LMFDB - Embedded newform 378.2.w.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	378.25
Dual form			378.2.w.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-1.70460 + 0.307144i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.61773 - 0.952774i) q^{5} +(1.49675 - 0.871628i) q^{6} +(-1.47144 - 2.19883i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.81133 - 1.04711i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.70460 + 0.307144i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.61773 - 0.952774i) q^{5} +(1.49675 - 0.871628i) q^{6} +(-1.47144 - 2.19883i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.81133 - 1.04711i) q^{9} +2.78573 q^{10} +(1.49059 - 0.542529i) q^{11} +(-1.10837 + 1.33098i) q^{12} +(0.943280 + 5.34960i) q^{13} +(2.13475 + 1.56297i) q^{14} +(4.75482 + 0.820082i) q^{15} +(0.173648 - 0.984808i) q^{16} -6.34941 q^{17} +(-2.28365 + 1.94550i) q^{18} +6.63466 q^{19} +(-2.61773 + 0.952774i) q^{20} +(3.18357 + 3.29619i) q^{21} +(-1.21514 + 1.01962i) q^{22} +(1.38675 + 7.86465i) q^{23} +(0.586306 - 1.62980i) q^{24} +(2.11449 + 1.77427i) q^{25} +(-2.71607 - 4.70436i) q^{26} +(-4.47057 + 2.64839i) q^{27} +(-2.54057 - 0.738582i) q^{28} +(-0.0620252 + 0.351762i) q^{29} +(-4.74855 + 0.855618i) q^{30} +(-1.90948 + 1.60224i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-2.37422 + 1.38262i) q^{33} +(5.96649 - 2.17162i) q^{34} +(1.75683 + 7.15789i) q^{35} +(1.48053 - 2.60922i) q^{36} +(1.98208 - 3.43307i) q^{37} +(-6.23454 + 2.26919i) q^{38} +(-3.25101 - 8.82922i) q^{39} +(2.13399 - 1.79063i) q^{40} +(-0.0866442 - 0.491383i) q^{41} +(-4.11894 - 2.00856i) q^{42} +(9.13494 + 7.66513i) q^{43} +(0.793124 - 1.37373i) q^{44} +(-8.35694 + 0.0624984i) q^{45} +(-3.99299 - 6.91606i) q^{46} +(8.50255 + 7.13449i) q^{47} +(0.00647654 + 1.73204i) q^{48} +(-2.66974 + 6.47090i) q^{49} +(-2.59380 - 0.944067i) q^{50} +(10.8232 - 1.95018i) q^{51} +(4.16125 + 3.49171i) q^{52} +(3.02977 - 5.24771i) q^{53} +(3.29516 - 4.01770i) q^{54} -4.41885 q^{55} +(2.63996 - 0.174886i) q^{56} +(-11.3094 + 2.03779i) q^{57} +(-0.0620252 - 0.351762i) q^{58} +(1.65619 + 9.39272i) q^{59} +(4.16954 - 2.42812i) q^{60} +(-4.30173 - 3.60958i) q^{61} +(1.24632 - 2.15869i) q^{62} +(-6.43912 - 4.64087i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.62772 - 14.9025i) q^{65} +(1.75815 - 2.11127i) q^{66} +(-2.15056 - 0.782738i) q^{67} +(-4.86393 + 4.08132i) q^{68} +(-4.77943 - 12.9802i) q^{69} +(-4.09902 - 6.12535i) q^{70} +(0.0982486 + 0.170172i) q^{71} +(-0.498836 + 2.95824i) q^{72} +(3.32722 + 5.76291i) q^{73} +(-0.688371 + 3.90394i) q^{74} +(-4.14931 - 2.37496i) q^{75} +(5.08245 - 4.26468i) q^{76} +(-3.38624 - 2.47925i) q^{77} +(6.07472 + 7.18484i) q^{78} +(-2.43040 + 0.884592i) q^{79} +(-1.39286 + 2.41251i) q^{80} +(6.80710 - 5.88756i) q^{81} +(0.249482 + 0.432115i) q^{82} +(3.07726 - 17.4520i) q^{83} +(4.55751 + 0.478667i) q^{84} +(16.6210 + 6.04955i) q^{85} +(-11.2057 - 4.07853i) q^{86} +(-0.00231335 - 0.618665i) q^{87} +(-0.275449 + 1.56215i) q^{88} -1.32558 q^{89} +(7.83158 - 2.91697i) q^{90} +(10.3749 - 9.94573i) q^{91} +(6.11761 + 5.13328i) q^{92} +(2.76278 - 3.31766i) q^{93} +(-10.4299 - 3.79618i) q^{94} +(-17.3677 - 6.32134i) q^{95} +(-0.598478 - 1.62537i) q^{96} +(-6.75544 - 5.66849i) q^{97} +(0.295555 - 6.99376i) q^{98} +(3.62243 - 3.08604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.70460	+	0.307144i	−0.984152	+	0.177329i
$3$	−1.70460	+	0.307144i	−0.984152	+	0.177329i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−2.61773	−	0.952774i	−1.17068	−	0.426094i	−0.317780	−	0.948164i	$-0.602937\pi$
$5$	−2.61773	−	0.952774i	−1.17068	−	0.426094i	−0.852902	+	0.522071i	$0.825160\pi$
$6$	1.49675	−	0.871628i	0.611046	−	0.355841i
$7$	−1.47144	−	2.19883i	−0.556152	−	0.831081i
$7$	−1.47144	−	2.19883i	−0.556152	−	0.831081i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.81133	−	1.04711i	0.937109	−	0.349038i
$10$	2.78573			0.880924
$11$	1.49059	−	0.542529i	0.449429	−	0.163579i	−0.107383	−	0.994218i	$-0.534247\pi$
$11$	1.49059	−	0.542529i	0.449429	−	0.163579i	0.556811	+	0.830639i	$0.312025\pi$
$12$	−1.10837	+	1.33098i	−0.319959	+	0.384221i
$13$	0.943280	+	5.34960i	0.261619	+	1.48371i	0.778494	+	0.627652i	$0.215984\pi$
$13$	0.943280	+	5.34960i	0.261619	+	1.48371i	−0.516875	+	0.856061i	$0.672905\pi$
$14$	2.13475	+	1.56297i	0.570535	+	0.417720i
$15$	4.75482	+	0.820082i	1.22769	+	0.211744i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−6.34941			−1.53996			−0.769979	−	0.638070i	$-0.779733\pi$
$17$	−6.34941			−1.53996			−0.769979	+	0.638070i	$0.779733\pi$
$18$	−2.28365	+	1.94550i	−0.538261	+	0.458558i
$19$	6.63466			1.52210			0.761048	−	0.648696i	$-0.224685\pi$
$19$	6.63466			1.52210			0.761048	+	0.648696i	$0.224685\pi$
$20$	−2.61773	+	0.952774i	−0.585341	+	0.213047i
$21$	3.18357	+	3.29619i	0.694712	+	0.719288i
$22$	−1.21514	+	1.01962i	−0.259068	+	0.217384i
$23$	1.38675	+	7.86465i	0.289157	+	1.63989i	0.690046	+	0.723766i	$0.257590\pi$
$23$	1.38675	+	7.86465i	0.289157	+	1.63989i	−0.400888	+	0.916127i	$0.631299\pi$
$24$	0.586306	−	1.62980i	0.119679	−	0.332681i
$25$	2.11449	+	1.77427i	0.422898	+	0.354853i
$26$	−2.71607	−	4.70436i	−0.532664	−	0.922601i
$27$	−4.47057	+	2.64839i	−0.860362	+	0.509683i
$28$	−2.54057	−	0.738582i	−0.480123	−	0.139579i
$29$	−0.0620252	+	0.351762i	−0.0115178	+	0.0653206i	−0.990025	−	0.140892i	$-0.955003\pi$
$29$	−0.0620252	+	0.351762i	−0.0115178	+	0.0653206i	0.978507	+	0.206213i	$0.0661140\pi$
$30$	−4.74855	+	0.855618i	−0.866963	+	0.156214i
$31$	−1.90948	+	1.60224i	−0.342952	+	0.287771i	−0.797953	−	0.602720i	$-0.794083\pi$
$31$	−1.90948	+	1.60224i	−0.342952	+	0.287771i	0.455001	+	0.890491i	$0.349639\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−2.37422	+	1.38262i	−0.413298	+	0.240683i
$34$	5.96649	−	2.17162i	1.02324	−	0.372431i
$35$	1.75683	+	7.15789i	0.296959	+	1.20990i
$36$	1.48053	−	2.60922i	0.246755	−	0.434870i
$37$	1.98208	−	3.43307i	0.325853	−	0.564393i	−0.655832	−	0.754907i	$-0.727682\pi$
$37$	1.98208	−	3.43307i	0.325853	−	0.564393i	0.981685	+	0.190514i	$0.0610154\pi$
$38$	−6.23454	+	2.26919i	−1.01138	+	0.368111i
$39$	−3.25101	−	8.82922i	−0.520578	−	1.41381i
$40$	2.13399	−	1.79063i	0.337413	−	0.283123i
$41$	−0.0866442	−	0.491383i	−0.0135315	−	0.0767412i	0.977294	−	0.211887i	$-0.0679609\pi$
$41$	−0.0866442	−	0.491383i	−0.0135315	−	0.0767412i	−0.990826	+	0.135146i	$0.956850\pi$
$42$	−4.11894	−	2.00856i	−0.635567	−	0.309927i
$43$	9.13494	+	7.66513i	1.39307	+	1.16892i	0.964081	+	0.265609i	$0.0855732\pi$
$43$	9.13494	+	7.66513i	1.39307	+	1.16892i	0.428985	+	0.903312i	$0.358871\pi$
$44$	0.793124	−	1.37373i	0.119568	−	0.207098i
$45$	−8.35694	+	0.0624984i	−1.24578	+	0.00931671i
$46$	−3.99299	−	6.91606i	−0.588734	−	1.01972i
$47$	8.50255	+	7.13449i	1.24022	+	1.04067i	0.997506	+	0.0705754i	$0.0224836\pi$
$47$	8.50255	+	7.13449i	1.24022	+	1.04067i	0.242718	+	0.970097i	$0.421961\pi$
$48$	0.00647654	+	1.73204i	0.000934808	+	0.249998i
$49$	−2.66974	+	6.47090i	−0.381391	+	0.924414i
$50$	−2.59380	−	0.944067i	−0.366819	−	0.133511i
$51$	10.8232	−	1.95018i	1.51555	−	0.273080i
$52$	4.16125	+	3.49171i	0.577062	+	0.484213i
$53$	3.02977	−	5.24771i	0.416171	−	0.720829i	−0.579380	−	0.815058i	$-0.696705\pi$
$53$	3.02977	−	5.24771i	0.416171	−	0.720829i	0.995551	+	0.0942287i	$0.0300385\pi$
$54$	3.29516	−	4.01770i	0.448415	−	0.546740i
$55$	−4.41885			−0.595838
$56$	2.63996	−	0.174886i	0.352780	−	0.0233702i
$57$	−11.3094	+	2.03779i	−1.49797	+	0.269912i
$58$	−0.0620252	−	0.351762i	−0.00814430	−	0.0461886i
$59$	1.65619	+	9.39272i	0.215617	+	1.22283i	0.879832	+	0.475285i	$0.157655\pi$
$59$	1.65619	+	9.39272i	0.215617	+	1.22283i	−0.664214	+	0.747542i	$0.731234\pi$
$60$	4.16954	−	2.42812i	0.538285	−	0.313469i
$61$	−4.30173	−	3.60958i	−0.550780	−	0.462159i	0.324425	−	0.945911i	$-0.394829\pi$
$61$	−4.30173	−	3.60958i	−0.550780	−	0.462159i	−0.875205	+	0.483752i	$0.839274\pi$
$62$	1.24632	−	2.15869i	0.158283	−	0.274154i
$63$	−6.43912	−	4.64087i	−0.811253	−	0.584695i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.62772	−	14.9025i	0.325928	−	1.84843i
$66$	1.75815	−	2.11127i	0.216414	−	0.259879i
$67$	−2.15056	−	0.782738i	−0.262732	−	0.0956267i	0.207295	−	0.978278i	$-0.433534\pi$
$67$	−2.15056	−	0.782738i	−0.262732	−	0.0956267i	−0.470028	+	0.882652i	$0.655756\pi$
$68$	−4.86393	+	4.08132i	−0.589838	+	0.494933i
$69$	−4.77943	−	12.9802i	−0.575376	−	1.56263i
$70$	−4.09902	−	6.12535i	−0.489927	−	0.732119i
$71$	0.0982486	+	0.170172i	0.0116600	+	0.0201956i	0.871797	−	0.489868i	$-0.162955\pi$
$71$	0.0982486	+	0.170172i	0.0116600	+	0.0201956i	−0.860137	+	0.510064i	$0.829622\pi$
$72$	−0.498836	+	2.95824i	−0.0587883	+	0.348632i
$73$	3.32722	+	5.76291i	0.389421	+	0.674498i	0.992372	−	0.123281i	$-0.0393416\pi$
$73$	3.32722	+	5.76291i	0.389421	+	0.674498i	−0.602950	+	0.797779i	$0.706008\pi$
$74$	−0.688371	+	3.90394i	−0.0800214	+	0.453824i
$75$	−4.14931	−	2.37496i	−0.479121	−	0.274237i
$76$	5.08245	−	4.26468i	0.582996	−	0.489192i
$77$	−3.38624	−	2.47925i	−0.385897	−	0.282537i
$78$	6.07472	+	7.18484i	0.687827	+	0.813523i
$79$	−2.43040	+	0.884592i	−0.273441	+	0.0995244i	−0.475101	−	0.879931i	$-0.657589\pi$
