LMFDB - Embedded newform 550.2.ba.f.399.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(49,550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.ba (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,4,0,-2,0,0,12,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + 75x^{12} - 554x^{10} + 2019x^{8} - 3874x^{6} + 9670x^{4} - 16456x^{2} + 14641 $ x^16 - x^14 + 75x^12 - 554x^10 + 2019x^8 - 3874x^6 + 9670x^4 - 16456x^2 + 14641
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			399.4
Root			$-0.874145 - 1.20316i$ of defining polynomial
Character	$\chi$	$=$	550.399
Dual form			550.2.ba.f.499.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.587785 + 0.809017i) q^{2} +(2.36545 - 0.768582i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.01217 + 1.46193i) q^{6} +(-0.410805 - 0.133479i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(2.57760 - 1.87274i) q^{9} +(1.92705 - 2.69935i) q^{11} +2.48718i q^{12} +(2.31792 + 3.19034i) q^{13} +(-0.133479 - 0.410805i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(2.01149 - 2.76858i) q^{17} +(3.03015 + 0.984555i) q^{18} +(1.89414 + 5.82957i) q^{19} -1.07433 q^{21} +(3.31651 - 0.0276194i) q^{22} -4.17025i q^{23} +(-2.01217 + 1.46193i) q^{24} +(-1.21860 + 3.75047i) q^{26} +(0.272048 - 0.374442i) q^{27} +(0.253891 - 0.349452i) q^{28} +(0.195878 - 0.602850i) q^{29} +(-8.34129 + 6.06030i) q^{31} -1.00000i q^{32} +(2.48368 - 7.86628i) q^{33} +3.42216 q^{34} +(0.984555 + 3.03015i) q^{36} +(-6.98198 - 2.26858i) q^{37} +(-3.60287 + 4.95892i) q^{38} +(7.93497 + 5.76509i) q^{39} +(0.821192 + 2.52737i) q^{41} +(-0.631475 - 0.869151i) q^{42} -11.5615i q^{43} +(1.97174 + 2.66688i) q^{44} +(3.37380 - 2.45121i) q^{46} +(-2.82379 + 0.917506i) q^{47} +(-2.36545 - 0.768582i) q^{48} +(-5.51217 - 4.00483i) q^{49} +(2.63021 - 8.09495i) q^{51} +(-3.75047 + 1.21860i) q^{52} +(-3.08268 - 4.24295i) q^{53} +0.462835 q^{54} +0.431946 q^{56} +(8.96100 + 12.3338i) q^{57} +(0.602850 - 0.195878i) q^{58} +(-3.35698 + 10.3317i) q^{59} +(-8.51153 - 6.18399i) q^{61} +(-9.80577 - 3.18609i) q^{62} +(-1.30886 + 0.425275i) q^{63} +(0.809017 - 0.587785i) q^{64} +(7.82382 - 2.61434i) q^{66} -10.9987i q^{67} +(2.01149 + 2.76858i) q^{68} +(-3.20518 - 9.86453i) q^{69} +(8.29982 + 6.03017i) q^{71} +(-1.87274 + 2.57760i) q^{72} +(10.5929 + 3.44186i) q^{73} +(-2.26858 - 6.98198i) q^{74} -6.12957 q^{76} +(-1.15195 + 0.851685i) q^{77} +9.80816i q^{78} +(-6.02435 + 4.37695i) q^{79} +(-2.59794 + 7.99563i) q^{81} +(-1.56200 + 2.14991i) q^{82} +(-4.63468 + 6.37909i) q^{83} +(0.331986 - 1.02175i) q^{84} +(9.35346 - 6.79569i) q^{86} -1.57656i q^{87} +(-0.998590 + 3.16272i) q^{88} -1.34257 q^{89} +(-0.526370 - 1.62000i) q^{91} +(3.96614 + 1.28868i) q^{92} +(-15.0731 + 20.7463i) q^{93} +(-2.40206 - 1.74520i) q^{94} +(-0.768582 - 2.36545i) q^{96} +(1.03059 + 1.41849i) q^{97} -6.81342i q^{98} +(-0.0879978 - 10.5667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 2 q^{6} + 12 q^{9} + 4 q^{11} - 2 q^{14} - 4 q^{16} + 14 q^{19} + 64 q^{21} + 2 q^{24} - 12 q^{26} + 44 q^{29} - 52 q^{31} - 4 q^{34} - 2 q^{36} + 96 q^{39} - 30 q^{41} - 14 q^{44} - 12 q^{46}+ \cdots - 72 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 2 * q^6 + 12 * q^9 + 4 * q^11 - 2 * q^14 - 4 * q^16 + 14 * q^19 + 64 * q^21 + 2 * q^24 - 12 * q^26 + 44 * q^29 - 52 * q^31 - 4 * q^34 - 2 * q^36 + 96 * q^39 - 30 * q^41 - 14 * q^44 - 12 * q^46 - 54 * q^49 - 10 * q^51 + 48 * q^54 + 12 * q^56 - 78 * q^59 - 40 * q^61 + 4 * q^64 + 72 * q^66 + 20 * q^69 + 4 * q^71 - 16 * q^74 + 16 * q^76 - 28 * q^79 - 62 * q^81 + 36 * q^84 + 34 * q^86 - 64 * q^89 + 106 * q^91 - 18 * q^94 + 8 * q^96 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	2.36545	−	0.768582i	1.36570	−	0.443741i	0.467755	−	0.883858i	$-0.345063\pi$
$3$	2.36545	−	0.768582i	1.36570	−	0.443741i	0.897940	+	0.440117i	$0.145063\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	2.01217	+	1.46193i	0.821467	+	0.596831i
$7$	−0.410805	−	0.133479i	−0.155270	−	0.0504502i	0.230351	−	0.973108i	$-0.426013\pi$
$7$	−0.410805	−	0.133479i	−0.155270	−	0.0504502i	−0.385621	+	0.922657i	$0.626013\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	2.57760	−	1.87274i	0.859200	−	0.624245i
$10$		0			0
$11$	1.92705	−	2.69935i	0.581028	−	0.813884i
$11$	1.92705	−	2.69935i	0.581028	−	0.813884i
$12$			2.48718i			0.717988i
$13$	2.31792	+	3.19034i	0.642875	+	0.884842i	0.998765	−	0.0496862i	$-0.0158221\pi$
$13$	2.31792	+	3.19034i	0.642875	+	0.884842i	−0.355890	+	0.934528i	$0.615822\pi$
$14$	−0.133479	−	0.410805i	−0.0356737	−	0.109792i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.01149	−	2.76858i	0.487859	−	0.671480i	−0.492133	−	0.870520i	$-0.663782\pi$
$17$	2.01149	−	2.76858i	0.487859	−	0.671480i	0.979991	+	0.199040i	$0.0637825\pi$
$18$	3.03015	+	0.984555i	0.714213	+	0.232062i
$19$	1.89414	+	5.82957i	0.434546	+	1.33739i	0.893551	+	0.448961i	$0.148206\pi$
$19$	1.89414	+	5.82957i	0.434546	+	1.33739i	−0.459006	+	0.888433i	$0.651794\pi$
$20$		0			0
$21$	−1.07433			−0.234438
$22$	3.31651	−	0.0276194i	0.707082	−	0.00588847i
$23$		−	4.17025i		−	0.869557i	−0.900537	−	0.434778i	$-0.856827\pi$
$23$		−	4.17025i		−	0.869557i	0.900537	−	0.434778i	$-0.143173\pi$
$24$	−2.01217	+	1.46193i	−0.410733	+	0.298415i
$25$		0			0
$26$	−1.21860	+	3.75047i	−0.238988	+	0.735528i
$27$	0.272048	−	0.374442i	0.0523556	−	0.0720613i
$28$	0.253891	−	0.349452i	0.0479810	−	0.0660402i
$29$	0.195878	−	0.602850i	0.0363736	−	0.111947i	−0.931221	−	0.364455i	$-0.881255\pi$
$29$	0.195878	−	0.602850i	0.0363736	−	0.111947i	0.967595	+	0.252508i	$0.0812554\pi$
$30$		0			0
$31$	−8.34129	+	6.06030i	−1.49814	+	1.08846i	−0.527024	+	0.849850i	$0.676692\pi$
$31$	−8.34129	+	6.06030i	−1.49814	+	1.08846i	−0.971115	+	0.238612i	$0.923308\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.48368	−	7.86628i	0.432353	−	1.36934i
$34$	3.42216			0.586895
$35$		0			0
$36$	0.984555	+	3.03015i	0.164093	+	0.505025i
$37$	−6.98198	−	2.26858i	−1.14783	−	0.372953i	−0.327505	−	0.944850i	$-0.606208\pi$
$37$	−6.98198	−	2.26858i	−1.14783	−	0.372953i	−0.820326	+	0.571897i	$0.806208\pi$
$38$	−3.60287	+	4.95892i	−0.584463	+	0.804444i
$39$	7.93497	+	5.76509i	1.27061	+	0.923154i
$40$		0			0
$41$	0.821192	+	2.52737i	0.128249	+	0.394709i	0.994479	−	0.104936i	$-0.0334639\pi$
$41$	0.821192	+	2.52737i	0.128249	+	0.394709i	−0.866230	+	0.499645i	$0.833464\pi$
$42$	−0.631475	−	0.869151i	−0.0974387	−	0.134113i
$43$		−	11.5615i		−	1.76311i	−0.472077	−	0.881557i	$-0.656496\pi$
$43$		−	11.5615i		−	1.76311i	0.472077	−	0.881557i	$-0.343504\pi$
$44$	1.97174	+	2.66688i	0.297251	+	0.402047i
$45$		0			0
$46$	3.37380	−	2.45121i	0.497440	−	0.361411i
$47$	−2.82379	+	0.917506i	−0.411892	+	0.133832i	−0.507631	−	0.861575i	$-0.669479\pi$
$47$	−2.82379	+	0.917506i	−0.411892	+	0.133832i	0.0957387	+	0.995407i	$0.469479\pi$
$48$	−2.36545	−	0.768582i	−0.341424	−	0.110935i
$49$	−5.51217	−	4.00483i	−0.787454	−	0.572118i
$50$		0			0
$51$	2.63021	−	8.09495i	0.368303	−	1.13352i
$52$	−3.75047	+	1.21860i	−0.520097	+	0.168990i
$53$	−3.08268	−	4.24295i	−0.423439	−	0.582814i	0.542992	−	0.839738i	$-0.317291\pi$
$53$	−3.08268	−	4.24295i	−0.423439	−	0.582814i	−0.966432	+	0.256923i	$0.917291\pi$
$54$	0.462835			0.0629839
$55$		0			0
$56$	0.431946			0.0577212
$57$	8.96100	+	12.3338i	1.18691	+	1.63365i
$58$	0.602850	−	0.195878i	0.0791581	−	0.0257200i
$59$	−3.35698	+	10.3317i	−0.437041	+	1.34507i	0.453939	+	0.891033i	$0.350018\pi$
$59$	−3.35698	+	10.3317i	−0.437041	+	1.34507i	−0.890981	+	0.454042i	$0.849982\pi$
$60$		0			0
$61$	−8.51153	−	6.18399i	−1.08979	−	0.791779i	−0.110426	−	0.993884i	$-0.535222\pi$
$61$	−8.51153	−	6.18399i	−1.08979	−	0.791779i	−0.979364	+	0.202105i	$0.935222\pi$
$62$	−9.80577	−	3.18609i	−1.24533	−	0.404634i
$63$	−1.30886	+	0.425275i	−0.164901	+	0.0535796i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$		0			0
$66$	7.82382	−	2.61434i	0.963046	−	0.321803i
$67$		−	10.9987i		−	1.34371i	−0.740684	−	0.671854i	$-0.765498\pi$
$67$		−	10.9987i		−	1.34371i	0.740684	−	0.671854i	$-0.234502\pi$
$68$	2.01149	+	2.76858i	0.243929	+	0.335740i
$69$	−3.20518	−	9.86453i	−0.385858	−	1.18755i
$70$		0			0
$71$	8.29982	+	6.03017i	0.985007	+	0.715649i	0.958822	−	0.284008i	$-0.0916641\pi$
