LMFDB - Embedded newform 441.2.bb.d.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(37,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 32]))

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

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

chi := DirichletCharacter("441.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bb (of order $21$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	441.109
Dual form			441.2.bb.d.352.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02480 - 0.950878i) q^{2} +(-0.00340854 + 0.0454838i) q^{4} +(1.11243 - 2.83442i) q^{5} +(2.44418 - 1.01290i) q^{7} +(1.78303 + 2.23585i) q^{8} +O(q^{10})$	\(q+(1.02480 - 0.950878i) q^{2} +(-0.00340854 + 0.0454838i) q^{4} +(1.11243 - 2.83442i) q^{5} +(2.44418 - 1.01290i) q^{7} +(1.78303 + 2.23585i) q^{8} +(-1.55517 - 3.96251i) q^{10} +(-4.91424 - 1.51584i) q^{11} +(0.369081 + 1.61705i) q^{13} +(1.54166 - 3.36214i) q^{14} +(3.86306 + 0.582263i) q^{16} +(2.42053 - 1.65029i) q^{17} +(-0.170770 - 0.295782i) q^{19} +(0.125128 + 0.0602587i) q^{20} +(-6.47751 + 3.11940i) q^{22} +(2.94916 + 2.01070i) q^{23} +(-3.13119 - 2.90532i) q^{25} +(1.91585 + 1.30621i) q^{26} +(0.0377395 + 0.114623i) q^{28} +(-5.41330 - 2.60691i) q^{29} +(1.30646 - 2.26286i) q^{31} +(-0.213141 + 0.145317i) q^{32} +(0.911342 - 3.99285i) q^{34} +(-0.152014 - 8.05463i) q^{35} +(-0.120508 - 1.60806i) q^{37} +(-0.456258 - 0.140737i) q^{38} +(8.32082 - 2.56663i) q^{40} +(2.03064 + 2.54634i) q^{41} +(-2.88168 + 3.61351i) q^{43} +(0.0856967 - 0.218352i) q^{44} +(4.93423 - 0.743716i) q^{46} +(-7.48457 + 6.94467i) q^{47} +(4.94806 - 4.95144i) q^{49} -5.97146 q^{50} +(-0.0748076 + 0.0112754i) q^{52} +(-0.217030 + 2.89606i) q^{53} +(-9.76328 + 12.2428i) q^{55} +(6.62274 + 3.65878i) q^{56} +(-8.02642 + 2.47582i) q^{58} +(3.40185 + 8.66778i) q^{59} +(0.385625 + 5.14581i) q^{61} +(-0.812835 - 3.56126i) q^{62} +(-1.81889 + 7.96909i) q^{64} +(4.99398 + 0.752722i) q^{65} +(-5.99203 + 10.3785i) q^{67} +(0.0668109 + 0.115720i) q^{68} +(-7.81475 - 8.10985i) q^{70} +(1.67332 - 0.805828i) q^{71} +(9.61611 + 8.92245i) q^{73} +(-1.65257 - 1.53336i) q^{74} +(0.0140354 - 0.00675907i) q^{76} +(-13.5467 + 1.27265i) q^{77} +(-6.91937 - 11.9847i) q^{79} +(5.94776 - 10.3018i) q^{80} +(4.50226 + 0.678606i) q^{82} +(-0.194494 + 0.852134i) q^{83} +(-1.98495 - 8.69663i) q^{85} +(0.482856 + 6.44326i) q^{86} +(-5.37304 - 13.6903i) q^{88} +(0.454630 - 0.140235i) q^{89} +(2.54002 + 3.57852i) q^{91} +(-0.101507 + 0.127285i) q^{92} +(-1.06668 + 14.2338i) q^{94} +(-1.02834 + 0.154997i) q^{95} +7.70896 q^{97} +(0.362570 - 9.77924i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	$ 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) $ 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{20}{21}\right)$	$1$

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 $

$2$	1.02480	−	0.950878i	0.724645	−	0.672372i	−0.228959	−	0.973436i	$-0.573532\pi$
$2$	1.02480	−	0.950878i	0.724645	−	0.672372i	0.953604	+	0.301064i	$0.0973418\pi$
$3$		0			0
$3$		0			0
$4$	−0.00340854	+	0.0454838i	−0.00170427	+	0.0227419i
$5$	1.11243	−	2.83442i	0.497493	−	1.26759i	−0.433037	−	0.901376i	$-0.642558\pi$
$5$	1.11243	−	2.83442i	0.497493	−	1.26759i	0.930530	−	0.366216i	$-0.119347\pi$
$6$		0			0
$7$	2.44418	−	1.01290i	0.923814	−	0.382841i
$7$	2.44418	−	1.01290i	0.923814	−	0.382841i
$8$	1.78303	+	2.23585i	0.630395	+	0.790491i
$9$		0			0
$10$	−1.55517	−	3.96251i	−0.491788	−	1.25305i
$11$	−4.91424	−	1.51584i	−1.48170	−	0.457044i	−0.554682	−	0.832062i	$-0.687160\pi$
$11$	−4.91424	−	1.51584i	−1.48170	−	0.457044i	−0.927017	+	0.375018i	$0.877636\pi$
$12$		0			0
$13$	0.369081	+	1.61705i	0.102365	+	0.448489i	0.999970	+	0.00768993i	$0.00244780\pi$
$13$	0.369081	+	1.61705i	0.102365	+	0.448489i	−0.897606	+	0.440799i	$0.854695\pi$
$14$	1.54166	−	3.36214i	0.412025	−	0.898571i
$15$		0			0
$16$	3.86306	+	0.582263i	0.965766	+	0.145566i
$17$	2.42053	−	1.65029i	0.587065	−	0.400254i	−0.233040	−	0.972467i	$-0.574867\pi$
$17$	2.42053	−	1.65029i	0.587065	−	0.400254i	0.820105	+	0.572213i	$0.193915\pi$
$18$		0			0
$19$	−0.170770	−	0.295782i	−0.0391773	−	0.0678571i	0.845772	−	0.533545i	$-0.179140\pi$
$19$	−0.170770	−	0.295782i	−0.0391773	−	0.0678571i	−0.884949	+	0.465688i	$0.845807\pi$
$20$	0.125128	+	0.0602587i	0.0279796	+	0.0134743i
$21$		0			0
$22$	−6.47751	+	3.11940i	−1.38101	+	0.665059i
$23$	2.94916	+	2.01070i	0.614941	+	0.419260i	0.830333	−	0.557268i	$-0.188150\pi$
$23$	2.94916	+	2.01070i	0.614941	+	0.419260i	−0.215391	+	0.976528i	$0.569103\pi$
$24$		0			0
$25$	−3.13119	−	2.90532i	−0.626238	−	0.581064i
$26$	1.91585	+	1.30621i	0.375730	+	0.256168i
$27$		0			0
$28$	0.0377395	+	0.114623i	0.00713210	+	0.0216617i
$29$	−5.41330	−	2.60691i	−1.00523	−	0.484091i	−0.142517	−	0.989792i	$-0.545519\pi$
$29$	−5.41330	−	2.60691i	−1.00523	−	0.484091i	−0.862709	+	0.505701i	$0.831234\pi$
$30$		0			0
$31$	1.30646	−	2.26286i	0.234647	−	0.406421i	−0.724523	−	0.689251i	$-0.757940\pi$
$31$	1.30646	−	2.26286i	0.234647	−	0.406421i	0.959170	+	0.282830i	$0.0912732\pi$
$32$	−0.213141	+	0.145317i	−0.0376784	+	0.0256887i
$33$		0			0
$34$	0.911342	−	3.99285i	0.156294	−	0.684768i
$35$	−0.152014	−	8.05463i	−0.0256951	−	1.36148i
$36$		0			0
$37$	−0.120508	−	1.60806i	−0.0198113	−	0.264364i	−0.998310	−	0.0581114i	$-0.981492\pi$
$37$	−0.120508	−	1.60806i	−0.0198113	−	0.264364i	0.978499	−	0.206253i	$-0.0661269\pi$
$38$	−0.456258	−	0.140737i	−0.0740148	−	0.0228305i
$39$		0			0
$40$	8.32082	−	2.56663i	1.31564	−	0.405820i
$41$	2.03064	+	2.54634i	0.317132	+	0.397671i	0.914691	−	0.404154i	$-0.132434\pi$
$41$	2.03064	+	2.54634i	0.317132	+	0.397671i	−0.597559	+	0.801825i	$0.703863\pi$
$42$		0			0
$43$	−2.88168	+	3.61351i	−0.439452	+	0.551055i	−0.951399	−	0.307962i	$-0.900353\pi$
$43$	−2.88168	+	3.61351i	−0.439452	+	0.551055i	0.511947	+	0.859017i	$0.328925\pi$
$44$	0.0856967	−	0.218352i	0.0129193	−	0.0329177i
$45$		0			0
$46$	4.93423	−	0.743716i	0.727513	−	0.109655i
$47$	−7.48457	+	6.94467i	−1.09174	+	1.01298i	−0.0918856	+	0.995770i	$0.529289\pi$
$47$	−7.48457	+	6.94467i	−1.09174	+	1.01298i	−0.999852	+	0.0172147i	$0.994520\pi$
$48$		0			0
$49$	4.94806	−	4.95144i	0.706865	−	0.707348i
$50$	−5.97146			−0.844492
$51$		0			0
$52$	−0.0748076	+	0.0112754i	−0.0103739	+	0.00156362i
$53$	−0.217030	+	2.89606i	−0.0298113	+	0.397804i	0.962260	+	0.272131i	$0.0877283\pi$
$53$	−0.217030	+	2.89606i	−0.0298113	+	0.397804i	−0.992072	+	0.125674i	$0.959891\pi$
$54$		0			0
$55$	−9.76328	+	12.2428i	−1.31648	+	1.65081i
$56$	6.62274	+	3.65878i	0.885000	+	0.488925i
$57$		0			0
$58$	−8.02642	+	2.47582i	−1.05392	+	0.325091i
$59$	3.40185	+	8.66778i	0.442883	+	1.12845i	0.961831	+	0.273643i	$0.0882286\pi$
$59$	3.40185	+	8.66778i	0.442883	+	1.12845i	−0.518948	+	0.854806i	$0.673676\pi$
$60$		0			0
$61$	0.385625	+	5.14581i	0.0493742	+	0.658854i	0.965906	+	0.258892i	$0.0833574\pi$
$61$	0.385625	+	5.14581i	0.0493742	+	0.658854i	−0.916532	+	0.399961i	$0.869024\pi$
$62$	−0.812835	−	3.56126i	−0.103230	−	0.452281i
$63$		0			0
$64$	−1.81889	+	7.96909i	−0.227362	+	0.996136i
$65$	4.99398	+	0.752722i	0.619427	+	0.0933636i
$66$		0			0
$67$	−5.99203	+	10.3785i	−0.732044	+	1.26794i	0.223965	+	0.974597i	$0.428100\pi$
$67$	−5.99203	+	10.3785i	−0.732044	+	1.26794i	−0.956008	+	0.293339i	$0.905233\pi$
$68$	0.0668109	+	0.115720i	0.00810201	+	0.0140331i
$69$		0			0
$70$	−7.81475	−	8.10985i	−0.934041	−	0.969313i
$71$	1.67332	−	0.805828i	0.198586	−	0.0956342i	−0.331948	−	0.943298i	$-0.607706\pi$
$71$	1.67332	−	0.805828i	0.198586	−	0.0956342i	0.530534	+	0.847664i	$0.321991\pi$
$72$		0			0
$73$	9.61611	+	8.92245i	1.12548	+	1.04429i	0.998628	+	0.0523724i	$0.0166783\pi$
$73$	9.61611	+	8.92245i	1.12548	+	1.04429i	0.126853	+	0.991921i	$0.459512\pi$
$74$	−1.65257	−	1.53336i	−0.192107	−	0.178249i
$75$		0			0
$76$	0.0140354	−	0.00675907i	0.00160997	−	0.000775319i
$77$	−13.5467	+	1.27265i	−1.54379	+	0.145032i
$78$		0			0
$79$	−6.91937	−	11.9847i	−0.778490	−	1.34838i	−0.932812	−	0.360364i	$-0.882652\pi$