$79$	−2.43040	+	0.884592i	−0.273441	+	0.0995244i	0.201660	+	0.979456i	$0.435366\pi$
$80$	−1.39286	+	2.41251i	−0.155727	+	0.269727i
$81$	6.80710	−	5.88756i	0.756345	−	0.654173i
$82$	0.249482	+	0.432115i	0.0275507	+	0.0477192i
$83$	3.07726	−	17.4520i	0.337773	−	1.91561i	−0.0601547	−	0.998189i	$-0.519159\pi$
$83$	3.07726	−	17.4520i	0.337773	−	1.91561i	0.397928	−	0.917417i	$-0.369729\pi$
$84$	4.55751	+	0.478667i	0.497265	+	0.0522269i
$85$	16.6210	+	6.04955i	1.80280	+	0.656166i
$86$	−11.2057	−	4.07853i	−1.20834	−	0.439799i
$87$	−0.00231335	−	0.618665i	−0.000248017	−	0.0663278i
$88$	−0.275449	+	1.56215i	−0.0293630	+	0.166526i
$89$	−1.32558			−0.140511			−0.0702556	−	0.997529i	$-0.522381\pi$
$89$	−1.32558			−0.140511			−0.0702556	+	0.997529i	$0.522381\pi$
$90$	7.83158	−	2.91697i	0.825521	−	0.307476i
$91$	10.3749	−	9.94573i	1.08759	−	1.04260i
$92$	6.11761	+	5.13328i	0.637805	+	0.535182i
$93$	2.76278	−	3.31766i	0.286486	−	0.344026i
$94$	−10.4299	−	3.79618i	−1.07576	−	0.391546i
$95$	−17.3677	−	6.32134i	−1.78189	−	0.648555i
$96$	−0.598478	−	1.62537i	−0.0610819	−	0.165889i
$97$	−6.75544	−	5.66849i	−0.685911	−	0.575548i	0.231816	−	0.972760i	$-0.425533\pi$
$97$	−6.75544	−	5.66849i	−0.685911	−	0.575548i	−0.917727	+	0.397212i	$0.869978\pi$
$98$	0.295555	−	6.99376i	0.0298556	−	0.706476i
$99$	3.62243	−	3.08604i	0.364068	−	0.310159i
$100$	2.76027			0.276027
$101$	−1.42499	+	8.08154i	−0.141792	+	0.804143i	0.828095	+	0.560588i	$0.189425\pi$
$101$	−1.42499	+	8.08154i	−0.141792	+	0.804143i	−0.969887	+	0.243555i	$0.921686\pi$
$102$	−9.50348	+	5.53432i	−0.940985	+	0.547979i
$103$	−7.61284	−	2.77085i	−0.750116	−	0.273020i	−0.0614613	−	0.998109i	$-0.519576\pi$
$103$	−7.61284	−	2.77085i	−0.750116	−	0.273020i	−0.688654	+	0.725090i	$0.741798\pi$
$104$	−5.10453	−	1.85790i	−0.500541	−	0.182182i
$105$	−5.19320	−	11.6617i	−0.506804	−	1.13807i
$106$	−1.05223	+	5.96748i	−0.102201	+	0.579613i
$107$	0.811790	+	1.40606i	0.0784787	+	0.135929i	0.902594	−	0.430493i	$-0.141660\pi$
$107$	0.811790	+	1.40606i	0.0784787	+	0.135929i	−0.824115	+	0.566422i	$0.808327\pi$
$108$	−1.72230	+	4.90241i	−0.165729	+	0.471735i
$109$	−4.63410	+	8.02650i	−0.443866	+	0.768799i	−0.997972	−	0.0636468i	$-0.979727\pi$
$109$	−4.63410	+	8.02650i	−0.443866	+	0.768799i	0.554106	+	0.832446i	$0.313060\pi$
$110$	4.15236	−	1.51134i	0.395912	−	0.144100i
$111$	−2.32422	+	6.46080i	−0.220605	+	0.613232i
$112$	−2.42094	+	1.06726i	−0.228757	+	0.100847i
$113$	1.67323	−	1.40401i	0.157404	−	0.132078i	−0.560684	−	0.828030i	$-0.689462\pi$
$113$	1.67323	−	1.40401i	0.157404	−	0.132078i	0.718088	+	0.695952i	$0.245017\pi$
$114$	9.93044	−	5.78296i	0.930071	−	0.541624i
$115$	3.86310	−	21.9088i	0.360236	−	2.04300i
$116$	0.178594	+	0.309334i	0.0165821	+	0.0287210i
$117$	8.25351	+	14.0518i	0.763037	+	1.29909i
$118$	−4.76881	−	8.25982i	−0.439004	−	0.760378i
$119$	9.34276	+	13.9613i	0.856449	+	1.27983i
$120$	−3.08762	+	3.70775i	−0.281860	+	0.338470i
$121$	−6.49898	+	5.45329i	−0.590816	+	0.495754i
$122$	5.27685	+	1.92062i	0.477744	+	0.173884i
$123$	0.298619	+	0.811000i	0.0269256	+	0.0731254i
$124$	−0.432843	+	2.45477i	−0.0388704	+	0.220445i
$125$	3.11964	+	5.40337i	0.279029	+	0.483292i
$126$	7.63807	+	2.15868i	0.680453	+	0.192311i
$127$	−6.62007	+	11.4663i	−0.587436	+	1.01747i	0.407131	+	0.913370i	$0.366529\pi$
$127$	−6.62007	+	11.4663i	−0.587436	+	1.01747i	−0.994567	+	0.104100i	$0.966804\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−17.9257	−	10.2602i	−1.57827	−	0.903364i
$130$	2.62772	+	14.9025i	0.230466	+	1.30704i
$131$	0.320367	+	1.81689i	0.0279906	+	0.158742i	0.995599	−	0.0937120i	$-0.0298733\pi$
$131$	0.320367	+	1.81689i	0.0279906	+	0.158742i	−0.967609	+	0.252455i	$0.918762\pi$
$132$	−0.930027	+	2.58527i	−0.0809485	+	0.225019i
$133$	−9.76250	−	14.5885i	−0.846516	−	1.26498i
$134$	2.28857			0.197703
$135$	14.2261	−	2.67332i	1.22438	−	0.230082i
$136$	3.17470	−	5.49875i	0.272229	−	0.471514i
$137$	4.42133	+	3.70994i	0.377740	+	0.316961i	0.811814	−	0.583916i	$-0.198480\pi$
$137$	4.42133	+	3.70994i	0.377740	+	0.316961i	−0.434075	+	0.900877i	$0.642925\pi$
$138$	8.93067	+	10.5627i	0.760229	+	0.899156i
$139$	17.9535	+	6.53454i	1.52280	+	0.554252i	0.961845	−	0.273597i	$-0.0882133\pi$
$139$	17.9535	+	6.53454i	1.52280	+	0.554252i	0.560951	+	0.827849i	$0.310436\pi$
$140$	5.94682	+	4.35399i	0.502598	+	0.367980i
$141$	−16.6848	−	9.54995i	−1.40511	−	0.804251i
$142$	−0.150526	−	0.126306i	−0.0126318	−	0.0105994i
$143$	4.30835	+	7.46229i	0.360283	+	0.624028i
$144$	−0.543024	−	2.95044i	−0.0452520	−	0.245870i
$145$	0.497515	−	0.861721i	0.0413164	−	0.0715620i
$146$	−5.09759	−	4.27739i	−0.421880	−	0.353999i
$147$	2.56334	−	11.8503i	0.211421	−	0.977395i
$148$	−0.688371	−	3.90394i	−0.0565837	−	0.320902i
$149$	−4.70806	+	3.95053i	−0.385699	+	0.323640i	−0.814935	−	0.579553i	$-0.803227\pi$
$149$	−4.70806	+	3.95053i	−0.385699	+	0.323640i	0.429236	+	0.903192i	$0.358783\pi$
$150$	4.71136	+	0.812588i	0.384681	+	0.0663475i
$151$	−3.14946	+	1.14631i	−0.256300	+	0.0932854i	−0.466975	−	0.884271i	$-0.654656\pi$
$151$	−3.14946	+	1.14631i	−0.256300	+	0.0932854i	0.210675	+	0.977556i	$0.432434\pi$
$152$	−3.31733	+	5.74579i	−0.269071	+	0.466045i
$153$	−17.8502	+	6.64855i	−1.44311	+	0.537504i
$154$	4.02998	+	1.17157i	0.324745	+	0.0944081i
$155$	6.52506	−	2.37493i	0.524105	−	0.190759i
$156$	−8.16573	−	4.67386i	−0.653782	−	0.374208i
$157$	1.29706	+	7.35600i	0.103517	+	0.587073i	0.991802	+	0.127781i	$0.0407856\pi$
$157$	1.29706	+	7.35600i	0.103517	+	0.587073i	−0.888286	+	0.459292i	$0.848103\pi$
$158$	1.98128	−	1.66249i	0.157622	−	0.132261i
$159$	−3.55275	+	9.87583i	−0.281751	+	0.783204i
$160$	0.483736	−	2.74340i	0.0382427	−	0.216885i
$161$	15.2525	−	14.6216i	1.20207	−	1.15234i
$162$	−4.38292	+	7.86066i	−0.344355	+	0.617592i
$163$	0.283776	+	0.491514i	0.0222271	+	0.0384984i	0.876925	−	0.480627i	$-0.159591\pi$
$163$	0.283776	+	0.491514i	0.0222271	+	0.0384984i	−0.854698	+	0.519126i	$0.826258\pi$
$164$	−0.382228	−	0.320728i	−0.0298470	−	0.0250446i
$165$	7.53238	−	1.35722i	0.586395	−	0.105660i
$166$	3.07726	+	17.4520i	0.238842	+	1.35454i
$167$	−8.03215	+	6.73978i	−0.621547	+	0.521540i	−0.898289	−	0.439404i	$-0.855190\pi$
$167$	−8.03215	+	6.73978i	−0.621547	+	0.521540i	0.276743	+	0.960944i	$0.410745\pi$
$168$	−4.44637	+	1.10896i	−0.343045	+	0.0855581i
$169$	−15.5125	+	5.64608i	−1.19327	+	0.434314i
$170$	−17.6877			−1.35658
$171$	18.6522	−	6.94725i	1.42637	−	0.531269i
$172$	11.9248			0.909259
$173$	0.241184	−	1.36782i	0.0183368	−	0.103993i	−0.974266	−	0.225403i	$-0.927630\pi$
$173$	0.241184	−	1.36782i	0.0183368	−	0.103993i	0.992603	+	0.121409i	$0.0387413\pi$
$174$	0.213770	+	0.580563i	0.0162058	+	0.0440124i
$175$	0.789977	−	7.26013i	0.0597166	−	0.548814i
$176$	−0.275449	−	1.56215i	−0.0207628	−	0.117751i
$177$	−5.70805	−	15.5021i	−0.429044	−	1.16521i
$178$	1.24564	−	0.453375i	0.0933645	−	0.0339819i
$179$	7.40325			0.553345			0.276673	−	0.960964i	$-0.410768\pi$
$179$	7.40325			0.553345			0.276673	+	0.960964i	$0.410768\pi$
$180$	−6.36162	+	5.41962i	−0.474167	+	0.403954i
$181$	−6.70877	+	11.6199i	−0.498659	+	0.863702i	−0.999999	−	0.00154822i	$-0.999507\pi$
$181$	−6.70877	+	11.6199i	−0.498659	+	0.863702i	0.501340	+	0.865250i	$0.332841\pi$
$182$	−6.34759	+	12.8944i	−0.470514	+	0.955793i
$183$	8.44139	+	4.83164i	0.624005	+	0.357165i
$184$	−7.50436	−	2.73136i	−0.553229	−	0.201359i
$185$	−8.45949	+	7.09836i	−0.621954	+	0.521882i
$186$	−1.46145	+	4.06251i	−0.107159	+	0.297878i
$187$	−9.46433	+	3.44474i	−0.692101	+	0.251904i
$188$	11.0993			0.809499
$189$	12.4015	+	5.93310i	0.902080	+	0.431570i
$190$	18.4823			1.34085
$191$	4.04269	−	1.47142i	0.292519	−	0.106468i	−0.191592	−	0.981475i	$-0.561365\pi$
$191$	4.04269	−	1.47142i	0.292519	−	0.106468i	0.484111	+	0.875006i	$0.339143\pi$
$192$	1.11829	+	1.32266i	0.0807059	+	0.0954544i
$193$	−14.7730	+	12.3961i	−1.06339	+	0.892287i	−0.994437	−	0.105333i	$-0.966409\pi$
$193$	−14.7730	+	12.3961i	−1.06339	+	0.892287i	−0.0689495	+	0.997620i	$0.521965\pi$
$194$	8.28677	+	3.01614i	0.594956	+	0.216546i
$195$	0.0980057	+	26.2099i	0.00701834	+	1.87693i
$196$	2.11428	+	6.67307i	0.151020	+	0.476648i
$197$	−6.79535	+	11.7699i	−0.484149	+	0.838570i	−0.999834	−	0.0182080i	$-0.994204\pi$
$197$	−6.79535	+	11.7699i	−0.484149	+	0.838570i	0.515686	+	0.856778i	$0.327537\pi$
$198$	−2.34849	+	4.13887i	−0.166900	+	0.294137i
$199$	−8.57078			−0.607566			−0.303783	−	0.952741i	$-0.598250\pi$
$199$	−8.57078			−0.607566			−0.303783	+	0.952741i	$0.598250\pi$
$200$	−2.59380	+	0.944067i	−0.183410	+	0.0667557i
$201$	3.90625	+	0.673727i	0.275526	+	0.0475210i
$202$	−1.42499	−	8.08154i	−0.100262	−	0.568615i
$203$	0.864733	−	0.381213i	0.0606923	−	0.0267559i
$204$	7.03750	−	8.45094i	0.492724	−	0.591684i
$205$	−0.241367	+	1.36886i	−0.0168578	+	0.0956053i
$206$	8.10142			0.564453
$207$	12.1338	+	20.6580i	0.843357	+	1.43583i
$208$	5.43213			0.376650
$209$	9.88953	−	3.59950i	0.684073	−	0.248982i
$210$	8.86856	+	9.18228i	0.611989	+	0.633638i
$211$	0.423929	−	0.355718i	0.0291844	−	0.0244887i	−0.628079	−	0.778150i	$-0.716158\pi$
$211$	0.423929	−	0.355718i	0.0291844	−	0.0244887i	0.657263	+	0.753661i	$0.271714\pi$
