LMFDB - Embedded newform 418.2.q.a.109.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(21,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("418.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.q (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			109.10
Character	$\chi$	$=$	418.109
Dual form			418.2.q.a.395.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(2.84334 + 0.501357i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.382944 - 0.321328i) q^{5} +(2.84334 - 0.501357i) q^{6} +(-0.682188 + 0.393861i) q^{7} +(0.500000 - 0.866025i) q^{8} +(5.01412 + 1.82499i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(2.84334 + 0.501357i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.382944 - 0.321328i) q^{5} +(2.84334 - 0.501357i) q^{6} +(-0.682188 + 0.393861i) q^{7} +(0.500000 - 0.866025i) q^{8} +(5.01412 + 1.82499i) q^{9} +(-0.469750 - 0.170975i) q^{10} +(-2.47575 + 2.20695i) q^{11} +(2.50039 - 1.44360i) q^{12} +(0.636404 + 3.60923i) q^{13} +(-0.506338 + 0.603431i) q^{14} +(-0.927739 - 1.10564i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-2.66319 - 7.31706i) q^{17} +5.33592 q^{18} +(-4.34422 + 0.357400i) q^{19} -0.499898 q^{20} +(-2.13715 + 0.777861i) q^{21} +(-1.57162 + 2.92062i) q^{22} +(5.12411 - 4.29964i) q^{23} +(1.85586 - 2.21172i) q^{24} +(-0.824847 - 4.67794i) q^{25} +(1.83245 + 3.17390i) q^{26} +(5.84070 + 3.37213i) q^{27} +(-0.269417 + 0.740217i) q^{28} +(3.72606 + 1.35618i) q^{29} +(-1.24994 - 0.721652i) q^{30} +(-9.28076 + 5.35825i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-8.14587 + 5.03388i) q^{33} +(-5.00517 - 5.96493i) q^{34} +(0.387799 + 0.0683793i) q^{35} +(5.01412 - 1.82499i) q^{36} -5.42973i q^{37} +(-3.96000 + 1.82166i) q^{38} +10.5813i q^{39} +(-0.469750 + 0.170975i) q^{40} +(-1.78113 + 10.1013i) q^{41} +(-1.74222 + 1.46190i) q^{42} +(3.84732 - 4.58506i) q^{43} +(-0.477934 + 3.28201i) q^{44} +(-1.33371 - 2.31005i) q^{45} +(3.34452 - 5.79289i) q^{46} +(-2.80828 - 1.02213i) q^{47} +(0.987480 - 2.71308i) q^{48} +(-3.18975 + 5.52480i) q^{49} +(-2.37505 - 4.11371i) q^{50} +(-3.90389 - 22.1401i) q^{51} +(2.80748 + 2.35576i) q^{52} +(7.20424 + 8.58567i) q^{53} +(6.64180 + 1.17113i) q^{54} +(1.65723 - 0.0496105i) q^{55} +0.787723i q^{56} +(-12.5313 - 1.16180i) q^{57} +3.96519 q^{58} +(-1.10701 - 3.04147i) q^{59} +(-1.42138 - 0.250627i) q^{60} +(2.48206 + 2.95801i) q^{61} +(-6.88843 + 8.20931i) q^{62} +(-4.13937 + 0.729882i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.916039 - 1.58663i) q^{65} +(-5.93293 + 7.51635i) q^{66} +(-0.303270 + 0.833227i) q^{67} +(-6.74344 - 3.89333i) q^{68} +(16.7252 - 9.65631i) q^{69} +(0.387799 - 0.0683793i) q^{70} +(-2.57716 + 3.07134i) q^{71} +(4.08755 - 3.42986i) q^{72} +(7.20898 + 1.27114i) q^{73} +(-1.85708 - 5.10227i) q^{74} -13.7145i q^{75} +(-3.09814 + 3.06620i) q^{76} +(0.819695 - 2.48066i) q^{77} +(3.61902 + 9.94318i) q^{78} +(-0.870146 + 4.93484i) q^{79} +(-0.382944 + 0.321328i) q^{80} +(2.65379 + 2.22679i) q^{81} +(1.78113 + 10.1013i) q^{82} +(11.7879 - 6.80575i) q^{83} +(-1.13716 + 1.96961i) q^{84} +(-1.33133 + 3.65779i) q^{85} +(2.04712 - 5.62441i) q^{86} +(9.91452 + 5.72415i) q^{87} +(0.673402 + 3.24754i) q^{88} +(-1.93725 + 0.341589i) q^{89} +(-2.04336 - 1.71458i) q^{90} +(-1.85568 - 2.21152i) q^{91} +(1.16154 - 6.58743i) q^{92} +(-29.0747 + 10.5823i) q^{93} -2.98851 q^{94} +(1.77844 + 1.25906i) q^{95} -2.88720i q^{96} +(-5.10117 - 14.0153i) q^{97} +(-1.10779 + 6.28257i) q^{98} +(-16.4414 + 6.54771i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9}+O(q^{10}) $ 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9	$ 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9} + 3 q^{11} + 6 q^{13} - 12 q^{14} + 24 q^{15} - 6 q^{17} + 60 q^{18} - 30 q^{19} - 12 q^{20} + 12 q^{21} + 12 q^{22} + 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} + 6 q^{28} - 3 q^{29} - 9 q^{31} - 42 q^{33} - 6 q^{34} - 24 q^{35} - 3 q^{36} + 6 q^{38} + 15 q^{41} + 6 q^{42} - 3 q^{43} + 12 q^{44} - 48 q^{45} + 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} + 36 q^{50} - 45 q^{51} - 3 q^{52} + 24 q^{53} - 27 q^{54} + 6 q^{55} + 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} + 54 q^{61} - 66 q^{63} - 30 q^{64} - 63 q^{66} + 9 q^{67} - 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 36 q^{79} - 93 q^{81} - 15 q^{82} - 36 q^{83} + 24 q^{84} - 60 q^{85} - 3 q^{86} + 54 q^{87} - 3 q^{88} - 3 q^{89} - 24 q^{90} - 12 q^{91} - 102 q^{93} - 12 q^{94} + 24 q^{95} - 6 q^{97} - 18 q^{98} - 78 q^{99}+O(q^{100}) $ 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9 + 3 * q^11 + 6 * q^13 - 12 * q^14 + 24 * q^15 - 6 * q^17 + 60 * q^18 - 30 * q^19 - 12 * q^20 + 12 * q^21 + 12 * q^22 + 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 + 6 * q^28 - 3 * q^29 - 9 * q^31 - 42 * q^33 - 6 * q^34 - 24 * q^35 - 3 * q^36 + 6 * q^38 + 15 * q^41 + 6 * q^42 - 3 * q^43 + 12 * q^44 - 48 * q^45 + 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 + 36 * q^50 - 45 * q^51 - 3 * q^52 + 24 * q^53 - 27 * q^54 + 6 * q^55 + 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 + 54 * q^61 - 66 * q^63 - 30 * q^64 - 63 * q^66 + 9 * q^67 - 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 36 * q^79 - 93 * q^81 - 15 * q^82 - 36 * q^83 + 24 * q^84 - 60 * q^85 - 3 * q^86 + 54 * q^87 - 3 * q^88 - 3 * q^89 - 24 * q^90 - 12 * q^91 - 102 * q^93 - 12 * q^94 + 24 * q^95 - 6 * q^97 - 18 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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
$3$	2.84334	+	0.501357i	1.64160	+	0.289459i	0.916754	−	0.399452i	$-0.130799\pi$
$3$	2.84334	+	0.501357i	1.64160	+	0.289459i	0.724847	+	0.688910i	$0.241911\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.382944	−	0.321328i	−0.171258	−	0.143702i	0.553130	−	0.833095i	$-0.313433\pi$
$5$	−0.382944	−	0.321328i	−0.171258	−	0.143702i	−0.724388	+	0.689392i	$0.757878\pi$
$6$	2.84334	−	0.501357i	1.16079	−	0.204678i
$7$	−0.682188	+	0.393861i	−0.257843	+	0.148866i	−0.623350	−	0.781943i	$-0.714229\pi$
$7$	−0.682188	+	0.393861i	−0.257843	+	0.148866i	0.365507	+	0.930808i	$0.380896\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	5.01412	+	1.82499i	1.67137	+	0.608331i
$10$	−0.469750	−	0.170975i	−0.148548	−	0.0540671i
$11$	−2.47575	+	2.20695i	−0.746468	+	0.665422i
$11$	−2.47575	+	2.20695i	−0.746468	+	0.665422i
$12$	2.50039	−	1.44360i	0.721800	−	0.416731i
$13$	0.636404	+	3.60923i	0.176507	+	1.00102i	0.936390	+	0.350960i	$0.114145\pi$
$13$	0.636404	+	3.60923i	0.176507	+	1.00102i	−0.759884	+	0.650059i	$0.774744\pi$
$14$	−0.506338	+	0.603431i	−0.135325	+	0.161274i
$15$	−0.927739	−	1.10564i	−0.239541	−	0.285474i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.66319	−	7.31706i	−0.645919	−	1.77465i	−0.632278	−	0.774742i	$-0.717880\pi$
$17$	−2.66319	−	7.31706i	−0.645919	−	1.77465i	−0.0136416	−	0.999907i	$-0.504342\pi$
$18$	5.33592			1.25769
$19$	−4.34422	+	0.357400i	−0.996633	+	0.0819931i
$19$	−4.34422	+	0.357400i	−0.996633	+	0.0819931i
$20$	−0.499898			−0.111781
$21$	−2.13715	+	0.777861i	−0.466365	+	0.169743i
$22$	−1.57162	+	2.92062i	−0.335071	+	0.622677i
$23$	5.12411	−	4.29964i	1.06845	−	0.896536i	0.0735392	−	0.997292i	$-0.476571\pi$
$23$	5.12411	−	4.29964i	1.06845	−	0.896536i	0.994911	+	0.100756i	$0.0321262\pi$
$24$	1.85586	−	2.21172i	0.378825	−	0.451466i
$25$	−0.824847	−	4.67794i	−0.164969	−	0.935587i
$26$	1.83245	+	3.17390i	0.359373	+	0.622453i
$27$	5.84070	+	3.37213i	1.12404	+	0.648967i
$28$	−0.269417	+	0.740217i	−0.0509150	+	0.139888i
$29$	3.72606	+	1.35618i	0.691912	+	0.251836i	0.663954	−	0.747774i	$-0.268877\pi$
$29$	3.72606	+	1.35618i	0.691912	+	0.251836i	0.0279585	+	0.999609i	$0.491099\pi$
$30$	−1.24994	−	0.721652i	−0.228207	−	0.131755i
$31$	−9.28076	+	5.35825i	−1.66687	+	0.962370i	−0.697564	+	0.716522i	$0.745733\pi$
$31$	−9.28076	+	5.35825i	−1.66687	+	0.962370i	−0.969309	+	0.245847i	$0.920934\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−8.14587	+	5.03388i	−1.41801	+	0.876285i
$34$	−5.00517	−	5.96493i	−0.858379	−	1.02298i
$35$	0.387799	+	0.0683793i	0.0655499	+	0.0115582i
$36$	5.01412	−	1.82499i	0.835687	−	0.304165i
$37$		−	5.42973i		−	0.892641i	−0.894873	−	0.446321i	$-0.852734\pi$
$37$		−	5.42973i		−	0.892641i	0.894873	−	0.446321i	$-0.147266\pi$
$38$	−3.96000	+	1.82166i	−0.642396	+	0.295512i
$39$			10.5813i			1.69437i
$40$	−0.469750	+	0.170975i	−0.0742741	+	0.0270335i
$41$	−1.78113	+	10.1013i	−0.278166	+	1.57756i	0.450554	+	0.892749i	$0.351227\pi$
$41$	−1.78113	+	10.1013i	−0.278166	+	1.57756i	−0.728720	+	0.684811i	$0.759885\pi$
$42$	−1.74222	+	1.46190i	−0.268831	+	0.225576i
$43$	3.84732	−	4.58506i	0.586711	−	0.699215i	−0.388259	−	0.921550i	$-0.626923\pi$
$43$	3.84732	−	4.58506i	0.586711	−	0.699215i	0.974970	+	0.222335i	$0.0713679\pi$
$44$	−0.477934	+	3.28201i	−0.0720513	+	0.494781i
$45$	−1.33371	−	2.31005i	−0.198817	−	0.344362i
$46$	3.34452	−	5.79289i	0.493123	−	0.854114i
$47$	−2.80828	−	1.02213i	−0.409629	−	0.149093i	0.128983	−	0.991647i	$-0.458829\pi$
$47$	−2.80828	−	1.02213i	−0.409629	−	0.149093i	−0.538612	+	0.842554i	$0.681051\pi$
$48$	0.987480	−	2.71308i	0.142531	−	0.391599i
$49$	−3.18975	+	5.52480i	−0.455678	+	0.789258i
$50$	−2.37505	−	4.11371i	−0.335883	−	0.581766i
$51$	−3.90389	−	22.1401i	−0.546655	−	3.10023i
$52$	2.80748	+	2.35576i	0.389327	+	0.326684i
$53$	7.20424	+	8.58567i	0.989578	+	1.17933i	0.983785	+	0.179350i	$0.0573994\pi$
$53$	7.20424	+	8.58567i	0.989578	+	1.17933i	0.00579266	+	0.999983i	$0.498156\pi$
$54$	6.64180	+	1.17113i	0.903835	+	0.159370i
$55$	1.65723	−	0.0496105i	0.223461	−	0.00668948i
$56$			0.787723i			0.105264i
