LMFDB - Embedded newform 272.3.bh.b.209.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,3,Mod(65,272)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 0, 9])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("272.65"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	272.bh (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.41146319060$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			209.1
Root			$-0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	272.209
Dual form			272.3.bh.b.177.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.88669 + 4.32023i) q^{3} +(-0.711297 + 3.57593i) q^{5} +(0.644047 + 3.23784i) q^{7} +(-6.88730 + 16.6274i) q^{9} +(-2.02046 - 1.35003i) q^{11} +(-7.73173 - 7.73173i) q^{13} +(-17.5022 + 7.24963i) q^{15} +(15.0347 - 7.93458i) q^{17} +(3.50319 + 8.45745i) q^{19} +(-12.1291 + 12.1291i) q^{21} +(1.91942 - 2.87262i) q^{23} +(10.8156 + 4.47998i) q^{25} +(-45.8512 + 9.12037i) q^{27} +(-23.5861 - 4.69157i) q^{29} +(23.0300 - 15.3882i) q^{31} -12.6260i q^{33} -12.0364 q^{35} +(-21.3995 - 32.0267i) q^{37} +(11.0838 - 55.7219i) q^{39} +(15.0157 + 75.4890i) q^{41} +(-20.7301 + 50.0470i) q^{43} +(-54.5596 - 36.4555i) q^{45} +(5.13810 + 5.13810i) q^{47} +(35.2013 - 14.5808i) q^{49} +(77.6797 + 42.0488i) q^{51} +(21.8223 + 52.6837i) q^{53} +(6.26475 - 6.26475i) q^{55} +(-26.4255 + 39.5486i) q^{57} +(21.2985 + 8.82213i) q^{59} +(40.6888 - 8.09351i) q^{61} +(-58.2726 - 11.5911i) q^{63} +(33.1477 - 22.1486i) q^{65} -17.3637i q^{67} +17.9512 q^{69} +(28.6631 + 42.8974i) q^{71} +(12.1277 - 60.9700i) q^{73} +(11.8668 + 59.6583i) q^{75} +(3.06990 - 7.41140i) q^{77} +(-98.5655 - 65.8593i) q^{79} +(-57.2255 - 57.2255i) q^{81} +(86.9369 - 36.0104i) q^{83} +(17.6794 + 59.4070i) q^{85} +(-47.8171 - 115.441i) q^{87} +(19.6021 - 19.6021i) q^{89} +(20.0545 - 30.0137i) q^{91} +(132.961 + 55.0742i) q^{93} +(-32.7351 + 6.51142i) q^{95} +(14.9417 + 2.97209i) q^{97} +(36.3629 - 24.2969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 24 q^{5} + 16 q^{7} + 8 q^{9} - 40 q^{11} - 32 q^{15} - 16 q^{17} + 32 q^{19} - 64 q^{21} + 8 q^{23} + 16 q^{25} - 96 q^{27} + 24 q^{29} - 32 q^{31} - 80 q^{35} - 168 q^{37} + 72 q^{39} - 96 q^{43}+ \cdots - 136 q^{99}+O(q^{100}) $ 8 * q - 24 * q^5 + 16 * q^7 + 8 * q^9 - 40 * q^11 - 32 * q^15 - 16 * q^17 + 32 * q^19 - 64 * q^21 + 8 * q^23 + 16 * q^25 - 96 * q^27 + 24 * q^29 - 32 * q^31 - 80 * q^35 - 168 * q^37 + 72 * q^39 - 96 * q^43 - 88 * q^45 + 80 * q^47 + 8 * q^49 + 176 * q^51 + 96 * q^53 + 8 * q^55 + 248 * q^57 - 8 * q^59 + 264 * q^61 - 8 * q^63 - 32 * q^65 - 208 * q^69 - 32 * q^71 + 24 * q^73 + 192 * q^75 - 216 * q^77 + 96 * q^79 - 224 * q^81 + 88 * q^83 + 512 * q^85 - 312 * q^87 + 288 * q^89 + 24 * q^91 + 280 * q^93 + 152 * q^95 - 344 * q^97 - 136 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{16}\right)$

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
$3$	2.88669	+	4.32023i	0.962229	+	1.44008i	0.896910	+	0.442213i	$0.145807\pi$
$3$	2.88669	+	4.32023i	0.962229	+	1.44008i	0.0653191	+	0.997864i	$0.479193\pi$
$4$		0			0
$5$	−0.711297	+	3.57593i	−0.142259	+	0.715187i	0.842143	+	0.539255i	$0.181294\pi$
$5$	−0.711297	+	3.57593i	−0.142259	+	0.715187i	−0.984402	+	0.175932i	$0.943706\pi$
$6$		0			0
$7$	0.644047	+	3.23784i	0.0920066	+	0.462549i	0.999131	+	0.0416855i	$0.0132727\pi$
$7$	0.644047	+	3.23784i	0.0920066	+	0.462549i	−0.907124	+	0.420863i	$0.861727\pi$
$8$		0			0
$9$	−6.88730	+	16.6274i	−0.765255	+	1.84749i
$10$		0			0
$11$	−2.02046	−	1.35003i	−0.183678	−	0.122730i	0.460332	−	0.887747i	$-0.347730\pi$
$11$	−2.02046	−	1.35003i	−0.183678	−	0.122730i	−0.644010	+	0.765017i	$0.722730\pi$
$12$		0			0
$13$	−7.73173	−	7.73173i	−0.594748	−	0.594748i	0.344162	−	0.938910i	$-0.388163\pi$
$13$	−7.73173	−	7.73173i	−0.594748	−	0.594748i	−0.938910	+	0.344162i	$0.888163\pi$
$14$		0			0
$15$	−17.5022	+	7.24963i	−1.16681	+	0.483309i
$16$		0			0
$17$	15.0347	−	7.93458i	0.884395	−	0.466740i
$17$	15.0347	−	7.93458i	0.884395	−	0.466740i
$18$		0			0
$19$	3.50319	+	8.45745i	0.184379	+	0.445129i	0.988860	−	0.148849i	$-0.0475567\pi$
$19$	3.50319	+	8.45745i	0.184379	+	0.445129i	−0.804481	+	0.593978i	$0.797557\pi$
$20$		0			0
$21$	−12.1291	+	12.1291i	−0.577574	+	0.577574i
$22$		0			0
$23$	1.91942	−	2.87262i	0.0834532	−	0.124897i	−0.787395	−	0.616449i	$-0.788571\pi$
$23$	1.91942	−	2.87262i	0.0834532	−	0.124897i	0.870848	+	0.491553i	$0.163571\pi$
$24$		0			0
$25$	10.8156	+	4.47998i	0.432625	+	0.179199i
$26$		0			0
$27$	−45.8512	+	9.12037i	−1.69819	+	0.337791i
$28$		0			0
$29$	−23.5861	−	4.69157i	−0.813314	−	0.161778i	−0.229126	−	0.973397i	$-0.573587\pi$
$29$	−23.5861	−	4.69157i	−0.813314	−	0.161778i	−0.584188	+	0.811618i	$0.698587\pi$
$30$		0			0
$31$	23.0300	−	15.3882i	0.742903	−	0.496392i	−0.125597	−	0.992081i	$-0.540085\pi$
$31$	23.0300	−	15.3882i	0.742903	−	0.496392i	0.868500	+	0.495689i	$0.165085\pi$
$32$		0			0
$33$		−	12.6260i		−	0.382605i
$34$		0			0
$35$	−12.0364			−0.343897
$36$		0			0
$37$	−21.3995	−	32.0267i	−0.578366	−	0.865586i	0.420769	−	0.907168i	$-0.361760\pi$
$37$	−21.3995	−	32.0267i	−0.578366	−	0.865586i	−0.999135	+	0.0415820i	$0.986760\pi$
$38$		0			0
$39$	11.0838	−	55.7219i	0.284200	−	1.42877i
$40$		0			0
$41$	15.0157	+	75.4890i	0.366237	+	1.84120i	0.521407	+	0.853308i	$0.325407\pi$
$41$	15.0157	+	75.4890i	0.366237	+	1.84120i	−0.155171	+	0.987888i	$0.549593\pi$
$42$		0			0
$43$	−20.7301	+	50.0470i	−0.482096	+	1.16388i	0.476515	+	0.879166i	$0.341900\pi$
$43$	−20.7301	+	50.0470i	−0.482096	+	1.16388i	−0.958612	+	0.284717i	$0.908100\pi$
$44$		0			0
$45$	−54.5596	−	36.4555i	−1.21244	−	0.810123i
$46$		0			0
$47$	5.13810	+	5.13810i	0.109321	+	0.109321i	0.759652	−	0.650330i	$-0.225369\pi$
$47$	5.13810	+	5.13810i	0.109321	+	0.109321i	−0.650330	+	0.759652i	$0.725369\pi$
$48$		0			0
$49$	35.2013	−	14.5808i	0.718394	−	0.297568i
$50$		0			0
$51$	77.6797	+	42.0488i	1.52313	+	0.824486i
$52$		0			0
$53$	21.8223	+	52.6837i	0.411742	+	0.994033i	0.984670	+	0.174427i	$0.0558074\pi$
$53$	21.8223	+	52.6837i	0.411742	+	0.994033i	−0.572928	+	0.819606i	$0.694193\pi$
$54$		0			0
$55$	6.26475	−	6.26475i	0.113905	−	0.113905i
$56$		0			0
$57$	−26.4255	+	39.5486i	−0.463606	+	0.693836i
$58$		0			0
$59$	21.2985	+	8.82213i	0.360992	+	0.149528i	0.555805	−	0.831313i	$-0.312410\pi$
$59$	21.2985	+	8.82213i	0.360992	+	0.149528i	−0.194813	+	0.980840i	$0.562410\pi$
$60$		0			0
$61$	40.6888	−	8.09351i	0.667030	−	0.132680i	0.150050	−	0.988678i	$-0.452056\pi$
$61$	40.6888	−	8.09351i	0.667030	−	0.132680i	0.516979	+	0.855998i	$0.327056\pi$
$62$		0			0
$63$	−58.2726	−	11.5911i	−0.924962	−	0.183986i
$64$		0			0
$65$	33.1477	−	22.1486i	0.509965	−	0.340747i
$66$		0			0
$67$		−	17.3637i		−	0.259160i	−0.991569	−	0.129580i	$-0.958637\pi$
$67$		−	17.3637i		−	0.259160i	0.991569	−	0.129580i	$-0.0413630\pi$
$68$		0			0
$69$	17.9512			0.260162
$70$		0			0
$71$	28.6631	+	42.8974i	0.403706	+	0.604188i	0.976502	−	0.215510i	$-0.0691413\pi$
