LMFDB - Embedded newform 336.3.bh.h.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,3,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, degree $2$, not 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:	$9.15533688251$
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:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$2.64247 + 0.131782i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.3.bh.h.241.2

$q$-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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	−2.05105	−	1.18418i	−0.410211	−	0.236835i	0.280670	−	0.959804i	$-0.409443\pi$
$5$	−2.05105	−	1.18418i	−0.410211	−	0.236835i	−0.690880	+	0.722969i	$0.742777\pi$
$6$		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	$-0.285404\pi$
$11$	−4.00876	−	6.94337i	−0.364433	−	0.631216i	−0.988685	+	0.150007i	$0.952070\pi$
$12$		0			0
$13$		−	23.8428i		−	1.83406i	−0.398814	−	0.917032i	$-0.630578\pi$
$13$		−	23.8428i		−	1.83406i	0.398814	−	0.917032i	$-0.369422\pi$
$14$		0			0
$15$	−4.10211			−0.273474
$16$		0			0
$17$	27.9857	−	16.1575i	1.64622	−	0.950444i	0.667660	−	0.744466i	$-0.267296\pi$
$17$	27.9857	−	16.1575i	1.64622	−	0.950444i	0.978557	−	0.205977i	$-0.0660373\pi$
$18$		0			0
$19$	−12.6133	−	7.28227i	−0.663856	−	0.383277i	0.129889	−	0.991529i	$-0.458538\pi$
$19$	−12.6133	−	7.28227i	−0.663856	−	0.383277i	−0.793745	+	0.608251i	$0.791871\pi$
$20$		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	$-0.794090\pi$
$23$	2.82843	−	4.89898i	0.122975	−	0.212999i	0.920940	+	0.389705i	$0.127423\pi$
$24$		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	$-0.811178\pi$
$31$	−23.5479	+	13.5954i	−0.759609	+	0.438561i	0.0695460	+	0.997579i	$0.477845\pi$
$32$		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	−0.806156	−	0.591702i	$-0.798456\pi$
$37$	4.04599	−	7.00786i	0.109351	−	0.189402i	0.915508	+	0.402301i	$0.131789\pi$
$38$		0			0
$39$	−20.6485	−	35.7642i	−0.529449	−	0.917032i
$40$		0			0
$41$			50.6069i			1.23431i	0.786840	+	0.617157i	$0.211716\pi$
$41$			50.6069i			1.23431i	−0.786840	+	0.617157i	$0.788284\pi$
$42$		0			0
$43$	39.8591			0.926957			0.463478	−	0.886108i	$-0.346601\pi$
$43$	39.8591			0.926957			0.463478	+	0.886108i	$0.346601\pi$
$44$		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	$-0.301453\pi$
$47$	8.13954	+	4.69937i	0.173182	+	0.0999865i	−0.410904	+	0.911679i	$0.634787\pi$
$48$		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	0.999925	+	0.0122274i	$0.00389219\pi$
$53$	27.0592	+	46.8680i	0.510552	+	0.884302i	−0.489373	+	0.872074i	$0.662774\pi$
$54$		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	$-0.544775\pi$
$59$	38.1831	−	22.0450i	0.647171	−	0.373644i	0.787371	+	0.616479i	$0.211441\pi$
$60$		0			0
$61$	−30.0000	−	17.3205i	−0.491803	−	0.283943i	0.233519	−	0.972352i	$-0.424976\pi$
$61$	−30.0000	−	17.3205i	−0.491803	−	0.283943i	−0.725322	+	0.688409i	$0.758309\pi$
$62$		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	−0.851581	−	0.524222i	$-0.824356\pi$
$67$	−58.9453	−	102.096i	−0.879781	−	1.52382i	−0.0281991	−	0.999602i	$-0.508977\pi$
$68$		0			0
$69$		−	9.79796i		−	0.141999i
$70$		0			0
$71$	38.2807			0.539165			0.269582	−	0.962977i	$-0.413114\pi$
$71$	38.2807			0.539165			0.269582	+	0.962977i	$0.413114\pi$
