LMFDB - Embedded newform 672.3.bh.a.481.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,3,Mod(481,672)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("672.481"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	672.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,-24,0,0,0,-12,0,24,0,-12,0,0,0,0,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$18.3106737650$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 76 x^{14} - 392 x^{13} + 1982 x^{12} - 7160 x^{11} + 23796 x^{10} - 61736 x^{9} + \cdots + 16807 $ x^16 - 8x^15 + 76x^14 - 392x^13 + 1982x^12 - 7160x^11 + 23796x^10 - 61736x^9 + 141869x^8 - 261520x^7 + 411696x^6 - 515296x^5 + 526280x^4 - 407176x^3 + 235396x^2 - 87808*x + 16807
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{18}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			481.6
Root			$0.500000 - 3.06833i$ of defining polynomial
Character	$\chi$	$=$	672.481
Dual form			672.3.bh.a.577.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 + 0.866025i) q^{3} +(3.60807 + 2.08312i) q^{5} +(3.89168 + 5.81849i) q^{7} +(1.50000 - 2.59808i) q^{9} +(3.55841 + 6.16335i) q^{11} -2.34453i q^{13} -7.21615 q^{15} +(9.39685 - 5.42527i) q^{17} +(20.0614 + 11.5824i) q^{19} +(-10.8765 - 5.35743i) q^{21} +(-6.35184 + 11.0017i) q^{23} +(-3.82120 - 6.61851i) q^{25} +5.19615i q^{27} -2.42670 q^{29} +(-16.7915 + 9.69460i) q^{31} +(-10.6752 - 6.16335i) q^{33} +(1.92087 + 29.1004i) q^{35} +(2.81291 - 4.87210i) q^{37} +(2.03042 + 3.51679i) q^{39} -32.1282i q^{41} +0.536222 q^{43} +(10.8242 - 6.24937i) q^{45} +(2.50339 + 1.44533i) q^{47} +(-18.7096 + 45.2874i) q^{49} +(-9.39685 + 16.2758i) q^{51} +(26.9278 + 46.6404i) q^{53} +29.6505i q^{55} -40.1228 q^{57} +(-72.8315 + 42.0493i) q^{59} +(81.5996 + 47.1116i) q^{61} +(20.9544 - 1.38316i) q^{63} +(4.88394 - 8.45924i) q^{65} +(44.0928 + 76.3709i) q^{67} -22.0034i q^{69} +62.2297 q^{71} +(-45.3916 + 26.2069i) q^{73} +(11.4636 + 6.61851i) q^{75} +(-22.0132 + 44.6904i) q^{77} +(-42.1596 + 73.0225i) q^{79} +(-4.50000 - 7.79423i) q^{81} +77.3283i q^{83} +45.2060 q^{85} +(3.64004 - 2.10158i) q^{87} +(-123.331 - 71.2053i) q^{89} +(13.6416 - 9.12417i) q^{91} +(16.7915 - 29.0838i) q^{93} +(48.2553 + 83.5806i) q^{95} +38.0431i q^{97} +21.3505 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{3} - 12 q^{7} + 24 q^{9} - 12 q^{11} - 48 q^{17} - 60 q^{19} + 24 q^{21} - 48 q^{23} + 52 q^{25} - 64 q^{29} - 60 q^{31} + 36 q^{33} - 4 q^{37} + 12 q^{39} + 72 q^{43} + 120 q^{47} - 8 q^{49}+ \cdots - 72 q^{99}+O(q^{100}) $ 16 * q - 24 * q^3 - 12 * q^7 + 24 * q^9 - 12 * q^11 - 48 * q^17 - 60 * q^19 + 24 * q^21 - 48 * q^23 + 52 * q^25 - 64 * q^29 - 60 * q^31 + 36 * q^33 - 4 * q^37 + 12 * q^39 + 72 * q^43 + 120 * q^47 - 8 * q^49 + 48 * q^51 - 72 * q^53 + 120 * q^57 - 228 * q^59 + 72 * q^61 - 36 * q^63 - 40 * q^65 + 12 * q^67 - 528 * q^71 - 36 * q^73 - 156 * q^75 - 96 * q^77 - 204 * q^79 - 72 * q^81 - 480 * q^85 + 96 * q^87 - 192 * q^89 - 276 * q^91 + 60 * q^93 - 48 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$		0			0
$5$	3.60807	+	2.08312i	0.721615	+	0.416625i	0.815347	−	0.578973i	$-0.196546\pi$
$5$	3.60807	+	2.08312i	0.721615	+	0.416625i	−0.0937318	+	0.995597i	$0.529880\pi$
$6$		0			0
$7$	3.89168	+	5.81849i	0.555955	+	0.831212i
$7$	3.89168	+	5.81849i	0.555955	+	0.831212i
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	3.55841	+	6.16335i	0.323492	+	0.560305i	0.981206	−	0.192963i	$-0.0618097\pi$
$11$	3.55841	+	6.16335i	0.323492	+	0.560305i	−0.657714	+	0.753268i	$0.728476\pi$
$12$		0			0
$13$		−	2.34453i		−	0.180348i	−0.995926	−	0.0901742i	$-0.971258\pi$
$13$		−	2.34453i		−	0.180348i	0.995926	−	0.0901742i	$-0.0287424\pi$
$14$		0			0
$15$	−7.21615			−0.481077
$16$		0			0
$17$	9.39685	−	5.42527i	0.552756	−	0.319134i	−0.197477	−	0.980308i	$-0.563275\pi$
$17$	9.39685	−	5.42527i	0.552756	−	0.319134i	0.750233	+	0.661174i	$0.229941\pi$
$18$		0			0
$19$	20.0614	+	11.5824i	1.05586	+	0.609602i	0.924285	−	0.381704i	$-0.124663\pi$
$19$	20.0614	+	11.5824i	1.05586	+	0.609602i	0.131577	+	0.991306i	$0.457996\pi$
$20$		0			0
$21$	−10.8765	−	5.35743i	−0.517928	−	0.255116i
$22$		0			0
$23$	−6.35184	+	11.0017i	−0.276167	+	0.478335i	−0.970429	−	0.241387i	$-0.922398\pi$
$23$	−6.35184	+	11.0017i	−0.276167	+	0.478335i	0.694262	+	0.719722i	$0.255731\pi$
$24$		0			0
$25$	−3.82120	−	6.61851i	−0.152848	−	0.264740i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−2.42670			−0.0836792			−0.0418396	−	0.999124i	$-0.513322\pi$
$29$	−2.42670			−0.0836792			−0.0418396	+	0.999124i	$0.513322\pi$
$30$		0			0
$31$	−16.7915	+	9.69460i	−0.541663	+	0.312729i	−0.745753	−	0.666223i	$-0.767910\pi$
$31$	−16.7915	+	9.69460i	−0.541663	+	0.312729i	0.204090	+	0.978952i	$0.434577\pi$
$32$		0			0
$33$	−10.6752	−	6.16335i	−0.323492	−	0.186768i
$34$		0			0
$35$	1.92087	+	29.1004i	0.0548819	+	0.831440i
$36$		0			0
$37$	2.81291	−	4.87210i	0.0760245	−	0.131678i	−0.825507	−	0.564392i	$-0.809111\pi$
$37$	2.81291	−	4.87210i	0.0760245	−	0.131678i	0.901531	+	0.432714i	$0.142444\pi$
$38$		0			0
$39$	2.03042	+	3.51679i	0.0520621	+	0.0901742i
$40$		0			0
$41$		−	32.1282i		−	0.783614i	−0.920047	−	0.391807i	$-0.871850\pi$
$41$		−	32.1282i		−	0.783614i	0.920047	−	0.391807i	$-0.128150\pi$
$42$		0			0
$43$	0.536222			0.0124703			0.00623514	−	0.999981i	$-0.498015\pi$
$43$	0.536222			0.0124703			0.00623514	+	0.999981i	$0.498015\pi$
$44$		0			0
$45$	10.8242	−	6.24937i	0.240538	−	0.138875i
$46$		0			0
$47$	2.50339	+	1.44533i	0.0532636	+	0.0307518i	0.526395	−	0.850240i	$-0.323543\pi$
$47$	2.50339	+	1.44533i	0.0532636	+	0.0307518i	−0.473132	+	0.880992i	$0.656877\pi$
$48$		0			0
$49$	−18.7096	+	45.2874i	−0.381828	+	0.924233i
$50$		0			0
$51$	−9.39685	+	16.2758i	−0.184252	+	0.319134i
$52$		0			0
$53$	26.9278	+	46.6404i	0.508072	+	0.880007i	0.999956	+	0.00934631i	$0.00297507\pi$
$53$	26.9278	+	46.6404i	0.508072	+	0.880007i	−0.491884	+	0.870661i	$0.663692\pi$
$54$		0			0
$55$			29.6505i			0.539099i
$56$		0			0
$57$	−40.1228			−0.703908
$58$		0			0
$59$	−72.8315	+	42.0493i	−1.23443	+	0.712700i	−0.967951	−	0.251140i	$-0.919195\pi$
$59$	−72.8315	+	42.0493i	−1.23443	+	0.712700i	−0.266482	+	0.963840i	$0.585861\pi$
$60$		0			0
$61$	81.5996	+	47.1116i	1.33770	+	0.772321i	0.986466	−	0.163967i	$-0.0524292\pi$
$61$	81.5996	+	47.1116i	1.33770	+	0.772321i	0.351233	+	0.936288i	$0.385763\pi$
$62$		0			0
$63$	20.9544	−	1.38316i	0.332610	−	0.0219550i
$64$		0			0
$65$	4.88394	−	8.45924i	0.0751376	−	0.130142i
$66$		0			0
