LMFDB - Embedded newform 560.2.ci.c.353.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(17,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("560.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.ci (of order $12$, degree $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.1
Root			$-0.144868 + 1.25092i$ of defining polynomial
Character	$\chi$	$=$	560.353
Dual form			560.2.ci.c.257.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.523277 - 1.95290i) q^{3} +(-2.03078 + 0.935904i) q^{5} +(-1.83959 - 1.90155i) q^{7} +(-0.941911 + 0.543813i) q^{9} +O(q^{10})$	\(q+(-0.523277 - 1.95290i) q^{3} +(-2.03078 + 0.935904i) q^{5} +(-1.83959 - 1.90155i) q^{7} +(-0.941911 + 0.543813i) q^{9} +(-2.01999 + 3.49872i) q^{11} +(0.204875 - 0.204875i) q^{13} +(2.89039 + 3.47617i) q^{15} +(-1.97024 + 0.527924i) q^{17} +(3.10166 + 5.37224i) q^{19} +(-2.75092 + 4.58757i) q^{21} +(-1.17456 + 4.38350i) q^{23} +(3.24817 - 3.80124i) q^{25} +(-2.73397 - 2.73397i) q^{27} +7.15869i q^{29} +(-6.33287 - 3.65628i) q^{31} +(7.88965 + 2.11403i) q^{33} +(5.51548 + 2.13996i) q^{35} +(-4.46814 - 1.19723i) q^{37} +(-0.507306 - 0.292893i) q^{39} -2.58745i q^{41} +(4.97801 + 4.97801i) q^{43} +(1.40386 - 1.98590i) q^{45} +(0.0815604 - 0.304388i) q^{47} +(-0.231803 + 6.99616i) q^{49} +(2.06196 + 3.57142i) q^{51} +(-8.00039 + 2.14370i) q^{53} +(0.827689 - 8.99566i) q^{55} +(8.86840 - 8.86840i) q^{57} +(-0.427702 + 0.740802i) q^{59} +(-5.99356 + 3.46038i) q^{61} +(2.76682 + 0.790700i) q^{63} +(-0.224313 + 0.607800i) q^{65} +(0.817530 + 3.05106i) q^{67} +9.17514 q^{69} -7.12240 q^{71} +(-2.98311 - 11.1331i) q^{73} +(-9.12312 - 4.35423i) q^{75} +(10.3690 - 2.59511i) q^{77} +(4.39618 - 2.53813i) q^{79} +(-5.53997 + 9.59552i) q^{81} +(3.85372 - 3.85372i) q^{83} +(3.50704 - 2.91605i) q^{85} +(13.9802 - 3.74598i) q^{87} +(-1.53615 - 2.66069i) q^{89} +(-0.766467 - 0.0126942i) q^{91} +(-3.82650 + 14.2807i) q^{93} +(-11.3267 - 8.00700i) q^{95} +(-6.63103 - 6.63103i) q^{97} -4.39398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 - 8 * q^7	$ 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53} + 8 q^{57} - 12 q^{61} + 36 q^{63} - 8 q^{65} - 32 q^{67} - 16 q^{71} - 12 q^{73} + 48 q^{75} + 16 q^{77} + 24 q^{85} + 24 q^{87} + 16 q^{91} + 28 q^{93} - 20 q^{95}+O(q^{100}) $ 16 * q - 12 * q^5 - 8 * q^7 + 12 * q^11 - 16 * q^15 - 36 * q^17 - 28 * q^21 + 4 * q^23 + 12 * q^25 - 24 * q^31 + 48 * q^33 - 8 * q^35 + 4 * q^37 + 8 * q^43 - 12 * q^45 - 12 * q^47 + 16 * q^51 - 28 * q^53 + 8 * q^57 - 12 * q^61 + 36 * q^63 - 8 * q^65 - 32 * q^67 - 16 * q^71 - 12 * q^73 + 48 * q^75 + 16 * q^77 + 24 * q^85 + 24 * q^87 + 16 * q^91 + 28 * q^93 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.523277	−	1.95290i	−0.302114	−	1.12751i	−0.935401	−	0.353588i	$-0.884961\pi$
$3$	−0.523277	−	1.95290i	−0.302114	−	1.12751i	0.633287	−	0.773917i	$-0.281705\pi$
$4$		0			0
$5$	−2.03078	+	0.935904i	−0.908194	+	0.418549i
$5$	−2.03078	+	0.935904i	−0.908194	+	0.418549i
$6$		0			0
$7$	−1.83959	−	1.90155i	−0.695300	−	0.718719i
$7$	−1.83959	−	1.90155i	−0.695300	−	0.718719i
$8$		0			0
$9$	−0.941911	+	0.543813i	−0.313970	+	0.181271i
$10$		0			0
$11$	−2.01999	+	3.49872i	−0.609049	+	1.05490i	0.382349	+	0.924018i	$0.375115\pi$
$11$	−2.01999	+	3.49872i	−0.609049	+	1.05490i	−0.991397	+	0.130886i	$0.958218\pi$
$12$		0			0
$13$	0.204875	−	0.204875i	0.0568221	−	0.0568221i	−0.678125	−	0.734947i	$-0.737207\pi$
$13$	0.204875	−	0.204875i	0.0568221	−	0.0568221i	0.734947	+	0.678125i	$0.237207\pi$
$14$		0			0
$15$	2.89039	+	3.47617i	0.746295	+	0.897544i
$16$		0			0
$17$	−1.97024	+	0.527924i	−0.477853	+	0.128040i	−0.489703	−	0.871890i	$-0.662895\pi$
$17$	−1.97024	+	0.527924i	−0.477853	+	0.128040i	0.0118498	+	0.999930i	$0.496228\pi$
$18$		0			0
$19$	3.10166	+	5.37224i	0.711571	+	1.23248i	0.964267	+	0.264931i	$0.0853491\pi$
$19$	3.10166	+	5.37224i	0.711571	+	1.23248i	−0.252697	+	0.967545i	$0.581318\pi$
$20$		0			0
$21$	−2.75092	+	4.58757i	−0.600300	+	1.00109i
$22$		0			0
$23$	−1.17456	+	4.38350i	−0.244912	+	0.914023i	0.728516	+	0.685029i	$0.240210\pi$
$23$	−1.17456	+	4.38350i	−0.244912	+	0.914023i	−0.973428	+	0.228994i	$0.926456\pi$
$24$		0			0
$25$	3.24817	−	3.80124i	0.649633	−	0.760248i
$26$		0			0
$27$	−2.73397	−	2.73397i	−0.526152	−	0.526152i
$28$		0			0
$29$			7.15869i			1.32934i	0.747139	+	0.664668i	$0.231427\pi$
$29$			7.15869i			1.32934i	−0.747139	+	0.664668i	$0.768573\pi$
$30$		0			0
$31$	−6.33287	−	3.65628i	−1.13742	−	0.656688i	−0.191627	−	0.981468i	$-0.561376\pi$
$31$	−6.33287	−	3.65628i	−1.13742	−	0.656688i	−0.945790	+	0.324780i	$0.894710\pi$
$32$		0			0
$33$	7.88965	+	2.11403i	1.37341	+	0.368005i
$34$		0			0
$35$	5.51548	+	2.13996i	0.932287	+	0.361719i
$36$		0			0
$37$	−4.46814	−	1.19723i	−0.734558	−	0.196824i	−0.127900	−	0.991787i	$-0.540824\pi$
$37$	−4.46814	−	1.19723i	−0.734558	−	0.196824i	−0.606658	+	0.794963i	$0.707490\pi$
$38$		0			0
$39$	−0.507306	−	0.292893i	−0.0812340	−	0.0469005i
$40$		0			0
$41$		−	2.58745i		−	0.404093i	−0.979376	−	0.202046i	$-0.935241\pi$
$41$		−	2.58745i		−	0.404093i	0.979376	−	0.202046i	$-0.0647591\pi$
$42$		0			0
$43$	4.97801	+	4.97801i	0.759140	+	0.759140i	0.976166	−	0.217026i	$-0.0696356\pi$
$43$	4.97801	+	4.97801i	0.759140	+	0.759140i	−0.217026	+	0.976166i	$0.569636\pi$
$44$		0			0
$45$	1.40386	−	1.98590i	0.209275	−	0.296041i
$46$		0			0
$47$	0.0815604	−	0.304388i	0.0118968	−	0.0443995i	−0.959722	−	0.280950i	$-0.909350\pi$
$47$	0.0815604	−	0.304388i	0.0118968	−	0.0443995i	0.971619	+	0.236551i	$0.0760170\pi$
$48$		0			0
$49$	−0.231803	+	6.99616i	−0.0331148	+	0.999452i
$50$		0			0
$51$	2.06196	+	3.57142i	0.288732	+	0.500099i
$52$		0			0
$53$	−8.00039	+	2.14370i	−1.09894	+	0.294460i	−0.762332	−	0.647186i	$-0.775946\pi$
$53$	−8.00039	+	2.14370i	−1.09894	+	0.294460i	−0.336606	+	0.941646i	$0.609279\pi$
$54$		0			0
$55$	0.827689	−	8.99566i	0.111606	−	1.21297i
$56$		0			0
$57$	8.86840	−	8.86840i	1.17465	−	1.17465i
$58$		0			0
$59$	−0.427702	+	0.740802i	−0.0556821	+	0.0964442i	−0.892523	−	0.451002i	$-0.851067\pi$
$59$	−0.427702	+	0.740802i	−0.0556821	+	0.0964442i	0.836841	+	0.547446i	$0.184400\pi$
$60$		0			0
$61$	−5.99356	+	3.46038i	−0.767397	+	0.443057i	−0.831945	−	0.554858i	$-0.812773\pi$
$61$	−5.99356	+	3.46038i	−0.767397	+	0.443057i	0.0645484	+	0.997915i	$0.479439\pi$
$62$		0			0
$63$	2.76682	+	0.790700i	0.348587	+	0.0996189i
$64$		0			0
$65$	−0.224313	+	0.607800i	−0.0278226	+	0.0753883i
$66$		0			0
$67$	0.817530	+	3.05106i	0.0998772	+	0.372747i	0.997714	−	0.0675822i	$-0.0215285\pi$
$67$	0.817530	+	3.05106i	0.0998772	+	0.372747i	−0.897837	+	0.440329i	$0.854862\pi$
$68$		0			0
$69$	9.17514			1.10456
$70$		0			0
$71$	−7.12240			−0.845273			−0.422637	−	0.906299i	$-0.638895\pi$
$71$	−7.12240			−0.845273			−0.422637	+	0.906299i	$0.638895\pi$
$72$		0			0
$73$	−2.98311	−	11.1331i	−0.349147	−	1.30303i	−0.887692	−	0.460438i	$-0.847693\pi$
$73$	−2.98311	−	11.1331i	−0.349147	−	1.30303i	0.538545	−	0.842597i	$-0.318974\pi$
$74$		0			0
