LMFDB - Embedded newform 368.2.m.e.257.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(49,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("368.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.m (of order $11$, degree $10$, 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			257.2
Character	$\chi$	$=$	368.257
Dual form			368.2.m.e.305.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.817468 + 0.240030i) q^{3} +(2.57662 + 1.65589i) q^{5} +(0.181823 + 1.26461i) q^{7} +(-1.91312 + 1.22949i) q^{9} +O(q^{10})$	\(q+(-0.817468 + 0.240030i) q^{3} +(2.57662 + 1.65589i) q^{5} +(0.181823 + 1.26461i) q^{7} +(-1.91312 + 1.22949i) q^{9} +(-0.0891963 + 0.195313i) q^{11} +(0.133237 - 0.926681i) q^{13} +(-2.50377 - 0.735173i) q^{15} +(1.65894 + 1.91452i) q^{17} +(-2.99577 + 3.45730i) q^{19} +(-0.452179 - 0.990134i) q^{21} +(3.67385 + 3.08267i) q^{23} +(1.81991 + 3.98505i) q^{25} +(2.94258 - 3.39592i) q^{27} +(-1.37099 - 1.58221i) q^{29} +(6.97977 + 2.04945i) q^{31} +(0.0260342 - 0.181072i) q^{33} +(-1.62557 + 3.55950i) q^{35} +(-8.67535 + 5.57531i) q^{37} +(0.113515 + 0.789513i) q^{39} +(4.48304 + 2.88108i) q^{41} +(9.26657 - 2.72091i) q^{43} -6.96529 q^{45} -5.35449 q^{47} +(5.15027 - 1.51226i) q^{49} +(-1.81567 - 1.16686i) q^{51} +(-2.04664 - 14.2347i) q^{53} +(-0.553242 + 0.355547i) q^{55} +(1.61909 - 3.54531i) q^{57} +(0.584927 - 4.06826i) q^{59} +(-6.83371 - 2.00656i) q^{61} +(-1.90267 - 2.19580i) q^{63} +(1.87778 - 2.16708i) q^{65} +(-1.66308 - 3.64163i) q^{67} +(-3.74319 - 1.63815i) q^{69} +(-2.94055 - 6.43891i) q^{71} +(2.53968 - 2.93095i) q^{73} +(-2.44425 - 2.82082i) q^{75} +(-0.263212 - 0.0772860i) q^{77} +(1.92588 - 13.3948i) q^{79} +(1.24378 - 2.72350i) q^{81} +(-8.81386 + 5.66433i) q^{83} +(1.10422 + 7.68000i) q^{85} +(1.50052 + 0.964324i) q^{87} +(4.62819 - 1.35896i) q^{89} +1.19611 q^{91} -6.19767 q^{93} +(-13.4439 + 3.94748i) q^{95} +(9.77480 + 6.28188i) q^{97} +(-0.0694913 - 0.483322i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9	$ 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41} + 47 q^{43} + 8 q^{45} + 72 q^{47} - 16 q^{49} + 7 q^{51} - 43 q^{53} + 9 q^{55} - 42 q^{57} + 11 q^{59} + 57 q^{61} + 62 q^{63} + 14 q^{65} + 27 q^{67} - 22 q^{69} - 48 q^{71} - 12 q^{73} - 87 q^{75} - 3 q^{77} - 8 q^{79} + 123 q^{81} + 18 q^{83} + 54 q^{85} - 137 q^{87} - 23 q^{89} - 142 q^{91} - 110 q^{93} - 119 q^{95} + 47 q^{97} + 17 q^{99}+O(q^{100}) $ 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.817468	+	0.240030i	−0.471965	+	0.138582i	−0.509061	−	0.860730i	$-0.670007\pi$
$3$	−0.817468	+	0.240030i	−0.471965	+	0.138582i	0.0370961	+	0.999312i	$0.488189\pi$
$4$		0			0
$5$	2.57662	+	1.65589i	1.15230	+	0.740538i	0.970096	−	0.242723i	$-0.0780406\pi$
$5$	2.57662	+	1.65589i	1.15230	+	0.740538i	0.182204	+	0.983261i	$0.441677\pi$
$6$		0			0
$7$	0.181823	+	1.26461i	0.0687227	+	0.477977i	0.994898	+	0.100884i	$0.0321672\pi$
$7$	0.181823	+	1.26461i	0.0687227	+	0.477977i	−0.926175	+	0.377093i	$0.876924\pi$
$8$		0			0
$9$	−1.91312	+	1.22949i	−0.637707	+	0.409829i
$10$		0			0
$11$	−0.0891963	+	0.195313i	−0.0268937	+	0.0588890i	−0.922602	−	0.385753i	$-0.873942\pi$
$11$	−0.0891963	+	0.195313i	−0.0268937	+	0.0588890i	0.895708	+	0.444642i	$0.146669\pi$
$12$		0			0
$13$	0.133237	−	0.926681i	0.0369532	−	0.257015i	−0.962967	−	0.269618i	$-0.913103\pi$
$13$	0.133237	−	0.926681i	0.0369532	−	0.257015i	0.999921	+	0.0126028i	$0.00401171\pi$
$14$		0			0
$15$	−2.50377	−	0.735173i	−0.646470	−	0.189821i
$16$		0			0
$17$	1.65894	+	1.91452i	0.402351	+	0.464338i	0.920380	−	0.391025i	$-0.127879\pi$
$17$	1.65894	+	1.91452i	0.402351	+	0.464338i	−0.518029	+	0.855363i	$0.673334\pi$
$18$		0			0
$19$	−2.99577	+	3.45730i	−0.687276	+	0.793159i	−0.986975	−	0.160875i	$-0.948568\pi$
$19$	−2.99577	+	3.45730i	−0.687276	+	0.793159i	0.299699	+	0.954034i	$0.403114\pi$
$20$		0			0
$21$	−0.452179	−	0.990134i	−0.0986736	−	0.216065i
$22$		0			0
$23$	3.67385	+	3.08267i	0.766050	+	0.642781i
$23$	3.67385	+	3.08267i	0.766050	+	0.642781i
$24$		0			0
$25$	1.81991	+	3.98505i	0.363982	+	0.797010i
$26$		0			0
$27$	2.94258	−	3.39592i	0.566301	−	0.653546i
$28$		0			0
$29$	−1.37099	−	1.58221i	−0.254586	−	0.293808i	0.614041	−	0.789274i	$-0.289543\pi$
$29$	−1.37099	−	1.58221i	−0.254586	−	0.293808i	−0.868627	+	0.495466i	$0.834997\pi$
$30$		0			0
$31$	6.97977	+	2.04945i	1.25360	+	0.368091i	0.840110	−	0.542416i	$-0.182490\pi$
$31$	6.97977	+	2.04945i	1.25360	+	0.368091i	0.413493	+	0.910507i	$0.364308\pi$
$32$		0			0
$33$	0.0260342	−	0.181072i	0.00453197	−	0.0315205i
$34$		0			0
$35$	−1.62557	+	3.55950i	−0.274771	+	0.601665i
$36$		0			0
$37$	−8.67535	+	5.57531i	−1.42622	+	0.916575i	−0.426291	+	0.904586i	$0.640180\pi$
$37$	−8.67535	+	5.57531i	−1.42622	+	0.916575i	−0.999928	+	0.0119889i	$0.996184\pi$
$38$		0			0
$39$	0.113515	+	0.789513i	0.0181769	+	0.126423i
$40$		0			0
$41$	4.48304	+	2.88108i	0.700133	+	0.449948i	0.841675	−	0.539984i	$-0.181570\pi$
$41$	4.48304	+	2.88108i	0.700133	+	0.449948i	−0.141542	+	0.989932i	$0.545206\pi$
$42$		0			0
$43$	9.26657	−	2.72091i	1.41314	−	0.414935i	0.515964	−	0.856610i	$-0.327434\pi$
$43$	9.26657	−	2.72091i	1.41314	−	0.414935i	0.897175	+	0.441675i	$0.145616\pi$
$44$		0			0
$45$	−6.96529			−1.03832
$46$		0			0
$47$	−5.35449			−0.781033			−0.390516	−	0.920596i	$-0.627703\pi$
$47$	−5.35449			−0.781033			−0.390516	+	0.920596i	$0.627703\pi$
$48$		0			0
$49$	5.15027	−	1.51226i	0.735754	−	0.216037i
$50$		0			0
$51$	−1.81567	−	1.16686i	−0.254245	−	0.163393i
$52$		0			0
$53$	−2.04664	−	14.2347i	−0.281128	−	1.95529i	−0.295345	−	0.955391i	$-0.595435\pi$
$53$	−2.04664	−	14.2347i	−0.281128	−	1.95529i	0.0142166	−	0.999899i	$-0.495475\pi$
$54$		0			0
$55$	−0.553242	+	0.355547i	−0.0745991	+	0.0479419i
$56$		0			0
$57$	1.61909	−	3.54531i	0.214453	−	0.469587i
$58$		0			0
$59$	0.584927	−	4.06826i	0.0761511	−	0.529642i	−0.915663	−	0.401948i	$-0.868333\pi$
$59$	0.584927	−	4.06826i	0.0761511	−	0.529642i	0.991814	−	0.127694i	$-0.0407576\pi$
$60$		0			0
$61$	−6.83371	−	2.00656i	−0.874967	−	0.256914i	−0.186741	−	0.982409i	$-0.559792\pi$
$61$	−6.83371	−	2.00656i	−0.874967	−	0.256914i	−0.688227	+	0.725496i	$0.741611\pi$
$62$		0			0
$63$	−1.90267	−	2.19580i	−0.239714	−	0.276645i
$64$		0			0
$65$	1.87778	−	2.16708i	0.232910	−	0.268793i
$66$		0			0
$67$	−1.66308	−	3.64163i	−0.203177	−	0.444896i	0.780425	−	0.625250i	$-0.215003\pi$
$67$	−1.66308	−	3.64163i	−0.203177	−	0.444896i	−0.983602	+	0.180354i	$0.942276\pi$
$68$		0			0
$69$	−3.74319	−	1.63815i	−0.450627	−	0.197210i
$70$		0			0
$71$	−2.94055	−	6.43891i	−0.348979	−	0.764158i	−0.999987	−	0.00508708i	$-0.998381\pi$
$71$	−2.94055	−	6.43891i	−0.348979	−	0.764158i	0.651008	−	0.759071i	$-0.274347\pi$
$72$		0			0
$73$	2.53968	−	2.93095i	0.297247	−	0.343042i	−0.587405	−	0.809293i	$-0.699850\pi$
$73$	2.53968	−	2.93095i	0.297247	−	0.343042i	0.884652	+	0.466251i	$0.154396\pi$
$74$		0			0
$75$	−2.44425	−	2.82082i	−0.282238	−	0.325720i