$67$	44.0928	+	76.3709i	0.658101	+	1.13986i	0.981107	+	0.193468i	$0.0619735\pi$
$67$	44.0928	+	76.3709i	0.658101	+	1.13986i	−0.323005	+	0.946397i	$0.604693\pi$
$68$		0			0
$69$		−	22.0034i		−	0.318890i
$70$		0			0
$71$	62.2297			0.876475			0.438238	−	0.898859i	$-0.355603\pi$
$71$	62.2297			0.876475			0.438238	+	0.898859i	$0.355603\pi$
$72$		0			0
$73$	−45.3916	+	26.2069i	−0.621803	+	0.358998i	−0.777571	−	0.628795i	$-0.783548\pi$
$73$	−45.3916	+	26.2069i	−0.621803	+	0.358998i	0.155767	+	0.987794i	$0.450215\pi$
$74$		0			0
$75$	11.4636	+	6.61851i	0.152848	+	0.0882468i
$76$		0			0
$77$	−22.0132	+	44.6904i	−0.285885	+	0.580395i
$78$		0			0
$79$	−42.1596	+	73.0225i	−0.533666	+	0.924336i	0.465561	+	0.885016i	$0.345853\pi$
$79$	−42.1596	+	73.0225i	−0.533666	+	0.924336i	−0.999227	+	0.0393201i	$0.987481\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			77.3283i			0.931666i	0.884873	+	0.465833i	$0.154245\pi$
$83$			77.3283i			0.931666i	−0.884873	+	0.465833i	$0.845755\pi$
$84$		0			0
$85$	45.2060			0.531836
$86$		0			0
$87$	3.64004	−	2.10158i	0.0418396	−	0.0241561i
$88$		0			0
$89$	−123.331	−	71.2053i	−1.38574	−	0.800059i	−0.392911	−	0.919577i	$-0.628532\pi$
$89$	−123.331	−	71.2053i	−1.38574	−	0.800059i	−0.992832	+	0.119517i	$0.961865\pi$
$90$		0			0
$91$	13.6416	−	9.12417i	0.149908	−	0.100266i
$92$		0			0
$93$	16.7915	−	29.0838i	0.180554	−	0.312729i
$94$		0			0
$95$	48.2553	+	83.5806i	0.507951	+	0.879796i
$96$		0			0
$97$			38.0431i			0.392197i	0.980584	+	0.196098i	$0.0628272\pi$
$97$			38.0431i			0.392197i	−0.980584	+	0.196098i	$0.937173\pi$
$98$		0			0
$99$	21.3505			0.215661
$100$		0			0
$101$	58.2112	−	33.6082i	0.576348	−	0.332755i	−0.183333	−	0.983051i	$-0.558689\pi$
$101$	58.2112	−	33.6082i	0.576348	−	0.332755i	0.759681	+	0.650296i	$0.225355\pi$
$102$		0			0
$103$	−41.7037	−	24.0776i	−0.404890	−	0.233763i	0.283702	−	0.958913i	$-0.408437\pi$
$103$	−41.7037	−	24.0776i	−0.404890	−	0.233763i	−0.688592	+	0.725149i	$0.741771\pi$
$104$		0			0
$105$	−28.0830	−	41.9871i	−0.267457	−	0.399877i
$106$		0			0
$107$	47.3769	−	82.0592i	0.442775	−	0.766909i	−0.555119	−	0.831771i	$-0.687327\pi$
$107$	47.3769	−	82.0592i	0.442775	−	0.766909i	0.997894	+	0.0648621i	$0.0206608\pi$
$108$		0			0
$109$	102.829	+	178.104i	0.943381	+	1.63398i	0.758961	+	0.651136i	$0.225707\pi$
$109$	102.829	+	178.104i	0.943381	+	1.63398i	0.184420	+	0.982848i	$0.440959\pi$
$110$		0			0
$111$			9.74420i			0.0877856i
$112$		0			0
$113$	−123.000			−1.08849			−0.544246	−	0.838925i	$-0.683184\pi$
$113$	−123.000			−1.08849			−0.544246	+	0.838925i	$0.683184\pi$
$114$		0			0
$115$	−45.8358	+	26.4633i	−0.398572	+	0.230116i
$116$		0			0
$117$	−6.09127	−	3.51679i	−0.0520621	−	0.0300581i
$118$		0			0
$119$	68.1365	+	33.5620i	0.572575	+	0.282033i
$120$		0			0
$121$	35.1754	−	60.9256i	0.290706	−	0.503517i
$122$		0			0
$123$	27.8238	+	48.1923i	0.226210	+	0.391807i
$124$		0			0
$125$		−	135.996i		−	1.08797i
$126$		0			0
$127$	−119.560			−0.941416			−0.470708	−	0.882289i	$-0.656002\pi$
$127$	−119.560			−0.941416			−0.470708	+	0.882289i	$0.656002\pi$
$128$		0			0
$129$	−0.804332	+	0.464382i	−0.00623514	+	0.00359986i
$130$		0			0
$131$	−49.2137	−	28.4135i	−0.375677	−	0.216897i	0.300259	−	0.953858i	$-0.402927\pi$
$131$	−49.2137	−	28.4135i	−0.375677	−	0.216897i	−0.675936	+	0.736961i	$0.736260\pi$
$132$		0			0
$133$	10.6803	+	161.802i	0.0803028	+	1.21656i
$134$		0			0
$135$	−10.8242	+	18.7481i	−0.0801794	+	0.138875i
$136$		0			0
$137$	−66.7779	−	115.663i	−0.487430	−	0.844254i	0.512465	−	0.858708i	$-0.328732\pi$
$137$	−66.7779	−	115.663i	−0.487430	−	0.844254i	−0.999896	+	0.0144542i	$0.995399\pi$
$138$		0			0
$139$		−	169.452i		−	1.21908i	−0.792756	−	0.609539i	$-0.791354\pi$
$139$		−	169.452i		−	1.21908i	0.792756	−	0.609539i	$-0.208646\pi$
$140$		0			0
$141$	−5.00678			−0.0355091
$142$		0			0
$143$	14.4502	−	8.34280i	0.101050	−	0.0583413i
$144$		0			0
$145$	−8.75570	−	5.05511i	−0.0603842	−	0.0348628i
$146$		0			0
$147$	−11.1557	−	84.1341i	−0.0758891	−	0.572341i
$148$		0			0
$149$	49.7596	−	86.1861i	0.333957	−	0.578430i	−0.649327	−	0.760509i	$-0.724949\pi$
$149$	49.7596	−	86.1861i	0.333957	−	0.578430i	0.983284	+	0.182079i	$0.0582827\pi$
$150$		0			0
$151$	30.3637	+	52.5915i	0.201084	+	0.348288i	0.948878	−	0.315643i	$-0.102220\pi$
$151$	30.3637	+	52.5915i	0.201084	+	0.348288i	−0.747794	+	0.663931i	$0.768887\pi$
$152$		0			0
$153$		−	32.5516i		−	0.212756i
$154$		0			0
$155$	−80.7802			−0.521163
$156$		0			0
$157$	163.990	−	94.6794i	1.04452	−	0.603054i	0.123410	−	0.992356i	$-0.460617\pi$
$157$	163.990	−	94.6794i	1.04452	−	0.603054i	0.921110	+	0.389302i	$0.127284\pi$
$158$		0			0
$159$	−80.7835	−	46.6404i	−0.508072	−	0.293336i
$160$		0			0
$161$	−88.7326	+	5.85709i	−0.551134	+	0.0363794i
$162$		0			0
$163$	80.5783	−	139.566i	0.494345	−	0.856231i	−0.505633	−	0.862748i	$-0.668741\pi$
$163$	80.5783	−	139.566i	0.494345	−	0.856231i	0.999979	+	0.00651719i	$0.00207450\pi$
$164$		0			0
$165$	−25.6780	−	44.4757i	−0.155625	−	0.269550i
$166$		0			0
$167$		−	242.581i		−	1.45258i	−0.687387	−	0.726291i	$-0.741242\pi$
$167$		−	242.581i		−	1.45258i	0.687387	−	0.726291i	$-0.258758\pi$
$168$		0			0
$169$	163.503			0.967474
$170$		0			0
$171$	60.1841	−	34.7473i	0.351954	−	0.203201i
$172$		0			0
$173$	−100.376	−	57.9522i	−0.580209	−	0.334984i	0.181008	−	0.983482i	$-0.442064\pi$
$173$	−100.376	−	57.9522i	−0.580209	−	0.334984i	−0.761216	+	0.648498i	$0.775397\pi$
$174$		0			0
$175$	23.6388	−	47.9907i	0.135079	−	0.274233i
$176$		0			0
$177$	72.8315	−	126.148i	0.411477	−	0.712700i
$178$		0			0
$179$	−145.575	−	252.144i	−0.813269	−	1.40862i	−0.910564	−	0.413368i	$-0.864352\pi$
$179$	−145.575	−	252.144i	−0.813269	−	1.40862i	0.0972946	−	0.995256i	$-0.468981\pi$
$180$		0			0
$181$			323.162i			1.78543i	0.450626	+	0.892713i	$0.351201\pi$
$181$			323.162i			1.78543i	−0.450626	+	0.892713i	$0.648799\pi$
$182$		0			0
$183$	−163.199			−0.891799
$184$		0			0
$185$	20.2984	−	11.7193i	0.109721	−	0.0633474i
$186$		0			0
$187$	66.8757	+	38.6107i	0.357624	+	0.206474i
$188$		0			0
$189$	−30.2337	+	20.2218i	−0.159967	+	0.106994i
$190$		0			0
$191$	12.5181	−	21.6819i	0.0655397	−	0.113518i	−0.831394	−	0.555684i	$-0.812456\pi$
$191$	12.5181	−	21.6819i	0.0655397	−	0.113518i	0.896933	+	0.442166i	$0.145790\pi$
$192$		0			0
$193$	163.103	+	282.503i	0.845095	+	1.46375i	0.885539	+	0.464565i	$0.153789\pi$
$193$	163.103	+	282.503i	0.845095	+	1.46375i	−0.0404445	+	0.999182i	$0.512877\pi$
$194$		0			0
$195$			16.9185i			0.0867614i
$196$		0			0
