LMFDB - Embedded newform 576.2.bb.e.529.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			529.3
Character	$\chi$	$=$	576.529
Dual form			576.2.bb.e.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45211 - 0.944122i) q^{3} +(-0.491749 - 0.131764i) q^{5} +(2.40518 + 1.38863i) q^{7} +(1.21727 + 2.74194i) q^{9} +O(q^{10})$	\(q+(-1.45211 - 0.944122i) q^{3} +(-0.491749 - 0.131764i) q^{5} +(2.40518 + 1.38863i) q^{7} +(1.21727 + 2.74194i) q^{9} +(-1.06358 - 3.96934i) q^{11} +(-0.596329 + 2.22553i) q^{13} +(0.589675 + 0.655607i) q^{15} +2.87908 q^{17} +(3.48018 + 3.48018i) q^{19} +(-2.18156 - 4.28723i) q^{21} +(3.85945 - 2.22826i) q^{23} +(-4.10567 - 2.37041i) q^{25} +(0.821118 - 5.13086i) q^{27} +(5.88383 - 1.57657i) q^{29} +(1.28296 + 2.22216i) q^{31} +(-2.20310 + 6.76808i) q^{33} +(-0.999773 - 0.999773i) q^{35} +(7.64112 - 7.64112i) q^{37} +(2.96711 - 2.66872i) q^{39} +(4.84731 - 2.79860i) q^{41} +(-0.911456 - 3.40160i) q^{43} +(-0.237302 - 1.50874i) q^{45} +(4.94233 - 8.56037i) q^{47} +(0.356586 + 0.617625i) q^{49} +(-4.18075 - 2.71820i) q^{51} +(-2.86564 + 2.86564i) q^{53} +2.09206i q^{55} +(-1.76790 - 8.33934i) q^{57} +(-2.15652 - 0.577838i) q^{59} +(4.79709 - 1.28538i) q^{61} +(-0.879800 + 8.28520i) q^{63} +(0.586489 - 1.01583i) q^{65} +(-3.96319 + 14.7908i) q^{67} +(-7.70811 - 0.408113i) q^{69} +13.2447i q^{71} +11.3768i q^{73} +(3.72395 + 7.31836i) q^{75} +(2.95384 - 11.0239i) q^{77} +(1.56750 - 2.71499i) q^{79} +(-6.03652 + 6.67536i) q^{81} +(-11.0286 + 2.95510i) q^{83} +(-1.41578 - 0.379358i) q^{85} +(-10.0325 - 3.26570i) q^{87} -2.37475i q^{89} +(-4.52472 + 4.52472i) q^{91} +(0.234979 - 4.43810i) q^{93} +(-1.25282 - 2.16994i) q^{95} +(-5.04313 + 8.73496i) q^{97} +(9.58904 - 7.74803i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) $ 72 * q - 2 * q^3 + 4 * q^5	$ 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) $ 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.45211	−	0.944122i	−0.838378	−	0.545089i
$3$	−1.45211	−	0.944122i	−0.838378	−	0.545089i
$4$		0			0
$5$	−0.491749	−	0.131764i	−0.219917	−	0.0589266i	0.147178	−	0.989110i	$-0.452981\pi$
$5$	−0.491749	−	0.131764i	−0.219917	−	0.0589266i	−0.367095	+	0.930183i	$0.619648\pi$
$6$		0			0
$7$	2.40518	+	1.38863i	0.909072	+	0.524853i	0.880132	−	0.474728i	$-0.157454\pi$
$7$	2.40518	+	1.38863i	0.909072	+	0.524853i	0.0289393	+	0.999581i	$0.490787\pi$
$8$		0			0
$9$	1.21727	+	2.74194i	0.405756	+	0.913981i
$10$		0			0
$11$	−1.06358	−	3.96934i	−0.320682	−	1.19680i	−0.918582	−	0.395230i	$-0.870665\pi$
$11$	−1.06358	−	3.96934i	−0.320682	−	1.19680i	0.597900	−	0.801570i	$-0.296002\pi$
$12$		0			0
$13$	−0.596329	+	2.22553i	−0.165392	+	0.617251i	0.832598	+	0.553878i	$0.186853\pi$
$13$	−0.596329	+	2.22553i	−0.165392	+	0.617251i	−0.997990	+	0.0633733i	$0.979814\pi$
$14$		0			0
$15$	0.589675	+	0.655607i	0.152253	+	0.169277i
$16$		0			0
$17$	2.87908			0.698279			0.349139	−	0.937071i	$-0.386474\pi$
$17$	2.87908			0.698279			0.349139	+	0.937071i	$0.386474\pi$
$18$		0			0
$19$	3.48018	+	3.48018i	0.798409	+	0.798409i	0.982845	−	0.184436i	$-0.0590457\pi$
$19$	3.48018	+	3.48018i	0.798409	+	0.798409i	−0.184436	+	0.982845i	$0.559046\pi$
$20$		0			0
$21$	−2.18156	−	4.28723i	−0.476054	−	0.935550i
$22$		0			0
$23$	3.85945	−	2.22826i	0.804752	−	0.464624i	−0.0403783	−	0.999184i	$-0.512856\pi$
$23$	3.85945	−	2.22826i	0.804752	−	0.464624i	0.845130	+	0.534561i	$0.179523\pi$
$24$		0			0
$25$	−4.10567	−	2.37041i	−0.821134	−	0.474082i
$26$		0			0
$27$	0.821118	−	5.13086i	0.158024	−	0.987435i
$28$		0			0
$29$	5.88383	−	1.57657i	1.09260	−	0.292761i	0.332852	−	0.942979i	$-0.391989\pi$
$29$	5.88383	−	1.57657i	1.09260	−	0.292761i	0.759748	+	0.650218i	$0.225323\pi$
$30$		0			0
$31$	1.28296	+	2.22216i	0.230427	+	0.399112i	0.957934	−	0.286989i	$-0.0926543\pi$
$31$	1.28296	+	2.22216i	0.230427	+	0.399112i	−0.727507	+	0.686101i	$0.759321\pi$
$32$		0			0
$33$	−2.20310	+	6.76808i	−0.383510	+	1.17817i
$34$		0			0
$35$	−0.999773	−	0.999773i	−0.168993	−	0.168993i
$36$		0			0
$37$	7.64112	−	7.64112i	1.25619	−	1.25619i	0.303297	−	0.952896i	$-0.401913\pi$
$37$	7.64112	−	7.64112i	1.25619	−	1.25619i	0.952896	−	0.303297i	$-0.0980873\pi$
$38$		0			0
$39$	2.96711	−	2.66872i	0.475118	−	0.427337i
$40$		0			0
$41$	4.84731	−	2.79860i	0.757023	−	0.437067i	−0.0712028	−	0.997462i	$-0.522684\pi$
$41$	4.84731	−	2.79860i	0.757023	−	0.437067i	0.828226	+	0.560394i	$0.189350\pi$
$42$		0			0
$43$	−0.911456	−	3.40160i	−0.138996	−	0.518739i	−0.999949	−	0.0100559i	$-0.996799\pi$
$43$	−0.911456	−	3.40160i	−0.138996	−	0.518739i	0.860954	−	0.508683i	$-0.169868\pi$
$44$		0			0
$45$	−0.237302	−	1.50874i	−0.0353748	−	0.224910i
$46$		0			0
$47$	4.94233	−	8.56037i	0.720913	−	1.24866i	−0.239721	−	0.970842i	$-0.577056\pi$
$47$	4.94233	−	8.56037i	0.720913	−	1.24866i	0.960634	−	0.277817i	$-0.0896108\pi$
$48$		0			0
$49$	0.356586	+	0.617625i	0.0509409	+	0.0882322i
$50$		0			0
$51$	−4.18075	−	2.71820i	−0.585422	−	0.380624i
$52$		0			0
$53$	−2.86564	+	2.86564i	−0.393626	+	0.393626i	−0.875978	−	0.482352i	$-0.839783\pi$
$53$	−2.86564	+	2.86564i	−0.393626	+	0.393626i	0.482352	+	0.875978i	$0.339783\pi$
$54$		0			0
$55$			2.09206i			0.282093i
$56$		0			0
$57$	−1.76790	−	8.33934i	−0.234165	−	1.10457i
$58$		0			0
$59$	−2.15652	−	0.577838i	−0.280755	−	0.0752281i	0.115694	−	0.993285i	$-0.463091\pi$
$59$	−2.15652	−	0.577838i	−0.280755	−	0.0752281i	−0.396449	+	0.918057i	$0.629758\pi$
$60$		0			0
$61$	4.79709	−	1.28538i	0.614204	−	0.164575i	0.0617124	−	0.998094i	$-0.480344\pi$
$61$	4.79709	−	1.28538i	0.614204	−	0.164575i	0.552491	+	0.833519i	$0.313677\pi$
$62$		0			0
$63$	−0.879800	+	8.28520i	−0.110844	+	1.04384i
$64$		0			0
$65$	0.586489	−	1.01583i	0.0727450	−	0.125998i
$66$		0			0
$67$	−3.96319	+	14.7908i	−0.484181	+	1.80699i	0.0995397	+	0.995034i	$0.468263\pi$
$67$	−3.96319	+	14.7908i	−0.484181	+	1.80699i	−0.583721	+	0.811955i	$0.698404\pi$
$68$		0			0
$69$	−7.70811	−	0.408113i	−0.927947	−	0.0491310i
$70$		0			0
$71$			13.2447i			1.57186i	0.618317	+	0.785929i	$0.287815\pi$
$71$			13.2447i			1.57186i	−0.618317	+	0.785929i	$0.712185\pi$
$72$		0			0
$73$			11.3768i			1.33155i	0.746152	+	0.665776i	$0.231899\pi$
$73$			11.3768i			1.33155i	−0.746152	+	0.665776i	$0.768101\pi$
$74$		0			0
$75$	3.72395	+	7.31836i	0.430004	+	0.845051i
$76$		0			0
$77$	2.95384	−	11.0239i	0.336621	−	1.25629i
$78$		0			0
$79$	1.56750	−	2.71499i	0.176358	−	0.305460i	−0.764273	−	0.644893i	$-0.776902\pi$
$79$	1.56750	−	2.71499i	0.176358	−	0.305460i	0.940630	+	0.339433i	$0.110235\pi$
$80$		0			0
$81$	−6.03652	+	6.67536i	−0.670724	+	0.741707i
$82$		0			0
$83$	−11.0286	+	2.95510i	−1.21055	+	0.324365i	−0.806976	−	0.590584i	$-0.798897\pi$
$83$	−11.0286	+	2.95510i	−1.21055	+	0.324365i	−0.403569	+	0.914949i	$0.632231\pi$
