LMFDB - Embedded newform 864.2.w.b.107.12

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			107.12
Character	$\chi$	$=$	864.107
Dual form			864.2.w.b.323.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654624 + 1.25358i) q^{2} +(-1.14293 - 1.64125i) q^{4} +(-0.0422264 - 0.0174907i) q^{5} +(-1.54323 + 1.54323i) q^{7} +(2.80563 - 0.358360i) q^{8} +O(q^{10})$	\(q+(-0.654624 + 1.25358i) q^{2} +(-1.14293 - 1.64125i) q^{4} +(-0.0422264 - 0.0174907i) q^{5} +(-1.54323 + 1.54323i) q^{7} +(2.80563 - 0.358360i) q^{8} +(0.0495684 - 0.0414843i) q^{10} +(2.36542 + 0.979788i) q^{11} +(-0.368489 - 0.889611i) q^{13} +(-0.924330 - 2.94480i) q^{14} +(-1.38740 + 3.75168i) q^{16} +4.89675 q^{17} +(-1.42602 + 0.590675i) q^{19} +(0.0195553 + 0.0892947i) q^{20} +(-2.77670 + 2.32385i) q^{22} +(1.43441 - 1.43441i) q^{23} +(-3.53406 - 3.53406i) q^{25} +(1.35642 + 0.120430i) q^{26} +(4.29664 + 0.769016i) q^{28} +(2.09126 + 5.04875i) q^{29} +8.87410i q^{31} +(-3.79481 - 4.19516i) q^{32} +(-3.20553 + 6.13848i) q^{34} +(0.0921573 - 0.0381728i) q^{35} +(-1.04239 + 2.51656i) q^{37} +(0.193045 - 2.17430i) q^{38} +(-0.124740 - 0.0339403i) q^{40} +(0.556667 + 0.556667i) q^{41} +(-1.48807 + 3.59253i) q^{43} +(-1.09544 - 5.00208i) q^{44} +(0.859153 + 2.73716i) q^{46} +11.2877i q^{47} +2.23687i q^{49} +(6.74371 - 2.11675i) q^{50} +(-1.03892 + 1.62155i) q^{52} +(-3.14759 + 7.59897i) q^{53} +(-0.0827458 - 0.0827458i) q^{55} +(-3.77671 + 4.88277i) q^{56} +(-7.69802 - 0.683468i) q^{58} +(0.698406 - 1.68610i) q^{59} +(2.19335 - 0.908515i) q^{61} +(-11.1244 - 5.80920i) q^{62} +(7.74316 - 2.01086i) q^{64} +0.0440102i q^{65} +(4.03963 + 9.75253i) q^{67} +(-5.59666 - 8.03679i) q^{68} +(-0.0124757 + 0.140516i) q^{70} +(4.06618 + 4.06618i) q^{71} +(5.63896 - 5.63896i) q^{73} +(-2.47233 - 2.95412i) q^{74} +(2.59929 + 1.66535i) q^{76} +(-5.16243 + 2.13835i) q^{77} -4.03294 q^{79} +(0.124205 - 0.134153i) q^{80} +(-1.06224 + 0.333420i) q^{82} +(2.22963 + 5.38280i) q^{83} +(-0.206772 - 0.0856477i) q^{85} +(-3.52940 - 4.21717i) q^{86} +(6.98761 + 1.90125i) q^{88} +(4.29985 - 4.29985i) q^{89} +(1.94154 + 0.804212i) q^{91} +(-3.99367 - 0.714790i) q^{92} +(-14.1501 - 7.38920i) q^{94} +0.0705468 q^{95} -10.5936 q^{97} +(-2.80410 - 1.46431i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) $ 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	−0.654624	+	1.25358i	−0.462889	+	0.886416i
$2$	−0.654624	+	1.25358i	−0.462889	+	0.886416i
$3$		0			0
$3$		0			0
$4$	−1.14293	−	1.64125i	−0.571467	−	0.820625i
$5$	−0.0422264	−	0.0174907i	−0.0188842	−	0.00782209i	0.373221	−	0.927742i	$-0.378253\pi$
$5$	−0.0422264	−	0.0174907i	−0.0188842	−	0.00782209i	−0.392106	+	0.919920i	$0.628253\pi$
$6$		0			0
$7$	−1.54323	+	1.54323i	−0.583287	+	0.583287i	−0.935805	−	0.352518i	$-0.885325\pi$
$7$	−1.54323	+	1.54323i	−0.583287	+	0.583287i	0.352518	+	0.935805i	$0.385325\pi$
$8$	2.80563	−	0.358360i	0.991941	−	0.126700i
$9$		0			0
$10$	0.0495684	−	0.0414843i	0.0156749	−	0.0131185i
$11$	2.36542	+	0.979788i	0.713200	+	0.295417i	0.709628	−	0.704576i	$-0.248863\pi$
$11$	2.36542	+	0.979788i	0.713200	+	0.295417i	0.00357225	+	0.999994i	$0.498863\pi$
$12$		0			0
$13$	−0.368489	−	0.889611i	−0.102200	−	0.246734i	0.864506	−	0.502623i	$-0.167632\pi$
$13$	−0.368489	−	0.889611i	−0.102200	−	0.246734i	−0.966706	+	0.255890i	$0.917632\pi$
$14$	−0.924330	−	2.94480i	−0.247038	−	0.787032i
$15$		0			0
$16$	−1.38740	+	3.75168i	−0.346850	+	0.937921i
$17$	4.89675			1.18764			0.593818	−	0.804599i	$-0.297620\pi$
$17$	4.89675			1.18764			0.593818	+	0.804599i	$0.297620\pi$
$18$		0			0
$19$	−1.42602	+	0.590675i	−0.327151	+	0.135510i	−0.540213	−	0.841528i	$-0.681656\pi$
$19$	−1.42602	+	0.590675i	−0.327151	+	0.135510i	0.213062	+	0.977039i	$0.431656\pi$
$20$	0.0195553	+	0.0892947i	0.00437270	+	0.0199669i
$21$		0			0
$22$	−2.77670	+	2.32385i	−0.591995	+	0.495447i
$23$	1.43441	−	1.43441i	0.299096	−	0.299096i	−0.541564	−	0.840660i	$-0.682168\pi$
$23$	1.43441	−	1.43441i	0.299096	−	0.299096i	0.840660	+	0.541564i	$0.182168\pi$
$24$		0			0
$25$	−3.53406	−	3.53406i	−0.706811	−	0.706811i
$26$	1.35642	+	0.120430i	0.266016	+	0.0236182i
$27$		0			0
$28$	4.29664	+	0.769016i	0.811989	+	0.145330i
$29$	2.09126	+	5.04875i	0.388338	+	0.937530i	0.990292	+	0.139000i	$0.0443887\pi$
$29$	2.09126	+	5.04875i	0.388338	+	0.937530i	−0.601955	+	0.798530i	$0.705611\pi$
$30$		0			0
$31$			8.87410i			1.59384i	0.604088	+	0.796918i	$0.293537\pi$
$31$			8.87410i			1.59384i	−0.604088	+	0.796918i	$0.706463\pi$
$32$	−3.79481	−	4.19516i	−0.670835	−	0.741607i
$33$		0			0
$34$	−3.20553	+	6.13848i	−0.549744	+	1.05274i
$35$	0.0921573	−	0.0381728i	0.0155774	−	0.00645238i
$36$		0			0
$37$	−1.04239	+	2.51656i	−0.171368	+	0.413719i	−0.986108	−	0.166108i	$-0.946880\pi$
$37$	−1.04239	+	2.51656i	−0.171368	+	0.413719i	0.814739	+	0.579827i	$0.196880\pi$
$38$	0.193045	−	2.17430i	0.0313160	−	0.352718i
$39$		0			0
$40$	−0.124740	−	0.0339403i	−0.0197231	−	0.00536644i
$41$	0.556667	+	0.556667i	0.0869368	+	0.0869368i	0.749238	−	0.662301i	$-0.230420\pi$
$41$	0.556667	+	0.556667i	0.0869368	+	0.0869368i	−0.662301	+	0.749238i	$0.730420\pi$
$42$		0			0
$43$	−1.48807	+	3.59253i	−0.226929	+	0.547855i	−0.995801	−	0.0915481i	$-0.970818\pi$
$43$	−1.48807	+	3.59253i	−0.226929	+	0.547855i	0.768872	+	0.639403i	$0.220818\pi$
$44$	−1.09544	−	5.00208i	−0.165144	−	0.754091i
$45$		0			0
$46$	0.859153	+	2.73716i	0.126675	+	0.403571i
$47$			11.2877i			1.64648i	0.567693	+	0.823240i	$0.307836\pi$
$47$			11.2877i			1.64648i	−0.567693	+	0.823240i	$0.692164\pi$
$48$		0			0
$49$			2.23687i			0.319553i
$50$	6.74371	−	2.11675i	0.953704	−	0.299354i
$51$		0			0
$52$	−1.03892	+	1.62155i	−0.144072	+	0.224868i
$53$	−3.14759	+	7.59897i	−0.432355	+	1.04380i	0.546170	+	0.837674i	$0.316085\pi$
$53$	−3.14759	+	7.59897i	−0.432355	+	1.04380i	−0.978526	+	0.206124i	$0.933915\pi$
$54$		0			0
$55$	−0.0827458	−	0.0827458i	−0.0111574	−	0.0111574i
$56$	−3.77671	+	4.88277i	−0.504684	+	0.652488i
$57$		0			0
$58$	−7.69802	−	0.683468i	−1.01080	−	0.0897437i
$59$	0.698406	−	1.68610i	0.0909247	−	0.219512i	−0.871875	−	0.489729i	$-0.837096\pi$
$59$	0.698406	−	1.68610i	0.0909247	−	0.219512i	0.962799	+	0.270218i	$0.0870956\pi$
$60$		0			0
$61$	2.19335	−	0.908515i	0.280830	−	0.116323i	−0.237823	−	0.971309i	$-0.576434\pi$
$61$	2.19335	−	0.908515i	0.280830	−	0.116323i	0.518653	+	0.854985i	$0.326434\pi$
$62$	−11.1244	−	5.80920i	−1.41280	−	0.737769i
$63$		0			0
$64$	7.74316	−	2.01086i	0.967894	−	0.251357i
$65$			0.0440102i			0.00545879i
$66$		0			0
$67$	4.03963	+	9.75253i	0.493520	+	1.19146i	0.952917	+	0.303231i	$0.0980653\pi$
$67$	4.03963	+	9.75253i	0.493520	+	1.19146i	−0.459398	+	0.888231i	$0.651935\pi$
$68$	−5.59666	−	8.03679i	−0.678695	−	0.974604i
$69$		0			0
$70$	−0.0124757	+	0.140516i	−0.00149113	+	0.0167948i
$71$	4.06618	+	4.06618i	0.482567	+	0.482567i	0.905951	−	0.423384i	$-0.139158\pi$
$71$	4.06618	+	4.06618i	0.482567	+	0.482567i	−0.423384	+	0.905951i	$0.639158\pi$
$72$		0			0
$73$	5.63896	−	5.63896i	0.659990	−	0.659990i	−0.295388	−	0.955377i	$-0.595449\pi$
$73$	5.63896	−	5.63896i	0.659990	−	0.659990i	0.955377	+	0.295388i	$0.0954488\pi$
$74$	−2.47233	−	2.95412i	−0.287403	−	0.343410i
$75$		0			0
$76$	2.59929	+	1.66535i	0.298159	+	0.191028i
$77$	−5.16243	+	2.13835i	−0.588313	+	0.243687i
$78$		0			0
$79$	−4.03294			−0.453742			−0.226871	−	0.973925i	$-0.572850\pi$
$79$	−4.03294			−0.453742			−0.226871	+	0.973925i	$0.572850\pi$
