LMFDB - Embedded newform 74.2.f.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, 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:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.1
Root			$-2.20976 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	74.49
Dual form			74.2.f.b.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-2.41262 - 2.02443i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.43969 + 0.524005i) q^{5} -3.14945 q^{6} +(4.53424 - 1.65033i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.20148 + 6.81391i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-2.41262 - 2.02443i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.43969 + 0.524005i) q^{5} -3.14945 q^{6} +(4.53424 - 1.65033i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.20148 + 6.81391i) q^{9} +(-0.766044 + 1.32683i) q^{10} +(0.546896 + 0.947252i) q^{11} +(-2.41262 + 2.02443i) q^{12} +(0.307284 - 1.74269i) q^{13} +(2.41262 - 4.17878i) q^{14} +(4.53424 + 1.65033i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.511542 + 2.90110i) q^{17} +(5.30028 + 4.44747i) q^{18} +(-0.632167 - 0.530451i) q^{19} +(0.266044 + 1.50881i) q^{20} +(-14.2804 - 5.19762i) q^{21} +(1.02783 + 0.374099i) q^{22} +(0.121620 - 0.210653i) q^{23} +(-0.546896 + 3.10160i) q^{24} +(-2.03209 + 1.70513i) q^{25} +(-0.884789 - 1.53250i) q^{26} +(6.17139 - 10.6892i) q^{27} +(-0.837893 - 4.75193i) q^{28} +(2.78587 + 4.82526i) q^{29} +(4.53424 - 1.65033i) q^{30} -5.73495 q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.598191 - 3.39251i) q^{33} +(2.25665 + 1.89356i) q^{34} +(-5.66313 + 4.75193i) q^{35} +6.91903 q^{36} +(5.84038 + 1.69999i) q^{37} -0.825235 q^{38} +(-4.26932 + 3.58238i) q^{39} +(1.17365 + 0.984808i) q^{40} +(0.505653 - 2.86770i) q^{41} +(-14.2804 + 5.19762i) q^{42} +4.37987 q^{43} +(1.02783 - 0.374099i) q^{44} +(-5.30028 - 9.18036i) q^{45} +(-0.0422383 - 0.239545i) q^{46} +(-1.13249 + 1.96153i) q^{47} +(1.57472 + 2.72750i) q^{48} +(12.4734 - 10.4664i) q^{49} +(-0.460637 + 2.61240i) q^{50} +(4.63890 - 8.03481i) q^{51} +(-1.66286 - 0.605232i) q^{52} +(-5.77859 - 2.10324i) q^{53} +(-2.14330 - 12.1553i) q^{54} +(-1.28373 - 1.07717i) q^{55} +(-3.69634 - 3.10160i) q^{56} +(0.451318 + 2.55955i) q^{57} +(5.23571 + 1.90564i) q^{58} +(-8.29301 - 3.01841i) q^{59} +(2.41262 - 4.17878i) q^{60} +(-2.04075 + 11.5737i) q^{61} +(-4.39322 + 3.68635i) q^{62} +(16.6930 + 28.9131i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.470787 + 2.66996i) q^{65} +(-1.72242 - 2.98332i) q^{66} +(-8.44220 + 3.07271i) q^{67} +2.94585 q^{68} +(-0.719875 + 0.262013i) q^{69} +(-1.28373 + 7.28038i) q^{70} +(-0.933535 - 0.783329i) q^{71} +(5.30028 - 4.44747i) q^{72} +8.79418 q^{73} +(5.56672 - 2.45185i) q^{74} +8.35455 q^{75} +(-0.632167 + 0.530451i) q^{76} +(4.04303 + 3.39251i) q^{77} +(-0.967776 + 5.48853i) q^{78} +(-2.02379 + 0.736599i) q^{79} +1.53209 q^{80} +(-17.0233 + 6.19599i) q^{81} +(-1.45597 - 2.52181i) q^{82} +(0.884528 + 5.01641i) q^{83} +(-7.59842 + 13.1608i) q^{84} +(-2.25665 - 3.90864i) q^{85} +(3.35518 - 2.81533i) q^{86} +(3.04716 - 17.2813i) q^{87} +(0.546896 - 0.947252i) q^{88} +(-8.43486 - 3.07004i) q^{89} +(-9.96127 - 3.62561i) q^{90} +(-1.48272 - 8.40891i) q^{91} +(-0.186333 - 0.156352i) q^{92} +(13.8362 + 11.6100i) q^{93} +(0.393310 + 2.23057i) q^{94} +(1.18809 + 0.432428i) q^{95} +(2.95951 + 1.07717i) q^{96} +(-2.17954 + 3.77507i) q^{97} +(2.82750 - 16.0355i) q^{98} +(-5.79741 + 4.86460i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 6 q^{30} + 42 q^{31} + 57 q^{33} - 3 q^{34} - 9 q^{35} + 24 q^{36} - 3 q^{37} + 42 q^{38} - 24 q^{39} + 12 q^{40} - 21 q^{41} - 33 q^{42} + 36 q^{43} - 3 q^{44} - 6 q^{45} + 3 q^{46} + 9 q^{47} - 12 q^{49} + 12 q^{50} + 3 q^{52} - 6 q^{53} - 27 q^{54} - 3 q^{56} - 36 q^{57} - 3 q^{58} - 6 q^{59} + 3 q^{60} - 18 q^{61} - 33 q^{62} + 36 q^{63} - 6 q^{64} + 3 q^{65} + 3 q^{66} - 27 q^{67} + 6 q^{68} - 12 q^{69} - 18 q^{71} + 6 q^{72} + 54 q^{73} + 3 q^{74} - 6 q^{75} - 3 q^{76} + 51 q^{77} - 33 q^{78} - 12 q^{79} - 36 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 3 q^{85} + 39 q^{87} + 3 q^{88} - 15 q^{89} - 15 q^{90} - 51 q^{91} - 6 q^{92} + 45 q^{93} - 12 q^{94} - 15 q^{95} + 6 q^{96} - 42 q^{97} + 51 q^{98} - 33 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−2.41262	−	2.02443i	−1.39293	−	1.16880i	−0.964139	−	0.265397i	$-0.914497\pi$
$3$	−2.41262	−	2.02443i	−1.39293	−	1.16880i	−0.428786	−	0.903406i	$-0.641059\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−1.43969	+	0.524005i	−0.643850	+	0.234342i	−0.643248	−	0.765658i	$-0.722414\pi$
$5$	−1.43969	+	0.524005i	−0.643850	+	0.234342i	−0.000601695		1.00000i	$0.500192\pi$
$6$	−3.14945			−1.28576
$7$	4.53424	−	1.65033i	1.71378	−	0.623765i	0.716509	−	0.697578i	$-0.245739\pi$
$7$	4.53424	−	1.65033i	1.71378	−	0.623765i	0.997272	+	0.0738128i	$0.0235167\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	1.20148	+	6.81391i	0.400492	+	2.27130i
$10$	−0.766044	+	1.32683i	−0.242245	+	0.419580i
$11$	0.546896	+	0.947252i	0.164895	+	0.285607i	0.936618	−	0.350352i	$-0.113938\pi$
$11$	0.546896	+	0.947252i	0.164895	+	0.285607i	−0.771723	+	0.635959i	$0.780605\pi$
$12$	−2.41262	+	2.02443i	−0.696463	+	0.584402i
$13$	0.307284	−	1.74269i	0.0852253	−	0.483337i	−0.912082	−	0.410007i	$-0.865526\pi$
$13$	0.307284	−	1.74269i	0.0852253	−	0.483337i	0.997308	−	0.0733298i	$-0.0233626\pi$
$14$	2.41262	−	4.17878i	0.644799	−	1.11682i
$15$	4.53424	+	1.65033i	1.17074	+	0.426113i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.511542	+	2.90110i	0.124067	+	0.703619i	0.981858	+	0.189620i	$0.0607255\pi$
$17$	0.511542	+	2.90110i	0.124067	+	0.703619i	−0.857791	+	0.513999i	$0.828163\pi$
$18$	5.30028	+	4.44747i	1.24929	+	1.04828i
$19$	−0.632167	−	0.530451i	−0.145029	−	0.121694i	0.567387	−	0.823451i	$-0.307954\pi$
$19$	−0.632167	−	0.530451i	−0.145029	−	0.121694i	−0.712416	+	0.701758i	$0.752399\pi$
$20$	0.266044	+	1.50881i	0.0594893	+	0.337381i
$21$	−14.2804	−	5.19762i	−3.11623	−	1.13421i
$22$	1.02783	+	0.374099i	0.219134	+	0.0797582i
$23$	0.121620	−	0.210653i	0.0253596	−	0.0439241i	−0.853067	−	0.521801i	$-0.825260\pi$
$23$	0.121620	−	0.210653i	0.0253596	−	0.0439241i	0.878427	+	0.477877i	$0.158594\pi$
$24$	−0.546896	+	3.10160i	−0.111635	+	0.633112i
$25$	−2.03209	+	1.70513i	−0.406418	+	0.341025i
$26$	−0.884789	−	1.53250i	−0.173521	−	0.300548i
$27$	6.17139	−	10.6892i	1.18768	−	2.05713i
$28$	−0.837893	−	4.75193i	−0.158347	−	0.898030i
$29$	2.78587	+	4.82526i	0.517322	+	0.896028i	0.999798	+	0.0201189i	$0.00640447\pi$
$29$	2.78587	+	4.82526i	0.517322	+	0.896028i	−0.482475	+	0.875910i	$0.660262\pi$
$30$	4.53424	−	1.65033i	0.827835	−	0.301307i
$31$	−5.73495			−1.03003			−0.515013	−	0.857182i	$-0.672213\pi$
$31$	−5.73495			−1.03003			−0.515013	+	0.857182i	$0.672213\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.598191	−	3.39251i	0.104132	−	0.590560i
$34$	2.25665	+	1.89356i	0.387013	+	0.324742i
$35$	−5.66313	+	4.75193i	−0.957243	+	0.803223i
$36$	6.91903			1.15317
$37$	5.84038	+	1.69999i	0.960152	+	0.279477i
$37$	5.84038	+	1.69999i	0.960152	+	0.279477i
$38$	−0.825235			−0.133871
$39$	−4.26932	+	3.58238i	−0.683638	+	0.573640i
$40$	1.17365	+	0.984808i	0.185570	+	0.155712i
$41$	0.505653	−	2.86770i	0.0789697	−	0.447859i	−0.919526	−	0.393029i	$-0.871427\pi$
$41$	0.505653	−	2.86770i	0.0789697	−	0.447859i	0.998496	−	0.0548301i	$-0.0174617\pi$
$42$	−14.2804	+	5.19762i	−2.20351	+	0.802011i
$43$	4.37987			0.667924			0.333962	−	0.942587i	$-0.391614\pi$
$43$	4.37987			0.667924			0.333962	+	0.942587i	$0.391614\pi$
$44$	1.02783	−	0.374099i	0.154951	−	0.0563975i
$45$	−5.30028	−	9.18036i	−0.790119	−	1.36853i
$46$	−0.0422383	−	0.239545i	−0.00622770	−	0.0353191i
$47$	−1.13249	+	1.96153i	−0.165191	+	0.286119i	−0.936723	−	0.350071i	$-0.886157\pi$
$47$	−1.13249	+	1.96153i	−0.165191	+	0.286119i	0.771532	+	0.636190i	$0.219491\pi$
$48$	1.57472	+	2.72750i	0.227292	+	0.393681i
$49$	12.4734	−	10.4664i	1.78192	−	1.49521i
$50$	−0.460637	+	2.61240i	−0.0651439	+	0.369450i
$51$	4.63890	−	8.03481i	0.649576	−	1.12510i
$52$	−1.66286	−	0.605232i	−0.230597	−	0.0839305i
$53$	−5.77859	−	2.10324i	−0.793751	−	0.288902i	−0.0868564	−	0.996221i	$-0.527682\pi$
$53$	−5.77859	−	2.10324i	−0.793751	−	0.288902i	−0.706894	+	0.707319i	$0.749904\pi$
$54$	−2.14330	−	12.1553i	−0.291666	−	1.65412i
$55$	−1.28373	−	1.07717i	−0.173098	−	0.145246i
$56$	−3.69634	−	3.10160i	−0.493945	−	0.414469i
$57$	0.451318	+	2.55955i	0.0597785	+	0.339021i
$58$	5.23571	+	1.90564i	0.687483	+	0.250223i
$59$	−8.29301	−	3.01841i	−1.07966	−	0.392963i	−0.259878	−	0.965642i	$-0.583682\pi$
$59$	−8.29301	−	3.01841i	−1.07966	−	0.392963i	−0.819780	+	0.572678i	$0.805904\pi$
$60$	2.41262	−	4.17878i	0.311468	−	0.539478i
$61$	−2.04075	+	11.5737i	−0.261292	+	1.48186i	0.518098	+	0.855321i	$0.326640\pi$
$61$	−2.04075	+	11.5737i	−0.261292	+	1.48186i	−0.779390	+	0.626539i	$0.784471\pi$
$62$	−4.39322	+	3.68635i	−0.557940	+	0.468167i
$63$	16.6930	+	28.9131i	2.10312	+	3.64270i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.470787	+	2.66996i	0.0583939	+	0.331168i
$66$	−1.72242	−	2.98332i	−0.212015	−	0.367221i
$67$	−8.44220	+	3.07271i	−1.03138	+	0.375391i	−0.801606	−	0.597853i	$-0.796021\pi$
$67$	−8.44220	+	3.07271i	−1.03138	+	0.375391i	−0.229773	+	0.973244i	$0.573798\pi$
