q^{4} +(-1.98784 + 1.02395i) q^{5} +(-1.03805 + 1.38652i) q^{6} -1.00000 q^{8} +(-0.844897 - 2.87857i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.03805 - 1.38652i) q^{3} +1.00000 q^{4} +(-1.98784 + 1.02395i) q^{5} +(-1.03805 + 1.38652i) q^{6} -1.00000 q^{8} +(-0.844897 - 2.87857i) q^{9} +(1.98784 - 1.02395i) q^{10} -1.27840i q^{11} +(1.03805 - 1.38652i) q^{12} -1.32254 q^{13} +(-0.643753 + 3.81911i) q^{15} +1.00000 q^{16} -5.76944i q^{17} +(0.844897 + 2.87857i) q^{18} +2.44195i q^{19} +(-1.98784 + 1.02395i) q^{20} +1.27840i q^{22} -0.680020 q^{23} +(-1.03805 + 1.38652i) q^{24} +(2.90305 - 4.07091i) q^{25} +1.32254 q^{26} +(-4.86825 - 1.81663i) q^{27} +6.12676i q^{29} +(0.643753 - 3.81911i) q^{30} +6.94293i q^{31} -1.00000 q^{32} +(-1.77253 - 1.32704i) q^{33} +5.76944i q^{34} +(-0.844897 - 2.87857i) q^{36} -4.67531i q^{37} -2.44195i q^{38} +(-1.37286 + 1.83373i) q^{39} +(1.98784 - 1.02395i) q^{40} -12.3285 q^{41} -1.87753i q^{43} -1.27840i q^{44} +(4.62703 + 4.85701i) q^{45} +0.680020 q^{46} +7.97726i q^{47} +(1.03805 - 1.38652i) q^{48} +(-2.90305 + 4.07091i) q^{50} +(-7.99947 - 5.98898i) q^{51} -1.32254 q^{52} -6.98682 q^{53} +(4.86825 + 1.81663i) q^{54} +(1.30902 + 2.54126i) q^{55} +(3.38582 + 2.53487i) q^{57} -6.12676i q^{58} -9.65619 q^{59} +(-0.643753 + 3.81911i) q^{60} -4.22958i q^{61} -6.94293i q^{62} +1.00000 q^{64} +(2.62899 - 1.35421i) q^{65} +(1.77253 + 1.32704i) q^{66} -12.9467i q^{67} -5.76944i q^{68} +(-0.705896 + 0.942863i) q^{69} +5.09896i q^{71} +(0.844897 + 2.87857i) q^{72} -16.4851 q^{73} +4.67531i q^{74} +(-2.63090 - 8.25096i) q^{75} +2.44195i q^{76} +(1.37286 - 1.83373i) q^{78} -15.5370 q^{79} +(-1.98784 + 1.02395i) q^{80} +(-7.57230 + 4.86419i) q^{81} +12.3285 q^{82} -3.33498i q^{83} +(5.90762 + 11.4688i) q^{85} +1.87753i q^{86} +(8.49490 + 6.35990i) q^{87} +1.27840i q^{88} +12.7400 q^{89} +(-4.62703 - 4.85701i) q^{90} -0.680020 q^{92} +(9.62654 + 7.20712i) q^{93} -7.97726i q^{94} +(-2.50043 - 4.85421i) q^{95} +(-1.03805 + 1.38652i) q^{96} -2.90682 q^{97} +(-3.67995 + 1.08011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9	\( 24 q - 24 q^{2} + 24 q^{4} - 24 q^{8} + 8 q^{9} + 24 q^{16} - 8 q^{18} - 16 q^{23} + 8 q^{25} - 24 q^{32} + 8 q^{36} + 16 q^{39} + 16 q^{46} - 8 q^{50} + 16 q^{51} + 16 q^{53} + 16 q^{57} + 24 q^{64} - 48 q^{65} - 8 q^{72} - 16 q^{78} - 48 q^{79} - 24 q^{81} + 16 q^{85} - 16 q^{92} + 64 q^{93} - 112 q^{95} - 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 24 * q^4 - 24 * q^8 + 8 * q^9 + 24 * q^16 - 8 * q^18 - 16 * q^23 + 8 * q^25 - 24 * q^32 + 8 * q^36 + 16 * q^39 + 16 * q^46 - 8 * q^50 + 16 * q^51 + 16 * q^53 + 16 * q^57 + 24 * q^64 - 48 * q^65 - 8 * q^72 - 16 * q^78 - 48 * q^79 - 24 * q^81 + 16 * q^85 - 16 * q^92 + 64 * q^93 - 112 * q^95 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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