LMFDB - Embedded newform 912.3.be.d.673.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.1
Root			$1.56632 - 2.71294i$ of defining polynomial
Character	$\chi$	$=$	912.673
Dual form			912.3.be.d.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{3} +(-3.13264 + 5.42589i) q^{5} -8.36156 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{3} +(-3.13264 + 5.42589i) q^{5} -8.36156 q^{7} +(1.50000 + 2.59808i) q^{9} -16.7958 q^{11} +(-14.4824 + 8.36142i) q^{13} +(9.39791 - 5.42589i) q^{15} +(-0.0962854 + 0.166771i) q^{17} +(6.09629 - 17.9954i) q^{19} +(12.5423 + 7.24132i) q^{21} +(2.77108 + 4.79965i) q^{23} +(-7.12684 - 12.3440i) q^{25} -5.19615i q^{27} +(13.4578 - 7.76989i) q^{29} +30.6078i q^{31} +(25.1937 + 14.5456i) q^{33} +(26.1937 - 45.3689i) q^{35} -65.6110i q^{37} +28.9648 q^{39} +(15.8801 + 9.16840i) q^{41} +(-4.63264 + 8.02396i) q^{43} -18.7958 q^{45} +(44.4111 + 76.9222i) q^{47} +20.9157 q^{49} +(0.288856 - 0.166771i) q^{51} +(-2.56727 + 1.48222i) q^{53} +(52.6152 - 91.1323i) q^{55} +(-24.7289 + 21.7136i) q^{57} +(-52.3983 - 30.2522i) q^{59} +(34.1587 + 59.1647i) q^{61} +(-12.5423 - 21.7240i) q^{63} -104.773i q^{65} +(-36.4053 + 21.0186i) q^{67} -9.59929i q^{69} +(49.9153 + 28.8186i) q^{71} +(25.0186 - 43.3334i) q^{73} +24.6881i q^{75} +140.439 q^{77} +(-21.5918 - 12.4661i) q^{79} +(-4.50000 + 7.79423i) q^{81} +61.2537 q^{83} +(-0.603254 - 1.04487i) q^{85} -26.9157 q^{87} +(98.6021 - 56.9279i) q^{89} +(121.096 - 69.9145i) q^{91} +(26.5072 - 45.9117i) q^{93} +(78.5437 + 89.4509i) q^{95} +(-98.4729 - 56.8534i) q^{97} +(-25.1937 - 43.6368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} - 2 q^{5} - 26 q^{7} + 9 q^{9}+O(q^{10}) $ 6 * q - 9 * q^3 - 2 * q^5 - 26 * q^7 + 9 * q^9	$ 6 q - 9 q^{3} - 2 q^{5} - 26 q^{7} + 9 q^{9} - 15 q^{13} + 6 q^{15} - 10 q^{17} + 46 q^{19} + 39 q^{21} + 24 q^{23} + 15 q^{25} + 66 q^{29} + 6 q^{35} + 30 q^{39} + 24 q^{41} - 11 q^{43} - 12 q^{45} + 26 q^{47} + 96 q^{49} + 30 q^{51} + 180 q^{53} + 176 q^{55} - 141 q^{57} - 162 q^{59} - 141 q^{61} - 39 q^{63} + 63 q^{67} + 372 q^{71} + 103 q^{73} - 16 q^{77} + 123 q^{79} - 27 q^{81} + 252 q^{83} + 116 q^{85} - 132 q^{87} + 642 q^{89} - 87 q^{91} - 21 q^{93} + 214 q^{95} - 12 q^{97}+O(q^{100}) $ 6 * q - 9 * q^3 - 2 * q^5 - 26 * q^7 + 9 * q^9 - 15 * q^13 + 6 * q^15 - 10 * q^17 + 46 * q^19 + 39 * q^21 + 24 * q^23 + 15 * q^25 + 66 * q^29 + 6 * q^35 + 30 * q^39 + 24 * q^41 - 11 * q^43 - 12 * q^45 + 26 * q^47 + 96 * q^49 + 30 * q^51 + 180 * q^53 + 176 * q^55 - 141 * q^57 - 162 * q^59 - 141 * q^61 - 39 * q^63 + 63 * q^67 + 372 * q^71 + 103 * q^73 - 16 * q^77 + 123 * q^79 - 27 * q^81 + 252 * q^83 + 116 * q^85 - 132 * q^87 + 642 * q^89 - 87 * q^91 - 21 * q^93 + 214 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$		0			0
$5$	−3.13264	+	5.42589i	−0.626527	+	1.08518i	0.361716	+	0.932288i	$0.382191\pi$
$5$	−3.13264	+	5.42589i	−0.626527	+	1.08518i	−0.988243	+	0.152889i	$0.951142\pi$
$6$		0			0
$7$	−8.36156			−1.19451			−0.597254	−	0.802052i	$-0.703742\pi$
$7$	−8.36156			−1.19451			−0.597254	+	0.802052i	$0.703742\pi$
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	−16.7958			−1.52689			−0.763447	−	0.645871i	$-0.776494\pi$
$11$	−16.7958			−1.52689			−0.763447	+	0.645871i	$0.776494\pi$
$12$		0			0
$13$	−14.4824	+	8.36142i	−1.11403	+	0.643186i	−0.939871	−	0.341531i	$-0.889055\pi$
$13$	−14.4824	+	8.36142i	−1.11403	+	0.643186i	−0.174161	+	0.984717i	$0.555721\pi$
$14$		0			0
$15$	9.39791	−	5.42589i	0.626527	−	0.361726i
$16$		0			0
$17$	−0.0962854	+	0.166771i	−0.00566384	+	0.00981007i	−0.868843	−	0.495087i	$-0.835136\pi$
$17$	−0.0962854	+	0.166771i	−0.00566384	+	0.00981007i	0.863180	+	0.504897i	$0.168470\pi$
$18$		0			0
$19$	6.09629	−	17.9954i	0.320857	−	0.947128i
$19$	6.09629	−	17.9954i	0.320857	−	0.947128i
$20$		0			0
$21$	12.5423	+	7.24132i	0.597254	+	0.344825i
$22$		0			0
$23$	2.77108	+	4.79965i	0.120482	+	0.208680i	0.919958	−	0.392018i	$-0.128223\pi$
$23$	2.77108	+	4.79965i	0.120482	+	0.208680i	−0.799476	+	0.600698i	$0.794889\pi$
$24$		0			0
$25$	−7.12684	−	12.3440i	−0.285073	−	0.493762i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	13.4578	−	7.76989i	0.464064	−	0.267927i	−0.249688	−	0.968326i	$-0.580328\pi$
$29$	13.4578	−	7.76989i	0.464064	−	0.267927i	0.713751	+	0.700399i	$0.246995\pi$
$30$		0			0
$31$			30.6078i			0.987349i	0.869647	+	0.493675i	$0.164347\pi$
$31$			30.6078i			0.987349i	−0.869647	+	0.493675i	$0.835653\pi$
$32$		0			0
$33$	25.1937	+	14.5456i	0.763447	+	0.440776i
$34$		0			0
$35$	26.1937	−	45.3689i	0.748392	−	1.29625i
$36$		0			0
$37$		−	65.6110i		−	1.77327i	−0.462471	−	0.886635i	$-0.653037\pi$
$37$		−	65.6110i		−	1.77327i	0.462471	−	0.886635i	$-0.346963\pi$
$38$		0			0
$39$	28.9648			0.742688
$40$		0			0
$41$	15.8801	+	9.16840i	0.387320	+	0.223619i	0.680998	−	0.732285i	$-0.261546\pi$
$41$	15.8801	+	9.16840i	0.387320	+	0.223619i	−0.293678	+	0.955904i	$0.594879\pi$
$42$		0			0
$43$	−4.63264	+	8.02396i	−0.107736	+	0.186604i	−0.914853	−	0.403788i	$-0.867693\pi$
$43$	−4.63264	+	8.02396i	−0.107736	+	0.186604i	0.807117	+	0.590392i	$0.201027\pi$
$44$		0			0
$45$	−18.7958			−0.417685
$46$		0			0
$47$	44.4111	+	76.9222i	0.944916	+	1.63664i	0.755919	+	0.654665i	$0.227190\pi$
$47$	44.4111	+	76.9222i	0.944916	+	1.63664i	0.188997	+	0.981978i	$0.439476\pi$
$48$		0			0
$49$	20.9157			0.426851
$50$		0			0
$51$	0.288856	−	0.166771i	0.00566384	−	0.00327002i
$52$		0			0
$53$	−2.56727	+	1.48222i	−0.0484391	+	0.0279664i	−0.524024	−	0.851703i	$-0.675570\pi$
$53$	−2.56727	+	1.48222i	−0.0484391	+	0.0279664i	0.475585	+	0.879670i	$0.342236\pi$
$54$		0			0
$55$	52.6152	−	91.1323i	0.956641	−	1.65695i
$56$		0			0
$57$	−24.7289	+	21.7136i	−0.433841	+	0.380940i
$58$		0			0
$59$	−52.3983	−	30.2522i	−0.888107	−	0.512749i	−0.0147838	−	0.999891i	$-0.504706\pi$
$59$	−52.3983	−	30.2522i	−0.888107	−	0.512749i	−0.873323	+	0.487142i	$0.838039\pi$
$60$		0			0
$61$	34.1587	+	59.1647i	0.559979	+	0.969913i	0.997497	+	0.0707030i	$0.0225243\pi$
$61$	34.1587	+	59.1647i	0.559979	+	0.969913i	−0.437518	+	0.899210i	$0.644142\pi$
$62$		0			0
$63$	−12.5423	−	21.7240i	−0.199085	−	0.344825i
$64$		0			0
$65$		−	104.773i		−	1.61190i
$66$		0			0
$67$	−36.4053	+	21.0186i	−0.543362	+	0.313710i	−0.746440	−	0.665452i	$-0.768239\pi$
$67$	−36.4053	+	21.0186i	−0.543362	+	0.313710i	0.203078	+	0.979162i	$0.434905\pi$
$68$		0			0
$69$		−	9.59929i		−	0.139120i
$70$		0			0
$71$	49.9153	+	28.8186i	0.703033	+	0.405896i	0.808476	−	0.588529i	$-0.200293\pi$
