LMFDB - Embedded newform 756.2.bq.a.25.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(25,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10, 12]))

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

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

chi := DirichletCharacter("756.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bq (of order $9$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.12
Character	$\chi$	$=$	756.25
Dual form			756.2.bq.a.121.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0456125 + 1.73145i) q^{3} +(2.25335 + 0.820154i) q^{5} +(-0.197469 - 2.63837i) q^{7} +(-2.99584 - 0.157952i) q^{9} +O(q^{10})$	\(q+(-0.0456125 + 1.73145i) q^{3} +(2.25335 + 0.820154i) q^{5} +(-0.197469 - 2.63837i) q^{7} +(-2.99584 - 0.157952i) q^{9} +(-0.101929 + 0.0370992i) q^{11} +(1.18564 + 6.72408i) q^{13} +(-1.52284 + 3.86416i) q^{15} +4.20368 q^{17} +1.48747 q^{19} +(4.57722 - 0.221565i) q^{21} +(1.45565 + 8.25539i) q^{23} +(0.574733 + 0.482259i) q^{25} +(0.410133 - 5.17994i) q^{27} +(0.608337 - 3.45005i) q^{29} +(1.82648 - 1.53260i) q^{31} +(-0.0595861 - 0.178177i) q^{33} +(1.71890 - 6.10714i) q^{35} +(-4.36645 + 7.56291i) q^{37} +(-11.6965 + 1.74617i) q^{39} +(0.990121 + 5.61525i) q^{41} +(0.908317 + 0.762168i) q^{43} +(-6.62114 - 2.81297i) q^{45} +(-3.90179 - 3.27399i) q^{47} +(-6.92201 + 1.04199i) q^{49} +(-0.191741 + 7.27847i) q^{51} +(3.18200 - 5.51139i) q^{53} -0.260110 q^{55} +(-0.0678472 + 2.57548i) q^{57} +(-1.26170 - 7.15548i) q^{59} +(6.37701 + 5.35095i) q^{61} +(0.174850 + 7.93533i) q^{63} +(-2.84312 + 16.1241i) q^{65} +(-3.94935 - 1.43745i) q^{67} +(-14.3602 + 2.14383i) q^{69} +(-4.13196 - 7.15676i) q^{71} +(6.86088 + 11.8834i) q^{73} +(-0.861222 + 0.973125i) q^{75} +(0.118009 + 0.261601i) q^{77} +(4.75591 - 1.73101i) q^{79} +(8.95010 + 0.946396i) q^{81} +(3.11284 - 17.6538i) q^{83} +(9.47239 + 3.44767i) q^{85} +(5.94585 + 1.21067i) q^{87} -13.3726 q^{89} +(17.5065 - 4.45595i) q^{91} +(2.57031 + 3.23236i) q^{93} +(3.35179 + 1.21995i) q^{95} +(6.78522 + 5.69348i) q^{97} +(0.311223 - 0.0950433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0456125	+	1.73145i	−0.0263344	+	0.999653i
$3$	−0.0456125	+	1.73145i	−0.0263344	+	0.999653i
$4$		0			0
$5$	2.25335	+	0.820154i	1.00773	+	0.366784i	0.792561	−	0.609793i	$-0.208747\pi$
$5$	2.25335	+	0.820154i	1.00773	+	0.366784i	0.215170	+	0.976577i	$0.430969\pi$
$6$		0			0
$7$	−0.197469	−	2.63837i	−0.0746363	−	0.997211i
$7$	−0.197469	−	2.63837i	−0.0746363	−	0.997211i
$8$		0			0
$9$	−2.99584	−	0.157952i	−0.998613	−	0.0526506i
$10$		0			0
$11$	−0.101929	+	0.0370992i	−0.0307328	+	0.0111858i	−0.357341	−	0.933974i	$-0.616317\pi$
$11$	−0.101929	+	0.0370992i	−0.0307328	+	0.0111858i	0.326608	+	0.945160i	$0.394094\pi$
$12$		0			0
$13$	1.18564	+	6.72408i	0.328836	+	1.86492i	0.481216	+	0.876602i	$0.340195\pi$
$13$	1.18564	+	6.72408i	0.328836	+	1.86492i	−0.152379	+	0.988322i	$0.548694\pi$
$14$		0			0
$15$	−1.52284	+	3.86416i	−0.393195	+	0.997722i
$16$		0			0
$17$	4.20368			1.01954			0.509771	−	0.860310i	$-0.329730\pi$
$17$	4.20368			1.01954			0.509771	+	0.860310i	$0.329730\pi$
$18$		0			0
$19$	1.48747			0.341249			0.170624	−	0.985336i	$-0.445422\pi$
$19$	1.48747			0.341249			0.170624	+	0.985336i	$0.445422\pi$
$20$		0			0
$21$	4.57722	−	0.221565i	0.998830	−	0.0483494i
$22$		0			0
$23$	1.45565	+	8.25539i	0.303524	+	1.72137i	0.630373	+	0.776292i	$0.282902\pi$
$23$	1.45565	+	8.25539i	0.303524	+	1.72137i	−0.326849	+	0.945076i	$0.605987\pi$
$24$		0			0
$25$	0.574733	+	0.482259i	0.114947	+	0.0964517i
$26$		0			0
$27$	0.410133	−	5.17994i	0.0789302	−	0.996880i
$28$		0			0
$29$	0.608337	−	3.45005i	0.112965	−	0.640659i	−0.874772	−	0.484535i	$-0.838989\pi$
$29$	0.608337	−	3.45005i	0.112965	−	0.640659i	0.987737	−	0.156124i	$-0.0499000\pi$
$30$		0			0
$31$	1.82648	−	1.53260i	0.328045	−	0.275263i	−0.463857	−	0.885910i	$-0.653535\pi$
$31$	1.82648	−	1.53260i	0.328045	−	0.275263i	0.791903	+	0.610647i	$0.209091\pi$
$32$		0			0
$33$	−0.0595861	−	0.178177i	−0.0103726	−	0.0310167i
$34$		0			0
$35$	1.71890	−	6.10714i	0.290548	−	1.03230i
$36$		0			0
$37$	−4.36645	+	7.56291i	−0.717840	+	1.24334i	0.244014	+	0.969772i	$0.421536\pi$
$37$	−4.36645	+	7.56291i	−0.717840	+	1.24334i	−0.961854	+	0.273564i	$0.911798\pi$
$38$		0			0
$39$	−11.6965	+	1.74617i	−1.87294	+	0.279611i
$40$		0			0
$41$	0.990121	+	5.61525i	0.154631	+	0.876955i	0.959122	+	0.282991i	$0.0913268\pi$
$41$	0.990121	+	5.61525i	0.154631	+	0.876955i	−0.804492	+	0.593964i	$0.797562\pi$
$42$		0			0
$43$	0.908317	+	0.762168i	0.138517	+	0.116230i	0.709414	−	0.704792i	$-0.248960\pi$
$43$	0.908317	+	0.762168i	0.138517	+	0.116230i	−0.570897	+	0.821022i	$0.693404\pi$
$44$		0			0
$45$	−6.62114	−	2.81297i	−0.987022	−	0.419333i
$46$		0			0
$47$	−3.90179	−	3.27399i	−0.569135	−	0.477561i	0.312224	−	0.950009i	$-0.398926\pi$
$47$	−3.90179	−	3.27399i	−0.569135	−	0.477561i	−0.881359	+	0.472448i	$0.843371\pi$
$48$		0			0
$49$	−6.92201	+	1.04199i	−0.988859	+	0.148856i
$50$		0			0
$51$	−0.191741	+	7.27847i	−0.0268491	+	1.01919i
$52$		0			0
$53$	3.18200	−	5.51139i	0.437082	−	0.757048i	−0.560381	−	0.828235i	$-0.689345\pi$
$53$	3.18200	−	5.51139i	0.437082	−	0.757048i	0.997463	+	0.0711869i	$0.0226787\pi$
$54$		0			0
$55$	−0.260110			−0.0350732
$56$		0			0
$57$	−0.0678472	+	2.57548i	−0.00898658	+	0.341130i
$58$		0			0
$59$	−1.26170	−	7.15548i	−0.164260	−	0.931564i	−0.949824	−	0.312784i	$-0.898738\pi$
$59$	−1.26170	−	7.15548i	−0.164260	−	0.931564i	0.785564	−	0.618780i	$-0.212373\pi$
$60$		0			0
$61$	6.37701	+	5.35095i	0.816492	+	0.685118i	0.952148	−	0.305638i	$-0.0988696\pi$
$61$	6.37701	+	5.35095i	0.816492	+	0.685118i	−0.135656	+	0.990756i	$0.543314\pi$
$62$		0			0
$63$	0.174850	+	7.93533i	0.0220290	+	0.999757i
$64$		0			0
$65$	−2.84312	+	16.1241i	−0.352646	+	1.99995i
$66$		0			0
$67$	−3.94935	−	1.43745i	−0.482490	−	0.175612i	0.0893117	−	0.996004i	$-0.471533\pi$
$67$	−3.94935	−	1.43745i	−0.482490	−	0.175612i	−0.571802	+	0.820392i	$0.693755\pi$
$68$		0			0
$69$	−14.3602	+	2.14383i	−1.72876	+	0.258087i
$70$		0			0
$71$	−4.13196	−	7.15676i	−0.490373	−	0.849351i	0.509565	−	0.860432i	$-0.329806\pi$
$71$	−4.13196	−	7.15676i	−0.490373	−	0.849351i	−0.999939	+	0.0110807i	$0.996473\pi$
$72$		0			0
$73$	6.86088	+	11.8834i	0.803005	+	1.39085i	0.917630	+	0.397437i	$0.130100\pi$
$73$	6.86088	+	11.8834i	0.803005	+	1.39085i	−0.114624	+	0.993409i	$0.536566\pi$
$74$		0			0
$75$	−0.861222	+	0.973125i	−0.0994453	+	0.112367i
$76$		0			0
$77$	0.118009	+	0.261601i	0.0134484	+	0.0298122i
$78$		0			0
$79$	4.75591	−	1.73101i	0.535082	−	0.194754i	−0.0603239	−	0.998179i	$-0.519213\pi$
$79$	4.75591	−	1.73101i	0.535082	−	0.194754i	0.595406	+	0.803425i	$0.296991\pi$
$80$		0			0