$197$	150.710			0.765026			0.382513	−	0.923950i	$-0.375059\pi$
$197$	150.710			0.765026			0.382513	+	0.923950i	$0.375059\pi$
$198$		0			0
$199$	265.167	−	153.094i	1.33250	−	0.769318i	0.346817	−	0.937933i	$-0.387263\pi$
$199$	265.167	−	153.094i	1.33250	−	0.769318i	0.985682	+	0.168615i	$0.0539293\pi$
$200$		0			0
$201$	−132.278	−	76.3709i	−0.658101	−	0.379955i
$202$		0			0
$203$	−9.44394	−	14.1197i	−0.0465219	−	0.0695552i
$204$		0			0
$205$	66.9269	−	115.921i	0.326473	−	0.565468i
$206$		0			0
$207$	19.0555	+	33.0051i	0.0920556	+	0.159445i
$208$		0			0
$209$			164.860i			0.788806i
$210$		0			0
$211$	3.55018			0.0168255			0.00841276	−	0.999965i	$-0.497322\pi$
$211$	3.55018			0.0168255			0.00841276	+	0.999965i	$0.497322\pi$
$212$		0			0
$213$	−93.3446	+	53.8925i	−0.438238	+	0.253017i
$214$		0			0
$215$	1.93473	+	1.11702i	0.00899873	+	0.00519542i
$216$		0			0
$217$	−121.755	−	59.9731i	−0.561085	−	0.276374i
$218$		0			0
$219$	45.3916	−	78.6206i	0.207268	−	0.358998i
$220$		0			0
$221$	−12.7197	−	22.0312i	−0.0575553	−	0.0996886i
$222$		0			0
$223$		−	201.520i		−	0.903675i	−0.892100	−	0.451838i	$-0.850769\pi$
$223$		−	201.520i		−	0.903675i	0.892100	−	0.451838i	$-0.149231\pi$
$224$		0			0
$225$	−22.9272			−0.101899
$226$		0			0
$227$	−357.131	+	206.190i	−1.57327	+	0.908325i	−0.577500	+	0.816390i	$0.695972\pi$
$227$	−357.131	+	206.190i	−1.57327	+	0.908325i	−0.995765	+	0.0919349i	$0.970695\pi$
$228$		0			0
$229$	−66.7344	−	38.5291i	−0.291417	−	0.168250i	0.347164	−	0.937804i	$-0.387145\pi$
$229$	−66.7344	−	38.5291i	−0.291417	−	0.168250i	−0.638581	+	0.769555i	$0.720478\pi$
$230$		0			0
$231$	−5.68328	−	86.0996i	−0.0246030	−	0.372725i
$232$		0			0
$233$	85.9698	−	148.904i	0.368969	−	0.639073i	−0.620436	−	0.784257i	$-0.713044\pi$
$233$	85.9698	−	148.904i	0.368969	−	0.639073i	0.989405	+	0.145184i	$0.0463775\pi$
$234$		0			0
$235$	6.02162	+	10.4297i	0.0256239	+	0.0443819i
$236$		0			0
$237$		−	146.045i		−	0.616224i
$238$		0			0
$239$	315.877			1.32166			0.660830	−	0.750536i	$-0.270204\pi$
$239$	315.877			1.32166			0.660830	+	0.750536i	$0.270204\pi$
$240$		0			0
$241$	−51.0128	+	29.4522i	−0.211671	+	0.122209i	−0.602088	−	0.798430i	$-0.705664\pi$
$241$	−51.0128	+	29.4522i	−0.211671	+	0.122209i	0.390417	+	0.920638i	$0.372331\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−161.845	+	124.426i	−0.660591	+	0.507862i
$246$		0			0
$247$	27.1554	−	47.0345i	0.109941	−	0.190423i
$248$		0			0
$249$	−66.9682	−	115.992i	−0.268949	−	0.465833i
$250$		0			0
$251$		−	162.195i		−	0.646195i	−0.946366	−	0.323097i	$-0.895276\pi$
$251$		−	162.195i		−	0.646195i	0.946366	−	0.323097i	$-0.104724\pi$
$252$		0			0
$253$	−90.4099			−0.357351
$254$		0			0
$255$	−67.8091	+	39.1496i	−0.265918	+	0.153528i
$256$		0			0
$257$	−372.367	−	214.986i	−1.44890	−	0.836523i	−0.450484	−	0.892784i	$-0.648749\pi$
$257$	−372.367	−	214.986i	−1.44890	−	0.836523i	−0.998416	+	0.0562613i	$0.982082\pi$
$258$		0			0
$259$	39.2952	−	2.59381i	0.151719	−	0.0100147i
$260$		0			0
$261$	−3.64004	+	6.30474i	−0.0139465	+	0.0241561i
$262$		0			0
$263$	−85.5110	−	148.109i	−0.325137	−	0.563154i	0.656403	−	0.754410i	$-0.272077\pi$
$263$	−85.5110	−	148.109i	−0.325137	−	0.563154i	−0.981540	+	0.191257i	$0.938744\pi$
$264$		0			0
$265$			224.376i			0.846702i
$266$		0			0
$267$	246.662			0.923829
$268$		0			0
$269$	−61.3494	+	35.4201i	−0.228065	+	0.131673i	−0.609679	−	0.792648i	$-0.708702\pi$
$269$	−61.3494	+	35.4201i	−0.228065	+	0.131673i	0.381614	+	0.924322i	$0.375368\pi$
$270$		0			0
$271$	−211.309	−	121.999i	−0.779736	−	0.450181i	0.0566006	−	0.998397i	$-0.481974\pi$
$271$	−211.309	−	121.999i	−0.779736	−	0.450181i	−0.836337	+	0.548216i	$0.815307\pi$
$272$		0			0
$273$	−12.5607	+	25.5002i	−0.0460097	+	0.0934075i
$274$		0			0
$275$	27.1948	−	47.1028i	0.0988902	−	0.171283i
$276$		0			0
$277$	164.231	+	284.457i	0.592892	+	1.02692i	0.993841	+	0.110819i	$0.0353473\pi$
$277$	164.231	+	284.457i	0.592892	+	1.02692i	−0.400949	+	0.916101i	$0.631319\pi$
$278$		0			0
$279$			58.1676i			0.208486i
$280$		0			0
$281$	451.831			1.60794			0.803970	−	0.594669i	$-0.202717\pi$
$281$	451.831			1.60794			0.803970	+	0.594669i	$0.202717\pi$
$282$		0			0
$283$	−60.1879	+	34.7495i	−0.212678	+	0.122790i	−0.602555	−	0.798077i	$-0.705851\pi$
$283$	−60.1879	+	34.7495i	−0.212678	+	0.122790i	0.389877	+	0.920867i	$0.372517\pi$
$284$		0			0
$285$	−144.766	−	83.5806i	−0.507951	−	0.293265i
$286$		0			0
$287$	186.937	−	125.033i	0.651350	−	0.435654i
$288$		0			0
$289$	−85.6328	+	148.320i	−0.296307	+	0.513219i
$290$		0			0
$291$	−32.9463	−	57.0646i	−0.113217	−	0.196098i
$292$		0			0
$293$			236.560i			0.807372i	0.914898	+	0.403686i	$0.132271\pi$
$293$			236.560i			0.807372i	−0.914898	+	0.403686i	$0.867729\pi$
$294$		0			0
$295$	−350.375			−1.18771
$296$		0			0
$297$	−32.0257	+	18.4901i	−0.107831	+	0.0622561i
$298$		0			0
$299$	25.7938	+	14.8921i	0.0862670	+	0.0498063i
$300$		0			0
$301$	2.08681	+	3.12000i	0.00693291	+	0.0103654i
$302$		0			0
$303$	−58.2112	+	100.825i	−0.192116	+	0.332755i
$304$		0			0
$305$	196.278	+	339.964i	0.643536	+	1.11464i
$306$		0			0
$307$		−	6.97393i		−	0.0227164i	−0.999935	−	0.0113582i	$-0.996384\pi$
$307$		−	6.97393i		−	0.0227164i	0.999935	−	0.0113582i	$-0.00361550\pi$
$308$		0			0
$309$	83.4073			0.269927
$310$		0			0
$311$	92.0662	−	53.1545i	0.296033	−	0.170915i	−0.344626	−	0.938740i	$-0.611994\pi$
$311$	92.0662	−	53.1545i	0.296033	−	0.170915i	0.640659	+	0.767825i	$0.278661\pi$
$312$		0			0
$313$	−273.310	−	157.796i	−0.873195	−	0.504139i	−0.00478623	−	0.999989i	$-0.501524\pi$
$313$	−273.310	−	157.796i	−0.873195	−	0.504139i	−0.868409	+	0.495849i	$0.834857\pi$
$314$		0			0
$315$	78.4863	+	38.6600i	0.249163	+	0.122730i
$316$		0			0
$317$	270.169	−	467.946i	0.852268	−	1.47617i	−0.0268886	−	0.999638i	$-0.508560\pi$
$317$	270.169	−	467.946i	0.852268	−	1.47617i	0.879157	−	0.476533i	$-0.158107\pi$
$318$		0			0
$319$	−8.63519	−	14.9566i	−0.0270696	−	0.0468859i
$320$		0			0
$321$			164.118i			0.511272i
$322$		0			0
$323$	251.352			0.778178
$324$		0			0
$325$	−15.5173	+	8.95891i	−0.0477455	+	0.0275659i
$326$		0			0
$327$	−308.486	−	178.104i	−0.943381	−	0.544661i
$328$		0			0
$329$	1.33276	+	20.1907i	0.00405093	+	0.0613700i
$330$		0			0
$331$	30.7015	−	53.1766i	0.0927539	−	0.160654i	−0.815915	−	0.578172i	$-0.803766\pi$
$331$	30.7015	−	53.1766i	0.0927539	−	0.160654i	0.908669	+	0.417517i	$0.137100\pi$
$332$		0			0
$333$	−8.43872	−	14.6163i	−0.0253415	−	0.0438928i
$334$		0			0
$335$			367.403i			1.09672i
$336$		0			0
