LMFDB - Embedded newform 672.3.bh.b.481.5

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)

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);

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")

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} + 120 x^{14} - 700 x^{13} + 5060 x^{12} - 21624 x^{11} + 95002 x^{10} - 292520 x^{9} + \cdots + 76783 $ x^16 - 8x^15 + 120x^14 - 700x^13 + 5060x^12 - 21624x^11 + 95002x^10 - 292520x^9 + 820115x^8 - 1736320x^7 + 3049290x^6 - 4089680x^5 + 4223014x^4 - 3175248x^3 + 1657766x^2 - 534268*x + 76783
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			481.5
Root			$0.500000 + 1.70210i$ of defining polynomial
Character	$\chi$	$=$	672.481
Dual form			672.3.bh.b.577.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 + 0.866025i) q^{3} +(-0.803356 - 0.463818i) q^{5} +(0.377407 - 6.98982i) q^{7} +(1.50000 - 2.59808i) q^{9} +(7.28297 + 12.6145i) q^{11} -14.4822i q^{13} +1.60671 q^{15} +(-18.8640 + 10.8912i) q^{17} +(8.69362 + 5.01926i) q^{19} +(5.48725 + 10.8116i) q^{21} +(2.65798 - 4.60375i) q^{23} +(-12.0697 - 20.9054i) q^{25} +5.19615i q^{27} -8.59590 q^{29} +(-39.7627 + 22.9570i) q^{31} +(-21.8489 - 12.6145i) q^{33} +(-3.54519 + 5.44026i) q^{35} +(18.8742 - 32.6910i) q^{37} +(12.5419 + 21.7232i) q^{39} -41.3390i q^{41} -14.8107 q^{43} +(-2.41007 + 1.39145i) q^{45} +(-24.7153 - 14.2694i) q^{47} +(-48.7151 - 5.27601i) q^{49} +(18.8640 - 32.6735i) q^{51} +(-41.3353 - 71.5948i) q^{53} -13.5119i q^{55} -17.3872 q^{57} +(48.8859 - 28.2243i) q^{59} +(-33.6563 - 19.4315i) q^{61} +(-17.5940 - 11.4653i) q^{63} +(-6.71708 + 11.6343i) q^{65} +(-31.5515 - 54.6488i) q^{67} +9.20751i q^{69} +91.5126 q^{71} +(-93.7022 + 54.0990i) q^{73} +(36.2092 + 20.9054i) q^{75} +(90.9215 - 46.1458i) q^{77} +(20.1148 - 34.8399i) q^{79} +(-4.50000 - 7.79423i) q^{81} +11.9047i q^{83} +20.2060 q^{85} +(12.8939 - 7.44427i) q^{87} +(-65.5180 - 37.8268i) q^{89} +(-101.228 - 5.46567i) q^{91} +(39.7627 - 68.8710i) q^{93} +(-4.65604 - 8.06451i) q^{95} -153.192i q^{97} +43.6978 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{3} - 12 q^{7} + 24 q^{9} - 12 q^{11} + 48 q^{17} + 36 q^{19} + 24 q^{21} + 48 q^{23} + 20 q^{25} + 64 q^{29} - 60 q^{31} + 36 q^{33} - 36 q^{37} + 12 q^{39} + 72 q^{43} - 72 q^{47} - 40 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 + 36 * q^19 + 24 * q^21 + 48 * q^23 + 20 * q^25 + 64 * q^29 - 60 * q^31 + 36 * q^33 - 36 * q^37 + 12 * q^39 + 72 * q^43 - 72 * q^47 - 40 * q^49 - 48 * q^51 + 56 * q^53 - 72 * q^57 - 36 * q^59 + 72 * q^61 - 36 * q^63 + 120 * q^65 + 12 * q^67 + 240 * q^71 + 156 * q^73 - 60 * q^75 + 224 * q^77 + 84 * q^79 - 72 * q^81 + 800 * q^85 - 96 * q^87 + 192 * q^89 + 300 * 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
$5$	−0.803356	−	0.463818i	−0.160671	−	0.0927635i	0.417509	−	0.908673i	$-0.362903\pi$
$5$	−0.803356	−	0.463818i	−0.160671	−	0.0927635i	−0.578180	+	0.815909i	$0.696237\pi$
$6$		0			0
$7$	0.377407	−	6.98982i	0.0539153	−	0.998546i
$7$	0.377407	−	6.98982i	0.0539153	−	0.998546i
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	7.28297	+	12.6145i	0.662088	+	1.14677i	0.980066	+	0.198672i	$0.0636627\pi$
$11$	7.28297	+	12.6145i	0.662088	+	1.14677i	−0.317978	+	0.948098i	$0.603004\pi$
$12$		0			0
$13$		−	14.4822i		−	1.11401i	−0.830508	−	0.557006i	$-0.811950\pi$
$13$		−	14.4822i		−	1.11401i	0.830508	−	0.557006i	$-0.188050\pi$
$14$		0			0
$15$	1.60671			0.107114
$16$		0			0
$17$	−18.8640	+	10.8912i	−1.10965	+	0.640656i	−0.938738	−	0.344631i	$-0.888004\pi$
$17$	−18.8640	+	10.8912i	−1.10965	+	0.640656i	−0.170910	+	0.985287i	$0.554671\pi$
$18$		0			0
$19$	8.69362	+	5.01926i	0.457559	+	0.264172i	0.711017	−	0.703175i	$-0.248235\pi$
$19$	8.69362	+	5.01926i	0.457559	+	0.264172i	−0.253458	+	0.967346i	$0.581568\pi$
$20$		0			0
$21$	5.48725	+	10.8116i	0.261298	+	0.514837i
$22$		0			0
$23$	2.65798	−	4.60375i	0.115564	−	0.200163i	−0.802441	−	0.596732i	$-0.796466\pi$
$23$	2.65798	−	4.60375i	0.115564	−	0.200163i	0.918005	+	0.396568i	$0.129799\pi$
$24$		0			0
$25$	−12.0697	−	20.9054i	−0.482790	−	0.836217i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−8.59590			−0.296410			−0.148205	−	0.988957i	$-0.547350\pi$
$29$	−8.59590			−0.296410			−0.148205	+	0.988957i	$0.547350\pi$
$30$		0			0
$31$	−39.7627	+	22.9570i	−1.28267	+	0.740549i	−0.977335	−	0.211697i	$-0.932101\pi$
$31$	−39.7627	+	22.9570i	−1.28267	+	0.740549i	−0.305332	+	0.952246i	$0.598768\pi$
$32$		0			0
$33$	−21.8489	−	12.6145i	−0.662088	−	0.382257i
$34$		0			0
$35$	−3.54519	+	5.44026i	−0.101291	+	0.155436i
$36$		0			0
$37$	18.8742	−	32.6910i	0.510113	−	0.883541i	−0.489819	−	0.871824i	$-0.662937\pi$
$37$	18.8742	−	32.6910i	0.510113	−	0.883541i	0.999931	−	0.0117167i	$-0.00372963\pi$
$38$		0			0
$39$	12.5419	+	21.7232i	0.321588	+	0.557006i
$40$		0			0
$41$		−	41.3390i		−	1.00827i	−0.863625	−	0.504134i	$-0.831812\pi$
$41$		−	41.3390i		−	1.00827i	0.863625	−	0.504134i	$-0.168188\pi$
$42$		0			0
$43$	−14.8107			−0.344435			−0.172217	−	0.985059i	$-0.555093\pi$
$43$	−14.8107			−0.344435			−0.172217	+	0.985059i	$0.555093\pi$
$44$		0			0
$45$	−2.41007	+	1.39145i	−0.0535570	+	0.0309212i
$46$		0			0
$47$	−24.7153	−	14.2694i	−0.525857	−	0.303604i	0.213471	−	0.976949i	$-0.431523\pi$
$47$	−24.7153	−	14.2694i	−0.525857	−	0.303604i	−0.739328	+	0.673346i	$0.764857\pi$
$48$		0			0
$49$	−48.7151	−	5.27601i	−0.994186	−	0.107674i
$50$		0			0
$51$	18.8640	−	32.6735i	0.369883	−	0.640656i
$52$		0			0
$53$	−41.3353	−	71.5948i	−0.779911	−	1.35084i	−0.931993	−	0.362477i	$-0.881931\pi$
$53$	−41.3353	−	71.5948i	−0.779911	−	1.35084i	0.152082	−	0.988368i	$-0.451402\pi$
$54$		0			0
$55$		−	13.5119i		−	0.245670i
$56$		0			0
$57$	−17.3872			−0.305039
$58$		0			0
$59$	48.8859	−	28.2243i	0.828574	−	0.478378i	−0.0247901	−	0.999693i	$-0.507892\pi$
$59$	48.8859	−	28.2243i	0.828574	−	0.478378i	0.853364	+	0.521315i	$0.174558\pi$
$60$		0			0
$61$	−33.6563	−	19.4315i	−0.551743	−	0.318549i	0.198082	−	0.980185i	$-0.436529\pi$
$61$	−33.6563	−	19.4315i	−0.551743	−	0.318549i	−0.749825	+	0.661637i	$0.769862\pi$
$62$		0			0
$63$	−17.5940	−	11.4653i	−0.279269	−	0.181988i
$64$		0			0
$65$	−6.71708	+	11.6343i	−0.103340	+	0.178990i
$66$		0			0
$67$	−31.5515	−	54.6488i	−0.470918	−	0.815654i	0.528529	−	0.848915i	$-0.322744\pi$
$67$	−31.5515	−	54.6488i	−0.470918	−	0.815654i	−0.999447	+	0.0332615i	$0.989411\pi$
$68$		0			0
$69$			9.20751i			0.133442i
$70$		0			0
$71$	91.5126			1.28891			0.644455	−	0.764642i	$-0.277084\pi$
