LMFDB - Embedded newform 168.3.z.a.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,3,Mod(73,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("168.73");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	168.z (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:	$4.57766844125$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.126303473664.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 9x^{6} + 2x^{5} + 92x^{4} + 14x^{3} - 441x^{2} - 686x + 2401 $ x^8 - 2x^7 - 9x^6 + 2x^5 + 92x^4 + 14x^3 - 441x^2 - 686*x + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.2
Root			$-1.43536 + 2.22255i$ of defining polynomial
Character	$\chi$	$=$	168.73
Dual form			168.3.z.a.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 - 0.866025i) q^{3} +(-2.05105 + 1.18418i) q^{5} +(4.55981 + 5.31113i) q^{7} +(1.50000 + 2.59808i) q^{9} +(4.00876 - 6.94337i) q^{11} +23.8428i q^{13} +4.10211 q^{15} +(27.9857 + 16.1575i) q^{17} +(12.6133 - 7.28227i) q^{19} +(-2.24014 - 11.9156i) q^{21} +(-2.82843 - 4.89898i) q^{23} +(-9.69545 + 16.7930i) q^{25} -5.19615i q^{27} -34.3864 q^{29} +(23.5479 + 13.5954i) q^{31} +(-12.0263 + 6.94337i) q^{33} +(-15.6417 - 5.49379i) q^{35} +(4.04599 + 7.00786i) q^{37} +(20.6485 - 35.7642i) q^{39} -50.6069i q^{41} -39.8591 q^{43} +(-6.15316 - 3.55253i) q^{45} +(-8.13954 + 4.69937i) q^{47} +(-7.41622 + 48.4355i) q^{49} +(-27.9857 - 48.4726i) q^{51} +(27.0592 - 46.8680i) q^{53} +18.9883i q^{55} -25.2265 q^{57} +(-38.1831 - 22.0450i) q^{59} +(-30.0000 + 17.3205i) q^{61} +(-6.95900 + 19.8134i) q^{63} +(-28.2341 - 48.9029i) q^{65} +(58.9453 - 102.096i) q^{67} +9.79796i q^{69} -38.2807 q^{71} +(50.4867 + 29.1485i) q^{73} +(29.0864 - 16.7930i) q^{75} +(55.1564 - 10.3694i) q^{77} +(38.2995 + 66.3366i) q^{79} +(-4.50000 + 7.79423i) q^{81} +58.2873i q^{83} -76.5335 q^{85} +(51.5796 + 29.7795i) q^{87} +(12.5005 - 7.21720i) q^{89} +(-126.632 + 108.719i) q^{91} +(-23.5479 - 40.7861i) q^{93} +(-17.2470 + 29.8727i) q^{95} -120.336i q^{97} +24.0526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} + 6 q^{5} - 4 q^{7} + 12 q^{9} + 14 q^{11} - 12 q^{15} + 12 q^{17} + 78 q^{19} + 18 q^{21} - 6 q^{25} - 4 q^{29} - 24 q^{31} - 42 q^{33} - 156 q^{35} + 50 q^{37} - 6 q^{39} - 20 q^{43} + 18 q^{45}+ \cdots + 84 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 + 6 * q^5 - 4 * q^7 + 12 * q^9 + 14 * q^11 - 12 * q^15 + 12 * q^17 + 78 * q^19 + 18 * q^21 - 6 * q^25 - 4 * q^29 - 24 * q^31 - 42 * q^33 - 156 * q^35 + 50 * q^37 - 6 * q^39 - 20 * q^43 + 18 * q^45 + 12 * q^47 + 220 * q^49 - 12 * q^51 - 50 * q^53 - 156 * q^57 - 186 * q^59 - 240 * q^61 - 42 * q^63 - 148 * q^65 + 34 * q^67 + 424 * q^71 + 294 * q^73 + 18 * q^75 + 126 * q^77 - 40 * q^79 - 36 * q^81 - 232 * q^85 + 6 * q^87 - 132 * q^89 - 378 * q^91 + 24 * q^93 + 144 * q^95 + 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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
$5$	−2.05105	+	1.18418i	−0.410211	+	0.236835i	−0.690880	−	0.722969i	$-0.742777\pi$
$5$	−2.05105	+	1.18418i	−0.410211	+	0.236835i	0.280670	+	0.959804i	$0.409443\pi$
$6$		0			0
$7$	4.55981	+	5.31113i	0.651402	+	0.758733i
$7$	4.55981	+	5.31113i	0.651402	+	0.758733i
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$	4.00876	−	6.94337i	0.364433	−	0.631216i	−0.624252	−	0.781223i	$-0.714596\pi$
$11$	4.00876	−	6.94337i	0.364433	−	0.631216i	0.988685	+	0.150007i	$0.0479296\pi$
$12$		0			0
$13$			23.8428i			1.83406i	0.398814	+	0.917032i	$0.369422\pi$
$13$			23.8428i			1.83406i	−0.398814	+	0.917032i	$0.630578\pi$
$14$		0			0
$15$	4.10211			0.273474
$16$		0			0
$17$	27.9857	+	16.1575i	1.64622	+	0.950444i	0.978557	+	0.205977i	$0.0660373\pi$
$17$	27.9857	+	16.1575i	1.64622	+	0.950444i	0.667660	+	0.744466i	$0.267296\pi$
$18$		0			0
$19$	12.6133	−	7.28227i	0.663856	−	0.383277i	−0.129889	−	0.991529i	$-0.541462\pi$
$19$	12.6133	−	7.28227i	0.663856	−	0.383277i	0.793745	+	0.608251i	$0.208129\pi$
$20$		0			0
$21$	−2.24014	−	11.9156i	−0.106674	−	0.567410i
$22$		0			0
$23$	−2.82843	−	4.89898i	−0.122975	−	0.212999i	0.797965	−	0.602704i	$-0.205910\pi$
$23$	−2.82843	−	4.89898i	−0.122975	−	0.212999i	−0.920940	+	0.389705i	$0.872577\pi$
$24$		0			0
$25$	−9.69545	+	16.7930i	−0.387818	+	0.671721i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	−34.3864			−1.18574			−0.592869	−	0.805299i	$-0.702005\pi$
$29$	−34.3864			−1.18574			−0.592869	+	0.805299i	$0.702005\pi$
$30$		0			0
$31$	23.5479	+	13.5954i	0.759609	+	0.438561i	0.829156	−	0.559018i	$-0.188822\pi$
$31$	23.5479	+	13.5954i	0.759609	+	0.438561i	−0.0695460	+	0.997579i	$0.522155\pi$
$32$		0			0
$33$	−12.0263	+	6.94337i	−0.364433	+	0.210405i
$34$		0			0
$35$	−15.6417	−	5.49379i	−0.446907	−	0.156965i
$36$		0			0
$37$	4.04599	+	7.00786i	0.109351	+	0.189402i	0.915508	−	0.402301i	$-0.131789\pi$
$37$	4.04599	+	7.00786i	0.109351	+	0.189402i	−0.806156	+	0.591702i	$0.798456\pi$
$38$		0			0
$39$	20.6485	−	35.7642i	0.529449	−	0.917032i
$40$		0			0
$41$		−	50.6069i		−	1.23431i	−0.786840	−	0.617157i	$-0.788284\pi$
$41$		−	50.6069i		−	1.23431i	0.786840	−	0.617157i	$-0.211716\pi$
$42$		0			0
$43$	−39.8591			−0.926957			−0.463478	−	0.886108i	$-0.653399\pi$
$43$	−39.8591			−0.926957			−0.463478	+	0.886108i	$0.653399\pi$
$44$		0			0
$45$	−6.15316	−	3.55253i	−0.136737	−	0.0789451i
$46$		0			0
$47$	−8.13954	+	4.69937i	−0.173182	+	0.0999865i	−0.584085	−	0.811692i	$-0.698547\pi$
$47$	−8.13954	+	4.69937i	−0.173182	+	0.0999865i	0.410904	+	0.911679i	$0.365213\pi$
$48$		0			0
$49$	−7.41622	+	48.4355i	−0.151351	+	0.988480i
$50$		0			0
$51$	−27.9857	−	48.4726i	−0.548739	−	0.950444i
$52$		0			0
$53$	27.0592	−	46.8680i	0.510552	−	0.884302i	−0.489373	−	0.872074i	$-0.662774\pi$
$53$	27.0592	−	46.8680i	0.510552	−	0.884302i	0.999925	−	0.0122274i	$-0.00389219\pi$
$54$		0			0
$55$			18.9883i			0.345242i
$56$		0			0
$57$	−25.2265			−0.442571
$58$		0			0
$59$	−38.1831	−	22.0450i	−0.647171	−	0.373644i	0.140201	−	0.990123i	$-0.455225\pi$
$59$	−38.1831	−	22.0450i	−0.647171	−	0.373644i	−0.787371	+	0.616479i	$0.788559\pi$
$60$		0			0
$61$	−30.0000	+	17.3205i	−0.491803	+	0.283943i	−0.725322	−	0.688409i	$-0.758309\pi$
$61$	−30.0000	+	17.3205i	−0.491803	+	0.283943i	0.233519	+	0.972352i	$0.424976\pi$
$62$		0			0
$63$	−6.95900	+	19.8134i	−0.110460	+	0.314499i
$64$		0			0
$65$	−28.2341	−	48.9029i	−0.434371	−	0.752353i
$66$		0			0
$67$	58.9453	−	102.096i	0.879781	−	1.52382i	0.0281991	−	0.999602i	$-0.491023\pi$
$67$	58.9453	−	102.096i	0.879781	−	1.52382i	0.851581	−	0.524222i	$-0.175644\pi$
$68$		0			0
$69$			9.79796i			0.141999i
$70$		0			0
