LMFDB - Embedded newform 114.2.l.a.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(29,114)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			59.1
Root			$-1.72388 - 0.168030i$ of defining polynomial
Character	$\chi$	$=$	114.59
Dual form			114.2.l.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(-0.716422 - 1.57694i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.14133 - 3.13578i) q^{5} +(1.67739 - 0.431705i) q^{6} +(-1.07356 - 1.85947i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.97348 + 2.25951i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 18 * q + 3 * q^6 + 9 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.880802	−	0.473484i	$-0.842996\pi$
$5$	−1.14133	−	3.13578i	−0.510418	−	1.40236i	0.370384	−	0.928879i	$-0.379226\pi$
$6$	1.67739	−	0.431705i	0.684791	−	0.176243i
$7$	−1.07356	−	1.85947i	−0.405769	−	0.702812i	0.588642	−	0.808394i	$-0.299663\pi$
$7$	−1.07356	−	1.85947i	−0.405769	−	0.702812i	−0.994411	+	0.105582i	$0.966330\pi$
$8$	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	0.982975	+	0.183740i	$0.0588203\pi$
$11$	5.41799	+	3.12808i	1.63359	+	0.943151i	0.650611	+	0.759412i	$0.274513\pi$
$12$	0.133871	+	1.72687i	0.0386453	+	0.498504i
$13$	−2.56208	−	3.05336i	−0.710592	−	0.846850i	0.283089	−	0.959094i	$-0.408641\pi$
$13$	−2.56208	−	3.05336i	−0.710592	−	0.846850i	−0.993681	+	0.112243i	$0.964196\pi$
$14$	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	0.222379	−	0.974960i	$-0.428618\pi$
$17$	0.403611	+	0.0711674i	0.0978899	+	0.0172606i	−0.124489	+	0.992221i	$0.539729\pi$
$18$	−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	−0.907019	−	0.421090i	$-0.861647\pi$
$23$	0.280411	−	0.770422i	0.0584697	−	0.160644i	0.965488	+	0.260446i	$0.0838697\pi$
$24$	−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	−0.963634	−	0.267226i	$-0.913893\pi$
$29$	−0.805141	−	4.56618i	−0.149511	−	0.847919i	0.814123	−	0.580693i	$-0.197218\pi$
$30$	−3.26819	−	4.76720i	−0.596686	−	0.870368i
$31$	−2.02597	+	1.16970i	−0.363875	+	0.210084i	−0.670779	−	0.741657i	$-0.734040\pi$
$31$	−2.02597	+	1.16970i	−0.363875	+	0.210084i	0.306904	+	0.951740i	$0.400707\pi$
$32$	−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	$0.164577\pi$
$37$			6.01346i			0.988607i	−0.869289	+	0.494303i	$0.835423\pi$
$38$	−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	0.567557	−	0.823334i	$-0.307889\pi$
$41$	−0.926617	−	0.777524i	−0.144713	−	0.121429i	−0.712270	+	0.701905i	$0.752333\pi$
$42$	−2.60352	−	2.65558i	−0.401733	−	0.409766i
$43$	5.87377	−	2.13788i	0.895741	−	0.326023i	0.147196	−	0.989107i	$-0.452975\pi$
$43$	5.87377	−	2.13788i	0.895741	−	0.326023i	0.748545	+	0.663084i	$0.230753\pi$
$44$	−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	0.410689	−	0.911776i	$-0.365288\pi$
$47$	7.59919	−	1.33994i	1.10846	−	0.195451i	0.697767	+	0.716325i	$0.254177\pi$
$48$	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	0.357121	−	0.934058i	$-0.383758\pi$
$53$	0.220516	+	0.0802612i	0.0302902	+	0.0110247i	−0.326831	+	0.945083i	$0.605981\pi$
$54$	−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	0.862410	+	0.506210i	$0.168954\pi$
$59$	−0.930375	+	5.27642i	−0.121124	+	0.686931i	−0.983534	+	0.180721i	$0.942157\pi$
$60$	5.26229	−	2.39072i	0.679359	−	0.308640i
$61$	7.30705	+	2.65955i	0.935572	+	0.340520i	0.764416	−	0.644723i	$-0.223027\pi$
$61$	7.30705	+	2.65955i	0.935572	+	0.340520i	0.171156	+	0.985244i	$0.445250\pi$
$62$	−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	0.0434574	−	0.999055i	$-0.486163\pi$
$67$	3.48689	−	0.614832i	0.425991	−	0.0751137i	0.382534	+	0.923942i	$0.375052\pi$
$68$	−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	−0.578889	−	0.815407i	$-0.696513\pi$
$71$	−4.19799	+	1.52794i	−0.498210	+	0.181334i	0.0806788	+	0.996740i	$0.474291\pi$
$72$	0.970052	+	2.83884i	0.114322	+	0.334560i
$73$	−4.33185	−	3.63485i	−0.507005	−	0.425427i	0.353069	−	0.935597i	$-0.385138\pi$
