LMFDB - Embedded newform 272.3.bh.c.129.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [272,3,Mod(65,272)]

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

lf = mfeigenbasis(mf)

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")

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

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			129.1
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	272.129
Dual form			272.3.bh.c.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.675577 + 0.451406i) q^{3} +(7.87510 - 1.56645i) q^{5} +(7.70353 + 1.53233i) q^{7} +(-3.19151 - 7.70500i) q^{9} +O(q^{10})$	\(q+(0.675577 + 0.451406i) q^{3} +(7.87510 - 1.56645i) q^{5} +(7.70353 + 1.53233i) q^{7} +(-3.19151 - 7.70500i) q^{9} +(-4.48649 - 6.71450i) q^{11} +(-0.798835 + 0.798835i) q^{13} +(6.02734 + 2.49661i) q^{15} +(-6.50562 + 15.7060i) q^{17} +(-1.07647 + 2.59882i) q^{19} +(4.51262 + 4.51262i) q^{21} +(7.13426 - 4.76696i) q^{23} +(36.4664 - 15.1049i) q^{25} +(2.74858 - 13.8181i) q^{27} +(-0.599020 - 3.01148i) q^{29} +(7.13254 - 10.6746i) q^{31} -6.56139i q^{33} +63.0663 q^{35} +(19.6817 + 13.1509i) q^{37} +(-0.900273 + 0.179075i) q^{39} +(21.4206 + 4.26082i) q^{41} +(8.89197 + 21.4671i) q^{43} +(-37.2030 - 55.6783i) q^{45} +(-55.6597 + 55.6597i) q^{47} +(11.7262 + 4.85715i) q^{49} +(-11.4848 + 7.67390i) q^{51} +(-22.9922 + 55.5080i) q^{53} +(-45.8495 - 45.8495i) q^{55} +(-1.90036 + 1.26978i) q^{57} +(25.3733 - 10.5100i) q^{59} +(7.11302 - 35.7596i) q^{61} +(-12.7793 - 64.2461i) q^{63} +(-5.03957 + 7.54224i) q^{65} +117.219i q^{67} +6.97157 q^{69} +(-88.1108 - 58.8738i) q^{71} +(-59.8620 + 11.9073i) q^{73} +(31.4543 + 6.25665i) q^{75} +(-24.2730 - 58.6001i) q^{77} +(-52.9382 - 79.2276i) q^{79} +(-44.9799 + 44.9799i) q^{81} +(109.791 + 45.4770i) q^{83} +(-26.6297 + 133.877i) q^{85} +(0.954715 - 2.30489i) q^{87} +(-61.4534 - 61.4534i) q^{89} +(-7.37792 + 4.92977i) q^{91} +(9.63715 - 3.99184i) q^{93} +(-4.40634 + 22.1522i) q^{95} +(4.79748 + 24.1185i) q^{97} +(-37.4165 + 55.9978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 16 q^{5} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 8 * q + 8 * q^3 + 16 * q^5 - 8 * q^7 - 16 * q^9	$ 8 q + 8 q^{3} + 16 q^{5} - 8 q^{7} - 16 q^{9} + 8 q^{11} + 16 q^{13} + 16 q^{15} - 64 q^{21} + 56 q^{23} + 64 q^{25} - 40 q^{27} + 48 q^{29} - 24 q^{31} + 160 q^{35} + 32 q^{37} - 48 q^{39} + 48 q^{41} + 232 q^{43} - 192 q^{47} + 16 q^{49} - 136 q^{51} - 32 q^{53} - 224 q^{55} + 24 q^{57} + 48 q^{59} - 160 q^{61} - 56 q^{63} - 96 q^{65} + 240 q^{69} - 40 q^{71} + 48 q^{73} + 296 q^{75} - 48 q^{77} + 136 q^{79} - 424 q^{81} + 264 q^{83} - 272 q^{85} - 208 q^{87} + 160 q^{89} - 320 q^{91} - 64 q^{93} - 272 q^{95} + 48 q^{97} + 224 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 16 * q^5 - 8 * q^7 - 16 * q^9 + 8 * q^11 + 16 * q^13 + 16 * q^15 - 64 * q^21 + 56 * q^23 + 64 * q^25 - 40 * q^27 + 48 * q^29 - 24 * q^31 + 160 * q^35 + 32 * q^37 - 48 * q^39 + 48 * q^41 + 232 * q^43 - 192 * q^47 + 16 * q^49 - 136 * q^51 - 32 * q^53 - 224 * q^55 + 24 * q^57 + 48 * q^59 - 160 * q^61 - 56 * q^63 - 96 * q^65 + 240 * q^69 - 40 * q^71 + 48 * q^73 + 296 * q^75 - 48 * q^77 + 136 * q^79 - 424 * q^81 + 264 * q^83 - 272 * q^85 - 208 * q^87 + 160 * q^89 - 320 * q^91 - 64 * q^93 - 272 * q^95 + 48 * q^97 + 224 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$69$	$239$	$241$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{16}\right)$

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
$3$	0.675577	+	0.451406i	0.225192	+	0.150469i	0.663049	−	0.748576i	$-0.269262\pi$
$3$	0.675577	+	0.451406i	0.225192	+	0.150469i	−0.437857	+	0.899045i	$0.644262\pi$
$4$		0			0
$5$	7.87510	−	1.56645i	1.57502	−	0.313291i	0.671224	−	0.741255i	$-0.265769\pi$
$5$	7.87510	−	1.56645i	1.57502	−	0.313291i	0.903796	+	0.427964i	$0.140769\pi$
$6$		0			0
$7$	7.70353	+	1.53233i	1.10050	+	0.218904i	0.711746	−	0.702436i	$-0.247904\pi$
$7$	7.70353	+	1.53233i	1.10050	+	0.218904i	0.388757	+	0.921340i	$0.372904\pi$
$8$		0			0
$9$	−3.19151	−	7.70500i	−0.354613	−	0.856111i
$10$		0			0
$11$	−4.48649	−	6.71450i	−0.407863	−	0.610410i	0.569497	−	0.821993i	$-0.307138\pi$
$11$	−4.48649	−	6.71450i	−0.407863	−	0.610410i	−0.977360	+	0.211584i	$0.932138\pi$
$12$		0			0
$13$	−0.798835	+	0.798835i	−0.0614489	+	0.0614489i	−0.737163	−	0.675715i	$-0.763835\pi$
$13$	−0.798835	+	0.798835i	−0.0614489	+	0.0614489i	0.675715	+	0.737163i	$0.263835\pi$
$14$		0			0
$15$	6.02734	+	2.49661i	0.401823	+	0.166440i
$16$		0			0
$17$	−6.50562	+	15.7060i	−0.382683	+	0.923880i
$17$	−6.50562	+	15.7060i	−0.382683	+	0.923880i
$18$		0			0
$19$	−1.07647	+	2.59882i	−0.0566561	+	0.136780i	−0.949673	−	0.313244i	$-0.898584\pi$
$19$	−1.07647	+	2.59882i	−0.0566561	+	0.136780i	0.893017	+	0.450023i	$0.148584\pi$
$20$		0			0
$21$	4.51262	+	4.51262i	0.214887	+	0.214887i
$22$		0			0
$23$	7.13426	−	4.76696i	0.310185	−	0.207259i	−0.390727	−	0.920507i	$-0.627776\pi$
$23$	7.13426	−	4.76696i	0.310185	−	0.207259i	0.700912	+	0.713247i	$0.252776\pi$
$24$		0			0
$25$	36.4664	−	15.1049i	1.45866	−	0.604195i
$26$		0			0
$27$	2.74858	−	13.8181i	0.101799	−	0.511780i
$28$		0			0
$29$	−0.599020	−	3.01148i	−0.0206559	−	0.103844i	0.969082	−	0.246739i	$-0.0793590\pi$
$29$	−0.599020	−	3.01148i	−0.0206559	−	0.103844i	−0.989738	+	0.142895i	$0.954359\pi$
$30$		0			0
$31$	7.13254	−	10.6746i	0.230082	−	0.344342i	−0.698408	−	0.715700i	$-0.746108\pi$
$31$	7.13254	−	10.6746i	0.230082	−	0.344342i	0.928490	+	0.371358i	$0.121108\pi$
$32$		0			0
$33$		−	6.56139i		−	0.198830i
$34$		0			0
$35$	63.0663			1.80190
$36$		0			0
$37$	19.6817	+	13.1509i	0.531938	+	0.355429i	0.792349	−	0.610068i	$-0.208858\pi$
$37$	19.6817	+	13.1509i	0.531938	+	0.355429i	−0.260411	+	0.965498i	$0.583858\pi$
$38$		0			0
$39$	−0.900273	+	0.179075i	−0.0230839	+	0.00459168i
$40$		0			0
$41$	21.4206	+	4.26082i	0.522453	+	0.103922i	0.449270	−	0.893396i	$-0.351684\pi$
$41$	21.4206	+	4.26082i	0.522453	+	0.103922i	0.0731833	+	0.997319i	$0.476684\pi$
$42$		0			0
$43$	8.89197	+	21.4671i	0.206790	+	0.499235i	0.992914	−	0.118833i	$-0.0379154\pi$
$43$	8.89197	+	21.4671i	0.206790	+	0.499235i	−0.786124	+	0.618069i	$0.787915\pi$
$44$		0			0
$45$	−37.2030	−	55.6783i	−0.826734	−	1.23729i
$46$		0			0
$47$	−55.6597	+	55.6597i	−1.18425	+	1.18425i	−0.205617	+	0.978632i	$0.565920\pi$
$47$	−55.6597	+	55.6597i	−1.18425	+	1.18425i	−0.978632	+	0.205617i	$0.934080\pi$
$48$		0			0
$49$	11.7262	+	4.85715i	0.239310	+	0.0991254i
$50$		0			0
$51$	−11.4848	+	7.67390i	−0.225192	+	0.150469i
$52$		0			0
$53$	−22.9922	+	55.5080i	−0.433815	+	1.04732i	0.544232	+	0.838935i	$0.316821\pi$
$53$	−22.9922	+	55.5080i	−0.433815	+	1.04732i	−0.978047	+	0.208386i	$0.933179\pi$
$54$		0			0
$55$	−45.8495	−	45.8495i	−0.833627	−	0.833627i
$56$		0			0
$57$	−1.90036	+	1.26978i	−0.0333396	+	0.0222768i
$58$		0			0
$59$	25.3733	−	10.5100i	0.430057	−	0.178135i	−0.157146	−	0.987575i	$-0.550229\pi$
$59$	25.3733	−	10.5100i	0.430057	−	0.178135i	0.587202	+	0.809440i	$0.300229\pi$
$60$		0			0
$61$	7.11302	−	35.7596i	0.116607	−	0.586223i	−0.877659	−	0.479286i	$-0.840896\pi$