$71$	28.6631	+	42.8974i	0.403706	+	0.604188i	−0.572796	+	0.819698i	$0.694141\pi$
$72$		0			0
$73$	12.1277	−	60.9700i	0.166133	−	0.835206i	−0.804372	−	0.594126i	$-0.797498\pi$
$73$	12.1277	−	60.9700i	0.166133	−	0.835206i	0.970505	−	0.241080i	$-0.0775018\pi$
$74$		0			0
$75$	11.8668	+	59.6583i	0.158224	+	0.795445i
$76$		0			0
$77$	3.06990	−	7.41140i	0.0398689	−	0.0962520i
$78$		0			0
$79$	−98.5655	−	65.8593i	−1.24766	−	0.833662i	−0.256531	−	0.966536i	$-0.582580\pi$
$79$	−98.5655	−	65.8593i	−1.24766	−	0.833662i	−0.991133	+	0.132874i	$0.957580\pi$
$80$		0			0
$81$	−57.2255	−	57.2255i	−0.706488	−	0.706488i
$82$		0			0
$83$	86.9369	−	36.0104i	1.04743	−	0.433861i	0.208458	−	0.978031i	$-0.433156\pi$
$83$	86.9369	−	36.0104i	1.04743	−	0.433861i	0.838975	+	0.544171i	$0.183156\pi$
$84$		0			0
$85$	17.6794	+	59.4070i	0.207993	+	0.698905i
$86$		0			0
$87$	−47.8171	−	115.441i	−0.549621	−	1.32690i
$88$		0			0
$89$	19.6021	−	19.6021i	0.220248	−	0.220248i	−0.588355	−	0.808603i	$-0.700224\pi$
$89$	19.6021	−	19.6021i	0.220248	−	0.220248i	0.808603	+	0.588355i	$0.200224\pi$
$90$		0			0
$91$	20.0545	−	30.0137i	0.220379	−	0.329821i
$92$		0			0
$93$	132.961	+	55.0742i	1.42969	+	0.592195i
$94$		0			0
$95$	−32.7351	+	6.51142i	−0.344580	+	0.0685412i
$96$		0			0
$97$	14.9417	+	2.97209i	0.154038	+	0.0306401i	0.271507	−	0.962437i	$-0.412478\pi$
$97$	14.9417	+	2.97209i	0.154038	+	0.0306401i	−0.117469	+	0.993077i	$0.537478\pi$
$98$		0			0
$99$	36.3629	−	24.2969i	0.367302	−	0.245424i
$100$		0			0
$101$		−	132.191i		−	1.30882i	−0.756140	−	0.654410i	$-0.772917\pi$
$101$		−	132.191i		−	1.30882i	0.756140	−	0.654410i	$-0.227083\pi$
$102$		0			0
$103$	185.135			1.79743			0.898713	−	0.438536i	$-0.144503\pi$
$103$	185.135			1.79743			0.898713	+	0.438536i	$0.144503\pi$
$104$		0			0
$105$	−34.7454	−	52.0001i	−0.330908	−	0.495239i
$106$		0			0
$107$	7.23785	−	36.3871i	0.0676434	−	0.340066i	−0.932112	−	0.362169i	$-0.882036\pi$
$107$	7.23785	−	36.3871i	0.0676434	−	0.340066i	0.999756	+	0.0221030i	$0.00703617\pi$
$108$		0			0
$109$	−8.89084	−	44.6973i	−0.0815673	−	0.410067i	−0.999898	−	0.0142535i	$-0.995463\pi$
$109$	−8.89084	−	44.6973i	−0.0815673	−	0.410067i	0.918331	−	0.395813i	$-0.129537\pi$
$110$		0			0
$111$	76.5889	−	184.902i	0.689990	−	1.66578i
$112$		0			0
$113$	−72.6645	−	48.5529i	−0.643049	−	0.429671i	0.190827	−	0.981624i	$-0.438883\pi$
$113$	−72.6645	−	48.5529i	−0.643049	−	0.429671i	−0.833876	+	0.551952i	$0.813883\pi$
$114$		0			0
$115$	8.90702	+	8.90702i	0.0774524	+	0.0774524i
$116$		0			0
$117$	181.809	−	75.3079i	1.55393	−	0.643657i
$118$		0			0
$119$	35.3739	+	43.5698i	0.297260	+	0.366132i
$120$		0			0
$121$	−44.0450	−	106.334i	−0.364008	−	0.878794i
$122$		0			0
$123$	−282.785	+	282.785i	−2.29906	+	2.29906i
$124$		0			0
$125$	−74.3533	+	111.278i	−0.594827	+	0.890221i
$126$		0			0
$127$	−102.264	−	42.3590i	−0.805226	−	0.333535i	−0.0581782	−	0.998306i	$-0.518529\pi$
$127$	−102.264	−	42.3590i	−0.805226	−	0.333535i	−0.747047	+	0.664771i	$0.768529\pi$
$128$		0			0
$129$	−276.056	+	54.9109i	−2.13997	+	0.425666i
$130$		0			0
$131$	44.0168	+	8.75549i	0.336006	+	0.0668358i	0.360210	−	0.932871i	$-0.382705\pi$
$131$	44.0168	+	8.75549i	0.336006	+	0.0668358i	−0.0242037	+	0.999707i	$0.507705\pi$
$132$		0			0
$133$	−25.1277	+	16.7898i	−0.188930	+	0.126239i
$134$		0			0
$135$		−	170.448i		−	1.26258i
$136$		0			0
$137$	61.5009			0.448911			0.224456	−	0.974484i	$-0.427940\pi$
$137$	61.5009			0.448911			0.224456	+	0.974484i	$0.427940\pi$
$138$		0			0
$139$	−48.5334	−	72.6354i	−0.349161	−	0.522557i	0.614770	−	0.788706i	$-0.289249\pi$
$139$	−48.5334	−	72.6354i	−0.349161	−	0.522557i	−0.963932	+	0.266149i	$0.914249\pi$
$140$		0			0
$141$	−7.36571	+	37.0299i	−0.0522391	+	0.262623i
$142$		0			0
$143$	5.18359	+	26.0597i	0.0362489	+	0.182235i
$144$		0			0
$145$	33.5535	−	81.0053i	0.231403	−	0.558657i
$146$		0			0
$147$	164.608	+	109.987i	1.11978	+	0.748213i
$148$		0			0
$149$	132.640	+	132.640i	0.890200	+	0.890200i	0.994541	−	0.104342i	$-0.0332736\pi$
$149$	132.640	+	132.640i	0.890200	+	0.890200i	−0.104342	+	0.994541i	$0.533274\pi$
$150$		0			0
$151$	199.707	−	82.7215i	1.32257	−	0.547824i	0.394040	−	0.919093i	$-0.371077\pi$
$151$	199.707	−	82.7215i	1.32257	−	0.547824i	0.928525	+	0.371269i	$0.121077\pi$
$152$		0			0
$153$	28.3829	+	304.636i	0.185509	+	1.99108i
$154$		0			0
$155$	38.6458	+	93.2993i	0.249328	+	0.601931i
$156$		0			0
$157$	−111.042	+	111.042i	−0.707276	+	0.707276i	−0.965961	−	0.258686i	$-0.916711\pi$
$157$	−111.042	+	111.042i	−0.707276	+	0.707276i	0.258686	+	0.965961i	$0.416711\pi$
$158$		0			0
$159$	−164.612	+	246.359i	−1.03529	+	1.54943i
$160$		0			0
$161$	10.5373	+	4.36469i	0.0654490	+	0.0271099i
$162$		0			0
$163$	−163.655	+	32.5530i	−1.00402	+	0.199712i	−0.669607	−	0.742715i	$-0.733538\pi$
$163$	−163.655	+	32.5530i	−1.00402	+	0.199712i	−0.334412	+	0.942427i	$0.608538\pi$
$164$		0			0
$165$	45.1496	+	8.98081i	0.273634	+	0.0544291i
$166$		0			0
$167$	44.7752	−	29.9178i	0.268115	−	0.179149i	−0.414244	−	0.910166i	$-0.635954\pi$
$167$	44.7752	−	29.9178i	0.268115	−	0.179149i	0.682359	+	0.731017i	$0.260954\pi$
$168$		0			0
$169$		−	49.4408i		−	0.292549i
$170$		0			0
$171$	−164.753			−0.963468
$172$		0			0
$173$	37.3651	+	55.9209i	0.215983	+	0.323242i	0.923602	−	0.383352i	$-0.125231\pi$
$173$	37.3651	+	55.9209i	0.215983	+	0.323242i	−0.707619	+	0.706594i	$0.750231\pi$
$174$		0			0
$175$	−7.53969	+	37.9046i	−0.0430840	+	0.216598i
$176$		0			0
$177$	23.3685	+	117.481i	0.132025	+	0.663736i
$178$		0			0
$179$	−96.0193	+	231.811i	−0.536421	+	1.29503i	0.390785	+	0.920482i	$0.372203\pi$
$179$	−96.0193	+	231.811i	−0.536421	+	1.29503i	−0.927206	+	0.374552i	$0.877797\pi$
$180$		0			0
$181$	−14.2421	−	9.51629i	−0.0786859	−	0.0525762i	0.515605	−	0.856826i	$-0.327567\pi$
$181$	−14.2421	−	9.51629i	−0.0786859	−	0.0525762i	−0.594291	+	0.804250i	$0.702567\pi$
$182$		0			0
$183$	152.422	+	152.422i	0.832905	+	0.832905i
$184$		0			0
$185$	129.747	−	53.7428i	0.701333	−	0.290502i
$186$		0			0
$187$	−41.0889	−	4.26578i	−0.219727	−	0.0228117i
$188$		0			0
$189$	−59.0606	−	142.585i	−0.312490	−	0.754417i
$190$		0			0
$191$	−79.7646	+	79.7646i	−0.417615	+	0.417615i	−0.884381	−	0.466766i	$-0.845419\pi$
$191$	−79.7646	+	79.7646i	−0.417615	+	0.417615i	0.466766	+	0.884381i	$0.345419\pi$
$192$		0			0
$193$	−11.3804	+	17.0319i	−0.0589656	+	0.0882482i	−0.859781	−	0.510663i	$-0.829400\pi$
$193$	−11.3804	+	17.0319i	−0.0589656	+	0.0882482i	0.800815	+	0.598911i	$0.204400\pi$
$194$		0			0
$195$	191.374	+	79.2697i	0.981406	+	0.406511i
$196$		0			0
$197$	−40.4361	+	8.04325i	−0.205260	+	0.0408287i	−0.296649	−	0.954987i	$-0.595869\pi$
$197$	−40.4361	+	8.04325i	−0.205260	+	0.0408287i	0.0913895	+	0.995815i	$0.470869\pi$
$198$		0			0
$199$	−359.028	−	71.4150i	−1.80416	−	0.358870i	−0.825507	−	0.564392i	$-0.809110\pi$
$199$	−359.028	−	71.4150i	−1.80416	−	0.358870i	−0.978652	+	0.205523i	$0.934110\pi$
$200$		0			0
$201$	75.0154	−	50.1237i	0.373211	−	0.249372i
$202$		0			0
$203$		−	79.3897i		−	0.391082i
$204$		0			0