$71$	49.9153	+	28.8186i	0.703033	+	0.405896i	−0.105443	+	0.994425i	$0.533626\pi$
$72$		0			0
$73$	25.0186	−	43.3334i	0.342720	−	0.593609i	−0.642217	−	0.766523i	$-0.721985\pi$
$73$	25.0186	−	43.3334i	0.342720	−	0.593609i	0.984937	+	0.172914i	$0.0553184\pi$
$74$		0			0
$75$			24.6881i			0.329174i
$76$		0			0
$77$	140.439			1.82389
$78$		0			0
$79$	−21.5918	−	12.4661i	−0.273314	−	0.157798i	0.357079	−	0.934074i	$-0.383773\pi$
$79$	−21.5918	−	12.4661i	−0.273314	−	0.157798i	−0.630393	+	0.776276i	$0.717106\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	61.2537			0.737996			0.368998	−	0.929430i	$-0.379701\pi$
$83$	61.2537			0.737996			0.368998	+	0.929430i	$0.379701\pi$
$84$		0			0
$85$	−0.603254	−	1.04487i	−0.00709711	−	0.0122926i
$86$		0			0
$87$	−26.9157			−0.309376
$88$		0			0
$89$	98.6021	−	56.9279i	1.10789	−	0.639640i	0.169607	−	0.985512i	$-0.445750\pi$
$89$	98.6021	−	56.9279i	1.10789	−	0.639640i	0.938282	+	0.345872i	$0.112417\pi$
$90$		0			0
$91$	121.096	−	69.9145i	1.33072	−	0.768292i
$92$		0			0
$93$	26.5072	−	45.9117i	0.285023	−	0.493675i
$94$		0			0
$95$	78.5437	+	89.4509i	0.826776	+	0.941588i
$96$		0			0
$97$	−98.4729	−	56.8534i	−1.01518	−	0.586117i	−0.102479	−	0.994735i	$-0.532677\pi$
$97$	−98.4729	−	56.8534i	−1.01518	−	0.586117i	−0.912705	+	0.408618i	$0.866011\pi$
$98$		0			0
$99$	−25.1937	−	43.6368i	−0.254482	−	0.440776i
$100$		0			0
$101$	2.97642	+	5.15531i	0.0294695	+	0.0510427i	0.880384	−	0.474262i	$-0.157285\pi$
$101$	2.97642	+	5.15531i	0.0294695	+	0.0510427i	−0.850915	+	0.525304i	$0.823952\pi$
$102$		0			0
$103$		−	152.063i		−	1.47634i	−0.674615	−	0.738170i	$-0.735690\pi$
$103$		−	152.063i		−	1.47634i	0.674615	−	0.738170i	$-0.264310\pi$
$104$		0			0
$105$	−78.5812	+	45.3689i	−0.748392	+	0.432085i
$106$		0			0
$107$		−	141.614i		−	1.32350i	−0.749726	−	0.661749i	$-0.769815\pi$
$107$		−	141.614i		−	1.32350i	0.749726	−	0.661749i	$-0.230185\pi$
$108$		0			0
$109$	−65.3032	−	37.7028i	−0.599112	−	0.345897i	0.169580	−	0.985516i	$-0.445759\pi$
$109$	−65.3032	−	37.7028i	−0.599112	−	0.345897i	−0.768692	+	0.639619i	$0.779092\pi$
$110$		0			0
$111$	−56.8208	+	98.4164i	−0.511899	+	0.886635i
$112$		0			0
$113$		−	8.95674i		−	0.0792632i	−0.999214	−	0.0396316i	$-0.987382\pi$
$113$		−	8.95674i		−	0.0792632i	0.999214	−	0.0396316i	$-0.0126184\pi$
$114$		0			0
$115$	−34.7231			−0.301940
$116$		0			0
$117$	−43.4472	−	25.0843i	−0.371344	−	0.214395i
$118$		0			0
$119$	0.805096	−	1.39447i	0.00676551	−	0.0117182i
$120$		0			0
$121$	161.100			1.33140
$122$		0			0
$123$	−15.8801	−	27.5052i	−0.129107	−	0.223619i
$124$		0			0
$125$	−67.3287			−0.538630
$126$		0			0
$127$	−142.015	+	81.9924i	−1.11823	+	0.645610i	−0.940948	−	0.338551i	$-0.890063\pi$
$127$	−142.015	+	81.9924i	−1.11823	+	0.645610i	−0.177281	+	0.984160i	$0.556730\pi$
$128$		0			0
$129$	13.8979	−	8.02396i	0.107736	−	0.0622013i
$130$		0			0
$131$	−17.9416	+	31.0758i	−0.136959	+	0.237220i	−0.926344	−	0.376679i	$-0.877066\pi$
$131$	−17.9416	+	31.0758i	−0.136959	+	0.237220i	0.789385	+	0.613898i	$0.210399\pi$
$132$		0			0
$133$	−50.9745	+	150.470i	−0.383267	+	1.13135i
$134$		0			0
$135$	28.1937	+	16.2777i	0.208842	+	0.120575i
$136$		0			0
$137$	−40.5425	−	70.2217i	−0.295931	−	0.512567i	0.679270	−	0.733888i	$-0.262296\pi$
$137$	−40.5425	−	70.2217i	−0.295931	−	0.512567i	−0.975201	+	0.221321i	$0.928963\pi$
$138$		0			0
$139$	38.6237	+	66.8983i	0.277869	+	0.481283i	0.970855	−	0.239668i	$-0.0770387\pi$
$139$	38.6237	+	66.8983i	0.277869	+	0.481283i	−0.692986	+	0.720951i	$0.743705\pi$
$140$		0			0
$141$		−	153.844i		−	1.09110i
$142$		0			0
$143$	243.244	−	140.437i	1.70101	−	0.982077i
$144$		0			0
$145$			97.3610i			0.671455i
$146$		0			0
$147$	−31.3735	−	18.1135i	−0.213425	−	0.123221i
$148$		0			0
$149$	89.3751	−	154.802i	0.599833	−	1.03894i	−0.393013	−	0.919533i	$-0.628567\pi$
$149$	89.3751	−	154.802i	0.599833	−	1.03894i	0.992845	−	0.119408i	$-0.0380995\pi$
$150$		0			0
$151$			14.9286i			0.0988646i	0.998777	+	0.0494323i	$0.0157412\pi$
$151$			14.9286i			0.0988646i	−0.998777	+	0.0494323i	$0.984259\pi$
$152$		0			0
$153$	−0.577712			−0.00377590
$154$		0			0
$155$	−166.075	−	95.8832i	−1.07145	−	0.618601i
$156$		0			0
$157$	−84.5435	+	146.434i	−0.538494	+	0.932698i	0.460492	+	0.887664i	$0.347673\pi$
$157$	−84.5435	+	146.434i	−0.538494	+	0.932698i	−0.998985	+	0.0450344i	$0.985660\pi$
$158$		0			0
$159$	5.13455			0.0322928
$160$		0			0
$161$	−23.1705	−	40.1325i	−0.143916	−	0.249270i
$162$		0			0
$163$	−193.054			−1.18438			−0.592191	−	0.805798i	$-0.701737\pi$
$163$	−193.054			−1.18438			−0.592191	+	0.805798i	$0.701737\pi$
$164$		0			0
$165$	−157.846	+	91.1323i	−0.956641	+	0.552317i
$166$		0			0
$167$	171.018	−	98.7374i	1.02406	−	0.591242i	0.108783	−	0.994065i	$-0.465305\pi$
$167$	171.018	−	98.7374i	1.02406	−	0.591242i	0.915278	+	0.402824i	$0.131971\pi$
$168$		0			0
$169$	55.3267	−	95.8287i	0.327377	−	0.567034i
$170$		0			0
$171$	55.8979	−	11.1545i	0.326888	−	0.0652311i
$172$		0			0
$173$	−16.8593	−	9.73370i	−0.0974524	−	0.0562641i	0.450482	−	0.892786i	$-0.351252\pi$
$173$	−16.8593	−	9.73370i	−0.0974524	−	0.0562641i	−0.547934	+	0.836521i	$0.684586\pi$
$174$		0			0
$175$	59.5915	+	103.215i	0.340523	+	0.589803i
$176$		0			0
$177$	52.3983	+	90.7565i	0.296036	+	0.512749i
$178$		0			0
$179$		−	14.8843i		−	0.0831526i	−0.999135	−	0.0415763i	$-0.986762\pi$
$179$		−	14.8843i		−	0.0831526i	0.999135	−	0.0415763i	$-0.0132380\pi$
$180$		0			0
$181$	10.6265	−	6.13519i	0.0587097	−	0.0338961i	−0.470358	−	0.882476i	$-0.655875\pi$
$181$	10.6265	−	6.13519i	0.0587097	−	0.0338961i	0.529068	+	0.848580i	$0.322542\pi$
$182$		0			0
$183$		−	118.329i		−	0.646608i
$184$		0			0
$185$	355.998	+	205.535i	1.92431	+	1.11100i
$186$		0			0
$187$	1.61719	−	2.80106i	0.00864809	−	0.0149789i
$188$		0			0
$189$			43.4479i			0.229883i
$190$		0			0
$191$	100.170			0.524451			0.262226	−	0.965007i	$-0.415544\pi$
$191$	100.170			0.524451			0.262226	+	0.965007i	$0.415544\pi$
$192$		0			0
$193$	137.346	+	79.2970i	0.711640	+	0.410865i	0.811668	−	0.584119i	$-0.198560\pi$
$193$	137.346	+	79.2970i	0.711640	+	0.410865i	−0.100028	+	0.994985i	$0.531893\pi$
$194$		0			0
$195$	−90.7363	+	157.160i	−0.465314	+	0.805948i
$196$		0			0
$197$	106.340			0.539799			0.269899	−	0.962889i	$-0.413010\pi$
$197$	106.340			0.539799			0.269899	+	0.962889i	$0.413010\pi$
$198$		0			0
$199$	38.8548	+	67.2984i	0.195250	+	0.338183i	0.946982	−	0.321285i	$-0.104115\pi$
$199$	38.8548	+	67.2984i	0.195250	+	0.338183i	−0.751732	+	0.659468i	$0.770781\pi$
