LMFDB - Embedded newform 448.2.z.a.47.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(47,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("448.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.z (of order $12$, 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:	$3.57729801055$
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			47.13
Character	$\chi$	$=$	448.47
Dual form			448.2.z.a.143.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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	−0.400521	−	0.916287i	$-0.631171\pi$
$3$	0.700587	−	2.61463i	0.404484	−	1.50955i	0.805005	−	0.593268i	$-0.202162\pi$
$4$		0			0
$5$	0.450647	−	0.120751i	0.201536	−	0.0540013i	−0.156639	−	0.987656i	$-0.550066\pi$
$5$	0.450647	−	0.120751i	0.201536	−	0.0540013i	0.358175	+	0.933655i	$0.383399\pi$
$6$		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	0.842627	+	0.538497i	$0.181008\pi$
$11$	−0.518581	+	1.93537i	−0.156358	+	0.583536i	−0.998985	+	0.0450390i	$0.985659\pi$
$12$		0			0
$13$	4.51607	−	4.51607i	1.25253	−	1.25253i	0.297952	−	0.954581i	$-0.403696\pi$
$13$	4.51607	−	4.51607i	1.25253	−	1.25253i	0.954581	−	0.297952i	$-0.0963035\pi$
$14$		0			0
$15$		−	1.26287i		−	0.326072i
$16$		0			0
$17$	−4.68066	+	2.70238i	−1.13523	+	0.655424i	−0.945244	−	0.326364i	$-0.894177\pi$
$17$	−4.68066	+	2.70238i	−1.13523	+	0.655424i	−0.189983	+	0.981787i	$0.560843\pi$
$18$		0			0
$19$	1.90476	−	0.510379i	0.436982	−	0.117089i	−0.0336198	−	0.999435i	$-0.510704\pi$
$19$	1.90476	−	0.510379i	0.436982	−	0.117089i	0.470602	+	0.882346i	$0.344037\pi$
$20$		0			0
$21$	−1.39503	−	7.02450i	−0.304420	−	1.53287i
$22$		0			0
$23$	−0.951245	+	1.64761i	−0.198348	+	0.343549i	−0.947993	−	0.318291i	$-0.896891\pi$
$23$	−0.951245	+	1.64761i	−0.198348	+	0.343549i	0.749645	+	0.661841i	$0.230224\pi$
$24$		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	$-0.297157\pi$
$29$	−1.12415	−	1.12415i	−0.208749	−	0.208749i	−0.803736	+	0.594986i	$0.797157\pi$
$30$		0			0
$31$	−0.434075	−	0.751840i	−0.0779622	−	0.135035i	0.824408	−	0.565995i	$-0.191508\pi$
$31$	−0.434075	−	0.751840i	−0.0779622	−	0.135035i	−0.902371	+	0.430961i	$0.858175\pi$
$32$		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	0.888683	+	0.458522i	$0.151621\pi$
$37$	2.11876	+	7.90732i	0.348322	+	1.29996i	−0.540361	+	0.841433i	$0.681712\pi$
$38$		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	$-0.490426\pi$
$43$	−6.35727	−	6.35727i	−0.969475	−	0.969475i	−0.999548	+	0.0300731i	$0.990426\pi$
$44$		0			0
$45$	−1.94999	−	0.522499i	−0.290688	−	0.0778895i
$46$		0			0
$47$	−1.49266	+	2.58536i	−0.217727	+	0.377114i	−0.954113	−	0.299448i	$-0.903198\pi$
$47$	−1.49266	+	2.58536i	−0.217727	+	0.377114i	0.736386	+	0.676562i	$0.236531\pi$
$48$		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	$-0.256555\pi$
$53$	6.77976	+	1.81663i	0.931272	+	0.249533i	0.238875	+	0.971050i	$0.423221\pi$
$54$		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	$-0.227884\pi$
$59$	8.29366	+	2.22228i	1.07974	+	0.289316i	0.325253	+	0.945627i	$0.394551\pi$
$60$		0			0
$61$	0.125856	+	0.469703i	0.0161143	+	0.0601393i	0.973515	−	0.228624i	$-0.0734226\pi$
$61$	0.125856	+	0.469703i	0.0161143	+	0.0601393i	−0.957401	+	0.288763i	$0.906756\pi$
$62$		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	$-0.495002\pi$
$67$	−3.85238	−	1.03224i	−0.470643	−	0.126108i	−0.486342	+	0.873768i	$0.661669\pi$
$68$		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	0.811408	+	0.584480i	$0.198701\pi$
$73$	7.79109	+	13.4946i	0.911878	+	1.57942i	0.100470	+	0.994940i	$0.467965\pi$
$74$		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	0.438522	−	0.898720i	$-0.355502\pi$
$79$	−1.07130	−	0.618516i	−0.120531	−	0.0695885i	−0.559053	+	0.829132i	$0.688835\pi$