$84$		0			0
$85$	−1.41578	−	0.379358i	−0.153563	−	0.0411472i
$86$		0			0
$87$	−10.0325	−	3.26570i	−1.07559	−	0.350119i
$88$		0			0
$89$		−	2.37475i		−	0.251723i	−0.992048	−	0.125862i	$-0.959830\pi$
$89$		−	2.37475i		−	0.251723i	0.992048	−	0.125862i	$-0.0401696\pi$
$90$		0			0
$91$	−4.52472	+	4.52472i	−0.474319	+	0.474319i
$92$		0			0
$93$	0.234979	−	4.43810i	0.0243662	−	0.460210i
$94$		0			0
$95$	−1.25282	−	2.16994i	−0.128536	−	0.222631i
$96$		0			0
$97$	−5.04313	+	8.73496i	−0.512052	+	0.886900i	0.487850	+	0.872927i	$0.337781\pi$
$97$	−5.04313	+	8.73496i	−0.512052	+	0.886900i	−0.999902	+	0.0139730i	$0.995552\pi$
$98$		0			0
$99$	9.58904	−	7.74803i	0.963735	−	0.778706i
$100$		0			0
$101$	1.55666	+	5.80953i	0.154893	+	0.578070i	0.999114	+	0.0420749i	$0.0133968\pi$
$101$	1.55666	+	5.80953i	0.154893	+	0.578070i	−0.844221	+	0.535995i	$0.819937\pi$
$102$		0			0
$103$	11.7431	−	6.77986i	1.15708	−	0.668039i	0.206476	−	0.978452i	$-0.433800\pi$
$103$	11.7431	−	6.77986i	1.15708	−	0.668039i	0.950602	+	0.310412i	$0.100467\pi$
$104$		0			0
$105$	0.507877	+	2.39569i	0.0495637	+	0.233796i
$106$		0			0
$107$	−2.81971	+	2.81971i	−0.272592	+	0.272592i	−0.830143	−	0.557551i	$-0.811741\pi$
$107$	−2.81971	+	2.81971i	−0.272592	+	0.272592i	0.557551	+	0.830143i	$0.311741\pi$
$108$		0			0
$109$	3.20455	+	3.20455i	0.306940	+	0.306940i	0.843721	−	0.536781i	$-0.180360\pi$
$109$	3.20455	+	3.20455i	0.306940	+	0.306940i	−0.536781	+	0.843721i	$0.680360\pi$
$110$		0			0
$111$	−18.3099	+	3.88163i	−1.73790	+	0.368428i
$112$		0			0
$113$	−5.07913	−	8.79731i	−0.477804	−	0.827581i	0.521872	−	0.853024i	$-0.325234\pi$
$113$	−5.07913	−	8.79731i	−0.477804	−	0.827581i	−0.999676	+	0.0254424i	$0.991901\pi$
$114$		0			0
$115$	−2.19149	+	0.587207i	−0.204357	+	0.0547573i
$116$		0			0
$117$	−6.82817	+	1.07397i	−0.631265	+	0.0992882i
$118$		0			0
$119$	6.92469	+	3.99797i	0.634785	+	0.366493i
$120$		0			0
$121$	−5.09817	+	2.94343i	−0.463470	+	0.267584i
$122$		0			0
$123$	−9.68107	−	0.512573i	−0.872912	−	0.0462171i
$124$		0			0
$125$	3.50655	+	3.50655i	0.313636	+	0.313636i
$126$		0			0
$127$	−7.32268			−0.649783			−0.324892	−	0.945751i	$-0.605328\pi$
$127$	−7.32268			−0.649783			−0.324892	+	0.945751i	$0.605328\pi$
$128$		0			0
$129$	−1.88799	+	5.80004i	−0.166228	+	0.510665i
$130$		0			0
$131$	5.31322	−	19.8292i	0.464218	−	1.73249i	−0.195250	−	0.980754i	$-0.562552\pi$
$131$	5.31322	−	19.8292i	0.464218	−	1.73249i	0.659468	−	0.751733i	$-0.270782\pi$
$132$		0			0
$133$	3.53777	+	13.2031i	0.306764	+	1.14486i
$134$		0			0
$135$	−1.07985	+	2.41490i	−0.0929384	+	0.207842i
$136$		0			0
$137$	−10.0888	−	5.82479i	−0.861947	−	0.497646i	0.00271649	−	0.999996i	$-0.499135\pi$
$137$	−10.0888	−	5.82479i	−0.861947	−	0.497646i	−0.864664	+	0.502351i	$0.832469\pi$
$138$		0			0
$139$	11.5413	+	3.09248i	0.978918	+	0.262300i	0.712589	−	0.701582i	$-0.247522\pi$
$139$	11.5413	+	3.09248i	0.978918	+	0.262300i	0.266329	+	0.963882i	$0.414189\pi$
$140$		0			0
$141$	−15.2589	+	7.76447i	−1.28503	+	0.653886i
$142$		0			0
$143$	9.46813			0.791765
$144$		0			0
$145$	−3.10110			−0.257533
$146$		0			0
$147$	0.0653099	−	1.23352i	0.00538667	−	0.101739i
$148$		0			0
$149$	1.01009	+	0.270654i	0.0827502	+	0.0221728i	0.299957	−	0.953953i	$-0.403028\pi$
$149$	1.01009	+	0.270654i	0.0827502	+	0.0221728i	−0.217206	+	0.976126i	$0.569694\pi$
$150$		0			0
$151$	−11.0495	−	6.37943i	−0.899195	−	0.519150i	−0.0222559	−	0.999752i	$-0.507085\pi$
$151$	−11.0495	−	6.37943i	−0.899195	−	0.519150i	−0.876939	+	0.480602i	$0.840418\pi$
$152$		0			0
$153$	3.50461	+	7.89427i	0.283331	+	0.638214i
$154$		0			0
$155$	−0.338097	−	1.26179i	−0.0271566	−	0.101350i
$156$		0			0
$157$	−2.95544	+	11.0299i	−0.235870	+	0.880279i	0.741885	+	0.670527i	$0.233932\pi$
$157$	−2.95544	+	11.0299i	−0.235870	+	0.880279i	−0.977755	+	0.209751i	$0.932735\pi$
$158$		0			0
$159$	6.86675	−	1.45572i	0.544569	−	0.115446i
$160$		0			0
$161$	12.3769			0.975436
$162$		0			0
$163$	4.61842	+	4.61842i	0.361742	+	0.361742i	0.864454	−	0.502712i	$-0.167664\pi$
$163$	4.61842	+	4.61842i	0.361742	+	0.361742i	−0.502712	+	0.864454i	$0.667664\pi$
$164$		0			0
$165$	1.97516	−	3.03791i	0.153766	−	0.236501i
$166$		0			0
$167$	6.85336	−	3.95679i	0.530329	−	0.306186i	−0.210821	−	0.977525i	$-0.567614\pi$
$167$	6.85336	−	3.95679i	0.530329	−	0.306186i	0.741150	+	0.671339i	$0.234280\pi$
$168$		0			0
$169$	6.66095	+	3.84570i	0.512381	+	0.295823i
$170$		0			0
$171$	−5.30615	+	13.7788i	−0.405772	+	1.05369i
$172$		0			0
$173$	−20.9267	+	5.60729i	−1.59103	+	0.426315i	−0.942317	−	0.334721i	$-0.891358\pi$
$173$	−20.9267	+	5.60729i	−1.59103	+	0.426315i	−0.648711	+	0.761035i	$0.724691\pi$
$174$		0			0
$175$	−6.58325	−	11.4025i	−0.497647	−	0.861949i
$176$		0			0
$177$	2.58596	+	2.87511i	0.194373	+	0.216106i
$178$		0			0
$179$	−4.24438	−	4.24438i	−0.317240	−	0.317240i	0.530466	−	0.847706i	$-0.322017\pi$
$179$	−4.24438	−	4.24438i	−0.317240	−	0.317240i	−0.847706	+	0.530466i	$0.822017\pi$
$180$		0			0
$181$	10.0752	−	10.0752i	0.748886	−	0.748886i	−0.225384	−	0.974270i	$-0.572364\pi$
$181$	10.0752	−	10.0752i	0.748886	−	0.748886i	0.974270	+	0.225384i	$0.0723638\pi$
$182$		0			0
$183$	−8.17946	−	2.66252i	−0.604643	−	0.196819i
$184$		0			0
$185$	−4.76434	+	2.75069i	−0.350281	+	0.202235i
$186$		0			0
$187$	−3.06213	−	11.4280i	−0.223925	−	0.835700i
$188$		0			0
$189$	9.09981	−	11.2004i	0.661914	−	0.814710i
$190$		0			0
$191$	−5.46820	+	9.47119i	−0.395665	+	0.685312i	−0.993186	−	0.116542i	$-0.962819\pi$
$191$	−5.46820	+	9.47119i	−0.395665	+	0.685312i	0.597521	+	0.801853i	$0.296152\pi$
$192$		0			0
$193$	−9.82326	−	17.0144i	−0.707094	−	1.22472i	−0.965931	−	0.258801i	$-0.916673\pi$
$193$	−9.82326	−	17.0144i	−0.707094	−	1.22472i	0.258837	−	0.965921i	$-0.416661\pi$
$194$		0			0
$195$	−1.81071	+	0.921381i	−0.129668	+	0.0659815i
$196$		0			0
$197$	−17.9489	+	17.9489i	−1.27881	+	1.27881i	−0.337472	+	0.941336i	$0.609572\pi$
$197$	−17.9489	+	17.9489i	−1.27881	+	1.27881i	−0.941336	+	0.337472i	$0.890428\pi$
$198$		0			0
$199$		−	10.7912i		−	0.764966i	−0.923963	−	0.382483i	$-0.875069\pi$
$199$		−	10.7912i		−	0.764966i	0.923963	−	0.382483i	$-0.124931\pi$
$200$		0			0
$201$	19.7194	−	17.7362i	1.39090	−	1.25102i
$202$		0			0
$203$	16.3409	+	4.37854i	1.14691	+	0.307313i
$204$		0			0
$205$	−2.75242	+	0.737508i	−0.192237	+	0.0515098i
$206$		0			0
$207$	10.8077	+	7.87002i	0.751190	+	0.547004i
$208$		0			0
$209$	10.1126	−	17.5155i	0.699501	−	1.21157i
$210$		0			0
$211$	−2.28982	+	8.54571i	−0.157637	+	0.588311i	0.841228	+	0.540681i	$0.181833\pi$
$211$	−2.28982	+	8.54571i	−0.157637	+	0.588311i	−0.998865	+	0.0476299i	$0.984833\pi$
$212$		0			0
$213$	12.5046	−	19.2328i	0.856802	−	1.31781i
$214$		0			0
