LMFDB - Embedded newform 864.2.w.a.323.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(107,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			323.4
Character	$\chi$	$=$	864.323
Dual form			864.2.w.a.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36834 - 0.357292i) q^{2} +(1.74468 + 0.977791i) q^{4} +(0.202568 - 0.0839066i) q^{5} +(-0.0119413 - 0.0119413i) q^{7} +(-2.03796 - 1.96131i) q^{8} +O(q^{10})$	\(q+(-1.36834 - 0.357292i) q^{2} +(1.74468 + 0.977791i) q^{4} +(0.202568 - 0.0839066i) q^{5} +(-0.0119413 - 0.0119413i) q^{7} +(-2.03796 - 1.96131i) q^{8} +(-0.307161 + 0.0424363i) q^{10} +(-3.46699 + 1.43608i) q^{11} +(1.44858 - 3.49717i) q^{13} +(0.0120732 + 0.0206062i) q^{14} +(2.08785 + 3.41187i) q^{16} -1.93975 q^{17} +(-2.32957 - 0.964939i) q^{19} +(0.435461 + 0.0516790i) q^{20} +(5.25711 - 0.726304i) q^{22} +(-4.79172 - 4.79172i) q^{23} +(-3.50154 + 3.50154i) q^{25} +(-3.23165 + 4.26774i) q^{26} +(-0.00915771 - 0.0325099i) q^{28} +(1.79276 - 4.32810i) q^{29} +0.213195i q^{31} +(-1.63784 - 5.41456i) q^{32} +(2.65423 + 0.693057i) q^{34} +(-0.00342088 - 0.00141698i) q^{35} +(1.04659 + 2.52670i) q^{37} +(2.84287 + 2.15270i) q^{38} +(-0.577392 - 0.226301i) q^{40} +(2.21601 - 2.21601i) q^{41} +(-1.38417 - 3.34169i) q^{43} +(-7.45299 - 0.884495i) q^{44} +(4.84464 + 8.26873i) q^{46} +2.42072i q^{47} -6.99971i q^{49} +(6.04235 - 3.54021i) q^{50} +(5.94681 - 4.68506i) q^{52} +(-1.24746 - 3.01163i) q^{53} +(-0.581807 + 0.581807i) q^{55} +(0.000915288 + 0.0477564i) q^{56} +(-3.99949 + 5.28175i) q^{58} +(1.49224 + 3.60257i) q^{59} +(-3.46424 - 1.43494i) q^{61} +(0.0761730 - 0.291723i) q^{62} +(0.306539 + 7.99412i) q^{64} -0.829962i q^{65} +(3.85824 - 9.31462i) q^{67} +(-3.38425 - 1.89667i) q^{68} +(0.00417464 + 0.00316115i) q^{70} +(-8.45626 + 8.45626i) q^{71} +(-11.0555 - 11.0555i) q^{73} +(-0.529321 - 3.83131i) q^{74} +(-3.12085 - 3.96135i) q^{76} +(0.0585490 + 0.0242518i) q^{77} -15.3461 q^{79} +(0.709211 + 0.515953i) q^{80} +(-3.82400 + 2.24048i) q^{82} +(1.25116 - 3.02056i) q^{83} +(-0.392932 + 0.162758i) q^{85} +(0.700054 + 5.06711i) q^{86} +(9.88217 + 3.87318i) q^{88} +(-1.44269 - 1.44269i) q^{89} +(-0.0590587 + 0.0244629i) q^{91} +(-3.67474 - 13.0453i) q^{92} +(0.864905 - 3.31236i) q^{94} -0.552862 q^{95} -11.8857 q^{97} +(-2.50094 + 9.57796i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) $ 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.36834	−	0.357292i	−0.967559	−	0.252644i
$2$	−1.36834	−	0.357292i	−0.967559	−	0.252644i
$3$		0			0
$3$		0			0
$4$	1.74468	+	0.977791i	0.872342	+	0.488896i
$5$	0.202568	−	0.0839066i	0.0905913	−	0.0375242i	−0.336928	−	0.941531i	$-0.609388\pi$
$5$	0.202568	−	0.0839066i	0.0905913	−	0.0375242i	0.427519	+	0.904006i	$0.359388\pi$
$6$		0			0
$7$	−0.0119413	−	0.0119413i	−0.00451339	−	0.00451339i	0.704846	−	0.709360i	$-0.251016\pi$
$7$	−0.0119413	−	0.0119413i	−0.00451339	−	0.00451339i	−0.709360	+	0.704846i	$0.751016\pi$
$8$	−2.03796	−	1.96131i	−0.720527	−	0.693427i
$9$		0			0
$10$	−0.307161	+	0.0424363i	−0.0971327	+	0.0134195i
$11$	−3.46699	+	1.43608i	−1.04534	+	0.432993i	−0.838225	−	0.545324i	$-0.816407\pi$
$11$	−3.46699	+	1.43608i	−1.04534	+	0.432993i	−0.207112	+	0.978317i	$0.566407\pi$
$12$		0			0
$13$	1.44858	−	3.49717i	0.401763	−	0.969941i	−0.585475	−	0.810690i	$-0.699092\pi$
$13$	1.44858	−	3.49717i	0.401763	−	0.969941i	0.987238	−	0.159251i	$-0.0509079\pi$
$14$	0.0120732	+	0.0206062i	0.00322669	+	0.00550725i
$15$		0			0
$16$	2.08785	+	3.41187i	0.521962	+	0.852969i
$17$	−1.93975			−0.470458			−0.235229	−	0.971940i	$-0.575584\pi$
$17$	−1.93975			−0.470458			−0.235229	+	0.971940i	$0.575584\pi$
$18$		0			0
$19$	−2.32957	−	0.964939i	−0.534440	−	0.221372i	0.0991068	−	0.995077i	$-0.468401\pi$
$19$	−2.32957	−	0.964939i	−0.534440	−	0.221372i	−0.633546	+	0.773705i	$0.718401\pi$
$20$	0.435461	+	0.0516790i	0.0973720	+	0.0115558i
$21$		0			0
$22$	5.25711	−	0.726304i	1.12082	−	0.154849i
$23$	−4.79172	−	4.79172i	−0.999143	−	0.999143i	0.000856866	−	1.00000i	$-0.499727\pi$
$23$	−4.79172	−	4.79172i	−0.999143	−	0.999143i	−1.00000		0.000856866i	$0.999727\pi$
$24$		0			0
$25$	−3.50154	+	3.50154i	−0.700308	+	0.700308i
$26$	−3.23165	+	4.26774i	−0.633779	+	0.836973i
$27$		0			0
$28$	−0.00915771	−	0.0325099i	−0.00173064	−	0.00614380i
$29$	1.79276	−	4.32810i	0.332906	−	0.803707i	−0.665453	−	0.746440i	$-0.731761\pi$
$29$	1.79276	−	4.32810i	0.332906	−	0.803707i	0.998359	−	0.0572669i	$-0.0182386\pi$
$30$		0			0
$31$			0.213195i			0.0382910i	0.999817	+	0.0191455i	$0.00609458\pi$
$31$			0.213195i			0.0382910i	−0.999817	+	0.0191455i	$0.993905\pi$
$32$	−1.63784	−	5.41456i	−0.289532	−	0.957168i
$33$		0			0
$34$	2.65423	+	0.693057i	0.455196	+	0.118858i
$35$	−0.00342088	−	0.00141698i	−0.000578235	−	0.000239513i
$36$		0			0
$37$	1.04659	+	2.52670i	0.172059	+	0.415386i	0.986261	−	0.165195i	$-0.0528253\pi$
$37$	1.04659	+	2.52670i	0.172059	+	0.415386i	−0.814202	+	0.580581i	$0.802825\pi$
$38$	2.84287	+	2.15270i	0.461174	+	0.349214i
$39$		0			0
$40$	−0.577392	−	0.226301i	−0.0912937	−	0.0357813i
$41$	2.21601	−	2.21601i	0.346082	−	0.346082i	−0.512566	−	0.858648i	$-0.671305\pi$
$41$	2.21601	−	2.21601i	0.346082	−	0.346082i	0.858648	+	0.512566i	$0.171305\pi$
$42$		0			0
$43$	−1.38417	−	3.34169i	−0.211085	−	0.509603i	0.782506	−	0.622643i	$-0.213941\pi$
$43$	−1.38417	−	3.34169i	−0.211085	−	0.509603i	−0.993590	+	0.113040i	$0.963941\pi$
$44$	−7.45299	−	0.884495i	−1.12358	−	0.133343i
$45$		0			0
$46$	4.84464	+	8.26873i	0.714303	+	1.21916i
$47$			2.42072i			0.353099i	0.984292	+	0.176549i	$0.0564935\pi$
$47$			2.42072i			0.353099i	−0.984292	+	0.176549i	$0.943506\pi$
$48$		0			0
$49$		−	6.99971i		−	0.999959i
$50$	6.04235	−	3.54021i	0.854518	−	0.500661i
$51$		0			0
$52$	5.94681	−	4.68506i	0.824675	−	0.649701i
$53$	−1.24746	−	3.01163i	−0.171352	−	0.413679i	0.814752	−	0.579809i	$-0.196873\pi$
$53$	−1.24746	−	3.01163i	−0.171352	−	0.413679i	−0.986104	+	0.166130i	$0.946873\pi$
$54$		0			0
$55$	−0.581807	+	0.581807i	−0.0784508	+	0.0784508i
$56$	0.000915288		0.0477564i	0.000122310		0.00638172i
$57$		0			0
$58$	−3.99949	+	5.28175i	−0.525158	+	0.693528i
$59$	1.49224	+	3.60257i	0.194272	+	0.469015i	0.990758	−	0.135643i	$-0.0433099\pi$
$59$	1.49224	+	3.60257i	0.194272	+	0.469015i	−0.796485	+	0.604658i	$0.793310\pi$
$60$		0			0
$61$	−3.46424	−	1.43494i	−0.443551	−	0.183725i	0.149719	−	0.988729i	$-0.452163\pi$
$61$	−3.46424	−	1.43494i	−0.443551	−	0.183725i	−0.593270	+	0.805004i	$0.702163\pi$
$62$	0.0761730	−	0.291723i	0.00967398	−	0.0370488i
$63$		0			0
$64$	0.306539	+	7.99412i	0.0383174	+	0.999266i
$65$		−	0.829962i		−	0.102944i
$66$		0			0
$67$	3.85824	−	9.31462i	0.471359	−	1.13796i	−0.492203	−	0.870480i	$-0.663808\pi$
$67$	3.85824	−	9.31462i	0.471359	−	1.13796i	0.963563	−	0.267482i	$-0.0861916\pi$
$68$	−3.38425	−	1.89667i	−0.410401	−	0.230005i
$69$		0			0
$70$	0.00417464	+	0.00316115i	0.000498965	+	0.000377830i
$71$	−8.45626	+	8.45626i	−1.00357	+	1.00357i	−0.00357951	+	0.999994i	$0.501139\pi$
$71$	−8.45626	+	8.45626i	−1.00357	+	1.00357i	−0.999994	+	0.00357951i	$0.998861\pi$
$72$		0			0
$73$	−11.0555	−	11.0555i	−1.29394	−	1.29394i	−0.932326	−	0.361618i	$-0.882224\pi$
$73$	−11.0555	−	11.0555i	−1.29394	−	1.29394i	−0.361618	−	0.932326i	$-0.617776\pi$
$74$	−0.529321	−	3.83131i	−0.0615323	−	0.445381i
$75$		0			0
$76$	−3.12085	−	3.96135i	−0.357987	−	0.454398i
$77$	0.0585490	+	0.0242518i	0.00667228	+	0.00276375i
$78$		0			0
$79$	−15.3461			−1.72658			−0.863288	−	0.504712i	$-0.831599\pi$
