LMFDB - Embedded newform 672.4.bl.b.31.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,4,Mod(31,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("672.31");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	672.bl (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$39.6492835239$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.9
Character	$\chi$	$=$	672.31
Dual form			672.4.bl.b.607.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(-4.30657 + 2.48640i) q^{5} +(-9.80887 - 15.7094i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{3} +(-4.30657 + 2.48640i) q^{5} +(-9.80887 - 15.7094i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(28.9632 + 16.7219i) q^{11} +19.9184i q^{13} +14.9184i q^{15} +(105.462 + 60.8886i) q^{17} +(0.472943 + 0.819161i) q^{19} +(-55.5276 + 1.92007i) q^{21} +(66.3780 - 38.3234i) q^{23} +(-50.1357 + 86.8375i) q^{25} -27.0000 q^{27} -41.8752 q^{29} +(94.8284 - 164.248i) q^{31} +(86.8895 - 50.1657i) q^{33} +(81.3025 + 43.2649i) q^{35} +(-85.6165 - 148.292i) q^{37} +(51.7494 + 29.8776i) q^{39} -496.810i q^{41} -165.386i q^{43} +(38.7591 + 22.3776i) q^{45} +(-94.3560 - 163.429i) q^{47} +(-150.572 + 308.184i) q^{49} +(316.386 - 182.666i) q^{51} +(209.370 - 362.640i) q^{53} -166.309 q^{55} +2.83766 q^{57} +(-60.1623 + 104.204i) q^{59} +(319.617 - 184.531i) q^{61} +(-78.3029 + 147.145i) q^{63} +(-49.5250 - 85.7798i) q^{65} +(822.793 + 475.040i) q^{67} -229.940i q^{69} -467.087i q^{71} +(-388.860 - 224.508i) q^{73} +(150.407 + 260.512i) q^{75} +(-21.4048 - 619.018i) q^{77} +(788.392 - 455.178i) q^{79} +(-40.5000 + 70.1481i) q^{81} +1052.65 q^{83} -605.573 q^{85} +(-62.8128 + 108.795i) q^{87} +(-1126.90 + 650.614i) q^{89} +(312.906 - 195.377i) q^{91} +(-284.485 - 492.743i) q^{93} +(-4.07352 - 2.35185i) q^{95} -950.793i q^{97} -300.994i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 72 q^{3} + 20 q^{7} - 216 q^{9}+O(q^{10}) $ 48 * q + 72 * q^3 + 20 * q^7 - 216 * q^9	$ 48 q + 72 q^{3} + 20 q^{7} - 216 q^{9} - 12 q^{11} + 28 q^{19} + 120 q^{21} + 684 q^{25} - 1296 q^{27} + 460 q^{31} - 36 q^{33} + 568 q^{35} + 252 q^{37} + 324 q^{39} + 280 q^{47} - 184 q^{49} - 392 q^{53} + 848 q^{55} + 168 q^{57} - 964 q^{59} - 600 q^{61} + 180 q^{63} + 280 q^{65} - 660 q^{67} + 324 q^{73} - 2052 q^{75} + 1568 q^{77} - 2652 q^{79} - 1944 q^{81} + 1336 q^{83} - 1056 q^{85} - 3004 q^{91} - 1380 q^{93} - 3984 q^{95}+O(q^{100}) $ 48 * q + 72 * q^3 + 20 * q^7 - 216 * q^9 - 12 * q^11 + 28 * q^19 + 120 * q^21 + 684 * q^25 - 1296 * q^27 + 460 * q^31 - 36 * q^33 + 568 * q^35 + 252 * q^37 + 324 * q^39 + 280 * q^47 - 184 * q^49 - 392 * q^53 + 848 * q^55 + 168 * q^57 - 964 * q^59 - 600 * q^61 + 180 * q^63 + 280 * q^65 - 660 * q^67 + 324 * q^73 - 2052 * q^75 + 1568 * q^77 - 2652 * q^79 - 1944 * q^81 + 1336 * q^83 - 1056 * q^85 - 3004 * q^91 - 1380 * q^93 - 3984 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$		0			0
$5$	−4.30657	+	2.48640i	−0.385191	+	0.222390i	−0.680074	−	0.733143i	$-0.738053\pi$
$5$	−4.30657	+	2.48640i	−0.385191	+	0.222390i	0.294883	+	0.955533i	$0.404719\pi$
$6$		0			0
$7$	−9.80887	−	15.7094i	−0.529629	−	0.848229i
$7$	−9.80887	−	15.7094i	−0.529629	−	0.848229i
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	28.9632	+	16.7219i	0.793884	+	0.458349i	0.841328	−	0.540525i	$-0.181774\pi$
$11$	28.9632	+	16.7219i	0.793884	+	0.458349i	−0.0474439	+	0.998874i	$0.515108\pi$
$12$		0			0
$13$			19.9184i			0.424951i	0.977166	+	0.212475i	$0.0681526\pi$
$13$			19.9184i			0.424951i	−0.977166	+	0.212475i	$0.931847\pi$
$14$		0			0
$15$			14.9184i			0.256794i
$16$		0			0
$17$	105.462	+	60.8886i	1.50461	+	0.868685i	0.999986	+	0.00534432i	$0.00170116\pi$
$17$	105.462	+	60.8886i	1.50461	+	0.868685i	0.504621	+	0.863341i	$0.331632\pi$
$18$		0			0
$19$	0.472943	+	0.819161i	0.00571056	+	0.00989097i	0.868867	−	0.495046i	$-0.164849\pi$
$19$	0.472943	+	0.819161i	0.00571056	+	0.00989097i	−0.863156	+	0.504937i	$0.831516\pi$
$20$		0			0
$21$	−55.5276	+	1.92007i	−0.577005	+	0.0199521i
$22$		0			0
$23$	66.3780	−	38.3234i	0.601773	−	0.347434i	−0.167966	−	0.985793i	$-0.553720\pi$
$23$	66.3780	−	38.3234i	0.601773	−	0.347434i	0.769739	+	0.638359i	$0.220387\pi$
$24$		0			0
$25$	−50.1357	+	86.8375i	−0.401085	+	0.694700i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−41.8752			−0.268139			−0.134070	−	0.990972i	$-0.542805\pi$
$29$	−41.8752			−0.268139			−0.134070	+	0.990972i	$0.542805\pi$
$30$		0			0
$31$	94.8284	−	164.248i	0.549409	−	0.951604i	−0.448906	−	0.893579i	$-0.648186\pi$
$31$	94.8284	−	164.248i	0.549409	−	0.951604i	0.998315	−	0.0580255i	$-0.0184805\pi$
$32$		0			0
$33$	86.8895	−	50.1657i	0.458349	−	0.264628i
$34$		0			0
$35$	81.3025	+	43.2649i	0.392646	+	0.208946i
$36$		0			0
$37$	−85.6165	−	148.292i	−0.380413	−	0.658894i	0.610709	−	0.791855i	$-0.290885\pi$
$37$	−85.6165	−	148.292i	−0.380413	−	0.658894i	−0.991121	+	0.132961i	$0.957551\pi$
$38$		0			0
$39$	51.7494	+	29.8776i	0.212475	+	0.122673i
$40$		0			0
$41$		−	496.810i		−	1.89241i	−0.323572	−	0.946204i	$-0.604884\pi$
$41$		−	496.810i		−	1.89241i	0.323572	−	0.946204i	$-0.395116\pi$
$42$		0			0
$43$		−	165.386i		−	0.586538i	−0.956030	−	0.293269i	$-0.905257\pi$
$43$		−	165.386i		−	0.586538i	0.956030	−	0.293269i	$-0.0947431\pi$
$44$		0			0
$45$	38.7591	+	22.3776i	0.128397	+	0.0741301i
$46$		0			0
$47$	−94.3560	−	163.429i	−0.292835	−	0.507205i	0.681644	−	0.731684i	$-0.261265\pi$
$47$	−94.3560	−	163.429i	−0.292835	−	0.507205i	−0.974479	+	0.224479i	$0.927932\pi$
$48$		0			0
$49$	−150.572	+	308.184i	−0.438985	+	0.898494i
$50$		0			0
$51$	316.386	−	182.666i	0.868685	−	0.501536i
$52$		0			0
$53$	209.370	−	362.640i	0.542627	−	0.939857i	−0.456126	−	0.889915i	$-0.650763\pi$
$53$	209.370	−	362.640i	0.542627	−	0.939857i	0.998752	−	0.0499414i	$-0.0159035\pi$
$54$		0			0
$55$	−166.309			−0.407730
$56$		0			0
$57$	2.83766			0.00659398
$58$		0			0
$59$	−60.1623	+	104.204i	−0.132754	+	0.229936i	−0.924737	−	0.380606i	$-0.875715\pi$
$59$	−60.1623	+	104.204i	−0.132754	+	0.229936i	0.791983	+	0.610543i	$0.209049\pi$
$60$		0			0
$61$	319.617	−	184.531i	0.670864	−	0.387324i	−0.125540	−	0.992089i	$-0.540066\pi$
$61$	319.617	−	184.531i	0.670864	−	0.387324i	0.796404	+	0.604765i	$0.206733\pi$
$62$		0			0
$63$	−78.3029	+	147.145i	−0.156591	+	0.294262i
$64$		0			0
$65$	−49.5250	−	85.7798i	−0.0945049	−	0.163687i
$66$		0			0
$67$	822.793	+	475.040i	1.50030	+	0.866199i	1.00000		0.000347228i	$0.000110526\pi$
$67$	822.793	+	475.040i	1.50030	+	0.866199i	0.500301	+	0.865852i	$0.333223\pi$
$68$		0			0
$69$		−	229.940i		−	0.401182i