$57$	−12.5313	−	1.16180i	−1.65981	−	0.153884i
$58$	3.96519			0.520655
$59$	−1.10701	−	3.04147i	−0.144120	−	0.395966i	0.846540	−	0.532326i	$-0.178682\pi$
$59$	−1.10701	−	3.04147i	−0.144120	−	0.395966i	−0.990659	+	0.136360i	$0.956460\pi$
$60$	−1.42138	−	0.250627i	−0.183499	−	0.0323558i
$61$	2.48206	+	2.95801i	0.317796	+	0.378734i	0.901167	−	0.433471i	$-0.142711\pi$
$61$	2.48206	+	2.95801i	0.317796	+	0.378734i	−0.583372	+	0.812205i	$0.698267\pi$
$62$	−6.88843	+	8.20931i	−0.874831	+	1.04258i
$63$	−4.13937	+	0.729882i	−0.521511	+	0.0919565i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.916039	−	1.58663i	0.113621	−	0.196797i
$66$	−5.93293	+	7.51635i	−0.730293	+	0.925198i
$67$	−0.303270	+	0.833227i	−0.0370503	+	0.101795i	−0.956838	−	0.290621i	$-0.906138\pi$
$67$	−0.303270	+	0.833227i	−0.0370503	+	0.101795i	0.919788	+	0.392416i	$0.128360\pi$
$68$	−6.74344	−	3.89333i	−0.817763	−	0.472135i
$69$	16.7252	−	9.65631i	2.01348	−	1.16248i
$70$	0.387799	−	0.0683793i	0.0463508	−	0.00817289i
$71$	−2.57716	+	3.07134i	−0.305852	+	0.364500i	−0.896975	−	0.442081i	$-0.854240\pi$
$71$	−2.57716	+	3.07134i	−0.305852	+	0.364500i	0.591123	+	0.806581i	$0.298685\pi$
$72$	4.08755	−	3.42986i	0.481723	−	0.404213i
$73$	7.20898	+	1.27114i	0.843747	+	0.148775i	0.578782	−	0.815483i	$-0.303528\pi$
$73$	7.20898	+	1.27114i	0.843747	+	0.148775i	0.264965	+	0.964258i	$0.414640\pi$
$74$	−1.85708	−	5.10227i	−0.215881	−	0.593127i
$75$		−	13.7145i		−	1.58361i
$76$	−3.09814	+	3.06620i	−0.355380	+	0.351717i
$77$	0.819695	−	2.48066i	0.0934129	−	0.282698i
$78$	3.61902	+	9.94318i	0.409773	+	1.12584i
$79$	−0.870146	+	4.93484i	−0.0978990	+	0.555213i	0.895921	+	0.444213i	$0.146517\pi$
$79$	−0.870146	+	4.93484i	−0.0978990	+	0.555213i	−0.993820	+	0.111000i	$0.964595\pi$
$80$	−0.382944	+	0.321328i	−0.0428144	+	0.0359256i
$81$	2.65379	+	2.22679i	0.294865	+	0.247421i
$82$	1.78113	+	10.1013i	0.196693	+	1.11550i
$83$	11.7879	−	6.80575i	1.29389	−	0.747029i	0.314550	−	0.949241i	$-0.398146\pi$
$83$	11.7879	−	6.80575i	1.29389	−	0.747029i	0.979342	+	0.202212i	$0.0648131\pi$
$84$	−1.13716	+	1.96961i	−0.124074	+	0.214902i
$85$	−1.33133	+	3.65779i	−0.144402	+	0.396743i
$86$	2.04712	−	5.62441i	0.220746	−	0.606496i
$87$	9.91452	+	5.72415i	1.06295	+	0.613693i
$88$	0.673402	+	3.24754i	0.0717848	+	0.346189i
$89$	−1.93725	+	0.341589i	−0.205348	+	0.0362084i	−0.275376	−	0.961337i	$-0.588802\pi$
$89$	−1.93725	+	0.341589i	−0.205348	+	0.0362084i	0.0700279	+	0.997545i	$0.477691\pi$
$90$	−2.04336	−	1.71458i	−0.215389	−	0.180733i
$91$	−1.85568	−	2.21152i	−0.194528	−	0.231830i
$92$	1.16154	−	6.58743i	0.121099	−	0.686787i
$93$	−29.0747	+	10.5823i	−3.01491	+	1.09734i
$94$	−2.98851			−0.308241
$95$	1.77844	+	1.25906i	0.182464	+	0.129177i
$96$		−	2.88720i		−	0.294674i
$97$	−5.10117	−	14.0153i	−0.517945	−	1.42304i	−0.872780	−	0.488114i	$-0.837685\pi$
$97$	−5.10117	−	14.0153i	−0.517945	−	1.42304i	0.354835	−	0.934929i	$-0.384537\pi$
$98$	−1.10779	+	6.28257i	−0.111903	+	0.634636i
$99$	−16.4414	+	6.54771i	−1.65242	+	0.658070i
$100$	−3.63879	−	3.05331i	−0.363879	−	0.305331i
$101$	8.89868	−	1.56908i	0.885452	−	0.156129i	0.287614	−	0.957746i	$-0.407138\pi$
$101$	8.89868	−	1.56908i	0.885452	−	0.156129i	0.597838	+	0.801617i	$0.296027\pi$
$102$	−11.2408	−	19.4697i	−1.11301	−	1.92778i
$103$	2.60616	+	1.50467i	0.256792	+	0.148259i	0.622871	−	0.782325i	$-0.285966\pi$
$103$	2.60616	+	1.50467i	0.256792	+	0.148259i	−0.366078	+	0.930584i	$0.619300\pi$
$104$	3.44388	+	1.25347i	0.337701	+	0.122913i
$105$	1.06836	+	0.388851i	0.104261	+	0.0379480i
$106$	9.70624	+	5.60390i	0.942754	+	0.544299i
$107$	0.807929	+	1.39937i	0.0781055	+	0.135283i	0.902433	−	0.430831i	$-0.141780\pi$
$107$	0.807929	+	1.39937i	0.0781055	+	0.135283i	−0.824327	+	0.566114i	$0.808446\pi$
$108$	6.64180	−	1.17113i	0.639108	−	0.112692i
$109$	−4.52846	−	3.79983i	−0.433748	−	0.363958i	0.399616	−	0.916683i	$-0.369144\pi$
$109$	−4.52846	−	3.79983i	−0.433748	−	0.363958i	−0.833364	+	0.552725i	$0.813588\pi$
$110$	1.54032	−	0.613425i	0.146864	−	0.0584878i
$111$	2.72223	−	15.4385i	0.258383	−	1.46536i
$112$	0.269417	+	0.740217i	0.0254575	+	0.0699439i
$113$			4.12316i			0.387874i	0.981014	+	0.193937i	$0.0621258\pi$
$113$			4.12316i			0.387874i	−0.981014	+	0.193937i	$0.937874\pi$
$114$	−12.1729	+	3.19421i	−1.14010	+	0.299165i
$115$	−3.34384			−0.311815
$116$	3.72606	−	1.35618i	0.345956	−	0.125918i
$117$	−3.39580	+	19.2585i	−0.313942	+	1.78045i
$118$	−2.08049	−	2.47943i	−0.191525	−	0.228250i
$119$	4.69871	+	3.94268i	0.430730	+	0.361425i
$120$	−1.42138	+	0.250627i	−0.129753	+	0.0228790i
$121$	1.25871	−	10.9277i	0.114428	−	0.993432i
$122$	3.34407	+	1.93070i	0.302758	+	0.174798i
$123$	−10.1287	+	27.8285i	−0.913277	+	2.50921i
$124$	−3.66526	+	10.0702i	−0.329150	+	0.904332i
$125$	−2.43703	+	4.22106i	−0.217974	+	0.377543i
$126$	−3.64010	+	2.10161i	−0.324286	+	0.187226i
$127$	3.31403	+	18.7948i	0.294073	+	1.66777i	0.670946	+	0.741506i	$0.265888\pi$
$127$	3.31403	+	18.7948i	0.294073	+	1.66777i	−0.376873	+	0.926265i	$0.623001\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	13.2380	−	11.1080i	1.16554	−	0.978004i
$130$	0.318137	−	1.80424i	0.0279025	−	0.158243i
$131$	−1.10650	−	3.04008i	−0.0966753	−	0.265613i	0.881923	−	0.471394i	$-0.156249\pi$
$131$	−1.10650	−	3.04008i	−0.0966753	−	0.265613i	−0.978598	+	0.205781i	$0.934027\pi$
$132$	−3.00439	+	9.09224i	−0.261498	+	0.791378i
$133$	2.82281	−	1.95483i	0.244769	−	0.169506i
$134$			0.886702i			0.0765994i
$135$	−1.15310	−	3.16812i	−0.0992432	−	0.272668i
$136$	−7.66836	−	1.35214i	−0.657556	−	0.115945i
$137$	3.03730	−	2.54860i	0.259494	−	0.217741i	−0.503754	−	0.863847i	$-0.668048\pi$
$137$	3.03730	−	2.54860i	0.259494	−	0.217741i	0.763248	+	0.646106i	$0.223604\pi$
$138$	12.4139	−	14.7943i	1.05674	−	1.25938i
$139$	−18.8682	+	3.32698i	−1.60038	+	0.282191i	−0.901413	−	0.432960i	$-0.857469\pi$
$139$	−18.8682	+	3.32698i	−1.60038	+	0.282191i	−0.698971	+	0.715150i	$0.746358\pi$
$140$	0.341024	−	0.196890i	0.0288218	−	0.0166403i
$141$	−7.47243	−	4.31421i	−0.629292	−	0.363322i
$142$	−1.37128	+	3.76755i	−0.115075	+	0.316166i
$143$	−9.54098	−	7.53104i	−0.797856	−	0.629777i
$144$	2.66796	−	4.62104i	0.222330	−	0.385087i
$145$	−0.991096	−	1.71663i	−0.0823060	−	0.142558i
$146$	7.20898	−	1.27114i	0.596619	−	0.105200i
$147$	−11.8394	+	14.1097i	−0.976499	+	1.16375i
$148$	−3.49016	−	4.15941i	−0.286889	−	0.341901i
$149$	14.1060	+	2.48726i	1.15561	+	0.203765i	0.718422	−	0.695608i	$-0.244865\pi$
$149$	14.1060	+	2.48726i	1.15561	+	0.203765i	0.437184	+	0.899372i	$0.355976\pi$
$150$	−4.69063	−	12.8874i	−0.382989	−	1.05225i
$151$	−9.33219			−0.759443			−0.379722	−	0.925101i	$-0.623980\pi$
$151$	−9.33219			−0.759443			−0.379722	+	0.925101i	$0.623980\pi$
$152$	−1.86259	+	3.94091i	−0.151076	+	0.319650i
$153$		−	41.5490i		−	3.35904i
$154$	−0.0781746	−	2.61141i	−0.00629949	−	0.210433i
$155$	5.27577	+	0.930260i	0.423760	+	0.0747203i
$156$	6.80153	+	8.10575i	0.544559	+	0.648980i
$157$	−0.931253	−	0.781414i	−0.0743221	−	0.0623636i	0.604870	−	0.796324i	$-0.293225\pi$
$157$	−0.931253	−	0.781414i	−0.0743221	−	0.0623636i	−0.679192	+	0.733961i	$0.737670\pi$
$158$	0.870146	+	4.93484i	0.0692251	+	0.392595i
$159$	16.1796	+	28.0239i	1.28312	+	2.22244i
$160$	−0.249949	+	0.432924i	−0.0197602	+	0.0342257i
$161$	−1.80214	+	4.95135i	−0.142029	+	0.390221i
$162$	3.25535	+	1.18485i	0.255765	+	0.0930907i
$163$	3.78849	−	6.56186i	0.296738	−	0.513965i	−0.678650	−	0.734462i	$-0.737435\pi$
$163$	3.78849	−	6.56186i	0.296738	−	0.513965i	0.975388	+	0.220497i	$0.0707680\pi$
$164$	5.12857	+	8.88295i	0.400474	+	0.693642i
$165$	4.73694	+	0.689805i	0.368770	+	0.0537012i
$166$	8.74931	−	10.4270i	0.679078	−	0.809294i
$167$	−2.85558	+	2.39611i	−0.220971	+	0.185417i	−0.746553	−	0.665326i	$-0.768292\pi$
$167$	−2.85558	+	2.39611i	−0.220971	+	0.185417i	0.525581	+	0.850743i	$0.323848\pi$
$168$	−0.394930	+	2.23976i	−0.0304695	+	0.172801i
$169$	−0.405499	+	0.147590i	−0.0311922	+	0.0113530i
$170$			3.89253i			0.298544i
$171$	−22.4347	−	6.13612i	−1.71563	−	0.469241i
$172$		−	5.98537i		−	0.456380i
$173$	4.05261	−	1.47503i	0.308114	−	0.112144i	−0.183335	−	0.983050i	$-0.558689\pi$
$173$	4.05261	−	1.47503i	0.308114	−	0.112144i	0.491450	+	0.870906i	$0.336467\pi$
$174$	11.2744	+	1.98798i	0.854708	+	0.150708i
$175$	2.40516	+	2.86636i	0.181813	+	0.216676i
$176$	1.74352	+	2.82137i	0.131422	+	0.212669i
$177$	−1.62273	−	9.20293i	−0.121972	−	0.691735i
$178$	−1.70359	+	0.983567i	−0.127689	+	0.0737214i
$179$	1.27390	+	0.735487i	0.0952158	+	0.0549729i	0.546852	−	0.837229i	$-0.315826\pi$
$179$	1.27390	+	0.735487i	0.0952158	+	0.0549729i	−0.451636	+	0.892202i	$0.649159\pi$
$180$	−2.50655	−	0.912310i	−0.186827	−	0.0679995i
$181$	0.848847	−	2.33219i	0.0630943	−	0.173350i	−0.904140	−	0.427237i	$-0.859487\pi$
$181$	0.848847	−	2.33219i	0.0630943	−	0.173350i	0.967234	+	0.253887i	$0.0817091\pi$
$182$	−2.50015	−	1.44346i	−0.185324	−	0.106997i
$183$	5.57432	+	9.65501i	0.412066	+	0.713719i
$184$	−1.16154	−	6.58743i	−0.0856299	−	0.485631i
$185$	−1.74472	+	2.07928i	−0.128275	+	0.152872i
$186$	−23.7019	+	19.8883i	−1.73791	+	1.45828i
$187$	22.7418	+	12.2377i	1.66305	+	0.894909i
$188$	−2.80828	+	1.02213i	−0.204815	+	0.0745465i
$189$	−5.31261			−0.386435
$190$	2.10181	+	0.574865i	0.152481	+	0.0417051i
$191$	13.1283			0.949931			0.474966	−	0.880004i	$-0.342461\pi$
$191$	13.1283			0.949931			0.474966	+	0.880004i	$0.342461\pi$
$192$	−0.987480	−	2.71308i	−0.0712653	−	0.195800i
$193$	2.59866	−	14.7377i	0.187056	−	1.06085i	−0.736230	−	0.676731i	$-0.763396\pi$
$193$	2.59866	−	14.7377i	0.187056	−	1.06085i	0.923286	−	0.384114i	$-0.125493\pi$