$81$	8.95010	+	0.946396i	0.994456	+	0.105155i
$82$		0			0
$83$	3.11284	−	17.6538i	0.341679	−	1.93776i	−0.00557061	−	0.999984i	$-0.501773\pi$
$83$	3.11284	−	17.6538i	0.341679	−	1.93776i	0.347249	−	0.937773i	$-0.387116\pi$
$84$		0			0
$85$	9.47239	+	3.44767i	1.02742	+	0.373952i
$86$		0			0
$87$	5.94585	+	1.21067i	0.637462	+	0.129798i
$88$		0			0
$89$	−13.3726			−1.41749			−0.708745	−	0.705465i	$-0.750738\pi$
$89$	−13.3726			−1.41749			−0.708745	+	0.705465i	$0.750738\pi$
$90$		0			0
$91$	17.5065	−	4.45595i	1.83518	−	0.467110i
$92$		0			0
$93$	2.57031	+	3.23236i	0.266528	+	0.335181i
$94$		0			0
$95$	3.35179	+	1.21995i	0.343887	+	0.125165i
$96$		0			0
$97$	6.78522	+	5.69348i	0.688935	+	0.578085i	0.918602	−	0.395184i	$-0.129319\pi$
$97$	6.78522	+	5.69348i	0.688935	+	0.578085i	−0.229667	+	0.973269i	$0.573764\pi$
$98$		0			0
$99$	0.311223	−	0.0950433i	0.0312791	−	0.00955221i
$100$		0			0
$101$	0.976297	−	5.53685i	0.0971451	−	0.550937i	−0.896924	−	0.442185i	$-0.854203\pi$
$101$	0.976297	−	5.53685i	0.0971451	−	0.550937i	0.994069	−	0.108752i	$-0.0346855\pi$
$102$		0			0
$103$	−4.26466	−	1.55221i	−0.420209	−	0.152944i	0.123257	−	0.992375i	$-0.460666\pi$
$103$	−4.26466	−	1.55221i	−0.420209	−	0.152944i	−0.543466	+	0.839431i	$0.682888\pi$
$104$		0			0
$105$	10.4958	+	3.25476i	1.02429	+	0.317632i
$106$		0			0
$107$	−1.71725	−	2.97436i	−0.166013	−	0.287542i	0.771002	−	0.636833i	$-0.219756\pi$
$107$	−1.71725	−	2.97436i	−0.166013	−	0.287542i	−0.937014	+	0.349291i	$0.886423\pi$
$108$		0			0
$109$	6.07605	−	10.5240i	0.581980	−	1.00802i	−0.413265	−	0.910611i	$-0.635612\pi$
$109$	6.07605	−	10.5240i	0.581980	−	1.00802i	0.995245	−	0.0974075i	$-0.0310550\pi$
$110$		0			0
$111$	−12.8956	−	7.90526i	−1.22400	−	0.750334i
$112$		0			0
$113$	4.91523	−	4.12437i	0.462386	−	0.387988i	−0.381622	−	0.924319i	$-0.624634\pi$
$113$	4.91523	−	4.12437i	0.462386	−	0.387988i	0.844008	+	0.536330i	$0.180190\pi$
$114$		0			0
$115$	−3.49060	+	19.7962i	−0.325500	+	1.84600i
$116$		0			0
$117$	−2.48990	−	20.3315i	−0.230191	−	1.87965i
$118$		0			0
$119$	−0.830097	−	11.0909i	−0.0760949	−	1.01670i
$120$		0			0
$121$	−8.41748	+	7.06310i	−0.765225	+	0.642100i
$122$		0			0
$123$	−9.76769	+	1.45822i	−0.880723	+	0.131483i
$124$		0			0
$125$	−5.09537	−	8.82545i	−0.455744	−	0.789372i
$126$		0			0
$127$	−2.35385	+	4.07699i	−0.208870	+	0.361774i	−0.951359	−	0.308085i	$-0.900312\pi$
$127$	−2.35385	+	4.07699i	−0.208870	+	0.361774i	0.742489	+	0.669859i	$0.233645\pi$
$128$		0			0
$129$	−1.36109	+	1.53794i	−0.119837	+	0.135408i
$130$		0			0
$131$	−0.0240379	−	0.136326i	−0.00210020	−	0.0119108i	0.983740	−	0.179600i	$-0.0574805\pi$
$131$	−0.0240379	−	0.136326i	−0.00210020	−	0.0119108i	−0.985840	+	0.167690i	$0.946369\pi$
$132$		0			0
$133$	−0.293729	−	3.92449i	−0.0254695	−	0.340297i
$134$		0			0
$135$	5.17253	−	11.3359i	0.445180	−	0.975637i
$136$		0			0
$137$	0.701983	+	0.589033i	0.0599744	+	0.0503245i	0.672282	−	0.740295i	$-0.265314\pi$
$137$	0.701983	+	0.589033i	0.0599744	+	0.0503245i	−0.612308	+	0.790620i	$0.709759\pi$
$138$		0			0
$139$	−14.5315	−	5.28903i	−1.23255	−	0.448610i	−0.358077	−	0.933692i	$-0.616567\pi$
$139$	−14.5315	−	5.28903i	−1.23255	−	0.448610i	−0.874469	+	0.485082i	$0.838790\pi$
$140$		0			0
$141$	5.84672	−	6.60642i	0.492383	−	0.556361i
$142$		0			0
$143$	−0.370309	−	0.641394i	−0.0309668	−	0.0536360i
$144$		0			0
$145$	4.20038	−	7.27526i	0.348822	−	0.604178i
$146$		0			0
$147$	−1.48843	−	12.0326i	−0.122764	−	0.992436i
$148$		0			0
$149$	15.6633	−	13.1431i	1.28319	−	1.07672i	0.290395	−	0.956907i	$-0.406213\pi$
$149$	15.6633	−	13.1431i	1.28319	−	1.07672i	0.992796	−	0.119818i	$-0.0382311\pi$
$150$		0			0
$151$	1.09180	−	0.397383i	0.0888495	−	0.0323386i	−0.297213	−	0.954811i	$-0.596057\pi$
$151$	1.09180	−	0.397383i	0.0888495	−	0.0323386i	0.386062	+	0.922473i	$0.373835\pi$
$152$		0			0
$153$	−12.5936	−	0.663979i	−1.01813	−	0.0536795i
$154$		0			0
$155$	5.37267	−	1.95549i	0.431543	−	0.157069i
$156$		0			0
$157$	−3.47536	−	19.7097i	−0.277364	−	1.57301i	−0.731351	−	0.682001i	$-0.761110\pi$
$157$	−3.47536	−	19.7097i	−0.277364	−	1.57301i	0.453987	−	0.891008i	$-0.350001\pi$
$158$		0			0
$159$	9.39756	+	5.76087i	0.745275	+	0.456867i
$160$		0			0
$161$	21.4934	−	5.47073i	1.69391	−	0.431154i
$162$		0			0
$163$	5.65790	+	9.79977i	0.443161	+	0.767577i	0.997922	−	0.0644325i	$-0.0205237\pi$
$163$	5.65790	+	9.79977i	0.443161	+	0.767577i	−0.554761	+	0.832010i	$0.687190\pi$
$164$		0			0
$165$	0.0118643	−	0.450367i	0.000923631	−	0.0350610i
$166$		0			0
$167$	5.41506	−	4.54377i	0.419030	−	0.351608i	−0.408764	−	0.912640i	$-0.634040\pi$
$167$	5.41506	−	4.54377i	0.419030	−	0.351608i	0.827794	+	0.561032i	$0.189596\pi$
$168$		0			0
$169$	−31.5915	+	11.4984i	−2.43012	+	0.884490i
$170$		0			0
$171$	−4.45621	−	0.234948i	−0.340775	−	0.0179669i
$172$		0			0
$173$	−0.669420	+	3.79647i	−0.0508951	+	0.288640i	−0.999623	−	0.0274533i	$-0.991260\pi$
$173$	−0.669420	+	3.79647i	−0.0508951	+	0.288640i	0.948728	+	0.316094i	$0.102371\pi$
$174$		0			0
$175$	1.15889	−	1.61159i	0.0876035	−	0.121825i
$176$		0			0
$177$	12.4469	−	1.85820i	0.935566	−	0.139671i
$178$		0			0
$179$	23.2874			1.74058			0.870290	−	0.492540i	$-0.163931\pi$
$179$	23.2874			1.74058			0.870290	+	0.492540i	$0.163931\pi$
$180$		0			0
$181$	1.88836	−	3.27073i	0.140361	−	0.243112i	−0.787272	−	0.616606i	$-0.788507\pi$
$181$	1.88836	−	3.27073i	0.140361	−	0.243112i	0.927632	+	0.373494i	$0.121840\pi$
$182$		0			0
$183$	−9.55577	+	10.7974i	−0.706383	+	0.798167i
$184$		0			0
$185$	−16.0419	+	13.4608i	−1.17943	+	0.989655i
$186$		0			0
$187$	−0.428478	+	0.155953i	−0.0313334	+	0.0114044i
$188$		0			0
$189$	−13.7476	−	0.0592062i	−0.999991	−	0.00430662i
$190$		0			0
$191$	−8.72685	+	3.17631i	−0.631453	+	0.229830i	−0.637863	−	0.770149i	$-0.720182\pi$
$191$	−8.72685	+	3.17631i	−0.631453	+	0.229830i	0.00641078	+	0.999979i	$0.497959\pi$
$192$		0			0
$193$	10.8209	−	9.07984i	0.778907	−	0.653581i	−0.164066	−	0.986449i	$-0.552461\pi$
$193$	10.8209	−	9.07984i	0.778907	−	0.653581i	0.942973	+	0.332869i	$0.108017\pi$
$194$		0			0
$195$	−27.7885	−	5.65819i	−1.98997	−	0.405191i
$196$		0			0
$197$	−4.50444	+	7.80191i	−0.320928	+	0.555863i	−0.980680	−	0.195620i	$-0.937328\pi$
$197$	−4.50444	+	7.80191i	−0.320928	+	0.555863i	0.659752	+	0.751483i	$0.270661\pi$
$198$		0			0
$199$	24.1799			1.71407			0.857034	−	0.515260i	$-0.172305\pi$
$199$	24.1799			1.71407			0.857034	+	0.515260i	$0.172305\pi$
$200$		0			0
$201$	2.66901	−	6.77254i	0.188257	−	0.477698i
$202$		0			0
$203$	−9.22265	−	0.923742i	−0.647303	−	0.0648340i
$204$		0			0
$205$	−2.37428	+	13.4652i	−0.165827	+	0.940451i
$206$		0			0
$207$	−3.05694	−	24.9618i	−0.212472	−	1.73496i
$208$		0			0
$209$	−0.151616	+	0.0551838i	−0.0104875	+	0.00381715i
