LMFDB - Embedded newform 672.3.bh.c.481.7

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} + 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			481.7
Root			$0.500000 - 2.54626i$ of defining polynomial
Character	$\chi$	$=$	672.481
Dual form			672.3.bh.c.577.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 - 0.866025i) q^{3} +(4.12320 + 2.38053i) q^{5} +(6.96231 + 0.725445i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-10.0157 - 17.3477i) q^{11} -8.03507i q^{13} +8.24641 q^{15} +(2.82192 - 1.62923i) q^{17} +(6.97874 + 4.02918i) q^{19} +(11.0717 - 4.94137i) q^{21} +(19.6162 - 33.9763i) q^{23} +(-1.16613 - 2.01979i) q^{25} -5.19615i q^{27} +14.6407 q^{29} +(-18.2308 + 10.5256i) q^{31} +(-30.0471 - 17.3477i) q^{33} +(26.9801 + 19.5652i) q^{35} +(-19.9254 + 34.5117i) q^{37} +(-6.95858 - 12.0526i) q^{39} +75.7892i q^{41} +57.6698 q^{43} +(12.3696 - 7.14160i) q^{45} +(22.9002 + 13.2214i) q^{47} +(47.9475 + 10.1015i) q^{49} +(2.82192 - 4.88770i) q^{51} +(-23.9789 - 41.5327i) q^{53} -95.3709i q^{55} +13.9575 q^{57} +(-3.68843 + 2.12952i) q^{59} +(-34.1223 - 19.7005i) q^{61} +(12.3282 - 17.0004i) q^{63} +(19.1277 - 33.1302i) q^{65} +(7.03215 + 12.1800i) q^{67} -67.9527i q^{69} +82.3201 q^{71} +(-78.1500 + 45.1199i) q^{73} +(-3.49838 - 2.01979i) q^{75} +(-57.1476 - 128.046i) q^{77} +(41.4414 - 71.7787i) q^{79} +(-4.50000 - 7.79423i) q^{81} -100.182i q^{83} +15.5138 q^{85} +(21.9611 - 12.6792i) q^{87} +(102.957 + 59.4420i) q^{89} +(5.82900 - 55.9426i) q^{91} +(-18.2308 + 31.5767i) q^{93} +(19.1832 + 33.2262i) q^{95} +182.783i q^{97} -60.0942 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	4.12320	+	2.38053i	0.824641	+	0.476107i	0.852014	−	0.523519i	$-0.175381\pi$
$5$	4.12320	+	2.38053i	0.824641	+	0.476107i	−0.0273734	+	0.999625i	$0.508714\pi$
$6$		0			0
$7$	6.96231	+	0.725445i	0.994615	+	0.103635i
$7$	6.96231	+	0.725445i	0.994615	+	0.103635i
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−10.0157	−	17.3477i	−0.910519	−	1.57706i	−0.813333	−	0.581798i	$-0.802349\pi$
$11$	−10.0157	−	17.3477i	−0.910519	−	1.57706i	−0.0971854	−	0.995266i	$-0.530984\pi$
$12$		0			0
$13$		−	8.03507i		−	0.618082i	−0.951049	−	0.309041i	$-0.899992\pi$
$13$		−	8.03507i		−	0.618082i	0.951049	−	0.309041i	$-0.100008\pi$
$14$		0			0
$15$	8.24641			0.549760
$16$		0			0
$17$	2.82192	−	1.62923i	0.165995	−	0.0958373i	−0.414701	−	0.909958i	$-0.636114\pi$
$17$	2.82192	−	1.62923i	0.165995	−	0.0958373i	0.580696	+	0.814120i	$0.302780\pi$
$18$		0			0
$19$	6.97874	+	4.02918i	0.367302	+	0.212062i	0.672279	−	0.740298i	$-0.265315\pi$
$19$	6.97874	+	4.02918i	0.367302	+	0.212062i	−0.304977	+	0.952360i	$0.598649\pi$
$20$		0			0
$21$	11.0717	−	4.94137i	0.527225	−	0.235303i
$22$		0			0
$23$	19.6162	−	33.9763i	0.852880	−	1.47723i	−0.0257172	−	0.999669i	$-0.508187\pi$
$23$	19.6162	−	33.9763i	0.852880	−	1.47723i	0.878598	−	0.477563i	$-0.158480\pi$
$24$		0			0
$25$	−1.16613	−	2.01979i	−0.0466451	−	0.0807917i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	14.6407			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$29$	14.6407			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$30$		0			0
$31$	−18.2308	+	10.5256i	−0.588091	+	0.339535i	−0.764342	−	0.644811i	$-0.776936\pi$
$31$	−18.2308	+	10.5256i	−0.588091	+	0.339535i	0.176251	+	0.984345i	$0.443603\pi$
$32$		0			0
$33$	−30.0471	−	17.3477i	−0.910519	−	0.525688i
$34$		0			0
$35$	26.9801	+	19.5652i	0.770859	+	0.559005i
$36$		0			0
$37$	−19.9254	+	34.5117i	−0.538523	+	0.932750i	0.460461	+	0.887680i	$0.347684\pi$
$37$	−19.9254	+	34.5117i	−0.538523	+	0.932750i	−0.998984	+	0.0450695i	$0.985649\pi$
$38$		0			0
$39$	−6.95858	−	12.0526i	−0.178425	−	0.309041i
$40$		0			0
$41$			75.7892i			1.84852i	0.381767	+	0.924259i	$0.375316\pi$
$41$			75.7892i			1.84852i	−0.381767	+	0.924259i	$0.624684\pi$
$42$		0			0
$43$	57.6698			1.34116			0.670579	−	0.741838i	$-0.266046\pi$
$43$	57.6698			1.34116			0.670579	+	0.741838i	$0.266046\pi$
$44$		0			0
$45$	12.3696	−	7.14160i	0.274880	−	0.158702i
$46$		0			0
$47$	22.9002	+	13.2214i	0.487238	+	0.281307i	0.723428	−	0.690400i	$-0.242565\pi$
$47$	22.9002	+	13.2214i	0.487238	+	0.281307i	−0.236190	+	0.971707i	$0.575899\pi$
$48$		0			0
$49$	47.9475	+	10.1015i	0.978520	+	0.206154i
$50$		0			0
$51$	2.82192	−	4.88770i	0.0553317	−	0.0958373i
$52$		0			0
$53$	−23.9789	−	41.5327i	−0.452433	−	0.783637i	0.546104	−	0.837718i	$-0.316110\pi$
$53$	−23.9789	−	41.5327i	−0.452433	−	0.783637i	−0.998537	+	0.0540809i	$0.982777\pi$
$54$		0			0
$55$		−	95.3709i		−	1.73402i
$56$		0			0
$57$	13.9575			0.244868
$58$		0			0
$59$	−3.68843	+	2.12952i	−0.0625158	+	0.0360935i	−0.530932	−	0.847414i	$-0.678158\pi$
$59$	−3.68843	+	2.12952i	−0.0625158	+	0.0360935i	0.468416	+	0.883508i	$0.344825\pi$
$60$		0			0
$61$	−34.1223	−	19.7005i	−0.559381	−	0.322959i	0.193516	−	0.981097i	$-0.438011\pi$
$61$	−34.1223	−	19.7005i	−0.559381	−	0.322959i	−0.752897	+	0.658138i	$0.771344\pi$
$62$		0			0
$63$	12.3282	−	17.0004i	0.195686	−	0.269848i
$64$		0			0
$65$	19.1277	−	33.1302i	0.294273	−	0.509696i
$66$		0			0
$67$	7.03215	+	12.1800i	0.104957	+	0.181792i	0.913721	−	0.406343i	$-0.133196\pi$
$67$	7.03215	+	12.1800i	0.104957	+	0.181792i	−0.808763	+	0.588134i	$0.799863\pi$
$68$		0			0
$69$		−	67.9527i		−	0.984821i
$70$		0			0
$71$	82.3201			1.15944			0.579719	−	0.814816i	$-0.303162\pi$
$71$	82.3201			1.15944			0.579719	+	0.814816i	$0.303162\pi$
$72$		0			0
$73$	−78.1500	+	45.1199i	−1.07055	+	0.618081i	−0.928331	−	0.371754i	$-0.878756\pi$
$73$	−78.1500	+	45.1199i	−1.07055	+	0.618081i	−0.142217	+	0.989836i	$0.545423\pi$
$74$		0			0
$75$	−3.49838	−	2.01979i	−0.0466451	−	0.0269306i
$76$		0			0
$77$	−57.1476	−	128.046i	−0.742177	−	1.66293i
$78$		0			0
$79$	41.4414	−	71.7787i	0.524575	−	0.908591i	−0.475016	−	0.879977i	$-0.657558\pi$
$79$	41.4414	−	71.7787i	0.524575	−	0.908591i	0.999591	−	0.0286132i	$-0.00910910\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	100.182i		−	1.20701i	−0.797360	−	0.603504i	$-0.793771\pi$
$83$		−	100.182i		−	1.20701i	0.797360	−	0.603504i	$-0.206229\pi$
$84$		0			0
$85$	15.5138			0.182515
$86$		0			0
$87$	21.9611	−	12.6792i	0.252426	−	0.145738i
$88$		0			0
$89$	102.957	+	59.4420i	1.15682	+	0.667888i	0.950539	−	0.310606i	$-0.100532\pi$