$72$		0			0
$73$	50.4867	−	29.1485i	0.691599	−	0.399295i	−0.112612	−	0.993639i	$-0.535922\pi$
$73$	50.4867	−	29.1485i	0.691599	−	0.399295i	0.804211	+	0.594344i	$0.202588\pi$
$74$		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	$-0.994442\pi$
$79$	−38.2995	+	66.3366i	−0.484803	+	0.839704i	0.515044	+	0.857164i	$0.327776\pi$
$80$		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	0.568581	−	0.822627i	$-0.307493\pi$
$89$	12.5005	+	7.21720i	0.140456	+	0.0810921i	−0.428126	+	0.903719i	$0.640826\pi$
$90$		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	$0.212985\pi$
$97$			120.336i			1.24058i	−0.784374	+	0.620289i	$0.787015\pi$
$98$		0			0
$99$	−24.0526			−0.242955
$100$		0			0
$101$	157.876	−	91.1498i	1.56313	−	0.902473i	0.566192	−	0.824274i	$-0.308416\pi$
$101$	157.876	−	91.1498i	1.56313	−	0.902473i	0.996938	−	0.0781997i	$-0.0249172\pi$
$102$		0			0
$103$	−21.0409	−	12.1479i	−0.204280	−	0.117941i	0.394370	−	0.918952i	$-0.370963\pi$
$103$	−21.0409	−	12.1479i	−0.204280	−	0.117941i	−0.598650	+	0.801010i	$0.704296\pi$
$104$		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	$-0.772145\pi$
$107$	20.4419	−	35.4064i	0.191046	−	0.330901i	0.945597	+	0.325340i	$0.105479\pi$
$108$		0			0
$109$	34.1243	+	59.1049i	0.313067	+	0.542247i	0.979025	−	0.203742i	$-0.0653104\pi$
$109$	34.1243	+	59.1049i	0.313067	+	0.542247i	−0.665958	+	0.745989i	$0.731977\pi$
$110$		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	$-0.759169\pi$
$127$	−184.703			−1.45436			−0.727178	+	0.686449i	$0.759169\pi$
$128$		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	$-0.0548326\pi$
$131$	174.145	+	100.543i	1.32935	+	0.767502i	0.344153	+	0.938913i	$0.388166\pi$
$132$		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	0.999979	+	0.00642244i	$0.00204434\pi$
$137$	69.2606	+	119.963i	0.505552	+	0.875641i	−0.494428	+	0.869219i	$0.664622\pi$
$138$		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	−0.677225	−	0.735776i	$-0.736818\pi$
$149$	44.4896	−	77.0583i	0.298588	−	0.517170i	0.975813	+	0.218606i	$0.0701510\pi$
$150$		0			0
$151$	−23.9271	−	41.4429i	−0.158458	−	0.274457i	0.775855	−	0.630911i	$-0.217319\pi$
$151$	−23.9271	−	41.4429i	−0.158458	−	0.274457i	−0.934313	+	0.356455i	$0.883985\pi$
$152$		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	−0.875748	−	0.482769i	$-0.839631\pi$
$157$	−140.598	+	81.1745i	−0.895531	+	0.517035i	−0.0197835	+	0.999804i	$0.506298\pi$
$158$		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	0.0150459	−	0.999887i	$-0.495211\pi$
$163$	142.372	−	246.596i	0.873450	−	1.51286i	0.858404	−	0.512974i	$-0.171456\pi$
$164$		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	−0.0266652	−	0.999644i	$-0.508489\pi$
$173$	−156.689	−	90.4643i	−0.905715	−	0.522915i	−0.879050	+	0.476729i	$0.841822\pi$
$174$		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	−0.894156	−	0.447755i	$-0.852224\pi$
$179$	−149.437	−	258.833i	−0.834845	−	1.44599i	0.0593107	−	0.998240i	$-0.481110\pi$
$180$		0			0
$181$			209.210i			1.15586i	0.816087	+	0.577928i	$0.196139\pi$
$181$			209.210i			1.15586i	−0.816087	+	0.577928i	$0.803861\pi$
$182$		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	0.0705895	−	0.997505i	$-0.477512\pi$
$191$	171.740	−	297.462i	0.899160	−	1.55739i	0.828570	−	0.559885i	$-0.189155\pi$
