LMFDB - Embedded newform 768.2.o.a.287.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(95,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("768.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.o (of order $8$, degree $4$, not 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			287.2
Character	$\chi$	$=$	768.287
Dual form			768.2.o.a.479.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67029 - 0.458417i) q^{3} +(0.632159 - 1.52617i) q^{5} +(2.65940 - 2.65940i) q^{7} +(2.57971 + 1.53137i) q^{9} +O(q^{10})$	\(q+(-1.67029 - 0.458417i) q^{3} +(0.632159 - 1.52617i) q^{5} +(2.65940 - 2.65940i) q^{7} +(2.57971 + 1.53137i) q^{9} +(-1.24221 + 2.99895i) q^{11} +(3.05737 - 1.26640i) q^{13} +(-1.75551 + 2.25934i) q^{15} +2.20920 q^{17} +(-1.68742 - 4.07379i) q^{19} +(-5.66108 + 3.22285i) q^{21} +(-3.48822 + 3.48822i) q^{23} +(1.60597 + 1.60597i) q^{25} +(-3.60684 - 3.74042i) q^{27} +(4.26699 - 1.76744i) q^{29} -6.66418i q^{31} +(3.44961 - 4.43965i) q^{33} +(-2.37753 - 5.73985i) q^{35} +(0.622792 + 0.257969i) q^{37} +(-5.68722 + 0.713706i) q^{39} +(-6.66609 - 6.66609i) q^{41} +(6.38285 + 2.64386i) q^{43} +(3.96792 - 2.96899i) q^{45} -6.25962i q^{47} -7.14484i q^{49} +(-3.68999 - 1.01273i) q^{51} +(-5.31326 - 2.20082i) q^{53} +(3.79163 + 3.79163i) q^{55} +(0.950977 + 7.57794i) q^{57} +(7.82249 + 3.24018i) q^{59} +(-3.06898 - 7.40918i) q^{61} +(10.9330 - 2.78794i) q^{63} -5.46663i q^{65} +(1.05391 - 0.436545i) q^{67} +(7.42538 - 4.22726i) q^{69} +(-4.95182 - 4.95182i) q^{71} +(3.80393 - 3.80393i) q^{73} +(-1.94623 - 3.41864i) q^{75} +(4.67189 + 11.2789i) q^{77} +3.76078 q^{79} +(4.30978 + 7.90100i) q^{81} +(7.01836 - 2.90710i) q^{83} +(1.39656 - 3.37160i) q^{85} +(-7.93732 + 0.996076i) q^{87} +(-5.24890 + 5.24890i) q^{89} +(4.76290 - 11.4987i) q^{91} +(-3.05498 + 11.1311i) q^{93} -7.28400 q^{95} -18.6426 q^{97} +(-7.79705 + 5.83413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9	$ 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9} + 8 q^{13} + 8 q^{15} - 8 q^{19} + 4 q^{21} - 8 q^{25} - 28 q^{27} - 8 q^{33} + 8 q^{37} + 28 q^{39} - 8 q^{43} + 4 q^{45} - 16 q^{51} - 24 q^{55} - 4 q^{57} + 40 q^{61} + 56 q^{67} + 4 q^{69} - 8 q^{73} + 16 q^{75} - 16 q^{79} + 48 q^{85} - 52 q^{87} + 40 q^{91} - 8 q^{93} - 16 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9 + 8 * q^13 + 8 * q^15 - 8 * q^19 + 4 * q^21 - 8 * q^25 - 28 * q^27 - 8 * q^33 + 8 * q^37 + 28 * q^39 - 8 * q^43 + 4 * q^45 - 16 * q^51 - 24 * q^55 - 4 * q^57 + 40 * q^61 + 56 * q^67 + 4 * q^69 - 8 * q^73 + 16 * q^75 - 16 * q^79 + 48 * q^85 - 52 * q^87 + 40 * q^91 - 8 * q^93 - 16 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.67029	−	0.458417i	−0.964340	−	0.264667i
$3$	−1.67029	−	0.458417i	−0.964340	−	0.264667i
$4$		0			0
$5$	0.632159	−	1.52617i	0.282710	−	0.682522i	−0.717187	−	0.696881i	$-0.754571\pi$
$5$	0.632159	−	1.52617i	0.282710	−	0.682522i	0.999897	+	0.0143585i	$0.00457062\pi$
$6$		0			0
$7$	2.65940	−	2.65940i	1.00516	−	1.00516i	0.00517297	−	0.999987i	$-0.498353\pi$
$7$	2.65940	−	2.65940i	1.00516	−	1.00516i	0.999987	−	0.00517297i	$-0.00164662\pi$
$8$		0			0
$9$	2.57971	+	1.53137i	0.859903	+	0.510458i
$10$		0			0
$11$	−1.24221	+	2.99895i	−0.374539	+	0.904218i	0.618430	+	0.785840i	$0.287769\pi$
$11$	−1.24221	+	2.99895i	−0.374539	+	0.904218i	−0.992969	+	0.118377i	$0.962231\pi$
$12$		0			0
$13$	3.05737	−	1.26640i	0.847962	−	0.351237i	0.0839742	−	0.996468i	$-0.473239\pi$
$13$	3.05737	−	1.26640i	0.847962	−	0.351237i	0.763988	+	0.645231i	$0.223239\pi$
$14$		0			0
$15$	−1.75551	+	2.25934i	−0.453270	+	0.583359i
$16$		0			0
$17$	2.20920			0.535809			0.267905	−	0.963445i	$-0.413669\pi$
$17$	2.20920			0.535809			0.267905	+	0.963445i	$0.413669\pi$
$18$		0			0
$19$	−1.68742	−	4.07379i	−0.387121	−	0.934592i	−0.990547	−	0.137173i	$-0.956198\pi$
$19$	−1.68742	−	4.07379i	−0.387121	−	0.934592i	0.603426	−	0.797419i	$-0.293802\pi$
$20$		0			0
$21$	−5.66108	+	3.22285i	−1.23535	+	0.703283i
$22$		0			0
$23$	−3.48822	+	3.48822i	−0.727343	+	0.727343i	−0.970090	−	0.242746i	$-0.921952\pi$
$23$	−3.48822	+	3.48822i	−0.727343	+	0.727343i	0.242746	+	0.970090i	$0.421952\pi$
$24$		0			0
$25$	1.60597	+	1.60597i	0.321195	+	0.321195i
$26$		0			0
$27$	−3.60684	−	3.74042i	−0.694137	−	0.719843i
$28$		0			0
$29$	4.26699	−	1.76744i	0.792360	−	0.328206i	0.0504679	−	0.998726i	$-0.483929\pi$
$29$	4.26699	−	1.76744i	0.792360	−	0.328206i	0.741892	+	0.670519i	$0.233929\pi$
$30$		0			0
$31$		−	6.66418i		−	1.19692i	−0.801152	−	0.598461i	$-0.795779\pi$
$31$		−	6.66418i		−	1.19692i	0.801152	−	0.598461i	$-0.204221\pi$
$32$		0			0
$33$	3.44961	−	4.43965i	0.600500	−	0.772845i
$34$		0			0
$35$	−2.37753	−	5.73985i	−0.401875	−	0.970213i
$36$		0			0
$37$	0.622792	+	0.257969i	0.102386	+	0.0424098i	0.433289	−	0.901255i	$-0.357353\pi$
$37$	0.622792	+	0.257969i	0.102386	+	0.0424098i	−0.330902	+	0.943665i	$0.607353\pi$
$38$		0			0
$39$	−5.68722	+	0.713706i	−0.910685	+	0.114284i
$40$		0			0
$41$	−6.66609	−	6.66609i	−1.04107	−	1.04107i	−0.999120	−	0.0419492i	$-0.986643\pi$
$41$	−6.66609	−	6.66609i	−1.04107	−	1.04107i	−0.0419492	−	0.999120i	$-0.513357\pi$
$42$		0			0
$43$	6.38285	+	2.64386i	0.973376	+	0.403185i	0.811968	−	0.583702i	$-0.198396\pi$
$43$	6.38285	+	2.64386i	0.973376	+	0.403185i	0.161408	+	0.986888i	$0.448396\pi$
$44$		0			0
$45$	3.96792	−	2.96899i	0.591502	−	0.442591i
$46$		0			0
$47$		−	6.25962i		−	0.913059i	−0.889708	−	0.456529i	$-0.849092\pi$
$47$		−	6.25962i		−	0.913059i	0.889708	−	0.456529i	$-0.150908\pi$
$48$		0			0
$49$		−	7.14484i		−	1.02069i
$50$		0			0
$51$	−3.68999	−	1.01273i	−0.516702	−	0.141811i
$52$		0			0
$53$	−5.31326	−	2.20082i	−0.729833	−	0.302307i	−0.0133494	−	0.999911i	$-0.504249\pi$
$53$	−5.31326	−	2.20082i	−0.729833	−	0.302307i	−0.716483	+	0.697604i	$0.754249\pi$
$54$		0			0
$55$	3.79163	+	3.79163i	0.511263	+	0.511263i
$56$		0			0
$57$	0.950977	+	7.57794i	0.125960	+	1.00372i
$58$		0			0
$59$	7.82249	+	3.24018i	1.01840	+	0.421836i	0.828513	−	0.559970i	$-0.189187\pi$
$59$	7.82249	+	3.24018i	1.01840	+	0.421836i	0.189889	+	0.981806i	$0.439187\pi$
$60$		0			0
$61$	−3.06898	−	7.40918i	−0.392943	−	0.948648i	−0.989296	−	0.145926i	$-0.953384\pi$
$61$	−3.06898	−	7.40918i	−0.392943	−	0.948648i	0.596353	−	0.802723i	$-0.296616\pi$
$62$		0			0
$63$	10.9330	−	2.78794i	1.37743	−	0.351247i
$64$		0			0
$65$		−	5.46663i		−	0.678051i
$66$		0			0
$67$	1.05391	−	0.436545i	0.128756	−	0.0533325i	−0.317375	−	0.948300i	$-0.602801\pi$
$67$	1.05391	−	0.436545i	0.128756	−	0.0533325i	0.446131	+	0.894968i	$0.352801\pi$
$68$		0			0
$69$	7.42538	−	4.22726i	0.893910	−	0.508902i
$70$		0			0
$71$	−4.95182	−	4.95182i	−0.587673	−	0.587673i	0.349328	−	0.937001i	$-0.386410\pi$
$71$	−4.95182	−	4.95182i	−0.587673	−	0.587673i	−0.937001	+	0.349328i	$0.886410\pi$
$72$		0			0