$194$	−9.58706	−	11.4254i	−0.688311	−	0.820297i
$195$	3.40007	−	4.05205i	0.243484	−	0.290173i
$196$	1.10779	+	6.28257i	0.0791277	+	0.448755i
$197$	18.3821	−	10.6129i	1.30967	−	0.756140i	0.327631	−	0.944806i	$-0.393750\pi$
$197$	18.3821	−	10.6129i	1.30967	−	0.756140i	0.982041	+	0.188666i	$0.0604164\pi$
$198$	−13.2104	+	11.7761i	−0.938824	+	0.836893i
$199$	20.0003	+	7.27952i	1.41778	+	0.516031i	0.933404	−	0.358826i	$-0.116823\pi$
$199$	20.0003	+	7.27952i	1.41778	+	0.516031i	0.484380	+	0.874858i	$0.339045\pi$
$200$	−4.46364	−	1.62463i	−0.315627	−	0.114879i
$201$	−1.28004	+	2.21710i	−0.0902872	+	0.156382i
$202$	7.82537	−	4.51798i	0.550591	−	0.317884i
$203$	−3.07602	+	0.542385i	−0.215894	+	0.0380680i
$204$	−17.2219	−	14.4509i	−1.20578	−	1.01177i
$205$	3.92791	−	3.29591i	0.274337	−	0.230196i
$206$	2.96361	+	0.522565i	0.206485	+	0.0364088i
$207$	33.5397	−	12.2075i	2.33117	−	0.848477i
$208$	3.66490			0.254115
$209$	9.96646	−	10.4723i	0.689394	−	0.724386i
$210$	1.13692			0.0784552
$211$	−8.90448	+	3.24097i	−0.613010	+	0.223117i	−0.629820	−	0.776741i	$-0.716871\pi$
$211$	−8.90448	+	3.24097i	−0.613010	+	0.223117i	0.0168099	+	0.999859i	$0.494649\pi$
$212$	11.0375	+	1.94621i	0.758061	+	0.133667i
$213$	−8.86756	+	7.44076i	−0.607595	+	0.509833i
$214$	1.23782	+	1.03865i	0.0846156	+	0.0710009i
$215$	−2.94662	+	0.519568i	−0.200958	+	0.0354343i
$216$	5.84070	−	3.37213i	0.397410	−	0.229444i
$217$	4.22081	−	7.31066i	0.286527	−	0.496280i
$218$	−5.55498	−	2.02185i	−0.376231	−	0.136937i
$219$	19.8602	+	7.22854i	1.34203	+	0.488459i
$220$	1.23762	−	1.10325i	0.0834406	−	0.0743812i
$221$	24.7141	−	14.2687i	1.66245	−	0.959815i
$222$	−2.72223	−	15.4385i	−0.182704	−	1.03617i
$223$	−6.30946	+	7.51932i	−0.422512	+	0.503531i	−0.934747	−	0.355315i	$-0.884374\pi$
$223$	−6.30946	+	7.51932i	−0.422512	+	0.503531i	0.512234	+	0.858846i	$0.328818\pi$
$224$	0.506338	+	0.603431i	0.0338312	+	0.0403184i
$225$	4.40131	−	24.9611i	0.293421	−	1.66407i
$226$	1.41020	+	3.87450i	0.0938054	+	0.257728i
$227$	−18.8139			−1.24872			−0.624360	−	0.781137i	$-0.714640\pi$
$227$	−18.8139			−1.24872			−0.624360	+	0.781137i	$0.714640\pi$
$228$	−10.3463	+	7.16495i	−0.685200	+	0.474511i
$229$	10.1958			0.673756			0.336878	−	0.941548i	$-0.390629\pi$
$229$	10.1958			0.673756			0.336878	+	0.941548i	$0.390629\pi$
$230$	−3.14218	+	1.14366i	−0.207189	+	0.0754108i
$231$	3.57436	−	6.64239i	0.235176	−	0.437037i
$232$	3.03751	−	2.54878i	0.199423	−	0.167335i
$233$	8.25297	−	9.83551i	0.540670	−	0.644346i	−0.424668	−	0.905349i	$-0.639609\pi$
$233$	8.25297	−	9.83551i	0.540670	−	0.644346i	0.965338	+	0.261004i	$0.0840534\pi$
$234$	3.39580	+	19.2585i	0.221990	+	1.25897i
$235$	0.746974	+	1.29380i	0.0487272	+	0.0843980i
$236$	−2.80304	−	1.61833i	−0.182462	−	0.105345i
$237$	−4.94823	+	13.5952i	−0.321422	+	0.883101i
$238$	5.76382	+	2.09786i	0.373613	+	0.135984i
$239$	11.1548	+	6.44024i	0.721545	+	0.416584i	0.815321	−	0.579009i	$-0.196560\pi$
$239$	11.1548	+	6.44024i	0.721545	+	0.416584i	−0.0937758	+	0.995593i	$0.529894\pi$
$240$	−1.24994	+	0.721652i	−0.0806832	+	0.0465825i
$241$	−4.42633	−	25.1030i	−0.285125	−	1.61702i	−0.704839	−	0.709368i	$-0.748981\pi$
$241$	−4.42633	−	25.1030i	−0.285125	−	1.61702i	0.419714	−	0.907657i	$-0.362131\pi$
$242$	−2.55471	−	10.6992i	−0.164223	−	0.687772i
$243$	−6.57619	−	7.83720i	−0.421863	−	0.502757i
$244$	3.80274	+	0.670526i	0.243446	+	0.0429260i
$245$	2.99677	−	1.09073i	0.191457	−	0.0696845i
$246$			29.6144i			1.88815i
$247$	−4.05462	−	15.4518i	−0.257989	−	0.983176i
$248$			10.7165i			0.680498i
$249$	36.9291	−	13.4411i	2.34029	−	0.851795i
$250$	−0.846371	+	4.80001i	−0.0535292	+	0.303579i
$251$	6.76166	−	5.67370i	0.426792	−	0.358121i	−0.403948	−	0.914782i	$-0.632362\pi$
$251$	6.76166	−	5.67370i	0.426792	−	0.358121i	0.830740	+	0.556661i	$0.187918\pi$
$252$	−2.70178	+	3.21986i	−0.170196	+	0.202832i
$253$	−3.19693	+	21.9535i	−0.200989	+	1.38021i
$254$	9.54238	+	16.5279i	0.598742	+	1.03705i
$255$	−5.61926	+	9.73284i	−0.351892	+	0.609494i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−4.59712	+	12.6305i	−0.286761	+	0.787868i	0.709754	+	0.704450i	$0.248806\pi$
$257$	−4.59712	+	12.6305i	−0.286761	+	0.787868i	−0.996515	+	0.0834185i	$0.973416\pi$
$258$	8.64048	−	14.9657i	0.537933	−	0.931727i
$259$	2.13856	+	3.70409i	0.132884	+	0.230161i
$260$	−0.318137	−	1.80424i	−0.0197300	−	0.111895i
$261$	16.2079	+	13.6001i	1.00325	+	0.841823i
$262$	−2.07954	−	2.47830i	−0.128474	−	0.153110i
$263$	−12.9705	−	2.28704i	−0.799793	−	0.141025i	−0.241209	−	0.970473i	$-0.577544\pi$
$263$	−12.9705	−	2.28704i	−0.799793	−	0.141025i	−0.558584	+	0.829448i	$0.688655\pi$
$264$	0.286529	+	9.57147i	0.0176347	+	0.589083i
$265$		−	5.60276i		−	0.344175i
$266$	1.98398	−	2.80240i	0.121646	−	0.171826i
$267$	−5.67951			−0.347580
$268$	0.303270	+	0.833227i	0.0185252	+	0.0508974i
$269$	13.4114	+	2.36479i	0.817708	+	0.144184i	0.566830	−	0.823835i	$-0.308170\pi$
$269$	13.4114	+	2.36479i	0.817708	+	0.144184i	0.250878	+	0.968019i	$0.419281\pi$
$270$	−2.16712	−	2.58268i	−0.131887	−	0.157177i
$271$	−10.5461	+	12.5683i	−0.640628	+	0.763471i	−0.984469	−	0.175557i	$-0.943827\pi$
$271$	−10.5461	+	12.5683i	−0.640628	+	0.763471i	0.343841	+	0.939028i	$0.388272\pi$
$272$	−7.66836	+	1.35214i	−0.464963	+	0.0819855i
$273$	−4.16757	−	7.21844i	−0.252233	−	0.436880i
$274$	1.98246	−	3.43372i	0.119765	−	0.207438i
$275$	12.3661	+	9.76102i	0.745704	+	0.588612i
$276$	6.60530	−	18.1479i	0.397592	−	1.09238i
$277$	−21.2057	−	12.2431i	−1.27413	−	0.735618i	−0.298366	−	0.954452i	$-0.596442\pi$
$277$	−21.2057	−	12.2431i	−1.27413	−	0.735618i	−0.975762	+	0.218833i	$0.929775\pi$
$278$	−16.5925	+	9.57966i	−0.995150	+	0.574550i
$279$	−56.3136	+	9.92961i	−3.37141	+	0.594470i
$280$	0.253118	−	0.301654i	0.0151267	−	0.0180273i
$281$	−17.3918	+	14.5934i	−1.03751	+	0.870571i	−0.991725	−	0.128380i	$-0.959022\pi$
$281$	−17.3918	+	14.5934i	−1.03751	+	0.870571i	−0.0457816	+	0.998951i	$0.514578\pi$
$282$	−8.49733	−	1.49831i	−0.506009	−	0.0892230i
$283$	−3.14369	−	8.63721i	−0.186873	−	0.513429i	0.810511	−	0.585724i	$-0.199190\pi$
$283$	−3.14369	−	8.63721i	−0.186873	−	0.513429i	−0.997383	+	0.0722955i	$0.976968\pi$
$284$			4.00934i			0.237911i
$285$	4.42546	+	4.47155i	0.262141	+	0.264872i
$286$	−11.5414	−	3.81366i	−0.682454	−	0.225506i
$287$	−2.76345	−	7.59252i	−0.163121	−	0.448172i
$288$	0.926573	−	5.25485i	0.0545988	−	0.309645i
$289$	−33.4241	+	28.0461i	−1.96612	+	1.64977i
$290$	−1.51845	−	1.27413i	−0.0891663	−	0.0748194i
$291$	−7.47765	−	42.4079i	−0.438348	−	2.48599i
$292$	6.33947	−	3.66009i	0.370989	−	0.214191i
$293$	5.77029	−	9.99443i	0.337104	−	0.583881i	−0.646783	−	0.762674i	$-0.723886\pi$
$293$	5.77029	−	9.99443i	0.337104	−	0.583881i	0.983887	+	0.178793i	$0.0572194\pi$
$294$	−6.29962	+	17.3081i	−0.367402	+	1.00943i
$295$	−0.553390	+	1.52043i	−0.0322196	+	0.0885226i
$296$	−4.70228	−	2.71486i	−0.273314	−	0.157798i
$297$	−21.9023	+	4.54160i	−1.27090	+	0.263530i
$298$	14.1060	−	2.48726i	0.817137	−	0.144083i
$299$	18.7794	+	15.7578i	1.08604	+	0.911295i
$300$	−8.81550	−	10.5059i	−0.508963	−	0.606559i
$301$	−0.818719	+	4.64318i	−0.0471902	+	0.267629i
$302$	−8.76939	+	3.19180i	−0.504622	+	0.183667i
$303$	26.0886			1.49875
$304$	−0.402396	+	4.34029i	−0.0230790	+	0.248932i
$305$		−	1.93031i		−	0.110529i
$306$	−14.2106	−	39.0433i	−0.812365	−	2.23195i
$307$	−3.53775	+	20.0636i	−0.201910	+	1.14509i	0.700318	+	0.713831i	$0.253042\pi$
$307$	−3.53775	+	20.0636i	−0.201910	+	1.14509i	−0.902228	+	0.431259i	$0.858070\pi$
$308$	−0.966615	−	2.42719i	−0.0550780	−	0.138302i
$309$	6.65581	+	5.58489i	0.378636	+	0.317713i
$310$	5.27577	−	0.930260i	0.299643	−	0.0528352i
$311$	6.53120	+	11.3124i	0.370350	+	0.641465i	0.989619	−	0.143713i	$-0.0459044\pi$
$311$	6.53120	+	11.3124i	0.370350	+	0.641465i	−0.619269	+	0.785179i	$0.712571\pi$
$312$	9.16368	+	5.29065i	0.518791	+	0.299524i
$313$	0.0546296	+	0.0198835i	0.00308785	+	0.00112388i	0.343564	−	0.939129i	$-0.388366\pi$
$313$	0.0546296	+	0.0198835i	0.00308785	+	0.00112388i	−0.340476	+	0.940253i	$0.610588\pi$
$314$	−1.14235	−	0.415782i	−0.0644666	−	0.0234639i
$315$	1.81968	+	1.05059i	0.102527	+	0.0591941i
$316$	2.50548	+	4.33963i	0.140945	+	0.244123i
$317$	−14.2013	+	2.50406i	−0.797622	+	0.140642i	−0.557583	−	0.830121i	$-0.688271\pi$
$317$	−14.2013	+	2.50406i	−0.797622	+	0.140642i	−0.240039	+	0.970763i	$0.577160\pi$
$318$	24.7886	+	20.8001i	1.39007	+	1.16641i
$319$	−12.2178	+	4.86569i	−0.684067	+	0.272426i
$320$	−0.0868064	+	0.492303i	−0.00485262	+	0.0275206i
$321$	1.59563	+	4.38395i	0.0890593	+	0.244688i
$322$			5.26911i			0.293636i
$323$	14.1846	+	30.8351i	0.789253	+	1.71571i
$324$	3.46427			0.192460
$325$	16.3588	−	5.95412i	0.907423	−	0.330275i
$326$	1.31573	−	7.46188i	0.0728715	−	0.413275i
$327$	−10.9709	−	13.0746i	−0.606690	−	0.723025i
$328$	7.85743	+	6.59317i	0.433854	+	0.364047i
$329$	2.31835	−	0.408788i	0.127815	−	0.0225372i
$330$	4.68719	−	0.971924i	0.258022	−	0.0535026i
$331$	6.18025	+	3.56817i	0.339697	+	0.196124i	0.660138	−	0.751144i	$-0.270498\pi$
$331$	6.18025	+	3.56817i	0.339697	+	0.196124i	−0.320441	+	0.947269i	$0.603831\pi$
$332$	4.65541	−	12.7906i	0.255499	−	0.701977i
$333$	9.90920	−	27.2253i	0.543021	−	1.49194i
$334$	−1.86385	+	3.22828i	−0.101985	+	0.176643i
$335$	0.383875	−	0.221630i	0.0209733	−	0.0121090i
$336$	0.394930	+	2.23976i	0.0215452	+	0.122189i
$337$	6.15116	+	5.16144i	0.335075	+	0.281161i	0.794764	−	0.606919i	$-0.207595\pi$
$337$	6.15116	+	5.16144i	0.335075	+	0.281161i	−0.459689	+	0.888080i	$0.652039\pi$
$338$	−0.330566	+	0.277378i	−0.0179804	+	0.0150874i
$339$	−2.06717	+	11.7235i	−0.112274	+	0.636735i
