LMFDB - Embedded newform 896.2.p.c.383.3

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			383.3
Root			$-1.29724 + 0.347596i$ of defining polynomial
Character	$\chi$	$=$	896.383
Dual form			896.2.p.c.255.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.779618 - 1.35034i) q^{3} +(3.14484 + 1.81567i) q^{5} +(-0.0694427 + 2.64484i) q^{7} +(0.284392 - 0.492581i) q^{9} +O(q^{10})$	\(q+(-0.779618 - 1.35034i) q^{3} +(3.14484 + 1.81567i) q^{5} +(-0.0694427 + 2.64484i) q^{7} +(0.284392 - 0.492581i) q^{9} +(-0.170031 + 0.0981673i) q^{11} +6.20968i q^{13} -5.66213i q^{15} +(0.588057 - 0.339515i) q^{17} +(-2.74836 + 4.76030i) q^{19} +(3.62557 - 1.96819i) q^{21} +(-2.05460 - 1.18622i) q^{23} +(4.09335 + 7.08988i) q^{25} -5.56458 q^{27} -7.22524 q^{29} +(2.86536 + 4.96296i) q^{31} +(0.265118 + 0.153066i) q^{33} +(-5.02055 + 8.19151i) q^{35} +(1.53222 - 2.65388i) q^{37} +(8.38516 - 4.84117i) q^{39} -1.33079i q^{41} -0.392669i q^{43} +(1.78873 - 1.03273i) q^{45} +(6.66953 - 11.5520i) q^{47} +(-6.99036 - 0.367330i) q^{49} +(-0.916920 - 0.529384i) q^{51} +(4.56112 + 7.90010i) q^{53} -0.712959 q^{55} +8.57068 q^{57} +(4.72267 + 8.17990i) q^{59} +(-0.757458 - 0.437319i) q^{61} +(1.28305 + 0.786377i) q^{63} +(-11.2747 + 19.5284i) q^{65} +(9.42874 - 5.44368i) q^{67} +3.69921i q^{69} -8.18669i q^{71} +(11.6665 - 6.73564i) q^{73} +(6.38249 - 11.0548i) q^{75} +(-0.247829 - 0.456521i) q^{77} +(8.09255 + 4.67224i) q^{79} +(3.48507 + 6.03631i) q^{81} -0.334493 q^{83} +2.46579 q^{85} +(5.63292 + 9.75651i) q^{87} +(0.613565 + 0.354242i) q^{89} +(-16.4236 - 0.431217i) q^{91} +(4.46778 - 7.73842i) q^{93} +(-17.2863 + 9.98025i) q^{95} -12.5145i q^{97} +0.111672i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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	$-0.315283\pi$
$3$	−0.779618	−	1.35034i	−0.450113	−	0.779618i	−0.998393	+	0.0566769i	$0.981950\pi$
$4$		0			0
$5$	3.14484	+	1.81567i	1.40642	+	0.811994i	0.995040	−	0.0994721i	$-0.0317154\pi$
$5$	3.14484	+	1.81567i	1.40642	+	0.811994i	0.411375	+	0.911466i	$0.365049\pi$
$6$		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	$-0.676090\pi$
$11$	−0.170031	+	0.0981673i	−0.0512662	+	0.0295986i	0.474148	+	0.880445i	$0.342756\pi$
$12$		0			0
$13$			6.20968i			1.72225i	0.508390	+	0.861127i	$0.330241\pi$
$13$			6.20968i			1.72225i	−0.508390	+	0.861127i	$0.669759\pi$
$14$		0			0
$15$		−	5.66213i		−	1.46196i
$16$		0			0
$17$	0.588057	−	0.339515i	0.142625	−	0.0823445i	−0.426990	−	0.904257i	$-0.640426\pi$
$17$	0.588057	−	0.339515i	0.142625	−	0.0823445i	0.569614	+	0.821912i	$0.307093\pi$
$18$		0			0
$19$	−2.74836	+	4.76030i	−0.630517	+	1.09209i	0.356930	+	0.934131i	$0.383824\pi$
$19$	−2.74836	+	4.76030i	−0.630517	+	1.09209i	−0.987446	+	0.157955i	$0.949510\pi$
$20$		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	$-0.412891\pi$
$23$	−2.05460	−	1.18622i	−0.428414	−	0.247345i	−0.698671	+	0.715443i	$0.746225\pi$
$24$		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	0.999856	+	0.0169819i	$0.00540575\pi$
$31$	2.86536	+	4.96296i	0.514635	+	0.891373i	−0.485221	+	0.874391i	$0.661261\pi$
$32$		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	−0.712152	−	0.702025i	$-0.752279\pi$
$37$	1.53222	−	2.65388i	0.251896	−	0.436296i	0.964048	+	0.265729i	$0.0856127\pi$
$38$		0			0
$39$	8.38516	−	4.84117i	1.34270	−	0.775208i
