LMFDB - Embedded newform 896.2.z.a.31.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [896,2,Mod(31,896)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("896.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [56,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	896.31
Dual form			896.2.z.a.607.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.700587 - 2.61463i) q^{3} +(-0.450647 - 0.120751i) q^{5} +(2.37326 + 1.16946i) q^{7} +(-3.74737 + 2.16355i) q^{9} +(0.518581 + 1.93537i) q^{11} +(-4.51607 - 4.51607i) q^{13} +1.26287i q^{15} +(-4.68066 - 2.70238i) q^{17} +(-1.90476 - 0.510379i) q^{19} +(1.39503 - 7.02450i) q^{21} +(-0.951245 - 1.64761i) q^{23} +(-4.14162 - 2.39117i) q^{25} +(2.54010 + 2.54010i) q^{27} +(1.12415 - 1.12415i) q^{29} +(-0.434075 + 0.751840i) q^{31} +(4.69696 - 2.71179i) q^{33} +(-0.928290 - 0.813586i) q^{35} +(-2.11876 + 7.90732i) q^{37} +(-8.64394 + 14.9717i) q^{39} -3.24226 q^{41} +(6.35727 - 6.35727i) q^{43} +(1.94999 - 0.522499i) q^{45} +(-1.49266 - 2.58536i) q^{47} +(4.26473 + 5.55087i) q^{49} +(-3.78650 + 14.1314i) q^{51} +(-6.77976 + 1.81663i) q^{53} -0.934789i q^{55} +5.33780i q^{57} +(-8.29366 + 2.22228i) q^{59} +(-0.125856 + 0.469703i) q^{61} +(-11.4237 + 0.752254i) q^{63} +(1.48984 + 2.58047i) q^{65} +(3.85238 - 1.03224i) q^{67} +(-3.64144 + 3.64144i) q^{69} +12.1916 q^{71} +(7.79109 - 13.4946i) q^{73} +(-3.35044 + 12.5040i) q^{75} +(-1.03261 + 5.19960i) q^{77} +(-1.07130 + 0.618516i) q^{79} +(-1.62878 + 2.82113i) q^{81} +(-9.03560 + 9.03560i) q^{83} +(1.78301 + 1.78301i) q^{85} +(-3.72680 - 2.15167i) q^{87} +(1.16364 + 2.01548i) q^{89} +(-5.43644 - 15.9992i) q^{91} +(2.26989 + 0.608215i) q^{93} +(0.796746 + 0.460002i) q^{95} -4.69704i q^{97} +(-6.13058 - 6.13058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Character values

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

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.700587	−	2.61463i	−0.404484	−	1.50955i	−0.805005	−	0.593268i	$-0.797838\pi$
$3$	−0.700587	−	2.61463i	−0.404484	−	1.50955i	0.400521	−	0.916287i	$-0.368829\pi$
$4$		0			0
$5$	−0.450647	−	0.120751i	−0.201536	−	0.0540013i	0.156639	−	0.987656i	$-0.449934\pi$
$5$	−0.450647	−	0.120751i	−0.201536	−	0.0540013i	−0.358175	+	0.933655i	$0.616601\pi$
$6$		0			0
$7$	2.37326	+	1.16946i	0.897008	+	0.442014i
$7$	2.37326	+	1.16946i	0.897008	+	0.442014i
$8$		0			0
$9$	−3.74737	+	2.16355i	−1.24912	+	0.721182i
$10$		0			0
$11$	0.518581	+	1.93537i	0.156358	+	0.583536i	0.998985	+	0.0450390i	$0.0143412\pi$
$11$	0.518581	+	1.93537i	0.156358	+	0.583536i	−0.842627	+	0.538497i	$0.818992\pi$
$12$		0			0
$13$	−4.51607	−	4.51607i	−1.25253	−	1.25253i	−0.954581	−	0.297952i	$-0.903696\pi$
$13$	−4.51607	−	4.51607i	−1.25253	−	1.25253i	−0.297952	−	0.954581i	$-0.596304\pi$
$14$		0			0
$15$			1.26287i			0.326072i
$16$		0			0
$17$	−4.68066	−	2.70238i	−1.13523	−	0.655424i	−0.189983	−	0.981787i	$-0.560843\pi$
$17$	−4.68066	−	2.70238i	−1.13523	−	0.655424i	−0.945244	+	0.326364i	$0.894177\pi$
$18$		0			0
$19$	−1.90476	−	0.510379i	−0.436982	−	0.117089i	0.0336198	−	0.999435i	$-0.489296\pi$
$19$	−1.90476	−	0.510379i	−0.436982	−	0.117089i	−0.470602	+	0.882346i	$0.655963\pi$
$20$		0			0
$21$	1.39503	−	7.02450i	0.304420	−	1.53287i
$22$		0			0
$23$	−0.951245	−	1.64761i	−0.198348	−	0.343549i	0.749645	−	0.661841i	$-0.230224\pi$
$23$	−0.951245	−	1.64761i	−0.198348	−	0.343549i	−0.947993	+	0.318291i	$0.896891\pi$
$24$		0			0
$25$	−4.14162	−	2.39117i	−0.828325	−	0.478234i
$26$		0			0
$27$	2.54010	+	2.54010i	0.488843	+	0.488843i
$28$		0			0
$29$	1.12415	−	1.12415i	0.208749	−	0.208749i	−0.594986	−	0.803736i	$-0.702843\pi$
$29$	1.12415	−	1.12415i	0.208749	−	0.208749i	0.803736	+	0.594986i	$0.202843\pi$
$30$		0			0
$31$	−0.434075	+	0.751840i	−0.0779622	+	0.135035i	−0.902371	−	0.430961i	$-0.858175\pi$
$31$	−0.434075	+	0.751840i	−0.0779622	+	0.135035i	0.824408	+	0.565995i	$0.191508\pi$
$32$		0			0
$33$	4.69696	−	2.71179i	0.817636	−	0.472062i
$34$		0			0
$35$	−0.928290	−	0.813586i	−0.156910	−	0.137521i
$36$		0			0
$37$	−2.11876	+	7.90732i	−0.348322	+	1.29996i	0.540361	+	0.841433i	$0.318288\pi$
$37$	−2.11876	+	7.90732i	−0.348322	+	1.29996i	−0.888683	+	0.458522i	$0.848379\pi$
$38$		0			0
$39$	−8.64394	+	14.9717i	−1.38414	+	2.39740i
$40$		0			0
$41$	−3.24226			−0.506356			−0.253178	−	0.967420i	$-0.581476\pi$
$41$	−3.24226			−0.506356			−0.253178	+	0.967420i	$0.581476\pi$
$42$		0			0
$43$	6.35727	−	6.35727i	0.969475	−	0.969475i	−0.0300731	−	0.999548i	$-0.509574\pi$
$43$	6.35727	−	6.35727i	0.969475	−	0.969475i	0.999548	+	0.0300731i	$0.00957401\pi$
$44$		0			0
$45$	1.94999	−	0.522499i	0.290688	−	0.0778895i
$46$		0			0
$47$	−1.49266	−	2.58536i	−0.217727	−	0.377114i	0.736386	−	0.676562i	$-0.236531\pi$
$47$	−1.49266	−	2.58536i	−0.217727	−	0.377114i	−0.954113	+	0.299448i	$0.903198\pi$
$48$		0			0
$49$	4.26473	+	5.55087i	0.609246	+	0.792981i
$50$		0			0
$51$	−3.78650	+	14.1314i	−0.530217	+	1.97880i
$52$		0			0
$53$	−6.77976	+	1.81663i	−0.931272	+	0.249533i	−0.692397	−	0.721517i	$-0.743445\pi$
$53$	−6.77976	+	1.81663i	−0.931272	+	0.249533i	−0.238875	+	0.971050i	$0.576779\pi$
$54$		0			0
$55$		−	0.934789i		−	0.126047i
$56$		0			0
$57$			5.33780i			0.707009i
$58$		0			0
$59$	−8.29366	+	2.22228i	−1.07974	+	0.289316i	−0.754491	−	0.656311i	$-0.772116\pi$
$59$	−8.29366	+	2.22228i	−1.07974	+	0.289316i	−0.325253	+	0.945627i	$0.605449\pi$
$60$		0			0
$61$	−0.125856	+	0.469703i	−0.0161143	+	0.0601393i	−0.973515	−	0.228624i	$-0.926577\pi$
$61$	−0.125856	+	0.469703i	−0.0161143	+	0.0601393i	0.957401	+	0.288763i	$0.0932440\pi$
$62$		0			0
$63$	−11.4237	+	0.752254i	−1.43925	+	0.0947751i
$64$		0			0
$65$	1.48984	+	2.58047i	0.184792	+	0.320068i
$66$		0			0
$67$	3.85238	−	1.03224i	0.470643	−	0.126108i	−0.0156996	−	0.999877i	$-0.504998\pi$
$67$	3.85238	−	1.03224i	0.470643	−	0.126108i	0.486342	+	0.873768i	$0.338331\pi$
$68$		0			0
$69$	−3.64144	+	3.64144i	−0.438378	+	0.438378i
$70$		0			0
$71$	12.1916			1.44687			0.723437	−	0.690390i	$-0.242561\pi$
$71$	12.1916			1.44687			0.723437	+	0.690390i	$0.242561\pi$
$72$		0			0
$73$	7.79109	−	13.4946i	0.911878	−	1.57942i	0.100470	−	0.994940i	$-0.467965\pi$
$73$	7.79109	−	13.4946i	0.911878	−	1.57942i	0.811408	−	0.584480i	$-0.198701\pi$
$74$		0			0
$75$	−3.35044	+	12.5040i	−0.386876	+	1.44384i
$76$		0			0
$77$	−1.03261	+	5.19960i	−0.117677	+	0.592549i
$78$		0			0
$79$	−1.07130	+	0.618516i	−0.120531	+	0.0695885i	−0.559053	−	0.829132i	$-0.688835\pi$
$79$	−1.07130	+	0.618516i	−0.120531	+	0.0695885i	0.438522	+	0.898720i	$0.355502\pi$
$80$		0			0
$81$	−1.62878	+	2.82113i	−0.180976	+	0.313459i
$82$		0			0
$83$	−9.03560	+	9.03560i	−0.991786	+	0.991786i	−0.999967	−	0.00818066i	$-0.997396\pi$
