LMFDB - Embedded newform 1216.2.i.n.961.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(577,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1216.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.2696112.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 $ x^6 - x^5 + 5x^4 + 18x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.3
Root			$0.235342 + 0.407624i$ of defining polynomial
Character	$\chi$	$=$	1216.961
Dual form			1216.2.i.n.577.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62457 - 2.81384i) q^{3} +(0.235342 - 0.407624i) q^{5} -3.30777 q^{7} +(-3.77846 - 6.54448i) q^{9} +O(q^{10})$	\(q+(1.62457 - 2.81384i) q^{3} +(0.235342 - 0.407624i) q^{5} -3.30777 q^{7} +(-3.77846 - 6.54448i) q^{9} -1.47068 q^{11} +(-1.41855 - 2.45699i) q^{13} +(-0.764658 - 1.32443i) q^{15} +(-3.35991 + 5.81954i) q^{17} +(0.206025 - 4.35403i) q^{19} +(-5.37371 + 9.30754i) q^{21} +(-0.235342 - 0.407624i) q^{23} +(2.38923 + 4.13827i) q^{25} -14.8061 q^{27} +(2.48448 + 4.30325i) q^{29} +6.74742 q^{31} +(-2.38923 + 4.13827i) q^{33} +(-0.778457 + 1.34833i) q^{35} -4.74742 q^{37} -9.21811 q^{39} +(0.250859 - 0.434501i) q^{41} +(1.94786 - 3.37380i) q^{43} -3.55691 q^{45} +(-5.95517 - 10.3146i) q^{47} +3.94137 q^{49} +(10.9168 + 18.9085i) q^{51} +(-2.35991 - 4.08749i) q^{53} +(-0.346113 + 0.599486i) q^{55} +(-11.9168 - 7.65314i) q^{57} +(3.62457 - 6.27794i) q^{59} +(-6.26294 - 10.8477i) q^{61} +(12.4983 + 21.6477i) q^{63} -1.33537 q^{65} +(-0.316797 - 0.548708i) q^{67} -1.52932 q^{69} +(1.88923 - 3.27224i) q^{71} +(1.97068 - 3.41332i) q^{73} +15.5259 q^{75} +4.86469 q^{77} +(4.41855 - 7.65314i) q^{79} +(-12.7181 + 22.0284i) q^{81} -9.14486 q^{83} +(1.58145 + 2.73916i) q^{85} +16.1449 q^{87} +(-1.47718 - 2.55855i) q^{89} +(4.69223 + 8.12717i) q^{91} +(10.9617 - 18.9862i) q^{93} +(-1.72632 - 1.10866i) q^{95} +(-0.0293166 + 0.0507778i) q^{97} +(5.55691 + 9.62486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + q^{5} - 4 q^{7} - 6 q^{9}+O(q^{10}) $ 6 * q + q^3 + q^5 - 4 * q^7 - 6 * q^9	$ 6 q + q^{3} + q^{5} - 4 q^{7} - 6 q^{9} - 8 q^{11} - q^{13} - 5 q^{15} - 11 q^{17} - 6 q^{21} - q^{23} + 6 q^{25} - 38 q^{27} - 3 q^{29} - 12 q^{31} - 6 q^{33} + 12 q^{35} + 24 q^{37} - 2 q^{39} + 19 q^{41} + 5 q^{43} + 12 q^{45} - 17 q^{47} + 22 q^{49} + 23 q^{51} - 5 q^{53} - 10 q^{55} - 29 q^{57} + 13 q^{59} - 3 q^{61} + 40 q^{63} + 42 q^{65} - 9 q^{67} - 10 q^{69} + 3 q^{71} + 11 q^{73} + 24 q^{75} - 20 q^{77} + 19 q^{79} - 23 q^{81} - 24 q^{83} + 17 q^{85} + 66 q^{87} - 3 q^{89} + 44 q^{91} + 42 q^{93} + 13 q^{95} - q^{97}+O(q^{100}) $ 6 * q + q^3 + q^5 - 4 * q^7 - 6 * q^9 - 8 * q^11 - q^13 - 5 * q^15 - 11 * q^17 - 6 * q^21 - q^23 + 6 * q^25 - 38 * q^27 - 3 * q^29 - 12 * q^31 - 6 * q^33 + 12 * q^35 + 24 * q^37 - 2 * q^39 + 19 * q^41 + 5 * q^43 + 12 * q^45 - 17 * q^47 + 22 * q^49 + 23 * q^51 - 5 * q^53 - 10 * q^55 - 29 * q^57 + 13 * q^59 - 3 * q^61 + 40 * q^63 + 42 * q^65 - 9 * q^67 - 10 * q^69 + 3 * q^71 + 11 * q^73 + 24 * q^75 - 20 * q^77 + 19 * q^79 - 23 * q^81 - 24 * q^83 + 17 * q^85 + 66 * q^87 - 3 * q^89 + 44 * q^91 + 42 * q^93 + 13 * q^95 - q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.62457	−	2.81384i	0.937946	−	1.62457i	0.168652	−	0.985676i	$-0.446059\pi$
$3$	1.62457	−	2.81384i	0.937946	−	1.62457i	0.769294	−	0.638895i	$-0.220608\pi$
$4$		0			0
$5$	0.235342	−	0.407624i	0.105248	−	0.182295i	−0.808591	−	0.588370i	$-0.799770\pi$
$5$	0.235342	−	0.407624i	0.105248	−	0.182295i	0.913840	+	0.406076i	$0.133103\pi$
$6$		0			0
$7$	−3.30777			−1.25022			−0.625110	−	0.780536i	$-0.714946\pi$
$7$	−3.30777			−1.25022			−0.625110	+	0.780536i	$0.714946\pi$
$8$		0			0
$9$	−3.77846	−	6.54448i	−1.25949	−	2.18149i
$10$		0			0
$11$	−1.47068			−0.443428			−0.221714	−	0.975112i	$-0.571165\pi$
$11$	−1.47068			−0.443428			−0.221714	+	0.975112i	$0.571165\pi$
$12$		0			0
$13$	−1.41855	−	2.45699i	−0.393434	−	0.681447i	0.599466	−	0.800400i	$-0.295380\pi$
$13$	−1.41855	−	2.45699i	−0.393434	−	0.681447i	−0.992900	+	0.118953i	$0.962046\pi$
$14$		0			0
$15$	−0.764658	−	1.32443i	−0.197434	−	0.341966i
$16$		0			0
$17$	−3.35991	+	5.81954i	−0.814898	+	1.41145i	0.0945025	+	0.995525i	$0.469874\pi$
$17$	−3.35991	+	5.81954i	−0.814898	+	1.41145i	−0.909401	+	0.415921i	$0.863459\pi$
$18$		0			0
$19$	0.206025	−	4.35403i	0.0472654	−	0.998882i
$19$	0.206025	−	4.35403i	0.0472654	−	0.998882i
$20$		0			0
$21$	−5.37371	+	9.30754i	−1.17264	+	2.03107i
$22$		0			0
$23$	−0.235342	−	0.407624i	−0.0490721	−	0.0849954i	0.840446	−	0.541895i	$-0.182293\pi$
$23$	−0.235342	−	0.407624i	−0.0490721	−	0.0849954i	−0.889518	+	0.456900i	$0.848960\pi$
$24$		0			0
$25$	2.38923	+	4.13827i	0.477846	+	0.827653i
$26$		0			0
$27$	−14.8061			−2.84943
$28$		0			0
$29$	2.48448	+	4.30325i	0.461357	+	0.799093i	0.999029	−	0.0440607i	$-0.0140295\pi$
$29$	2.48448	+	4.30325i	0.461357	+	0.799093i	−0.537672	+	0.843154i	$0.680696\pi$
$30$		0			0
$31$	6.74742			1.21187			0.605936	−	0.795513i	$-0.292799\pi$
$31$	6.74742			1.21187			0.605936	+	0.795513i	$0.292799\pi$
$32$		0			0
$33$	−2.38923	+	4.13827i	−0.415911	+	0.720380i
$34$		0			0
$35$	−0.778457	+	1.34833i	−0.131583	+	0.227909i
$36$		0			0
$37$	−4.74742			−0.780471			−0.390236	−	0.920715i	$-0.627606\pi$
$37$	−4.74742			−0.780471			−0.390236	+	0.920715i	$0.627606\pi$
$38$		0			0
$39$	−9.21811			−1.47608
$40$		0			0
$41$	0.250859	−	0.434501i	0.0391777	−	0.0678577i	−0.845772	−	0.533545i	$-0.820860\pi$
$41$	0.250859	−	0.434501i	0.0391777	−	0.0678577i	0.884949	+	0.465687i	$0.154193\pi$
$42$		0			0
$43$	1.94786	−	3.37380i	0.297046	−	0.514499i	−0.678413	−	0.734681i	$-0.737332\pi$
$43$	1.94786	−	3.37380i	0.297046	−	0.514499i	0.975459	+	0.220182i	$0.0706652\pi$
$44$		0			0
$45$	−3.55691			−0.530233
$46$		0			0
$47$	−5.95517	−	10.3146i	−0.868650	−	1.50455i	−0.863377	−	0.504560i	$-0.831655\pi$
$47$	−5.95517	−	10.3146i	−0.868650	−	1.50455i	−0.00527366	−	0.999986i	$-0.501679\pi$
$48$		0			0
$49$	3.94137			0.563052
$50$		0			0
$51$	10.9168	+	18.9085i	1.52866	+	2.64772i
$52$		0			0
$53$	−2.35991	−	4.08749i	−0.324159	−	0.561460i	0.657183	−	0.753731i	$-0.271748\pi$
$53$	−2.35991	−	4.08749i	−0.324159	−	0.561460i	−0.981342	+	0.192272i	$0.938415\pi$
$54$		0			0
$55$	−0.346113	+	0.599486i	−0.0466699	+	0.0808346i
$56$		0			0
$57$	−11.9168	−	7.65314i	−1.57842	−	1.01368i
$58$		0			0
$59$	3.62457	−	6.27794i	0.471879	−	0.817318i	−0.527603	−	0.849491i	$-0.676909\pi$
$59$	3.62457	−	6.27794i	0.471879	−	0.817318i	0.999482	+	0.0321726i	$0.0102426\pi$
$60$		0			0
$61$	−6.26294	−	10.8477i	−0.801887	−	1.38891i	−0.918373	−	0.395717i	$-0.870496\pi$
$61$	−6.26294	−	10.8477i	−0.801887	−	1.38891i	0.116485	−	0.993192i	$-0.462837\pi$