$71$	−38.2807			−0.539165			−0.269582	−	0.962977i	$-0.586886\pi$
$71$	−38.2807			−0.539165			−0.269582	+	0.962977i	$0.586886\pi$
$72$		0			0
$73$	50.4867	+	29.1485i	0.691599	+	0.399295i	0.804211	−	0.594344i	$-0.202588\pi$
$73$	50.4867	+	29.1485i	0.691599	+	0.399295i	−0.112612	+	0.993639i	$0.535922\pi$
$74$		0			0
$75$	29.0864	−	16.7930i	0.387818	−	0.223907i
$76$		0			0
$77$	55.1564	−	10.3694i	0.716316	−	0.134668i
$78$		0			0
$79$	38.2995	+	66.3366i	0.484803	+	0.839704i	0.999848	−	0.0174596i	$-0.00555783\pi$
$79$	38.2995	+	66.3366i	0.484803	+	0.839704i	−0.515044	+	0.857164i	$0.672224\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			58.2873i			0.702257i	0.936327	+	0.351129i	$0.114202\pi$
$83$			58.2873i			0.702257i	−0.936327	+	0.351129i	$0.885798\pi$
$84$		0			0
$85$	−76.5335			−0.900394
$86$		0			0
$87$	51.5796	+	29.7795i	0.592869	+	0.342293i
$88$		0			0
$89$	12.5005	−	7.21720i	0.140456	−	0.0810921i	−0.428126	−	0.903719i	$-0.640826\pi$
$89$	12.5005	−	7.21720i	0.140456	−	0.0810921i	0.568581	+	0.822627i	$0.307493\pi$
$90$		0			0
$91$	−126.632	+	108.719i	−1.39156	+	1.19471i
$92$		0			0
$93$	−23.5479	−	40.7861i	−0.253203	−	0.438561i
$94$		0			0
$95$	−17.2470	+	29.8727i	−0.181547	+	0.314449i
$96$		0			0
$97$		−	120.336i		−	1.24058i	−0.784374	−	0.620289i	$-0.787015\pi$
$97$		−	120.336i		−	1.24058i	0.784374	−	0.620289i	$-0.212985\pi$
$98$		0			0
$99$	24.0526			0.242955
$100$		0			0
$101$	157.876	+	91.1498i	1.56313	+	0.902473i	0.996938	+	0.0781997i	$0.0249172\pi$
$101$	157.876	+	91.1498i	1.56313	+	0.902473i	0.566192	+	0.824274i	$0.308416\pi$
$102$		0			0
$103$	21.0409	−	12.1479i	0.204280	−	0.117941i	−0.394370	−	0.918952i	$-0.629037\pi$
$103$	21.0409	−	12.1479i	0.204280	−	0.117941i	0.598650	+	0.801010i	$0.295704\pi$
$104$		0			0
$105$	18.7048	+	21.7868i	0.178141	+	0.207494i
$106$		0			0
$107$	−20.4419	−	35.4064i	−0.191046	−	0.330901i	0.754551	−	0.656241i	$-0.227855\pi$
$107$	−20.4419	−	35.4064i	−0.191046	−	0.330901i	−0.945597	+	0.325340i	$0.894521\pi$
$108$		0			0
$109$	34.1243	−	59.1049i	0.313067	−	0.542247i	−0.665958	−	0.745989i	$-0.731977\pi$
$109$	34.1243	−	59.1049i	0.313067	−	0.542247i	0.979025	+	0.203742i	$0.0653104\pi$
$110$		0			0
$111$		−	14.0157i		−	0.126268i
$112$		0			0
$113$	−36.4622			−0.322674			−0.161337	−	0.986899i	$-0.551581\pi$
$113$	−36.4622			−0.322674			−0.161337	+	0.986899i	$0.551581\pi$
$114$		0			0
$115$	11.6025	+	6.69871i	0.100891	+	0.0582497i
$116$		0			0
$117$	−61.9455	+	35.7642i	−0.529449	+	0.305677i
$118$		0			0
$119$	41.7947	+	222.311i	0.351216	+	1.86816i
$120$		0			0
$121$	28.3597	+	49.1204i	0.234378	+	0.405954i
$122$		0			0
$123$	−43.8268	+	75.9103i	−0.356316	+	0.617157i
$124$		0			0
$125$		−	105.133i		−	0.841066i
$126$		0			0
$127$	184.703			1.45436			0.727178	−	0.686449i	$-0.240831\pi$
$127$	184.703			1.45436			0.727178	+	0.686449i	$0.240831\pi$
$128$		0			0
$129$	59.7887	+	34.5190i	0.463478	+	0.267589i
$130$		0			0
$131$	−174.145	+	100.543i	−1.32935	+	0.767502i	−0.985200	−	0.171411i	$-0.945167\pi$
$131$	−174.145	+	100.543i	−1.32935	+	0.767502i	−0.344153	+	0.938913i	$0.611834\pi$
$132$		0			0
$133$	96.1912	+	33.7849i	0.723242	+	0.254022i
$134$		0			0
$135$	6.15316	+	10.6576i	0.0455790	+	0.0789451i
$136$		0			0
$137$	69.2606	−	119.963i	0.505552	−	0.875641i	−0.494428	−	0.869219i	$-0.664622\pi$
$137$	69.2606	−	119.963i	0.505552	−	0.875641i	0.999979	−	0.00642244i	$-0.00204434\pi$
$138$		0			0
$139$		−	53.0062i		−	0.381340i	−0.981654	−	0.190670i	$-0.938934\pi$
$139$		−	53.0062i		−	0.381340i	0.981654	−	0.190670i	$-0.0610660\pi$
$140$		0			0
$141$	16.2791			0.115454
$142$		0			0
$143$	165.550	+	95.5802i	1.15769	+	0.668393i
$144$		0			0
$145$	70.5283	−	40.7195i	0.486402	−	0.280824i
$146$		0			0
$147$	53.0707	−	66.2306i	0.361025	−	0.450549i
$148$		0			0
$149$	44.4896	+	77.0583i	0.298588	+	0.517170i	0.975813	−	0.218606i	$-0.0701510\pi$
$149$	44.4896	+	77.0583i	0.298588	+	0.517170i	−0.677225	+	0.735776i	$0.736818\pi$
$150$		0			0
$151$	23.9271	−	41.4429i	0.158458	−	0.274457i	−0.775855	−	0.630911i	$-0.782681\pi$
$151$	23.9271	−	41.4429i	0.158458	−	0.274457i	0.934313	+	0.356455i	$0.116015\pi$
$152$		0			0
$153$			96.9453i			0.633629i
$154$		0			0
$155$	−64.3973			−0.415467
$156$		0			0
$157$	−140.598	−	81.1745i	−0.895531	−	0.517035i	−0.0197835	−	0.999804i	$-0.506298\pi$
$157$	−140.598	−	81.1745i	−0.895531	−	0.517035i	−0.875748	+	0.482769i	$0.839631\pi$
$158$		0			0
$159$	−81.1777	+	46.8680i	−0.510552	+	0.294767i
$160$		0			0
$161$	13.1220	−	37.3606i	0.0815032	−	0.232053i
$162$		0			0
$163$	−142.372	−	246.596i	−0.873450	−	1.51286i	−0.858404	−	0.512974i	$-0.828544\pi$
$163$	−142.372	−	246.596i	−0.873450	−	1.51286i	−0.0150459	−	0.999887i	$-0.504789\pi$
$164$		0			0
$165$	16.4444	−	28.4825i	0.0996628	−	0.172621i
$166$		0			0
$167$			240.554i			1.44044i	0.693743	+	0.720222i	$0.255960\pi$
$167$			240.554i			1.44044i	−0.693743	+	0.720222i	$0.744040\pi$
$168$		0			0
$169$	−399.481			−2.36379
$170$		0			0
$171$	37.8398	+	21.8468i	0.221285	+	0.127759i
$172$		0			0
$173$	−156.689	+	90.4643i	−0.905715	+	0.522915i	−0.879050	−	0.476729i	$-0.841822\pi$
$173$	−156.689	+	90.4643i	−0.905715	+	0.522915i	−0.0266652	+	0.999644i	$0.508489\pi$
$174$		0			0
$175$	−133.399	+	25.0792i	−0.762282	+	0.143310i
$176$		0			0
$177$	38.1831	+	66.1350i	0.215724	+	0.373644i
$178$		0			0
$179$	149.437	−	258.833i	0.834845	−	1.44599i	−0.0593107	−	0.998240i	$-0.518890\pi$
$179$	149.437	−	258.833i	0.834845	−	1.44599i	0.894156	−	0.447755i	$-0.147776\pi$
$180$		0			0
$181$		−	209.210i		−	1.15586i	−0.816087	−	0.577928i	$-0.803861\pi$
$181$		−	209.210i		−	1.15586i	0.816087	−	0.577928i	$-0.196139\pi$
$182$		0			0
$183$	60.0000			0.327869
$184$		0			0
$185$	−16.5971	−	9.58233i	−0.0897139	−	0.0517964i
$186$		0			0
$187$	224.376	−	129.543i	1.19987	−	0.692745i
$188$		0			0
$189$	27.5974	−	23.6935i	0.146018	−	0.125362i
$190$		0			0
$191$	−171.740	−	297.462i	−0.899160	−	1.55739i	−0.828570	−	0.559885i	$-0.810845\pi$
$191$	−171.740	−	297.462i	−0.899160	−	1.55739i	−0.0705895	−	0.997505i	$-0.522488\pi$
$192$		0			0
$193$	46.9612	−	81.3392i	0.243322	−	0.421447i	−0.718336	−	0.695696i	$-0.755096\pi$
$193$	46.9612	−	81.3392i	0.243322	−	0.421447i	0.961659	+	0.274249i	$0.0884294\pi$
$194$		0			0
$195$			97.8058i			0.501568i
$196$		0			0
$197$	163.468			0.829786			0.414893	−	0.909870i	$-0.363819\pi$
$197$	163.468			0.829786			0.414893	+	0.909870i	$0.363819\pi$
$198$		0			0
$199$	−235.308	−	135.855i	−1.18245	−	0.682690i	−0.225872	−	0.974157i	$-0.572523\pi$
$199$	−235.308	−	135.855i	−1.18245	−	0.682690i	−0.956581	+	0.291467i	$0.905857\pi$
