LMFDB - Embedded newform 471.2.q.b.19.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(19,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 62]))

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

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

chi := DirichletCharacter("471.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.q (of order $39$, degree $24$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	471.19
Dual form			471.2.q.b.124.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.92606 + 0.474730i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.71341 + 0.899266i) q^{4} +(-2.98759 + 2.24503i) q^{5} +(-1.37416 - 1.43065i) q^{6} +(-2.68643 + 1.40995i) q^{7} +(-0.0964276 - 0.0854274i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(1.92606 + 0.474730i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.71341 + 0.899266i) q^{4} +(-2.98759 + 2.24503i) q^{5} +(-1.37416 - 1.43065i) q^{6} +(-2.68643 + 1.40995i) q^{7} +(-0.0964276 - 0.0854274i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-6.82004 + 2.90575i) q^{10} +(0.499260 + 0.519785i) q^{11} +(-0.967529 - 1.67581i) q^{12} +(-0.440234 + 0.762508i) q^{13} +(-5.84357 + 1.44031i) q^{14} +(3.72497 - 0.300710i) q^{15} +(-2.34365 - 3.39536i) q^{16} +(-0.393479 + 0.295680i) q^{17} +(0.396791 + 1.94361i) q^{18} +(-1.25829 + 6.16354i) q^{19} +(-7.13783 + 1.16001i) q^{20} +(3.02412 + 0.244132i) q^{21} +(0.714845 + 1.23815i) q^{22} +(-2.23989 - 3.24504i) q^{23} +(0.0358416 + 0.123740i) q^{24} +(2.49444 - 8.61182i) q^{25} +(-1.20990 + 1.25964i) q^{26} +(0.120537 - 0.992709i) q^{27} -5.87088 q^{28} +(-0.333954 + 2.75036i) q^{29} +(7.31725 + 1.18917i) q^{30} +(6.43639 + 7.88315i) q^{31} +(-2.81075 - 7.41134i) q^{32} +(-0.144162 - 0.706154i) q^{33} +(-0.898231 + 0.382701i) q^{34} +(4.86058 - 10.2435i) q^{35} +(-0.0779169 + 1.93349i) q^{36} +(3.14440 + 2.36286i) q^{37} +(-5.34956 + 11.2740i) q^{38} +(0.779616 - 0.409174i) q^{39} +(0.479872 + 0.0387393i) q^{40} +(0.340630 - 0.493488i) q^{41} +(5.70872 + 1.90585i) q^{42} +(4.28072 - 2.70696i) q^{43} +(0.388011 + 1.33957i) q^{44} +(-3.30902 - 1.73671i) q^{45} +(-2.77363 - 7.31347i) q^{46} +(0.891752 + 0.379940i) q^{47} +(0.166124 + 4.12232i) q^{48} +(1.25252 - 1.81459i) q^{49} +(8.89273 - 15.4027i) q^{50} +(0.490596 - 0.0396050i) q^{51} +(-1.44000 + 0.910600i) q^{52} +(-11.4367 + 3.81815i) q^{53} +(0.703429 - 1.85479i) q^{54} +(-2.65851 - 0.432050i) q^{55} +(0.379495 + 0.0935370i) q^{56} +(4.35770 - 4.53684i) q^{57} +(-1.94889 + 5.13881i) q^{58} +(9.86676 - 8.74119i) q^{59} +(6.65281 + 2.83450i) q^{60} +(-1.48032 + 7.25108i) q^{61} +(8.65448 + 18.2389i) q^{62} +(-2.42547 - 1.82263i) q^{63} +(-0.900686 - 7.41782i) q^{64} +(-0.396612 - 3.26639i) q^{65} +(0.0575678 - 1.42853i) q^{66} +(-3.35085 - 2.96860i) q^{67} +(-0.940086 + 0.152779i) q^{68} +(0.158769 + 3.93982i) q^{69} +(14.2246 - 17.4220i) q^{70} +(-0.211858 + 0.0707285i) q^{71} +(0.0358416 - 0.123740i) q^{72} +(-2.64296 - 1.67130i) q^{73} +(4.93456 + 6.04374i) q^{74} +(-6.71100 + 5.94543i) q^{75} +(-7.69863 + 9.42911i) q^{76} +(-2.07410 - 0.692436i) q^{77} +(1.69583 - 0.417985i) q^{78} +(-8.58712 + 2.11653i) q^{79} +(14.6245 + 4.88238i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(0.890345 - 0.788777i) q^{82} +(1.31182 + 1.60668i) q^{83} +(4.96201 + 3.13778i) q^{84} +(0.511743 - 1.76674i) q^{85} +(9.52998 - 3.18157i) q^{86} +(1.75223 - 2.14609i) q^{87} +(-0.00373858 - 0.0927720i) q^{88} +(-18.2685 + 2.96892i) q^{89} +(-5.54890 - 4.91589i) q^{90} +(0.107562 - 2.66914i) q^{91} +(-0.919691 - 7.57433i) q^{92} +(-1.22670 - 10.1028i) q^{93} +(1.53719 + 1.15513i) q^{94} +(-10.0780 - 21.2390i) q^{95} +(-1.58549 + 7.76624i) q^{96} +(4.25139 + 1.81135i) q^{97} +(3.27386 - 2.90039i) q^{98} +(-0.255571 + 0.673884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) $ 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{31}{39}\right)$

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 $

$2$	1.92606	+	0.474730i	1.36193	+	0.335685i	0.851553	−	0.524268i	$-0.175661\pi$
$2$	1.92606	+	0.474730i	1.36193	+	0.335685i	0.510373	+	0.859953i	$0.329507\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	1.71341	+	0.899266i	0.856704	+	0.449633i
$5$	−2.98759	+	2.24503i	−1.33609	+	1.00401i	−0.338068	+	0.941122i	$0.609773\pi$
$5$	−2.98759	+	2.24503i	−1.33609	+	1.00401i	−0.998021	+	0.0628842i	$0.979970\pi$
$6$	−1.37416	−	1.43065i	−0.560997	−	0.584060i
$7$	−2.68643	+	1.40995i	−1.01538	+	0.532911i	−0.888437	−	0.458999i	$-0.848208\pi$
$7$	−2.68643	+	1.40995i	−1.01538	+	0.532911i	−0.126940	+	0.991910i	$0.540516\pi$
$8$	−0.0964276	−	0.0854274i	−0.0340923	−	0.0302031i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−6.82004	+	2.90575i	−2.15668	+	0.918878i
$11$	0.499260	+	0.519785i	0.150533	+	0.156721i	0.792199	−	0.610263i	$-0.208936\pi$
$11$	0.499260	+	0.519785i	0.150533	+	0.156721i	−0.641667	+	0.766984i	$0.721757\pi$
$12$	−0.967529	−	1.67581i	−0.279302	−	0.483764i
$13$	−0.440234	+	0.762508i	−0.122099	+	0.211482i	−0.920595	−	0.390518i	$-0.872296\pi$
$13$	−0.440234	+	0.762508i	−0.122099	+	0.211482i	0.798496	+	0.602000i	$0.205629\pi$
$14$	−5.84357	+	1.44031i	−1.56176	+	0.384939i
$15$	3.72497	−	0.300710i	0.961782	−	0.0776431i
$16$	−2.34365	−	3.39536i	−0.585912	−	0.848839i
$17$	−0.393479	+	0.295680i	−0.0954327	+	0.0717131i	−0.647388	−	0.762161i	$-0.724138\pi$
$17$	−0.393479	+	0.295680i	−0.0954327	+	0.0717131i	0.551955	+	0.833874i	$0.313882\pi$
$18$	0.396791	+	1.94361i	0.0935244	+	0.458113i
$19$	−1.25829	+	6.16354i	−0.288673	+	1.41401i	0.533994	+	0.845488i	$0.320690\pi$
$19$	−1.25829	+	6.16354i	−0.288673	+	1.41401i	−0.822667	+	0.568524i	$0.807515\pi$
$20$	−7.13783	+	1.16001i	−1.59607	+	0.259386i
$21$	3.02412	+	0.244132i	0.659917	+	0.0532740i
$22$	0.714845	+	1.23815i	0.152405	+	0.263974i
$23$	−2.23989	−	3.24504i	−0.467049	−	0.676637i	0.516704	−	0.856164i	$-0.327159\pi$
$23$	−2.23989	−	3.24504i	−0.467049	−	0.676637i	−0.983753	+	0.179527i	$0.942543\pi$
$24$	0.0358416	+	0.123740i	0.00731614	+	0.0252582i
$25$	2.49444	−	8.61182i	0.498889	−	1.72236i
$26$	−1.20990	+	1.25964i	−0.237281	+	0.247036i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−5.87088			−1.10949
$29$	−0.333954	+	2.75036i	−0.0620138	+	0.510729i	0.928295	+	0.371845i	$0.121275\pi$