$215$			1.79283i			0.122270i
$216$		0			0
$217$			7.12625i			0.483762i
$218$		0			0
$219$	10.7411	−	16.5204i	0.725814	−	1.11634i
$220$		0			0
$221$	−1.71688	+	6.40747i	−0.115490	+	0.431013i
$222$		0			0
$223$	−7.53363	+	13.0486i	−0.504489	+	0.873800i	0.495498	+	0.868609i	$0.334986\pi$
$223$	−7.53363	+	13.0486i	−0.504489	+	0.873800i	−0.999987	+	0.00519105i	$0.998348\pi$
$224$		0			0
$225$	1.50183	−	14.1429i	0.100122	−	0.942863i
$226$		0			0
$227$	−5.94741	+	1.59360i	−0.394743	+	0.105771i	−0.450730	−	0.892660i	$-0.648836\pi$
$227$	−5.94741	+	1.59360i	−0.394743	+	0.105771i	0.0559866	+	0.998432i	$0.482170\pi$
$228$		0			0
$229$	4.03435	+	1.08100i	0.266597	+	0.0714345i	0.389641	−	0.920967i	$-0.372599\pi$
$229$	4.03435	+	1.08100i	0.266597	+	0.0714345i	−0.123044	+	0.992401i	$0.539266\pi$
$230$		0			0
$231$	−14.6972	+	13.2191i	−0.967005	+	0.869756i
$232$		0			0
$233$			1.71937i			0.112640i	0.998413	+	0.0563200i	$0.0179367\pi$
$233$			1.71937i			0.112640i	−0.998413	+	0.0563200i	$0.982063\pi$
$234$		0			0
$235$	−3.55834	+	3.55834i	−0.232120	+	0.232120i
$236$		0			0
$237$	−4.83947	+	2.46256i	−0.314357	+	0.159961i
$238$		0			0
$239$	−4.99586	−	8.65308i	−0.323155	−	0.559721i	0.657982	−	0.753034i	$-0.271410\pi$
$239$	−4.99586	−	8.65308i	−0.323155	−	0.559721i	−0.981137	+	0.193312i	$0.938077\pi$
$240$		0			0
$241$	10.9017	−	18.8822i	0.702238	−	1.21631i	−0.265442	−	0.964127i	$-0.585518\pi$
$241$	10.9017	−	18.8822i	0.702238	−	1.21631i	0.967679	−	0.252184i	$-0.0811489\pi$
$242$		0			0
$243$	15.0681	−	3.99418i	0.966617	−	0.256226i
$244$		0			0
$245$	−0.0939703	−	0.350702i	−0.00600354	−	0.0224055i
$246$		0			0
$247$	−9.82059	+	5.66992i	−0.624869	+	0.360768i
$248$		0			0
$249$	18.8047	+	6.12119i	1.19170	+	0.387915i
$250$		0			0
$251$	−0.351987	+	0.351987i	−0.0222172	+	0.0222172i	−0.718128	−	0.695911i	$-0.755001\pi$
$251$	−0.351987	+	0.351987i	−0.0222172	+	0.0222172i	0.695911	+	0.718128i	$0.255001\pi$
$252$		0			0
$253$	−12.9495	−	12.9495i	−0.814131	−	0.814131i
$254$		0			0
$255$	1.69772	+	1.88754i	0.106315	+	0.118203i
$256$		0			0
$257$	5.69516	+	9.86431i	0.355254	+	0.615319i	0.987161	−	0.159726i	$-0.0510609\pi$
$257$	5.69516	+	9.86431i	0.355254	+	0.615319i	−0.631907	+	0.775044i	$0.717728\pi$
$258$		0			0
$259$	28.9889	−	7.76756i	1.80129	−	0.482653i
$260$		0			0
$261$	11.4851	+	14.2140i	0.710907	+	0.879826i
$262$		0			0
$263$	−4.43754	−	2.56201i	−0.273630	−	0.157980i	0.356906	−	0.934140i	$-0.383832\pi$
$263$	−4.43754	−	2.56201i	−0.273630	−	0.157980i	−0.630536	+	0.776160i	$0.717165\pi$
$264$		0			0
$265$	1.78676	−	1.03159i	0.109760	−	0.0633700i
$266$		0			0
$267$	−2.24206	+	3.44841i	−0.137212	+	0.211039i
$268$		0			0
$269$	8.67269	+	8.67269i	0.528784	+	0.528784i	0.920210	−	0.391426i	$-0.128018\pi$
$269$	8.67269	+	8.67269i	0.528784	+	0.528784i	−0.391426	+	0.920210i	$0.628018\pi$
$270$		0			0
$271$	19.6128			1.19139			0.595696	−	0.803210i	$-0.296876\pi$
$271$	19.6128			1.19139			0.595696	+	0.803210i	$0.296876\pi$
$272$		0			0
$273$	10.8423	−	2.29852i	0.656205	−	0.139113i
$274$		0			0
$275$	−5.04225	+	18.8179i	−0.304059	+	1.13476i
$276$		0			0
$277$	4.36219	+	16.2799i	0.262099	+	0.978165i	0.964002	+	0.265893i	$0.0856669\pi$
$277$	4.36219	+	16.2799i	0.262099	+	0.978165i	−0.701904	+	0.712272i	$0.747666\pi$
$278$		0			0
$279$	−4.53133	+	6.22278i	−0.271283	+	0.372548i
$280$		0			0
$281$	−14.0437	−	8.10816i	−0.837780	−	0.483692i	0.0187292	−	0.999825i	$-0.494038\pi$
$281$	−14.0437	−	8.10816i	−0.837780	−	0.483692i	−0.856509	+	0.516132i	$0.827371\pi$
$282$		0			0
$283$	0.905572	+	0.242647i	0.0538307	+	0.0144239i	0.285634	−	0.958339i	$-0.407796\pi$
$283$	0.905572	+	0.242647i	0.0538307	+	0.0144239i	−0.231803	+	0.972763i	$0.574463\pi$
$284$		0			0
$285$	−0.229457	+	4.33381i	−0.0135919	+	0.256713i
$286$		0			0
$287$	15.5449			0.917584
$288$		0			0
$289$	−8.71092			−0.512407
$290$		0			0
$291$	15.5701	−	7.92282i	0.912733	−	0.464444i
$292$		0			0
$293$	9.76797	+	2.61732i	0.570651	+	0.152905i	0.532595	−	0.846370i	$-0.321217\pi$
$293$	9.76797	+	2.61732i	0.570651	+	0.152905i	0.0380557	+	0.999276i	$0.487884\pi$
$294$		0			0
$295$	0.984330	+	0.568303i	0.0573099	+	0.0330879i
$296$		0			0
$297$	−21.2395	+	2.19779i	−1.23244	+	0.127529i
$298$		0			0
$299$	2.65755	+	9.91811i	0.153690	+	0.573579i
$300$		0			0
$301$	2.53135	−	9.44713i	0.145905	−	0.544524i
$302$		0			0
$303$	3.22446	−	9.90578i	0.185240	−	0.569072i
$304$		0			0
$305$	−2.52833			−0.144772
$306$		0			0
$307$	−16.1653	−	16.1653i	−0.922603	−	0.922603i	0.0746101	−	0.997213i	$-0.476229\pi$
$307$	−16.1653	−	16.1653i	−0.922603	−	0.922603i	−0.997213	+	0.0746101i	$0.976229\pi$
$308$		0			0
$309$	−23.4533	−	1.24175i	−1.33421	−	0.0706409i
$310$		0			0
$311$	−11.8457	+	6.83912i	−0.671708	+	0.387811i	−0.796724	−	0.604344i	$-0.793435\pi$
$311$	−11.8457	+	6.83912i	−0.671708	+	0.387811i	0.125015	+	0.992155i	$0.460102\pi$
$312$		0			0
$313$	−22.5829	−	13.0383i	−1.27646	−	0.736966i	−0.300266	−	0.953855i	$-0.597075\pi$
$313$	−22.5829	−	13.0383i	−1.27646	−	0.736966i	−0.976196	+	0.216890i	$0.930409\pi$
$314$		0			0
$315$	1.52433	−	3.95831i	0.0858863	−	0.223026i
$316$		0			0
$317$	−14.9639	+	4.00957i	−0.840457	+	0.225200i	−0.653270	−	0.757125i	$-0.726604\pi$
$317$	−14.9639	+	4.00957i	−0.840457	+	0.225200i	−0.187187	+	0.982324i	$0.559937\pi$
$318$		0			0
$319$	−12.5159	−	21.6781i	−0.700753	−	1.21374i
$320$		0			0
$321$	6.75670	−	1.43239i	0.377122	−	0.0799483i
$322$		0			0
$323$	10.0197	+	10.0197i	0.557512	+	0.557512i
$324$		0			0
$325$	7.72375	−	7.72375i	0.428437	−	0.428437i
$326$		0			0
$327$	−1.62788	−	7.67885i	−0.0900222	−	0.424641i
$328$		0			0
$329$	23.7744	−	13.7261i	1.31072	−	0.756747i
$330$		0			0
$331$	2.82670	+	10.5494i	0.155370	+	0.579847i	0.999073	+	0.0430383i	$0.0137038\pi$
$331$	2.82670	+	10.5494i	0.155370	+	0.579847i	−0.843704	+	0.536809i	$0.819630\pi$
$332$		0			0
$333$	30.2528	+	11.6502i	1.65784	+	0.638429i
$334$		0			0
$335$	3.89779	−	6.75118i	0.212959	−	0.368856i
$336$		0			0
$337$	−2.81502	−	4.87577i	−0.153344	−	0.265600i	0.779111	−	0.626886i	$-0.215671\pi$
$337$	−2.81502	−	4.87577i	−0.153344	−	0.265600i	−0.932455	+	0.361287i	$0.882338\pi$
$338$		0			0
$339$	−0.930260	+	17.5700i	−0.0505248	+	0.954272i
$340$		0			0
$341$	7.45597	−	7.45597i	0.403763	−	0.403763i
$342$		0			0
$343$		−	17.4602i		−	0.942760i
$344$		0			0
$345$	3.73668	+	1.21634i	0.201176	+	0.0654855i
$346$		0			0
$347$	−1.40004	−	0.375139i	−0.0751579	−	0.0201385i	0.221044	−	0.975264i	$-0.429054\pi$
$347$	−1.40004	−	0.375139i	−0.0751579	−	0.0201385i	−0.296202	+	0.955125i	$0.595720\pi$
$348$		0			0
$349$	4.05103	−	1.08547i	0.216847	−	0.0581039i	−0.148760	−	0.988873i	$-0.547528\pi$
$349$	4.05103	−	1.08547i	0.216847	−	0.0581039i	0.365607	+	0.930769i	$0.380861\pi$