$68$	2.94585			0.357237
$69$	−0.719875	+	0.262013i	−0.0866627	+	0.0315427i
$70$	−1.28373	+	7.28038i	−0.153435	+	0.870172i
$71$	−0.933535	−	0.783329i	−0.110790	−	0.0929640i	0.585710	−	0.810521i	$-0.300816\pi$
$71$	−0.933535	−	0.783329i	−0.110790	−	0.0929640i	−0.696500	+	0.717557i	$0.745260\pi$
$72$	5.30028	−	4.44747i	0.624644	−	0.524139i
$73$	8.79418			1.02928			0.514640	−	0.857406i	$-0.327925\pi$
$73$	8.79418			1.02928			0.514640	+	0.857406i	$0.327925\pi$
$74$	5.56672	−	2.45185i	0.647119	−	0.285022i
$75$	8.35455			0.964701
$76$	−0.632167	+	0.530451i	−0.0725145	+	0.0608469i
$77$	4.04303	+	3.39251i	0.460746	+	0.386612i
$78$	−0.967776	+	5.48853i	−0.109579	+	0.621453i
$79$	−2.02379	+	0.736599i	−0.227694	+	0.0828739i	−0.453348	−	0.891334i	$-0.649770\pi$
$79$	−2.02379	+	0.736599i	−0.227694	+	0.0828739i	0.225654	+	0.974208i	$0.427548\pi$
$80$	1.53209			0.171293
$81$	−17.0233	+	6.19599i	−1.89148	+	0.688443i
$82$	−1.45597	−	2.52181i	−0.160785	−	0.278488i
$83$	0.884528	+	5.01641i	0.0970895	+	0.550622i	0.994087	+	0.108586i	$0.0346324\pi$
$83$	0.884528	+	5.01641i	0.0970895	+	0.550622i	−0.896997	+	0.442036i	$0.854256\pi$
$84$	−7.59842	+	13.1608i	−0.829055	+	1.43597i
$85$	−2.25665	−	3.90864i	−0.244768	−	0.423951i
$86$	3.35518	−	2.81533i	0.361798	−	0.303584i
$87$	3.04716	−	17.2813i	0.326690	−	1.85275i
$88$	0.546896	−	0.947252i	0.0582993	−	0.100977i
$89$	−8.43486	−	3.07004i	−0.894093	−	0.325423i	−0.146210	−	0.989254i	$-0.546708\pi$
$89$	−8.43486	−	3.07004i	−0.894093	−	0.325423i	−0.747883	+	0.663830i	$0.768930\pi$
$90$	−9.96127	−	3.62561i	−1.05001	−	0.382173i
$91$	−1.48272	−	8.40891i	−0.155431	−	0.881494i
$92$	−0.186333	−	0.156352i	−0.0194266	−	0.0163008i
$93$	13.8362	+	11.6100i	1.43475	+	1.20390i
$94$	0.393310	+	2.23057i	0.0405669	+	0.230066i
$95$	1.18809	+	0.432428i	0.121895	+	0.0443661i
$96$	2.95951	+	1.07717i	0.302054	+	0.109939i
$97$	−2.17954	+	3.77507i	−0.221298	+	0.383300i	−0.955203	−	0.295953i	$-0.904363\pi$
$97$	−2.17954	+	3.77507i	−0.221298	+	0.383300i	0.733904	+	0.679253i	$0.237696\pi$
$98$	2.82750	−	16.0355i	0.285620	−	1.61983i
$99$	−5.79741	+	4.86460i	−0.582661	+	0.488911i
$100$	1.32635	+	2.29731i	0.132635	+	0.229731i
$101$	2.19444	−	3.80089i	0.218355	−	0.378203i	−0.735950	−	0.677036i	$-0.763264\pi$
$101$	2.19444	−	3.80089i	0.218355	−	0.378203i	0.954305	+	0.298833i	$0.0965975\pi$
$102$	−1.61107	−	9.13685i	−0.159520	−	0.904683i
$103$	−6.32262	−	10.9511i	−0.622987	−	1.07904i	−0.988927	−	0.148406i	$-0.952586\pi$
$103$	−6.32262	−	10.9511i	−0.622987	−	1.07904i	0.365940	−	0.930638i	$-0.380748\pi$
$104$	−1.66286	+	0.605232i	−0.163057	+	0.0593478i
$105$	23.2829			2.27218
$106$	−5.77859	+	2.10324i	−0.561266	+	0.204284i
$107$	3.27495	−	18.5731i	0.316601	−	1.79553i	−0.246497	−	0.969144i	$-0.579279\pi$
$107$	3.27495	−	18.5731i	0.316601	−	1.79553i	0.563098	−	0.826390i	$-0.309609\pi$
$108$	−9.45512	−	7.93378i	−0.909819	−	0.763429i
$109$	−6.44574	+	5.40862i	−0.617390	+	0.518052i	−0.896982	−	0.442067i	$-0.854245\pi$
$109$	−6.44574	+	5.40862i	−0.617390	+	0.518052i	0.279592	+	0.960119i	$0.409801\pi$
$110$	−1.67579			−0.159780
$111$	−10.6491	−	15.9249i	−1.01077	−	1.51152i
$112$	−4.82524			−0.455942
$113$	−4.89090	+	4.10395i	−0.460097	+	0.386067i	−0.843167	−	0.537652i	$-0.819311\pi$
$113$	−4.89090	+	4.10395i	−0.460097	+	0.386067i	0.383070	+	0.923719i	$0.374867\pi$
$114$	1.99098	+	1.67063i	0.186472	+	0.156469i
$115$	−0.0647129	+	0.367005i	−0.00603451	+	0.0342234i
$116$	5.23571	−	1.90564i	0.486124	−	0.176935i
$117$	12.2438			1.13194
$118$	−8.29301	+	3.01841i	−0.763433	+	0.277867i
$119$	7.10721	+	12.3100i	0.651517	+	1.12846i
$120$	−0.837893	−	4.75193i	−0.0764888	−	0.433790i
$121$	4.90181	−	8.49018i	0.445619	−	0.771835i
$122$	5.87612	+	10.1777i	0.531999	+	0.921449i
$123$	−7.02539	+	5.89500i	−0.633458	+	0.531535i
$124$	−0.995863	+	5.64782i	−0.0894312	+	0.507189i
$125$	5.86231	−	10.1538i	0.524341	−	0.908185i
$126$	31.3725	+	11.4187i	2.79489	+	1.01726i
$127$	4.46592	+	1.62546i	0.396287	+	0.144237i	0.532474	−	0.846447i	$-0.321263\pi$
$127$	4.46592	+	1.62546i	0.396287	+	0.144237i	−0.136187	+	0.990683i	$0.543485\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−10.5670	−	8.86673i	−0.930368	−	0.780672i
$130$	2.07686	+	1.74269i	0.182153	+	0.152844i
$131$	3.12341	+	17.7137i	0.272893	+	1.54765i	0.745575	+	0.666422i	$0.232175\pi$
$131$	3.12341	+	17.7137i	0.272893	+	1.54765i	−0.472682	+	0.881233i	$0.656714\pi$
$132$	−3.23709	−	1.17821i	−0.281753	−	0.102550i
$133$	−3.74181	−	1.36191i	−0.324456	−	0.118092i
$134$	−4.49200	+	7.78037i	−0.388050	+	0.672122i
$135$	−3.28373	+	18.6229i	−0.282618	+	1.60281i
$136$	2.25665	−	1.89356i	0.193506	−	0.162371i
$137$	−11.0546	−	19.1471i	−0.944456	−	1.63585i	−0.756837	−	0.653603i	$-0.773256\pi$
$137$	−11.0546	−	19.1471i	−0.944456	−	1.63585i	−0.187619	−	0.982242i	$-0.560077\pi$
$138$	−0.383037	+	0.663440i	−0.0326063	+	0.0564758i
$139$	−0.462854	−	2.62497i	−0.0392587	−	0.222647i	0.958866	−	0.283859i	$-0.0916147\pi$
$139$	−0.462854	−	2.62497i	−0.0392587	−	0.222647i	−0.998125	+	0.0612114i	$0.980504\pi$
$140$	3.69634	+	6.40226i	0.312398	+	0.541089i
$141$	6.70325	−	2.43978i	0.564516	−	0.205467i
$142$	−1.21864			−0.102266
$143$	1.81882	−	0.661998i	0.152098	−	0.0553590i
$144$	1.20148	−	6.81391i	0.100123	−	0.567826i
$145$	−6.53925	−	5.48708i	−0.543055	−	0.455678i
$146$	6.73673	−	5.65279i	0.557536	−	0.467828i
$147$	−51.2822			−4.22968
$148$	2.68834	−	5.45645i	0.220980	−	0.448517i
$149$	6.13622			0.502699			0.251349	−	0.967896i	$-0.419126\pi$
$149$	6.13622			0.502699			0.251349	+	0.967896i	$0.419126\pi$
$150$	6.39996	−	5.37020i	0.522555	−	0.438475i
$151$	−0.334584	−	0.280749i	−0.0272281	−	0.0228471i	0.629072	−	0.777347i	$-0.283435\pi$
$151$	−0.334584	−	0.280749i	−0.0272281	−	0.0228471i	−0.656300	+	0.754500i	$0.727879\pi$
$152$	−0.143301	+	0.812698i	−0.0116232	+	0.0659185i
$153$	−19.1532	+	6.97120i	−1.54845	+	0.563588i
$154$	5.27780			0.425298
$155$	8.25656	−	3.00514i	0.663183	−	0.241379i
$156$	2.78660	+	4.82653i	0.223106	+	0.386432i
$157$	1.05255	+	5.96930i	0.0840025	+	0.476402i	0.997567	+	0.0697089i	$0.0222070\pi$
$157$	1.05255	+	5.96930i	0.0840025	+	0.476402i	−0.913565	+	0.406693i	$0.866682\pi$
$158$	−1.07684	+	1.86513i	−0.0856684	+	0.148382i
$159$	9.68369	+	16.7726i	0.767966	+	1.33016i
$160$	1.17365	−	0.984808i	0.0927850	−	0.0778559i
$161$	0.203810	−	1.15586i	0.0160625	−	0.0910948i
$162$	−9.05793	+	15.6888i	−0.711658	+	1.23263i
$163$	−12.9066	−	4.69763i	−1.01093	−	0.367947i	−0.217137	−	0.976141i	$-0.569672\pi$
$163$	−12.9066	−	4.69763i	−1.01093	−	0.367947i	−0.793788	+	0.608194i	$0.791894\pi$
$164$	−2.73633	−	0.995941i	−0.213671	−	0.0777699i
$165$	0.916481	+	5.19762i	0.0713480	+	0.404634i
$166$	3.90207	+	3.27423i	0.302859	+	0.254129i
$167$	18.2471	+	15.3112i	1.41201	+	1.18481i	0.955463	+	0.295112i	$0.0953570\pi$
$167$	18.2471	+	15.3112i	1.41201	+	1.18481i	0.456543	+	0.889701i	$0.349087\pi$
$168$	2.63890	+	14.9660i	0.203596	+	1.15465i
$169$	9.27344	+	3.37526i	0.713342	+	0.259635i
$170$	−4.24112	−	1.54364i	−0.325279	−	0.118392i
$171$	2.85491	−	4.94486i	0.218321	−	0.378143i
$172$	0.760556	−	4.31333i	0.0579919	−	0.328888i
$173$	16.4280	−	13.7847i	1.24899	−	1.04803i	0.252229	−	0.967668i	$-0.418836\pi$
$173$	16.4280	−	13.7847i	1.24899	−	1.04803i	0.996766	−	0.0803630i	$-0.0256080\pi$
$174$	−8.77394	−	15.1969i	−0.665151	−	1.15207i
$175$	−6.39996	+	11.0851i	−0.483791	+	0.837951i
$176$	−0.189935	−	1.07717i	−0.0143169	−	0.0811951i
$177$	13.8973	+	24.0709i	1.04459	+	1.80928i
$178$	−8.43486	+	3.07004i	−0.632220	+	0.230109i
$179$	11.5247			0.861400			0.430700	−	0.902495i	$-0.358267\pi$
$179$	11.5247			0.861400			0.430700	+	0.902495i	$0.358267\pi$
$180$	−9.96127	+	3.62561i	−0.742469	+	0.270237i
$181$	−3.08553	+	17.4989i	−0.229346	+	1.30068i	0.624855	+	0.780740i	$0.285158\pi$
$181$	−3.08553	+	17.4989i	−0.229346	+	1.30068i	−0.854201	+	0.519943i	$0.825953\pi$
$182$	−6.54097	−	5.48853i	−0.484849	−	0.406837i
$183$	28.3537	−	23.7915i	2.09596	−	1.75872i
$184$	−0.243241			−0.0179320
$185$	−9.29916	+	0.612921i	−0.683688	+	0.0450629i
$186$	18.0619			1.32436
$187$	−2.46831	+	2.07116i	−0.180501	+	0.151458i
$188$	1.73508	+	1.45590i	0.126544	+	0.106183i
$189$	10.3419	−	58.6520i	0.752265	−	4.26631i
$190$	1.18809	−	0.432428i	0.0861928	−	0.0313716i
$191$	−25.9113			−1.87487			−0.937437	−	0.348155i	$-0.886808\pi$
$191$	−25.9113			−1.87487			−0.937437	+	0.348155i	$0.886808\pi$
$192$	2.95951	−	1.07717i	0.213585	−	0.0777384i
$193$	−5.45149	−	9.44225i	−0.392407	−	0.679668i	0.600360	−	0.799730i	$-0.295024\pi$
$193$	−5.45149	−	9.44225i	−0.392407	−	0.679668i	−0.992766	+	0.120062i	$0.961691\pi$
$194$	0.756945	+	4.29285i	0.0543455	+	0.308209i
$195$	4.26932	−	7.39467i	0.305732	−	0.529544i
$196$	−8.14145	−	14.1014i	−0.581532	−	1.00724i
$197$	−4.93573	+	4.14157i	−0.351656	+	0.295075i	−0.801455	−	0.598055i	$-0.795940\pi$
$197$	−4.93573	+	4.14157i	−0.351656	+	0.295075i	0.449798	+	0.893130i	$0.351496\pi$
$198$	−1.31417	+	7.45300i	−0.0933937	+	0.529662i
$199$	−9.42779	+	16.3294i	−0.668318	+	1.15756i	0.310056	+	0.950718i	$0.399652\pi$
$199$	−9.42779	+	16.3294i	−0.668318	+	1.15756i	−0.978374	+	0.206843i	$0.933681\pi$
$200$	2.49273	+	0.907278i	0.176262	+	0.0641542i
$201$	26.5883	+	9.67734i	1.87539	+	0.682587i