$80$	0.124205	−	0.134153i	0.0138865	−	0.0149988i
$81$		0			0
$82$	−1.06224	+	0.333420i	−0.117304	+	0.0368201i
$83$	2.22963	+	5.38280i	0.244734	+	0.590839i	0.997741	−	0.0671726i	$-0.0213978\pi$
$83$	2.22963	+	5.38280i	0.244734	+	0.590839i	−0.753008	+	0.658012i	$0.771398\pi$
$84$		0			0
$85$	−0.206772	−	0.0856477i	−0.0224276	−	0.00928980i
$86$	−3.52940	−	4.21717i	−0.380585	−	0.454750i
$87$		0			0
$88$	6.98761	+	1.90125i	0.744882	+	0.202674i
$89$	4.29985	−	4.29985i	0.455783	−	0.455783i	−0.441485	−	0.897268i	$-0.645548\pi$
$89$	4.29985	−	4.29985i	0.455783	−	0.455783i	0.897268	+	0.441485i	$0.145548\pi$
$90$		0			0
$91$	1.94154	+	0.804212i	0.203529	+	0.0843043i
$92$	−3.99367	−	0.714790i	−0.416369	−	0.0745220i
$93$		0			0
$94$	−14.1501	−	7.38920i	−1.45947	−	0.762138i
$95$	0.0705468			0.00723795
$96$		0			0
$97$	−10.5936			−1.07562			−0.537810	−	0.843066i	$-0.680748\pi$
$97$	−10.5936			−1.07562			−0.537810	+	0.843066i	$0.680748\pi$
$98$	−2.80410	−	1.46431i	−0.283257	−	0.147918i
$99$		0			0
$100$	−1.76107	+	9.83947i	−0.176107	+	0.983947i
$101$	−6.60514	−	2.73594i	−0.657236	−	0.272236i	0.0290390	−	0.999578i	$-0.490755\pi$
$101$	−6.60514	−	2.73594i	−0.657236	−	0.272236i	−0.686275	+	0.727342i	$0.740755\pi$
$102$		0			0
$103$	8.13450	−	8.13450i	0.801516	−	0.801516i	−0.181816	−	0.983333i	$-0.558198\pi$
$103$	8.13450	−	8.13450i	0.801516	−	0.801516i	0.983333	+	0.181816i	$0.0581976\pi$
$104$	−1.35265	−	2.36387i	−0.132638	−	0.231797i
$105$		0			0
$106$	−7.46543	−	8.92023i	−0.725107	−	0.866410i
$107$	−7.60654	−	3.15073i	−0.735352	−	0.304593i	−0.0166025	−	0.999862i	$-0.505285\pi$
$107$	−7.60654	−	3.15073i	−0.735352	−	0.304593i	−0.718749	+	0.695270i	$0.755285\pi$
$108$		0			0
$109$	−7.67143	−	18.5205i	−0.734790	−	1.77394i	−0.625925	−	0.779883i	$-0.715278\pi$
$109$	−7.67143	−	18.5205i	−0.734790	−	1.77394i	−0.108865	−	0.994057i	$-0.534722\pi$
$110$	0.157896	−	0.0495612i	0.0150548	−	0.00472548i
$111$		0			0
$112$	−3.64863	−	7.93079i	−0.344763	−	0.749390i
$113$	10.4742			0.985331			0.492666	−	0.870219i	$-0.336023\pi$
$113$	10.4742			0.985331			0.492666	+	0.870219i	$0.336023\pi$
$114$		0			0
$115$	−0.0856589	+	0.0354811i	−0.00798774	+	0.00330863i
$116$	5.89609	−	9.20268i	0.547438	−	0.854447i
$117$		0			0
$118$	1.65647	+	1.97927i	0.152491	+	0.182207i
$119$	−7.55682	+	7.55682i	−0.692732	+	0.692732i
$120$		0			0
$121$	−3.14296	−	3.14296i	−0.285723	−	0.285723i
$122$	−0.296922	+	3.34428i	−0.0268820	+	0.302777i
$123$		0			0
$124$	14.5646	−	10.1425i	1.30794	−	0.910825i
$125$	0.174871	+	0.422175i	0.0156409	+	0.0377605i
$126$		0			0
$127$			11.1840i			0.992422i	0.868202	+	0.496211i	$0.165276\pi$
$127$			11.1840i			0.992422i	−0.868202	+	0.496211i	$0.834724\pi$
$128$	−2.54808	+	11.0230i	−0.225221	+	0.974308i
$129$		0			0
$130$	−0.0551703	−	0.0288101i	−0.00483876	−	0.00252681i
$131$	8.24207	−	3.41398i	0.720113	−	0.298280i	0.00763072	−	0.999971i	$-0.497571\pi$
$131$	8.24207	−	3.41398i	0.720113	−	0.298280i	0.712482	+	0.701690i	$0.247571\pi$
$132$		0			0
$133$	1.28912	−	3.11222i	0.111781	−	0.269864i
$134$	−14.8700	−	1.32023i	−1.28458	−	0.114051i
$135$		0			0
$136$	13.7385	−	1.75480i	1.17807	−	0.150473i
$137$	5.44839	+	5.44839i	0.465488	+	0.465488i	0.900449	−	0.434961i	$-0.143238\pi$
$137$	5.44839	+	5.44839i	0.465488	+	0.465488i	−0.434961	+	0.900449i	$0.643238\pi$
$138$		0			0
$139$	−2.47429	+	5.97346i	−0.209867	+	0.506663i	−0.993402	−	0.114685i	$-0.963414\pi$
$139$	−2.47429	+	5.97346i	−0.209867	+	0.506663i	0.783535	+	0.621347i	$0.213414\pi$
$140$	−0.167981	−	0.107624i	−0.0141970	−	0.00909590i
$141$		0			0
$142$	−7.75911	+	2.43547i	−0.651130	+	0.204380i
$143$		−	2.46534i		−	0.206162i
$144$		0			0
$145$		−	0.249768i		−	0.0207421i
$146$	3.37750	+	10.7603i	0.279524	+	0.890528i
$147$		0			0
$148$	5.32168	−	1.16543i	0.437440	−	0.0957981i
$149$	0.734041	−	1.77213i	0.0601350	−	0.145179i	−0.890956	−	0.454090i	$-0.849965\pi$
$149$	0.734041	−	1.77213i	0.0601350	−	0.145179i	0.951091	+	0.308911i	$0.0999645\pi$
$150$		0			0
$151$	−1.46383	−	1.46383i	−0.119125	−	0.119125i	0.645031	−	0.764156i	$-0.276844\pi$
$151$	−1.46383	−	1.46383i	−0.119125	−	0.119125i	−0.764156	+	0.645031i	$0.776844\pi$
$152$	−3.78921	+	2.16825i	−0.307345	+	0.175868i
$153$		0			0
$154$	0.698856	−	7.87134i	0.0563154	−	0.634291i
$155$	0.155214	−	0.374721i	0.0124671	−	0.0300983i
$156$		0			0
$157$	14.5329	−	6.01971i	1.15985	−	0.480425i	0.282025	−	0.959407i	$-0.408994\pi$
$157$	14.5329	−	6.01971i	1.15985	−	0.480425i	0.877825	+	0.478982i	$0.158994\pi$
$158$	2.64006	−	5.05562i	0.210032	−	0.402204i
$159$		0			0
$160$	0.0868647	+	0.243520i	0.00686726	+	0.0192520i
$161$			4.42726i			0.348917i
$162$		0			0
$163$	−3.29257	−	7.94896i	−0.257894	−	0.622611i	0.740905	−	0.671610i	$-0.234397\pi$
$163$	−3.29257	−	7.94896i	−0.257894	−	0.622611i	−0.998799	+	0.0489990i	$0.984397\pi$
$164$	0.277396	−	1.54986i	0.0216610	−	0.121024i
$165$		0			0
$166$	−8.20735	−	0.728688i	−0.637014	−	0.0565572i
$167$	10.9855	+	10.9855i	0.850086	+	0.850086i	0.990143	−	0.140057i	$-0.0447286\pi$
$167$	10.9855	+	10.9855i	0.850086	+	0.850086i	−0.140057	+	0.990143i	$0.544729\pi$
$168$		0			0
$169$	8.53676	−	8.53676i	0.656674	−	0.656674i
$170$	0.242724	−	0.203138i	0.0186161	−	0.0155800i
$171$		0			0
$172$	7.59700	−	1.66372i	0.579266	−	0.126858i
$173$	−10.2040	+	4.22666i	−0.775799	+	0.321347i	−0.735219	−	0.677830i	$-0.762921\pi$
$173$	−10.2040	+	4.22666i	−0.775799	+	0.321347i	−0.0405804	+	0.999176i	$0.512921\pi$
$174$		0			0
$175$	10.9077			0.824547
$176$	−6.95764	+	7.51494i	−0.524452	+	0.566460i
$177$		0			0
$178$	2.57543	+	8.20500i	0.193037	+	0.614991i
$179$	−9.52358	−	22.9920i	−0.711826	−	1.71850i	−0.695388	−	0.718635i	$-0.744767\pi$
$179$	−9.52358	−	22.9920i	−0.711826	−	1.71850i	−0.0164379	−	0.999865i	$-0.505233\pi$
$180$		0			0
$181$	−14.3423	−	5.94076i	−1.06605	−	0.441573i	−0.220456	−	0.975397i	$-0.570755\pi$
$181$	−14.3423	−	5.94076i	−1.06605	−	0.441573i	−0.845596	+	0.533824i	$0.820755\pi$
$182$	−2.27912	+	1.90742i	−0.168940	+	0.141388i
$183$		0			0
$184$	3.51040	−	4.53847i	0.258790	−	0.334581i
$185$	0.0880328	−	0.0880328i	0.00647230	−	0.00647230i
$186$		0			0
$187$	11.5829	+	4.79778i	0.847023	+	0.350848i
$188$	18.5259	−	12.9011i	1.35114	−	0.940910i
$189$		0			0
$190$	−0.0461817	+	0.0884362i	−0.00335037	+	0.00641584i
$191$	17.7384			1.28350			0.641752	−	0.766912i	$-0.278208\pi$
$191$	17.7384			1.28350			0.641752	+	0.766912i	$0.278208\pi$
$192$		0			0
$193$	26.6932			1.92142			0.960709	−	0.277559i	$-0.0895254\pi$
$193$	26.6932			1.92142			0.960709	+	0.277559i	$0.0895254\pi$
$194$	6.93485	−	13.2800i	0.497893	−	0.953447i
$195$		0			0
$196$	3.67127	−	2.55660i	0.262233	−	0.182614i
$197$	8.73578	+	3.61848i	0.622398	+	0.257806i	0.671519	−	0.740987i	$-0.265642\pi$
$197$	8.73578	+	3.61848i	0.622398	+	0.257806i	−0.0491211	+	0.998793i	$0.515642\pi$
$198$		0			0
$199$	−0.749357	+	0.749357i	−0.0531205	+	0.0531205i	−0.733168	−	0.680048i	$-0.761959\pi$
$199$	−0.749357	+	0.749357i	−0.0531205	+	0.0531205i	0.680048	+	0.733168i	$0.261959\pi$
$200$	−11.1817	−	8.64880i	−0.790668	−	0.611563i
$201$		0			0
$202$	7.75361	−	6.48907i	0.545542	−	0.456569i
$203$	−11.0187	−	4.56409i	−0.773361	−	0.320337i
$204$		0			0
$205$	−0.0137695	−	0.0332425i	−0.000961704	−	0.00232176i
$206$	4.87222	+	15.5223i	0.339464	+	1.08149i
$207$		0			0
$208$	3.84878	−	0.148206i	0.266865	−	0.0102762i
$209$	−3.95186			−0.273356
$210$		0			0
$211$	−11.2680	+	4.66737i	−0.775723	+	0.321315i	−0.735188	−	0.677863i	$-0.762906\pi$
