LMFDB - Embedded newform 888.2.bo.c.673.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [888,2,Mod(49,888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(888, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 14]))

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

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

chi := DirichletCharacter("888.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.bo (of order $9$, degree $6$, 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:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			673.3
Character	$\chi$	$=$	888.673
Dual form			888.2.bo.c.793.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{3} +(0.139923 + 0.793545i) q^{5} +(-0.580155 - 3.29022i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{3} +(0.139923 + 0.793545i) q^{5} +(-0.580155 - 3.29022i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-2.31584 + 4.01115i) q^{11} +(3.55370 - 2.98191i) q^{13} +(0.139923 - 0.793545i) q^{15} +(-3.21791 - 2.70014i) q^{17} +(-1.11559 - 0.406043i) q^{19} +(-0.580155 + 3.29022i) q^{21} +(-1.67049 - 2.89337i) q^{23} +(4.08833 - 1.48803i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-0.410050 + 0.710228i) q^{29} -10.7099 q^{31} +(3.54807 - 2.97719i) q^{33} +(2.52976 - 0.920758i) q^{35} +(-2.49164 - 5.54903i) q^{37} +(-4.35926 + 1.58664i) q^{39} +(-3.23742 + 2.71652i) q^{41} +4.12571 q^{43} +(-0.402893 + 0.697832i) q^{45} +(-6.37119 - 11.0352i) q^{47} +(-3.91114 + 1.42354i) q^{49} +(2.10034 + 3.63789i) q^{51} +(0.807180 - 4.57775i) q^{53} +(-3.50707 - 1.27647i) q^{55} +(0.909440 + 0.763111i) q^{57} +(0.449582 - 2.54971i) q^{59} +(-4.78942 + 4.01880i) q^{61} +(1.67049 - 2.89337i) q^{63} +(2.86353 + 2.40278i) q^{65} +(-2.54638 - 14.4412i) q^{67} +(0.580155 + 3.29022i) q^{69} +(11.0217 + 4.01156i) q^{71} -9.68731 q^{73} -4.35071 q^{75} +(14.5411 + 5.29254i) q^{77} +(-2.45893 - 13.9453i) q^{79} +(0.173648 + 0.984808i) q^{81} +(2.98412 + 2.50398i) q^{83} +(1.69242 - 2.93137i) q^{85} +(0.628233 - 0.527150i) q^{87} +(-0.904762 + 5.13116i) q^{89} +(-11.8729 - 9.96251i) q^{91} +(10.0640 + 3.66300i) q^{93} +(0.166115 - 0.942088i) q^{95} +(4.48901 + 7.77519i) q^{97} +(-4.35235 + 1.58413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) $ 24 * q + 3 * q^5 + 15 * q^7	$ 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) $ 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$	$1$	$1$

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
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$		0			0
$5$	0.139923	+	0.793545i	0.0625756	+	0.354884i	0.999978	+	0.00663578i	$0.00211225\pi$
$5$	0.139923	+	0.793545i	0.0625756	+	0.354884i	−0.937402	+	0.348248i	$0.886777\pi$
$6$		0			0
$7$	−0.580155	−	3.29022i	−0.219278	−	1.24359i	−0.873327	−	0.487135i	$-0.838042\pi$
$7$	−0.580155	−	3.29022i	−0.219278	−	1.24359i	0.654049	−	0.756453i	$-0.273069\pi$
$8$		0			0
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$		0			0
$11$	−2.31584	+	4.01115i	−0.698252	+	1.20941i	0.270820	+	0.962630i	$0.412705\pi$
$11$	−2.31584	+	4.01115i	−0.698252	+	1.20941i	−0.969072	+	0.246778i	$0.920628\pi$
$12$		0			0
$13$	3.55370	−	2.98191i	0.985620	−	0.827033i	0.000692395	−	1.00000i	$-0.499780\pi$
$13$	3.55370	−	2.98191i	0.985620	−	0.827033i	0.984928	+	0.172966i	$0.0553352\pi$
$14$		0			0
$15$	0.139923	−	0.793545i	0.0361281	−	0.204892i
$16$		0			0
$17$	−3.21791	−	2.70014i	−0.780457	−	0.654881i	0.162907	−	0.986641i	$-0.447913\pi$
$17$	−3.21791	−	2.70014i	−0.780457	−	0.654881i	−0.943364	+	0.331760i	$0.892357\pi$
$18$		0			0
$19$	−1.11559	−	0.406043i	−0.255935	−	0.0931526i	0.210867	−	0.977515i	$-0.432371\pi$
$19$	−1.11559	−	0.406043i	−0.255935	−	0.0931526i	−0.466801	+	0.884362i	$0.654594\pi$
$20$		0			0
$21$	−0.580155	+	3.29022i	−0.126600	+	0.717986i
$22$		0			0
$23$	−1.67049	−	2.89337i	−0.348321	−	0.603310i	0.637630	−	0.770343i	$-0.279915\pi$
$23$	−1.67049	−	2.89337i	−0.348321	−	0.603310i	−0.985951	+	0.167032i	$0.946582\pi$
$24$		0			0
$25$	4.08833	−	1.48803i	0.817666	−	0.297606i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	−0.410050	+	0.710228i	−0.0761444	+	0.131886i	−0.901583	−	0.432605i	$-0.857594\pi$
$29$	−0.410050	+	0.710228i	−0.0761444	+	0.131886i	0.825439	+	0.564491i	$0.190928\pi$
$30$		0			0
$31$	−10.7099			−1.92355			−0.961777	−	0.273834i	$-0.911708\pi$
$31$	−10.7099			−1.92355			−0.961777	+	0.273834i	$0.911708\pi$
$32$		0			0
$33$	3.54807	−	2.97719i	0.617640	−	0.518261i
$34$		0			0
$35$	2.52976	−	0.920758i	0.427608	−	0.155637i
$36$		0			0
$37$	−2.49164	−	5.54903i	−0.409623	−	0.912255i
$37$	−2.49164	−	5.54903i	−0.409623	−	0.912255i
$38$		0			0
$39$	−4.35926	+	1.58664i	−0.698041	+	0.254066i
$40$		0			0
$41$	−3.23742	+	2.71652i	−0.505601	+	0.424249i	−0.859578	−	0.511005i	$-0.829273\pi$
$41$	−3.23742	+	2.71652i	−0.505601	+	0.424249i	0.353977	+	0.935254i	$0.384829\pi$
$42$		0			0
$43$	4.12571			0.629165			0.314582	−	0.949230i	$-0.398136\pi$
$43$	4.12571			0.629165			0.314582	+	0.949230i	$0.398136\pi$
$44$		0			0
$45$	−0.402893	+	0.697832i	−0.0600598	+	0.104027i
$46$		0			0
$47$	−6.37119	−	11.0352i	−0.929334	−	1.60965i	−0.784438	−	0.620207i	$-0.787048\pi$
$47$	−6.37119	−	11.0352i	−0.929334	−	1.60965i	−0.144896	−	0.989447i	$-0.546285\pi$
$48$		0			0
$49$	−3.91114	+	1.42354i	−0.558735	+	0.203363i
$50$		0			0
$51$	2.10034	+	3.63789i	0.294106	+	0.509407i
$52$		0			0
$53$	0.807180	−	4.57775i	0.110875	−	0.628802i	−0.877836	−	0.478962i	$-0.841013\pi$
$53$	0.807180	−	4.57775i	0.110875	−	0.628802i	0.988710	−	0.149840i	$-0.0478758\pi$
$54$		0			0
$55$	−3.50707	−	1.27647i	−0.472893	−	0.172119i
$56$		0			0
$57$	0.909440	+	0.763111i	0.120458	+	0.101076i
$58$		0			0
$59$	0.449582	−	2.54971i	0.0585306	−	0.331943i	−0.941456	−	0.337136i	$-0.890542\pi$
$59$	0.449582	−	2.54971i	0.0585306	−	0.331943i	0.999987	+	0.00519264i	$0.00165288\pi$
$60$		0			0
$61$	−4.78942	+	4.01880i	−0.613222	+	0.514555i	−0.895665	−	0.444730i	$-0.853300\pi$
$61$	−4.78942	+	4.01880i	−0.613222	+	0.514555i	0.282443	+	0.959284i	$0.408855\pi$
$62$		0			0
$63$	1.67049	−	2.89337i	0.210462	−	0.364531i
$64$		0			0
$65$	2.86353	+	2.40278i	0.355177	+	0.298029i
$66$		0			0
$67$	−2.54638	−	14.4412i	−0.311089	−	1.76428i	−0.593357	−	0.804940i	$-0.702198\pi$
$67$	−2.54638	−	14.4412i	−0.311089	−	1.76428i	0.282267	−	0.959336i	$-0.408913\pi$
$68$		0			0
$69$	0.580155	+	3.29022i	0.0698425	+	0.396096i
$70$		0			0
$71$	11.0217	+	4.01156i	1.30803	+	0.476085i	0.899604	−	0.436706i	$-0.143855\pi$
$71$	11.0217	+	4.01156i	1.30803	+	0.476085i	0.408427	+	0.912791i	$0.366077\pi$
$72$		0			0
$73$	−9.68731			−1.13381			−0.566907	−	0.823782i	$-0.691860\pi$
$73$	−9.68731			−1.13381			−0.566907	+	0.823782i	$0.691860\pi$