$73$	3.80393	−	3.80393i	0.445216	−	0.445216i	−0.448544	−	0.893761i	$-0.648057\pi$
$73$	3.80393	−	3.80393i	0.445216	−	0.445216i	0.893761	+	0.448544i	$0.148057\pi$
$74$		0			0
$75$	−1.94623	−	3.41864i	−0.224731	−	0.394751i
$76$		0			0
$77$	4.67189	+	11.2789i	0.532411	+	1.28535i
$78$		0			0
$79$	3.76078			0.423121			0.211561	−	0.977365i	$-0.432145\pi$
$79$	3.76078			0.423121			0.211561	+	0.977365i	$0.432145\pi$
$80$		0			0
$81$	4.30978	+	7.90100i	0.478865	+	0.877889i
$82$		0			0
$83$	7.01836	−	2.90710i	0.770365	−	0.319095i	0.0373445	−	0.999302i	$-0.488110\pi$
$83$	7.01836	−	2.90710i	0.770365	−	0.319095i	0.733020	+	0.680207i	$0.238110\pi$
$84$		0			0
$85$	1.39656	−	3.37160i	0.151479	−	0.365702i
$86$		0			0
$87$	−7.93732	+	0.996076i	−0.850970	+	0.106791i
$88$		0			0
$89$	−5.24890	+	5.24890i	−0.556382	+	0.556382i	−0.928276	−	0.371893i	$-0.878709\pi$
$89$	−5.24890	+	5.24890i	−0.556382	+	0.556382i	0.371893	+	0.928276i	$0.378709\pi$
$90$		0			0
$91$	4.76290	−	11.4987i	0.499288	−	1.20539i
$92$		0			0
$93$	−3.05498	+	11.1311i	−0.316786	+	1.15424i
$94$		0			0
$95$	−7.28400			−0.747323
$96$		0			0
$97$	−18.6426			−1.89287			−0.946433	−	0.322899i	$-0.895342\pi$
$97$	−18.6426			−1.89287			−0.946433	+	0.322899i	$0.895342\pi$
$98$		0			0
$99$	−7.79705	+	5.83413i	−0.783633	+	0.586352i
$100$		0			0
$101$	−2.57298	+	6.21173i	−0.256021	+	0.618090i	−0.998668	−	0.0515932i	$-0.983570\pi$
$101$	−2.57298	+	6.21173i	−0.256021	+	0.618090i	0.742647	+	0.669683i	$0.233570\pi$
$102$		0			0
$103$	−5.77137	+	5.77137i	−0.568670	+	0.568670i	−0.931756	−	0.363085i	$-0.881723\pi$
$103$	−5.77137	+	5.77137i	−0.568670	+	0.568670i	0.363085	+	0.931756i	$0.381723\pi$
$104$		0			0
$105$	1.33990	+	10.6771i	0.130761	+	1.04198i
$106$		0			0
$107$	−7.25959	+	17.5262i	−0.701811	+	1.69432i	0.0177034	+	0.999843i	$0.494365\pi$
$107$	−7.25959	+	17.5262i	−0.701811	+	1.69432i	−0.719514	+	0.694478i	$0.755635\pi$
$108$		0			0
$109$	0.819975	−	0.339645i	0.0785393	−	0.0325320i	−0.343068	−	0.939311i	$-0.611466\pi$
$109$	0.819975	−	0.339645i	0.0785393	−	0.0325320i	0.421607	+	0.906779i	$0.361466\pi$
$110$		0			0
$111$	−0.921983	−	0.716380i	−0.0875108	−	0.0679958i
$112$		0			0
$113$	1.38780			0.130553			0.0652767	−	0.997867i	$-0.479207\pi$
$113$	1.38780			0.130553			0.0652767	+	0.997867i	$0.479207\pi$
$114$		0			0
$115$	3.11849	+	7.52870i	0.290801	+	0.702055i
$116$		0			0
$117$	9.82646	+	1.41503i	0.908457	+	0.130819i
$118$		0			0
$119$	5.87515	−	5.87515i	0.538574	−	0.538574i
$120$		0			0
$121$	0.327547	+	0.327547i	0.0297770	+	0.0297770i
$122$		0			0
$123$	8.07843	+	14.1901i	0.728407	+	1.27948i
$124$		0			0
$125$	11.0970	−	4.59655i	0.992550	−	0.411128i
$126$		0			0
$127$			1.41832i			0.125856i	0.998018	+	0.0629278i	$0.0200438\pi$
$127$			1.41832i			0.125856i	−0.998018	+	0.0629278i	$0.979956\pi$
$128$		0			0
$129$	−9.44919	−	7.34202i	−0.831955	−	0.646429i
$130$		0			0
$131$	−2.02810	−	4.89628i	−0.177196	−	0.427790i	0.810180	−	0.586181i	$-0.199369\pi$
$131$	−2.02810	−	4.89628i	−0.177196	−	0.427790i	−0.987376	+	0.158391i	$0.949369\pi$
$132$		0			0
$133$	−15.3214	−	6.34632i	−1.32853	−	0.550296i
$134$		0			0
$135$	−7.98859	+	3.14010i	−0.687548	+	0.270257i
$136$		0			0
$137$	4.79832	+	4.79832i	0.409948	+	0.409948i	0.881720	−	0.471772i	$-0.156386\pi$
$137$	4.79832	+	4.79832i	0.409948	+	0.409948i	−0.471772	+	0.881720i	$0.656386\pi$
$138$		0			0
$139$	3.72205	+	1.54172i	0.315700	+	0.130767i	0.534907	−	0.844911i	$-0.320347\pi$
$139$	3.72205	+	1.54172i	0.315700	+	0.130767i	−0.219206	+	0.975679i	$0.570347\pi$
$140$		0			0
$141$	−2.86952	+	10.4553i	−0.241657	+	0.880499i
$142$		0			0
$143$			10.7420i			0.898294i
$144$		0			0
$145$		−	7.62944i		−	0.633590i
$146$		0			0
$147$	−3.27532	+	11.9339i	−0.270144	+	0.984294i
$148$		0			0
$149$	−6.33143	−	2.62257i	−0.518691	−	0.214849i	0.107951	−	0.994156i	$-0.465571\pi$
$149$	−6.33143	−	2.62257i	−0.518691	−	0.214849i	−0.626642	+	0.779307i	$0.715571\pi$
$150$		0			0
$151$	3.93949	+	3.93949i	0.320591	+	0.320591i	0.848994	−	0.528403i	$-0.177209\pi$
$151$	3.93949	+	3.93949i	0.320591	+	0.320591i	−0.528403	+	0.848994i	$0.677209\pi$
$152$		0			0
$153$	5.69909	+	3.38311i	0.460744	+	0.273508i
$154$		0			0
$155$	−10.1707	−	4.21282i	−0.816927	−	0.338382i
$156$		0			0
$157$	1.37232	+	3.31308i	0.109523	+	0.264413i	0.969133	−	0.246539i	$-0.0792932\pi$
$157$	1.37232	+	3.31308i	0.109523	+	0.264413i	−0.859610	+	0.510951i	$0.829293\pi$
$158$		0			0
$159$	7.86577	+	6.11170i	0.623796	+	0.484689i
$160$		0			0
$161$			18.5531i			1.46219i
$162$		0			0
$163$	3.75647	−	1.55598i	0.294230	−	0.121874i	−0.230686	−	0.973028i	$-0.574097\pi$
$163$	3.75647	−	1.55598i	0.294230	−	0.121874i	0.524915	+	0.851154i	$0.324097\pi$
$164$		0			0
$165$	−4.59495	−	8.07124i	−0.357716	−	0.628345i
$166$		0			0
$167$	15.3293	+	15.3293i	1.18622	+	1.18622i	0.978105	+	0.208110i	$0.0667311\pi$
$167$	15.3293	+	15.3293i	1.18622	+	1.18622i	0.208110	+	0.978105i	$0.433269\pi$
$168$		0			0
$169$	−1.44865	+	1.44865i	−0.111435	+	0.111435i
$170$		0			0
$171$	1.88545	−	13.0933i	0.144184	−	1.00127i
$172$		0			0
$173$	−5.26974	−	12.7223i	−0.400651	−	0.967257i	−0.987508	−	0.157567i	$-0.949635\pi$
$173$	−5.26974	−	12.7223i	−0.400651	−	0.967257i	0.586857	−	0.809690i	$-0.300365\pi$
$174$		0			0
$175$	8.54187			0.645704
$176$		0			0
$177$	−11.5804	−	8.99799i	−0.870439	−	0.676331i
$178$		0			0
$179$	11.0109	−	4.56087i	0.822994	−	0.340895i	0.0688683	−	0.997626i	$-0.478061\pi$
$179$	11.0109	−	4.56087i	0.822994	−	0.340895i	0.754125	+	0.656731i	$0.228061\pi$
$180$		0			0
$181$	−4.46761	+	10.7858i	−0.332075	+	0.801700i	0.666352	+	0.745637i	$0.267855\pi$
$181$	−4.46761	+	10.7858i	−0.332075	+	0.801700i	−0.998427	+	0.0560630i	$0.982145\pi$
$182$		0			0
$183$	1.72958	+	13.7823i	0.127854	+	1.01882i
$184$		0			0
$185$	0.787407	−	0.787407i	0.0578913	−	0.0578913i
$186$		0			0
$187$	−2.74428	+	6.62528i	−0.200682	+	0.484488i
$188$		0			0
$189$	−19.5393	−	0.355231i	−1.42128	−	0.0258393i
$190$		0			0
$191$	12.4770			0.902804			0.451402	−	0.892321i	$-0.350924\pi$
$191$	12.4770			0.902804			0.451402	+	0.892321i	$0.350924\pi$
$192$		0			0
$193$	26.3839			1.89915			0.949576	−	0.313537i	$-0.101514\pi$
$193$	26.3839			1.89915			0.949576	+	0.313537i	$0.101514\pi$
$194$		0			0
$195$	−2.50599	+	9.13083i	−0.179458	+	0.653872i
$196$		0			0
$197$	−8.49181	+	20.5010i	−0.605017	+	1.46064i	0.263342	+	0.964702i	$0.415175\pi$
$197$	−8.49181	+	20.5010i	−0.605017	+	1.46064i	−0.868359	+	0.495937i	$0.834825\pi$
$198$		0			0
$199$	5.26709	−	5.26709i	0.373374	−	0.373374i	−0.495331	−	0.868705i	$-0.664953\pi$
$199$	5.26709	−	5.26709i	0.373374	−	0.373374i	0.868705	+	0.495331i	$0.164953\pi$
$200$		0			0
$201$	−1.96046	+	0.246023i	−0.138280	+	0.0173531i
$202$		0			0
$203$	6.64729	−	16.0480i	0.466549	−	1.12635i
$204$		0			0