$350$		0			0
$351$	10.9292	+	4.88711i	0.583360	+	0.260854i
$352$		0			0
$353$	−5.70555	+	9.88230i	−0.303676	+	0.525982i	−0.976966	−	0.213397i	$-0.931547\pi$
$353$	−5.70555	+	9.88230i	−0.303676	+	0.525982i	0.673290	+	0.739379i	$0.264881\pi$
$354$		0			0
$355$	1.74517	−	6.51307i	0.0926242	−	0.345678i
$356$		0			0
$357$	−6.28086	−	12.3433i	−0.332419	−	0.653275i
$358$		0			0
$359$		−	1.05572i		−	0.0557189i	−0.999612	−	0.0278594i	$-0.991131\pi$
$359$		−	1.05572i		−	0.0557189i	0.999612	−	0.0278594i	$-0.00886909\pi$
$360$		0			0
$361$			5.22336i			0.274914i
$362$		0			0
$363$	10.1821	+	0.539099i	0.534420	+	0.0282953i
$364$		0			0
$365$	1.49905	−	5.59452i	0.0784638	−	0.292831i
$366$		0			0
$367$	−4.67503	+	8.09739i	−0.244035	+	0.422680i	−0.961860	−	0.273543i	$-0.911804\pi$
$367$	−4.67503	+	8.09739i	−0.244035	+	0.422680i	0.717825	+	0.696223i	$0.245138\pi$
$368$		0			0
$369$	13.5741	+	9.88442i	0.706638	+	0.514562i
$370$		0			0
$371$	−10.8717	+	2.91306i	−0.564430	+	0.151239i
$372$		0			0
$373$	5.80682	+	1.55593i	0.300666	+	0.0805631i	0.405998	−	0.913874i	$-0.366924\pi$
$373$	5.80682	+	1.55593i	0.300666	+	0.0805631i	−0.105332	+	0.994437i	$0.533591\pi$
$374$		0			0
$375$	−1.78130	−	8.40253i	−0.0919860	−	0.433905i
$376$		0			0
$377$			14.0348i			0.722828i
$378$		0			0
$379$	−6.35334	+	6.35334i	−0.326349	+	0.326349i	−0.851196	−	0.524847i	$-0.824122\pi$
$379$	−6.35334	+	6.35334i	−0.326349	+	0.326349i	0.524847	+	0.851196i	$0.324122\pi$
$380$		0			0
$381$	10.6334	+	6.91350i	0.544764	+	0.354190i
$382$		0			0
$383$	10.8961	+	18.8725i	0.556762	+	0.964341i	0.997764	+	0.0668344i	$0.0212899\pi$
$383$	10.8961	+	18.8725i	0.556762	+	0.964341i	−0.441002	+	0.897506i	$0.645377\pi$
$384$		0			0
$385$	−2.90510	+	5.03178i	−0.148058	+	0.256443i
$386$		0			0
$387$	8.21751	−	6.63982i	0.417720	−	0.337521i
$388$		0			0
$389$	−1.30926	−	4.88623i	−0.0663822	−	0.247742i	0.924759	−	0.380553i	$-0.124266\pi$
$389$	−1.30926	−	4.88623i	−0.0663822	−	0.247742i	−0.991141	+	0.132811i	$0.957600\pi$
$390$		0			0
$391$	11.1117	−	6.41532i	0.561941	−	0.324437i
$392$		0			0
$393$	−26.4366	+	23.7779i	−1.33355	+	1.19944i
$394$		0			0
$395$	−1.12855	+	1.12855i	−0.0567837	+	0.0567837i
$396$		0			0
$397$	2.11018	+	2.11018i	0.105907	+	0.105907i	0.758075	−	0.652168i	$-0.226140\pi$
$397$	2.11018	+	2.11018i	0.105907	+	0.105907i	−0.652168	+	0.758075i	$0.726140\pi$
$398$		0			0
$399$	7.32813	−	22.5126i	0.366865	−	1.12704i
$400$		0			0
$401$	4.22120	+	7.31133i	0.210797	+	0.365110i	0.951964	−	0.306210i	$-0.0990609\pi$
$401$	4.22120	+	7.31133i	0.210797	+	0.365110i	−0.741168	+	0.671320i	$0.765728\pi$
$402$		0			0
$403$	−5.71055	+	1.53014i	−0.284463	+	0.0762216i
$404$		0			0
$405$	3.84802	−	2.48721i	0.191210	−	0.123590i
$406$		0			0
$407$	−38.4572	−	22.2032i	−1.90625	−	1.10057i
$408$		0			0
$409$	34.4821	−	19.9082i	1.70503	−	0.984399i	0.764539	−	0.644577i	$-0.222967\pi$
$409$	34.4821	−	19.9082i	1.70503	−	0.984399i	0.940490	−	0.339822i	$-0.110367\pi$
$410$		0			0
$411$	9.15082	+	17.9834i	0.451377	+	0.887053i
$412$		0			0
$413$	−4.38441	−	4.38441i	−0.215743	−	0.215743i
$414$		0			0
$415$	5.81268			0.285333
$416$		0			0
$417$	−13.8396	−	15.3870i	−0.677727	−	0.753505i
$418$		0			0
$419$	1.69652	−	6.33148i	0.0828802	−	0.309313i	−0.912024	−	0.410137i	$-0.865481\pi$
$419$	1.69652	−	6.33148i	0.0828802	−	0.309313i	0.994904	+	0.100823i	$0.0321477\pi$
$420$		0			0
$421$	−8.71468	−	32.5236i	−0.424727	−	1.58510i	−0.764518	−	0.644603i	$-0.777023\pi$
$421$	−8.71468	−	32.5236i	−0.424727	−	1.58510i	0.339790	−	0.940501i	$-0.389644\pi$
$422$		0			0
$423$	29.4882	+	3.13134i	1.43377	+	0.152251i
$424$		0			0
$425$	−11.8205	−	6.82459i	−0.573380	−	0.331041i
$426$		0			0
$427$	13.3228	+	3.56982i	0.644733	+	0.172756i
$428$		0			0
$429$	−13.7488	−	8.93907i	−0.663798	−	0.431582i
$430$		0			0
$431$	−19.0914			−0.919602			−0.459801	−	0.888022i	$-0.652079\pi$
$431$	−19.0914			−0.919602			−0.459801	+	0.888022i	$0.652079\pi$
$432$		0			0
$433$	−4.98594			−0.239609			−0.119805	−	0.992797i	$-0.538227\pi$
$433$	−4.98594			−0.239609			−0.119805	+	0.992797i	$0.538227\pi$
$434$		0			0
$435$	4.50315	+	2.92782i	0.215910	+	0.140378i
$436$		0			0
$437$	21.1863	+	5.67687i	1.01348	+	0.271561i
$438$		0			0
$439$	11.1893	+	6.46017i	0.534038	+	0.308327i	0.742659	−	0.669670i	$-0.233564\pi$
$439$	11.1893	+	6.46017i	0.534038	+	0.308327i	−0.208621	+	0.977997i	$0.566898\pi$
$440$		0			0
$441$	−1.25943	+	1.72955i	−0.0599730	+	0.0823597i
$442$		0			0
$443$	−3.84803	−	14.3610i	−0.182825	−	0.682314i	−0.995086	−	0.0990185i	$-0.968430\pi$
$443$	−3.84803	−	14.3610i	−0.182825	−	0.682314i	0.812260	−	0.583295i	$-0.198237\pi$
$444$		0			0
$445$	−0.312907	+	1.16778i	−0.0148332	+	0.0553583i
$446$		0			0
$447$	−1.21124	−	1.34667i	−0.0572898	−	0.0636954i
$448$		0			0
$449$	−3.60684			−0.170217			−0.0851086	−	0.996372i	$-0.527124\pi$
$449$	−3.60684			−0.170217			−0.0851086	+	0.996372i	$0.527124\pi$
$450$		0			0
$451$	−16.2641	−	16.2641i	−0.765846	−	0.765846i
$452$		0			0
$453$	10.0222	+	19.6957i	0.470882	+	0.925385i
$454$		0			0
$455$	2.82122	−	1.62883i	0.132261	−	0.0763608i
$456$		0			0
$457$	−4.13238	−	2.38583i	−0.193304	−	0.111604i	0.400224	−	0.916417i	$-0.368932\pi$
$457$	−4.13238	−	2.38583i	−0.193304	−	0.111604i	−0.593529	+	0.804813i	$0.702266\pi$
$458$		0			0
$459$	2.36406	−	14.7721i	0.110345	−	0.689505i
$460$		0			0
$461$	22.7740	−	6.10228i	1.06069	−	0.284212i	0.314029	−	0.949413i	$-0.398321\pi$
$461$	22.7740	−	6.10228i	1.06069	−	0.284212i	0.746664	+	0.665202i	$0.231655\pi$
$462$		0			0
$463$	−15.9602	−	27.6439i	−0.741735	−	1.28472i	−0.951705	−	0.307014i	$-0.900670\pi$
$463$	−15.9602	−	27.6439i	−0.741735	−	1.28472i	0.209970	−	0.977708i	$-0.432663\pi$
$464$		0			0
$465$	−0.700332	+	2.15147i	−0.0324771	+	0.0997721i
$466$		0			0
$467$	−7.26104	−	7.26104i	−0.336001	−	0.336001i	0.518859	−	0.854860i	$-0.326357\pi$
$467$	−7.26104	−	7.26104i	−0.336001	−	0.336001i	−0.854860	+	0.518859i	$0.826357\pi$
$468$		0			0
$469$	−30.0712	+	30.0712i	−1.38856	+	1.38856i
$470$		0			0
$471$	14.7052	−	13.2263i	0.677579	−	0.609436i
$472$		0			0
$473$	−12.5327	+	7.23576i	−0.576254	+	0.332700i
$474$		0			0
$475$	−6.03903	−	22.5380i	−0.277090	−	1.03411i
$476$		0			0
$477$	−11.3457	−	4.36917i	−0.519483	−	0.200051i
$478$		0			0
$479$	−13.4733	+	23.3364i	−0.615609	+	1.06627i	0.374669	+	0.927159i	$0.377756\pi$
$479$	−13.4733	+	23.3364i	−0.615609	+	1.06627i	−0.990277	+	0.139107i	$0.955577\pi$
$480$		0			0
$481$	12.4489	+	21.5622i	0.567622	+	0.983151i
$482$		0			0
$483$	−17.9727	−	11.6853i	−0.817784	−	0.531699i
$484$		0			0
$485$	3.63091	−	3.63091i	0.164871	−	0.164871i
$486$		0			0
$487$			33.3405i			1.51080i	0.655264	+	0.755400i	$0.272558\pi$
$487$			33.3405i			1.51080i	−0.655264	+	0.755400i	$0.727442\pi$