$79$	−6.91937	−	11.9847i	−0.778490	−	1.34838i	0.154321	−	0.988021i	$-0.450681\pi$
$80$	5.94776	−	10.3018i	0.664980	−	1.15178i
$81$		0			0
$82$	4.50226	+	0.678606i	0.497191	+	0.0749395i
$83$	−0.194494	+	0.852134i	−0.0213485	+	0.0935338i	−0.984480	−	0.175498i	$-0.943846\pi$
$83$	−0.194494	+	0.852134i	−0.0213485	+	0.0935338i	0.963131	+	0.269032i	$0.0867036\pi$
$84$		0			0
$85$	−1.98495	−	8.69663i	−0.215298	−	0.943282i
$86$	0.482856	+	6.44326i	0.0520677	+	0.694795i
$87$		0			0
$88$	−5.37304	−	13.6903i	−0.572768	−	1.45939i
$89$	0.454630	−	0.140235i	0.0481907	−	0.0148648i	−0.270566	−	0.962701i	$-0.587211\pi$
$89$	0.454630	−	0.140235i	0.0481907	−	0.0148648i	0.318757	+	0.947837i	$0.396735\pi$
$90$		0			0
$91$	2.54002	+	3.57852i	0.266266	+	0.375131i
$92$	−0.101507	+	0.127285i	−0.0105828	+	0.0132704i
$93$		0			0
$94$	−1.06668	+	14.2338i	−0.110019	+	1.46811i
$95$	−1.02834	+	0.154997i	−0.105506	+	0.0159024i
$96$		0			0
$97$	7.70896			0.782726			0.391363	−	0.920236i	$-0.372004\pi$
$97$	7.70896			0.782726			0.391363	+	0.920236i	$0.372004\pi$
$98$	0.362570	−	9.77924i	0.0366251	−	0.987853i
$99$		0			0
$100$	0.142818	−	0.132515i	0.0142818	−	0.0132515i
$101$	0.812223	−	0.122423i	0.0808192	−	0.0121815i	−0.108508	−	0.994096i	$-0.534607\pi$
$101$	0.812223	−	0.122423i	0.0808192	−	0.0121815i	0.189327	+	0.981914i	$0.439369\pi$
$102$		0			0
$103$	0.469049	−	1.19512i	0.0462168	−	0.117758i	−0.905901	−	0.423489i	$-0.860805\pi$
$103$	0.469049	−	1.19512i	0.0462168	−	0.117758i	0.952118	+	0.305730i	$0.0989006\pi$
$104$	−2.95739	+	3.70845i	−0.289996	+	0.363644i
$105$		0			0
$106$	2.53139	+	3.17426i	0.245870	+	0.308311i
$107$	−8.31467	+	2.56474i	−0.803810	+	0.247942i	−0.669322	−	0.742973i	$-0.733415\pi$
$107$	−8.31467	+	2.56474i	−0.803810	+	0.247942i	−0.134488	+	0.990915i	$0.542939\pi$
$108$		0			0
$109$	−14.5211	−	4.47918i	−1.39087	−	0.429028i	−0.493287	−	0.869866i	$-0.664205\pi$
$109$	−14.5211	−	4.47918i	−1.39087	−	0.429028i	−0.897586	+	0.440839i	$0.854681\pi$
$110$	1.63594	+	21.8301i	0.155981	+	2.08142i
$111$		0			0
$112$	10.0318	−	2.48975i	0.947917	−	0.235259i
$113$	−2.37904	+	10.4232i	−0.223801	+	0.980536i	0.730787	+	0.682606i	$0.239153\pi$
$113$	−2.37904	+	10.4232i	−0.223801	+	0.980536i	−0.954588	+	0.297930i	$0.903704\pi$
$114$		0			0
$115$	8.97990	−	6.12239i	0.837380	−	0.570916i
$116$	0.137024	−	0.237332i	0.0127223	−	0.0220357i
$117$		0			0
$118$	11.7282	+	5.64801i	1.07967	+	0.519942i
$119$	4.24463	−	6.48537i	0.389105	−	0.594513i
$120$		0			0
$121$	12.7634	+	8.70192i	1.16031	+	0.791084i
$122$	5.28823	+	4.90676i	0.478774	+	0.444237i
$123$		0			0
$124$	0.0984701	+	0.0671358i	0.00884287	+	0.00602897i
$125$	1.99869	−	0.962519i	0.178768	−	0.0860903i
$126$		0			0
$127$	4.39159	+	2.11488i	0.389691	+	0.187665i	0.618461	−	0.785815i	$-0.287756\pi$
$127$	4.39159	+	2.11488i	0.389691	+	0.187665i	−0.228771	+	0.973480i	$0.573471\pi$
$128$	5.45566	+	9.44948i	0.482217	+	0.835224i
$129$		0			0
$130$	5.83359	−	3.97727i	0.511640	−	0.348830i
$131$	−4.74215	−	0.714764i	−0.414324	−	0.0624493i	−0.0614271	−	0.998112i	$-0.519565\pi$
$131$	−4.74215	−	0.714764i	−0.414324	−	0.0624493i	−0.352897	+	0.935662i	$0.614803\pi$
$132$		0			0
$133$	−0.716991	−	0.549972i	−0.0621710	−	0.0476886i
$134$	3.72804	+	16.3336i	0.322054	+	1.41101i
$135$		0			0
$136$	8.00566	+	2.46942i	0.686480	+	0.211751i
$137$	−6.46097	−	16.4623i	−0.551998	−	1.40647i	−0.885908	−	0.463862i	$-0.846463\pi$
$137$	−6.46097	−	16.4623i	−0.551998	−	1.40647i	0.333910	−	0.942605i	$-0.391632\pi$
$138$		0			0
$139$	−6.10524	−	7.65573i	−0.517840	−	0.649350i	0.452309	−	0.891861i	$-0.350600\pi$
$139$	−6.10524	−	7.65573i	−0.517840	−	0.649350i	−0.970149	+	0.242511i	$0.922029\pi$
$140$	0.366873	+	0.0205403i	0.0310064	+	0.00173597i
$141$		0			0
$142$	0.948577	−	2.41694i	0.0796029	−	0.202825i
$143$	0.637440	−	8.50605i	0.0533054	−	0.711312i
$144$		0			0
$145$	−13.4110	+	12.4436i	−1.11372	+	1.03338i
$146$	18.3388			1.51773
$147$		0			0
$148$	0.0735516			0.00604590
$149$	3.46035	−	3.21074i	0.283483	−	0.263034i	−0.525595	−	0.850735i	$-0.676157\pi$
$149$	3.46035	−	3.21074i	0.283483	−	0.263034i	0.809078	+	0.587701i	$0.199967\pi$
$150$		0			0
$151$	0.915924	−	12.2222i	0.0745368	−	0.994625i	−0.827079	−	0.562086i	$-0.809999\pi$
$151$	0.915924	−	12.2222i	0.0745368	−	0.994625i	0.901615	−	0.432539i	$-0.142382\pi$
$152$	0.356836	−	0.909203i	0.0289432	−	0.0737461i
$153$		0			0
$154$	−12.6726	+	14.1855i	−1.02118	+	1.14310i
$155$	−4.96054	−	6.22032i	−0.398440	−	0.499628i
$156$		0			0
$157$	−6.63852	−	16.9147i	−0.529811	−	1.34994i	−0.905954	−	0.423376i	$-0.860845\pi$
$157$	−6.63852	−	16.9147i	−0.529811	−	1.34994i	0.376143	−	0.926562i	$-0.377250\pi$
$158$	−18.4870	−	5.70248i	−1.47075	−	0.453665i
$159$		0			0
$160$	0.174786	+	0.765788i	0.0138181	+	0.0605408i
$161$	9.24492	+	1.92731i	0.728602	+	0.151893i
$162$		0			0
$163$	−2.29461	−	0.345857i	−0.179728	−	0.0270896i	0.0585616	−	0.998284i	$-0.481349\pi$
$163$	−2.29461	−	0.345857i	−0.179728	−	0.0270896i	−0.238289	+	0.971194i	$0.576587\pi$
$164$	−0.122738	+	0.0836817i	−0.00958427	+	0.00653444i
$165$		0			0
$166$	0.610957	+	1.05821i	0.0474195	+	0.0821329i
$167$	10.9122	+	5.25502i	0.844409	+	0.406646i	0.805499	−	0.592597i	$-0.201897\pi$
$167$	10.9122	+	5.25502i	0.844409	+	0.406646i	0.0389096	+	0.999243i	$0.487612\pi$
$168$		0			0
$169$	9.23396	−	4.44684i	0.710305	−	0.342065i
$170$	−10.3036	−	7.02489i	−0.790251	−	0.538784i
$171$		0			0
$172$	−0.154534	−	0.143386i	−0.0117831	−	0.0109331i
$173$	−2.39542	−	1.63317i	−0.182120	−	0.124168i	0.468828	−	0.883289i	$-0.344676\pi$
$173$	−2.39542	−	1.63317i	−0.182120	−	0.124168i	−0.650949	+	0.759122i	$0.725629\pi$
$174$		0			0
$175$	−10.5960	−	3.92954i	−0.800983	−	0.297046i
$176$	−18.1014	−	8.71718i	−1.36444	−	0.657082i
$177$		0			0
$178$	0.332560	−	0.576010i	0.0249264	−	0.0431738i
$179$	−6.37293	+	4.34499i	−0.476335	+	0.324760i	−0.777577	−	0.628788i	$-0.783551\pi$
$179$	−6.37293	+	4.34499i	−0.476335	+	0.324760i	0.301241	+	0.953548i	$0.402599\pi$
$180$		0			0
$181$	4.32264	−	18.9387i	0.321300	−	1.40771i	−0.513943	−	0.857824i	$-0.671816\pi$
$181$	4.32264	−	18.9387i	0.321300	−	1.40771i	0.835243	−	0.549881i	$-0.185327\pi$
$182$	6.00575	+	1.25203i	0.445176	+	0.0928070i
$183$		0			0
$184$	0.762810	+	10.1790i	0.0562351	+	0.750405i
$185$	−4.69199	−	1.44729i	−0.344962	−	0.106407i
$186$		0			0
$187$	−14.3967	+	4.44078i	−1.05279	+	0.324742i
$188$	−0.290358	−	0.364098i	−0.0211766	−	0.0265546i
$189$		0			0
$190$	−0.906462	+	1.13667i	−0.0657617	+	0.0824626i
$191$	−0.714386	+	1.82023i	−0.0516912	+	0.131707i	−0.954387	−	0.298572i	$-0.903490\pi$
$191$	−0.714386	+	1.82023i	−0.0516912	+	0.131707i	0.902696	+	0.430279i	$0.141585\pi$
$192$		0			0
$193$	−3.50075	+	0.527653i	−0.251989	+	0.0379813i	−0.273822	−	0.961780i	$-0.588288\pi$
$193$	−3.50075	+	0.527653i	−0.251989	+	0.0379813i	0.0218327	+	0.999762i	$0.493050\pi$
$194$	7.90016	−	7.33028i	0.567199	−	0.526283i
$195$		0			0
$196$	0.208344	+	0.241933i	0.0148817	+	0.0172810i
$197$	23.0280			1.64068			0.820339	−	0.571877i	$-0.193785\pi$
$197$	23.0280			1.64068			0.820339	+	0.571877i	$0.193785\pi$
$198$		0			0
$199$	−16.0129	+	2.41355i	−1.13512	+	0.171092i	−0.689609	−	0.724182i	$-0.742217\pi$
$199$	−16.0129	+	2.41355i	−1.13512	+	0.171092i	−0.445515	+	0.895275i	$0.646979\pi$
$200$	0.912849	−	12.1811i	0.0645482	−	0.861336i
$201$		0			0
$202$	0.715959	−	0.897784i	0.0503747	−	0.0631679i
$203$	−15.8716	−	0.888614i	−1.11397	−	0.0623685i
$204$		0			0
$205$	9.47633	−	2.92306i	0.661856	−	0.204155i
$206$	−0.655728	−	1.67077i	−0.0456867	−	0.116408i
$207$		0			0
$208$	0.484235	+	6.46167i	0.0335757	+	0.448036i
$209$	0.390845	+	1.71241i	0.0270353	+	0.118450i
$210$		0			0
$211$	−4.38992	+	19.2335i	−0.302215	+	1.32409i	0.564561	+	0.825391i	$0.309045\pi$
$211$	−4.38992	+	19.2335i	−0.302215	+	1.32409i	−0.866776	+	0.498698i	$0.833812\pi$
$212$	−0.130984	−	0.0197427i	−0.00899601	−	0.00135593i
$213$		0			0
$214$	−6.08215	+	10.5346i	−0.415767	+	0.720129i
$215$	7.03655	+	12.1877i	0.479889	+	0.831192i
