LMFDB - Embedded newform 336.3.bh.g.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:	8.0.35911766016.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 7x^{6} - 2x^{5} + 78x^{4} - 18x^{3} - 153x^{2} - 230x + 529 $ x^8 - 2x^7 - 7x^6 - 2x^5 + 78x^4 - 18x^3 - 153x^2 - 230*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 7 $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$-1.90015 + 1.67440i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.3.bh.g.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 + 0.866025i) q^{3} +(-4.68140 - 2.70281i) q^{5} +(6.12873 + 3.38210i) q^{7} +(1.50000 - 2.59808i) q^{9} +(5.26719 + 9.12303i) q^{11} -12.0366i q^{13} +9.36280 q^{15} +(-20.8464 + 12.0357i) q^{17} +(-30.9077 - 17.8446i) q^{19} +(-12.1221 + 0.234486i) q^{21} +(-20.6552 + 35.7759i) q^{23} +(2.11033 + 3.65520i) q^{25} +5.19615i q^{27} -28.6732 q^{29} +(4.50233 - 2.59942i) q^{31} +(-15.8016 - 9.12303i) q^{33} +(-19.5499 - 32.3978i) q^{35} +(1.90932 - 3.30704i) q^{37} +(10.4240 + 18.0550i) q^{39} -9.20741i q^{41} -54.2960 q^{43} +(-14.0442 + 8.10842i) q^{45} +(-14.3350 - 8.27632i) q^{47} +(26.1228 + 41.4560i) q^{49} +(20.8464 - 36.1071i) q^{51} +(-9.58322 - 16.5986i) q^{53} -56.9447i q^{55} +61.8154 q^{57} +(-10.8261 + 6.25043i) q^{59} +(84.1179 + 48.5655i) q^{61} +(17.9801 - 10.8498i) q^{63} +(-32.5327 + 56.3483i) q^{65} +(0.499078 + 0.864429i) q^{67} -71.5517i q^{69} +14.8401 q^{71} +(-51.0987 + 29.5018i) q^{73} +(-6.33099 - 3.65520i) q^{75} +(1.42615 + 73.7268i) q^{77} +(-50.7558 + 87.9116i) q^{79} +(-4.50000 - 7.79423i) q^{81} -22.7269i q^{83} +130.121 q^{85} +(43.0098 - 24.8317i) q^{87} +(-98.7518 - 57.0144i) q^{89} +(40.7092 - 73.7694i) q^{91} +(-4.50233 + 7.79826i) q^{93} +(96.4608 + 167.075i) q^{95} -153.333i q^{97} +31.6031 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} - 6 q^{5} - 8 q^{7} + 12 q^{9} + 22 q^{11} + 12 q^{15} + 36 q^{17} - 42 q^{19} + 6 q^{21} - 48 q^{23} + 42 q^{25} + 68 q^{29} + 60 q^{31} - 66 q^{33} + 12 q^{35} - 118 q^{37} + 18 q^{39}+ \cdots + 132 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 - 6 * q^5 - 8 * q^7 + 12 * q^9 + 22 * q^11 + 12 * q^15 + 36 * q^17 - 42 * q^19 + 6 * q^21 - 48 * q^23 + 42 * q^25 + 68 * q^29 + 60 * q^31 - 66 * q^33 + 12 * q^35 - 118 * q^37 + 18 * q^39 + 92 * q^43 - 18 * q^45 + 12 * q^47 - 20 * q^49 - 36 * q^51 + 10 * q^53 + 84 * q^57 + 54 * q^59 + 24 * q^61 + 6 * q^63 - 148 * q^65 - 22 * q^67 + 392 * q^71 - 138 * q^73 - 126 * q^75 - 126 * q^77 - 164 * q^79 - 36 * q^81 + 200 * q^85 - 102 * q^87 - 60 * q^89 - 90 * q^91 - 60 * q^93 + 132 * 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
$5$	−4.68140	−	2.70281i	−0.936280	−	0.540561i	−0.0474876	−	0.998872i	$-0.515121\pi$
$5$	−4.68140	−	2.70281i	−0.936280	−	0.540561i	−0.888792	+	0.458310i	$0.848455\pi$
$6$		0			0
$7$	6.12873	+	3.38210i	0.875533	+	0.483158i
$7$	6.12873	+	3.38210i	0.875533	+	0.483158i
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	5.26719	+	9.12303i	0.478835	+	0.829367i	0.999705	−	0.0242691i	$-0.00772586\pi$
$11$	5.26719	+	9.12303i	0.478835	+	0.829367i	−0.520870	+	0.853636i	$0.674393\pi$
$12$		0			0
$13$		−	12.0366i		−	0.925896i	−0.886386	−	0.462948i	$-0.846792\pi$
$13$		−	12.0366i		−	0.925896i	0.886386	−	0.462948i	$-0.153208\pi$
$14$		0			0
$15$	9.36280			0.624187
$16$		0			0
$17$	−20.8464	+	12.0357i	−1.22626	+	0.707982i	−0.966246	−	0.257622i	$-0.917061\pi$
$17$	−20.8464	+	12.0357i	−1.22626	+	0.707982i	−0.260015	+	0.965605i	$0.583728\pi$
$18$		0			0
$19$	−30.9077	−	17.8446i	−1.62672	−	0.939187i	−0.985063	−	0.172195i	$-0.944914\pi$
$19$	−30.9077	−	17.8446i	−1.62672	−	0.939187i	−0.641657	−	0.766992i	$-0.721753\pi$
$20$		0			0
$21$	−12.1221	+	0.234486i	−0.577242	+	0.0111660i
$22$		0			0
$23$	−20.6552	+	35.7759i	−0.898053	+	1.55547i	−0.0680720	+	0.997680i	$0.521685\pi$
$23$	−20.6552	+	35.7759i	−0.898053	+	1.55547i	−0.829981	+	0.557792i	$0.811649\pi$
$24$		0			0
$25$	2.11033	+	3.65520i	0.0844132	+	0.146208i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−28.6732			−0.988732			−0.494366	−	0.869254i	$-0.664600\pi$
$29$	−28.6732			−0.988732			−0.494366	+	0.869254i	$0.664600\pi$
$30$		0			0
$31$	4.50233	−	2.59942i	0.145236	−	0.0838522i	−0.425621	−	0.904902i	$-0.639944\pi$
$31$	4.50233	−	2.59942i	0.145236	−	0.0838522i	0.570857	+	0.821049i	$0.306611\pi$
$32$		0			0
$33$	−15.8016	−	9.12303i	−0.478835	−	0.276456i
$34$		0			0
$35$	−19.5499	−	32.3978i	−0.558568	−	0.925650i
$36$		0			0
$37$	1.90932	−	3.30704i	0.0516033	−	0.0893795i	−0.839070	−	0.544024i	$-0.816900\pi$
$37$	1.90932	−	3.30704i	0.0516033	−	0.0893795i	0.890673	+	0.454644i	$0.150234\pi$
$38$		0			0
$39$	10.4240	+	18.0550i	0.267283	+	0.462948i
$40$		0			0
$41$		−	9.20741i		−	0.224571i	−0.993676	−	0.112286i	$-0.964183\pi$
$41$		−	9.20741i		−	0.224571i	0.993676	−	0.112286i	$-0.0358171\pi$
$42$		0			0
$43$	−54.2960			−1.26270			−0.631349	−	0.775499i	$-0.717498\pi$
$43$	−54.2960			−1.26270			−0.631349	+	0.775499i	$0.717498\pi$
$44$		0			0
$45$	−14.0442	+	8.10842i	−0.312093	+	0.180187i
$46$		0			0
$47$	−14.3350	−	8.27632i	−0.305000	−	0.176092i	0.339687	−	0.940539i	$-0.389679\pi$
$47$	−14.3350	−	8.27632i	−0.305000	−	0.176092i	−0.644687	+	0.764447i	$0.723012\pi$
$48$		0			0
$49$	26.1228	+	41.4560i	0.533118	+	0.846041i
$50$		0			0
$51$	20.8464	−	36.1071i	0.408754	−	0.707982i
$52$		0			0
$53$	−9.58322	−	16.5986i	−0.180815	−	0.313182i	0.761343	−	0.648349i	$-0.224540\pi$
$53$	−9.58322	−	16.5986i	−0.180815	−	0.313182i	−0.942158	+	0.335168i	$0.891207\pi$
$54$		0			0
$55$		−	56.9447i		−	1.03536i
$56$		0			0
$57$	61.8154			1.08448
$58$		0			0
$59$	−10.8261	+	6.25043i	−0.183493	+	0.105939i	−0.588933	−	0.808182i	$-0.700452\pi$
$59$	−10.8261	+	6.25043i	−0.183493	+	0.105939i	0.405440	+	0.914122i	$0.367118\pi$
$60$		0			0
$61$	84.1179	+	48.5655i	1.37898	+	0.796156i	0.992037	−	0.125947i	$-0.0401969\pi$
$61$	84.1179	+	48.5655i	1.37898	+	0.796156i	0.386945	+	0.922103i	$0.373530\pi$
$62$		0			0
$63$	17.9801	−	10.8498i	0.285398	−	0.172218i
$64$		0			0
$65$	−32.5327	+	56.3483i	−0.500503	+	0.866897i
$66$		0			0
$67$	0.499078	+	0.864429i	0.00744893	+	0.0129019i	0.869726	−	0.493535i	$-0.164296\pi$
$67$	0.499078	+	0.864429i	0.00744893	+	0.0129019i	−0.862277	+	0.506437i	$0.830962\pi$
$68$		0			0
$69$		−	71.5517i		−	1.03698i
$70$		0			0
$71$	14.8401			0.209015			0.104507	−	0.994524i	$-0.466673\pi$
$71$	14.8401			0.209015			0.104507	+	0.994524i	$0.466673\pi$
$72$		0			0
$73$	−51.0987	+	29.5018i	−0.699982	+	0.404135i	−0.807341	−	0.590085i	$-0.799094\pi$