$79$	−15.3461			−1.72658			−0.863288	+	0.504712i	$0.831599\pi$
$80$	0.709211	+	0.515953i	0.0792922	+	0.0576854i
$81$		0			0
$82$	−3.82400	+	2.24048i	−0.422290	+	0.247420i
$83$	1.25116	−	3.02056i	0.137332	−	0.331549i	−0.840219	−	0.542247i	$-0.817574\pi$
$83$	1.25116	−	3.02056i	0.137332	−	0.331549i	0.977551	+	0.210698i	$0.0675736\pi$
$84$		0			0
$85$	−0.392932	+	0.162758i	−0.0426194	+	0.0176536i
$86$	0.700054	+	5.06711i	0.0754888	+	0.546400i
$87$		0			0
$88$	9.88217	+	3.87318i	1.05344	+	0.412882i
$89$	−1.44269	−	1.44269i	−0.152925	−	0.152925i	0.626498	−	0.779423i	$-0.284488\pi$
$89$	−1.44269	−	1.44269i	−0.152925	−	0.152925i	−0.779423	+	0.626498i	$0.784488\pi$
$90$		0			0
$91$	−0.0590587	+	0.0244629i	−0.00619103	+	0.00256441i
$92$	−3.67474	−	13.0453i	−0.383118	−	1.36007i
$93$		0			0
$94$	0.864905	−	3.31236i	0.0892081	−	0.341644i
$95$	−0.552862			−0.0567224
$96$		0			0
$97$	−11.8857			−1.20681			−0.603404	−	0.797436i	$-0.706189\pi$
$97$	−11.8857			−1.20681			−0.603404	+	0.797436i	$0.706189\pi$
$98$	−2.50094	+	9.57796i	−0.252633	+	0.967520i
$99$		0			0
$100$	−9.53286	+	2.68531i	−0.953286	+	0.268531i
$101$	9.63369	−	3.99041i	0.958588	−	0.397060i	0.152136	−	0.988360i	$-0.451385\pi$
$101$	9.63369	−	3.99041i	0.958588	−	0.397060i	0.806452	+	0.591299i	$0.201385\pi$
$102$		0			0
$103$	1.67304	+	1.67304i	0.164850	+	0.164850i	0.784711	−	0.619861i	$-0.212811\pi$
$103$	1.67304	+	1.67304i	0.164850	+	0.164850i	−0.619861	+	0.784711i	$0.712811\pi$
$104$	−9.81117	+	4.28598i	−0.962065	+	0.420275i
$105$		0			0
$106$	0.630910	+	4.56663i	0.0612794	+	0.443550i
$107$	−14.0152	+	5.80527i	−1.35490	+	0.561217i	−0.937651	−	0.347577i	$-0.887005\pi$
$107$	−14.0152	+	5.80527i	−1.35490	+	0.561217i	−0.417246	+	0.908794i	$0.637005\pi$
$108$		0			0
$109$	−2.85189	+	6.88507i	−0.273161	+	0.659470i	−0.999615	−	0.0277456i	$-0.991167\pi$
$109$	−2.85189	+	6.88507i	−0.273161	+	0.659470i	0.726454	+	0.687215i	$0.241167\pi$
$110$	1.00398	−	0.588232i	0.0957259	−	0.0560857i
$111$		0			0
$112$	0.0158106	−	0.0656739i	0.00149396	−	0.00620560i
$113$	14.2128			1.33703			0.668514	−	0.743700i	$-0.266931\pi$
$113$	14.2128			1.33703			0.668514	+	0.743700i	$0.266931\pi$
$114$		0			0
$115$	−1.37271	−	0.568594i	−0.128006	−	0.0530217i
$116$	7.35977	−	5.79822i	0.683337	−	0.538351i
$117$		0			0
$118$	−0.754707	−	5.46269i	−0.0694764	−	0.502882i
$119$	0.0231631	+	0.0231631i	0.00212336	+	0.00212336i
$120$		0			0
$121$	2.17955	−	2.17955i	0.198141	−	0.198141i
$122$	4.22755	+	3.20122i	0.382745	+	0.289825i
$123$		0			0
$124$	−0.208461	+	0.371959i	−0.0187203	+	0.0334029i
$125$	−0.835032	+	2.01595i	−0.0746875	+	0.180312i
$126$		0			0
$127$		−	0.594874i		−	0.0527865i	−0.999652	−	0.0263933i	$-0.991598\pi$
$127$		−	0.594874i		−	0.0527865i	0.999652	−	0.0263933i	$-0.00840222\pi$
$128$	2.43679	−	11.0482i	0.215384	−	0.976529i
$129$		0			0
$130$	−0.296539	+	1.13567i	−0.0260082	+	0.0996045i
$131$	−11.9207	−	4.93770i	−1.04151	−	0.431409i	−0.204658	−	0.978833i	$-0.565608\pi$
$131$	−11.9207	−	4.93770i	−1.04151	−	0.431409i	−0.836855	+	0.547424i	$0.815608\pi$
$132$		0			0
$133$	0.0162955	+	0.0393407i	0.00141300	+	0.00341127i
$134$	−8.60741	+	11.3670i	−0.743567	+	0.981960i
$135$		0			0
$136$	3.95313	+	3.80445i	0.338978	+	0.326229i
$137$	10.8258	−	10.8258i	0.924915	−	0.924915i	−0.0724568	−	0.997372i	$-0.523084\pi$
$137$	10.8258	−	10.8258i	0.924915	−	0.924915i	0.997372	+	0.0724568i	$0.0230840\pi$
$138$		0			0
$139$	−3.55148	−	8.57403i	−0.301232	−	0.727239i	−0.999930	−	0.0118224i	$-0.996237\pi$
$139$	−3.55148	−	8.57403i	−0.301232	−	0.727239i	0.698698	−	0.715417i	$-0.253763\pi$
$140$	−0.00458286	−	0.00581709i	−0.000387322	−	0.000491634i
$141$		0			0
$142$	14.5924	−	8.54964i	1.22456	−	0.717470i
$143$			14.2049i			1.18788i
$144$		0			0
$145$		−	1.02716i		−	0.0853009i
$146$	11.1776	+	19.0776i	0.925061	+	1.57888i
$147$		0			0
$148$	−0.644608	+	5.43164i	−0.0529865	+	0.446478i
$149$	4.25928	+	10.2828i	0.348933	+	0.842400i	0.996746	+	0.0806006i	$0.0256838\pi$
$149$	4.25928	+	10.2828i	0.348933	+	0.842400i	−0.647813	+	0.761799i	$0.724316\pi$
$150$		0			0
$151$	−9.71514	+	9.71514i	−0.790607	+	0.790607i	−0.981593	−	0.190986i	$-0.938831\pi$
$151$	−9.71514	+	9.71514i	−0.790607	+	0.790607i	0.190986	+	0.981593i	$0.438831\pi$
$152$	2.85502	+	6.53551i	0.231573	+	0.530100i
$153$		0			0
$154$	−0.0714497	−	0.0541037i	−0.00575758	−	0.00435980i
$155$	0.0178885	+	0.0431866i	0.00143684	+	0.00346883i
$156$		0			0
$157$	11.4671	+	4.74982i	0.915172	+	0.379077i	0.790034	−	0.613063i	$-0.210063\pi$
$157$	11.4671	+	4.74982i	0.915172	+	0.379077i	0.125138	+	0.992139i	$0.460063\pi$
$158$	20.9987	+	5.48305i	1.67056	+	0.436208i
$159$		0			0
$160$	−0.786092	−	0.959393i	−0.0621461	−	0.0758467i
$161$			0.114439i			0.00901904i
$162$		0			0
$163$	3.79553	−	9.16322i	0.297289	−	0.717719i	−0.702692	−	0.711494i	$-0.748019\pi$
$163$	3.79553	−	9.16322i	0.297289	−	0.717719i	0.999981	−	0.00622432i	$-0.00198128\pi$
$164$	6.03302	−	1.69944i	0.471100	−	0.132704i
$165$		0			0
$166$	−2.79122	+	3.68611i	−0.216641	+	0.286097i
$167$	8.08092	−	8.08092i	0.625320	−	0.625320i	−0.321567	−	0.946887i	$-0.604209\pi$
$167$	8.08092	−	8.08092i	0.625320	−	0.625320i	0.946887	+	0.321567i	$0.104209\pi$
$168$		0			0
$169$	−0.939459	−	0.939459i	−0.0722661	−	0.0722661i
$170$	0.595815	−	0.0823157i	0.0456969	−	0.00631333i
$171$		0			0
$172$	0.852529	−	7.18363i	0.0650047	−	0.547747i
$173$	−1.73554	−	0.718885i	−0.131951	−	0.0546558i	0.315731	−	0.948849i	$-0.397750\pi$
$173$	−1.73554	−	0.718885i	−0.131951	−	0.0546558i	−0.447682	+	0.894193i	$0.647750\pi$
$174$		0			0
$175$	0.0836259			0.00632153
$176$	−12.1383	−	8.83063i	−0.914956	−	0.665634i
$177$		0			0
$178$	1.45862	+	2.48954i	0.109328	+	0.186599i
$179$	−2.93125	+	7.07665i	−0.219092	+	0.528934i	−0.994764	−	0.102202i	$-0.967411\pi$
$179$	−2.93125	+	7.07665i	−0.219092	+	0.528934i	0.775672	+	0.631136i	$0.217411\pi$
$180$		0			0
$181$	20.2266	−	8.37811i	1.50343	−	0.622740i	0.529239	−	0.848473i	$-0.322478\pi$
$181$	20.2266	−	8.37811i	1.50343	−	0.622740i	0.974189	+	0.225733i	$0.0724777\pi$
$182$	0.0895525	−	0.0123723i	0.00663808	−	0.000917094i
$183$		0			0
$184$	0.367280	+	19.1634i	0.0270762	+	1.41274i
$185$	0.424013	+	0.424013i	0.0311741	+	0.0311741i
$186$		0			0
$187$	6.72510	−	2.78563i	0.491788	−	0.203705i
$188$	−2.36696	+	4.22340i	−0.172628	+	0.308023i
$189$		0			0
$190$	0.756500	+	0.197533i	0.0548823	+	0.0143306i
$191$	2.52579			0.182760			0.0913800	−	0.995816i	$-0.470872\pi$
$191$	2.52579			0.182760			0.0913800	+	0.995816i	$0.470872\pi$
$192$		0			0
$193$	−6.18898			−0.445492			−0.222746	−	0.974876i	$-0.571502\pi$
$193$	−6.18898			−0.445492			−0.222746	+	0.974876i	$0.571502\pi$
$194$	16.2636	+	4.24666i	1.16766	+	0.304892i
$195$		0			0
$196$	6.84426	−	12.2123i	0.488876	−	0.872307i
$197$	22.6357	−	9.37602i	1.61273	−	0.668014i	0.619586	−	0.784929i	$-0.287301\pi$
$197$	22.6357	−	9.37602i	1.61273	−	0.668014i	0.993142	+	0.116915i	$0.0373005\pi$
$198$		0			0
$199$	−1.71266	−	1.71266i	−0.121407	−	0.121407i	0.643793	−	0.765200i	$-0.277360\pi$
$199$	−1.71266	−	1.71266i	−0.121407	−	0.121407i	−0.765200	+	0.643793i	$0.777360\pi$
$200$	14.0036	−	0.268389i	0.990203	−	0.0189780i
$201$		0			0
$202$	−14.6079	+	2.01817i	−1.02781	+	0.141998i
$203$	−0.0730909	+	0.0302753i	−0.00512998	+	0.00212491i
$204$		0			0
$205$	0.262955	−	0.634830i	0.0183656	−	0.0443385i
$206$	−1.69152	−	2.88705i	−0.117854	−	0.201150i
$207$		0			0
$208$	14.9563	−	2.35921i	1.03703	−	0.163582i