$62$		0			0
$63$	12.4983	+	21.6477i	1.57464	+	2.72735i
$64$		0			0
$65$	−1.33537			−0.165632
$66$		0			0
$67$	−0.316797	−	0.548708i	−0.0387029	−	0.0670353i	0.846025	−	0.533143i	$-0.178989\pi$
$67$	−0.316797	−	0.548708i	−0.0387029	−	0.0670353i	−0.884728	+	0.466108i	$0.845656\pi$
$68$		0			0
$69$	−1.52932			−0.184108
$70$		0			0
$71$	1.88923	−	3.27224i	0.224210	−	0.388343i	−0.731872	−	0.681442i	$-0.761353\pi$
$71$	1.88923	−	3.27224i	0.224210	−	0.388343i	0.956082	+	0.293099i	$0.0946865\pi$
$72$		0			0
$73$	1.97068	−	3.41332i	0.230651	−	0.399499i	−0.727349	−	0.686268i	$-0.759248\pi$
$73$	1.97068	−	3.41332i	0.230651	−	0.399499i	0.958000	+	0.286769i	$0.0925811\pi$
$74$		0			0
$75$	15.5259			1.79277
$76$		0			0
$77$	4.86469			0.554383
$78$		0			0
$79$	4.41855	−	7.65314i	0.497125	−	0.861046i	−0.502869	−	0.864362i	$-0.667722\pi$
$79$	4.41855	−	7.65314i	0.497125	−	0.861046i	0.999995	+	0.00331640i	$0.00105564\pi$
$80$		0			0
$81$	−12.7181	+	22.0284i	−1.41312	+	2.44760i
$82$		0			0
$83$	−9.14486			−1.00378			−0.501890	−	0.864932i	$-0.667362\pi$
$83$	−9.14486			−1.00378			−0.501890	+	0.864932i	$0.667362\pi$
$84$		0			0
$85$	1.58145	+	2.73916i	0.171533	+	0.297104i
$86$		0			0
$87$	16.1449			1.73091
$88$		0			0
$89$	−1.47718	−	2.55855i	−0.156581	−	0.271206i	0.777053	−	0.629435i	$-0.216714\pi$
$89$	−1.47718	−	2.55855i	−0.156581	−	0.271206i	−0.933633	+	0.358230i	$0.883380\pi$
$90$		0			0
$91$	4.69223	+	8.12717i	0.491879	+	0.851959i
$92$		0			0
$93$	10.9617	−	18.9862i	1.13667	−	1.96877i
$94$		0			0
$95$	−1.72632	−	1.10866i	−0.177117	−	0.113747i
$96$		0			0
$97$	−0.0293166	+	0.0507778i	−0.00297665	+	0.00515571i	−0.867510	−	0.497420i	$-0.834281\pi$
$97$	−0.0293166	+	0.0507778i	−0.00297665	+	0.00515571i	0.864533	+	0.502576i	$0.167614\pi$
$98$		0			0
$99$	5.55691	+	9.62486i	0.558491	+	0.967335i
$100$		0			0
$101$	5.79226	+	10.0325i	0.576351	+	0.998269i	0.995893	+	0.0905335i	$0.0288572\pi$
$101$	5.79226	+	10.0325i	0.576351	+	0.998269i	−0.419542	+	0.907736i	$0.637809\pi$
$102$		0			0
$103$	−8.17246			−0.805257			−0.402628	−	0.915364i	$-0.631903\pi$
$103$	−8.17246			−0.805257			−0.402628	+	0.915364i	$0.631903\pi$
$104$		0			0
$105$	2.52932	+	4.38090i	0.246836	+	0.427533i
$106$		0			0
$107$	−0.498281			−0.0481706			−0.0240853	−	0.999710i	$-0.507667\pi$
$107$	−0.498281			−0.0481706			−0.0240853	+	0.999710i	$0.507667\pi$
$108$		0			0
$109$	−4.19700	+	7.26942i	−0.402000	+	0.696284i	−0.993967	−	0.109678i	$-0.965018\pi$
$109$	−4.19700	+	7.26942i	−0.402000	+	0.696284i	0.591967	+	0.805962i	$0.298351\pi$
$110$		0			0
$111$	−7.71252	+	13.3585i	−0.732040	+	1.26793i
$112$		0			0
$113$	4.83365			0.454712			0.227356	−	0.973812i	$-0.426992\pi$
$113$	4.83365			0.454712			0.227356	+	0.973812i	$0.426992\pi$
$114$		0			0
$115$	−0.221543			−0.0206590
$116$		0			0
$117$	−10.7198	+	18.5673i	−0.991048	+	1.71655i
$118$		0			0
$119$	11.1138	−	19.2497i	1.01880	−	1.76462i
$120$		0			0
$121$	−8.83709			−0.803372
$122$		0			0
$123$	−0.815078	−	1.41176i	−0.0734931	−	0.127294i
$124$		0			0
$125$	4.60256			0.411665
$126$		0			0
$127$	9.22460	+	15.9775i	0.818551	+	1.41777i	0.906750	+	0.421669i	$0.138556\pi$
$127$	9.22460	+	15.9775i	0.818551	+	1.41777i	−0.0881990	+	0.996103i	$0.528111\pi$
$128$		0			0
$129$	−6.32888	−	10.9619i	−0.557227	−	0.965145i
$130$		0			0
$131$	0.434063	−	0.751819i	0.0379243	−	0.0656867i	−0.846440	−	0.532484i	$-0.821259\pi$
$131$	0.434063	−	0.751819i	0.0379243	−	0.0656867i	0.884365	+	0.466797i	$0.154592\pi$
$132$		0			0
$133$	−0.681485	+	14.4021i	−0.0590922	+	1.24882i
$134$		0			0
$135$	−3.48448	+	6.03530i	−0.299896	+	0.519436i
$136$		0			0
$137$	−2.27846	−	3.94640i	−0.194662	−	0.337164i	0.752128	−	0.659017i	$-0.229028\pi$
$137$	−2.27846	−	3.94640i	−0.194662	−	0.337164i	−0.946790	+	0.321853i	$0.895694\pi$
$138$		0			0
$139$	−8.15389	−	14.1229i	−0.691604	−	1.19789i	−0.971312	−	0.237808i	$-0.923571\pi$
$139$	−8.15389	−	14.1229i	−0.691604	−	1.19789i	0.279709	−	0.960085i	$-0.409762\pi$
$140$		0			0
$141$	−38.6983			−3.25899
$142$		0			0
$143$	2.08623	+	3.61346i	0.174459	+	0.302173i
$144$		0			0
$145$	2.33881			0.194228
$146$		0			0
$147$	6.40303	−	11.0904i	0.528113	−	0.914718i
$148$		0			0
$149$	10.4534	−	18.1059i	0.856380	−	1.48329i	−0.0189794	−	0.999820i	$-0.506042\pi$
$149$	10.4534	−	18.1059i	0.856380	−	1.48329i	0.875359	−	0.483473i	$-0.160625\pi$
$150$		0			0
$151$	1.75086			0.142483			0.0712415	−	0.997459i	$-0.477304\pi$
$151$	1.75086			0.142483			0.0712415	+	0.997459i	$0.477304\pi$
$152$		0			0
$153$	50.7811			4.10541
$154$		0			0
$155$	1.58795	−	2.75041i	0.127547	−	0.220918i
$156$		0			0
$157$	−0.0797359	+	0.138107i	−0.00636362	+	0.0110221i	−0.869190	−	0.494479i	$-0.835359\pi$
$157$	−0.0797359	+	0.138107i	−0.00636362	+	0.0110221i	0.862826	+	0.505501i	$0.168692\pi$
$158$		0			0
$159$	−15.3354			−1.21617
$160$		0			0
$161$	0.778457	+	1.34833i	0.0613510	+	0.106263i
$162$		0			0
$163$	0.0862308			0.00675412			0.00337706	−	0.999994i	$-0.498925\pi$
$163$	0.0862308			0.00675412			0.00337706	+	0.999994i	$0.498925\pi$
$164$		0			0
$165$	1.12457	+	1.94781i	0.0875477	+	0.151637i
$166$		0			0
$167$	3.13837	+	5.43581i	0.242854	+	0.420636i	0.961526	−	0.274713i	$-0.0885830\pi$
$167$	3.13837	+	5.43581i	0.242854	+	0.420636i	−0.718672	+	0.695349i	$0.755250\pi$
$168$		0			0
$169$	2.47546	−	4.28762i	0.190420	−	0.329817i
$170$		0			0
$171$	−29.2733	+	15.1032i	−2.23859	+	1.15497i
$172$		0			0
$173$	−5.41855	+	9.38520i	−0.411964	+	0.713543i	−0.995104	−	0.0988284i	$-0.968491\pi$
$173$	−5.41855	+	9.38520i	−0.411964	+	0.713543i	0.583140	+	0.812372i	$0.301824\pi$
$174$		0			0
$175$	−7.90303	−	13.6884i	−0.597413	−	1.03475i
$176$		0			0
$177$	−11.7767	−	20.3979i	−0.885194	−	1.53320i
$178$		0			0
$179$	−7.08967			−0.529907			−0.264953	−	0.964261i	$-0.585357\pi$
$179$	−7.08967			−0.529907			−0.264953	+	0.964261i	$0.585357\pi$
$180$		0			0
$181$	−6.17671	−	10.6984i	−0.459111	−	0.795204i	0.539803	−	0.841791i	$-0.318499\pi$
$181$	−6.17671	−	10.6984i	−0.459111	−	0.795204i	−0.998914	+	0.0465875i	$0.985165\pi$
$182$		0			0
$183$	−40.6983			−3.00851
$184$		0			0
$185$	−1.11727	+	1.93516i	−0.0821431	+	0.142276i
$186$		0			0
$187$	4.94137	−	8.55870i	0.361349	−	0.625874i
$188$		0			0
$189$	48.9751			3.56241
$190$		0			0
$191$	8.99656			0.650968			0.325484	−	0.945547i	$-0.394473\pi$
$191$	8.99656			0.650968			0.325484	+	0.945547i	$0.394473\pi$
$192$		0			0
$193$	1.58145	−	2.73916i	0.113836	−	0.197169i	−0.803478	−	0.595334i	$-0.797020\pi$
$193$	1.58145	−	2.73916i	0.113836	−	0.197169i	0.917314	+	0.398165i	$0.130353\pi$
$194$		0			0
$195$	−2.16940	+	3.75752i	−0.155354	+	0.269082i
$196$		0			0
