LMFDB - Embedded newform 114.2.l.a.71.3

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			71.3
Root			$-0.396613 - 1.68603i$ of defining polynomial
Character	$\chi$	$=$	114.71
Dual form			114.2.l.a.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(1.26184 - 1.18649i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.86241 + 2.21954i) q^{5} +(0.779936 - 1.54651i) q^{6} +(0.562083 + 0.973556i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.184473 - 2.99432i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(1.26184 - 1.18649i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.86241 + 2.21954i) q^{5} +(0.779936 - 1.54651i) q^{6} +(0.562083 + 0.973556i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.184473 - 2.99432i) q^{9} +(-0.990970 + 2.72267i) q^{10} +(-2.70920 - 1.56416i) q^{11} +(0.203962 - 1.72000i) q^{12} +(-5.18404 + 0.914087i) q^{13} +(0.861160 + 0.722599i) q^{14} +(0.283400 + 5.01044i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.880484 + 2.41911i) q^{17} +(-0.850771 - 2.87684i) q^{18} +(4.13617 - 1.37554i) q^{19} +2.89740i q^{20} +(1.86437 + 0.561563i) q^{21} +(-3.08079 - 0.543226i) q^{22} +(4.31710 + 5.14492i) q^{23} +(-0.396613 - 1.68603i) q^{24} +(-0.589524 - 3.34336i) q^{25} +(-4.55877 + 2.63201i) q^{26} +(-3.31997 - 3.99723i) q^{27} +(1.05637 + 0.384487i) q^{28} +(1.09635 + 0.399039i) q^{29} +(1.97998 + 4.61134i) q^{30} +(-3.90801 + 2.25629i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-5.27443 + 1.24073i) q^{33} +(1.65477 + 1.97208i) q^{34} +(-3.20767 - 0.565599i) q^{35} +(-1.78340 - 2.41236i) q^{36} -12.0703i q^{37} +(3.41626 - 2.70724i) q^{38} +(-5.45687 + 7.30426i) q^{39} +(0.990970 + 2.72267i) q^{40} +(1.06170 - 6.02118i) q^{41} +(1.94400 - 0.109956i) q^{42} +(2.21295 + 1.85688i) q^{43} +(-3.08079 + 0.543226i) q^{44} +(6.30245 + 5.98611i) q^{45} +(5.81642 + 3.35811i) q^{46} +(-0.377793 + 1.03798i) q^{47} +(-0.949351 - 1.44870i) q^{48} +(2.86813 - 4.96774i) q^{49} +(-1.69747 - 2.94010i) q^{50} +(3.98128 + 2.00784i) q^{51} +(-3.38365 + 4.03247i) q^{52} +(5.66806 - 4.75606i) q^{53} +(-4.48688 - 2.62067i) q^{54} +(8.51736 - 3.10007i) q^{55} +1.12417 q^{56} +(3.58710 - 6.64324i) q^{57} +1.16671 q^{58} +(-6.41833 + 2.33608i) q^{59} +(3.43774 + 3.65605i) q^{60} +(-5.58223 + 4.68405i) q^{61} +(-2.90063 + 3.45684i) q^{62} +(3.01883 - 1.50346i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(7.62598 - 13.2086i) q^{65} +(-4.53199 + 2.96987i) q^{66} +(-2.42040 + 6.64999i) q^{67} +(2.22946 + 1.28718i) q^{68} +(11.5519 + 1.36985i) q^{69} +(-3.20767 + 0.565599i) q^{70} +(-3.31294 - 2.77989i) q^{71} +(-2.50092 - 1.65692i) q^{72} +(-1.30735 + 7.41438i) q^{73} +(-4.12829 - 11.3424i) q^{74} +(-4.71075 - 3.51931i) q^{75} +(2.28431 - 3.71240i) q^{76} -3.51674i q^{77} +(-2.62958 + 8.73012i) q^{78} +(4.30920 + 0.759829i) q^{79} +(1.86241 + 2.21954i) q^{80} +(-8.93194 - 1.10474i) q^{81} +(-1.06170 - 6.02118i) q^{82} +(12.5112 - 7.22333i) q^{83} +(1.78916 - 0.768214i) q^{84} +(-7.00913 - 2.55111i) q^{85} +(2.71458 + 0.988026i) q^{86} +(1.85688 - 0.797290i) q^{87} +(-2.70920 + 1.56416i) q^{88} +(2.38095 + 13.5030i) q^{89} +(7.96974 + 3.46954i) q^{90} +(-3.80378 - 4.53316i) q^{91} +(6.61418 + 1.16626i) q^{92} +(-2.25420 + 7.48389i) q^{93} +1.10459i q^{94} +(-4.65018 + 11.7422i) q^{95} +(-1.38758 - 1.03664i) q^{96} +(-1.47287 - 4.04669i) q^{97} +(0.996090 - 5.64911i) q^{98} +(-5.18337 + 7.82368i) 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 $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	1.26184	−	1.18649i	0.728523	−	0.685022i
$3$	1.26184	−	1.18649i	0.728523	−	0.685022i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−1.86241	+	2.21954i	−0.832897	+	0.992608i	0.167081	+	0.985943i	$0.446566\pi$
$5$	−1.86241	+	2.21954i	−0.832897	+	0.992608i	−0.999978	+	0.00666440i	$0.997879\pi$
$6$	0.779936	−	1.54651i	0.318408	−	0.631361i
$7$	0.562083	+	0.973556i	0.212447	+	0.367969i	0.952480	−	0.304602i	$-0.0985233\pi$
$7$	0.562083	+	0.973556i	0.212447	+	0.367969i	−0.740033	+	0.672571i	$0.765190\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.184473	−	2.99432i	0.0614909	−	0.998108i
$10$	−0.990970	+	2.72267i	−0.313372	+	0.860983i
$11$	−2.70920	−	1.56416i	−0.816855	−	0.471611i	0.0324759	−	0.999473i	$-0.489661\pi$
$11$	−2.70920	−	1.56416i	−0.816855	−	0.471611i	−0.849331	+	0.527861i	$0.822994\pi$
$12$	0.203962	−	1.72000i	0.0588787	−	0.496521i
$13$	−5.18404	+	0.914087i	−1.43780	+	0.253522i	−0.837579	−	0.546316i	$-0.816030\pi$
$13$	−5.18404	+	0.914087i	−1.43780	+	0.253522i	−0.600216	+	0.799838i	$0.704919\pi$
$14$	0.861160	+	0.722599i	0.230155	+	0.193123i
$15$	0.283400	+	5.01044i	0.0731734	+	1.29369i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	0.880484	+	2.41911i	0.213549	+	0.586720i	0.999502	−	0.0315662i	$-0.0100495\pi$
$17$	0.880484	+	2.41911i	0.213549	+	0.586720i	−0.785953	+	0.618286i	$0.787827\pi$
$18$	−0.850771	−	2.87684i	−0.200529	−	0.678077i
$19$	4.13617	−	1.37554i	0.948902	−	0.315571i
$19$	4.13617	−	1.37554i	0.948902	−	0.315571i
$20$			2.89740i			0.647879i
$21$	1.86437	+	0.561563i	0.406840	+	0.122543i
$22$	−3.08079	−	0.543226i	−0.656826	−	0.115816i
$23$	4.31710	+	5.14492i	0.900178	+	1.07279i	0.996993	+	0.0774881i	$0.0246900\pi$
$23$	4.31710	+	5.14492i	0.900178	+	1.07279i	−0.0968152	+	0.995302i	$0.530866\pi$
$24$	−0.396613	−	1.68603i	−0.0809583	−	0.344159i
$25$	−0.589524	−	3.34336i	−0.117905	−	0.668671i
$26$	−4.55877	+	2.63201i	−0.894049	+	0.516179i
$27$	−3.31997	−	3.99723i	−0.638928	−	0.769267i
$28$	1.05637	+	0.384487i	0.199635	+	0.0726612i
$29$	1.09635	+	0.399039i	0.203587	+	0.0740998i	0.441801	−	0.897113i	$-0.354340\pi$
$29$	1.09635	+	0.399039i	0.203587	+	0.0740998i	−0.238214	+	0.971213i	$0.576562\pi$
$30$	1.97998	+	4.61134i	0.361493	+	0.841912i
$31$	−3.90801	+	2.25629i	−0.701899	+	0.405241i	−0.808054	−	0.589108i	$-0.799479\pi$
$31$	−3.90801	+	2.25629i	−0.701899	+	0.405241i	0.106155	+	0.994350i	$0.466146\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−5.27443	+	1.24073i	−0.918161	+	0.215984i
$34$	1.65477	+	1.97208i	0.283790	+	0.338208i
$35$	−3.20767	−	0.565599i	−0.542196	−	0.0956038i
$36$	−1.78340	−	2.41236i	−0.297233	−	0.402060i
$37$		−	12.0703i		−	1.98435i	−0.124859	−	0.992174i	$-0.539848\pi$
$37$		−	12.0703i		−	1.98435i	0.124859	−	0.992174i	$-0.460152\pi$
$38$	3.41626	−	2.70724i	0.554191	−	0.439173i
$39$	−5.45687	+	7.30426i	−0.873799	+	1.16962i
$40$	0.990970	+	2.72267i	0.156686	+	0.430491i
$41$	1.06170	−	6.02118i	0.165809	−	0.940350i	−0.782417	−	0.622755i	$-0.786014\pi$
$41$	1.06170	−	6.02118i	0.165809	−	0.940350i	0.948226	−	0.317595i	$-0.102875\pi$
$42$	1.94400	−	0.109956i	0.299966	−	0.0169666i
$43$	2.21295	+	1.85688i	0.337471	+	0.283172i	0.795736	−	0.605644i	$-0.207084\pi$
$43$	2.21295	+	1.85688i	0.337471	+	0.283172i	−0.458265	+	0.888816i	$0.651529\pi$
$44$	−3.08079	+	0.543226i	−0.464446	+	0.0818944i
$45$	6.30245	+	5.98611i	0.939514	+	0.892357i
$46$	5.81642	+	3.35811i	0.857584	+	0.495126i
$47$	−0.377793	+	1.03798i	−0.0551068	+	0.151405i	−0.964192	−	0.265206i	$-0.914560\pi$
$47$	−0.377793	+	1.03798i	−0.0551068	+	0.151405i	0.909085	+	0.416611i	$0.136782\pi$
$48$	−0.949351	−	1.44870i	−0.137027	−	0.209102i
$49$	2.86813	−	4.96774i	0.409732	−	0.709677i
$50$	−1.69747	−	2.94010i	−0.240058	−	0.415793i
$51$	3.98128	+	2.00784i	0.557491	+	0.281153i
$52$	−3.38365	+	4.03247i	−0.469227	+	0.559203i
$53$	5.66806	−	4.75606i	0.778568	−	0.653296i	−0.164320	−	0.986407i	$-0.552543\pi$
$53$	5.66806	−	4.75606i	0.778568	−	0.653296i	0.942887	+	0.333111i	$0.108099\pi$
$54$	−4.48688	−	2.62067i	−0.610587	−	0.356628i
$55$	8.51736	−	3.10007i	1.14848	−	0.418013i
$56$	1.12417			0.150223
$57$	3.58710	−	6.64324i	0.475123	−	0.879919i
$58$	1.16671			0.153197
$59$	−6.41833	+	2.33608i	−0.835596	+	0.304132i	−0.724153	−	0.689639i	$-0.757769\pi$
$59$	−6.41833	+	2.33608i	−0.835596	+	0.304132i	−0.111442	+	0.993771i	$0.535547\pi$
$60$	3.43774	+	3.65605i	0.443811	+	0.471994i
$61$	−5.58223	+	4.68405i	−0.714732	+	0.599731i	−0.925922	−	0.377714i	$-0.876710\pi$
$61$	−5.58223	+	4.68405i	−0.714732	+	0.599731i	0.211191	+	0.977445i	$0.432266\pi$
$62$	−2.90063	+	3.45684i	−0.368380	+	0.439019i
$63$	3.01883	−	1.50346i	0.380337	−	0.189418i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	7.62598	−	13.2086i	0.945887	−	1.63832i
$66$	−4.53199	+	2.96987i	−0.557850	+	0.365566i
$67$	−2.42040	+	6.64999i	−0.295699	+	0.812425i	0.699508	+	0.714625i	$0.253403\pi$
$67$	−2.42040	+	6.64999i	−0.295699	+	0.812425i	−0.995206	+	0.0977999i	$0.968819\pi$
$68$	2.22946	+	1.28718i	0.270362	+	0.156094i
$69$	11.5519	+	1.36985i	1.39068	+	0.164911i
$70$	−3.20767	+	0.565599i	−0.383390	+	0.0676021i
$71$	−3.31294	−	2.77989i	−0.393174	−	0.329912i	0.424674	−	0.905346i	$-0.360389\pi$
$71$	−3.31294	−	2.77989i	−0.393174	−	0.329912i	−0.817848	+	0.575434i	$0.804833\pi$
$72$	−2.50092	−	1.65692i	−0.294737	−	0.195270i
$73$	−1.30735	+	7.41438i	−0.153014	+	0.867787i	0.807565	+	0.589779i	$0.200785\pi$
$73$	−1.30735	+	7.41438i	−0.153014	+	0.867787i	−0.960579	+	0.278008i	$0.910326\pi$
$74$	−4.12829	−	11.3424i	−0.479904	−	1.31853i
$75$	−4.71075	−	3.51931i	−0.543950	−	0.406375i
$76$	2.28431	−	3.71240i	0.262028	−	0.425842i
$77$		−	3.51674i		−	0.400770i
