LMFDB - Embedded newform 114.2.l.a.29.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [114,2,Mod(29,114)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("114.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(114, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.l (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.1
Root			$-1.72388 + 0.168030i$ of defining polynomial
Character	$\chi$	$=$	114.29
Dual form			114.2.l.a.59.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.716422 + 1.57694i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.14133 + 3.13578i) q^{5} +(1.67739 + 0.431705i) q^{6} +(-1.07356 + 1.85947i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.97348 - 2.25951i) q^{9} +(3.28633 + 0.579469i) q^{10} +(5.41799 - 3.12808i) q^{11} +(0.133871 - 1.72687i) q^{12} +(-2.56208 + 3.05336i) q^{13} +(2.01764 + 0.734361i) q^{14} +(-4.12726 - 4.04635i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.403611 - 0.0711674i) q^{17} +(-1.88249 + 2.33586i) q^{18} +(4.34640 + 0.329887i) q^{19} -3.33703i q^{20} +(-2.16314 - 3.02511i) q^{21} +(-4.02138 - 4.79249i) q^{22} +(0.280411 + 0.770422i) q^{23} +(-1.72388 + 0.168030i) q^{24} +(-4.70025 - 3.94398i) q^{25} +(3.45187 + 1.99294i) q^{26} +(4.97695 - 1.49330i) q^{27} +(0.372845 - 2.11451i) q^{28} +(-0.805141 + 4.56618i) q^{29} +(-3.26819 + 4.76720i) q^{30} +(-2.02597 - 1.16970i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(1.05122 + 10.7849i) q^{33} +(-0.140172 - 0.385121i) q^{34} +(-4.60559 - 5.48872i) q^{35} +(2.62726 + 1.44827i) q^{36} -6.01346i q^{37} +(-0.429869 - 4.33765i) q^{38} +(-2.97944 - 6.22774i) q^{39} +(-3.28633 + 0.579469i) q^{40} +(-0.926617 + 0.777524i) q^{41} +(-2.60352 + 2.65558i) q^{42} +(5.87377 + 2.13788i) q^{43} +(-4.02138 + 4.79249i) q^{44} +(9.33771 - 3.60955i) q^{45} +(0.710025 - 0.409933i) q^{46} +(7.59919 + 1.33994i) q^{47} +(0.464826 + 1.66851i) q^{48} +(1.19492 + 2.06967i) q^{49} +(-3.06787 + 5.31371i) q^{50} +(-0.176929 + 0.687455i) q^{51} +(1.36325 - 3.74550i) q^{52} +(0.220516 - 0.0802612i) q^{53} +(-2.33485 - 4.64203i) q^{54} +(3.62525 + 20.5598i) q^{55} -2.14713 q^{56} +(-3.63407 + 6.61767i) q^{57} +4.63662 q^{58} +(-0.930375 - 5.27642i) q^{59} +(5.26229 + 2.39072i) q^{60} +(7.30705 - 2.65955i) q^{61} +(-0.800119 + 2.19831i) q^{62} +(6.32014 - 1.24389i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-6.65050 - 11.5190i) q^{65} +(10.4385 - 2.90803i) q^{66} +(3.48689 + 0.614832i) q^{67} +(-0.354929 + 0.204918i) q^{68} +(-1.41580 - 0.109756i) q^{69} +(-4.60559 + 5.48872i) q^{70} +(-4.19799 - 1.52794i) q^{71} +(0.970052 - 2.83884i) q^{72} +(-4.33185 + 3.63485i) q^{73} +(-5.92210 + 1.04423i) q^{74} +(9.58679 - 4.58646i) q^{75} +(-4.19711 + 1.17656i) q^{76} +13.4328i q^{77} +(-5.61575 + 4.01561i) q^{78} +(-8.05412 - 9.59853i) q^{79} +(1.14133 + 3.13578i) q^{80} +(-1.21076 + 8.91819i) q^{81} +(0.926617 + 0.777524i) q^{82} +(-8.01579 - 4.62792i) q^{83} +(3.06734 + 2.10283i) q^{84} +(-0.237488 + 1.34686i) q^{85} +(1.08543 - 6.15577i) q^{86} +(-6.62378 - 4.54097i) q^{87} +(5.41799 + 3.12808i) q^{88} +(5.61888 + 4.71480i) q^{89} +(-5.17619 - 8.56906i) q^{90} +(-2.92708 - 8.04207i) q^{91} +(-0.527000 - 0.628054i) q^{92} +(3.29599 - 2.35684i) q^{93} -7.71642i q^{94} +(-5.99513 + 13.2528i) q^{95} +(1.56245 - 0.747499i) q^{96} +(-16.0734 + 2.83418i) q^{97} +(1.83073 - 1.53616i) q^{98} +(-17.7602 - 6.06880i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38}+ \cdots - 30 q^{99}+O(q^{100}) $ 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	−0.716422	+	1.57694i	−0.413626	+	0.910447i
$3$	−0.716422	+	1.57694i	−0.413626	+	0.910447i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−1.14133	+	3.13578i	−0.510418	+	1.40236i	0.370384	+	0.928879i	$0.379226\pi$
$5$	−1.14133	+	3.13578i	−0.510418	+	1.40236i	−0.880802	+	0.473484i	$0.842996\pi$
$6$	1.67739	+	0.431705i	0.684791	+	0.176243i
$7$	−1.07356	+	1.85947i	−0.405769	+	0.702812i	−0.994411	−	0.105582i	$-0.966330\pi$
$7$	−1.07356	+	1.85947i	−0.405769	+	0.702812i	0.588642	+	0.808394i	$0.299663\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.97348	−	2.25951i	−0.657826	−	0.753170i
$10$	3.28633	+	0.579469i	1.03923	+	0.183244i
$11$	5.41799	−	3.12808i	1.63359	−	0.943151i	0.650611	−	0.759412i	$-0.274513\pi$
$11$	5.41799	−	3.12808i	1.63359	−	0.943151i	0.982975	−	0.183740i	$-0.0588203\pi$
$12$	0.133871	−	1.72687i	0.0386453	−	0.498504i
$13$	−2.56208	+	3.05336i	−0.710592	+	0.846850i	−0.993681	−	0.112243i	$-0.964196\pi$
$13$	−2.56208	+	3.05336i	−0.710592	+	0.846850i	0.283089	+	0.959094i	$0.408641\pi$
$14$	2.01764	+	0.734361i	0.539237	+	0.196266i
$15$	−4.12726	−	4.04635i	−1.06565	−	1.04476i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.403611	−	0.0711674i	0.0978899	−	0.0172606i	−0.124489	−	0.992221i	$-0.539729\pi$
$17$	0.403611	−	0.0711674i	0.0978899	−	0.0172606i	0.222379	+	0.974960i	$0.428618\pi$
$18$	−1.88249	+	2.33586i	−0.443707	+	0.550567i
$19$	4.34640	+	0.329887i	0.997132	+	0.0756812i
$19$	4.34640	+	0.329887i	0.997132	+	0.0756812i
$20$		−	3.33703i		−	0.746182i
$21$	−2.16314	−	3.02511i	−0.472037	−	0.660133i
$22$	−4.02138	−	4.79249i	−0.857361	−	1.02176i
$23$	0.280411	+	0.770422i	0.0584697	+	0.160644i	0.965488	−	0.260446i	$-0.0838697\pi$
$23$	0.280411	+	0.770422i	0.0584697	+	0.160644i	−0.907019	+	0.421090i	$0.861647\pi$
$24$	−1.72388	+	0.168030i	−0.351886	+	0.0342991i
$25$	−4.70025	−	3.94398i	−0.940051	−	0.788796i
$26$	3.45187	+	1.99294i	0.676968	+	0.390848i
$27$	4.97695	−	1.49330i	0.957815	−	0.287385i
$28$	0.372845	−	2.11451i	0.0704610	−	0.399604i
$29$	−0.805141	+	4.56618i	−0.149511	+	0.847919i	0.814123	+	0.580693i	$0.197218\pi$
$29$	−0.805141	+	4.56618i	−0.149511	+	0.847919i	−0.963634	+	0.267226i	$0.913893\pi$
$30$	−3.26819	+	4.76720i	−0.596686	+	0.870368i
$31$	−2.02597	−	1.16970i	−0.363875	−	0.210084i	0.306904	−	0.951740i	$-0.400707\pi$
$31$	−2.02597	−	1.16970i	−0.363875	−	0.210084i	−0.670779	+	0.741657i	$0.734040\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	1.05122	+	10.7849i	0.182995	+	1.87740i
$34$	−0.140172	−	0.385121i	−0.0240394	−	0.0660477i
$35$	−4.60559	−	5.48872i	−0.778486	−	0.927764i
$36$	2.62726	+	1.44827i	0.437877	+	0.241379i
$37$		−	6.01346i		−	0.988607i	−0.869289	−	0.494303i	$-0.835423\pi$
$37$		−	6.01346i		−	0.988607i	0.869289	−	0.494303i	$-0.164577\pi$
$38$	−0.429869	−	4.33765i	−0.0697340	−	0.703660i
$39$	−2.97944	−	6.22774i	−0.477093	−	0.997236i
$40$	−3.28633	+	0.579469i	−0.519614	+	0.0916220i
$41$	−0.926617	+	0.777524i	−0.144713	+	0.121429i	−0.712270	−	0.701905i	$-0.752333\pi$
$41$	−0.926617	+	0.777524i	−0.144713	+	0.121429i	0.567557	+	0.823334i	$0.307889\pi$
$42$	−2.60352	+	2.65558i	−0.401733	+	0.409766i
$43$	5.87377	+	2.13788i	0.895741	+	0.326023i	0.748545	−	0.663084i	$-0.230753\pi$
$43$	5.87377	+	2.13788i	0.895741	+	0.326023i	0.147196	+	0.989107i	$0.452975\pi$
$44$	−4.02138	+	4.79249i	−0.606246	+	0.722496i
$45$	9.33771	−	3.60955i	1.39198	−	0.538080i
$46$	0.710025	−	0.409933i	0.104687	−	0.0604413i
$47$	7.59919	+	1.33994i	1.10846	+	0.195451i	0.697767	−	0.716325i	$-0.254177\pi$
$47$	7.59919	+	1.33994i	1.10846	+	0.195451i	0.410689	+	0.911776i	$0.365288\pi$
$48$	0.464826	+	1.66851i	0.0670919	+	0.240829i
$49$	1.19492	+	2.06967i	0.170703	+	0.295666i
$50$	−3.06787	+	5.31371i	−0.433863	+	0.751472i
$51$	−0.176929	+	0.687455i	−0.0247750	+	0.0962630i
$52$	1.36325	−	3.74550i	0.189049	−	0.519408i
$53$	0.220516	−	0.0802612i	0.0302902	−	0.0110247i	−0.326831	−	0.945083i	$-0.605981\pi$
$53$	0.220516	−	0.0802612i	0.0302902	−	0.0110247i	0.357121	+	0.934058i	$0.383758\pi$
$54$	−2.33485	−	4.64203i	−0.317733	−	0.631701i
$55$	3.62525	+	20.5598i	0.488828	+	2.77228i
$56$	−2.14713			−0.286922
$57$	−3.63407	+	6.61767i	−0.481344	+	0.876532i
$58$	4.63662			0.608819
$59$	−0.930375	−	5.27642i	−0.121124	−	0.686931i	−0.983534	−	0.180721i	$-0.942157\pi$
$59$	−0.930375	−	5.27642i	−0.121124	−	0.686931i	0.862410	−	0.506210i	$-0.168954\pi$
$60$	5.26229	+	2.39072i	0.679359	+	0.308640i
$61$	7.30705	−	2.65955i	0.935572	−	0.340520i	0.171156	−	0.985244i	$-0.445250\pi$
$61$	7.30705	−	2.65955i	0.935572	−	0.340520i	0.764416	+	0.644723i	$0.223027\pi$
$62$	−0.800119	+	2.19831i	−0.101615	+	0.279186i
$63$	6.32014	−	1.24389i	0.796262	−	0.156716i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−6.65050	−	11.5190i	−0.824893	−	1.42876i
$66$	10.4385	−	2.90803i	1.28489	−	0.357953i
$67$	3.48689	+	0.614832i	0.425991	+	0.0751137i	0.382534	−	0.923942i	$-0.375052\pi$
$67$	3.48689	+	0.614832i	0.425991	+	0.0751137i	0.0434574	+	0.999055i	$0.486163\pi$
$68$	−0.354929	+	0.204918i	−0.0430415	+	0.0248500i
$69$	−1.41580	−	0.109756i	−0.170443	−	0.0132131i
$70$	−4.60559	+	5.48872i	−0.550473	+	0.656028i
$71$	−4.19799	−	1.52794i	−0.498210	−	0.181334i	0.0806788	−	0.996740i	$-0.474291\pi$
$71$	−4.19799	−	1.52794i	−0.498210	−	0.181334i	−0.578889	+	0.815407i	$0.696513\pi$
$72$	0.970052	−	2.83884i	0.114322	−	0.334560i
$73$	−4.33185	+	3.63485i	−0.507005	+	0.425427i	−0.860074	−	0.510170i	$-0.829583\pi$
$73$	−4.33185	+	3.63485i	−0.507005	+	0.425427i	0.353069	+	0.935597i	$0.385138\pi$
$74$	−5.92210	+	1.04423i	−0.688430	+	0.121389i
$75$	9.58679	−	4.58646i	1.10699	−	0.529599i
$76$	−4.19711	+	1.17656i	−0.481441	+	0.134961i