$73$	−4.33185	−	3.63485i	−0.507005	−	0.425427i	−0.860074	+	0.510170i	$0.829583\pi$
$74$	−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	0.0903059	+	0.995914i	$0.471216\pi$
$79$	−8.05412	+	9.59853i	−0.906159	+	1.07992i	−0.996465	+	0.0840047i	$0.973229\pi$
$80$	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	−0.870608	−	0.491977i	$-0.836274\pi$
$83$	−8.01579	+	4.62792i	−0.879848	+	0.507980i	−0.00923947	+	0.999957i	$0.502941\pi$
$84$	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	−0.294428	−	0.955674i	$-0.595129\pi$
$89$	5.61888	−	4.71480i	0.595600	−	0.499767i	0.890028	+	0.455906i	$0.150685\pi$
$90$	−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	−0.718786	−	0.695231i	$-0.755302\pi$
$97$	−16.0734	−	2.83418i	−1.63201	−	0.287767i	−0.913221	+	0.407464i	$0.866413\pi$
$98$	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	0.917787	−	0.397073i	$-0.129974\pi$
$101$	3.69207	+	4.40004i	0.367375	+	0.437820i	−0.550412	+	0.834893i	$0.685529\pi$
$102$	0.707735	−	0.0548653i	0.0700762	−	0.00543248i
$103$	−0.957127	−	0.552597i	−0.0943085	−	0.0544490i	0.452104	−	0.891965i	$-0.350674\pi$
$103$	−0.957127	−	0.552597i	−0.0943085	−	0.0544490i	−0.546413	+	0.837516i	$0.684007\pi$
$104$	−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	0.983688	−	0.179881i	$-0.0575713\pi$
$107$	3.47626	+	6.02105i	0.336062	+	0.582077i	−0.647626	+	0.761958i	$0.724238\pi$
$108$	−4.16607	−	3.10546i	−0.400880	−	0.298823i
$109$	2.42887	+	6.67327i	0.232644	+	0.639183i	0.999998	−	0.00204008i	$-0.000649379\pi$
$109$	2.42887	+	6.67327i	0.232644	+	0.639183i	−0.767354	+	0.641223i	$0.778427\pi$
$110$	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	0.800045	−	0.599941i	$-0.204809\pi$
$127$	0.792153	+	0.944052i	0.0702922	+	0.0837710i	−0.729752	+	0.683712i	$0.760365\pi$
$128$	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	−0.110472	−	0.993879i	$-0.535236\pi$
$131$	−6.34320	−	1.11848i	−0.554208	−	0.0977218i	−0.443736	+	0.896157i	$0.646347\pi$
$132$	−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	0.676882	+	0.736091i	$0.263331\pi$
$137$	−3.68452	+	10.1231i	−0.314790	+	0.864878i	−0.991672	+	0.128787i	$0.958892\pi$
$138$	0.137762	−	1.41335i	0.0117271	−	0.120313i
$139$	6.45972	−	5.42035i	0.547906	−	0.459748i	−0.326325	−	0.945258i	$-0.605810\pi$
$139$	6.45972	−	5.42035i	0.547906	−	0.459748i	0.874231	+	0.485510i	$0.161366\pi$
$140$	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	−0.607920	−	0.793998i	$-0.707996\pi$
$149$	3.41271	−	4.06711i	0.279580	−	0.333190i	0.887500	+	0.460808i	$0.152440\pi$
$150$	−6.18151	+	8.64471i	−0.504718	+	0.705838i
$151$		−	2.55987i		−	0.208319i	−0.994561	−	0.104160i	$-0.966785\pi$
$151$		−	2.55987i		−	0.208319i	0.994561	−	0.104160i	$-0.0332153\pi$
$152$	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	0.374573	−	0.927197i	$-0.377789\pi$
$157$	15.7565	−	5.73489i	1.25750	−	0.457694i	0.882931	+	0.469503i	$0.155567\pi$
$158$	−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	−0.581365	−	0.813643i	$-0.697481\pi$
$163$	5.28499	−	9.15387i	0.413952	−	0.716987i	0.995318	+	0.0966559i	$0.0308146\pi$
$164$	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	0.715298	−	0.698820i	$-0.246291\pi$
$167$	10.5199	+	3.82893i	0.814054	+	0.296292i	0.0987568	+	0.995112i	$0.468513\pi$
$168$	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	0.400051	+	0.916493i	$0.368993\pi$
$173$	−3.80558	+	21.5825i	−0.289333	+	1.64089i	−0.689384	+	0.724396i	$0.742119\pi$
$174$	−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	−0.120833	−	0.992673i	$-0.538557\pi$
$179$	10.6934	−	18.5215i	0.799263	−	1.38436i	0.920097	−	0.391692i	$-0.128110\pi$
$180$	−7.54004	−	6.58555i	−0.562001	−	0.490858i
$181$	−18.0057	+	3.17489i	−1.33835	+	0.235988i	−0.796578	−	0.604536i	$-0.793359\pi$
$181$	−18.0057	+	3.17489i	−1.33835	+	0.235988i	−0.541775	+	0.840523i	$0.682248\pi$
$182$	−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	$-0.960036\pi$