$89$	102.957	+	59.4420i	1.15682	+	0.667888i	0.206276	+	0.978494i	$0.433865\pi$
$90$		0			0
$91$	5.82900	−	55.9426i	0.0640549	−	0.614754i
$92$		0			0
$93$	−18.2308	+	31.5767i	−0.196030	+	0.339535i
$94$		0			0
$95$	19.1832	+	33.2262i	0.201928	+	0.349750i
$96$		0			0
$97$			182.783i			1.88436i	0.335100	+	0.942182i	$0.391230\pi$
$97$			182.783i			1.88436i	−0.335100	+	0.942182i	$0.608770\pi$
$98$		0			0
$99$	−60.0942			−0.607012
$100$		0			0
$101$	−45.6915	+	26.3800i	−0.452391	+	0.261188i	−0.708840	−	0.705370i	$-0.750781\pi$
$101$	−45.6915	+	26.3800i	−0.452391	+	0.261188i	0.256448	+	0.966558i	$0.417448\pi$
$102$		0			0
$103$	−0.649827	−	0.375178i	−0.00630900	−	0.00364251i	0.496842	−	0.867841i	$-0.334493\pi$
$103$	−0.649827	−	0.375178i	−0.00630900	−	0.00364251i	−0.503151	+	0.864198i	$0.667826\pi$
$104$		0			0
$105$	57.4140	+	5.98231i	0.546800	+	0.0569744i
$106$		0			0
$107$	20.5176	−	35.5375i	0.191753	−	0.332126i	−0.754078	−	0.656785i	$-0.771916\pi$
$107$	20.5176	−	35.5375i	0.191753	−	0.332126i	0.945831	+	0.324658i	$0.105249\pi$
$108$		0			0
$109$	−10.5758	−	18.3179i	−0.0970258	−	0.168054i	0.813426	−	0.581668i	$-0.197600\pi$
$109$	−10.5758	−	18.3179i	−0.0970258	−	0.168054i	−0.910452	+	0.413614i	$0.864266\pi$
$110$		0			0
$111$			69.0235i			0.621833i
$112$		0			0
$113$	−32.5548			−0.288096			−0.144048	−	0.989571i	$-0.546012\pi$
$113$	−32.5548			−0.288096			−0.144048	+	0.989571i	$0.546012\pi$
$114$		0			0
$115$	161.764	−	93.3942i	1.40664	−	0.812124i
$116$		0			0
$117$	−20.8757	−	12.0526i	−0.178425	−	0.103014i
$118$		0			0
$119$	20.8290	−	9.29609i	0.175033	−	0.0781184i
$120$		0			0
$121$	−140.129	+	242.710i	−1.15809	+	2.00587i
$122$		0			0
$123$	65.6354	+	113.684i	0.533621	+	0.924259i
$124$		0			0
$125$		−	130.131i		−	1.04105i
$126$		0			0
$127$	−180.800			−1.42362			−0.711811	−	0.702371i	$-0.752125\pi$
$127$	−180.800			−1.42362			−0.711811	+	0.702371i	$0.752125\pi$
$128$		0			0
$129$	86.5047	−	49.9435i	0.670579	−	0.387159i
$130$		0			0
$131$	−143.214	−	82.6846i	−1.09324	−	0.631180i	−0.158800	−	0.987311i	$-0.550762\pi$
$131$	−143.214	−	82.6846i	−1.09324	−	0.631180i	−0.934436	+	0.356131i	$0.884096\pi$
$132$		0			0
$133$	45.6652	+	33.1151i	0.343347	+	0.248985i
$134$		0			0
$135$	12.3696	−	21.4248i	0.0916267	−	0.158702i
$136$		0			0
$137$	−50.7716	−	87.9391i	−0.370596	−	0.641891i	0.619061	−	0.785343i	$-0.287513\pi$
$137$	−50.7716	−	87.9391i	−0.370596	−	0.641891i	−0.989657	+	0.143452i	$0.954180\pi$
$138$		0			0
$139$			69.1168i			0.497243i	0.968601	+	0.248622i	$0.0799776\pi$
$139$			69.1168i			0.497243i	−0.968601	+	0.248622i	$0.920022\pi$
$140$		0			0
$141$	45.8003			0.324825
$142$		0			0
$143$	−139.390	+	80.4769i	−0.974756	+	0.562776i
$144$		0			0
$145$	60.3667	+	34.8527i	0.416322	+	0.240364i
$146$		0			0
$147$	80.6694	−	26.3714i	0.548771	−	0.179397i
$148$		0			0
$149$	120.048	−	207.930i	0.805694	−	1.39550i	−0.110128	−	0.993917i	$-0.535126\pi$
$149$	120.048	−	207.930i	0.805694	−	1.39550i	0.915822	−	0.401585i	$-0.131541\pi$
$150$		0			0
$151$	127.578	+	220.972i	0.844890	+	1.46339i	0.885717	+	0.464226i	$0.153667\pi$
$151$	127.578	+	220.972i	0.844890	+	1.46339i	−0.0408273	+	0.999166i	$0.512999\pi$
$152$		0			0
$153$		−	9.77541i		−	0.0638916i
$154$		0			0
$155$	−100.226			−0.646619
$156$		0			0
$157$	−24.4349	+	14.1075i	−0.155636	+	0.0898566i	−0.575795	−	0.817594i	$-0.695308\pi$
$157$	−24.4349	+	14.1075i	−0.155636	+	0.0898566i	0.420159	+	0.907450i	$0.361974\pi$
$158$		0			0
$159$	−71.9368	−	41.5327i	−0.452433	−	0.261212i
$160$		0			0
$161$	161.222	−	222.323i	1.00138	−	1.38089i
$162$		0			0
$163$	−147.881	+	256.138i	−0.907246	+	1.57140i	−0.0893731	+	0.995998i	$0.528486\pi$
$163$	−147.881	+	256.138i	−0.907246	+	1.57140i	−0.817873	+	0.575399i	$0.804847\pi$
$164$		0			0
$165$	−82.5936	−	143.056i	−0.500567	−	0.867008i
$166$		0			0
$167$			197.655i			1.18356i	0.806099	+	0.591781i	$0.201575\pi$
$167$			197.655i			1.18356i	−0.806099	+	0.591781i	$0.798425\pi$
$168$		0			0
$169$	104.438			0.617974
$170$		0			0
$171$	20.9362	−	12.0875i	0.122434	−	0.0706873i
$172$		0			0
$173$	143.301	+	82.7350i	0.828331	+	0.478237i	0.853281	−	0.521451i	$-0.174609\pi$
$173$	143.301	+	82.7350i	0.828331	+	0.478237i	−0.0249497	+	0.999689i	$0.507943\pi$
$174$		0			0
$175$	−6.65369	−	14.9084i	−0.0380211	−	0.0851907i
$176$		0			0
$177$	−3.68843	+	6.38856i	−0.0208386	+	0.0360935i
$178$		0			0
$179$	−0.973062	−	1.68539i	−0.00543610	−	0.00941561i	0.863295	−	0.504700i	$-0.168397\pi$
$179$	−0.973062	−	1.68539i	−0.00543610	−	0.00941561i	−0.868731	+	0.495285i	$0.835064\pi$
$180$		0			0
$181$			7.57563i			0.0418543i	0.999781	+	0.0209271i	$0.00666180\pi$
$181$			7.57563i			0.0418543i	−0.999781	+	0.0209271i	$0.993338\pi$
$182$		0			0
$183$	−68.2445			−0.372921
$184$		0			0
$185$	−164.313	+	94.8660i	−0.888176	+	0.512789i
$186$		0			0
$187$	−56.5270	−	32.6359i	−0.302283	−	0.174523i
$188$		0			0
$189$	3.76952	−	36.1772i	0.0199446	−	0.191414i
$190$		0			0
$191$	−27.1913	+	47.0967i	−0.142363	+	0.246580i	−0.928386	−	0.371617i	$-0.878803\pi$
$191$	−27.1913	+	47.0967i	−0.142363	+	0.246580i	0.786023	+	0.618197i	$0.212137\pi$
$192$		0			0
$193$	88.1806	+	152.733i	0.456894	+	0.791364i	0.998795	−	0.0490784i	$-0.0156284\pi$
$193$	88.1806	+	152.733i	0.456894	+	0.791364i	−0.541901	+	0.840443i	$0.682295\pi$
$194$		0			0
$195$		−	66.2605i		−	0.339797i
$196$		0			0
$197$	−98.7425			−0.501231			−0.250616	−	0.968087i	$-0.580633\pi$
$197$	−98.7425			−0.501231			−0.250616	+	0.968087i	$0.580633\pi$
$198$		0			0
$199$	−297.560	+	171.796i	−1.49528	+	0.863298i	−0.999985	−	0.00542881i	$-0.998272\pi$
$199$	−297.560	+	171.796i	−1.49528	+	0.863298i	−0.495291	+	0.868727i	$0.664939\pi$
$200$		0			0
$201$	21.0965	+	12.1800i	0.104957	+	0.0605972i
$202$		0			0
$203$	101.933	+	10.6210i	0.502134	+	0.0523204i
$204$		0			0
$205$	−180.419	+	312.494i	−0.880091	+	1.52436i
$206$		0			0
$207$	−58.8487	−	101.929i	−0.284293	−	0.492411i
$208$		0			0
$209$		−	161.420i		−	0.772346i
$210$		0			0
$211$	−184.550			−0.874645			−0.437323	−	0.899305i	$-0.644073\pi$
$211$	−184.550			−0.874645			−0.437323	+	0.899305i	$0.644073\pi$
$212$		0			0
$213$	123.480	−	71.2913i	0.579719	−	0.334701i
$214$		0			0
$215$	237.784	+	137.285i	1.10597	+	0.638534i
$216$		0			0
$217$	−134.564	+	60.0568i	−0.620112	+	0.276760i