$75$	−9.12312	−	4.35423i	−1.05345	−	0.502783i
$76$		0			0
$77$	10.3690	−	2.59511i	1.18165	−	0.295740i
$78$		0			0
$79$	4.39618	−	2.53813i	0.494609	−	0.285562i	−0.231876	−	0.972745i	$-0.574486\pi$
$79$	4.39618	−	2.53813i	0.494609	−	0.285562i	0.726484	+	0.687183i	$0.241153\pi$
$80$		0			0
$81$	−5.53997	+	9.59552i	−0.615553	+	1.06617i
$82$		0			0
$83$	3.85372	−	3.85372i	0.423001	−	0.423001i	−0.463235	−	0.886236i	$-0.653311\pi$
$83$	3.85372	−	3.85372i	0.423001	−	0.423001i	0.886236	+	0.463235i	$0.153311\pi$
$84$		0			0
$85$	3.50704	−	2.91605i	0.380392	−	0.316290i
$86$		0			0
$87$	13.9802	−	3.74598i	1.49883	−	0.401611i
$88$		0			0
$89$	−1.53615	−	2.66069i	−0.162832	−	0.282033i	0.773051	−	0.634343i	$-0.218729\pi$
$89$	−1.53615	−	2.66069i	−0.162832	−	0.282033i	−0.935883	+	0.352310i	$0.885396\pi$
$90$		0			0
$91$	−0.766467	−	0.0126942i	−0.0803475	−	0.00133071i
$92$		0			0
$93$	−3.82650	+	14.2807i	−0.396789	+	1.48084i
$94$		0			0
$95$	−11.3267	−	8.00700i	−1.16210	−	0.821501i
$96$		0			0
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	0.285191	−	0.958471i	$-0.407943\pi$
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	−0.958471	+	0.285191i	$0.907943\pi$
$98$		0			0
$99$		−	4.39398i		−	0.441611i
$100$		0			0
$101$	−8.56364	−	4.94422i	−0.852114	−	0.491968i	0.00924966	−	0.999957i	$-0.497056\pi$
$101$	−8.56364	−	4.94422i	−0.852114	−	0.491968i	−0.861364	+	0.507989i	$0.830389\pi$
$102$		0			0
$103$	−4.13612	−	1.10827i	−0.407544	−	0.109201i	0.0492221	−	0.998788i	$-0.484326\pi$
$103$	−4.13612	−	1.10827i	−0.407544	−	0.109201i	−0.456766	+	0.889587i	$0.650992\pi$
$104$		0			0
$105$	1.29299	−	11.8910i	0.126183	−	1.16044i
$106$		0			0
$107$	−14.3653	−	3.84918i	−1.38875	−	0.372114i	−0.514457	−	0.857516i	$-0.672007\pi$
$107$	−14.3653	−	3.84918i	−1.38875	−	0.372114i	−0.874291	+	0.485402i	$0.838673\pi$
$108$		0			0
$109$	−11.4586	−	6.61564i	−1.09754	−	0.633664i	−0.161964	−	0.986797i	$-0.551783\pi$
$109$	−11.4586	−	6.61564i	−1.09754	−	0.633664i	−0.935573	+	0.353133i	$0.885116\pi$
$110$		0			0
$111$			9.35230i			0.887681i
$112$		0			0
$113$	9.75336	+	9.75336i	0.917519	+	0.917519i	0.996848	−	0.0793296i	$-0.0252780\pi$
$113$	9.75336	+	9.75336i	0.917519	+	0.917519i	−0.0793296	+	0.996848i	$0.525278\pi$
$114$		0			0
$115$	−1.71727	−	10.0012i	−0.160136	−	0.932618i
$116$		0			0
$117$	−0.0815604	+	0.304388i	−0.00754026	+	0.0281406i
$118$		0			0
$119$	4.62831	+	2.77535i	0.424276	+	0.254416i
$120$		0			0
$121$	−2.66069	−	4.60846i	−0.241881	−	0.418951i
$122$		0			0
$123$	−5.05303	+	1.35396i	−0.455617	+	0.122082i
$124$		0			0
$125$	−3.03873	+	10.7595i	−0.271792	+	0.962356i
$126$		0			0
$127$	2.19984	−	2.19984i	0.195204	−	0.195204i	−0.602736	−	0.797940i	$-0.705923\pi$
$127$	2.19984	−	2.19984i	0.195204	−	0.195204i	0.797940	+	0.602736i	$0.205923\pi$
$128$		0			0
$129$	7.11667	−	12.3264i	0.626587	−	1.08528i
$130$		0			0
$131$	6.32091	−	3.64938i	0.552260	−	0.318848i	−0.197773	−	0.980248i	$-0.563371\pi$
$131$	6.32091	−	3.64938i	0.552260	−	0.318848i	0.750033	+	0.661400i	$0.230037\pi$
$132$		0			0
$133$	4.50980	−	15.7807i	0.391049	−	1.36836i
$134$		0			0
$135$	8.11083	+	2.99337i	0.698069	+	0.257628i
$136$		0			0
$137$	1.85804	+	6.93431i	0.158743	+	0.592438i	0.998756	+	0.0498710i	$0.0158810\pi$
$137$	1.85804	+	6.93431i	0.158743	+	0.592438i	−0.840012	+	0.542567i	$0.817452\pi$
$138$		0			0
$139$	−12.4172			−1.05321			−0.526605	−	0.850110i	$-0.676535\pi$
$139$	−12.4172			−1.05321			−0.526605	+	0.850110i	$0.676535\pi$
$140$		0			0
$141$	−0.637116			−0.0536549
$142$		0			0
$143$	0.302955	+	1.13064i	0.0253344	+	0.0945492i
$144$		0			0
$145$	−6.69985	−	14.5378i	−0.556392	−	1.20730i
$146$		0			0
$147$	13.7841	−	3.20824i	1.13689	−	0.264611i
$148$		0			0
$149$	20.7399	−	11.9742i	1.69908	−	0.980963i	0.752440	−	0.658661i	$-0.228877\pi$
$149$	20.7399	−	11.9742i	1.69908	−	0.980963i	0.946637	−	0.322302i	$-0.104457\pi$
$150$		0			0
$151$	−1.77167	+	3.06862i	−0.144176	+	0.249721i	−0.929065	−	0.369916i	$-0.879387\pi$
$151$	−1.77167	+	3.06862i	−0.144176	+	0.249721i	0.784889	+	0.619636i	$0.212720\pi$
$152$		0			0
$153$	1.56870	−	1.56870i	0.126822	−	0.126822i
$154$		0			0
$155$	16.2826	+	1.49816i	1.30785	+	0.120335i
$156$		0			0
$157$	−5.91389	+	1.58462i	−0.471980	+	0.126467i	−0.486966	−	0.873421i	$-0.661896\pi$
$157$	−5.91389	+	1.58462i	−0.471980	+	0.126467i	0.0149859	+	0.999888i	$0.495230\pi$
$158$		0			0
$159$	8.37284	+	14.5022i	0.664010	+	1.15010i
$160$		0			0
$161$	10.4962	−	5.83037i	0.827213	−	0.459498i
$162$		0			0
$163$	4.28549	−	15.9937i	0.335666	−	1.25272i	−0.567480	−	0.823387i	$-0.692082\pi$
$163$	4.28549	−	15.9937i	0.335666	−	1.25272i	0.903146	−	0.429334i	$-0.141252\pi$
$164$		0			0
$165$	−18.0007	+	3.09083i	−1.40135	+	0.240621i
$166$		0			0
$167$	10.2873	+	10.2873i	0.796056	+	0.796056i	0.982471	−	0.186415i	$-0.0596869\pi$
$167$	10.2873	+	10.2873i	0.796056	+	0.796056i	−0.186415	+	0.982471i	$0.559687\pi$
$168$		0			0
$169$			12.9161i			0.993543i
$170$		0			0
$171$	−5.84298	−	3.37345i	−0.446824	−	0.257974i
$172$		0			0
$173$	7.50720	+	2.01155i	0.570762	+	0.152935i	0.532646	−	0.846338i	$-0.321198\pi$
$173$	7.50720	+	2.01155i	0.570762	+	0.152935i	0.0381159	+	0.999273i	$0.487864\pi$
$174$		0			0
$175$	−13.2036	+	0.816171i	−0.998095	+	0.0616967i
$176$		0			0
$177$	1.67052	+	0.447613i	0.125564	+	0.0336447i
$178$		0			0
$179$	−3.34695	−	1.93236i	−0.250163	−	0.144431i	0.369676	−	0.929161i	$-0.379469\pi$
$179$	−3.34695	−	1.93236i	−0.250163	−	0.144431i	−0.619839	+	0.784729i	$0.712802\pi$
$180$		0			0
$181$			6.99107i			0.519642i	0.965657	+	0.259821i	$0.0836636\pi$
$181$			6.99107i			0.519642i	−0.965657	+	0.259821i	$0.916336\pi$
$182$		0			0
$183$	9.89407	+	9.89407i	0.731390	+	0.731390i
$184$		0			0
$185$	10.1943	−	1.75043i	0.749502	−	0.128694i
$186$		0			0
$187$	2.13280	−	7.95971i	0.155966	−	0.582071i
$188$		0			0
$189$	−0.169398	+	10.2282i	−0.0123219	+	0.743990i
$190$		0			0
$191$	2.23721	+	3.87496i	0.161879	+	0.280383i	0.935543	−	0.353214i	$-0.114911\pi$
$191$	2.23721	+	3.87496i	0.161879	+	0.280383i	−0.773664	+	0.633597i	$0.781578\pi$
$192$		0			0
$193$	19.3907	−	5.19573i	1.39577	−	0.373997i	0.518949	−	0.854805i	$-0.326324\pi$
$193$	19.3907	−	5.19573i	1.39577	−	0.373997i	0.876825	+	0.480809i	$0.159657\pi$
$194$		0			0
$195$	1.30435	+	0.120013i	0.0934064	+	0.00859431i
$196$		0			0
$197$	−7.84901	+	7.84901i	−0.559219	+	0.559219i	−0.929085	−	0.369866i	$-0.879404\pi$
$197$	−7.84901	+	7.84901i	−0.559219	+	0.559219i	0.369866	+	0.929085i	$0.379404\pi$
$198$		0			0
$199$	5.40103	−	9.35485i	0.382869	−	0.663148i	−0.608602	−	0.793475i	$-0.708270\pi$
$199$	5.40103	−	9.35485i	0.382869	−	0.663148i	0.991471	+	0.130327i	$0.0416028\pi$
$200$		0			0
$201$	5.53062	−	3.19310i	0.390100	−	0.225224i
$202$		0			0
$203$	13.6126	−	13.1691i	0.955419	−	0.924288i
$204$		0			0
$205$	2.42161	+	5.25456i	0.169133	+	0.366995i
$206$		0			0
$207$	−1.27748	−	4.76761i	−0.0887908	−	0.331372i
$208$		0			0
$209$	−25.0613			−1.73353
$210$		0			0
$211$	−7.56555			−0.520834			−0.260417	−	0.965496i	$-0.583860\pi$