$197$	21.2457			1.51369			0.756847	−	0.653592i	$-0.226739\pi$
$197$	21.2457			1.51369			0.756847	+	0.653592i	$0.226739\pi$
$198$		0			0
$199$	−4.94786	−	8.56995i	−0.350745	−	0.607507i	0.635635	−	0.771989i	$-0.280738\pi$
$199$	−4.94786	−	8.56995i	−0.350745	−	0.607507i	−0.986380	+	0.164482i	$0.947405\pi$
$200$		0			0
$201$	−2.05863			−0.145205
$202$		0			0
$203$	−8.21811	−	14.2342i	−0.576798	−	0.999043i
$204$		0			0
$205$	−0.118075	−	0.204513i	−0.00824674	−	0.0142838i
$206$		0			0
$207$	−1.77846	+	3.08038i	−0.123611	+	0.214101i
$208$		0			0
$209$	−0.302998	+	6.40340i	−0.0209588	+	0.442932i
$210$		0			0
$211$	9.55042	−	16.5418i	0.657478	−	1.13879i	−0.323788	−	0.946130i	$-0.604957\pi$
$211$	9.55042	−	16.5418i	0.657478	−	1.13879i	0.981266	−	0.192656i	$-0.0617101\pi$
$212$		0			0
$213$	−6.13837	−	10.6320i	−0.420594	−	0.728490i
$214$		0			0
$215$	−0.916826	−	1.58799i	−0.0625270	−	0.108300i
$216$		0			0
$217$	−22.3189			−1.51511
$218$		0			0
$219$	−6.40303	−	11.0904i	−0.432676	−	0.749418i
$220$		0			0
$221$	19.0647			1.28243
$222$		0			0
$223$	8.48448	−	14.6956i	0.568163	−	0.984087i	−0.428585	−	0.903502i	$-0.640988\pi$
$223$	8.48448	−	14.6956i	0.568163	−	0.984087i	0.996748	−	0.0805855i	$-0.0256790\pi$
$224$		0			0
$225$	18.0552	−	31.2725i	1.20368	−	2.08483i
$226$		0			0
$227$	−0.646583			−0.0429152			−0.0214576	−	0.999770i	$-0.506831\pi$
$227$	−0.646583			−0.0429152			−0.0214576	+	0.999770i	$0.506831\pi$
$228$		0			0
$229$	8.55348			0.565230			0.282615	−	0.959233i	$-0.408798\pi$
$229$	8.55348			0.565230			0.282615	+	0.959233i	$0.408798\pi$
$230$		0			0
$231$	7.90303	−	13.6884i	0.519981	−	0.900634i
$232$		0			0
$233$	1.85342	−	3.21021i	0.121421	−	0.210308i	−0.798907	−	0.601455i	$-0.794588\pi$
$233$	1.85342	−	3.21021i	0.121421	−	0.210308i	0.920328	+	0.391147i	$0.127921\pi$
$234$		0			0
$235$	−5.60600			−0.365695
$236$		0			0
$237$	−14.3565	−	24.8661i	−0.932553	−	1.61523i
$238$		0			0
$239$	15.7655			1.01978			0.509892	−	0.860239i	$-0.329685\pi$
$239$	15.7655			1.01978			0.509892	+	0.860239i	$0.329685\pi$
$240$		0			0
$241$	8.05691	+	13.9550i	0.518991	+	0.898920i	0.999756	+	0.0220701i	$0.00702570\pi$
$241$	8.05691	+	13.9550i	0.518991	+	0.898920i	−0.480765	+	0.876850i	$0.659641\pi$
$242$		0			0
$243$	19.1138	+	33.1061i	1.22615	+	2.12376i
$244$		0			0
$245$	0.927568	−	1.60659i	0.0592601	−	0.102642i
$246$		0			0
$247$	−10.9901	+	5.67018i	−0.699281	+	0.360785i
$248$		0			0
$249$	−14.8565	+	25.7322i	−0.941491	+	1.63071i
$250$		0			0
$251$	−7.82807	−	13.5586i	−0.494103	−	0.855812i	0.505874	−	0.862608i	$-0.331170\pi$
$251$	−7.82807	−	13.5586i	−0.494103	−	0.855812i	−0.999977	+	0.00679567i	$0.997837\pi$
$252$		0			0
$253$	0.346113	+	0.599486i	0.0217599	+	0.0376893i
$254$		0			0
$255$	10.2767			0.643554
$256$		0			0
$257$	13.9086	+	24.0904i	0.867595	+	1.50272i	0.864447	+	0.502724i	$0.167669\pi$
$257$	13.9086	+	24.0904i	0.867595	+	1.50272i	0.00314859	+	0.999995i	$0.498998\pi$
$258$		0			0
$259$	15.7034			0.975762
$260$		0			0
$261$	18.7750	−	32.5193i	1.16214	−	2.01289i
$262$		0			0
$263$	−8.42585	+	14.5940i	−0.519560	+	0.899905i	0.480181	+	0.877169i	$0.340571\pi$
$263$	−8.42585	+	14.5940i	−0.519560	+	0.899905i	−0.999742	+	0.0227353i	$0.992763\pi$
$264$		0			0
$265$	−2.22154			−0.136468
$266$		0			0
$267$	−9.59912			−0.587457
$268$		0			0
$269$	−14.8125	+	25.6561i	−0.903137	+	1.56428i	−0.0797386	+	0.996816i	$0.525409\pi$
$269$	−14.8125	+	25.6561i	−0.903137	+	1.56428i	−0.823399	+	0.567464i	$0.807925\pi$
$270$		0			0
$271$	−7.23534	+	12.5320i	−0.439516	+	0.761264i	−0.997652	−	0.0684857i	$-0.978183\pi$
$271$	−7.23534	+	12.5320i	−0.439516	+	0.761264i	0.558136	+	0.829749i	$0.311517\pi$
$272$		0			0
$273$	30.4914			1.84542
$274$		0			0
$275$	−3.51380	−	6.08608i	−0.211890	−	0.367004i
$276$		0			0
$277$	12.4216			0.746342			0.373171	−	0.927763i	$-0.378271\pi$
$277$	12.4216			0.746342			0.373171	+	0.927763i	$0.378271\pi$
$278$		0			0
$279$	−25.4948	−	44.1584i	−1.52634	−	2.64369i
$280$		0			0
$281$	5.14658	+	8.91414i	0.307019	+	0.531773i	0.977709	−	0.209965i	$-0.0673350\pi$
$281$	5.14658	+	8.91414i	0.307019	+	0.531773i	−0.670690	+	0.741738i	$0.734002\pi$
$282$		0			0
$283$	−7.93234	+	13.7392i	−0.471529	+	0.816712i	−0.999469	−	0.0325693i	$-0.989631\pi$
$283$	−7.93234	+	13.7392i	−0.471529	+	0.816712i	0.527941	+	0.849281i	$0.322964\pi$
$284$		0			0
$285$	−5.92413	+	3.05648i	−0.350915	+	0.181050i
$286$		0			0
$287$	−0.829786	+	1.43723i	−0.0489807	+	0.0848371i
$288$		0			0
$289$	−14.0780	−	24.3838i	−0.828119	−	1.43434i
$290$		0			0
$291$	0.0952537	+	0.164984i	0.00558387	+	0.00967155i
$292$		0			0
$293$	12.1579			0.710269			0.355135	−	0.934815i	$-0.384435\pi$
$293$	12.1579			0.710269			0.355135	+	0.934815i	$0.384435\pi$
$294$		0			0
$295$	−1.70603	−	2.95492i	−0.0993286	−	0.172042i
$296$		0			0
$297$	21.7750			1.26351
$298$		0			0
$299$	−0.667686	+	1.15647i	−0.0386133	+	0.0668801i
$300$		0			0
$301$	−6.44309	+	11.1598i	−0.371373	+	0.643237i
$302$		0			0
$303$	37.6397			2.16234
$304$		0			0
$305$	−5.89572			−0.337588
$306$		0			0
$307$	−6.15045	+	10.6529i	−0.351025	+	0.607993i	−0.986429	−	0.164187i	$-0.947500\pi$
$307$	−6.15045	+	10.6529i	−0.351025	+	0.607993i	0.635405	+	0.772179i	$0.280833\pi$
$308$		0			0
$309$	−13.2767	+	22.9960i	−0.755287	+	1.30820i
$310$		0			0
$311$	−0.519765			−0.0294732			−0.0147366	−	0.999891i	$-0.504691\pi$
$311$	−0.519765			−0.0294732			−0.0147366	+	0.999891i	$0.504691\pi$
$312$		0			0
$313$	−9.30605	−	16.1186i	−0.526009	−	0.911075i	−0.999541	−	0.0302980i	$-0.990354\pi$
$313$	−9.30605	−	16.1186i	−0.526009	−	0.911075i	0.473532	−	0.880777i	$-0.342979\pi$
$314$		0			0
$315$	11.7655			0.662909
$316$		0			0
$317$	−1.41855	−	2.45699i	−0.0796734	−	0.137998i	0.823436	−	0.567410i	$-0.192054\pi$
$317$	−1.41855	−	2.45699i	−0.0796734	−	0.137998i	−0.903109	+	0.429411i	$0.858721\pi$
$318$		0			0
$319$	−3.65389	−	6.32872i	−0.204578	−	0.354340i
$320$		0			0
$321$	−0.809493	+	1.40208i	−0.0451815	+	0.0782566i
$322$		0			0
$323$	24.6462	+	15.8281i	1.37135	+	0.880700i
$324$		0			0
$325$	6.77846	−	11.7406i	0.376001	−	0.651253i
$326$		0			0
$327$	13.6367	+	23.6194i	0.754108	+	1.30615i
$328$		0			0
$329$	19.6983	+	34.1185i	1.08600	+	1.88102i
$330$		0			0
$331$	19.0276			1.04585			0.522926	−	0.852378i	$-0.324841\pi$
$331$	19.0276			1.04585			0.522926	+	0.852378i	$0.324841\pi$
$332$		0			0
$333$	17.9379	+	31.0694i	0.982992	+	1.70259i
$334$		0			0
$335$	−0.298222			−0.0162936
$336$		0			0
$337$	7.36469	−	12.7560i	0.401180	−	0.694864i	−0.592689	−	0.805432i	$-0.701933\pi$
$337$	7.36469	−	12.7560i	0.401180	−	0.694864i	0.993869	+	0.110567i	$0.0352668\pi$
$338$		0			0