$71$	8.29982	+	6.03017i	0.985007	+	0.715649i	0.0261849	+	0.999657i	$0.491664\pi$
$72$	−1.87274	+	2.57760i	−0.220704	+	0.303773i
$73$	10.5929	+	3.44186i	1.23981	+	0.402839i	0.854259	−	0.519848i	$-0.174011\pi$
$73$	10.5929	+	3.44186i	1.23981	+	0.402839i	0.385551	+	0.922686i	$0.374011\pi$
$74$	−2.26858	−	6.98198i	−0.263717	−	0.811639i
$75$		0			0
$76$	−6.12957			−0.703110
$77$	−1.15195	+	0.851685i	−0.131277	+	0.0970585i
$78$			9.80816i			1.11056i
$79$	−6.02435	+	4.37695i	−0.677792	+	0.492445i	−0.872625	−	0.488392i	$-0.837584\pi$
$79$	−6.02435	+	4.37695i	−0.677792	+	0.492445i	0.194832	+	0.980837i	$0.437584\pi$
$80$		0			0
$81$	−2.59794	+	7.99563i	−0.288660	+	0.888404i
$82$	−1.56200	+	2.14991i	−0.172494	+	0.237418i
$83$	−4.63468	+	6.37909i	−0.508722	+	0.700196i	−0.983703	−	0.179800i	$-0.942455\pi$
$83$	−4.63468	+	6.37909i	−0.508722	+	0.700196i	0.474981	+	0.879996i	$0.342455\pi$
$84$	0.331986	−	1.02175i	0.0362226	−	0.111482i
$85$		0			0
$86$	9.35346	−	6.79569i	1.00861	−	0.732798i
$87$		−	1.57656i		−	0.169025i
$88$	−0.998590	+	3.16272i	−0.106450	+	0.337147i
$89$	−1.34257			−0.142312			−0.0711559	−	0.997465i	$-0.522669\pi$
$89$	−1.34257			−0.142312			−0.0711559	+	0.997465i	$0.522669\pi$
$90$		0			0
$91$	−0.526370	−	1.62000i	−0.0551786	−	0.169822i
$92$	3.96614	+	1.28868i	0.413499	+	0.134354i
$93$	−15.0731	+	20.7463i	−1.56301	+	2.15129i
$94$	−2.40206	−	1.74520i	−0.247754	−	0.180004i
$95$		0			0
$96$	−0.768582	−	2.36545i	−0.0784431	−	0.241423i
$97$	1.03059	+	1.41849i	0.104641	+	0.144026i	0.858126	−	0.513439i	$-0.171629\pi$
$97$	1.03059	+	1.41849i	0.104641	+	0.144026i	−0.753485	+	0.657465i	$0.771629\pi$
$98$		−	6.81342i		−	0.688260i
$99$	−0.0879978	−	10.5667i	−0.00884411	−	1.06199i
$100$		0			0
$101$	1.00000	−	0.726543i	0.0995037	−	0.0722937i	−0.536921	−	0.843633i	$-0.680413\pi$
$101$	1.00000	−	0.726543i	0.0995037	−	0.0722937i	0.636425	+	0.771339i	$0.280413\pi$
$102$	8.09495	−	2.63021i	0.801519	−	0.260429i
$103$	2.55872	+	0.831378i	0.252118	+	0.0819181i	0.432349	−	0.901706i	$-0.357685\pi$
$103$	2.55872	+	0.831378i	0.252118	+	0.0819181i	−0.180232	+	0.983624i	$0.557685\pi$
$104$	−3.19034	−	2.31792i	−0.312839	−	0.227291i
$105$		0			0
$106$	1.62066	−	4.98789i	0.157413	−	0.484467i
$107$	0.309518	−	0.100568i	0.0299222	−	0.00972232i	−0.294018	−	0.955800i	$-0.594992\pi$
$107$	0.309518	−	0.100568i	0.0299222	−	0.00972232i	0.323940	+	0.946078i	$0.394992\pi$
$108$	0.272048	+	0.374442i	0.0261778	+	0.0360307i
$109$	10.0487			0.962491			0.481245	−	0.876586i	$-0.340185\pi$
$109$	10.0487			0.962491			0.481245	+	0.876586i	$0.340185\pi$
$110$		0			0
$111$	−18.2591			−1.73308
$112$	0.253891	+	0.349452i	0.0239905	+	0.0330201i
$113$	−8.08064	+	2.62556i	−0.760162	+	0.246992i	−0.663348	−	0.748311i	$-0.730865\pi$
$113$	−8.08064	+	2.62556i	−0.760162	+	0.246992i	−0.0968141	+	0.995302i	$0.530865\pi$
$114$	−4.71108	+	14.4992i	−0.441233	+	1.35798i
$115$		0			0
$116$	0.512815	+	0.372582i	0.0476137	+	0.0345934i
$117$	11.9493	+	3.88257i	1.10472	+	0.358944i
$118$	−10.3317	+	3.35698i	−0.951111	+	0.309035i
$119$	−1.19588	+	0.868856i	−0.109626	+	0.0796479i
$120$		0			0
$121$	−3.57295	−	10.4036i	−0.324814	−	0.945778i
$122$		−	10.5208i		−	0.952512i
$123$	3.88498	+	5.34722i	0.350297	+	0.482142i
$124$	−3.18609	−	9.80577i	−0.286119	−	0.880584i
$125$		0			0
$126$	−1.11338	−	0.808921i	−0.0991881	−	0.0720644i
$127$	−5.07796	+	6.98921i	−0.450596	+	0.620192i	−0.972525	−	0.232797i	$-0.925212\pi$
$127$	−5.07796	+	6.98921i	−0.450596	+	0.620192i	0.521930	+	0.852988i	$0.325212\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−8.88598	−	27.3482i	−0.782367	−	2.40788i
$130$		0			0
$131$	16.3347			1.42717			0.713587	−	0.700567i	$-0.247069\pi$
$131$	16.3347			1.42717			0.713587	+	0.700567i	$0.247069\pi$
$132$	6.71377	+	4.79293i	0.584359	+	0.417171i
$133$		−	2.64764i		−	0.229580i
$134$	8.89815	−	6.46488i	0.768683	−	0.558481i
$135$		0			0
$136$	−1.05750	+	3.25466i	−0.0906803	+	0.279085i
$137$	10.0272	−	13.8012i	0.856681	−	1.17912i	−0.125670	−	0.992072i	$-0.540108\pi$
$137$	10.0272	−	13.8012i	0.856681	−	1.17912i	0.982351	−	0.187048i	$-0.0598920\pi$
$138$	6.09661	−	8.39127i	0.518978	−	0.714312i
$139$	−1.73646	+	5.34429i	−0.147285	+	0.453296i	−0.997298	−	0.0734656i	$-0.976594\pi$
$139$	−1.73646	+	5.34429i	−0.147285	+	0.453296i	0.850013	+	0.526762i	$0.176594\pi$
$140$		0			0
$141$	−5.97437	+	4.34063i	−0.503133	+	0.365547i
$142$			10.2591i			0.860928i
$143$	13.0786	−	0.108917i	1.09369	−	0.00910806i
$144$	−3.18609			−0.265507
$145$		0			0
$146$	3.44186	+	10.5929i	0.284850	+	0.876678i
$147$	−16.1168	−	5.23668i	−1.32929	−	0.431914i
$148$	4.31510	−	5.93923i	0.354699	−	0.488201i
$149$	8.00930	+	5.81910i	0.656147	+	0.476719i	0.865360	−	0.501151i	$-0.167090\pi$
$149$	8.00930	+	5.81910i	0.656147	+	0.476719i	−0.209212	+	0.977870i	$0.567090\pi$
$150$		0			0
$151$	−3.54695	−	10.9164i	−0.288647	−	0.888364i	−0.985282	−	0.170938i	$-0.945320\pi$
$151$	−3.54695	−	10.9164i	−0.288647	−	0.888364i	0.696635	−	0.717426i	$-0.254680\pi$
$152$	−3.60287	−	4.95892i	−0.292231	−	0.402222i
$153$		−	10.9033i		−	0.881479i
$154$	−1.36613	−	0.431337i	−0.110086	−	0.0347581i
$155$		0			0
$156$	−7.93497	+	5.76509i	−0.635306	+	0.461577i
$157$	7.18764	−	2.33541i	0.573636	−	0.186386i	−0.00781135	−	0.999969i	$-0.502486\pi$
$157$	7.18764	−	2.33541i	0.573636	−	0.186386i	0.581448	+	0.813584i	$0.302486\pi$
$158$	−7.08205	−	2.30110i	−0.563417	−	0.183065i
$159$	−10.5530	−	7.66721i	−0.836908	−	0.608049i
$160$		0			0
$161$	−0.556639	+	1.71316i	−0.0438693	+	0.135016i
$162$	−7.99563	+	2.59794i	−0.628196	+	0.204113i
$163$	−1.85149	−	2.54835i	−0.145020	−	0.199603i	0.730328	−	0.683097i	$-0.239367\pi$
$163$	−1.85149	−	2.54835i	−0.145020	−	0.199603i	−0.875347	+	0.483494i	$0.839367\pi$
$164$	−2.65743			−0.207511
$165$		0			0
$166$	−7.88499			−0.611994
$167$	3.20447	+	4.41057i	0.247969	+	0.341300i	0.914799	−	0.403910i	$-0.132349\pi$
$167$	3.20447	+	4.41057i	0.247969	+	0.341300i	−0.666830	+	0.745210i	$0.732349\pi$
$168$	1.02175	−	0.331986i	0.0788296	−	0.0256133i
$169$	−0.788314	+	2.42618i	−0.0606395	+	0.186629i
$170$		0			0
$171$	15.7996	+	11.4791i	1.20822	+	0.877826i
$172$	10.9957	+	3.57270i	0.838411	+	0.272416i
$173$	−14.2309	+	4.62391i	−1.08196	+	0.351550i	−0.795134	−	0.606434i	$-0.792600\pi$
$173$	−14.2309	+	4.62391i	−1.08196	+	0.351550i	−0.286824	+	0.957983i	$0.592600\pi$
$174$	1.27547	−	0.926680i	0.0966928	−	0.0702515i
$175$		0			0
$176$	−3.14565	+	1.05113i	−0.237113	+	0.0792316i
$177$			27.0193i			2.03089i
$178$	−0.789142	−	1.08616i	−0.0591487	−	0.0814111i
$179$	−3.75329	−	11.5514i	−0.280534	−	0.863395i	−0.987702	−	0.156349i	$-0.950027\pi$
$179$	−3.75329	−	11.5514i	−0.280534	−	0.863395i	0.707168	−	0.707046i	$-0.249973\pi$
$180$		0			0
$181$	11.5274	+	8.37513i	0.856823	+	0.622518i	0.927019	−	0.375015i	$-0.122362\pi$
$181$	11.5274	+	8.37513i	0.856823	+	0.622518i	−0.0701958	+	0.997533i	$0.522362\pi$
$182$	1.00122	−	1.37806i	0.0742151	−	0.102148i
$183$	−24.8865	−	8.08613i	−1.83967	−	0.597744i
$184$	1.28868	+	3.96614i	0.0950026	+	0.292388i
$185$		0			0
$186$	−25.6439			−1.88030
$187$	−3.59712	−	10.7649i	−0.263047	−	0.787209i
$188$		−	2.96911i		−	0.216545i
$189$	−0.161739	+	0.117510i	−0.0117647	+	0.00854759i
$190$		0			0
$191$	−0.341287	+	1.05037i	−0.0246946	+	0.0760023i	−0.962644	−	0.270769i	$-0.912722\pi$
$191$	−0.341287	+	1.05037i	−0.0246946	+	0.0760023i	0.937950	+	0.346771i	$0.112722\pi$
$192$	1.46193	−	2.01217i	0.105506	−	0.145216i
$193$	6.43288	−	8.85410i	0.463049	−	0.637332i	−0.512089	−	0.858933i	$-0.671128\pi$
$193$	6.43288	−	8.85410i	0.463049	−	0.637332i	0.975138	+	0.221600i	$0.0711281\pi$
$194$	−0.541815	+	1.66754i	−0.0389001	+	0.119722i
$195$		0			0
$196$	5.51217	−	4.00483i	0.393727	−	0.286059i
$197$		−	16.0572i		−	1.14403i	−0.820244	−	0.572014i	$-0.806162\pi$
$197$		−	16.0572i		−	1.14403i	0.820244	−	0.572014i	$-0.193838\pi$
$198$	8.49691	−	6.28214i	0.603849	−	0.446452i
$199$	−27.1521			−1.92476			−0.962382	−	0.271699i	$-0.912415\pi$
$199$	−27.1521			−1.92476			−0.962382	+	0.271699i	$0.912415\pi$
$200$		0			0
$201$	−8.45342	−	26.0170i	−0.596258	−	1.83509i
$202$	1.17557	+	0.381966i	0.0827129	+	0.0268750i
$203$	−0.160935	+	0.221508i	−0.0112954	+	0.0155468i