$61$	7.11302	−	35.7596i	0.116607	−	0.586223i	0.994266	−	0.106937i	$-0.0341043\pi$
$62$		0			0
$63$	−12.7793	−	64.2461i	−0.202847	−	1.01978i
$64$		0			0
$65$	−5.03957	+	7.54224i	−0.0775318	+	0.116035i
$66$		0			0
$67$			117.219i			1.74953i	0.484544	+	0.874767i	$0.338985\pi$
$67$			117.219i			1.74953i	−0.484544	+	0.874767i	$0.661015\pi$
$68$		0			0
$69$	6.97157			0.101037
$70$		0			0
$71$	−88.1108	−	58.8738i	−1.24100	−	0.829208i	−0.250685	−	0.968069i	$-0.580656\pi$
$71$	−88.1108	−	58.8738i	−1.24100	−	0.829208i	−0.990312	+	0.138861i	$0.955656\pi$
$72$		0			0
$73$	−59.8620	+	11.9073i	−0.820028	+	0.163114i	−0.587239	−	0.809414i	$-0.699785\pi$
$73$	−59.8620	+	11.9073i	−0.820028	+	0.163114i	−0.232789	+	0.972527i	$0.574785\pi$
$74$		0			0
$75$	31.4543	+	6.25665i	0.419390	+	0.0834220i
$76$		0			0
$77$	−24.2730	−	58.6001i	−0.315233	−	0.761041i
$78$		0			0
$79$	−52.9382	−	79.2276i	−0.670103	−	1.00288i	−0.998301	−	0.0582714i	$-0.981441\pi$
$79$	−52.9382	−	79.2276i	−0.670103	−	1.00288i	0.328197	−	0.944609i	$-0.393559\pi$
$80$		0			0
$81$	−44.9799	+	44.9799i	−0.555308	+	0.555308i
$82$		0			0
$83$	109.791	+	45.4770i	1.32279	+	0.547916i	0.928589	−	0.371110i	$-0.121023\pi$
$83$	109.791	+	45.4770i	1.32279	+	0.547916i	0.394197	+	0.919026i	$0.371023\pi$
$84$		0			0
$85$	−26.6297	+	133.877i	−0.313291	+	1.57502i
$86$		0			0
$87$	0.954715	−	2.30489i	0.0109737	−	0.0264929i
$88$		0			0
$89$	−61.4534	−	61.4534i	−0.690488	−	0.690488i	0.271851	−	0.962339i	$-0.412364\pi$
$89$	−61.4534	−	61.4534i	−0.690488	−	0.690488i	−0.962339	+	0.271851i	$0.912364\pi$
$90$		0			0
$91$	−7.37792	+	4.92977i	−0.0810761	+	0.0541733i
$92$		0			0
$93$	9.63715	−	3.99184i	0.103625	−	0.0429230i
$94$		0			0
$95$	−4.40634	+	22.1522i	−0.0463826	+	0.233181i
$96$		0			0
$97$	4.79748	+	24.1185i	0.0494585	+	0.248645i	0.997603	−	0.0691943i	$-0.0220428\pi$
$97$	4.79748	+	24.1185i	0.0494585	+	0.248645i	−0.948145	+	0.317839i	$0.897043\pi$
$98$		0			0
$99$	−37.4165	+	55.9978i	−0.377945	+	0.565635i
$100$		0			0
$101$			7.70266i			0.0762640i	0.999273	+	0.0381320i	$0.0121407\pi$
$101$			7.70266i			0.0762640i	−0.999273	+	0.0381320i	$0.987859\pi$
$102$		0			0
$103$	−41.5688			−0.403581			−0.201790	−	0.979429i	$-0.564676\pi$
$103$	−41.5688			−0.403581			−0.201790	+	0.979429i	$0.564676\pi$
$104$		0			0
$105$	42.6061	+	28.4685i	0.405773	+	0.271129i
$106$		0			0
$107$	−86.7136	+	17.2484i	−0.810407	+	0.161200i	−0.582866	−	0.812568i	$-0.698069\pi$
$107$	−86.7136	+	17.2484i	−0.810407	+	0.161200i	−0.227541	+	0.973768i	$0.573069\pi$
$108$		0			0
$109$	18.2754	+	3.63521i	0.167665	+	0.0333506i	0.278209	−	0.960521i	$-0.410259\pi$
$109$	18.2754	+	3.63521i	0.167665	+	0.0333506i	−0.110544	+	0.993871i	$0.535259\pi$
$110$		0			0
$111$	7.36011	+	17.7689i	0.0663073	+	0.160080i
$112$		0			0
$113$	−33.6909	−	50.4220i	−0.298150	−	0.446212i	0.651903	−	0.758302i	$-0.273971\pi$
$113$	−33.6909	−	50.4220i	−0.298150	−	0.446212i	−0.950053	+	0.312090i	$0.898971\pi$
$114$		0			0
$115$	48.7158	−	48.7158i	0.423615	−	0.423615i
$116$		0			0
$117$	8.70452	+	3.60553i	0.0743976	+	0.0308165i
$118$		0			0
$119$	−74.1828	+	111.022i	−0.623385	+	0.932962i
$120$		0			0
$121$	21.3487	−	51.5403i	0.176436	−	0.425953i
$122$		0			0
$123$	12.5479	+	12.5479i	0.102015	+	0.102015i
$124$		0			0
$125$	96.6108	−	64.5533i	0.772886	−	0.516426i
$126$		0			0
$127$	−110.168	+	45.6333i	−0.867468	+	0.359317i	−0.771624	−	0.636079i	$-0.780555\pi$
$127$	−110.168	+	45.6333i	−0.867468	+	0.359317i	−0.0958444	+	0.995396i	$0.530555\pi$
$128$		0			0
$129$	−3.68317	+	18.5166i	−0.0285517	+	0.143539i
$130$		0			0
$131$	−33.4238	−	168.033i	−0.255144	−	1.28269i	−0.869605	−	0.493748i	$-0.835627\pi$
$131$	−33.4238	−	168.033i	−0.255144	−	1.28269i	0.614461	−	0.788947i	$-0.289373\pi$
$132$		0			0
$133$	−12.2748	+	18.3706i	−0.0922919	+	0.138125i
$134$		0			0
$135$		−	113.124i		−	0.837956i
$136$		0			0
$137$	−173.113			−1.26360			−0.631799	−	0.775132i	$-0.717683\pi$
$137$	−173.113			−1.26360			−0.631799	+	0.775132i	$0.717683\pi$
$138$		0			0
$139$	149.307	+	99.7637i	1.07415	+	0.717724i	0.961193	−	0.275876i	$-0.0889678\pi$
$139$	149.307	+	99.7637i	1.07415	+	0.717724i	0.112957	+	0.993600i	$0.463968\pi$
$140$		0			0
$141$	−62.7276	+	12.4773i	−0.444876	+	0.0884914i
$142$		0			0
$143$	8.94775	+	1.77982i	0.0625717	+	0.0124463i
$144$		0			0
$145$	−9.43469	−	22.7774i	−0.0650668	−	0.157085i
$146$		0			0
$147$	5.72939	+	8.57464i	0.0389755	+	0.0583309i
$148$		0			0
$149$	31.6842	−	31.6842i	0.212646	−	0.212646i	−0.592745	−	0.805391i	$-0.701956\pi$
$149$	31.6842	−	31.6842i	0.212646	−	0.212646i	0.805391	+	0.592745i	$0.201956\pi$
$150$		0			0
$151$	121.384	+	50.2789i	0.803868	+	0.332973i	0.746504	−	0.665380i	$-0.231731\pi$
$151$	121.384	+	50.2789i	0.803868	+	0.332973i	0.0573634	+	0.998353i	$0.481731\pi$
$152$		0			0
$153$	141.777			0.926648
$154$		0			0
$155$	39.4482	−	95.2363i	0.254504	−	0.614428i
$156$		0			0
$157$	25.4694	+	25.4694i	0.162225	+	0.162225i	0.783552	−	0.621327i	$-0.213406\pi$
$157$	25.4694	+	25.4694i	0.162225	+	0.162225i	−0.621327	+	0.783552i	$0.713406\pi$
$158$		0			0
$159$	−40.5896	+	27.1211i	−0.255281	+	0.170573i
$160$		0			0
$161$	62.2635	−	25.7904i	0.386730	−	0.160189i
$162$		0			0
$163$	−31.1596	+	156.650i	−0.191163	+	0.961041i	0.759427	+	0.650592i	$0.225479\pi$
$163$	−31.1596	+	156.650i	−0.191163	+	0.961041i	−0.950590	+	0.310449i	$0.899521\pi$
$164$		0			0
$165$	−10.2781	−	51.6716i	−0.0622916	−	0.313161i
$166$		0			0
$167$	61.5214	−	92.0734i	0.368392	−	0.551337i	−0.600246	−	0.799816i	$-0.704930\pi$
$167$	61.5214	−	92.0734i	0.368392	−	0.551337i	0.968637	+	0.248478i	$0.0799305\pi$
$168$		0			0
$169$			167.724i			0.992448i
$170$		0			0
$171$	23.4594			0.137190
$172$		0			0
$173$	−148.047	−	98.9216i	−0.855761	−	0.571801i	0.0484797	−	0.998824i	$-0.484562\pi$
$173$	−148.047	−	98.9216i	−0.855761	−	0.571801i	−0.904241	+	0.427023i	$0.859562\pi$
$174$		0			0
$175$	304.066	−	60.4824i	1.73752	−	0.345614i
$176$		0			0
$177$	21.8859	+	4.35338i	0.123649	+	0.0245954i
$178$		0			0
$179$	−96.5028	−	232.978i	−0.539122	−	1.30155i	−0.925337	−	0.379146i	$-0.876218\pi$
$179$	−96.5028	−	232.978i	−0.539122	−	1.30155i	0.386215	−	0.922409i	$-0.373782\pi$
$180$		0			0
$181$	167.421	+	250.563i	0.924977	+	1.38433i	0.923197	+	0.384328i	$0.125567\pi$
$181$	167.421	+	250.563i	0.924977	+	1.38433i	0.00178027	+	0.999998i	$0.499433\pi$
$182$		0			0
$183$	20.9475	−	20.9475i	0.114467	−	0.114467i
$184$		0			0
$185$	175.596	+	72.7341i	0.949165	+	0.393157i
$186$		0			0
$187$	134.645	−	26.7826i	0.720027	−	0.143222i
$188$		0			0
$189$	42.3476	−	102.236i	0.224061	−	0.540931i
$190$		0			0
$191$	−93.7287	−	93.7287i	−0.490726	−	0.490726i	0.417809	−	0.908535i	$-0.362798\pi$
$191$	−93.7287	−	93.7287i	−0.490726	−	0.490726i	−0.908535	+	0.417809i	$0.862798\pi$
$192$		0			0
$193$	264.917	−	177.012i	1.37263	−	0.917161i	0.372687	−	0.927957i	$-0.378436\pi$
$193$	264.917	−	177.012i	1.37263	−	0.917161i	0.999942	+	0.0107958i	$0.00343648\pi$
$194$		0			0
$195$	−6.80923	+	2.82047i	−0.0349191	+	0.0144640i
$196$		0			0
$197$	22.5650	−	113.442i	0.114543	−	0.575847i	−0.880300	−	0.474418i	$-0.842659\pi$
$197$	22.5650	−	113.442i	0.114543	−	0.575847i	0.994843	−	0.101429i	$-0.0323415\pi$