$73$	−51.0987	+	29.5018i	−0.699982	+	0.404135i	0.107359	+	0.994220i	$0.465761\pi$
$74$		0			0
$75$	−6.33099	−	3.65520i	−0.0844132	−	0.0487360i
$76$		0			0
$77$	1.42615	+	73.7268i	0.0185214	+	0.957491i
$78$		0			0
$79$	−50.7558	+	87.9116i	−0.642478	+	1.11281i	0.342399	+	0.939555i	$0.388760\pi$
$79$	−50.7558	+	87.9116i	−0.642478	+	1.11281i	−0.984878	+	0.173251i	$0.944573\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	22.7269i		−	0.273818i	−0.990584	−	0.136909i	$-0.956283\pi$
$83$		−	22.7269i		−	0.273818i	0.990584	−	0.136909i	$-0.0437168\pi$
$84$		0			0
$85$	130.121			1.53083
$86$		0			0
$87$	43.0098	−	24.8317i	0.494366	−	0.285422i
$88$		0			0
$89$	−98.7518	−	57.0144i	−1.10957	−	0.640611i	−0.170853	−	0.985297i	$-0.554652\pi$
$89$	−98.7518	−	57.0144i	−1.10957	−	0.640611i	−0.938718	+	0.344685i	$0.887986\pi$
$90$		0			0
$91$	40.7092	−	73.7694i	0.447353	−	0.810653i
$92$		0			0
$93$	−4.50233	+	7.79826i	−0.0484121	+	0.0838522i
$94$		0			0
$95$	96.4608	+	167.075i	1.01538	+	1.75868i
$96$		0			0
$97$		−	153.333i		−	1.58075i	−0.612621	−	0.790377i	$-0.709885\pi$
$97$		−	153.333i		−	1.58075i	0.612621	−	0.790377i	$-0.290115\pi$
$98$		0			0
$99$	31.6031			0.319223
$100$		0			0
$101$	−15.2778	+	8.82063i	−0.151265	+	0.0873329i	−0.573722	−	0.819050i	$-0.694501\pi$
$101$	−15.2778	+	8.82063i	−0.151265	+	0.0873329i	0.422457	+	0.906383i	$0.361168\pi$
$102$		0			0
$103$	119.710	+	69.1149i	1.16224	+	0.671018i	0.951839	−	0.306598i	$-0.0991907\pi$
$103$	119.710	+	69.1149i	1.16224	+	0.671018i	0.210398	+	0.977616i	$0.432524\pi$
$104$		0			0
$105$	57.3821	+	31.6659i	0.546496	+	0.301580i
$106$		0			0
$107$	−41.0743	+	71.1428i	−0.383872	+	0.664886i	−0.991612	−	0.129250i	$-0.958743\pi$
$107$	−41.0743	+	71.1428i	−0.383872	+	0.664886i	0.607740	+	0.794136i	$0.292076\pi$
$108$		0			0
$109$	−45.1889	−	78.2695i	−0.414577	−	0.718069i	0.580807	−	0.814042i	$-0.302737\pi$
$109$	−45.1889	−	78.2695i	−0.414577	−	0.718069i	−0.995384	+	0.0959724i	$0.969404\pi$
$110$		0			0
$111$			6.61408i			0.0595863i
$112$		0			0
$113$	206.994			1.83180			0.915901	−	0.401405i	$-0.131478\pi$
$113$	206.994			1.83180			0.915901	+	0.401405i	$0.131478\pi$
$114$		0			0
$115$	193.391	−	111.654i	1.68166	−	0.970905i
$116$		0			0
$117$	−31.2721	−	18.0550i	−0.267283	−	0.154316i
$118$		0			0
$119$	−168.468	+	3.25879i	−1.41570	+	0.0273848i
$120$		0			0
$121$	5.01351	−	8.68366i	0.0414340	−	0.0717658i
$122$		0			0
$123$	7.97385	+	13.8111i	0.0648281	+	0.112286i
$124$		0			0
$125$			112.325i			0.898601i
$126$		0			0
$127$	155.159			1.22172			0.610862	−	0.791737i	$-0.290823\pi$
$127$	155.159			1.22172			0.610862	+	0.791737i	$0.290823\pi$
$128$		0			0
$129$	81.4440	−	47.0217i	0.631349	−	0.364509i
$130$		0			0
$131$	−62.0353	−	35.8161i	−0.473552	−	0.273405i	0.244174	−	0.969732i	$-0.421483\pi$
$131$	−62.0353	−	35.8161i	−0.473552	−	0.273405i	−0.717725	+	0.696326i	$0.754817\pi$
$132$		0			0
$133$	−129.073	−	213.897i	−0.970472	−	1.60825i
$134$		0			0
$135$	14.0442	−	24.3253i	0.104031	−	0.180187i
$136$		0			0
$137$	−76.1226	−	131.848i	−0.555639	−	0.962395i	−0.997853	−	0.0654859i	$-0.979140\pi$
$137$	−76.1226	−	131.848i	−0.555639	−	0.962395i	0.442214	−	0.896909i	$-0.354193\pi$
$138$		0			0
$139$		−	119.318i		−	0.858401i	−0.903209	−	0.429200i	$-0.858795\pi$
$139$		−	119.318i		−	0.858401i	0.903209	−	0.429200i	$-0.141205\pi$
$140$		0			0
$141$	28.6700			0.203333
$142$		0			0
$143$	109.811	−	63.3992i	0.767907	−	0.443351i
$144$		0			0
$145$	134.231	+	77.4982i	0.925729	+	0.534470i
$146$		0			0
$147$	−75.0861	−	39.5610i	−0.510790	−	0.269123i
$148$		0			0
$149$	27.0510	−	46.8537i	0.181550	−	0.314455i	−0.760858	−	0.648918i	$-0.775222\pi$
$149$	27.0510	−	46.8537i	0.181550	−	0.314455i	0.942409	+	0.334464i	$0.108555\pi$
$150$		0			0
$151$	65.8756	+	114.100i	0.436262	+	0.755629i	0.997398	−	0.0720954i	$-0.0229686\pi$
$151$	65.8756	+	114.100i	0.436262	+	0.755629i	−0.561135	+	0.827724i	$0.689635\pi$
$152$		0			0
$153$			72.2142i			0.471988i
$154$		0			0
$155$	−28.1029			−0.181309
$156$		0			0
$157$	−208.180	+	120.193i	−1.32599	+	0.765558i	−0.984676	−	0.174393i	$-0.944204\pi$
$157$	−208.180	+	120.193i	−1.32599	+	0.765558i	−0.341309	+	0.939951i	$0.610870\pi$
$158$		0			0
$159$	28.7497	+	16.5986i	0.180815	+	0.104394i
$160$		0			0
$161$	−247.588	+	149.403i	−1.53781	+	0.927968i
$162$		0			0
$163$	−134.585	+	233.108i	−0.825674	+	1.43011i	0.0757286	+	0.997128i	$0.475872\pi$
$163$	−134.585	+	233.108i	−0.825674	+	1.43011i	−0.901403	+	0.432981i	$0.857462\pi$
$164$		0			0
$165$	49.3156	+	85.4171i	0.298882	+	0.517679i
$166$		0			0
$167$			123.116i			0.737219i	0.929584	+	0.368609i	$0.120166\pi$
$167$			123.116i			0.737219i	−0.929584	+	0.368609i	$0.879834\pi$
$168$		0			0
$169$	24.1192			0.142717
$170$		0			0
$171$	−92.7230	+	53.5337i	−0.542240	+	0.313062i
$172$		0			0
$173$	195.401	+	112.815i	1.12949	+	0.652109i	0.943805	−	0.330502i	$-0.107218\pi$
$173$	195.401	+	112.815i	1.12949	+	0.652109i	0.185680	+	0.982610i	$0.440551\pi$
$174$		0			0
$175$	0.571395	+	29.5391i	0.00326511	+	0.168795i
$176$		0			0
$177$	10.8261	−	18.7513i	0.0611642	−	0.105939i
$178$		0			0
$179$	−133.624	−	231.444i	−0.746505	−	1.29298i	−0.949488	−	0.313803i	$-0.898397\pi$
$179$	−133.624	−	231.444i	−0.746505	−	1.29298i	0.202983	−	0.979182i	$-0.434936\pi$
$180$		0			0
$181$			64.5441i			0.356597i	0.983976	+	0.178299i	$0.0570593\pi$
$181$			64.5441i			0.356597i	−0.983976	+	0.178299i	$0.942941\pi$
$182$		0			0
$183$	−168.236			−0.919321
$184$		0			0
$185$	−17.8766	+	10.3211i	−0.0966302	+	0.0557895i
$186$		0			0
$187$	−219.604	−	126.788i	−1.17435	−	0.678013i
$188$		0			0
$189$	−17.5739	+	31.8458i	−0.0929837	+	0.168496i
$190$		0			0
$191$	74.3710	−	128.814i	0.389377	−	0.674421i	−0.602989	−	0.797750i	$-0.706024\pi$
$191$	74.3710	−	128.814i	0.389377	−	0.674421i	0.992366	+	0.123329i	$0.0393570\pi$
$192$		0			0
$193$	−14.9315	−	25.8622i	−0.0773655	−	0.134001i	0.824747	−	0.565502i	$-0.191318\pi$
$193$	−14.9315	−	25.8622i	−0.0773655	−	0.134001i	−0.902112	+	0.431501i	$0.857984\pi$
$194$		0			0
$195$		−	112.697i		−	0.577932i
$196$		0			0
$197$	191.905			0.974138			0.487069	−	0.873364i	$-0.338066\pi$
$197$	191.905			0.974138			0.487069	+	0.873364i	$0.338066\pi$
$198$		0			0
$199$	−18.5965	+	10.7367i	−0.0934495	+	0.0539531i	−0.545996	−	0.837787i	$-0.683849\pi$
$199$	−18.5965	+	10.7367i	−0.0934495	+	0.0539531i	0.452547	+	0.891741i	$0.350515\pi$
$200$		0			0
$201$	−1.49723	−	0.864429i	−0.00744893	−	0.00430064i
$202$		0			0
$203$	−175.731	−	96.9758i	−0.865668	−	0.477713i
$204$		0			0
$205$	−24.8859	+	43.1036i	−0.121394	+	0.210261i
$206$		0			0