$211$	−11.2680	+	4.66737i	−0.775723	+	0.321315i	−0.0405351	+	0.999178i	$0.512906\pi$
$212$	16.0693	−	3.51913i	1.10364	−	0.241695i
$213$		0			0
$214$	8.92912	−	7.47287i	0.610382	−	0.510835i
$215$	0.125672	−	0.125672i	0.00857074	−	0.00857074i
$216$		0			0
$217$	−13.6948	−	13.6948i	−0.929663	−	0.929663i
$218$	28.2388	+	2.50718i	1.91258	+	0.169808i
$219$		0			0
$220$	−0.0412335	+	0.230379i	−0.00277996	+	0.0155322i
$221$	−1.80440	−	4.35620i	−0.121377	−	0.293030i
$222$		0			0
$223$			17.7737i			1.19021i	0.803646	+	0.595107i	$0.202890\pi$
$223$			17.7737i			1.19021i	−0.803646	+	0.595107i	$0.797110\pi$
$224$	12.3304	+	0.617830i	0.823858	+	0.0412805i
$225$		0			0
$226$	−6.85667	+	13.1303i	−0.456099	+	0.873414i
$227$	−12.1012	+	5.01248i	−0.803184	+	0.332690i	−0.746231	−	0.665687i	$-0.768139\pi$
$227$	−12.1012	+	5.01248i	−0.803184	+	0.332690i	−0.0569532	+	0.998377i	$0.518139\pi$
$228$		0			0
$229$	−0.704087	+	1.69982i	−0.0465274	+	0.112327i	−0.945435	−	0.325812i	$-0.894362\pi$
$229$	−0.704087	+	1.69982i	−0.0465274	+	0.112327i	0.898907	+	0.438139i	$0.144362\pi$
$230$	0.0115960	−	0.130607i	0.000764615	−	0.00861199i
$231$		0			0
$232$	7.67659	+	13.4155i	0.503993	+	0.880772i
$233$	15.8621	+	15.8621i	1.03916	+	1.03916i	0.999201	+	0.0399589i	$0.0127227\pi$
$233$	15.8621	+	15.8621i	1.03916	+	1.03916i	0.0399589	+	0.999201i	$0.487277\pi$
$234$		0			0
$235$	0.197430	−	0.476639i	0.0128789	−	0.0310925i
$236$	−3.56555	+	0.780845i	−0.232097	+	0.0508287i
$237$		0			0
$238$	−4.52621	−	14.4200i	−0.293391	−	0.934708i
$239$			16.2607i			1.05181i	0.850542	+	0.525907i	$0.176274\pi$
$239$			16.2607i			1.05181i	−0.850542	+	0.525907i	$0.823726\pi$
$240$		0			0
$241$		−	13.2742i		−	0.855064i	−0.904000	−	0.427532i	$-0.859383\pi$
$241$		−	13.2742i		−	0.855064i	0.904000	−	0.427532i	$-0.140617\pi$
$242$	5.99741	−	1.88250i	0.385528	−	0.121012i
$243$		0			0
$244$	−3.99796	−	2.56146i	−0.255943	−	0.163981i
$245$	0.0391245	−	0.0944550i	0.00249958	−	0.00603451i
$246$		0			0
$247$	1.05094	+	1.05094i	0.0668699	+	0.0668699i
$248$	3.18012	+	24.8975i	0.201938	+	1.58099i
$249$		0			0
$250$	−0.643706	−	0.0571514i	−0.0407115	−	0.00361457i
$251$	8.24217	−	19.8984i	0.520241	−	1.25597i	−0.417512	−	0.908671i	$-0.637098\pi$
$251$	8.24217	−	19.8984i	0.520241	−	1.25597i	0.937753	−	0.347302i	$-0.112902\pi$
$252$		0			0
$253$	4.79841	−	1.98757i	0.301673	−	0.124957i
$254$	−14.0201	−	7.32134i	−0.879699	−	0.459381i
$255$		0			0
$256$	−12.1502	−	10.4102i	−0.759390	−	0.650636i
$257$		−	21.9312i		−	1.36803i	−0.729467	−	0.684016i	$-0.760232\pi$
$257$		−	21.9312i		−	1.36803i	0.729467	−	0.684016i	$-0.239768\pi$
$258$		0			0
$259$	−2.27498	−	5.49228i	−0.141360	−	0.341274i
$260$	0.0722317	−	0.0503007i	0.00447962	−	0.00311952i
$261$		0			0
$262$	−1.11576	+	12.5670i	−0.0689317	+	0.776390i
$263$	13.7329	+	13.7329i	0.846805	+	0.846805i	0.989733	−	0.142928i	$-0.0456517\pi$
$263$	13.7329	+	13.7329i	0.846805	+	0.846805i	−0.142928	+	0.989733i	$0.545652\pi$
$264$		0			0
$265$	0.265823	−	0.265823i	0.0163294	−	0.0163294i
$266$	3.05753	+	3.65336i	0.187469	+	0.224002i
$267$		0			0
$268$	11.3893	−	17.7766i	0.695713	−	1.08588i
$269$	−11.9724	+	4.95911i	−0.729967	+	0.302362i	−0.716539	−	0.697547i	$-0.754275\pi$
$269$	−11.9724	+	4.95911i	−0.729967	+	0.302362i	−0.0134288	+	0.999910i	$0.504275\pi$
$270$		0			0
$271$	−2.43778			−0.148085			−0.0740423	−	0.997255i	$-0.523590\pi$
$271$	−2.43778			−0.148085			−0.0740423	+	0.997255i	$0.523590\pi$
$272$	−6.79376	+	18.3710i	−0.411932	+	1.11391i
$273$		0			0
$274$	−10.3967	+	3.26336i	−0.628085	+	0.197147i
$275$	−4.89690	−	11.8222i	−0.295294	−	0.712903i
$276$		0			0
$277$	3.18945	+	1.32112i	0.191636	+	0.0793781i	0.476438	−	0.879208i	$-0.341928\pi$
$277$	3.18945	+	1.32112i	0.191636	+	0.0793781i	−0.284802	+	0.958586i	$0.591928\pi$
$278$	−5.86850	−	7.01210i	−0.351969	−	0.420558i
$279$		0			0
$280$	0.244880	−	0.140124i	0.0146344	−	0.00837403i
$281$	20.3108	−	20.3108i	1.21164	−	1.21164i	0.241152	−	0.970487i	$-0.422475\pi$
$281$	20.3108	−	20.3108i	1.21164	−	1.21164i	0.970487	−	0.241152i	$-0.0775254\pi$
$282$		0			0
$283$	28.9481	+	11.9907i	1.72079	+	0.712773i	0.999804	+	0.0198193i	$0.00630911\pi$
$283$	28.9481	+	11.9907i	1.72079	+	0.712773i	0.720982	+	0.692953i	$0.243691\pi$
$284$	2.02624	−	11.3210i	0.120235	−	0.671778i
$285$		0			0
$286$	3.09051	+	1.61387i	0.182746	+	0.0954303i
$287$	−1.71813			−0.101418
$288$		0			0
$289$	6.97816			0.410480
$290$	0.313105	+	0.163504i	0.0183861	+	0.00960130i
$291$		0			0
$292$	−15.6999	−	2.80998i	−0.918767	−	0.164441i
$293$	−20.5940	−	8.53033i	−1.20312	−	0.498347i	−0.311112	−	0.950373i	$-0.600701\pi$
$293$	−20.5940	−	8.53033i	−1.20312	−	0.498347i	−0.892005	+	0.452026i	$0.850701\pi$
$294$		0			0
$295$	−0.0589823	+	0.0589823i	−0.00343408	+	0.00343408i
$296$	−2.02273	+	7.43408i	−0.117569	+	0.432097i
$297$		0			0
$298$	1.74099	+	2.08026i	0.100853	+	0.120506i
$299$	−1.80463	−	0.747504i	−0.104365	−	0.0432293i
$300$		0			0
$301$	−3.24766	−	7.84054i	−0.187192	−	0.451921i
$302$	2.79330	−	0.876775i	0.160736	−	0.0504527i
$303$		0			0
$304$	−0.237569	−	6.16947i	−0.0136255	−	0.353843i
$305$	−0.108508			−0.00621314
$306$		0			0
$307$	−31.1815	+	12.9158i	−1.77962	+	0.737144i	−0.786850	+	0.617144i	$0.788289\pi$
$307$	−31.1815	+	12.9158i	−1.77962	+	0.737144i	−0.992774	+	0.120000i	$0.961711\pi$
$308$	9.40988	+	6.02884i	0.536178	+	0.343525i
$309$		0			0
$310$	0.368136	+	0.439875i	0.0209087	+	0.0249832i
$311$	−1.85109	+	1.85109i	−0.104966	+	0.104966i	−0.757639	−	0.652674i	$-0.773647\pi$
$311$	−1.85109	+	1.85109i	−0.104966	+	0.104966i	0.652674	+	0.757639i	$0.273647\pi$
$312$		0			0
$313$	−23.3448	−	23.3448i	−1.31953	−	1.31953i	−0.914148	−	0.405380i	$-0.867139\pi$
$313$	−23.3448	−	23.3448i	−1.31953	−	1.31953i	−0.405380	−	0.914148i	$-0.632861\pi$
$314$	−1.96737	+	22.1588i	−0.111025	+	1.25049i
$315$		0			0
$316$	4.60939	+	6.61907i	0.259299	+	0.372352i
$317$	−8.95027	−	21.6079i	−0.502697	−	1.21362i	−0.948009	−	0.318243i	$-0.896907\pi$
$317$	−8.95027	−	21.6079i	−0.502697	−	1.21362i	0.445312	−	0.895375i	$-0.353093\pi$
$318$		0			0
$319$			13.9914i			0.783368i
$320$	−0.362137	−	0.0505223i	−0.0202440	−	0.00282428i
$321$		0			0
$322$	−5.54993	−	2.89819i	−0.309286	−	0.161510i
$323$	−6.98285	+	2.89239i	−0.388536	+	0.160937i
$324$		0			0
$325$	−1.84167	+	4.44620i	−0.102158	+	0.246631i
$326$	12.1201	+	1.07608i	0.671269	+	0.0595985i
$327$		0			0
$328$	1.76129	+	1.36232i	0.0972510	+	0.0752213i
$329$	−17.4195	−	17.4195i	−0.960370	−	0.960370i
$330$		0			0
$331$	8.10357	−	19.5637i	0.445412	−	1.07532i	−0.528609	−	0.848865i	$-0.677286\pi$
$331$	8.10357	−	19.5637i	0.445412	−	1.07532i	0.974022	−	0.226455i	$-0.0727137\pi$
$332$	6.28620	−	9.81156i	0.345000	−	0.538480i
$333$		0			0
$334$	−20.9627	+	6.57987i	−1.14703	+	0.360035i
$335$		−	0.482470i		−	0.0263602i
$336$		0			0
$337$			23.6220i			1.28677i	0.765541	+	0.643387i	$0.222471\pi$
$337$			23.6220i			1.28677i	−0.765541	+	0.643387i	$0.777529\pi$
$338$	5.11316	+	16.2899i	0.278119	+	0.886054i
$339$		0			0
$340$	0.0957574	+	0.437254i	0.00519318	+	0.0237134i
$341$	−8.69474	+	20.9910i	−0.470846	+	1.13672i
$342$		0			0
$343$	−14.2546	−	14.2546i	−0.769678	−	0.769678i
$344$	−2.88757	+	10.6126i	−0.155687	+	0.572192i
$345$		0			0
$346$	1.38136	−	15.5585i	0.0742623	−	0.836429i
$347$	−1.69754	+	4.09823i	−0.0911289	+	0.220005i	−0.962872	−	0.269959i	$-0.912990\pi$