$211$	−7.56555			−0.520834			−0.260417	+	0.965496i	$0.583860\pi$
$212$		0			0
$213$	3.72699	+	13.9093i	0.255369	+	0.953050i
$214$		0			0
$215$	−14.7682	−	5.45032i	−1.00718	−	0.371709i
$216$		0			0
$217$	4.69728	+	18.7683i	0.318872	+	1.27408i
$218$		0			0
$219$	−20.1809	+	11.6514i	−1.36370	+	0.787330i
$220$		0			0
$221$	−0.295494	+	0.511811i	−0.0198771	+	0.0344281i
$222$		0			0
$223$	−9.35230	+	9.35230i	−0.626277	+	0.626277i	−0.947129	−	0.320853i	$-0.896031\pi$
$223$	−9.35230	+	9.35230i	−0.626277	+	0.626277i	0.320853	+	0.947129i	$0.396031\pi$
$224$		0			0
$225$	−0.992322	+	5.34682i	−0.0661548	+	0.356455i
$226$		0			0
$227$	−15.6420	+	4.19127i	−1.03820	+	0.278184i	−0.737367	−	0.675493i	$-0.763931\pi$
$227$	−15.6420	+	4.19127i	−1.03820	+	0.278184i	−0.300832	+	0.953677i	$0.597264\pi$
$228$		0			0
$229$	5.88820	+	10.1987i	0.389103	+	0.673947i	0.992329	−	0.123624i	$-0.0394515\pi$
$229$	5.88820	+	10.1987i	0.389103	+	0.673947i	−0.603226	+	0.797570i	$0.706118\pi$
$230$		0			0
$231$	−10.4938	−	18.8915i	−0.690442	−	1.24297i
$232$		0			0
$233$	−1.48154	+	5.52920i	−0.0970591	+	0.362230i	−0.997324	−	0.0731138i	$-0.976706\pi$
$233$	−1.48154	+	5.52920i	−0.0970591	+	0.362230i	0.900264	+	0.435343i	$0.143373\pi$
$234$		0			0
$235$	0.119246	+	0.694478i	0.00777876	+	0.0453028i
$236$		0			0
$237$	−7.25713	−	7.25713i	−0.471402	−	0.471402i
$238$		0			0
$239$			8.33794i			0.539337i	0.962953	+	0.269668i	$0.0869141\pi$
$239$			8.33794i			0.539337i	−0.962953	+	0.269668i	$0.913086\pi$
$240$		0			0
$241$	2.56723	+	1.48219i	0.165370	+	0.0954763i	0.580401	−	0.814331i	$-0.302896\pi$
$241$	2.56723	+	1.48219i	0.165370	+	0.0954763i	−0.415031	+	0.909807i	$0.636229\pi$
$242$		0			0
$243$	10.4340	+	2.79578i	0.669340	+	0.179349i
$244$		0			0
$245$	−6.07700	−	14.4246i	−0.388245	−	0.921556i
$246$		0			0
$247$	1.73609	+	0.465184i	0.110465	+	0.0295989i
$248$		0			0
$249$	−9.54248	−	5.50936i	−0.604730	−	0.349141i
$250$		0			0
$251$			16.1800i			1.02127i	0.859796	+	0.510637i	$0.170590\pi$
$251$			16.1800i			1.02127i	−0.859796	+	0.510637i	$0.829410\pi$
$252$		0			0
$253$	−12.9641	−	12.9641i	−0.815043	−	0.815043i
$254$		0			0
$255$	−7.52990	−	5.32298i	−0.471541	−	0.333338i
$256$		0			0
$257$	−1.50754	+	5.62621i	−0.0940377	+	0.350954i	−0.996872	−	0.0790355i	$-0.974816\pi$
$257$	−1.50754	+	5.62621i	−0.0940377	+	0.350954i	0.902834	+	0.429989i	$0.141483\pi$
$258$		0			0
$259$	5.94295	+	10.6988i	0.369277	+	0.664793i
$260$		0			0
$261$	−3.89299	−	6.74285i	−0.240970	−	0.417372i
$262$		0			0
$263$	1.67793	−	0.449601i	0.103466	−	0.0277236i	−0.206715	−	0.978401i	$-0.566277\pi$
$263$	1.67793	−	0.449601i	0.103466	−	0.0277236i	0.310180	+	0.950678i	$0.399611\pi$
$264$		0			0
$265$	14.2408	−	11.8410i	0.874803	−	0.727386i
$266$		0			0
$267$	−4.39223	+	4.39223i	−0.268800	+	0.268800i
$268$		0			0
$269$	−1.89169	+	3.27650i	−0.115338	+	0.199772i	−0.917915	−	0.396777i	$-0.870128\pi$
$269$	−1.89169	+	3.27650i	−0.115338	+	0.199772i	0.802577	+	0.596549i	$0.203462\pi$
$270$		0			0
$271$	18.4029	−	10.6249i	1.11789	−	0.645416i	0.177032	−	0.984205i	$-0.443351\pi$
$271$	18.4029	−	10.6249i	1.11789	−	0.645416i	0.940862	+	0.338789i	$0.110017\pi$
$272$		0			0
$273$	0.376284	+	1.50347i	0.0227737	+	0.0909943i
$274$		0			0
$275$	6.73822	+	19.0429i	0.406330	+	1.14833i
$276$		0			0
$277$	−1.26567	−	4.72353i	−0.0760465	−	0.283810i	0.917422	−	0.397916i	$-0.130266\pi$
$277$	−1.26567	−	4.72353i	−0.0760465	−	0.283810i	−0.993469	+	0.114106i	$0.963600\pi$
$278$		0			0
$279$	7.95333			0.476153
$280$		0			0
$281$	−29.4776			−1.75849			−0.879243	−	0.476373i	$-0.841951\pi$
$281$	−29.4776			−1.75849			−0.879243	+	0.476373i	$0.841951\pi$
$282$		0			0
$283$	2.92041	+	10.8991i	0.173601	+	0.647886i	0.996786	+	0.0801133i	$0.0255282\pi$
$283$	2.92041	+	10.8991i	0.173601	+	0.647886i	−0.823185	+	0.567773i	$0.807805\pi$
$284$		0			0
$285$	−9.70983	+	26.3098i	−0.575161	+	1.55846i
$286$		0			0
$287$	−4.92018	+	4.75986i	−0.290429	+	0.280966i
$288$		0			0
$289$	−11.1193	+	6.41973i	−0.654076	+	0.377631i
$290$		0			0
$291$	−9.47985	+	16.4196i	−0.555719	+	0.962533i
$292$		0			0
$293$	−7.23407	+	7.23407i	−0.422619	+	0.422619i	−0.886105	−	0.463485i	$-0.846599\pi$
$293$	−7.23407	+	7.23407i	−0.422619	+	0.422619i	0.463485	+	0.886105i	$0.346599\pi$
$294$		0			0
$295$	0.175251	−	1.90470i	0.0102035	−	0.110896i
$296$		0			0
$297$	15.0880	−	4.04281i	0.875493	−	0.234588i
$298$		0			0
$299$	0.657432	+	1.13871i	0.0380203	+	0.0658531i
$300$		0			0
$301$	0.308440	−	18.6235i	0.0177782	−	1.07344i
$302$		0			0
$303$	−5.17439	+	19.3111i	−0.297261	+	1.10939i
$304$		0			0
$305$	8.93304	−	12.6367i	0.511504	−	0.723575i
$306$		0			0
$307$	1.07859	+	1.07859i	0.0615584	+	0.0615584i	0.737216	−	0.675657i	$-0.236140\pi$
$307$	1.07859	+	1.07859i	0.0615584	+	0.0615584i	−0.675657	+	0.737216i	$0.736140\pi$
$308$		0			0
$309$			8.65735i			0.492500i
$310$		0			0
$311$	8.33830	+	4.81412i	0.472821	+	0.272984i	0.717420	−	0.696641i	$-0.245323\pi$
$311$	8.33830	+	4.81412i	0.472821	+	0.272984i	−0.244599	+	0.969624i	$0.578656\pi$
$312$		0			0
$313$	2.92361	+	0.783378i	0.165252	+	0.0442791i	0.340496	−	0.940246i	$-0.389405\pi$
$313$	2.92361	+	0.783378i	0.165252	+	0.0442791i	−0.175244	+	0.984525i	$0.556072\pi$
$314$		0			0
$315$	−6.35883	+	0.983739i	−0.358280	+	0.0554274i
$316$		0			0
$317$	−1.88227	−	0.504353i	−0.105719	−	0.0283273i	0.205572	−	0.978642i	$-0.434095\pi$
$317$	−1.88227	−	0.504353i	−0.105719	−	0.0283273i	−0.311291	+	0.950315i	$0.600761\pi$
$318$		0			0
$319$	−25.0463	−	14.4605i	−1.40232	−	0.809631i
$320$		0			0
$321$			30.0682i			1.67824i
$322$		0			0
$323$	−8.94715	−	8.94715i	−0.497833	−	0.497833i
$324$		0			0
$325$	−0.113311	−	1.44425i	−0.00628535	−	0.0801124i
$326$		0			0
$327$	−6.92363	+	25.8393i	−0.382878	+	1.42892i
$328$		0			0
$329$	−0.728847	+	0.404858i	−0.0401826	+	0.0223205i
$330$		0			0
$331$	−14.4468	−	25.0225i	−0.794066	−	1.37536i	−0.923431	−	0.383765i	$-0.874627\pi$
$331$	−14.4468	−	25.0225i	−0.794066	−	1.37536i	0.129365	−	0.991597i	$-0.458706\pi$
$332$		0			0
$333$	4.85966	−	1.30214i	0.266308	−	0.0713570i
$334$		0			0
$335$	−4.51573	−	5.43092i	−0.246721	−	0.296723i
$336$		0			0
$337$	−0.823226	+	0.823226i	−0.0448440	+	0.0448440i	−0.729173	−	0.684329i	$-0.760095\pi$
$337$	−0.823226	+	0.823226i	−0.0448440	+	0.0448440i	0.684329	+	0.729173i	$0.260095\pi$
$338$		0			0
$339$	13.9436	−	24.1510i	0.757312	−	1.31170i
$340$		0			0
$341$	25.5846	−	14.7713i	1.38548	−	0.799910i
$342$		0			0
$343$	13.7300	−	12.4293i	0.741350	−	0.671119i
$344$		0			0
$345$	−18.6327	+	8.58706i	−1.00315	+	0.462312i
$346$		0			0
$347$	4.32336	+	16.1350i	0.232090	+	0.866172i	0.979439	+	0.201740i	$0.0646597\pi$
$347$	4.32336	+	16.1350i	0.232090	+	0.866172i	−0.747349	+	0.664432i	$0.768674\pi$
$348$		0			0
$349$	36.7146			1.96529			0.982644	−	0.185503i	$-0.0593916\pi$
$349$	36.7146			1.96529			0.982644	+	0.185503i	$0.0593916\pi$
$350$		0			0
$351$	−1.12024			−0.0597942
$352$		0			0