$207$	61.9656	+	107.328i	0.299351	+	0.518491i
$208$		0			0
$209$		−	375.962i		−	1.79886i
$210$		0			0
$211$	179.565			0.851020			0.425510	−	0.904954i	$-0.360095\pi$
$211$	179.565			0.851020			0.425510	+	0.904954i	$0.360095\pi$
$212$		0			0
$213$	−22.2601	+	12.8519i	−0.104507	+	0.0603374i
$214$		0			0
$215$	254.181	+	146.752i	1.18224	+	0.682565i
$216$		0			0
$217$	36.3851	−	0.703821i	0.167673	−	0.00324341i
$218$		0			0
$219$	51.0987	−	88.5055i	0.233327	−	0.404135i
$220$		0			0
$221$	144.869	+	250.921i	0.655518	+	1.13539i
$222$		0			0
$223$		−	296.009i		−	1.32739i	−0.748001	−	0.663697i	$-0.768986\pi$
$223$		−	296.009i		−	1.32739i	0.748001	−	0.663697i	$-0.231014\pi$
$224$		0			0
$225$	12.6620			0.0562755
$226$		0			0
$227$	−152.738	+	88.1834i	−0.672855	+	0.388473i	−0.797158	−	0.603771i	$-0.793664\pi$
$227$	−152.738	+	88.1834i	−0.672855	+	0.388473i	0.124302	+	0.992244i	$0.460331\pi$
$228$		0			0
$229$	−41.8862	−	24.1830i	−0.182909	−	0.105603i	0.405750	−	0.913984i	$-0.367011\pi$
$229$	−41.8862	−	24.1830i	−0.182909	−	0.105603i	−0.588659	+	0.808382i	$0.700344\pi$
$230$		0			0
$231$	−65.9885	−	109.355i	−0.285665	−	0.473399i
$232$		0			0
$233$	−229.214	+	397.011i	−0.983753	+	1.70391i	−0.336401	+	0.941719i	$0.609210\pi$
$233$	−229.214	+	397.011i	−0.983753	+	1.70391i	−0.647352	+	0.762191i	$0.724123\pi$
$234$		0			0
$235$	44.7386	+	77.4895i	0.190377	+	0.329743i
$236$		0			0
$237$		−	175.823i		−	0.741870i
$238$		0			0
$239$	−124.419			−0.520581			−0.260291	−	0.965530i	$-0.583818\pi$
$239$	−124.419			−0.520581			−0.260291	+	0.965530i	$0.583818\pi$
$240$		0			0
$241$	−190.318	+	109.880i	−0.789702	+	0.455935i	−0.839858	−	0.542807i	$-0.817362\pi$
$241$	−190.318	+	109.880i	−0.789702	+	0.455935i	0.0501556	+	0.998741i	$0.484028\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−10.2435	−	264.677i	−0.0418101	−	1.08031i
$246$		0			0
$247$	−214.789	+	372.025i	−0.869589	+	1.50617i
$248$		0			0
$249$	19.6821	+	34.0904i	0.0790445	+	0.136909i
$250$		0			0
$251$		−	69.5582i		−	0.277124i	−0.990354	−	0.138562i	$-0.955752\pi$
$251$		−	69.5582i		−	0.277124i	0.990354	−	0.138562i	$-0.0442481\pi$
$252$		0			0
$253$	−435.179			−1.72008
$254$		0			0
$255$	−195.181	+	112.688i	−0.765416	+	0.441913i
$256$		0			0
$257$	−88.1589	−	50.8985i	−0.343031	−	0.198049i	0.318581	−	0.947896i	$-0.396794\pi$
$257$	−88.1589	−	50.8985i	−0.343031	−	0.198049i	−0.661611	+	0.749847i	$0.730127\pi$
$258$		0			0
$259$	22.8865	−	13.8105i	0.0883648	−	0.0533222i
$260$		0			0
$261$	−43.0098	+	74.4952i	−0.164789	+	0.285422i
$262$		0			0
$263$	−105.787	−	183.229i	−0.402233	−	0.696688i	0.591762	−	0.806113i	$-0.298432\pi$
$263$	−105.787	−	183.229i	−0.402233	−	0.696688i	−0.993995	+	0.109425i	$0.965099\pi$
$264$		0			0
$265$			103.606i			0.390967i
$266$		0			0
$267$	197.504			0.739714
$268$		0			0
$269$	270.057	−	155.918i	1.00393	−	0.579620i	0.0945219	−	0.995523i	$-0.469868\pi$
$269$	270.057	−	155.918i	1.00393	−	0.579620i	0.909409	+	0.415903i	$0.136534\pi$
$270$		0			0
$271$	−222.199	−	128.287i	−0.819924	−	0.473383i	0.0304661	−	0.999536i	$-0.490301\pi$
$271$	−222.199	−	128.287i	−0.819924	−	0.473383i	−0.850390	+	0.526152i	$0.823634\pi$
$272$		0			0
$273$	2.82242	+	145.909i	0.0103385	+	0.534466i
$274$		0			0
$275$	−22.2310	+	38.5052i	−0.0808400	+	0.140019i
$276$		0			0
$277$	139.547	+	241.702i	0.503778	+	0.872570i	0.999990	+	0.00436839i	$0.00139050\pi$
$277$	139.547	+	241.702i	0.503778	+	0.872570i	−0.496212	+	0.868201i	$0.665276\pi$
$278$		0			0
$279$		−	15.5965i		−	0.0559015i
$280$		0			0
$281$	−84.1671			−0.299527			−0.149763	−	0.988722i	$-0.547851\pi$
$281$	−84.1671			−0.299527			−0.149763	+	0.988722i	$0.547851\pi$
$282$		0			0
$283$	−403.071	+	232.713i	−1.42428	+	0.822309i	−0.996661	−	0.0816501i	$-0.973981\pi$
$283$	−403.071	+	232.713i	−1.42428	+	0.822309i	−0.427619	+	0.903959i	$0.640648\pi$
$284$		0			0
$285$	−289.382	−	167.075i	−1.01538	−	0.586228i
$286$		0			0
$287$	31.1404	−	56.4298i	0.108503	−	0.196619i
$288$		0			0
$289$	145.216	−	251.521i	0.502477	−	0.870316i
$290$		0			0
$291$	132.790	+	230.000i	0.456324	+	0.790377i
$292$		0			0
$293$		−	289.553i		−	0.988237i	−0.869395	−	0.494119i	$-0.835491\pi$
$293$		−	289.553i		−	0.988237i	0.869395	−	0.494119i	$-0.164509\pi$
$294$		0			0
$295$	67.5748			0.229067
$296$		0			0
$297$	−47.4047	+	27.3691i	−0.159612	+	0.0921518i
$298$		0			0
$299$	430.621	+	248.619i	1.44021	+	0.831503i
$300$		0			0
$301$	−332.766	−	183.635i	−1.10553	−	0.610082i
$302$		0			0
$303$	15.2778	−	26.4619i	0.0504217	−	0.0873329i
$304$		0			0
$305$	−262.526	−	454.709i	−0.860742	−	1.49085i
$306$		0			0
$307$			339.471i			1.10577i	0.833258	+	0.552884i	$0.186473\pi$
$307$			339.471i			1.10577i	−0.833258	+	0.552884i	$0.813527\pi$
$308$		0			0
$309$	−239.421			−0.774825
$310$		0			0
$311$	−85.5013	+	49.3642i	−0.274924	+	0.158727i	−0.631123	−	0.775683i	$-0.717406\pi$
$311$	−85.5013	+	49.3642i	−0.274924	+	0.158727i	0.356199	+	0.934410i	$0.384072\pi$
$312$		0			0
$313$	185.867	+	107.310i	0.593824	+	0.342845i	0.766608	−	0.642115i	$-0.221943\pi$
$313$	185.867	+	107.310i	0.593824	+	0.342845i	−0.172784	+	0.984960i	$0.555276\pi$
$314$		0			0
$315$	−113.497	+	2.19544i	−0.360307	+	0.00696966i
$316$		0			0
$317$	−96.8033	+	167.668i	−0.305373	+	0.528922i	−0.977344	−	0.211655i	$-0.932115\pi$
$317$	−96.8033	+	167.668i	−0.305373	+	0.528922i	0.671971	+	0.740577i	$0.265448\pi$
$318$		0			0
$319$	−151.027	−	261.587i	−0.473439	−	0.820021i
$320$		0			0
$321$		−	142.286i		−	0.443257i
$322$		0			0
$323$	859.086			2.65971
$324$		0			0
$325$	43.9964	−	25.4013i	0.135373	−	0.0781579i
$326$		0			0
$327$	135.567	+	78.2695i	0.414577	+	0.239356i
$328$		0			0
$329$	−59.8641	−	99.2058i	−0.181958	−	0.301537i
$330$		0			0
$331$	244.085	−	422.768i	0.737417	−	1.27724i	−0.216238	−	0.976341i	$-0.569379\pi$
$331$	244.085	−	422.768i	0.737417	−	1.27724i	0.953655	−	0.300903i	$-0.0972879\pi$
$332$		0			0
$333$	−5.72796	−	9.92112i	−0.0172011	−	0.0297932i
$334$		0			0
$335$		−	5.39565i		−	0.0161064i
$336$		0			0
$337$	535.060			1.58771			0.793857	−	0.608104i	$-0.208070\pi$
$337$	535.060			1.58771			0.793857	+	0.608104i	$0.208070\pi$
$338$		0			0
$339$	−310.490	+	179.262i	−0.915901	+	0.528796i
$340$		0			0
$341$	47.4292	+	27.3832i	0.139088	+	0.0803028i
$342$		0			0
$343$	19.8910	+	342.423i	0.0579912	+	0.998317i
$344$		0			0
$345$	−193.391	+	334.962i	−0.560552	+	0.970905i
$346$		0			0
$347$	167.692	+	290.451i	0.483262	+	0.837034i	0.999815	−	0.0192209i	$-0.00611857\pi$
$347$	167.692	+	290.451i	0.483262	+	0.837034i	−0.516553	+	0.856255i	$0.672785\pi$
$348$		0			0