$71$	91.5126			1.28891			0.644455	+	0.764642i	$0.277084\pi$
$72$		0			0
$73$	−93.7022	+	54.0990i	−1.28359	+	0.741082i	−0.977503	−	0.210921i	$-0.932354\pi$
$73$	−93.7022	+	54.0990i	−1.28359	+	0.741082i	−0.306088	+	0.952003i	$0.599020\pi$
$74$		0			0
$75$	36.2092	+	20.9054i	0.482790	+	0.278739i
$76$		0			0
$77$	90.9215	−	46.1458i	1.18080	−	0.599296i
$78$		0			0
$79$	20.1148	−	34.8399i	0.254618	−	0.441011i	−0.710174	−	0.704026i	$-0.751384\pi$
$79$	20.1148	−	34.8399i	0.254618	−	0.441011i	0.964792	+	0.263015i	$0.0847169\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			11.9047i			0.143430i	0.997425	+	0.0717152i	$0.0228473\pi$
$83$			11.9047i			0.143430i	−0.997425	+	0.0717152i	$0.977153\pi$
$84$		0			0
$85$	20.2060			0.237718
$86$		0			0
$87$	12.8939	−	7.44427i	0.148205	−	0.0855663i
$88$		0			0
$89$	−65.5180	−	37.8268i	−0.736157	−	0.425021i	0.0845132	−	0.996422i	$-0.473066\pi$
$89$	−65.5180	−	37.8268i	−0.736157	−	0.425021i	−0.820670	+	0.571402i	$0.806400\pi$
$90$		0			0
$91$	−101.228	−	5.46567i	−1.11239	−	0.0600623i
$92$		0			0
$93$	39.7627	−	68.8710i	0.427556	−	0.740549i
$94$		0			0
$95$	−4.65604	−	8.06451i	−0.0490110	−	0.0848895i
$96$		0			0
$97$		−	153.192i		−	1.57930i	−0.613555	−	0.789652i	$-0.710261\pi$
$97$		−	153.192i		−	1.57930i	0.613555	−	0.789652i	$-0.289739\pi$
$98$		0			0
$99$	43.6978			0.441392
$100$		0			0
$101$	19.9204	−	11.5011i	0.197232	−	0.113872i	−0.398132	−	0.917328i	$-0.630341\pi$
$101$	19.9204	−	11.5011i	0.197232	−	0.113872i	0.595364	+	0.803456i	$0.297008\pi$
$102$		0			0
$103$	−154.703	−	89.3180i	−1.50197	−	0.867165i	−0.999997	−	0.00228358i	$-0.999273\pi$
$103$	−154.703	−	89.3180i	−1.50197	−	0.867165i	−0.501976	−	0.864881i	$-0.667394\pi$
$104$		0			0
$105$	0.606384	−	11.2306i	0.00577509	−	0.106958i
$106$		0			0
$107$	−60.6271	+	105.009i	−0.566609	+	0.981395i	0.430289	+	0.902691i	$0.358411\pi$
$107$	−60.6271	+	105.009i	−0.566609	+	0.981395i	−0.996898	+	0.0787039i	$0.974922\pi$
$108$		0			0
$109$	89.1390	+	154.393i	0.817789	+	1.41645i	0.907308	+	0.420467i	$0.138134\pi$
$109$	89.1390	+	154.393i	0.817789	+	1.41645i	−0.0895187	+	0.995985i	$0.528533\pi$
$110$		0			0
$111$			65.3820i			0.589027i
$112$		0			0
$113$	−173.570			−1.53602			−0.768011	−	0.640437i	$-0.778753\pi$
$113$	−173.570			−1.53602			−0.768011	+	0.640437i	$0.778753\pi$
$114$		0			0
$115$	−4.27060	+	2.46563i	−0.0371357	+	0.0214403i
$116$		0			0
$117$	−37.6257	−	21.7232i	−0.321588	−	0.185669i
$118$		0			0
$119$	69.0077	+	135.967i	0.579897	+	1.14258i
$120$		0			0
$121$	−45.5832	+	78.9524i	−0.376720	+	0.652499i
$122$		0			0
$123$	35.8006	+	62.0085i	0.291062	+	0.504134i
$124$		0			0
$125$			45.5835i			0.364668i
$126$		0			0
$127$	−81.9650			−0.645394			−0.322697	−	0.946502i	$-0.604589\pi$
$127$	−81.9650			−0.645394			−0.322697	+	0.946502i	$0.604589\pi$
$128$		0			0
$129$	22.2160	−	12.8264i	0.172217	−	0.0994298i
$130$		0			0
$131$	−137.288	−	79.2635i	−1.04800	−	0.605065i	−0.125913	−	0.992041i	$-0.540186\pi$
$131$	−137.288	−	79.2635i	−1.04800	−	0.605065i	−0.922089	+	0.386977i	$0.873519\pi$
$132$		0			0
$133$	38.3648	−	58.8725i	0.288457	−	0.442651i
$134$		0			0
$135$	2.41007	−	4.17436i	0.0178523	−	0.0309212i
$136$		0			0
$137$	82.2387	+	142.442i	0.600282	+	1.03972i	0.992778	+	0.119966i	$0.0382784\pi$
$137$	82.2387	+	142.442i	0.600282	+	1.03972i	−0.392496	+	0.919754i	$0.628388\pi$
$138$		0			0
$139$			72.2545i			0.519817i	0.965633	+	0.259908i	$0.0836924\pi$
$139$			72.2545i			0.519817i	−0.965633	+	0.259908i	$0.916308\pi$
$140$		0			0
$141$	49.4306			0.350571
$142$		0			0
$143$	182.685	−	105.473i	1.27752	−	0.737574i
$144$		0			0
$145$	6.90556	+	3.98693i	0.0476246	+	0.0274961i
$146$		0			0
$147$	77.6419	−	34.2745i	0.528176	−	0.233160i
$148$		0			0
$149$	1.18929	−	2.05991i	0.00798182	−	0.0138249i	−0.862007	−	0.506897i	$-0.830793\pi$
$149$	1.18929	−	2.05991i	0.00798182	−	0.0138249i	0.869989	+	0.493072i	$0.164126\pi$
$150$		0			0
$151$	43.6360	+	75.5798i	0.288980	+	0.500529i	0.973567	−	0.228403i	$-0.0733505\pi$
$151$	43.6360	+	75.5798i	0.288980	+	0.500529i	−0.684586	+	0.728932i	$0.740017\pi$
$152$		0			0
$153$			65.3469i			0.427104i
$154$		0			0
$155$	42.5914			0.274784
$156$		0			0
$157$	121.900	−	70.3789i	0.776432	−	0.448273i	−0.0587326	−	0.998274i	$-0.518706\pi$
$157$	121.900	−	70.3789i	0.776432	−	0.448273i	0.835164	+	0.550001i	$0.185373\pi$
$158$		0			0
$159$	124.006	+	71.5948i	0.779911	+	0.450282i
$160$		0			0
$161$	−31.1763	−	20.3163i	−0.193641	−	0.126188i
$162$		0			0
$163$	98.9970	−	171.468i	0.607343	−	1.05195i	−0.384333	−	0.923194i	$-0.625569\pi$
$163$	98.9970	−	171.468i	0.607343	−	1.05195i	0.991676	−	0.128755i	$-0.0410981\pi$
$164$		0			0
$165$	11.7016	+	20.2678i	0.0709189	+	0.122835i
$166$		0			0
$167$		−	5.76908i		−	0.0345454i	−0.999851	−	0.0172727i	$-0.994502\pi$
$167$		−	5.76908i		−	0.0345454i	0.999851	−	0.0172727i	$-0.00549835\pi$
$168$		0			0
$169$	−40.7328			−0.241023
$170$		0			0
$171$	26.0809	−	15.0578i	0.152520	−	0.0880573i
$172$		0			0
$173$	151.729	+	87.6005i	0.877044	+	0.506362i	0.869683	−	0.493611i	$-0.164323\pi$
$173$	151.729	+	87.6005i	0.877044	+	0.506362i	0.00736129	+	0.999973i	$0.497657\pi$
$174$		0			0
$175$	−150.680	+	76.4755i	−0.861030	+	0.437003i
$176$		0			0
$177$	−48.8859	+	84.6728i	−0.276191	+	0.478378i
$178$		0			0
$179$	160.382	+	277.791i	0.895991	+	1.55190i	0.832573	+	0.553915i	$0.186867\pi$
$179$	160.382	+	277.791i	0.895991	+	1.55190i	0.0634182	+	0.997987i	$0.479800\pi$
$180$		0			0
$181$		−	33.4249i		−	0.184668i	−0.995728	−	0.0923338i	$-0.970567\pi$
$181$		−	33.4249i		−	0.184668i	0.995728	−	0.0923338i	$-0.0294327\pi$
$182$		0			0
$183$	67.3126			0.367828
$184$		0			0
$185$	−30.3253	+	17.5083i	−0.163921	+	0.0946397i
$186$		0			0
$187$	−274.772	−	158.640i	−1.46937	−	0.848341i
$188$		0			0
$189$	36.3202	+	1.96106i	0.192170	+	0.0103760i
$190$		0			0
$191$	135.932	−	235.441i	0.711686	−	1.23268i	−0.252537	−	0.967587i	$-0.581265\pi$
$191$	135.932	−	235.441i	0.711686	−	1.23268i	0.964224	−	0.265090i	$-0.0854016\pi$
$192$		0			0
$193$	43.8766	+	75.9966i	0.227340	+	0.393765i	0.957019	−	0.290025i	$-0.0936638\pi$
$193$	43.8766	+	75.9966i	0.227340	+	0.393765i	−0.729679	+	0.683790i	$0.760330\pi$
$194$		0			0
$195$		−	23.2686i		−	0.119326i
$196$		0			0
$197$	228.881			1.16183			0.580915	−	0.813964i	$-0.302695\pi$
$197$	228.881			1.16183			0.580915	+	0.813964i	$0.302695\pi$
$198$		0			0
$199$	−283.498	+	163.678i	−1.42461	+	0.822501i	−0.996689	−	0.0813136i	$-0.974088\pi$