$353$	−3.69356	−	13.7845i	−0.196588	−	0.733677i	−0.991850	−	0.127411i	$-0.959333\pi$
$353$	−3.69356	−	13.7845i	−0.196588	−	0.733677i	0.795262	−	0.606266i	$-0.207333\pi$
$354$		0			0
$355$	14.4640	−	6.66588i	0.767672	−	0.353788i
$356$		0			0
$357$	2.99808	−	10.4909i	0.158675	−	0.555236i
$358$		0			0
$359$	23.4596	−	13.5444i	1.23815	−	0.714847i	0.269435	−	0.963019i	$-0.413163\pi$
$359$	23.4596	−	13.5444i	1.23815	−	0.714847i	0.968716	+	0.248172i	$0.0798298\pi$
$360$		0			0
$361$	−9.74064	+	16.8713i	−0.512665	+	0.887962i
$362$		0			0
$363$	−7.60756	+	7.60756i	−0.399293	+	0.399293i
$364$		0			0
$365$	16.4776	+	19.8171i	0.862477	+	1.03727i
$366$		0			0
$367$	−21.8990	+	5.86782i	−1.14312	+	0.306298i	−0.780204	−	0.625525i	$-0.784885\pi$
$367$	−21.8990	+	5.86782i	−1.14312	+	0.306298i	−0.362914	+	0.931823i	$0.618218\pi$
$368$		0			0
$369$	1.40709	+	2.43715i	0.0732502	+	0.126873i
$370$		0			0
$371$	18.7938	+	11.2696i	0.975726	+	0.585090i
$372$		0			0
$373$	−3.32215	+	12.3984i	−0.172014	+	0.641966i	0.825027	+	0.565094i	$0.191160\pi$
$373$	−3.32215	+	12.3984i	−0.172014	+	0.641966i	−0.997041	+	0.0768720i	$0.975507\pi$
$374$		0			0
$375$	22.6022	+	0.304135i	1.16717	+	0.0157055i
$376$		0			0
$377$	1.46664	+	1.46664i	0.0755356	+	0.0755356i
$378$		0			0
$379$			14.4739i			0.743476i	0.928338	+	0.371738i	$0.121238\pi$
$379$			14.4739i			0.743476i	−0.928338	+	0.371738i	$0.878762\pi$
$380$		0			0
$381$	−5.44718	−	3.14493i	−0.279068	−	0.161120i
$382$		0			0
$383$	−1.69189	−	0.453341i	−0.0864517	−	0.0231647i	0.215334	−	0.976540i	$-0.430916\pi$
$383$	−1.69189	−	0.453341i	−0.0864517	−	0.0231647i	−0.301786	+	0.953376i	$0.597583\pi$
$384$		0			0
$385$	−18.6283	+	14.9744i	−0.949387	+	0.763168i
$386$		0			0
$387$	−7.39595	−	1.98174i	−0.375957	−	0.100737i
$388$		0			0
$389$	−2.40954	−	1.39115i	−0.122169	−	0.0705341i	0.437670	−	0.899135i	$-0.355804\pi$
$389$	−2.40954	−	1.39115i	−0.122169	−	0.0705341i	−0.559839	+	0.828601i	$0.689137\pi$
$390$		0			0
$391$		−	9.25661i		−	0.468127i
$392$		0			0
$393$	−10.4344	−	10.4344i	−0.526348	−	0.526348i
$394$		0			0
$395$	−6.55224	+	9.26881i	−0.329679	+	0.466364i
$396$		0			0
$397$	10.2668	−	38.3163i	0.515277	−	1.92304i	0.165486	−	0.986212i	$-0.447081\pi$
$397$	10.2668	−	38.3163i	0.515277	−	1.92304i	0.349791	−	0.936828i	$-0.386253\pi$
$398$		0			0
$399$	−33.1780	−	0.549491i	−1.66098	−	0.0275089i
$400$		0			0
$401$	9.98528	+	17.2950i	0.498641	+	0.863672i	0.999999	−	0.00156835i	$-0.000499221\pi$
$401$	9.98528	+	17.2950i	0.498641	+	0.863672i	−0.501358	+	0.865240i	$0.667166\pi$
$402$		0			0
$403$	−2.04653	+	0.548365i	−0.101945	+	0.0273160i
$404$		0			0
$405$	2.27000	−	24.6713i	0.112797	−	1.22593i
$406$		0			0
$407$	13.2144	−	13.2144i	0.655012	−	0.655012i
$408$		0			0
$409$	−7.65280	+	13.2550i	−0.378407	+	0.655419i	−0.990831	−	0.135110i	$-0.956861\pi$
$409$	−7.65280	+	13.2550i	−0.378407	+	0.655419i	0.612424	+	0.790529i	$0.290195\pi$
$410$		0			0
$411$	12.5697	−	7.25713i	0.620019	−	0.357968i
$412$		0			0
$413$	2.19547	−	0.549475i	0.108032	−	0.0270379i
$414$		0			0
$415$	−4.21936	+	11.4328i	−0.207120	+	0.561214i
$416$		0			0
$417$	6.49762	+	24.2495i	0.318190	+	1.18750i
$418$		0			0
$419$	27.7027			1.35337			0.676684	−	0.736274i	$-0.263416\pi$
$419$	27.7027			1.35337			0.676684	+	0.736274i	$0.263416\pi$
$420$		0			0
$421$	33.0159			1.60910			0.804549	−	0.593887i	$-0.202407\pi$
$421$	33.0159			1.60910			0.804549	+	0.593887i	$0.202407\pi$
$422$		0			0
$423$	0.0887072	+	0.331060i	0.00431309	+	0.0160967i
$424$		0			0
$425$	−4.39289	+	9.20413i	−0.213087	+	0.446466i
$426$		0			0
$427$	17.6058	+	5.03138i	0.852005	+	0.243485i
$428$		0			0
$429$	2.04950	−	1.18328i	0.0989509	−	0.0571293i
$430$		0			0
$431$	11.9586	−	20.7129i	0.576027	−	0.997708i	−0.419902	−	0.907569i	$-0.637936\pi$
$431$	11.9586	−	20.7129i	0.576027	−	0.997708i	0.995929	−	0.0901384i	$-0.0287309\pi$
$432$		0			0
$433$	−13.2515	+	13.2515i	−0.636829	+	0.636829i	−0.949772	−	0.312943i	$-0.898685\pi$
$433$	−13.2515	+	13.2515i	−0.636829	+	0.636829i	0.312943	+	0.949772i	$0.398685\pi$
$434$		0			0
$435$	−24.8849	+	20.6914i	−1.19314	+	0.992077i
$436$		0			0
$437$	−27.1923	+	7.28615i	−1.30078	+	0.348544i
$438$		0			0
$439$	7.05383	+	12.2176i	0.336661	+	0.583114i	0.983802	−	0.179256i	$-0.0573690\pi$
$439$	7.05383	+	12.2176i	0.336661	+	0.583114i	−0.647141	+	0.762370i	$0.724036\pi$
$440$		0			0
$441$	−3.58626	−	6.71582i	−0.170774	−	0.319801i
$442$		0			0
$443$	−5.45161	+	20.3457i	−0.259014	+	0.966652i	0.706800	+	0.707414i	$0.250138\pi$
$443$	−5.45161	+	20.3457i	−0.259014	+	0.966652i	−0.965813	+	0.259238i	$0.916528\pi$
$444$		0			0
$445$	5.60975	+	3.96560i	0.265928	+	0.187988i
$446$		0			0
$447$	−34.2370	−	34.2370i	−1.61936	−	1.61936i
$448$		0			0
$449$		−	31.3247i		−	1.47831i	−0.673538	−	0.739153i	$-0.735226\pi$
$449$		−	31.3247i		−	1.47831i	0.673538	−	0.739153i	$-0.264774\pi$
$450$		0			0
$451$	9.05278	+	5.22662i	0.426279	+	0.246112i
$452$		0			0
$453$	6.91977	+	1.85415i	0.325119	+	0.0871154i
$454$		0			0
$455$	1.56841	−	0.691560i	0.0735281	−	0.0324209i
$456$		0			0
$457$	2.76404	+	0.740622i	0.129296	+	0.0346448i	0.322887	−	0.946438i	$-0.395347\pi$
$457$	2.76404	+	0.740622i	0.129296	+	0.0346448i	−0.193591	+	0.981082i	$0.562013\pi$
$458$		0			0
$459$	6.82989	+	3.94324i	0.318792	+	0.184055i
$460$		0			0
$461$			3.02674i			0.140969i	0.997513	+	0.0704846i	$0.0224546\pi$
$461$			3.02674i			0.140969i	−0.997513	+	0.0704846i	$0.977545\pi$
$462$		0			0
$463$	−19.2889	−	19.2889i	−0.896431	−	0.896431i	0.0986876	−	0.995118i	$-0.468536\pi$
$463$	−19.2889	−	19.2889i	−0.896431	−	0.896431i	−0.995118	+	0.0986876i	$0.968536\pi$
$464$		0			0
$465$	−5.59457	−	32.5822i	−0.259442	−	1.51096i
$466$		0			0
$467$	6.50385	−	24.2727i	0.300962	−	1.12321i	−0.635403	−	0.772180i	$-0.719166\pi$
$467$	6.50385	−	24.2727i	0.300962	−	1.12321i	0.936366	−	0.351026i	$-0.114167\pi$
$468$		0			0
$469$	4.29784	−	7.16729i	0.198456	−	0.330955i
$470$		0			0
$471$	6.18921	+	10.7200i	0.285184	+	0.493953i
$472$		0			0
$473$	−27.4722	+	7.36115i	−1.26317	+	0.338466i
$474$		0			0
$475$	30.4959	+	5.65976i	1.39925	+	0.259688i
$476$		0			0
$477$	6.36989	−	6.36989i	0.291657	−	0.291657i
$478$		0			0
$479$	4.14346	−	7.17668i	0.189319	−	0.327911i	−0.755704	−	0.654913i	$-0.772705\pi$
$479$	4.14346	−	7.17668i	0.189319	−	0.327911i	0.945024	+	0.327002i	$0.106039\pi$
$480$		0			0
$481$	−1.16069	+	0.670127i	−0.0529231	+	0.0305551i
$482$		0			0
$483$	−16.8785	−	17.4470i	−0.767999	−	0.793867i
$484$		0			0
$485$	19.6722	+	7.26018i	0.893269	+	0.329668i
$486$		0			0
$487$	−2.76375	−	10.3144i	−0.125237	−	0.467392i	0.874611	−	0.484826i	$-0.161117\pi$
$487$	−2.76375	−	10.3144i	−0.125237	−	0.467392i	−0.999848	+	0.0174340i	$0.994450\pi$
$488$		0			0
$489$	−33.4765			−1.51386
$490$		0			0
$491$	−25.7259			−1.16100			−0.580498	−	0.814262i	$-0.697142\pi$
$491$	−25.7259			−1.16100			−0.580498	+	0.814262i	$0.697142\pi$
$492$		0			0
$493$	−3.77924	−	14.1043i	−0.170209	−	0.635227i
$494$		0			0
$495$	4.11234	+	8.92322i	0.184836	+	0.401069i
$496$		0			0