$198$		0			0
$199$	57.7166	+	290.161i	0.290033	+	1.45809i	0.801088	+	0.598547i	$0.204255\pi$
$199$	57.7166	+	290.161i	0.290033	+	1.45809i	−0.511055	+	0.859548i	$0.670745\pi$
$200$		0			0
$201$	−52.9132	+	79.1902i	−0.263250	+	0.393981i
$202$		0			0
$203$		−	24.1169i		−	0.118802i
$204$		0			0
$205$	175.364			0.855432
$206$		0			0
$207$	−59.4985	−	39.7556i	−0.287432	−	0.192056i
$208$		0			0
$209$	22.2793	−	4.43163i	0.106600	−	0.0212040i
$210$		0			0
$211$	225.325	+	44.8199i	1.06789	+	0.212417i	0.697592	−	0.716495i	$-0.254255\pi$
$211$	225.325	+	44.8199i	1.06789	+	0.212417i	0.370300	+	0.928912i	$0.379255\pi$
$212$		0			0
$213$	−32.9496	−	79.5475i	−0.154693	−	0.373462i
$214$		0			0
$215$	103.652	+	155.127i	0.482104	+	0.721520i
$216$		0			0
$217$	71.3026	−	71.3026i	0.328584	−	0.328584i
$218$		0			0
$219$	−45.8164	−	18.9778i	−0.209207	−	0.0866565i
$220$		0			0
$221$	−7.34955	−	17.7434i	−0.0332559	−	0.0802868i
$222$		0			0
$223$	139.061	−	335.723i	0.623593	−	1.50549i	−0.223863	−	0.974621i	$-0.571867\pi$
$223$	139.061	−	335.723i	0.623593	−	1.50549i	0.847456	−	0.530865i	$-0.178133\pi$
$224$		0			0
$225$	−232.766	−	232.766i	−1.03452	−	1.03452i
$226$		0			0
$227$	80.5890	−	53.8478i	0.355017	−	0.237215i	−0.365253	−	0.930908i	$-0.619018\pi$
$227$	80.5890	−	53.8478i	0.355017	−	0.237215i	0.720271	+	0.693693i	$0.244018\pi$
$228$		0			0
$229$	−334.120	+	138.397i	−1.45904	+	0.604353i	−0.964329	−	0.264706i	$-0.914725\pi$
$229$	−334.120	+	138.397i	−1.45904	+	0.604353i	−0.494708	+	0.869059i	$0.664725\pi$
$230$		0			0
$231$	10.0542	−	50.5458i	0.0435246	−	0.218813i
$232$		0			0
$233$	54.6542	+	274.765i	0.234567	+	1.17925i	0.901045	+	0.433725i	$0.142801\pi$
$233$	54.6542	+	274.765i	0.234567	+	1.17925i	−0.666478	+	0.745525i	$0.732199\pi$
$234$		0			0
$235$	−351.137	+	525.514i	−1.49420	+	2.23623i
$236$		0			0
$237$		−	77.4209i		−	0.326670i
$238$		0			0
$239$	−328.551			−1.37469			−0.687345	−	0.726331i	$-0.741224\pi$
$239$	−328.551			−1.37469			−0.687345	+	0.726331i	$0.741224\pi$
$240$		0			0
$241$	−201.560	−	134.678i	−0.836349	−	0.558831i	0.0620186	−	0.998075i	$-0.480246\pi$
$241$	−201.560	−	134.678i	−0.836349	−	0.558831i	−0.898368	+	0.439244i	$0.855246\pi$
$242$		0			0
$243$	−175.054	+	34.8204i	−0.720387	+	0.143294i
$244$		0			0
$245$	99.9534	+	19.8820i	0.407973	+	0.0811509i
$246$		0			0
$247$	−1.21611	−	2.93595i	−0.00492352	−	0.0118864i
$248$		0			0
$249$	53.6438	+	80.2836i	0.215437	+	0.322424i
$250$		0			0
$251$	155.463	−	155.463i	0.619375	−	0.619375i	−0.325996	−	0.945371i	$-0.605700\pi$
$251$	155.463	−	155.463i	0.619375	−	0.619375i	0.945371	+	0.325996i	$0.105700\pi$
$252$		0			0
$253$	−64.0155	−	26.5161i	−0.253026	−	0.104807i
$254$		0			0
$255$	−78.4231	+	78.4231i	−0.307542	+	0.307542i
$256$		0			0
$257$	124.463	−	300.480i	0.484292	−	1.16918i	−0.473260	−	0.880923i	$-0.656923\pi$
$257$	124.463	−	300.480i	0.484292	−	1.16918i	0.957552	−	0.288261i	$-0.0930772\pi$
$258$		0			0
$259$	131.467	+	131.467i	0.507595	+	0.507595i
$260$		0			0
$261$	−21.2917	+	14.2266i	−0.0815772	+	0.0545082i
$262$		0			0
$263$	−128.172	+	53.0907i	−0.487347	+	0.201866i	−0.612806	−	0.790233i	$-0.709959\pi$
$263$	−128.172	+	53.0907i	−0.487347	+	0.201866i	0.125460	+	0.992099i	$0.459959\pi$
$264$		0			0
$265$	−94.1149	+	473.147i	−0.355150	+	1.78546i
$266$		0			0
$267$	−13.7761	−	69.2570i	−0.0515957	−	0.259389i
$268$		0			0
$269$	−180.493	+	270.126i	−0.670976	+	1.00419i	0.327267	+	0.944932i	$0.393872\pi$
$269$	−180.493	+	270.126i	−0.670976	+	1.00419i	−0.998243	+	0.0592547i	$0.981128\pi$
$270$		0			0
$271$		−	19.1867i		−	0.0707996i	−0.999373	−	0.0353998i	$-0.988730\pi$
$271$		−	19.1867i		−	0.0707996i	0.999373	−	0.0353998i	$-0.0112705\pi$
$272$		0			0
$273$	−7.20968			−0.0264091
$274$		0			0
$275$	−265.028	−	177.086i	−0.963738	−	0.643949i
$276$		0			0
$277$	302.084	−	60.0883i	1.09056	−	0.216925i	0.383118	−	0.923700i	$-0.374850\pi$
$277$	302.084	−	60.0883i	1.09056	−	0.216925i	0.707439	+	0.706774i	$0.249850\pi$
$278$		0			0
$279$	−105.011	−	20.8880i	−0.376385	−	0.0748676i
$280$		0			0
$281$	−33.1106	−	79.9361i	−0.117831	−	0.284470i	0.853949	−	0.520356i	$-0.174201\pi$
$281$	−33.1106	−	79.9361i	−0.117831	−	0.284470i	−0.971781	+	0.235886i	$0.924201\pi$
$282$		0			0
$283$	−4.15656	−	6.22073i	−0.0146875	−	0.0219814i	0.824053	−	0.566512i	$-0.191708\pi$
$283$	−4.15656	−	6.22073i	−0.0146875	−	0.0219814i	−0.838741	+	0.544531i	$0.816708\pi$
$284$		0			0
$285$	−12.9764	+	12.9764i	−0.0455314	+	0.0455314i
$286$		0			0
$287$	158.485	+	65.6466i	0.552213	+	0.228734i
$288$		0			0
$289$	−204.354	−	204.354i	−0.707107	−	0.707107i
$290$		0			0
$291$	−7.64619	+	18.4595i	−0.0262756	+	0.0634348i
$292$		0			0
$293$	54.4583	+	54.4583i	0.185864	+	0.185864i	0.793906	−	0.608041i	$-0.208044\pi$
$293$	54.4583	+	54.4583i	0.185864	+	0.185864i	−0.608041	+	0.793906i	$0.708044\pi$
$294$		0			0
$295$	183.354	−	122.513i	0.621540	−	0.415300i
$296$		0			0
$297$	−105.113	+	43.5392i	−0.353915	+	0.146597i
$298$		0			0
$299$	−1.89108	+	9.50711i	−0.00632469	+	0.0317964i
$300$		0			0
$301$	35.6049	+	178.998i	0.118289	+	0.594677i
$302$		0			0
$303$	−3.47703	+	5.20374i	−0.0114753	+	0.0171741i
$304$		0			0
$305$		−	292.752i		−	0.959844i
$306$		0			0
$307$	159.680			0.520132			0.260066	−	0.965591i	$-0.416256\pi$
$307$	159.680			0.520132			0.260066	+	0.965591i	$0.416256\pi$
$308$		0			0
$309$	−28.0829	−	18.7644i	−0.0908832	−	0.0607262i
$310$		0			0
$311$	326.615	−	64.9678i	1.05021	−	0.208900i	0.360331	−	0.932825i	$-0.382664\pi$
$311$	326.615	−	64.9678i	1.05021	−	0.208900i	0.689879	+	0.723925i	$0.257664\pi$
$312$		0			0
$313$	386.986	+	76.9763i	1.23638	+	0.245931i	0.769647	−	0.638470i	$-0.220432\pi$
$313$	386.986	+	76.9763i	1.23638	+	0.245931i	0.466729	+	0.884400i	$0.345432\pi$
$314$		0			0
$315$	−201.277	−	485.926i	−0.638975	−	1.54262i
$316$		0			0
$317$	−77.2775	−	115.654i	−0.243778	−	0.364839i	0.689323	−	0.724454i	$-0.257908\pi$
$317$	−77.2775	−	115.654i	−0.243778	−	0.364839i	−0.933101	+	0.359615i	$0.882908\pi$
$318$		0			0
$319$	−17.5331	+	17.5331i	−0.0549627	+	0.0549627i
$320$		0			0
$321$	−66.3677	−	27.4904i	−0.206753	−	0.0856399i
$322$		0			0
$323$	−33.8138	−	33.8138i	−0.104687	−	0.104687i
$324$		0			0
$325$	−17.0643	+	41.1970i	−0.0525057	+	0.126760i
$326$		0			0
$327$	10.7055	+	10.7055i	0.0327385	+	0.0327385i
$328$		0			0
$329$	−514.065	+	343.487i	−1.56251	+	1.04403i
$330$		0			0
$331$	−146.717	+	60.7720i	−0.443252	+	0.183601i	−0.593136	−	0.805103i	$-0.702110\pi$
$331$	−146.717	+	60.7720i	−0.443252	+	0.183601i	0.149883	+	0.988704i	$0.452110\pi$
$332$		0			0
$333$	38.5132	−	193.619i	0.115655	−	0.581438i
$334$		0			0
$335$	183.618	+	923.109i	0.548113	+	2.75555i
$336$		0			0
$337$	−267.981	+	401.062i	−0.795195	+	1.19009i	0.183144	+	0.983086i	$0.441372\pi$
$337$	−267.981	+	401.062i	−0.795195	+	1.19009i	−0.978339	+	0.207008i	$0.933628\pi$
$338$		0			0
$339$		−	49.2722i		−	0.145346i
$340$		0			0
$341$	−103.675			−0.304031
$342$		0			0
$343$	−237.116	−	158.436i	−0.691299	−	0.461912i
$344$		0			0
$345$	54.9018	−	10.9207i	0.159136	−	0.0316541i
$346$		0			0
$347$	19.4096	+	3.86080i	0.0559353	+	0.0111262i	0.222979	−	0.974823i	$-0.428422\pi$