$80$		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	$-0.00260402\pi$
$83$	9.03560	+	9.03560i	0.991786	+	0.991786i	−0.00818066	+	0.999967i	$0.502604\pi$
$84$		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	−0.797740	−	0.603002i	$-0.793971\pi$
$89$	1.16364	−	2.01548i	0.123345	−	0.213640i	0.921085	+	0.389362i	$0.127304\pi$
$90$		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	$0.0766414\pi$
$97$			4.69704i			0.476912i	−0.971153	+	0.238456i	$0.923359\pi$
$98$		0			0
$99$	6.13058	−	6.13058i	0.616146	−	0.616146i
$100$		0			0
$101$	1.43509	−	5.35584i	0.142797	−	0.532926i	−0.857047	−	0.515239i	$-0.827703\pi$
$101$	1.43509	−	5.35584i	0.142797	−	0.532926i	0.999844	−	0.0176866i	$-0.00563013\pi$
$102$		0			0
$103$	0.958115	+	0.553168i	0.0944059	+	0.0545053i	0.546460	−	0.837485i	$-0.315975\pi$
$103$	0.958115	+	0.553168i	0.0944059	+	0.0545053i	−0.452054	+	0.891991i	$0.649308\pi$
$104$		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	$-0.679937\pi$
$107$	−5.97202	+	1.60020i	−0.577337	+	0.154697i	−0.0416773	+	0.999131i	$0.513270\pi$
$108$		0			0
$109$	2.81979	−	10.5236i	0.270087	−	1.00798i	−0.688975	−	0.724785i	$-0.741939\pi$
$109$	2.81979	−	10.5236i	0.270087	−	1.00798i	0.959063	−	0.283194i	$-0.0913941\pi$
$110$		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	$0.136119\pi$
$127$			9.34725i			0.829434i	−0.909950	+	0.414717i	$0.863881\pi$
$128$		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	$-0.884121\pi$
$131$	−17.9203	+	4.80174i	−1.56571	+	0.419530i	−0.631242	+	0.775586i	$0.717455\pi$
$132$		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	−0.942376	−	0.334555i	$-0.891414\pi$
$137$	−13.1541	+	7.59453i	−1.12383	+	0.648844i	−0.181455	+	0.983399i	$0.558081\pi$
$138$		0			0
$139$	1.13113	−	1.13113i	0.0959413	−	0.0959413i	−0.657507	−	0.753448i	$-0.728389\pi$
$139$	1.13113	−	1.13113i	0.0959413	−	0.0959413i	0.753448	+	0.657507i	$0.228389\pi$
$140$		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	0.986016	+	0.166648i	$0.0532944\pi$
$149$	2.62960	+	9.81380i	0.215425	+	0.803978i	−0.770591	+	0.637330i	$0.780039\pi$
$150$		0			0
$151$	5.83900	+	10.1134i	0.475171	+	0.823020i	0.999596	−	0.0284368i	$-0.00905293\pi$
$151$	5.83900	+	10.1134i	0.475171	+	0.823020i	−0.524425	+	0.851457i	$0.675720\pi$
$152$		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	$-0.388340\pi$
$157$	2.15127	+	0.576431i	0.171690	+	0.0460042i	−0.171950	+	0.985106i	$0.555007\pi$
$158$		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	−0.939231	−	0.343286i	$-0.888460\pi$
$163$	−3.79792	−	14.1740i	−0.297476	−	1.11020i	0.641755	−	0.766910i	$-0.278207\pi$
$164$		0			0
$165$	2.44412	+	0.654901i	0.190275	+	0.0509839i
$166$		0			0
$167$			5.94995i			0.460421i	0.973141	+	0.230210i	$0.0739415\pi$
$167$			5.94995i			0.460421i	−0.973141	+	0.230210i	$0.926059\pi$
$168$		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	−0.995503	−	0.0947304i	$-0.969801\pi$
$173$	−2.37723	−	8.87194i	−0.180737	−	0.674521i	0.814766	−	0.579790i	$-0.196866\pi$
$174$		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	$-0.462080\pi$
$179$	−3.67501	−	0.984716i	−0.274683	−	0.0736011i	−0.393531	+	0.919311i	$0.628747\pi$
$180$		0			0
$181$	−5.13439	−	5.13439i	−0.381636	−	0.381636i	0.490055	−	0.871691i	$-0.336977\pi$
$181$	−5.13439	−	5.13439i	−0.381636	−	0.381636i	−0.871691	+	0.490055i	$0.836977\pi$
$182$		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	−0.165791	−	0.986161i	$-0.553018\pi$
$191$	−15.2400	−	8.79882i	−1.10273	−	0.636660i	−0.936936	+	0.349501i	$0.886351\pi$
$192$		0			0
$193$	3.28968	+	5.69790i	0.236797	+	0.410144i	0.959793	−	0.280708i	$-0.0905692\pi$
$193$	3.28968	+	5.69790i	0.236797	+	0.410144i	−0.722997	+	0.690851i	$0.757236\pi$
$194$		0			0
$195$	−5.70321	−	5.70321i	−0.408415	−	0.408415i
$196$		0			0