$78$	−2.62958	+	8.73012i	−0.297741	+	0.988491i
$79$	4.30920	+	0.759829i	0.484823	+	0.0854874i	0.410717	−	0.911763i	$-0.365278\pi$
$79$	4.30920	+	0.759829i	0.484823	+	0.0854874i	0.0741064	+	0.997250i	$0.476390\pi$
$80$	1.86241	+	2.21954i	0.208224	+	0.248152i
$81$	−8.93194	−	1.10474i	−0.992438	−	0.122749i
$82$	−1.06170	−	6.02118i	−0.117245	−	0.664928i
$83$	12.5112	−	7.22333i	1.37328	−	0.792863i	0.381940	−	0.924187i	$-0.375256\pi$
$83$	12.5112	−	7.22333i	1.37328	−	0.792863i	0.991340	+	0.131324i	$0.0419227\pi$
$84$	1.78916	−	0.768214i	0.195213	−	0.0838190i
$85$	−7.00913	−	2.55111i	−0.760247	−	0.276707i
$86$	2.71458	+	0.988026i	0.292721	+	0.106542i
$87$	1.85688	−	0.797290i	0.199078	−	0.0854784i
$88$	−2.70920	+	1.56416i	−0.288802	+	0.166740i
$89$	2.38095	+	13.5030i	0.252380	+	1.43132i	0.802710	+	0.596369i	$0.203391\pi$
$89$	2.38095	+	13.5030i	0.252380	+	1.43132i	−0.550331	+	0.834947i	$0.685498\pi$
$90$	7.96974	+	3.46954i	0.840084	+	0.365722i
$91$	−3.80378	−	4.53316i	−0.398744	−	0.475205i
$92$	6.61418	+	1.16626i	0.689576	+	0.121591i
$93$	−2.25420	+	7.48389i	−0.233750	+	0.776043i
$94$			1.10459i			0.113930i
$95$	−4.65018	+	11.7422i	−0.477098	+	1.20473i
$96$	−1.38758	−	1.03664i	−0.141620	−	0.105801i
$97$	−1.47287	−	4.04669i	−0.149548	−	0.410879i	0.842187	−	0.539186i	$-0.181268\pi$
$97$	−1.47287	−	4.04669i	−0.149548	−	0.410879i	−0.991735	+	0.128307i	$0.959046\pi$
$98$	0.996090	−	5.64911i	0.100620	−	0.570646i
$99$	−5.18337	+	7.82368i	−0.520948	+	0.786309i
$100$	−2.60067	−	2.18222i	−0.260067	−	0.218222i
$101$	−5.82418	+	1.02696i	−0.579528	+	0.102186i	−0.455725	−	0.890121i	$-0.650620\pi$
$101$	−5.82418	+	1.02696i	−0.579528	+	0.102186i	−0.123802	+	0.992307i	$0.539509\pi$
$102$	4.42790	+	0.525072i	0.438428	+	0.0519898i
$103$	17.2614	+	9.96588i	1.70082	+	0.981967i	0.944934	+	0.327261i	$0.106126\pi$
$103$	17.2614	+	9.96588i	1.70082	+	0.981967i	0.755884	+	0.654706i	$0.227208\pi$
$104$	−1.80040	+	4.94656i	−0.176544	+	0.485050i
$105$	−4.71865	+	3.09218i	−0.460493	+	0.301766i
$106$	3.69956	−	6.40783i	0.359333	−	0.622383i
$107$	−2.39183	−	4.14277i	−0.231227	−	0.400496i	0.726943	−	0.686698i	$-0.240941\pi$
$107$	−2.39183	−	4.14277i	−0.231227	−	0.400496i	−0.958169	+	0.286202i	$0.907607\pi$
$108$	−5.11261	−	0.928020i	−0.491961	−	0.0892988i
$109$	−5.52889	+	6.58908i	−0.529572	+	0.631119i	−0.962816	−	0.270157i	$-0.912924\pi$
$109$	−5.52889	+	6.58908i	−0.529572	+	0.631119i	0.433244	+	0.901276i	$0.357369\pi$
$110$	6.94341	−	5.82622i	0.662029	−	0.555508i
$111$	−14.3213	−	15.2308i	−1.35932	−	1.44564i
$112$	1.05637	−	0.384487i	0.0998176	−	0.0363306i
$113$	−16.1668			−1.52085			−0.760424	−	0.649427i	$-0.775009\pi$
$113$	−16.1668			−1.52085			−0.760424	+	0.649427i	$0.775009\pi$
$114$	1.09865	−	7.46947i	0.102898	−	0.699580i
$115$	−19.4596			−1.81462
$116$	1.09635	−	0.399039i	0.101794	−	0.0370499i
$117$	1.78076	+	15.6913i	0.164631	+	1.45066i
$118$	−5.23227	+	4.39040i	−0.481670	+	0.404169i
$119$	−1.86023	+	2.21694i	−0.170527	+	0.203226i
$120$	4.48087	+	2.25979i	0.409045	+	0.206289i
$121$	−0.606822	−	1.05105i	−0.0551656	−	0.0955496i
$122$	−3.64354	+	6.31080i	−0.329871	+	0.571353i
$123$	−5.80439	−	8.85745i	−0.523364	−	0.798649i
$124$	−1.54339	+	4.24044i	−0.138601	+	0.380802i
$125$	−4.02747	−	2.32526i	−0.360228	−	0.207978i
$126$	2.32256	−	2.44529i	0.206910	−	0.217844i
$127$	7.59392	−	1.33901i	0.673852	−	0.118818i	0.173756	−	0.984789i	$-0.444409\pi$
$127$	7.59392	−	1.33901i	0.673852	−	0.118818i	0.500095	+	0.865970i	$0.333298\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	4.99556	−	0.282558i	0.439834	−	0.0248778i
$130$	2.64848	−	15.0203i	0.232287	−	1.31736i
$131$	0.757267	+	2.08057i	0.0661627	+	0.181781i	0.968368	−	0.249526i	$-0.0802749\pi$
$131$	0.757267	+	2.08057i	0.0661627	+	0.181781i	−0.902205	+	0.431307i	$0.858053\pi$
$132$	−3.24292	+	4.34080i	−0.282260	+	0.377818i
$133$	3.66404	+	3.25362i	0.317712	+	0.282125i
$134$			7.07677i			0.611340i
$135$	15.0551	+	0.0756985i	1.29574	+	0.00651509i
$136$	2.53525	+	0.447033i	0.217396	+	0.0383328i
$137$	−0.138747	−	0.165352i	−0.0118540	−	0.0141270i	0.760085	−	0.649824i	$-0.225157\pi$
$137$	−0.138747	−	0.165352i	−0.0118540	−	0.0141270i	−0.771939	+	0.635697i	$0.780713\pi$
$138$	11.3237	−	2.66374i	0.963942	−	0.226753i
$139$	3.25695	+	18.4711i	0.276251	+	1.56670i	0.734961	+	0.678110i	$0.237201\pi$
$139$	3.25695	+	18.4711i	0.276251	+	1.56670i	−0.458710	+	0.888586i	$0.651688\pi$
$140$	−2.82078	+	1.62858i	−0.238400	+	0.137640i
$141$	0.754839	+	1.75801i	0.0635689	+	0.148051i
$142$	−4.06393	−	1.47915i	−0.341037	−	0.124127i
$143$	15.4744	+	5.63222i	1.29403	+	0.470990i
$144$	−2.91680	−	0.701629i	−0.243067	−	0.0584691i
$145$	−2.92754	+	1.69022i	−0.243119	+	0.140365i
$146$	1.30735	+	7.41438i	0.108197	+	0.613618i
$147$	−2.27507	−	9.67150i	−0.187645	−	0.797692i
$148$	−7.75865	−	9.24640i	−0.637757	−	0.760050i
$149$	−4.18590	−	0.738088i	−0.342923	−	0.0604665i	−0.000465272	−	1.00000i	$-0.500148\pi$
$149$	−4.18590	−	0.738088i	−0.342923	−	0.0604665i	−0.342457	+	0.939533i	$0.611259\pi$
$150$	−5.63033	−	1.69590i	−0.459715	−	0.138469i
$151$		−	8.94139i		−	0.727640i	−0.931469	−	0.363820i	$-0.881472\pi$
$151$		−	8.94139i		−	0.727640i	0.931469	−	0.363820i	$-0.118528\pi$
$152$	0.876827	−	4.26980i	0.0711201	−	0.346326i
$153$	7.40602	−	2.19019i	0.598741	−	0.177067i
$154$	−1.20280	−	3.30466i	−0.0969241	−	0.266297i
$155$	2.27041	−	12.8761i	0.182363	−	1.03423i
$156$	0.514882	+	9.10300i	0.0412236	+	0.728823i
$157$	1.55311	+	1.30322i	0.123952	+	0.104008i	0.702656	−	0.711529i	$-0.251997\pi$
$157$	1.55311	+	1.30322i	0.123952	+	0.104008i	−0.578705	+	0.815537i	$0.696442\pi$
$158$	4.30920	−	0.759829i	0.342822	−	0.0604487i
$159$	1.50914	−	12.7265i	0.119682	−	1.00928i
$160$	2.50922	+	1.44870i	0.198371	+	0.114530i
$161$	−2.58230	+	7.09481i	−0.203514	+	0.559149i
$162$	−8.77112	+	2.01679i	−0.689124	+	0.158454i
$163$	−4.66573	+	8.08128i	−0.365448	+	0.632975i	−0.988848	−	0.148929i	$-0.952418\pi$
$163$	−4.66573	+	8.08128i	−0.365448	+	0.632975i	0.623400	+	0.781903i	$0.285751\pi$
$164$	−3.05703	−	5.29493i	−0.238714	−	0.413465i
$165$	7.06933	−	14.0176i	0.550346	−	1.09127i
$166$	9.28613	−	11.0668i	0.720744	−	0.858949i
$167$	−9.70512	+	8.14356i	−0.751005	+	0.630168i	−0.935768	−	0.352615i	$-0.885292\pi$
$167$	−9.70512	+	8.14356i	−0.751005	+	0.630168i	0.184764	+	0.982783i	$0.440848\pi$
$168$	1.41851	−	1.33381i	0.109441	−	0.102906i
$169$	13.8228	−	5.03107i	1.06329	−	0.387006i
$170$	−7.45896			−0.572076
$171$	−3.35581	−	12.6388i	−0.256626	−	0.966511i
$172$	2.88880			0.220269
$173$	8.86150	−	3.22532i	0.673727	−	0.245217i	0.0175755	−	0.999846i	$-0.494405\pi$
$173$	8.86150	−	3.22532i	0.673727	−	0.245217i	0.656152	+	0.754629i	$0.272183\pi$
$174$	1.47220	−	1.38430i	0.111607	−	0.104943i
$175$	2.92358	−	2.45318i	0.221002	−	0.185443i
$176$	−2.01084	+	2.39643i	−0.151573	+	0.180638i
$177$	−5.32716	+	10.5631i	−0.400414	+	0.793968i
$178$	6.85566	+	11.8743i	0.513853	+	0.890020i
$179$	3.74454	−	6.48573i	0.279880	−	0.484766i	−0.691475	−	0.722401i	$-0.743039\pi$
$179$	3.74454	−	6.48573i	0.279880	−	0.484766i	0.971355	+	0.237634i	$0.0763720\pi$
$180$	8.67575	+	0.534491i	0.646653	+	0.0398386i
$181$	5.46326	−	15.0102i	0.406081	−	1.11570i	−0.553151	−	0.833081i	$-0.686575\pi$
$181$	5.46326	−	15.0102i	0.406081	−	1.11570i	0.959232	−	0.282618i	$-0.0912030\pi$
$182$	−5.12481	−	2.95881i	−0.379876	−	0.219322i
$183$	−1.48629	+	12.5338i	−0.109870	+	0.926524i
$184$	6.61418	−	1.16626i	0.487604	−	0.0859778i
$185$	26.7905	+	22.4799i	1.96968	+	1.65276i
$186$	0.441383	+	7.80354i	0.0323637	+	0.572183i
$187$	1.39846	−	7.93107i	0.102266	−	0.579977i
$188$	0.377793	+	1.03798i	0.0275534	+	0.0757023i
$189$	2.02543	−	5.47894i	0.147328	−	0.398534i
$190$	−0.353668	+	12.6245i	−0.0256577	+	0.915879i
$191$		−	7.61751i		−	0.551184i	−0.961275	−	0.275592i	$-0.911126\pi$
$191$		−	7.61751i		−	0.551184i	0.961275	−	0.275592i	$-0.0888738\pi$
$192$	−1.65845	−	0.499538i	−0.119688	−	0.0360511i
$193$	11.8171	+	2.08368i	0.850616	+	0.149987i	0.581928	−	0.813241i	$-0.302299\pi$
$193$	11.8171	+	2.08368i	0.850616	+	0.149987i	0.268688	+	0.963227i	$0.413410\pi$
$194$	−2.76810	−	3.29889i	−0.198738	−	0.236847i
$195$	−6.04913	−	25.7153i	−0.433187	−	1.84151i
$196$	−0.996090	−	5.64911i	−0.0711493	−	0.403508i
$197$	−15.2618	+	8.81139i	−1.08736	+	0.627786i	−0.932871	−	0.360210i	$-0.882705\pi$
$197$	−15.2618	+	8.81139i	−1.08736	+	0.627786i	−0.154485	+	0.987995i	$0.549372\pi$
$198$	−2.19492	+	9.12467i	−0.155986	+	0.648462i
$199$	−2.12679	−	0.774087i	−0.150764	−	0.0548736i	0.265536	−	0.964101i	$-0.414451\pi$
$199$	−2.12679	−	0.774087i	−0.150764	−	0.0548736i	−0.416300	+	0.909227i	$0.636673\pi$
$200$	−3.19019	−	1.16114i	−0.225581	−	0.0821047i
$201$	4.83601	+	11.2630i	0.341106	+	0.794430i
$202$	−5.12170	+	2.95701i	−0.360361	+	0.208055i
$203$	0.227753	+	1.29165i	0.0159851	+	0.0906562i
$204$	4.34045	−	1.02103i	0.303892	−	0.0714861i
$205$	11.3869	+	13.5704i	0.795297	+	0.947798i
$206$	19.6290	+	3.46111i	1.36761	+	0.241147i
$207$	16.2019	−	11.9777i	1.12611	−	0.832508i
$208$			5.26402i			0.364994i
$209$	−13.3573	−	2.74299i	−0.923942	−	0.189737i
$210$	−3.37649	+	4.51957i	−0.233000	+	0.311880i
$211$	−1.31716	−	3.61886i	−0.0906769	−	0.249133i	0.886061	−	0.463568i	$-0.153431\pi$