$192$		0			0
$193$	46.9612	+	81.3392i	0.243322	+	0.421447i	0.961659	−	0.274249i	$-0.0884294\pi$
$193$	46.9612	+	81.3392i	0.243322	+	0.421447i	−0.718336	+	0.695696i	$0.755096\pi$
$194$		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	$-0.427477\pi$
$199$	235.308	−	135.855i	1.18245	−	0.682690i	0.956581	+	0.291467i	$0.0941435\pi$
$200$		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	$-0.406520\pi$
$211$	122.158			0.578947			0.289474	+	0.957186i	$0.406520\pi$
$212$		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	$-0.650906\pi$
$227$	19.4602	−	11.2353i	0.0857277	−	0.0494949i	0.542251	+	0.840217i	$0.317572\pi$
$228$		0			0
$229$	248.673	+	143.571i	1.08591	+	0.626949i	0.932484	−	0.361212i	$-0.117637\pi$
$229$	248.673	+	143.571i	1.08591	+	0.626949i	0.153423	+	0.988161i	$0.450970\pi$
$230$		0			0
$231$	91.7147	−	32.2126i	0.397034	−	0.139449i
$232$		0			0
$233$	−26.7700	+	46.3669i	−0.114893	+	0.199000i	−0.917737	−	0.397189i	$-0.869986\pi$
$233$	−26.7700	+	46.3669i	−0.114893	+	0.199000i	0.802844	+	0.596189i	$0.203319\pi$
$234$		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	$-0.752070\pi$
$239$	−340.188			−1.42338			−0.711691	+	0.702493i	$0.752070\pi$
$240$		0			0
$241$	−22.3377	+	12.8967i	−0.0926877	+	0.0535132i	−0.545627	−	0.838028i	$-0.683709\pi$
$241$	−22.3377	+	12.8967i	−0.0926877	+	0.0535132i	0.452940	+	0.891541i	$0.350375\pi$
$242$		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	0.564776	−	0.825244i	$-0.308963\pi$
$257$	34.0477	+	19.6575i	0.132481	+	0.0764882i	−0.432295	+	0.901732i	$0.642296\pi$
$258$		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	$-0.273070\pi$
$263$	−86.2864	−	149.452i	−0.328085	−	0.568260i	−0.982132	+	0.188194i	$0.939737\pi$
$264$		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	−0.247899	−	0.968786i	$-0.579740\pi$
$269$	125.662	−	72.5509i	0.467144	−	0.269706i	0.715043	+	0.699080i	$0.246407\pi$
$270$		0			0
$271$	3.61372	+	2.08638i	0.0133348	+	0.00769883i	0.506653	−	0.862150i	$-0.330883\pi$
$271$	3.61372	+	2.08638i	0.0133348	+	0.00769883i	−0.493318	+	0.869849i	$0.664216\pi$
$272$		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	0.851093	−	0.525015i	$-0.175940\pi$
$277$	−8.06909	−	13.9761i	−0.0291303	−	0.0504551i	−0.880223	+	0.474560i	$0.842607\pi$
$278$		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	$-0.673672\pi$
$283$	−10.7861	+	6.22734i	−0.0381133	+	0.0220047i	0.480822	+	0.876818i	$0.340338\pi$
$284$		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	$-0.849307\pi$
$293$		−	267.174i		−	0.911858i	0.890016	−	0.455929i	$-0.150693\pi$
$294$		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	0.541004	−	0.841020i	$-0.318044\pi$
$311$	478.894	−	276.489i	1.53985	−	0.889033i	0.998847	−	0.0480134i	$-0.0152890\pi$
$312$		0			0
$313$	133.600	+	77.1343i	0.426839	+	0.246435i	0.697999	−	0.716099i	$-0.254074\pi$
$313$	133.600	+	77.1343i	0.426839	+	0.246435i	−0.271160	+	0.962534i	$0.587407\pi$
$314$		0			0
$315$	9.18931	−	48.8791i	0.0291724	−	0.155172i
$316$		0			0
$317$	82.1807	−	142.341i	0.259245	−	0.449026i	−0.706795	−	0.707419i	$-0.749860\pi$
$317$	82.1807	−	142.341i	0.259245	−	0.449026i	0.966040	+	0.258393i	$0.0831929\pi$