$347$	−1.69754	+	4.09823i	−0.0911289	+	0.220005i	0.871743	+	0.489964i	$0.162990\pi$
$348$		0			0
$349$	26.1350	−	10.8255i	1.39898	−	0.579475i	0.449491	−	0.893285i	$-0.351605\pi$
$349$	26.1350	−	10.8255i	1.39898	−	0.579475i	0.949486	+	0.313810i	$0.101605\pi$
$350$	−7.14047	+	13.6737i	−0.381674	+	0.730892i
$351$		0			0
$352$	−4.86595	−	13.6414i	−0.259356	−	0.727091i
$353$		−	3.83846i		−	0.204300i	−0.994769	−	0.102150i	$-0.967428\pi$
$353$		−	3.83846i		−	0.204300i	0.994769	−	0.102150i	$-0.0325722\pi$
$354$		0			0
$355$	−0.100580	−	0.242820i	−0.00533821	−	0.0128876i
$356$	−11.9716	−	2.14268i	−0.634492	−	0.113562i
$357$		0			0
$358$	35.0567	+	3.11250i	1.85280	+	0.164501i
$359$	−16.6932	−	16.6932i	−0.881036	−	0.881036i	0.112604	−	0.993640i	$-0.464081\pi$
$359$	−16.6932	−	16.6932i	−0.881036	−	0.881036i	−0.993640	+	0.112604i	$0.964081\pi$
$360$		0			0
$361$	−11.7504	+	11.7504i	−0.618442	+	0.618442i
$362$	16.8360	−	14.0902i	0.884881	−	0.740566i
$363$		0			0
$364$	−0.899140	−	4.10571i	−0.0471277	−	0.215198i
$365$	−0.336742	+	0.139483i	−0.0176259	+	0.00730088i
$366$		0			0
$367$	−25.6693			−1.33993			−0.669963	−	0.742394i	$-0.733690\pi$
$367$	−25.6693			−1.33993			−0.669963	+	0.742394i	$0.733690\pi$
$368$	3.39135	+	7.37157i	0.176787	+	0.384269i
$369$		0			0
$370$	0.0527279	+	0.167985i	0.00274119	+	0.00873311i
$371$	−6.86950	−	16.5844i	−0.356646	−	0.861021i
$372$		0			0
$373$	−8.82848	−	3.65687i	−0.457121	−	0.189346i	0.142227	−	0.989834i	$-0.454574\pi$
$373$	−8.82848	−	3.65687i	−0.457121	−	0.189346i	−0.599348	+	0.800488i	$0.704574\pi$
$374$	−13.5968	+	11.3793i	−0.703075	+	0.588411i
$375$		0			0
$376$	4.04507	+	31.6692i	0.208608	+	1.63321i
$377$	3.72082	−	3.72082i	0.191632	−	0.191632i
$378$		0			0
$379$	7.76023	+	3.21439i	0.398616	+	0.165112i	0.572981	−	0.819569i	$-0.305787\pi$
$379$	7.76023	+	3.21439i	0.398616	+	0.165112i	−0.174364	+	0.984681i	$0.555787\pi$
$380$	−0.0806304	−	0.115785i	−0.00413625	−	0.00593964i
$381$		0			0
$382$	−11.6120	+	22.2365i	−0.594120	+	1.13772i
$383$	−12.6514			−0.646456			−0.323228	−	0.946321i	$-0.604768\pi$
$383$	−12.6514			−0.646456			−0.323228	+	0.946321i	$0.604768\pi$
$384$		0			0
$385$	0.255392			0.0130160
$386$	−17.4740	+	33.4621i	−0.889403	+	1.70318i
$387$		0			0
$388$	12.1078	+	17.3868i	0.614682	+	0.882681i
$389$	−21.9846	−	9.10632i	−1.11466	−	0.461709i	−0.252122	−	0.967695i	$-0.581128\pi$
$389$	−21.9846	−	9.10632i	−1.11466	−	0.461709i	−0.862541	+	0.505987i	$0.831128\pi$
$390$		0			0
$391$	7.02396	−	7.02396i	0.355217	−	0.355217i
$392$	0.801607	+	6.27585i	0.0404873	+	0.316978i
$393$		0			0
$394$	−10.2547	+	8.58227i	−0.516625	+	0.432368i
$395$	0.170297	+	0.0705391i	0.00856855	+	0.00354921i
$396$		0			0
$397$	5.19713	+	12.5470i	0.260837	+	0.629715i	0.998991	−	0.0449169i	$-0.0143023\pi$
$397$	5.19713	+	12.5470i	0.260837	+	0.629715i	−0.738154	+	0.674632i	$0.764302\pi$
$398$	−0.448833	−	1.42993i	−0.0224980	−	0.0716758i
$399$		0			0
$400$	18.1618	−	8.35550i	0.908091	−	0.417775i
$401$	30.6133			1.52876			0.764379	−	0.644767i	$-0.223046\pi$
$401$	30.6133			1.52876			0.764379	+	0.644767i	$0.223046\pi$
$402$		0			0
$403$	7.89449	−	3.27001i	0.393253	−	0.162891i
$404$	3.05888	+	13.9677i	0.152185	+	0.694918i
$405$		0			0
$406$	12.9346	−	10.8251i	0.641932	−	0.537239i
$407$	−4.93138	+	4.93138i	−0.244440	+	0.244440i
$408$		0			0
$409$	8.30704	+	8.30704i	0.410757	+	0.410757i	0.882002	−	0.471245i	$-0.156195\pi$
$409$	8.30704	+	8.30704i	0.410757	+	0.410757i	−0.471245	+	0.882002i	$0.656195\pi$
$410$	0.0506861	+	0.00450016i	0.00250321	+	0.000222247i
$411$		0			0
$412$	−22.6480	−	4.05355i	−1.11578	−	0.199704i
$413$	1.52424	+	3.67985i	0.0750031	+	0.181073i
$414$		0			0
$415$		−	0.266294i		−	0.0130718i
$416$	−2.33372	+	4.92178i	−0.114420	+	0.241310i
$417$		0			0
$418$	2.58698	−	4.95398i	0.126534	−	0.242307i
$419$	5.63076	−	2.33234i	0.275081	−	0.113942i	−0.240879	−	0.970555i	$-0.577436\pi$
$419$	5.63076	−	2.33234i	0.275081	−	0.113942i	0.515959	+	0.856613i	$0.327436\pi$
$420$		0			0
$421$	−12.7909	+	30.8800i	−0.623391	+	1.50500i	0.224306	+	0.974519i	$0.427989\pi$
$421$	−12.7909	+	30.8800i	−0.623391	+	1.50500i	−0.847697	+	0.530481i	$0.822011\pi$
$422$	1.52539	−	17.1808i	0.0742550	−	0.836347i
$423$		0			0
$424$	−6.10783	+	22.4479i	−0.296622	+	1.09017i
$425$	−17.3054	−	17.3054i	−0.839435	−	0.839435i
$426$		0			0
$427$	−1.98280	+	4.78690i	−0.0959543	+	0.231654i
$428$	3.52264	+	16.0853i	0.170273	+	0.777512i
$429$		0			0
$430$	0.0752721	+	0.239808i	0.00362994	+	0.0115645i
$431$		−	22.0507i		−	1.06215i	−0.847326	−	0.531073i	$-0.821789\pi$
$431$		−	22.0507i		−	1.06215i	0.847326	−	0.531073i	$-0.178211\pi$
$432$		0			0
$433$			18.5224i			0.890128i	0.895499	+	0.445064i	$0.146819\pi$
$433$			18.5224i			0.890128i	−0.895499	+	0.445064i	$0.853181\pi$
$434$	26.1325	−	8.20260i	1.25440	−	0.393737i
$435$		0			0
$436$	−21.6288	+	33.7584i	−1.03583	+	1.61674i
$437$	−1.19822	+	2.89277i	−0.0573188	+	0.138380i
$438$		0			0
$439$	0.0826752	+	0.0826752i	0.00394587	+	0.00394587i	0.709077	−	0.705131i	$-0.249112\pi$
$439$	0.0826752	+	0.0826752i	0.00394587	+	0.00394587i	−0.705131	+	0.709077i	$0.749112\pi$
$440$	−0.261807	−	0.202501i	−0.0124812	−	0.00965388i
$441$		0			0
$442$	6.64206	+	0.589714i	0.315931	+	0.0280499i
$443$	10.6384	−	25.6833i	0.505445	−	1.22025i	−0.441035	−	0.897490i	$-0.645389\pi$
$443$	10.6384	−	25.6833i	0.505445	−	1.22025i	0.946480	−	0.322762i	$-0.104611\pi$
$444$		0			0
$445$	−0.256775	+	0.106359i	−0.0121723	+	0.00504192i
$446$	−22.2808	−	11.6351i	−1.05503	−	0.550937i
$447$		0			0
$448$	−8.84627	+	15.0527i	−0.417947	+	0.711173i
$449$			11.9793i			0.565338i	0.959218	+	0.282669i	$0.0912198\pi$
$449$			11.9793i			0.565338i	−0.959218	+	0.282669i	$0.908780\pi$
$450$		0			0
$451$	0.771334	+	1.86217i	0.0363207	+	0.0876860i
$452$	−11.9713	−	17.1908i	−0.563085	−	0.808587i
$453$		0			0
$454$	1.63818	−	18.4511i	0.0768836	−	0.865954i
$455$	−0.0679179	−	0.0679179i	−0.00318404	−	0.00318404i
$456$		0			0
$457$	−15.4727	+	15.4727i	−0.723782	+	0.723782i	−0.969373	−	0.245591i	$-0.921018\pi$
$457$	−15.4727	+	15.4727i	−0.723782	+	0.723782i	0.245591	+	0.969373i	$0.421018\pi$
$458$	−1.66995	−	1.99537i	−0.0780315	−	0.0932376i
$459$		0			0
$460$	0.156136	+	0.100035i	0.00727987	+	0.00466416i
$461$	−9.20868	+	3.81436i	−0.428891	+	0.177653i	−0.586677	−	0.809821i	$-0.699564\pi$
$461$	−9.20868	+	3.81436i	−0.428891	+	0.177653i	0.157786	+	0.987473i	$0.449564\pi$
$462$		0			0
$463$	13.8046			0.641556			0.320778	−	0.947154i	$-0.396056\pi$
$463$	13.8046			0.641556			0.320778	+	0.947154i	$0.396056\pi$
$464$	−21.8427	+	0.841104i	−1.01402	+	0.0390473i
$465$		0			0
$466$	−30.2681	+	9.50072i	−1.40214	+	0.440112i
$467$	−12.4800	−	30.1295i	−0.577507	−	1.39423i	−0.895043	−	0.445980i	$-0.852855\pi$
$467$	−12.4800	−	30.1295i	−0.577507	−	1.39423i	0.317536	−	0.948246i	$-0.397145\pi$
$468$		0			0
$469$	−21.2845	−	8.81633i	−0.982827	−	0.407100i
$470$	0.468263	+	0.559514i	0.0215994	+	0.0258085i
$471$		0			0
$472$	1.35524	−	4.98086i	0.0623800	−	0.229263i
$473$	−7.03983	+	7.03983i	−0.323692	+	0.323692i
$474$		0			0
$475$	7.12711	+	2.95214i	0.327014	+	0.135454i
$476$	21.0396	+	3.76568i	0.964347	+	0.172600i
$477$		0			0
$478$	−20.3841	−	10.6446i	−0.932345	−	0.486874i
$479$	5.83947			0.266812			0.133406	−	0.991061i	$-0.457409\pi$
$479$	5.83947			0.266812			0.133406	+	0.991061i	$0.457409\pi$
$480$		0			0
$481$	2.62287			0.119592
$482$	16.6402	+	8.68958i	0.757942	+	0.395800i
$483$		0			0