$210$		0			0
$211$	−4.02124	+	3.37422i	−0.276833	+	0.232291i	−0.770624	−	0.637290i	$-0.780055\pi$
$211$	−4.02124	+	3.37422i	−0.276833	+	0.232291i	0.493791	+	0.869581i	$0.335611\pi$
$212$		0			0
$213$	12.5800	−	6.82784i	0.861970	−	0.467836i
$214$		0			0
$215$	1.42166	+	2.46239i	0.0969567	+	0.167934i
$216$		0			0
$217$	−4.40424	−	4.51629i	−0.298979	−	0.306586i
$218$		0			0
$219$	−20.8884	+	11.3372i	−1.41151	+	0.766100i
$220$		0			0
$221$	4.98404	+	28.2659i	0.335263	+	1.90137i
$222$		0			0
$223$	0.418474	−	0.152312i	0.0280231	−	0.0101996i	−0.327971	−	0.944688i	$-0.606365\pi$
$223$	0.418474	−	0.152312i	0.0280231	−	0.0101996i	0.355994	+	0.934488i	$0.384142\pi$
$224$		0			0
$225$	−1.64564	−	1.53555i	−0.109709	−	0.102370i
$226$		0			0
$227$	−12.9064	+	4.69754i	−0.856628	+	0.311787i	−0.732739	−	0.680509i	$-0.761759\pi$
$227$	−12.9064	+	4.69754i	−0.856628	+	0.311787i	−0.123888	+	0.992296i	$0.539536\pi$
$228$		0			0
$229$	14.0449	−	11.7851i	0.928114	−	0.778780i	−0.0473643	−	0.998878i	$-0.515082\pi$
$229$	14.0449	−	11.7851i	0.928114	−	0.778780i	0.975478	+	0.220098i	$0.0706377\pi$
$230$		0			0
$231$	−0.458332	+	0.192395i	−0.0301560	+	0.0126587i
$232$		0			0
$233$	9.65552	−	16.7238i	0.632554	−	1.09562i	−0.354474	−	0.935066i	$-0.615340\pi$
$233$	9.65552	−	16.7238i	0.632554	−	1.09562i	0.987028	−	0.160549i	$-0.0513266\pi$
$234$		0			0
$235$	−6.10694	−	10.5775i	−0.398373	−	0.690002i
$236$		0			0
$237$	2.78023	+	8.31359i	0.180595	+	0.540025i
$238$		0			0
$239$	−1.80124	−	0.655599i	−0.116513	−	0.0424072i	0.283106	−	0.959089i	$-0.408635\pi$
$239$	−1.80124	−	0.655599i	−0.116513	−	0.0424072i	−0.399619	+	0.916681i	$0.630857\pi$
$240$		0			0
$241$	−14.5492	−	12.2082i	−0.937195	−	0.786400i	0.0399001	−	0.999204i	$-0.487296\pi$
$241$	−14.5492	−	12.2082i	−0.937195	−	0.786400i	−0.977095	+	0.212804i	$0.931740\pi$
$242$		0			0
$243$	−2.04687	+	15.4535i	−0.131307	+	0.991342i
$244$		0			0
$245$	−16.4523	−	3.32914i	−1.05110	−	0.212691i
$246$		0			0
$247$	1.76360	+	10.0019i	0.112215	+	0.636403i
$248$		0			0
$249$	30.4247	+	6.19497i	1.92809	+	0.392590i
$250$		0			0
$251$	2.32477	−	4.02663i	0.146738	−	0.254158i	−0.783282	−	0.621667i	$-0.786456\pi$
$251$	2.32477	−	4.02663i	0.146738	−	0.254158i	0.930020	+	0.367508i	$0.119789\pi$
$252$		0			0
$253$	−0.454641	−	0.787462i	−0.0285831	−	0.0495073i
$254$		0			0
$255$	−6.40152	+	16.2437i	−0.400879	+	1.01722i
$256$		0			0
$257$	15.3947	−	12.9177i	0.960296	−	0.805784i	−0.0207050	−	0.999786i	$-0.506591\pi$
$257$	15.3947	−	12.9177i	0.960296	−	0.805784i	0.981001	+	0.194001i	$0.0621466\pi$
$258$		0			0
$259$	20.8160	+	10.0269i	1.29344	+	0.623040i
$260$		0			0
$261$	−2.36742	+	10.2397i	−0.146540	+	0.633823i
$262$		0			0
$263$	2.62008	−	14.8592i	0.161561	−	0.916258i	−0.790979	−	0.611843i	$-0.790428\pi$
$263$	2.62008	−	14.8592i	0.161561	−	0.916258i	0.952540	−	0.304414i	$-0.0984607\pi$
$264$		0			0
$265$	11.6904	−	9.80939i	0.718134	−	0.602586i
$266$		0			0
$267$	0.609957	−	23.1539i	0.0373288	−	1.41700i
$268$		0			0
$269$	−0.0124310	+	0.0215312i	−0.000757933	+	0.00131278i	−0.866404	−	0.499343i	$-0.833575\pi$
$269$	−0.0124310	+	0.0215312i	−0.000757933	+	0.00131278i	0.865646	+	0.500656i	$0.166908\pi$
$270$		0			0
$271$	−10.0401	−	17.3899i	−0.609892	−	1.05636i	−0.991258	−	0.131939i	$-0.957880\pi$
$271$	−10.0401	−	17.3899i	−0.609892	−	1.05636i	0.381366	−	0.924424i	$-0.375454\pi$
$272$		0			0
$273$	6.91674	+	30.5149i	0.418620	+	1.84684i
$274$		0			0
$275$	−0.0764735	−	0.0278341i	−0.00461152	−	0.00167846i
$276$		0			0
$277$	−0.707885	+	4.01462i	−0.0425327	+	0.241215i	−0.998661	−	0.0517336i	$-0.983525\pi$
$277$	−0.707885	+	4.01462i	−0.0425327	+	0.241215i	0.956128	+	0.292948i	$0.0946364\pi$
$278$		0			0
$279$	−5.71391	+	4.30292i	−0.342083	+	0.257609i
$280$		0			0
$281$	2.80901	+	2.35704i	0.167571	+	0.140609i	0.722717	−	0.691144i	$-0.242893\pi$
$281$	2.80901	+	2.35704i	0.167571	+	0.140609i	−0.555146	+	0.831753i	$0.687337\pi$
$282$		0			0
$283$	−21.4307	−	7.80012i	−1.27392	−	0.463669i	−0.385504	−	0.922706i	$-0.625972\pi$
$283$	−21.4307	−	7.80012i	−1.27392	−	0.463669i	−0.888417	+	0.459037i	$0.848195\pi$
$284$		0			0
$285$	−2.26517	+	5.74782i	−0.134177	+	0.340471i
$286$		0			0
$287$	14.6196	−	3.72115i	0.862968	−	0.219652i
$288$		0			0
$289$	0.670948			0.0394675
$290$		0			0
$291$	−10.1675	+	11.4886i	−0.596027	+	0.673472i
$292$		0			0
$293$	−29.8516	−	10.8651i	−1.74395	−	0.634746i	−0.744492	−	0.667632i	$-0.767308\pi$
$293$	−29.8516	−	10.8651i	−1.74395	−	0.634746i	−0.999459	+	0.0328857i	$0.989530\pi$
$294$		0			0
$295$	3.02553	−	17.1586i	0.176153	−	0.999013i
$296$		0			0
$297$	0.150367	+	0.543203i	0.00872518	+	0.0315198i
$298$		0			0
$299$	−53.7841	+	19.5758i	−3.11041	+	1.13210i
$300$		0			0
$301$	1.83152	−	2.54698i	0.105567	−	0.146806i
$302$		0			0
$303$	9.54225	+	1.94296i	0.548188	+	0.111620i
$304$		0			0
$305$	9.98106	+	17.2877i	0.571514	+	0.989891i
$306$		0			0
$307$	1.51123	+	2.61753i	0.0862505	+	0.149390i	0.905923	−	0.423442i	$-0.139178\pi$
$307$	1.51123	+	2.61753i	0.0862505	+	0.149390i	−0.819673	+	0.572832i	$0.805845\pi$
$308$		0			0
$309$	2.88209	−	7.31324i	0.163957	−	0.416036i
$310$		0			0
$311$	0.00501264	+	0.00182445i	0.000284241	+	0.000103455i	0.342162	−	0.939641i	$-0.388841\pi$
$311$	0.00501264	+	0.00182445i	0.000284241	+	0.000103455i	−0.341878	+	0.939744i	$0.611063\pi$
$312$		0			0
$313$	−1.83706	+	10.4185i	−0.103837	+	0.588889i	0.887841	+	0.460149i	$0.152204\pi$
$313$	−1.83706	+	10.4185i	−0.103837	+	0.588889i	−0.991678	+	0.128739i	$0.958907\pi$
$314$		0			0
$315$	−6.11419	+	18.0245i	−0.344496	+	1.01557i
$316$		0			0
$317$	20.0172	+	16.7964i	1.12428	+	0.943381i	0.998813	−	0.0487165i	$-0.0155131\pi$
$317$	20.0172	+	16.7964i	1.12428	+	0.943381i	0.125466	+	0.992098i	$0.459958\pi$
$318$		0			0
$319$	0.0659868	+	0.374230i	0.00369455	+	0.0209528i
$320$		0			0
$321$	5.22828	−	2.83766i	0.291814	−	0.158383i
$322$		0			0
$323$	6.25284			0.347918
$324$		0			0
$325$	−2.56132	+	4.43634i	−0.142076	+	0.246084i
$326$		0			0
$327$	17.9447	+	11.0004i	0.992343	+	0.608323i
$328$		0			0
$329$	−7.86752	+	10.9409i	−0.433751	+	0.603191i
$330$		0			0
$331$	14.0382	+	11.7795i	0.771612	+	0.647459i	0.941121	−	0.338069i	$-0.109774\pi$
$331$	14.0382	+	11.7795i	0.771612	+	0.647459i	−0.169509	+	0.985529i	$0.554218\pi$
$332$		0			0
$333$	14.2758	−	21.9676i	0.782307	−	1.20382i
$334$		0			0
$335$	−7.72037	−	6.47816i	−0.421809	−	0.353940i
$336$		0			0
$337$	−4.24322	−	24.0645i	−0.231143	−	1.31088i	−0.850586	−	0.525836i	$-0.823753\pi$
$337$	−4.24322	−	24.0645i	−0.231143	−	1.31088i	0.619443	−	0.785042i	$-0.287359\pi$
$338$		0			0
$339$	6.91694	+	8.69860i	0.375677	+	0.472443i
$340$		0			0
$341$	−0.129313	+	0.223977i	−0.00700271	+	0.0121291i
$342$		0			0