$76$		0			0
$77$	−0.263212	−	0.0772860i	−0.0299958	−	0.00880756i
$78$		0			0
$79$	1.92588	−	13.3948i	0.216678	−	1.50703i	−0.533504	−	0.845798i	$-0.679125\pi$
$79$	1.92588	−	13.3948i	0.216678	−	1.50703i	0.750182	−	0.661232i	$-0.229966\pi$
$80$		0			0
$81$	1.24378	−	2.72350i	0.138198	−	0.302611i
$82$		0			0
$83$	−8.81386	+	5.66433i	−0.967447	+	0.621741i	−0.926049	−	0.377402i	$-0.876817\pi$
$83$	−8.81386	+	5.66433i	−0.967447	+	0.621741i	−0.0413978	+	0.999143i	$0.513181\pi$
$84$		0			0
$85$	1.10422	+	7.68000i	0.119769	+	0.833013i
$86$		0			0
$87$	1.50052	+	0.964324i	0.160872	+	0.103386i
$88$		0			0
$89$	4.62819	−	1.35896i	0.490587	−	0.144049i	−0.0270770	−	0.999633i	$-0.508620\pi$
$89$	4.62819	−	1.35896i	0.490587	−	0.144049i	0.517664	+	0.855584i	$0.326802\pi$
$90$		0			0
$91$	1.19611			0.125387
$92$		0			0
$93$	−6.19767			−0.642668
$94$		0			0
$95$	−13.4439	+	3.94748i	−1.37931	+	0.405002i
$96$		0			0
$97$	9.77480	+	6.28188i	0.992481	+	0.637829i	0.932802	−	0.360389i	$-0.117356\pi$
$97$	9.77480	+	6.28188i	0.992481	+	0.637829i	0.0596787	+	0.998218i	$0.480992\pi$
$98$		0			0
$99$	−0.0694913	−	0.483322i	−0.00698414	−	0.0485757i
$100$		0			0
$101$	14.0411	−	9.02369i	1.39714	−	0.897890i	0.397340	−	0.917671i	$-0.369933\pi$
$101$	14.0411	−	9.02369i	1.39714	−	0.897890i	0.999804	+	0.0197809i	$0.00629688\pi$
$102$		0			0
$103$	−0.832916	+	1.82383i	−0.0820697	+	0.179708i	−0.946218	−	0.323530i	$-0.895130\pi$
$103$	−0.832916	+	1.82383i	−0.0820697	+	0.179708i	0.864148	+	0.503237i	$0.167858\pi$
$104$		0			0
$105$	0.474462	−	3.29996i	0.0463028	−	0.322043i
$106$		0			0
$107$	−3.16458	−	0.929204i	−0.305931	−	0.0898295i	0.125164	−	0.992136i	$-0.460054\pi$
$107$	−3.16458	−	0.929204i	−0.305931	−	0.0898295i	−0.431095	+	0.902307i	$0.641873\pi$
$108$		0			0
$109$	0.314835	+	0.363339i	0.0301557	+	0.0348016i	0.770627	−	0.637286i	$-0.219943\pi$
$109$	0.314835	+	0.363339i	0.0301557	+	0.0348016i	−0.740471	+	0.672088i	$0.765398\pi$
$110$		0			0
$111$	5.75358	−	6.63998i	0.546105	−	0.630239i
$112$		0			0
$113$	1.23410	+	2.70231i	0.116095	+	0.254212i	0.958755	−	0.284234i	$-0.0917391\pi$
$113$	1.23410	+	2.70231i	0.116095	+	0.254212i	−0.842660	+	0.538445i	$0.819012\pi$
$114$		0			0
$115$	4.36153	+	14.0264i	0.406715	+	1.30797i
$116$		0			0
$117$	0.884446	+	1.93667i	0.0817670	+	0.179045i
$118$		0			0
$119$	−2.11948	+	2.44601i	−0.194292	+	0.224225i
$120$		0			0
$121$	7.17328	+	8.27840i	0.652116	+	0.752582i
$122$		0			0
$123$	−4.35629	−	1.27912i	−0.392793	−	0.115334i
$124$		0			0
$125$	0.269836	−	1.87675i	0.0241349	−	0.167862i
$126$		0			0
$127$	−6.03876	+	13.2230i	−0.535853	+	1.17335i	0.427228	+	0.904144i	$0.359490\pi$
$127$	−6.03876	+	13.2230i	−0.535853	+	1.17335i	−0.963081	+	0.269211i	$0.913237\pi$
$128$		0			0
$129$	−6.92202	+	4.44851i	−0.609450	+	0.391670i
$130$		0			0
$131$	−2.67418	−	18.5993i	−0.233644	−	1.62503i	−0.682123	−	0.731237i	$-0.738943\pi$
$131$	−2.67418	−	18.5993i	−0.233644	−	1.62503i	0.448479	−	0.893793i	$-0.351966\pi$
$132$		0			0
$133$	−4.91683	−	3.15986i	−0.426343	−	0.273994i
$134$		0			0
$135$	13.2052	−	3.87740i	1.13652	−	0.333713i
$136$		0			0
$137$	−20.9794			−1.79239			−0.896197	−	0.443657i	$-0.853681\pi$
$137$	−20.9794			−1.79239			−0.896197	+	0.443657i	$0.853681\pi$
$138$		0			0
$139$	13.7231			1.16398			0.581991	−	0.813195i	$-0.302274\pi$
$139$	13.7231			1.16398			0.581991	+	0.813195i	$0.302274\pi$
$140$		0			0
$141$	4.37712	−	1.28524i	0.368620	−	0.108237i
$142$		0			0
$143$	0.169108	+	0.108679i	0.0141415	+	0.00908822i
$144$		0			0
$145$	−0.912554	−	6.34695i	−0.0757835	−	0.527086i
$146$		0			0
$147$	−3.84720	+	2.47244i	−0.317311	+	0.203924i
$148$		0			0
$149$	−3.84541	+	8.42027i	−0.315028	+	0.689815i	−0.999220	−	0.0394868i	$-0.987428\pi$
$149$	−3.84541	+	8.42027i	−0.315028	+	0.689815i	0.684192	+	0.729302i	$0.260155\pi$
$150$		0			0
$151$	1.14815	−	7.98559i	0.0934354	−	0.649858i	−0.888252	−	0.459357i	$-0.848080\pi$
$151$	1.14815	−	7.98559i	0.0934354	−	0.649858i	0.981687	−	0.190501i	$-0.0610111\pi$
$152$		0			0
$153$	−5.52762	−	1.62306i	−0.446882	−	0.131216i
$154$		0			0
$155$	14.5905	+	16.8384i	1.17194	+	1.35249i
$156$		0			0
$157$	−1.89961	+	2.19227i	−0.151606	+	0.174962i	−0.826472	−	0.562978i	$-0.809656\pi$
$157$	−1.89961	+	2.19227i	−0.151606	+	0.174962i	0.674867	+	0.737940i	$0.264201\pi$
$158$		0			0
$159$	5.08983	+	11.1452i	0.403650	+	0.883870i
$160$		0			0
$161$	−3.23038	+	5.20648i	−0.254590	+	0.410328i
$162$		0			0
$163$	9.42959	+	20.6479i	0.738583	+	1.61727i	0.785872	+	0.618390i	$0.212215\pi$
$163$	9.42959	+	20.6479i	0.738583	+	1.61727i	−0.0472888	+	0.998881i	$0.515058\pi$
$164$		0			0
$165$	0.366915	−	0.423443i	0.0285643	−	0.0329650i
$166$		0			0
$167$	−13.2667	−	15.3106i	−1.02661	−	1.18477i	−0.982599	−	0.185737i	$-0.940533\pi$
$167$	−13.2667	−	15.3106i	−1.02661	−	1.18477i	−0.0440081	−	0.999031i	$-0.514013\pi$
$168$		0			0
$169$	11.6324	+	3.41559i	0.894802	+	0.262738i
$170$		0			0
$171$	1.48056	−	10.2975i	0.113221	−	0.787469i
$172$		0			0
$173$	3.50720	−	7.67969i	0.266647	−	0.583876i	−0.728188	−	0.685377i	$-0.759637\pi$
$173$	3.50720	−	7.67969i	0.266647	−	0.583876i	0.994835	+	0.101501i	$0.0323646\pi$
$174$		0			0
$175$	−4.70863	+	3.02605i	−0.355939	+	0.228748i
$176$		0			0
$177$	0.498346	+	3.46607i	0.0374580	+	0.260526i
$178$		0			0
$179$	−15.1054	−	9.70767i	−1.12903	−	0.725585i	−0.163674	−	0.986514i	$-0.552335\pi$
$179$	−15.1054	−	9.70767i	−1.12903	−	0.725585i	−0.965358	+	0.260929i	$0.915971\pi$
$180$		0			0
$181$	4.22286	−	1.23994i	0.313882	−	0.0921642i	−0.120997	−	0.992653i	$-0.538609\pi$
$181$	4.22286	−	1.23994i	0.313882	−	0.0921642i	0.434879	+	0.900489i	$0.356791\pi$
$182$		0			0
$183$	6.06798			0.448558
$184$		0			0
$185$	−31.5852			−2.32219
$186$		0			0
$187$	−0.521900	+	0.153244i	−0.0381651	+	0.0112063i
$188$		0			0
$189$	4.82954	+	3.10376i	0.351298	+	0.225765i
$190$		0			0
$191$	2.18842	+	15.2208i	0.158349	+	1.10134i	0.901676	+	0.432412i	$0.142337\pi$
$191$	2.18842	+	15.2208i	0.158349	+	1.10134i	−0.743328	+	0.668928i	$0.766754\pi$
$192$		0			0
$193$	10.8363	−	6.96406i	0.780013	−	0.501284i	−0.0890250	−	0.996029i	$-0.528375\pi$
$193$	10.8363	−	6.96406i	0.780013	−	0.501284i	0.869038	+	0.494746i	$0.164739\pi$
$194$		0			0
$195$	−1.01486	+	2.22224i	−0.0726759	+	0.159138i
$196$		0			0
$197$	−0.371997	+	2.58730i	−0.0265037	+	0.184337i	−0.998773	−	0.0495278i	$-0.984228\pi$
$197$	−0.371997	+	2.58730i	−0.0265037	+	0.184337i	0.972269	+	0.233865i	$0.0751374\pi$
$198$		0			0
$199$	17.4615	+	5.12714i	1.23781	+	0.363454i	0.834192	−	0.551474i	$-0.185934\pi$
$199$	17.4615	+	5.12714i	1.23781	+	0.363454i	0.403617	+	0.914928i	$0.367753\pi$
$200$		0			0
$201$	2.23361	+	2.57773i	0.157547	+	0.181819i
$202$		0			0
$203$	1.75159	−	2.02145i	0.122938	−	0.141878i
$204$		0			0
$205$	6.78034	+	14.8469i	0.473559	+	1.03695i
$206$		0			0
$207$	−10.8186	−	1.38057i	−0.751946	−	0.0959564i
$208$		0			0
$209$	−0.408043	−	0.893489i	−0.0282249	−	0.0618039i
$210$		0			0