$202$	−0.762122	−	4.32221i	−0.0536227	−	0.304110i
$203$	20.5950	+	17.2813i	1.44549	+	1.21291i
$204$	−7.10721	−	5.96366i	−0.497604	−	0.417540i
$205$	0.774705	+	4.39357i	0.0541077	+	0.306860i
$206$	−11.8826	−	4.32493i	−0.827903	−	0.301332i
$207$	1.58149	+	0.575617i	0.109921	+	0.0400081i
$208$	−0.884789	+	1.53250i	−0.0613491	+	0.106260i
$209$	0.156741	−	0.888923i	0.0108420	−	0.0614881i
$210$	17.8357	−	14.9660i	1.23078	−	1.03275i
$211$	0.707251	+	1.22499i	0.0486891	+	0.0843321i	0.889343	−	0.457241i	$-0.151162\pi$
$211$	0.707251	+	1.22499i	0.0486891	+	0.0843321i	−0.840654	+	0.541573i	$0.817829\pi$
$212$	−3.07472	+	5.32558i	−0.211173	+	0.365762i
$213$	0.666471	+	3.77975i	0.0456659	+	0.258984i
$214$	−9.42983	−	16.3330i	−0.644610	−	1.11650i
$215$	−6.30567	+	2.29507i	−0.430043	+	0.156523i
$216$	−12.3428			−0.839820
$217$	−26.0036	+	9.46454i	−1.76524	+	0.642495i
$218$	−1.46113	+	8.28649i	−0.0989603	+	0.561232i
$219$	−21.2170	−	17.8032i	−1.43371	−	1.20303i
$220$	−1.28373	+	1.07717i	−0.0865489	+	0.0726231i
$221$	5.21291			0.350659
$222$	−18.3940	−	5.35404i	−1.23452	−	0.359340i
$223$	−12.1750			−0.815302			−0.407651	−	0.913138i	$-0.633652\pi$
$223$	−12.1750			−0.815302			−0.407651	+	0.913138i	$0.633652\pi$
$224$	−3.69634	+	3.10160i	−0.246972	+	0.207234i
$225$	−14.0601	−	11.7978i	−0.937339	−	0.786520i
$226$	−1.10868	+	6.28761i	−0.0737480	+	0.418246i
$227$	20.0154	−	7.28501i	1.32847	−	0.483523i	0.422306	−	0.906453i	$-0.361221\pi$
$227$	20.0154	−	7.28501i	1.32847	−	0.483523i	0.906162	+	0.422930i	$0.138998\pi$
$228$	2.59904			0.172125
$229$	2.67775	−	0.974622i	0.176951	−	0.0644048i	−0.252025	−	0.967721i	$-0.581097\pi$
$229$	2.67775	−	0.974622i	0.176951	−	0.0644048i	0.428976	+	0.903316i	$0.358874\pi$
$230$	0.186333	+	0.322739i	0.0122865	+	0.0212808i
$231$	−2.88641	−	16.3696i	−0.189912	−	1.07704i
$232$	2.78587	−	4.82526i	0.182901	−	0.316794i
$233$	−11.7583	−	20.3659i	−0.770310	−	1.33422i	−0.937393	−	0.348273i	$-0.886768\pi$
$233$	−11.7583	−	20.3659i	−0.770310	−	1.33422i	0.167083	−	0.985943i	$-0.446565\pi$
$234$	9.37927	−	7.87014i	0.613142	−	0.514487i
$235$	0.602587	−	3.41744i	0.0393084	−	0.222929i
$236$	−4.41262	+	7.64288i	−0.287237	+	0.497509i
$237$	6.37382	+	2.31988i	0.414024	+	0.150692i
$238$	13.3572	+	4.86162i	0.865818	+	0.315132i
$239$	1.39581	+	7.91601i	0.0902872	+	0.512044i	0.996090	+	0.0883447i	$0.0281577\pi$
$239$	1.39581	+	7.91601i	0.0902872	+	0.512044i	−0.905803	+	0.423700i	$0.860731\pi$
$240$	−3.69634	−	3.10160i	−0.238598	−	0.200208i
$241$	14.1349	+	11.8606i	0.910511	+	0.764010i	0.972216	−	0.234085i	$-0.0752093\pi$
$241$	14.1349	+	11.8606i	0.910511	+	0.764010i	−0.0617048	+	0.998094i	$0.519654\pi$
$242$	−1.70238	−	9.65468i	−0.109433	−	0.620626i
$243$	18.8189	+	6.84951i	1.20723	+	0.439397i
$244$	11.0435	+	4.01950i	0.706987	+	0.257322i
$245$	−12.4734	+	21.6046i	−0.796898	+	1.38027i
$246$	−1.59253	+	9.03167i	−0.101536	+	0.575838i
$247$	−1.11867	+	0.938675i	−0.0711792	+	0.0597265i
$248$	2.86747	+	4.96661i	0.182085	+	0.315380i
$249$	8.02132	−	13.8933i	0.508330	−	0.880454i
$250$	−2.03596	−	11.5465i	−0.128765	−	0.730265i
$251$	−11.6472	−	20.1736i	−0.735167	−	1.27335i	−0.954650	−	0.297731i	$-0.903770\pi$
$251$	−11.6472	−	20.1736i	−0.735167	−	1.27335i	0.219483	−	0.975616i	$-0.429563\pi$
$252$	31.3725	−	11.4187i	1.97628	−	0.719308i
$253$	0.266055			0.0167267
$254$	4.46592	−	1.62546i	0.280217	−	0.101991i
$255$	−2.46831	+	13.9985i	−0.154571	+	0.876618i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−3.26092	+	2.73624i	−0.203411	+	0.170682i	−0.738803	−	0.673922i	$-0.764608\pi$
$257$	−3.26092	+	2.73624i	−0.203411	+	0.170682i	0.535392	+	0.844604i	$0.320164\pi$
$258$	−13.7942			−0.858788
$259$	29.2872	−	1.93036i	1.81982	−	0.119947i
$260$	2.71115			0.168139
$261$	−29.5317	+	24.7801i	−1.82797	+	1.53385i
$262$	13.7788	+	11.5618i	0.851259	+	0.714291i
$263$	−1.19565	+	6.78086i	−0.0737269	+	0.418126i	0.925498	+	0.378753i	$0.123647\pi$
$263$	−1.19565	+	6.78086i	−0.0737269	+	0.418126i	−0.999225	+	0.0393727i	$0.987464\pi$
$264$	−3.23709	+	1.17821i	−0.199229	+	0.0725135i
$265$	9.42150			0.578758
$266$	−3.74181	+	1.36191i	−0.229425	+	0.0835040i
$267$	14.1350	+	24.4826i	0.865050	+	1.49831i
$268$	1.56006	+	8.84751i	0.0952955	+	0.540448i
$269$	−4.83783	+	8.37936i	−0.294968	+	0.510899i	−0.974977	−	0.222304i	$-0.928642\pi$
$269$	−4.83783	+	8.37936i	−0.294968	+	0.510899i	0.680010	+	0.733203i	$0.261976\pi$
$270$	9.45512	+	16.3767i	0.575420	+	0.996657i
$271$	5.87002	−	4.92553i	0.356578	−	0.299205i	−0.446847	−	0.894610i	$-0.647453\pi$
$271$	5.87002	−	4.92553i	0.356578	−	0.299205i	0.803425	+	0.595406i	$0.203009\pi$
$272$	0.511542	−	2.90110i	0.0310168	−	0.175905i
$273$	−13.4460	+	23.2891i	−0.813789	+	1.40952i
$274$	−20.7758	−	7.56177i	−1.25511	−	0.456823i
$275$	−2.72652	−	0.992374i	−0.164416	−	0.0598424i
$276$	0.133027	+	0.754436i	0.00800731	+	0.0454117i
$277$	3.07917	+	2.58373i	0.185009	+	0.155241i	0.730589	−	0.682818i	$-0.239246\pi$
$277$	3.07917	+	2.58373i	0.185009	+	0.155241i	−0.545579	+	0.838059i	$0.683690\pi$
$278$	−2.04187	−	1.71333i	−0.122463	−	0.102759i
$279$	−6.89040	−	39.0774i	−0.412518	−	2.33950i
$280$	6.94686	+	2.52845i	0.415154	+	0.151104i
$281$	6.57717	+	2.39389i	0.392361	+	0.142808i	0.530664	−	0.847582i	$-0.321943\pi$
$281$	6.57717	+	2.39389i	0.392361	+	0.142808i	−0.138303	+	0.990390i	$0.544165\pi$
$282$	3.56673	−	6.17775i	0.212395	−	0.367880i
$283$	−0.816946	+	4.63313i	−0.0485624	+	0.275411i	−0.999414	−	0.0342367i	$-0.989100\pi$
$283$	−0.816946	+	4.63313i	−0.0485624	+	0.275411i	0.950851	+	0.309648i	$0.100211\pi$
$284$	−0.933535	+	0.783329i	−0.0553951	+	0.0464820i
$285$	−1.99098	−	3.44847i	−0.117935	−	0.204270i
$286$	0.967776	−	1.67624i	0.0572258	−	0.0991179i
$287$	−2.43989	−	13.8373i	−0.144022	−	0.816791i
$288$	−3.45951	−	5.99205i	−0.203854	−	0.353085i
$289$	7.82009	−	2.84628i	0.460005	−	0.167428i
$290$	−8.53639			−0.501274
$291$	12.9007	−	4.69549i	0.756255	−	0.275254i
$292$	1.52709	−	8.66057i	0.0893663	−	0.506822i
$293$	−10.9016	−	9.14751i	−0.636877	−	0.534403i	0.266180	−	0.963923i	$-0.414238\pi$
$293$	−10.9016	−	9.14751i	−0.636877	−	0.534403i	−0.903057	+	0.429520i	$0.858683\pi$
$294$	−39.2844	+	32.9635i	−2.29111	+	1.92247i
$295$	13.5210			0.787226
$296$	−1.44795	−	5.90791i	−0.0841605	−	0.343390i
$297$	13.5004			0.783374
$298$	4.70062	−	3.94429i	0.272299	−	0.228486i
$299$	−0.329731	−	0.276678i	−0.0190689	−	0.0160007i
$300$	1.45075	−	8.22763i	0.0837593	−	0.475022i
$301$	19.8594	−	7.22822i	1.14468	−	0.416628i
$302$	−0.436768			−0.0251332
$303$	−12.9890	+	4.72760i	−0.746197	+	0.271594i
$304$	0.412618	+	0.714675i	0.0236652	+	0.0409894i
$305$	−3.12662	−	17.7319i	−0.179030	−	1.01533i
$306$	−10.1912	+	17.6517i	−0.582593	+	1.00908i
$307$	−0.401308	−	0.695086i	−0.0229039	−	0.0396707i	0.854346	−	0.519704i	$-0.173958\pi$
$307$	−0.401308	−	0.695086i	−0.0229039	−	0.0396707i	−0.877250	+	0.480034i	$0.840624\pi$
$308$	4.04303	−	3.39251i	0.230373	−	0.193306i
$309$	−6.91563	+	39.2205i	−0.393417	+	2.23118i
$310$	4.39322	−	7.60929i	0.249518	−	0.432179i
$311$	2.32051	+	0.844598i	0.131584	+	0.0478928i	0.406973	−	0.913440i	$-0.366584\pi$
$311$	2.32051	+	0.844598i	0.131584	+	0.0478928i	−0.275389	+	0.961333i	$0.588807\pi$
$312$	5.23709	+	1.90615i	0.296492	+	0.107914i
$313$	−3.09856	−	17.5728i	−0.175141	−	0.993273i	−0.937981	−	0.346686i	$-0.887307\pi$
$313$	−3.09856	−	17.5728i	−0.175141	−	0.993273i	0.762840	−	0.646587i	$-0.223804\pi$
$314$	4.64329	+	3.89618i	0.262036	+	0.219874i
$315$	−39.1833	−	32.8787i	−2.20773	−	1.85251i
$316$	0.373981	+	2.12095i	0.0210381	+	0.119313i
$317$	−3.32609	−	1.21060i	−0.186812	−	0.0679940i	0.246920	−	0.969036i	$-0.420581\pi$
$317$	−3.32609	−	1.21060i	−0.186812	−	0.0679940i	−0.433732	+	0.901042i	$0.642804\pi$
$318$	18.1994	+	6.62403i	1.02057	+	0.371457i
$319$	−3.04716	+	5.27783i	−0.170608	+	0.295502i
$320$	0.266044	−	1.50881i	0.0148723	−	0.0843452i
$321$	−45.5012	+	38.1800i	−2.53963	+	2.13100i
$322$	−0.586847	−	1.01645i	−0.0327037	−	0.0566445i
$323$	1.21551	−	2.10533i	0.0676328	−	0.117143i
$324$	3.14579	+	17.8406i	0.174766	+	0.991147i
$325$	2.34708	+	4.06527i	0.130193	+	0.225501i
$326$	−12.9066	+	4.69763i	−0.714832	+	0.260178i
$327$	26.5005			1.46548
$328$	−2.73633	+	0.995941i	−0.151088	+	0.0549917i
$329$	−1.89782	+	10.7630i	−0.104630	+	0.593386i
$330$	4.04303	+	3.39251i	0.222562	+	0.186751i
$331$	2.93110	−	2.45948i	0.161108	−	0.135185i	−0.558670	−	0.829390i	$-0.688688\pi$
$331$	2.93110	−	2.45948i	0.161108	−	0.135185i	0.719778	+	0.694205i	$0.244244\pi$
$332$	5.09379			0.279558
$333$	−4.56653	+	41.8383i	−0.250244	+	2.29273i
$334$	23.8199			1.30337
$335$	10.5441	−	8.84751i	0.576083	−	0.483391i
$336$	11.6414	+	9.76834i	0.635093	+	0.532906i
$337$	−3.71542	+	21.0712i	−0.202392	+	1.14782i	0.699100	+	0.715024i	$0.253584\pi$
$337$	−3.71542	+	21.0712i	−0.202392	+	1.14782i	−0.901492	+	0.432797i	$0.857527\pi$
$338$	9.27344	−	3.37526i	0.504409	−	0.183590i
$339$	20.1080			1.09212
$340$	−4.24112	+	1.54364i	−0.230007	+	0.0837157i
$341$	−3.13642	−	5.43244i	−0.169847	−	0.294183i
$342$	−0.991501	−	5.62308i	−0.0536142	−	0.304061i
$343$	22.3961	−	38.7912i	1.20927	−	2.09453i
$344$	−2.18994	−	3.79308i	−0.118073	−	0.204509i
$345$	0.899102	−	0.754436i	0.0484060	−	0.0406175i
$346$	3.72392	−	21.1194i	0.200199	−	1.13538i