$200$		0			0
$201$	−176.836	+	102.096i	−0.879781	+	0.507942i
$202$		0			0
$203$	−156.795	−	182.631i	−0.772391	−	0.899658i
$204$		0			0
$205$	59.9274	+	103.797i	0.292329	+	0.506329i
$206$		0			0
$207$	8.48528	−	14.6969i	0.0409917	−	0.0709997i
$208$		0			0
$209$		−	116.771i		−	0.558715i
$210$		0			0
$211$	−122.158			−0.578947			−0.289474	−	0.957186i	$-0.593480\pi$
$211$	−122.158			−0.578947			−0.289474	+	0.957186i	$0.593480\pi$
$212$		0			0
$213$	57.4210	+	33.1521i	0.269582	+	0.155643i
$214$		0			0
$215$	81.7532	−	47.2002i	0.380247	−	0.219536i
$216$		0			0
$217$	35.1671	+	187.058i	0.162061	+	0.862020i
$218$		0			0
$219$	−50.4867	−	87.4455i	−0.230533	−	0.399295i
$220$		0			0
$221$	−385.242	+	667.258i	−1.74317	+	3.01927i
$222$		0			0
$223$		−	182.325i		−	0.817603i	−0.912623	−	0.408801i	$-0.865947\pi$
$223$		−	182.325i		−	0.817603i	0.912623	−	0.408801i	$-0.134053\pi$
$224$		0			0
$225$	−58.1727			−0.258545
$226$		0			0
$227$	−19.4602	−	11.2353i	−0.0857277	−	0.0494949i	0.456523	−	0.889711i	$-0.349094\pi$
$227$	−19.4602	−	11.2353i	−0.0857277	−	0.0494949i	−0.542251	+	0.840217i	$0.682428\pi$
$228$		0			0
$229$	248.673	−	143.571i	1.08591	−	0.626949i	0.153423	−	0.988161i	$-0.450970\pi$
$229$	248.673	−	143.571i	1.08591	−	0.626949i	0.932484	+	0.361212i	$0.117637\pi$
$230$		0			0
$231$	−91.7147	−	32.2126i	−0.397034	−	0.139449i
$232$		0			0
$233$	−26.7700	−	46.3669i	−0.114893	−	0.199000i	0.802844	−	0.596189i	$-0.203319\pi$
$233$	−26.7700	−	46.3669i	−0.114893	−	0.199000i	−0.917737	+	0.397189i	$0.869986\pi$
$234$		0			0
$235$	11.1298	−	19.2773i	0.0473607	−	0.0820311i
$236$		0			0
$237$		−	132.673i		−	0.559803i
$238$		0			0
$239$	340.188			1.42338			0.711691	−	0.702493i	$-0.247930\pi$
$239$	340.188			1.42338			0.711691	+	0.702493i	$0.247930\pi$
$240$		0			0
$241$	−22.3377	−	12.8967i	−0.0926877	−	0.0535132i	0.452940	−	0.891541i	$-0.350375\pi$
$241$	−22.3377	−	12.8967i	−0.0926877	−	0.0535132i	−0.545627	+	0.838028i	$0.683709\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−42.1451	−	108.126i	−0.172021	−	0.441330i
$246$		0			0
$247$	173.630	+	300.736i	0.702955	+	1.21755i
$248$		0			0
$249$	50.4783	−	87.4310i	0.202724	−	0.351129i
$250$		0			0
$251$			143.218i			0.570590i	0.958440	+	0.285295i	$0.0920915\pi$
$251$			143.218i			0.570590i	−0.958440	+	0.285295i	$0.907908\pi$
$252$		0			0
$253$	−45.3539			−0.179265
$254$		0			0
$255$	114.800	+	66.2800i	0.450197	+	0.259921i
$256$		0			0
$257$	34.0477	−	19.6575i	0.132481	−	0.0764882i	−0.432295	−	0.901732i	$-0.642296\pi$
$257$	34.0477	−	19.6575i	0.132481	−	0.0764882i	0.564776	+	0.825244i	$0.308963\pi$
$258$		0			0
$259$	−18.7707	+	53.4433i	−0.0724737	+	0.206345i
$260$		0			0
$261$	−51.5796	−	89.3384i	−0.197623	−	0.342293i
$262$		0			0
$263$	86.2864	−	149.452i	0.328085	−	0.568260i	−0.654047	−	0.756454i	$-0.726930\pi$
$263$	86.2864	−	149.452i	0.328085	−	0.568260i	0.982132	+	0.188194i	$0.0602634\pi$
$264$		0			0
$265$			128.172i			0.483667i
$266$		0			0
$267$	−25.0011			−0.0936371
$268$		0			0
$269$	125.662	+	72.5509i	0.467144	+	0.269706i	0.715043	−	0.699080i	$-0.246407\pi$
$269$	125.662	+	72.5509i	0.467144	+	0.269706i	−0.247899	+	0.968786i	$0.579740\pi$
$270$		0			0
$271$	−3.61372	+	2.08638i	−0.0133348	+	0.00769883i	−0.506653	−	0.862150i	$-0.669117\pi$
$271$	−3.61372	+	2.08638i	−0.0133348	+	0.00769883i	0.493318	+	0.869849i	$0.335784\pi$
$272$		0			0
$273$	284.102	−	53.4114i	1.04067	−	0.195646i
$274$		0			0
$275$	77.7335	+	134.638i	0.282667	+	0.489594i
$276$		0			0
$277$	−8.06909	+	13.9761i	−0.0291303	+	0.0504551i	−0.880223	−	0.474560i	$-0.842607\pi$
$277$	−8.06909	+	13.9761i	−0.0291303	+	0.0504551i	0.851093	+	0.525015i	$0.175940\pi$
$278$		0			0
$279$			81.5723i			0.292374i
$280$		0			0
$281$	−404.197			−1.43843			−0.719213	−	0.694790i	$-0.755497\pi$
$281$	−404.197			−1.43843			−0.719213	+	0.694790i	$0.755497\pi$
$282$		0			0
$283$	10.7861	+	6.22734i	0.0381133	+	0.0220047i	0.518936	−	0.854813i	$-0.326328\pi$
$283$	10.7861	+	6.22734i	0.0381133	+	0.0220047i	−0.480822	+	0.876818i	$0.659662\pi$
$284$		0			0
$285$	51.7409	−	29.8727i	0.181547	−	0.104816i
$286$		0			0
$287$	268.780	−	230.758i	0.936515	−	0.804034i
$288$		0			0
$289$	377.632	+	654.078i	1.30669	+	2.26325i
$290$		0			0
$291$	−104.214	+	180.504i	−0.358124	+	0.620289i
$292$		0			0
$293$			267.174i			0.911858i	0.890016	+	0.455929i	$0.150693\pi$
$293$			267.174i			0.911858i	−0.890016	+	0.455929i	$0.849307\pi$
$294$		0			0
$295$	104.421			0.353968
$296$		0			0
$297$	−36.0788	−	20.8301i	−0.121478	−	0.0701351i
$298$		0			0
$299$	116.806	−	67.4377i	0.390654	−	0.225544i
$300$		0			0
$301$	−181.750	−	211.697i	−0.603821	−	0.703312i
$302$		0			0
$303$	−157.876	−	273.449i	−0.521043	−	0.902473i
$304$		0			0
$305$	41.0211	−	71.0506i	0.134495	−	0.232953i
$306$		0			0
$307$			417.532i			1.36004i	0.733193	+	0.680020i	$0.238029\pi$
$307$			417.532i			1.36004i	−0.733193	+	0.680020i	$0.761971\pi$
$308$		0			0
$309$	−42.0817			−0.136187
$310$		0			0
$311$	−478.894	−	276.489i	−1.53985	−	0.889033i	−0.998847	−	0.0480134i	$-0.984711\pi$
$311$	−478.894	−	276.489i	−1.53985	−	0.889033i	−0.541004	−	0.841020i	$-0.681956\pi$
$312$		0			0
$313$	133.600	−	77.1343i	0.426839	−	0.246435i	−0.271160	−	0.962534i	$-0.587407\pi$
$313$	133.600	−	77.1343i	0.426839	−	0.246435i	0.697999	+	0.716099i	$0.254074\pi$
$314$		0			0
$315$	−9.18931	−	48.8791i	−0.0291724	−	0.155172i
$316$		0			0
$317$	82.1807	+	142.341i	0.259245	+	0.449026i	0.966040	−	0.258393i	$-0.0831929\pi$
$317$	82.1807	+	142.341i	0.259245	+	0.449026i	−0.706795	+	0.707419i	$0.749860\pi$
$318$		0			0
$319$	−137.847	+	238.758i	−0.432121	+	0.748456i
$320$		0			0
$321$			70.8128i			0.220601i
$322$		0			0
$323$	470.654			1.45713
$324$		0			0
$325$	−400.393	−	231.167i	−1.23198	−	0.711283i
$326$		0			0
$327$	−102.373	+	59.1049i	−0.313067	+	0.180749i
$328$		0			0
$329$	−62.0737	−	21.8019i	−0.188674	−	0.0662673i
$330$		0			0
$331$	262.136	+	454.033i	0.791952	+	1.37170i	0.924757	+	0.380558i	$0.124268\pi$
$331$	262.136	+	454.033i	0.791952	+	1.37170i	−0.132805	+	0.991142i	$0.542398\pi$
$332$		0			0
$333$	−12.1380	+	21.0236i	−0.0364503	+	0.0631339i
$334$		0			0
$335$			279.206i			0.833452i
$336$		0			0
$337$	479.725			1.42352			0.711758	−	0.702424i	$-0.247899\pi$
$337$	479.725			1.42352			0.711758	+	0.702424i	$0.247899\pi$
$338$		0			0
$339$	54.6933	+	31.5772i	0.161337	+	0.0931481i
$340$		0			0
$341$	188.796	−	109.001i	0.553653	−	0.319652i
$342$		0			0
$343$	−291.064	+	181.468i	−0.848583	+	0.529062i
$344$		0			0
$345$	−11.6025	−	20.0961i	−0.0336305	−	0.0582497i
$346$		0			0