$205$	−14.3876	+	5.95954i	−1.00487	+	0.416232i
$206$		0			0
$207$	−14.3403	+	3.65681i	−0.996723	+	0.254166i
$208$		0			0
$209$	14.3132			0.990067
$210$		0			0
$211$	1.35356	+	3.26778i	0.0931829	+	0.224964i	0.963598	−	0.267355i	$-0.0861496\pi$
$211$	1.35356	+	3.26778i	0.0931829	+	0.224964i	−0.870415	+	0.492318i	$0.836150\pi$
$212$		0			0
$213$	6.00096	+	10.5410i	0.411179	+	0.722254i
$214$		0			0
$215$	8.06995	−	8.06995i	0.550366	−	0.550366i
$216$		0			0
$217$	−17.7227	−	17.7227i	−1.20310	−	1.20310i
$218$		0			0
$219$	−8.09743	+	4.60986i	−0.547174	+	0.311505i
$220$		0			0
$221$	6.75434	−	2.79774i	0.454346	−	0.188196i
$222$		0			0
$223$			7.02678i			0.470548i	0.971929	+	0.235274i	$0.0755988\pi$
$223$			7.02678i			0.470548i	−0.971929	+	0.235274i	$0.924401\pi$
$224$		0			0
$225$	1.68360	+	6.60230i	0.112240	+	0.440153i
$226$		0			0
$227$	−0.128954	−	0.311323i	−0.00855899	−	0.0206632i	0.919542	−	0.392991i	$-0.128560\pi$
$227$	−0.128954	−	0.311323i	−0.00855899	−	0.0206632i	−0.928101	+	0.372328i	$0.878560\pi$
$228$		0			0
$229$	8.32315	+	3.44756i	0.550009	+	0.227821i	0.640341	−	0.768090i	$-0.278793\pi$
$229$	8.32315	+	3.44756i	0.550009	+	0.227821i	−0.0903321	+	0.995912i	$0.528793\pi$
$230$		0			0
$231$	−2.63293	−	20.9807i	−0.173234	−	1.38043i
$232$		0			0
$233$	−3.72476	−	3.72476i	−0.244017	−	0.244017i	0.574493	−	0.818510i	$-0.305199\pi$
$233$	−3.72476	−	3.72476i	−0.244017	−	0.244017i	−0.818510	+	0.574493i	$0.805199\pi$
$234$		0			0
$235$	−9.55322	−	3.95707i	−0.623183	−	0.258131i
$236$		0			0
$237$	−6.28158	−	1.72401i	−0.408033	−	0.111986i
$238$		0			0
$239$		−	10.6096i		−	0.686277i	−0.939285	−	0.343138i	$-0.888510\pi$
$239$		−	10.6096i		−	0.686277i	0.939285	−	0.343138i	$-0.111490\pi$
$240$		0			0
$241$			10.2565i			0.660681i	0.943862	+	0.330341i	$0.107164\pi$
$241$			10.2565i			0.660681i	−0.943862	+	0.330341i	$0.892836\pi$
$242$		0			0
$243$	−3.57661	−	15.1726i	−0.229440	−	0.973323i
$244$		0			0
$245$	−10.9042	−	4.51667i	−0.696645	−	0.288560i
$246$		0			0
$247$	−10.3181	−	10.3181i	−0.656527	−	0.656527i
$248$		0			0
$249$	−13.0553	+	1.63835i	−0.827347	+	0.103826i
$250$		0			0
$251$	−1.53857	−	0.637297i	−0.0971138	−	0.0402258i	0.333598	−	0.942716i	$-0.391737\pi$
$251$	−1.53857	−	0.637297i	−0.0971138	−	0.0402258i	−0.430711	+	0.902490i	$0.641737\pi$
$252$		0			0
$253$	−6.12790	−	14.7941i	−0.385258	−	0.930095i
$254$		0			0
$255$	−3.87826	+	4.99133i	−0.242866	+	0.312569i
$256$		0			0
$257$			15.0434i			0.938379i	0.883098	+	0.469189i	$0.155454\pi$
$257$			15.0434i			0.938379i	−0.883098	+	0.469189i	$0.844546\pi$
$258$		0			0
$259$	2.34230	−	0.970212i	0.145543	−	0.0602860i
$260$		0			0
$261$	13.7142	+	1.97487i	0.848888	+	0.122241i
$262$		0			0
$263$	17.1521	+	17.1521i	1.05764	+	1.05764i	0.998234	+	0.0594075i	$0.0189211\pi$
$263$	17.1521	+	17.1521i	1.05764	+	1.05764i	0.0594075	+	0.998234i	$0.481079\pi$
$264$		0			0
$265$	−6.71765	+	6.71765i	−0.412662	+	0.412662i
$266$		0			0
$267$	11.1734	−	6.36098i	0.683798	−	0.389286i
$268$		0			0
$269$	−3.67246	−	8.86611i	−0.223914	−	0.540576i	0.771501	−	0.636228i	$-0.219506\pi$
$269$	−3.67246	−	8.86611i	−0.223914	−	0.540576i	−0.995415	+	0.0956522i	$0.969506\pi$
$270$		0			0
$271$	−0.446617			−0.0271300			−0.0135650	−	0.999908i	$-0.504318\pi$
$271$	−0.446617			−0.0271300			−0.0135650	+	0.999908i	$0.504318\pi$
$272$		0			0
$273$	−13.2266	+	17.0226i	−0.800509	+	1.03026i
$274$		0			0
$275$	−6.81119	+	2.82129i	−0.410730	+	0.170130i
$276$		0			0
$277$	7.09792	−	17.1359i	0.426473	−	1.02960i	−0.553925	−	0.832567i	$-0.686871\pi$
$277$	7.09792	−	17.1359i	0.426473	−	1.02960i	0.980398	−	0.197029i	$-0.0631294\pi$
$278$		0			0
$279$	10.2054	−	17.1916i	0.610979	−	1.02924i
$280$		0			0
$281$	21.8515	−	21.8515i	1.30355	−	1.30355i	0.377570	−	0.925981i	$-0.376760\pi$
$281$	21.8515	−	21.8515i	1.30355	−	1.30355i	0.925981	−	0.377570i	$-0.123240\pi$
$282$		0			0
$283$	−8.71809	+	21.0473i	−0.518237	+	1.25113i	0.420748	+	0.907177i	$0.361768\pi$
$283$	−8.71809	+	21.0473i	−0.518237	+	1.25113i	−0.938985	+	0.343957i	$0.888232\pi$
$284$		0			0
$285$	12.1664	+	3.33911i	0.720673	+	0.197792i
$286$		0			0
$287$	−35.4557			−2.09288
$288$		0			0
$289$	−12.1194			−0.712908
$290$		0			0
$291$	31.1384	+	8.54607i	1.82537	+	0.500980i
$292$		0			0
$293$	8.00942	−	19.3364i	0.467915	−	1.12965i	−0.497156	−	0.867661i	$-0.665622\pi$
$293$	8.00942	−	19.3364i	0.467915	−	1.12965i	0.965072	−	0.261986i	$-0.0843775\pi$
$294$		0			0
$295$	9.89011	−	9.89011i	0.575825	−	0.575825i
$296$		0			0
$297$	15.6978	−	6.17037i	0.910876	−	0.358041i
$298$		0			0
$299$	−6.24728	+	15.0823i	−0.361289	+	0.872230i
$300$		0			0
$301$	24.0057	−	9.94347i	1.38366	−	0.573132i
$302$		0			0
$303$	7.14518	−	9.19586i	0.410480	−	0.528288i
$304$		0			0
$305$	−13.2477			−0.758563
$306$		0			0
$307$	−1.33094	−	3.21317i	−0.0759606	−	0.183385i	0.881338	−	0.472487i	$-0.156643\pi$
$307$	−1.33094	−	3.21317i	−0.0759606	−	0.183385i	−0.957298	+	0.289102i	$0.906643\pi$
$308$		0			0
$309$	12.2855	−	6.99415i	0.698900	−	0.397883i
$310$		0			0
$311$	1.04002	−	1.04002i	0.0589739	−	0.0589739i	−0.677005	−	0.735979i	$-0.736722\pi$
$311$	1.04002	−	1.04002i	0.0589739	−	0.0589739i	0.735979	+	0.677005i	$0.236722\pi$
$312$		0			0
$313$	−2.18573	−	2.18573i	−0.123545	−	0.123545i	0.642631	−	0.766176i	$-0.277843\pi$
$313$	−2.18573	−	2.18573i	−0.123545	−	0.123545i	−0.766176	+	0.642631i	$0.777843\pi$
$314$		0			0
$315$	2.65655	−	18.4480i	0.149680	−	1.03943i
$316$		0			0
$317$	−28.4555	+	11.7866i	−1.59822	+	0.662004i	−0.991162	−	0.132656i	$-0.957650\pi$
$317$	−28.4555	+	11.7866i	−1.59822	+	0.662004i	−0.607056	+	0.794659i	$0.707650\pi$
$318$		0			0
$319$			14.9920i			0.839392i
$320$		0			0
$321$	20.1599	−	25.9458i	1.12522	−	1.44815i
$322$		0			0
$323$	−3.72785	−	8.99982i	−0.207423	−	0.500763i
$324$		0			0
$325$	6.94387	+	2.87625i	0.385177	+	0.159545i
$326$		0			0
$327$	−1.52529	+	0.191413i	−0.0843488	+	0.0105852i
$328$		0			0
$329$	−16.6468	−	16.6468i	−0.917770	−	0.917770i
$330$		0			0
$331$	1.77145	+	0.733760i	0.0973678	+	0.0403311i	0.430836	−	0.902430i	$-0.358219\pi$
$331$	1.77145	+	0.733760i	0.0973678	+	0.0403311i	−0.333468	+	0.942761i	$0.608219\pi$
$332$		0			0
$333$	1.21157	+	1.61921i	0.0663939	+	0.0887323i
$334$		0			0
$335$		−	1.88441i		−	0.102956i
$336$		0			0
$337$			30.3584i			1.65373i	0.562401	+	0.826865i	$0.309878\pi$
$337$			30.3584i			1.65373i	−0.562401	+	0.826865i	$0.690122\pi$
$338$		0			0
$339$	−2.31802	−	0.636192i	−0.125898	−	0.0345532i
$340$		0			0
$341$	19.9856	+	8.27829i	1.08228	+	0.448294i
$342$		0			0
$343$	−0.385191	−	0.385191i	−0.0207984	−	0.0207984i
$344$		0			0
$345$	−1.75748	−	14.0047i	−0.0946198	−	0.753985i
$346$		0			0
$347$	8.49692	+	3.51954i	0.456138	+	0.188939i	0.598909	−	0.800817i	$-0.295601\pi$
$347$	8.49692	+	3.51954i	0.456138	+	0.188939i	−0.142771	+	0.989756i	$0.545601\pi$