$211$	−1.31716	−	3.61886i	−0.0906769	−	0.249133i	−0.976738	+	0.214435i	$0.931209\pi$
$212$	1.28484	−	7.28671i	0.0882435	−	0.500454i
$213$	−7.47872	+	0.423010i	−0.512433	+	0.0289842i
$214$	−3.66449	−	3.07487i	−0.250500	−	0.210194i
$215$	−8.24284	+	1.45344i	−0.562157	+	0.0991235i
$216$	−5.12168	+	0.876562i	−0.348486	+	0.0596425i
$217$	−4.39325	−	2.53644i	−0.298233	−	0.172185i
$218$	−2.94186	+	8.08270i	−0.199248	+	0.547429i
$219$	7.14743	+	10.9069i	0.482979	+	0.737021i
$220$	4.53199	−	7.84964i	0.305547	−	0.529223i
$221$	−6.77574	−	11.7359i	−0.455786	−	0.789444i
$222$	−18.6669	−	9.41408i	−1.25284	−	0.631832i
$223$	−3.57822	+	4.26435i	−0.239615	+	0.285562i	−0.872428	−	0.488743i	$-0.837456\pi$
$223$	−3.57822	+	4.26435i	−0.239615	+	0.285562i	0.632813	+	0.774305i	$0.281900\pi$
$224$	0.861160	−	0.722599i	0.0575387	−	0.0482807i
$225$	−10.1198	+	1.14847i	−0.674656	+	0.0765645i
$226$	−15.1919	+	5.52938i	−1.01055	+	0.367809i
$227$	24.7738			1.64430			0.822148	−	0.569274i	$-0.192776\pi$
$227$	24.7738			1.64430			0.822148	+	0.569274i	$0.192776\pi$
$228$	−1.52232	−	7.39477i	−0.100818	−	0.489730i
$229$	−24.7947			−1.63848			−0.819241	−	0.573449i	$-0.805605\pi$
$229$	−24.7947			−1.63848			−0.819241	+	0.573449i	$0.805605\pi$
$230$	−18.2860	+	6.65557i	−1.20574	+	0.438855i
$231$	−4.17259	−	4.43756i	−0.274536	−	0.291970i
$232$	0.893754	−	0.749949i	0.0586778	−	0.0492366i
$233$	−13.8205	+	16.4706i	−0.905410	+	1.07903i	0.0911239	+	0.995840i	$0.470954\pi$
$233$	−13.8205	+	16.4706i	−0.905410	+	1.07903i	−0.996534	+	0.0831862i	$0.973490\pi$
$234$	7.04012	+	14.1360i	0.460227	+	0.924097i
$235$	−1.60022	−	2.77167i	−0.104387	−	0.180804i
$236$	−3.41512	+	5.91517i	−0.222306	+	0.385045i
$237$	6.33905	−	4.15406i	0.411766	−	0.269835i
$238$	−0.989809	+	2.71948i	−0.0641598	+	0.176278i
$239$	−10.5128	−	6.06955i	−0.680015	−	0.392607i	0.119846	−	0.992793i	$-0.461760\pi$
$239$	−10.5128	−	6.06955i	−0.680015	−	0.392607i	−0.799861	+	0.600186i	$0.795093\pi$
$240$	4.98353	+	0.590959i	0.321685	+	0.0381463i
$241$	−21.4162	+	3.77626i	−1.37954	+	0.243250i	−0.813709	−	0.581272i	$-0.802555\pi$
$241$	−21.4162	+	3.77626i	−1.37954	+	0.243250i	−0.565830	+	0.824522i	$0.691444\pi$
$242$	−0.929705	−	0.780115i	−0.0597637	−	0.0501477i
$243$	−12.5814	+	9.20367i	−0.807099	+	0.590416i
$244$	−1.26539	+	7.17638i	−0.0810083	+	0.459421i
$245$	5.68445	+	15.6179i	0.363166	+	0.997791i
$246$	−8.48377	−	6.33806i	−0.540905	−	0.404100i
$247$	−20.1847	+	10.9117i	−1.28432	+	0.694295i
$248$			4.51258i			0.286549i
$249$	7.21666	−	23.9591i	0.457337	−	1.51835i
$250$	−4.57987	−	0.807555i	−0.289657	−	0.0510743i
$251$	−12.5021	−	14.8994i	−0.789127	−	0.940445i	0.210181	−	0.977663i	$-0.432595\pi$
$251$	−12.5021	−	14.8994i	−0.789127	−	0.940445i	−0.999307	+	0.0372181i	$0.988150\pi$
$252$	1.34615	−	3.09218i	0.0847995	−	0.194789i
$253$	−3.64843	−	20.6913i	−0.229375	−	1.30085i
$254$	6.67798	−	3.85554i	0.419014	−	0.241918i
$255$	−11.8713	+	5.09718i	−0.743407	+	0.319198i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	10.1861	+	3.70746i	0.635395	+	0.231265i	0.639578	−	0.768727i	$-0.279109\pi$
$257$	10.1861	+	3.70746i	0.635395	+	0.231265i	−0.00418306	+	0.999991i	$0.501332\pi$
$258$	4.59765	−	1.97410i	0.286237	−	0.122902i
$259$	11.7511	−	6.78452i	0.730180	−	0.421569i
$260$	−2.64848	−	15.0203i	−0.164252	−	0.931517i
$261$	1.39710	−	3.20922i	0.0864783	−	0.198646i
$262$	1.42320	+	1.69610i	0.0879253	+	0.104785i
$263$	30.4663	+	5.37204i	1.87863	+	0.331254i	0.991484	−	0.130227i	$-0.0415706\pi$
$263$	30.4663	+	5.37204i	1.87863	+	0.331254i	0.887150	+	0.461481i	$0.152682\pi$
$264$	−1.56271	+	5.18816i	−0.0961783	+	0.319309i
$265$			21.4382i			1.31694i
$266$	4.55587	+	1.80423i	0.279338	+	0.110624i
$267$	19.0256	+	14.2136i	1.16435	+	0.869861i
$268$	2.42040	+	6.64999i	0.147849	+	0.406213i
$269$	−0.880210	+	4.99192i	−0.0536673	+	0.304363i	−0.999812	−	0.0193811i	$-0.993830\pi$
$269$	−0.880210	+	4.99192i	−0.0536673	+	0.304363i	0.946145	+	0.323744i	$0.104942\pi$
$270$	14.1731	−	5.07803i	0.862547	−	0.309039i
$271$	4.01481	+	3.36882i	0.243882	+	0.204641i	0.756533	−	0.653956i	$-0.226892\pi$
$271$	4.01481	+	3.36882i	0.243882	+	0.204641i	−0.512650	+	0.858597i	$0.671336\pi$
$272$	2.53525	−	0.447033i	0.153722	−	0.0271054i
$273$	−10.1783	−	1.20697i	−0.616020	−	0.0730491i
$274$	−0.186934	−	0.107926i	−0.0112931	−	0.00652006i
$275$	−3.63240	+	9.97993i	−0.219042	+	0.601812i
$276$	9.72979	−	6.37605i	0.585665	−	0.383793i
$277$	2.15677	−	3.73563i	0.129588	−	0.224453i	−0.793929	−	0.608010i	$-0.791968\pi$
$277$	2.15677	−	3.73563i	0.129588	−	0.224453i	0.923517	+	0.383558i	$0.125301\pi$
$278$	9.37801	+	16.2432i	0.562456	+	0.974202i
$279$	6.03514	+	12.1181i	0.361314	+	0.725489i
$280$	−2.09366	+	2.49513i	−0.125120	+	0.149112i
$281$	8.43804	−	7.08036i	0.503371	−	0.422379i	−0.355418	−	0.934707i	$-0.615661\pi$
$281$	8.43804	−	7.08036i	0.503371	−	0.422379i	0.858789	+	0.512329i	$0.171217\pi$
$282$	1.31059	+	1.39382i	0.0780445	+	0.0830006i
$283$	−3.71261	+	1.35128i	−0.220691	+	0.0803251i	−0.450000	−	0.893029i	$-0.648576\pi$
$283$	−3.71261	+	1.35128i	−0.220691	+	0.0803251i	0.229308	+	0.973354i	$0.426354\pi$
$284$	−4.32474			−0.256626
$285$	8.06427	+	20.3342i	0.477686	+	1.20449i
$286$	16.4675			0.973744
$287$	6.45871	−	2.35078i	0.381246	−	0.138762i
$288$	−2.98087	+	0.338289i	−0.175649	+	0.0199339i
$289$	7.94592	−	6.66742i	0.467407	−	0.392201i
$290$	−2.17290	+	2.58956i	−0.127597	+	0.152064i
$291$	−6.65990	−	3.35871i	−0.390410	−	0.196891i
$292$	3.76438	+	6.52009i	0.220294	+	0.381560i
$293$	10.0719	−	17.4450i	0.588406	−	1.01915i	−0.406036	−	0.913857i	$-0.633089\pi$
$293$	10.0719	−	17.4450i	0.588406	−	1.01915i	0.994441	−	0.105291i	$-0.0335775\pi$
$294$	−5.44572	−	8.31011i	−0.317601	−	0.484656i
$295$	6.76857	−	18.5965i	0.394081	−	1.08273i
$296$	−10.4532	−	6.03516i	−0.607580	−	0.350787i
$297$	2.74216	+	16.0222i	0.159116	+	0.929705i
$298$	−4.18590	+	0.738088i	−0.242483	+	0.0427563i
$299$	−27.0830	−	22.7253i	−1.56625	−	1.31424i
$300$	−5.87081	+	0.332064i	−0.338951	+	0.0191717i
$301$	−0.563920	+	3.19815i	−0.0325038	+	0.184338i
$302$	−3.05814	−	8.40216i	−0.175976	−	0.483490i
$303$	−6.13070	+	8.20620i	−0.352199	+	0.471434i
$304$	−0.636409	−	4.31219i	−0.0365005	−	0.247321i
$305$		−	21.1136i		−	1.20896i
$306$	6.21029	−	4.59112i	0.355019	−	0.262457i
$307$	−6.45677	−	1.13850i	−0.368508	−	0.0649778i	−0.0136720	−	0.999907i	$-0.504352\pi$
$307$	−6.45677	−	1.13850i	−0.368508	−	0.0649778i	−0.354836	+	0.934929i	$0.615463\pi$
$308$	−2.26052	−	2.69398i	−0.128805	−	0.153504i
$309$	33.6056	−	7.90520i	1.91175	−	0.449711i
$310$	−2.27041	−	12.8761i	−0.128950	−	0.731314i
$311$	−1.86672	+	1.07775i	−0.105852	+	0.0611137i	−0.551991	−	0.833850i	$-0.686132\pi$
$311$	−1.86672	+	1.07775i	−0.105852	+	0.0611137i	0.446139	+	0.894963i	$0.352799\pi$
$312$	3.59724	+	8.37792i	0.203654	+	0.474306i
$313$	15.9106	+	5.79098i	0.899320	+	0.327326i	0.749980	−	0.661460i	$-0.230063\pi$
$313$	15.9106	+	5.79098i	0.899320	+	0.327326i	0.149340	+	0.988786i	$0.452285\pi$
$314$	1.90517	+	0.693426i	0.107515	+	0.0391323i
$315$	−2.28532	+	9.50047i	−0.128763	+	0.535291i
$316$	3.78945	−	2.18784i	0.213173	−	0.123076i
$317$	−0.961500	−	5.45293i	−0.0540032	−	0.306267i	0.945827	−	0.324670i	$-0.105253\pi$
$317$	−0.961500	−	5.45293i	−0.0540032	−	0.306267i	−0.999831	+	0.0184023i	$0.994142\pi$
$318$	−2.93459	−	12.4751i	−0.164564	−	0.699571i
$319$	−2.34608	−	2.79595i	−0.131355	−	0.156543i
$320$	2.85338	+	0.503128i	0.159509	+	0.0281257i
$321$	−7.93346	−	2.38962i	−0.442803	−	0.133375i
$322$			7.55014i			0.420753i
$323$	6.96942	+	8.79469i	0.387789	+	0.489350i
$324$	−7.55238	+	4.89506i	−0.419576	+	0.271948i
$325$	6.11224	+	16.7932i	0.339046	+	0.931521i
$326$	−1.62039	+	9.18969i	−0.0897451	+	0.508970i
$327$	0.841320	+	14.8743i	0.0465251	+	0.822553i
$328$	−4.68364	−	3.93004i	−0.258611	−	0.217000i
$329$	−1.22288	+	0.215627i	−0.0674195	+	0.0118879i
$330$	1.84871	−	15.5901i	0.101768	−	0.858204i
$331$	−6.67525	−	3.85396i	−0.366905	−	0.211833i	0.305200	−	0.952288i	$-0.401277\pi$
$331$	−6.67525	−	3.85396i	−0.366905	−	0.211833i	−0.672106	+	0.740455i	$0.734610\pi$
$332$	4.94105	−	13.5754i	0.271175	−	0.745048i
$333$	−36.1424	−	2.22664i	−1.98059	−	0.122019i
$334$	−6.33457	+	10.9718i	−0.346612	+	0.600350i
$335$	−10.2521	−	17.7572i	−0.560133	−	0.970179i
$336$	0.876777	−	1.73854i	0.0478321	−	0.0948449i
$337$	8.14195	−	9.70320i	0.443520	−	0.528567i	−0.497252	−	0.867606i	$-0.665657\pi$
$337$	8.14195	−	9.70320i	0.443520	−	0.528567i	0.940772	+	0.339039i	$0.110102\pi$
$338$	11.2684	−	9.45533i	0.612921	−	0.514302i
$339$	−20.3999	+	19.1818i	−1.10797	+	1.04181i
$340$	−7.00913	+	2.55111i	−0.380123	+	0.138354i
$341$	14.1168			0.764466
$342$	−7.47615	−	10.7288i	−0.404264	−	0.580147i
$343$	14.3177			0.773081
$344$	2.71458	−	0.988026i	0.146360	−	0.0532708i
$345$	−24.5548	+	23.0886i	−1.32199	+	1.24305i
$346$	7.22396	−	6.06162i	0.388363	−	0.325875i
$347$	2.93143	−	3.49354i	0.157367	−	0.187543i	−0.681600	−	0.731725i	$-0.738716\pi$
$347$	2.93143	−	3.49354i	0.157367	−	0.187543i	0.838967	+	0.544182i	$0.183160\pi$
$348$	0.909962	−	1.80434i	0.0487791	−	0.0967226i
$349$	0.809906	+	1.40280i	0.0433533	+	0.0750901i	0.886888	−	0.461985i	$-0.152863\pi$