$29$	−0.333954	+	2.75036i	−0.0620138	+	0.510729i	−0.990309	+	0.138884i	$0.955648\pi$
$30$	7.31725	+	1.18917i	1.33594	+	0.217112i
$31$	6.43639	+	7.88315i	1.15601	+	1.41585i	0.892412	+	0.451222i	$0.149012\pi$
$31$	6.43639	+	7.88315i	1.15601	+	1.41585i	0.263598	+	0.964633i	$0.415091\pi$
$32$	−2.81075	−	7.41134i	−0.496875	−	1.31015i
$33$	−0.144162	−	0.706154i	−0.0250955	−	0.122926i
$34$	−0.898231	+	0.382701i	−0.154045	+	0.0656326i
$35$	4.86058	−	10.2435i	0.821588	−	1.73146i
$36$	−0.0779169	+	1.93349i	−0.0129862	+	0.322248i
$37$	3.14440	+	2.36286i	0.516936	+	0.388452i	0.826946	−	0.562281i	$-0.190076\pi$
$37$	3.14440	+	2.36286i	0.516936	+	0.388452i	−0.310010	+	0.950733i	$0.600333\pi$
$38$	−5.34956	+	11.2740i	−0.867813	+	1.82888i
$39$	0.779616	−	0.409174i	0.124838	−	0.0655203i
$40$	0.479872	+	0.0387393i	0.0758745	+	0.00612522i
$41$	0.340630	−	0.493488i	0.0531975	−	0.0770698i	−0.795482	−	0.605977i	$-0.792783\pi$
$41$	0.340630	−	0.493488i	0.0531975	−	0.0770698i	0.848680	+	0.528907i	$0.177398\pi$
$42$	5.70872	+	1.90585i	0.880875	+	0.294079i
$43$	4.28072	−	2.70696i	0.652803	−	0.412808i	−0.166600	−	0.986024i	$-0.553279\pi$
$43$	4.28072	−	2.70696i	0.652803	−	0.412808i	0.819404	+	0.573217i	$0.194305\pi$
$44$	0.388011	+	1.33957i	0.0584949	+	0.201948i
$45$	−3.30902	−	1.73671i	−0.493280	−	0.258893i
$46$	−2.77363	−	7.31347i	−0.408950	−	1.07831i
$47$	0.891752	+	0.379940i	0.130075	+	0.0554199i	0.456024	−	0.889968i	$-0.349273\pi$
$47$	0.891752	+	0.379940i	0.130075	+	0.0554199i	−0.325948	+	0.945388i	$0.605684\pi$
$48$	0.166124	+	4.12232i	0.0239779	+	0.595006i
$49$	1.25252	−	1.81459i	0.178931	−	0.259227i
$50$	8.89273	−	15.4027i	1.25762	−	2.17826i
$51$	0.490596	−	0.0396050i	0.0686972	−	0.00554581i
$52$	−1.44000	+	0.910600i	−0.199692	+	0.126277i
$53$	−11.4367	+	3.81815i	−1.57096	+	0.524463i	−0.962999	−	0.269506i	$-0.913140\pi$
$53$	−11.4367	+	3.81815i	−1.57096	+	0.524463i	−0.607959	+	0.793969i	$0.708011\pi$
$54$	0.703429	−	1.85479i	0.0957246	−	0.252405i
$55$	−2.65851	−	0.432050i	−0.358474	−	0.0582576i
$56$	0.379495	+	0.0935370i	0.0507121	+	0.0124994i
$57$	4.35770	−	4.53684i	0.577191	−	0.600920i
$58$	−1.94889	+	5.13881i	−0.255902	+	0.674759i
$59$	9.86676	−	8.74119i	1.28454	−	1.13801i	0.301731	−	0.953393i	$-0.402435\pi$
$59$	9.86676	−	8.74119i	1.28454	−	1.13801i	0.982811	−	0.184612i	$-0.0591030\pi$
$60$	6.65281	+	2.83450i	0.858874	+	0.365932i
$61$	−1.48032	+	7.25108i	−0.189535	+	0.928405i	0.768080	+	0.640354i	$0.221212\pi$
$61$	−1.48032	+	7.25108i	−0.189535	+	0.928405i	−0.957615	+	0.288051i	$0.906993\pi$
$62$	8.65448	+	18.2389i	1.09912	+	2.31635i
$63$	−2.42547	−	1.82263i	−0.305581	−	0.229629i
$64$	−0.900686	−	7.41782i	−0.112586	−	0.927227i
$65$	−0.396612	−	3.26639i	−0.0491937	−	0.405146i
$66$	0.0575678	−	1.42853i	0.00708611	−	0.175840i
$67$	−3.35085	−	2.96860i	−0.409372	−	0.362672i	0.433161	−	0.901317i	$-0.357398\pi$
$67$	−3.35085	−	2.96860i	−0.409372	−	0.362672i	−0.842533	+	0.538645i	$0.818937\pi$
$68$	−0.940086	+	0.152779i	−0.114002	+	0.0185272i
$69$	0.158769	+	3.93982i	0.0191136	+	0.474298i
$70$	14.2246	−	17.4220i	1.70017	−	2.08233i
