LMFDB - Embedded newform 896.2.p.c.255.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(255,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("896.255");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.p (of order $6$, degree $2$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			255.6
Root			$-0.347596 + 1.29724i$ of defining polynomial
Character	$\chi$	$=$	896.255
Dual form			896.2.p.c.383.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.779618 - 1.35034i) q^{3} +(3.14484 - 1.81567i) q^{5} +(0.0694427 + 2.64484i) q^{7} +(0.284392 + 0.492581i) q^{9} +O(q^{10})$	\(q+(0.779618 - 1.35034i) q^{3} +(3.14484 - 1.81567i) q^{5} +(0.0694427 + 2.64484i) q^{7} +(0.284392 + 0.492581i) q^{9} +(0.170031 + 0.0981673i) q^{11} -6.20968i q^{13} -5.66213i q^{15} +(0.588057 + 0.339515i) q^{17} +(2.74836 + 4.76030i) q^{19} +(3.62557 + 1.96819i) q^{21} +(2.05460 - 1.18622i) q^{23} +(4.09335 - 7.08988i) q^{25} +5.56458 q^{27} -7.22524 q^{29} +(-2.86536 + 4.96296i) q^{31} +(0.265118 - 0.153066i) q^{33} +(5.02055 + 8.19151i) q^{35} +(1.53222 + 2.65388i) q^{37} +(-8.38516 - 4.84117i) q^{39} +1.33079i q^{41} -0.392669i q^{43} +(1.78873 + 1.03273i) q^{45} +(-6.66953 - 11.5520i) q^{47} +(-6.99036 + 0.367330i) q^{49} +(0.916920 - 0.529384i) q^{51} +(4.56112 - 7.90010i) q^{53} +0.712959 q^{55} +8.57068 q^{57} +(-4.72267 + 8.17990i) q^{59} +(-0.757458 + 0.437319i) q^{61} +(-1.28305 + 0.786377i) q^{63} +(-11.2747 - 19.5284i) q^{65} +(-9.42874 - 5.44368i) q^{67} -3.69921i q^{69} -8.18669i q^{71} +(11.6665 + 6.73564i) q^{73} +(-6.38249 - 11.0548i) q^{75} +(-0.247829 + 0.456521i) q^{77} +(-8.09255 + 4.67224i) q^{79} +(3.48507 - 6.03631i) q^{81} +0.334493 q^{83} +2.46579 q^{85} +(-5.63292 + 9.75651i) q^{87} +(0.613565 - 0.354242i) q^{89} +(16.4236 - 0.431217i) q^{91} +(4.46778 + 7.73842i) q^{93} +(17.2863 + 9.98025i) q^{95} +12.5145i q^{97} +0.111672i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} - 16 q^{9}+O(q^{10}) $ 16 * q + 12 * q^5 - 16 * q^9	$ 16 q + 12 q^{5} - 16 q^{9} - 12 q^{21} - 48 q^{29} - 48 q^{33} + 20 q^{37} - 24 q^{45} + 8 q^{49} + 12 q^{53} + 48 q^{57} + 60 q^{61} - 40 q^{65} + 48 q^{73} - 20 q^{77} - 8 q^{81} - 56 q^{85} - 48 q^{89} + 76 q^{93}+O(q^{100}) $ 16 * q + 12 * q^5 - 16 * q^9 - 12 * q^21 - 48 * q^29 - 48 * q^33 + 20 * q^37 - 24 * q^45 + 8 * q^49 + 12 * q^53 + 48 * q^57 + 60 * q^61 - 40 * q^65 + 48 * q^73 - 20 * q^77 - 8 * q^81 - 56 * q^85 - 48 * q^89 + 76 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	0.779618	−	1.35034i	0.450113	−	0.779618i	−0.548280	−	0.836295i	$-0.684717\pi$
$3$	0.779618	−	1.35034i	0.450113	−	0.779618i	0.998393	+	0.0566769i	$0.0180505\pi$
$4$		0			0
$5$	3.14484	−	1.81567i	1.40642	−	0.811994i	0.411375	−	0.911466i	$-0.365049\pi$
$5$	3.14484	−	1.81567i	1.40642	−	0.811994i	0.995040	+	0.0994721i	$0.0317154\pi$
$6$		0			0
$7$	0.0694427	+	2.64484i	0.0262469	+	0.999655i
$7$	0.0694427	+	2.64484i	0.0262469	+	0.999655i
$8$		0			0
$9$	0.284392	+	0.492581i	0.0947972	+	0.164194i
$10$		0			0
$11$	0.170031	+	0.0981673i	0.0512662	+	0.0295986i	0.525414	−	0.850847i	$-0.323910\pi$
$11$	0.170031	+	0.0981673i	0.0512662	+	0.0295986i	−0.474148	+	0.880445i	$0.657244\pi$
$12$		0			0
$13$		−	6.20968i		−	1.72225i	−0.508390	−	0.861127i	$-0.669759\pi$
$13$		−	6.20968i		−	1.72225i	0.508390	−	0.861127i	$-0.330241\pi$
$14$		0			0
$15$		−	5.66213i		−	1.46196i
$16$		0			0
$17$	0.588057	+	0.339515i	0.142625	+	0.0823445i	0.569614	−	0.821912i	$-0.307093\pi$
$17$	0.588057	+	0.339515i	0.142625	+	0.0823445i	−0.426990	+	0.904257i	$0.640426\pi$
$18$		0			0
$19$	2.74836	+	4.76030i	0.630517	+	1.09209i	0.987446	+	0.157955i	$0.0504903\pi$
$19$	2.74836	+	4.76030i	0.630517	+	1.09209i	−0.356930	+	0.934131i	$0.616176\pi$
$20$		0			0
$21$	3.62557	+	1.96819i	0.791163	+	0.429495i
$22$		0			0
$23$	2.05460	−	1.18622i	0.428414	−	0.247345i	−0.270257	−	0.962788i	$-0.587109\pi$
$23$	2.05460	−	1.18622i	0.428414	−	0.247345i	0.698671	+	0.715443i	$0.253775\pi$
$24$		0			0
$25$	4.09335	−	7.08988i	0.818669	−	1.41798i
$26$		0			0
$27$	5.56458			1.07090
$28$		0			0
$29$	−7.22524			−1.34169			−0.670846	−	0.741596i	$-0.734069\pi$
$29$	−7.22524			−1.34169			−0.670846	+	0.741596i	$0.734069\pi$
$30$		0			0
$31$	−2.86536	+	4.96296i	−0.514635	+	0.891373i	0.485221	+	0.874391i	$0.338739\pi$
$31$	−2.86536	+	4.96296i	−0.514635	+	0.891373i	−0.999856	+	0.0169819i	$0.994594\pi$
$32$		0			0
$33$	0.265118	−	0.153066i	0.0461511	−	0.0266454i
$34$		0			0
$35$	5.02055	+	8.19151i	0.848628	+	1.38462i
$36$		0			0
$37$	1.53222	+	2.65388i	0.251896	+	0.436296i	0.964048	−	0.265729i	$-0.0856127\pi$
$37$	1.53222	+	2.65388i	0.251896	+	0.436296i	−0.712152	+	0.702025i	$0.752279\pi$
$38$		0			0
$39$	−8.38516	−	4.84117i	−1.34270	−	0.775208i
$40$		0			0
$41$			1.33079i			0.207835i	0.994586	+	0.103917i	$0.0331378\pi$
$41$			1.33079i			0.207835i	−0.994586	+	0.103917i	$0.966862\pi$
$42$		0			0
$43$		−	0.392669i		−	0.0598815i	−0.999552	−	0.0299408i	$-0.990468\pi$
$43$		−	0.392669i		−	0.0598815i	0.999552	−	0.0299408i	$-0.00953186\pi$
$44$		0			0
$45$	1.78873	+	1.03273i	0.266649	+	0.153950i
$46$		0			0
$47$	−6.66953	−	11.5520i	−0.972851	−	1.68503i	−0.686853	−	0.726796i	$-0.741008\pi$
$47$	−6.66953	−	11.5520i	−0.972851	−	1.68503i	−0.285997	−	0.958230i	$-0.592325\pi$
$48$		0			0
$49$	−6.99036	+	0.367330i	−0.998622	+	0.0524757i
$50$		0			0
$51$	0.916920	−	0.529384i	0.128394	−	0.0741286i
$52$		0			0
$53$	4.56112	−	7.90010i	0.626519	−	1.08516i	−0.361727	−	0.932284i	$-0.617813\pi$
$53$	4.56112	−	7.90010i	0.626519	−	1.08516i	0.988245	−	0.152878i	$-0.0488541\pi$
$54$		0			0
$55$	0.712959			0.0961354
$56$		0			0
$57$	8.57068			1.13521
$58$		0			0
$59$	−4.72267	+	8.17990i	−0.614839	+	1.06493i	0.375574	+	0.926792i	$0.377446\pi$
$59$	−4.72267	+	8.17990i	−0.614839	+	1.06493i	−0.990413	+	0.138140i	$0.955888\pi$
$60$		0			0
$61$	−0.757458	+	0.437319i	−0.0969826	+	0.0559929i	−0.547707	−	0.836670i	$-0.684499\pi$
$61$	−0.757458	+	0.437319i	−0.0969826	+	0.0559929i	0.450724	+	0.892663i	$0.351166\pi$
$62$		0			0
$63$	−1.28305	+	0.786377i	−0.161649	+	0.0990742i
$64$		0			0
$65$	−11.2747	−	19.5284i	−1.39846	−	2.42220i
$66$		0			0
$67$	−9.42874	−	5.44368i	−1.15190	−	0.665052i	−0.202553	−	0.979271i	$-0.564924\pi$
$67$	−9.42874	−	5.44368i	−1.15190	−	0.665052i	−0.949350	+	0.314220i	$0.898257\pi$
$68$		0			0
$69$		−	3.69921i		−	0.445332i
$70$		0			0
$71$		−	8.18669i		−	0.971581i	−0.874075	−	0.485791i	$-0.838532\pi$
$71$		−	8.18669i		−	0.971581i	0.874075	−	0.485791i	$-0.161468\pi$
$72$		0			0