$216$		0			0
$217$	0.901175	−	6.85415i	0.0611758	−	0.465290i
$218$	−19.1405	+	9.21756i	−1.29636	+	0.624292i
$219$		0			0
$220$	−0.523569	−	0.485801i	−0.0352990	−	0.0327527i
$221$	3.56197	+	3.30503i	0.239604	+	0.222320i
$222$		0			0
$223$	7.53918	−	3.63068i	0.504861	−	0.243128i	−0.164076	−	0.986448i	$-0.552464\pi$
$223$	7.53918	−	3.63068i	0.504861	−	0.243128i	0.668936	+	0.743320i	$0.266750\pi$
$224$	−0.373764	+	0.571074i	−0.0249732	+	0.0381565i
$225$		0			0
$226$	7.47319	+	12.9439i	0.497109	+	0.861018i
$227$	13.1924	−	22.8500i	0.875613	−	1.51661i	0.0195053	−	0.999810i	$-0.493791\pi$
$227$	13.1924	−	22.8500i	0.875613	−	1.51661i	0.856108	−	0.516797i	$-0.172876\pi$
$228$		0			0
$229$	3.78238	+	0.570102i	0.249947	+	0.0376734i	0.272820	−	0.962065i	$-0.412044\pi$
$229$	3.78238	+	0.570102i	0.249947	+	0.0376734i	−0.0228739	+	0.999738i	$0.507282\pi$
$230$	3.38098	−	14.8130i	0.222935	−	0.976742i
$231$		0			0
$232$	−3.82342	−	16.7515i	−0.251020	−	1.09979i
$233$	0.0329808	+	0.440098i	0.00216064	+	0.0288318i	0.998180	−	0.0603064i	$-0.0192078\pi$
$233$	0.0329808	+	0.440098i	0.00216064	+	0.0288318i	−0.996019	+	0.0891382i	$0.971589\pi$
$234$		0			0
$235$	11.3581	+	28.9399i	0.740919	+	1.88783i
$236$	−0.405839	+	0.125185i	−0.0264178	+	0.00814883i
$237$		0			0
$238$	−1.81688	−	10.6824i	−0.117771	−	0.692434i
$239$	−3.94650	+	4.94875i	−0.255278	+	0.320108i	−0.892912	−	0.450231i	$-0.851342\pi$
$239$	−3.94650	+	4.94875i	−0.255278	+	0.320108i	0.637634	+	0.770339i	$0.279913\pi$
$240$		0			0
$241$	1.03222	−	13.7741i	0.0664913	−	0.887265i	−0.859842	−	0.510560i	$-0.829438\pi$
$241$	1.03222	−	13.7741i	0.0664913	−	0.887265i	0.926333	−	0.376705i	$-0.122943\pi$
$242$	21.3544	−	3.21866i	1.37271	−	0.206903i
$243$		0			0
$244$	−0.235365			−0.0150677
$245$	−8.53010	−	19.5330i	−0.544968	−	1.24792i
$246$		0			0
$247$	0.415267	−	0.385311i	0.0264228	−	0.0245168i
$248$	7.38885	−	1.11369i	0.469192	−	0.0707194i
$249$		0			0
$250$	1.13303	−	2.88690i	0.0716588	−	0.182584i
$251$	−7.71990	+	9.68045i	−0.487276	+	0.611025i	−0.963306	−	0.268404i	$-0.913504\pi$
$251$	−7.71990	+	9.68045i	−0.487276	+	0.611025i	0.476030	+	0.879429i	$0.342075\pi$
$252$		0			0
$253$	−11.4450	−	14.3515i	−0.719538	−	0.902273i
$254$	6.51150	−	2.00853i	0.408568	−	0.126027i
$255$		0			0
$256$	−1.04549	−	0.322491i	−0.0653431	−	0.0201557i
$257$	−1.43568	−	19.1578i	−0.0895553	−	1.19503i	−0.843145	−	0.537687i	$-0.819298\pi$
$257$	−1.43568	−	19.1578i	−0.0895553	−	1.19503i	0.753589	−	0.657345i	$-0.228321\pi$
$258$		0			0
$259$	−1.92335	−	3.80834i	−0.119511	−	0.236639i
$260$	−0.0512588	+	0.224579i	−0.00317894	+	0.0139278i
$261$		0			0
$262$	−5.53942	+	3.77671i	−0.342227	+	0.233326i
$263$	−4.59200	+	7.95358i	−0.283155	+	0.490439i	−0.972160	−	0.234318i	$-0.924714\pi$
$263$	−4.59200	+	7.95358i	−0.283155	+	0.490439i	0.689005	+	0.724756i	$0.258048\pi$
$264$		0			0
$265$	7.96722	+	3.83681i	0.489423	+	0.235693i
$266$	−1.25773	+	0.118158i	−0.0771164	+	0.00724474i
$267$		0			0
$268$	−0.451630	−	0.307916i	−0.0275877	−	0.0188090i
$269$	−13.0942	−	12.1497i	−0.798369	−	0.740778i	0.171295	−	0.985220i	$-0.445205\pi$
$269$	−13.0942	−	12.1497i	−0.798369	−	0.740778i	−0.969664	+	0.244441i	$0.921395\pi$
$270$		0			0
$271$	0.0206336	+	0.0140677i	0.00125340	+	0.000854554i	0.563947	−	0.825811i	$-0.309282\pi$
$271$	0.0206336	+	0.0140677i	0.00125340	+	0.000854554i	−0.562693	+	0.826666i	$0.690235\pi$
$272$	10.3116	−	4.96579i	0.625230	−	0.301095i
$273$		0			0
$274$	−22.2748	−	10.7270i	−1.34567	−	0.648041i
$275$	10.9834	+	19.0238i	0.662325	+	1.14718i
$276$		0			0
$277$	4.95931	−	3.38120i	0.297976	−	0.203156i	−0.405098	−	0.914273i	$-0.632763\pi$
$277$	4.95931	−	3.38120i	0.297976	−	0.203156i	0.703074	+	0.711117i	$0.251810\pi$
$278$	−13.5363	−	2.04027i	−0.811855	−	0.122367i
$279$		0			0
$280$	17.7379	−	14.7015i	1.06004	−	0.878583i
$281$	−5.27888	−	23.1283i	−0.314912	−	1.37972i	−0.846353	−	0.532623i	$-0.821207\pi$
$281$	−5.27888	−	23.1283i	−0.314912	−	1.37972i	0.531441	−	0.847095i	$-0.321651\pi$
$282$		0			0
$283$	19.7093	+	6.07951i	1.17160	+	0.361390i	0.818672	−	0.574262i	$-0.194711\pi$
$283$	19.7093	+	6.07951i	1.17160	+	0.361390i	0.352925	+	0.935652i	$0.385187\pi$
$284$	0.0309485	+	0.0788556i	0.00183646	+	0.00467922i
$285$		0			0
$286$	−7.43496	−	9.32315i	−0.439639	−	0.551289i
$287$	7.54243	+	4.16688i	0.445216	+	0.245963i
$288$		0			0
$289$	−3.07529	+	7.83570i	−0.180899	+	0.460924i
$290$	−1.91129	+	25.5044i	−0.112235	+	1.49767i
$291$		0			0
$292$	−0.438604	+	0.406965i	−0.0256673	+	0.0238158i
$293$	9.60232			0.560974			0.280487	−	0.959858i	$-0.409504\pi$
$293$	9.60232			0.560974			0.280487	+	0.959858i	$0.409504\pi$
$294$		0			0
$295$	28.3525			1.65074
$296$	3.38051	−	3.13666i	0.196488	−	0.182315i
$297$		0			0
$298$	0.493159	−	6.58075i	0.0285679	−	0.381212i
$299$	−2.16293	+	5.51105i	−0.125085	+	0.318712i
$300$		0			0
$301$	−3.38322	+	11.7509i	−0.195005	+	0.677313i
$302$	−10.6831	−	13.3962i	−0.614745	−	0.770866i
$303$		0			0
$304$	−0.487472	−	1.24206i	−0.0279584	−	0.0712369i
$305$	15.0144	+	4.63132i	0.859721	+	0.265189i
$306$		0			0
$307$	−0.340557	−	1.49208i	−0.0194366	−	0.0851573i	0.964279	−	0.264887i	$-0.0853347\pi$
$307$	−0.340557	−	1.49208i	−0.0194366	−	0.0851573i	−0.983716	+	0.179730i	$0.942478\pi$
$308$	−0.0117105	−	0.620493i	−0.000667269	−	0.0353559i
$309$		0			0
$310$	−10.9983	−	1.65773i	−0.624664	−	0.0941529i
$311$	9.03816	−	6.16211i	0.512507	−	0.349421i	−0.279289	−	0.960207i	$-0.590099\pi$
$311$	9.03816	−	6.16211i	0.512507	−	0.349421i	0.791796	+	0.610786i	$0.209146\pi$
$312$		0			0
$313$	−13.2243	−	22.9052i	−0.747482	−	1.29468i	−0.949026	−	0.315197i	$-0.897929\pi$
$313$	−13.2243	−	22.9052i	−0.747482	−	1.29468i	0.201544	−	0.979479i	$-0.435404\pi$
$314$	−22.8869	−	11.0218i	−1.29159	−	0.621995i
$315$		0			0
$316$	0.568695	−	0.273869i	0.0319916	−	0.0154063i
$317$	14.0501	+	9.57916i	0.789130	+	0.538019i	0.889502	−	0.456930i	$-0.151051\pi$
$317$	14.0501	+	9.57916i	0.789130	+	0.538019i	−0.100373	+	0.994950i	$0.532004\pi$
$318$		0			0
$319$	22.6506	+	21.0167i	1.26819	+	1.17671i
$320$	20.5644	+	14.0206i	1.14958	+	0.783773i
$321$		0			0
$322$	11.3069	−	6.81567i	0.630106	−	0.379823i
$323$	−0.901480	−	0.434130i	−0.0501597	−	0.0241556i
$324$		0			0
$325$	3.54239	−	6.13559i	0.196496	−	0.340342i
$326$	−2.68039	+	1.82746i	−0.148453	+	0.101214i
$327$		0			0
$328$	−2.07254	+	9.08037i	−0.114437	+	0.501380i
$329$	−11.2594	+	24.5552i	−0.620750	+	1.35377i
$330$		0			0
$331$	1.02548	+	13.6840i	0.0563653	+	0.752142i	0.951755	+	0.306859i	$0.0992780\pi$
$331$	1.02548	+	13.6840i	0.0563653	+	0.752142i	−0.895390	+	0.445283i	$0.853103\pi$
$332$	−0.0380953	−	0.0117508i	−0.00209075	−	0.000644912i
$333$		0			0
$334$	16.1797	−	4.99078i	0.885314	−	0.273083i
$335$	22.7514	+	28.5293i	1.24304	+	1.55872i
$336$		0			0
$337$	7.18694	−	9.01214i	0.391498	−	0.490923i	−0.546551	−	0.837426i	$-0.684060\pi$
$337$	7.18694	−	9.01214i	0.391498	−	0.490923i	0.938049	+	0.346503i	$0.112631\pi$
$338$	5.23458	−	13.3375i	0.284724	−	0.725465i
$339$		0			0
$340$	0.402321	−	0.0606402i	0.0218189	−	0.00328868i
$341$	−9.85040	+	9.13983i	−0.533429	+	0.494950i
$342$		0			0
$343$	7.07863	−	17.1141i	0.382210	−	0.924075i
$344$	−13.2174			−0.712633
$345$		0			0
$346$	−4.00778	+	0.604075i	−0.215459	+	0.0324753i
$347$	−0.645582	+	8.61470i	−0.0346567	+	0.462461i	0.952696	+	0.303924i	$0.0982969\pi$
$347$	−0.645582	+	8.61470i	−0.0346567	+	0.462461i	−0.987353	+	0.158537i	$0.949322\pi$
$348$		0			0
$349$	−21.9262	+	27.4946i	−1.17368	+	1.47175i	−0.322741	+	0.946487i	$0.604604\pi$
$349$	−21.9262	+	27.4946i	−1.17368	+	1.47175i	−0.850940	+	0.525263i	$0.823967\pi$
$350$	−14.5953	+	6.04850i	−0.780153	+	0.323306i
$351$		0			0
$352$	1.26771	−	0.391036i	0.0675690	−	0.0208423i
$353$	−7.56928	−	19.2862i	−0.402872	−	1.02650i	−0.978031	−	0.208460i	$-0.933155\pi$
$353$	−7.56928	−	19.2862i	−0.402872	−	1.02650i	0.575158	−	0.818042i	$-0.304940\pi$
$354$		0			0
$355$	−0.422608	−	5.63932i	−0.0224297	−	0.299304i
$356$	0.00482878	+	0.0211563i	0.000255925	+	0.00112128i