$339$	7.85261	−	13.6011i	0.426495	−	0.738711i
$340$		0			0
$341$	−9.92332			−0.537378
$342$		0			0
$343$	10.1173			0.546281
$344$		0			0
$345$	−0.359912	+	0.623386i	−0.0193770	+	0.0335620i
$346$		0			0
$347$	−5.06766	+	8.77744i	−0.272046	+	0.471198i	−0.969386	−	0.245543i	$-0.921034\pi$
$347$	−5.06766	+	8.77744i	−0.272046	+	0.471198i	0.697340	+	0.716741i	$0.254367\pi$
$348$		0			0
$349$	−2.56035			−0.137053			−0.0685263	−	0.997649i	$-0.521830\pi$
$349$	−2.56035			−0.137053			−0.0685263	+	0.997649i	$0.521830\pi$
$350$		0			0
$351$	21.0031	+	36.3784i	1.12106	+	1.94173i
$352$		0			0
$353$	20.4458			1.08822			0.544109	−	0.839015i	$-0.316868\pi$
$353$	20.4458			1.08822			0.544109	+	0.839015i	$0.316868\pi$
$354$		0			0
$355$	−0.889229	−	1.54019i	−0.0471954	−	0.0817447i
$356$		0			0
$357$	−36.1104	−	62.5450i	−1.91116	−	3.31023i
$358$		0			0
$359$	7.29397	−	12.6335i	0.384961	−	0.666772i	−0.606803	−	0.794853i	$-0.707548\pi$
$359$	7.29397	−	12.6335i	0.384961	−	0.666772i	0.991764	+	0.128080i	$0.0408815\pi$
$360$		0			0
$361$	−18.9151	−	1.79408i	−0.995532	−	0.0944252i
$362$		0			0
$363$	−14.3565	+	24.8661i	−0.753519	+	1.30513i
$364$		0			0
$365$	−0.927568	−	1.60659i	−0.0485511	−	0.0840930i
$366$		0			0
$367$	−14.5397	−	25.1835i	−0.758965	−	1.31457i	−0.943379	−	0.331717i	$-0.892372\pi$
$367$	−14.5397	−	25.1835i	−0.758965	−	1.31457i	0.184414	−	0.982849i	$-0.440961\pi$
$368$		0			0
$369$	−3.79145			−0.197375
$370$		0			0
$371$	7.80605	+	13.5205i	0.405270	+	0.701949i
$372$		0			0
$373$	−20.7880			−1.07636			−0.538181	−	0.842829i	$-0.680888\pi$
$373$	−20.7880			−1.07636			−0.538181	+	0.842829i	$0.680888\pi$
$374$		0			0
$375$	7.47718	−	12.9509i	0.386120	−	0.668779i
$376$		0			0
$377$	7.04870	−	12.2087i	0.363027	−	0.628780i
$378$		0			0
$379$	−19.7034			−1.01210			−0.506048	−	0.862505i	$-0.668894\pi$
$379$	−19.7034			−1.01210			−0.506048	+	0.862505i	$0.668894\pi$
$380$		0			0
$381$	59.9440			3.07103
$382$		0			0
$383$	−14.2319	+	24.6504i	−0.727216	+	1.25958i	0.230839	+	0.972992i	$0.425853\pi$
$383$	−14.2319	+	24.6504i	−0.727216	+	1.25958i	−0.958055	+	0.286584i	$0.907480\pi$
$384$		0			0
$385$	1.14486	−	1.98296i	0.0583477	−	0.101061i
$386$		0			0
$387$	−29.4396			−1.49650
$388$		0			0
$389$	1.85819	+	3.21848i	0.0942141	+	0.163184i	0.909280	−	0.416184i	$-0.136633\pi$
$389$	1.85819	+	3.21848i	0.0942141	+	0.163184i	−0.815066	+	0.579368i	$0.803300\pi$
$390$		0			0
$391$	3.16291			0.159955
$392$		0			0
$393$	−1.41033	−	2.44277i	−0.0711418	−	0.123221i
$394$		0			0
$395$	−2.07974	−	3.60221i	−0.104643	−	0.181247i
$396$		0			0
$397$	8.81985	−	15.2764i	0.442656	−	0.766702i	−0.555230	−	0.831697i	$-0.687370\pi$
$397$	8.81985	−	15.2764i	0.442656	−	0.766702i	0.997886	+	0.0649947i	$0.0207030\pi$
$398$		0			0
$399$	39.4182	+	25.3149i	1.97338	+	1.26733i
$400$		0			0
$401$	15.2785	−	26.4631i	0.762970	−	1.32150i	−0.178344	−	0.983968i	$-0.557074\pi$
$401$	15.2785	−	26.4631i	0.762970	−	1.32150i	0.941313	−	0.337534i	$-0.109593\pi$
$402$		0			0
$403$	−9.57152	−	16.5784i	−0.476791	−	0.825827i
$404$		0			0
$405$	5.98620	+	10.3684i	0.297457	+	0.515210i
$406$		0			0
$407$	6.98195			0.346083
$408$		0			0
$409$	15.6138	+	27.0439i	0.772054	+	1.33724i	0.936435	+	0.350840i	$0.114104\pi$
$409$	15.6138	+	27.0439i	0.772054	+	1.33724i	−0.164381	+	0.986397i	$0.552563\pi$
$410$		0			0
$411$	−14.8061			−0.730329
$412$		0			0
$413$	−11.9893	+	20.7660i	−0.589953	+	1.02183i
$414$		0			0
$415$	−2.15217	+	3.72766i	−0.105646	+	0.182984i
$416$		0			0
$417$	−52.9862			−2.59475
$418$		0			0
$419$	28.9966			1.41657			0.708287	−	0.705924i	$-0.249468\pi$
$419$	28.9966			1.41657			0.708287	+	0.705924i	$0.249468\pi$
$420$		0			0
$421$	15.6293	−	27.0708i	0.761728	−	1.31935i	−0.180232	−	0.983624i	$-0.557685\pi$
$421$	15.6293	−	27.0708i	0.761728	−	1.31935i	0.941959	−	0.335727i	$-0.108982\pi$
$422$		0			0
$423$	−45.0027	+	77.9469i	−2.18810	+	3.78991i
$424$		0			0
$425$	−32.1104			−1.55758
$426$		0			0
$427$	20.7164	+	35.8818i	1.00254	+	1.73644i
$428$		0			0
$429$	13.5569			0.654534
$430$		0			0
$431$	7.43315	+	12.8746i	0.358042	+	0.620148i	0.987634	−	0.156779i	$-0.0501110\pi$
$431$	7.43315	+	12.8746i	0.358042	+	0.620148i	−0.629591	+	0.776926i	$0.716778\pi$
$432$		0			0
$433$	−19.7815	−	34.2626i	−0.950639	−	1.64655i	−0.744047	−	0.668128i	$-0.767096\pi$
$433$	−19.7815	−	34.2626i	−0.950639	−	1.64655i	−0.206592	−	0.978427i	$-0.566237\pi$
$434$		0			0
$435$	3.79956	−	6.58103i	0.182175	−	0.315536i
$436$		0			0
$437$	−1.82329	+	0.940703i	−0.0872199	+	0.0450000i
$438$		0			0
$439$	5.79226	−	10.0325i	0.276449	−	0.478824i	−0.694050	−	0.719926i	$-0.744176\pi$
$439$	5.79226	−	10.0325i	0.276449	−	0.478824i	0.970500	+	0.241102i	$0.0775089\pi$
$440$		0			0
$441$	−14.8923	−	25.7942i	−0.709156	−	1.22830i
$442$		0			0
$443$	14.4617	+	25.0483i	0.687094	+	1.19008i	0.972774	+	0.231757i	$0.0744474\pi$
$443$	14.4617	+	25.0483i	0.687094	+	1.19008i	−0.285680	+	0.958325i	$0.592219\pi$
$444$		0			0
$445$	−1.39057			−0.0659192
$446$		0			0
$447$	−33.9647	−	58.8286i	−1.60648	−	2.78250i
$448$		0			0
$449$	31.2147			1.47311			0.736556	−	0.676377i	$-0.236451\pi$
$449$	31.2147			1.47311			0.736556	+	0.676377i	$0.236451\pi$
$450$		0			0
$451$	−0.368935	+	0.639014i	−0.0173725	+	0.0300900i
$452$		0			0
$453$	2.84439	−	4.92664i	0.133641	−	0.231474i
$454$		0			0
$455$	4.41711			0.207077
$456$		0			0
$457$	17.2215			0.805590			0.402795	−	0.915290i	$-0.368039\pi$
$457$	17.2215			0.805590			0.402795	+	0.915290i	$0.368039\pi$
$458$		0			0
$459$	49.7470	−	86.1644i	2.32199	−	4.02181i
$460$		0			0
$461$	−16.4151	+	28.4318i	−0.764528	+	1.32420i	0.175968	+	0.984396i	$0.443694\pi$
$461$	−16.4151	+	28.4318i	−0.764528	+	1.32420i	−0.940496	+	0.339805i	$0.889639\pi$
$462$		0			0
$463$	6.28973			0.292308			0.146154	−	0.989262i	$-0.453310\pi$
$463$	6.28973			0.292308			0.146154	+	0.989262i	$0.453310\pi$
$464$		0			0
$465$	−5.15947	−	8.93647i	−0.239265	−	0.414419i
$466$		0			0
$467$	9.47068			0.438251			0.219125	−	0.975697i	$-0.429680\pi$
$467$	9.47068			0.438251			0.219125	+	0.975697i	$0.429680\pi$
$468$		0			0
$469$	1.04789	+	1.81500i	0.0483871	+	0.0838090i
$470$		0			0
$471$	0.259073	+	0.448728i	0.0119375	+	0.0206763i
$472$		0			0
$473$	−2.86469	+	4.96179i	−0.131718	+	0.228143i
$474$		0			0
$475$	18.5104	−	9.55018i	0.849314	−	0.438192i
$476$		0			0
$477$	−17.8337	+	30.8888i	−0.816547	+	1.41430i
$478$		0			0
$479$	−13.0341	−	22.5757i	−0.595543	−	1.03151i	−0.993470	−	0.114094i	$-0.963604\pi$
$479$	−13.0341	−	22.5757i	−0.595543	−	1.03151i	0.397927	−	0.917417i	$-0.369730\pi$
$480$		0			0
$481$	6.73443	+	11.6644i	0.307064	+	0.531850i
$482$		0			0
$483$	5.05863			0.230176
$484$		0			0