$211$	4.55158	−	5.25281i	0.313344	−	0.361618i	−0.577130	−	0.816652i	$-0.695827\pi$
$211$	4.55158	−	5.25281i	0.313344	−	0.361618i	0.890474	+	0.455034i	$0.150373\pi$
$212$		0			0
$213$	3.94934	+	4.55778i	0.270604	+	0.312294i
$214$		0			0
$215$	28.3820	+	8.33370i	1.93563	+	0.568353i
$216$		0			0
$217$	−1.32266	+	9.19932i	−0.0897881	+	0.624490i
$218$		0			0
$219$	−1.37259	+	3.00556i	−0.0927512	+	0.203097i
$220$		0			0
$221$	1.99518	−	1.28222i	0.134210	−	0.0862516i
$222$		0			0
$223$	1.98436	+	13.8015i	0.132883	+	0.924219i	0.941771	+	0.336256i	$0.109161\pi$
$223$	1.98436	+	13.8015i	0.132883	+	0.924219i	−0.808888	+	0.587963i	$0.799930\pi$
$224$		0			0
$225$	−8.38129	−	5.38632i	−0.558752	−	0.359088i
$226$		0			0
$227$	10.2991	−	3.02408i	0.683574	−	0.200715i	0.0785350	−	0.996911i	$-0.474976\pi$
$227$	10.2991	−	3.02408i	0.683574	−	0.200715i	0.605039	+	0.796196i	$0.293158\pi$
$228$		0			0
$229$	−5.31107			−0.350965			−0.175483	−	0.984483i	$-0.556149\pi$
$229$	−5.31107			−0.350965			−0.175483	+	0.984483i	$0.556149\pi$
$230$		0			0
$231$	0.233718			0.0153775
$232$		0			0
$233$	5.68951	−	1.67059i	0.372732	−	0.109444i	−0.0900010	−	0.995942i	$-0.528687\pi$
$233$	5.68951	−	1.67059i	0.372732	−	0.109444i	0.462733	+	0.886498i	$0.346869\pi$
$234$		0			0
$235$	−13.7965	−	8.86646i	−0.899983	−	0.578384i
$236$		0			0
$237$	1.64081	+	11.4121i	0.106582	+	0.741293i
$238$		0			0
$239$	−16.1486	+	10.3781i	−1.04457	+	0.671301i	−0.946112	−	0.323840i	$-0.895026\pi$
$239$	−16.1486	+	10.3781i	−1.04457	+	0.671301i	−0.0984534	+	0.995142i	$0.531390\pi$
$240$		0			0
$241$	−5.02220	+	10.9971i	−0.323508	+	0.708384i	−0.999596	−	0.0284371i	$-0.990947\pi$
$241$	−5.02220	+	10.9971i	−0.323508	+	0.708384i	0.676087	+	0.736822i	$0.263674\pi$
$242$		0			0
$243$	−2.28148	+	15.8681i	−0.146357	+	1.01794i
$244$		0			0
$245$	15.7744	+	4.63179i	1.00779	+	0.295914i
$246$		0			0
$247$	2.80467	+	3.23676i	0.178457	+	0.205950i
$248$		0			0
$249$	5.84544	−	6.74600i	0.370440	−	0.427510i
$250$		0			0
$251$	0.853487	+	1.86888i	0.0538716	+	0.117962i	0.934654	−	0.355560i	$-0.115710\pi$
$251$	0.853487	+	1.86888i	0.0538716	+	0.117962i	−0.880782	+	0.473522i	$0.842982\pi$
$252$		0			0
$253$	−0.929778	+	0.442586i	−0.0584546	+	0.0278251i
$254$		0			0
$255$	−2.74610	−	6.01311i	−0.171967	−	0.376556i
$256$		0			0
$257$	−7.19600	+	8.30462i	−0.448874	+	0.518028i	−0.934415	−	0.356186i	$-0.884077\pi$
$257$	−7.19600	+	8.30462i	−0.448874	+	0.518028i	0.485541	+	0.874214i	$0.338623\pi$
$258$		0			0
$259$	−8.62797	−	9.95720i	−0.536116	−	0.618711i
$260$		0			0
$261$	4.56817	+	1.34134i	0.282763	+	0.0830266i
$262$		0			0
$263$	2.58595	−	17.9857i	0.159457	−	1.10904i	−0.740181	−	0.672408i	$-0.765260\pi$
$263$	2.58595	−	17.9857i	0.159457	−	1.10904i	0.899638	−	0.436637i	$-0.143831\pi$
$264$		0			0
$265$	18.2978	−	40.0665i	1.12402	−	2.46126i
$266$		0			0
$267$	−3.45720	+	2.22181i	−0.211577	+	0.135973i
$268$		0			0
$269$	1.08848	+	7.57056i	0.0663660	+	0.461585i	0.995722	+	0.0924005i	$0.0294540\pi$
$269$	1.08848	+	7.57056i	0.0663660	+	0.461585i	−0.929356	+	0.369185i	$0.879637\pi$
$270$		0			0
$271$	−22.1011	−	14.2035i	−1.34255	−	0.862804i	−0.345414	−	0.938450i	$-0.612262\pi$
$271$	−22.1011	−	14.2035i	−1.34255	−	0.862804i	−0.997135	+	0.0756463i	$0.975898\pi$
$272$		0			0
$273$	−0.977785	+	0.287104i	−0.0591783	+	0.0173763i
$274$		0			0
$275$	−0.940660			−0.0567239
$276$		0			0
$277$	−6.45543			−0.387869			−0.193935	−	0.981014i	$-0.562125\pi$
$277$	−6.45543			−0.387869			−0.193935	+	0.981014i	$0.562125\pi$
$278$		0			0
$279$	−15.8729	+	4.66071i	−0.950287	+	0.279029i
$280$		0			0
$281$	15.8457	+	10.1834i	0.945273	+	0.607490i	0.919885	−	0.392188i	$-0.128282\pi$
$281$	15.8457	+	10.1834i	0.945273	+	0.607490i	0.0253875	+	0.999678i	$0.491918\pi$
$282$		0			0
$283$	1.21577	+	8.45586i	0.0722700	+	0.502649i	0.993518	+	0.113674i	$0.0362618\pi$
$283$	1.21577	+	8.45586i	0.0722700	+	0.502649i	−0.921248	+	0.388975i	$0.872829\pi$
$284$		0			0
$285$	10.0424	−	6.45387i	0.594861	−	0.382294i
$286$		0			0
$287$	−2.82831	+	6.19314i	−0.166950	+	0.365569i
$288$		0			0
$289$	1.50605	−	10.4748i	0.0885914	−	0.616167i
$290$		0			0
$291$	−9.49843	−	2.78899i	−0.556808	−	0.163494i
$292$		0			0
$293$	−7.92115	−	9.14150i	−0.462759	−	0.534052i	0.475625	−	0.879648i	$-0.342222\pi$
$293$	−7.92115	−	9.14150i	−0.462759	−	0.534052i	−0.938383	+	0.345596i	$0.887677\pi$
$294$		0			0
$295$	8.24374	−	9.51378i	0.479969	−	0.553914i
$296$		0			0
$297$	0.400799	+	0.877627i	0.0232567	+	0.0509251i
$298$		0			0
$299$	3.34614	−	2.99376i	0.193512	−	0.173134i
$300$		0			0
$301$	5.12577	+	11.2239i	0.295444	+	0.646933i
$302$		0			0
$303$	−9.31222	+	10.7469i	−0.534973	+	0.617392i
$304$		0			0
$305$	−14.2852	−	16.4860i	−0.817970	−	0.943988i
$306$		0			0
$307$	−24.6469	−	7.23697i	−1.40667	−	0.413036i	−0.511701	−	0.859163i	$-0.670985\pi$
$307$	−24.6469	−	7.23697i	−1.40667	−	0.413036i	−0.894969	+	0.446128i	$0.852803\pi$
$308$		0			0
$309$	0.243107	−	1.69085i	0.0138299	−	0.0961891i
$310$		0			0
$311$	12.7221	−	27.8575i	0.721405	−	1.57966i	−0.0905202	−	0.995895i	$-0.528853\pi$
$311$	12.7221	−	27.8575i	0.721405	−	1.57966i	0.811925	−	0.583762i	$-0.198420\pi$
$312$		0			0
$313$	−22.3933	+	14.3913i	−1.26574	+	0.813444i	−0.989060	−	0.147516i	$-0.952872\pi$
$313$	−22.3933	+	14.3913i	−1.26574	+	0.813444i	−0.276685	+	0.960961i	$0.589236\pi$
$314$		0			0
$315$	−1.26645	−	8.80836i	−0.0713564	−	0.496295i
$316$		0			0
$317$	−2.74808	−	1.76608i	−0.154347	−	0.0991931i	0.461187	−	0.887303i	$-0.347424\pi$
$317$	−2.74808	−	1.76608i	−0.154347	−	0.0991931i	−0.615535	+	0.788110i	$0.711060\pi$
$318$		0			0
$319$	0.431312	−	0.126645i	0.0241488	−	0.00709074i
$320$		0			0
$321$	2.80998			0.156838
$322$		0			0
$323$	−11.5888			−0.644821
$324$		0			0
$325$	3.93535	−	1.15552i	0.218294	−	0.0640969i
$326$		0			0
$327$	−0.344580	−	0.221448i	−0.0190553	−	0.0122461i
$328$		0			0
$329$	−0.973571	−	6.77134i	−0.0536747	−	0.373316i
$330$		0			0
$331$	23.5588	−	15.1403i	1.29491	−	0.832188i	0.302261	−	0.953225i	$-0.402258\pi$
$331$	23.5588	−	15.1403i	1.29491	−	0.832188i	0.992648	+	0.121037i	$0.0386221\pi$
$332$		0			0
$333$	9.74222	−	21.3325i	0.533870	−	1.16901i
$334$		0			0
$335$	1.74503	−	12.1370i	0.0953414	−	0.663114i
$336$		0			0
$337$	12.5077	+	3.67259i	0.681337	+	0.200059i	0.604046	−	0.796950i	$-0.293554\pi$
$337$	12.5077	+	3.67259i	0.681337	+	0.200059i	0.0772919	+	0.997009i	$0.475373\pi$
$338$		0			0
$339$	−1.65748	−	1.91283i	−0.0900217	−	0.103891i
$340$		0			0
$341$	−1.02285	+	1.18043i	−0.0553905	+	0.0639241i
$342$		0			0
$343$	6.56403	+	14.3732i	0.354424	+	0.776081i
$344$		0			0
$345$	−6.93216	−	10.4192i	−0.373215	−	0.560951i
$346$		0			0
$347$	12.4894	+	27.3479i	0.670464	+	1.46811i	0.872441	+	0.488720i	$0.162536\pi$
$347$	12.4894	+	27.3479i	0.670464	+	1.46811i	−0.201977	+	0.979390i	$0.564737\pi$
$348$		0			0
$349$	−7.00288	+	8.08175i	−0.374855	+	0.432606i	−0.911562	−	0.411163i	$-0.865123\pi$