$347$	12.8181	−	22.2016i	0.688113	−	1.19185i	−0.284334	−	0.958725i	$-0.591773\pi$
$347$	12.8181	−	22.2016i	0.688113	−	1.19185i	0.972448	−	0.233122i	$-0.0748941\pi$
$348$	−16.4896	−	6.00173i	−0.883936	−	0.321726i
$349$	−14.5983	−	5.31334i	−0.781428	−	0.284417i	−0.0796600	−	0.996822i	$-0.525383\pi$
$349$	−14.5983	−	5.31334i	−0.781428	−	0.284417i	−0.701768	+	0.712406i	$0.747606\pi$
$350$	2.22268	+	12.6055i	0.118807	+	0.673790i
$351$	−16.7316	−	14.0395i	−0.893065	−	0.749371i
$352$	−0.837893	−	0.703076i	−0.0446599	−	0.0374741i
$353$	−0.235520	−	1.33570i	−0.0125355	−	0.0710923i	0.977898	−	0.209081i	$-0.0670473\pi$
$353$	−0.235520	−	1.33570i	−0.0125355	−	0.0710923i	−0.990434	+	0.137989i	$0.955936\pi$
$354$	26.1184	+	9.50632i	1.38818	+	0.505255i
$355$	1.75447	+	0.638576i	0.0931177	+	0.0338921i
$356$	−4.48810	+	7.77361i	−0.237869	+	0.412000i
$357$	7.77381	−	44.0875i	0.411434	−	2.33336i
$358$	8.82847	−	7.40796i	0.466599	−	0.391523i
$359$	11.1573	+	19.3251i	0.588862	+	1.01994i	0.994382	+	0.105853i	$0.0337573\pi$
$359$	11.1573	+	19.3251i	0.588862	+	1.01994i	−0.405519	+	0.914086i	$0.632909\pi$
$360$	−5.30028	+	9.18036i	−0.279349	+	0.483847i
$361$	−3.18106	−	18.0407i	−0.167424	−	0.949509i
$362$	8.88443	+	15.3883i	0.466955	+	0.808790i
$363$	−29.0139	+	10.5602i	−1.52284	+	0.554267i
$364$	−8.53863			−0.447546
$365$	−12.6609	+	4.60819i	−0.662702	+	0.241204i
$366$	6.42725	−	36.4508i	0.335958	−	1.90531i
$367$	5.53730	+	4.64635i	0.289045	+	0.242538i	0.775767	−	0.631019i	$-0.217363\pi$
$367$	5.53730	+	4.64635i	0.289045	+	0.242538i	−0.486722	+	0.873557i	$0.661808\pi$
$368$	−0.186333	+	0.156352i	−0.00971329	+	0.00815042i
$369$	20.1478			1.04885
$370$	−6.72959	+	6.44691i	−0.349855	+	0.335159i
$371$	−29.6725			−1.54052
$372$	13.8362	−	11.6100i	0.717375	−	0.601949i
$373$	−8.98788	−	7.54173i	−0.465375	−	0.390496i	0.379729	−	0.925098i	$-0.376017\pi$
$373$	−8.98788	−	7.54173i	−0.465375	−	0.390496i	−0.845104	+	0.534602i	$0.820462\pi$
$374$	−0.559520	+	3.17320i	−0.0289321	+	0.164082i
$375$	−34.6992	+	12.6295i	−1.79186	+	0.652183i
$376$	2.26498			0.116808
$377$	9.26501	−	3.37219i	0.477172	−	0.173677i
$378$	−29.7784	−	51.5777i	−1.53164	−	2.65287i
$379$	−0.480627	−	2.72577i	−0.0246881	−	0.140013i	0.969972	−	0.243216i	$-0.0782022\pi$
$379$	−0.480627	−	2.72577i	−0.0246881	−	0.140013i	−0.994660	+	0.103202i	$0.967091\pi$
$380$	0.632167	−	1.09495i	0.0324295	−	0.0561695i
$381$	−7.48394	−	12.9626i	−0.383414	−	0.664092i
$382$	−19.8492	+	16.6554i	−1.01557	+	0.852167i
$383$	3.38122	−	19.1758i	0.172772	−	0.979840i	−0.767912	−	0.640556i	$-0.778704\pi$
$383$	3.38122	−	19.1758i	0.172772	−	0.979840i	0.940684	−	0.339284i	$-0.110185\pi$
$384$	1.57472	−	2.72750i	0.0803598	−	0.139187i
$385$	−7.59842	−	2.76560i	−0.387251	−	0.140948i
$386$	−10.2454	−	3.72904i	−0.521479	−	0.189803i
$387$	5.26231	+	29.8440i	0.267498	+	1.51706i
$388$	3.33924	+	2.80196i	0.169524	+	0.142248i
$389$	−1.79849	−	1.50911i	−0.0911870	−	0.0765150i	0.596055	−	0.802944i	$-0.296734\pi$
$389$	−1.79849	−	1.50911i	−0.0911870	−	0.0765150i	−0.687242	+	0.726429i	$0.741179\pi$
$390$	−1.48272	−	8.40891i	−0.0750804	−	0.425802i
$391$	0.673338	+	0.245075i	0.0340522	+	0.0123940i
$392$	−15.3009	−	5.56908i	−0.772813	−	0.281281i
$393$	28.3245	−	49.0595i	1.42878	−	2.47473i
$394$	−1.11884	+	6.34525i	−0.0563663	+	0.319669i
$395$	2.52765	−	2.12095i	0.127180	−	0.106717i
$396$	3.78399	+	6.55406i	0.190153	+	0.329354i
$397$	−1.13774	+	1.97062i	−0.0571015	+	0.0989026i	−0.893163	−	0.449733i	$-0.851519\pi$
$397$	−1.13774	+	1.97062i	−0.0571015	+	0.0989026i	0.836062	+	0.548635i	$0.184853\pi$
$398$	3.27424	+	18.5691i	0.164123	+	0.930786i
$399$	6.27048	+	10.8608i	0.313917	+	0.543720i
$400$	2.49273	−	0.907278i	0.124636	−	0.0453639i
$401$	17.5482			0.876316			0.438158	−	0.898898i	$-0.355631\pi$
$401$	17.5482			0.876316			0.438158	+	0.898898i	$0.355631\pi$
$402$	26.5883	−	9.67734i	1.32610	−	0.482662i
$403$	−1.76226	+	9.99426i	−0.0877843	+	0.497850i
$404$	−3.36208	−	2.82112i	−0.167270	−	0.140356i
$405$	21.2616	−	17.8406i	1.05650	−	0.886508i
$406$	26.8849			1.33428
$407$	1.58376	+	6.46203i	0.0785040	+	0.320311i
$408$	−9.27780			−0.459320
$409$	17.3730	−	14.5777i	0.859041	−	0.720821i	−0.102720	−	0.994710i	$-0.532755\pi$
$409$	17.3730	−	14.5777i	0.859041	−	0.720821i	0.961761	+	0.273889i	$0.0883102\pi$
$410$	3.41759	+	2.86770i	0.168783	+	0.141626i
$411$	−12.0914	+	68.5738i	−0.596425	+	3.38249i
$412$	−11.8826	+	4.32493i	−0.585416	+	0.213074i
$413$	−42.5838			−2.09541
$414$	1.58149	−	0.575617i	0.0777262	−	0.0282900i
$415$	−3.90207	−	6.75859i	−0.191545	−	0.331766i
$416$	0.307284	+	1.74269i	0.0150658	+	0.0854426i
$417$	−4.19738	+	7.27007i	−0.205547	+	0.356017i
$418$	−0.451318	−	0.781706i	−0.0220747	−	0.0382345i
$419$	14.4180	−	12.0981i	0.704365	−	0.591032i	−0.218647	−	0.975804i	$-0.570164\pi$
$419$	14.4180	−	12.0981i	0.704365	−	0.591032i	0.923012	+	0.384772i	$0.125720\pi$
$420$	4.04303	−	22.9292i	0.197280	−	1.11883i
$421$	8.96330	−	15.5249i	0.436844	−	0.756637i	−0.560600	−	0.828087i	$-0.689429\pi$
$421$	8.96330	−	15.5249i	0.436844	−	0.756637i	0.997444	+	0.0714502i	$0.0227627\pi$
$422$	1.32920	+	0.483788i	0.0647043	+	0.0235504i
$423$	−14.7264	−	5.35997i	−0.716021	−	0.260610i
$424$	1.06784	+	6.05602i	0.0518589	+	0.294107i
$425$	−5.98623	−	5.02304i	−0.290375	−	0.243653i
$426$	2.94012	+	2.46705i	0.142449	+	0.119529i
$427$	9.84712	+	55.8458i	0.476536	+	2.70257i
$428$	−17.7223	−	6.45039i	−0.856639	−	0.311791i
$429$	−5.72829	−	2.08493i	−0.276564	−	0.100661i
$430$	−3.35518	+	5.81133i	−0.161801	+	0.280247i
$431$	2.12908	−	12.0746i	0.102554	−	0.581613i	−0.889615	−	0.456711i	$-0.849027\pi$
$431$	2.12908	−	12.0746i	0.102554	−	0.581613i	0.992169	−	0.124902i	$-0.0398616\pi$
$432$	−9.45512	+	7.93378i	−0.454909	+	0.381714i
$433$	−10.5573	−	18.2858i	−0.507351	−	0.878758i	−0.999964	−	0.00850909i	$-0.997291\pi$
$433$	−10.5573	−	18.2858i	−0.507351	−	0.878758i	0.492613	−	0.870249i	$-0.336042\pi$
$434$	−13.8362	+	23.9651i	−0.664161	+	1.15036i
$435$	4.66852	+	26.4765i	0.223838	+	1.26945i
$436$	4.20716	+	7.28702i	0.201486	+	0.348985i
$437$	−0.188625	+	0.0686540i	−0.00902318	+	0.00328417i
$438$	−27.6968			−1.32340
$439$	22.6396	−	8.24015i	1.08053	−	0.393281i	0.260425	−	0.965494i	$-0.416137\pi$
$439$	22.6396	−	8.24015i	1.08053	−	0.393281i	0.820105	+	0.572213i	$0.193915\pi$
$440$	−0.290997	+	1.65033i	−0.0138728	+	0.0786763i
$441$	86.3040	+	72.4176i	4.10971	+	3.44846i
$442$	3.99332	−	3.35080i	0.189943	−	0.159381i
$443$	19.2348			0.913871			0.456936	−	0.889500i	$-0.348947\pi$
$443$	19.2348			0.913871			0.456936	+	0.889500i	$0.348947\pi$
$444$	−17.5321	+	7.72198i	−0.832037	+	0.366469i
$445$	13.7523			0.651923
$446$	−9.32663	+	7.82597i	−0.441629	+	0.370570i
$447$	−14.8043	−	12.4223i	−0.700222	−	0.587556i
$448$	−0.837893	+	4.75193i	−0.0395867	+	0.224508i
$449$	6.19008	−	2.25301i	0.292128	−	0.106326i	−0.191799	−	0.981434i	$-0.561432\pi$
$449$	6.19008	−	2.25301i	0.292128	−	0.106326i	0.483927	+	0.875108i	$0.339210\pi$
$450$	−18.3541			−0.865222
$451$	2.99297	−	1.08935i	0.140934	−	0.0512956i
$452$	3.19231	+	5.52924i	0.150153	+	0.260073i
$453$	0.238867	+	1.35468i	0.0112229	+	0.0636485i
$454$	10.6500	−	18.4463i	0.499828	−	0.865727i
$455$	6.54097	+	11.3293i	0.306646	+	0.531126i
$456$	1.99098	−	1.67063i	0.0932361	−	0.0782344i
$457$	−5.03427	+	28.5507i	−0.235493	+	1.33555i	0.606080	+	0.795404i	$0.292741\pi$
$457$	−5.03427	+	28.5507i	−0.235493	+	1.33555i	−0.841573	+	0.540144i	$0.818370\pi$
$458$	1.42480	−	2.46783i	0.0665766	−	0.115314i
$459$	34.1672	+	12.4358i	1.59479	+	0.580455i
$460$	0.350192	+	0.127459i	0.0163278	+	0.00594283i
$461$	6.22553	+	35.3067i	0.289952	+	1.64440i	0.687041	+	0.726618i	$0.258909\pi$
$461$	6.22553	+	35.3067i	0.289952	+	1.64440i	−0.397089	+	0.917780i	$0.629980\pi$
$462$	−12.7333	−	10.6845i	−0.592408	−	0.497089i
$463$	−14.2350	−	11.9446i	−0.661556	−	0.555111i	0.248997	−	0.968504i	$-0.419899\pi$
$463$	−14.2350	−	11.9446i	−0.661556	−	0.555111i	−0.910553	+	0.413393i	$0.864344\pi$
$464$	−0.967521	−	5.48708i	−0.0449160	−	0.254731i
$465$	−26.0036	−	9.46454i	−1.20589	−	0.438908i
$466$	−22.0983	−	8.04313i	−1.02369	−	0.372591i
$467$	0.823127	−	1.42570i	0.0380898	−	0.0659734i	−0.846352	−	0.532624i	$-0.821206\pi$
$467$	0.823127	−	1.42570i	0.0380898	−	0.0659734i	0.884442	+	0.466650i	$0.154539\pi$
$468$	2.12611	−	12.0578i	0.0982793	−	0.557370i
$469$	−33.2080	+	27.8648i	−1.53340	+	1.28668i
$470$	−1.73508	−	3.00524i	−0.0800332	−	0.138622i
$471$	9.54501	−	16.5324i	0.439811	−	0.761775i
$472$	1.53249	+	8.69116i	0.0705384	+	0.400043i
$473$	2.39533	+	4.14884i	0.110138	+	0.190764i
$474$	6.37382	−	2.31988i	0.292759	−	0.106556i
$475$	2.18911			0.100443
$476$	13.3572	−	4.86162i	0.612226	−	0.222832i
$477$	7.38842	−	41.9018i	0.338292	−	1.91855i
$478$	6.15757	+	5.16681i	0.281640	+	0.236324i
$479$	−26.1002	+	21.9007i	−1.19255	+	1.00067i	−0.192737	+	0.981250i	$0.561736\pi$
$479$	−26.1002	+	21.9007i	−1.19255	+	1.00067i	−0.999811	+	0.0194166i	$0.993819\pi$
$480$	−4.82524			−0.220241
$481$	4.75723	−	9.65562i	0.216911	−	0.440258i
$482$	18.4519			0.840459
$483$	−2.83168	+	2.37606i	−0.128846	+	0.108114i
$484$	−7.51001	−	6.30164i	−0.341364	−	0.286438i
$485$	1.15971	−	6.57703i	0.0526596	−	0.298647i
$486$	18.8189	−	6.84951i	0.853642	−	0.310700i
$487$	−31.0898			−1.40881			−0.704407	−	0.709796i	$-0.748787\pi$
