LMFDB - Embedded newform 550.2.h.l.301.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(201,550)] 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([0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.201"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,4,-2,0,-1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.1
Root			$-1.20316 - 0.874145i$ of defining polynomial
Character	$\chi$	$=$	550.301
Dual form			550.2.h.l.201.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.768582 + 2.36545i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.01217 - 1.46193i) q^{6} +(0.133479 + 0.410805i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.57760 - 1.87274i) q^{9} +(1.92705 + 2.69935i) q^{11} -2.48718 q^{12} +(3.19034 + 2.31792i) q^{13} +(0.133479 - 0.410805i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(2.76858 - 2.01149i) q^{17} +(0.984555 + 3.03015i) q^{18} +(-1.89414 + 5.82957i) q^{19} -1.07433 q^{21} +(0.0276194 - 3.31651i) q^{22} -4.17025 q^{23} +(2.01217 + 1.46193i) q^{24} +(-1.21860 - 3.75047i) q^{26} +(0.374442 - 0.272048i) q^{27} +(-0.349452 + 0.253891i) q^{28} +(-0.195878 - 0.602850i) q^{29} +(-8.34129 - 6.06030i) q^{31} +1.00000 q^{32} +(-7.86628 + 2.48368i) q^{33} -3.42216 q^{34} +(0.984555 - 3.03015i) q^{36} +(2.26858 + 6.98198i) q^{37} +(4.95892 - 3.60287i) q^{38} +(-7.93497 + 5.76509i) q^{39} +(0.821192 - 2.52737i) q^{41} +(0.869151 + 0.631475i) q^{42} -11.5615 q^{43} +(-1.97174 + 2.66688i) q^{44} +(3.37380 + 2.45121i) q^{46} +(-0.917506 + 2.82379i) q^{47} +(-0.768582 - 2.36545i) q^{48} +(5.51217 - 4.00483i) q^{49} +(2.63021 + 8.09495i) q^{51} +(-1.21860 + 3.75047i) q^{52} +(-4.24295 - 3.08268i) q^{53} -0.462835 q^{54} +0.431946 q^{56} +(-12.3338 - 8.96100i) q^{57} +(-0.195878 + 0.602850i) q^{58} +(3.35698 + 10.3317i) q^{59} +(-8.51153 + 6.18399i) q^{61} +(3.18609 + 9.80577i) q^{62} +(0.425275 - 1.30886i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(7.82382 + 2.61434i) q^{66} +10.9987 q^{67} +(2.76858 + 2.01149i) q^{68} +(3.20518 - 9.86453i) q^{69} +(8.29982 - 6.03017i) q^{71} +(-2.57760 + 1.87274i) q^{72} +(3.44186 + 10.5929i) q^{73} +(2.26858 - 6.98198i) q^{74} -6.12957 q^{76} +(-0.851685 + 1.15195i) q^{77} +9.80816 q^{78} +(6.02435 + 4.37695i) q^{79} +(-2.59794 - 7.99563i) q^{81} +(-2.14991 + 1.56200i) q^{82} +(6.37909 - 4.63468i) q^{83} +(-0.331986 - 1.02175i) q^{84} +(9.35346 + 6.79569i) q^{86} +1.57656 q^{87} +(3.16272 - 0.998590i) q^{88} +1.34257 q^{89} +(-0.526370 + 1.62000i) q^{91} +(-1.28868 - 3.96614i) q^{92} +(20.7463 - 15.0731i) q^{93} +(2.40206 - 1.74520i) q^{94} +(-0.768582 + 2.36545i) q^{96} +(-1.41849 - 1.03059i) q^{97} -6.81342 q^{98} +(0.0879978 - 10.5667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - q^{6} + q^{7} - 2 q^{8} - 6 q^{9} + 2 q^{11} - 6 q^{12} - q^{13} + q^{14} - 2 q^{16} + 12 q^{17} - q^{18} - 7 q^{19} + 32 q^{21} - 8 q^{22} - 26 q^{23} - q^{24}+ \cdots + 36 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - q^6 + q^7 - 2 * q^8 - 6 * q^9 + 2 * q^11 - 6 * q^12 - q^13 + q^14 - 2 * q^16 + 12 * q^17 - q^18 - 7 * q^19 + 32 * q^21 - 8 * q^22 - 26 * q^23 - q^24 - 6 * q^26 + q^27 - 4 * q^28 - 22 * q^29 - 26 * q^31 + 8 * q^32 - 19 * q^33 + 2 * q^34 - q^36 + 8 * q^37 + 3 * q^38 - 48 * q^39 - 15 * q^41 + 2 * q^42 - 38 * q^43 + 7 * q^44 - 6 * q^46 - 6 * q^47 + 4 * q^48 + 27 * q^49 - 5 * q^51 - 6 * q^52 + 4 * q^53 - 24 * q^54 + 6 * q^56 - 47 * q^57 - 22 * q^58 + 39 * q^59 - 20 * q^61 + 14 * q^62 + 57 * q^63 - 2 * q^64 + 36 * q^66 + 26 * q^67 + 12 * q^68 - 10 * q^69 + 2 * q^71 - 6 * q^72 - 8 * q^73 + 8 * q^74 + 8 * q^76 - 16 * q^77 + 12 * q^78 + 14 * q^79 - 31 * q^81 + 15 * q^82 + 21 * q^83 - 18 * q^84 + 17 * q^86 - 20 * q^87 + 7 * q^88 + 32 * q^89 + 53 * q^91 + 19 * q^92 + 38 * q^93 + 9 * q^94 + 4 * q^96 + 31 * q^97 + 22 * q^98 + 36 * q^99

Character values

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

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

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.768582	+	2.36545i	−0.443741	+	1.36570i	0.440117	+	0.897940i	$0.354937\pi$
$3$	−0.768582	+	2.36545i	−0.443741	+	1.36570i	−0.883858	+	0.467755i	$0.845063\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	2.01217	−	1.46193i	0.821467	−	0.596831i
$7$	0.133479	+	0.410805i	0.0504502	+	0.155270i	0.973108	−	0.230351i	$-0.0739874\pi$
$7$	0.133479	+	0.410805i	0.0504502	+	0.155270i	−0.922657	+	0.385621i	$0.873987\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−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
$12$	−2.48718			−0.717988
$13$	3.19034	+	2.31792i	0.884842	+	0.642875i	0.934528	−	0.355890i	$-0.115822\pi$
$13$	3.19034	+	2.31792i	0.884842	+	0.642875i	−0.0496862	+	0.998765i	$0.515822\pi$
$14$	0.133479	−	0.410805i	0.0356737	−	0.109792i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.76858	−	2.01149i	0.671480	−	0.487859i	−0.199040	−	0.979991i	$-0.563782\pi$
$17$	2.76858	−	2.01149i	0.671480	−	0.487859i	0.870520	+	0.492133i	$0.163782\pi$
$18$	0.984555	+	3.03015i	0.232062	+	0.714213i
$19$	−1.89414	+	5.82957i	−0.434546	+	1.33739i	0.459006	+	0.888433i	$0.348206\pi$
$19$	−1.89414	+	5.82957i	−0.434546	+	1.33739i	−0.893551	+	0.448961i	$0.851794\pi$
$20$		0			0
$21$	−1.07433			−0.234438
$22$	0.0276194	−	3.31651i	0.00588847	−	0.707082i
$23$	−4.17025			−0.869557			−0.434778	−	0.900537i	$-0.643173\pi$
$23$	−4.17025			−0.869557			−0.434778	+	0.900537i	$0.643173\pi$
$24$	2.01217	+	1.46193i	0.410733	+	0.298415i
$25$		0			0
$26$	−1.21860	−	3.75047i	−0.238988	−	0.735528i
$27$	0.374442	−	0.272048i	0.0720613	−	0.0523556i
$28$	−0.349452	+	0.253891i	−0.0660402	+	0.0479810i
$29$	−0.195878	−	0.602850i	−0.0363736	−	0.111947i	0.931221	−	0.364455i	$-0.118745\pi$
$29$	−0.195878	−	0.602850i	−0.0363736	−	0.111947i	−0.967595	+	0.252508i	$0.918745\pi$
$30$		0			0
$31$	−8.34129	−	6.06030i	−1.49814	−	1.08846i	−0.971115	−	0.238612i	$-0.923308\pi$
$31$	−8.34129	−	6.06030i	−1.49814	−	1.08846i	−0.527024	−	0.849850i	$-0.676692\pi$
$32$	1.00000			0.176777
$33$	−7.86628	+	2.48368i	−1.36934	+	0.432353i
$34$	−3.42216			−0.586895
$35$		0			0
$36$	0.984555	−	3.03015i	0.164093	−	0.505025i
$37$	2.26858	+	6.98198i	0.372953	+	1.14783i	0.944850	+	0.327505i	$0.106208\pi$
$37$	2.26858	+	6.98198i	0.372953	+	1.14783i	−0.571897	+	0.820326i	$0.693792\pi$
$38$	4.95892	−	3.60287i	0.804444	−	0.584463i
$39$	−7.93497	+	5.76509i	−1.27061	+	0.923154i
$40$		0			0
$41$	0.821192	−	2.52737i	0.128249	−	0.394709i	−0.866230	−	0.499645i	$-0.833464\pi$
$41$	0.821192	−	2.52737i	0.128249	−	0.394709i	0.994479	+	0.104936i	$0.0334639\pi$
$42$	0.869151	+	0.631475i	0.134113	+	0.0974387i
$43$	−11.5615			−1.76311			−0.881557	−	0.472077i	$-0.843504\pi$
$43$	−11.5615			−1.76311			−0.881557	+	0.472077i	$0.843504\pi$
$44$	−1.97174	+	2.66688i	−0.297251	+	0.402047i
$45$		0			0
$46$	3.37380	+	2.45121i	0.497440	+	0.361411i
$47$	−0.917506	+	2.82379i	−0.133832	+	0.411892i	−0.995407	−	0.0957387i	$-0.969479\pi$
$47$	−0.917506	+	2.82379i	−0.133832	+	0.411892i	0.861575	+	0.507631i	$0.169479\pi$
$48$	−0.768582	−	2.36545i	−0.110935	−	0.341424i
$49$	5.51217	−	4.00483i	0.787454	−	0.572118i
$50$		0			0
$51$	2.63021	+	8.09495i	0.368303	+	1.13352i
$52$	−1.21860	+	3.75047i	−0.168990	+	0.520097i
$53$	−4.24295	−	3.08268i	−0.582814	−	0.423439i	0.256923	−	0.966432i	$-0.417291\pi$
$53$	−4.24295	−	3.08268i	−0.582814	−	0.423439i	−0.839738	+	0.542992i	$0.817291\pi$
$54$	−0.462835			−0.0629839
$55$		0			0
$56$	0.431946			0.0577212
$57$	−12.3338	−	8.96100i	−1.63365	−	1.18691i
$58$	−0.195878	+	0.602850i	−0.0257200	+	0.0791581i
$59$	3.35698	+	10.3317i	0.437041	+	1.34507i	0.890981	+	0.454042i	$0.150018\pi$
$59$	3.35698	+	10.3317i	0.437041	+	1.34507i	−0.453939	+	0.891033i	$0.649982\pi$
$60$		0			0
$61$	−8.51153	+	6.18399i	−1.08979	+	0.791779i	−0.979364	−	0.202105i	$-0.935222\pi$
$61$	−8.51153	+	6.18399i	−1.08979	+	0.791779i	−0.110426	+	0.993884i	$0.535222\pi$
$62$	3.18609	+	9.80577i	0.404634	+	1.24533i
$63$	0.425275	−	1.30886i	0.0535796	−	0.164901i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$		0			0
$66$	7.82382	+	2.61434i	0.963046	+	0.321803i
$67$	10.9987			1.34371			0.671854	−	0.740684i	$-0.265498\pi$