$484$	−1.56618	+	8.75057i	−0.0711901	+	0.397753i
$485$	0.447330	+	0.185290i	0.0203122	+	0.00841360i
$486$		0			0
$487$	23.2157	−	23.2157i	1.05200	−	1.05200i	0.0534306	−	0.998572i	$-0.482984\pi$
$487$	23.2157	−	23.2157i	1.05200	−	1.05200i	0.998572	−	0.0534306i	$-0.0170156\pi$
$488$	5.82816	−	3.33497i	0.263828	−	0.150967i
$489$		0			0
$490$	0.0927952	+	0.110878i	0.00419206	+	0.00500897i
$491$	−23.2326	−	9.62327i	−1.04847	−	0.434292i	−0.209127	−	0.977888i	$-0.567062\pi$
$491$	−23.2326	−	9.62327i	−1.04847	−	0.434292i	−0.839347	+	0.543596i	$0.817062\pi$
$492$		0			0
$493$	10.2404	+	24.7225i	0.461204	+	1.11344i
$494$	−2.00542	+	0.629470i	−0.0902279	+	0.0283212i
$495$		0			0
$496$	−33.2928	−	12.3119i	−1.49489	−	0.552822i
$497$	−12.5501			−0.562950
$498$		0			0
$499$	−31.8618	+	13.1976i	−1.42633	+	0.590805i	−0.956442	−	0.291921i	$-0.905705\pi$
$499$	−31.8618	+	13.1976i	−1.42633	+	0.590805i	−0.469887	+	0.882726i	$0.655705\pi$
$500$	0.493029	−	0.769525i	0.0220489	−	0.0344142i
$501$		0			0
$502$	19.5487	+	23.3582i	0.872501	+	1.04253i
$503$	−12.5463	+	12.5463i	−0.559414	+	0.559414i	−0.929140	−	0.369727i	$-0.879451\pi$
$503$	−12.5463	+	12.5463i	−0.559414	+	0.559414i	0.369727	+	0.929140i	$0.379451\pi$
$504$		0			0
$505$	0.231057	+	0.231057i	0.0102819	+	0.0102819i
$506$	−0.649577	+	7.31630i	−0.0288772	+	0.325249i
$507$		0			0
$508$	18.3558	−	12.7826i	0.814406	−	0.567137i
$509$	5.02812	+	12.1390i	0.222868	+	0.538050i	0.995277	−	0.0970749i	$-0.0309486\pi$
$509$	5.02812	+	12.1390i	0.222868	+	0.538050i	−0.772409	+	0.635125i	$0.780949\pi$
$510$		0			0
$511$			17.4044i			0.769927i
$512$	21.0038	−	8.41656i	0.928248	−	0.371963i
$513$		0			0
$514$	27.4926	+	14.3567i	1.21265	+	0.633247i
$515$	−0.485769	+	0.201212i	−0.0214055	+	0.00886646i
$516$		0			0
$517$	−11.0596	+	26.7001i	−0.486399	+	1.17427i
$518$	8.37428	+	0.743509i	0.367945	+	0.0326679i
$519$		0			0
$520$	0.0157715	+	0.123476i	0.000691626	+	0.00541480i
$521$	10.9131	+	10.9131i	0.478112	+	0.478112i	0.904528	−	0.426415i	$-0.140224\pi$
$521$	10.9131	+	10.9131i	0.478112	+	0.478112i	−0.426415	+	0.904528i	$0.640224\pi$
$522$		0			0
$523$	−1.50942	+	3.64406i	−0.0660024	+	0.159344i	−0.953439	−	0.301586i	$-0.902484\pi$
$523$	−1.50942	+	3.64406i	−0.0660024	+	0.159344i	0.887437	+	0.460930i	$0.152484\pi$
$524$	−15.0233	−	9.62534i	−0.656297	−	0.420485i
$525$		0			0
$526$	−26.2051	+	8.22541i	−1.14260	+	0.358645i
$527$			43.4542i			1.89290i
$528$		0			0
$529$			18.8849i			0.821083i
$530$	0.159217	+	0.507245i	0.00691593	+	0.0220333i
$531$		0			0
$532$	−6.58132	+	1.44129i	−0.285336	+	0.0624879i
$533$	0.290091	−	0.700343i	0.0125653	−	0.0303352i
$534$		0			0
$535$	0.266088	+	0.266088i	0.0115040	+	0.0115040i
$536$	14.8286	+	25.9144i	0.640500	+	1.11933i
$537$		0			0
$538$	1.62074	−	18.2547i	0.0698751	−	0.787015i
$539$	−2.19166	+	5.29114i	−0.0944016	+	0.227906i
$540$		0			0
$541$	9.58662	−	3.97091i	0.412161	−	0.170723i	−0.166961	−	0.985963i	$-0.553395\pi$
$541$	9.58662	−	3.97091i	0.412161	−	0.170723i	0.579122	+	0.815241i	$0.303395\pi$
$542$	1.59583	−	3.05596i	0.0685468	−	0.131265i
$543$		0			0
$544$	−18.5823	−	20.5427i	−0.796708	−	0.880759i
$545$			0.916231i			0.0392470i
$546$		0			0
$547$	−13.3463	−	32.2208i	−0.570646	−	1.37766i	−0.901007	−	0.433806i	$-0.857170\pi$
$547$	−13.3463	−	32.2208i	−0.570646	−	1.37766i	0.330361	−	0.943855i	$-0.392830\pi$
$548$	2.71502	−	15.1693i	0.115980	−	0.648002i
$549$		0			0
$550$	18.0257	+	1.60041i	0.768617	+	0.0682416i
$551$	−5.96435	−	5.96435i	−0.254090	−	0.254090i
$552$		0			0
$553$	6.22377	−	6.22377i	0.264661	−	0.264661i
$554$	−3.74402	+	3.13341i	−0.159068	+	0.133126i
$555$		0			0
$556$	12.6319	−	2.76635i	0.535712	−	0.117319i
$557$	5.38229	−	2.22942i	0.228055	−	0.0944635i	−0.265730	−	0.964048i	$-0.585613\pi$
$557$	5.38229	−	2.22942i	0.228055	−	0.0944635i	0.493785	+	0.869584i	$0.335613\pi$
$558$		0			0
$559$	3.74429			0.158367
$560$	0.0153531	+	0.398706i	0.000648786	+	0.0168484i
$561$		0			0
$562$	12.1653	+	38.7572i	0.513162	+	1.63487i
$563$	17.6342	+	42.5728i	0.743194	+	1.79423i	0.592366	+	0.805669i	$0.298194\pi$
$563$	17.6342	+	42.5728i	0.743194	+	1.79423i	0.150829	+	0.988560i	$0.451806\pi$
$564$		0			0
$565$	−0.442288	−	0.183202i	−0.0186072	−	0.00770735i
$566$	−33.9814	+	28.4394i	−1.42835	+	1.19540i
$567$		0			0
$568$	12.8654	+	9.95106i	0.539819	+	0.417537i
$569$	23.2904	−	23.2904i	0.976386	−	0.976386i	−0.0233414	−	0.999728i	$-0.507430\pi$
$569$	23.2904	−	23.2904i	0.976386	−	0.976386i	0.999728	+	0.0233414i	$0.00743047\pi$
$570$		0			0
$571$	3.51014	+	1.45395i	0.146895	+	0.0608458i	0.454920	−	0.890533i	$-0.349668\pi$
$571$	3.51014	+	1.45395i	0.146895	+	0.0608458i	−0.308025	+	0.951378i	$0.599668\pi$
$572$	−4.04624	+	2.81773i	−0.169182	+	0.117815i
$573$		0			0
$574$	1.12473	−	2.15382i	0.0469453	−	0.0898987i
$575$	−10.1386			−0.422809
$576$		0			0
$577$	22.2939			0.928109			0.464054	−	0.885807i	$-0.346394\pi$
$577$	22.2939			0.928109			0.464054	+	0.885807i	$0.346394\pi$
$578$	−4.56807	+	8.74769i	−0.190007	+	0.363856i
$579$		0			0
$580$	−0.409932	+	0.285469i	−0.0170215	+	0.0118534i
$581$	−11.7477	−	4.86607i	−0.487378	−	0.201879i
$582$		0			0
$583$	−14.8908	+	14.8908i	−0.616712	+	0.616712i
$584$	13.8001	−	17.8416i	0.571051	−	0.738291i
$585$		0			0
$586$	24.1748	−	20.2322i	0.998653	−	0.835783i
$587$	17.0966	+	7.08164i	0.705652	+	0.292291i	0.706504	−	0.707709i	$-0.250271\pi$
$587$	17.0966	+	7.08164i	0.705652	+	0.292291i	−0.000851907		1.00000i	$0.500271\pi$
$588$		0			0
$589$	−5.24171	−	12.6546i	−0.215981	−	0.521424i
$590$	−0.0353279	−	0.112550i	−0.00145443	−	0.00463362i
$591$		0			0
$592$	−7.99510	−	7.40219i	−0.328597	−	0.304228i
$593$	15.4109			0.632850			0.316425	−	0.948617i	$-0.397517\pi$
$593$	15.4109			0.632850			0.316425	+	0.948617i	$0.397517\pi$
$594$		0			0
$595$	0.451271	−	0.186923i	0.0185003	−	0.00766308i
$596$	−3.74747	+	0.820686i	−0.153502	+	0.0336166i
$597$		0			0
$598$	2.11841	−	1.77292i	0.0866284	−	0.0725002i
$599$	31.4125	−	31.4125i	1.28348	−	1.28348i	0.344807	−	0.938674i	$-0.387944\pi$
$599$	31.4125	−	31.4125i	1.28348	−	1.28348i	0.938674	−	0.344807i	$-0.112056\pi$
$600$		0			0
$601$	−19.8887	−	19.8887i	−0.811276	−	0.811276i	0.173549	−	0.984825i	$-0.444476\pi$
$601$	−19.8887	−	19.8887i	−0.811276	−	0.811276i	−0.984825	+	0.173549i	$0.944476\pi$
$602$	11.9548	+	1.06140i	0.487239	+	0.0432595i
$603$		0			0
$604$	−0.729451	+	4.07558i	−0.0296809	+	0.165833i
$605$	0.0777430	+	0.187688i	0.00316070	+	0.00763061i
$606$		0			0
$607$		−	32.4626i		−	1.31761i	−0.752312	−	0.658807i	$-0.771061\pi$
$607$		−	32.4626i		−	1.31761i	0.752312	−	0.658807i	$-0.228939\pi$
$608$	7.88945	+	3.74087i	0.319959	+	0.151712i
$609$		0			0
$610$	0.0710318	−	0.136023i	0.00287599	−	0.00550742i
$611$	10.0417	−	4.15939i	0.406242	−	0.168271i
$612$		0			0
$613$	0.755880	−	1.82486i	0.0305297	−	0.0737053i	−0.907879	−	0.419231i	$-0.862300\pi$
$613$	0.755880	−	1.82486i	0.0305297	−	0.0737053i	0.938409	+	0.345526i	$0.112300\pi$
$614$	4.22115	−	47.5436i	0.170352	−	1.91870i
$615$		0			0
$616$	−13.7176	+	7.84943i	−0.552697	+	0.316263i
$617$	6.74247	+	6.74247i	0.271442	+	0.271442i	0.829680	−	0.558239i	$-0.188523\pi$
$617$	6.74247	+	6.74247i	0.271442	+	0.271442i	−0.558239	+	0.829680i	$0.688523\pi$
$618$		0			0
$619$	12.9820	−	31.3414i	0.521792	−	1.25972i	−0.414998	−	0.909823i	$-0.636218\pi$
$619$	12.9820	−	31.3414i	0.521792	−	1.25972i	0.936789	−	0.349894i	$-0.113782\pi$
$620$	−0.792410	+	0.173536i	−0.0318240	+	0.00696936i