$485$	0.0137988	+	0.0239003i	0.000626573	+	0.00108526i
$486$		0			0
$487$	16.8939			0.765536			0.382768	−	0.923845i	$-0.374971\pi$
$487$	16.8939			0.765536			0.382768	+	0.923845i	$0.374971\pi$
$488$		0			0
$489$	0.140088	−	0.242640i	0.00633500	−	0.0109725i
$490$		0			0
$491$	8.94442	−	15.4922i	0.403656	−	0.699153i	−0.590508	−	0.807032i	$-0.701073\pi$
$491$	8.94442	−	15.4922i	0.403656	−	0.699153i	0.994164	+	0.107879i	$0.0344059\pi$
$492$		0			0
$493$	−33.3906			−1.50384
$494$		0			0
$495$	5.23109			0.235120
$496$		0			0
$497$	−6.24914	+	10.8238i	−0.280312	+	0.485515i
$498$		0			0
$499$	−14.7108	+	25.4799i	−0.658546	+	1.14063i	0.322446	+	0.946588i	$0.395495\pi$
$499$	−14.7108	+	25.4799i	−0.658546	+	1.14063i	−0.980992	+	0.194047i	$0.937839\pi$
$500$		0			0
$501$	20.3940			0.911137
$502$		0			0
$503$	−4.53968	−	7.86295i	−0.202414	−	0.350592i	0.746892	−	0.664946i	$-0.231545\pi$
$503$	−4.53968	−	7.86295i	−0.202414	−	0.350592i	−0.949306	+	0.314354i	$0.898212\pi$
$504$		0			0
$505$	5.45264			0.242639
$506$		0			0
$507$	−8.04312	−	13.9311i	−0.357207	−	0.618701i
$508$		0			0
$509$	−10.1970	−	17.6617i	−0.451974	−	0.782842i	0.546534	−	0.837437i	$-0.315947\pi$
$509$	−10.1970	−	17.6617i	−0.451974	−	0.782842i	−0.998509	+	0.0545944i	$0.982613\pi$
$510$		0			0
$511$	−6.51857	+	11.2905i	−0.288365	+	0.499462i
$512$		0			0
$513$	−3.05042	+	64.4660i	−0.134679	+	2.84624i
$514$		0			0
$515$	−1.92332	+	3.33129i	−0.0847517	+	0.146794i
$516$		0			0
$517$	8.75816	+	15.1696i	0.385184	+	0.667158i
$518$		0			0
$519$	17.6056	+	30.4938i	0.772801	+	1.33853i
$520$		0			0
$521$	−14.8697			−0.651455			−0.325728	−	0.945464i	$-0.605609\pi$
$521$	−14.8697			−0.651455			−0.325728	+	0.945464i	$0.605609\pi$
$522$		0			0
$523$	−5.44958	−	9.43895i	−0.238294	−	0.412736i	0.721931	−	0.691965i	$-0.243255\pi$
$523$	−5.44958	−	9.43895i	−0.238294	−	0.412736i	−0.960225	+	0.279228i	$0.909921\pi$
$524$		0			0
$525$	−51.3561			−2.24136
$526$		0			0
$527$	−22.6707	+	39.2669i	−0.987553	+	1.71049i
$528$		0			0
$529$	11.3892	−	19.7267i	0.495184	−	0.857684i
$530$		0			0
$531$	−54.7811			−2.37730
$532$		0			0
$533$	−1.42342			−0.0616552
$534$		0			0
$535$	−0.117266	+	0.203111i	−0.00506987	+	0.00878126i
$536$		0			0
$537$	−11.5177	+	19.9492i	−0.497024	+	0.860871i
$538$		0			0
$539$	−5.79650			−0.249673
$540$		0			0
$541$	5.97546	+	10.3498i	0.256905	+	0.444973i	0.965411	−	0.260732i	$-0.0839639\pi$
$541$	5.97546	+	10.3498i	0.256905	+	0.444973i	−0.708506	+	0.705705i	$0.750631\pi$
$542$		0			0
$543$	−40.1380			−1.72249
$544$		0			0
$545$	1.97546	+	3.42160i	0.0846194	+	0.146565i
$546$		0			0
$547$	−2.00306	−	3.46940i	−0.0856445	−	0.148341i	0.820021	−	0.572333i	$-0.193962\pi$
$547$	−2.00306	−	3.46940i	−0.0856445	−	0.148341i	−0.905666	+	0.423993i	$0.860628\pi$
$548$		0			0
$549$	−47.3285	+	81.9754i	−2.01993	+	3.49862i
$550$		0			0
$551$	19.2483	−	9.93093i	0.820006	−	0.423072i
$552$		0			0
$553$	−14.6155	+	25.3149i	−0.621516	+	1.07650i
$554$		0			0
$555$	3.63016	+	6.28761i	0.154092	+	0.266894i
$556$		0			0
$557$	5.35991	+	9.28364i	0.227107	+	0.393360i	0.956949	−	0.290255i	$-0.0937400\pi$
$557$	5.35991	+	9.28364i	0.227107	+	0.393360i	−0.729843	+	0.683615i	$0.760407\pi$
$558$		0			0
$559$	−11.0525			−0.467472
$560$		0			0
$561$	−16.0552	−	27.8084i	−0.677851	−	1.17407i
$562$		0			0
$563$	−7.18096			−0.302641			−0.151321	−	0.988485i	$-0.548353\pi$
$563$	−7.18096			−0.302641			−0.151321	+	0.988485i	$0.548353\pi$
$564$		0			0
$565$	1.13756	−	1.97031i	0.0478575	−	0.0828916i
$566$		0			0
$567$	42.0686	−	72.8650i	1.76672	−	3.06004i
$568$		0			0
$569$	31.4328			1.31773			0.658865	−	0.752261i	$-0.271037\pi$
$569$	31.4328			1.31773			0.658865	+	0.752261i	$0.271037\pi$
$570$		0			0
$571$	−8.08623			−0.338398			−0.169199	−	0.985582i	$-0.554118\pi$
$571$	−8.08623			−0.338398			−0.169199	+	0.985582i	$0.554118\pi$
$572$		0			0
$573$	14.6155	−	25.3149i	0.610573	−	1.05754i
$574$		0			0
$575$	1.12457	−	1.94781i	0.0468978	−	0.0812294i
$576$		0			0
$577$	4.95779			0.206396			0.103198	−	0.994661i	$-0.467093\pi$
$577$	4.95779			0.206396			0.103198	+	0.994661i	$0.467093\pi$
$578$		0			0
$579$	−5.13837	−	8.89992i	−0.213543	−	0.369868i
$580$		0			0
$581$	30.2491			1.25495
$582$		0			0
$583$	3.47068	+	6.01140i	0.143741	+	0.248967i
$584$		0			0
$585$	5.04564	+	8.73931i	0.208612	+	0.361326i
$586$		0			0
$587$	11.8858	−	20.5868i	0.490579	−	0.849708i	−0.509362	−	0.860552i	$-0.670119\pi$
$587$	11.8858	−	20.5868i	0.490579	−	0.849708i	0.999941	+	0.0108444i	$0.00345194\pi$
$588$		0			0
$589$	1.39014	−	29.3785i	0.0572797	−	1.21052i
$590$		0			0
$591$	34.5151	−	59.7820i	1.41976	−	2.45910i
$592$		0			0
$593$	21.2018	+	36.7226i	0.870653	+	1.50801i	0.861323	+	0.508058i	$0.169637\pi$
$593$	21.2018	+	36.7226i	0.870653	+	1.50801i	0.00932994	+	0.999956i	$0.497030\pi$
$594$		0			0
$595$	−5.23109	−	9.06052i	−0.214454	−	0.371445i
$596$		0			0
$597$	−32.1526			−1.31592
$598$		0			0
$599$	−21.4258	−	37.1107i	−0.875436	−	1.51630i	−0.856297	−	0.516484i	$-0.827241\pi$
$599$	−21.4258	−	37.1107i	−0.875436	−	1.51630i	−0.0191394	−	0.999817i	$-0.506093\pi$
$600$		0			0
$601$	−15.1855			−0.619427			−0.309714	−	0.950830i	$-0.600233\pi$
$601$	−15.1855			−0.619427			−0.309714	+	0.950830i	$0.600233\pi$
$602$		0			0
$603$	−2.39400	+	4.14654i	−0.0974914	+	0.168860i
$604$		0			0
$605$	−2.07974	+	3.60221i	−0.0845533	+	0.146451i
$606$		0			0
$607$	−32.3336			−1.31238			−0.656189	−	0.754596i	$-0.727833\pi$
$607$	−32.3336			−1.31238			−0.656189	+	0.754596i	$0.727833\pi$
$608$		0			0
$609$	−53.4036			−2.16402
$610$		0			0
$611$	−16.8953	+	29.2636i	−0.683512	+	1.18388i
$612$		0			0
$613$	−3.91683	+	6.78414i	−0.158199	+	0.274009i	−0.934219	−	0.356699i	$-0.883902\pi$
$613$	−3.91683	+	6.78414i	−0.158199	+	0.274009i	0.776020	+	0.630708i	$0.217235\pi$
$614$		0			0
$615$	−0.767287			−0.0309400
$616$		0			0
$617$	2.13359	+	3.69549i	0.0858952	+	0.148775i	0.905772	−	0.423765i	$-0.139292\pi$
$617$	2.13359	+	3.69549i	0.0858952	+	0.148775i	−0.819877	+	0.572540i	$0.805958\pi$
$618$		0			0
$619$	−42.8363			−1.72174			−0.860869	−	0.508827i	$-0.830079\pi$
$619$	−42.8363			−1.72174			−0.860869	+	0.508827i	$0.830079\pi$
$620$		0			0
$621$	3.48448	+	6.03530i	0.139827	+	0.242188i
$622$		0			0
$623$	4.88617	+	8.46310i	0.195760	+	0.339067i
$624$		0			0
$625$	−10.8630	+	18.8152i	−0.434519	+	0.752609i
$626$		0			0
$627$	17.5259	+	11.2554i	0.699916	+	0.449496i
$628$		0			0
$629$	15.9509	−	27.6278i	0.636005	−	1.10159i
$630$		0			0
$631$	18.1552	+	31.4458i	0.722748	+	1.25184i	0.959894	+	0.280362i	$0.0904546\pi$
$631$	18.1552	+	31.4458i	0.722748	+	1.25184i	−0.237146	+	0.971474i	$0.576212\pi$
$632$		0			0