$74$		0			0
$75$	−4.35071			−0.502377
$76$		0			0
$77$	14.5411	+	5.29254i	1.65712	+	0.603141i
$78$		0			0
$79$	−2.45893	−	13.9453i	−0.276651	−	1.56896i	−0.733669	−	0.679507i	$-0.762194\pi$
$79$	−2.45893	−	13.9453i	−0.276651	−	1.56896i	0.457018	−	0.889458i	$-0.348918\pi$
$80$		0			0
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$		0			0
$83$	2.98412	+	2.50398i	0.327550	+	0.274847i	0.791701	−	0.610909i	$-0.209196\pi$
$83$	2.98412	+	2.50398i	0.327550	+	0.274847i	−0.464151	+	0.885756i	$0.653640\pi$
$84$		0			0
$85$	1.69242	−	2.93137i	0.183569	−	0.317951i
$86$		0			0
$87$	0.628233	−	0.527150i	0.0673537	−	0.0565164i
$88$		0			0
$89$	−0.904762	+	5.13116i	−0.0959046	+	0.543902i	0.898562	+	0.438847i	$0.144613\pi$
$89$	−0.904762	+	5.13116i	−0.0959046	+	0.543902i	−0.994466	+	0.105055i	$0.966498\pi$
$90$		0			0
$91$	−11.8729	−	9.96251i	−1.24461	−	1.04435i
$92$		0			0
$93$	10.0640	+	3.66300i	1.04359	+	0.379835i
$94$		0			0
$95$	0.166115	−	0.942088i	0.0170431	−	0.0966562i
$96$		0			0
$97$	4.48901	+	7.77519i	0.455790	+	0.789451i	0.998733	−	0.0503180i	$-0.0160235\pi$
$97$	4.48901	+	7.77519i	0.455790	+	0.789451i	−0.542943	+	0.839769i	$0.682690\pi$
$98$		0			0
$99$	−4.35235	+	1.58413i	−0.437428	+	0.159211i
$100$		0			0
$101$	−6.76312	−	11.7141i	−0.672955	−	1.16559i	−0.977062	−	0.212955i	$-0.931691\pi$
$101$	−6.76312	−	11.7141i	−0.672955	−	1.16559i	0.304107	−	0.952638i	$-0.401642\pi$
$102$		0			0
$103$	0.685157	−	1.18673i	0.0675106	−	0.116932i	−0.830294	−	0.557325i	$-0.811828\pi$
$103$	0.685157	−	1.18673i	0.0675106	−	0.116932i	0.897805	+	0.440393i	$0.145161\pi$
$104$		0			0
$105$	−2.69212			−0.262724
$106$		0			0
$107$	−13.2209	+	11.0937i	−1.27811	+	1.07247i	−0.284613	+	0.958642i	$0.591865\pi$
$107$	−13.2209	+	11.0937i	−1.27811	+	1.07247i	−0.993501	+	0.113823i	$0.963690\pi$
$108$		0			0
$109$	9.80153	−	3.56747i	0.938817	−	0.341701i	0.173118	−	0.984901i	$-0.444616\pi$
$109$	9.80153	−	3.56747i	0.938817	−	0.341701i	0.765698	+	0.643200i	$0.222394\pi$
$110$		0			0
$111$	0.443494	+	6.06657i	0.0420946	+	0.575814i
$112$		0			0
$113$	−11.6223	+	4.23016i	−1.09333	+	0.397940i	−0.824854	−	0.565346i	$-0.808743\pi$
$113$	−11.6223	+	4.23016i	−1.09333	+	0.397940i	−0.268477	+	0.963286i	$0.586520\pi$
$114$		0			0
$115$	2.06228	−	1.73046i	0.192309	−	0.161366i
$116$		0			0
$117$	4.63903			0.428879
$118$		0			0
$119$	−7.01719	+	12.1541i	−0.643265	+	1.11417i
$120$		0			0
$121$	−5.22622	−	9.05208i	−0.475111	−	0.822917i
$122$		0			0
$123$	3.97129	−	1.44543i	0.358079	−	0.130330i
$124$		0			0
$125$	3.76734	+	6.52522i	0.336961	+	0.583633i
$126$		0			0
$127$	−3.16164	+	17.9306i	−0.280550	+	1.59108i	0.440209	+	0.897895i	$0.354904\pi$
$127$	−3.16164	+	17.9306i	−0.280550	+	1.59108i	−0.720759	+	0.693185i	$0.756207\pi$
$128$		0			0
$129$	−3.87690	−	1.41108i	−0.341342	−	0.124238i
$130$		0			0
$131$	10.8801	+	9.12948i	0.950598	+	0.797646i	0.979398	−	0.201939i	$-0.0647243\pi$
$131$	10.8801	+	9.12948i	0.950598	+	0.797646i	−0.0288004	+	0.999585i	$0.509169\pi$
$132$		0			0
$133$	−0.688754	+	3.90612i	−0.0597226	+	0.338703i
$134$		0			0
$135$	0.617268	−	0.517950i	0.0531260	−	0.0445780i
$136$		0			0
$137$	5.98167	−	10.3606i	0.511049	−	0.885162i	−0.488869	−	0.872357i	$-0.662591\pi$
$137$	5.98167	−	10.3606i	0.511049	−	0.885162i	0.999918	−	0.0128051i	$-0.00407611\pi$
$138$		0			0
$139$	1.79585	+	1.50690i	0.152322	+	0.127813i	0.715764	−	0.698342i	$-0.246079\pi$
$139$	1.79585	+	1.50690i	0.152322	+	0.127813i	−0.563442	+	0.826156i	$0.690523\pi$
$140$		0			0
$141$	2.21269	+	12.5488i	0.186342	+	1.05680i
$142$		0			0
$143$	3.73109	+	21.1601i	0.312010	+	1.76949i
$144$		0			0
$145$	−0.620973	−	0.226016i	−0.0515690	−	0.0187696i
$146$		0			0
$147$	4.16215			0.343289
$148$		0			0
$149$	7.02131			0.575208			0.287604	−	0.957749i	$-0.407141\pi$
$149$	7.02131			0.575208			0.287604	+	0.957749i	$0.407141\pi$
$150$		0			0
$151$	10.2471	+	3.72962i	0.833894	+	0.303513i	0.723456	−	0.690370i	$-0.242552\pi$
$151$	10.2471	+	3.72962i	0.833894	+	0.303513i	0.110438	+	0.993883i	$0.464775\pi$
$152$		0			0
$153$	−0.729440	−	4.13686i	−0.0589717	−	0.334445i
$154$		0			0
$155$	−1.49856	−	8.49878i	−0.120368	−	0.682638i
$156$		0			0
$157$	12.6382	+	10.6047i	1.00863	+	0.846345i	0.988157	−	0.153445i	$-0.0490369\pi$
$157$	12.6382	+	10.6047i	1.00863	+	0.846345i	0.0204775	+	0.999790i	$0.493481\pi$
$158$		0			0
$159$	−2.32418	+	4.02560i	−0.184320	+	0.319251i
$160$		0			0
$161$	−8.55071	+	7.17489i	−0.673890	+	0.565461i
$162$		0			0
$163$	2.19040	−	12.4224i	0.171566	−	0.972997i	−0.770468	−	0.637479i	$-0.779977\pi$
$163$	2.19040	−	12.4224i	0.171566	−	0.972997i	0.942034	−	0.335518i	$-0.108911\pi$
$164$		0			0
$165$	2.85899	+	2.39898i	0.222572	+	0.186760i
$166$		0			0
$167$	15.4148	+	5.61053i	1.19283	+	0.434156i	0.860717	−	0.509083i	$-0.170015\pi$
$167$	15.4148	+	5.61053i	1.19283	+	0.434156i	0.332115	+	0.943239i	$0.392238\pi$
$168$		0			0
$169$	1.47959	−	8.39116i	0.113814	−	0.645474i
$170$		0			0
$171$	−0.593595	−	1.02814i	−0.0453933	−	0.0786235i
$172$		0			0
$173$	10.7877	−	3.92642i	0.820176	−	0.298520i	0.102356	−	0.994748i	$-0.467362\pi$
$173$	10.7877	−	3.92642i	0.820176	−	0.298520i	0.717821	+	0.696228i	$0.245140\pi$
$174$		0			0
$175$	−7.26782	−	12.5882i	−0.549395	−	0.951581i
$176$		0			0
$177$	−1.29452	+	2.24217i	−0.0973020	+	0.168532i
$178$		0			0
$179$	7.94734			0.594012			0.297006	−	0.954876i	$-0.404012\pi$
$179$	7.94734			0.594012			0.297006	+	0.954876i	$0.404012\pi$
$180$		0			0
$181$	4.32428	−	3.62850i	0.321421	−	0.269705i	−0.467772	−	0.883849i	$-0.654943\pi$
$181$	4.32428	−	3.62850i	0.321421	−	0.269705i	0.789194	+	0.614144i	$0.210499\pi$
$182$		0			0
$183$	5.87509	−	2.13836i	0.434299	−	0.158072i
$184$		0			0
$185$	4.05477	−	2.75367i	0.298112	−	0.202454i
$186$		0			0
$187$	18.2828	−	6.65441i	1.33697	−	0.486619i
$188$		0			0
$189$	−2.55934	+	2.14754i	−0.186165	+	0.156211i
$190$		0			0
$191$	−9.21524			−0.666791			−0.333396	−	0.942787i	$-0.608194\pi$
$191$	−9.21524			−0.666791			−0.333396	+	0.942787i	$0.608194\pi$
$192$		0			0
$193$	7.49758	−	12.9862i	0.539688	−	0.934767i	−0.459233	−	0.888316i	$-0.651876\pi$
$193$	7.49758	−	12.9862i	0.539688	−	0.934767i	0.998921	−	0.0464508i	$-0.0147911\pi$
$194$		0			0
$195$	−1.86903	−	3.23726i	−0.133844	−	0.231825i
$196$		0			0
$197$	15.0206	−	5.46706i	1.07017	−	0.389512i	0.253933	−	0.967222i	$-0.418276\pi$
$197$	15.0206	−	5.46706i	1.07017	−	0.389512i	0.816242	+	0.577710i	$0.196054\pi$
$198$		0			0
$199$	2.48283	+	4.30039i	0.176003	+	0.304846i	0.940508	−	0.339772i	$-0.110350\pi$
$199$	2.48283	+	4.30039i	0.176003	+	0.304846i	−0.764505	+	0.644618i	$0.777016\pi$
$200$		0			0
$201$	−2.54638	+	14.4412i	−0.179608	+	1.01860i
$202$		0			0