$349$		−	105.238i		−	0.301542i	−0.988569	−	0.150771i	$-0.951824\pi$
$349$		−	105.238i		−	0.301542i	0.988569	−	0.150771i	$-0.0481756\pi$
$350$		0			0
$351$	62.5442			0.178189
$352$		0			0
$353$	284.108	−	164.030i	0.804840	−	0.464674i	−0.0403210	−	0.999187i	$-0.512838\pi$
$353$	284.108	−	164.030i	0.804840	−	0.464674i	0.845161	+	0.534512i	$0.179505\pi$
$354$		0			0
$355$	−69.4722	−	40.1098i	−0.195696	−	0.112985i
$356$		0			0
$357$	249.880	−	150.786i	0.699944	−	0.422370i
$358$		0			0
$359$	267.417	−	463.180i	0.744895	−	1.29020i	−0.205349	−	0.978689i	$-0.565833\pi$
$359$	267.417	−	463.180i	0.744895	−	1.29020i	0.950244	−	0.311507i	$-0.100834\pi$
$360$		0			0
$361$	456.356	+	790.432i	1.26414	+	2.18956i
$362$		0			0
$363$			17.3673i			0.0478439i
$364$		0			0
$365$	318.951			0.873839
$366$		0			0
$367$	−72.0037	+	41.5714i	−0.196195	+	0.113274i	−0.594880	−	0.803815i	$-0.702800\pi$
$367$	−72.0037	+	41.5714i	−0.196195	+	0.113274i	0.398684	+	0.917088i	$0.369467\pi$
$368$		0			0
$369$	−23.9216	−	13.8111i	−0.0648281	−	0.0374285i
$370$		0			0
$371$	−2.59476	−	134.140i	−0.00699396	−	0.361563i
$372$		0			0
$373$	270.334	−	468.233i	0.724757	−	1.25532i	−0.234317	−	0.972160i	$-0.575285\pi$
$373$	270.334	−	468.233i	0.724757	−	1.25532i	0.959074	−	0.283156i	$-0.0913814\pi$
$374$		0			0
$375$	−97.2764	−	168.488i	−0.259404	−	0.449300i
$376$		0			0
$377$			345.129i			0.915462i
$378$		0			0
$379$	−74.8470			−0.197486			−0.0987428	−	0.995113i	$-0.531482\pi$
$379$	−74.8470			−0.197486			−0.0987428	+	0.995113i	$0.531482\pi$
$380$		0			0
$381$	−232.738	+	134.372i	−0.610862	+	0.352681i
$382$		0			0
$383$	−101.467	−	58.5818i	−0.264926	−	0.152955i	0.361654	−	0.932313i	$-0.382212\pi$
$383$	−101.467	−	58.5818i	−0.264926	−	0.152955i	−0.626580	+	0.779357i	$0.715546\pi$
$384$		0			0
$385$	192.593	−	348.999i	0.500241	−	0.906491i
$386$		0			0
$387$	−81.4440	+	141.065i	−0.210450	+	0.364509i
$388$		0			0
$389$	264.804	+	458.653i	0.680729	+	1.17906i	0.974759	+	0.223261i	$0.0716703\pi$
$389$	264.804	+	458.653i	0.680729	+	1.17906i	−0.294029	+	0.955796i	$0.594996\pi$
$390$		0			0
$391$		−	994.399i		−	2.54322i
$392$		0			0
$393$	124.071			0.315701
$394$		0			0
$395$	475.216	−	274.366i	1.20308	−	0.694598i
$396$		0			0
$397$	301.419	+	174.024i	0.759241	+	0.438348i	0.829023	−	0.559214i	$-0.188897\pi$
$397$	301.419	+	174.024i	0.759241	+	0.438348i	−0.0697819	+	0.997562i	$0.522230\pi$
$398$		0			0
$399$	378.850	+	209.066i	0.949498	+	0.523975i
$400$		0			0
$401$	226.644	−	392.559i	0.565197	−	0.978950i	−0.431834	−	0.901953i	$-0.642134\pi$
$401$	226.644	−	392.559i	0.565197	−	0.978950i	0.997031	−	0.0769969i	$-0.0245332\pi$
$402$		0			0
$403$	−31.2883	−	54.1929i	−0.0776384	−	0.134474i
$404$		0			0
$405$			48.6505i			0.120125i
$406$		0			0
$407$	40.2270			0.0988378
$408$		0			0
$409$	−481.022	+	277.718i	−1.17609	+	0.679018i	−0.955108	−	0.296259i	$-0.904261\pi$
$409$	−481.022	+	277.718i	−1.17609	+	0.679018i	−0.220986	+	0.975277i	$0.570927\pi$
$410$		0			0
$411$	228.368	+	131.848i	0.555639	+	0.320798i
$412$		0			0
$413$	−87.4896	+	1.69237i	−0.211839	+	0.00409775i
$414$		0			0
$415$	−61.4264	+	106.394i	−0.148016	+	0.256370i
$416$		0			0
$417$	103.332	+	178.977i	0.247799	+	0.429200i
$418$		0			0
$419$			54.3155i			0.129631i	0.997897	+	0.0648156i	$0.0206459\pi$
$419$			54.3155i			0.129631i	−0.997897	+	0.0648156i	$0.979354\pi$
$420$		0			0
$421$	−578.890			−1.37504			−0.687518	−	0.726168i	$-0.741300\pi$
$421$	−578.890			−1.37504			−0.687518	+	0.726168i	$0.741300\pi$
$422$		0			0
$423$	−43.0050	+	24.8290i	−0.101667	+	0.0586973i
$424$		0			0
$425$	−87.9858	−	50.7986i	−0.207025	−	0.119526i
$426$		0			0
$427$	351.283	+	582.140i	0.822676	+	1.36333i
$428$		0			0
$429$	−109.811	+	190.198i	−0.255969	+	0.443351i
$430$		0			0
$431$	−266.699	−	461.936i	−0.618791	−	1.07178i	−0.989707	−	0.143111i	$-0.954289\pi$
$431$	−266.699	−	461.936i	−0.618791	−	1.07178i	0.370916	−	0.928667i	$-0.379044\pi$
$432$		0			0
$433$			110.744i			0.255760i	0.991790	+	0.127880i	$0.0408173\pi$
$433$			110.744i			0.255760i	−0.991790	+	0.127880i	$0.959183\pi$
$434$		0			0
$435$	−268.462			−0.617153
$436$		0			0
$437$	1276.81	−	737.166i	2.92176	−	1.68688i
$438$		0			0
$439$	−539.160	−	311.284i	−1.22816	−	0.709076i	−0.261512	−	0.965200i	$-0.584221\pi$
$439$	−539.160	−	311.284i	−1.22816	−	0.709076i	−0.966644	+	0.256124i	$0.917554\pi$
$440$		0			0
$441$	146.890	−	5.68491i	0.333084	−	0.0128910i
$442$		0			0
$443$	−211.173	+	365.762i	−0.476688	+	0.825647i	−0.999643	−	0.0267129i	$-0.991496\pi$
$443$	−211.173	+	365.762i	−0.476688	+	0.825647i	0.522956	+	0.852360i	$0.324829\pi$
$444$		0			0
$445$	308.198	+	533.814i	0.692579	+	1.19958i
$446$		0			0
$447$			93.7075i			0.209636i
$448$		0			0
$449$	−365.850			−0.814810			−0.407405	−	0.913248i	$-0.633566\pi$
$449$	−365.850			−0.814810			−0.407405	+	0.913248i	$0.633566\pi$
$450$		0			0
$451$	83.9995	−	48.4971i	0.186252	−	0.107532i
$452$		0			0
$453$	−197.627	−	114.100i	−0.436262	−	0.251876i
$454$		0			0
$455$	−389.960	+	235.315i	−0.857056	+	0.517176i
$456$		0			0
$457$	16.3276	−	28.2803i	0.0357279	−	0.0618825i	−0.847609	−	0.530622i	$-0.821958\pi$
$457$	16.3276	−	28.2803i	0.0357279	−	0.0618825i	0.883336	+	0.468740i	$0.155292\pi$
$458$		0			0
$459$	−62.5393	−	108.321i	−0.136251	−	0.235994i
$460$		0			0
$461$			770.259i			1.67084i	0.549609	+	0.835422i	$0.314777\pi$
$461$			770.259i			1.67084i	−0.549609	+	0.835422i	$0.685223\pi$
$462$		0			0
$463$	308.030			0.665292			0.332646	−	0.943052i	$-0.392059\pi$
$463$	308.030			0.665292			0.332646	+	0.943052i	$0.392059\pi$
$464$		0			0
$465$	42.1544	−	24.3378i	0.0906546	−	0.0523394i
$466$		0			0
$467$	81.0507	+	46.7947i	0.173556	+	0.100203i	0.584262	−	0.811565i	$-0.301384\pi$
$467$	81.0507	+	46.7947i	0.173556	+	0.100203i	−0.410705	+	0.911768i	$0.634718\pi$
$468$		0			0
$469$	0.135131	+	6.98579i	0.000288125	+	0.0148951i
$470$		0			0
$471$	208.180	−	360.578i	0.441995	−	0.765558i
$472$		0			0
$473$	−285.987	−	495.344i	−0.604624	−	1.04724i
$474$		0			0
$475$		−	150.632i		−	0.317119i
$476$		0			0
$477$	−57.4993			−0.120544
$478$		0			0
$479$	66.5254	−	38.4084i	0.138884	−	0.0801846i	−0.428948	−	0.903329i	$-0.641116\pi$
$479$	66.5254	−	38.4084i	0.138884	−	0.0801846i	0.567832	+	0.823145i	$0.307782\pi$
$480$		0			0
$481$	−39.8057	−	22.9818i	−0.0827561	−	0.0477792i
$482$		0			0
$483$	241.995	−	438.522i	0.501026	−	0.907912i
$484$		0			0
$485$	−414.430	+	717.813i	−0.854494	+	1.48003i
$486$		0			0
$487$	304.987	+	528.253i	0.626256	+	1.08471i	0.988296	+	0.152545i	$0.0487470\pi$