$40$		0			0
$41$		−	1.33079i		−	0.207835i	−0.994586	−	0.103917i	$-0.966862\pi$
$41$		−	1.33079i		−	0.207835i	0.994586	−	0.103917i	$-0.0331378\pi$
$42$		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	0.285997	−	0.958230i	$-0.407675\pi$
$47$	6.66953	−	11.5520i	0.972851	−	1.68503i	0.686853	−	0.726796i	$-0.258992\pi$
$48$		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	0.988245	+	0.152878i	$0.0488541\pi$
$53$	4.56112	+	7.90010i	0.626519	+	1.08516i	−0.361727	+	0.932284i	$0.617813\pi$
$54$		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	0.990413	+	0.138140i	$0.0441123\pi$
$59$	4.72267	+	8.17990i	0.614839	+	1.06493i	−0.375574	+	0.926792i	$0.622554\pi$
$60$		0			0
$61$	−0.757458	−	0.437319i	−0.0969826	−	0.0559929i	0.450724	−	0.892663i	$-0.351166\pi$
$61$	−0.757458	−	0.437319i	−0.0969826	−	0.0559929i	−0.547707	+	0.836670i	$0.684499\pi$
$62$		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	$-0.435076\pi$
$67$	9.42874	−	5.44368i	1.15190	−	0.665052i	0.949350	+	0.314220i	$0.101743\pi$
$68$		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	0.375113	−	0.926979i	$-0.377604\pi$
$73$	11.6665	−	6.73564i	1.36546	−	0.788347i	0.990344	+	0.138632i	$0.0442706\pi$
$74$		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	$-0.157149\pi$
$79$	8.09255	+	4.67224i	0.910484	+	0.525668i	0.0298968	+	0.999553i	$0.490482\pi$
$80$		0			0
$81$	3.48507	+	6.03631i	0.387230	+	0.670702i
$82$		0			0
$83$	−0.334493			−0.0367154			−0.0183577	−	0.999831i	$-0.505844\pi$
$83$	−0.334493			−0.0367154			−0.0183577	+	0.999831i	$0.505844\pi$
$84$		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	0.532166	−	0.846640i	$-0.321378\pi$
$89$	0.613565	+	0.354242i	0.0650378	+	0.0375496i	−0.467128	+	0.884189i	$0.654711\pi$
$90$		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	$-0.780866\pi$
$97$		−	12.5145i		−	1.27065i	0.772244	−	0.635326i	$-0.219134\pi$
$98$		0			0
$99$			0.111672i			0.0112234i
$100$		0			0
$101$	7.90031	−	4.56125i	0.786111	−	0.453861i	−0.0524809	−	0.998622i	$-0.516713\pi$
$101$	7.90031	−	4.56125i	0.786111	−	0.453861i	0.838591	+	0.544761i	$0.183380\pi$
$102$		0			0
$103$	−1.57675	+	2.73101i	−0.155362	+	0.269094i	−0.933191	−	0.359382i	$-0.882988\pi$
$103$	−1.57675	+	2.73101i	−0.155362	+	0.269094i	0.777829	+	0.628476i	$0.216321\pi$
$104$		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	$-0.182644\pi$
$107$	8.16848	+	4.71607i	0.789677	+	0.455920i	−0.0501720	+	0.998741i	$0.515977\pi$
$108$		0			0
$109$	−0.772391	−	1.33782i	−0.0739816	−	0.128140i	0.826661	−	0.562700i	$-0.190237\pi$
$109$	−0.772391	−	1.33782i	−0.0739816	−	0.128140i	−0.900643	+	0.434560i	$0.856904\pi$
$110$		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	−0.268220	−	0.963358i	$-0.586435\pi$
$131$	8.01395	−	13.8806i	0.700182	−	1.21275i	0.968402	−	0.249394i	$-0.0802313\pi$
$132$		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	−0.945283	−	0.326251i	$-0.894215\pi$
$137$	−8.83919	−	15.3099i	−0.755183	−	1.30802i	0.190100	−	0.981765i	$-0.439119\pi$
$138$		0			0
$139$	2.16276			0.183443			0.0917216	−	0.995785i	$-0.470763\pi$
$139$	2.16276			0.183443			0.0917216	+	0.995785i	$0.470763\pi$
$140$		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	−0.677492	−	0.735530i	$-0.736933\pi$
$149$	3.64050	−	6.30553i	0.298241	−	0.516569i	0.975734	+	0.218961i	$0.0702667\pi$
$150$		0			0