$218$		0			0
$219$	−78.1500	+	135.360i	−0.356849	+	0.618081i
$220$		0			0
$221$	−13.0910	−	22.6743i	−0.0592354	−	0.102599i
$222$		0			0
$223$		−	201.934i		−	0.905534i	−0.891629	−	0.452767i	$-0.850437\pi$
$223$		−	201.934i		−	0.905534i	0.891629	−	0.452767i	$-0.149563\pi$
$224$		0			0
$225$	−6.99677			−0.0310967
$226$		0			0
$227$	−321.629	+	185.693i	−1.41687	+	0.818029i	−0.996022	−	0.0891028i	$-0.971600\pi$
$227$	−321.629	+	185.693i	−1.41687	+	0.818029i	−0.420846	+	0.907132i	$0.638267\pi$
$228$		0			0
$229$	316.879	+	182.950i	1.38375	+	0.798910i	0.992602	−	0.121417i	$-0.0387438\pi$
$229$	316.879	+	182.950i	1.38375	+	0.798910i	0.391151	+	0.920327i	$0.372077\pi$
$230$		0			0
$231$	−196.612	−	142.578i	−0.851136	−	0.617219i
$232$		0			0
$233$	−162.550	+	281.545i	−0.697640	+	1.20835i	0.271643	+	0.962398i	$0.412433\pi$
$233$	−162.550	+	281.545i	−0.697640	+	1.20835i	−0.969283	+	0.245949i	$0.920900\pi$
$234$		0			0
$235$	62.9481	+	109.029i	0.267864	+	0.463954i
$236$		0			0
$237$		−	143.557i		−	0.605727i
$238$		0			0
$239$	262.345			1.09768			0.548840	−	0.835928i	$-0.315070\pi$
$239$	262.345			1.09768			0.548840	+	0.835928i	$0.315070\pi$
$240$		0			0
$241$	−12.5187	+	7.22765i	−0.0519446	+	0.0299902i	−0.525747	−	0.850641i	$-0.676214\pi$
$241$	−12.5187	+	7.22765i	−0.0519446	+	0.0299902i	0.473803	+	0.880631i	$0.342881\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	173.650	+	155.791i	0.708776	+	0.635882i
$246$		0			0
$247$	32.3747	−	56.0747i	0.131072	−	0.227023i
$248$		0			0
$249$	−86.7599	−	150.273i	−0.348433	−	0.603504i
$250$		0			0
$251$		−	88.1019i		−	0.351004i	−0.984479	−	0.175502i	$-0.943845\pi$
$251$		−	88.1019i		−	0.351004i	0.984479	−	0.175502i	$-0.0561548\pi$
$252$		0			0
$253$	−785.882			−3.10625
$254$		0			0
$255$	23.2707	−	13.4353i	0.0912576	−	0.0526876i
$256$		0			0
$257$	48.1756	+	27.8142i	0.187454	+	0.108226i	0.590790	−	0.806825i	$-0.298816\pi$
$257$	48.1756	+	27.8142i	0.187454	+	0.108226i	−0.403336	+	0.915052i	$0.632150\pi$
$258$		0			0
$259$	−163.763	+	225.827i	−0.632289	+	0.871917i
$260$		0			0
$261$	21.9611	−	38.0377i	0.0841422	−	0.145738i
$262$		0			0
$263$	−220.150	−	381.311i	−0.837072	−	1.44985i	−0.892332	−	0.451380i	$-0.850932\pi$
$263$	−220.150	−	381.311i	−0.837072	−	1.44985i	0.0552594	−	0.998472i	$-0.482401\pi$
$264$		0			0
$265$		−	228.331i		−	0.861625i
$266$		0			0
$267$	205.913			0.771210
$268$		0			0
$269$	69.0223	−	39.8501i	0.256589	−	0.148141i	−0.366189	−	0.930541i	$-0.619338\pi$
$269$	69.0223	−	39.8501i	0.256589	−	0.148141i	0.622777	+	0.782399i	$0.286004\pi$
$270$		0			0
$271$	46.4151	+	26.7978i	0.171274	+	0.0988848i	0.583186	−	0.812339i	$-0.301806\pi$
$271$	46.4151	+	26.7978i	0.171274	+	0.0988848i	−0.411913	+	0.911223i	$0.635139\pi$
$272$		0			0
$273$	−39.7042	−	88.9620i	−0.145437	−	0.325868i
$274$		0			0
$275$	−23.3592	+	40.4593i	−0.0849425	+	0.147125i
$276$		0			0
$277$	−186.167	−	322.450i	−0.672082	−	1.16408i	−0.977313	−	0.211801i	$-0.932067\pi$
$277$	−186.167	−	322.450i	−0.672082	−	1.16408i	0.305231	−	0.952278i	$-0.401266\pi$
$278$		0			0
$279$			63.1534i			0.226356i
$280$		0			0
$281$	12.1407			0.0432053			0.0216026	−	0.999767i	$-0.493123\pi$
$281$	12.1407			0.0432053			0.0216026	+	0.999767i	$0.493123\pi$
$282$		0			0
$283$	115.266	−	66.5486i	0.407299	−	0.235154i	−0.282330	−	0.959317i	$-0.591107\pi$
$283$	115.266	−	66.5486i	0.407299	−	0.235154i	0.689629	+	0.724163i	$0.257774\pi$
$284$		0			0
$285$	57.5495	+	33.2262i	0.201928	+	0.116583i
$286$		0			0
$287$	−54.9809	+	527.668i	−0.191571	+	1.83856i
$288$		0			0
$289$	−139.191	+	241.086i	−0.481630	+	0.834208i
$290$		0			0
$291$	158.295	+	274.175i	0.543969	+	0.942182i
$292$		0			0
$293$		−	312.457i		−	1.06640i	−0.845988	−	0.533202i	$-0.820988\pi$
$293$		−	312.457i		−	1.06640i	0.845988	−	0.533202i	$-0.179012\pi$
$294$		0			0
$295$	−20.2776			−0.0687375
$296$		0			0
$297$	−90.1413	+	52.0431i	−0.303506	+	0.175229i
$298$		0			0
$299$	−273.002	−	157.618i	−0.913051	−	0.527150i
$300$		0			0
$301$	401.515	+	41.8362i	1.33394	+	0.138991i
$302$		0			0
$303$	−45.6915	+	79.1400i	−0.150797	+	0.261188i
$304$		0			0
$305$	−93.7953	−	162.458i	−0.307526	−	0.532650i
$306$		0			0
$307$			74.1852i			0.241646i	0.992674	+	0.120823i	$0.0385533\pi$
$307$			74.1852i			0.241646i	−0.992674	+	0.120823i	$0.961447\pi$
$308$		0			0
$309$	−1.29965			−0.00420600
$310$		0			0
$311$	−291.157	+	168.099i	−0.936195	+	0.540512i	−0.888766	−	0.458362i	$-0.848436\pi$
$311$	−291.157	+	168.099i	−0.936195	+	0.540512i	−0.0474295	+	0.998875i	$0.515103\pi$
$312$		0			0
$313$	306.481	+	176.947i	0.979174	+	0.565326i	0.902021	−	0.431693i	$-0.142084\pi$
$313$	306.481	+	176.947i	0.979174	+	0.565326i	0.0771532	+	0.997019i	$0.475417\pi$
$314$		0			0
$315$	91.3019	−	40.7485i	0.289847	−	0.129360i
$316$		0			0
$317$	−264.435	+	458.014i	−0.834179	+	1.44484i	0.0605186	+	0.998167i	$0.480725\pi$
$317$	−264.435	+	458.014i	−0.834179	+	1.44484i	−0.894697	+	0.446673i	$0.852609\pi$
$318$		0			0
$319$	−146.637	−	253.983i	−0.459678	−	0.796186i
$320$		0			0
$321$		−	71.0750i		−	0.221418i
$322$		0			0
$323$	26.2579			0.0812938
$324$		0			0
$325$	−16.2292	+	9.36992i	−0.0499359	+	0.0288305i
$326$		0			0
$327$	−31.7275	−	18.3179i	−0.0970258	−	0.0560179i
$328$		0			0
$329$	149.847	+	108.664i	0.455461	+	0.330287i
$330$		0			0
$331$	120.511	−	208.730i	0.364080	−	0.630605i	−0.624548	−	0.780987i	$-0.714717\pi$
$331$	120.511	−	208.730i	0.364080	−	0.630605i	0.988628	+	0.150381i	$0.0480501\pi$
$332$		0			0
$333$	59.7761	+	103.535i	0.179508	+	0.310917i
$334$		0			0
$335$			66.9611i			0.199884i
$336$		0			0
$337$	−12.7531			−0.0378429			−0.0189215	−	0.999821i	$-0.506023\pi$
$337$	−12.7531			−0.0378429			−0.0189215	+	0.999821i	$0.506023\pi$
$338$		0			0
$339$	−48.8322	+	28.1933i	−0.144048	+	0.0831660i
$340$		0			0
$341$	365.189	+	210.842i	1.07094	+	0.618305i
$342$		0			0
$343$	326.497	+	105.113i	0.951886	+	0.306453i
$344$		0			0
$345$	161.764	−	280.183i	0.468880	−	0.812124i
$346$		0			0
$347$	−131.657	−	228.037i	−0.379416	−	0.657168i	0.611561	−	0.791197i	$-0.290542\pi$
$347$	−131.657	−	228.037i	−0.379416	−	0.657168i	−0.990977	+	0.134029i	$0.957209\pi$
$348$		0			0
$349$			455.175i			1.30423i	0.758122	+	0.652113i	$0.226117\pi$
$349$			455.175i			1.30423i	−0.758122	+	0.652113i	$0.773883\pi$