$197$	14.8776	−	14.8776i	1.05998	−	1.05998i	0.0619015	−	0.998082i	$-0.480284\pi$
$197$	14.8776	−	14.8776i	1.05998	−	1.05998i	0.998082	−	0.0619015i	$-0.0197165\pi$
$198$		0			0
$199$	−6.43322	+	3.71422i	−0.456039	+	0.263294i	−0.710377	−	0.703821i	$-0.751476\pi$
$199$	−6.43322	+	3.71422i	−0.456039	+	0.263294i	0.254338	+	0.967115i	$0.418142\pi$
$200$		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	$-0.603622\pi$
$211$	9.11727	−	9.11727i	0.627659	−	0.627659i	0.947478	+	0.319820i	$0.103622\pi$
$212$		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	$-0.834106\pi$
$227$	2.00024	−	7.46500i	0.132761	−	0.495469i	0.999997	+	0.00242728i	$0.000772628\pi$
$228$		0			0
$229$	−14.7233	+	3.94509i	−0.972941	+	0.260699i	−0.710069	−	0.704132i	$-0.751336\pi$
$229$	−14.7233	+	3.94509i	−0.972941	+	0.260699i	−0.262872	+	0.964831i	$0.584670\pi$
$230$		0			0
$231$	14.3184	+	0.942877i	0.942084	+	0.0620367i
$232$		0			0
$233$	−12.7954	−	7.38741i	−0.838253	−	0.483965i	0.0184173	−	0.999830i	$-0.494137\pi$
$233$	−12.7954	−	7.38741i	−0.838253	−	0.483965i	−0.856670	+	0.515865i	$0.827471\pi$
$234$		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	$-0.625453\pi$
$239$		−	28.5488i		−	1.84667i	0.383998	−	0.923334i	$-0.374547\pi$
$240$		0			0
$241$	19.8792	−	11.4772i	1.28053	−	0.739314i	0.303584	−	0.952805i	$-0.401817\pi$
$241$	19.8792	−	11.4772i	1.28053	−	0.739314i	0.976945	+	0.213491i	$0.0684834\pi$
$242$		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	$-0.901740\pi$
$251$	−10.2808	+	10.2808i	−0.648918	+	0.648918i	0.303813	+	0.952732i	$0.401740\pi$
$252$		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	0.566393	−	0.824135i	$-0.308338\pi$
$257$	2.17812	+	1.25754i	0.135867	+	0.0784431i	−0.430526	+	0.902578i	$0.641672\pi$
$258$		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	0.971491	−	0.237078i	$-0.0761897\pi$
$263$	4.54781	+	7.87703i	0.280430	+	0.485718i	−0.691061	+	0.722797i	$0.742856\pi$
$264$		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	$-0.361065\pi$
$269$	5.50656	+	1.47548i	0.335741	+	0.0899615i	−0.0870099	+	0.996207i	$0.527731\pi$
$270$		0			0
$271$	−5.76007	+	9.97673i	−0.349899	+	0.606043i	−0.986231	−	0.165372i	$-0.947118\pi$
$271$	−5.76007	+	9.97673i	−0.349899	+	0.606043i	0.636332	+	0.771415i	$0.280451\pi$
$272$		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	$-0.632681\pi$
$277$	−20.1829	−	5.40800i	−1.21268	−	0.324935i	−0.807811	+	0.589442i	$0.799348\pi$
$278$		0			0
$279$			3.75657i			0.224900i
$280$		0			0
$281$			19.8360i			1.18331i	0.806190	+	0.591657i	$0.201526\pi$
$281$			19.8360i			1.18331i	−0.806190	+	0.591657i	$0.798474\pi$
$282$		0			0
$283$	−19.6531	−	5.26602i	−1.16825	−	0.313033i	−0.377996	−	0.925807i	$-0.623387\pi$
$283$	−19.6531	−	5.26602i	−1.16825	−	0.313033i	−0.790258	+	0.612775i	$0.790053\pi$
$284$		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	$-0.159980\pi$
$293$	6.75509	+	6.75509i	0.394636	+	0.394636i	−0.481700	+	0.876336i	$0.659980\pi$
$294$		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	$-0.219517\pi$
$307$	2.36930	+	2.36930i	0.135223	+	0.135223i	−0.636255	+	0.771479i	$0.719517\pi$
$308$		0			0
$309$	2.11757	−	2.11757i	0.120464	−	0.120464i
$310$		0			0
$311$	13.1239	−	7.57707i	0.744186	−	0.429656i	−0.0794032	−	0.996843i	$-0.525301\pi$
$311$	13.1239	−	7.57707i	0.744186	−	0.429656i	0.823589	+	0.567186i	$0.191968\pi$
$312$		0			0
$313$	3.32791	−	5.76411i	0.188105	−	0.325807i	−0.756514	−	0.653978i	$-0.773099\pi$
$313$	3.32791	−	5.76411i	0.188105	−	0.325807i	0.944618	+	0.328171i	$0.106432\pi$
$314$		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	$-0.850687\pi$
$317$	−25.6106	+	6.86233i	−1.43843	+	0.385427i	−0.546449	+	0.837493i	$0.684021\pi$
$318$		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	$-0.499375\pi$