$204$	6.88598	+	5.00295i	0.482115	+	0.350277i
$205$		0			0
$206$	0.831378	+	2.55872i	0.0579248	+	0.178274i
$207$	−7.80977	−	10.7492i	−0.542817	−	0.747123i
$208$		−	3.94348i		−	0.273431i
$209$	19.3861	+	6.12093i	1.34097	+	0.423393i
$210$		0			0
$211$	−2.14302	+	1.55700i	−0.147532	+	0.107188i	−0.659103	−	0.752053i	$-0.729064\pi$
$211$	−2.14302	+	1.55700i	−0.147532	+	0.107188i	0.511571	+	0.859241i	$0.329064\pi$
$212$	4.98789	−	1.62066i	0.342570	−	0.111308i
$213$	24.2675	+	7.88499i	1.66278	+	0.540271i
$214$	0.263292	+	0.191292i	0.0179982	+	0.0130765i
$215$		0			0
$216$	−0.143024	+	0.440183i	−0.00973155	+	0.0299506i
$217$	4.23556	−	1.37622i	0.287529	−	0.0934238i
$218$	5.90648	+	8.12957i	0.400037	+	0.550604i
$219$	27.7025			1.87196
$220$		0			0
$221$	13.4952			0.907786
$222$	−10.7325	−	14.7720i	−0.720315	−	0.991428i
$223$	−5.97576	+	1.94164i	−0.400167	+	0.130022i	−0.502184	−	0.864761i	$-0.667470\pi$
$223$	−5.97576	+	1.94164i	−0.400167	+	0.130022i	0.102018	+	0.994783i	$0.467470\pi$
$224$	−0.133479	+	0.410805i	−0.00891842	+	0.0274481i
$225$		0			0
$226$	−6.87380	−	4.99411i	−0.457238	−	0.332203i
$227$	−13.4430	−	4.36790i	−0.892245	−	0.289908i	−0.173212	−	0.984885i	$-0.555415\pi$
$227$	−13.4430	−	4.36790i	−0.892245	−	0.289908i	−0.719032	+	0.694977i	$0.755415\pi$
$228$	−14.4992	+	4.71108i	−0.960233	+	0.311999i
$229$	−3.14462	+	2.28470i	−0.207802	+	0.150977i	−0.686819	−	0.726829i	$-0.740993\pi$
$229$	−3.14462	+	2.28470i	−0.207802	+	0.150977i	0.479017	+	0.877806i	$0.340993\pi$
$230$		0			0
$231$	−2.07029	+	2.89999i	−0.136215	+	0.190805i
$232$			0.633874i			0.0416159i
$233$	15.0356	+	20.6947i	0.985016	+	1.35576i	0.934083	+	0.357056i	$0.116219\pi$
$233$	15.0356	+	20.6947i	0.985016	+	1.35576i	0.0509329	+	0.998702i	$0.483781\pi$
$234$	3.88257	+	11.9493i	0.253812	+	0.781153i
$235$		0			0
$236$	−8.78868	−	6.38535i	−0.572094	−	0.415651i
$237$	−10.8863	+	14.9837i	−0.707139	+	0.973294i
$238$	−1.40584	−	0.456785i	−0.0911270	−	0.0296090i
$239$	3.73255	+	11.4876i	0.241439	+	0.743072i	0.996202	+	0.0870747i	$0.0277519\pi$
$239$	3.73255	+	11.4876i	0.241439	+	0.743072i	−0.754763	+	0.655998i	$0.772248\pi$
$240$		0			0
$241$	23.5597			1.51762			0.758808	−	0.651314i	$-0.225782\pi$
$241$	23.5597			1.51762			0.758808	+	0.651314i	$0.225782\pi$
$242$	6.31653	−	9.00563i	0.406042	−	0.578904i
$243$			22.2985i			1.43045i
$244$	8.51153	−	6.18399i	0.544895	−	0.395889i
$245$		0			0
$246$	−2.04246	+	6.28603i	−0.130222	+	0.400783i
$247$	−14.2078	+	19.5554i	−0.904024	+	1.24428i
$248$	6.06030	−	8.34129i	0.384829	−	0.529672i
$249$	−6.06027	+	18.6516i	−0.384054	+	1.18200i
$250$		0			0
$251$	2.77289	−	2.01462i	0.175023	−	0.127162i	−0.496825	−	0.867851i	$-0.665501\pi$
$251$	2.77289	−	2.01462i	0.175023	−	0.127162i	0.671848	+	0.740689i	$0.265501\pi$
$252$		−	1.37622i		−	0.0866936i
$253$	−11.2569	−	8.03628i	−0.707718	−	0.505237i
$254$	−8.63913			−0.542067
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	1.55003	+	0.503634i	0.0966879	+	0.0314158i	0.356961	−	0.934119i	$-0.383813\pi$
$257$	1.55003	+	0.503634i	0.0966879	+	0.0314158i	−0.260274	+	0.965535i	$0.583813\pi$
$258$	16.9021	−	23.2638i	1.05228	−	1.44834i
$259$	2.56542	+	1.86389i	0.159408	+	0.115816i
$260$		0			0
$261$	−0.624085	−	1.92073i	−0.0386299	−	0.118890i
$262$	9.60132	+	13.2151i	0.593172	+	0.816431i
$263$			1.65168i			0.101847i	0.998703	+	0.0509236i	$0.0162165\pi$
$263$			1.65168i			0.101847i	−0.998703	+	0.0509236i	$0.983783\pi$
$264$	0.0686945	+	8.24877i	0.00422786	+	0.507677i
$265$		0			0
$266$	2.14199	−	1.55625i	0.131334	−	0.0954195i
$267$	−3.17578	+	1.03187i	−0.194355	+	0.0631497i
$268$	10.4604	+	3.39879i	0.638971	+	0.207614i
$269$	17.9324	+	13.0287i	1.09336	+	0.794371i	0.979963	−	0.199179i	$-0.0638274\pi$
$269$	17.9324	+	13.0287i	1.09336	+	0.794371i	0.113395	+	0.993550i	$0.463827\pi$
$270$		0			0
$271$	−2.27021	+	6.98698i	−0.137905	+	0.424429i	−0.996031	−	0.0890115i	$-0.971629\pi$
$271$	−2.27021	+	6.98698i	−0.137905	+	0.424429i	0.858125	+	0.513440i	$0.171629\pi$
$272$	−3.25466	+	1.05750i	−0.197343	+	0.0641206i
$273$	−2.49021	−	3.42748i	−0.150714	−	0.207440i
$274$	17.0593			1.03059
$275$		0			0
$276$	10.3722			0.624332
$277$	9.12054	+	12.5533i	0.548000	+	0.754258i	0.989739	−	0.142886i	$-0.0456382\pi$
$277$	9.12054	+	12.5533i	0.548000	+	0.754258i	−0.441739	+	0.897144i	$0.645638\pi$
$278$	−5.34429	+	1.73646i	−0.320529	+	0.104146i
$279$	−10.1512	+	31.2420i	−0.607734	+	1.87041i
$280$		0			0
$281$	18.5343	+	13.4660i	1.10566	+	0.803311i	0.981975	−	0.189010i	$-0.0605278\pi$
$281$	18.5343	+	13.4660i	1.10566	+	0.803311i	0.123688	+	0.992321i	$0.460528\pi$
$282$	−7.02329	−	2.28201i	−0.418231	−	0.135891i
$283$	−2.66497	+	0.865901i	−0.158416	+	0.0514724i	−0.387151	−	0.922016i	$-0.626541\pi$
$283$	−2.66497	+	0.865901i	−0.158416	+	0.0514724i	0.228735	+	0.973489i	$0.426541\pi$
$284$	−8.29982	+	6.03017i	−0.492503	+	0.357825i
$285$		0			0
$286$	7.77552	+	10.5168i	0.459776	+	0.621870i
$287$		−	1.14787i		−	0.0677565i
$288$	−1.87274	−	2.57760i	−0.110352	−	0.151886i
$289$	1.63434	+	5.02999i	0.0961379	+	0.295882i
$290$		0			0
$291$	3.52805	+	2.56328i	0.206818	+	0.150262i
$292$	−6.54680	+	9.01089i	−0.383122	+	0.527323i
$293$	20.2349	+	6.57473i	1.18214	+	0.384100i	0.833160	−	0.553032i	$-0.186529\pi$
$293$	20.2349	+	6.57473i	1.18214	+	0.384100i	0.348977	+	0.937131i	$0.386529\pi$
$294$	−5.23668	−	16.1168i	−0.305409	−	0.939953i
$295$		0			0
$296$	7.34129			0.426704
$297$	−0.486498	−	1.45592i	−0.0282295	−	0.0844810i
$298$			9.90004i			0.573494i
$299$	13.3045	−	9.66630i	0.769420	−	0.559016i
$300$		0			0
$301$	−1.54322	+	4.74953i	−0.0889494	+	0.273758i
$302$	6.74671	−	9.28605i	0.388229	−	0.534352i
$303$	1.80705	−	2.48718i	0.103812	−	0.142885i
$304$	1.89414	−	5.82957i	0.108636	−	0.334349i
$305$		0			0
$306$	8.82095	−	6.40879i	0.504260	−	0.366366i
$307$		−	2.92114i		−	0.166718i	−0.996520	−	0.0833591i	$-0.973435\pi$
$307$		−	2.92114i		−	0.166718i	0.996520	−	0.0833591i	$-0.0265649\pi$
$308$	−0.454029	−	1.35875i	−0.0258707	−	0.0774221i
$309$	6.69151			0.380667
$310$		0			0
$311$	−1.18284	−	3.64040i	−0.0670726	−	0.206428i	0.911903	−	0.410406i	$-0.134613\pi$
$311$	−1.18284	−	3.64040i	−0.0670726	−	0.206428i	−0.978976	+	0.203978i	$0.934613\pi$
$312$	−9.32812	−	3.03089i	−0.528101	−	0.171590i
$313$	16.0395	−	22.0764i	0.906604	−	1.24783i	−0.0617096	−	0.998094i	$-0.519655\pi$
$313$	16.0395	−	22.0764i	0.906604	−	1.24783i	0.968313	−	0.249739i	$-0.0803447\pi$
$314$	6.11418	+	4.44221i	0.345043	+	0.250688i
$315$		0			0
$316$	−2.30110	−	7.08205i	−0.129447	−	0.398396i
$317$	16.9018	+	23.2634i	0.949302	+	1.30660i	0.951837	+	0.306605i	$0.0991932\pi$
$317$	16.9018	+	23.2634i	0.949302	+	1.30660i	−0.00253464	+	0.999997i	$0.500807\pi$
$318$		−	13.0442i		−	0.731484i
$319$	−1.24984	−	1.69047i	−0.0699774	−	0.0946479i
$320$		0			0
$321$	0.654855	−	0.475780i	0.0365504	−	0.0265554i
$322$	−1.71316	+	0.556639i	−0.0954706	+	0.0310203i
$323$	19.9497	+	6.48205i	1.11003	+	0.360671i
$324$	−6.80149	−	4.94157i	−0.377861	−	0.274532i
$325$		0			0
$326$	0.973385	−	2.99577i	0.0539108	−	0.165920i
$327$	23.7697	−	7.72325i	1.31447	−	0.427097i
$328$	−1.56200	−	2.14991i	−0.0862470	−	0.118709i
$329$	1.28250			0.0707063
$330$		0			0
$331$	−15.2961			−0.840752			−0.420376	−	0.907350i	$-0.638102\pi$
$331$	−15.2961			−0.840752			−0.420376	+	0.907350i	$0.638102\pi$
$332$	−4.63468	−	6.37909i	−0.254361	−	0.350098i
$333$	−22.2452	+	7.22790i	−1.21903	+	0.396087i
$334$	−1.68469	+	5.18494i	−0.0921820	+	0.283707i
$335$		0			0
$336$	0.869151	+	0.631475i	0.0474161	+	0.0344498i
$337$	−18.4878	−	6.00704i	−1.00709	−	0.327224i	−0.241396	−	0.970427i	$-0.577605\pi$
$337$	−18.4878	−	6.00704i	−1.00709	−	0.327224i	−0.765696	+	0.643203i	$0.777605\pi$
$338$	−2.42618	+	0.788314i	−0.131967	+	0.0428786i
$339$	−17.0964	+	12.4213i	−0.928550	+	0.674631i
$340$		0			0
$341$	0.284767	+	34.1945i	0.0154210	+	1.85174i
$342$			19.5293i			1.05603i
$343$	3.50711	+	4.82712i	0.189366	+	0.260640i
$344$	3.57270	+	10.9957i	0.192627	+	0.592846i
$345$		0			0
$346$	−12.1056	−	8.79521i	−0.650799	−	0.472833i
$347$	5.42452	−	7.46620i	0.291203	−	0.400807i	−0.638201	−	0.769870i	$-0.720321\pi$
$347$	5.42452	−	7.46620i	0.291203	−	0.400807i	0.929405	+	0.369063i	$0.120321\pi$