$151$	1.45615	−	0.840709i	0.118500	−	0.0684159i	−0.439579	−	0.898204i	$-0.644872\pi$
$151$	1.45615	−	0.840709i	0.118500	−	0.0684159i	0.558078	+	0.829788i	$0.311539\pi$
$152$		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	−0.961025	−	0.276461i	$-0.910838\pi$
$157$	−15.0625	+	8.69631i	−1.20211	+	0.694041i	−0.241090	+	0.970503i	$0.577505\pi$
$158$		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	−0.999995	−	0.00317884i	$-0.998988\pi$
$163$	−19.1858	−	11.0769i	−1.50275	−	0.867610i	−0.502750	−	0.864432i	$-0.667679\pi$
$164$		0			0
$165$	0.555836	+	0.962736i	0.0432718	+	0.0749489i
$166$		0			0
$167$	−3.93748			−0.304691			−0.152346	−	0.988327i	$-0.548683\pi$
$167$	−3.93748			−0.304691			−0.152346	+	0.988327i	$0.548683\pi$
$168$		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	0.422347	−	0.906434i	$-0.361206\pi$
$173$	−1.99234	−	1.15028i	−0.151475	−	0.0874540i	−0.573822	+	0.818980i	$0.694540\pi$
$174$		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	$-0.765762\pi$
$179$	−7.09823	+	4.09817i	−0.530547	+	0.306311i	0.210692	+	0.977552i	$0.432428\pi$
$180$		0			0
$181$		−	11.1837i		−	0.831277i	−0.909530	−	0.415638i	$-0.863558\pi$
$181$		−	11.1837i		−	0.831277i	0.909530	−	0.415638i	$-0.136442\pi$
$182$		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	$-0.516795\pi$
$191$	−13.0454	−	7.53174i	−0.943929	−	0.544978i	−0.891190	+	0.453631i	$0.850129\pi$
$192$		0			0
$193$	−2.60828	−	4.51767i	−0.187748	−	0.325189i	0.756751	−	0.653703i	$-0.226785\pi$
$193$	−2.60828	−	4.51767i	−0.187748	−	0.325189i	−0.944499	+	0.328514i	$0.893452\pi$
$194$		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	0.952291	+	0.305192i	$0.0987208\pi$
$199$	10.4453	+	18.0918i	0.740450	+	1.28250i	−0.211841	+	0.977304i	$0.567946\pi$
$200$		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	$-0.218709\pi$
$223$	23.0894			1.54618			0.773091	+	0.634295i	$0.218709\pi$
$224$		0			0
$225$	4.65645			0.310430
$226$		0			0
$227$	3.45575	+	5.98553i	0.229366	+	0.397274i	0.957620	−	0.288033i	$-0.0930014\pi$
$227$	3.45575	+	5.98553i	0.229366	+	0.397274i	−0.728254	+	0.685307i	$0.759668\pi$
$228$		0			0
$229$	14.4383	+	8.33596i	0.954110	+	0.550856i	0.894355	−	0.447358i	$-0.147635\pi$
$229$	14.4383	+	8.33596i	0.954110	+	0.550856i	0.0597546	+	0.998213i	$0.480968\pi$
$230$		0			0
$231$	−0.423246	+	0.690566i	−0.0278475	+	0.0454359i
$232$		0			0
$233$	8.29931	−	14.3748i	0.543706	−	0.941726i	−0.454981	−	0.890501i	$-0.650354\pi$
$233$	8.29931	−	14.3748i	0.543706	−	0.941726i	0.998687	−	0.0512251i	$-0.0163126\pi$
$234$		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	−0.168675	−	0.985672i	$-0.553949\pi$
$241$	9.32389	−	5.38315i	0.600604	−	0.346759i	0.769279	+	0.638913i	$0.220615\pi$
$242$		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	$-0.516297\pi$
$251$	−1.62153			−0.102350			−0.0511749	+	0.998690i	$0.516297\pi$
$252$		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	0.738373	−	0.674392i	$-0.235594\pi$
$257$	8.39265	+	4.84550i	0.523519	+	0.302254i	−0.214854	+	0.976646i	$0.568928\pi$
$258$		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	$-0.642604\pi$
$263$	2.12137	−	1.22477i	0.130809	−	0.0755227i	0.563977	+	0.825791i	$0.309271\pi$
$264$		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	−0.420814	−	0.907147i	$-0.638255\pi$