$348$		0			0
$349$	10.0493	+	24.2611i	0.537926	+	1.29867i	0.926168	+	0.377111i	$0.123082\pi$
$349$	10.0493	+	24.2611i	0.537926	+	1.29867i	−0.388242	+	0.921557i	$0.626918\pi$
$350$		0			0
$351$	−15.7643	−	6.86812i	−0.841437	−	0.366593i
$352$		0			0
$353$			14.8788i			0.791921i	0.918268	+	0.395961i	$0.129588\pi$
$353$			14.8788i			0.791921i	−0.918268	+	0.395961i	$0.870412\pi$
$354$		0			0
$355$	−10.6876	+	4.42697i	−0.567241	+	0.234959i
$356$		0			0
$357$	−12.5064	+	7.11990i	−0.661911	+	0.376825i
$358$		0			0
$359$	0.751643	+	0.751643i	0.0396702	+	0.0396702i	0.726664	−	0.686993i	$-0.241070\pi$
$359$	0.751643	+	0.751643i	0.0396702	+	0.0396702i	−0.686993	+	0.726664i	$0.741070\pi$
$360$		0			0
$361$	−0.313372	+	0.313372i	−0.0164933	+	0.0164933i
$362$		0			0
$363$	−0.396944	−	0.697251i	−0.0208342	−	0.0365962i
$364$		0			0
$365$	−3.40074	−	8.21011i	−0.178003	−	0.429737i
$366$		0			0
$367$	−21.0438			−1.09848			−0.549239	−	0.835665i	$-0.685082\pi$
$367$	−21.0438			−1.09848			−0.549239	+	0.835665i	$0.685082\pi$
$368$		0			0
$369$	−6.98828	−	27.4049i	−0.363796	−	1.42664i
$370$		0			0
$371$	−19.9830	+	8.27722i	−1.03746	+	0.429732i
$372$		0			0
$373$	−0.0584700	+	0.141159i	−0.00302746	+	0.00730894i	−0.925386	−	0.379026i	$-0.876259\pi$
$373$	−0.0584700	+	0.141159i	−0.00302746	+	0.00730894i	0.922359	+	0.386335i	$0.126259\pi$
$374$		0			0
$375$	−20.6424	+	2.59047i	−1.06597	+	0.133771i
$376$		0			0
$377$	10.8075	−	10.8075i	0.556613	−	0.556613i
$378$		0			0
$379$	7.39031	−	17.8418i	0.379615	−	0.916471i	−0.612423	−	0.790530i	$-0.709805\pi$
$379$	7.39031	−	17.8418i	0.379615	−	0.916471i	0.992038	−	0.125941i	$-0.0401949\pi$
$380$		0			0
$381$	0.650182	−	2.36900i	0.0333098	−	0.121368i
$382$		0			0
$383$	−24.2018			−1.23666			−0.618328	−	0.785920i	$-0.712190\pi$
$383$	−24.2018			−1.23666			−0.618328	+	0.785920i	$0.712190\pi$
$384$		0			0
$385$	20.1669			1.02780
$386$		0			0
$387$	12.4171	+	16.5949i	0.631199	+	0.843568i
$388$		0			0
$389$	−0.103603	+	0.250119i	−0.00525287	+	0.0126815i	−0.926484	−	0.376334i	$-0.877185\pi$
$389$	−0.103603	+	0.250119i	−0.00525287	+	0.0126815i	0.921231	+	0.389015i	$0.127185\pi$
$390$		0			0
$391$	−7.70616	+	7.70616i	−0.389717	+	0.389717i
$392$		0			0
$393$	1.14298	+	9.10790i	0.0576555	+	0.459433i
$394$		0			0
$395$	2.37741	−	5.73958i	0.119621	−	0.288790i
$396$		0			0
$397$	−24.7102	+	10.2353i	−1.24017	+	0.513694i	−0.903767	−	0.428024i	$-0.859210\pi$
$397$	−24.7102	+	10.2353i	−1.24017	+	0.513694i	−0.336401	+	0.941719i	$0.609210\pi$
$398$		0			0
$399$	22.6818	+	17.6238i	1.13551	+	0.882291i
$400$		0			0
$401$	6.89411			0.344275			0.172138	−	0.985073i	$-0.444933\pi$
$401$	6.89411			0.344275			0.172138	+	0.985073i	$0.444933\pi$
$402$		0			0
$403$	−8.43955	−	20.3749i	−0.420404	−	1.01495i
$404$		0			0
$405$	14.7827	−	1.58276i	0.734559	−	0.0786479i
$406$		0			0
$407$	−1.54727	+	1.54727i	−0.0766954	+	0.0766954i
$408$		0			0
$409$	26.6691	+	26.6691i	1.31870	+	1.31870i	0.914804	+	0.403897i	$0.132345\pi$
$409$	26.6691	+	26.6691i	1.31870	+	1.31870i	0.403897	+	0.914804i	$0.367655\pi$
$410$		0			0
$411$	−5.81493	−	10.2142i	−0.286830	−	0.503829i
$412$		0			0
$413$	29.4201	−	12.1862i	1.44767	−	0.599644i
$414$		0			0
$415$		−	12.5489i		−	0.616003i
$416$		0			0
$417$	−5.51013	−	4.28137i	−0.269832	−	0.209660i
$418$		0			0
$419$	5.68960	+	13.7359i	0.277955	+	0.671043i	0.999779	−	0.0210342i	$-0.00669590\pi$
$419$	5.68960	+	13.7359i	0.277955	+	0.671043i	−0.721824	+	0.692077i	$0.756696\pi$
$420$		0			0
$421$	19.2802	+	7.98613i	0.939661	+	0.389220i	0.799335	−	0.600885i	$-0.205185\pi$
$421$	19.2802	+	7.98613i	0.939661	+	0.389220i	0.140325	+	0.990105i	$0.455185\pi$
$422$		0			0
$423$	9.58582	−	16.1480i	0.466078	−	0.785142i
$424$		0			0
$425$	3.54792	+	3.54792i	0.172099	+	0.172099i
$426$		0			0
$427$	−27.8657	−	11.5423i	−1.34851	−	0.558573i
$428$		0			0
$429$	4.92433	−	17.9423i	0.237749	−	0.866261i
$430$		0			0
$431$			0.896539i			0.0431848i	0.999767	+	0.0215924i	$0.00687361\pi$
$431$			0.896539i			0.0431848i	−0.999767	+	0.0215924i	$0.993126\pi$
$432$		0			0
$433$		−	15.1990i		−	0.730416i	−0.930926	−	0.365208i	$-0.880998\pi$
$433$		−	15.1990i		−	0.730416i	0.930926	−	0.365208i	$-0.119002\pi$
$434$		0			0
$435$	−3.49747	+	12.7433i	−0.167691	+	0.610997i
$436$		0			0
$437$	20.0964	+	8.32418i	0.961339	+	0.398200i
$438$		0			0
$439$	−19.4573	−	19.4573i	−0.928645	−	0.928645i	0.0689738	−	0.997618i	$-0.478028\pi$
$439$	−19.4573	−	19.4573i	−0.928645	−	0.928645i	−0.997618	+	0.0689738i	$0.978028\pi$
$440$		0			0
$441$	10.9414	−	18.4316i	0.521021	−	0.877695i
$442$		0			0
$443$	−29.1034	−	12.0550i	−1.38274	−	0.572751i	−0.437529	−	0.899204i	$-0.644146\pi$
$443$	−29.1034	−	12.0550i	−1.38274	−	0.572751i	−0.945213	+	0.326453i	$0.894146\pi$
$444$		0			0
$445$	4.69256	+	11.3288i	0.222449	+	0.537038i
$446$		0			0
$447$	9.37307	+	7.28287i	0.443331	+	0.344468i
$448$		0			0
$449$		−	15.3710i		−	0.725405i	−0.931905	−	0.362702i	$-0.881854\pi$
$449$		−	15.3710i		−	0.725405i	0.931905	−	0.362702i	$-0.118146\pi$
$450$		0			0
$451$	28.2719	−	11.7106i	1.33127	−	0.551432i
$452$		0			0
$453$	−4.77415	−	8.38601i	−0.224309	−	0.394009i
$454$		0			0
$455$	−14.5380	−	14.5380i	−0.681550	−	0.681550i
$456$		0			0
$457$	7.57684	−	7.57684i	0.354430	−	0.354430i	−0.507325	−	0.861755i	$-0.669366\pi$
$457$	7.57684	−	7.57684i	0.354430	−	0.354430i	0.861755	+	0.507325i	$0.169366\pi$
$458$		0			0
$459$	−7.96822	−	8.26332i	−0.371925	−	0.385699i
$460$		0			0
$461$	2.98247	+	7.20032i	0.138908	+	0.335352i	0.977990	−	0.208652i	$-0.0669075\pi$
$461$	2.98247	+	7.20032i	0.138908	+	0.335352i	−0.839082	+	0.544004i	$0.816908\pi$
$462$		0			0
$463$	−14.2866			−0.663957			−0.331978	−	0.943287i	$-0.607716\pi$
$463$	−14.2866			−0.663957			−0.331978	+	0.943287i	$0.607716\pi$
$464$		0			0
$465$	15.0567	+	11.6990i	0.698236	+	0.542529i
$466$		0			0
$467$	3.05479	−	1.26534i	0.141359	−	0.0585527i	−0.310883	−	0.950448i	$-0.600625\pi$
$467$	3.05479	−	1.26534i	0.141359	−	0.0585527i	0.452241	+	0.891896i	$0.350625\pi$
$468$		0			0
$469$	1.64183	−	3.96373i	0.0758127	−	0.183028i
$470$		0			0
$471$	−0.773398	−	6.16289i	−0.0356363	−	0.283971i
$472$		0			0
$473$	−15.8576	+	15.8576i	−0.729135	+	0.729135i
$474$		0			0
$475$	3.83245	−	9.25236i	0.175845	−	0.424528i
$476$		0			0
$477$	−10.3364	−	13.8141i	−0.473270	−	0.632503i
$478$		0			0
$479$	26.6399			1.21721			0.608605	−	0.793473i	$-0.291729\pi$
$479$	26.6399			1.21721			0.608605	+	0.793473i	$0.291729\pi$
$480$		0			0
$481$	2.23080			0.101716
$482$		0			0
$483$	8.50508	−	30.9890i	0.386994	−	1.41005i
$484$		0			0
$485$	−11.7851	+	28.4517i	−0.535132	+	1.29192i
$486$		0			0
$487$	−7.36014	+	7.36014i	−0.333520	+	0.333520i	−0.853922	−	0.520402i	$-0.825782\pi$
$487$	−7.36014	+	7.36014i	−0.333520	+	0.333520i	0.520402	+	0.853922i	$0.325782\pi$