$347$	−21.5704	+	37.3610i	−0.0621624	+	0.107669i	−0.895432	−	0.445199i	$-0.853133\pi$
$347$	−21.5704	+	37.3610i	−0.0621624	+	0.107669i	0.833269	+	0.552867i	$0.186466\pi$
$348$		0			0
$349$		−	20.2166i		−	0.0579273i	−0.999580	−	0.0289636i	$-0.990779\pi$
$349$		−	20.2166i		−	0.0579273i	0.999580	−	0.0289636i	$-0.00922070\pi$
$350$		0			0
$351$	123.891			0.352966
$352$		0			0
$353$	227.795	+	131.517i	0.645310	+	0.372570i	0.786657	−	0.617390i	$-0.211810\pi$
$353$	227.795	+	131.517i	0.645310	+	0.372570i	−0.141347	+	0.989960i	$0.545143\pi$
$354$		0			0
$355$	78.5157	−	45.3311i	0.221171	−	0.127693i
$356$		0			0
$357$	129.835	−	369.662i	0.363683	−	1.03547i
$358$		0			0
$359$	−256.794	−	444.781i	−0.715305	−	1.23894i	−0.962842	−	0.270066i	$-0.912954\pi$
$359$	−256.794	−	444.781i	−0.715305	−	1.23894i	0.247537	−	0.968878i	$-0.420379\pi$
$360$		0			0
$361$	−74.4371	+	128.929i	−0.206197	+	0.357143i
$362$		0			0
$363$		−	98.2409i		−	0.270636i
$364$		0			0
$365$	−138.068			−0.378268
$366$		0			0
$367$	−76.4289	−	44.1262i	−0.208253	−	0.120235i	0.392246	−	0.919860i	$-0.371698\pi$
$367$	−76.4289	−	44.1262i	−0.208253	−	0.120235i	−0.600499	+	0.799625i	$0.705031\pi$
$368$		0			0
$369$	131.481	−	75.9103i	0.356316	−	0.205719i
$370$		0			0
$371$	372.307	−	69.9941i	1.00352	−	0.188663i
$372$		0			0
$373$	193.918	+	335.877i	0.519889	+	0.900474i	0.999733	+	0.0231198i	$0.00735993\pi$
$373$	193.918	+	335.877i	0.519889	+	0.900474i	−0.479844	+	0.877354i	$0.659307\pi$
$374$		0			0
$375$	−91.0481	+	157.700i	−0.242795	+	0.420533i
$376$		0			0
$377$		−	819.869i		−	2.17472i
$378$		0			0
$379$	215.531			0.568682			0.284341	−	0.958723i	$-0.408225\pi$
$379$	215.531			0.568682			0.284341	+	0.958723i	$0.408225\pi$
$380$		0			0
$381$	−277.055	−	159.958i	−0.727178	−	0.419836i
$382$		0			0
$383$	−448.533	+	258.961i	−1.17111	+	0.676138i	−0.953940	−	0.299997i	$-0.903014\pi$
$383$	−448.533	+	258.961i	−1.17111	+	0.676138i	−0.217165	+	0.976135i	$0.569681\pi$
$384$		0			0
$385$	−100.849	+	86.5831i	−0.261946	+	0.224891i
$386$		0			0
$387$	−59.7887	−	103.557i	−0.154493	−	0.267589i
$388$		0			0
$389$	−148.316	+	256.891i	−0.381275	+	0.660387i	−0.991245	−	0.132037i	$-0.957848\pi$
$389$	−148.316	+	256.891i	−0.381275	+	0.660387i	0.609970	+	0.792424i	$0.291181\pi$
$390$		0			0
$391$		−	182.802i		−	0.467524i
$392$		0			0
$393$	348.291			0.886235
$394$		0			0
$395$	−157.108	−	90.7066i	−0.397743	−	0.229637i
$396$		0			0
$397$	140.243	−	80.9692i	0.353256	−	0.203953i	−0.312862	−	0.949799i	$-0.601288\pi$
$397$	140.243	−	80.9692i	0.353256	−	0.203953i	0.666119	+	0.745846i	$0.267954\pi$
$398$		0			0
$399$	−115.028	−	133.981i	−0.288291	−	0.335793i
$400$		0			0
$401$	−370.716	−	642.098i	−0.924478	−	1.60124i	−0.792399	−	0.610004i	$-0.791168\pi$
$401$	−370.716	−	642.098i	−0.924478	−	1.60124i	−0.132079	−	0.991239i	$-0.542165\pi$
$402$		0			0
$403$	−324.152	+	561.448i	−0.804348	+	1.39317i
$404$		0			0
$405$		−	21.3152i		−	0.0526301i
$406$		0			0
$407$	64.8776			0.159404
$408$		0			0
$409$	−143.889	−	83.0741i	−0.351806	−	0.203115i	0.313675	−	0.949531i	$-0.398440\pi$
$409$	−143.889	−	83.0741i	−0.351806	−	0.203115i	−0.665480	+	0.746415i	$0.731773\pi$
$410$		0			0
$411$	−207.782	+	119.963i	−0.505552	+	0.291880i
$412$		0			0
$413$	−57.0237	−	303.316i	−0.138072	−	0.734422i
$414$		0			0
$415$	−69.0225	−	119.550i	−0.166319	−	0.288073i
$416$		0			0
$417$	−45.9047	+	79.5094i	−0.110083	+	0.190670i
$418$		0			0
$419$			210.967i			0.503502i	0.967792	+	0.251751i	$0.0810064\pi$
$419$			210.967i			0.503502i	−0.967792	+	0.251751i	$0.918994\pi$
$420$		0			0
$421$	191.145			0.454027			0.227013	−	0.973892i	$-0.427104\pi$
$421$	191.145			0.454027			0.227013	+	0.973892i	$0.427104\pi$
$422$		0			0
$423$	−24.4186	−	14.0981i	−0.0577272	−	0.0333288i
$424$		0			0
$425$	−542.668	+	313.309i	−1.27687	+	0.737199i
$426$		0			0
$427$	−228.786	−	80.3556i	−0.535798	−	0.188187i
$428$		0			0
$429$	−165.550	−	286.741i	−0.385897	−	0.668393i
$430$		0			0
$431$	47.6578	−	82.5457i	0.110575	−	0.191521i	−0.805427	−	0.592695i	$-0.798064\pi$
$431$	47.6578	−	82.5457i	0.110575	−	0.191521i	0.916002	+	0.401173i	$0.131397\pi$
$432$		0			0
$433$		−	393.461i		−	0.908685i	−0.890827	−	0.454343i	$-0.849874\pi$
$433$		−	393.461i		−	0.908685i	0.890827	−	0.454343i	$-0.150126\pi$
$434$		0			0
$435$	−141.057			−0.324268
$436$		0			0
$437$	−71.3514	−	41.1947i	−0.163275	−	0.0942672i
$438$		0			0
$439$	540.002	−	311.770i	1.23007	−	0.710183i	0.263028	−	0.964788i	$-0.415279\pi$
$439$	540.002	−	311.770i	1.23007	−	0.710183i	0.967045	+	0.254605i	$0.0819455\pi$
$440$		0			0
$441$	−136.964	+	53.3854i	−0.310575	+	0.121055i
$442$		0			0
$443$	280.200	+	485.321i	0.632507	+	1.09553i	0.987038	+	0.160489i	$0.0513072\pi$
$443$	280.200	+	485.321i	0.632507	+	1.09553i	−0.354531	+	0.935044i	$0.615359\pi$
$444$		0			0
$445$	−17.0929	+	29.6057i	−0.0384109	+	0.0665297i
$446$		0			0
$447$		−	154.117i		−	0.344780i
$448$		0			0
$449$	387.654			0.863372			0.431686	−	0.902024i	$-0.357919\pi$
$449$	387.654			0.863372			0.431686	+	0.902024i	$0.357919\pi$
$450$		0			0
$451$	−351.382	−	202.871i	−0.779119	−	0.449824i
$452$		0			0
$453$	−71.7813	+	41.4429i	−0.158458	+	0.0914855i
$454$		0			0
$455$	130.988	−	372.943i	0.287885	−	0.819655i
$456$		0			0
$457$	−243.867	−	422.391i	−0.533627	−	0.924268i	−0.999228	−	0.0392740i	$-0.987495\pi$
$457$	−243.867	−	422.391i	−0.533627	−	0.924268i	0.465602	−	0.884994i	$-0.345838\pi$
$458$		0			0
$459$	83.9571	−	145.418i	0.182913	−	0.316815i
$460$		0			0
$461$			300.713i			0.652307i	0.945317	+	0.326153i	$0.105753\pi$
$461$			300.713i			0.652307i	−0.945317	+	0.326153i	$0.894247\pi$
$462$		0			0
$463$	−661.184			−1.42804			−0.714022	−	0.700124i	$-0.753128\pi$
$463$	−661.184			−1.42804			−0.714022	+	0.700124i	$0.753128\pi$
$464$		0			0
$465$	96.5960	+	55.7697i	0.207733	+	0.119935i
$466$		0			0
$467$	286.324	−	165.309i	0.613114	−	0.353982i	−0.161069	−	0.986943i	$-0.551494\pi$
$467$	286.324	−	165.309i	0.613114	−	0.353982i	0.774183	+	0.632961i	$0.218161\pi$
$468$		0			0
$469$	811.026	−	152.474i	1.72927	−	0.325104i
$470$		0			0
$471$	140.598	+	243.524i	0.298510	+	0.517035i
$472$		0			0
$473$	−159.786	+	276.757i	−0.337813	+	0.585110i
$474$		0			0
$475$			282.420i			0.594568i
$476$		0			0
$477$	162.355			0.340368
$478$		0			0
$479$	−542.813	−	313.393i	−1.13322	−	0.654266i	−0.188479	−	0.982077i	$-0.560356\pi$
$479$	−542.813	−	313.393i	−1.13322	−	0.654266i	−0.944743	+	0.327811i	$0.893689\pi$
$480$		0			0
$481$	−167.087	+	96.4678i	−0.347375	+	0.200557i
$482$		0			0
$483$	−52.0382	+	44.6769i	−0.107740	+	0.0924987i
$484$		0			0