$269$	2.53222	−	1.46198i	0.154392	−	0.0891384i	0.575206	+	0.818009i	$0.304922\pi$
$270$		0			0
$271$	−5.40261	+	9.35760i	−0.328185	+	0.568433i	−0.982152	−	0.188090i	$-0.939770\pi$
$271$	−5.40261	+	9.35760i	−0.328185	+	0.568433i	0.653967	+	0.756523i	$0.273104\pi$
$272$		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	0.583443	−	0.812154i	$-0.301705\pi$
$277$	−6.85080	−	11.8659i	−0.411625	−	0.712955i	−0.995068	+	0.0991991i	$0.968372\pi$
$278$		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	$-0.0773690\pi$
$283$	4.65770	+	8.06737i	0.276871	+	0.479555i	−0.693734	+	0.720231i	$0.744036\pi$
$284$		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	$-0.850161\pi$
$293$		−	15.5267i		−	0.907079i	0.891236	−	0.453539i	$-0.149839\pi$
$294$		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	$-0.414386\pi$
$307$	9.31202			0.531465			0.265732	+	0.964047i	$0.414386\pi$
$308$		0			0
$309$	4.91704			0.279721
$310$		0			0
$311$	5.38539	+	9.32776i	0.305377	+	0.528929i	0.977345	−	0.211651i	$-0.0678841\pi$
$311$	5.38539	+	9.32776i	0.305377	+	0.528929i	−0.671968	+	0.740580i	$0.734551\pi$
$312$		0			0
$313$	−22.8292	−	13.1804i	−1.29038	−	0.745001i	−0.311659	−	0.950194i	$-0.600885\pi$
$313$	−22.8292	−	13.1804i	−1.29038	−	0.745001i	−0.978722	+	0.205193i	$0.934218\pi$
$314$		0			0
$315$	2.60718	+	4.80263i	0.146898	+	0.270597i
$316$		0			0
$317$	12.8017	−	22.1732i	0.719014	−	1.24537i	−0.242377	−	0.970182i	$-0.577927\pi$
$317$	12.8017	−	22.1732i	0.719014	−	1.24537i	0.961391	−	0.275187i	$-0.0887396\pi$
$318$		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	$-0.531548\pi$
$331$	−18.3790	−	10.6111i	−1.01020	−	0.583240i	−0.911250	+	0.411853i	$0.864882\pi$
$332$		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	$-0.916256\pi$
$347$	−22.7850	+	13.1549i	−1.22316	+	0.706194i	−0.257573	+	0.966259i	$0.582923\pi$
$348$		0			0
$349$			0.985162i			0.0527345i	0.999652	+	0.0263673i	$0.00839393\pi$
$349$			0.985162i			0.0527345i	−0.999652	+	0.0263673i	$0.991606\pi$
$350$		0			0
$351$		−	34.5542i		−	1.84437i
$352$		0			0
$353$	3.72262	−	2.14925i	0.198135	−	0.114393i	−0.397650	−	0.917537i	$-0.630174\pi$
$353$	3.72262	−	2.14925i	0.198135	−	0.114393i	0.595785	+	0.803144i	$0.296841\pi$
$354$		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	$-0.141528\pi$
$359$	18.5999	+	10.7387i	0.981665	+	0.566764i	0.0788923	+	0.996883i	$0.474862\pi$
$360$		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	−0.779876	−	0.625934i	$-0.784718\pi$
$367$	−17.8548	−	30.9254i	−0.932013	−	1.61429i	−0.152137	−	0.988359i	$-0.548615\pi$
$368$		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	0.175317	+	0.984512i	$0.443905\pi$
$373$	−14.7737	+	25.5888i	−0.764954	+	1.32494i	−0.940271	+	0.340427i	$0.889429\pi$
$374$		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	0.00760054	−	0.999971i	$-0.497581\pi$
$383$	17.0223	−	29.4835i	0.869801	−	1.50654i	0.862200	−	0.506568i	$-0.169086\pi$
$384$		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	0.991092	−	0.133176i	$-0.0425175\pi$
$389$	7.49896	+	12.9886i	0.380212	+	0.658547i	−0.610880	+	0.791723i	$0.709184\pi$
$390$		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	0.435775	−	0.900056i	$-0.356474\pi$
$397$	−2.50671	−	1.44725i	−0.125808	−	0.0726355i	−0.561583	+	0.827420i	$0.689808\pi$
$398$		0			0
$399$	−0.595171	+	22.6681i	−0.0297958	+	1.13482i
$400$		0			0