$203$	2.57470	+	0.937114i	0.180709	+	0.0657725i
$204$		0			0
$205$	−2.60867	−	2.18894i	−0.182198	−	0.152882i
$206$		0			0
$207$	0.580155	−	3.29022i	0.0403236	−	0.228686i
$208$		0			0
$209$	4.21223	−	3.53448i	0.291366	−	0.244485i
$210$		0			0
$211$	−9.18344	+	15.9062i	−0.632214	+	1.09503i	0.354884	+	0.934910i	$0.384520\pi$
$211$	−9.18344	+	15.9062i	−0.632214	+	1.09503i	−0.987098	+	0.160117i	$0.948813\pi$
$212$		0			0
$213$	−8.98495	−	7.53927i	−0.615638	−	0.516582i
$214$		0			0
$215$	0.577283	+	3.27394i	0.0393704	+	0.223281i
$216$		0			0
$217$	6.21340	+	35.2380i	0.421793	+	2.39211i
$218$		0			0
$219$	9.10309	+	3.31325i	0.615130	+	0.223889i
$220$		0			0
$221$	−19.4871			−1.31084
$222$		0			0
$223$	−0.363961			−0.0243726			−0.0121863	−	0.999926i	$-0.503879\pi$
$223$	−0.363961			−0.0243726			−0.0121863	+	0.999926i	$0.503879\pi$
$224$		0			0
$225$	4.08833	+	1.48803i	0.272555	+	0.0992020i
$226$		0			0
$227$	0.214687	+	1.21755i	0.0142493	+	0.0808116i	0.991103	−	0.133096i	$-0.0424919\pi$
$227$	0.214687	+	1.21755i	0.0142493	+	0.0808116i	−0.976854	+	0.213908i	$0.931381\pi$
$228$		0			0
$229$	3.02405	+	17.1503i	0.199835	+	1.13332i	0.905363	+	0.424639i	$0.139599\pi$
$229$	3.02405	+	17.1503i	0.199835	+	1.13332i	−0.705528	+	0.708682i	$0.749290\pi$
$230$		0			0
$231$	−11.8540	−	9.94672i	−0.779938	−	0.654446i
$232$		0			0
$233$	−6.83301	+	11.8351i	−0.447645	+	0.775344i	−0.998232	−	0.0594334i	$-0.981071\pi$
$233$	−6.83301	+	11.8351i	−0.447645	+	0.775344i	0.550587	+	0.834778i	$0.314404\pi$
$234$		0			0
$235$	7.86547	−	6.59991i	0.513087	−	0.430531i
$236$		0			0
$237$	−2.45893	+	13.9453i	−0.159724	+	0.905842i
$238$		0			0
$239$	11.8304	+	9.92689i	0.765245	+	0.642117i	0.939486	−	0.342586i	$-0.111303\pi$
$239$	11.8304	+	9.92689i	0.765245	+	0.642117i	−0.174241	+	0.984703i	$0.555747\pi$
$240$		0			0
$241$	−7.26196	−	2.64314i	−0.467784	−	0.170259i	0.0973643	−	0.995249i	$-0.468959\pi$
$241$	−7.26196	−	2.64314i	−0.467784	−	0.170259i	−0.565148	+	0.824989i	$0.691181\pi$
$242$		0			0
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$		0			0
$245$	−1.67690	−	2.90448i	−0.107133	−	0.185561i
$246$		0			0
$247$	−5.17527	+	1.88364i	−0.329295	+	0.119853i
$248$		0			0
$249$	−1.94775	−	3.37360i	−0.123434	−	0.213793i
$250$		0			0
$251$	5.00052	−	8.66116i	0.315630	−	0.546687i	−0.663941	−	0.747785i	$-0.731117\pi$
$251$	5.00052	−	8.66116i	0.315630	−	0.546687i	0.979571	+	0.201097i	$0.0644508\pi$
$252$		0			0
$253$	15.4743			0.972864
$254$		0			0
$255$	−2.59295	+	2.17574i	−0.162377	+	0.136250i
$256$		0			0
$257$	−18.6568	+	6.79053i	−1.16378	+	0.423582i	−0.850447	−	0.526061i	$-0.823668\pi$
$257$	−18.6568	+	6.79053i	−1.16378	+	0.423582i	−0.313335	+	0.949643i	$0.601446\pi$
$258$		0			0
$259$	−16.8120	+	11.4173i	−1.04465	+	0.709439i
$260$		0			0
$261$	−0.770642	+	0.280491i	−0.0477016	+	0.0173619i
$262$		0			0
$263$	10.5323	−	8.83765i	0.649449	−	0.544953i	−0.257455	−	0.966290i	$-0.582884\pi$
$263$	10.5323	−	8.83765i	0.649449	−	0.544953i	0.906904	+	0.421338i	$0.138439\pi$
$264$		0			0
$265$	3.74559			0.230090
$266$		0			0
$267$	2.60516	−	4.51227i	0.159433	−	0.276146i
$268$		0			0
$269$	−7.59877	−	13.1615i	−0.463305	−	0.802468i	0.535818	−	0.844333i	$-0.320003\pi$
$269$	−7.59877	−	13.1615i	−0.463305	−	0.802468i	−0.999123	+	0.0418655i	$0.986670\pi$
$270$		0			0
$271$	−5.06425	+	1.84324i	−0.307631	+	0.111969i	−0.491223	−	0.871034i	$-0.663450\pi$
$271$	−5.06425	+	1.84324i	−0.307631	+	0.111969i	0.183591	+	0.983003i	$0.441228\pi$
$272$		0			0
$273$	7.74946	+	13.4225i	0.469018	+	0.812364i
$274$		0			0
$275$	−3.49920	+	19.8449i	−0.211010	+	1.19669i
$276$		0			0
$277$	−17.8369	−	6.49211i	−1.07172	−	0.390073i	−0.254898	−	0.966968i	$-0.582042\pi$
$277$	−17.8369	−	6.49211i	−1.07172	−	0.390073i	−0.816818	+	0.576895i	$0.804264\pi$
$278$		0			0
$279$	−8.20426	−	6.88419i	−0.491176	−	0.412146i
$280$		0			0
$281$	2.44551	−	13.8692i	0.145887	−	0.827367i	−0.820763	−	0.571268i	$-0.806452\pi$
$281$	2.44551	−	13.8692i	0.145887	−	0.827367i	0.966651	−	0.256099i	$-0.0824373\pi$
$282$		0			0
$283$	−5.97019	+	5.00959i	−0.354891	+	0.297789i	−0.802751	−	0.596315i	$-0.796631\pi$
$283$	−5.97019	+	5.00959i	−0.354891	+	0.297789i	0.447859	+	0.894104i	$0.352187\pi$
$284$		0			0
$285$	−0.478310	+	0.828458i	−0.0283327	+	0.0490736i
$286$		0			0
$287$	10.8162	+	9.07584i	0.638458	+	0.535730i
$288$		0			0
$289$	0.112124	+	0.635887i	0.00659554	+	0.0374051i
$290$		0			0
$291$	−1.55902	−	8.84162i	−0.0913912	−	0.518305i
$292$		0			0
$293$	−8.24728	−	3.00176i	−0.481811	−	0.175365i	0.0896841	−	0.995970i	$-0.471414\pi$
$293$	−8.24728	−	3.00176i	−0.481811	−	0.175365i	−0.571495	+	0.820605i	$0.693636\pi$
$294$		0			0
$295$	2.08621			0.121464
$296$		0			0
$297$	4.63168			0.268757
$298$		0			0
$299$	−14.5642	−	5.30094i	−0.842270	−	0.306561i
$300$		0			0
$301$	−2.39355	−	13.5745i	−0.137962	−	0.782422i
$302$		0			0
$303$	2.34881	+	13.3207i	0.134935	+	0.765257i
$304$		0			0
$305$	−3.85925	−	3.23829i	−0.220980	−	0.185424i
$306$		0			0
$307$	6.47755	−	11.2195i	0.369693	−	0.640328i	−0.619824	−	0.784741i	$-0.712796\pi$
$307$	6.47755	−	11.2195i	0.369693	−	0.640328i	0.989518	+	0.144413i	$0.0461294\pi$
$308$		0			0
$309$	−1.04972	+	0.880821i	−0.0597166	+	0.0501082i
$310$		0			0
$311$	−3.86591	+	21.9247i	−0.219216	+	1.24323i	0.654223	+	0.756301i	$0.272996\pi$
$311$	−3.86591	+	21.9247i	−0.219216	+	1.24323i	−0.873439	+	0.486933i	$0.838115\pi$
$312$		0			0
$313$	−24.7859	−	20.7978i	−1.40098	−	1.17556i	−0.960662	−	0.277719i	$-0.910422\pi$
$313$	−24.7859	−	20.7978i	−1.40098	−	1.17556i	−0.440317	−	0.897842i	$-0.645134\pi$
$314$		0			0
$315$	2.52976	+	0.920758i	0.142536	+	0.0518788i
$316$		0			0
$317$	−3.25232	+	18.4448i	−0.182668	+	1.03596i	0.746246	+	0.665670i	$0.231854\pi$
$317$	−3.25232	+	18.4448i	−0.182668	+	1.03596i	−0.928915	+	0.370294i	$0.879257\pi$
$318$		0			0
$319$	−1.89922	−	3.28955i	−0.106336	−	0.184179i
$320$		0			0
$321$	16.2179	−	5.90282i	0.905192	−	0.329463i
$322$		0			0
$323$	2.49350	+	4.31887i	0.138742	+	0.240308i
$324$		0			0
$325$	10.0915	−	17.4791i	0.559778	−	0.969563i
$326$		0			0
$327$	−10.4306			−0.576812
$328$		0			0
$329$	−32.6121	+	27.3648i	−1.79796	+	1.50867i
$330$		0			0
$331$	23.8178	−	8.66899i	1.30915	−	0.476491i	0.409182	−	0.912453i	$-0.365814\pi$
$331$	23.8178	−	8.66899i	1.30915	−	0.476491i	0.899965	+	0.435962i	$0.143592\pi$
$332$		0			0
$333$	1.65814	−	5.85240i	0.0908656	−	0.320709i
$334$		0			0
$335$	11.1035	−	4.04133i	0.606646	−	0.220801i
$336$		0			0
$337$	−7.85862	+	6.59417i	−0.428086	+	0.359207i	−0.831229	−	0.555930i	$-0.812362\pi$
$337$	−7.85862	+	6.59417i	−0.428086	+	0.359207i	0.403143	+	0.915137i	$0.367918\pi$
$338$		0			0
$339$	12.3682			0.671746