$67$	10.9987			1.34371			0.671854	+	0.740684i	$0.265498\pi$
$68$	2.76858	+	2.01149i	0.335740	+	0.243929i
$69$	3.20518	−	9.86453i	0.385858	−	1.18755i
$70$		0			0
$71$	8.29982	−	6.03017i	0.985007	−	0.715649i	0.0261849	−	0.999657i	$-0.491664\pi$
$71$	8.29982	−	6.03017i	0.985007	−	0.715649i	0.958822	+	0.284008i	$0.0916641\pi$
$72$	−2.57760	+	1.87274i	−0.303773	+	0.220704i
$73$	3.44186	+	10.5929i	0.402839	+	1.23981i	0.922686	+	0.385551i	$0.125989\pi$
$73$	3.44186	+	10.5929i	0.402839	+	1.23981i	−0.519848	+	0.854259i	$0.674011\pi$
$74$	2.26858	−	6.98198i	0.263717	−	0.811639i
$75$		0			0
$76$	−6.12957			−0.703110
$77$	−0.851685	+	1.15195i	−0.0970585	+	0.131277i
$78$	9.80816			1.11056
$79$	6.02435	+	4.37695i	0.677792	+	0.492445i	0.872625	−	0.488392i	$-0.162416\pi$
$79$	6.02435	+	4.37695i	0.677792	+	0.492445i	−0.194832	+	0.980837i	$0.562416\pi$
$80$		0			0
$81$	−2.59794	−	7.99563i	−0.288660	−	0.888404i
$82$	−2.14991	+	1.56200i	−0.237418	+	0.172494i
$83$	6.37909	−	4.63468i	0.700196	−	0.508722i	−0.179800	−	0.983703i	$-0.557545\pi$
$83$	6.37909	−	4.63468i	0.700196	−	0.508722i	0.879996	+	0.474981i	$0.157545\pi$
$84$	−0.331986	−	1.02175i	−0.0362226	−	0.111482i
$85$		0			0
$86$	9.35346	+	6.79569i	1.00861	+	0.732798i
$87$	1.57656			0.169025
$88$	3.16272	−	0.998590i	0.337147	−	0.106450i
$89$	1.34257			0.142312			0.0711559	−	0.997465i	$-0.477331\pi$
$89$	1.34257			0.142312			0.0711559	+	0.997465i	$0.477331\pi$
$90$		0			0
$91$	−0.526370	+	1.62000i	−0.0551786	+	0.169822i
$92$	−1.28868	−	3.96614i	−0.134354	−	0.413499i
$93$	20.7463	−	15.0731i	2.15129	−	1.56301i
$94$	2.40206	−	1.74520i	0.247754	−	0.180004i
$95$		0			0
$96$	−0.768582	+	2.36545i	−0.0784431	+	0.241423i
$97$	−1.41849	−	1.03059i	−0.144026	−	0.104641i	0.513439	−	0.858126i	$-0.328371\pi$
$97$	−1.41849	−	1.03059i	−0.144026	−	0.104641i	−0.657465	+	0.753485i	$0.728371\pi$
$98$	−6.81342			−0.688260
$99$	0.0879978	−	10.5667i	0.00884411	−	1.06199i
$100$		0			0
$101$	1.00000	+	0.726543i	0.0995037	+	0.0722937i	0.636425	−	0.771339i	$-0.280413\pi$
$101$	1.00000	+	0.726543i	0.0995037	+	0.0722937i	−0.536921	+	0.843633i	$0.680413\pi$
$102$	2.63021	−	8.09495i	0.260429	−	0.801519i
$103$	0.831378	+	2.55872i	0.0819181	+	0.252118i	0.983624	−	0.180232i	$-0.0576847\pi$
$103$	0.831378	+	2.55872i	0.0819181	+	0.252118i	−0.901706	+	0.432349i	$0.857685\pi$
$104$	3.19034	−	2.31792i	0.312839	−	0.227291i
$105$		0			0
$106$	1.62066	+	4.98789i	0.157413	+	0.484467i
$107$	0.100568	−	0.309518i	0.00972232	−	0.0299222i	−0.946078	−	0.323940i	$-0.894992\pi$
$107$	0.100568	−	0.309518i	0.00972232	−	0.0299222i	0.955800	+	0.294018i	$0.0949924\pi$
$108$	0.374442	+	0.272048i	0.0360307	+	0.0261778i
$109$	−10.0487			−0.962491			−0.481245	−	0.876586i	$-0.659815\pi$
$109$	−10.0487			−0.962491			−0.481245	+	0.876586i	$0.659815\pi$
$110$		0			0
$111$	−18.2591			−1.73308
$112$	−0.349452	−	0.253891i	−0.0330201	−	0.0239905i
$113$	2.62556	−	8.08064i	0.246992	−	0.760162i	−0.748311	−	0.663348i	$-0.769135\pi$
$113$	2.62556	−	8.08064i	0.246992	−	0.760162i	0.995302	−	0.0968141i	$-0.0308652\pi$
$114$	4.71108	+	14.4992i	0.441233	+	1.35798i
$115$		0			0
$116$	0.512815	−	0.372582i	0.0476137	−	0.0345934i
$117$	−3.88257	−	11.9493i	−0.358944	−	1.10472i
$118$	3.35698	−	10.3317i	0.309035	−	0.951111i
$119$	1.19588	+	0.868856i	0.109626	+	0.0796479i
$120$		0			0
$121$	−3.57295	+	10.4036i	−0.324814	+	0.945778i
$122$	10.5208			0.952512
$123$	5.34722	+	3.88498i	0.482142	+	0.350297i
$124$	3.18609	−	9.80577i	0.286119	−	0.880584i
$125$		0			0
$126$	−1.11338	+	0.808921i	−0.0991881	+	0.0720644i
$127$	−6.98921	+	5.07796i	−0.620192	+	0.450596i	−0.852988	−	0.521930i	$-0.825212\pi$
$127$	−6.98921	+	5.07796i	−0.620192	+	0.450596i	0.232797	+	0.972525i	$0.425212\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	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	$0.247069\pi$
$132$	−4.79293	−	6.71377i	−0.417171	−	0.584359i
$133$	−2.64764			−0.229580
$134$	−8.89815	−	6.46488i	−0.768683	−	0.558481i
$135$		0			0
$136$	−1.05750	−	3.25466i	−0.0906803	−	0.279085i
$137$	13.8012	−	10.0272i	1.17912	−	0.856681i	0.187048	−	0.982351i	$-0.440108\pi$
$137$	13.8012	−	10.0272i	1.17912	−	0.856681i	0.992072	+	0.125670i	$0.0401080\pi$
$138$	−8.39127	+	6.09661i	−0.714312	+	0.518978i
$139$	1.73646	+	5.34429i	0.147285	+	0.453296i	0.997298	−	0.0734656i	$-0.0234059\pi$
$139$	1.73646	+	5.34429i	0.147285	+	0.453296i	−0.850013	+	0.526762i	$0.823406\pi$
$140$		0			0
$141$	−5.97437	−	4.34063i	−0.503133	−	0.365547i
$142$	−10.2591			−0.860928
$143$	−0.108917	+	13.0786i	−0.00910806	+	1.09369i
$144$	3.18609			0.265507
$145$		0			0
$146$	3.44186	−	10.5929i	0.284850	−	0.876678i
$147$	5.23668	+	16.1168i	0.431914	+	1.32929i
$148$	−5.93923	+	4.31510i	−0.488201	+	0.354699i
$149$	−8.00930	+	5.81910i	−0.656147	+	0.476719i	−0.865360	−	0.501151i	$-0.832910\pi$
$149$	−8.00930	+	5.81910i	−0.656147	+	0.476719i	0.209212	+	0.977870i	$0.432910\pi$
$150$		0			0
$151$	−3.54695	+	10.9164i	−0.288647	+	0.888364i	0.696635	+	0.717426i	$0.254680\pi$
$151$	−3.54695	+	10.9164i	−0.288647	+	0.888364i	−0.985282	+	0.170938i	$0.945320\pi$
$152$	4.95892	+	3.60287i	0.402222	+	0.292231i
$153$	−10.9033			−0.881479
$154$	1.36613	−	0.431337i	0.110086	−	0.0347581i
$155$		0			0
$156$	−7.93497	−	5.76509i	−0.635306	−	0.461577i
$157$	2.33541	−	7.18764i	0.186386	−	0.573636i	−0.813584	−	0.581448i	$-0.802486\pi$
$157$	2.33541	−	7.18764i	0.186386	−	0.573636i	0.999969	+	0.00781135i	$0.00248645\pi$
$158$	−2.30110	−	7.08205i	−0.183065	−	0.563417i
$159$	10.5530	−	7.66721i	0.836908	−	0.608049i
$160$		0			0
$161$	−0.556639	−	1.71316i	−0.0438693	−	0.135016i
$162$	−2.59794	+	7.99563i	−0.204113	+	0.628196i
$163$	−2.54835	−	1.85149i	−0.199603	−	0.145020i	0.483494	−	0.875347i	$-0.339367\pi$
$163$	−2.54835	−	1.85149i	−0.199603	−	0.145020i	−0.683097	+	0.730328i	$0.739367\pi$
$164$	2.65743			0.207511
$165$		0			0
$166$	−7.88499			−0.611994
$167$	−4.41057	−	3.20447i	−0.341300	−	0.247969i	0.403910	−	0.914799i	$-0.367651\pi$
$167$	−4.41057	−	3.20447i	−0.341300	−	0.247969i	−0.745210	+	0.666830i	$0.767651\pi$
$168$	−0.331986	+	1.02175i	−0.0256133	+	0.0788296i
$169$	0.788314	+	2.42618i	0.0606395	+	0.186629i
$170$		0			0
$171$	15.7996	−	11.4791i	1.20822	−	0.877826i
$172$	−3.57270	−	10.9957i	−0.272416	−	0.838411i
$173$	4.62391	−	14.2309i	0.351550	−	1.08196i	−0.606434	−	0.795134i	$-0.707400\pi$
$173$	4.62391	−	14.2309i	0.351550	−	1.08196i	0.957983	−	0.286824i	$-0.0925996\pi$
$174$	−1.27547	−	0.926680i	−0.0966928	−	0.0702515i
$175$		0			0
$176$	−3.14565	−	1.05113i	−0.237113	−	0.0792316i
$177$	−27.0193			−2.03089
$178$	−1.08616	−	0.789142i	−0.0814111	−	0.0591487i
$179$	3.75329	−	11.5514i	0.280534	−	0.863395i	−0.707168	−	0.707046i	$-0.750027\pi$
$179$	3.75329	−	11.5514i	0.280534	−	0.863395i	0.987702	−	0.156349i	$-0.0499725\pi$
$180$		0			0
$181$	11.5274	−	8.37513i	0.856823	−	0.622518i	−0.0701958	−	0.997533i	$-0.522362\pi$
$181$	11.5274	−	8.37513i	0.856823	−	0.622518i	0.927019	+	0.375015i	$0.122362\pi$
$182$	1.37806	−	1.00122i	0.102148	−	0.0742151i
$183$	−8.08613	−	24.8865i	−0.597744	−	1.83967i
$184$	−1.28868	+	3.96614i	−0.0950026	+	0.292388i
$185$		0			0
$186$	−25.6439			−1.88030
$187$	10.7649	+	3.59712i	0.787209	+	0.263047i
$188$	−2.96911			−0.216545
$189$	0.161739	+	0.117510i	0.0117647	+	0.00854759i
$190$		0			0
$191$	−0.341287	−	1.05037i	−0.0246946	−	0.0760023i	0.937950	−	0.346771i	$-0.112722\pi$
$191$	−0.341287	−	1.05037i	−0.0246946	−	0.0760023i	−0.962644	+	0.270769i	$0.912722\pi$
$192$	2.01217	−	1.46193i	0.145216	−	0.105506i
$193$	−8.85410	+	6.43288i	−0.637332	+	0.463049i	−0.858933	−	0.512089i	$-0.828872\pi$
$193$	−8.85410	+	6.43288i	−0.637332	+	0.463049i	0.221600	+	0.975138i	$0.428872\pi$
$194$	0.541815	+	1.66754i	0.0389001	+	0.119722i
$195$		0			0
$196$	5.51217	+	4.00483i	0.393727	+	0.286059i
$197$	16.0572			1.14403			0.572014	−	0.820244i	$-0.306162\pi$
$197$	16.0572			1.14403			0.572014	+	0.820244i	$0.306162\pi$
$198$	−6.28214	+	8.49691i	−0.446452	+	0.603849i
$199$	27.1521			1.92476			0.962382	−	0.271699i	$-0.0875854\pi$
$199$	27.1521			1.92476			0.962382	+	0.271699i	$0.0875854\pi$
$200$		0			0
$201$	−8.45342	+	26.0170i	−0.596258	+	1.83509i