$331$	9.16331	−	2.45530i	0.503661	−	0.134956i	0.501699	+	0.865043i	$0.332709\pi$
$332$		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	$-0.943822\pi$
$347$	−0.821629	+	3.06636i	−0.0441074	+	0.164611i	0.940359	+	0.340183i	$0.110489\pi$
$348$		0			0
$349$	2.21348	−	2.21348i	0.118485	−	0.118485i	−0.645378	−	0.763863i	$-0.723300\pi$
$349$	2.21348	−	2.21348i	0.118485	−	0.118485i	0.763863	+	0.645378i	$0.223300\pi$
$350$		0			0
$351$			22.9426i			1.22458i
$352$		0			0
$353$	−7.11770	+	4.10941i	−0.378837	+	0.218722i	−0.677312	−	0.735696i	$-0.736855\pi$
$353$	−7.11770	+	4.10941i	−0.378837	+	0.218722i	0.298475	+	0.954417i	$0.403522\pi$
$354$		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	0.104245	+	0.994552i	$0.466757\pi$
$359$	−15.3319	+	26.5556i	−0.809184	+	1.40155i	−0.913430	+	0.406997i	$0.866576\pi$
$360$		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	0.999210	−	0.0397435i	$-0.0126541\pi$
$367$	8.91168	+	15.4355i	0.465186	+	0.805726i	−0.534024	+	0.845469i	$0.679321\pi$
$368$		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	$-0.103818\pi$
$373$	−0.642914	−	2.39939i	−0.0332888	−	0.124236i	−0.980571	+	0.196166i	$0.937151\pi$
$374$		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	$-0.243917\pi$
$379$	0.526070	+	0.526070i	0.0270224	+	0.0270224i	−0.693466	+	0.720489i	$0.743917\pi$
$380$		0			0
$381$	24.4396	+	6.54856i	1.25208	+	0.335493i
$382$		0			0
$383$	11.8928	−	20.5989i	0.607692	−	1.05255i	−0.383928	−	0.923363i	$-0.625429\pi$
$383$	11.8928	−	20.5989i	0.607692	−	1.05255i	0.991620	−	0.129190i	$-0.0412377\pi$
$384$		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	$-0.627364\pi$
$389$	−23.4190	−	6.27509i	−1.18739	−	0.318160i	−0.797853	+	0.602852i	$0.794031\pi$
$390$		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	$-0.0495585\pi$
$397$	1.09232	+	4.07659i	0.0548219	+	0.204598i	−0.933082	+	0.359662i	$0.882892\pi$
$398$		0			0
$399$	−6.24235	−	12.6680i	−0.312508	−	0.634193i
$400$		0			0
$401$	−9.01163	+	15.6086i	−0.450019	+	0.779456i	−0.998387	−	0.0567812i	$-0.981916\pi$
$401$	−9.01163	+	15.6086i	−0.450019	+	0.779456i	0.548367	+	0.836238i	$0.315250\pi$
$402$		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	−0.971354	−	0.237639i	$-0.923626\pi$
$409$	−13.9843	−	24.2215i	−0.691478	−	1.19768i	0.279875	−	0.960036i	$-0.409707\pi$
$410$		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	$-0.367760\pi$
$419$	−10.4669	−	10.4669i	−0.511342	−	0.511342i	−0.914937	+	0.403596i	$0.867760\pi$
$420$		0			0
$421$	12.3722	−	12.3722i	0.602984	−	0.602984i	−0.338119	−	0.941103i	$-0.609791\pi$
$421$	12.3722	−	12.3722i	0.602984	−	0.602984i	0.941103	+	0.338119i	$0.109791\pi$
$422$		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	−0.756675	−	0.653791i	$-0.773178\pi$
$431$	−11.8089	+	6.81786i	−0.568814	+	0.328405i	0.187862	+	0.982195i	$0.439844\pi$
$432$		0			0
$433$			19.1575i			0.920649i	0.887751	+	0.460325i	$0.152267\pi$
$433$			19.1575i			0.920649i	−0.887751	+	0.460325i	$0.847733\pi$
$434$		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	0.312265	−	0.949995i	$-0.398912\pi$
$439$	−7.42387	−	4.28617i	−0.354322	−	0.204568i	−0.666587	+	0.745427i	$0.732246\pi$
$440$		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	$-0.749102\pi$
$443$	−20.2310	+	5.42088i	−0.961204	+	0.257554i	−0.256094	+	0.966652i	$0.582436\pi$
$444$		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	0.425056	−	0.905167i	$-0.360254\pi$
$457$	−3.12783	−	1.80585i	−0.146314	−	0.0844743i	−0.571370	+	0.820693i	$0.693588\pi$
$458$		0			0
$459$	5.02503	−	18.7537i	0.234548	−	0.875347i
$460$		0			0
$461$	25.2872	−	25.2872i	1.17774	−	1.17774i	0.197423	−	0.980318i	$-0.436743\pi$
$461$	25.2872	−	25.2872i	1.17774	−	1.17774i	0.980318	−	0.197423i	$-0.0632574\pi$
$462$		0			0