$621$		0			0
$622$	−1.10872	−	3.53226i	−0.0444558	−	0.141631i
$623$			13.2713i			0.531705i
$624$		0			0
$625$			24.9687i			0.998747i
$626$	44.5467	−	13.9826i	1.78045	−	0.558856i
$627$		0			0
$628$	−26.4900	−	16.9719i	−1.05706	−	0.677254i
$629$	−5.10433	+	12.3229i	−0.203523	+	0.491348i
$630$		0			0
$631$	−5.56375	−	5.56375i	−0.221489	−	0.221489i	0.587636	−	0.809125i	$-0.300059\pi$
$631$	−5.56375	−	5.56375i	−0.221489	−	0.221489i	−0.809125	+	0.587636i	$0.800059\pi$
$632$	−11.3150	+	1.44525i	−0.450085	+	0.0574888i
$633$		0			0
$634$	32.9463	+	2.92513i	1.30846	+	0.116172i
$635$	0.195617	−	0.472261i	0.00776282	−	0.0187411i
$636$		0			0
$637$	1.98995	−	0.824263i	0.0788446	−	0.0326585i
$638$	−17.5394	−	9.15911i	−0.694390	−	0.362613i
$639$		0			0
$640$	0.300397	−	0.420895i	0.0118742	−	0.0166373i
$641$		−	49.9154i		−	1.97154i	−0.168097	−	0.985771i	$-0.553762\pi$
$641$		−	49.9154i		−	1.97154i	0.168097	−	0.985771i	$-0.446238\pi$
$642$		0			0
$643$	−14.7227	−	35.5437i	−0.580606	−	1.40171i	−0.892265	−	0.451512i	$-0.850885\pi$
$643$	−14.7227	−	35.5437i	−0.580606	−	1.40171i	0.311659	−	0.950194i	$-0.399115\pi$
$644$	7.26624	−	5.06007i	0.286330	−	0.199395i
$645$		0			0
$646$	0.945293	−	10.6470i	0.0371920	−	0.418901i
$647$	18.9322	+	18.9322i	0.744303	+	0.744303i	0.973403	−	0.229100i	$-0.0735783\pi$
$647$	18.9322	+	18.9322i	0.744303	+	0.744303i	−0.229100	+	0.973403i	$0.573578\pi$
$648$		0			0
$649$	3.30405	−	3.30405i	0.129695	−	0.129695i
$650$	−4.36807	−	5.21928i	−0.171330	−	0.204717i
$651$		0			0
$652$	−9.28304	+	14.4891i	−0.363552	+	0.567436i
$653$	−29.8393	+	12.3598i	−1.16770	+	0.483677i	−0.880432	−	0.474173i	$-0.842747\pi$
$653$	−29.8393	+	12.3598i	−1.16770	+	0.483677i	−0.287269	+	0.957850i	$0.592747\pi$
$654$		0			0
$655$	−0.407745			−0.0159319
$656$	−2.86076	+	1.31612i	−0.111694	+	0.0513857i
$657$		0			0
$658$	33.2401	−	10.4336i	1.29583	−	0.406743i
$659$	4.43254	+	10.7011i	0.172667	+	0.416855i	0.986395	−	0.164390i	$-0.0525656\pi$
$659$	4.43254	+	10.7011i	0.172667	+	0.416855i	−0.813728	+	0.581245i	$0.802566\pi$
$660$		0			0
$661$	−28.9783	−	12.0032i	−1.12713	−	0.466871i	−0.260322	−	0.965522i	$-0.583829\pi$
$661$	−28.9783	−	12.0032i	−1.12713	−	0.466871i	−0.866803	+	0.498651i	$0.833829\pi$
$662$	19.2200	+	22.9654i	0.747005	+	0.892575i
$663$		0			0
$664$	8.18450	+	14.3031i	0.317620	+	0.555070i
$665$	−0.108870	+	0.108870i	−0.00422180	+	0.00422180i
$666$		0			0
$667$	10.2417	+	4.24226i	0.396561	+	0.164261i
$668$	5.47426	−	30.5858i	0.211805	−	1.18340i
$669$		0			0
$670$	0.604816	+	0.315837i	0.0233661	+	0.0122018i
$671$	6.07834			0.234652
$672$		0			0
$673$	36.0517			1.38969			0.694845	−	0.719159i	$-0.255473\pi$
$673$	36.0517			1.38969			0.694845	+	0.719159i	$0.255473\pi$
$674$	−29.6122	−	15.4636i	−1.14062	−	0.595634i
$675$		0			0
$676$	−23.7679	−	4.25400i	−0.914151	−	0.163615i
$677$	18.0256	+	7.46647i	0.692782	+	0.286960i	0.701159	−	0.713005i	$-0.252666\pi$
$677$	18.0256	+	7.46647i	0.692782	+	0.286960i	−0.00837691	+	0.999965i	$0.502666\pi$
$678$		0			0
$679$	16.3484	−	16.3484i	0.627395	−	0.627395i
$680$	−0.610819	−	0.166197i	−0.0234238	−	0.00637337i
$681$		0			0
$682$	−20.6221	−	24.6407i	−0.789661	−	0.943543i
$683$	−10.1455	−	4.20240i	−0.388207	−	0.160800i	0.180039	−	0.983659i	$-0.442378\pi$
$683$	−10.1455	−	4.20240i	−0.388207	−	0.160800i	−0.568246	+	0.822859i	$0.692378\pi$
$684$		0			0
$685$	−0.134769	−	0.325362i	−0.00514928	−	0.0124315i
$686$	27.2008	−	8.53792i	1.03853	−	0.325979i
$687$		0			0
$688$	−11.4135	−	10.5670i	−0.435134	−	0.402865i
$689$	7.91998			0.301727
$690$		0			0
$691$	−7.43659	+	3.08034i	−0.282901	+	0.117182i	−0.519622	−	0.854396i	$-0.673927\pi$
$691$	−7.43659	+	3.08034i	−0.282901	+	0.117182i	0.236721	+	0.971578i	$0.423927\pi$
$692$	18.5996	+	11.9166i	0.707049	+	0.453001i
$693$		0			0
$694$	−4.02622	−	4.81081i	−0.152833	−	0.182616i
$695$	0.208960	−	0.208960i	0.00792632	−	0.00792632i
$696$		0			0
$697$	2.72586	+	2.72586i	0.103249	+	0.103249i
$698$	−3.53799	+	39.8490i	−0.133915	+	1.50831i
$699$		0			0
$700$	−12.4668	−	17.9023i	−0.471202	−	0.676644i
$701$	−1.64786	−	3.97828i	−0.0622387	−	0.150258i	0.889700	−	0.456545i	$-0.150913\pi$
$701$	−1.64786	−	3.97828i	−0.0622387	−	0.150258i	−0.951939	+	0.306287i	$0.900913\pi$
$702$		0			0
$703$		−	4.20437i		−	0.158571i
$704$	20.2860	+	2.83014i	0.764558	+	0.106665i
$705$		0			0
$706$	4.81182	+	2.51275i	0.181095	+	0.0945684i
$707$	14.4154	−	5.97107i	0.542149	−	0.224565i
$708$		0			0
$709$	−9.56825	+	23.0998i	−0.359343	+	0.867531i	0.636050	+	0.771648i	$0.280567\pi$
$709$	−9.56825	+	23.0998i	−0.359343	+	0.867531i	−0.995393	+	0.0958828i	$0.969433\pi$
$710$	0.370237	+	0.0328715i	0.0138948	+	0.00123364i
$711$		0			0
$712$	10.5229	−	13.6047i	0.394363	−	0.509858i
$713$	12.7291	+	12.7291i	0.476709	+	0.476709i
$714$		0			0
$715$	−0.0431206	+	0.104102i	−0.00161262	+	0.00389321i
$716$	−26.8507	+	41.9089i	−1.00346	+	1.56621i
$717$		0			0
$718$	31.8541	−	9.99854i	1.18879	−	0.373142i
$719$		−	23.2267i		−	0.866208i	−0.901344	−	0.433104i	$-0.857418\pi$
$719$		−	23.2267i		−	0.866208i	0.901344	−	0.433104i	$-0.142582\pi$
$720$		0			0
$721$			25.1068i			0.935028i
$722$	−7.03799	−	22.4222i	−0.261927	−	0.834467i
$723$		0			0
$724$	6.64200	+	30.3291i	0.246848	+	1.12717i
$725$	10.4519	−	25.2332i	0.388175	−	0.937138i
$726$		0			0
$727$	−34.9490	−	34.9490i	−1.29619	−	1.29619i	−0.930893	−	0.365293i	$-0.880969\pi$
$727$	−34.9490	−	34.9490i	−1.29619	−	1.29619i	−0.365293	−	0.930893i	$-0.619031\pi$
$728$	5.73544	+	1.56055i	0.212570	+	0.0578379i
$729$		0			0
$730$	0.0455859	−	0.513443i	0.00168721	−	0.0190034i
$731$	−7.28672	+	17.5917i	−0.269509	+	0.650652i
$732$		0			0
$733$	8.53994	−	3.53736i	0.315430	−	0.130655i	−0.219351	−	0.975646i	$-0.570394\pi$
$733$	8.53994	−	3.53736i	0.315430	−	0.130655i	0.534781	+	0.844991i	$0.320394\pi$
$734$	16.8037	−	32.1786i	0.620237	−	1.18773i
$735$		0			0
$736$	−11.4609	−	0.574265i	−0.422455	−	0.0211677i
$737$			27.0268i			0.995545i
$738$		0			0
$739$	−1.90375	−	4.59605i	−0.0700305	−	0.169069i	0.884989	−	0.465612i	$-0.154166\pi$
$739$	−1.90375	−	4.59605i	−0.0700305	−	0.169069i	−0.955019	+	0.296544i	$0.904166\pi$
$740$	−0.245099	−	0.0438681i	−0.00901004	−	0.00161262i
$741$		0			0
$742$	25.2869	+	2.24509i	0.928310	+	0.0824199i
$743$	−0.557193	−	0.557193i	−0.0204414	−	0.0204414i	0.696812	−	0.717254i	$-0.254601\pi$
$743$	−0.557193	−	0.557193i	−0.0204414	−	0.0204414i	−0.717254	+	0.696812i	$0.754601\pi$
$744$		0			0
$745$	−0.0619917	+	0.0619917i	−0.00227120	+	0.00227120i
$746$	10.3635	−	8.67334i	0.379436	−	0.317554i
$747$		0			0
$748$	−5.36410	−	24.4939i	−0.196131	−	0.895586i
$749$	16.6010	−	6.87634i	0.606586	−	0.251256i
$750$		0			0
$751$	−3.97299			−0.144976			−0.0724882	−	0.997369i	$-0.523094\pi$
$751$	−3.97299			−0.144976			−0.0724882	+	0.997369i	$0.523094\pi$
$752$	−42.3479	−	15.6606i	−1.54427	−	0.571082i
$753$		0			0
$754$	2.22861	+	7.10009i	0.0811613	+	0.258570i
$755$	0.0362088	+	0.0874159i	0.00131777	+	0.00318139i
$756$		0			0
$757$	27.8541	+	11.5375i	1.01237	+	0.419339i	0.826320	−	0.563200i	$-0.190430\pi$
$757$	27.8541	+	11.5375i	1.01237	+	0.419339i	0.186054	+	0.982540i	$0.440430\pi$
$758$	−9.10954	+	7.62386i	−0.330873	+	0.276911i
$759$		0			0
$760$	0.197929	−	0.0252812i	0.00717962	−	0.000917045i
$761$	−21.8585	+	21.8585i	−0.792369	+	0.792369i	−0.981879	−	0.189510i	$-0.939310\pi$
$761$	−21.8585	+	21.8585i	−0.792369	+	0.792369i	0.189510	+	0.981879i	$0.439310\pi$
$762$		0			0