$73$	11.6665	+	6.73564i	1.36546	+	0.788347i	0.990344	−	0.138632i	$-0.0442706\pi$
$73$	11.6665	+	6.73564i	1.36546	+	0.788347i	0.375113	+	0.926979i	$0.377604\pi$
$74$		0			0
$75$	−6.38249	−	11.0548i	−0.736987	−	1.27650i
$76$		0			0
$77$	−0.247829	+	0.456521i	−0.0282428	+	0.0520254i
$78$		0			0
$79$	−8.09255	+	4.67224i	−0.910484	+	0.525668i	−0.880587	−	0.473885i	$-0.842851\pi$
$79$	−8.09255	+	4.67224i	−0.910484	+	0.525668i	−0.0298968	+	0.999553i	$0.509518\pi$
$80$		0			0
$81$	3.48507	−	6.03631i	0.387230	−	0.670702i
$82$		0			0
$83$	0.334493			0.0367154			0.0183577	−	0.999831i	$-0.494156\pi$
$83$	0.334493			0.0367154			0.0183577	+	0.999831i	$0.494156\pi$
$84$		0			0
$85$	2.46579			0.267453
$86$		0			0
$87$	−5.63292	+	9.75651i	−0.603913	+	1.04601i
$88$		0			0
$89$	0.613565	−	0.354242i	0.0650378	−	0.0375496i	−0.467128	−	0.884189i	$-0.654711\pi$
$89$	0.613565	−	0.354242i	0.0650378	−	0.0375496i	0.532166	+	0.846640i	$0.321378\pi$
$90$		0			0
$91$	16.4236	−	0.431217i	1.72166	−	0.0452038i
$92$		0			0
$93$	4.46778	+	7.73842i	0.463287	+	0.802437i
$94$		0			0
$95$	17.2863	+	9.98025i	1.77354	+	1.02395i
$96$		0			0
$97$			12.5145i			1.27065i	0.772244	+	0.635326i	$0.219134\pi$
$97$			12.5145i			1.27065i	−0.772244	+	0.635326i	$0.780866\pi$
$98$		0			0
$99$			0.111672i			0.0112234i
$100$		0			0
$101$	7.90031	+	4.56125i	0.786111	+	0.453861i	0.838591	−	0.544761i	$-0.183380\pi$
$101$	7.90031	+	4.56125i	0.786111	+	0.453861i	−0.0524809	+	0.998622i	$0.516713\pi$
$102$		0			0
$103$	1.57675	+	2.73101i	0.155362	+	0.269094i	0.933191	−	0.359382i	$-0.117012\pi$
$103$	1.57675	+	2.73101i	0.155362	+	0.269094i	−0.777829	+	0.628476i	$0.783679\pi$
$104$		0			0
$105$	14.9754	−	0.393193i	1.46145	−	0.0383717i
$106$		0			0
$107$	−8.16848	+	4.71607i	−0.789677	+	0.455920i	−0.839849	−	0.542821i	$-0.817356\pi$
$107$	−8.16848	+	4.71607i	−0.789677	+	0.455920i	0.0501720	+	0.998741i	$0.484023\pi$
$108$		0			0
$109$	−0.772391	+	1.33782i	−0.0739816	+	0.128140i	−0.900643	−	0.434560i	$-0.856904\pi$
$109$	−0.772391	+	1.33782i	−0.0739816	+	0.128140i	0.826661	+	0.562700i	$0.190237\pi$
$110$		0			0
$111$	4.77819			0.453526
$112$		0			0
$113$	−0.216555			−0.0203718			−0.0101859	−	0.999948i	$-0.503242\pi$
$113$	−0.216555			−0.0203718			−0.0101859	+	0.999948i	$0.503242\pi$
$114$		0			0
$115$	4.30759	−	7.46097i	0.401685	−	0.695739i
$116$		0			0
$117$	3.05877	−	1.76598i	0.282783	−	0.163265i
$118$		0			0
$119$	−0.857126	+	1.57889i	−0.0785726	+	0.144737i
$120$		0			0
$121$	−5.48073	−	9.49290i	−0.498248	−	0.862991i
$122$		0			0
$123$	1.79702	+	1.03751i	0.162032	+	0.0935490i
$124$		0			0
$125$		−	11.5720i		−	1.03503i
$126$		0			0
$127$			8.31557i			0.737888i	0.929452	+	0.368944i	$0.120281\pi$
$127$			8.31557i			0.737888i	−0.929452	+	0.368944i	$0.879719\pi$
$128$		0			0
$129$	−0.530236	−	0.306132i	−0.0466847	−	0.0269534i
$130$		0			0
$131$	−8.01395	−	13.8806i	−0.700182	−	1.21275i	−0.968402	−	0.249394i	$-0.919769\pi$
$131$	−8.01395	−	13.8806i	−0.700182	−	1.21275i	0.268220	−	0.963358i	$-0.413565\pi$
$132$		0			0
$133$	−12.3994	+	7.59953i	−1.07516	+	0.658963i
$134$		0			0
$135$	17.4997	−	10.1035i	1.50613	−	0.869567i
$136$		0			0
$137$	−8.83919	+	15.3099i	−0.755183	+	1.30802i	0.190100	+	0.981765i	$0.439119\pi$
$137$	−8.83919	+	15.3099i	−0.755183	+	1.30802i	−0.945283	+	0.326251i	$0.894215\pi$
$138$		0			0
$139$	−2.16276			−0.183443			−0.0917216	−	0.995785i	$-0.529237\pi$
$139$	−2.16276			−0.183443			−0.0917216	+	0.995785i	$0.529237\pi$
$140$		0			0
$141$	−20.7987			−1.75157
$142$		0			0
$143$	0.609587	−	1.05584i	0.0509762	−	0.0882934i
$144$		0			0
$145$	−22.7222	+	13.1187i	−1.88698	+	1.08945i
$146$		0			0
$147$	−4.95379	+	9.72572i	−0.408582	+	0.802164i
$148$		0			0
$149$	3.64050	+	6.30553i	0.298241	+	0.516569i	0.975734	−	0.218961i	$-0.0702667\pi$
$149$	3.64050	+	6.30553i	0.298241	+	0.516569i	−0.677492	+	0.735530i	$0.736933\pi$
$150$		0			0
$151$	−1.45615	−	0.840709i	−0.118500	−	0.0684159i	0.439579	−	0.898204i	$-0.355128\pi$
$151$	−1.45615	−	0.840709i	−0.118500	−	0.0684159i	−0.558078	+	0.829788i	$0.688461\pi$
$152$		0			0
$153$			0.386221i			0.0312241i
$154$		0			0
$155$			20.8103i			1.67152i
$156$		0			0
$157$	−15.0625	−	8.69631i	−1.20211	−	0.694041i	−0.241090	−	0.970503i	$-0.577505\pi$
$157$	−15.0625	−	8.69631i	−1.20211	−	0.694041i	−0.961025	+	0.276461i	$0.910838\pi$
$158$		0			0
$159$	−7.11187	−	12.3181i	−0.564008	−	0.976890i
$160$		0			0
$161$	3.28005	+	5.35172i	0.258504	+	0.421774i
$162$		0			0
$163$	19.1858	−	11.0769i	1.50275	−	0.867610i	0.502750	−	0.864432i	$-0.332321\pi$
$163$	19.1858	−	11.0769i	1.50275	−	0.867610i	0.999995	−	0.00317884i	$-0.00101186\pi$
$164$		0			0
$165$	0.555836	−	0.962736i	0.0432718	−	0.0749489i
$166$		0			0
$167$	3.93748			0.304691			0.152346	−	0.988327i	$-0.451317\pi$
$167$	3.93748			0.304691			0.152346	+	0.988327i	$0.451317\pi$
$168$		0			0
$169$	−25.5601			−1.96616
$170$		0			0
$171$	−1.56322	+	2.70758i	−0.119542	+	0.207054i
$172$		0			0
$173$	−1.99234	+	1.15028i	−0.151475	+	0.0874540i	−0.573822	−	0.818980i	$-0.694540\pi$
$173$	−1.99234	+	1.15028i	−0.151475	+	0.0874540i	0.422347	+	0.906434i	$0.361206\pi$
$174$		0			0
$175$	19.0359	+	10.3339i	1.43898	+	0.781170i
$176$		0			0
$177$	7.36375	+	12.7544i	0.553493	+	0.958679i
$178$		0			0
$179$	7.09823	+	4.09817i	0.530547	+	0.306311i	0.741239	−	0.671241i	$-0.234238\pi$
$179$	7.09823	+	4.09817i	0.530547	+	0.306311i	−0.210692	+	0.977552i	$0.567572\pi$
$180$		0			0
$181$			11.1837i			0.831277i	0.909530	+	0.415638i	$0.136442\pi$
$181$			11.1837i			0.831277i	−0.909530	+	0.415638i	$0.863558\pi$
$182$		0			0
$183$			1.36377i			0.100813i
$184$		0			0
$185$	9.63718	+	5.56403i	0.708540	+	0.409076i
$186$		0			0
$187$	0.0666585	+	0.115456i	0.00487455	+	0.00844298i
$188$		0			0
$189$	0.386419	+	14.7174i	0.0281078	+	1.07053i
$190$		0			0
$191$	13.0454	−	7.53174i	0.943929	−	0.544978i	0.0527391	−	0.998608i	$-0.483205\pi$
$191$	13.0454	−	7.53174i	0.943929	−	0.544978i	0.891190	+	0.453631i	$0.149871\pi$
$192$		0			0
$193$	−2.60828	+	4.51767i	−0.187748	+	0.325189i	−0.944499	−	0.328514i	$-0.893452\pi$
$193$	−2.60828	+	4.51767i	−0.187748	+	0.325189i	0.756751	+	0.653703i	$0.226785\pi$
$194$		0			0
$195$	−35.1600			−2.51786
$196$		0			0
$197$	6.74412			0.480499			0.240249	−	0.970711i	$-0.422771\pi$
$197$	6.74412			0.480499			0.240249	+	0.970711i	$0.422771\pi$
$198$		0			0
$199$	−10.4453	+	18.0918i	−0.740450	+	1.28250i	0.211841	+	0.977304i	$0.432054\pi$
$199$	−10.4453	+	18.0918i	−0.740450	+	1.28250i	−0.952291	+	0.305192i	$0.901279\pi$