$202$	−0.381966	−	1.17557i	−0.0268750	−	0.0827129i
$203$	0.221508	−	0.160935i	0.0155468	−	0.0112954i
$204$	−6.88598	+	5.00295i	−0.482115	+	0.350277i
$205$		0			0
$206$	0.831378	−	2.55872i	0.0579248	−	0.178274i
$207$	10.7492	+	7.80977i	0.747123	+	0.542817i
$208$	−3.94348			−0.273431
$209$	−19.3861	+	6.12093i	−1.34097	+	0.423393i
$210$		0			0
$211$	−2.14302	−	1.55700i	−0.147532	−	0.107188i	0.511571	−	0.859241i	$-0.329064\pi$
$211$	−2.14302	−	1.55700i	−0.147532	−	0.107188i	−0.659103	+	0.752053i	$0.729064\pi$
$212$	1.62066	−	4.98789i	0.111308	−	0.342570i
$213$	7.88499	+	24.2675i	0.540271	+	1.66278i
$214$	−0.263292	+	0.191292i	−0.0179982	+	0.0130765i
$215$		0			0
$216$	−0.143024	−	0.440183i	−0.00973155	−	0.0299506i
$217$	1.37622	−	4.23556i	0.0934238	−	0.287529i
$218$	8.12957	+	5.90648i	0.550604	+	0.400037i
$219$	−27.7025			−1.87196
$220$		0			0
$221$	13.4952			0.907786
$222$	14.7720	+	10.7325i	0.991428	+	0.720315i
$223$	1.94164	−	5.97576i	0.130022	−	0.400167i	−0.864761	−	0.502184i	$-0.832530\pi$
$223$	1.94164	−	5.97576i	0.130022	−	0.400167i	0.994783	+	0.102018i	$0.0325299\pi$
$224$	0.133479	+	0.410805i	0.00891842	+	0.0274481i
$225$		0			0
$226$	−6.87380	+	4.99411i	−0.457238	+	0.332203i
$227$	4.36790	+	13.4430i	0.289908	+	0.892245i	0.984885	+	0.173212i	$0.0554147\pi$
$227$	4.36790	+	13.4430i	0.289908	+	0.892245i	−0.694977	+	0.719032i	$0.744585\pi$
$228$	4.71108	−	14.4992i	0.311999	−	0.960233i
$229$	3.14462	+	2.28470i	0.207802	+	0.150977i	0.686819	−	0.726829i	$-0.259007\pi$
$229$	3.14462	+	2.28470i	0.207802	+	0.150977i	−0.479017	+	0.877806i	$0.659007\pi$
$230$		0			0
$231$	−2.07029	−	2.89999i	−0.136215	−	0.190805i
$232$	−0.633874			−0.0416159
$233$	20.6947	+	15.0356i	1.35576	+	0.985016i	0.998702	+	0.0509329i	$0.0162195\pi$
$233$	20.6947	+	15.0356i	1.35576	+	0.985016i	0.357056	+	0.934083i	$0.383781\pi$
$234$	−3.88257	+	11.9493i	−0.253812	+	0.781153i
$235$		0			0
$236$	−8.78868	+	6.38535i	−0.572094	+	0.415651i
$237$	−14.9837	+	10.8863i	−0.973294	+	0.707139i
$238$	−0.456785	−	1.40584i	−0.0296090	−	0.0911270i
$239$	−3.73255	+	11.4876i	−0.241439	+	0.743072i	0.754763	+	0.655998i	$0.227752\pi$
$239$	−3.73255	+	11.4876i	−0.241439	+	0.743072i	−0.996202	+	0.0870747i	$0.972248\pi$
$240$		0			0
$241$	23.5597			1.51762			0.758808	−	0.651314i	$-0.225782\pi$
$241$	23.5597			1.51762			0.758808	+	0.651314i	$0.225782\pi$
$242$	9.00563	−	6.31653i	0.578904	−	0.406042i
$243$	22.2985			1.43045
$244$	−8.51153	−	6.18399i	−0.544895	−	0.395889i
$245$		0			0
$246$	−2.04246	−	6.28603i	−0.130222	−	0.400783i
$247$	−19.5554	+	14.2078i	−1.24428	+	0.904024i
$248$	−8.34129	+	6.06030i	−0.529672	+	0.384829i
$249$	6.06027	+	18.6516i	0.384054	+	1.18200i
$250$		0			0
$251$	2.77289	+	2.01462i	0.175023	+	0.127162i	0.671848	−	0.740689i	$-0.265501\pi$
$251$	2.77289	+	2.01462i	0.175023	+	0.127162i	−0.496825	+	0.867851i	$0.665501\pi$
$252$	1.37622			0.0866936
$253$	−8.03628	−	11.2569i	−0.505237	−	0.707718i
$254$	8.63913			0.542067
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−0.503634	−	1.55003i	−0.0314158	−	0.0966879i	0.934119	−	0.356961i	$-0.116187\pi$
$257$	−0.503634	−	1.55003i	−0.0314158	−	0.0966879i	−0.965535	+	0.260274i	$0.916187\pi$
$258$	−23.2638	+	16.9021i	−1.44834	+	1.05228i
$259$	−2.56542	+	1.86389i	−0.159408	+	0.115816i
$260$		0			0
$261$	−0.624085	+	1.92073i	−0.0386299	+	0.118890i
$262$	−13.2151	−	9.60132i	−0.816431	−	0.593172i
$263$	1.65168			0.101847			0.0509236	−	0.998703i	$-0.483783\pi$
$263$	1.65168			0.101847			0.0509236	+	0.998703i	$0.483783\pi$
$264$	−0.0686945	+	8.24877i	−0.00422786	+	0.507677i
$265$		0			0
$266$	2.14199	+	1.55625i	0.131334	+	0.0954195i
$267$	−1.03187	+	3.17578i	−0.0631497	+	0.194355i
$268$	3.39879	+	10.4604i	0.207614	+	0.638971i
$269$	−17.9324	+	13.0287i	−1.09336	+	0.794371i	−0.979963	−	0.199179i	$-0.936173\pi$
$269$	−17.9324	+	13.0287i	−1.09336	+	0.794371i	−0.113395	+	0.993550i	$0.536173\pi$
$270$		0			0
$271$	−2.27021	−	6.98698i	−0.137905	−	0.424429i	0.858125	−	0.513440i	$-0.171629\pi$
$271$	−2.27021	−	6.98698i	−0.137905	−	0.424429i	−0.996031	+	0.0890115i	$0.971629\pi$
$272$	−1.05750	+	3.25466i	−0.0641206	+	0.197343i
$273$	−3.42748	−	2.49021i	−0.207440	−	0.150714i
$274$	−17.0593			−1.03059
$275$		0			0
$276$	10.3722			0.624332
$277$	−12.5533	−	9.12054i	−0.754258	−	0.548000i	0.142886	−	0.989739i	$-0.454362\pi$
$277$	−12.5533	−	9.12054i	−0.754258	−	0.548000i	−0.897144	+	0.441739i	$0.854362\pi$
$278$	1.73646	−	5.34429i	0.104146	−	0.320529i
$279$	10.1512	+	31.2420i	0.607734	+	1.87041i
$280$		0			0
$281$	18.5343	−	13.4660i	1.10566	−	0.803311i	0.123688	−	0.992321i	$-0.460528\pi$
$281$	18.5343	−	13.4660i	1.10566	−	0.803311i	0.981975	+	0.189010i	$0.0605278\pi$
$282$	2.28201	+	7.02329i	0.135891	+	0.418231i
$283$	0.865901	−	2.66497i	0.0514724	−	0.158416i	−0.922016	−	0.387151i	$-0.873459\pi$
$283$	0.865901	−	2.66497i	0.0514724	−	0.158416i	0.973489	+	0.228735i	$0.0734591\pi$
$284$	8.29982	+	6.03017i	0.492503	+	0.357825i
$285$		0			0
$286$	7.77552	−	10.5168i	0.459776	−	0.621870i
$287$	1.14787			0.0677565
$288$	−2.57760	−	1.87274i	−0.151886	−	0.110352i
$289$	−1.63434	+	5.02999i	−0.0961379	+	0.295882i
$290$		0			0
$291$	3.52805	−	2.56328i	0.206818	−	0.150262i
$292$	−9.01089	+	6.54680i	−0.527323	+	0.383122i
$293$	6.57473	+	20.2349i	0.384100	+	1.18214i	0.937131	+	0.348977i	$0.113471\pi$
$293$	6.57473	+	20.2349i	0.384100	+	1.18214i	−0.553032	+	0.833160i	$0.686529\pi$
$294$	5.23668	−	16.1168i	0.305409	−	0.939953i
$295$		0			0
$296$	7.34129			0.426704
$297$	1.45592	+	0.486498i	0.0844810	+	0.0282295i
$298$	9.90004			0.573494
$299$	−13.3045	−	9.66630i	−0.769420	−	0.559016i
$300$		0			0
$301$	−1.54322	−	4.74953i	−0.0889494	−	0.273758i
$302$	9.28605	−	6.74671i	0.534352	−	0.388229i
$303$	−2.48718	+	1.80705i	−0.142885	+	0.103812i
$304$	−1.89414	−	5.82957i	−0.108636	−	0.334349i
$305$		0			0
$306$	8.82095	+	6.40879i	0.504260	+	0.366366i
$307$	2.92114			0.166718			0.0833591	−	0.996520i	$-0.473435\pi$
$307$	2.92114			0.166718			0.0833591	+	0.996520i	$0.473435\pi$
$308$	−1.35875	−	0.454029i	−0.0774221	−	0.0258707i
$309$	−6.69151			−0.380667
$310$		0			0
$311$	−1.18284	+	3.64040i	−0.0670726	+	0.206428i	−0.978976	−	0.203978i	$-0.934613\pi$
$311$	−1.18284	+	3.64040i	−0.0670726	+	0.206428i	0.911903	+	0.410406i	$0.134613\pi$
$312$	3.03089	+	9.32812i	0.171590	+	0.528101i
$313$	−22.0764	+	16.0395i	−1.24783	+	0.906604i	−0.998094	−	0.0617096i	$-0.980345\pi$
$313$	−22.0764	+	16.0395i	−1.24783	+	0.906604i	−0.249739	+	0.968313i	$0.580345\pi$
$314$	−6.11418	+	4.44221i	−0.345043	+	0.250688i
$315$		0			0
$316$	−2.30110	+	7.08205i	−0.129447	+	0.398396i
$317$	−23.2634	−	16.9018i	−1.30660	−	0.949302i	−0.306605	−	0.951837i	$-0.599193\pi$
$317$	−23.2634	−	16.9018i	−1.30660	−	0.949302i	−0.999997	+	0.00253464i	$0.999193\pi$
$318$	−13.0442			−0.731484
$319$	1.24984	−	1.69047i	0.0699774	−	0.0946479i
$320$		0			0
$321$	0.654855	+	0.475780i	0.0365504	+	0.0265554i
$322$	−0.556639	+	1.71316i	−0.0310203	+	0.0954706i
$323$	6.48205	+	19.9497i	0.360671	+	1.11003i
$324$	6.80149	−	4.94157i	0.377861	−	0.274532i
$325$		0			0
$326$	0.973385	+	2.99577i	0.0539108	+	0.165920i
$327$	7.72325	−	23.7697i	0.427097	−	1.31447i
$328$	−2.14991	−	1.56200i	−0.118709	−	0.0862470i
$329$	−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	$0.638102\pi$
$332$	6.37909	+	4.63468i	0.350098	+	0.254361i
$333$	7.22790	−	22.2452i	0.396087	−	1.21903i
$334$	1.68469	+	5.18494i	0.0921820	+	0.283707i
$335$		0			0
$336$	0.869151	−	0.631475i	0.0474161	−	0.0344498i
$337$	6.00704	+	18.4878i	0.327224	+	1.00709i	0.970427	+	0.241396i	$0.0776053\pi$
$337$	6.00704	+	18.4878i	0.327224	+	1.00709i	−0.643203	+	0.765696i	$0.722395\pi$
$338$	0.788314	−	2.42618i	0.0428786	−	0.131967i
$339$	17.0964	+	12.4213i	0.928550	+	0.674631i
$340$		0			0
$341$	0.284767	−	34.1945i	0.0154210	−	1.85174i
$342$	−19.5293			−1.05603
$343$	4.82712	+	3.50711i	0.260640	+	0.189366i
$344$	−3.57270	+	10.9957i	−0.192627	+	0.592846i
$345$		0			0
$346$	−12.1056	+	8.79521i	−0.650799	+	0.472833i
$347$	7.46620	−	5.42452i	0.400807	−	0.291203i	−0.369063	−	0.929405i	$-0.620321\pi$
$347$	7.46620	−	5.42452i	0.400807	−	0.291203i	0.769870	+	0.638201i	$0.220321\pi$