$209$	9.46232			0.654522
$210$		0			0
$211$	8.84986	+	3.66573i	0.609249	+	0.252359i	0.665908	−	0.746034i	$-0.268045\pi$
$211$	8.84986	+	3.66573i	0.609249	+	0.252359i	−0.0566581	+	0.998394i	$0.518045\pi$
$212$	0.768324	−	6.47410i	0.0527687	−	0.444643i
$213$		0			0
$214$	21.2516	−	2.93605i	1.45273	−	0.200704i
$215$	−0.560780	−	0.560780i	−0.0382449	−	0.0382449i
$216$		0			0
$217$	0.00254583	−	0.00254583i	0.000172822	−	0.000172822i
$218$	6.36232	−	8.40213i	0.430911	−	0.569064i
$219$		0			0
$220$	−1.58395	+	0.446184i	−0.106790	+	0.0300817i
$221$	−2.80988	+	6.78364i	−0.189013	+	0.456317i
$222$		0			0
$223$			25.7423i			1.72383i	0.507049	+	0.861917i	$0.330736\pi$
$223$			25.7423i			1.72383i	−0.507049	+	0.861917i	$0.669264\pi$
$224$	−0.0450989	+	0.0842149i	−0.00301330	+	0.00562684i
$225$		0			0
$226$	−19.4479	−	5.07812i	−1.29365	−	0.337792i
$227$	20.1573	+	8.34944i	1.33789	+	0.554172i	0.932895	−	0.360147i	$-0.117274\pi$
$227$	20.1573	+	8.34944i	1.33789	+	0.554172i	0.404994	+	0.914319i	$0.367274\pi$
$228$		0			0
$229$	2.08085	+	5.02362i	0.137507	+	0.331970i	0.977600	−	0.210471i	$-0.0674999\pi$
$229$	2.08085	+	5.02362i	0.137507	+	0.331970i	−0.840093	+	0.542442i	$0.817500\pi$
$230$	1.67517	+	1.26849i	0.110457	+	0.0836414i
$231$		0			0
$232$	−12.1423	+	5.30433i	−0.797180	+	0.348246i
$233$	11.8444	−	11.8444i	0.775951	−	0.775951i	−0.203188	−	0.979140i	$-0.565130\pi$
$233$	11.8444	−	11.8444i	0.775951	−	0.775951i	0.979140	+	0.203188i	$0.0651304\pi$
$234$		0			0
$235$	0.203114	+	0.490362i	0.0132497	+	0.0319877i
$236$	−0.919085	+	7.74445i	−0.0598273	+	0.504121i
$237$		0			0
$238$	−0.0234189	−	0.0399709i	−0.00151802	−	0.00259093i
$239$			10.0203i			0.648161i	0.946030	+	0.324080i	$0.105055\pi$
$239$			10.0203i			0.648161i	−0.946030	+	0.324080i	$0.894945\pi$
$240$		0			0
$241$		−	2.24829i		−	0.144825i	−0.997375	−	0.0724124i	$-0.976930\pi$
$241$		−	2.24829i		−	0.144825i	0.997375	−	0.0724124i	$-0.0230698\pi$
$242$	−3.76109	+	2.20362i	−0.241772	+	0.141654i
$243$		0			0
$244$	−4.64094	−	5.89081i	−0.297106	−	0.377121i
$245$	−0.587322	−	1.41792i	−0.0375226	−	0.0905876i
$246$		0			0
$247$	−6.74912	+	6.74912i	−0.429436	+	0.429436i
$248$	0.418142	−	0.434483i	0.0265520	−	0.0275897i
$249$		0			0
$250$	1.86289	−	2.46014i	0.117819	−	0.155593i
$251$	7.33649	+	17.7119i	0.463075	+	1.11796i	0.967128	+	0.254290i	$0.0818418\pi$
$251$	7.33649	+	17.7119i	0.463075	+	1.11796i	−0.504053	+	0.863673i	$0.668158\pi$
$252$		0			0
$253$	23.4941	+	9.73159i	1.47706	+	0.611820i
$254$	−0.212544	+	0.813988i	−0.0133362	+	0.0510741i
$255$		0			0
$256$	−7.28177	+	14.2470i	−0.455111	+	0.890435i
$257$			26.7917i			1.67122i	0.549325	+	0.835609i	$0.314885\pi$
$257$			26.7917i			1.67122i	−0.549325	+	0.835609i	$0.685115\pi$
$258$		0			0
$259$	0.0176744	−	0.0426697i	0.00109823	−	0.00265137i
$260$	0.811529	−	1.44802i	0.0503289	−	0.0898025i
$261$		0			0
$262$	14.5473	+	11.0156i	0.898733	+	0.680546i
$263$	−17.1686	+	17.1686i	−1.05866	+	1.05866i	−0.0604905	+	0.998169i	$0.519266\pi$
$263$	−17.1686	+	17.1686i	−1.05866	+	1.05866i	−0.998169	+	0.0604905i	$0.980734\pi$
$264$		0			0
$265$	−0.505391	−	0.505391i	−0.0310459	−	0.0310459i
$266$	−0.00824153	−	0.0596535i	−0.000505321	−	0.00365759i
$267$		0			0
$268$	15.8392	−	12.4785i	0.967531	−	0.762247i
$269$	−20.0795	−	8.31721i	−1.22427	−	0.507109i	−0.325505	−	0.945540i	$-0.605534\pi$
$269$	−20.0795	−	8.31721i	−1.22427	−	0.507109i	−0.898765	+	0.438431i	$0.855534\pi$
$270$		0			0
$271$	27.7852			1.68783			0.843915	−	0.536476i	$-0.180245\pi$
$271$	27.7852			1.68783			0.843915	+	0.536476i	$0.180245\pi$
$272$	−4.04990	−	6.61818i	−0.245562	−	0.401286i
$273$		0			0
$274$	−18.6814	+	10.9454i	−1.12858	+	0.661236i
$275$	7.11134	−	17.1683i	0.428830	−	1.03529i
$276$		0			0
$277$	−14.1201	+	5.84875i	−0.848396	+	0.351417i	−0.764158	−	0.645029i	$-0.776845\pi$
$277$	−14.1201	+	5.84875i	−0.848396	+	0.351417i	−0.0842374	+	0.996446i	$0.526845\pi$
$278$	1.79618	+	13.0011i	0.107728	+	0.779752i
$279$		0			0
$280$	0.00419249	+	0.00959715i	0.000250549	+	0.000573539i
$281$	−17.2705	−	17.2705i	−1.03027	−	1.03027i	−0.999527	−	0.0307455i	$-0.990212\pi$
$281$	−17.2705	−	17.2705i	−1.03027	−	1.03027i	−0.0307455	−	0.999527i	$-0.509788\pi$
$282$		0			0
$283$	26.6752	−	11.0492i	1.58568	−	0.656808i	0.596376	−	0.802705i	$-0.296607\pi$
$283$	26.6752	−	11.0492i	1.58568	−	0.656808i	0.989300	+	0.145897i	$0.0466067\pi$
$284$	−23.0220	+	6.48505i	−1.36610	+	0.384817i
$285$		0			0
$286$	5.07531	−	19.4371i	0.300109	−	1.14934i
$287$	−0.0529240			−0.00312401
$288$		0			0
$289$	−13.2374			−0.778669
$290$	−0.366996	+	1.40550i	−0.0215507	+	0.0825337i
$291$		0			0
$292$	−8.47837	−	30.0982i	−0.496159	−	1.76137i
$293$	25.5733	−	10.5928i	1.49401	−	0.618838i	0.521823	−	0.853054i	$-0.325252\pi$
$293$	25.5733	−	10.5928i	1.49401	−	0.618838i	0.972185	+	0.234215i	$0.0752520\pi$
$294$		0			0
$295$	0.604559	+	0.604559i	0.0351988	+	0.0351988i
$296$	2.82272	−	7.20199i	0.164067	−	0.418607i
$297$		0			0
$298$	−2.15416	−	15.5921i	−0.124787	−	0.903228i
$299$	−23.6987	+	9.81630i	−1.37053	+	0.567691i
$300$		0			0
$301$	−0.0233753	+	0.0564330i	−0.00134733	+	0.00325274i
$302$	16.7647	−	9.82243i	0.964701	−	0.565217i
$303$		0			0
$304$	−1.57154	−	9.96284i	−0.0901339	−	0.571408i
$305$	−0.822146			−0.0470760
$306$		0			0
$307$	−1.03022	−	0.426730i	−0.0587976	−	0.0243548i	0.353091	−	0.935589i	$-0.385131\pi$
$307$	−1.03022	−	0.426730i	−0.0587976	−	0.0243548i	−0.411888	+	0.911234i	$0.635131\pi$
$308$	0.0784364	+	0.0995604i	0.00446933	+	0.00567298i
$309$		0			0
$310$	−0.00904721	−	0.0654852i	−0.000513847	−	0.00371931i
$311$	−23.9114	−	23.9114i	−1.35589	−	1.35589i	−0.878919	−	0.476971i	$-0.841735\pi$
$311$	−23.9114	−	23.9114i	−1.35589	−	1.35589i	−0.476971	−	0.878919i	$-0.658265\pi$
$312$		0			0
$313$	−4.43744	+	4.43744i	−0.250819	+	0.250819i	−0.821306	−	0.570487i	$-0.806754\pi$
$313$	−4.43744	+	4.43744i	−0.250819	+	0.250819i	0.570487	+	0.821306i	$0.306754\pi$
$314$	−13.9937	−	10.5964i	−0.789712	−	0.597991i
$315$		0			0
$316$	−26.7742	−	15.0053i	−1.50616	−	0.844115i
$317$	2.38033	−	5.74662i	0.133693	−	0.322763i	−0.842829	−	0.538181i	$-0.819112\pi$
$317$	2.38033	−	5.74662i	0.133693	−	0.322763i	0.976522	+	0.215419i	$0.0691116\pi$
$318$		0			0
$319$			17.5800i			0.984291i
$320$	0.732855	+	1.59364i	0.0409678	+	0.0890870i
$321$		0			0
$322$	0.0408881	−	0.156591i	0.00227860	−	0.00872646i
$323$	4.51878	+	1.87174i	0.251432	+	0.104146i
$324$		0			0
$325$	7.17324	+	17.3177i	0.397900	+	0.960616i
$326$	−8.46750	+	11.1822i	−0.468972	+	0.619327i
$327$		0			0
$328$	−8.86240	+	0.169854i	−0.489344	+	0.00937864i
$329$	0.0289066	−	0.0289066i	0.00159367	−	0.00159367i
$330$		0			0
$331$	−6.95616	−	16.7937i	−0.382345	−	0.923063i	−0.991511	−	0.130021i	$-0.958496\pi$
$331$	−6.95616	−	16.7937i	−0.382345	−	0.923063i	0.609166	−	0.793043i	$-0.291504\pi$
$332$	5.13635	−	4.04655i	0.281894	−	0.222083i
$333$		0			0
$334$	−13.9447	+	8.17016i	−0.763018	+	0.447051i
$335$		−	2.21058i		−	0.120777i
$336$		0			0
$337$			19.6482i			1.07030i	0.844756	+	0.535152i	$0.179746\pi$
$337$			19.6482i			1.07030i	−0.844756	+	0.535152i	$0.820254\pi$
$338$	0.949834	+	1.62116i	0.0516641	+	0.0881793i
$339$		0			0
$340$	−0.844685	−	0.100244i	−0.0458095	−	0.00543651i
$341$	−0.306165	−	0.739147i	−0.0165797	−	0.0400270i
$342$		0			0
$343$	−0.167175	+	0.167175i	−0.00902659	+	0.00902659i
$344$	−3.73320	+	9.52501i	−0.201281	+	0.513554i
$345$		0			0
$346$	2.11795	+	1.60377i	0.113862	+	0.0862193i