$357$		0			0
$358$	−2.39944	+	10.5126i	−0.126814	+	0.555610i
$359$	−29.0737	−	4.38216i	−1.53445	−	0.231282i	−0.673201	−	0.739459i	$-0.735081\pi$
$359$	−29.0737	−	4.38216i	−1.53445	−	0.231282i	−0.861252	+	0.508178i	$0.830319\pi$
$360$		0			0
$361$	9.44168	−	16.3535i	0.496930	−	0.860708i
$362$	−13.5786	−	23.5188i	−0.713674	−	1.23612i
$363$		0			0
$364$	−0.171423	+	0.103332i	−0.00898498	+	0.00541607i
$365$	35.9872	−	17.3305i	1.88366	−	0.907122i
$366$		0			0
$367$	−24.3137	−	22.5599i	−1.26917	−	1.17762i	−0.975084	−	0.221835i	$-0.928795\pi$
$367$	−24.3137	−	22.5599i	−1.26917	−	1.17762i	−0.294083	−	0.955780i	$-0.595014\pi$
$368$	10.2220	+	9.48464i	0.532859	+	0.494421i
$369$		0			0
$370$	−6.18455	+	2.97832i	−0.321520	+	0.154836i
$371$	2.40297	+	7.29833i	0.124756	+	0.378910i
$372$		0			0
$373$	4.74746	+	8.22284i	0.245814	+	0.425762i	0.962360	−	0.271777i	$-0.0876114\pi$
$373$	4.74746	+	8.22284i	0.245814	+	0.425762i	−0.716546	+	0.697540i	$0.754278\pi$
$374$	−10.5311	+	18.2404i	−0.544549	+	0.943187i
$375$		0			0
$376$	−28.8724	−	4.35182i	−1.48898	−	0.224428i
$377$	2.21756	−	9.71575i	0.114210	−	0.500387i
$378$		0			0
$379$	2.94125	+	12.8865i	0.151082	+	0.661934i	0.992572	+	0.121661i	$0.0388219\pi$
$379$	2.94125	+	12.8865i	0.151082	+	0.661934i	−0.841490	+	0.540273i	$0.818321\pi$
$380$	−0.00354473	−	0.0473011i	−0.000181841	−	0.00242650i
$381$		0			0
$382$	0.998708	+	2.54467i	0.0510983	+	0.130196i
$383$	−2.79180	+	0.861157i	−0.142655	+	0.0440031i	−0.365260	−	0.930905i	$-0.619020\pi$
$383$	−2.79180	+	0.861157i	−0.142655	+	0.0440031i	0.222606	+	0.974909i	$0.428544\pi$
$384$		0			0
$385$	−11.4625	+	39.8128i	−0.584184	+	2.02905i
$386$	−3.08584	+	3.86952i	−0.157065	+	0.196954i
$387$		0			0
$388$	−0.0262763	+	0.350633i	−0.00133398	+	0.0178007i
$389$	−13.0024	+	1.95980i	−0.659248	+	0.0993657i	−0.470142	−	0.882591i	$-0.655797\pi$
$389$	−13.0024	+	1.95980i	−0.659248	+	0.0993657i	−0.189106	+	0.981957i	$0.560559\pi$
$390$		0			0
$391$	10.4568			0.528821
$392$	19.8932	+	2.23454i	1.00476	+	0.112861i
$393$		0			0
$394$	23.5992	−	21.8968i	1.18891	−	1.10315i
$395$	−41.6670	+	6.28029i	−2.09650	+	0.315996i
$396$		0			0
$397$	−3.67103	+	9.35362i	−0.184244	+	0.469445i	−0.992917	−	0.118813i	$-0.962091\pi$
$397$	−3.67103	+	9.35362i	−0.184244	+	0.469445i	0.808673	+	0.588258i	$0.200186\pi$
$398$	−14.1150	+	17.6997i	−0.707523	+	0.887206i
$399$		0			0
$400$	−10.4043	−	13.0466i	−0.520216	−	0.652331i
$401$	15.9236	−	4.91179i	0.795188	−	0.245283i	0.129565	−	0.991571i	$-0.458642\pi$
$401$	15.9236	−	4.91179i	0.795188	−	0.245283i	0.665623	+	0.746288i	$0.268166\pi$
$402$		0			0
$403$	4.14134	+	1.27743i	0.206295	+	0.0636336i
$404$	0.00279976	+	0.0373603i	0.000139293	+	0.00185874i
$405$		0			0
$406$	−17.1103	+	14.1813i	−0.849168	+	0.703808i
$407$	−1.84537	+	8.08509i	−0.0914715	+	0.400763i
$408$		0			0
$409$	−8.01635	+	5.46545i	−0.396383	+	0.270249i	−0.745065	−	0.666992i	$-0.767582\pi$
$409$	−8.01635	+	5.46545i	−0.396383	+	0.270249i	0.348682	+	0.937241i	$0.386629\pi$
$410$	6.93189	−	12.0064i	0.342342	−	0.592953i
$411$		0			0
$412$	0.0527597	+	0.0254077i	0.00259928	+	0.00125175i
$413$	17.0944	+	17.7399i	0.841159	+	0.872923i
$414$		0			0
$415$	2.19895	+	1.49922i	0.107942	+	0.0735936i
$416$	−0.313652	−	0.291027i	−0.0153781	−	0.0142688i
$417$		0			0
$418$	2.02883	+	1.38323i	0.0992332	+	0.0676560i
$419$	18.6164	−	8.96520i	0.909472	−	0.437979i	0.0801714	−	0.996781i	$-0.474453\pi$
$419$	18.6164	−	8.96520i	0.909472	−	0.437979i	0.829301	+	0.558802i	$0.188739\pi$
$420$		0			0
$421$	−4.75730	−	2.29099i	−0.231856	−	0.111656i	0.314349	−	0.949308i	$-0.398214\pi$
$421$	−4.75730	−	2.29099i	−0.231856	−	0.111656i	−0.546205	+	0.837651i	$0.683928\pi$
$422$	13.7899	+	23.8848i	0.671282	+	1.16269i
$423$		0			0
$424$	−6.86211	+	4.67851i	−0.333253	+	0.227208i
$425$	−12.3738	−	1.86504i	−0.600216	−	0.0904679i
$426$		0			0
$427$	6.15474	+	12.1867i	0.297849	+	0.589756i
$428$	−0.0883130	−	0.386925i	−0.00426877	−	0.0187027i
$429$		0			0
$430$	18.8001	+	5.79905i	0.906619	+	0.279655i
$431$	7.99907	+	20.3813i	0.385302	+	0.981733i	0.983585	+	0.180448i	$0.0577547\pi$
$431$	7.99907	+	20.3813i	0.385302	+	0.981733i	−0.598283	+	0.801285i	$0.704150\pi$
$432$		0			0
$433$	20.7707	+	26.0456i	0.998175	+	1.25167i	0.967692	+	0.252136i	$0.0811331\pi$
$433$	20.7707	+	26.0456i	0.998175	+	1.25167i	0.0304828	+	0.999535i	$0.490296\pi$
$434$	−5.59393	−	7.88106i	−0.268517	−	0.378303i
$435$		0			0
$436$	0.253226	−	0.645209i	0.0121273	−	0.0308999i
$437$	0.0911022	−	1.21567i	0.00435801	−	0.0581536i
$438$		0			0
$439$	13.6710	−	12.6848i	0.652482	−	0.605414i	−0.282860	−	0.959161i	$-0.591283\pi$
$439$	13.6710	−	12.6848i	0.652482	−	0.605414i	0.935341	+	0.353747i	$0.115093\pi$
$440$	−44.7811			−2.13486
$441$		0			0
$442$	6.79300			0.323110
$443$	−27.9415	+	25.9259i	−1.32754	+	1.23178i	−0.375125	+	0.926974i	$0.622400\pi$
$443$	−27.9415	+	25.9259i	−1.32754	+	1.23178i	−0.952415	+	0.304803i	$0.901409\pi$
$444$		0			0
$445$	0.108259	−	1.44461i	0.00513196	−	0.0684813i
$446$	4.27384	−	10.8896i	0.202372	−	0.515636i
$447$		0			0
$448$	3.62620	+	21.3203i	0.171322	+	1.00729i
$449$	8.94093	+	11.2116i	0.421949	+	0.529107i	0.946686	−	0.322157i	$-0.104408\pi$
$449$	8.94093	+	11.2116i	0.421949	+	0.529107i	−0.524738	+	0.851264i	$0.675837\pi$
$450$		0			0
$451$	−6.11919	−	15.5914i	−0.288141	−	0.734172i
$452$	−0.465979	−	0.143736i	−0.0219178	−	0.00676076i
$453$		0			0
$454$	−8.20789	−	35.9611i	−0.385215	−	1.68774i
$455$	12.9686	−	3.21863i	0.607979	−	0.150892i
$456$		0			0
$457$	−17.4292	−	2.62703i	−0.815305	−	0.122887i	−0.271865	−	0.962335i	$-0.587640\pi$
$457$	−17.4292	−	2.62703i	−0.815305	−	0.122887i	−0.543440	+	0.839448i	$0.682878\pi$
$458$	4.41829	−	3.01234i	0.206453	−	0.140757i
$459$		0			0
$460$	0.247861	+	0.429308i	0.0115566	+	0.0200166i
$461$	1.39891	+	0.673680i	0.0651538	+	0.0313764i	0.466177	−	0.884692i	$-0.345631\pi$
$461$	1.39891	+	0.673680i	0.0651538	+	0.0313764i	−0.401023	+	0.916068i	$0.631345\pi$
$462$		0			0
$463$	12.7074	−	6.11956i	0.590562	−	0.284400i	−0.114639	−	0.993407i	$-0.536571\pi$
$463$	12.7074	−	6.11956i	0.590562	−	0.284400i	0.705201	+	0.709007i	$0.250857\pi$
$464$	−19.3940	−	13.2226i	−0.900345	−	0.613845i
$465$		0			0
$466$	0.452278	+	0.419653i	0.0209514	+	0.0194401i
$467$	10.2320	+	6.97609i	0.473483	+	0.322815i	0.776442	−	0.630188i	$-0.217022\pi$
$467$	10.2320	+	6.97609i	0.473483	+	0.322815i	−0.302960	+	0.953003i	$0.597975\pi$
$468$		0			0
$469$	−4.13321	+	31.4363i	−0.190854	+	1.45159i
$470$	39.1581	+	18.8575i	1.80623	+	0.869833i
$471$		0			0
$472$	−13.3142	+	23.0609i	−0.612836	+	1.06146i
$473$	19.6388	−	13.3895i	0.902992	−	0.615650i
$474$		0			0
$475$	−0.324629	+	1.42229i	−0.0148950	+	0.0652592i
$476$	0.280511	+	0.215168i	0.0128572	+	0.00986219i
$477$		0			0
$478$	0.661277	+	8.82413i	0.0302461	+	0.403606i
$479$	35.4006	+	10.9196i	1.61749	+	0.498930i	0.965742	−	0.259503i	$-0.0835587\pi$
$479$	35.4006	+	10.9196i	1.61749	+	0.498930i	0.651751	+	0.758433i	$0.274035\pi$
$480$		0			0
$481$	2.55584	−	0.788373i	0.116536	−	0.0359467i
$482$	−12.0396	−	15.0972i	−0.548389	−	0.687659i
$483$		0			0
$484$	−0.439301	+	0.550866i	−0.0199682	+	0.0250393i
$485$	8.57567	−	21.8504i	0.389401	−	0.992178i
$486$		0			0
$487$	−29.0923	+	4.38496i	−1.31830	+	0.198702i	−0.770249	−	0.637744i	$-0.779868\pi$
$487$	−29.0923	+	4.38496i	−1.31830	+	0.198702i	−0.548051	+	0.836445i	$0.684630\pi$
$488$	−10.8177	+	10.0373i	−0.489692	+	0.454368i
$489$		0			0
$490$	−27.3152	−	11.9064i	−1.23397	−	0.537876i
$491$	19.1247			0.863086			0.431543	−	0.902092i	$-0.357969\pi$
$491$	19.1247			0.863086			0.431543	+	0.902092i	$0.357969\pi$
$492$		0			0
$493$	−17.4052	+	2.62341i	−0.783892	+	0.118153i
$494$	0.0591825	−	0.789736i	0.00266275	−	0.0355319i
$495$		0			0
$496$	6.36451	−	7.98085i	0.285775	−	0.358351i
$497$	3.27367	−	3.66450i	0.146844	−	0.164375i
$498$		0			0
$499$	−29.6128	+	9.13434i	−1.32565	+	0.408909i	−0.875144	−	0.483863i	$-0.839233\pi$
$499$	−29.6128	+	9.13434i	−1.32565	+	0.408909i	−0.450508	+	0.892772i	$0.648757\pi$