$71$	−0.211858	+	0.0707285i	−0.0251429	+	0.00839393i	−0.329212	−	0.944256i	$-0.606783\pi$
$71$	−0.211858	+	0.0707285i	−0.0251429	+	0.00839393i	0.304069	+	0.952650i	$0.401655\pi$
$72$	0.0358416	−	0.123740i	0.00422397	−	0.0145829i
$73$	−2.64296	−	1.67130i	−0.309335	−	0.195611i	0.370773	−	0.928723i	$-0.379093\pi$
$73$	−2.64296	−	1.67130i	−0.309335	−	0.195611i	−0.680108	+	0.733112i	$0.738067\pi$
$74$	4.93456	+	6.04374i	0.573631	+	0.702571i
$75$	−6.71100	+	5.94543i	−0.774920	+	0.686519i
$76$	−7.69863	+	9.42911i	−0.883094	+	1.08159i
$77$	−2.07410	−	0.692436i	−0.236366	−	0.0789104i
$78$	1.69583	−	0.417985i	0.192015	−	0.0473274i
$79$	−8.58712	+	2.11653i	−0.966126	+	0.238129i	−0.690658	−	0.723181i	$-0.742679\pi$
$79$	−8.58712	+	2.11653i	−0.966126	+	0.238129i	−0.275468	+	0.961310i	$0.588833\pi$
$80$	14.6245	+	4.88238i	1.63507	+	0.545866i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	0.890345	−	0.788777i	0.0983222	−	0.0871059i
$83$	1.31182	+	1.60668i	0.143991	+	0.176357i	0.841565	−	0.540156i	$-0.181635\pi$
$83$	1.31182	+	1.60668i	0.143991	+	0.176357i	−0.697574	+	0.716512i	$0.745737\pi$
$84$	4.96201	+	3.13778i	0.541400	+	0.342360i
$85$	0.511743	−	1.76674i	0.0555063	−	0.191630i
$86$	9.52998	−	3.18157i	1.02764	−	0.343078i
$87$	1.75223	−	2.14609i	0.187859	−	0.230085i
$88$	−0.00373858	−	0.0927720i	−0.000398534	−	0.00988953i
$89$	−18.2685	+	2.96892i	−1.93646	+	0.314705i	−0.999405	−	0.0344857i	$-0.989021\pi$
$89$	−18.2685	+	2.96892i	−1.93646	+	0.314705i	−0.937052	+	0.349191i	$0.886457\pi$
$90$	−5.54890	−	4.91589i	−0.584905	−	0.518181i
$91$	0.107562	−	2.66914i	0.0112756	−	0.279801i
$92$	−0.919691	−	7.57433i	−0.0958844	−	0.789679i
$93$	−1.22670	−	10.1028i	−0.127203	−	1.04761i
$94$	1.53719	+	1.15513i	0.158550	+	0.119142i
$95$	−10.0780	−	21.2390i	−1.03398	−	2.17907i
$96$	−1.58549	+	7.76624i	−0.161818	+	0.792638i
$97$	4.25139	+	1.81135i	0.431663	+	0.183914i	0.596859	−	0.802346i	$-0.296415\pi$
$97$	4.25139	+	1.81135i	0.431663	+	0.183914i	−0.165196	+	0.986261i	$0.552826\pi$
$98$	3.27386	−	2.90039i	0.330710	−	0.292983i
$99$	−0.255571	+	0.673884i	−0.0256858	+	0.0677279i
$100$	12.0183	−	12.5124i	1.20183	−	1.25124i
$101$	2.05782	+	0.507208i	0.204761	+	0.0504691i	0.340362	−	0.940294i	$-0.389450\pi$
$101$	2.05782	+	0.507208i	0.204761	+	0.0504691i	−0.135601	+	0.990764i	$0.543297\pi$
$102$	0.963717	+	0.156619i	0.0954222	+	0.0155076i
$103$	3.23546	−	8.53121i	0.318799	−	0.840605i	−0.675826	−	0.737062i	$-0.736213\pi$
$103$	3.23546	−	8.53121i	0.318799	−	0.840605i	0.994625	−	0.103543i	$-0.0330180\pi$
$104$	0.107590	−	0.0359187i	0.0105500	−	0.00352212i
$105$	−9.58289	+	6.05986i	−0.935195	+	0.591381i
$106$	−23.8404	+	1.92459i	−2.31558	+	0.186933i
$107$	−3.29486	+	5.70686i	−0.318526	+	0.551703i	−0.980181	−	0.198105i	$-0.936521\pi$
$107$	−3.29486	+	5.70686i	−0.318526	+	0.551703i	0.661655	+	0.749809i	$0.269854\pi$
$108$	1.09924	−	1.59252i	0.105774	−	0.153240i
$109$	0.613186	+	15.2160i	0.0587325	+	1.45743i	0.712997	+	0.701167i	$0.247337\pi$
$109$	0.613186	+	15.2160i	0.0587325	+	1.45743i	−0.654264	+	0.756266i	$0.727022\pi$
$110$	−4.91533	−	2.09423i	−0.468659	−	0.199677i