$348$	0.487185	+	1.49940i	0.0261158	+	0.0803763i
$349$	4.72374	−	14.5382i	0.252856	−	0.778211i	−0.741388	−	0.671076i	$-0.765832\pi$
$349$	4.72374	−	14.5382i	0.252856	−	0.778211i	0.994244	−	0.107135i	$-0.0341677\pi$
$350$		0			0
$351$	1.82518			0.0974210
$352$	1.92705	+	2.69935i	0.102712	+	0.143876i
$353$	−6.10571			−0.324974			−0.162487	−	0.986711i	$-0.551952\pi$
$353$	−6.10571			−0.324974			−0.162487	+	0.986711i	$0.551952\pi$
$354$	21.8591	+	15.8815i	1.16180	+	0.844094i
$355$		0			0
$356$	0.414876	+	1.27686i	0.0219884	+	0.0676733i
$357$	−2.97437	+	2.16101i	−0.157420	+	0.114373i
$358$	−9.82624	+	7.13918i	−0.519333	+	0.377317i
$359$	−8.32545	−	25.6231i	−0.439400	−	1.35233i	−0.888510	−	0.458858i	$-0.848259\pi$
$359$	−8.32545	−	25.6231i	−0.439400	−	1.35233i	0.449109	−	0.893477i	$-0.351741\pi$
$360$		0			0
$361$	−15.0247	−	10.9161i	−0.790776	−	0.574532i
$362$	−14.2486			−0.748891
$363$	−21.8630	−	16.4476i	−1.14751	−	0.863277i
$364$	−1.70337			−0.0892809
$365$		0			0
$366$	−8.08613	+	24.8865i	−0.422669	+	1.30084i
$367$	−7.72900	−	23.7874i	−0.403451	−	1.24169i	−0.922182	−	0.386756i	$-0.873596\pi$
$367$	−7.72900	−	23.7874i	−0.403451	−	1.24169i	0.518732	−	0.854937i	$-0.326404\pi$
$368$	3.37380	−	2.45121i	0.175872	−	0.127778i
$369$	−6.84980	+	4.97667i	−0.356586	+	0.259075i
$370$		0			0
$371$	0.700039	−	2.15450i	0.0363442	−	0.111856i
$372$	20.7463	+	15.0731i	1.07565	+	0.781503i
$373$	27.5557			1.42678			0.713389	−	0.700768i	$-0.247159\pi$
$373$	27.5557			1.42678			0.713389	+	0.700768i	$0.247159\pi$
$374$	−6.59467	−	9.23759i	−0.341002	−	0.477664i
$375$		0			0
$376$	2.40206	+	1.74520i	0.123877	+	0.0900018i
$377$	0.772441	−	2.37733i	0.0397827	−	0.122439i
$378$	−0.0617786	−	0.190135i	−0.00317755	−	0.00977949i
$379$	19.0027	−	13.8063i	0.976105	−	0.709182i	0.0192700	−	0.999814i	$-0.493866\pi$
$379$	19.0027	−	13.8063i	0.976105	−	0.709182i	0.956835	+	0.290633i	$0.0938658\pi$
$380$		0			0
$381$	−6.63989	−	20.4355i	−0.340172	−	1.04694i
$382$	−0.341287	+	1.05037i	−0.0174617	+	0.0537417i
$383$	−15.1470	−	11.0050i	−0.773977	−	0.562327i	0.129188	−	0.991620i	$-0.458763\pi$
$383$	−15.1470	−	11.0050i	−0.773977	−	0.562327i	−0.903165	+	0.429293i	$0.858763\pi$
$384$	−2.48718			−0.126924
$385$		0			0
$386$	10.9443			0.557049
$387$	29.8010	+	21.6517i	1.51487	+	1.10062i
$388$	0.541815	−	1.66754i	0.0275065	−	0.0846563i
$389$	2.29210	+	7.05435i	0.116214	+	0.357670i	0.992198	−	0.124670i	$-0.0397871\pi$
$389$	2.29210	+	7.05435i	0.116214	+	0.357670i	−0.875984	+	0.482340i	$0.839787\pi$
$390$		0			0
$391$	−11.5457	+	8.38842i	−0.583890	+	0.424221i
$392$	−2.10546	−	6.47995i	−0.106342	−	0.327287i
$393$	−12.5546	+	38.6391i	−0.633296	+	1.94908i
$394$	−12.9906	−	9.43819i	−0.654455	−	0.475489i
$395$		0			0
$396$	10.0767	−	3.18160i	0.506374	−	0.159881i
$397$	22.6398			1.13626			0.568130	−	0.822939i	$-0.307667\pi$
$397$	22.6398			1.13626			0.568130	+	0.822939i	$0.307667\pi$
$398$	−21.9665	−	15.9596i	−1.10108	−	0.799984i
$399$	2.03493	−	6.26287i	0.101874	−	0.313536i
$400$		0			0
$401$	−21.8299	+	15.8603i	−1.09013	+	0.792026i	−0.979421	−	0.201826i	$-0.935312\pi$
$401$	−21.8299	+	15.8603i	−1.09013	+	0.792026i	−0.110709	+	0.993853i	$0.535312\pi$
$402$	22.1313	−	16.0794i	1.10381	−	0.801966i
$403$	−12.5643	−	38.6689i	−0.625871	−	1.92623i
$404$	−0.381966	+	1.17557i	−0.0190035	+	0.0584868i
$405$		0			0
$406$	−0.273800			−0.0135884
$407$	−14.4751	+	19.5783i	−0.717505	+	0.970461i
$408$	8.51153			0.421384
$409$	7.55854	+	5.49160i	0.373746	+	0.271542i	0.758762	−	0.651367i	$-0.225804\pi$
$409$	7.55854	+	5.49160i	0.373746	+	0.271542i	−0.385017	+	0.922910i	$0.625804\pi$
$410$		0			0
$411$	13.1115	+	40.3529i	0.646741	+	1.99046i
$412$	−2.17657	+	1.58137i	−0.107232	+	0.0779087i
$413$	−3.79623	+	2.75813i	−0.186800	+	0.135718i
$414$	−4.10584	−	12.6365i	−0.201791	−	0.621049i
$415$		0			0
$416$	3.19034	+	2.31792i	0.156419	+	0.113645i
$417$	−13.9763			−0.684421
$418$	19.2815	+	6.44295i	0.943089	+	0.315135i
$419$	16.5607			0.809044			0.404522	−	0.914528i	$-0.367438\pi$
$419$	16.5607			0.809044			0.404522	+	0.914528i	$0.367438\pi$
$420$		0			0
$421$	0.581094	−	1.78842i	0.0283208	−	0.0871624i	−0.935897	−	0.352274i	$-0.885409\pi$
$421$	0.581094	−	1.78842i	0.0283208	−	0.0871624i	0.964218	+	0.265111i	$0.0854087\pi$
$422$	0.818562	+	2.51928i	0.0398470	+	0.122636i
$423$	7.65318	−	5.56036i	0.372110	−	0.270354i
$424$	−4.24295	+	3.08268i	−0.206056	+	0.149708i
$425$		0			0
$426$	7.88499	−	24.2675i	0.382029	−	1.17576i
$427$	−3.67652	−	2.67115i	−0.177919	−	0.129266i
$428$	0.325446			0.0157310
$429$	−30.8531	−	10.3096i	−1.48960	−	0.497753i
$430$		0			0
$431$	−19.0974	−	13.8751i	−0.919889	−	0.668339i	0.0236072	−	0.999721i	$-0.492485\pi$
$431$	−19.0974	−	13.8751i	−0.919889	−	0.668339i	−0.943496	+	0.331383i	$0.892485\pi$
$432$	−0.143024	+	0.440183i	−0.00688124	+	0.0211783i
$433$	4.90556	+	15.0977i	0.235746	+	0.725551i	0.997022	+	0.0771230i	$0.0245734\pi$
$433$	4.90556	+	15.0977i	0.235746	+	0.725551i	−0.761276	+	0.648428i	$0.775427\pi$
$434$	−3.60299	+	2.61772i	−0.172949	+	0.125655i
$435$		0			0
$436$	−3.10522	−	9.55688i	−0.148713	−	0.457692i
$437$	7.89904	−	24.3107i	0.377862	−	1.16294i
$438$	22.4118	+	16.2831i	1.07088	+	0.778036i
$439$	−11.6082			−0.554031			−0.277016	−	0.960865i	$-0.589345\pi$
$439$	−11.6082			−0.554031			−0.277016	+	0.960865i	$0.589345\pi$
$440$		0			0
$441$	−21.7082			−1.03372
$442$	−10.9178	−	7.93228i	−0.519309	−	0.377300i
$443$	−2.94892	+	9.07585i	−0.140108	+	0.431207i	−0.996349	−	0.0853684i	$-0.972793\pi$
$443$	−2.94892	+	9.07585i	−0.140108	+	0.431207i	0.856242	+	0.516575i	$0.172793\pi$
$444$	−5.64238	−	17.3655i	−0.267776	−	0.824129i
$445$		0			0
$446$	−5.08329	+	3.69322i	−0.240701	+	0.174879i
$447$	−7.60900	−	23.4181i	−0.359893	−	1.10764i
$448$	0.133479	−	0.410805i	0.00630627	−	0.0194087i
$449$	−16.0576	−	11.6665i	−0.757805	−	0.550578i	0.140431	−	0.990090i	$-0.455151\pi$
$449$	−16.0576	−	11.6665i	−0.757805	−	0.550578i	−0.898236	+	0.439513i	$0.855151\pi$
$450$		0			0
$451$	8.40472	−	2.65369i	0.395763	−	0.124957i
$452$	8.49649			0.399641
$453$	−23.0961	−	16.7803i	−1.08515	−	0.788408i
$454$	4.36790	−	13.4430i	0.204996	−	0.630912i
$455$		0			0
$456$	−12.3338	+	8.96100i	−0.577581	+	0.419637i
$457$	3.40265	−	2.47217i	0.159169	−	0.115643i	−0.505350	−	0.862915i	$-0.668636\pi$
$457$	3.40265	−	2.47217i	0.159169	−	0.115643i	0.664519	+	0.747271i	$0.268636\pi$
$458$	−1.20114	−	3.69672i	−0.0561254	−	0.172736i
$459$	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	$0.429388\pi$
$462$	−0.0296723	+	3.56302i	−0.00138048	+	0.165767i
$463$	26.5879			1.23564			0.617822	−	0.786318i	$-0.288015\pi$
$463$	26.5879			1.23564			0.617822	+	0.786318i	$0.288015\pi$
$464$	0.512815	+	0.372582i	0.0238068	+	0.0172967i
$465$		0			0
$466$	−7.90469	−	24.3281i	−0.366178	−	1.12698i
$467$	14.7476	−	10.7148i	0.682438	−	0.495820i	−0.191728	−	0.981448i	$-0.561409\pi$
$467$	14.7476	−	10.7148i	0.682438	−	0.495820i	0.874165	+	0.485628i	$0.161409\pi$
$468$	10.1647	−	7.38510i	0.469864	−	0.341376i
$469$	1.46809	+	4.51833i	0.0677903	+	0.208637i
$470$		0			0
$471$	15.2071	+	11.0486i	0.700705	+	0.509092i
$472$	10.8634			0.500029
$473$	−22.2796	−	31.2085i	−1.02442	−	1.43497i
$474$	18.5208			0.850690
$475$		0			0
$476$	−0.456785	+	1.40584i	−0.0209367	+	0.0644365i
$477$	5.16358	+	15.8919i	0.236424	+	0.727638i
$478$	9.77195	−	7.09974i	0.446959	−	0.324734i
$479$	10.5221	−	7.64476i	0.480768	−	0.349298i	−0.320855	−	0.947128i	$-0.603970\pi$
$479$	10.5221	−	7.64476i	0.480768	−	0.349298i	0.801623	+	0.597830i	$0.203970\pi$
$480$		0			0
$481$	−8.94611	+	27.5333i	−0.407907	+	1.25541i
$482$	−19.0602	−	13.8481i	−0.868170	−	0.630762i
$483$	4.48022			0.203857
$484$	−10.9985	−	0.183200i	−0.499931	−	0.00832727i
$485$		0			0
$486$	−18.0399	−	13.1067i	−0.818306	−	0.594534i
$487$	2.38148	−	7.32943i	0.107915	−	0.332128i	−0.882489	−	0.470334i	$-0.844133\pi$
$487$	2.38148	−	7.32943i	0.107915	−	0.332128i	0.990404	+	0.138206i	$0.0441335\pi$
$488$	3.25112	+	10.0059i	0.147171	+	0.452946i
$489$	6.33823	−	4.60499i	0.286625	−	0.208245i
$490$		0			0
$491$	4.16722	+	12.8254i	0.188064	+	0.578802i	0.999988	−	0.00496193i	$-0.00157944\pi$