$191$		−	3.46116i		−	0.250441i	0.992129	−	0.125220i	$-0.0399638\pi$
$192$	−1.00746	+	1.40891i	−0.0727071	+	0.101679i
$193$	6.64414	−	7.91818i	0.478256	−	0.569963i	−0.471934	−	0.881634i	$-0.656444\pi$
$193$	6.64414	−	7.91818i	0.478256	−	0.569963i	0.950190	+	0.311671i	$0.100889\pi$
$194$	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	−0.819506	−	0.573070i	$-0.805752\pi$
$197$	−10.2877	+	5.93959i	−0.732966	+	0.423178i	0.0865400	+	0.996248i	$0.472419\pi$
$198$	−2.89257	−	18.5442i	−0.205566	−	1.31788i
$199$	4.24330	+	24.0650i	0.300800	+	1.70592i	0.642645	+	0.766164i	$0.277837\pi$
$199$	4.24330	+	24.0650i	0.300800	+	1.70592i	−0.341845	+	0.939756i	$0.611052\pi$
$200$	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	−0.419028	−	0.907973i	$-0.637629\pi$
$211$	−16.3173	−	2.87718i	−1.12333	−	0.198074i	−0.704303	+	0.709900i	$0.748740\pi$
$212$	−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	−0.998275	−	0.0587091i	$-0.981302\pi$
$223$	−4.05122	−	11.1306i	−0.271290	−	0.745362i	0.726986	−	0.686653i	$-0.240921\pi$
$224$	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	0.860792	+	0.508958i	$0.169969\pi$
$233$	8.06779	+	22.1661i	0.528539	+	1.45215i	−0.332253	+	0.943190i	$0.607809\pi$
$234$	−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	0.999497	+	0.0317050i	$0.0100937\pi$
$239$	23.6023	+	13.6268i	1.52670	+	0.881443i	0.527206	+	0.849738i	$0.323240\pi$
$240$	−5.76261	+	0.446732i	−0.371975	+	0.0288364i
$241$	13.6728	+	16.2946i	0.880739	+	1.04962i	0.998399	+	0.0565704i	$0.0180165\pi$
$241$	13.6728	+	16.2946i	0.880739	+	1.04962i	−0.117659	+	0.993054i	$0.537539\pi$
$242$	−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	−0.963598	−	0.267355i	$-0.913850\pi$
$251$	−0.848967	+	2.33252i	−0.0535863	+	0.147227i	0.910012	+	0.414583i	$0.136072\pi$
$252$	−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	−0.983085	−	0.183149i	$-0.941371\pi$
$257$	−1.95465	−	11.0854i	−0.121928	−	0.691488i	0.861157	−	0.508339i	$-0.169740\pi$
$258$	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	−0.947252	−	0.320490i	$-0.896153\pi$
$263$	−7.57578	+	9.02847i	−0.467143	+	0.556719i	0.480109	+	0.877209i	$0.340597\pi$
$264$	−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	0.327175	−	0.944964i	$-0.393903\pi$
$269$	−8.96522	−	7.52271i	−0.546619	−	0.458668i	−0.873794	+	0.486296i	$0.838348\pi$
$270$	17.2212	+	2.02348i	1.04805	+	0.123145i
$271$	−29.1999	+	10.6279i	−1.77377	+	0.645598i	−0.773841	+	0.633380i	$0.781667\pi$
$271$	−29.1999	+	10.6279i	−1.77377	+	0.645598i	−0.999925	+	0.0122180i	$0.996111\pi$
$272$	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	−0.802575	−	0.596551i	$-0.796537\pi$
$277$	1.91965	−	3.32494i	0.115341	−	0.199776i	0.917916	+	0.396775i	$0.129871\pi$
$278$	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	−0.455031	−	0.890475i	$-0.650372\pi$
$281$	−23.0658	−	8.39528i	−1.37599	−	0.500820i	−0.920961	+	0.389655i	$0.872594\pi$
$282$	12.1683	−	5.52821i	0.724614	−	0.329200i
$283$	−4.03563	+	22.8872i	−0.239894	+	1.36050i	0.592165	+	0.805817i	$0.298273\pi$
$283$	−4.03563	+	22.8872i	−0.239894	+	1.36050i	−0.832059	+	0.554688i	$0.812838\pi$
$284$	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	−0.980598	−	0.196031i	$-0.937195\pi$
$293$	−5.48661	+	9.50309i	−0.320531	+	0.555177i	0.660066	+	0.751207i	$0.270528\pi$
$294$	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	−0.775983	−	0.630754i	$-0.782746\pi$
$307$	−0.351542	+	0.418952i	−0.0200636	+	0.0239108i	0.755919	+	0.654665i	$0.227190\pi$
$308$	−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	−0.804090	−	0.594507i	$-0.797347\pi$
$311$	−12.1908	+	7.03836i	−0.691277	+	0.399109i	0.112813	+	0.993616i	$0.464014\pi$
$312$	3.90366	+	5.69414i	0.221001	+	0.322367i
$313$	−3.23018	−	18.3193i	−0.182580	−	1.03547i	−0.929025	−	0.370018i	$-0.879352\pi$
$313$	−3.23018	−	18.3193i	−0.182580	−	1.03547i	0.746444	−	0.665448i	$-0.231759\pi$