$488$		0			0
$489$	−6.98767	+	0.876903i	−0.315993	+	0.0396549i
$490$		0			0
$491$	4.20682	−	10.1562i	0.189851	−	0.458342i	−0.800079	−	0.599894i	$-0.795209\pi$
$491$	4.20682	−	10.1562i	0.189851	−	0.458342i	0.989931	+	0.141553i	$0.0452094\pi$
$492$		0			0
$493$	9.42662	−	3.90464i	0.424554	−	0.175856i
$494$		0			0
$495$	3.97488	+	15.5877i	0.178658	+	0.700614i
$496$		0			0
$497$	−26.3378			−1.18141
$498$		0			0
$499$	12.5040	+	30.1873i	0.559756	+	1.35137i	0.909960	+	0.414697i	$0.136112\pi$
$499$	12.5040	+	30.1873i	0.559756	+	1.35137i	−0.350204	+	0.936673i	$0.613888\pi$
$500$		0			0
$501$	−18.5771	−	32.6315i	−0.829962	−	1.45787i
$502$		0			0
$503$	7.17279	−	7.17279i	0.319819	−	0.319819i	−0.528879	−	0.848697i	$-0.677387\pi$
$503$	7.17279	−	7.17279i	0.319819	−	0.319819i	0.848697	+	0.528879i	$0.177387\pi$
$504$		0			0
$505$	7.85360	+	7.85360i	0.349480	+	0.349480i
$506$		0			0
$507$	3.08375	−	1.75558i	0.136954	−	0.0779678i
$508$		0			0
$509$	−9.07957	+	3.76088i	−0.402445	+	0.166698i	−0.574719	−	0.818351i	$-0.694889\pi$
$509$	−9.07957	+	3.76088i	−0.402445	+	0.166698i	0.172274	+	0.985049i	$0.444889\pi$
$510$		0			0
$511$		−	20.2323i		−	0.895026i
$512$		0			0
$513$	−9.15142	+	21.0052i	−0.404045	+	0.927401i
$514$		0			0
$515$	5.15965	+	12.4565i	0.227361	+	0.548899i
$516$		0			0
$517$	18.7723	+	7.77573i	0.825604	+	0.341976i
$518$		0			0
$519$	2.96986	+	23.6656i	0.130362	+	1.03880i
$520$		0			0
$521$	−9.65370	−	9.65370i	−0.422936	−	0.422936i	0.463277	−	0.886214i	$-0.346673\pi$
$521$	−9.65370	−	9.65370i	−0.422936	−	0.422936i	−0.886214	+	0.463277i	$0.846673\pi$
$522$		0			0
$523$	−10.1079	−	4.18681i	−0.441986	−	0.183077i	0.150581	−	0.988598i	$-0.451885\pi$
$523$	−10.1079	−	4.18681i	−0.441986	−	0.183077i	−0.592567	+	0.805521i	$0.701885\pi$
$524$		0			0
$525$	−14.2674	−	3.91574i	−0.622678	−	0.170897i
$526$		0			0
$527$		−	14.7225i		−	0.641322i
$528$		0			0
$529$		−	1.33531i		−	0.0580568i
$530$		0			0
$531$	15.2178	+	20.3379i	0.660397	+	0.882589i
$532$		0			0
$533$	−28.8227	−	11.9388i	−1.24845	−	0.517125i
$534$		0			0
$535$	22.1587	+	22.1587i	0.958003	+	0.958003i
$536$		0			0
$537$	−20.4821	+	2.57036i	−0.883869	+	0.110919i
$538$		0			0
$539$	21.4270	+	8.87536i	0.922927	+	0.382289i
$540$		0			0
$541$	13.6712	+	33.0051i	0.587769	+	1.41900i	0.885630	+	0.464391i	$0.153727\pi$
$541$	13.6712	+	33.0051i	0.587769	+	1.41900i	−0.297861	+	0.954609i	$0.596273\pi$
$542$		0			0
$543$	12.4066	−	15.9673i	0.532417	−	0.685222i
$544$		0			0
$545$		−	1.46613i		−	0.0628020i
$546$		0			0
$547$	−25.3638	+	10.5060i	−1.08448	+	0.449205i	−0.852078	−	0.523415i	$-0.824658\pi$
$547$	−25.3638	+	10.5060i	−1.08448	+	0.449205i	−0.232399	+	0.972620i	$0.574658\pi$
$548$		0			0
$549$	3.42915	−	23.8133i	0.146353	−	1.01633i
$550$		0			0
$551$	−14.4004	−	14.4004i	−0.613478	−	0.613478i
$552$		0			0
$553$	10.0014	−	10.0014i	0.425304	−	0.425304i
$554$		0			0
$555$	−1.67616	+	0.954234i	−0.0711488	+	0.0405050i
$556$		0			0
$557$	−11.6829	−	28.2051i	−0.495022	−	1.19509i	−0.952135	−	0.305679i	$-0.901116\pi$
$557$	−11.6829	−	28.2051i	−0.495022	−	1.19509i	0.457113	−	0.889409i	$-0.348884\pi$
$558$		0			0
$559$	22.8629			0.967000
$560$		0			0
$561$	7.62087	−	9.80808i	0.321753	−	0.414097i
$562$		0			0
$563$	22.1299	−	9.16651i	0.932664	−	0.386322i	0.135976	−	0.990712i	$-0.456583\pi$
$563$	22.1299	−	9.16651i	0.932664	−	0.386322i	0.796689	+	0.604390i	$0.206583\pi$
$564$		0			0
$565$	0.877311	−	2.11802i	0.0369087	−	0.0891056i
$566$		0			0
$567$	32.4734	+	9.55049i	1.36375	+	0.401083i
$568$		0			0
$569$	−1.57829	+	1.57829i	−0.0661653	+	0.0661653i	−0.739415	−	0.673250i	$-0.764898\pi$
$569$	−1.57829	+	1.57829i	−0.0661653	+	0.0661653i	0.673250	+	0.739415i	$0.264898\pi$
$570$		0			0
$571$	−9.32640	+	22.5159i	−0.390298	+	0.942262i	0.599577	+	0.800317i	$0.295336\pi$
$571$	−9.32640	+	22.5159i	−0.390298	+	0.942262i	−0.989875	+	0.141945i	$0.954664\pi$
$572$		0			0
$573$	−20.8402	−	5.71967i	−0.870610	−	0.238943i
$574$		0			0
$575$	−11.2040			−0.467238
$576$		0			0
$577$	−3.55080			−0.147822			−0.0739109	−	0.997265i	$-0.523548\pi$
$577$	−3.55080			−0.147822			−0.0739109	+	0.997265i	$0.523548\pi$
$578$		0			0
$579$	−44.0686	−	12.0948i	−1.83143	−	0.502643i
$580$		0			0
$581$	10.9335	−	26.3958i	0.453597	−	1.09508i
$582$		0			0
$583$	13.2003	−	13.2003i	0.546702	−	0.546702i
$584$		0			0
$585$	8.37145	−	14.1023i	0.346117	−	0.583058i
$586$		0			0
$587$	1.41290	−	3.41105i	0.0583167	−	0.140789i	−0.892035	−	0.451965i	$-0.850723\pi$
$587$	1.41290	−	3.41105i	0.0583167	−	0.140789i	0.950352	+	0.311176i	$0.100723\pi$
$588$		0			0
$589$	−27.1485	+	11.2453i	−1.11863	+	0.463354i
$590$		0			0
$591$	23.5818	−	30.3498i	0.970025	−	1.24842i
$592$		0			0
$593$	21.2489			0.872588			0.436294	−	0.899804i	$-0.356291\pi$
$593$	21.2489			0.872588			0.436294	+	0.899804i	$0.356291\pi$
$594$		0			0
$595$	−5.25243	−	12.6805i	−0.215328	−	0.519849i
$596$		0			0
$597$	−11.2121	+	6.38302i	−0.458879	+	0.261240i
$598$		0			0
$599$	−17.2746	+	17.2746i	−0.705821	+	0.705821i	−0.965654	−	0.259833i	$-0.916333\pi$
$599$	−17.2746	+	17.2746i	−0.705821	+	0.705821i	0.259833	+	0.965654i	$0.416333\pi$
$600$		0			0
$601$	8.14843	+	8.14843i	0.332382	+	0.332382i	0.853490	−	0.521109i	$-0.174481\pi$
$601$	8.14843	+	8.14843i	0.332382	+	0.332382i	−0.521109	+	0.853490i	$0.674481\pi$
$602$		0			0
$603$	3.38730	+	0.487777i	0.137942	+	0.0198638i
$604$		0			0
$605$	0.706954	−	0.292830i	0.0287417	−	0.0119052i
$606$		0			0
$607$			43.9202i			1.78267i	0.453347	+	0.891334i	$0.350230\pi$
$607$			43.9202i			1.78267i	−0.453347	+	0.891334i	$0.649770\pi$
$608$		0			0
$609$	−18.4595	+	23.7575i	−0.748019	+	0.962702i
$610$		0			0
$611$	−7.92721	−	19.1380i	−0.320700	−	0.774239i
$612$		0			0
$613$	−36.0966	−	14.9517i	−1.45793	−	0.603894i	−0.493859	−	0.869542i	$-0.664414\pi$
$613$	−36.0966	−	14.9517i	−1.45793	−	0.603894i	−0.964070	+	0.265648i	$0.914414\pi$
$614$		0			0
$615$	26.7634	−	3.35861i	1.07920	−	0.135432i
$616$		0			0
$617$	23.8220	+	23.8220i	0.959036	+	0.959036i	0.999193	−	0.0401577i	$-0.0127860\pi$
$617$	23.8220	+	23.8220i	0.959036	+	0.959036i	−0.0401577	+	0.999193i	$0.512786\pi$
$618$		0			0
$619$	21.1101	+	8.74408i	0.848485	+	0.351454i	0.764194	−	0.644987i	$-0.223137\pi$
$619$	21.1101	+	8.74408i	0.848485	+	0.351454i	0.0842919	+	0.996441i	$0.473137\pi$
$620$		0			0
$621$	25.6288	+	0.465941i	1.02845	+	0.0186976i
$622$		0			0
$623$			27.9179i			1.11851i
$624$		0			0
$625$		−	8.48573i		−	0.339429i
$626$		0			0
$627$	−23.9072	−	6.56143i	−0.954761	−	0.262038i
$628$		0			0
$629$	1.37587	+	0.569904i	0.0548596	+	0.0227236i
$630$		0			0
$631$	−14.1380	−	14.1380i	−0.562826	−	0.562826i	0.367283	−	0.930109i	$-0.380288\pi$
$631$	−14.1380	−	14.1380i	−0.562826	−	0.562826i	−0.930109	+	0.367283i	$0.880288\pi$
$632$		0			0