$205$	−280.624			−1.36890
$206$		0			0
$207$	34.5446	+	51.6997i	0.166882	+	0.249757i
$208$		0			0
$209$	4.33974	−	21.8173i	0.0207643	−	0.104389i
$210$		0			0
$211$	−62.5770	−	314.596i	−0.296574	−	1.49098i	−0.785615	−	0.618716i	$-0.787653\pi$
$211$	−62.5770	−	314.596i	−0.296574	−	1.49098i	0.489041	−	0.872261i	$-0.337347\pi$
$212$		0			0
$213$	−102.585	+	247.663i	−0.481621	+	1.16274i
$214$		0			0
$215$	−164.219	−	109.728i	−0.763811	−	0.510362i
$216$		0			0
$217$	64.6568	+	64.6568i	0.297958	+	0.297958i
$218$		0			0
$219$	298.414	−	123.607i	1.36262	−	0.564415i
$220$		0			0
$221$	−177.592	−	54.8963i	−0.803585	−	0.248399i
$222$		0			0
$223$	41.5859	+	100.397i	0.186484	+	0.450211i	0.989278	−	0.146045i	$-0.0466543\pi$
$223$	41.5859	+	100.397i	0.186484	+	0.450211i	−0.802794	+	0.596256i	$0.796654\pi$
$224$		0			0
$225$	−148.981	+	148.981i	−0.662137	+	0.662137i
$226$		0			0
$227$	109.633	−	164.078i	0.482966	−	0.722810i	−0.507335	−	0.861749i	$-0.669369\pi$
$227$	109.633	−	164.078i	0.482966	−	0.722810i	0.990301	+	0.138939i	$0.0443693\pi$
$228$		0			0
$229$	−167.322	−	69.3072i	−0.730665	−	0.302651i	−0.0138399	−	0.999904i	$-0.504406\pi$
$229$	−167.322	−	69.3072i	−0.730665	−	0.302651i	−0.716825	+	0.697253i	$0.754406\pi$
$230$		0			0
$231$	40.8808	−	8.13170i	0.176973	−	0.0352022i
$232$		0			0
$233$	5.74492	+	1.14274i	0.0246563	+	0.00490444i	0.207403	−	0.978256i	$-0.433499\pi$
$233$	5.74492	+	1.14274i	0.0246563	+	0.00490444i	−0.182747	+	0.983160i	$0.558499\pi$
$234$		0			0
$235$	−22.0282	+	14.7188i	−0.0937372	+	0.0626332i
$236$		0			0
$237$		−	615.941i		−	2.59891i
$238$		0			0
$239$	−68.9414			−0.288458			−0.144229	−	0.989544i	$-0.546070\pi$
$239$	−68.9414			−0.288458			−0.144229	+	0.989544i	$0.546070\pi$
$240$		0			0
$241$	−172.160	−	257.655i	−0.714355	−	1.06911i	−0.994040	−	0.109016i	$-0.965230\pi$
$241$	−172.160	−	257.655i	−0.714355	−	1.06911i	0.279685	−	0.960092i	$-0.409770\pi$
$242$		0			0
$243$	−0.0479123	+	0.240872i	−0.000197170	+	0.000991241i
$244$		0			0
$245$	27.1016	+	136.249i	0.110619	+	0.556117i
$246$		0			0
$247$	38.3050	−	92.4764i	0.155081	−	0.374399i
$248$		0			0
$249$	406.533	+	271.637i	1.63266	+	1.09091i
$250$		0			0
$251$	−149.892	−	149.892i	−0.597178	−	0.597178i	0.342382	−	0.939561i	$-0.388766\pi$
$251$	−149.892	−	149.892i	−0.597178	−	0.597178i	−0.939561	+	0.342382i	$0.888766\pi$
$252$		0			0
$253$	−7.75623	+	3.21274i	−0.0306571	+	0.0126986i
$254$		0			0
$255$	−205.617	+	247.868i	−0.806342	+	0.972033i
$256$		0			0
$257$	92.4689	+	223.240i	0.359801	+	0.868637i	0.995327	+	0.0965575i	$0.0307832\pi$
$257$	92.4689	+	223.240i	0.359801	+	0.868637i	−0.635526	+	0.772079i	$0.719217\pi$
$258$		0			0
$259$	89.9150	−	89.9150i	0.347162	−	0.347162i
$260$		0			0
$261$	240.453	−	359.864i	0.921277	−	1.37879i
$262$		0			0
$263$	221.046	+	91.5602i	0.840479	+	0.348138i	0.761042	−	0.648702i	$-0.224688\pi$
$263$	221.046	+	91.5602i	0.840479	+	0.348138i	0.0794365	+	0.996840i	$0.474688\pi$
$264$		0			0
$265$	−203.916	+	40.5614i	−0.769493	+	0.153062i
$266$		0			0
$267$	141.271	+	28.1005i	0.529103	+	0.105245i
$268$		0			0
$269$	9.41947	−	6.29389i	0.0350166	−	0.0233973i	−0.537939	−	0.842984i	$-0.680797\pi$
$269$	9.41947	−	6.29389i	0.0350166	−	0.0233973i	0.572955	+	0.819587i	$0.305797\pi$
$270$		0			0
$271$		−	352.304i		−	1.30001i	−0.759929	−	0.650007i	$-0.774766\pi$
$271$		−	352.304i		−	1.30001i	0.759929	−	0.650007i	$-0.225234\pi$
$272$		0			0
$273$	187.557			0.687023
$274$		0			0
$275$	−15.8044	−	23.6530i	−0.0574707	−	0.0860109i
$276$		0			0
$277$	−18.1940	+	91.4673i	−0.0656823	+	0.330207i	−0.999630	−	0.0272028i	$-0.991340\pi$
$277$	−18.1940	+	91.4673i	−0.0656823	+	0.330207i	0.933948	+	0.357410i	$0.116340\pi$
$278$		0			0
$279$	97.2506	+	488.912i	0.348569	+	1.75237i
$280$		0			0
$281$	85.1913	−	205.670i	0.303172	−	0.731922i	−0.696722	−	0.717341i	$-0.745359\pi$
$281$	85.1913	−	205.670i	0.303172	−	0.731922i	0.999894	−	0.0145802i	$-0.00464119\pi$
$282$		0			0
$283$	−104.017	−	69.5017i	−0.367550	−	0.245589i	0.358055	−	0.933700i	$-0.383440\pi$
$283$	−104.017	−	69.5017i	−0.367550	−	0.245589i	−0.725605	+	0.688111i	$0.758440\pi$
$284$		0			0
$285$	−122.627	−	122.627i	−0.430270	−	0.430270i
$286$		0			0
$287$	−234.751	+	97.2369i	−0.817946	+	0.338804i
$288$		0			0
$289$	163.085	−	238.588i	0.564308	−	0.825564i
$290$		0			0
$291$	30.2919	+	73.1311i	0.104096	+	0.251309i
$292$		0			0
$293$	−84.7101	+	84.7101i	−0.289113	+	0.289113i	−0.836729	−	0.547617i	$-0.815535\pi$
$293$	−84.7101	+	84.7101i	−0.289113	+	0.289113i	0.547617	+	0.836729i	$0.315535\pi$
$294$		0			0
$295$	−46.6969	+	69.8869i	−0.158295	+	0.236905i
$296$		0			0
$297$	104.953	+	43.4730i	0.353378	+	0.146374i
$298$		0			0
$299$	−37.0508	+	7.36986i	−0.123916	+	0.0246484i
$300$		0			0
$301$	−175.395	−	34.8883i	−0.582709	−	0.115908i
$302$		0			0
$303$	571.095	−	381.594i	1.88480	−	1.25938i
$304$		0			0
$305$			151.257i			0.495926i
$306$		0			0
$307$	−237.264			−0.772846			−0.386423	−	0.922322i	$-0.626289\pi$
$307$	−237.264			−0.772846			−0.386423	+	0.922322i	$0.626289\pi$
$308$		0			0
$309$	534.427	+	799.826i	1.72954	+	2.58843i
$310$		0			0
$311$	−62.8072	+	315.753i	−0.201953	+	1.01528i	0.738213	+	0.674567i	$0.235670\pi$
$311$	−62.8072	+	315.753i	−0.201953	+	1.01528i	−0.940166	+	0.340717i	$0.889330\pi$
$312$		0			0
$313$	61.4642	+	309.001i	0.196371	+	0.987225i	0.945703	+	0.325031i	$0.105375\pi$
$313$	61.4642	+	309.001i	0.196371	+	0.987225i	−0.749332	+	0.662194i	$0.769625\pi$
$314$		0			0
$315$	82.8983	−	200.134i	0.263169	−	0.635347i
$316$		0			0
$317$	−266.949	−	178.370i	−0.842111	−	0.562681i	0.0580122	−	0.998316i	$-0.481524\pi$
$317$	−266.949	−	178.370i	−0.842111	−	0.562681i	−0.900123	+	0.435635i	$0.856524\pi$
$318$		0			0
$319$	41.3210	+	41.3210i	0.129533	+	0.129533i
$320$		0			0
$321$	178.094	−	73.7690i	0.554811	−	0.229810i
$322$		0			0
$323$	119.776	+	99.3590i	0.370823	+	0.307613i
$324$		0			0
$325$	−48.9855	−	118.262i	−0.150725	−	0.363882i
$326$		0			0
$327$	167.437	−	167.437i	0.512041	−	0.512041i
$328$		0			0
$329$	−13.3272	+	19.9455i	−0.0405082	+	0.0606247i
$330$		0			0
$331$	−24.6962	−	10.2295i	−0.0746109	−	0.0309049i	0.345066	−	0.938578i	$-0.387857\pi$
$331$	−24.6962	−	10.2295i	−0.0746109	−	0.0309049i	−0.419677	+	0.907674i	$0.637857\pi$
$332$		0			0
$333$	679.905	−	135.242i	2.04176	−	0.406131i
$334$		0			0
$335$	62.0916	+	12.3508i	0.185348	+	0.0368680i
$336$		0			0
$337$	406.888	−	271.874i	1.20738	−	0.806748i	0.221661	−	0.975124i	$-0.428852\pi$
$337$	406.888	−	271.874i	1.20738	−	0.806748i	0.985723	+	0.168375i	$0.0538521\pi$
$338$		0			0
$339$		−	454.084i		−	1.33948i
$340$		0			0
$341$	−67.3056			−0.197377
$342$		0			0
$343$	159.752	+	239.086i	0.465750	+	0.697043i
$344$		0			0
$345$	−12.7686	+	64.1922i	−0.0370105	+	0.186064i
$346$		0			0
$347$	47.1829	+	237.204i	0.135974	+	0.683586i	0.987289	+	0.158932i	$0.0508052\pi$
$347$	47.1829	+	237.204i	0.135974	+	0.683586i	−0.851316	+	0.524654i	$0.824195\pi$
$348$		0			0
$349$	−15.1979	+	36.6909i	−0.0435470	+	0.105132i	−0.944156	−	0.329498i	$-0.893121\pi$