$314$	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	0.169940	−	0.985454i	$-0.445643\pi$
$317$	20.8301	−	17.4785i	1.16993	−	0.981690i	0.999993	+	0.00376423i	$0.00119819\pi$
$318$	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	0.994112	−	0.108360i	$-0.0345598\pi$
$331$	25.4221	+	14.6775i	1.39733	+	0.806746i	0.403214	+	0.915106i	$0.367893\pi$
$332$	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	0.999643	+	0.0267031i	$0.00850087\pi$
$337$	4.60842	+	12.6615i	0.251037	+	0.689717i	−0.748607	+	0.663014i	$0.769277\pi$
$338$	−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	0.872033	−	0.489447i	$-0.162801\pi$
$347$	−2.06013	−	5.66016i	−0.110594	−	0.303854i	−0.982627	+	0.185594i	$0.940579\pi$
$348$	7.77742	−	2.00165i	0.416913	−	0.107300i
$349$	−14.3065	−	24.7795i	−0.765808	−	1.32642i	−0.939818	−	0.341675i	$-0.889006\pi$
$349$	−14.3065	−	24.7795i	−0.765808	−	1.32642i	0.174010	−	0.984744i	$-0.444328\pi$
$350$	−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	0.0580867	−	0.998312i	$-0.481500\pi$
$353$	−14.6066	−	8.43315i	−0.777433	−	0.448851i	−0.835520	+	0.549460i	$0.814833\pi$
$354$	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	0.585898	−	0.810385i	$-0.300742\pi$
$359$	16.2813	+	2.87084i	0.859295	+	0.151517i	0.273397	+	0.961901i	$0.411853\pi$
$360$	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	−0.813614	−	0.581405i	$-0.802503\pi$
$367$	−7.32428	+	6.14580i	−0.382324	+	0.320808i	0.431290	+	0.902213i	$0.358059\pi$
$368$	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	−0.399710	−	0.916642i	$-0.630889\pi$
$373$	3.75197	−	2.16620i	0.194270	−	0.112162i	0.593980	+	0.804480i	$0.297556\pi$
$374$	−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	$-0.951016\pi$
$379$		−	5.96818i		−	0.306565i	0.988182	−	0.153282i	$-0.0489844\pi$
$380$	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	0.552614	−	0.833437i	$-0.313630\pi$
$383$	−3.37004	−	2.82780i	−0.172201	−	0.144494i	−0.724815	+	0.688944i	$0.758075\pi$
$384$	−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	0.206515	−	0.978443i	$-0.433788\pi$
$389$	14.5009	−	2.55689i	0.735223	−	0.129640i	0.528708	+	0.848804i	$0.322677\pi$
$390$	−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	−0.909035	−	0.416719i	$-0.863180\pi$
$397$	1.74751	−	9.91059i	0.0877048	−	0.497398i	0.996740	−	0.0806794i	$-0.0257090\pi$
$398$	−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	−0.850041	−	0.526717i	$-0.823423\pi$
$401$	2.58090	−	14.6370i	0.128884	−	0.730937i	0.978925	−	0.204221i	$-0.0654660\pi$
$402$	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	−0.410874	−	0.911692i	$-0.634777\pi$
$409$	−9.81162	+	1.73005i	−0.485153	+	0.0855456i	−0.0742787	+	0.997238i	$0.523665\pi$
$410$	−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	$-0.934630\pi$
$419$		−	8.34847i		−	0.407849i	0.978987	−	0.203925i	$-0.0653698\pi$
$420$	−10.0949	−	7.21847i	−0.492579	−	0.352225i
$421$	23.4446	−	27.9402i	1.14262	−	1.36172i	0.220234	−	0.975447i	$-0.429318\pi$
$421$	23.4446	−	27.9402i	1.14262	−	1.36172i	0.922384	−	0.386273i	$-0.126238\pi$
$422$	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	−0.815879	−	0.578223i	$-0.803746\pi$
$431$	−8.05751	+	6.76105i	−0.388116	+	0.325668i	0.427762	+	0.903891i	$0.359302\pi$
$432$	2.85269	+	4.34306i	0.137250	+	0.208955i
$433$	−12.6127	+	34.6530i	−0.606126	+	1.66532i	0.132485	+	0.991185i	$0.457704\pi$
$433$	−12.6127	+	34.6530i	−0.606126	+	1.66532i	−0.738611	+	0.674132i	$0.764518\pi$
$434$	−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	0.477522	−	0.878620i	$-0.341535\pi$
$439$	13.1107	+	2.31177i	0.625739	+	0.110335i	0.148218	+	0.988955i	$0.452646\pi$
$440$	−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	0.639899	−	0.768459i	$-0.278976\pi$
$443$	−4.79891	−	5.71912i	−0.228003	−	0.271724i	−0.867902	+	0.496736i	$0.834532\pi$
$444$	−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	−0.996072	−	0.0885490i	$-0.971777\pi$