$318$		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	0.132805	+	0.991142i	$0.457602\pi$
$331$	−262.136	+	454.033i	−0.791952	+	1.37170i	−0.924757	+	0.380558i	$0.875732\pi$
$332$		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	$-0.146867\pi$
$347$	21.5704	+	37.3610i	0.0621624	+	0.107669i	−0.833269	+	0.552867i	$0.813534\pi$
$348$		0			0
$349$			20.2166i			0.0579273i	0.999580	+	0.0289636i	$0.00922070\pi$
$349$			20.2166i			0.0579273i	−0.999580	+	0.0289636i	$0.990779\pi$
$350$		0			0
$351$	−123.891			−0.352966
$352$		0			0
$353$	227.795	−	131.517i	0.645310	−	0.372570i	−0.141347	−	0.989960i	$-0.545143\pi$
$353$	227.795	−	131.517i	0.645310	−	0.372570i	0.786657	+	0.617390i	$0.211810\pi$
$354$		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	−0.247537	−	0.968878i	$-0.579621\pi$
$359$	256.794	−	444.781i	0.715305	−	1.23894i	0.962842	−	0.270066i	$-0.0870456\pi$
$360$		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	$-0.628302\pi$
$367$	76.4289	−	44.1262i	0.208253	−	0.120235i	0.600499	+	0.799625i	$0.294969\pi$
$368$		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	−0.479844	−	0.877354i	$-0.659307\pi$
$373$	193.918	−	335.877i	0.519889	−	0.900474i	0.999733	−	0.0231198i	$-0.00735993\pi$
$374$		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	$-0.591775\pi$
$379$	−215.531			−0.568682			−0.284341	+	0.958723i	$0.591775\pi$
$380$		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	$-0.0969856\pi$
$383$	448.533	+	258.961i	1.17111	+	0.676138i	0.217165	+	0.976135i	$0.430319\pi$
$384$		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	0.609970	−	0.792424i	$-0.291181\pi$
$389$	−148.316	−	256.891i	−0.381275	−	0.660387i	−0.991245	+	0.132037i	$0.957848\pi$
$390$		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	0.666119	−	0.745846i	$-0.267954\pi$
$397$	140.243	+	80.9692i	0.353256	+	0.203953i	−0.312862	+	0.949799i	$0.601288\pi$
$398$		0			0
$399$	115.028	−	133.981i	0.288291	−	0.335793i
$400$		0			0
$401$	−370.716	+	642.098i	−0.924478	+	1.60124i	−0.132079	+	0.991239i	$0.542165\pi$
$401$	−370.716	+	642.098i	−0.924478	+	1.60124i	−0.792399	+	0.610004i	$0.791168\pi$
$402$		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	−0.665480	−	0.746415i	$-0.731773\pi$
$409$	−143.889	+	83.0741i	−0.351806	+	0.203115i	0.313675	+	0.949531i	$0.398440\pi$
$410$		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	$-0.201936\pi$
$431$	−47.6578	−	82.5457i	−0.110575	−	0.191521i	−0.916002	+	0.401173i	$0.868603\pi$
$432$		0			0
$433$			393.461i			0.908685i	0.890827	+	0.454343i	$0.150126\pi$
$433$			393.461i			0.908685i	−0.890827	+	0.454343i	$0.849874\pi$
$434$		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	$-0.584721\pi$
$439$	−540.002	−	311.770i	−1.23007	−	0.710183i	−0.967045	+	0.254605i	$0.918054\pi$
$440$		0			0
$441$	−136.964	−	53.3854i	−0.310575	−	0.121055i
$442$		0			0
$443$	−280.200	+	485.321i	−0.632507	+	1.09553i	0.354531	+	0.935044i	$0.384641\pi$
$443$	−280.200	+	485.321i	−0.632507	+	1.09553i	−0.987038	+	0.160489i	$0.948693\pi$
$444$		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	0.465602	+	0.884994i	$0.345838\pi$
$457$	−243.867	+	422.391i	−0.533627	+	0.924268i	−0.999228	+	0.0392740i	$0.987495\pi$
$458$		0			0
$459$	−83.9571	−	145.418i	−0.182913	−	0.316815i
$460$		0			0