$200$		0			0
$201$	72.8105			0.362241
$202$		0			0
$203$	−112.529	+	64.9684i	−0.554328	+	0.320041i
$204$		0			0
$205$	−99.4934	+	57.4425i	−0.485334	+	0.280208i
$206$		0			0
$207$	−8.31323	+	14.3989i	−0.0401605	+	0.0695601i
$208$		0			0
$209$	−102.392	+	302.248i	−0.489915	+	1.44616i
$210$		0			0
$211$	136.914	+	79.0472i	0.648880	+	0.374631i	0.788027	−	0.615641i	$-0.211103\pi$
$211$	136.914	+	79.0472i	0.648880	+	0.374631i	−0.139147	+	0.990272i	$0.544436\pi$
$212$		0			0
$213$	−49.9153	−	86.4559i	−0.234344	−	0.405896i
$214$		0			0
$215$	−29.0247	−	50.2723i	−0.134999	−	0.233825i
$216$		0			0
$217$		−	255.929i		−	1.17940i
$218$		0			0
$219$	−75.0557	+	43.3334i	−0.342720	+	0.197870i
$220$		0			0
$221$		−	3.22033i		−	0.0145716i
$222$		0			0
$223$	158.473	+	91.4947i	0.710643	+	0.410290i	0.811299	−	0.584631i	$-0.198761\pi$
$223$	158.473	+	91.4947i	0.710643	+	0.410290i	−0.100656	+	0.994921i	$0.532094\pi$
$224$		0			0
$225$	21.3805	−	37.0321i	0.0950245	−	0.164587i
$226$		0			0
$227$		−	203.575i		−	0.896807i	−0.893831	−	0.448403i	$-0.851993\pi$
$227$		−	203.575i		−	0.896807i	0.893831	−	0.448403i	$-0.148007\pi$
$228$		0			0
$229$	−214.754			−0.937792			−0.468896	−	0.883253i	$-0.655348\pi$
$229$	−214.754			−0.937792			−0.468896	+	0.883253i	$0.655348\pi$
$230$		0			0
$231$	−210.659	−	121.624i	−0.911944	−	0.526511i
$232$		0			0
$233$	−150.857	+	261.293i	−0.647456	+	1.12143i	0.336272	+	0.941765i	$0.390834\pi$
$233$	−150.857	+	261.293i	−0.647456	+	1.12143i	−0.983728	+	0.179662i	$0.942500\pi$
$234$		0			0
$235$	−556.495			−2.36806
$236$		0			0
$237$	21.5918	+	37.3982i	0.0911048	+	0.157798i
$238$		0			0
$239$	189.275			0.791944			0.395972	−	0.918263i	$-0.370408\pi$
$239$	189.275			0.791944			0.395972	+	0.918263i	$0.370408\pi$
$240$		0			0
$241$	−132.570	+	76.5395i	−0.550085	+	0.317591i	−0.749156	−	0.662394i	$-0.769541\pi$
$241$	−132.570	+	76.5395i	−0.550085	+	0.317591i	0.199072	+	0.979985i	$0.436207\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−65.5213	+	113.486i	−0.267434	+	0.463209i
$246$		0			0
$247$	62.1784	+	311.591i	0.251735	+	1.26150i
$248$		0			0
$249$	−91.8805	−	53.0472i	−0.368998	−	0.213041i
$250$		0			0
$251$	84.8855	+	147.026i	0.338189	+	0.585761i	0.984092	−	0.177658i	$-0.0568522\pi$
$251$	84.8855	+	147.026i	0.338189	+	0.585761i	−0.645903	+	0.763420i	$0.723519\pi$
$252$		0			0
$253$	−46.5425	−	80.6140i	−0.183963	−	0.318632i
$254$		0			0
$255$			2.08973i			0.00819504i
$256$		0			0
$257$	146.666	−	84.6778i	0.570686	−	0.329486i	−0.186737	−	0.982410i	$-0.559791\pi$
$257$	146.666	−	84.6778i	0.570686	−	0.329486i	0.757423	+	0.652924i	$0.226458\pi$
$258$		0			0
$259$			548.610i			2.11819i
$260$		0			0
$261$	40.3735	+	23.3097i	0.154688	+	0.0893091i
$262$		0			0
$263$	−198.645	+	344.064i	−0.755306	+	1.30823i	0.189916	+	0.981800i	$0.439178\pi$
$263$	−198.645	+	344.064i	−0.755306	+	1.30823i	−0.945222	+	0.326428i	$0.894155\pi$
$264$		0			0
$265$		−	18.5730i		−	0.0700868i
$266$		0			0
$267$	−197.204			−0.738592
$268$		0			0
$269$	13.6937	+	7.90606i	0.0509060	+	0.0293906i	0.525237	−	0.850956i	$-0.323977\pi$
$269$	13.6937	+	7.90606i	0.0509060	+	0.0293906i	−0.474331	+	0.880347i	$0.657310\pi$
$270$		0			0
$271$	5.79816	−	10.0427i	0.0213954	−	0.0370580i	−0.855129	−	0.518415i	$-0.826522\pi$
$271$	5.79816	−	10.0427i	0.0213954	−	0.0370580i	0.876525	+	0.481357i	$0.159856\pi$
$272$		0			0
$273$	−242.191			−0.887147
$274$		0			0
$275$	119.701	+	207.328i	0.435277	+	0.753921i
$276$		0			0
$277$	−213.637			−0.771254			−0.385627	−	0.922655i	$-0.626015\pi$
$277$	−213.637			−0.771254			−0.385627	+	0.922655i	$0.626015\pi$
$278$		0			0
$279$	−79.5215	+	45.9117i	−0.285023	+	0.164558i
$280$		0			0
$281$	8.30555	−	4.79521i	0.0295571	−	0.0170648i	−0.485149	−	0.874432i	$-0.661235\pi$
$281$	8.30555	−	4.79521i	0.0295571	−	0.0170648i	0.514706	+	0.857367i	$0.327901\pi$
$282$		0			0
$283$	34.3782	−	59.5448i	0.121478	−	0.210406i	−0.798873	−	0.601500i	$-0.794570\pi$
$283$	34.3782	−	59.5448i	0.121478	−	0.210406i	0.920351	+	0.391094i	$0.127903\pi$
$284$		0			0
$285$	−40.3488	−	202.197i	−0.141575	−	0.709464i
$286$		0			0
$287$	−132.783	−	76.6621i	−0.462657	−	0.267115i
$288$		0			0
$289$	144.481	+	250.249i	0.499936	+	0.865914i
$290$		0			0
$291$	98.4729	+	170.560i	0.338395	+	0.586117i
$292$		0			0
$293$			220.596i			0.752886i	0.926440	+	0.376443i	$0.122853\pi$
$293$			220.596i			0.752886i	−0.926440	+	0.376443i	$0.877147\pi$
$294$		0			0
$295$	328.290	−	189.538i	1.11285	−	0.642502i
$296$		0			0
$297$			87.2737i			0.293851i
$298$		0			0
$299$	−80.2637	−	46.3403i	−0.268441	−	0.154984i
$300$		0			0
$301$	38.7361	−	67.0929i	0.128691	−	0.222900i
$302$		0			0
$303$		−	10.3106i		−	0.0340284i
$304$		0			0
$305$	−428.028			−1.40337
$306$		0			0
$307$	−351.943	−	203.194i	−1.14639	−	0.661871i	−0.198389	−	0.980123i	$-0.563571\pi$
$307$	−351.943	−	203.194i	−1.14639	−	0.661871i	−0.948006	+	0.318252i	$0.896904\pi$
$308$		0			0
$309$	−131.690	+	228.095i	−0.426183	+	0.738170i
$310$		0			0
$311$	124.527			0.400407			0.200204	−	0.979754i	$-0.435840\pi$
$311$	124.527			0.400407			0.200204	+	0.979754i	$0.435840\pi$
$312$		0			0
$313$	−306.564	−	530.985i	−0.979438	−	1.69644i	−0.664434	−	0.747347i	$-0.731327\pi$
$313$	−306.564	−	530.985i	−0.979438	−	1.69644i	−0.315004	−	0.949090i	$-0.602006\pi$
$314$		0			0
$315$	157.162			0.498928
$316$		0			0
$317$	148.214	−	85.5713i	0.467552	−	0.269941i	−0.247663	−	0.968846i	$-0.579662\pi$
$317$	148.214	−	85.5713i	0.467552	−	0.269941i	0.715214	+	0.698905i	$0.246329\pi$
$318$		0			0
$319$	−226.036	+	130.502i	−0.708576	+	0.409096i
$320$		0			0
$321$	−122.642	+	212.421i	−0.382061	+	0.661749i
$322$		0			0
$323$	2.41413	+	2.74938i	0.00747410	+	0.00851201i
$324$		0			0
$325$	206.427	+	119.181i	0.635161	+	0.366711i
$326$		0			0
$327$	65.3032	+	113.108i	0.199704	+	0.345897i
$328$		0			0
$329$	−371.346	−	643.190i	−1.12871	−	1.95498i
$330$		0			0
$331$		−	460.487i		−	1.39120i	−0.718429	−	0.695600i	$-0.755138\pi$
$331$		−	460.487i		−	1.39120i	0.718429	−	0.695600i	$-0.244862\pi$
$332$		0			0
$333$	170.462	−	98.4164i	0.511899	−	0.295545i
$334$		0			0
$335$		−	263.374i		−	0.786192i
$336$		0			0
$337$	−133.635	−	77.1544i	−0.396544	−	0.228945i	0.288448	−	0.957496i	$-0.406861\pi$
$337$	−133.635	−	77.1544i	−0.396544	−	0.228945i	−0.684992	+	0.728551i	$0.740194\pi$
$338$		0			0
$339$	−7.75677	+	13.4351i	−0.0228813	+	0.0396316i
$340$		0			0
$341$		−	514.084i		−	1.50758i
$342$		0			0
$343$	234.829			0.684632
$344$		0			0