$199$	−283.498	+	163.678i	−1.42461	+	0.822501i	−0.427925	+	0.903814i	$0.640755\pi$
$200$		0			0
$201$	94.6545	+	54.6488i	0.470918	+	0.271885i
$202$		0			0
$203$	−3.24415	+	60.0838i	−0.0159811	+	0.295979i
$204$		0			0
$205$	−19.1738	+	33.2099i	−0.0935306	+	0.162000i
$206$		0			0
$207$	−7.97394	−	13.8113i	−0.0385214	−	0.0667211i
$208$		0			0
$209$			146.220i			0.699620i
$210$		0			0
$211$	−151.304			−0.717079			−0.358539	−	0.933515i	$-0.616725\pi$
$211$	−151.304			−0.717079			−0.358539	+	0.933515i	$0.616725\pi$
$212$		0			0
$213$	−137.269	+	79.2522i	−0.644455	+	0.372076i
$214$		0			0
$215$	11.8983	+	6.86946i	0.0553407	+	0.0319510i
$216$		0			0
$217$	145.459	+	286.598i	0.670316	+	1.32073i
$218$		0			0
$219$	93.7022	−	162.297i	0.427864	−	0.741082i
$220$		0			0
$221$	157.727	+	273.192i	0.713698	+	1.23616i
$222$		0			0
$223$		−	86.0826i		−	0.386021i	−0.981197	−	0.193010i	$-0.938175\pi$
$223$		−	86.0826i		−	0.386021i	0.981197	−	0.193010i	$-0.0618251\pi$
$224$		0			0
$225$	−72.4185			−0.321860
$226$		0			0
$227$	−216.852	+	125.199i	−0.955294	+	0.551539i	−0.894721	−	0.446625i	$-0.852626\pi$
$227$	−216.852	+	125.199i	−0.955294	+	0.551539i	−0.0605724	+	0.998164i	$0.519293\pi$
$228$		0			0
$229$	111.215	+	64.2100i	0.485655	+	0.280393i	0.722770	−	0.691088i	$-0.242869\pi$
$229$	111.215	+	64.2100i	0.485655	+	0.280393i	−0.237115	+	0.971482i	$0.576202\pi$
$230$		0			0
$231$	−96.4188	+	147.959i	−0.417397	+	0.640515i
$232$		0			0
$233$	96.6534	−	167.409i	0.414822	−	0.718492i	−0.580588	−	0.814197i	$-0.697177\pi$
$233$	96.6534	−	167.409i	0.414822	−	0.718492i	0.995410	+	0.0957053i	$0.0305106\pi$
$234$		0			0
$235$	13.2368	+	22.9268i	0.0563267	+	0.0975607i
$236$		0			0
$237$			69.6798i			0.294008i
$238$		0			0
$239$	308.972			1.29277			0.646386	−	0.763011i	$-0.276280\pi$
$239$	308.972			1.29277			0.646386	+	0.763011i	$0.276280\pi$
$240$		0			0
$241$	32.5677	−	18.8029i	0.135136	−	0.0780205i	−0.430908	−	0.902396i	$-0.641807\pi$
$241$	32.5677	−	18.8029i	0.135136	−	0.0780205i	0.566044	+	0.824375i	$0.308473\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	36.6885	+	26.8334i	0.149749	+	0.109524i
$246$		0			0
$247$	72.6898	−	125.902i	0.294291	−	0.509726i
$248$		0			0
$249$	−10.3098	−	17.8571i	−0.0414048	−	0.0717152i
$250$		0			0
$251$			165.618i			0.659833i	0.944010	+	0.329916i	$0.107021\pi$
$251$			165.618i			0.659833i	−0.944010	+	0.329916i	$0.892979\pi$
$252$		0			0
$253$	77.4319			0.306055
$254$		0			0
$255$	−30.3090	+	17.4989i	−0.118859	+	0.0686233i
$256$		0			0
$257$	−100.539	−	58.0462i	−0.391202	−	0.225861i	0.291479	−	0.956577i	$-0.405853\pi$
$257$	−100.539	−	58.0462i	−0.391202	−	0.225861i	−0.682681	+	0.730717i	$0.739186\pi$
$258$		0			0
$259$	−221.381	−	144.265i	−0.854753	−	0.557007i
$260$		0			0
$261$	−12.8939	+	22.3328i	−0.0494017	+	0.0855663i
$262$		0			0
$263$	−7.36005	−	12.7480i	−0.0279850	−	0.0484714i	0.851694	−	0.524040i	$-0.175576\pi$
$263$	−7.36005	−	12.7480i	−0.0279850	−	0.0484714i	−0.879679	+	0.475568i	$0.842242\pi$
$264$		0			0
$265$			76.6881i			0.289389i
$266$		0			0
$267$	131.036			0.490772
$268$		0			0
$269$	−141.670	+	81.7935i	−0.526656	+	0.304065i	−0.739654	−	0.672988i	$-0.765011\pi$
$269$	−141.670	+	81.7935i	−0.526656	+	0.304065i	0.212998	+	0.977053i	$0.431677\pi$
$270$		0			0
$271$	−234.623	−	135.460i	−0.865767	−	0.499851i	0.000171980	−	1.00000i	$-0.499945\pi$
$271$	−234.623	−	135.460i	−0.865767	−	0.499851i	−0.865939	+	0.500149i	$0.833279\pi$
$272$		0			0
$273$	156.575	−	79.4672i	0.573534	−	0.291089i
$274$		0			0
$275$	175.807	−	304.507i	0.639299	−	1.10730i
$276$		0			0
$277$	−101.203	−	175.289i	−0.365355	−	0.632813i	0.623478	−	0.781841i	$-0.285719\pi$
$277$	−101.203	−	175.289i	−0.365355	−	0.632813i	−0.988833	+	0.149028i	$0.952386\pi$
$278$		0			0
$279$			137.742i			0.493699i
$280$		0			0
$281$	334.869			1.19171			0.595853	−	0.803093i	$-0.296814\pi$
$281$	334.869			1.19171			0.595853	+	0.803093i	$0.296814\pi$
$282$		0			0
$283$	451.162	−	260.479i	1.59421	−	0.920420i	0.601641	−	0.798767i	$-0.294514\pi$
$283$	451.162	−	260.479i	1.59421	−	0.920420i	0.992573	−	0.121653i	$-0.0388195\pi$
$284$		0			0
$285$	13.9681	+	8.06451i	0.0490110	+	0.0282965i
$286$		0			0
$287$	−288.952	−	15.6016i	−1.00680	−	0.0543611i
$288$		0			0
$289$	92.7343	−	160.621i	0.320880	−	0.555780i
$290$		0			0
$291$	132.669	+	229.789i	0.455906	+	0.789652i
$292$		0			0
$293$		−	90.1677i		−	0.307740i	−0.988091	−	0.153870i	$-0.950826\pi$
$293$		−	90.1677i		−	0.307740i	0.988091	−	0.153870i	$-0.0491736\pi$
$294$		0			0
$295$	−52.3636			−0.177504
$296$		0			0
$297$	−65.5467	+	37.8434i	−0.220696	+	0.127419i
$298$		0			0
$299$	−66.6723	−	38.4933i	−0.222984	−	0.128740i
$300$		0			0
$301$	−5.58966	+	103.524i	−0.0185703	+	0.343934i
$302$		0			0
$303$	−19.9204	+	34.5032i	−0.0657440	+	0.113872i
$304$		0			0
$305$	18.0253	+	31.2208i	0.0590994	+	0.102363i
$306$		0			0
$307$			55.1367i			0.179598i	0.995960	+	0.0897992i	$0.0286225\pi$
$307$			55.1367i			0.179598i	−0.995960	+	0.0897992i	$0.971377\pi$
$308$		0			0
$309$	309.407			1.00132
$310$		0			0
$311$	283.214	−	163.513i	0.910654	−	0.525767i	0.0300128	−	0.999550i	$-0.490445\pi$
$311$	283.214	−	163.513i	0.910654	−	0.525767i	0.880642	+	0.473783i	$0.157112\pi$
$312$		0			0
$313$	489.375	+	282.541i	1.56350	+	0.902687i	0.996899	+	0.0786936i	$0.0250749\pi$
$313$	489.375	+	282.541i	1.56350	+	0.902687i	0.566600	+	0.823993i	$0.308258\pi$
$314$		0			0
$315$	8.81642	+	17.3711i	0.0279887	+	0.0551463i
$316$		0			0
$317$	−190.180	+	329.402i	−0.599938	+	1.03912i	0.392892	+	0.919585i	$0.371475\pi$
$317$	−190.180	+	329.402i	−0.599938	+	1.03912i	−0.992830	+	0.119538i	$0.961859\pi$
$318$		0			0
$319$	−62.6036	−	108.433i	−0.196250	−	0.339914i
$320$		0			0
$321$		−	210.018i		−	0.654263i
$322$		0			0
$323$	−218.662			−0.676973
$324$		0			0
$325$	−302.755	+	174.796i	−0.931555	+	0.537834i
$326$		0			0
$327$	−267.417	−	154.393i	−0.817789	−	0.472151i
$328$		0			0
$329$	−109.068	+	167.370i	−0.331514	+	0.508723i
$330$		0			0
$331$	−24.4903	+	42.4185i	−0.0739890	+	0.128153i	−0.900646	−	0.434553i	$-0.856906\pi$
$331$	−24.4903	+	42.4185i	−0.0739890	+	0.128153i	0.826657	+	0.562706i	$0.190240\pi$
$332$		0			0
$333$	−56.6225	−	98.0731i	−0.170038	−	0.294514i
$334$		0			0
$335$			58.5366i			0.174736i
$336$		0			0
$337$	−483.294			−1.43411			−0.717054	−	0.697018i	$-0.754510\pi$
$337$	−483.294			−1.43411			−0.717054	+	0.697018i	$0.754510\pi$
$338$		0			0
$339$	260.356	−	150.316i	0.768011	−	0.443411i