$340$		0			0
$341$	24.8024	−	42.9590i	1.34312	−	2.32636i
$342$		0			0
$343$	−4.74060	−	8.21095i	−0.255968	−	0.443350i
$344$		0			0
$345$	−2.52976	+	0.920758i	−0.136198	+	0.0495720i
$346$		0			0
$347$	−8.82672	−	15.2883i	−0.473843	−	0.820721i	0.525708	−	0.850665i	$-0.323800\pi$
$347$	−8.82672	−	15.2883i	−0.473843	−	0.820721i	−0.999552	+	0.0299443i	$0.990467\pi$
$348$		0			0
$349$	2.32360	−	13.1778i	0.124379	−	0.705391i	−0.857295	−	0.514826i	$-0.827857\pi$
$349$	2.32360	−	13.1778i	0.124379	−	0.705391i	0.981674	−	0.190566i	$-0.0610322\pi$
$350$		0			0
$351$	−4.35926	−	1.58664i	−0.232680	−	0.0846887i
$352$		0			0
$353$	−14.4667	−	12.1390i	−0.769982	−	0.646092i	0.170722	−	0.985319i	$-0.445390\pi$
$353$	−14.4667	−	12.1390i	−0.769982	−	0.646092i	−0.940704	+	0.339227i	$0.889834\pi$
$354$		0			0
$355$	−1.64116	+	9.30750i	−0.0871039	+	0.493991i
$356$		0			0
$357$	10.7510	−	9.02113i	0.569001	−	0.477449i
$358$		0			0
$359$	14.4170	−	24.9709i	0.760898	−	1.31791i	−0.181490	−	0.983393i	$-0.558092\pi$
$359$	14.4170	−	24.9709i	0.760898	−	1.31791i	0.942388	−	0.334522i	$-0.108575\pi$
$360$		0			0
$361$	−13.4752	−	11.3070i	−0.709219	−	0.595106i
$362$		0			0
$363$	1.81505	+	10.2936i	0.0952653	+	0.540276i
$364$		0			0
$365$	−1.35548	−	7.68731i	−0.0709491	−	0.402372i
$366$		0			0
$367$	1.85047	+	0.673516i	0.0965938	+	0.0351573i	0.389865	−	0.920872i	$-0.372522\pi$
$367$	1.85047	+	0.673516i	0.0965938	+	0.0351573i	−0.293271	+	0.956029i	$0.594744\pi$
$368$		0			0
$369$	−4.22616			−0.220005
$370$		0			0
$371$	−15.5301			−0.806283
$372$		0			0
$373$	4.22551	+	1.53796i	0.218789	+	0.0796326i	0.449089	−	0.893487i	$-0.351749\pi$
$373$	4.22551	+	1.53796i	0.218789	+	0.0796326i	−0.230300	+	0.973120i	$0.573971\pi$
$374$		0			0
$375$	−1.30838	−	7.42021i	−0.0675646	−	0.383178i
$376$		0			0
$377$	0.660639	+	3.74667i	0.0340247	+	0.192963i
$378$		0			0
$379$	19.3281	+	16.2182i	0.992820	+	0.833075i	0.985974	−	0.166902i	$-0.0533763\pi$
$379$	19.3281	+	16.2182i	0.992820	+	0.833075i	0.00684633	+	0.999977i	$0.497821\pi$
$380$		0			0
$381$	9.10359	−	15.7679i	0.466391	−	0.807813i
$382$		0			0
$383$	1.14016	−	0.956706i	0.0582594	−	0.0488854i	−0.613193	−	0.789933i	$-0.710115\pi$
$383$	1.14016	−	0.956706i	0.0582594	−	0.0488854i	0.671452	+	0.741048i	$0.265671\pi$
$384$		0			0
$385$	−2.16522	+	12.2796i	−0.110350	+	0.625826i
$386$		0			0
$387$	3.16048	+	2.65196i	0.160656	+	0.134806i
$388$		0			0
$389$	18.4650	+	6.72072i	0.936215	+	0.340754i	0.764670	−	0.644422i	$-0.222902\pi$
$389$	18.4650	+	6.72072i	0.936215	+	0.340754i	0.171545	+	0.985176i	$0.445124\pi$
$390$		0			0
$391$	−2.43705	+	13.8212i	−0.123247	+	0.698967i
$392$		0			0
$393$	−7.10147	−	12.3001i	−0.358222	−	0.620459i
$394$		0			0
$395$	10.7221	−	3.90254i	0.539489	−	0.196358i
$396$		0			0
$397$	16.2118	+	28.0797i	0.813647	+	1.40928i	0.910295	+	0.413959i	$0.135854\pi$
$397$	16.2118	+	28.0797i	0.813647	+	1.40928i	−0.0966486	+	0.995319i	$0.530812\pi$
$398$		0			0
$399$	1.98319	−	3.43498i	0.0992836	−	0.171964i
$400$		0			0
$401$	7.59897			0.379474			0.189737	−	0.981835i	$-0.439236\pi$
$401$	7.59897			0.379474			0.189737	+	0.981835i	$0.439236\pi$
$402$		0			0
$403$	−38.0598	+	31.9360i	−1.89589	+	1.59084i
$404$		0			0
$405$	−0.757192	+	0.275595i	−0.0376252	+	0.0136944i
$406$		0			0
$407$	28.0282	+	2.85632i	1.38931	+	0.141583i
$408$		0			0
$409$	20.2829	−	7.38237i	1.00292	−	0.365035i	0.212213	−	0.977223i	$-0.431933\pi$
$409$	20.2829	−	7.38237i	1.00292	−	0.365035i	0.790712	+	0.612189i	$0.209711\pi$
$410$		0			0
$411$	−9.16445	+	7.68989i	−0.452049	+	0.379314i
$412$		0			0
$413$	−8.64993			−0.425635
$414$		0			0
$415$	−1.56947	+	2.71840i	−0.0770422	+	0.133441i
$416$		0			0
$417$	−1.17216	−	2.03024i	−0.0574009	−	0.0994212i
$418$		0			0
$419$	−33.3116	+	12.1244i	−1.62738	+	0.592318i	−0.984768	−	0.173873i	$-0.944372\pi$
$419$	−33.3116	+	12.1244i	−1.62738	+	0.592318i	−0.642612	+	0.766191i	$0.722149\pi$
$420$		0			0
$421$	13.1783	+	22.8255i	0.642271	+	1.11245i	0.984925	+	0.172985i	$0.0553411\pi$
$421$	13.1783	+	22.8255i	0.642271	+	1.11245i	−0.342653	+	0.939462i	$0.611326\pi$
$422$		0			0
$423$	2.21269	−	12.5488i	0.107585	−	0.610144i
$424$		0			0
$425$	−17.1738	−	6.25073i	−0.833049	−	0.303205i
$426$		0			0
$427$	16.0014	+	13.4267i	0.774360	+	0.649765i
$428$		0			0
$429$	3.73109	−	21.1601i	0.180139	−	1.02162i
$430$		0			0
$431$	7.92363	−	6.64871i	0.381668	−	0.320257i	−0.431689	−	0.902023i	$-0.642082\pi$
$431$	7.92363	−	6.64871i	0.381668	−	0.320257i	0.813357	+	0.581765i	$0.197638\pi$
$432$		0			0
$433$	−4.22908	+	7.32498i	−0.203237	+	0.352016i	−0.949569	−	0.313557i	$-0.898479\pi$
$433$	−4.22908	+	7.32498i	−0.203237	+	0.352016i	0.746333	+	0.665573i	$0.231813\pi$
$434$		0			0
$435$	0.506222	+	0.424771i	0.0242715	+	0.0203662i
$436$		0			0
$437$	0.688754	+	3.90612i	0.0329476	+	0.186855i
$438$		0			0
$439$	−5.51069	−	31.2527i	−0.263011	−	1.49161i	−0.774640	−	0.632403i	$-0.782069\pi$
$439$	−5.51069	−	31.2527i	−0.263011	−	1.49161i	0.511629	−	0.859207i	$-0.329042\pi$
$440$		0			0
$441$	−3.91114	−	1.42354i	−0.186245	−	0.0677876i
$442$		0			0
$443$	23.9862			1.13962			0.569808	−	0.821778i	$-0.307017\pi$
$443$	23.9862			1.13962			0.569808	+	0.821778i	$0.307017\pi$
$444$		0			0
$445$	−4.19840			−0.199023
$446$		0			0
$447$	−6.59787	−	2.40143i	−0.312069	−	0.113584i
$448$		0			0
$449$	−4.42937	−	25.1202i	−0.209035	−	1.18550i	−0.890963	−	0.454077i	$-0.849969\pi$
$449$	−4.42937	−	25.1202i	−0.209035	−	1.18550i	0.681928	−	0.731420i	$-0.261142\pi$
$450$		0			0
$451$	−3.39902	−	19.2768i	−0.160054	−	0.907710i
$452$		0			0
$453$	−8.35348	−	7.00940i	−0.392481	−	0.329330i
$454$		0			0
$455$	6.24441	−	10.8156i	0.292742	−	0.507045i
$456$		0			0
$457$	−19.0473	+	15.9825i	−0.890993	+	0.747632i	−0.968409	−	0.249367i	$-0.919777\pi$
$457$	−19.0473	+	15.9825i	−0.890993	+	0.747632i	0.0774162	+	0.996999i	$0.475333\pi$
$458$		0			0
$459$	−0.729440	+	4.13686i	−0.0340473	+	0.193092i
$460$		0			0
$461$	−25.1780	−	21.1269i	−1.17266	−	0.983976i	−0.172658	−	0.984982i	$-0.555236\pi$
$461$	−25.1780	−	21.1269i	−1.17266	−	0.983976i	−0.999999	+	0.00100546i	$0.999680\pi$
$462$		0			0
$463$	−29.4169	−	10.7069i	−1.36712	−	0.497590i	−0.448870	−	0.893597i	$-0.648173\pi$
$463$	−29.4169	−	10.7069i	−1.36712	−	0.497590i	−0.918248	+	0.396007i	$0.870396\pi$
$464$		0			0
$465$	−1.49856	+	8.49878i	−0.0694943	+	0.394122i
$466$		0			0
$467$	6.17323	+	10.6923i	0.285663	+	0.494782i	0.972770	−	0.231774i	$-0.0744529\pi$
$467$	6.17323	+	10.6923i	0.285663	+	0.494782i	−0.687107	+	0.726556i	$0.741120\pi$
$468$		0			0
$469$	−46.0375	+	16.7563i	−2.12582	+	0.773734i
$470$		0			0
$471$	−8.24897	−	14.2876i	−0.380093	−	0.658340i
$472$		0			0