$77$			13.4328i			1.53081i
$78$	−5.61575	+	4.01561i	−0.635858	+	0.454679i
$79$	−8.05412	−	9.59853i	−0.906159	−	1.07992i	−0.996465	−	0.0840047i	$-0.973229\pi$
$79$	−8.05412	−	9.59853i	−0.906159	−	1.07992i	0.0903059	−	0.995914i	$-0.471216\pi$
$80$	1.14133	+	3.13578i	0.127605	+	0.350591i
$81$	−1.21076	+	8.91819i	−0.134529	+	0.990910i
$82$	0.926617	+	0.777524i	0.102328	+	0.0858631i
$83$	−8.01579	−	4.62792i	−0.879848	−	0.507980i	−0.00923947	−	0.999957i	$-0.502941\pi$
$83$	−8.01579	−	4.62792i	−0.879848	−	0.507980i	−0.870608	+	0.491977i	$0.836274\pi$
$84$	3.06734	+	2.10283i	0.334674	+	0.229438i
$85$	−0.237488	+	1.34686i	−0.0257591	+	0.146087i
$86$	1.08543	−	6.15577i	0.117045	−	0.663794i
$87$	−6.62378	−	4.54097i	−0.710143	−	0.486843i
$88$	5.41799	+	3.12808i	0.577560	+	0.333454i
$89$	5.61888	+	4.71480i	0.595600	+	0.499767i	0.890028	−	0.455906i	$-0.150685\pi$
$89$	5.61888	+	4.71480i	0.595600	+	0.499767i	−0.294428	+	0.955674i	$0.595129\pi$
$90$	−5.17619	−	8.56906i	−0.545618	−	0.903258i
$91$	−2.92708	−	8.04207i	−0.306841	−	0.843038i
$92$	−0.527000	−	0.628054i	−0.0549435	−	0.0654792i
$93$	3.29599	−	2.35684i	0.341778	−	0.244393i
$94$		−	7.71642i		−	0.795888i
$95$	−5.99513	+	13.2528i	−0.615087	+	1.35971i
$96$	1.56245	−	0.747499i	0.159467	−	0.0762913i
$97$	−16.0734	+	2.83418i	−1.63201	+	0.287767i	−0.913221	−	0.407464i	$-0.866413\pi$
$97$	−16.0734	+	2.83418i	−1.63201	+	0.287767i	−0.718786	+	0.695231i	$0.755302\pi$
$98$	1.83073	−	1.53616i	0.184931	−	0.155176i
$99$	−17.7602	−	6.06880i	−1.78497	−	0.609937i
$100$	5.76571	+	2.09855i	0.576571	+	0.209855i
$101$	3.69207	−	4.40004i	0.367375	−	0.437820i	−0.550412	−	0.834893i	$-0.685529\pi$
$101$	3.69207	−	4.40004i	0.367375	−	0.437820i	0.917787	+	0.397073i	$0.129974\pi$
$102$	0.707735	+	0.0548653i	0.0700762	+	0.00543248i
$103$	−0.957127	+	0.552597i	−0.0943085	+	0.0544490i	−0.546413	−	0.837516i	$-0.684007\pi$
$103$	−0.957127	+	0.552597i	−0.0943085	+	0.0544490i	0.452104	+	0.891965i	$0.350674\pi$
$104$	−3.92533	−	0.692141i	−0.384910	−	0.0678700i
$105$	11.9549	−	3.33049i	1.16668	−	0.325023i
$106$	−0.117334	−	0.203228i	−0.0113965	−	0.0197393i
$107$	3.47626	−	6.02105i	0.336062	−	0.582077i	−0.647626	−	0.761958i	$-0.724238\pi$
$107$	3.47626	−	6.02105i	0.336062	−	0.582077i	0.983688	+	0.179881i	$0.0575713\pi$
$108$	−4.16607	+	3.10546i	−0.400880	+	0.298823i
$109$	2.42887	−	6.67327i	0.232644	−	0.639183i	−0.767354	−	0.641223i	$-0.778427\pi$
$109$	2.42887	−	6.67327i	0.232644	−	0.639183i	0.999998	+	0.00204008i	$0.000649379\pi$
$110$	19.6179	−	7.14034i	1.87050	−	0.680805i
$111$	9.48286	+	4.30817i	0.900074	+	0.408914i
$112$	0.372845	+	2.11451i	0.0352305	+	0.199802i
$113$	−2.33000			−0.219188			−0.109594	−	0.993976i	$-0.534955\pi$
$113$	−2.33000			−0.219188			−0.109594	+	0.993976i	$0.534955\pi$
$114$	7.14818	+	2.42971i	0.669489	+	0.227563i
$115$	−2.73592			−0.255125
$116$	−0.805141	−	4.56618i	−0.0747555	−	0.423960i
$117$	11.9553	−	0.236716i	1.10527	−	0.0218844i
$118$	−5.03470	+	1.83248i	−0.463482	+	0.168693i
$119$	−0.300968	+	0.826903i	−0.0275897	+	0.0758021i
$120$	1.44061	−	5.59749i	0.131509	−	0.510978i
$121$	14.0697	−	24.3695i	1.27907	−	2.21541i
$122$	−3.88800	−	6.73422i	−0.352003	−	0.609687i
$123$	−0.562260	−	2.01825i	−0.0506973	−	0.181980i
$124$	2.30385	+	0.406231i	0.206892	+	0.0364806i
$125$	3.28225	−	1.89501i	0.293573	−	0.169495i
$126$	−2.32248	−	6.00812i	−0.206903	−	0.535246i
$127$	0.792153	−	0.944052i	0.0702922	−	0.0837710i	−0.729752	−	0.683712i	$-0.760365\pi$
$127$	0.792153	−	0.944052i	0.0702922	−	0.0837710i	0.800045	+	0.599941i	$0.204809\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	−7.57940	+	7.73096i	−0.667329	+	0.680673i
$130$	−10.1892	+	8.54971i	−0.893648	+	0.749859i
$131$	−6.34320	+	1.11848i	−0.554208	+	0.0977218i	−0.443736	−	0.896157i	$-0.646347\pi$
$131$	−6.34320	+	1.11848i	−0.554208	+	0.0977218i	−0.110472	+	0.993879i	$0.535236\pi$
$132$	−4.67647	−	9.77492i	−0.407035	−	0.850798i
$133$	−5.27955	+	7.72783i	−0.457795	+	0.670088i
$134$		−	3.54068i		−	0.305868i
$135$	−0.997698	+	17.3110i	−0.0858682	+	1.48989i
$136$	0.263438	+	0.313953i	0.0225896	+	0.0269213i
$137$	−3.68452	−	10.1231i	−0.314790	−	0.864878i	−0.991672	−	0.128787i	$-0.958892\pi$
$137$	−3.68452	−	10.1231i	−0.314790	−	0.864878i	0.676882	−	0.736091i	$-0.263331\pi$
$138$	0.137762	+	1.41335i	0.0117271	+	0.120313i
$139$	6.45972	+	5.42035i	0.547906	+	0.459748i	0.874231	−	0.485510i	$-0.161366\pi$
$139$	6.45972	+	5.42035i	0.547906	+	0.459748i	−0.326325	+	0.945258i	$0.605810\pi$
$140$	6.20509	+	3.58251i	0.524426	+	0.302777i
$141$	−7.55723	+	11.0235i	−0.636434	+	0.928346i
$142$	−0.775757	+	4.39954i	−0.0651001	+	0.369201i
$143$	−4.33014	+	24.5575i	−0.362105	+	2.05360i
$144$	−2.96416	−	0.462356i	−0.247013	−	0.0385297i
$145$	−13.3996	−	7.73627i	−1.11278	−	0.642462i
$146$	4.33185	+	3.63485i	0.358506	+	0.300823i
$147$	−4.11981	+	0.401566i	−0.339796	+	0.0331206i
$148$	2.05672	+	5.65080i	0.169062	+	0.464493i
$149$	3.41271	+	4.06711i	0.279580	+	0.333190i	0.887500	−	0.460808i	$-0.152440\pi$
$149$	3.41271	+	4.06711i	0.279580	+	0.333190i	−0.607920	+	0.793998i	$0.707996\pi$
$150$	−6.18151	−	8.64471i	−0.504718	−	0.705838i
$151$			2.55987i			0.208319i	0.994561	+	0.104160i	$0.0332153\pi$
$151$			2.55987i			0.208319i	−0.994561	+	0.104160i	$0.966785\pi$
$152$	1.88751	+	3.92903i	0.153097	+	0.318687i
$153$	−0.957320	−	0.771514i	−0.0773948	−	0.0623732i
$154$	13.2287	−	2.33258i	1.06600	−	0.187964i
$155$	5.98021	−	5.01799i	0.480342	−	0.403055i
$156$	4.92977	+	4.83313i	0.394698	+	0.386960i
$157$	15.7565	+	5.73489i	1.25750	+	0.457694i	0.882931	−	0.469503i	$-0.155567\pi$
$157$	15.7565	+	5.73489i	1.25750	+	0.457694i	0.374573	+	0.927197i	$0.377789\pi$
$158$	−8.05412	+	9.59853i	−0.640751	+	0.763618i
$159$	−0.0314153	+	0.405241i	−0.00249139	+	0.0321377i
$160$	2.88995	−	1.66851i	0.228471	−	0.131908i
$161$	−1.73361	−	0.305683i	−0.136628	−	0.0240912i
$162$	8.99295	−	0.356262i	0.706553	−	0.0279906i
$163$	5.28499	+	9.15387i	0.413952	+	0.716987i	0.995318	−	0.0966559i	$-0.0308146\pi$
$163$	5.28499	+	9.15387i	0.413952	+	0.716987i	−0.581365	+	0.813643i	$0.697481\pi$
$164$	0.604806	−	1.04755i	0.0472274	−	0.0818003i
$165$	−35.0188	−	9.01269i	−2.72621	−	0.701637i
$166$	−3.16568	+	8.69765i	−0.245705	+	0.675068i
$167$	10.5199	−	3.82893i	0.814054	−	0.296292i	0.0987568	−	0.995112i	$-0.468513\pi$
$167$	10.5199	−	3.82893i	0.814054	−	0.296292i	0.715298	+	0.698820i	$0.246291\pi$
$168$	1.53825	−	3.38589i	0.118678	−	0.261227i
$169$	−0.501366	−	2.84339i	−0.0385666	−	0.218722i
$170$	1.36764			0.104893
$171$	−7.83214	−	10.4717i	−0.598939	−	0.800795i
$172$	−6.25073			−0.476614
$173$	−3.80558	−	21.5825i	−0.289333	−	1.64089i	−0.689384	−	0.724396i	$-0.742119\pi$
$173$	−3.80558	−	21.5825i	−0.289333	−	1.64089i	0.400051	−	0.916493i	$-0.368993\pi$
$174$	−3.32178	+	7.31168i	−0.251823	+	0.554297i
$175$	12.3797	−	4.50585i	0.935819	−	0.340610i
$176$	2.13973	−	5.87886i	0.161288	−	0.443136i
$177$	8.98713	+	2.31300i	0.675514	+	0.173855i
$178$	3.66746	−	6.35223i	0.274888	−	0.476120i
$179$	10.6934	+	18.5215i	0.799263	+	1.38436i	0.920097	+	0.391692i	$0.128110\pi$
$179$	10.6934	+	18.5215i	0.799263	+	1.38436i	−0.120833	+	0.992673i	$0.538557\pi$
$180$	−7.54004	+	6.58555i	−0.562001	+	0.490858i
$181$	−18.0057	−	3.17489i	−1.33835	−	0.235988i	−0.541775	−	0.840523i	$-0.682248\pi$
$181$	−18.0057	−	3.17489i	−1.33835	−	0.235988i	−0.796578	+	0.604536i	$0.793359\pi$
$182$	−7.41162	+	4.27910i	−0.549386	+	0.317188i
$183$	−1.04098	+	13.4281i	−0.0769516	+	0.992637i
$184$	−0.527000	+	0.628054i	−0.0388509	+	0.0463008i
$185$	18.8569	+	6.86334i	1.38639	+	0.504603i
$186$	−2.89338	−	2.83666i	−0.212153	−	0.207994i
$187$	1.96414	−	1.64811i	0.143632	−	0.120522i
$188$	−7.59919	+	1.33994i	−0.554228	+	0.0977253i
$189$	−2.56634	+	10.8576i	−0.186674	+	0.789776i
$190$	14.0925	+	3.60272i	1.02238	+	0.261369i
$191$			3.46116i			0.250441i	0.992129	+	0.125220i	$0.0399638\pi$
$191$			3.46116i			0.250441i	−0.992129	+	0.125220i	$0.960036\pi$
$192$	−1.00746	−	1.40891i	−0.0727071	−	0.101679i
$193$	6.64414	+	7.91818i	0.478256	+	0.569963i	0.950190	−	0.311671i	$-0.100889\pi$
$193$	6.64414	+	7.91818i	0.478256	+	0.569963i	−0.471934	+	0.881634i	$0.656444\pi$
$194$	5.58224	+	15.3371i	0.400781	+	1.10114i
$195$	22.9293	−	2.23497i	1.64200	−	0.160050i
$196$	−1.83073	−	1.53616i	−0.130766	−	0.109726i
$197$	−10.2877	−	5.93959i	−0.732966	−	0.423178i	0.0865400	−	0.996248i	$-0.472419\pi$
$197$	−10.2877	−	5.93959i	−0.732966	−	0.423178i	−0.819506	+	0.573070i	$0.805752\pi$
$198$	−2.89257	+	18.5442i	−0.205566	+	1.31788i
$199$	4.24330	−	24.0650i	0.300800	−	1.70592i	−0.341845	−	0.939756i	$-0.611052\pi$
$199$	4.24330	−	24.0650i	0.300800	−	1.70592i	0.642645	−	0.766164i	$-0.277837\pi$
$200$	1.06546	−	6.04253i	0.0753395	−	0.427271i
$201$	−3.46764	+	5.05813i	−0.244588	+	0.356773i
$202$	−4.97432	−	2.87192i	−0.349992	−	0.202068i
$203$	−7.62630	−	6.39922i	−0.535261	−	0.449137i
$204$	−0.0688651	−	0.706510i	−0.00482152	−	0.0494656i
$205$	−1.38057	−	3.79308i	−0.0964230	−	0.264920i
$206$	0.710405	+	0.846628i	0.0494963	+	0.0589874i
$207$	1.18739	−	2.15400i	0.0825294	−	0.149714i
$208$			3.98588i			0.276371i
$209$	24.5807	−	11.8085i	1.70028	−	0.816814i