$449$	−12.1781	−	21.0931i	−0.574722	−	0.995447i	0.421350	−	0.906898i	$-0.361556\pi$
$450$	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	0.920601	−	0.390503i	$-0.127699\pi$
$461$	−0.765028	−	2.10190i	−0.0356309	−	0.0978951i	−0.956232	+	0.292608i	$0.905477\pi$
$462$	−5.79899	−	22.5320i	−0.269794	−	1.04828i
$463$	1.84091	+	3.18854i	0.0855541	+	0.148184i	0.905627	−	0.424075i	$-0.139401\pi$
$463$	1.84091	+	3.18854i	0.0855541	+	0.148184i	−0.820073	+	0.572259i	$0.806067\pi$
$464$	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	0.739911	−	0.672704i	$-0.234867\pi$
$467$	11.3948	+	6.57879i	0.527288	+	0.304430i	−0.212623	+	0.977134i	$0.568201\pi$
$468$	−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	−0.342424	−	0.939546i	$-0.611248\pi$
$479$	11.4643	−	31.4978i	0.523816	−	1.43917i	0.866240	−	0.499628i	$-0.166530\pi$
$480$	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	−0.803243	−	0.595651i	$-0.796894\pi$
$487$	−15.2052	+	8.77875i	−0.689015	+	0.397803i	0.114228	+	0.993455i	$0.463561\pi$
$488$	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	−0.994030	−	0.109112i	$-0.965199\pi$
$491$	−15.8204	+	18.8540i	−0.713964	+	0.850869i	0.280065	+	0.959981i	$0.409644\pi$
$492$	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	−0.0141259	−	0.999900i	$-0.504497\pi$
$499$	13.8001	−	5.02282i	0.617777	−	0.224852i	0.631902	+	0.775048i	$0.282274\pi$
$500$	−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	−0.0782748	−	0.996932i	$-0.524941\pi$
$503$	4.24201	−	0.747980i	0.189142	−	0.0333508i	0.267417	+	0.963581i	$0.413830\pi$
$504$	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	0.436782	−	0.899567i	$-0.356118\pi$
$509$	4.35756	+	1.58602i	0.193145	+	0.0702991i	−0.243637	+	0.969867i	$0.578340\pi$
$510$	−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	−0.861478	−	0.507794i	$-0.830461\pi$
$521$	0.205968	−	0.356747i	0.00902363	−	0.0156294i	0.870502	+	0.492165i	$0.163794\pi$
$522$	−9.15028	+	10.4765i	−0.400497	+	0.458544i
$523$	−19.2248	+	3.38986i	−0.840643	+	0.148228i	−0.577359	−	0.816490i	$-0.695917\pi$
$523$	−19.2248	+	3.38986i	−0.840643	+	0.148228i	−0.263284	+	0.964718i	$0.584806\pi$
$524$	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	−0.974369	−	0.224957i	$-0.927776\pi$
$541$	−3.15633	−	17.9005i	−0.135701	−	0.769601i	0.838667	−	0.544644i	$-0.183335\pi$
$542$	−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	−0.905510	−	0.424324i	$-0.860512\pi$
$547$	1.42436	−	3.91340i	0.0609014	−	0.167325i	0.966412	+	0.256999i	$0.0827338\pi$
$548$	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	0.536181	−	0.844103i	$-0.319866\pi$
$557$	−9.16196	−	10.9188i	−0.388205	−	0.462644i	−0.924386	+	0.381459i	$0.875422\pi$
$558$	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	0.926878	−	0.375363i	$-0.122482\pi$
$563$	3.28307	+	5.68645i	0.138365	+	0.239655i	−0.788513	+	0.615018i	$0.789149\pi$
$564$	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	−0.949276	−	0.314446i	$-0.898181\pi$
$577$	−17.9425	−	31.0773i	−0.746956	−	1.29377i	0.202320	−	0.979319i	$-0.435152\pi$
$578$	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	−0.474118	−	0.880461i	$-0.657233\pi$
$587$	−29.5771	−	5.21525i	−1.22078	−	0.215256i	−0.746661	+	0.665205i	$0.768344\pi$
$588$	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	−0.934059	−	0.357119i	$-0.883759\pi$
$593$	0.268437	−	0.737526i	0.0110234	−	0.0302866i	0.945082	+	0.326832i	$0.105981\pi$
$594$	−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	0.994308	+	0.106548i	$0.0339798\pi$
$599$	2.35948	+	13.3813i	0.0964057	+	0.546744i	−0.897902	+	0.440196i	$0.854909\pi$
$600$	8.76539	−	6.00917i	0.357845	−	0.245323i
$601$	1.41283	−	0.815696i	0.0576304	−	0.0332729i	−0.470908	−	0.882182i	$-0.656074\pi$
$601$	1.41283	−	0.815696i	0.0576304	−	0.0332729i	0.528538	+	0.848909i	$0.322740\pi$
$602$	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	$0.159475\pi$