$83$	−9.03560	+	9.03560i	−0.991786	+	0.991786i	0.00818066	+	0.999967i	$0.497396\pi$
$84$		0			0
$85$	1.78301	+	1.78301i	0.193395	+	0.193395i
$86$		0			0
$87$	−3.72680	−	2.15167i	−0.399554	−	0.230683i
$88$		0			0
$89$	1.16364	+	2.01548i	0.123345	+	0.213640i	0.921085	−	0.389362i	$-0.127304\pi$
$89$	1.16364	+	2.01548i	0.123345	+	0.213640i	−0.797740	+	0.603002i	$0.793971\pi$
$90$		0			0
$91$	−5.43644	−	15.9992i	−0.569894	−	1.67717i
$92$		0			0
$93$	2.26989	+	0.608215i	0.235376	+	0.0630689i
$94$		0			0
$95$	0.796746	+	0.460002i	0.0817444	+	0.0471952i
$96$		0			0
$97$		−	4.69704i		−	0.476912i	−0.971153	−	0.238456i	$-0.923359\pi$
$97$		−	4.69704i		−	0.476912i	0.971153	−	0.238456i	$-0.0766414\pi$
$98$		0			0
$99$	−6.13058	−	6.13058i	−0.616146	−	0.616146i
$100$		0			0
$101$	−1.43509	−	5.35584i	−0.142797	−	0.532926i	−0.999844	−	0.0176866i	$-0.994370\pi$
$101$	−1.43509	−	5.35584i	−0.142797	−	0.532926i	0.857047	−	0.515239i	$-0.172297\pi$
$102$		0			0
$103$	0.958115	−	0.553168i	0.0944059	−	0.0545053i	−0.452054	−	0.891991i	$-0.649308\pi$
$103$	0.958115	−	0.553168i	0.0944059	−	0.0545053i	0.546460	+	0.837485i	$0.315975\pi$
$104$		0			0
$105$	−1.47688	+	2.99712i	−0.144128	+	0.292489i
$106$		0			0
$107$	5.97202	+	1.60020i	0.577337	+	0.154697i	0.535659	−	0.844434i	$-0.320063\pi$
$107$	5.97202	+	1.60020i	0.577337	+	0.154697i	0.0416773	+	0.999131i	$0.486730\pi$
$108$		0			0
$109$	−2.81979	−	10.5236i	−0.270087	−	1.00798i	−0.959063	−	0.283194i	$-0.908606\pi$
$109$	−2.81979	−	10.5236i	−0.270087	−	1.00798i	0.688975	−	0.724785i	$-0.258061\pi$
$110$		0			0
$111$	22.1591			2.10324
$112$		0			0
$113$	−2.81872			−0.265163			−0.132582	−	0.991172i	$-0.542327\pi$
$113$	−2.81872			−0.265163			−0.132582	+	0.991172i	$0.542327\pi$
$114$		0			0
$115$	0.229727	+	0.857352i	0.0214221	+	0.0799485i
$116$		0			0
$117$	26.6941	+	7.15267i	2.46787	+	0.661264i
$118$		0			0
$119$	−7.94810	−	11.8873i	−0.728601	−	1.08971i
$120$		0			0
$121$	6.04954	−	3.49271i	0.549958	−	0.317519i
$122$		0			0
$123$	2.27149	+	8.47731i	0.204813	+	0.764373i
$124$		0			0
$125$	3.22716	+	3.22716i	0.288646	+	0.288646i
$126$		0			0
$127$		−	9.34725i		−	0.829434i	−0.909950	−	0.414717i	$-0.863881\pi$
$127$		−	9.34725i		−	0.829434i	0.909950	−	0.414717i	$-0.136119\pi$
$128$		0			0
$129$	−21.0757	−	12.1681i	−1.85561	−	1.07134i
$130$		0			0
$131$	17.9203	+	4.80174i	1.56571	+	0.419530i	0.934465	−	0.356056i	$-0.115879\pi$
$131$	17.9203	+	4.80174i	1.56571	+	0.419530i	0.631242	+	0.775586i	$0.282545\pi$
$132$		0			0
$133$	−3.92362	−	3.43880i	−0.340221	−	0.298182i
$134$		0			0
$135$	−0.837971	−	1.45141i	−0.0721211	−	0.124917i
$136$		0			0
$137$	−13.1541	−	7.59453i	−1.12383	−	0.648844i	−0.181455	−	0.983399i	$-0.558081\pi$
$137$	−13.1541	−	7.59453i	−1.12383	−	0.648844i	−0.942376	+	0.334555i	$0.891414\pi$
$138$		0			0
$139$	−1.13113	−	1.13113i	−0.0959413	−	0.0959413i	0.657507	−	0.753448i	$-0.271611\pi$
$139$	−1.13113	−	1.13113i	−0.0959413	−	0.0959413i	−0.753448	+	0.657507i	$0.771611\pi$
$140$		0			0
$141$	−5.71402	+	5.71402i	−0.481207	+	0.481207i
$142$		0			0
$143$	6.39833	−	11.0822i	0.535055	−	0.926742i
$144$		0			0
$145$	−0.642337	+	0.370853i	−0.0533431	+	0.0307977i
$146$		0			0
$147$	11.5256	−	15.0395i	0.950618	−	1.24044i
$148$		0			0
$149$	−2.62960	+	9.81380i	−0.215425	+	0.803978i	0.770591	+	0.637330i	$0.219961\pi$
$149$	−2.62960	+	9.81380i	−0.215425	+	0.803978i	−0.986016	+	0.166648i	$0.946706\pi$
$150$		0			0
$151$	5.83900	−	10.1134i	0.475171	−	0.823020i	−0.524425	−	0.851457i	$-0.675720\pi$
$151$	5.83900	−	10.1134i	0.475171	−	0.823020i	0.999596	+	0.0284368i	$0.00905293\pi$
$152$		0			0
$153$	23.3869			1.89072
$154$		0			0
$155$	0.286400	−	0.286400i	0.0230042	−	0.0230042i
$156$		0			0
$157$	−2.15127	+	0.576431i	−0.171690	+	0.0460042i	−0.343640	−	0.939101i	$-0.611660\pi$
$157$	−2.15127	+	0.576431i	−0.171690	+	0.0460042i	0.171950	+	0.985106i	$0.444993\pi$
$158$		0			0
$159$	9.49962	+	16.4538i	0.753369	+	1.30487i
$160$		0			0
$161$	−0.330743	−	5.02264i	−0.0260662	−	0.395839i
$162$		0			0
$163$	3.79792	−	14.1740i	0.297476	−	1.11020i	−0.641755	−	0.766910i	$-0.721793\pi$
$163$	3.79792	−	14.1740i	0.297476	−	1.11020i	0.939231	−	0.343286i	$-0.111540\pi$
$164$		0			0
$165$	−2.44412	+	0.654901i	−0.190275	+	0.0509839i
$166$		0			0
$167$		−	5.94995i		−	0.460421i	−0.973141	−	0.230210i	$-0.926059\pi$
$167$		−	5.94995i		−	0.460421i	0.973141	−	0.230210i	$-0.0739415\pi$
$168$		0			0
$169$			27.7898i			2.13768i
$170$		0			0
$171$	8.24207	−	2.20846i	0.630287	−	0.168885i
$172$		0			0
$173$	2.37723	−	8.87194i	0.180737	−	0.674521i	−0.814766	−	0.579790i	$-0.803134\pi$
$173$	2.37723	−	8.87194i	0.180737	−	0.674521i	0.995503	−	0.0947304i	$-0.0301989\pi$
$174$		0			0
$175$	−7.03278	−	10.5183i	−0.531628	−	0.795111i
$176$		0			0
$177$	11.6209	+	20.1279i	0.873478	+	1.51291i
$178$		0			0
$179$	3.67501	−	0.984716i	0.274683	−	0.0736011i	−0.118848	−	0.992912i	$-0.537920\pi$
$179$	3.67501	−	0.984716i	0.274683	−	0.0736011i	0.393531	+	0.919311i	$0.371253\pi$
$180$		0			0
$181$	5.13439	−	5.13439i	0.381636	−	0.381636i	−0.490055	−	0.871691i	$-0.663023\pi$
$181$	5.13439	−	5.13439i	0.381636	−	0.381636i	0.871691	+	0.490055i	$0.163023\pi$
$182$		0			0
$183$	1.31627			0.0973015
$184$		0			0
$185$	1.90963	−	3.30757i	0.140398	−	0.243177i
$186$		0			0
$187$	2.80281	−	10.4602i	0.204962	−	0.764927i
$188$		0			0
$189$	3.05777	+	8.99887i	0.222420	+	0.654572i
$190$		0			0
$191$	−15.2400	+	8.79882i	−1.10273	+	0.636660i	−0.936936	−	0.349501i	$-0.886351\pi$
$191$	−15.2400	+	8.79882i	−1.10273	+	0.636660i	−0.165791	+	0.986161i	$0.553018\pi$
$192$		0			0
$193$	3.28968	−	5.69790i	0.236797	−	0.410144i	−0.722997	−	0.690851i	$-0.757236\pi$
$193$	3.28968	−	5.69790i	0.236797	−	0.410144i	0.959793	+	0.280708i	$0.0905692\pi$
$194$		0			0
$195$	5.70321	−	5.70321i	0.408415	−	0.408415i
$196$		0			0
$197$	−14.8776	−	14.8776i	−1.05998	−	1.05998i	−0.998082	−	0.0619015i	$-0.980284\pi$
$197$	−14.8776	−	14.8776i	−1.05998	−	1.05998i	−0.0619015	−	0.998082i	$-0.519716\pi$
$198$		0			0
$199$	−6.43322	−	3.71422i	−0.456039	−	0.263294i	0.254338	−	0.967115i	$-0.418142\pi$
$199$	−6.43322	−	3.71422i	−0.456039	−	0.263294i	−0.710377	+	0.703821i	$0.751476\pi$
$200$		0			0
$201$	−5.39785	−	9.34935i	−0.380735	−	0.659452i
$202$		0			0
$203$	3.98255	−	1.35325i	0.279520	−	0.0949796i
$204$		0			0
$205$	1.46112	+	0.391505i	0.102049	+	0.0273439i
$206$		0			0
$207$	7.12934	+	4.11612i	0.495523	+	0.286090i
$208$		0			0
$209$		−	3.95109i		−	0.273303i
$210$		0			0
$211$	−9.11727	−	9.11727i	−0.627659	−	0.627659i	0.319820	−	0.947478i	$-0.396378\pi$
$211$	−9.11727	−	9.11727i	−0.627659	−	0.627659i	−0.947478	+	0.319820i	$0.896378\pi$
$212$		0			0
$213$	−8.54126	−	31.8764i	−0.585237	−	2.18414i
$214$		0			0