$210$	−5.35585	−	11.1950i	−0.369588	−	0.772527i
$211$	−16.3173	+	2.87718i	−1.12333	+	0.198074i	−0.704303	−	0.709900i	$-0.748740\pi$
$211$	−16.3173	+	2.87718i	−1.12333	+	0.198074i	−0.419028	+	0.907973i	$0.637629\pi$
$212$	−0.179766	+	0.150842i	−0.0123464	+	0.0103598i
$213$	5.41701	−	5.52533i	0.371167	−	0.378589i
$214$	−6.53323	−	2.37790i	−0.446602	−	0.162550i
$215$	−13.4078	+	15.9788i	−0.914405	+	1.08975i
$216$	3.78171	+	3.56352i	0.257313	+	0.242467i
$217$	4.35002	−	2.51149i	0.295299	−	0.170491i
$218$	−6.99366	−	1.23317i	−0.473670	−	0.0835208i
$219$	−2.62851	−	9.43516i	−0.177619	−	0.637569i
$220$	−10.4385	−	18.0800i	−0.703762	−	1.21895i
$221$	−0.816781	+	1.41471i	−0.0549426	+	0.0951634i
$222$	2.59604	−	10.0869i	0.174235	−	0.676989i
$223$	−4.05122	+	11.1306i	−0.271290	+	0.745362i	0.726986	+	0.686653i	$0.240921\pi$
$223$	−4.05122	+	11.1306i	−0.271290	+	0.745362i	−0.998275	+	0.0587091i	$0.981302\pi$
$224$	2.01764	−	0.734361i	0.134809	−	0.0490665i
$225$	0.364394	+	18.4036i	0.0242929	+	1.22691i
$226$	0.404601	+	2.29460i	0.0269136	+	0.152635i
$227$	23.0722			1.53135			0.765676	−	0.643226i	$-0.222405\pi$
$227$	23.0722			1.53135			0.765676	+	0.643226i	$0.222405\pi$
$228$	1.15153	−	7.46150i	0.0762618	−	0.494150i
$229$	14.0461			0.928192			0.464096	−	0.885785i	$-0.346379\pi$
$229$	14.0461			0.928192			0.464096	+	0.885785i	$0.346379\pi$
$230$	0.475087	+	2.69435i	0.0313263	+	0.177660i
$231$	−21.1827	−	9.62353i	−1.39372	−	0.633182i
$232$	−4.35700	+	1.58582i	−0.286051	+	0.104114i
$233$	8.06779	−	22.1661i	0.528539	−	1.45215i	−0.332253	−	0.943190i	$-0.607809\pi$
$233$	8.06779	−	22.1661i	0.528539	−	1.45215i	0.860792	−	0.508958i	$-0.169969\pi$
$234$	−2.30914	−	11.7326i	−0.150953	−	0.766982i
$235$	−12.8749	+	22.3001i	−0.839869	+	1.45470i
$236$	2.67891	+	4.64000i	0.174382	+	0.302038i
$237$	20.9065	−	5.82427i	1.35802	−	0.378327i
$238$	0.866603	+	0.152806i	0.0561735	+	0.00990491i
$239$	23.6023	−	13.6268i	1.52670	−	0.881443i	0.527206	−	0.849738i	$-0.323240\pi$
$239$	23.6023	−	13.6268i	1.52670	−	0.881443i	0.999497	−	0.0317050i	$-0.0100937\pi$
$240$	−5.76261	−	0.446732i	−0.371975	−	0.0288364i
$241$	13.6728	−	16.2946i	0.880739	−	1.04962i	−0.117659	−	0.993054i	$-0.537539\pi$
$241$	13.6728	−	16.2946i	0.880739	−	1.04962i	0.998399	−	0.0565704i	$-0.0180165\pi$
$242$	−26.4425	−	9.62427i	−1.69979	−	0.618672i
$243$	−13.1960	−	8.29848i	−0.846526	−	0.532348i
$244$	−5.95676	+	4.99832i	−0.381343	+	0.319985i
$245$	−7.85381	+	1.38484i	−0.501762	+	0.0884741i
$246$	−1.88996	+	0.904184i	−0.120499	+	0.0576487i
$247$	−12.1431	+	12.4259i	−0.772645	+	0.790643i
$248$		−	2.33939i		−	0.148552i
$249$	13.0406	−	9.32488i	0.826417	−	0.590940i
$250$	−2.43617	−	2.90332i	−0.154077	−	0.183622i
$251$	−0.848967	−	2.33252i	−0.0535863	−	0.147227i	0.910012	−	0.414583i	$-0.136072\pi$
$251$	−0.848967	−	2.33252i	−0.0535863	−	0.147227i	−0.963598	+	0.267355i	$0.913850\pi$
$252$	−5.51355	+	3.33049i	−0.347321	+	0.209801i
$253$	3.92920	+	3.29699i	0.247027	+	0.207280i
$254$	−1.06727	−	0.616186i	−0.0669662	−	0.0386629i
$255$	−1.95377	−	1.33942i	−0.122350	−	0.0838779i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−1.95465	+	11.0854i	−0.121928	+	0.691488i	0.861157	+	0.508339i	$0.169740\pi$
$257$	−1.95465	+	11.0854i	−0.121928	+	0.691488i	−0.983085	+	0.183149i	$0.941371\pi$
$258$	8.92965	+	6.12178i	0.555936	+	0.381126i
$259$	11.1818	+	6.45583i	0.694805	+	0.401146i
$260$	10.1892	+	8.54971i	0.631904	+	0.530231i
$261$	11.9063	−	7.19205i	0.736979	−	0.445176i
$262$	2.20297	+	6.05261i	0.136100	+	0.373931i
$263$	−7.57578	−	9.02847i	−0.467143	−	0.556719i	0.480109	−	0.877209i	$-0.340597\pi$
$263$	−7.57578	−	9.02847i	−0.467143	−	0.556719i	−0.947252	+	0.320490i	$0.896153\pi$
$264$	−8.81436	+	6.30282i	−0.542486	+	0.387912i
$265$			0.783093i			0.0481050i
$266$	8.52721	+	3.85742i	0.522837	+	0.236513i
$267$	−11.4604	+	5.48285i	−0.701367	+	0.335545i
$268$	−3.48689	+	0.614832i	−0.212996	+	0.0375569i
$269$	−8.96522	+	7.52271i	−0.546619	+	0.458668i	−0.873794	−	0.486296i	$-0.838348\pi$
$269$	−8.96522	+	7.52271i	−0.546619	+	0.458668i	0.327175	+	0.944964i	$0.393903\pi$
$270$	17.2212	−	2.02348i	1.04805	−	0.123145i
$271$	−29.1999	−	10.6279i	−1.77377	−	0.645598i	−0.999925	−	0.0122180i	$-0.996111\pi$
$271$	−29.1999	−	10.6279i	−1.77377	−	0.645598i	−0.773841	−	0.633380i	$-0.781667\pi$
$272$	0.263438	−	0.313953i	0.0159733	−	0.0190362i
$273$	14.7789	+	1.14570i	0.894459	+	0.0693406i
$274$	−9.32954	+	5.38641i	−0.563618	+	0.325405i
$275$	−37.8030	−	6.66569i	−2.27961	−	0.401956i
$276$	1.36796	−	0.381096i	0.0823414	−	0.0229393i
$277$	1.91965	+	3.32494i	0.115341	+	0.199776i	0.917916	−	0.396775i	$-0.129871\pi$
$277$	1.91965	+	3.32494i	0.115341	+	0.199776i	−0.802575	+	0.596551i	$0.796537\pi$
$278$	4.21628	−	7.30281i	0.252876	−	0.437994i
$279$	1.35528	+	6.88607i	0.0811383	+	0.412258i
$280$	2.45058	−	6.73292i	0.146450	−	0.402369i
$281$	−23.0658	+	8.39528i	−1.37599	+	0.500820i	−0.920961	−	0.389655i	$-0.872594\pi$
$281$	−23.0658	+	8.39528i	−1.37599	+	0.500820i	−0.455031	+	0.890475i	$0.650372\pi$
$282$	12.1683	+	5.52821i	0.724614	+	0.329200i
$283$	−4.03563	−	22.8872i	−0.239894	−	1.36050i	−0.832059	−	0.554688i	$-0.812838\pi$
$283$	−4.03563	−	22.8872i	−0.239894	−	1.36050i	0.592165	−	0.805817i	$-0.298273\pi$
$284$	4.46741			0.265092
$285$	−16.6039	−	18.9486i	−0.983529	−	1.12242i
$286$	24.9363			1.47451
$287$	−0.450998	−	2.55773i	−0.0266215	−	0.150978i
$288$	0.0593887	+	2.99941i	0.00349951	+	0.176742i
$289$	−15.8169	+	5.75689i	−0.930408	+	0.338641i
$290$	−5.29192	+	14.5394i	−0.310752	+	0.853785i
$291$	7.04602	−	27.3773i	0.413045	−	1.60488i
$292$	2.82741	−	4.89723i	0.165462	−	0.286588i
$293$	−5.48661	−	9.50309i	−0.320531	−	0.555177i	0.660066	−	0.751207i	$-0.270528\pi$
$293$	−5.48661	−	9.50309i	−0.320531	−	0.555177i	−0.980598	+	0.196031i	$0.937195\pi$
$294$	1.11086	+	3.98749i	0.0647868	+	0.232555i
$295$	17.6075	+	3.10468i	1.02515	+	0.180762i
$296$	5.20781	−	3.00673i	0.302698	−	0.174763i
$297$	22.2939	−	23.6590i	1.29363	−	1.37283i
$298$	3.41271	−	4.06711i	0.197693	−	0.235601i
$299$	−3.07081	−	1.11768i	−0.177590	−	0.0646374i
$300$	−7.43997	+	7.58874i	−0.429547	+	0.438136i
$301$	−10.2812	+	8.62693i	−0.592597	+	0.497248i
$302$	2.52098	−	0.444517i	0.145066	−	0.0255791i
$303$	4.29352	+	8.97446i	0.246656	+	0.515569i
$304$	3.54158	−	2.54110i	0.203124	−	0.145742i
$305$			25.9487i			1.48582i
$306$	−0.593556	+	1.07675i	−0.0339313	+	0.0615536i
$307$	−0.351542	−	0.418952i	−0.0200636	−	0.0239108i	0.755919	−	0.654665i	$-0.227190\pi$
$307$	−0.351542	−	0.418952i	−0.0200636	−	0.0239108i	−0.775983	+	0.630754i	$0.782746\pi$
$308$	−4.59428	−	12.6227i	−0.261783	−	0.719243i
$309$	−0.185706	−	1.90522i	−0.0105645	−	0.108384i
$310$	−5.98021	−	5.01799i	−0.339653	−	0.285003i
$311$	−12.1908	−	7.03836i	−0.691277	−	0.399109i	0.112813	−	0.993616i	$-0.464014\pi$
$311$	−12.1908	−	7.03836i	−0.691277	−	0.399109i	−0.804090	+	0.594507i	$0.797347\pi$
$312$	3.90366	−	5.69414i	0.221001	−	0.322367i
$313$	−3.23018	+	18.3193i	−0.182580	+	1.03547i	0.746444	+	0.665448i	$0.231759\pi$
$313$	−3.23018	+	18.3193i	−0.182580	+	1.03547i	−0.929025	+	0.370018i	$0.879352\pi$
$314$	2.91168	−	16.5130i	0.164316	−	0.931880i
$315$	−3.31279	+	21.2382i	−0.186655	+	1.19664i
$316$	10.8513	+	6.26499i	0.610433	+	0.352433i
$317$	20.8301	+	17.4785i	1.16993	+	0.981690i	0.999993	−	0.00376423i	$-0.00119819\pi$
$317$	20.8301	+	17.4785i	1.16993	+	0.981690i	0.169940	+	0.985454i	$0.445643\pi$
$318$	0.404540	−	0.0394314i	0.0226855	−	0.00221120i
$319$	9.92113	+	27.2581i	0.555477	+	1.52616i
$320$	−2.14500	−	2.55631i	−0.119909	−	0.142902i
$321$	7.00437	+	9.79546i	0.390946	+	0.546730i
$322$			1.76036i			0.0981009i
$323$	1.77773	−	0.176176i	0.0989155	−	0.00980270i
$324$	−1.91246	−	8.79446i	−0.106248	−	0.488581i
$325$	24.0848	−	4.24680i	1.33598	−	0.235570i
$326$	8.09708	−	6.79425i	0.448456	−	0.376299i
$327$	8.78325	+	8.61106i	0.485715	+	0.476193i
$328$	−1.13666	−	0.413712i	−0.0627618	−	0.0228434i
$329$	−10.6498	+	12.6919i	−0.587142	+	0.699729i
$330$	−2.79482	+	36.0518i	−0.153850	+	1.98459i
$331$	25.4221	−	14.6775i	1.39733	−	0.806746i	0.403214	−	0.915106i	$-0.367893\pi$
$331$	25.4221	−	14.6775i	1.39733	−	0.806746i	0.994112	+	0.108360i	$0.0345598\pi$
$332$	9.11522	+	1.60726i	0.500263	+	0.0882098i
$333$	−13.5875	+	11.8674i	−0.744588	+	0.650332i
$334$	−5.59752	−	9.69519i	−0.306283	−	0.530497i
$335$	−5.90767	+	10.2324i	−0.322770	+	0.559055i
$336$	−3.60157	−	0.926926i	−0.196482	−	0.0505680i
$337$	4.60842	−	12.6615i	0.251037	−	0.689717i	−0.748607	−	0.663014i	$-0.769277\pi$
$337$	4.60842	−	12.6615i	0.251037	−	0.689717i	0.999643	−	0.0267031i	$-0.00850087\pi$
$338$	−2.71313	+	0.987499i	−0.147575	+	0.0537129i
$339$	1.66926	−	3.67427i	0.0906620	−	0.199559i
$340$	−0.237488	−	1.34686i	−0.0128796	−	0.0730437i
$341$	−14.6356			−0.792562
$342$	−8.95262	+	9.53156i	−0.484102	+	0.515408i
$343$	−20.1612			−1.08860
$344$	1.08543	+	6.15577i	0.0585224	+	0.331897i
$345$	1.96007	−	4.31437i	0.105527	−	0.232278i
$346$	−20.5938	+	7.49553i	−1.10713	+	0.402962i
$347$	−2.06013	+	5.66016i	−0.110594	+	0.303854i	−0.982627	−	0.185594i	$-0.940579\pi$
$347$	−2.06013	+	5.66016i	−0.110594	+	0.303854i	0.872033	+	0.489447i	$0.162801\pi$
$348$	7.77742	+	2.00165i	0.416913	+	0.107300i