$340$		0			0
$341$	−579.181	−	334.390i	−1.69848	−	0.980616i
$342$		0			0
$343$	−55.2638	+	338.519i	−0.161119	+	0.986935i
$344$		0			0
$345$	4.27060	−	7.39690i	0.0123786	−	0.0214403i
$346$		0			0
$347$	238.871	+	413.738i	0.688390	+	1.19233i	0.972358	+	0.233493i	$0.0750157\pi$
$347$	238.871	+	413.738i	0.688390	+	1.19233i	−0.283968	+	0.958834i	$0.591651\pi$
$348$		0			0
$349$			231.968i			0.664664i	0.943162	+	0.332332i	$0.107835\pi$
$349$			231.968i			0.664664i	−0.943162	+	0.332332i	$0.892165\pi$
$350$		0			0
$351$	75.2515			0.214392
$352$		0			0
$353$	188.059	−	108.576i	0.532745	−	0.307581i	−0.209388	−	0.977833i	$-0.567147\pi$
$353$	188.059	−	108.576i	0.532745	−	0.307581i	0.742134	+	0.670252i	$0.233814\pi$
$354$		0			0
$355$	−73.5172	−	42.4452i	−0.207091	−	0.119564i
$356$		0			0
$357$	−221.262	−	144.187i	−0.619782	−	0.403886i
$358$		0			0
$359$	274.439	−	475.343i	0.764455	−	1.32407i	−0.176079	−	0.984376i	$-0.556342\pi$
$359$	274.439	−	475.343i	0.764455	−	1.32407i	0.940534	−	0.339699i	$-0.110325\pi$
$360$		0			0
$361$	−130.114	−	225.364i	−0.360427	−	0.624277i
$362$		0			0
$363$		−	157.905i		−	0.434999i
$364$		0			0
$365$	100.368			0.274981
$366$		0			0
$367$	−273.519	+	157.916i	−0.745282	+	0.430289i	−0.823987	−	0.566609i	$-0.808255\pi$
$367$	−273.519	+	157.916i	−0.745282	+	0.430289i	0.0787045	+	0.996898i	$0.474922\pi$
$368$		0			0
$369$	−107.402	−	62.0085i	−0.291062	−	0.168045i
$370$		0			0
$371$	−516.035	+	261.906i	−1.39093	+	0.705945i
$372$		0			0
$373$	69.2168	−	119.887i	0.185568	−	0.321413i	−0.758200	−	0.652022i	$-0.773921\pi$
$373$	69.2168	−	119.887i	0.185568	−	0.321413i	0.943768	+	0.330609i	$0.107254\pi$
$374$		0			0
$375$	−39.4765	−	68.3753i	−0.105271	−	0.182334i
$376$		0			0
$377$			124.487i			0.330205i
$378$		0			0
$379$	219.084			0.578058			0.289029	−	0.957320i	$-0.406668\pi$
$379$	219.084			0.578058			0.289029	+	0.957320i	$0.406668\pi$
$380$		0			0
$381$	122.948	−	70.9838i	0.322697	−	0.186309i
$382$		0			0
$383$	−16.8847	−	9.74836i	−0.0440853	−	0.0254526i	0.477795	−	0.878471i	$-0.341436\pi$
$383$	−16.8847	−	9.74836i	−0.0440853	−	0.0254526i	−0.521881	+	0.853019i	$0.674769\pi$
$384$		0			0
$385$	−94.4455	−	5.09947i	−0.245313	−	0.0132454i
$386$		0			0
$387$	−22.2160	+	38.4793i	−0.0574058	+	0.0994298i
$388$		0			0
$389$	−356.540	−	617.545i	−0.916555	−	1.58752i	−0.804608	−	0.593806i	$-0.797625\pi$
$389$	−356.540	−	617.545i	−0.916555	−	1.58752i	−0.111947	−	0.993714i	$-0.535709\pi$
$390$		0			0
$391$			115.794i			0.296148i
$392$		0			0
$393$	274.577			0.698668
$394$		0			0
$395$	−32.3187	+	18.6592i	−0.0818195	+	0.0472385i
$396$		0			0
$397$	−45.1763	−	26.0826i	−0.113794	−	0.0656992i	0.442023	−	0.897004i	$-0.354261\pi$
$397$	−45.1763	−	26.0826i	−0.113794	−	0.0656992i	−0.555817	+	0.831305i	$0.687594\pi$
$398$		0			0
$399$	−6.56207	+	121.534i	−0.0164463	+	0.304596i
$400$		0			0
$401$	155.741	−	269.752i	0.388382	−	0.672697i	−0.603850	−	0.797098i	$-0.706367\pi$
$401$	155.741	−	269.752i	0.388382	−	0.672697i	0.992232	+	0.124401i	$0.0397008\pi$
$402$		0			0
$403$	332.467	+	575.850i	0.824980	+	1.42891i
$404$		0			0
$405$			8.34872i			0.0206141i
$406$		0			0
$407$	549.840			1.35096
$408$		0			0
$409$	521.110	−	300.863i	1.27411	−	0.735607i	0.298350	−	0.954457i	$-0.403564\pi$
$409$	521.110	−	300.863i	1.27411	−	0.735607i	0.975759	+	0.218850i	$0.0702304\pi$
$410$		0			0
$411$	−246.716	−	142.442i	−0.600282	−	0.346573i
$412$		0			0
$413$	−178.833	−	352.355i	−0.433009	−	0.853161i
$414$		0			0
$415$	5.52162	−	9.56372i	0.0133051	−	0.0230451i
$416$		0			0
$417$	−62.5743	−	108.382i	−0.150058	−	0.259908i
$418$		0			0
$419$			308.844i			0.737099i	0.929608	+	0.368549i	$0.120145\pi$
$419$			308.844i			0.737099i	−0.929608	+	0.368549i	$0.879855\pi$
$420$		0			0
$421$	−782.558			−1.85881			−0.929404	−	0.369064i	$-0.879678\pi$
$421$	−782.558			−1.85881			−0.929404	+	0.369064i	$0.879678\pi$
$422$		0			0
$423$	−74.1458	+	42.8081i	−0.175286	+	0.101201i
$424$		0			0
$425$	455.368	+	262.907i	1.07145	+	0.618604i
$426$		0			0
$427$	−148.525	+	227.918i	−0.347833	+	0.533765i
$428$		0			0
$429$	−182.685	+	316.419i	−0.425838	+	0.737574i
$430$		0			0
$431$	67.0084	+	116.062i	0.155472	+	0.269285i	0.933231	−	0.359278i	$-0.116977\pi$
$431$	67.0084	+	116.062i	0.155472	+	0.269285i	−0.777759	+	0.628563i	$0.783644\pi$
$432$		0			0
$433$		−	700.146i		−	1.61697i	−0.588519	−	0.808483i	$-0.700289\pi$
$433$		−	700.146i		−	1.61697i	0.588519	−	0.808483i	$-0.299711\pi$
$434$		0			0
$435$	−13.8111			−0.0317497
$436$		0			0
$437$	46.2149	−	26.6822i	0.105755	−	0.0610576i
$438$		0			0
$439$	−401.282	−	231.680i	−0.914083	−	0.527746i	−0.0323403	−	0.999477i	$-0.510296\pi$
$439$	−401.282	−	231.680i	−0.914083	−	0.527746i	−0.881743	+	0.471731i	$0.843629\pi$
$440$		0			0
$441$	−86.7802	+	118.652i	−0.196780	+	0.269051i
$442$		0			0
$443$	−48.2414	+	83.5566i	−0.108897	+	0.188615i	−0.915324	−	0.402719i	$-0.868065\pi$
$443$	−48.2414	+	83.5566i	−0.108897	+	0.188615i	0.806427	+	0.591334i	$0.201399\pi$
$444$		0			0
$445$	35.0895	+	60.7768i	0.0788528	+	0.136577i
$446$		0			0
$447$			4.11982i			0.00921661i
$448$		0			0
$449$	−208.259			−0.463828			−0.231914	−	0.972736i	$-0.574499\pi$
$449$	−208.259			−0.463828			−0.231914	+	0.972736i	$0.574499\pi$
$450$		0			0
$451$	521.470	−	301.071i	1.15625	−	0.667563i
$452$		0			0
$453$	−130.908	−	75.5798i	−0.288980	−	0.166843i
$454$		0			0
$455$	78.7867	+	51.3420i	0.173158	+	0.112840i
$456$		0			0
$457$	77.9698	−	135.048i	0.170612	−	0.295509i	−0.768022	−	0.640424i	$-0.778759\pi$
$457$	77.9698	−	135.048i	0.170612	−	0.295509i	0.938634	+	0.344915i	$0.112092\pi$
$458$		0			0
$459$	−56.5921	−	98.0204i	−0.123294	−	0.213552i
$460$		0			0
$461$			125.104i			0.271375i	0.990752	+	0.135688i	$0.0433244\pi$
$461$			125.104i			0.271375i	−0.990752	+	0.135688i	$0.956676\pi$
$462$		0			0
$463$	725.921			1.56786			0.783932	−	0.620846i	$-0.213211\pi$
$463$	725.921			1.56786			0.783932	+	0.620846i	$0.213211\pi$
$464$		0			0
$465$	−63.8872	+	36.8853i	−0.137392	+	0.0793232i
$466$		0			0
$467$	−695.521	−	401.559i	−1.48934	−	0.859870i	−0.489413	−	0.872052i	$-0.662789\pi$
$467$	−695.521	−	401.559i	−1.48934	−	0.859870i	−0.999926	+	0.0121816i	$0.996122\pi$
$468$		0			0
$469$	−393.893	+	199.914i	−0.839857	+	0.426257i
$470$		0			0
$471$	−121.900	+	211.137i	−0.258811	+	0.448273i
$472$		0			0
$473$	−107.866	−	186.829i	−0.228046	−	0.394987i
$474$		0			0
$475$		−	242.325i		−	0.510158i
$476$		0			0