$461$		−	300.713i		−	0.652307i	−0.945317	−	0.326153i	$-0.894247\pi$
$461$		−	300.713i		−	0.652307i	0.945317	−	0.326153i	$-0.105753\pi$
$462$		0			0
$463$	661.184			1.42804			0.714022	−	0.700124i	$-0.246872\pi$
$463$	661.184			1.42804			0.714022	+	0.700124i	$0.246872\pi$
$464$		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	$-0.448506\pi$
$467$	−286.324	−	165.309i	−0.613114	−	0.353982i	−0.774183	+	0.632961i	$0.781839\pi$
$468$		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	$-0.439644\pi$
$479$	542.813	−	313.393i	1.13322	−	0.654266i	0.944743	+	0.327811i	$0.106311\pi$
$480$		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	$-0.155854\pi$
$487$	16.5404	+	28.6488i	0.0339639	+	0.0588272i	−0.848544	+	0.529125i	$0.822520\pi$
$488$		0			0
$489$		−	493.192i		−	1.00857i
$490$		0			0
$491$	460.309			0.937493			0.468747	−	0.883333i	$-0.344706\pi$
$491$	460.309			0.937493			0.468747	+	0.883333i	$0.344706\pi$
$492$		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	$-0.833628\pi$
$499$	−0.462513	+	0.801097i	−0.000926881	+	0.00160540i	0.865562	+	0.500802i	$0.166962\pi$
$500$		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	0.527643	−	0.849466i	$-0.323076\pi$
$509$	28.4048	+	16.3995i	0.0558051	+	0.0322191i	−0.471838	+	0.881685i	$0.656409\pi$
$510$		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	−0.0438448	−	0.999038i	$-0.513961\pi$
$521$	416.501	−	240.467i	0.799425	−	0.461548i	0.843270	+	0.537490i	$0.180627\pi$
$522$		0			0
$523$	−370.870	−	214.122i	−0.709120	−	0.409411i	0.101615	−	0.994824i	$-0.467599\pi$
$523$	−370.870	−	214.122i	−0.709120	−	0.409411i	−0.810735	+	0.585413i	$0.800932\pi$
$524$		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	−0.601804	−	0.798644i	$-0.705551\pi$
$541$	211.392	−	366.142i	0.390743	−	0.676787i	0.992548	+	0.121856i	$0.0388846\pi$
$542$		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	$-0.842207\pi$
$547$	−962.311			−1.75925			−0.879626	+	0.475665i	$0.842207\pi$
$548$		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	−0.903060	−	0.429515i	$-0.858685\pi$
$557$	−458.690	−	794.474i	−0.823501	−	1.42634i	0.0795593	−	0.996830i	$-0.474649\pi$
$558$		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	$-0.779315\pi$
$563$	−337.941	+	195.111i	−0.600251	+	0.346555i	0.168889	+	0.985635i	$0.445982\pi$
$564$		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	−0.925692	−	0.378278i	$-0.876516\pi$
$569$	−76.9559	+	133.292i	−0.135248	+	0.234256i	0.790444	+	0.612534i	$0.209850\pi$
$570$		0			0
$571$	−179.223	−	310.424i	−0.313876	−	0.543650i	0.665322	−	0.746557i	$-0.268294\pi$
$571$	−179.223	−	310.424i	−0.313876	−	0.543650i	−0.979198	+	0.202907i	$0.934961\pi$
$572$		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	0.350494	−	0.936565i	$-0.386014\pi$
$577$	771.351	−	445.340i	1.33683	−	0.771820i	0.986336	+	0.164745i	$0.0526802\pi$
$578$		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	0.991165	+	0.132637i	$0.0423444\pi$
$593$	949.757	+	548.343i	1.60161	+	0.924692i	0.610449	+	0.792055i	$0.290989\pi$
$594$		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	$-0.186082\pi$
$599$	−36.5134	−	63.2431i	−0.0609573	−	0.105581i	−0.894894	+	0.446280i	$0.852749\pi$
$600$		0			0
$601$		−	911.924i		−	1.51734i	−0.651472	−	0.758672i	$-0.725848\pi$