$350$		0			0
$351$	−41.7515			−0.118950
$352$		0			0
$353$	480.103	−	277.188i	1.36007	−	0.785234i	0.370434	−	0.928859i	$-0.379209\pi$
$353$	480.103	−	277.188i	1.36007	−	0.785234i	0.989632	+	0.143625i	$0.0458758\pi$
$354$		0			0
$355$	339.423	+	195.966i	0.956120	+	0.552016i
$356$		0			0
$357$	23.1928	−	31.9826i	0.0649659	−	0.0895870i
$358$		0			0
$359$	100.706	−	174.428i	0.280518	−	0.485872i	−0.690994	−	0.722860i	$-0.742827\pi$
$359$	100.706	−	174.428i	0.280518	−	0.485872i	0.971512	+	0.236989i	$0.0761604\pi$
$360$		0			0
$361$	−148.031	−	256.398i	−0.410059	−	0.710244i
$362$		0			0
$363$			485.420i			1.33725i
$364$		0			0
$365$	−429.638			−1.17709
$366$		0			0
$367$	95.7746	−	55.2955i	0.260966	−	0.150669i	−0.363809	−	0.931474i	$-0.618524\pi$
$367$	95.7746	−	55.2955i	0.260966	−	0.150669i	0.624775	+	0.780805i	$0.285191\pi$
$368$		0			0
$369$	196.906	+	113.684i	0.533621	+	0.308086i
$370$		0			0
$371$	−136.819	−	306.559i	−0.368784	−	0.826305i
$372$		0			0
$373$	135.293	−	234.334i	0.362715	−	0.628241i	−0.625692	−	0.780070i	$-0.715183\pi$
$373$	135.293	−	234.334i	0.362715	−	0.628241i	0.988407	+	0.151830i	$0.0485165\pi$
$374$		0			0
$375$	−112.696	−	195.196i	−0.300524	−	0.520523i
$376$		0			0
$377$		−	117.639i		−	0.312041i
$378$		0			0
$379$	−477.970			−1.26114			−0.630568	−	0.776134i	$-0.717178\pi$
$379$	−477.970			−1.26114			−0.630568	+	0.776134i	$0.717178\pi$
$380$		0			0
$381$	−271.200	+	156.577i	−0.711811	+	0.410964i
$382$		0			0
$383$	300.104	+	173.265i	0.783560	+	0.452389i	0.837691	−	0.546145i	$-0.183905\pi$
$383$	300.104	+	173.265i	0.783560	+	0.452389i	−0.0541302	+	0.998534i	$0.517239\pi$
$384$		0			0
$385$	69.1863	−	664.001i	0.179705	−	1.72468i
$386$		0			0
$387$	86.5047	−	149.830i	0.223526	−	0.387159i
$388$		0			0
$389$	−145.824	−	252.574i	−0.374868	−	0.649290i	0.615439	−	0.788184i	$-0.288979\pi$
$389$	−145.824	−	252.574i	−0.374868	−	0.649290i	−0.990307	+	0.138894i	$0.955645\pi$
$390$		0			0
$391$		−	127.838i		−	0.326951i
$392$		0			0
$393$	−286.428			−0.728824
$394$		0			0
$395$	341.743	−	197.305i	0.865172	−	0.499507i
$396$		0			0
$397$	479.019	+	276.561i	1.20660	+	0.696628i	0.962014	−	0.273000i	$-0.0880160\pi$
$397$	479.019	+	276.561i	1.20660	+	0.696628i	0.244582	+	0.969629i	$0.421349\pi$
$398$		0			0
$399$	97.1763	+	10.1254i	0.243550	+	0.0253769i
$400$		0			0
$401$	−120.143	+	208.093i	−0.299608	+	0.518936i	−0.976046	−	0.217563i	$-0.930189\pi$
$401$	−120.143	+	208.093i	−0.299608	+	0.518936i	0.676439	+	0.736499i	$0.263522\pi$
$402$		0			0
$403$	84.5737	+	146.486i	0.209860	+	0.363489i
$404$		0			0
$405$		−	42.8496i		−	0.105801i
$406$		0			0
$407$	798.266			1.96134
$408$		0			0
$409$	−551.423	+	318.364i	−1.34822	+	0.778396i	−0.987998	−	0.154469i	$-0.950633\pi$
$409$	−551.423	+	318.364i	−1.34822	+	0.778396i	−0.360224	+	0.932866i	$0.617300\pi$
$410$		0			0
$411$	−152.315	−	87.9391i	−0.370596	−	0.213964i
$412$		0			0
$413$	−27.2249	+	12.1506i	−0.0659198	+	0.0294204i
$414$		0			0
$415$	238.486	−	413.070i	0.574665	−	0.995348i
$416$		0			0
$417$	59.8569	+	103.675i	0.143542	+	0.248622i
$418$		0			0
$419$		−	187.780i		−	0.448163i	−0.974570	−	0.224081i	$-0.928062\pi$
$419$		−	187.780i		−	0.448163i	0.974570	−	0.224081i	$-0.0719381\pi$
$420$		0			0
$421$	278.920			0.662517			0.331258	−	0.943540i	$-0.392527\pi$
$421$	278.920			0.662517			0.331258	+	0.943540i	$0.392527\pi$
$422$		0			0
$423$	68.7005	−	39.6643i	0.162413	−	0.0937689i
$424$		0			0
$425$	−6.58143	−	3.79979i	−0.0154857	−	0.00894069i
$426$		0			0
$427$	−223.278	−	161.915i	−0.522899	−	0.379191i
$428$		0			0
$429$	−139.390	+	241.431i	−0.324919	+	0.562776i
$430$		0			0
$431$	152.459	+	264.066i	0.353733	+	0.612683i	0.986900	−	0.161332i	$-0.0515790\pi$
$431$	152.459	+	264.066i	0.353733	+	0.612683i	−0.633168	+	0.774015i	$0.718246\pi$
$432$		0			0
$433$		−	803.297i		−	1.85519i	−0.373588	−	0.927595i	$-0.621873\pi$
$433$		−	803.297i		−	1.85519i	0.373588	−	0.927595i	$-0.378127\pi$
$434$		0			0
$435$	120.733			0.277548
$436$		0			0
$437$	273.793	−	158.075i	0.626530	−	0.361727i
$438$		0			0
$439$	−253.391	−	146.296i	−0.577201	−	0.333247i	0.182819	−	0.983147i	$-0.441478\pi$
$439$	−253.391	−	146.296i	−0.577201	−	0.333247i	−0.760020	+	0.649899i	$0.774811\pi$
$440$		0			0
$441$	98.1658	−	109.419i	0.222598	−	0.248115i
$442$		0			0
$443$	−10.0891	+	17.4748i	−0.0227745	+	0.0394466i	−0.877188	−	0.480147i	$-0.840583\pi$
$443$	−10.0891	+	17.4748i	−0.0227745	+	0.0394466i	0.854414	+	0.519594i	$0.173917\pi$
$444$		0			0
$445$	283.007	+	490.183i	0.635971	+	1.10153i
$446$		0			0
$447$		−	415.860i		−	0.930335i
$448$		0			0
$449$	−140.081			−0.311984			−0.155992	−	0.987758i	$-0.549857\pi$
$449$	−140.081			−0.311984			−0.155992	+	0.987758i	$0.549857\pi$
$450$		0			0
$451$	1314.77	−	759.082i	2.91523	−	1.68311i
$452$		0			0
$453$	382.735	+	220.972i	0.844890	+	0.487797i
$454$		0			0
$455$	157.207	−	216.787i	0.345511	−	0.476454i
$456$		0			0
$457$	−45.9491	+	79.5862i	−0.100545	+	0.174149i	−0.911909	−	0.410392i	$-0.865392\pi$
$457$	−45.9491	+	79.5862i	−0.100545	+	0.174149i	0.811364	+	0.584541i	$0.198725\pi$
$458$		0			0
$459$	−8.46575	−	14.6631i	−0.0184439	−	0.0319458i
$460$		0			0
$461$			217.149i			0.471040i	0.971870	+	0.235520i	$0.0756793\pi$
$461$			217.149i			0.471040i	−0.971870	+	0.235520i	$0.924321\pi$
$462$		0			0
$463$	−90.4223			−0.195297			−0.0976483	−	0.995221i	$-0.531132\pi$
$463$	−90.4223			−0.195297			−0.0976483	+	0.995221i	$0.531132\pi$
$464$		0			0
$465$	−150.339	+	86.7982i	−0.323309	+	0.186663i
$466$		0			0
$467$	−143.220	−	82.6880i	−0.306681	−	0.177062i	0.338760	−	0.940873i	$-0.389993\pi$
$467$	−143.220	−	82.6880i	−0.306681	−	0.177062i	−0.645440	+	0.763811i	$0.723326\pi$
$468$		0			0
$469$	40.1241	+	89.9027i	0.0855524	+	0.191690i
$470$		0			0
$471$	−24.4349	+	42.3225i	−0.0518787	+	0.0898566i
$472$		0			0
$473$	−577.603	−	1000.44i	−1.22115	−	2.11509i
$474$		0			0
$475$		−	18.7941i		−	0.0395666i
$476$		0			0
$477$	−143.874			−0.301622
$478$		0			0
$479$	318.129	−	183.672i	0.664152	−	0.383448i	−0.129705	−	0.991553i	$-0.541403\pi$
$479$	318.129	−	183.672i	0.664152	−	0.383448i	0.793857	+	0.608104i	$0.208070\pi$
$480$		0			0
$481$	277.304	+	160.102i	0.576516	+	0.332852i
$482$		0			0
$483$	49.2959	−	473.107i	0.102062	−	0.979519i