$497$	13.1023	+	13.5436i	0.587719	+	0.607514i
$498$		0			0
$499$	12.6429	−	7.29940i	0.565975	−	0.326766i	−0.189565	−	0.981868i	$-0.560708\pi$
$499$	12.6429	−	7.29940i	0.565975	−	0.326766i	0.755540	+	0.655102i	$0.227374\pi$
$500$		0			0
$501$	14.7069	−	25.4732i	0.657058	−	1.13806i
$502$		0			0
$503$	−13.9891	+	13.9891i	−0.623744	+	0.623744i	−0.946487	−	0.322743i	$-0.895395\pi$
$503$	−13.9891	+	13.9891i	−0.623744	+	0.623744i	0.322743	+	0.946487i	$0.395395\pi$
$504$		0			0
$505$	22.0182	+	2.02589i	0.979798	+	0.0901510i
$506$		0			0
$507$	25.2237	−	6.75868i	1.12022	−	0.300163i
$508$		0			0
$509$	1.42883	+	2.47481i	0.0633319	+	0.109694i	0.895953	−	0.444149i	$-0.146494\pi$
$509$	1.42883	+	2.47481i	0.0633319	+	0.109694i	−0.832621	+	0.553843i	$0.813161\pi$
$510$		0			0
$511$	−15.6825	+	26.1530i	−0.693754	+	1.15694i
$512$		0			0
$513$	6.20768	−	23.1674i	0.274076	−	1.02287i
$514$		0			0
$515$	9.43680	−	1.62036i	0.415835	−	0.0714015i
$516$		0			0
$517$	0.900216	+	0.900216i	0.0395914	+	0.0395914i
$518$		0			0
$519$		−	15.7134i		−	0.689741i
$520$		0			0
$521$	24.7917	+	14.3135i	1.08614	+	0.627084i	0.932547	−	0.361049i	$-0.117581\pi$
$521$	24.7917	+	14.3135i	1.08614	+	0.627084i	0.153595	+	0.988134i	$0.450915\pi$
$522$		0			0
$523$	−30.5069	−	8.17429i	−1.33397	−	0.357437i	−0.479777	−	0.877390i	$-0.659283\pi$
$523$	−30.5069	−	8.17429i	−1.33397	−	0.357437i	−0.854195	+	0.519954i	$0.825949\pi$
$524$		0			0
$525$	8.50302	+	25.3581i	0.371102	+	1.10672i
$526$		0			0
$527$	14.4075	+	3.86048i	0.627600	+	0.168165i
$528$		0			0
$529$	2.08308	+	1.20267i	0.0905687	+	0.0522899i
$530$		0			0
$531$		−	0.930359i		−	0.0403742i
$532$		0			0
$533$	−0.530105	−	0.530105i	−0.0229614	−	0.0229614i
$534$		0			0
$535$	32.7753	−	5.62772i	1.41700	−	0.243308i
$536$		0			0
$537$	−2.02232	+	7.54741i	−0.0872696	+	0.325695i
$538$		0			0
$539$	−24.0094	−	14.9432i	−1.03416	−	0.643648i
$540$		0			0
$541$	−18.4994	−	32.0420i	−0.795353	−	1.37759i	−0.922615	−	0.385722i	$-0.873952\pi$
$541$	−18.4994	−	32.0420i	−0.795353	−	1.37759i	0.127262	−	0.991869i	$-0.459381\pi$
$542$		0			0
$543$	13.6528	−	3.65827i	0.585899	−	0.156991i
$544$		0			0
$545$	29.4616	+	2.71076i	1.26200	+	0.116116i
$546$		0			0
$547$	20.0765	−	20.0765i	0.858409	−	0.858409i	−0.132742	−	0.991151i	$-0.542378\pi$
$547$	20.0765	−	20.0765i	0.858409	−	0.858409i	0.991151	+	0.132742i	$0.0423781\pi$
$548$		0			0
$549$	3.76360	−	6.51875i	0.160627	−	0.278213i
$550$		0			0
$551$	−38.4582	+	22.2039i	−1.63838	+	0.945916i
$552$		0			0
$553$	−12.9136	−	3.69043i	−0.549141	−	0.156933i
$554$		0			0
$555$	−8.75286	−	18.9925i	−0.371538	−	0.806187i
$556$		0			0
$557$	−6.65499	−	24.8367i	−0.281981	−	1.05237i	−0.951017	−	0.309137i	$-0.899960\pi$
$557$	−6.65499	−	24.8367i	−0.281981	−	1.05237i	0.669037	−	0.743229i	$-0.266707\pi$
$558$		0			0
$559$	2.03974			0.0862718
$560$		0			0
$561$	−16.6605			−0.703408
$562$		0			0
$563$	−1.38907	−	5.18407i	−0.0585422	−	0.218482i	0.930458	−	0.366400i	$-0.119410\pi$
$563$	−1.38907	−	5.18407i	−0.0585422	−	0.218482i	−0.989000	+	0.147917i	$0.952743\pi$
$564$		0			0
$565$	−28.9352	−	10.6788i	−1.21731	−	0.449258i
$566$		0			0
$567$	28.4377	−	7.11728i	1.19427	−	0.298898i
$568$		0			0
$569$	22.0839	−	12.7502i	0.925806	−	0.534514i	0.0403234	−	0.999187i	$-0.487161\pi$
$569$	22.0839	−	12.7502i	0.925806	−	0.534514i	0.885483	+	0.464672i	$0.153828\pi$
$570$		0			0
$571$	7.95235	−	13.7739i	0.332795	−	0.576419i	−0.650263	−	0.759709i	$-0.725341\pi$
$571$	7.95235	−	13.7739i	0.332795	−	0.576419i	0.983059	+	0.183290i	$0.0586748\pi$
$572$		0			0
$573$	6.39672	−	6.39672i	0.267227	−	0.267227i
$574$		0			0
$575$	12.8476	+	18.7031i	0.535781	+	0.779973i
$576$		0			0
$577$	−22.2641	+	5.96565i	−0.926867	+	0.248353i	−0.690518	−	0.723315i	$-0.742617\pi$
$577$	−22.2641	+	5.96565i	−0.926867	+	0.248353i	−0.236349	+	0.971668i	$0.575951\pi$
$578$		0			0
$579$	−20.2934	−	35.1493i	−0.843366	−	1.46075i
$580$		0			0
$581$	−14.4173	−	0.238779i	−0.598132	−	0.00990621i
$582$		0			0
$583$	8.66048	−	32.3214i	0.358681	−	1.33861i
$584$		0			0
$585$	−0.119246	−	0.694478i	−0.00493022	−	0.0287131i
$586$		0			0
$587$	−28.2277	−	28.2277i	−1.16508	−	1.16508i	−0.983348	−	0.181734i	$-0.941829\pi$
$587$	−28.2277	−	28.2277i	−1.16508	−	1.16508i	−0.181734	−	0.983348i	$-0.558171\pi$
$588$		0			0
$589$		−	45.3622i		−	1.86912i
$590$		0			0
$591$	19.4355	+	11.2211i	0.799471	+	0.461575i
$592$		0			0
$593$	−34.2220	−	9.16977i	−1.40533	−	0.376557i	−0.525075	−	0.851056i	$-0.675963\pi$
$593$	−34.2220	−	9.16977i	−1.40533	−	0.376557i	−0.880256	+	0.474499i	$0.842629\pi$
$594$		0			0
$595$	−11.9965	−	1.30447i	−0.491811	−	0.0534782i
$596$		0			0
$597$	−21.0953	−	5.65247i	−0.863373	−	0.231340i
$598$		0			0
$599$	−14.5339	−	8.39115i	−0.593839	−	0.342853i	0.172775	−	0.984961i	$-0.444727\pi$
$599$	−14.5339	−	8.39115i	−0.593839	−	0.342853i	−0.766614	+	0.642108i	$0.778060\pi$
$600$		0			0
$601$			1.73528i			0.0707833i	0.999374	+	0.0353917i	$0.0112679\pi$
$601$			1.73528i			0.0707833i	−0.999374	+	0.0353917i	$0.988732\pi$
$602$		0			0
$603$	−2.42925	−	2.42925i	−0.0989266	−	0.0989266i
$604$		0			0
$605$	9.71637	+	6.86862i	0.395027	+	0.279249i
$606$		0			0
$607$	−10.2070	+	38.0930i	−0.414288	+	1.54615i	0.371968	+	0.928245i	$0.378683\pi$
$607$	−10.2070	+	38.0930i	−0.414288	+	1.54615i	−0.786257	+	0.617900i	$0.787984\pi$
$608$		0			0
$609$	−32.8410	−	19.6930i	−1.33079	−	0.798000i
$610$		0			0
$611$	−0.0456517	−	0.0790711i	−0.00184687	−	0.00319887i
$612$		0			0
$613$	−0.330293	+	0.0885018i	−0.0133404	+	0.00357455i	−0.265483	−	0.964116i	$-0.585531\pi$
$613$	−0.330293	+	0.0885018i	−0.0133404	+	0.00357455i	0.252143	+	0.967690i	$0.418865\pi$
$614$		0			0
$615$	8.99444	−	7.47875i	0.362691	−	0.301572i
$616$		0			0
$617$	11.1876	−	11.1876i	0.450397	−	0.450397i	−0.445089	−	0.895486i	$-0.646828\pi$
$617$	11.1876	−	11.1876i	0.450397	−	0.450397i	0.895486	+	0.445089i	$0.146828\pi$
$618$		0			0
$619$	−18.2682	+	31.6414i	−0.734260	+	1.27178i	0.220787	+	0.975322i	$0.429138\pi$
$619$	−18.2682	+	31.6414i	−0.734260	+	1.27178i	−0.955047	+	0.296454i	$0.904196\pi$
$620$		0			0
$621$	15.1956	−	8.77316i	0.609777	−	0.352055i
$622$		0			0
$623$	−2.23356	+	7.81566i	−0.0894855	+	0.313128i
$624$		0			0
$625$	−3.89884	−	24.6941i	−0.155953	−	0.987764i
$626$		0			0
$627$	13.1140	+	48.9421i	0.523723	+	1.95456i
$628$		0			0
$629$	9.43535			0.376212
$630$		0			0
$631$	35.8189			1.42593			0.712964	−	0.701201i	$-0.247352\pi$
$631$	35.8189			1.42593			0.712964	+	0.701201i	$0.247352\pi$
$632$		0			0
$633$	3.95888	+	14.7747i	0.157351	+	0.587243i
$634$		0			0
$635$	−2.40856	+	6.52623i	−0.0955807	+	0.258986i
$636$		0			0
$637$	1.38585	+	1.48083i	0.0549093	+	0.0586726i
$638$		0			0
$639$	6.70867	−	3.87325i	0.265391	−	0.153223i
$640$		0			0
$641$	7.16573	−	12.4114i	0.283029	−	0.490221i	−0.689100	−	0.724666i	$-0.741994\pi$
$641$	7.16573	−	12.4114i	0.283029	−	0.490221i	0.972129	+	0.234445i	$0.0753272\pi$
$642$		0			0
$643$	−7.65201	+	7.65201i	−0.301766	+	0.301766i	−0.841704	−	0.539939i	$-0.818447\pi$