$601$		−	911.924i		−	1.51734i	0.651472	−	0.758672i	$-0.274152\pi$
$602$		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	$-0.364140\pi$
$607$	−101.592	−	58.6544i	−0.167368	−	0.0966299i	−0.581344	+	0.813658i	$0.697473\pi$
$608$		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	0.858152	−	0.513396i	$-0.171613\pi$
$613$	−9.52481	−	16.4975i	−0.0155380	−	0.0269127i	−0.873690	+	0.486483i	$0.838279\pi$
$614$		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	$-0.710092\pi$
$619$	−145.813	+	84.1853i	−0.235562	+	0.136002i	0.377573	+	0.925980i	$0.376759\pi$
$620$		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	$-0.303452\pi$
$631$	730.669			1.15795			0.578977	+	0.815344i	$0.303452\pi$
$632$		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	0.953777	−	0.300517i	$-0.0971591\pi$
$641$	138.862	+	240.516i	0.216633	+	0.375220i	−0.737143	+	0.675736i	$0.763826\pi$
$642$		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	$-0.895579\pi$
$647$	−738.214	+	426.208i	−1.14098	+	0.658745i	−0.194307	+	0.980941i	$0.562246\pi$
$648$		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	−0.924058	−	0.382252i	$-0.875149\pi$
$653$	−85.5358	+	148.152i	−0.130989	+	0.226880i	0.793069	+	0.609132i	$0.208482\pi$
$654$		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	$-0.112067\pi$
$659$	1237.16			1.87732			0.938661	+	0.344840i	$0.112067\pi$
$660$		0			0
$661$	−222.784	+	128.624i	−0.337040	+	0.194590i	−0.658962	−	0.752176i	$-0.729004\pi$
$661$	−222.784	+	128.624i	−0.337040	+	0.194590i	0.321922	+	0.946766i	$0.395671\pi$
$662$		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	0.646308	−	0.763076i	$-0.276312\pi$
$677$	208.935	+	120.629i	0.308619	+	0.178181i	−0.337689	+	0.941258i	$0.609645\pi$
$678$		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	$-0.315550\pi$
$683$	−307.939	−	533.366i	−0.450863	−	0.780917i	−0.998440	+	0.0558381i	$0.982217\pi$
$684$		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	$-0.327970\pi$
$691$	20.1639	+	11.6416i	0.0291807	+	0.0168475i	−0.485339	+	0.874326i	$0.661304\pi$
$692$		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	0.450018	+	0.893020i	$0.351418\pi$
$709$	−388.793	+	673.410i	−0.548369	+	0.949802i	−0.998387	+	0.0567828i	$0.981916\pi$
$710$		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	$-0.204310\pi$
$719$	491.076	+	283.523i	0.682998	+	0.394329i	−0.117985	+	0.993015i	$0.537644\pi$
$720$		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	0.00313844	−	0.999995i	$-0.499001\pi$
$733$	−631.343	−	364.506i	−0.861313	−	0.497280i	−0.864452	+	0.502716i	$0.832334\pi$
$734$		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	$-0.0586792\pi$
$739$	245.926	+	425.957i	0.332782	+	0.576396i	−0.650274	+	0.759700i	$0.725346\pi$
$740$		0			0
$741$			601.472i			0.811703i
$742$		0			0
$743$	1124.25			1.51313			0.756563	−	0.653920i	$-0.226877\pi$
$743$	1124.25			1.51313			0.756563	+	0.653920i	$0.226877\pi$
$744$		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	0.379184	+	0.925321i	$0.376205\pi$
$751$	−459.432	+	795.759i	−0.611760	+	1.05960i	−0.990944	+	0.134278i	$0.957129\pi$
$752$		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	0.384972	−	0.922928i	$-0.374211\pi$
$761$	−168.805	−	97.4598i	−0.221820	−	0.128068i	−0.606793	+	0.794860i	$0.707544\pi$