$401$	−10.5342	+	18.2458i	−0.526052	+	0.911149i	0.473487	+	0.880801i	$0.342995\pi$
$401$	−10.5342	+	18.2458i	−0.526052	+	0.911149i	−0.999539	+	0.0303486i	$0.990338\pi$
$402$		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	−0.898305	−	0.439373i	$-0.855201\pi$
$409$	−19.5553	+	11.2903i	−0.966949	+	0.558269i	−0.0686446	+	0.997641i	$0.521867\pi$
$410$		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	$-0.607432\pi$
$419$	−13.5564			−0.662272			−0.331136	+	0.943583i	$0.607432\pi$
$420$		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	$-0.699936\pi$
$431$	−3.75150	+	2.16593i	−0.180703	+	0.104329i	0.406920	+	0.913464i	$0.366603\pi$
$432$		0			0
$433$			20.8029i			0.999725i	0.866105	+	0.499862i	$0.166616\pi$
$433$			20.8029i			0.999725i	−0.866105	+	0.499862i	$0.833384\pi$
$434$		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	$-0.755438\pi$
$439$	5.07636	−	8.79252i	0.242282	−	0.419644i	0.961364	+	0.275281i	$0.0887709\pi$
$440$		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	$-0.580397\pi$
$443$	−25.5390	−	14.7450i	−1.21340	−	0.700555i	−0.963498	+	0.267717i	$0.913731\pi$
$444$		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	−0.951006	−	0.309172i	$-0.899948\pi$
$457$	−4.44123	+	7.69244i	−0.207752	+	0.359837i	0.743254	+	0.669009i	$0.233281\pi$
$458$		0			0
$459$	−3.27229	+	1.88926i	−0.152737	+	0.0881829i
$460$		0			0
$461$			31.1184i			1.44933i	0.689102	+	0.724665i	$0.258005\pi$
$461$			31.1184i			1.44933i	−0.689102	+	0.724665i	$0.741995\pi$
$462$		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	−0.0434446	−	0.999056i	$-0.513833\pi$
$467$	18.2279	−	31.5716i	0.843485	−	1.46096i	0.886930	−	0.461904i	$-0.152833\pi$
$468$		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	$-0.0719596\pi$
$479$	6.41613	+	11.1131i	0.293161	+	0.507769i	−0.681395	+	0.731916i	$0.738626\pi$
$480$		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	$-0.392898\pi$
$487$	28.9688	−	16.7251i	1.31270	−	0.757889i	0.982543	+	0.186037i	$0.0595644\pi$
$488$		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	$-0.352875\pi$
$499$	−2.37388	−	1.37056i	−0.106269	−	0.0613546i	−0.552193	+	0.833717i	$0.686209\pi$
$500$		0			0
$501$	3.06973	+	5.31693i	0.137145	+	0.237543i
$502$		0			0
$503$	−17.5215			−0.781244			−0.390622	−	0.920551i	$-0.627740\pi$
$503$	−17.5215			−0.781244			−0.390622	+	0.920551i	$0.627740\pi$
$504$		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	0.866366	−	0.499409i	$-0.166449\pi$
$509$	19.5615	+	11.2938i	0.867049	+	0.500591i	0.000682339		1.00000i	$0.499783\pi$
$510$		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	−0.706306	−	0.707906i	$-0.749640\pi$
$521$	−10.1891	+	5.88270i	−0.446394	+	0.257726i	0.259912	+	0.965632i	$0.416306\pi$
$522$		0			0
$523$	−4.51991	+	7.82871i	−0.197642	+	0.342326i	−0.947763	−	0.318974i	$-0.896662\pi$
$523$	−4.51991	+	7.82871i	−0.197642	+	0.342326i	0.750122	+	0.661300i	$0.229995\pi$
$524$		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	−0.516240	−	0.856444i	$-0.672669\pi$
$541$	11.2478	−	19.4818i	0.483582	−	0.837589i	0.999822	+	0.0188553i	$0.00600218\pi$
$542$		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	0.919992	−	0.391937i	$-0.128195\pi$
$557$	2.84552	+	4.92858i	0.120568	+	0.208831i	−0.799424	+	0.600768i	$0.794862\pi$
$558$		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	$-0.291475\pi$