$70$		0			0
$71$		−	467.087i		−	0.780747i	−0.920657	−	0.390374i	$-0.872346\pi$
$71$		−	467.087i		−	0.780747i	0.920657	−	0.390374i	$-0.127654\pi$
$72$		0			0
$73$	−388.860	−	224.508i	−0.623460	−	0.359955i	0.154755	−	0.987953i	$-0.450541\pi$
$73$	−388.860	−	224.508i	−0.623460	−	0.359955i	−0.778215	+	0.627998i	$0.783875\pi$
$74$		0			0
$75$	150.407	+	260.512i	0.231567	+	0.401085i
$76$		0			0
$77$	−21.4048	−	619.018i	−0.0316793	−	0.916151i
$78$		0			0
$79$	788.392	−	455.178i	1.12280	−	0.648248i	0.180684	−	0.983541i	$-0.442169\pi$
$79$	788.392	−	455.178i	1.12280	−	0.648248i	0.942114	+	0.335294i	$0.108835\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	1052.65			1.39209			0.696043	−	0.718000i	$-0.254942\pi$
$83$	1052.65			1.39209			0.696043	+	0.718000i	$0.254942\pi$
$84$		0			0
$85$	−605.573			−0.772748
$86$		0			0
$87$	−62.8128	+	108.795i	−0.0774051	+	0.134070i
$88$		0			0
$89$	−1126.90	+	650.614i	−1.34214	+	0.774887i	−0.987122	−	0.159971i	$-0.948860\pi$
$89$	−1126.90	+	650.614i	−1.34214	+	0.774887i	−0.355022	+	0.934858i	$0.615527\pi$
$90$		0			0
$91$	312.906	−	195.377i	0.360456	−	0.225067i
$92$		0			0
$93$	−284.485	−	492.743i	−0.317201	−	0.549409i
$94$		0			0
$95$	−4.07352	−	2.35185i	−0.00439931	−	0.00253994i
$96$		0			0
$97$		−	950.793i		−	0.995242i	−0.867395	−	0.497621i	$-0.834207\pi$
$97$		−	950.793i		−	0.995242i	0.867395	−	0.497621i	$-0.165793\pi$
$98$		0			0
$99$		−	300.994i		−	0.305566i
$100$		0			0
$101$	−310.107	−	179.040i	−0.305513	−	0.176388i	0.339404	−	0.940641i	$-0.389775\pi$
$101$	−310.107	−	179.040i	−0.305513	−	0.176388i	−0.644917	+	0.764253i	$0.723108\pi$
$102$		0			0
$103$	537.408	+	930.818i	0.514101	+	0.890449i	0.999866	+	0.0163595i	$0.00520763\pi$
$103$	537.408	+	930.818i	0.514101	+	0.890449i	−0.485765	+	0.874089i	$0.661459\pi$
$104$		0			0
$105$	234.359	−	146.333i	0.217820	−	0.136006i
$106$		0			0
$107$	−381.168	+	220.068i	−0.344383	+	0.198829i	−0.662208	−	0.749320i	$-0.730381\pi$
$107$	−381.168	+	220.068i	−0.344383	+	0.198829i	0.317826	+	0.948149i	$0.397047\pi$
$108$		0			0
$109$	4.06875	−	7.04727i	0.00357537	−	0.00619272i	−0.864232	−	0.503093i	$-0.832195\pi$
$109$	4.06875	−	7.04727i	0.00357537	−	0.00619272i	0.867808	+	0.496900i	$0.165529\pi$
$110$		0			0
$111$	−513.699			−0.439263
$112$		0			0
$113$	206.244			0.171697			0.0858486	−	0.996308i	$-0.472640\pi$
$113$	206.244			0.171697			0.0858486	+	0.996308i	$0.472640\pi$
$114$		0			0
$115$	−190.574	+	330.084i	−0.154532	+	0.267657i
$116$		0			0
$117$	155.248	−	89.6327i	0.122673	−	0.0708252i
$118$		0			0
$119$	−77.9401	−	2254.00i	−0.0600400	−	1.73633i
$120$		0			0
$121$	−106.256	−	184.041i	−0.0798318	−	0.138273i
$122$		0			0
$123$	−1290.75	−	745.215i	−0.946204	−	0.546291i
$124$		0			0
$125$		−	1120.23i		−	0.801570i
$126$		0			0
$127$			139.196i			0.0972568i	0.998817	+	0.0486284i	$0.0154850\pi$
$127$			139.196i			0.0972568i	−0.998817	+	0.0486284i	$0.984515\pi$
$128$		0			0
$129$	−429.685	−	248.079i	−0.293269	−	0.169319i
$130$		0			0
$131$	358.948	+	621.717i	0.239400	+	0.414654i	0.960542	−	0.278134i	$-0.0897158\pi$
$131$	358.948	+	621.717i	0.239400	+	0.414654i	−0.721142	+	0.692787i	$0.756382\pi$
$132$		0			0
$133$	8.22951	−	15.4647i	0.00536533	−	0.0100824i
$134$		0			0
$135$	116.277	−	67.1327i	0.0741301	−	0.0427990i
$136$		0			0
$137$	961.682	−	1665.68i	0.599723	−	1.03875i	−0.393139	−	0.919479i	$-0.628611\pi$
$137$	961.682	−	1665.68i	0.599723	−	1.03875i	0.992862	−	0.119271i	$-0.0380557\pi$
$138$		0			0
$139$	2775.81			1.69382			0.846912	−	0.531733i	$-0.178459\pi$
$139$	2775.81			1.69382			0.846912	+	0.531733i	$0.178459\pi$
$140$		0			0
$141$	−566.136			−0.338136
$142$		0			0
$143$	−333.073	+	576.899i	−0.194776	+	0.337362i
$144$		0			0
$145$	180.338	−	104.118i	0.103285	−	0.0596315i
$146$		0			0
$147$	574.826	+	853.473i	0.322523	+	0.478866i
$148$		0			0
$149$	−425.524	−	737.029i	−0.233961	−	0.405233i	0.725009	−	0.688740i	$-0.241836\pi$
$149$	−425.524	−	737.029i	−0.233961	−	0.405233i	−0.958970	+	0.283506i	$0.908502\pi$
$150$		0			0
$151$	−2030.26	−	1172.17i	−1.09417	−	0.631721i	−0.159488	−	0.987200i	$-0.550984\pi$
$151$	−2030.26	−	1172.17i	−1.09417	−	0.631721i	−0.934684	+	0.355479i	$0.884318\pi$
$152$		0			0
$153$		−	1095.99i		−	0.579123i
$154$		0			0
$155$			943.124i			0.488733i
$156$		0			0
$157$	134.779	+	77.8149i	0.0685131	+	0.0395561i	0.533865	−	0.845570i	$-0.320739\pi$
$157$	134.779	+	77.8149i	0.0685131	+	0.0395561i	−0.465352	+	0.885126i	$0.654072\pi$
$158$		0			0
$159$	−628.111	−	1087.92i	−0.313286	−	0.542627i
$160$		0			0
$161$	−1253.13	−	666.851i	−0.613420	−	0.326430i
$162$		0			0
$163$	3054.30	−	1763.40i	1.46768	−	0.847364i	0.468332	−	0.883553i	$-0.344855\pi$
$163$	3054.30	−	1763.40i	1.46768	−	0.847364i	0.999345	+	0.0361888i	$0.0115218\pi$
$164$		0			0
$165$	−249.464	+	432.084i	−0.117701	+	0.203865i
$166$		0			0
$167$	−1186.63			−0.549845			−0.274923	−	0.961466i	$-0.588652\pi$
$167$	−1186.63			−0.549845			−0.274923	+	0.961466i	$0.588652\pi$
$168$		0			0
$169$	1800.26			0.819417
$170$		0			0
$171$	4.25649	−	7.37245i	0.00190352	−	0.00329699i
$172$		0			0
$173$	−1357.56	+	783.790i	−0.596611	+	0.344453i	−0.767707	−	0.640801i	$-0.778602\pi$
$173$	−1357.56	+	783.790i	−0.596611	+	0.344453i	0.171096	+	0.985254i	$0.445269\pi$
$174$		0			0
$175$	1855.94	−	64.1759i	0.801691	−	0.0277214i
$176$		0			0
$177$	180.487	+	312.613i	0.0766454	+	0.132754i
$178$		0			0
$179$	1015.61	+	586.365i	0.424082	+	0.244844i	0.696822	−	0.717244i	$-0.254597\pi$
$179$	1015.61	+	586.365i	0.424082	+	0.244844i	−0.272741	+	0.962088i	$0.587930\pi$
$180$		0			0
$181$			2290.66i			0.940682i	0.882485	+	0.470341i	$0.155869\pi$
$181$			2290.66i			0.940682i	−0.882485	+	0.470341i	$0.844131\pi$
$182$		0			0
$183$		−	1107.18i		−	0.447243i
$184$		0			0
$185$	737.427	+	425.753i	0.293063	+	0.169200i
$186$		0			0
$187$	2036.35	+	3527.05i	0.796323	+	1.37927i
$188$		0			0
$189$	264.840	+	424.154i	0.101927	+	0.163242i
$190$		0			0
$191$	−1341.10	+	774.287i	−0.508057	+	0.293327i	−0.732035	−	0.681267i	$-0.761429\pi$
$191$	−1341.10	+	774.287i	−0.508057	+	0.293327i	0.223978	+	0.974594i	$0.428096\pi$
$192$		0			0
$193$	−1641.86	+	2843.79i	−0.612352	+	1.06063i	0.378491	+	0.925605i	$0.376443\pi$
$193$	−1641.86	+	2843.79i	−0.612352	+	1.06063i	−0.990843	+	0.135020i	$0.956890\pi$
$194$		0			0
$195$	−297.150			−0.109125
$196$		0			0
$197$	4435.77			1.60424			0.802121	−	0.597161i	$-0.203705\pi$
$197$	4435.77			1.60424			0.802121	+	0.597161i	$0.203705\pi$
$198$		0			0
$199$	1389.85	−	2407.29i	0.495096	−	0.857531i	−0.504888	−	0.863185i	$-0.668466\pi$