$200$		0			0
$201$	−14.7016	+	8.48799i	−1.03697	+	0.598696i
$202$		0			0
$203$	−0.501740	−	19.1096i	−0.0352152	−	1.34123i
$204$		0			0
$205$	2.41628	+	4.18513i	0.168761	+	0.292302i
$206$		0			0
$207$	1.16862	+	0.674705i	0.0812249	+	0.0468952i
$208$		0			0
$209$			1.07920i			0.0746495i
$210$		0			0
$211$		−	8.18669i		−	0.563595i	−0.959474	−	0.281797i	$-0.909069\pi$
$211$		−	8.18669i		−	0.563595i	0.959474	−	0.281797i	$-0.0909306\pi$
$212$		0			0
$213$	−11.0548	−	6.38249i	−0.757462	−	0.437321i
$214$		0			0
$215$	−0.712959	−	1.23488i	−0.0486234	−	0.0842182i
$216$		0			0
$217$	−13.3252	−	7.23379i	−0.904574	−	0.491062i
$218$		0			0
$219$	18.1908	−	10.5025i	1.22922	−	0.709690i
$220$		0			0
$221$	2.10828	−	3.65164i	0.141818	−	0.245636i
$222$		0			0
$223$	−23.0894			−1.54618			−0.773091	−	0.634295i	$-0.781291\pi$
$223$	−23.0894			−1.54618			−0.773091	+	0.634295i	$0.781291\pi$
$224$		0			0
$225$	4.65645			0.310430
$226$		0			0
$227$	−3.45575	+	5.98553i	−0.229366	+	0.397274i	−0.957620	−	0.288033i	$-0.906999\pi$
$227$	−3.45575	+	5.98553i	−0.229366	+	0.397274i	0.728254	+	0.685307i	$0.240332\pi$
$228$		0			0
$229$	14.4383	−	8.33596i	0.954110	−	0.550856i	0.0597546	−	0.998213i	$-0.480968\pi$
$229$	14.4383	−	8.33596i	0.954110	−	0.550856i	0.894355	+	0.447358i	$0.147635\pi$
$230$		0			0
$231$	0.423246	+	0.690566i	0.0278475	+	0.0454359i
$232$		0			0
$233$	8.29931	+	14.3748i	0.543706	+	0.941726i	0.998687	+	0.0512251i	$0.0163126\pi$
$233$	8.29931	+	14.3748i	0.543706	+	0.941726i	−0.454981	+	0.890501i	$0.650354\pi$
$234$		0			0
$235$	−41.9492	−	24.2194i	−2.73646	−	1.57990i
$236$		0			0
$237$			14.5702i			0.946439i
$238$		0			0
$239$			25.2299i			1.63199i	0.578059	+	0.815995i	$0.303810\pi$
$239$			25.2299i			1.63199i	−0.578059	+	0.815995i	$0.696190\pi$
$240$		0			0
$241$	9.32389	+	5.38315i	0.600604	+	0.346759i	0.769279	−	0.638913i	$-0.220615\pi$
$241$	9.32389	+	5.38315i	0.600604	+	0.346759i	−0.168675	+	0.985672i	$0.553949\pi$
$242$		0			0
$243$	2.91282	+	5.04515i	0.186858	+	0.323647i
$244$		0			0
$245$	−21.3166	+	13.8474i	−1.36187	+	0.884678i
$246$		0			0
$247$	29.5599	−	17.0664i	1.88085	−	1.08591i
$248$		0			0
$249$	0.260777	−	0.451679i	0.0165261	−	0.0286240i
$250$		0			0
$251$	1.62153			0.102350			0.0511749	−	0.998690i	$-0.483703\pi$
$251$	1.62153			0.102350			0.0511749	+	0.998690i	$0.483703\pi$
$252$		0			0
$253$	0.465794			0.0292842
$254$		0			0
$255$	1.92238	−	3.32965i	0.120384	−	0.208511i
$256$		0			0
$257$	8.39265	−	4.84550i	0.523519	−	0.302254i	−0.214854	−	0.976646i	$-0.568928\pi$
$257$	8.39265	−	4.84550i	0.523519	−	0.302254i	0.738373	+	0.674392i	$0.235594\pi$
$258$		0			0
$259$	−6.91270	+	4.23677i	−0.429534	+	0.263260i
$260$		0			0
$261$	−2.05480	−	3.55901i	−0.127189	−	0.220297i
$262$		0			0
$263$	−2.12137	−	1.22477i	−0.130809	−	0.0755227i	0.433168	−	0.901313i	$-0.357396\pi$
$263$	−2.12137	−	1.22477i	−0.130809	−	0.0755227i	−0.563977	+	0.825791i	$0.690729\pi$
$264$		0			0
$265$		−	33.1261i		−	2.03492i
$266$		0			0
$267$		−	1.10469i		−	0.0676062i
$268$		0			0
$269$	2.53222	+	1.46198i	0.154392	+	0.0891384i	0.575206	−	0.818009i	$-0.304922\pi$
$269$	2.53222	+	1.46198i	0.154392	+	0.0891384i	−0.420814	+	0.907147i	$0.638255\pi$
$270$		0			0
$271$	5.40261	+	9.35760i	0.328185	+	0.568433i	0.982152	−	0.188090i	$-0.0602297\pi$
$271$	5.40261	+	9.35760i	0.328185	+	0.568433i	−0.653967	+	0.756523i	$0.726896\pi$
$272$		0			0
$273$	12.2218	−	22.5136i	0.739700	−	1.36258i
$274$		0			0
$275$	1.39199	−	0.803665i	0.0839401	−	0.0484628i
$276$		0			0
$277$	−6.85080	+	11.8659i	−0.411625	+	0.712955i	−0.995068	−	0.0991991i	$-0.968372\pi$
$277$	−6.85080	+	11.8659i	−0.411625	+	0.712955i	0.583443	+	0.812154i	$0.301705\pi$
$278$		0			0
$279$	−3.25954			−0.195144
$280$		0			0
$281$	9.22524			0.550332			0.275166	−	0.961397i	$-0.411267\pi$
$281$	9.22524			0.550332			0.275166	+	0.961397i	$0.411267\pi$
$282$		0			0
$283$	−4.65770	+	8.06737i	−0.276871	+	0.479555i	−0.970606	−	0.240676i	$-0.922631\pi$
$283$	−4.65770	+	8.06737i	−0.276871	+	0.479555i	0.693734	+	0.720231i	$0.255964\pi$
$284$		0			0
$285$	26.9534	−	15.5616i	1.59658	−	0.921787i
$286$		0			0
$287$	−3.51973	+	0.0924137i	−0.207763	+	0.00545501i
$288$		0			0
$289$	−8.26946	−	14.3231i	−0.486439	−	0.842537i
$290$		0			0
$291$	16.8988	+	9.75651i	0.990624	+	0.571937i
$292$		0			0
$293$			15.5267i			0.907079i	0.891236	+	0.453539i	$0.149839\pi$
$293$			15.5267i			0.907079i	−0.891236	+	0.453539i	$0.850161\pi$
$294$		0			0
$295$			34.2993i			1.99698i
$296$		0			0
$297$	0.946149	+	0.546259i	0.0549011	+	0.0316972i
$298$		0			0
$299$	−7.36607	−	12.7584i	−0.425991	−	0.737838i
$300$		0			0
$301$	1.03855	−	0.0272680i	0.0598609	−	0.00157170i
$302$		0			0
$303$	12.3185	−	7.11206i	0.707677	−	0.408577i
$304$		0			0
$305$	−1.58806	+	2.75060i	−0.0909319	+	0.157499i
$306$		0			0
$307$	−9.31202			−0.531465			−0.265732	−	0.964047i	$-0.585614\pi$
$307$	−9.31202			−0.531465			−0.265732	+	0.964047i	$0.585614\pi$
$308$		0			0
$309$	4.91704			0.279721
$310$		0			0
$311$	−5.38539	+	9.32776i	−0.305377	+	0.528929i	−0.977345	−	0.211651i	$-0.932116\pi$
$311$	−5.38539	+	9.32776i	−0.305377	+	0.528929i	0.671968	+	0.740580i	$0.265449\pi$
$312$		0			0
$313$	−22.8292	+	13.1804i	−1.29038	+	0.745001i	−0.978722	−	0.205193i	$-0.934218\pi$
$313$	−22.8292	+	13.1804i	−1.29038	+	0.745001i	−0.311659	+	0.950194i	$0.600885\pi$
$314$		0			0
$315$	−2.60718	+	4.80263i	−0.146898	+	0.270597i
$316$		0			0
$317$	12.8017	+	22.1732i	0.719014	+	1.24537i	0.961391	+	0.275187i	$0.0887396\pi$
$317$	12.8017	+	22.1732i	0.719014	+	1.24537i	−0.242377	+	0.970182i	$0.577927\pi$
$318$		0			0
$319$	−1.22851	−	0.709282i	−0.0687835	−	0.0397122i
$320$		0			0
$321$			14.7069i			0.820862i
$322$		0			0
$323$			3.73243i			0.207678i
$324$		0			0
$325$	−44.0259	−	25.4183i	−2.44212	−	1.40996i
$326$		0			0
$327$	1.20434	+	2.08598i	0.0666001	+	0.115355i
$328$		0			0
$329$	30.0899	−	18.4420i	1.65891	−	1.01674i
$330$		0			0
$331$	18.3790	−	10.6111i	1.01020	−	0.583240i	0.0989502	−	0.995092i	$-0.468452\pi$
$331$	18.3790	−	10.6111i	1.01020	−	0.583240i	0.911250	+	0.411853i	$0.135118\pi$
$332$		0			0
$333$	−0.871502	+	1.50949i	−0.0477580	+	0.0827193i
$334$		0			0
$335$	−39.5358			−2.16007
$336$		0			0
$337$	10.6266			0.578867			0.289434	−	0.957198i	$-0.406533\pi$
$337$	10.6266			0.578867			0.289434	+	0.957198i	$0.406533\pi$
$338$		0			0
$339$	−0.168830	+	0.292422i	−0.00916960	+	0.0158822i
$340$		0			0
$341$	−0.974400	+	0.562570i	−0.0527667	+	0.0304649i
$342$		0			0
$343$	−1.45696	−	18.4629i	−0.0786683	−	0.996901i