$485$	142.499	+	246.816i	0.293812	+	0.508898i
$486$		0			0
$487$	−16.5404	+	28.6488i	−0.0339639	+	0.0588272i	−0.882508	−	0.470298i	$-0.844146\pi$
$487$	−16.5404	+	28.6488i	−0.0339639	+	0.0588272i	0.848544	+	0.529125i	$0.177480\pi$
$488$		0			0
$489$			493.192i			1.00857i
$490$		0			0
$491$	−460.309			−0.937493			−0.468747	−	0.883333i	$-0.655294\pi$
$491$	−460.309			−0.937493			−0.468747	+	0.883333i	$0.655294\pi$
$492$		0			0
$493$	−962.326	−	555.599i	−1.95198	−	1.12698i
$494$		0			0
$495$	−49.3331	+	28.4825i	−0.0996628	+	0.0575403i
$496$		0			0
$497$	−174.553	−	203.314i	−0.351213	−	0.409082i
$498$		0			0
$499$	0.462513	+	0.801097i	0.000926881	+	0.00160540i	0.866488	−	0.499197i	$-0.166372\pi$
$499$	0.462513	+	0.801097i	0.000926881	+	0.00160540i	−0.865562	+	0.500802i	$0.833038\pi$
$500$		0			0
$501$	208.326	−	360.831i	0.415820	−	0.720222i
$502$		0			0
$503$		−	457.206i		−	0.908959i	−0.890757	−	0.454479i	$-0.849825\pi$
$503$		−	457.206i		−	0.908959i	0.890757	−	0.454479i	$-0.150175\pi$
$504$		0			0
$505$	−431.750			−0.854950
$506$		0			0
$507$	599.221	+	345.960i	1.18190	+	0.682368i
$508$		0			0
$509$	28.4048	−	16.3995i	0.0558051	−	0.0322191i	−0.471838	−	0.881685i	$-0.656409\pi$
$509$	28.4048	−	16.3995i	0.0558051	−	0.0322191i	0.527643	+	0.849466i	$0.323076\pi$
$510$		0			0
$511$	75.3984	+	401.053i	0.147551	+	0.784840i
$512$		0			0
$513$	−37.8398	−	65.5404i	−0.0737618	−	0.127759i
$514$		0			0
$515$	−28.7706	+	49.8321i	−0.0558652	+	0.0967614i
$516$		0			0
$517$			75.3545i			0.145753i
$518$		0			0
$519$	313.377			0.603810
$520$		0			0
$521$	416.501	+	240.467i	0.799425	+	0.461548i	0.843270	−	0.537490i	$-0.180627\pi$
$521$	416.501	+	240.467i	0.799425	+	0.461548i	−0.0438448	+	0.999038i	$0.513961\pi$
$522$		0			0
$523$	370.870	−	214.122i	0.709120	−	0.409411i	−0.101615	−	0.994824i	$-0.532401\pi$
$523$	370.870	−	214.122i	0.709120	−	0.409411i	0.810735	+	0.585413i	$0.199068\pi$
$524$		0			0
$525$	221.818	+	77.9084i	0.422511	+	0.148397i
$526$		0			0
$527$	439.336	+	760.952i	0.833655	+	1.44393i
$528$		0			0
$529$	248.500	−	430.415i	0.469754	−	0.813638i
$530$		0			0
$531$		−	132.270i		−	0.249096i
$532$		0			0
$533$	1206.61			2.26381
$534$		0			0
$535$	83.8548	+	48.4136i	0.156738	+	0.0904927i
$536$		0			0
$537$	−448.312	+	258.833i	−0.834845	+	0.481998i
$538$		0			0
$539$	306.576	+	245.660i	0.568787	+	0.455770i
$540$		0			0
$541$	211.392	+	366.142i	0.390743	+	0.676787i	0.992548	−	0.121856i	$-0.0388846\pi$
$541$	211.392	+	366.142i	0.390743	+	0.676787i	−0.601804	+	0.798644i	$0.705551\pi$
$542$		0			0
$543$	−181.181	+	313.815i	−0.333667	+	0.577928i
$544$		0			0
$545$			161.637i			0.296581i
$546$		0			0
$547$	962.311			1.75925			0.879626	−	0.475665i	$-0.157793\pi$
$547$	962.311			1.75925			0.879626	+	0.475665i	$0.157793\pi$
$548$		0			0
$549$	−90.0000	−	51.9615i	−0.163934	−	0.0946476i
$550$		0			0
$551$	−433.724	+	250.411i	−0.787159	+	0.454466i
$552$		0			0
$553$	−177.684	+	505.896i	−0.321309	+	0.914821i
$554$		0			0
$555$	16.5971	+	28.7470i	0.0299046	+	0.0517964i
$556$		0			0
$557$	−458.690	+	794.474i	−0.823501	+	1.42634i	0.0795593	+	0.996830i	$0.474649\pi$
$557$	−458.690	+	794.474i	−0.823501	+	1.42634i	−0.903060	+	0.429515i	$0.858685\pi$
$558$		0			0
$559$		−	950.355i		−	1.70010i
$560$		0			0
$561$	−448.751			−0.799914
$562$		0			0
$563$	337.941	+	195.111i	0.600251	+	0.346555i	0.769140	−	0.639080i	$-0.220685\pi$
$563$	337.941	+	195.111i	0.600251	+	0.346555i	−0.168889	+	0.985635i	$0.554018\pi$
$564$		0			0
$565$	74.7859	−	43.1777i	0.132364	−	0.0764207i
$566$		0			0
$567$	−61.9153	+	11.6401i	−0.109198	+	0.0205293i
$568$		0			0
$569$	−76.9559	−	133.292i	−0.135248	−	0.234256i	0.790444	−	0.612534i	$-0.209850\pi$
$569$	−76.9559	−	133.292i	−0.135248	−	0.234256i	−0.925692	+	0.378278i	$0.876516\pi$
$570$		0			0
$571$	179.223	−	310.424i	0.313876	−	0.543650i	−0.665322	−	0.746557i	$-0.731706\pi$
$571$	179.223	−	310.424i	0.313876	−	0.543650i	0.979198	+	0.202907i	$0.0650389\pi$
$572$		0			0
$573$			594.923i			1.03826i
$574$		0			0
$575$	109.692			0.190768
$576$		0			0
$577$	771.351	+	445.340i	1.33683	+	0.771820i	0.986336	−	0.164745i	$-0.0526802\pi$
$577$	771.351	+	445.340i	1.33683	+	0.771820i	0.350494	+	0.936565i	$0.386014\pi$
$578$		0			0
$579$	−140.884	+	81.3392i	−0.243322	+	0.140482i
$580$		0			0
$581$	−309.572	+	265.779i	−0.532826	+	0.457451i
$582$		0			0
$583$	−216.948	−	375.765i	−0.372124	−	0.644537i
$584$		0			0
$585$	84.7023	−	146.709i	0.144790	−	0.250784i
$586$		0			0
$587$			85.2525i			0.145234i	0.997360	+	0.0726171i	$0.0231351\pi$
$587$			85.2525i			0.145234i	−0.997360	+	0.0726171i	$0.976865\pi$
$588$		0			0
$589$	396.021			0.672362
$590$		0			0
$591$	−245.202	−	141.567i	−0.414893	−	0.239539i
$592$		0			0
$593$	949.757	−	548.343i	1.60161	−	0.924692i	0.610449	−	0.792055i	$-0.290989\pi$
$593$	949.757	−	548.343i	1.60161	−	0.924692i	0.991165	−	0.132637i	$-0.0423444\pi$
$594$		0			0
$595$	−348.978	−	406.479i	−0.586518	−	0.683159i
$596$		0			0
$597$	235.308	+	407.566i	0.394151	+	0.682690i
$598$		0			0
$599$	36.5134	−	63.2431i	0.0609573	−	0.105581i	−0.833936	−	0.551861i	$-0.813918\pi$
$599$	36.5134	−	63.2431i	0.0609573	−	0.105581i	0.894894	+	0.446280i	$0.147251\pi$
$600$		0			0
$601$			911.924i			1.51734i	0.651472	+	0.758672i	$0.274152\pi$
$601$			911.924i			1.51734i	−0.651472	+	0.758672i	$0.725848\pi$
$602$		0			0
$603$	353.672			0.586520
$604$		0			0
$605$	−116.334	−	67.1658i	−0.192288	−	0.111018i
$606$		0			0
$607$	101.592	−	58.6544i	0.167368	−	0.0966299i	−0.413976	−	0.910288i	$-0.635860\pi$
$607$	101.592	−	58.6544i	0.167368	−	0.0966299i	0.581344	+	0.813658i	$0.302527\pi$
$608$		0			0
$609$	77.0305	+	409.735i	0.126487	+	0.672799i
$610$		0			0
$611$	−112.046	−	194.070i	−0.183382	−	0.317626i
$612$		0			0
$613$	−9.52481	+	16.4975i	−0.0155380	+	0.0269127i	−0.873690	−	0.486483i	$-0.838279\pi$
$613$	−9.52481	+	16.4975i	−0.0155380	+	0.0269127i	0.858152	+	0.513396i	$0.171613\pi$
$614$		0			0
$615$		−	207.595i		−	0.337552i
$616$		0			0
$617$	−688.725			−1.11625			−0.558124	−	0.829758i	$-0.688479\pi$
$617$	−688.725			−1.11625			−0.558124	+	0.829758i	$0.688479\pi$
$618$		0			0
$619$	145.813	+	84.1853i	0.235562	+	0.136002i	0.613135	−	0.789978i	$-0.289908\pi$
$619$	145.813	+	84.1853i	0.235562	+	0.136002i	−0.377573	+	0.925980i	$0.623241\pi$
$620$		0			0
$621$	−25.4558	+	14.6969i	−0.0409917	+	0.0236666i
$622$		0			0
$623$	95.3316	+	33.4830i	0.153020	+	0.0537448i
$624$		0			0
$625$	−117.890	−	204.191i	−0.188624	−	0.326706i
$626$		0			0
$627$	−101.127	+	175.157i	−0.161287	+	0.279358i
$628$		0			0
$629$			261.493i			0.415728i