$633$	−0.762824	−	6.07863i	−0.0303195	−	0.241604i
$634$		0			0
$635$	2.16459	+	0.896604i	0.0858992	+	0.0355806i
$636$		0			0
$637$	−9.04826	−	21.8444i	−0.358505	−	0.865508i
$638$		0			0
$639$	−5.19116	−	20.3573i	−0.205359	−	0.805324i
$640$		0			0
$641$		−	44.1735i		−	1.74475i	−0.488839	−	0.872374i	$-0.662579\pi$
$641$		−	44.1735i		−	1.74475i	0.488839	−	0.872374i	$-0.337421\pi$
$642$		0			0
$643$	−19.0014	+	7.87062i	−0.749341	+	0.310387i	−0.724473	−	0.689304i	$-0.757917\pi$
$643$	−19.0014	+	7.87062i	−0.749341	+	0.310387i	−0.0248682	+	0.999691i	$0.507917\pi$
$644$		0			0
$645$	−17.1785	+	9.77972i	−0.676404	+	0.385076i
$646$		0			0
$647$	12.5375	+	12.5375i	0.492899	+	0.492899i	0.909218	−	0.416319i	$-0.136680\pi$
$647$	12.5375	+	12.5375i	0.492899	+	0.492899i	−0.416319	+	0.909218i	$0.636680\pi$
$648$		0			0
$649$	−19.4343	+	19.4343i	−0.762863	+	0.762863i
$650$		0			0
$651$	21.4776	+	37.7265i	0.841775	+	1.47862i
$652$		0			0
$653$	15.6644	+	37.8172i	0.612996	+	1.47990i	0.859694	+	0.510810i	$0.170654\pi$
$653$	15.6644	+	37.8172i	0.612996	+	1.47990i	−0.246698	+	0.969092i	$0.579346\pi$
$654$		0			0
$655$	−8.75462			−0.342071
$656$		0			0
$657$	15.6383	−	3.98778i	0.610107	−	0.155578i
$658$		0			0
$659$	3.44904	−	1.42864i	0.134356	−	0.0556519i	−0.314493	−	0.949260i	$-0.601834\pi$
$659$	3.44904	−	1.42864i	0.134356	−	0.0556519i	0.448848	+	0.893608i	$0.351834\pi$
$660$		0			0
$661$	−17.8323	+	43.0509i	−0.693595	+	1.67449i	0.0438153	+	0.999040i	$0.486049\pi$
$661$	−17.8323	+	43.0509i	−0.693595	+	1.67449i	−0.737410	+	0.675446i	$0.763951\pi$
$662$		0			0
$663$	−12.5642	+	1.57672i	−0.487953	+	0.0612347i
$664$		0			0
$665$	−19.3711	+	19.3711i	−0.751179	+	0.751179i
$666$		0			0
$667$	−8.71895	+	21.0494i	−0.337599	+	0.815036i
$668$		0			0
$669$	3.22120	−	11.7367i	0.124539	−	0.453768i
$670$		0			0
$671$	26.0321			1.00496
$672$		0			0
$673$	−26.3444			−1.01550			−0.507751	−	0.861504i	$-0.669523\pi$
$673$	−26.3444			−1.01550			−0.507751	+	0.861504i	$0.669523\pi$
$674$		0			0
$675$	0.214519	−	11.7995i	0.00825685	−	0.454163i
$676$		0			0
$677$	0.895317	−	2.16149i	0.0344098	−	0.0830726i	−0.905740	−	0.423833i	$-0.860684\pi$
$677$	0.895317	−	2.16149i	0.0344098	−	0.0830726i	0.940150	+	0.340760i	$0.110684\pi$
$678$		0			0
$679$	−49.5781	+	49.5781i	−1.90263	+	1.90263i
$680$		0			0
$681$	0.0726746	+	0.579113i	0.00278490	+	0.0221917i
$682$		0			0
$683$	0.147686	−	0.356545i	0.00565103	−	0.0136428i	−0.921029	−	0.389494i	$-0.872650\pi$
$683$	0.147686	−	0.356545i	0.00565103	−	0.0136428i	0.926680	+	0.375852i	$0.122650\pi$
$684$		0			0
$685$	10.3563	−	4.28974i	0.395695	−	0.163902i
$686$		0			0
$687$	−12.3216	−	9.57389i	−0.470099	−	0.365267i
$688$		0			0
$689$	−19.0317			−0.725052
$690$		0			0
$691$	−10.0387	−	24.2355i	−0.381889	−	0.921961i	−0.991601	−	0.129338i	$-0.958715\pi$
$691$	−10.0387	−	24.2355i	−0.381889	−	0.921961i	0.609712	−	0.792623i	$-0.291285\pi$
$692$		0			0
$693$	−5.22018	+	36.2508i	−0.198298	+	1.37705i
$694$		0			0
$695$	4.70585	−	4.70585i	0.178503	−	0.178503i
$696$		0			0
$697$	−14.7267	−	14.7267i	−0.557814	−	0.557814i
$698$		0			0
$699$	4.51391	+	7.92890i	0.170732	+	0.299898i
$700$		0			0
$701$	−3.41867	+	1.41606i	−0.129121	+	0.0534839i	−0.446309	−	0.894879i	$-0.647262\pi$
$701$	−3.41867	+	1.41606i	−0.129121	+	0.0534839i	0.317187	+	0.948363i	$0.397262\pi$
$702$		0			0
$703$		−	2.97243i		−	0.112107i
$704$		0			0
$705$	14.1426	+	10.9888i	0.532641	+	0.413862i
$706$		0			0
$707$	9.67689	+	23.3621i	0.363937	+	0.878621i
$708$		0			0
$709$	−22.1344	−	9.16837i	−0.831275	−	0.344325i	−0.0738674	−	0.997268i	$-0.523534\pi$
$709$	−22.1344	−	9.16837i	−0.831275	−	0.344325i	−0.757407	+	0.652943i	$0.773534\pi$
$710$		0			0
$711$	9.70172	+	5.75917i	0.363843	+	0.215986i
$712$		0			0
$713$	23.2461	+	23.2461i	0.870574	+	0.870574i
$714$		0			0
$715$	16.3941	+	6.79067i	0.613106	+	0.253957i
$716$		0			0
$717$	−4.86361	+	17.7210i	−0.181635	+	0.661804i
$718$		0			0
$719$			15.2182i			0.567543i	0.958892	+	0.283771i	$0.0915857\pi$
$719$			15.2182i			0.567543i	−0.958892	+	0.283771i	$0.908414\pi$
$720$		0			0
$721$			30.6968i			1.14321i
$722$		0			0
$723$	4.70177	−	17.1313i	0.174861	−	0.637121i
$724$		0			0
$725$	9.69115	+	4.01420i	0.359920	+	0.149084i
$726$		0			0
$727$	8.89557	+	8.89557i	0.329918	+	0.329918i	0.852555	−	0.522637i	$-0.175052\pi$
$727$	8.89557	+	8.89557i	0.329918	+	0.329918i	−0.522637	+	0.852555i	$0.675052\pi$
$728$		0			0
$729$	−0.981415	+	26.9822i	−0.0363487	+	0.999339i
$730$		0			0
$731$	14.1010	+	5.84082i	0.521544	+	0.216031i
$732$		0			0
$733$	−7.20455	−	17.3933i	−0.266106	−	0.642437i	0.733187	−	0.680027i	$-0.238032\pi$
$733$	−7.20455	−	17.3933i	−0.266106	−	0.642437i	−0.999293	+	0.0375899i	$0.988032\pi$
$734$		0			0
$735$	16.1426	+	12.5428i	0.595430	+	0.462649i
$736$		0			0
$737$			3.70291i			0.136399i
$738$		0			0
$739$	−31.3226	+	12.9743i	−1.15222	+	0.477266i	−0.875278	−	0.483621i	$-0.839321\pi$
$739$	−31.3226	+	12.9743i	−1.15222	+	0.477266i	−0.276943	+	0.960886i	$0.589321\pi$
$740$		0			0
$741$	12.5042	+	21.9642i	0.459354	+	0.806877i
$742$		0			0
$743$	−11.8953	−	11.8953i	−0.436397	−	0.436397i	0.454401	−	0.890797i	$-0.349853\pi$
$743$	−11.8953	−	11.8953i	−0.436397	−	0.436397i	−0.890797	+	0.454401i	$0.849853\pi$
$744$		0			0
$745$	−8.00494	+	8.00494i	−0.293278	+	0.293278i
$746$		0			0
$747$	22.5572	+	3.24827i	0.825323	+	0.118848i
$748$		0			0
$749$	27.3030	+	65.9154i	0.997631	+	2.40849i
$750$		0			0
$751$	−33.7037			−1.22987			−0.614933	−	0.788580i	$-0.710817\pi$
$751$	−33.7037			−1.22987			−0.614933	+	0.788580i	$0.710817\pi$
$752$		0			0
$753$	2.27771	+	1.76978i	0.0830042	+	0.0644942i
$754$		0			0
$755$	8.50271	−	3.52194i	0.309445	−	0.128176i
$756$		0			0
$757$	−3.44482	+	8.31653i	−0.125204	+	0.302269i	−0.974036	−	0.226394i	$-0.927306\pi$
$757$	−3.44482	+	8.31653i	−0.125204	+	0.302269i	0.848832	+	0.528663i	$0.177306\pi$
$758$		0			0
$759$	3.45350	+	27.5195i	0.125354	+	0.998893i
$760$		0			0
$761$	−12.4231	+	12.4231i	−0.450337	+	0.450337i	−0.895466	−	0.445129i	$-0.853158\pi$
$761$	−12.4231	+	12.4231i	−0.450337	+	0.450337i	0.445129	+	0.895466i	$0.353158\pi$
$762$		0			0
$763$	1.27739	−	3.08389i	0.0462446	−	0.111644i
$764$		0			0
$765$	8.76592	−	6.55909i	0.316932	−	0.237144i
$766$		0			0
$767$	28.0196			1.01173
$768$		0			0
$769$	11.9632			0.431404			0.215702	−	0.976459i	$-0.430796\pi$
$769$	11.9632			0.431404			0.215702	+	0.976459i	$0.430796\pi$
$770$		0			0
$771$	6.89613	−	25.1267i	0.248358	−	0.904916i
$772$		0			0
$773$	3.08489	−	7.44759i	0.110956	−	0.267871i	−0.858642	−	0.512576i	$-0.828691\pi$
$773$	3.08489	−	7.44759i	0.110956	−	0.267871i	0.969598	+	0.244705i	$0.0786912\pi$
$774$		0			0
$775$	10.7025	−	10.7025i	0.384446	−	0.384446i
$776$		0			0
$777$	−4.35707	+	0.546781i	−0.156309	+	0.0196157i
$778$		0			0