$345$	52.0847	+	30.0711i	0.150970	+	0.0871626i
$346$		0			0
$347$	−201.934	+	349.760i	−0.581942	+	1.00795i	0.413307	+	0.910592i	$0.364374\pi$
$347$	−201.934	+	349.760i	−0.581942	+	1.00795i	−0.995249	+	0.0973614i	$0.968960\pi$
$348$		0			0
$349$	472.207			1.35303			0.676514	−	0.736430i	$-0.263490\pi$
$349$	472.207			1.35303			0.676514	+	0.736430i	$0.263490\pi$
$350$		0			0
$351$	43.4472	+	75.2528i	0.123781	+	0.214395i
$352$		0			0
$353$	327.128			0.926707			0.463354	−	0.886174i	$-0.346646\pi$
$353$	327.128			0.926707			0.463354	+	0.886174i	$0.346646\pi$
$354$		0			0
$355$	−312.733	+	180.557i	−0.880939	+	0.508610i
$356$		0			0
$357$	−2.41529	+	1.39447i	−0.00676551	+	0.00390607i
$358$		0			0
$359$	301.887	−	522.884i	0.840911	−	1.45650i	−0.0482145	−	0.998837i	$-0.515353\pi$
$359$	301.887	−	522.884i	0.840911	−	1.45650i	0.889125	−	0.457664i	$-0.151314\pi$
$360$		0			0
$361$	−286.671	−	219.410i	−0.794101	−	0.607785i
$362$		0			0
$363$	−241.650	−	139.516i	−0.665701	−	0.384343i
$364$		0			0
$365$	156.748	+	271.496i	0.429447	+	0.743824i
$366$		0			0
$367$	−283.537	−	491.100i	−0.772579	−	1.33815i	−0.936145	−	0.351614i	$-0.885633\pi$
$367$	−283.537	−	491.100i	−0.772579	−	1.33815i	0.163566	−	0.986532i	$-0.447700\pi$
$368$		0			0
$369$			55.0104i			0.149080i
$370$		0			0
$371$	21.4664	−	12.3936i	0.0578610	−	0.0334060i
$372$		0			0
$373$			468.494i			1.25602i	0.778207	+	0.628008i	$0.216130\pi$
$373$			468.494i			1.25602i	−0.778207	+	0.628008i	$0.783870\pi$
$374$		0			0
$375$	100.993	+	58.3084i	0.269315	+	0.155489i
$376$		0			0
$377$	−129.935	+	225.053i	−0.344654	+	0.596959i
$378$		0			0
$379$			5.35549i			0.0141306i	0.999975	+	0.00706528i	$0.00224897\pi$
$379$			5.35549i			0.0141306i	−0.999975	+	0.00706528i	$0.997751\pi$
$380$		0			0
$381$	284.030			0.745486
$382$		0			0
$383$	−276.130	−	159.424i	−0.720967	−	0.416250i	0.0941416	−	0.995559i	$-0.469989\pi$
$383$	−276.130	−	159.424i	−0.720967	−	0.416250i	−0.815108	+	0.579308i	$0.803323\pi$
$384$		0			0
$385$	−439.945	+	762.008i	−1.14272	+	1.97924i
$386$		0			0
$387$	−27.7958			−0.0718238
$388$		0			0
$389$	323.659	+	560.594i	0.832029	+	1.44112i	0.896427	+	0.443192i	$0.146154\pi$
$389$	323.659	+	560.594i	0.832029	+	1.44112i	−0.0643974	+	0.997924i	$0.520513\pi$
$390$		0			0
$391$	−1.06726			−0.00272956
$392$		0			0
$393$	53.8248	−	31.0758i	0.136959	−	0.0790732i
$394$		0			0
$395$	135.279	−	78.1032i	0.342478	−	0.197730i
$396$		0			0
$397$	92.8463	−	160.815i	0.233870	−	0.405074i	−0.725074	−	0.688671i	$-0.758194\pi$
$397$	92.8463	−	160.815i	0.233870	−	0.405074i	0.958944	+	0.283597i	$0.0915277\pi$
$398$		0			0
$399$	206.772	−	181.560i	0.518227	−	0.455037i
$400$		0			0
$401$	−53.1582	−	30.6909i	−0.132564	−	0.0765359i	0.432251	−	0.901753i	$-0.357719\pi$
$401$	−53.1582	−	30.6909i	−0.132564	−	0.0765359i	−0.564815	+	0.825217i	$0.691053\pi$
$402$		0			0
$403$	−255.925	−	443.275i	−0.635049	−	1.09994i
$404$		0			0
$405$	−28.1937	−	48.8330i	−0.0696142	−	0.120575i
$406$		0			0
$407$			1101.99i			2.70759i
$408$		0			0
$409$	402.506	−	232.387i	0.984123	−	0.568184i	0.0806106	−	0.996746i	$-0.474313\pi$
$409$	402.506	−	232.387i	0.984123	−	0.568184i	0.903512	+	0.428562i	$0.140980\pi$
$410$		0			0
$411$			140.443i			0.341712i
$412$		0			0
$413$	438.131	+	252.955i	1.06085	+	0.612483i
$414$		0			0
$415$	−191.886	+	332.356i	−0.462375	+	0.800857i
$416$		0			0
$417$		−	133.797i		−	0.320855i
$418$		0			0
$419$	−315.309			−0.752528			−0.376264	−	0.926512i	$-0.622791\pi$
$419$	−315.309			−0.752528			−0.376264	+	0.926512i	$0.622791\pi$
$420$		0			0
$421$	−564.214	−	325.749i	−1.34018	−	0.773751i	−0.353343	−	0.935494i	$-0.614955\pi$
$421$	−564.214	−	325.749i	−1.34018	−	0.773751i	−0.986833	+	0.161743i	$0.948289\pi$
$422$		0			0
$423$	−133.233	+	230.767i	−0.314972	+	0.545548i
$424$		0			0
$425$	2.74484			0.00645845
$426$		0			0
$427$	−285.620	−	494.709i	−0.668900	−	1.15857i
$428$		0			0
$429$	−486.488			−1.13400
$430$		0			0
$431$	690.530	−	398.678i	1.60216	−	0.925006i	0.611103	−	0.791551i	$-0.290726\pi$
$431$	690.530	−	398.678i	1.60216	−	0.925006i	0.991055	−	0.133456i	$-0.0426074\pi$
$432$		0			0
$433$	−716.064	+	413.420i	−1.65373	+	0.954780i	−0.678207	+	0.734871i	$0.737243\pi$
$433$	−716.064	+	413.420i	−1.65373	+	0.954780i	−0.975520	+	0.219909i	$0.929424\pi$
$434$		0			0
$435$	84.3171	−	146.042i	0.193832	−	0.335728i
$436$		0			0
$437$	103.265	−	20.6067i	0.236304	−	0.0471549i
$438$		0			0
$439$	52.9272	+	30.5575i	0.120563	+	0.0696071i	0.559069	−	0.829121i	$-0.311159\pi$
$439$	52.9272	+	30.5575i	0.120563	+	0.0696071i	−0.438506	+	0.898728i	$0.644492\pi$
$440$		0			0
$441$	31.3735	+	54.3406i	0.0711418	+	0.123221i
$442$		0			0
$443$	−244.293	−	423.128i	−0.551451	−	0.955141i	−0.998170	−	0.0604669i	$-0.980741\pi$
$443$	−244.293	−	423.128i	−0.551451	−	0.955141i	0.446719	−	0.894674i	$-0.352592\pi$
$444$		0			0
$445$			713.338i			1.60301i
$446$		0			0
$447$	−268.125	+	154.802i	−0.599833	+	0.346314i
$448$		0			0
$449$		−	358.968i		−	0.799482i	−0.916628	−	0.399741i	$-0.869100\pi$
$449$		−	358.968i		−	0.799482i	0.916628	−	0.399741i	$-0.130900\pi$
$450$		0			0
$451$	−266.720	−	153.991i	−0.591397	−	0.341443i
$452$		0			0
$453$	12.9285	−	22.3928i	0.0285398	−	0.0494323i
$454$		0			0
$455$			876.068i			1.92542i
$456$		0			0
$457$	46.1801			0.101051			0.0505253	−	0.998723i	$-0.483910\pi$
$457$	46.1801			0.101051			0.0505253	+	0.998723i	$0.483910\pi$
$458$		0			0
$459$	0.866568	+	0.500313i	0.00188795	+	0.00109001i
$460$		0			0
$461$	105.292	−	182.372i	0.228400	−	0.395600i	−0.728934	−	0.684584i	$-0.759984\pi$
$461$	105.292	−	182.372i	0.228400	−	0.395600i	0.957334	+	0.288984i	$0.0933174\pi$
$462$		0			0
$463$	756.768			1.63449			0.817244	−	0.576291i	$-0.195501\pi$
$463$	756.768			1.63449			0.817244	+	0.576291i	$0.195501\pi$
$464$		0			0
$465$	166.075	+	287.650i	0.357150	+	0.618601i
$466$		0			0
$467$	564.886			1.20961			0.604803	−	0.796375i	$-0.293252\pi$
$467$	564.886			1.20961			0.604803	+	0.796375i	$0.293252\pi$
$468$		0			0
$469$	304.405	−	175.748i	0.649051	−	0.374730i
$470$		0			0
$471$	253.631	−	146.434i	0.538494	−	0.310899i
$472$		0			0
$473$	77.8090	−	134.769i	0.164501	−	0.284924i
$474$		0			0
$475$	−265.583	+	52.9976i	−0.559123	+	0.111574i
$476$		0			0
$477$	−7.70182	−	4.44665i	−0.0161464	−	0.00932212i
$478$		0			0
$479$	127.894	+	221.520i	0.267003	+	0.462463i	0.968086	−	0.250616i	$-0.0806333\pi$
$479$	127.894	+	221.520i	0.267003	+	0.462463i	−0.701083	+	0.713079i	$0.747300\pi$
$480$		0			0
$481$	548.601	+	950.205i	1.14054	+	1.97548i