$607$			23.6670i			0.960615i	−0.877100	+	0.480308i	$0.840525\pi$
$608$	−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	−0.0273321	−	0.999626i	$-0.508701\pi$
$613$	14.7136	−	5.35532i	0.594278	−	0.216299i	0.621610	+	0.783327i	$0.286479\pi$
$614$	−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	−0.554117	−	0.832439i	$-0.686944\pi$
$617$	−19.6258	+	3.46056i	−0.790105	+	0.139317i	−0.235988	+	0.971756i	$0.575833\pi$
$618$	−1.84403	−	0.513724i	−0.0741778	−	0.0206650i
$619$	−3.55524	+	6.15786i	−0.142897	+	0.247505i	−0.928587	−	0.371116i	$-0.878975\pi$
$619$	−3.55524	+	6.15786i	−0.142897	+	0.247505i	0.785689	+	0.618621i	$0.212309\pi$
$620$	−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	0.318692	−	0.947858i	$-0.396756\pi$
$631$	−1.16675	−	0.424661i	−0.0464474	−	0.0169055i	−0.365139	+	0.930953i	$0.618979\pi$
$632$	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	−0.198708	−	0.980059i	$-0.563675\pi$
$641$	7.06477	−	2.57137i	0.279042	−	0.101563i	0.477750	+	0.878496i	$0.341452\pi$
$642$	8.43035	+	8.59893i	0.332719	+	0.339373i
$643$	−9.31005	−	7.81206i	−0.367153	−	0.308078i	0.440481	−	0.897762i	$-0.354808\pi$
$643$	−9.31005	−	7.81206i	−0.367153	−	0.308078i	−0.807634	+	0.589684i	$0.799252\pi$
$644$	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	$0.269715\pi$
$647$			38.1298i			1.49904i	−0.661983	+	0.749519i	$0.730285\pi$
$648$	−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	−0.558063	+	0.829798i	$0.688455\pi$
$653$	−39.7547	+	22.9524i	−1.55572	+	0.898196i	−0.997658	+	0.0683980i	$0.978211\pi$
$654$	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	−0.318779	−	0.947829i	$-0.603273\pi$
$659$	14.3577	−	12.0475i	0.559295	−	0.469304i	0.878074	+	0.478525i	$0.158828\pi$
$660$	35.9894	+	3.50796i	1.40089	+	0.136547i
$661$	4.05073	−	11.1293i	0.157555	−	0.432879i	−0.835649	−	0.549263i	$-0.814908\pi$
$661$	4.05073	−	11.1293i	0.157555	−	0.432879i	0.993204	+	0.116385i	$0.0371306\pi$
$662$	−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	0.315917	−	0.948787i	$-0.397688\pi$
$673$	−9.02264	−	5.20922i	−0.347797	−	0.200801i	−0.663715	+	0.747986i	$0.731021\pi$
$674$	−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	0.595097	−	0.803654i	$-0.297114\pi$
$677$	−10.3670	−	17.9562i	−0.398437	−	0.690112i	−0.993533	+	0.113542i	$0.963780\pi$
$678$	−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	0.774968	−	0.632001i	$-0.217766\pi$
$691$	−4.20182	−	7.27776i	−0.159845	−	0.276859i	−0.934813	+	0.355142i	$0.884433\pi$
$692$	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	−0.115912	−	0.993259i	$-0.536979\pi$
$701$	−14.9472	−	2.63560i	−0.564549	−	0.0995451i	−0.448636	+	0.893714i	$0.648090\pi$
$702$	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	−0.997451	−	0.0713544i	$-0.977268\pi$
$709$	−29.3000	+	24.5857i	−1.10039	+	0.923334i	−0.102935	+	0.994688i	$0.532823\pi$
$710$	−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	0.0628501	+	0.998023i	$0.479981\pi$
$719$	−24.9620	+	29.7485i	−0.930924	+	1.10943i	−0.993775	+	0.111410i	$0.964463\pi$
$720$	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	0.425818	−	0.904809i	$-0.359986\pi$
$727$	35.9582	−	13.0877i	1.33361	−	0.485396i	0.907796	+	0.419413i	$0.137764\pi$
$728$	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	−0.972558	−	0.232660i	$-0.925257\pi$
$733$	−7.71039	+	13.3548i	−0.284790	+	0.493270i	0.687768	+	0.725930i	$0.258590\pi$
$734$	−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	0.744892	+	0.667185i	$0.232501\pi$
$739$	−4.98207	+	28.2547i	−0.183268	+	1.03937i	−0.928160	+	0.372181i	$0.878610\pi$
$740$	−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	−0.748006	−	0.663691i	$-0.768989\pi$
$743$	4.95784	−	28.1173i	0.181886	−	1.03152i	0.929892	−	0.367833i	$-0.119900\pi$
$744$	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	0.0585987	−	0.998282i	$-0.481337\pi$
$751$	12.4716	−	2.19908i	0.455096	−	0.0802457i	0.396497	+	0.918036i	$0.370226\pi$