$349$	−15.1979	+	36.6909i	−0.0435470	+	0.105132i	0.900609	+	0.434629i	$0.143121\pi$
$350$		0			0
$351$	425.025	+	283.993i	1.21090	+	0.809096i
$352$		0			0
$353$	−451.955	−	451.955i	−1.28033	−	1.28033i	−0.940482	−	0.339843i	$-0.889626\pi$
$353$	−451.955	−	451.955i	−1.28033	−	1.28033i	−0.339843	−	0.940482i	$-0.610374\pi$
$354$		0			0
$355$	−173.786	+	71.9846i	−0.489538	+	0.202773i
$356$		0			0
$357$	−86.1179	+	278.596i	−0.241227	+	0.780381i
$358$		0			0
$359$	−78.0349	−	188.393i	−0.217367	−	0.524771i	0.777153	−	0.629311i	$-0.216663\pi$
$359$	−78.0349	−	188.393i	−0.217367	−	0.524771i	−0.994521	+	0.104540i	$0.966663\pi$
$360$		0			0
$361$	196.009	−	196.009i	0.542962	−	0.542962i
$362$		0			0
$363$	332.244	−	497.238i	0.915272	−	1.36980i
$364$		0			0
$365$	209.398	+	86.7357i	0.573694	+	0.237632i
$366$		0			0
$367$	276.557	−	55.0107i	0.753563	−	0.149893i	0.196661	−	0.980472i	$-0.436990\pi$
$367$	276.557	−	55.0107i	0.753563	−	0.149893i	0.556901	+	0.830579i	$0.311990\pi$
$368$		0			0
$369$	−1358.60	−	270.243i	−3.68185	−	0.732366i
$370$		0			0
$371$	−156.527	+	104.588i	−0.421906	+	0.281908i
$372$		0			0
$373$		−	340.976i		−	0.914144i	−0.889430	−	0.457072i	$-0.848898\pi$
$373$		−	340.976i		−	0.914144i	0.889430	−	0.457072i	$-0.151102\pi$
$374$		0			0
$375$	−695.380			−1.85435
$376$		0			0
$377$	146.087	+	218.635i	0.387500	+	0.579935i
$378$		0			0
$379$	69.8686	−	351.253i	0.184350	−	0.926790i	−0.772235	−	0.635337i	$-0.780861\pi$
$379$	69.8686	−	351.253i	0.184350	−	0.926790i	0.956585	−	0.291453i	$-0.0941387\pi$
$380$		0			0
$381$	−112.202	−	564.080i	−0.294495	−	1.48052i
$382$		0			0
$383$	−92.5645	+	223.470i	−0.241683	+	0.583474i	−0.997450	−	0.0713664i	$-0.977264\pi$
$383$	−92.5645	+	223.470i	−0.241683	+	0.583474i	0.755767	+	0.654840i	$0.227264\pi$
$384$		0			0
$385$	24.3191	+	16.2495i	0.0631664	+	0.0422064i
$386$		0			0
$387$	−689.377	−	689.377i	−1.78134	−	1.78134i
$388$		0			0
$389$	−619.174	+	256.470i	−1.59171	+	0.659307i	−0.990212	−	0.139570i	$-0.955428\pi$
$389$	−619.174	+	256.470i	−1.59171	+	0.659307i	−0.601495	+	0.798877i	$0.705428\pi$
$390$		0			0
$391$	6.06495	−	58.4189i	0.0155114	−	0.149409i
$392$		0			0
$393$	89.2370	+	215.437i	0.227066	+	0.548186i
$394$		0			0
$395$	305.618	−	305.618i	0.773716	−	0.773716i
$396$		0			0
$397$	248.868	−	372.457i	0.626871	−	0.938179i	−0.373075	−	0.927801i	$-0.621697\pi$
$397$	248.868	−	372.457i	0.626871	−	0.938179i	0.999946	−	0.0103776i	$-0.00330334\pi$
$398$		0			0
$399$	−145.071	−	60.0906i	−0.363588	−	0.150603i
$400$		0			0
$401$	136.334	−	27.1185i	0.339985	−	0.0676272i	−0.0221452	−	0.999755i	$-0.507050\pi$
$401$	136.334	−	27.1185i	0.339985	−	0.0676272i	0.362130	+	0.932128i	$0.382050\pi$
$402$		0			0
$403$	−297.039	−	59.0847i	−0.737069	−	0.146612i
$404$		0			0
$405$	245.339	−	163.930i	0.605775	−	0.404766i
$406$		0			0
$407$			93.5985i			0.229972i
$408$		0			0
$409$	−404.559			−0.989142			−0.494571	−	0.869137i	$-0.664675\pi$
$409$	−404.559			−0.989142			−0.494571	+	0.869137i	$0.664675\pi$
$410$		0			0
$411$	177.534	+	265.698i	0.431956	+	0.646467i
$412$		0			0
$413$	−14.8474	+	74.6430i	−0.0359502	+	0.180734i
$414$		0			0
$415$	66.9330	+	336.495i	0.161284	+	0.810831i
$416$		0			0
$417$	173.701	−	419.352i	0.416549	−	1.00564i
$418$		0			0
$419$	217.250	+	145.162i	0.518496	+	0.346448i	0.787123	−	0.616796i	$-0.211570\pi$
$419$	217.250	+	145.162i	0.518496	+	0.346448i	−0.268627	+	0.963244i	$0.586570\pi$
$420$		0			0
$421$	429.955	+	429.955i	1.02127	+	1.02127i	0.999769	+	0.0215010i	$0.00684449\pi$
$421$	429.955	+	429.955i	1.02127	+	1.02127i	0.0215010	+	0.999769i	$0.493156\pi$
$422$		0			0
$423$	−120.821	+	50.0457i	−0.285629	+	0.118311i
$424$		0			0
$425$	198.157	−	18.4623i	0.466251	−	0.0434406i
$426$		0			0
$427$	52.4110	+	126.531i	0.122742	+	0.296326i
$428$		0			0
$429$	−97.6204	+	97.6204i	−0.227553	+	0.227553i
$430$		0			0
$431$	355.752	−	532.421i	0.825412	−	1.23532i	−0.143927	−	0.989588i	$-0.545973\pi$
$431$	355.752	−	532.421i	0.825412	−	1.23532i	0.969339	−	0.245728i	$-0.0790269\pi$
$432$		0			0
$433$	−590.594	−	244.632i	−1.36396	−	0.564971i	−0.423816	−	0.905748i	$-0.639310\pi$
$433$	−590.594	−	244.632i	−1.36396	−	0.564971i	−0.940144	+	0.340778i	$0.889310\pi$
$434$		0			0
$435$	446.820	−	88.8780i	1.02717	−	0.204317i
$436$		0			0
$437$	31.0192	+	6.17010i	0.0709821	+	0.0141192i
$438$		0			0
$439$	−586.307	+	391.758i	−1.33555	+	0.892386i	−0.998789	−	0.0492039i	$-0.984332\pi$
$439$	−586.307	+	391.758i	−1.33555	+	0.892386i	−0.336761	+	0.941590i	$0.609332\pi$
$440$		0			0
$441$			685.729i			1.55494i
$442$		0			0
$443$	317.185			0.715994			0.357997	−	0.933723i	$-0.383460\pi$
$443$	317.185			0.715994			0.357997	+	0.933723i	$0.383460\pi$
$444$		0			0
$445$	56.1528	+	84.0386i	0.126186	+	0.188851i
$446$		0			0
$447$	−190.145	+	955.924i	−0.425381	+	2.13853i
$448$		0			0
$449$	−47.9801	−	241.212i	−0.106860	−	0.537222i	−0.996716	−	0.0809796i	$-0.974195\pi$
$449$	−47.9801	−	241.212i	−0.106860	−	0.537222i	0.889856	−	0.456242i	$-0.150805\pi$
$450$		0			0
$451$	71.5736	−	172.794i	0.158700	−	0.383135i
$452$		0			0
$453$	933.869	+	623.991i	2.06152	+	1.37746i
$454$		0			0
$455$	93.0622	+	93.0622i	0.204532	+	0.204532i
$456$		0			0
$457$	343.798	−	142.406i	0.752293	−	0.311610i	0.0266163	−	0.999646i	$-0.491527\pi$
$457$	343.798	−	142.406i	0.752293	−	0.311610i	0.725677	+	0.688036i	$0.241527\pi$
$458$		0			0
$459$	−616.993	+	500.932i	−1.34421	+	1.09135i
$460$		0			0
$461$	329.689	+	795.940i	0.715161	+	1.72655i	0.686683	+	0.726957i	$0.259066\pi$
$461$	329.689	+	795.940i	0.715161	+	1.72655i	0.0284783	+	0.999594i	$0.490934\pi$
$462$		0			0
$463$	386.172	−	386.172i	0.834065	−	0.834065i	−0.154005	−	0.988070i	$-0.549217\pi$
$463$	386.172	−	386.172i	0.834065	−	0.834065i	0.988070	+	0.154005i	$0.0492172\pi$
$464$		0			0
$465$	−291.516	+	436.285i	−0.626917	+	0.938247i
$466$		0			0
$467$	−374.194	−	154.996i	−0.801272	−	0.331898i	−0.0558061	−	0.998442i	$-0.517773\pi$
$467$	−374.194	−	154.996i	−0.801272	−	0.331898i	−0.745466	+	0.666544i	$0.767773\pi$
$468$		0			0
$469$	56.2210	−	11.1831i	0.119874	−	0.0238445i
$470$		0			0
$471$	−800.273	−	159.184i	−1.69909	−	0.337971i
$472$		0			0
$473$	109.449	−	73.1316i	0.231394	−	0.154612i
$474$		0			0
$475$			107.167i			0.225615i
$476$		0			0
$477$	−1026.29			−2.15155
$478$		0			0
$479$	−66.8122	−	99.9916i	−0.139483	−	0.208751i	0.755151	−	0.655551i	$-0.227564\pi$
$479$	−66.8122	−	99.9916i	−0.139483	−	0.208751i	−0.894634	+	0.446800i	$0.852564\pi$
$480$		0			0
$481$	−82.1661	+	413.077i	−0.170823	+	0.858788i
$482$		0			0
$483$	11.5614	+	58.1230i	0.0239366	+	0.120338i
$484$		0			0
$485$	−21.2560	+	51.3164i	−0.0438267	+	0.105807i
$486$		0			0
$487$	673.901	+	450.287i	1.38378	+	0.924613i	0.999999	+	0.00118928i	$0.000378561\pi$
$487$	673.901	+	450.287i	1.38378	+	0.924613i	0.383782	+	0.923424i	$0.374621\pi$
$488$		0			0
$489$	−613.058	−	613.058i	−1.25370	−	1.25370i
$490$		0			0
$491$	139.166	−	57.6444i	0.283433	−	0.117402i	−0.236438	−	0.971647i	$-0.575980\pi$