$337$	638.027			1.89326			0.946628	−	0.322329i	$-0.104466\pi$
$337$	638.027			1.89326			0.946628	+	0.322329i	$0.104466\pi$
$338$		0			0
$339$	184.499	−	106.521i	0.544246	−	0.314221i
$340$		0			0
$341$	−119.503	−	68.9948i	−0.350447	−	0.202331i
$342$		0			0
$343$	−336.316	+	67.3830i	−0.980513	+	0.196452i
$344$		0			0
$345$	45.8358	−	79.3900i	0.132857	−	0.230116i
$346$		0			0
$347$	−202.855	−	351.355i	−0.584597	−	1.01255i	−0.994926	−	0.100614i	$-0.967919\pi$
$347$	−202.855	−	351.355i	−0.584597	−	1.01255i	0.410329	−	0.911938i	$-0.365414\pi$
$348$		0			0
$349$		−	103.045i		−	0.295258i	−0.989043	−	0.147629i	$-0.952836\pi$
$349$		−	103.045i		−	0.295258i	0.989043	−	0.147629i	$-0.0471642\pi$
$350$		0			0
$351$	12.1825			0.0347081
$352$		0			0
$353$	−21.1953	+	12.2371i	−0.0600433	+	0.0346660i	−0.529721	−	0.848172i	$-0.677703\pi$
$353$	−21.1953	+	12.2371i	−0.0600433	+	0.0346660i	0.469678	+	0.882838i	$0.344370\pi$
$354$		0			0
$355$	224.530	+	129.632i	0.632478	+	0.365161i
$356$		0			0
$357$	−131.270	+	8.66492i	−0.367704	+	0.0242715i
$358$		0			0
$359$	93.1536	−	161.347i	0.259481	−	0.449434i	−0.706622	−	0.707591i	$-0.749782\pi$
$359$	93.1536	−	161.347i	0.259481	−	0.449434i	0.966103	+	0.258157i	$0.0831152\pi$
$360$		0			0
$361$	87.8059	+	152.084i	0.243230	+	0.421286i
$362$		0			0
$363$			121.851i			0.335678i
$364$		0			0
$365$	−218.369			−0.598270
$366$		0			0
$367$	88.8880	−	51.3195i	0.242202	−	0.139835i	−0.373987	−	0.927434i	$-0.622009\pi$
$367$	88.8880	−	51.3195i	0.242202	−	0.139835i	0.616188	+	0.787599i	$0.288676\pi$
$368$		0			0
$369$	−83.4715	−	48.1923i	−0.226210	−	0.130602i
$370$		0			0
$371$	−166.582	+	338.189i	−0.449007	+	0.911560i
$372$		0			0
$373$	169.415	−	293.436i	0.454197	−	0.786692i	−0.544445	−	0.838797i	$-0.683260\pi$
$373$	169.415	−	293.436i	0.454197	−	0.786692i	0.998642	+	0.0521050i	$0.0165931\pi$
$374$		0			0
$375$	117.776	+	203.994i	0.314070	+	0.543985i
$376$		0			0
$377$			5.68946i			0.0150914i
$378$		0			0
$379$	−93.7837			−0.247451			−0.123725	−	0.992317i	$-0.539484\pi$
$379$	−93.7837			−0.247451			−0.123725	+	0.992317i	$0.539484\pi$
$380$		0			0
$381$	179.340	−	103.542i	0.470708	−	0.271763i
$382$		0			0
$383$	171.537	+	99.0368i	0.447877	+	0.258582i	0.706933	−	0.707281i	$-0.250078\pi$
$383$	171.537	+	99.0368i	0.447877	+	0.258582i	−0.259056	+	0.965862i	$0.583412\pi$
$384$		0			0
$385$	−172.521	+	115.390i	−0.448106	+	0.299715i
$386$		0			0
$387$	0.804332	−	1.39314i	0.00207838	−	0.00359986i
$388$		0			0
$389$	173.187	+	299.969i	0.445211	+	0.771128i	0.998067	−	0.0621491i	$-0.0197954\pi$
$389$	173.187	+	299.969i	0.445211	+	0.771128i	−0.552856	+	0.833277i	$0.686462\pi$
$390$		0			0
$391$			137.842i			0.352537i
$392$		0			0
$393$	98.4273			0.250451
$394$		0			0
$395$	−304.230	+	175.647i	−0.770202	+	0.444676i
$396$		0			0
$397$	−648.234	−	374.258i	−1.63283	−	0.942715i	−0.983215	−	0.182453i	$-0.941596\pi$
$397$	−648.234	−	374.258i	−1.63283	−	0.942715i	−0.649616	−	0.760262i	$-0.725070\pi$
$398$		0			0
$399$	−156.145	−	233.454i	−0.391341	−	0.585097i
$400$		0			0
$401$	134.341	−	232.686i	0.335015	−	0.580263i	−0.648473	−	0.761238i	$-0.724592\pi$
$401$	134.341	−	232.686i	0.335015	−	0.580263i	0.983488	+	0.180975i	$0.0579252\pi$
$402$		0			0
$403$	22.7293	+	39.3683i	0.0564002	+	0.0976880i
$404$		0			0
$405$		−	37.4962i		−	0.0925832i
$406$		0			0
$407$	40.0380			0.0983734
$408$		0			0
$409$	274.742	−	158.622i	0.671741	−	0.387830i	−0.124995	−	0.992157i	$-0.539892\pi$
$409$	274.742	−	158.622i	0.671741	−	0.387830i	0.796736	+	0.604328i	$0.206558\pi$
$410$		0			0
$411$	200.334	+	115.663i	0.487430	+	0.281418i
$412$		0			0
$413$	−528.101	−	260.127i	−1.27869	−	0.629846i
$414$		0			0
$415$	−161.084	+	279.006i	−0.388155	+	0.672304i
$416$		0			0
$417$	146.750	+	254.178i	0.351918	+	0.609539i
$418$		0			0
$419$			360.703i			0.860866i	0.902623	+	0.430433i	$0.141639\pi$
$419$			360.703i			0.860866i	−0.902623	+	0.430433i	$0.858361\pi$
$420$		0			0
$421$	−66.7260			−0.158494			−0.0792470	−	0.996855i	$-0.525252\pi$
$421$	−66.7260			−0.158494			−0.0792470	+	0.996855i	$0.525252\pi$
$422$		0			0
$423$	7.51017	−	4.33600i	0.0177545	−	0.0102506i
$424$		0			0
$425$	−71.8144	−	41.4621i	−0.168975	−	0.0975578i
$426$		0			0
$427$	43.4420	+	658.130i	0.101738	+	1.54129i
$428$		0			0
$429$	−14.4502	+	25.0284i	−0.0336834	+	0.0583413i
$430$		0			0
$431$	279.892	+	484.787i	0.649401	+	1.12480i	0.983266	+	0.182175i	$0.0583137\pi$
$431$	279.892	+	484.787i	0.649401	+	1.12480i	−0.333865	+	0.942621i	$0.608353\pi$
$432$		0			0
$433$			80.8669i			0.186760i	0.995631	+	0.0933798i	$0.0297671\pi$
$433$			80.8669i			0.186760i	−0.995631	+	0.0933798i	$0.970233\pi$
$434$		0			0
$435$	17.5114			0.0402561
$436$		0			0
$437$	−254.853	+	147.140i	−0.583188	+	0.336704i
$438$		0			0
$439$	547.230	+	315.943i	1.24654	+	0.719689i	0.970417	−	0.241434i	$-0.0776177\pi$
$439$	547.230	+	315.943i	1.24654	+	0.719689i	0.276121	+	0.961123i	$0.410951\pi$
$440$		0			0
$441$	89.5958	+	116.540i	0.203165	+	0.264263i
$442$		0			0
$443$	−322.186	+	558.042i	−0.727282	+	1.25969i	0.230746	+	0.973014i	$0.425883\pi$
$443$	−322.186	+	558.042i	−0.727282	+	1.25969i	−0.958028	+	0.286675i	$0.907450\pi$
$444$		0			0
$445$	−296.659	−	513.828i	−0.666649	−	1.15467i
$446$		0			0
$447$			172.372i			0.385620i
$448$		0			0
$449$	321.769			0.716635			0.358317	−	0.933600i	$-0.383351\pi$
$449$	321.769			0.716635			0.358317	+	0.933600i	$0.383351\pi$
$450$		0			0
$451$	198.017	−	114.325i	0.439063	−	0.253493i
$452$		0			0
$453$	−91.0912	−	52.5915i	−0.201084	−	0.116096i
$454$		0			0
$455$	68.2267	−	4.50353i	0.149949	−	0.00989787i
$456$		0			0
$457$	304.964	−	528.213i	0.667318	−	1.15583i	−0.311334	−	0.950301i	$-0.600776\pi$
$457$	304.964	−	528.213i	0.667318	−	1.15583i	0.978651	−	0.205527i	$-0.0658910\pi$
$458$		0			0
$459$	28.1905	+	48.8275i	0.0614173	+	0.106378i
$460$		0			0
$461$		−	187.544i		−	0.406821i	−0.979094	−	0.203410i	$-0.934797\pi$
$461$		−	187.544i		−	0.406821i	0.979094	−	0.203410i	$-0.0652025\pi$
$462$		0			0
$463$	−533.296			−1.15183			−0.575913	−	0.817511i	$-0.695353\pi$
$463$	−533.296			−1.15183			−0.575913	+	0.817511i	$0.695353\pi$
$464$		0			0
$465$	121.170	−	69.9577i	0.260581	−	0.150447i
$466$		0			0
$467$	−222.902	−	128.692i	−0.477306	−	0.275573i	0.241987	−	0.970279i	$-0.422201\pi$
$467$	−222.902	−	128.692i	−0.477306	−	0.275573i	−0.719293	+	0.694707i	$0.755534\pi$
$468$		0			0
$469$	−272.768	+	553.765i	−0.581595	+	1.18074i
$470$		0			0
$471$	−163.990	+	284.038i	−0.348173	+	0.603054i
$472$		0			0