$463$			8.01165i			0.372333i	0.982518	+	0.186166i	$0.0596064\pi$
$463$			8.01165i			0.372333i	−0.982518	+	0.186166i	$0.940394\pi$
$464$		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	$-0.442280\pi$
$467$	17.9002	−	4.79633i	0.828321	−	0.221948i	0.647981	+	0.761657i	$0.275614\pi$
$468$		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	0.988457	+	0.151501i	$0.0484106\pi$
$479$	13.6882	+	23.7087i	0.625432	+	1.08328i	−0.363025	+	0.931779i	$0.618256\pi$
$480$		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	0.997585	−	0.0694492i	$-0.0221242\pi$
$487$	9.68012	+	16.7665i	0.438648	+	0.759761i	−0.558938	+	0.829210i	$0.688791\pi$
$488$		0			0
$489$	−39.7206			−1.79623
$490$		0			0
$491$	17.1950	+	17.1950i	0.775998	+	0.775998i	0.979148	−	0.203149i	$-0.0651177\pi$
$491$	17.1950	+	17.1950i	0.775998	+	0.775998i	−0.203149	+	0.979148i	$0.565118\pi$
$492$		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	$-0.0617429\pi$
$499$	0.783708	+	2.92484i	0.0350836	+	0.130934i	−0.946163	+	0.323691i	$0.895076\pi$
$500$		0			0
$501$	15.5569	+	4.16846i	0.695031	+	0.186233i
$502$		0			0
$503$		−	34.5673i		−	1.54128i	−0.637272	−	0.770639i	$-0.719937\pi$
$503$		−	34.5673i		−	1.54128i	0.637272	−	0.770639i	$-0.280063\pi$
$504$		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	−0.995473	−	0.0950424i	$-0.969701\pi$
$509$	−4.08105	−	15.2307i	−0.180889	−	0.675088i	0.814584	−	0.580046i	$-0.196965\pi$
$510$		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	0.984106	−	0.177584i	$-0.0568281\pi$
$521$	7.72095	+	13.3731i	0.338261	+	0.585885i	−0.645845	+	0.763469i	$0.723495\pi$
$522$		0			0
$523$	−0.527773	−	1.96968i	−0.0230779	−	0.0861280i	0.953426	−	0.301626i	$-0.0975293\pi$
$523$	−0.527773	−	1.96968i	−0.0230779	−	0.0861280i	−0.976504	+	0.215498i	$0.930863\pi$
$524$		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	$-0.731606\pi$
$541$	−20.1819	+	5.40772i	−0.867686	+	0.232496i	−0.202599	+	0.979262i	$0.564939\pi$
$542$		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	$-0.879283\pi$
$547$	−13.0675	+	13.0675i	−0.558728	+	0.558728i	0.370217	+	0.928945i	$0.379283\pi$
$548$		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	$-0.834121\pi$
$557$	3.13271	−	11.6914i	0.132737	−	0.495381i	0.999997	+	0.00247440i	$0.000787626\pi$
$558$		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	0.623821	+	0.781567i	$0.285579\pi$
$563$	−7.28930	+	27.2040i	−0.307207	+	1.14651i	−0.931029	+	0.364946i	$0.881087\pi$
$564$		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	0.862797	−	0.505551i	$-0.168711\pi$
$569$	20.4277	+	11.7940i	0.856375	+	0.494428i	−0.00642167	+	0.999979i	$0.502044\pi$
$570$		0			0
$571$	5.83253	−	21.7673i	0.244084	−	0.910933i	−0.729758	−	0.683705i	$-0.760367\pi$
$571$	5.83253	−	21.7673i	0.244084	−	0.910933i	0.973842	−	0.227227i	$-0.0729660\pi$
$572$		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	−0.799151	−	0.601130i	$-0.794717\pi$
$577$	−16.2893	+	9.40463i	−0.678132	+	0.391520i	0.121019	+	0.992650i	$0.461384\pi$
$578$		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	$-0.629948\pi$
$587$	12.6185	−	12.6185i	0.520820	−	0.520820i	0.917819	+	0.396999i	$0.129948\pi$
$588$		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	−0.0258409	−	0.999666i	$-0.508226\pi$
$593$	−22.0260	−	12.7167i	−0.904498	−	0.522212i	−0.878657	+	0.477454i	$0.841560\pi$
$594$		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	−0.869864	−	0.493292i	$-0.835793\pi$
$599$	−21.1003	−	36.5468i	−0.862135	−	1.49326i	0.00772853	−	0.999970i	$-0.497540\pi$
$600$		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	−0.396018	−	0.918243i	$-0.629608\pi$
$607$	14.7137	−	25.4850i	0.597212	−	1.03440i	0.993231	−	0.116160i	$-0.0370584\pi$
$608$		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	$-0.570215\pi$