$488$		0			0
$489$	−2.34612	−	11.0668i	−0.106095	−	0.500459i
$490$		0			0
$491$	−22.4169	−	6.00659i	−1.01166	−	0.271074i	−0.285338	−	0.958427i	$-0.592106\pi$
$491$	−22.4169	−	6.00659i	−1.01166	−	0.271074i	−0.726323	+	0.687353i	$0.758772\pi$
$492$		0			0
$493$	16.9400	−	4.53906i	0.762939	−	0.204429i
$494$		0			0
$495$	−5.73631	+	2.54660i	−0.257828	+	0.114461i
$496$		0			0
$497$	−18.3920	+	31.8559i	−0.824994	+	1.42893i
$498$		0			0
$499$	−4.03564	+	15.0612i	−0.180660	+	0.674233i	0.814858	+	0.579661i	$0.196815\pi$
$499$	−4.03564	+	15.0612i	−0.180660	+	0.674233i	−0.995518	+	0.0945722i	$0.969852\pi$
$500$		0			0
$501$	−13.6876	−	0.724700i	−0.611515	−	0.0323772i
$502$		0			0
$503$			26.2715i			1.17139i	0.810533	+	0.585693i	$0.199178\pi$
$503$			26.2715i			1.17139i	−0.810533	+	0.585693i	$0.800822\pi$
$504$		0			0
$505$		−	3.06194i		−	0.136255i
$506$		0			0
$507$	−6.04165	−	11.8731i	−0.268319	−	0.527305i
$508$		0			0
$509$	−7.08716	+	26.4496i	−0.314133	+	1.17236i	0.610661	+	0.791892i	$0.290904\pi$
$509$	−7.08716	+	26.4496i	−0.314133	+	1.17236i	−0.924794	+	0.380468i	$0.875763\pi$
$510$		0			0
$511$	−15.7981	+	27.3632i	−0.698869	+	1.21048i
$512$		0			0
$513$	20.7140	−	14.9987i	0.914545	−	0.662209i
$514$		0			0
$515$	−6.66798	+	1.78668i	−0.293826	+	0.0787305i
$516$		0			0
$517$	−39.2356	−	10.5131i	−1.72558	−	0.462368i
$518$		0			0
$519$	35.6819	+	11.6149i	1.56626	+	0.509839i
$520$		0			0
$521$			13.9069i			0.609272i	0.952469	+	0.304636i	$0.0985348\pi$
$521$			13.9069i			0.609272i	−0.952469	+	0.304636i	$0.901465\pi$
$522$		0			0
$523$	−14.8539	+	14.8539i	−0.649517	+	0.649517i	−0.952876	−	0.303359i	$-0.901892\pi$
$523$	−14.8539	+	14.8539i	−0.649517	+	0.649517i	0.303359	+	0.952876i	$0.401892\pi$
$524$		0			0
$525$	−1.20574	+	22.7731i	−0.0526230	+	0.993901i
$526$		0			0
$527$	3.69375	+	6.39777i	0.160902	+	0.278691i
$528$		0			0
$529$	−1.56975	+	2.71888i	−0.0682499	+	0.118212i
$530$		0			0
$531$	−1.04066	−	6.61645i	−0.0451610	−	0.287129i
$532$		0			0
$533$	3.33777	+	12.4567i	0.144575	+	0.539561i
$534$		0			0
$535$	1.75813	−	1.01506i	0.0760105	−	0.0438847i
$536$		0			0
$537$	2.15611	+	10.1705i	0.0930430	+	0.438891i
$538$		0			0
$539$	2.07230	−	2.07230i	0.0892605	−	0.0892605i
$540$		0			0
$541$	−30.6206	−	30.6206i	−1.31648	−	1.31648i	−0.916542	−	0.399939i	$-0.869031\pi$
$541$	−30.6206	−	30.6206i	−1.31648	−	1.31648i	−0.399939	−	0.916542i	$-0.630969\pi$
$542$		0			0
$543$	−24.1426	+	5.11813i	−1.03606	+	0.219640i
$544$		0			0
$545$	−1.15359	−	1.99808i	−0.0494144	−	0.0855882i
$546$		0			0
$547$	−0.751802	+	0.201445i	−0.0321447	+	0.00861315i	−0.274856	−	0.961486i	$-0.588630\pi$
$547$	−0.751802	+	0.201445i	−0.0321447	+	0.00861315i	0.242711	+	0.970099i	$0.421963\pi$
$548$		0			0
$549$	9.36376	+	11.5887i	0.399636	+	0.494593i
$550$		0			0
$551$	25.9635	+	14.9901i	1.10608	+	0.638598i
$552$		0			0
$553$	7.54023	−	4.35336i	0.320643	−	0.185124i
$554$		0			0
$555$	9.51535	+	0.503799i	0.403904	+	0.0213851i
$556$		0			0
$557$	−15.1991	−	15.1991i	−0.644006	−	0.644006i	0.307532	−	0.951538i	$-0.400497\pi$
$557$	−15.1991	−	15.1991i	−0.644006	−	0.644006i	−0.951538	+	0.307532i	$0.900497\pi$
$558$		0			0
$559$	8.11390			0.343181
$560$		0			0
$561$	−6.34289	+	19.4858i	−0.267797	+	0.822692i
$562$		0			0
$563$	−2.92996	+	10.9348i	−0.123483	+	0.460846i	−0.999781	−	0.0209240i	$-0.993339\pi$
$563$	−2.92996	+	10.9348i	−0.123483	+	0.460846i	0.876298	+	0.481770i	$0.160006\pi$
$564$		0			0
$565$	1.33849	+	4.99532i	0.0563107	+	0.210155i
$566$		0			0
$567$	−23.7885	+	7.67294i	−0.999023	+	0.322233i
$568$		0			0
$569$	38.8985	+	22.4581i	1.63071	+	0.941491i	0.983874	+	0.178861i	$0.0572413\pi$
$569$	38.8985	+	22.4581i	1.63071	+	0.941491i	0.646835	+	0.762630i	$0.276092\pi$
$570$		0			0
$571$	−22.0647	−	5.91221i	−0.923378	−	0.247418i	−0.234349	−	0.972152i	$-0.575296\pi$
$571$	−22.0647	−	5.91221i	−0.923378	−	0.247418i	−0.689029	+	0.724734i	$0.741963\pi$
$572$		0			0
$573$	16.8824	−	8.59061i	0.705273	−	0.358878i
$574$		0			0
$575$	−21.1275			−0.881079
$576$		0			0
$577$	−13.2304			−0.550790			−0.275395	−	0.961331i	$-0.588809\pi$
$577$	−13.2304			−0.550790			−0.275395	+	0.961331i	$0.588809\pi$
$578$		0			0
$579$	−1.79916	+	33.9812i	−0.0747707	+	1.41221i
$580$		0			0
$581$	−30.6293	−	8.20709i	−1.27072	−	0.340487i
$582$		0			0
$583$	14.4225	+	8.32685i	0.597320	+	0.344863i
$584$		0			0
$585$	3.49926	+	0.371584i	0.144677	+	0.0153631i
$586$		0			0
$587$	0.899168	+	3.35574i	0.0371126	+	0.138506i	0.981996	−	0.188900i	$-0.0604922\pi$
$587$	0.899168	+	3.35574i	0.0371126	+	0.138506i	−0.944884	+	0.327406i	$0.893825\pi$
$588$		0			0
$589$	−3.26857	+	12.1985i	−0.134679	+	0.502630i
$590$		0			0
$591$	43.0098	−	9.11790i	1.76919	−	0.375060i
$592$		0			0
$593$	−43.3013			−1.77817			−0.889086	−	0.457740i	$-0.848659\pi$
$593$	−43.3013			−1.77817			−0.889086	+	0.457740i	$0.848659\pi$
$594$		0			0
$595$	−2.87842	−	2.87842i	−0.118004	−	0.118004i
$596$		0			0
$597$	−10.1882	+	15.6700i	−0.416974	+	0.641331i
$598$		0			0
$599$	15.9727	−	9.22187i	0.652629	−	0.376795i	−0.136834	−	0.990594i	$-0.543693\pi$
$599$	15.9727	−	9.22187i	0.652629	−	0.376795i	0.789463	+	0.613799i	$0.210359\pi$
$600$		0			0
$601$	−17.7246	−	10.2333i	−0.723003	−	0.417426i	0.0928541	−	0.995680i	$-0.470401\pi$
$601$	−17.7246	−	10.2333i	−0.723003	−	0.417426i	−0.815857	+	0.578254i	$0.803734\pi$
$602$		0			0
$603$	−45.3799	+	7.13756i	−1.84801	+	0.290664i
$604$		0			0
$605$	2.89486	−	0.775674i	0.117693	−	0.0315357i
$606$		0			0
$607$	8.07865	+	13.9926i	0.327902	+	0.567944i	0.982095	−	0.188384i	$-0.0603249\pi$
$607$	8.07865	+	13.9926i	0.327902	+	0.567944i	−0.654193	+	0.756328i	$0.726992\pi$
$608$		0			0
$609$	−19.5950	−	21.7859i	−0.794029	−	0.882811i
$610$		0			0
$611$	16.1041	+	16.1041i	0.651503	+	0.651503i
$612$		0			0
$613$	22.2010	−	22.2010i	0.896689	−	0.896689i	−0.0984526	−	0.995142i	$-0.531389\pi$
$613$	22.2010	−	22.2010i	0.896689	−	0.896689i	0.995142	+	0.0984526i	$0.0313893\pi$
$614$		0			0
$615$	4.69312	+	1.52767i	0.189245	+	0.0616017i
$616$		0			0
$617$	0.887087	−	0.512160i	0.0357128	−	0.0206188i	−0.482037	−	0.876151i	$-0.660103\pi$
$617$	0.887087	−	0.512160i	0.0357128	−	0.0206188i	0.517750	+	0.855532i	$0.326770\pi$
$618$		0			0
$619$	2.14654	+	8.01100i	0.0862768	+	0.321989i	0.995553	−	0.0942040i	$-0.0300306\pi$
$619$	2.14654	+	8.01100i	0.0862768	+	0.321989i	−0.909276	+	0.416193i	$0.863364\pi$
$620$		0			0
$621$	−8.26381	−	21.6320i	−0.331615	−	0.868062i
$622$		0			0
$623$	3.29766	−	5.71171i	0.132118	−	0.228835i
$624$		0			0
$625$	10.5897	+	18.3420i	0.423590	+	0.733679i
$626$		0			0
$627$	−31.2214	+	15.8870i	−1.24686	+	0.634465i
$628$		0			0
$629$	21.9994	−	21.9994i	0.877172	−	0.877172i
$630$		0			0