$111$	−1.39475	−	3.67764i	−0.132383	−	0.349066i
$112$	11.0833	+	5.81698i	1.04728	+	0.549653i
$113$	0.184733	+	0.637771i	0.0173782	+	0.0599964i	0.968739	−	0.248084i	$-0.0798007\pi$
$113$	0.184733	+	0.637771i	0.0173782	+	0.0599964i	−0.951360	+	0.308080i	$0.900314\pi$
$114$	10.5469	−	6.66948i	0.987812	−	0.624654i
$115$	13.9771	+	4.66623i	1.30337	+	0.435128i
$116$	−3.04551	+	4.41218i	−0.282768	+	0.409661i
$117$	−0.877613	−	0.0708482i	−0.0811354	−	0.00654992i
$118$	23.1536	−	12.1520i	2.13146	−	1.11868i
$119$	0.640162	−	1.34911i	0.0586835	−	0.123673i
$120$	−0.384878	−	0.289217i	−0.0351344	−	0.0264018i
$121$	0.422010	−	10.4721i	0.0383645	−	0.952006i
$122$	−6.29348	+	13.2632i	−0.569785	+	1.20080i
$123$	−0.551649	+	0.235036i	−0.0497405	+	0.0211925i
$124$	3.93912	+	19.2951i	0.353743	+	1.73275i
$125$	5.25544	+	13.8575i	0.470061	+	1.23945i
$126$	−3.80634	−	4.66192i	−0.339096	−	0.415317i
$127$	17.8473	+	2.90047i	1.58369	+	0.257375i	0.887613	−	0.460590i	$-0.152362\pi$
$127$	17.8473	+	2.90047i	1.58369	+	0.257375i	0.696079	+	0.717965i	$0.254926\pi$
$128$	−0.124160	+	1.02255i	−0.0109743	+	0.0903818i
$129$	−5.06480			−0.445931
$130$	0.786759	−	6.47954i	0.0690033	−	0.568293i
$131$	−7.40454	+	7.70894i	−0.646937	+	0.673533i	−0.961216	−	0.275798i	$-0.911058\pi$
$131$	−7.40454	+	7.70894i	−0.646937	+	0.673533i	0.314278	+	0.949331i	$0.398237\pi$
$132$	0.388011	−	1.33957i	0.0337721	−	0.116595i
$133$	−5.30995	−	18.3321i	−0.460431	−	1.58959i
$134$	−5.04465	−	7.30844i	−0.435791	−	0.631353i
$135$	1.86854	+	3.23641i	0.160819	+	0.278546i
$136$	0.0632015	+	0.00510215i	0.00541948	+	0.000437506i
$137$	−1.83724	+	0.298580i	−0.156966	+	0.0255094i	−0.238386	−	0.971170i	$-0.576618\pi$
$137$	−1.83724	+	0.298580i	−0.156966	+	0.0255094i	0.0814205	+	0.996680i	$0.474054\pi$
$138$	−1.56455	+	7.66368i	−0.133183	+	0.652376i
$139$	4.15044	+	20.3302i	0.352036	+	1.72439i	0.641435	+	0.767177i	$0.278339\pi$
$139$	4.15044	+	20.3302i	0.352036	+	1.72439i	−0.289399	+	0.957208i	$0.593456\pi$
$140$	17.5398	−	13.1803i	1.48238	−	1.11394i
$141$	−0.550635	−	0.797732i	−0.0463718	−	0.0671812i
$142$	−0.441626	+	0.0356518i	−0.0370605	+	0.00299183i
$143$	−0.616131	+	0.151863i	−0.0515235	+	0.0126994i
$144$	2.06283	−	3.57293i	0.171903	−	0.297744i
$145$	−5.17691	−	8.96668i	−0.429919	−	0.744642i
$146$	−4.29706	−	4.47372i	−0.355628	−	0.370247i
$147$	−2.02845	+	0.864243i	−0.167304	+	0.0712815i
$148$	3.26280	+	6.87620i	0.268200	+	0.565220i
$149$	−16.2377	−	14.3853i	−1.33024	−	1.17849i	−0.969294	−	0.245906i	$-0.920914\pi$
$149$	−16.2377	−	14.3853i	−1.33024	−	1.17849i	−0.360949	−	0.932586i	$-0.617547\pi$
$150$	−15.7482	+	8.26531i	−1.28584	+	0.674860i
$151$	11.5087	+	11.9818i	0.936562	+	0.975064i	0.999737	−	0.0229383i	$-0.00730213\pi$
$151$	11.5087	+	11.9818i	0.936562	+	0.975064i	−0.0631750	+	0.998002i	$0.520123\pi$
$152$	0.647869	−	0.486842i	0.0525491	−	0.0394881i
$153$	−0.435814	−	0.228733i	−0.0352335	−	0.0184920i
$154$	−3.66611	−	2.31831i	−0.295424	−	0.186815i
$155$	−36.9271	−	9.10172i	−2.96606	−	0.731068i
$156$	1.70376			0.136410
$157$	−6.78664	+	10.5329i	−0.541633	+	0.840615i