$779$	−15.9078	+	38.4048i	−0.569956	+	1.37599i
$780$		0			0
$781$	21.0015	−	8.69909i	0.751491	−	0.311278i
$782$		0			0
$783$	−22.0013	−	9.58542i	−0.786263	−	0.342555i
$784$		0			0
$785$	5.92384			0.211431
$786$		0			0
$787$	8.69388	+	20.9889i	0.309903	+	0.748173i	0.999708	+	0.0241769i	$0.00769649\pi$
$787$	8.69388	+	20.9889i	0.309903	+	0.748173i	−0.689804	+	0.723996i	$0.742304\pi$
$788$		0			0
$789$	−20.7860	−	36.5116i	−0.740003	−	1.29985i
$790$		0			0
$791$	3.69072	−	3.69072i	0.131227	−	0.131227i
$792$		0			0
$793$	−18.7660	−	18.7660i	−0.666402	−	0.666402i
$794$		0			0
$795$	14.2999	−	8.14091i	0.507164	−	0.288728i
$796$		0			0
$797$	16.1204	−	6.67729i	0.571014	−	0.236522i	−0.0784449	−	0.996918i	$-0.524995\pi$
$797$	16.1204	−	6.67729i	0.571014	−	0.236522i	0.649459	+	0.760397i	$0.274995\pi$
$798$		0			0
$799$		−	13.8287i		−	0.489225i
$800$		0			0
$801$	−21.5787	+	5.50259i	−0.762445	+	0.194425i
$802$		0			0
$803$	6.68253	+	16.1331i	0.235821	+	0.569323i
$804$		0			0
$805$	28.3152	+	11.7285i	0.997979	+	0.413376i
$806$		0			0
$807$	2.06968	+	16.4924i	0.0728563	+	0.580562i
$808$		0			0
$809$	−24.1279	−	24.1279i	−0.848293	−	0.848293i	0.141627	−	0.989920i	$-0.454767\pi$
$809$	−24.1279	−	24.1279i	−0.848293	−	0.848293i	−0.989920	+	0.141627i	$0.954767\pi$
$810$		0			0
$811$	35.2705	+	14.6095i	1.23851	+	0.513010i	0.903250	−	0.429114i	$-0.141174\pi$
$811$	35.2705	+	14.6095i	1.23851	+	0.513010i	0.335265	+	0.942124i	$0.391174\pi$
$812$		0			0
$813$	0.745977	+	0.204737i	0.0261626	+	0.00718043i
$814$		0			0
$815$		−	6.71663i		−	0.235273i
$816$		0			0
$817$		−	30.4637i		−	1.06579i
$818$		0			0
$819$	29.8956	−	22.3694i	1.04464	−	0.781650i
$820$		0			0
$821$	16.5547	+	6.85716i	0.577761	+	0.239317i	0.652375	−	0.757896i	$-0.273773\pi$
$821$	16.5547	+	6.85716i	0.577761	+	0.239317i	−0.0746142	+	0.997212i	$0.523773\pi$
$822$		0			0
$823$	33.2669	+	33.2669i	1.15961	+	1.15961i	0.984559	+	0.175053i	$0.0560097\pi$
$823$	33.2669	+	33.2669i	1.15961	+	1.15961i	0.175053	+	0.984559i	$0.443990\pi$
$824$		0			0
$825$	12.6700	−	1.58999i	0.441111	−	0.0553563i
$826$		0			0
$827$	35.9603	+	14.8953i	1.25046	+	0.517959i	0.906970	−	0.421196i	$-0.138390\pi$
$827$	35.9603	+	14.8953i	1.25046	+	0.517959i	0.343494	+	0.939155i	$0.388390\pi$
$828$		0			0
$829$	−19.2504	−	46.4747i	−0.668596	−	1.61413i	−0.783961	−	0.620810i	$-0.786804\pi$
$829$	−19.2504	−	46.4747i	−0.668596	−	1.61413i	0.115366	−	0.993323i	$-0.463196\pi$
$830$		0			0
$831$	−19.7109	+	25.3680i	−0.683765	+	0.880007i
$832$		0			0
$833$		−	15.7844i		−	0.546896i
$834$		0			0
$835$	33.0856	−	13.7045i	1.14497	−	0.474263i
$836$		0			0
$837$	−24.9268	+	24.0366i	−0.861597	+	0.830828i
$838$		0			0
$839$	−39.7662	−	39.7662i	−1.37288	−	1.37288i	−0.856144	−	0.516738i	$-0.827146\pi$
$839$	−39.7662	−	39.7662i	−1.37288	−	1.37288i	−0.516738	−	0.856144i	$-0.672854\pi$
$840$		0			0
$841$	−5.42277	+	5.42277i	−0.186992	+	0.186992i
$842$		0			0
$843$	−46.5153	+	26.4811i	−1.60207	+	0.912059i
$844$		0			0
$845$	1.29511	+	3.12666i	0.0445530	+	0.107560i
$846$		0			0
$847$	1.74216			0.0598613
$848$		0			0
$849$	24.2102	−	31.1585i	0.830891	−	1.06936i
$850$		0			0
$851$	−3.07228	+	1.27258i	−0.105317	+	0.0436236i
$852$		0			0
$853$	−6.17946	+	14.9185i	−0.211581	+	0.510801i	−0.993666	−	0.112370i	$-0.964156\pi$
$853$	−6.17946	+	14.9185i	−0.211581	+	0.510801i	0.782086	+	0.623171i	$0.214156\pi$
$854$		0			0
$855$	−18.7906	−	11.1545i	−0.642625	−	0.381477i
$856$		0			0
$857$	8.03815	−	8.03815i	0.274578	−	0.274578i	−0.556362	−	0.830940i	$-0.687803\pi$
$857$	8.03815	−	8.03815i	0.274578	−	0.274578i	0.830940	+	0.556362i	$0.187803\pi$
$858$		0			0
$859$	4.97384	−	12.0079i	0.169705	−	0.409705i	−0.816030	−	0.578010i	$-0.803829\pi$
$859$	4.97384	−	12.0079i	0.169705	−	0.409705i	0.985735	+	0.168305i	$0.0538295\pi$
$860$		0			0
$861$	59.2211	+	16.2535i	2.01825	+	0.553917i
$862$		0			0
$863$	41.3031			1.40597			0.702987	−	0.711203i	$-0.251849\pi$
$863$	41.3031			1.40597			0.702987	+	0.711203i	$0.251849\pi$
$864$		0			0
$865$	−22.7476			−0.773442
$866$		0			0
$867$	20.2429	+	5.55576i	0.687486	+	0.188684i
$868$		0			0
$869$	−4.67167	+	11.2784i	−0.158475	+	0.382594i
$870$		0			0
$871$	2.66936	−	2.66936i	0.0904478	−	0.0904478i
$872$		0			0
$873$	−48.0924	−	28.5488i	−1.62768	−	0.966229i
$874$		0			0
$875$	17.2874	−	41.7356i	0.584422	−	1.41092i
$876$		0			0
$877$	37.0892	−	15.3629i	1.25241	−	0.518767i	0.344841	−	0.938661i	$-0.387933\pi$
$877$	37.0892	−	15.3629i	1.25241	−	0.518767i	0.907573	+	0.419894i	$0.137933\pi$
$878$		0			0
$879$	−22.2422	+	28.6257i	−0.750210	+	0.965522i
$880$		0			0
$881$	37.4808			1.26276			0.631381	−	0.775473i	$-0.282489\pi$
$881$	37.4808			1.26276			0.631381	+	0.775473i	$0.282489\pi$
$882$		0			0
$883$	11.9352	+	28.8142i	0.401653	+	0.969676i	0.987265	+	0.159085i	$0.0508543\pi$
$883$	11.9352	+	28.8142i	0.401653	+	0.969676i	−0.585612	+	0.810592i	$0.699146\pi$
$884$		0			0
$885$	−21.0531	+	11.9855i	−0.707693	+	0.402889i
$886$		0			0
$887$	−31.1207	+	31.1207i	−1.04493	+	1.04493i	−0.0459903	+	0.998942i	$0.514644\pi$
$887$	−31.1207	+	31.1207i	−1.04493	+	1.04493i	−0.998942	+	0.0459903i	$0.985356\pi$
$888$		0			0
$889$	3.77188	+	3.77188i	0.126505	+	0.126505i
$890$		0			0
$891$	−29.0483	+	3.11015i	−0.973156	+	0.104194i
$892$		0			0
$893$	−25.5004	+	10.5626i	−0.853338	+	0.353464i
$894$		0			0
$895$		−	19.6877i		−	0.658086i
$896$		0			0
$897$	17.3487	−	22.3278i	0.579256	−	0.745504i
$898$		0			0
$899$	−11.7786	−	28.4360i	−0.392837	−	0.948394i
$900$		0			0
$901$	−11.7380	−	4.86206i	−0.391051	−	0.161979i
$902$		0			0
$903$	−44.6546	+	5.60383i	−1.48601	+	0.186484i
$904$		0			0
$905$	13.6366	+	13.6366i	0.453297	+	0.453297i
$906$		0			0
$907$	−40.2044	−	16.6532i	−1.33497	−	0.552961i	−0.402898	−	0.915245i	$-0.631997\pi$
$907$	−40.2044	−	16.6532i	−1.33497	−	0.552961i	−0.932068	+	0.362284i	$0.881997\pi$
$908$		0			0
$909$	−16.1500	+	12.0842i	−0.535662	+	0.400809i
$910$		0			0
$911$		−	54.2050i		−	1.79589i	−0.440106	−	0.897946i	$-0.645059\pi$
$911$		−	54.2050i		−	1.79589i	0.440106	−	0.897946i	$-0.354941\pi$
$912$		0			0
$913$			24.6589i			0.816091i
$914$		0			0
$915$	22.1275	+	6.07298i	0.731512	+	0.200767i
$916$		0			0
$917$	−18.4147	−	7.62762i	−0.608107	−	0.251886i
$918$		0			0
$919$	−0.537488	−	0.537488i	−0.0177301	−	0.0177301i	0.698186	−	0.715916i	$-0.253991\pi$
$919$	−0.537488	−	0.537488i	−0.0177301	−	0.0177301i	−0.715916	+	0.698186i	$0.753991\pi$
$920$		0			0
$921$	0.750074	+	5.97703i	0.0247158	+	0.196950i
$922$		0			0
$923$	−21.4106	−	8.86855i	−0.704737	−	0.291912i
$924$		0			0
$925$	0.585897	+	1.41448i	0.0192642	+	0.0465078i
$926$		0			0
$927$	−23.7266	+	6.05032i	−0.779284	+	0.198719i
$928$		0			0
$929$			7.98688i			0.262041i	0.991380	+	0.131021i	$0.0418254\pi$
$929$			7.98688i			0.262041i	−0.991380	+	0.131021i	$0.958175\pi$