$491$	4.16722	+	12.8254i	0.188064	+	0.578802i	−0.811924	+	0.583764i	$0.801579\pi$
$492$	−2.04246	+	6.28603i	−0.0920810	+	0.283396i
$493$	−1.75493	−	1.27503i	−0.0790382	−	0.0574246i
$494$	24.1718			1.08754
$495$		0			0
$496$	10.3104			0.462951
$497$	3.58507	+	2.60471i	0.160812	+	0.116837i
$498$	6.06027	−	18.6516i	0.271567	−	0.835797i
$499$	4.25919	+	13.1084i	0.190667	+	0.586814i	1.00000		0.000536806i	$-0.000170871\pi$
$499$	4.25919	+	13.1084i	0.190667	+	0.586814i	−0.809332	+	0.587351i	$0.800171\pi$
$500$		0			0
$501$	10.9699	−	7.97010i	0.490099	−	0.356078i
$502$	−1.05915	−	3.25973i	−0.0472721	−	0.145489i
$503$	−1.95116	+	6.00504i	−0.0869977	+	0.267752i	−0.985086	−	0.172064i	$-0.944956\pi$
$503$	−1.95116	+	6.00504i	−0.0869977	+	0.267752i	0.898088	+	0.439816i	$0.144956\pi$
$504$	−1.11338	−	0.808921i	−0.0495940	−	0.0360322i
$505$		0			0
$506$	−0.115180	+	13.8307i	−0.00512036	+	0.614848i
$507$	−6.34490			−0.281787
$508$	−6.98921	−	5.07796i	−0.310096	−	0.225298i
$509$	13.3957	−	41.2278i	0.593755	−	1.82739i	0.0329295	−	0.999458i	$-0.489516\pi$
$509$	13.3957	−	41.2278i	0.593755	−	1.82739i	0.560826	−	0.827934i	$-0.310484\pi$
$510$		0			0
$511$	−3.89222	+	2.82786i	−0.172182	+	0.125097i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	0.876675	+	2.69813i	0.0387062	+	0.119125i
$514$	−0.503634	+	1.55003i	−0.0222143	+	0.0683687i
$515$		0			0
$516$	28.7556			1.26590
$517$	−9.39047	+	2.96493i	−0.412993	+	0.130397i
$518$	3.17104			0.139327
$519$	30.1088	+	21.8753i	1.32163	+	0.960219i
$520$		0			0
$521$	6.70203	+	20.6267i	0.293621	+	0.903673i	0.983681	+	0.179921i	$0.0575842\pi$
$521$	6.70203	+	20.6267i	0.293621	+	0.903673i	−0.690060	+	0.723752i	$0.742416\pi$
$522$	1.63387	−	1.18708i	0.0715127	−	0.0519570i
$523$	12.3618	−	8.98136i	0.540543	−	0.392727i	−0.283744	−	0.958900i	$-0.591577\pi$
$523$	12.3618	−	8.98136i	0.540543	−	0.392727i	0.824287	+	0.566173i	$0.191577\pi$
$524$	5.04771	+	15.5353i	0.220510	+	0.678661i
$525$		0			0
$526$	−1.33624	−	0.970836i	−0.0582629	−	0.0423304i
$527$	−35.2838			−1.53699
$528$	4.90408	−	6.63302i	0.213423	−	0.288665i
$529$	−5.60904			−0.243871
$530$		0			0
$531$	10.6956	−	32.9177i	0.464150	−	1.42851i
$532$	−0.818166	−	2.51806i	−0.0354720	−	0.109172i
$533$	8.47812	−	6.15971i	0.367228	−	0.266807i
$534$	2.70148	−	1.96274i	0.116905	−	0.0849361i
$535$		0			0
$536$	3.39879	−	10.4604i	0.146805	−	0.451821i
$537$	24.4397	+	17.7565i	1.05465	+	0.766248i
$538$	22.1657			0.955630
$539$	21.4327	+	7.16176i	0.923170	+	0.308479i
$540$		0			0
$541$	19.5314	+	14.1904i	0.839721	+	0.610093i	0.922293	−	0.386492i	$-0.126313\pi$
$541$	19.5314	+	14.1904i	0.839721	+	0.610093i	−0.0825716	+	0.996585i	$0.526313\pi$
$542$	−2.27021	+	6.98698i	−0.0975138	+	0.300116i
$543$	10.9512	+	33.7044i	0.469963	+	1.44640i
$544$	2.76858	−	2.01149i	0.118702	−	0.0862420i
$545$		0			0
$546$	1.30918	+	4.02924i	0.0560277	+	0.172436i
$547$	−10.3431	+	31.8327i	−0.442237	+	1.36107i	0.443248	+	0.896399i	$0.353826\pi$
$547$	−10.3431	+	31.8327i	−0.442237	+	1.36107i	−0.885485	+	0.464668i	$0.846174\pi$
$548$	13.8012	+	10.0272i	0.589560	+	0.428340i
$549$	33.5203			1.43061
$550$		0			0
$551$	3.88538			0.165523
$552$	−8.39127	−	6.09661i	−0.357156	−	0.259489i
$553$	−0.993949	+	3.05906i	−0.0422670	+	0.130085i
$554$	4.79495	+	14.7573i	0.203718	+	0.626980i
$555$		0			0
$556$	−4.54612	+	3.30295i	−0.192798	+	0.140076i
$557$	1.27788	+	3.93292i	0.0541456	+	0.166643i	0.974472	−	0.224507i	$-0.0720772\pi$
$557$	1.27788	+	3.93292i	0.0541456	+	0.166643i	−0.920327	+	0.391150i	$0.872077\pi$
$558$	10.1512	−	31.2420i	0.429733	−	1.32258i
$559$	−36.8852	−	26.7987i	−1.56008	−	1.13346i
$560$		0			0
$561$	−16.7825	+	22.6992i	−0.708559	+	0.958362i
$562$	−22.9096			−0.966385
$563$	22.3363	+	16.2283i	0.941364	+	0.683941i	0.948749	−	0.316031i	$-0.102350\pi$
$563$	22.3363	+	16.2283i	0.941364	+	0.683941i	−0.00738424	+	0.999973i	$0.502350\pi$
$564$	2.28201	−	7.02329i	0.0960898	−	0.295734i
$565$		0			0
$566$	−2.26696	+	1.64704i	−0.0952873	+	0.0692303i
$567$	2.93788	−	2.13449i	0.123379	−	0.0896403i
$568$	−3.17025	−	9.75702i	−0.133021	−	0.409395i
$569$	−2.40142	+	7.39081i	−0.100673	+	0.309839i	−0.988691	−	0.149970i	$-0.952082\pi$
$569$	−2.40142	+	7.39081i	−0.100673	+	0.309839i	0.888018	+	0.459809i	$0.152082\pi$
$570$		0			0
$571$	−1.73373			−0.0725544			−0.0362772	−	0.999342i	$-0.511550\pi$
$571$	−1.73373			−0.0725544			−0.0362772	+	0.999342i	$0.511550\pi$
$572$	−12.4721	+	3.93792i	−0.521486	+	0.164653i
$573$	2.74691			0.114754
$574$	−0.928644	−	0.674699i	−0.0387609	−	0.0281614i
$575$		0			0
$576$	0.984555	+	3.03015i	0.0410231	+	0.126256i
$577$	5.45036	−	3.95992i	0.226902	−	0.164854i	−0.468526	−	0.883450i	$-0.655215\pi$
$577$	5.45036	−	3.95992i	0.226902	−	0.164854i	0.695428	+	0.718596i	$0.255215\pi$
$578$	4.27877	−	3.10871i	0.177973	−	0.129305i
$579$	−8.41157	−	25.8882i	−0.349573	−	1.07588i
$580$		0			0
$581$	2.75542	+	2.00193i	0.114314	+	0.0830541i
$582$	−4.36091			−0.180765
$583$	0.144852	−	17.3937i	0.00599916	−	0.720373i
$584$	11.1381			0.460897
$585$		0			0
$586$	6.57473	−	20.2349i	0.271599	−	0.835897i
$587$	−10.8498	−	33.3923i	−0.447820	−	1.37825i	−0.879361	−	0.476156i	$-0.842030\pi$
$587$	−10.8498	−	33.3923i	−0.447820	−	1.37825i	0.431541	−	0.902093i	$-0.357970\pi$
$588$	−13.7098	+	9.96075i	−0.565382	+	0.410774i
$589$	51.1285	−	37.1470i	2.10671	−	1.53062i
$590$		0			0
$591$	−12.3413	+	37.9826i	−0.507653	+	1.56239i
$592$	−5.93923	−	4.31510i	−0.244101	−	0.177350i
$593$	5.17098			0.212347			0.106173	−	0.994348i	$-0.466140\pi$
$593$	5.17098			0.212347			0.106173	+	0.994348i	$0.466140\pi$
$594$	−0.891907	−	1.24935i	−0.0365954	−	0.0512616i
$595$		0			0
$596$	−8.00930	−	5.81910i	−0.328074	−	0.238360i
$597$	−20.8687	+	64.2271i	−0.854097	+	2.62864i
$598$	5.08187	+	15.6404i	0.207813	+	0.639583i
$599$	−13.5879	+	9.87221i	−0.555188	+	0.403368i	−0.829695	−	0.558217i	$-0.811485\pi$
$599$	−13.5879	+	9.87221i	−0.555188	+	0.403368i	0.274507	+	0.961585i	$0.411485\pi$
$600$		0			0
$601$	−8.19285	−	25.2150i	−0.334193	−	1.02854i	−0.967118	−	0.254328i	$-0.918146\pi$
$601$	−8.19285	−	25.2150i	−0.334193	−	1.02854i	0.632925	−	0.774213i	$-0.281854\pi$
$602$	−1.54322	+	4.74953i	−0.0628968	+	0.193576i
$603$	−28.3503	−	20.5977i	−1.15451	−	0.838803i
$604$	−11.4782			−0.467041
$605$		0			0
$606$	3.07433			0.124886
$607$	36.2383	+	26.3287i	1.47087	+	1.06865i	0.980361	+	0.197212i	$0.0631887\pi$
$607$	36.2383	+	26.3287i	1.47087	+	1.06865i	0.490508	+	0.871437i	$0.336811\pi$
$608$	−1.89414	+	5.82957i	−0.0768176	+	0.236420i
$609$	0.210437	+	0.647660i	0.00852736	+	0.0262445i
$610$		0			0
$611$	−9.47248	+	6.88216i	−0.383216	+	0.278422i
$612$	−3.36930	−	10.3696i	−0.136196	−	0.419168i
$613$	−0.354366	+	1.09063i	−0.0143127	+	0.0440500i	−0.957958	−	0.286909i	$-0.907372\pi$
$613$	−0.354366	+	1.09063i	−0.0143127	+	0.0440500i	0.943645	+	0.330959i	$0.107372\pi$
$614$	−2.36325	−	1.71700i	−0.0953731	−	0.0692926i
$615$		0			0
$616$	0.832382	+	1.16597i	0.0335376	+	0.0469784i
$617$	23.3790			0.941202			0.470601	−	0.882346i	$-0.344037\pi$
$617$	23.3790			0.941202			0.470601	+	0.882346i	$0.344037\pi$
$618$	5.41354	+	3.93317i	0.217765	+	0.158215i
$619$	−7.30246	+	22.4747i	−0.293511	+	0.903334i	0.690207	+	0.723612i	$0.257520\pi$
$619$	−7.30246	+	22.4747i	−0.293511	+	0.903334i	−0.983718	+	0.179721i	$0.942480\pi$
$620$		0			0
$621$	−1.56151	+	1.13451i	−0.0626614	+	0.0455262i
$622$	3.09671	−	2.24989i	0.124167	−	0.0902124i
$623$	0.179204	+	0.551534i	0.00717966	+	0.0220967i
$624$	3.03089	−	9.32812i	0.121333	−	0.373424i
$625$		0			0
$626$	27.2880			1.09065
$627$	0.421068	−	50.5614i	0.0168158	−	2.01923i
$628$	7.55754			0.301579
$629$	20.3250	+	14.7669i	0.810409	+	0.588797i
$630$		0			0
$631$	−4.16946	−	12.8323i	−0.165983	−	0.510844i	0.833124	−	0.553086i	$-0.186550\pi$
$631$	−4.16946	−	12.8323i	−0.165983	−	0.510844i	−0.999107	+	0.0422418i	$0.986550\pi$
$632$	6.02435	−	4.37695i	0.239636	−	0.174106i
$633$	5.33010	−	3.87254i	0.211852	−	0.153920i
$634$	8.88582	+	27.3478i	0.352901	+	1.08612i
$635$		0			0
$636$	10.5530	+	7.66721i	0.418454	+	0.304025i
$637$	26.8686			1.06457
$638$	−2.00477	+	0.632981i	−0.0793696	+	0.0250600i
$639$	−32.6865			−1.29306