$631$			17.1003i			0.680750i	0.940290	+	0.340375i	$0.110554\pi$
$631$			17.1003i			0.680750i	−0.940290	+	0.340375i	$0.889446\pi$
$632$		0			0
$633$	11.3933	−	10.2475i	0.452842	−	0.407301i
$634$		0			0
$635$	3.60092	+	0.964865i	0.142898	+	0.0382895i
$636$		0			0
$637$	−1.58719	+	0.425285i	−0.0628866	+	0.0168504i
$638$		0			0
$639$	−36.3162	+	16.1224i	−1.43665	+	0.637790i
$640$		0			0
$641$	−4.96926	+	8.60701i	−0.196274	+	0.339956i	−0.947317	−	0.320296i	$-0.896217\pi$
$641$	−4.96926	+	8.60701i	−0.196274	+	0.339956i	0.751044	+	0.660253i	$0.229551\pi$
$642$		0			0
$643$	8.95763	−	33.4303i	0.353254	−	1.31836i	−0.529413	−	0.848364i	$-0.677588\pi$
$643$	8.95763	−	33.4303i	0.353254	−	1.31836i	0.882667	−	0.469999i	$-0.155746\pi$
$644$		0			0
$645$	1.69265	−	2.60340i	0.0666481	−	0.102509i
$646$		0			0
$647$		−	41.6750i		−	1.63841i	−0.573498	−	0.819207i	$-0.694414\pi$
$647$		−	41.6750i		−	1.63841i	0.573498	−	0.819207i	$-0.305586\pi$
$648$		0			0
$649$			9.17454i			0.360132i
$650$		0			0
$651$	6.72805	−	10.3481i	0.263693	−	0.405575i
$652$		0			0
$653$	10.9418	−	40.8352i	0.428184	−	1.59800i	−0.328687	−	0.944439i	$-0.606606\pi$
$653$	10.9418	−	40.8352i	0.428184	−	1.59800i	0.756871	−	0.653565i	$-0.226727\pi$
$654$		0			0
$655$	−5.22555	+	9.05091i	−0.204179	+	0.353648i
$656$		0			0
$657$	−31.1945	+	13.8486i	−1.21701	+	0.540285i
$658$		0			0
$659$	25.4089	−	6.80828i	0.989789	−	0.265213i	0.272627	−	0.962120i	$-0.412108\pi$
$659$	25.4089	−	6.80828i	0.989789	−	0.265213i	0.717162	+	0.696907i	$0.245441\pi$
$660$		0			0
$661$	−12.8649	−	3.44715i	−0.500388	−	0.134079i	−0.000208061	−	1.00000i	$-0.500066\pi$
$661$	−12.8649	−	3.44715i	−0.500388	−	0.134079i	−0.500180	+	0.865921i	$0.666733\pi$
$662$		0			0
$663$	8.54254	−	7.68344i	0.331765	−	0.298400i
$664$		0			0
$665$		−	6.95879i		−	0.269850i
$666$		0			0
$667$	19.1954	−	19.1954i	0.743247	−	0.743247i
$668$		0			0
$669$	23.2592	−	11.8354i	0.899251	−	0.457584i
$670$		0			0
$671$	−10.2042	−	17.6742i	−0.393928	−	0.682303i
$672$		0			0
$673$	−6.35961	+	11.0152i	−0.245145	+	0.424604i	−0.962172	−	0.272441i	$-0.912169\pi$
$673$	−6.35961	+	11.0152i	−0.245145	+	0.424604i	0.717027	+	0.697045i	$0.245502\pi$
$674$		0			0
$675$	−15.5335	+	19.1193i	−0.597885	+	0.735900i
$676$		0			0
$677$	−11.3408	−	42.3243i	−0.435861	−	1.62665i	−0.738998	−	0.673708i	$-0.764701\pi$
$677$	−11.3408	−	42.3243i	−0.435861	−	1.62665i	0.303137	−	0.952947i	$-0.401966\pi$
$678$		0			0
$679$	−24.2592	+	14.0061i	−0.930984	+	0.537504i
$680$		0			0
$681$	10.1409	+	3.30098i	0.388599	+	0.126494i
$682$		0			0
$683$	−4.22715	+	4.22715i	−0.161748	+	0.161748i	−0.783340	−	0.621593i	$-0.786486\pi$
$683$	−4.22715	+	4.22715i	−0.161748	+	0.161748i	0.621593	+	0.783340i	$0.286486\pi$
$684$		0			0
$685$	4.19368	+	4.19368i	0.160232	+	0.160232i
$686$		0			0
$687$	−4.83773	−	5.37865i	−0.184571	−	0.205208i
$688$		0			0
$689$	−4.66870	−	8.08643i	−0.177863	−	0.308069i
$690$		0			0
$691$	3.57753	−	0.958595i	0.136096	−	0.0364667i	−0.190128	−	0.981759i	$-0.560890\pi$
$691$	3.57753	−	0.958595i	0.136096	−	0.0364667i	0.326224	+	0.945293i	$0.394224\pi$
$692$		0			0
$693$	33.8225	−	5.31975i	1.28481	−	0.202081i
$694$		0			0
$695$	−5.26794	−	3.04145i	−0.199824	−	0.115369i
$696$		0			0
$697$	13.9558	−	8.05738i	0.528613	−	0.305195i
$698$		0			0
$699$	1.62330	−	2.49673i	0.0613988	−	0.0944349i
$700$		0			0
$701$	22.6596	+	22.6596i	0.855842	+	0.855842i	0.990845	−	0.135003i	$-0.0431044\pi$
$701$	22.6596	+	22.6596i	0.855842	+	0.855842i	−0.135003	+	0.990845i	$0.543104\pi$
$702$		0			0
$703$	53.1850			2.00591
$704$		0			0
$705$	8.52661	−	1.80761i	0.321131	−	0.0680784i
$706$		0			0
$707$	−4.32325	+	16.1346i	−0.162592	+	0.606803i
$708$		0			0
$709$	5.72683	+	21.3728i	0.215076	+	0.802673i	0.986140	+	0.165916i	$0.0530580\pi$
$709$	5.72683	+	21.3728i	0.215076	+	0.802673i	−0.771064	+	0.636757i	$0.780275\pi$
$710$		0			0
$711$	9.35242	+	0.993128i	0.350743	+	0.0372452i
$712$		0			0
$713$	9.90308	+	5.71755i	0.370873	+	0.214124i
$714$		0			0
$715$	−4.65595	−	1.24756i	−0.174122	−	0.0466560i
$716$		0			0
$717$	−0.915008	+	17.2820i	−0.0341716	+	0.645407i
$718$		0			0
$719$	−8.65067			−0.322616			−0.161308	−	0.986904i	$-0.551571\pi$
$719$	−8.65067			−0.322616			−0.161308	+	0.986904i	$0.551571\pi$
$720$		0			0
$721$	37.6589			1.40249
$722$		0			0
$723$	−33.6576	+	17.1266i	−1.25174	+	0.636947i
$724$		0			0
$725$	−27.8942	−	7.47422i	−1.03596	−	0.277586i
$726$		0			0
$727$	−2.70356	−	1.56090i	−0.100269	−	0.0578905i	0.449027	−	0.893518i	$-0.351771\pi$
$727$	−2.70356	−	1.56090i	−0.100269	−	0.0578905i	−0.549296	+	0.835628i	$0.685104\pi$
$728$		0			0
$729$	−25.6515	−	8.42609i	−0.950057	−	0.312077i
$730$		0			0
$731$	−2.62415	−	9.79347i	−0.0970578	−	0.362225i
$732$		0			0
$733$	−0.888818	+	3.31711i	−0.0328292	+	0.122520i	−0.980396	−	0.197038i	$-0.936868\pi$
$733$	−0.888818	+	3.31711i	−0.0328292	+	0.122520i	0.947567	+	0.319558i	$0.103534\pi$
$734$		0			0
$735$	−0.194650	+	0.597978i	−0.00717976	+	0.0220568i
$736$		0			0
$737$	62.9250			2.31787
$738$		0			0
$739$	−11.1765	−	11.1765i	−0.411133	−	0.411133i	0.471000	−	0.882133i	$-0.343893\pi$
$739$	−11.1765	−	11.1765i	−0.411133	−	0.411133i	−0.882133	+	0.471000i	$0.843893\pi$
$740$		0			0
$741$	19.6137	+	1.03847i	0.720528	+	0.0381490i
$742$		0			0
$743$	8.55561	−	4.93958i	0.313875	−	0.181216i	−0.334784	−	0.942295i	$-0.608663\pi$
$743$	8.55561	−	4.93958i	0.313875	−	0.181216i	0.648659	+	0.761079i	$0.275330\pi$
$744$		0			0
$745$	−0.461051	−	0.266188i	−0.0168916	−	0.00975237i
$746$		0			0
$747$	−21.5275	−	26.6426i	−0.787649	−	0.974803i
$748$		0			0
$749$	−10.6974	+	2.86637i	−0.390876	+	0.104735i
$750$		0			0
$751$	23.4223	+	40.5685i	0.854690	+	1.48037i	0.876932	+	0.480615i	$0.159586\pi$
$751$	23.4223	+	40.5685i	0.854690	+	1.48037i	−0.0222416	+	0.999753i	$0.507080\pi$
$752$		0			0
$753$	0.843443	−	0.178806i	0.0307368	−	0.00651606i
$754$		0			0
$755$	4.59300	+	4.59300i	0.167156	+	0.167156i
$756$		0			0
$757$	−14.0064	+	14.0064i	−0.509071	+	0.509071i	−0.914241	−	0.405170i	$-0.867212\pi$
$757$	−14.0064	+	14.0064i	−0.509071	+	0.509071i	0.405170	+	0.914241i	$0.367212\pi$
$758$		0			0
$759$	6.57826	+	31.0302i	0.238776	+	1.12632i
$760$		0			0
$761$	−24.1008	+	13.9146i	−0.873655	+	0.504405i	−0.868561	−	0.495582i	$-0.834955\pi$
$761$	−24.1008	+	13.9146i	−0.873655	+	0.504405i	−0.00509371	+	0.999987i	$0.501621\pi$
$762$		0			0
$763$	3.25757	+	12.1574i	0.117932	+	0.440129i
$764$		0			0
$765$	−0.683209	−	4.34378i	−0.0247015	−	0.157050i
$766$		0			0
$767$	2.57199	−	4.45482i	0.0928693	−	0.160854i
$768$		0			0
$769$	8.70836	+	15.0833i	0.314031	+	0.543918i	0.979231	−	0.202747i	$-0.0649869\pi$
$769$	8.70836	+	15.0833i	0.314031	+	0.543918i	−0.665200	+	0.746666i	$0.731654\pi$
$770$		0			0