$349$	0.809906	+	1.40280i	0.0433533	+	0.0750901i	−0.843535	+	0.537075i	$0.819529\pi$
$350$	1.90823	−	3.30516i	0.101999	−	0.176668i
$351$	20.8647	+	17.6871i	1.11367	+	0.944066i
$352$	−1.06995	+	2.93965i	−0.0570284	+	0.156684i
$353$	−5.92549	−	3.42108i	−0.315382	−	0.182086i	0.333950	−	0.942591i	$-0.391618\pi$
$353$	−5.92549	−	3.42108i	−0.315382	−	0.182086i	−0.649332	+	0.760505i	$0.724952\pi$
$354$	−1.39311	+	11.7480i	−0.0740430	+	0.624400i
$355$	12.3401	−	2.17590i	0.654947	−	0.115485i
$356$	10.5035	+	8.81346i	0.556683	+	0.467113i
$357$	0.283068	+	5.00457i	0.0149815	+	0.264870i
$358$	1.30046	−	7.37530i	0.0687317	−	0.389797i
$359$	−1.39824	−	3.84165i	−0.0737965	−	0.202754i	0.897310	−	0.441401i	$-0.145518\pi$
$359$	−1.39824	−	3.84165i	−0.0737965	−	0.202754i	−0.971106	+	0.238647i	$0.923296\pi$
$360$	8.33535	−	2.46503i	0.439311	−	0.129918i
$361$	15.2158	−	11.3790i	0.800829	−	0.598893i
$362$		−	15.9735i		−	0.839549i
$363$	−2.01277	−	0.606261i	−0.105643	−	0.0318205i
$364$	−5.82772	−	1.02758i	−0.305456	−	0.0538601i
$365$	−14.0217	−	16.7104i	−0.733927	−	0.874660i
$366$	2.89015	+	12.2863i	0.151071	+	0.642213i
$367$	−1.71891	−	9.74845i	−0.0897266	−	0.508865i	−0.996236	−	0.0866798i	$-0.972374\pi$
$367$	−1.71891	−	9.74845i	−0.0897266	−	0.508865i	0.906510	−	0.422185i	$-0.138737\pi$
$368$	5.81642	−	3.35811i	0.303202	−	0.175054i
$369$	−17.8335	−	4.28980i	−0.928375	−	0.223318i
$370$	32.8635	+	11.9613i	1.70849	+	0.621840i
$371$	7.81621	+	2.84487i	0.405797	+	0.147698i
$372$	3.08373	+	7.18197i	0.159884	+	0.372368i
$373$	6.90673	−	3.98760i	0.357617	−	0.206470i	−0.310418	−	0.950600i	$-0.600469\pi$
$373$	6.90673	−	3.98760i	0.357617	−	0.206470i	0.668035	+	0.744130i	$0.267136\pi$
$374$	−1.39846	−	7.93107i	−0.0723127	−	0.410106i
$375$	−7.84092	+	1.84446i	−0.404904	+	0.0952475i
$376$	0.710018	+	0.846167i	0.0366164	+	0.0436377i
$377$	−6.04829	−	1.06648i	−0.311503	−	0.0549264i
$378$	0.0293703	−	5.84126i	0.00151065	−	0.300442i
$379$		−	10.7490i		−	0.552141i	−0.961137	−	0.276071i	$-0.910968\pi$
$379$		−	10.7490i		−	0.552141i	0.961137	−	0.276071i	$-0.0890323\pi$
$380$	3.98550	+	11.9841i	0.204452	+	0.614773i
$381$	7.99358	−	10.6997i	0.409523	−	0.548165i
$382$	−2.60534	−	7.15812i	−0.133301	−	0.366241i
$383$	−0.913805	+	5.18245i	−0.0466933	+	0.264811i	−0.999213	−	0.0396663i	$-0.987371\pi$
$383$	−0.913805	+	5.18245i	−0.0466933	+	0.264811i	0.952520	+	0.304477i	$0.0984816\pi$
$384$	−1.72929	+	0.0978116i	−0.0882473	+	0.00499143i
$385$	7.80554	+	6.54963i	0.397807	+	0.333800i
$386$	11.8171	−	2.08368i	0.601476	−	0.106057i
$387$	5.96833	−	6.28373i	0.303387	−	0.319420i
$388$	−3.72945	−	2.15320i	−0.189334	−	0.109312i
$389$	−5.43196	+	14.9242i	−0.275411	+	0.756686i	0.722457	+	0.691416i	$0.243013\pi$
$389$	−5.43196	+	14.9242i	−0.275411	+	0.756686i	−0.997868	+	0.0652695i	$0.979209\pi$
$390$	−14.4795	−	22.0955i	−0.733196	−	1.11885i
$391$	−8.64499	+	14.9736i	−0.437196	+	0.757245i
$392$	−2.86813	−	4.96774i	−0.144862	−	0.250909i
$393$	3.42413	+	1.72686i	0.172725	+	0.0871084i
$394$	−11.3277	+	13.4998i	−0.570681	+	0.680112i
$395$	−9.71199	+	8.14933i	−0.488663	+	0.410037i
$396$	1.05827	+	9.32509i	0.0531803	+	0.468603i
$397$	−33.6599	+	12.2512i	−1.68934	+	0.614870i	−0.994542	−	0.104334i	$-0.966729\pi$
$397$	−33.6599	+	12.2512i	−1.68934	+	0.614870i	−0.694799	+	0.719204i	$0.744507\pi$
$398$	−2.26328			−0.113448
$399$	8.48382	−	0.241809i	0.424722	−	0.0121056i
$400$	−3.39493			−0.169747
$401$	−5.57564	+	2.02937i	−0.278434	+	0.101342i	−0.477463	−	0.878652i	$-0.658443\pi$
$401$	−5.57564	+	2.02937i	−0.278434	+	0.101342i	0.199029	+	0.979994i	$0.436221\pi$
$402$	8.39653	+	8.92974i	0.418781	+	0.445375i
$403$	18.1968	−	15.2690i	0.906449	−	0.760601i
$404$	−3.80146	+	4.53041i	−0.189130	+	0.225396i
$405$	19.0870	−	17.7673i	0.948440	−	0.882864i
$406$	0.655789	+	1.13586i	0.0325463	+	0.0563718i
$407$	−18.8799	+	32.7009i	−0.935841	+	1.62092i
$408$	3.72948	−	2.44397i	0.184637	−	0.120995i
$409$	9.06715	−	24.9118i	0.448342	−	1.23181i	−0.485536	−	0.874217i	$-0.661375\pi$
$409$	9.06715	−	24.9118i	0.448342	−	1.23181i	0.933878	−	0.357592i	$-0.116402\pi$
$410$	15.3415	+	8.85745i	0.757665	+	0.437438i
$411$	−0.371266	−	0.0440256i	−0.0183132	−	0.00217162i
$412$	19.6290	−	3.46111i	0.967049	−	0.170517i
$413$	−5.88194	−	4.93553i	−0.289431	−	0.242862i
$414$	11.1282	−	16.7968i	0.546923	−	0.825515i
$415$	−7.26852	+	41.2218i	−0.356798	+	2.02350i
$416$	1.80040	+	4.94656i	0.0882719	+	0.242525i
$417$	26.0255	+	19.4432i	1.27448	+	0.952136i
$418$	−13.4899	+	1.99089i	−0.659812	+	0.0973775i
$419$		−	8.21543i		−	0.401350i	−0.979658	−	0.200675i	$-0.935686\pi$
$419$		−	8.21543i		−	0.401350i	0.979658	−	0.200675i	$-0.0643135\pi$
$420$	−1.62707	+	5.40184i	−0.0793931	+	0.263583i
$421$	−16.5911	−	2.92547i	−0.808603	−	0.142578i	−0.245961	−	0.969280i	$-0.579104\pi$
$421$	−16.5911	−	2.92547i	−0.808603	−	0.142578i	−0.562641	+	0.826701i	$0.690215\pi$
$422$	−2.47545	−	2.95012i	−0.120503	−	0.143610i
$423$	3.03835	+	1.32271i	0.147730	+	0.0643125i
$424$	−1.28484	−	7.28671i	−0.0623976	−	0.353874i
$425$	7.56888	−	4.36989i	0.367144	−	0.211971i
$426$	−6.88302	+	2.95537i	−0.333483	+	0.143188i
$427$	−7.69786	−	2.80179i	−0.372526	−	0.135588i
$428$	−4.49517	−	1.63611i	−0.217282	−	0.0790842i
$429$	26.2088	−	11.2533i	1.26537	−	0.543314i
$430$	−7.24863	+	4.18500i	−0.349560	+	0.201819i
$431$	5.03223	+	28.5392i	0.242394	+	1.37469i	0.826467	+	0.562985i	$0.190347\pi$
$431$	5.03223	+	28.5392i	0.242394	+	1.37469i	−0.584073	+	0.811701i	$0.698542\pi$
$432$	−4.51301	+	2.57542i	−0.217132	+	0.123910i
$433$	−17.6845	−	21.0756i	−0.849863	−	1.01283i	−0.999709	−	0.0241176i	$-0.992322\pi$
$433$	−17.6845	−	21.0756i	−0.849863	−	1.01283i	0.149846	−	0.988709i	$-0.452122\pi$
$434$	−4.99581	−	0.880897i	−0.239807	−	0.0422844i
$435$	−1.68866	+	5.60629i	−0.0809649	+	0.268801i
$436$			8.60143i			0.411934i
$437$	24.9333	+	15.3419i	1.19272	+	0.733902i
$438$	10.4468	+	7.80458i	0.499166	+	0.372917i
$439$	−5.19707	−	14.2788i	−0.248042	−	0.681491i	−0.999758	−	0.0220034i	$-0.992996\pi$
$439$	−5.19707	−	14.2788i	−0.248042	−	0.681491i	0.751715	−	0.659488i	$-0.229227\pi$
$440$	1.57394	−	8.92628i	0.0750348	−	0.425544i
$441$	−14.3459	−	9.50451i	−0.683139	−	0.452596i
$442$	−10.3810	−	8.71073i	−0.493776	−	0.414327i
$443$	−4.75117	+	0.837760i	−0.225735	+	0.0398032i	−0.285371	−	0.958417i	$-0.592117\pi$
$443$	−4.75117	+	0.837760i	−0.225735	+	0.0398032i	0.0596365	+	0.998220i	$0.481006\pi$
$444$	−20.7610	−	2.46189i	−0.985271	−	0.116836i
$445$	−34.4047	−	19.8636i	−1.63094	−	0.941624i
$446$	−1.90393	+	5.23100i	−0.0901537	+	0.247695i
$447$	−6.15767	+	4.03519i	−0.291248	+	0.190858i
$448$	0.562083	−	0.973556i	0.0265559	−	0.0459962i
$449$	−1.78666	−	3.09458i	−0.0843176	−	0.146042i	0.820783	−	0.571241i	$-0.193538\pi$
$449$	−1.78666	−	3.09458i	−0.0843176	−	0.146042i	−0.905100	+	0.425198i	$0.860204\pi$
$450$	−9.11674	+	4.54039i	−0.429767	+	0.214036i
$451$	−12.2944	+	14.6519i	−0.578921	+	0.689932i
$452$	−12.3845	+	10.3918i	−0.582519	+	0.488791i
$453$	−10.6089	−	11.2826i	−0.498449	−	0.530103i
$454$	23.2798	−	8.47314i	1.09257	−	0.397664i
$455$	17.1457			0.803804
$456$	−3.95967	−	6.42814i	−0.185428	−	0.301025i
$457$	26.0709			1.21955			0.609774	−	0.792576i	$-0.291260\pi$
$457$	26.0709			1.21955			0.609774	+	0.792576i	$0.291260\pi$
$458$	−23.2994	+	8.48030i	−1.08871	+	0.396258i
$459$	6.74655	−	11.5509i	0.314902	−	0.539148i
$460$	−14.9069	+	12.5084i	−0.695038	+	0.583206i
$461$	−8.46456	+	10.0877i	−0.394234	+	0.469830i	−0.926253	−	0.376903i	$-0.876989\pi$
$461$	−8.46456	+	10.0877i	−0.394234	+	0.469830i	0.532019	+	0.846732i	$0.321433\pi$
$462$	−5.43869	−	2.74283i	−0.253031	−	0.127608i
$463$	−10.6868	−	18.5101i	−0.496659	−	0.860238i	0.503334	−	0.864092i	$-0.332107\pi$
$463$	−10.6868	−	18.5101i	−0.496659	−	0.860238i	−0.999993	+	0.00385369i	$0.998773\pi$
$464$	0.583357	−	1.01040i	0.0270817	−	0.0469068i
$465$	−12.4125	−	18.9414i	−0.575617	−	0.878386i
$466$	−7.35373	+	20.2042i	−0.340655	+	0.935941i
$467$	8.01942	+	4.63001i	0.371094	+	0.214251i	0.673936	−	0.738789i	$-0.264602\pi$
$467$	8.01942	+	4.63001i	0.371094	+	0.214251i	−0.302842	+	0.953041i	$0.597935\pi$
$468$	11.4503	+	10.8756i	0.529292	+	0.502725i
$469$	−7.83459	+	1.38145i	−0.361768	+	0.0637894i
$470$	−2.45169	−	2.05721i	−0.113088	−	0.0948919i
$471$	3.50603	−	0.198308i	0.161549	−	0.00913753i
$472$	−1.18606	+	6.72648i	−0.0545928	+	0.309611i
$473$	−3.09086	−	8.49206i	−0.142118	−	0.390465i
$474$	4.53599	−	6.07162i	0.208345	−	0.278879i
$475$	−7.03730	−	13.0178i	−0.322894	−	0.597296i
$476$			2.89401i			0.132647i
$477$	−13.1956	−	17.8494i	−0.604185	−	0.817266i
$478$	−11.9547	−	2.10793i	−0.546795	−	0.0964147i
$479$	3.61743	+	4.31108i	0.165284	+	0.196978i	0.842329	−	0.538964i	$-0.181184\pi$
$479$	3.61743	+	4.31108i	0.165284	+	0.196978i	−0.677045	+	0.735942i	$0.736740\pi$
$480$	4.88511	−	1.14915i	0.222974	−	0.0524512i
$481$	11.0333	+	62.5731i	0.503076	+	2.85309i
$482$	−18.8331	+	10.8733i	−0.857824	+	0.495265i
$483$	5.15949	+	12.0164i	0.234765	+	0.546764i
$484$	−1.14045	−	0.415090i	−0.0518387	−	0.0188677i
$485$	11.7249	+	4.26751i	0.532400	+	0.193778i
$486$	−8.67484	+	12.9517i	−0.393499	+	0.587502i
$487$	17.7438	−	10.2444i	0.804048	−	0.464217i	−0.0408365	−	0.999166i	$-0.513002\pi$