$484$		0			0
$485$	−435.122	+	753.653i	−0.897159	+	1.55392i
$486$		0			0
$487$	−198.591	−	343.970i	−0.407784	−	0.706303i	0.586857	−	0.809691i	$-0.300365\pi$
$487$	−198.591	−	343.970i	−0.407784	−	0.706303i	−0.994641	+	0.103388i	$0.967032\pi$
$488$		0			0
$489$			512.275i			1.04760i
$490$		0			0
$491$	202.970			0.413381			0.206691	−	0.978406i	$-0.433731\pi$
$491$	202.970			0.413381			0.206691	+	0.978406i	$0.433731\pi$
$492$		0			0
$493$	41.3149	−	23.8532i	0.0838031	−	0.0483838i
$494$		0			0
$495$	−247.781	−	143.056i	−0.500567	−	0.289003i
$496$		0			0
$497$	573.138	+	59.7187i	1.15320	+	0.120158i
$498$		0			0
$499$	−79.9083	+	138.405i	−0.160137	+	0.277365i	−0.934918	−	0.354865i	$-0.884527\pi$
$499$	−79.9083	+	138.405i	−0.160137	+	0.277365i	0.774781	+	0.632230i	$0.217860\pi$
$500$		0			0
$501$	171.174	+	296.482i	0.341665	+	0.591781i
$502$		0			0
$503$			119.831i			0.238233i	0.992880	+	0.119116i	$0.0380061\pi$
$503$			119.831i			0.238233i	−0.992880	+	0.119116i	$0.961994\pi$
$504$		0			0
$505$	−251.194			−0.497414
$506$		0			0
$507$	156.656	−	90.4456i	0.308987	−	0.178394i
$508$		0			0
$509$	27.6729	+	15.9769i	0.0543671	+	0.0313889i	0.526937	−	0.849904i	$-0.323340\pi$
$509$	27.6729	+	15.9769i	0.0543671	+	0.0313889i	−0.472570	+	0.881293i	$0.656674\pi$
$510$		0			0
$511$	−576.836	+	257.445i	−1.12884	+	0.503807i
$512$		0			0
$513$	20.9362	−	36.2626i	0.0408113	−	0.0706873i
$514$		0			0
$515$	−1.78625	−	3.09387i	−0.00346844	−	0.00600752i
$516$		0			0
$517$		−	529.687i		−	1.02454i
$518$		0			0
$519$	286.603			0.552221
$520$		0			0
$521$	25.4676	−	14.7037i	0.0488821	−	0.0282221i	−0.475360	−	0.879791i	$-0.657682\pi$
$521$	25.4676	−	14.7037i	0.0488821	−	0.0282221i	0.524242	+	0.851569i	$0.324349\pi$
$522$		0			0
$523$	708.823	+	409.239i	1.35530	+	0.782484i	0.988986	−	0.148007i	$-0.0472857\pi$
$523$	708.823	+	409.239i	1.35530	+	0.782484i	0.366316	+	0.930491i	$0.380619\pi$
$524$		0			0
$525$	−22.8916	−	16.6003i	−0.0436030	−	0.0316196i
$526$		0			0
$527$	−34.2973	+	59.4046i	−0.0650802	+	0.112722i
$528$		0			0
$529$	−505.094	−	874.849i	−0.954810	−	1.65378i
$530$		0			0
$531$			12.7771i			0.0240624i
$532$		0			0
$533$	608.972			1.14254
$534$		0			0
$535$	169.196	−	97.6856i	0.316255	−	0.182590i
$536$		0			0
$537$	−2.91919	−	1.68539i	−0.00543610	−	0.00313854i
$538$		0			0
$539$	−304.989	−	932.953i	−0.565842	−	1.73090i
$540$		0			0
$541$	−4.73933	+	8.20876i	−0.00876032	+	0.0151733i	−0.870372	−	0.492394i	$-0.836122\pi$
$541$	−4.73933	+	8.20876i	−0.00876032	+	0.0151733i	0.861612	+	0.507567i	$0.169455\pi$
$542$		0			0
$543$	6.56069	+	11.3634i	0.0120823	+	0.0209271i
$544$		0			0
$545$		−	100.704i		−	0.184779i
$546$		0			0
$547$	−390.922			−0.714666			−0.357333	−	0.933977i	$-0.616314\pi$
$547$	−390.922			−0.714666			−0.357333	+	0.933977i	$0.616314\pi$
$548$		0			0
$549$	−102.367	+	59.1015i	−0.186460	+	0.107653i
$550$		0			0
$551$	102.174	+	58.9901i	0.185434	+	0.107060i
$552$		0			0
$553$	340.599	−	469.682i	0.615912	−	0.849334i
$554$		0			0
$555$	−164.313	+	284.598i	−0.296059	+	0.512789i
$556$		0			0
$557$	153.953	+	266.655i	0.276397	+	0.478734i	0.970487	−	0.241155i	$-0.0775262\pi$
$557$	153.953	+	266.655i	0.276397	+	0.478734i	−0.694090	+	0.719889i	$0.744193\pi$
$558$		0			0
$559$		−	463.381i		−	0.828946i
$560$		0			0
$561$	−113.054			−0.201522
$562$		0			0
$563$	383.039	−	221.148i	0.680353	−	0.392802i	−0.119635	−	0.992818i	$-0.538172\pi$
$563$	383.039	−	221.148i	0.680353	−	0.392802i	0.799988	+	0.600016i	$0.204839\pi$
$564$		0			0
$565$	−134.230	−	77.4978i	−0.237575	−	0.137164i
$566$		0			0
$567$	−25.6761	−	57.5303i	−0.0452841	−	0.101464i
$568$		0			0
$569$	−341.194	+	590.965i	−0.599637	+	1.03860i	0.393237	+	0.919437i	$0.371355\pi$
$569$	−341.194	+	590.965i	−0.599637	+	1.03860i	−0.992874	+	0.119165i	$0.961978\pi$
$570$		0			0
$571$	537.999	+	931.841i	0.942205	+	1.63195i	0.761254	+	0.648454i	$0.224584\pi$
$571$	537.999	+	931.841i	0.942205	+	1.63195i	0.180951	+	0.983492i	$0.442082\pi$
$572$		0			0
$573$			94.1934i			0.164386i
$574$		0			0
$575$	−91.5002			−0.159131
$576$		0			0
$577$	376.559	−	217.406i	0.652614	−	0.376787i	−0.136843	−	0.990593i	$-0.543695\pi$
$577$	376.559	−	217.406i	0.652614	−	0.376787i	0.789457	+	0.613806i	$0.210362\pi$
$578$		0			0
$579$	264.542	+	152.733i	0.456894	+	0.263788i
$580$		0			0
$581$	72.6763	−	697.496i	0.125088	−	1.20051i
$582$		0			0
$583$	−480.332	+	831.959i	−0.823897	+	1.42703i
$584$		0			0
$585$	−57.3832	−	99.3907i	−0.0980910	−	0.169899i
$586$		0			0
$587$			661.370i			1.12670i	0.826220	+	0.563348i	$0.190487\pi$
$587$			661.370i			1.12670i	−0.826220	+	0.563348i	$0.809513\pi$
$588$		0			0
$589$	−169.638			−0.288010
$590$		0			0
$591$	−148.114	+	85.5135i	−0.250616	+	0.144693i
$592$		0			0
$593$	−463.867	−	267.814i	−0.782238	−	0.451626i	0.0549845	−	0.998487i	$-0.482489\pi$
$593$	−463.867	−	267.814i	−0.782238	−	0.451626i	−0.837223	+	0.546862i	$0.815822\pi$
$594$		0			0
$595$	108.012	+	11.2544i	0.181532	+	0.0189150i
$596$		0			0
$597$	−297.560	+	515.389i	−0.498425	+	0.863298i
$598$		0			0
$599$	−273.471	−	473.666i	−0.456546	−	0.790761i	0.542229	−	0.840231i	$-0.317580\pi$
$599$	−273.471	−	473.666i	−0.456546	−	0.790761i	−0.998776	+	0.0494691i	$0.984247\pi$
$600$		0			0
$601$			643.284i			1.07036i	0.844739	+	0.535178i	$0.179755\pi$
$601$			643.284i			1.07036i	−0.844739	+	0.535178i	$0.820245\pi$
$602$		0			0
$603$	42.1929			0.0699717
$604$		0			0
$605$	−1155.56	+	667.162i	−1.91001	+	1.10275i
$606$		0			0
$607$	683.386	+	394.553i	1.12584	+	0.650005i	0.942886	−	0.333116i	$-0.108100\pi$
$607$	683.386	+	394.553i	1.12584	+	0.650005i	0.182955	+	0.983121i	$0.441434\pi$
$608$		0			0
$609$	162.098	−	72.3453i	0.266171	−	0.118794i
$610$		0			0
$611$	106.235	−	184.005i	0.173871	−	0.301153i
$612$		0			0
$613$	−529.746	−	917.546i	−0.864185	−	1.49681i	−0.867854	−	0.496820i	$-0.834501\pi$
$613$	−529.746	−	917.546i	−0.864185	−	1.49681i	0.00366824	−	0.999993i	$-0.498832\pi$
$614$		0			0
$615$			624.989i			1.01624i
$616$		0			0
$617$	−459.828			−0.745265			−0.372632	−	0.927979i	$-0.621545\pi$
$617$	−459.828			−0.745265			−0.372632	+	0.927979i	$0.621545\pi$
$618$		0			0
$619$	−581.867	+	335.941i	−0.940011	+	0.542716i	−0.889964	−	0.456031i	$-0.849271\pi$