$343$	4.11605	+	18.0571i	0.222246	+	0.974991i
$344$		0			0
$345$	−34.1169	−	6.94676i	−1.83679	−	0.374001i
$346$		0			0
$347$	7.14977	−	5.99937i	0.383820	−	0.322063i	−0.430380	−	0.902648i	$-0.641620\pi$
$347$	7.14977	−	5.99937i	0.383820	−	0.322063i	0.814200	+	0.580585i	$0.197176\pi$
$348$		0			0
$349$	−2.88546	+	16.3643i	−0.154455	+	0.875959i	0.804827	+	0.593510i	$0.202258\pi$
$349$	−2.88546	+	16.3643i	−0.154455	+	0.875959i	−0.959282	+	0.282450i	$0.908853\pi$
$350$		0			0
$351$	35.3166	−	3.38376i	1.88506	−	0.180612i
$352$		0			0
$353$	6.54243	+	5.48975i	0.348218	+	0.292190i	0.800074	−	0.599901i	$-0.204793\pi$
$353$	6.54243	+	5.48975i	0.348218	+	0.292190i	−0.451856	+	0.892091i	$0.649238\pi$
$354$		0			0
$355$	−3.44112	−	19.5156i	−0.182636	−	1.03578i
$356$		0			0
$357$	19.2412	−	0.931389i	1.01835	−	0.0492943i
$358$		0			0
$359$	−24.8713			−1.31265			−0.656327	−	0.754476i	$-0.727891\pi$
$359$	−24.8713			−1.31265			−0.656327	+	0.754476i	$0.727891\pi$
$360$		0			0
$361$	−16.7874			−0.883549
$362$		0			0
$363$	−11.8455	−	14.8966i	−0.621726	−	0.781869i
$364$		0			0
$365$	5.71378	+	32.4045i	0.299073	+	1.69613i
$366$		0			0
$367$	−29.5186	+	10.7439i	−1.54086	+	0.560827i	−0.966251	−	0.257603i	$-0.917067\pi$
$367$	−29.5186	+	10.7439i	−1.54086	+	0.560827i	−0.574607	+	0.818429i	$0.694845\pi$
$368$		0			0
$369$	−2.07930	−	16.9788i	−0.108244	−	0.883880i
$370$		0			0
$371$	−15.1694	−	7.30698i	−0.787559	−	0.379359i
$372$		0			0
$373$	17.5233	+	6.37796i	0.907322	+	0.330238i	0.753183	−	0.657811i	$-0.228517\pi$
$373$	17.5233	+	6.37796i	0.907322	+	0.330238i	0.154139	+	0.988049i	$0.450740\pi$
$374$		0			0
$375$	15.5132	−	8.41983i	0.801100	−	0.434798i
$376$		0			0
$377$	23.9197			1.23193
$378$		0			0
$379$	−12.6614			−0.650375			−0.325187	−	0.945650i	$-0.605427\pi$
$379$	−12.6614			−0.650375			−0.325187	+	0.945650i	$0.605427\pi$
$380$		0			0
$381$	−6.95174	−	4.26154i	−0.356148	−	0.218325i
$382$		0			0
$383$	16.9975	+	6.18657i	0.868530	+	0.316119i	0.737572	−	0.675269i	$-0.235972\pi$
$383$	16.9975	+	6.18657i	0.868530	+	0.316119i	0.130958	+	0.991388i	$0.458195\pi$
$384$		0			0
$385$	0.0513636	+	0.686266i	0.00261773	+	0.0349753i
$386$		0			0
$387$	−2.60078	−	2.42680i	−0.132205	−	0.123361i
$388$		0			0
$389$	2.90947	−	1.05896i	0.147516	−	0.0536914i	−0.267207	−	0.963639i	$-0.586101\pi$
$389$	2.90947	−	1.05896i	0.147516	−	0.0536914i	0.414723	+	0.909948i	$0.363879\pi$
$390$		0			0
$391$	6.11909	+	34.7031i	0.309455	+	1.75501i
$392$		0			0
$393$	0.237138	−	0.0354023i	0.0119620	−	0.00178581i
$394$		0			0
$395$	12.1365			0.610652
$396$		0			0
$397$	13.5366			0.679381			0.339690	−	0.940537i	$-0.389678\pi$
$397$	13.5366			0.679381			0.339690	+	0.940537i	$0.389678\pi$
$398$		0			0
$399$	6.80846	−	0.329571i	0.340849	−	0.0164992i
$400$		0			0
$401$	6.58952	+	37.3710i	0.329065	+	1.86622i	0.479415	+	0.877588i	$0.340849\pi$
$401$	6.58952	+	37.3710i	0.329065	+	1.86622i	−0.150350	+	0.988633i	$0.548040\pi$
$402$		0			0
$403$	12.4709	+	10.4643i	0.621218	+	0.521263i
$404$		0			0
$405$	19.3916	+	9.47303i	0.963575	+	0.470719i
$406$		0			0
$407$	0.164491	−	0.932873i	0.00815350	−	0.0462408i
$408$		0			0
$409$	−20.8763	+	17.5173i	−1.03227	+	0.866173i	−0.991119	−	0.132980i	$-0.957545\pi$
$409$	−20.8763	+	17.5173i	−1.03227	+	0.866173i	−0.0411465	+	0.999153i	$0.513101\pi$
$410$		0			0
$411$	−1.05190	+	1.18858i	−0.0518864	+	0.0586284i
$412$		0			0
$413$	−18.6297	+	4.74183i	−0.916706	+	0.233330i
$414$		0			0
$415$	21.4932	−	37.2273i	1.05506	−	1.82742i
$416$		0			0
$417$	9.82051	−	24.9193i	0.480913	−	1.22030i
$418$		0			0
$419$	0.00285723	+	0.0162041i	0.000139585	+	0.000791624i	0.984877	−	0.173252i	$-0.0554276\pi$
$419$	0.00285723	+	0.0162041i	0.000139585	+	0.000791624i	−0.984738	+	0.174044i	$0.944317\pi$
$420$		0			0
$421$	−20.0476	−	16.8219i	−0.977061	−	0.819851i	0.00658257	−	0.999978i	$-0.497905\pi$
$421$	−20.0476	−	16.8219i	−0.977061	−	0.819851i	−0.983643	+	0.180127i	$0.942349\pi$
$422$		0			0
$423$	11.1720	+	10.4246i	0.543202	+	0.506864i
$424$		0			0
$425$	2.41600	+	2.02726i	0.117193	+	0.0983366i
$426$		0			0
$427$	12.8585	−	17.8816i	0.622267	−	0.865350i
$428$		0			0
$429$	1.12743	−	0.611916i	0.0544329	−	0.0295436i
$430$		0			0
$431$	−7.90416	+	13.6904i	−0.380730	+	0.659444i	−0.991167	−	0.132621i	$-0.957661\pi$
$431$	−7.90416	+	13.6904i	−0.380730	+	0.659444i	0.610437	+	0.792065i	$0.290994\pi$
$432$		0			0
$433$	19.1952			0.922461			0.461231	−	0.887280i	$-0.347408\pi$
$433$	19.1952			0.922461			0.461231	+	0.887280i	$0.347408\pi$
$434$		0			0
$435$	12.4052	+	7.60458i	0.594782	+	0.364612i
$436$		0			0
$437$	2.16523	+	12.2796i	0.103577	+	0.587415i
$438$		0			0
$439$	24.9517	+	20.9370i	1.19088	+	0.999268i	0.999844	+	0.0176851i	$0.00562964\pi$
$439$	24.9517	+	20.9370i	1.19088	+	0.999268i	0.191037	+	0.981583i	$0.438815\pi$
$440$		0			0
$441$	20.9018	−	2.02830i	0.995325	−	0.0965858i
$442$		0			0
$443$	1.56210	−	8.85914i	0.0742178	−	0.420910i	−0.924949	−	0.380092i	$-0.875892\pi$
$443$	1.56210	−	8.85914i	0.0742178	−	0.420910i	0.999167	−	0.0408184i	$-0.0129965\pi$
$444$		0			0
$445$	−30.1332	−	10.9676i	−1.42845	−	0.519913i
$446$		0			0
$447$	22.0422	+	27.7198i	1.04256	+	1.31110i
$448$		0			0
$449$	−9.97480	−	17.2769i	−0.470740	−	0.815345i	0.528700	−	0.848809i	$-0.322680\pi$
$449$	−9.97480	−	17.2769i	−0.470740	−	0.815345i	−0.999440	+	0.0334634i	$0.989346\pi$
$450$		0			0
$451$	−0.309243	−	0.535625i	−0.0145617	−	0.0252216i
$452$		0			0
$453$	0.638249	+	1.90852i	0.0299875	+	0.0896703i
$454$		0			0
$455$	43.1029	+	4.31719i	2.02070	+	0.202393i
$456$		0			0
$457$	−36.6502	+	13.3396i	−1.71442	+	0.623999i	−0.997333	−	0.0729807i	$-0.976749\pi$
$457$	−36.6502	+	13.3396i	−1.71442	+	0.623999i	−0.717091	+	0.696980i	$0.754527\pi$
$458$		0			0
$459$	1.72407	−	21.7748i	0.0804727	−	1.01636i
$460$		0			0
$461$	−2.67190	+	15.1531i	−0.124443	+	0.705751i	0.857194	+	0.514993i	$0.172206\pi$
$461$	−2.67190	+	15.1531i	−0.124443	+	0.705751i	−0.981637	+	0.190758i	$0.938906\pi$
$462$		0			0
$463$	26.0820	+	9.49308i	1.21213	+	0.441181i	0.867444	−	0.497535i	$-0.165761\pi$
$463$	26.0820	+	9.49308i	1.21213	+	0.441181i	0.344691	+	0.938716i	$0.387984\pi$
$464$		0			0
$465$	3.14078	+	9.39171i	0.145650	+	0.435530i
$466$		0			0
$467$	−24.3758			−1.12798			−0.563988	−	0.825783i	$-0.690734\pi$
$467$	−24.3758			−1.12798			−0.563988	+	0.825783i	$0.690734\pi$
$468$		0			0
$469$	−3.01265	+	10.7037i	−0.139111	+	0.494252i
$470$		0			0
$471$	34.2850	−	5.11840i	1.57977	−	0.235843i
$472$		0			0
$473$	−0.120860	−	0.0439893i	−0.00555714	−	0.00202263i
$474$		0			0
$475$	0.854897	+	0.717344i	0.0392254	+	0.0329140i
$476$		0			0
$477$	−10.4033	+	16.0086i	−0.476335	+	0.732985i
$478$		0			0
$479$	−5.95146	+	33.7524i	−0.271929	+	1.54219i	0.476620	+	0.879109i	$0.341862\pi$