$347$	19.4096	+	3.86080i	0.0559353	+	0.0111262i	−0.167043	+	0.985950i	$0.553422\pi$
$348$		0			0
$349$	−149.801	−	361.651i	−0.429229	−	1.03625i	−0.979533	−	0.201286i	$-0.935488\pi$
$349$	−149.801	−	361.651i	−0.429229	−	1.03625i	0.550304	−	0.834965i	$-0.314512\pi$
$350$		0			0
$351$	8.84268	+	13.2340i	0.0251928	+	0.0377037i
$352$		0			0
$353$	138.024	−	138.024i	0.391003	−	0.391003i	−0.484042	−	0.875045i	$-0.660832\pi$
$353$	138.024	−	138.024i	0.391003	−	0.391003i	0.875045	+	0.484042i	$0.160832\pi$
$354$		0			0
$355$	−786.104	−	325.615i	−2.21438	−	0.917226i
$356$		0			0
$357$	−100.232	+	41.5176i	−0.280763	+	0.116296i
$358$		0			0
$359$	−136.163	+	328.726i	−0.379284	+	0.915672i	0.612817	+	0.790225i	$0.290036\pi$
$359$	−136.163	+	328.726i	−0.379284	+	0.915672i	−0.992100	+	0.125447i	$0.959964\pi$
$360$		0			0
$361$	249.670	+	249.670i	0.691608	+	0.691608i
$362$		0			0
$363$	37.6883	−	25.1825i	0.103824	−	0.0693733i
$364$		0			0
$365$	−452.767	+	187.542i	−1.24046	+	0.513814i
$366$		0			0
$367$	15.9442	−	80.1568i	0.0434446	−	0.218411i	−0.952964	−	0.303083i	$-0.901984\pi$
$367$	15.9442	−	80.1568i	0.0434446	−	0.218411i	0.996409	+	0.0846717i	$0.0269842\pi$
$368$		0			0
$369$	−35.5345	−	178.644i	−0.0962994	−	0.484130i
$370$		0			0
$371$	−262.177	+	392.376i	−0.706677	+	1.05762i
$372$		0			0
$373$			76.8209i			0.205954i	0.994684	+	0.102977i	$0.0328368\pi$
$373$			76.8209i			0.205954i	−0.994684	+	0.102977i	$0.967163\pi$
$374$		0			0
$375$	94.4077			0.251754
$376$		0			0
$377$	2.88419	+	1.92716i	0.00765038	+	0.00511182i
$378$		0			0
$379$	−577.940	+	114.959i	−1.52491	+	0.303323i	−0.885169	−	0.465269i	$-0.845957\pi$
$379$	−577.940	+	114.959i	−1.52491	+	0.303323i	−0.639739	+	0.768592i	$0.720957\pi$
$380$		0			0
$381$	−95.0264	−	18.9019i	−0.249413	−	0.0496113i
$382$		0			0
$383$	89.4016	+	215.834i	0.233424	+	0.563537i	0.996576	−	0.0826832i	$-0.0263490\pi$
$383$	89.4016	+	215.834i	0.233424	+	0.563537i	−0.763151	+	0.646220i	$0.776349\pi$
$384$		0			0
$385$	−282.946	−	423.459i	−0.734926	−	1.09989i
$386$		0			0
$387$	137.025	−	137.025i	0.354070	−	0.354070i
$388$		0			0
$389$	372.916	+	154.467i	0.958653	+	0.397087i	0.806477	−	0.591266i	$-0.201372\pi$
$389$	372.916	+	154.467i	0.958653	+	0.397087i	0.152177	+	0.988353i	$0.451372\pi$
$390$		0			0
$391$	28.4569	+	143.062i	0.0727797	+	0.365888i
$392$		0			0
$393$	53.2707	−	128.607i	0.135549	−	0.327244i
$394$		0			0
$395$	−541.000	−	541.000i	−1.36962	−	1.36962i
$396$		0			0
$397$	219.332	−	146.553i	0.552474	−	0.369151i	−0.247776	−	0.968817i	$-0.579700\pi$
$397$	219.332	−	146.553i	0.552474	−	0.369151i	0.800251	+	0.599666i	$0.204700\pi$
$398$		0			0
$399$	−16.5852	+	6.86980i	−0.0415668	+	0.0172175i
$400$		0			0
$401$	46.6830	−	234.691i	0.116416	−	0.585265i	−0.877904	−	0.478837i	$-0.841059\pi$
$401$	46.6830	−	234.691i	0.116416	−	0.585265i	0.994320	−	0.106428i	$-0.0339414\pi$
$402$		0			0
$403$	2.82952	+	14.2250i	0.00702114	+	0.0352977i
$404$		0			0
$405$	−283.762	+	424.680i	−0.700648	+	1.04859i
$406$		0			0
$407$		−	191.154i		−	0.469666i
$408$		0			0
$409$	259.903			0.635461			0.317730	−	0.948181i	$-0.397079\pi$
$409$	259.903			0.635461			0.317730	+	0.948181i	$0.397079\pi$
$410$		0			0
$411$	−116.951	−	78.1442i	−0.284552	−	0.190132i
$412$		0			0
$413$	211.569	−	42.0837i	0.512274	−	0.101898i
$414$		0			0
$415$	935.855	+	186.153i	2.25507	+	0.448562i
$416$		0			0
$417$	55.8343	+	134.796i	0.133895	+	0.323252i
$418$		0			0
$419$	95.3087	+	142.640i	0.227467	+	0.340429i	0.927594	−	0.373590i	$-0.121873\pi$
$419$	95.3087	+	142.640i	0.227467	+	0.340429i	−0.700127	+	0.714018i	$0.746873\pi$
$420$		0			0
$421$	443.214	−	443.214i	1.05276	−	1.05276i	0.0542356	−	0.998528i	$-0.482728\pi$
$421$	443.214	−	443.214i	1.05276	−	1.05276i	0.998528	−	0.0542356i	$-0.0172722\pi$
$422$		0			0
$423$	606.497	+	251.219i	1.43380	+	0.593899i
$424$		0			0
$425$			671.006i			1.57884i
$426$		0			0
$427$	109.591	−	264.575i	0.256653	−	0.619614i
$428$		0			0
$429$	5.24147	+	5.24147i	0.0122179	+	0.0122179i
$430$		0			0
$431$	633.734	−	423.447i	1.47038	−	0.982477i	0.475684	−	0.879616i	$-0.342201\pi$
$431$	633.734	−	423.447i	1.47038	−	0.982477i	0.994696	−	0.102860i	$-0.0327995\pi$
$432$		0			0
$433$	87.4681	−	36.2305i	0.202005	−	0.0836732i	−0.279387	−	0.960179i	$-0.590131\pi$
$433$	87.4681	−	36.2305i	0.202005	−	0.0836732i	0.481392	+	0.876505i	$0.340131\pi$
$434$		0			0
$435$	3.90798	−	19.6467i	0.00898385	−	0.0451649i
$436$		0			0
$437$	4.70868	+	23.6721i	0.0107750	+	0.0541696i
$438$		0			0
$439$	20.5441	−	30.7465i	0.0467976	−	0.0700375i	−0.807333	−	0.590096i	$-0.799090\pi$
$439$	20.5441	−	30.7465i	0.0467976	−	0.0700375i	0.854131	+	0.520059i	$0.174090\pi$
$440$		0			0
$441$		−	105.852i		−	0.240027i
$442$		0			0
$443$	634.146			1.43148			0.715740	−	0.698367i	$-0.246089\pi$
$443$	634.146			1.43148			0.715740	+	0.698367i	$0.246089\pi$
$444$		0			0
$445$	−580.216	−	387.688i	−1.30386	−	0.871209i
$446$		0			0
$447$	35.7076	−	7.10268i	0.0798828	−	0.0158897i
$448$		0			0
$449$	433.336	+	86.1959i	0.965114	+	0.191973i	0.652400	−	0.757874i	$-0.273762\pi$
$449$	433.336	+	86.1959i	0.965114	+	0.191973i	0.312713	+	0.949848i	$0.398762\pi$
$450$		0			0
$451$	−67.4939	−	162.945i	−0.149654	−	0.361296i
$452$		0			0
$453$	59.3080	+	88.7607i	0.130923	+	0.195940i
$454$		0			0
$455$	−50.3796	+	50.3796i	−0.110724	+	0.110724i
$456$		0			0
$457$	246.501	+	102.104i	0.539390	+	0.223423i	0.635710	−	0.771928i	$-0.280707\pi$
$457$	246.501	+	102.104i	0.539390	+	0.223423i	−0.0963202	+	0.995350i	$0.530707\pi$
$458$		0			0
$459$	199.145	+	133.064i	0.433866	+	0.289900i
$460$		0			0
$461$	172.768	−	417.100i	0.374769	−	0.904772i	−0.618159	−	0.786053i	$-0.712121\pi$
$461$	172.768	−	417.100i	0.374769	−	0.904772i	0.992928	−	0.118719i	$-0.0378787\pi$
$462$		0			0
$463$	57.1171	+	57.1171i	0.123363	+	0.123363i	0.766093	−	0.642730i	$-0.222198\pi$
$463$	57.1171	+	57.1171i	0.123363	+	0.123363i	−0.642730	+	0.766093i	$0.722198\pi$
$464$		0			0
$465$	69.6405	−	46.5323i	0.149764	−	0.100069i
$466$		0			0
$467$	−76.1879	+	31.5580i	−0.163143	+	0.0675761i	−0.462760	−	0.886483i	$-0.653141\pi$
$467$	−76.1879	+	31.5580i	−0.163143	+	0.0675761i	0.299617	+	0.954059i	$0.403141\pi$
$468$		0			0
$469$	−179.617	+	902.998i	−0.382979	+	1.92537i
$470$		0			0
$471$	5.70949	+	28.7035i	0.0121221	+	0.0609417i
$472$		0			0
$473$	104.247	−	156.017i	0.220396	−	0.329846i
$474$		0			0
$475$			111.029i			0.233746i
$476$		0			0
$477$	501.069			1.05046
$478$		0			0
$479$	−382.794	−	255.775i	−0.799153	−	0.533977i	0.0876357	−	0.996153i	$-0.472069\pi$
$479$	−382.794	−	255.775i	−0.799153	−	0.533977i	−0.886788	+	0.462176i	$0.847069\pi$
$480$		0			0
$481$	−26.2278	+	5.21704i	−0.0545277	+	0.0108462i
$482$		0			0
$483$	53.7057	+	10.6827i	0.111192	+	0.0221174i
$484$		0			0
$485$	75.5612	+	182.421i	0.155796	+	0.376125i
$486$		0			0
$487$	−290.646	−	434.982i	−0.596809	−	0.893187i	0.402948	−	0.915223i	$-0.367985\pi$
$487$	−290.646	−	434.982i	−0.596809	−	0.893187i	−0.999757	+	0.0220352i	$0.992985\pi$
$488$		0			0
$489$	−91.7633	+	91.7633i	−0.187655	+	0.187655i
$490$		0			0
$491$	451.862	+	187.167i	0.920289	+	0.381196i	0.791986	−	0.610539i	$-0.209047\pi$