$473$	1.90810	+	3.30492i	0.00403403	+	0.00698715i
$474$		0			0
$475$		−	177.035i		−	0.372706i
$476$		0			0
$477$	161.567			0.338715
$478$		0			0
$479$	576.578	−	332.888i	1.20371	−	0.694964i	0.242334	−	0.970193i	$-0.422087\pi$
$479$	576.578	−	332.888i	1.20371	−	0.694964i	0.961379	+	0.275229i	$0.0887537\pi$
$480$		0			0
$481$	−11.4228	−	6.59495i	−0.0237480	−	0.0137109i
$482$		0			0
$483$	128.027	−	85.6304i	0.265065	−	0.177289i
$484$		0			0
$485$	−79.2484	+	137.262i	−0.163399	+	0.283015i
$486$		0			0
$487$	450.640	+	780.531i	0.925338	+	1.60273i	0.791016	+	0.611795i	$0.209552\pi$
$487$	450.640	+	780.531i	0.925338	+	1.60273i	0.134322	+	0.990938i	$0.457114\pi$
$488$		0			0
$489$			279.131i			0.570821i
$490$		0			0
$491$	−42.5398			−0.0866391			−0.0433195	−	0.999061i	$-0.513793\pi$
$491$	−42.5398			−0.0866391			−0.0433195	+	0.999061i	$0.513793\pi$
$492$		0			0
$493$	−22.8033	+	13.1655i	−0.0462542	+	0.0267049i
$494$		0			0
$495$	77.0341	+	44.4757i	0.155625	+	0.0898499i
$496$		0			0
$497$	242.179	+	362.083i	0.487281	+	0.728537i
$498$		0			0
$499$	61.6165	−	106.723i	0.123480	−	0.213874i	−0.797658	−	0.603110i	$-0.793928\pi$
$499$	61.6165	−	106.723i	0.123480	−	0.213874i	0.921138	+	0.389237i	$0.127261\pi$
$500$		0			0
$501$	210.082	+	363.872i	0.419325	+	0.726291i
$502$		0			0
$503$			613.084i			1.21885i	0.792842	+	0.609427i	$0.208601\pi$
$503$			613.084i			1.21885i	−0.792842	+	0.609427i	$0.791399\pi$
$504$		0			0
$505$	280.040			0.554535
$506$		0			0
$507$	−245.255	+	141.598i	−0.483737	+	0.279286i
$508$		0			0
$509$	−452.131	−	261.038i	−0.888274	−	0.512845i	−0.0148964	−	0.999889i	$-0.504742\pi$
$509$	−452.131	−	261.038i	−0.888274	−	0.512845i	−0.873378	+	0.487044i	$0.838075\pi$
$510$		0			0
$511$	−329.134	−	162.122i	−0.644099	−	0.317264i
$512$		0			0
$513$	−60.1841	+	104.242i	−0.117318	+	0.203201i
$514$		0			0
$515$	−100.313	−	173.748i	−0.194783	−	0.337374i
$516$		0			0
$517$			20.5724i			0.0397918i
$518$		0			0
$519$	200.752			0.386806
$520$		0			0
$521$	386.266	−	223.011i	0.741394	−	0.428044i	−0.0811821	−	0.996699i	$-0.525870\pi$
$521$	386.266	−	223.011i	0.741394	−	0.428044i	0.822576	+	0.568655i	$0.192536\pi$
$522$		0			0
$523$	584.557	+	337.494i	1.11770	+	0.645305i	0.940813	−	0.338926i	$-0.110064\pi$
$523$	584.557	+	337.494i	1.11770	+	0.645305i	0.176888	+	0.984231i	$0.443397\pi$
$524$		0			0
$525$	6.10299	+	92.4579i	0.0116247	+	0.176110i
$526$		0			0
$527$	−105.192	+	182.197i	−0.199605	+	0.345726i
$528$		0			0
$529$	183.808	+	318.365i	0.347464	+	0.601825i
$530$		0			0
$531$			252.296i			0.475133i
$532$		0			0
$533$	−75.3255			−0.141324
$534$		0			0
$535$	341.879	−	197.384i	0.639026	−	0.368942i
$536$		0			0
$537$	436.726	+	252.144i	0.813269	+	0.469541i
$538$		0			0
$539$	−345.699	+	45.8377i	−0.641371	+	0.0850421i
$540$		0			0
$541$	287.306	−	497.629i	0.531065	−	0.919832i	−0.468277	−	0.883582i	$-0.655125\pi$
$541$	287.306	−	497.629i	0.531065	−	0.919832i	0.999343	−	0.0362508i	$-0.0115415\pi$
$542$		0			0
$543$	−279.866	−	484.743i	−0.515408	−	0.892713i
$544$		0			0
$545$			856.818i			1.57214i
$546$		0			0
$547$	307.808			0.562721			0.281360	−	0.959602i	$-0.409214\pi$
$547$	307.808			0.562721			0.281360	+	0.959602i	$0.409214\pi$
$548$		0			0
$549$	244.799	−	141.335i	0.445900	−	0.257440i
$550$		0			0
$551$	−48.6829	−	28.1071i	−0.0883537	−	0.0510110i
$552$		0			0
$553$	−588.952	+	38.8757i	−1.06501	+	0.0702997i
$554$		0			0
$555$	−20.2984	+	35.1578i	−0.0365736	+	0.0633474i
$556$		0			0
$557$	332.333	+	575.618i	0.596649	+	1.03343i	0.993312	+	0.115462i	$0.0368348\pi$
$557$	332.333	+	575.618i	0.596649	+	1.03343i	−0.396663	+	0.917964i	$0.629832\pi$
$558$		0			0
$559$		−	1.25719i		−	0.00224899i
$560$		0			0
$561$	−133.751			−0.238416
$562$		0			0
$563$	−485.470	+	280.286i	−0.862291	+	0.497844i	−0.864779	−	0.502153i	$-0.832541\pi$
$563$	−485.470	+	280.286i	−0.862291	+	0.497844i	0.00248813	+	0.999997i	$0.499208\pi$
$564$		0			0
$565$	−443.792	−	256.223i	−0.785473	−	0.453493i
$566$		0			0
$567$	27.8380	−	56.5159i	0.0490971	−	0.0996753i
$568$		0			0
$569$	252.749	−	437.774i	0.444198	−	0.769374i	−0.553798	−	0.832651i	$-0.686822\pi$
$569$	252.749	−	437.774i	0.444198	−	0.769374i	0.997996	+	0.0632770i	$0.0201552\pi$
$570$		0			0
$571$	−309.204	−	535.556i	−0.541512	−	0.937927i	−0.998817	−	0.0486171i	$-0.984519\pi$
$571$	−309.204	−	535.556i	−0.541512	−	0.937927i	0.457305	−	0.889310i	$-0.348815\pi$
$572$		0			0
$573$			43.3639i			0.0756787i
$574$		0			0
$575$	97.0865			0.168846
$576$		0			0
$577$	−438.092	+	252.933i	−0.759259	+	0.438358i	−0.829030	−	0.559205i	$-0.811107\pi$
$577$	−438.092	+	252.933i	−0.759259	+	0.438358i	0.0697707	+	0.997563i	$0.477773\pi$
$578$		0			0
$579$	−489.310	−	282.503i	−0.845095	−	0.487916i
$580$		0			0
$581$	−449.933	+	300.937i	−0.774412	+	0.517964i
$582$		0			0
$583$	−191.641	+	331.931i	−0.328715	+	0.569351i
$584$		0			0
$585$	−14.6518	−	25.3777i	−0.0250459	−	0.0433807i
$586$		0			0
$587$		−	222.198i		−	0.378532i	−0.981926	−	0.189266i	$-0.939389\pi$
$587$		−	222.198i		−	0.378532i	0.981926	−	0.189266i	$-0.0606108\pi$
$588$		0			0
$589$	−449.149			−0.762562
$590$		0			0
$591$	−226.065	+	130.519i	−0.382513	+	0.220844i
$592$		0			0
$593$	129.129	+	74.5527i	0.217756	+	0.125721i	0.604911	−	0.796293i	$-0.293209\pi$
$593$	129.129	+	74.5527i	0.217756	+	0.125721i	−0.387155	+	0.922015i	$0.626542\pi$
$594$		0			0
$595$	175.928	+	263.031i	0.295677	+	0.442069i
$596$		0			0
$597$	−265.167	+	459.283i	−0.444166	+	0.769318i
$598$		0			0
$599$	107.113	+	185.525i	0.178819	+	0.309724i	0.941476	−	0.337079i	$-0.109439\pi$
$599$	107.113	+	185.525i	0.178819	+	0.309724i	−0.762657	+	0.646803i	$0.776106\pi$
$600$		0			0
$601$		−	886.830i		−	1.47559i	−0.675024	−	0.737796i	$-0.735867\pi$
$601$		−	886.830i		−	1.47559i	0.675024	−	0.737796i	$-0.264133\pi$
$602$		0			0
$603$	264.557			0.438734
$604$		0			0
$605$	253.831	−	146.549i	0.419555	−	0.242230i
$606$		0			0
$607$	94.4477	+	54.5294i	0.155598	+	0.0898343i	0.575777	−	0.817607i	$-0.304700\pi$
$607$	94.4477	+	54.5294i	0.155598	+	0.0898343i	−0.420180	+	0.907441i	$0.638033\pi$
$608$		0			0
$609$	26.3939	+	13.0009i	0.0433398	+	0.0213479i
$610$		0			0
$611$	3.38863	−	5.86927i	0.00554603	−	0.00960601i
$612$		0			0
$613$	−233.714	−	404.805i	−0.381263	−	0.660367i	0.609980	−	0.792417i	$-0.291177\pi$
$613$	−233.714	−	404.805i	−0.381263	−	0.660367i	−0.991243	+	0.132050i	$0.957844\pi$
$614$		0			0
$615$			231.842i			0.376978i
$616$		0			0
$617$	−832.398			−1.34911			−0.674553	−	0.738227i	$-0.735663\pi$