$479$	−5.95146	+	33.7524i	−0.271929	+	1.54219i	−0.748550	+	0.663079i	$0.769249\pi$
$480$		0			0
$481$	−56.0307	−	20.3935i	−2.55478	−	0.929863i
$482$		0			0
$483$	8.49193	+	37.4642i	0.386396	+	1.70468i
$484$		0			0
$485$	10.6200	+	18.3944i	0.482229	+	0.835244i
$486$		0			0
$487$	−7.98852	+	13.8365i	−0.361994	+	0.626993i	−0.988289	−	0.152594i	$-0.951237\pi$
$487$	−7.98852	+	13.8365i	−0.361994	+	0.626993i	0.626295	+	0.779586i	$0.284571\pi$
$488$		0			0
$489$	−17.2259	+	9.34938i	−0.778981	+	0.422793i
$490$		0			0
$491$	−30.5982	+	25.6749i	−1.38088	+	1.15869i	−0.411990	+	0.911188i	$0.635166\pi$
$491$	−30.5982	+	25.6749i	−1.38088	+	1.15869i	−0.968887	+	0.247505i	$0.920389\pi$
$492$		0			0
$493$	2.55726	−	14.5029i	0.115173	−	0.653179i
$494$		0			0
$495$	0.779246	+	0.0410847i	0.0350245	+	0.00184662i
$496$		0			0
$497$	−18.0663	+	12.3149i	−0.810383	+	0.552398i
$498$		0			0
$499$	−30.1748	+	25.3197i	−1.35081	+	1.13347i	−0.372107	+	0.928190i	$0.621365\pi$
$499$	−30.1748	+	25.3197i	−1.35081	+	1.13347i	−0.978704	+	0.205275i	$0.934191\pi$
$500$		0			0
$501$	7.62032	+	9.58316i	0.340451	+	0.428144i
$502$		0			0
$503$	−12.0254	−	20.8287i	−0.536188	−	0.928705i	−0.999105	−	0.0423033i	$-0.986530\pi$
$503$	−12.0254	−	20.8287i	−0.536188	−	0.928705i	0.462917	−	0.886402i	$-0.346803\pi$
$504$		0			0
$505$	6.74102	−	11.6758i	0.299971	−	0.519565i
$506$		0			0
$507$	−18.4679	−	55.2236i	−0.820188	−	2.45257i
$508$		0			0
$509$	−6.97993	−	39.5852i	−0.309380	−	1.75458i	−0.602136	−	0.798394i	$-0.705683\pi$
$509$	−6.97993	−	39.5852i	−0.309380	−	1.75458i	0.292756	−	0.956187i	$-0.405428\pi$
$510$		0			0
$511$	29.9980	−	20.4482i	1.32703	−	0.904573i
$512$		0			0
$513$	0.610060	−	7.70500i	0.0269348	−	0.340184i
$514$		0			0
$515$	−8.33674	−	6.99535i	−0.367361	−	0.308252i
$516$		0			0
$517$	0.519169	+	0.188962i	0.0228330	+	0.00831054i
$518$		0			0
$519$	−6.54287	−	1.33223i	−0.287200	−	0.0584786i
$520$		0			0
$521$	−3.86061	−	6.68677i	−0.169136	−	0.292953i	0.768980	−	0.639273i	$-0.220764\pi$
$521$	−3.86061	−	6.68677i	−0.169136	−	0.292953i	−0.938116	+	0.346320i	$0.887431\pi$
$522$		0			0
$523$	2.53189	−	4.38537i	0.110712	−	0.191759i	−0.805346	−	0.592806i	$-0.798020\pi$
$523$	2.53189	−	4.38537i	0.110712	−	0.191759i	0.916058	+	0.401047i	$0.131354\pi$
$524$		0			0
$525$	2.73753	+	2.08006i	0.119476	+	0.0907813i
$526$		0			0
$527$	7.67794	−	6.44256i	0.334456	−	0.280642i
$528$		0			0
$529$	−44.4197	+	16.1674i	−1.93129	+	0.702932i
$530$		0			0
$531$	2.64964	+	21.6359i	0.114985	+	0.938920i
$532$		0			0
$533$	−36.5835	+	13.3153i	−1.58461	+	0.576750i
$534$		0			0
$535$	−1.43013	−	8.11069i	−0.0618301	−	0.350656i
$536$		0			0
$537$	−1.06220	+	40.3209i	−0.0458371	+	1.73998i
$538$		0			0
$539$	0.666898	−	0.363010i	0.0287253	−	0.0156360i
$540$		0			0
$541$	−4.99627	−	8.65380i	−0.214806	−	0.372056i	0.738406	−	0.674356i	$-0.235579\pi$
$541$	−4.99627	−	8.65380i	−0.214806	−	0.372056i	−0.953213	+	0.302300i	$0.902245\pi$
$542$		0			0
$543$	5.57698	+	3.41879i	0.239331	+	0.146714i
$544$		0			0
$545$	22.3228	−	18.7311i	0.956204	−	0.802350i
$546$		0			0
$547$	21.1584	−	7.70104i	0.904669	−	0.329273i	0.152547	−	0.988296i	$-0.451253\pi$
$547$	21.1584	−	7.70104i	0.904669	−	0.329273i	0.752122	+	0.659024i	$0.229030\pi$
$548$		0			0
$549$	−18.2593	−	17.0378i	−0.779288	−	0.727157i
$550$		0			0
$551$	0.904883	−	5.13184i	0.0385493	−	0.218624i
$552$		0			0
$553$	−5.50620	−	12.2061i	−0.234147	−	0.519054i
$554$		0			0
$555$	−22.5749	−	28.3898i	−0.958253	−	1.20508i
$556$		0			0
$557$	−1.67247			−0.0708646			−0.0354323	−	0.999372i	$-0.511281\pi$
$557$	−1.67247			−0.0708646			−0.0354323	+	0.999372i	$0.511281\pi$
$558$		0			0
$559$	−4.04795	+	7.01125i	−0.171210	+	0.296544i
$560$		0			0
$561$	−0.250481	−	0.749001i	−0.0105753	−	0.0316229i
$562$		0			0
$563$	−5.38135	+	4.51549i	−0.226797	+	0.190305i	−0.749104	−	0.662452i	$-0.769516\pi$
$563$	−5.38135	+	4.51549i	−0.226797	+	0.190305i	0.522307	+	0.852757i	$0.325071\pi$
$564$		0			0
$565$	14.4584	−	5.26242i	0.608269	−	0.221392i
$566$		0			0
$567$	0.729576	−	23.8006i	0.0306393	−	0.999531i
$568$		0			0
$569$	23.9481	−	8.71640i	1.00396	−	0.365411i	0.212848	−	0.977085i	$-0.431726\pi$
$569$	23.9481	−	8.71640i	1.00396	−	0.365411i	0.791109	+	0.611675i	$0.209504\pi$
$570$		0			0
$571$	−21.4001	+	17.9569i	−0.895568	+	0.751471i	−0.969319	−	0.245806i	$-0.920947\pi$
$571$	−21.4001	+	17.9569i	−0.895568	+	0.751471i	0.0737509	+	0.997277i	$0.476503\pi$
$572$		0			0
$573$	−5.10157	−	15.2550i	−0.213121	−	0.637286i
$574$		0			0
$575$	−3.14462	+	5.44665i	−0.131140	+	0.227141i
$576$		0			0
$577$	−7.43822			−0.309657			−0.154829	−	0.987941i	$-0.549483\pi$
$577$	−7.43822			−0.309657			−0.154829	+	0.987941i	$0.549483\pi$
$578$		0			0
$579$	15.2277	+	19.1500i	0.632842	+	0.795849i
$580$		0			0
$581$	−47.1920	−	4.72676i	−1.95785	−	0.196099i
$582$		0			0
$583$	−0.119871	+	0.679821i	−0.00496454	+	0.0281553i
$584$		0			0
$585$	11.0644	−	47.8563i	0.457455	−	1.97861i
$586$		0			0
$587$	26.9780	−	9.81918i	1.11350	−	0.405281i	0.281224	−	0.959642i	$-0.409260\pi$
$587$	26.9780	−	9.81918i	1.11350	−	0.405281i	0.832276	+	0.554361i	$0.187037\pi$
$588$		0			0
$589$	2.71683	−	2.27969i	0.111945	−	0.0939330i
$590$		0			0
$591$	−13.3032	−	8.15507i	−0.547219	−	0.335455i
$592$		0			0
$593$	3.74703	+	6.49005i	0.153872	+	0.266514i	0.932648	−	0.360788i	$-0.117492\pi$
$593$	3.74703	+	6.49005i	0.153872	+	0.266514i	−0.778776	+	0.627303i	$0.784159\pi$
$594$		0			0
$595$	7.22573	−	25.6725i	0.296226	−	1.05247i
$596$		0			0
$597$	−1.10291	+	41.8663i	−0.0451390	+	1.71347i
$598$		0			0
$599$	7.26241	+	41.1872i	0.296734	+	1.68286i	0.660069	+	0.751205i	$0.270527\pi$
$599$	7.26241	+	41.1872i	0.296734	+	1.68286i	−0.363335	+	0.931659i	$0.618362\pi$
$600$		0			0
$601$	3.69330	−	1.34425i	0.150653	−	0.0548331i	−0.265593	−	0.964085i	$-0.585568\pi$
$601$	3.69330	−	1.34425i	0.150653	−	0.0548331i	0.416246	+	0.909252i	$0.363346\pi$
$602$		0			0
$603$	11.6046	+	4.93017i	0.472575	+	0.200772i
$604$		0			0
$605$	−24.7604	+	9.01205i	−1.00665	+	0.366392i
$606$		0			0
$607$	30.0634	−	25.2262i	1.22024	−	1.02390i	0.221425	−	0.975177i	$-0.428929\pi$
$607$	30.0634	−	25.2262i	1.22024	−	1.02390i	0.998812	−	0.0487231i	$-0.0155152\pi$
$608$		0			0
$609$	2.02008	−	15.9264i	0.0818578	−	0.645371i
$610$		0			0
$611$	17.3885	−	30.1177i	0.703462	−	1.21843i
$612$		0			0
$613$	−10.3420	−	17.9129i	−0.417710	−	0.723495i	0.577999	−	0.816038i	$-0.303834\pi$
$613$	−10.3420	−	17.9129i	−0.417710	−	0.723495i	−0.995709	+	0.0925430i	$0.970500\pi$
$614$		0			0
$615$	−23.2060	−	4.72513i	−0.935758	−	0.190536i
$616$		0			0
$617$	−0.0829542	−	0.0301929i	−0.00333961	−	0.00121552i	0.340350	−	0.940299i	$-0.389455\pi$
$617$	−0.0829542	−	0.0301929i	−0.00333961	−	0.00121552i	−0.343689	+	0.939083i	$0.611677\pi$