$771$	1.04309	−	19.7010i	0.0375659	−	0.709515i
$772$		0			0
$773$	2.74550	−	2.74550i	0.0987489	−	0.0987489i	−0.656006	−	0.754755i	$-0.727756\pi$
$773$	2.74550	−	2.74550i	0.0987489	−	0.0987489i	0.754755	+	0.656006i	$0.227756\pi$
$774$		0			0
$775$		−	12.1646i		−	0.436966i
$776$		0			0
$777$	−49.4288	−	16.0897i	−1.77325	−	0.577215i
$778$		0			0
$779$	26.6092	+	7.12991i	0.953373	+	0.255455i
$780$		0			0
$781$	52.5727	−	14.0868i	1.88120	−	0.504066i
$782$		0			0
$783$	−3.25783	−	31.4837i	−0.116425	−	1.12513i
$784$		0			0
$785$	2.90667	−	5.03451i	0.103744	−	0.179689i
$786$		0			0
$787$	−0.187023	+	0.697981i	−0.00666666	+	0.0248803i	−0.969179	−	0.246357i	$-0.920766\pi$
$787$	−0.187023	+	0.697981i	−0.00666666	+	0.0248803i	0.962512	+	0.271238i	$0.0874330\pi$
$788$		0			0
$789$	4.02495	+	7.90991i	0.143292	+	0.281600i
$790$		0			0
$791$		−	28.2121i		−	1.00311i
$792$		0			0
$793$			11.4426i			0.406337i
$794$		0			0
$795$	−3.56853	−	0.188939i	−0.126563	−	0.00670097i
$796$		0			0
$797$	−4.56209	+	17.0260i	−0.161598	+	0.603090i	0.836852	+	0.547429i	$0.184393\pi$
$797$	−4.56209	+	17.0260i	−0.161598	+	0.603090i	−0.998450	+	0.0556613i	$0.982273\pi$
$798$		0			0
$799$	14.2294	−	24.6460i	0.503398	−	0.871912i
$800$		0			0
$801$	6.51145	−	2.89071i	0.230071	−	0.102138i
$802$		0			0
$803$	45.1583	−	12.1001i	1.59360	−	0.427004i
$804$		0			0
$805$	−6.08633	−	1.63083i	−0.214515	−	0.0574791i
$806$		0			0
$807$	−4.40566	−	20.7818i	−0.155086	−	0.731555i
$808$		0			0
$809$		−	34.5309i		−	1.21404i	−0.794685	−	0.607022i	$-0.792364\pi$
$809$		−	34.5309i		−	1.21404i	0.794685	−	0.607022i	$-0.207636\pi$
$810$		0			0
$811$	21.6237	−	21.6237i	0.759310	−	0.759310i	−0.216887	−	0.976197i	$-0.569590\pi$
$811$	21.6237	−	21.6237i	0.759310	−	0.759310i	0.976197	+	0.216887i	$0.0695902\pi$
$812$		0			0
$813$	−28.4800	−	18.5168i	−0.998836	−	0.649414i
$814$		0			0
$815$	−1.66256	−	2.87964i	−0.0582371	−	0.100870i
$816$		0			0
$817$	8.66616	−	15.0102i	0.303191	−	0.525142i
$818$		0			0
$819$	−17.9143	−	6.89873i	−0.625977	−	0.241061i
$820$		0			0
$821$	−2.88421	−	10.7640i	−0.100660	−	0.375667i	0.897157	−	0.441712i	$-0.145629\pi$
$821$	−2.88421	−	10.7640i	−0.100660	−	0.375667i	−0.997817	+	0.0660446i	$0.978962\pi$
$822$		0			0
$823$	−22.0500	+	12.7306i	−0.768616	+	0.443760i	−0.832381	−	0.554205i	$-0.813023\pi$
$823$	−22.0500	+	12.7306i	−0.768616	+	0.443760i	0.0637649	+	0.997965i	$0.479689\pi$
$824$		0			0
$825$	25.0883	−	22.5653i	0.873464	−	0.785622i
$826$		0			0
$827$	15.8750	−	15.8750i	0.552029	−	0.552029i	−0.374997	−	0.927026i	$-0.622356\pi$
$827$	15.8750	−	15.8750i	0.552029	−	0.552029i	0.927026	+	0.374997i	$0.122356\pi$
$828$		0			0
$829$	28.3270	+	28.3270i	0.983836	+	0.983836i	0.999871	−	0.0160352i	$-0.00510438\pi$
$829$	28.3270	+	28.3270i	0.983836	+	0.983836i	−0.0160352	+	0.999871i	$0.505104\pi$
$830$		0			0
$831$	9.03583	−	27.7587i	0.313449	−	0.962939i
$832$		0			0
$833$	1.02664	+	1.77819i	0.0355709	+	0.0616106i
$834$		0			0
$835$	−3.89150	+	1.04272i	−0.134671	+	0.0360849i
$836$		0			0
$837$	12.4551	−	4.75806i	0.430510	−	0.164463i
$838$		0			0
$839$	17.2154	+	9.93933i	0.594342	+	0.343144i	0.766813	−	0.641871i	$-0.221842\pi$
$839$	17.2154	+	9.93933i	0.594342	+	0.343144i	−0.172470	+	0.985015i	$0.555175\pi$
$840$		0			0
$841$	7.01912	−	4.05249i	0.242039	−	0.139741i
$842$		0			0
$843$	12.7380	+	25.0330i	0.438721	+	0.862182i
$844$		0			0
$845$	−2.76879	−	2.76879i	−0.0952494	−	0.0952494i
$846$		0			0
$847$	−16.3493			−0.561769
$848$		0			0
$849$	−1.08591	−	1.20732i	−0.0372682	−	0.0414352i
$850$		0			0
$851$	12.4642	−	46.5169i	0.427266	−	1.59458i
$852$		0			0
$853$	6.83749	+	25.5178i	0.234111	+	0.873715i	0.978548	+	0.206021i	$0.0660516\pi$
$853$	6.83749	+	25.5178i	0.234111	+	0.873715i	−0.744436	+	0.667693i	$0.767282\pi$
$854$		0			0
$855$	4.42484	−	6.07655i	0.151326	−	0.207814i
$856$		0			0
$857$	6.38473	+	3.68622i	0.218098	+	0.125919i	0.605069	−	0.796173i	$-0.293145\pi$
$857$	6.38473	+	3.68622i	0.218098	+	0.125919i	−0.386971	+	0.922092i	$0.626479\pi$
$858$		0			0
$859$	24.1370	+	6.46749i	0.823544	+	0.220668i	0.645895	−	0.763426i	$-0.276484\pi$
$859$	24.1370	+	6.46749i	0.823544	+	0.220668i	0.177649	+	0.984094i	$0.443151\pi$
$860$		0			0
$861$	−22.5729	−	14.6762i	−0.769283	−	0.500165i
$862$		0			0
$863$	22.7407			0.774104			0.387052	−	0.922058i	$-0.373493\pi$
$863$	22.7407			0.774104			0.387052	+	0.922058i	$0.373493\pi$
$864$		0			0
$865$	11.0295			0.375015
$866$		0			0
$867$	12.6492	+	8.22417i	0.429591	+	0.279307i
$868$		0			0
$869$	−12.4439	−	3.33433i	−0.422130	−	0.113109i
$870$		0			0
$871$	−30.5541	−	17.6404i	−1.03529	−	0.597723i
$872$		0			0
$873$	−30.0896	−	3.19520i	−1.01838	−	0.108141i
$874$		0			0
$875$	3.56458	+	13.3032i	0.120505	+	0.449730i
$876$		0			0
$877$	−5.79980	+	21.6451i	−0.195845	+	0.730905i	0.796201	+	0.605032i	$0.206840\pi$
$877$	−5.79980	+	21.6451i	−0.195845	+	0.730905i	−0.992046	+	0.125873i	$0.959827\pi$
$878$		0			0
$879$	−11.7131	−	13.0228i	−0.395074	−	0.439248i
$880$		0			0
$881$	−55.9231			−1.88410			−0.942048	−	0.335477i	$-0.891102\pi$
$881$	−55.9231			−1.88410			−0.942048	+	0.335477i	$0.891102\pi$
$882$		0			0
$883$	7.12196	+	7.12196i	0.239673	+	0.239673i	0.816715	−	0.577042i	$-0.195793\pi$
$883$	7.12196	+	7.12196i	0.239673	+	0.239673i	−0.577042	+	0.816715i	$0.695793\pi$
$884$		0			0
$885$	−0.892811	−	1.75457i	−0.0300115	−	0.0589791i
$886$		0			0
$887$	1.13549	−	0.655576i	0.0381260	−	0.0220121i	−0.480816	−	0.876822i	$-0.659659\pi$
$887$	1.13549	−	0.655576i	0.0381260	−	0.0220121i	0.518942	+	0.854810i	$0.326326\pi$
$888$		0			0
$889$	−17.6124	−	10.1685i	−0.590699	−	0.341040i
$890$		0			0
$891$	32.9171	+	16.8612i	1.10276	+	0.564871i
$892$		0			0
$893$	46.9919	−	12.5914i	1.57252	−	0.421357i
$894$		0			0
$895$	1.52791	+	2.64642i	0.0510725	+	0.0884602i
$896$		0			0
$897$	5.50484	−	16.9113i	0.183801	−	0.564651i
$898$		0			0
$899$	11.0521	+	11.0521i	0.368609	+	0.368609i
$900$		0			0
$901$	−8.25040	+	8.25040i	−0.274861	+	0.274861i
$902$		0			0
$903$	−12.5951	+	11.3284i	−0.419137	+	0.376986i
$904$		0			0
$905$	−6.28204	+	3.62693i	−0.208822	+	0.120563i
$906$		0			0
$907$	−4.81582	−	17.9729i	−0.159907	−	0.596780i	−0.998635	−	0.0522300i	$-0.983367\pi$
$907$	−4.81582	−	17.9729i	−0.159907	−	0.596780i	0.838728	−	0.544550i	$-0.183300\pi$
$908$		0			0
$909$	−14.0345	+	11.3400i	−0.465496	+	0.376125i
$910$		0			0
$911$	−1.56545	+	2.71143i	−0.0518656	+	0.0898338i	−0.890793	−	0.454410i	$-0.849850\pi$
$911$	−1.56545	+	2.71143i	−0.0518656	+	0.0898338i	0.838927	+	0.544244i	$0.183183\pi$
$912$		0			0
$913$	23.4596	+	40.6332i	0.776400	+	1.34476i
$914$		0			0
$915$	3.67142	+	2.38705i	0.121373	+	0.0789135i
$916$		0			0
$917$	40.3147	−	40.3147i	1.33131	−	1.33131i
$918$		0			0