$563$	−9.06697	−	15.7045i	−0.382127	−	0.661864i	−0.991366	+	0.131123i	$0.958142\pi$
$564$		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	0.0899815	+	0.995943i	$0.471319\pi$
$569$	−19.5009	+	33.7766i	−0.817522	+	1.41599i	−0.907503	+	0.420045i	$0.862014\pi$
$570$		0			0
$571$	28.7914	−	16.6227i	1.20488	−	0.695640i	0.243246	−	0.969965i	$-0.421788\pi$
$571$	28.7914	−	16.6227i	1.20488	−	0.695640i	0.961637	+	0.274325i	$0.0884544\pi$
$572$		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	−0.612163	−	0.790731i	$-0.709701\pi$
$577$	−5.60770	+	3.23761i	−0.233452	+	0.134783i	0.378712	+	0.925515i	$0.376367\pi$
$578$		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	$-0.502183\pi$
$587$	−0.332307			−0.0137158			−0.00685788	+	0.999976i	$0.502183\pi$
$588$		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	0.917319	−	0.398154i	$-0.130349\pi$
$593$	25.1105	+	14.4976i	1.03117	+	0.595344i	0.113848	+	0.993498i	$0.463682\pi$
$594$		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	$-0.537263\pi$
$599$	16.7626	−	9.67791i	0.684903	−	0.395429i	0.801700	+	0.597727i	$0.203929\pi$
$600$		0			0
$601$		−	43.3124i		−	1.76675i	−0.468669	−	0.883374i	$-0.655266\pi$
$601$		−	43.3124i		−	1.76675i	0.468669	−	0.883374i	$-0.344734\pi$
$602$		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	0.384900	+	0.922958i	$0.374236\pi$
$607$	−14.9513	+	25.8964i	−0.606855	+	1.05110i	−0.991755	+	0.128146i	$0.959097\pi$
$608$		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	0.883617	−	0.468211i	$-0.155101\pi$
$613$	0.899382	+	1.55778i	0.0363257	+	0.0629180i	−0.847291	+	0.531129i	$0.821768\pi$
$614$		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	$-0.132269\pi$
$619$	2.68339	+	4.64777i	0.107855	+	0.186810i	−0.807046	+	0.590488i	$0.798935\pi$
$620$		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	0.993756	+	0.111571i	$0.0355884\pi$
$641$	15.0263	+	26.0263i	0.593502	+	1.02798i	−0.400255	+	0.916404i	$0.631078\pi$
$642$		0			0
$643$	−3.33057			−0.131345			−0.0656724	−	0.997841i	$-0.520919\pi$
$643$	−3.33057			−0.131345			−0.0656724	+	0.997841i	$0.520919\pi$
$644$		0			0
$645$	−2.22334			−0.0875441
$646$		0			0
$647$	−7.19695	−	12.4655i	−0.282941	−	0.490069i	0.689167	−	0.724603i	$-0.257977\pi$
$647$	−7.19695	−	12.4655i	−0.282941	−	0.490069i	−0.972108	+	0.234534i	$0.924644\pi$
$648$		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	0.488968	+	0.872302i	$0.337373\pi$
$653$	−13.0568	+	22.6150i	−0.510951	+	0.884994i	−0.999919	+	0.0126921i	$0.995960\pi$
$654$		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	−0.631957	−	0.775003i	$-0.717748\pi$
$661$	−7.11555	+	4.10816i	−0.276763	+	0.159789i	0.355194	+	0.934793i	$0.384415\pi$
$662$		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	0.578286	−	0.815834i	$-0.303722\pi$
$677$	4.18639	+	2.41702i	0.160896	+	0.0928935i	−0.417390	+	0.908727i	$0.637055\pi$
$678$		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	$-0.531990\pi$
$683$	18.5857	−	10.7304i	0.711160	−	0.410589i	0.811490	+	0.584366i	$0.198657\pi$
$684$		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	$-0.696501\pi$
$691$	10.9551	−	18.9749i	0.416753	−	0.721837i	0.995611	+	0.0935912i	$0.0298347\pi$
$692$		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	−0.972856	−	0.231409i	$-0.925666\pi$