$487$	304.987	+	528.253i	0.626256	+	1.08471i	−0.362040	+	0.932162i	$0.617920\pi$
$488$		0			0
$489$		−	466.216i		−	0.953407i
$490$		0			0
$491$	−132.287			−0.269424			−0.134712	−	0.990885i	$-0.543011\pi$
$491$	−132.287			−0.269424			−0.134712	+	0.990885i	$0.543011\pi$
$492$		0			0
$493$	597.734	−	345.102i	1.21244	−	0.700004i
$494$		0			0
$495$	−147.947	−	85.4171i	−0.298882	−	0.172560i
$496$		0			0
$497$	90.9508	+	50.1906i	0.183000	+	0.100987i
$498$		0			0
$499$	−196.807	+	340.880i	−0.394403	+	0.683126i	−0.993025	−	0.117906i	$-0.962382\pi$
$499$	−196.807	+	340.880i	−0.394403	+	0.683126i	0.598622	+	0.801032i	$0.295715\pi$
$500$		0			0
$501$	−106.621	−	184.673i	−0.212817	−	0.368609i
$502$		0			0
$503$		−	79.0334i		−	0.157124i	−0.996909	−	0.0785620i	$-0.974967\pi$
$503$		−	79.0334i		−	0.157124i	0.996909	−	0.0785620i	$-0.0250329\pi$
$504$		0			0
$505$	95.3618			0.188835
$506$		0			0
$507$	−36.1788	+	20.8878i	−0.0713586	+	0.0411989i
$508$		0			0
$509$	−278.660	−	160.884i	−0.547465	−	0.316079i	0.200634	−	0.979666i	$-0.435700\pi$
$509$	−278.660	−	160.884i	−0.547465	−	0.316079i	−0.748099	+	0.663587i	$0.769033\pi$
$510$		0			0
$511$	−412.949	+	7.98794i	−0.808119	+	0.0156320i
$512$		0			0
$513$	92.7230	−	160.601i	0.180747	−	0.313062i
$514$		0			0
$515$	−373.608	−	647.108i	−0.725453	−	1.25652i
$516$		0			0
$517$		−	174.372i		−	0.337276i
$518$		0			0
$519$	−390.802			−0.752990
$520$		0			0
$521$	−433.474	+	250.266i	−0.832004	+	0.480358i	−0.854538	−	0.519388i	$-0.826160\pi$
$521$	−433.474	+	250.266i	−0.832004	+	0.480358i	0.0225341	+	0.999746i	$0.492827\pi$
$522$		0			0
$523$	115.191	+	66.5054i	0.220250	+	0.127161i	0.606066	−	0.795414i	$-0.292747\pi$
$523$	115.191	+	66.5054i	0.220250	+	0.127161i	−0.385816	+	0.922576i	$0.626080\pi$
$524$		0			0
$525$	−26.4387	−	43.8138i	−0.0503595	−	0.0834549i
$526$		0			0
$527$	−62.5716	+	108.377i	−0.118732	+	0.205649i
$528$		0			0
$529$	−588.775	−	1019.79i	−1.11300	−	1.92777i
$530$		0			0
$531$			37.5026i			0.0706263i
$532$		0			0
$533$	−110.826			−0.207929
$534$		0			0
$535$	384.571	−	222.032i	0.718823	−	0.415013i
$536$		0			0
$537$	400.873	+	231.444i	0.746505	+	0.430995i
$538$		0			0
$539$	−240.611	+	456.675i	−0.446403	+	0.847264i
$540$		0			0
$541$	−449.836	+	779.140i	−0.831491	+	1.44018i	0.0653652	+	0.997861i	$0.479179\pi$
$541$	−449.836	+	779.140i	−0.831491	+	1.44018i	−0.896856	+	0.442323i	$0.854155\pi$
$542$		0			0
$543$	−55.8968	−	96.8161i	−0.102941	−	0.178299i
$544$		0			0
$545$			488.548i			0.896418i
$546$		0			0
$547$	59.3373			0.108478			0.0542388	−	0.998528i	$-0.482727\pi$
$547$	59.3373			0.108478			0.0542388	+	0.998528i	$0.482727\pi$
$548$		0			0
$549$	252.354	−	145.697i	0.459661	−	0.265385i
$550$		0			0
$551$	886.223	+	511.661i	1.60839	+	0.928604i
$552$		0			0
$553$	−608.395	+	367.126i	−1.10017	+	0.663880i
$554$		0			0
$555$	17.8766	−	30.9632i	0.0322101	−	0.0557895i
$556$		0			0
$557$	−348.483	−	603.590i	−0.625643	−	1.08364i	−0.988416	−	0.151767i	$-0.951504\pi$
$557$	−348.483	−	603.590i	−0.625643	−	1.08364i	0.362774	−	0.931877i	$-0.381830\pi$
$558$		0			0
$559$			653.541i			1.16913i
$560$		0			0
$561$	439.208			0.782902
$562$		0			0
$563$	−74.3002	+	42.8972i	−0.131972	+	0.0761940i	−0.564532	−	0.825411i	$-0.690944\pi$
$563$	−74.3002	+	42.8972i	−0.131972	+	0.0761940i	0.432561	+	0.901605i	$0.357610\pi$
$564$		0			0
$565$	−969.020	−	559.464i	−1.71508	−	0.990201i
$566$		0			0
$567$	−1.21842	−	62.9882i	−0.00214889	−	0.111090i
$568$		0			0
$569$	260.352	−	450.943i	0.457561	−	0.792518i	−0.541271	−	0.840848i	$-0.682057\pi$
$569$	260.352	−	450.943i	0.457561	−	0.792518i	0.998831	+	0.0483301i	$0.0153899\pi$
$570$		0			0
$571$	−90.3719	−	156.529i	−0.158270	−	0.274131i	0.775975	−	0.630763i	$-0.217258\pi$
$571$	−90.3719	−	156.529i	−0.158270	−	0.274131i	−0.934245	+	0.356632i	$0.883925\pi$
$572$		0			0
$573$			257.629i			0.449614i
$574$		0			0
$575$	−174.357			−0.303230
$576$		0			0
$577$	−448.898	+	259.171i	−0.777986	+	0.449170i	−0.835716	−	0.549162i	$-0.814947\pi$
$577$	−448.898	+	259.171i	−0.777986	+	0.449170i	0.0577301	+	0.998332i	$0.481614\pi$
$578$		0			0
$579$	44.7946	+	25.8622i	0.0773655	+	0.0446670i
$580$		0			0
$581$	76.8647	−	139.287i	0.132297	−	0.239737i
$582$		0			0
$583$	100.953	−	174.856i	0.173162	−	0.299925i
$584$		0			0
$585$	97.5982	+	169.045i	0.166834	+	0.288966i
$586$		0			0
$587$			1072.05i			1.82632i	0.407602	+	0.913160i	$0.366365\pi$
$587$			1072.05i			1.82632i	−0.407602	+	0.913160i	$0.633635\pi$
$588$		0			0
$589$	−185.542			−0.315012
$590$		0			0
$591$	−287.858	+	166.195i	−0.487069	+	0.281209i
$592$		0			0
$593$	230.489	+	133.073i	0.388682	+	0.224406i	0.681589	−	0.731735i	$-0.261289\pi$
$593$	230.489	+	133.073i	0.388682	+	0.224406i	−0.292907	+	0.956141i	$0.594623\pi$
$594$		0			0
$595$	797.475	+	440.081i	1.34029	+	0.739633i
$596$		0			0
$597$	18.5965	−	32.2100i	0.0311498	−	0.0539531i
$598$		0			0
$599$	−453.423	−	785.351i	−0.756966	−	1.31110i	−0.944391	−	0.328825i	$-0.893347\pi$
$599$	−453.423	−	785.351i	−0.756966	−	1.31110i	0.187425	−	0.982279i	$-0.439986\pi$
$600$		0			0
$601$		−	472.642i		−	0.786426i	−0.919448	−	0.393213i	$-0.871364\pi$
$601$		−	472.642i		−	0.786426i	0.919448	−	0.393213i	$-0.128636\pi$
$602$		0			0
$603$	2.99447			0.00496595
$604$		0			0
$605$	−46.9405	+	27.1011i	−0.0775876	+	0.0447952i
$606$		0			0
$607$	19.5830	+	11.3063i	0.0322620	+	0.0186264i	0.516044	−	0.856562i	$-0.327404\pi$
$607$	19.5830	+	11.3063i	0.0322620	+	0.0186264i	−0.483782	+	0.875188i	$0.660737\pi$
$608$		0			0
$609$	347.579	−	6.72346i	0.570738	−	0.0110402i
$610$		0			0
$611$	−99.6191	+	172.545i	−0.163043	+	0.282398i
$612$		0			0
$613$	2.39151	+	4.14221i	0.00390132	+	0.00675728i	0.867969	−	0.496618i	$-0.165425\pi$
$613$	2.39151	+	4.14221i	0.00390132	+	0.00675728i	−0.864068	+	0.503375i	$0.832092\pi$
$614$		0			0
$615$		−	86.2071i		−	0.140174i
$616$		0			0
$617$	−537.983			−0.871934			−0.435967	−	0.899963i	$-0.643594\pi$
$617$	−537.983			−0.871934			−0.435967	+	0.899963i	$0.643594\pi$
$618$		0			0
$619$	363.363	−	209.788i	0.587016	−	0.338914i	−0.176901	−	0.984229i	$-0.556607\pi$
$619$	363.363	−	209.788i	0.587016	−	0.338914i	0.763917	+	0.645315i	$0.223274\pi$
$620$		0			0
$621$	−185.897	−	107.328i	−0.299351	−	0.172830i
$622$		0			0
$623$	−412.395	−	683.415i	−0.661951	−	1.09697i
$624$		0			0
$625$	356.351	−	617.219i	0.570162	−	0.987550i
$626$		0			0
$627$	325.593	+	563.943i	0.519287	+	0.899431i
$628$		0			0
$629$			91.9200i			0.146137i
$630$		0			0
$631$	−346.433			−0.549022			−0.274511	−	0.961584i	$-0.588516\pi$
$631$	−346.433			−0.549022			−0.274511	+	0.961584i	$0.588516\pi$