$212$	−1.05223	−	5.96748i	−0.0722673	−	0.409848i
$213$	−0.219742	−	0.259898i	−0.0150564	−	0.0178079i
$214$	−1.24373	−	1.04362i	−0.0850200	−	0.0713402i
$215$	−16.6096	−	28.7687i	−1.13277	−	1.96201i
$216$	−0.0582878	−	5.19583i	−0.00396598	−	0.353531i
$217$	6.33274	+	1.84102i	0.429894	+	0.124977i
$218$	1.60941	−	9.12740i	0.109003	−	0.618185i
$219$	−7.44162	−	8.80153i	−0.502858	−	0.594752i
$220$	−3.38504	+	2.84038i	−0.228219	+	0.191499i
$221$	−5.98926	−	33.9668i	−0.402882	−	2.28485i
$222$	−0.0256741	−	6.86609i	−0.00172313	−	0.460822i
$223$	−12.9524	+	4.71428i	−0.867355	+	0.315691i	−0.737096	−	0.675789i	$-0.763803\pi$
$223$	−12.9524	+	4.71428i	−0.867355	+	0.315691i	−0.130259	+	0.991480i	$0.541581\pi$
$224$	1.90992	−	1.83091i	0.127612	−	0.122333i
$225$	7.80237	+	2.77393i	0.520158	+	0.184929i
$226$	−1.09212	+	1.89161i	−0.0726470	+	0.125828i
$227$	13.4772	−	4.90529i	0.894511	−	0.325575i	0.146460	−	0.989217i	$-0.453212\pi$
$227$	13.4772	−	4.90529i	0.894511	−	0.325575i	0.748051	+	0.663641i	$0.230990\pi$
$228$	−7.35367	+	8.83061i	−0.487009	+	0.584822i
$229$	12.7199	−	10.6732i	0.840552	−	0.705307i	−0.117136	−	0.993116i	$-0.537371\pi$
$229$	12.7199	−	10.6732i	0.840552	−	0.705307i	0.957688	+	0.287809i	$0.0929268\pi$
$230$	3.86310	+	21.9088i	0.254726	+	1.44462i
$231$	6.53367	+	3.18607i	0.429884	+	0.209628i
$232$	−0.273622	−	0.229596i	−0.0179642	−	0.0150737i
$233$	5.49626	−	9.51981i	0.360072	−	0.623663i	−0.627900	−	0.778294i	$-0.716085\pi$
$233$	5.49626	−	9.51981i	0.360072	−	0.623663i	0.987972	+	0.154631i	$0.0494187\pi$
$234$	−12.5617	−	10.3815i	−0.821187	−	0.678658i
$235$	−15.4598	−	26.7772i	−1.00849	−	1.74675i
$236$	7.30624	+	6.13066i	0.475596	+	0.399072i
$237$	3.87116	−	2.25436i	0.251459	−	0.146436i
$238$	−13.5544	−	9.92391i	−0.878599	−	0.643271i
$239$	7.37903	+	2.68575i	0.477310	+	0.173727i	0.569461	−	0.822019i	$-0.307152\pi$
$239$	7.37903	+	2.68575i	0.477310	+	0.173727i	−0.0921511	+	0.995745i	$0.529374\pi$
$240$	1.63329	−	4.54017i	0.105428	−	0.293067i
$241$	−5.53356	−	4.64321i	−0.356448	−	0.299095i	0.446925	−	0.894571i	$-0.352519\pi$
$241$	−5.53356	−	4.64321i	−0.356448	−	0.299095i	−0.803373	+	0.595476i	$0.796963\pi$
$242$	4.24191	−	7.34720i	0.272680	−	0.472296i
$243$	−9.79507	+	12.1267i	−0.628354	+	0.777928i
$244$	−5.61551			−0.359496
$245$	13.1539	−	14.3954i	0.840375	−	0.919687i
$246$	−0.557988	−	0.659957i	−0.0355760	−	0.0420773i
$247$	6.25834	+	35.4928i	0.398209	+	2.25835i
$248$	−0.432843	−	2.45477i	−0.0274856	−	0.155878i
$249$	0.114772	+	30.6938i	0.00727339	+	1.94514i
$250$	−4.77956	−	4.01053i	−0.302286	−	0.253648i
$251$	13.8030	−	23.9075i	0.871237	−	1.50903i	0.0105180	−	0.999945i	$-0.496652\pi$
$251$	13.8030	−	23.9075i	0.871237	−	1.50903i	0.860718	−	0.509081i	$-0.170015\pi$
$252$	−7.91575	+	0.583873i	−0.498645	+	0.0367805i
$253$	6.33387	+	10.9706i	0.398207	+	0.689715i
$254$	2.29913	−	13.0390i	0.144260	−	0.818139i
$255$	−30.1903	−	5.20703i	−1.89059	−	0.326077i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−6.89934	+	5.78924i	−0.430369	+	0.361123i	−0.832091	−	0.554639i	$-0.812856\pi$
$257$	−6.89934	+	5.78924i	−0.430369	+	0.361123i	0.401722	+	0.915762i	$0.368412\pi$
$258$	20.3539	+	3.51052i	1.26718	+	0.218555i
$259$	−10.4653	+	0.693279i	−0.650280	+	0.0430783i
$260$	−7.56621	−	13.1051i	−0.469237	−	0.812742i
$261$	0.193962	+	1.05387i	0.0120060	+	0.0652326i
$262$	−0.922460	−	1.59775i	−0.0569897	−	0.0987091i
$263$	−0.185051	+	1.04948i	−0.0114107	+	0.0647135i	−0.989981	−	0.141198i	$-0.954905\pi$
$263$	−0.185051	+	1.04948i	−0.0114107	+	0.0647135i	0.978571	+	0.205911i	$0.0660158\pi$
$264$	−0.0102734	−	2.74744i	−0.000632284	−	0.169093i
$265$	−12.9310	+	10.8504i	−0.794345	+	0.666534i
$266$	14.1633	+	10.3697i	0.868408	+	0.635810i
$267$	2.25958	−	0.407143i	0.138284	−	0.0249168i
$268$	−2.15056	+	0.782738i	−0.131366	+	0.0478134i
$269$	−5.72064	+	9.90845i	−0.348794	+	0.604129i	−0.986035	−	0.166535i	$-0.946742\pi$
$269$	−5.72064	+	9.90845i	−0.348794	+	0.604129i	0.637242	+	0.770664i	$0.280075\pi$
$270$	−12.4538	+	7.37769i	−0.757914	+	0.448992i
$271$	0.632743	+	1.09594i	0.0384364	+	0.0665738i	0.884604	−	0.466344i	$-0.154429\pi$
$271$	0.632743	+	1.09594i	0.0384364	+	0.0665738i	−0.846167	+	0.532917i	$0.821096\pi$
$272$	−1.10256	+	6.25294i	−0.0668527	+	0.379140i
$273$	−14.6303	+	20.1401i	−0.885467	+	1.21893i
$274$	−5.42356	−	1.97402i	−0.327649	−	0.119255i
$275$	4.11442	+	1.49753i	0.248109	+	0.0903042i
$276$	−12.0047	−	6.87122i	−0.722600	−	0.413599i
$277$	−0.461722	+	2.61856i	−0.0277422	+	0.157334i	−0.995532	−	0.0944263i	$-0.969898\pi$
$277$	−0.461722	+	2.61856i	−0.0277422	+	0.157334i	0.967790	+	0.251760i	$0.0810094\pi$
$278$	−19.1057			−1.14588
$279$	−3.69043	+	6.50386i	−0.220940	+	0.389376i
$280$	−7.07733	−	2.05749i	−0.422951	−	0.122958i
$281$	15.1420	+	12.7057i	0.903297	+	0.757956i	0.970832	−	0.239761i	$-0.0770691\pi$
$281$	15.1420	+	12.7057i	0.903297	+	0.757956i	−0.0675354	+	0.997717i	$0.521514\pi$
$282$	18.9448	+	3.26749i	1.12815	+	0.194576i
$283$	11.9941	+	4.36550i	0.712976	+	0.259502i	0.672941	−	0.739696i	$-0.265031\pi$
$283$	11.9941	+	4.36550i	0.712976	+	0.259502i	0.0400349	+	0.999198i	$0.487253\pi$
$284$	0.184647	+	0.0672060i	0.0109568	+	0.00398794i
$285$	31.5466	+	5.44097i	1.86866	+	0.322295i
$286$	−6.60078	−	5.53871i	−0.390312	−	0.327511i
$287$	−0.952979	+	0.913557i	−0.0562526	+	0.0539255i
$288$	1.51939	+	2.58679i	0.0895308	+	0.152428i
$289$	23.3150			1.37147
$290$	−0.172785	+	0.979913i	−0.0101463	+	0.0575425i
$291$	13.2564	+	7.58761i	0.777102	+	0.444794i
$292$	6.25312	+	2.27595i	0.365936	+	0.133190i
$293$	20.1819	+	7.34561i	1.17904	+	0.429135i	0.855863	−	0.517203i	$-0.173027\pi$
$293$	20.1819	+	7.34561i	1.17904	+	0.429135i	0.323177	+	0.946339i	$0.395249\pi$
$294$	1.64428	+	12.0123i	0.0958966	+	0.700574i
$295$	4.61369	−	26.1655i	0.268619	−	1.52342i
$296$	1.98208	+	3.43307i	0.115206	+	0.199543i
$297$	−5.22694	+	6.37307i	−0.303298	+	0.369803i
$298$	3.07297	−	5.32253i	0.178012	−	0.308326i
$299$	−40.7647	+	14.8371i	−2.35748	+	0.858053i
$300$	−4.70516	+	0.847799i	−0.271652	+	0.0489477i
$301$	3.41283	−	31.3650i	0.196712	−	1.80785i
$302$	2.56747	−	2.15436i	0.147741	−	0.123969i
$303$	−0.0531478	−	14.2135i	−0.00305326	−	0.816542i
$304$	1.15210	−	6.53387i	0.0660773	−	0.374743i
$305$	7.82163	+	13.5475i	0.447865	+	0.775725i
$306$	14.4998	−	12.3527i	0.828899	−	0.706159i
$307$	−17.0932	−	29.6062i	−0.975558	−	1.68972i	−0.678081	−	0.734987i	$-0.737188\pi$
$307$	−17.0932	−	29.6062i	−0.975558	−	1.68972i	−0.297477	−	0.954729i	$-0.596145\pi$
$308$	−4.18764	+	0.277413i	−0.238613	+	0.0158071i
$309$	13.8279	+	2.38495i	0.786642	+	0.135675i
$310$	−5.31928	+	4.46340i	−0.302115	+	0.253504i
$311$	−8.17599	−	2.97582i	−0.463618	−	0.168743i	0.0996413	−	0.995023i	$-0.468230\pi$
$311$	−8.17599	−	2.97582i	−0.463618	−	0.168743i	−0.563259	+	0.826280i	$0.690453\pi$
$312$	9.27183	+	1.59915i	0.524914	+	0.0905340i
$313$	2.18873	−	12.4129i	0.123714	−	0.701618i	−0.858349	−	0.513066i	$-0.828510\pi$
$313$	2.18873	−	12.4129i	0.123714	−	0.701618i	0.982063	−	0.188552i	$-0.0603793\pi$
$314$	−3.73474	−	6.46876i	−0.210764	−	0.365053i
$315$	12.4342	+	18.2836i	0.700585	+	1.03016i
$316$	−1.29319	+	2.23987i	−0.0727474	+	0.126002i
$317$	−13.9130	−	11.6744i	−0.781434	−	0.655701i	0.162175	−	0.986762i	$-0.448149\pi$
$317$	−13.9130	−	11.6744i	−0.781434	−	0.655701i	−0.943609	+	0.331061i	$0.892593\pi$
$318$	−0.0392448	−	10.4954i	−0.00220074	−	0.588550i
$319$	0.0983873	+	0.557982i	0.00550863	+	0.0312410i
$320$	0.483736	+	2.74340i	0.0270417	+	0.153361i
$321$	−1.81564	−	2.14744i	−0.101339	−	0.119858i
$322$	−9.33182	+	18.9565i	−0.520042	+	1.05640i
$323$	−42.1262			−2.34396
$324$	1.43010	−	8.88565i	0.0794498	−	0.493647i
$325$	−7.49707	+	12.9853i	−0.415863	+	0.720295i
$326$	−0.434770	−	0.364815i	−0.0240797	−	0.0202053i
$327$	5.43401	−	15.1053i	0.300501	−	0.835326i
$328$	0.468873	+	0.170656i	0.0258892	+	0.00942288i
$329$	3.17657	−	29.1937i	0.175130	−	1.60950i
$330$	−6.61392	+	3.85160i	−0.364085	+	0.212023i
$331$	17.5556	+	14.7309i	0.964942	+	0.809682i	0.981750	−	0.190176i	$-0.0609060\pi$
$331$	17.5556	+	14.7309i	0.964942	+	0.809682i	−0.0168082	+	0.999859i	$0.505350\pi$
$332$	−8.86061	−	15.3470i	−0.486289	−	0.842278i
$333$	1.97747	−	11.7269i	0.108365	−	0.642633i
$334$	5.24262	−	9.08048i	0.286863	−	0.496862i
$335$	4.88379	+	4.09799i	0.266830	+	0.223897i
$336$	3.79893	−	2.56283i	0.207249	−	0.139814i
$337$	−5.11480	−	29.0075i	−0.278621	−	1.58014i	−0.727220	−	0.686404i	$-0.759188\pi$
$337$	−5.11480	−	29.0075i	−0.278621	−	1.58014i	0.448599	−	0.893733i	$-0.351923\pi$
$338$	12.6459	−	10.6112i	0.687846	−	0.577171i
$339$	−2.42096	+	2.90719i	−0.131488	+	0.157897i
$340$	16.6210	−	6.04955i	0.901401	−	0.328083i
$341$	−1.97698	+	3.42422i	−0.107059	+	0.185432i
$342$	−15.1512	+	12.9077i	−0.819285	+	0.697969i
$343$	18.1568	−	3.65122i	0.980374	−	0.197147i
$344$	−11.2057	+	4.07853i	−0.604169	+	0.219900i
$345$	0.144082	+	38.5322i	0.00775711	+	2.07450i
$346$	0.241184	+	1.36782i	0.0129661	+	0.0735345i
$347$	0.456269	−	0.382855i	0.0244938	−	0.0205527i	−0.630459	−	0.776223i	$-0.717133\pi$
$347$	0.456269	−	0.382855i	0.0244938	−	0.0205527i	0.654952	+	0.755670i	$0.272689\pi$
$348$	−0.399442	−	0.472438i	−0.0214123	−	0.0253253i