$473$	−9.55448	+	16.5488i	−0.439316	+	0.760917i
$474$		0			0
$475$	−5.16511			−0.236992
$476$		0			0
$477$	3.56085	−	2.98791i	0.163040	−	0.136807i
$478$		0			0
$479$	−3.99190	+	1.45293i	−0.182394	+	0.0663862i	−0.431603	−	0.902064i	$-0.642052\pi$
$479$	−3.99190	+	1.45293i	−0.182394	+	0.0663862i	0.249208	+	0.968450i	$0.419830\pi$
$480$		0			0
$481$	−25.4013	−	12.2898i	−1.15820	−	0.560365i
$482$		0			0
$483$	10.4890	−	3.81768i	0.477266	−	0.173711i
$484$		0			0
$485$	−5.54185	+	4.65016i	−0.251642	+	0.211153i
$486$		0			0
$487$	21.8843			0.991671			0.495836	−	0.868416i	$-0.334862\pi$
$487$	21.8843			0.991671			0.495836	+	0.868416i	$0.334862\pi$
$488$		0			0
$489$	−6.30701	+	10.9241i	−0.285213	+	0.494003i
$490$		0			0
$491$	−17.2027	−	29.7959i	−0.776346	−	1.34467i	−0.934035	−	0.357183i	$-0.883737\pi$
$491$	−17.2027	−	29.7959i	−0.776346	−	1.34467i	0.157688	−	0.987489i	$-0.449596\pi$
$492$		0			0
$493$	3.23722	−	1.17825i	0.145797	−	0.0530658i
$494$		0			0
$495$	−1.86607	−	3.23213i	−0.0838737	−	0.145273i
$496$		0			0
$497$	6.80465	−	38.5911i	0.305230	−	1.73105i
$498$		0			0
$499$	33.6579	+	12.2505i	1.50673	+	0.548407i	0.957794	−	0.287455i	$-0.0928090\pi$
$499$	33.6579	+	12.2505i	1.50673	+	0.548407i	0.548941	+	0.835861i	$0.315031\pi$
$500$		0			0
$501$	−12.5663	−	10.5443i	−0.561419	−	0.471086i
$502$		0			0
$503$	3.53053	−	20.0226i	0.157418	−	0.892764i	−0.799123	−	0.601168i	$-0.794702\pi$
$503$	3.53053	−	20.0226i	0.157418	−	0.892764i	0.956541	−	0.291597i	$-0.0941865\pi$
$504$		0			0
$505$	8.34931	−	7.00591i	0.371540	−	0.311759i
$506$		0			0
$507$	−4.26030	+	7.37906i	−0.189207	+	0.327716i
$508$		0			0
$509$	−4.49569	−	3.77233i	−0.199268	−	0.167206i	0.537694	−	0.843140i	$-0.319296\pi$
$509$	−4.49569	−	3.77233i	−0.199268	−	0.167206i	−0.736962	+	0.675935i	$0.763740\pi$
$510$		0			0
$511$	5.62014	+	31.8734i	0.248620	+	1.41000i
$512$		0			0
$513$	0.206153	+	1.16915i	0.00910189	+	0.0516194i
$514$		0			0
$515$	1.03759	+	0.377652i	0.0457217	+	0.0166413i
$516$		0			0
$517$	59.0187			2.59564
$518$		0			0
$519$	−11.4801			−0.503919
$520$		0			0
$521$	−25.5550	−	9.30126i	−1.11958	−	0.407495i	−0.285084	−	0.958503i	$-0.592022\pi$
$521$	−25.5550	−	9.30126i	−1.11958	−	0.407495i	−0.834501	+	0.551007i	$0.814244\pi$
$522$		0			0
$523$	−3.48567	−	19.7682i	−0.152418	−	0.864405i	−0.961109	−	0.276171i	$-0.910935\pi$
$523$	−3.48567	−	19.7682i	−0.152418	−	0.864405i	0.808691	−	0.588234i	$-0.200177\pi$
$524$		0			0
$525$	2.52409	+	14.3148i	0.110160	+	0.624749i
$526$		0			0
$527$	34.4634	+	28.9183i	1.50125	+	1.25970i
$528$		0			0
$529$	5.91892	−	10.2519i	0.257345	−	0.445734i
$530$		0			0
$531$	1.98332	−	1.66420i	0.0860687	−	0.0722202i
$532$		0			0
$533$	−3.40442	+	19.3074i	−0.147462	+	0.836297i
$534$		0			0
$535$	−10.6532	−	8.93913i	−0.460579	−	0.386472i
$536$		0			0
$537$	−7.46806	−	2.71815i	−0.322271	−	0.117297i
$538$		0			0
$539$	3.34755	−	18.9849i	0.144189	−	0.817737i
$540$		0			0
$541$	−5.05682	−	8.75867i	−0.217410	−	0.376565i	0.736606	−	0.676323i	$-0.236427\pi$
$541$	−5.05682	−	8.75867i	−0.217410	−	0.376565i	−0.954015	+	0.299758i	$0.903094\pi$
$542$		0			0
$543$	−5.30452	+	1.93069i	−0.227639	+	0.0828537i
$544$		0			0
$545$	4.20241	+	7.27878i	0.180011	+	0.311789i
$546$		0			0
$547$	6.41022	−	11.1028i	0.274081	−	0.474722i	−0.695822	−	0.718214i	$-0.744960\pi$
$547$	6.41022	−	11.1028i	0.274081	−	0.474722i	0.969903	+	0.243492i	$0.0782930\pi$
$548$		0			0
$549$	−6.25214			−0.266835
$550$		0			0
$551$	0.745832	−	0.625827i	0.0317735	−	0.0266611i
$552$		0			0
$553$	−44.4565	+	16.1808i	−1.89048	+	0.688079i
$554$		0			0
$555$	−4.75204	+	1.20079i	−0.201713	+	0.0509706i
$556$		0			0
$557$	1.45078	−	0.528040i	0.0614714	−	0.0223738i	−0.311101	−	0.950377i	$-0.600698\pi$
$557$	1.45078	−	0.528040i	0.0614714	−	0.0223738i	0.372573	+	0.928003i	$0.378476\pi$
$558$		0			0
$559$	14.6616	−	12.3025i	0.620118	−	0.520340i
$560$		0			0
$561$	−19.4562			−0.821441
$562$		0			0
$563$	−12.3585	+	21.4056i	−0.520850	+	0.902139i	0.478856	+	0.877894i	$0.341052\pi$
$563$	−12.3585	+	21.4056i	−0.520850	+	0.902139i	−0.999706	+	0.0242454i	$0.992282\pi$
$564$		0			0
$565$	−4.98305	−	8.63089i	−0.209638	−	0.363104i
$566$		0			0
$567$	3.13950	−	1.14268i	0.131846	−	0.0479882i
$568$		0			0
$569$	−18.6121	−	32.2371i	−0.780261	−	1.35145i	−0.931790	−	0.362999i	$-0.881753\pi$
$569$	−18.6121	−	32.2371i	−0.780261	−	1.35145i	0.151529	−	0.988453i	$-0.451580\pi$
$570$		0			0
$571$	−3.20029	+	18.1497i	−0.133928	+	0.759543i	0.841672	+	0.539989i	$0.181571\pi$
$571$	−3.20029	+	18.1497i	−0.133928	+	0.759543i	−0.975600	+	0.219554i	$0.929540\pi$
$572$		0			0
$573$	8.65949	+	3.15180i	0.361756	+	0.131668i
$574$		0			0
$575$	−11.1349	−	9.34332i	−0.464359	−	0.389644i
$576$		0			0
$577$	−5.18181	+	29.3875i	−0.215722	+	1.22342i	0.663928	+	0.747796i	$0.268888\pi$
$577$	−5.18181	+	29.3875i	−0.215722	+	1.22342i	−0.879650	+	0.475622i	$0.842223\pi$
$578$		0			0
$579$	−11.4870	+	9.63871i	−0.477382	+	0.400571i
$580$		0			0
$581$	6.50739	−	11.2711i	0.269972	−	0.467605i
$582$		0			0
$583$	16.4927	+	13.8390i	0.683059	+	0.573155i
$584$		0			0
$585$	0.649109	+	3.68128i	0.0268373	+	0.152202i
$586$		0			0
$587$	−2.05795	−	11.6712i	−0.0849407	−	0.481722i	−0.997369	−	0.0724867i	$-0.976906\pi$
$587$	−2.05795	−	11.6712i	−0.0849407	−	0.481722i	0.912429	−	0.409236i	$-0.134205\pi$
$588$		0			0
$589$	11.9479	+	4.34867i	0.492304	+	0.179184i
$590$		0			0
$591$	−15.9846			−0.657519
$592$		0			0
$593$	15.0779			0.619177			0.309588	−	0.950871i	$-0.399809\pi$
$593$	15.0779			0.619177			0.309588	+	0.950871i	$0.399809\pi$
$594$		0			0
$595$	−10.6267	−	3.86781i	−0.435653	−	0.158565i
$596$		0			0
$597$	−0.862278	−	4.89022i	−0.0352907	−	0.200143i
$598$		0			0
$599$	7.59287	+	43.0613i	0.310236	+	1.75944i	0.597772	+	0.801666i	$0.296053\pi$
$599$	7.59287	+	43.0613i	0.310236	+	1.75944i	−0.287536	+	0.957770i	$0.592836\pi$
$600$		0			0
$601$	10.1790	+	8.54118i	0.415209	+	0.348402i	0.826337	−	0.563176i	$-0.190421\pi$
$601$	10.1790	+	8.54118i	0.415209	+	0.348402i	−0.411128	+	0.911578i	$0.634865\pi$
$602$		0			0
$603$	7.33200	−	12.6994i	0.298582	−	0.517159i
$604$		0			0
$605$	6.45196	−	5.41384i	0.262310	−	0.220104i
$606$		0			0
$607$	0.582548	−	3.30379i	0.0236449	−	0.134097i	−0.970700	−	0.240294i	$-0.922756\pi$
$607$	0.582548	−	3.30379i	0.0236449	−	0.134097i	0.994345	+	0.106197i	$0.0338674\pi$
$608$		0			0
$609$	−2.09892	−	1.76120i	−0.0850523	−	0.0713674i
$610$		0			0
$611$	−55.5474	−	20.2176i	−2.24721	−	0.817917i
$612$		0			0
$613$	−0.393187	+	2.22988i	−0.0158807	+	0.0900638i	−0.991718	−	0.128435i	$-0.959005\pi$
$613$	−0.393187	+	2.22988i	−0.0158807	+	0.0900638i	0.975837	+	0.218498i	$0.0701159\pi$
$614$		0			0
$615$	1.70269	+	2.94915i	0.0686591	+	0.118921i