$630$		0			0
$631$	−730.669			−1.15795			−0.578977	−	0.815344i	$-0.696548\pi$
$631$	−730.669			−1.15795			−0.578977	+	0.815344i	$0.696548\pi$
$632$		0			0
$633$	183.237	+	105.792i	0.289474	+	0.167128i
$634$		0			0
$635$	−378.836	+	218.721i	−0.596592	+	0.344443i
$636$		0			0
$637$	−1154.84	−	176.824i	−1.81294	−	0.277588i
$638$		0			0
$639$	−57.4210	−	99.4562i	−0.0898608	−	0.155643i
$640$		0			0
$641$	138.862	−	240.516i	0.216633	−	0.375220i	−0.737143	−	0.675736i	$-0.763826\pi$
$641$	138.862	−	240.516i	0.216633	−	0.375220i	0.953777	+	0.300517i	$0.0971591\pi$
$642$		0			0
$643$		−	1069.73i		−	1.66366i	−0.555029	−	0.831831i	$-0.687293\pi$
$643$		−	1069.73i		−	1.66366i	0.555029	−	0.831831i	$-0.312707\pi$
$644$		0			0
$645$	−163.506			−0.253498
$646$		0			0
$647$	738.214	+	426.208i	1.14098	+	0.658745i	0.946673	−	0.322195i	$-0.104421\pi$
$647$	738.214	+	426.208i	1.14098	+	0.658745i	0.194307	+	0.980941i	$0.437754\pi$
$648$		0			0
$649$	−306.134	+	176.746i	−0.471700	+	0.272336i
$650$		0			0
$651$	109.247	−	311.043i	0.167813	−	0.477793i
$652$		0			0
$653$	−85.5358	−	148.152i	−0.130989	−	0.226880i	0.793069	−	0.609132i	$-0.208482\pi$
$653$	−85.5358	−	148.152i	−0.130989	−	0.226880i	−0.924058	+	0.382252i	$0.875149\pi$
$654$		0			0
$655$	238.121	−	412.437i	0.363543	−	0.629675i
$656$		0			0
$657$			174.891i			0.266196i
$658$		0			0
$659$	−1237.16			−1.87732			−0.938661	−	0.344840i	$-0.887933\pi$
$659$	−1237.16			−1.87732			−0.938661	+	0.344840i	$0.887933\pi$
$660$		0			0
$661$	−222.784	−	128.624i	−0.337040	−	0.194590i	0.321922	−	0.946766i	$-0.395671\pi$
$661$	−222.784	−	128.624i	−0.337040	−	0.194590i	−0.658962	+	0.752176i	$0.729004\pi$
$662$		0			0
$663$	1155.72	−	667.258i	1.74317	−	1.00642i
$664$		0			0
$665$	−237.301	+	44.6127i	−0.356843	+	0.0670868i
$666$		0			0
$667$	97.2594	+	168.458i	0.145816	+	0.252561i
$668$		0			0
$669$	−157.898	+	273.488i	−0.236022	+	0.408801i
$670$		0			0
$671$			277.735i			0.413912i
$672$		0			0
$673$	−792.478			−1.17753			−0.588765	−	0.808304i	$-0.700386\pi$
$673$	−792.478			−1.17753			−0.588765	+	0.808304i	$0.700386\pi$
$674$		0			0
$675$	87.2591	+	50.3791i	0.129273	+	0.0746356i
$676$		0			0
$677$	208.935	−	120.629i	0.308619	−	0.178181i	−0.337689	−	0.941258i	$-0.609645\pi$
$677$	208.935	−	120.629i	0.308619	−	0.178181i	0.646308	+	0.763076i	$0.276312\pi$
$678$		0			0
$679$	639.120	−	548.710i	0.941267	−	0.808114i
$680$		0			0
$681$	19.4602	+	33.7060i	0.0285759	+	0.0494949i
$682$		0			0
$683$	307.939	−	533.366i	0.450863	−	0.780917i	−0.547577	−	0.836755i	$-0.684450\pi$
$683$	307.939	−	533.366i	0.450863	−	0.780917i	0.998440	+	0.0558381i	$0.0177831\pi$
$684$		0			0
$685$			328.067i			0.478930i
$686$		0			0
$687$	−497.345			−0.723938
$688$		0			0
$689$	1117.47	+	645.169i	1.62187	+	0.936385i
$690$		0			0
$691$	−20.1639	+	11.6416i	−0.0291807	+	0.0168475i	−0.514519	−	0.857479i	$-0.672030\pi$
$691$	−20.1639	+	11.6416i	−0.0291807	+	0.0168475i	0.485339	+	0.874326i	$0.338696\pi$
$692$		0			0
$693$	109.675	+	127.746i	0.158261	+	0.184338i
$694$		0			0
$695$	62.7687	+	108.719i	0.0903147	+	0.156430i
$696$		0			0
$697$	817.683	−	1416.27i	1.17315	−	2.03195i
$698$		0			0
$699$			92.7339i			0.132666i
$700$		0			0
$701$	164.723			0.234983			0.117491	−	0.993074i	$-0.462515\pi$
$701$	164.723			0.234983			0.117491	+	0.993074i	$0.462515\pi$
$702$		0			0
$703$	102.066	+	58.9280i	0.145187	+	0.0838236i
$704$		0			0
$705$	−33.3893	+	19.2773i	−0.0473607	+	0.0273437i
$706$		0			0
$707$	235.777	+	1254.13i	0.333489	+	1.77387i
$708$		0			0
$709$	−388.793	−	673.410i	−0.548369	−	0.949802i	−0.998387	−	0.0567828i	$-0.981916\pi$
$709$	−388.793	−	673.410i	−0.548369	−	0.949802i	0.450018	−	0.893020i	$-0.351418\pi$
$710$		0			0
$711$	−114.898	+	199.010i	−0.161601	+	0.279901i
$712$		0			0
$713$		−	153.814i		−	0.215728i
$714$		0			0
$715$	−452.735			−0.633196
$716$		0			0
$717$	−510.282	−	294.612i	−0.711691	−	0.410895i
$718$		0			0
$719$	−491.076	+	283.523i	−0.682998	+	0.394329i	−0.800984	−	0.598686i	$-0.795690\pi$
$719$	−491.076	+	283.523i	−0.682998	+	0.394329i	0.117985	+	0.993015i	$0.462356\pi$
$720$		0			0
$721$	160.462	+	56.3584i	0.222554	+	0.0781670i
$722$		0			0
$723$	22.3377	+	38.6901i	0.0308959	+	0.0535132i
$724$		0			0
$725$	333.392	−	577.451i	0.459850	−	0.796484i
$726$		0			0
$727$		−	175.123i		−	0.240884i	−0.992720	−	0.120442i	$-0.961569\pi$
$727$		−	175.123i		−	0.240884i	0.992720	−	0.120442i	$-0.0384313\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−1115.49	−	644.026i	−1.52597	−	0.881020i
$732$		0			0
$733$	−631.343	+	364.506i	−0.861313	+	0.497280i	−0.864452	−	0.502716i	$-0.832334\pi$
$733$	−631.343	+	364.506i	−0.861313	+	0.497280i	0.00313844	+	0.999995i	$0.499001\pi$
$734$		0			0
$735$	−30.4221	+	198.688i	−0.0413906	+	0.270323i
$736$		0			0
$737$	−472.595	−	818.559i	−0.641242	−	1.11066i
$738$		0			0
$739$	−245.926	+	425.957i	−0.332782	+	0.576396i	−0.983056	−	0.183304i	$-0.941321\pi$
$739$	−245.926	+	425.957i	−0.332782	+	0.576396i	0.650274	+	0.759700i	$0.274654\pi$
$740$		0			0
$741$		−	601.472i		−	0.811703i
$742$		0			0
$743$	−1124.25			−1.51313			−0.756563	−	0.653920i	$-0.773123\pi$
$743$	−1124.25			−1.51313			−0.756563	+	0.653920i	$0.773123\pi$
$744$		0			0
$745$	−182.501	−	105.367i	−0.244968	−	0.141432i
$746$		0			0
$747$	−151.435	+	87.4310i	−0.202724	+	0.117043i
$748$		0			0
$749$	94.8368	−	270.016i	0.126618	−	0.360502i
$750$		0			0
$751$	459.432	+	795.759i	0.611760	+	1.05960i	0.990944	+	0.134278i	$0.0428714\pi$
$751$	459.432	+	795.759i	0.611760	+	1.05960i	−0.379184	+	0.925321i	$0.623795\pi$
$752$		0			0
$753$	124.030	−	214.827i	0.164715	−	0.285295i
$754$		0			0
$755$			113.336i			0.150113i
$756$		0			0
$757$	544.690			0.719538			0.359769	−	0.933041i	$-0.382856\pi$
$757$	544.690			0.719538			0.359769	+	0.933041i	$0.382856\pi$
$758$		0			0
$759$	68.0309	+	39.2777i	0.0896323	+	0.0517492i
$760$		0			0
$761$	−168.805	+	97.4598i	−0.221820	+	0.128068i	−0.606793	−	0.794860i	$-0.707544\pi$
$761$	−168.805	+	97.4598i	−0.221820	+	0.128068i	0.384972	+	0.922928i	$0.374211\pi$
$762$		0			0
$763$	469.514	−	88.2691i	0.615353	−	0.115687i
$764$		0			0
$765$	−114.800	−	198.840i	−0.150066	−	0.259921i
$766$		0			0
$767$	525.615	−	910.393i	0.685287	−	1.18695i
$768$		0			0
$769$			450.642i			0.586010i	0.956111	+	0.293005i	$0.0946553\pi$
$769$			450.642i			0.586010i	−0.956111	+	0.293005i	$0.905345\pi$
$770$		0			0
$771$	−68.0954			−0.0883209
$772$		0			0
$773$	−132.382	−	76.4306i	−0.171257	−	0.0988754i	0.411921	−	0.911219i	$-0.364858\pi$
$773$	−132.382	−	76.4306i	−0.171257	−	0.0988754i	−0.583178	+	0.812344i	$0.698191\pi$