$349$	−2.79952	+	15.8769i	−0.149855	+	0.849870i	0.813485	+	0.581586i	$0.197568\pi$
$349$	−2.79952	+	15.8769i	−0.149855	+	0.849870i	−0.963340	+	0.268284i	$0.913544\pi$
$350$	1.74078	+	7.09248i	0.0930484	+	0.379109i
$351$	−18.3848	−	21.4176i	−0.981310	−	1.14319i
$352$	0.793124	+	1.37373i	0.0422737	+	0.0732201i
$353$	7.29346	+	6.11994i	0.388191	+	0.325731i	0.815908	−	0.578182i	$-0.196237\pi$
$353$	7.29346	+	6.11994i	0.388191	+	0.325731i	−0.427717	+	0.903913i	$0.640682\pi$
$354$	10.6659	+	12.6150i	0.566884	+	0.670479i
$355$	−0.0950528	−	0.539071i	−0.00504488	−	0.0286109i
$356$	−1.01545	+	0.852066i	−0.0538189	+	0.0451594i
$357$	−20.2138	−	20.9288i	−1.06983	−	1.10767i
$358$	−6.95678	+	2.53206i	−0.367677	+	0.133824i
$359$	5.98325			0.315784			0.157892	−	0.987456i	$-0.449530\pi$
$359$	5.98325			0.315784			0.157892	+	0.987456i	$0.449530\pi$
$360$	4.12435	−	7.26857i	0.217372	−	0.383088i
$361$	25.0187			1.31678
$362$	2.32993	−	13.2137i	0.122458	−	0.694496i
$363$	9.40322	−	11.2918i	0.493541	−	0.592666i
$364$	1.55465	−	14.2877i	0.0814859	−	0.748881i
$365$	−3.21899	−	18.2558i	−0.168490	−	0.955553i
$366$	−9.58483	−	1.65313i	−0.501007	−	0.0864107i
$367$	11.4038	−	4.15065i	0.595274	−	0.216662i	−0.0267733	−	0.999642i	$-0.508523\pi$
$367$	11.4038	−	4.15065i	0.595274	−	0.216662i	0.622048	+	0.782979i	$0.286301\pi$
$368$	7.98597			0.416298
$369$	−0.758119	−	1.29071i	−0.0394661	−	0.0671918i
$370$	5.52154	−	9.56359i	0.287051	−	0.497187i
$371$	−15.9970	+	1.05973i	−0.830521	+	0.0550185i
$372$	−0.0161437	−	4.31735i	−0.000837012	−	0.223844i
$373$	−30.0025	−	10.9200i	−1.55347	−	0.565417i	−0.584243	−	0.811579i	$-0.698608\pi$
$373$	−30.0025	−	10.9200i	−1.55347	−	0.565417i	−0.969229	+	0.246162i	$0.920831\pi$
$374$	7.71540	−	6.47399i	0.398954	−	0.334762i
$375$	−6.97735	−	8.25242i	−0.360309	−	0.426153i
$376$	−10.4299	+	3.79618i	−0.537882	+	0.195773i
$377$	−1.94030			−0.0999303
$378$	−13.6829	−	1.33371i	−0.703771	−	0.0685987i
$379$	−9.11400			−0.468154			−0.234077	−	0.972218i	$-0.575207\pi$
$379$	−9.11400			−0.468154			−0.234077	+	0.972218i	$0.575207\pi$
$380$	−17.3677	+	6.32134i	−0.890946	+	0.324278i
$381$	7.76278	−	21.5788i	0.397699	−	1.10551i
$382$	−3.29563	+	2.76537i	−0.168619	+	0.141488i
$383$	5.19462	+	1.89069i	0.265433	+	0.0966097i	0.471308	−	0.881969i	$-0.343782\pi$
$383$	5.19462	+	1.89069i	0.265433	+	0.0966097i	−0.205875	+	0.978578i	$0.566004\pi$
$384$	−1.50323	−	0.860411i	−0.0767113	−	0.0439076i
$385$	6.50207	+	9.71632i	0.331376	+	0.495190i
$386$	9.64242	−	16.7012i	0.490786	−	0.850066i
$387$	33.7076	+	11.9838i	1.71345	+	0.609173i
$388$	−8.81860			−0.447697
$389$	−10.3661	+	3.77296i	−0.525583	+	0.191297i	−0.591165	−	0.806551i	$-0.701332\pi$
$389$	−10.3661	+	3.77296i	−0.525583	+	0.191297i	0.0655819	+	0.997847i	$0.479110\pi$
$390$	−9.05643	−	24.5958i	−0.458590	−	1.24546i
$391$	−8.80504	−	49.9358i	−0.445290	−	2.52536i
$392$	−4.26909	−	5.54751i	−0.215622	−	0.280191i
$393$	−1.10414	−	2.99867i	−0.0556967	−	0.151263i
$394$	2.36000	−	13.3842i	0.118895	−	0.674287i
$395$	7.20493			0.362519
$396$	0.791277	−	4.69250i	0.0397632	−	0.235807i
$397$	11.6325			0.583820			0.291910	−	0.956446i	$-0.405709\pi$
$397$	11.6325			0.583820			0.291910	+	0.956446i	$0.405709\pi$
$398$	8.05389	−	2.93138i	0.403705	−	0.146937i
$399$	21.1219	+	21.8691i	1.05742	+	1.09482i
$400$	2.11449	−	1.77427i	0.105724	−	0.0887133i
$401$	−1.48903	−	8.44470i	−0.0743586	−	0.421708i	−0.999150	−	0.0412329i	$-0.986871\pi$
$401$	−1.48903	−	8.44470i	−0.0743586	−	0.421708i	0.924791	−	0.380476i	$-0.124240\pi$
$402$	−3.90110	+	0.702921i	−0.194569	+	0.0350585i
$403$	−10.3725	−	8.70358i	−0.516692	−	0.433556i
$404$	4.10310	+	7.10678i	0.204137	+	0.353576i
$405$	−23.4286	+	8.92638i	−1.16418	+	0.443555i
$406$	−0.682200	+	0.653979i	−0.0338570	+	0.0324565i
$407$	1.09193	−	6.19262i	0.0541248	−	0.306957i
$408$	−3.72270	+	10.3483i	−0.184301	+	0.512315i
$409$	24.7065	−	20.7312i	1.22166	−	1.02509i	0.222919	−	0.974837i	$-0.428441\pi$
$409$	24.7065	−	20.7312i	1.22166	−	1.02509i	0.998736	−	0.0502537i	$-0.0160030\pi$
$410$	−0.241367	−	1.36886i	−0.0119203	−	0.0676032i
$411$	−8.67608	−	4.96598i	−0.427960	−	0.244954i
$412$	−7.61284	+	2.77085i	−0.375058	+	0.136510i
$413$	18.2160	−	17.4625i	0.896353	−	0.859273i
$414$	−18.4675	−	15.2622i	−0.907627	−	0.750095i
$415$	−24.6832	+	42.7526i	−1.21165	+	2.09864i
$416$	−5.10453	+	1.85790i	−0.250270	+	0.0910909i
$417$	−32.6106	−	5.62448i	−1.59695	−	0.275432i
$418$	−8.06202	+	6.76484i	−0.394326	+	0.330879i
$419$	2.99828	+	17.0041i	0.146475	+	0.830703i	0.966171	+	0.257903i	$0.0830316\pi$
$419$	2.99828	+	17.0041i	0.146475	+	0.830703i	−0.819695	+	0.572800i	$0.805857\pi$
$420$	−11.4742	−	5.59530i	−0.559886	−	0.273022i
$421$	25.5691	+	21.4550i	1.24616	+	1.04565i	0.997016	+	0.0771891i	$0.0245945\pi$
$421$	25.5691	+	21.4550i	1.24616	+	1.04565i	0.249147	+	0.968466i	$0.419850\pi$
$422$	−0.276700	+	0.479258i	−0.0134695	+	0.0233299i
$423$	31.3741	+	11.1542i	1.52546	+	0.542337i
$424$	3.02977	+	5.24771i	0.147139	+	0.254852i
$425$	−13.4257	−	11.2655i	−0.651244	−	0.546459i
$426$	0.295380	+	0.169068i	0.0143112	+	0.00819138i
$427$	−1.60713	+	14.7701i	−0.0777746	+	0.714773i
$428$	1.52567	+	0.555297i	0.0737459	+	0.0268413i
$429$	−9.63601	−	11.3969i	−0.465231	−	0.550249i
$430$	25.4474	+	21.3529i	1.22718	+	1.02973i
$431$	−11.4752	+	19.8756i	−0.552741	+	0.957375i	0.445334	+	0.895364i	$0.353085\pi$
$431$	−11.4752	+	19.8756i	−0.552741	+	0.957375i	−0.998075	+	0.0620112i	$0.980249\pi$
$432$	1.83185	+	4.86254i	0.0881349	+	0.233949i
$433$	−15.4656			−0.743231			−0.371615	−	0.928387i	$-0.621196\pi$
$433$	−15.4656			−0.743231			−0.371615	+	0.928387i	$0.621196\pi$
$434$	−6.58049	+	0.435930i	−0.315874	+	0.0209253i
$435$	−0.583392	+	1.62170i	−0.0279715	+	0.0777545i
$436$	1.60941	+	9.12740i	0.0770766	+	0.437123i
$437$	9.20062	+	52.1793i	0.440125	+	2.49607i
$438$	10.0031	+	5.72555i	0.477968	+	0.273577i
$439$	−11.9673	−	10.0418i	−0.571168	−	0.479267i	0.310865	−	0.950454i	$-0.399381\pi$
$439$	−11.9673	−	10.0418i	−0.571168	−	0.479267i	−0.882033	+	0.471187i	$0.843826\pi$
$440$	2.20943	−	3.82684i	0.105330	−	0.182437i
$441$	−0.729734	+	20.9873i	−0.0347492	+	0.999396i
$442$	17.2454	+	29.8699i	0.820280	+	1.42077i
$443$	1.85572	−	10.5243i	0.0881678	−	0.500024i	−0.908460	−	0.417971i	$-0.862741\pi$
$443$	1.85572	−	10.5243i	0.0881678	−	0.500024i	0.996628	−	0.0820529i	$-0.0261476\pi$
$444$	2.37247	+	6.44323i	0.112592	+	0.305782i
$445$	3.47001	+	1.26298i	0.164494	+	0.0598709i
$446$	10.5589	−	8.85994i	0.499977	−	0.419531i
$447$	6.81198	−	8.18012i	0.322195	−	0.386906i
$448$	−1.16853	+	2.37372i	−0.0552077	+	0.112148i
$449$	6.55973	+	11.3618i	0.309573	+	0.536196i	0.978269	−	0.207340i	$-0.0664807\pi$
$449$	6.55973	+	11.3618i	0.309573	+	0.536196i	−0.668696	+	0.743536i	$0.733147\pi$
$450$	−8.28057	+	0.0619273i	−0.390350	+	0.00291928i
$451$	−0.395740	−	0.685442i	−0.0186347	−	0.0322762i
$452$	0.379291	−	2.15106i	0.0178403	−	0.101178i
$453$	5.01649	−	2.92134i	0.235695	−	0.137256i
$454$	−10.9867	+	9.21892i	−0.515631	+	0.432665i
$455$	−36.6347	+	16.1502i	−1.71746	+	0.757135i
$456$	3.88994	−	10.8132i	0.182163	−	0.506373i
$457$	1.93915	−	0.705792i	0.0907094	−	0.0330155i	−0.296267	−	0.955105i	$-0.595742\pi$
$457$	1.93915	−	0.705792i	0.0907094	−	0.0330155i	0.386976	+	0.922090i	$0.373520\pi$
$458$	−8.30230	+	14.3800i	−0.387941	+	0.671933i
$459$	28.3855	−	16.8157i	1.32492	−	0.784890i
$460$	−11.1234	−	19.2662i	−0.518630	−	0.898293i
$461$	−0.665461	+	3.77402i	−0.0309936	+	0.175774i	−0.996375	−	0.0850685i	$-0.972889\pi$
$461$	−0.665461	+	3.77402i	−0.0309936	+	0.175774i	0.965381	+	0.260842i	$0.0840002\pi$
$462$	−7.22934	−	0.759285i	−0.336339	−	0.0353251i
$463$	13.3257	+	4.85018i	0.619300	+	0.225407i	0.632568	−	0.774505i	$-0.282001\pi$
$463$	13.3257	+	4.85018i	0.619300	+	0.225407i	−0.0132675	+	0.999912i	$0.504223\pi$
$464$	0.335648	+	0.122166i	0.0155820	+	0.00567140i
$465$	−10.3932	+	6.05243i	−0.481972	+	0.280675i
$466$	−1.90883	+	10.8255i	−0.0884249	+	0.501483i
$467$	4.19968			0.194338			0.0971690	−	0.995268i	$-0.469021\pi$
$467$	4.19968			0.194338			0.0971690	+	0.995268i	$0.469021\pi$
$468$	15.3549	+	5.45902i	0.709778	+	0.252343i
$469$	1.44330	+	5.88047i	0.0666454	+	0.271535i
$470$	23.6858	+	19.8747i	1.09254	+	0.916753i
$471$	−4.47032	−	12.1407i	−0.205981	−	0.559412i
$472$	−8.96243	−	3.26206i	−0.412529	−	0.150148i
$473$	17.7750	+	6.46956i	0.817294	+	0.297471i
$474$	−2.86666	+	3.44242i	−0.131670	+	0.158115i
$475$	14.0289	+	11.7717i	0.643691	+	0.540121i
$476$	16.1311	+	4.68955i	0.739368	+	0.214945i
$477$	3.02271	−	17.9255i	0.138401	−	0.820755i
$478$	−7.85260			−0.359169
$479$	−7.56592	+	42.9084i	−0.345696	+	1.96054i	−0.0784009	+	0.996922i	$0.524981\pi$
$479$	−7.56592	+	42.9084i	−0.345696	+	1.96054i	−0.267295	+	0.963615i	$0.586130\pi$
$480$	0.0180419	+	4.82499i	0.000823495	+	0.220229i
$481$	20.2352	+	7.36502i	0.922647	+	0.335816i
$482$	6.78791	+	2.47060i	0.309181	+	0.112533i
$483$	−21.5086	+	29.6087i	−0.978673	+	1.34724i
$484$	−1.47320	+	8.35493i	−0.0669636	+	0.379769i
$485$	12.2831	+	21.2750i	0.557747	+	0.966046i
$486$	5.05678	−	14.7455i	0.229380	−	0.668868i
$487$	7.51091	−	13.0093i	0.340352	−	0.589507i	−0.644146	−	0.764902i	$-0.722787\pi$