$199$	1389.85	−	2407.29i	0.495096	−	0.857531i	0.999984	+	0.00565397i	$0.00179972\pi$
$200$		0			0
$201$	2468.38	−	1425.12i	0.866199	−	0.500100i
$202$		0			0
$203$	410.749	+	657.836i	0.142014	+	0.227443i
$204$		0			0
$205$	1235.27	+	2139.55i	0.420853	+	0.728938i
$206$		0			0
$207$	−597.402	−	344.910i	−0.200591	−	0.115811i
$208$		0			0
$209$			31.6340i			0.0104697i
$210$		0			0
$211$			69.9294i			0.0228158i	0.999935	+	0.0114079i	$0.00363133\pi$
$211$			69.9294i			0.0228158i	−0.999935	+	0.0114079i	$0.996369\pi$
$212$		0			0
$213$	−1213.53	−	700.631i	−0.390374	−	0.225382i
$214$		0			0
$215$	411.215	+	712.246i	0.130440	+	0.225929i
$216$		0			0
$217$	−3510.39	+	121.385i	−1.09816	+	0.0379729i
$218$		0			0
$219$	−1166.58	+	673.524i	−0.359955	+	0.207820i
$220$		0			0
$221$	−1212.80	+	2100.63i	−0.369149	+	0.639384i
$222$		0			0
$223$	−3043.66			−0.913985			−0.456992	−	0.889471i	$-0.651073\pi$
$223$	−3043.66			−0.913985			−0.456992	+	0.889471i	$0.651073\pi$
$224$		0			0
$225$	902.442			0.267390
$226$		0			0
$227$	1175.84	−	2036.61i	0.343802	−	0.595483i	−0.641333	−	0.767262i	$-0.721618\pi$
$227$	1175.84	−	2036.61i	0.343802	−	0.595483i	0.985135	+	0.171780i	$0.0549518\pi$
$228$		0			0
$229$	−3674.13	+	2121.26i	−1.06023	+	0.612125i	−0.925496	−	0.378756i	$-0.876352\pi$
$229$	−3674.13	+	2121.26i	−1.06023	+	0.612125i	−0.134736	+	0.990882i	$0.543019\pi$
$230$		0			0
$231$	−1640.36	−	872.916i	−0.467221	−	0.248630i
$232$		0			0
$233$	−183.707	−	318.190i	−0.0516525	−	0.0894648i	0.839043	−	0.544065i	$-0.183115\pi$
$233$	−183.707	−	318.190i	−0.0516525	−	0.0894648i	−0.890696	+	0.454600i	$0.849782\pi$
$234$		0			0
$235$	812.701	+	469.213i	0.225595	+	0.130247i
$236$		0			0
$237$		−	2731.07i		−	0.748532i
$238$		0			0
$239$		−	4210.06i		−	1.13944i	−0.821839	−	0.569720i	$-0.807052\pi$
$239$		−	4210.06i		−	1.13944i	0.821839	−	0.569720i	$-0.192948\pi$
$240$		0			0
$241$	3898.76	+	2250.95i	1.04208	+	0.601645i	0.920422	−	0.390927i	$-0.127846\pi$
$241$	3898.76	+	2250.95i	1.04208	+	0.601645i	0.121658	+	0.992572i	$0.461179\pi$
$242$		0			0
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−117.819	−	1701.59i	−0.0307231	−	0.443718i
$246$		0			0
$247$	−16.3164	+	9.42025i	−0.00420318	+	0.00242671i
$248$		0			0
$249$	1578.97	−	2734.86i	0.401860	−	0.696043i
$250$		0			0
$251$	154.212			0.0387801			0.0193900	−	0.999812i	$-0.493828\pi$
$251$	154.212			0.0387801			0.0193900	+	0.999812i	$0.493828\pi$
$252$		0			0
$253$	2563.36			0.636984
$254$		0			0
$255$	−908.359	+	1573.32i	−0.223073	+	0.386374i
$256$		0			0
$257$	327.313	−	188.974i	0.0794445	−	0.0458673i	−0.459752	−	0.888048i	$-0.652062\pi$
$257$	327.313	−	188.974i	0.0794445	−	0.0458673i	0.539196	+	0.842180i	$0.318728\pi$
$258$		0			0
$259$	−1489.78	+	2799.56i	−0.357415	+	0.671647i
$260$		0			0
$261$	188.439	+	326.385i	0.0446899	+	0.0774051i
$262$		0			0
$263$	−5621.20	−	3245.40i	−1.31794	−	0.760913i	−0.334542	−	0.942381i	$-0.608582\pi$
$263$	−5621.20	−	3245.40i	−1.31794	−	0.760913i	−0.983397	+	0.181468i	$0.941915\pi$
$264$		0			0
$265$			2082.31i			0.482699i
$266$		0			0
$267$			3903.69i			0.894763i
$268$		0			0
$269$	7386.37	+	4264.52i	1.67418	+	0.966590i	0.965256	+	0.261308i	$0.0841538\pi$
$269$	7386.37	+	4264.52i	1.67418	+	0.966590i	0.708927	+	0.705282i	$0.249180\pi$
$270$		0			0
$271$	−669.102	−	1158.92i	−0.149982	−	0.259776i	0.781239	−	0.624232i	$-0.214588\pi$
$271$	−669.102	−	1158.92i	−0.149982	−	0.259776i	−0.931220	+	0.364456i	$0.881255\pi$
$272$		0			0
$273$	−38.2446	−	1106.02i	−0.00847865	−	0.245199i
$274$		0			0
$275$	−2904.18	+	1676.73i	−0.636830	+	0.367674i
$276$		0			0
$277$	−2892.57	+	5010.08i	−0.627428	+	1.08674i	0.360638	+	0.932706i	$0.382559\pi$
$277$	−2892.57	+	5010.08i	−0.627428	+	1.08674i	−0.988066	+	0.154031i	$0.950774\pi$
$278$		0			0
$279$	−1706.91			−0.366273
$280$		0			0
$281$	−6452.76			−1.36989			−0.684945	−	0.728595i	$-0.740174\pi$
$281$	−6452.76			−1.36989			−0.684945	+	0.728595i	$0.740174\pi$
$282$		0			0
$283$	−3360.26	+	5820.14i	−0.705818	+	1.22251i	0.260577	+	0.965453i	$0.416087\pi$
$283$	−3360.26	+	5820.14i	−0.705818	+	1.22251i	−0.966395	+	0.257060i	$0.917246\pi$
$284$		0			0
$285$	−12.2206	+	7.05555i	−0.00253994	+	0.00146644i
$286$		0			0
$287$	−7804.60	+	4873.15i	−1.60520	+	1.00227i
$288$		0			0
$289$	4958.34	+	8588.09i	1.00923	+	1.74803i
$290$		0			0
$291$	−2470.23	−	1426.19i	−0.497621	−	0.287301i
$292$		0			0
$293$		−	5406.60i		−	1.07801i	−0.842303	−	0.539005i	$-0.818801\pi$
$293$		−	5406.60i		−	1.07801i	0.842303	−	0.539005i	$-0.181199\pi$
$294$		0			0
$295$		−	598.350i		−	0.118092i
$296$		0			0
$297$	−782.006	−	451.491i	−0.152783	−	0.0882094i
$298$		0			0
$299$	763.339	+	1322.14i	0.147642	+	0.255724i
$300$		0			0
$301$	−2598.12	+	1622.25i	−0.497518	+	0.310648i
$302$		0			0
$303$	−930.320	+	537.121i	−0.176388	+	0.101838i
$304$		0			0
$305$	−917.634	+	1589.39i	−0.172274	+	0.298387i
$306$		0			0
$307$	767.110			0.142610			0.0713050	−	0.997455i	$-0.477284\pi$
$307$	767.110			0.142610			0.0713050	+	0.997455i	$0.477284\pi$
$308$		0			0
$309$	3224.45			0.593633
$310$		0			0
$311$	−3962.67	+	6863.54i	−0.722515	+	1.25143i	0.237473	+	0.971394i	$0.423681\pi$
$311$	−3962.67	+	6863.54i	−0.722515	+	1.25143i	−0.959989	+	0.280039i	$0.909653\pi$
$312$		0			0
$313$	−1659.12	+	957.891i	−0.299613	+	0.172982i	−0.642269	−	0.766479i	$-0.722007\pi$
$313$	−1659.12	+	957.891i	−0.299613	+	0.172982i	0.342656	+	0.939461i	$0.388673\pi$
$314$		0			0
$315$	−28.6443	−	828.382i	−0.00512357	−	0.148172i
$316$		0			0
$317$	−399.219	−	691.468i	−0.0707331	−	0.122513i	0.828490	−	0.560004i	$-0.189201\pi$
$317$	−399.219	−	691.468i	−0.0707331	−	0.122513i	−0.899223	+	0.437491i	$0.855867\pi$
$318$		0			0
$319$	−1212.84	−	700.233i	−0.212871	−	0.122901i
$320$		0			0
$321$			1320.41i			0.229588i
$322$		0			0
$323$			115.187i			0.0198427i
$324$		0			0
$325$	−1729.66	−	998.620i	−0.295213	−	0.170442i
$326$		0			0
$327$	−12.2062	−	21.1418i	−0.00206424	−	0.00357537i
$328$		0			0
$329$	−1641.85	+	3085.34i	−0.275132	+	0.517021i
$330$		0			0
$331$	7373.90	−	4257.33i	1.22449	−	0.706960i	0.258619	−	0.965980i	$-0.416733\pi$
$331$	7373.90	−	4257.33i	1.22449	−	0.706960i	0.965872	+	0.259020i	$0.0833994\pi$
$332$		0			0
$333$	−770.549	+	1334.63i	−0.126804	+	0.219631i
$334$		0			0
$335$	−4724.55			−0.770537
$336$		0			0
$337$	−1742.77			−0.281706			−0.140853	−	0.990031i	$-0.544984\pi$
$337$	−1742.77			−0.281706			−0.140853	+	0.990031i	$0.544984\pi$
$338$		0			0
$339$	309.366	−	535.837i	0.0495647	−	0.0858486i
$340$		0			0
$341$	5493.06	−	3171.42i	0.872334	−	0.503643i