$344$		0			0
$345$	−6.71656	−	11.6334i	−0.361607	−	0.626322i
$346$		0			0
$347$	22.7850	+	13.1549i	1.22316	+	0.706194i	0.965591	−	0.260065i	$-0.0837440\pi$
$347$	22.7850	+	13.1549i	1.22316	+	0.706194i	0.257573	+	0.966259i	$0.417077\pi$
$348$		0			0
$349$		−	0.985162i		−	0.0527345i	−0.999652	−	0.0263673i	$-0.991606\pi$
$349$		−	0.985162i		−	0.0527345i	0.999652	−	0.0263673i	$-0.00839393\pi$
$350$		0			0
$351$		−	34.5542i		−	1.84437i
$352$		0			0
$353$	3.72262	+	2.14925i	0.198135	+	0.114393i	0.595785	−	0.803144i	$-0.296841\pi$
$353$	3.72262	+	2.14925i	0.198135	+	0.114393i	−0.397650	+	0.917537i	$0.630174\pi$
$354$		0			0
$355$	−14.8644	−	25.7458i	−0.788918	−	1.36645i
$356$		0			0
$357$	1.46381	+	2.38834i	0.0774730	+	0.126405i
$358$		0			0
$359$	−18.5999	+	10.7387i	−0.981665	+	0.566764i	−0.902772	−	0.430119i	$-0.858472\pi$
$359$	−18.5999	+	10.7387i	−0.981665	+	0.566764i	−0.0788923	+	0.996883i	$0.525138\pi$
$360$		0			0
$361$	−5.60694	+	9.71151i	−0.295102	+	0.511132i
$362$		0			0
$363$	−17.0915			−0.897071
$364$		0			0
$365$	48.9189			2.56053
$366$		0			0
$367$	17.8548	−	30.9254i	0.932013	−	1.61429i	0.152137	−	0.988359i	$-0.451385\pi$
$367$	17.8548	−	30.9254i	0.932013	−	1.61429i	0.779876	−	0.625934i	$-0.215282\pi$
$368$		0			0
$369$	−0.655523	+	0.378466i	−0.0341251	+	0.0197022i
$370$		0			0
$371$	21.2112	+	11.5148i	1.10123	+	0.597821i
$372$		0			0
$373$	−14.7737	−	25.5888i	−0.764954	−	1.32494i	−0.940271	−	0.340427i	$-0.889429\pi$
$373$	−14.7737	−	25.5888i	−0.764954	−	1.32494i	0.175317	−	0.984512i	$-0.443905\pi$
$374$		0			0
$375$	−15.6261	−	9.02172i	−0.806928	−	0.465880i
$376$		0			0
$377$			44.8664i			2.31074i
$378$		0			0
$379$			4.57542i			0.235024i	0.993071	+	0.117512i	$0.0374918\pi$
$379$			4.57542i			0.235024i	−0.993071	+	0.117512i	$0.962508\pi$
$380$		0			0
$381$	11.2288	+	6.48297i	0.575271	+	0.332133i
$382$		0			0
$383$	−17.0223	−	29.4835i	−0.869801	−	1.50654i	−0.862200	−	0.506568i	$-0.830914\pi$
$383$	−17.0223	−	29.4835i	−0.869801	−	1.50654i	−0.00760054	−	0.999971i	$-0.502419\pi$
$384$		0			0
$385$	0.0495098	+	1.88566i	0.00252325	+	0.0961023i
$386$		0			0
$387$	0.193421	−	0.111672i	0.00983216	−	0.00567660i
$388$		0			0
$389$	7.49896	−	12.9886i	0.380212	−	0.658547i	−0.610880	−	0.791723i	$-0.709184\pi$
$389$	7.49896	−	12.9886i	0.380212	−	0.658547i	0.991092	+	0.133176i	$0.0425175\pi$
$390$		0			0
$391$	1.61096			0.0814699
$392$		0			0
$393$	−24.9913			−1.26064
$394$		0			0
$395$	−16.9665	+	29.3869i	−0.853679	+	1.47861i
$396$		0			0
$397$	−2.50671	+	1.44725i	−0.125808	+	0.0726355i	−0.561583	−	0.827420i	$-0.689808\pi$
$397$	−2.50671	+	1.44725i	−0.125808	+	0.0726355i	0.435775	+	0.900056i	$0.356474\pi$
$398$		0			0
$399$	0.595171	+	22.6681i	0.0297958	+	1.13482i
$400$		0			0
$401$	−10.5342	−	18.2458i	−0.526052	−	0.911149i	−0.999539	−	0.0303486i	$-0.990338\pi$
$401$	−10.5342	−	18.2458i	−0.526052	−	0.911149i	0.473487	−	0.880801i	$-0.342995\pi$
$402$		0			0
$403$	30.8183	+	17.7930i	1.53517	+	0.886332i
$404$		0			0
$405$		−	25.3110i		−	1.25771i
$406$		0			0
$407$			0.601656i			0.0298230i
$408$		0			0
$409$	−19.5553	−	11.2903i	−0.966949	−	0.558269i	−0.0686446	−	0.997641i	$-0.521867\pi$
$409$	−19.5553	−	11.2903i	−0.966949	−	0.558269i	−0.898305	+	0.439373i	$0.855201\pi$
$410$		0			0
$411$	13.7824	+	23.8718i	0.679835	+	1.17751i
$412$		0			0
$413$	−21.9625	−	11.9227i	−1.08070	−	0.586676i
$414$		0			0
$415$	1.05193	−	0.607331i	0.0516371	−	0.0298127i
$416$		0			0
$417$	−1.68613	+	2.92046i	−0.0825701	+	0.143016i
$418$		0			0
$419$	13.5564			0.662272			0.331136	−	0.943583i	$-0.392568\pi$
$419$	13.5564			0.662272			0.331136	+	0.943583i	$0.392568\pi$
$420$		0			0
$421$	−22.9826			−1.12010			−0.560052	−	0.828458i	$-0.689219\pi$
$421$	−22.9826			−1.12010			−0.560052	+	0.828458i	$0.689219\pi$
$422$		0			0
$423$	3.79352	−	6.57056i	0.184447	−	0.319472i
$424$		0			0
$425$	4.81424	−	2.77950i	0.233525	−	0.134826i
$426$		0			0
$427$	−1.20924	−	1.97299i	−0.0585191	−	0.0954796i
$428$		0			0
$429$	−0.950490	−	1.64630i	−0.0458901	−	0.0794840i
$430$		0			0
$431$	3.75150	+	2.16593i	0.180703	+	0.104329i	0.587623	−	0.809135i	$-0.300064\pi$
$431$	3.75150	+	2.16593i	0.180703	+	0.104329i	−0.406920	+	0.913464i	$0.633397\pi$
$432$		0			0
$433$		−	20.8029i		−	0.999725i	−0.866105	−	0.499862i	$-0.833384\pi$
$433$		−	20.8029i		−	0.999725i	0.866105	−	0.499862i	$-0.166616\pi$
$434$		0			0
$435$			40.9102i			1.96150i
$436$		0			0
$437$	11.2936	+	6.52034i	0.540244	+	0.311910i
$438$		0			0
$439$	−5.07636	−	8.79252i	−0.242282	−	0.419644i	0.719082	−	0.694925i	$-0.244562\pi$
$439$	−5.07636	−	8.79252i	−0.242282	−	0.419644i	−0.961364	+	0.275281i	$0.911229\pi$
$440$		0			0
$441$	−2.16894	−	3.33885i	−0.103283	−	0.158993i
$442$		0			0
$443$	25.5390	−	14.7450i	1.21340	−	0.700555i	0.249899	−	0.968272i	$-0.419603\pi$
$443$	25.5390	−	14.7450i	1.21340	−	0.700555i	0.963498	+	0.267717i	$0.0862692\pi$
$444$		0			0
$445$	1.28638	−	2.22807i	0.0609801	−	0.105621i
$446$		0			0
$447$	11.3528			0.536969
$448$		0			0
$449$	29.6871			1.40102			0.700510	−	0.713643i	$-0.252956\pi$
$449$	29.6871			1.40102			0.700510	+	0.713643i	$0.252956\pi$
$450$		0			0
$451$	−0.130640	+	0.226276i	−0.00615161	+	0.0106549i
$452$		0			0
$453$	−2.27048	+	1.31086i	−0.106677	+	0.0615897i
$454$		0			0
$455$	50.8666	−	31.1760i	2.38466	−	1.46155i
$456$		0			0
$457$	−4.44123	−	7.69244i	−0.207752	−	0.359837i	0.743254	−	0.669009i	$-0.233281\pi$
$457$	−4.44123	−	7.69244i	−0.207752	−	0.359837i	−0.951006	+	0.309172i	$0.899948\pi$
$458$		0			0
$459$	3.27229	+	1.88926i	0.152737	+	0.0881829i
$460$		0			0
$461$		−	31.1184i		−	1.44933i	−0.689102	−	0.724665i	$-0.741995\pi$
$461$		−	31.1184i		−	1.44933i	0.689102	−	0.724665i	$-0.258005\pi$
$462$		0			0
$463$			17.5170i			0.814082i	0.913410	+	0.407041i	$0.133439\pi$
$463$			17.5170i			0.814082i	−0.913410	+	0.407041i	$0.866561\pi$
$464$		0			0
$465$	28.1009	+	16.2241i	1.30315	+	0.752373i
$466$		0			0
$467$	−18.2279	−	31.5716i	−0.843485	−	1.46096i	−0.886930	−	0.461904i	$-0.847167\pi$
$467$	−18.2279	−	31.5716i	−0.843485	−	1.46096i	0.0434446	−	0.999056i	$-0.486167\pi$
$468$		0			0
$469$	13.7429	−	25.3155i	0.634589	−	1.16896i
$470$		0			0
$471$	−23.4859	+	13.5596i	−1.08217	+	0.624794i
$472$		0			0
$473$	0.0385473	−	0.0667659i	0.00177241	−	0.00306990i
$474$		0			0
$475$	44.9999			2.06474
$476$		0			0
$477$	5.18858			0.237569
$478$		0			0
$479$	−6.41613	+	11.1131i	−0.293161	+	0.507769i	−0.974555	−	0.224147i	$-0.928040\pi$
$479$	−6.41613	+	11.1131i	−0.293161	+	0.507769i	0.681395	+	0.731916i	$0.261374\pi$