$487$	7.51091	−	13.0093i	0.340352	−	0.589507i	0.984498	+	0.175396i	$0.0561205\pi$
$488$	5.27685	−	1.92062i	0.238872	−	0.0869422i
$489$	−0.634690	−	0.750676i	−0.0287017	−	0.0339467i
$490$	−7.43716	+	18.0261i	−0.335976	+	0.814338i
$491$	−21.7701	+	18.2672i	−0.982469	+	0.824389i	−0.984460	−	0.175609i	$-0.943811\pi$
$491$	−21.7701	+	18.2672i	−0.982469	+	0.824389i	0.00199135	+	0.999998i	$0.499366\pi$
$492$	0.750056	+	0.429314i	0.0338151	+	0.0193550i
$493$	0.393823	−	2.23348i	0.0177369	−	0.100591i
$494$	−18.0202	−	31.2119i	−0.810766	−	1.40429i
$495$	−12.4228	+	4.62704i	−0.558365	+	0.207970i
$496$	1.24632	+	2.15869i	0.0559615	+	0.0969282i
$497$	0.229612	−	0.466429i	0.0102995	−	0.0209222i
$498$	−10.6058	−	28.8035i	−0.475256	−	1.29072i
$499$	−13.4601	+	11.2944i	−0.602557	+	0.505605i	−0.892266	−	0.451509i	$-0.850886\pi$
$499$	−13.4601	+	11.2944i	−0.602557	+	0.505605i	0.289710	+	0.957115i	$0.406441\pi$
$500$	5.86300	+	2.13396i	0.262201	+	0.0954335i
$501$	11.6215	−	13.9557i	0.519212	−	0.623493i
$502$	−4.79373	+	27.1866i	−0.213954	+	1.21340i
$503$	−12.3330	−	21.3614i	−0.549902	−	0.952457i	−0.998281	−	0.0586140i	$-0.981332\pi$
$503$	−12.3330	−	21.3614i	−0.549902	−	0.952457i	0.448379	−	0.893843i	$-0.352001\pi$
$504$	7.23868	−	3.25601i	0.322436	−	0.145034i
$505$	11.4301	−	19.7975i	0.508634	−	0.880979i
$506$	−9.70405	−	8.14266i	−0.431398	−	0.361986i
$507$	24.7084	−	14.3889i	1.09734	−	0.639032i
$508$	2.29913	+	13.0390i	0.102007	+	0.578512i
$509$	−4.18884	−	23.7561i	−0.185667	−	1.05297i	−0.925096	−	0.379734i	$-0.876015\pi$
$509$	−4.18884	−	23.7561i	−0.185667	−	1.05297i	0.739429	−	0.673235i	$-0.235096\pi$
$510$	30.1505	−	5.43266i	1.33509	−	0.240562i
$511$	7.77588	−	15.7958i	0.343985	−	0.698764i
$512$	1.00000			0.0441942
$513$	−29.6607	+	17.5712i	−1.30955	+	0.775787i
$514$	4.50323	−	7.79982i	0.198629	−	0.344035i
$515$	17.2883	+	14.5066i	0.761816	+	0.639239i
$516$	−20.3271	+	3.66263i	−0.894849	+	0.161238i
$517$	16.5445	+	6.02169i	0.727624	+	0.264834i
$518$	9.59702	−	4.23080i	0.421669	−	0.185891i
$519$	0.00899540	+	2.40566i	0.000394854	+	0.105597i
$520$	11.5921	+	9.72694i	0.508348	+	0.426554i
$521$	−3.76199	−	6.51596i	−0.164816	−	0.285469i	0.771774	−	0.635897i	$-0.219370\pi$
$521$	−3.76199	−	6.51596i	−0.164816	−	0.285469i	−0.936590	+	0.350427i	$0.886036\pi$
$522$	−0.542708	−	0.923971i	−0.0237537	−	0.0404411i
$523$	−12.3031	+	21.3095i	−0.537975	+	0.931800i	0.461038	+	0.887380i	$0.347477\pi$
$523$	−12.3031	+	21.3095i	−0.537975	+	0.931800i	−0.999013	+	0.0444197i	$0.985856\pi$
$524$	1.41329	+	1.18589i	0.0617399	+	0.0518059i
$525$	0.883308	+	12.6183i	0.0385507	+	0.550706i
$526$	−0.185051	−	1.04948i	−0.00806861	−	0.0457594i
$527$	12.1240	−	10.1733i	0.528131	−	0.443155i
$528$	0.949335	+	2.57824i	0.0413145	+	0.112203i
$529$	−38.3167	+	13.9461i	−1.66594	+	0.606354i
$530$	8.44011	−	14.6187i	0.366615	−	0.634996i
$531$	14.4913	+	24.6718i	0.628870	+	1.07066i
$532$	−16.8558	−	4.90024i	−0.730793	−	0.212452i
$533$	2.54698	−	0.927024i	0.110322	−	0.0401539i
$534$	−1.98406	+	1.15541i	−0.0858588	+	0.0499996i
$535$	−0.785385	−	4.45414i	−0.0339551	−	0.192569i
$536$	1.75315	−	1.47107i	0.0757245	−	0.0635404i
$537$	−12.6196	+	2.27386i	−0.544575	+	0.0981243i
$538$	1.98676	−	11.2675i	0.0856552	−	0.485775i
$539$	−0.468824	+	11.0938i	−0.0201937	+	0.477845i
$540$	9.17942	−	11.1922i	0.395019	−	0.481636i
$541$	19.9879	+	34.6201i	0.859347	+	1.48843i	0.872552	+	0.488520i	$0.162463\pi$
$541$	19.9879	+	34.6201i	0.859347	+	1.48843i	−0.0132052	+	0.999913i	$0.504203\pi$
$542$	−0.969419	−	0.813439i	−0.0416401	−	0.0349402i
$543$	7.86678	−	21.8679i	0.337596	−	0.938441i
$544$	−1.10256	−	6.25294i	−0.0472720	−	0.268093i
$545$	19.7783	−	16.5959i	0.847207	−	0.710891i
$546$	6.85968	−	23.9293i	0.293567	−	1.02408i
$547$	−6.60822	+	2.40520i	−0.282547	+	0.102839i	−0.479406	−	0.877593i	$-0.659148\pi$
$547$	−6.60822	+	2.40520i	−0.282547	+	0.102839i	0.196859	+	0.980432i	$0.436926\pi$
$548$	5.77164			0.246552
$549$	−15.8732	−	5.64330i	−0.677452	−	0.240850i
$550$	−4.37847			−0.186699
$551$	−0.411516	+	2.33382i	−0.0175312	+	0.0994242i
$552$	13.6309	+	2.35097i	0.580168	+	0.100064i
$553$	5.52125	+	4.04241i	0.234787	+	0.171901i
$554$	−0.461722	−	2.61856i	−0.0196167	−	0.111252i
$555$	12.2398	−	14.6981i	0.519552	−	0.623901i
$556$	17.9535	−	6.53454i	0.761398	−	0.277126i
$557$	−10.1099			−0.428372			−0.214186	−	0.976793i	$-0.568710\pi$
$557$	−10.1099			−0.428372			−0.214186	+	0.976793i	$0.568710\pi$
$558$	1.24342	−	7.37383i	0.0526381	−	0.312159i
$559$	−32.3886	+	56.0987i	−1.36989	+	2.37272i
$560$	7.35422	−	0.487186i	0.310772	−	0.0205874i
$561$	15.0749	−	8.77881i	0.636462	−	0.370642i
$562$	−18.5744	−	6.76054i	−0.783515	−	0.285176i
$563$	8.12820	−	6.82037i	0.342563	−	0.287444i	−0.455233	−	0.890373i	$-0.650444\pi$
$563$	8.12820	−	6.82037i	0.342563	−	0.287444i	0.797796	+	0.602928i	$0.205999\pi$
$564$	−18.9199	+	3.40908i	−0.796670	+	0.143548i
$565$	−5.71776	+	2.08109i	−0.240548	+	0.0875523i
$566$	−12.7639			−0.536505
$567$	−22.9620	−	6.30451i	−0.964313	−	0.264765i
$568$	−0.196497			−0.00824484
$569$	−17.0912	+	6.22068i	−0.716500	+	0.260785i	−0.674439	−	0.738330i	$-0.735614\pi$
$569$	−17.0912	+	6.22068i	−0.716500	+	0.260785i	−0.0420606	+	0.999115i	$0.513392\pi$
$570$	−31.5050	+	5.67673i	−1.31960	+	0.237772i
$571$	35.0227	−	29.3875i	1.46565	−	1.22983i	0.545597	−	0.838048i	$-0.316303\pi$
$571$	35.0227	−	29.3875i	1.46565	−	1.22983i	0.920058	−	0.391782i	$-0.128141\pi$
$572$	8.09706	+	2.94709i	0.338555	+	0.123224i
$573$	−6.43924	+	3.74987i	−0.269003	+	0.156653i
$574$	0.583052	−	1.18440i	0.0243361	−	0.0494359i
$575$	−11.0217	+	19.0902i	−0.459637	+	0.796115i
$576$	−2.31249	−	1.91112i	−0.0963538	−	0.0796301i
$577$	19.1058			0.795385			0.397693	−	0.917519i	$-0.369811\pi$
$577$	19.1058			0.795385			0.397693	+	0.917519i	$0.369811\pi$
$578$	−21.9089	+	7.97418i	−0.911290	+	0.331682i
$579$	21.3748	−	25.6678i	0.888305	−	1.06672i
$580$	−0.172785	−	0.979913i	−0.00717451	−	0.0406887i
$581$	−42.9020	+	18.9132i	−1.77988	+	0.784650i
$582$	−15.0520	−	2.59608i	−0.623926	−	0.107611i
$583$	1.66909	−	9.46591i	0.0691268	−	0.392038i
$584$	−6.65444			−0.275363
$585$	−8.21728	−	44.6474i	−0.339743	−	1.84594i
$586$	−21.4771			−0.887212
$587$	29.0244	−	10.5640i	1.19797	−	0.436024i	0.335453	−	0.942057i	$-0.391111\pi$
$587$	29.0244	−	10.5640i	1.19797	−	0.436024i	0.862514	+	0.506033i	$0.168889\pi$
$588$	−5.65358	−	10.7255i	−0.233150	−	0.442313i
$589$	−12.6687	+	10.6303i	−0.522006	+	0.438015i
$590$	4.61369	+	26.1655i	0.189943	+	1.07722i
$591$	7.96831	−	22.1501i	0.327772	−	0.911134i
$592$	−3.03673	−	2.54812i	−0.124809	−	0.104727i
$593$	9.09010	+	15.7445i	0.373286	+	0.646550i	0.990069	−	0.140583i	$-0.0448978\pi$
$593$	9.09010	+	15.7445i	0.373286	+	0.646550i	−0.616783	+	0.787133i	$0.711564\pi$
$594$	2.73200	−	7.77645i	0.112095	−	0.319071i
$595$	−11.1548	−	45.4484i	−0.457304	−	1.86320i
$596$	−1.06723	+	6.05256i	−0.0437154	+	0.247923i
$597$	14.6097	−	2.63246i	0.597937	−	0.107739i
$598$	33.2317	−	27.8847i	1.35894	−	1.14029i
$599$	0.984888	+	5.58558i	0.0402414	+	0.228220i	0.998295	−	0.0583683i	$-0.0185898\pi$
$599$	0.984888	+	5.58558i	0.0402414	+	0.228220i	−0.958054	+	0.286589i	$0.907479\pi$
$600$	4.13144	−	2.40593i	0.168665	−	0.0982216i
$601$	35.0446	−	12.7552i	1.42950	−	0.520295i	0.492711	−	0.870193i	$-0.336006\pi$
$601$	35.0446	−	12.7552i	1.42950	−	0.520295i	0.936788	+	0.349898i	$0.113784\pi$
$602$	7.52044	+	30.6407i	0.306510	+	1.24882i
$603$	−6.86553	+	0.0513447i	−0.279586	+	0.00209092i
$604$	−1.67579	+	2.90256i	−0.0681871	+	0.118104i
$605$	22.2083	−	8.08316i	0.902896	−	0.328627i
$606$	4.91123	+	13.3381i	0.199505	+	0.541824i
$607$	19.8872	−	16.6874i	0.807197	−	0.677319i	−0.142740	−	0.989760i	$-0.545591\pi$
$607$	19.8872	−	16.6874i	0.807197	−	0.677319i	0.949937	+	0.312441i	$0.101147\pi$
$608$	1.15210	+	6.53387i	0.0467237	+	0.264983i
$609$	−1.35694	+	0.915414i	−0.0549858	+	0.0370944i
$610$	−11.9834	−	10.0553i	−0.485195	−	0.407127i
$611$	−30.1464	+	52.2151i	−1.21959	+	2.11240i
$612$	−9.40048	+	16.5670i	−0.379992	+	0.669681i
$613$	−1.95987	−	3.39459i	−0.0791583	−	0.137106i	0.823729	−	0.566984i	$-0.191890\pi$
$613$	−1.95987	−	3.39459i	−0.0791583	−	0.137106i	−0.902887	+	0.429878i	$0.858557\pi$
$614$	26.1882	+	21.9745i	1.05687	+	0.886820i
$615$	−0.00900224	−	2.40749i	−0.000363005	−	0.0970795i
$616$	3.84021	−	1.69294i	0.154727	−	0.0682105i
$617$	−34.4264	−	12.5302i	−1.38595	−	0.504446i	−0.461976	−	0.886892i	$-0.652859\pi$
$617$	−34.4264	−	12.5302i	−1.38595	−	0.504446i	−0.923978	+	0.382446i	$0.875082\pi$
$618$	−13.8097	+	2.48830i	−0.555507	+	0.100094i
$619$	37.8419	+	31.7531i	1.52099	+	1.27627i	0.837713	+	0.546111i	$0.183892\pi$
$619$	37.8419	+	31.7531i	1.52099	+	1.27627i	0.683282	+	0.730155i	$0.260552\pi$
$620$	3.47191	−	6.01353i	0.139435	−	0.241509i
$621$	−27.0282	−	31.4868i	−1.08461	−	1.26352i
$622$	8.70071			0.348867
$623$	1.95051	+	2.91473i	0.0781455	+	0.116776i
$624$	−9.25961	+	1.66844i	−0.370681	+	0.0667912i
$625$	−5.41474	−	30.7085i	−0.216590	−	1.22834i
$626$	2.18873	+	12.4129i	0.0874791	+	0.496119i
$627$	−15.7521	+	9.17321i	−0.629080	+	0.366343i
$628$	5.72195	+	4.80129i	0.228331	+	0.191592i