$491$	139.166	−	57.6444i	0.283433	−	0.117402i	0.519871	+	0.854245i	$0.325980\pi$
$492$		0			0
$493$	−391.836	+	116.609i	−0.794799	+	0.236530i
$494$		0			0
$495$	61.0194	+	147.314i	0.123271	+	0.297604i
$496$		0			0
$497$	−120.434	+	120.434i	−0.242323	+	0.242323i
$498$		0			0
$499$	−457.780	+	685.116i	−0.917394	+	1.37298i	0.0104246	+	0.999946i	$0.496682\pi$
$499$	−457.780	+	685.116i	−0.917394	+	1.37298i	−0.927819	+	0.373032i	$0.878318\pi$
$500$		0			0
$501$	258.504	+	107.076i	0.515976	+	0.213724i
$502$		0			0
$503$	−663.866	+	132.051i	−1.31981	+	0.262527i	−0.804233	−	0.594314i	$-0.797424\pi$
$503$	−663.866	+	132.051i	−1.31981	+	0.262527i	−0.515580	+	0.856841i	$0.672424\pi$
$504$		0			0
$505$	472.706	+	94.0270i	0.936051	+	0.186192i
$506$		0			0
$507$	213.596	−	142.720i	0.421293	−	0.281499i
$508$		0			0
$509$		−	340.603i		−	0.669161i	−0.942367	−	0.334581i	$-0.891405\pi$
$509$		−	340.603i		−	0.669161i	0.942367	−	0.334581i	$-0.108595\pi$
$510$		0			0
$511$	205.222			0.401609
$512$		0			0
$513$	−237.761	−	355.834i	−0.463471	−	0.693633i
$514$		0			0
$515$	−131.686	+	662.030i	−0.255701	+	1.28550i
$516$		0			0
$517$	−3.44475	−	17.3179i	−0.00666295	−	0.0334969i
$518$		0			0
$519$	−133.730	+	322.852i	−0.257668	+	0.622066i
$520$		0			0
$521$	374.731	+	250.387i	0.719253	+	0.480590i	0.860542	−	0.509379i	$-0.170125\pi$
$521$	374.731	+	250.387i	0.719253	+	0.480590i	−0.141289	+	0.989968i	$0.545125\pi$
$522$		0			0
$523$	−425.914	−	425.914i	−0.814367	−	0.814367i	0.170918	−	0.985285i	$-0.445327\pi$
$523$	−425.914	−	425.914i	−0.814367	−	0.814367i	−0.985285	+	0.170918i	$0.945327\pi$
$524$		0			0
$525$	−185.521	+	76.8455i	−0.353374	+	0.146372i
$526$		0			0
$527$	224.151	−	414.090i	0.425334	−	0.785749i
$528$		0			0
$529$	197.872	+	477.705i	0.374049	+	0.903033i
$530$		0			0
$531$	−293.378	+	293.378i	−0.552501	+	0.552501i
$532$		0			0
$533$	467.563	−	699.758i	0.877229	−	1.31287i
$534$		0			0
$535$	124.970	+	51.7641i	0.233588	+	0.0967554i
$536$		0			0
$537$	−1278.66	+	254.340i	−2.38111	+	0.473632i
$538$		0			0
$539$	−90.8073	−	18.0627i	−0.168474	−	0.0335115i
$540$		0			0
$541$	−406.212	+	271.422i	−0.750855	+	0.501705i	−0.871140	−	0.491034i	$-0.836619\pi$
$541$	−406.212	+	271.422i	−0.750855	+	0.501705i	0.120286	+	0.992739i	$0.461619\pi$
$542$		0			0
$543$		−	88.9999i		−	0.163904i
$544$		0			0
$545$	166.158			0.304878
$546$		0			0
$547$	209.264	+	313.185i	0.382566	+	0.572551i	0.971916	−	0.235327i	$-0.0756161\pi$
$547$	209.264	+	313.185i	0.382566	+	0.572551i	−0.589350	+	0.807878i	$0.700616\pi$
$548$		0			0
$549$	−145.662	+	732.292i	−0.265322	+	1.33386i
$550$		0			0
$551$	−42.9480	−	215.914i	−0.0779455	−	0.391858i
$552$		0			0
$553$	149.761	−	361.556i	0.270816	−	0.653808i
$554$		0			0
$555$	606.720	+	405.397i	1.09319	+	0.730445i
$556$		0			0
$557$	58.1418	+	58.1418i	0.104384	+	0.104384i	0.757370	−	0.652986i	$-0.226484\pi$
$557$	58.1418	+	58.1418i	0.104384	+	0.104384i	−0.652986	+	0.757370i	$0.726484\pi$
$558$		0			0
$559$	547.229	−	226.670i	0.978943	−	0.405492i
$560$		0			0
$561$	−100.182	−	189.828i	−0.178577	−	0.338374i
$562$		0			0
$563$	−93.7832	−	226.413i	−0.166578	−	0.402154i	0.818444	−	0.574587i	$-0.194837\pi$
$563$	−93.7832	−	226.413i	−0.166578	−	0.402154i	−0.985021	+	0.172433i	$0.944837\pi$
$564$		0			0
$565$	225.308	−	225.308i	0.398775	−	0.398775i
$566$		0			0
$567$	148.431	−	222.143i	0.261783	−	0.391787i
$568$		0			0
$569$	−35.1685	−	14.5673i	−0.0618076	−	0.0256015i	0.351565	−	0.936163i	$-0.385649\pi$
$569$	−35.1685	−	14.5673i	−0.0618076	−	0.0256015i	−0.413373	+	0.910562i	$0.635649\pi$
$570$		0			0
$571$	55.6344	−	11.0664i	0.0974332	−	0.0193807i	−0.146133	−	0.989265i	$-0.546683\pi$
$571$	55.6344	−	11.0664i	0.0974332	−	0.0193807i	0.243566	+	0.969884i	$0.421683\pi$
$572$		0			0
$573$	−574.857	−	114.346i	−1.00324	−	0.199557i
$574$		0			0
$575$	33.6291	−	22.4702i	0.0584854	−	0.0390787i
$576$		0			0
$577$			711.158i			1.23251i	0.787547	+	0.616255i	$0.211351\pi$
$577$			711.158i			1.23251i	−0.787547	+	0.616255i	$0.788649\pi$
$578$		0			0
$579$	−106.433			−0.183823
$580$		0			0
$581$	172.587	+	258.295i	0.297052	+	0.444570i
$582$		0			0
$583$	27.0334	−	135.906i	0.0463694	−	0.233115i
$584$		0			0
$585$	139.975	+	703.704i	0.239274	+	1.20291i
$586$		0			0
$587$	358.692	−	865.959i	0.611060	−	1.47523i	−0.250778	−	0.968045i	$-0.580686\pi$
$587$	358.692	−	865.959i	0.611060	−	1.47523i	0.861838	−	0.507184i	$-0.169314\pi$
$588$		0			0
$589$	210.823	+	140.868i	0.357934	+	0.239164i
$590$		0			0
$591$	−151.475	−	151.475i	−0.256303	−	0.256303i
$592$		0			0
$593$	858.785	−	355.720i	1.44820	−	0.599865i	0.486432	−	0.873719i	$-0.338298\pi$
$593$	858.785	−	355.720i	1.44820	−	0.599865i	0.961772	+	0.273853i	$0.0882982\pi$
$594$		0			0
$595$	−180.964	+	95.5038i	−0.304141	+	0.160511i
$596$		0			0
$597$	−727.871	−	1757.24i	−1.21921	−	2.94344i
$598$		0			0
$599$	278.647	−	278.647i	0.465187	−	0.465187i	−0.435164	−	0.900351i	$-0.643310\pi$
$599$	278.647	−	278.647i	0.465187	−	0.465187i	0.900351	+	0.435164i	$0.143310\pi$
$600$		0			0
$601$	280.477	−	419.764i	0.466684	−	0.698442i	−0.521235	−	0.853413i	$-0.674528\pi$
$601$	280.477	−	419.764i	0.466684	−	0.698442i	0.987919	+	0.154971i	$0.0495284\pi$
$602$		0			0
$603$	288.714	+	119.589i	0.478796	+	0.198324i
$604$		0			0
$605$	411.573	−	81.8669i	0.680285	−	0.135317i
$606$		0			0
$607$	302.742	+	60.2190i	0.498750	+	0.0992076i	0.438054	−	0.898949i	$-0.355668\pi$
$607$	302.742	+	60.2190i	0.498750	+	0.0992076i	0.0606964	+	0.998156i	$0.480668\pi$
$608$		0			0
$609$	342.982	−	229.173i	0.563189	−	0.376311i
$610$		0			0
$611$		−	79.4528i		−	0.130037i
$612$		0			0
$613$	116.450			0.189967			0.0949835	−	0.995479i	$-0.469720\pi$
$613$	116.450			0.189967			0.0949835	+	0.995479i	$0.469720\pi$
$614$		0			0
$615$	−810.075	−	1212.36i	−1.31719	−	1.97132i
$616$		0			0
$617$	−124.062	+	623.701i	−0.201073	+	1.01086i	0.739987	+	0.672621i	$0.234831\pi$
$617$	−124.062	+	623.701i	−0.201073	+	1.01086i	−0.941060	+	0.338239i	$0.890169\pi$
$618$		0			0
$619$	−114.897	−	577.626i	−0.185617	−	0.933160i	−0.955504	−	0.294980i	$-0.904687\pi$
$619$	−114.897	−	577.626i	−0.185617	−	0.933160i	0.769886	−	0.638181i	$-0.220313\pi$
$620$		0			0
$621$	−61.8085	+	149.219i	−0.0995306	+	0.240288i
$622$		0			0
$623$	76.0930	+	50.8437i	0.122140	+	0.0816111i
$624$		0			0
$625$	−138.086	−	138.086i	−0.220938	−	0.220938i
$626$		0			0
$627$	106.783	−	44.2311i	0.170309	−	0.0705441i
$628$		0			0
$629$	−575.854	−	311.715i	−0.915507	−	0.495573i
$630$		0			0
$631$	414.694	+	1001.16i	0.657201	+	1.58662i	0.802108	+	0.597179i	$0.203712\pi$
$631$	414.694	+	1001.16i	0.657201	+	1.58662i	−0.144906	+	0.989445i	$0.546288\pi$
$632$		0			0
$633$	1178.49	−	1178.49i	1.86175	−	1.86175i
$634$		0			0
$635$	224.213	−	335.558i	0.353091	−	0.528438i
$636$		0			0
$637$	−384.902	−	159.432i	−0.604242	−	0.250285i
$638$		0			0
$639$	−910.683	+	181.146i	−1.42517	+	0.283484i
$640$		0			0
$641$	−545.664	−	108.539i	−0.851269	−	0.169328i	−0.249873	−	0.968279i	$-0.580389\pi$