$709$	−7.61592	+	13.1912i	−0.286022	+	0.495405i	0.686835	+	0.726814i	$0.259000\pi$
$710$		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	$-0.831345\pi$
$719$	0.167533	−	0.290176i	0.00624794	−	0.0108217i	0.869132	+	0.494579i	$0.164678\pi$
$720$		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	$-0.716783\pi$
$727$	−33.9519			−1.25921			−0.629604	+	0.776916i	$0.716783\pi$
$728$		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	0.474041	−	0.880503i	$-0.342795\pi$
$733$	−1.39369	−	0.804648i	−0.0514772	−	0.0297204i	−0.525518	+	0.850783i	$0.676128\pi$
$734$		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	$-0.782825\pi$
$739$	−16.8035	+	9.70153i	−0.618128	+	0.356876i	0.158012	+	0.987437i	$0.449492\pi$
$740$		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	$-0.439522\pi$
$751$	−15.5426	−	8.97353i	−0.567158	−	0.327449i	−0.756013	+	0.654556i	$0.772856\pi$
$752$		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	0.823959	−	0.566649i	$-0.191761\pi$
$761$	20.5574	+	11.8688i	0.745206	+	0.430245i	−0.0787532	+	0.996894i	$0.525094\pi$
$762$		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	$-0.966006\pi$
$769$		−	5.91182i		−	0.213186i	0.994303	−	0.106593i	$-0.0339941\pi$
$770$		0			0
$771$		−	15.1106i		−	0.544193i
$772$		0			0
$773$	23.9341	−	13.8184i	0.860850	−	0.497012i	−0.00344660	−	0.999994i	$-0.501097\pi$
$773$	23.9341	−	13.8184i	0.860850	−	0.497012i	0.864297	+	0.502982i	$0.167764\pi$
$774$		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	0.614413	+	0.788985i	$0.289393\pi$
$787$	27.7867	+	48.1279i	0.990487	+	1.71557i	0.376074	+	0.926590i	$0.377274\pi$
$788$		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	$-0.946985\pi$
$797$		−	9.36041i		−	0.331563i	0.986163	−	0.165781i	$-0.0530146\pi$
$798$		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	0.947981	−	0.318326i	$-0.103121\pi$
$809$	5.64057	+	9.76976i	0.198312	+	0.343487i	−0.749669	+	0.661813i	$0.769787\pi$
$810$		0			0
$811$	−20.7846			−0.729846			−0.364923	−	0.931038i	$-0.618905\pi$
$811$	−20.7846			−0.729846			−0.364923	+	0.931038i	$0.618905\pi$
$812$		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	−0.974057	−	0.226304i	$-0.927336\pi$
$821$	−8.33928	+	14.4441i	−0.291043	+	0.504101i	0.683014	+	0.730406i	$0.260669\pi$
$822$		0			0
$823$	−46.6810	+	26.9513i	−1.62720	+	0.939464i	−0.642275	+	0.766474i	$0.722009\pi$
$823$	−46.6810	+	26.9513i	−1.62720	+	0.939464i	−0.984924	+	0.172989i	$0.944657\pi$
$824$		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	−0.720319	−	0.693643i	$-0.756005\pi$
$829$	−13.8136	+	7.97529i	−0.479766	+	0.276993i	0.240553	+	0.970636i	$0.422671\pi$
$830$		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	$-0.618313\pi$
$839$	−21.0401			−0.726385			−0.363193	+	0.931714i	$0.618313\pi$
$840$		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	$-0.949189\pi$
$853$		−	9.28475i		−	0.317904i	0.987286	−	0.158952i	$-0.0508115\pi$
$854$		0			0
$855$			11.3532i			0.388271i
$856$		0			0
$857$	28.9820	−	16.7328i	0.990007	−	0.571581i	0.0847304	−	0.996404i	$-0.472997\pi$
$857$	28.9820	−	16.7328i	0.990007	−	0.571581i	0.905276	+	0.424823i	$0.139664\pi$
$858$		0			0
$859$	10.7118	−	18.5534i	0.365481	−	0.633032i	−0.623372	−	0.781925i	$-0.714238\pi$
$859$	10.7118	−	18.5534i	0.365481	−	0.633032i	0.988853	+	0.148893i	$0.0475711\pi$
$860$		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	$-0.205519\pi$