$348$	1.49940	+	0.487185i	0.0803763	+	0.0261158i
$349$	−4.72374	−	14.5382i	−0.252856	−	0.778211i	−0.994244	−	0.107135i	$-0.965832\pi$
$349$	−4.72374	−	14.5382i	−0.252856	−	0.778211i	0.741388	−	0.671076i	$-0.234168\pi$
$350$		0			0
$351$	1.82518			0.0974210
$352$	−2.69935	−	1.92705i	−0.143876	−	0.102712i
$353$		−	6.10571i		−	0.324974i	−0.986711	−	0.162487i	$-0.948048\pi$
$353$		−	6.10571i		−	0.324974i	0.986711	−	0.162487i	$-0.0519516\pi$
$354$	−21.8591	+	15.8815i	−1.16180	+	0.844094i
$355$		0			0
$356$	0.414876	−	1.27686i	0.0219884	−	0.0676733i
$357$	−2.16101	+	2.97437i	−0.114373	+	0.157420i
$358$	7.13918	−	9.82624i	0.377317	−	0.519333i
$359$	8.32545	−	25.6231i	0.439400	−	1.35233i	−0.449109	−	0.893477i	$-0.648259\pi$
$359$	8.32545	−	25.6231i	0.439400	−	1.35233i	0.888510	−	0.458858i	$-0.151741\pi$
$360$		0			0
$361$	−15.0247	+	10.9161i	−0.790776	+	0.574532i
$362$			14.2486i			0.748891i
$363$	−16.4476	−	21.8630i	−0.863277	−	1.14751i
$364$	1.70337			0.0892809
$365$		0			0
$366$	−8.08613	−	24.8865i	−0.422669	−	1.30084i
$367$	23.7874	+	7.72900i	1.24169	+	0.403451i	0.854937	−	0.518732i	$-0.173596\pi$
$367$	23.7874	+	7.72900i	1.24169	+	0.403451i	0.386756	+	0.922182i	$0.373596\pi$
$368$	−2.45121	+	3.37380i	−0.127778	+	0.175872i
$369$	6.84980	+	4.97667i	0.356586	+	0.259075i
$370$		0			0
$371$	0.700039	+	2.15450i	0.0363442	+	0.111856i
$372$	−15.0731	−	20.7463i	−0.781503	−	1.07565i
$373$			27.5557i			1.42678i	0.700768	+	0.713389i	$0.252841\pi$
$373$			27.5557i			1.42678i	−0.700768	+	0.713389i	$0.747159\pi$
$374$	6.59467	−	9.23759i	0.341002	−	0.477664i
$375$		0			0
$376$	2.40206	−	1.74520i	0.123877	−	0.0900018i
$377$	2.37733	−	0.772441i	0.122439	−	0.0397827i
$378$	−0.190135	−	0.0617786i	−0.00977949	−	0.00317755i
$379$	−19.0027	−	13.8063i	−0.976105	−	0.709182i	−0.0192700	−	0.999814i	$-0.506134\pi$
$379$	−19.0027	−	13.8063i	−0.976105	−	0.709182i	−0.956835	+	0.290633i	$0.906134\pi$
$380$		0			0
$381$	−6.63989	+	20.4355i	−0.340172	+	1.04694i
$382$	−1.05037	+	0.341287i	−0.0537417	+	0.0174617i
$383$	−11.0050	−	15.1470i	−0.562327	−	0.773977i	0.429293	−	0.903165i	$-0.358763\pi$
$383$	−11.0050	−	15.1470i	−0.562327	−	0.773977i	−0.991620	+	0.129188i	$0.958763\pi$
$384$	2.48718			0.126924
$385$		0			0
$386$	10.9443			0.557049
$387$	−21.6517	−	29.8010i	−1.10062	−	1.51487i
$388$	−1.66754	+	0.541815i	−0.0846563	+	0.0275065i
$389$	−2.29210	+	7.05435i	−0.116214	+	0.357670i	−0.992198	−	0.124670i	$-0.960213\pi$
$389$	−2.29210	+	7.05435i	−0.116214	+	0.357670i	0.875984	+	0.482340i	$0.160213\pi$
$390$		0			0
$391$	−11.5457	−	8.38842i	−0.583890	−	0.424221i
$392$	6.47995	+	2.10546i	0.327287	+	0.106342i
$393$	38.6391	−	12.5546i	1.94908	−	0.633296i
$394$	12.9906	−	9.43819i	0.654455	−	0.475489i
$395$		0			0
$396$	10.0767	+	3.18160i	0.506374	+	0.159881i
$397$		−	22.6398i		−	1.13626i	−0.822939	−	0.568130i	$-0.807667\pi$
$397$		−	22.6398i		−	1.13626i	0.822939	−	0.568130i	$-0.192333\pi$
$398$	−15.9596	−	21.9665i	−0.799984	−	1.10108i
$399$	−2.03493	−	6.26287i	−0.101874	−	0.313536i
$400$		0			0
$401$	−21.8299	−	15.8603i	−1.09013	−	0.792026i	−0.110709	−	0.993853i	$-0.535312\pi$
$401$	−21.8299	−	15.8603i	−1.09013	−	0.792026i	−0.979421	+	0.201826i	$0.935312\pi$
$402$	16.0794	−	22.1313i	0.801966	−	1.10381i
$403$	−38.6689	−	12.5643i	−1.92623	−	0.625871i
$404$	0.381966	+	1.17557i	0.0190035	+	0.0584868i
$405$		0			0
$406$	−0.273800			−0.0135884
$407$	−19.5783	+	14.4751i	−0.970461	+	0.717505i
$408$			8.51153i			0.421384i
$409$	−7.55854	+	5.49160i	−0.373746	+	0.271542i	−0.758762	−	0.651367i	$-0.774196\pi$
$409$	−7.55854	+	5.49160i	−0.373746	+	0.271542i	0.385017	+	0.922910i	$0.374196\pi$
$410$		0			0
$411$	13.1115	−	40.3529i	0.646741	−	1.99046i
$412$	−1.58137	+	2.17657i	−0.0779087	+	0.107232i
$413$	2.75813	−	3.79623i	0.135718	−	0.186800i
$414$	4.10584	−	12.6365i	0.201791	−	0.621049i
$415$		0			0
$416$	3.19034	−	2.31792i	0.156419	−	0.113645i
$417$			13.9763i			0.684421i
$418$	6.44295	+	19.2815i	0.315135	+	0.943089i
$419$	−16.5607			−0.809044			−0.404522	−	0.914528i	$-0.632562\pi$
$419$	−16.5607			−0.809044			−0.404522	+	0.914528i	$0.632562\pi$
$420$		0			0
$421$	0.581094	+	1.78842i	0.0283208	+	0.0871624i	0.964218	−	0.265111i	$-0.0854087\pi$
$421$	0.581094	+	1.78842i	0.0283208	+	0.0871624i	−0.935897	+	0.352274i	$0.885409\pi$
$422$	−2.51928	−	0.818562i	−0.122636	−	0.0398470i
$423$	−5.56036	+	7.65318i	−0.270354	+	0.372110i
$424$	4.24295	+	3.08268i	0.206056	+	0.149708i
$425$		0			0
$426$	7.88499	+	24.2675i	0.382029	+	1.17576i
$427$	2.67115	+	3.67652i	0.129266	+	0.177919i
$428$			0.325446i			0.0157310i
$429$	30.8531	−	10.3096i	1.48960	−	0.497753i
$430$		0			0
$431$	−19.0974	+	13.8751i	−0.919889	+	0.668339i	−0.943496	−	0.331383i	$-0.892485\pi$
$431$	−19.0974	+	13.8751i	−0.919889	+	0.668339i	0.0236072	+	0.999721i	$0.492485\pi$
$432$	−0.440183	+	0.143024i	−0.0211783	+	0.00688124i
$433$	15.0977	+	4.90556i	0.725551	+	0.235746i	0.648428	−	0.761276i	$-0.275427\pi$
$433$	15.0977	+	4.90556i	0.725551	+	0.235746i	0.0771230	+	0.997022i	$0.475427\pi$
$434$	3.60299	+	2.61772i	0.172949	+	0.125655i
$435$		0			0
$436$	−3.10522	+	9.55688i	−0.148713	+	0.457692i
$437$	24.3107	−	7.89904i	1.16294	−	0.377862i
$438$	16.2831	+	22.4118i	0.778036	+	1.07088i
$439$	11.6082			0.554031			0.277016	−	0.960865i	$-0.410655\pi$
$439$	11.6082			0.554031			0.277016	+	0.960865i	$0.410655\pi$
$440$		0			0
$441$	−21.7082			−1.03372
$442$	7.93228	+	10.9178i	0.377300	+	0.519309i
$443$	9.07585	−	2.94892i	0.431207	−	0.140108i	−0.0853684	−	0.996349i	$-0.527207\pi$
$443$	9.07585	−	2.94892i	0.431207	−	0.140108i	0.516575	+	0.856242i	$0.327207\pi$
$444$	5.64238	−	17.3655i	0.267776	−	0.824129i
$445$		0			0
$446$	−5.08329	−	3.69322i	−0.240701	−	0.174879i
$447$	23.4181	+	7.60900i	1.10764	+	0.359893i
$448$	−0.410805	+	0.133479i	−0.0194087	+	0.00630627i
$449$	16.0576	−	11.6665i	0.757805	−	0.550578i	−0.140431	−	0.990090i	$-0.544849\pi$
$449$	16.0576	−	11.6665i	0.757805	−	0.550578i	0.898236	+	0.439513i	$0.144849\pi$
$450$		0			0
$451$	8.40472	+	2.65369i	0.395763	+	0.124957i
$452$		−	8.49649i		−	0.399641i
$453$	−16.7803	−	23.0961i	−0.788408	−	1.08515i
$454$	−4.36790	−	13.4430i	−0.204996	−	0.630912i
$455$		0			0
$456$	−12.3338	−	8.96100i	−0.577581	−	0.419637i
$457$	2.47217	−	3.40265i	0.115643	−	0.159169i	−0.747271	−	0.664519i	$-0.768636\pi$
$457$	2.47217	−	3.40265i	0.115643	−	0.159169i	0.862915	+	0.505350i	$0.168636\pi$
$458$	−3.69672	−	1.20114i	−0.172736	−	0.0561254i
$459$	−0.489450	−	1.50637i	−0.0228456	−	0.0703115i
$460$		0			0
$461$	9.44809			0.440041			0.220021	−	0.975495i	$-0.429388\pi$
$461$	9.44809			0.440041			0.220021	+	0.975495i	$0.429388\pi$
$462$	−3.56302	+	0.0296723i	−0.165767	+	0.00138048i
$463$			26.5879i			1.23564i	0.786318	+	0.617822i	$0.211985\pi$
$463$			26.5879i			1.23564i	−0.786318	+	0.617822i	$0.788015\pi$
$464$	−0.512815	+	0.372582i	−0.0238068	+	0.0172967i
$465$		0			0
$466$	−7.90469	+	24.3281i	−0.366178	+	1.12698i
$467$	10.7148	−	14.7476i	0.495820	−	0.682438i	−0.485628	−	0.874165i	$-0.661409\pi$
$467$	10.7148	−	14.7476i	0.495820	−	0.682438i	0.981448	+	0.191728i	$0.0614091\pi$
$468$	−7.38510	+	10.1647i	−0.341376	+	0.469864i
$469$	−1.46809	+	4.51833i	−0.0677903	+	0.208637i
$470$		0			0
$471$	15.2071	−	11.0486i	0.700705	−	0.509092i
$472$		−	10.8634i		−	0.500029i
$473$	−31.2085	−	22.2796i	−1.43497	−	1.02442i
$474$	−18.5208			−0.850690
$475$		0			0
$476$	−0.456785	−	1.40584i	−0.0209367	−	0.0644365i
$477$	−15.8919	−	5.16358i	−0.727638	−	0.236424i
$478$	−7.09974	+	9.77195i	−0.324734	+	0.446959i
$479$	−10.5221	−	7.64476i	−0.480768	−	0.349298i	0.320855	−	0.947128i	$-0.396030\pi$
$479$	−10.5221	−	7.64476i	−0.480768	−	0.349298i	−0.801623	+	0.597830i	$0.796030\pi$
$480$		0			0
$481$	−8.94611	−	27.5333i	−0.407907	−	1.25541i
$482$	13.8481	+	19.0602i	0.630762	+	0.868170i
$483$			4.48022i			0.203857i
$484$	10.9985	−	0.183200i	0.499931	−	0.00832727i
$485$		0			0
$486$	−18.0399	+	13.1067i	−0.818306	+	0.594534i
$487$	7.32943	−	2.38148i	0.332128	−	0.107915i	−0.138206	−	0.990404i	$-0.544133\pi$
$487$	7.32943	−	2.38148i	0.332128	−	0.107915i	0.470334	+	0.882489i	$0.344133\pi$
$488$	10.0059	+	3.25112i	0.452946	+	0.147171i
$489$	−6.33823	−	4.60499i	−0.286625	−	0.208245i