$618$		0			0
$619$	0.512729	+	0.430230i	0.0206083	+	0.0172924i	0.653034	−	0.757329i	$-0.273496\pi$
$619$	0.512729	+	0.430230i	0.0206083	+	0.0172924i	−0.632425	+	0.774621i	$0.717940\pi$
$620$		0			0
$621$	43.3595	−	4.15436i	1.73996	−	0.166709i
$622$		0			0
$623$	2.64067	+	35.2818i	0.105796	+	1.41354i
$624$		0			0
$625$	−4.89487	−	27.7602i	−0.195795	−	1.11041i
$626$		0			0
$627$	−0.0886324	−	0.265033i	−0.00353964	−	0.0105844i
$628$		0			0
$629$	−18.3552	+	31.7921i	−0.731869	+	1.26763i
$630$		0			0
$631$	−13.0587	−	22.6184i	−0.519860	−	0.900424i	−0.999733	−	0.0230865i	$-0.992651\pi$
$631$	−13.0587	−	22.6184i	−0.519860	−	0.900424i	0.479873	−	0.877338i	$-0.340683\pi$
$632$		0			0
$633$	−5.65887	−	7.11648i	−0.224920	−	0.282855i
$634$		0			0
$635$	−8.64782	+	7.25638i	−0.343178	+	0.287961i
$636$		0			0
$637$	−15.2134	−	45.3087i	−0.602778	−	1.79520i
$638$		0			0
$639$	11.2483	+	22.0932i	0.444974	+	0.873992i
$640$		0			0
$641$	1.53662	−	8.71458i	0.0606927	−	0.344205i	−0.939307	−	0.343079i	$-0.888530\pi$
$641$	1.53662	−	8.71458i	0.0606927	−	0.344205i	0.999999	−	0.00112667i	$-0.000358631\pi$
$642$		0			0
$643$	−14.1884	+	11.9055i	−0.559537	+	0.469507i	−0.878155	−	0.478376i	$-0.841226\pi$
$643$	−14.1884	+	11.9055i	−0.559537	+	0.469507i	0.318618	+	0.947883i	$0.396781\pi$
$644$		0			0
$645$	−4.32836	+	2.34922i	−0.170429	+	0.0925006i
$646$		0			0
$647$	20.1791	−	34.9513i	0.793323	−	1.37408i	−0.130576	−	0.991438i	$-0.541683\pi$
$647$	20.1791	−	34.9513i	0.793323	−	1.37408i	0.923899	−	0.382637i	$-0.124984\pi$
$648$		0			0
$649$	0.394067	+	0.682543i	0.0154685	+	0.0267922i
$650$		0			0
$651$	8.02062	−	7.41972i	0.314353	−	0.290802i
$652$		0			0
$653$	−5.16011	−	1.87812i	−0.201931	−	0.0734967i	0.239075	−	0.971001i	$-0.423156\pi$
$653$	−5.16011	−	1.87812i	−0.201931	−	0.0734967i	−0.441005	+	0.897504i	$0.645378\pi$
$654$		0			0
$655$	0.0576422	−	0.326905i	0.00225227	−	0.0127732i
$656$		0			0
$657$	−18.6771	−	36.6844i	−0.728663	−	1.43120i
$658$		0			0
$659$	−2.29246	−	1.92361i	−0.0893017	−	0.0749330i	0.597044	−	0.802209i	$-0.296342\pi$
$659$	−2.29246	−	1.92361i	−0.0893017	−	0.0749330i	−0.686346	+	0.727276i	$0.740786\pi$
$660$		0			0
$661$	18.4901	+	6.72985i	0.719182	+	0.261761i	0.675579	−	0.737288i	$-0.263894\pi$
$661$	18.4901	+	6.72985i	0.719182	+	0.261761i	0.0436037	+	0.999049i	$0.486116\pi$
$662$		0			0
$663$	−49.1683	+	7.34034i	−1.90954	+	0.285075i
$664$		0			0
$665$	2.55681	−	9.08418i	0.0991490	−	0.352269i
$666$		0			0
$667$	29.3671			1.13710
$668$		0			0
$669$	0.244633	+	0.731514i	0.00945807	+	0.0282820i
$670$		0			0
$671$	−0.848519	−	0.308835i	−0.0327567	−	0.0119225i
$672$		0			0
$673$	2.31457	−	13.1266i	0.0892201	−	0.505992i	−0.907146	−	0.420816i	$-0.861744\pi$
$673$	2.31457	−	13.1266i	0.0892201	−	0.505992i	0.996366	−	0.0851760i	$-0.0271452\pi$
$674$		0			0
$675$	2.73379	−	2.77929i	0.105224	−	0.106975i
$676$		0			0
$677$	35.9742	−	13.0935i	1.38260	−	0.503226i	0.459636	−	0.888108i	$-0.347980\pi$
$677$	35.9742	−	13.0935i	1.38260	−	0.503226i	0.922966	+	0.384882i	$0.125758\pi$
$678$		0			0
$679$	13.6816	−	19.0262i	0.525053	−	0.730159i
$680$		0			0
$681$	−7.54487	−	22.5610i	−0.289120	−	0.864541i
$682$		0			0
$683$	12.3486	+	21.3885i	0.472508	+	0.818408i	0.999505	−	0.0314595i	$-0.0100155\pi$
$683$	12.3486	+	21.3885i	0.472508	+	0.818408i	−0.526997	+	0.849867i	$0.676682\pi$
$684$		0			0
$685$	1.09872	+	1.90303i	0.0419798	+	0.0727112i
$686$		0			0
$687$	19.7646	+	24.8556i	0.754068	+	0.948300i
$688$		0			0
$689$	40.8317	+	14.8615i	1.55557	+	0.566180i
$690$		0			0
$691$	1.31092	−	7.43459i	0.0498697	−	0.282825i	−0.949667	−	0.313261i	$-0.898578\pi$
$691$	1.31092	−	7.43459i	0.0498697	−	0.282825i	0.999537	+	0.0304360i	$0.00968957\pi$
$692$		0			0
$693$	−0.312216	−	0.802354i	−0.0118601	−	0.0304789i
$694$		0			0
$695$	−28.4068	−	23.8361i	−1.07753	−	0.904156i
$696$		0			0
$697$	4.16215	+	23.6047i	0.157653	+	0.894093i
$698$		0			0
$699$	28.5161	+	17.4809i	1.07858	+	0.661187i
$700$		0			0
$701$	−14.9996			−0.566525			−0.283263	−	0.959042i	$-0.591417\pi$
$701$	−14.9996			−0.566525			−0.283263	+	0.959042i	$0.591417\pi$
$702$		0			0
$703$	−6.49496	+	11.2496i	−0.244962	+	0.424286i
$704$		0			0
$705$	18.5930	−	10.0914i	0.700254	−	0.380064i
$706$		0			0
$707$	−14.8011	−	1.48248i	−0.556651	−	0.0557543i
$708$		0			0
$709$	−15.2150	−	12.7669i	−0.571412	−	0.479471i	0.310702	−	0.950507i	$-0.399436\pi$
$709$	−15.2150	−	12.7669i	−0.571412	−	0.479471i	−0.882114	+	0.471036i	$0.843880\pi$
$710$		0			0
$711$	−14.5214	+	4.43463i	−0.544594	+	0.166312i
$712$		0			0
$713$	15.3109	+	12.8474i	0.573398	+	0.481138i
$714$		0			0
$715$	−0.308395	−	1.74900i	−0.0115333	−	0.0654088i
$716$		0			0
$717$	1.21730	−	3.08886i	0.0454608	−	0.115356i
$718$		0			0
$719$	18.1996	−	31.5227i	0.678732	−	1.17560i	−0.296631	−	0.954992i	$-0.595863\pi$
$719$	18.1996	−	31.5227i	0.678732	−	1.17560i	0.975363	−	0.220606i	$-0.0708036\pi$
$720$		0			0
$721$	−3.25317	+	11.5583i	−0.121154	+	0.430452i
$722$		0			0
$723$	21.8015	−	24.6343i	0.810808	−	0.916160i
$724$		0			0
$725$	2.01345	−	1.68948i	0.0747776	−	0.0627459i
$726$		0			0
$727$	−1.25226	+	7.10194i	−0.0464439	+	0.263396i	−0.999184	−	0.0403902i	$-0.987140\pi$
$727$	−1.25226	+	7.10194i	−0.0464439	+	0.263396i	0.952740	+	0.303787i	$0.0982510\pi$
$728$		0			0
$729$	−26.6636	−	4.24893i	−0.987540	−	0.157368i
$730$		0			0
$731$	3.81827	+	3.20391i	0.141224	+	0.118501i
$732$		0			0
$733$	−5.77966	−	32.7781i	−0.213477	−	1.21069i	−0.883531	−	0.468374i	$-0.844840\pi$
$733$	−5.77966	−	32.7781i	−0.213477	−	1.21069i	0.670054	−	0.742312i	$-0.266271\pi$
$734$		0			0
$735$	6.51467	−	28.3346i	0.240297	−	1.04514i
$736$		0			0
$737$	0.455882			0.0167926
$738$		0			0
$739$	−16.3838			−0.602689			−0.301344	−	0.953515i	$-0.597435\pi$
$739$	−16.3838			−0.602689			−0.301344	+	0.953515i	$0.597435\pi$
$740$		0			0
$741$	−17.3982	+	2.59737i	−0.639137	+	0.0954168i
$742$		0			0
$743$	6.87041	+	38.9641i	0.252051	+	1.42945i	0.803530	+	0.595264i	$0.202952\pi$
$743$	6.87041	+	38.9641i	0.252051	+	1.42945i	−0.551479	+	0.834189i	$0.685936\pi$
$744$		0			0
$745$	46.0744	−	16.7697i	1.68804	−	0.614395i
$746$		0			0
$747$	−12.1140	+	52.3963i	−0.443229	+	1.91708i
$748$		0			0
$749$	−7.50836	+	5.11808i	−0.274350	+	0.187011i
$750$		0			0
$751$	−24.1136	−	8.77664i	−0.879918	−	0.320264i	−0.137741	−	0.990468i	$-0.543984\pi$
$751$	−24.1136	−	8.77664i	−0.879918	−	0.320264i	−0.742177	+	0.670204i	$0.766207\pi$
$752$		0			0
$753$	6.86586	+	4.20889i	0.250206	+	0.153381i
$754$		0			0
$755$	2.78613			0.101398
$756$		0			0
$757$	30.7898			1.11908			0.559538	−	0.828805i	$-0.310979\pi$
$757$	30.7898			1.11908			0.559538	+	0.828805i	$0.310979\pi$
$758$		0			0
$759$	1.38419	−	0.751271i	0.0502429	−	0.0272694i