$340$	1.33133	+	3.65779i	0.0722012	+	0.198371i
$341$	11.1515	−	33.7479i	0.603885	−	1.82755i
$342$	−23.1804	+	1.90706i	−1.25345	+	0.103122i
$343$		−	10.5393i		−	0.569070i
$344$	−2.04712	−	5.62441i	−0.110373	−	0.303248i
$345$	−9.50766	−	1.67646i	−0.511875	−	0.0902575i
$346$	3.30372	−	2.77215i	0.177609	−	0.149032i
$347$	12.2160	−	14.5585i	0.655792	−	0.781542i	−0.330983	−	0.943637i	$-0.607380\pi$
$347$	12.2160	−	14.5585i	0.655792	−	0.781542i	0.986775	+	0.162094i	$0.0518249\pi$
$348$	11.2744	−	1.98798i	0.604370	−	0.106567i
$349$	−12.7057	+	7.33565i	−0.680122	+	0.392669i	−0.799901	−	0.600132i	$-0.795115\pi$
$349$	−12.7057	+	7.33565i	−0.680122	+	0.392669i	0.119779	+	0.992801i	$0.461781\pi$
$350$	3.24046	+	1.87088i	0.173210	+	0.100003i
$351$	−8.45374	+	23.2265i	−0.451227	+	1.23974i
$352$	2.60334	+	2.05491i	0.138758	+	0.109527i
$353$	11.3850	−	19.7194i	0.605962	−	1.04956i	−0.385936	−	0.922525i	$-0.626122\pi$
$353$	11.3850	−	19.7194i	0.605962	−	1.04956i	0.991899	−	0.127032i	$-0.0405452\pi$
$354$	−4.67245	−	8.09292i	−0.248338	−	0.430134i
$355$	1.97381	−	0.348037i	0.104759	−	0.0184719i
$356$	−1.26445	+	1.50691i	−0.0670157	+	0.0798661i
$357$	11.3833	+	13.5661i	0.602469	+	0.717994i
$358$	1.44863	+	0.255432i	0.0765623	+	0.0135000i
$359$	−2.51111	−	6.89921i	−0.132531	−	0.364126i	0.855621	−	0.517602i	$-0.173175\pi$
$359$	−2.51111	−	6.89921i	−0.132531	−	0.364126i	−0.988152	+	0.153476i	$0.950953\pi$
$360$	−2.66741			−0.140585
$361$	18.7445	−	3.10525i	0.986554	−	0.163434i
$362$		−	2.48186i		−	0.130444i
$363$	9.05763	−	30.4402i	0.475402	−	1.59770i
$364$	−2.84307	−	0.501310i	−0.149017	−	0.0262758i
$365$	−2.35218	−	2.80322i	−0.123119	−	0.146727i
$366$	8.54036	+	7.16621i	0.446412	+	0.374584i
$367$	−0.260646	−	1.47820i	−0.0136056	−	0.0771613i	0.977249	−	0.212096i	$-0.0680288\pi$
$367$	−0.260646	−	1.47820i	−0.0136056	−	0.0771613i	−0.990855	+	0.134934i	$0.956918\pi$
$368$	−3.34452	−	5.79289i	−0.174345	−	0.301975i
$369$	−27.3656	+	47.3987i	−1.42460	+	2.46748i
$370$	−0.928348	+	2.55062i	−0.0482625	+	0.132600i
$371$	−8.29621	−	3.01957i	−0.430718	−	0.156768i
$372$	−15.4703	+	26.7954i	−0.802099	+	1.38928i
$373$	−5.10142	−	8.83591i	−0.264141	−	0.457506i	0.703197	−	0.710995i	$-0.251755\pi$
$373$	−5.10142	−	8.83591i	−0.264141	−	0.457506i	−0.967338	+	0.253489i	$0.918422\pi$
$374$	25.5559	+	3.72151i	1.32146	+	0.192435i
$375$	−9.04555	+	10.7801i	−0.467110	+	0.556680i
$376$	−2.28933	+	1.92098i	−0.118063	+	0.0990667i
$377$	−2.52346	+	14.3113i	−0.129965	+	0.737068i
$378$	−4.99222	+	1.81702i	−0.256772	+	0.0934574i
$379$			8.58017i			0.440734i	0.975417	+	0.220367i	$0.0707255\pi$
$379$			8.58017i			0.440734i	−0.975417	+	0.220367i	$0.929275\pi$
$380$	2.17167	−	0.178663i	0.111404	−	0.00916524i
$381$			55.1015i			2.82294i
$382$	12.3366	−	4.49015i	0.631194	−	0.229736i
$383$	−20.4717	−	3.60971i	−1.04605	−	0.184448i	−0.375893	−	0.926663i	$-0.622664\pi$
$383$	−20.4717	−	3.60971i	−1.04605	−	0.184448i	−0.670161	+	0.742215i	$0.733775\pi$
$384$	−1.85586	−	2.21172i	−0.0947062	−	0.112867i
$385$	−1.11100	+	0.686563i	−0.0566220	+	0.0349905i
$386$	−2.59866	−	14.7377i	−0.132268	−	0.750131i
$387$	27.6586	−	15.9687i	1.40597	−	0.811736i
$388$	−12.9166	−	7.45741i	−0.655742	−	0.378593i
$389$	−27.6889	−	10.0779i	−1.40388	−	0.510971i	−0.474554	−	0.880226i	$-0.657391\pi$
$389$	−27.6889	−	10.0779i	−1.40388	−	0.510971i	−0.929328	+	0.369255i	$0.879613\pi$
$390$	1.80914	−	4.97057i	0.0916094	−	0.251695i
$391$	−45.1072	−	26.0427i	−2.28117	−	1.31703i
$392$	3.18975	+	5.52480i	0.161107	+	0.279045i
$393$	−1.62198	−	9.19873i	−0.0818183	−	0.464014i
$394$	13.6437	−	16.2599i	0.687360	−	0.819164i
$395$	1.91892	−	1.61017i	0.0965514	−	0.0810162i
$396$	−8.38606	+	15.5842i	−0.421415	+	0.783134i
$397$	−15.8506	+	5.76913i	−0.795517	+	0.289544i	−0.707627	−	0.706586i	$-0.750234\pi$
$397$	−15.8506	+	5.76913i	−0.795517	+	0.289544i	−0.0878895	+	0.996130i	$0.528012\pi$
$398$	21.2839			1.06686
$399$	9.00627	−	4.14302i	0.450877	−	0.207410i
$400$	−4.75010			−0.237505
$401$	5.61554	+	15.4286i	0.280427	+	0.770466i	0.997312	+	0.0732747i	$0.0233450\pi$
$401$	5.61554	+	15.4286i	0.280427	+	0.770466i	−0.716885	+	0.697191i	$0.754433\pi$
$402$	−0.444554	+	2.52119i	−0.0221723	+	0.125746i
$403$	−25.2454	−	30.0863i	−1.25756	−	1.49871i
$404$	5.80820	−	6.92195i	0.288969	−	0.344380i
$405$	−0.300721	−	1.70547i	−0.0149430	−	0.0847457i
$406$	−2.70501	+	1.56174i	−0.134247	+	0.0775077i
$407$	11.9832	+	13.4427i	0.593983	+	0.666328i
$408$	−21.1258	−	7.68917i	−1.04588	−	0.380671i
$409$	25.1036	+	9.13696i	1.24129	+	0.451794i	0.877451	−	0.479667i	$-0.159242\pi$
$409$	25.1036	+	9.13696i	1.24129	+	0.451794i	0.363843	+	0.931460i	$0.381465\pi$
$410$	2.56376	−	4.44057i	0.126615	−	0.219304i
$411$	9.91383	−	5.72375i	0.489013	−	0.282332i
$412$	2.96361	−	0.522565i	0.146007	−	0.0257449i
$413$	1.95310	+	1.63885i	0.0961060	+	0.0806425i
$414$	27.3418	−	22.9425i	1.34378	−	1.12756i
$415$	−6.70099	−	1.18157i	−0.328939	−	0.0580008i
$416$	3.44388	−	1.25347i	0.168850	−	0.0614565i
$417$	−55.3168			−2.70887
$418$	5.78366	−	13.2495i	0.282888	−	0.648054i
$419$	−1.46621			−0.0716290			−0.0358145	−	0.999358i	$-0.511403\pi$
$419$	−1.46621			−0.0716290			−0.0358145	+	0.999358i	$0.511403\pi$
$420$	1.06836	−	0.388851i	0.0521306	−	0.0189740i
$421$	−33.7064	−	5.94335i	−1.64275	−	0.289661i	−0.725574	−	0.688145i	$-0.758425\pi$
$421$	−33.7064	−	5.94335i	−1.64275	−	0.289661i	−0.917175	+	0.398484i	$0.869537\pi$
$422$	−7.25900	+	6.09102i	−0.353363	+	0.296506i
$423$	−12.2157	−	10.2502i	−0.593946	−	0.498380i
$424$	11.0375	−	1.94621i	0.536030	−	0.0945165i
$425$	−32.0320	+	18.4937i	−1.55378	+	0.897077i
$426$	−5.78789	+	10.0249i	−0.280424	+	0.485709i
$427$	−2.85828	−	1.04033i	−0.138322	−	0.0503450i
$428$	1.51841	+	0.552656i	0.0733951	+	0.0267136i
$429$	−23.3525	−	26.1967i	−1.12747	−	1.26479i
$430$	−2.59121	+	1.49604i	−0.124959	+	0.0721453i
$431$	4.83822	+	27.4389i	0.233049	+	1.32169i	0.846684	+	0.532096i	$0.178596\pi$
$431$	4.83822	+	27.4389i	0.233049	+	1.32169i	−0.613635	+	0.789590i	$0.710293\pi$
$432$	4.33513	−	5.16641i	0.208574	−	0.248569i
$433$	11.9003	+	14.1822i	0.571890	+	0.681552i	0.972018	−	0.234908i	$-0.0754788\pi$
$433$	11.9003	+	14.1822i	0.571890	+	0.681552i	−0.400128	+	0.916459i	$0.631034\pi$
$434$	1.46587	−	8.31338i	0.0703641	−	0.399055i
$435$	−1.95738	−	5.37784i	−0.0938490	−	0.257848i
$436$	−5.91149			−0.283109
$437$	−20.7236	+	20.5099i	−0.991343	+	0.981123i
$438$	21.1348			1.00986
$439$	−27.3289	+	9.94689i	−1.30434	+	0.474739i	−0.898406	−	0.439166i	$-0.855274\pi$
$439$	−27.3289	+	9.94689i	−1.30434	+	0.474739i	−0.405929	+	0.913905i	$0.633052\pi$
$440$	0.785652	−	1.46001i	0.0374545	−	0.0696032i
$441$	−26.0765	+	21.8808i	−1.24174	+	1.04194i
$442$	18.3435	−	21.8609i	0.872509	−	1.03982i
$443$	3.87426	+	21.9720i	0.184072	+	1.04392i	0.927142	+	0.374710i	$0.122258\pi$
$443$	3.87426	+	21.9720i	0.184072	+	1.04392i	−0.743070	+	0.669213i	$0.766631\pi$
$444$	−7.83835	−	13.5764i	−0.371992	−	0.644308i
$445$	0.851620	+	0.491683i	0.0403706	+	0.0233080i
$446$	−3.35719	+	9.22381i	−0.158968	+	0.436760i
$447$	38.8610	+	14.1442i	1.83806	+	0.669000i
$448$	0.682188	+	0.393861i	0.0322303	+	0.0186082i
$449$	27.4647	−	15.8568i	1.29614	−	0.748327i	0.316405	−	0.948624i	$-0.397524\pi$
$449$	27.4647	−	15.8568i	1.29614	−	0.748327i	0.979735	+	0.200297i	$0.0641908\pi$
$450$	−4.40131	−	24.9611i	−0.207480	−	1.17668i
$451$	−17.8835	−	28.9392i	−0.842101	−	1.36270i
$452$	2.65032	+	3.15852i	0.124660	+	0.148564i
$453$	−26.5346	−	4.67876i	−1.24670	−	0.219827i
$454$	−17.6793	+	6.43472i	−0.829728	+	0.301996i
$455$			1.44317i			0.0676568i
$456$	−7.27178	+	10.2715i	−0.340532	+	0.481007i
$457$		−	9.59857i		−	0.449002i	−0.974474	−	0.224501i	$-0.927925\pi$
$457$		−	9.59857i		−	0.449002i	0.974474	−	0.224501i	$-0.0720752\pi$
$458$	9.58090	−	3.48716i	0.447686	−	0.162944i
$459$	9.11918	−	51.7174i	0.425647	−	2.41396i
$460$	−2.56153	+	2.14938i	−0.119432	+	0.100215i
$461$	15.9711	−	19.0336i	0.743847	−	0.886483i	−0.252865	−	0.967502i	$-0.581373\pi$
$461$	15.9711	−	19.0336i	0.743847	−	0.886483i	0.996713	+	0.0810186i	$0.0258173\pi$
$462$	1.08697	−	7.46431i	0.0505705	−	0.347271i
$463$	7.51676	+	13.0194i	0.349334	+	0.605063i	0.986131	−	0.165967i	$-0.0530747\pi$
$463$	7.51676	+	13.0194i	0.349334	+	0.605063i	−0.636798	+	0.771031i	$0.719741\pi$
$464$	1.98260	−	3.43396i	0.0920397	−	0.159417i
$465$	14.5344	+	5.29008i	0.674016	+	0.245322i
$466$	4.39132	−	12.0650i	0.203424	−	0.558902i
$467$	−15.5919	+	27.0060i	−0.721508	+	1.24969i	0.238888	+	0.971047i	$0.423217\pi$
$467$	−15.5919	+	27.0060i	−0.721508	+	1.24969i	−0.960395	+	0.278641i	$0.910116\pi$
$468$	9.77782	+	16.9357i	0.451980	+	0.782852i
$469$	−0.121289	−	0.687864i	−0.00560060	−	0.0317626i
$470$	1.14443	+	0.960292i	0.0527887	+	0.0442949i
$471$	−2.25610	−	2.68871i	−0.103956	−	0.123889i
$472$	−3.18750	−	0.562041i	−0.146716	−	0.0258701i
$473$	0.593996	+	19.8423i	0.0273120	+	0.912352i
$474$			14.4677i			0.664522i
$475$	5.25521	+	20.0272i	0.241126	+	0.918911i
$476$	6.13373			0.281139
$477$	20.4541	+	56.1973i	0.936531	+	2.57310i
$478$	12.6848	+	2.23667i	0.580189	+	0.102303i
$479$	−10.5411	−	12.5624i	−0.481637	−	0.573993i	0.469433	−	0.882968i	$-0.344458\pi$
$479$	−10.5411	−	12.5624i	−0.481637	−	0.573993i	−0.951070	+	0.308975i	$0.900014\pi$
$480$	−0.927739	+	1.10564i	−0.0423453	+	0.0504651i
$481$	19.5971	−	3.45550i	0.893551	−	0.157557i
$482$	−12.7451	−	22.0752i	−0.580524	−	1.00550i
$483$	−7.60649	+	13.1748i	−0.346107	+	0.599476i
$484$	−6.05999	−	9.18022i	−0.275454	−	0.417283i
$485$	−2.55006	+	7.00624i	−0.115792	+	0.318137i
$486$	−8.86008	−	5.11537i	−0.401901	−	0.232038i