$490$		0			0
$491$	4.16722	−	12.8254i	0.188064	−	0.578802i	−0.811924	−	0.583764i	$-0.801579\pi$
$491$	4.16722	−	12.8254i	0.188064	−	0.578802i	0.999988	+	0.00496193i	$0.00157944\pi$
$492$	−6.28603	+	2.04246i	−0.283396	+	0.0920810i
$493$	−1.27503	−	1.75493i	−0.0574246	−	0.0790382i
$494$	−24.1718			−1.08754
$495$		0			0
$496$	10.3104			0.462951
$497$	−2.60471	−	3.58507i	−0.116837	−	0.160812i
$498$	−18.6516	+	6.06027i	−0.835797	+	0.271567i
$499$	−4.25919	+	13.1084i	−0.190667	+	0.586814i	−1.00000		0.000536806i	$-0.999829\pi$
$499$	−4.25919	+	13.1084i	−0.190667	+	0.586814i	0.809332	+	0.587351i	$0.199829\pi$
$500$		0			0
$501$	10.9699	+	7.97010i	0.490099	+	0.356078i
$502$	3.25973	+	1.05915i	0.145489	+	0.0472721i
$503$	6.00504	−	1.95116i	0.267752	−	0.0869977i	−0.172064	−	0.985086i	$-0.555044\pi$
$503$	6.00504	−	1.95116i	0.267752	−	0.0869977i	0.439816	+	0.898088i	$0.355044\pi$
$504$	1.11338	−	0.808921i	0.0495940	−	0.0360322i
$505$		0			0
$506$	−0.115180	−	13.8307i	−0.00512036	−	0.614848i
$507$			6.34490i			0.281787i
$508$	−5.07796	−	6.98921i	−0.225298	−	0.310096i
$509$	−13.3957	−	41.2278i	−0.593755	−	1.82739i	−0.560826	−	0.827934i	$-0.689516\pi$
$509$	−13.3957	−	41.2278i	−0.593755	−	1.82739i	−0.0329295	−	0.999458i	$-0.510484\pi$
$510$		0			0
$511$	−3.89222	−	2.82786i	−0.172182	−	0.125097i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	2.69813	+	0.876675i	0.119125	+	0.0387062i
$514$	0.503634	+	1.55003i	0.0222143	+	0.0683687i
$515$		0			0
$516$	28.7556			1.26590
$517$	−2.96493	+	9.39047i	−0.130397	+	0.412993i
$518$			3.17104i			0.139327i
$519$	−30.1088	+	21.8753i	−1.32163	+	0.960219i
$520$		0			0
$521$	6.70203	−	20.6267i	0.293621	−	0.903673i	−0.690060	−	0.723752i	$-0.742416\pi$
$521$	6.70203	−	20.6267i	0.293621	−	0.903673i	0.983681	−	0.179921i	$-0.0575842\pi$
$522$	1.18708	−	1.63387i	0.0519570	−	0.0715127i
$523$	−8.98136	+	12.3618i	−0.392727	+	0.540543i	−0.958900	−	0.283744i	$-0.908423\pi$
$523$	−8.98136	+	12.3618i	−0.392727	+	0.540543i	0.566173	+	0.824287i	$0.308423\pi$
$524$	−5.04771	+	15.5353i	−0.220510	+	0.678661i
$525$		0			0
$526$	−1.33624	+	0.970836i	−0.0582629	+	0.0423304i
$527$			35.2838i			1.53699i
$528$	−6.63302	+	4.90408i	−0.288665	+	0.213423i
$529$	5.60904			0.243871
$530$		0			0
$531$	10.6956	+	32.9177i	0.464150	+	1.42851i
$532$	2.51806	+	0.818166i	0.109172	+	0.0354720i
$533$	−6.15971	+	8.47812i	−0.266807	+	0.367228i
$534$	−2.70148	−	1.96274i	−0.116905	−	0.0849361i
$535$		0			0
$536$	3.39879	+	10.4604i	0.146805	+	0.451821i
$537$	−17.7565	−	24.4397i	−0.766248	−	1.05465i
$538$			22.1657i			0.955630i
$539$	−21.4327	+	7.16176i	−0.923170	+	0.308479i
$540$		0			0
$541$	19.5314	−	14.1904i	0.839721	−	0.610093i	−0.0825716	−	0.996585i	$-0.526313\pi$
$541$	19.5314	−	14.1904i	0.839721	−	0.610093i	0.922293	+	0.386492i	$0.126313\pi$
$542$	−6.98698	+	2.27021i	−0.300116	+	0.0975138i
$543$	33.7044	+	10.9512i	1.44640	+	0.469963i
$544$	−2.76858	−	2.01149i	−0.118702	−	0.0862420i
$545$		0			0
$546$	1.30918	−	4.02924i	0.0560277	−	0.172436i
$547$	−31.8327	+	10.3431i	−1.36107	+	0.442237i	−0.896399	−	0.443248i	$-0.853826\pi$
$547$	−31.8327	+	10.3431i	−1.36107	+	0.442237i	−0.464668	+	0.885485i	$0.653826\pi$
$548$	10.0272	+	13.8012i	0.428340	+	0.589560i
$549$	−33.5203			−1.43061
$550$		0			0
$551$	3.88538			0.165523
$552$	6.09661	+	8.39127i	0.259489	+	0.357156i
$553$	3.05906	−	0.993949i	0.130085	−	0.0422670i
$554$	−4.79495	+	14.7573i	−0.203718	+	0.626980i
$555$		0			0
$556$	−4.54612	−	3.30295i	−0.192798	−	0.140076i
$557$	−3.93292	−	1.27788i	−0.166643	−	0.0541456i	0.224507	−	0.974472i	$-0.427923\pi$
$557$	−3.93292	−	1.27788i	−0.166643	−	0.0541456i	−0.391150	+	0.920327i	$0.627923\pi$
$558$	−31.2420	+	10.1512i	−1.32258	+	0.429733i
$559$	36.8852	−	26.7987i	1.56008	−	1.13346i
$560$		0			0
$561$	−16.7825	−	22.6992i	−0.708559	−	0.958362i
$562$			22.9096i			0.966385i
$563$	16.2283	+	22.3363i	0.683941	+	0.941364i	0.999973	−	0.00738424i	$-0.00235050\pi$
$563$	16.2283	+	22.3363i	0.683941	+	0.941364i	−0.316031	+	0.948749i	$0.602350\pi$
$564$	−2.28201	−	7.02329i	−0.0960898	−	0.295734i
$565$		0			0
$566$	−2.26696	−	1.64704i	−0.0952873	−	0.0692303i
$567$	2.13449	−	2.93788i	0.0896403	−	0.123379i
$568$	−9.75702	−	3.17025i	−0.409395	−	0.133021i
$569$	2.40142	+	7.39081i	0.100673	+	0.309839i	0.988691	−	0.149970i	$-0.0479178\pi$
$569$	2.40142	+	7.39081i	0.100673	+	0.309839i	−0.888018	+	0.459809i	$0.847918\pi$
$570$		0			0
$571$	−1.73373			−0.0725544			−0.0362772	−	0.999342i	$-0.511550\pi$
$571$	−1.73373			−0.0725544			−0.0362772	+	0.999342i	$0.511550\pi$
$572$	−3.93792	+	12.4721i	−0.164653	+	0.521486i
$573$			2.74691i			0.114754i
$574$	0.928644	−	0.674699i	0.0387609	−	0.0281614i
$575$		0			0
$576$	0.984555	−	3.03015i	0.0410231	−	0.126256i
$577$	3.95992	−	5.45036i	0.164854	−	0.226902i	−0.718596	−	0.695428i	$-0.755215\pi$
$577$	3.95992	−	5.45036i	0.164854	−	0.226902i	0.883450	+	0.468526i	$0.155215\pi$
$578$	−3.10871	+	4.27877i	−0.129305	+	0.177973i
$579$	8.41157	−	25.8882i	0.349573	−	1.07588i
$580$		0			0
$581$	2.75542	−	2.00193i	0.114314	−	0.0830541i
$582$			4.36091i			0.180765i
$583$	−17.3937	+	0.144852i	−0.720373	+	0.00599916i
$584$	−11.1381			−0.460897
$585$		0			0
$586$	6.57473	+	20.2349i	0.271599	+	0.835897i
$587$	33.3923	+	10.8498i	1.37825	+	0.447820i	0.902093	−	0.431541i	$-0.142030\pi$
$587$	33.3923	+	10.8498i	1.37825	+	0.447820i	0.476156	+	0.879361i	$0.342030\pi$
$588$	9.96075	−	13.7098i	0.410774	−	0.565382i
$589$	−51.1285	−	37.1470i	−2.10671	−	1.53062i
$590$		0			0
$591$	−12.3413	−	37.9826i	−0.507653	−	1.56239i
$592$	4.31510	+	5.93923i	0.177350	+	0.244101i
$593$			5.17098i			0.212347i	0.994348	+	0.106173i	$0.0338598\pi$
$593$			5.17098i			0.212347i	−0.994348	+	0.106173i	$0.966140\pi$
$594$	0.891907	−	1.24935i	0.0365954	−	0.0512616i
$595$		0			0
$596$	−8.00930	+	5.81910i	−0.328074	+	0.238360i
$597$	−64.2271	+	20.8687i	−2.62864	+	0.854097i
$598$	15.6404	+	5.08187i	0.639583	+	0.207813i
$599$	13.5879	+	9.87221i	0.555188	+	0.403368i	0.829695	−	0.558217i	$-0.188515\pi$
$599$	13.5879	+	9.87221i	0.555188	+	0.403368i	−0.274507	+	0.961585i	$0.588515\pi$
$600$		0			0
$601$	−8.19285	+	25.2150i	−0.334193	+	1.02854i	0.632925	+	0.774213i	$0.281854\pi$
$601$	−8.19285	+	25.2150i	−0.334193	+	1.02854i	−0.967118	+	0.254328i	$0.918146\pi$
$602$	−4.74953	+	1.54322i	−0.193576	+	0.0628968i
$603$	−20.5977	−	28.3503i	−0.838803	−	1.15451i
$604$	11.4782			0.467041
$605$		0			0
$606$	3.07433			0.124886
$607$	−26.3287	−	36.2383i	−1.06865	−	1.47087i	−0.871437	−	0.490508i	$-0.836811\pi$
$607$	−26.3287	−	36.2383i	−1.06865	−	1.47087i	−0.197212	−	0.980361i	$-0.563189\pi$
$608$	5.82957	−	1.89414i	0.236420	−	0.0768176i
$609$	−0.210437	+	0.647660i	−0.00852736	+	0.0262445i
$610$		0			0
$611$	−9.47248	−	6.88216i	−0.383216	−	0.278422i
$612$	10.3696	+	3.36930i	0.419168	+	0.136196i
$613$	1.09063	−	0.354366i	0.0440500	−	0.0143127i	−0.286909	−	0.957958i	$-0.592628\pi$
$613$	1.09063	−	0.354366i	0.0440500	−	0.0143127i	0.330959	+	0.943645i	$0.392628\pi$
$614$	2.36325	−	1.71700i	0.0953731	−	0.0692926i
$615$		0			0
$616$	0.832382	−	1.16597i	0.0335376	−	0.0469784i
$617$		−	23.3790i		−	0.941202i	−0.882346	−	0.470601i	$-0.844037\pi$
$617$		−	23.3790i		−	0.941202i	0.882346	−	0.470601i	$-0.155963\pi$
$618$	3.93317	+	5.41354i	0.158215	+	0.217765i
$619$	7.30246	+	22.4747i	0.293511	+	0.903334i	0.983718	+	0.179721i	$0.0575196\pi$
$619$	7.30246	+	22.4747i	0.293511	+	0.903334i	−0.690207	+	0.723612i	$0.742480\pi$
$620$		0			0
$621$	−1.56151	−	1.13451i	−0.0626614	−	0.0455262i
$622$	2.24989	−	3.09671i	0.0902124	−	0.124167i
$623$	0.551534	+	0.179204i	0.0220967	+	0.00717966i
$624$	−3.03089	−	9.32812i	−0.121333	−	0.373424i
$625$		0			0
$626$	27.2880			1.09065
$627$	50.5614	−	0.421068i	2.01923	−	0.0168158i
$628$			7.55754i			0.301579i
$629$	−20.3250	+	14.7669i	−0.810409	+	0.588797i
$630$		0			0
$631$	−4.16946	+	12.8323i	−0.165983	+	0.510844i	−0.999107	−	0.0422418i	$-0.986550\pi$
$631$	−4.16946	+	12.8323i	−0.165983	+	0.510844i	0.833124	+	0.553086i	$0.186550\pi$
$632$	4.37695	−	6.02435i	0.174106	−	0.239636i
$633$	−3.87254	+	5.33010i	−0.153920	+	0.211852i
$634$	−8.88582	+	27.3478i	−0.352901	+	1.08612i
$635$		0			0
$636$	10.5530	−	7.66721i	0.418454	−	0.304025i