$349$	−7.00288	+	8.08175i	−0.374855	+	0.432606i	0.536707	+	0.843769i	$0.319668\pi$
$350$		0			0
$351$	−2.75488	−	3.17930i	−0.147044	−	0.169698i
$352$		0			0
$353$	−31.3397	−	9.20215i	−1.66804	−	0.489781i	−0.694730	−	0.719270i	$-0.744476\pi$
$353$	−31.3397	−	9.20215i	−1.66804	−	0.489781i	−0.973311	+	0.229489i	$0.926294\pi$
$354$		0			0
$355$	3.08546	−	21.4599i	0.163759	−	1.13897i
$356$		0			0
$357$	1.14549	−	2.50827i	0.0606258	−	0.132752i
$358$		0			0
$359$	11.6822	−	7.50772i	0.616565	−	0.396242i	−0.194749	−	0.980853i	$-0.562389\pi$
$359$	11.6822	−	7.50772i	0.616565	−	0.396242i	0.811314	+	0.584611i	$0.198753\pi$
$360$		0			0
$361$	−0.274317	−	1.90791i	−0.0144377	−	0.100417i
$362$		0			0
$363$	−7.85099	−	5.04553i	−0.412070	−	0.264821i
$364$		0			0
$365$	11.3971	−	3.34650i	0.596553	−	0.175164i
$366$		0			0
$367$	8.70583			0.454441			0.227220	−	0.973843i	$-0.427036\pi$
$367$	8.70583			0.454441			0.227220	+	0.973843i	$0.427036\pi$
$368$		0			0
$369$	−12.1188			−0.630882
$370$		0			0
$371$	17.6292	−	5.17641i	0.915264	−	0.268746i
$372$		0			0
$373$	−0.779682	−	0.501071i	−0.0403704	−	0.0259445i	0.520300	−	0.853984i	$-0.325820\pi$
$373$	−0.779682	−	0.501071i	−0.0403704	−	0.0259445i	−0.560670	+	0.828039i	$0.689457\pi$
$374$		0			0
$375$	0.229895	+	1.59895i	0.0118717	+	0.0825697i
$376$		0			0
$377$	−1.64887	+	1.05966i	−0.0849209	+	0.0545754i
$378$		0			0
$379$	−13.3906	+	29.3212i	−0.687827	+	1.50613i	0.166306	+	0.986074i	$0.446816\pi$
$379$	−13.3906	+	29.3212i	−0.687827	+	1.50613i	−0.854132	+	0.520056i	$0.825911\pi$
$380$		0			0
$381$	1.76256	−	12.2589i	0.0902988	−	0.628042i
$382$		0			0
$383$	9.56563	+	2.80872i	0.488781	+	0.143519i	0.516831	−	0.856087i	$-0.327112\pi$
$383$	9.56563	+	2.80872i	0.488781	+	0.143519i	−0.0280499	+	0.999607i	$0.508930\pi$
$384$		0			0
$385$	−0.550220	−	0.634987i	−0.0280418	−	0.0323620i
$386$		0			0
$387$	−14.3827	+	16.5986i	−0.731116	+	0.843753i
$388$		0			0
$389$	13.7724	+	30.1572i	0.698286	+	1.52903i	0.842037	+	0.539419i	$0.181356\pi$
$389$	13.7724	+	30.1572i	0.698286	+	1.52903i	−0.143751	+	0.989614i	$0.545917\pi$
$390$		0			0
$391$	0.192858	+	12.1476i	0.00975324	+	0.614330i
$392$		0			0
$393$	6.65046	+	14.5625i	0.335471	+	0.734579i
$394$		0			0
$395$	27.1426	−	31.3242i	1.36569	−	1.57609i
$396$		0			0
$397$	−11.1983	−	12.9235i	−0.562024	−	0.648610i	0.401618	−	0.915807i	$-0.368448\pi$
$397$	−11.1983	−	12.9235i	−0.562024	−	0.648610i	−0.963642	+	0.267197i	$0.913903\pi$
$398$		0			0
$399$	4.77781	+	1.40289i	0.239190	+	0.0702325i
$400$		0			0
$401$	3.09765	−	21.5446i	0.154689	−	1.07589i	−0.753536	−	0.657406i	$-0.771654\pi$
$401$	3.09765	−	21.5446i	0.154689	−	1.07589i	0.908226	−	0.418481i	$-0.137437\pi$
$402$		0			0
$403$	2.82914	−	6.19496i	0.140930	−	0.308593i
$404$		0			0
$405$	7.71458	−	4.95786i	0.383340	−	0.246358i
$406$		0			0
$407$	−0.315119	−	2.19170i	−0.0156199	−	0.108639i
$408$		0			0
$409$	−28.4862	−	18.3070i	−1.40855	−	0.905223i	−0.408582	−	0.912721i	$-0.633977\pi$
$409$	−28.4862	−	18.3070i	−1.40855	−	0.905223i	−0.999972	+	0.00749867i	$0.997613\pi$
$410$		0			0
$411$	17.1500	−	5.03570i	0.845948	−	0.248393i
$412$		0			0
$413$	5.25111			0.258390
$414$		0			0
$415$	−32.0895			−1.57521
$416$		0			0
$417$	−11.2182	+	3.29397i	−0.549359	+	0.161306i
$418$		0			0
$419$	−2.00403	−	1.28791i	−0.0979030	−	0.0629185i	0.490773	−	0.871287i	$-0.336714\pi$
$419$	−2.00403	−	1.28791i	−0.0979030	−	0.0629185i	−0.588676	+	0.808369i	$0.700351\pi$
$420$		0			0
$421$	−3.64913	−	25.3803i	−0.177848	−	1.23696i	−0.861731	−	0.507366i	$-0.830619\pi$
$421$	−3.64913	−	25.3803i	−0.177848	−	1.23696i	0.683883	−	0.729592i	$-0.260290\pi$
$422$		0			0
$423$	10.2438	−	6.58328i	0.498070	−	0.320090i
$424$		0			0
$425$	−4.61032	+	10.0952i	−0.223634	+	0.489689i
$426$		0			0
$427$	1.29498	−	9.00681i	0.0626687	−	0.435870i
$428$		0			0
$429$	−0.164327	−	0.0482507i	−0.00793378	−	0.00232957i
$430$		0			0
$431$	0.0218038	+	0.0251629i	0.00105025	+	0.00121206i	0.756274	−	0.654254i	$-0.227017\pi$
$431$	0.0218038	+	0.0251629i	0.00105025	+	0.00121206i	−0.755224	+	0.655467i	$0.772472\pi$
$432$		0			0
$433$	0.783279	−	0.903952i	0.0376420	−	0.0434412i	−0.736616	−	0.676311i	$-0.763578\pi$
$433$	0.783279	−	0.903952i	0.0376420	−	0.0434412i	0.774258	+	0.632870i	$0.218123\pi$
$434$		0			0
$435$	2.26944	+	4.96939i	0.108812	+	0.238264i
$436$		0			0
$437$	−21.6637	+	3.46662i	−1.03632	+	0.165831i
$438$		0			0
$439$	−6.41264	−	14.0417i	−0.306059	−	0.670175i	0.692634	−	0.721289i	$-0.256450\pi$
$439$	−6.41264	−	14.0417i	−0.306059	−	0.670175i	−0.998693	+	0.0511142i	$0.983723\pi$
$440$		0			0
$441$	−7.99380	+	9.22533i	−0.380657	+	0.439302i
$442$		0			0
$443$	4.63685	+	5.35121i	0.220304	+	0.254244i	0.855133	−	0.518408i	$-0.173475\pi$
$443$	4.63685	+	5.35121i	0.220304	+	0.254244i	−0.634830	+	0.772652i	$0.718930\pi$
$444$		0			0
$445$	14.1754	+	4.16226i	0.671977	+	0.197310i
$446$		0			0
$447$	1.12238	−	7.80631i	0.0530867	−	0.369226i
$448$		0			0
$449$	−4.02515	+	8.81386i	−0.189959	+	0.415952i	−0.980517	−	0.196436i	$-0.937063\pi$
$449$	−4.02515	+	8.81386i	−0.189959	+	0.415952i	0.790558	+	0.612387i	$0.209791\pi$
$450$		0			0
$451$	−0.962581	+	0.618613i	−0.0453262	+	0.0291294i
$452$		0			0
$453$	0.978203	+	6.80355i	0.0459600	+	0.319659i
$454$		0			0
$455$	3.08193	+	1.98064i	0.144483	+	0.0928537i
$456$		0			0
$457$	−13.4522	+	3.94992i	−0.629266	+	0.184769i	−0.580788	−	0.814055i	$-0.697255\pi$
$457$	−13.4522	+	3.94992i	−0.629266	+	0.184769i	−0.0484785	+	0.998824i	$0.515437\pi$
$458$		0			0
$459$	11.3831			0.531318
$460$		0			0
$461$	−0.854133			−0.0397809			−0.0198905	−	0.999802i	$-0.506332\pi$
$461$	−0.854133			−0.0397809			−0.0198905	+	0.999802i	$0.506332\pi$
$462$		0			0
$463$	−6.67547	+	1.96010i	−0.310236	+	0.0910934i	−0.433144	−	0.901325i	$-0.642596\pi$
$463$	−6.67547	+	1.96010i	−0.310236	+	0.0910934i	0.122909	+	0.992418i	$0.460778\pi$
$464$		0			0
$465$	−15.9690	−	10.2627i	−0.740546	−	0.475920i
$466$		0			0
$467$	4.10379	+	28.5425i	0.189901	+	1.32079i	0.832260	+	0.554385i	$0.187046\pi$
$467$	4.10379	+	28.5425i	0.189901	+	1.32079i	−0.642360	+	0.766403i	$0.722044\pi$
$468$		0			0
$469$	4.30285	−	2.76528i	0.198687	−	0.127689i
$470$		0			0
$471$	1.02666	−	2.24807i	0.0473061	−	0.103586i
$472$		0			0
$473$	−0.295115	+	2.05257i	−0.0135694	+	0.0943774i
$474$		0			0
$475$	−19.2295	−	5.64630i	−0.882312	−	0.259070i
$476$		0			0
$477$	21.4169	+	24.7164i	0.980613	+	1.13169i
$478$		0			0
$479$	−2.39860	+	2.76814i	−0.109595	+	0.126479i	−0.807897	−	0.589324i	$-0.799394\pi$
$479$	−2.39860	+	2.76814i	−0.109595	+	0.126479i	0.698302	+	0.715804i	$0.253939\pi$
$480$		0			0
$481$	4.01066	+	8.78212i	0.182870	+	0.400430i
$482$		0			0
$483$	1.39102	−	5.03152i	0.0632937	−	0.228942i
$484$		0			0
$485$	14.7838	+	32.3720i	0.671299	+	1.46994i
$486$		0			0
$487$	−20.3349	+	23.4677i	−0.921463	+	1.06342i	0.0763341	+	0.997082i	$0.475678\pi$
$487$	−20.3349	+	23.4677i	−0.921463	+	1.06342i	−0.997797	+	0.0663425i	$0.978867\pi$
$488$		0			0