$762$		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	$-0.905345\pi$
$769$		−	450.642i		−	0.586010i	0.956111	−	0.293005i	$-0.0946553\pi$
$770$		0			0
$771$	68.0954			0.0883209
$772$		0			0
$773$	−132.382	+	76.4306i	−0.171257	+	0.0988754i	−0.583178	−	0.812344i	$-0.698191\pi$
$773$	−132.382	+	76.4306i	−0.171257	+	0.0988754i	0.411921	+	0.911219i	$0.364858\pi$
$774$		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	$-0.867008\pi$
$787$	−802.406	+	463.269i	−1.01958	+	0.588652i	−0.105595	+	0.994409i	$0.533675\pi$
$788$		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	$0.295803\pi$
$797$			1277.11i			1.60239i	−0.598401	+	0.801197i	$0.704197\pi$
$798$		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	0.995025	−	0.0996258i	$-0.0317646\pi$
$809$	332.688	+	576.233i	0.411234	+	0.712278i	−0.583791	+	0.811904i	$0.698431\pi$
$810$		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	−0.966214	−	0.257742i	$-0.917022\pi$
$821$	−213.374	+	369.575i	−0.259896	+	0.450153i	0.706318	+	0.707895i	$0.250355\pi$
$822$		0			0
$823$	489.430	+	847.717i	0.594690	+	1.03003i	0.993591	+	0.113039i	$0.0360585\pi$
$823$	489.430	+	847.717i	0.594690	+	1.03003i	−0.398901	+	0.916994i	$0.630608\pi$
$824$		0			0
$825$			269.277i			0.326396i
$826$		0			0
$827$	660.437			0.798594			0.399297	−	0.916822i	$-0.369254\pi$
$827$	660.437			0.798594			0.399297	+	0.916822i	$0.369254\pi$
$828$		0			0
$829$	993.501	−	573.598i	1.19843	−	0.691916i	0.238227	−	0.971209i	$-0.423434\pi$
$829$	993.501	−	573.598i	1.19843	−	0.691916i	0.960206	+	0.279294i	$0.0901004\pi$
$830$		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	$-0.882307\pi$
$853$		−	616.510i		−	0.722755i	0.932420	−	0.361378i	$-0.117693\pi$
$854$		0			0
$855$	103.482			0.121031
$856$		0			0
$857$	−150.722	+	87.0195i	−0.175872	+	0.101540i	−0.585352	−	0.810780i	$-0.699044\pi$
$857$	−150.722	+	87.0195i	−0.175872	+	0.101540i	0.409480	+	0.912319i	$0.365710\pi$
$858$		0			0
$859$	1284.90	+	741.836i	1.49581	+	0.863605i	0.999988	−	0.00482143i	$-0.00153472\pi$
$859$	1284.90	+	741.836i	1.49581	+	0.863605i	0.495819	+	0.868426i	$0.334868\pi$
$860$		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	$-0.984519\pi$
$863$	−394.655	+	683.562i	−0.457305	+	0.792076i	0.541512	+	0.840693i	$0.317852\pi$
$864$		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	−0.909174	−	0.416417i	$-0.863285\pi$
$877$	−82.4017	+	142.724i	−0.0939586	+	0.162741i	0.815215	+	0.579159i	$0.196619\pi$
$878$		0			0
$879$	−231.380	−	400.762i	−0.263231	−	0.455929i
$880$		0			0
$881$			150.440i			0.170761i	0.996348	+	0.0853804i	$0.0272105\pi$
$881$			150.440i			0.170761i	−0.996348	+	0.0853804i	$0.972789\pi$
$882$		0			0
$883$	1260.13			1.42710			0.713550	−	0.700604i	$-0.247086\pi$
$883$	1260.13			1.42710			0.713550	+	0.700604i	$0.247086\pi$
$884$		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	$-0.229076\pi$
$887$	494.249	+	285.355i	0.557214	+	0.321708i	−0.194812	+	0.980841i	$0.562410\pi$
$888$		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	$-0.214413\pi$
$907$	−135.539	−	234.761i	−0.149437	−	0.258832i	−0.931019	+	0.364970i	$0.881079\pi$
$908$		0			0
$909$		−	546.899i		−	0.601649i
$910$		0			0
$911$	−1152.78			−1.26540			−0.632699	−	0.774398i	$-0.718053\pi$