$613$	−22.1882	−	5.94532i	−0.896175	−	0.240129i	−0.677373	+	0.735640i	$0.736882\pi$
$614$		0			0
$615$			4.09456i			0.165108i
$616$		0			0
$617$		−	31.2064i		−	1.25632i	−0.778084	−	0.628161i	$-0.783808\pi$
$617$		−	31.2064i		−	1.25632i	0.778084	−	0.628161i	$-0.216192\pi$
$618$		0			0
$619$	17.7087	+	4.74503i	0.711772	+	0.190719i	0.596498	−	0.802615i	$-0.296559\pi$
$619$	17.7087	+	4.74503i	0.711772	+	0.190719i	0.115275	+	0.993334i	$0.463225\pi$
$620$		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	−0.997928	−	0.0643416i	$-0.979505\pi$
$641$	−14.0435	−	24.3241i	−0.554685	−	0.960743i	0.443242	−	0.896402i	$-0.353828\pi$
$642$		0			0
$643$	21.6759	+	21.6759i	0.854812	+	0.854812i	0.990721	−	0.135909i	$-0.0433955\pi$
$643$	21.6759	+	21.6759i	0.854812	+	0.854812i	−0.135909	+	0.990721i	$0.543395\pi$
$644$		0			0
$645$	−8.02841	+	8.02841i	−0.316118	+	0.316118i
$646$		0			0
$647$	39.8543	−	23.0099i	1.56683	−	0.904612i	0.570299	−	0.821437i	$-0.306827\pi$
$647$	39.8543	−	23.0099i	1.56683	−	0.904612i	0.996535	−	0.0831749i	$-0.0265060\pi$
$648$		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	$-0.785271\pi$
$653$	−29.2593	+	7.84001i	−1.14501	+	0.306803i	−0.364043	+	0.931382i	$0.618604\pi$
$654$		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	$-0.683887\pi$
$659$	7.48634	−	7.48634i	0.291626	−	0.291626i	0.837723	+	0.546096i	$0.183887\pi$
$660$		0			0
$661$	2.73446	−	10.2052i	0.106358	−	0.396934i	−0.892137	−	0.451764i	$-0.850795\pi$
$661$	2.73446	−	10.2052i	0.106358	−	0.396934i	0.998496	+	0.0548296i	$0.0174616\pi$
$662$		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	$-0.457590\pi$
$677$	19.3441	−	5.18323i	0.743453	−	0.199208i	0.610612	+	0.791930i	$0.290923\pi$
$678$		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	$-0.922534\pi$
$683$	−0.249364	+	0.930638i	−0.00954164	+	0.0356099i	0.960991	+	0.276580i	$0.0892011\pi$
$684$		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	$-0.353986\pi$
$691$	33.5048	−	8.97758i	1.27458	−	0.341523i	0.831784	+	0.555099i	$0.187320\pi$
$692$		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	0.964947	+	0.262444i	$0.0845286\pi$
$701$	32.4969	+	32.4969i	1.22739	+	1.22739i	0.262444	+	0.964947i	$0.415471\pi$
$702$		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	$-0.111492\pi$
$709$	−1.21770	−	4.54454i	−0.0457319	−	0.170674i	−0.985015	+	0.172470i	$0.944825\pi$
$710$		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	−0.639603	−	0.768706i	$-0.720901\pi$
$719$	9.27548	−	16.0656i	0.345917	−	0.599146i	0.985520	+	0.169559i	$0.0542345\pi$
$720$		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	$-0.964711\pi$
$727$		−	5.96613i		−	0.221272i	0.993861	−	0.110636i	$-0.0352887\pi$
$728$		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	0.988955	+	0.148218i	$0.0473536\pi$
$733$	5.59358	+	20.8755i	0.206604	+	0.771055i	−0.782351	+	0.622838i	$0.785980\pi$
$734$		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	$-0.648697\pi$
$739$	−34.9804	−	9.37297i	−1.28677	−	0.344790i	−0.836434	+	0.548067i	$0.815364\pi$
$740$		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	0.760504	−	0.649334i	$-0.224952\pi$
$751$	15.8511	+	9.15166i	0.578416	+	0.333949i	−0.182087	+	0.983282i	$0.558285\pi$
$752$		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	$-0.891151\pi$
$757$	−16.6944	+	16.6944i	−0.606767	+	0.606767i	0.335333	+	0.942100i	$0.391151\pi$
$758$		0			0
$759$	−8.93593	+	5.15916i	−0.324354	+	0.187266i
$760$		0			0
$761$	4.43390	−	7.67974i	0.160729	−	0.278390i	−0.774401	−	0.632695i	$-0.781949\pi$
$761$	4.43390	−	7.67974i	0.160729	−	0.278390i	0.935130	+	0.354304i	$0.115282\pi$
$762$		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	$0.00656298\pi$
$769$			1.14344i			0.0412335i	−0.999787	+	0.0206167i	$0.993437\pi$