$616$		0			0
$617$	25.1343	−	9.14812i	1.01187	−	0.368290i	0.217718	−	0.976012i	$-0.430139\pi$
$617$	25.1343	−	9.14812i	1.01187	−	0.368290i	0.794150	+	0.607722i	$0.207917\pi$
$618$		0			0
$619$	14.4668	+	25.0572i	0.581470	+	1.00714i	0.995305	+	0.0967835i	$0.0308554\pi$
$619$	14.4668	+	25.0572i	0.581470	+	1.00714i	−0.413836	+	0.910352i	$0.635811\pi$
$620$		0			0
$621$	−1.67049	+	2.89337i	−0.0670345	+	0.116107i
$622$		0			0
$623$	17.4076			0.697420
$624$		0			0
$625$	12.0133	−	10.0803i	0.480531	−	0.403213i
$626$		0			0
$627$	−5.16707	+	1.88066i	−0.206353	+	0.0751063i
$628$		0			0
$629$	−6.96532	+	24.5840i	−0.277725	+	0.980230i
$630$		0			0
$631$	21.5573	−	7.84620i	0.858181	−	0.312352i	0.124810	−	0.992181i	$-0.460168\pi$
$631$	21.5573	−	7.84620i	0.858181	−	0.312352i	0.733371	+	0.679828i	$0.237946\pi$
$632$		0			0
$633$	14.0698	−	11.8060i	0.559226	−	0.469246i
$634$		0			0
$635$	−14.6711			−0.582205
$636$		0			0
$637$	−9.65418	+	16.7215i	−0.382512	+	0.662531i
$638$		0			0
$639$	5.86451	+	10.1576i	0.231996	+	0.401829i
$640$		0			0
$641$	37.6528	−	13.7045i	1.48720	−	0.541295i	0.534487	−	0.845177i	$-0.320505\pi$
$641$	37.6528	−	13.7045i	1.48720	−	0.541295i	0.952710	+	0.303882i	$0.0982828\pi$
$642$		0			0
$643$	14.2864	+	24.7447i	0.563400	+	0.975838i	0.997197	+	0.0748267i	$0.0238404\pi$
$643$	14.2864	+	24.7447i	0.563400	+	0.975838i	−0.433796	+	0.901011i	$0.642826\pi$
$644$		0			0
$645$	0.577283	−	3.27394i	0.0227305	−	0.128911i
$646$		0			0
$647$	−30.1142	−	10.9607i	−1.18391	−	0.430908i	−0.326328	−	0.945256i	$-0.605812\pi$
$647$	−30.1142	−	10.9607i	−1.18391	−	0.430908i	−0.857581	+	0.514349i	$0.828034\pi$
$648$		0			0
$649$	9.18610	+	7.70805i	0.360586	+	0.302567i
$650$		0			0
$651$	6.21340	−	35.2380i	0.243522	−	1.38108i
$652$		0			0
$653$	−22.1298	+	18.5691i	−0.866006	+	0.726665i	−0.963253	−	0.268595i	$-0.913441\pi$
$653$	−22.1298	+	18.5691i	−0.866006	+	0.726665i	0.0972474	+	0.995260i	$0.468996\pi$
$654$		0			0
$655$	−5.72227	+	9.91126i	−0.223588	+	0.387265i
$656$		0			0
$657$	−7.42091	−	6.22688i	−0.289517	−	0.242934i
$658$		0			0
$659$	3.11700	+	17.6774i	0.121421	+	0.688614i	0.983369	+	0.181617i	$0.0581332\pi$
$659$	3.11700	+	17.6774i	0.121421	+	0.688614i	−0.861948	+	0.506997i	$0.830756\pi$
$660$		0			0
$661$	−3.64195	−	20.6545i	−0.141656	−	0.803369i	−0.969992	−	0.243137i	$-0.921823\pi$
$661$	−3.64195	−	20.6545i	−0.141656	−	0.803369i	0.828336	−	0.560231i	$-0.189288\pi$
$662$		0			0
$663$	18.3119	+	6.66497i	0.711174	+	0.258846i
$664$		0			0
$665$	−3.19605			−0.123938
$666$		0			0
$667$	2.73994			0.106091
$668$		0			0
$669$	0.342011	+	0.124482i	0.0132229	+	0.00481275i
$670$		0			0
$671$	−5.02849	−	28.5180i	−0.194123	−	1.10092i
$672$		0			0
$673$	−2.30399	−	13.0666i	−0.0888122	−	0.503679i	−0.996469	−	0.0839652i	$-0.973242\pi$
$673$	−2.30399	−	13.0666i	−0.0888122	−	0.503679i	0.907656	−	0.419714i	$-0.137870\pi$
$674$		0			0
$675$	−3.33284	−	2.79658i	−0.128281	−	0.107640i
$676$		0			0
$677$	18.3880	−	31.8489i	0.706707	−	1.22405i	−0.259365	−	0.965779i	$-0.583513\pi$
$677$	18.3880	−	31.8489i	0.706707	−	1.22405i	0.966072	−	0.258273i	$-0.0831533\pi$
$678$		0			0
$679$	22.9778	−	19.2807i	0.881807	−	0.739924i
$680$		0			0
$681$	0.214687	−	1.21755i	0.00822682	−	0.0466566i
$682$		0			0
$683$	4.04138	+	3.39112i	0.154639	+	0.129758i	0.716825	−	0.697254i	$-0.245595\pi$
$683$	4.04138	+	3.39112i	0.154639	+	0.129758i	−0.562185	+	0.827011i	$0.690039\pi$
$684$		0			0
$685$	9.05854	+	3.29704i	0.346109	+	0.125973i
$686$		0			0
$687$	3.02405	−	17.1503i	0.115375	−	0.654323i
$688$		0			0
$689$	−10.7820	−	18.6749i	−0.410760	−	0.711457i
$690$		0			0
$691$	5.42798	−	1.97562i	0.206490	−	0.0751562i	−0.236704	−	0.971582i	$-0.576067\pi$
$691$	5.42798	−	1.97562i	0.206490	−	0.0751562i	0.443195	+	0.896425i	$0.353845\pi$
$692$		0			0
$693$	7.73717	+	13.4012i	0.293911	+	0.509069i
$694$		0			0
$695$	−0.944510	+	1.63594i	−0.0358273	+	0.0620547i
$696$		0			0
$697$	17.7527			0.672432
$698$		0			0
$699$	10.4688	−	8.78435i	0.395966	−	0.332255i
$700$		0			0
$701$	−39.2342	+	14.2801i	−1.48186	+	0.539351i	−0.951291	−	0.308293i	$-0.900242\pi$
$701$	−39.2342	+	14.2801i	−1.48186	+	0.539351i	−0.530564	+	0.847645i	$0.678020\pi$
$702$		0			0
$703$	0.526512	+	7.20217i	0.0198578	+	0.271635i
$704$		0			0
$705$	−9.64843	+	3.51174i	−0.363381	+	0.132260i
$706$		0			0
$707$	−34.6182	+	29.0481i	−1.30195	+	1.09247i
$708$		0			0
$709$	15.0711			0.566006			0.283003	−	0.959119i	$-0.408669\pi$
$709$	15.0711			0.566006			0.283003	+	0.959119i	$0.408669\pi$
$710$		0			0
$711$	7.08020	−	12.2633i	0.265528	−	0.459908i
$712$		0			0
$713$	17.8908	+	30.9877i	0.670015	+	1.16050i
$714$		0			0
$715$	−16.2694	+	5.92158i	−0.608441	+	0.221454i
$716$		0			0
$717$	−7.72175	−	13.3745i	−0.288374	−	0.499478i
$718$		0			0
$719$	5.81520	−	32.9796i	0.216870	−	1.22993i	−0.660761	−	0.750596i	$-0.729766\pi$
$719$	5.81520	−	32.9796i	0.216870	−	1.22993i	0.877631	−	0.479336i	$-0.159123\pi$
$720$		0			0
$721$	−4.30210	−	1.56584i	−0.160218	−	0.0583147i
$722$		0			0
$723$	5.92000	+	4.96747i	0.220167	+	0.184742i
$724$		0			0
$725$	−0.619580	+	3.51381i	−0.0230106	+	0.130500i
$726$		0			0
$727$	−4.45096	+	3.73479i	−0.165077	+	0.138516i	−0.721584	−	0.692327i	$-0.756586\pi$
$727$	−4.45096	+	3.73479i	−0.165077	+	0.138516i	0.556507	+	0.830843i	$0.312141\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	−13.2761	−	11.1400i	−0.491036	−	0.412028i
$732$		0			0
$733$	−3.40820	−	19.3288i	−0.125885	−	0.713927i	−0.980779	−	0.195124i	$-0.937489\pi$
$733$	−3.40820	−	19.3288i	−0.125885	−	0.713927i	0.854894	−	0.518803i	$-0.173622\pi$
$734$		0			0
$735$	0.582382	+	3.30285i	0.0214815	+	0.121828i
$736$		0			0
$737$	63.8229	+	23.2296i	2.35095	+	0.855675i
$738$		0			0
$739$	31.9318			1.17463			0.587314	−	0.809359i	$-0.300185\pi$
$739$	31.9318			1.17463			0.587314	+	0.809359i	$0.300185\pi$
$740$		0			0
$741$	5.50741			0.202320
$742$		0			0
$743$	−23.7115	−	8.63026i	−0.869889	−	0.316614i	−0.131767	−	0.991281i	$-0.542065\pi$
$743$	−23.7115	−	8.63026i	−0.869889	−	0.316614i	−0.738122	+	0.674667i	$0.764287\pi$
$744$		0			0
$745$	0.982445	+	5.57172i	0.0359940	+	0.204132i
$746$		0			0
$747$	0.676446	+	3.83632i	0.0247499	+	0.140363i
$748$		0			0
$749$	44.1708	+	37.0637i	1.61397	+	1.35428i
$750$		0			0
$751$	−10.0314	+	17.3748i	−0.366050	+	0.634017i	−0.988944	−	0.148289i	$-0.952623\pi$
$751$	−10.0314	+	17.3748i	−0.366050	+	0.634017i	0.622894	+	0.782306i	$0.285957\pi$
$752$		0			0
$753$	−7.66124	+	6.42855i	−0.279191	+	0.234269i
$754$		0			0
$755$	−1.52582	+	8.65336i	−0.0555303	+	0.314928i
$756$		0			0
$757$	23.1941	+	19.4622i	0.843005	+	0.707365i	0.958237	−	0.285974i	$-0.0923170\pi$