$632$		0			0
$633$	−269.348	+	155.508i	−0.425510	+	0.245668i
$634$		0			0
$635$	−726.361	−	419.365i	−1.14388	−	0.660417i
$636$		0			0
$637$	498.991	−	314.430i	0.783346	−	0.493611i
$638$		0			0
$639$	22.2601	−	38.5556i	0.0348358	−	0.0603374i
$640$		0			0
$641$	−413.473	−	716.157i	−0.645044	−	1.11725i	−0.984291	−	0.176552i	$-0.943506\pi$
$641$	−413.473	−	716.157i	−0.645044	−	1.11725i	0.339247	−	0.940697i	$-0.389828\pi$
$642$		0			0
$643$			1041.58i			1.61988i	0.586514	+	0.809939i	$0.300500\pi$
$643$			1041.58i			1.61988i	−0.586514	+	0.809939i	$0.699500\pi$
$644$		0			0
$645$	−508.362			−0.788159
$646$		0			0
$647$	−464.511	+	268.186i	−0.717946	+	0.414507i	−0.813996	−	0.580870i	$-0.802712\pi$
$647$	−464.511	+	268.186i	−0.717946	+	0.414507i	0.0960500	+	0.995377i	$0.469379\pi$
$648$		0			0
$649$	−114.046	−	65.8443i	−0.175725	−	0.101455i
$650$		0			0
$651$	−53.9681	+	32.5661i	−0.0829003	+	0.0500248i
$652$		0			0
$653$	−398.410	+	690.067i	−0.610123	+	1.05676i	0.381096	+	0.924535i	$0.375547\pi$
$653$	−398.410	+	690.067i	−0.610123	+	1.05676i	−0.991219	+	0.132229i	$0.957787\pi$
$654$		0			0
$655$	193.608	+	335.339i	0.295585	+	0.511968i
$656$		0			0
$657$			177.011i			0.269423i
$658$		0			0
$659$	−668.820			−1.01490			−0.507451	−	0.861681i	$-0.669412\pi$
$659$	−668.820			−1.01490			−0.507451	+	0.861681i	$0.669412\pi$
$660$		0			0
$661$	227.421	−	131.302i	0.344056	−	0.198641i	−0.318008	−	0.948088i	$-0.603014\pi$
$661$	227.421	−	131.302i	0.344056	−	0.198641i	0.662064	+	0.749447i	$0.269681\pi$
$662$		0			0
$663$	−434.608	−	250.921i	−0.655518	−	0.378463i
$664$		0			0
$665$	26.1178	+	1350.20i	0.0392749	+	2.03037i
$666$		0			0
$667$	592.251	−	1025.81i	0.887933	−	1.53795i
$668$		0			0
$669$	256.351	+	444.013i	0.383186	+	0.663697i
$670$		0			0
$671$			1023.21i			1.52491i
$672$		0			0
$673$	−234.458			−0.348378			−0.174189	−	0.984712i	$-0.555730\pi$
$673$	−234.458			−0.348378			−0.174189	+	0.984712i	$0.555730\pi$
$674$		0			0
$675$	−18.9930	+	10.9656i	−0.0281377	+	0.0162453i
$676$		0			0
$677$	453.701	+	261.944i	0.670164	+	0.386919i	0.796139	−	0.605114i	$-0.206873\pi$
$677$	453.701	+	261.944i	0.670164	+	0.386919i	−0.125975	+	0.992033i	$0.540206\pi$
$678$		0			0
$679$	518.588	−	939.738i	0.763753	−	1.38400i
$680$		0			0
$681$	152.738	−	264.550i	0.224285	−	0.388473i
$682$		0			0
$683$	112.693	+	195.190i	0.164997	+	0.285783i	0.936654	−	0.350256i	$-0.113905\pi$
$683$	112.693	+	195.190i	0.164997	+	0.285783i	−0.771657	+	0.636038i	$0.780572\pi$
$684$		0			0
$685$			822.978i			1.20143i
$686$		0			0
$687$	83.7724			0.121939
$688$		0			0
$689$	−199.792	+	115.350i	−0.289973	+	0.167416i
$690$		0			0
$691$	−484.078	−	279.483i	−0.700547	−	0.404461i	0.107004	−	0.994259i	$-0.465874\pi$
$691$	−484.078	−	279.483i	−0.700547	−	0.404461i	−0.807551	+	0.589798i	$0.799208\pi$
$692$		0			0
$693$	193.687	+	106.885i	0.279491	+	0.154235i
$694$		0			0
$695$	−322.493	+	558.574i	−0.464018	+	0.803703i
$696$		0			0
$697$	110.818	+	191.942i	0.158992	+	0.275383i
$698$		0			0
$699$		−	794.022i		−	1.13594i
$700$		0			0
$701$	−270.005			−0.385171			−0.192585	−	0.981280i	$-0.561687\pi$
$701$	−270.005			−0.385171			−0.192585	+	0.981280i	$0.561687\pi$
$702$		0			0
$703$	−118.025	+	68.1420i	−0.167888	+	0.0969303i
$704$		0			0
$705$	−134.216	−	77.4895i	−0.190377	−	0.109914i
$706$		0			0
$707$	−123.466	+	2.38828i	−0.174633	+	0.00337805i
$708$		0			0
$709$	626.647	−	1085.38i	0.883846	−	1.53087i	0.0368152	−	0.999322i	$-0.488279\pi$
$709$	626.647	−	1085.38i	0.883846	−	1.53087i	0.847031	−	0.531544i	$-0.178388\pi$
$710$		0			0
$711$	152.267	+	263.735i	0.214159	+	0.370935i
$712$		0			0
$713$			214.766i			0.301215i
$714$		0			0
$715$	−685.424			−0.958634
$716$		0			0
$717$	186.628	−	107.750i	0.260291	−	0.150279i
$718$		0			0
$719$	−513.681	−	296.574i	−0.714438	−	0.412481i	0.0982644	−	0.995160i	$-0.468671\pi$
$719$	−513.681	−	296.574i	−0.714438	−	0.412481i	−0.812702	+	0.582680i	$0.802004\pi$
$720$		0			0
$721$	499.920	+	828.460i	0.693370	+	1.14904i
$722$		0			0
$723$	190.318	−	329.641i	0.263234	−	0.455935i
$724$		0			0
$725$	−60.5100	−	104.806i	−0.0834620	−	0.144561i
$726$		0			0
$727$		−	752.400i		−	1.03494i	−0.855702	−	0.517469i	$-0.826874\pi$
$727$		−	752.400i		−	1.03494i	0.855702	−	0.517469i	$-0.173126\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	1131.88	−	653.490i	1.54840	−	0.893967i
$732$		0			0
$733$	−636.602	−	367.542i	−0.868488	−	0.501422i	−0.00164274	−	0.999999i	$-0.500523\pi$
$733$	−636.602	−	367.542i	−0.868488	−	0.501422i	−0.866846	+	0.498577i	$0.833856\pi$
$734$		0			0
$735$	244.582	+	388.144i	0.332765	+	0.528087i
$736$		0			0
$737$	−5.25747	+	9.10621i	−0.00713362	+	0.0123558i
$738$		0			0
$739$	−34.3763	−	59.5415i	−0.0465173	−	0.0805703i	0.841829	−	0.539744i	$-0.181479\pi$
$739$	−34.3763	−	59.5415i	−0.0465173	−	0.0805703i	−0.888347	+	0.459174i	$0.848146\pi$
$740$		0			0
$741$		−	744.049i		−	1.00412i
$742$		0			0
$743$	−1023.37			−1.37735			−0.688674	−	0.725071i	$-0.741807\pi$
$743$	−1023.37			−1.37735			−0.688674	+	0.725071i	$0.741807\pi$
$744$		0			0
$745$	−253.273	+	146.227i	−0.339964	+	0.196278i
$746$		0			0
$747$	−59.0462	−	34.0904i	−0.0790445	−	0.0456364i
$748$		0			0
$749$	−492.346	+	297.098i	−0.657338	+	0.396659i
$750$		0			0
$751$	−36.8175	+	63.7697i	−0.0490246	+	0.0849131i	−0.889496	−	0.456942i	$-0.848945\pi$
$751$	−36.8175	+	63.7697i	−0.0490246	+	0.0849131i	0.840472	+	0.541855i	$0.182278\pi$
$752$		0			0
$753$	60.2392	+	104.337i	0.0799989	+	0.138562i
$754$		0			0
$755$		−	712.196i		−	0.943307i
$756$		0			0
$757$	14.6651			0.0193727			0.00968634	−	0.999953i	$-0.496917\pi$
$757$	14.6651			0.0193727			0.00968634	+	0.999953i	$0.496917\pi$
$758$		0			0
$759$	652.769	−	376.876i	0.860038	−	0.496543i
$760$		0			0
$761$	692.428	+	399.774i	0.909893	+	0.525327i	0.880397	−	0.474238i	$-0.157276\pi$
$761$	692.428	+	399.774i	0.909893	+	0.525327i	0.0294962	+	0.999565i	$0.490610\pi$
$762$		0			0
$763$	−12.2354	−	632.527i	−0.0160359	−	0.829000i
$764$		0			0
$765$	195.181	−	338.063i	0.255139	−	0.441913i
$766$		0			0
$767$	75.2342	+	130.309i	0.0980889	+	0.169895i
$768$		0			0
$769$			665.988i			0.866044i	0.901383	+	0.433022i	$0.142553\pi$
$769$			665.988i			0.866044i	−0.901383	+	0.433022i	$0.857447\pi$
$770$		0			0
$771$	176.318			0.228687
$772$		0			0
$773$	−47.3482	+	27.3365i	−0.0612525	+	0.0353642i	−0.530314	−	0.847802i	$-0.677926\pi$
$773$	−47.3482	+	27.3365i	−0.0612525	+	0.0353642i	0.469061	+	0.883166i	$0.344592\pi$
$774$		0			0
$775$	19.0028	+	10.9713i	0.0245197	+	0.0141565i