$640$		0			0
$641$	−0.719738	+	2.21513i	−0.0284279	+	0.0874922i	−0.964264	−	0.264944i	$-0.914647\pi$
$641$	−0.719738	+	2.21513i	−0.0284279	+	0.0874922i	0.935836	+	0.352436i	$0.114647\pi$
$642$	−0.250132	−	0.769828i	−0.00987193	−	0.0303827i
$643$	22.9946	−	16.7065i	0.906817	−	0.658841i	−0.0333908	−	0.999442i	$-0.510631\pi$
$643$	22.9946	−	16.7065i	0.906817	−	0.658841i	0.940208	+	0.340601i	$0.110631\pi$
$644$	1.45730	−	1.05879i	0.0574257	−	0.0417222i
$645$		0			0
$646$	6.48205	−	19.9497i	0.255033	−	0.784910i
$647$	20.1803	+	14.6619i	0.793371	+	0.576418i	0.908962	−	0.416879i	$-0.136876\pi$
$647$	20.1803	+	14.6619i	0.793371	+	0.576418i	−0.115591	+	0.993297i	$0.536876\pi$
$648$	−8.40711			−0.330262
$649$	−21.4198	+	28.9714i	−0.840801	+	1.13723i
$650$		0			0
$651$	8.96129	+	6.51076i	0.351221	+	0.255177i
$652$	0.973385	−	2.99577i	0.0381207	−	0.117323i
$653$	−12.3022	−	37.8624i	−0.481424	−	1.48167i	−0.837095	−	0.547058i	$-0.815748\pi$
$653$	−12.3022	−	37.8624i	−0.481424	−	1.48167i	0.355671	−	0.934611i	$-0.384252\pi$
$654$	−20.2197	+	14.6905i	−0.790654	+	0.574444i
$655$		0			0
$656$	0.821192	+	2.52737i	0.0320622	+	0.0986772i
$657$	10.9661	−	33.7500i	0.427826	−	1.31671i
$658$	1.03756	+	0.753832i	0.0404483	+	0.0293874i
$659$	−28.4602			−1.10865			−0.554327	−	0.832299i	$-0.687024\pi$
$659$	−28.4602			−1.10865			−0.554327	+	0.832299i	$0.687024\pi$
$660$		0			0
$661$	22.1958			0.863316			0.431658	−	0.902037i	$-0.357929\pi$
$661$	22.1958			0.863316			0.431658	+	0.902037i	$0.357929\pi$
$662$	12.3748	+	8.99085i	0.480962	+	0.349439i
$663$	−10.3722	+	31.9223i	−0.402822	+	1.23976i
$664$	−2.43660	−	7.49907i	−0.0945583	−	0.291020i
$665$		0			0
$666$	−18.9229	+	13.7483i	−0.733247	+	0.532735i
$667$	0.816860	+	2.51404i	0.0316289	+	0.0973439i
$668$	1.68469	−	5.18494i	0.0651825	−	0.200611i
$669$	12.6431	+	9.18573i	0.488809	+	0.355141i
$670$		0			0
$671$	−33.0949	−	11.0587i	−1.27761	−	0.426917i
$672$	−1.07433			−0.0414432
$673$	−14.6642	−	10.6541i	−0.565262	−	0.410687i	0.268119	−	0.963386i	$-0.413598\pi$
$673$	−14.6642	−	10.6541i	−0.565262	−	0.410687i	−0.833381	+	0.552699i	$0.813598\pi$
$674$	6.00704	−	18.4878i	0.231382	−	0.712122i
$675$		0			0
$676$	−2.06383	+	1.49946i	−0.0793781	+	0.0576716i
$677$	−14.2420	+	10.3474i	−0.547365	+	0.397684i	−0.826813	−	0.562477i	$-0.809849\pi$
$677$	−14.2420	+	10.3474i	−0.547365	+	0.397684i	0.279448	+	0.960161i	$0.409849\pi$
$678$	−6.53025	−	20.0980i	−0.250793	−	0.771861i
$679$	0.234035	−	0.720285i	0.00898143	−	0.0276420i
$680$		0			0
$681$	−35.1559			−1.34718
$682$	−20.3294	+	27.4966i	−0.778454	+	1.05290i
$683$	−37.4782			−1.43406			−0.717031	−	0.697041i	$-0.754500\pi$
$683$	−37.4782			−1.43406			−0.717031	+	0.697041i	$0.754500\pi$
$684$	15.7996	+	11.4791i	0.604112	+	0.438913i
$685$		0			0
$686$	−1.84380	−	5.67462i	−0.0703965	−	0.216658i
$687$	−7.82124	+	5.68247i	−0.298399	+	0.216800i
$688$	9.35346	−	6.79569i	0.356597	−	0.259083i
$689$	−6.39105	−	19.6696i	−0.243480	−	0.749354i
$690$		0			0
$691$	−9.75191	−	7.08518i	−0.370980	−	0.269533i	0.386637	−	0.922232i	$-0.373637\pi$
$691$	−9.75191	−	7.08518i	−0.370980	−	0.269533i	−0.757617	+	0.652699i	$0.773637\pi$
$692$	14.9633			0.568819
$693$	4.35260	−	1.37428i	0.165341	−	0.0522045i
$694$	−9.22874			−0.350318
$695$		0			0
$696$	0.487185	−	1.49940i	0.0184667	−	0.0568346i
$697$	−2.81025	−	8.64905i	−0.106446	−	0.327606i
$698$	−12.3669	+	8.98509i	−0.468095	+	0.340091i
$699$	−51.4717	+	37.3964i	−1.94684	+	1.41446i
$700$		0			0
$701$	−8.60170	+	26.4733i	−0.324882	+	0.999884i	0.646612	+	0.762819i	$0.276185\pi$
$701$	−8.60170	+	26.4733i	−0.324882	+	0.999884i	−0.971494	+	0.237065i	$0.923815\pi$
$702$	−1.47660	−	1.07281i	−0.0557308	−	0.0404908i
$703$	−44.9989			−1.69717
$704$	0.0276194	−	3.31651i	0.00104095	−	0.124996i
$705$		0			0
$706$	4.93962	+	3.58885i	0.185905	+	0.135068i
$707$	−0.164989	+	0.507783i	−0.00620504	+	0.0190971i
$708$	−8.34942	−	25.6969i	−0.313790	−	0.965748i
$709$	−22.1770	+	16.1125i	−0.832874	+	0.605119i	−0.920371	−	0.391046i	$-0.872113\pi$
$709$	−22.1770	+	16.1125i	−0.832874	+	0.605119i	0.0874968	+	0.996165i	$0.472113\pi$
$710$		0			0
$711$	−7.33150	−	22.5640i	−0.274953	−	0.846217i
$712$	0.414876	−	1.27686i	0.0155481	−	0.0478523i
$713$	34.7852	+	25.2729i	1.30272	+	0.946479i
$714$	3.67652			0.137590
$715$		0			0
$716$	12.1459			0.453914
$717$	−24.3046	−	17.6584i	−0.907674	−	0.659464i
$718$	−8.32545	+	25.6231i	−0.310703	+	0.956245i
$719$	−12.0166	−	36.9832i	−0.448142	−	1.37924i	−0.879001	−	0.476821i	$-0.841789\pi$
$719$	−12.0166	−	36.9832i	−0.448142	−	1.37924i	0.430858	−	0.902420i	$-0.358211\pi$
$720$		0			0
$721$	−0.940163	+	0.683068i	−0.0350135	+	0.0254388i
$722$	5.73894	+	17.6626i	0.213581	+	0.657336i
$723$	−18.1076	+	55.7295i	−0.673429	+	2.07260i
$724$	11.5274	+	8.37513i	0.428412	+	0.311259i
$725$		0			0
$726$	8.01988	+	26.1572i	0.297646	+	0.970784i
$727$	32.3326			1.19915			0.599575	−	0.800319i	$-0.295336\pi$
$727$	32.3326			1.19915			0.599575	+	0.800319i	$0.295336\pi$
$728$	1.37806	+	1.00122i	0.0510741	+	0.0371075i
$729$	−9.34444	+	28.7592i	−0.346090	+	1.06516i
$730$		0			0
$731$	−32.0090	+	23.2559i	−1.18390	+	0.860151i
$732$	21.1698	−	15.3807i	0.782457	−	0.568488i
$733$	3.39701	+	10.4549i	0.125472	+	0.386162i	0.993987	−	0.109501i	$-0.0349252\pi$
$733$	3.39701	+	10.4549i	0.125472	+	0.386162i	−0.868515	+	0.495663i	$0.834925\pi$
$734$	−7.72900	+	23.7874i	−0.285283	+	0.878010i
$735$		0			0
$736$	−4.17025			−0.153717
$737$	21.1951	+	29.6894i	0.780731	+	1.09362i
$738$	8.46681			0.311668
$739$	−15.0306	−	10.9204i	−0.552910	−	0.401713i	0.275947	−	0.961173i	$-0.411009\pi$
$739$	−15.0306	−	10.9204i	−0.552910	−	0.401713i	−0.828857	+	0.559460i	$0.811009\pi$
$740$		0			0
$741$	−18.5780	−	57.1773i	−0.682481	−	2.10046i
$742$	−1.83273	+	1.33155i	−0.0672815	+	0.0488829i
$743$	−16.4936	+	11.9833i	−0.605091	+	0.439624i	−0.847682	−	0.530504i	$-0.822003\pi$
$743$	−16.4936	+	11.9833i	−0.605091	+	0.439624i	0.242591	+	0.970129i	$0.422003\pi$
$744$	−7.92439	−	24.3888i	−0.290522	−	0.894135i
$745$		0			0
$746$	−22.2930	−	16.1968i	−0.816205	−	0.593007i
$747$	−25.1223			−0.919176
$748$	−0.0945179	+	11.3496i	−0.00345592	+	0.414983i
$749$	0.140575			0.00513651
$750$		0			0
$751$	12.9995	−	40.0084i	0.474359	−	1.45993i	−0.372462	−	0.928048i	$-0.621486\pi$
$751$	12.9995	−	40.0084i	0.474359	−	1.45993i	0.846820	−	0.531879i	$-0.178514\pi$
$752$	−0.917506	−	2.82379i	−0.0334580	−	0.102973i
$753$	−6.89669	+	5.01074i	−0.251329	+	0.182601i
$754$	−2.02228	+	1.46927i	−0.0736470	+	0.0535077i
$755$		0			0
$756$	−0.0617786	+	0.190135i	−0.00224687	+	0.00691515i
$757$	−1.27328	−	0.925095i	−0.0462783	−	0.0336232i	0.564406	−	0.825498i	$-0.309105\pi$
$757$	−1.27328	−	0.925095i	−0.0462783	−	0.0336232i	−0.610684	+	0.791874i	$0.709105\pi$
$758$	−23.4887			−0.853147
$759$	32.8043	−	10.3576i	1.19072	−	0.375955i
$760$		0			0
$761$	11.7245	+	8.51838i	0.425015	+	0.308791i	0.779652	−	0.626213i	$-0.215396\pi$
$761$	11.7245	+	8.51838i	0.425015	+	0.308791i	−0.354638	+	0.935004i	$0.615396\pi$
$762$	−6.63989	+	20.4355i	−0.240538	+	0.740299i
$763$	−1.34129	−	4.12806i	−0.0485578	−	0.149446i
$764$	0.893500	−	0.649166i	0.0323257	−	0.0234860i
$765$		0			0
$766$	5.78565	+	17.8064i	0.209044	+	0.643372i
$767$	−13.2382	+	40.7429i	−0.478003	+	1.47114i
$768$	2.01217	+	1.46193i	0.0726081	+	0.0527529i
$769$	50.5632			1.82335			0.911677	−	0.410907i	$-0.134788\pi$
$769$	50.5632			1.82335			0.911677	+	0.410907i	$0.134788\pi$
$770$		0			0
$771$	4.05360			0.145987
$772$	−8.85410	−	6.43288i	−0.318666	−	0.231524i
$773$	10.9064	−	33.5665i	0.392276	−	1.20730i	−0.538786	−	0.842443i	$-0.681117\pi$
$773$	10.9064	−	33.5665i	0.392276	−	1.20730i	0.931063	−	0.364860i	$-0.118883\pi$
$774$	−11.3830	−	35.0331i	−0.409152	−	1.25924i
$775$		0			0
$776$	−1.41849	+	1.03059i	−0.0509208	+	0.0369961i
$777$	−2.43720	−	7.50095i	−0.0874342	−	0.269095i
$778$	2.29210	−	7.05435i	0.0821757	−	0.252911i
$779$	13.1780	+	9.57438i	0.472151	+	0.343038i
$780$		0			0
$781$	32.2717	+	10.7836i	1.15477	+	0.385869i
$782$	14.2712			0.510338
$783$	−0.237349	−	0.172444i	−0.00848216	−	0.00616265i
$784$	−2.10546	+	6.47995i	−0.0751951	+	0.231427i
$785$		0			0