$487$	−31.0898			−1.40881			−0.704407	+	0.709796i	$0.748787\pi$
$488$	11.0435	−	4.01950i	0.499915	−	0.181954i
$489$	21.6288	+	37.4621i	0.978086	+	1.69409i
$490$	4.33197	+	24.5678i	0.195699	+	1.10986i
$491$	−17.5270	+	30.3576i	−0.790981	+	1.37002i	0.134379	+	0.990930i	$0.457096\pi$
$491$	−17.5270	+	30.3576i	−0.790981	+	1.37002i	−0.925360	+	0.379089i	$0.876237\pi$
$492$	4.58550	+	7.94232i	0.206730	+	0.358067i
$493$	−12.5735	+	10.5504i	−0.566280	+	0.475165i
$494$	−0.253582	+	1.43813i	−0.0114092	+	0.0647047i
$495$	5.79741	−	10.0414i	0.260574	−	0.451328i
$496$	5.38909	+	1.96147i	0.241977	+	0.0880725i
$497$	−5.52562	−	2.01116i	−0.247858	−	0.0902129i
$498$	−2.78577	−	15.7989i	−0.124834	−	0.707966i
$499$	−26.9427	−	22.6076i	−1.20612	−	1.01205i	−0.999434	−	0.0336472i	$-0.989288\pi$
$499$	−26.9427	−	22.6076i	−1.20612	−	1.01205i	−0.206686	−	0.978407i	$-0.566268\pi$
$500$	−8.98158	−	7.53644i	−0.401669	−	0.337040i
$501$	−13.0270	−	73.8800i	−0.582005	−	3.30071i
$502$	−21.8897	−	7.96718i	−0.976983	−	0.355593i
$503$	−4.35300	−	1.58436i	−0.194091	−	0.0706432i	0.243146	−	0.969990i	$-0.421821\pi$
$503$	−4.35300	−	1.58436i	−0.194091	−	0.0706432i	−0.437237	+	0.899346i	$0.644043\pi$
$504$	16.6930	−	28.9131i	0.743564	−	1.28789i
$505$	−1.16764	+	6.62201i	−0.0519593	+	0.294676i
$506$	0.203810	−	0.171017i	0.00906045	−	0.00760262i
$507$	−15.5403	−	26.9166i	−0.690169	−	1.19541i
$508$	2.37627	−	4.11582i	0.105430	−	0.182610i
$509$	−4.14162	−	23.4883i	−0.183574	−	1.04110i	−0.927774	−	0.373144i	$-0.878280\pi$
$509$	−4.14162	−	23.4883i	−0.183574	−	1.04110i	0.744199	−	0.667958i	$-0.232831\pi$
$510$	7.10721	+	12.3100i	0.314713	+	0.545098i
$511$	39.8749	−	14.5133i	1.76396	−	0.642029i
$512$	1.00000			0.0441942
$513$	−9.57142	+	3.48371i	−0.422589	+	0.153810i
$514$	−0.739191	+	4.19216i	−0.0326043	+	0.184908i
$515$	14.8411	+	12.4531i	0.653976	+	0.548751i
$516$	−10.5670	+	8.86673i	−0.465184	+	0.390336i
$517$	−2.47742			−0.108957
$518$	21.1945	−	20.3042i	0.931233	−	0.892115i
$519$	−67.5405			−2.96470
$520$	2.07686	−	1.74269i	0.0910765	−	0.0764222i
$521$	14.8610	+	12.4698i	0.651071	+	0.546313i	0.907396	−	0.420278i	$-0.138067\pi$
$521$	14.8610	+	12.4698i	0.651071	+	0.546313i	−0.256325	+	0.966591i	$0.582512\pi$
$522$	−6.69430	+	37.9653i	−0.293002	+	1.66170i
$523$	−1.82296	+	0.663503i	−0.0797125	+	0.0290130i	−0.381569	−	0.924341i	$-0.624616\pi$
$523$	−1.82296	+	0.663503i	−0.0797125	+	0.0290130i	0.301856	+	0.953353i	$0.402394\pi$
$524$	17.9870			0.785765
$525$	37.8815	−	13.7878i	1.65329	−	0.601747i
$526$	3.44273	+	5.96299i	0.150110	+	0.259999i
$527$	−2.93366	−	16.6376i	−0.127792	−	0.724747i
$528$	−1.72242	+	2.98332i	−0.0749588	+	0.129832i
$529$	11.4704	+	19.8673i	0.498714	+	0.863798i
$530$	7.21729	−	6.05602i	0.313499	−	0.263057i
$531$	10.6033	−	60.1344i	0.460145	−	2.60961i
$532$	−1.99098	+	3.44847i	−0.0863198	+	0.149510i
$533$	−4.84214	−	1.76240i	−0.209737	−	0.0763379i
$534$	26.5652	+	9.66893i	1.14959	+	0.418415i
$535$	5.01751	+	28.4557i	0.216926	+	1.23025i
$536$	6.88214	+	5.77480i	0.297263	+	0.249434i
$537$	−27.8048	−	23.3310i	−1.19987	−	1.00681i
$538$	1.68016	+	9.52866i	0.0724368	+	0.410810i
$539$	16.7360	+	6.09141i	0.720872	+	0.262376i
$540$	17.7698	+	6.46768i	0.764691	+	0.278325i
$541$	2.15605	−	3.73439i	0.0926958	−	0.160554i	−0.815949	−	0.578124i	$-0.803785\pi$
$541$	2.15605	−	3.73439i	0.0926958	−	0.160554i	0.908645	+	0.417570i	$0.137118\pi$
$542$	1.33063	−	7.54635i	0.0571553	−	0.324144i
$543$	42.8694	−	35.9717i	1.83970	−	1.54370i
$544$	−1.47293	−	2.55118i	−0.0631511	−	0.109381i
$545$	6.44574	−	11.1644i	0.276105	−	0.478228i
$546$	4.66975	+	26.4834i	0.199847	+	1.13339i
$547$	−8.75830	−	15.1698i	−0.374478	−	0.648615i	0.615771	−	0.787925i	$-0.288845\pi$
$547$	−8.75830	−	15.1698i	−0.374478	−	0.648615i	−0.990249	+	0.139311i	$0.955511\pi$
$548$	−20.7758	+	7.56177i	−0.887498	+	0.323023i
$549$	−81.3141			−3.47040
$550$	−2.72652	+	0.992374i	−0.116259	+	0.0423150i
$551$	0.798433	−	4.52814i	0.0340144	−	0.192905i
$552$	0.586847	+	0.492423i	0.0249779	+	0.0209589i
$553$	−7.96071	+	6.67983i	−0.338524	+	0.284055i
$554$	4.01957			0.170775
$555$	23.6761	+	17.3467i	1.00500	+	0.736327i
$556$	−2.66547			−0.113041
$557$	17.4740	−	14.6624i	0.740398	−	0.621268i	−0.192546	−	0.981288i	$-0.561675\pi$
$557$	17.4740	−	14.6624i	0.740398	−	0.621268i	0.932945	+	0.360020i	$0.117230\pi$
$558$	−30.3968	−	25.5060i	−1.28680	−	1.07975i
$559$	1.34586	−	7.63278i	0.0569240	−	0.322832i
$560$	6.94686	−	2.52845i	0.293558	−	0.106846i
$561$	10.1480			0.428448
$562$	6.57717	−	2.39389i	0.277441	−	0.100980i
$563$	13.2921	+	23.0226i	0.560195	+	0.970287i	0.997479	+	0.0709631i	$0.0226073\pi$
$563$	13.2921	+	23.0226i	0.560195	+	0.970287i	−0.437284	+	0.899324i	$0.644059\pi$
$564$	−1.23871	−	7.02508i	−0.0521591	−	0.295809i
$565$	4.89090	−	8.47128i	0.205762	−	0.356389i
$566$	2.35230	+	4.07430i	0.0988746	+	0.171256i
$567$	−66.9625	+	56.1882i	−2.81216	+	2.35968i
$568$	−0.211615	+	1.20013i	−0.00887918	+	0.0503563i
$569$	6.98492	−	12.0982i	0.292823	−	0.507184i	−0.681653	−	0.731676i	$-0.738739\pi$
$569$	6.98492	−	12.0982i	0.292823	−	0.507184i	0.974476	+	0.224491i	$0.0720720\pi$
$570$	−3.74181	−	1.36191i	−0.156727	−	0.0570441i
$571$	−20.6390	−	7.51199i	−0.863717	−	0.314367i	−0.128097	−	0.991762i	$-0.540887\pi$
$571$	−20.6390	−	7.51199i	−0.863717	−	0.314367i	−0.735620	+	0.677395i	$0.763109\pi$
$572$	−0.336105	−	1.90615i	−0.0140533	−	0.0797000i
$573$	62.5140	+	52.4555i	2.61156	+	2.19136i
$574$	−10.7635	−	9.03167i	−0.449261	−	0.376975i
$575$	0.112046	+	0.635443i	0.00467263	+	0.0264998i
$576$	−6.50176	−	2.36645i	−0.270907	−	0.0986019i
$577$	−29.6115	−	10.7777i	−1.23274	−	0.448682i	−0.358207	−	0.933642i	$-0.616612\pi$
$577$	−29.6115	−	10.7777i	−1.23274	−	0.448682i	−0.874536	+	0.484961i	$0.838834\pi$
$578$	4.16098	−	7.20703i	0.173074	−	0.299773i
$579$	−5.96279	+	33.8167i	−0.247805	+	1.40537i
$580$	−6.53925	+	5.48708i	−0.271528	+	0.227839i
$581$	12.2894	+	21.2858i	0.509849	+	0.883085i
$582$	6.86434	−	11.8894i	0.284536	−	0.492831i
$583$	−1.16800	−	6.62403i	−0.0483734	−	0.274339i
$584$	−4.39709	−	7.61598i	−0.181953	−	0.315151i
$585$	−17.6273	+	6.41580i	−0.728797	+	0.265261i
$586$	−14.2310			−0.587877
$587$	39.3494	−	14.3220i	1.62412	−	0.591133i	0.639963	−	0.768406i	$-0.278950\pi$
$587$	39.3494	−	14.3220i	1.62412	−	0.591133i	0.984162	+	0.177273i	$0.0567274\pi$
$588$	−8.90505	+	50.5031i	−0.367238	+	2.08271i
$589$	3.62544	+	3.04211i	0.149384	+	0.125348i
$590$	10.3577	−	8.69116i	0.426421	−	0.357809i
$591$	20.2923			0.834715
$592$	−4.90673	−	3.59500i	−0.201665	−	0.147754i
$593$	−30.7471			−1.26263			−0.631316	−	0.775525i	$-0.717485\pi$
$593$	−30.7471			−1.26263			−0.631316	+	0.775525i	$0.717485\pi$
$594$	10.3419	−	8.67791i	0.424335	−	0.356059i
$595$	−16.6827	−	13.9985i	−0.683925	−	0.573881i
$596$	1.06554	−	6.04300i	0.0436463	−	0.247531i
$597$	55.8033	−	20.3108i	2.28388	−	0.831264i
$598$	−0.430434			−0.0176017
$599$	−28.2700	+	10.2894i	−1.15508	+	0.420415i	−0.847337	−	0.531055i	$-0.821796\pi$
$599$	−28.2700	+	10.2894i	−1.15508	+	0.420415i	−0.307742	+	0.951470i	$0.599573\pi$
$600$	−4.17728	−	7.23526i	−0.170537	−	0.295378i
$601$	5.27054	+	29.8907i	0.214990	+	1.21927i	0.880924	+	0.473257i	$0.156922\pi$
$601$	5.27054	+	29.8907i	0.214990	+	1.21927i	−0.665935	+	0.746010i	$0.731967\pi$
$602$	10.5670	−	18.3025i	0.430677	−	0.745954i
$603$	−31.0803	−	53.8326i	−1.26569	−	2.19223i
$604$	−0.334584	+	0.280749i	−0.0136140	+	0.0114235i
$605$	−2.60820	+	14.7918i	−0.106038	+	0.601373i
$606$	−6.91129	+	11.9707i	−0.280752	+	0.486277i
$607$	1.08095	+	0.393434i	0.0438744	+	0.0159690i	0.363864	−	0.931452i	$-0.381457\pi$
$607$	1.08095	+	0.393434i	0.0438744	+	0.0159690i	−0.319990	+	0.947421i	$0.603679\pi$
$608$	0.775468	+	0.282247i	0.0314494	+	0.0114466i
$609$	−14.7033	−	83.3863i	−0.595806	−	3.37898i
$610$	−13.7930	−	11.5737i	−0.558462	−	0.468605i
$611$	3.07036	+	2.57634i	0.124213	+	0.104227i
$612$	3.53937	+	20.0728i	0.143071	+	0.811393i
$613$	14.5282	+	5.28784i	0.586789	+	0.213574i	0.618317	−	0.785929i	$-0.287815\pi$
$613$	14.5282	+	5.28784i	0.586789	+	0.213574i	−0.0315273	+	0.999503i	$0.510037\pi$
$614$	−0.754213	−	0.274511i	−0.0304375	−	0.0110784i
$615$	7.02539	−	12.1683i	0.283291	−	0.490675i
$616$	0.916481	−	5.19762i	0.0369261	−	0.209418i
$617$	16.0733	−	13.4871i	0.647086	−	0.542970i	−0.259099	−	0.965851i	$-0.583426\pi$
$617$	16.0733	−	13.4871i	0.647086	−	0.542970i	0.906185	+	0.422881i	$0.138981\pi$
$618$	19.9128	+	34.4899i	0.801009	+	1.38739i
$619$	−15.4275	+	26.7212i	−0.620084	+	1.07402i	0.369386	+	0.929276i	$0.379568\pi$
$619$	−15.4275	+	26.7212i	−0.620084	+	1.07402i	−0.989470	+	0.144741i	$0.953765\pi$
$620$	−1.52575	−	8.65296i	−0.0612756	−	0.347511i
$621$	−1.50113	−	2.60004i	−0.0602384	−	0.104336i
$622$	2.32051	−	0.844598i	0.0930441	−	0.0338653i
$623$	−43.3122			−1.73527
$624$	5.23709	−	1.90615i	0.209651	−	0.0763069i
$625$	−0.816085	+	4.62825i	−0.0326434	+	0.185130i
$626$	−13.6692	−	11.4698i	−0.546331	−	0.458426i
$627$	−2.17772	+	1.82732i	−0.0869696	+	0.0729761i
$628$	6.06139			0.241876
$629$	−1.94425	+	17.8131i	−0.0775222	+	0.710255i
$630$	−51.1502			−2.03787
$631$	4.47641	−	3.75615i	0.178203	−	0.149530i	−0.549323	−	0.835610i	$-0.685114\pi$
$631$	4.47641	−	3.75615i	0.178203	−	0.149530i	0.727526	+	0.686080i	$0.240670\pi$