$919$		−	20.2458i		−	0.667847i	−0.942600	−	0.333924i	$-0.891627\pi$
$919$		−	20.2458i		−	0.667847i	0.942600	−	0.333924i	$-0.108373\pi$
$920$		0			0
$921$	8.21184	+	38.7359i	0.270589	+	1.27639i
$922$		0			0
$923$	−29.4765	−	7.89820i	−0.970231	−	0.259973i
$924$		0			0
$925$	−49.4845	+	13.2593i	−1.62704	+	0.435964i
$926$		0			0
$927$	32.8844	+	23.9459i	1.08007	+	0.786487i
$928$		0			0
$929$	7.78745	−	13.4883i	0.255498	−	0.442535i	−0.709533	−	0.704672i	$-0.751094\pi$
$929$	7.78745	−	13.4883i	0.255498	−	0.442535i	0.965031	+	0.262137i	$0.0844273\pi$
$930$		0			0
$931$	−0.908464	+	3.39043i	−0.0297737	+	0.111117i
$932$		0			0
$933$	23.6583	+	1.25261i	0.774537	+	0.0410085i
$934$		0			0
$935$			6.02320i			0.196980i
$936$		0			0
$937$			40.1896i			1.31294i	0.754354	+	0.656468i	$0.227950\pi$
$937$			40.1896i			1.31294i	−0.754354	+	0.656468i	$0.772050\pi$
$938$		0			0
$939$	20.4833	+	40.2541i	0.668446	+	1.31364i
$940$		0			0
$941$	0.547985	−	2.04511i	0.0178638	−	0.0666686i	−0.956419	−	0.291999i	$-0.905680\pi$
$941$	0.547985	−	2.04511i	0.0178638	−	0.0666686i	0.974282	+	0.225331i	$0.0723462\pi$
$942$		0			0
$943$	12.4720	−	21.6021i	0.406144	−	0.703462i
$944$		0			0
$945$	−5.95063	+	4.30877i	−0.193574	+	0.140164i
$946$		0			0
$947$	46.7422	−	12.5245i	1.51892	−	0.406993i	0.599532	−	0.800350i	$-0.295353\pi$
$947$	46.7422	−	12.5245i	1.51892	−	0.406993i	0.919386	+	0.393358i	$0.128687\pi$
$948$		0			0
$949$	−25.3194	−	6.78431i	−0.821902	−	0.220228i
$950$		0			0
$951$	25.5148	+	8.30541i	0.827375	+	0.269321i
$952$		0			0
$953$			41.3167i			1.33838i	0.743091	+	0.669190i	$0.233359\pi$
$953$			41.3167i			1.33838i	−0.743091	+	0.669190i	$0.766641\pi$
$954$		0			0
$955$	3.93694	−	3.93694i	0.127396	−	0.127396i
$956$		0			0
$957$	−2.29232	+	43.2955i	−0.0741002	+	1.39955i
$958$		0			0
$959$	−16.1770	−	28.0193i	−0.522381	−	0.904791i
$960$		0			0
$961$	12.2080	−	21.1449i	0.393807	−	0.682093i
$962$		0			0
$963$	−11.1638	−	4.29915i	−0.359750	−	0.138538i
$964$		0			0
$965$	2.58870	+	9.66116i	0.0833332	+	0.311004i
$966$		0			0
$967$	−15.5967	+	9.00476i	−0.501556	+	0.289574i	−0.729356	−	0.684134i	$-0.760180\pi$
$967$	−15.5967	+	9.00476i	−0.501556	+	0.289574i	0.227800	+	0.973708i	$0.426847\pi$
$968$		0			0
$969$	−5.08993	−	24.0096i	−0.163512	−	0.771299i
$970$		0			0
$971$	−26.1482	+	26.1482i	−0.839134	+	0.839134i	−0.988745	−	0.149611i	$-0.952198\pi$
$971$	−26.1482	+	26.1482i	−0.839134	+	0.839134i	0.149611	+	0.988745i	$0.452198\pi$
$972$		0			0
$973$	23.4645	+	23.4645i	0.752238	+	0.752238i
$974$		0			0
$975$	−18.5079	+	3.92360i	−0.592728	+	0.125656i
$976$		0			0
$977$	−9.85534	−	17.0699i	−0.315300	−	0.546116i	0.664201	−	0.747554i	$-0.268772\pi$
$977$	−9.85534	−	17.0699i	−0.315300	−	0.546116i	−0.979501	+	0.201438i	$0.935439\pi$
$978$		0			0
$979$	−9.42621	+	2.52574i	−0.301263	+	0.0807231i
$980$		0			0
$981$	−4.88590	+	12.6875i	−0.155995	+	0.405080i
$982$		0			0
$983$	−5.03257	−	2.90556i	−0.160514	−	0.0926729i	0.417591	−	0.908635i	$-0.362874\pi$
$983$	−5.03257	−	2.90556i	−0.160514	−	0.0926729i	−0.578105	+	0.815962i	$0.696208\pi$
$984$		0			0
$985$	11.1914	−	6.46135i	0.356587	−	0.205876i
$986$		0			0
$987$	−47.4823	−	2.51399i	−1.51138	−	0.0800212i
$988$		0			0
$989$	−11.0974	−	11.0974i	−0.352876	−	0.352876i
$990$		0			0
$991$	28.5729			0.907648			0.453824	−	0.891091i	$-0.350060\pi$
$991$	28.5729			0.907648			0.453824	+	0.891091i	$0.350060\pi$
$992$		0			0
$993$	5.85522	−	17.9877i	0.185810	−	0.570822i
$994$		0			0
$995$	−1.42189	+	5.30655i	−0.0450768	+	0.168229i
$996$		0			0
$997$	−6.86935	−	25.6368i	−0.217555	−	0.811925i	−0.985252	−	0.171112i	$-0.945264\pi$
$997$	−6.86935	−	25.6368i	−0.217555	−	0.811925i	0.767697	−	0.640813i	$-0.221403\pi$
$998$		0			0
$999$	−32.9313	−	45.4798i	−1.04190	−	1.43892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.529.3		72
3.2	odd	2		1728.2.bc.e.721.11		72
4.3	odd	2		144.2.x.e.61.14	yes	72
9.4	even	3	inner	576.2.bb.e.337.7		72
9.5	odd	6		1728.2.bc.e.145.8		72
12.11	even	2		432.2.y.e.397.5		72
16.5	even	4	inner	576.2.bb.e.241.7		72
16.11	odd	4		144.2.x.e.133.9	yes	72
36.23	even	6		432.2.y.e.253.10		72
36.31	odd	6		144.2.x.e.13.9	✓	72
48.5	odd	4		1728.2.bc.e.1585.8		72
48.11	even	4		432.2.y.e.181.10		72
144.5	odd	12		1728.2.bc.e.1009.11		72
144.59	even	12		432.2.y.e.37.5		72
144.85	even	12	inner	576.2.bb.e.49.3		72
144.139	odd	12		144.2.x.e.85.14	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.9	✓	72	36.31	odd	6
144.2.x.e.61.14	yes	72	4.3	odd	2
144.2.x.e.85.14	yes	72	144.139	odd	12
144.2.x.e.133.9	yes	72	16.11	odd	4
432.2.y.e.37.5		72	144.59	even	12
432.2.y.e.181.10		72	48.11	even	4
432.2.y.e.253.10		72	36.23	even	6
432.2.y.e.397.5		72	12.11	even	2
576.2.bb.e.49.3		72	144.85	even	12	inner
576.2.bb.e.241.7		72	16.5	even	4	inner
576.2.bb.e.337.7		72	9.4	even	3	inner
576.2.bb.e.529.3		72	1.1	even	1	trivial
1728.2.bc.e.145.8		72	9.5	odd	6
1728.2.bc.e.721.11		72	3.2	odd	2
1728.2.bc.e.1009.11		72	144.5	odd	12
1728.2.bc.e.1585.8		72	48.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.45211 - 0.944122i) q^{3} +(-0.491749 - 0.131764i) q^{5} +(2.40518 + 1.38863i) q^{7} +(1.21727 + 2.74194i) q^{9} +O(q^{10})\)	\(q+(-1.45211 - 0.944122i) q^{3} +(-0.491749 - 0.131764i) q^{5} +(2.40518 + 1.38863i) q^{7} +(1.21727 + 2.74194i) q^{9} +(-1.06358 - 3.96934i) q^{11} +(-0.596329 + 2.22553i) q^{13} +(0.589675 + 0.655607i) q^{15} +2.87908 q^{17} +(3.48018 + 3.48018i) q^{19} +(-2.18156 - 4.28723i) q^{21} +(3.85945 - 2.22826i) q^{23} +(-4.10567 - 2.37041i) q^{25} +(0.821118 - 5.13086i) q^{27} +(5.88383 - 1.57657i) q^{29} +(1.28296 + 2.22216i) q^{31} +(-2.20310 + 6.76808i) q^{33} +(-0.999773 - 0.999773i) q^{35} +(7.64112 - 7.64112i) q^{37} +(2.96711 - 2.66872i) q^{39} +(4.84731 - 2.79860i) q^{41} +(-0.911456 - 3.40160i) q^{43} +(-0.237302 - 1.50874i) q^{45} +(4.94233 - 8.56037i) q^{47} +(0.356586 + 0.617625i) q^{49} +(-4.18075 - 2.71820i) q^{51} +(-2.86564 + 2.86564i) q^{53} +2.09206i q^{55} +(-1.76790 - 8.33934i) q^{57} +(-2.15652 - 0.577838i) q^{59} +(4.79709 - 1.28538i) q^{61} +(-0.879800 + 8.28520i) q^{63} +(0.586489 - 1.01583i) q^{65} +(-3.96319 + 14.7908i) q^{67} +(-7.70811 - 0.408113i) q^{69} +13.2447i q^{71} +11.3768i q^{73} +(3.72395 + 7.31836i) q^{75} +(2.95384 - 11.0239i) q^{77} +(1.56750 - 2.71499i) q^{79} +(-6.03652 + 6.67536i) q^{81} +(-11.0286 + 2.95510i) q^{83} +(-1.41578 - 0.379358i) q^{85} +(-10.0325 - 3.26570i) q^{87} -2.37475i q^{89} +(-4.52472 + 4.52472i) q^{91} +(0.234979 - 4.43810i) q^{93} +(-1.25282 - 2.16994i) q^{95} +(-5.04313 + 8.73496i) q^{97} +(9.58904 - 7.74803i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 72 * q - 2 * q^3 + 4 * q^5	\( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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