$774$		0			0
$775$	−456.615	+	263.627i	−0.589181	+	0.340164i
$776$		0			0
$777$	74.4393	−	63.9090i	0.0958035	−	0.0822510i
$778$		0			0
$779$	−368.533	−	638.318i	−0.473085	−	0.819407i
$780$		0			0
$781$	−153.458	+	265.797i	−0.196489	+	0.340329i
$782$		0			0
$783$			178.677i			0.228195i
$784$		0			0
$785$	384.500			0.489809
$786$		0			0
$787$	802.406	+	463.269i	1.01958	+	0.588652i	0.913981	−	0.405757i	$-0.132992\pi$
$787$	802.406	+	463.269i	1.01958	+	0.588652i	0.105595	+	0.994409i	$0.466325\pi$
$788$		0			0
$789$	−258.859	+	149.452i	−0.328085	+	0.189420i
$790$		0			0
$791$	−166.261	−	193.656i	−0.210191	−	0.244824i
$792$		0			0
$793$	−412.970	−	715.285i	−0.520769	−	0.901999i
$794$		0			0
$795$	111.000	−	192.257i	0.139623	−	0.241833i
$796$		0			0
$797$		−	1277.11i		−	1.60239i	−0.598401	−	0.801197i	$-0.704197\pi$
$797$		−	1277.11i		−	1.60239i	0.598401	−	0.801197i	$-0.295803\pi$
$798$		0			0
$799$	−303.721			−0.380126
$800$		0			0
$801$	37.5016	+	21.6516i	0.0468185	+	0.0270307i
$802$		0			0
$803$	404.778	−	233.699i	0.504082	−	0.291032i
$804$		0			0
$805$	17.3275	+	92.1673i	0.0215249	+	0.114494i
$806$		0			0
$807$	−125.662	−	217.653i	−0.155715	−	0.269706i
$808$		0			0
$809$	332.688	−	576.233i	0.411234	−	0.712278i	−0.583791	−	0.811904i	$-0.698431\pi$
$809$	332.688	−	576.233i	0.411234	−	0.712278i	0.995025	+	0.0996258i	$0.0317646\pi$
$810$		0			0
$811$		−	355.325i		−	0.438132i	−0.975710	−	0.219066i	$-0.929699\pi$
$811$		−	355.325i		−	0.438132i	0.975710	−	0.219066i	$-0.0703010\pi$
$812$		0			0
$813$	7.22744			0.00888984
$814$		0			0
$815$	584.027	+	337.188i	0.716597	+	0.413728i
$816$		0			0
$817$	−502.754	+	290.265i	−0.615366	+	0.355282i
$818$		0			0
$819$	−472.408	−	165.922i	−0.576811	−	0.202591i
$820$		0			0
$821$	−213.374	−	369.575i	−0.259896	−	0.450153i	0.706318	−	0.707895i	$-0.250355\pi$
$821$	−213.374	−	369.575i	−0.259896	−	0.450153i	−0.966214	+	0.257742i	$0.917022\pi$
$822$		0			0
$823$	−489.430	+	847.717i	−0.594690	+	1.03003i	0.398901	+	0.916994i	$0.369392\pi$
$823$	−489.430	+	847.717i	−0.594690	+	1.03003i	−0.993591	+	0.113039i	$0.963942\pi$
$824$		0			0
$825$		−	269.277i		−	0.326396i
$826$		0			0
$827$	−660.437			−0.798594			−0.399297	−	0.916822i	$-0.630746\pi$
$827$	−660.437			−0.798594			−0.399297	+	0.916822i	$0.630746\pi$
$828$		0			0
$829$	993.501	+	573.598i	1.19843	+	0.691916i	0.960206	−	0.279294i	$-0.0901004\pi$
$829$	993.501	+	573.598i	1.19843	+	0.691916i	0.238227	+	0.971209i	$0.423434\pi$
$830$		0			0
$831$	24.2073	−	13.9761i	0.0291303	−	0.0168184i
$832$		0			0
$833$	−990.147	+	1235.67i	−1.18865	+	1.48340i
$834$		0			0
$835$	−284.859	−	493.389i	−0.341148	−	0.590886i
$836$		0			0
$837$	70.6437	−	122.358i	0.0844011	−	0.146187i
$838$		0			0
$839$			1522.06i			1.81413i	0.420988	+	0.907066i	$0.361683\pi$
$839$			1522.06i			1.81413i	−0.420988	+	0.907066i	$0.638317\pi$
$840$		0			0
$841$	341.423			0.405973
$842$		0			0
$843$	606.296	+	350.045i	0.719213	+	0.415238i
$844$		0			0
$845$	819.356	−	473.055i	0.969652	−	0.559829i
$846$		0			0
$847$	−131.570	+	374.602i	−0.155337	+	0.442269i
$848$		0			0
$849$	−10.7861	−	18.6820i	−0.0127044	−	0.0220047i
$850$		0			0
$851$	22.8876	−	39.6424i	0.0268949	−	0.0465833i
$852$		0			0
$853$			616.510i			0.722755i	0.932420	+	0.361378i	$0.117693\pi$
$853$			616.510i			0.722755i	−0.932420	+	0.361378i	$0.882307\pi$
$854$		0			0
$855$	−103.482			−0.121031
$856$		0			0
$857$	−150.722	−	87.0195i	−0.175872	−	0.101540i	0.409480	−	0.912319i	$-0.365710\pi$
$857$	−150.722	−	87.0195i	−0.175872	−	0.101540i	−0.585352	+	0.810780i	$0.699044\pi$
$858$		0			0
$859$	−1284.90	+	741.836i	−1.49581	+	0.863605i	−0.999988	−	0.00482143i	$-0.998465\pi$
$859$	−1284.90	+	741.836i	−1.49581	+	0.863605i	−0.495819	+	0.868426i	$0.665132\pi$
$860$		0			0
$861$	−603.012	+	113.367i	−0.700362	+	0.131669i
$862$		0			0
$863$	394.655	+	683.562i	0.457305	+	0.792076i	0.998818	−	0.0486167i	$-0.0154813\pi$
$863$	394.655	+	683.562i	0.457305	+	0.792076i	−0.541512	+	0.840693i	$0.682148\pi$
$864$		0			0
$865$	214.251	−	371.094i	0.247689	−	0.429011i
$866$		0			0
$867$		−	1308.16i		−	1.50883i
$868$		0			0
$869$	614.133			0.706713
$870$		0			0
$871$	2434.26	+	1405.42i	2.79479	+	1.61357i
$872$		0			0
$873$	312.642	−	180.504i	0.358124	−	0.206763i
$874$		0			0
$875$	558.377	−	479.388i	0.638145	−	0.547872i
$876$		0			0
$877$	−82.4017	−	142.724i	−0.0939586	−	0.162741i	0.815215	−	0.579159i	$-0.196619\pi$
$877$	−82.4017	−	142.724i	−0.0939586	−	0.162741i	−0.909174	+	0.416417i	$0.863285\pi$
$878$		0			0
$879$	231.380	−	400.762i	0.263231	−	0.455929i
$880$		0			0
$881$		−	150.440i		−	0.170761i	−0.996348	−	0.0853804i	$-0.972789\pi$
$881$		−	150.440i		−	0.170761i	0.996348	−	0.0853804i	$-0.0272105\pi$
$882$		0			0
$883$	−1260.13			−1.42710			−0.713550	−	0.700604i	$-0.752914\pi$
$883$	−1260.13			−1.42710			−0.713550	+	0.700604i	$0.752914\pi$
$884$		0			0
$885$	−156.631	−	90.4310i	−0.176984	−	0.102182i
$886$		0			0
$887$	−494.249	+	285.355i	−0.557214	+	0.321708i	−0.752027	−	0.659133i	$-0.770924\pi$
$887$	−494.249	+	285.355i	−0.557214	+	0.321708i	0.194812	+	0.980841i	$0.437590\pi$
$888$		0			0
$889$	842.212	+	980.983i	0.947370	+	1.10347i
$890$		0			0
$891$	36.0788	+	62.4904i	0.0404925	+	0.0701351i
$892$		0			0
$893$	−68.4441	+	118.549i	−0.0766451	+	0.132753i
$894$		0			0
$895$			707.841i			0.790883i
$896$		0			0
$897$	−233.611			−0.260436
$898$		0			0
$899$	−809.727	−	467.496i	−0.900697	−	0.520018i
$900$		0			0
$901$	1514.54	−	874.422i	1.68096	−	0.970502i
$902$		0			0
$903$	89.2902	+	474.946i	0.0988818	+	0.525964i
$904$		0			0
$905$	247.742	+	429.101i	0.273748	+	0.474145i
$906$		0			0
$907$	135.539	−	234.761i	0.149437	−	0.258832i	−0.781583	−	0.623802i	$-0.785587\pi$
$907$	135.539	−	234.761i	0.149437	−	0.258832i	0.931019	+	0.364970i	$0.118921\pi$
$908$		0			0
$909$			546.899i			0.601649i
$910$		0			0
$911$	1152.78			1.26540			0.632699	−	0.774398i	$-0.281947\pi$
$911$	1152.78			1.26540			0.632699	+	0.774398i	$0.281947\pi$
$912$		0			0
$913$	404.711	+	233.660i	0.443276	+	0.255925i
$914$		0			0
$915$	−123.063	+	71.0506i	−0.134495	+	0.0776509i
$916$		0			0
$917$	−1328.07	−	466.452i	−1.44827	−	0.508672i
$918$		0			0
$919$	−179.916	−	311.624i	−0.195774	−	0.339090i	0.751380	−	0.659870i	$-0.229388\pi$
$919$	−179.916	−	311.624i	−0.195774	−	0.339090i	−0.947154	+	0.320780i	$0.896055\pi$
$920$		0			0
$921$	361.594	−	626.299i	0.392610	−	0.680020i
$922$		0			0
$923$		−	912.720i		−	0.988863i
$924$		0			0
$925$	−156.911			−0.169633
$926$		0			0
$927$	63.1226	+	36.4438i	0.0680934	+	0.0393137i
$928$		0			0