$342$		0			0
$343$	6318.33	−	657.535i	0.994629	−	0.103509i
$344$		0			0
$345$	571.723	+	990.253i	0.0892189	+	0.154532i
$346$		0			0
$347$	−8128.44	−	4692.95i	−1.25751	−	0.726026i	−0.284923	−	0.958550i	$-0.591968\pi$
$347$	−8128.44	−	4692.95i	−1.25751	−	0.726026i	−0.972591	+	0.232524i	$0.925301\pi$
$348$		0			0
$349$			9429.62i			1.44629i	0.690695	+	0.723146i	$0.257305\pi$
$349$			9429.62i			1.44629i	−0.690695	+	0.723146i	$0.742695\pi$
$350$		0			0
$351$		−	537.796i		−	0.0817818i
$352$		0			0
$353$	−971.440	−	560.861i	−0.146472	−	0.0845655i	0.424973	−	0.905206i	$-0.360284\pi$
$353$	−971.440	−	560.861i	−0.146472	−	0.0845655i	−0.571445	+	0.820640i	$0.693617\pi$
$354$		0			0
$355$	1161.36	+	2011.54i	0.173631	+	0.300737i
$356$		0			0
$357$	−5972.97	−	3178.50i	−0.885498	−	0.471216i
$358$		0			0
$359$	5933.52	−	3425.72i	0.872309	−	0.503628i	0.00419433	−	0.999991i	$-0.498665\pi$
$359$	5933.52	−	3425.72i	0.872309	−	0.503628i	0.868115	+	0.496363i	$0.165332\pi$
$360$		0			0
$361$	3429.05	−	5939.29i	0.499935	−	0.865912i
$362$		0			0
$363$	−637.537			−0.0921818
$364$		0			0
$365$	2232.87			0.320202
$366$		0			0
$367$	−1531.09	+	2651.93i	−0.217772	+	0.377192i	−0.954127	−	0.299404i	$-0.903212\pi$
$367$	−1531.09	+	2651.93i	−0.217772	+	0.377192i	0.736354	+	0.676596i	$0.236546\pi$
$368$		0			0
$369$	−3872.25	+	2235.65i	−0.546291	+	0.315401i
$370$		0			0
$371$	−7750.55	+	268.003i	−1.08460	+	0.0375042i
$372$		0			0
$373$	2872.17	+	4974.75i	0.398701	+	0.690570i	0.993566	−	0.113255i	$-0.0361278\pi$
$373$	2872.17	+	4974.75i	0.398701	+	0.690570i	−0.594865	+	0.803826i	$0.702794\pi$
$374$		0			0
$375$	−2910.44	−	1680.34i	−0.400785	−	0.231393i
$376$		0			0
$377$		−	834.086i		−	0.113946i
$378$		0			0
$379$			7365.74i			0.998291i	0.866518	+	0.499146i	$0.166353\pi$
$379$			7365.74i			0.998291i	−0.866518	+	0.499146i	$0.833647\pi$
$380$		0			0
$381$	361.641	+	208.793i	0.0486284	+	0.0280756i
$382$		0			0
$383$	3386.37	+	5865.36i	0.451789	+	0.782522i	0.998497	−	0.0548014i	$-0.0174526\pi$
$383$	3386.37	+	5865.36i	0.451789	+	0.782522i	−0.546708	+	0.837323i	$0.684119\pi$
$384$		0			0
$385$	1631.31	+	2612.62i	0.215946	+	0.345848i
$386$		0			0
$387$	−1289.06	+	744.237i	−0.169319	+	0.0977563i
$388$		0			0
$389$	6645.07	−	11509.6i	0.866114	−	1.50015i	0.000176464	−	1.00000i	$-0.499944\pi$
$389$	6645.07	−	11509.6i	0.866114	−	1.50015i	0.865937	−	0.500153i	$-0.166723\pi$
$390$		0			0
$391$	9333.82			1.20724
$392$		0			0
$393$	2153.69			0.276436
$394$		0			0
$395$	−2263.51	+	3920.51i	−0.288328	+	0.499398i
$396$		0			0
$397$	−9128.38	+	5270.27i	−1.15401	+	0.666266i	−0.949860	−	0.312675i	$-0.898775\pi$
$397$	−9128.38	+	5270.27i	−1.15401	+	0.666266i	−0.204146	+	0.978940i	$0.565442\pi$
$398$		0			0
$399$	−27.8342	−	44.5780i	−0.00349237	−	0.00559321i
$400$		0			0
$401$	1861.92	+	3224.93i	0.231869	+	0.401610i	0.958358	−	0.285569i	$-0.0921824\pi$
$401$	1861.92	+	3224.93i	0.231869	+	0.401610i	−0.726489	+	0.687178i	$0.758849\pi$
$402$		0			0
$403$	3271.54	+	1888.83i	0.404385	+	0.233472i
$404$		0			0
$405$		−	402.796i		−	0.0494200i
$406$		0			0
$407$		−	5726.68i		−	0.697447i
$408$		0			0
$409$	10451.8	+	6034.35i	1.26359	+	0.729534i	0.973767	−	0.227546i	$-0.0730701\pi$
$409$	10451.8	+	6034.35i	1.26359	+	0.729534i	0.289823	+	0.957080i	$0.406403\pi$
$410$		0			0
$411$	−2885.04	−	4997.04i	−0.346250	−	0.599723i
$412$		0			0
$413$	2227.11	−	77.0105i	0.265349	−	0.00917540i
$414$		0			0
$415$	−4533.30	+	2617.30i	−0.536219	+	0.309586i
$416$		0			0
$417$	4163.72	−	7211.78i	0.488965	−	0.846912i
$418$		0			0
$419$	−1298.82			−0.151435			−0.0757177	−	0.997129i	$-0.524125\pi$
$419$	−1298.82			−0.151435			−0.0757177	+	0.997129i	$0.524125\pi$
$420$		0			0
$421$	−6628.23			−0.767316			−0.383658	−	0.923475i	$-0.625336\pi$
$421$	−6628.23			−0.767316			−0.383658	+	0.923475i	$0.625336\pi$
$422$		0			0
$423$	−849.204	+	1470.86i	−0.0976116	+	0.169068i
$424$		0			0
$425$	−10574.8	+	6105.38i	−1.20695	+	0.696834i
$426$		0			0
$427$	−6033.95	−	3210.95i	−0.683849	−	0.363909i
$428$		0			0
$429$	999.219	+	1730.70i	0.112454	+	0.194776i
$430$		0			0
$431$	−786.502	−	454.087i	−0.0878990	−	0.0507485i	0.455406	−	0.890284i	$-0.349494\pi$
$431$	−786.502	−	454.087i	−0.0878990	−	0.0507485i	−0.543305	+	0.839535i	$0.682827\pi$
$432$		0			0
$433$			466.437i			0.0517680i	0.999665	+	0.0258840i	$0.00824005\pi$
$433$			466.437i			0.0517680i	−0.999665	+	0.0258840i	$0.991760\pi$
$434$		0			0
$435$		−	624.711i		−	0.0688565i
$436$		0			0
$437$	62.7860	+	36.2495i	0.00687291	+	0.00396808i
$438$		0			0
$439$	9047.30	+	15670.4i	0.983608	+	1.70366i	0.647965	+	0.761670i	$0.275620\pi$
$439$	9047.30	+	15670.4i	0.983608	+	1.70366i	0.335643	+	0.941989i	$0.391047\pi$
$440$		0			0
$441$	3079.63	−	213.234i	0.332537	−	0.0230249i
$442$		0			0
$443$	13326.1	−	7693.81i	1.42921	−	0.825156i	0.432153	−	0.901800i	$-0.357754\pi$
$443$	13326.1	−	7693.81i	1.42921	−	0.825156i	0.997058	+	0.0766446i	$0.0244207\pi$
$444$		0			0
$445$	3235.37	−	5603.83i	0.344655	−	0.596959i
$446$		0			0
$447$	−2553.14			−0.270155
$448$		0			0
$449$	2326.87			0.244570			0.122285	−	0.992495i	$-0.460978\pi$
$449$	2326.87			0.244570			0.122285	+	0.992495i	$0.460978\pi$
$450$		0			0
$451$	8307.61	−	14389.2i	0.867384	−	1.50235i
$452$		0			0
$453$	−6090.77	+	3516.51i	−0.631721	+	0.364724i
$454$		0			0
$455$	−861.767	+	1619.41i	−0.0887918	+	0.166855i
$456$		0			0
$457$	171.175	+	296.483i	0.0175213	+	0.0303477i	0.874653	−	0.484749i	$-0.161089\pi$
$457$	171.175	+	296.483i	0.0175213	+	0.0303477i	−0.857132	+	0.515097i	$0.827756\pi$
$458$		0			0
$459$	−2847.48	−	1643.99i	−0.289562	−	0.167179i
$460$		0			0
$461$			3365.88i			0.340053i	0.985439	+	0.170027i	$0.0543854\pi$
$461$			3365.88i			0.340053i	−0.985439	+	0.170027i	$0.945615\pi$
$462$		0			0
$463$		−	8521.95i		−	0.855397i	−0.903921	−	0.427698i	$-0.859325\pi$
$463$		−	8521.95i		−	0.855397i	0.903921	−	0.427698i	$-0.140675\pi$
$464$		0			0
$465$	2450.31	+	1414.69i	0.244366	+	0.141085i
$466$		0			0
$467$	−631.959	−	1094.58i	−0.0626201	−	0.108461i	0.833016	−	0.553249i	$-0.186612\pi$
$467$	−631.959	−	1094.58i	−0.0626201	−	0.108461i	−0.895636	+	0.444788i	$0.853279\pi$
$468$		0			0
$469$	−608.072	−	17585.2i	−0.0598682	−	1.73136i
$470$		0			0
$471$	404.338	−	233.445i	0.0395561	−	0.0228377i
$472$		0			0
$473$	2765.57	−	4790.10i	0.268839	−	0.465643i
$474$		0			0
$475$	−94.8452			−0.00916168
$476$		0			0
$477$	−3768.66			−0.361751
$478$		0			0
$479$	5647.64	−	9782.00i	0.538721	−	0.933092i	−0.460252	−	0.887788i	$-0.652241\pi$