$215$	−3.63253	+	2.09724i	−0.247736	+	0.143031i
$216$		0			0
$217$	−1.90942	+	1.27668i	−0.129620	+	0.0866666i
$218$		0			0
$219$	−40.7416	−	10.9167i	−2.75306	−	0.737681i
$220$		0			0
$221$	8.93405	+	33.3423i	0.600969	+	2.24285i
$222$		0			0
$223$	−6.72926			−0.450624			−0.225312	−	0.974287i	$-0.572340\pi$
$223$	−6.72926			−0.450624			−0.225312	+	0.974287i	$0.572340\pi$
$224$		0			0
$225$	20.6936			1.37957
$226$		0			0
$227$	−2.00024	−	7.46500i	−0.132761	−	0.495469i	0.867236	−	0.497896i	$-0.165894\pi$
$227$	−2.00024	−	7.46500i	−0.132761	−	0.495469i	−0.999997	+	0.00242728i	$0.999227\pi$
$228$		0			0
$229$	14.7233	+	3.94509i	0.972941	+	0.260699i	0.710069	−	0.704132i	$-0.248664\pi$
$229$	14.7233	+	3.94509i	0.972941	+	0.260699i	0.262872	+	0.964831i	$0.415330\pi$
$230$		0			0
$231$	14.3184	−	0.942877i	0.942084	−	0.0620367i
$232$		0			0
$233$	−12.7954	+	7.38741i	−0.838253	+	0.483965i	−0.856670	−	0.515865i	$-0.827471\pi$
$233$	−12.7954	+	7.38741i	−0.838253	+	0.483965i	0.0184173	+	0.999830i	$0.494137\pi$
$234$		0			0
$235$	0.360479	+	1.34533i	0.0235151	+	0.0877594i
$236$		0			0
$237$	2.36773	+	2.36773i	0.153800	+	0.153800i
$238$		0			0
$239$			28.5488i			1.84667i	0.383998	+	0.923334i	$0.374547\pi$
$239$			28.5488i			1.84667i	−0.383998	+	0.923334i	$0.625453\pi$
$240$		0			0
$241$	19.8792	+	11.4772i	1.28053	+	0.739314i	0.976945	−	0.213491i	$-0.0684834\pi$
$241$	19.8792	+	11.4772i	1.28053	+	0.739314i	0.303584	+	0.952805i	$0.401817\pi$
$242$		0			0
$243$	18.9268	+	5.07143i	1.21416	+	0.325332i
$244$		0			0
$245$	−1.25162	−	3.01645i	−0.0799628	−	0.192714i
$246$		0			0
$247$	6.29713	+	10.9069i	0.400676	+	0.693992i
$248$		0			0
$249$	29.9549	+	17.2945i	1.89832	+	1.09599i
$250$		0			0
$251$	10.2808	+	10.2808i	0.648918	+	0.648918i	0.952732	−	0.303813i	$-0.0982599\pi$
$251$	10.2808	+	10.2808i	0.648918	+	0.648918i	−0.303813	+	0.952732i	$0.598260\pi$
$252$		0			0
$253$	2.69543	−	2.69543i	0.169460	−	0.169460i
$254$		0			0
$255$	3.41276	−	5.91107i	0.213715	−	0.370165i
$256$		0			0
$257$	2.17812	−	1.25754i	0.135867	−	0.0784431i	−0.430526	−	0.902578i	$-0.641672\pi$
$257$	2.17812	−	1.25754i	0.135867	−	0.0784431i	0.566393	+	0.824135i	$0.308338\pi$
$258$		0			0
$259$	−14.2757	+	16.2883i	−0.887046	+	1.01211i
$260$		0			0
$261$	−1.78046	+	6.64475i	−0.110207	+	0.411300i
$262$		0			0
$263$	4.54781	−	7.87703i	0.280430	−	0.485718i	−0.691061	−	0.722797i	$-0.742856\pi$
$263$	4.54781	−	7.87703i	0.280430	−	0.485718i	0.971491	+	0.237078i	$0.0761897\pi$
$264$		0			0
$265$	3.27464			0.201159
$266$		0			0
$267$	4.45449	−	4.45449i	0.272611	−	0.272611i
$268$		0			0
$269$	−5.50656	+	1.47548i	−0.335741	+	0.0899615i	−0.422751	−	0.906246i	$-0.638935\pi$
$269$	−5.50656	+	1.47548i	−0.335741	+	0.0899615i	0.0870099	+	0.996207i	$0.472269\pi$
$270$		0			0
$271$	−5.76007	−	9.97673i	−0.349899	−	0.606043i	0.636332	−	0.771415i	$-0.280451\pi$
$271$	−5.76007	−	9.97673i	−0.349899	−	0.606043i	−0.986231	+	0.165372i	$0.947118\pi$
$272$		0			0
$273$	−38.0232	+	25.4231i	−2.30127	+	1.53868i
$274$		0			0
$275$	2.48003	−	9.25560i	0.149551	−	0.558134i
$276$		0			0
$277$	20.1829	−	5.40800i	1.21268	−	0.324935i	0.404864	−	0.914377i	$-0.367319\pi$
$277$	20.1829	−	5.40800i	1.21268	−	0.324935i	0.807811	+	0.589442i	$0.200652\pi$
$278$		0			0
$279$		−	3.75657i		−	0.224900i
$280$		0			0
$281$		−	19.8360i		−	1.18331i	−0.806190	−	0.591657i	$-0.798474\pi$
$281$		−	19.8360i		−	1.18331i	0.806190	−	0.591657i	$-0.201526\pi$
$282$		0			0
$283$	19.6531	−	5.26602i	1.16825	−	0.313033i	0.377996	−	0.925807i	$-0.376613\pi$
$283$	19.6531	−	5.26602i	1.16825	−	0.313033i	0.790258	+	0.612775i	$0.209947\pi$
$284$		0			0
$285$	0.644542	−	2.40546i	0.0381794	−	0.142487i
$286$		0			0
$287$	−7.69473	−	3.79170i	−0.454206	−	0.223817i
$288$		0			0
$289$	6.10572	+	10.5754i	0.359160	+	0.622083i
$290$		0			0
$291$	−12.2810	+	3.29069i	−0.719926	+	0.192903i
$292$		0			0
$293$	−6.75509	+	6.75509i	−0.394636	+	0.394636i	−0.876336	−	0.481700i	$-0.840020\pi$
$293$	−6.75509	+	6.75509i	−0.394636	+	0.394636i	0.481700	+	0.876336i	$0.340020\pi$
$294$		0			0
$295$	4.00586			0.233230
$296$		0			0
$297$	−3.59879	+	6.23329i	−0.208823	+	0.361692i
$298$		0			0
$299$	−3.14481	+	11.7366i	−0.181869	+	0.678745i
$300$		0			0
$301$	22.5220	−	7.65288i	1.29815	−	0.441105i
$302$		0			0
$303$	−12.9981	+	7.50446i	−0.746721	+	0.431120i
$304$		0			0
$305$	0.113434	−	0.196473i	0.00649520	−	0.0112500i
$306$		0			0
$307$	−2.36930	+	2.36930i	−0.135223	+	0.135223i	−0.771479	−	0.636255i	$-0.780483\pi$
$307$	−2.36930	+	2.36930i	−0.135223	+	0.135223i	0.636255	+	0.771479i	$0.280483\pi$
$308$		0			0
$309$	−2.11757	−	2.11757i	−0.120464	−	0.120464i
$310$		0			0
$311$	13.1239	+	7.57707i	0.744186	+	0.429656i	0.823589	−	0.567186i	$-0.191968\pi$
$311$	13.1239	+	7.57707i	0.744186	+	0.429656i	−0.0794032	+	0.996843i	$0.525301\pi$
$312$		0			0
$313$	3.32791	+	5.76411i	0.188105	+	0.325807i	0.944618	−	0.328171i	$-0.106432\pi$
$313$	3.32791	+	5.76411i	0.188105	+	0.325807i	−0.756514	+	0.653978i	$0.773099\pi$
$314$		0			0
$315$	5.23888	+	1.04041i	0.295177	+	0.0586206i
$316$		0			0
$317$	25.6106	+	6.86233i	1.43843	+	0.385427i	0.891985	−	0.452065i	$-0.149313\pi$
$317$	25.6106	+	6.86233i	1.43843	+	0.385427i	0.546449	+	0.837493i	$0.315979\pi$
$318$		0			0
$319$	2.75861	+	1.59268i	0.154453	+	0.0891732i
$320$		0			0
$321$		−	16.7357i		−	0.934094i
$322$		0			0
$323$	7.53630	+	7.53630i	0.419331	+	0.419331i
$324$		0			0
$325$	7.90519	+	29.5026i	0.438501	+	1.63651i
$326$		0			0
$327$	−25.5398	+	14.7454i	−1.41235	+	0.815423i
$328$		0			0
$329$	−0.518991	−	7.88134i	−0.0286129	−	0.434513i
$330$		0			0
$331$	−9.16331	−	2.45530i	−0.503661	−	0.134956i	−0.00196237	−	0.999998i	$-0.500625\pi$
$331$	−9.16331	−	2.45530i	−0.503661	−	0.134956i	−0.501699	+	0.865043i	$0.667291\pi$
$332$		0			0
$333$	−9.16806	−	34.2157i	−0.502407	−	1.87501i
$334$		0			0
$335$	−1.86071			−0.101661
$336$		0			0
$337$	−16.0354			−0.873502			−0.436751	−	0.899582i	$-0.643871\pi$
$337$	−16.0354			−0.873502			−0.436751	+	0.899582i	$0.643871\pi$
$338$		0			0
$339$	1.97476	+	7.36991i	0.107254	+	0.400278i
$340$		0			0
$341$	−1.68019	−	0.450207i	−0.0909876	−	0.0243801i
$342$		0			0
$343$	3.62978	+	18.1611i	0.195990	+	0.980606i
$344$		0			0
$345$	2.08071	−	1.20130i	0.112022	−	0.0646758i
$346$		0			0
$347$	0.821629	+	3.06636i	0.0441074	+	0.164611i	0.984467	−	0.175572i	$-0.0561776\pi$
$347$	0.821629	+	3.06636i	0.0441074	+	0.164611i	−0.940359	+	0.340183i	$0.889511\pi$
$348$		0			0
$349$	−2.21348	−	2.21348i	−0.118485	−	0.118485i	0.645378	−	0.763863i	$-0.276700\pi$
$349$	−2.21348	−	2.21348i	−0.118485	−	0.118485i	−0.763863	+	0.645378i	$0.776700\pi$
$350$		0			0
$351$		−	22.9426i		−	1.22458i
$352$		0			0
$353$	−7.11770	−	4.10941i	−0.378837	−	0.218722i	0.298475	−	0.954417i	$-0.403522\pi$