$629$	−12.5851	+	21.7980i	−0.501799	+	0.869141i
$630$	−17.9376	−	12.9282i	−0.714652	−	0.515072i
$631$	−10.3646	−	17.9519i	−0.412606	−	0.714655i	0.582568	−	0.812782i	$-0.302048\pi$
$631$	−10.3646	−	17.9519i	−0.412606	−	0.714655i	−0.995174	+	0.0981271i	$0.968715\pi$
$632$	0.449119	−	2.54708i	0.0178650	−	0.101317i
$633$	−0.613372	+	0.736565i	−0.0243794	+	0.0292758i
$634$	17.0669	+	6.21183i	0.677812	+	0.246703i
$635$	28.2543	−	23.7082i	1.12124	−	0.940831i
$636$	3.62650	+	9.84899i	0.143800	+	0.390538i
$637$	−37.1350	−	8.17817i	−1.47134	−	0.324031i
$638$	−0.283295	−	0.490681i	−0.0112158	−	0.0194263i
$639$	0.454398	+	0.375530i	0.0179757	+	0.0148557i
$640$	−1.39286	−	2.41251i	−0.0550577	−	0.0953628i
$641$	4.00954	−	22.7392i	0.158367	−	0.898146i	−0.797275	−	0.603616i	$-0.793726\pi$
$641$	4.00954	−	22.7392i	0.158367	−	0.898146i	0.955642	−	0.294530i	$-0.0951630\pi$
$642$	2.44061	+	1.39695i	0.0963232	+	0.0551330i
$643$	8.83350	−	7.41219i	0.348359	−	0.292308i	−0.451772	−	0.892134i	$-0.649208\pi$
$643$	8.83350	−	7.41219i	0.348359	−	0.292308i	0.800131	+	0.599826i	$0.204763\pi$
$644$	2.28555	−	21.0049i	0.0900633	−	0.827710i
$645$	37.1489	+	43.9377i	1.46274	+	1.73004i
$646$	39.5856	−	14.4080i	1.55748	−	0.566875i
$647$	9.88562	−	17.1224i	0.388644	−	0.673151i	−0.603624	−	0.797269i	$-0.706277\pi$
$647$	9.88562	−	17.1224i	0.388644	−	0.673151i	0.992267	+	0.124119i	$0.0396103\pi$
$648$	1.69522	+	8.83890i	0.0665946	+	0.347225i
$649$	7.56451	+	13.1021i	0.296933	+	0.514303i
$650$	2.60370	−	14.7663i	0.102126	−	0.579184i
$651$	−11.3602	−	1.19315i	−0.445243	−	0.0467631i
$652$	0.533324	+	0.194114i	0.0208866	+	0.00760210i
$653$	5.99251	+	2.18110i	0.234505	+	0.0853529i	0.456600	−	0.889672i	$-0.349067\pi$
$653$	5.99251	+	2.18110i	0.234505	+	0.0853529i	−0.222095	+	0.975025i	$0.571289\pi$
$654$	0.0600259	+	16.0529i	0.00234720	+	0.627718i
$655$	0.892454	−	5.06136i	0.0348711	−	0.197764i
$656$	−0.498964			−0.0194813
$657$	15.3883	+	12.7174i	0.600355	+	0.496155i
$658$	6.99982	+	28.5195i	0.272881	+	1.11181i
$659$	−16.9418	−	14.2158i	−0.659958	−	0.553770i	0.250116	−	0.968216i	$-0.419531\pi$
$659$	−16.9418	−	14.2158i	−0.659958	−	0.553770i	−0.910074	+	0.414445i	$0.863976\pi$
$660$	4.89773	−	5.88141i	0.190644	−	0.228934i
$661$	22.2354	+	8.09303i	0.864857	+	0.314782i	0.736083	−	0.676892i	$-0.236673\pi$
$661$	22.2354	+	8.09303i	0.864857	+	0.314782i	0.128774	+	0.991674i	$0.458896\pi$
$662$	−21.5351	−	7.83814i	−0.836986	−	0.304638i
$663$	20.6420	+	56.0603i	0.801668	+	2.17720i
$664$	13.5752	+	11.3910i	0.526822	+	0.442056i
$665$	11.6560	+	47.4902i	0.451999	+	1.84159i
$666$	2.15264	+	11.6961i	0.0834131	+	0.453213i
$667$	−2.85250			−0.110449
$668$	−1.82074	+	10.3259i	−0.0704466	+	0.399523i
$669$	20.6307	−	12.0142i	0.797627	−	0.464496i
$670$	−5.99086	−	2.18049i	−0.231447	−	0.0842398i
$671$	−8.37039	−	3.04657i	−0.323136	−	0.117612i
$672$	−2.69329	+	3.70758i	−0.103896	+	0.143023i
$673$	−1.50081	+	8.51150i	−0.0578518	+	0.328094i	−0.999974	−	0.00717497i	$-0.997716\pi$
$673$	−1.50081	+	8.51150i	−0.0578518	+	0.328094i	0.942122	+	0.335269i	$0.108827\pi$
$674$	14.7275	+	25.5087i	0.567281	+	0.982560i
$675$	−14.1519	−	2.33199i	−0.544708	−	0.0897585i
$676$	−8.25402	+	14.2964i	−0.317462	+	0.549861i
$677$	1.10810	−	0.403314i	0.0425876	−	0.0155006i	−0.320639	−	0.947202i	$-0.603897\pi$
$677$	1.10810	−	0.403314i	0.0425876	−	0.0155006i	0.363226	+	0.931701i	$0.381675\pi$
$678$	1.28064	−	3.55988i	0.0491826	−	0.136717i
$679$	−2.52384	+	23.1949i	−0.0968562	+	0.890139i
$680$	−13.5496	+	11.3694i	−0.519602	+	0.435998i
$681$	−21.4666	+	12.5010i	−0.822600	+	0.479038i
$682$	0.686596	−	3.89388i	0.0262911	−	0.149104i
$683$	18.3722	+	31.8216i	0.702992	+	1.21762i	0.967411	+	0.253211i	$0.0814866\pi$
$683$	18.3722	+	31.8216i	0.702992	+	1.21762i	−0.264419	+	0.964408i	$0.585180\pi$
$684$	9.82281	−	17.3113i	0.375584	−	0.661914i
$685$	−8.03910	−	13.9241i	−0.307158	−	0.532014i
$686$	−15.8130	+	9.64101i	−0.603743	+	0.368095i
$687$	−18.4041	+	22.1004i	−0.702159	+	0.843183i
$688$	9.13494	−	7.66513i	0.348266	−	0.292230i
$689$	30.9311	+	11.2580i	1.17838	+	0.428896i
$690$	−13.3142	−	36.1591i	−0.506862	−	1.37656i
$691$	6.02215	−	34.1533i	0.229094	−	1.29925i	−0.625609	−	0.780136i	$-0.715150\pi$
$691$	6.02215	−	34.1533i	0.229094	−	1.29925i	0.854703	−	0.519117i	$-0.173739\pi$
$692$	−0.694460	−	1.20284i	−0.0263994	−	0.0457251i
$693$	−12.1159	−	3.42421i	−0.460244	−	0.130075i
$694$	−0.297809	+	0.515819i	−0.0113047	+	0.0195802i
$695$	−40.7714	−	34.2113i	−1.54655	−	1.29771i
$696$	0.536936	+	0.307329i	0.0203525	+	0.0116493i
$697$	0.550139	+	3.11999i	0.0208380	+	0.118178i
$698$	−2.79952	−	15.8769i	−0.105963	−	0.600949i
$699$	−6.44499	+	17.9156i	−0.243772	+	0.677631i
$700$	−4.06157	−	6.06937i	−0.153513	−	0.229401i
$701$	−14.0402			−0.530292			−0.265146	−	0.964208i	$-0.585420\pi$
$701$	−14.0402			−0.530292			−0.265146	+	0.964208i	$0.585420\pi$
$702$	24.6014	+	13.8380i	0.928519	+	0.522281i
$703$	13.1505	−	22.7773i	0.495979	−	0.859061i
$704$	−1.21514	−	1.01962i	−0.0457972	−	0.0384284i
$705$	34.5772	+	40.8960i	1.30225	+	1.54023i
$706$	−8.94675	−	3.25635i	−0.336715	−	0.122554i
$707$	19.8667	−	8.75816i	0.747166	−	0.329385i
$708$	−14.3372	−	8.20626i	−0.538825	−	0.308410i
$709$	−23.8662	−	20.0261i	−0.896313	−	0.752096i	0.0731531	−	0.997321i	$-0.476694\pi$
$709$	−23.8662	−	20.0261i	−0.896313	−	0.752096i	−0.969466	+	0.245225i	$0.921138\pi$
$710$	0.273694	+	0.474051i	0.0102715	+	0.0177908i
$711$	−5.90637	+	5.03178i	−0.221506	+	0.188706i
$712$	0.662790	−	1.14799i	0.0248391	−	0.0430226i
$713$	−15.2490	−	12.7954i	−0.571080	−	0.479193i
$714$	26.1528	+	12.7532i	0.978745	+	0.477275i
$715$	−4.16821	−	23.6391i	−0.155882	−	0.884053i
$716$	5.67122	−	4.75872i	0.211943	−	0.177842i
$717$	−13.4032	−	2.31170i	−0.500552	−	0.0863322i
$718$	−5.62242	+	2.04639i	−0.209827	+	0.0763707i
$719$	7.16345	−	12.4075i	0.267152	−	0.462720i	−0.700974	−	0.713187i	$-0.747251\pi$
$719$	7.16345	−	12.4075i	0.267152	−	0.462720i	0.968125	+	0.250467i	$0.0805842\pi$
$720$	−1.38962	+	8.24084i	−0.0517880	+	0.307118i
$721$	5.10920	+	20.8165i	0.190276	+	0.775247i
$722$	−23.5099	+	8.55691i	−0.874949	+	0.318455i
$723$	10.8586	+	6.21522i	0.403837	+	0.231146i
$724$	2.32993	+	13.2137i	0.0865912	+	0.491083i
$725$	−0.755271	+	0.633748i	−0.0280501	+	0.0235368i
$726$	−4.97411	+	13.8269i	−0.184607	+	0.513165i
$727$	−0.936272	+	5.30986i	−0.0347244	+	0.196932i	−0.997235	−	0.0743121i	$-0.976324\pi$
$727$	−0.936272	+	5.30986i	−0.0347244	+	0.196932i	0.962511	+	0.271244i	$0.0874350\pi$
$728$	3.42580	+	13.9578i	0.126969	+	0.517310i
$729$	12.9720	−	23.6797i	0.480446	−	0.877024i
$730$	9.26872	+	16.0539i	0.343051	+	0.594181i
$731$	−58.0015	−	48.6690i	−2.14526	−	1.80009i
$732$	9.57220	−	1.72477i	0.353799	−	0.0637492i
$733$	3.09844	+	17.5721i	0.114443	+	0.649041i	0.987024	+	0.160571i	$0.0513336\pi$
$733$	3.09844	+	17.5721i	0.114443	+	0.649041i	−0.872581	+	0.488470i	$0.837555\pi$
$734$	−9.29648	+	7.80067i	−0.343139	+	0.287928i
$735$	−18.0008	+	28.5785i	−0.663969	+	1.05413i
$736$	−7.50436	+	2.73136i	−0.276614	+	0.100679i
$737$	−3.63025			−0.133722
$738$	1.15385	+	0.953581i	0.0424738	+	0.0351018i
$739$	−40.6410			−1.49500			−0.747501	−	0.664260i	$-0.768747\pi$
$739$	−40.6410			−1.49500			−0.747501	+	0.664260i	$0.768747\pi$
$740$	−1.91761	+	10.8753i	−0.0704928	+	0.399785i
$741$	−21.5694	−	58.5789i	−0.792370	−	2.15195i
$742$	14.6698	−	6.46711i	0.538545	−	0.237415i
$743$	−5.13821	−	29.1402i	−0.188502	−	1.06905i	−0.921372	−	0.388682i	$-0.872931\pi$
$743$	−5.13821	−	29.1402i	−0.188502	−	1.06905i	0.732870	−	0.680369i	$-0.238180\pi$
$744$	1.49179	+	4.05146i	0.0546918	+	0.148534i
$745$	16.0884	−	5.85568i	0.589432	−	0.214536i
$746$	31.9280			1.16897
$747$	−9.62306	−	52.2855i	−0.352089	−	1.91303i
$748$	−5.03587	+	8.72238i	−0.184130	+	0.318922i
$749$	1.89720	−	3.85393i	0.0693221	−	0.140819i
$750$	9.37906	+	5.36834i	0.342475	+	0.196024i
$751$	−17.3305	−	6.30777i	−0.632397	−	0.230174i	0.00587717	−	0.999983i	$-0.498129\pi$
$751$	−17.3305	−	6.30777i	−0.632397	−	0.230174i	−0.638274	+	0.769809i	$0.720351\pi$
$752$	8.50255	−	7.13449i	0.310056	−	0.260168i
$753$	−16.1855	+	44.9922i	−0.589834	+	1.63961i
$754$	1.82328	−	0.663620i	0.0664000	−	0.0241676i
$755$	9.33661			0.339794
$756$	13.3139	−	3.42654i	0.484220	−	0.124622i
$757$	−27.3164			−0.992830			−0.496415	−	0.868085i	$-0.665351\pi$
$757$	−27.3164			−0.992830			−0.496415	+	0.868085i	$0.665351\pi$
$758$	8.56435	−	3.11717i	0.311071	−	0.113221i
$759$	−14.1663	−	16.7551i	−0.514203	−	0.608170i
$760$	14.1583	−	11.8802i	0.513576	−	0.430941i
$761$	−39.4821	−	14.3703i	−1.43123	−	0.520923i	−0.493943	−	0.869494i	$-0.664445\pi$
$761$	−39.4821	−	14.3703i	−1.43123	−	0.520923i	−0.937282	+	0.348571i	$0.886667\pi$
$762$	0.0857503	+	22.9324i	0.00310641	+	0.830755i
$763$	24.4677	−	1.62088i	0.885791	−	0.0586799i
$764$	2.15107	−	3.72577i	0.0778231	−	0.134794i
$765$	53.0616	−	0.396828i	1.91845	−	0.0143473i
$766$	−5.52800			−0.199735
$767$	−48.6851	+	17.7199i	−1.75792	+	0.639829i
$768$	1.70685	+	0.294387i	0.0615906	+	0.0106228i
$769$	3.36957	+	19.1098i	0.121510	+	0.689116i	0.983320	+	0.181885i	$0.0582198\pi$
$769$	3.36957	+	19.1098i	0.121510	+	0.689116i	−0.861810	+	0.507231i	$0.830669\pi$