$641$	−545.664	−	108.539i	−0.851269	−	0.169328i	−0.601397	+	0.798951i	$0.705389\pi$
$642$		0			0
$643$	90.3509	−	60.3706i	0.140515	−	0.0938889i	−0.483326	−	0.875440i	$-0.660571\pi$
$643$	90.3509	−	60.3706i	0.140515	−	0.0938889i	0.623841	+	0.781552i	$0.285571\pi$
$644$		0			0
$645$		−	1026.22i		−	1.59103i
$646$		0			0
$647$	−1175.55			−1.81693			−0.908463	−	0.417966i	$-0.862743\pi$
$647$	−1175.55			−1.81693			−0.908463	+	0.417966i	$0.862743\pi$
$648$		0			0
$649$	−31.1226	−	46.5783i	−0.0479547	−	0.0717693i
$650$		0			0
$651$	−92.6884	+	465.976i	−0.142379	+	0.715785i
$652$		0			0
$653$	−132.779	−	667.525i	−0.203337	−	1.02224i	−0.938743	−	0.344617i	$-0.888009\pi$
$653$	−132.779	−	667.525i	−0.203337	−	1.02224i	0.735407	−	0.677626i	$-0.236991\pi$
$654$		0			0
$655$	−62.6181	+	151.173i	−0.0956001	+	0.230799i
$656$		0			0
$657$	930.246	+	621.571i	1.41590	+	0.946074i
$658$		0			0
$659$	542.829	+	542.829i	0.823716	+	0.823716i	0.986639	−	0.162923i	$-0.0520921\pi$
$659$	542.829	+	542.829i	0.823716	+	0.823716i	−0.162923	+	0.986639i	$0.552092\pi$
$660$		0			0
$661$	84.7509	−	35.1050i	0.128216	−	0.0531089i	−0.317653	−	0.948207i	$-0.602895\pi$
$661$	84.7509	−	35.1050i	0.128216	−	0.0531089i	0.445869	+	0.895098i	$0.352895\pi$
$662$		0			0
$663$	−275.489	−	925.708i	−0.415518	−	1.39624i
$664$		0			0
$665$	−42.1659	−	101.797i	−0.0634073	−	0.153079i
$666$		0			0
$667$	−58.7489	+	58.7489i	−0.0880793	+	0.0880793i
$668$		0			0
$669$	−313.694	+	469.476i	−0.468899	+	0.701757i
$670$		0			0
$671$	−93.1365	−	38.5784i	−0.138803	−	0.0574939i
$672$		0			0
$673$	−166.460	+	33.1109i	−0.247340	+	0.0491990i	−0.317203	−	0.948358i	$-0.602744\pi$
$673$	−166.460	+	33.1109i	−0.247340	+	0.0491990i	0.0698631	+	0.997557i	$0.477744\pi$
$674$		0			0
$675$	−536.768	−	106.770i	−0.795213	−	0.158178i
$676$		0			0
$677$	−378.084	+	252.628i	−0.558470	+	0.373158i	−0.802539	−	0.596600i	$-0.796518\pi$
$677$	−378.084	+	252.628i	−0.558470	+	0.373158i	0.244068	+	0.969758i	$0.421518\pi$
$678$		0			0
$679$			50.2930i			0.0740692i
$680$		0			0
$681$	1025.33			1.50563
$682$		0			0
$683$	746.009	+	1116.48i	1.09225	+	1.63467i	0.698779	+	0.715337i	$0.253727\pi$
$683$	746.009	+	1116.48i	1.09225	+	1.63467i	0.393474	+	0.919336i	$0.371273\pi$
$684$		0			0
$685$	−43.7454	+	219.923i	−0.0638619	+	0.321055i
$686$		0			0
$687$	−183.584	−	922.940i	−0.267226	−	1.34343i
$688$		0			0
$689$	238.612	−	576.061i	0.346317	−	0.836082i
$690$		0			0
$691$	163.058	+	108.952i	0.235975	+	0.157673i	0.667936	−	0.744219i	$-0.267178\pi$
$691$	163.058	+	108.952i	0.235975	+	0.157673i	−0.431961	+	0.901892i	$0.642178\pi$
$692$		0			0
$693$	102.089	+	102.089i	0.147315	+	0.147315i
$694$		0			0
$695$	294.261	−	121.887i	0.423397	−	0.175377i
$696$		0			0
$697$	824.730	+	1015.81i	1.18326	+	1.45741i
$698$		0			0
$699$	11.6469	+	28.1181i	0.0166622	+	0.0402262i
$700$		0			0
$701$	−164.717	+	164.717i	−0.234975	+	0.234975i	−0.814766	−	0.579791i	$-0.803134\pi$
$701$	−164.717	+	164.717i	−0.234975	+	0.234975i	0.579791	+	0.814766i	$0.303134\pi$
$702$		0			0
$703$	195.897	−	293.181i	0.278659	−	0.417043i
$704$		0			0
$705$	−127.177	−	52.6786i	−0.180393	−	0.0747214i
$706$		0			0
$707$	428.013	−	85.1370i	0.605393	−	0.120420i
$708$		0			0
$709$	737.675	+	146.733i	1.04044	+	0.206957i	0.685608	−	0.727971i	$-0.259537\pi$
$709$	737.675	+	146.733i	1.04044	+	0.206957i	0.354836	+	0.934928i	$0.384537\pi$
$710$		0			0
$711$	1773.92	−	1185.29i	2.49496	−	1.66708i
$712$		0			0
$713$		−	95.6929i		−	0.134212i
$714$		0			0
$715$	−96.8747			−0.135489
$716$		0			0
$717$	−199.012	−	297.843i	−0.277562	−	0.415402i
$718$		0			0
$719$	104.310	−	524.403i	0.145077	−	0.729351i	−0.837929	−	0.545779i	$-0.816234\pi$
$719$	104.310	−	524.403i	0.145077	−	0.729351i	0.983006	−	0.183572i	$-0.0587661\pi$
$720$		0			0
$721$	119.236	+	599.437i	0.165375	+	0.831397i
$722$		0			0
$723$	616.159	−	1487.54i	0.852225	−	2.05745i
$724$		0			0
$725$	−234.081	−	156.408i	−0.322870	−	0.215735i
$726$		0			0
$727$	883.793	+	883.793i	1.21567	+	1.21567i	0.969133	+	0.246538i	$0.0792932\pi$
$727$	883.793	+	883.793i	1.21567	+	1.21567i	0.246538	+	0.969133i	$0.420707\pi$
$728$		0			0
$729$	−674.098	+	279.220i	−0.924688	+	0.383018i
$730$		0			0
$731$	85.4300	+	916.927i	0.116867	+	1.25435i
$732$		0			0
$733$	249.714	+	602.864i	0.340674	+	0.822460i	0.997648	+	0.0685469i	$0.0218363\pi$
$733$	249.714	+	602.864i	0.340674	+	0.822460i	−0.656974	+	0.753914i	$0.728164\pi$
$734$		0			0
$735$	−510.393	+	510.393i	−0.694412	+	0.694412i
$736$		0			0
$737$	−23.4415	+	35.0827i	−0.0318067	+	0.0476021i
$738$		0			0
$739$	−710.562	−	294.324i	−0.961518	−	0.398274i	−0.153970	−	0.988075i	$-0.549206\pi$
$739$	−710.562	−	294.324i	−0.961518	−	0.398274i	−0.807548	+	0.589802i	$0.799206\pi$
$740$		0			0
$741$	510.094	−	101.464i	0.688386	−	0.136929i
$742$		0			0
$743$	−66.1835	−	13.1647i	−0.0890760	−	0.0177183i	0.150351	−	0.988633i	$-0.451960\pi$
$743$	−66.1835	−	13.1647i	−0.0890760	−	0.0177183i	−0.239427	+	0.970914i	$0.576960\pi$
$744$		0			0
$745$	−568.657	+	379.965i	−0.763298	+	0.510020i
$746$		0			0
$747$			1693.55i			2.26713i
$748$		0			0
$749$	122.477			0.163521
$750$		0			0
$751$	−155.202	−	232.276i	−0.206660	−	0.309289i	0.713632	−	0.700521i	$-0.247049\pi$
$751$	−155.202	−	232.276i	−0.206660	−	0.309289i	−0.920292	+	0.391232i	$0.872049\pi$
$752$		0			0
$753$	214.877	−	1080.26i	0.285361	−	1.43461i
$754$		0			0
$755$	153.755	+	772.980i	0.203649	+	1.02381i
$756$		0			0
$757$	−222.495	+	537.150i	−0.293917	+	0.709577i	0.706082	+	0.708130i	$0.250461\pi$
$757$	−222.495	+	537.150i	−0.293917	+	0.709577i	−0.999999	+	0.00144764i	$0.999539\pi$
$758$		0			0
$759$	−36.2696	−	24.2346i	−0.0477860	−	0.0319296i
$760$		0			0
$761$	−64.7670	−	64.7670i	−0.0851078	−	0.0851078i	0.663271	−	0.748379i	$-0.269168\pi$
$761$	−64.7670	−	64.7670i	−0.0851078	−	0.0851078i	−0.748379	+	0.663271i	$0.769168\pi$
$762$		0			0
$763$	138.996	−	57.5742i	0.182171	−	0.0754577i
$764$		0			0
$765$	−1109.55	−	115.191i	−1.45039	−	0.150577i
$766$		0			0
$767$	−96.4639	−	232.884i	−0.125768	−	0.303630i
$768$		0			0
$769$	−8.68658	+	8.68658i	−0.0112959	+	0.0112959i	−0.712732	−	0.701436i	$-0.752543\pi$
$769$	−8.68658	+	8.68658i	−0.0112959	+	0.0112959i	0.701436	+	0.712732i	$0.252543\pi$
$770$		0			0
$771$	−697.518	+	1043.91i	−0.904693	+	1.35397i
$772$		0			0
$773$	−256.725	−	106.339i	−0.332115	−	0.137567i	0.210393	−	0.977617i	$-0.432526\pi$
$773$	−256.725	−	106.339i	−0.332115	−	0.137567i	−0.542509	+	0.840050i	$0.682526\pi$
$774$		0			0
$775$	318.023	−	63.2586i	0.410352	−	0.0816240i
$776$		0			0
$777$	648.010	+	128.897i	0.833990	+	0.165891i
$778$		0			0
$779$	−585.842	+	391.447i	−0.752044	+	0.502500i
$780$		0			0
$781$		−	125.368i		−	0.160523i
$782$		0			0
$783$	1124.24			1.43581
$784$		0			0
$785$	−318.096	−	476.064i	−0.405217	−	0.606451i
$786$		0			0
$787$	25.8529	−	129.971i	0.0328499	−	0.165148i	−0.960878	−	0.276971i	$-0.910669\pi$
$787$	25.8529	−	129.971i	0.0328499	−	0.165148i	0.993728	+	0.111824i	$0.0356692\pi$
$788$		0			0