$633$	−31.0307	−	53.7467i	−1.23336	−	2.13624i
$634$		0			0
$635$	8.68373			0.344603
$636$		0			0
$637$	−5.59101	−	9.68391i	−0.221524	−	0.383690i
$638$		0			0
$639$	−28.5535			−1.12956
$640$		0			0
$641$	24.8043	−	42.9624i	0.979712	−	1.69691i	0.316297	−	0.948660i	$-0.397560\pi$
$641$	24.8043	−	42.9624i	0.979712	−	1.69691i	0.663415	−	0.748251i	$-0.269106\pi$
$642$		0			0
$643$	−2.49270	+	4.31748i	−0.0983023	+	0.170265i	−0.910982	−	0.412446i	$-0.864675\pi$
$643$	−2.49270	+	4.31748i	−0.0983023	+	0.170265i	0.812680	+	0.582711i	$0.198008\pi$
$644$		0			0
$645$	−5.95779			−0.234588
$646$		0			0
$647$	−43.2863			−1.70176			−0.850880	−	0.525360i	$-0.823931\pi$
$647$	−43.2863			−1.70176			−0.850880	+	0.525360i	$0.823931\pi$
$648$		0			0
$649$	−5.33060	+	9.23286i	−0.209244	+	0.362422i
$650$		0			0
$651$	−36.2587	+	62.8019i	−1.42109	+	2.46140i
$652$		0			0
$653$	5.43965			0.212870			0.106435	−	0.994320i	$-0.466056\pi$
$653$	5.43965			0.212870			0.106435	+	0.994320i	$0.466056\pi$
$654$		0			0
$655$	−0.204306	−	0.353869i	−0.00798290	−	0.0138268i
$656$		0			0
$657$	−29.7846			−1.16201
$658$		0			0
$659$	−2.87462	−	4.97899i	−0.111979	−	0.193954i	0.804589	−	0.593832i	$-0.202386\pi$
$659$	−2.87462	−	4.97899i	−0.111979	−	0.193954i	−0.916568	+	0.399878i	$0.869052\pi$
$660$		0			0
$661$	−5.12763	−	8.88131i	−0.199442	−	0.345443i	0.748906	−	0.662676i	$-0.230579\pi$
$661$	−5.12763	−	8.88131i	−0.199442	−	0.345443i	−0.948348	+	0.317233i	$0.897246\pi$
$662$		0			0
$663$	30.9720	−	53.6451i	1.20285	−	2.08340i
$664$		0			0
$665$	5.71027	+	3.66721i	0.221435	+	0.142208i
$666$		0			0
$667$	1.16940	−	2.02547i	0.0452795	−	0.0784264i
$668$		0			0
$669$	−27.5673	−	47.7479i	−1.06581	−	1.84604i
$670$		0			0
$671$	9.21080	+	15.9536i	0.355579	+	0.615881i
$672$		0			0
$673$	−29.9379			−1.15402			−0.577011	−	0.816736i	$-0.695781\pi$
$673$	−29.9379			−1.15402			−0.577011	+	0.816736i	$0.695781\pi$
$674$		0			0
$675$	−35.3750	−	61.2714i	−1.36159	−	2.35834i
$676$		0			0
$677$	11.8827			0.456691			0.228345	−	0.973580i	$-0.426668\pi$
$677$	11.8827			0.456691			0.228345	+	0.973580i	$0.426668\pi$
$678$		0			0
$679$	0.0969726	−	0.167961i	0.00372147	−	0.00644577i
$680$		0			0
$681$	−1.05042	+	1.81938i	−0.0402522	+	0.0697188i
$682$		0			0
$683$	−6.35180			−0.243045			−0.121522	−	0.992589i	$-0.538778\pi$
$683$	−6.35180			−0.243045			−0.121522	+	0.992589i	$0.538778\pi$
$684$		0			0
$685$	−2.14486			−0.0819510
$686$		0			0
$687$	13.8957	−	24.0681i	0.530155	−	0.918255i
$688$		0			0
$689$	−6.69528	+	11.5966i	−0.255070	+	0.441794i
$690$		0			0
$691$	−28.9966			−1.10308			−0.551541	−	0.834148i	$-0.685960\pi$
$691$	−28.9966			−1.10308			−0.551541	+	0.834148i	$0.685960\pi$
$692$		0			0
$693$	−18.3810	−	31.8369i	−0.698237	−	1.20938i
$694$		0			0
$695$	−7.67580			−0.291160
$696$		0			0
$697$	1.68573	+	2.91977i	0.0638516	+	0.110594i
$698$		0			0
$699$	−6.02201	−	10.4304i	−0.227773	−	0.394515i
$700$		0			0
$701$	2.00081	−	3.46550i	0.0755695	−	0.130890i	−0.825764	−	0.564015i	$-0.809256\pi$
$701$	2.00081	−	3.46550i	0.0755695	−	0.130890i	0.901334	+	0.433125i	$0.142589\pi$
$702$		0			0
$703$	−0.978088	+	20.6704i	−0.0368893	+	0.779599i
$704$		0			0
$705$	−9.10733	+	15.7744i	−0.343002	+	0.594097i
$706$		0			0
$707$	−19.1595	−	33.1852i	−0.720566	−	1.24806i
$708$		0			0
$709$	−8.23190	−	14.2581i	−0.309156	−	0.535473i	0.669022	−	0.743242i	$-0.266713\pi$
$709$	−8.23190	−	14.2581i	−0.309156	−	0.535473i	−0.978178	+	0.207769i	$0.933380\pi$
$710$		0			0
$711$	−66.7811			−2.50449
$712$		0			0
$713$	−1.58795	−	2.75041i	−0.0594692	−	0.103004i
$714$		0			0
$715$	1.96391			0.0734460
$716$		0			0
$717$	25.6121	−	44.3615i	0.956502	−	1.65671i
$718$		0			0
$719$	−9.60561	+	16.6374i	−0.358229	+	0.620471i	−0.987665	−	0.156581i	$-0.949953\pi$
$719$	−9.60561	+	16.6374i	−0.358229	+	0.620471i	0.629436	+	0.777052i	$0.283286\pi$
$720$		0			0
$721$	27.0327			1.00675
$722$		0			0
$723$	52.3561			1.94714
$724$		0			0
$725$	−11.8720	+	20.5629i	−0.440915	+	0.763687i
$726$		0			0
$727$	−9.08317	+	15.7325i	−0.336876	+	0.583487i	−0.983843	−	0.179031i	$-0.942704\pi$
$727$	−9.08317	+	15.7325i	−0.336876	+	0.583487i	0.646967	+	0.762518i	$0.276037\pi$
$728$		0			0
$729$	47.8984			1.77401
$730$		0			0
$731$	13.0893	+	22.6713i	0.484125	+	0.838529i
$732$		0			0
$733$	−50.2423			−1.85574			−0.927870	−	0.372903i	$-0.878362\pi$
$733$	−50.2423			−1.85574			−0.927870	+	0.372903i	$0.878362\pi$
$734$		0			0
$735$	−3.01380	−	5.22005i	−0.111166	−	0.192545i
$736$		0			0
$737$	0.465907	+	0.806975i	0.0171619	+	0.0297253i
$738$		0			0
$739$	−14.8883	+	25.7873i	−0.547676	+	0.948602i	0.450758	+	0.892646i	$0.351154\pi$
$739$	−14.8883	+	25.7873i	−0.547676	+	0.948602i	−0.998433	+	0.0559557i	$0.982179\pi$
$740$		0			0
$741$	−1.89916	+	40.1359i	−0.0697674	+	1.47443i
$742$		0			0
$743$	−19.7578	+	34.2215i	−0.724843	+	1.25546i	0.234196	+	0.972189i	$0.424754\pi$
$743$	−19.7578	+	34.2215i	−0.724843	+	1.25546i	−0.959039	+	0.283275i	$0.908579\pi$
$744$		0			0
$745$	−4.92026	−	8.52215i	−0.180265	−	0.312227i
$746$		0			0
$747$	34.5535	+	59.8484i	1.26425	+	2.18974i
$748$		0			0
$749$	1.64820			0.0602240
$750$		0			0
$751$	9.05214	+	15.6788i	0.330317	+	0.572126i	0.982574	−	0.185872i	$-0.0595109\pi$
$751$	9.05214	+	15.6788i	0.330317	+	0.572126i	−0.652257	+	0.757998i	$0.726178\pi$
$752$		0			0
$753$	−50.8690			−1.85377
$754$		0			0
$755$	0.412050	−	0.713692i	0.0149960	−	0.0259739i
$756$		0			0
$757$	−11.7996	+	20.4374i	−0.428862	+	0.742811i	−0.996772	−	0.0802793i	$-0.974419\pi$
$757$	−11.7996	+	20.4374i	−0.428862	+	0.742811i	0.567910	+	0.823091i	$0.307752\pi$
$758$		0			0
$759$	2.24914			0.0816386
$760$		0			0
$761$	−1.69061			−0.0612845			−0.0306422	−	0.999530i	$-0.509755\pi$
$761$	−1.69061			−0.0612845			−0.0306422	+	0.999530i	$0.509755\pi$
$762$		0			0
$763$	13.8827	−	24.0456i	0.502589	−	0.870509i
$764$		0			0
$765$	11.9509	−	20.6996i	0.432086	−	0.748396i
$766$		0			0
$767$	−20.5665			−0.742612
$768$		0			0
$769$	26.0583	+	45.1342i	0.939685	+	1.62758i	0.766059	+	0.642770i	$0.222215\pi$
$769$	26.0583	+	45.1342i	0.939685	+	1.62758i	0.173625	+	0.984812i	$0.444452\pi$
$770$		0			0
$771$	90.3821			3.25503
$772$		0			0
$773$	22.5397	+	39.0399i	0.810696	+	1.40417i	0.912378	+	0.409349i	$0.134244\pi$
$773$	22.5397	+	39.0399i	0.810696	+	1.40417i	−0.101682	+	0.994817i	$0.532422\pi$
$774$		0			0
$775$	16.1211	+	27.9226i	0.579088	+	1.00301i
$776$		0			0
$777$	25.5113	−	44.1868i	0.915212	−	1.58519i
$778$		0			0
$779$	−1.84015	−	1.18177i	−0.0659301	−	0.0423412i
$780$		0			0
$781$	−2.77846	+	4.81243i	−0.0994210	+	0.172202i
$782$		0			0
$783$	−36.7854	−	63.7141i	−1.31460	−	2.27696i
$784$		0			0