$786$	32.8684	−	23.8803i	1.17238	−	0.851781i
$787$	0.304466	−	0.221208i	0.0108530	−	0.00788520i	−0.582346	−	0.812941i	$-0.697865\pi$
$787$	0.304466	−	0.221208i	0.0108530	−	0.00788520i	0.593199	+	0.805056i	$0.297865\pi$
$788$	4.96195	+	15.2713i	0.176762	+	0.544018i
$789$	−1.26946	+	3.90698i	−0.0451938	+	0.139092i
$790$		0			0
$791$	3.67002			0.130491
$792$	−10.0223	−	3.34898i	−0.356128	−	0.119001i
$793$	−41.4887			−1.47331
$794$	−18.3160	−	13.3074i	−0.650011	−	0.472260i
$795$		0			0
$796$	8.39047	+	25.8232i	0.297393	+	0.915280i
$797$	−17.2167	+	12.5086i	−0.609845	+	0.443079i	−0.849360	−	0.527814i	$-0.823012\pi$
$797$	−17.2167	+	12.5086i	−0.609845	+	0.443079i	0.239514	+	0.970893i	$0.423012\pi$
$798$	−5.32752	+	3.87067i	−0.188592	+	0.137020i
$799$	3.13985	+	9.66346i	0.111080	+	0.341869i
$800$		0			0
$801$	−3.46060	−	2.51427i	−0.122274	−	0.0888375i
$802$	26.9832			0.952809
$803$	−21.9614	+	29.7039i	−0.775001	+	1.04823i
$804$	−27.3558			−0.964766
$805$		0			0
$806$	−12.5643	+	38.6689i	−0.442558	+	1.36205i
$807$	−17.0361	−	52.4319i	−0.599701	−	1.84569i
$808$	1.00000	−	0.726543i	0.0351799	−	0.0255597i
$809$	10.5822	−	7.68843i	0.372051	−	0.270311i	−0.386010	−	0.922495i	$-0.626147\pi$
$809$	10.5822	−	7.68843i	0.372051	−	0.270311i	0.758061	+	0.652184i	$0.226147\pi$
$810$		0			0
$811$	12.6338	−	38.8829i	0.443634	−	1.36536i	−0.440342	−	0.897830i	$-0.645143\pi$
$811$	12.6338	−	38.8829i	0.443634	−	1.36536i	0.883975	−	0.467533i	$-0.154857\pi$
$812$	0.221508	+	0.160935i	0.00777342	+	0.00564772i
$813$	18.2722			0.640835
$814$	23.2185	−	7.33094i	0.813807	−	0.256949i
$815$		0			0
$816$	−6.88598	−	5.00295i	−0.241057	−	0.175138i
$817$	21.8991	−	67.3986i	0.766154	−	2.35798i
$818$	−2.88711	−	8.88560i	−0.100945	−	0.310678i
$819$	4.39061	−	3.18996i	0.153420	−	0.111466i
$820$		0			0
$821$	8.77898	+	27.0189i	0.306389	+	0.942967i	0.979155	+	0.203112i	$0.0651057\pi$
$821$	8.77898	+	27.0189i	0.306389	+	0.942967i	−0.672767	+	0.739855i	$0.734894\pi$
$822$	13.1115	−	40.3529i	0.457315	−	1.40747i
$823$	−9.60724	−	6.98007i	−0.334887	−	0.243310i	0.407614	−	0.913154i	$-0.366361\pi$
$823$	−9.60724	−	6.98007i	−0.334887	−	0.243310i	−0.742502	+	0.669844i	$0.766361\pi$
$824$	2.69039			0.0937243
$825$		0			0
$826$	4.69240			0.163270
$827$	−45.5209	−	33.0728i	−1.58292	−	1.15006i	−0.913256	−	0.407387i	$-0.866440\pi$
$827$	−45.5209	−	33.0728i	−1.58292	−	1.15006i	−0.669659	−	0.742668i	$-0.733560\pi$
$828$	−4.10584	+	12.6365i	−0.142688	+	0.439148i
$829$	4.24409	+	13.0620i	0.147403	+	0.453661i	0.997312	−	0.0732690i	$-0.0233432\pi$
$829$	4.24409	+	13.0620i	0.147403	+	0.453661i	−0.849909	+	0.526930i	$0.823343\pi$
$830$		0			0
$831$	31.2225	−	22.6845i	1.08310	−	0.786916i
$832$	−1.21860	−	3.75047i	−0.0422474	−	0.130024i
$833$	7.20522	−	22.1754i	0.249646	−	0.768332i
$834$	11.3070	+	8.21505i	0.391531	+	0.284464i
$835$		0			0
$836$	−11.8120	−	16.5458i	−0.408526	−	0.572250i
$837$	−4.77202			−0.164945
$838$	−13.3979	−	9.73415i	−0.462823	−	0.336261i
$839$	−9.95199	+	30.6291i	−0.343581	+	1.05743i	0.618758	+	0.785581i	$0.287636\pi$
$839$	−9.95199	+	30.6291i	−0.343581	+	1.05743i	−0.962339	+	0.271852i	$0.912364\pi$
$840$		0			0
$841$	23.1364	−	16.8096i	0.797808	−	0.579641i
$842$	−1.52132	+	1.10531i	−0.0524283	+	0.0380914i
$843$	17.6079	+	54.1917i	0.606450	+	1.86646i
$844$	0.818562	−	2.51928i	0.0281761	−	0.0867170i
$845$		0			0
$846$	−9.45985			−0.325236
$847$	−4.75075	−	0.0791325i	−0.163238	−	0.00271902i
$848$	5.24458			0.180100
$849$	5.63834	+	4.09649i	0.193507	+	0.140591i
$850$		0			0
$851$	−9.46055	−	29.1166i	−0.324303	−	0.998103i
$852$	−20.6432	+	14.9981i	−0.707224	+	0.513828i
$853$	25.6606	−	18.6435i	0.878604	−	0.638343i	−0.0542781	−	0.998526i	$-0.517286\pi$
$853$	25.6606	−	18.6435i	0.878604	−	0.638343i	0.932882	+	0.360183i	$0.117286\pi$
$854$	1.40431	+	4.32201i	0.0480544	+	0.147896i
$855$		0			0
$856$	−0.263292	−	0.191292i	−0.00899912	−	0.00653824i
$857$	−25.5670			−0.873353			−0.436677	−	0.899619i	$-0.643845\pi$
$857$	−25.5670			−0.873353			−0.436677	+	0.899619i	$0.643845\pi$
$858$	18.9008	+	26.4756i	0.645264	+	0.903863i
$859$	35.0484			1.19584			0.597919	−	0.801557i	$-0.295995\pi$
$859$	35.0484			1.19584			0.597919	+	0.801557i	$0.295995\pi$
$860$		0			0
$861$	−0.882230	+	2.71523i	−0.0300663	+	0.0925347i
$862$	7.29456	+	22.4503i	0.248454	+	0.764662i
$863$	17.5376	−	12.7418i	0.596986	−	0.433736i	−0.247822	−	0.968806i	$-0.579715\pi$
$863$	17.5376	−	12.7418i	0.596986	−	0.433736i	0.844808	+	0.535070i	$0.179715\pi$
$864$	0.374442	−	0.272048i	0.0127388	−	0.00925525i
$865$		0			0
$866$	4.90556	−	15.0977i	0.166698	−	0.513042i
$867$	−10.6421	−	7.73193i	−0.361424	−	0.262590i
$868$	4.45353			0.151163
$869$	−0.205668	+	24.6964i	−0.00697681	+	0.837768i
$870$		0			0
$871$	35.0897	+	25.4941i	1.18897	+	0.863836i
$872$	−3.10522	+	9.55688i	−0.105156	+	0.323637i
$873$	1.72627	+	5.31291i	0.0584254	+	0.179815i
$874$	−20.6799	+	15.0249i	−0.699510	+	0.508223i
$875$		0			0
$876$	−8.56053	−	26.3466i	−0.289233	−	0.890169i
$877$	−8.01263	+	24.6603i	−0.270567	+	0.832721i	0.719791	+	0.694191i	$0.244238\pi$
$877$	−8.01263	+	24.6603i	−0.270567	+	0.832721i	−0.990358	+	0.138530i	$0.955762\pi$
$878$	9.39127	+	6.82315i	0.316940	+	0.230270i
$879$	−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	$0.795548\pi$
$882$	17.5623	+	12.7597i	0.591353	+	0.429643i
$883$	−6.75830	+	20.7999i	−0.227435	+	0.699973i	0.770600	+	0.637319i	$0.219957\pi$
$883$	−6.75830	+	20.7999i	−0.227435	+	0.699973i	−0.998035	+	0.0626542i	$0.980043\pi$
$884$	4.17025	+	12.8347i	0.140261	+	0.431678i
$885$		0			0
$886$	7.72038	−	5.60918i	0.259371	−	0.188444i
$887$	−2.14278	−	6.59480i	−0.0719475	−	0.221432i	0.908616	−	0.417632i	$-0.137140\pi$
$887$	−2.14278	−	6.59480i	−0.0719475	−	0.221432i	−0.980564	+	0.196200i	$0.937140\pi$
$888$	−5.64238	+	17.3655i	−0.189346	+	0.582747i
$889$	−3.01896	−	2.19340i	−0.101253	−	0.0735644i
$890$		0			0
$891$	16.5766	−	22.4207i	0.555338	−	0.751123i
$892$	6.28329			0.210380
$893$	−14.7236	−	10.6973i	−0.492706	−	0.357972i
$894$	−7.60900	+	23.4181i	−0.254483	+	0.783218i
$895$		0			0
$896$	−0.349452	+	0.253891i	−0.0116744	+	0.00848192i
$897$	33.0908	−	24.0419i	1.10487	−	0.802735i
$898$	6.13346	+	18.8768i	0.204676	+	0.629928i
$899$	−2.01958	+	6.21563i	−0.0673568	+	0.207303i
$900$		0			0
$901$	−17.9478			−0.597927
$902$	−8.35936	−	2.79329i	−0.278336	−	0.0930065i
$903$	12.4209			0.413341
$904$	−6.87380	−	4.99411i	−0.228619	−	0.166102i
$905$		0			0
$906$	8.82193	+	27.1511i	0.293089	+	0.902035i
$907$	−34.2462	+	24.8813i	−1.13713	+	0.826170i	−0.986716	−	0.162454i	$-0.948059\pi$
$907$	−34.2462	+	24.8813i	−1.13713	+	0.826170i	−0.150409	+	0.988624i	$0.548059\pi$
$908$	−11.4353	+	8.30824i	−0.379494	+	0.275719i
$909$	−1.21698	−	3.74547i	−0.0403646	−	0.124229i
$910$		0			0
$911$	7.64031	+	5.55101i	0.253135	+	0.183913i	0.707115	−	0.707099i	$-0.249996\pi$
$911$	7.64031	+	5.55101i	0.253135	+	0.183913i	−0.453980	+	0.891012i	$0.649996\pi$
$912$	15.2454			0.504825
$913$	24.8034	+	8.28812i	0.820874	+	0.274297i
$914$	−4.20591			−0.139119
$915$		0			0
$916$	−1.20114	+	3.69672i	−0.0396867	+	0.122143i
$917$	2.18034	+	6.71040i	0.0720012	+	0.221597i
$918$	−1.28140	+	0.930990i	−0.0422924	+	0.0307272i
$919$	14.1560	−	10.2849i	0.466963	−	0.339269i	−0.329294	−	0.944228i	$-0.606811\pi$
$919$	14.1560	−	10.2849i	0.466963	−	0.339269i	0.796257	+	0.604959i	$0.206811\pi$
$920$		0			0
$921$	−2.24514	+	6.90982i	−0.0739798	+	0.227686i
$922$	−7.64366	−	5.55345i	−0.251731	−	0.182893i
$923$	40.4567			1.33165
$924$	2.11830	−	2.86511i	0.0696869	−	0.0942551i
$925$		0			0
$926$	−21.5100	−	15.6280i	−0.706864	−	0.513567i
$927$	2.64884	−	8.15230i	0.0869994	−	0.267757i
$928$	−0.195878	−	0.602850i	−0.00643001	−	0.0197895i
$929$	−15.9892	+	11.6168i	−0.524587	+	0.381135i	−0.818329	−	0.574750i	$-0.805099\pi$
$929$	−15.9892	+	11.6168i	−0.524587	+	0.381135i	0.293742	+	0.955885i	$0.405099\pi$
$930$		0			0
$931$	12.9056	+	39.7193i	0.422963	+	1.30175i
$932$	−7.90469	+	24.3281i	−0.258927	+	0.796895i
$933$	−7.70209	−	5.59590i	−0.252155	−	0.183201i
$934$	−18.2290			−0.596472
$935$		0			0
$936$	−12.5643			−0.410676
$937$	23.0660	+	16.7584i	0.753533	+	0.547474i	0.896920	−	0.442193i	$-0.145799\pi$