$482$		0			0
$483$			80.2651i			0.166180i
$484$		0			0
$485$	616.960	−	356.202i	1.27208	−	0.734437i
$486$		0			0
$487$			409.229i			0.840306i	0.907453	+	0.420153i	$0.138024\pi$
$487$			409.229i			0.840306i	−0.907453	+	0.420153i	$0.861976\pi$
$488$		0			0
$489$	289.581	+	167.190i	0.592191	+	0.341901i
$490$		0			0
$491$	170.835	−	295.895i	0.347932	−	0.602637i	−0.637950	−	0.770078i	$-0.720217\pi$
$491$	170.835	−	295.895i	0.347932	−	0.602637i	0.985882	+	0.167441i	$0.0535505\pi$
$492$		0			0
$493$			2.99251i			0.00606999i
$494$		0			0
$495$	315.691			0.637760
$496$		0			0
$497$	−417.370	−	240.969i	−0.839779	−	0.484846i
$498$		0			0
$499$	−21.9180	+	37.9632i	−0.0439239	+	0.0760785i	−0.887152	−	0.461478i	$-0.847319\pi$
$499$	−21.9180	+	37.9632i	−0.0439239	+	0.0760785i	0.843228	+	0.537557i	$0.180653\pi$
$500$		0			0
$501$	−342.036			−0.682707
$502$		0			0
$503$	−102.279	−	177.153i	−0.203338	−	0.352192i	0.746264	−	0.665650i	$-0.231846\pi$
$503$	−102.279	−	177.153i	−0.203338	−	0.352192i	−0.949602	+	0.313458i	$0.898512\pi$
$504$		0			0
$505$	−37.2962			−0.0738538
$506$		0			0
$507$	−165.980	+	95.8287i	−0.327377	+	0.189011i
$508$		0			0
$509$	478.607	−	276.324i	0.940290	−	0.542877i	0.0502386	−	0.998737i	$-0.484002\pi$
$509$	478.607	−	276.324i	0.940290	−	0.542877i	0.890051	+	0.455861i	$0.150668\pi$
$510$		0			0
$511$	−209.194	+	362.335i	−0.409382	+	0.709071i
$512$		0			0
$513$	−93.5070	−	31.6772i	−0.182275	−	0.0617490i
$514$		0			0
$515$	825.077	+	476.358i	1.60209	+	0.924968i
$516$		0			0
$517$	−745.920	−	1291.97i	−1.44279	−	2.49898i
$518$		0			0
$519$	16.8593	+	29.2011i	0.0324841	+	0.0562641i
$520$		0			0
$521$		−	94.6044i		−	0.181582i	−0.995870	−	0.0907911i	$-0.971060\pi$
$521$		−	94.6044i		−	0.181582i	0.995870	−	0.0907911i	$-0.0289396\pi$
$522$		0			0
$523$	505.303	−	291.737i	0.966162	−	0.557814i	0.0680980	−	0.997679i	$-0.478307\pi$
$523$	505.303	−	291.737i	0.966162	−	0.557814i	0.898064	+	0.439865i	$0.144974\pi$
$524$		0			0
$525$		−	206.431i		−	0.393202i
$526$		0			0
$527$	−5.10450	−	2.94709i	−0.00968596	−	0.00559219i
$528$		0			0
$529$	249.142	−	431.527i	0.470968	−	0.815741i
$530$		0			0
$531$		−	181.513i		−	0.341832i
$532$		0			0
$533$	−306.643			−0.575316
$534$		0			0
$535$	768.383	+	443.626i	1.43623	+	0.829208i
$536$		0			0
$537$	−12.8902	+	22.3265i	−0.0240041	+	0.0415763i
$538$		0			0
$539$	−351.296			−0.651756
$540$		0			0
$541$	−426.677	−	739.026i	−0.788682	−	1.36604i	−0.926775	−	0.375618i	$-0.877431\pi$
$541$	−426.677	−	739.026i	−0.788682	−	1.36604i	0.138093	−	0.990419i	$-0.455903\pi$
$542$		0			0
$543$	−21.2529			−0.0391398
$544$		0			0
$545$	409.142	−	236.218i	0.750720	−	0.433428i
$546$		0			0
$547$	81.4532	−	47.0270i	0.148909	−	0.0859726i	−0.423694	−	0.905805i	$-0.639267\pi$
$547$	81.4532	−	47.0270i	0.148909	−	0.0859726i	0.572603	+	0.819833i	$0.305934\pi$
$548$		0			0
$549$	−102.476	+	177.494i	−0.186660	+	0.323304i
$550$		0			0
$551$	−57.7796	−	289.547i	−0.104863	−	0.525494i
$552$		0			0
$553$	180.541	+	104.236i	0.326476	+	0.188491i
$554$		0			0
$555$	−355.998	−	616.606i	−0.641437	−	1.11100i
$556$		0			0
$557$	371.642	+	643.702i	0.667220	+	1.15566i	0.978678	+	0.205399i	$0.0658493\pi$
$557$	371.642	+	643.702i	0.667220	+	1.15566i	−0.311458	+	0.950260i	$0.600817\pi$
$558$		0			0
$559$		−	154.942i		−	0.277177i
$560$		0			0
$561$	−4.85158	+	2.80106i	−0.00864809	+	0.00499297i
$562$		0			0
$563$			258.369i			0.458914i	0.973319	+	0.229457i	$0.0736950\pi$
$563$			258.369i			0.458914i	−0.973319	+	0.229457i	$0.926305\pi$
$564$		0			0
$565$	48.5983	+	28.0582i	0.0860147	+	0.0496606i
$566$		0			0
$567$	37.6270	−	65.1719i	0.0663616	−	0.114942i
$568$		0			0
$569$		−	105.229i		−	0.184936i	−0.995716	−	0.0924682i	$-0.970524\pi$
$569$		−	105.229i		−	0.184936i	0.995716	−	0.0924682i	$-0.0294756\pi$
$570$		0			0
$571$	−219.177			−0.383848			−0.191924	−	0.981410i	$-0.561473\pi$
$571$	−219.177			−0.383848			−0.191924	+	0.981410i	$0.561473\pi$
$572$		0			0
$573$	−150.255	−	86.7499i	−0.262226	−	0.151396i
$574$		0			0
$575$	39.4980	−	68.4126i	0.0686922	−	0.118978i
$576$		0			0
$577$	693.596			1.20207			0.601036	−	0.799222i	$-0.294755\pi$
$577$	693.596			1.20207			0.601036	+	0.799222i	$0.294755\pi$
$578$		0			0
$579$	−137.346	−	237.891i	−0.237213	−	0.410865i
$580$		0			0
$581$	−512.176			−0.881543
$582$		0			0
$583$	43.1195	−	24.8951i	0.0739614	−	0.0427016i
$584$		0			0
$585$	272.209	−	157.160i	0.465314	−	0.268649i
$586$		0			0
$587$	−239.393	+	414.641i	−0.407824	+	0.706372i	−0.994646	−	0.103344i	$-0.967046\pi$
$587$	−239.393	+	414.641i	−0.407824	+	0.706372i	0.586821	+	0.809716i	$0.300379\pi$
$588$		0			0
$589$	550.801	+	186.594i	0.935146	+	0.316798i
$590$		0			0
$591$	−159.510	−	92.0934i	−0.269899	−	0.155826i
$592$		0			0
$593$	−249.374	−	431.928i	−0.420529	−	0.728378i	0.575462	−	0.817829i	$-0.304822\pi$
$593$	−249.374	−	431.928i	−0.420529	−	0.728378i	−0.995991	+	0.0894503i	$0.971489\pi$
$594$		0			0
$595$	5.04415	+	8.73672i	0.00847756	+	0.0146836i
$596$		0			0
$597$		−	134.597i		−	0.225455i
$598$		0			0
$599$	710.026	−	409.934i	1.18535	−	0.684363i	0.228106	−	0.973636i	$-0.426747\pi$
$599$	710.026	−	409.934i	1.18535	−	0.684363i	0.957247	+	0.289273i	$0.0934136\pi$
$600$		0			0
$601$			159.689i			0.265706i	0.991136	+	0.132853i	$0.0424138\pi$
$601$			159.689i			0.265706i	−0.991136	+	0.132853i	$0.957586\pi$
$602$		0			0
$603$	−109.216	−	63.0557i	−0.181121	−	0.104570i
$604$		0			0
$605$	−504.667	+	874.109i	−0.834160	+	1.44481i
$606$		0			0
$607$		−	346.659i		−	0.571102i	−0.958364	−	0.285551i	$-0.907823\pi$
$607$		−	346.659i		−	0.571102i	0.958364	−	0.285551i	$-0.0921766\pi$
$608$		0			0
$609$	225.057			0.369552
$610$		0			0
$611$	−1286.36	−	742.679i	−2.10533	−	1.21551i
$612$		0			0
$613$	−2.74278	+	4.75063i	−0.00447436	+	0.00774981i	−0.868254	−	0.496120i	$-0.834758\pi$
$613$	−2.74278	+	4.75063i	−0.00447436	+	0.00774981i	0.863780	+	0.503870i	$0.168091\pi$
$614$		0			0
$615$	198.987			0.323556
$616$		0			0
$617$	−251.948	−	436.387i	−0.408344	−	0.707272i	0.586360	−	0.810050i	$-0.300560\pi$
$617$	−251.948	−	436.387i	−0.408344	−	0.707272i	−0.994704	+	0.102778i	$0.967227\pi$
$618$		0			0
$619$	978.911			1.58144			0.790720	−	0.612178i	$-0.209707\pi$
$619$	978.911			1.58144			0.790720	+	0.612178i	$0.209707\pi$
$620$		0			0
$621$	24.9397	−	14.3989i	0.0401605	−	0.0231867i
$622$		0			0
$623$	−824.467	+	476.006i	−1.32338	+	0.764055i
$624$		0			0
$625$	389.087	−	673.919i	0.622540	−	1.07827i
$626$		0			0
$627$	415.343	−	364.698i	0.662428	−	0.581655i