$487$	17.7438	−	10.2444i	0.804048	−	0.464217i	0.844885	+	0.534948i	$0.179669\pi$
$488$	1.26539	+	7.17638i	0.0572815	+	0.324859i
$489$	3.70098	+	15.7331i	0.167364	+	0.711476i
$490$	10.6833	+	12.7318i	0.482621	+	0.575165i
$491$	32.2309	+	5.68317i	1.45456	+	0.256478i	0.844363	−	0.535772i	$-0.179979\pi$
$491$	32.2309	+	5.68317i	1.45456	+	0.256478i	0.610196	+	0.792250i	$0.291091\pi$
$492$	−10.1399	−	3.05421i	−0.457141	−	0.137694i
$493$			3.00354i			0.135273i
$494$	−15.2354	+	17.1572i	−0.685473	+	0.771940i
$495$	−7.71138	−	26.0756i	−0.346601	−	1.17201i
$496$	1.54339	+	4.24044i	0.0693004	+	0.190401i
$497$	0.844229	−	4.78786i	0.0378689	−	0.214765i
$498$	−1.41305	−	24.9824i	−0.0633203	−	1.11949i
$499$	15.7157	+	13.1871i	0.703533	+	0.590334i	0.922776	−	0.385336i	$-0.125914\pi$
$499$	15.7157	+	13.1871i	0.703533	+	0.590334i	−0.219243	+	0.975670i	$0.570359\pi$
$500$	−4.57987	+	0.807555i	−0.204818	+	0.0361150i
$501$	−2.58402	+	21.7909i	−0.115446	+	0.973546i
$502$	−16.8441	−	9.72492i	−0.751787	−	0.434044i
$503$	7.95923	−	21.8678i	0.354885	−	0.975037i	−0.625893	−	0.779909i	$-0.715265\pi$
$503$	7.95923	−	21.8678i	0.354885	−	0.975037i	0.980778	−	0.195128i	$-0.0625124\pi$
$504$	0.207378	−	3.36611i	0.00923733	−	0.149939i
$505$	8.56766	−	14.8396i	0.381256	−	0.660354i
$506$	−10.5052	−	18.1956i	−0.467014	−	0.808892i
$507$	11.4728	−	22.7490i	0.509523	−	1.01032i
$508$	4.95658	−	5.90702i	0.219913	−	0.262082i
$509$	16.6553	−	13.9754i	0.738232	−	0.619450i	−0.194130	−	0.980976i	$-0.562188\pi$
$509$	16.6553	−	13.9754i	0.738232	−	0.619450i	0.932362	+	0.361525i	$0.117744\pi$
$510$	−9.41200	+	8.85000i	−0.416770	+	0.391884i
$511$	−7.95315	+	2.89471i	−0.351827	+	0.128054i
$512$	−1.00000			−0.0441942
$513$	−19.2303	−	11.9664i	−0.849038	−	0.528331i
$514$	10.8399			0.478126
$515$	−54.2675	+	19.7518i	−2.39131	+	0.870367i
$516$	3.64519	−	3.42753i	0.160471	−	0.150889i
$517$	2.64708	−	2.22116i	0.116418	−	0.0976866i
$518$	8.72201	−	10.3945i	0.383223	−	0.456707i
$519$	7.35496	−	14.5839i	0.322847	−	0.640164i
$520$	−7.62598	−	13.2086i	−0.334422	−	0.579235i
$521$	7.53777	−	13.0558i	0.330236	−	0.571985i	−0.652322	−	0.757942i	$-0.726205\pi$
$521$	7.53777	−	13.0558i	0.330236	−	0.571985i	0.982558	+	0.185957i	$0.0595384\pi$
$522$	0.215227	−	3.49352i	0.00942021	−	0.152907i
$523$	2.38040	−	6.54010i	0.104088	−	0.285979i	−0.876706	−	0.481027i	$-0.840264\pi$
$523$	2.38040	−	6.54010i	0.104088	−	0.285979i	0.980794	+	0.195048i	$0.0624862\pi$
$524$	1.91747	+	1.10705i	0.0837649	+	0.0483617i
$525$	0.778413	−	6.56432i	0.0339727	−	0.286490i
$526$	30.4663	−	5.37204i	1.32840	−	0.234232i
$527$	−8.89914	−	7.46727i	−0.387653	−	0.325279i
$528$	0.305986	+	5.40975i	0.0133163	+	0.235429i
$529$	−3.83894	+	21.7717i	−0.166911	+	0.946597i
$530$	7.33231	+	20.1453i	0.318495	+	0.875058i
$531$	5.81098	+	19.6495i	0.252175	+	0.852716i
$532$	4.89820	+	0.137220i	0.212364	+	0.00594923i
$533$			32.1845i			1.39407i
$534$	22.7396	+	6.84932i	0.984037	+	0.296399i
$535$	13.6496	+	2.40679i	0.590124	+	0.104055i
$536$	4.54886	+	5.42112i	0.196481	+	0.234157i
$537$	−2.97027	−	12.6268i	−0.128176	−	0.544887i
$538$	0.880210	+	4.99192i	0.0379485	+	0.215217i
$539$	−15.5407	+	8.97240i	−0.669384	+	0.386469i
$540$	11.5816	−	9.61927i	0.498391	−	0.413948i
$541$	−4.63626	−	1.68746i	−0.199328	−	0.0725495i	0.240427	−	0.970667i	$-0.422713\pi$
$541$	−4.63626	−	1.68746i	−0.199328	−	0.0725495i	−0.439755	+	0.898118i	$0.644935\pi$
$542$	4.92489	+	1.79251i	0.211542	+	0.0769950i
$543$	−10.9157	−	25.4226i	−0.468439	−	1.09099i
$544$	2.22946	−	1.28718i	0.0955874	−	0.0551874i
$545$	−4.32762	−	24.5432i	−0.185375	−	1.05131i
$546$	−9.97729	+	2.34701i	−0.426989	+	0.100443i
$547$	9.08478	+	10.8268i	0.388437	+	0.462922i	0.924458	−	0.381283i	$-0.124518\pi$
$547$	9.08478	+	10.8268i	0.388437	+	0.462922i	−0.536021	+	0.844205i	$0.680073\pi$
$548$	−0.212573	−	0.0374824i	−0.00908067	−	0.00160117i
$549$	12.9958	+	17.5791i	0.554647	+	0.750257i
$550$			10.6204i			0.452856i
$551$	5.08359	+	0.142413i	0.216568	+	0.00606701i
$552$	6.96228	−	9.31931i	0.296334	−	0.396656i
$553$	1.68239	+	4.62234i	0.0715426	+	0.196562i
$554$	0.749038	−	4.24801i	0.0318236	−	0.180481i
$555$	60.4776	−	3.42072i	2.56713	−	0.145202i
$556$	14.3679	+	12.0561i	0.609336	+	0.511294i
$557$	−0.424076	+	0.0747760i	−0.0179687	+	0.00316836i	−0.182625	−	0.983183i	$-0.558460\pi$
$557$	−0.424076	+	0.0747760i	−0.0179687	+	0.00316836i	0.164657	+	0.986351i	$0.447348\pi$
$558$	9.81580	+	9.32311i	0.415536	+	0.394679i
$559$	−13.1694	−	7.60334i	−0.557005	−	0.321587i
$560$	−1.11401	+	3.06073i	−0.0470757	+	0.129339i
$561$	−7.64552	−	11.6670i	−0.322794	−	0.492581i
$562$	5.50754	−	9.53934i	0.232322	−	0.402393i
$563$	2.44919	+	4.24212i	0.103221	+	0.178784i	0.913010	−	0.407937i	$-0.133752\pi$
$563$	2.44919	+	4.24212i	0.103221	+	0.178784i	−0.809789	+	0.586721i	$0.800418\pi$
$564$	1.70827	+	0.861512i	0.0719310	+	0.0362762i
$565$	30.1093	−	35.8829i	1.26671	−	1.50961i
$566$	−3.02654	+	2.53957i	−0.127215	+	0.106746i
$567$	−3.94496	−	9.31670i	−0.165673	−	0.391264i
$568$	−4.06393	+	1.47915i	−0.170519	+	0.0620637i
$569$	−9.33523			−0.391353			−0.195677	−	0.980668i	$-0.562690\pi$
$569$	−9.33523			−0.391353			−0.195677	+	0.980668i	$0.562690\pi$
$570$	14.5326	+	16.3497i	0.608705	+	0.684815i
$571$	23.4478			0.981260			0.490630	−	0.871368i	$-0.336767\pi$
$571$	23.4478			0.981260			0.490630	+	0.871368i	$0.336767\pi$
$572$	15.4744	−	5.63222i	0.647017	−	0.235495i
$573$	−9.03812	−	9.61207i	−0.377573	−	0.401550i
$574$	5.26519	−	4.41802i	0.219765	−	0.184405i
$575$	14.6563	−	17.4667i	0.611209	−	0.728410i
$576$	−2.68540	+	1.33740i	−0.111892	+	0.0557251i
$577$	−1.23938	−	2.14667i	−0.0515960	−	0.0893669i	0.839074	−	0.544017i	$-0.183097\pi$
$577$	−1.23938	−	2.14667i	−0.0515960	−	0.0893669i	−0.890670	+	0.454651i	$0.849764\pi$
$578$	5.18633	−	8.98299i	0.215723	−	0.373643i
$579$	17.3836	−	11.3917i	0.722437	−	0.473422i
$580$	−1.15618	+	3.17657i	−0.0480076	+	0.131900i
$581$	14.0646	+	8.12021i	0.583499	+	0.336883i
$582$	−7.40700	−	0.878341i	−0.307030	−	0.0364084i
$583$	−22.7951	+	4.01940i	−0.944078	+	0.166466i
$584$	5.76736	+	4.83939i	0.238655	+	0.200255i
$585$	−38.1440	−	25.2713i	−1.57706	−	1.04484i
$586$	3.49793	−	19.8377i	0.144498	−	0.819489i
$587$	13.2139	+	36.3050i	0.545398	+	1.49847i	0.839859	+	0.542804i	$0.182637\pi$
$587$	13.2139	+	36.3050i	0.545398	+	1.49847i	−0.294462	+	0.955663i	$0.595140\pi$
$588$	−7.95952	−	5.94641i	−0.328245	−	0.245226i
$589$	−13.0605	+	14.7080i	−0.538150	+	0.606034i
$590$		−	19.7900i		−	0.814740i
$591$	−8.80325	+	29.2265i	−0.362117	+	1.20222i
$592$	−11.8869	−	2.09599i	−0.488551	−	0.0861446i
$593$	−2.81505	−	3.35484i	−0.115600	−	0.137767i	0.705141	−	0.709067i	$-0.250884\pi$
$593$	−2.81505	−	3.35484i	−0.115600	−	0.137767i	−0.820741	+	0.571300i	$0.806439\pi$
$594$	8.05672	+	14.1181i	0.330571	+	0.579273i
$595$	−1.45606	−	8.25771i	−0.0596925	−	0.338533i
$596$	−3.68102	+	2.12524i	−0.150781	+	0.0870532i
$597$	−3.60211	+	1.54664i	−0.147424	+	0.0632999i
$598$	−33.2222	−	12.0919i	−1.35856	−	0.494474i
$599$	−40.2689	−	14.6567i	−1.64534	−	0.598855i	−0.657380	−	0.753559i	$-0.728335\pi$
$599$	−40.2689	−	14.6567i	−1.64534	−	0.598855i	−0.987961	+	0.154704i	$0.950558\pi$
$600$	−5.40319	+	2.31997i	−0.220584	+	0.0947125i
$601$	−24.0390	+	13.8789i	−0.980571	+	0.566133i	−0.902443	−	0.430810i	$-0.858228\pi$
$601$	−24.0390	+	13.8789i	−0.980571	+	0.566133i	−0.0781288	+	0.996943i	$0.524895\pi$
$602$	0.563920	+	3.19815i	0.0229836	+	0.130347i
$603$	19.4657	+	8.47419i	0.792705	+	0.345096i
$604$	−5.74742	−	6.84951i	−0.233859	−	0.278702i
$605$	3.46299	+	0.610618i	0.140791	+	0.0248252i
$606$	−2.95428	+	9.80813i	−0.120010	+	0.398428i
$607$			16.1090i			0.653844i	0.945051	+	0.326922i	$0.106011\pi$
$607$			16.1090i			0.653844i	−0.945051	+	0.326922i	$0.893989\pi$
$608$	−2.07288	−	3.83447i	−0.0840666	−	0.155508i
$609$	1.81992	+	1.35963i	0.0737470	+	0.0550950i
$610$	−7.22128	−	19.8403i	−0.292381	−	0.803311i
$611$	1.00969	−	5.72626i	0.0408478	−	0.231660i
$612$	4.26551	−	6.43828i	0.172423	−	0.260252i
$613$	17.2068	+	14.4382i	0.694975	+	0.583154i	0.920339	−	0.391121i	$-0.127913\pi$
$613$	17.2068	+	14.4382i	0.694975	+	0.583154i	−0.225364	+	0.974275i	$0.572357\pi$
$614$	−6.45677	+	1.13850i	−0.260574	+	0.0459463i
$615$	30.4696	+	3.61316i	1.22865	+	0.145697i
$616$	−3.04559	−	1.75837i	−0.122710	−	0.0708468i
$617$	15.8059	−	43.4264i	0.636322	−	1.74828i	−0.0266596	−	0.999645i	$-0.508487\pi$
$617$	15.8059	−	43.4264i	0.636322	−	1.74828i	0.662982	−	0.748636i	$-0.269291\pi$
$618$	28.8752	−	18.9222i	1.16153	−	0.761164i
$619$	−20.8534	+	36.1192i	−0.838170	+	1.45175i	0.0532532	+	0.998581i	$0.483041\pi$
$619$	−20.8534	+	36.1192i	−0.838170	+	1.45175i	−0.891423	+	0.453172i	$0.850292\pi$
$620$	−6.53737	−	11.3231i	−0.262547	−	0.454745i
$621$	6.23279	−	34.3374i	0.250113	−	1.37791i
$622$	−1.38553	+	1.65121i	−0.0555547	+	0.0662076i
$623$	−11.8076	+	9.90779i	−0.473063	+	0.396947i
$624$	6.24572	+	6.64234i	0.250029	+	0.265906i
$625$	28.6128	−	10.4142i	1.14451	−	0.416568i
$626$	16.9317			0.676727
$627$	−20.1093	+	12.3871i	−0.803087	+	0.494693i
$628$	2.02744			0.0809038
$629$	29.1994	−	10.6277i	1.16426	−	0.423755i
$630$	1.10186	+	9.70915i	0.0438991	+	0.386822i