$929$	103.571	−	59.7966i	0.111486	−	0.0643667i	−0.443220	−	0.896413i	$-0.646164\pi$
$929$	103.571	−	59.7966i	0.111486	−	0.0643667i	0.554706	+	0.832046i	$0.312831\pi$
$930$		0			0
$931$	259.178	+	664.937i	0.278387	+	0.714218i
$932$		0			0
$933$	478.894	+	829.468i	0.513284	+	0.889033i
$934$		0			0
$935$	−306.804	+	531.401i	−0.328133	+	0.568343i
$936$		0			0
$937$			968.840i			1.03398i	0.855991	+	0.516990i	$0.172948\pi$
$937$			968.840i			1.03398i	−0.855991	+	0.516990i	$0.827052\pi$
$938$		0			0
$939$	−267.201			−0.284559
$940$		0			0
$941$	285.043	+	164.570i	0.302915	+	0.174888i	0.643752	−	0.765235i	$-0.277377\pi$
$941$	285.043	+	164.570i	0.302915	+	0.174888i	−0.340837	+	0.940123i	$0.610710\pi$
$942$		0			0
$943$	−247.922	+	143.138i	−0.262908	+	0.151790i
$944$		0			0
$945$	−28.5466	+	81.2768i	−0.0302080	+	0.0860072i
$946$		0			0
$947$	898.178	+	1555.69i	0.948445	+	1.64276i	0.748702	+	0.662907i	$0.230678\pi$
$947$	898.178	+	1555.69i	0.948445	+	1.64276i	0.199743	+	0.979848i	$0.435989\pi$
$948$		0			0
$949$	−694.983	+	1203.75i	−0.732332	+	1.26844i
$950$		0			0
$951$		−	284.682i		−	0.299351i
$952$		0			0
$953$	121.924			0.127938			0.0639688	−	0.997952i	$-0.479624\pi$
$953$	121.924			0.127938			0.0639688	+	0.997952i	$0.479624\pi$
$954$		0			0
$955$	704.494	+	406.740i	0.737690	+	0.425905i
$956$		0			0
$957$	413.540	−	238.758i	0.432121	−	0.249485i
$958$		0			0
$959$	952.954	−	179.156i	0.993695	−	0.186816i
$960$		0			0
$961$	−110.831	−	191.965i	−0.115329	−	0.199756i
$962$		0			0
$963$	61.3257	−	106.219i	0.0636819	−	0.110300i
$964$		0			0
$965$			222.441i			0.230509i
$966$		0			0
$967$	1228.86			1.27080			0.635399	−	0.772184i	$-0.280836\pi$
$967$	1228.86			1.27080			0.635399	+	0.772184i	$0.280836\pi$
$968$		0			0
$969$	−705.982	−	407.599i	−0.728567	−	0.420638i
$970$		0			0
$971$	−317.288	+	183.186i	−0.326764	+	0.188658i	−0.654404	−	0.756145i	$-0.727080\pi$
$971$	−317.288	+	183.186i	−0.326764	+	0.188658i	0.327639	+	0.944803i	$0.393747\pi$
$972$		0			0
$973$	281.523	−	241.698i	0.289335	−	0.248405i
$974$		0			0
$975$	400.393	+	693.501i	0.410660	+	0.711283i
$976$		0			0
$977$	771.097	−	1335.58i	0.789249	−	1.36702i	−0.137178	−	0.990546i	$-0.543803\pi$
$977$	771.097	−	1335.58i	0.789249	−	1.36702i	0.926427	−	0.376474i	$-0.122863\pi$
$978$		0			0
$979$		−	115.728i		−	0.118210i
$980$		0			0
$981$	204.746			0.208711
$982$		0			0
$983$	−378.028	−	218.255i	−0.384566	−	0.222029i	0.295237	−	0.955424i	$-0.404601\pi$
$983$	−378.028	−	218.255i	−0.384566	−	0.222029i	−0.679803	+	0.733395i	$0.737935\pi$
$984$		0			0
$985$	−335.281	+	193.575i	−0.340387	+	0.196523i
$986$		0			0
$987$	74.2296	+	86.4603i	0.0752073	+	0.0875991i
$988$		0			0
$989$	112.739	+	195.269i	0.113993	+	0.197441i
$990$		0			0
$991$	41.9624	−	72.6811i	0.0423435	−	0.0733411i	−0.844077	−	0.536222i	$-0.819851\pi$
$991$	41.9624	−	72.6811i	0.0423435	−	0.0733411i	0.886420	+	0.462881i	$0.153184\pi$
$992$		0			0
$993$		−	908.066i		−	0.914467i
$994$		0			0
$995$	643.506			0.646740
$996$		0			0
$997$	−431.750	−	249.271i	−0.433050	−	0.250021i	0.267595	−	0.963531i	$-0.413771\pi$
$997$	−431.750	−	249.271i	−0.433050	−	0.250021i	−0.700645	+	0.713510i	$0.747104\pi$
$998$		0			0
$999$	36.4139	−	21.0236i	0.0364503	−	0.0210446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.3.z.a.73.2	✓	8
3.2	odd	2		504.3.by.a.73.3		8
4.3	odd	2		336.3.bh.h.241.2		8
7.2	even	3		1176.3.z.d.313.3		8
7.3	odd	6		1176.3.f.a.97.3		8
7.4	even	3		1176.3.f.a.97.6		8
7.5	odd	6	inner	168.3.z.a.145.2	yes	8
7.6	odd	2		1176.3.z.d.913.3		8
12.11	even	2		1008.3.cg.n.577.3		8
21.5	even	6		504.3.by.a.145.3		8
21.11	odd	6		3528.3.f.f.2449.6		8
21.17	even	6		3528.3.f.f.2449.3		8
28.3	even	6		2352.3.f.k.97.7		8
28.11	odd	6		2352.3.f.k.97.2		8
28.19	even	6		336.3.bh.h.145.2		8
84.47	odd	6		1008.3.cg.n.145.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.z.a.73.2	✓	8	1.1	even	1	trivial
168.3.z.a.145.2	yes	8	7.5	odd	6	inner
336.3.bh.h.145.2		8	28.19	even	6
336.3.bh.h.241.2		8	4.3	odd	2
504.3.by.a.73.3		8	3.2	odd	2
504.3.by.a.145.3		8	21.5	even	6
1008.3.cg.n.145.3		8	84.47	odd	6
1008.3.cg.n.577.3		8	12.11	even	2
1176.3.f.a.97.3		8	7.3	odd	6
1176.3.f.a.97.6		8	7.4	even	3
1176.3.z.d.313.3		8	7.2	even	3
1176.3.z.d.913.3		8	7.6	odd	2
2352.3.f.k.97.2		8	28.11	odd	6
2352.3.f.k.97.7		8	28.3	even	6
3528.3.f.f.2449.3		8	21.17	even	6
3528.3.f.f.2449.6		8	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	168.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-2.05105 + 1.18418i) q^{5} +(4.55981 + 5.31113i) q^{7} +(1.50000 + 2.59808i) q^{9} +(4.00876 - 6.94337i) q^{11} +23.8428i q^{13} +4.10211 q^{15} +(27.9857 + 16.1575i) q^{17} +(12.6133 - 7.28227i) q^{19} +(-2.24014 - 11.9156i) q^{21} +(-2.82843 - 4.89898i) q^{23} +(-9.69545 + 16.7930i) q^{25} -5.19615i q^{27} -34.3864 q^{29} +(23.5479 + 13.5954i) q^{31} +(-12.0263 + 6.94337i) q^{33} +(-15.6417 - 5.49379i) q^{35} +(4.04599 + 7.00786i) q^{37} +(20.6485 - 35.7642i) q^{39} -50.6069i q^{41} -39.8591 q^{43} +(-6.15316 - 3.55253i) q^{45} +(-8.13954 + 4.69937i) q^{47} +(-7.41622 + 48.4355i) q^{49} +(-27.9857 - 48.4726i) q^{51} +(27.0592 - 46.8680i) q^{53} +18.9883i q^{55} -25.2265 q^{57} +(-38.1831 - 22.0450i) q^{59} +(-30.0000 + 17.3205i) q^{61} +(-6.95900 + 19.8134i) q^{63} +(-28.2341 - 48.9029i) q^{65} +(58.9453 - 102.096i) q^{67} +9.79796i q^{69} -38.2807 q^{71} +(50.4867 + 29.1485i) q^{73} +(29.0864 - 16.7930i) q^{75} +(55.1564 - 10.3694i) q^{77} +(38.2995 + 66.3366i) q^{79} +(-4.50000 + 7.79423i) q^{81} +58.2873i q^{83} -76.5335 q^{85} +(51.5796 + 29.7795i) q^{87} +(12.5005 - 7.21720i) q^{89} +(-126.632 + 108.719i) q^{91} +(-23.5479 - 40.7861i) q^{93} +(-17.2470 + 29.8727i) q^{95} -120.336i q^{97} +24.0526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} + 6 q^{5} - 4 q^{7} + 12 q^{9} + 14 q^{11} - 12 q^{15} + 12 q^{17} + 78 q^{19} + 18 q^{21} - 6 q^{25} - 4 q^{29} - 24 q^{31} - 42 q^{33} - 156 q^{35} + 50 q^{37} - 6 q^{39} - 20 q^{43} + 18 q^{45}+ \cdots + 84 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 + 6 * q^5 - 4 * q^7 + 12 * q^9 + 14 * q^11 - 12 * q^15 + 12 * q^17 + 78 * q^19 + 18 * q^21 - 6 * q^25 - 4 * q^29 - 24 * q^31 - 42 * q^33 - 156 * q^35 + 50 * q^37 - 6 * q^39 - 20 * q^43 + 18 * q^45 + 12 * q^47 + 220 * q^49 - 12 * q^51 - 50 * q^53 - 156 * q^57 - 186 * q^59 - 240 * q^61 - 42 * q^63 - 148 * q^65 + 34 * q^67 + 424 * q^71 + 294 * q^73 + 18 * q^75 + 126 * q^77 - 40 * q^79 - 36 * q^81 - 232 * q^85 + 6 * q^87 - 132 * q^89 - 378 * q^91 + 24 * q^93 + 144 * q^95 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more