$480$		0			0
$481$	16.4798	−	9.51460i	0.751413	−	0.433828i
$482$		0			0
$483$	9.78381	−	0.256883i	0.445179	−	0.0116886i
$484$		0			0
$485$	22.7222	+	39.3560i	1.03176	+	1.78707i
$486$		0			0
$487$	−28.9688	−	16.7251i	−1.31270	−	0.757889i	−0.330159	−	0.943925i	$-0.607102\pi$
$487$	−28.9688	−	16.7251i	−1.31270	−	0.757889i	−0.982543	+	0.186037i	$0.940436\pi$
$488$		0			0
$489$		−	34.5430i		−	1.56209i
$490$		0			0
$491$		−	26.4851i		−	1.19525i	−0.801774	−	0.597627i	$-0.796110\pi$
$491$		−	26.4851i		−	1.19525i	0.801774	−	0.597627i	$-0.203890\pi$
$492$		0			0
$493$	−4.24885	−	2.45308i	−0.191359	−	0.110481i
$494$		0			0
$495$	0.202760	+	0.351190i	0.00911337	+	0.0157848i
$496$		0			0
$497$	21.6525	−	0.568506i	0.971247	−	0.0255010i
$498$		0			0
$499$	2.37388	−	1.37056i	0.106269	−	0.0613546i	−0.445923	−	0.895071i	$-0.647125\pi$
$499$	2.37388	−	1.37056i	0.106269	−	0.0613546i	0.552193	+	0.833717i	$0.313791\pi$
$500$		0			0
$501$	3.06973	−	5.31693i	0.137145	−	0.237543i
$502$		0			0
$503$	17.5215			0.781244			0.390622	−	0.920551i	$-0.372260\pi$
$503$	17.5215			0.781244			0.390622	+	0.920551i	$0.372260\pi$
$504$		0			0
$505$	33.1270			1.47413
$506$		0			0
$507$	−19.9271	+	34.5147i	−0.884993	+	1.53285i
$508$		0			0
$509$	19.5615	−	11.2938i	0.867049	−	0.500591i	0.000682339	−	1.00000i	$-0.499783\pi$
$509$	19.5615	−	11.2938i	0.867049	−	0.500591i	0.866366	+	0.499409i	$0.166449\pi$
$510$		0			0
$511$	−17.0045	+	31.3237i	−0.752236	+	1.38568i
$512$		0			0
$513$	15.2934	+	26.4890i	0.675222	+	1.16952i
$514$		0			0
$515$	9.91724	+	5.72572i	0.437006	+	0.252305i
$516$		0			0
$517$		−	2.61892i		−	0.115180i
$518$		0			0
$519$			3.58711i			0.157457i
$520$		0			0
$521$	−10.1891	−	5.88270i	−0.446394	−	0.257726i	0.259912	−	0.965632i	$-0.416306\pi$
$521$	−10.1891	−	5.88270i	−0.446394	−	0.257726i	−0.706306	+	0.707906i	$0.749640\pi$
$522$		0			0
$523$	4.51991	+	7.82871i	0.197642	+	0.342326i	0.947763	−	0.318974i	$-0.103338\pi$
$523$	4.51991	+	7.82871i	0.197642	+	0.342326i	−0.750122	+	0.661300i	$0.770005\pi$
$524$		0			0
$525$	28.7950	−	17.6483i	1.25671	−	0.770237i
$526$		0			0
$527$	−3.37000	+	1.94567i	−0.146799	+	0.0847546i
$528$		0			0
$529$	−8.68574	+	15.0441i	−0.377641	+	0.654093i
$530$		0			0
$531$	−5.37235			−0.233140
$532$		0			0
$533$	8.26378			0.357944
$534$		0			0
$535$	−17.1257	+	29.6626i	−0.740409	+	1.28243i
$536$		0			0
$537$	11.0678	−	6.39001i	0.477612	−	0.275749i
$538$		0			0
$539$	−1.22464	−	0.623767i	−0.0527488	−	0.0268676i
$540$		0			0
$541$	11.2478	+	19.4818i	0.483582	+	0.837589i	0.999822	−	0.0188553i	$-0.00600218\pi$
$541$	11.2478	+	19.4818i	0.483582	+	0.837589i	−0.516240	+	0.856444i	$0.672669\pi$
$542$		0			0
$543$	15.1018	+	8.71900i	0.648078	+	0.374168i
$544$		0			0
$545$			5.60964i			0.240291i
$546$		0			0
$547$		−	32.0557i		−	1.37060i	−0.728259	−	0.685302i	$-0.759670\pi$
$547$		−	32.0557i		−	1.37060i	0.728259	−	0.685302i	$-0.240330\pi$
$548$		0			0
$549$	−0.430830	−	0.248740i	−0.0183874	−	0.0106160i
$550$		0			0
$551$	−19.8575	−	34.3943i	−0.845960	−	1.46525i
$552$		0			0
$553$	−12.9193	−	21.0791i	−0.549384	−	0.896373i
$554$		0			0
$555$	15.0266	−	8.67563i	0.637845	−	0.368260i
$556$		0			0
$557$	2.84552	−	4.92858i	0.120568	−	0.208831i	−0.799424	−	0.600768i	$-0.794862\pi$
$557$	2.84552	−	4.92858i	0.120568	−	0.208831i	0.919992	+	0.391937i	$0.128195\pi$
$558$		0			0
$559$	−2.43835			−0.103131
$560$		0			0
$561$	0.207873			0.00877639
$562$		0			0
$563$	9.06697	−	15.7045i	0.382127	−	0.661864i	−0.609239	−	0.792987i	$-0.708525\pi$
$563$	9.06697	−	15.7045i	0.382127	−	0.661864i	0.991366	+	0.131123i	$0.0418582\pi$
$564$		0			0
$565$	−0.681031	+	0.393193i	−0.0286512	+	0.0165418i
$566$		0			0
$567$	16.2071	+	8.79827i	0.680634	+	0.369493i
$568$		0			0
$569$	−19.5009	−	33.7766i	−0.817522	−	1.41599i	−0.907503	−	0.420045i	$-0.862014\pi$
$569$	−19.5009	−	33.7766i	−0.817522	−	1.41599i	0.0899815	−	0.995943i	$-0.471319\pi$
$570$		0			0
$571$	−28.7914	−	16.6227i	−1.20488	−	0.695640i	−0.243246	−	0.969965i	$-0.578212\pi$
$571$	−28.7914	−	16.6227i	−1.20488	−	0.695640i	−0.961637	+	0.274325i	$0.911546\pi$
$572$		0			0
$573$		−	23.4875i		−	0.981205i
$574$		0			0
$575$		−	19.4225i		−	0.809974i
$576$		0			0
$577$	−5.60770	−	3.23761i	−0.233452	−	0.134783i	0.378712	−	0.925515i	$-0.376367\pi$
$577$	−5.60770	−	3.23761i	−0.233452	−	0.134783i	−0.612163	+	0.790731i	$0.709701\pi$
$578$		0			0
$579$	4.06692	+	7.04411i	0.169015	+	0.292743i
$580$		0			0
$581$	0.0232281	+	0.884681i	0.000963664	+	0.0367028i
$582$		0			0
$583$	1.55106	−	0.895507i	0.0642385	−	0.0370881i
$584$		0			0
$585$	6.41289	−	11.1075i	0.265140	−	0.459237i
$586$		0			0
$587$	0.332307			0.0137158			0.00685788	−	0.999976i	$-0.497817\pi$
$587$	0.332307			0.0137158			0.00685788	+	0.999976i	$0.497817\pi$
$588$		0			0
$589$	−31.5002			−1.29794
$590$		0			0
$591$	5.25784	−	9.10685i	0.216279	−	0.374606i
$592$		0			0
$593$	25.1105	−	14.4976i	1.03117	−	0.595344i	0.113848	−	0.993498i	$-0.463682\pi$
$593$	25.1105	−	14.4976i	1.03117	−	0.595344i	0.917319	+	0.398154i	$0.130349\pi$
$594$		0			0
$595$	0.171231	+	6.52163i	0.00701980	+	0.267361i
$596$		0			0
$597$	16.2867	+	28.2094i	0.666572	+	1.15454i
$598$		0			0
$599$	−16.7626	−	9.67791i	−0.684903	−	0.395429i	0.116797	−	0.993156i	$-0.462737\pi$
$599$	−16.7626	−	9.67791i	−0.684903	−	0.395429i	−0.801700	+	0.597727i	$0.796071\pi$
$600$		0			0
$601$			43.3124i			1.76675i	0.468669	+	0.883374i	$0.344734\pi$
$601$			43.3124i			1.76675i	−0.468669	+	0.883374i	$0.655266\pi$
$602$		0			0
$603$		−	6.19255i		−	0.252180i
$604$		0			0
$605$	−34.4720	−	19.9024i	−1.40149	−	0.809149i
$606$		0			0
$607$	14.9513	+	25.8964i	0.606855	+	1.05110i	0.991755	+	0.128146i	$0.0409025\pi$
$607$	14.9513	+	25.8964i	0.606855	+	1.05110i	−0.384900	+	0.922958i	$0.625764\pi$
$608$		0			0
$609$	−26.1956	−	14.2207i	−1.06150	−	0.576250i
$610$		0			0
$611$	−71.7339	+	41.4156i	−2.90204	+	1.67550i
$612$		0			0
$613$	0.899382	−	1.55778i	0.0363257	−	0.0629180i	−0.847291	−	0.531129i	$-0.821768\pi$
$613$	0.899382	−	1.55778i	0.0363257	−	0.0629180i	0.883617	+	0.468211i	$0.155101\pi$
$614$		0			0
$615$	7.53511			0.303845
$616$		0			0
$617$	9.86240			0.397045			0.198523	−	0.980096i	$-0.436386\pi$
$617$	9.86240			0.397045			0.198523	+	0.980096i	$0.436386\pi$
$618$		0			0
$619$	−2.68339	+	4.64777i	−0.107855	+	0.186810i	−0.914901	−	0.403679i	$-0.867731\pi$
$619$	−2.68339	+	4.64777i	−0.107855	+	0.186810i	0.807046	+	0.590488i	$0.201065\pi$
$620$		0			0
$621$	11.4330	−	6.60083i	0.458790	−	0.264882i