$500$	0.0369664	+	0.0941888i	0.00165319	+	0.00421225i
$501$		0			0
$502$	1.29355	+	17.2612i	0.0577340	+	0.770407i
$503$	−7.33332	−	32.1294i	−0.326977	−	1.43258i	−0.824862	−	0.565335i	$-0.808747\pi$
$503$	−7.33332	−	32.1294i	−0.326977	−	1.43258i	0.497885	−	0.867243i	$-0.334110\pi$
$504$		0			0
$505$	0.556542	−	2.43837i	0.0247658	−	0.108506i
$506$	−25.3754	−	3.82472i	−1.12807	−	0.170030i
$507$		0			0
$508$	−0.111162	+	0.192538i	−0.00493200	+	0.00854247i
$509$	−8.19506	−	14.1943i	−0.363240	−	0.629150i	0.625252	−	0.780423i	$-0.284996\pi$
$509$	−8.19506	−	14.1943i	−0.363240	−	0.629150i	−0.988492	+	0.151273i	$0.951663\pi$
$510$		0			0
$511$	32.5411	+	12.0679i	1.43953	+	0.533853i
$512$	−21.0396	+	10.1321i	−0.929827	+	0.447781i
$513$		0			0
$514$	−19.6880	−	18.2678i	−0.868402	−	0.805759i
$515$	−2.86568	−	2.65897i	−0.126277	−	0.117168i
$516$		0			0
$517$	47.3080	−	22.7824i	2.08061	−	1.00197i
$518$	−5.59232	−	2.07392i	−0.245713	−	0.0911228i
$519$		0			0
$520$	7.22143	+	12.5079i	0.316681	+	0.548507i
$521$	−17.7234	+	30.6977i	−0.776474	+	1.34489i	0.157488	+	0.987521i	$0.449660\pi$
$521$	−17.7234	+	30.6977i	−0.776474	+	1.34489i	−0.933962	+	0.357372i	$0.883673\pi$
$522$		0			0
$523$	−30.4104	−	4.58362i	−1.32975	−	0.200428i	−0.554555	−	0.832147i	$-0.687111\pi$
$523$	−30.4104	−	4.58362i	−1.32975	−	0.200428i	−0.775197	+	0.631719i	$0.782350\pi$
$524$	0.0486740	−	0.213255i	0.00212633	−	0.00931607i
$525$		0			0
$526$	2.85699	+	12.5173i	0.124571	+	0.545779i
$527$	−0.572040	−	7.63335i	−0.0249185	−	0.332514i
$528$		0			0
$529$	−3.74824	−	9.55036i	−0.162967	−	0.415233i
$530$	11.8132	−	3.64388i	0.513131	−	0.158280i
$531$		0			0
$532$	0.0274587	−	0.0307369i	0.00119049	−	0.00133261i
$533$	−3.36809	+	4.22345i	−0.145888	+	0.182938i
$534$		0			0
$535$	−1.97993	+	26.4204i	−0.0856000	+	1.14225i
$536$	−33.8887	+	5.10790i	−1.46377	+	0.220628i
$537$		0			0
$538$	−24.9718			−1.07661
$539$	−31.8216	+	16.8321i	−1.37065	+	0.725009i
$540$		0			0
$541$	7.90059	−	7.33068i	0.339673	−	0.315171i	−0.491829	−	0.870692i	$-0.663672\pi$
$541$	7.90059	−	7.33068i	0.339673	−	0.315171i	0.831503	+	0.555521i	$0.187481\pi$
$542$	0.0345220	−	0.00520336i	0.00148285	−	0.000223503i
$543$		0			0
$544$	−0.276099	+	0.703490i	−0.0118377	+	0.0301619i
$545$	−28.8496	+	36.1763i	−1.23578	+	1.54962i
$546$		0			0
$547$	−10.5375	−	13.2136i	−0.450550	−	0.564972i	0.503739	−	0.863856i	$-0.331957\pi$
$547$	−10.5375	−	13.2136i	−0.450550	−	0.564972i	−0.954290	+	0.298883i	$0.903386\pi$
$548$	0.770789	−	0.237757i	0.0329265	−	0.0101565i
$549$		0			0
$550$	29.3452	+	9.05179i	1.25128	+	0.385970i
$551$	0.153352	+	2.04634i	0.00653301	+	0.0871770i
$552$		0			0
$553$	−29.0516	−	22.2842i	−1.23540	−	0.947619i
$554$	1.86720	−	8.18075i	0.0793299	−	0.347567i
$555$		0			0
$556$	0.369021	−	0.251595i	0.0156500	−	0.0106700i
$557$	−9.10664	+	15.7732i	−0.385861	+	0.668331i	−0.991888	−	0.127113i	$-0.959429\pi$
$557$	−9.10664	+	15.7732i	−0.385861	+	0.668331i	0.606027	+	0.795444i	$0.292762\pi$
$558$		0			0
$559$	−6.90681	−	3.32614i	−0.292127	−	0.140681i
$560$	4.10267	−	31.2040i	0.173369	−	1.31861i
$561$		0			0
$562$	−27.4020	−	18.6824i	−1.15588	−	0.788068i
$563$	8.33631	+	7.73497i	0.351334	+	0.325990i	0.836021	−	0.548698i	$-0.184876\pi$
$563$	8.33631	+	7.73497i	0.351334	+	0.325990i	−0.484687	+	0.874687i	$0.661067\pi$
$564$		0			0
$565$	26.8974	+	18.3383i	1.13158	+	0.771499i
$566$	25.9790	−	12.5108i	1.09198	−	0.525870i
$567$		0			0
$568$	4.78528	+	2.30447i	0.200786	+	0.0966934i
$569$	6.66633	+	11.5464i	0.279467	+	0.484051i	0.971252	−	0.238052i	$-0.0765089\pi$
$569$	6.66633	+	11.5464i	0.279467	+	0.484051i	−0.691785	+	0.722103i	$0.743176\pi$
$570$		0			0
$571$	27.1898	−	18.5377i	1.13786	−	0.775778i	0.160429	−	0.987047i	$-0.448712\pi$
$571$	27.1898	−	18.5377i	1.13786	−	0.775778i	0.977428	+	0.211269i	$0.0677597\pi$
$572$	0.384715	+	0.0579864i	0.0160857	+	0.00242453i
$573$		0			0
$574$	11.6917	−	2.90171i	0.488002	−	0.121115i
$575$	−3.39264	−	14.8641i	−0.141483	−	0.619877i
$576$		0			0
$577$	9.29316	+	2.86656i	0.386879	+	0.119336i	0.482092	−	0.876120i	$-0.339877\pi$
$577$	9.29316	+	2.86656i	0.386879	+	0.119336i	−0.0952130	+	0.995457i	$0.530353\pi$
$578$	4.29924	+	10.9543i	0.178825	+	0.455638i
$579$		0			0
$580$	−0.520269	−	0.652397i	−0.0216030	−	0.0270893i
$581$	0.387750	+	2.27977i	0.0160866	+	0.0945809i
$582$		0			0
$583$	5.45651	−	13.9030i	0.225985	−	0.575801i
$584$	−2.80343	+	37.4091i	−0.116007	+	1.54800i
$585$		0			0
$586$	9.84048	−	9.13063i	0.406507	−	0.377183i
$587$	−9.81759			−0.405216			−0.202608	−	0.979260i	$-0.564942\pi$
$587$	−9.81759			−0.405216			−0.202608	+	0.979260i	$0.564942\pi$
$588$		0			0
$589$	−0.892416			−0.0367714
$590$	29.0557	−	26.9597i	1.19620	−	1.10991i
$591$		0			0
$592$	0.470787	−	6.28222i	0.0193492	−	0.258198i
$593$	12.3327	−	31.4232i	0.506443	−	1.29039i	−0.417783	−	0.908547i	$-0.637193\pi$
$593$	12.3327	−	31.4232i	0.506443	−	1.29039i	0.924225	−	0.381848i	$-0.124712\pi$
$594$		0			0
$595$	−13.6604	−	19.2456i	−0.560023	−	0.788993i
$596$	0.134242	+	0.168334i	0.00549876	+	0.00689523i
$597$		0			0
$598$	3.02376	+	7.70441i	0.123651	+	0.315057i
$599$	7.81225	+	2.40976i	0.319200	+	0.0984602i	0.450215	−	0.892920i	$-0.351347\pi$
$599$	7.81225	+	2.40976i	0.319200	+	0.0984602i	−0.131015	+	0.991380i	$0.541824\pi$
$600$		0			0
$601$	5.90190	+	25.8579i	0.240743	+	1.05477i	0.940342	+	0.340230i	$0.110505\pi$
$601$	5.90190	+	25.8579i	0.240743	+	1.05477i	−0.699599	+	0.714536i	$0.746638\pi$
$602$	7.70658	+	15.2594i	0.314097	+	0.621927i
$603$		0			0
$604$	0.552788	+	0.0833194i	0.0224926	+	0.00339022i
$605$	38.8633	−	26.4965i	1.58002	−	1.07724i
$606$		0			0
$607$	15.9130	+	27.5622i	0.645890	+	1.11871i	0.984095	+	0.177642i	$0.0568468\pi$
$607$	15.9130	+	27.5622i	0.645890	+	1.11871i	−0.338205	+	0.941072i	$0.609820\pi$
$608$	0.0793804	+	0.0382276i	0.00321930	+	0.00155033i
$609$		0			0
$610$	19.7906	−	9.53065i	0.801298	−	0.385885i
$611$	−13.9923	−	9.53979i	−0.566068	−	0.385939i
$612$		0			0
$613$	−28.4261	−	26.3756i	−1.14812	−	1.06530i	−0.997048	−	0.0767756i	$-0.975537\pi$
$613$	−28.4261	−	26.3756i	−1.14812	−	1.06530i	−0.151070	−	0.988523i	$-0.548272\pi$
$614$	−1.76779	−	1.20526i	−0.0713420	−	0.0486402i
$615$		0			0
$616$	−26.9996	−	28.0192i	−1.08784	−	1.12892i
$617$	5.08147	+	2.44710i	0.204572	+	0.0985167i	0.533365	−	0.845885i	$-0.320927\pi$
$617$	5.08147	+	2.44710i	0.204572	+	0.0985167i	−0.328792	+	0.944402i	$0.606642\pi$
$618$		0			0
$619$	11.6348	−	20.1521i	0.467644	−	0.809983i	−0.531673	−	0.846950i	$-0.678436\pi$
$619$	11.6348	−	20.1521i	0.467644	−	0.809983i	0.999316	+	0.0369673i	$0.0117697\pi$
$620$	0.299832	−	0.204422i	0.0120415	−	0.00820979i
$621$		0			0
$622$	3.40291	−	14.9091i	0.136444	−	0.597802i
$623$	0.969154	−	0.803255i	0.0388283	−	0.0321817i
$624$		0			0
$625$	−2.10081	−	28.0334i	−0.0840324	−	1.12133i
$626$	−35.3323	−	10.8986i	−1.41216	−	0.435595i
$627$		0			0
$628$	0.791970	−	0.244291i	0.0316031	−	0.00974825i
$629$	−2.94546	−	3.69349i	−0.117443	−	0.147269i
$630$		0			0
$631$	−5.36560	+	6.72825i	−0.213601	+	0.267848i	−0.877076	−	0.480351i	$-0.840509\pi$
$631$	−5.36560	+	6.72825i	−0.213601	+	0.267848i	0.663475	+	0.748198i	$0.269081\pi$
$632$	14.4585	−	36.8397i	0.575129	−	1.46540i
$633$		0			0
$634$	23.5071	−	3.54313i	0.933588	−	0.140716i
$635$	10.8798	−	10.0950i	0.431751	−	0.400607i
$636$		0			0
$637$	9.83296	+	6.17378i	0.389596	+	0.244614i
$638$	43.1967			1.71017
$639$		0			0
$640$	32.8528	−	4.95177i	1.29862	−	0.195736i
$641$	−0.113511	+	1.51470i	−0.00448343	+	0.0598272i	−0.998997	−	0.0447829i	$-0.985740\pi$
$641$	−0.113511	+	1.51470i	−0.00448343	+	0.0598272i	0.994513	+	0.104610i	$0.0333595\pi$
$642$		0			0
$643$	17.3518	−	21.7585i	0.684289	−	0.858071i	−0.311452	−	0.950262i	$-0.600815\pi$
$643$	17.3518	−	21.7585i	0.684289	−	0.858071i	0.995741	+	0.0921906i	$0.0293869\pi$
$644$	−0.119173	+	0.413924i	−0.00469608	+	0.0163109i
$645$		0			0
$646$	−1.33664	+	0.412300i	−0.0525895	+	0.0162217i