$157$	−6.78664	+	10.5329i	−0.541633	+	0.840615i
$158$	−17.5441			−1.39573
$159$	11.7069	+	2.88549i	0.928417	+	0.228834i
$160$	25.0360	+	15.8318i	1.97927	+	1.25161i
$161$	10.5927	+	5.55945i	0.834818	+	0.438146i
$162$	−1.58585	+	1.19169i	−0.124596	+	0.0936281i
$163$	6.17736	+	6.43132i	0.483848	+	0.503740i	0.917716	−	0.397237i	$-0.130031\pi$
$163$	6.17736	+	6.43132i	0.483848	+	0.503740i	−0.433868	+	0.900977i	$0.642851\pi$
$164$	1.02741	−	0.539229i	0.0802276	−	0.0421067i
$165$	2.01603	+	1.78605i	0.156948	+	0.139044i
$166$	1.76389	+	3.71732i	0.136905	+	0.288520i
$167$	1.07172	−	0.456617i	0.0829321	−	0.0353340i	−0.350102	−	0.936711i	$-0.613853\pi$
$167$	1.07172	−	0.456617i	0.0829321	−	0.0353340i	0.433034	+	0.901377i	$0.357443\pi$
$168$	−0.270753	−	0.281883i	−0.0208890	−	0.0217478i
$169$	6.11239	+	10.5870i	0.470184	+	0.814382i
$170$	1.82437	−	3.15990i	0.139923	−	0.242353i
$171$	−6.10787	+	1.50545i	−0.467081	+	0.115125i
$172$	9.76890	−	0.788627i	0.744871	−	0.0601322i
$173$	9.49294	+	13.7529i	0.721735	+	1.04561i	0.996458	+	0.0840901i	$0.0267984\pi$
$173$	9.49294	+	13.7529i	0.721735	+	1.04561i	−0.274723	+	0.961523i	$0.588586\pi$
$174$	4.39371	−	3.30166i	0.333086	−	0.250298i
$175$	5.44107	+	26.6521i	0.411306	+	2.01471i
$176$	0.594766	−	2.91336i	0.0448322	−	0.219603i
$177$	−13.0112	+	2.11452i	−0.977978	+	0.158937i
$178$	−36.5956	−	2.95430i	−2.74295	−	0.221434i
$179$	9.84456	+	17.0513i	0.735817	+	1.27447i	0.954364	+	0.298646i	$0.0965350\pi$
$179$	9.84456	+	17.0513i	0.735817	+	1.27447i	−0.218547	+	0.975826i	$0.570132\pi$
$180$	−4.10795	−	5.95139i	−0.306188	−	0.443590i
$181$	−1.23837	−	4.27535i	−0.0920472	−	0.317784i	0.901261	−	0.433276i	$-0.142643\pi$
$181$	−1.23837	−	4.27535i	−0.0920472	−	0.317784i	−0.993308	+	0.115492i	$0.963155\pi$
$182$	1.47429	−	5.08984i	0.109282	−	0.377284i
$183$	5.12660	−	5.33736i	0.378969	−	0.394549i
$184$	−0.0612281	+	0.504259i	−0.00451380	+	0.0371745i
$185$	−14.6988			−1.08068
$186$	2.43340	−	20.0409i	0.178426	−	1.46947i
$187$	−0.350139	−	0.0569031i	−0.0256047	−	0.00416116i
$188$	1.18627	+	1.45291i	0.0865175	+	0.105965i
$189$	1.07586	+	2.83680i	0.0782570	+	0.206347i
$190$	−9.32805	−	45.6918i	−0.676728	−	3.31483i
$191$	−20.9187	+	8.91263i	−1.51363	+	0.644895i	−0.979670	−	0.200617i	$-0.935705\pi$
$191$	−20.9187	+	8.91263i	−1.51363	+	0.644895i	−0.533956	+	0.845513i	$0.679295\pi$
$192$	−3.20332	+	6.75085i	−0.231180	+	0.487201i
$193$	0.677246	−	16.8057i	0.0487492	−	1.20970i	−0.770946	−	0.636900i	$-0.780216\pi$
$193$	0.677246	−	16.8057i	0.0487492	−	1.20970i	0.819696	−	0.572799i	$-0.194143\pi$
$194$	7.32851	+	5.50702i	0.526156	+	0.395381i
$195$	−1.41056	+	2.97270i	−0.101013	+	0.212879i
$196$	3.77787	−	1.98278i	0.269848	−	0.141627i
$197$	−0.165148	−	0.0133321i	−0.0117663	−	0.000949874i	0.0745820	−	0.997215i	$-0.476238\pi$
$197$	−0.165148	−	0.0133321i	−0.0117663	−	0.000949874i	−0.0863483	+	0.996265i	$0.527520\pi$
$198$	−0.812156	+	1.17661i	−0.0577174	+	0.0836181i
$199$	8.73360	+	2.91570i	0.619108	+	0.206689i	0.608884	−	0.793259i	$-0.291617\pi$
$199$	8.73360	+	2.91570i	0.619108	+	0.206689i	0.0102240	+	0.999948i	$0.496746\pi$