$489$	−12.6645	−	14.6156i	−0.572709	−	0.660942i
$490$		0			0
$491$	−18.5161	−	5.43682i	−0.835620	−	0.245360i	−0.164190	−	0.986429i	$-0.552501\pi$
$491$	−18.5161	−	5.43682i	−0.835620	−	0.245360i	−0.671429	+	0.741069i	$0.734319\pi$
$492$		0			0
$493$	0.754773	−	5.24956i	0.0339933	−	0.236428i
$494$		0			0
$495$	0.621278	−	1.36041i	0.0279243	−	0.0611458i
$496$		0			0
$497$	7.60804	−	4.88939i	0.341267	−	0.219319i
$498$		0			0
$499$	4.26024	+	29.6306i	0.190714	+	1.32645i	0.830123	+	0.557580i	$0.188270\pi$
$499$	4.26024	+	29.6306i	0.190714	+	1.32645i	−0.639409	+	0.768867i	$0.720821\pi$
$500$		0			0
$501$	14.5201	+	9.33150i	0.648710	+	0.416901i
$502$		0			0
$503$	−4.42136	+	1.29823i	−0.197139	+	0.0578852i	−0.378811	−	0.925474i	$-0.623667\pi$
$503$	−4.42136	+	1.29823i	−0.197139	+	0.0578852i	0.181673	+	0.983359i	$0.441849\pi$
$504$		0			0
$505$	51.1209			2.27485
$506$		0			0
$507$	−10.3290			−0.458726
$508$		0			0
$509$	−3.92130	+	1.15140i	−0.173809	+	0.0510349i	−0.367479	−	0.930032i	$-0.619779\pi$
$509$	−3.92130	+	1.15140i	−0.173809	+	0.0510349i	0.193670	+	0.981067i	$0.437961\pi$
$510$		0			0
$511$	4.16828	+	2.67879i	0.184394	+	0.118503i
$512$		0			0
$513$	2.92543	+	20.3468i	0.129161	+	0.898333i
$514$		0			0
$515$	−5.16618	+	3.32010i	−0.227649	+	0.146301i
$516$		0			0
$517$	0.477601	−	1.04580i	0.0210048	−	0.0459942i
$518$		0			0
$519$	−1.02366	+	7.11973i	−0.0449338	+	0.312522i
$520$		0			0
$521$	−4.28290	−	1.25757i	−0.187637	−	0.0550953i	0.186564	−	0.982443i	$-0.440265\pi$
$521$	−4.28290	−	1.25757i	−0.187637	−	0.0550953i	−0.374201	+	0.927348i	$0.622083\pi$
$522$		0			0
$523$	9.47424	+	10.9339i	0.414280	+	0.478104i	0.924086	−	0.382185i	$-0.124828\pi$
$523$	9.47424	+	10.9339i	0.414280	+	0.478104i	−0.509806	+	0.860289i	$0.670283\pi$
$524$		0			0
$525$	3.12281	−	3.60391i	0.136291	−	0.157288i
$526$		0			0
$527$	7.65531	+	16.7628i	0.333470	+	0.730198i
$528$		0			0
$529$	3.99428	+	22.6505i	0.173664	+	0.984805i
$530$		0			0
$531$	3.88284	+	8.50223i	0.168501	+	0.368966i
$532$		0			0
$533$	3.26714	−	3.77048i	0.141516	−	0.163318i
$534$		0			0
$535$	−6.61525	−	7.63440i	−0.286002	−	0.330064i
$536$		0			0
$537$	14.6783	+	4.30995i	0.633417	+	0.185988i
$538$		0			0
$539$	−0.164022	+	1.14080i	−0.00706495	+	0.0491378i
$540$		0			0
$541$	1.34391	−	2.94275i	0.0577791	−	0.126519i	−0.878540	−	0.477669i	$-0.841482\pi$
$541$	1.34391	−	2.94275i	0.0577791	−	0.126519i	0.936319	+	0.351150i	$0.114209\pi$
$542$		0			0
$543$	−3.15443	+	2.02723i	−0.135369	+	0.0869966i
$544$		0			0
$545$	0.209560	+	1.45752i	0.00897655	+	0.0624333i
$546$		0			0
$547$	−2.73914	−	1.76034i	−0.117117	−	0.0752667i	0.480771	−	0.876846i	$-0.340357\pi$
$547$	−2.73914	−	1.76034i	−0.117117	−	0.0752667i	−0.597888	+	0.801580i	$0.703993\pi$
$548$		0			0
$549$	15.5408	−	4.56318i	0.663264	−	0.194752i
$550$		0			0
$551$	9.57732			0.408008
$552$		0			0
$553$	17.2893			0.735216
$554$		0			0
$555$	25.8199	−	7.58140i	1.09599	−	0.321813i
$556$		0			0
$557$	−9.12124	−	5.86187i	−0.386479	−	0.248375i	0.332945	−	0.942946i	$-0.391958\pi$
$557$	−9.12124	−	5.86187i	−0.386479	−	0.248375i	−0.719424	+	0.694571i	$0.755594\pi$
$558$		0			0
$559$	−1.28677	−	8.94968i	−0.0544246	−	0.378531i
$560$		0			0
$561$	0.389854	−	0.250544i	0.0164596	−	0.0105780i
$562$		0			0
$563$	−2.15378	+	4.71611i	−0.0907709	+	0.198760i	−0.949572	−	0.313548i	$-0.898482\pi$
$563$	−2.15378	+	4.71611i	−0.0907709	+	0.198760i	0.858801	+	0.512309i	$0.171210\pi$
$564$		0			0
$565$	−1.29492	+	9.00636i	−0.0544777	+	0.378901i
$566$		0			0
$567$	3.67031	+	1.07770i	0.154139	+	0.0452592i
$568$		0			0
$569$	17.8093	+	20.5530i	0.746604	+	0.861627i	0.994234	−	0.107228i	$-0.0341974\pi$
$569$	17.8093	+	20.5530i	0.746604	+	0.861627i	−0.247631	+	0.968854i	$0.579652\pi$
$570$		0			0
$571$	−0.258462	+	0.298281i	−0.0108163	+	0.0124827i	−0.761132	−	0.648597i	$-0.775356\pi$
$571$	−0.258462	+	0.298281i	−0.0108163	+	0.0124827i	0.750316	+	0.661080i	$0.229902\pi$
$572$		0			0
$573$	−5.44242	−	11.9172i	−0.227360	−	0.497850i
$574$		0			0
$575$	−5.59852	+	20.2506i	−0.233475	+	0.844510i
$576$		0			0
$577$	−2.45463	−	5.37489i	−0.102188	−	0.223760i	0.851632	−	0.524141i	$-0.175613\pi$
$577$	−2.45463	−	5.37489i	−0.102188	−	0.223760i	−0.953819	+	0.300381i	$0.902886\pi$
$578$		0			0
$579$	−7.18673	+	8.29393i	−0.298670	+	0.344684i
$580$		0			0
$581$	−8.76572	−	10.1162i	−0.363663	−	0.419690i
$582$		0			0
$583$	2.96277	+	0.869949i	0.122706	+	0.0360296i
$584$		0			0
$585$	−0.928031	+	6.45460i	−0.0383694	+	0.266865i
$586$		0			0
$587$	14.7226	−	32.2381i	0.607669	−	1.33061i	−0.316488	−	0.948596i	$-0.602504\pi$
$587$	14.7226	−	32.2381i	0.607669	−	1.33061i	0.924157	−	0.382013i	$-0.124769\pi$
$588$		0			0
$589$	−27.9953	+	17.9915i	−1.15353	+	0.741326i
$590$		0			0
$591$	−0.316934	−	2.20432i	−0.0130369	−	0.0906738i
$592$		0			0
$593$	25.6347	+	16.4744i	1.05269	+	0.676524i	0.948094	−	0.317991i	$-0.103008\pi$
$593$	25.6347	+	16.4744i	1.05269	+	0.676524i	0.104598	+	0.994515i	$0.466644\pi$
$594$		0			0
$595$	−9.51143	+	2.79281i	−0.389930	+	0.114494i
$596$		0			0
$597$	−15.5048			−0.634571
$598$		0			0
$599$	−22.6521			−0.925539			−0.462770	−	0.886479i	$-0.653144\pi$
$599$	−22.6521			−0.925539			−0.462770	+	0.886479i	$0.653144\pi$
$600$		0			0
$601$	14.1372	−	4.15104i	0.576666	−	0.169325i	0.0196223	−	0.999807i	$-0.493754\pi$
$601$	14.1372	−	4.15104i	0.576666	−	0.169325i	0.557044	+	0.830483i	$0.311935\pi$
$602$		0			0
$603$	7.65901	+	4.92215i	0.311899	+	0.200445i
$604$		0			0
$605$	4.77466	+	33.2085i	0.194117	+	1.35012i
$606$		0			0
$607$	33.7455	−	21.6869i	1.36969	−	0.880244i	0.370861	−	0.928689i	$-0.379063\pi$
$607$	33.7455	−	21.6869i	1.36969	−	0.880244i	0.998826	+	0.0484446i	$0.0154264\pi$
$608$		0			0
$609$	−0.946663	+	2.07290i	−0.0383607	+	0.0839983i
$610$		0			0
$611$	−0.713414	+	4.96190i	−0.0288616	+	0.200737i
$612$		0			0
$613$	−26.2068	−	7.69500i	−1.05848	−	0.310798i	−0.294242	−	0.955731i	$-0.595067\pi$
$613$	−26.2068	−	7.69500i	−1.05848	−	0.310798i	−0.764239	+	0.644933i	$0.776885\pi$
$614$		0			0
$615$	−9.10641	−	10.5094i	−0.367206	−	0.423778i
$616$		0			0
$617$	7.75272	−	8.94711i	0.312113	−	0.360197i	−0.577920	−	0.816093i	$-0.696136\pi$
$617$	7.75272	−	8.94711i	0.312113	−	0.360197i	0.890033	+	0.455896i	$0.150681\pi$
$618$		0			0
$619$	−4.18050	−	9.15401i	−0.168028	−	0.367931i	0.806821	−	0.590796i	$-0.201186\pi$
$619$	−4.18050	−	9.15401i	−0.168028	−	0.367931i	−0.974849	+	0.222865i	$0.928459\pi$
$620$		0			0
$621$	21.2791	−	3.40508i	0.853901	−	0.136641i
$622$		0			0
$623$	2.56006	+	5.60576i	0.102567	+	0.224590i
$624$		0			0
$625$	18.1475	−	20.9434i	0.725901	−	0.837734i
$626$		0			0
$627$	0.548026	+	0.632456i	0.0218861	+	0.0252579i
$628$		0			0
$629$	−25.0659	−	7.36001i	−0.999442	−	0.293463i
$630$		0			0
$631$	−4.01100	+	27.8971i	−0.159675	+	1.11057i	0.739557	+	0.673094i	$0.235035\pi$
$631$	−4.01100	+	27.8971i	−0.159675	+	1.11057i	−0.899232	+	0.437472i	$0.855874\pi$
$632$		0			0
$633$	−2.45994	+	5.38652i	−0.0977739	+	0.214095i