$491$	451.862	+	187.167i	0.920289	+	0.381196i	0.128303	+	0.991735i	$0.459047\pi$
$492$		0			0
$493$	51.1951	+	10.1833i	0.103844	+	0.0206559i
$494$		0			0
$495$	−206.941	+	499.600i	−0.418063	+	1.00929i
$496$		0			0
$497$	−588.550	−	588.550i	−1.18421	−	1.18421i
$498$		0			0
$499$	421.610	−	281.711i	0.844910	−	0.564551i	−0.0560623	−	0.998427i	$-0.517855\pi$
$499$	421.610	−	281.711i	0.844910	−	0.564551i	0.900972	+	0.433876i	$0.142855\pi$
$500$		0			0
$501$	83.1249	−	34.4315i	0.165918	−	0.0687255i
$502$		0			0
$503$	131.577	−	661.484i	0.261585	−	1.31508i	−0.596932	−	0.802292i	$-0.703614\pi$
$503$	131.577	−	661.484i	0.261585	−	1.31508i	0.858517	−	0.512785i	$-0.171386\pi$
$504$		0			0
$505$	12.0659	+	60.6592i	0.0238928	+	0.120117i
$506$		0			0
$507$	−75.7115	+	113.310i	−0.149332	+	0.223492i
$508$		0			0
$509$		−	349.504i		−	0.686648i	−0.939217	−	0.343324i	$-0.888447\pi$
$509$		−	349.504i		−	0.686648i	0.939217	−	0.343324i	$-0.111553\pi$
$510$		0			0
$511$	−479.395			−0.938150
$512$		0			0
$513$	32.9519	+	22.0177i	0.0642337	+	0.0429196i
$514$		0			0
$515$	−327.358	+	65.1157i	−0.635648	+	0.126438i
$516$		0			0
$517$	623.444	+	124.011i	1.20589	+	0.239866i
$518$		0			0
$519$	−55.3631	−	133.658i	−0.106673	−	0.257530i
$520$		0			0
$521$	−175.223	−	262.240i	−0.336320	−	0.503339i	0.624307	−	0.781179i	$-0.285381\pi$
$521$	−175.223	−	262.240i	−0.336320	−	0.503339i	−0.960627	+	0.277840i	$0.910381\pi$
$522$		0			0
$523$	145.221	−	145.221i	0.277669	−	0.277669i	−0.554509	−	0.832178i	$-0.687094\pi$
$523$	145.221	−	145.221i	0.277669	−	0.277669i	0.832178	+	0.554509i	$0.187094\pi$
$524$		0			0
$525$	232.722	+	96.3965i	0.443279	+	0.183612i
$526$		0			0
$527$	121.253	+	181.468i	0.230082	+	0.344342i
$528$		0			0
$529$	−174.266	+	420.715i	−0.329425	+	0.795302i
$530$		0			0
$531$	−161.959	−	161.959i	−0.305007	−	0.305007i
$532$		0			0
$533$	−20.5152	+	13.7078i	−0.0384901	+	0.0257182i
$534$		0			0
$535$	−655.859	+	271.666i	−1.22590	+	0.507786i
$536$		0			0
$537$	39.9728	−	200.957i	0.0744372	−	0.374221i
$538$		0			0
$539$	−19.9961	−	100.527i	−0.0370985	−	0.186507i
$540$		0			0
$541$	439.282	−	657.431i	0.811981	−	1.21522i	−0.161596	−	0.986857i	$-0.551664\pi$
$541$	439.282	−	657.431i	0.811981	−	1.21522i	0.973577	−	0.228358i	$-0.0733358\pi$
$542$		0			0
$543$			244.849i			0.450919i
$544$		0			0
$545$	149.615			0.274523
$546$		0			0
$547$	783.860	+	523.758i	1.43302	+	0.957511i	0.998380	+	0.0569051i	$0.0181232\pi$
$547$	783.860	+	523.758i	1.43302	+	0.957511i	0.434637	+	0.900606i	$0.356877\pi$
$548$		0			0
$549$	−298.229	+	59.3214i	−0.543222	+	0.108054i
$550$		0			0
$551$	8.47111	+	1.68501i	0.0153741	+	0.00305809i
$552$		0			0
$553$	−286.408	−	691.450i	−0.517917	−	1.25036i
$554$		0			0
$555$	85.7957	+	128.402i	0.154587	+	0.231356i
$556$		0			0
$557$	−303.284	+	303.284i	−0.544495	+	0.544495i	−0.924843	−	0.380348i	$-0.875804\pi$
$557$	−303.284	+	303.284i	−0.544495	+	0.544495i	0.380348	+	0.924843i	$0.375804\pi$
$558$		0			0
$559$	−24.2519	−	10.0455i	−0.0433844	−	0.0179704i
$560$		0			0
$561$	103.053	+	42.6859i	0.183695	+	0.0760889i
$562$		0			0
$563$	264.879	−	639.473i	0.470477	−	1.13583i	−0.493476	−	0.869759i	$-0.664274\pi$
$563$	264.879	−	639.473i	0.470477	−	1.13583i	0.963953	−	0.266072i	$-0.0857260\pi$
$564$		0			0
$565$	−344.303	−	344.303i	−0.609386	−	0.609386i
$566$		0			0
$567$	−415.428	+	277.580i	−0.732677	+	0.489559i
$568$		0			0
$569$	−370.173	+	153.331i	−0.650567	+	0.269474i	−0.683463	−	0.729985i	$-0.739527\pi$
$569$	−370.173	+	153.331i	−0.650567	+	0.269474i	0.0328958	+	0.999459i	$0.489527\pi$
$570$		0			0
$571$	−127.142	+	639.187i	−0.222666	+	1.11942i	0.694065	+	0.719912i	$0.255818\pi$
$571$	−127.142	+	639.187i	−0.222666	+	1.11942i	−0.916731	+	0.399505i	$0.869182\pi$
$572$		0			0
$573$	−21.0112	−	105.631i	−0.0366688	−	0.184347i
$574$		0			0
$575$	188.156	−	281.596i	0.327229	−	0.489732i
$576$		0			0
$577$			684.109i			1.18563i	0.805339	+	0.592815i	$0.201983\pi$
$577$			684.109i			1.18563i	−0.805339	+	0.592815i	$0.798017\pi$
$578$		0			0
$579$	258.876			0.447109
$580$		0			0
$581$	776.094	+	518.569i	1.33579	+	0.892546i
$582$		0			0
$583$	475.863	−	94.6550i	0.816232	−	0.162359i
$584$		0			0
$585$	74.1968	+	14.7587i	0.126832	+	0.0252285i
$586$		0			0
$587$	141.750	+	342.216i	0.241483	+	0.582991i	0.997430	−	0.0716408i	$-0.0228235\pi$
$587$	141.750	+	342.216i	0.241483	+	0.582991i	−0.755948	+	0.654632i	$0.772824\pi$
$588$		0			0
$589$	20.0634	+	30.0270i	0.0340635	+	0.0509796i
$590$		0			0
$591$	66.4527	−	66.4527i	0.112441	−	0.112441i
$592$		0			0
$593$	585.245	+	242.416i	0.986922	+	0.408797i	0.816985	−	0.576658i	$-0.195644\pi$
$593$	585.245	+	242.416i	0.986922	+	0.408797i	0.169937	+	0.985455i	$0.445644\pi$
$594$		0			0
$595$	−410.286	+	990.517i	−0.689556	+	1.66473i
$596$		0			0
$597$	−91.9883	+	222.080i	−0.154084	+	0.371992i
$598$		0			0
$599$	−315.855	−	315.855i	−0.527304	−	0.527304i	0.392463	−	0.919768i	$-0.371623\pi$
$599$	−315.855	−	315.855i	−0.527304	−	0.527304i	−0.919768	+	0.392463i	$0.871623\pi$
$600$		0			0
$601$	362.279	−	242.067i	0.602794	−	0.402774i	−0.216388	−	0.976307i	$-0.569428\pi$
$601$	362.279	−	242.067i	0.602794	−	0.402774i	0.819182	+	0.573533i	$0.194428\pi$
$602$		0			0
$603$	903.170	−	374.105i	1.49779	−	0.620407i
$604$		0			0
$605$	87.3876	−	439.327i	0.144442	−	0.726160i
$606$		0			0
$607$	−123.803	−	622.400i	−0.203959	−	1.02537i	−0.938098	−	0.346371i	$-0.887414\pi$
$607$	−123.803	−	622.400i	−0.203959	−	1.02537i	0.734139	−	0.679000i	$-0.237586\pi$
$608$		0			0
$609$	10.8865	−	16.2928i	0.0178760	−	0.0267534i
$610$		0			0
$611$		−	88.9259i		−	0.145542i
$612$		0			0
$613$	−692.422			−1.12956			−0.564782	−	0.825240i	$-0.691040\pi$
$613$	−692.422			−1.12956			−0.564782	+	0.825240i	$0.691040\pi$
$614$		0			0
$615$	118.472	+	79.1601i	0.192637	+	0.128716i
$616$		0			0
$617$	−263.077	+	52.3292i	−0.426381	+	0.0848124i	−0.403616	−	0.914928i	$-0.632247\pi$
$617$	−263.077	+	52.3292i	−0.426381	+	0.0848124i	−0.0227645	+	0.999741i	$0.507247\pi$
$618$		0			0
$619$	153.549	+	30.5428i	0.248060	+	0.0493422i	0.317554	−	0.948240i	$-0.397138\pi$
$619$	153.549	+	30.5428i	0.248060	+	0.0493422i	−0.0694940	+	0.997582i	$0.522138\pi$
$620$		0			0
$621$	−46.2610	−	111.684i	−0.0744944	−	0.179845i
$622$		0			0
$623$	−379.241	−	567.575i	−0.608734	−	0.911035i
$624$		0			0
$625$	−38.0547	+	38.0547i	−0.0608875	+	0.0608875i
$626$		0			0
$627$	17.0519	+	7.06311i	0.0271959	+	0.0112649i
$628$		0			0
$629$	−334.589	+	223.565i	−0.531938	+	0.355429i
$630$		0			0
$631$	119.803	−	289.230i	0.189862	−	0.458368i	−0.800071	−	0.599906i	$-0.795205\pi$
$631$	119.803	−	289.230i	0.189862	−	0.458368i	0.989933	+	0.141538i	$0.0452048\pi$
$632$		0			0
$633$	131.992	+	131.992i	0.208519	+	0.208519i
$634$		0			0
$635$	−796.105	+	531.940i	−1.25371	+	0.837701i
$636$		0			0
$637$	−13.2473	+	5.48723i	−0.0207965	+	0.00861418i
$638$		0			0
$639$	−172.415	+	866.790i	−0.269820	+	1.35648i
$640$		0			0
$641$	−72.2074	−	363.011i	−0.112648	−	0.566320i	−0.995345	−	0.0963771i	$-0.969275\pi$
$641$	−72.2074	−	363.011i	−0.112648	−	0.566320i	0.882697	−	0.469943i	$-0.155725\pi$
$642$		0			0