$770$	−9.43313	−	6.90652i	−0.339946	−	0.248894i
$771$	9.98250	−	11.9874i	0.359511	−	0.431717i
$772$	−3.34878	+	18.9919i	−0.120525	+	0.683532i
$773$	−32.9235			−1.18418			−0.592088	−	0.805873i	$-0.701696\pi$
$773$	−32.9235			−1.18418			−0.592088	+	0.805873i	$0.701696\pi$
$774$	−35.7735	+	0.267536i	−1.28585	+	0.00961639i
$775$	−6.88037			−0.247150
$776$	8.28677	−	3.01614i	0.297478	−	0.108273i
$777$	17.6262	−	4.39610i	0.632335	−	0.157709i
$778$	8.45054	−	7.09084i	0.302966	−	0.254219i
$779$	−0.574855	−	3.26016i	−0.0205963	−	0.116807i
$780$	16.9225	+	20.0150i	0.605923	+	0.716652i
$781$	0.238771	+	0.200353i	0.00854389	+	0.00716918i
$782$	25.3531	+	43.9128i	0.906625	+	1.57032i
$783$	−0.654316	−	1.73685i	−0.0233833	−	0.0620698i
$784$	5.90899	+	3.75284i	0.211036	+	0.134030i
$785$	3.61326	−	20.4918i	0.128963	−	0.731384i
$786$	2.06316	+	2.44019i	0.0735906	+	0.0870388i
$787$	−24.3924	+	20.4677i	−0.869495	+	0.729593i	−0.963992	−	0.265932i	$-0.914320\pi$
$787$	−24.3924	+	20.4677i	−0.869495	+	0.729593i	0.0944967	+	0.995525i	$0.469876\pi$
$788$	2.36000	+	13.3842i	0.0840715	+	0.476793i
$789$	−0.00690184	−	1.84578i	−0.000245712	−	0.0657114i
$790$	−6.77042	+	2.46423i	−0.240881	+	0.0876734i
$791$	−5.54923	−	1.61324i	−0.197308	−	0.0573604i
$792$	0.861371	+	4.68014i	0.0306075	+	0.166301i
$793$	15.2521	−	26.4174i	0.541617	−	0.938109i
$794$	−10.9310	+	3.97856i	−0.387927	+	0.141194i
$795$	18.7096	−	22.4673i	0.663559	−	0.796831i
$796$	−6.56559	+	5.50919i	−0.232711	+	0.195268i
$797$	−0.723329	−	4.10221i	−0.0256216	−	0.145308i	0.969313	−	0.245829i	$-0.0790601\pi$
$797$	−0.723329	−	4.10221i	−0.0256216	−	0.145308i	−0.994935	+	0.100521i	$0.967949\pi$
$798$	−27.3278	−	13.3261i	−0.967393	−	0.471739i
$799$	−53.9862	−	45.2998i	−1.90989	−	1.60259i
$800$	−1.38013	+	2.39046i	−0.0487951	+	0.0845156i
$801$	−3.72664	+	1.38803i	−0.131674	+	0.0490437i
$802$	4.28749	+	7.42615i	0.151396	+	0.262226i
$803$	8.08605	+	6.78500i	0.285350	+	0.239437i
$804$	3.42543	−	1.99479i	0.120805	−	0.0703507i
$805$	−53.8580	+	23.7431i	−1.89825	+	0.836833i
$806$	12.7238	+	4.63108i	0.448176	+	0.163123i
$807$	6.70810	−	18.6470i	0.236136	−	0.656405i
$808$	−6.28632	−	5.27485i	−0.221152	−	0.185568i
$809$	10.2560	−	17.7639i	0.360582	−	0.624547i	−0.627475	−	0.778637i	$-0.715911\pi$
$809$	10.2560	−	17.7639i	0.360582	−	0.624547i	0.988057	+	0.154090i	$0.0492447\pi$
$810$	18.9627	−	16.4011i	0.666282	−	0.576277i
$811$	43.6906			1.53418			0.767092	−	0.641538i	$-0.221703\pi$
$811$	43.6906			1.53418			0.767092	+	0.641538i	$0.221703\pi$
$812$	0.417384	−	0.847866i	0.0146473	−	0.0297543i
$813$	−1.41519	−	1.67380i	−0.0496328	−	0.0587028i
$814$	1.09193	+	6.19262i	0.0382720	+	0.217051i
$815$	−0.274545	−	1.55702i	−0.00961691	−	0.0545402i
$816$	−0.0411222	−	10.9974i	−0.00143956	−	0.384987i
$817$	60.6073	+	50.8555i	2.12038	+	1.77921i
$818$	−16.1260	+	27.9310i	−0.563832	+	0.976586i
$819$	18.7529	−	38.8244i	0.655281	−	1.35663i
$820$	0.694988	+	1.20375i	0.0242700	+	0.0420369i
$821$	2.31703	−	13.1406i	0.0808650	−	0.458608i	−0.917307	−	0.398180i	$-0.869642\pi$
$821$	2.31703	−	13.1406i	0.0808650	−	0.458608i	0.998173	−	0.0604288i	$-0.0192468\pi$
$822$	9.85132	+	1.69910i	0.343604	+	0.0592628i
$823$	−9.39951	−	3.42114i	−0.327646	−	0.119253i	0.172959	−	0.984929i	$-0.444667\pi$
$823$	−9.39951	−	3.42114i	−0.327646	−	0.119253i	−0.500606	+	0.865676i	$0.666889\pi$
$824$	6.20605	−	5.20749i	0.216198	−	0.181412i
$825$	−7.47339	−	1.28897i	−0.260190	−	0.0448760i
$826$	−11.1450	+	22.6396i	−0.387783	+	0.787733i
$827$	0.709907	+	1.22959i	0.0246859	+	0.0427572i	0.878104	−	0.478469i	$-0.158808\pi$
$827$	0.709907	+	1.22959i	0.0246859	+	0.0427572i	−0.853419	+	0.521226i	$0.825475\pi$
$828$	22.5737	+	8.02550i	0.784491	+	0.278905i
$829$	−22.4314	−	38.8523i	−0.779075	−	1.34940i	−0.932476	−	0.361233i	$-0.882356\pi$
$829$	−22.4314	−	38.8523i	−0.779075	−	1.34940i	0.153401	−	0.988164i	$-0.450977\pi$
$830$	8.57240	−	48.6165i	0.297552	−	1.68750i
$831$	−0.0172208	−	4.60541i	−0.000597384	−	0.159760i
$832$	4.16125	−	3.49171i	0.144265	−	0.121053i
$833$	16.9512	−	41.0863i	0.587326	−	1.42356i
$834$	32.5676	−	5.86820i	1.12772	−	0.203199i
$835$	27.4475	−	9.99006i	0.949859	−	0.345720i
$836$	5.26211	−	9.11424i	0.181994	−	0.315223i
$837$	4.29309	−	12.2200i	0.148391	−	0.422384i
$838$	−8.63319	−	14.9531i	−0.298229	−	0.516547i
$839$	−7.61327	+	43.1770i	−0.262839	+	1.49064i	0.512279	+	0.858819i	$0.328801\pi$
$839$	−7.61327	+	43.1770i	−0.262839	+	1.49064i	−0.775118	+	0.631816i	$0.782310\pi$
$840$	12.6960	+	1.33344i	0.438052	+	0.0460079i
$841$	27.1312	+	9.87495i	0.935558	+	0.340515i
$842$	−31.3652	−	11.4160i	−1.08092	−	0.393421i
$843$	−29.7135	−	17.0073i	−1.02339	−	0.585762i
$844$	0.0960968	−	0.544992i	0.00330779	−	0.0187594i
$845$	45.9869			1.58200
$846$	−33.2970	+	0.249015i	−1.14477	+	0.00856132i
$847$	21.5537	+	6.26599i	0.740595	+	0.215302i
$848$	−4.64188	−	3.89500i	−0.159403	−	0.133755i
$849$	−21.7860	−	3.75752i	−0.747693	−	0.128958i
$850$	16.4691	+	5.99427i	0.564886	+	0.205602i
$851$	29.7485	+	10.8276i	1.01977	+	0.371165i
$852$	−0.335391	−	0.0578462i	−0.0114903	−	0.00198178i
$853$	42.6198	+	35.7623i	1.45927	+	1.22448i	0.925443	+	0.378886i	$0.123693\pi$
$853$	42.6198	+	35.7623i	1.45927	+	1.22448i	0.533832	+	0.845591i	$0.320752\pi$
$854$	−3.54145	−	14.4290i	−0.121186	−	0.493750i
$855$	−55.4455	+	0.414656i	−1.89620	+	0.0141809i
$856$	−1.62358			−0.0554928
$857$	6.19991	−	35.1615i	0.211785	−	1.20109i	−0.674614	−	0.738171i	$-0.735690\pi$
$857$	6.19991	−	35.1615i	0.211785	−	1.20109i	0.886399	−	0.462922i	$-0.153199\pi$
$858$	12.9529	+	7.41391i	0.442204	+	0.253107i
$859$	−15.7853	−	5.74537i	−0.538586	−	0.196029i	0.0583819	−	0.998294i	$-0.481406\pi$
$859$	−15.7853	−	5.74537i	−0.538586	−	0.196029i	−0.596968	+	0.802265i	$0.703628\pi$
$860$	−31.2159	−	11.3617i	−1.06445	−	0.387430i
$861$	1.34386	−	1.84995i	0.0457985	−	0.0630461i
$862$	3.98530	−	22.6017i	0.135740	−	0.769818i
$863$	−4.78225	−	8.28309i	−0.162790	−	0.281960i	0.773079	−	0.634310i	$-0.218716\pi$
$863$	−4.78225	−	8.28309i	−0.162790	−	0.281960i	−0.935868	+	0.352351i	$0.885382\pi$
$864$	−3.38446	−	3.94277i	−0.115142	−	0.134136i
$865$	−1.93458	+	3.35078i	−0.0657776	+	0.113930i
$866$	14.5329	−	5.28956i	0.493849	−	0.179746i
$867$	−39.7427	+	7.16104i	−1.34973	+	0.243202i
$868$	6.03454	−	2.66030i	0.204826	−	0.0902965i
$869$	−3.14280	+	2.63712i	−0.106612	+	0.0894582i
$870$	−0.00644435	−	1.72343i	−0.000218484	−	0.0584297i
$871$	2.15876	−	12.2430i	0.0731469	−	0.414837i
$872$	−4.63410	−	8.02650i	−0.156930	−	0.271812i
$873$	−24.9273	−	8.86225i	−0.843661	−	0.299942i
$874$	−26.4921	−	45.8857i	−0.896109	−	1.55211i
$875$	7.29076	−	14.8103i	0.246473	−	0.500679i
$876$	−11.3581	−	1.95898i	−0.383755	−	0.0661878i
$877$	14.3578	−	12.0476i	0.484828	−	0.406819i	−0.367341	−	0.930086i	$-0.619732\pi$
$877$	14.3578	−	12.0476i	0.484828	−	0.406819i	0.852168	+	0.523268i	$0.175287\pi$
$878$	14.6801	+	5.34311i	0.495428	+	0.180321i
$879$	−36.6582	−	6.32259i	−1.23645	−	0.213256i
$880$	−0.767326	+	4.35172i	−0.0258665	+	0.146696i
$881$	−18.6948	−	32.3803i	−0.629843	−	1.09092i	−0.987583	−	0.157099i	$-0.949786\pi$
$881$	−18.6948	−	32.3803i	−0.629843	−	1.09092i	0.357740	−	0.933821i	$-0.383548\pi$
$882$	−6.49236	−	19.9712i	−0.218609	−	0.672466i
$883$	−11.5451	+	19.9968i	−0.388525	+	0.672945i	−0.992251	−	0.124247i	$-0.960349\pi$
$883$	−11.5451	+	19.9968i	−0.388525	+	0.672945i	0.603726	+	0.797192i	$0.293682\pi$
$884$	−26.4215	−	22.1703i	−0.888651	−	0.745666i
$885$	0.172076	+	46.0188i	0.00578428	+	1.54691i
$886$	1.85572	+	10.5243i	0.0623440	+	0.353570i
$887$	9.55660	+	54.1982i	0.320879	+	1.81980i	0.537178	+	0.843469i	$0.319490\pi$
$887$	9.55660	+	54.1982i	0.320879	+	1.81980i	−0.216299	+	0.976327i	$0.569399\pi$
$888$	−4.43311	−	5.24323i	−0.148765	−	0.175951i
$889$	34.9535	−	2.31552i	1.17230	−	0.0776601i
$890$	−3.69270			−0.123780
$891$	6.95240	−	12.4690i	0.232914	−	0.417726i
$892$	−6.89181	+	11.9370i	−0.230755	+	0.399679i
$893$	56.4116	+	47.3349i	1.88774	+	1.58400i
$894$	−3.60340	+	10.0166i	−0.120516	+	0.335006i
$895$	−19.3797	−	7.05363i	−0.647792	−	0.235777i
$896$	0.286196	−	2.63023i	0.00956112	−	0.0878697i
$897$	64.9303	−	37.8120i	2.16796	−	1.26250i
$898$	−10.0501	−	8.43302i	−0.335376	−	0.281414i
$899$	−0.445172	−	0.771060i	−0.0148473	−	0.0257163i
$900$	7.76001	−	2.89032i	0.258667	−	0.0963439i
$901$	−19.2372	+	33.3199i	−0.640885	+	1.11005i
$902$	0.606309	+	0.508754i	0.0201879	+	0.0169397i
$903$	3.81604	+	54.5130i	0.126990	+	1.81408i
$904$	0.379291	+	2.15106i	0.0126150	+	0.0715433i
$905$	28.6329	−	24.0258i	0.951789	−	0.798646i
$906$	−3.71481	+	4.46090i	−0.123416	+	0.148204i
$907$	−19.7000	+	7.17020i	−0.654127	+	0.238083i	−0.647699	−	0.761897i	$-0.724268\pi$
$907$	−19.7000	+	7.17020i	−0.654127	+	0.238083i	−0.00642823	+	0.999979i	$0.502046\pi$
$908$	7.17105	−	12.4206i	0.237980	−	0.412193i
$909$	4.45617	+	24.2120i	0.147802	+	0.803060i
$910$	28.9017	−	27.7061i	0.958081	−	0.918447i
$911$	−21.7296	+	7.90894i	−0.719935	+	0.262035i	−0.675898	−	0.736995i	$-0.736244\pi$
$911$	−21.7296	+	7.90894i	−0.719935	+	0.262035i	−0.0440369	+	0.999030i	$0.514022\pi$
$912$	0.0429696	+	11.4915i	0.00142287	+	0.380521i
$913$	−4.88130	−	27.6832i	−0.161547	−	0.916180i