$628$		0			0
$629$	10.9420	+	6.31737i	0.0173959	+	0.0100435i
$630$		0			0
$631$	95.3152	+	165.091i	0.151054	+	0.261634i	0.931615	−	0.363446i	$-0.118400\pi$
$631$	95.3152	+	165.091i	0.151054	+	0.261634i	−0.780561	+	0.625080i	$0.785067\pi$
$632$		0			0
$633$	−136.914	−	237.142i	−0.216293	−	0.374631i
$634$		0			0
$635$		−	1027.41i		−	1.61797i
$636$		0			0
$637$	−302.910	+	174.885i	−0.475525	+	0.274545i
$638$		0			0
$639$			172.912i			0.270597i
$640$		0			0
$641$	313.170	+	180.809i	0.488565	+	0.282073i	0.723979	−	0.689822i	$-0.242311\pi$
$641$	313.170	+	180.809i	0.488565	+	0.282073i	−0.235414	+	0.971895i	$0.575645\pi$
$642$		0			0
$643$	−163.125	+	282.540i	−0.253693	+	0.439410i	−0.964540	−	0.263937i	$-0.914979\pi$
$643$	−163.125	+	282.540i	−0.253693	+	0.439410i	0.710846	+	0.703347i	$0.248312\pi$
$644$		0			0
$645$			100.545i			0.155883i
$646$		0			0
$647$	−378.348			−0.584773			−0.292386	−	0.956300i	$-0.594449\pi$
$647$	−378.348			−0.584773			−0.292386	+	0.956300i	$0.594449\pi$
$648$		0			0
$649$	880.072	+	508.110i	1.35604	+	0.782912i
$650$		0			0
$651$	−221.641	+	383.894i	−0.340463	+	0.589699i
$652$		0			0
$653$	−837.036			−1.28183			−0.640915	−	0.767612i	$-0.721445\pi$
$653$	−837.036			−1.28183			−0.640915	+	0.767612i	$0.721445\pi$
$654$		0			0
$655$	−112.409	−	194.698i	−0.171617	−	0.297249i
$656$		0			0
$657$	150.111			0.228480
$658$		0			0
$659$	243.410	−	140.533i	0.369363	−	0.213252i	−0.303817	−	0.952730i	$-0.598261\pi$
$659$	243.410	−	140.533i	0.369363	−	0.213252i	0.673180	+	0.739479i	$0.264928\pi$
$660$		0			0
$661$	977.164	−	564.166i	1.47831	−	0.853504i	0.478613	−	0.878026i	$-0.341140\pi$
$661$	977.164	−	564.166i	1.47831	−	0.853504i	0.999699	+	0.0245221i	$0.00780641\pi$
$662$		0			0
$663$	−2.78889	+	4.83049i	−0.00420647	+	0.00728581i
$664$		0			0
$665$	−656.748	−	747.949i	−0.987591	−	1.12474i
$666$		0			0
$667$	74.5855	+	43.0619i	0.111822	+	0.0645606i
$668$		0			0
$669$	−158.473	−	274.484i	−0.236881	−	0.410290i
$670$		0			0
$671$	−573.724	−	993.719i	−0.855029	−	1.48095i
$672$		0			0
$673$		−	255.733i		−	0.379990i	−0.981785	−	0.189995i	$-0.939153\pi$
$673$		−	255.733i		−	0.379990i	0.981785	−	0.189995i	$-0.0608472\pi$
$674$		0			0
$675$	−64.1415	+	37.0321i	−0.0950245	+	0.0548624i
$676$		0			0
$677$			55.5306i			0.0820245i	0.999159	+	0.0410122i	$0.0130583\pi$
$677$			55.5306i			0.0820245i	−0.999159	+	0.0410122i	$0.986942\pi$
$678$		0			0
$679$	823.387	+	475.383i	1.21265	+	0.700122i
$680$		0			0
$681$	−176.301	+	305.363i	−0.258886	+	0.448403i
$682$		0			0
$683$			1074.74i			1.57355i	0.617239	+	0.786776i	$0.288251\pi$
$683$			1074.74i			1.57355i	−0.617239	+	0.786776i	$0.711749\pi$
$684$		0			0
$685$	508.020			0.741635
$686$		0			0
$687$	322.132	+	185.983i	0.468896	+	0.270717i
$688$		0			0
$689$	24.7869	−	42.9321i	0.0359751	−	0.0623108i
$690$		0			0
$691$	1158.59			1.67669			0.838345	−	0.545140i	$-0.183524\pi$
$691$	1158.59			1.67669			0.838345	+	0.545140i	$0.183524\pi$
$692$		0			0
$693$	210.659	+	364.872i	0.303981	+	0.526511i
$694$		0			0
$695$	−483.977			−0.696369
$696$		0			0
$697$	−3.05805	+	1.76557i	−0.00438744	+	0.00253309i
$698$		0			0
$699$	452.572	−	261.293i	0.647456	−	0.373809i
$700$		0			0
$701$	−401.853	+	696.031i	−0.573257	+	0.992911i	0.422971	+	0.906143i	$0.360987\pi$
$701$	−401.853	+	696.031i	−0.573257	+	0.992911i	−0.996229	+	0.0867678i	$0.972346\pi$
$702$		0			0
$703$	−1180.70	−	399.983i	−1.67951	−	0.568966i
$704$		0			0
$705$	834.742	+	481.939i	1.18403	+	0.683601i
$706$		0			0
$707$	−24.8875	−	43.1064i	−0.0352016	−	0.0609709i
$708$		0			0
$709$	−445.022	−	770.800i	−0.627675	−	1.08716i	−0.988017	−	0.154345i	$-0.950673\pi$
$709$	−445.022	−	770.800i	−0.627675	−	1.08716i	0.360342	−	0.932820i	$-0.382660\pi$
$710$		0			0
$711$		−	74.7963i		−	0.105199i
$712$		0			0
$713$	−146.907	+	84.8166i	−0.206040	+	0.118957i
$714$		0			0
$715$			1759.75i			2.46119i
$716$		0			0
$717$	−283.912	−	163.917i	−0.395972	−	0.228614i
$718$		0			0
$719$	132.626	−	229.715i	0.184459	−	0.319492i	−0.758935	−	0.651166i	$-0.774280\pi$
$719$	132.626	−	229.715i	0.184459	−	0.319492i	0.943394	+	0.331674i	$0.107613\pi$
$720$		0			0
$721$			1271.48i			1.76350i
$722$		0			0
$723$	265.141			0.366723
$724$		0			0
$725$	−191.824	−	110.749i	−0.264584	−	0.152758i
$726$		0			0
$727$	579.383	−	1003.52i	0.796950	−	1.38036i	−0.124644	−	0.992202i	$-0.539779\pi$
$727$	579.383	−	1003.52i	0.796950	−	1.38036i	0.921594	−	0.388156i	$-0.126888\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−0.892110	−	1.54518i	−0.00122040	−	0.00211379i
$732$		0			0
$733$	−412.148			−0.562275			−0.281138	−	0.959667i	$-0.590712\pi$
$733$	−412.148			−0.562275			−0.281138	+	0.959667i	$0.590712\pi$
$734$		0			0
$735$	196.564	−	113.486i	0.267434	−	0.154403i
$736$		0			0
$737$	611.456	−	353.024i	0.829656	−	0.479002i
$738$		0			0
$739$	−20.8862	+	36.1760i	−0.0282628	+	0.0489526i	−0.879811	−	0.475324i	$-0.842331\pi$
$739$	−20.8862	+	36.1760i	−0.0282628	+	0.0489526i	0.851548	+	0.524277i	$0.175664\pi$
$740$		0			0
$741$	176.578	−	521.234i	0.238297	−	0.703420i
$742$		0			0
$743$	−843.004	−	486.709i	−1.13460	−	0.655059i	−0.189509	−	0.981879i	$-0.560690\pi$
$743$	−843.004	−	486.709i	−1.13460	−	0.655059i	−0.945087	+	0.326820i	$0.894023\pi$
$744$		0			0
$745$	559.959	+	969.878i	0.751623	+	1.30185i
$746$		0			0
$747$	91.8805	+	159.142i	0.122999	+	0.213041i
$748$		0			0
$749$			1184.12i			1.58093i
$750$		0			0
$751$	33.8884	−	19.5655i	0.0451243	−	0.0260525i	−0.477268	−	0.878758i	$-0.658373\pi$
$751$	33.8884	−	19.5655i	0.0451243	−	0.0260525i	0.522392	+	0.852705i	$0.325040\pi$
$752$		0			0
$753$		−	294.052i		−	0.390508i
$754$		0			0
$755$	−81.0007	−	46.7658i	−0.107286	−	0.0619414i
$756$		0			0
$757$	712.001	−	1233.22i	0.940556	−	1.62909i	0.176143	−	0.984365i	$-0.443638\pi$
$757$	712.001	−	1233.22i	0.940556	−	1.62909i	0.764413	−	0.644727i	$-0.223029\pi$
$758$		0			0
$759$			161.228i			0.212422i
$760$		0			0
$761$	−894.712			−1.17571			−0.587853	−	0.808968i	$-0.700027\pi$
$761$	−894.712			−1.17571			−0.587853	+	0.808968i	$0.700027\pi$
$762$		0			0
$763$	546.036	+	315.254i	0.715644	+	0.413177i
$764$		0			0
$765$	1.80976	−	3.13460i	0.00236570	−	0.00409752i
$766$		0			0
$767$	1011.80			1.31917
$768$		0			0
$769$	259.833	+	450.043i	0.337884	+	0.585232i	0.984034	−	0.177978i	$-0.0569556\pi$
$769$	259.833	+	450.043i	0.337884	+	0.585232i	−0.646151	+	0.763210i	$0.723622\pi$
$770$		0			0
$771$	−293.333			−0.380457
$772$		0			0