$789$	242.529	+	1219.28i	0.307388	+	1.54534i
$790$		0			0
$791$	110.407	−	266.546i	0.139579	−	0.336974i
$792$		0			0
$793$	−377.172	−	252.018i	−0.475626	−	0.317803i
$794$		0			0
$795$	−763.875	−	763.875i	−0.960850	−	0.960850i
$796$		0			0
$797$	1137.33	−	471.097i	1.42701	−	0.591087i	0.470400	−	0.882453i	$-0.344110\pi$
$797$	1137.33	−	471.097i	1.42701	−	0.591087i	0.956612	+	0.291366i	$0.0941097\pi$
$798$		0			0
$799$	118.019	+	36.4812i	0.147708	+	0.0456586i
$800$		0			0
$801$	190.926	+	460.937i	0.238360	+	0.575452i
$802$		0			0
$803$	−106.815	+	106.815i	−0.133020	+	0.133020i
$804$		0			0
$805$	−23.1030	+	34.5761i	−0.0286994	+	0.0429516i
$806$		0			0
$807$	54.3821	+	22.5258i	0.0673880	+	0.0279130i
$808$		0			0
$809$	−1547.48	+	307.812i	−1.91282	+	0.380485i	−0.999634	−	0.0270477i	$-0.991389\pi$
$809$	−1547.48	+	307.812i	−1.91282	+	0.380485i	−0.913191	+	0.407532i	$0.866389\pi$
$810$		0			0
$811$	−590.002	−	117.359i	−0.727499	−	0.144709i	−0.182573	−	0.983192i	$-0.558442\pi$
$811$	−590.002	−	117.359i	−0.727499	−	0.144709i	−0.544926	+	0.838484i	$0.683442\pi$
$812$		0			0
$813$	1522.03	−	1016.99i	1.87212	−	1.25091i
$814$		0			0
$815$		−	608.375i		−	0.746472i
$816$		0			0
$817$	−495.892			−0.606966
$818$		0			0
$819$	360.928	+	540.168i	0.440694	+	0.659545i
$820$		0			0
$821$	153.360	−	770.993i	0.186797	−	0.939090i	−0.767687	−	0.640826i	$-0.778592\pi$
$821$	153.360	−	770.993i	0.186797	−	0.939090i	0.954483	−	0.298265i	$-0.0964078\pi$
$822$		0			0
$823$	54.7382	+	275.188i	0.0665106	+	0.334371i	0.999686	−	0.0250494i	$-0.00797432\pi$
$823$	54.7382	+	275.188i	0.0665106	+	0.334371i	−0.933176	+	0.359421i	$0.882974\pi$
$824$		0			0
$825$	56.5640	−	136.558i	0.0685625	−	0.165524i
$826$		0			0
$827$	−1229.32	−	821.409i	−1.48649	−	0.993239i	−0.992297	−	0.123886i	$-0.960464\pi$
$827$	−1229.32	−	821.409i	−1.48649	−	0.993239i	−0.494191	−	0.869354i	$-0.664536\pi$
$828$		0			0
$829$	−331.030	−	331.030i	−0.399312	−	0.399312i	0.478678	−	0.877990i	$-0.341116\pi$
$829$	−331.030	−	331.030i	−0.399312	−	0.399312i	−0.877990	+	0.478678i	$0.841116\pi$
$830$		0			0
$831$	−447.681	+	185.435i	−0.538725	+	0.223147i
$832$		0			0
$833$	413.548	−	498.526i	0.496456	−	0.598471i
$834$		0			0
$835$	75.1357	+	181.394i	0.0899828	+	0.217238i
$836$		0			0
$837$	−915.607	+	915.607i	−1.09392	+	1.09392i
$838$		0			0
$839$	117.506	−	175.861i	0.140055	−	0.209608i	−0.754810	−	0.655943i	$-0.772271\pi$
$839$	117.506	−	175.861i	0.140055	−	0.209608i	0.894866	+	0.446335i	$0.147271\pi$
$840$		0			0
$841$	−242.689	−	100.525i	−0.288572	−	0.119530i
$842$		0			0
$843$	1134.46	−	225.659i	1.34574	−	0.267685i
$844$		0			0
$845$	176.797	+	35.1671i	0.209227	+	0.0416179i
$846$		0			0
$847$	315.926	−	211.095i	0.372994	−	0.249226i
$848$		0			0
$849$		−	650.006i		−	0.765613i
$850$		0			0
$851$	−133.075			−0.156375
$852$		0			0
$853$	556.064	+	832.209i	0.651892	+	0.975626i	0.999281	+	0.0379048i	$0.0120684\pi$
$853$	556.064	+	832.209i	0.651892	+	0.975626i	−0.347389	+	0.937721i	$0.612932\pi$
$854$		0			0
$855$	117.188	−	589.146i	0.137062	−	0.689060i
$856$		0			0
$857$	145.210	+	730.021i	0.169440	+	0.851833i	0.968199	+	0.250181i	$0.0804903\pi$
$857$	145.210	+	730.021i	0.169440	+	0.851833i	−0.798759	+	0.601651i	$0.794510\pi$
$858$		0			0
$859$	−374.100	+	903.157i	−0.435506	+	1.05141i	0.541977	+	0.840393i	$0.317676\pi$
$859$	−374.100	+	903.157i	−0.435506	+	1.05141i	−0.977483	+	0.211012i	$0.932324\pi$
$860$		0			0
$861$	−1097.74	−	733.485i	−1.27496	−	0.851899i
$862$		0			0
$863$	−799.269	−	799.269i	−0.926152	−	0.926152i	0.0713024	−	0.997455i	$-0.477284\pi$
$863$	−799.269	−	799.269i	−0.926152	−	0.926152i	−0.997455	+	0.0713024i	$0.977284\pi$
$864$		0			0
$865$	−226.547	+	93.8388i	−0.261904	+	0.108484i
$866$		0			0
$867$	1501.53	+	15.8356i	1.73187	+	0.0182649i
$868$		0			0
$869$	110.236	+	266.132i	0.126853	+	0.306251i
$870$		0			0
$871$	−134.252	+	134.252i	−0.154135	+	0.154135i
$872$		0			0
$873$	−152.326	+	227.972i	−0.174486	+	0.261136i
$874$		0			0
$875$	−408.186	−	169.076i	−0.466499	−	0.193230i
$876$		0			0
$877$	1320.03	−	262.571i	1.50517	−	0.299397i	0.627483	−	0.778630i	$-0.284085\pi$
$877$	1320.03	−	262.571i	1.50517	−	0.299397i	0.877688	+	0.479233i	$0.159085\pi$
$878$		0			0
$879$	−610.499	−	121.436i	−0.694538	−	0.138152i
$880$		0			0
$881$	−880.918	+	588.611i	−0.999907	+	0.668116i	−0.943872	−	0.330312i	$-0.892846\pi$
$881$	−880.918	+	588.611i	−0.999907	+	0.668116i	−0.0560352	+	0.998429i	$0.517846\pi$
$882$		0			0
$883$		−	658.553i		−	0.745813i	−0.927869	−	0.372907i	$-0.878361\pi$
$883$		−	658.553i		−	0.745813i	0.927869	−	0.372907i	$-0.121639\pi$
$884$		0			0
$885$	−436.727			−0.493477
$886$		0			0
$887$	370.614	+	554.662i	0.417828	+	0.625324i	0.979358	−	0.202132i	$-0.0647871\pi$
$887$	370.614	+	554.662i	0.417828	+	0.625324i	−0.561530	+	0.827456i	$0.689787\pi$
$888$		0			0
$889$	71.2891	−	358.395i	0.0801902	−	0.403143i
$890$		0			0
$891$	38.3658	+	192.878i	0.0430592	+	0.216473i
$892$		0			0
$893$	−25.4555	+	61.4550i	−0.0285056	+	0.0688186i
$894$		0			0
$895$	−760.643	−	508.245i	−0.849880	−	0.567872i
$896$		0			0
$897$	−138.794	−	138.794i	−0.154731	−	0.154731i
$898$		0			0
$899$	−615.383	+	254.900i	−0.684519	+	0.283537i
$900$		0			0
$901$	746.115	+	618.934i	0.828097	+	0.686941i
$902$		0			0
$903$	−355.586	−	858.460i	−0.393783	−	0.950676i
$904$		0			0
$905$	44.1600	−	44.1600i	0.0487956	−	0.0487956i
$906$		0			0
$907$	100.245	−	150.028i	0.110524	−	0.165411i	−0.772084	−	0.635521i	$-0.780786\pi$
$907$	100.245	−	150.028i	0.110524	−	0.165411i	0.882608	+	0.470109i	$0.155786\pi$
$908$		0			0
$909$	2197.99	+	910.437i	2.41803	+	1.00158i
$910$		0			0
$911$	−1620.68	+	322.374i	−1.77901	+	0.353868i	−0.971693	−	0.236246i	$-0.924083\pi$
$911$	−1620.68	+	322.374i	−1.77901	+	0.353868i	−0.807320	+	0.590114i	$0.799083\pi$
$912$		0			0
$913$	−224.267	−	44.6096i	−0.245638	−	0.0488604i
$914$		0			0
$915$	−653.467	+	436.633i	−0.714172	+	0.477194i
$916$		0			0
$917$			148.158i			0.161569i
$918$		0			0
$919$	630.155			0.685697			0.342848	−	0.939391i	$-0.388608\pi$
$919$	630.155			0.685697			0.342848	+	0.939391i	$0.388608\pi$
$920$		0			0
$921$	−684.906	−	1025.03i	−0.743655	−	1.11296i
$922$		0			0
$923$	110.055	−	553.286i	0.119237	−	0.599443i
$924$		0			0
$925$	−87.9706	−	442.258i	−0.0951034	−	0.478117i
$926$		0			0
$927$	−1275.08	+	3078.31i	−1.37549	+	3.32073i
$928$		0			0
$929$	−1303.36	−	870.877i	−1.40297	−	0.937435i	−0.999751	−	0.0223314i	$-0.992891\pi$
$929$	−1303.36	−	870.877i	−1.40297	−	0.937435i	−0.403220	−	0.915103i	$-0.632109\pi$
$930$		0			0
$931$	246.634	+	246.634i	0.264913	+	0.264913i
$932$		0			0
$933$	−1545.43	+	640.139i	−1.65641	+	0.686109i
$934$		0			0
$935$	44.4806	−	143.897i	0.0475728	−	0.153900i
$936$		0			0
$937$	−291.961	−	704.857i	−0.311591	−	0.752248i	−0.999646	−	0.0265897i	$-0.991535\pi$
$937$	−291.961	−	704.857i	−0.311591	−	0.752248i	0.688055	−	0.725659i	$-0.258465\pi$
$938$		0			0
$939$	−1157.53	+	1157.53i	−1.23273	+	1.23273i
$940$		0			0