$637$		−	26.8686i		−	1.06457i
$638$	0.632981	−	2.00477i	0.0250600	−	0.0793696i
$639$	32.6865			1.29306
$640$		0			0
$641$	−0.719738	−	2.21513i	−0.0284279	−	0.0874922i	0.935836	−	0.352436i	$-0.114647\pi$
$641$	−0.719738	−	2.21513i	−0.0284279	−	0.0874922i	−0.964264	+	0.264944i	$0.914647\pi$
$642$	0.769828	+	0.250132i	0.0303827	+	0.00987193i
$643$	−16.7065	+	22.9946i	−0.658841	+	0.906817i	−0.999442	−	0.0333908i	$-0.989369\pi$
$643$	−16.7065	+	22.9946i	−0.658841	+	0.906817i	0.340601	+	0.940208i	$0.389369\pi$
$644$	−1.45730	−	1.05879i	−0.0574257	−	0.0417222i
$645$		0			0
$646$	6.48205	+	19.9497i	0.255033	+	0.784910i
$647$	−14.6619	−	20.1803i	−0.576418	−	0.793371i	0.416879	−	0.908962i	$-0.363124\pi$
$647$	−14.6619	−	20.1803i	−0.576418	−	0.793371i	−0.993297	+	0.115591i	$0.963124\pi$
$648$		−	8.40711i		−	0.330262i
$649$	21.4198	+	28.9714i	0.840801	+	1.13723i
$650$		0			0
$651$	8.96129	−	6.51076i	0.351221	−	0.255177i
$652$	2.99577	−	0.973385i	0.117323	−	0.0381207i
$653$	−37.8624	−	12.3022i	−1.48167	−	0.481424i	−0.547058	−	0.837095i	$-0.684252\pi$
$653$	−37.8624	−	12.3022i	−1.48167	−	0.481424i	−0.934611	+	0.355671i	$0.884252\pi$
$654$	20.2197	+	14.6905i	0.790654	+	0.574444i
$655$		0			0
$656$	0.821192	−	2.52737i	0.0320622	−	0.0986772i
$657$	33.7500	−	10.9661i	1.31671	−	0.427826i
$658$	0.753832	+	1.03756i	0.0293874	+	0.0404483i
$659$	28.4602			1.10865			0.554327	−	0.832299i	$-0.312976\pi$
$659$	28.4602			1.10865			0.554327	+	0.832299i	$0.312976\pi$
$660$		0			0
$661$	22.1958			0.863316			0.431658	−	0.902037i	$-0.357929\pi$
$661$	22.1958			0.863316			0.431658	+	0.902037i	$0.357929\pi$
$662$	−8.99085	−	12.3748i	−0.349439	−	0.480962i
$663$	31.9223	−	10.3722i	1.23976	−	0.402822i
$664$	2.43660	−	7.49907i	0.0945583	−	0.291020i
$665$		0			0
$666$	−18.9229	−	13.7483i	−0.733247	−	0.532735i
$667$	−2.51404	−	0.816860i	−0.0973439	−	0.0316289i
$668$	−5.18494	+	1.68469i	−0.200611	+	0.0651825i
$669$	−12.6431	+	9.18573i	−0.488809	+	0.355141i
$670$		0			0
$671$	−33.0949	+	11.0587i	−1.27761	+	0.426917i
$672$			1.07433i			0.0414432i
$673$	−10.6541	−	14.6642i	−0.410687	−	0.565262i	0.552699	−	0.833381i	$-0.313598\pi$
$673$	−10.6541	−	14.6642i	−0.410687	−	0.565262i	−0.963386	+	0.268119i	$0.913598\pi$
$674$	−6.00704	−	18.4878i	−0.231382	−	0.712122i
$675$		0			0
$676$	−2.06383	−	1.49946i	−0.0793781	−	0.0576716i
$677$	−10.3474	+	14.2420i	−0.397684	+	0.547365i	−0.960161	−	0.279448i	$-0.909849\pi$
$677$	−10.3474	+	14.2420i	−0.397684	+	0.547365i	0.562477	+	0.826813i	$0.309849\pi$
$678$	−20.0980	−	6.53025i	−0.771861	−	0.250793i
$679$	−0.234035	−	0.720285i	−0.00898143	−	0.0276420i
$680$		0			0
$681$	−35.1559			−1.34718
$682$	−27.4966	+	20.3294i	−1.05290	+	0.778454i
$683$		−	37.4782i		−	1.43406i	−0.697041	−	0.717031i	$-0.745500\pi$
$683$		−	37.4782i		−	1.43406i	0.697041	−	0.717031i	$-0.254500\pi$
$684$	−15.7996	+	11.4791i	−0.604112	+	0.438913i
$685$		0			0
$686$	−1.84380	+	5.67462i	−0.0703965	+	0.216658i
$687$	−5.68247	+	7.82124i	−0.216800	+	0.298399i
$688$	−6.79569	+	9.35346i	−0.259083	+	0.356597i
$689$	6.39105	−	19.6696i	0.243480	−	0.749354i
$690$		0			0
$691$	−9.75191	+	7.08518i	−0.370980	+	0.269533i	−0.757617	−	0.652699i	$-0.773637\pi$
$691$	−9.75191	+	7.08518i	−0.370980	+	0.269533i	0.386637	+	0.922232i	$0.373637\pi$
$692$		−	14.9633i		−	0.568819i
$693$	−1.37428	+	4.35260i	−0.0522045	+	0.165341i
$694$	9.22874			0.350318
$695$		0			0
$696$	0.487185	+	1.49940i	0.0184667	+	0.0568346i
$697$	8.64905	+	2.81025i	0.327606	+	0.106446i
$698$	8.98509	−	12.3669i	0.340091	−	0.468095i
$699$	51.4717	+	37.3964i	1.94684	+	1.41446i
$700$		0			0
$701$	−8.60170	−	26.4733i	−0.324882	−	0.999884i	−0.971494	−	0.237065i	$-0.923815\pi$
$701$	−8.60170	−	26.4733i	−0.324882	−	0.999884i	0.646612	−	0.762819i	$-0.276185\pi$
$702$	1.07281	+	1.47660i	0.0404908	+	0.0557308i
$703$		−	44.9989i		−	1.69717i
$704$	−0.0276194	−	3.31651i	−0.00104095	−	0.124996i
$705$		0			0
$706$	4.93962	−	3.58885i	0.185905	−	0.135068i
$707$	−0.507783	+	0.164989i	−0.0190971	+	0.00620504i
$708$	−25.6969	−	8.34942i	−0.965748	−	0.313790i
$709$	22.1770	+	16.1125i	0.832874	+	0.605119i	0.920371	−	0.391046i	$-0.127887\pi$
$709$	22.1770	+	16.1125i	0.832874	+	0.605119i	−0.0874968	+	0.996165i	$0.527887\pi$
$710$		0			0
$711$	−7.33150	+	22.5640i	−0.274953	+	0.846217i
$712$	1.27686	−	0.414876i	0.0478523	−	0.0155481i
$713$	25.2729	+	34.7852i	0.946479	+	1.30272i
$714$	−3.67652			−0.137590
$715$		0			0
$716$	12.1459			0.453914
$717$	17.6584	+	24.3046i	0.659464	+	0.907674i
$718$	25.6231	−	8.32545i	0.956245	−	0.310703i
$719$	12.0166	−	36.9832i	0.448142	−	1.37924i	−0.430858	−	0.902420i	$-0.641789\pi$
$719$	12.0166	−	36.9832i	0.448142	−	1.37924i	0.879001	−	0.476821i	$-0.158211\pi$
$720$		0			0
$721$	−0.940163	−	0.683068i	−0.0350135	−	0.0254388i
$722$	−17.6626	−	5.73894i	−0.657336	−	0.213581i
$723$	55.7295	−	18.1076i	2.07260	−	0.673429i
$724$	−11.5274	+	8.37513i	−0.428412	+	0.311259i
$725$		0			0
$726$	8.01988	−	26.1572i	0.297646	−	0.970784i
$727$		−	32.3326i		−	1.19915i	−0.800319	−	0.599575i	$-0.795336\pi$
$727$		−	32.3326i		−	1.19915i	0.800319	−	0.599575i	$-0.204664\pi$
$728$	1.00122	+	1.37806i	0.0371075	+	0.0510741i
$729$	9.34444	+	28.7592i	0.346090	+	1.06516i
$730$		0			0
$731$	−32.0090	−	23.2559i	−1.18390	−	0.860151i
$732$	15.3807	−	21.1698i	0.568488	−	0.782457i
$733$	10.4549	+	3.39701i	0.386162	+	0.125472i	0.495663	−	0.868515i	$-0.334925\pi$
$733$	10.4549	+	3.39701i	0.386162	+	0.125472i	−0.109501	+	0.993987i	$0.534925\pi$
$734$	7.72900	+	23.7874i	0.285283	+	0.878010i
$735$		0			0
$736$	−4.17025			−0.153717
$737$	−29.6894	−	21.1951i	−1.09362	−	0.780731i
$738$			8.46681i			0.311668i
$739$	15.0306	−	10.9204i	0.552910	−	0.401713i	−0.275947	−	0.961173i	$-0.588991\pi$
$739$	15.0306	−	10.9204i	0.552910	−	0.401713i	0.828857	+	0.559460i	$0.188991\pi$
$740$		0			0
$741$	−18.5780	+	57.1773i	−0.682481	+	2.10046i
$742$	−1.33155	+	1.83273i	−0.0488829	+	0.0672815i
$743$	11.9833	−	16.4936i	0.439624	−	0.605091i	−0.530504	−	0.847682i	$-0.677997\pi$
$743$	11.9833	−	16.4936i	0.439624	−	0.605091i	0.970129	+	0.242591i	$0.0779974\pi$
$744$	7.92439	−	24.3888i	0.290522	−	0.894135i
$745$		0			0
$746$	−22.2930	+	16.1968i	−0.816205	+	0.593007i
$747$			25.1223i			0.919176i
$748$	11.3496	−	0.0945179i	0.414983	−	0.00345592i
$749$	−0.140575			−0.00513651
$750$		0			0
$751$	12.9995	+	40.0084i	0.474359	+	1.45993i	0.846820	+	0.531879i	$0.178514\pi$
$751$	12.9995	+	40.0084i	0.474359	+	1.45993i	−0.372462	+	0.928048i	$0.621486\pi$
$752$	2.82379	+	0.917506i	0.102973	+	0.0334580i
$753$	5.01074	−	6.89669i	0.182601	−	0.251329i
$754$	2.02228	+	1.46927i	0.0736470	+	0.0535077i
$755$		0			0
$756$	−0.0617786	−	0.190135i	−0.00224687	−	0.00691515i
$757$	0.925095	+	1.27328i	0.0336232	+	0.0462783i	0.825498	−	0.564406i	$-0.190895\pi$
$757$	0.925095	+	1.27328i	0.0336232	+	0.0462783i	−0.791874	+	0.610684i	$0.790895\pi$
$758$		−	23.4887i		−	0.853147i
$759$	−32.8043	−	10.3576i	−1.19072	−	0.375955i
$760$		0			0
$761$	11.7245	−	8.51838i	0.425015	−	0.308791i	−0.354638	−	0.935004i	$-0.615396\pi$
$761$	11.7245	−	8.51838i	0.425015	−	0.308791i	0.779652	+	0.626213i	$0.215396\pi$
$762$	−20.4355	+	6.63989i	−0.740299	+	0.240538i
$763$	−4.12806	−	1.34129i	−0.149446	−	0.0485578i
$764$	−0.893500	−	0.649166i	−0.0323257	−	0.0234860i
$765$		0			0
$766$	5.78565	−	17.8064i	0.209044	−	0.643372i
$767$	−40.7429	+	13.2382i	−1.47114	+	0.478003i
$768$	1.46193	+	2.01217i	0.0527529	+	0.0726081i
$769$	−50.5632			−1.82335			−0.911677	−	0.410907i	$-0.865212\pi$
$769$	−50.5632			−1.82335			−0.911677	+	0.410907i	$0.865212\pi$
$770$		0			0
$771$	4.05360			0.145987
$772$	6.43288	+	8.85410i	0.231524	+	0.318666i
$773$	−33.5665	+	10.9064i	−1.20730	+	0.392276i	−0.842443	−	0.538786i	$-0.818883\pi$
$773$	−33.5665	+	10.9064i	−1.20730	+	0.392276i	−0.364860	+	0.931063i	$0.618883\pi$
$774$	11.3830	−	35.0331i	0.409152	−	1.25924i
$775$		0			0
$776$	−1.41849	−	1.03059i	−0.0509208	−	0.0369961i
$777$	7.50095	+	2.43720i	0.269095	+	0.0874342i
$778$	−7.05435	+	2.29210i	−0.252911	+	0.0821757i
$779$	−13.1780	+	9.57438i	−0.472151	+	0.343038i
$780$		0			0
$781$	32.2717	−	10.7836i	1.15477	−	0.385869i
$782$		−	14.2712i		−	0.510338i