$760$		0			0
$761$	10.6887	+	3.89037i	0.387466	+	0.141026i	0.528405	−	0.848992i	$-0.322790\pi$
$761$	10.6887	+	3.89037i	0.387466	+	0.141026i	−0.140940	+	0.990018i	$0.545012\pi$
$762$		0			0
$763$	−28.9661	−	13.9527i	−1.04864	−	0.505122i
$764$		0			0
$765$	−27.8332	−	11.8248i	−1.00631	−	0.427528i
$766$		0			0
$767$	46.6181	−	16.9676i	1.68328	−	0.612664i
$768$		0			0
$769$	−2.38400	−	13.5203i	−0.0859692	−	0.487555i	−0.997143	−	0.0755338i	$-0.975934\pi$
$769$	−2.38400	−	13.5203i	−0.0859692	−	0.487555i	0.911174	−	0.412022i	$-0.135177\pi$
$770$		0			0
$771$	21.6642	+	27.2444i	0.780216	+	0.981183i
$772$		0			0
$773$	30.5531			1.09892			0.549459	−	0.835521i	$-0.314834\pi$
$773$	30.5531			1.09892			0.549459	+	0.835521i	$0.314834\pi$
$774$		0			0
$775$	1.78885			0.0642573
$776$		0			0
$777$	−18.3105	+	35.5845i	−0.656886	+	1.27659i
$778$		0			0
$779$	1.47277	+	8.35251i	0.0527676	+	0.299260i
$780$		0			0
$781$	0.686677	+	0.576190i	0.0245712	+	0.0206177i
$782$		0			0
$783$	−17.6216	−	4.56613i	−0.629744	−	0.163180i
$784$		0			0
$785$	8.33381	−	47.2634i	0.297446	−	1.68690i
$786$		0			0
$787$	−18.2909	+	15.3479i	−0.652000	+	0.547093i	−0.907677	−	0.419669i	$-0.862146\pi$
$787$	−18.2909	+	15.3479i	−0.652000	+	0.547093i	0.255677	+	0.966762i	$0.417702\pi$
$788$		0			0
$789$	25.6085	+	5.21430i	0.911685	+	0.185634i
$790$		0			0
$791$	−11.8522	−	12.1538i	−0.421417	−	0.432139i
$792$		0			0
$793$	−28.4194	+	49.2238i	−1.00920	+	1.74799i
$794$		0			0
$795$	16.4512	+	20.6887i	0.583465	+	0.733754i
$796$		0			0
$797$	−7.84905	−	44.5142i	−0.278028	−	1.57677i	−0.729178	−	0.684324i	$-0.760097\pi$
$797$	−7.84905	−	44.5142i	−0.278028	−	1.57677i	0.451150	−	0.892448i	$-0.351014\pi$
$798$		0			0
$799$	−16.4019	−	13.7628i	−0.580257	−	0.486894i
$800$		0			0
$801$	40.0621	+	2.11222i	1.41552	+	0.0746317i
$802$		0			0
$803$	−1.14019	−	0.956731i	−0.0402363	−	0.0337623i
$804$		0			0
$805$	52.9190	+	5.30037i	1.86515	+	0.186814i
$806$		0			0
$807$	−0.0367131	−	0.0225058i	−0.00129236	−	0.000792241i
$808$		0			0
$809$	−26.6197	+	46.1067i	−0.935899	+	1.62102i	−0.162877	+	0.986646i	$0.552077\pi$
$809$	−26.6197	+	46.1067i	−0.935899	+	1.62102i	−0.773023	+	0.634378i	$0.781256\pi$
$810$		0			0
$811$	−2.51071			−0.0881629			−0.0440815	−	0.999028i	$-0.514036\pi$
$811$	−2.51071			−0.0881629			−0.0440815	+	0.999028i	$0.514036\pi$
$812$		0			0
$813$	30.5678	−	16.5907i	1.07206	−	0.581861i
$814$		0			0
$815$	4.71193	+	26.7227i	0.165052	+	0.936056i
$816$		0			0
$817$	1.35109	+	1.13370i	0.0472687	+	0.0396632i
$818$		0			0
$819$	−53.1505	+	10.5841i	−1.85723	+	0.369839i
$820$		0			0
$821$	1.50090	−	8.51204i	0.0523819	−	0.297072i	−0.947351	−	0.320198i	$-0.896251\pi$
$821$	1.50090	−	8.51204i	0.0523819	−	0.297072i	0.999733	+	0.0231255i	$0.00736172\pi$
$822$		0			0
$823$	20.7374	+	7.54780i	0.722861	+	0.263100i	0.677140	−	0.735854i	$-0.263219\pi$
$823$	20.7374	+	7.54780i	0.722861	+	0.263100i	0.0457211	+	0.998954i	$0.485441\pi$
$824$		0			0
$825$	0.0516814	−	0.131140i	0.00179932	−	0.00456572i
$826$		0			0
$827$	−0.660727	−	1.14441i	−0.0229757	−	0.0397951i	0.854309	−	0.519766i	$-0.173981\pi$
$827$	−0.660727	−	1.14441i	−0.0229757	−	0.0397951i	−0.877285	+	0.479970i	$0.840647\pi$
$828$		0			0
$829$	3.75325	+	6.50082i	0.130356	+	0.225783i	0.923814	−	0.382842i	$-0.125055\pi$
$829$	3.75325	+	6.50082i	0.130356	+	0.225783i	−0.793458	+	0.608625i	$0.791721\pi$
$830$		0			0
$831$	−6.91882	−	1.40878i	−0.240011	−	0.0488702i
$832$		0			0
$833$	−29.0979	+	4.38021i	−1.00818	+	0.151765i
$834$		0			0
$835$	15.9286	−	5.79755i	0.551233	−	0.200633i
$836$		0			0
$837$	−7.18967	−	10.0896i	−0.248511	−	0.348748i
$838$		0			0
$839$	9.31444	−	52.8248i	0.321570	−	1.82372i	−0.211185	−	0.977446i	$-0.567732\pi$
$839$	9.31444	−	52.8248i	0.321570	−	1.82372i	0.532755	−	0.846269i	$-0.321157\pi$
$840$		0			0
$841$	15.7183	+	5.72099i	0.542010	+	0.197276i
$842$		0			0
$843$	−4.20922	+	4.75614i	−0.144973	+	0.163810i
$844$		0			0
$845$	−80.6173			−2.77332
$846$		0			0
$847$	20.2973	+	20.8137i	0.697423	+	0.715167i
$848$		0			0
$849$	14.4830	−	36.7503i	0.497056	−	1.26127i
$850$		0			0
$851$	−68.7909	−	25.0378i	−2.35812	−	0.858286i
$852$		0			0
$853$	5.65192	+	4.74252i	0.193518	+	0.162381i	0.734398	−	0.678719i	$-0.237464\pi$
$853$	5.65192	+	4.74252i	0.193518	+	0.162381i	−0.540880	+	0.841100i	$0.681909\pi$
$854$		0			0
$855$	−9.84874	−	4.18420i	−0.336820	−	0.143097i
$856$		0			0
$857$	5.80904	−	32.9447i	0.198433	−	1.12537i	−0.709011	−	0.705197i	$-0.750859\pi$
$857$	5.80904	−	32.9447i	0.198433	−	1.12537i	0.907444	−	0.420172i	$-0.138030\pi$
$858$		0			0
$859$	−4.04497	−	1.47225i	−0.138013	−	0.0502325i	0.272090	−	0.962272i	$-0.412285\pi$
$859$	−4.04497	−	1.47225i	−0.138013	−	0.0502325i	−0.410103	+	0.912039i	$0.634507\pi$
$860$		0			0
$861$	5.77614	+	25.4829i	0.196850	+	0.868453i
$862$		0			0
$863$	9.88580	+	17.1227i	0.336516	+	0.582864i	0.983775	−	0.179407i	$-0.0574179\pi$
$863$	9.88580	+	17.1227i	0.336516	+	0.582864i	−0.647259	+	0.762271i	$0.724085\pi$
$864$		0			0
$865$	−4.62213	+	8.00577i	−0.157157	+	0.272204i
$866$		0			0
$867$	−0.0306036	+	1.16171i	−0.00103935	+	0.0394538i
$868$		0			0
$869$	−0.420547	+	0.352881i	−0.0142661	+	0.0119707i
$870$		0			0
$871$	4.98301	−	28.2601i	0.168843	−	0.957556i
$872$		0			0
$873$	−19.4281	−	18.1285i	−0.657543	−	0.613556i
$874$		0			0
$875$	−22.2786	+	15.1862i	−0.753155	+	0.513389i
$876$		0			0
$877$	−9.28013	+	7.78695i	−0.313368	+	0.262947i	−0.785882	−	0.618376i	$-0.787791\pi$
$877$	−9.28013	+	7.78695i	−0.313368	+	0.262947i	0.472515	+	0.881323i	$0.343346\pi$
$878$		0			0
$879$	20.1740	−	51.1910i	0.680452	−	1.72663i
$880$		0			0
$881$	−7.58168	−	13.1319i	−0.255433	−	0.442423i	0.709580	−	0.704625i	$-0.248885\pi$
$881$	−7.58168	−	13.1319i	−0.255433	−	0.442423i	−0.965013	+	0.262202i	$0.915551\pi$
$882$		0			0
$883$	2.25302	−	3.90234i	0.0758200	−	0.131324i	−0.825623	−	0.564223i	$-0.809176\pi$
$883$	2.25302	−	3.90234i	0.0758200	−	0.131324i	0.901443	+	0.432899i	$0.142509\pi$
$884$		0			0
$885$	29.5713	+	6.02120i	0.994028	+	0.202400i
$886$		0			0
$887$	−0.768527	−	4.35854i	−0.0258046	−	0.146345i	0.969183	−	0.246341i	$-0.0792283\pi$
$887$	−0.768527	−	4.35854i	−0.0258046	−	0.146345i	−0.994988	+	0.0999955i	$0.968117\pi$
$888$		0			0
$889$	11.2214	+	5.40525i	0.376355	+	0.181286i
$890$		0			0
$891$	−0.947387	+	0.235576i	−0.0317386	+	0.00789210i
$892$		0			0
$893$	−5.80379	−	4.86996i	−0.194216	−	0.162967i
$894$		0			0
$895$	52.4747	+	19.0992i	1.75404	+	0.638417i
$896$		0			0
$897$	−31.4413	−	94.0173i	−1.04979	−	3.13915i
$898$		0			0
$899$	−4.17643	−	7.23379i	−0.139292	−	0.241260i
$900$		0			0
$901$	13.3761	−	23.1681i	0.445624	−	0.771843i
$902$		0			0
$903$	4.32643	+	3.28736i	0.143975	+	0.109396i
$904$		0			0