$863$	19.8867	+	11.4816i	0.676950	+	0.390837i	−0.121755	+	0.992560i	$0.538852\pi$
$864$		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	0.0686157	+	0.997643i	$0.478142\pi$
$877$	−24.5702	+	42.5568i	−0.829676	+	1.43704i	−0.898292	+	0.439399i	$0.855192\pi$
$878$		0			0
$879$	−20.9663	+	12.1049i	−0.707175	+	0.408288i
$880$		0			0
$881$			5.91577i			0.199307i	0.995022	+	0.0996537i	$0.0317735\pi$
$881$			5.91577i			0.199307i	−0.995022	+	0.0996537i	$0.968226\pi$
$882$		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	$-0.992587\pi$
$887$	−14.2866	+	24.7451i	−0.479697	+	0.830859i	0.520032	+	0.854147i	$0.325920\pi$
$888$		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	$-0.479771\pi$
$907$	28.8980	−	16.6842i	0.959541	−	0.553991i	0.896032	+	0.443990i	$0.146437\pi$
$908$		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	$-0.425367\pi$
$919$	−14.9708	−	8.64341i	−0.493842	−	0.285120i	−0.726167	+	0.687518i	$0.758700\pi$
$920$		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	0.0667478	−	0.997770i	$-0.478738\pi$
$929$	−23.2855	−	13.4439i	−0.763972	−	0.441080i	−0.830720	+	0.556690i	$0.812071\pi$
$930$		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	$-0.926686\pi$
$937$		−	13.9762i		−	0.456582i	0.973593	−	0.228291i	$-0.0733138\pi$
$938$		0			0
$939$			41.1028i			1.34134i
$940$		0			0
$941$	−6.44074	+	3.71856i	−0.209962	+	0.121222i	−0.601294	−	0.799028i	$-0.705348\pi$
$941$	−6.44074	+	3.71856i	−0.209962	+	0.121222i	0.391332	+	0.920250i	$0.372015\pi$
$942$		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	$-0.249137\pi$
$947$	13.9349	+	8.04534i	0.452825	+	0.261438i	−0.256198	+	0.966624i	$0.582470\pi$
$948$		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	$-0.751837\pi$
$971$	7.89120	−	13.6680i	0.253241	−	0.438626i	0.964416	+	0.264389i	$0.0851702\pi$
$972$		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	−0.986070	−	0.166330i	$-0.946808\pi$
$977$	−19.9132	−	34.4908i	−0.637081	−	1.10346i	0.348989	−	0.937127i	$-0.386525\pi$
$978$		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	0.997956	+	0.0639080i	$0.0203564\pi$
$983$	17.3796	+	30.1024i	0.554324	+	0.960117i	−0.443632	+	0.896209i	$0.646310\pi$
$984$		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	$-0.699976\pi$
$991$	−5.69542	+	3.28825i	−0.180921	+	0.104455i	0.406804	+	0.913515i	$0.366643\pi$
$992$		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	0.0871054	−	0.996199i	$-0.472238\pi$
$997$	31.3667	−	18.1095i	0.993392	−	0.573535i	0.906286	+	0.422664i	$0.138905\pi$
$998$		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.383.3	yes	16
4.3	odd	2	inner	896.2.p.c.383.6	yes	16
7.3	odd	6	inner	896.2.p.c.255.6	yes	16
8.3	odd	2		896.2.p.a.383.3	yes	16
8.5	even	2		896.2.p.a.383.6	yes	16
28.3	even	6	inner	896.2.p.c.255.3	yes	16
56.3	even	6		896.2.p.a.255.6	yes	16
56.45	odd	6		896.2.p.a.255.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.p.a.255.3	✓	16	56.45	odd	6
896.2.p.a.255.6	yes	16	56.3	even	6
896.2.p.a.383.3	yes	16	8.3	odd	2
896.2.p.a.383.6	yes	16	8.5	even	2
896.2.p.c.255.3	yes	16	28.3	even	6	inner
896.2.p.c.255.6	yes	16	7.3	odd	6	inner
896.2.p.c.383.3	yes	16	1.1	even	1	trivial
896.2.p.c.383.6	yes	16	4.3	odd	2	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

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