$619$	−581.867	+	335.941i	−0.940011	+	0.542716i	−0.0500475	+	0.998747i	$0.515937\pi$
$620$		0			0
$621$	−176.546	−	101.929i	−0.284293	−	0.164137i
$622$		0			0
$623$	673.693	+	488.543i	1.08137	+	0.784178i
$624$		0			0
$625$	280.627	−	486.060i	0.449003	−	0.777697i
$626$		0			0
$627$	−139.794	−	242.130i	−0.222957	−	0.386173i
$628$		0			0
$629$			129.852i			0.206443i
$630$		0			0
$631$	5.44649			0.00863152			0.00431576	−	0.999991i	$-0.498626\pi$
$631$	5.44649			0.00863152			0.00431576	+	0.999991i	$0.498626\pi$
$632$		0			0
$633$	−276.825	+	159.825i	−0.437323	+	0.252488i
$634$		0			0
$635$	−745.475	−	430.400i	−1.17398	−	0.677796i
$636$		0			0
$637$	81.1666	−	385.261i	0.127420	−	0.604806i
$638$		0			0
$639$	123.480	−	213.874i	0.193240	−	0.334701i
$640$		0			0
$641$	414.375	+	717.718i	0.646450	+	1.11969i	0.983964	+	0.178365i	$0.0570806\pi$
$641$	414.375	+	717.718i	0.646450	+	1.11969i	−0.337514	+	0.941321i	$0.609586\pi$
$642$		0			0
$643$		−	1003.09i		−	1.56001i	−0.625773	−	0.780005i	$-0.715216\pi$
$643$		−	1003.09i		−	1.56001i	0.625773	−	0.780005i	$-0.284784\pi$
$644$		0			0
$645$	475.568			0.737315
$646$		0			0
$647$	−167.179	+	96.5208i	−0.258391	+	0.149182i	−0.623600	−	0.781743i	$-0.714331\pi$
$647$	−167.179	+	96.5208i	−0.258391	+	0.149182i	0.365209	+	0.930925i	$0.380997\pi$
$648$		0			0
$649$	73.8846	+	42.6573i	0.113844	+	0.0657277i
$650$		0			0
$651$	−149.836	+	206.621i	−0.230163	+	0.317391i
$652$		0			0
$653$	−261.555	+	453.027i	−0.400544	+	0.693763i	−0.993792	−	0.111257i	$-0.964512\pi$
$653$	−261.555	+	453.027i	−0.400544	+	0.693763i	0.593247	+	0.805020i	$0.297846\pi$
$654$		0			0
$655$	−393.667	−	681.851i	−0.601018	−	1.04099i
$656$		0			0
$657$			270.720i			0.412054i
$658$		0			0
$659$	−1140.04			−1.72995			−0.864976	−	0.501813i	$-0.832666\pi$
$659$	−1140.04			−1.72995			−0.864976	+	0.501813i	$0.832666\pi$
$660$		0			0
$661$	186.400	−	107.618i	0.281997	−	0.162811i	−0.352330	−	0.935876i	$-0.614610\pi$
$661$	186.400	−	107.618i	0.281997	−	0.162811i	0.634327	+	0.773065i	$0.281277\pi$
$662$		0			0
$663$	−39.2731	−	22.6743i	−0.0592354	−	0.0341996i
$664$		0			0
$665$	109.455	+	245.248i	0.164595	+	0.368793i
$666$		0			0
$667$	287.196	−	497.439i	0.430579	−	0.745785i
$668$		0			0
$669$	−174.880	−	302.901i	−0.261405	−	0.452767i
$670$		0			0
$671$			789.257i			1.17624i
$672$		0			0
$673$	981.407			1.45826			0.729128	−	0.684377i	$-0.239926\pi$
$673$	981.407			1.45826			0.729128	+	0.684377i	$0.239926\pi$
$674$		0			0
$675$	−10.4951	+	6.05938i	−0.0155484	+	0.00897685i
$676$		0			0
$677$	1118.63	+	645.842i	1.65234	+	0.953976i	0.976109	+	0.217282i	$0.0697191\pi$
$677$	1118.63	+	645.842i	1.65234	+	0.953976i	0.676226	+	0.736694i	$0.263614\pi$
$678$		0			0
$679$	−132.599	+	1272.59i	−0.195286	+	1.87422i
$680$		0			0
$681$	−321.629	+	557.078i	−0.472289	+	0.818029i
$682$		0			0
$683$	−46.1542	−	79.9415i	−0.0675758	−	0.117045i	0.830258	−	0.557379i	$-0.188193\pi$
$683$	−46.1542	−	79.9415i	−0.0675758	−	0.117045i	−0.897834	+	0.440335i	$0.854860\pi$
$684$		0			0
$685$		−	483.454i		−	0.705773i
$686$		0			0
$687$	633.758			0.922501
$688$		0			0
$689$	−333.719	+	192.672i	−0.484352	+	0.279641i
$690$		0			0
$691$	130.766	+	75.4977i	0.189241	+	0.109259i	0.591627	−	0.806212i	$-0.298486\pi$
$691$	130.766	+	75.4977i	0.189241	+	0.109259i	−0.402386	+	0.915470i	$0.631819\pi$
$692$		0			0
$693$	−418.395	−	43.5950i	−0.603744	−	0.0629077i
$694$		0			0
$695$	−164.535	+	284.983i	−0.236741	+	0.410047i
$696$		0			0
$697$	123.478	+	213.871i	0.177157	+	0.306845i
$698$		0			0
$699$			563.090i			0.805565i
$700$		0			0
$701$	518.111			0.739103			0.369551	−	0.929210i	$-0.379511\pi$
$701$	518.111			0.739103			0.369551	+	0.929210i	$0.379511\pi$
$702$		0			0
$703$	−278.108	+	160.566i	−0.395601	+	0.228401i
$704$		0			0
$705$	188.844	+	109.029i	0.267864	+	0.154651i
$706$		0			0
$707$	−337.256	+	150.519i	−0.477024	+	0.212898i
$708$		0			0
$709$	−183.389	+	317.638i	−0.258658	+	0.448009i	−0.965883	−	0.258980i	$-0.916614\pi$
$709$	−183.389	+	317.638i	−0.258658	+	0.448009i	0.707225	+	0.706989i	$0.249947\pi$
$710$		0			0
$711$	−124.324	−	215.336i	−0.174858	−	0.302864i
$712$		0			0
$713$			825.889i			1.15833i
$714$		0			0
$715$	−766.312			−1.07176
$716$		0			0
$717$	393.518	−	227.198i	0.548840	−	0.316873i
$718$		0			0
$719$	−940.161	−	542.802i	−1.30760	−	0.754940i	−0.325901	−	0.945404i	$-0.605668\pi$
$719$	−940.161	−	542.802i	−1.30760	−	0.754940i	−0.981694	+	0.190464i	$0.939001\pi$
$720$		0			0
$721$	−4.25213	−	3.08352i	−0.00589754	−	0.00427673i
$722$		0			0
$723$	−12.5187	+	21.6829i	−0.0173149	+	0.0299902i
$724$		0			0
$725$	−17.0730	−	29.5712i	−0.0235489	−	0.0407879i
$726$		0			0
$727$		−	964.388i		−	1.32653i	−0.748384	−	0.663265i	$-0.769170\pi$
$727$		−	964.388i		−	1.32653i	0.748384	−	0.663265i	$-0.230830\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	162.739	−	93.9576i	0.222626	−	0.128533i
$732$		0			0
$733$	−897.332	−	518.075i	−1.22419	−	0.706787i	−0.258382	−	0.966043i	$-0.583189\pi$
$733$	−897.332	−	518.075i	−1.22419	−	0.706787i	−0.965809	+	0.259256i	$0.916523\pi$
$734$		0			0
$735$	395.394	+	83.3014i	0.537951	+	0.113335i
$736$		0			0
$737$	140.864	−	243.983i	0.191131	−	0.331049i
$738$		0			0
$739$	90.8990	+	157.442i	0.123003	+	0.213047i	0.920950	−	0.389680i	$-0.127414\pi$
$739$	90.8990	+	157.442i	0.123003	+	0.213047i	−0.797948	+	0.602727i	$0.794081\pi$
$740$		0			0
$741$		−	112.149i		−	0.151349i
$742$		0			0
$743$	756.385			1.01801			0.509007	−	0.860762i	$-0.330013\pi$
$743$	756.385			1.01801			0.509007	+	0.860762i	$0.330013\pi$
$744$		0			0
$745$	989.968	−	571.558i	1.32882	−	0.767192i
$746$		0			0
$747$	−260.280	−	150.273i	−0.348433	−	0.201168i
$748$		0			0
$749$	168.630	−	232.539i	0.225141	−	0.310466i
$750$		0			0
$751$	590.565	−	1022.89i	0.786372	−	1.36204i	−0.141804	−	0.989895i	$-0.545290\pi$
$751$	590.565	−	1022.89i	0.786372	−	1.36204i	0.928176	−	0.372141i	$-0.121376\pi$
$752$		0			0
$753$	−76.2985	−	132.153i	−0.101326	−	0.175502i
$754$		0			0
$755$			1214.82i			1.60903i
$756$		0			0
$757$	519.548			0.686325			0.343163	−	0.939276i	$-0.388502\pi$
$757$	519.548			0.686325			0.343163	+	0.939276i	$0.388502\pi$
$758$		0			0
$759$	−1178.82	+	680.594i	−1.55313	+	0.896698i
$760$		0			0
$761$	−194.150	−	112.093i	−0.255125	−	0.147296i	0.366984	−	0.930227i	$-0.380390\pi$