$632$	1.64981	+	1.38435i	0.0656258	+	0.0550666i
$633$	0.773585	−	4.38722i	0.0307472	−	0.174376i
$634$	−3.32609	+	1.21060i	−0.132096	+	0.0480790i
$635$	−7.28131			−0.288950
$636$	18.1994	−	6.62403i	0.721652	−	0.262660i
$637$	−14.4069	−	24.9535i	−0.570824	−	0.988695i
$638$	1.05827	+	6.00173i	0.0418972	+	0.237611i
$639$	4.21591	−	7.30218i	0.166779	−	0.288870i
$640$	−0.766044	−	1.32683i	−0.0302806	−	0.0524475i
$641$	22.8599	−	19.1817i	0.902912	−	0.757633i	−0.0678451	−	0.997696i	$-0.521612\pi$
$641$	22.8599	−	19.1817i	0.902912	−	0.757633i	0.970757	+	0.240062i	$0.0771679\pi$
$642$	−10.3143	+	58.4952i	−0.407072	+	2.30862i
$643$	−7.18117	+	12.4382i	−0.283198	+	0.490513i	−0.972171	−	0.234274i	$-0.924729\pi$
$643$	−7.18117	+	12.4382i	−0.283198	+	0.490513i	0.688973	+	0.724787i	$0.258062\pi$
$644$	−1.10291	−	0.401427i	−0.0434608	−	0.0158184i
$645$	19.8594	+	7.22822i	0.781962	+	0.284611i
$646$	−0.422142	−	2.39409i	−0.0166090	−	0.0941941i
$647$	7.11852	+	5.97315i	0.279858	+	0.234829i	0.771902	−	0.635742i	$-0.219306\pi$
$647$	7.11852	+	5.97315i	0.279858	+	0.234829i	−0.492044	+	0.870570i	$0.663750\pi$
$648$	13.8776	+	11.6446i	0.545162	+	0.457445i
$649$	−1.67622	−	9.50632i	−0.0657974	−	0.373156i
$650$	4.41108	+	1.60550i	0.173017	+	0.0629729i
$651$	81.8971	+	29.8081i	3.20980	+	1.16827i
$652$	−6.86747	+	11.8948i	−0.268951	+	0.465837i
$653$	−7.38987	+	41.9101i	−0.289188	+	1.64007i	0.400742	+	0.916191i	$0.368752\pi$
$653$	−7.38987	+	41.9101i	−0.289188	+	1.64007i	−0.689930	+	0.723876i	$0.742359\pi$
$654$	20.3005	−	17.0342i	0.793814	−	0.666089i
$655$	−13.7788	−	23.8656i	−0.538383	−	0.932507i
$656$	−1.45597	+	2.52181i	−0.0568460	+	0.0984602i
$657$	10.5660	+	59.9227i	0.412219	+	2.33781i
$658$	5.46454	+	9.46486i	0.213030	+	0.368979i
$659$	−10.3196	+	3.75603i	−0.401995	+	0.146314i	−0.535102	−	0.844788i	$-0.679727\pi$
$659$	−10.3196	+	3.75603i	−0.401995	+	0.146314i	0.133107	+	0.991102i	$0.457505\pi$
$660$	5.27780			0.205438
$661$	−31.5074	+	11.4678i	−1.22550	+	0.446044i	−0.872053	−	0.489412i	$-0.837212\pi$
$661$	−31.5074	+	11.4678i	−1.22550	+	0.446044i	−0.353444	+	0.935456i	$0.614989\pi$
$662$	0.664426	−	3.76815i	0.0258237	−	0.146453i
$663$	−12.5768	−	10.5532i	−0.488441	−	0.409851i
$664$	3.90207	−	3.27423i	0.151430	−	0.127065i
$665$	6.10071			0.236575
$666$	23.3950	+	34.9853i	0.906538	+	1.35565i
$667$	1.35527			0.0524764
$668$	18.2471	−	15.3112i	0.706003	−	0.592407i
$669$	29.3737	+	24.6475i	1.13565	+	0.952927i
$670$	2.39014	−	13.5552i	0.0923393	−	0.523682i
$671$	−12.0793	+	4.39650i	−0.466316	+	0.169725i
$672$	15.1968			0.586231
$673$	41.1753	−	14.9866i	1.58719	−	0.577691i	0.610440	−	0.792063i	$-0.290993\pi$
$673$	41.1753	−	14.9866i	1.58719	−	0.577691i	0.976752	+	0.214372i	$0.0687704\pi$
$674$	10.6981	+	18.5297i	0.412076	+	0.713737i
$675$	5.68554	+	32.2443i	0.218837	+	1.24108i
$676$	4.93430	−	8.54645i	0.189781	−	0.328710i
$677$	1.08790	+	1.88429i	0.0418113	+	0.0724192i	0.886174	−	0.463353i	$-0.153354\pi$
$677$	1.08790	+	1.88429i	0.0418113	+	0.0724192i	−0.844362	+	0.535772i	$0.820021\pi$
$678$	15.4036	−	12.9252i	0.591573	−	0.496388i
$679$	−3.65244	+	20.7140i	−0.140168	+	0.794931i
$680$	−2.25665	+	3.90864i	−0.0865387	+	0.149889i
$681$	−63.0375	−	22.9438i	−2.41560	−	0.879207i
$682$	−5.89454	−	2.14544i	−0.225714	−	0.0821531i
$683$	−5.50558	−	31.2237i	−0.210665	−	1.19474i	−0.888272	−	0.459318i	$-0.848094\pi$
$683$	−5.50558	−	31.2237i	−0.210665	−	1.19474i	0.677607	−	0.735424i	$-0.263017\pi$
$684$	−4.37398	−	3.67021i	−0.167243	−	0.140334i
$685$	25.9484	+	21.7733i	0.991436	+	0.831913i
$686$	−7.77808	−	44.1117i	−0.296968	−	1.68419i
$687$	−8.43344	−	3.06952i	−0.321756	−	0.117110i
$688$	−4.11573	−	1.49800i	−0.156911	−	0.0571109i
$689$	−5.44097	+	9.42403i	−0.207284	+	0.359027i
$690$	0.203810	−	1.15586i	0.00775891	−	0.0440030i
$691$	19.5271	−	16.3852i	0.742847	−	0.623323i	−0.190754	−	0.981638i	$-0.561093\pi$
$691$	19.5271	−	16.3852i	0.742847	−	0.623323i	0.933601	+	0.358315i	$0.116649\pi$
$692$	−10.7226	−	18.5721i	−0.407612	−	0.706004i
$693$	−18.2586	+	31.6249i	−0.693588	+	1.20133i
$694$	−4.45169	−	25.2468i	−0.168984	−	0.958355i
$695$	2.04187	+	3.53662i	0.0774525	+	0.134152i
$696$	−16.4896	+	6.00173i	−0.625037	+	0.227495i
$697$	8.57813			0.324920
$698$	−14.5983	+	5.31334i	−0.552553	+	0.201113i
$699$	−12.8611	+	72.9390i	−0.486452	+	2.75880i
$700$	9.80531	+	8.22763i	0.370606	+	0.310975i
$701$	−13.7802	+	11.5629i	−0.520470	+	0.436726i	−0.864796	−	0.502124i	$-0.832552\pi$
$701$	−13.7802	+	11.5629i	−0.520470	+	0.436726i	0.344325	+	0.938850i	$0.388108\pi$
$702$	−21.8415			−0.824355
$703$	−2.79033	−	4.17272i	−0.105239	−	0.157377i
$704$	−1.09379			−0.0412238
$705$	−8.37216	+	7.02508i	−0.315314	+	0.264580i
$706$	−1.03899	−	0.871818i	−0.0391030	−	0.0328113i
$707$	3.67742	−	20.8557i	0.138304	−	0.784359i
$708$	26.1184	−	9.50632i	0.981590	−	0.357269i
$709$	27.8902			1.04744			0.523719	−	0.851891i	$-0.324544\pi$
$709$	27.8902			1.04744			0.523719	+	0.851891i	$0.324544\pi$
$710$	1.75447	−	0.638576i	0.0658442	−	0.0239653i
$711$	−7.45066	−	12.9049i	−0.279421	−	0.483972i
$712$	1.55870	+	8.83982i	0.0584147	+	0.331286i
$713$	−0.697487	+	1.20808i	−0.0261211	+	0.0452430i
$714$	−22.3838	−	38.7699i	−0.837692	−	1.45093i
$715$	−2.27166	+	1.90615i	−0.0849551	+	0.0712858i
$716$	2.00125	−	11.3497i	0.0747903	−	0.424157i
$717$	12.6578	−	21.9240i	0.472716	−	0.818768i
$718$	20.9690	+	7.63208i	0.782555	+	0.284827i
$719$	25.7753	+	9.38145i	0.961257	+	0.349869i	0.774526	−	0.632542i	$-0.217988\pi$
$719$	25.7753	+	9.38145i	0.961257	+	0.349869i	0.186731	+	0.982411i	$0.440211\pi$
$720$	1.84077	+	10.4395i	0.0686014	+	0.389058i
$721$	−46.7412	−	39.2205i	−1.74073	−	1.46065i
$722$	−14.0332	−	11.7752i	−0.522260	−	0.438228i
$723$	−10.0912	−	57.2303i	−0.375297	−	2.12842i
$724$	16.6973	+	6.07731i	0.620549	+	0.225861i
$725$	−13.8888	−	5.05511i	−0.515817	−	0.187742i
$726$	−15.4380	+	26.7394i	−0.572958	+	0.992392i
$727$	1.76832	−	10.0286i	0.0655832	−	0.371941i	−0.934298	−	0.356494i	$-0.883972\pi$
$727$	1.76832	−	10.0286i	0.0655832	−	0.371941i	0.999881	−	0.0154465i	$-0.00491696\pi$
$728$	−6.54097	+	5.48853i	−0.242425	+	0.203418i
$729$	−4.36265	−	7.55633i	−0.161580	−	0.279864i
$730$	−6.73673	+	11.6684i	−0.249338	+	0.431865i
$731$	2.24049	+	12.7064i	0.0828673	+	0.469964i
$732$	−18.5065	−	32.0543i	−0.684021	−	1.18476i
$733$	33.0879	−	12.0430i	1.22213	−	0.444819i	0.351234	−	0.936288i	$-0.385762\pi$
$733$	33.0879	−	12.0430i	1.22213	−	0.444819i	0.870895	+	0.491469i	$0.163540\pi$
$734$	7.22844			0.266807
$735$	73.8305	−	26.8721i	2.72328	−	0.991193i
$736$	−0.0422383	+	0.239545i	−0.00155693	+	0.00882976i
$737$	−7.52763	−	6.31643i	−0.277284	−	0.232669i
$738$	15.4341	−	12.9507i	0.568137	−	0.476723i
$739$	−8.78122			−0.323022			−0.161511	−	0.986871i	$-0.551637\pi$
$739$	−8.78122			−0.323022			−0.161511	+	0.986871i	$0.551637\pi$
$740$	−1.01117	+	9.26431i	−0.0371714	+	0.340563i
$741$	4.59920			0.168956
$742$	−22.7305	+	19.0731i	−0.834462	+	0.700197i
$743$	11.2952	+	9.47778i	0.414380	+	0.347706i	0.826020	−	0.563640i	$-0.190600\pi$
$743$	11.2952	+	9.47778i	0.414380	+	0.347706i	−0.411640	+	0.911346i	$0.635044\pi$
$744$	3.13642	−	17.7875i	0.114987	−	0.652122i
$745$	−8.83427	+	3.21541i	−0.323663	+	0.117804i
$746$	−11.7328			−0.429570
$747$	−33.1186	+	12.0542i	−1.21175	+	0.441040i
$748$	1.61107	+	2.79046i	0.0589067	+	0.102029i
$749$	−15.8024	−	89.6198i	−0.577407	−	3.27464i
$750$	−18.4630	+	31.9789i	−0.674175	+	1.16771i
$751$	17.4428	+	30.2118i	0.636496	+	1.10244i	0.986196	+	0.165582i	$0.0529503\pi$
$751$	17.4428	+	30.2118i	0.636496	+	1.10244i	−0.349700	+	0.936862i	$0.613716\pi$
$752$	1.73508	−	1.45590i	0.0632718	−	0.0530914i
$753$	−12.7397	+	72.2502i	−0.464259	+	2.63294i
$754$	4.92981	−	8.53868i	0.179533	−	0.310960i
$755$	0.628812	+	0.228869i	0.0228848	+	0.00832939i
$756$	−55.9651	−	20.3696i	−2.03543	−	0.740836i
$757$	9.03260	+	51.2264i	0.328296	+	1.86186i	0.485425	+	0.874278i	$0.338665\pi$
$757$	9.03260	+	51.2264i	0.328296	+	1.86186i	−0.157129	+	0.987578i	$0.550224\pi$
$758$	−2.12027	−	1.77912i	−0.0770117	−	0.0646205i
$759$	−0.641889	−	0.538609i	−0.0232991	−	0.0195503i
$760$	−0.219549	−	1.24513i	−0.00796389	−	0.0451655i
$761$	−5.60441	−	2.03984i	−0.203160	−	0.0739441i	0.238436	−	0.971158i	$-0.423365\pi$
$761$	−5.60441	−	2.03984i	−0.203160	−	0.0739441i	−0.441596	+	0.897214i	$0.645587\pi$
$762$	−14.0652	−	5.11931i	−0.509528	−	0.185453i
$763$	−20.3005	+	35.1616i	−0.734929	+	1.27293i
$764$	−4.49945	+	25.5176i	−0.162784	+	0.923195i
$765$	23.9218	−	20.0728i	0.864894	−	0.725732i
$766$	−9.73583	−	16.8629i	−0.351770	−	0.609283i
$767$	−7.80847	+	13.5247i	−0.281948	+	0.488348i
$768$	−0.546896	−	3.10160i	−0.0197344	−	0.111919i
$769$	−18.5451	−	32.1210i	−0.668753	−	1.15831i	−0.978253	−	0.207415i	$-0.933495\pi$
$769$	−18.5451	−	32.1210i	−0.668753	−	1.15831i	0.309500	−	0.950900i	$-0.399838\pi$
$770$	−7.59842	+	2.76560i	−0.273828	+	0.0996652i
$771$	13.4067			0.482830
$772$	−10.2454	+	3.72904i	−0.368742	+	0.134211i
$773$	−0.552148	+	3.13139i	−0.0198594	+	0.112628i	−0.993126	−	0.117050i	$-0.962656\pi$
$773$	−0.552148	+	3.13139i	−0.0198594	+	0.112628i	0.973267	+	0.229678i	$0.0737673\pi$
$774$	23.2145	+	19.4793i	0.834430	+	0.700170i
$775$	11.6539	−	9.77880i	0.418621	−	0.351265i
$776$	4.35907			0.156482