$477$	−248.012			−0.519940
$478$		0			0
$479$	−743.964	+	429.528i	−1.55316	+	0.896718i	−0.555279	+	0.831664i	$0.687389\pi$
$479$	−743.964	+	429.528i	−1.55316	+	0.896718i	−0.997882	+	0.0650537i	$0.979278\pi$
$480$		0			0
$481$	−473.436	−	273.339i	−0.984275	−	0.568272i
$482$		0			0
$483$	64.3588	+	3.47498i	0.133248	+	0.00719457i
$484$		0			0
$485$	−71.0534	+	123.068i	−0.146502	+	0.253749i
$486$		0			0
$487$	211.745	+	366.754i	0.434795	+	0.753087i	0.997279	−	0.0737210i	$-0.0234874\pi$
$487$	211.745	+	366.754i	0.434795	+	0.753087i	−0.562484	+	0.826808i	$0.690154\pi$
$488$		0			0
$489$			342.936i			0.701300i
$490$		0			0
$491$	−523.819			−1.06684			−0.533421	−	0.845850i	$-0.679094\pi$
$491$	−523.819			−1.06684			−0.533421	+	0.845850i	$0.679094\pi$
$492$		0			0
$493$	162.153	−	93.6193i	0.328911	−	0.189897i
$494$		0			0
$495$	−35.1049	−	20.2678i	−0.0709189	−	0.0409451i
$496$		0			0
$497$	34.5375	−	639.657i	0.0694920	−	1.28704i
$498$		0			0
$499$	281.331	−	487.279i	0.563789	−	0.976511i	−0.433372	−	0.901215i	$-0.642677\pi$
$499$	281.331	−	487.279i	0.563789	−	0.976511i	0.997161	−	0.0752960i	$-0.0239902\pi$
$500$		0			0
$501$	4.99617	+	8.65362i	0.00997240	+	0.0172727i
$502$		0			0
$503$		−	265.960i		−	0.528748i	−0.964420	−	0.264374i	$-0.914835\pi$
$503$		−	265.960i		−	0.528748i	0.964420	−	0.264374i	$-0.0851653\pi$
$504$		0			0
$505$	−21.3376			−0.0422526
$506$		0			0
$507$	61.0992	−	35.2757i	0.120511	−	0.0695772i
$508$		0			0
$509$	−328.983	−	189.939i	−0.646333	−	0.373160i	0.140717	−	0.990050i	$-0.455059\pi$
$509$	−328.983	−	189.939i	−0.646333	−	0.373160i	−0.787050	+	0.616890i	$0.788393\pi$
$510$		0			0
$511$	342.778	+	675.378i	0.670799	+	1.32168i
$512$		0			0
$513$	−26.0809	+	45.1734i	−0.0508399	+	0.0880573i
$514$		0			0
$515$	82.8545	+	143.508i	0.160883	+	0.278657i
$516$		0			0
$517$		−	415.693i		−	0.804049i
$518$		0			0
$519$	−303.457			−0.584696
$520$		0			0
$521$	153.871	−	88.8376i	0.295338	−	0.170514i	−0.345009	−	0.938600i	$-0.612124\pi$
$521$	153.871	−	88.8376i	0.295338	−	0.170514i	0.640347	+	0.768086i	$0.278791\pi$
$522$		0			0
$523$	−503.405	−	290.641i	−0.962534	−	0.555719i	−0.0655817	−	0.997847i	$-0.520890\pi$
$523$	−503.405	−	290.641i	−0.962534	−	0.555719i	−0.896952	+	0.442128i	$0.854224\pi$
$524$		0			0
$525$	159.791	−	245.206i	0.304363	−	0.467059i
$526$		0			0
$527$	500.056	−	866.123i	0.948874	−	1.64350i
$528$		0			0
$529$	250.370	+	433.654i	0.473290	+	0.819762i
$530$		0			0
$531$		−	169.346i		−	0.318918i
$532$		0			0
$533$	−598.678			−1.12322
$534$		0			0
$535$	97.4103	−	56.2398i	0.182075	−	0.105121i
$536$		0			0
$537$	−481.147	−	277.791i	−0.895991	−	0.517301i
$538$		0			0
$539$	−288.236	−	652.940i	−0.534762	−	1.21139i
$540$		0			0
$541$	277.646	−	480.897i	0.513209	−	0.888905i	−0.486673	−	0.873584i	$-0.661790\pi$
$541$	277.646	−	480.897i	0.513209	−	0.888905i	0.999883	−	0.0153206i	$-0.00487690\pi$
$542$		0			0
$543$	28.9468	+	50.1373i	0.0533090	+	0.0923338i
$544$		0			0
$545$		−	165.377i		−	0.303444i
$546$		0			0
$547$	598.458			1.09407			0.547036	−	0.837109i	$-0.315756\pi$
$547$	598.458			1.09407			0.547036	+	0.837109i	$0.315756\pi$
$548$		0			0
$549$	−100.969	+	58.2944i	−0.183914	+	0.106183i
$550$		0			0
$551$	−74.7295	−	43.1451i	−0.135625	−	0.0783033i
$552$		0			0
$553$	−235.933	−	153.748i	−0.426642	−	0.278025i
$554$		0			0
$555$	30.3253	−	52.5250i	0.0546402	−	0.0946397i
$556$		0			0
$557$	122.186	+	211.632i	0.219364	+	0.379950i	0.954614	−	0.297846i	$-0.0962683\pi$
$557$	122.186	+	211.632i	0.219364	+	0.379950i	−0.735249	+	0.677797i	$0.762935\pi$
$558$		0			0
$559$			214.491i			0.383705i
$560$		0			0
$561$	549.544			0.979580
$562$		0			0
$563$	583.333	−	336.787i	1.03611	−	0.598201i	0.117384	−	0.993087i	$-0.462549\pi$
$563$	583.333	−	336.787i	1.03611	−	0.598201i	0.918730	+	0.394886i	$0.129216\pi$
$564$		0			0
$565$	139.439	+	80.5050i	0.246794	+	0.142487i
$566$		0			0
$567$	−56.1786	+	28.5126i	−0.0990804	+	0.0502867i
$568$		0			0
$569$	−413.759	+	716.651i	−0.727168	+	1.25949i	0.230907	+	0.972976i	$0.425831\pi$
$569$	−413.759	+	716.651i	−0.727168	+	1.25949i	−0.958075	+	0.286516i	$0.907503\pi$
$570$		0			0
$571$	164.966	+	285.729i	0.288907	+	0.500401i	0.973549	−	0.228478i	$-0.0733749\pi$
$571$	164.966	+	285.729i	0.288907	+	0.500401i	−0.684642	+	0.728879i	$0.740042\pi$
$572$		0			0
$573$			470.883i			0.821785i
$574$		0			0
$575$	−128.325			−0.223173
$576$		0			0
$577$	459.266	−	265.157i	0.795955	−	0.459545i	−0.0460996	−	0.998937i	$-0.514679\pi$
$577$	459.266	−	265.157i	0.795955	−	0.459545i	0.842055	+	0.539392i	$0.181346\pi$
$578$		0			0
$579$	−131.630	−	75.9966i	−0.227340	−	0.131255i
$580$		0			0
$581$	83.2118	+	4.49292i	0.143222	+	0.00773309i
$582$		0			0
$583$	602.087	−	1042.84i	1.03274	−	1.78876i
$584$		0			0
$585$	20.1512	+	34.9030i	0.0344466	+	0.0596632i
$586$		0			0
$587$			647.575i			1.10319i	0.834111	+	0.551597i	$0.185981\pi$
$587$			647.575i			1.10319i	−0.834111	+	0.551597i	$0.814019\pi$
$588$		0			0
$589$	−460.909			−0.782528
$590$		0			0
$591$	−343.321	+	198.216i	−0.580915	+	0.335391i
$592$		0			0
$593$	199.413	+	115.131i	0.336278	+	0.194150i	0.658625	−	0.752471i	$-0.271138\pi$
$593$	199.413	+	115.131i	0.336278	+	0.194150i	−0.322347	+	0.946622i	$0.604472\pi$
$594$		0			0
$595$	7.62590	−	141.236i	0.0128166	−	0.237372i
$596$		0			0
$597$	283.498	−	491.033i	0.474871	−	0.822501i
$598$		0			0
$599$	−178.277	−	308.785i	−0.297624	−	0.515500i	0.677968	−	0.735092i	$-0.262861\pi$
$599$	−178.277	−	308.785i	−0.297624	−	0.515500i	−0.975592	+	0.219591i	$0.929528\pi$
$600$		0			0
$601$		−	124.839i		−	0.207720i	−0.994592	−	0.103860i	$-0.966881\pi$
$601$		−	124.839i		−	0.207720i	0.994592	−	0.103860i	$-0.0331193\pi$
$602$		0			0
$603$	−189.309			−0.313945
$604$		0			0
$605$	73.2390	−	42.2845i	0.121056	−	0.0698918i
$606$		0			0
$607$	533.565	+	308.054i	0.879020	+	0.507502i	0.870335	−	0.492460i	$-0.163902\pi$
$607$	533.565	+	308.054i	0.879020	+	0.507502i	0.00868458	+	0.999962i	$0.497236\pi$
$608$		0			0
$609$	−47.1679	−	92.9352i	−0.0774513	−	0.152603i
$610$		0			0
$611$	−206.651	+	357.931i	−0.338218	+	0.585811i
$612$		0			0
$613$	−531.540	−	920.654i	−0.867112	−	1.50188i	−0.864934	−	0.501885i	$-0.832640\pi$
$613$	−531.540	−	920.654i	−0.867112	−	1.50188i	−0.00217812	−	0.999998i	$-0.500693\pi$
$614$		0			0
$615$		−	66.4199i		−	0.108000i
$616$		0			0
$617$	575.402			0.932580			0.466290	−	0.884632i	$-0.345590\pi$
$617$	575.402			0.932580			0.466290	+	0.884632i	$0.345590\pi$
$618$		0			0