$353$	−7.11770	−	4.10941i	−0.378837	−	0.218722i	−0.677312	+	0.735696i	$0.736855\pi$
$354$		0			0
$355$	−5.49410	−	1.47214i	−0.291597	−	0.0781331i
$356$		0			0
$357$	−25.5125	+	29.1094i	−1.35026	+	1.54063i
$358$		0			0
$359$	−15.3319	−	26.5556i	−0.809184	−	1.40155i	−0.913430	−	0.406997i	$-0.866576\pi$
$359$	−15.3319	−	26.5556i	−0.809184	−	1.40155i	0.104245	−	0.994552i	$-0.466757\pi$
$360$		0			0
$361$	−13.0869	−	7.55570i	−0.688782	−	0.397668i
$362$		0			0
$363$	−13.3703	−	13.3703i	−0.701761	−	0.701761i
$364$		0			0
$365$	−5.14051	+	5.14051i	−0.269067	+	0.269067i
$366$		0			0
$367$	8.91168	−	15.4355i	0.465186	−	0.805726i	−0.534024	−	0.845469i	$-0.679321\pi$
$367$	8.91168	−	15.4355i	0.465186	−	0.805726i	0.999210	+	0.0397435i	$0.0126541\pi$
$368$		0			0
$369$	12.1500	−	7.01478i	0.632502	−	0.365175i
$370$		0			0
$371$	−18.2146	−	3.61732i	−0.945656	−	0.187802i
$372$		0			0
$373$	0.642914	−	2.39939i	0.0332888	−	0.124236i	−0.947282	−	0.320401i	$-0.896182\pi$
$373$	0.642914	−	2.39939i	0.0332888	−	0.124236i	0.980571	+	0.196166i	$0.0628490\pi$
$374$		0			0
$375$	6.17691	−	10.6987i	0.318974	−	0.552480i
$376$		0			0
$377$	−10.1535			−0.522931
$378$		0			0
$379$	−0.526070	+	0.526070i	−0.0270224	+	0.0270224i	−0.720489	−	0.693466i	$-0.756083\pi$
$379$	−0.526070	+	0.526070i	−0.0270224	+	0.0270224i	0.693466	+	0.720489i	$0.256083\pi$
$380$		0			0
$381$	−24.4396	+	6.54856i	−1.25208	+	0.335493i
$382$		0			0
$383$	11.8928	+	20.5989i	0.607692	+	1.05255i	0.991620	+	0.129190i	$0.0412377\pi$
$383$	11.8928	+	20.5989i	0.607692	+	1.05255i	−0.383928	+	0.923363i	$0.625429\pi$
$384$		0			0
$385$	1.09320	−	2.21850i	0.0557145	−	0.113065i
$386$		0			0
$387$	−10.0688	+	37.5773i	−0.511826	+	1.91016i
$388$		0			0
$389$	23.4190	−	6.27509i	1.18739	−	0.318160i	0.389535	−	0.921012i	$-0.372636\pi$
$389$	23.4190	−	6.27509i	1.18739	−	0.318160i	0.797853	+	0.602852i	$0.205969\pi$
$390$		0			0
$391$			10.2825i			0.520009i
$392$		0			0
$393$		−	50.2190i		−	2.53321i
$394$		0			0
$395$	0.557465	−	0.149372i	0.0280491	−	0.00751574i
$396$		0			0
$397$	−1.09232	+	4.07659i	−0.0548219	+	0.204598i	−0.987904	−	0.155064i	$-0.950442\pi$
$397$	−1.09232	+	4.07659i	−0.0548219	+	0.204598i	0.933082	+	0.359662i	$0.117108\pi$
$398$		0			0
$399$	−6.24235	+	12.6680i	−0.312508	+	0.634193i
$400$		0			0
$401$	−9.01163	−	15.6086i	−0.450019	−	0.779456i	0.548367	−	0.836238i	$-0.315250\pi$
$401$	−9.01163	−	15.6086i	−0.450019	−	0.779456i	−0.998387	+	0.0567812i	$0.981916\pi$
$402$		0			0
$403$	5.35568	−	1.43505i	0.266785	−	0.0714849i
$404$		0			0
$405$	1.07466	−	1.07466i	0.0534002	−	0.0534002i
$406$		0			0
$407$	−16.4023			−0.813034
$408$		0			0
$409$	−13.9843	+	24.2215i	−0.691478	+	1.19768i	0.279875	+	0.960036i	$0.409707\pi$
$409$	−13.9843	+	24.2215i	−0.691478	+	1.19768i	−0.971354	+	0.237639i	$0.923626\pi$
$410$		0			0
$411$	−10.6412	+	39.7137i	−0.524894	+	1.95893i
$412$		0			0
$413$	−22.2819	−	4.42506i	−1.09642	−	0.217743i
$414$		0			0
$415$	5.16292	−	2.98081i	0.253438	−	0.146322i
$416$		0			0
$417$	−2.16503	+	3.74994i	−0.106022	+	0.183635i
$418$		0			0
$419$	10.4669	−	10.4669i	0.511342	−	0.511342i	−0.403596	−	0.914937i	$-0.632240\pi$
$419$	10.4669	−	10.4669i	0.511342	−	0.511342i	0.914937	+	0.403596i	$0.132240\pi$
$420$		0			0
$421$	−12.3722	−	12.3722i	−0.602984	−	0.602984i	0.338119	−	0.941103i	$-0.390209\pi$
$421$	−12.3722	−	12.3722i	−0.602984	−	0.602984i	−0.941103	+	0.338119i	$0.890209\pi$
$422$		0			0
$423$	11.1871	+	6.45887i	0.543935	+	0.314041i
$424$		0			0
$425$	12.9237	+	22.3845i	0.626891	+	1.08581i
$426$		0			0
$427$	−0.847989	+	0.967542i	−0.0410370	+	0.0468227i
$428$		0			0
$429$	−33.4585	−	8.96517i	−1.61539	−	0.432842i
$430$		0			0
$431$	−11.8089	−	6.81786i	−0.568814	−	0.328405i	0.187862	−	0.982195i	$-0.439844\pi$
$431$	−11.8089	−	6.81786i	−0.568814	−	0.328405i	−0.756675	+	0.653791i	$0.773178\pi$
$432$		0			0
$433$		−	19.1575i		−	0.920649i	−0.887751	−	0.460325i	$-0.847733\pi$
$433$		−	19.1575i		−	0.920649i	0.887751	−	0.460325i	$-0.152267\pi$
$434$		0			0
$435$	1.41965	+	1.41965i	0.0680672	+	0.0680672i
$436$		0			0
$437$	0.970991	+	3.62379i	0.0464488	+	0.173349i
$438$		0			0
$439$	−7.42387	+	4.28617i	−0.354322	+	0.204568i	−0.666587	−	0.745427i	$-0.732246\pi$
$439$	−7.42387	+	4.28617i	−0.354322	+	0.204568i	0.312265	+	0.949995i	$0.398912\pi$
$440$		0			0
$441$	−27.9911	−	11.5742i	−1.33291	−	0.551154i
$442$		0			0
$443$	20.2310	+	5.42088i	0.961204	+	0.257554i	0.705110	−	0.709098i	$-0.250898\pi$
$443$	20.2310	+	5.42088i	0.961204	+	0.257554i	0.256094	+	0.966652i	$0.417564\pi$
$444$		0			0
$445$	−0.281020	−	1.04878i	−0.0133216	−	0.0497169i
$446$		0			0
$447$	27.5017			1.30079
$448$		0			0
$449$	−24.4270			−1.15278			−0.576391	−	0.817174i	$-0.695539\pi$
$449$	−24.4270			−1.15278			−0.576391	+	0.817174i	$0.695539\pi$
$450$		0			0
$451$	−1.68138	−	6.27498i	−0.0791729	−	0.295477i
$452$		0			0
$453$	−30.5336	−	8.18145i	−1.43459	−	0.384398i
$454$		0			0
$455$	0.518009	+	7.86644i	0.0242846	+	0.368784i
$456$		0			0
$457$	−3.12783	+	1.80585i	−0.146314	+	0.0844743i	−0.571370	−	0.820693i	$-0.693588\pi$
$457$	−3.12783	+	1.80585i	−0.146314	+	0.0844743i	0.425056	+	0.905167i	$0.360254\pi$
$458$		0			0
$459$	−5.02503	−	18.7537i	−0.234548	−	0.875347i
$460$		0			0
$461$	−25.2872	−	25.2872i	−1.17774	−	1.17774i	−0.980318	−	0.197423i	$-0.936743\pi$
$461$	−25.2872	−	25.2872i	−1.17774	−	1.17774i	−0.197423	−	0.980318i	$-0.563257\pi$
$462$		0			0
$463$		−	8.01165i		−	0.372333i	−0.982518	−	0.186166i	$-0.940394\pi$
$463$		−	8.01165i		−	0.372333i	0.982518	−	0.186166i	$-0.0596064\pi$
$464$		0			0
$465$	−0.949477	−	0.548181i	−0.0440309	−	0.0254213i
$466$		0			0
$467$	−17.9002	−	4.79633i	−0.828321	−	0.221948i	−0.180340	−	0.983604i	$-0.557720\pi$
$467$	−17.9002	−	4.79633i	−0.828321	−	0.221948i	−0.647981	+	0.761657i	$0.724386\pi$
$468$		0			0
$469$	10.3499	+	2.05542i	0.477912	+	0.0949107i
$470$		0			0
$471$	3.01430	+	5.22093i	0.138892	+	0.240568i
$472$		0			0
$473$	15.6004	+	9.00692i	0.717309	+	0.414139i
$474$		0			0
$475$	6.66840	+	6.66840i	0.305967	+	0.305967i
$476$		0			0
$477$	21.4759	−	21.4759i	0.983314	−	0.983314i
$478$		0			0
$479$	13.6882	−	23.7087i	0.625432	−	1.08328i	−0.363025	−	0.931779i	$-0.618256\pi$
$479$	13.6882	−	23.7087i	0.625432	−	1.08328i	0.988457	−	0.151501i	$-0.0484106\pi$
$480$		0			0
$481$	45.2785	−	26.1415i	2.06452	−	1.19195i
$482$		0			0
$483$	−12.9006	+	4.38357i	−0.586998	+	0.199459i
$484$		0			0
$485$	−0.567171	+	2.11671i	−0.0257539	+	0.0961148i
$486$		0			0
$487$	9.68012	−	16.7665i	0.438648	−	0.759761i	−0.558938	−	0.829210i	$-0.688791\pi$
$487$	9.68012	−	16.7665i	0.438648	−	0.759761i	0.997585	+	0.0694492i	$0.0221242\pi$
$488$		0			0
$489$	−39.7206			−1.79623
$490$		0			0