$643$	−7.65201	+	7.65201i	−0.301766	+	0.301766i	0.539939	+	0.841704i	$0.318447\pi$
$644$		0			0
$645$	−2.91605	+	31.6928i	−0.114819	+	1.24790i
$646$		0			0
$647$	−31.2468	+	8.37254i	−1.22844	+	0.329159i	−0.813971	−	0.580906i	$-0.802698\pi$
$647$	−31.2468	+	8.37254i	−1.22844	+	0.329159i	−0.414466	+	0.910065i	$0.636032\pi$
$648$		0			0
$649$	−1.72791	−	2.99282i	−0.0678262	−	0.117478i
$650$		0			0
$651$	34.1947	−	18.9943i	1.34019	−	0.744447i
$652$		0			0
$653$	−0.132578	+	0.494788i	−0.00518818	+	0.0193625i	−0.968471	−	0.249125i	$-0.919857\pi$
$653$	−0.132578	+	0.494788i	−0.00518818	+	0.0193625i	0.963283	+	0.268487i	$0.0865237\pi$
$654$		0			0
$655$	−9.42093	+	13.3269i	−0.368106	+	0.520724i
$656$		0			0
$657$	8.86417	+	8.86417i	0.345824	+	0.345824i
$658$		0			0
$659$			19.5542i			0.761723i	0.924632	+	0.380862i	$0.124373\pi$
$659$			19.5542i			0.761723i	−0.924632	+	0.380862i	$0.875627\pi$
$660$		0			0
$661$	34.0324	+	19.6486i	1.32371	+	0.764242i	0.984318	−	0.176405i	$-0.0564468\pi$
$661$	34.0324	+	19.6486i	1.32371	+	0.764242i	0.339388	+	0.940647i	$0.389780\pi$
$662$		0			0
$663$	1.15414	+	0.309250i	0.0448230	+	0.0120103i
$664$		0			0
$665$	5.61080	+	36.2679i	0.217578	+	1.40641i
$666$		0			0
$667$	−31.3801	−	8.40828i	−1.21504	−	0.325570i
$668$		0			0
$669$	23.1579	+	13.3702i	0.895337	+	0.516923i
$670$		0			0
$671$		−	27.9597i		−	1.07937i
$672$		0			0
$673$	18.4813	+	18.4813i	0.712401	+	0.712401i	0.967037	−	0.254636i	$-0.0819556\pi$
$673$	18.4813	+	18.4813i	0.712401	+	0.712401i	−0.254636	+	0.967037i	$0.581956\pi$
$674$		0			0
$675$	−19.2729	+	1.51208i	−0.741812	+	0.0582002i
$676$		0			0
$677$	−10.6631	+	39.7951i	−0.409815	+	1.52945i	0.385183	+	0.922840i	$0.374138\pi$
$677$	−10.6631	+	39.7951i	−0.409815	+	1.52945i	−0.794999	+	0.606611i	$0.792528\pi$
$678$		0			0
$679$	−0.410862	+	24.8076i	−0.0157674	+	0.952030i
$680$		0			0
$681$	16.3702	+	28.3541i	0.627309	+	1.08653i
$682$		0			0
$683$	−8.81689	+	2.36248i	−0.337369	+	0.0903978i	−0.423526	−	0.905884i	$-0.639208\pi$
$683$	−8.81689	+	2.36248i	−0.337369	+	0.0903978i	0.0861573	+	0.996282i	$0.472541\pi$
$684$		0			0
$685$	−10.2631	−	12.3431i	−0.392134	−	0.471607i
$686$		0			0
$687$	16.8358	−	16.8358i	0.642325	−	0.642325i
$688$		0			0
$689$	−1.19989	+	2.07827i	−0.0457121	+	0.0791758i
$690$		0			0
$691$	41.9971	−	24.2470i	1.59765	−	0.922401i	0.605706	−	0.795689i	$-0.292891\pi$
$691$	41.9971	−	24.2470i	1.59765	−	0.922401i	0.991940	−	0.126712i	$-0.0404424\pi$
$692$		0			0
$693$	−8.35538	+	8.08313i	−0.317395	+	0.307053i
$694$		0			0
$695$	25.2166	−	11.6213i	0.956520	−	0.440821i
$696$		0			0
$697$	1.36598	+	5.09790i	0.0517401	+	0.193097i
$698$		0			0
$699$	11.5732			0.437739
$700$		0			0
$701$	−30.8898			−1.16669			−0.583347	−	0.812223i	$-0.698257\pi$
$701$	−30.8898			−1.16669			−0.583347	+	0.812223i	$0.698257\pi$
$702$		0			0
$703$	−7.42684	−	27.7173i	−0.280109	−	1.04538i
$704$		0			0
$705$	1.29385	−	0.596280i	0.0487290	−	0.0224572i
$706$		0			0
$707$	6.35191	+	25.3796i	0.238888	+	0.954496i
$708$		0			0
$709$	−12.7354	+	7.35277i	−0.478287	+	0.276139i	−0.719702	−	0.694283i	$-0.755722\pi$
$709$	−12.7354	+	7.35277i	−0.478287	+	0.276139i	0.241416	+	0.970422i	$0.422388\pi$
$710$		0			0
$711$	−2.76054	+	4.78140i	−0.103528	+	0.179316i
$712$		0			0
$713$	23.4656	−	23.4656i	0.878795	−	0.878795i
$714$		0			0
$715$	−1.67341	−	2.01256i	−0.0625821	−	0.0752654i
$716$		0			0
$717$	16.2831	−	4.36306i	0.608105	−	0.162941i
$718$		0			0
$719$	−11.7360	−	20.3273i	−0.437679	−	0.758082i	0.559831	−	0.828607i	$-0.310866\pi$
$719$	−11.7360	−	20.3273i	−0.437679	−	0.758082i	−0.997510	+	0.0705247i	$0.977533\pi$
$720$		0			0
$721$	5.50134	+	9.90382i	0.204881	+	0.368837i
$722$		0			0
$723$	1.55119	−	5.78913i	0.0576895	−	0.215300i
$724$		0			0
$725$	27.2119	+	23.2526i	1.01062	+	0.863581i
$726$		0			0
$727$	14.1380	+	14.1380i	0.524349	+	0.524349i	0.918882	−	0.394533i	$-0.129093\pi$
$727$	14.1380	+	14.1380i	0.524349	+	0.524349i	−0.394533	+	0.918882i	$0.629093\pi$
$728$		0			0
$729$			11.4004i			0.422236i
$730$		0			0
$731$	−12.4359	−	7.17986i	−0.459958	−	0.265557i
$732$		0			0
$733$	−26.7908	−	7.17859i	−0.989543	−	0.265147i	−0.272484	−	0.962160i	$-0.587845\pi$
$733$	−26.7908	−	7.17859i	−0.989543	−	0.265147i	−0.717058	+	0.697013i	$0.754512\pi$
$734$		0			0
$735$	−24.9899	+	19.4158i	−0.921765	+	0.716164i
$736$		0			0
$737$	−12.3262	−	3.30280i	−0.454042	−	0.121660i
$738$		0			0
$739$	11.7451	+	6.78102i	0.432050	+	0.249444i	0.700219	−	0.713928i	$-0.253085\pi$
$739$	11.7451	+	6.78102i	0.432050	+	0.249444i	−0.268170	+	0.963372i	$0.586419\pi$
$740$		0			0
$741$		−	3.63383i		−	0.133492i
$742$		0			0
$743$	−13.5961	−	13.5961i	−0.498791	−	0.498791i	0.412270	−	0.911062i	$-0.364736\pi$
$743$	−13.5961	−	13.5961i	−0.498791	−	0.498791i	−0.911062	+	0.412270i	$0.864736\pi$
$744$		0			0
$745$	−30.9115	+	43.7275i	−1.13251	+	1.60205i
$746$		0			0
$747$	−1.53416	+	5.72557i	−0.0561320	+	0.209488i
$748$		0			0
$749$	19.1069	+	34.3973i	0.698152	+	1.25685i
$750$		0			0
$751$	21.8309	+	37.8123i	0.796622	+	1.37979i	0.921804	+	0.387656i	$0.126715\pi$
$751$	21.8309	+	37.8123i	0.796622	+	1.37979i	−0.125182	+	0.992134i	$0.539951\pi$
$752$		0			0
$753$	31.5979	−	8.46663i	1.15149	−	0.308541i
$754$		0			0
$755$	0.725941	−	7.88981i	0.0264197	−	0.287140i
$756$		0			0
$757$	7.88896	−	7.88896i	0.286729	−	0.286729i	−0.549056	−	0.835785i	$-0.685013\pi$
$757$	7.88896	−	7.88896i	0.286729	−	0.286729i	0.835785	+	0.549056i	$0.185013\pi$
$758$		0			0
$759$	−18.5337	+	32.1013i	−0.672730	+	1.16520i
$760$		0			0
$761$	−1.70923	+	0.986825i	−0.0619596	+	0.0357724i	−0.530660	−	0.847585i	$-0.678056\pi$
$761$	−1.70923	+	0.986825i	−0.0619596	+	0.0357724i	0.468700	+	0.883357i	$0.344722\pi$
$762$		0			0
$763$	8.49921	+	33.9593i	0.307692	+	1.22941i
$764$		0			0
$765$	−1.71753	+	4.65384i	−0.0620976	+	0.168260i
$766$		0			0
$767$	0.0641463	+	0.239397i	0.00231619	+	0.00864413i
$768$		0			0
$769$	−17.4914			−0.630756			−0.315378	−	0.948966i	$-0.602131\pi$
$769$	−17.4914			−0.630756			−0.315378	+	0.948966i	$0.602131\pi$
$770$		0			0
$771$	11.7763			0.424112
$772$		0			0
$773$	11.5736	+	43.1933i	0.416274	+	1.55355i	0.782271	+	0.622939i	$0.214061\pi$
$773$	11.5736	+	43.1933i	0.416274	+	1.55355i	−0.365997	+	0.930616i	$0.619272\pi$
$774$		0			0
$775$	−34.4686	+	12.1965i	−1.23815	+	0.438112i
$776$		0			0
$777$	17.7839	−	17.2044i	0.637994	−	0.617205i
$778$		0			0
$779$	13.9004	−	8.02542i	0.498035	−	0.287540i
$780$		0			0
$781$	14.3871	−	24.9193i	0.514813	−	0.891682i
$782$		0			0
$783$	19.5716	−	19.5716i	0.699433	−	0.699433i
$784$		0			0
$785$	10.5268	−	8.75286i	0.375717	−	0.312403i
$786$		0			0
$787$	−25.0643	+	6.71595i	−0.893445	+	0.239398i	−0.676199	−	0.736719i	$-0.736374\pi$
$787$	−25.0643	+	6.71595i	−0.893445	+	0.239398i	−0.217246	+	0.976117i	$0.569707\pi$
$788$		0			0
$789$	−1.75605	−	3.04156i	−0.0625170	−	0.108283i
$790$		0			0
$791$	0.604323	−	36.4887i	0.0214873	−	1.29739i
$792$		0			0
$793$	−0.518984	+	1.93688i	−0.0184297	+	0.0687805i