$617$	−832.398			−1.34911			−0.674553	+	0.738227i	$0.735663\pi$
$618$		0			0
$619$	295.530	−	170.624i	0.477431	−	0.275645i	−0.241914	−	0.970298i	$-0.577775\pi$
$619$	295.530	−	170.624i	0.477431	−	0.275645i	0.719345	+	0.694653i	$0.244442\pi$
$620$		0			0
$621$	−57.1666	−	33.0051i	−0.0920556	−	0.0531483i
$622$		0			0
$623$	−65.6590	−	994.709i	−0.105392	−	1.59664i
$624$		0			0
$625$	187.767	−	325.222i	0.300427	−	0.520355i
$626$		0			0
$627$	−142.773	−	247.291i	−0.227709	−	0.394403i
$628$		0			0
$629$		−	61.0432i		−	0.0970480i
$630$		0			0
$631$	−1249.74			−1.98057			−0.990284	−	0.139063i	$-0.955591\pi$
$631$	−1249.74			−1.98057			−0.990284	+	0.139063i	$0.955591\pi$
$632$		0			0
$633$	−5.32527	+	3.07455i	−0.00841276	+	0.00485711i
$634$		0			0
$635$	−431.381	−	249.058i	−0.679340	−	0.392217i
$636$		0			0
$637$	106.178	+	43.8652i	0.166684	+	0.0688621i
$638$		0			0
$639$	93.3446	−	161.678i	0.146079	−	0.253017i
$640$		0			0
$641$	448.374	+	776.606i	0.699491	+	1.21155i	0.968643	+	0.248457i	$0.0799234\pi$
$641$	448.374	+	776.606i	0.699491	+	1.21155i	−0.269152	+	0.963098i	$0.586743\pi$
$642$		0			0
$643$		−	422.098i		−	0.656451i	−0.944599	−	0.328225i	$-0.893549\pi$
$643$		−	422.098i		−	0.656451i	0.944599	−	0.328225i	$-0.106451\pi$
$644$		0			0
$645$	−3.86946			−0.00599916
$646$		0			0
$647$	390.884	−	225.677i	0.604148	−	0.348805i	−0.166524	−	0.986037i	$-0.553254\pi$
$647$	390.884	−	225.677i	0.604148	−	0.348805i	0.770672	+	0.637233i	$0.219921\pi$
$648$		0			0
$649$	−518.329	−	299.258i	−0.798658	−	0.461106i
$650$		0			0
$651$	234.571	−	15.4836i	0.360324	−	0.0237844i
$652$		0			0
$653$	266.155	−	460.994i	0.407588	−	0.705964i	−0.587031	−	0.809565i	$-0.699703\pi$
$653$	266.155	−	460.994i	0.407588	−	0.705964i	0.994619	+	0.103601i	$0.0330365\pi$
$654$		0			0
$655$	−118.378	−	205.036i	−0.180729	−	0.313032i
$656$		0			0
$657$			157.241i			0.239332i
$658$		0			0
$659$	1311.97			1.99085			0.995424	−	0.0955521i	$-0.0304616\pi$
$659$	1311.97			1.99085			0.995424	+	0.0955521i	$0.0304616\pi$
$660$		0			0
$661$	143.074	−	82.6039i	0.216451	−	0.124968i	−0.387855	−	0.921720i	$-0.626784\pi$
$661$	143.074	−	82.6039i	0.216451	−	0.124968i	0.604306	+	0.796752i	$0.293450\pi$
$662$		0			0
$663$	38.1591	+	22.0312i	0.0575553	+	0.0332295i
$664$		0			0
$665$	−298.518	+	606.042i	−0.448900	+	0.911342i
$666$		0			0
$667$	15.4140	−	26.6978i	0.0231094	−	0.0400267i
$668$		0			0
$669$	174.521	+	302.279i	0.260869	+	0.451838i
$670$		0			0
$671$			670.570i			0.999359i
$672$		0			0
$673$	−917.460			−1.36324			−0.681620	−	0.731707i	$-0.738724\pi$
$673$	−917.460			−1.36324			−0.681620	+	0.731707i	$0.738724\pi$
$674$		0			0
$675$	34.3908	−	19.8555i	0.0509493	−	0.0294156i
$676$		0			0
$677$	973.160	+	561.854i	1.43746	+	0.829918i	0.997673	−	0.0681842i	$-0.0217205\pi$
$677$	973.160	+	561.854i	1.43746	+	0.829918i	0.439787	+	0.898102i	$0.355054\pi$
$678$		0			0
$679$	−221.353	+	148.052i	−0.325999	+	0.218044i
$680$		0			0
$681$	357.131	−	618.569i	0.524422	−	0.908325i
$682$		0			0
$683$	−297.019	−	514.452i	−0.434874	−	0.753225i	0.562411	−	0.826858i	$-0.309874\pi$
$683$	−297.019	−	514.452i	−0.434874	−	0.753225i	−0.997285	+	0.0736333i	$0.976541\pi$
$684$		0			0
$685$		−	556.427i		−	0.812302i
$686$		0			0
$687$	133.469			0.194278
$688$		0			0
$689$	109.350	−	63.1331i	0.158708	−	0.0916300i
$690$		0			0
$691$	−221.826	−	128.072i	−0.321022	−	0.185342i	0.330826	−	0.943692i	$-0.392673\pi$
$691$	−221.826	−	128.072i	−0.321022	−	0.185342i	−0.651848	+	0.758350i	$0.726006\pi$
$692$		0			0
$693$	83.0893	+	124.227i	0.119898	+	0.179260i
$694$		0			0
$695$	352.989	−	611.395i	0.507898	−	0.879706i
$696$		0			0
$697$	−174.304	−	301.904i	−0.250078	−	0.433147i
$698$		0			0
$699$			297.808i			0.426049i
$700$		0			0
$701$	1035.70			1.47746			0.738732	−	0.674000i	$-0.235425\pi$
$701$	1035.70			1.47746			0.738732	+	0.674000i	$0.235425\pi$
$702$		0			0
$703$	112.862	−	65.1607i	0.160543	−	0.0926895i
$704$		0			0
$705$	−18.0648	−	10.4297i	−0.0256239	−	0.0147940i
$706$		0			0
$707$	422.089	+	207.908i	0.597014	+	0.294071i
$708$		0			0
$709$	123.811	−	214.447i	0.174627	−	0.302464i	−0.765405	−	0.643549i	$-0.777461\pi$
$709$	123.811	−	214.447i	0.174627	−	0.302464i	0.940032	+	0.341086i	$0.110795\pi$
$710$		0			0
$711$	126.479	+	219.068i	0.177889	+	0.308112i
$712$		0			0
$713$		−	246.314i		−	0.345462i
$714$		0			0
$715$	69.5164			0.0972257
$716$		0			0
$717$	−473.815	+	273.557i	−0.660830	+	0.381530i
$718$		0			0
$719$	49.8292	+	28.7689i	0.0693035	+	0.0400124i	0.534251	−	0.845326i	$-0.320594\pi$
$719$	49.8292	+	28.7689i	0.0693035	+	0.0400124i	−0.464948	+	0.885338i	$0.653927\pi$
$720$		0			0
$721$	−22.2022	−	336.355i	−0.0307936	−	0.466511i
$722$		0			0
$723$	51.0128	−	88.3567i	0.0705571	−	0.122209i
$724$		0			0
$725$	9.27288	+	16.0611i	0.0127902	+	0.0221533i
$726$		0			0
$727$		−	1226.15i		−	1.68659i	−0.537455	−	0.843293i	$-0.680614\pi$
$727$		−	1226.15i		−	1.68659i	0.537455	−	0.843293i	$-0.319386\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	5.03879	−	2.90915i	0.00689301	−	0.00397968i
$732$		0			0
$733$	−510.729	−	294.869i	−0.696765	−	0.402277i	0.109376	−	0.994000i	$-0.465115\pi$
$733$	−510.729	−	294.869i	−0.696765	−	0.402277i	−0.806141	+	0.591723i	$0.798448\pi$
$734$		0			0
$735$	135.011	−	326.801i	0.183689	−	0.444627i
$736$		0			0
$737$	−313.801	+	543.519i	−0.425781	+	0.737475i
$738$		0			0
$739$	−455.898	−	789.638i	−0.616912	−	1.06852i	−0.990046	−	0.140745i	$-0.955050\pi$
$739$	−455.898	−	789.638i	−0.616912	−	1.06852i	0.373134	−	0.927777i	$-0.378283\pi$
$740$		0			0
$741$			94.0690i			0.126949i
$742$		0			0
$743$	−778.225			−1.04741			−0.523705	−	0.851900i	$-0.675450\pi$
$743$	−778.225			−1.04741			−0.523705	+	0.851900i	$0.675450\pi$
$744$		0			0
$745$	359.072	−	207.311i	0.481976	−	0.278269i
$746$		0			0
$747$	200.905	+	115.992i	0.268949	+	0.155278i
$748$		0			0
$749$	661.837	−	43.6867i	0.883627	−	0.0583267i
$750$		0			0
$751$	330.897	−	573.130i	0.440608	−	0.763156i	−0.557126	−	0.830428i	$-0.688096\pi$
$751$	330.897	−	573.130i	0.440608	−	0.763156i	0.997735	+	0.0672717i	$0.0214294\pi$
$752$		0			0
$753$	140.465	+	243.292i	0.186540	+	0.323097i
$754$		0			0
$755$			253.006i			0.335107i
$756$		0			0
$757$	227.313			0.300282			0.150141	−	0.988665i	$-0.452027\pi$
$757$	227.313			0.300282			0.150141	+	0.988665i	$0.452027\pi$
$758$		0			0
$759$	135.615	−	78.2972i	0.178676	−	0.103158i
$760$		0			0
$761$	−663.592	−	383.125i	−0.872000	−	0.503450i	−0.00398792	−	0.999992i	$-0.501269\pi$