$757$	23.1941	+	19.4622i	0.843005	+	0.707365i	−0.115233	+	0.993338i	$0.536761\pi$
$758$		0			0
$759$	−14.5411	−	5.29254i	−0.527810	−	0.192107i
$760$		0			0
$761$	1.01119	−	5.73472i	0.0366555	−	0.207883i	−0.960979	−	0.276620i	$-0.910786\pi$
$761$	1.01119	−	5.73472i	0.0366555	−	0.207883i	0.997635	+	0.0687365i	$0.0218968\pi$
$762$		0			0
$763$	−17.4242	−	30.1796i	−0.630797	−	1.09257i
$764$		0			0
$765$	3.18072	−	1.15769i	0.114999	−	0.0418563i
$766$		0			0
$767$	−6.00532	−	10.4015i	−0.216839	−	0.375577i
$768$		0			0
$769$	−4.68374	+	8.11248i	−0.168900	+	0.292544i	−0.938033	−	0.346545i	$-0.887355\pi$
$769$	−4.68374	+	8.11248i	−0.168900	+	0.292544i	0.769133	+	0.639088i	$0.220688\pi$
$770$		0			0
$771$	19.8542			0.715031
$772$		0			0
$773$	−13.0568	+	10.9560i	−0.469622	+	0.394059i	−0.846657	−	0.532140i	$-0.821388\pi$
$773$	−13.0568	+	10.9560i	−0.469622	+	0.394059i	0.377035	+	0.926199i	$0.376944\pi$
$774$		0			0
$775$	−43.7856	+	15.9366i	−1.57282	+	0.572461i
$776$		0			0
$777$	19.7031	−	4.97875i	0.706844	−	0.178612i
$778$		0			0
$779$	4.71467	−	1.71600i	0.168921	−	0.0614821i
$780$		0			0
$781$	−41.6154	+	34.9195i	−1.48912	+	1.24952i
$782$		0			0
$783$	0.820100			0.0293080
$784$		0			0
$785$	−6.64691	+	11.5128i	−0.237238	+	0.410909i
$786$		0			0
$787$	−6.85359	−	11.8708i	−0.244304	−	0.423147i	0.717632	−	0.696423i	$-0.245226\pi$
$787$	−6.85359	−	11.8708i	−0.244304	−	0.423147i	−0.961936	+	0.273276i	$0.911893\pi$
$788$		0			0
$789$	−12.9198	+	4.70241i	−0.459956	+	0.167410i
$790$		0			0
$791$	20.6609	+	35.7857i	0.734617	+	1.27239i
$792$		0			0
$793$	−5.03647	+	28.5633i	−0.178850	+	1.01431i
$794$		0			0
$795$	−3.51970	−	1.28107i	−0.124831	−	0.0454348i
$796$		0			0
$797$	−8.83860	−	7.41647i	−0.313079	−	0.262705i	0.472684	−	0.881232i	$-0.343285\pi$
$797$	−8.83860	−	7.41647i	−0.313079	−	0.262705i	−0.785763	+	0.618527i	$0.787730\pi$
$798$		0			0
$799$	−9.29481	+	52.7135i	−0.328827	+	1.86487i
$800$		0			0
$801$	−3.99133	+	3.34913i	−0.141027	+	0.118336i
$802$		0			0
$803$	22.4342	−	38.8573i	0.791687	−	1.37124i
$804$		0			0
$805$	−6.89004	−	5.78143i	−0.242842	−	0.203769i
$806$		0			0
$807$	2.63902	+	14.9667i	0.0928981	+	0.526851i
$808$		0			0
$809$	2.95222	+	16.7429i	0.103795	+	0.588649i	0.991695	+	0.128613i	$0.0410524\pi$
$809$	2.95222	+	16.7429i	0.103795	+	0.588649i	−0.887900	+	0.460036i	$0.847836\pi$
$810$		0			0
$811$	6.94433	+	2.52753i	0.243848	+	0.0887535i	0.461053	−	0.887373i	$-0.347472\pi$
$811$	6.94433	+	2.52753i	0.243848	+	0.0887535i	−0.217205	+	0.976126i	$0.569694\pi$
$812$		0			0
$813$	5.38926			0.189010
$814$		0			0
$815$	10.1642			0.356037
$816$		0			0
$817$	−4.60261	−	1.67521i	−0.161025	−	0.0586083i
$818$		0			0
$819$	−2.69136	−	15.2635i	−0.0940437	−	0.533348i
$820$		0			0
$821$	4.73561	+	26.8570i	0.165274	+	0.937316i	0.948781	+	0.315933i	$0.102318\pi$
$821$	4.73561	+	26.8570i	0.165274	+	0.937316i	−0.783507	+	0.621383i	$0.786571\pi$
$822$		0			0
$823$	18.7522	+	15.7349i	0.653659	+	0.548485i	0.908179	−	0.418583i	$-0.137473\pi$
$823$	18.7522	+	15.7349i	0.653659	+	0.548485i	−0.254520	+	0.967068i	$0.581917\pi$
$824$		0			0
$825$	10.0755	−	17.4513i	0.350785	−	0.607578i
$826$		0			0
$827$	−32.5931	+	27.3489i	−1.13337	+	0.951014i	−0.999202	−	0.0399441i	$-0.987282\pi$
$827$	−32.5931	+	27.3489i	−1.13337	+	0.951014i	−0.134172	+	0.990958i	$0.542838\pi$
$828$		0			0
$829$	1.63593	−	9.27784i	0.0568183	−	0.322233i	−0.943130	−	0.332425i	$-0.892133\pi$
$829$	1.63593	−	9.27784i	0.0568183	−	0.322233i	0.999948	+	0.0101922i	$0.00324432\pi$
$830$		0			0
$831$	14.5408	+	12.2012i	0.504414	+	0.423254i
$832$		0			0
$833$	16.4295	+	5.97983i	0.569247	+	0.207189i
$834$		0			0
$835$	−2.29531	+	13.0174i	−0.0794326	+	0.450485i
$836$		0			0
$837$	5.35495	+	9.27504i	0.185094	+	0.320592i
$838$		0			0
$839$	28.7472	−	10.4631i	0.992464	−	0.361227i	0.205790	−	0.978596i	$-0.434023\pi$
$839$	28.7472	−	10.4631i	0.992464	−	0.361227i	0.786674	+	0.617369i	$0.211801\pi$
$840$		0			0
$841$	14.1637	+	24.5323i	0.488404	+	0.845941i
$842$		0			0
$843$	−7.04158	+	12.1964i	−0.242525	+	0.420065i
$844$		0			0
$845$	6.86579			0.236190
$846$		0			0
$847$	−26.7514	+	22.4471i	−0.919187	+	0.771290i
$848$		0			0
$849$	7.32353	−	2.66555i	0.251343	−	0.0914813i
$850$		0			0
$851$	−11.8932	+	16.4788i	−0.407692	+	0.564888i
$852$		0			0
$853$	29.9884	−	10.9149i	1.02678	−	0.373719i	0.226928	−	0.973911i	$-0.427132\pi$
$853$	29.9884	−	10.9149i	1.02678	−	0.373719i	0.799856	+	0.600193i	$0.204909\pi$
$854$		0			0
$855$	0.732814	−	0.614904i	0.0250617	−	0.0210293i
$856$		0			0
$857$	−0.224683			−0.00767503			−0.00383752	−	0.999993i	$-0.501222\pi$
$857$	−0.224683			−0.00767503			−0.00383752	+	0.999993i	$0.501222\pi$
$858$		0			0
$859$	−9.18306	+	15.9055i	−0.313322	+	0.542690i	−0.979079	−	0.203479i	$-0.934775\pi$
$859$	−9.18306	+	15.9055i	−0.313322	+	0.542690i	0.665757	+	0.746168i	$0.268109\pi$
$860$		0			0
$861$	−7.05975	−	12.2279i	−0.240596	−	0.416724i
$862$		0			0
$863$	−26.0949	+	9.49777i	−0.888281	+	0.323308i	−0.745547	−	0.666453i	$-0.767812\pi$
$863$	−26.0949	+	9.49777i	−0.888281	+	0.323308i	−0.142734	+	0.989761i	$0.545589\pi$
$864$		0			0
$865$	4.62524	+	8.01115i	0.157263	+	0.272387i
$866$		0			0
$867$	0.112124	−	0.635887i	0.00380793	−	0.0215959i
$868$		0			0
$869$	61.6310	+	22.4319i	2.09069	+	0.760949i
$870$		0			0
$871$	−52.1115	−	43.7267i	−1.76573	−	1.48162i
$872$		0			0
$873$	−1.55902	+	8.84162i	−0.0527647	+	0.299244i
$874$		0			0
$875$	19.2838	−	16.1810i	0.651911	−	0.547018i
$876$		0			0
$877$	7.25012	−	12.5576i	0.244819	−	0.424039i	−0.717262	−	0.696804i	$-0.754605\pi$
$877$	7.25012	−	12.5576i	0.244819	−	0.424039i	0.962081	+	0.272765i	$0.0879381\pi$
$878$		0			0
$879$	6.72324	+	5.64147i	0.226769	+	0.190282i
$880$		0			0
$881$	−1.83291	−	10.3949i	−0.0617523	−	0.350215i	−0.999991	−	0.00422624i	$-0.998655\pi$
$881$	−1.83291	−	10.3949i	−0.0617523	−	0.350215i	0.938239	−	0.345988i	$-0.112456\pi$
$882$		0			0
$883$	3.19036	+	18.0935i	0.107364	+	0.608893i	0.990250	+	0.139304i	$0.0444867\pi$
$883$	3.19036	+	18.0935i	0.107364	+	0.608893i	−0.882885	+	0.469589i	$0.844402\pi$
$884$		0			0
$885$	−1.96040	−	0.713527i	−0.0658981	−	0.0239849i
$886$		0			0
$887$	7.70995			0.258875			0.129437	−	0.991588i	$-0.458683\pi$
$887$	7.70995			0.258875			0.129437	+	0.991588i	$0.458683\pi$
$888$		0			0
$889$	60.8298			2.04017
$890$		0			0
$891$	−4.35235	−	1.58413i	−0.145809	−	0.0530703i
$892$		0			0
$893$	2.62689	+	14.8978i	0.0879054	+	0.498536i
$894$		0			0
$895$	1.11202	+	6.30657i	0.0371707	+	0.210805i
$896$		0			0
$897$	11.8729	+	9.96251i	0.396423	+	0.332639i
$898$		0			0
$899$	4.39159	−	7.60646i	0.146468	−	0.253690i
$900$		0			0
$901$	−14.9580	+	12.5513i	−0.498323	+	0.418143i
$902$		0			0