$647$	−1.17939	−	3.00503i	−0.0463664	−	0.118140i	0.905814	−	0.423675i	$-0.139260\pi$
$647$	−1.17939	−	3.00503i	−0.0463664	−	0.118140i	−0.952181	+	0.305535i	$0.901165\pi$
$648$		0			0
$649$	−3.57854	−	47.7522i	−0.140470	−	1.87444i
$650$	−2.20395	−	9.65615i	−0.0864462	−	0.378745i
$651$		0			0
$652$	0.0235522	−	0.103189i	0.000922374	−	0.00404118i
$653$	−34.8590	−	5.25415i	−1.36414	−	0.205611i	−0.574159	−	0.818744i	$-0.694671\pi$
$653$	−34.8590	−	5.25415i	−1.36414	−	0.205611i	−0.789980	+	0.613133i	$0.789909\pi$
$654$		0			0
$655$	−7.30125	+	12.6461i	−0.285283	+	0.494125i
$656$	6.36183	+	11.0190i	0.248388	+	0.430220i
$657$		0			0
$658$	11.8103	+	35.8705i	0.460414	+	1.39838i
$659$	15.6565	−	7.53979i	0.609892	−	0.293709i	−0.103329	−	0.994647i	$-0.532950\pi$
$659$	15.6565	−	7.53979i	0.609892	−	0.293709i	0.713222	+	0.700939i	$0.247235\pi$
$660$		0			0
$661$	35.3902	+	32.8373i	1.37652	+	1.27722i	0.922377	+	0.386292i	$0.126244\pi$
$661$	35.3902	+	32.8373i	1.37652	+	1.27722i	0.454141	+	0.890930i	$0.349946\pi$
$662$	14.0627	+	13.0483i	0.546564	+	0.507137i
$663$		0			0
$664$	−2.25203	+	1.08452i	−0.0873956	+	0.0420875i
$665$	−2.35645	+	1.42045i	−0.0913794	+	0.0550827i
$666$		0			0
$667$	−10.7230	−	18.5727i	−0.415195	−	0.719138i
$668$	−0.276213	+	0.478415i	−0.0106870	+	0.0185104i
$669$		0			0
$670$	50.4435	+	7.60314i	1.94880	+	0.293735i
$671$	5.90519	−	25.8723i	0.227967	−	0.998789i
$672$		0			0
$673$	8.18221	+	35.8486i	0.315401	+	1.38186i	0.845522	+	0.533940i	$0.179289\pi$
$673$	8.18221	+	35.8486i	0.315401	+	1.38186i	−0.530121	+	0.847922i	$0.677854\pi$
$674$	−1.20425	−	16.0696i	−0.0463859	−	0.618977i
$675$		0			0
$676$	0.170785	+	0.435153i	0.00656865	+	0.0167366i
$677$	38.6014	−	11.9069i	1.48357	−	0.457621i	0.555973	−	0.831200i	$-0.312346\pi$
$677$	38.6014	−	11.9069i	1.48357	−	0.457621i	0.927598	+	0.373579i	$0.121870\pi$
$678$		0			0
$679$	18.8421	−	7.80843i	0.723094	−	0.299660i
$680$	15.9051	−	19.9444i	0.609933	−	0.764832i
$681$		0			0
$682$	−1.40385	+	18.7330i	−0.0537561	+	0.717325i
$683$	36.0182	−	5.42887i	1.37820	−	0.207730i	0.582208	−	0.813040i	$-0.302189\pi$
$683$	36.0182	−	5.42887i	1.37820	−	0.207730i	0.795990	+	0.605310i	$0.206951\pi$
$684$		0			0
$685$	−53.8484			−2.05744
$686$	−9.01923	−	24.2695i	−0.344356	−	0.926614i
$687$		0			0
$688$	−13.2361	+	12.2813i	−0.504622	+	0.468221i
$689$	−4.76318	+	0.717933i	−0.181463	+	0.0273511i
$690$		0			0
$691$	−1.10637	+	2.81900i	−0.0420885	+	0.107240i	−0.950372	−	0.311115i	$-0.899298\pi$
$691$	−1.10637	+	2.81900i	−0.0420885	+	0.107240i	0.908284	+	0.418354i	$0.137393\pi$
$692$	0.0824476	−	0.103386i	0.00313419	−	0.00393015i
$693$		0			0
$694$	7.52993	+	9.44223i	0.285832	+	0.358422i
$695$	−28.4912	+	8.78837i	−1.08073	+	0.333362i
$696$		0			0
$697$	9.11741	+	2.81235i	0.345346	+	0.106525i
$698$	3.67396	+	49.0256i	0.139061	+	1.85565i
$699$		0			0
$700$	0.214847	−	0.468553i	0.00812047	−	0.0177096i
$701$	3.61315	−	15.8302i	0.136467	−	0.597900i	−0.859729	−	0.510751i	$-0.829367\pi$
$701$	3.61315	−	15.8302i	0.136467	−	0.597900i	0.996195	−	0.0871485i	$-0.0277755\pi$
$702$		0			0
$703$	−0.455057	+	0.310253i	−0.0171628	+	0.0117014i
$704$	21.0184	−	36.4049i	0.792160	−	1.37206i
$705$		0			0
$706$	−26.0959	−	12.5671i	−0.982131	−	0.472969i
$707$	1.86122	−	1.12193i	0.0699984	−	0.0421944i
$708$		0			0
$709$	14.4669	+	9.86335i	0.543315	+	0.370426i	0.803659	−	0.595090i	$-0.202884\pi$
$709$	14.4669	+	9.86335i	0.543315	+	0.370426i	−0.260344	+	0.965516i	$0.583836\pi$
$710$	−5.79539	−	5.37734i	−0.217497	−	0.201808i
$711$		0			0
$712$	1.12416	+	0.766439i	0.0421297	+	0.0287235i
$713$	8.40288	−	4.04661i	0.314690	−	0.151547i
$714$		0			0
$715$	−23.4006	−	11.2691i	−0.875134	−	0.421442i
$716$	−0.175904	−	0.304675i	−0.00657385	−	0.0113862i
$717$		0			0
$718$	−33.9617	+	23.1547i	−1.26744	+	0.864127i
$719$	−1.21104	−	0.182536i	−0.0451643	−	0.00680743i	0.126421	−	0.991977i	$-0.459651\pi$
$719$	−1.21104	−	0.182536i	−0.0451643	−	0.00680743i	−0.171586	+	0.985169i	$0.554889\pi$
$720$		0			0
$721$	−0.0640960	−	3.39619i	−0.00238706	−	0.126481i
$722$	−5.87429	−	25.7369i	−0.218618	−	0.957830i
$723$		0			0
$724$	0.846672	+	0.261164i	0.0314663	+	0.00970607i
$725$	9.37618	+	23.8901i	0.348223	+	0.887257i
$726$		0			0
$727$	16.1712	+	20.2780i	0.599755	+	0.752069i	0.985340	−	0.170603i	$-0.0545716\pi$
$727$	16.1712	+	20.2780i	0.599755	+	0.752069i	−0.385585	+	0.922673i	$0.626000\pi$
$728$	−3.47211	+	12.0597i	−0.128685	+	0.446962i
$729$		0			0
$730$	20.4006	−	51.9798i	0.755059	−	1.92386i
$731$	−1.01185	+	13.5022i	−0.0374247	+	0.499398i
$732$		0			0
$733$	16.5224	−	15.3306i	0.610269	−	0.566247i	−0.313312	−	0.949650i	$-0.601438\pi$
$733$	16.5224	−	15.3306i	0.610269	−	0.566247i	0.923581	+	0.383403i	$0.125248\pi$
$734$	−46.3685			−1.71149
$735$		0			0
$736$	−0.920777			−0.0339403
$737$	45.1785	−	41.9195i	1.66417	−	1.54413i
$738$		0			0
$739$	0.944643	−	12.6054i	0.0347493	−	0.463697i	−0.952503	−	0.304531i	$-0.901500\pi$
$739$	0.944643	−	12.6054i	0.0347493	−	0.463697i	0.987252	−	0.159166i	$-0.0508805\pi$
$740$	0.0818209	−	0.208476i	0.00300779	−	0.00766374i
$741$		0			0
$742$	9.40238	+	5.19442i	0.345172	+	0.190693i
$743$	−10.2591	−	12.8645i	−0.376371	−	0.471954i	0.557184	−	0.830389i	$-0.311882\pi$
$743$	−10.2591	−	12.8645i	−0.376371	−	0.471954i	−0.933555	+	0.358435i	$0.883310\pi$
$744$		0			0
$745$	−5.25119	−	13.3798i	−0.192389	−	0.490199i
$746$	12.6841	+	3.91253i	0.464399	+	0.143248i
$747$		0			0
$748$	−0.152912	−	0.669951i	−0.00559101	−	0.0244958i
$749$	−17.7247	+	14.6906i	−0.647648	+	0.536784i
$750$		0			0
$751$	−45.8791	−	6.91516i	−1.67415	−	0.252338i	−0.757734	−	0.652563i	$-0.773694\pi$
$751$	−45.8791	−	6.91516i	−1.67415	−	0.252338i	−0.916417	+	0.400226i	$0.868932\pi$
$752$	−32.9570	+	22.4697i	−1.20182	+	0.819386i
$753$		0			0
$754$	−6.96593	−	12.0653i	−0.253684	−	0.439394i
$755$	−33.6238	−	16.1924i	−1.22370	−	0.589301i
$756$		0			0
$757$	45.7806	−	22.0468i	1.66393	−	0.801304i	0.665430	−	0.746460i	$-0.268248\pi$
$757$	45.7806	−	22.0468i	1.66393	−	0.801304i	0.998495	−	0.0548444i	$-0.0174663\pi$
$758$	15.2677	+	10.4093i	0.554547	+	0.378083i
$759$		0			0
$760$	−2.18011	−	2.02285i	−0.0790809	−	0.0733763i
$761$	−35.5545	−	24.2406i	−1.28885	−	0.878722i	−0.291874	−	0.956457i	$-0.594279\pi$
$761$	−35.5545	−	24.2406i	−1.28885	−	0.878722i	−0.996974	+	0.0777348i	$0.975231\pi$
$762$		0			0
$763$	−40.0293	+	3.76057i	−1.44916	+	0.136142i
$764$	−0.0803558	−	0.0386973i	−0.00290717	−	0.00140002i
$765$		0			0
$766$	−2.04219	+	3.53718i	−0.0737874	+	0.127804i
$767$	−12.7607	+	8.70008i	−0.460761	+	0.314142i
$768$		0			0
$769$	−3.74912	+	16.4260i	−0.135197	+	0.592336i	0.861255	+	0.508173i	$0.169679\pi$
$769$	−3.74912	+	16.4260i	−0.135197	+	0.592336i	−0.996452	+	0.0841633i	$0.973178\pi$
$770$	26.1103	+	51.6997i	0.940950	+	1.86313i
$771$		0			0
$772$	−0.0120672	−	0.161026i	−0.000434309	−	0.00579545i
$773$	−8.48457	−	2.61714i	−0.305169	−	0.0941321i	0.138389	−	0.990378i	$-0.455808\pi$
$773$	−8.48457	−	2.61714i	−0.305169	−	0.0941321i	−0.443558	+	0.896246i	$0.646284\pi$
$774$		0			0
$775$	−10.6651	+	3.28975i	−0.383102	+	0.118171i
$776$	13.7453	+	17.2360i	0.493427	+	0.618738i
$777$		0			0
$778$	−11.4614	+	14.3721i	−0.410910	+	0.515265i
$779$	0.406389	−	1.03546i	0.0145604	−	0.0370993i
$780$		0			0
$781$	−9.44460	+	1.42354i	−0.337954	+	0.0509384i
$782$	10.7161	−	9.94310i	0.383207	−	0.355564i
$783$		0			0
$784$	21.9977	−	16.2466i	0.785632	−	0.580237i
$785$	−55.3282			−1.97475
$786$		0			0
$787$	−34.9249	+	5.26408i	−1.24494	+	0.187644i	−0.738275	−	0.674500i	$-0.764359\pi$
$787$	−34.9249	+	5.26408i	−1.24494	+	0.187644i	−0.506664	+	0.862144i	$0.669121\pi$
$788$	−0.0784919	+	1.04740i	−0.00279616	+	0.0373121i
$789$		0			0
$790$	−36.7287	+	46.0563i	−1.30675	+	1.63861i
$791$	4.74293	+	27.8860i	0.168639	+	0.991514i
$792$		0			0
$793$	−8.17871	+	2.52280i	−0.290435	+	0.0895872i
$794$	5.13208	+	13.0763i	0.182131	+	0.464061i
$795$		0			0
$796$	−0.0551970	−	0.736553i	−0.00195641	−	0.0261064i
$797$	10.7720	+	47.1953i	0.381564	+	1.67174i	0.692582	+	0.721339i	$0.256473\pi$