$761$	−194.150	−	112.093i	−0.255125	−	0.147296i	−0.622109	+	0.782931i	$0.713724\pi$
$762$		0			0
$763$	−60.3435	−	135.207i	−0.0790872	−	0.177204i
$764$		0			0
$765$	23.2707	−	40.3060i	0.0304192	−	0.0526876i
$766$		0			0
$767$	17.1108	+	29.6368i	0.0223088	+	0.0386399i
$768$		0			0
$769$		−	1323.88i		−	1.72155i	−0.508982	−	0.860777i	$-0.669978\pi$
$769$		−	1323.88i		−	1.72155i	0.508982	−	0.860777i	$-0.330022\pi$
$770$		0			0
$771$	96.3511			0.124969
$772$		0			0
$773$	−344.501	+	198.898i	−0.445668	+	0.257306i	−0.705999	−	0.708213i	$-0.749502\pi$
$773$	−344.501	+	198.898i	−0.445668	+	0.257306i	0.260331	+	0.965519i	$0.416168\pi$
$774$		0			0
$775$	42.5189	+	24.5483i	0.0548632	+	0.0316753i
$776$		0			0
$777$	−50.0727	+	480.563i	−0.0644436	+	0.618485i
$778$		0			0
$779$	−305.368	+	528.913i	−0.392000	+	0.678964i
$780$		0			0
$781$	−824.494	−	1428.07i	−1.05569	−	1.82851i
$782$		0			0
$783$		−	76.0755i		−	0.0971590i
$784$		0			0
$785$	−134.333			−0.171125
$786$		0			0
$787$	−646.379	+	373.187i	−0.821320	+	0.474189i	−0.850871	−	0.525374i	$-0.823925\pi$
$787$	−646.379	+	373.187i	−0.821320	+	0.474189i	0.0295516	+	0.999563i	$0.490592\pi$
$788$		0			0
$789$	−660.450	−	381.311i	−0.837072	−	0.483284i
$790$		0			0
$791$	−226.657	−	23.6167i	−0.286544	−	0.0298568i
$792$		0			0
$793$	−158.295	+	274.175i	−0.199615	+	0.345744i
$794$		0			0
$795$	−197.740	−	342.496i	−0.248730	−	0.430812i
$796$		0			0
$797$		−	159.247i		−	0.199808i	−0.994997	−	0.0999040i	$-0.968146\pi$
$797$		−	159.247i		−	0.199808i	0.994997	−	0.0999040i	$-0.0318536\pi$
$798$		0			0
$799$	86.1632			0.107839
$800$		0			0
$801$	308.870	−	178.326i	0.385605	−	0.222629i
$802$		0			0
$803$	1565.45	+	903.816i	1.94951	+	1.12555i
$804$		0			0
$805$	1194.00	−	532.889i	1.48323	−	0.661974i
$806$		0			0
$807$	69.0223	−	119.550i	0.0855295	−	0.148141i
$808$		0			0
$809$	535.657	+	927.785i	0.662122	+	1.14683i	0.980057	+	0.198717i	$0.0636774\pi$
$809$	535.657	+	927.785i	0.662122	+	1.14683i	−0.317935	+	0.948113i	$0.602989\pi$
$810$		0			0
$811$			466.486i			0.575199i	0.957751	+	0.287599i	$0.0928572\pi$
$811$			466.486i			0.575199i	−0.957751	+	0.287599i	$0.907143\pi$
$812$		0			0
$813$	92.8302			0.114182
$814$		0			0
$815$	−1219.49	+	704.072i	−1.49630	+	0.863892i
$816$		0			0
$817$	402.462	+	232.362i	0.492610	+	0.284409i
$818$		0			0
$819$	−136.600	−	99.0581i	−0.166788	−	0.120950i
$820$		0			0
$821$	743.425	−	1287.65i	0.905512	−	1.56839i	0.0852835	−	0.996357i	$-0.472820\pi$
$821$	743.425	−	1287.65i	0.905512	−	1.56839i	0.820229	−	0.572036i	$-0.193846\pi$
$822$		0			0
$823$	−430.852	−	746.258i	−0.523514	−	0.906753i	−0.999625	−	0.0273681i	$-0.991287\pi$
$823$	−430.852	−	746.258i	−0.523514	−	0.906753i	0.476111	−	0.879385i	$-0.342046\pi$
$824$		0			0
$825$			80.9186i			0.0980831i
$826$		0			0
$827$	621.169			0.751111			0.375556	−	0.926800i	$-0.377452\pi$
$827$	621.169			0.751111			0.375556	+	0.926800i	$0.377452\pi$
$828$		0			0
$829$	574.498	−	331.687i	0.693001	−	0.400105i	−0.111734	−	0.993738i	$-0.535640\pi$
$829$	574.498	−	331.687i	0.693001	−	0.400105i	0.804735	+	0.593634i	$0.202307\pi$
$830$		0			0
$831$	−558.500	−	322.450i	−0.672082	−	0.388027i
$832$		0			0
$833$	151.762	−	49.6120i	0.182187	−	0.0595582i
$834$		0			0
$835$	−470.524	+	814.971i	−0.563501	+	0.976013i
$836$		0			0
$837$	54.6925	+	94.7302i	0.0653435	+	0.113178i
$838$		0			0
$839$		−	543.556i		−	0.647862i	−0.946081	−	0.323931i	$-0.894996\pi$
$839$		−	543.556i		−	0.647862i	0.946081	−	0.323931i	$-0.105004\pi$
$840$		0			0
$841$	−626.649			−0.745124
$842$		0			0
$843$	18.2110	−	10.5141i	0.0216026	−	0.0124723i
$844$		0			0
$845$	430.618	+	248.617i	0.509607	+	0.294222i
$846$		0			0
$847$	−1151.69	+	1588.17i	−1.35973	+	1.87505i
$848$		0			0
$849$	115.266	−	199.646i	0.135766	−	0.235154i
$850$		0			0
$851$	781.722	+	1353.98i	0.918592	+	1.59105i
$852$		0			0
$853$			712.546i			0.835341i	0.908599	+	0.417670i	$0.137153\pi$
$853$			712.546i			0.835341i	−0.908599	+	0.417670i	$0.862847\pi$
$854$		0			0
$855$	115.099			0.134619
$856$		0			0
$857$	−173.885	+	100.393i	−0.202900	+	0.117144i	−0.598008	−	0.801490i	$-0.704041\pi$
$857$	−173.885	+	100.393i	−0.202900	+	0.117144i	0.395107	+	0.918635i	$0.370707\pi$
$858$		0			0
$859$	−765.085	−	441.722i	−0.890669	−	0.514228i	−0.0165077	−	0.999864i	$-0.505255\pi$
$859$	−765.085	−	441.722i	−0.890669	−	0.514228i	−0.874161	+	0.485636i	$0.838588\pi$
$860$		0			0
$861$	374.502	+	839.117i	0.434962	+	0.974584i
$862$		0			0
$863$	−196.473	+	340.302i	−0.227663	+	0.394324i	−0.957115	−	0.289708i	$-0.906442\pi$
$863$	−196.473	+	340.302i	−0.227663	+	0.394324i	0.729452	+	0.684032i	$0.239775\pi$
$864$		0			0
$865$	393.907	+	682.267i	0.455384	+	0.788748i
$866$		0			0
$867$			482.172i			0.556139i
$868$		0			0
$869$	−1660.26			−1.91054
$870$		0			0
$871$	97.8675	−	56.5038i	0.112362	−	0.0648724i
$872$		0			0
$873$	474.885	+	274.175i	0.543969	+	0.314061i
$874$		0			0
$875$	94.4026	−	906.010i	0.107889	−	1.03544i
$876$		0			0
$877$	106.581	−	184.604i	0.121529	−	0.210494i	−0.798842	−	0.601541i	$-0.794554\pi$
$877$	106.581	−	184.604i	0.121529	−	0.210494i	0.920371	+	0.391047i	$0.127887\pi$
$878$		0			0
$879$	−270.595	−	468.685i	−0.307844	−	0.533202i
$880$		0			0
$881$			595.779i			0.676254i	0.941101	+	0.338127i	$0.109793\pi$
$881$			595.779i			0.676254i	−0.941101	+	0.338127i	$0.890207\pi$
$882$		0			0
$883$	−973.948			−1.10300			−0.551500	−	0.834175i	$-0.685944\pi$
$883$	−973.948			−1.10300			−0.551500	+	0.834175i	$0.685944\pi$
$884$		0			0
$885$	−30.4163	+	17.5609i	−0.0343687	+	0.0198428i
$886$		0			0
$887$	−668.226	−	385.801i	−0.753356	−	0.434950i	0.0735495	−	0.997292i	$-0.476567\pi$
$887$	−668.226	−	385.801i	−0.753356	−	0.434950i	−0.826905	+	0.562342i	$0.809901\pi$
$888$		0			0
$889$	−1258.79	−	131.160i	−1.41596	−	0.147537i
$890$		0			0
$891$	−90.1413	+	156.129i	−0.101169	+	0.175229i
$892$		0			0
$893$	106.543	+	184.538i	0.119309	+	0.206649i
$894$		0			0
$895$		−	9.26563i		−	0.0103527i
$896$		0			0
$897$	−546.005			−0.608701
$898$		0			0
$899$	−266.913	+	154.102i	−0.296900	+	0.171415i
$900$		0			0
$901$	−135.333	−	78.1347i	−0.150203	−	0.0867199i
$902$		0			0
$903$	638.503	−	284.968i	0.707091	−	0.315579i
$904$		0			0
$905$	−18.0340	+	31.2359i	−0.0199271	+	0.0345148i