$903$	−2.39355	+	13.5745i	−0.0796524	+	0.451731i
$904$		0			0
$905$	3.48445	+	2.92380i	0.115827	+	0.0971904i
$906$		0			0
$907$	43.3356	+	15.7729i	1.43894	+	0.523730i	0.939478	−	0.342608i	$-0.111310\pi$
$907$	43.3356	+	15.7729i	1.43894	+	0.523730i	0.499458	+	0.866338i	$0.333532\pi$
$908$		0			0
$909$	2.34881	−	13.3207i	0.0779050	−	0.441821i
$910$		0			0
$911$	−18.5530	−	32.1348i	−0.614689	−	1.06467i	−0.990439	−	0.137952i	$-0.955948\pi$
$911$	−18.5530	−	32.1348i	−0.614689	−	1.06467i	0.375750	−	0.926721i	$-0.377385\pi$
$912$		0			0
$913$	−16.9546	+	6.17096i	−0.561115	+	0.204229i
$914$		0			0
$915$	2.51895	+	4.36294i	0.0832738	+	0.144234i
$916$		0			0
$917$	23.7259	−	41.0944i	0.783498	−	1.35706i
$918$		0			0
$919$	27.6014			0.910486			0.455243	−	0.890367i	$-0.349552\pi$
$919$	27.6014			0.910486			0.455243	+	0.890367i	$0.349552\pi$
$920$		0			0
$921$	−9.92419	+	8.32738i	−0.327013	+	0.274397i
$922$		0			0
$923$	51.1299	−	18.6097i	1.68296	−	0.612547i
$924$		0			0
$925$	−18.4438	−	18.9786i	−0.606427	−	0.624013i
$926$		0			0
$927$	1.28767	−	0.468675i	0.0422928	−	0.0153933i
$928$		0			0
$929$	−28.9432	+	24.2863i	−0.949596	+	0.796806i	−0.979230	−	0.202755i	$-0.935011\pi$
$929$	−28.9432	+	24.2863i	−0.949596	+	0.796806i	0.0296331	+	0.999561i	$0.490566\pi$
$930$		0			0
$931$	4.94126			0.161943
$932$		0			0
$933$	11.1315	−	19.2802i	0.364427	−	0.631207i
$934$		0			0
$935$	7.83877	+	13.5771i	0.256355	+	0.444020i
$936$		0			0
$937$	9.26681	−	3.37284i	0.302733	−	0.110186i	−0.186187	−	0.982514i	$-0.559613\pi$
$937$	9.26681	−	3.37284i	0.302733	−	0.110186i	0.488920	+	0.872328i	$0.337391\pi$
$938$		0			0
$939$	16.1778	+	28.0208i	0.527943	+	0.914424i
$940$		0			0
$941$	−5.14704	+	29.1903i	−0.167789	+	0.951576i	0.778354	+	0.627826i	$0.216055\pi$
$941$	−5.14704	+	29.1903i	−0.167789	+	0.951576i	−0.946142	+	0.323751i	$0.895056\pi$
$942$		0			0
$943$	13.2680	+	4.82916i	0.432065	+	0.157259i
$944$		0			0
$945$	−2.06228	−	1.73046i	−0.0670860	−	0.0562919i
$946$		0			0
$947$	0.751456	−	4.26172i	0.0244190	−	0.138487i	−0.970161	−	0.242462i	$-0.922045\pi$
$947$	0.751456	−	4.26172i	0.0244190	−	0.138487i	0.994580	+	0.103975i	$0.0331561\pi$
$948$		0			0
$949$	−34.4258	+	28.8867i	−1.11751	+	0.937702i
$950$		0			0
$951$	9.36467	−	16.2201i	0.303670	−	0.525972i
$952$		0			0
$953$	−4.14895	−	3.48138i	−0.134398	−	0.112773i	0.573111	−	0.819478i	$-0.305736\pi$
$953$	−4.14895	−	3.48138i	−0.134398	−	0.112773i	−0.707509	+	0.706705i	$0.750181\pi$
$954$		0			0
$955$	−1.28943	−	7.31271i	−0.0417249	−	0.236634i
$956$		0			0
$957$	0.659592	+	3.74073i	0.0213216	+	0.120921i
$958$		0			0
$959$	−37.5588	−	13.6703i	−1.21284	−	0.441437i
$960$		0			0
$961$	83.7018			2.70006
$962$		0			0
$963$	−17.2587			−0.556153
$964$		0			0
$965$	11.3542	+	4.13260i	0.365505	+	0.133033i
$966$		0			0
$967$	−6.74131	−	38.2319i	−0.216786	−	1.22945i	−0.877780	−	0.479064i	$-0.840976\pi$
$967$	−6.74131	−	38.2319i	−0.216786	−	1.22945i	0.660994	−	0.750391i	$-0.270135\pi$
$968$		0			0
$969$	−0.865983	−	4.91124i	−0.0278194	−	0.157772i
$970$		0			0
$971$	−32.3209	−	27.1205i	−1.03723	−	0.870337i	−0.0455339	−	0.998963i	$-0.514499\pi$
$971$	−32.3209	−	27.1205i	−1.03723	−	0.870337i	−0.991693	+	0.128626i	$0.958943\pi$
$972$		0			0
$973$	3.91616	−	6.78299i	0.125546	−	0.217453i
$974$		0			0
$975$	−15.4611	+	12.9734i	−0.495152	+	0.415482i
$976$		0			0
$977$	−0.930966	+	5.27977i	−0.0297842	+	0.168915i	−0.996072	−	0.0885510i	$-0.971776\pi$
$977$	−0.930966	+	5.27977i	−0.0297842	+	0.168915i	0.966287	+	0.257466i	$0.0828875\pi$
$978$		0			0
$979$	−18.4866	−	15.5121i	−0.590834	−	0.495768i
$980$		0			0
$981$	9.80153	+	3.56747i	0.312939	+	0.113900i
$982$		0			0
$983$	8.05130	−	45.6612i	0.256796	−	1.45637i	−0.534623	−	0.845091i	$-0.679546\pi$
$983$	8.05130	−	45.6612i	0.256796	−	1.45637i	0.791419	−	0.611274i	$-0.209343\pi$
$984$		0			0
$985$	6.44009	+	11.1546i	0.205198	+	0.355414i
$986$		0			0
$987$	40.0047	−	14.5605i	1.27336	−	0.463466i
$988$		0			0
$989$	−6.89196	−	11.9372i	−0.219152	−	0.379582i
$990$		0			0
$991$	0.441431	−	0.764580i	0.0140225	−	0.0242877i	−0.858929	−	0.512095i	$-0.828870\pi$
$991$	0.441431	−	0.764580i	0.0140225	−	0.0242877i	0.872952	+	0.487807i	$0.162203\pi$
$992$		0			0
$993$	−25.3464			−0.804344
$994$		0			0
$995$	−3.06514	+	2.57196i	−0.0971716	+	0.0815366i
$996$		0			0
$997$	21.2712	−	7.74210i	0.673667	−	0.245195i	0.0175409	−	0.999846i	$-0.494416\pi$
$997$	21.2712	−	7.74210i	0.673667	−	0.245195i	0.656126	+	0.754652i	$0.272194\pi$
$998$		0			0
$999$	−3.55978	+	4.93234i	−0.112627	+	0.156052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.bo.c.673.3	✓	24
37.16	even	9	inner	888.2.bo.c.793.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.bo.c.673.3	✓	24	1.1	even	1	trivial
888.2.bo.c.793.3	yes	24	37.16	even	9	inner

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:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{3} +(0.139923 + 0.793545i) q^{5} +(-0.580155 - 3.29022i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{3} +(0.139923 + 0.793545i) q^{5} +(-0.580155 - 3.29022i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-2.31584 + 4.01115i) q^{11} +(3.55370 - 2.98191i) q^{13} +(0.139923 - 0.793545i) q^{15} +(-3.21791 - 2.70014i) q^{17} +(-1.11559 - 0.406043i) q^{19} +(-0.580155 + 3.29022i) q^{21} +(-1.67049 - 2.89337i) q^{23} +(4.08833 - 1.48803i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-0.410050 + 0.710228i) q^{29} -10.7099 q^{31} +(3.54807 - 2.97719i) q^{33} +(2.52976 - 0.920758i) q^{35} +(-2.49164 - 5.54903i) q^{37} +(-4.35926 + 1.58664i) q^{39} +(-3.23742 + 2.71652i) q^{41} +4.12571 q^{43} +(-0.402893 + 0.697832i) q^{45} +(-6.37119 - 11.0352i) q^{47} +(-3.91114 + 1.42354i) q^{49} +(2.10034 + 3.63789i) q^{51} +(0.807180 - 4.57775i) q^{53} +(-3.50707 - 1.27647i) q^{55} +(0.909440 + 0.763111i) q^{57} +(0.449582 - 2.54971i) q^{59} +(-4.78942 + 4.01880i) q^{61} +(1.67049 - 2.89337i) q^{63} +(2.86353 + 2.40278i) q^{65} +(-2.54638 - 14.4412i) q^{67} +(0.580155 + 3.29022i) q^{69} +(11.0217 + 4.01156i) q^{71} -9.68731 q^{73} -4.35071 q^{75} +(14.5411 + 5.29254i) q^{77} +(-2.45893 - 13.9453i) q^{79} +(0.173648 + 0.984808i) q^{81} +(2.98412 + 2.50398i) q^{83} +(1.69242 - 2.93137i) q^{85} +(0.628233 - 0.527150i) q^{87} +(-0.904762 + 5.13116i) q^{89} +(-11.8729 - 9.96251i) q^{91} +(10.0640 + 3.66300i) q^{93} +(0.166115 - 0.942088i) q^{95} +(4.48901 + 7.77519i) q^{97} +(-4.35235 + 1.58413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) \) 24 * q + 3 * q^5 + 15 * q^7	\( 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) \) 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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