$773$	682.951	−	394.302i	0.883508	−	0.510093i	0.0116943	−	0.999932i	$-0.496278\pi$
$773$	682.951	−	394.302i	0.883508	−	0.510093i	0.871813	+	0.489838i	$0.162944\pi$
$774$		0			0
$775$	377.824	−	218.137i	0.487515	−	0.281467i
$776$		0			0
$777$	475.110	−	822.915i	0.611467	−	1.05909i
$778$		0			0
$779$	261.799	−	229.877i	0.336071	−	0.295092i
$780$		0			0
$781$	−838.369	−	484.033i	−1.07346	−	0.619760i
$782$		0			0
$783$	−40.3735	−	69.9290i	−0.0515626	−	0.0893091i
$784$		0			0
$785$	−529.688	−	917.447i	−0.674762	−	1.16872i
$786$		0			0
$787$		−	1449.11i		−	1.84131i	−0.390373	−	0.920657i	$-0.627654\pi$
$787$		−	1449.11i		−	1.84131i	0.390373	−	0.920657i	$-0.372346\pi$
$788$		0			0
$789$	595.936	−	344.064i	0.755306	−	0.436076i
$790$		0			0
$791$			74.8923i			0.0946806i
$792$		0			0
$793$	−989.402	−	571.231i	−1.24767	−	0.720342i
$794$		0			0
$795$	−16.0847	+	27.8595i	−0.0202323	+	0.0350434i
$796$		0			0
$797$			882.703i			1.10753i	0.832672	+	0.553766i	$0.186810\pi$
$797$			882.703i			1.10753i	−0.832672	+	0.553766i	$0.813190\pi$
$798$		0			0
$799$	−17.1045			−0.0214074
$800$		0			0
$801$	295.806	+	170.784i	0.369296	+	0.213213i
$802$		0			0
$803$	−420.208	+	727.821i	−0.523297	+	0.906377i
$804$		0			0
$805$	290.339			0.360670
$806$		0			0
$807$	−13.6937	−	23.7182i	−0.0169687	−	0.0293906i
$808$		0			0
$809$	−1181.51			−1.46045			−0.730227	−	0.683204i	$-0.760586\pi$
$809$	−1181.51			−1.46045			−0.730227	+	0.683204i	$0.760586\pi$
$810$		0			0
$811$	851.956	−	491.877i	1.05050	−	0.606507i	0.127711	−	0.991811i	$-0.459237\pi$
$811$	851.956	−	491.877i	1.05050	−	0.606507i	0.922789	+	0.385305i	$0.125904\pi$
$812$		0			0
$813$	−17.3945	+	10.0427i	−0.0213954	+	0.0123527i
$814$		0			0
$815$	604.769	−	1047.49i	0.742047	−	1.28526i
$816$		0			0
$817$	116.153	+	132.283i	0.142170	+	0.161913i
$818$		0			0
$819$	363.287	+	209.744i	0.443573	+	0.256097i
$820$		0			0
$821$	−162.034	−	280.651i	−0.197362	−	0.341841i	0.750310	−	0.661086i	$-0.229904\pi$
$821$	−162.034	−	280.651i	−0.197362	−	0.341841i	−0.947672	+	0.319245i	$0.896571\pi$
$822$		0			0
$823$	−794.171	−	1375.54i	−0.964971	−	1.67138i	−0.709693	−	0.704511i	$-0.751167\pi$
$823$	−794.171	−	1375.54i	−0.964971	−	1.67138i	−0.255278	−	0.966868i	$-0.582167\pi$
$824$		0			0
$825$		−	414.657i		−	0.502614i
$826$		0			0
$827$	−414.532	+	239.330i	−0.501248	+	0.289396i	−0.729229	−	0.684270i	$-0.760121\pi$
$827$	−414.532	+	239.330i	−0.501248	+	0.289396i	0.227981	+	0.973666i	$0.426788\pi$
$828$		0			0
$829$			377.806i			0.455737i	0.973692	+	0.227869i	$0.0731757\pi$
$829$			377.806i			0.455737i	−0.973692	+	0.227869i	$0.926824\pi$
$830$		0			0
$831$	320.456	+	185.015i	0.385627	+	0.222642i
$832$		0			0
$833$	−2.01387	+	3.48813i	−0.00241762	+	0.00418744i
$834$		0			0
$835$			1237.23i			1.48172i
$836$		0			0
$837$	159.043			0.190015
$838$		0			0
$839$	177.113	+	102.256i	0.211100	+	0.121879i	0.601822	−	0.798630i	$-0.294441\pi$
$839$	177.113	+	102.256i	0.211100	+	0.121879i	−0.390723	+	0.920508i	$0.627775\pi$
$840$		0			0
$841$	−299.758	+	519.195i	−0.356430	+	0.617355i
$842$		0			0
$843$	−16.6111			−0.0197047
$844$		0			0
$845$	346.637	+	600.393i	0.410222	+	0.710525i
$846$		0			0
$847$	−1347.05			−1.59037
$848$		0			0
$849$	−103.135	+	59.5448i	−0.121478	+	0.0701352i
$850$		0			0
$851$	314.909	−	181.813i	0.370046	−	0.213646i
$852$		0			0
$853$	29.4624	−	51.0303i	0.0345397	−	0.0598245i	−0.848239	−	0.529614i	$-0.822337\pi$
$853$	29.4624	−	51.0303i	0.0345397	−	0.0598245i	0.882779	+	0.469789i	$0.155670\pi$
$854$		0			0
$855$	−114.585	+	338.239i	−0.134017	+	0.395601i
$856$		0			0
$857$	828.169	+	478.143i	0.966358	+	0.557927i	0.898124	−	0.439743i	$-0.144930\pi$
$857$	828.169	+	478.143i	0.966358	+	0.557927i	0.0682338	+	0.997669i	$0.478264\pi$
$858$		0			0
$859$	235.888	+	408.571i	0.274608	+	0.475635i	0.970036	−	0.242961i	$-0.0781186\pi$
$859$	235.888	+	408.571i	0.274608	+	0.475635i	−0.695428	+	0.718596i	$0.744785\pi$
$860$		0			0
$861$	132.783	+	229.986i	0.154219	+	0.267115i
$862$		0			0
$863$			1033.90i			1.19803i	0.800737	+	0.599017i	$0.204442\pi$
$863$			1033.90i			1.19803i	−0.800737	+	0.599017i	$0.795558\pi$
$864$		0			0
$865$	105.628	−	60.9843i	0.122113	−	0.0705021i
$866$		0			0
$867$		−	500.498i		−	0.577276i
$868$		0			0
$869$	362.653	+	209.378i	0.417322	+	0.240941i
$870$		0			0
$871$	351.490	−	608.799i	0.403548	−	0.698966i
$872$		0			0
$873$		−	341.120i		−	0.390745i
$874$		0			0
$875$	562.973			0.643398
$876$		0			0
$877$	1141.55	+	659.075i	1.30165	+	0.751510i	0.980688	−	0.195580i	$-0.0626589\pi$
$877$	1141.55	+	659.075i	1.30165	+	0.751510i	0.320967	+	0.947091i	$0.395992\pi$
$878$		0			0
$879$	191.041	−	330.893i	0.217340	−	0.376443i
$880$		0			0
$881$	867.615			0.984807			0.492403	−	0.870367i	$-0.336119\pi$
$881$	867.615			0.984807			0.492403	+	0.870367i	$0.336119\pi$
$882$		0			0
$883$	−365.349	−	632.804i	−0.413759	−	0.716652i	0.581538	−	0.813519i	$-0.302451\pi$
$883$	−365.349	−	632.804i	−0.413759	−	0.716652i	−0.995297	+	0.0968671i	$0.969118\pi$
$884$		0			0
$885$	−656.579			−0.741898
$886$		0			0
$887$	−985.378	+	568.908i	−1.11091	+	0.641385i	−0.939065	−	0.343739i	$-0.888306\pi$
$887$	−985.378	+	568.908i	−1.11091	+	0.641385i	−0.171846	+	0.985124i	$0.554973\pi$
$888$		0			0
$889$	1187.47	−	685.585i	1.33573	−	0.771186i
$890$		0			0
$891$	75.5812	−	130.910i	0.0848274	−	0.146925i
$892$		0			0
$893$	1654.99	−	330.256i	1.85329	−	0.369828i
$894$		0			0
$895$	80.7606	+	46.6272i	0.0902354	+	0.0520974i
$896$		0			0
$897$	80.2637	+	139.021i	0.0894802	+	0.154984i
$898$		0			0
$899$	237.819	+	411.915i	0.264538	+	0.458193i
$900$		0			0
$901$		−	0.570863i		−	0.000633588i
$902$		0			0
$903$	−116.208	+	67.0929i	−0.128691	+	0.0743000i
$904$		0			0
$905$			76.8773i			0.0849473i
$906$		0			0
$907$	−135.953	−	78.4924i	−0.149893	−	0.0865407i	0.423178	−	0.906047i	$-0.360915\pi$
$907$	−135.953	−	78.4924i	−0.149893	−	0.0865407i	−0.573071	+	0.819506i	$0.694248\pi$
$908$		0			0
$909$	−8.92926	+	15.4659i	−0.00982316	+	0.0170142i
$910$		0			0
$911$		−	65.1730i		−	0.0715400i	−0.999360	−	0.0357700i	$-0.988612\pi$
$911$		−	65.1730i		−	0.0715400i	0.999360	−	0.0357700i	$-0.0113884\pi$
$912$		0			0
$913$	−1028.81			−1.12684
$914$		0			0
$915$	642.042	+	370.683i	0.701685	+	0.405118i
$916$		0			0
$917$	150.020	−	259.842i	0.163598	−	0.283361i
$918$		0			0
$919$	−1516.82			−1.65051			−0.825255	−	0.564761i	$-0.808969\pi$
$919$	−1516.82			−1.65051			−0.825255	+	0.564761i	$0.808969\pi$
$920$		0			0
$921$	351.943	+	609.583i	0.382132	+	0.661871i
$922$		0			0
$923$	−963.859			−1.04427