$643$	122.220	−	182.915i	0.190077	−	0.284471i	−0.724175	−	0.689616i	$-0.757779\pi$
$643$	122.220	−	182.915i	0.190077	−	0.284471i	0.914252	+	0.405146i	$0.132779\pi$
$644$		0			0
$645$			151.589i			0.235022i
$646$		0			0
$647$	−769.098			−1.18871			−0.594357	−	0.804201i	$-0.702593\pi$
$647$	−769.098			−1.18871			−0.594357	+	0.804201i	$0.702593\pi$
$648$		0			0
$649$	−184.407	−	123.217i	−0.284140	−	0.189856i
$650$		0			0
$651$	80.3568	−	15.9840i	0.123436	−	0.0245529i
$652$		0			0
$653$	−41.6201	−	8.27876i	−0.0637368	−	0.0126780i	0.163119	−	0.986606i	$-0.447845\pi$
$653$	−41.6201	−	8.27876i	−0.0637368	−	0.0126780i	−0.226856	+	0.973928i	$0.572845\pi$
$654$		0			0
$655$	−526.432	−	1270.92i	−0.803713	−	1.94033i
$656$		0			0
$657$	282.796	+	423.234i	0.430436	+	0.644192i
$658$		0			0
$659$	−472.719	+	472.719i	−0.717328	+	0.717328i	−0.968057	−	0.250729i	$-0.919330\pi$
$659$	−472.719	+	472.719i	−0.717328	+	0.717328i	0.250729	+	0.968057i	$0.419330\pi$
$660$		0			0
$661$	−380.158	−	157.467i	−0.575126	−	0.238225i	0.0761113	−	0.997099i	$-0.475750\pi$
$661$	−380.158	−	157.467i	−0.575126	−	0.238225i	−0.651237	+	0.758874i	$0.725750\pi$
$662$		0			0
$663$	3.04428	−	15.3046i	0.00459168	−	0.0230839i
$664$		0			0
$665$	−67.8888	+	163.898i	−0.102088	+	0.246463i
$666$		0			0
$667$	−18.6292	−	18.6292i	−0.0279298	−	0.0279298i
$668$		0			0
$669$	245.494	−	164.034i	0.366957	−	0.245193i
$670$		0			0
$671$	−272.020	+	112.675i	−0.405395	+	0.167920i
$672$		0			0
$673$	3.16371	−	15.9051i	0.00470091	−	0.0236331i	−0.978364	−	0.206893i	$-0.933665\pi$
$673$	3.16371	−	15.9051i	0.00470091	−	0.0236331i	0.983065	+	0.183260i	$0.0586649\pi$
$674$		0			0
$675$	−108.489	−	545.412i	−0.160725	−	0.808018i
$676$		0			0
$677$	−571.240	+	854.921i	−0.843782	+	1.26281i	0.119099	+	0.992882i	$0.461999\pi$
$677$	−571.240	+	854.921i	−0.843782	+	1.26281i	−0.962881	+	0.269926i	$0.913001\pi$
$678$		0			0
$679$			193.149i			0.284461i
$680$		0			0
$681$	78.7512			0.115641
$682$		0			0
$683$	−188.201	−	125.752i	−0.275551	−	0.184117i	0.410114	−	0.912034i	$-0.365489\pi$
$683$	−188.201	−	125.752i	−0.275551	−	0.184117i	−0.685666	+	0.727917i	$0.740489\pi$
$684$		0			0
$685$	−1363.28	+	271.173i	−1.99019	+	0.395874i
$686$		0			0
$687$	−288.197	−	57.3259i	−0.419500	−	0.0834438i
$688$		0			0
$689$	−25.9748	−	62.7087i	−0.0376993	−	0.0910141i
$690$		0			0
$691$	21.7058	+	32.4851i	0.0314122	+	0.0470117i	0.846843	−	0.531842i	$-0.178500\pi$
$691$	21.7058	+	32.4851i	0.0314122	+	0.0470117i	−0.815431	+	0.578854i	$0.803500\pi$
$692$		0			0
$693$	−374.046	+	374.046i	−0.539749	+	0.539749i
$694$		0			0
$695$	1332.08	+	551.766i	1.91666	+	0.793908i
$696$		0			0
$697$	−206.274	+	308.711i	−0.295946	+	0.442914i
$698$		0			0
$699$	−87.1075	+	210.296i	−0.124617	+	0.300853i
$700$		0			0
$701$	−401.261	−	401.261i	−0.572412	−	0.572412i	0.360390	−	0.932802i	$-0.382644\pi$
$701$	−401.261	−	401.261i	−0.572412	−	0.572412i	−0.932802	+	0.360390i	$0.882644\pi$
$702$		0			0
$703$	−55.3634	+	36.9927i	−0.0787531	+	0.0526212i
$704$		0			0
$705$	−474.441	+	196.520i	−0.672965	+	0.278751i
$706$		0			0
$707$	−11.8030	+	59.3377i	−0.0166945	+	0.0839288i
$708$		0			0
$709$	55.6759	+	279.901i	0.0785273	+	0.394783i	0.999980	+	0.00629329i	$0.00200323\pi$
$709$	55.6759	+	279.901i	0.0785273	+	0.394783i	−0.921453	+	0.388490i	$0.872997\pi$
$710$		0			0
$711$	−441.495	+	660.744i	−0.620950	+	0.929317i
$712$		0			0
$713$		−	110.156i		−	0.154496i
$714$		0			0
$715$	73.2524			0.102451
$716$		0			0
$717$	−221.961	−	148.310i	−0.309569	−	0.206848i
$718$		0			0
$719$	−601.644	+	119.674i	−0.836779	+	0.166446i	−0.594838	−	0.803845i	$-0.702784\pi$
$719$	−601.644	+	119.674i	−0.836779	+	0.166446i	−0.241941	+	0.970291i	$0.577784\pi$
$720$		0			0
$721$	−320.226	−	63.6970i	−0.444142	−	0.0883453i
$722$		0			0
$723$	−75.3748	−	181.971i	−0.104253	−	0.251689i
$724$		0			0
$725$	−67.3322	−	100.770i	−0.0928719	−	0.138993i
$726$		0			0
$727$	−244.413	+	244.413i	−0.336194	+	0.336194i	−0.854933	−	0.518739i	$-0.826402\pi$
$727$	−244.413	+	244.413i	−0.336194	+	0.336194i	0.518739	+	0.854933i	$0.326402\pi$
$728$		0			0
$729$	394.941	+	163.590i	0.541758	+	0.224403i
$730$		0			0
$731$	−395.009			−0.540368
$732$		0			0
$733$	516.266	−	1246.38i	0.704319	−	1.70038i	−0.00941053	−	0.999956i	$-0.502996\pi$
$733$	516.266	−	1246.38i	0.704319	−	1.70038i	0.713730	−	0.700421i	$-0.247004\pi$
$734$		0			0
$735$	58.5513	+	58.5513i	0.0796617	+	0.0796617i
$736$		0			0
$737$	787.066	−	525.901i	1.06793	−	0.713569i
$738$		0			0
$739$	−602.925	+	249.740i	−0.815866	+	0.337943i	−0.751292	−	0.659970i	$-0.770569\pi$
$739$	−602.925	+	249.740i	−0.815866	+	0.337943i	−0.0645741	+	0.997913i	$0.520569\pi$
$740$		0			0
$741$	0.503729	−	2.53241i	0.000679796	−	0.00341756i
$742$		0			0
$743$	43.5044	+	218.711i	0.0585523	+	0.294362i	0.998955	−	0.0456999i	$-0.0145518\pi$
$743$	43.5044	+	218.711i	0.0585523	+	0.294362i	−0.940403	+	0.340062i	$0.889552\pi$
$744$		0			0
$745$	199.885	−	299.149i	0.268302	−	0.401542i
$746$		0			0
$747$		−	991.082i		−	1.32675i
$748$		0			0
$749$	−694.430			−0.927143
$750$		0			0
$751$	373.353	+	249.467i	0.497142	+	0.332180i	0.778734	−	0.627355i	$-0.215862\pi$
$751$	373.353	+	249.467i	0.497142	+	0.332180i	−0.281592	+	0.959534i	$0.590862\pi$
$752$		0			0
$753$	175.204	−	34.8503i	0.232675	−	0.0462820i
$754$		0			0
$755$	1034.67	+	205.809i	1.37043	+	0.272595i
$756$		0			0
$757$	−17.6369	−	42.5792i	−0.0232984	−	0.0562473i	0.911802	−	0.410630i	$-0.134691\pi$
$757$	−17.6369	−	42.5792i	−0.0232984	−	0.0562473i	−0.935101	+	0.354382i	$0.884691\pi$
$758$		0			0
$759$	−31.2779	−	46.8107i	−0.0412093	−	0.0616741i
$760$		0			0
$761$	−552.081	+	552.081i	−0.725467	+	0.725467i	−0.969713	−	0.244246i	$-0.921460\pi$
$761$	−552.081	+	552.081i	−0.725467	+	0.725467i	0.244246	+	0.969713i	$0.421460\pi$
$762$		0			0
$763$	135.215	+	56.0079i	0.177215	+	0.0734048i
$764$		0			0
$765$	1116.51	−	222.087i	1.45949	−	0.290310i
$766$		0			0
$767$	−11.8734	+	28.6649i	−0.0154803	+	0.0373727i
$768$		0			0
$769$	−625.504	−	625.504i	−0.813400	−	0.813400i	0.171742	−	0.985142i	$-0.445060\pi$
$769$	−625.504	−	625.504i	−0.813400	−	0.813400i	−0.985142	+	0.171742i	$0.945060\pi$
$770$		0			0
$771$	219.723	−	146.814i	0.284984	−	0.190420i
$772$		0			0
$773$	1123.75	−	465.474i	1.45376	−	0.602166i	0.490667	−	0.871347i	$-0.336753\pi$
$773$	1123.75	−	465.474i	1.45376	−	0.602166i	0.963090	+	0.269181i	$0.0867531\pi$
$774$		0			0
$775$	98.8595	−	497.000i	0.127561	−	0.641291i
$776$		0			0
$777$	29.4711	+	148.161i	0.0379293	+	0.190683i
$778$		0			0
$779$	−34.1316	+	51.0816i	−0.0438146	+	0.0655733i
$780$		0			0
$781$			855.757i			1.09572i
$782$		0			0
$783$	−43.2592			−0.0552481
$784$		0			0
$785$	240.470	+	160.677i	0.306332	+	0.204684i
$786$		0			0
$787$	190.336	−	37.8601i	0.241850	−	0.0481069i	−0.0726771	−	0.997356i	$-0.523154\pi$
$787$	190.336	−	37.8601i	0.241850	−	0.0481069i	0.314527	+	0.949249i	$0.398154\pi$
$788$		0			0
$789$	−110.556	−	21.9909i	−0.140121	−	0.0278718i
$790$		0			0
$791$	−182.276	−	440.053i	−0.230437	−	0.556324i
$792$		0			0
$793$	22.8839	+	34.2481i	0.0288573	+	0.0431881i
$794$		0			0
$795$	−277.163	+	277.163i	−0.348633	+	0.348633i
$796$		0			0