$783$	−0.172444	−	0.237349i	−0.00616265	−	0.00848216i
$784$	2.10546	+	6.47995i	0.0751951	+	0.231427i
$785$		0			0
$786$	32.8684	+	23.8803i	1.17238	+	0.851781i
$787$	0.221208	−	0.304466i	0.00788520	−	0.0108530i	−0.805056	−	0.593199i	$-0.797865\pi$
$787$	0.221208	−	0.304466i	0.00788520	−	0.0108530i	0.812941	+	0.582346i	$0.197865\pi$
$788$	15.2713	+	4.96195i	0.544018	+	0.176762i
$789$	1.26946	+	3.90698i	0.0451938	+	0.139092i
$790$		0			0
$791$	3.67002			0.130491
$792$	3.34898	+	10.0223i	0.119001	+	0.356128i
$793$		−	41.4887i		−	1.47331i
$794$	18.3160	−	13.3074i	0.650011	−	0.472260i
$795$		0			0
$796$	8.39047	−	25.8232i	0.297393	−	0.915280i
$797$	−12.5086	+	17.2167i	−0.443079	+	0.609845i	−0.970893	−	0.239514i	$-0.923012\pi$
$797$	−12.5086	+	17.2167i	−0.443079	+	0.609845i	0.527814	+	0.849360i	$0.323012\pi$
$798$	3.87067	−	5.32752i	0.137020	−	0.188592i
$799$	−3.13985	+	9.66346i	−0.111080	+	0.341869i
$800$		0			0
$801$	−3.46060	+	2.51427i	−0.122274	+	0.0888375i
$802$		−	26.9832i		−	0.952809i
$803$	29.7039	−	21.9614i	1.04823	−	0.775001i
$804$	27.3558			0.964766
$805$		0			0
$806$	−12.5643	−	38.6689i	−0.442558	−	1.36205i
$807$	52.4319	+	17.0361i	1.84569	+	0.599701i
$808$	−0.726543	+	1.00000i	−0.0255597	+	0.0351799i
$809$	−10.5822	−	7.68843i	−0.372051	−	0.270311i	0.386010	−	0.922495i	$-0.373853\pi$
$809$	−10.5822	−	7.68843i	−0.372051	−	0.270311i	−0.758061	+	0.652184i	$0.773853\pi$
$810$		0			0
$811$	12.6338	+	38.8829i	0.443634	+	1.36536i	0.883975	+	0.467533i	$0.154857\pi$
$811$	12.6338	+	38.8829i	0.443634	+	1.36536i	−0.440342	+	0.897830i	$0.645143\pi$
$812$	−0.160935	−	0.221508i	−0.00564772	−	0.00777342i
$813$			18.2722i			0.640835i
$814$	−23.2185	−	7.33094i	−0.813807	−	0.256949i
$815$		0			0
$816$	−6.88598	+	5.00295i	−0.241057	+	0.175138i
$817$	67.3986	−	21.8991i	2.35798	−	0.766154i
$818$	−8.88560	−	2.88711i	−0.310678	−	0.100945i
$819$	−4.39061	−	3.18996i	−0.153420	−	0.111466i
$820$		0			0
$821$	8.77898	−	27.0189i	0.306389	−	0.942967i	−0.672767	−	0.739855i	$-0.734894\pi$
$821$	8.77898	−	27.0189i	0.306389	−	0.942967i	0.979155	−	0.203112i	$-0.0651057\pi$
$822$	40.3529	−	13.1115i	1.40747	−	0.457315i
$823$	−6.98007	−	9.60724i	−0.243310	−	0.334887i	0.669844	−	0.742502i	$-0.266361\pi$
$823$	−6.98007	−	9.60724i	−0.243310	−	0.334887i	−0.913154	+	0.407614i	$0.866361\pi$
$824$	−2.69039			−0.0937243
$825$		0			0
$826$	4.69240			0.163270
$827$	33.0728	+	45.5209i	1.15006	+	1.58292i	0.742668	+	0.669659i	$0.233560\pi$
$827$	33.0728	+	45.5209i	1.15006	+	1.58292i	0.407387	+	0.913256i	$0.366440\pi$
$828$	12.6365	−	4.10584i	0.439148	−	0.142688i
$829$	−4.24409	+	13.0620i	−0.147403	+	0.453661i	−0.997312	−	0.0732690i	$-0.976657\pi$
$829$	−4.24409	+	13.0620i	−0.147403	+	0.453661i	0.849909	+	0.526930i	$0.176657\pi$
$830$		0			0
$831$	31.2225	+	22.6845i	1.08310	+	0.786916i
$832$	3.75047	+	1.21860i	0.130024	+	0.0422474i
$833$	−22.1754	+	7.20522i	−0.768332	+	0.249646i
$834$	−11.3070	+	8.21505i	−0.391531	+	0.284464i
$835$		0			0
$836$	−11.8120	+	16.5458i	−0.408526	+	0.572250i
$837$			4.77202i			0.164945i
$838$	−9.73415	−	13.3979i	−0.336261	−	0.462823i
$839$	9.95199	+	30.6291i	0.343581	+	1.05743i	0.962339	+	0.271852i	$0.0876360\pi$
$839$	9.95199	+	30.6291i	0.343581	+	1.05743i	−0.618758	+	0.785581i	$0.712364\pi$
$840$		0			0
$841$	23.1364	+	16.8096i	0.797808	+	0.579641i
$842$	−1.10531	+	1.52132i	−0.0380914	+	0.0524283i
$843$	54.1917	+	17.6079i	1.86646	+	0.606450i
$844$	−0.818562	−	2.51928i	−0.0281761	−	0.0867170i
$845$		0			0
$846$	−9.45985			−0.325236
$847$	0.0791325	+	4.75075i	0.00271902	+	0.163238i
$848$			5.24458i			0.180100i
$849$	−5.63834	+	4.09649i	−0.193507	+	0.140591i
$850$		0			0
$851$	−9.46055	+	29.1166i	−0.324303	+	0.998103i
$852$	−14.9981	+	20.6432i	−0.513828	+	0.707224i
$853$	−18.6435	+	25.6606i	−0.638343	+	0.878604i	−0.998526	−	0.0542781i	$-0.982714\pi$
$853$	−18.6435	+	25.6606i	−0.638343	+	0.878604i	0.360183	+	0.932882i	$0.382714\pi$
$854$	−1.40431	+	4.32201i	−0.0480544	+	0.147896i
$855$		0			0
$856$	−0.263292	+	0.191292i	−0.00899912	+	0.00653824i
$857$			25.5670i			0.873353i	0.899619	+	0.436677i	$0.143845\pi$
$857$			25.5670i			0.873353i	−0.899619	+	0.436677i	$0.856155\pi$
$858$	26.4756	+	18.9008i	0.903863	+	0.645264i
$859$	−35.0484			−1.19584			−0.597919	−	0.801557i	$-0.704005\pi$
$859$	−35.0484			−1.19584			−0.597919	+	0.801557i	$0.704005\pi$
$860$		0			0
$861$	−0.882230	−	2.71523i	−0.0300663	−	0.0925347i
$862$	−22.4503	−	7.29456i	−0.764662	−	0.248454i
$863$	−12.7418	+	17.5376i	−0.433736	+	0.596986i	−0.968806	−	0.247822i	$-0.920285\pi$
$863$	−12.7418	+	17.5376i	−0.433736	+	0.596986i	0.535070	+	0.844808i	$0.320285\pi$
$864$	−0.374442	−	0.272048i	−0.0127388	−	0.00925525i
$865$		0			0
$866$	4.90556	+	15.0977i	0.166698	+	0.513042i
$867$	7.73193	+	10.6421i	0.262590	+	0.361424i
$868$			4.45353i			0.151163i
$869$	0.205668	+	24.6964i	0.00697681	+	0.837768i
$870$		0			0
$871$	35.0897	−	25.4941i	1.18897	−	0.863836i
$872$	−9.55688	+	3.10522i	−0.323637	+	0.105156i
$873$	5.31291	+	1.72627i	0.179815	+	0.0584254i
$874$	20.6799	+	15.0249i	0.699510	+	0.508223i
$875$		0			0
$876$	−8.56053	+	26.3466i	−0.289233	+	0.890169i
$877$	−24.6603	+	8.01263i	−0.832721	+	0.270567i	−0.694191	−	0.719791i	$-0.744238\pi$
$877$	−24.6603	+	8.01263i	−0.832721	+	0.270567i	−0.138530	+	0.990358i	$0.544238\pi$
$878$	6.82315	+	9.39127i	0.230270	+	0.316940i
$879$	52.9180			1.78488
$880$		0			0
$881$	−47.5332			−1.60143			−0.800717	−	0.599042i	$-0.795548\pi$
$881$	−47.5332			−1.60143			−0.800717	+	0.599042i	$0.795548\pi$
$882$	−12.7597	−	17.5623i	−0.429643	−	0.591353i
$883$	20.7999	−	6.75830i	0.699973	−	0.227435i	0.0626542	−	0.998035i	$-0.480043\pi$
$883$	20.7999	−	6.75830i	0.699973	−	0.227435i	0.637319	+	0.770600i	$0.280043\pi$
$884$	−4.17025	+	12.8347i	−0.140261	+	0.431678i
$885$		0			0
$886$	7.72038	+	5.60918i	0.259371	+	0.188444i
$887$	6.59480	+	2.14278i	0.221432	+	0.0719475i	0.417632	−	0.908616i	$-0.362860\pi$
$887$	6.59480	+	2.14278i	0.221432	+	0.0719475i	−0.196200	+	0.980564i	$0.562860\pi$
$888$	17.3655	−	5.64238i	0.582747	−	0.189346i
$889$	3.01896	−	2.19340i	0.101253	−	0.0735644i
$890$		0			0
$891$	16.5766	+	22.4207i	0.555338	+	0.751123i
$892$		−	6.28329i		−	0.210380i
$893$	−10.6973	−	14.7236i	−0.357972	−	0.492706i
$894$	7.60900	+	23.4181i	0.254483	+	0.783218i
$895$		0			0
$896$	−0.349452	−	0.253891i	−0.0116744	−	0.00848192i
$897$	24.0419	−	33.0908i	0.802735	−	1.10487i
$898$	18.8768	+	6.13346i	0.629928	+	0.204676i
$899$	2.01958	+	6.21563i	0.0673568	+	0.207303i
$900$		0			0
$901$	−17.9478			−0.597927
$902$	2.79329	+	8.35936i	0.0930065	+	0.278336i
$903$			12.4209i			0.413341i
$904$	6.87380	−	4.99411i	0.228619	−	0.166102i
$905$		0			0
$906$	8.82193	−	27.1511i	0.293089	−	0.902035i
$907$	−24.8813	+	34.2462i	−0.826170	+	1.13713i	0.162454	+	0.986716i	$0.448059\pi$
$907$	−24.8813	+	34.2462i	−0.826170	+	1.13713i	−0.988624	+	0.150409i	$0.951941\pi$
$908$	8.30824	−	11.4353i	0.275719	−	0.379494i
$909$	1.21698	−	3.74547i	0.0403646	−	0.124229i
$910$		0			0
$911$	7.64031	−	5.55101i	0.253135	−	0.183913i	−0.453980	−	0.891012i	$-0.649996\pi$
$911$	7.64031	−	5.55101i	0.253135	−	0.183913i	0.707115	+	0.707099i	$0.249996\pi$
$912$		−	15.2454i		−	0.504825i
$913$	8.28812	+	24.8034i	0.274297	+	0.820874i
$914$	4.20591			0.139119
$915$		0			0
$916$	−1.20114	−	3.69672i	−0.0396867	−	0.122143i
$917$	−6.71040	−	2.18034i	−0.221597	−	0.0720012i
$918$	0.930990	−	1.28140i	0.0307272	−	0.0422924i
$919$	−14.1560	−	10.2849i	−0.466963	−	0.339269i	0.329294	−	0.944228i	$-0.393189\pi$
$919$	−14.1560	−	10.2849i	−0.466963	−	0.339269i	−0.796257	+	0.604959i	$0.793189\pi$
$920$		0			0
$921$	−2.24514	−	6.90982i	−0.0739798	−	0.227686i
$922$	5.55345	+	7.64366i	0.182893	+	0.251731i
$923$			40.4567i			1.33165i
$924$	−2.11830	−	2.86511i	−0.0696869	−	0.0942551i
$925$		0			0
$926$	−21.5100	+	15.6280i	−0.706864	+	0.513567i
$927$	8.15230	−	2.64884i	0.267757	−	0.0869994i
$928$	−0.602850	−	0.195878i	−0.0197895	−	0.00643001i
$929$	15.9892	+	11.6168i	0.524587	+	0.381135i	0.818329	−	0.574750i	$-0.194901\pi$
$929$	15.9892	+	11.6168i	0.524587	+	0.381135i	−0.293742	+	0.955885i	$0.594901\pi$
$930$		0			0
$931$	12.9056	−	39.7193i	0.422963	−	1.30175i
$932$	−24.3281	+	7.90469i	−0.796895	+	0.258927i