$911$	−1152.78			−1.26540			−0.632699	+	0.774398i	$0.718053\pi$
$912$		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	$-0.770612\pi$
$919$	179.916	−	311.624i	0.195774	−	0.339090i	0.947154	+	0.320780i	$0.103945\pi$
$920$		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	0.554706	−	0.832046i	$-0.312831\pi$
$929$	103.571	+	59.7966i	0.111486	+	0.0643667i	−0.443220	+	0.896413i	$0.646164\pi$
$930$		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	$-0.827052\pi$
$937$		−	968.840i		−	1.03398i	0.855991	−	0.516990i	$-0.172948\pi$
$938$		0			0
$939$	267.201			0.284559
$940$		0			0
$941$	285.043	−	164.570i	0.302915	−	0.174888i	−0.340837	−	0.940123i	$-0.610710\pi$
$941$	285.043	−	164.570i	0.302915	−	0.174888i	0.643752	+	0.765235i	$0.277377\pi$
$942$		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	−0.199743	+	0.979848i	$0.564011\pi$
$947$	−898.178	+	1555.69i	−0.948445	+	1.64276i	−0.748702	+	0.662907i	$0.769322\pi$
$948$		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	$-0.719164\pi$
$967$	−1228.86			−1.27080			−0.635399	+	0.772184i	$0.719164\pi$
$968$		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	$-0.272920\pi$
$971$	317.288	+	183.186i	0.326764	+	0.188658i	−0.327639	+	0.944803i	$0.606253\pi$
$972$		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	0.926427	+	0.376474i	$0.122863\pi$
$977$	771.097	+	1335.58i	0.789249	+	1.36702i	−0.137178	+	0.990546i	$0.543803\pi$
$978$		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	$-0.595399\pi$
$983$	378.028	−	218.255i	0.384566	−	0.222029i	0.679803	+	0.733395i	$0.262065\pi$
$984$		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	$-0.180149\pi$
$991$	−41.9624	−	72.6811i	−0.0423435	−	0.0733411i	−0.886420	+	0.462881i	$0.846816\pi$
$992$		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	−0.700645	−	0.713510i	$-0.747104\pi$
$997$	−431.750	+	249.271i	−0.433050	+	0.250021i	0.267595	+	0.963531i	$0.413771\pi$
$998$		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	336.3.bh.h.145.2		8
3.2	odd	2		1008.3.cg.n.145.3		8
4.3	odd	2		168.3.z.a.145.2	yes	8
7.2	even	3		2352.3.f.k.97.7		8
7.3	odd	6	inner	336.3.bh.h.241.2		8
7.5	odd	6		2352.3.f.k.97.2		8
12.11	even	2		504.3.by.a.145.3		8
21.17	even	6		1008.3.cg.n.577.3		8
28.3	even	6		168.3.z.a.73.2	✓	8
28.11	odd	6		1176.3.z.d.913.3		8
28.19	even	6		1176.3.f.a.97.6		8
28.23	odd	6		1176.3.f.a.97.3		8
28.27	even	2		1176.3.z.d.313.3		8
84.23	even	6		3528.3.f.f.2449.3		8
84.47	odd	6		3528.3.f.f.2449.6		8
84.59	odd	6		504.3.by.a.73.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.z.a.73.2	✓	8	28.3	even	6
168.3.z.a.145.2	yes	8	4.3	odd	2
336.3.bh.h.145.2		8	1.1	even	1	trivial
336.3.bh.h.241.2		8	7.3	odd	6	inner
504.3.by.a.73.3		8	84.59	odd	6
504.3.by.a.145.3		8	12.11	even	2
1008.3.cg.n.145.3		8	3.2	odd	2
1008.3.cg.n.577.3		8	21.17	even	6
1176.3.f.a.97.3		8	28.23	odd	6
1176.3.f.a.97.6		8	28.19	even	6
1176.3.z.d.313.3		8	28.27	even	2
1176.3.z.d.913.3		8	28.11	odd	6
2352.3.f.k.97.2		8	7.5	odd	6
2352.3.f.k.97.7		8	7.2	even	3
3528.3.f.f.2449.3		8	84.23	even	6
3528.3.f.f.2449.6		8	84.47	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not 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

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