$770$		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	$-0.947836\pi$
$773$	−1.40701	+	5.25103i	−0.0506066	+	0.188866i	0.935995	+	0.352012i	$0.114503\pi$
$774$		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	−0.167221	−	0.985919i	$-0.553479\pi$
$787$	13.2008	−	49.2659i	0.470556	−	1.75614i	0.637778	−	0.770220i	$-0.279854\pi$
$788$		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	$-0.518504\pi$
$797$	26.5433	−	26.5433i	0.940211	−	0.940211i	0.998311	+	0.0581002i	$0.0185043\pi$
$798$		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	−0.156869	−	0.987619i	$-0.550140\pi$
$809$	17.6346	−	10.1813i	0.620000	−	0.357957i	0.776869	+	0.629662i	$0.216807\pi$
$810$		0			0
$811$	−31.8932	+	31.8932i	−1.11992	+	1.11992i	−0.128171	+	0.991752i	$0.540911\pi$
$811$	−31.8932	+	31.8932i	−1.11992	+	1.11992i	−0.991752	+	0.128171i	$0.959089\pi$
$812$		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	−0.983806	−	0.179234i	$-0.942638\pi$
$821$	−6.34443	−	23.6777i	−0.221422	−	0.826359i	0.762384	−	0.647125i	$-0.224029\pi$
$822$		0			0
$823$	5.16976	+	8.95429i	0.180207	+	0.312127i	0.941951	−	0.335751i	$-0.108990\pi$
$823$	5.16976	+	8.95429i	0.180207	+	0.312127i	−0.761744	+	0.647878i	$0.775657\pi$
$824$		0			0
$825$	−25.9374			−0.903024
$826$		0			0
$827$	−33.0264	−	33.0264i	−1.14844	−	1.14844i	−0.986859	−	0.161581i	$-0.948341\pi$
$827$	−33.0264	−	33.0264i	−1.14844	−	1.14844i	−0.161581	−	0.986859i	$-0.551659\pi$
$828$		0			0
$829$	36.2050	+	9.70111i	1.25745	+	0.336934i	0.825211	−	0.564824i	$-0.191056\pi$
$829$	36.2050	+	9.70111i	1.25745	+	0.336934i	0.432242	+	0.901758i	$0.357723\pi$
$830$		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	$0.254830\pi$
$839$			41.5802i			1.43551i	−0.696296	+	0.717754i	$0.745170\pi$
$840$		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	$-0.220779\pi$
$853$	3.78632	+	3.78632i	0.129641	+	0.129641i	−0.639309	+	0.768950i	$0.720779\pi$
$854$		0			0
$855$	−3.98094			−0.136145
$856$		0			0
$857$	9.93943	+	17.2156i	0.339524	+	0.588073i	0.984343	−	0.176262i	$-0.0564006\pi$
$857$	9.93943	+	17.2156i	0.339524	+	0.588073i	−0.644819	+	0.764335i	$0.723067\pi$
$858$		0			0
$859$	3.31449	+	12.3699i	0.113089	+	0.422054i	0.999137	−	0.0415399i	$-0.0132264\pi$
$859$	3.31449	+	12.3699i	0.113089	+	0.422054i	−0.886048	+	0.463594i	$0.846560\pi$
$860$		0			0
$861$	4.52304	+	22.7753i	0.154145	+	0.776179i
$862$		0			0
$863$	20.9940	+	12.1209i	0.714643	+	0.412599i	0.812778	−	0.582574i	$-0.197954\pi$
$863$	20.9940	+	12.1209i	0.714643	+	0.412599i	−0.0981346	+	0.995173i	$0.531288\pi$
$864$		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	$-0.464132\pi$
$877$	20.9270	−	5.60738i	0.706656	−	0.189348i	0.594210	+	0.804310i	$0.297465\pi$
$878$		0			0
$879$	22.3946	−	12.9295i	0.755349	−	0.436101i
$880$		0			0
$881$			15.3375i			0.516733i	0.966047	+	0.258367i	$0.0831842\pi$
$881$			15.3375i			0.516733i	−0.966047	+	0.258367i	$0.916816\pi$
$882$		0			0
$883$	−35.7596	+	35.7596i	−1.20341	+	1.20341i	−0.230282	+	0.973124i	$0.573965\pi$
$883$	−35.7596	+	35.7596i	−1.20341	+	1.20341i	−0.973124	+	0.230282i	$0.926035\pi$
$884$		0			0
$885$	2.80645	−	10.4738i	0.0943378	−	0.352074i
$886$		0			0
$887$	−28.0000	−	16.1658i	−0.940148	−	0.542795i	−0.0501414	−	0.998742i	$-0.515967\pi$
$887$	−28.0000	−	16.1658i	−0.940148	−	0.542795i	−0.890007	+	0.455947i	$0.849301\pi$
$888$		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	0.685693	+	0.727891i	$0.259499\pi$
$907$	−8.19408	+	30.5807i	−0.272080	+	1.01542i	−0.957773	+	0.287525i	$0.907168\pi$
$908$		0			0
$909$	−16.9654	+	16.9654i	−0.562707	+	0.562707i
$910$		0			0
$911$			7.17911i			0.237854i	0.992903	+	0.118927i	$0.0379455\pi$
$911$			7.17911i			0.237854i	−0.992903	+	0.118927i	$0.962054\pi$
$912$		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	−0.845864	−	0.533398i	$-0.820915\pi$