$777$	−74.5667	−	54.6326i	−2.67507	−	1.95993i
$778$	−2.34776			−0.0841713
$779$	−1.84083	+	1.54464i	−0.0659546	+	0.0553425i
$780$	−6.54097	−	5.48853i	−0.234204	−	0.196521i
$781$	0.231463	−	1.31269i	0.00828240	−	0.0469718i
$782$	0.673338	−	0.245075i	0.0240785	−	0.00876386i
$783$	68.7706			2.45766
$784$	−15.3009	+	5.56908i	−0.546461	+	0.198896i
$785$	−4.64329	−	8.04242i	−0.165726	−	0.287046i
$786$	−9.83701	−	55.7884i	−0.350874	−	1.98991i
$787$	2.62525	−	4.54707i	0.0935802	−	0.162086i	−0.815435	−	0.578849i	$-0.803502\pi$
$787$	2.62525	−	4.54707i	0.0935802	−	0.162086i	0.909015	+	0.416763i	$0.136836\pi$
$788$	3.22157	+	5.57992i	0.114764	+	0.198777i
$789$	16.6120	−	13.9391i	0.591403	−	0.496246i
$790$	0.572972	−	3.24949i	0.0203854	−	0.115612i
$791$	−15.4036	+	26.6799i	−0.547690	+	0.948627i
$792$	7.11157	+	2.58840i	0.252699	+	0.0919748i
$793$	19.5423	+	7.11283i	0.693968	+	0.252584i
$794$	0.395132	+	2.24091i	0.0140227	+	0.0795268i
$795$	−22.7305	−	19.0731i	−0.806167	−	0.676455i
$796$	14.4442	+	12.1201i	0.511961	+	0.429587i
$797$	4.62443	+	26.2264i	0.163806	+	0.928988i	0.950287	+	0.311375i	$0.100789\pi$
$797$	4.62443	+	26.2264i	0.163806	+	0.928988i	−0.786482	+	0.617614i	$0.788100\pi$
$798$	11.7847	+	4.28926i	0.417172	+	0.151838i
$799$	−6.26992	−	2.28206i	−0.221814	−	0.0807336i
$800$	1.32635	−	2.29731i	0.0468936	−	0.0812221i
$801$	10.7847	−	61.1630i	0.381058	−	2.16109i
$802$	13.4427	−	11.2798i	0.474679	−	0.398303i
$803$	4.80950	+	8.33030i	0.169724	+	0.293970i
$804$	14.1473	−	24.5039i	0.498938	−	0.864185i
$805$	0.312255	+	1.77089i	0.0110055	+	0.0624155i
$806$	5.07422	+	8.78881i	0.178732	+	0.309573i
$807$	28.6352	−	10.4224i	1.00801	−	0.366885i
$808$	−4.38889			−0.154401
$809$	14.5826	−	5.30762i	0.512696	−	0.186606i	−0.0726995	−	0.997354i	$-0.523161\pi$
$809$	14.5826	−	5.30762i	0.512696	−	0.186606i	0.585396	+	0.810748i	$0.300939\pi$
$810$	4.81962	−	27.3334i	0.169344	−	0.960399i
$811$	25.0817	+	21.0460i	0.880737	+	0.739026i	0.966330	−	0.257304i	$-0.0828343\pi$
$811$	25.0817	+	21.0460i	0.880737	+	0.739026i	−0.0855938	+	0.996330i	$0.527279\pi$
$812$	20.5950	−	17.2813i	0.722744	−	0.606454i
$813$	−24.1335			−0.846399
$814$	5.36694	+	3.93218i	0.188111	+	0.137823i
$815$	21.0432			0.737110
$816$	−7.10721	+	5.96366i	−0.248802	+	0.208770i
$817$	−2.76881	−	2.32331i	−0.0968684	−	0.0812822i
$818$	3.93815	−	22.3343i	0.137694	−	0.780902i
$819$	55.5161	−	20.2062i	1.93989	−	0.706063i
$820$	4.46135			0.155797
$821$	11.4303	−	4.16028i	0.398920	−	0.145195i	−0.134767	−	0.990877i	$-0.543028\pi$
$821$	11.4303	−	4.16028i	0.398920	−	0.145195i	0.533686	+	0.845682i	$0.320806\pi$
$822$	34.8158	+	60.3027i	1.21434	+	2.10330i
$823$	3.78732	+	21.4790i	0.132018	+	0.748709i	0.976890	+	0.213742i	$0.0685651\pi$
$823$	3.78732	+	21.4790i	0.132018	+	0.748709i	−0.844873	+	0.534968i	$0.820324\pi$
$824$	−6.32262	+	10.9511i	−0.220259	+	0.381500i
$825$	4.56907	+	7.91387i	0.159075	+	0.275525i
$826$	−32.6211	+	27.3724i	−1.13503	+	0.952406i
$827$	−2.00178	+	11.3526i	−0.0696086	+	0.394770i	0.930020	+	0.367509i	$0.119789\pi$
$827$	−2.00178	+	11.3526i	−0.0696086	+	0.394770i	−0.999628	+	0.0272604i	$0.991322\pi$
$828$	0.841495	−	1.45751i	0.0292440	−	0.0506520i
$829$	9.86084	+	3.58905i	0.342481	+	0.124653i	0.507534	−	0.861632i	$-0.330557\pi$
$829$	9.86084	+	3.58905i	0.342481	+	0.124653i	−0.165053	+	0.986285i	$0.552779\pi$
$830$	−7.33349	−	2.66917i	−0.254549	−	0.0926484i
$831$	−2.19829	−	12.4671i	−0.0762578	−	0.432479i
$832$	1.35558	+	1.13746i	0.0469961	+	0.0394344i
$833$	36.7448	+	30.8326i	1.27313	+	1.06829i
$834$	1.45773	+	8.26722i	0.0504772	+	0.286270i
$835$	−34.2934	−	12.4818i	−1.18677	−	0.431950i
$836$	−0.848200	−	0.308720i	−0.0293356	−	0.0106773i
$837$	−35.3926	+	61.3018i	−1.22335	+	2.11890i
$838$	3.26829	−	18.5354i	0.112901	−	0.640295i
$839$	−21.1557	+	17.7517i	−0.730375	+	0.612857i	−0.930234	−	0.366968i	$-0.880396\pi$
$839$	−21.1557	+	17.7517i	−0.730375	+	0.612857i	0.199859	+	0.979825i	$0.435952\pi$
$840$	−11.6414	−	20.1636i	−0.401668	−	0.695710i
$841$	−1.02209	+	1.77032i	−0.0352446	+	0.0610455i
$842$	−3.11292	−	17.6543i	−0.107278	−	0.608406i
$843$	−11.0219	−	19.0905i	−0.379615	−	0.657513i
$844$	1.32920	−	0.483788i	0.0457528	−	0.0166527i
$845$	−15.1196			−0.520129
$846$	−14.7264	+	5.35997i	−0.506304	+	0.184279i
$847$	8.21439	−	46.5861i	0.282250	−	1.60072i
$848$	4.71075	+	3.95279i	0.161768	+	0.135739i
$849$	11.3504	−	9.52412i	0.389545	−	0.326867i
$850$	−7.81447			−0.268034
$851$	1.06842	−	1.02354i	0.0366249	−	0.0350864i
$852$	3.83806			0.131490
$853$	15.8103	−	13.2664i	0.541334	−	0.454233i	−0.330660	−	0.943750i	$-0.607271\pi$
$853$	15.8103	−	13.2664i	0.541334	−	0.454233i	0.871994	+	0.489517i	$0.162827\pi$
$854$	43.4403	+	36.4508i	1.48650	+	1.24732i
$855$	−1.51907	+	8.61506i	−0.0519510	+	0.294629i
$856$	−17.7223	+	6.45039i	−0.605735	+	0.220470i
$857$	31.3189			1.06983			0.534917	−	0.844905i	$-0.320343\pi$
$857$	31.3189			1.06983			0.534917	+	0.844905i	$0.320343\pi$
$858$	−5.72829	+	2.08493i	−0.195561	+	0.0711782i
$859$	−22.7736	−	39.4450i	−0.777025	−	1.34585i	−0.933649	−	0.358189i	$-0.883394\pi$
$859$	−22.7736	−	39.4450i	−0.777025	−	1.34585i	0.156624	−	0.987658i	$-0.449939\pi$
$860$	1.16524	+	6.60840i	0.0397344	+	0.225345i
$861$	−22.1261	+	38.3235i	−0.754056	+	1.30606i
$862$	−6.13043	−	10.6182i	−0.208803	−	0.361658i
$863$	−38.4587	+	32.2707i	−1.30915	+	1.09851i	−0.320664	+	0.947193i	$0.603906\pi$
$863$	−38.4587	+	32.2707i	−1.30915	+	1.09851i	−0.988486	+	0.151314i	$0.951650\pi$
$864$	−2.14330	+	12.1553i	−0.0729166	+	0.413530i
$865$	−16.4280	+	28.4541i	−0.558567	+	0.967467i
$866$	−19.8412	−	7.22161i	−0.674232	−	0.245400i
$867$	−24.6290	−	8.96421i	−0.836444	−	0.304441i
$868$	4.80527	+	27.2521i	0.163102	+	0.924995i
$869$	−1.80455	−	1.51419i	−0.0612151	−	0.0513655i
$870$	20.5950	+	17.2813i	0.698237	+	0.585891i
$871$	2.76064	+	15.6564i	0.0935407	+	0.530496i
$872$	7.90687	+	2.87787i	0.267761	+	0.0974569i
$873$	−28.3417	−	10.3155i	−0.959220	−	0.349127i
$874$	−0.100365	+	0.173838i	−0.00339491	+	0.00588016i
$875$	9.82398	−	55.7146i	0.332111	−	1.88350i
$876$	−21.2170	+	17.8032i	−0.716856	+	0.601513i
$877$	−15.8566	−	27.4644i	−0.535439	−	0.927408i	−0.999142	−	0.0414174i	$-0.986813\pi$
$877$	−15.8566	−	27.4644i	−0.535439	−	0.927408i	0.463702	−	0.885991i	$-0.346521\pi$
$878$	12.0463	−	20.8648i	0.406543	−	0.704153i
$879$	7.78288	+	44.1389i	0.262510	+	1.48877i
$880$	0.837893	+	1.45127i	0.0282454	+	0.0489224i
$881$	−27.9167	+	10.1609i	−0.940538	+	0.342328i	−0.766378	−	0.642390i	$-0.777943\pi$
$881$	−27.9167	+	10.1609i	−0.940538	+	0.342328i	−0.174160	+	0.984717i	$0.555721\pi$
$882$	112.662			3.79352
$883$	−14.6477	+	5.33132i	−0.492934	+	0.179413i	−0.576513	−	0.817088i	$-0.695587\pi$
$883$	−14.6477	+	5.33132i	−0.492934	+	0.179413i	0.0835793	+	0.996501i	$0.473365\pi$
$884$	0.905213	−	5.13372i	0.0304456	−	0.172666i
$885$	−32.6211	−	27.3724i	−1.09655	−	0.920112i
$886$	14.7347	−	12.3639i	0.495021	−	0.415372i
$887$	−39.8038			−1.33648			−0.668240	−	0.743946i	$-0.732952\pi$
$887$	−39.8038			−1.33648			−0.668240	+	0.743946i	$0.732952\pi$
$888$	−8.46678	+	17.1848i	−0.284127	+	0.576684i
$889$	22.9321			0.769118
$890$	10.5349	−	8.83982i	0.353130	−	0.296312i
$891$	−15.1792	−	12.7368i	−0.508521	−	0.426700i
$892$	−2.11418	+	11.9901i	−0.0707878	+	0.401458i
$893$	1.75642	−	0.639285i	0.0587764	−	0.0213929i
$894$	−19.3257			−0.646348
$895$	−16.5921	+	6.03903i	−0.554612	+	0.201862i
$896$	2.41262	+	4.17878i	0.0805999	+	0.139603i
$897$	0.235403	+	1.33503i	0.00785986	+	0.0445755i
$898$	3.29367	−	5.70481i	0.109911	−	0.190372i
$899$	−15.9768	−	27.6726i	−0.532856	−	0.922933i
$900$	−14.0601	+	11.7978i	−0.468669	+	0.393260i
$901$	3.14570	−	17.8401i	0.104798	−	0.594341i
$902$	1.59253	−	2.75834i	0.0530253	−	0.0918426i
$903$	−62.5461	−	22.7649i	−2.08140	−	0.757569i
$904$	5.99957	+	2.18367i	0.199543	+	0.0726276i
$905$	−4.72730	−	26.8099i	−0.157141	−	0.891190i
$906$	1.05376	+	0.884206i	0.0350087	+	0.0293758i
$907$	34.4417	+	28.9000i	1.14362	+	0.959610i	0.999551	−	0.0299580i	$-0.00953737\pi$
$907$	34.4417	+	28.9000i	1.14362	+	0.959610i	0.144067	+	0.989568i	$0.453982\pi$
$908$	−3.69870	−	20.9763i	−0.122746	−	0.696124i
$909$	28.5355	+	10.3861i	0.946463	+	0.344484i
$910$	12.2930	+	4.47429i	0.407509	+	0.148321i
$911$	7.10212	−	12.3012i	0.235304	−	0.407558i	−0.724057	−	0.689740i	$-0.757725\pi$
$911$	7.10212	−	12.3012i	0.235304	−	0.407558i	0.959361	+	0.282182i	$0.0910582\pi$
$912$	0.451318	−	2.55955i	0.0149446	−	0.0847552i
$913$	−4.26805	+	3.58132i	−0.141252	+	0.118524i
$914$	14.4956	+	25.1071i	0.479472	+	0.830469i
$915$	−28.3537	+	49.1100i	−0.937343	+	1.62353i
$916$	−0.494828	−	2.80631i	−0.0163496	−	0.0927231i
$917$	43.3957	+	75.1636i	1.43305	+	2.48212i
$918$	34.1672	−	12.4358i	1.12769	−	0.410444i
$919$	46.2177			1.52458			0.762291	−	0.647235i	$-0.224075\pi$
$919$	46.2177			1.52458			0.762291	+	0.647235i	$0.224075\pi$
$920$	0.350192	−	0.127459i	0.0115455	−	0.00420221i
$921$	−0.438948	+	2.48940i	−0.0144638	+	0.0820284i
$922$	27.4638	+	23.0448i	0.904471	+	0.758941i
$923$	−1.65196	+	1.38616i	−0.0543750	+	0.0456261i
$924$	−16.6222			−0.546829
$925$	−14.7669	+	6.50404i	−0.485532	+	0.213851i
$926$	−18.5824			−0.610657
$927$	67.0234	−	56.2393i	2.20134	−	1.84714i
$928$	−4.26819	−	3.58144i	−0.140110	−	0.117567i