$491$	−17.1950	+	17.1950i	−0.775998	+	0.775998i	−0.979148	−	0.203149i	$-0.934882\pi$
$491$	−17.1950	+	17.1950i	−0.775998	+	0.775998i	0.203149	+	0.979148i	$0.434882\pi$
$492$		0			0
$493$	−8.29964	+	2.22388i	−0.373797	+	0.100159i
$494$		0			0
$495$	2.02246	+	3.50300i	0.0909027	+	0.157448i
$496$		0			0
$497$	28.9338	+	14.2576i	1.29786	+	0.639539i
$498$		0			0
$499$	−0.783708	+	2.92484i	−0.0350836	+	0.130934i	−0.981247	−	0.192757i	$-0.938257\pi$
$499$	−0.783708	+	2.92484i	−0.0350836	+	0.130934i	0.946163	+	0.323691i	$0.104924\pi$
$500$		0			0
$501$	−15.5569	+	4.16846i	−0.695031	+	0.186233i
$502$		0			0
$503$			34.5673i			1.54128i	0.637272	+	0.770639i	$0.280063\pi$
$503$			34.5673i			1.54128i	−0.637272	+	0.770639i	$0.719937\pi$
$504$		0			0
$505$			2.58688i			0.115115i
$506$		0			0
$507$	72.6599	−	19.4692i	3.22694	−	0.864656i
$508$		0			0
$509$	4.08105	−	15.2307i	0.180889	−	0.675088i	−0.814584	−	0.580046i	$-0.803035\pi$
$509$	4.08105	−	15.2307i	0.180889	−	0.675088i	0.995473	−	0.0950424i	$-0.0302987\pi$
$510$		0			0
$511$	34.2717	−	22.9147i	1.51609	−	1.01369i
$512$		0			0
$513$	−3.54187	−	6.13470i	−0.156377	−	0.270854i
$514$		0			0
$515$	−0.498567	+	0.133591i	−0.0219695	+	0.00588671i
$516$		0			0
$517$	4.22957	−	4.22957i	0.186016	−	0.186016i
$518$		0			0
$519$	−24.8623			−1.09133
$520$		0			0
$521$	7.72095	−	13.3731i	0.338261	−	0.585885i	−0.645845	−	0.763469i	$-0.723495\pi$
$521$	7.72095	−	13.3731i	0.338261	−	0.585885i	0.984106	+	0.177584i	$0.0568281\pi$
$522$		0			0
$523$	0.527773	−	1.96968i	0.0230779	−	0.0861280i	−0.953426	−	0.301626i	$-0.902471\pi$
$523$	0.527773	−	1.96968i	0.0230779	−	0.0861280i	0.976504	+	0.215498i	$0.0691374\pi$
$524$		0			0
$525$	−22.5744	+	25.7571i	−0.985229	+	1.12413i
$526$		0			0
$527$	4.06352	−	2.34607i	0.177010	−	0.102197i
$528$		0			0
$529$	9.69026	−	16.7840i	0.421316	−	0.729740i
$530$		0			0
$531$	26.2714	−	26.2714i	1.14008	−	1.14008i
$532$		0			0
$533$	14.6423	+	14.6423i	0.634228	+	0.634228i
$534$		0			0
$535$	−2.49805	−	1.44225i	−0.108000	−	0.0623538i
$536$		0			0
$537$	−5.14933	−	8.91890i	−0.222210	−	0.384879i
$538$		0			0
$539$	−8.53138	+	11.1324i	−0.367473	+	0.479507i
$540$		0			0
$541$	20.1819	+	5.40772i	0.867686	+	0.232496i	0.665087	−	0.746766i	$-0.268394\pi$
$541$	20.1819	+	5.40772i	0.867686	+	0.232496i	0.202599	+	0.979262i	$0.435061\pi$
$542$		0			0
$543$	−17.0216	−	9.82741i	−0.730466	−	0.421735i
$544$		0			0
$545$			5.08293i			0.217729i
$546$		0			0
$547$	13.0675	+	13.0675i	0.558728	+	0.558728i	0.928945	−	0.370217i	$-0.120717\pi$
$547$	13.0675	+	13.0675i	0.558728	+	0.558728i	−0.370217	+	0.928945i	$0.620717\pi$
$548$		0			0
$549$	−0.544592	−	2.03245i	−0.0232426	−	0.0867427i
$550$		0			0
$551$	−2.71498	+	1.56749i	−0.115662	+	0.0667775i
$552$		0			0
$553$	−3.26581	+	0.215055i	−0.138876	+	0.00914507i
$554$		0			0
$555$	−9.98591	−	2.67572i	−0.423878	−	0.113578i
$556$		0			0
$557$	−3.13271	−	11.6914i	−0.132737	−	0.495381i	0.867260	−	0.497856i	$-0.165879\pi$
$557$	−3.13271	−	11.6914i	−0.132737	−	0.495381i	−0.999997	+	0.00247440i	$0.999212\pi$
$558$		0			0
$559$	−57.4198			−2.42860
$560$		0			0
$561$	−29.3132			−1.23760
$562$		0			0
$563$	7.28930	+	27.2040i	0.307207	+	1.14651i	0.931029	+	0.364946i	$0.118913\pi$
$563$	7.28930	+	27.2040i	0.307207	+	1.14651i	−0.623821	+	0.781567i	$0.714421\pi$
$564$		0			0
$565$	1.27025	+	0.340362i	0.0534398	+	0.0143192i
$566$		0			0
$567$	−7.16472	+	4.79048i	−0.300890	+	0.201181i
$568$		0			0
$569$	20.4277	−	11.7940i	0.856375	−	0.494428i	−0.00642167	−	0.999979i	$-0.502044\pi$
$569$	20.4277	−	11.7940i	0.856375	−	0.494428i	0.862797	+	0.505551i	$0.168711\pi$
$570$		0			0
$571$	−5.83253	−	21.7673i	−0.244084	−	0.910933i	−0.973842	−	0.227227i	$-0.927034\pi$
$571$	−5.83253	−	21.7673i	−0.244084	−	0.910933i	0.729758	−	0.683705i	$-0.239633\pi$
$572$		0			0
$573$	33.6826	+	33.6826i	1.40711	+	1.40711i
$574$		0			0
$575$			9.09835i			0.379427i
$576$		0			0
$577$	−16.2893	−	9.40463i	−0.678132	−	0.391520i	0.121019	−	0.992650i	$-0.461384\pi$
$577$	−16.2893	−	9.40463i	−0.678132	−	0.391520i	−0.799151	+	0.601130i	$0.794717\pi$
$578$		0			0
$579$	−17.2026	−	4.60942i	−0.714915	−	0.191561i
$580$		0			0
$581$	−32.0106	+	10.8771i	−1.32802	+	0.451256i
$582$		0			0
$583$	−7.03171	−	12.1793i	−0.291224	−	0.504414i
$584$		0			0
$585$	−11.1659	−	6.44666i	−0.461655	−	0.266537i
$586$		0			0
$587$	−12.6185	−	12.6185i	−0.520820	−	0.520820i	0.396999	−	0.917819i	$-0.370052\pi$
$587$	−12.6185	−	12.6185i	−0.520820	−	0.520820i	−0.917819	+	0.396999i	$0.870052\pi$
$588$		0			0
$589$	1.21053	−	1.21053i	0.0498791	−	0.0498791i
$590$		0			0
$591$	−28.4763	+	49.3223i	−1.17136	+	2.02885i
$592$		0			0
$593$	−22.0260	+	12.7167i	−0.904498	+	0.522212i	−0.878657	−	0.477454i	$-0.841560\pi$
$593$	−22.0260	+	12.7167i	−0.904498	+	0.522212i	−0.0258409	+	0.999666i	$0.508226\pi$
$594$		0			0
$595$	2.14639	+	6.31671i	0.0879934	+	0.258960i
$596$		0			0
$597$	−5.20427	+	19.4226i	−0.212997	+	0.794914i
$598$		0			0
$599$	−21.1003	+	36.5468i	−0.862135	+	1.49326i	0.00772853	+	0.999970i	$0.497540\pi$
$599$	−21.1003	+	36.5468i	−0.862135	+	1.49326i	−0.869864	+	0.493292i	$0.835793\pi$
$600$		0			0
$601$	29.8695			1.21840			0.609202	−	0.793015i	$-0.291490\pi$
$601$	29.8695			1.21840			0.609202	+	0.793015i	$0.291490\pi$
$602$		0			0
$603$	−12.2030	+	12.2030i	−0.496944	+	0.496944i
$604$		0			0
$605$	−3.14796	+	0.843492i	−0.127983	+	0.0342928i
$606$		0			0
$607$	14.7137	+	25.4850i	0.597212	+	1.03440i	0.993231	+	0.116160i	$0.0370584\pi$
$607$	14.7137	+	25.4850i	0.597212	+	1.03440i	−0.396018	+	0.918243i	$0.629608\pi$
$608$		0			0
$609$	−6.32837	−	9.46480i	−0.256438	−	0.383533i
$610$		0			0
$611$	−4.93472	+	18.4166i	−0.199638	+	0.745058i
$612$		0			0
$613$	22.1882	−	5.94532i	0.896175	−	0.240129i	0.218802	−	0.975769i	$-0.429785\pi$
$613$	22.1882	−	5.94532i	0.896175	−	0.240129i	0.677373	+	0.735640i	$0.263118\pi$
$614$		0			0
$615$		−	4.09456i		−	0.165108i
$616$		0			0
$617$			31.2064i			1.25632i	0.778084	+	0.628161i	$0.216192\pi$
$617$			31.2064i			1.25632i	−0.778084	+	0.628161i	$0.783808\pi$
$618$		0			0
$619$	−17.7087	+	4.74503i	−0.711772	+	0.190719i	−0.596498	−	0.802615i	$-0.703441\pi$
$619$	−17.7087	+	4.74503i	−0.711772	+	0.190719i	−0.115275	+	0.993334i	$0.536775\pi$
$620$		0			0
$621$	1.76883	−	6.60135i	0.0709805	−	0.264903i
$622$		0			0
$623$	0.404591	+	6.14408i	0.0162096	+	0.246157i
$624$		0			0
$625$	10.8912	+	18.8641i	0.435648	+	0.754565i
$626$		0			0
$627$	−10.3306	+	2.76808i	−0.412565	+	0.110547i
$628$		0			0
$629$	31.2858	−	31.2858i	1.24745	−	1.24745i
$630$		0			0
$631$	−8.10970			−0.322842			−0.161421	−	0.986886i	$-0.551608\pi$
$631$	−8.10970			−0.322842			−0.161421	+	0.986886i	$0.551608\pi$
$632$		0			0