$349$	−14.3065	+	24.7795i	−0.765808	+	1.32642i	0.174010	+	0.984744i	$0.444328\pi$
$349$	−14.3065	+	24.7795i	−0.765808	+	1.32642i	−0.939818	+	0.341675i	$0.889006\pi$
$350$	−6.58711	−	11.4092i	−0.352096	−	0.609848i
$351$	−8.19175	+	19.0224i	−0.437243	+	1.01534i
$352$	−6.16111	−	1.08637i	−0.328388	−	0.0579037i
$353$	−14.6066	+	8.43315i	−0.777433	+	0.448851i	−0.835520	−	0.549460i	$-0.814833\pi$
$353$	−14.6066	+	8.43315i	−0.777433	+	0.448851i	0.0580867	+	0.998312i	$0.481500\pi$
$354$	0.717257	−	9.25225i	0.0381218	−	0.491751i
$355$	9.58259	−	11.4201i	0.508591	−	0.606115i
$356$	−6.89257	−	2.50869i	−0.365306	−	0.132960i
$357$	−1.08836	−	1.06702i	−0.0576019	−	0.0564727i
$358$	16.3833	−	13.7472i	0.865882	−	0.726561i
$359$	16.2813	−	2.87084i	0.859295	−	0.151517i	0.273397	−	0.961901i	$-0.411853\pi$
$359$	16.2813	−	2.87084i	0.859295	−	0.151517i	0.585898	+	0.810385i	$0.300742\pi$
$360$	7.79482	+	6.28192i	0.410823	+	0.331086i
$361$	18.7823	+	2.86764i	0.988545	+	0.150928i
$362$			18.2835i			0.960958i
$363$	28.3494	+	39.6460i	1.48796	+	2.08088i
$364$	5.50110	+	6.55596i	0.288336	+	0.343626i
$365$	−6.45403	−	17.7323i	−0.337819	−	0.928151i
$366$	13.4049	−	1.30661i	0.700686	−	0.0682974i
$367$	−7.32428	−	6.14580i	−0.382324	−	0.320808i	0.431290	−	0.902213i	$-0.358059\pi$
$367$	−7.32428	−	6.14580i	−0.382324	−	0.320808i	−0.813614	+	0.581405i	$0.802503\pi$
$368$	0.710025	+	0.409933i	0.0370126	+	0.0213692i
$369$	3.58548	+	0.559271i	0.186653	+	0.0291145i
$370$	3.48461	−	19.7622i	0.181156	−	1.02739i
$371$	−0.0874947	+	0.496207i	−0.00454250	+	0.0257618i
$372$	−2.29113	+	3.34200i	−0.118790	+	0.173275i
$373$	3.75197	+	2.16620i	0.194270	+	0.112162i	0.593980	−	0.804480i	$-0.297556\pi$
$373$	3.75197	+	2.16620i	0.194270	+	0.112162i	−0.399710	+	0.916642i	$0.630889\pi$
$374$	−1.96414	−	1.64811i	−0.101563	−	0.0852217i
$375$	0.636837	+	6.53353i	0.0328861	+	0.337390i
$376$	2.63917	+	7.25106i	0.136105	+	0.373945i
$377$	−11.8794	−	14.1573i	−0.611819	−	0.729138i
$378$	11.1383	+	0.641944i	0.572893	+	0.0330180i
$379$			5.96818i			0.306565i	0.988182	+	0.153282i	$0.0489844\pi$
$379$			5.96818i			0.306565i	−0.988182	+	0.153282i	$0.951016\pi$
$380$	1.10084	−	14.5040i	0.0564719	−	0.744042i
$381$	0.921197	+	1.92552i	0.0471943	+	0.0986472i
$382$	3.40858	−	0.601025i	0.174398	−	0.0307511i
$383$	−3.37004	+	2.82780i	−0.172201	+	0.144494i	−0.724815	−	0.688944i	$-0.758075\pi$
$383$	−3.37004	+	2.82780i	−0.172201	+	0.144494i	0.552614	+	0.833437i	$0.313630\pi$
$384$	−1.21256	+	1.23681i	−0.0618783	+	0.0631156i
$385$	−42.1222	−	15.3312i	−2.14675	−	0.781351i
$386$	6.64414	−	7.91818i	0.338178	−	0.403025i
$387$	−6.76121	−	17.4909i	−0.343692	−	0.889112i
$388$	14.1347	−	8.16068i	0.717582	−	0.414296i
$389$	14.5009	+	2.55689i	0.735223	+	0.129640i	0.528708	−	0.848804i	$-0.322677\pi$
$389$	14.5009	+	2.55689i	0.735223	+	0.129640i	0.206515	+	0.978443i	$0.433788\pi$
$390$	−6.18265	−	22.1929i	−0.313071	−	1.12378i
$391$	0.168006	+	0.290994i	0.00849641	+	0.0147162i
$392$	−1.19492	+	2.06967i	−0.0603527	+	0.104534i
$393$	2.78064	−	10.8041i	0.140264	−	0.544997i
$394$	−4.06292	+	11.1628i	−0.204687	+	0.562373i
$395$	39.2913	−	14.3009i	1.97696	−	0.719554i
$396$	18.7648	−	0.371545i	0.942966	−	0.0186708i
$397$	1.74751	+	9.91059i	0.0877048	+	0.497398i	0.996740	+	0.0806794i	$0.0257090\pi$
$397$	1.74751	+	9.91059i	0.0877048	+	0.497398i	−0.909035	+	0.416719i	$0.863180\pi$
$398$	−24.4362			−1.22488
$399$	−8.40394	−	13.8619i	−0.420723	−	0.693964i
$400$	−6.13575			−0.306787
$401$	2.58090	+	14.6370i	0.128884	+	0.730937i	0.978925	+	0.204221i	$0.0654660\pi$
$401$	2.58090	+	14.6370i	0.128884	+	0.730937i	−0.850041	+	0.526717i	$0.823423\pi$
$402$	5.58344	+	2.53662i	0.278476	+	0.126515i
$403$	8.76220	−	3.18918i	0.436476	−	0.158864i
$404$	−1.96451	+	5.39745i	−0.0977381	+	0.268533i
$405$	−26.5836	−	13.9753i	−1.32095	−	0.694437i
$406$	−4.97771	+	8.62165i	−0.247040	+	0.427885i
$407$	−18.8106	−	32.5809i	−0.932405	−	1.61497i
$408$	−0.683818	+	0.190503i	−0.0338540	+	0.00943130i
$409$	−9.81162	−	1.73005i	−0.485153	−	0.0855456i	−0.0742787	−	0.997238i	$-0.523665\pi$
$409$	−9.81162	−	1.73005i	−0.485153	−	0.0855456i	−0.410874	+	0.911692i	$0.634777\pi$
$410$	−3.49572	+	2.01825i	−0.172641	+	0.0996745i
$411$	18.6033	+	1.44217i	0.917631	+	0.0711370i
$412$	0.710405	−	0.846628i	0.0349992	−	0.0417104i
$413$	10.8101	+	3.93457i	0.531932	+	0.193607i
$414$	−2.32747	−	0.795313i	−0.114389	−	0.0390875i
$415$	23.6608	−	19.8538i	1.16146	−	0.974583i
$416$	3.92533	−	0.692141i	0.192455	−	0.0339350i
$417$	−13.1754	+	6.30333i	−0.645204	+	0.308676i
$418$	−15.8975	−	22.1567i	−0.777574	−	1.08372i
$419$			8.34847i			0.407849i	0.978987	+	0.203925i	$0.0653698\pi$
$419$			8.34847i			0.407849i	−0.978987	+	0.203925i	$0.934630\pi$
$420$	−10.0949	+	7.21847i	−0.492579	+	0.352225i
$421$	23.4446	+	27.9402i	1.14262	+	1.36172i	0.922384	+	0.386273i	$0.126238\pi$
$421$	23.4446	+	27.9402i	1.14262	+	1.36172i	0.220234	+	0.975447i	$0.429318\pi$
$422$	5.66695	+	15.5698i	0.275863	+	0.757926i
$423$	−11.9692	−	19.8148i	−0.581964	−	0.963428i
$424$	0.179766	+	0.150842i	0.00873021	+	0.00732552i
$425$	−2.17775	−	1.25733i	−0.105637	−	0.0609893i
$426$	−6.38204	−	4.37525i	−0.309211	−	0.211981i
$427$	−2.89924	+	16.4424i	−0.140304	+	0.795705i
$428$	−1.20729	+	6.84689i	−0.0583566	+	0.330957i
$429$	−35.6234	−	24.4219i	−1.71992	−	1.17910i
$430$	18.0643	+	10.4294i	0.871138	+	0.502952i
$431$	−8.05751	−	6.76105i	−0.388116	−	0.325668i	0.427762	−	0.903891i	$-0.359302\pi$
$431$	−8.05751	−	6.76105i	−0.388116	−	0.325668i	−0.815879	+	0.578223i	$0.803746\pi$
$432$	2.85269	−	4.34306i	0.137250	−	0.208955i
$433$	−12.6127	−	34.6530i	−0.606126	−	1.66532i	−0.738611	−	0.674132i	$-0.764518\pi$
$433$	−12.6127	−	34.6530i	−0.606126	−	1.66532i	0.132485	−	0.991185i	$-0.457704\pi$
$434$	−3.22870	−	3.84782i	−0.154983	−	0.184701i
$435$	21.7994	−	15.5879i	1.04520	−	0.747385i
$436$			7.10155i			0.340102i
$437$	0.964625	+	3.44107i	0.0461443	+	0.164608i
$438$	−8.83538	+	4.22698i	−0.422171	+	0.201973i
$439$	13.1107	−	2.31177i	0.625739	−	0.110335i	0.148218	−	0.988955i	$-0.452646\pi$
$439$	13.1107	−	2.31177i	0.625739	−	0.110335i	0.477522	+	0.878620i	$0.341535\pi$
$440$	−15.9927	+	13.4195i	−0.762421	+	0.639747i
$441$	2.31827	−	6.78438i	0.110394	−	0.323066i
$442$	1.53505	+	0.558711i	0.0730147	+	0.0265752i
$443$	−4.79891	+	5.71912i	−0.228003	+	0.271724i	−0.867902	−	0.496736i	$-0.834532\pi$
$443$	−4.79891	+	5.71912i	−0.228003	+	0.271724i	0.639899	+	0.768459i	$0.278976\pi$
$444$	−10.3845	−	0.805029i	−0.492825	−	0.0382050i
$445$	−21.1976	+	12.2384i	−1.00486	+	0.580156i
$446$	11.6650	+	2.05686i	0.552354	+	0.0973950i
$447$	−8.85852	+	2.46787i	−0.418994	+	0.116726i
$448$	−1.07356	−	1.85947i	−0.0507211	−	0.0878516i
$449$	−12.1781	+	21.0931i	−0.574722	+	0.995447i	0.421350	+	0.906898i	$0.361556\pi$
$449$	−12.1781	+	21.0931i	−0.574722	+	0.995447i	−0.996072	+	0.0885490i	$0.971777\pi$
$450$	18.0608	−	3.55461i	0.851392	−	0.167566i
$451$	−2.58825	+	7.11115i	−0.121876	+	0.334851i
$452$	2.18949	−	0.796908i	0.102985	−	0.0374834i
$453$	−4.03676	−	1.83395i	−0.189664	−	0.0861664i
$454$	−4.00644	−	22.7216i	−0.188031	−	1.06638i
$455$	28.5589			1.33886
$456$	−7.54810	+	0.161642i	−0.353472	+	0.00756956i
$457$	−34.8127			−1.62847			−0.814236	−	0.580534i	$-0.802844\pi$
$457$	−34.8127			−1.62847			−0.814236	+	0.580534i	$0.802844\pi$
$458$	−2.43908	−	13.8327i	−0.113971	−	0.646360i
$459$	1.90248	−	0.956907i	0.0888000	−	0.0446646i
$460$	2.57092	−	0.935738i	0.119870	−	0.0436290i
$461$	−0.765028	+	2.10190i	−0.0356309	+	0.0978951i	−0.956232	−	0.292608i	$-0.905477\pi$
$461$	−0.765028	+	2.10190i	−0.0356309	+	0.0978951i	0.920601	+	0.390503i	$0.127699\pi$
$462$	−5.79899	+	22.5320i	−0.269794	+	1.04828i
$463$	1.84091	−	3.18854i	0.0855541	−	0.148184i	−0.820073	−	0.572259i	$-0.806067\pi$
$463$	1.84091	−	3.18854i	0.0855541	−	0.148184i	0.905627	+	0.424075i	$0.139401\pi$
$464$	2.31831	+	4.01543i	0.107625	+	0.186412i
$465$	3.62872	+	13.0254i	0.168278	+	0.604040i
$466$	−23.2303	−	4.09613i	−1.07612	−	0.189749i
$467$	11.3948	−	6.57879i	0.527288	−	0.304430i	−0.212623	−	0.977134i	$-0.568201\pi$
$467$	11.3948	−	6.57879i	0.527288	−	0.304430i	0.739911	+	0.672704i	$0.234867\pi$
$468$	−11.1533	+	4.31139i	−0.515564	+	0.199294i
$469$	−4.88666	+	5.82369i	−0.225645	+	0.268913i
$470$	24.1970	+	8.80698i	1.11612	+	0.406236i
$471$	−20.3319	+	20.7384i	−0.936843	+	0.955576i
$472$	4.10432	−	3.44394i	0.188917	−	0.158520i
$473$	38.5115	−	6.79061i	1.77076	−	0.312233i
$474$	−9.36615	−	19.5775i	−0.430202	−	0.899223i
$475$	−19.1281	−	18.6927i	−0.877658	−	0.857678i
$476$		−	0.879972i		−	0.0403335i
$477$	−0.616534	−	0.339864i	−0.0282292	−	0.0155613i
$478$	−17.5182	−	20.8774i	−0.801266	−	0.954911i
$479$	11.4643	+	31.4978i	0.523816	+	1.43917i	0.866240	+	0.499628i	$0.166530\pi$
$479$	11.4643	+	31.4978i	0.523816	+	1.43917i	−0.342424	+	0.939546i	$0.611248\pi$
$480$	0.560722	+	5.75264i	0.0255933	+	0.262571i
$481$	18.3613	+	15.4069i	0.837202	+	0.702496i
$482$	−18.4213	−	10.6355i	−0.839065	−	0.484434i
$483$	1.72404	−	2.51481i	0.0784466	−	0.114428i
$484$	−4.88637	+	27.7120i	−0.222108	+	1.25964i
$485$	9.45772	−	53.6374i	0.429453	−	2.43555i
$486$	−5.88094	+	14.4366i	−0.266765	+	0.654856i