$487$	1.39554	−	0.805713i	0.0632378	−	0.0365104i	−0.468048	−	0.883703i	$-0.655042\pi$
$487$	1.39554	−	0.805713i	0.0632378	−	0.0365104i	0.531286	+	0.847193i	$0.321709\pi$
$488$	3.80274	−	0.670526i	0.172142	−	0.0303533i
$489$	14.0618	−	16.7582i	0.635896	−	0.757832i
$490$	2.44299	−	2.04991i	0.110363	−	0.0926055i
$491$	−6.34089	−	1.11807i	−0.286160	−	0.0504578i	0.0287255	−	0.999587i	$-0.490855\pi$
$491$	−6.34089	−	1.11807i	−0.286160	−	0.0504578i	−0.314886	+	0.949130i	$0.601966\pi$
$492$	10.1287	+	27.8285i	0.456638	+	1.25460i
$493$		−	30.8756i		−	1.39057i
$494$	−9.09493	−	13.1332i	−0.409200	−	0.590891i
$495$	8.40010	+	2.77568i	0.377557	+	0.124758i
$496$	3.66526	+	10.0702i	0.164575	+	0.452166i
$497$	0.548424	−	3.11027i	0.0246002	−	0.139515i
$498$	30.1049	−	25.2610i	1.34903	−	1.13197i
$499$	−14.0844	−	11.8182i	−0.630505	−	0.529057i	0.270581	−	0.962697i	$-0.412784\pi$
$499$	−14.0844	−	11.8182i	−0.630505	−	0.529057i	−0.901086	+	0.433641i	$0.857229\pi$
$500$	0.846371	+	4.80001i	0.0378509	+	0.214663i
$501$	−9.32068	+	5.38130i	−0.416417	+	0.240419i
$502$	4.41336	−	7.64416i	0.196978	−	0.341176i
$503$	8.26632	−	22.7115i	0.368577	−	1.01266i	−0.607326	−	0.794453i	$-0.707758\pi$
$503$	8.26632	−	22.7115i	0.368577	−	1.01266i	0.975903	−	0.218204i	$-0.0700200\pi$
$504$	−1.43759	+	3.94974i	−0.0640352	+	0.175935i
$505$	−3.91189	−	2.25853i	−0.174077	−	0.100503i
$506$	4.50442	+	21.7230i	0.200246	+	0.965704i
$507$	−1.22697	+	0.216347i	−0.0544914	+	0.00960831i
$508$	14.6198	+	12.2675i	0.648648	+	0.544280i
$509$	0.242071	+	0.288489i	0.0107296	+	0.0127871i	0.771383	−	0.636372i	$-0.219566\pi$
$509$	0.242071	+	0.288489i	0.0107296	+	0.0127871i	−0.760653	+	0.649159i	$0.775121\pi$
$510$	−1.95155	+	11.0678i	−0.0864160	+	0.490090i
$511$	−5.41853	+	1.97218i	−0.239702	+	0.0872442i
$512$	−1.00000			−0.0441942
$513$	−26.5785	−	12.5618i	−1.17347	−	0.554618i
$514$			13.4411i			0.592861i
$515$	−0.514521	−	1.41364i	−0.0226725	−	0.0622922i
$516$	3.00081	−	17.0184i	0.132103	−	0.749194i
$517$	9.20840	−	3.66720i	0.404985	−	0.161283i
$518$	3.27646	+	2.74928i	0.143959	+	0.120796i
$519$	12.2625	−	2.16220i	0.538262	−	0.0949101i
$520$	−0.916039	−	1.58663i	−0.0401710	−	0.0695782i
$521$	−19.4949	−	11.2554i	−0.854087	−	0.493107i	0.00794059	−	0.999968i	$-0.497472\pi$
$521$	−19.4949	−	11.2554i	−0.854087	−	0.493107i	−0.862028	+	0.506861i	$0.830806\pi$
$522$	19.8820	+	7.23644i	0.870210	+	0.316731i
$523$	−15.0650	−	5.48321i	−0.658746	−	0.239764i	−0.00905134	−	0.999959i	$-0.502881\pi$
$523$	−15.0650	−	5.48321i	−0.658746	−	0.239764i	−0.649695	+	0.760195i	$0.725103\pi$
$524$	−2.80176	−	1.61759i	−0.122395	−	0.0706649i
$525$	5.40161	+	9.35586i	0.235745	+	0.408323i
$526$	−12.9705	+	2.28704i	−0.565539	+	0.0997198i
$527$	63.9231	+	53.6378i	2.78453	+	2.33650i
$528$	3.54288	+	8.89624i	0.154184	+	0.387159i
$529$	3.77569	−	21.4130i	0.164161	−	0.931001i
$530$	−1.91626	−	5.26487i	−0.0832368	−	0.228691i
$531$		−	17.2706i		−	0.749480i
$532$	0.905854	−	3.31196i	0.0392738	−	0.143592i
$533$	−37.5915			−1.62827
$534$	−5.33699	+	1.94251i	−0.230954	+	0.0840604i
$535$	0.140267	−	0.795493i	0.00606426	−	0.0343921i
$536$	0.569961	+	0.679253i	0.0246186	+	0.0293393i
$537$	3.25339	+	2.72991i	0.140394	+	0.117805i
$538$	13.4114	−	2.36479i	0.578207	−	0.101954i
$539$	−4.29596	−	20.7177i	−0.185040	−	0.892373i
$540$	−2.91976	−	1.68572i	−0.125646	−	0.0725419i
$541$	−1.33857	+	3.67770i	−0.0575497	+	0.158117i	−0.965136	−	0.261749i	$-0.915701\pi$
$541$	−1.33857	+	3.67770i	−0.0575497	+	0.158117i	0.907586	+	0.419866i	$0.137923\pi$
$542$	−5.61145	+	15.4173i	−0.241032	+	0.662231i
$543$	3.58282	−	6.20562i	0.153753	−	0.266309i
$544$	−6.74344	+	3.89333i	−0.289123	+	0.166925i
$545$	0.513155	+	2.91024i	0.0219811	+	0.124661i
$546$	−6.38509	−	5.35772i	−0.273256	−	0.229289i
$547$	−16.8396	+	14.1301i	−0.720008	+	0.604159i	−0.927388	−	0.374102i	$-0.877951\pi$
$547$	−16.8396	+	14.1301i	−0.720008	+	0.604159i	0.207379	+	0.978261i	$0.433507\pi$
$548$	0.688500	−	3.90468i	0.0294113	−	0.166800i
$549$	7.04703	+	19.3616i	0.300760	+	0.826331i
$550$	14.9588	+	4.94290i	0.637846	+	0.210766i
$551$	−16.6715	−	4.55984i	−0.710231	−	0.194256i
$552$		−	19.3126i		−	0.821999i
$553$	−1.35004	−	3.70921i	−0.0574096	−	0.157731i
$554$	−24.1143	−	4.25199i	−1.02452	−	0.180650i
$555$	−6.00330	+	5.03737i	−0.254826	+	0.213824i
$556$	−12.3154	+	14.6769i	−0.522288	+	0.622439i
$557$	−12.5220	+	2.20797i	−0.530575	+	0.0935546i	−0.432516	−	0.901626i	$-0.642374\pi$
$557$	−12.5220	+	2.20797i	−0.530575	+	0.0935546i	−0.0980582	+	0.995181i	$0.531263\pi$
$558$	−49.5214	+	28.5912i	−2.09641	+	1.21036i
$559$	18.9970	+	10.9679i	0.803486	+	0.463893i
$560$	0.134681	−	0.370033i	0.00569131	−	0.0156368i
$561$	58.5272	+	46.1977i	2.47102	+	1.95047i
$562$	−11.3517	+	19.6617i	−0.478842	+	0.829378i
$563$	−6.18515	−	10.7130i	−0.260673	−	0.451499i	0.705748	−	0.708463i	$-0.250611\pi$
$563$	−6.18515	−	10.7130i	−0.260673	−	0.451499i	−0.966421	+	0.256964i	$0.917278\pi$
$564$	−8.49733	+	1.49831i	−0.357802	+	0.0630902i
$565$	1.32489	−	1.57894i	0.0557384	−	0.0664265i
$566$	−5.90820	−	7.04112i	−0.248340	−	0.295960i
$567$	−2.68743	−	0.473866i	−0.112861	−	0.0199005i
$568$	1.37128	+	3.76755i	0.0575375	+	0.158083i
$569$	−7.91935			−0.331996			−0.165998	−	0.986126i	$-0.553085\pi$
$569$	−7.91935			−0.331996			−0.165998	+	0.986126i	$0.553085\pi$
$570$	5.68793	+	2.68829i	0.238241	+	0.112600i
$571$			21.6809i			0.907317i	0.891175	+	0.453659i	$0.149881\pi$
$571$			21.6809i			0.907317i	−0.891175	+	0.453659i	$0.850119\pi$
$572$	−12.1497	+	0.363710i	−0.508003	+	0.0152075i
$573$	37.3282	+	6.58197i	1.55941	+	0.274966i
$574$	−5.19359	−	6.18948i	−0.216776	−	0.258344i
$575$	−24.3400	−	20.4237i	−1.01505	−	0.851728i
$576$	−0.926573	−	5.25485i	−0.0386072	−	0.218952i
$577$	12.8630	+	22.2793i	0.535492	+	0.927499i	0.999139	+	0.0414795i	$0.0132071\pi$
$577$	12.8630	+	22.2793i	0.535492	+	0.927499i	−0.463647	+	0.886020i	$0.653460\pi$
$578$	−21.8160	+	37.7864i	−0.907427	+	1.57171i
$579$	14.7777	−	40.6015i	0.614141	−	1.68734i
$580$	−1.86265	−	0.677949i	−0.0773424	−	0.0281503i
$581$	−5.36105	+	9.28561i	−0.222414	+	0.385232i
$582$	−21.5310	−	37.2928i	−0.892490	−	1.54584i
$583$	−36.7841	−	5.35659i	−1.52344	−	0.221847i
$584$	4.70532	−	5.60759i	0.194708	−	0.232044i
$585$	7.48871	−	6.28378i	0.309620	−	0.259802i
$586$	2.00400	−	11.3652i	0.0827845	−	0.469494i
$587$	19.5686	−	7.12239i	0.807683	−	0.293972i	0.0950163	−	0.995476i	$-0.469710\pi$
$587$	19.5686	−	7.12239i	0.807683	−	0.293972i	0.712666	+	0.701503i	$0.247487\pi$
$588$			18.4189i			0.759581i
$589$	38.4026	−	26.5944i	1.58235	−	1.09580i
$590$			1.61800i			0.0666122i
$591$	57.5874	−	20.9601i	2.36883	−	0.862184i
$592$	−5.34724	−	0.942862i	−0.219770	−	0.0387514i
$593$	−12.2461	−	14.5943i	−0.502886	−	0.599316i	0.453560	−	0.891226i	$-0.350154\pi$
$593$	−12.2461	−	14.5943i	−0.502886	−	0.599316i	−0.956446	+	0.291910i	$0.905709\pi$
$594$	−19.0281	+	11.7587i	−0.780732	+	0.482466i
$595$	−0.532447	−	3.01965i	−0.0218282	−	0.123794i
$596$	12.4046	−	7.16179i	0.508111	−	0.293358i
$597$	53.2180	+	30.7254i	2.17807	+	1.25751i
$598$	23.0363	+	8.38453i	0.942024	+	0.342869i
$599$	11.9577	−	32.8534i	0.488577	−	1.34235i	−0.413392	−	0.910553i	$-0.635656\pi$
$599$	11.9577	−	32.8534i	0.488577	−	1.34235i	0.901969	−	0.431801i	$-0.142122\pi$
$600$	−11.8771	−	6.85725i	−0.484880	−	0.279946i
$601$	11.5704	+	20.0405i	0.471965	+	0.817467i	0.999485	−	0.0320749i	$-0.0102115\pi$
$601$	11.5704	+	20.0405i	0.471965	+	0.817467i	−0.527520	+	0.849542i	$0.676878\pi$
$602$	0.818719	+	4.64318i	0.0333685	+	0.189242i
$603$	−3.04127	+	3.62444i	−0.123850	+	0.147599i
$604$	−7.14887	+	5.99862i	−0.290884	+	0.244080i
$605$	−3.99341	+	3.78026i	−0.162355	+	0.153689i
$606$	24.5153	−	8.92283i	0.995865	−	0.362465i
$607$	−24.8612			−1.00909			−0.504543	−	0.863387i	$-0.668339\pi$
$607$	−24.8612			−1.00909			−0.504543	+	0.863387i	$0.668339\pi$
$608$	1.10634	+	4.21616i	0.0448679	+	0.170988i
$609$	−9.01809			−0.365431
$610$	−0.660204	−	1.81390i	−0.0267309	−	0.0734425i
$611$	1.90190	−	10.7862i	0.0769425	−	0.436363i
$612$	−26.7072	−	31.8284i	−1.07957	−	1.28659i
$613$	14.9708	−	17.8415i	0.604665	−	0.720612i	−0.373688	−	0.927554i	$-0.621907\pi$
$613$	14.9708	−	17.8415i	0.604665	−	0.720612i	0.978353	+	0.206943i	$0.0663514\pi$
$614$	3.53775	+	20.0636i	0.142772	+	0.809701i
$615$	12.8208	−	7.40209i	0.516985	−	0.298481i
$616$	−1.73847	−	1.95021i	−0.0700449	−	0.0785761i
$617$	5.54368	+	2.01773i	0.223180	+	0.0812309i	0.451190	−	0.892428i	$-0.351000\pi$
$617$	5.54368	+	2.01773i	0.223180	+	0.0812309i	−0.228010	+	0.973659i	$0.573222\pi$
$618$	8.16456	+	2.97166i	0.328427	+	0.119538i
$619$	−8.61180	+	14.9161i	−0.346137	+	0.599527i	−0.985560	−	0.169328i	$-0.945840\pi$
$619$	−8.61180	+	14.9161i	−0.346137	+	0.599527i	0.639422	+	0.768856i	$0.279174\pi$
$620$	4.63943	−	2.67858i	0.186324	−	0.107574i
$621$	44.4273	−	7.83374i	1.78281	−	0.314357i
$622$	10.0064	+	8.39634i	0.401219	+	0.336663i
$623$	1.18703	−	0.996035i	0.0475573	−	0.0399053i
$624$	10.4206	+	1.83742i	0.417156	+	0.0735559i
$625$	−20.0286	+	7.28981i	−0.801144	+	0.291592i
$626$	0.0581356			0.00232357
$627$	33.5884	−	24.7796i	1.34139	−	0.989602i
$628$	−1.21566			−0.0485103
$629$	−39.7297	+	14.4604i	−1.58412	+	0.576574i
$630$	2.06926	+	0.364867i	0.0824414	+	0.0145366i
$631$	28.1646	−	23.6329i	1.12121	−	0.940810i	0.122549	−	0.992462i	$-0.460893\pi$
$631$	28.1646	−	23.6329i	1.12121	−	0.940810i	0.998665	+	0.0516520i	$0.0164486\pi$
$632$	3.83863	+	3.22099i	0.152692	+	0.128124i
$633$	−26.9433	+	4.75083i	−1.07090	+	0.188829i
$634$	−12.4884	+	7.21017i	−0.495977	+	0.286352i
$635$	4.77022	−	8.26226i	0.189300	−	0.327878i