$479$	5647.64	−	9782.00i	0.538721	−	0.933092i	0.998973	−	0.0453039i	$-0.0144256\pi$
$480$		0			0
$481$	2953.74	−	1705.34i	0.279998	−	0.161657i
$482$		0			0
$483$	−3612.23	+	2255.45i	−0.340294	+	0.212478i
$484$		0			0
$485$	2364.05	+	4094.66i	0.221332	+	0.383358i
$486$		0			0
$487$	2589.66	+	1495.14i	0.240963	+	0.139120i	0.615619	−	0.788044i	$-0.288906\pi$
$487$	2589.66	+	1495.14i	0.240963	+	0.139120i	−0.374656	+	0.927164i	$0.622239\pi$
$488$		0			0
$489$		−	10580.4i		−	0.978451i
$490$		0			0
$491$			3839.89i			0.352936i	0.984306	+	0.176468i	$0.0564672\pi$
$491$			3839.89i			0.352936i	−0.984306	+	0.176468i	$0.943533\pi$
$492$		0			0
$493$	−4416.25	−	2549.72i	−0.403444	−	0.232928i
$494$		0			0
$495$	748.391	+	1296.25i	0.0679549	+	0.117701i
$496$		0			0
$497$	−7337.67	+	4581.60i	−0.662252	+	0.413507i
$498$		0			0
$499$	1495.79	−	863.597i	0.134190	−	0.0774748i	−0.431402	−	0.902160i	$-0.641981\pi$
$499$	1495.79	−	863.597i	0.134190	−	0.0774748i	0.565592	+	0.824685i	$0.308648\pi$
$500$		0			0
$501$	−1779.94	+	3082.95i	−0.158727	+	0.274923i
$502$		0			0
$503$	−5651.51			−0.500971			−0.250485	−	0.968120i	$-0.580590\pi$
$503$	−5651.51			−0.500971			−0.250485	+	0.968120i	$0.580590\pi$
$504$		0			0
$505$	1780.66			0.156908
$506$		0			0
$507$	2700.39	−	4677.21i	0.236545	−	0.409708i
$508$		0			0
$509$	3547.89	−	2048.38i	0.308954	−	0.178375i	−0.337504	−	0.941324i	$-0.609583\pi$
$509$	3547.89	−	2048.38i	0.308954	−	0.178375i	0.646458	+	0.762949i	$0.276249\pi$
$510$		0			0
$511$	287.381	+	8310.93i	0.0248786	+	0.719479i
$512$		0			0
$513$	−12.7695	−	22.1174i	−0.00109900	−	0.00190352i
$514$		0			0
$515$	−4628.77	−	2672.42i	−0.396054	−	0.228662i
$516$		0			0
$517$		−	6311.24i		−	0.536882i
$518$		0			0
$519$			4702.74i			0.397741i
$520$		0			0
$521$	−11501.5	−	6640.40i	−0.967159	−	0.558390i	−0.0687902	−	0.997631i	$-0.521914\pi$
$521$	−11501.5	−	6640.40i	−0.967159	−	0.558390i	−0.898369	+	0.439241i	$0.855247\pi$
$522$		0			0
$523$	−1676.16	−	2903.20i	−0.140141	−	0.242731i	0.787409	−	0.616431i	$-0.211422\pi$
$523$	−1676.16	−	2903.20i	−0.140141	−	0.242731i	−0.927549	+	0.373700i	$0.878089\pi$
$524$		0			0
$525$	2617.18	−	4918.14i	0.217568	−	0.408848i
$526$		0			0
$527$	20001.6	−	11547.9i	1.65329	−	0.954527i
$528$		0			0
$529$	−3146.14	+	5449.27i	−0.258580	+	0.447873i
$530$		0			0
$531$	1082.92			0.0885024
$532$		0			0
$533$	9895.65			0.804180
$534$		0			0
$535$	1094.35	−	1895.47i	0.0884354	−	0.153175i
$536$		0			0
$537$	3046.84	−	1759.10i	0.244844	−	0.141361i
$538$		0			0
$539$	−9514.46	+	6408.13i	−0.760328	+	0.512092i
$540$		0			0
$541$	11412.4	+	19766.8i	0.906943	+	1.57087i	0.818288	+	0.574809i	$0.194924\pi$
$541$	11412.4	+	19766.8i	0.906943	+	1.57087i	0.0886555	+	0.996062i	$0.471743\pi$
$542$		0			0
$543$	5951.31	+	3435.99i	0.470341	+	0.271552i
$544$		0			0
$545$			40.4661i			0.00318051i
$546$		0			0
$547$		−	14723.1i		−	1.15085i	−0.817856	−	0.575423i	$-0.804837\pi$
$547$		−	14723.1i		−	1.15085i	0.817856	−	0.575423i	$-0.195163\pi$
$548$		0			0
$549$	−2876.55	−	1660.78i	−0.223621	−	0.129108i
$550$		0			0
$551$	−19.8046	−	34.3026i	−0.00153122	−	0.00265216i
$552$		0			0
$553$	−14883.8	−	7920.40i	−1.14453	−	0.609059i
$554$		0			0
$555$	2212.28	−	1277.26i	0.169200	−	0.0976877i
$556$		0			0
$557$	3803.43	−	6587.74i	0.289330	−	0.501134i	−0.684320	−	0.729182i	$-0.739901\pi$
$557$	3803.43	−	6587.74i	0.289330	−	0.501134i	0.973650	+	0.228048i	$0.0732343\pi$
$558$		0			0
$559$	3294.22			0.249250
$560$		0			0
$561$	12218.1			0.919514
$562$		0			0
$563$	−753.915	+	1305.82i	−0.0564365	+	0.0977509i	−0.892863	−	0.450328i	$-0.851307\pi$
$563$	−753.915	+	1305.82i	−0.0564365	+	0.0977509i	0.836427	+	0.548079i	$0.184641\pi$
$564$		0			0
$565$	−888.202	+	512.804i	−0.0661362	+	0.0381838i
$566$		0			0
$567$	1499.24	−	51.8418i	0.111045	−	0.00383978i
$568$		0			0
$569$	−4836.05	−	8376.29i	−0.356306	−	0.617140i	0.631035	−	0.775755i	$-0.282630\pi$
$569$	−4836.05	−	8376.29i	−0.356306	−	0.617140i	−0.987341	+	0.158615i	$0.949297\pi$
$570$		0			0
$571$	−10863.1	−	6271.82i	−0.796159	−	0.459663i	0.0459671	−	0.998943i	$-0.485363\pi$
$571$	−10863.1	−	6271.82i	−0.796159	−	0.459663i	−0.842126	+	0.539280i	$0.818696\pi$
$572$		0			0
$573$			4645.72i			0.338705i
$574$		0			0
$575$			7685.47i			0.557402i
$576$		0			0
$577$	4457.96	+	2573.81i	0.321642	+	0.185700i	0.652124	−	0.758112i	$-0.273878\pi$
$577$	4457.96	+	2573.81i	0.321642	+	0.185700i	−0.330482	+	0.943812i	$0.607211\pi$
$578$		0			0
$579$	4925.59	+	8531.38i	0.353542	+	0.612352i
$580$		0			0
$581$	−10325.3	−	16536.5i	−0.737289	−	1.18081i
$582$		0			0
$583$	12128.1	−	7002.14i	0.861565	−	0.497425i
$584$		0			0
$585$	−445.725	+	772.018i	−0.0315016	+	0.0545624i
$586$		0			0
$587$	4377.91			0.307829			0.153915	−	0.988084i	$-0.450812\pi$
$587$	4377.91			0.307829			0.153915	+	0.988084i	$0.450812\pi$
$588$		0			0
$589$	179.394			0.0125497
$590$		0			0
$591$	6653.66	−	11524.5i	0.463105	−	0.802121i
$592$		0			0
$593$	−18761.9	+	10832.2i	−1.29925	+	0.750124i	−0.980275	−	0.197638i	$-0.936673\pi$
$593$	−18761.9	+	10832.2i	−1.29925	+	0.750124i	−0.318978	+	0.947762i	$0.603340\pi$
$594$		0			0
$595$	5939.99	+	9513.20i	0.409270	+	0.655468i
$596$		0			0
$597$	−4169.56	−	7221.88i	−0.285844	−	0.495096i
$598$		0			0
$599$	14592.1	+	8424.76i	0.995355	+	0.574668i	0.906871	−	0.421409i	$-0.138464\pi$
$599$	14592.1	+	8424.76i	0.995355	+	0.574668i	0.0884841	+	0.996078i	$0.471798\pi$
$600$		0			0
$601$		−	19969.1i		−	1.35534i	−0.735368	−	0.677668i	$-0.762991\pi$
$601$		−	19969.1i		−	1.35534i	0.735368	−	0.677668i	$-0.237009\pi$
$602$		0			0
$603$		−	8550.71i		−	0.577466i
$604$		0			0
$605$	915.199	+	528.390i	0.0615010	+	0.0355076i
$606$		0			0
$607$	9588.04	+	16607.0i	0.641131	+	1.11047i	0.985181	+	0.171520i	$0.0548678\pi$
$607$	9588.04	+	16607.0i	0.641131	+	1.11047i	−0.344050	+	0.938951i	$0.611799\pi$
$608$		0			0
$609$	2325.23	−	80.4033i	0.154718	−	0.00534993i
$610$		0			0
$611$	3255.25	−	1879.42i	0.215537	−	0.124440i
$612$		0			0
$613$	−3370.29	+	5837.52i	−0.222063	+	0.384625i	−0.955434	−	0.295204i	$-0.904613\pi$
$613$	−3370.29	+	5837.52i	−0.222063	+	0.384625i	0.733371	+	0.679829i	$0.237946\pi$
$614$		0			0
$615$	7411.61			0.485959
$616$		0			0
$617$	−22084.1			−1.44096			−0.720481	−	0.693474i	$-0.756079\pi$
$617$	−22084.1			−1.44096			−0.720481	+	0.693474i	$0.756079\pi$
$618$		0			0
$619$	9128.06	−	15810.3i	0.592711	−	1.02660i	−0.401155	−	0.916010i	$-0.631391\pi$
$619$	9128.06	−	15810.3i	0.592711	−	1.02660i	0.993866	−	0.110595i	$-0.0352755\pi$
$620$		0			0
$621$	−1792.21	+	1034.73i	−0.115811	+	0.0668636i