$487$	−15.2052	−	8.77875i	−0.689015	−	0.397803i	0.114228	−	0.993455i	$-0.463561\pi$
$487$	−15.2052	−	8.77875i	−0.689015	−	0.397803i	−0.803243	+	0.595651i	$0.796894\pi$
$488$	5.95676	+	4.99832i	0.269650	+	0.226263i
$489$	−18.2214	+	1.77608i	−0.824000	+	0.0803171i
$490$	2.72760	+	7.49402i	0.123220	+	0.338545i
$491$	−15.8204	−	18.8540i	−0.713964	−	0.850869i	0.280065	−	0.959981i	$-0.409644\pi$
$491$	−15.8204	−	18.8540i	−0.713964	−	0.850869i	−0.994030	+	0.109112i	$0.965199\pi$
$492$	1.21863	+	1.70423i	0.0549403	+	0.0768328i
$493$			1.90026i			0.0855834i
$494$	14.3458	+	9.80084i	0.645447	+	0.440961i
$495$	39.3007	−	48.7656i	1.76643	−	2.19185i
$496$	−2.30385	+	0.406231i	−0.103446	+	0.0182403i
$497$	7.34797	−	6.16568i	0.329602	−	0.276569i
$498$	−11.4477	−	11.2233i	−0.512984	−	0.502927i
$499$	13.8001	+	5.02282i	0.617777	+	0.224852i	0.631902	−	0.775048i	$-0.282274\pi$
$499$	13.8001	+	5.02282i	0.617777	+	0.224852i	−0.0141259	+	0.999900i	$0.504497\pi$
$500$	−2.43617	+	2.90332i	−0.108949	+	0.129840i
$501$	−1.49869	+	19.3324i	−0.0669567	+	0.863707i
$502$	−2.14966	+	1.24111i	−0.0959440	+	0.0553933i
$503$	4.24201	+	0.747980i	0.189142	+	0.0333508i	0.267417	−	0.963581i	$-0.413830\pi$
$503$	4.24201	+	0.747980i	0.189142	+	0.0333508i	−0.0782748	+	0.996932i	$0.524941\pi$
$504$	4.23731	+	4.85145i	0.188745	+	0.216101i
$505$	9.58368	+	16.5994i	0.426468	+	0.738665i
$506$	2.56461	−	4.44203i	0.114011	−	0.197472i
$507$	4.84305	+	1.24644i	0.215087	+	0.0553564i
$508$	−0.421496	+	1.15805i	−0.0187009	+	0.0513802i
$509$	4.35756	−	1.58602i	0.193145	−	0.0702991i	−0.243637	−	0.969867i	$-0.578340\pi$
$509$	4.35756	−	1.58602i	0.193145	−	0.0702991i	0.436782	+	0.899567i	$0.356118\pi$
$510$	−0.979805	+	2.15668i	−0.0433865	+	0.0954994i
$511$	−2.10837	−	11.9572i	−0.0932690	−	0.528955i
$512$	−1.00000			−0.0441942
$513$	22.1244	−	4.84863i	0.976818	−	0.214072i
$514$	11.2564			0.496498
$515$	−0.640425	−	3.63203i	−0.0282205	−	0.160047i
$516$	4.47816	−	9.85703i	0.197140	−	0.433932i
$517$	45.3638	−	16.5111i	1.99510	−	0.726156i
$518$	4.41605	−	12.1330i	0.194030	−	0.533093i
$519$	36.7608	+	9.46102i	1.61362	+	0.415293i
$520$	6.65050	−	11.5190i	0.291644	−	0.505141i
$521$	0.205968	+	0.356747i	0.00902363	+	0.0156294i	0.870502	−	0.492165i	$-0.163794\pi$
$521$	0.205968	+	0.356747i	0.00902363	+	0.0156294i	−0.861478	+	0.507794i	$0.830461\pi$
$522$	−9.15028	−	10.4765i	−0.400497	−	0.458544i
$523$	−19.2248	−	3.38986i	−0.840643	−	0.148228i	−0.263284	−	0.964718i	$-0.584806\pi$
$523$	−19.2248	−	3.38986i	−0.840643	−	0.148228i	−0.577359	+	0.816490i	$0.695917\pi$
$524$	5.57811	−	3.22053i	0.243681	−	0.140689i
$525$	−1.76365	+	22.7502i	−0.0769719	+	0.992899i
$526$	−7.57578	+	9.02847i	−0.330320	+	0.393660i
$527$	−0.900948	−	0.327918i	−0.0392459	−	0.0142843i
$528$	7.73767	+	7.58597i	0.336739	+	0.330137i
$529$	17.1041	−	14.3520i	0.743657	−	0.624002i
$530$	0.771196	−	0.135983i	0.0334986	−	0.00590671i
$531$	−10.0860	+	12.5151i	−0.437697	+	0.543109i
$532$	2.31808	−	9.06750i	0.100502	−	0.393126i
$533$		−	4.82137i		−	0.208837i
$534$	7.38963	+	10.3342i	0.319781	+	0.447206i
$535$	14.9131	+	17.7728i	0.644751	+	0.768385i
$536$	1.21098	+	3.32715i	0.0523065	+	0.143711i
$537$	−36.8683	+	3.59364i	−1.59099	+	0.155077i
$538$	8.96522	+	7.52271i	0.386518	+	0.324327i
$539$	12.9481	+	7.47562i	0.557716	+	0.321998i
$540$	−4.98317	−	16.6082i	−0.214442	−	0.714704i
$541$	−3.15633	+	17.9005i	−0.135701	+	0.769601i	0.838667	+	0.544644i	$0.183335\pi$
$541$	−3.15633	+	17.9005i	−0.135701	+	0.769601i	−0.974369	+	0.224957i	$0.927776\pi$
$542$	−5.39592	+	30.6018i	−0.231775	+	1.31446i
$543$	17.9063	−	26.1194i	0.768433	−	1.12089i
$544$	−0.354929	−	0.204918i	−0.0152175	−	0.00878581i
$545$	18.1538	+	15.2328i	0.777622	+	0.652502i
$546$	−1.43804	−	14.7533i	−0.0615423	−	0.631383i
$547$	1.42436	+	3.91340i	0.0609014	+	0.167325i	0.966412	−	0.256999i	$-0.0827338\pi$
$547$	1.42436	+	3.91340i	0.0609014	+	0.167325i	−0.905510	+	0.424324i	$0.860512\pi$
$548$	6.92464	+	8.25246i	0.295806	+	0.352528i
$549$	−20.4296	−	11.2618i	−0.871914	−	0.480641i
$550$			38.3862i			1.63679i
$551$	−5.00579	+	19.5808i	−0.213254	+	0.834172i
$552$	−0.612849	−	1.28100i	−0.0260846	−	0.0545229i
$553$	26.4948	−	4.67174i	1.12667	−	0.198663i
$554$	2.94108	−	2.46786i	0.124955	−	0.104849i
$555$	−24.3326	+	24.8191i	−1.03286	+	1.05351i
$556$	−7.92402	−	2.88411i	−0.336053	−	0.122313i
$557$	−9.16196	+	10.9188i	−0.388205	+	0.462644i	−0.924386	−	0.381459i	$-0.875422\pi$
$557$	−9.16196	+	10.9188i	−0.388205	+	0.462644i	0.536181	+	0.844103i	$0.319866\pi$
$558$	6.54612	−	2.53044i	0.277119	−	0.107122i
$559$	−21.5767	+	12.4573i	−0.912599	+	0.526889i
$560$	−7.05617	−	1.24419i	−0.298178	−	0.0525767i
$561$	1.19182	+	4.27807i	0.0503185	+	0.180620i
$562$	12.2731	+	21.2576i	0.517708	+	0.896697i
$563$	3.28307	−	5.68645i	0.138365	−	0.239655i	−0.788513	−	0.615018i	$-0.789149\pi$
$563$	3.28307	−	5.68645i	0.138365	−	0.239655i	0.926878	+	0.375363i	$0.122482\pi$
$564$	3.33122	−	12.9434i	0.140270	−	0.545017i
$565$	2.65930	−	7.30637i	0.111878	−	0.307381i
$566$	−21.8387	+	7.94865i	−0.917950	+	0.334107i
$567$	−15.2832	−	11.8256i	−0.641836	−	0.496629i
$568$	−0.775757	−	4.39954i	−0.0325501	−	0.184601i
$569$	−45.7506			−1.91797			−0.958983	−	0.283465i	$-0.908516\pi$
$569$	−45.7506			−1.91797			−0.958983	+	0.283465i	$0.908516\pi$
$570$	−15.7775	+	19.6420i	−0.660846	+	0.822714i
$571$	5.82547			0.243788			0.121894	−	0.992543i	$-0.461103\pi$
$571$	5.82547			0.243788			0.121894	+	0.992543i	$0.461103\pi$
$572$	−4.33014	−	24.5575i	−0.181052	−	1.02680i
$573$	−5.45805	−	2.47965i	−0.228013	−	0.103589i
$574$	−2.44056	+	0.888292i	−0.101867	+	0.0370766i
$575$	1.72053	−	4.72712i	0.0717510	−	0.197134i
$576$	2.94353	−	0.579329i	0.122647	−	0.0241387i
$577$	−17.9425	+	31.0773i	−0.746956	+	1.29377i	0.202320	+	0.979319i	$0.435152\pi$
$577$	−17.9425	+	31.0773i	−0.746956	+	1.29377i	−0.949276	+	0.314446i	$0.898181\pi$
$578$	8.41602	+	14.5770i	0.350060	+	0.606322i
$579$	−17.2465	+	4.80465i	−0.716740	+	0.199675i
$580$	15.2375	+	2.68678i	0.632702	+	0.111562i
$581$	17.2109	−	9.93674i	0.714030	−	0.412245i
$582$	−28.1849	−	2.18496i	−1.16830	−	0.0905695i
$583$	0.943689	−	1.12464i	0.0390836	−	0.0465780i
$584$	−5.31380	−	1.93407i	−0.219887	−	0.0800322i
$585$	−12.9027	+	37.7594i	−0.533459	+	1.56116i
$586$	−8.40598	+	7.05345i	−0.347248	+	0.291376i
$587$	−29.5771	+	5.21525i	−1.22078	+	0.215256i	−0.746661	−	0.665205i	$-0.768344\pi$
$587$	−29.5771	+	5.21525i	−1.22078	+	0.215256i	−0.474118	+	0.880461i	$0.657233\pi$
$588$	3.73401	−	1.78641i	0.153988	−	0.0736701i
$589$	−8.41982	−	5.75231i	−0.346932	−	0.237020i
$590$		−	17.8792i		−	0.736074i
$591$	16.7367	−	11.9678i	0.688456	−	0.492289i
$592$	−3.86538	−	4.60658i	−0.158866	−	0.189329i
$593$	0.268437	+	0.737526i	0.0110234	+	0.0302866i	0.945082	−	0.326832i	$-0.105981\pi$
$593$	0.268437	+	0.737526i	0.0110234	+	0.0302866i	−0.934059	+	0.357119i	$0.883759\pi$
$594$	−27.1708	−	17.8469i	−1.11483	−	0.732267i
$595$	−2.24948	−	1.88754i	−0.0922198	−	0.0773816i
$596$	−4.59793	−	2.65462i	−0.188339	−	0.108737i
$597$	34.9090	+	23.9321i	1.42873	+	0.979476i
$598$	−0.567463	+	3.21824i	−0.0232053	+	0.131604i
$599$	2.35948	−	13.3813i	0.0964057	−	0.546744i	−0.897902	−	0.440196i	$-0.854909\pi$
$599$	2.35948	−	13.3813i	0.0964057	−	0.546744i	0.994308	−	0.106548i	$-0.0339798\pi$
$600$	8.76539	+	6.00917i	0.357845	+	0.245323i
$601$	1.41283	+	0.815696i	0.0576304	+	0.0332729i	0.528538	−	0.848909i	$-0.322740\pi$
$601$	1.41283	+	0.815696i	0.0576304	+	0.0332729i	−0.470908	+	0.882182i	$0.656074\pi$
$602$	10.2812	+	8.62693i	0.419029	+	0.351607i
$603$	−5.49208	−	9.09201i	−0.223655	−	0.370255i
$604$	−0.875527	−	2.40549i	−0.0356247	−	0.0978781i
$605$	60.3592	+	71.9333i	2.45395	+	2.92450i
$606$	8.09256	−	5.78669i	0.328738	−	0.235068i
$607$		−	23.6670i		−	0.960615i	−0.877100	−	0.480308i	$-0.840525\pi$
$607$		−	23.6670i		−	0.960615i	0.877100	−	0.480308i	$-0.159475\pi$
$608$	−3.11749	−	3.04652i	−0.126431	−	0.123553i
$609$	15.5548	−	7.44167i	0.630314	−	0.301552i
$610$	25.5545	−	4.50595i	1.03467	−	0.182441i
$611$	−23.5610	+	19.7700i	−0.953177	+	0.799811i
$612$	1.16346	+	0.397563i	0.0470301	+	0.0160705i
$613$	14.7136	+	5.35532i	0.594278	+	0.216299i	0.621610	−	0.783327i	$-0.286479\pi$
$613$	14.7136	+	5.35532i	0.594278	+	0.216299i	−0.0273321	+	0.999626i	$0.508701\pi$
$614$	−0.351542	+	0.418952i	−0.0141871	+	0.0169075i
$615$	6.97052	+	0.540372i	0.281079	+	0.0217899i
$616$	−11.6331	+	6.71638i	−0.468712	+	0.270611i
$617$	−19.6258	−	3.46056i	−0.790105	−	0.139317i	−0.235988	−	0.971756i	$-0.575833\pi$
$617$	−19.6258	−	3.46056i	−0.790105	−	0.139317i	−0.554117	+	0.832439i	$0.686944\pi$
$618$	−1.84403	+	0.513724i	−0.0741778	+	0.0206650i
$619$	−3.55524	−	6.15786i	−0.142897	−	0.247505i	0.785689	−	0.618621i	$-0.212309\pi$
$619$	−3.55524	−	6.15786i	−0.142897	−	0.247505i	−0.928587	+	0.371116i	$0.878975\pi$
$620$	−3.90331	+	6.76072i	−0.156761	+	0.271517i
$621$	2.54606	+	3.41562i	0.102170	+	0.137064i
$622$	−4.81452	+	13.2278i	−0.193045	+	0.530386i
$623$	−14.7992	+	5.38648i	−0.592919	+	0.215805i
$624$	−6.28550	−	2.85557i	−0.251621	−	0.114314i
$625$	−3.13111	−	17.7574i	−0.125244	−	0.710297i
$626$	18.6019			0.743480
$627$	1.01125	+	47.2221i	0.0403856	+	1.88587i