$919$	1.18242	−	2.04801i	0.0390044	−	0.0675576i	0.884869	+	0.465841i	$0.154248\pi$
$920$		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	−0.971906	−	0.235367i	$-0.924371\pi$
$929$	−50.6476	−	29.2414i	−1.66169	−	0.959379i	−0.689787	−	0.724012i	$-0.742296\pi$
$930$		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	$-0.497675\pi$
$941$	−14.9193	−	3.99761i	−0.486355	−	0.130318i	−0.493660	+	0.869655i	$0.664341\pi$
$942$		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	−0.963655	−	0.267151i	$-0.913918\pi$
$947$	−8.08357	−	30.1683i	−0.262681	−	0.980338i	0.700974	−	0.713187i	$-0.252749\pi$
$948$		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	$0.0822680\pi$
$953$			15.7802i			0.511170i	−0.966787	+	0.255585i	$0.917732\pi$
$954$		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	−0.586761	−	0.809761i	$-0.699597\pi$
$971$	−15.0660	−	56.2271i	−0.483491	−	1.80441i	0.103269	−	0.994653i	$-0.467070\pi$
$972$		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	0.983259	−	0.182215i	$-0.0583267\pi$
$977$	10.4344	+	18.0729i	0.333827	+	0.578204i	−0.649432	+	0.760420i	$0.724993\pi$
$978$		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	−0.952474	−	0.304619i	$-0.901471\pi$
$983$	−36.5230	+	21.0866i	−1.16490	+	0.672558i	−0.212430	+	0.977176i	$0.568138\pi$
$984$		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	−0.716280	−	0.697813i	$-0.754156\pi$
$991$	−14.7987	+	8.54402i	−0.470095	+	0.271410i	0.246184	+	0.969223i	$0.420823\pi$
$992$		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	0.746214	+	0.665707i	$0.231870\pi$
$997$	−7.35325	+	27.4427i	−0.232880	+	0.869119i	−0.979093	+	0.203412i	$0.934797\pi$
$998$		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	448.2.z.a.47.13		56
4.3	odd	2		112.2.v.a.19.13	yes	56
7.3	odd	6	inner	448.2.z.a.367.13		56
8.3	odd	2		896.2.z.b.607.13		56
8.5	even	2		896.2.z.a.607.2		56
16.3	odd	4		896.2.z.a.159.2		56
16.5	even	4		112.2.v.a.75.7	yes	56
16.11	odd	4	inner	448.2.z.a.271.13		56
16.13	even	4		896.2.z.b.159.13		56
28.3	even	6		112.2.v.a.3.7	✓	56
28.11	odd	6		784.2.w.f.227.7		56
28.19	even	6		784.2.j.a.195.8		56
28.23	odd	6		784.2.j.a.195.7		56
28.27	even	2		784.2.w.f.19.13		56
56.3	even	6		896.2.z.b.479.13		56
56.45	odd	6		896.2.z.a.479.2		56
112.3	even	12		896.2.z.a.31.2		56
112.5	odd	12		784.2.j.a.587.7		56
112.37	even	12		784.2.j.a.587.8		56
112.45	odd	12		896.2.z.b.31.13		56
112.53	even	12		784.2.w.f.619.13		56
112.59	even	12	inner	448.2.z.a.143.13		56
112.69	odd	4		784.2.w.f.411.7		56
112.101	odd	12		112.2.v.a.59.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.7	✓	56	28.3	even	6
112.2.v.a.19.13	yes	56	4.3	odd	2
112.2.v.a.59.13	yes	56	112.101	odd	12
112.2.v.a.75.7	yes	56	16.5	even	4
448.2.z.a.47.13		56	1.1	even	1	trivial
448.2.z.a.143.13		56	112.59	even	12	inner
448.2.z.a.271.13		56	16.11	odd	4	inner
448.2.z.a.367.13		56	7.3	odd	6	inner
784.2.j.a.195.7		56	28.23	odd	6
784.2.j.a.195.8		56	28.19	even	6
784.2.j.a.587.7		56	112.5	odd	12
784.2.j.a.587.8		56	112.37	even	12
784.2.w.f.19.13		56	28.27	even	2
784.2.w.f.227.7		56	28.11	odd	6
784.2.w.f.411.7		56	112.69	odd	4
784.2.w.f.619.13		56	112.53	even	12
896.2.z.a.31.2		56	112.3	even	12
896.2.z.a.159.2		56	16.3	odd	4
896.2.z.a.479.2		56	56.45	odd	6
896.2.z.a.607.2		56	8.5	even	2
896.2.z.b.31.13		56	112.45	odd	12
896.2.z.b.159.13		56	16.13	even	4
896.2.z.b.479.13		56	56.3	even	6
896.2.z.b.607.13		56	8.3	odd	2

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.z (of order \(12\), degree \(4\), not minimal)

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

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Representations

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Database

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