$633$	−17.4508	+	30.2257i	−0.693608	+	1.20136i
$634$		0			0
$635$	−1.12869	+	4.21231i	−0.0447905	+	0.167160i
$636$		0			0
$637$	5.80831	−	44.3279i	0.230134	−	1.75634i
$638$		0			0
$639$	−45.6864	+	26.3770i	−1.80732	+	1.04346i
$640$		0			0
$641$	−14.0435	+	24.3241i	−0.554685	+	0.960743i	0.443242	+	0.896402i	$0.353828\pi$
$641$	−14.0435	+	24.3241i	−0.554685	+	0.960743i	−0.997928	+	0.0643416i	$0.979505\pi$
$642$		0			0
$643$	−21.6759	+	21.6759i	−0.854812	+	0.854812i	−0.990721	−	0.135909i	$-0.956605\pi$
$643$	−21.6759	+	21.6759i	−0.854812	+	0.854812i	0.135909	+	0.990721i	$0.456605\pi$
$644$		0			0
$645$	8.02841	+	8.02841i	0.316118	+	0.316118i
$646$		0			0
$647$	39.8543	+	23.0099i	1.56683	+	0.904612i	0.996535	+	0.0831749i	$0.0265060\pi$
$647$	39.8543	+	23.0099i	1.56683	+	0.904612i	0.570299	+	0.821437i	$0.306827\pi$
$648$		0			0
$649$	−8.60188	−	14.8989i	−0.337653	−	0.584833i
$650$		0			0
$651$	4.67575	+	4.09800i	0.183257	+	0.160613i
$652$		0			0
$653$	29.2593	+	7.84001i	1.14501	+	0.306803i	0.780962	−	0.624579i	$-0.214729\pi$
$653$	29.2593	+	7.84001i	1.14501	+	0.306803i	0.364043	+	0.931382i	$0.381396\pi$
$654$		0			0
$655$	−7.49594	−	4.32778i	−0.292890	−	0.169100i
$656$		0			0
$657$			67.4255i			2.63052i
$658$		0			0
$659$	−7.48634	−	7.48634i	−0.291626	−	0.291626i	0.546096	−	0.837723i	$-0.316113\pi$
$659$	−7.48634	−	7.48634i	−0.291626	−	0.291626i	−0.837723	+	0.546096i	$0.816113\pi$
$660$		0			0
$661$	−2.73446	−	10.2052i	−0.106358	−	0.396934i	0.892137	−	0.451764i	$-0.149205\pi$
$661$	−2.73446	−	10.2052i	−0.106358	−	0.396934i	−0.998496	+	0.0548296i	$0.982538\pi$
$662$		0			0
$663$	80.9187	−	46.7184i	3.14262	−	1.81439i
$664$		0			0
$665$	1.35293	+	2.02347i	0.0524645	+	0.0784667i
$666$		0			0
$667$	−2.92150	−	0.782813i	−0.113121	−	0.0303106i
$668$		0			0
$669$	4.71443	+	17.5945i	0.182270	+	0.680242i
$670$		0			0
$671$	−0.974316			−0.0376130
$672$		0			0
$673$	17.2027			0.663115			0.331557	−	0.943435i	$-0.392426\pi$
$673$	17.2027			0.663115			0.331557	+	0.943435i	$0.392426\pi$
$674$		0			0
$675$	−4.44634	−	16.5940i	−0.171140	−	0.638702i
$676$		0			0
$677$	−19.3441	−	5.18323i	−0.743453	−	0.199208i	−0.132841	−	0.991137i	$-0.542410\pi$
$677$	−19.3441	−	5.18323i	−0.743453	−	0.199208i	−0.610612	+	0.791930i	$0.709077\pi$
$678$		0			0
$679$	5.49301	−	11.1473i	0.210802	−	0.427794i
$680$		0			0
$681$	−18.1168	+	10.4598i	−0.694238	+	0.400819i
$682$		0			0
$683$	0.249364	+	0.930638i	0.00954164	+	0.0356099i	0.970533	−	0.240970i	$-0.0774656\pi$
$683$	0.249364	+	0.930638i	0.00954164	+	0.0356099i	−0.960991	+	0.276580i	$0.910799\pi$
$684$		0			0
$685$	5.01082	+	5.01082i	0.191453	+	0.191453i
$686$		0			0
$687$		−	41.2597i		−	1.57416i
$688$		0			0
$689$	38.8219	+	22.4138i	1.47900	+	0.853899i
$690$		0			0
$691$	−33.5048	−	8.97758i	−1.27458	−	0.341523i	−0.442797	−	0.896622i	$-0.646014\pi$
$691$	−33.5048	−	8.97758i	−1.27458	−	0.341523i	−0.831784	+	0.555099i	$0.812680\pi$
$692$		0			0
$693$	−7.37999	−	21.7189i	−0.280343	−	0.825034i
$694$		0			0
$695$	0.373156	+	0.646326i	0.0141546	+	0.0245165i
$696$		0			0
$697$	15.1759	+	8.76183i	0.574829	+	0.331878i
$698$		0			0
$699$	28.2796	+	28.2796i	1.06963	+	1.06963i
$700$		0			0
$701$	−32.4969	+	32.4969i	−1.22739	+	1.22739i	−0.262444	+	0.964947i	$0.584529\pi$
$701$	−32.4969	+	32.4969i	−1.22739	+	1.22739i	−0.964947	+	0.262444i	$0.915471\pi$
$702$		0			0
$703$	8.07146	−	13.9802i	0.304421	−	0.527272i
$704$		0			0
$705$	3.26498	−	1.88504i	0.122966	−	0.0709945i
$706$		0			0
$707$	2.85759	−	14.3891i	0.107471	−	0.541157i
$708$		0			0
$709$	1.21770	−	4.54454i	0.0457319	−	0.170674i	−0.939283	−	0.343144i	$-0.888508\pi$
$709$	1.21770	−	4.54454i	0.0457319	−	0.170674i	0.985015	+	0.172470i	$0.0551748\pi$
$710$		0			0
$711$	2.67638	−	4.63562i	0.100372	−	0.173849i
$712$		0			0
$713$	1.65165			0.0618547
$714$		0			0
$715$	−4.22157	+	4.22157i	−0.157878	+	0.157878i
$716$		0			0
$717$	74.6444	−	20.0009i	2.78765	−	0.746947i
$718$		0			0
$719$	9.27548	+	16.0656i	0.345917	+	0.599146i	0.985520	−	0.169559i	$-0.0542345\pi$
$719$	9.27548	+	16.0656i	0.345917	+	0.599146i	−0.639603	+	0.768706i	$0.720901\pi$
$720$		0			0
$721$	2.92076	−	0.192334i	0.108775	−	0.00716289i
$722$		0			0
$723$	16.0816	−	60.0174i	0.598081	−	2.23207i
$724$		0			0
$725$	−7.34384	+	1.96778i	−0.272743	+	0.0730813i
$726$		0			0
$727$			5.96613i			0.221272i	0.993861	+	0.110636i	$0.0352887\pi$
$727$			5.96613i			0.221272i	−0.993861	+	0.110636i	$0.964711\pi$
$728$		0			0
$729$		−	43.2669i		−	1.60248i
$730$		0			0
$731$	−46.9360	+	12.5765i	−1.73599	+	0.465157i
$732$		0			0
$733$	−5.59358	+	20.8755i	−0.206604	+	0.771055i	0.782351	+	0.622838i	$0.214020\pi$
$733$	−5.59358	+	20.8755i	−0.206604	+	0.771055i	−0.988955	+	0.148218i	$0.952646\pi$
$734$		0			0
$735$	−7.01002	+	5.38579i	−0.258569	+	0.198658i
$736$		0			0
$737$	3.99554	+	6.92048i	0.147178	+	0.254919i
$738$		0			0
$739$	34.9804	−	9.37297i	1.28677	−	0.344790i	0.450340	−	0.892857i	$-0.351303\pi$
$739$	34.9804	−	9.37297i	1.28677	−	0.344790i	0.836434	+	0.548067i	$0.184636\pi$
$740$		0			0
$741$	24.1059	−	24.1059i	0.885552	−	0.885552i
$742$		0			0
$743$	−16.2749			−0.597067			−0.298533	−	0.954399i	$-0.596497\pi$
$743$	−16.2749			−0.597067			−0.298533	+	0.954399i	$0.596497\pi$
$744$		0			0
$745$	2.37004	−	4.10504i	0.0868317	−	0.150397i
$746$		0			0
$747$	14.3108	−	53.4087i	0.523605	−	1.95412i
$748$		0			0
$749$	12.3018	+	10.7817i	0.449497	+	0.393955i
$750$		0			0
$751$	15.8511	−	9.15166i	0.578416	−	0.333949i	−0.182087	−	0.983282i	$-0.558285\pi$
$751$	15.8511	−	9.15166i	0.578416	−	0.333949i	0.760504	+	0.649334i	$0.224952\pi$
$752$		0			0
$753$	19.6778	−	34.0830i	0.717101	−	1.24205i
$754$		0			0
$755$	−3.85253	+	3.85253i	−0.140208	+	0.140208i
$756$		0			0
$757$	16.6944	+	16.6944i	0.606767	+	0.606767i	0.942100	−	0.335333i	$-0.108849\pi$
$757$	16.6944	+	16.6944i	0.606767	+	0.606767i	−0.335333	+	0.942100i	$0.608849\pi$
$758$		0			0
$759$	−8.93593	−	5.15916i	−0.324354	−	0.187266i
$760$		0			0
$761$	4.43390	+	7.67974i	0.160729	+	0.278390i	0.935130	−	0.354304i	$-0.115282\pi$
$761$	4.43390	+	7.67974i	0.160729	+	0.278390i	−0.774401	+	0.632695i	$0.781949\pi$
$762$		0			0
$763$	5.61484	−	28.2729i	0.203271	−	1.02355i
$764$		0			0
$765$	−10.5392	−	2.82398i	−0.381047	−	0.102101i
$766$		0			0
$767$	47.4908	+	27.4188i	1.71479	+	0.990036i
$768$		0			0
$769$		−	1.14344i		−	0.0412335i	−0.999787	−	0.0206167i	$-0.993437\pi$
$769$		−	1.14344i		−	0.0412335i	0.999787	−	0.0206167i	$-0.00656298\pi$
$770$		0			0
$771$	−4.81396	−	4.81396i	−0.173370	−	0.173370i
$772$		0			0
$773$	1.40701	+	5.25103i	0.0506066	+	0.188866i	0.986602	−	0.163146i	$-0.0521641\pi$
$773$	1.40701	+	5.25103i	0.0506066	+	0.188866i	−0.935995	+	0.352012i	$0.885497\pi$
$774$		0			0
$775$	3.59555	−	2.07589i	0.129156	−	0.0745683i