$797$	10.7720	+	47.1953i	0.381564	+	1.67174i	−0.311018	+	0.950404i	$0.600670\pi$
$798$		0			0
$799$	−6.65592	+	29.1615i	−0.235470	+	1.03166i
$800$	1.08958	+	0.164228i	0.0385225	+	0.00580633i
$801$		0			0
$802$	11.6481	−	20.1750i	0.411308	−	0.712406i
$803$	−33.7309	−	58.4236i	−1.19034	−	2.06172i
$804$		0			0
$805$	15.7471	−	24.0600i	0.555013	−	0.848004i
$806$	5.45874	−	2.62879i	0.192276	−	0.0925952i
$807$		0			0
$808$	1.72193	+	1.59772i	0.0605775	+	0.0562077i
$809$	−23.5119	−	21.8159i	−0.826636	−	0.767006i	0.148430	−	0.988923i	$-0.452578\pi$
$809$	−23.5119	−	21.8159i	−0.826636	−	0.767006i	−0.975066	+	0.221917i	$0.928769\pi$
$810$		0			0
$811$	−21.7322	+	10.4657i	−0.763120	+	0.367499i	−0.774614	−	0.632435i	$-0.782056\pi$
$811$	−21.7322	+	10.4657i	−0.763120	+	0.367499i	0.0114935	+	0.999934i	$0.496341\pi$
$812$	0.0945166	−	0.718874i	0.00331688	−	0.0252275i
$813$		0			0
$814$	5.79679	+	10.0403i	0.203177	+	0.351914i
$815$	−3.53290	+	6.11916i	−0.123752	+	0.214345i
$816$		0			0
$817$	1.56092	+	0.235270i	0.0546095	+	0.00823106i
$818$	−3.01819	+	13.2236i	−0.105529	+	0.462351i
$819$		0			0
$820$	0.100651	+	0.440983i	0.00351490	+	0.0153998i
$821$	3.72987	+	49.7717i	0.130173	+	1.73704i	0.555073	+	0.831802i	$0.312690\pi$
$821$	3.72987	+	49.7717i	0.130173	+	1.73704i	−0.424899	+	0.905241i	$0.639690\pi$
$822$		0			0
$823$	4.28836	+	10.9266i	0.149483	+	0.380876i	0.985927	−	0.167176i	$-0.0534648\pi$
$823$	4.28836	+	10.9266i	0.149483	+	0.380876i	−0.836444	+	0.548052i	$0.815370\pi$
$824$	3.50842	−	1.08221i	0.122222	−	0.0377004i
$825$		0			0
$826$	34.3868	+	1.92523i	1.19647	+	0.0669874i
$827$	2.42448	−	3.04021i	0.0843075	−	0.105718i	−0.737889	−	0.674922i	$-0.764177\pi$
$827$	2.42448	−	3.04021i	0.0843075	−	0.105718i	0.822196	+	0.569204i	$0.192749\pi$
$828$		0			0
$829$	−0.731090	+	9.75572i	−0.0253918	+	0.338830i	0.970012	+	0.243059i	$0.0781508\pi$
$829$	−0.731090	+	9.75572i	−0.0253918	+	0.338830i	−0.995403	+	0.0957714i	$0.969468\pi$
$830$	3.67906	−	0.554528i	0.127702	−	0.0192480i
$831$		0			0
$832$	−13.5577			−0.470030
$833$	3.80562	−	20.1508i	0.131857	−	0.698185i
$834$		0			0
$835$	27.0340	−	25.0838i	0.935549	−	0.868062i
$836$	−0.0792189	+	0.0119403i	−0.00273984	+	0.000412965i
$837$		0			0
$838$	10.5534	−	26.8895i	0.364560	−	0.928883i
$839$	3.47047	−	4.35183i	0.119814	−	0.150242i	−0.718307	−	0.695726i	$-0.755083\pi$
$839$	3.47047	−	4.35183i	0.119814	−	0.150242i	0.838121	+	0.545484i	$0.183654\pi$
$840$		0			0
$841$	4.42667	+	5.55087i	0.152644	+	0.191409i
$842$	−7.05374	+	2.17579i	−0.243088	+	0.0749827i
$843$		0			0
$844$	−0.859849	−	0.265228i	−0.0295972	−	0.00912953i
$845$	−2.33210	−	31.1197i	−0.0802268	−	1.07055i
$846$		0			0
$847$	40.0102	+	8.34103i	1.37477	+	0.286601i
$848$	−2.52467	+	11.0613i	−0.0866974	+	0.379846i
$849$		0			0
$850$	−14.4541	+	9.85463i	−0.495771	+	0.338011i
$851$	2.87794	−	4.98473i	0.0986544	−	0.170874i
$852$		0			0
$853$	−41.8538	−	20.1557i	−1.43305	−	0.690119i	−0.453486	−	0.891263i	$-0.649820\pi$
$853$	−41.8538	−	20.1557i	−1.43305	−	0.690119i	−0.979562	+	0.201144i	$0.935534\pi$
$854$	17.8955	+	6.63655i	0.612370	+	0.227098i
$855$		0			0
$856$	−20.5596	−	14.0173i	−0.702714	−	0.479102i
$857$	20.0940	+	18.6445i	0.686398	+	0.636884i	0.944223	−	0.329307i	$-0.106815\pi$
$857$	20.0940	+	18.6445i	0.686398	+	0.636884i	−0.257825	+	0.966192i	$0.583006\pi$
$858$		0			0
$859$	−7.90752	−	5.39126i	−0.269801	−	0.183947i	0.420860	−	0.907125i	$-0.361728\pi$
$859$	−7.90752	−	5.39126i	−0.269801	−	0.183947i	−0.690662	+	0.723178i	$0.742681\pi$
$860$	−0.578326	+	0.278507i	−0.0197207	+	0.00949701i
$861$		0			0
$862$	27.5776	+	13.2807i	0.939297	+	0.452341i
$863$	1.05265	+	1.82324i	0.0358326	+	0.0620639i	0.883386	−	0.468647i	$-0.155258\pi$
$863$	1.05265	+	1.82324i	0.0358326	+	0.0620639i	−0.847553	+	0.530711i	$0.821925\pi$
$864$		0			0
$865$	−7.29382	+	4.97285i	−0.247997	+	0.169082i
$866$	46.0520	+	6.94122i	1.56491	+	0.235872i
$867$		0			0
$868$	0.308681	+	0.0643515i	0.0104773	+	0.00218423i
$869$	15.8365	+	69.3844i	0.537218	+	2.35371i
$870$		0			0
$871$	−18.9941	−	5.85891i	−0.643591	−	0.198522i
$872$	−15.8768	−	40.4535i	−0.537658	−	1.36993i
$873$		0			0
$874$	−1.06260	−	1.33245i	−0.0359428	−	0.0450709i
$875$	3.91023	−	4.37705i	0.132190	−	0.147971i
$876$		0			0
$877$	−4.59063	+	11.6967i	−0.155015	+	0.394971i	−0.987192	−	0.159539i	$-0.948999\pi$
$877$	−4.59063	+	11.6967i	−0.155015	+	0.394971i	0.832177	+	0.554510i	$0.187094\pi$
$878$	1.94835	−	25.9989i	0.0657536	−	0.877421i
$879$		0			0
$880$	−44.8447	+	41.6098i	−1.51171	+	1.40267i
$881$	7.94150			0.267556			0.133778	−	0.991011i	$-0.457289\pi$
$881$	7.94150			0.267556			0.133778	+	0.991011i	$0.457289\pi$
$882$		0			0
$883$	−3.75050			−0.126215			−0.0631073	−	0.998007i	$-0.520101\pi$
$883$	−3.75050			−0.126215			−0.0631073	+	0.998007i	$0.520101\pi$
$884$	−0.162466	+	0.150747i	−0.00546433	+	0.00507016i
$885$		0			0
$886$	−3.98213	+	53.1379i	−0.133782	+	1.78520i
$887$	−6.62764	+	16.8869i	−0.222534	+	0.567008i	−0.997919	−	0.0644812i	$-0.979461\pi$
$887$	−6.62764	+	16.8869i	−0.222534	+	0.567008i	0.775385	+	0.631489i	$0.217556\pi$
$888$		0			0
$889$	12.8760	+	0.720896i	0.431848	+	0.0241781i
$890$	−1.26271	−	1.58338i	−0.0423260	−	0.0530752i
$891$		0			0
$892$	0.139439	+	0.355285i	0.00466877	+	0.0118958i
$893$	3.33225	+	1.02786i	0.111509	+	0.0343961i
$894$		0			0
$895$	5.22611	+	22.8971i	0.174690	+	0.765365i
$896$	22.9060	+	17.5702i	0.765237	+	0.586979i
$897$		0			0
$898$	19.8235	+	2.98791i	0.661519	+	0.0997080i
$899$	−12.9713	+	8.84370i	−0.432618	+	0.294954i
$900$		0			0
$901$	4.25401	+	7.36816i	0.141722	+	0.245469i
$902$	−21.0965	−	10.1595i	−0.702437	−	0.338276i
$903$		0			0
$904$	−27.5466	+	13.2658i	−0.916188	+	0.441213i
$905$	−48.8718	−	33.3202i	−1.62455	−	1.10760i
$906$		0			0
$907$	−13.2897	−	12.3311i	−0.441278	−	0.409446i	0.427993	−	0.903782i	$-0.359221\pi$
$907$	−13.2897	−	12.3311i	−0.441278	−	0.409446i	−0.869271	+	0.494336i	$0.835411\pi$
$908$	0.994337	+	0.677927i	0.0329982	+	0.0224978i
$909$		0			0
$910$	10.2298	−	15.6300i	0.339114	−	0.518131i
$911$	9.12745	+	4.39555i	0.302406	+	0.145631i	0.578933	−	0.815375i	$-0.303469\pi$
$911$	9.12745	+	4.39555i	0.302406	+	0.145631i	−0.276527	+	0.961006i	$0.589184\pi$
$912$		0			0
$913$	2.24749	−	3.89277i	0.0743811	−	0.128832i
$914$	−20.3595	+	13.8809i	−0.673432	+	0.459138i
$915$		0			0
$916$	−0.0388227	+	0.170094i	−0.00128274	+	0.00562005i
$917$	−12.3147	+	3.05632i	−0.406666	+	0.100929i
$918$		0			0
$919$	1.59100	+	21.2305i	0.0524824	+	0.700329i	0.959944	+	0.280193i	$0.0903985\pi$
$919$	1.59100	+	21.2305i	0.0524824	+	0.700329i	−0.907461	+	0.420136i	$0.861982\pi$
$920$	29.7001	+	9.16127i	0.979184	+	0.302038i
$921$		0			0
$922$	2.07420	−	0.639805i	0.0683100	−	0.0210708i
$923$	1.92066	+	2.40843i	0.0632191	+	0.0792743i
$924$		0			0
$925$	−4.29461	+	5.38527i	−0.141206	+	0.177067i
$926$	7.20361	−	18.3545i	0.236725	−	0.603167i
$927$		0			0
$928$	1.53263	−	0.231007i	0.0503110	−	0.00758316i
$929$	−34.0305	+	31.5757i	−1.11650	+	1.03597i	−0.117425	+	0.993082i	$0.537464\pi$
$929$	−34.0305	+	31.5757i	−1.11650	+	1.03597i	−0.999080	+	0.0428834i	$0.986346\pi$
$930$		0			0
$931$	−2.30953	−	0.617990i	−0.0756916	−	0.0202538i
$932$	−0.0201297			−0.000659372
$933$		0			0
$934$	17.1192	−	2.58031i	0.560159	−	0.0844303i
$935$	−3.42821	+	45.7462i	−0.112114	+	1.49606i
$936$		0			0
$937$	−7.82128	+	9.80757i	−0.255510	+	0.320399i	−0.892998	−	0.450061i	$-0.851402\pi$
$937$	−7.82128	+	9.80757i	−0.255510	+	0.320399i	0.637488	+	0.770460i	$0.279974\pi$
$938$	25.6564	+	36.1462i	0.837710	+	1.18022i
$939$		0			0
$940$	−1.35501	+	0.417965i	−0.0441956	+	0.0136325i
$941$	−9.36589	−	23.8639i	−0.305319	−	0.777941i	−0.998371	−	0.0570533i	$-0.981830\pi$
$941$	−9.36589	−	23.8639i	−0.305319	−	0.777941i	0.693052	−	0.720888i	$-0.256266\pi$
$942$		0			0
$943$	0.868741	+	11.5925i	0.0282901	+	0.377505i
$944$	8.09464	+	35.4649i	0.263458	+	1.15429i
$945$		0			0
$946$	7.39410	−	32.3957i	0.240403	−	1.05327i