$636$	30.4077	+	11.0675i	1.20574	+	0.438854i
$637$	−21.9702	−	7.99651i	−0.870492	−	0.316833i
$638$	−9.81684	+	8.75100i	−0.388652	+	0.346455i
$639$	−18.5273	+	10.6968i	−0.732930	+	0.423157i
$640$	0.0868064	+	0.492303i	0.00343132	+	0.0194600i
$641$	26.4693	−	31.5449i	1.04548	−	1.24595i	0.0769499	−	0.997035i	$-0.475482\pi$
$641$	26.4693	−	31.5449i	1.04548	−	1.24595i	0.968526	−	0.248914i	$-0.0800737\pi$
$642$	2.99880	+	3.57383i	0.118353	+	0.141048i
$643$	−2.91259	+	16.5181i	−0.114861	+	0.651411i	0.871957	+	0.489582i	$0.162851\pi$
$643$	−2.91259	+	16.5181i	−0.114861	+	0.651411i	−0.986819	+	0.161830i	$0.948261\pi$
$644$	1.80214	+	4.95135i	0.0710144	+	0.195110i
$645$	−8.63872			−0.340149
$646$	23.8754	+	24.1241i	0.939366	+	0.949151i
$647$	−14.5065			−0.570311			−0.285156	−	0.958481i	$-0.592045\pi$
$647$	−14.5065			−0.570311			−0.285156	+	0.958481i	$0.592045\pi$
$648$	3.25535	−	1.18485i	0.127882	−	0.0465454i
$649$	9.45306	+	5.08683i	0.371065	+	0.199675i
$650$	13.3358	−	11.1901i	0.523074	−	0.438911i
$651$	15.6664	−	18.6705i	0.614016	−	0.731756i
$652$	−1.31573	−	7.46188i	−0.0515280	−	0.292230i
$653$	−6.68284	−	11.5750i	−0.261520	−	0.452965i	0.705126	−	0.709082i	$-0.250890\pi$
$653$	−6.68284	−	11.5750i	−0.261520	−	0.452965i	−0.966646	+	0.256116i	$0.917557\pi$
$654$	−14.7810	−	8.53382i	−0.577983	−	0.333699i
$655$	−0.553137	+	1.51973i	−0.0216128	+	0.0593808i
$656$	9.63856	+	3.50815i	0.376323	+	0.136970i
$657$	33.8269	+	19.5300i	1.31971	+	0.761936i
$658$	2.03872	−	1.17706i	0.0794777	−	0.0458865i
$659$	0.999779	+	5.67003i	0.0389459	+	0.220873i	0.998069	−	0.0621164i	$-0.0197850\pi$
$659$	0.999779	+	5.67003i	0.0389459	+	0.220873i	−0.959123	+	0.282989i	$0.908674\pi$
$660$	4.07210	−	2.51642i	0.158506	−	0.0979517i
$661$	3.10063	+	3.69519i	0.120600	+	0.143726i	0.822966	−	0.568090i	$-0.192317\pi$
$661$	3.10063	+	3.69519i	0.120600	+	0.143726i	−0.702366	+	0.711816i	$0.747873\pi$
$662$	7.02792	+	1.23921i	0.273148	+	0.0481634i
$663$	77.4241	−	28.1801i	3.00690	−	1.09442i
$664$		−	13.6115i		−	0.528229i
$665$	−1.70912	−	0.158456i	−0.0662769	−	0.00614466i
$666$		−	28.9726i		−	1.12266i
$667$	24.9238	−	9.07152i	0.965054	−	0.351251i
$668$	−0.647307	+	3.67106i	−0.0250451	+	0.142038i
$669$	−21.7098	+	18.2167i	−0.839348	+	0.704297i
$670$	0.284922	−	0.339557i	0.0110075	−	0.0131182i
$671$	−12.6732	−	1.84550i	−0.489242	−	0.0712447i
$672$	1.13716	+	1.96961i	0.0438667	+	0.0759794i
$673$	−14.8054	+	25.6438i	−0.570707	+	0.988494i	0.425786	+	0.904824i	$0.359998\pi$
$673$	−14.8054	+	25.6438i	−0.570707	+	0.988494i	−0.996493	+	0.0836704i	$0.973336\pi$
$674$	7.54552	+	2.74634i	0.290642	+	0.105785i
$675$	10.9569	−	30.1039i	0.421733	−	1.15870i
$676$	−0.215762	+	0.373710i	−0.00829852	+	0.0143735i
$677$	20.8524	+	36.1174i	0.801423	+	1.38811i	0.918679	+	0.395004i	$0.129257\pi$
$677$	20.8524	+	36.1174i	0.801423	+	1.38811i	−0.117256	+	0.993102i	$0.537410\pi$
$678$	2.06717	+	11.7235i	0.0793894	+	0.450239i
$679$	9.00006	+	7.55195i	0.345391	+	0.289817i
$680$	2.50207	+	2.98185i	0.0959501	+	0.114349i
$681$	−53.4941	−	9.43246i	−2.04990	−	0.361453i
$682$	−1.06352	−	35.5267i	−0.0407242	−	1.36039i
$683$			4.77644i			0.182765i	0.995816	+	0.0913827i	$0.0291286\pi$
$683$			4.77644i			0.182765i	−0.995816	+	0.0913827i	$0.970871\pi$
$684$	−21.1302	+	9.72022i	−0.807934	+	0.371662i
$685$	−1.98205			−0.0757304
$686$	−3.60466	−	9.90373i	−0.137627	−	0.378126i
$687$	28.9900	+	5.11172i	1.10604	+	0.195024i
$688$	−3.84732	−	4.58506i	−0.146678	−	0.174804i
$689$	−26.4028	+	31.4657i	−1.00587	+	1.19875i
$690$	−9.50766	+	1.67646i	−0.361951	+	0.0638217i
$691$	13.2420	+	22.9358i	0.503750	+	0.872520i	0.999991	+	0.00433510i	$0.00137991\pi$
$691$	13.2420	+	22.9358i	0.503750	+	0.872520i	−0.496241	+	0.868185i	$0.665287\pi$
$692$	2.15635	−	3.73491i	0.0819721	−	0.141980i
$693$	8.63724	−	10.9424i	0.328102	−	0.415668i
$694$	6.50002	−	17.8587i	0.246738	−	0.677906i
$695$	8.29454	+	4.78885i	0.314630	+	0.181652i
$696$	9.91452	−	5.72415i	0.375809	−	0.216973i
$697$	78.6555	−	13.8691i	2.97929	−	0.525329i
$698$	−9.43053	+	11.2389i	−0.356951	+	0.425398i
$699$	28.3971	−	23.8280i	1.07408	−	0.901257i
$700$	3.68492	+	0.649750i	0.139277	+	0.0245583i
$701$	−13.7893	−	37.8857i	−0.520814	−	1.43092i	−0.869617	−	0.493728i	$-0.835634\pi$
$701$	−13.7893	−	37.8857i	−0.520814	−	1.43092i	0.348803	−	0.937196i	$-0.386588\pi$
$702$			24.7171i			0.932886i
$703$	1.94058	+	23.5879i	0.0731904	+	0.889636i
$704$	3.14915	+	1.04059i	0.118688	+	0.0392186i
$705$	1.47524	+	4.05320i	0.0555609	+	0.152652i
$706$	3.95397	−	22.4241i	0.148810	−	0.843941i
$707$	−5.45257	+	4.57525i	−0.205065	+	0.172070i
$708$	−7.15861	−	6.00679i	−0.269037	−	0.225749i
$709$	0.169225	+	0.959725i	0.00635539	+	0.0360432i	0.987821	−	0.155597i	$-0.0497303\pi$
$709$	0.169225	+	0.959725i	0.00635539	+	0.0360432i	−0.981465	+	0.191641i	$0.938619\pi$
$710$	1.73574	−	1.00213i	0.0651412	−	0.0376093i
$711$	−13.3691	+	23.1559i	−0.501379	+	0.868414i
$712$	−0.672799	+	1.84850i	−0.0252142	+	0.0692755i
$713$	−24.5171	+	67.3601i	−0.918172	+	2.52266i
$714$	15.3367	+	8.85465i	0.573961	+	0.331377i
$715$	1.23372	+	5.94975i	0.0461387	+	0.222508i
$716$	1.44863	−	0.255432i	0.0541377	−	0.00954594i
$717$	28.4880	+	23.9043i	1.06391	+	0.892723i
$718$	−4.71934	−	5.62429i	−0.176124	−	0.209897i
$719$	4.31581	−	24.4762i	0.160953	−	0.912808i	−0.792187	−	0.610278i	$-0.791058\pi$
$719$	4.31581	−	24.4762i	0.160953	−	0.912808i	0.953140	−	0.302530i	$-0.0978312\pi$
$720$	−2.50655	+	0.912310i	−0.0934136	+	0.0339998i
$721$	−2.37052			−0.0882828
$722$	16.5520	−	9.32899i	0.616003	−	0.347189i
$723$		−	73.5954i		−	2.73704i
$724$	−0.848847	−	2.33219i	−0.0315472	−	0.0866751i
$725$	3.27068	−	18.5489i	0.121470	−	0.688890i
$726$	−1.89977	−	31.7023i	−0.0705071	−	1.17658i
$727$	−31.3409	−	26.2981i	−1.16237	−	0.975344i	−0.162435	−	0.986719i	$-0.551935\pi$
$727$	−31.3409	−	26.2981i	−1.16237	−	0.975344i	−0.999935	+	0.0113751i	$0.996379\pi$
$728$	−2.84307	+	0.501310i	−0.105371	+	0.0185798i
$729$	−19.9655	−	34.5813i	−0.739463	−	1.28079i
$730$	−3.16909	−	1.82967i	−0.117293	−	0.0677192i
$731$	−43.7953	−	15.9402i	−1.61983	−	0.589570i
$732$	10.4763	+	3.81306i	0.387215	+	0.140935i
$733$	14.4049	+	8.31667i	0.532057	+	0.307183i	0.741854	−	0.670562i	$-0.233947\pi$
$733$	14.4049	+	8.31667i	0.532057	+	0.307183i	−0.209797	+	0.977745i	$0.567280\pi$
$734$	−0.750500	−	1.29990i	−0.0277015	−	0.0479804i
$735$	9.06767	−	1.59887i	0.334466	−	0.0589754i
$736$	−5.12411	−	4.29964i	−0.188877	−	0.158487i
$737$	−1.08807	−	2.73217i	−0.0400797	−	0.100641i
$738$	−9.50399	+	53.8998i	−0.349847	+	1.98408i
$739$	−2.48978	−	6.84061i	−0.0915880	−	0.251636i	0.885437	−	0.464759i	$-0.153859\pi$
$739$	−2.48978	−	6.84061i	−0.0915880	−	0.251636i	−0.977025	+	0.213122i	$0.931637\pi$
$740$			2.71431i			0.0997800i
$741$	−3.78176	−	45.9676i	−0.138926	−	1.68866i
$742$	−8.82864			−0.324110
$743$	22.4314	−	8.16437i	0.822929	−	0.299522i	0.103975	−	0.994580i	$-0.466844\pi$
$743$	22.4314	−	8.16437i	0.822929	−	0.299522i	0.718953	+	0.695058i	$0.244621\pi$
$744$	−5.37279	+	30.4706i	−0.196976	+	1.11711i
$745$	−4.60257	−	5.48513i	−0.168625	−	0.200960i
$746$	−7.81582	−	6.55825i	−0.286158	−	0.240115i
$747$	71.5265	−	12.6121i	2.61702	−	0.461451i
$748$	25.2875	−	5.24355i	0.924603	−	0.191723i
$749$	−1.10232	−	0.636424i	−0.0402779	−	0.0232544i
$750$	−4.81303	+	13.2237i	−0.175747	+	0.482861i
$751$	−7.57596	+	20.8148i	−0.276451	+	0.759542i	0.721307	+	0.692615i	$0.243542\pi$
$751$	−7.57596	+	20.8148i	−0.276451	+	0.759542i	−0.997758	+	0.0669265i	$0.978681\pi$
$752$	−1.49425	+	2.58812i	−0.0544898	+	0.0943791i
$753$	22.0702	−	12.7422i	0.804283	−	0.464353i
$754$	2.52346	+	14.3113i	0.0918991	+	0.521186i
$755$	3.57371	+	2.99870i	0.130061	+	0.109134i
$756$	−4.06969	+	3.41488i	−0.148013	+	0.124198i
$757$	−2.84816	+	16.1527i	−0.103518	+	0.587080i	0.888284	+	0.459295i	$0.151898\pi$
$757$	−2.84816	+	16.1527i	−0.103518	+	0.587080i	−0.991802	+	0.127785i	$0.959213\pi$
$758$	2.93459	+	8.06272i	0.106589	+	0.292851i
$759$	−20.0965	+	60.8184i	−0.729456	+	2.20757i
$760$	1.97959	−	0.910643i	0.0718074	−	0.0330325i
$761$			1.78365i			0.0646573i	0.999477	+	0.0323287i	$0.0102923\pi$
$761$			1.78365i			0.0646573i	−0.999477	+	0.0323287i	$0.989708\pi$
$762$	18.8458	+	51.7785i	0.682712	+	1.87574i
$763$	4.58587	+	0.808612i	0.166020	+	0.0292737i
$764$	10.0569	−	8.43871i	0.363845	−	0.305302i
$765$	−13.3509	+	15.9109i	−0.482701	+	0.575261i
$766$	−20.4717	+	3.60971i	−0.739672	+	0.130424i
$767$	10.2729	−	5.93104i	0.370931	−	0.214157i
$768$	−2.50039	−	1.44360i	−0.0902250	−	0.0520914i
$769$	−13.2854	+	36.5012i	−0.479082	+	1.31627i	0.431191	+	0.902261i	$0.358093\pi$
$769$	−13.2854	+	36.5012i	−0.479082	+	1.31627i	−0.910274	+	0.414007i	$0.864129\pi$
$770$	−0.809183	+	1.02514i	−0.0291609	+	0.0369436i
$771$	−19.4035	+	33.6079i	−0.698801	+	1.21036i
$772$	−7.48254	−	12.9601i	−0.269303	−	0.466446i
$773$	−32.6300	+	5.75355i	−1.17362	+	0.206941i	−0.726264	−	0.687416i	$-0.758745\pi$
$773$	−32.6300	+	5.75355i	−1.17362	+	0.206941i	−0.447355	+	0.894357i	$0.647634\pi$
$774$	20.5290	−	24.4655i	0.737900	−	0.879395i
$775$	32.7207	+	38.9951i	1.17536	+	1.40074i
$776$	−14.6882	−	2.58993i	−0.527277	−	0.0929731i
$777$	4.22357	+	11.6042i	0.151520	+	0.416297i
$778$	−29.4659			−1.05640
$779$	4.12744	−	44.5189i	0.147881	−	1.59506i
$780$		−	5.28957i		−	0.189397i
$781$	−0.397892	−	13.2915i	−0.0142377	−	0.475608i
$782$	−51.2940	−	9.04452i	−1.83427	−	0.323431i
$783$	17.1896	+	20.4858i	0.614307	+	0.732102i
$784$	4.88698	+	4.10066i	0.174535	+	0.146452i
$785$	0.105527	+	0.598476i	0.00376644	+	0.0213605i
$786$	−4.67032	−	8.08923i	−0.166585	−	0.288533i