$797$	118.577	+	49.1164i	0.148780	+	0.0616266i	0.455831	−	0.890066i	$-0.349342\pi$
$797$	118.577	+	49.1164i	0.148780	+	0.0616266i	−0.307051	+	0.951693i	$0.599342\pi$
$798$		0			0
$799$	−512.088	−	1236.29i	−0.640911	−	1.54730i
$800$		0			0
$801$	−277.369	+	669.628i	−0.346278	+	0.835990i
$802$		0			0
$803$	348.522	+	348.522i	0.434025	+	0.434025i
$804$		0			0
$805$	449.932	−	300.635i	0.558921	−	0.373459i
$806$		0			0
$807$	−243.873	+	101.016i	−0.302197	+	0.125174i
$808$		0			0
$809$	68.1098	−	342.411i	0.0841902	−	0.423253i	−0.915587	−	0.402121i	$-0.868273\pi$
$809$	68.1098	−	342.411i	0.0841902	−	0.423253i	0.999777	−	0.0211316i	$-0.00672688\pi$
$810$		0			0
$811$	−36.2150	−	182.065i	−0.0446547	−	0.224494i	0.952014	−	0.306056i	$-0.0990094\pi$
$811$	−36.2150	−	182.065i	−0.0446547	−	0.224494i	−0.996668	+	0.0815613i	$0.974009\pi$
$812$		0			0
$813$	8.66099	−	12.9621i	0.0106531	−	0.0159435i
$814$		0			0
$815$			1282.44i			1.57355i
$816$		0			0
$817$	−65.3610			−0.0800013
$818$		0			0
$819$	61.5306	+	41.1134i	0.0751290	+	0.0501996i
$820$		0			0
$821$	1545.78	−	307.474i	1.88280	−	0.374512i	0.886669	−	0.462404i	$-0.153013\pi$
$821$	1545.78	−	307.474i	1.88280	−	0.374512i	0.996130	+	0.0878920i	$0.0280130\pi$
$822$		0			0
$823$	−986.291	−	196.185i	−1.19841	−	0.238378i	−0.444757	−	0.895651i	$-0.646710\pi$
$823$	−986.291	−	196.185i	−1.19841	−	0.238378i	−0.753653	+	0.657273i	$0.771710\pi$
$824$		0			0
$825$	−99.1090	−	239.270i	−0.120132	−	0.290025i
$826$		0			0
$827$	883.014	+	1321.52i	1.06773	+	1.59797i	0.764001	+	0.645216i	$0.223232\pi$
$827$	883.014	+	1321.52i	1.06773	+	1.59797i	0.303731	+	0.952758i	$0.401768\pi$
$828$		0			0
$829$	−269.747	+	269.747i	−0.325388	+	0.325388i	−0.850830	−	0.525442i	$-0.823900\pi$
$829$	−269.747	+	269.747i	−0.325388	+	0.325388i	0.525442	+	0.850830i	$0.323900\pi$
$830$		0			0
$831$	231.205	+	95.7684i	0.278225	+	0.115245i
$832$		0			0
$833$	−152.572	+	152.572i	−0.183160	+	0.183160i
$834$		0			0
$835$	340.259	−	821.457i	0.407495	−	0.983781i
$836$		0			0
$837$	−127.898	−	127.898i	−0.152805	−	0.152805i
$838$		0			0
$839$	30.7798	−	20.5664i	0.0366862	−	0.0245130i	−0.537092	−	0.843524i	$-0.680477\pi$
$839$	30.7798	−	20.5664i	0.0366862	−	0.0245130i	0.573778	+	0.819011i	$0.305477\pi$
$840$		0			0
$841$	768.273	−	318.229i	0.913523	−	0.378393i
$842$		0			0
$843$	13.7149	−	68.9493i	0.0162691	−	0.0817904i
$844$		0			0
$845$	262.732	+	1320.84i	0.310925	+	1.56313i
$846$		0			0
$847$	243.437	−	364.329i	0.287411	−	0.430141i
$848$		0			0
$849$		−	6.07887i		−	0.00716004i
$850$		0			0
$851$	203.104			0.238665
$852$		0			0
$853$	−65.5718	−	43.8137i	−0.0768720	−	0.0513642i	0.516540	−	0.856263i	$-0.327220\pi$
$853$	−65.5718	−	43.8137i	−0.0768720	−	0.0513642i	−0.593412	+	0.804899i	$0.702220\pi$
$854$		0			0
$855$	184.745	−	36.7481i	0.216077	−	0.0429803i
$856$		0			0
$857$	−653.288	−	129.947i	−0.762297	−	0.151630i	−0.201392	−	0.979511i	$-0.564547\pi$
$857$	−653.288	−	129.947i	−0.762297	−	0.151630i	−0.560905	+	0.827880i	$0.689547\pi$
$858$		0			0
$859$	530.649	+	1281.10i	0.617752	+	1.49138i	0.854308	+	0.519767i	$0.173981\pi$
$859$	530.649	+	1281.10i	0.617752	+	1.49138i	−0.236556	+	0.971618i	$0.576019\pi$
$860$		0			0
$861$	77.4355	+	115.890i	0.0899367	+	0.134600i
$862$		0			0
$863$	375.548	−	375.548i	0.435166	−	0.435166i	−0.455215	−	0.890381i	$-0.650438\pi$
$863$	375.548	−	375.548i	0.435166	−	0.435166i	0.890381	+	0.455215i	$0.150438\pi$
$864$		0			0
$865$	−1320.84	−	547.109i	−1.52698	−	0.632496i
$866$		0			0
$867$	−45.8102	−	230.303i	−0.0528376	−	0.265632i
$868$		0			0
$869$	−294.467	+	710.907i	−0.338858	+	0.818075i
$870$		0			0
$871$	−93.6384	−	93.6384i	−0.107507	−	0.107507i
$872$		0			0
$873$	170.522	−	113.939i	0.195329	−	0.130515i
$874$		0			0
$875$	843.160	−	349.249i	0.963612	−	0.399141i
$876$		0			0
$877$	−48.4908	+	243.780i	−0.0552917	+	0.277970i	−0.998534	−	0.0541366i	$-0.982759\pi$
$877$	−48.4908	+	243.780i	−0.0552917	+	0.277970i	0.943242	+	0.332107i	$0.107759\pi$
$878$		0			0
$879$	12.2080	+	61.3735i	0.0138885	+	0.0698220i
$880$		0			0
$881$	−81.3688	+	121.777i	−0.0923595	+	0.138226i	−0.874772	−	0.484535i	$-0.838989\pi$
$881$	−81.3688	+	121.777i	−0.0923595	+	0.138226i	0.782412	+	0.622761i	$0.213989\pi$
$882$		0			0
$883$		−	322.505i		−	0.365237i	−0.983184	−	0.182619i	$-0.941543\pi$
$883$		−	322.505i		−	0.365237i	0.983184	−	0.182619i	$-0.0584574\pi$
$884$		0			0
$885$	179.173			0.202455
$886$		0			0
$887$	52.2618	+	34.9202i	0.0589197	+	0.0393689i	0.584681	−	0.811263i	$-0.301220\pi$
$887$	52.2618	+	34.9202i	0.0589197	+	0.0393689i	−0.525762	+	0.850632i	$0.676220\pi$
$888$		0			0
$889$	−918.610	+	182.723i	−1.03331	+	0.205538i
$890$		0			0
$891$	503.820	+	100.216i	0.565454	+	0.112476i
$892$		0			0
$893$	−84.7337	−	204.565i	−0.0948866	−	0.229077i
$894$		0			0
$895$	−1124.92	−	1683.56i	−1.25689	−	1.88107i
$896$		0			0
$897$	−5.56914	+	5.56914i	−0.00620863	+	0.00620863i
$898$		0			0
$899$	−36.4189	−	15.0852i	−0.0405104	−	0.0167800i
$900$		0			0
$901$	−722.228	−	722.228i	−0.801585	−	0.801585i
$902$		0			0
$903$	−56.7469	+	136.999i	−0.0628426	+	0.151715i
$904$		0			0
$905$	1710.95	+	1710.95i	1.89055	+	1.89055i
$906$		0			0
$907$	182.765	−	122.120i	0.201505	−	0.134641i	−0.450724	−	0.892663i	$-0.648834\pi$
$907$	182.765	−	122.120i	0.201505	−	0.134641i	0.652229	+	0.758022i	$0.273834\pi$
$908$		0			0
$909$	59.3490	−	24.5832i	0.0652904	−	0.0270442i
$910$		0			0
$911$	−98.5913	+	495.652i	−0.108223	+	0.544074i	0.888192	+	0.459473i	$0.151962\pi$
$911$	−98.5913	+	495.652i	−0.108223	+	0.544074i	−0.996415	+	0.0846014i	$0.973038\pi$
$912$		0			0
$913$	−187.221	−	941.226i	−0.205062	−	1.03092i
$914$		0			0
$915$	132.150	−	197.777i	0.144426	−	0.216149i
$916$		0			0
$917$		−	1345.66i		−	1.46746i
$918$		0			0
$919$	930.196			1.01218			0.506091	−	0.862480i	$-0.331090\pi$
$919$	930.196			1.01218			0.506091	+	0.862480i	$0.331090\pi$
$920$		0			0
$921$	107.876	+	72.0807i	0.117130	+	0.0782635i
$922$		0			0
$923$	117.416	−	23.3556i	0.127212	−	0.0253040i
$924$		0			0
$925$	916.364	+	182.276i	0.990663	+	0.197055i
$926$		0			0
$927$	132.667	+	320.288i	0.143115	+	0.345510i
$928$		0			0
$929$	637.592	+	954.224i	0.686321	+	1.02715i	0.997058	+	0.0766557i	$0.0244242\pi$
$929$	637.592	+	954.224i	0.686321	+	1.02715i	−0.310737	+	0.950496i	$0.600576\pi$
$930$		0			0
$931$	−25.2457	+	25.2457i	−0.0271167	+	0.0271167i
$932$		0			0
$933$	249.980	+	103.545i	0.267932	+	0.110981i
$934$		0			0
$935$	1018.39	−	421.831i	1.08919	−	0.451156i
$936$		0			0
$937$	517.380	−	1249.07i	0.552166	−	1.33305i	−0.363682	−	0.931523i	$-0.618481\pi$
$937$	517.380	−	1249.07i	0.552166	−	1.33305i	0.915848	−	0.401524i	$-0.131519\pi$
$938$		0			0
$939$	226.691	+	226.691i	0.241418	+	0.241418i
$940$		0			0
$941$	−1529.70	+	1022.11i	−1.62561	+	1.08620i	−0.695743	+	0.718291i	$0.744925\pi$
$941$	−1529.70	+	1022.11i	−1.62561	+	1.08620i	−0.929864	+	0.367905i	$0.880075\pi$
$942$		0			0
$943$	173.131	−	71.7133i	0.183596	−	0.0760480i
$944$		0			0
$945$	173.343	−	871.454i	0.183432	−	0.922174i
$946$		0			0
$947$	7.67691	+	38.5945i	0.00810656	+	0.0407544i	0.984627	−	0.174671i	$-0.0558862\pi$