$200$	−0.976218	+	0.617323i	−0.0690291	+	0.0436513i
$201$	1.24549	+	4.29995i	0.0878504	+	0.303295i
$202$	3.72269	+	1.95382i	0.261928	+	0.137470i
$203$	−2.98073	−	7.85953i	−0.209206	−	0.551631i
$204$	0.876207	+	0.373317i	0.0613467	+	0.0261374i
$205$	0.0902310	+	2.23906i	0.00630201	+	0.156383i
$206$	10.2817	−	14.8956i	0.716360	−	1.03783i
$207$	1.97151	−	3.41475i	0.137029	−	0.237342i
$208$	3.62074	−	0.292296i	0.251053	−	0.0202671i
$209$	−3.83193	+	2.42316i	−0.265060	+	0.167614i
$210$	−21.3340	+	7.12233i	−1.47218	+	0.491487i
$211$	10.0500	−	26.4996i	0.691868	−	1.82430i	0.140426	−	0.990091i	$-0.455153\pi$
$211$	10.0500	−	26.4996i	0.691868	−	1.82430i	0.551441	−	0.834214i	$-0.314078\pi$
$212$	−23.0293	−	3.74263i	−1.58166	−	0.257045i
$213$	0.216862	+	0.0534517i	0.0148591	+	0.00366245i
$214$	−9.05530	+	9.42756i	−0.619007	+	0.644455i
$215$	−6.71181	+	17.6976i	−0.457742	+	1.20697i
$216$	−0.0964276	+	0.0854274i	−0.00656106	+	0.00581260i
$217$	−28.4058	−	12.1026i	−1.92831	−	0.821576i
$218$	−6.04248	+	29.5980i	−0.409249	+	2.00463i
$219$	1.34055	+	2.82514i	0.0905857	+	0.190905i
$220$	−4.16659	−	3.13099i	−0.280911	−	0.211091i
$221$	−0.0522357	−	0.430200i	−0.00351375	−	0.0289384i
$222$	−0.940470	−	7.74547i	−0.0631202	−	0.519842i
$223$	0.750081	−	18.6131i	0.0502291	−	1.24642i	−0.755901	−	0.654686i	$-0.772801\pi$
$223$	0.750081	−	18.6131i	0.0502291	−	1.24642i	0.806131	−	0.591738i	$-0.201558\pi$
$224$	18.0005	+	15.9471i	1.20271	+	1.06551i
$225$	8.84970	−	1.43822i	0.589980	−	0.0958811i
$226$	0.0530362	+	1.31608i	0.00352792	+	0.0875443i
$227$	17.3541	−	21.2549i	1.15183	−	1.41074i	0.255812	−	0.966727i	$-0.417657\pi$
$227$	17.3541	−	21.2549i	1.15183	−	1.41074i	0.896021	−	0.444012i	$-0.146445\pi$
$228$	11.5463	−	3.85474i	0.764675	−	0.255286i
$229$	3.87870	−	13.3908i	0.256312	−	0.884892i	−0.724391	−	0.689389i	$-0.757879\pi$
$229$	3.87870	−	13.3908i	0.256312	−	0.884892i	0.980703	−	0.195503i	$-0.0626338\pi$
$230$	24.7054	+	15.6227i	1.62902	+	1.03013i
$231$	1.38292	+	1.69378i	0.0909898	+	0.111442i
$232$	0.267159	−	0.236682i	0.0175398	−	0.0155389i
$233$	13.1543	−	16.1111i	0.861766	−	1.05547i	−0.136133	−	0.990691i	$-0.543468\pi$
$233$	13.1543	−	16.1111i	0.861766	−	1.05547i	0.997899	−	0.0647815i	$-0.0206351\pi$
$234$	−1.65670	−	0.553087i	−0.108302	−	0.0361564i
$235$	−3.51716	+	0.866902i	−0.229434	+	0.0565505i
$236$	24.7664	−	6.10438i	1.61216	−	0.397361i
$237$	8.38896	+	2.80065i	0.544922	+	0.181922i
$238$	1.87345	−	2.29456i	0.121438	−	0.148734i
$239$	18.7632	−	16.6227i	1.21369	−	1.07523i	0.218644	−	0.975805i	$-0.429837\pi$
$239$	18.7632	−	16.6227i	1.21369	−	1.07523i	0.995045	−	0.0994292i	$-0.0317017\pi$
$240$	−9.75102	−	11.9428i	−0.629426	−	0.770907i
$241$	−13.5248	−	8.55259i	−0.871212	−	0.550921i	0.0224063	−	0.999749i	$-0.492867\pi$
$241$	−13.5248	−	8.55259i	−0.871212	−	0.550921i	−0.893618	+	0.448828i	$0.851842\pi$
$242$	5.78422	−	19.9694i	0.371824	−	1.28368i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−9.05704	+	11.0929i	−0.579818	+	0.710148i
$245$	0.331786	+	8.23317i	0.0211970	+	0.525998i
$246$	−1.17409	+	0.190807i	−0.0748570	+	0.0121654i
$247$	−4.14580	−	3.67286i	−0.263791	−	0.233698i