$937$	23.0660	+	16.7584i	0.753533	+	0.547474i	−0.143387	+	0.989667i	$0.545799\pi$
$938$	1.46809	−	4.51833i	0.0479350	−	0.147529i
$939$	−20.9730	−	64.5484i	−0.684429	−	2.10646i
$940$		0			0
$941$	24.5781	−	17.8571i	0.801225	−	0.582124i	−0.110048	−	0.993926i	$-0.535101\pi$
$941$	24.5781	−	17.8571i	0.801225	−	0.582124i	0.911273	+	0.411802i	$0.135101\pi$
$942$	−5.80859	−	17.8770i	−0.189254	−	0.582464i
$943$	−3.42457	+	10.5398i	−0.111519	+	0.343222i
$944$	−8.78868	−	6.38535i	−0.286047	−	0.207825i
$945$		0			0
$946$	−0.319322	+	38.3439i	−0.0103821	+	1.24667i
$947$	−2.37805			−0.0772763			−0.0386382	−	0.999253i	$-0.512302\pi$
$947$	−2.37805			−0.0772763			−0.0386382	+	0.999253i	$0.512302\pi$
$948$	−14.9837	−	10.8863i	−0.486647	−	0.353570i
$949$	−13.5729	+	41.7731i	−0.440595	+	1.35601i
$950$		0			0
$951$	57.8604	−	42.0380i	1.87625	−	1.36318i
$952$	1.19588	−	0.868856i	0.0387586	−	0.0281598i
$953$	13.7214	+	42.2300i	0.444479	+	1.36796i	0.883055	+	0.469270i	$0.155483\pi$
$953$	13.7214	+	42.2300i	0.444479	+	1.36796i	−0.438576	+	0.898694i	$0.644517\pi$
$954$	5.16358	−	15.8919i	0.167177	−	0.514518i
$955$		0			0
$956$	−12.0788			−0.390656
$957$	3.03812	+	4.25569i	0.0982084	+	0.137567i
$958$	−13.0061			−0.420206
$959$	5.96139	+	4.33121i	0.192503	+	0.139862i
$960$		0			0
$961$	23.2703	+	71.6186i	0.750655	+	2.31028i
$962$	23.4212	−	17.0165i	0.755130	−	0.548634i
$963$	−0.838870	+	0.609475i	−0.0270322	+	0.0196400i
$964$	7.28036	+	22.4066i	0.234485	+	0.721670i
$965$		0			0
$966$	−3.62457	−	2.63341i	−0.116619	−	0.0847285i
$967$	−11.4834			−0.369283			−0.184641	−	0.982806i	$-0.559112\pi$
$967$	−11.4834			−0.369283			−0.184641	+	0.982806i	$0.559112\pi$
$968$	8.79027	+	6.61295i	0.282530	+	0.212548i
$969$	−52.1720			−1.67601
$970$		0			0
$971$	−1.38789	+	4.27147i	−0.0445394	+	0.137078i	−0.970853	−	0.239674i	$-0.922959\pi$
$971$	−1.38789	+	4.27147i	−0.0445394	+	0.137078i	0.926314	+	0.376753i	$0.122959\pi$
$972$	6.89063	+	21.2072i	0.221017	+	0.680220i
$973$	−1.96368	+	1.42670i	−0.0629527	+	0.0457378i
$974$	−6.23479	+	4.52984i	−0.199775	+	0.145145i
$975$		0			0
$976$	3.25112	−	10.0059i	0.104066	−	0.320281i
$977$	5.74228	+	4.17201i	0.183712	+	0.133474i	0.675840	−	0.737048i	$-0.263781\pi$
$977$	5.74228	+	4.17201i	0.183712	+	0.133474i	−0.492128	+	0.870523i	$0.663781\pi$
$978$	−7.83448			−0.250519
$979$	2.58720	+	3.62406i	0.0826872	+	0.115825i
$980$		0			0
$981$	25.9015	+	18.8186i	0.826972	+	0.600830i
$982$	4.16722	−	12.8254i	0.132981	−	0.409275i
$983$	−17.1375	−	52.7437i	−0.546600	−	1.68226i	−0.717155	−	0.696914i	$-0.754556\pi$
$983$	−17.1375	−	52.7437i	−0.546600	−	1.68226i	0.170555	−	0.985348i	$-0.445444\pi$
$984$	5.34722	−	3.88498i	0.170463	−	0.123849i
$985$		0			0
$986$	0.670325	+	2.06305i	0.0213475	+	0.0657008i
$987$	0.985703	−	3.03368i	0.0313753	−	0.0965632i
$988$	−19.5554	−	14.2078i	−0.622141	−	0.452012i
$989$	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	$0.493729\pi$
$992$	−8.34129	−	6.06030i	−0.264836	−	0.192415i
$993$	11.7563	−	36.1823i	0.373076	−	1.14821i
$994$	−1.36938	−	4.21450i	−0.0434340	−	0.133676i
$995$		0			0
$996$	−15.8660	+	11.5273i	−0.502733	+	0.365257i
$997$	10.2928	+	31.6781i	0.325977	+	1.00325i	0.970998	+	0.239089i	$0.0768488\pi$
$997$	10.2928	+	31.6781i	0.325977	+	1.00325i	−0.645021	+	0.764165i	$0.723151\pi$
$998$	4.25919	−	13.1084i	0.134822	−	0.414940i
$999$	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.h.l.301.1		8
5.2	odd	4		550.2.ba.f.499.4		16
5.3	odd	4		550.2.ba.f.499.1		16
5.4	even	2		110.2.g.c.81.2	✓	8
11.3	even	5	inner	550.2.h.l.201.1		8
11.5	even	5		6050.2.a.dh.1.2		4
11.6	odd	10		6050.2.a.cy.1.2		4
15.14	odd	2		990.2.n.j.631.2		8
20.19	odd	2		880.2.bo.g.81.1		8
55.3	odd	20		550.2.ba.f.399.4		16
55.14	even	10		110.2.g.c.91.2	yes	8
55.39	odd	10		1210.2.a.v.1.3		4
55.47	odd	20		550.2.ba.f.399.1		16
55.49	even	10		1210.2.a.u.1.3		4
165.14	odd	10		990.2.n.j.91.2		8
220.39	even	10		9680.2.a.ci.1.2		4
220.159	odd	10		9680.2.a.cj.1.2		4
220.179	odd	10		880.2.bo.g.641.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.c.81.2	✓	8	5.4	even	2
110.2.g.c.91.2	yes	8	55.14	even	10
550.2.h.l.201.1		8	11.3	even	5	inner
550.2.h.l.301.1		8	1.1	even	1	trivial
550.2.ba.f.399.1		16	55.47	odd	20
550.2.ba.f.399.4		16	55.3	odd	20
550.2.ba.f.499.1		16	5.3	odd	4
550.2.ba.f.499.4		16	5.2	odd	4
880.2.bo.g.81.1		8	20.19	odd	2
880.2.bo.g.641.1		8	220.179	odd	10
990.2.n.j.91.2		8	165.14	odd	10
990.2.n.j.631.2		8	15.14	odd	2
1210.2.a.u.1.3		4	55.49	even	10
1210.2.a.v.1.3		4	55.39	odd	10
6050.2.a.cy.1.2		4	11.6	odd	10
6050.2.a.dh.1.2		4	11.5	even	5
9680.2.a.ci.1.2		4	220.39	even	10
9680.2.a.cj.1.2		4	220.159	odd	10

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.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.768582 + 2.36545i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.01217 - 1.46193i) q^{6} +(0.133479 + 0.410805i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.57760 - 1.87274i) q^{9} +(1.92705 + 2.69935i) q^{11} -2.48718 q^{12} +(3.19034 + 2.31792i) q^{13} +(0.133479 - 0.410805i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(2.76858 - 2.01149i) q^{17} +(0.984555 + 3.03015i) q^{18} +(-1.89414 + 5.82957i) q^{19} -1.07433 q^{21} +(0.0276194 - 3.31651i) q^{22} -4.17025 q^{23} +(2.01217 + 1.46193i) q^{24} +(-1.21860 - 3.75047i) q^{26} +(0.374442 - 0.272048i) q^{27} +(-0.349452 + 0.253891i) q^{28} +(-0.195878 - 0.602850i) q^{29} +(-8.34129 - 6.06030i) q^{31} +1.00000 q^{32} +(-7.86628 + 2.48368i) q^{33} -3.42216 q^{34} +(0.984555 - 3.03015i) q^{36} +(2.26858 + 6.98198i) q^{37} +(4.95892 - 3.60287i) q^{38} +(-7.93497 + 5.76509i) q^{39} +(0.821192 - 2.52737i) q^{41} +(0.869151 + 0.631475i) q^{42} -11.5615 q^{43} +(-1.97174 + 2.66688i) q^{44} +(3.37380 + 2.45121i) q^{46} +(-0.917506 + 2.82379i) q^{47} +(-0.768582 - 2.36545i) q^{48} +(5.51217 - 4.00483i) q^{49} +(2.63021 + 8.09495i) q^{51} +(-1.21860 + 3.75047i) q^{52} +(-4.24295 - 3.08268i) q^{53} -0.462835 q^{54} +0.431946 q^{56} +(-12.3338 - 8.96100i) q^{57} +(-0.195878 + 0.602850i) q^{58} +(3.35698 + 10.3317i) q^{59} +(-8.51153 + 6.18399i) q^{61} +(3.18609 + 9.80577i) q^{62} +(0.425275 - 1.30886i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(7.82382 + 2.61434i) q^{66} +10.9987 q^{67} +(2.76858 + 2.01149i) q^{68} +(3.20518 - 9.86453i) q^{69} +(8.29982 - 6.03017i) q^{71} +(-2.57760 + 1.87274i) q^{72} +(3.44186 + 10.5929i) q^{73} +(2.26858 - 6.98198i) q^{74} -6.12957 q^{76} +(-0.851685 + 1.15195i) q^{77} +9.80816 q^{78} +(6.02435 + 4.37695i) q^{79} +(-2.59794 - 7.99563i) q^{81} +(-2.14991 + 1.56200i) q^{82} +(6.37909 - 4.63468i) q^{83} +(-0.331986 - 1.02175i) q^{84} +(9.35346 + 6.79569i) q^{86} +1.57656 q^{87} +(3.16272 - 0.998590i) q^{88} +1.34257 q^{89} +(-0.526370 + 1.62000i) q^{91} +(-1.28868 - 3.96614i) q^{92} +(20.7463 - 15.0731i) q^{93} +(2.40206 - 1.74520i) q^{94} +(-0.768582 + 2.36545i) q^{96} +(-1.41849 - 1.03059i) q^{97} -6.81342 q^{98} +(0.0879978 - 10.5667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - q^{6} + q^{7} - 2 q^{8} - 6 q^{9} + 2 q^{11} - 6 q^{12} - q^{13} + q^{14} - 2 q^{16} + 12 q^{17} - q^{18} - 7 q^{19} + 32 q^{21} - 8 q^{22} - 26 q^{23} - q^{24}+ \cdots + 36 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - q^6 + q^7 - 2 * q^8 - 6 * q^9 + 2 * q^11 - 6 * q^12 - q^13 + q^14 - 2 * q^16 + 12 * q^17 - q^18 - 7 * q^19 + 32 * q^21 - 8 * q^22 - 26 * q^23 - q^24 - 6 * q^26 + q^27 - 4 * q^28 - 22 * q^29 - 26 * q^31 + 8 * q^32 - 19 * q^33 + 2 * q^34 - q^36 + 8 * q^37 + 3 * q^38 - 48 * q^39 - 15 * q^41 + 2 * q^42 - 38 * q^43 + 7 * q^44 - 6 * q^46 - 6 * q^47 + 4 * q^48 + 27 * q^49 - 5 * q^51 - 6 * q^52 + 4 * q^53 - 24 * q^54 + 6 * q^56 - 47 * q^57 - 22 * q^58 + 39 * q^59 - 20 * q^61 + 14 * q^62 + 57 * q^63 - 2 * q^64 + 36 * q^66 + 26 * q^67 + 12 * q^68 - 10 * q^69 + 2 * q^71 - 6 * q^72 - 8 * q^73 + 8 * q^74 + 8 * q^76 - 16 * q^77 + 12 * q^78 + 14 * q^79 - 31 * q^81 + 15 * q^82 + 21 * q^83 - 18 * q^84 + 17 * q^86 - 20 * q^87 + 7 * q^88 + 32 * q^89 + 53 * q^91 + 19 * q^92 + 38 * q^93 + 9 * q^94 + 4 * q^96 + 31 * q^97 + 22 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more