$761$	−663.592	−	383.125i	−0.872000	−	0.503450i	−0.868012	+	0.496542i	$0.834603\pi$
$762$		0			0
$763$	−636.121	+	1291.43i	−0.833710	+	1.69257i
$764$		0			0
$765$	67.8091	−	117.449i	0.0886393	−	0.153528i
$766$		0			0
$767$	98.5858	+	170.756i	0.128534	+	0.222628i
$768$		0			0
$769$		−	455.642i		−	0.592512i	−0.955109	−	0.296256i	$-0.904262\pi$
$769$		−	455.642i		−	0.592512i	0.955109	−	0.296256i	$-0.0957381\pi$
$770$		0			0
$771$	744.735			0.965934
$772$		0			0
$773$	87.5476	−	50.5456i	0.113257	−	0.0653889i	−0.442301	−	0.896866i	$-0.645838\pi$
$773$	87.5476	−	50.5456i	0.113257	−	0.0653889i	0.555558	+	0.831478i	$0.312505\pi$
$774$		0			0
$775$	128.328	+	74.0900i	0.165584	+	0.0956000i
$776$		0			0
$777$	−56.6965	+	37.9214i	−0.0729685	+	0.0488048i
$778$		0			0
$779$	372.123	−	644.535i	0.477693	−	0.827388i
$780$		0			0
$781$	221.439	+	383.544i	0.283533	+	0.491093i
$782$		0			0
$783$		−	12.6095i		−	0.0161041i
$784$		0			0
$785$	788.916			1.00499
$786$		0			0
$787$	−543.871	+	314.004i	−0.691068	+	0.398988i	−0.804012	−	0.594613i	$-0.797305\pi$
$787$	−543.871	+	314.004i	−0.691068	+	0.398988i	0.112944	+	0.993601i	$0.463972\pi$
$788$		0			0
$789$	256.533	+	148.109i	0.325137	+	0.187718i
$790$		0			0
$791$	−478.676	−	715.672i	−0.605153	−	0.904769i
$792$		0			0
$793$	110.454	−	191.313i	0.139287	−	0.241252i
$794$		0			0
$795$	−194.315	−	336.564i	−0.244422	−	0.423351i
$796$		0			0
$797$			420.720i			0.527880i	0.964539	+	0.263940i	$0.0850221\pi$
$797$			420.720i			0.527880i	−0.964539	+	0.263940i	$0.914978\pi$
$798$		0			0
$799$	31.3653			0.0392557
$800$		0			0
$801$	−369.993	+	213.616i	−0.461914	+	0.266686i
$802$		0			0
$803$	−323.044	−	186.510i	−0.402297	−	0.232266i
$804$		0			0
$805$	−332.355	−	163.708i	−0.412863	−	0.203364i
$806$		0			0
$807$	61.3494	−	106.260i	0.0760216	−	0.131673i
$808$		0			0
$809$	−288.910	−	500.406i	−0.357120	−	0.618549i	0.630359	−	0.776304i	$-0.282908\pi$
$809$	−288.910	−	500.406i	−0.357120	−	0.618549i	−0.987478	+	0.157755i	$0.949574\pi$
$810$		0			0
$811$		−	1263.65i		−	1.55814i	−0.626937	−	0.779070i	$-0.715692\pi$
$811$		−	1263.65i		−	1.55814i	0.626937	−	0.779070i	$-0.284308\pi$
$812$		0			0
$813$	422.617			0.519824
$814$		0			0
$815$	581.465	−	335.709i	0.713454	−	0.411913i
$816$		0			0
$817$	10.7573	+	6.21076i	0.0131669	+	0.00760190i
$818$		0			0
$819$	−3.24287	−	49.1282i	−0.00395955	−	0.0599856i
$820$		0			0
$821$	69.8461	−	120.977i	0.0850745	−	0.147353i	−0.820348	−	0.571864i	$-0.806221\pi$
$821$	69.8461	−	120.977i	0.0850745	−	0.147353i	0.905423	+	0.424511i	$0.139554\pi$
$822$		0			0
$823$	200.176	+	346.716i	0.243228	+	0.421283i	0.961632	−	0.274343i	$-0.0884604\pi$
$823$	200.176	+	346.716i	0.243228	+	0.421283i	−0.718404	+	0.695626i	$0.755127\pi$
$824$		0			0
$825$			94.2055i			0.114189i
$826$		0			0
$827$	−484.494			−0.585845			−0.292922	−	0.956136i	$-0.594628\pi$
$827$	−484.494			−0.585845			−0.292922	+	0.956136i	$0.594628\pi$
$828$		0			0
$829$	322.222	−	186.035i	0.388687	−	0.224409i	−0.292904	−	0.956142i	$-0.594622\pi$
$829$	322.222	−	186.035i	0.388687	−	0.224409i	0.681591	+	0.731733i	$0.261288\pi$
$830$		0			0
$831$	−492.693	−	284.457i	−0.592892	−	0.342306i
$832$		0			0
$833$	69.8856	+	527.064i	0.0838963	+	0.632730i
$834$		0			0
$835$	505.327	−	875.252i	0.605182	−	1.04821i
$836$		0			0
$837$	−50.3746	−	87.2514i	−0.0601848	−	0.104243i
$838$		0			0
$839$		−	1119.49i		−	1.33432i	−0.744916	−	0.667159i	$-0.767510\pi$
$839$		−	1119.49i		−	1.33432i	0.744916	−	0.667159i	$-0.232490\pi$
$840$		0			0
$841$	−835.111			−0.992998
$842$		0			0
$843$	−677.747	+	391.297i	−0.803970	+	0.464172i
$844$		0			0
$845$	589.932	+	340.597i	0.698144	+	0.403074i
$846$		0			0
$847$	491.386	−	32.4356i	0.580149	−	0.0382946i
$848$		0			0
$849$	60.1879	−	104.248i	0.0708926	−	0.122790i
$850$		0			0
$851$	35.7343	+	61.8936i	0.0419909	+	0.0727304i
$852$		0			0
$853$			511.521i			0.599673i	0.953991	+	0.299837i	$0.0969322\pi$
$853$			511.521i			0.599673i	−0.953991	+	0.299837i	$0.903068\pi$
$854$		0			0
$855$	289.532			0.338634
$856$		0			0
$857$	750.430	−	433.261i	0.875648	−	0.505556i	0.00642697	−	0.999979i	$-0.497954\pi$
$857$	750.430	−	433.261i	0.875648	−	0.505556i	0.869221	+	0.494424i	$0.164621\pi$
$858$		0			0
$859$	1069.10	+	617.244i	1.24459	+	0.718562i	0.970024	−	0.243008i	$-0.0781341\pi$
$859$	1069.10	+	617.244i	1.24459	+	0.718562i	0.274561	+	0.961570i	$0.411467\pi$
$860$		0			0
$861$	−172.125	+	349.442i	−0.199912	+	0.405856i
$862$		0			0
$863$	−687.116	+	1190.12i	−0.796194	+	1.37905i	0.125884	+	0.992045i	$0.459823\pi$
$863$	−687.116	+	1190.12i	−0.796194	+	1.37905i	−0.922078	+	0.387004i	$0.873510\pi$
$864$		0			0
$865$	−241.443	−	418.192i	−0.279125	−	0.483458i
$866$		0			0
$867$		−	296.641i		−	0.342146i
$868$		0			0
$869$	−600.085			−0.690546
$870$		0			0
$871$	179.054	−	103.377i	0.205573	−	0.118688i
$872$		0			0
$873$	98.8388	+	57.0646i	0.113217	+	0.0653661i
$874$		0			0
$875$	791.292	−	529.255i	0.904334	−	0.604862i
$876$		0			0
$877$	−124.971	+	216.456i	−0.142499	+	0.246815i	−0.928437	−	0.371490i	$-0.878847\pi$
$877$	−124.971	+	216.456i	−0.142499	+	0.246815i	0.785938	+	0.618305i	$0.212180\pi$
$878$		0			0
$879$	−204.867	−	354.840i	−0.233068	−	0.403686i
$880$		0			0
$881$		−	1070.84i		−	1.21548i	−0.794135	−	0.607742i	$-0.792076\pi$
$881$		−	1070.84i		−	1.21548i	0.794135	−	0.607742i	$-0.207924\pi$
$882$		0			0
$883$	−1034.20			−1.17123			−0.585614	−	0.810590i	$-0.699147\pi$
$883$	−1034.20			−1.17123			−0.585614	+	0.810590i	$0.699147\pi$
$884$		0			0
$885$	525.563	−	303.434i	0.593857	−	0.342863i
$886$		0			0
$887$	−1407.11	−	812.396i	−1.58637	−	0.915891i	−0.993898	−	0.110300i	$-0.964819\pi$
$887$	−1407.11	−	812.396i	−1.58637	−	0.915891i	−0.592472	−	0.805591i	$-0.701848\pi$
$888$		0			0
$889$	−465.289	−	695.658i	−0.523385	−	0.782517i
$890$		0			0
$891$	32.0257	−	55.4702i	0.0359436	−	0.0622561i
$892$		0			0
$893$	33.4810	+	57.9908i	0.0374927	+	0.0649393i
$894$		0			0
$895$		−	1213.00i		−	1.35531i
$896$		0			0
$897$	−51.5877			−0.0575113
$898$		0			0
$899$	40.7480	−	23.5259i	0.0453259	−	0.0261689i
$900$		0			0
$901$	506.074	+	292.182i	0.561680	+	0.324286i
$902$		0			0
$903$	−5.83221	−	2.87277i	−0.00645870	−	0.00318136i
$904$		0			0
$905$	−673.186	+	1165.99i	−0.743852	+	1.28839i
$906$		0			0
$907$	192.221	+	332.937i	0.211931	+	0.367075i	0.952319	−	0.305105i	$-0.0986915\pi$
$907$	192.221	+	332.937i	0.211931	+	0.367075i	−0.740388	+	0.672180i	$0.765358\pi$
$908$		0			0
$909$		−	201.649i		−	0.221837i
$910$		0			0
$911$	−528.605			−0.580247			−0.290123	−	0.956989i	$-0.593696\pi$