$619$	−9.06057	+	5.23112i	−0.0146374	+	0.00845093i	−0.507301	−	0.861769i	$-0.669357\pi$
$619$	−9.06057	+	5.23112i	−0.0146374	+	0.00845093i	0.492663	+	0.870220i	$0.336023\pi$
$620$		0			0
$621$	23.9218	+	13.8113i	0.0385214	+	0.0222404i
$622$		0			0
$623$	−289.130	+	443.683i	−0.464093	+	0.712171i
$624$		0			0
$625$	−280.601	+	486.016i	−0.448962	+	0.777625i
$626$		0			0
$627$	−126.631	−	219.331i	−0.201963	−	0.349810i
$628$		0			0
$629$			822.246i			1.30723i
$630$		0			0
$631$	432.829			0.685942			0.342971	−	0.939346i	$-0.388567\pi$
$631$	432.829			0.685942			0.342971	+	0.939346i	$0.388567\pi$
$632$		0			0
$633$	226.955	−	131.033i	0.358539	−	0.207003i
$634$		0			0
$635$	65.8470	+	38.0168i	0.103696	+	0.0598690i
$636$		0			0
$637$	−76.4080	+	705.500i	−0.119950	+	1.10754i
$638$		0			0
$639$	137.269	−	237.757i	0.214818	−	0.372076i
$640$		0			0
$641$	−514.252	−	890.710i	−0.802264	−	1.38956i	−0.918122	−	0.396297i	$-0.870295\pi$
$641$	−514.252	−	890.710i	−0.802264	−	1.38956i	0.115858	−	0.993266i	$-0.463038\pi$
$642$		0			0
$643$			1139.29i			1.77183i	0.463846	+	0.885916i	$0.346469\pi$
$643$			1139.29i			1.77183i	−0.463846	+	0.885916i	$0.653531\pi$
$644$		0			0
$645$	−23.7965			−0.0368938
$646$		0			0
$647$	−323.493	+	186.769i	−0.499989	+	0.288669i	−0.728709	−	0.684823i	$-0.759879\pi$
$647$	−323.493	+	186.769i	−0.499989	+	0.288669i	0.228720	+	0.973492i	$0.426546\pi$
$648$		0			0
$649$	712.068	+	411.113i	1.09718	+	0.633456i
$650$		0			0
$651$	−466.389	−	303.926i	−0.716420	−	0.466861i
$652$		0			0
$653$	−140.836	+	243.935i	−0.215675	+	0.373560i	−0.953481	−	0.301453i	$-0.902528\pi$
$653$	−140.836	+	243.935i	−0.215675	+	0.373560i	0.737806	+	0.675013i	$0.235862\pi$
$654$		0			0
$655$	73.5276	+	127.353i	0.112256	+	0.194433i
$656$		0			0
$657$			324.594i			0.494055i
$658$		0			0
$659$	−827.336			−1.25544			−0.627721	−	0.778438i	$-0.716012\pi$
$659$	−827.336			−1.25544			−0.627721	+	0.778438i	$0.716012\pi$
$660$		0			0
$661$	377.510	−	217.955i	0.571119	−	0.329736i	−0.186477	−	0.982459i	$-0.559707\pi$
$661$	377.510	−	217.955i	0.571119	−	0.329736i	0.757596	+	0.652724i	$0.226374\pi$
$662$		0			0
$663$	−473.182	−	273.192i	−0.713698	−	0.412054i
$664$		0			0
$665$	−58.1267	+	29.5013i	−0.0874085	+	0.0443629i
$666$		0			0
$667$	−22.8477	+	39.5734i	−0.0342545	+	0.0593305i
$668$		0			0
$669$	74.5497	+	129.124i	0.111435	+	0.193010i
$670$		0			0
$671$		−	566.075i		−	0.843629i
$672$		0			0
$673$	283.719			0.421574			0.210787	−	0.977532i	$-0.432397\pi$
$673$	283.719			0.421574			0.210787	+	0.977532i	$0.432397\pi$
$674$		0			0
$675$	108.628	−	62.7162i	0.160930	−	0.0929130i
$676$		0			0
$677$	17.7669	+	10.2577i	0.0262436	+	0.0151517i	0.513064	−	0.858350i	$-0.328510\pi$
$677$	17.7669	+	10.2577i	0.0262436	+	0.0151517i	−0.486821	+	0.873502i	$0.661844\pi$
$678$		0			0
$679$	−1070.79	−	57.8159i	−1.57701	−	0.0851486i
$680$		0			0
$681$	216.852	−	375.598i	0.318431	−	0.551539i
$682$		0			0
$683$	293.050	+	507.577i	0.429063	+	0.743159i	0.996790	−	0.0800579i	$-0.0255105\pi$
$683$	293.050	+	507.577i	0.429063	+	0.743159i	−0.567727	+	0.823217i	$0.692177\pi$
$684$		0			0
$685$		−	152.575i		−	0.222737i
$686$		0			0
$687$	−222.430			−0.323770
$688$		0			0
$689$	−1036.85	+	598.624i	−1.50486	+	0.868830i
$690$		0			0
$691$	418.908	+	241.857i	0.606235	+	0.350010i	0.771490	−	0.636241i	$-0.219512\pi$
$691$	418.908	+	241.857i	0.606235	+	0.350010i	−0.165256	+	0.986251i	$0.552845\pi$
$692$		0			0
$693$	16.4919	−	305.440i	0.0237978	−	0.440750i
$694$		0			0
$695$	33.5129	−	58.0461i	0.0482200	−	0.0835195i
$696$		0			0
$697$	450.230	+	779.820i	0.645953	+	1.11882i
$698$		0			0
$699$			334.817i			0.478995i
$700$		0			0
$701$	1298.30			1.85207			0.926036	−	0.377435i	$-0.123194\pi$
$701$	1298.30			1.85207			0.926036	+	0.377435i	$0.123194\pi$
$702$		0			0
$703$	328.170	−	189.469i	0.466813	−	0.269515i
$704$		0			0
$705$	−39.7103	−	22.9268i	−0.0563267	−	0.0325202i
$706$		0			0
$707$	−72.8722	−	143.581i	−0.103072	−	0.203084i
$708$		0			0
$709$	−313.580	+	543.136i	−0.442285	+	0.766059i	−0.997859	−	0.0654077i	$-0.979165\pi$
$709$	−313.580	+	543.136i	−0.442285	+	0.766059i	0.555574	+	0.831467i	$0.312499\pi$
$710$		0			0
$711$	−60.3445	−	104.520i	−0.0848727	−	0.147004i
$712$		0			0
$713$			244.077i			0.342324i
$714$		0			0
$715$	−195.681			−0.273680
$716$		0			0
$717$	−463.459	+	267.578i	−0.646386	+	0.373191i
$718$		0			0
$719$	−448.725	−	259.072i	−0.624097	−	0.360322i	0.154366	−	0.988014i	$-0.450667\pi$
$719$	−448.725	−	259.072i	−0.624097	−	0.360322i	−0.778462	+	0.627691i	$0.784000\pi$
$720$		0			0
$721$	−682.703	+	1047.64i	−0.946883	+	1.45304i
$722$		0			0
$723$	−32.5677	+	56.4088i	−0.0450452	+	0.0780205i
$724$		0			0
$725$	103.750	+	179.701i	0.143104	+	0.247863i
$726$		0			0
$727$			630.122i			0.866742i	0.901216	+	0.433371i	$0.142676\pi$
$727$			630.122i			0.866742i	−0.901216	+	0.433371i	$0.857324\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	279.389	−	161.306i	0.382202	−	0.220664i
$732$		0			0
$733$	1128.34	+	651.450i	1.53935	+	0.888745i	0.998877	+	0.0473848i	$0.0150887\pi$
$733$	1128.34	+	651.450i	1.53935	+	0.888745i	0.540475	+	0.841360i	$0.318245\pi$
$734$		0			0
$735$	−78.2711	−	8.47703i	−0.106491	−	0.0115334i
$736$		0			0
$737$	459.577	−	796.011i	0.623578	−	1.08007i
$738$		0			0
$739$	666.314	+	1154.09i	0.901643	+	1.56169i	0.825361	+	0.564605i	$0.190972\pi$
$739$	666.314	+	1154.09i	0.901643	+	1.56169i	0.0762820	+	0.997086i	$0.475695\pi$
$740$		0			0
$741$			251.805i			0.339817i
$742$		0			0
$743$	1288.12			1.73368			0.866840	−	0.498586i	$-0.166147\pi$
$743$	1288.12			1.73368			0.866840	+	0.498586i	$0.166147\pi$
$744$		0			0
$745$	−1.91085	+	1.10323i	−0.00256489	+	0.00148084i
$746$		0			0
$747$	30.9294	+	17.8571i	0.0414048	+	0.0239051i
$748$		0			0
$749$	711.114	+	463.404i	0.949419	+	0.618697i
$750$		0			0
$751$	−298.030	+	516.202i	−0.396844	+	0.687353i	−0.993335	−	0.115267i	$-0.963228\pi$
$751$	−298.030	+	516.202i	−0.396844	+	0.687353i	0.596491	+	0.802620i	$0.296561\pi$
$752$		0			0
$753$	−143.429	−	248.427i	−0.190477	−	0.329916i
$754$		0			0
$755$		−	80.9566i		−	0.107227i
$756$		0			0
$757$	439.074			0.580019			0.290009	−	0.957024i	$-0.406342\pi$
$757$	439.074			0.580019			0.290009	+	0.957024i	$0.406342\pi$
$758$		0			0
$759$	−116.148	+	67.0580i	−0.153027	+	0.0883504i
$760$		0			0
$761$	207.931	+	120.049i	0.273235	+	0.157752i	0.630357	−	0.776306i	$-0.282909\pi$
$761$	207.931	+	120.049i	0.273235	+	0.157752i	−0.357122	+	0.934058i	$0.616242\pi$