$622$		0			0
$623$	0.979521	+	1.59818i	0.0392437	+	0.0640298i
$624$		0			0
$625$	−0.544222	−	0.942620i	−0.0217689	−	0.0377048i
$626$		0			0
$627$	1.45728	+	0.841360i	0.0581981	+	0.0336007i
$628$		0			0
$629$			2.08085i			0.0829688i
$630$		0			0
$631$		−	12.4909i		−	0.497255i	−0.968599	−	0.248628i	$-0.920020\pi$
$631$		−	12.4909i		−	0.497255i	0.968599	−	0.248628i	$-0.0799796\pi$
$632$		0			0
$633$	−11.0548	−	6.38249i	−0.439389	−	0.253681i
$634$		0			0
$635$	15.0984	+	26.1512i	0.599161	+	1.03778i
$636$		0			0
$637$	2.28100	+	43.4078i	0.0903764	+	1.71988i
$638$		0			0
$639$	4.03261	−	2.32823i	0.159527	−	0.0921032i
$640$		0			0
$641$	15.0263	−	26.0263i	0.593502	−	1.02798i	−0.400255	−	0.916404i	$-0.631078\pi$
$641$	15.0263	−	26.0263i	0.593502	−	1.02798i	0.993756	−	0.111571i	$-0.0355884\pi$
$642$		0			0
$643$	3.33057			0.131345			0.0656724	−	0.997841i	$-0.479081\pi$
$643$	3.33057			0.131345			0.0656724	+	0.997841i	$0.479081\pi$
$644$		0			0
$645$	−2.22334			−0.0875441
$646$		0			0
$647$	7.19695	−	12.4655i	0.282941	−	0.490069i	−0.689167	−	0.724603i	$-0.742023\pi$
$647$	7.19695	−	12.4655i	0.282941	−	0.490069i	0.972108	+	0.234534i	$0.0753565\pi$
$648$		0			0
$649$	−1.60600	+	0.927223i	−0.0630409	+	0.0363967i
$650$		0			0
$651$	−20.1566	+	12.3539i	−0.790000	+	0.484189i
$652$		0			0
$653$	−13.0568	−	22.6150i	−0.510951	−	0.884994i	−0.999919	−	0.0126921i	$-0.995960\pi$
$653$	−13.0568	−	22.6150i	−0.510951	−	0.884994i	0.488968	−	0.872302i	$-0.337373\pi$
$654$		0			0
$655$	−50.4052	−	29.1015i	−1.96949	−	1.13709i
$656$		0			0
$657$			7.66224i			0.298932i
$658$		0			0
$659$		−	16.5601i		−	0.645089i	−0.946554	−	0.322544i	$-0.895462\pi$
$659$		−	16.5601i		−	0.645089i	0.946554	−	0.322544i	$-0.104538\pi$
$660$		0			0
$661$	−7.11555	−	4.10816i	−0.276763	−	0.159789i	0.355194	−	0.934793i	$-0.384415\pi$
$661$	−7.11555	−	4.10816i	−0.276763	−	0.159789i	−0.631957	+	0.775003i	$0.717748\pi$
$662$		0			0
$663$	−3.28730	−	5.69377i	−0.127668	−	0.221128i
$664$		0			0
$665$	−25.1957	+	46.4125i	−0.977049	+	1.79980i
$666$		0			0
$667$	−14.8450	+	8.57075i	−0.574800	+	0.331861i
$668$		0			0
$669$	−18.0009	+	31.1785i	−0.695956	+	1.20543i
$670$		0			0
$671$	−0.171722			−0.00662924
$672$		0			0
$673$	12.6784			0.488716			0.244358	−	0.969685i	$-0.421423\pi$
$673$	12.6784			0.488716			0.244358	+	0.969685i	$0.421423\pi$
$674$		0			0
$675$	22.7777	−	39.4522i	0.876715	−	1.51852i
$676$		0			0
$677$	4.18639	−	2.41702i	0.160896	−	0.0928935i	−0.417390	−	0.908727i	$-0.637055\pi$
$677$	4.18639	−	2.41702i	0.160896	−	0.0928935i	0.578286	+	0.815834i	$0.303722\pi$
$678$		0			0
$679$	−33.0988	+	0.869039i	−1.27021	+	0.0333507i
$680$		0			0
$681$	5.38833	+	9.33286i	0.206481	+	0.357636i
$682$		0			0
$683$	−18.5857	−	10.7304i	−0.711160	−	0.410589i	0.100330	−	0.994954i	$-0.468010\pi$
$683$	−18.5857	−	10.7304i	−0.711160	−	0.410589i	−0.811490	+	0.584366i	$0.801343\pi$
$684$		0			0
$685$			64.1964i			2.45282i
$686$		0			0
$687$		−	25.9954i		−	0.991788i
$688$		0			0
$689$	−49.0570	−	28.3231i	−1.86892	−	1.07902i
$690$		0			0
$691$	−10.9551	−	18.9749i	−0.416753	−	0.721837i	0.578858	−	0.815429i	$-0.303499\pi$
$691$	−10.9551	−	18.9749i	−0.416753	−	0.721837i	−0.995611	+	0.0935912i	$0.970165\pi$
$692$		0			0
$693$	−0.295354	+	0.00775480i	−0.0112196	+	0.000294580i
$694$		0			0
$695$	−6.80155	+	3.92688i	−0.257997	+	0.148955i
$696$		0			0
$697$	−0.451824	+	0.782582i	−0.0171140	+	0.0296424i
$698$		0			0
$699$	25.8812			0.978915
$700$		0			0
$701$	−26.9354			−1.01734			−0.508668	−	0.860963i	$-0.669862\pi$
$701$	−26.9354			−1.01734			−0.508668	+	0.860963i	$0.669862\pi$
$702$		0			0
$703$	−8.42218	+	14.5877i	−0.317649	+	0.550184i
$704$		0			0
$705$	−65.4087	+	37.7637i	−2.46343	+	1.42226i
$706$		0			0
$707$	−11.5152	+	21.2118i	−0.433072	+	0.797752i
$708$		0			0
$709$	−7.61592	−	13.1912i	−0.286022	−	0.495405i	0.686835	−	0.726814i	$-0.259000\pi$
$709$	−7.61592	−	13.1912i	−0.286022	−	0.495405i	−0.972856	+	0.231409i	$0.925666\pi$
$710$		0			0
$711$	−4.60291	−	2.65749i	−0.172623	−	0.0996637i
$712$		0			0
$713$			13.5959i			0.509169i
$714$		0			0
$715$		−	4.42725i		−	0.165570i
$716$		0			0
$717$	34.0690	+	19.6697i	1.27233	+	0.734579i
$718$		0			0
$719$	−0.167533	−	0.290176i	−0.00624794	−	0.0108217i	0.862885	−	0.505401i	$-0.168655\pi$
$719$	−0.167533	−	0.290176i	−0.00624794	−	0.0108217i	−0.869132	+	0.494579i	$0.835322\pi$
$720$		0			0
$721$	−7.11358	+	4.35989i	−0.264924	+	0.162371i
$722$		0			0
$723$	14.5381	−	8.39360i	0.540679	−	0.312161i
$724$		0			0
$725$	−29.5754	+	51.2261i	−1.09840	+	1.90249i
$726$		0			0
$727$	33.9519			1.25921			0.629604	−	0.776916i	$-0.283217\pi$
$727$	33.9519			1.25921			0.629604	+	0.776916i	$0.283217\pi$
$728$		0			0
$729$	29.9940			1.11089
$730$		0			0
$731$	0.133317	−	0.230912i	0.00493091	−	0.00854059i
$732$		0			0
$733$	−1.39369	+	0.804648i	−0.0514772	+	0.0297204i	−0.525518	−	0.850783i	$-0.676128\pi$
$733$	−1.39369	+	0.804648i	−0.0514772	+	0.0297204i	0.474041	+	0.880503i	$0.342795\pi$
$734$		0			0
$735$	2.07987	+	39.5803i	0.0767171	+	1.45994i
$736$		0			0
$737$	−1.06878	−	1.85119i	−0.0393691	−	0.0681894i
$738$		0			0
$739$	16.8035	+	9.70153i	0.618128	+	0.356876i	0.776140	−	0.630561i	$-0.217175\pi$
$739$	16.8035	+	9.70153i	0.618128	+	0.356876i	−0.158012	+	0.987437i	$0.550508\pi$
$740$		0			0
$741$		−	53.2211i		−	1.95513i
$742$		0			0
$743$			15.4917i			0.568334i	0.958775	+	0.284167i	$0.0917170\pi$
$743$			15.4917i			0.568334i	−0.958775	+	0.284167i	$0.908283\pi$
$744$		0			0
$745$	22.8976	+	13.2199i	0.838902	+	0.484340i
$746$		0			0
$747$	0.0951271	+	0.164765i	0.00348052	+	0.00602844i
$748$		0			0
$749$	−13.0405	−	21.2768i	−0.476490	−	0.777438i
$750$		0			0
$751$	15.5426	−	8.97353i	0.567158	−	0.327449i	−0.188855	−	0.982005i	$-0.560478\pi$
$751$	15.5426	−	8.97353i	0.567158	−	0.327449i	0.756013	+	0.654556i	$0.227144\pi$
$752$		0			0
$753$	1.26417	−	2.18961i	0.0460690	−	0.0797938i
$754$		0			0
$755$	−6.10581			−0.222213
$756$		0			0
$757$	−31.0113			−1.12713			−0.563563	−	0.826073i	$-0.690570\pi$
$757$	−31.0113			−1.12713			−0.563563	+	0.826073i	$0.690570\pi$
$758$		0			0
$759$	0.363141	−	0.628979i	0.0131812	−	0.0228305i
$760$		0			0
$761$	20.5574	−	11.8688i	0.745206	−	0.430245i	−0.0787532	−	0.996894i	$-0.525094\pi$
$761$	20.5574	−	11.8688i	0.745206	−	0.430245i	0.823959	+	0.566649i	$0.191761\pi$
$762$		0			0
$763$	−3.59196	−	1.94995i	−0.130038	−	0.0705929i
$764$		0			0
$765$	0.701251	+	1.21460i	0.0253538	+	0.0439141i
$766$		0			0
$767$	50.7945	+	29.3262i	1.83408	+	1.05891i