$347$	−6.02247	−	14.5395i	−0.323303	−	0.780523i	−0.999058	−	0.0433963i	$-0.986182\pi$
$347$	−6.02247	−	14.5395i	−0.323303	−	0.780523i	0.675755	−	0.737126i	$-0.263818\pi$
$348$		0			0
$349$	10.4951	+	4.34720i	0.561788	+	0.232700i	0.645461	−	0.763793i	$-0.276665\pi$
$349$	10.4951	+	4.34720i	0.561788	+	0.232700i	−0.0836734	+	0.996493i	$0.526665\pi$
$350$	−0.114428	−	0.0298789i	−0.00611645	−	0.00159709i
$351$		0			0
$352$	13.4541	+	16.4202i	0.717106	+	0.875198i
$353$			30.0234i			1.59798i	0.601342	+	0.798992i	$0.294633\pi$
$353$			30.0234i			1.59798i	−0.601342	+	0.798992i	$0.705367\pi$
$354$		0			0
$355$	−1.00343	+	2.42251i	−0.0532568	+	0.128573i
$356$	−1.10639	−	3.92769i	−0.0586385	−	0.208167i
$357$		0			0
$358$	6.53936	−	8.63593i	0.345616	−	0.456423i
$359$	10.5864	−	10.5864i	0.558730	−	0.558730i	−0.370216	−	0.928946i	$-0.620716\pi$
$359$	10.5864	−	10.5864i	0.558730	−	0.558730i	0.928946	+	0.370216i	$0.120716\pi$
$360$		0			0
$361$	−8.93925	−	8.93925i	−0.470487	−	0.470487i
$362$	−30.6701	+	4.23728i	−1.61199	+	0.222707i
$363$		0			0
$364$	−0.126958	−	0.0150670i	−0.00665443	−	0.000789725i
$365$	−3.16711	−	1.31186i	−0.165774	−	0.0686660i
$366$		0			0
$367$	−3.82385			−0.199604			−0.0998018	−	0.995007i	$-0.531821\pi$
$367$	−3.82385			−0.199604			−0.0998018	+	0.995007i	$0.531821\pi$
$368$	6.34436	−	26.3531i	0.330722	−	1.37375i
$369$		0			0
$370$	−0.428696	−	0.731689i	−0.0222868	−	0.0380387i
$371$	−0.0210665	+	0.0508591i	−0.00109372	+	0.00264047i
$372$		0			0
$373$	23.5062	−	9.73660i	1.21711	−	0.504142i	0.320617	−	0.947209i	$-0.396110\pi$
$373$	23.5062	−	9.73660i	1.21711	−	0.504142i	0.896489	+	0.443067i	$0.146110\pi$
$374$	−10.1975	+	1.40885i	−0.527299	+	0.0728498i
$375$		0			0
$376$	4.74778	−	4.93333i	0.244848	−	0.254417i
$377$	−12.5392	−	12.5392i	−0.645799	−	0.645799i
$378$		0			0
$379$	−2.96668	+	1.22884i	−0.152388	+	0.0631212i	−0.457574	−	0.889172i	$-0.651281\pi$
$379$	−2.96668	+	1.22884i	−0.152388	+	0.0631212i	0.305186	+	0.952293i	$0.401281\pi$
$380$	−0.964569	−	0.540583i	−0.0494814	−	0.0277313i
$381$		0			0
$382$	−3.45613	−	0.902446i	−0.176831	−	0.0461731i
$383$	4.97811			0.254369			0.127185	−	0.991879i	$-0.459406\pi$
$383$	4.97811			0.254369			0.127185	+	0.991879i	$0.459406\pi$
$384$		0			0
$385$	0.0138951			0.000708158
$386$	8.46860	+	2.21127i	0.431040	+	0.112551i
$387$		0			0
$388$	−20.7368	−	11.6217i	−1.05275	−	0.590003i
$389$	−8.47226	+	3.50933i	−0.429561	+	0.177930i	−0.586979	−	0.809602i	$-0.699683\pi$
$389$	−8.47226	+	3.50933i	−0.429561	+	0.177930i	0.157418	+	0.987532i	$0.449683\pi$
$390$		0			0
$391$	9.29474	+	9.29474i	0.470055	+	0.470055i
$392$	−13.7286	+	14.2651i	−0.693399	+	0.720497i
$393$		0			0
$394$	−34.3232	+	4.74198i	−1.72918	+	0.238897i
$395$	−3.10864	+	1.28764i	−0.156413	+	0.0647883i
$396$		0			0
$397$	−1.22095	+	2.94765i	−0.0612780	+	0.147938i	−0.951553	−	0.307486i	$-0.900512\pi$
$397$	−1.22095	+	2.94765i	−0.0612780	+	0.147938i	0.890275	+	0.455424i	$0.150512\pi$
$398$	1.73157	+	2.95541i	0.0867958	+	0.148141i
$399$		0			0
$400$	−19.2575	−	4.63613i	−0.962875	−	0.231806i
$401$	−27.8490			−1.39071			−0.695356	−	0.718665i	$-0.744753\pi$
$401$	−27.8490			−1.39071			−0.695356	+	0.718665i	$0.744753\pi$
$402$		0			0
$403$	0.745581	+	0.308830i	0.0371400	+	0.0153839i
$404$	20.7095	+	2.45774i	1.03034	+	0.122277i
$405$		0			0
$406$	0.110830	−	0.0153119i	0.00550040	−	0.000759917i
$407$	−7.25705	−	7.25705i	−0.359719	−	0.359719i
$408$		0			0
$409$	−0.776560	+	0.776560i	−0.0383984	+	0.0383984i	−0.726045	−	0.687647i	$-0.758644\pi$
$409$	−0.776560	+	0.776560i	−0.0383984	+	0.0383984i	0.687647	+	0.726045i	$0.258644\pi$
$410$	−0.586631	+	0.774709i	−0.0289716	+	0.0382602i
$411$		0			0
$412$	1.28305	+	4.55482i	0.0632111	+	0.224400i
$413$	0.0252002	−	0.0608387i	0.00124002	−	0.00299368i
$414$		0			0
$415$		−	0.716849i		−	0.0351888i
$416$	−21.3082	−	2.11559i	−1.04472	−	0.103725i
$417$		0			0
$418$	−12.9476	−	3.38081i	−0.633289	−	0.165361i
$419$	−6.17161	−	2.55636i	−0.301503	−	0.124887i	0.226803	−	0.973941i	$-0.427173\pi$
$419$	−6.17161	−	2.55636i	−0.301503	−	0.124887i	−0.528306	+	0.849054i	$0.677173\pi$
$420$		0			0
$421$	4.54054	+	10.9618i	0.221293	+	0.534248i	0.995066	−	0.0992148i	$-0.0316331\pi$
$421$	4.54054	+	10.9618i	0.221293	+	0.534248i	−0.773773	+	0.633462i	$0.781633\pi$
$422$	−10.7998	−	8.17794i	−0.525728	−	0.398096i
$423$		0			0
$424$	−3.36447	+	8.58423i	−0.163393	+	0.416887i
$425$	6.79211	−	6.79211i	0.329466	−	0.329466i
$426$		0			0
$427$	0.0242326	+	0.0585026i	0.00117270	+	0.00283114i
$428$	−30.1284	−	3.57553i	−1.45631	−	0.172830i
$429$		0			0
$430$	0.566973	+	0.967697i	0.0273418	+	0.0466665i
$431$			14.2802i			0.687851i	0.938997	+	0.343925i	$0.111757\pi$
$431$			14.2802i			0.687851i	−0.938997	+	0.343925i	$0.888243\pi$
$432$		0			0
$433$		−	36.5612i		−	1.75702i	−0.477723	−	0.878510i	$-0.658538\pi$
$433$		−	36.5612i		−	1.75702i	0.477723	−	0.878510i	$-0.341462\pi$
$434$	−0.00439316	+	0.00257395i	−0.000210878	+	0.000123553i
$435$		0			0
$436$	−11.7078	+	9.22372i	−0.560702	+	0.441736i
$437$	6.53892	+	15.7864i	0.312799	+	0.755164i
$438$		0			0
$439$	−19.9584	+	19.9584i	−0.952563	+	0.952563i	−0.998925	−	0.0463616i	$-0.985237\pi$
$439$	−19.9584	+	19.9584i	−0.952563	+	0.952563i	0.0463616	+	0.998925i	$0.485237\pi$
$440$	2.32680	−	0.0445948i	0.110926	−	0.00212598i
$441$		0			0
$442$	6.26859	−	8.27835i	0.298167	−	0.393761i
$443$	1.86847	+	4.51089i	0.0887737	+	0.214319i	0.962031	−	0.272941i	$-0.0879965\pi$
$443$	1.86847	+	4.51089i	0.0887737	+	0.214319i	−0.873257	+	0.487260i	$0.837996\pi$
$444$		0			0
$445$	−0.413294	−	0.171192i	−0.0195920	−	0.00811528i
$446$	9.19753	−	35.2241i	0.435516	−	1.66791i
$447$		0			0
$448$	0.0917998	−	0.0991208i	0.00433713	−	0.00468302i
$449$		−	18.5243i		−	0.874217i	−0.899409	−	0.437109i	$-0.856003\pi$
$449$		−	18.5243i		−	0.874217i	0.899409	−	0.437109i	$-0.143997\pi$
$450$		0			0
$451$	−4.50053	+	10.8652i	−0.211921	+	0.511624i
$452$	24.7969	+	13.8971i	1.16635	+	0.653667i
$453$		0			0
$454$	−24.5988	−	18.6269i	−1.15448	−	0.874204i
$455$	−0.00991083	+	0.00991083i	−0.000464627	+	0.000464627i
$456$		0			0
$457$	4.31755	+	4.31755i	0.201967	+	0.201967i	0.800842	−	0.598876i	$-0.204386\pi$
$457$	4.31755	+	4.31755i	0.201967	+	0.201967i	−0.598876	+	0.800842i	$0.704386\pi$
$458$	−1.05240	−	7.61748i	−0.0491756	−	0.355941i
$459$		0			0
$460$	−1.83898	−	2.33424i	−0.0857427	−	0.108834i
$461$	−8.85130	−	3.66633i	−0.412246	−	0.170758i	0.166915	−	0.985971i	$-0.446620\pi$
$461$	−8.85130	−	3.66633i	−0.412246	−	0.170758i	−0.579161	+	0.815213i	$0.696620\pi$
$462$		0			0
$463$	−30.4291			−1.41416			−0.707080	−	0.707134i	$-0.749988\pi$
$463$	−30.4291			−1.41416			−0.707080	+	0.707134i	$0.749988\pi$
$464$	18.5099	−	2.91975i	0.859301	−	0.135546i
$465$		0			0
$466$	−20.4390	+	11.9752i	−0.946818	+	0.554740i
$467$	11.8108	−	28.5138i	0.546539	−	1.31946i	−0.373499	−	0.927631i	$-0.621842\pi$
$467$	11.8108	−	28.5138i	0.546539	−	1.31946i	0.920038	−	0.391830i	$-0.128158\pi$
$468$		0			0
$469$	−0.157301	+	0.0651563i	−0.00726349	+	0.00300864i
$470$	−0.102726	−	0.743551i	−0.00473842	−	0.0342974i
$471$		0			0
$472$	4.02465	−	10.2686i	0.185249	−	0.472652i
$473$	9.59784	+	9.59784i	0.441309	+	0.441309i
$474$		0			0
$475$	11.5359	−	4.77831i	0.529301	−	0.219244i
$476$	0.0177637	+	0.0630611i	0.000814196	+	0.00289040i
$477$		0			0
$478$	3.58018	−	13.7112i	0.163754	−	0.627134i
$479$	33.1421			1.51430			0.757151	−	0.653240i	$-0.226591\pi$
$479$	33.1421			1.51430			0.757151	+	0.653240i	$0.226591\pi$