$762$		0			0
$763$	1112.82	−	564.796i	1.45848	−	0.740231i
$764$		0			0
$765$	30.3090	−	52.4968i	0.0396197	−	0.0686233i
$766$		0			0
$767$	−408.748	−	707.973i	−0.532918	−	0.923042i
$768$		0			0
$769$		−	524.552i		−	0.682122i	−0.940041	−	0.341061i	$-0.889214\pi$
$769$		−	524.552i		−	0.682122i	0.940041	−	0.341061i	$-0.110786\pi$
$770$		0			0
$771$	201.078			0.260801
$772$		0			0
$773$	713.035	−	411.671i	0.922425	−	0.532562i	0.0380172	−	0.999277i	$-0.487896\pi$
$773$	713.035	−	411.671i	0.922425	−	0.532562i	0.884408	+	0.466715i	$0.154563\pi$
$774$		0			0
$775$	959.851	+	554.171i	1.23852	+	0.715059i
$776$		0			0
$777$	457.009	+	24.6756i	0.588171	+	0.0317576i
$778$		0			0
$779$	207.491	−	359.386i	0.266356	−	0.461342i
$780$		0			0
$781$	666.483	+	1154.38i	0.853372	+	1.47808i
$782$		0			0
$783$		−	44.6656i		−	0.0570442i
$784$		0			0
$785$	−130.572			−0.166333
$786$		0			0
$787$	615.173	−	355.170i	0.781668	−	0.451296i	−0.0553531	−	0.998467i	$-0.517628\pi$
$787$	615.173	−	355.170i	0.781668	−	0.451296i	0.837021	+	0.547171i	$0.184295\pi$
$788$		0			0
$789$	22.0801	+	12.7480i	0.0279850	+	0.0161571i
$790$		0			0
$791$	−65.5067	+	1213.23i	−0.0828151	+	1.53379i
$792$		0			0
$793$	−281.410	+	487.416i	−0.354867	+	0.614648i
$794$		0			0
$795$	−66.4138	−	115.032i	−0.0835394	−	0.144694i
$796$		0			0
$797$			30.1730i			0.0378582i	0.999821	+	0.0189291i	$0.00602569\pi$
$797$			30.1730i			0.0378582i	−0.999821	+	0.0189291i	$0.993974\pi$
$798$		0			0
$799$	621.640			0.778022
$800$		0			0
$801$	−196.554	+	113.481i	−0.245386	+	0.141674i
$802$		0			0
$803$	−1364.86	−	788.002i	−1.69970	−	0.981322i
$804$		0			0
$805$	15.6226	+	30.7813i	0.0194069	+	0.0382376i
$806$		0			0
$807$	141.670	−	245.380i	0.175552	−	0.304065i
$808$		0			0
$809$	339.811	+	588.569i	0.420038	+	0.727527i	0.995943	−	0.0899899i	$-0.0286835\pi$
$809$	339.811	+	588.569i	0.420038	+	0.727527i	−0.575905	+	0.817517i	$0.695350\pi$
$810$		0			0
$811$		−	899.207i		−	1.10876i	−0.832263	−	0.554382i	$-0.812955\pi$
$811$		−	899.207i		−	1.10876i	0.832263	−	0.554382i	$-0.187045\pi$
$812$		0			0
$813$	469.246			0.577178
$814$		0			0
$815$	−159.060	+	91.8330i	−0.195165	+	0.112679i
$816$		0			0
$817$	−128.759	−	74.3388i	−0.157599	−	0.0909900i
$818$		0			0
$819$	−166.042	+	254.799i	−0.202737	+	0.311109i
$820$		0			0
$821$	314.955	−	545.518i	0.383624	−	0.664456i	−0.607954	−	0.793973i	$-0.708009\pi$
$821$	314.955	−	545.518i	0.383624	−	0.664456i	0.991577	+	0.129517i	$0.0413427\pi$
$822$		0			0
$823$	−770.412	−	1334.39i	−0.936102	−	1.62138i	−0.772657	−	0.634824i	$-0.781073\pi$
$823$	−770.412	−	1334.39i	−0.936102	−	1.62138i	−0.163446	−	0.986552i	$-0.552261\pi$
$824$		0			0
$825$			609.014i			0.738198i
$826$		0			0
$827$	812.768			0.982791			0.491396	−	0.870936i	$-0.336487\pi$
$827$	812.768			0.982791			0.491396	+	0.870936i	$0.336487\pi$
$828$		0			0
$829$	−604.000	+	348.720i	−0.728589	+	0.420651i	−0.817906	−	0.575352i	$-0.804865\pi$
$829$	−604.000	+	348.720i	−0.728589	+	0.420651i	0.0893166	+	0.996003i	$0.471532\pi$
$830$		0			0
$831$	303.610	+	175.289i	0.365355	+	0.210938i
$832$		0			0
$833$	976.425	−	431.037i	1.17218	−	0.517451i
$834$		0			0
$835$	−2.67580	+	4.63462i	−0.00320455	+	0.00555045i
$836$		0			0
$837$	−119.288	−	206.613i	−0.142519	−	0.246850i
$838$		0			0
$839$			731.636i			0.872034i	0.899938	+	0.436017i	$0.143611\pi$
$839$			731.636i			0.872034i	−0.899938	+	0.436017i	$0.856389\pi$
$840$		0			0
$841$	−767.110			−0.912141
$842$		0			0
$843$	−502.304	+	290.005i	−0.595853	+	0.344016i
$844$		0			0
$845$	32.7229	+	18.8926i	0.0387254	+	0.0223581i
$846$		0			0
$847$	534.659	+	348.415i	0.631239	+	0.411352i
$848$		0			0
$849$	−451.162	+	781.436i	−0.531405	+	0.920420i
$850$		0			0
$851$	−100.334	−	173.784i	−0.117902	−	0.204212i
$852$		0			0
$853$		−	1525.90i		−	1.78886i	−0.447207	−	0.894430i	$-0.647581\pi$
$853$		−	1525.90i		−	1.78886i	0.447207	−	0.894430i	$-0.352419\pi$
$854$		0			0
$855$	−27.9363			−0.0326740
$856$		0			0
$857$	−853.233	+	492.614i	−0.995605	+	0.574813i	−0.906945	−	0.421249i	$-0.861592\pi$
$857$	−853.233	+	492.614i	−0.995605	+	0.574813i	−0.0886598	+	0.996062i	$0.528258\pi$
$858$		0			0
$859$	246.510	+	142.322i	0.286973	+	0.165684i	0.636576	−	0.771214i	$-0.280350\pi$
$859$	246.510	+	142.322i	0.286973	+	0.165684i	−0.349603	+	0.936898i	$0.613684\pi$
$860$		0			0
$861$	446.940	−	226.838i	0.519094	−	0.263458i
$862$		0			0
$863$	−514.903	+	891.839i	−0.596644	+	1.03342i	0.396669	+	0.917962i	$0.370166\pi$
$863$	−514.903	+	891.839i	−0.596644	+	1.03342i	−0.993313	+	0.115455i	$0.963167\pi$
$864$		0			0
$865$	−81.2613	−	140.749i	−0.0939437	−	0.162715i
$866$		0			0
$867$			321.241i			0.370520i
$868$		0			0
$869$	585.982			0.674318
$870$		0			0
$871$	−791.433	+	456.934i	−0.908648	+	0.524608i
$872$		0			0
$873$	−398.006	−	229.789i	−0.455906	−	0.263217i
$874$		0			0
$875$	318.621	+	17.2035i	0.364138	+	0.0196612i
$876$		0			0
$877$	254.000	−	439.941i	0.289624	−	0.501643i	−0.684096	−	0.729392i	$-0.739803\pi$
$877$	254.000	−	439.941i	0.289624	−	0.501643i	0.973720	+	0.227749i	$0.0731365\pi$
$878$		0			0
$879$	78.0875	+	135.252i	0.0888368	+	0.153870i
$880$		0			0
$881$			1681.72i			1.90888i	0.298402	+	0.954440i	$0.403546\pi$
$881$			1681.72i			1.90888i	−0.298402	+	0.954440i	$0.596454\pi$
$882$		0			0
$883$	−921.458			−1.04355			−0.521777	−	0.853082i	$-0.674731\pi$
$883$	−921.458			−1.04355			−0.521777	+	0.853082i	$0.674731\pi$
$884$		0			0
$885$	78.5455	−	45.3482i	0.0887519	−	0.0512410i
$886$		0			0
$887$	−514.831	−	297.238i	−0.580419	−	0.335105i	0.180881	−	0.983505i	$-0.442105\pi$
$887$	−514.831	−	297.238i	−0.580419	−	0.335105i	−0.761300	+	0.648400i	$0.775438\pi$
$888$		0			0
$889$	−30.9342	+	572.921i	−0.0347966	+	0.644455i
$890$		0			0
$891$	65.5467	−	113.530i	0.0735653	−	0.127419i
$892$		0			0
$893$	−143.244	−	248.105i	−0.160407	−	0.277833i
$894$		0			0
$895$		−	297.553i		−	0.332461i
$896$		0			0
$897$	133.345			0.148656
$898$		0			0
$899$	341.796	−	197.336i	0.380196	−	0.219506i
$900$		0			0
$901$	1559.50	+	900.377i	1.73085	+	0.999309i
$902$		0			0
$903$	−81.2700	−	160.127i	−0.0900000	−	0.177328i
$904$		0			0
$905$	−15.5030	+	26.8520i	−0.0171304	+	0.0296708i
$906$		0			0
$907$	575.946	+	997.568i	0.635002	+	1.09985i	0.986515	+	0.163672i	$0.0523339\pi$
$907$	575.946	+	997.568i	0.635002	+	1.09985i	−0.351513	+	0.936183i	$0.614333\pi$
$908$		0			0
$909$		−	69.0064i		−	0.0759146i
$910$		0			0
$911$	−1393.09			−1.52919			−0.764595	−	0.644511i	$-0.777061\pi$