$787$	14.2687	−	24.7141i	0.508625	−	0.880964i	−0.491326	−	0.870976i	$-0.663487\pi$
$787$	14.2687	−	24.7141i	0.508625	−	0.880964i	0.999950	−	0.00998763i	$-0.00317921\pi$
$788$	7.25967	−	19.9458i	0.258615	−	0.710539i
$789$	−35.7328	−	13.0057i	−1.27212	−	0.463014i
$790$	1.25249	−	2.16937i	0.0445615	−	0.0771827i
$791$	−1.62395	−	2.81277i	−0.0577411	−	0.100011i
$792$	−2.55022	+	17.5125i	−0.0906181	+	0.622281i
$793$	−9.09652	+	10.8408i	−0.323027	+	0.384969i
$794$	−12.9215	+	10.8424i	−0.458567	+	0.384783i
$795$	2.80898	−	15.9305i	0.0996243	−	0.564997i
$796$	20.0003	−	7.27952i	0.708892	−	0.258016i
$797$		−	3.27299i		−	0.115935i	−0.998318	−	0.0579676i	$-0.981538\pi$
$797$		−	3.27299i		−	0.115935i	0.998318	−	0.0579676i	$-0.0184620\pi$
$798$	7.04613	−	6.97349i	0.249430	−	0.246859i
$799$			23.2705i			0.823250i
$800$	−4.46364	+	1.62463i	−0.157813	+	0.0574394i
$801$	−10.3370	−	1.82269i	−0.365240	−	0.0644016i
$802$	10.5538	+	12.5775i	0.372666	+	0.444126i
$803$	−20.6530	+	12.7629i	−0.728828	+	0.450391i
$804$	0.444554	+	2.52119i	0.0156782	+	0.0889156i
$805$	2.28113	−	1.31701i	0.0803992	−	0.0464185i
$806$	−34.0131	−	19.6375i	−1.19806	−	0.691700i
$807$	36.9476	+	13.4478i	1.30062	+	0.473385i
$808$	3.09048	−	8.49102i	0.108723	−	0.298713i
$809$	−7.33202	−	4.23314i	−0.257780	−	0.148829i	0.365541	−	0.930795i	$-0.380884\pi$
$809$	−7.33202	−	4.23314i	−0.257780	−	0.148829i	−0.623321	+	0.781966i	$0.714217\pi$
$810$	−0.865892	−	1.49977i	−0.0304243	−	0.0526965i
$811$	−4.34357	−	24.6336i	−0.152523	−	0.865003i	−0.961015	−	0.276496i	$-0.910827\pi$
$811$	−4.34357	−	24.6336i	−0.152523	−	0.865003i	0.808492	−	0.588507i	$-0.200284\pi$
$812$	−2.00773	+	2.39272i	−0.0704575	+	0.0839680i
$813$	−36.2872	+	30.4486i	−1.27265	+	1.06788i
$814$	15.8581	+	8.53349i	0.555828	+	0.299099i
$815$	−3.55929	+	1.29548i	−0.124677	+	0.0453786i
$816$	−22.4816			−0.787014
$817$	−15.0749	+	21.2936i	−0.527405	+	0.744967i
$818$	26.7147			0.934058
$819$	−5.26862	−	14.4754i	−0.184100	−	0.505812i
$820$	0.890386	−	5.04963i	0.0310936	−	0.176341i
$821$	−28.9790	−	34.5358i	−1.01137	−	1.20531i	−0.978584	−	0.205846i	$-0.934005\pi$
$821$	−28.9790	−	34.5358i	−1.01137	−	1.20531i	−0.0327891	−	0.999462i	$-0.510439\pi$
$822$	7.35831	−	8.76929i	0.256651	−	0.305864i
$823$	−0.364500	−	2.06718i	−0.0127057	−	0.0720575i	0.977796	−	0.209561i	$-0.0672034\pi$
$823$	−0.364500	−	2.06718i	−0.0127057	−	0.0720575i	−0.990501	+	0.137503i	$0.956092\pi$
$824$	2.60616	−	1.50467i	0.0907899	−	0.0524175i
$825$	30.2672	+	33.9537i	1.05377	+	1.18212i
$826$	2.39584	+	0.872013i	0.0833618	+	0.0303412i
$827$	−15.6696	−	5.70329i	−0.544887	−	0.198323i	0.0548863	−	0.998493i	$-0.482520\pi$
$827$	−15.6696	−	5.70329i	−0.544887	−	0.198323i	−0.599773	+	0.800170i	$0.704743\pi$
$828$	17.8461	−	30.9104i	0.620195	−	1.07421i
$829$	−7.45885	+	4.30637i	−0.259056	+	0.149566i	−0.623904	−	0.781501i	$-0.714454\pi$
$829$	−7.45885	+	4.30637i	−0.259056	+	0.149566i	0.364848	+	0.931067i	$0.381121\pi$
$830$	−6.70099	+	1.18157i	−0.232595	+	0.0410127i
$831$	−54.1568	−	45.4430i	−1.87868	−	1.57640i
$832$	2.80748	−	2.35576i	0.0973318	−	0.0816711i
$833$	48.9203	+	8.62596i	1.69499	+	0.298872i
$834$	−51.9808	+	18.9195i	−1.79995	+	0.655127i
$835$	1.86347			0.0644879
$836$	0.903264	−	14.4286i	0.0312400	−	0.499023i
$837$	−72.2749			−2.49818
$838$	−1.37779	+	0.501473i	−0.0475948	+	0.0173231i
$839$	−32.4599	−	5.72355i	−1.12064	−	0.197599i	−0.417518	−	0.908669i	$-0.637100\pi$
$839$	−32.4599	−	5.72355i	−1.12064	−	0.197599i	−0.703121	+	0.711070i	$0.748211\pi$
$840$	0.870934	−	0.730801i	0.0300501	−	0.0252150i
$841$	−10.1710	−	8.53445i	−0.350723	−	0.294291i
$842$	−33.7064	+	5.94335i	−1.16160	+	0.204821i
$843$	−56.7672	+	32.7746i	−1.95517	+	1.12882i
$844$	−4.73797	+	8.20641i	−0.163088	+	0.282476i
$845$	0.202708	+	0.0737797i	0.00697337	+	0.00253810i
$846$	−14.9847	−	5.45400i	−0.515186	−	0.187512i
$847$	3.44534	+	7.95053i	0.118383	+	0.273184i
$848$	9.70624	−	5.60390i	0.333314	−	0.192439i
$849$	−4.60823	−	26.1346i	−0.158154	−	0.896937i
$850$	−23.7751	+	28.3340i	−0.815478	+	0.971848i
$851$	−23.3458	−	27.8225i	−0.800285	−	0.953743i
$852$	−2.01011	+	11.3999i	−0.0688653	+	0.390554i
$853$	14.6382	+	40.2180i	0.501201	+	1.37704i	0.890103	+	0.455760i	$0.150632\pi$
$853$	14.6382	+	40.2180i	0.501201	+	1.37704i	−0.388902	+	0.921279i	$0.627145\pi$
$854$	−3.04172			−0.104085
$855$	6.61953	+	9.55870i	0.226383	+	0.326901i
$856$	1.61586			0.0552289
$857$	−15.1134	+	5.50082i	−0.516263	+	0.187904i	−0.586994	−	0.809591i	$-0.699689\pi$
$857$	−15.1134	+	5.50082i	−0.516263	+	0.187904i	0.0707314	+	0.997495i	$0.477467\pi$
$858$	−30.9039	−	16.6298i	−1.05504	−	0.567733i
$859$	28.5637	−	23.9678i	0.974580	−	0.817770i	−0.00868267	−	0.999962i	$-0.502764\pi$
$859$	28.5637	−	23.9678i	0.974580	−	0.817770i	0.983263	+	0.182192i	$0.0583194\pi$
$860$	−1.92327	+	2.29206i	−0.0655829	+	0.0781587i
$861$	−4.05086	−	22.9735i	−0.138053	−	0.782936i
$862$	13.9311	+	24.1294i	0.474495	+	0.821850i
$863$	−11.7449	−	6.78092i	−0.399801	−	0.230825i	0.286597	−	0.958051i	$-0.407476\pi$
$863$	−11.7449	−	6.78092i	−0.399801	−	0.230825i	−0.686398	+	0.727226i	$0.740809\pi$
$864$	2.30667	−	6.33753i	0.0784746	−	0.215607i
$865$	−2.02589	−	0.737364i	−0.0688824	−	0.0250711i
$866$	16.0332	+	9.25675i	0.544829	+	0.314557i
$867$	−109.097	+	62.9872i	−3.70513	+	2.13916i
$868$	−1.46587	−	8.31338i	−0.0497550	−	0.282174i
$869$	−8.73670	−	14.1378i	−0.296372	−	0.479593i
$870$	−3.67866	−	4.38406i	−0.124718	−	0.148634i
$871$	−3.20031	−	0.564300i	−0.108438	−	0.0191206i
$872$	−5.55498	+	2.02185i	−0.188115	+	0.0684684i
$873$		−	79.5843i		−	2.69352i
$874$	−12.4590	+	26.3609i	−0.421431	+	0.891671i
$875$		−	3.83940i		−	0.129796i
$876$	19.8602	−	7.22854i	0.671016	−	0.244230i
$877$	8.89263	−	50.4326i	0.300283	−	1.70299i	−0.344635	−	0.938737i	$-0.611997\pi$
$877$	8.89263	−	50.4326i	0.300283	−	1.70299i	0.644918	−	0.764252i	$-0.276892\pi$
$878$	−22.2787	+	18.6940i	−0.751869	+	0.630893i
$879$	21.4176	−	25.5245i	0.722399	−	0.860922i
$880$	0.238918	−	1.64067i	0.00805394	−	0.0553069i
$881$	−7.53399	−	13.0493i	−0.253827	−	0.439641i	0.710749	−	0.703445i	$-0.248356\pi$
$881$	−7.53399	−	13.0493i	−0.253827	−	0.439641i	−0.964576	+	0.263804i	$0.915023\pi$
$882$	−17.0202	+	29.4799i	−0.573101	+	0.992640i
$883$	−24.2866	−	8.83960i	−0.817309	−	0.297476i	−0.100669	−	0.994920i	$-0.532098\pi$
$883$	−24.2866	−	8.83960i	−0.817309	−	0.297476i	−0.716639	+	0.697444i	$0.754321\pi$
$884$	9.76035	−	26.8163i	0.328276	−	0.901931i
$885$	−2.33575	+	4.04564i	−0.0785154	+	0.135993i
$886$	11.1555	+	19.3219i	0.374776	+	0.649132i
$887$	5.20281	+	29.5066i	0.174693	+	0.990735i	0.938497	+	0.345287i	$0.112218\pi$
$887$	5.20281	+	29.5066i	0.174693	+	0.990735i	−0.763804	+	0.645448i	$0.776671\pi$
$888$	−12.0090	−	10.0768i	−0.402997	−	0.338155i
$889$	−9.66335	−	11.5163i	−0.324098	−	0.386245i
$890$	0.968426	+	0.170760i	0.0324617	+	0.00572388i
$891$	−11.4846	+	0.343799i	−0.384747	+	0.0115177i
$892$			9.81577i			0.328656i
$893$	12.5651	+	3.43668i	0.420475	+	0.115004i
$894$	41.3550			1.38312
$895$	−0.251500	−	0.690990i	−0.00840672	−	0.0230973i
$896$	0.775755	+	0.136787i	0.0259162	+	0.00456972i
$897$	45.4958	+	54.2198i	1.51906	+	1.81035i
$898$	20.3851	−	24.2940i	0.680258	−	0.810700i
$899$	−41.8474	+	7.37882i	−1.39569	+	0.246098i
$900$	−12.6731	−	21.9504i	−0.422436	−	0.731681i
$901$	43.6357	−	75.5792i	1.45371	−	2.51791i
$902$	−26.7028	−	21.0775i	−0.889106	−	0.701803i
$903$	−4.65578	+	12.7917i	−0.154935	+	0.425680i
$904$	3.57076	+	2.06158i	0.118762	+	0.0685671i
$905$	−1.07446	+	0.620339i	−0.0357162	+	0.0206208i
$906$	−26.5346	+	4.67876i	−0.881552	+	0.155441i
$907$	−15.5355	+	18.5144i	−0.515846	+	0.614762i	−0.959593	−	0.281390i	$-0.909204\pi$
$907$	−15.5355	+	18.5144i	−0.515846	+	0.614762i	0.443747	+	0.896152i	$0.353649\pi$
$908$	−14.4123	+	12.0933i	−0.478288	+	0.401331i
$909$	47.4826	+	8.37247i	1.57490	+	0.277697i
$910$	0.493593	+	1.35614i	0.0163624	+	0.0449555i
$911$			26.2708i			0.870390i	0.900336	+	0.435195i	$0.143321\pi$
$911$			26.2708i			0.870390i	−0.900336	+	0.435195i	$0.856679\pi$
$912$	−3.32018	+	12.1391i	−0.109942	+	0.401967i
$913$	−14.1640	+	42.8647i	−0.468759	+	1.41862i
$914$	−3.28290	−	9.01971i	−0.108589	−	0.298345i
$915$	0.967773	−	5.48852i	0.0319936	−	0.181445i
$916$	7.81042	−	6.55372i	0.258063	−	0.216541i
$917$	1.95221	+	1.63810i	0.0644677	+	0.0540948i
$918$	−9.11918	−	51.7174i	−0.300978	−	1.70693i
$919$	−29.9493	+	17.2912i	−0.987935	+	0.570385i	−0.904656	−	0.426142i	$-0.859872\pi$
$919$	−29.9493	+	17.2912i	−0.987935	+	0.570385i	−0.0832786	+	0.996526i	$0.526539\pi$
$920$	−1.67192	+	2.89585i	−0.0551216	+	0.0954734i
$921$	−20.1180	+	55.2739i	−0.662912	+	1.82134i
$922$	8.49804	−	23.3482i	0.279868	−	0.768931i
$923$	−12.7253	−	7.34693i	−0.418857	−	0.241827i
$924$	−1.53153	−	7.38592i	−0.0503835	−	0.242979i
$925$	−25.3999	+	4.47869i	−0.835144	+	0.147258i
$926$	11.5163	+	9.66336i	0.378451	+	0.317558i
$927$	10.3216	+	12.3008i	0.339006	+	0.404011i
$928$	0.688548	−	3.90495i	0.0226027	−	0.128186i
$929$	−10.6555	+	3.87827i	−0.349595	+	0.127242i	−0.510848	−	0.859671i	$-0.670669\pi$
$929$	−10.6555	+	3.87827i	−0.349595	+	0.127242i	0.161253	+	0.986913i	$0.448446\pi$
$930$	15.4672			0.507188
$931$	11.8824	−	25.1410i	0.389430	−	0.823963i
$932$		−	12.8393i		−	0.420567i
$933$	12.8989	+	35.4393i	0.422290	+	1.16023i
$934$	−5.41502	+	30.7101i	−0.177185	+	1.00486i
$935$	−4.77653	−	11.9939i	−0.156209	−	0.392244i
$936$	14.9805	+	12.5701i	0.489652	+	0.410867i
$937$	−25.7464	+	4.53978i	−0.841098	+	0.148308i	−0.577568	−	0.816343i	$-0.695998\pi$
$937$	−25.7464	+	4.53978i	−0.841098	+	0.148308i	−0.263530	+	0.964651i	$0.584887\pi$