$933$	−5.59590	−	7.70209i	−0.183201	−	0.252155i
$934$	18.2290			0.596472
$935$		0			0
$936$	−12.5643			−0.410676
$937$	−16.7584	−	23.0660i	−0.547474	−	0.753533i	0.442193	−	0.896920i	$-0.354201\pi$
$937$	−16.7584	−	23.0660i	−0.547474	−	0.753533i	−0.989667	+	0.143387i	$0.954201\pi$
$938$	−4.51833	+	1.46809i	−0.147529	+	0.0479350i
$939$	20.9730	−	64.5484i	0.684429	−	2.10646i
$940$		0			0
$941$	24.5781	+	17.8571i	0.801225	+	0.582124i	0.911273	−	0.411802i	$-0.135101\pi$
$941$	24.5781	+	17.8571i	0.801225	+	0.582124i	−0.110048	+	0.993926i	$0.535101\pi$
$942$	17.8770	+	5.80859i	0.582464	+	0.189254i
$943$	10.5398	−	3.42457i	0.343222	−	0.111519i
$944$	8.78868	−	6.38535i	0.286047	−	0.207825i
$945$		0			0
$946$	−0.319322	−	38.3439i	−0.0103821	−	1.24667i
$947$			2.37805i			0.0772763i	0.999253	+	0.0386382i	$0.0123020\pi$
$947$			2.37805i			0.0772763i	−0.999253	+	0.0386382i	$0.987698\pi$
$948$	−10.8863	−	14.9837i	−0.353570	−	0.486647i
$949$	13.5729	+	41.7731i	0.440595	+	1.35601i
$950$		0			0
$951$	57.8604	+	42.0380i	1.87625	+	1.36318i
$952$	0.868856	−	1.19588i	0.0281598	−	0.0387586i
$953$	42.2300	+	13.7214i	1.36796	+	0.444479i	0.898694	−	0.438576i	$-0.144517\pi$
$953$	42.2300	+	13.7214i	1.36796	+	0.444479i	0.469270	+	0.883055i	$0.344517\pi$
$954$	−5.16358	−	15.8919i	−0.167177	−	0.514518i
$955$		0			0
$956$	−12.0788			−0.390656
$957$	−4.25569	−	3.03812i	−0.137567	−	0.0982084i
$958$		−	13.0061i		−	0.420206i
$959$	−5.96139	+	4.33121i	−0.192503	+	0.139862i
$960$		0			0
$961$	23.2703	−	71.6186i	0.750655	−	2.31028i
$962$	17.0165	−	23.4212i	0.548634	−	0.755130i
$963$	0.609475	−	0.838870i	0.0196400	−	0.0270322i
$964$	−7.28036	+	22.4066i	−0.234485	+	0.721670i
$965$		0			0
$966$	−3.62457	+	2.63341i	−0.116619	+	0.0847285i
$967$			11.4834i			0.369283i	0.982806	+	0.184641i	$0.0591124\pi$
$967$			11.4834i			0.369283i	−0.982806	+	0.184641i	$0.940888\pi$
$968$	6.61295	+	8.79027i	0.212548	+	0.282530i
$969$	52.1720			1.67601
$970$		0			0
$971$	−1.38789	−	4.27147i	−0.0445394	−	0.137078i	0.926314	−	0.376753i	$-0.122959\pi$
$971$	−1.38789	−	4.27147i	−0.0445394	−	0.137078i	−0.970853	+	0.239674i	$0.922959\pi$
$972$	−21.2072	−	6.89063i	−0.680220	−	0.221017i
$973$	1.42670	−	1.96368i	0.0457378	−	0.0629527i
$974$	6.23479	+	4.52984i	0.199775	+	0.145145i
$975$		0			0
$976$	3.25112	+	10.0059i	0.104066	+	0.320281i
$977$	−4.17201	−	5.74228i	−0.133474	−	0.183712i	0.737048	−	0.675840i	$-0.236219\pi$
$977$	−4.17201	−	5.74228i	−0.133474	−	0.183712i	−0.870523	+	0.492128i	$0.836219\pi$
$978$		−	7.83448i		−	0.250519i
$979$	−2.58720	+	3.62406i	−0.0826872	+	0.115825i
$980$		0			0
$981$	25.9015	−	18.8186i	0.826972	−	0.600830i
$982$	12.8254	−	4.16722i	0.409275	−	0.132981i
$983$	−52.7437	−	17.1375i	−1.68226	−	0.546600i	−0.696914	−	0.717155i	$-0.745444\pi$
$983$	−52.7437	−	17.1375i	−1.68226	−	0.546600i	−0.985348	+	0.170555i	$0.945444\pi$
$984$	−5.34722	−	3.88498i	−0.170463	−	0.123849i
$985$		0			0
$986$	0.670325	−	2.06305i	0.0213475	−	0.0657008i
$987$	3.03368	−	0.985703i	0.0965632	−	0.0313753i
$988$	−14.2078	−	19.5554i	−0.452012	−	0.622141i
$989$	−48.2144			−1.53313
$990$		0			0
$991$	1.24021			0.0393967			0.0196983	−	0.999806i	$-0.493729\pi$
$991$	1.24021			0.0393967			0.0196983	+	0.999806i	$0.493729\pi$
$992$	6.06030	+	8.34129i	0.192415	+	0.264836i
$993$	−36.1823	+	11.7563i	−1.14821	+	0.373076i
$994$	1.36938	−	4.21450i	0.0434340	−	0.133676i
$995$		0			0
$996$	−15.8660	−	11.5273i	−0.502733	−	0.365257i
$997$	−31.6781	−	10.2928i	−1.00325	−	0.325977i	−0.239089	−	0.970998i	$-0.576849\pi$
$997$	−31.6781	−	10.2928i	−1.00325	−	0.325977i	−0.764165	+	0.645021i	$0.776849\pi$
$998$	−13.1084	+	4.25919i	−0.414940	+	0.134822i
$999$	−2.74888	+	1.99718i	−0.0869708	+	0.0631880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.ba.f.399.4		16
5.2	odd	4		550.2.h.l.201.1		8
5.3	odd	4		110.2.g.c.91.2	yes	8
5.4	even	2	inner	550.2.ba.f.399.1		16
11.4	even	5	inner	550.2.ba.f.499.1		16
15.8	even	4		990.2.n.j.91.2		8
20.3	even	4		880.2.bo.g.641.1		8
55.2	even	20		6050.2.a.cy.1.2		4
55.4	even	10	inner	550.2.ba.f.499.4		16
55.13	even	20		1210.2.a.v.1.3		4
55.37	odd	20		550.2.h.l.301.1		8
55.42	odd	20		6050.2.a.dh.1.2		4
55.48	odd	20		110.2.g.c.81.2	✓	8
55.53	odd	20		1210.2.a.u.1.3		4
165.158	even	20		990.2.n.j.631.2		8
220.103	even	20		880.2.bo.g.81.1		8
220.123	odd	20		9680.2.a.ci.1.2		4
220.163	even	20		9680.2.a.cj.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.c.81.2	✓	8	55.48	odd	20
110.2.g.c.91.2	yes	8	5.3	odd	4
550.2.h.l.201.1		8	5.2	odd	4
550.2.h.l.301.1		8	55.37	odd	20
550.2.ba.f.399.1		16	5.4	even	2	inner
550.2.ba.f.399.4		16	1.1	even	1	trivial
550.2.ba.f.499.1		16	11.4	even	5	inner
550.2.ba.f.499.4		16	55.4	even	10	inner
880.2.bo.g.81.1		8	220.103	even	20
880.2.bo.g.641.1		8	20.3	even	4
990.2.n.j.91.2		8	15.8	even	4
990.2.n.j.631.2		8	165.158	even	20
1210.2.a.u.1.3		4	55.53	odd	20
1210.2.a.v.1.3		4	55.13	even	20
6050.2.a.cy.1.2		4	55.2	even	20
6050.2.a.dh.1.2		4	55.42	odd	20
9680.2.a.ci.1.2		4	220.123	odd	20
9680.2.a.cj.1.2		4	220.163	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.ba (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(2.36545 - 0.768582i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.01217 + 1.46193i) q^{6} +(-0.410805 - 0.133479i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(2.57760 - 1.87274i) q^{9} +(1.92705 - 2.69935i) q^{11} +2.48718i q^{12} +(2.31792 + 3.19034i) q^{13} +(-0.133479 - 0.410805i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(2.01149 - 2.76858i) q^{17} +(3.03015 + 0.984555i) q^{18} +(1.89414 + 5.82957i) q^{19} -1.07433 q^{21} +(3.31651 - 0.0276194i) q^{22} -4.17025i q^{23} +(-2.01217 + 1.46193i) q^{24} +(-1.21860 + 3.75047i) q^{26} +(0.272048 - 0.374442i) q^{27} +(0.253891 - 0.349452i) q^{28} +(0.195878 - 0.602850i) q^{29} +(-8.34129 + 6.06030i) q^{31} -1.00000i q^{32} +(2.48368 - 7.86628i) q^{33} +3.42216 q^{34} +(0.984555 + 3.03015i) q^{36} +(-6.98198 - 2.26858i) q^{37} +(-3.60287 + 4.95892i) q^{38} +(7.93497 + 5.76509i) q^{39} +(0.821192 + 2.52737i) q^{41} +(-0.631475 - 0.869151i) q^{42} -11.5615i q^{43} +(1.97174 + 2.66688i) q^{44} +(3.37380 - 2.45121i) q^{46} +(-2.82379 + 0.917506i) q^{47} +(-2.36545 - 0.768582i) q^{48} +(-5.51217 - 4.00483i) q^{49} +(2.63021 - 8.09495i) q^{51} +(-3.75047 + 1.21860i) q^{52} +(-3.08268 - 4.24295i) q^{53} +0.462835 q^{54} +0.431946 q^{56} +(8.96100 + 12.3338i) q^{57} +(0.602850 - 0.195878i) q^{58} +(-3.35698 + 10.3317i) q^{59} +(-8.51153 - 6.18399i) q^{61} +(-9.80577 - 3.18609i) q^{62} +(-1.30886 + 0.425275i) q^{63} +(0.809017 - 0.587785i) q^{64} +(7.82382 - 2.61434i) q^{66} -10.9987i q^{67} +(2.01149 + 2.76858i) q^{68} +(-3.20518 - 9.86453i) q^{69} +(8.29982 + 6.03017i) q^{71} +(-1.87274 + 2.57760i) q^{72} +(10.5929 + 3.44186i) q^{73} +(-2.26858 - 6.98198i) q^{74} -6.12957 q^{76} +(-1.15195 + 0.851685i) q^{77} +9.80816i q^{78} +(-6.02435 + 4.37695i) q^{79} +(-2.59794 + 7.99563i) q^{81} +(-1.56200 + 2.14991i) q^{82} +(-4.63468 + 6.37909i) q^{83} +(0.331986 - 1.02175i) q^{84} +(9.35346 - 6.79569i) q^{86} -1.57656i q^{87} +(-0.998590 + 3.16272i) q^{88} -1.34257 q^{89} +(-0.526370 - 1.62000i) q^{91} +(3.96614 + 1.28868i) q^{92} +(-15.0731 + 20.7463i) q^{93} +(-2.40206 - 1.74520i) q^{94} +(-0.768582 - 2.36545i) q^{96} +(1.03059 + 1.41849i) q^{97} -6.81342i q^{98} +(-0.0879978 - 10.5667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 2 q^{6} + 12 q^{9} + 4 q^{11} - 2 q^{14} - 4 q^{16} + 14 q^{19} + 64 q^{21} + 2 q^{24} - 12 q^{26} + 44 q^{29} - 52 q^{31} - 4 q^{34} - 2 q^{36} + 96 q^{39} - 30 q^{41} - 14 q^{44} - 12 q^{46}+ \cdots - 72 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 2 * q^6 + 12 * q^9 + 4 * q^11 - 2 * q^14 - 4 * q^16 + 14 * q^19 + 64 * q^21 + 2 * q^24 - 12 * q^26 + 44 * q^29 - 52 * q^31 - 4 * q^34 - 2 * q^36 + 96 * q^39 - 30 * q^41 - 14 * q^44 - 12 * q^46 - 54 * q^49 - 10 * q^51 + 48 * q^54 + 12 * q^56 - 78 * q^59 - 40 * q^61 + 4 * q^64 + 72 * q^66 + 20 * q^69 + 4 * q^71 - 16 * q^74 + 16 * q^76 - 28 * q^79 - 62 * q^81 + 36 * q^84 + 34 * q^86 - 64 * q^89 + 106 * q^91 - 18 * q^94 + 8 * q^96 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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