$794$		0			0
$795$	−30.5761	−	21.6146i	−1.08442	−	0.766592i
$796$		0			0
$797$	−37.3374	−	37.3374i	−1.32256	−	1.32256i	−0.911698	−	0.410861i	$-0.865228\pi$
$797$	−37.3374	−	37.3374i	−1.32256	−	1.32256i	−0.410861	−	0.911698i	$-0.634772\pi$
$798$		0			0
$799$			0.642773i			0.0227397i
$800$		0			0
$801$	2.89384	+	1.67076i	0.102249	+	0.0590333i
$802$		0			0
$803$	44.9776	+	12.0517i	1.58722	+	0.425295i
$804$		0			0
$805$	−15.8588	+	21.6636i	−0.558948	+	0.763543i
$806$		0			0
$807$	7.38854	+	1.97975i	0.260089	+	0.0696906i
$808$		0			0
$809$	−13.9001	−	8.02525i	−0.488703	−	0.282153i	0.235333	−	0.971915i	$-0.424382\pi$
$809$	−13.9001	−	8.02525i	−0.488703	−	0.282153i	−0.724036	+	0.689762i	$0.757715\pi$
$810$		0			0
$811$			35.4040i			1.24320i	0.783334	+	0.621602i	$0.213518\pi$
$811$			35.4040i			1.24320i	−0.783334	+	0.621602i	$0.786482\pi$
$812$		0			0
$813$	−30.3791	−	30.3791i	−1.06544	−	1.06544i
$814$		0			0
$815$	6.26564	+	36.4905i	0.219476	+	1.27821i
$816$		0			0
$817$	−11.3030	+	42.1832i	−0.395440	+	1.47580i
$818$		0			0
$819$	0.728847	−	0.404858i	0.0254680	−	0.0141469i
$820$		0			0
$821$	−13.4231	−	23.2495i	−0.468469	−	0.811412i	0.530881	−	0.847446i	$-0.321861\pi$
$821$	−13.4231	−	23.2495i	−0.468469	−	0.811412i	−0.999351	+	0.0360337i	$0.988528\pi$
$822$		0			0
$823$	27.0285	−	7.24225i	0.942153	−	0.252449i	0.245124	−	0.969492i	$-0.421171\pi$
$823$	27.0285	−	7.24225i	0.942153	−	0.252449i	0.697029	+	0.717043i	$0.254505\pi$
$824$		0			0
$825$	33.6628	−	23.1237i	1.17199	−	0.805066i
$826$		0			0
$827$	−16.8901	+	16.8901i	−0.587325	+	0.587325i	−0.936906	−	0.349581i	$-0.886324\pi$
$827$	−16.8901	+	16.8901i	−0.587325	+	0.587325i	0.349581	+	0.936906i	$0.386324\pi$
$828$		0			0
$829$	7.08412	−	12.2701i	0.246042	−	0.426157i	−0.716382	−	0.697708i	$-0.754203\pi$
$829$	7.08412	−	12.2701i	0.246042	−	0.426157i	0.962424	+	0.271551i	$0.0875367\pi$
$830$		0			0
$831$	−8.56228	+	4.94343i	−0.297022	+	0.171486i
$832$		0			0
$833$	−3.23673	−	13.9065i	−0.112146	−	0.481831i
$834$		0			0
$835$	−30.5192	−	11.2634i	−1.05616	−	0.389785i
$836$		0			0
$837$	7.31770	+	27.3100i	0.252937	+	0.943972i
$838$		0			0
$839$	−18.1874			−0.627900			−0.313950	−	0.949439i	$-0.601652\pi$
$839$	−18.1874			−0.627900			−0.313950	+	0.949439i	$0.601652\pi$
$840$		0			0
$841$	−22.2469			−0.767134
$842$		0			0
$843$	15.4250	+	57.5667i	0.531264	+	1.98270i
$844$		0			0
$845$	−12.0882	−	26.2297i	−0.415846	−	0.902329i
$846$		0			0
$847$	−3.86863	+	13.5371i	−0.132928	+	0.465141i
$848$		0			0
$849$	19.7567	−	11.4065i	0.678048	−	0.391471i
$850$		0			0
$851$	10.4962	−	18.1799i	0.359804	−	0.623198i
$852$		0			0
$853$	−17.4820	+	17.4820i	−0.598574	+	0.598574i	−0.939933	−	0.341359i	$-0.889113\pi$
$853$	−17.4820	+	17.4820i	−0.598574	+	0.598574i	0.341359	+	0.939933i	$0.389113\pi$
$854$		0			0
$855$	15.0231	+	1.38227i	0.513778	+	0.0472726i
$856$		0			0
$857$	−25.2634	+	6.76932i	−0.862982	+	0.231235i	−0.663051	−	0.748574i	$-0.730739\pi$
$857$	−25.2634	+	6.76932i	−0.862982	+	0.231235i	−0.199932	+	0.979810i	$0.564072\pi$
$858$		0			0
$859$	−24.4126	−	42.2838i	−0.832946	−	1.44271i	−0.895692	−	0.444676i	$-0.853319\pi$
$859$	−24.4126	−	42.2838i	−0.832946	−	1.44271i	0.0627455	−	0.998030i	$-0.480014\pi$
$860$		0			0
$861$	11.8701	+	7.11788i	0.404533	+	0.242577i
$862$		0			0
$863$	−3.97256	+	14.8258i	−0.135228	+	0.504676i	0.864769	+	0.502169i	$0.167465\pi$
$863$	−3.97256	+	14.8258i	−0.135228	+	0.504676i	−0.999997	+	0.00250685i	$0.999202\pi$
$864$		0			0
$865$	−17.1281	+	2.94100i	−0.582373	+	0.0999971i
$866$		0			0
$867$	18.3555	+	18.3555i	0.623387	+	0.623387i
$868$		0			0
$869$			20.5080i			0.695686i
$870$		0			0
$871$	0.792578	+	0.457595i	0.0268555	+	0.0155050i
$872$		0			0
$873$	9.85188	+	2.63980i	0.333436	+	0.0893438i
$874$		0			0
$875$	26.0497	−	14.0147i	0.880641	−	0.473784i
$876$		0			0
$877$	38.1169	+	10.2134i	1.28712	+	0.344882i	0.836565	−	0.547868i	$-0.184560\pi$
$877$	38.1169	+	10.2134i	1.28712	+	0.344882i	0.450552	+	0.892750i	$0.351227\pi$
$878$		0			0
$879$	17.9128	+	10.3420i	0.604185	+	0.348826i
$880$		0			0
$881$		−	52.5926i		−	1.77189i	−0.463791	−	0.885945i	$-0.653511\pi$
$881$		−	52.5926i		−	1.77189i	0.463791	−	0.885945i	$-0.346489\pi$
$882$		0			0
$883$	−13.0940	−	13.0940i	−0.440649	−	0.440649i	0.451581	−	0.892230i	$-0.350860\pi$
$883$	−13.0940	−	13.0940i	−0.440649	−	0.440649i	−0.892230	+	0.451581i	$0.850860\pi$
$884$		0			0
$885$	−3.81138	+	0.654437i	−0.128118	+	0.0219987i
$886$		0			0
$887$	−9.56553	+	35.6990i	−0.321179	+	1.19866i	0.596919	+	0.802302i	$0.296391\pi$
$887$	−9.56553	+	35.6990i	−0.321179	+	1.19866i	−0.918098	+	0.396354i	$0.870275\pi$
$888$		0			0
$889$	−8.22991	−	0.136303i	−0.276022	−	0.00457146i
$890$		0			0
$891$	−22.3813	−	38.7656i	−0.749803	−	1.29870i
$892$		0			0
$893$	1.88822	−	0.505946i	0.0631867	−	0.0169308i
$894$		0			0
$895$	8.60543	+	0.791785i	0.287648	+	0.0264664i
$896$		0			0
$897$	1.87976	−	1.87976i	0.0627633	−	0.0627633i
$898$		0			0
$899$	26.1742	−	45.3351i	0.872959	−	1.51201i
$900$		0			0
$901$	14.6310	−	8.44719i	0.487428	−	0.281417i
$902$		0			0
$903$	−36.5311	+	9.14288i	−1.21568	+	0.304256i
$904$		0			0
$905$	−6.54297	−	14.1974i	−0.217496	−	0.471936i
$906$		0			0
$907$	4.28883	+	16.0061i	0.142408	+	0.531474i	0.999857	+	0.0169054i	$0.00538141\pi$
$907$	4.28883	+	16.0061i	0.142408	+	0.531474i	−0.857449	+	0.514569i	$0.827952\pi$
$908$		0			0
$909$	10.7549			0.356718
$910$		0			0
$911$	1.46770			0.0486270			0.0243135	−	0.999704i	$-0.492260\pi$
$911$	1.46770			0.0486270			0.0243135	+	0.999704i	$0.492260\pi$
$912$		0			0
$913$	5.69862	+	21.2676i	0.188597	+	0.703853i
$914$		0			0
$915$	−29.3526	−	10.8328i	−0.970367	−	0.358122i
$916$		0			0
$917$	−18.5674	−	5.30617i	−0.613149	−	0.175225i
$918$		0			0
$919$	−24.1523	+	13.9443i	−0.796710	+	0.459981i	−0.842319	−	0.538979i	$-0.818810\pi$
$919$	−24.1523	+	13.9443i	−0.796710	+	0.459981i	0.0456096	+	0.998959i	$0.485477\pi$
$920$		0			0
$921$	1.54197	−	2.67078i	0.0508098	−	0.0880051i
$922$		0			0
$923$	−1.45920	+	1.45920i	−0.0480302	+	0.0480302i
$924$		0			0
$925$	−19.0642	+	13.0957i	−0.626828	+	0.430582i
$926$		0			0
$927$	4.49855	−	1.20538i	0.147752	−	0.0395900i
$928$		0			0
$929$	−16.6468	−	28.8331i	−0.546164	−	0.945984i	−0.998533	−	0.0541530i	$-0.982754\pi$
$929$	−16.6468	−	28.8331i	−0.546164	−	0.945984i	0.452368	−	0.891831i	$-0.350579\pi$
$930$		0			0
$931$	−38.3040	+	20.4544i	−1.25536	+	0.670367i
$932$		0			0
$933$	5.03824	−	18.8030i	0.164944	−	0.615581i
$934$		0			0
$935$	3.11828	+	18.1605i	0.101979	+	0.593913i
$936$		0			0
$937$	25.6651	+	25.6651i	0.838442	+	0.838442i	0.988654	−	0.150212i	$-0.0479957\pi$
$937$	25.6651	+	25.6651i	0.838442	+	0.838442i	−0.150212	+	0.988654i	$0.547996\pi$
$938$		0			0
$939$		−	6.11942i		−	0.199700i
$940$		0			0
$941$	−21.0732	−	12.1666i	−0.686967	−	0.396621i	0.115508	−	0.993307i	$-0.463151\pi$
$941$	−21.0732	−	12.1666i	−0.686967	−	0.396621i	−0.802475	+	0.596686i	$0.796484\pi$
$942$		0			0
$943$	11.3421	+	3.03911i	0.369350	+	0.0989670i