$622$		0			0
$623$	21274.4	+	11321.1i	1.36812	+	0.728043i
$624$		0			0
$625$	−3481.62	−	6030.35i	−0.222824	−	0.385942i
$626$		0			0
$627$	82.1876	+	47.4510i	0.00523486	+	0.00302235i
$628$		0			0
$629$		−	20852.3i		−	1.32184i
$630$		0			0
$631$		−	15516.1i		−	0.978898i	−0.872032	−	0.489449i	$-0.837198\pi$
$631$		−	15516.1i		−	0.978898i	0.872032	−	0.489449i	$-0.162802\pi$
$632$		0			0
$633$	181.682	+	104.894i	0.0114079	+	0.00658636i
$634$		0			0
$635$	−346.096	−	599.455i	−0.0216289	−	0.0374624i
$636$		0			0
$637$	−6138.51	−	2999.15i	−0.381816	−	0.186547i
$638$		0			0
$639$	−3640.58	+	2101.89i	−0.225382	+	0.130125i
$640$		0			0
$641$	8848.14	−	15325.4i	0.545211	−	0.944334i	−0.453382	−	0.891316i	$-0.649783\pi$
$641$	8848.14	−	15325.4i	0.545211	−	0.944334i	0.998594	−	0.0530177i	$-0.0168840\pi$
$642$		0			0
$643$	−22939.0			−1.40688			−0.703440	−	0.710754i	$-0.748354\pi$
$643$	−22939.0			−1.40688			−0.703440	+	0.710754i	$0.748354\pi$
$644$		0			0
$645$	2467.29			0.150619
$646$		0			0
$647$	1665.72	−	2885.11i	0.101215	−	0.175309i	−0.810971	−	0.585087i	$-0.801060\pi$
$647$	1665.72	−	2885.11i	0.101215	−	0.175309i	0.912185	+	0.409778i	$0.134394\pi$
$648$		0			0
$649$	−3484.98	+	2012.06i	−0.210782	+	0.121695i
$650$		0			0
$651$	−4950.23	+	9302.35i	−0.298026	+	0.560043i
$652$		0			0
$653$	12177.9	+	21092.8i	0.729800	+	1.26405i	0.956967	+	0.290195i	$0.0937203\pi$
$653$	12177.9	+	21092.8i	0.729800	+	1.26405i	−0.227167	+	0.973856i	$0.572946\pi$
$654$		0			0
$655$	−3091.67	−	1784.98i	−0.184430	−	0.106481i
$656$		0			0
$657$			4041.15i			0.239970i
$658$		0			0
$659$		−	12209.3i		−	0.721707i	−0.932622	−	0.360854i	$-0.882485\pi$
$659$		−	12209.3i		−	0.721707i	0.932622	−	0.360854i	$-0.117515\pi$
$660$		0			0
$661$	−21962.3	−	12680.0i	−1.29234	−	0.746132i	−0.313270	−	0.949664i	$-0.601425\pi$
$661$	−21962.3	−	12680.0i	−1.29234	−	0.746132i	−0.979068	+	0.203532i	$0.934758\pi$
$662$		0			0
$663$	3638.40	+	6301.90i	0.213128	+	0.369149i
$664$		0			0
$665$	3.01047	+	87.0617i	0.000175551	+	0.00507685i
$666$		0			0
$667$	−2779.59	+	1604.80i	−0.161359	+	0.0931605i
$668$		0			0
$669$	−4565.49	+	7907.66i	−0.263845	+	0.456992i
$670$		0			0
$671$	12342.8			0.710118
$672$		0			0
$673$	−747.690			−0.0428252			−0.0214126	−	0.999771i	$-0.506816\pi$
$673$	−747.690			−0.0428252			−0.0214126	+	0.999771i	$0.506816\pi$
$674$		0			0
$675$	1353.66	−	2344.61i	0.0771889	−	0.133695i
$676$		0			0
$677$	−2391.40	+	1380.67i	−0.135759	+	0.0783805i	−0.566341	−	0.824171i	$-0.691642\pi$
$677$	−2391.40	+	1380.67i	−0.135759	+	0.0783805i	0.430582	+	0.902551i	$0.358308\pi$
$678$		0			0
$679$	−14936.4	+	9326.21i	−0.844193	+	0.527109i
$680$		0			0
$681$	−3527.51	−	6109.83i	−0.198494	−	0.343802i
$682$		0			0
$683$	337.194	+	194.679i	0.0188907	+	0.0109066i	0.509416	−	0.860521i	$-0.329862\pi$
$683$	337.194	+	194.679i	0.0188907	+	0.0109066i	−0.490525	+	0.871427i	$0.663195\pi$
$684$		0			0
$685$			9564.49i			0.533490i
$686$		0			0
$687$			12727.6i			0.706821i
$688$		0			0
$689$	7223.19	+	4170.31i	0.399393	+	0.230590i
$690$		0			0
$691$	6572.13	+	11383.3i	0.361817	+	0.626686i	0.988260	−	0.152781i	$-0.0488231\pi$
$691$	6572.13	+	11383.3i	0.361817	+	0.626686i	−0.626443	+	0.779468i	$0.715490\pi$
$692$		0			0
$693$	−4728.45	+	2952.41i	−0.259190	+	0.161837i
$694$		0			0
$695$	−11954.2	+	6901.78i	−0.652446	+	0.376690i
$696$		0			0
$697$	30250.1	−	52394.6i	1.64391	−	2.84733i
$698$		0			0
$699$	−1102.24			−0.0596432
$700$		0			0
$701$	27202.0			1.46563			0.732813	−	0.680430i	$-0.238207\pi$
$701$	27202.0			1.46563			0.732813	+	0.680430i	$0.238207\pi$
$702$		0			0
$703$	80.9835	−	140.267i	0.00434474	−	0.00752530i
$704$		0			0
$705$	2438.10	−	1407.64i	0.130247	−	0.0751982i
$706$		0			0
$707$	229.180	+	6627.78i	0.0121912	+	0.352565i
$708$		0			0
$709$	−13296.5	−	23030.1i	−0.704314	−	1.21991i	−0.966938	−	0.255010i	$-0.917921\pi$
$709$	−13296.5	−	23030.1i	−0.704314	−	1.21991i	0.262624	−	0.964898i	$-0.415412\pi$
$710$		0			0
$711$	−7095.53	−	4096.60i	−0.374266	−	0.216083i
$712$		0			0
$713$		−	14536.6i		−	0.763533i
$714$		0			0
$715$		−	3312.61i		−	0.173265i
$716$		0			0
$717$	−10938.0	−	6315.09i	−0.569720	−	0.328928i
$718$		0			0
$719$	6224.10	+	10780.5i	0.322837	+	0.559170i	0.981072	−	0.193642i	$-0.0620302\pi$
$719$	6224.10	+	10780.5i	0.322837	+	0.559170i	−0.658235	+	0.752812i	$0.728697\pi$
$720$		0			0
$721$	9351.25	−	17572.6i	0.483022	−	0.907683i
$722$		0			0
$723$	11696.3	−	6752.85i	0.601645	−	0.347360i
$724$		0			0
$725$	2099.44	−	3636.34i	0.107547	−	0.186276i
$726$		0			0
$727$	−36106.8			−1.84199			−0.920995	−	0.389575i	$-0.872622\pi$
$727$	−36106.8			−1.84199			−0.920995	+	0.389575i	$0.872622\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	10070.1	−	17441.9i	0.509517	−	0.882509i
$732$		0			0
$733$	−20109.9	+	11610.5i	−1.01334	+	0.585051i	−0.912167	−	0.409819i	$-0.865592\pi$
$733$	−20109.9	+	11610.5i	−1.01334	+	0.585051i	−0.101170	+	0.994869i	$0.532259\pi$
$734$		0			0
$735$	−4597.60	−	2246.29i	−0.230728	−	0.112729i
$736$		0			0
$737$	15887.1	+	27517.3i	0.794043	+	1.37532i
$738$		0			0
$739$	−33233.8	−	19187.6i	−1.65430	−	0.955109i	−0.975276	−	0.220992i	$-0.929070\pi$
$739$	−33233.8	−	19187.6i	−1.65430	−	0.955109i	−0.679023	−	0.734117i	$-0.737596\pi$
$740$		0			0
$741$			56.5215i			0.00280212i
$742$		0			0
$743$			10558.8i			0.521352i	0.965426	+	0.260676i	$0.0839454\pi$
$743$			10558.8i			0.521352i	−0.965426	+	0.260676i	$0.916055\pi$
$744$		0			0
$745$	3665.09	+	2116.04i	0.180240	+	0.104061i
$746$		0			0
$747$	−4736.91	−	8204.58i	−0.232014	−	0.401860i
$748$		0			0
$749$	7195.97	+	3829.32i	0.351048	+	0.186809i
$750$		0			0
$751$	26802.6	−	15474.5i	1.30232	−	0.751893i	0.321515	−	0.946904i	$-0.395808\pi$
$751$	26802.6	−	15474.5i	1.30232	−	0.751893i	0.980801	+	0.195012i	$0.0624745\pi$
$752$		0			0
$753$	231.319	−	400.655i	0.0111948	−	0.0193900i
$754$		0			0
$755$	11657.9			0.561954
$756$		0			0
$757$	16987.8			0.815633			0.407816	−	0.913064i	$-0.366290\pi$
$757$	16987.8			0.815633			0.407816	+	0.913064i	$0.366290\pi$
$758$		0			0
$759$	3845.04	−	6659.80i	0.183881	−	0.318492i
$760$		0			0
$761$	−25984.3	+	15002.0i	−1.23775	+	0.714617i	−0.968634	−	0.248491i	$-0.920065\pi$
$761$	−25984.3	+	15002.0i	−1.23775	+	0.714617i	−0.269118	+	0.963107i	$0.586732\pi$
$762$		0			0
$763$	−150.618	+	5.20818i	−0.00714647	+	0.000247115i
$764$		0			0
$765$	2725.08	+	4719.97i	0.128791	+	0.223073i
$766$		0			0
$767$	−2075.58	−	1198.34i	−0.0977116	−	0.0564138i
$768$		0			0
$769$			26163.2i			1.22688i	0.789743	+	0.613438i	$0.210214\pi$