$634$		0			0
$635$	−37.4555	+	24.0712i	−1.48638	+	0.955236i
$636$		0			0
$637$	−0.715175	−	4.97415i	−0.0283363	−	0.197083i
$638$		0			0
$639$	13.5422	+	8.70304i	0.535721	+	0.344287i
$640$		0			0
$641$	30.9702	−	9.09367i	1.22325	−	0.359178i	0.394551	−	0.918874i	$-0.370900\pi$
$641$	30.9702	−	9.09367i	1.22325	−	0.359178i	0.828698	+	0.559696i	$0.189082\pi$
$642$		0			0
$643$	−37.3247			−1.47194			−0.735971	−	0.677013i	$-0.763274\pi$
$643$	−37.3247			−1.47194			−0.735971	+	0.677013i	$0.763274\pi$
$644$		0			0
$645$	−25.2017			−0.992315
$646$		0			0
$647$	−24.0258	+	7.05462i	−0.944552	+	0.277346i	−0.717517	−	0.696541i	$-0.754721\pi$
$647$	−24.0258	+	7.05462i	−0.944552	+	0.277346i	−0.227035	+	0.973887i	$0.572903\pi$
$648$		0			0
$649$	0.742409	+	0.477117i	0.0291421	+	0.0187285i
$650$		0			0
$651$	−1.12688	−	7.83762i	−0.0441659	−	0.307181i
$652$		0			0
$653$	−11.2051	+	7.20110i	−0.438491	+	0.281801i	−0.741203	−	0.671281i	$-0.765744\pi$
$653$	−11.2051	+	7.20110i	−0.438491	+	0.281801i	0.302712	+	0.953082i	$0.402108\pi$
$654$		0			0
$655$	23.9081	−	52.3515i	0.934169	−	2.04554i
$656$		0			0
$657$	−1.25515	+	8.72977i	−0.0489681	+	0.340581i
$658$		0			0
$659$	−19.6457	−	5.76848i	−0.765286	−	0.224708i	−0.124283	−	0.992247i	$-0.539663\pi$
$659$	−19.6457	−	5.76848i	−0.765286	−	0.224708i	−0.641003	+	0.767539i	$0.721481\pi$
$660$		0			0
$661$	−13.5785	−	15.6705i	−0.528143	−	0.609510i	0.427507	−	0.904012i	$-0.359392\pi$
$661$	−13.5785	−	15.6705i	−0.528143	−	0.609510i	−0.955651	+	0.294502i	$0.904846\pi$
$662$		0			0
$663$	−1.32322	+	1.52708i	−0.0513896	+	0.0593068i
$664$		0			0
$665$	−7.43642	−	16.2835i	−0.288372	−	0.631447i
$666$		0			0
$667$	−0.159383	−	10.0391i	−0.00617133	−	0.388715i
$668$		0			0
$669$	−4.93493	−	10.8060i	−0.190796	−	0.417784i
$670$		0			0
$671$	1.00145	−	1.15573i	0.0386605	−	0.0446166i
$672$		0			0
$673$	7.73728	+	8.92930i	0.298250	+	0.344199i	0.885019	−	0.465556i	$-0.154145\pi$
$673$	7.73728	+	8.92930i	0.298250	+	0.344199i	−0.586768	+	0.809755i	$0.699600\pi$
$674$		0			0
$675$	18.8882	+	5.54607i	0.727006	+	0.213468i
$676$		0			0
$677$	3.92414	−	27.2930i	0.150817	−	1.04895i	−0.764038	−	0.645171i	$-0.776786\pi$
$677$	3.92414	−	27.2930i	0.150817	−	1.04895i	0.914855	−	0.403783i	$-0.132305\pi$
$678$		0			0
$679$	−6.16684	+	13.5035i	−0.236662	+	0.518217i
$680$		0			0
$681$	−7.69329	+	4.94418i	−0.294808	+	0.189461i
$682$		0			0
$683$	−1.33135	−	9.25976i	−0.0509428	−	0.354315i	−0.999310	−	0.0371406i	$-0.988175\pi$
$683$	−1.33135	−	9.25976i	−0.0509428	−	0.354315i	0.948367	−	0.317174i	$-0.102734\pi$
$684$		0			0
$685$	−54.0560	−	34.7397i	−2.06537	−	1.32734i
$686$		0			0
$687$	4.34163	−	1.27482i	0.165643	−	0.0486373i
$688$		0			0
$689$	−13.4637			−0.512927
$690$		0			0
$691$	25.0171			0.951696			0.475848	−	0.879528i	$-0.342141\pi$
$691$	25.0171			0.951696			0.475848	+	0.879528i	$0.342141\pi$
$692$		0			0
$693$	0.598579	−	0.175759i	0.0227381	−	0.00667652i
$694$		0			0
$695$	35.3593	+	22.7241i	1.34126	+	0.861973i
$696$		0			0
$697$	1.92122	+	13.3624i	0.0727714	+	0.506136i
$698$		0			0
$699$	−4.25000	+	2.73131i	−0.160750	+	0.103308i
$700$		0			0
$701$	0.688924	−	1.50853i	0.0260203	−	0.0569765i	−0.896176	−	0.443699i	$-0.853666\pi$
$701$	0.688924	−	1.50853i	0.0260203	−	0.0569765i	0.922196	+	0.386723i	$0.126393\pi$
$702$		0			0
$703$	6.71381	−	46.6956i	0.253216	−	1.76116i
$704$		0			0
$705$	13.4064	+	3.93647i	0.504914	+	0.148256i
$706$		0			0
$707$	13.9644	+	16.1158i	0.525187	+	0.606098i
$708$		0			0
$709$	−23.1676	+	26.7368i	−0.870078	+	1.00412i	0.129843	+	0.991535i	$0.458553\pi$
$709$	−23.1676	+	26.7368i	−0.870078	+	1.00412i	−0.999921	+	0.0125888i	$0.995993\pi$
$710$		0			0
$711$	12.7843	+	27.9937i	0.479448	+	1.04984i
$712$		0			0
$713$	19.3248	+	29.0457i	0.723721	+	1.08777i
$714$		0			0
$715$	0.255766	+	0.560050i	0.00956512	+	0.0209447i
$716$		0			0
$717$	10.7099	−	12.3599i	0.399969	−	0.461588i
$718$		0			0
$719$	−1.12354	−	1.29663i	−0.0419009	−	0.0483563i	0.734412	−	0.678704i	$-0.237458\pi$
$719$	−1.12354	−	1.29663i	−0.0419009	−	0.0483563i	−0.776313	+	0.630347i	$0.782912\pi$
$720$		0			0
$721$	−2.45788	−	0.721698i	−0.0915361	−	0.0268774i
$722$		0			0
$723$	1.46585	−	10.1952i	0.0545157	−	0.379165i
$724$		0			0
$725$	3.81009	−	8.34294i	0.141503	−	0.309849i
$726$		0			0
$727$	−15.5564	+	9.99747i	−0.576954	+	0.370786i	−0.796337	−	0.604853i	$-0.793232\pi$
$727$	−15.5564	+	9.99747i	−0.576954	+	0.370786i	0.219383	+	0.975639i	$0.429595\pi$
$728$		0			0
$729$	−0.665474	−	4.62847i	−0.0246472	−	0.171425i
$730$		0			0
$731$	20.5819	+	13.2272i	0.761249	+	0.489225i
$732$		0			0
$733$	−19.4340	+	5.70635i	−0.717813	+	0.210769i	−0.620187	−	0.784454i	$-0.712943\pi$
$733$	−19.4340	+	5.70635i	−0.717813	+	0.210769i	−0.0976263	+	0.995223i	$0.531125\pi$
$734$		0			0
$735$	−14.0069			−0.516651
$736$		0			0
$737$	0.859597			0.0316637
$738$		0			0
$739$	45.2056	−	13.2736i	1.66292	−	0.488276i	0.690853	−	0.722995i	$-0.257235\pi$
$739$	45.2056	−	13.2736i	1.66292	−	0.488276i	0.972063	+	0.234719i	$0.0754171\pi$
$740$		0			0
$741$	−3.06965	−	1.97274i	−0.112766	−	0.0724705i
$742$		0			0
$743$	−6.44028	−	44.7931i	−0.236271	−	1.64330i	−0.670075	−	0.742293i	$-0.733738\pi$
$743$	−6.44028	−	44.7931i	−0.236271	−	1.64330i	0.433805	−	0.901007i	$-0.357171\pi$
$744$		0			0
$745$	−23.8512	+	15.3282i	−0.873841	+	0.561583i
$746$		0			0
$747$	9.89777	−	21.6731i	0.362140	−	0.792977i
$748$		0			0
$749$	0.599685	−	4.17090i	0.0219120	−	0.152401i
$750$		0			0
$751$	39.0441	+	11.4644i	1.42474	+	0.418341i	0.901105	−	0.433602i	$-0.142758\pi$
$751$	39.0441	+	11.4644i	1.42474	+	0.418341i	0.523634	+	0.851943i	$0.324576\pi$
$752$		0			0
$753$	−1.14628	−	1.32288i	−0.0417729	−	0.0482085i
$754$		0			0
$755$	16.1816	−	18.6746i	0.588910	−	0.679638i
$756$		0			0
$757$	6.01044	+	13.1610i	0.218453	+	0.478346i	0.986852	−	0.161625i	$-0.0516736\pi$
$757$	6.01044	+	13.1610i	0.218453	+	0.478346i	−0.768399	+	0.639971i	$0.778946\pi$
$758$		0			0
$759$	0.653830	−	0.584974i	0.0237325	−	0.0212332i
$760$		0			0
$761$	−13.7044	−	30.0084i	−0.496782	−	1.08780i	−0.977502	−	0.210927i	$-0.932352\pi$
$761$	−13.7044	−	30.0084i	−0.496782	−	1.08780i	0.480719	−	0.876875i	$-0.340376\pi$
$762$		0			0
$763$	−0.402237	+	0.464207i	−0.0145620	+	0.0168054i
$764$		0			0
$765$	−11.5550	−	13.3352i	−0.417771	−	0.482133i
$766$		0			0
$767$	−3.69204	−	1.08408i	−0.133312	−	0.0391439i
$768$		0			0
$769$	7.07162	−	49.1842i	0.255009	−	1.77363i	−0.312164	−	0.950028i	$-0.601054\pi$
$769$	7.07162	−	49.1842i	0.255009	−	1.77363i	0.567173	−	0.823599i	$-0.308037\pi$
$770$		0			0
$771$	3.88914	−	8.51602i	0.140064	−	0.306697i
$772$		0			0
$773$	11.4533	−	7.36059i	0.411947	−	0.264742i	−0.318212	−	0.948020i	$-0.603082\pi$
$773$	11.4533	−	7.36059i	0.411947	−	0.264742i	0.730159	+	0.683278i	$0.239446\pi$
$774$		0			0
$775$	4.53542	+	31.5445i	0.162917	+	1.13311i
$776$		0			0
$777$	9.44312	+	6.06872i	0.338770	+	0.217714i
$778$		0			0