$763$	40.4202	+	16.7426i	1.46331	+	0.606122i
$764$	−20.2738	−	29.1131i	−0.733481	−	1.05328i
$765$		0			0
$766$	8.28191	−	15.8596i	0.299238	−	0.573029i
$767$	−1.75733			−0.0634535
$768$		0			0
$769$	3.63950			0.131244			0.0656218	−	0.997845i	$-0.479097\pi$
$769$	3.63950			0.131244			0.0656218	+	0.997845i	$0.479097\pi$
$770$	−0.167186	+	0.320154i	−0.00602495	+	0.0115376i
$771$		0			0
$772$	−30.5086	−	43.8102i	−1.09803	−	1.57676i
$773$	30.8863	+	12.7935i	1.11090	+	0.460151i	0.861249	−	0.508183i	$-0.169683\pi$
$773$	30.8863	+	12.7935i	1.11090	+	0.460151i	0.249655	+	0.968335i	$0.419683\pi$
$774$		0			0
$775$	31.3616	−	31.3616i	1.12654	−	1.12654i
$776$	−29.7218	+	3.79634i	−1.06695	+	0.136281i
$777$		0			0
$778$	25.8072	−	21.5983i	0.925232	−	0.774336i
$779$	−1.12263	−	0.465007i	−0.0402223	−	0.0166606i
$780$		0			0
$781$	5.63422	+	13.6022i	0.201608	+	0.486726i
$782$	4.20706	+	13.4032i	0.150444	+	0.479296i
$783$		0			0
$784$	−8.39204	−	3.10344i	−0.299716	−	0.110837i
$785$	−0.718959			−0.0256608
$786$		0			0
$787$	−15.1622	+	6.28040i	−0.540475	+	0.223872i	−0.636184	−	0.771537i	$-0.719488\pi$
$787$	−15.1622	+	6.28040i	−0.540475	+	0.223872i	0.0957090	+	0.995409i	$0.469488\pi$
$788$	−4.04560	−	18.4733i	−0.144118	−	0.658083i
$789$		0			0
$790$	−0.199907	+	0.167304i	−0.00711236	+	0.00595241i
$791$	−16.1641	+	16.1641i	−0.574731	+	0.574731i
$792$		0			0
$793$	−1.61645	−	1.61645i	−0.0574018	−	0.0574018i
$794$	−19.1308	−	1.69853i	−0.678928	−	0.0602786i
$795$		0			0
$796$	2.08635	+	0.373416i	0.0739486	+	0.0132354i
$797$	18.9327	+	45.7076i	0.670631	+	1.61905i	0.780540	+	0.625105i	$0.214944\pi$
$797$	18.9327	+	45.7076i	0.670631	+	1.61905i	−0.109909	+	0.993942i	$0.535056\pi$
$798$		0			0
$799$			55.2731i			1.95542i
$800$	−1.41485	+	28.2370i	−0.0500226	+	0.998330i
$801$		0			0
$802$	−20.0402	+	38.3763i	−0.707645	+	1.35512i
$803$	18.8635	−	7.81351i	0.665678	−	0.275733i
$804$		0			0
$805$	0.0774360	−	0.186947i	0.00272926	−	0.00658902i
$806$	−1.06871	+	12.0370i	−0.0376435	+	0.423986i
$807$		0			0
$808$	−19.5121	−	5.30902i	−0.686432	−	0.186771i
$809$	1.51342	+	1.51342i	0.0532091	+	0.0532091i	0.733211	−	0.680002i	$-0.238021\pi$
$809$	1.51342	+	1.51342i	0.0532091	+	0.0532091i	−0.680002	+	0.733211i	$0.738021\pi$
$810$		0			0
$811$	3.43406	−	8.29055i	0.120586	−	0.291121i	−0.852048	−	0.523464i	$-0.824639\pi$
$811$	3.43406	−	8.29055i	0.120586	−	0.291121i	0.972634	+	0.232344i	$0.0746394\pi$
$812$	5.10283	+	23.3009i	0.179074	+	0.817701i
$813$		0			0
$814$	−2.95369	−	9.41010i	−0.103527	−	0.329824i
$815$			0.393245i			0.0137748i
$816$		0			0
$817$		−	6.00197i		−	0.209982i
$818$	−15.8515	+	4.97557i	−0.554236	+	0.173967i
$819$		0			0
$820$	−0.0388216	+	0.0605932i	−0.00135571	+	0.00211601i
$821$	9.67787	−	23.3644i	0.337760	−	0.815425i	−0.660170	−	0.751116i	$-0.729516\pi$
$821$	9.67787	−	23.3644i	0.337760	−	0.815425i	0.997930	−	0.0643086i	$-0.0204842\pi$
$822$		0			0
$823$	−24.0051	−	24.0051i	−0.836764	−	0.836764i	0.151667	−	0.988432i	$-0.451536\pi$
$823$	−24.0051	−	24.0051i	−0.836764	−	0.836764i	−0.988432	+	0.151667i	$0.951536\pi$
$824$	19.9073	−	25.7375i	0.693505	−	0.896609i
$825$		0			0
$826$	−5.61079	−	0.498154i	−0.195225	−	0.0173330i
$827$	−2.21129	+	5.33852i	−0.0768941	+	0.185639i	−0.957652	−	0.287928i	$-0.907034\pi$
$827$	−2.21129	+	5.33852i	−0.0768941	+	0.185639i	0.880758	+	0.473567i	$0.157034\pi$
$828$		0			0
$829$	46.7091	−	19.3475i	1.62227	−	0.671968i	0.627939	−	0.778263i	$-0.283899\pi$
$829$	46.7091	−	19.3475i	1.62227	−	0.671968i	0.994335	+	0.106295i	$0.0338989\pi$
$830$	0.333821	+	0.174322i	0.0115871	+	0.00605082i
$831$		0			0
$832$	−4.64215	−	6.14742i	−0.160937	−	0.213123i
$833$			10.9534i			0.379513i
$834$		0			0
$835$	−0.271734	−	0.656024i	−0.00940375	−	0.0227027i
$836$	4.51672	+	6.48599i	0.156214	+	0.224323i
$837$		0			0
$838$	−0.762256	+	8.58542i	−0.0263317	+	0.296578i
$839$	12.9401	+	12.9401i	0.446743	+	0.446743i	0.894270	−	0.447527i	$-0.147695\pi$
$839$	12.9401	+	12.9401i	0.446743	+	0.446743i	−0.447527	+	0.894270i	$0.647695\pi$
$840$		0			0
$841$	−0.610434	+	0.610434i	−0.0210495	+	0.0210495i
$842$	−30.3374	−	36.2493i	−1.04549	−	1.24923i
$843$		0			0
$844$	20.5389	+	13.1592i	0.706980	+	0.452957i
$845$	−0.509791	+	0.211162i	−0.0175373	+	0.00726420i
$846$		0			0
$847$	9.70062			0.333317
$848$	−24.1419	−	22.3516i	−0.829037	−	0.767557i
$849$		0			0
$850$	33.0223	−	10.3652i	1.13265	−	0.355523i
$851$	2.11456	+	5.10500i	0.0724862	+	0.174997i
$852$		0			0
$853$	33.9325	+	14.0553i	1.16183	+	0.481245i	0.878483	−	0.477773i	$-0.158556\pi$
$853$	33.9325	+	14.0553i	1.16183	+	0.481245i	0.283345	+	0.959018i	$0.408556\pi$
$854$	−4.70278	−	5.61922i	−0.160926	−	0.192286i
$855$		0			0
$856$	−22.4702	−	6.11391i	−0.768017	−	0.208969i
$857$	−37.2438	+	37.2438i	−1.27223	+	1.27223i	−0.327307	+	0.944918i	$0.606141\pi$
$857$	−37.2438	+	37.2438i	−1.27223	+	1.27223i	−0.944918	+	0.327307i	$0.893859\pi$
$858$		0			0
$859$	−33.3526	−	13.8151i	−1.13798	−	0.471366i	−0.267492	−	0.963560i	$-0.586195\pi$
$859$	−33.3526	−	13.8151i	−1.13798	−	0.471366i	−0.870485	+	0.492194i	$0.836195\pi$
$860$	−0.349893	−	0.0626241i	−0.0119313	−	0.00213547i
$861$		0			0
$862$	27.6424	+	14.4349i	0.941503	+	0.491656i
$863$	30.7896			1.04809			0.524045	−	0.851691i	$-0.324422\pi$
$863$	30.7896			1.04809			0.524045	+	0.851691i	$0.324422\pi$
$864$		0			0
$865$	0.504807			0.0171640
$866$	−23.2193	−	12.1252i	−0.789024	−	0.412030i
$867$		0			0
$868$	−6.82432	+	38.1288i	−0.231632	+	1.29418i
$869$	−9.53960	−	3.95143i	−0.323609	−	0.134043i
$870$		0			0
$871$	7.18740	−	7.18740i	0.243536	−	0.243536i
$872$	−28.1602	−	49.2125i	−0.953626	−	1.66655i
$873$		0			0
$874$	−2.84194	−	3.39575i	−0.0961299	−	0.114863i
$875$	−0.921380	−	0.381648i	−0.0311483	−	0.0129021i
$876$		0			0
$877$	−11.0969	−	26.7902i	−0.374714	−	0.904640i	−0.992938	−	0.118638i	$-0.962147\pi$
$877$	−11.0969	−	26.7902i	−0.374714	−	0.904640i	0.618223	−	0.786002i	$-0.287853\pi$
$878$	−0.157761	+	0.0495189i	−0.00532418	+	0.00167118i
$879$		0			0
$880$	0.425237	−	0.195634i	0.0143348	−	0.00659483i
$881$	−28.8189			−0.970934			−0.485467	−	0.874255i	$-0.661350\pi$
$881$	−28.8189			−0.970934			−0.485467	+	0.874255i	$0.661350\pi$
$882$		0			0
$883$	9.07984	−	3.76099i	0.305561	−	0.126567i	−0.224634	−	0.974443i	$-0.572119\pi$
$883$	9.07984	−	3.76099i	0.305561	−	0.126567i	0.530195	+	0.847876i	$0.322119\pi$
$884$	−5.08731	+	7.94032i	−0.171105	+	0.267062i
$885$		0			0
$886$	25.2320	+	30.1490i	0.847686	+	1.01288i
$887$	−8.48772	+	8.48772i	−0.284990	+	0.284990i	−0.835095	−	0.550106i	$-0.814587\pi$
$887$	−8.48772	+	8.48772i	−0.284990	+	0.284990i	0.550106	+	0.835095i	$0.314587\pi$
$888$		0			0
$889$	−17.2595	−	17.2595i	−0.578867	−	0.578867i
$890$	0.0347605	−	0.391513i	0.00116517	−	0.0131236i
$891$		0			0
$892$	29.1711	−	20.3142i	0.976719	−	0.680168i
$893$	−6.66737	−	16.0965i	−0.223115	−	0.538647i
$894$		0			0
$895$			1.13744i			0.0380205i
$896$	−13.0788	−	20.9434i	−0.436932	−	0.699669i
$897$		0			0
$898$	−15.0170	−	7.84193i	−0.501125	−	0.261689i
$899$	−44.8031	+	18.5581i	−1.49427	+	0.618946i
$900$		0			0
$901$	−15.4130	+	37.2102i	−0.513481	+	1.23965i
$902$	−2.83931	−	0.252088i	−0.0945387	−	0.00839361i
$903$		0			0
$904$	29.3868	−	3.75354i	0.977391	−	0.124841i
$905$	0.501713	+	0.501713i	0.0166775	+	0.0166775i
$906$		0			0
$907$	19.2498	−	46.4730i	0.639177	−	1.54311i	−0.188600	−	0.982054i	$-0.560395\pi$
$907$	19.2498	−	46.4730i	0.639177	−	1.54311i	0.827777	−	0.561057i	$-0.189605\pi$