$768$		0			0
$769$			5.91182i			0.213186i	0.994303	+	0.106593i	$0.0339941\pi$
$769$			5.91182i			0.213186i	−0.994303	+	0.106593i	$0.966006\pi$
$770$		0			0
$771$		−	15.1106i		−	0.544193i
$772$		0			0
$773$	23.9341	+	13.8184i	0.860850	+	0.497012i	0.864297	−	0.502982i	$-0.167764\pi$
$773$	23.9341	+	13.8184i	0.860850	+	0.497012i	−0.00344660	+	0.999994i	$0.501097\pi$
$774$		0			0
$775$	23.4578	+	40.6302i	0.842631	+	1.45948i
$776$		0			0
$777$	0.331810	+	12.6375i	0.0119036	+	0.453369i
$778$		0			0
$779$	−6.33496	+	3.65749i	−0.226974	+	0.131043i
$780$		0			0
$781$	0.803665	−	1.39199i	0.0287574	−	0.0498093i
$782$		0			0
$783$	−40.2054			−1.43682
$784$		0			0
$785$	−63.1587			−2.25423
$786$		0			0
$787$	−27.7867	+	48.1279i	−0.990487	+	1.71557i	−0.376074	+	0.926590i	$0.622726\pi$
$787$	−27.7867	+	48.1279i	−0.990487	+	1.71557i	−0.614413	+	0.788985i	$0.710607\pi$
$788$		0			0
$789$	−3.30771	+	1.90971i	−0.117758	+	0.0679874i
$790$		0			0
$791$	−0.0150382	−	0.572753i	−0.000534696	−	0.0203648i
$792$		0			0
$793$	2.71561	+	4.70357i	0.0964341	+	0.167029i
$794$		0			0
$795$	−44.7314	−	25.8257i	−1.58646	−	0.915942i
$796$		0			0
$797$			9.36041i			0.331563i	0.986163	+	0.165781i	$0.0530146\pi$
$797$			9.36041i			0.331563i	−0.986163	+	0.165781i	$0.946985\pi$
$798$		0			0
$799$		−	9.05762i		−	0.320435i
$800$		0			0
$801$	0.348986	+	0.201487i	0.0123308	+	0.00711920i
$802$		0			0
$803$	1.32244	+	2.29053i	0.0466679	+	0.0808311i
$804$		0			0
$805$	20.0322	+	10.8748i	0.706042	+	0.383286i
$806$		0			0
$807$	3.94833	−	2.27957i	0.138988	−	0.0802446i
$808$		0			0
$809$	5.64057	−	9.76976i	0.198312	−	0.343487i	−0.749669	−	0.661813i	$-0.769787\pi$
$809$	5.64057	−	9.76976i	0.198312	−	0.343487i	0.947981	+	0.318326i	$0.103121\pi$
$810$		0			0
$811$	20.7846			0.729846			0.364923	−	0.931038i	$-0.381095\pi$
$811$	20.7846			0.729846			0.364923	+	0.931038i	$0.381095\pi$
$812$		0			0
$813$	16.8479			0.590881
$814$		0			0
$815$	40.2241	−	69.6702i	1.40899	−	2.44044i
$816$		0			0
$817$	1.86922	−	1.07920i	0.0653958	−	0.0377563i
$818$		0			0
$819$	4.88314	+	7.96732i	0.170631	+	0.278401i
$820$		0			0
$821$	−8.33928	−	14.4441i	−0.291043	−	0.504101i	0.683014	−	0.730406i	$-0.260669\pi$
$821$	−8.33928	−	14.4441i	−0.291043	−	0.504101i	−0.974057	+	0.226304i	$0.927336\pi$
$822$		0			0
$823$	46.6810	+	26.9513i	1.62720	+	0.939464i	0.984924	+	0.172989i	$0.0553427\pi$
$823$	46.6810	+	26.9513i	1.62720	+	0.939464i	0.642275	+	0.766474i	$0.277991\pi$
$824$		0			0
$825$		−	2.50621i		−	0.0872550i
$826$		0			0
$827$		−	13.2260i		−	0.459913i	−0.973201	−	0.229957i	$-0.926142\pi$
$827$		−	13.2260i		−	0.459913i	0.973201	−	0.229957i	$-0.0738585\pi$
$828$		0			0
$829$	−13.8136	−	7.97529i	−0.479766	−	0.276993i	0.240553	−	0.970636i	$-0.422671\pi$
$829$	−13.8136	−	7.97529i	−0.479766	−	0.276993i	−0.720319	+	0.693643i	$0.756005\pi$
$830$		0			0
$831$	10.6820	+	18.5018i	0.370555	+	0.641820i
$832$		0			0
$833$	−4.23544	−	2.15732i	−0.146749	−	0.0747467i
$834$		0			0
$835$	12.3827	−	7.14918i	0.428523	−	0.247408i
$836$		0			0
$837$	−15.9445	+	27.6167i	−0.551124	+	0.954574i
$838$		0			0
$839$	21.0401			0.726385			0.363193	−	0.931714i	$-0.381687\pi$
$839$	21.0401			0.726385			0.363193	+	0.931714i	$0.381687\pi$
$840$		0			0
$841$	23.2041			0.800140
$842$		0			0
$843$	7.19216	−	12.4572i	0.247711	−	0.429048i
$844$		0			0
$845$	−80.3823	+	46.4088i	−2.76524	+	1.59651i
$846$		0			0
$847$	24.7266	−	15.1549i	0.849616	−	0.520727i
$848$		0			0
$849$	7.26245	+	12.5789i	0.249247	+	0.431708i
$850$		0			0
$851$	6.29621	+	3.63512i	0.215831	+	0.124610i
$852$		0			0
$853$			9.28475i			0.317904i	0.987286	+	0.158952i	$0.0508115\pi$
$853$			9.28475i			0.317904i	−0.987286	+	0.158952i	$0.949189\pi$
$854$		0			0
$855$			11.3532i			0.388271i
$856$		0			0
$857$	28.9820	+	16.7328i	0.990007	+	0.571581i	0.905276	−	0.424823i	$-0.139664\pi$
$857$	28.9820	+	16.7328i	0.990007	+	0.571581i	0.0847304	+	0.996404i	$0.472997\pi$
$858$		0			0
$859$	−10.7118	−	18.5534i	−0.365481	−	0.633032i	0.623372	−	0.781925i	$-0.285762\pi$
$859$	−10.7118	−	18.5534i	−0.365481	−	0.633032i	−0.988853	+	0.148893i	$0.952429\pi$
$860$		0			0
$861$	−2.61926	+	4.82487i	−0.0892640	+	0.164431i
$862$		0			0
$863$	−19.8867	+	11.4816i	−0.676950	+	0.390837i	−0.798705	−	0.601723i	$-0.794481\pi$
$863$	−19.8867	+	11.4816i	−0.676950	+	0.390837i	0.121755	+	0.992560i	$0.461148\pi$
$864$		0			0
$865$	−4.17706	+	7.23488i	−0.142024	+	0.245993i
$866$		0			0
$867$	−25.7881			−0.875809
$868$		0			0
$869$	−1.83464			−0.0622361
$870$		0			0
$871$	−33.8035	+	58.5494i	−1.14539	+	1.98387i
$872$		0			0
$873$	−6.16439	+	3.55901i	−0.208633	+	0.120454i
$874$		0			0
$875$	30.6060	−	0.803589i	1.03467	−	0.0271663i
$876$		0			0
$877$	−24.5702	−	42.5568i	−0.829676	−	1.43704i	−0.898292	−	0.439399i	$-0.855192\pi$
$877$	−24.5702	−	42.5568i	−0.829676	−	1.43704i	0.0686157	−	0.997643i	$-0.478142\pi$
$878$		0			0
$879$	20.9663	+	12.1049i	0.707175	+	0.408288i
$880$		0			0
$881$		−	5.91577i		−	0.199307i	−0.995022	−	0.0996537i	$-0.968226\pi$
$881$		−	5.91577i		−	0.199307i	0.995022	−	0.0996537i	$-0.0317735\pi$
$882$		0			0
$883$		−	39.1183i		−	1.31643i	−0.752828	−	0.658217i	$-0.771311\pi$
$883$		−	39.1183i		−	1.31643i	0.752828	−	0.658217i	$-0.228689\pi$
$884$		0			0
$885$	46.3156	+	26.7403i	1.55688	+	0.898867i
$886$		0			0
$887$	14.2866	+	24.7451i	0.479697	+	0.830859i	0.999729	−	0.0232876i	$-0.00741335\pi$
$887$	14.2866	+	24.7451i	0.479697	+	0.830859i	−0.520032	+	0.854147i	$0.674080\pi$
$888$		0			0
$889$	−21.9934	+	0.577456i	−0.737634	+	0.0193672i
$890$		0			0
$891$	1.18514	−	0.684239i	0.0397036	−	0.0229229i
$892$		0			0
$893$	36.6605	−	63.4978i	1.22680	−	2.12487i
$894$		0			0
$895$	29.7637			0.994892
$896$		0			0
$897$	−22.9709			−0.766975
$898$		0			0
$899$	20.7029	−	35.8585i	0.690482	−	1.19595i
$900$		0			0
$901$	5.36440	−	3.09714i	0.178714	−	0.103181i
$902$		0			0
$903$	0.772849	−	1.42365i	0.0257188	−	0.0473761i
$904$		0			0
$905$	20.3059	+	35.1709i	0.674992	+	1.16912i
$906$		0			0
$907$	−28.8980	−	16.6842i	−0.959541	−	0.553991i	−0.0635090	−	0.997981i	$-0.520229\pi$
$907$	−28.8980	−	16.6842i	−0.959541	−	0.553991i	−0.896032	+	0.443990i	$0.853563\pi$
$908$		0			0
$909$			5.18872i			0.172099i
$910$		0			0
$911$			23.8038i			0.788656i	0.918970	+	0.394328i	$0.129023\pi$
$911$			23.8038i			0.788656i	−0.918970	+	0.394328i	$0.870977\pi$
$912$		0			0
$913$	0.0568741	+	0.0328363i	0.00188226	+	0.00108672i
$914$		0			0
$915$	2.47616	+	4.28883i	0.0818592	+	0.141784i
$916$		0			0