$776$		0			0
$777$	−22.3695	+	40.5360i	−0.0287896	+	0.0521698i
$778$		0			0
$779$	−164.302	+	284.580i	−0.210914	+	0.365314i
$780$		0			0
$781$	78.1653	+	135.386i	0.100084	+	0.173350i
$782$		0			0
$783$		−	148.990i		−	0.190281i
$784$		0			0
$785$	1299.43			1.65532
$786$		0			0
$787$	−380.225	+	219.523i	−0.483132	+	0.278936i	−0.721721	−	0.692184i	$-0.756648\pi$
$787$	−380.225	+	219.523i	−0.483132	+	0.278936i	0.238589	+	0.971121i	$0.423315\pi$
$788$		0			0
$789$	317.362	+	183.229i	0.402233	+	0.232229i
$790$		0			0
$791$	1268.61	+	700.074i	1.60380	+	0.885049i
$792$		0			0
$793$	584.566	−	1012.50i	0.737157	−	1.27679i
$794$		0			0
$795$	−89.7258	−	155.410i	−0.112863	−	0.195484i
$796$		0			0
$797$			479.187i			0.601239i	0.953744	+	0.300619i	$0.0971934\pi$
$797$			479.187i			0.601239i	−0.953744	+	0.300619i	$0.902807\pi$
$798$		0			0
$799$	398.445			0.498680
$800$		0			0
$801$	−296.255	+	171.043i	−0.369857	+	0.213537i
$802$		0			0
$803$	−538.293	−	310.783i	−0.670352	−	0.387028i
$804$		0			0
$805$	1562.86	−	30.2315i	1.94145	−	0.0375547i
$806$		0			0
$807$	−270.057	+	467.753i	−0.334644	+	0.579620i
$808$		0			0
$809$	−370.116	−	641.060i	−0.457498	−	0.792410i	0.541330	−	0.840810i	$-0.317921\pi$
$809$	−370.116	−	641.060i	−0.457498	−	0.792410i	−0.998828	+	0.0484003i	$0.984588\pi$
$810$		0			0
$811$		−	157.469i		−	0.194166i	−0.995276	−	0.0970831i	$-0.969049\pi$
$811$		−	157.469i		−	0.194166i	0.995276	−	0.0970831i	$-0.0309513\pi$
$812$		0			0
$813$	444.399			0.546616
$814$		0			0
$815$	1260.09	−	727.514i	1.54612	−	0.892655i
$816$		0			0
$817$	1678.16	+	968.888i	2.05405	+	1.18591i
$818$		0			0
$819$	−130.595	−	216.420i	−0.159456	−	0.264249i
$820$		0			0
$821$	416.699	−	721.744i	0.507551	−	0.879104i	−0.492411	−	0.870363i	$-0.663884\pi$
$821$	416.699	−	721.744i	0.507551	−	0.879104i	0.999962	−	0.00874120i	$-0.00278245\pi$
$822$		0			0
$823$	290.180	+	502.607i	0.352588	+	0.610701i	0.986702	−	0.162539i	$-0.0519684\pi$
$823$	290.180	+	502.607i	0.352588	+	0.610701i	−0.634114	+	0.773240i	$0.718635\pi$
$824$		0			0
$825$		−	77.0105i		−	0.0933460i
$826$		0			0
$827$	−310.093			−0.374962			−0.187481	−	0.982268i	$-0.560032\pi$
$827$	−310.093			−0.374962			−0.187481	+	0.982268i	$0.560032\pi$
$828$		0			0
$829$	−510.938	+	294.990i	−0.616330	+	0.355838i	−0.775439	−	0.631423i	$-0.782471\pi$
$829$	−510.938	+	294.990i	−0.616330	+	0.355838i	0.159109	+	0.987261i	$0.449138\pi$
$830$		0			0
$831$	−418.640	−	241.702i	−0.503778	−	0.290857i
$832$		0			0
$833$	−1043.52	−	549.804i	−1.25272	−	0.660029i
$834$		0			0
$835$	332.758	−	576.353i	0.398512	−	0.690243i
$836$		0			0
$837$	13.5070	+	23.3948i	0.0161374	+	0.0279507i
$838$		0			0
$839$			1658.50i			1.97676i	0.152018	+	0.988378i	$0.451423\pi$
$839$			1658.50i			1.97676i	−0.152018	+	0.988378i	$0.548577\pi$
$840$		0			0
$841$	−18.8466			−0.0224098
$842$		0			0
$843$	126.251	−	72.8908i	0.149763	−	0.0864660i
$844$		0			0
$845$	−112.912	−	65.1895i	−0.133623	−	0.0771474i
$846$		0			0
$847$	60.0955	−	36.2636i	0.0709510	−	0.0428142i
$848$		0			0
$849$	403.071	−	698.140i	0.474760	−	0.822309i
$850$		0			0
$851$	78.8749	+	136.615i	0.0926849	+	0.160535i
$852$		0			0
$853$		−	921.244i		−	1.08001i	−0.841663	−	0.540003i	$-0.818423\pi$
$853$		−	921.244i		−	1.08001i	0.841663	−	0.540003i	$-0.181577\pi$
$854$		0			0
$855$	578.765			0.676918
$856$		0			0
$857$	−1107.38	+	639.346i	−1.29216	+	0.746028i	−0.979037	−	0.203685i	$-0.934708\pi$
$857$	−1107.38	+	639.346i	−1.29216	+	0.746028i	−0.313122	+	0.949713i	$0.601375\pi$
$858$		0			0
$859$	800.548	+	462.197i	0.931953	+	0.538064i	0.887429	−	0.460945i	$-0.152489\pi$
$859$	800.548	+	462.197i	0.931953	+	0.538064i	0.0445245	+	0.999008i	$0.485823\pi$
$860$		0			0
$861$	2.15901	+	111.613i	0.00250756	+	0.129632i
$862$		0			0
$863$	611.344	−	1058.88i	0.708394	−	1.22697i	−0.257059	−	0.966396i	$-0.582753\pi$
$863$	611.344	−	1058.88i	0.708394	−	1.22697i	0.965453	−	0.260579i	$-0.0839134\pi$
$864$		0			0
$865$	−609.833	−	1056.26i	−0.705009	−	1.22111i
$866$		0			0
$867$			503.043i			0.580211i
$868$		0			0
$869$	−1069.36			−1.23056
$870$		0			0
$871$	10.4048	−	6.00723i	0.0119458	−	0.00689693i
$872$		0			0
$873$	−398.371	−	230.000i	−0.456324	−	0.263459i
$874$		0			0
$875$	−379.895	+	688.411i	−0.434166	+	0.786755i
$876$		0			0
$877$	−565.185	+	978.929i	−0.644453	+	1.11622i	0.339975	+	0.940434i	$0.389581\pi$
$877$	−565.185	+	978.929i	−0.644453	+	1.11622i	−0.984428	+	0.175790i	$0.943752\pi$
$878$		0			0
$879$	250.761	+	434.330i	0.285280	+	0.494119i
$880$		0			0
$881$		−	37.1187i		−	0.0421325i	−0.999778	−	0.0210663i	$-0.993294\pi$
$881$		−	37.1187i		−	0.0421325i	0.999778	−	0.0210663i	$-0.00670609\pi$
$882$		0			0
$883$	−1517.07			−1.71809			−0.859045	−	0.511901i	$-0.828942\pi$
$883$	−1517.07			−1.71809			−0.859045	+	0.511901i	$0.828942\pi$
$884$		0			0
$885$	−101.362	+	58.5215i	−0.114534	+	0.0661260i
$886$		0			0
$887$	1153.86	+	666.179i	1.30085	+	0.751047i	0.980550	−	0.196268i	$-0.0628823\pi$
$887$	1153.86	+	666.179i	1.30085	+	0.751047i	0.320302	+	0.947316i	$0.396216\pi$
$888$		0			0
$889$	950.928	+	524.764i	1.06966	+	0.590285i
$890$		0			0
$891$	47.4047	−	82.1073i	0.0532039	−	0.0921518i
$892$		0			0
$893$	295.374	+	511.604i	0.330766	+	0.572904i
$894$		0			0
$895$			1444.64i			1.61413i
$896$		0			0
$897$	−861.243			−0.960137
$898$		0			0
$899$	−129.096	+	74.5337i	−0.143600	+	0.0829074i
$900$		0			0
$901$	399.552	+	230.681i	0.443454	+	0.256028i
$902$		0			0
$903$	658.181	−	12.7316i	0.728882	−	0.0140993i
$904$		0			0
$905$	174.450	−	302.157i	0.192763	−	0.333875i
$906$		0			0
$907$	32.7414	+	56.7098i	0.0360986	+	0.0625246i	0.883510	−	0.468412i	$-0.155174\pi$
$907$	32.7414	+	56.7098i	0.0360986	+	0.0625246i	−0.847412	+	0.530936i	$0.821840\pi$
$908$		0			0
$909$			52.9238i			0.0582220i
$910$		0			0
$911$	242.277			0.265946			0.132973	−	0.991120i	$-0.457548\pi$
$911$	242.277			0.265946			0.132973	+	0.991120i	$0.457548\pi$
$912$		0			0
$913$	207.338	−	119.707i	0.227096	−	0.131114i
$914$		0			0
$915$	787.579	+	454.709i	0.860742	+	0.496950i
$916$		0			0
$917$	−259.064	−	429.317i	−0.282513	−	0.468176i
$918$		0			0
$919$	−401.585	+	695.566i	−0.436981	+	0.756873i	−0.997455	−	0.0712988i	$-0.977286\pi$
$919$	−401.585	+	695.566i	−0.436981	+	0.756873i	0.560474	+	0.828172i	$0.310619\pi$
$920$		0			0
$921$	−293.990	−	509.206i	−0.319208	−	0.552884i
$922$		0			0
$923$		−	178.624i		−	0.193526i
$924$		0			0
$925$	16.1172			0.0174240
$926$		0			0
$927$	359.131	−	207.345i	0.387412	−	0.223673i
$928$		0			0
$929$	−544.851	−	314.570i	−0.586492	−	0.338611i	0.177217	−	0.984172i	$-0.443291\pi$