$628$	−16.7677			−0.669104
$629$	−0.427962	−	2.42710i	−0.0170640	−	0.0967746i
$630$	21.4909	−	0.425521i	0.856216	−	0.0169532i
$631$	−1.16675	+	0.424661i	−0.0464474	+	0.0169055i	−0.365139	−	0.930953i	$-0.618979\pi$
$631$	−1.16675	+	0.424661i	−0.0464474	+	0.0169055i	0.318692	+	0.947858i	$0.396756\pi$
$632$	4.28551	−	11.7743i	0.170468	−	0.468358i
$633$	7.15294	−	27.7927i	0.284304	−	1.10466i
$634$	13.5959	−	23.5487i	0.539960	−	0.935239i
$635$	2.05623	+	3.56149i	0.0815989	+	0.141334i
$636$	−0.109080	−	0.391547i	−0.00432530	−	0.0155258i
$637$	−9.38092	−	1.65411i	−0.371685	−	0.0655382i
$638$	25.1212	−	14.5037i	0.994557	−	0.574208i
$639$	4.83225	+	12.5008i	0.191161	+	0.494522i
$640$	−2.14500	+	2.55631i	−0.0847885	+	0.101047i
$641$	7.06477	+	2.57137i	0.279042	+	0.101563i	0.477750	−	0.878496i	$-0.341452\pi$
$641$	7.06477	+	2.57137i	0.279042	+	0.101563i	−0.198708	+	0.980059i	$0.563675\pi$
$642$	8.43035	−	8.59893i	0.332719	−	0.339373i
$643$	−9.31005	+	7.81206i	−0.367153	+	0.308078i	−0.807634	−	0.589684i	$-0.799252\pi$
$643$	−9.31005	+	7.81206i	−0.367153	+	0.308078i	0.440481	+	0.897762i	$0.354808\pi$
$644$	1.73361	−	0.305683i	0.0683139	−	0.0120456i
$645$	−15.5920	−	32.5909i	−0.613933	−	1.28327i
$646$	−0.482199	−	1.72013i	−0.0189719	−	0.0676776i
$647$		−	38.1298i		−	1.49904i	−0.661983	−	0.749519i	$-0.730285\pi$
$647$		−	38.1298i		−	1.49904i	0.661983	−	0.749519i	$-0.269715\pi$
$648$	−8.32876	+	3.41055i	−0.327184	+	0.133979i
$649$	−21.5458	−	25.6773i	−0.845747	−	1.00792i
$650$	−8.36457	−	22.9815i	−0.328085	−	0.901407i
$651$	0.844012	+	8.65901i	0.0330794	+	0.339373i
$652$	−8.09708	−	6.79425i	−0.317106	−	0.266084i
$653$	−39.7547	−	22.9524i	−1.55572	−	0.898196i	−0.997658	−	0.0683980i	$-0.978211\pi$
$653$	−39.7547	−	22.9524i	−1.55572	−	0.898196i	−0.558063	−	0.829798i	$-0.688455\pi$
$654$	6.95505	−	10.1451i	0.271964	−	0.396705i
$655$	3.73239	−	21.1674i	0.145836	−	0.827080i
$656$	−0.210047	+	1.19124i	−0.00820096	+	0.0465099i
$657$	16.7618	+	2.61454i	0.653940	+	0.102003i
$658$	14.3484	+	8.28407i	0.559360	+	0.322947i
$659$	14.3577	+	12.0475i	0.559295	+	0.469304i	0.878074	−	0.478525i	$-0.158828\pi$
$659$	14.3577	+	12.0475i	0.559295	+	0.469304i	−0.318779	+	0.947829i	$0.603273\pi$
$660$	35.9894	−	3.50796i	1.40089	−	0.136547i
$661$	4.05073	+	11.1293i	0.157555	+	0.432879i	0.993204	−	0.116385i	$-0.0371306\pi$
$661$	4.05073	+	11.1293i	0.157555	+	0.432879i	−0.835649	+	0.549263i	$0.814908\pi$
$662$	−18.8690	−	22.4872i	−0.733364	−	0.873989i
$663$	−1.64575	−	2.30154i	−0.0639155	−	0.0893844i
$664$		−	9.25584i		−	0.359196i
$665$	−18.2071	−	25.3755i	−0.706039	−	0.984020i
$666$	14.0466	+	11.3203i	0.544294	+	0.438652i
$667$	−3.74366	+	0.660108i	−0.144955	+	0.0255595i
$668$	−8.57590	+	7.19604i	−0.331812	+	0.278423i
$669$	−14.6499	−	14.3627i	−0.566400	−	0.555296i
$670$	11.1028	+	4.04108i	0.428938	+	0.156121i
$671$	31.2703	−	37.2665i	1.20718	−	1.43866i
$672$	−0.287438	+	3.70781i	−0.0110882	+	0.143032i
$673$	−9.02264	+	5.20922i	−0.347797	+	0.200801i	−0.663715	−	0.747986i	$-0.731021\pi$
$673$	−9.02264	+	5.20922i	−0.347797	+	0.200801i	0.315917	+	0.948787i	$0.397688\pi$
$674$	−13.2694	−	2.33976i	−0.511119	−	0.0901240i
$675$	−29.2825	−	12.6101i	−1.12708	−	0.485364i
$676$	1.44363	+	2.50044i	0.0555241	+	0.0961706i
$677$	−10.3670	+	17.9562i	−0.398437	+	0.690112i	−0.993533	−	0.113542i	$-0.963780\pi$
$677$	−10.3670	+	17.9562i	−0.398437	+	0.690112i	0.595097	+	0.803654i	$0.297114\pi$
$678$	−3.90832	−	1.00587i	−0.150098	−	0.0386303i
$679$	11.9858	−	32.9306i	0.459972	−	1.26376i
$680$	−1.28516	+	0.467759i	−0.0492836	+	0.0179377i
$681$	−16.5294	+	36.3834i	−0.633408	+	1.39421i
$682$	2.54145	+	14.4133i	0.0973170	+	0.551912i
$683$	2.79983			0.107132			0.0535662	−	0.998564i	$-0.482941\pi$
$683$	2.79983			0.107132			0.0535662	+	0.998564i	$0.482941\pi$
$684$	10.9414	+	7.16147i	0.418353	+	0.273826i
$685$	35.9492			1.37355
$686$	3.50095	+	19.8549i	0.133667	+	0.758064i
$687$	−10.0629	+	22.1499i	−0.383925	+	0.845070i
$688$	5.87377	−	2.13788i	0.223935	−	0.0815058i
$689$	−0.319912	+	0.878950i	−0.0121877	+	0.0334853i
$690$	−4.58919	−	1.18111i	−0.174708	−	0.0449640i
$691$	−4.20182	+	7.27776i	−0.159845	+	0.276859i	−0.934813	−	0.355142i	$-0.884433\pi$
$691$	−4.20182	+	7.27776i	−0.159845	+	0.276859i	0.774968	+	0.632001i	$0.217766\pi$
$692$	10.9577	+	18.9794i	0.416551	+	0.721487i
$693$	30.3514	−	26.5093i	1.15296	−	1.00700i
$694$	5.93191	+	1.04596i	0.225172	+	0.0397040i
$695$	−24.3697	+	14.0698i	−0.924395	+	0.533700i
$696$	0.620710	−	8.00685i	0.0235280	−	0.303499i
$697$	−0.318658	+	0.379762i	−0.0120700	+	0.0143845i
$698$	26.8874	+	9.78621i	1.01770	+	0.370413i
$699$	29.1746	+	28.6027i	1.10349	+	1.08185i
$700$	−10.0920	+	8.46823i	−0.381443	+	0.320069i
$701$	−14.9472	+	2.63560i	−0.564549	+	0.0995451i	−0.448636	−	0.893714i	$-0.648090\pi$
$701$	−14.9472	+	2.63560i	−0.564549	+	0.0995451i	−0.115912	+	0.993259i	$0.536979\pi$
$702$	20.1559	+	4.76410i	0.760734	+	0.179809i
$703$	1.98376	−	26.1369i	0.0748190	−	0.985771i
$704$			6.25616i			0.235788i
$705$	−25.9420	−	36.2793i	−0.977031	−	1.36636i
$706$	10.8414	+	12.9203i	0.408023	+	0.486263i
$707$	4.21806	+	11.5890i	0.158636	+	0.435850i
$708$	−9.23623	+	0.900276i	−0.347119	+	0.0338344i
$709$	−29.3000	−	24.5857i	−1.10039	−	0.923334i	−0.102935	−	0.994688i	$-0.532823\pi$
$709$	−29.3000	−	24.5857i	−1.10039	−	0.923334i	−0.997451	+	0.0713544i	$0.977268\pi$
$710$	−12.9106	−	7.45393i	−0.484526	−	0.279741i
$711$	−5.79331	+	37.1409i	−0.217266	+	1.39289i
$712$	−1.27370	+	7.22349i	−0.0477338	+	0.270712i
$713$	0.333055	−	1.88885i	0.0124730	−	0.0707380i
$714$	−0.861819	+	1.25711i	−0.0322528	+	0.0470461i
$715$	−72.0647	−	41.6065i	−2.69507	−	1.55600i
$716$	−16.3833	−	13.7472i	−0.612271	−	0.513756i
$717$	4.57942	+	46.9819i	0.171022	+	1.75457i
$718$	−5.65444	−	15.5354i	−0.211022	−	0.579778i
$719$	−24.9620	−	29.7485i	−0.930924	−	1.10943i	−0.993775	−	0.111410i	$-0.964463\pi$
$719$	−24.9620	−	29.7485i	−0.930924	−	1.10943i	0.0628501	−	0.998023i	$-0.479981\pi$
$720$	4.83293	−	8.76724i	0.180113	−	0.326736i
$721$		−	2.37299i		−	0.0883749i
$722$	−0.437448	−	18.9950i	−0.0162801	−	0.706919i
$723$	15.9001	+	33.2349i	0.591330	+	1.23602i
$724$	18.0057	−	3.17489i	0.669177	−	0.117994i
$725$	21.7933	−	18.2868i	0.809383	−	0.679153i
$726$	34.1209	−	34.8032i	1.26634	−	1.29167i
$727$	35.9582	+	13.0877i	1.33361	+	0.485396i	0.907796	−	0.419413i	$-0.137764\pi$
$727$	35.9582	+	13.0877i	1.33361	+	0.485396i	0.425818	+	0.904809i	$0.359986\pi$
$728$	5.50110	−	6.55596i	0.203884	−	0.242980i
$729$	22.5401	−	14.8641i	0.834820	−	0.550524i
$730$	−16.3422	+	9.43516i	−0.604851	+	0.349211i
$731$	2.52286	+	0.444849i	0.0933114	+	0.0164533i
$732$	−3.61449	−	12.9744i	−0.133595	−	0.479546i
$733$	−7.71039	−	13.3548i	−0.284790	−	0.493270i	0.687768	−	0.725930i	$-0.258590\pi$
$733$	−7.71039	−	13.3548i	−0.284790	−	0.493270i	−0.972558	+	0.232660i	$0.925257\pi$
$734$	−4.78059	+	8.28022i	−0.176455	+	0.305628i
$735$	3.44284	−	13.3771i	0.126991	−	0.493423i
$736$	0.280411	−	0.770422i	0.0103361	−	0.0283981i
$737$	20.8152	−	7.57610i	0.766736	−	0.279069i
$738$	−0.0718373	−	3.62813i	−0.00264437	−	0.133553i
$739$	−4.98207	−	28.2547i	−0.183268	−	1.03937i	−0.928160	−	0.372181i	$-0.878610\pi$
$739$	−4.98207	−	28.2547i	−0.183268	−	1.03937i	0.744892	−	0.667185i	$-0.232501\pi$
$740$	−20.0671			−0.737680
$741$	−10.8954	−	28.0511i	−0.400252	−	1.03048i
$742$	0.503862			0.0184974
$743$	4.95784	+	28.1173i	0.181886	+	1.03152i	0.929892	+	0.367833i	$0.119900\pi$
$743$	4.95784	+	28.1173i	0.181886	+	1.03152i	−0.748006	+	0.663691i	$0.768989\pi$
$744$	3.68908	+	1.67599i	0.135248	+	0.0614448i
$745$	−16.6486	+	6.05959i	−0.609957	+	0.222006i
$746$	1.48177	−	4.07112i	0.0542514	−	0.149054i
$747$	5.36218	+	27.2449i	0.196192	+	0.996837i
$748$	−1.28200	+	2.22049i	−0.0468746	+	0.0811892i
$749$	7.46397	+	12.9280i	0.272727	+	0.472378i
$750$	6.32369	−	1.76170i	0.230908	−	0.0643281i
$751$	12.4716	+	2.19908i	0.455096	+	0.0802457i	0.396497	−	0.918036i	$-0.370226\pi$
$751$	12.4716	+	2.19908i	0.455096	+	0.0802457i	0.0585987	+	0.998282i	$0.481337\pi$
$752$	6.68262	−	3.85821i	0.243690	−	0.140694i
$753$	4.28646	+	0.332297i	0.156207	+	0.0121096i
$754$	−11.8794	+	14.1573i	−0.432622	+	0.515578i
$755$	−8.02719	−	2.92166i	−0.292139	−	0.106330i
$756$	−1.30196	−	11.0806i	−0.0473517	−	0.402997i
$757$	38.4432	−	32.2577i	1.39724	−	1.17243i	0.434934	−	0.900462i	$-0.356772\pi$
$757$	38.4432	−	32.2577i	1.39724	−	1.17243i	0.962308	−	0.271963i	$-0.0876729\pi$
$758$	5.87751	−	1.03636i	0.213481	−	0.0376424i
$759$	−8.01413	+	3.83408i	−0.290894	+	0.139168i
$760$	−14.4749	+	1.43448i	−0.525058	+	0.0520342i
$761$		−	26.6803i		−	0.967159i	−0.875300	−	0.483580i	$-0.839336\pi$
$761$		−	26.6803i		−	0.967159i	0.875300	−	0.483580i	$-0.160664\pi$
$762$	1.73630	−	1.24156i	0.0628995	−	0.0449771i
$763$	9.80118	+	11.6806i	0.354826	+	0.422866i
$764$	−1.18379	−	3.25243i	−0.0428279	−	0.117669i
$765$	3.51192	−	2.12139i	0.126974	−	0.0766991i
$766$	3.37004	+	2.82780i	0.121764	+	0.102172i
$767$	18.4945	+	10.6778i	0.667798	+	0.385553i
$768$	1.42858	+	0.979371i	0.0515493	+	0.0353400i
$769$	−6.83201	+	38.7463i	−0.246369	+	1.39723i	0.570924	+	0.821003i	$0.306585\pi$