$752$	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	0.962308	+	0.271963i	$0.0876729\pi$
$757$	38.4432	+	32.2577i	1.39724	+	1.17243i	0.434934	+	0.900462i	$0.356772\pi$
$758$	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	$0.160664\pi$
$761$			26.6803i			0.967159i	−0.875300	+	0.483580i	$0.839336\pi$
$762$	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	−0.817292	−	0.576223i	$-0.804526\pi$
$769$	−6.83201	−	38.7463i	−0.246369	−	1.39723i	0.570924	−	0.821003i	$-0.306585\pi$
$770$	−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	−0.597095	−	0.802170i	$-0.703679\pi$
$773$	2.48012	−	2.08107i	0.0892039	−	0.0748509i	0.686299	+	0.727319i	$0.259234\pi$
$774$	−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	0.0337179	−	0.999431i	$-0.489265\pi$
$787$	−22.8624	−	13.1996i	−0.814956	−	0.470515i	−0.848674	+	0.528916i	$0.822599\pi$
$788$	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	−0.164156	−	0.986434i	$-0.552490\pi$
$809$	−31.3018	−	18.0721i	−1.10051	−	0.635380i	−0.936355	+	0.351054i	$0.885823\pi$
$810$	−9.14676	−	28.6065i	−0.321384	−	1.00513i
$811$	16.3764	+	19.5167i	0.575054	+	0.685323i	0.972660	−	0.232233i	$-0.0746033\pi$
$811$	16.3764	+	19.5167i	0.575054	+	0.685323i	−0.397606	+	0.917556i	$0.630159\pi$
$812$	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	−0.985986	−	0.166827i	$-0.946648\pi$
$821$	−3.53702	+	9.71788i	−0.123443	+	0.339156i	0.862543	+	0.505983i	$0.168870\pi$
$822$	−1.81016	+	18.5711i	−0.0631366	+	0.647740i
$823$	11.1336	−	9.34221i	0.388093	−	0.325649i	−0.427776	−	0.903885i	$-0.640703\pi$
$823$	11.1336	−	9.34221i	0.388093	−	0.325649i	0.815870	+	0.578235i	$0.196259\pi$
$824$	−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	−0.965958	−	0.258699i	$-0.916706\pi$
$827$	−4.21974	−	23.9313i	−0.146735	−	0.832174i	0.819223	−	0.573475i	$-0.194405\pi$
$828$	−0.379070	−	2.43021i	−0.0131736	−	0.0844557i
$829$	43.3587	−	25.0331i	1.50591	−	0.869437i	0.505932	−	0.862573i	$-0.331149\pi$
$829$	43.3587	−	25.0331i	1.50591	−	0.869437i	0.999976	−	0.00686327i	$-0.00218466\pi$
$830$	−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	0.964676	−	0.263440i	$-0.0848572\pi$
$839$	25.2797	+	21.2122i	0.872752	+	0.732326i	−0.0919238	+	0.995766i	$0.529302\pi$
$840$	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	−0.761566	−	0.648088i	$-0.775569\pi$
$853$	5.13243	−	29.1074i	0.175731	−	0.996620i	0.937297	−	0.348532i	$-0.113320\pi$
$854$	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	0.396019	+	0.918242i	$0.370392\pi$
$857$	−8.49473	+	48.1760i	−0.290175	+	1.64566i	−0.686193	+	0.727419i	$0.740720\pi$
$858$	−17.8649	−	39.3230i	−0.609898	−	1.34247i
$859$	−36.8403	−	13.4088i	−1.25698	−	0.457502i	−0.374222	−	0.927339i	$-0.622090\pi$
$859$	−36.8403	−	13.4088i	−1.25698	−	0.457502i	−0.882753	+	0.469837i	$0.844313\pi$
$860$	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	0.392525	+	0.919741i	$0.371602\pi$
$863$	−17.6337	+	30.5424i	−0.600257	+	1.03967i	−0.992782	+	0.119934i	$0.961732\pi$
$864$	−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	−0.464050	−	0.885809i	$-0.653604\pi$
$877$	14.4779	−	17.2541i	0.488883	−	0.582628i	0.952933	+	0.303181i	$0.0980486\pi$
$878$	−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	0.589765	−	0.807575i	$-0.299220\pi$
$881$	47.0165	−	27.1450i	1.58403	−	0.914539i	0.994263	−	0.106964i	$-0.0341129\pi$
$882$	−7.08387	+	1.10496i	−0.238526	+	0.0372059i
$883$	4.51473	+	25.6043i	0.151933	+	0.861653i	0.961537	+	0.274677i	$0.0885708\pi$
$883$	4.51473	+	25.6043i	0.151933	+	0.861653i	−0.809604	+	0.586977i	$0.800318\pi$
$884$	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	−0.569577	−	0.821938i	$-0.692893\pi$
$887$	4.19836	−	3.52284i	0.140967	−	0.118286i	0.710545	+	0.703652i	$0.248449\pi$
$888$	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	0.547928	+	0.836526i	$0.315417\pi$
$907$	20.0545	+	55.0993i	0.665899	+	1.82954i	0.117971	+	0.993017i	$0.462361\pi$