$480$		0			0
$481$	10.3524			0.472027
$482$	−0.803295	+	3.07641i	−0.0365891	+	0.140127i
$483$		0			0
$484$	5.93377	−	1.67148i	0.269717	−	0.0759764i
$485$	−2.40766	+	0.997286i	−0.109326	+	0.0452844i
$486$		0			0
$487$	8.33714	+	8.33714i	0.377792	+	0.377792i	0.870305	−	0.492513i	$-0.163922\pi$
$487$	8.33714	+	8.33714i	0.377792	+	0.377792i	−0.492513	+	0.870305i	$0.663922\pi$
$488$	4.24562	+	9.71878i	0.192190	+	0.439949i
$489$		0			0
$490$	0.297042	+	2.15004i	0.0134190	+	0.0971288i
$491$	−9.27696	+	3.84264i	−0.418664	+	0.173416i	−0.582063	−	0.813144i	$-0.697754\pi$
$491$	−9.27696	+	3.84264i	−0.418664	+	0.173416i	0.163399	+	0.986560i	$0.447754\pi$
$492$		0			0
$493$	−3.47750	+	8.39542i	−0.156619	+	0.378111i
$494$	11.6465	−	6.82365i	0.523999	−	0.307011i
$495$		0			0
$496$	−0.727396	+	0.445120i	−0.0326610	+	0.0199865i
$497$	0.201957			0.00905903
$498$		0			0
$499$	10.2993	+	4.26612i	0.461061	+	0.190978i	0.601109	−	0.799167i	$-0.294726\pi$
$499$	10.2993	+	4.26612i	0.461061	+	0.190978i	−0.140048	+	0.990145i	$0.544726\pi$
$500$	−3.42804	+	2.70070i	−0.153307	+	0.120779i
$501$		0			0
$502$	−3.71048	−	26.8570i	−0.165607	−	1.19869i
$503$	−17.7557	−	17.7557i	−0.791687	−	0.791687i	0.190082	−	0.981768i	$-0.439125\pi$
$503$	−17.7557	−	17.7557i	−0.791687	−	0.791687i	−0.981768	+	0.190082i	$0.939125\pi$
$504$		0			0
$505$	1.61666	−	1.61666i	0.0719404	−	0.0719404i
$506$	−28.6708	−	21.7103i	−1.27457	−	0.965142i
$507$		0			0
$508$	0.581663	−	1.03787i	0.0258071	−	0.0460479i
$509$	−16.3316	+	39.4279i	−0.723884	+	1.74761i	−0.0619134	+	0.998082i	$0.519720\pi$
$509$	−16.3316	+	39.4279i	−0.723884	+	1.74761i	−0.661971	+	0.749530i	$0.730280\pi$
$510$		0			0
$511$			0.264033i			0.0116801i
$512$	15.0542	−	16.8929i	0.665309	−	0.746568i
$513$		0			0
$514$	9.57245	−	36.6600i	0.422223	−	1.61700i
$515$	0.479285	+	0.198526i	0.0211198	+	0.00874811i
$516$		0			0
$517$	−3.47634	−	8.39262i	−0.152889	−	0.369107i
$518$	−0.0394301	+	0.0520716i	−0.00173246	+	0.00228790i
$519$		0			0
$520$	−1.62781	+	1.69143i	−0.0713842	+	0.0741740i
$521$	2.59199	−	2.59199i	0.113557	−	0.113557i	−0.648045	−	0.761602i	$-0.724413\pi$
$521$	2.59199	−	2.59199i	0.113557	−	0.113557i	0.761602	+	0.648045i	$0.224413\pi$
$522$		0			0
$523$	6.55437	+	15.8236i	0.286602	+	0.691919i	0.999961	−	0.00888020i	$-0.00282669\pi$
$523$	6.55437	+	15.8236i	0.286602	+	0.691919i	−0.713358	+	0.700800i	$0.752827\pi$
$524$	−15.9698	−	20.2707i	−0.697642	−	0.885528i
$525$		0			0
$526$	29.6266	−	17.3582i	1.29178	−	0.756852i
$527$		−	0.413546i		−	0.0180143i
$528$		0			0
$529$			22.9212i			0.996573i
$530$	0.510973	+	0.872117i	0.0221952	+	0.0378823i
$531$		0			0
$532$	−0.0100366	+	0.0845707i	−0.000435140	+	0.00366661i
$533$	−4.53970	−	10.9598i	−0.196636	−	0.474722i
$534$		0			0
$535$	−2.35193	+	2.35193i	−0.101683	+	0.101683i
$536$	−26.1318	+	11.4156i	−1.12872	+	0.493079i
$537$		0			0
$538$	24.5039	+	18.5550i	1.05644	+	0.799962i
$539$	10.0521	+	24.2680i	0.432975	+	1.04529i
$540$		0			0
$541$	31.3688	+	12.9934i	1.34865	+	0.558628i	0.935916	−	0.352224i	$-0.114574\pi$
$541$	31.3688	+	12.9934i	1.34865	+	0.558628i	0.412733	+	0.910852i	$0.364574\pi$
$542$	−38.0195	−	9.92743i	−1.63308	−	0.426420i
$543$		0			0
$544$	3.17700	+	10.5029i	0.136213	+	0.450308i
$545$			1.63399i			0.0699924i
$546$		0			0
$547$	16.7932	−	40.5423i	0.718024	−	1.73346i	0.0391202	−	0.999235i	$-0.487544\pi$
$547$	16.7932	−	40.5423i	0.718024	−	1.73346i	0.678903	−	0.734228i	$-0.262456\pi$
$548$	29.4731	−	8.30228i	1.25903	−	0.354656i
$549$		0			0
$550$	−15.8648	+	20.9512i	−0.676477	+	0.893360i
$551$	−8.35270	+	8.35270i	−0.355837	+	0.355837i
$552$		0			0
$553$	0.183253	+	0.183253i	0.00779271	+	0.00779271i
$554$	21.4108	−	2.95804i	0.909657	−	0.125675i
$555$		0			0
$556$	2.18740	−	18.4316i	0.0927663	−	0.781673i
$557$	−23.9875	−	9.93595i	−1.01638	−	0.421000i	−0.188604	−	0.982053i	$-0.560396\pi$
$557$	−23.9875	−	9.93595i	−1.01638	−	0.421000i	−0.827780	+	0.561053i	$0.810396\pi$
$558$		0			0
$559$	−13.6916			−0.579091
$560$	−0.00230775	−	0.0146301i	−9.75200e−5	−	0.000618233i
$561$		0			0
$562$	17.4612	+	29.8025i	0.736558	+	1.25714i
$563$	15.7397	−	37.9991i	0.663350	−	1.60147i	−0.129169	−	0.991623i	$-0.541231\pi$
$563$	15.7397	−	37.9991i	0.663350	−	1.60147i	0.792519	−	0.609847i	$-0.208769\pi$
$564$		0			0
$565$	2.87906	−	1.19255i	0.121123	−	0.0501708i
$566$	−40.4484	+	5.58822i	−1.70017	+	0.234890i
$567$		0			0
$568$	33.8188	−	0.648163i	1.41901	−	0.0271963i
$569$	−26.5263	−	26.5263i	−1.11204	−	1.11204i	−0.992874	−	0.119168i	$-0.961977\pi$
$569$	−26.5263	−	26.5263i	−1.11204	−	1.11204i	−0.119168	−	0.992874i	$-0.538023\pi$
$570$		0			0
$571$	4.44812	−	1.84247i	0.186148	−	0.0771050i	−0.287663	−	0.957732i	$-0.592878\pi$
$571$	4.44812	−	1.84247i	0.186148	−	0.0771050i	0.473811	+	0.880627i	$0.342878\pi$
$572$	−13.8895	+	24.7831i	−0.580747	+	1.03624i
$573$		0			0
$574$	0.0724178	+	0.0189093i	0.00302266	+	0.000789260i
$575$	33.5568			1.39942
$576$		0			0
$577$	−27.0428			−1.12581			−0.562903	−	0.826523i	$-0.690315\pi$
$577$	−27.0428			−1.12581			−0.562903	+	0.826523i	$0.690315\pi$
$578$	18.1132	+	4.72961i	0.753408	+	0.196726i
$579$		0			0
$580$	1.00435	−	1.79207i	0.0417032	−	0.0744116i
$581$	−0.0510098	+	0.0211290i	−0.00211624	+	0.000876577i
$582$		0			0
$583$	8.64986	+	8.64986i	0.358240	+	0.358240i
$584$	0.847389	+	44.2137i	0.0350652	+	1.82958i
$585$		0			0
$586$	−38.7776	+	5.35738i	−1.60189	+	0.221311i
$587$	−24.7371	+	10.2464i	−1.02101	+	0.422915i	−0.829459	−	0.558568i	$-0.811351\pi$
$587$	−24.7371	+	10.2464i	−1.02101	+	0.422915i	−0.191549	+	0.981483i	$0.561351\pi$
$588$		0			0
$589$	0.205721	−	0.496653i	0.00847657	−	0.0204642i
$590$	−0.611236	−	1.04324i	−0.0251642	−	0.0429497i
$591$		0			0
$592$	−6.43565	+	8.84620i	−0.264503	+	0.363577i
$593$	14.7443			0.605477			0.302738	−	0.953074i	$-0.402099\pi$
$593$	14.7443			0.605477			0.302738	+	0.953074i	$0.402099\pi$
$594$		0			0
$595$	0.00663566	+	0.00274858i	0.000272035	+	0.000112681i
$596$	−2.62334	+	22.1049i	−0.107456	+	0.905453i
$597$		0			0
$598$	35.9350	−	4.96466i	1.46949	−	0.203020i
$599$	−3.57851	−	3.57851i	−0.146214	−	0.146214i	0.630210	−	0.776424i	$-0.282969\pi$
$599$	−3.57851	−	3.57851i	−0.146214	−	0.146214i	−0.776424	+	0.630210i	$0.782969\pi$
$600$		0			0
$601$	−2.91144	+	2.91144i	−0.118760	+	0.118760i	−0.763989	−	0.645229i	$-0.776762\pi$
$601$	−2.91144	+	2.91144i	−0.118760	+	0.118760i	0.645229	+	0.763989i	$0.276762\pi$
$602$	0.0521483	−	0.0688675i	0.00212541	−	0.00280683i
$603$		0			0
$604$	−26.4492	+	7.45048i	−1.07620	+	0.303156i
$605$	0.258629	−	0.624386i	0.0105148	−	0.0253849i
$606$		0			0
$607$		−	4.29692i		−	0.174406i	−0.996191	−	0.0872032i	$-0.972207\pi$
$607$		−	4.29692i		−	0.174406i	0.996191	−	0.0872032i	$-0.0277929\pi$
$608$	−1.40925	+	14.1940i	−0.0571527	+	0.575643i
$609$		0			0
$610$	1.12497	+	0.293746i	0.0455488	+	0.0118934i
$611$	8.46568	+	3.50660i	0.342485	+	0.141862i
$612$		0			0
$613$	15.8444	+	38.2518i	0.639949	+	1.54497i	0.826746	+	0.562575i	$0.190189\pi$
$613$	15.8444	+	38.2518i	0.639949	+	1.54497i	−0.186797	+	0.982399i	$0.559811\pi$
$614$	1.25722	+	0.951998i	0.0507371	+	0.0384195i
$615$		0			0
$616$	−0.0717551	−	0.164257i	−0.00289110	−	0.00661810i
$617$	−16.9817	+	16.9817i	−0.683659	+	0.683659i	−0.960823	−	0.277163i	$-0.910606\pi$
$617$	−16.9817	+	16.9817i	−0.683659	+	0.683659i	0.277163	+	0.960823i	$0.410606\pi$
$618$		0			0
$619$	5.89007	+	14.2199i	0.236742	+	0.571545i	0.996942	−	0.0781434i	$-0.0248992\pi$