$924$		0			0
$925$	−809.904	+	467.599i	−0.875572	+	0.505512i
$926$		0			0
$927$	395.071	−	228.095i	0.426183	−	0.246057i
$928$		0			0
$929$	−175.213	+	303.477i	−0.188603	+	0.326671i	−0.944785	−	0.327691i	$-0.893729\pi$
$929$	−175.213	+	303.477i	−0.188603	+	0.326671i	0.756181	+	0.654362i	$0.227063\pi$
$930$		0			0
$931$	127.508	−	376.387i	0.136958	−	0.404282i
$932$		0			0
$933$	−186.790	−	107.843i	−0.200204	−	0.115588i
$934$		0			0
$935$	10.1322	+	17.5494i	0.0108365	+	0.0187694i
$936$		0			0
$937$	−698.630	−	1210.06i	−0.745603	−	1.29142i	−0.949912	−	0.312516i	$-0.898828\pi$
$937$	−698.630	−	1210.06i	−0.745603	−	1.29142i	0.204309	−	0.978906i	$-0.434505\pi$
$938$		0			0
$939$			1061.97i			1.13096i
$940$		0			0
$941$	−1455.24	+	840.185i	−1.54649	+	0.892864i	−0.548079	+	0.836426i	$0.684641\pi$
$941$	−1455.24	+	840.185i	−1.54649	+	0.892864i	−0.998406	+	0.0564375i	$0.982026\pi$
$942$		0			0
$943$			101.625i			0.107768i
$944$		0			0
$945$	−235.744	−	136.107i	−0.249464	−	0.144028i
$946$		0			0
$947$	689.782	−	1194.74i	0.728387	−	1.26160i	−0.229178	−	0.973384i	$-0.573604\pi$
$947$	689.782	−	1194.74i	0.728387	−	1.26160i	0.957565	−	0.288218i	$-0.0930628\pi$
$948$		0			0
$949$			836.763i			0.881732i
$950$		0			0
$951$	−296.428			−0.311701
$952$		0			0
$953$	−1452.87	−	838.815i	−1.52452	−	0.880184i	−0.999578	−	0.0290471i	$-0.990753\pi$
$953$	−1452.87	−	838.815i	−1.52452	−	0.880184i	−0.524945	−	0.851136i	$-0.675914\pi$
$954$		0			0
$955$	−313.797	+	543.512i	−0.328583	+	0.569123i
$956$		0			0
$957$	452.071			0.472384
$958$		0			0
$959$	338.999	+	587.163i	0.353492	+	0.612266i
$960$		0			0
$961$	24.1610			0.0251415
$962$		0			0
$963$	367.925	−	212.421i	0.382061	−	0.220583i
$964$		0			0
$965$	−860.513	+	496.818i	−0.891724	+	0.514837i
$966$		0			0
$967$	−574.798	+	995.579i	−0.594414	+	1.02955i	0.399216	+	0.916857i	$0.369282\pi$
$967$	−574.798	+	995.579i	−0.594414	+	1.02955i	−0.993629	+	0.112698i	$0.964051\pi$
$968$		0			0
$969$	−1.24017	−	6.21477i	−0.00127984	−	0.00641359i
$970$		0			0
$971$	312.116	+	180.200i	0.321438	+	0.185582i	0.652033	−	0.758190i	$-0.273916\pi$
$971$	312.116	+	180.200i	0.321438	+	0.185582i	−0.330595	+	0.943773i	$0.607250\pi$
$972$		0			0
$973$	−322.955	−	559.374i	−0.331916	−	0.574896i
$974$		0			0
$975$	−206.427	−	357.543i	−0.211720	−	0.366711i
$976$		0			0
$977$			1322.71i			1.35385i	0.736054	+	0.676923i	$0.236687\pi$
$977$			1322.71i			1.35385i	−0.736054	+	0.676923i	$0.763313\pi$
$978$		0			0
$979$	−1656.10	+	956.152i	−1.69163	+	0.976662i
$980$		0			0
$981$		−	226.217i		−	0.230598i
$982$		0			0
$983$	−583.104	−	336.655i	−0.593188	−	0.342478i	0.173169	−	0.984892i	$-0.444599\pi$
$983$	−583.104	−	336.655i	−0.593188	−	0.342478i	−0.766357	+	0.642415i	$0.777933\pi$
$984$		0			0
$985$	−333.126	+	576.991i	−0.338199	+	0.585777i
$986$		0			0
$987$			1286.38i			1.30332i
$988$		0			0
$989$	−51.3496			−0.0519207
$990$		0			0
$991$	243.449	+	140.556i	0.245660	+	0.141832i	0.617776	−	0.786355i	$-0.288034\pi$
$991$	243.449	+	140.556i	0.245660	+	0.141832i	−0.372115	+	0.928187i	$0.621367\pi$
$992$		0			0
$993$	−398.794	+	690.731i	−0.401605	+	0.695600i
$994$		0			0
$995$	−486.872			−0.489318
$996$		0			0
$997$	493.422	+	854.632i	0.494907	+	0.857204i	0.999983	−	0.00587106i	$-0.00186883\pi$
$997$	493.422	+	854.632i	0.494907	+	0.857204i	−0.505076	+	0.863075i	$0.668535\pi$
$998$		0			0
$999$	−340.925			−0.341266

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.d.673.1		6
4.3	odd	2		57.3.g.a.46.1	yes	6
12.11	even	2		171.3.p.e.46.3		6
19.12	odd	6	inner	912.3.be.d.145.1		6
76.31	even	6		57.3.g.a.31.1	✓	6
228.107	odd	6		171.3.p.e.145.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.g.a.31.1	✓	6	76.31	even	6
57.3.g.a.46.1	yes	6	4.3	odd	2
171.3.p.e.46.3		6	12.11	even	2
171.3.p.e.145.3		6	228.107	odd	6
912.3.be.d.145.1		6	19.12	odd	6	inner
912.3.be.d.673.1		6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-3.13264 + 5.42589i) q^{5} -8.36156 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-3.13264 + 5.42589i) q^{5} -8.36156 q^{7} +(1.50000 + 2.59808i) q^{9} -16.7958 q^{11} +(-14.4824 + 8.36142i) q^{13} +(9.39791 - 5.42589i) q^{15} +(-0.0962854 + 0.166771i) q^{17} +(6.09629 - 17.9954i) q^{19} +(12.5423 + 7.24132i) q^{21} +(2.77108 + 4.79965i) q^{23} +(-7.12684 - 12.3440i) q^{25} -5.19615i q^{27} +(13.4578 - 7.76989i) q^{29} +30.6078i q^{31} +(25.1937 + 14.5456i) q^{33} +(26.1937 - 45.3689i) q^{35} -65.6110i q^{37} +28.9648 q^{39} +(15.8801 + 9.16840i) q^{41} +(-4.63264 + 8.02396i) q^{43} -18.7958 q^{45} +(44.4111 + 76.9222i) q^{47} +20.9157 q^{49} +(0.288856 - 0.166771i) q^{51} +(-2.56727 + 1.48222i) q^{53} +(52.6152 - 91.1323i) q^{55} +(-24.7289 + 21.7136i) q^{57} +(-52.3983 - 30.2522i) q^{59} +(34.1587 + 59.1647i) q^{61} +(-12.5423 - 21.7240i) q^{63} -104.773i q^{65} +(-36.4053 + 21.0186i) q^{67} -9.59929i q^{69} +(49.9153 + 28.8186i) q^{71} +(25.0186 - 43.3334i) q^{73} +24.6881i q^{75} +140.439 q^{77} +(-21.5918 - 12.4661i) q^{79} +(-4.50000 + 7.79423i) q^{81} +61.2537 q^{83} +(-0.603254 - 1.04487i) q^{85} -26.9157 q^{87} +(98.6021 - 56.9279i) q^{89} +(121.096 - 69.9145i) q^{91} +(26.5072 - 45.9117i) q^{93} +(78.5437 + 89.4509i) q^{95} +(-98.4729 - 56.8534i) q^{97} +(-25.1937 - 43.6368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} - 2 q^{5} - 26 q^{7} + 9 q^{9}+O(q^{10}) \) 6 * q - 9 * q^3 - 2 * q^5 - 26 * q^7 + 9 * q^9	\( 6 q - 9 q^{3} - 2 q^{5} - 26 q^{7} + 9 q^{9} - 15 q^{13} + 6 q^{15} - 10 q^{17} + 46 q^{19} + 39 q^{21} + 24 q^{23} + 15 q^{25} + 66 q^{29} + 6 q^{35} + 30 q^{39} + 24 q^{41} - 11 q^{43} - 12 q^{45} + 26 q^{47} + 96 q^{49} + 30 q^{51} + 180 q^{53} + 176 q^{55} - 141 q^{57} - 162 q^{59} - 141 q^{61} - 39 q^{63} + 63 q^{67} + 372 q^{71} + 103 q^{73} - 16 q^{77} + 123 q^{79} - 27 q^{81} + 252 q^{83} + 116 q^{85} - 132 q^{87} + 642 q^{89} - 87 q^{91} - 21 q^{93} + 214 q^{95} - 12 q^{97}+O(q^{100}) \) 6 * q - 9 * q^3 - 2 * q^5 - 26 * q^7 + 9 * q^9 - 15 * q^13 + 6 * q^15 - 10 * q^17 + 46 * q^19 + 39 * q^21 + 24 * q^23 + 15 * q^25 + 66 * q^29 + 6 * q^35 + 30 * q^39 + 24 * q^41 - 11 * q^43 - 12 * q^45 + 26 * q^47 + 96 * q^49 + 30 * q^51 + 180 * q^53 + 176 * q^55 - 141 * q^57 - 162 * q^59 - 141 * q^61 - 39 * q^63 + 63 * q^67 + 372 * q^71 + 103 * q^73 - 16 * q^77 + 123 * q^79 - 27 * q^81 + 252 * q^83 + 116 * q^85 - 132 * q^87 + 642 * q^89 - 87 * q^91 - 21 * q^93 + 214 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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