$908$	−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	0.910555	−	0.413389i	$-0.135655\pi$
$919$	2.94881	+	5.10749i	0.0972722	+	0.168480i	−0.813282	+	0.581869i	$0.802322\pi$
$920$	−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	0.528776	−	0.848762i	$-0.322651\pi$
$929$	22.4137	+	3.95214i	0.735369	+	0.129665i	0.206593	+	0.978427i	$0.433762\pi$
$930$	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	−0.997042	−	0.0768570i	$-0.975512\pi$
$937$	−33.5028	+	28.1122i	−1.09449	+	0.918384i	−0.0974452	+	0.995241i	$0.531067\pi$
$938$	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	0.962616	−	0.270870i	$-0.0873115\pi$
$941$	−1.06108	−	6.01769i	−0.0345903	−	0.196171i	−0.997206	+	0.0746992i	$0.976200\pi$
$942$	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	−0.337586	−	0.941295i	$-0.609611\pi$
$947$	19.9420	−	23.7660i	0.648029	−	0.772291i	0.985615	+	0.169004i	$0.0540550\pi$
$948$	−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	0.997797	+	0.0663415i	$0.0211327\pi$
$953$	38.1684	+	32.0271i	1.23640	+	1.03746i	0.238599	+	0.971118i	$0.423312\pi$
$954$	−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	0.937390	+	0.348280i	$0.113234\pi$
$967$	−1.94625	+	11.0377i	−0.0625873	+	0.354950i	−0.999978	+	0.00666987i	$0.997877\pi$
$968$	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	−0.495528	−	0.868592i	$-0.665026\pi$
$971$	8.32593	−	47.2187i	0.267192	−	1.51532i	0.762720	−	0.646729i	$-0.223863\pi$
$972$	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	−0.766714	−	0.641989i	$-0.778110\pi$
$977$	5.39563	−	9.34550i	0.172621	−	0.298989i	0.939336	+	0.343000i	$0.111443\pi$
$978$	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	−0.825748	−	0.564039i	$-0.809247\pi$
$983$	−34.3549	+	12.5042i	−1.09575	+	0.398821i	−0.270003	+	0.962860i	$0.587025\pi$
$984$	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	−0.825375	−	0.564584i	$-0.809036\pi$
$991$	−3.96786	+	4.72871i	−0.126043	+	0.150213i	0.699332	+	0.714797i	$0.253481\pi$
$992$	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	0.992821	+	0.119610i	$0.0381643\pi$
$997$	3.18227	+	18.0475i	0.100783	+	0.571571i	−0.892038	+	0.451961i	$0.850725\pi$
$998$	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.59.1	yes	18
3.2	odd	2		114.2.l.b.59.3	yes	18
4.3	odd	2		912.2.cc.d.401.3		18
12.11	even	2		912.2.cc.c.401.1		18
19.10	odd	18		114.2.l.b.29.3	yes	18
57.29	even	18	inner	114.2.l.a.29.1	✓	18
76.67	even	18		912.2.cc.c.257.1		18
228.143	odd	18		912.2.cc.d.257.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.29.1	✓	18	57.29	even	18	inner
114.2.l.a.59.1	yes	18	1.1	even	1	trivial
114.2.l.b.29.3	yes	18	19.10	odd	18
114.2.l.b.59.3	yes	18	3.2	odd	2
912.2.cc.c.257.1		18	76.67	even	18
912.2.cc.c.401.1		18	12.11	even	2
912.2.cc.d.257.3		18	228.143	odd	18
912.2.cc.d.401.3		18	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.716422 - 1.57694i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.14133 - 3.13578i) q^{5} +(1.67739 - 0.431705i) q^{6} +(-1.07356 - 1.85947i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.97348 + 2.25951i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{6} + 9 q^{8}+O(q^{10}) \) 18 * q + 3 * q^6 + 9 * q^8	\( 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38} + 6 q^{39} - 3 q^{41} - 6 q^{43} - 24 q^{44} + 54 q^{45} + 18 q^{46} - 30 q^{47} + 6 q^{48} + 21 q^{49} - 3 q^{50} - 33 q^{51} - 6 q^{52} + 60 q^{53} + 30 q^{55} + 12 q^{57} + 12 q^{58} - 3 q^{59} + 18 q^{60} + 54 q^{61} - 6 q^{62} + 84 q^{63} - 9 q^{64} - 24 q^{65} + 30 q^{66} - 15 q^{67} + 27 q^{68} + 24 q^{69} + 24 q^{70} - 36 q^{71} - 42 q^{73} - 6 q^{74} - 18 q^{78} - 6 q^{79} + 3 q^{82} - 36 q^{83} - 24 q^{84} + 6 q^{86} - 54 q^{87} + 60 q^{89} - 12 q^{90} - 18 q^{91} - 84 q^{93} - 6 q^{95} + 9 q^{97} - 12 q^{98} - 30 q^{99}+O(q^{100}) \) 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

Related objects

Downloads

Learn more