$776$		0			0
$777$	52.5892	+	25.9141i	1.88663	+	0.929664i
$778$		0			0
$779$	6.17573	+	1.65478i	0.221269	+	0.0592888i
$780$		0			0
$781$	6.32232	+	23.5952i	0.226231	+	0.844304i
$782$		0			0
$783$	5.71091			0.204091
$784$		0			0
$785$	1.03907			0.0370859
$786$		0			0
$787$	−13.2008	−	49.2659i	−0.470556	−	1.75614i	−0.637778	−	0.770220i	$-0.720146\pi$
$787$	−13.2008	−	49.2659i	−0.470556	−	1.75614i	0.167221	−	0.985919i	$-0.446521\pi$
$788$		0			0
$789$	−23.7816	−	6.37227i	−0.846648	−	0.226859i
$790$		0			0
$791$	−6.68956	−	3.29639i	−0.237854	−	0.117206i
$792$		0			0
$793$	2.68959	−	1.55283i	0.0955101	−	0.0551428i
$794$		0			0
$795$	−2.29417	−	8.56196i	−0.0813658	−	0.303661i
$796$		0			0
$797$	−26.5433	−	26.5433i	−0.940211	−	0.940211i	0.0581002	−	0.998311i	$-0.481496\pi$
$797$	−26.5433	−	26.5433i	−0.940211	−	0.940211i	−0.998311	+	0.0581002i	$0.981496\pi$
$798$		0			0
$799$			16.1349i			0.570813i
$800$		0			0
$801$	−8.72116	−	5.03516i	−0.308147	−	0.177909i
$802$		0			0
$803$	30.1573	+	8.08063i	1.06423	+	0.285159i
$804$		0			0
$805$	−0.457438	+	2.30338i	−0.0161226	+	0.0811833i
$806$		0			0
$807$	7.71565	+	13.3639i	0.271604	+	0.470432i
$808$		0			0
$809$	17.6346	+	10.1813i	0.620000	+	0.357957i	0.776869	−	0.629662i	$-0.216807\pi$
$809$	17.6346	+	10.1813i	0.620000	+	0.357957i	−0.156869	+	0.987619i	$0.550140\pi$
$810$		0			0
$811$	31.8932	+	31.8932i	1.11992	+	1.11992i	0.991752	+	0.128171i	$0.0409107\pi$
$811$	31.8932	+	31.8932i	1.11992	+	1.11992i	0.128171	+	0.991752i	$0.459089\pi$
$812$		0			0
$813$	−22.0500	+	22.0500i	−0.773327	+	0.773327i
$814$		0			0
$815$	−3.42304	+	5.92889i	−0.119904	+	0.207680i
$816$		0			0
$817$	−15.3537	+	8.86446i	−0.537158	+	0.310128i
$818$		0			0
$819$	54.9873	+	48.1928i	1.92141	+	1.68399i
$820$		0			0
$821$	6.34443	−	23.6777i	0.221422	−	0.826359i	−0.762384	−	0.647125i	$-0.775971\pi$
$821$	6.34443	−	23.6777i	0.221422	−	0.826359i	0.983806	−	0.179234i	$-0.0573620\pi$
$822$		0			0
$823$	5.16976	−	8.95429i	0.180207	−	0.312127i	−0.761744	−	0.647878i	$-0.775657\pi$
$823$	5.16976	−	8.95429i	0.180207	−	0.312127i	0.941951	+	0.335751i	$0.108990\pi$
$824$		0			0
$825$	−25.9374			−0.903024
$826$		0			0
$827$	33.0264	−	33.0264i	1.14844	−	1.14844i	0.161581	−	0.986859i	$-0.448341\pi$
$827$	33.0264	−	33.0264i	1.14844	−	1.14844i	0.986859	−	0.161581i	$-0.0516594\pi$
$828$		0			0
$829$	−36.2050	+	9.70111i	−1.25745	+	0.336934i	−0.825211	−	0.564824i	$-0.808944\pi$
$829$	−36.2050	+	9.70111i	−1.25745	+	0.336934i	−0.432242	+	0.901758i	$0.642277\pi$
$830$		0			0
$831$	−28.2798	−	48.9821i	−0.981015	−	1.69917i
$832$		0			0
$833$	−4.96118	−	37.5066i	−0.171895	−	1.29953i
$834$		0			0
$835$	−0.718460	+	2.68133i	−0.0248633	+	0.0927912i
$836$		0			0
$837$	−3.01235	+	0.807156i	−0.104122	+	0.0278994i
$838$		0			0
$839$		−	41.5802i		−	1.43551i	−0.696296	−	0.717754i	$-0.745170\pi$
$839$		−	41.5802i		−	1.43551i	0.696296	−	0.717754i	$-0.254830\pi$
$840$		0			0
$841$			26.4726i			0.912847i
$842$		0			0
$843$	−51.8636	+	13.8968i	−1.78628	+	0.478632i
$844$		0			0
$845$	3.35563	−	12.5234i	0.115437	−	0.430818i
$846$		0			0
$847$	18.4417	−	1.21440i	0.633665	−	0.0417272i
$848$		0			0
$849$	−27.5374	−	47.6961i	−0.945080	−	1.63693i
$850$		0			0
$851$	15.0436	−	4.03092i	0.515688	−	0.138178i
$852$		0			0
$853$	−3.78632	+	3.78632i	−0.129641	+	0.129641i	−0.768950	−	0.639309i	$-0.779221\pi$
$853$	−3.78632	+	3.78632i	−0.129641	+	0.129641i	0.639309	+	0.768950i	$0.279221\pi$
$854$		0			0
$855$	−3.98094			−0.136145
$856$		0			0
$857$	9.93943	−	17.2156i	0.339524	−	0.588073i	−0.644819	−	0.764335i	$-0.723067\pi$
$857$	9.93943	−	17.2156i	0.339524	−	0.588073i	0.984343	+	0.176262i	$0.0564006\pi$
$858$		0			0
$859$	−3.31449	+	12.3699i	−0.113089	+	0.422054i	−0.999137	−	0.0415399i	$-0.986774\pi$
$859$	−3.31449	+	12.3699i	−0.113089	+	0.422054i	0.886048	+	0.463594i	$0.153440\pi$
$860$		0			0
$861$	−4.52304	+	22.7753i	−0.154145	+	0.776179i
$862$		0			0
$863$	20.9940	−	12.1209i	0.714643	−	0.412599i	−0.0981346	−	0.995173i	$-0.531288\pi$
$863$	20.9940	−	12.1209i	0.714643	−	0.412599i	0.812778	+	0.582574i	$0.197954\pi$
$864$		0			0
$865$	−2.14258	+	3.71106i	−0.0728500	+	0.126180i
$866$		0			0
$867$	23.3732	−	23.3732i	0.793794	−	0.793794i
$868$		0			0
$869$	−1.75262	−	1.75262i	−0.0594534	−	0.0594534i
$870$		0			0
$871$	−22.0593	−	12.7359i	−0.747450	−	0.431541i
$872$		0			0
$873$	10.1623	+	17.6016i	0.343941	+	0.595723i
$874$		0			0
$875$	3.88485	+	11.4329i	0.131332	+	0.386503i
$876$		0			0
$877$	−20.9270	−	5.60738i	−0.706656	−	0.189348i	−0.112446	−	0.993658i	$-0.535868\pi$
$877$	−20.9270	−	5.60738i	−0.706656	−	0.189348i	−0.594210	+	0.804310i	$0.702535\pi$
$878$		0			0
$879$	22.3946	+	12.9295i	0.755349	+	0.436101i
$880$		0			0
$881$		−	15.3375i		−	0.516733i	−0.966047	−	0.258367i	$-0.916816\pi$
$881$		−	15.3375i		−	0.516733i	0.966047	−	0.258367i	$-0.0831842\pi$
$882$		0			0
$883$	35.7596	+	35.7596i	1.20341	+	1.20341i	0.973124	+	0.230282i	$0.0739648\pi$
$883$	35.7596	+	35.7596i	1.20341	+	1.20341i	0.230282	+	0.973124i	$0.426035\pi$
$884$		0			0
$885$	−2.80645	−	10.4738i	−0.0943378	−	0.352074i
$886$		0			0
$887$	−28.0000	+	16.1658i	−0.940148	+	0.542795i	−0.890007	−	0.455947i	$-0.849301\pi$
$887$	−28.0000	+	16.1658i	−0.940148	+	0.542795i	−0.0501414	+	0.998742i	$0.515967\pi$
$888$		0			0
$889$	10.9312	−	22.1835i	0.366622	−	0.744009i
$890$		0			0
$891$	−6.30459	−	1.68931i	−0.211212	−	0.0565940i
$892$		0			0
$893$	1.52364	+	5.68632i	0.0509868	+	0.190285i
$894$		0			0
$895$	−1.77504			−0.0593330
$896$		0			0
$897$	32.8900			1.09817
$898$		0			0
$899$	0.357216	+	1.33315i	0.0119138	+	0.0444629i
$900$		0			0
$901$	36.6430	+	9.81846i	1.22075	+	0.327100i
$902$		0			0
$903$	−35.7881	−	53.5252i	−1.19095	−	1.78121i
$904$		0			0
$905$	−2.93378	+	1.69382i	−0.0975220	+	0.0563044i
$906$		0			0
$907$	8.19408	+	30.5807i	0.272080	+	1.01542i	0.957773	+	0.287525i	$0.0928325\pi$
$907$	8.19408	+	30.5807i	0.272080	+	1.01542i	−0.685693	+	0.727891i	$0.740501\pi$
$908$		0			0
$909$	16.9654	+	16.9654i	0.562707	+	0.562707i
$910$		0			0
$911$		−	7.17911i		−	0.237854i	−0.992903	−	0.118927i	$-0.962054\pi$
$911$		−	7.17911i		−	0.237854i	0.992903	−	0.118927i	$-0.0379455\pi$
$912$		0			0
$913$	−22.1729	−	12.8015i	−0.733817	−	0.423669i
$914$		0			0
$915$	−0.593173	−	0.158940i	−0.0196097	−	0.00525441i
$916$		0			0
$917$	36.9142	+	32.3529i	1.21901	+	1.06839i
$918$		0			0
$919$	1.18242	+	2.04801i	0.0390044	+	0.0675576i	0.884869	−	0.465841i	$-0.154248\pi$
$919$	1.18242	+	2.04801i	0.0390044	+	0.0675576i	−0.845864	+	0.533398i	$0.820915\pi$
$920$		0			0
$921$	7.85475	+	4.53494i	0.258823	+	0.149431i
$922$		0			0
$923$	−55.0580	−	55.0580i	−1.81226	−	1.81226i
$924$		0			0
$925$	27.6828	−	27.6828i	0.910206	−	0.910206i