$619$	5.89007	+	14.2199i	0.236742	+	0.571545i	−0.760200	+	0.649689i	$0.774899\pi$
$620$	−0.0110177	+	0.0928383i	−0.000442483	+	0.00372847i
$621$		0			0
$622$	24.1754	+	41.2621i	0.969347	+	1.65446i
$623$			0.0344552i			0.00138042i
$624$		0			0
$625$		−	24.2812i		−	0.971248i
$626$	7.65737	−	4.48645i	0.306050	−	0.179314i
$627$		0			0
$628$	15.3621	+	19.4993i	0.613014	+	0.778108i
$629$	−2.03013	−	4.90116i	−0.0809464	−	0.195422i
$630$		0			0
$631$	23.5566	−	23.5566i	0.937772	−	0.937772i	−0.0604020	−	0.998174i	$-0.519238\pi$
$631$	23.5566	−	23.5566i	0.937772	−	0.937772i	0.998174	+	0.0604020i	$0.0192383\pi$
$632$	31.2748	+	30.0985i	1.24404	+	1.19725i
$633$		0			0
$634$	−5.31031	+	7.01284i	−0.210900	+	0.278515i
$635$	−0.0499139	−	0.120503i	−0.00198077	−	0.00478200i
$636$		0			0
$637$	−24.4792	−	10.1396i	−0.969902	−	0.401746i
$638$	6.28120	−	24.0553i	0.248675	−	0.952360i
$639$		0			0
$640$	−0.433398	−	2.44247i	−0.0171315	−	0.0965472i
$641$			32.1521i			1.26993i	0.772540	+	0.634966i	$0.218986\pi$
$641$			32.1521i			1.26993i	−0.772540	+	0.634966i	$0.781014\pi$
$642$		0			0
$643$	17.0638	−	41.1958i	0.672932	−	1.62460i	−0.103670	−	0.994612i	$-0.533059\pi$
$643$	17.0638	−	41.1958i	0.672932	−	1.62460i	0.776603	−	0.629991i	$-0.216941\pi$
$644$	−0.111897	+	0.199660i	−0.00440937	+	0.00786769i
$645$		0			0
$646$	−5.51445	−	4.17569i	−0.216963	−	0.164290i
$647$	10.0224	−	10.0224i	0.394023	−	0.394023i	−0.482096	−	0.876119i	$-0.660124\pi$
$647$	10.0224	−	10.0224i	0.394023	−	0.394023i	0.876119	+	0.482096i	$0.160124\pi$
$648$		0			0
$649$	−10.3471	−	10.3471i	−0.406161	−	0.406161i
$650$	−3.62791	−	26.2594i	−0.142298	−	1.02998i
$651$		0			0
$652$	15.5817	−	12.2757i	0.610227	−	0.480753i
$653$	−32.9549	−	13.6503i	−1.28962	−	0.534179i	−0.370750	−	0.928733i	$-0.620899\pi$
$653$	−32.9549	−	13.6503i	−1.28962	−	0.534179i	−0.918873	+	0.394553i	$0.870899\pi$
$654$		0			0
$655$	−2.82906			−0.110540
$656$	12.1874	+	2.93405i	0.475839	+	0.114555i
$657$		0			0
$658$	−0.0498820	+	0.0292258i	−0.00194460	+	0.00113934i
$659$	12.1112	−	29.2389i	0.471784	−	1.13899i	−0.491590	−	0.870827i	$-0.663584\pi$
$659$	12.1112	−	29.2389i	0.471784	−	1.13899i	0.963374	−	0.268161i	$-0.0864159\pi$
$660$		0			0
$661$	−1.46878	+	0.608388i	−0.0571289	+	0.0236636i	−0.411065	−	0.911606i	$-0.634843\pi$
$661$	−1.46878	+	0.608388i	−0.0571289	+	0.0236636i	0.353936	+	0.935270i	$0.384843\pi$
$662$	3.51812	+	25.4648i	0.136736	+	0.989716i
$663$		0			0
$664$	−8.47405	+	3.70186i	−0.328857	+	0.143660i
$665$	0.00660189	+	0.00660189i	0.000256010	+	0.000256010i
$666$		0			0
$667$	−29.3294	+	12.1486i	−1.13564	+	0.470397i
$668$	22.0001	−	6.19721i	0.851210	−	0.239777i
$669$		0			0
$670$	−0.789823	+	3.02482i	−0.0305135	+	0.116859i
$671$	14.0712			0.543212
$672$		0			0
$673$	18.9627			0.730957			0.365478	−	0.930820i	$-0.380905\pi$
$673$	18.9627			0.730957			0.365478	+	0.930820i	$0.380905\pi$
$674$	7.02014	−	26.8853i	0.270406	−	1.03558i
$675$		0			0
$676$	−0.720465	−	2.55765i	−0.0277102	−	0.0983713i
$677$	−30.8482	+	12.7778i	−1.18559	+	0.491089i	−0.886318	−	0.463077i	$-0.846745\pi$
$677$	−30.8482	+	12.7778i	−1.18559	+	0.491089i	−0.299276	+	0.954166i	$0.596745\pi$
$678$		0			0
$679$	0.141930	+	0.141930i	0.00544679	+	0.00544679i
$680$	1.12000	+	0.438967i	0.0429499	+	0.0168336i
$681$		0			0
$682$	0.154845	+	1.12079i	0.00592931	+	0.0429173i
$683$	23.3005	−	9.65139i	0.891570	−	0.369300i	0.110597	−	0.993865i	$-0.464724\pi$
$683$	23.3005	−	9.65139i	0.891570	−	0.369300i	0.780973	+	0.624565i	$0.214724\pi$
$684$		0			0
$685$	1.28461	−	3.10133i	0.0490826	−	0.118496i
$686$	0.288482	−	0.169021i	0.0110143	−	0.00645325i
$687$		0			0
$688$	8.51148	−	11.6996i	0.324497	−	0.446042i
$689$	−12.3392			−0.470087
$690$		0			0
$691$	17.6321	+	7.30344i	0.670756	+	0.277836i	0.691957	−	0.721939i	$-0.256749\pi$
$691$	17.6321	+	7.30344i	0.670756	+	0.277836i	−0.0212009	+	0.999775i	$0.506749\pi$
$692$	−2.32506	−	2.95123i	−0.0883854	−	0.112189i
$693$		0			0
$694$	3.04590	+	22.0467i	0.115621	+	0.836883i
$695$	−1.43883	−	1.43883i	−0.0545781	−	0.0545781i
$696$		0			0
$697$	−4.29850	+	4.29850i	−0.162817	+	0.162817i
$698$	−12.8075	−	9.69823i	−0.484773	−	0.367083i
$699$		0			0
$700$	0.145901	+	0.0817687i	0.00551453	+	0.00309057i
$701$	3.99504	−	9.64488i	0.150891	−	0.364282i	−0.830302	−	0.557314i	$-0.811832\pi$
$701$	3.99504	−	9.64488i	0.150891	−	0.364282i	0.981192	+	0.193032i	$0.0618321\pi$
$702$		0			0
$703$		−	6.89601i		−	0.260088i
$704$	−12.5429	−	27.2754i	−0.472730	−	1.02798i
$705$		0			0
$706$	10.7271	−	41.0821i	0.403721	−	1.54614i
$707$	−0.162689	−	0.0673882i	−0.00611857	−	0.00253439i
$708$		0			0
$709$	−13.5796	−	32.7841i	−0.509994	−	1.23123i	−0.943887	−	0.330270i	$-0.892860\pi$
$709$	−13.5796	−	32.7841i	−0.509994	−	1.23123i	0.433893	−	0.900965i	$-0.357140\pi$
$710$	2.23858	−	2.95628i	0.0840123	−	0.110947i
$711$		0			0
$712$	0.110581	+	5.76970i	0.00414418	+	0.216229i
$713$	1.02157	−	1.02157i	0.0382582	−	0.0382582i
$714$		0			0
$715$	1.19189	+	2.87747i	0.0445741	+	0.107611i
$716$	−12.0336	+	9.48038i	−0.449716	+	0.354299i
$717$		0			0
$718$	−18.2682	+	10.7033i	−0.681764	+	0.399445i
$719$			33.9773i			1.26714i	0.773686	+	0.633570i	$0.218411\pi$
$719$			33.9773i			1.26714i	−0.773686	+	0.633570i	$0.781589\pi$
$720$		0			0
$721$		−	0.0399566i		−	0.00148806i
$722$	9.03797	+	15.4258i	0.336358	+	0.574089i
$723$		0			0
$724$	43.4810	+	5.16018i	1.61596	+	0.191776i
$725$	8.87759	+	21.4324i	0.329706	+	0.795980i
$726$		0			0
$727$	−6.66650	+	6.66650i	−0.247247	+	0.247247i	−0.819840	−	0.572593i	$-0.805938\pi$
$727$	−6.66650	+	6.66650i	−0.247247	+	0.247247i	0.572593	+	0.819840i	$0.305938\pi$
$728$	0.168338	+	0.0659780i	0.00623904	+	0.00244531i
$729$		0			0
$730$	3.86496	+	2.92665i	0.143048	+	0.108320i
$731$	2.68495	+	6.48204i	0.0993065	+	0.239747i
$732$		0			0
$733$	−20.4629	−	8.47602i	−0.755815	−	0.313069i	−0.0287034	−	0.999588i	$-0.509138\pi$
$733$	−20.4629	−	8.47602i	−0.755815	−	0.313069i	−0.727112	+	0.686519i	$0.759138\pi$
$734$	5.23232	+	1.36623i	0.193128	+	0.0504286i
$735$		0			0
$736$	−18.0970	+	33.7931i	−0.667063	+	1.24563i
$737$			37.8345i			1.39365i
$738$		0			0
$739$	−14.5912	+	35.2264i	−0.536748	+	1.29582i	0.390234	+	0.920716i	$0.372394\pi$
$739$	−14.5912	+	35.2264i	−0.536748	+	1.29582i	−0.926981	+	0.375108i	$0.877606\pi$
$740$	0.325173	+	1.15437i	0.0119536	+	0.0424353i
$741$		0			0
$742$	0.0469976	−	0.0620654i	0.00172534	−	0.00227849i
$743$	30.0108	−	30.0108i	1.10099	−	1.10099i	0.106696	−	0.994292i	$-0.465973\pi$
$743$	30.0108	−	30.0108i	1.10099	−	1.10099i	0.994292	−	0.106696i	$-0.0340272\pi$
$744$		0			0
$745$	1.72559	+	1.72559i	0.0632207	+	0.0632207i
$746$	−35.6432	+	4.92434i	−1.30499	+	0.180293i
$747$		0			0
$748$	14.4569	+	1.71570i	0.528598	+	0.0627322i
$749$	0.236682	+	0.0980368i	0.00864817	+	0.00358219i
$750$		0			0
$751$	36.3413			1.32611			0.663056	−	0.748570i	$-0.269259\pi$
$751$	36.3413			1.32611			0.663056	+	0.748570i	$0.269259\pi$
$752$	−8.25920	+	5.05410i	−0.301182	+	0.184304i
$753$		0			0
$754$	12.6776	+	21.6379i	0.461692	+	0.788006i
$755$	−1.15282	+	2.78314i	−0.0419553	+	0.101289i
$756$		0			0
$757$	−20.0419	+	8.30162i	−0.728435	+	0.301728i	−0.715909	−	0.698194i	$-0.753987\pi$
$757$	−20.0419	+	8.30162i	−0.728435	+	0.301728i	−0.0125261	+	0.999922i	$0.503987\pi$
$758$	4.49847	−	0.621493i	0.163392	−	0.0225736i
$759$		0			0
$760$	1.12671	+	1.08433i	0.0408700	+	0.0393329i
$761$	29.5308	+	29.5308i	1.07049	+	1.07049i	0.997319	+	0.0731706i	$0.0233118\pi$