$941$	−656.274	+	982.184i	−0.697422	+	1.04377i	0.298575	+	0.954386i	$0.403489\pi$
$941$	−656.274	+	982.184i	−0.697422	+	1.04377i	−0.995998	+	0.0893803i	$0.971511\pi$
$942$		0			0
$943$	245.673	+	101.761i	0.260523	+	0.107912i
$944$		0			0
$945$	551.884	−	109.776i	0.584004	−	0.116166i
$946$		0			0
$947$	1709.91	+	340.121i	1.80560	+	0.359157i	0.979037	−	0.203684i	$-0.0652914\pi$
$947$	1709.91	+	340.121i	1.80560	+	0.359157i	0.826566	+	0.562840i	$0.190291\pi$
$948$		0			0
$949$	−565.172	+	377.636i	−0.595544	+	0.397930i
$950$		0			0
$951$		−	1668.18i		−	1.75413i
$952$		0			0
$953$	−1007.14			−1.05681			−0.528405	−	0.848992i	$-0.677210\pi$
$953$	−1007.14			−1.05681			−0.528405	+	0.848992i	$0.677210\pi$
$954$		0			0
$955$	−228.496	−	341.969i	−0.239263	−	0.358083i
$956$		0			0
$957$	−59.2356	+	297.797i	−0.0618971	+	0.311178i
$958$		0			0
$959$	39.6094	+	199.130i	0.0413028	+	0.207643i
$960$		0			0
$961$	−74.1731	+	179.070i	−0.0771833	+	0.186337i
$962$		0			0
$963$	555.174	+	370.955i	0.576505	+	0.385208i
$964$		0			0
$965$	−52.8101	−	52.8101i	−0.0547255	−	0.0547255i
$966$		0			0
$967$	−499.135	+	206.749i	−0.516169	+	0.213804i	−0.625533	−	0.780198i	$-0.715118\pi$
$967$	−499.135	+	206.749i	−0.516169	+	0.213804i	0.109364	+	0.994002i	$0.465118\pi$
$968$		0			0
$969$	−83.4988	+	804.278i	−0.0861700	+	0.830008i
$970$		0			0
$971$	−153.655	−	370.956i	−0.158244	−	0.382035i	0.824795	−	0.565432i	$-0.191291\pi$
$971$	−153.655	−	370.956i	−0.158244	−	0.382035i	−0.983039	+	0.183397i	$0.941291\pi$
$972$		0			0
$973$	203.924	−	203.924i	0.209583	−	0.209583i
$974$		0			0
$975$	369.511	−	553.013i	0.378986	−	0.567193i
$976$		0			0
$977$	880.902	+	364.881i	0.901639	+	0.373471i	0.784850	−	0.619686i	$-0.212740\pi$
$977$	880.902	+	364.881i	0.901639	+	0.373471i	0.116789	+	0.993157i	$0.462740\pi$
$978$		0			0
$979$	−66.0685	+	13.1418i	−0.0674857	+	0.0134237i
$980$		0			0
$981$	804.433	+	160.012i	0.820014	+	0.163111i
$982$		0			0
$983$	−1186.50	+	792.797i	−1.20702	+	0.806507i	−0.985670	−	0.168686i	$-0.946048\pi$
$983$	−1186.50	+	792.797i	−1.20702	+	0.806507i	−0.221354	+	0.975194i	$0.571048\pi$
$984$		0			0
$985$		−	150.318i		−	0.152607i
$986$		0			0
$987$	−124.641			−0.126282
$988$		0			0
$989$	103.976	+	155.611i	0.105133	+	0.157342i
$990$		0			0
$991$	−54.9030	+	276.016i	−0.0554016	+	0.278523i	−0.998549	−	0.0538524i	$-0.982850\pi$
$991$	−54.9030	+	276.016i	−0.0554016	+	0.278523i	0.943147	+	0.332375i	$0.107850\pi$
$992$		0			0
$993$	−27.0964	−	136.223i	−0.0272874	−	0.137183i
$994$		0			0
$995$	510.751	−	1233.06i	0.513317	−	1.23926i
$996$		0			0
$997$	−447.153	−	298.778i	−0.448499	−	0.299677i	0.310734	−	0.950497i	$-0.399425\pi$
$997$	−447.153	−	298.778i	−0.448499	−	0.299677i	−0.759232	+	0.650820i	$0.774425\pi$
$998$		0			0
$999$	1273.29	+	1273.29i	1.27456	+	1.27456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.3.bh.b.209.1		8
4.3	odd	2		17.3.e.b.5.1	✓	8
12.11	even	2		153.3.p.a.73.1		8
17.7	odd	16	inner	272.3.bh.b.177.1		8
20.3	even	4		425.3.t.d.124.1		8
20.7	even	4		425.3.t.b.124.1		8
20.19	odd	2		425.3.u.a.226.1		8
68.3	even	16		289.3.e.n.249.1		8
68.7	even	16		17.3.e.b.7.1	yes	8
68.11	even	16		289.3.e.h.214.1		8
68.15	odd	8		289.3.e.e.224.1		8
68.19	odd	8		289.3.e.a.224.1		8
68.23	even	16		289.3.e.f.214.1		8
68.27	even	16		289.3.e.g.75.1		8
68.31	even	16		289.3.e.j.249.1		8
68.39	even	16		289.3.e.e.40.1		8
68.43	odd	8		289.3.e.j.65.1		8
68.47	odd	4		289.3.e.h.131.1		8
68.55	odd	4		289.3.e.f.131.1		8
68.59	odd	8		289.3.e.n.65.1		8
68.63	even	16		289.3.e.a.40.1		8
68.67	odd	2		289.3.e.g.158.1		8
204.143	odd	16		153.3.p.a.109.1		8
340.7	odd	16		425.3.t.d.24.1		8
340.143	odd	16		425.3.t.b.24.1		8
340.279	even	16		425.3.u.a.126.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.5.1	✓	8	4.3	odd	2
17.3.e.b.7.1	yes	8	68.7	even	16
153.3.p.a.73.1		8	12.11	even	2
153.3.p.a.109.1		8	204.143	odd	16
272.3.bh.b.177.1		8	17.7	odd	16	inner
272.3.bh.b.209.1		8	1.1	even	1	trivial
289.3.e.a.40.1		8	68.63	even	16
289.3.e.a.224.1		8	68.19	odd	8
289.3.e.e.40.1		8	68.39	even	16
289.3.e.e.224.1		8	68.15	odd	8
289.3.e.f.131.1		8	68.55	odd	4
289.3.e.f.214.1		8	68.23	even	16
289.3.e.g.75.1		8	68.27	even	16
289.3.e.g.158.1		8	68.67	odd	2
289.3.e.h.131.1		8	68.47	odd	4
289.3.e.h.214.1		8	68.11	even	16
289.3.e.j.65.1		8	68.43	odd	8
289.3.e.j.249.1		8	68.31	even	16
289.3.e.n.65.1		8	68.59	odd	8
289.3.e.n.249.1		8	68.3	even	16
425.3.t.b.24.1		8	340.143	odd	16
425.3.t.b.124.1		8	20.7	even	4
425.3.t.d.24.1		8	340.7	odd	16
425.3.t.d.124.1		8	20.3	even	4
425.3.u.a.126.1		8	340.279	even	16
425.3.u.a.226.1		8	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	272.bh (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.88669 + 4.32023i) q^{3} +(-0.711297 + 3.57593i) q^{5} +(0.644047 + 3.23784i) q^{7} +(-6.88730 + 16.6274i) q^{9} +(-2.02046 - 1.35003i) q^{11} +(-7.73173 - 7.73173i) q^{13} +(-17.5022 + 7.24963i) q^{15} +(15.0347 - 7.93458i) q^{17} +(3.50319 + 8.45745i) q^{19} +(-12.1291 + 12.1291i) q^{21} +(1.91942 - 2.87262i) q^{23} +(10.8156 + 4.47998i) q^{25} +(-45.8512 + 9.12037i) q^{27} +(-23.5861 - 4.69157i) q^{29} +(23.0300 - 15.3882i) q^{31} -12.6260i q^{33} -12.0364 q^{35} +(-21.3995 - 32.0267i) q^{37} +(11.0838 - 55.7219i) q^{39} +(15.0157 + 75.4890i) q^{41} +(-20.7301 + 50.0470i) q^{43} +(-54.5596 - 36.4555i) q^{45} +(5.13810 + 5.13810i) q^{47} +(35.2013 - 14.5808i) q^{49} +(77.6797 + 42.0488i) q^{51} +(21.8223 + 52.6837i) q^{53} +(6.26475 - 6.26475i) q^{55} +(-26.4255 + 39.5486i) q^{57} +(21.2985 + 8.82213i) q^{59} +(40.6888 - 8.09351i) q^{61} +(-58.2726 - 11.5911i) q^{63} +(33.1477 - 22.1486i) q^{65} -17.3637i q^{67} +17.9512 q^{69} +(28.6631 + 42.8974i) q^{71} +(12.1277 - 60.9700i) q^{73} +(11.8668 + 59.6583i) q^{75} +(3.06990 - 7.41140i) q^{77} +(-98.5655 - 65.8593i) q^{79} +(-57.2255 - 57.2255i) q^{81} +(86.9369 - 36.0104i) q^{83} +(17.6794 + 59.4070i) q^{85} +(-47.8171 - 115.441i) q^{87} +(19.6021 - 19.6021i) q^{89} +(20.0545 - 30.0137i) q^{91} +(132.961 + 55.0742i) q^{93} +(-32.7351 + 6.51142i) q^{95} +(14.9417 + 2.97209i) q^{97} +(36.3629 - 24.2969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 24 q^{5} + 16 q^{7} + 8 q^{9} - 40 q^{11} - 32 q^{15} - 16 q^{17} + 32 q^{19} - 64 q^{21} + 8 q^{23} + 16 q^{25} - 96 q^{27} + 24 q^{29} - 32 q^{31} - 80 q^{35} - 168 q^{37} + 72 q^{39} - 96 q^{43}+ \cdots - 136 q^{99}+O(q^{100}) \) 8 * q - 24 * q^5 + 16 * q^7 + 8 * q^9 - 40 * q^11 - 32 * q^15 - 16 * q^17 + 32 * q^19 - 64 * q^21 + 8 * q^23 + 16 * q^25 - 96 * q^27 + 24 * q^29 - 32 * q^31 - 80 * q^35 - 168 * q^37 + 72 * q^39 - 96 * q^43 - 88 * q^45 + 80 * q^47 + 8 * q^49 + 176 * q^51 + 96 * q^53 + 8 * q^55 + 248 * q^57 - 8 * q^59 + 264 * q^61 - 8 * q^63 - 32 * q^65 - 208 * q^69 - 32 * q^71 + 24 * q^73 + 192 * q^75 - 216 * q^77 + 96 * q^79 - 224 * q^81 + 88 * q^83 + 512 * q^85 - 312 * q^87 + 288 * q^89 + 24 * q^91 + 280 * q^93 + 152 * q^95 - 344 * q^97 - 136 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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