$769$			26163.2i			1.22688i	−0.789743	+	0.613438i	$0.789786\pi$
$770$		0			0
$771$		−	1133.85i		−	0.0529630i
$772$		0			0
$773$	−32953.0	−	19025.4i	−1.53330	−	0.885249i	−0.999207	−	0.0398204i	$-0.987321\pi$
$773$	−32953.0	−	19025.4i	−1.53330	−	0.885249i	−0.534089	−	0.845428i	$-0.679345\pi$
$774$		0			0
$775$	9508.57	+	16469.3i	0.440720	+	0.763349i
$776$		0			0
$777$	5038.81	+	8069.92i	0.232646	+	0.372595i
$778$		0			0
$779$	406.968	−	234.963i	0.0187178	−	0.0108067i
$780$		0			0
$781$	7810.58	−	13528.3i	0.357855	−	0.619823i
$782$		0			0
$783$	1130.63			0.0516034
$784$		0			0
$785$	−773.915			−0.0351875
$786$		0			0
$787$	−13392.5	+	23196.6i	−0.606598	+	1.05066i	0.385198	+	0.922834i	$0.374133\pi$
$787$	−13392.5	+	23196.6i	−0.606598	+	1.05066i	−0.991797	+	0.127825i	$0.959200\pi$
$788$		0			0
$789$	−16863.6	+	9736.20i	−0.760913	+	0.439313i
$790$		0			0
$791$	−2023.02	−	3239.97i	−0.0909358	−	0.145638i
$792$		0			0
$793$	3675.55	+	6366.24i	0.164594	+	0.285084i
$794$		0			0
$795$	5410.00	+	3123.47i	0.241350	+	0.139343i
$796$		0			0
$797$			11406.4i			0.506947i	0.967342	+	0.253473i	$0.0815731\pi$
$797$			11406.4i			0.506947i	−0.967342	+	0.253473i	$0.918427\pi$
$798$		0			0
$799$		−	22980.8i		−	1.01752i
$800$		0			0
$801$	10142.1	+	5855.53i	0.447381	+	0.258296i
$802$		0			0
$803$	−7508.41	−	13004.9i	−0.329970	−	0.571525i
$804$		0			0
$805$	7054.75	−	243.944i	0.308879	−	0.0106806i
$806$		0			0
$807$	22159.1	−	12793.6i	0.966590	−	0.558061i
$808$		0			0
$809$	7836.06	−	13572.5i	0.340545	−	0.589842i	−0.643989	−	0.765035i	$-0.722722\pi$
$809$	7836.06	−	13572.5i	0.340545	−	0.589842i	0.984534	+	0.175193i	$0.0560550\pi$
$810$		0			0
$811$	−23645.9			−1.02382			−0.511912	−	0.859038i	$-0.671062\pi$
$811$	−23645.9			−1.02382			−0.511912	+	0.859038i	$0.671062\pi$
$812$		0			0
$813$	−4014.61			−0.173184
$814$		0			0
$815$	−8769.04	+	15188.4i	−0.376891	+	0.652794i
$816$		0			0
$817$	135.478	−	78.2181i	0.00580143	−	0.00334946i
$818$		0			0
$819$	−2930.89	−	1559.67i	−0.125047	−	0.0665435i
$820$		0			0
$821$	23149.8	+	40096.7i	0.984086	+	1.70449i	0.645930	+	0.763396i	$0.276470\pi$
$821$	23149.8	+	40096.7i	0.984086	+	1.70449i	0.338155	+	0.941090i	$0.390197\pi$
$822$		0			0
$823$	21582.4	+	12460.6i	0.914112	+	0.527763i	0.881752	−	0.471714i	$-0.156364\pi$
$823$	21582.4	+	12460.6i	0.914112	+	0.527763i	0.0323599	+	0.999476i	$0.489698\pi$
$824$		0			0
$825$			10060.4i			0.424554i
$826$		0			0
$827$		−	30279.0i		−	1.27316i	−0.771210	−	0.636581i	$-0.780348\pi$
$827$		−	30279.0i		−	1.27316i	0.771210	−	0.636581i	$-0.219652\pi$
$828$		0			0
$829$	−3100.58	−	1790.12i	−0.129901	−	0.0749981i	0.433642	−	0.901085i	$-0.357228\pi$
$829$	−3100.58	−	1790.12i	−0.129901	−	0.0749981i	−0.563542	+	0.826087i	$0.690562\pi$
$830$		0			0
$831$	8677.70	+	15030.2i	0.362246	+	0.627428i
$832$		0			0
$833$	−34644.5	+	23333.6i	−1.44101	+	0.970541i
$834$		0			0
$835$	5110.30	−	2950.43i	0.211795	−	0.122280i
$836$		0			0
$837$	−2560.37	+	4434.68i	−0.105734	+	0.183136i
$838$		0			0
$839$	−24560.9			−1.01065			−0.505325	−	0.862929i	$-0.668627\pi$
$839$	−24560.9			−1.01065			−0.505325	+	0.862929i	$0.668627\pi$
$840$		0			0
$841$	−22635.5			−0.928101
$842$		0			0
$843$	−9679.14	+	16764.8i	−0.395453	+	0.684945i
$844$		0			0
$845$	−7752.93	+	4476.16i	−0.315632	+	0.182230i
$846$		0			0
$847$	−1848.93	+	3474.46i	−0.0750057	+	0.140949i
$848$		0			0
$849$	10080.8	+	17460.4i	0.407504	+	0.705818i
$850$		0			0
$851$	−11366.1	−	6562.22i	−0.457844	−	0.264336i
$852$		0			0
$853$		−	5489.29i		−	0.220339i	−0.993913	−	0.110170i	$-0.964861\pi$
$853$		−	5489.29i		−	0.220339i	0.993913	−	0.110170i	$-0.0351394\pi$
$854$		0			0
$855$			42.3333i			0.00169330i
$856$		0			0
$857$	28019.1	+	16176.9i	1.11682	+	0.644797i	0.940587	−	0.339552i	$-0.110275\pi$
$857$	28019.1	+	16176.9i	1.11682	+	0.644797i	0.176233	+	0.984348i	$0.443609\pi$
$858$		0			0
$859$	6643.25	+	11506.4i	0.263870	+	0.457037i	0.967267	−	0.253761i	$-0.0816675\pi$
$859$	6643.25	+	11506.4i	0.263870	+	0.457037i	−0.703397	+	0.710798i	$0.748334\pi$
$860$		0			0
$861$	953.909	+	27586.7i	0.0377574	+	1.09193i
$862$		0			0
$863$	20491.8	−	11830.9i	0.808283	−	0.466662i	−0.0380762	−	0.999275i	$-0.512123\pi$
$863$	20491.8	−	11830.9i	0.808283	−	0.466662i	0.846359	+	0.532612i	$0.178790\pi$
$864$		0			0
$865$	3897.63	−	6750.89i	0.153206	−	0.265361i
$866$		0			0
$867$	29750.0			1.16536
$868$		0			0
$869$	30445.8			1.18850
$870$		0			0
$871$	−9462.02	+	16388.7i	−0.368092	+	0.637554i
$872$		0			0
$873$	−7410.70	+	4278.57i	−0.287301	+	0.165874i
$874$		0			0
$875$	−17598.1	+	10988.2i	−0.679915	+	0.424535i
$876$		0			0
$877$	16008.4	+	27727.4i	0.616380	+	1.06760i	0.990141	+	0.140076i	$0.0447347\pi$
$877$	16008.4	+	27727.4i	0.616380	+	1.06760i	−0.373761	+	0.927525i	$0.621932\pi$
$878$		0			0
$879$	−14046.7	−	8109.89i	−0.539005	−	0.311194i
$880$		0			0
$881$			20954.6i			0.801336i	0.916223	+	0.400668i	$0.131222\pi$
$881$			20954.6i			0.801336i	−0.916223	+	0.400668i	$0.868778\pi$
$882$		0			0
$883$			14392.3i			0.548518i	0.961656	+	0.274259i	$0.0884325\pi$
$883$			14392.3i			0.548518i	−0.961656	+	0.274259i	$0.911568\pi$
$884$		0			0
$885$	−1554.56	−	897.525i	−0.0590462	−	0.0340904i
$886$		0			0
$887$	4578.13	+	7929.55i	0.173301	+	0.300167i	0.939572	−	0.342351i	$-0.111223\pi$
$887$	4578.13	+	7929.55i	0.173301	+	0.300167i	−0.766271	+	0.642518i	$0.777890\pi$
$888$		0			0
$889$	2186.68	−	1365.35i	0.0824960	−	0.0515100i
$890$		0			0
$891$	−2346.02	+	1354.47i	−0.0882094	+	0.0509277i
$892$		0			0
$893$	89.2500	−	154.586i	0.00334450	−	0.00579284i
$894$		0			0
$895$	−5831.75			−0.217803
$896$		0			0
$897$	4580.03			0.170483
$898$		0			0
$899$	−3970.96	+	6877.91i	−0.147318	+	0.255162i
$900$		0			0
$901$	44161.2	−	25496.5i	1.63288	−	0.942743i
$902$		0			0
$903$	317.552	+	9183.48i	0.0117026	+	0.338435i
$904$		0			0
$905$	−5695.50	−	9864.89i	−0.209199	−	0.362342i
$906$		0			0
$907$	−420.151	−	242.574i	−0.0153813	−	0.00888042i	0.492290	−	0.870431i	$-0.336160\pi$
$907$	−420.151	−	242.574i	−0.0153813	−	0.00888042i	−0.507671	+	0.861551i	$0.669493\pi$
$908$		0			0
$909$			3222.72i			0.117592i
$910$		0			0
$911$			1645.90i			0.0598585i	0.999552	+	0.0299292i	$0.00952819\pi$
$911$			1645.90i			0.0598585i	−0.999552	+	0.0299292i	$0.990472\pi$
$912$		0			0
$913$	30488.0	+	17602.3i	1.10515	+	0.638061i
$914$		0			0
$915$	2752.90	+	4768.17i	0.0994624	+	0.172274i
$916$		0			0
$917$	6245.93	−	11737.2i	0.224928	−	0.422679i
$918$		0			0
$919$	−39639.0	+	22885.6i	−1.42282	+	0.821465i	−0.996539	−	0.0831261i	$-0.973510\pi$