$761$	29.5308	+	29.5308i	1.07049	+	1.07049i	0.0731706	+	0.997319i	$0.476688\pi$
$762$		0			0
$763$	0.116272	−	0.0481614i	0.00420933	−	0.00174356i
$764$	4.40671	+	2.46970i	0.159429	+	0.0893505i
$765$		0			0
$766$	−6.81172	−	1.77864i	−0.246118	−	0.0642648i
$767$	14.7604			0.532969
$768$		0			0
$769$	−4.12972			−0.148922			−0.0744608	−	0.997224i	$-0.523724\pi$
$769$	−4.12972			−0.148922			−0.0744608	+	0.997224i	$0.523724\pi$
$770$	−0.0190131	−	0.00496460i	−0.000685185	−	0.000178912i
$771$		0			0
$772$	−10.7978	−	6.05153i	−0.388622	−	0.217799i
$773$	40.0041	−	16.5702i	1.43885	−	0.595990i	0.479329	−	0.877635i	$-0.340880\pi$
$773$	40.0041	−	16.5702i	1.43885	−	0.595990i	0.959519	+	0.281645i	$0.0908800\pi$
$774$		0			0
$775$	−0.746512	−	0.746512i	−0.0268155	−	0.0268155i
$776$	24.2225	+	23.3115i	0.869537	+	0.836833i
$777$		0			0
$778$	12.8468	−	1.77486i	0.460579	−	0.0636319i
$779$	−7.30065	+	3.02403i	−0.261573	+	0.108347i
$780$		0			0
$781$	17.1740	−	41.4616i	0.614532	−	1.48361i
$782$	−9.39738	−	16.0393i	−0.336050	−	0.573563i
$783$		0			0
$784$	23.8821	−	14.6144i	0.852934	−	0.521941i
$785$	2.72141			0.0971311
$786$		0			0
$787$	−35.6785	−	14.7785i	−1.27180	−	0.526797i	−0.358290	−	0.933610i	$-0.616640\pi$
$787$	−35.6785	−	14.7785i	−1.27180	−	0.526797i	−0.913511	+	0.406813i	$0.866640\pi$
$788$	48.6600	+	5.77480i	1.73344	+	0.205719i
$789$		0			0
$790$	4.71373	−	0.651233i	0.167707	−	0.0231698i
$791$	−0.169719	−	0.169719i	−0.00603453	−	0.00603453i
$792$		0			0
$793$	−10.0364	+	10.0364i	−0.356404	+	0.356404i
$794$	2.72385	−	3.59713i	0.0966657	−	0.127657i
$795$		0			0
$796$	−1.31343	−	4.66267i	−0.0465531	−	0.165264i
$797$	−18.5765	+	44.8475i	−0.658012	+	1.58858i	0.142858	+	0.989743i	$0.454371\pi$
$797$	−18.5765	+	44.8475i	−0.658012	+	1.58858i	−0.800870	+	0.598838i	$0.795629\pi$
$798$		0			0
$799$		−	4.69559i		−	0.166118i
$800$	24.6943	+	13.2243i	0.873075	+	0.467551i
$801$		0			0
$802$	38.1068	+	9.95023i	1.34560	+	0.351355i
$803$	54.2057	+	22.4527i	1.91288	+	0.792340i
$804$		0			0
$805$	0.00960217	+	0.0231817i	0.000338432	+	0.000817047i
$806$	−0.909863	−	0.688973i	−0.0320485	−	0.0242680i
$807$		0			0
$808$	−27.4595	−	10.7624i	−0.966021	−	0.378619i
$809$	21.0608	−	21.0608i	0.740458	−	0.740458i	−0.232208	−	0.972666i	$-0.574595\pi$
$809$	21.0608	−	21.0608i	0.740458	−	0.740458i	0.972666	+	0.232208i	$0.0745951\pi$
$810$		0			0
$811$	−13.0466	−	31.4972i	−0.458126	−	1.10602i	−0.969155	−	0.246451i	$-0.920735\pi$
$811$	−13.0466	−	31.4972i	−0.458126	−	1.10602i	0.511029	−	0.859564i	$-0.329265\pi$
$812$	−0.157124	−	0.0186469i	−0.00551395	−	0.000654377i
$813$		0			0
$814$	7.33720	+	12.5230i	0.257169	+	0.438930i
$815$		−	2.17465i		−	0.0761746i
$816$		0			0
$817$			9.12034i			0.319080i
$818$	1.34005	−	0.785136i	0.0468539	−	0.0274516i
$819$		0			0
$820$	1.07951	−	0.850463i	0.0376980	−	0.0296995i
$821$	19.7064	+	47.5755i	0.687758	+	1.66040i	0.749249	+	0.662288i	$0.230414\pi$
$821$	19.7064	+	47.5755i	0.687758	+	1.66040i	−0.0614909	+	0.998108i	$0.519586\pi$
$822$		0			0
$823$	−8.83221	+	8.83221i	−0.307872	+	0.307872i	−0.844083	−	0.536212i	$-0.819855\pi$
$823$	−8.83221	+	8.83221i	−0.307872	+	0.307872i	0.536212	+	0.844083i	$0.319855\pi$
$824$	−0.128237	−	6.69094i	−0.00446734	−	0.233090i
$825$		0			0
$826$	−0.0562195	+	0.0742439i	−0.00195613	+	0.00258328i
$827$	−4.85317	−	11.7166i	−0.168761	−	0.407426i	0.816760	−	0.576977i	$-0.195768\pi$
$827$	−4.85317	−	11.7166i	−0.168761	−	0.407426i	−0.985521	+	0.169552i	$0.945768\pi$
$828$		0			0
$829$	−29.5493	−	12.2397i	−1.02629	−	0.425102i	−0.194917	−	0.980820i	$-0.562444\pi$
$829$	−29.5493	−	12.2397i	−1.02629	−	0.425102i	−0.831371	+	0.555717i	$0.812444\pi$
$830$	−0.256125	+	0.980891i	−0.00889022	+	0.0340472i
$831$		0			0
$832$	28.4009	+	10.5081i	0.984624	+	0.364302i
$833$			13.5777i			0.470439i
$834$		0			0
$835$	0.958897	−	2.31498i	0.0331840	−	0.0801132i
$836$	16.5088	+	9.25217i	0.570968	+	0.319993i
$837$		0			0
$838$	7.53146	+	5.70303i	0.260170	+	0.197008i
$839$	1.90644	−	1.90644i	0.0658177	−	0.0658177i	−0.673432	−	0.739249i	$-0.735180\pi$
$839$	1.90644	−	1.90644i	0.0658177	−	0.0658177i	0.739249	+	0.673432i	$0.235180\pi$
$840$		0			0
$841$	4.98766	+	4.98766i	0.171988	+	0.171988i
$842$	−2.29641	−	16.6218i	−0.0791395	−	0.572824i
$843$		0			0
$844$	11.8559	+	15.0489i	0.408097	+	0.518003i
$845$	−0.269131	−	0.111478i	−0.00925840	−	0.00383496i
$846$		0			0
$847$	−0.0520533			−0.00178857
$848$	7.67080	−	10.5440i	0.263416	−	0.362083i
$849$		0			0
$850$	−11.7207	+	6.86712i	−0.402015	+	0.235540i
$851$	7.09225	−	17.1222i	0.243119	−	0.586942i
$852$		0			0
$853$	33.4447	−	13.8532i	1.14512	−	0.474326i	0.272228	−	0.962233i	$-0.412239\pi$
$853$	33.4447	−	13.8532i	1.14512	−	0.474326i	0.872896	+	0.487907i	$0.162239\pi$
$854$	−0.0122558	−	0.0887093i	−0.000419384	−	0.00303557i
$855$		0			0
$856$	39.9482	+	15.6572i	1.36540	+	0.535151i
$857$	−34.3898	−	34.3898i	−1.17473	−	1.17473i	−0.981067	−	0.193667i	$-0.937962\pi$
$857$	−34.3898	−	34.3898i	−1.17473	−	1.17473i	−0.193667	−	0.981067i	$-0.562038\pi$
$858$		0			0
$859$	−34.8239	+	14.4245i	−1.18818	+	0.492158i	−0.887160	−	0.461461i	$-0.847325\pi$
$859$	−34.8239	+	14.4245i	−1.18818	+	0.492158i	−0.301015	+	0.953619i	$0.597325\pi$
$860$	−0.430058	−	1.52671i	−0.0146649	−	0.0520603i
$861$		0			0
$862$	5.10219	−	19.5400i	0.173781	−	0.665537i
$863$	18.2887			0.622556			0.311278	−	0.950319i	$-0.399243\pi$
$863$	18.2887			0.622556			0.311278	+	0.950319i	$0.399243\pi$
$864$		0			0
$865$	−0.411885			−0.0140045
$866$	−13.0630	+	50.0280i	−0.443900	+	1.70002i
$867$		0			0
$868$	0.00693096	−	0.00195238i	0.000235252	−	6.62681e-5i
$869$	53.2049	−	22.0382i	1.80485	−	0.747595i
$870$		0			0
$871$	−26.9859	−	26.9859i	−0.914382	−	0.914382i
$872$	19.3158	−	8.43804i	0.654114	−	0.285748i
$873$		0			0
$874$	−3.30710	−	23.9373i	−0.111864	−	0.809693i
$875$	0.0340444	−	0.0141016i	0.00115091	−	0.000476723i
$876$		0			0
$877$	−1.49573	+	3.61102i	−0.0505073	+	0.121935i	−0.947119	−	0.320882i	$-0.896021\pi$
$877$	−1.49573	+	3.61102i	−0.0505073	+	0.121935i	0.896612	+	0.442817i	$0.146021\pi$
$878$	34.4408	−	20.1788i	1.16232	−	0.681002i
$879$		0			0
$880$	−3.19978	−	0.770327i	−0.107864	−	0.0259677i
$881$	−38.4824			−1.29650			−0.648252	−	0.761426i	$-0.724500\pi$
$881$	−38.4824			−1.29650			−0.648252	+	0.761426i	$0.724500\pi$
$882$		0			0
$883$	−45.9974	−	19.0528i	−1.54794	−	0.641177i	−0.564995	−	0.825094i	$-0.691122\pi$
$883$	−45.9974	−	19.0528i	−1.54794	−	0.641177i	−0.982942	+	0.183918i	$0.941122\pi$
$884$	−11.5353	+	9.08784i	−0.387975	+	0.305657i
$885$		0			0
$886$	−0.944990	−	6.83999i	−0.0317476	−	0.229794i
$887$	−22.1513	−	22.1513i	−0.743769	−	0.743769i	0.229532	−	0.973301i	$-0.426280\pi$
$887$	−22.1513	−	22.1513i	−0.743769	−	0.743769i	−0.973301	+	0.229532i	$0.926280\pi$
$888$		0			0
$889$	−0.00710357	+	0.00710357i	−0.000238246	+	0.000238246i
$890$	0.504360	+	0.381915i	0.0169062	+	0.0128018i
$891$		0			0
$892$	−25.1706	+	44.9123i	−0.842775	+	1.50377i
$893$	2.33585	−	5.63924i	0.0781662	−	0.188710i
$894$		0			0
$895$			1.67946i			0.0561381i
$896$	−0.161028	+	0.102831i	−0.00537957	+	0.00343535i
$897$		0			0
$898$	−6.61860	+	25.3475i	−0.220865	+	0.845857i
$899$	0.922730	+	0.382207i	0.0307748	+	0.0127473i
$900$		0			0
$901$	2.41976	+	5.84181i	0.0806138	+	0.194619i
$902$	10.0403	−	13.2593i	0.334305	−	0.441486i
$903$		0			0
$904$	−28.9651	−	27.8757i	−0.963364	−	0.927131i
$905$	3.39428	−	3.39428i	0.112830	−	0.112830i
$906$		0			0