$947$	7.67691	+	38.5945i	0.00810656	+	0.0407544i	−0.976520	+	0.215425i	$0.930886\pi$
$948$		0			0
$949$	38.3079	−	57.3319i	0.0403666	−	0.0604129i
$950$		0			0
$951$		−	113.017i		−	0.118840i
$952$		0			0
$953$	183.445			0.192492			0.0962458	−	0.995358i	$-0.469317\pi$
$953$	183.445			0.192492			0.0962458	+	0.995358i	$0.469317\pi$
$954$		0			0
$955$	−884.944	−	591.301i	−0.926643	−	0.619163i
$956$		0			0
$957$	−19.7595	+	3.93041i	−0.0206473	+	0.00410701i
$958$		0			0
$959$	−1333.58	−	265.266i	−1.39059	−	0.276606i
$960$		0			0
$961$	304.685	+	735.574i	0.317050	+	0.765426i
$962$		0			0
$963$	409.646	+	613.079i	0.425386	+	0.636635i
$964$		0			0
$965$	1808.97	−	1808.97i	1.87458	−	1.87458i
$966$		0			0
$967$	−1181.69	−	489.471i	−1.22201	−	0.506175i	−0.323965	−	0.946069i	$-0.605016\pi$
$967$	−1181.69	−	489.471i	−1.22201	−	0.506175i	−0.898050	+	0.439894i	$0.855016\pi$
$968$		0			0
$969$	−7.58007	−	38.1076i	−0.00782257	−	0.0393267i
$970$		0			0
$971$	349.777	−	844.437i	0.360224	−	0.869657i	−0.635043	−	0.772477i	$-0.719018\pi$
$971$	349.777	−	844.437i	0.360224	−	0.869657i	0.995267	−	0.0971803i	$-0.0309823\pi$
$972$		0			0
$973$	997.319	+	997.319i	1.02499	+	1.02499i
$974$		0			0
$975$	−30.1248	+	20.1288i	−0.0308972	+	0.0206449i
$976$		0			0
$977$	−408.510	+	169.210i	−0.418126	+	0.173194i	−0.581820	−	0.813318i	$-0.697659\pi$
$977$	−408.510	+	169.210i	−0.418126	+	0.173194i	0.163694	+	0.986511i	$0.447659\pi$
$978$		0			0
$979$	−136.919	+	688.340i	−0.139856	+	0.703105i
$980$		0			0
$981$	−30.3170	−	152.414i	−0.0309042	−	0.155366i
$982$		0			0
$983$	−369.695	+	553.287i	−0.376088	+	0.562856i	−0.970438	−	0.241351i	$-0.922410\pi$
$983$	−369.695	+	553.287i	−0.376088	+	0.562856i	0.594350	+	0.804207i	$0.297410\pi$
$984$		0			0
$985$		−	928.713i		−	0.942856i
$986$		0			0
$987$	−502.343			−0.508959
$988$		0			0
$989$	165.770	+	110.764i	0.167614	+	0.111996i
$990$		0			0
$991$	1534.80	−	305.291i	1.54874	−	0.308063i	0.654642	−	0.755939i	$-0.272819\pi$
$991$	1534.80	−	305.291i	1.54874	−	0.308063i	0.894096	+	0.447876i	$0.147819\pi$
$992$		0			0
$993$	−126.551	−	25.1726i	−0.127443	−	0.0253500i
$994$		0			0
$995$	909.048	+	2194.64i	0.913616	+	2.20566i
$996$		0			0
$997$	−855.639	−	1280.55i	−0.858213	−	1.28441i	−0.957232	−	0.289321i	$-0.906570\pi$
$997$	−855.639	−	1280.55i	−0.858213	−	1.28441i	0.0990189	−	0.995086i	$-0.468430\pi$
$998$		0			0
$999$	235.817	−	235.817i	0.236053	−	0.236053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.3.bh.c.129.1		8
4.3	odd	2		17.3.e.a.10.1	✓	8
12.11	even	2		153.3.p.b.10.1		8
17.12	odd	16	inner	272.3.bh.c.97.1		8
20.3	even	4		425.3.t.c.299.1		8
20.7	even	4		425.3.t.a.299.1		8
20.19	odd	2		425.3.u.b.401.1		8
68.3	even	16		289.3.e.i.158.1		8
68.7	even	16		289.3.e.k.65.1		8
68.11	even	16		289.3.e.b.224.1		8
68.15	odd	8		289.3.e.b.40.1		8
68.19	odd	8		289.3.e.d.40.1		8
68.23	even	16		289.3.e.d.224.1		8
68.27	even	16		289.3.e.l.65.1		8
68.31	even	16		289.3.e.m.158.1		8
68.39	even	16		289.3.e.c.131.1		8
68.43	odd	8		289.3.e.k.249.1		8
68.47	odd	4		289.3.e.m.75.1		8
68.55	odd	4		289.3.e.i.75.1		8
68.59	odd	8		289.3.e.l.249.1		8
68.63	even	16		17.3.e.a.12.1	yes	8
68.67	odd	2		289.3.e.c.214.1		8
204.131	odd	16		153.3.p.b.46.1		8
340.63	odd	16		425.3.t.a.199.1		8
340.199	even	16		425.3.u.b.301.1		8
340.267	odd	16		425.3.t.c.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.10.1	✓	8	4.3	odd	2
17.3.e.a.12.1	yes	8	68.63	even	16
153.3.p.b.10.1		8	12.11	even	2
153.3.p.b.46.1		8	204.131	odd	16
272.3.bh.c.97.1		8	17.12	odd	16	inner
272.3.bh.c.129.1		8	1.1	even	1	trivial
289.3.e.b.40.1		8	68.15	odd	8
289.3.e.b.224.1		8	68.11	even	16
289.3.e.c.131.1		8	68.39	even	16
289.3.e.c.214.1		8	68.67	odd	2
289.3.e.d.40.1		8	68.19	odd	8
289.3.e.d.224.1		8	68.23	even	16
289.3.e.i.75.1		8	68.55	odd	4
289.3.e.i.158.1		8	68.3	even	16
289.3.e.k.65.1		8	68.7	even	16
289.3.e.k.249.1		8	68.43	odd	8
289.3.e.l.65.1		8	68.27	even	16
289.3.e.l.249.1		8	68.59	odd	8
289.3.e.m.75.1		8	68.47	odd	4
289.3.e.m.158.1		8	68.31	even	16
425.3.t.a.199.1		8	340.63	odd	16
425.3.t.a.299.1		8	20.7	even	4
425.3.t.c.199.1		8	340.267	odd	16
425.3.t.c.299.1		8	20.3	even	4
425.3.u.b.301.1		8	340.199	even	16
425.3.u.b.401.1		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.675577 + 0.451406i) q^{3} +(7.87510 - 1.56645i) q^{5} +(7.70353 + 1.53233i) q^{7} +(-3.19151 - 7.70500i) q^{9} +O(q^{10})\)	\(q+(0.675577 + 0.451406i) q^{3} +(7.87510 - 1.56645i) q^{5} +(7.70353 + 1.53233i) q^{7} +(-3.19151 - 7.70500i) q^{9} +(-4.48649 - 6.71450i) q^{11} +(-0.798835 + 0.798835i) q^{13} +(6.02734 + 2.49661i) q^{15} +(-6.50562 + 15.7060i) q^{17} +(-1.07647 + 2.59882i) q^{19} +(4.51262 + 4.51262i) q^{21} +(7.13426 - 4.76696i) q^{23} +(36.4664 - 15.1049i) q^{25} +(2.74858 - 13.8181i) q^{27} +(-0.599020 - 3.01148i) q^{29} +(7.13254 - 10.6746i) q^{31} -6.56139i q^{33} +63.0663 q^{35} +(19.6817 + 13.1509i) q^{37} +(-0.900273 + 0.179075i) q^{39} +(21.4206 + 4.26082i) q^{41} +(8.89197 + 21.4671i) q^{43} +(-37.2030 - 55.6783i) q^{45} +(-55.6597 + 55.6597i) q^{47} +(11.7262 + 4.85715i) q^{49} +(-11.4848 + 7.67390i) q^{51} +(-22.9922 + 55.5080i) q^{53} +(-45.8495 - 45.8495i) q^{55} +(-1.90036 + 1.26978i) q^{57} +(25.3733 - 10.5100i) q^{59} +(7.11302 - 35.7596i) q^{61} +(-12.7793 - 64.2461i) q^{63} +(-5.03957 + 7.54224i) q^{65} +117.219i q^{67} +6.97157 q^{69} +(-88.1108 - 58.8738i) q^{71} +(-59.8620 + 11.9073i) q^{73} +(31.4543 + 6.25665i) q^{75} +(-24.2730 - 58.6001i) q^{77} +(-52.9382 - 79.2276i) q^{79} +(-44.9799 + 44.9799i) q^{81} +(109.791 + 45.4770i) q^{83} +(-26.6297 + 133.877i) q^{85} +(0.954715 - 2.30489i) q^{87} +(-61.4534 - 61.4534i) q^{89} +(-7.37792 + 4.92977i) q^{91} +(9.63715 - 3.99184i) q^{93} +(-4.40634 + 22.1522i) q^{95} +(4.79748 + 24.1185i) q^{97} +(-37.4165 + 55.9978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 16 q^{5} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 8 * q + 8 * q^3 + 16 * q^5 - 8 * q^7 - 16 * q^9	\( 8 q + 8 q^{3} + 16 q^{5} - 8 q^{7} - 16 q^{9} + 8 q^{11} + 16 q^{13} + 16 q^{15} - 64 q^{21} + 56 q^{23} + 64 q^{25} - 40 q^{27} + 48 q^{29} - 24 q^{31} + 160 q^{35} + 32 q^{37} - 48 q^{39} + 48 q^{41} + 232 q^{43} - 192 q^{47} + 16 q^{49} - 136 q^{51} - 32 q^{53} - 224 q^{55} + 24 q^{57} + 48 q^{59} - 160 q^{61} - 56 q^{63} - 96 q^{65} + 240 q^{69} - 40 q^{71} + 48 q^{73} + 296 q^{75} - 48 q^{77} + 136 q^{79} - 424 q^{81} + 264 q^{83} - 272 q^{85} - 208 q^{87} + 160 q^{89} - 320 q^{91} - 64 q^{93} - 272 q^{95} + 48 q^{97} + 224 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 16 * q^5 - 8 * q^7 - 16 * q^9 + 8 * q^11 + 16 * q^13 + 16 * q^15 - 64 * q^21 + 56 * q^23 + 64 * q^25 - 40 * q^27 + 48 * q^29 - 24 * q^31 + 160 * q^35 + 32 * q^37 - 48 * q^39 + 48 * q^41 + 232 * q^43 - 192 * q^47 + 16 * q^49 - 136 * q^51 - 32 * q^53 - 224 * q^55 + 24 * q^57 + 48 * q^59 - 160 * q^61 - 56 * q^63 - 96 * q^65 + 240 * q^69 - 40 * q^71 + 48 * q^73 + 296 * q^75 - 48 * q^77 + 136 * q^79 - 424 * q^81 + 264 * q^83 - 272 * q^85 - 208 * q^87 + 160 * q^89 - 320 * q^91 - 64 * q^93 - 272 * q^95 + 48 * q^97 + 224 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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