$919$	−39639.0	+	22885.6i	−1.42282	+	0.821465i	−0.426280	+	0.904591i	$0.640176\pi$
$920$		0			0
$921$	1150.66	−	1993.01i	0.0411679	−	0.0713050i
$922$		0			0
$923$	9303.62			0.331779
$924$		0			0
$925$	17169.8			0.610311
$926$		0			0
$927$	4836.67	−	8377.36i	0.171367	−	0.296816i
$928$		0			0
$929$	−35669.7	+	20593.9i	−1.25973	+	0.727303i	−0.973021	−	0.230716i	$-0.925893\pi$
$929$	−35669.7	+	20593.9i	−1.25973	+	0.727303i	−0.286705	+	0.958019i	$0.592560\pi$
$930$		0			0
$931$	−323.664	+	22.4105i	−0.0113938	+	0.000788910i
$932$		0			0
$933$	11888.0	+	20590.6i	0.417144	+	0.722515i
$934$		0			0
$935$	−17539.3	−	10126.3i	−0.613473	−	0.354189i
$936$		0			0
$937$		−	2545.59i		−	0.0887523i	−0.999015	−	0.0443761i	$-0.985870\pi$
$937$		−	2545.59i		−	0.0887523i	0.999015	−	0.0443761i	$-0.0141300\pi$
$938$		0			0
$939$			5747.35i			0.199742i
$940$		0			0
$941$	4507.93	+	2602.65i	0.156168	+	0.0901637i	0.576048	−	0.817416i	$-0.304594\pi$
$941$	4507.93	+	2602.65i	0.156168	+	0.0901637i	−0.419879	+	0.907580i	$0.637928\pi$
$942$		0			0
$943$	−19039.4	−	32977.3i	−0.657486	−	1.13880i
$944$		0			0
$945$	−2195.17	−	1168.15i	−0.0755648	−	0.0402117i
$946$		0			0
$947$	−9404.38	+	5429.62i	−0.322705	+	0.186314i	−0.652597	−	0.757705i	$-0.726321\pi$
$947$	−9404.38	+	5429.62i	−0.322705	+	0.186314i	0.329893	+	0.944018i	$0.392987\pi$
$948$		0			0
$949$	4471.84	−	7745.45i	0.152963	−	0.264940i
$950$		0			0
$951$	−2395.32			−0.0816755
$952$		0			0
$953$	−3621.29			−0.123090			−0.0615452	−	0.998104i	$-0.519603\pi$
$953$	−3621.29			−0.123090			−0.0615452	+	0.998104i	$0.519603\pi$
$954$		0			0
$955$	3850.37	−	6669.04i	0.130466	−	0.225974i
$956$		0			0
$957$	−3638.52	+	2100.70i	−0.122901	+	0.0709571i
$958$		0			0
$959$	−35599.9	+	1231.00i	−1.19873	+	0.0414504i
$960$		0			0
$961$	−3089.35	−	5350.91i	−0.103701	−	0.179615i
$962$		0			0
$963$	3430.52	+	1980.61i	0.114794	+	0.0662765i
$964$		0			0
$965$		−	16329.3i		−	0.544725i
$966$		0			0
$967$		−	39475.5i		−	1.31277i	−0.754427	−	0.656384i	$-0.772085\pi$
$967$		−	39475.5i		−	1.31277i	0.754427	−	0.656384i	$-0.227915\pi$
$968$		0			0
$969$	299.265	+	172.781i	0.00992135	+	0.00572809i
$970$		0			0
$971$	12949.3	+	22428.9i	0.427975	+	0.741275i	0.996693	−	0.0812578i	$-0.0258937\pi$
$971$	12949.3	+	22428.9i	0.427975	+	0.741275i	−0.568718	+	0.822533i	$0.692560\pi$
$972$		0			0
$973$	−27227.6	−	43606.4i	−0.897099	−	1.43675i
$974$		0			0
$975$	−5188.98	+	2995.86i	−0.170442	+	0.0984045i
$976$		0			0
$977$	−14445.1	+	25019.6i	−0.473018	+	0.819290i	−0.999523	−	0.0308813i	$-0.990169\pi$
$977$	−14445.1	+	25019.6i	−0.473018	+	0.819290i	0.526506	+	0.850172i	$0.323502\pi$
$978$		0			0
$979$	−43518.0			−1.42068
$980$		0			0
$981$	−73.2374			−0.00238358
$982$		0			0
$983$	9662.90	−	16736.6i	0.313529	−	0.543048i	−0.665595	−	0.746313i	$-0.731822\pi$
$983$	9662.90	−	16736.6i	0.313529	−	0.543048i	0.979124	+	0.203266i	$0.0651555\pi$
$984$		0			0
$985$	−19103.0	+	11029.1i	−0.617940	+	0.356768i
$986$		0			0
$987$	5553.16	+	8893.67i	0.179087	+	0.286817i
$988$		0			0
$989$	−6338.14	−	10978.0i	−0.203783	−	0.352962i
$990$		0			0
$991$	−50483.8	−	29146.9i	−1.61824	−	0.934289i	−0.987376	−	0.158392i	$-0.949369\pi$
$991$	−50483.8	−	29146.9i	−1.61824	−	0.934289i	−0.630860	−	0.775897i	$-0.717298\pi$
$992$		0			0
$993$		−	25544.0i		−	0.816327i
$994$		0			0
$995$			13822.9i			0.440418i
$996$		0			0
$997$	7827.39	+	4519.15i	0.248642	+	0.143554i	0.619142	−	0.785279i	$-0.287480\pi$
$997$	7827.39	+	4519.15i	0.248642	+	0.143554i	−0.370500	+	0.928832i	$0.620814\pi$
$998$		0			0
$999$	2311.65	+	4003.89i	0.0732104	+	0.126804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.4.bl.b.31.9	yes	48
4.3	odd	2		672.4.bl.a.31.9	✓	48
7.5	odd	6		672.4.bl.a.607.9	yes	48
28.19	even	6	inner	672.4.bl.b.607.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.4.bl.a.31.9	✓	48	4.3	odd	2
672.4.bl.a.607.9	yes	48	7.5	odd	6
672.4.bl.b.31.9	yes	48	1.1	even	1	trivial
672.4.bl.b.607.9	yes	48	28.19	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	672.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(-4.30657 + 2.48640i) q^{5} +(-9.80887 - 15.7094i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{3} +(-4.30657 + 2.48640i) q^{5} +(-9.80887 - 15.7094i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(28.9632 + 16.7219i) q^{11} +19.9184i q^{13} +14.9184i q^{15} +(105.462 + 60.8886i) q^{17} +(0.472943 + 0.819161i) q^{19} +(-55.5276 + 1.92007i) q^{21} +(66.3780 - 38.3234i) q^{23} +(-50.1357 + 86.8375i) q^{25} -27.0000 q^{27} -41.8752 q^{29} +(94.8284 - 164.248i) q^{31} +(86.8895 - 50.1657i) q^{33} +(81.3025 + 43.2649i) q^{35} +(-85.6165 - 148.292i) q^{37} +(51.7494 + 29.8776i) q^{39} -496.810i q^{41} -165.386i q^{43} +(38.7591 + 22.3776i) q^{45} +(-94.3560 - 163.429i) q^{47} +(-150.572 + 308.184i) q^{49} +(316.386 - 182.666i) q^{51} +(209.370 - 362.640i) q^{53} -166.309 q^{55} +2.83766 q^{57} +(-60.1623 + 104.204i) q^{59} +(319.617 - 184.531i) q^{61} +(-78.3029 + 147.145i) q^{63} +(-49.5250 - 85.7798i) q^{65} +(822.793 + 475.040i) q^{67} -229.940i q^{69} -467.087i q^{71} +(-388.860 - 224.508i) q^{73} +(150.407 + 260.512i) q^{75} +(-21.4048 - 619.018i) q^{77} +(788.392 - 455.178i) q^{79} +(-40.5000 + 70.1481i) q^{81} +1052.65 q^{83} -605.573 q^{85} +(-62.8128 + 108.795i) q^{87} +(-1126.90 + 650.614i) q^{89} +(312.906 - 195.377i) q^{91} +(-284.485 - 492.743i) q^{93} +(-4.07352 - 2.35185i) q^{95} -950.793i q^{97} -300.994i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 72 q^{3} + 20 q^{7} - 216 q^{9}+O(q^{10}) \) 48 * q + 72 * q^3 + 20 * q^7 - 216 * q^9	\( 48 q + 72 q^{3} + 20 q^{7} - 216 q^{9} - 12 q^{11} + 28 q^{19} + 120 q^{21} + 684 q^{25} - 1296 q^{27} + 460 q^{31} - 36 q^{33} + 568 q^{35} + 252 q^{37} + 324 q^{39} + 280 q^{47} - 184 q^{49} - 392 q^{53} + 848 q^{55} + 168 q^{57} - 964 q^{59} - 600 q^{61} + 180 q^{63} + 280 q^{65} - 660 q^{67} + 324 q^{73} - 2052 q^{75} + 1568 q^{77} - 2652 q^{79} - 1944 q^{81} + 1336 q^{83} - 1056 q^{85} - 3004 q^{91} - 1380 q^{93} - 3984 q^{95}+O(q^{100}) \) 48 * q + 72 * q^3 + 20 * q^7 - 216 * q^9 - 12 * q^11 + 28 * q^19 + 120 * q^21 + 684 * q^25 - 1296 * q^27 + 460 * q^31 - 36 * q^33 + 568 * q^35 + 252 * q^37 + 324 * q^39 + 280 * q^47 - 184 * q^49 - 392 * q^53 + 848 * q^55 + 168 * q^57 - 964 * q^59 - 600 * q^61 + 180 * q^63 + 280 * q^65 - 660 * q^67 + 324 * q^73 - 2052 * q^75 + 1568 * q^77 - 2652 * q^79 - 1944 * q^81 + 1336 * q^83 - 1056 * q^85 - 3004 * q^91 - 1380 * q^93 - 3984 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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