$779$	−23.3909	+	6.86818i	−0.838065	+	0.246078i
$780$		0			0
$781$	1.51989			0.0543858
$782$		0			0
$783$	−9.40730			−0.336189
$784$		0			0
$785$	−8.52474	+	2.50309i	−0.304261	+	0.0893391i
$786$		0			0
$787$	−2.11128	−	1.35684i	−0.0752592	−	0.0483661i	0.502470	−	0.864595i	$-0.332425\pi$
$787$	−2.11128	−	1.35684i	−0.0752592	−	0.0483661i	−0.577729	+	0.816228i	$0.696061\pi$
$788$		0			0
$789$	2.20318	+	15.3234i	0.0784351	+	0.545528i
$790$		0			0
$791$	−3.19297	+	2.05200i	−0.113529	+	0.0729607i
$792$		0			0
$793$	−2.76994	+	6.06532i	−0.0983635	+	0.215386i
$794$		0			0
$795$	−5.34066	+	37.1451i	−0.189414	+	1.31740i
$796$		0			0
$797$	−20.7587	−	6.09530i	−0.735311	−	0.215907i	−0.107426	−	0.994213i	$-0.534261\pi$
$797$	−20.7587	−	6.09530i	−0.735311	−	0.215907i	−0.627885	+	0.778306i	$0.716079\pi$
$798$		0			0
$799$	−8.88276	−	10.2513i	−0.314250	−	0.362663i
$800$		0			0
$801$	−7.18346	+	8.29016i	−0.253815	+	0.292918i
$802$		0			0
$803$	0.345921	+	0.757462i	0.0122073	+	0.0267303i
$804$		0			0
$805$	−16.9448	+	8.06595i	−0.597227	+	0.284287i
$806$		0			0
$807$	−2.70696	−	5.92743i	−0.0952897	−	0.208655i
$808$		0			0
$809$	25.2910	−	29.1873i	0.889183	−	1.02617i	−0.110297	−	0.993899i	$-0.535180\pi$
$809$	25.2910	−	29.1873i	0.889183	−	1.02617i	0.999479	−	0.0322726i	$-0.0102745\pi$
$810$		0			0
$811$	−17.9636	−	20.7311i	−0.630788	−	0.727969i	0.346930	−	0.937891i	$-0.387224\pi$
$811$	−17.9636	−	20.7311i	−0.630788	−	0.727969i	−0.977718	+	0.209923i	$0.932679\pi$
$812$		0			0
$813$	21.4763	+	6.30600i	0.753205	+	0.221161i
$814$		0			0
$815$	−9.89428	+	68.8163i	−0.346582	+	2.41053i
$816$		0			0
$817$	−18.3535	+	40.1885i	−0.642107	+	1.40602i
$818$		0			0
$819$	−2.28831	+	1.47061i	−0.0799601	+	0.0513872i
$820$		0			0
$821$	−2.64575	−	18.4016i	−0.0923374	−	0.642221i	−0.982456	−	0.186492i	$-0.940288\pi$
$821$	−2.64575	−	18.4016i	−0.0923374	−	0.642221i	0.890119	−	0.455728i	$-0.150621\pi$
$822$		0			0
$823$	−31.3972	−	20.1778i	−1.09444	−	0.703353i	−0.136590	−	0.990628i	$-0.543614\pi$
$823$	−31.3972	−	20.1778i	−1.09444	−	0.703353i	−0.957848	+	0.287275i	$0.907251\pi$
$824$		0			0
$825$	0.768959	−	0.225787i	0.0267717	−	0.00786089i
$826$		0			0
$827$	−19.9983			−0.695409			−0.347704	−	0.937604i	$-0.613039\pi$
$827$	−19.9983			−0.695409			−0.347704	+	0.937604i	$0.613039\pi$
$828$		0			0
$829$	31.7857			1.10396			0.551982	−	0.833856i	$-0.313872\pi$
$829$	31.7857			1.10396			0.551982	+	0.833856i	$0.313872\pi$
$830$		0			0
$831$	5.27711	−	1.54950i	0.183061	−	0.0537515i
$832$		0			0
$833$	11.4392	+	7.35154i	0.396346	+	0.254716i
$834$		0			0
$835$	−8.83054	−	61.4178i	−0.305593	−	2.12545i
$836$		0			0
$837$	27.4983	−	17.6721i	0.950481	−	0.610837i
$838$		0			0
$839$	9.12250	−	19.9755i	0.314944	−	0.689631i	−0.684272	−	0.729227i	$-0.739880\pi$
$839$	9.12250	−	19.9755i	0.314944	−	0.689631i	0.999216	+	0.0395962i	$0.0126072\pi$
$840$		0			0
$841$	3.50337	−	24.3664i	0.120806	−	0.840222i
$842$		0			0
$843$	−15.3976	−	4.52115i	−0.530323	−	0.155717i
$844$		0			0
$845$	24.3165	+	28.0627i	0.836512	+	0.965387i
$846$		0			0
$847$	−9.16467	+	10.5766i	−0.314902	+	0.363416i
$848$		0			0
$849$	−3.02352	−	6.62058i	−0.103767	−	0.227218i
$850$		0			0
$851$	−49.0587	−	6.26042i	−1.68171	−	0.214605i
$852$		0			0
$853$	−21.7166	−	47.5526i	−0.743561	−	1.62817i	−0.777607	−	0.628751i	$-0.783566\pi$
$853$	−21.7166	−	47.5526i	−0.743561	−	1.62817i	0.0340455	−	0.999420i	$-0.489161\pi$
$854$		0			0
$855$	20.8664	−	24.0811i	0.713615	−	0.823555i
$856$		0			0
$857$	12.7263	+	14.6869i	0.434722	+	0.501696i	0.930265	−	0.366887i	$-0.119577\pi$
$857$	12.7263	+	14.6869i	0.434722	+	0.501696i	−0.495544	+	0.868583i	$0.665031\pi$
$858$		0			0
$859$	−13.3259	−	3.91284i	−0.454674	−	0.133504i	0.0463733	−	0.998924i	$-0.485234\pi$
$859$	−13.3259	−	3.91284i	−0.454674	−	0.133504i	−0.501047	+	0.865420i	$0.667052\pi$
$860$		0			0
$861$	0.825514	−	5.74157i	0.0281334	−	0.195672i
$862$		0			0
$863$	8.72736	−	19.1103i	0.297083	−	0.650521i	−0.700950	−	0.713210i	$-0.747240\pi$
$863$	8.72736	−	19.1103i	0.297083	−	0.650521i	0.998033	+	0.0626894i	$0.0199677\pi$
$864$		0			0
$865$	21.7534	−	13.9801i	0.739639	−	0.475337i
$866$		0			0
$867$	1.28313	+	8.92434i	0.0435773	+	0.303087i
$868$		0			0
$869$	2.44439	+	1.57091i	0.0829201	+	0.0532895i
$870$		0			0
$871$	−3.59621	+	1.05594i	−0.121853	+	0.0357793i
$872$		0			0
$873$	−26.4239			−0.894313
$874$		0			0
$875$	2.42242			0.0818928
$876$		0			0
$877$	−27.8078	+	8.16509i	−0.939001	+	0.275716i	−0.715200	−	0.698919i	$-0.753665\pi$
$877$	−27.8078	+	8.16509i	−0.939001	+	0.275716i	−0.223801	+	0.974635i	$0.571846\pi$
$878$		0			0
$879$	8.66953	+	5.57157i	0.292416	+	0.187924i
$880$		0			0
$881$	1.19897	+	8.33903i	0.0403944	+	0.280949i	1.00000		0.000399892i	$-0.000127290\pi$
$881$	1.19897	+	8.33903i	0.0403944	+	0.280949i	−0.959606	+	0.281349i	$0.909218\pi$
$882$		0			0
$883$	7.97555	−	5.12557i	0.268399	−	0.172489i	−0.399518	−	0.916725i	$-0.630823\pi$
$883$	7.97555	−	5.12557i	0.268399	−	0.172489i	0.667917	+	0.744236i	$0.267186\pi$
$884$		0			0
$885$	−4.45540	+	9.75596i	−0.149766	+	0.327943i
$886$		0			0
$887$	−0.00756554	+	0.0526195i	−0.000254026	+	0.00176679i	−0.989948	−	0.141431i	$-0.954830\pi$
$887$	−0.00756554	+	0.0526195i	−0.000254026	+	0.00176679i	0.989694	+	0.143198i	$0.0457386\pi$
$888$		0			0
$889$	−17.8200	−	5.23241i	−0.597662	−	0.175489i
$890$		0			0
$891$	0.420993	+	0.485852i	0.0141038	+	0.0162767i
$892$		0			0
$893$	16.0408	−	18.5121i	0.536785	−	0.619483i
$894$		0			0
$895$	−22.8461	−	50.0259i	−0.763660	−	1.67218i
$896$		0			0
$897$	−2.01677	+	3.25048i	−0.0673381	+	0.108530i
$898$		0			0
$899$	−6.32654	−	13.8532i	−0.211002	−	0.462030i
$900$		0			0
$901$	23.8574	−	27.5329i	0.794804	−	0.917252i
$902$		0			0
$903$	−6.88422	−	7.94481i	−0.229092	−	0.264387i
$904$		0			0
$905$	12.9339	+	3.79774i	0.429938	+	0.126241i
$906$		0			0
$907$	1.65663	−	11.5221i	0.0550077	−	0.382587i	−0.943657	−	0.330925i	$-0.892639\pi$
$907$	1.65663	−	11.5221i	0.0550077	−	0.382587i	0.998665	−	0.0516615i	$-0.0164517\pi$
$908$		0			0
$909$	−15.7679	+	34.5268i	−0.522987	+	1.14518i
$910$		0			0
$911$	−18.6436	+	11.9815i	−0.617691	+	0.396966i	−0.811734	−	0.584027i	$-0.801476\pi$
$911$	−18.6436	+	11.9815i	−0.617691	+	0.396966i	0.194043	+	0.980993i	$0.437840\pi$
$912$		0			0
$913$	−0.320150	−	2.22670i	−0.0105954	−	0.0736929i
$914$		0			0
$915$	15.6349	+	10.0479i	0.516873	+	0.332174i
$916$		0			0
$917$	23.0346	−	6.76358i	0.760671	−	0.223353i
$918$		0			0
$919$	−6.37804			−0.210392			−0.105196	−	0.994451i	$-0.533547\pi$
$919$	−6.37804			−0.210392			−0.105196	+	0.994451i	$0.533547\pi$
$920$		0			0
$921$	21.8851			0.721139
$922$		0			0
$923$	−6.35861	+	1.86706i	−0.209296	+	0.0614549i
$924$		0			0
$925$	−38.0063	−	24.4251i	−1.24964	−	0.803094i
$926$		0			0
$927$	−0.648911	−	4.51327i	−0.0213130	−	0.148235i
$928$		0			0
$929$	7.02396	−	4.51402i	0.230449	−	0.148100i	−0.420321	−	0.907375i	$-0.638083\pi$