$905$	6.93765	−	5.82138i	0.230615	−	0.193509i
$906$		0			0
$907$	30.1532	−	10.9749i	1.00122	−	0.364415i	0.211166	−	0.977450i	$-0.432274\pi$
$907$	30.1532	−	10.9749i	1.00122	−	0.364415i	0.790056	+	0.613035i	$0.210052\pi$
$908$		0			0
$909$	−3.79938	+	16.4333i	−0.126018	+	0.545059i
$910$		0			0
$911$	−13.8067	+	5.02523i	−0.457437	+	0.166493i	−0.560453	−	0.828186i	$-0.689373\pi$
$911$	−13.8067	+	5.02523i	−0.457437	+	0.166493i	0.103016	+	0.994680i	$0.467151\pi$
$912$		0			0
$913$	0.337652	+	1.91492i	0.0111747	+	0.0633746i
$914$		0			0
$915$	−30.3881	+	16.4932i	−1.00460	+	0.545248i
$916$		0			0
$917$	−0.354931	+	0.0903411i	−0.0117209	+	0.00298333i
$918$		0			0
$919$	−2.99944	−	5.19519i	−0.0989425	−	0.171373i	0.812305	−	0.583233i	$-0.198213\pi$
$919$	−2.99944	−	5.19519i	−0.0989425	−	0.171373i	−0.911247	+	0.411860i	$0.864879\pi$
$920$		0			0
$921$	−4.60105	+	2.49723i	−0.151610	+	0.0822864i
$922$		0			0
$923$	43.2236	−	36.2689i	1.42272	−	1.19381i
$924$		0			0
$925$	−6.15682	+	2.24090i	−0.202435	+	0.0736804i
$926$		0			0
$927$	12.5311	+	5.32378i	0.411574	+	0.174856i
$928$		0			0
$929$	−6.62283	+	37.5599i	−0.217288	+	1.23230i	0.659604	+	0.751613i	$0.270724\pi$
$929$	−6.62283	+	37.5599i	−0.217288	+	1.23230i	−0.876892	+	0.480688i	$0.840387\pi$
$930$		0			0
$931$	−10.2963	+	1.54993i	−0.337447	+	0.0507970i
$932$		0			0
$933$	−0.00338758	+	0.00859591i	−0.000110905	+	0.000281418i
$934$		0			0
$935$	−1.09342			−0.0357586
$936$		0			0
$937$	−1.51360	+	2.62163i	−0.0494471	+	0.0856448i	−0.889690	−	0.456566i	$-0.849079\pi$
$937$	−1.51360	+	2.62163i	−0.0494471	+	0.0856448i	0.840243	+	0.542211i	$0.182413\pi$
$938$		0			0
$939$	−17.9553	−	3.65600i	−0.585950	−	0.119309i
$940$		0			0
$941$	34.5993	−	29.0322i	1.12790	−	0.946424i	0.128928	−	0.991654i	$-0.458846\pi$
$941$	34.5993	−	29.0322i	1.12790	−	0.946424i	0.998977	+	0.0452297i	$0.0144020\pi$
$942$		0			0
$943$	−44.9149	+	16.3477i	−1.46263	+	0.532354i
$944$		0			0
$945$	−30.9297	−	11.4086i	−1.00614	−	0.371121i
$946$		0			0
$947$	22.4922	−	8.18648i	0.730897	−	0.266025i	0.0503525	−	0.998732i	$-0.483966\pi$
$947$	22.4922	−	8.18648i	0.730897	−	0.266025i	0.680544	+	0.732707i	$0.261743\pi$
$948$		0			0
$949$	−71.7704	+	60.2225i	−2.32976	+	1.95490i
$950$		0			0
$951$	−29.9952	+	33.8927i	−0.972662	+	1.09904i
$952$		0			0
$953$	−5.62372	+	9.74057i	−0.182170	+	0.315528i	−0.942619	−	0.333870i	$-0.891645\pi$
$953$	−5.62372	+	9.74057i	−0.182170	+	0.315528i	0.760449	+	0.649397i	$0.224979\pi$
$954$		0			0
$955$	−22.2698			−0.720632
$956$		0			0
$957$	−0.650970	+	0.0971833i	−0.0210429	+	0.00314149i
$958$		0			0
$959$	1.41547	−	1.96841i	0.0457079	−	0.0635632i
$960$		0			0
$961$	−4.39592	+	24.9305i	−0.141804	+	0.804210i
$962$		0			0
$963$	4.67479	+	9.18194i	0.150643	+	0.295884i
$964$		0			0
$965$	31.8303	−	11.5853i	1.02465	−	0.372943i
$966$		0			0
$967$	−20.5079	+	17.2082i	−0.659489	+	0.553377i	−0.909934	−	0.414754i	$-0.863868\pi$
$967$	−20.5079	+	17.2082i	−0.659489	+	0.553377i	0.250444	+	0.968131i	$0.419423\pi$
$968$		0			0
$969$	−0.285208	+	10.8265i	−0.00916220	+	0.347797i
$970$		0			0
$971$	22.4155	+	38.8248i	0.719347	+	1.24595i	0.961259	+	0.275648i	$0.0888924\pi$
$971$	22.4155	+	38.8248i	0.719347	+	1.24595i	−0.241911	+	0.970298i	$0.577774\pi$
$972$		0			0
$973$	−11.0849	+	39.3839i	−0.355366	+	1.26259i
$974$		0			0
$975$	−7.56447	−	4.63715i	−0.242257	−	0.148508i
$976$		0			0
$977$	−6.94729	−	39.4000i	−0.222264	−	1.26052i	−0.867848	−	0.496830i	$-0.834497\pi$
$977$	−6.94729	−	39.4000i	−0.222264	−	1.26052i	0.645584	−	0.763689i	$-0.276614\pi$
$978$		0			0
$979$	1.36306	−	0.496111i	0.0435634	−	0.0158558i
$980$		0			0
$981$	−19.8651	+	30.5685i	−0.634245	+	0.975979i
$982$		0			0
$983$	9.28605	−	3.37984i	0.296179	−	0.107800i	−0.189657	−	0.981850i	$-0.560738\pi$
$983$	9.28605	−	3.37984i	0.296179	−	0.107800i	0.485836	+	0.874050i	$0.338515\pi$
$984$		0			0
$985$	−16.5489	+	13.8861i	−0.527291	+	0.442449i
$986$		0			0
$987$	−18.5847	−	14.1213i	−0.591559	−	0.449485i
$988$		0			0
$989$	−4.96981	+	8.60796i	−0.158031	+	0.273717i
$990$		0			0
$991$	−8.21727	−	14.2327i	−0.261030	−	0.452118i	0.705486	−	0.708724i	$-0.250729\pi$
$991$	−8.21727	−	14.2327i	−0.261030	−	0.452118i	−0.966516	+	0.256606i	$0.917396\pi$
$992$		0			0
$993$	−21.0359	+	23.7692i	−0.667555	+	0.754294i
$994$		0			0
$995$	54.4859	+	19.8312i	1.72732	+	0.628693i
$996$		0			0
$997$	19.5738	+	16.4244i	0.619910	+	0.520166i	0.897775	−	0.440454i	$-0.145182\pi$
$997$	19.5738	+	16.4244i	0.619910	+	0.520166i	−0.277865	+	0.960620i	$0.589627\pi$
$998$		0			0
$999$	37.3846	+	25.7198i	1.18280	+	0.813737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bq.a.25.12	yes	144
7.2	even	3		756.2.bp.a.457.4	yes	144
27.13	even	9		756.2.bp.a.445.4	✓	144
189.121	even	9	inner	756.2.bq.a.121.12	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.445.4	✓	144	27.13	even	9
756.2.bp.a.457.4	yes	144	7.2	even	3
756.2.bq.a.25.12	yes	144	1.1	even	1	trivial
756.2.bq.a.121.12	yes	144	189.121	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bq (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0456125 + 1.73145i) q^{3} +(2.25335 + 0.820154i) q^{5} +(-0.197469 - 2.63837i) q^{7} +(-2.99584 - 0.157952i) q^{9} +O(q^{10})\)	\(q+(-0.0456125 + 1.73145i) q^{3} +(2.25335 + 0.820154i) q^{5} +(-0.197469 - 2.63837i) q^{7} +(-2.99584 - 0.157952i) q^{9} +(-0.101929 + 0.0370992i) q^{11} +(1.18564 + 6.72408i) q^{13} +(-1.52284 + 3.86416i) q^{15} +4.20368 q^{17} +1.48747 q^{19} +(4.57722 - 0.221565i) q^{21} +(1.45565 + 8.25539i) q^{23} +(0.574733 + 0.482259i) q^{25} +(0.410133 - 5.17994i) q^{27} +(0.608337 - 3.45005i) q^{29} +(1.82648 - 1.53260i) q^{31} +(-0.0595861 - 0.178177i) q^{33} +(1.71890 - 6.10714i) q^{35} +(-4.36645 + 7.56291i) q^{37} +(-11.6965 + 1.74617i) q^{39} +(0.990121 + 5.61525i) q^{41} +(0.908317 + 0.762168i) q^{43} +(-6.62114 - 2.81297i) q^{45} +(-3.90179 - 3.27399i) q^{47} +(-6.92201 + 1.04199i) q^{49} +(-0.191741 + 7.27847i) q^{51} +(3.18200 - 5.51139i) q^{53} -0.260110 q^{55} +(-0.0678472 + 2.57548i) q^{57} +(-1.26170 - 7.15548i) q^{59} +(6.37701 + 5.35095i) q^{61} +(0.174850 + 7.93533i) q^{63} +(-2.84312 + 16.1241i) q^{65} +(-3.94935 - 1.43745i) q^{67} +(-14.3602 + 2.14383i) q^{69} +(-4.13196 - 7.15676i) q^{71} +(6.86088 + 11.8834i) q^{73} +(-0.861222 + 0.973125i) q^{75} +(0.118009 + 0.261601i) q^{77} +(4.75591 - 1.73101i) q^{79} +(8.95010 + 0.946396i) q^{81} +(3.11284 - 17.6538i) q^{83} +(9.47239 + 3.44767i) q^{85} +(5.94585 + 1.21067i) q^{87} -13.3726 q^{89} +(17.5065 - 4.45595i) q^{91} +(2.57031 + 3.23236i) q^{93} +(3.35179 + 1.21995i) q^{95} +(6.78522 + 5.69348i) q^{97} +(0.311223 - 0.0950433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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