$785$	0.0375304	+	0.0650045i	0.00133952	+	0.00232011i
$786$		0			0
$787$	38.1414			1.35960			0.679798	−	0.733400i	$-0.262068\pi$
$787$	38.1414			1.35960			0.679798	+	0.733400i	$0.262068\pi$
$788$		0			0
$789$	27.3768	+	47.4180i	0.974639	+	1.68812i
$790$		0			0
$791$	−15.9886			−0.568490
$792$		0			0
$793$	−17.7685	+	30.7760i	−0.630979	+	1.09289i
$794$		0			0
$795$	−3.60905	+	6.25106i	−0.128000	+	0.221702i
$796$		0			0
$797$	13.7148			0.485802			0.242901	−	0.970051i	$-0.421901\pi$
$797$	13.7148			0.485802			0.242901	+	0.970051i	$0.421901\pi$
$798$		0			0
$799$	80.0353			2.83145
$800$		0			0
$801$	−11.1629	+	19.3347i	−0.394422	+	0.683159i
$802$		0			0
$803$	−2.89825	+	5.01992i	−0.102277	+	0.177149i
$804$		0			0
$805$	0.732814			0.0258283
$806$		0			0
$807$	48.1281	+	83.3602i	1.69419	+	2.93442i
$808$		0			0
$809$	−21.6285			−0.760419			−0.380209	−	0.924900i	$-0.624148\pi$
$809$	−21.6285			−0.760419			−0.380209	+	0.924900i	$0.624148\pi$
$810$		0			0
$811$	−3.27024	−	5.66423i	−0.114834	−	0.198898i	0.802880	−	0.596141i	$-0.203300\pi$
$811$	−3.27024	−	5.66423i	−0.114834	−	0.198898i	−0.917713	+	0.397243i	$0.869967\pi$
$812$		0			0
$813$	23.5086	+	40.7182i	0.824484	+	1.42805i
$814$		0			0
$815$	0.0202937	−	0.0351497i	0.000710858	−	0.00123124i
$816$		0			0
$817$	−14.2883	−	9.17613i	−0.499884	−	0.321032i
$818$		0			0
$819$	35.4588	−	61.4164i	1.23903	−	2.14606i
$820$		0			0
$821$	20.8091	+	36.0424i	0.726243	+	1.25789i	0.958460	+	0.285226i	$0.0920686\pi$
$821$	20.8091	+	36.0424i	0.726243	+	1.25789i	−0.232217	+	0.972664i	$0.574598\pi$
$822$		0			0
$823$	2.72632	+	4.72212i	0.0950335	+	0.164603i	0.909623	−	0.415436i	$-0.136371\pi$
$823$	2.72632	+	4.72212i	0.0950335	+	0.164603i	−0.814589	+	0.580038i	$0.803038\pi$
$824$		0			0
$825$	−22.8337			−0.794966
$826$		0			0
$827$	−1.34439	−	2.32856i	−0.0467492	−	0.0809719i	0.841704	−	0.539939i	$-0.181553\pi$
$827$	−1.34439	−	2.32856i	−0.0467492	−	0.0809719i	−0.888453	+	0.458967i	$0.848219\pi$
$828$		0			0
$829$	27.4328			0.952780			0.476390	−	0.879234i	$-0.341945\pi$
$829$	27.4328			0.952780			0.476390	+	0.879234i	$0.341945\pi$
$830$		0			0
$831$	20.1798	−	34.9524i	0.700028	−	1.21248i
$832$		0			0
$833$	−13.2426	+	22.9369i	−0.458830	+	0.794718i
$834$		0			0
$835$	2.95436			0.102240
$836$		0			0
$837$	−99.9027			−3.45314
$838$		0			0
$839$	13.7206	−	23.7648i	0.473689	−	0.820453i	−0.525857	−	0.850573i	$-0.676255\pi$
$839$	13.7206	−	23.7648i	0.473689	−	0.820453i	0.999546	+	0.0301195i	$0.00958880\pi$
$840$		0			0
$841$	2.15470	−	3.73204i	0.0742999	−	0.128691i
$842$		0			0
$843$	33.4439			1.15187
$844$		0			0
$845$	−1.16516	−	2.01811i	−0.0400826	−	0.0694252i
$846$		0			0
$847$	29.2311			1.00439
$848$		0			0
$849$	25.7733	+	44.6407i	0.884537	+	1.53206i
$850$		0			0
$851$	1.11727	+	1.93516i	0.0382994	+	0.0663365i
$852$		0			0
$853$	18.1936	−	31.5122i	0.622936	−	1.07896i	−0.366000	−	0.930615i	$-0.619273\pi$
$853$	18.1936	−	31.5122i	0.622936	−	1.07896i	0.988936	−	0.148342i	$-0.0473936\pi$
$854$		0			0
$855$	−0.732814	+	15.4869i	−0.0250617	+	0.529641i
$856$		0			0
$857$	24.5647	−	42.5474i	0.839116	−	1.45339i	−0.0515191	−	0.998672i	$-0.516406\pi$
$857$	24.5647	−	42.5474i	0.839116	−	1.45339i	0.890635	−	0.454719i	$-0.150260\pi$
$858$		0			0
$859$	25.9565	+	44.9580i	0.885624	+	1.53395i	0.844996	+	0.534772i	$0.179603\pi$
$859$	25.9565	+	44.9580i	0.885624	+	1.53395i	0.0406283	+	0.999174i	$0.487064\pi$
$860$		0			0
$861$	2.69609	+	4.66977i	0.0918826	+	0.159145i
$862$		0			0
$863$	27.9785			0.952400			0.476200	−	0.879337i	$-0.342014\pi$
$863$	27.9785			0.952400			0.476200	+	0.879337i	$0.342014\pi$
$864$		0			0
$865$	2.55042	+	4.41746i	0.0867169	+	0.150198i
$866$		0			0
$867$	−91.4829			−3.10692
$868$		0			0
$869$	−6.49828	+	11.2554i	−0.220439	+	0.381812i
$870$		0			0
$871$	−0.898780	+	1.55673i	−0.0304540	+	0.0527479i
$872$		0			0
$873$	0.443086			0.0149962
$874$		0			0
$875$	−15.2242			−0.514673
$876$		0			0
$877$	−6.20087	+	10.7402i	−0.209388	+	0.362671i	−0.951522	−	0.307581i	$-0.900481\pi$
$877$	−6.20087	+	10.7402i	−0.209388	+	0.362671i	0.742134	+	0.670252i	$0.233814\pi$
$878$		0			0
$879$	19.7513	−	34.2102i	0.666194	−	1.15388i
$880$		0			0
$881$	17.8923			0.602806			0.301403	−	0.953497i	$-0.402545\pi$
$881$	17.8923			0.602806			0.301403	+	0.953497i	$0.402545\pi$
$882$		0			0
$883$	−5.51686	−	9.55547i	−0.185657	−	0.321567i	0.758141	−	0.652091i	$-0.226108\pi$
$883$	−5.51686	−	9.55547i	−0.185657	−	0.321567i	−0.943798	+	0.330524i	$0.892775\pi$
$884$		0			0
$885$	−11.0862			−0.372660
$886$		0			0
$887$	20.1970	+	34.9822i	0.678149	+	1.17459i	0.975538	+	0.219832i	$0.0705509\pi$
$887$	20.1970	+	34.9822i	0.678149	+	1.17459i	−0.297389	+	0.954756i	$0.596116\pi$
$888$		0			0
$889$	−30.5129	−	52.8499i	−1.02337	−	1.77253i
$890$		0			0
$891$	18.7043	−	32.3968i	0.626618	−	1.08533i
$892$		0			0
$893$	−46.1372	+	23.8039i	−1.54392	+	0.796566i
$894$		0			0
$895$	−1.66849	+	2.88992i	−0.0557716	+	0.0965993i
$896$		0			0
$897$	2.16940	+	3.75752i	0.0724343	+	0.125460i
$898$		0			0
$899$	16.7638	+	29.0358i	0.559106	+	0.968399i
$900$		0			0
$901$	31.7164			1.05663
$902$		0			0
$903$	20.9345	+	36.2596i	0.696656	+	1.20664i
$904$		0			0
$905$	−5.81455			−0.193282
$906$		0			0
$907$	−19.5755	+	33.9057i	−0.649993	+	1.12582i	0.333130	+	0.942881i	$0.391895\pi$
$907$	−19.5755	+	33.9057i	−0.649993	+	1.12582i	−0.983124	+	0.182941i	$0.941438\pi$
$908$		0			0
$909$	43.7716	−	75.8146i	1.45181	−	2.51461i
$910$		0			0
$911$	−27.3561			−0.906348			−0.453174	−	0.891422i	$-0.649708\pi$
$911$	−27.3561			−0.906348			−0.453174	+	0.891422i	$0.649708\pi$
$912$		0			0
$913$	13.4492			0.445104
$914$		0			0
$915$	−9.57802	+	16.5896i	−0.316639	+	0.548436i
$916$		0			0
$917$	−1.43578	+	2.48685i	−0.0474137	+	0.0821229i
$918$		0			0
$919$	−0.948243			−0.0312796			−0.0156398	−	0.999878i	$-0.504979\pi$
$919$	−0.948243			−0.0312796			−0.0156398	+	0.999878i	$0.504979\pi$
$920$		0			0
$921$	19.9837	+	34.6127i	0.658484	+	1.14053i
$922$		0			0
$923$	−10.7198			−0.352847
$924$		0			0
$925$	−11.3427	−	19.6461i	−0.372945	−	0.645959i
$926$		0			0
$927$	30.8793	+	53.4845i	1.01421	+	1.75666i
$928$		0			0
$929$	−2.63026	+	4.55574i	−0.0862959	+	0.149469i	−0.905943	−	0.423400i	$-0.860836\pi$
$929$	−2.63026	+	4.55574i	−0.0862959	+	0.149469i	0.819647	+	0.572869i	$0.194170\pi$
$930$		0			0
$931$	0.812021	−	17.1608i	0.0266129	−	0.562423i
$932$		0			0
$933$	−0.844394	+	1.46253i	−0.0276442	+	0.0478812i
$934$		0			0
$935$	−2.32582	−	4.02844i	−0.0760624	−	0.131744i
$936$		0			0
$937$	−22.9638	−	39.7745i	−0.750195	−	1.29938i	−0.947728	−	0.319079i	$-0.896626\pi$
$937$	−22.9638	−	39.7745i	−0.750195	−	1.29938i	0.197533	−	0.980296i	$-0.436707\pi$