$938$	−0.349238	−	0.604897i	−0.0114030	−	0.0197506i
$939$	0.145362	+	0.0839245i	0.00474370	+	0.00273877i
$940$	1.40385	+	0.510960i	0.0457886	+	0.0166657i
$941$	22.5350	+	8.20206i	0.734619	+	0.267380i	0.682119	−	0.731241i	$-0.261059\pi$
$941$	22.5350	+	8.20206i	0.734619	+	0.267380i	0.0525004	+	0.998621i	$0.483281\pi$
$942$	−3.03963	−	1.75493i	−0.0990366	−	0.0571788i
$943$	34.3053	+	59.4185i	1.11713	+	1.93493i
$944$	−3.18750	+	0.562041i	−0.103744	+	0.0182929i
$945$	2.03443	+	1.70709i	0.0661801	+	0.0555317i
$946$	7.34465	+	18.4425i	0.238795	+	0.599619i
$947$	5.64264	−	32.0010i	0.183361	−	1.03989i	−0.744681	−	0.667420i	$-0.767399\pi$
$947$	5.64264	−	32.0010i	0.183361	−	1.03989i	0.928043	−	0.372474i	$-0.121490\pi$
$948$	4.94823	+	13.5952i	0.160711	+	0.441550i
$949$			26.8278i			0.870867i
$950$	11.7880	+	17.0220i	0.382453	+	0.552267i
$951$	−41.6344			−1.35009
$952$	5.76382	−	2.09786i	0.186806	−	0.0679920i
$953$	−3.69961	+	20.9815i	−0.119842	+	0.679659i	0.864396	+	0.502811i	$0.167701\pi$
$953$	−3.69961	+	20.9815i	−0.119842	+	0.679659i	−0.984238	+	0.176847i	$0.943410\pi$
$954$	38.4412	+	45.8125i	1.24458	+	1.48323i
$955$	−5.02741	−	4.21850i	−0.162683	−	0.136507i
$956$	12.6848	−	2.23667i	0.410256	−	0.0723391i
$957$	−37.1788	+	7.70930i	−1.20182	+	0.249206i
$958$	−14.2020	−	8.19955i	−0.458847	−	0.264916i
$959$	−1.06822	+	2.93490i	−0.0344945	+	0.0947728i
$960$	−0.493639	+	1.35626i	−0.0159321	+	0.0437732i
$961$	41.9216	−	72.6104i	1.35231	−	2.34227i
$962$	17.2334	−	9.94971i	0.555627	−	0.320792i
$963$	1.49721	+	8.49110i	0.0482469	+	0.273622i
$964$	−19.5266	−	16.3848i	−0.628911	−	0.527719i
$965$	−5.73079	+	4.80870i	−0.184481	+	0.154798i
$966$	−2.64171	+	14.9819i	−0.0849955	+	0.482034i
$967$	6.74565	+	18.5335i	0.216926	+	0.595998i	0.999652	−	0.0263674i	$-0.00839398\pi$
$967$	6.74565	+	18.5335i	0.216926	+	0.595998i	−0.782727	+	0.622366i	$0.786172\pi$
$968$	−8.83435	−	6.55395i	−0.283947	−	0.210652i
$969$	24.8722	+	94.7862i	0.799012	+	3.04497i
$970$			7.45589i			0.239394i
$971$	−4.49698	−	12.3554i	−0.144315	−	0.396502i	0.846384	−	0.532573i	$-0.178775\pi$
$971$	−4.49698	−	12.3554i	−0.144315	−	0.396502i	−0.990699	+	0.136071i	$0.956553\pi$
$972$	−10.0753	−	1.77655i	−0.323166	−	0.0569828i
$973$	11.5613	−	9.70110i	0.370639	−	0.311003i
$974$	1.03581	−	1.23442i	0.0331893	−	0.0395535i
$975$	49.4987	−	8.72796i	1.58523	−	0.279518i
$976$	3.34407	−	1.93070i	0.107041	−	0.0618003i
$977$	17.3067	+	9.99203i	0.553690	+	0.319673i	0.750609	−	0.660747i	$-0.229760\pi$
$977$	17.3067	+	9.99203i	0.553690	+	0.319673i	−0.196919	+	0.980420i	$0.563094\pi$
$978$	7.48212	−	20.5570i	0.239252	−	0.657339i
$979$	4.04228	−	5.12111i	0.129192	−	0.163671i
$980$	1.59455	−	2.76184i	0.0509360	−	0.0882237i
$981$	−15.7716	−	27.3172i	−0.503549	−	0.872172i
$982$	−6.34089	+	1.11807i	−0.202346	+	0.0356790i
$983$	6.24814	−	7.44624i	0.199285	−	0.237498i	−0.657142	−	0.753767i	$-0.728235\pi$
$983$	6.24814	−	7.44624i	0.199285	−	0.237498i	0.856427	+	0.516268i	$0.172679\pi$
$984$	19.0358	+	22.6860i	0.606839	+	0.723202i
$985$	−10.4496	−	1.84254i	−0.332951	−	0.0587082i
$986$	−10.5601	−	29.0136i	−0.336301	−	0.923980i
$987$	6.79680			0.216344
$988$	−13.0383	−	9.23053i	−0.414802	−	0.293662i
$989$		−	40.0364i		−	1.27308i
$990$	8.84285	−	0.264718i	0.281044	−	0.00841328i
$991$	36.0836	+	6.36251i	1.14623	+	0.202112i	0.714330	−	0.699809i	$-0.246732\pi$
$991$	36.0836	+	6.36251i	1.14623	+	0.202112i	0.431902	+	0.901921i	$0.357843\pi$
$992$	6.88843	+	8.20931i	0.218708	+	0.260646i
$993$	15.7836	+	13.2440i	0.500878	+	0.420286i
$994$	−0.548424	−	3.11027i	−0.0173950	−	0.0986518i
$995$	−5.31989	−	9.21431i	−0.168652	−	0.292113i
$996$	19.6496	−	34.0340i	0.622620	−	1.07841i
$997$	13.3167	−	36.5872i	0.421743	−	1.15873i	−0.528965	−	0.848643i	$-0.677420\pi$
$997$	13.3167	−	36.5872i	0.421743	−	1.15873i	0.950708	−	0.310086i	$-0.100358\pi$
$998$	−17.2771	−	6.28835i	−0.546897	−	0.199054i
$999$	18.3097	−	31.7134i	0.579295	−	1.00337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.q.a.109.10	✓	60
11.10	odd	2		418.2.q.b.109.10	yes	60
19.15	odd	18		418.2.q.b.395.10	yes	60
209.186	even	18	inner	418.2.q.a.395.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.q.a.109.10	✓	60	1.1	even	1	trivial
418.2.q.a.395.10	yes	60	209.186	even	18	inner
418.2.q.b.109.10	yes	60	11.10	odd	2
418.2.q.b.395.10	yes	60	19.15	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.q (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(2.84334 + 0.501357i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.382944 - 0.321328i) q^{5} +(2.84334 - 0.501357i) q^{6} +(-0.682188 + 0.393861i) q^{7} +(0.500000 - 0.866025i) q^{8} +(5.01412 + 1.82499i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(2.84334 + 0.501357i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.382944 - 0.321328i) q^{5} +(2.84334 - 0.501357i) q^{6} +(-0.682188 + 0.393861i) q^{7} +(0.500000 - 0.866025i) q^{8} +(5.01412 + 1.82499i) q^{9} +(-0.469750 - 0.170975i) q^{10} +(-2.47575 + 2.20695i) q^{11} +(2.50039 - 1.44360i) q^{12} +(0.636404 + 3.60923i) q^{13} +(-0.506338 + 0.603431i) q^{14} +(-0.927739 - 1.10564i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-2.66319 - 7.31706i) q^{17} +5.33592 q^{18} +(-4.34422 + 0.357400i) q^{19} -0.499898 q^{20} +(-2.13715 + 0.777861i) q^{21} +(-1.57162 + 2.92062i) q^{22} +(5.12411 - 4.29964i) q^{23} +(1.85586 - 2.21172i) q^{24} +(-0.824847 - 4.67794i) q^{25} +(1.83245 + 3.17390i) q^{26} +(5.84070 + 3.37213i) q^{27} +(-0.269417 + 0.740217i) q^{28} +(3.72606 + 1.35618i) q^{29} +(-1.24994 - 0.721652i) q^{30} +(-9.28076 + 5.35825i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-8.14587 + 5.03388i) q^{33} +(-5.00517 - 5.96493i) q^{34} +(0.387799 + 0.0683793i) q^{35} +(5.01412 - 1.82499i) q^{36} -5.42973i q^{37} +(-3.96000 + 1.82166i) q^{38} +10.5813i q^{39} +(-0.469750 + 0.170975i) q^{40} +(-1.78113 + 10.1013i) q^{41} +(-1.74222 + 1.46190i) q^{42} +(3.84732 - 4.58506i) q^{43} +(-0.477934 + 3.28201i) q^{44} +(-1.33371 - 2.31005i) q^{45} +(3.34452 - 5.79289i) q^{46} +(-2.80828 - 1.02213i) q^{47} +(0.987480 - 2.71308i) q^{48} +(-3.18975 + 5.52480i) q^{49} +(-2.37505 - 4.11371i) q^{50} +(-3.90389 - 22.1401i) q^{51} +(2.80748 + 2.35576i) q^{52} +(7.20424 + 8.58567i) q^{53} +(6.64180 + 1.17113i) q^{54} +(1.65723 - 0.0496105i) q^{55} +0.787723i q^{56} +(-12.5313 - 1.16180i) q^{57} +3.96519 q^{58} +(-1.10701 - 3.04147i) q^{59} +(-1.42138 - 0.250627i) q^{60} +(2.48206 + 2.95801i) q^{61} +(-6.88843 + 8.20931i) q^{62} +(-4.13937 + 0.729882i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.916039 - 1.58663i) q^{65} +(-5.93293 + 7.51635i) q^{66} +(-0.303270 + 0.833227i) q^{67} +(-6.74344 - 3.89333i) q^{68} +(16.7252 - 9.65631i) q^{69} +(0.387799 - 0.0683793i) q^{70} +(-2.57716 + 3.07134i) q^{71} +(4.08755 - 3.42986i) q^{72} +(7.20898 + 1.27114i) q^{73} +(-1.85708 - 5.10227i) q^{74} -13.7145i q^{75} +(-3.09814 + 3.06620i) q^{76} +(0.819695 - 2.48066i) q^{77} +(3.61902 + 9.94318i) q^{78} +(-0.870146 + 4.93484i) q^{79} +(-0.382944 + 0.321328i) q^{80} +(2.65379 + 2.22679i) q^{81} +(1.78113 + 10.1013i) q^{82} +(11.7879 - 6.80575i) q^{83} +(-1.13716 + 1.96961i) q^{84} +(-1.33133 + 3.65779i) q^{85} +(2.04712 - 5.62441i) q^{86} +(9.91452 + 5.72415i) q^{87} +(0.673402 + 3.24754i) q^{88} +(-1.93725 + 0.341589i) q^{89} +(-2.04336 - 1.71458i) q^{90} +(-1.85568 - 2.21152i) q^{91} +(1.16154 - 6.58743i) q^{92} +(-29.0747 + 10.5823i) q^{93} -2.98851 q^{94} +(1.77844 + 1.25906i) q^{95} -2.88720i q^{96} +(-5.10117 - 14.0153i) q^{97} +(-1.10779 + 6.28257i) q^{98} +(-16.4414 + 6.54771i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9}+O(q^{10}) \) 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9	\( 60 q - 3 q^{3} - 3 q^{6} - 18 q^{7} + 30 q^{8} - 3 q^{9} + 3 q^{11} + 6 q^{13} - 12 q^{14} + 24 q^{15} - 6 q^{17} + 60 q^{18} - 30 q^{19} - 12 q^{20} + 12 q^{21} + 12 q^{22} + 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} + 6 q^{28} - 3 q^{29} - 9 q^{31} - 42 q^{33} - 6 q^{34} - 24 q^{35} - 3 q^{36} + 6 q^{38} + 15 q^{41} + 6 q^{42} - 3 q^{43} + 12 q^{44} - 48 q^{45} + 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} + 36 q^{50} - 45 q^{51} - 3 q^{52} + 24 q^{53} - 27 q^{54} + 6 q^{55} + 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} + 54 q^{61} - 66 q^{63} - 30 q^{64} - 63 q^{66} + 9 q^{67} - 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 36 q^{79} - 93 q^{81} - 15 q^{82} - 36 q^{83} + 24 q^{84} - 60 q^{85} - 3 q^{86} + 54 q^{87} - 3 q^{88} - 3 q^{89} - 24 q^{90} - 12 q^{91} - 102 q^{93} - 12 q^{94} + 24 q^{95} - 6 q^{97} - 18 q^{98} - 78 q^{99}+O(q^{100}) \) 60 * q - 3 * q^3 - 3 * q^6 - 18 * q^7 + 30 * q^8 - 3 * q^9 + 3 * q^11 + 6 * q^13 - 12 * q^14 + 24 * q^15 - 6 * q^17 + 60 * q^18 - 30 * q^19 - 12 * q^20 + 12 * q^21 + 12 * q^22 + 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 + 6 * q^28 - 3 * q^29 - 9 * q^31 - 42 * q^33 - 6 * q^34 - 24 * q^35 - 3 * q^36 + 6 * q^38 + 15 * q^41 + 6 * q^42 - 3 * q^43 + 12 * q^44 - 48 * q^45 + 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 + 36 * q^50 - 45 * q^51 - 3 * q^52 + 24 * q^53 - 27 * q^54 + 6 * q^55 + 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 + 54 * q^61 - 66 * q^63 - 30 * q^64 - 63 * q^66 + 9 * q^67 - 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 36 * q^79 - 93 * q^81 - 15 * q^82 - 36 * q^83 + 24 * q^84 - 60 * q^85 - 3 * q^86 + 54 * q^87 - 3 * q^88 - 3 * q^89 - 24 * q^90 - 12 * q^91 - 102 * q^93 - 12 * q^94 + 24 * q^95 - 6 * q^97 - 18 * q^98 - 78 * q^99

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