$930$		0			0
$931$	−29.1066	+	12.0563i	−0.953930	+	0.395131i
$932$		0			0
$933$	−2.21389	+	1.26036i	−0.0724794	+	0.0412624i
$934$		0			0
$935$	8.37645	+	8.37645i	0.273939	+	0.273939i
$936$		0			0
$937$	−14.1066	+	14.1066i	−0.460841	+	0.460841i	−0.898931	−	0.438090i	$-0.855655\pi$
$937$	−14.1066	+	14.1066i	−0.460841	+	0.460841i	0.438090	+	0.898931i	$0.355655\pi$
$938$		0			0
$939$	2.64881	+	4.65276i	0.0864407	+	0.151837i
$940$		0			0
$941$	−19.7820	−	47.7580i	−0.644875	−	1.55687i	−0.820027	−	0.572324i	$-0.806042\pi$
$941$	−19.7820	−	47.7580i	−0.644875	−	1.55687i	0.175153	−	0.984541i	$-0.443958\pi$
$942$		0			0
$943$	46.5056			1.51443
$944$		0			0
$945$	−12.8941	+	29.5957i	−0.419445	+	0.962747i
$946$		0			0
$947$	−42.9582	+	17.7939i	−1.39596	+	0.578224i	−0.948699	−	0.316182i	$-0.897599\pi$
$947$	−42.9582	+	17.7939i	−1.39596	+	0.578224i	−0.447257	+	0.894406i	$0.647599\pi$
$948$		0			0
$949$	6.81271	−	16.4473i	0.221150	−	0.533903i
$950$		0			0
$951$	52.9319	−	6.64258i	1.71644	−	0.215400i
$952$		0			0
$953$	−32.3259	+	32.3259i	−1.04714	+	1.04714i	−0.0483060	+	0.998833i	$0.515382\pi$
$953$	−32.3259	+	32.3259i	−1.04714	+	1.04714i	−0.998833	+	0.0483060i	$0.984618\pi$
$954$		0			0
$955$	7.88745	−	19.0420i	0.255232	−	0.616184i
$956$		0			0
$957$	6.87260	−	25.0409i	0.222159	−	0.809459i
$958$		0			0
$959$	25.5213			0.824127
$960$		0			0
$961$	−13.4114			−0.432624
$962$		0			0
$963$	−45.5668	+	34.0953i	−1.46837	+	1.09871i
$964$		0			0
$965$	16.6788	−	40.2662i	0.536909	−	1.29621i
$966$		0			0
$967$	35.6925	−	35.6925i	1.14779	−	1.14779i	0.160806	−	0.986986i	$-0.448591\pi$
$967$	35.6925	−	35.6925i	1.14779	−	1.14779i	0.986986	−	0.160806i	$-0.0514095\pi$
$968$		0			0
$969$	2.10090	+	16.7412i	0.0674905	+	0.537804i
$970$		0			0
$971$	−7.88604	+	19.0386i	−0.253075	+	0.610977i	−0.998449	−	0.0556691i	$-0.982271\pi$
$971$	−7.88604	+	19.0386i	−0.253075	+	0.610977i	0.745374	+	0.666646i	$0.232271\pi$
$972$		0			0
$973$	13.9985	−	5.79836i	0.448771	−	0.185887i
$974$		0			0
$975$	−10.2797	−	7.98734i	−0.329215	−	0.255800i
$976$		0			0
$977$	−56.7561			−1.81579			−0.907894	−	0.419200i	$-0.862311\pi$
$977$	−56.7561			−1.81579			−0.907894	+	0.419200i	$0.862311\pi$
$978$		0			0
$979$	−9.22098	−	22.2614i	−0.294704	−	0.711478i
$980$		0			0
$981$	2.63542	+	0.379505i	0.0841424	+	0.0121167i
$982$		0			0
$983$	−24.5354	+	24.5354i	−0.782557	+	0.782557i	−0.980262	−	0.197704i	$-0.936651\pi$
$983$	−24.5354	+	24.5354i	−0.782557	+	0.782557i	0.197704	+	0.980262i	$0.436651\pi$
$984$		0			0
$985$	25.9198	+	25.9198i	0.825875	+	0.825875i
$986$		0			0
$987$	20.1738	+	35.4362i	0.642138	+	1.12795i
$988$		0			0
$989$	−31.4871	+	13.0424i	−1.00123	+	0.414724i
$990$		0			0
$991$		−	42.2948i		−	1.34354i	−0.740761	−	0.671769i	$-0.765535\pi$
$991$		−	42.2948i		−	1.34354i	0.740761	−	0.671769i	$-0.234465\pi$
$992$		0			0
$993$	−2.62246	−	2.03765i	−0.0832214	−	0.0646629i
$994$		0			0
$995$	−4.70882	−	11.3681i	−0.149280	−	0.360393i
$996$		0			0
$997$	−23.1872	−	9.60447i	−0.734347	−	0.304177i	−0.0160101	−	0.999872i	$-0.505096\pi$
$997$	−23.1872	−	9.60447i	−0.734347	−	0.304177i	−0.718337	+	0.695695i	$0.755096\pi$
$998$		0			0
$999$	−1.28140	−	3.25995i	−0.0405417	−	0.103140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.a.287.2		56
3.2	odd	2	inner	768.2.o.a.287.5		56
4.3	odd	2		768.2.o.b.287.13		56
8.3	odd	2		96.2.o.a.59.1	✓	56
8.5	even	2		384.2.o.a.143.13		56
12.11	even	2		768.2.o.b.287.10		56
24.5	odd	2		384.2.o.a.143.10		56
24.11	even	2		96.2.o.a.59.14	yes	56
32.3	odd	8		384.2.o.a.239.10		56
32.13	even	8		768.2.o.b.479.10		56
32.19	odd	8	inner	768.2.o.a.479.5		56
32.29	even	8		96.2.o.a.83.14	yes	56
96.29	odd	8		96.2.o.a.83.1	yes	56
96.35	even	8		384.2.o.a.239.13		56
96.77	odd	8		768.2.o.b.479.13		56
96.83	even	8	inner	768.2.o.a.479.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.59.1	✓	56	8.3	odd	2
96.2.o.a.59.14	yes	56	24.11	even	2
96.2.o.a.83.1	yes	56	96.29	odd	8
96.2.o.a.83.14	yes	56	32.29	even	8
384.2.o.a.143.10		56	24.5	odd	2
384.2.o.a.143.13		56	8.5	even	2
384.2.o.a.239.10		56	32.3	odd	8
384.2.o.a.239.13		56	96.35	even	8
768.2.o.a.287.2		56	1.1	even	1	trivial
768.2.o.a.287.5		56	3.2	odd	2	inner
768.2.o.a.479.2		56	96.83	even	8	inner
768.2.o.a.479.5		56	32.19	odd	8	inner
768.2.o.b.287.10		56	12.11	even	2
768.2.o.b.287.13		56	4.3	odd	2
768.2.o.b.479.10		56	32.13	even	8
768.2.o.b.479.13		56	96.77	odd	8

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.67029 - 0.458417i) q^{3} +(0.632159 - 1.52617i) q^{5} +(2.65940 - 2.65940i) q^{7} +(2.57971 + 1.53137i) q^{9} +O(q^{10})\)	\(q+(-1.67029 - 0.458417i) q^{3} +(0.632159 - 1.52617i) q^{5} +(2.65940 - 2.65940i) q^{7} +(2.57971 + 1.53137i) q^{9} +(-1.24221 + 2.99895i) q^{11} +(3.05737 - 1.26640i) q^{13} +(-1.75551 + 2.25934i) q^{15} +2.20920 q^{17} +(-1.68742 - 4.07379i) q^{19} +(-5.66108 + 3.22285i) q^{21} +(-3.48822 + 3.48822i) q^{23} +(1.60597 + 1.60597i) q^{25} +(-3.60684 - 3.74042i) q^{27} +(4.26699 - 1.76744i) q^{29} -6.66418i q^{31} +(3.44961 - 4.43965i) q^{33} +(-2.37753 - 5.73985i) q^{35} +(0.622792 + 0.257969i) q^{37} +(-5.68722 + 0.713706i) q^{39} +(-6.66609 - 6.66609i) q^{41} +(6.38285 + 2.64386i) q^{43} +(3.96792 - 2.96899i) q^{45} -6.25962i q^{47} -7.14484i q^{49} +(-3.68999 - 1.01273i) q^{51} +(-5.31326 - 2.20082i) q^{53} +(3.79163 + 3.79163i) q^{55} +(0.950977 + 7.57794i) q^{57} +(7.82249 + 3.24018i) q^{59} +(-3.06898 - 7.40918i) q^{61} +(10.9330 - 2.78794i) q^{63} -5.46663i q^{65} +(1.05391 - 0.436545i) q^{67} +(7.42538 - 4.22726i) q^{69} +(-4.95182 - 4.95182i) q^{71} +(3.80393 - 3.80393i) q^{73} +(-1.94623 - 3.41864i) q^{75} +(4.67189 + 11.2789i) q^{77} +3.76078 q^{79} +(4.30978 + 7.90100i) q^{81} +(7.01836 - 2.90710i) q^{83} +(1.39656 - 3.37160i) q^{85} +(-7.93732 + 0.996076i) q^{87} +(-5.24890 + 5.24890i) q^{89} +(4.76290 - 11.4987i) q^{91} +(-3.05498 + 11.1311i) q^{93} -7.28400 q^{95} -18.6426 q^{97} +(-7.79705 + 5.83413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9	\( 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9} + 8 q^{13} + 8 q^{15} - 8 q^{19} + 4 q^{21} - 8 q^{25} - 28 q^{27} - 8 q^{33} + 8 q^{37} + 28 q^{39} - 8 q^{43} + 4 q^{45} - 16 q^{51} - 24 q^{55} - 4 q^{57} + 40 q^{61} + 56 q^{67} + 4 q^{69} - 8 q^{73} + 16 q^{75} - 16 q^{79} + 48 q^{85} - 52 q^{87} + 40 q^{91} - 8 q^{93} - 16 q^{97} + 60 q^{99}+O(q^{100}) \) 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9 + 8 * q^13 + 8 * q^15 - 8 * q^19 + 4 * q^21 - 8 * q^25 - 28 * q^27 - 8 * q^33 + 8 * q^37 + 28 * q^39 - 8 * q^43 + 4 * q^45 - 16 * q^51 - 24 * q^55 - 4 * q^57 + 40 * q^61 + 56 * q^67 + 4 * q^69 - 8 * q^73 + 16 * q^75 - 16 * q^79 + 48 * q^85 - 52 * q^87 + 40 * q^91 - 8 * q^93 - 16 * q^97 + 60 * q^99

Introduction

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