$917$	36.1554	−	22.1595i	1.19396	−	0.731772i
$918$		0			0
$919$	14.9708	−	8.64341i	0.493842	−	0.285120i	−0.232325	−	0.972638i	$-0.574633\pi$
$919$	14.9708	−	8.64341i	0.493842	−	0.285120i	0.726167	+	0.687518i	$0.241300\pi$
$920$		0			0
$921$	−7.25981	+	12.5744i	−0.239219	+	0.414340i
$922$		0			0
$923$	−50.8367			−1.67331
$924$		0			0
$925$	25.0876			0.824877
$926$		0			0
$927$	−0.896828	+	1.55335i	−0.0294557	+	0.0510187i
$928$		0			0
$929$	−23.2855	+	13.4439i	−0.763972	+	0.441080i	−0.830720	−	0.556690i	$-0.812071\pi$
$929$	−23.2855	+	13.4439i	−0.763972	+	0.441080i	0.0667478	+	0.997770i	$0.478738\pi$
$930$		0			0
$931$	−20.9606	−	32.2666i	−0.686956	−	1.05750i
$932$		0			0
$933$	8.39709	+	14.5442i	0.274908	+	0.476155i
$934$		0			0
$935$	0.419261	+	0.242060i	0.0137113	+	0.00791622i
$936$		0			0
$937$			13.9762i			0.456582i	0.973593	+	0.228291i	$0.0733138\pi$
$937$			13.9762i			0.456582i	−0.973593	+	0.228291i	$0.926686\pi$
$938$		0			0
$939$			41.1028i			1.34134i
$940$		0			0
$941$	−6.44074	−	3.71856i	−0.209962	−	0.121222i	0.391332	−	0.920250i	$-0.372015\pi$
$941$	−6.44074	−	3.71856i	−0.209962	−	0.121222i	−0.601294	+	0.799028i	$0.705348\pi$
$942$		0			0
$943$	1.57862	+	2.73425i	0.0514069	+	0.0890393i
$944$		0			0
$945$	27.9372	+	45.5823i	0.908799	+	1.48279i
$946$		0			0
$947$	−13.9349	+	8.04534i	−0.452825	+	0.261438i	−0.709022	−	0.705186i	$-0.750863\pi$
$947$	−13.9349	+	8.04534i	−0.452825	+	0.261438i	0.256198	+	0.966624i	$0.417530\pi$
$948$		0			0
$949$	41.8261	−	72.4450i	1.35773	−	2.35166i
$950$		0			0
$951$	39.9217			1.29455
$952$		0			0
$953$	−15.4539			−0.500601			−0.250301	−	0.968168i	$-0.580529\pi$
$953$	−15.4539			−0.500601			−0.250301	+	0.968168i	$0.580529\pi$
$954$		0			0
$955$	27.3504	−	47.3722i	0.885037	−	1.53293i
$956$		0			0
$957$	−1.91554	+	1.10594i	−0.0619206	+	0.0357499i
$958$		0			0
$959$	−41.1061	−	22.3151i	−1.32739	−	0.720591i
$960$		0			0
$961$	−0.920625	−	1.59457i	−0.0296976	−	0.0514377i
$962$		0			0
$963$	−4.64610	−	2.68242i	−0.149718	−	0.0864399i
$964$		0			0
$965$			18.9431i			0.609801i
$966$		0			0
$967$		−	48.9546i		−	1.57427i	−0.616778	−	0.787137i	$-0.711562\pi$
$967$		−	48.9546i		−	1.57427i	0.616778	−	0.787137i	$-0.288438\pi$
$968$		0			0
$969$	5.04005	+	2.90987i	0.161910	+	0.0934786i
$970$		0			0
$971$	−7.89120	−	13.6680i	−0.253241	−	0.438626i	0.711176	−	0.703014i	$-0.248163\pi$
$971$	−7.89120	−	13.6680i	−0.253241	−	0.438626i	−0.964416	+	0.264389i	$0.914830\pi$
$972$		0			0
$973$	−0.150188	−	5.72017i	−0.00481481	−	0.183380i
$974$		0			0
$975$	−68.6467	+	39.6332i	−2.19845	+	1.26928i
$976$		0			0
$977$	−19.9132	+	34.4908i	−0.637081	+	1.10346i	0.348989	+	0.937127i	$0.386525\pi$
$977$	−19.9132	+	34.4908i	−0.637081	+	1.10346i	−0.986070	+	0.166330i	$0.946808\pi$
$978$		0			0
$979$	0.139100			0.00444566
$980$		0			0
$981$	−0.878646			−0.0280530
$982$		0			0
$983$	−17.3796	+	30.1024i	−0.554324	+	0.960117i	0.443632	+	0.896209i	$0.353690\pi$
$983$	−17.3796	+	30.1024i	−0.554324	+	0.960117i	−0.997956	+	0.0639080i	$0.979644\pi$
$984$		0			0
$985$	21.2092	−	12.2451i	0.675781	−	0.390162i
$986$		0			0
$987$	−1.44432	−	55.0093i	−0.0459732	−	1.75097i
$988$		0			0
$989$	−0.465794	−	0.806779i	−0.0148114	−	0.0256541i
$990$		0			0
$991$	5.69542	+	3.28825i	0.180921	+	0.104455i	0.587725	−	0.809061i	$-0.300024\pi$
$991$	5.69542	+	3.28825i	0.180921	+	0.104455i	−0.406804	+	0.913515i	$0.633357\pi$
$992$		0			0
$993$		−	33.0905i		−	1.05009i
$994$		0			0
$995$			75.8613i			2.40496i
$996$		0			0
$997$	31.3667	+	18.1095i	0.993392	+	0.573535i	0.906286	−	0.422664i	$-0.138905\pi$
$997$	31.3667	+	18.1095i	0.993392	+	0.573535i	0.0871054	+	0.996199i	$0.472238\pi$
$998$		0			0
$999$	8.52616	+	14.7677i	0.269756	+	0.467231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.p.c.255.6	yes	16
4.3	odd	2	inner	896.2.p.c.255.3	yes	16
7.5	odd	6	inner	896.2.p.c.383.3	yes	16
8.3	odd	2		896.2.p.a.255.6	yes	16
8.5	even	2		896.2.p.a.255.3	✓	16
28.19	even	6	inner	896.2.p.c.383.6	yes	16
56.5	odd	6		896.2.p.a.383.6	yes	16
56.19	even	6		896.2.p.a.383.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.p.a.255.3	✓	16	8.5	even	2
896.2.p.a.255.6	yes	16	8.3	odd	2
896.2.p.a.383.3	yes	16	56.19	even	6
896.2.p.a.383.6	yes	16	56.5	odd	6
896.2.p.c.255.3	yes	16	4.3	odd	2	inner
896.2.p.c.255.6	yes	16	1.1	even	1	trivial
896.2.p.c.383.3	yes	16	7.5	odd	6	inner
896.2.p.c.383.6	yes	16	28.19	even	6	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.779618 - 1.35034i) q^{3} +(3.14484 - 1.81567i) q^{5} +(0.0694427 + 2.64484i) q^{7} +(0.284392 + 0.492581i) q^{9} +O(q^{10})\)	\(q+(0.779618 - 1.35034i) q^{3} +(3.14484 - 1.81567i) q^{5} +(0.0694427 + 2.64484i) q^{7} +(0.284392 + 0.492581i) q^{9} +(0.170031 + 0.0981673i) q^{11} -6.20968i q^{13} -5.66213i q^{15} +(0.588057 + 0.339515i) q^{17} +(2.74836 + 4.76030i) q^{19} +(3.62557 + 1.96819i) q^{21} +(2.05460 - 1.18622i) q^{23} +(4.09335 - 7.08988i) q^{25} +5.56458 q^{27} -7.22524 q^{29} +(-2.86536 + 4.96296i) q^{31} +(0.265118 - 0.153066i) q^{33} +(5.02055 + 8.19151i) q^{35} +(1.53222 + 2.65388i) q^{37} +(-8.38516 - 4.84117i) q^{39} +1.33079i q^{41} -0.392669i q^{43} +(1.78873 + 1.03273i) q^{45} +(-6.66953 - 11.5520i) q^{47} +(-6.99036 + 0.367330i) q^{49} +(0.916920 - 0.529384i) q^{51} +(4.56112 - 7.90010i) q^{53} +0.712959 q^{55} +8.57068 q^{57} +(-4.72267 + 8.17990i) q^{59} +(-0.757458 + 0.437319i) q^{61} +(-1.28305 + 0.786377i) q^{63} +(-11.2747 - 19.5284i) q^{65} +(-9.42874 - 5.44368i) q^{67} -3.69921i q^{69} -8.18669i q^{71} +(11.6665 + 6.73564i) q^{73} +(-6.38249 - 11.0548i) q^{75} +(-0.247829 + 0.456521i) q^{77} +(-8.09255 + 4.67224i) q^{79} +(3.48507 - 6.03631i) q^{81} +0.334493 q^{83} +2.46579 q^{85} +(-5.63292 + 9.75651i) q^{87} +(0.613565 - 0.354242i) q^{89} +(16.4236 - 0.431217i) q^{91} +(4.46778 + 7.73842i) q^{93} +(17.2863 + 9.98025i) q^{95} +12.5145i q^{97} +0.111672i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} - 16 q^{9}+O(q^{10}) \) 16 * q + 12 * q^5 - 16 * q^9	\( 16 q + 12 q^{5} - 16 q^{9} - 12 q^{21} - 48 q^{29} - 48 q^{33} + 20 q^{37} - 24 q^{45} + 8 q^{49} + 12 q^{53} + 48 q^{57} + 60 q^{61} - 40 q^{65} + 48 q^{73} - 20 q^{77} - 8 q^{81} - 56 q^{85} - 48 q^{89} + 76 q^{93}+O(q^{100}) \) 16 * q + 12 * q^5 - 16 * q^9 - 12 * q^21 - 48 * q^29 - 48 * q^33 + 20 * q^37 - 24 * q^45 + 8 * q^49 + 12 * q^53 + 48 * q^57 + 60 * q^61 - 40 * q^65 + 48 * q^73 - 20 * q^77 - 8 * q^81 - 56 * q^85 - 48 * q^89 + 76 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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