$929$	−9.34083	+	52.9745i	−0.306463	+	1.73804i	0.310076	+	0.950712i	$0.399645\pi$
$929$	−9.34083	+	52.9745i	−0.306463	+	1.73804i	−0.616539	+	0.787325i	$0.711466\pi$
$930$	−26.0036	+	9.46454i	−0.852692	+	0.310355i
$931$	−13.4372			−0.440387
$932$	−22.0983	+	8.04313i	−0.723855	+	0.263462i
$933$	−3.88869	−	6.73540i	−0.127310	−	0.220507i
$934$	−0.285869	−	1.62124i	−0.00935392	−	0.0530487i
$935$	2.46831	−	4.27524i	0.0807223	−	0.139815i
$936$	−6.12188	−	10.6034i	−0.200100	−	0.346583i
$937$	−30.8185	+	25.8598i	−1.00680	+	0.844803i	−0.987912	−	0.155018i	$-0.950456\pi$
$937$	−30.8185	+	25.8598i	−1.00680	+	0.844803i	−0.0188857	+	0.999822i	$0.506012\pi$
$938$	−7.52763	+	42.6913i	−0.245786	+	1.39392i
$939$	−28.0992	+	48.6692i	−0.916983	+	1.58826i
$940$	−3.26088	−	1.18686i	−0.106358	−	0.0387112i
$941$	1.65197	+	0.601267i	0.0538526	+	0.0196007i	0.368806	−	0.929506i	$-0.379767\pi$
$941$	1.65197	+	0.601267i	0.0538526	+	0.0196007i	−0.314953	+	0.949107i	$0.601989\pi$
$942$	−3.31495	−	18.8000i	−0.108007	−	0.612537i
$943$	−0.542591	−	0.455288i	−0.0176692	−	0.0148262i
$944$	6.76052	+	5.67275i	0.220036	+	0.184632i
$945$	15.8448	+	89.8601i	0.515430	+	2.92315i
$946$	4.50175	+	1.63850i	0.146365	+	0.0532724i
$947$	−47.7122	−	17.3658i	−1.55044	−	0.564313i	−0.581917	−	0.813248i	$-0.697697\pi$
$947$	−47.7122	−	17.3658i	−1.55044	−	0.564313i	−0.968520	+	0.248935i	$0.919920\pi$
$948$	3.39144	−	5.87414i	0.110149	−	0.190783i
$949$	2.70231	−	15.3256i	0.0877207	−	0.497489i
$950$	1.67695	−	1.40713i	0.0544075	−	0.0456533i
$951$	5.57382	+	9.65415i	0.180744	+	0.313057i
$952$	7.10721	−	12.3100i	0.230346	−	0.398971i
$953$	4.28306	+	24.2904i	0.138742	+	0.786845i	0.972181	+	0.234233i	$0.0752577\pi$
$953$	4.28306	+	24.2904i	0.138742	+	0.786845i	−0.833439	+	0.552612i	$0.813631\pi$
$954$	−21.2741	−	36.8478i	−0.688775	−	1.19299i
$955$	37.3043	−	13.5776i	1.20714	−	0.439362i
$956$	8.03813			0.259972
$957$	18.0362	−	6.56464i	0.583028	−	0.212205i
$958$	−5.91643	+	33.5538i	−0.191151	+	1.08407i
$959$	−81.7230	−	68.5738i	−2.63897	−	2.21436i
$960$	−3.69634	+	3.10160i	−0.119299	+	0.100104i
$961$	1.88962			0.0609556
$962$	−2.56227	−	10.4545i	−0.0826107	−	0.337067i
$963$	130.491			4.20500
$964$	14.1349	−	11.8606i	0.455256	−	0.382005i
$965$	12.7963	+	10.7373i	0.411926	+	0.345647i
$966$	−0.641889	+	3.64033i	−0.0206524	+	0.117126i
$967$	29.2331	−	10.6400i	0.940073	−	0.342158i	0.173878	−	0.984767i	$-0.444370\pi$
$967$	29.2331	−	10.6400i	0.940073	−	0.342158i	0.766194	+	0.642609i	$0.222148\pi$
$968$	−9.80362			−0.315100
$969$	−7.19464	+	2.61863i	−0.231125	+	0.0841226i
$970$	−3.33924	−	5.78374i	−0.107217	−	0.185705i
$971$	3.59887	+	20.4102i	0.115493	+	0.654995i	0.986505	+	0.163732i	$0.0523534\pi$
$971$	3.59887	+	20.4102i	0.115493	+	0.654995i	−0.871011	+	0.491263i	$0.836536\pi$
$972$	10.0133	−	17.3436i	0.321177	−	0.556296i
$973$	−6.43076	−	11.1384i	−0.206161	−	0.357081i
$974$	−23.8162	+	19.9842i	−0.763120	+	0.640334i
$975$	2.56722	−	14.5594i	0.0822169	−	0.466275i
$976$	5.87612	−	10.1777i	0.188090	−	0.325781i
$977$	25.9583	+	9.44805i	0.830480	+	0.302270i	0.722056	−	0.691835i	$-0.243197\pi$
$977$	25.9583	+	9.44805i	0.830480	+	0.302270i	0.108424	+	0.994105i	$0.465420\pi$
$978$	40.6488	+	14.7949i	1.29980	+	0.473090i
$979$	−1.70489	−	9.66893i	−0.0544886	−	0.309020i
$980$	19.1104	+	16.0355i	0.610459	+	0.512236i
$981$	−44.5983	−	37.4224i	−1.42391	−	1.19481i
$982$	6.08705	+	34.5214i	0.194246	+	1.10162i
$983$	29.9156	+	10.8884i	0.954159	+	0.347285i	0.771742	−	0.635936i	$-0.219386\pi$
$983$	29.9156	+	10.8884i	0.954159	+	0.347285i	0.182417	+	0.983221i	$0.441608\pi$
$984$	8.61792	+	3.13667i	0.274729	+	0.0999933i
$985$	4.93573	−	8.54894i	0.157265	−	0.272392i
$986$	−2.85017	+	16.1641i	−0.0907680	+	0.514771i
$987$	26.3677	−	22.1251i	0.839293	−	0.704251i
$988$	0.730160	+	1.26467i	0.0232295	+	0.0402346i
$989$	0.532682	−	0.922632i	0.0169383	−	0.0293380i
$990$	−2.01342	−	11.4187i	−0.0639906	−	0.362909i
$991$	−0.0451636	−	0.0782257i	−0.00143467	−	0.00248492i	0.865307	−	0.501242i	$-0.167123\pi$
$991$	−0.0451636	−	0.0782257i	−0.00143467	−	0.00248492i	−0.866742	+	0.498757i	$0.833790\pi$
$992$	5.38909	−	1.96147i	0.171104	−	0.0622767i
$993$	−12.0507			−0.382416
$994$	−5.52562	+	2.01116i	−0.175262	+	0.0637902i
$995$	5.01642	−	28.4495i	0.159031	−	0.901911i
$996$	−12.2894	−	10.3120i	−0.389404	−	0.326748i
$997$	35.7709	−	30.0153i	1.13288	−	0.950595i	0.133693	−	0.991023i	$-0.457316\pi$
$997$	35.7709	−	30.0153i	1.13288	−	0.950595i	0.999182	+	0.0404277i	$0.0128720\pi$
$998$	−35.1712			−1.11332
$999$	54.2147	−	51.9374i	1.71528	−	1.64323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.f.b.49.1	✓	12
3.2	odd	2		666.2.x.g.271.2		12
4.3	odd	2		592.2.bc.d.49.2		12
37.16	even	9		2738.2.a.t.1.1		6
37.21	even	18		2738.2.a.q.1.1		6
37.34	even	9	inner	74.2.f.b.71.1	yes	12
111.71	odd	18		666.2.x.g.145.2		12
148.71	odd	18		592.2.bc.d.145.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.49.1	✓	12	1.1	even	1	trivial
74.2.f.b.71.1	yes	12	37.34	even	9	inner
592.2.bc.d.49.2		12	4.3	odd	2
592.2.bc.d.145.2		12	148.71	odd	18
666.2.x.g.145.2		12	111.71	odd	18
666.2.x.g.271.2		12	3.2	odd	2
2738.2.a.q.1.1		6	37.21	even	18
2738.2.a.t.1.1		6	37.16	even	9

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-2.41262 - 2.02443i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.43969 + 0.524005i) q^{5} -3.14945 q^{6} +(4.53424 - 1.65033i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.20148 + 6.81391i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-2.41262 - 2.02443i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-1.43969 + 0.524005i) q^{5} -3.14945 q^{6} +(4.53424 - 1.65033i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.20148 + 6.81391i) q^{9} +(-0.766044 + 1.32683i) q^{10} +(0.546896 + 0.947252i) q^{11} +(-2.41262 + 2.02443i) q^{12} +(0.307284 - 1.74269i) q^{13} +(2.41262 - 4.17878i) q^{14} +(4.53424 + 1.65033i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.511542 + 2.90110i) q^{17} +(5.30028 + 4.44747i) q^{18} +(-0.632167 - 0.530451i) q^{19} +(0.266044 + 1.50881i) q^{20} +(-14.2804 - 5.19762i) q^{21} +(1.02783 + 0.374099i) q^{22} +(0.121620 - 0.210653i) q^{23} +(-0.546896 + 3.10160i) q^{24} +(-2.03209 + 1.70513i) q^{25} +(-0.884789 - 1.53250i) q^{26} +(6.17139 - 10.6892i) q^{27} +(-0.837893 - 4.75193i) q^{28} +(2.78587 + 4.82526i) q^{29} +(4.53424 - 1.65033i) q^{30} -5.73495 q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.598191 - 3.39251i) q^{33} +(2.25665 + 1.89356i) q^{34} +(-5.66313 + 4.75193i) q^{35} +6.91903 q^{36} +(5.84038 + 1.69999i) q^{37} -0.825235 q^{38} +(-4.26932 + 3.58238i) q^{39} +(1.17365 + 0.984808i) q^{40} +(0.505653 - 2.86770i) q^{41} +(-14.2804 + 5.19762i) q^{42} +4.37987 q^{43} +(1.02783 - 0.374099i) q^{44} +(-5.30028 - 9.18036i) q^{45} +(-0.0422383 - 0.239545i) q^{46} +(-1.13249 + 1.96153i) q^{47} +(1.57472 + 2.72750i) q^{48} +(12.4734 - 10.4664i) q^{49} +(-0.460637 + 2.61240i) q^{50} +(4.63890 - 8.03481i) q^{51} +(-1.66286 - 0.605232i) q^{52} +(-5.77859 - 2.10324i) q^{53} +(-2.14330 - 12.1553i) q^{54} +(-1.28373 - 1.07717i) q^{55} +(-3.69634 - 3.10160i) q^{56} +(0.451318 + 2.55955i) q^{57} +(5.23571 + 1.90564i) q^{58} +(-8.29301 - 3.01841i) q^{59} +(2.41262 - 4.17878i) q^{60} +(-2.04075 + 11.5737i) q^{61} +(-4.39322 + 3.68635i) q^{62} +(16.6930 + 28.9131i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.470787 + 2.66996i) q^{65} +(-1.72242 - 2.98332i) q^{66} +(-8.44220 + 3.07271i) q^{67} +2.94585 q^{68} +(-0.719875 + 0.262013i) q^{69} +(-1.28373 + 7.28038i) q^{70} +(-0.933535 - 0.783329i) q^{71} +(5.30028 - 4.44747i) q^{72} +8.79418 q^{73} +(5.56672 - 2.45185i) q^{74} +8.35455 q^{75} +(-0.632167 + 0.530451i) q^{76} +(4.04303 + 3.39251i) q^{77} +(-0.967776 + 5.48853i) q^{78} +(-2.02379 + 0.736599i) q^{79} +1.53209 q^{80} +(-17.0233 + 6.19599i) q^{81} +(-1.45597 - 2.52181i) q^{82} +(0.884528 + 5.01641i) q^{83} +(-7.59842 + 13.1608i) q^{84} +(-2.25665 - 3.90864i) q^{85} +(3.35518 - 2.81533i) q^{86} +(3.04716 - 17.2813i) q^{87} +(0.546896 - 0.947252i) q^{88} +(-8.43486 - 3.07004i) q^{89} +(-9.96127 - 3.62561i) q^{90} +(-1.48272 - 8.40891i) q^{91} +(-0.186333 - 0.156352i) q^{92} +(13.8362 + 11.6100i) q^{93} +(0.393310 + 2.23057i) q^{94} +(1.18809 + 0.432428i) q^{95} +(2.95951 + 1.07717i) q^{96} +(-2.17954 + 3.77507i) q^{97} +(2.82750 - 16.0355i) q^{98} +(-5.79741 + 4.86460i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 6 q^{30} + 42 q^{31} + 57 q^{33} - 3 q^{34} - 9 q^{35} + 24 q^{36} - 3 q^{37} + 42 q^{38} - 24 q^{39} + 12 q^{40} - 21 q^{41} - 33 q^{42} + 36 q^{43} - 3 q^{44} - 6 q^{45} + 3 q^{46} + 9 q^{47} - 12 q^{49} + 12 q^{50} + 3 q^{52} - 6 q^{53} - 27 q^{54} - 3 q^{56} - 36 q^{57} - 3 q^{58} - 6 q^{59} + 3 q^{60} - 18 q^{61} - 33 q^{62} + 36 q^{63} - 6 q^{64} + 3 q^{65} + 3 q^{66} - 27 q^{67} + 6 q^{68} - 12 q^{69} - 18 q^{71} + 6 q^{72} + 54 q^{73} + 3 q^{74} - 6 q^{75} - 3 q^{76} + 51 q^{77} - 33 q^{78} - 12 q^{79} - 36 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 3 q^{85} + 39 q^{87} + 3 q^{88} - 15 q^{89} - 15 q^{90} - 51 q^{91} - 6 q^{92} + 45 q^{93} - 12 q^{94} - 15 q^{95} + 6 q^{96} - 42 q^{97} + 51 q^{98} - 33 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

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