$906$		0			0
$907$	720.104	+	1247.26i	0.793941	+	1.37515i	0.923510	+	0.383575i	$0.125307\pi$
$907$	720.104	+	1247.26i	0.793941	+	1.37515i	−0.129569	+	0.991570i	$0.541359\pi$
$908$		0			0
$909$			158.280i			0.174125i
$910$		0			0
$911$	351.853			0.386227			0.193114	−	0.981176i	$-0.438141\pi$
$911$	351.853			0.386227			0.193114	+	0.981176i	$0.438141\pi$
$912$		0			0
$913$	−1737.92	+	1003.39i	−1.90353	+	1.09900i
$914$		0			0
$915$	−281.386	−	162.458i	−0.307526	−	0.177550i
$916$		0			0
$917$	−937.116	−	679.569i	−1.02194	−	0.741079i
$918$		0			0
$919$	−311.224	+	539.056i	−0.338655	+	0.586568i	−0.984180	−	0.177171i	$-0.943305\pi$
$919$	−311.224	+	539.056i	−0.338655	+	0.586568i	0.645525	+	0.763739i	$0.276639\pi$
$920$		0			0
$921$	64.2463	+	111.278i	0.0697571	+	0.120823i
$922$		0			0
$923$		−	661.448i		−	0.716628i
$924$		0			0
$925$	92.9421			0.100478
$926$		0			0
$927$	−1.94948	+	1.12553i	−0.00210300	+	0.00121417i
$928$		0			0
$929$	1342.02	+	774.818i	1.44459	+	0.834035i	0.998151	−	0.0607792i	$-0.0193585\pi$
$929$	1342.02	+	774.818i	1.44459	+	0.834035i	0.446439	+	0.894814i	$0.352692\pi$
$930$		0			0
$931$	293.912	+	263.685i	0.315695	+	0.283228i
$932$		0			0
$933$	−291.157	+	504.298i	−0.312065	+	0.540512i
$934$		0			0
$935$	−155.382	−	269.129i	−0.166183	−	0.287838i
$936$		0			0
$937$			430.581i			0.459532i	0.973246	+	0.229766i	$0.0737960\pi$
$937$			430.581i			0.459532i	−0.973246	+	0.229766i	$0.926204\pi$
$938$		0			0
$939$	612.963			0.652783
$940$		0			0
$941$	−979.433	+	565.476i	−1.04084	+	0.600931i	−0.920072	−	0.391750i	$-0.871870\pi$
$941$	−979.433	+	565.476i	−1.04084	+	0.600931i	−0.120771	+	0.992680i	$0.538537\pi$
$942$		0			0
$943$	2575.04	+	1486.70i	2.73069	+	1.57656i
$944$		0			0
$945$	101.664	−	140.193i	0.107580	−	0.148352i
$946$		0			0
$947$	−691.847	+	1198.31i	−0.730568	+	1.26538i	0.226073	+	0.974110i	$0.427411\pi$
$947$	−691.847	+	1198.31i	−0.730568	+	1.26538i	−0.956641	+	0.291270i	$0.905922\pi$
$948$		0			0
$949$	362.542	+	627.941i	0.382025	+	0.661687i
$950$		0			0
$951$			916.029i			0.963227i
$952$		0			0
$953$	800.947			0.840448			0.420224	−	0.907420i	$-0.361952\pi$
$953$	800.947			0.840448			0.420224	+	0.907420i	$0.361952\pi$
$954$		0			0
$955$	−224.231	+	129.460i	−0.234796	+	0.135560i
$956$		0			0
$957$	−439.912	−	253.983i	−0.459678	−	0.265395i
$958$		0			0
$959$	−289.693	−	649.091i	−0.302078	−	0.676841i
$960$		0			0
$961$	−258.925	+	448.471i	−0.269432	+	0.466671i
$962$		0			0
$963$	−61.5528	−	106.613i	−0.0639177	−	0.110709i
$964$		0			0
$965$			839.667i			0.870121i
$966$		0			0
$967$	−285.981			−0.295740			−0.147870	−	0.989007i	$-0.547242\pi$
$967$	−285.981			−0.295740			−0.147870	+	0.989007i	$0.547242\pi$
$968$		0			0
$969$	39.3869	−	22.7400i	0.0406469	−	0.0234675i
$970$		0			0
$971$	−1465.09	−	845.873i	−1.50885	−	0.871136i	−0.999947	−	0.0103123i	$-0.996717\pi$
$971$	−1465.09	−	845.873i	−1.50885	−	0.871136i	−0.508904	−	0.860823i	$-0.669949\pi$
$972$		0			0
$973$	−50.1404	+	481.213i	−0.0515318	+	0.494566i
$974$		0			0
$975$	−16.2292	+	28.1098i	−0.0166453	+	0.0288305i
$976$		0			0
$977$	−726.742	−	1258.75i	−0.743851	−	1.28839i	−0.950730	−	0.310021i	$-0.899664\pi$
$977$	−726.742	−	1258.75i	−0.743851	−	1.28839i	0.206879	−	0.978366i	$-0.433669\pi$
$978$		0			0
$979$		−	2381.41i		−	2.43250i
$980$		0			0
$981$	−63.4549			−0.0646839
$982$		0			0
$983$	−269.568	+	155.635i	−0.274230	+	0.158327i	−0.630808	−	0.775939i	$-0.717277\pi$
$983$	−269.568	+	155.635i	−0.274230	+	0.158327i	0.356579	+	0.934265i	$0.383943\pi$
$984$		0			0
$985$	−407.136	−	235.060i	−0.413336	−	0.238639i
$986$		0			0
$987$	318.876	+	33.2256i	0.323076	+	0.0336632i
$988$		0			0
$989$	1131.26	−	1959.41i	1.14385	−	1.98120i
$990$		0			0
$991$	384.739	+	666.388i	0.388234	+	0.672440i	0.992212	−	0.124560i	$-0.0397521\pi$
$991$	384.739	+	666.388i	0.388234	+	0.672440i	−0.603979	+	0.797001i	$0.706419\pi$
$992$		0			0
$993$		−	417.461i		−	0.420404i
$994$		0			0
$995$	−1635.87			−1.64409
$996$		0			0
$997$	1289.12	−	744.274i	1.29300	−	0.746514i	0.313815	−	0.949484i	$-0.398393\pi$
$997$	1289.12	−	744.274i	1.29300	−	0.746514i	0.979185	+	0.202971i	$0.0650596\pi$
$998$		0			0
$999$	179.328	+	103.535i	0.179508	+	0.103639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.3.bh.c.481.7	yes	16
4.3	odd	2		672.3.bh.a.481.7	✓	16
7.3	odd	6	inner	672.3.bh.c.577.7	yes	16
28.3	even	6		672.3.bh.a.577.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.3.bh.a.481.7	✓	16	4.3	odd	2
672.3.bh.a.577.7	yes	16	28.3	even	6
672.3.bh.c.481.7	yes	16	1.1	even	1	trivial
672.3.bh.c.577.7	yes	16	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(4.12320 + 2.38053i) q^{5} +(6.96231 + 0.725445i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-10.0157 - 17.3477i) q^{11} -8.03507i q^{13} +8.24641 q^{15} +(2.82192 - 1.62923i) q^{17} +(6.97874 + 4.02918i) q^{19} +(11.0717 - 4.94137i) q^{21} +(19.6162 - 33.9763i) q^{23} +(-1.16613 - 2.01979i) q^{25} -5.19615i q^{27} +14.6407 q^{29} +(-18.2308 + 10.5256i) q^{31} +(-30.0471 - 17.3477i) q^{33} +(26.9801 + 19.5652i) q^{35} +(-19.9254 + 34.5117i) q^{37} +(-6.95858 - 12.0526i) q^{39} +75.7892i q^{41} +57.6698 q^{43} +(12.3696 - 7.14160i) q^{45} +(22.9002 + 13.2214i) q^{47} +(47.9475 + 10.1015i) q^{49} +(2.82192 - 4.88770i) q^{51} +(-23.9789 - 41.5327i) q^{53} -95.3709i q^{55} +13.9575 q^{57} +(-3.68843 + 2.12952i) q^{59} +(-34.1223 - 19.7005i) q^{61} +(12.3282 - 17.0004i) q^{63} +(19.1277 - 33.1302i) q^{65} +(7.03215 + 12.1800i) q^{67} -67.9527i q^{69} +82.3201 q^{71} +(-78.1500 + 45.1199i) q^{73} +(-3.49838 - 2.01979i) q^{75} +(-57.1476 - 128.046i) q^{77} +(41.4414 - 71.7787i) q^{79} +(-4.50000 - 7.79423i) q^{81} -100.182i q^{83} +15.5138 q^{85} +(21.9611 - 12.6792i) q^{87} +(102.957 + 59.4420i) q^{89} +(5.82900 - 55.9426i) q^{91} +(-18.2308 + 31.5767i) q^{93} +(19.1832 + 33.2262i) q^{95} +182.783i q^{97} -60.0942 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 24 q^{3} + 12 q^{7} + 24 q^{9} + 12 q^{11} - 48 q^{17} + 60 q^{19} + 24 q^{21} + 48 q^{23} + 52 q^{25} - 64 q^{29} + 60 q^{31} + 36 q^{33} - 4 q^{37} - 12 q^{39} - 72 q^{43} - 120 q^{47} - 8 q^{49}+ \cdots + 72 q^{99}+O(q^{100}) \) 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

Related objects

Downloads

Learn more