$769$	−6.83201	+	38.7463i	−0.246369	+	1.39723i	−0.817292	+	0.576223i	$0.804526\pi$
$770$	−7.78387	+	44.1445i	−0.280511	+	1.59086i
$771$	−16.0806	−	11.0242i	−0.579130	−	0.397026i
$772$	−8.95163	−	5.16822i	−0.322176	−	0.186008i
$773$	2.48012	+	2.08107i	0.0892039	+	0.0748509i	0.686299	−	0.727319i	$-0.259234\pi$
$773$	2.48012	+	2.08107i	0.0892039	+	0.0748509i	−0.597095	+	0.802170i	$0.703679\pi$
$774$	−16.0511	+	9.69575i	−0.576944	+	0.348507i
$775$	4.90933	+	13.4883i	0.176348	+	0.484513i
$776$	−10.4912	−	12.5029i	−0.376611	−	0.448828i
$777$	−18.1914	+	13.0080i	−0.652612	+	0.466658i
$778$		−	14.7246i		−	0.527901i
$779$	−4.28394	+	3.07375i	−0.153488	+	0.110128i
$780$	−20.7821	+	9.94248i	−0.744119	+	0.355998i
$781$	−27.5242	+	4.85326i	−0.984893	+	0.173663i
$782$	0.257400	−	0.215984i	0.00920459	−	0.00772357i
$783$	2.81152	+	23.9280i	0.100475	+	0.855117i
$784$	2.24572	+	0.817375i	0.0802042	+	0.0291919i
$785$	−35.9667	+	42.8634i	−1.28371	+	1.52986i
$786$	−11.1229	−	0.862271i	−0.396739	−	0.0307562i
$787$	−22.8624	+	13.1996i	−0.814956	+	0.470515i	−0.848674	−	0.528916i	$-0.822599\pi$
$787$	−22.8624	+	13.1996i	−0.814956	+	0.470515i	0.0337179	+	0.999431i	$0.489265\pi$
$788$	11.6987	+	2.06280i	0.416749	+	0.0734842i
$789$	19.6648	−	5.47836i	0.700086	−	0.195035i
$790$	−20.9065	−	36.2110i	−0.743818	−	1.28833i
$791$	2.50141	−	4.33256i	0.0889397	−	0.154048i
$792$	−3.62437	−	18.4152i	−0.128786	−	0.654355i
$793$	−10.6007	+	29.1251i	−0.376440	+	1.03426i
$794$	9.45658	−	3.44191i	0.335601	−	0.122149i
$795$	−1.23489	−	0.561025i	−0.0437971	−	0.0198975i
$796$	4.24330	+	24.0650i	0.150400	+	0.852960i
$797$	−9.50783			−0.336785			−0.168392	−	0.985720i	$-0.553858\pi$
$797$	−9.50783			−0.336785			−0.168392	+	0.985720i	$0.553858\pi$
$798$	−12.1920	+	10.6834i	−0.431592	+	0.378187i
$799$	3.16247			0.111880
$800$	1.06546	+	6.04253i	0.0376697	+	0.213636i
$801$	−0.435612	−	22.0005i	−0.0153916	−	0.777348i
$802$	13.9665	−	5.08338i	0.493173	−	0.179500i
$803$	−12.0998	+	33.2440i	−0.426993	+	1.17315i
$804$	1.52853	−	5.93909i	0.0539070	−	0.209456i
$805$	2.93718	−	5.08734i	0.103522	−	0.179305i
$806$	−4.66227	−	8.07529i	−0.164221	−	0.284440i
$807$	−5.43998	−	19.5270i	−0.191497	−	0.687384i
$808$	5.65658	+	0.997408i	0.198998	+	0.0350887i
$809$	−31.3018	+	18.0721i	−1.10051	+	0.635380i	−0.936355	−	0.351054i	$-0.885823\pi$
$809$	−31.3018	+	18.0721i	−1.10051	+	0.635380i	−0.164156	+	0.986434i	$0.552490\pi$
$810$	−9.14676	+	28.6065i	−0.321384	+	1.00513i
$811$	16.3764	−	19.5167i	0.575054	−	0.685323i	−0.397606	−	0.917556i	$-0.630159\pi$
$811$	16.3764	−	19.5167i	0.575054	−	0.685323i	0.972660	+	0.232233i	$0.0746033\pi$
$812$	9.35504	+	3.40496i	0.328297	+	0.119491i
$813$	37.6790	−	38.4324i	1.32146	−	1.34788i
$814$	−28.8195	+	24.1824i	−1.01012	+	0.847593i
$815$	−34.7364	+	6.12497i	−1.21676	+	0.214548i
$816$	0.306353	+	0.640349i	0.0107245	+	0.0224167i
$817$	24.8245	+	11.2297i	0.868498	+	0.392879i
$818$			9.96298i			0.348347i
$819$	−12.3946	+	22.4846i	−0.433103	+	0.785676i
$820$	2.59462	+	3.09214i	0.0906080	+	0.107982i
$821$	−3.53702	−	9.71788i	−0.123443	−	0.339156i	0.862543	−	0.505983i	$-0.168870\pi$
$821$	−3.53702	−	9.71788i	−0.123443	−	0.339156i	−0.985986	+	0.166827i	$0.946648\pi$
$822$	−1.81016	−	18.5711i	−0.0631366	−	0.647740i
$823$	11.1336	+	9.34221i	0.388093	+	0.325649i	0.815870	−	0.578235i	$-0.196259\pi$
$823$	11.1336	+	9.34221i	0.388093	+	0.325649i	−0.427776	+	0.903885i	$0.640703\pi$
$824$	−0.957127	−	0.552597i	−0.0333431	−	0.0192506i
$825$	37.5943	−	54.8376i	1.30887	−	1.90920i
$826$	1.99763	−	11.3291i	0.0695065	−	0.394191i
$827$	−4.21974	+	23.9313i	−0.146735	+	0.832174i	0.819223	+	0.573475i	$0.194405\pi$
$827$	−4.21974	+	23.9313i	−0.146735	+	0.832174i	−0.965958	+	0.258699i	$0.916706\pi$
$828$	−0.379070	+	2.43021i	−0.0131736	+	0.0844557i
$829$	43.3587	+	25.0331i	1.50591	+	0.869437i	0.999976	+	0.00686327i	$0.00218466\pi$
$829$	43.3587	+	25.0331i	1.50591	+	0.869437i	0.505932	+	0.862573i	$0.331149\pi$
$830$	−23.6608	−	19.8538i	−0.821279	−	0.689134i
$831$	−6.61851	+	0.645121i	−0.229594	+	0.0223790i
$832$	−1.36325	−	3.74550i	−0.0472623	−	0.129852i
$833$	0.629576	+	0.750299i	0.0218135	+	0.0259963i
$834$	8.49546	+	11.8807i	0.294174	+	0.411396i
$835$			37.3582i			1.29283i
$836$	−19.0595	+	19.5035i	−0.659186	+	0.674542i
$837$	−11.8299	−	2.79614i	−0.408900	−	0.0966488i
$838$	8.22164	−	1.44970i	0.284012	−	0.0500789i
$839$	25.2797	−	21.2122i	0.872752	−	0.732326i	−0.0919238	−	0.995766i	$-0.529302\pi$
$839$	25.2797	−	21.2122i	0.872752	−	0.732326i	0.964676	+	0.263440i	$0.0848572\pi$
$840$	8.86176	+	8.68803i	0.305760	+	0.299766i
$841$	7.04931	+	2.56574i	0.243080	+	0.0884737i
$842$	23.4446	−	27.9402i	0.807954	−	0.962882i
$843$	3.28602	−	42.3880i	0.113177	−	1.45992i
$844$	14.3492	−	8.28452i	0.493920	−	0.285165i
$845$	9.48847	+	1.67307i	0.326413	+	0.0575555i
$846$	−17.4353	+	15.2282i	−0.599439	+	0.523556i
$847$	30.2095	+	52.3245i	1.03801	+	1.79789i
$848$	0.117334	−	0.203228i	0.00402927	−	0.00697889i
$849$	38.9830	+	10.0330i	1.33789	+	0.344330i
$850$	−0.860063	+	2.36300i	−0.0294999	+	0.0810503i
$851$	4.63290	−	1.68624i	0.158814	−	0.0578035i
$852$	−3.20055	+	7.04483i	−0.109649	+	0.241352i
$853$	5.13243	+	29.1074i	0.175731	+	0.996620i	0.937297	+	0.348532i	$0.113320\pi$
$853$	5.13243	+	29.1074i	0.175731	+	0.996620i	−0.761566	+	0.648088i	$0.775569\pi$
$854$	16.6961			0.571328
$855$	41.7762	−	12.6082i	1.42871	−	0.431190i
$856$	6.95251			0.237632
$857$	−8.49473	−	48.1760i	−0.290175	−	1.64566i	−0.686193	−	0.727419i	$-0.740720\pi$
$857$	−8.49473	−	48.1760i	−0.290175	−	1.64566i	0.396019	−	0.918242i	$-0.370392\pi$
$858$	−17.8649	+	39.3230i	−0.609898	+	1.34247i
$859$	−36.8403	+	13.4088i	−1.25698	+	0.457502i	−0.882753	−	0.469837i	$-0.844313\pi$
$859$	−36.8403	+	13.4088i	−1.25698	+	0.457502i	−0.374222	+	0.927339i	$0.622090\pi$
$860$	7.13415	−	19.6009i	0.243272	−	0.668386i
$861$	4.35650	+	1.12122i	0.148469	+	0.0382111i
$862$	−5.25916	+	9.10914i	−0.179128	+	0.310258i
$863$	−17.6337	−	30.5424i	−0.600257	−	1.03967i	−0.992782	−	0.119934i	$-0.961732\pi$
$863$	−17.6337	−	30.5424i	−0.600257	−	1.03967i	0.392525	−	0.919741i	$-0.371602\pi$
$864$	−4.77244	−	2.05519i	−0.162362	−	0.0699191i
$865$	72.0215	+	12.6993i	2.44880	+	0.431790i
$866$	−31.9364	+	18.4385i	−1.08524	+	0.626565i
$867$	2.25332	−	29.0667i	0.0765269	−	0.987158i
$868$	−3.22870	+	3.84782i	−0.109589	+	0.130604i
$869$	−73.6621	−	26.8108i	−2.49882	−	0.909494i
$870$	−19.1366	−	18.7614i	−0.648790	−	0.636071i
$871$	−10.8110	+	9.07148i	−0.366316	+	0.307375i
$872$	6.99366	−	1.23317i	0.236835	−	0.0417604i
$873$	38.1244	+	30.7248i	1.29031	+	1.03988i
$874$	3.22128	−	1.54750i	0.108962	−	0.0523451i
$875$			8.13764i			0.275102i
$876$	5.69701	+	7.96714i	0.192484	+	0.269185i
$877$	14.4779	+	17.2541i	0.488883	+	0.582628i	0.952933	−	0.303181i	$-0.0980486\pi$
$877$	14.4779	+	17.2541i	0.488883	+	0.582628i	−0.464050	+	0.885809i	$0.653604\pi$
$878$	−4.55330	−	12.5101i	−0.153666	−	0.422195i
$879$	18.9165	−	1.84384i	0.638039	−	0.0621910i
$880$	15.9927	+	13.4195i	0.539113	+	0.452370i
$881$	47.0165	+	27.1450i	1.58403	+	0.914539i	0.994263	+	0.106964i	$0.0341129\pi$
$881$	47.0165	+	27.1450i	1.58403	+	0.914539i	0.589765	+	0.807575i	$0.299220\pi$
$882$	−7.08387	−	1.10496i	−0.238526	−	0.0372059i
$883$	4.51473	−	25.6043i	0.151933	−	0.861653i	−0.809604	−	0.586977i	$-0.800318\pi$
$883$	4.51473	−	25.6043i	0.151933	−	0.861653i	0.961537	−	0.274677i	$-0.0885708\pi$
$884$	0.283665	−	1.60874i	0.00954068	−	0.0541079i
$885$	−17.5103	+	25.5418i	−0.588603	+	0.858577i
$886$	6.46556	+	3.73289i	0.217215	+	0.125409i
$887$	4.19836	+	3.52284i	0.140967	+	0.118286i	0.710545	−	0.703652i	$-0.248449\pi$
$887$	4.19836	+	3.52284i	0.140967	+	0.118286i	−0.569577	+	0.821938i	$0.692893\pi$
$888$	1.01044	+	10.3665i	0.0339083	+	0.347877i
$889$	0.905006	+	2.48648i	0.0303529	+	0.0833939i
$890$	15.7334	+	18.7503i	0.527385	+	0.628513i
$891$	21.3369	+	52.1060i	0.714813	+	1.74562i
$892$		−	11.8450i		−	0.396599i
$893$	32.5871	+	8.33079i	1.09048	+	0.278779i
$894$	3.96864	+	8.29540i	0.132731	+	0.277440i
$895$	−70.2842	+	12.3930i	−2.34934	+	0.414252i
$896$	−1.64480	+	1.38015i	−0.0549487	+	0.0461075i
$897$	3.96252	−	4.04175i	0.132305	−	0.134950i
$898$	22.8874	+	8.33033i	0.763763	+	0.277987i
$899$	6.97224	−	8.30919i	0.232537	−	0.277127i
$900$	−6.63683	−	17.1691i	−0.221228	−	0.572304i
$901$	0.0832905	−	0.0480878i	0.00277481	−	0.00160204i
$902$	7.45256	+	1.31409i	0.248143	+	0.0437543i
$903$	−6.23849	−	22.3933i	−0.207604	−	0.745203i
$904$	−1.16500	−	2.01784i	−0.0387474	−	0.0671124i
$905$	30.5062	−	52.8383i	1.01406	−	1.75640i
$906$	−1.10511	+	4.29390i	−0.0367148	+	0.142655i
$907$	20.0545	−	55.0993i	0.665899	−	1.82954i	0.117971	−	0.993017i	$-0.462361\pi$
$907$	20.0545	−	55.0993i	0.665899	−	1.82954i	0.547928	−	0.836526i	$-0.315417\pi$
$908$	−21.6807	+	7.89114i	−0.719500	+	0.261877i
$909$	−17.2282	+	0.341120i	−0.571422	+	0.0113142i
$910$	−4.95921	−	28.1251i	−0.164396	−	0.932336i
$911$	2.91388			0.0965412			0.0482706	−	0.998834i	$-0.484629\pi$
$911$	2.91388			0.0965412			0.0482706	+	0.998834i	$0.484629\pi$
$912$	1.46990	+	7.40536i	0.0486733	+	0.245216i
$913$	−57.9060			−1.91641
$914$	6.04517	+	34.2839i	0.199956	+	1.13401i
$915$	−40.9196	−	18.5902i	−1.35276	−	0.614574i