$914$	−1.58081	+	1.32645i	−0.0522884	+	0.0438752i
$915$	−17.4938	−	20.6906i	−0.578326	−	0.684012i
$916$	2.88336	−	16.3523i	0.0952688	−	0.540296i
$917$	3.52364	−	3.37788i	0.116361	−	0.111547i
$918$	−20.9223	+	25.5100i	−0.690539	+	0.841956i
$919$	4.97400	+	8.61521i	0.164077	+	0.284190i	0.936327	−	0.351129i	$-0.114202\pi$
$919$	4.97400	+	8.61521i	0.164077	+	0.284190i	−0.772250	+	0.635319i	$0.780869\pi$
$920$	17.0420	+	14.2999i	0.561858	+	0.471455i
$921$	38.2304	+	45.2167i	1.25973	+	1.48994i
$922$	−0.665461	−	3.77402i	−0.0219158	−	0.124291i
$923$	−0.817674	+	0.686110i	−0.0269141	+	0.0225836i
$924$	7.05305	−	1.75909i	0.232028	−	0.0578697i
$925$	10.2823	−	3.74244i	0.338079	−	0.123051i
$926$	−14.1810			−0.466015
$927$	−24.3036	+	0.181757i	−0.798234	+	0.00596969i
$928$	−0.357189			−0.0117253
$929$	0.698067	−	3.95894i	0.0229028	−	0.129888i	−0.971213	−	0.238214i	$-0.923438\pi$
$929$	0.698067	−	3.95894i	0.0229028	−	0.129888i	0.994115	+	0.108326i	$0.0345490\pi$
$930$	7.69633	−	9.24210i	0.252373	−	0.303060i
$931$	−17.7128	+	42.9322i	−0.580514	+	1.40705i
$932$	−1.90883	−	10.8255i	−0.0625259	−	0.354602i
$933$	14.8508	+	2.56138i	0.486193	+	0.0838557i
$934$	−3.94641	+	1.43637i	−0.129130	+	0.0469996i
$935$	28.0571			0.917565
$936$	−16.2959	+	0.121871i	−0.532649	+	0.00398348i
$937$	19.0888	−	33.0627i	0.623602	−	1.08011i	−0.365207	−	0.930926i	$-0.619002\pi$
$937$	19.0888	−	33.0627i	0.623602	−	1.08011i	0.988809	−	0.149185i	$-0.0476649\pi$
$938$	−3.36750	−	5.03219i	−0.109953	−	0.164307i
$939$	0.0816327	+	21.8313i	0.00266398	+	0.712436i
$940$	−29.0549	−	10.5751i	−0.947667	−	0.344923i
$941$	10.9638	−	9.19975i	0.357411	−	0.299903i	−0.446347	−	0.894860i	$-0.647275\pi$
$941$	10.9638	−	9.19975i	0.357411	−	0.299903i	0.803758	+	0.594957i	$0.202831\pi$
$942$	8.35308	+	9.87955i	0.272158	+	0.321893i
$943$	3.74440	−	1.36285i	0.121935	−	0.0443806i
$944$	9.53761			0.310423
$945$	−26.8109	−	27.3471i	−0.872160	−	0.889601i
$946$	−18.9157			−0.615003
$947$	−28.7309	+	10.4572i	−0.933629	+	0.339813i	−0.763647	−	0.645634i	$-0.776593\pi$
$947$	−28.7309	+	10.4572i	−0.933629	+	0.339813i	−0.169982	+	0.985447i	$0.554371\pi$
$948$	1.51641	−	4.21527i	0.0492506	−	0.136906i
$949$	−27.6908	+	23.2353i	−0.898881	+	0.754251i
$950$	−17.2090	−	6.26357i	−0.558334	−	0.203217i
$951$	27.3019	+	15.6269i	0.885324	+	0.506738i
$952$	−16.7622	+	1.11043i	−0.543266	+	0.0359891i
$953$	10.4786	−	18.1494i	0.339434	−	0.587918i	−0.644892	−	0.764274i	$-0.723098\pi$
$953$	10.4786	−	18.1494i	0.339434	−	0.587918i	0.984326	+	0.176356i	$0.0564310\pi$
$954$	3.29048	+	17.8783i	0.106533	+	0.578832i
$955$	−11.9846			−0.387812
$956$	7.37903	−	2.68575i	0.238655	−	0.0868633i
$957$	−0.339092	−	0.920918i	−0.0109613	−	0.0297690i
$958$	−7.56592	−	42.9084i	−0.244444	−	1.38631i
$959$	1.65182	−	15.1807i	0.0533399	−	0.490211i
$960$	−1.66720	−	4.52783i	−0.0538085	−	0.146135i
$961$	−4.30417	+	24.4102i	−0.138844	+	0.787425i
$962$	−21.5339			−0.694280
$963$	3.75451	+	3.10286i	0.120988	+	0.0999883i
$964$	−7.22355			−0.232655
$965$	50.4824	−	18.3741i	1.62509	−	0.591483i
$966$	10.0847	−	35.1794i	0.324469	−	1.13188i
$967$	−8.66337	+	7.26943i	−0.278595	+	0.233769i	−0.771369	−	0.636388i	$-0.780428\pi$
$967$	−8.66337	+	7.26943i	−0.278595	+	0.233769i	0.492774	+	0.870158i	$0.335983\pi$
$968$	−1.47320	−	8.35493i	−0.0473504	−	0.268538i
$969$	71.8083	−	12.9388i	2.30681	−	0.415653i
$970$	−18.8188	−	15.7908i	−0.604235	−	0.507014i
$971$	−25.1116	−	43.4947i	−0.805871	−	1.39581i	−0.915701	−	0.401859i	$-0.868364\pi$
$971$	−25.1116	−	43.4947i	−0.805871	−	1.39581i	0.109830	−	0.993950i	$-0.464969\pi$
$972$	0.291428	+	15.5857i	0.00934756	+	0.499913i
$973$	−12.0491	−	49.0919i	−0.386277	−	1.57381i
$974$	−2.60851	+	14.7936i	−0.0835821	+	0.474018i
$975$	8.79116	−	24.4374i	0.281542	−	0.782624i
$976$	−4.30173	+	3.60958i	−0.137695	+	0.115540i
$977$	−2.73885	−	15.5328i	−0.0876235	−	0.496938i	−0.996760	−	0.0804384i	$-0.974368\pi$
$977$	−2.73885	−	15.5328i	−0.0876235	−	0.496938i	0.909136	−	0.416499i	$-0.136743\pi$
$978$	0.853160	+	0.488328i	0.0272810	+	0.0156150i
$979$	−1.97589	+	0.719165i	−0.0631497	+	0.0229846i
$980$	0.823336	−	19.4827i	0.0263005	−	0.622352i
$981$	−4.62331	+	27.4175i	−0.147611	+	0.875375i
$982$	14.2094	−	24.6114i	0.453440	−	0.785381i
$983$	−9.11837	+	3.31881i	−0.290831	+	0.105854i	−0.483316	−	0.875446i	$-0.660568\pi$
$983$	−9.11837	+	3.31881i	−0.290831	+	0.105854i	0.192485	+	0.981300i	$0.438345\pi$
$984$	−0.851656	−	0.146889i	−0.0271498	−	0.00468264i
$985$	29.0024	−	24.3359i	0.924094	−	0.775407i
$986$	0.393823	+	2.23348i	0.0125419	+	0.0711285i
$987$	3.55186	+	50.7392i	0.113057	+	1.61505i
$988$	27.6085	+	23.1663i	0.878344	+	0.737018i
$989$	−47.6157	+	82.4727i	−1.51409	+	2.62248i
$990$	10.0911	−	8.59686i	0.320716	−	0.273226i
$991$	−4.56303	−	7.90340i	−0.144949	−	0.251060i	0.784405	−	0.620249i	$-0.212969\pi$
$991$	−4.56303	−	7.90340i	−0.144949	−	0.251060i	−0.929354	+	0.369190i	$0.879635\pi$
$992$	−1.90948	−	1.60224i	−0.0606259	−	0.0508712i
$993$	−34.4497	−	19.7182i	−1.09323	−	0.625738i
$994$	−0.0562366	+	0.516832i	−0.00178372	+	0.0163929i
$995$	22.4359	+	8.16601i	0.711267	+	0.258880i
$996$	19.8175	+	23.4391i	0.627943	+	0.742696i
$997$	−37.4888	−	31.4568i	−1.18728	−	0.996248i	−0.999903	−	0.0139602i	$-0.995556\pi$
$997$	−37.4888	−	31.4568i	−1.18728	−	0.996248i	−0.187379	−	0.982288i	$-0.559999\pi$
$998$	8.78546	−	15.2169i	0.278099	−	0.481681i
$999$	0.231062	+	20.5971i	0.00731049	+	0.651664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.a.25.1	yes	72
7.2	even	3		378.2.v.b.79.7	yes	72
27.13	even	9		378.2.v.b.67.7	✓	72
189.121	even	9	inner	378.2.w.a.121.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.7	✓	72	27.13	even	9
378.2.v.b.79.7	yes	72	7.2	even	3
378.2.w.a.25.1	yes	72	1.1	even	1	trivial
378.2.w.a.121.1	yes	72	189.121	even	9	inner

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.70460 + 0.307144i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.61773 - 0.952774i) q^{5} +(1.49675 - 0.871628i) q^{6} +(-1.47144 - 2.19883i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.81133 - 1.04711i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.70460 + 0.307144i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.61773 - 0.952774i) q^{5} +(1.49675 - 0.871628i) q^{6} +(-1.47144 - 2.19883i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.81133 - 1.04711i) q^{9} +2.78573 q^{10} +(1.49059 - 0.542529i) q^{11} +(-1.10837 + 1.33098i) q^{12} +(0.943280 + 5.34960i) q^{13} +(2.13475 + 1.56297i) q^{14} +(4.75482 + 0.820082i) q^{15} +(0.173648 - 0.984808i) q^{16} -6.34941 q^{17} +(-2.28365 + 1.94550i) q^{18} +6.63466 q^{19} +(-2.61773 + 0.952774i) q^{20} +(3.18357 + 3.29619i) q^{21} +(-1.21514 + 1.01962i) q^{22} +(1.38675 + 7.86465i) q^{23} +(0.586306 - 1.62980i) q^{24} +(2.11449 + 1.77427i) q^{25} +(-2.71607 - 4.70436i) q^{26} +(-4.47057 + 2.64839i) q^{27} +(-2.54057 - 0.738582i) q^{28} +(-0.0620252 + 0.351762i) q^{29} +(-4.74855 + 0.855618i) q^{30} +(-1.90948 + 1.60224i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-2.37422 + 1.38262i) q^{33} +(5.96649 - 2.17162i) q^{34} +(1.75683 + 7.15789i) q^{35} +(1.48053 - 2.60922i) q^{36} +(1.98208 - 3.43307i) q^{37} +(-6.23454 + 2.26919i) q^{38} +(-3.25101 - 8.82922i) q^{39} +(2.13399 - 1.79063i) q^{40} +(-0.0866442 - 0.491383i) q^{41} +(-4.11894 - 2.00856i) q^{42} +(9.13494 + 7.66513i) q^{43} +(0.793124 - 1.37373i) q^{44} +(-8.35694 + 0.0624984i) q^{45} +(-3.99299 - 6.91606i) q^{46} +(8.50255 + 7.13449i) q^{47} +(0.00647654 + 1.73204i) q^{48} +(-2.66974 + 6.47090i) q^{49} +(-2.59380 - 0.944067i) q^{50} +(10.8232 - 1.95018i) q^{51} +(4.16125 + 3.49171i) q^{52} +(3.02977 - 5.24771i) q^{53} +(3.29516 - 4.01770i) q^{54} -4.41885 q^{55} +(2.63996 - 0.174886i) q^{56} +(-11.3094 + 2.03779i) q^{57} +(-0.0620252 - 0.351762i) q^{58} +(1.65619 + 9.39272i) q^{59} +(4.16954 - 2.42812i) q^{60} +(-4.30173 - 3.60958i) q^{61} +(1.24632 - 2.15869i) q^{62} +(-6.43912 - 4.64087i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.62772 - 14.9025i) q^{65} +(1.75815 - 2.11127i) q^{66} +(-2.15056 - 0.782738i) q^{67} +(-4.86393 + 4.08132i) q^{68} +(-4.77943 - 12.9802i) q^{69} +(-4.09902 - 6.12535i) q^{70} +(0.0982486 + 0.170172i) q^{71} +(-0.498836 + 2.95824i) q^{72} +(3.32722 + 5.76291i) q^{73} +(-0.688371 + 3.90394i) q^{74} +(-4.14931 - 2.37496i) q^{75} +(5.08245 - 4.26468i) q^{76} +(-3.38624 - 2.47925i) q^{77} +(6.07472 + 7.18484i) q^{78} +(-2.43040 + 0.884592i) q^{79} +(-1.39286 + 2.41251i) q^{80} +(6.80710 - 5.88756i) q^{81} +(0.249482 + 0.432115i) q^{82} +(3.07726 - 17.4520i) q^{83} +(4.55751 + 0.478667i) q^{84} +(16.6210 + 6.04955i) q^{85} +(-11.2057 - 4.07853i) q^{86} +(-0.00231335 - 0.618665i) q^{87} +(-0.275449 + 1.56215i) q^{88} -1.32558 q^{89} +(7.83158 - 2.91697i) q^{90} +(10.3749 - 9.94573i) q^{91} +(6.11761 + 5.13328i) q^{92} +(2.76278 - 3.31766i) q^{93} +(-10.4299 - 3.79618i) q^{94} +(-17.3677 - 6.32134i) q^{95} +(-0.598478 - 1.62537i) q^{96} +(-6.75544 - 5.66849i) q^{97} +(0.295555 - 6.99376i) q^{98} +(3.62243 - 3.08604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

Introduction

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