$929$	−544.851	−	314.570i	−0.586492	−	0.338611i	−0.763709	+	0.645560i	$0.776624\pi$
$930$		0			0
$931$	−67.6298	−	1747.46i	−0.0726421	−	1.87697i
$932$		0			0
$933$	85.5013	−	148.093i	0.0916413	−	0.158727i
$934$		0			0
$935$	685.370	+	1187.09i	0.733016	+	1.26962i
$936$		0			0
$937$			217.501i			0.232124i	0.993242	+	0.116062i	$0.0370272\pi$
$937$			217.501i			0.232124i	−0.993242	+	0.116062i	$0.962973\pi$
$938$		0			0
$939$	−371.734			−0.395883
$940$		0			0
$941$	1549.14	−	894.399i	1.64628	−	0.950477i	0.667741	−	0.744394i	$-0.267262\pi$
$941$	1549.14	−	894.399i	1.64628	−	0.950477i	0.978534	−	0.206083i	$-0.0660718\pi$
$942$		0			0
$943$	329.403	+	190.181i	0.349314	+	0.201677i
$944$		0			0
$945$	168.344	−	101.584i	0.178141	−	0.107496i
$946$		0			0
$947$	542.609	−	939.826i	0.572976	−	0.992424i	−0.423282	−	0.905998i	$-0.639122\pi$
$947$	542.609	−	939.826i	0.572976	−	0.992424i	0.996258	−	0.0864261i	$-0.0275446\pi$
$948$		0			0
$949$	355.103	+	615.057i	0.374187	+	0.648111i
$950$		0			0
$951$		−	335.336i		−	0.352615i
$952$		0			0
$953$	1638.91			1.71973			0.859867	−	0.510518i	$-0.170546\pi$
$953$	1638.91			1.71973			0.859867	+	0.510518i	$0.170546\pi$
$954$		0			0
$955$	−696.321	+	402.021i	−0.729132	+	0.420964i
$956$		0			0
$957$	453.081	+	261.587i	0.473439	+	0.273340i
$958$		0			0
$959$	−20.6110	−	1065.52i	−0.0214922	−	1.11107i
$960$		0			0
$961$	−466.986	+	808.844i	−0.485938	+	0.841669i
$962$		0			0
$963$	123.223	+	213.428i	0.127957	+	0.221629i
$964$		0			0
$965$			161.428i			0.167283i
$966$		0			0
$967$	−486.560			−0.503164			−0.251582	−	0.967836i	$-0.580951\pi$
$967$	−486.560			−0.503164			−0.251582	+	0.967836i	$0.580951\pi$
$968$		0			0
$969$	−1288.63	+	743.991i	−1.32986	+	0.767792i
$970$		0			0
$971$	−302.690	−	174.758i	−0.311730	−	0.179978i	0.335970	−	0.941873i	$-0.390936\pi$
$971$	−302.690	−	174.758i	−0.311730	−	0.179978i	−0.647700	+	0.761895i	$0.724269\pi$
$972$		0			0
$973$	403.545	−	731.266i	0.414743	−	0.751559i
$974$		0			0
$975$	−43.9964	+	76.2039i	−0.0451245	+	0.0781579i
$976$		0			0
$977$	120.146	+	208.099i	0.122974	+	0.212998i	0.920939	−	0.389706i	$-0.127423\pi$
$977$	120.146	+	208.099i	0.122974	+	0.212998i	−0.797965	+	0.602704i	$0.794090\pi$
$978$		0			0
$979$		−	1201.22i		−	1.22699i
$980$		0			0
$981$	−271.134			−0.276385
$982$		0			0
$983$	520.831	−	300.702i	0.529838	−	0.305902i	−0.211113	−	0.977462i	$-0.567709\pi$
$983$	520.831	−	300.702i	0.529838	−	0.305902i	0.740950	+	0.671560i	$0.234375\pi$
$984$		0			0
$985$	−898.384	−	518.682i	−0.912065	−	0.526581i
$986$		0			0
$987$	175.711	+	96.9649i	0.178025	+	0.0982421i
$988$		0			0
$989$	1121.49	−	1942.49i	1.13397	−	1.96409i
$990$		0			0
$991$	225.882	+	391.238i	0.227933	+	0.394791i	0.957195	−	0.289443i	$-0.0934700\pi$
$991$	225.882	+	391.238i	0.227933	+	0.394791i	−0.729262	+	0.684234i	$0.760137\pi$
$992$		0			0
$993$			845.535i			0.851496i
$994$		0			0
$995$	116.077			0.116660
$996$		0			0
$997$	−442.742	+	255.617i	−0.444074	+	0.256386i	−0.705324	−	0.708885i	$-0.749199\pi$
$997$	−442.742	+	255.617i	−0.444074	+	0.256386i	0.261250	+	0.965271i	$0.415865\pi$
$998$		0			0
$999$	17.1839	+	9.92112i	0.0172011	+	0.00993105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bh.g.145.2		8
3.2	odd	2		1008.3.cg.p.145.3		8
4.3	odd	2		168.3.z.b.145.2	yes	8
7.2	even	3		2352.3.f.g.97.3		8
7.3	odd	6	inner	336.3.bh.g.241.2		8
7.5	odd	6		2352.3.f.g.97.6		8
12.11	even	2		504.3.by.c.145.3		8
21.17	even	6		1008.3.cg.p.577.3		8
28.3	even	6		168.3.z.b.73.2	✓	8
28.11	odd	6		1176.3.z.c.913.3		8
28.19	even	6		1176.3.f.c.97.2		8
28.23	odd	6		1176.3.f.c.97.7		8
28.27	even	2		1176.3.z.c.313.3		8
84.23	even	6		3528.3.f.b.2449.3		8
84.47	odd	6		3528.3.f.b.2449.6		8
84.59	odd	6		504.3.by.c.73.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.z.b.73.2	✓	8	28.3	even	6
168.3.z.b.145.2	yes	8	4.3	odd	2
336.3.bh.g.145.2		8	1.1	even	1	trivial
336.3.bh.g.241.2		8	7.3	odd	6	inner
504.3.by.c.73.3		8	84.59	odd	6
504.3.by.c.145.3		8	12.11	even	2
1008.3.cg.p.145.3		8	3.2	odd	2
1008.3.cg.p.577.3		8	21.17	even	6
1176.3.f.c.97.2		8	28.19	even	6
1176.3.f.c.97.7		8	28.23	odd	6
1176.3.z.c.313.3		8	28.27	even	2
1176.3.z.c.913.3		8	28.11	odd	6
2352.3.f.g.97.3		8	7.2	even	3
2352.3.f.g.97.6		8	7.5	odd	6
3528.3.f.b.2449.3		8	84.23	even	6
3528.3.f.b.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)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-4.68140 - 2.70281i) q^{5} +(6.12873 + 3.38210i) q^{7} +(1.50000 - 2.59808i) q^{9} +(5.26719 + 9.12303i) q^{11} -12.0366i q^{13} +9.36280 q^{15} +(-20.8464 + 12.0357i) q^{17} +(-30.9077 - 17.8446i) q^{19} +(-12.1221 + 0.234486i) q^{21} +(-20.6552 + 35.7759i) q^{23} +(2.11033 + 3.65520i) q^{25} +5.19615i q^{27} -28.6732 q^{29} +(4.50233 - 2.59942i) q^{31} +(-15.8016 - 9.12303i) q^{33} +(-19.5499 - 32.3978i) q^{35} +(1.90932 - 3.30704i) q^{37} +(10.4240 + 18.0550i) q^{39} -9.20741i q^{41} -54.2960 q^{43} +(-14.0442 + 8.10842i) q^{45} +(-14.3350 - 8.27632i) q^{47} +(26.1228 + 41.4560i) q^{49} +(20.8464 - 36.1071i) q^{51} +(-9.58322 - 16.5986i) q^{53} -56.9447i q^{55} +61.8154 q^{57} +(-10.8261 + 6.25043i) q^{59} +(84.1179 + 48.5655i) q^{61} +(17.9801 - 10.8498i) q^{63} +(-32.5327 + 56.3483i) q^{65} +(0.499078 + 0.864429i) q^{67} -71.5517i q^{69} +14.8401 q^{71} +(-51.0987 + 29.5018i) q^{73} +(-6.33099 - 3.65520i) q^{75} +(1.42615 + 73.7268i) q^{77} +(-50.7558 + 87.9116i) q^{79} +(-4.50000 - 7.79423i) q^{81} -22.7269i q^{83} +130.121 q^{85} +(43.0098 - 24.8317i) q^{87} +(-98.7518 - 57.0144i) q^{89} +(40.7092 - 73.7694i) q^{91} +(-4.50233 + 7.79826i) q^{93} +(96.4608 + 167.075i) q^{95} -153.333i q^{97} +31.6031 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} - 6 q^{5} - 8 q^{7} + 12 q^{9} + 22 q^{11} + 12 q^{15} + 36 q^{17} - 42 q^{19} + 6 q^{21} - 48 q^{23} + 42 q^{25} + 68 q^{29} + 60 q^{31} - 66 q^{33} + 12 q^{35} - 118 q^{37} + 18 q^{39}+ \cdots + 132 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 - 6 * q^5 - 8 * q^7 + 12 * q^9 + 22 * q^11 + 12 * q^15 + 36 * q^17 - 42 * q^19 + 6 * q^21 - 48 * q^23 + 42 * q^25 + 68 * q^29 + 60 * q^31 - 66 * q^33 + 12 * q^35 - 118 * q^37 + 18 * q^39 + 92 * q^43 - 18 * q^45 + 12 * q^47 - 20 * q^49 - 36 * q^51 + 10 * q^53 + 84 * q^57 + 54 * q^59 + 24 * q^61 + 6 * q^63 - 148 * q^65 - 22 * q^67 + 392 * q^71 - 138 * q^73 - 126 * q^75 - 126 * q^77 - 164 * q^79 - 36 * q^81 + 200 * q^85 - 102 * q^87 - 60 * q^89 - 90 * q^91 - 60 * q^93 + 132 * q^99

Introduction

L-functions

Modular forms

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