$907$	0.313807	+	0.757598i	0.0104198	+	0.0251556i	0.929004	−	0.370070i	$-0.120666\pi$
$907$	0.313807	+	0.757598i	0.0104198	+	0.0251556i	−0.918584	+	0.395226i	$0.870666\pi$
$908$	27.0042	+	34.2768i	0.896165	+	1.13752i
$909$		0			0
$910$	0.0171024	−	0.0100203i	0.000566939	−	0.000332169i
$911$		−	19.5639i		−	0.648182i	−0.946026	−	0.324091i	$-0.894942\pi$
$911$		−	19.5639i		−	0.648182i	0.946026	−	0.324091i	$-0.105058\pi$
$912$		0			0
$913$			12.2690i			0.406045i
$914$	−4.36523	−	7.45049i	−0.144389	−	0.246440i
$915$		0			0
$916$	−1.28162	+	10.7993i	−0.0423460	+	0.356818i
$917$	0.0833857	+	0.201311i	0.00275364	+	0.00664787i
$918$		0			0
$919$	29.8704	−	29.8704i	0.985333	−	0.985333i	−0.0145606	−	0.999894i	$-0.504635\pi$
$919$	29.8704	−	29.8704i	0.985333	−	0.985333i	0.999894	+	0.0145606i	$0.00463493\pi$
$920$	1.68233	+	3.85107i	0.0554648	+	0.126966i
$921$		0			0
$922$	10.8016	+	8.17927i	0.355732	+	0.269370i
$923$	17.3235	+	41.8225i	0.570209	+	1.37661i
$924$		0			0
$925$	−12.5120	−	5.18265i	−0.411393	−	0.170404i
$926$	41.6372	+	10.8721i	1.36828	+	0.357278i
$927$		0			0
$928$	−26.3710	−	2.61824i	−0.865670	−	0.0859481i
$929$			32.3872i			1.06259i	0.847187	+	0.531295i	$0.178294\pi$
$929$			32.3872i			1.06259i	−0.847187	+	0.531295i	$0.821706\pi$
$930$		0			0
$931$	−6.75430	+	16.3063i	−0.221363	+	0.534418i
$932$	32.2460	−	9.08338i	1.05625	−	0.297536i
$933$		0			0
$934$	−26.3489	+	34.7965i	−0.862162	+	1.13858i
$935$	1.12856	−	1.12856i	0.0369078	−	0.0369078i
$936$		0			0
$937$	−25.5697	−	25.5697i	−0.835326	−	0.835326i	0.152914	−	0.988240i	$-0.451134\pi$
$937$	−25.5697	−	25.5697i	−0.835326	−	0.835326i	−0.988240	+	0.152914i	$0.951134\pi$
$938$	0.238521	−	0.0329532i	0.00778798	−	0.00107596i
$939$		0			0
$940$	−0.125101	+	1.05413i	−0.00408033	+	0.0343819i
$941$	−36.3130	−	15.0413i	−1.18377	−	0.490334i	−0.298048	−	0.954551i	$-0.596336\pi$
$941$	−36.3130	−	15.0413i	−1.18377	−	0.490334i	−0.885721	+	0.464217i	$0.846336\pi$
$942$		0			0
$943$	−21.2370			−0.691571
$944$	−9.17597	+	12.6130i	−0.298652	+	0.410517i
$945$		0			0
$946$	−9.70383	−	16.5623i	−0.315499	−	0.538487i
$947$	0.876633	−	2.11638i	0.0284868	−	0.0687731i	−0.908996	−	0.416805i	$-0.863150\pi$
$947$	0.876633	−	2.11638i	0.0284868	−	0.0687731i	0.937483	+	0.348032i	$0.113150\pi$
$948$		0			0
$949$	−54.6776	+	22.6482i	−1.77491	+	0.735191i
$950$	−17.4922	+	2.41666i	−0.567521	+	0.0784067i
$951$		0			0
$952$	−0.00177543	−	0.0926355i	−5.75420e−5	−	0.00300233i
$953$	−26.6396	−	26.6396i	−0.862941	−	0.862941i	0.128738	−	0.991679i	$-0.458907\pi$
$953$	−26.6396	−	26.6396i	−0.862941	−	0.862941i	−0.991679	+	0.128738i	$0.958907\pi$
$954$		0			0
$955$	0.511646	−	0.211931i	0.0165565	−	0.00685791i
$956$	−9.79778	+	17.4823i	−0.316883	+	0.565418i
$957$		0			0
$958$	−45.3496	−	11.8414i	−1.46518	−	0.382579i
$959$	−0.258550			−0.00834900
$960$		0			0
$961$	30.9545			0.998534
$962$	−14.1655	−	3.69882i	−0.456714	−	0.119255i
$963$		0			0
$964$	2.19835	−	3.92255i	0.0708042	−	0.126337i
$965$	−1.25369	+	0.519296i	−0.0403578	+	0.0167167i
$966$		0			0
$967$	−35.6148	−	35.6148i	−1.14529	−	1.14529i	−0.987467	−	0.157828i	$-0.949551\pi$
$967$	−35.6148	−	35.6148i	−1.14529	−	1.14529i	−0.157828	−	0.987467i	$-0.550449\pi$
$968$	−8.71659	+	0.167060i	−0.280162	+	0.00536951i
$969$		0			0
$970$	3.65081	−	0.504384i	0.117220	−	0.0161948i
$971$	−6.57654	+	2.72409i	−0.211051	+	0.0874203i	−0.485705	−	0.874123i	$-0.661437\pi$
$971$	−6.57654	+	2.72409i	−0.211051	+	0.0874203i	0.274653	+	0.961543i	$0.411437\pi$
$972$		0			0
$973$	−0.0599758	+	0.144794i	−0.00192274	+	0.00464189i
$974$	−8.42921	−	14.3868i	−0.270089	−	0.460983i
$975$		0			0
$976$	−2.33699	−	14.8155i	−0.0748054	−	0.474232i
$977$	11.5407			0.369220			0.184610	−	0.982812i	$-0.440898\pi$
$977$	11.5407			0.369220			0.184610	+	0.982812i	$0.440898\pi$
$978$		0			0
$979$	7.07360	+	2.92998i	0.226073	+	0.0936426i
$980$	0.361738	−	3.04810i	0.0115553	−	0.0973681i
$981$		0			0
$982$	14.0669	−	1.94344i	0.448894	−	0.0620177i
$983$	15.7142	+	15.7142i	0.501204	+	0.501204i	0.911812	−	0.410608i	$-0.134684\pi$
$983$	15.7142	+	15.7142i	0.501204	+	0.501204i	−0.410608	+	0.911812i	$0.634684\pi$
$984$		0			0
$985$	3.79857	−	3.79857i	0.121033	−	0.121033i
$986$	7.75800	−	10.2453i	0.247065	−	0.326276i
$987$		0			0
$988$	−18.3743	+	5.17586i	−0.584565	+	0.164666i
$989$	−9.37988	+	22.6450i	−0.298263	+	0.720070i
$990$		0			0
$991$		−	30.5998i		−	0.972033i	−0.873950	−	0.486017i	$-0.838449\pi$
$991$		−	30.5998i		−	0.972033i	0.873950	−	0.486017i	$-0.161551\pi$
$992$	1.15436	−	0.349181i	0.0366509	−	0.0110865i
$993$		0			0
$994$	−0.276346	−	0.0721578i	−0.00876515	−	0.00228871i
$995$	−0.490633	−	0.203227i	−0.0155541	−	0.00644273i
$996$		0			0
$997$	−16.7966	−	40.5506i	−0.531954	−	1.28425i	−0.930227	−	0.366984i	$-0.880390\pi$
$997$	−16.7966	−	40.5506i	−0.531954	−	1.28425i	0.398273	−	0.917267i	$-0.369610\pi$
$998$	−12.5687	−	9.51735i	−0.397855	−	0.301267i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.a.323.4	yes	128
3.2	odd	2	inner	864.2.w.a.323.29	yes	128
32.11	odd	8	inner	864.2.w.a.107.29	yes	128
96.11	even	8	inner	864.2.w.a.107.4	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.a.107.4	✓	128	96.11	even	8	inner
864.2.w.a.107.29	yes	128	32.11	odd	8	inner
864.2.w.a.323.4	yes	128	1.1	even	1	trivial
864.2.w.a.323.29	yes	128	3.2	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36834 - 0.357292i) q^{2} +(1.74468 + 0.977791i) q^{4} +(0.202568 - 0.0839066i) q^{5} +(-0.0119413 - 0.0119413i) q^{7} +(-2.03796 - 1.96131i) q^{8} +O(q^{10})\)	\(q+(-1.36834 - 0.357292i) q^{2} +(1.74468 + 0.977791i) q^{4} +(0.202568 - 0.0839066i) q^{5} +(-0.0119413 - 0.0119413i) q^{7} +(-2.03796 - 1.96131i) q^{8} +(-0.307161 + 0.0424363i) q^{10} +(-3.46699 + 1.43608i) q^{11} +(1.44858 - 3.49717i) q^{13} +(0.0120732 + 0.0206062i) q^{14} +(2.08785 + 3.41187i) q^{16} -1.93975 q^{17} +(-2.32957 - 0.964939i) q^{19} +(0.435461 + 0.0516790i) q^{20} +(5.25711 - 0.726304i) q^{22} +(-4.79172 - 4.79172i) q^{23} +(-3.50154 + 3.50154i) q^{25} +(-3.23165 + 4.26774i) q^{26} +(-0.00915771 - 0.0325099i) q^{28} +(1.79276 - 4.32810i) q^{29} +0.213195i q^{31} +(-1.63784 - 5.41456i) q^{32} +(2.65423 + 0.693057i) q^{34} +(-0.00342088 - 0.00141698i) q^{35} +(1.04659 + 2.52670i) q^{37} +(2.84287 + 2.15270i) q^{38} +(-0.577392 - 0.226301i) q^{40} +(2.21601 - 2.21601i) q^{41} +(-1.38417 - 3.34169i) q^{43} +(-7.45299 - 0.884495i) q^{44} +(4.84464 + 8.26873i) q^{46} +2.42072i q^{47} -6.99971i q^{49} +(6.04235 - 3.54021i) q^{50} +(5.94681 - 4.68506i) q^{52} +(-1.24746 - 3.01163i) q^{53} +(-0.581807 + 0.581807i) q^{55} +(0.000915288 + 0.0477564i) q^{56} +(-3.99949 + 5.28175i) q^{58} +(1.49224 + 3.60257i) q^{59} +(-3.46424 - 1.43494i) q^{61} +(0.0761730 - 0.291723i) q^{62} +(0.306539 + 7.99412i) q^{64} -0.829962i q^{65} +(3.85824 - 9.31462i) q^{67} +(-3.38425 - 1.89667i) q^{68} +(0.00417464 + 0.00316115i) q^{70} +(-8.45626 + 8.45626i) q^{71} +(-11.0555 - 11.0555i) q^{73} +(-0.529321 - 3.83131i) q^{74} +(-3.12085 - 3.96135i) q^{76} +(0.0585490 + 0.0242518i) q^{77} -15.3461 q^{79} +(0.709211 + 0.515953i) q^{80} +(-3.82400 + 2.24048i) q^{82} +(1.25116 - 3.02056i) q^{83} +(-0.392932 + 0.162758i) q^{85} +(0.700054 + 5.06711i) q^{86} +(9.88217 + 3.87318i) q^{88} +(-1.44269 - 1.44269i) q^{89} +(-0.0590587 + 0.0244629i) q^{91} +(-3.67474 - 13.0453i) q^{92} +(0.864905 - 3.31236i) q^{94} -0.552862 q^{95} -11.8857 q^{97} +(-2.50094 + 9.57796i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more