$926$		0			0
$927$	−2.39361	+	4.14585i	−0.0786164	+	0.136168i
$928$		0			0
$929$	−50.6476	+	29.2414i	−1.66169	+	0.959379i	−0.689787	+	0.724012i	$0.742296\pi$
$929$	−50.6476	+	29.2414i	−1.66169	+	0.959379i	−0.971906	+	0.235367i	$0.924371\pi$
$930$		0			0
$931$	−5.29023	−	12.7497i	−0.173380	−	0.417854i
$932$		0			0
$933$	10.6168	−	39.6224i	0.347578	−	1.29718i
$934$		0			0
$935$	−2.52615	+	4.37543i	−0.0826141	+	0.143092i
$936$		0			0
$937$	13.4613			0.439761			0.219881	−	0.975527i	$-0.429433\pi$
$937$	13.4613			0.439761			0.219881	+	0.975527i	$0.429433\pi$
$938$		0			0
$939$	12.7395	−	12.7395i	0.415738	−	0.415738i
$940$		0			0
$941$	14.9193	−	3.99761i	0.486355	−	0.130318i	−0.00730539	−	0.999973i	$-0.502325\pi$
$941$	14.9193	−	3.99761i	0.486355	−	0.130318i	0.493660	+	0.869655i	$0.335659\pi$
$942$		0			0
$943$	3.08419	+	5.34197i	0.100435	+	0.173959i
$944$		0			0
$945$	−0.291359	−	4.42454i	−0.00947790	−	0.143930i
$946$		0			0
$947$	8.08357	−	30.1683i	0.262681	−	0.980338i	−0.700974	−	0.713187i	$-0.747251\pi$
$947$	8.08357	−	30.1683i	0.262681	−	0.980338i	0.963655	−	0.267151i	$-0.0860823\pi$
$948$		0			0
$949$	−96.1276	+	25.7573i	−3.12043	+	0.836118i
$950$		0			0
$951$		−	71.7697i		−	2.32729i
$952$		0			0
$953$		−	15.7802i		−	0.511170i	−0.966787	−	0.255585i	$-0.917732\pi$
$953$		−	15.7802i		−	0.511170i	0.966787	−	0.255585i	$-0.0822680\pi$
$954$		0			0
$955$	7.93032	−	2.12492i	0.256619	−	0.0687609i
$956$		0			0
$957$	2.23163	−	8.32855i	0.0721383	−	0.269224i
$958$		0			0
$959$	−22.3366	−	33.4070i	−0.721287	−	1.07877i
$960$		0			0
$961$	15.1232	+	26.1941i	0.487844	+	0.844970i
$962$		0			0
$963$	−25.8415	+	6.92420i	−0.832729	+	0.223129i
$964$		0			0
$965$	−2.17051	+	2.17051i	−0.0698712	+	0.0698712i
$966$		0			0
$967$	44.7046			1.43760			0.718801	−	0.695216i	$-0.244691\pi$
$967$	44.7046			1.43760			0.718801	+	0.695216i	$0.244691\pi$
$968$		0			0
$969$	14.4248	−	24.9844i	0.463390	−	0.802615i
$970$		0			0
$971$	15.0660	−	56.2271i	0.483491	−	1.80441i	−0.103269	−	0.994653i	$-0.532930\pi$
$971$	15.0660	−	56.2271i	0.483491	−	1.80441i	0.586761	−	0.809761i	$-0.300403\pi$
$972$		0			0
$973$	−1.36166	−	4.00728i	−0.0436527	−	0.128468i
$974$		0			0
$975$	71.5999	−	41.3382i	2.29303	−	1.32388i
$976$		0			0
$977$	10.4344	−	18.0729i	0.333827	−	0.578204i	−0.649432	−	0.760420i	$-0.724993\pi$
$977$	10.4344	−	18.0729i	0.333827	−	0.578204i	0.983259	+	0.182215i	$0.0583267\pi$
$978$		0			0
$979$	−3.29726	+	3.29726i	−0.105381	+	0.105381i
$980$		0			0
$981$	33.3351	+	33.3351i	1.06431	+	1.06431i
$982$		0			0
$983$	−36.5230	−	21.0866i	−1.16490	−	0.672558i	−0.212430	−	0.977176i	$-0.568138\pi$
$983$	−36.5230	−	21.0866i	−1.16490	−	0.672558i	−0.952474	+	0.304619i	$0.901471\pi$
$984$		0			0
$985$	4.90806	+	8.50102i	0.156384	+	0.270865i
$986$		0			0
$987$	−20.2432	+	6.87853i	−0.644347	+	0.218946i
$988$		0			0
$989$	−16.5216	−	4.42695i	−0.525356	−	0.140769i
$990$		0			0
$991$	−14.7987	−	8.54402i	−0.470095	−	0.271410i	0.246184	−	0.969223i	$-0.420823\pi$
$991$	−14.7987	−	8.54402i	−0.470095	−	0.271410i	−0.716280	+	0.697813i	$0.754156\pi$
$992$		0			0
$993$			25.6788i			0.814891i
$994$		0			0
$995$	2.45062	+	2.45062i	0.0776898	+	0.0776898i
$996$		0			0
$997$	7.35325	+	27.4427i	0.232880	+	0.869119i	0.979093	+	0.203412i	$0.0652031\pi$
$997$	7.35325	+	27.4427i	0.232880	+	0.869119i	−0.746214	+	0.665707i	$0.768130\pi$
$998$		0			0
$999$	−25.4673	+	14.7035i	−0.805749	+	0.465199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.z.a.31.2		56
4.3	odd	2		896.2.z.b.31.13		56
7.5	odd	6	inner	896.2.z.a.159.2		56
8.3	odd	2		112.2.v.a.59.13	yes	56
8.5	even	2		448.2.z.a.143.13		56
16.3	odd	4	inner	896.2.z.a.479.2		56
16.5	even	4		112.2.v.a.3.7	✓	56
16.11	odd	4		448.2.z.a.367.13		56
16.13	even	4		896.2.z.b.479.13		56
28.19	even	6		896.2.z.b.159.13		56
56.3	even	6		784.2.j.a.587.8		56
56.5	odd	6		448.2.z.a.271.13		56
56.11	odd	6		784.2.j.a.587.7		56
56.19	even	6		112.2.v.a.75.7	yes	56
56.27	even	2		784.2.w.f.619.13		56
56.51	odd	6		784.2.w.f.411.7		56
112.5	odd	12		112.2.v.a.19.13	yes	56
112.19	even	12	inner	896.2.z.a.607.2		56
112.37	even	12		784.2.w.f.19.13		56
112.53	even	12		784.2.j.a.195.8		56
112.61	odd	12		896.2.z.b.607.13		56
112.69	odd	4		784.2.w.f.227.7		56
112.75	even	12		448.2.z.a.47.13		56
112.101	odd	12		784.2.j.a.195.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.7	✓	56	16.5	even	4
112.2.v.a.19.13	yes	56	112.5	odd	12
112.2.v.a.59.13	yes	56	8.3	odd	2
112.2.v.a.75.7	yes	56	56.19	even	6
448.2.z.a.47.13		56	112.75	even	12
448.2.z.a.143.13		56	8.5	even	2
448.2.z.a.271.13		56	56.5	odd	6
448.2.z.a.367.13		56	16.11	odd	4
784.2.j.a.195.7		56	112.101	odd	12
784.2.j.a.195.8		56	112.53	even	12
784.2.j.a.587.7		56	56.11	odd	6
784.2.j.a.587.8		56	56.3	even	6
784.2.w.f.19.13		56	112.37	even	12
784.2.w.f.227.7		56	112.69	odd	4
784.2.w.f.411.7		56	56.51	odd	6
784.2.w.f.619.13		56	56.27	even	2
896.2.z.a.31.2		56	1.1	even	1	trivial
896.2.z.a.159.2		56	7.5	odd	6	inner
896.2.z.a.479.2		56	16.3	odd	4	inner
896.2.z.a.607.2		56	112.19	even	12	inner
896.2.z.b.31.13		56	4.3	odd	2
896.2.z.b.159.13		56	28.19	even	6
896.2.z.b.479.13		56	16.13	even	4
896.2.z.b.607.13		56	112.61	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.700587 - 2.61463i) q^{3} +(-0.450647 - 0.120751i) q^{5} +(2.37326 + 1.16946i) q^{7} +(-3.74737 + 2.16355i) q^{9} +(0.518581 + 1.93537i) q^{11} +(-4.51607 - 4.51607i) q^{13} +1.26287i q^{15} +(-4.68066 - 2.70238i) q^{17} +(-1.90476 - 0.510379i) q^{19} +(1.39503 - 7.02450i) q^{21} +(-0.951245 - 1.64761i) q^{23} +(-4.14162 - 2.39117i) q^{25} +(2.54010 + 2.54010i) q^{27} +(1.12415 - 1.12415i) q^{29} +(-0.434075 + 0.751840i) q^{31} +(4.69696 - 2.71179i) q^{33} +(-0.928290 - 0.813586i) q^{35} +(-2.11876 + 7.90732i) q^{37} +(-8.64394 + 14.9717i) q^{39} -3.24226 q^{41} +(6.35727 - 6.35727i) q^{43} +(1.94999 - 0.522499i) q^{45} +(-1.49266 - 2.58536i) q^{47} +(4.26473 + 5.55087i) q^{49} +(-3.78650 + 14.1314i) q^{51} +(-6.77976 + 1.81663i) q^{53} -0.934789i q^{55} +5.33780i q^{57} +(-8.29366 + 2.22228i) q^{59} +(-0.125856 + 0.469703i) q^{61} +(-11.4237 + 0.752254i) q^{63} +(1.48984 + 2.58047i) q^{65} +(3.85238 - 1.03224i) q^{67} +(-3.64144 + 3.64144i) q^{69} +12.1916 q^{71} +(7.79109 - 13.4946i) q^{73} +(-3.35044 + 12.5040i) q^{75} +(-1.03261 + 5.19960i) q^{77} +(-1.07130 + 0.618516i) q^{79} +(-1.62878 + 2.82113i) q^{81} +(-9.03560 + 9.03560i) q^{83} +(1.78301 + 1.78301i) q^{85} +(-3.72680 - 2.15167i) q^{87} +(1.16364 + 2.01548i) q^{89} +(-5.43644 - 15.9992i) q^{91} +(2.26989 + 0.608215i) q^{93} +(0.796746 + 0.460002i) q^{95} -4.69704i q^{97} +(-6.13058 - 6.13058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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