$631$	−3.34686	+	2.80835i	−0.133236	+	0.111799i	−0.706971	−	0.707243i	$-0.749939\pi$
$631$	−3.34686	+	2.80835i	−0.133236	+	0.111799i	0.573734	+	0.819042i	$0.305494\pi$
$632$	2.81263	−	3.35197i	0.111881	−	0.133334i
$633$	−5.95579	−	3.00362i	−0.236722	−	0.119383i
$634$	−2.76853	−	4.79523i	−0.109952	−	0.190443i
$635$	−11.1710	+	19.3488i	−0.443309	+	0.767834i
$636$	−7.02436	−	10.7191i	−0.278534	−	0.425040i
$637$	−10.3275	+	28.3747i	−0.409192	+	1.12425i
$638$	−3.16086	−	1.82492i	−0.125140	−	0.0722494i
$639$	−8.93504	+	9.40721i	−0.353465	+	0.372144i
$640$	2.85338	−	0.503128i	0.112790	−	0.0198879i
$641$	−2.18494	−	1.83339i	−0.0863001	−	0.0724144i	0.598617	−	0.801035i	$-0.295717\pi$
$641$	−2.18494	−	1.83339i	−0.0863001	−	0.0724144i	−0.684917	+	0.728621i	$0.740162\pi$
$642$	−8.27231	+	0.467897i	−0.326482	+	0.0184664i
$643$	7.65253	−	43.3997i	0.301786	−	1.71152i	−0.336471	−	0.941694i	$-0.609234\pi$
$643$	7.65253	−	43.3997i	0.301786	−	1.71152i	0.638258	−	0.769823i	$-0.279655\pi$
$644$	2.58230	+	7.09481i	0.101757	+	0.279575i
$645$	−8.67664	+	11.6141i	−0.341643	+	0.457303i
$646$	9.55707	+	5.88063i	0.376018	+	0.231370i
$647$		−	20.3269i		−	0.799131i	−0.916705	−	0.399566i	$-0.869161\pi$
$647$		−	20.3269i		−	0.799131i	0.916705	−	0.399566i	$-0.130839\pi$
$648$	−5.42270	+	7.18292i	−0.213024	+	0.282172i
$649$	21.0426	+	3.71037i	0.825992	+	0.145645i
$650$	11.4872	+	13.6900i	0.450567	+	0.536965i
$651$	−8.55303	+	2.01197i	−0.335220	+	0.0788554i
$652$	1.62039	+	9.18969i	0.0634594	+	0.359896i
$653$	−35.1702	+	20.3055i	−1.37632	+	0.794617i	−0.991714	−	0.128465i	$-0.958995\pi$
$653$	−35.1702	+	20.3055i	−1.37632	+	0.794617i	−0.384603	+	0.923082i	$0.625662\pi$
$654$	5.87790	+	13.6896i	0.229844	+	0.535304i
$655$	−6.02826	−	2.19411i	−0.235543	−	0.0857308i
$656$	−5.74534	−	2.09113i	−0.224318	−	0.0816450i
$657$	21.9599	+	5.28239i	0.856736	+	0.206086i
$658$	−1.07538	+	0.620872i	−0.0419228	+	0.0242041i
$659$	6.33474	+	35.9261i	0.246766	+	1.39948i	0.816354	+	0.577552i	$0.195992\pi$
$659$	6.33474	+	35.9261i	0.246766	+	1.39948i	−0.569588	+	0.821930i	$0.692897\pi$
$660$	−3.59490	−	15.2822i	−0.139931	−	0.594857i
$661$	−2.71797	−	3.23916i	−0.105717	−	0.125989i	0.710591	−	0.703605i	$-0.248427\pi$
$661$	−2.71797	−	3.23916i	−0.105717	−	0.125989i	−0.816308	+	0.577616i	$0.803983\pi$
$662$	−7.59082	−	1.33847i	−0.295026	−	0.0520210i
$663$	−22.4745	−	6.76948i	−0.872837	−	0.262905i
$664$		−	14.4467i		−	0.560639i
$665$	−14.0455	+	2.07288i	−0.544660	+	0.0803830i
$666$	−34.7243	+	10.2691i	−1.34554	+	0.397919i
$667$	2.68004	+	7.36334i	0.103771	+	0.285110i
$668$	−2.19997	+	12.4767i	−0.0851195	+	0.482737i
$669$	0.544490	+	9.62645i	0.0210512	+	0.372180i
$670$	−15.7072	−	13.1799i	−0.606820	−	0.509183i
$671$	22.4500	−	3.95854i	0.866672	−	0.152818i
$672$	0.229287	−	1.93356i	0.00884493	−	0.0745888i
$673$	22.4627	+	12.9688i	0.865874	+	0.499912i	0.865975	−	0.500088i	$-0.166699\pi$
$673$	22.4627	+	12.9688i	0.865874	+	0.499912i	−0.000101249		1.00000i	$0.500032\pi$
$674$	4.33224	−	11.9027i	0.166872	−	0.458476i
$675$	−11.4070	+	13.4563i	−0.439054	+	0.517933i
$676$	7.35494	−	12.7391i	0.282882	−	0.489966i
$677$	16.1874	+	28.0374i	0.622132	+	1.07756i	0.989088	+	0.147326i	$0.0470665\pi$
$677$	16.1874	+	28.0374i	0.622132	+	1.07756i	−0.366956	+	0.930238i	$0.619600\pi$
$678$	−12.6091	+	25.0022i	−0.484249	+	0.960204i
$679$	3.11180	−	3.70850i	0.119420	−	0.142319i
$680$	−5.71389	+	4.79453i	−0.219118	+	0.183862i
$681$	31.2605	−	29.3939i	1.19791	−	1.12638i
$682$	13.2654	−	4.82822i	0.507959	−	0.184882i
$683$	12.5635			0.480728			0.240364	−	0.970683i	$-0.422733\pi$
$683$	12.5635			0.480728			0.240364	+	0.970683i	$0.422733\pi$
$684$	−10.6947	−	7.52478i	−0.408924	−	0.287717i
$685$	0.625411			0.0238957
$686$	13.4542	−	4.89693i	0.513683	−	0.186965i
$687$	−31.2869	+	29.4188i	−1.19367	+	1.12240i
$688$	2.21295	−	1.85688i	0.0843678	−	0.0707930i
$689$	−25.0360	+	29.8367i	−0.953796	+	1.13669i
$690$	−15.1772	+	30.0945i	−0.577787	+	1.14568i
$691$	−7.86815	−	13.6280i	−0.299319	−	0.518435i	0.676662	−	0.736294i	$-0.263426\pi$
$691$	−7.86815	−	13.6280i	−0.299319	−	0.518435i	−0.975980	+	0.217859i	$0.930093\pi$
$692$	4.71511	−	8.16680i	0.179241	−	0.310455i
$693$	−10.5303	−	0.648743i	−0.400012	−	0.0246437i
$694$	1.55978	−	4.28546i	0.0592084	−	0.162674i
$695$	−47.0630	−	27.1719i	−1.78520	−	1.03069i
$696$	0.237965	−	2.00675i	0.00902004	−	0.0760655i
$697$	15.5007	−	2.73319i	0.587130	−	0.103527i
$698$	1.24085	+	1.04120i	0.0469668	+	0.0394098i
$699$	2.10303	+	37.1812i	0.0795441	+	1.40632i
$700$	0.662722	−	3.75848i	0.0250485	−	0.142057i
$701$	−10.8602	−	29.8381i	−0.410183	−	1.12697i	−0.957094	−	0.289777i	$-0.906419\pi$
$701$	−10.8602	−	29.8381i	−0.410183	−	1.12697i	0.546911	−	0.837191i	$-0.315803\pi$
$702$	25.6557	+	9.48427i	0.968312	+	0.357961i
$703$	−16.6033	−	49.9249i	−0.626204	−	1.88295i
$704$			3.12832i			0.117903i
$705$	−5.30779	−	1.59875i	−0.199903	−	0.0602122i
$706$	−6.73822	−	1.18813i	−0.253596	−	0.0447159i
$707$	−4.27347	−	5.09293i	−0.160721	−	0.191539i
$708$	2.70897	+	11.5160i	0.101809	+	0.432798i
$709$	6.11366	+	34.6723i	0.229603	+	1.30214i	0.853687	+	0.520787i	$0.174361\pi$
$709$	6.11366	+	34.6723i	0.229603	+	1.30214i	−0.624084	+	0.781358i	$0.714528\pi$
$710$	10.8517	−	6.26526i	0.407259	−	0.235131i
$711$	3.07010	−	12.7630i	0.115138	−	0.478649i
$712$	12.8844	+	4.68955i	0.482864	+	0.175748i
$713$	−28.4797	−	10.3658i	−1.06657	−	0.388201i
$714$	1.97766	+	4.60594i	0.0740121	+	0.172373i
$715$	−41.3206	+	23.8565i	−1.54530	+	0.892182i
$716$	−1.30046	−	7.37530i	−0.0486007	−	0.275628i
$717$	−20.4669	+	4.81453i	−0.764350	+	0.179802i
$718$	−2.62784	−	3.13174i	−0.0980701	−	0.116875i
$719$	14.7056	+	2.59299i	0.548426	+	0.0967023i	0.440994	−	0.897510i	$-0.354626\pi$
$719$	14.7056	+	2.59299i	0.548426	+	0.0967023i	0.107432	+	0.994212i	$0.465737\pi$
$720$	6.98958	−	5.16722i	0.260486	−	0.192571i
$721$			22.4066i			0.834465i
$722$	10.4063	−	15.8968i	0.387282	−	0.591618i
$723$	−22.5433	+	30.1752i	−0.838394	+	1.12223i
$724$	−5.46326	−	15.0102i	−0.203041	−	0.557850i
$725$	0.687805	−	3.90074i	0.0255444	−	0.144870i
$726$	−2.09874	+	0.118708i	−0.0778915	+	0.00440568i
$727$	−22.7799	−	19.1146i	−0.844860	−	0.708922i	0.113791	−	0.993505i	$-0.463700\pi$
$727$	−22.7799	−	19.1146i	−0.844860	−	0.708922i	−0.958651	+	0.284583i	$0.908145\pi$
$728$	−5.82772	+	1.02758i	−0.215990	+	0.0380848i
$729$	−4.95565	+	26.5413i	−0.183543	+	0.983012i
$730$	−18.8913	−	10.9069i	−0.699199	−	0.403683i
$731$	−2.54354	+	6.98831i	−0.0940761	+	0.258472i
$732$	6.91800	+	10.5568i	0.255697	+	0.390191i
$733$	1.63062	−	2.82432i	0.0602284	−	0.104319i	−0.834339	−	0.551252i	$-0.814150\pi$
$733$	1.63062	−	2.82432i	0.0602284	−	0.104319i	0.894567	+	0.446933i	$0.147484\pi$
$734$	−4.94942	−	8.57264i	−0.182686	−	0.316422i
$735$	25.7034	+	12.9627i	0.948083	+	0.478137i
$736$	4.31710	−	5.14492i	0.159131	−	0.189644i
$737$	16.9590	−	14.2303i	0.624692	−	0.524178i
$738$	−18.2252	+	2.06832i	−0.670879	+	0.0761359i
$739$	−5.54154	+	2.01696i	−0.203849	+	0.0741950i	−0.441927	−	0.897051i	$-0.645705\pi$
$739$	−5.54154	+	2.01696i	−0.203849	+	0.0741950i	0.238078	+	0.971246i	$0.423483\pi$
$740$	34.9726			1.28562
$741$	−12.5232	+	37.7178i	−0.460051	+	1.38560i
$742$	8.31784			0.305357
$743$	27.7676	−	10.1066i	1.01870	−	0.370775i	0.221930	−	0.975063i	$-0.428764\pi$
$743$	27.7676	−	10.1066i	1.01870	−	0.370775i	0.796766	+	0.604288i	$0.206542\pi$
$744$	5.35414	+	5.69414i	0.196292	+	0.208757i
$745$	9.43410	−	7.91615i	0.345639	−	0.290025i
$746$	5.12636	−	6.10936i	0.187689	−	0.223680i
$747$	−19.3210	−	38.7950i	−0.706919	−	1.41943i
$748$	−4.02671	−	6.97446i	−0.147231	−	0.255012i
$749$	2.68881	−	4.65716i	0.0982470	−	0.170169i
$750$	−6.73722	+	4.41498i	−0.246008	+	0.161212i
$751$	−6.20481	+	17.0476i	−0.226417	+	0.622074i	−0.999932	−	0.0117037i	$-0.996275\pi$
$751$	−6.20481	+	17.0476i	−0.226417	+	0.622074i	0.773515	+	0.633778i	$0.218497\pi$
$752$	0.956605	+	0.552296i	0.0348838	+	0.0201402i
$753$	−33.4537	−	3.96703i	−1.21912	−	0.144566i
$754$	−6.04829	+	1.06648i	−0.220266	+	0.0388388i
$755$	19.8458	+	16.6526i	0.722261	+	0.606049i
$756$	−1.97023	−	5.49903i	−0.0716566	−	0.199998i
$757$	−3.70068	+	20.9876i	−0.134504	+	0.762807i	0.840701	+	0.541500i	$0.182143\pi$
$757$	−3.70068	+	20.9876i	−0.134504	+	0.762807i	−0.975204	+	0.221307i	$0.928968\pi$
$758$	−3.67639	−	10.1008i	−0.133532	−	0.366877i
$759$	−29.1537	−	21.7802i	−1.05821	−	0.790571i
$760$	7.84396	+	9.89828i	0.284530	+	0.359048i
$761$			29.1728i			1.05751i	0.848774	+	0.528757i	$0.177342\pi$
$761$			29.1728i			1.05751i	−0.848774	+	0.528757i	$0.822658\pi$
$762$	3.85197	−	12.7884i	0.139542	−	0.463276i
$763$	−9.52252	−	1.67908i	−0.344739	−	0.0607867i
$764$	−4.89644	−	5.83535i	−0.177147	−	0.211116i
$765$	−8.93185	+	20.5170i	−0.322932	+	0.741793i
$766$	0.913805	+	5.18245i	0.0330171	+	0.187249i
$767$	31.1375	−	17.9773i	1.12431	−	0.649122i
$768$	−1.59154	+	0.683364i	−0.0574299	+	0.0246588i
$769$	−25.9596	−	9.44854i	−0.936129	−	0.340723i	−0.171493	−	0.985185i	$-0.554859\pi$
$769$	−25.9596	−	9.44854i	−0.936129	−	0.340723i	−0.764636	+	0.644462i	$0.777081\pi$
$770$	9.57492	+	3.48499i	0.345056	+	0.125590i
$771$	17.2521	−	7.40758i	0.621321	−	0.266777i