$911$	−528.605			−0.580247			−0.290123	+	0.956989i	$0.593696\pi$
$912$		0			0
$913$	−476.601	+	275.166i	−0.522017	+	0.301387i
$914$		0			0
$915$	−588.835	−	339.964i	−0.643536	−	0.371545i
$916$		0			0
$917$	−26.2004	−	396.926i	−0.0285718	−	0.432852i
$918$		0			0
$919$	616.329	−	1067.51i	0.670652	−	1.16160i	−0.307068	−	0.951688i	$-0.599348\pi$
$919$	616.329	−	1067.51i	0.670652	−	1.16160i	0.977720	−	0.209915i	$-0.0673188\pi$
$920$		0			0
$921$	6.03960	+	10.4609i	0.00655766	+	0.0113582i
$922$		0			0
$923$		−	145.899i		−	0.158071i
$924$		0			0
$925$	−42.9947			−0.0464808
$926$		0			0
$927$	−125.111	+	72.2329i	−0.134963	+	0.0779211i
$928$		0			0
$929$	−672.470	−	388.251i	−0.723865	−	0.417924i	0.0923087	−	0.995730i	$-0.470575\pi$
$929$	−672.470	−	388.251i	−0.723865	−	0.417924i	−0.816173	+	0.577807i	$0.803909\pi$
$930$		0			0
$931$	−899.879	+	691.826i	−0.966572	+	0.743100i
$932$		0			0
$933$	−92.0662	+	159.463i	−0.0986776	+	0.170915i
$934$		0			0
$935$	160.862	+	278.621i	0.172045	+	0.297990i
$936$		0			0
$937$			4.02080i			0.00429114i	0.999998	+	0.00214557i	$0.000682957\pi$
$937$			4.02080i			0.00429114i	−0.999998	+	0.00214557i	$0.999317\pi$
$938$		0			0
$939$	546.620			0.582130
$940$		0			0
$941$	−1404.37	+	810.814i	−1.49242	+	0.861651i	−0.999962	−	0.00868298i	$-0.997236\pi$
$941$	−1404.37	+	810.814i	−1.49242	+	0.861651i	−0.492461	+	0.870334i	$0.663903\pi$
$942$		0			0
$943$	353.465	+	204.073i	0.374830	+	0.216408i
$944$		0			0
$945$	−151.210	+	9.98112i	−0.160011	+	0.0105620i
$946$		0			0
$947$	58.0509	−	100.547i	0.0612998	−	0.106174i	−0.833747	−	0.552147i	$-0.813809\pi$
$947$	58.0509	−	100.547i	0.0612998	−	0.106174i	0.895047	+	0.445973i	$0.147142\pi$
$948$		0			0
$949$	61.4428	+	106.422i	0.0647448	+	0.112141i
$950$		0			0
$951$			935.893i			0.984114i
$952$		0			0
$953$	118.987			0.124855			0.0624274	−	0.998050i	$-0.480116\pi$
$953$	118.987			0.124855			0.0624274	+	0.998050i	$0.480116\pi$
$954$		0			0
$955$	90.3323	−	52.1534i	0.0945888	−	0.0546109i
$956$		0			0
$957$	25.9056	+	14.9566i	0.0270696	+	0.0156286i
$958$		0			0
$959$	413.104	−	838.669i	0.430765	−	0.874525i
$960$		0			0
$961$	−292.529	+	506.676i	−0.304401	+	0.527238i
$962$		0			0
$963$	−142.131	−	246.178i	−0.147592	−	0.255636i
$964$		0			0
$965$			1359.06i			1.40835i
$966$		0			0
$967$	−470.206			−0.486253			−0.243126	−	0.969995i	$-0.578173\pi$
$967$	−470.206			−0.486253			−0.243126	+	0.969995i	$0.578173\pi$
$968$		0			0
$969$	−377.027	+	217.677i	−0.389089	+	0.224641i
$970$		0			0
$971$	254.174	+	146.748i	0.261766	+	0.151130i	0.625140	−	0.780513i	$-0.285042\pi$
$971$	254.174	+	146.748i	0.261766	+	0.151130i	−0.363374	+	0.931643i	$0.618375\pi$
$972$		0			0
$973$	985.954	−	659.454i	1.01331	−	0.677753i
$974$		0			0
$975$	15.5173	−	26.8767i	0.0159152	−	0.0275659i
$976$		0			0
$977$	−551.134	−	954.592i	−0.564109	−	0.977065i	−0.997132	−	0.0756821i	$-0.975887\pi$
$977$	−551.134	−	954.592i	−0.564109	−	0.977065i	0.433023	−	0.901383i	$-0.357447\pi$
$978$		0			0
$979$		−	1013.51i		−	1.03525i
$980$		0			0
$981$	616.971			0.628921
$982$		0			0
$983$	−179.042	+	103.370i	−0.182138	+	0.105157i	−0.588297	−	0.808645i	$-0.700201\pi$
$983$	−179.042	+	103.370i	−0.182138	+	0.105157i	0.406159	+	0.913803i	$0.366868\pi$
$984$		0			0
$985$	543.774	+	313.948i	0.552054	+	0.318729i
$986$		0			0
$987$	−19.4848	−	29.1319i	−0.0197415	−	0.0295156i
$988$		0			0
$989$	−3.40599	+	5.89935i	−0.00344388	+	0.00596497i
$990$		0			0
$991$	607.808	+	1052.75i	0.613328	+	1.06232i	0.990675	+	0.136244i	$0.0435030\pi$
$991$	607.808	+	1052.75i	0.613328	+	1.06232i	−0.377347	+	0.926072i	$0.623164\pi$
$992$		0			0
$993$			106.353i			0.107103i
$994$		0			0
$995$	1275.66			1.28207
$996$		0			0
$997$	52.2095	−	30.1432i	0.0523666	−	0.0302339i	−0.473588	−	0.880746i	$-0.657041\pi$
$997$	52.2095	−	30.1432i	0.0523666	−	0.0302339i	0.525955	+	0.850513i	$0.323708\pi$
$998$		0			0
$999$	25.3162	+	14.6163i	0.0253415	+	0.0146309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.3.bh.a.481.6	✓	16
4.3	odd	2		672.3.bh.c.481.6	yes	16
7.3	odd	6	inner	672.3.bh.a.577.6	yes	16
28.3	even	6		672.3.bh.c.577.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.3.bh.a.481.6	✓	16	1.1	even	1	trivial
672.3.bh.a.577.6	yes	16	7.3	odd	6	inner
672.3.bh.c.481.6	yes	16	4.3	odd	2
672.3.bh.c.577.6	yes	16	28.3	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	672.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(3.60807 + 2.08312i) q^{5} +(3.89168 + 5.81849i) q^{7} +(1.50000 - 2.59808i) q^{9} +(3.55841 + 6.16335i) q^{11} -2.34453i q^{13} -7.21615 q^{15} +(9.39685 - 5.42527i) q^{17} +(20.0614 + 11.5824i) q^{19} +(-10.8765 - 5.35743i) q^{21} +(-6.35184 + 11.0017i) q^{23} +(-3.82120 - 6.61851i) q^{25} +5.19615i q^{27} -2.42670 q^{29} +(-16.7915 + 9.69460i) q^{31} +(-10.6752 - 6.16335i) q^{33} +(1.92087 + 29.1004i) q^{35} +(2.81291 - 4.87210i) q^{37} +(2.03042 + 3.51679i) q^{39} -32.1282i q^{41} +0.536222 q^{43} +(10.8242 - 6.24937i) q^{45} +(2.50339 + 1.44533i) q^{47} +(-18.7096 + 45.2874i) q^{49} +(-9.39685 + 16.2758i) q^{51} +(26.9278 + 46.6404i) q^{53} +29.6505i q^{55} -40.1228 q^{57} +(-72.8315 + 42.0493i) q^{59} +(81.5996 + 47.1116i) q^{61} +(20.9544 - 1.38316i) q^{63} +(4.88394 - 8.45924i) q^{65} +(44.0928 + 76.3709i) q^{67} -22.0034i q^{69} +62.2297 q^{71} +(-45.3916 + 26.2069i) q^{73} +(11.4636 + 6.61851i) q^{75} +(-22.0132 + 44.6904i) q^{77} +(-42.1596 + 73.0225i) q^{79} +(-4.50000 - 7.79423i) q^{81} +77.3283i q^{83} +45.2060 q^{85} +(3.64004 - 2.10158i) q^{87} +(-123.331 - 71.2053i) q^{89} +(13.6416 - 9.12417i) q^{91} +(16.7915 - 29.0838i) q^{93} +(48.2553 + 83.5806i) q^{95} +38.0431i q^{97} +21.3505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{3} - 12 q^{7} + 24 q^{9} - 12 q^{11} - 48 q^{17} - 60 q^{19} + 24 q^{21} - 48 q^{23} + 52 q^{25} - 64 q^{29} - 60 q^{31} + 36 q^{33} - 4 q^{37} + 12 q^{39} + 72 q^{43} + 120 q^{47} - 8 q^{49}+ \cdots - 72 q^{99}+O(q^{100}) \) 16 * q - 24 * q^3 - 12 * q^7 + 24 * q^9 - 12 * q^11 - 48 * q^17 - 60 * q^19 + 24 * q^21 - 48 * q^23 + 52 * q^25 - 64 * q^29 - 60 * q^31 + 36 * q^33 - 4 * q^37 + 12 * q^39 + 72 * q^43 + 120 * q^47 - 8 * q^49 + 48 * q^51 - 72 * q^53 + 120 * q^57 - 228 * q^59 + 72 * q^61 - 36 * q^63 - 40 * q^65 + 12 * q^67 - 528 * q^71 - 36 * q^73 - 156 * q^75 - 96 * q^77 - 204 * q^79 - 72 * q^81 - 480 * q^85 + 96 * q^87 - 192 * q^89 - 276 * q^91 + 60 * q^93 - 48 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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