$911$	−1393.09			−1.52919			−0.764595	+	0.644511i	$0.777061\pi$
$912$		0			0
$913$	−150.172	+	86.7017i	−0.164482	+	0.0949635i
$914$		0			0
$915$	−54.0759	−	31.2208i	−0.0590994	−	0.0341211i
$916$		0			0
$917$	−605.851	+	929.706i	−0.660688	+	1.01386i
$918$		0			0
$919$	166.446	−	288.292i	0.181116	−	0.313702i	−0.761145	−	0.648582i	$-0.775362\pi$
$919$	166.446	−	288.292i	0.181116	−	0.313702i	0.942261	+	0.334880i	$0.108696\pi$
$920$		0			0
$921$	−47.7498	−	82.7051i	−0.0518456	−	0.0897992i
$922$		0			0
$923$		−	1325.30i		−	1.43586i
$924$		0			0
$925$	−911.226			−0.985109
$926$		0			0
$927$	−464.110	+	267.954i	−0.500658	+	0.289055i
$928$		0			0
$929$	−543.880	−	314.009i	−0.585447	−	0.338008i	0.177848	−	0.984058i	$-0.443086\pi$
$929$	−543.880	−	314.009i	−0.585447	−	0.338008i	−0.763295	+	0.646050i	$0.776420\pi$
$930$		0			0
$931$	−397.029	−	290.382i	−0.426454	−	0.311903i
$932$		0			0
$933$	−283.214	+	490.540i	−0.303551	+	0.525767i
$934$		0			0
$935$	147.160	+	254.888i	0.157390	+	0.272608i
$936$		0			0
$937$		−	750.509i		−	0.800970i	−0.916303	−	0.400485i	$-0.868842\pi$
$937$		−	750.509i		−	0.800970i	0.916303	−	0.400485i	$-0.131158\pi$
$938$		0			0
$939$	−978.750			−1.04233
$940$		0			0
$941$	296.607	−	171.246i	0.315205	−	0.181983i	−0.334049	−	0.942556i	$-0.608415\pi$
$941$	296.607	−	171.246i	0.315205	−	0.181983i	0.649253	+	0.760572i	$0.275082\pi$
$942$		0			0
$943$	−190.315	−	109.878i	−0.201818	−	0.116520i
$944$		0			0
$945$	−28.2684	−	18.4214i	−0.0299137	−	0.0194935i
$946$		0			0
$947$	−791.417	+	1370.78i	−0.835710	+	1.44749i	0.0577411	+	0.998332i	$0.481610\pi$
$947$	−791.417	+	1370.78i	−0.835710	+	1.44749i	−0.893451	+	0.449161i	$0.851723\pi$
$948$		0			0
$949$	783.470	+	1357.01i	0.825574	+	1.42994i
$950$		0			0
$951$		−	658.804i		−	0.692749i
$952$		0			0
$953$	−208.540			−0.218824			−0.109412	−	0.993996i	$-0.534897\pi$
$953$	−208.540			−0.218824			−0.109412	+	0.993996i	$0.534897\pi$
$954$		0			0
$955$	−218.404	+	126.095i	−0.228695	+	0.132037i
$956$		0			0
$957$	187.811	+	108.433i	0.196250	+	0.113305i
$958$		0			0
$959$	1026.68	−	521.075i	1.07057	−	0.543352i
$960$		0			0
$961$	573.548	−	993.415i	0.596824	−	1.03373i
$962$		0			0
$963$	181.881	+	315.028i	0.188870	+	0.327132i
$964$		0			0
$965$		−	81.4030i		−	0.0843554i
$966$		0			0
$967$	777.868			0.804414			0.402207	−	0.915549i	$-0.368243\pi$
$967$	777.868			0.804414			0.402207	+	0.915549i	$0.368243\pi$
$968$		0			0
$969$	327.993	−	189.367i	0.338486	−	0.195425i
$970$		0			0
$971$	860.430	+	496.770i	0.886128	+	0.511606i	0.872674	−	0.488303i	$-0.162384\pi$
$971$	860.430	+	496.770i	0.886128	+	0.511606i	0.0134541	+	0.999909i	$0.495717\pi$
$972$		0			0
$973$	505.046	+	27.2694i	0.519061	+	0.0280261i
$974$		0			0
$975$	302.755	−	524.388i	0.310518	−	0.537834i
$976$		0			0
$977$	273.883	+	474.380i	0.280331	+	0.485548i	0.971466	−	0.237178i	$-0.0762224\pi$
$977$	273.883	+	474.380i	0.280331	+	0.485548i	−0.691135	+	0.722726i	$0.742889\pi$
$978$		0			0
$979$		−	1101.97i		−	1.12560i
$980$		0			0
$981$	534.834			0.545193
$982$		0			0
$983$	−363.054	+	209.609i	−0.369333	+	0.213234i	−0.673167	−	0.739491i	$-0.735066\pi$
$983$	−363.054	+	209.609i	−0.369333	+	0.213234i	0.303834	+	0.952725i	$0.401733\pi$
$984$		0			0
$985$	−183.872	−	106.159i	−0.186673	−	0.107775i
$986$		0			0
$987$	18.6554	−	345.511i	0.0189012	−	0.350061i
$988$		0			0
$989$	−39.3665	+	68.1848i	−0.0398044	+	0.0689432i
$990$		0			0
$991$	−376.704	−	652.471i	−0.380125	−	0.658396i	0.610954	−	0.791666i	$-0.290786\pi$
$991$	−376.704	−	652.471i	−0.380125	−	0.658396i	−0.991080	+	0.133269i	$0.957452\pi$
$992$		0			0
$993$		−	84.8370i		−	0.0854351i
$994$		0			0
$995$	303.666			0.305192
$996$		0			0
$997$	1360.04	−	785.221i	1.36413	−	0.787584i	0.373963	−	0.927443i	$-0.377999\pi$
$997$	1360.04	−	785.221i	1.36413	−	0.787584i	0.990171	+	0.139860i	$0.0446652\pi$
$998$		0			0
$999$	169.868	+	98.0731i	0.170038	+	0.0981712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.3.bh.b.481.5	✓	16
4.3	odd	2		672.3.bh.d.481.5	yes	16
7.3	odd	6	inner	672.3.bh.b.577.5	yes	16
28.3	even	6		672.3.bh.d.577.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.3.bh.b.481.5	✓	16	1.1	even	1	trivial
672.3.bh.b.577.5	yes	16	7.3	odd	6	inner
672.3.bh.d.481.5	yes	16	4.3	odd	2
672.3.bh.d.577.5	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)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-0.803356 - 0.463818i) q^{5} +(0.377407 - 6.98982i) q^{7} +(1.50000 - 2.59808i) q^{9} +(7.28297 + 12.6145i) q^{11} -14.4822i q^{13} +1.60671 q^{15} +(-18.8640 + 10.8912i) q^{17} +(8.69362 + 5.01926i) q^{19} +(5.48725 + 10.8116i) q^{21} +(2.65798 - 4.60375i) q^{23} +(-12.0697 - 20.9054i) q^{25} +5.19615i q^{27} -8.59590 q^{29} +(-39.7627 + 22.9570i) q^{31} +(-21.8489 - 12.6145i) q^{33} +(-3.54519 + 5.44026i) q^{35} +(18.8742 - 32.6910i) q^{37} +(12.5419 + 21.7232i) q^{39} -41.3390i q^{41} -14.8107 q^{43} +(-2.41007 + 1.39145i) q^{45} +(-24.7153 - 14.2694i) q^{47} +(-48.7151 - 5.27601i) q^{49} +(18.8640 - 32.6735i) q^{51} +(-41.3353 - 71.5948i) q^{53} -13.5119i q^{55} -17.3872 q^{57} +(48.8859 - 28.2243i) q^{59} +(-33.6563 - 19.4315i) q^{61} +(-17.5940 - 11.4653i) q^{63} +(-6.71708 + 11.6343i) q^{65} +(-31.5515 - 54.6488i) q^{67} +9.20751i q^{69} +91.5126 q^{71} +(-93.7022 + 54.0990i) q^{73} +(36.2092 + 20.9054i) q^{75} +(90.9215 - 46.1458i) q^{77} +(20.1148 - 34.8399i) q^{79} +(-4.50000 - 7.79423i) q^{81} +11.9047i q^{83} +20.2060 q^{85} +(12.8939 - 7.44427i) q^{87} +(-65.5180 - 37.8268i) q^{89} +(-101.228 - 5.46567i) q^{91} +(39.7627 - 68.8710i) q^{93} +(-4.65604 - 8.06451i) q^{95} -153.192i q^{97} +43.6978 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{3} - 12 q^{7} + 24 q^{9} - 12 q^{11} + 48 q^{17} + 36 q^{19} + 24 q^{21} + 48 q^{23} + 20 q^{25} + 64 q^{29} - 60 q^{31} + 36 q^{33} - 36 q^{37} + 12 q^{39} + 72 q^{43} - 72 q^{47} - 40 q^{49}+ \cdots - 72 q^{99}+O(q^{100}) \) 16 * q - 24 * q^3 - 12 * q^7 + 24 * q^9 - 12 * q^11 + 48 * q^17 + 36 * q^19 + 24 * q^21 + 48 * q^23 + 20 * q^25 + 64 * q^29 - 60 * q^31 + 36 * q^33 - 36 * q^37 + 12 * q^39 + 72 * q^43 - 72 * q^47 - 40 * q^49 - 48 * q^51 + 56 * q^53 - 72 * q^57 - 36 * q^59 + 72 * q^61 - 36 * q^63 + 120 * q^65 + 12 * q^67 + 240 * q^71 + 156 * q^73 - 60 * q^75 + 224 * q^77 + 84 * q^79 - 72 * q^81 + 800 * q^85 - 96 * q^87 + 192 * q^89 + 300 * 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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