$772$	10.3918	−	5.99972i	0.374010	−	0.215935i
$773$	−7.60654	−	43.1388i	−0.273588	−	1.55160i	−0.743411	−	0.668835i	$-0.766793\pi$
$773$	−7.60654	−	43.1388i	−0.273588	−	1.55160i	0.469823	−	0.882761i	$-0.344318\pi$
$774$	3.45924	−	7.94607i	0.124340	−	0.285615i
$775$	9.84744	+	11.7357i	0.353731	+	0.421560i
$776$	−4.24097	−	0.747798i	−0.152242	−	0.0268444i
$777$	6.77825	−	22.5036i	0.243168	−	0.807312i
$778$			15.8820i			0.569396i
$779$	−3.89104	−	26.3650i	−0.139411	−	0.944624i
$780$	−21.1634	−	15.8107i	−0.757770	−	0.566115i
$781$	4.62724	+	12.7132i	0.165576	+	0.454916i
$782$	−3.00237	+	17.0273i	−0.107365	+	0.608895i
$783$	−2.04480	−	5.70716i	−0.0730752	−	0.203957i
$784$	−4.39422	−	3.68719i	−0.156937	−	0.131685i
$785$	−5.78507	+	1.02006i	−0.206478	+	0.0364077i
$786$	3.80825	+	0.451592i	0.135836	+	0.0161078i
$787$	31.9379	+	18.4393i	1.13846	+	0.657291i	0.946049	−	0.324023i	$-0.105036\pi$
$787$	31.9379	+	18.4393i	1.13846	+	0.657291i	0.192412	+	0.981314i	$0.438369\pi$
$788$	−6.02735	+	16.5600i	−0.214715	+	0.589925i
$789$	44.8175	−	29.3694i	1.59554	−	1.04558i
$790$	−6.33905	+	10.9796i	−0.225533	+	0.390635i
$791$	−9.08710	−	15.7393i	−0.323100	−	0.559626i
$792$	4.18382	+	8.40077i	0.148666	+	0.298508i
$793$	24.6569	−	29.3850i	0.875593	−	1.04349i
$794$	−27.4398	+	23.0247i	−0.973802	+	0.817117i
$795$	25.4363	+	27.0516i	0.902132	+	0.959421i
$796$	−2.12679	+	0.774087i	−0.0753819	+	0.0274368i
$797$	−47.4368			−1.68030			−0.840148	−	0.542357i	$-0.817532\pi$
$797$	−47.4368			−1.68030			−0.840148	+	0.542357i	$0.817532\pi$
$798$	7.88948	−	3.12886i	0.279284	−	0.110761i
$799$	−2.84362			−0.100600
$800$	−3.19019	+	1.16114i	−0.112790	+	0.0410523i
$801$	40.8716	−	4.63838i	1.44413	−	0.163889i
$802$	−4.54530	+	3.81396i	−0.160500	+	0.134676i
$803$	15.1391	−	18.0421i	0.534249	−	0.636693i
$804$	10.9443	+	5.51943i	0.385976	+	0.194655i
$805$	−10.9379	−	18.9450i	−0.385510	−	0.667723i
$806$	11.8771	−	20.5718i	0.418355	−	0.724611i
$807$	4.81219	+	7.34335i	0.169397	+	0.258498i
$808$	−2.02272	+	5.55737i	−0.0711589	+	0.195508i
$809$	46.6699	+	26.9449i	1.64083	+	0.947331i	0.980540	+	0.196317i	$0.0628981\pi$
$809$	46.6699	+	26.9449i	1.64083	+	0.947331i	0.660286	+	0.751015i	$0.270435\pi$
$810$	11.8591	−	23.2239i	0.416687	−	0.816006i
$811$	5.26849	−	0.928977i	0.185002	−	0.0326208i	−0.0803796	−	0.996764i	$-0.525613\pi$
$811$	5.26849	−	0.928977i	0.185002	−	0.0326208i	0.265381	+	0.964144i	$0.414502\pi$
$812$	1.00473	+	0.843066i	0.0352590	+	0.0295858i
$813$	9.06312	−	0.512626i	0.317857	−	0.0179786i
$814$	−6.55692	+	37.1861i	−0.229820	+	1.30337i
$815$	−9.24719	−	25.4064i	−0.323915	−	0.889949i
$816$	2.66868	−	3.57214i	0.0934224	−	0.125050i
$817$	11.7073	+	4.63637i	0.409588	+	0.162206i
$818$		−	26.5106i		−	0.926921i
$819$	−14.2754	+	10.5535i	−0.498825	+	0.368769i
$820$	17.4458	+	3.07616i	0.609233	+	0.107424i
$821$	14.7984	+	17.6360i	0.516468	+	0.615502i	0.959742	−	0.280884i	$-0.0906276\pi$
$821$	14.7984	+	17.6360i	0.516468	+	0.615502i	−0.443274	+	0.896386i	$0.646183\pi$
$822$	−0.363933	+	0.0856099i	−0.0126936	+	0.00298599i
$823$	1.89577	+	10.7514i	0.0660824	+	0.374772i	0.999857	+	0.0169103i	$0.00538296\pi$
$823$	1.89577	+	10.7514i	0.0660824	+	0.374772i	−0.933775	+	0.357862i	$0.883506\pi$
$824$	17.2614	−	9.96588i	0.601330	−	0.347178i
$825$	7.25761	+	16.9029i	0.252678	+	0.588482i
$826$	−7.21527	−	2.62614i	−0.251051	−	0.0913752i
$827$	−0.866657	−	0.315437i	−0.0301366	−	0.0109688i	0.326908	−	0.945056i	$-0.393993\pi$
$827$	−0.866657	−	0.315437i	−0.0301366	−	0.0109688i	−0.357044	+	0.934087i	$0.616216\pi$
$828$	4.71229	−	19.5899i	0.163763	−	0.680795i
$829$	36.7431	−	21.2136i	1.27614	−	0.736780i	0.300004	−	0.953938i	$-0.403012\pi$
$829$	36.7431	−	21.2136i	1.27614	−	0.736780i	0.976137	+	0.217158i	$0.0696786\pi$
$830$	7.26852	+	41.2218i	0.252294	+	1.43083i
$831$	−1.71081	−	7.27276i	−0.0593472	−	0.252289i
$832$	3.38365	+	4.03247i	0.117307	+	0.139801i
$833$	14.5428	+	2.56430i	0.503880	+	0.0888476i
$834$	31.1059	+	9.36934i	1.07711	+	0.324434i
$835$		−	36.7076i		−	1.27032i
$836$	−11.9954	+	6.48464i	−0.414871	+	0.224276i
$837$	21.9934	+	8.13039i	0.760201	+	0.281027i
$838$	−2.80984	−	7.71998i	−0.0970644	−	0.266682i
$839$	2.73490	−	15.5104i	0.0944194	−	0.535479i	−0.900504	−	0.434847i	$-0.856802\pi$
$839$	2.73490	−	15.5104i	0.0944194	−	0.535479i	0.994924	−	0.100632i	$-0.0320864\pi$
$840$	0.318588	+	5.63256i	0.0109923	+	0.194342i
$841$	−21.1725	−	17.7659i	−0.730087	−	0.612616i
$842$	−16.5911	+	2.92547i	−0.571769	+	0.100818i
$843$	2.24666	−	18.9459i	0.0773790	−	0.652533i
$844$	−3.33516	−	1.92556i	−0.114801	−	0.0662804i
$845$	−14.5770	+	40.0501i	−0.501465	+	1.37776i
$846$	3.30751	+	0.203767i	0.113714	+	0.00700565i
$847$	0.682168	−	1.18155i	0.0234396	−	0.0405985i
$848$	−3.69956	−	6.40783i	−0.127043	−	0.220046i
$849$	−3.08143	+	6.11007i	−0.105754	+	0.209697i
$850$	5.61783	−	6.69506i	0.192690	−	0.229639i
$851$	62.1009	−	52.1088i	2.12879	−	1.78627i
$852$	−5.45713	+	5.13127i	−0.186958	+	0.175794i
$853$	−30.2008	+	10.9922i	−1.03405	+	0.376365i	−0.802623	−	0.596486i	$-0.796563\pi$
$853$	−30.2008	+	10.9922i	−1.03405	+	0.376365i	−0.231431	+	0.972851i	$0.574341\pi$
$854$	−8.19189			−0.280321
$855$	34.3021	+	16.0903i	1.17311	+	0.550275i
$856$	−4.78366			−0.163502
$857$	−23.1422	+	8.42308i	−0.790524	+	0.287727i	−0.705554	−	0.708656i	$-0.749302\pi$
$857$	−23.1422	+	8.42308i	−0.790524	+	0.287727i	−0.0849699	+	0.996384i	$0.527079\pi$
$858$	20.7793	−	19.5386i	0.709395	−	0.667036i
$859$	−11.9557	+	10.0320i	−0.407923	+	0.342288i	−0.823547	−	0.567248i	$-0.808008\pi$
$859$	−11.9557	+	10.0320i	−0.407923	+	0.342288i	0.415623	+	0.909537i	$0.363563\pi$
$860$	−5.38013	+	6.41179i	−0.183461	+	0.218640i
$861$	5.36067	−	10.6295i	0.182691	−	0.362253i
$862$	14.4897	+	25.0970i	0.493522	+	0.854806i
$863$	−7.05542	+	12.2203i	−0.240169	+	0.415985i	−0.960762	−	0.277373i	$-0.910536\pi$
$863$	−7.05542	+	12.2203i	−0.240169	+	0.415985i	0.720593	+	0.693358i	$0.243870\pi$
$864$	−3.35999	+	3.96364i	−0.114309	+	0.134846i
$865$	−9.34505	+	25.6753i	−0.317741	+	0.872987i
$866$	−23.8263	−	13.7561i	−0.809649	−	0.467451i
$867$	2.11563	−	17.8410i	0.0718505	−	0.605911i
$868$	−4.99581	+	0.880897i	−0.169569	+	0.0298996i
$869$	−10.4860	−	8.79880i	−0.355713	−	0.298479i
$870$	0.330646	+	5.84574i	0.0112099	+	0.198189i
$871$	6.46878	−	36.6863i	0.219186	−	1.24307i
$872$	2.94186	+	8.08270i	0.0996240	+	0.273715i
$873$	−12.3888	+	3.66376i	−0.419297	+	0.123999i
$874$	28.6769	+	5.88896i	0.970011	+	0.199197i
$875$		−	5.22796i		−	0.176737i
$876$	12.4861	+	3.76090i	0.421865	+	0.127069i
$877$	17.9817	+	3.17067i	0.607200	+	0.107066i	0.468791	−	0.883309i	$-0.344690\pi$
$877$	17.9817	+	3.17067i	0.607200	+	0.107066i	0.138410	+	0.990375i	$0.455801\pi$
$878$	−9.76729	−	11.6402i	−0.329630	−	0.392838i
$879$	−7.98928	−	33.9630i	−0.269472	−	1.14554i
$880$	−1.57394	−	8.92628i	−0.0530577	−	0.300905i
$881$	5.32331	−	3.07342i	0.179347	−	0.103546i	−0.407639	−	0.913143i	$-0.633648\pi$
$881$	5.32331	−	3.07342i	0.179347	−	0.103546i	0.586986	+	0.809597i	$0.300314\pi$
$882$	−16.7315	−	4.02472i	−0.563379	−	0.135519i
$883$	51.4745	+	18.7352i	1.73225	+	0.630489i	0.998787	−	0.0492352i	$-0.0156784\pi$
$883$	51.4745	+	18.7352i	1.73225	+	0.630489i	0.733468	+	0.679724i	$0.237901\pi$
$884$	−12.7342	−	4.63488i	−0.428299	−	0.155888i
$885$	−13.5237	−	31.4966i	−0.454596	−	1.05875i
$886$	−4.17811	+	2.41223i	−0.140366	+	0.0810405i
$887$	−7.62578	−	43.2479i	−0.256049	−	1.45212i	−0.793367	−	0.608744i	$-0.791674\pi$
$887$	−7.62578	−	43.2479i	−0.256049	−	1.45212i	0.537318	−	0.843379i	$-0.319437\pi$
$888$	−20.3509	+	4.78725i	−0.682933	+	0.160650i
$889$	5.57202	+	6.64047i	0.186879	+	0.222714i
$890$	−39.1236	−	6.89855i	−1.31143	−	0.231240i
$891$	22.4704	+	16.9639i	0.752788	+	0.568313i
$892$			5.56672i			0.186387i
$893$	−0.134831	+	4.81292i	−0.00451194	+	0.161058i
$894$	−4.40620	+	5.89789i	−0.147365	+	0.197255i
$895$	7.42145	+	20.3903i	0.248072	+	0.681571i
$896$	0.195209	−	1.10709i	0.00652148	−	0.0369852i
$897$	−61.1377	+	3.45806i	−2.04133	+	0.115461i
$898$	−2.73732	−	2.29688i	−0.0913455	−	0.0766480i
$899$	−5.18490	+	0.914238i	−0.172926	+	0.0304915i
$900$	−7.01403	+	7.38468i	−0.233801	+	0.246156i
$901$	16.4961	+	9.52401i	0.549564	+	0.317291i
$902$	−6.54172	+	17.9732i	−0.217816	+	0.598443i
$903$	3.08300	+	4.70463i	0.102596	+	0.156560i
$904$	−8.08342	+	14.0009i	−0.268850	+	0.465663i
$905$	23.1408	+	40.0811i	0.769228	+	1.33234i
$906$	−13.8280	−	6.97372i	−0.459404	−	0.231686i
$907$	−21.7940	+	25.9730i	−0.723656	+	0.862420i	−0.994981	−	0.100068i	$-0.968094\pi$
$907$	−21.7940	+	25.9730i	−0.723656	+	0.862420i	0.271324	+	0.962488i	$0.412538\pi$
$908$	18.9778	−	15.9243i	0.629802	−	0.528466i
$909$	2.00065	+	17.6289i	0.0663573	+	0.584715i
$910$	16.1117	−	5.86419i	0.534098	−	0.194396i
$911$	−15.3654			−0.509077			−0.254539	−	0.967063i	$-0.581924\pi$
$911$	−15.3654			−0.509077			−0.254539	+	0.967063i	$0.581924\pi$
$912$	−5.91942	−	4.68619i	−0.196012	−	0.155175i
$913$	−45.1937			−1.49569
$914$	24.4987	−	8.91679i	0.810344	−	0.294941i
$915$	−25.0511	−	26.6420i	−0.828165	−	0.880756i
$916$	−18.9939	+	15.9377i	−0.627575	+	0.526598i
$917$	−1.59991	+	1.90670i	−0.0528336	+	0.0629646i
$918$	2.38906	−	13.1617i	0.0788507	−	0.434401i