$929$	7.02396	−	4.51402i	0.230449	−	0.148100i	0.650770	+	0.759275i	$0.274446\pi$
$930$		0			0
$931$	−10.2007	+	22.3364i	−0.334314	+	0.732046i
$932$		0			0
$933$	−3.71327	+	25.8263i	−0.121567	+	0.845516i
$934$		0			0
$935$	−1.59849	−	0.469360i	−0.0522763	−	0.0153497i
$936$		0			0
$937$	−23.2527	−	26.8350i	−0.759632	−	0.876662i	0.235833	−	0.971794i	$-0.424218\pi$
$937$	−23.2527	−	26.8350i	−0.759632	−	0.876662i	−0.995465	+	0.0951315i	$0.969673\pi$
$938$		0			0
$939$	14.8515	−	17.1395i	0.484659	−	0.559326i
$940$		0			0
$941$	−17.2715	−	37.8192i	−0.563033	−	1.23287i	−0.950424	−	0.310956i	$-0.899351\pi$
$941$	−17.2715	−	37.8192i	−0.563033	−	1.23287i	0.387391	−	0.921916i	$-0.373376\pi$
$942$		0			0
$943$	7.58859	+	24.4044i	0.247119	+	0.794715i
$944$		0			0
$945$	7.30440	+	15.9944i	0.237612	+	0.520298i
$946$		0			0
$947$	9.41531	−	10.8658i	0.305956	−	0.353092i	−0.581861	−	0.813288i	$-0.697675\pi$
$947$	9.41531	−	10.8658i	0.305956	−	0.353092i	0.887818	+	0.460196i	$0.152221\pi$
$948$		0			0
$949$	−2.37768	−	2.74399i	−0.0771827	−	0.0890736i
$950$		0			0
$951$	2.67038	+	0.784094i	0.0865930	+	0.0254260i
$952$		0			0
$953$	−1.92224	+	13.3695i	−0.0622676	+	0.433081i	0.934711	+	0.355408i	$0.115658\pi$
$953$	−1.92224	+	13.3695i	−0.0622676	+	0.433081i	−0.996979	+	0.0776728i	$0.975251\pi$
$954$		0			0
$955$	−19.5653	+	42.8420i	−0.633118	+	1.38634i
$956$		0			0
$957$	−0.322185	+	0.207056i	−0.0104148	+	0.00669316i
$958$		0			0
$959$	−3.81455	−	26.5308i	−0.123178	−	0.856723i
$960$		0			0
$961$	18.4381	+	11.8494i	0.594777	+	0.382240i
$962$		0			0
$963$	7.19666	−	2.11313i	0.231909	−	0.0680947i
$964$		0			0
$965$	39.4527			1.27003
$966$		0			0
$967$	−20.6391			−0.663709			−0.331855	−	0.943331i	$-0.607674\pi$
$967$	−20.6391			−0.663709			−0.331855	+	0.943331i	$0.607674\pi$
$968$		0			0
$969$	9.47351	−	2.78167i	0.304333	−	0.0893602i
$970$		0			0
$971$	35.2773	+	22.6713i	1.13210	+	0.727558i	0.965998	−	0.258551i	$-0.0832449\pi$
$971$	35.2773	+	22.6713i	1.13210	+	0.727558i	0.166104	+	0.986108i	$0.446881\pi$
$972$		0			0
$973$	2.49519	+	17.3544i	0.0799921	+	0.556357i
$974$		0			0
$975$	−2.93966	+	1.88921i	−0.0941445	+	0.0605030i
$976$		0			0
$977$	−5.15187	+	11.2810i	−0.164823	+	0.360912i	−0.973964	−	0.226702i	$-0.927206\pi$
$977$	−5.15187	+	11.2810i	−0.164823	+	0.360912i	0.809141	+	0.587615i	$0.199933\pi$
$978$		0			0
$979$	−0.147395	+	1.02516i	−0.00471078	+	0.0327642i
$980$		0			0
$981$	−1.04904	−	0.308026i	−0.0334932	−	0.00983450i
$982$		0			0
$983$	−24.3582	−	28.1109i	−0.776907	−	0.896598i	0.219975	−	0.975506i	$-0.429402\pi$
$983$	−24.3582	−	28.1109i	−0.776907	−	0.896598i	−0.996882	+	0.0789071i	$0.974857\pi$
$984$		0			0
$985$	−5.24278	+	6.05050i	−0.167049	+	0.192785i
$986$		0			0
$987$	2.42119	+	5.30166i	0.0770673	+	0.168754i
$988$		0			0
$989$	42.4316	+	18.5696i	1.34925	+	0.590478i
$990$		0			0
$991$	−8.00306	−	17.5243i	−0.254226	−	0.556677i	0.738888	−	0.673828i	$-0.235351\pi$
$991$	−8.00306	−	17.5243i	−0.254226	−	0.556677i	−0.993114	+	0.117151i	$0.962624\pi$
$992$		0			0
$993$	−15.6244	+	18.0316i	−0.495826	+	0.572214i
$994$		0			0
$995$	36.5015	+	42.1250i	1.15718	+	1.33545i
$996$		0			0
$997$	16.5154	+	4.84936i	0.523048	+	0.153581i	0.532589	−	0.846374i	$-0.321219\pi$
$997$	16.5154	+	4.84936i	0.523048	+	0.153581i	−0.00954163	+	0.999954i	$0.503037\pi$
$998$		0			0
$999$	−6.59463	+	45.8666i	−0.208645	+	1.45116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.e.257.2		30
4.3	odd	2		184.2.i.b.73.2	✓	30
23.6	even	11	inner	368.2.m.e.305.2		30
23.11	odd	22		8464.2.a.ch.1.10		15
23.12	even	11		8464.2.a.cg.1.10		15
92.11	even	22		4232.2.a.ba.1.6		15
92.35	odd	22		4232.2.a.bb.1.6		15
92.75	odd	22		184.2.i.b.121.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.i.b.73.2	✓	30	4.3	odd	2
184.2.i.b.121.2	yes	30	92.75	odd	22
368.2.m.e.257.2		30	1.1	even	1	trivial
368.2.m.e.305.2		30	23.6	even	11	inner
4232.2.a.ba.1.6		15	92.11	even	22
4232.2.a.bb.1.6		15	92.35	odd	22
8464.2.a.cg.1.10		15	23.12	even	11
8464.2.a.ch.1.10		15	23.11	odd	22

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.m (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.817468 + 0.240030i) q^{3} +(2.57662 + 1.65589i) q^{5} +(0.181823 + 1.26461i) q^{7} +(-1.91312 + 1.22949i) q^{9} +O(q^{10})\)	\(q+(-0.817468 + 0.240030i) q^{3} +(2.57662 + 1.65589i) q^{5} +(0.181823 + 1.26461i) q^{7} +(-1.91312 + 1.22949i) q^{9} +(-0.0891963 + 0.195313i) q^{11} +(0.133237 - 0.926681i) q^{13} +(-2.50377 - 0.735173i) q^{15} +(1.65894 + 1.91452i) q^{17} +(-2.99577 + 3.45730i) q^{19} +(-0.452179 - 0.990134i) q^{21} +(3.67385 + 3.08267i) q^{23} +(1.81991 + 3.98505i) q^{25} +(2.94258 - 3.39592i) q^{27} +(-1.37099 - 1.58221i) q^{29} +(6.97977 + 2.04945i) q^{31} +(0.0260342 - 0.181072i) q^{33} +(-1.62557 + 3.55950i) q^{35} +(-8.67535 + 5.57531i) q^{37} +(0.113515 + 0.789513i) q^{39} +(4.48304 + 2.88108i) q^{41} +(9.26657 - 2.72091i) q^{43} -6.96529 q^{45} -5.35449 q^{47} +(5.15027 - 1.51226i) q^{49} +(-1.81567 - 1.16686i) q^{51} +(-2.04664 - 14.2347i) q^{53} +(-0.553242 + 0.355547i) q^{55} +(1.61909 - 3.54531i) q^{57} +(0.584927 - 4.06826i) q^{59} +(-6.83371 - 2.00656i) q^{61} +(-1.90267 - 2.19580i) q^{63} +(1.87778 - 2.16708i) q^{65} +(-1.66308 - 3.64163i) q^{67} +(-3.74319 - 1.63815i) q^{69} +(-2.94055 - 6.43891i) q^{71} +(2.53968 - 2.93095i) q^{73} +(-2.44425 - 2.82082i) q^{75} +(-0.263212 - 0.0772860i) q^{77} +(1.92588 - 13.3948i) q^{79} +(1.24378 - 2.72350i) q^{81} +(-8.81386 + 5.66433i) q^{83} +(1.10422 + 7.68000i) q^{85} +(1.50052 + 0.964324i) q^{87} +(4.62819 - 1.35896i) q^{89} +1.19611 q^{91} -6.19767 q^{93} +(-13.4439 + 3.94748i) q^{95} +(9.77480 + 6.28188i) q^{97} +(-0.0694913 - 0.483322i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9	\( 30 q - 2 q^{3} + 13 q^{7} + 21 q^{9} - 2 q^{11} + 2 q^{15} - 22 q^{17} - 3 q^{19} + 2 q^{21} - q^{23} + 13 q^{25} + 31 q^{27} + 7 q^{29} - 18 q^{31} - 8 q^{33} - 41 q^{35} - 62 q^{37} - 6 q^{39} - 15 q^{41} + 47 q^{43} + 8 q^{45} + 72 q^{47} - 16 q^{49} + 7 q^{51} - 43 q^{53} + 9 q^{55} - 42 q^{57} + 11 q^{59} + 57 q^{61} + 62 q^{63} + 14 q^{65} + 27 q^{67} - 22 q^{69} - 48 q^{71} - 12 q^{73} - 87 q^{75} - 3 q^{77} - 8 q^{79} + 123 q^{81} + 18 q^{83} + 54 q^{85} - 137 q^{87} - 23 q^{89} - 142 q^{91} - 110 q^{93} - 119 q^{95} + 47 q^{97} + 17 q^{99}+O(q^{100}) \) 30 * q - 2 * q^3 + 13 * q^7 + 21 * q^9 - 2 * q^11 + 2 * q^15 - 22 * q^17 - 3 * q^19 + 2 * q^21 - q^23 + 13 * q^25 + 31 * q^27 + 7 * q^29 - 18 * q^31 - 8 * q^33 - 41 * q^35 - 62 * q^37 - 6 * q^39 - 15 * q^41 + 47 * q^43 + 8 * q^45 + 72 * q^47 - 16 * q^49 + 7 * q^51 - 43 * q^53 + 9 * q^55 - 42 * q^57 + 11 * q^59 + 57 * q^61 + 62 * q^63 + 14 * q^65 + 27 * q^67 - 22 * q^69 - 48 * q^71 - 12 * q^73 - 87 * q^75 - 3 * q^77 - 8 * q^79 + 123 * q^81 + 18 * q^83 + 54 * q^85 - 137 * q^87 - 23 * q^89 - 142 * q^91 - 110 * q^93 - 119 * q^95 + 47 * q^97 + 17 * q^99

Introduction

L-functions

Modular forms

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