$944$		0			0
$945$	−9.22858	−	20.9297i	−0.300206	−	0.680845i
$946$		0			0
$947$	−2.07680	−	0.556477i	−0.0674869	−	0.0180831i	0.224918	−	0.974378i	$-0.427789\pi$
$947$	−2.07680	−	0.556477i	−0.0674869	−	0.0180831i	−0.292405	+	0.956295i	$0.594455\pi$
$948$		0			0
$949$	−2.89206	−	1.66973i	−0.0938804	−	0.0542019i
$950$		0			0
$951$			3.93980i			0.127757i
$952$		0			0
$953$	−13.1863	−	13.1863i	−0.427146	−	0.427146i	0.460509	−	0.887655i	$-0.347667\pi$
$953$	−13.1863	−	13.1863i	−0.427146	−	0.427146i	−0.887655	+	0.460509i	$0.847667\pi$
$954$		0			0
$955$	−8.16989	−	5.77540i	−0.264371	−	0.186887i
$956$		0			0
$957$	−15.1337	+	56.4796i	−0.489202	+	1.82573i
$958$		0			0
$959$	9.76792	−	16.2895i	0.315423	−	0.526015i
$960$		0			0
$961$	11.2368	+	19.4627i	0.362477	+	0.627829i
$962$		0			0
$963$	15.6241	−	4.18646i	0.503479	−	0.134907i
$964$		0			0
$965$	−34.5156	+	28.6993i	−1.11110	+	0.923862i
$966$		0			0
$967$	27.7931	−	27.7931i	0.893766	−	0.893766i	−0.101109	−	0.994875i	$-0.532239\pi$
$967$	27.7931	−	27.7931i	0.893766	−	0.893766i	0.994875	+	0.101109i	$0.0322392\pi$
$968$		0			0
$969$	−12.7910	+	22.1547i	−0.410907	+	0.711711i
$970$		0			0
$971$	−12.1029	+	6.98760i	−0.388400	+	0.224243i	−0.681467	−	0.731849i	$-0.738658\pi$
$971$	−12.1029	+	6.98760i	−0.388400	+	0.224243i	0.293067	+	0.956092i	$0.405324\pi$
$972$		0			0
$973$	22.8425	+	23.6119i	0.732298	+	0.756963i
$974$		0			0
$975$	−2.76117	+	0.977025i	−0.0884282	+	0.0312899i
$976$		0			0
$977$	2.16089	+	8.06456i	0.0691331	+	0.258008i	0.991839	−	0.127496i	$-0.0406941\pi$
$977$	2.16089	+	8.06456i	0.0691331	+	0.258008i	−0.922706	+	0.385505i	$0.874027\pi$
$978$		0			0
$979$	12.4120			0.396690
$980$		0			0
$981$	14.3907			0.459459
$982$		0			0
$983$	6.30383	+	23.5262i	0.201061	+	0.750370i	0.990614	+	0.136688i	$0.0436457\pi$
$983$	6.30383	+	23.5262i	0.201061	+	0.750370i	−0.789553	+	0.613682i	$0.789688\pi$
$984$		0			0
$985$	8.59372	−	23.2856i	0.273819	−	0.741940i
$986$		0			0
$987$	1.17203	+	1.21151i	0.0373062	+	0.0385628i
$988$		0			0
$989$	−27.6681	+	15.9742i	−0.879794	+	0.507949i
$990$		0			0
$991$	8.72002	−	15.1035i	0.277000	−	0.479779i	−0.693637	−	0.720324i	$-0.743993\pi$
$991$	8.72002	−	15.1035i	0.277000	−	0.479779i	0.970638	+	0.240545i	$0.0773263\pi$
$992$		0			0
$993$	−41.3067	+	41.3067i	−1.31083	+	1.31083i
$994$		0			0
$995$	−2.21307	+	24.0525i	−0.0701590	+	0.762516i
$996$		0			0
$997$	25.2781	−	6.77324i	0.800565	−	0.214511i	0.164733	−	0.986338i	$-0.447324\pi$
$997$	25.2781	−	6.77324i	0.800565	−	0.214511i	0.635832	+	0.771827i	$0.280657\pi$
$998$		0			0
$999$	8.94255	+	15.4890i	0.282930	+	0.490049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.ci.c.353.1		16
4.3	odd	2		70.2.k.a.3.2	✓	16
5.2	odd	4	inner	560.2.ci.c.17.1		16
7.5	odd	6	inner	560.2.ci.c.33.1		16
12.11	even	2		630.2.bv.c.73.4		16
20.3	even	4		350.2.o.c.157.1		16
20.7	even	4		70.2.k.a.17.4	yes	16
20.19	odd	2		350.2.o.c.143.3		16
28.3	even	6		490.2.g.c.293.5		16
28.11	odd	6		490.2.g.c.293.8		16
28.19	even	6		70.2.k.a.33.4	yes	16
28.23	odd	6		490.2.l.c.313.3		16
28.27	even	2		490.2.l.c.423.1		16
35.12	even	12	inner	560.2.ci.c.257.1		16
60.47	odd	4		630.2.bv.c.577.2		16
84.47	odd	6		630.2.bv.c.523.2		16
140.19	even	6		350.2.o.c.243.1		16
140.27	odd	4		490.2.l.c.227.3		16
140.47	odd	12		70.2.k.a.47.2	yes	16
140.67	even	12		490.2.g.c.97.5		16
140.87	odd	12		490.2.g.c.97.8		16
140.103	odd	12		350.2.o.c.257.3		16
140.107	even	12		490.2.l.c.117.1		16
420.47	even	12		630.2.bv.c.397.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.2	✓	16	4.3	odd	2
70.2.k.a.17.4	yes	16	20.7	even	4
70.2.k.a.33.4	yes	16	28.19	even	6
70.2.k.a.47.2	yes	16	140.47	odd	12
350.2.o.c.143.3		16	20.19	odd	2
350.2.o.c.157.1		16	20.3	even	4
350.2.o.c.243.1		16	140.19	even	6
350.2.o.c.257.3		16	140.103	odd	12
490.2.g.c.97.5		16	140.67	even	12
490.2.g.c.97.8		16	140.87	odd	12
490.2.g.c.293.5		16	28.3	even	6
490.2.g.c.293.8		16	28.11	odd	6
490.2.l.c.117.1		16	140.107	even	12
490.2.l.c.227.3		16	140.27	odd	4
490.2.l.c.313.3		16	28.23	odd	6
490.2.l.c.423.1		16	28.27	even	2
560.2.ci.c.17.1		16	5.2	odd	4	inner
560.2.ci.c.33.1		16	7.5	odd	6	inner
560.2.ci.c.257.1		16	35.12	even	12	inner
560.2.ci.c.353.1		16	1.1	even	1	trivial
630.2.bv.c.73.4		16	12.11	even	2
630.2.bv.c.397.4		16	420.47	even	12
630.2.bv.c.523.2		16	84.47	odd	6
630.2.bv.c.577.2		16	60.47	odd	4

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.ci (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.523277 - 1.95290i) q^{3} +(-2.03078 + 0.935904i) q^{5} +(-1.83959 - 1.90155i) q^{7} +(-0.941911 + 0.543813i) q^{9} +O(q^{10})\)	\(q+(-0.523277 - 1.95290i) q^{3} +(-2.03078 + 0.935904i) q^{5} +(-1.83959 - 1.90155i) q^{7} +(-0.941911 + 0.543813i) q^{9} +(-2.01999 + 3.49872i) q^{11} +(0.204875 - 0.204875i) q^{13} +(2.89039 + 3.47617i) q^{15} +(-1.97024 + 0.527924i) q^{17} +(3.10166 + 5.37224i) q^{19} +(-2.75092 + 4.58757i) q^{21} +(-1.17456 + 4.38350i) q^{23} +(3.24817 - 3.80124i) q^{25} +(-2.73397 - 2.73397i) q^{27} +7.15869i q^{29} +(-6.33287 - 3.65628i) q^{31} +(7.88965 + 2.11403i) q^{33} +(5.51548 + 2.13996i) q^{35} +(-4.46814 - 1.19723i) q^{37} +(-0.507306 - 0.292893i) q^{39} -2.58745i q^{41} +(4.97801 + 4.97801i) q^{43} +(1.40386 - 1.98590i) q^{45} +(0.0815604 - 0.304388i) q^{47} +(-0.231803 + 6.99616i) q^{49} +(2.06196 + 3.57142i) q^{51} +(-8.00039 + 2.14370i) q^{53} +(0.827689 - 8.99566i) q^{55} +(8.86840 - 8.86840i) q^{57} +(-0.427702 + 0.740802i) q^{59} +(-5.99356 + 3.46038i) q^{61} +(2.76682 + 0.790700i) q^{63} +(-0.224313 + 0.607800i) q^{65} +(0.817530 + 3.05106i) q^{67} +9.17514 q^{69} -7.12240 q^{71} +(-2.98311 - 11.1331i) q^{73} +(-9.12312 - 4.35423i) q^{75} +(10.3690 - 2.59511i) q^{77} +(4.39618 - 2.53813i) q^{79} +(-5.53997 + 9.59552i) q^{81} +(3.85372 - 3.85372i) q^{83} +(3.50704 - 2.91605i) q^{85} +(13.9802 - 3.74598i) q^{87} +(-1.53615 - 2.66069i) q^{89} +(-0.766467 - 0.0126942i) q^{91} +(-3.82650 + 14.2807i) q^{93} +(-11.3267 - 8.00700i) q^{95} +(-6.63103 - 6.63103i) q^{97} -4.39398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} - 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 - 8 * q^7	\( 16 q - 12 q^{5} - 8 q^{7} + 12 q^{11} - 16 q^{15} - 36 q^{17} - 28 q^{21} + 4 q^{23} + 12 q^{25} - 24 q^{31} + 48 q^{33} - 8 q^{35} + 4 q^{37} + 8 q^{43} - 12 q^{45} - 12 q^{47} + 16 q^{51} - 28 q^{53} + 8 q^{57} - 12 q^{61} + 36 q^{63} - 8 q^{65} - 32 q^{67} - 16 q^{71} - 12 q^{73} + 48 q^{75} + 16 q^{77} + 24 q^{85} + 24 q^{87} + 16 q^{91} + 28 q^{93} - 20 q^{95}+O(q^{100}) \) 16 * q - 12 * q^5 - 8 * q^7 + 12 * q^11 - 16 * q^15 - 36 * q^17 - 28 * q^21 + 4 * q^23 + 12 * q^25 - 24 * q^31 + 48 * q^33 - 8 * q^35 + 4 * q^37 + 8 * q^43 - 12 * q^45 - 12 * q^47 + 16 * q^51 - 28 * q^53 + 8 * q^57 - 12 * q^61 + 36 * q^63 - 8 * q^65 - 32 * q^67 - 16 * q^71 - 12 * q^73 + 48 * q^75 + 16 * q^77 + 24 * q^85 + 24 * q^87 + 16 * q^91 + 28 * q^93 - 20 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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