$919$	−6.10344	−	10.5715i	−0.201334	−	0.348720i	0.747625	−	0.664121i	$-0.231194\pi$
$919$	−6.10344	−	10.5715i	−0.201334	−	0.348720i	−0.948958	+	0.315401i	$0.897861\pi$
$920$	−9.72979	+	16.8525i	−0.320782	+	0.555610i
$921$	−9.49823	+	6.22431i	−0.312977	+	0.205098i
$922$	−4.50390	+	12.3744i	−0.148328	+	0.407528i
$923$	19.7155	+	11.3828i	0.648944	+	0.374668i
$924$	−6.04880	−	0.717281i	−0.198991	−	0.0235968i
$925$	−40.3554	+	7.11574i	−1.32688	+	0.233964i
$926$	−16.3732	−	13.7387i	−0.538056	−	0.451482i
$927$	33.0253	−	49.8478i	1.08469	−	1.63722i
$928$	0.202598	−	1.14899i	0.00665059	−	0.0377174i
$929$	−6.30750	−	17.3297i	−0.206942	−	0.568569i	0.792188	−	0.610278i	$-0.208942\pi$
$929$	−6.30750	−	17.3297i	−0.206942	−	0.568569i	−0.999130	+	0.0417085i	$0.986720\pi$
$930$	−18.1423	−	13.5538i	−0.594909	−	0.444445i
$931$	5.02970	−	24.4926i	0.164842	−	0.802714i
$932$			21.5009i			0.704284i
$933$	−1.07676	+	3.57480i	−0.0352514	+	0.117034i
$934$	9.11934	+	1.60799i	0.298394	+	0.0526149i
$935$	14.9988	+	17.8749i	0.490513	+	0.584570i
$936$	14.4795	+	6.30348i	0.473276	+	0.206036i
$937$	−4.35606	−	24.7045i	−0.142306	−	0.807060i	−0.969491	−	0.245129i	$-0.921170\pi$
$937$	−4.35606	−	24.7045i	−0.142306	−	0.807060i	0.827184	−	0.561931i	$-0.189941\pi$
$938$	−6.88963	+	3.97773i	−0.224954	+	0.129877i
$939$	26.9476	−	11.5705i	0.879400	−	0.377589i
$940$	−3.00744	−	1.09462i	−0.0980918	−	0.0357025i
$941$	43.7853	+	15.9365i	1.42736	+	0.519517i	0.936174	−	0.351538i	$-0.114341\pi$
$941$	43.7853	+	15.9365i	1.42736	+	0.519517i	0.491187	+	0.871054i	$0.336563\pi$
$942$	3.22677	−	1.38548i	0.105134	−	0.0451414i
$943$	35.5619	−	20.5317i	1.15806	−	0.668604i
$944$	1.18606	+	6.72648i	0.0386030	+	0.218928i
$945$	8.38854	+	14.6996i	0.272879	+	0.478177i
$946$	−5.80891	−	6.92279i	−0.188864	−	0.225079i
$947$	−54.8110	−	9.66466i	−1.78112	−	0.314059i	−0.816429	−	0.577446i	$-0.804049\pi$
$947$	−54.8110	−	9.66466i	−1.78112	−	0.314059i	−0.964690	+	0.263387i	$0.915160\pi$
$948$	2.18582	−	7.25685i	0.0709921	−	0.235692i
$949$		−	39.6315i		−	1.28649i
$950$	−11.0652	−	9.82580i	−0.359004	−	0.318791i
$951$	−7.68312	−	5.73991i	−0.249142	−	0.186129i
$952$	0.989809	+	2.71948i	0.0320799	+	0.0881388i
$953$	−3.28854	+	18.6502i	−0.106526	+	0.604140i	0.884074	+	0.467348i	$0.154790\pi$
$953$	−3.28854	+	18.6502i	−0.106526	+	0.604140i	−0.990600	+	0.136792i	$0.956321\pi$
$954$	−18.5046	−	12.2598i	−0.599110	−	0.396924i
$955$	16.9074	+	14.1870i	0.547109	+	0.459079i
$956$	−11.9547	+	2.10793i	−0.386642	+	0.0681755i
$957$	−6.27774	−	0.744430i	−0.202930	−	0.0240640i
$958$	4.87374	+	2.81386i	0.157464	+	0.0909116i
$959$	0.0829924	−	0.228020i	0.00267997	−	0.00736314i
$960$	4.19747	−	2.75065i	0.135473	−	0.0887768i
$961$	−5.31832	+	9.21160i	−0.171559	+	0.297148i
$962$	31.7692	+	55.0259i	1.02428	+	1.77410i
$963$	−12.8460	+	6.39768i	−0.413957	+	0.206162i
$964$	−13.9784	+	16.6589i	−0.450215	+	0.536546i
$965$	−26.6332	+	22.3479i	−0.857353	+	0.719405i
$966$	8.95818	+	9.52706i	0.288225	+	0.306528i
$967$	−23.9285	+	8.70925i	−0.769488	+	0.280071i	−0.696782	−	0.717283i	$-0.745386\pi$
$967$	−23.9285	+	8.70925i	−0.769488	+	0.280071i	−0.0727056	+	0.997353i	$0.523163\pi$
$968$	−1.21364			−0.0390080
$969$	19.2291	+	2.82832i	0.617728	+	0.0908588i
$970$	12.4774			0.400624
$971$	−14.6975	+	5.34944i	−0.471664	+	0.171672i	−0.566906	−	0.823782i	$-0.691860\pi$
$971$	−14.6975	+	5.34944i	−0.471664	+	0.171672i	0.0952419	+	0.995454i	$0.469638\pi$
$972$	−3.72193	+	15.1376i	−0.119381	+	0.485539i
$973$	−16.1519	+	13.5531i	−0.517807	+	0.434492i
$974$	13.1699	−	15.6953i	0.421992	−	0.502910i
$975$	27.6377	+	13.9382i	0.885115	+	0.446380i
$976$	3.64354	+	6.31080i	0.116627	+	0.202004i
$977$	−10.2781	+	17.8022i	−0.328827	+	0.569544i	−0.982279	−	0.187423i	$-0.939986\pi$
$977$	−10.2781	+	17.8022i	−0.328827	+	0.569544i	0.653453	+	0.756967i	$0.273320\pi$
$978$	8.85882	+	13.5185i	0.283274	+	0.432273i
$979$	14.6704	−	40.3065i	0.468867	−	1.28820i
$980$	14.3935	+	8.31011i	0.459785	+	0.265457i
$981$	18.7099	+	17.7708i	0.597361	+	0.567378i
$982$	32.2309	−	5.68317i	1.02853	−	0.181357i
$983$	14.5443	+	12.2041i	0.463890	+	0.389250i	0.844560	−	0.535461i	$-0.179862\pi$
$983$	14.5443	+	12.2041i	0.463890	+	0.389250i	−0.380670	+	0.924711i	$0.624307\pi$
$984$	−10.5730	+	0.598026i	−0.337054	+	0.0190644i
$985$	8.86652	−	50.2845i	0.282511	−	1.60220i
$986$	1.02727	+	2.82241i	0.0327150	+	0.0898837i
$987$	−1.28724	+	1.72302i	−0.0409732	+	0.0548444i
$988$	−8.44848	+	21.3333i	−0.268782	+	0.678704i
$989$			19.4018i			0.616941i
$990$	−16.1647	−	21.8656i	−0.513748	−	0.694934i
$991$	−41.2131	−	7.26698i	−1.30918	−	0.230843i	−0.524852	−	0.851193i	$-0.675879\pi$
$991$	−41.2131	−	7.26698i	−1.30918	−	0.230843i	−0.784325	+	0.620350i	$0.786991\pi$
$992$	2.90063	+	3.45684i	0.0920951	+	0.109755i
$993$	−12.9958	+	3.05706i	−0.412409	+	0.0970129i
$994$	−0.844229	−	4.78786i	−0.0267773	−	0.151862i
$995$	5.67907	−	3.27881i	0.180039	−	0.103945i
$996$	−9.87232	−	22.9925i	−0.312817	−	0.728545i
$997$	14.4637	+	5.26435i	0.458069	+	0.166724i	0.560740	−	0.827992i	$-0.310517\pi$
$997$	14.4637	+	5.26435i	0.458069	+	0.166724i	−0.102671	+	0.994715i	$0.532739\pi$
$998$	19.2782	+	7.01669i	0.610241	+	0.222110i
$999$	−48.2478	+	40.0731i	−1.52649	+	1.26786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.l.a.71.3	yes	18
3.2	odd	2		114.2.l.b.71.2	yes	18
4.3	odd	2		912.2.cc.d.641.1		18
12.11	even	2		912.2.cc.c.641.2		18
19.15	odd	18		114.2.l.b.53.2	yes	18
57.53	even	18	inner	114.2.l.a.53.3	✓	18
76.15	even	18		912.2.cc.c.737.2		18
228.167	odd	18		912.2.cc.d.737.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.53.3	✓	18	57.53	even	18	inner
114.2.l.a.71.3	yes	18	1.1	even	1	trivial
114.2.l.b.53.2	yes	18	19.15	odd	18
114.2.l.b.71.2	yes	18	3.2	odd	2
912.2.cc.c.641.2		18	12.11	even	2
912.2.cc.c.737.2		18	76.15	even	18
912.2.cc.d.641.1		18	4.3	odd	2
912.2.cc.d.737.1		18	228.167	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.26184 - 1.18649i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.86241 + 2.21954i) q^{5} +(0.779936 - 1.54651i) q^{6} +(0.562083 + 0.973556i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.184473 - 2.99432i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.26184 - 1.18649i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.86241 + 2.21954i) q^{5} +(0.779936 - 1.54651i) q^{6} +(0.562083 + 0.973556i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.184473 - 2.99432i) q^{9} +(-0.990970 + 2.72267i) q^{10} +(-2.70920 - 1.56416i) q^{11} +(0.203962 - 1.72000i) q^{12} +(-5.18404 + 0.914087i) q^{13} +(0.861160 + 0.722599i) q^{14} +(0.283400 + 5.01044i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.880484 + 2.41911i) q^{17} +(-0.850771 - 2.87684i) q^{18} +(4.13617 - 1.37554i) q^{19} +2.89740i q^{20} +(1.86437 + 0.561563i) q^{21} +(-3.08079 - 0.543226i) q^{22} +(4.31710 + 5.14492i) q^{23} +(-0.396613 - 1.68603i) q^{24} +(-0.589524 - 3.34336i) q^{25} +(-4.55877 + 2.63201i) q^{26} +(-3.31997 - 3.99723i) q^{27} +(1.05637 + 0.384487i) q^{28} +(1.09635 + 0.399039i) q^{29} +(1.97998 + 4.61134i) q^{30} +(-3.90801 + 2.25629i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-5.27443 + 1.24073i) q^{33} +(1.65477 + 1.97208i) q^{34} +(-3.20767 - 0.565599i) q^{35} +(-1.78340 - 2.41236i) q^{36} -12.0703i q^{37} +(3.41626 - 2.70724i) q^{38} +(-5.45687 + 7.30426i) q^{39} +(0.990970 + 2.72267i) q^{40} +(1.06170 - 6.02118i) q^{41} +(1.94400 - 0.109956i) q^{42} +(2.21295 + 1.85688i) q^{43} +(-3.08079 + 0.543226i) q^{44} +(6.30245 + 5.98611i) q^{45} +(5.81642 + 3.35811i) q^{46} +(-0.377793 + 1.03798i) q^{47} +(-0.949351 - 1.44870i) q^{48} +(2.86813 - 4.96774i) q^{49} +(-1.69747 - 2.94010i) q^{50} +(3.98128 + 2.00784i) q^{51} +(-3.38365 + 4.03247i) q^{52} +(5.66806 - 4.75606i) q^{53} +(-4.48688 - 2.62067i) q^{54} +(8.51736 - 3.10007i) q^{55} +1.12417 q^{56} +(3.58710 - 6.64324i) q^{57} +1.16671 q^{58} +(-6.41833 + 2.33608i) q^{59} +(3.43774 + 3.65605i) q^{60} +(-5.58223 + 4.68405i) q^{61} +(-2.90063 + 3.45684i) q^{62} +(3.01883 - 1.50346i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(7.62598 - 13.2086i) q^{65} +(-4.53199 + 2.96987i) q^{66} +(-2.42040 + 6.64999i) q^{67} +(2.22946 + 1.28718i) q^{68} +(11.5519 + 1.36985i) q^{69} +(-3.20767 + 0.565599i) q^{70} +(-3.31294 - 2.77989i) q^{71} +(-2.50092 - 1.65692i) q^{72} +(-1.30735 + 7.41438i) q^{73} +(-4.12829 - 11.3424i) q^{74} +(-4.71075 - 3.51931i) q^{75} +(2.28431 - 3.71240i) q^{76} -3.51674i q^{77} +(-2.62958 + 8.73012i) q^{78} +(4.30920 + 0.759829i) q^{79} +(1.86241 + 2.21954i) q^{80} +(-8.93194 - 1.10474i) q^{81} +(-1.06170 - 6.02118i) q^{82} +(12.5112 - 7.22333i) q^{83} +(1.78916 - 0.768214i) q^{84} +(-7.00913 - 2.55111i) q^{85} +(2.71458 + 0.988026i) q^{86} +(1.85688 - 0.797290i) q^{87} +(-2.70920 + 1.56416i) q^{88} +(2.38095 + 13.5030i) q^{89} +(7.96974 + 3.46954i) q^{90} +(-3.80378 - 4.53316i) q^{91} +(6.61418 + 1.16626i) q^{92} +(-2.25420 + 7.48389i) q^{93} +1.10459i q^{94} +(-4.65018 + 11.7422i) q^{95} +(-1.38758 - 1.03664i) q^{96} +(-1.47287 - 4.04669i) q^{97} +(0.996090 - 5.64911i) q^{98} +(-5.18337 + 7.82368i) 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

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