$938$		0			0
$939$	−60.4734			−1.97347
$940$		0			0
$941$	−22.2978	−	38.6210i	−0.726889	−	1.25901i	−0.958192	−	0.286127i	$-0.907632\pi$
$941$	−22.2978	−	38.6210i	−0.726889	−	1.25901i	0.231303	−	0.972882i	$-0.425701\pi$
$942$		0			0
$943$	−0.236151			−0.00769013
$944$		0			0
$945$	11.5259	−	19.9634i	0.374937	−	0.649410i
$946$		0			0
$947$	−7.00811	+	12.1384i	−0.227733	+	0.394445i	−0.957136	−	0.289639i	$-0.906465\pi$
$947$	−7.00811	+	12.1384i	−0.227733	+	0.394445i	0.729403	+	0.684084i	$0.239798\pi$
$948$		0			0
$949$	−11.1820			−0.362984
$950$		0			0
$951$	−9.21811			−0.298918
$952$		0			0
$953$	−1.42332	+	2.46526i	−0.0461059	+	0.0798577i	−0.888157	−	0.459539i	$-0.848014\pi$
$953$	−1.42332	+	2.46526i	−0.0461059	+	0.0798577i	0.842051	+	0.539397i	$0.181348\pi$
$954$		0			0
$955$	2.11727	−	3.66721i	0.0685131	−	0.118668i
$956$		0			0
$957$	−23.7440			−0.767534
$958$		0			0
$959$	7.53662	+	13.0538i	0.243370	+	0.421529i
$960$		0			0
$961$	14.5277			0.468635
$962$		0			0
$963$	1.88273	+	3.26099i	0.0606702	+	0.105084i
$964$		0			0
$965$	−0.744365	−	1.28928i	−0.0239619	−	0.0415033i
$966$		0			0
$967$	0.830595	−	1.43863i	0.0267101	−	0.0462633i	−0.852361	−	0.522953i	$-0.824830\pi$
$967$	0.830595	−	1.43863i	0.0267101	−	0.0462633i	0.879071	+	0.476690i	$0.158164\pi$
$968$		0			0
$969$	84.5773	−	43.6365i	2.71701	−	1.40181i
$970$		0			0
$971$	20.2091	−	35.0032i	0.648540	−	1.12330i	−0.334931	−	0.942243i	$-0.608713\pi$
$971$	20.2091	−	35.0032i	0.648540	−	1.12330i	0.983472	−	0.181062i	$-0.0579535\pi$
$972$		0			0
$973$	26.9712	+	46.7155i	0.864657	+	1.49763i
$974$		0			0
$975$	−22.0242	−	38.1470i	−0.705338	−	1.22168i
$976$		0			0
$977$	10.5439			0.337330			0.168665	−	0.985673i	$-0.446054\pi$
$977$	10.5439			0.337330			0.168665	+	0.985673i	$0.446054\pi$
$978$		0			0
$979$	2.17246	+	3.76281i	0.0694322	+	0.120260i
$980$		0			0
$981$	63.4328			2.02525
$982$		0			0
$983$	4.91683	−	8.51619i	0.156822	−	0.271624i	−0.776899	−	0.629626i	$-0.783208\pi$
$983$	4.91683	−	8.51619i	0.156822	−	0.271624i	0.933721	+	0.358001i	$0.116542\pi$
$984$		0			0
$985$	5.00000	−	8.66025i	0.159313	−	0.275939i
$986$		0			0
$987$	128.005			4.07446
$988$		0			0
$989$	−1.83365			−0.0583068
$990$		0			0
$991$	−10.1349	+	17.5542i	−0.321947	+	0.557628i	−0.980890	−	0.194565i	$-0.937671\pi$
$991$	−10.1349	+	17.5542i	−0.321947	+	0.557628i	0.658943	+	0.752193i	$0.271004\pi$
$992$		0			0
$993$	30.9117	−	53.5406i	0.980952	−	1.69906i
$994$		0			0
$995$	−4.65775			−0.147661
$996$		0			0
$997$	7.66038	+	13.2682i	0.242607	+	0.420207i	0.961456	−	0.274959i	$-0.0886642\pi$
$997$	7.66038	+	13.2682i	0.242607	+	0.420207i	−0.718849	+	0.695166i	$0.755331\pi$
$998$		0			0
$999$	70.2906			2.22390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.i.n.961.3		6
4.3	odd	2		1216.2.i.m.961.1		6
8.3	odd	2		304.2.i.f.49.3		6
8.5	even	2		152.2.i.c.49.1	✓	6
19.7	even	3	inner	1216.2.i.n.577.3		6
24.5	odd	2		1368.2.s.k.505.2		6
24.11	even	2		2736.2.s.y.1873.2		6
76.7	odd	6		1216.2.i.m.577.1		6
152.11	odd	6		5776.2.a.bk.1.1		3
152.27	even	6		5776.2.a.bq.1.3		3
152.45	even	6		152.2.i.c.121.1	yes	6
152.83	odd	6		304.2.i.f.273.3		6
152.125	even	6		2888.2.a.r.1.3		3
152.141	odd	6		2888.2.a.n.1.1		3
456.83	even	6		2736.2.s.y.577.2		6
456.197	odd	6		1368.2.s.k.577.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.i.c.49.1	✓	6	8.5	even	2
152.2.i.c.121.1	yes	6	152.45	even	6
304.2.i.f.49.3		6	8.3	odd	2
304.2.i.f.273.3		6	152.83	odd	6
1216.2.i.m.577.1		6	76.7	odd	6
1216.2.i.m.961.1		6	4.3	odd	2
1216.2.i.n.577.3		6	19.7	even	3	inner
1216.2.i.n.961.3		6	1.1	even	1	trivial
1368.2.s.k.505.2		6	24.5	odd	2
1368.2.s.k.577.2		6	456.197	odd	6
2736.2.s.y.577.2		6	456.83	even	6
2736.2.s.y.1873.2		6	24.11	even	2
2888.2.a.n.1.1		3	152.141	odd	6
2888.2.a.r.1.3		3	152.125	even	6
5776.2.a.bk.1.1		3	152.11	odd	6
5776.2.a.bq.1.3		3	152.27	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.62457 - 2.81384i) q^{3} +(0.235342 - 0.407624i) q^{5} -3.30777 q^{7} +(-3.77846 - 6.54448i) q^{9} +O(q^{10})\)	\(q+(1.62457 - 2.81384i) q^{3} +(0.235342 - 0.407624i) q^{5} -3.30777 q^{7} +(-3.77846 - 6.54448i) q^{9} -1.47068 q^{11} +(-1.41855 - 2.45699i) q^{13} +(-0.764658 - 1.32443i) q^{15} +(-3.35991 + 5.81954i) q^{17} +(0.206025 - 4.35403i) q^{19} +(-5.37371 + 9.30754i) q^{21} +(-0.235342 - 0.407624i) q^{23} +(2.38923 + 4.13827i) q^{25} -14.8061 q^{27} +(2.48448 + 4.30325i) q^{29} +6.74742 q^{31} +(-2.38923 + 4.13827i) q^{33} +(-0.778457 + 1.34833i) q^{35} -4.74742 q^{37} -9.21811 q^{39} +(0.250859 - 0.434501i) q^{41} +(1.94786 - 3.37380i) q^{43} -3.55691 q^{45} +(-5.95517 - 10.3146i) q^{47} +3.94137 q^{49} +(10.9168 + 18.9085i) q^{51} +(-2.35991 - 4.08749i) q^{53} +(-0.346113 + 0.599486i) q^{55} +(-11.9168 - 7.65314i) q^{57} +(3.62457 - 6.27794i) q^{59} +(-6.26294 - 10.8477i) q^{61} +(12.4983 + 21.6477i) q^{63} -1.33537 q^{65} +(-0.316797 - 0.548708i) q^{67} -1.52932 q^{69} +(1.88923 - 3.27224i) q^{71} +(1.97068 - 3.41332i) q^{73} +15.5259 q^{75} +4.86469 q^{77} +(4.41855 - 7.65314i) q^{79} +(-12.7181 + 22.0284i) q^{81} -9.14486 q^{83} +(1.58145 + 2.73916i) q^{85} +16.1449 q^{87} +(-1.47718 - 2.55855i) q^{89} +(4.69223 + 8.12717i) q^{91} +(10.9617 - 18.9862i) q^{93} +(-1.72632 - 1.10866i) q^{95} +(-0.0293166 + 0.0507778i) q^{97} +(5.55691 + 9.62486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + q^{5} - 4 q^{7} - 6 q^{9}+O(q^{10}) \) 6 * q + q^3 + q^5 - 4 * q^7 - 6 * q^9	\( 6 q + q^{3} + q^{5} - 4 q^{7} - 6 q^{9} - 8 q^{11} - q^{13} - 5 q^{15} - 11 q^{17} - 6 q^{21} - q^{23} + 6 q^{25} - 38 q^{27} - 3 q^{29} - 12 q^{31} - 6 q^{33} + 12 q^{35} + 24 q^{37} - 2 q^{39} + 19 q^{41} + 5 q^{43} + 12 q^{45} - 17 q^{47} + 22 q^{49} + 23 q^{51} - 5 q^{53} - 10 q^{55} - 29 q^{57} + 13 q^{59} - 3 q^{61} + 40 q^{63} + 42 q^{65} - 9 q^{67} - 10 q^{69} + 3 q^{71} + 11 q^{73} + 24 q^{75} - 20 q^{77} + 19 q^{79} - 23 q^{81} - 24 q^{83} + 17 q^{85} + 66 q^{87} - 3 q^{89} + 44 q^{91} + 42 q^{93} + 13 q^{95} - q^{97}+O(q^{100}) \) 6 * q + q^3 + q^5 - 4 * q^7 - 6 * q^9 - 8 * q^11 - q^13 - 5 * q^15 - 11 * q^17 - 6 * q^21 - q^23 + 6 * q^25 - 38 * q^27 - 3 * q^29 - 12 * q^31 - 6 * q^33 + 12 * q^35 + 24 * q^37 - 2 * q^39 + 19 * q^41 + 5 * q^43 + 12 * q^45 - 17 * q^47 + 22 * q^49 + 23 * q^51 - 5 * q^53 - 10 * q^55 - 29 * q^57 + 13 * q^59 - 3 * q^61 + 40 * q^63 + 42 * q^65 - 9 * q^67 - 10 * q^69 + 3 * q^71 + 11 * q^73 + 24 * q^75 - 20 * q^77 + 19 * q^79 - 23 * q^81 - 24 * q^83 + 17 * q^85 + 66 * q^87 - 3 * q^89 + 44 * q^91 + 42 * q^93 + 13 * q^95 - q^97

Introduction

L-functions

Modular forms

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