$947$	−37.9832	−	5.72504i	−1.23429	−	0.186039i	−0.500692	−	0.865626i	$-0.666921\pi$
$947$	−37.9832	−	5.72504i	−1.23429	−	0.186039i	−0.733595	+	0.679587i	$0.762159\pi$
$948$		0			0
$949$	−10.8789	+	18.8429i	−0.353145	+	0.611665i
$950$	1.01974	+	1.76625i	0.0330849	+	0.0573047i
$951$		0			0
$952$	22.0686	−	2.07324i	0.715247	−	0.0671942i
$953$	25.9101	−	12.4776i	0.839311	−	0.404191i	0.0357118	−	0.999362i	$-0.488630\pi$
$953$	25.9101	−	12.4776i	0.839311	−	0.404191i	0.803599	+	0.595171i	$0.202916\pi$
$954$		0			0
$955$	4.36459	+	4.04974i	0.141235	+	0.131047i
$956$	−0.211636	−	0.196370i	−0.00684480	−	0.00635105i
$957$		0			0
$958$	46.6618	−	22.4711i	1.50757	−	0.726010i
$959$	−32.4665	−	33.6925i	−1.04840	−	1.08799i
$960$		0			0
$961$	12.0863	+	20.9341i	0.389881	+	0.675294i
$962$	1.86959	−	3.23822i	0.0602779	−	0.104404i
$963$		0			0
$964$	0.622978	+	0.0938988i	0.0200648	+	0.00302428i
$965$	−2.39874	+	10.5096i	−0.0772182	+	0.338315i
$966$		0			0
$967$	−7.14644	−	31.3106i	−0.229814	−	1.00688i	−0.949791	−	0.312884i	$-0.898705\pi$
$967$	−7.14644	−	31.3106i	−0.229814	−	1.00688i	0.719977	−	0.693997i	$-0.244152\pi$
$968$	3.30129	+	44.0527i	0.106108	+	1.41591i
$969$		0			0
$970$	−11.9887	−	30.5468i	−0.384935	−	0.980799i
$971$	49.5535	−	15.2852i	1.59025	−	0.490526i	0.631640	−	0.775262i	$-0.282382\pi$
$971$	49.5535	−	15.2852i	1.59025	−	0.490526i	0.958606	+	0.284735i	$0.0919058\pi$
$972$		0			0
$973$	−22.6768	−	12.5280i	−0.726986	−	0.401629i
$974$	−25.6443	+	32.1570i	−0.821697	+	1.03038i
$975$		0			0
$976$	−1.50652	+	20.1031i	−0.0482226	+	0.643485i
$977$	4.94384	−	0.745164i	0.158167	−	0.0238399i	−0.0694812	−	0.997583i	$-0.522134\pi$
$977$	4.94384	−	0.745164i	0.158167	−	0.0238399i	0.227649	+	0.973743i	$0.426896\pi$
$978$		0			0
$979$	−2.44673			−0.0781980
$980$	0.917510	−	0.321402i	0.0293088	−	0.0102668i
$981$		0			0
$982$	19.5990	−	18.1853i	0.625431	−	0.580315i
$983$	−31.3557	+	4.72612i	−1.00009	+	0.150740i	−0.628627	−	0.777707i	$-0.716383\pi$
$983$	−31.3557	+	4.72612i	−1.00009	+	0.150740i	−0.371466	+	0.928447i	$0.621145\pi$
$984$		0			0
$985$	25.6170	−	65.2711i	0.816226	−	2.07971i
$986$	−15.3424	+	19.2387i	−0.488600	+	0.612686i
$987$		0			0
$988$	0.0161100	+	0.0202012i	0.000512526	+	0.000642687i
$989$	−15.7642	+	4.86261i	−0.501273	+	0.154622i
$990$		0			0
$991$	12.9092	+	3.98196i	0.410074	+	0.126491i	0.492927	−	0.870071i	$-0.335927\pi$
$991$	12.9092	+	3.98196i	0.410074	+	0.126491i	−0.0828529	+	0.996562i	$0.526403\pi$
$992$	0.0503714	+	0.672159i	0.00159929	+	0.0213411i
$993$		0			0
$994$	−0.129624	−	6.86825i	−0.00411142	−	0.217848i
$995$	−10.9722	+	48.0722i	−0.347841	+	1.52399i
$996$		0			0
$997$	27.7122	−	18.8939i	0.877654	−	0.598375i	−0.0384739	−	0.999260i	$-0.512250\pi$
$997$	27.7122	−	18.8939i	0.877654	−	0.598375i	0.916128	+	0.400885i	$0.131297\pi$
$998$	−21.6616	+	37.5191i	−0.685687	+	1.18765i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bb.d.109.3		48
3.2	odd	2		49.2.g.a.11.2	yes	48
12.11	even	2		784.2.bg.c.305.3		48
21.2	odd	6		343.2.g.i.128.3		48
21.5	even	6		343.2.g.h.128.3		48
21.11	odd	6		343.2.e.d.246.2		48
21.17	even	6		343.2.e.c.246.2		48
21.20	even	2		343.2.g.g.312.2		48
49.9	even	21	inner	441.2.bb.d.352.3		48
147.74	odd	42		343.2.e.d.99.2		48
147.83	even	14		343.2.g.h.67.3		48
147.89	even	42		343.2.g.g.177.2		48
147.95	odd	42		2401.2.a.h.1.19		24
147.101	even	42		2401.2.a.i.1.19		24
147.107	odd	42		49.2.g.a.9.2	✓	48
147.113	odd	14		343.2.g.i.67.3		48
147.122	even	42		343.2.e.c.99.2		48
588.107	even	42		784.2.bg.c.401.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.g.a.9.2	✓	48	147.107	odd	42
49.2.g.a.11.2	yes	48	3.2	odd	2
343.2.e.c.99.2		48	147.122	even	42
343.2.e.c.246.2		48	21.17	even	6
343.2.e.d.99.2		48	147.74	odd	42
343.2.e.d.246.2		48	21.11	odd	6
343.2.g.g.177.2		48	147.89	even	42
343.2.g.g.312.2		48	21.20	even	2
343.2.g.h.67.3		48	147.83	even	14
343.2.g.h.128.3		48	21.5	even	6
343.2.g.i.67.3		48	147.113	odd	14
343.2.g.i.128.3		48	21.2	odd	6
441.2.bb.d.109.3		48	1.1	even	1	trivial
441.2.bb.d.352.3		48	49.9	even	21	inner
784.2.bg.c.305.3		48	12.11	even	2
784.2.bg.c.401.3		48	588.107	even	42
2401.2.a.h.1.19		24	147.95	odd	42
2401.2.a.i.1.19		24	147.101	even	42

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02480 - 0.950878i) q^{2} +(-0.00340854 + 0.0454838i) q^{4} +(1.11243 - 2.83442i) q^{5} +(2.44418 - 1.01290i) q^{7} +(1.78303 + 2.23585i) q^{8} +O(q^{10})\)	\(q+(1.02480 - 0.950878i) q^{2} +(-0.00340854 + 0.0454838i) q^{4} +(1.11243 - 2.83442i) q^{5} +(2.44418 - 1.01290i) q^{7} +(1.78303 + 2.23585i) q^{8} +(-1.55517 - 3.96251i) q^{10} +(-4.91424 - 1.51584i) q^{11} +(0.369081 + 1.61705i) q^{13} +(1.54166 - 3.36214i) q^{14} +(3.86306 + 0.582263i) q^{16} +(2.42053 - 1.65029i) q^{17} +(-0.170770 - 0.295782i) q^{19} +(0.125128 + 0.0602587i) q^{20} +(-6.47751 + 3.11940i) q^{22} +(2.94916 + 2.01070i) q^{23} +(-3.13119 - 2.90532i) q^{25} +(1.91585 + 1.30621i) q^{26} +(0.0377395 + 0.114623i) q^{28} +(-5.41330 - 2.60691i) q^{29} +(1.30646 - 2.26286i) q^{31} +(-0.213141 + 0.145317i) q^{32} +(0.911342 - 3.99285i) q^{34} +(-0.152014 - 8.05463i) q^{35} +(-0.120508 - 1.60806i) q^{37} +(-0.456258 - 0.140737i) q^{38} +(8.32082 - 2.56663i) q^{40} +(2.03064 + 2.54634i) q^{41} +(-2.88168 + 3.61351i) q^{43} +(0.0856967 - 0.218352i) q^{44} +(4.93423 - 0.743716i) q^{46} +(-7.48457 + 6.94467i) q^{47} +(4.94806 - 4.95144i) q^{49} -5.97146 q^{50} +(-0.0748076 + 0.0112754i) q^{52} +(-0.217030 + 2.89606i) q^{53} +(-9.76328 + 12.2428i) q^{55} +(6.62274 + 3.65878i) q^{56} +(-8.02642 + 2.47582i) q^{58} +(3.40185 + 8.66778i) q^{59} +(0.385625 + 5.14581i) q^{61} +(-0.812835 - 3.56126i) q^{62} +(-1.81889 + 7.96909i) q^{64} +(4.99398 + 0.752722i) q^{65} +(-5.99203 + 10.3785i) q^{67} +(0.0668109 + 0.115720i) q^{68} +(-7.81475 - 8.10985i) q^{70} +(1.67332 - 0.805828i) q^{71} +(9.61611 + 8.92245i) q^{73} +(-1.65257 - 1.53336i) q^{74} +(0.0140354 - 0.00675907i) q^{76} +(-13.5467 + 1.27265i) q^{77} +(-6.91937 - 11.9847i) q^{79} +(5.94776 - 10.3018i) q^{80} +(4.50226 + 0.678606i) q^{82} +(-0.194494 + 0.852134i) q^{83} +(-1.98495 - 8.69663i) q^{85} +(0.482856 + 6.44326i) q^{86} +(-5.37304 - 13.6903i) q^{88} +(0.454630 - 0.140235i) q^{89} +(2.54002 + 3.57852i) q^{91} +(-0.101507 + 0.127285i) q^{92} +(-1.06668 + 14.2338i) q^{94} +(-1.02834 + 0.154997i) q^{95} +7.70896 q^{97} +(0.362570 - 9.77924i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8}+O(q^{10}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8	\( 48 q + 13 q^{2} - 9 q^{4} + 14 q^{5} - 14 q^{7} + 20 q^{8} - 14 q^{10} + 3 q^{11} - 14 q^{13} - 21 q^{14} - 3 q^{16} + 7 q^{17} + 21 q^{19} - 14 q^{20} - 20 q^{22} - 15 q^{23} - 4 q^{25} + 28 q^{28} - 12 q^{29} + 35 q^{31} - 45 q^{32} + 70 q^{34} + 15 q^{37} + 28 q^{38} - 42 q^{40} + 42 q^{41} - 30 q^{43} + 50 q^{44} - 78 q^{46} - 21 q^{47} - 70 q^{49} - 40 q^{50} - 70 q^{52} - 11 q^{53} - 7 q^{55} + 28 q^{56} + 16 q^{58} + 28 q^{59} + 7 q^{61} + 28 q^{62} - 32 q^{64} - 14 q^{65} + 11 q^{67} - 77 q^{68} + 70 q^{70} - 19 q^{71} + 7 q^{73} - 34 q^{74} + 119 q^{76} - 7 q^{77} + 15 q^{79} - 70 q^{80} - 14 q^{82} - 26 q^{85} + 33 q^{86} - 77 q^{88} + 14 q^{89} + 84 q^{91} + 38 q^{92} + 14 q^{94} + 61 q^{95} + 161 q^{98}+O(q^{100}) \) 48 * q + 13 * q^2 - 9 * q^4 + 14 * q^5 - 14 * q^7 + 20 * q^8 - 14 * q^10 + 3 * q^11 - 14 * q^13 - 21 * q^14 - 3 * q^16 + 7 * q^17 + 21 * q^19 - 14 * q^20 - 20 * q^22 - 15 * q^23 - 4 * q^25 + 28 * q^28 - 12 * q^29 + 35 * q^31 - 45 * q^32 + 70 * q^34 + 15 * q^37 + 28 * q^38 - 42 * q^40 + 42 * q^41 - 30 * q^43 + 50 * q^44 - 78 * q^46 - 21 * q^47 - 70 * q^49 - 40 * q^50 - 70 * q^52 - 11 * q^53 - 7 * q^55 + 28 * q^56 + 16 * q^58 + 28 * q^59 + 7 * q^61 + 28 * q^62 - 32 * q^64 - 14 * q^65 + 11 * q^67 - 77 * q^68 + 70 * q^70 - 19 * q^71 + 7 * q^73 - 34 * q^74 + 119 * q^76 - 7 * q^77 + 15 * q^79 - 70 * q^80 - 14 * q^82 - 26 * q^85 + 33 * q^86 - 77 * q^88 + 14 * q^89 + 84 * q^91 + 38 * q^92 + 14 * q^94 + 61 * q^95 + 161 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more