$908$	22.0576	+	14.1321i	0.732007	+	0.468992i
$909$		0			0
$910$	0.129601	−	0.0406799i	0.00429624	−	0.00134853i
$911$		−	2.30224i		−	0.0762766i	−0.999272	−	0.0381383i	$-0.987857\pi$
$911$		−	2.30224i		−	0.0762766i	0.999272	−	0.0381383i	$-0.0121427\pi$
$912$		0			0
$913$			14.9171i			0.493685i
$914$	−9.26749	−	29.5251i	−0.306541	−	0.976603i
$915$		0			0
$916$	3.59455	−	0.787196i	0.118767	−	0.0260097i
$917$	−7.45086	+	17.9880i	−0.246049	+	0.594015i
$918$		0			0
$919$	−5.18147	−	5.18147i	−0.170921	−	0.170921i	0.616463	−	0.787384i	$-0.288565\pi$
$919$	−5.18147	−	5.18147i	−0.170921	−	0.170921i	−0.787384	+	0.616463i	$0.788565\pi$
$920$	−0.227613	+	0.130244i	−0.00750416	+	0.00429401i
$921$		0			0
$922$	1.24661	−	14.0408i	0.0410550	−	0.462410i
$923$	2.11898	−	5.11566i	0.0697470	−	0.168384i
$924$		0			0
$925$	12.5775	−	5.20978i	0.413546	−	0.171297i
$926$	−9.03685	+	17.3053i	−0.296969	+	0.568686i
$927$		0			0
$928$	13.2444	−	27.9323i	0.434768	−	0.916921i
$929$			42.8476i			1.40578i	0.711297	+	0.702891i	$0.248108\pi$
$929$			42.8476i			1.40578i	−0.711297	+	0.702891i	$0.751892\pi$
$930$		0			0
$931$	−1.32127	−	3.18982i	−0.0433028	−	0.104542i
$932$	7.90432	−	44.1630i	0.258915	−	1.44661i
$933$		0			0
$934$	45.9395	+	4.07873i	1.50319	+	0.133460i
$935$	−0.405185	−	0.405185i	−0.0132510	−	0.0132510i
$936$		0			0
$937$	−1.61726	+	1.61726i	−0.0528335	+	0.0528335i	−0.733030	−	0.680196i	$-0.761894\pi$
$937$	−1.61726	+	1.61726i	−0.0528335	+	0.0528335i	0.680196	+	0.733030i	$0.261894\pi$
$938$	24.9853	−	20.9105i	0.815800	−	0.682751i
$939$		0			0
$940$	−1.00793	+	0.220735i	−0.0328751	+	0.00719957i
$941$	25.9080	−	10.7314i	0.844576	−	0.349835i	0.0819196	−	0.996639i	$-0.473895\pi$
$941$	25.9080	−	10.7314i	0.844576	−	0.349835i	0.762656	+	0.646804i	$0.223895\pi$
$942$		0			0
$943$	1.59698			0.0520048
$944$	5.35675	+	4.95950i	0.174347	+	0.161418i
$945$		0			0
$946$	−4.21656	−	13.4334i	−0.137092	−	0.436759i
$947$	2.54074	+	6.13390i	0.0825631	+	0.199325i	0.959770	−	0.280788i	$-0.0905957\pi$
$947$	2.54074	+	6.13390i	0.0825631	+	0.199325i	−0.877207	+	0.480113i	$0.840596\pi$
$948$		0			0
$949$	−7.09437	−	2.93858i	−0.230293	−	0.0953905i
$950$	−8.36633	+	7.00186i	−0.271440	+	0.227170i
$951$		0			0
$952$	−18.4936	+	23.9097i	−0.599381	+	0.774919i
$953$	14.7075	−	14.7075i	0.476422	−	0.476422i	−0.427563	−	0.903985i	$-0.640628\pi$
$953$	14.7075	−	14.7075i	0.476422	−	0.476422i	0.903985	+	0.427563i	$0.140628\pi$
$954$		0			0
$955$	−0.749027	−	0.310257i	−0.0242379	−	0.0100397i
$956$	26.6878	−	18.5849i	0.863145	−	0.601078i
$957$		0			0
$958$	−3.82266	+	7.32025i	−0.123504	+	0.236507i
$959$	−16.8163			−0.543026
$960$		0			0
$961$	−47.7496			−1.54031
$962$	−1.71699	+	3.28798i	−0.0553580	+	0.106009i
$963$		0			0
$964$	−21.7862	+	15.1715i	−0.701686	+	0.488641i
$965$	−1.12716	−	0.466883i	−0.0362844	−	0.0150295i
$966$		0			0
$967$	33.1078	−	33.1078i	1.06467	−	1.06467i	0.0669159	−	0.997759i	$-0.478684\pi$
$967$	33.1078	−	33.1078i	1.06467	−	1.06467i	0.997759	−	0.0669159i	$-0.0213159\pi$
$968$	−9.94429	−	7.69167i	−0.319622	−	0.247220i
$969$		0			0
$970$	−0.525110	+	0.439470i	−0.0168603	+	0.0141105i
$971$	36.0754	+	14.9429i	1.15772	+	0.479542i	0.877114	−	0.480283i	$-0.159466\pi$
$971$	36.0754	+	14.9429i	1.15772	+	0.479542i	0.280602	+	0.959824i	$0.409466\pi$
$972$		0			0
$973$	−5.40004	−	13.0368i	−0.173117	−	0.417942i
$974$	13.9052	+	44.3003i	0.445551	+	1.41947i
$975$		0			0
$976$	0.365404	+	9.48923i	0.0116963	+	0.303743i
$977$	4.19698			0.134273			0.0671367	−	0.997744i	$-0.478614\pi$
$977$	4.19698			0.134273			0.0671367	+	0.997744i	$0.478614\pi$
$978$		0			0
$979$	14.3839	−	5.95800i	0.459711	−	0.190419i
$980$	−0.199741	+	0.0437427i	−0.00638049	+	0.00139731i
$981$		0			0
$982$	27.2722	−	22.8244i	0.870291	−	0.728355i
$983$	−5.65941	+	5.65941i	−0.180507	+	0.180507i	−0.791577	−	0.611070i	$-0.790740\pi$
$983$	−5.65941	+	5.65941i	−0.180507	+	0.180507i	0.611070	+	0.791577i	$0.290740\pi$
$984$		0			0
$985$	−0.305590	−	0.305590i	−0.00973691	−	0.00973691i
$986$	−37.6953	−	3.34677i	−1.20046	−	0.106583i
$987$		0			0
$988$	0.523701	−	2.92602i	0.0166611	−	0.0930890i
$989$	3.01865	+	7.28767i	0.0959876	+	0.231735i
$990$		0			0
$991$			0.0753046i			0.00239213i	0.999999	+	0.00119606i	$0.000380719\pi$
$991$			0.0753046i			0.00239213i	−0.999999	+	0.00119606i	$0.999619\pi$
$992$	37.2283	−	33.6756i	1.18200	−	1.06920i
$993$		0			0
$994$	8.21561	−	15.7326i	0.260583	−	0.499008i
$995$	0.0447494	−	0.0185358i	0.00141865	−	0.000587625i
$996$		0			0
$997$	−13.2343	+	31.9504i	−0.419134	+	1.01188i	0.563465	+	0.826140i	$0.309468\pi$
$997$	−13.2343	+	31.9504i	−0.419134	+	1.01188i	−0.982599	+	0.185739i	$0.940532\pi$
$998$	4.31324	−	48.5808i	0.136533	−	1.53780i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.b.107.12	✓	128
3.2	odd	2	inner	864.2.w.b.107.21	yes	128
32.3	odd	8	inner	864.2.w.b.323.21	yes	128
96.35	even	8	inner	864.2.w.b.323.12	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.b.107.12	✓	128	1.1	even	1	trivial
864.2.w.b.107.21	yes	128	3.2	odd	2	inner
864.2.w.b.323.12	yes	128	96.35	even	8	inner
864.2.w.b.323.21	yes	128	32.3	odd	8	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)

\(f(q)\)	\(=\)	\(q+(-0.654624 + 1.25358i) q^{2} +(-1.14293 - 1.64125i) q^{4} +(-0.0422264 - 0.0174907i) q^{5} +(-1.54323 + 1.54323i) q^{7} +(2.80563 - 0.358360i) q^{8} +O(q^{10})\)	\(q+(-0.654624 + 1.25358i) q^{2} +(-1.14293 - 1.64125i) q^{4} +(-0.0422264 - 0.0174907i) q^{5} +(-1.54323 + 1.54323i) q^{7} +(2.80563 - 0.358360i) q^{8} +(0.0495684 - 0.0414843i) q^{10} +(2.36542 + 0.979788i) q^{11} +(-0.368489 - 0.889611i) q^{13} +(-0.924330 - 2.94480i) q^{14} +(-1.38740 + 3.75168i) q^{16} +4.89675 q^{17} +(-1.42602 + 0.590675i) q^{19} +(0.0195553 + 0.0892947i) q^{20} +(-2.77670 + 2.32385i) q^{22} +(1.43441 - 1.43441i) q^{23} +(-3.53406 - 3.53406i) q^{25} +(1.35642 + 0.120430i) q^{26} +(4.29664 + 0.769016i) q^{28} +(2.09126 + 5.04875i) q^{29} +8.87410i q^{31} +(-3.79481 - 4.19516i) q^{32} +(-3.20553 + 6.13848i) q^{34} +(0.0921573 - 0.0381728i) q^{35} +(-1.04239 + 2.51656i) q^{37} +(0.193045 - 2.17430i) q^{38} +(-0.124740 - 0.0339403i) q^{40} +(0.556667 + 0.556667i) q^{41} +(-1.48807 + 3.59253i) q^{43} +(-1.09544 - 5.00208i) q^{44} +(0.859153 + 2.73716i) q^{46} +11.2877i q^{47} +2.23687i q^{49} +(6.74371 - 2.11675i) q^{50} +(-1.03892 + 1.62155i) q^{52} +(-3.14759 + 7.59897i) q^{53} +(-0.0827458 - 0.0827458i) q^{55} +(-3.77671 + 4.88277i) q^{56} +(-7.69802 - 0.683468i) q^{58} +(0.698406 - 1.68610i) q^{59} +(2.19335 - 0.908515i) q^{61} +(-11.1244 - 5.80920i) q^{62} +(7.74316 - 2.01086i) q^{64} +0.0440102i q^{65} +(4.03963 + 9.75253i) q^{67} +(-5.59666 - 8.03679i) q^{68} +(-0.0124757 + 0.140516i) q^{70} +(4.06618 + 4.06618i) q^{71} +(5.63896 - 5.63896i) q^{73} +(-2.47233 - 2.95412i) q^{74} +(2.59929 + 1.66535i) q^{76} +(-5.16243 + 2.13835i) q^{77} -4.03294 q^{79} +(0.124205 - 0.134153i) q^{80} +(-1.06224 + 0.333420i) q^{82} +(2.22963 + 5.38280i) q^{83} +(-0.206772 - 0.0856477i) q^{85} +(-3.52940 - 4.21717i) q^{86} +(6.98761 + 1.90125i) q^{88} +(4.29985 - 4.29985i) q^{89} +(1.94154 + 0.804212i) q^{91} +(-3.99367 - 0.714790i) q^{92} +(-14.1501 - 7.38920i) q^{94} +0.0705468 q^{95} -10.5936 q^{97} +(-2.80410 - 1.46431i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) \) 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

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