$916$	−13.1990	+	4.80405i	−0.436108	+	0.158730i
$917$	4.73006	−	12.9957i	0.156200	−	0.429157i
$918$	−1.27273	−	1.70741i	−0.0420064	−	0.0563529i
$919$	2.94881	−	5.10749i	0.0972722	−	0.168480i	−0.813282	−	0.581869i	$-0.802322\pi$
$919$	2.94881	−	5.10749i	0.0972722	−	0.168480i	0.910555	+	0.413389i	$0.135655\pi$
$920$	−1.36796	−	2.36937i	−0.0451002	−	0.0781159i
$921$	0.912514	−	0.254215i	0.0300684	−	0.00837666i
$922$	2.20281	+	0.388415i	0.0725457	+	0.0127918i
$923$	15.4209	−	8.90328i	0.507586	−	0.293055i
$924$	23.1966	+	1.79826i	0.763113	+	0.0591584i
$925$	−23.7170	+	28.2648i	−0.779809	+	0.929340i
$926$	−3.45977	−	1.25925i	−0.113695	−	0.0413816i
$927$	3.13747	+	1.07210i	0.103048	+	0.0352123i
$928$	3.55186	−	2.98036i	0.116596	−	0.0978353i
$929$	22.4137	−	3.95214i	0.735369	−	0.129665i	0.206593	−	0.978427i	$-0.433762\pi$
$929$	22.4137	−	3.95214i	0.735369	−	0.129665i	0.528776	+	0.848762i	$0.322651\pi$
$930$	12.1974	−	5.83543i	0.399969	−	0.191351i
$931$	4.51085	+	9.38978i	0.147837	+	0.307738i
$932$			23.5886i			0.772672i
$933$	19.8328	−	14.1817i	0.649298	−	0.464289i
$934$	−8.45753	−	10.0793i	−0.276739	−	0.329804i
$935$	2.92637	+	8.04015i	0.0957027	+	0.262941i
$936$	6.18265	+	10.2352i	0.202086	+	0.334549i
$937$	−33.5028	−	28.1122i	−1.09449	−	0.918384i	−0.0974452	−	0.995241i	$-0.531067\pi$
$937$	−33.5028	−	28.1122i	−1.09449	−	0.918384i	−0.997042	+	0.0768570i	$0.975512\pi$
$938$	6.58377	+	3.80114i	0.214968	+	0.124112i
$939$	−26.5742	−	18.2181i	−0.867216	−	0.594526i
$940$	4.47142	−	25.3587i	0.145842	−	0.827110i
$941$	−1.06108	+	6.01769i	−0.0345903	+	0.196171i	−0.997206	−	0.0746992i	$-0.976200\pi$
$941$	−1.06108	+	6.01769i	−0.0345903	+	0.196171i	0.962616	+	0.270870i	$0.0873115\pi$
$942$	23.9540	+	16.4218i	0.780462	+	0.535051i
$943$	−0.858855	−	0.495860i	−0.0279682	−	0.0161474i
$944$	−4.10432	−	3.44394i	−0.133584	−	0.112091i
$945$	−31.1181	−	20.4396i	−1.01227	−	0.664901i
$946$	−13.3749	−	36.7472i	−0.434855	−	1.19475i
$947$	19.9420	+	23.7660i	0.648029	+	0.772291i	0.985615	−	0.169004i	$-0.0540550\pi$
$947$	19.9420	+	23.7660i	0.648029	+	0.772291i	−0.337586	+	0.941295i	$0.609611\pi$
$948$	−17.6536	+	12.6235i	−0.573363	+	0.409991i
$949$		−	22.5395i		−	0.731662i
$950$	−15.0871	+	22.0835i	−0.489491	+	0.716482i
$951$	−42.4857	+	20.3258i	−1.37769	+	0.659109i
$952$	−0.866603	+	0.152806i	−0.0280868	+	0.00495246i
$953$	38.1684	−	32.0271i	1.23640	−	1.03746i	0.238599	−	0.971118i	$-0.423312\pi$
$953$	38.1684	−	32.0271i	1.23640	−	1.03746i	0.997797	−	0.0663415i	$-0.0211327\pi$
$954$	−0.227640	+	0.666184i	−0.00737012	+	0.0215685i
$955$	−10.8534	−	3.95033i	−0.351209	−	0.127830i
$956$	−17.5182	+	20.8774i	−0.566580	+	0.675224i
$957$	−50.0921	−	3.88326i	−1.61925	−	0.125528i
$958$	29.0286	−	16.7597i	0.937871	−	0.541480i
$959$	22.7792	+	4.01659i	0.735579	+	0.129702i
$960$	5.56787	−	1.55114i	0.179702	−	0.0500628i
$961$	−12.7636	−	22.1072i	−0.411730	−	0.713137i
$962$	11.9845	−	20.7577i	0.386395	−	0.669255i
$963$	−20.4649	+	4.02779i	−0.659474	+	0.129794i
$964$	−7.27512	+	19.9882i	−0.234316	+	0.643777i
$965$	−32.4128	+	11.7973i	−1.04341	+	0.379769i
$966$	−2.77598	−	1.26116i	−0.0893156	−	0.0405771i
$967$	−1.94625	−	11.0377i	−0.0625873	−	0.354950i	−0.999978	−	0.00666987i	$-0.997877\pi$
$967$	−1.94625	−	11.0377i	−0.0625873	−	0.354950i	0.937390	−	0.348280i	$-0.113234\pi$
$968$	28.1395			0.904438
$969$	−0.995785	+	2.92959i	−0.0319892	+	0.0941119i
$970$	−54.4648			−1.74876
$971$	8.32593	+	47.2187i	0.267192	+	1.51532i	0.762720	+	0.646729i	$0.223863\pi$
$971$	8.32593	+	47.2187i	0.267192	+	1.51532i	−0.495528	+	0.868592i	$0.665026\pi$
$972$	15.2385	+	3.28471i	0.488774	+	0.105357i
$973$	−17.0139	+	6.19254i	−0.545440	+	0.198524i
$974$	−6.00502	+	16.4987i	−0.192413	+	0.528651i
$975$	−10.5579	+	41.0228i	−0.338124	+	1.31378i
$976$	3.88800	−	6.73422i	0.124452	−	0.215557i
$977$	5.39563	+	9.34550i	0.172621	+	0.298989i	0.939336	−	0.343000i	$-0.111443\pi$
$977$	5.39563	+	9.34550i	0.172621	+	0.298989i	−0.766714	+	0.641989i	$0.778110\pi$
$978$	4.91321	+	17.6362i	0.157107	+	0.563942i
$979$	45.1913	+	7.96844i	1.44432	+	0.254672i
$980$	6.90653	−	3.98749i	0.220621	−	0.127376i
$981$	−19.8716	+	7.68150i	−0.634453	+	0.245252i
$982$	−15.8204	+	18.8540i	−0.504849	+	0.601656i
$983$	−34.3549	−	12.5042i	−1.09575	−	0.398821i	−0.270003	−	0.962860i	$-0.587025\pi$
$983$	−34.3549	−	12.5042i	−1.09575	−	0.398821i	−0.825748	+	0.564039i	$0.809247\pi$
$984$	1.46673	−	1.49606i	0.0467576	−	0.0476926i
$985$	30.3669	−	25.4808i	0.967569	−	0.811887i
$986$	1.87139	−	0.329977i	0.0595972	−	0.0105086i
$987$	−12.3847	−	25.8869i	−0.394208	−	0.823988i
$988$	7.16083	−	15.8297i	0.227816	−	0.503611i
$989$			5.12476i			0.162958i
$990$	−54.8492	−	30.2356i	−1.74322	−	0.960949i
$991$	−3.96786	−	4.72871i	−0.126043	−	0.150213i	0.699332	−	0.714797i	$-0.253481\pi$
$991$	−3.96786	−	4.72871i	−0.126043	−	0.150213i	−0.825375	+	0.564584i	$0.809036\pi$
$992$	0.800119	+	2.19831i	0.0254038	+	0.0697964i
$993$	4.93252	+	50.6044i	0.156529	+	1.60588i
$994$	−7.34797	−	6.16568i	−0.233063	−	0.195563i
$995$	70.6194	+	40.7721i	2.23879	+	1.29256i
$996$	−9.06490	+	13.2227i	−0.287232	+	0.418977i
$997$	3.18227	−	18.0475i	0.100783	−	0.571571i	−0.892038	−	0.451961i	$-0.850725\pi$
$997$	3.18227	−	18.0475i	0.100783	−	0.571571i	0.992821	−	0.119610i	$-0.0381643\pi$
$998$	2.55015	−	14.4626i	0.0807237	−	0.457807i
$999$	−8.97988	−	29.9287i	−0.284111	−	0.946902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.l.a.29.1	✓	18
3.2	odd	2		114.2.l.b.29.3	yes	18
4.3	odd	2		912.2.cc.d.257.3		18
12.11	even	2		912.2.cc.c.257.1		18
19.2	odd	18		114.2.l.b.59.3	yes	18
57.2	even	18	inner	114.2.l.a.59.1	yes	18
76.59	even	18		912.2.cc.c.401.1		18
228.59	odd	18		912.2.cc.d.401.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.29.1	✓	18	1.1	even	1	trivial
114.2.l.a.59.1	yes	18	57.2	even	18	inner
114.2.l.b.29.3	yes	18	3.2	odd	2
114.2.l.b.59.3	yes	18	19.2	odd	18
912.2.cc.c.257.1		18	12.11	even	2
912.2.cc.c.401.1		18	76.59	even	18
912.2.cc.d.257.3		18	4.3	odd	2
912.2.cc.d.401.3		18	228.59	odd	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.716422 + 1.57694i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.14133 + 3.13578i) q^{5} +(1.67739 + 0.431705i) q^{6} +(-1.07356 + 1.85947i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.97348 - 2.25951i) q^{9} +(3.28633 + 0.579469i) q^{10} +(5.41799 - 3.12808i) q^{11} +(0.133871 - 1.72687i) q^{12} +(-2.56208 + 3.05336i) q^{13} +(2.01764 + 0.734361i) q^{14} +(-4.12726 - 4.04635i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.403611 - 0.0711674i) q^{17} +(-1.88249 + 2.33586i) q^{18} +(4.34640 + 0.329887i) q^{19} -3.33703i q^{20} +(-2.16314 - 3.02511i) q^{21} +(-4.02138 - 4.79249i) q^{22} +(0.280411 + 0.770422i) q^{23} +(-1.72388 + 0.168030i) q^{24} +(-4.70025 - 3.94398i) q^{25} +(3.45187 + 1.99294i) q^{26} +(4.97695 - 1.49330i) q^{27} +(0.372845 - 2.11451i) q^{28} +(-0.805141 + 4.56618i) q^{29} +(-3.26819 + 4.76720i) q^{30} +(-2.02597 - 1.16970i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(1.05122 + 10.7849i) q^{33} +(-0.140172 - 0.385121i) q^{34} +(-4.60559 - 5.48872i) q^{35} +(2.62726 + 1.44827i) q^{36} -6.01346i q^{37} +(-0.429869 - 4.33765i) q^{38} +(-2.97944 - 6.22774i) q^{39} +(-3.28633 + 0.579469i) q^{40} +(-0.926617 + 0.777524i) q^{41} +(-2.60352 + 2.65558i) q^{42} +(5.87377 + 2.13788i) q^{43} +(-4.02138 + 4.79249i) q^{44} +(9.33771 - 3.60955i) q^{45} +(0.710025 - 0.409933i) q^{46} +(7.59919 + 1.33994i) q^{47} +(0.464826 + 1.66851i) q^{48} +(1.19492 + 2.06967i) q^{49} +(-3.06787 + 5.31371i) q^{50} +(-0.176929 + 0.687455i) q^{51} +(1.36325 - 3.74550i) q^{52} +(0.220516 - 0.0802612i) q^{53} +(-2.33485 - 4.64203i) q^{54} +(3.62525 + 20.5598i) q^{55} -2.14713 q^{56} +(-3.63407 + 6.61767i) q^{57} +4.63662 q^{58} +(-0.930375 - 5.27642i) q^{59} +(5.26229 + 2.39072i) q^{60} +(7.30705 - 2.65955i) q^{61} +(-0.800119 + 2.19831i) q^{62} +(6.32014 - 1.24389i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-6.65050 - 11.5190i) q^{65} +(10.4385 - 2.90803i) q^{66} +(3.48689 + 0.614832i) q^{67} +(-0.354929 + 0.204918i) q^{68} +(-1.41580 - 0.109756i) q^{69} +(-4.60559 + 5.48872i) q^{70} +(-4.19799 - 1.52794i) q^{71} +(0.970052 - 2.83884i) q^{72} +(-4.33185 + 3.63485i) q^{73} +(-5.92210 + 1.04423i) q^{74} +(9.58679 - 4.58646i) q^{75} +(-4.19711 + 1.17656i) q^{76} +13.4328i q^{77} +(-5.61575 + 4.01561i) q^{78} +(-8.05412 - 9.59853i) q^{79} +(1.14133 + 3.13578i) q^{80} +(-1.21076 + 8.91819i) q^{81} +(0.926617 + 0.777524i) q^{82} +(-8.01579 - 4.62792i) q^{83} +(3.06734 + 2.10283i) q^{84} +(-0.237488 + 1.34686i) q^{85} +(1.08543 - 6.15577i) q^{86} +(-6.62378 - 4.54097i) q^{87} +(5.41799 + 3.12808i) q^{88} +(5.61888 + 4.71480i) q^{89} +(-5.17619 - 8.56906i) q^{90} +(-2.92708 - 8.04207i) q^{91} +(-0.527000 - 0.628054i) q^{92} +(3.29599 - 2.35684i) q^{93} -7.71642i q^{94} +(-5.99513 + 13.2528i) q^{95} +(1.56245 - 0.747499i) q^{96} +(-16.0734 + 2.83418i) q^{97} +(1.83073 - 1.53616i) q^{98} +(-17.7602 - 6.06880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38}+ \cdots - 30 q^{99}+O(q^{100}) \) 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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