$248$	0.0527911	−	1.31000i	0.00335224	−	0.0831849i
$249$	−0.250017	−	2.05908i	−0.0158442	−	0.130489i
$250$	3.54372	+	29.1852i	0.224125	+	1.84583i
$251$	−1.08527	−	0.815529i	−0.0685017	−	0.0514757i	0.565940	−	0.824447i	$-0.308513\pi$
$251$	−1.08527	−	0.815529i	−0.0685017	−	0.0514757i	−0.634442	+	0.772971i	$0.718770\pi$
$252$	−2.51680	−	5.30405i	−0.158544	−	0.334124i
$253$	0.568435	−	2.78438i	0.0357372	−	0.175052i
$254$	32.9980	+	14.0591i	2.07048	+	0.882148i
$255$	−1.37678	+	1.21972i	−0.0862175	+	0.0763820i
$256$	−6.02401	+	15.8840i	−0.376500	+	0.992750i
$257$	−12.0825	+	12.5793i	−0.753688	+	0.784673i	−0.981993	−	0.188917i	$-0.939502\pi$
$257$	−12.0825	+	12.5793i	−0.753688	+	0.784673i	0.228305	+	0.973590i	$0.426682\pi$
$258$	−9.75508	−	2.40441i	−0.607325	−	0.149692i
$259$	−11.7787	−	1.91423i	−0.731895	−	0.118945i
$260$	2.25780	−	5.95333i	0.140023	−	0.369210i
$261$	−2.62798	+	0.877349i	−0.162668	+	0.0543065i
$262$	−17.9212	+	11.3327i	−1.10718	+	0.700136i
$263$	−13.5735	+	1.09576i	−0.836976	+	0.0675677i	−0.491519	−	0.870867i	$-0.663558\pi$
$263$	−13.5735	+	1.09576i	−0.836976	+	0.0675677i	−0.345457	+	0.938435i	$0.612276\pi$
$264$	−0.0464237	+	0.0804081i	−0.00285718	+	0.00494878i
$265$	25.5964	−	37.0828i	1.57238	−	2.27798i
$266$	−1.52447	−	37.8294i	−0.0934713	−	2.31947i
$267$	17.0271	+	7.25459i	1.04204	+	0.443973i
$268$	−3.07182	−	8.09973i	−0.187641	−	0.494770i
$269$	9.23653	+	4.84770i	0.563161	+	0.295570i	0.722179	−	0.691706i	$-0.243141\pi$
$269$	9.23653	+	4.84770i	0.563161	+	0.295570i	−0.159018	+	0.987276i	$0.550833\pi$
$270$	2.06250	+	7.12056i	0.125519	+	0.433343i
$271$	−19.8122	+	12.5285i	−1.20351	+	0.761052i	−0.977059	−	0.212971i	$-0.931686\pi$
$271$	−19.8122	+	12.5285i	−1.20351	+	0.761052i	−0.226449	+	0.974023i	$0.572712\pi$
$272$	1.92612	+	0.643032i	0.116788	+	0.0389896i
$273$	−1.51747	+	2.19844i	−0.0918416	+	0.133056i
$274$	−3.68037	−	0.297110i	−0.222339	−	0.0179491i
$275$	5.72167	−	3.00296i	0.345030	−	0.181085i
$276$	−3.27091	+	6.89330i	−0.196886	+	0.414928i
$277$	6.86547	+	5.15906i	0.412506	+	0.309978i	0.786658	−	0.617389i	$-0.211810\pi$
$277$	6.86547	+	5.15906i	0.412506	+	0.309978i	−0.374152	+	0.927367i	$0.622066\pi$
$278$	−1.65738	+	41.1274i	−0.0994030	+	2.46666i
$279$	−4.36280	+	9.19441i	−0.261194	+	0.550455i
$280$	−1.34377	+	0.572525i	−0.0803054	+	0.0342149i
$281$	−5.50104	−	26.9459i	−0.328165	−	1.60746i	−0.724449	−	0.689328i	$-0.757906\pi$
$281$	−5.50104	−	26.9459i	−0.328165	−	1.60746i	0.396284	−	0.918128i	$-0.370299\pi$
$282$	−0.681846	−	1.79788i	−0.0406033	−	0.107062i
$283$	8.08242	+	9.89916i	0.480450	+	0.588444i	0.956777	−	0.290824i	$-0.0939295\pi$
$283$	8.08242	+	9.89916i	0.480450	+	0.588444i	−0.476327	+	0.879268i	$0.658032\pi$
$284$	−0.426602	−	0.0693296i	−0.0253142	−	0.00411396i
$285$	−2.83367	+	23.3374i	−0.167852	+	1.38239i
$286$	−1.25880			−0.0744342
$287$	−0.219287	+	1.80599i	−0.0129441	+	0.106604i
$288$	5.49083	−	5.71656i	0.323550	−	0.336851i
$289$	−4.66230	+	16.0961i	−0.274253	+	0.946831i
$290$	−5.71427	−	19.7280i	−0.335554	−	1.15847i
$291$	−2.62513	−	3.80315i	−0.153888	−	0.222945i
$292$	−3.02552	−	5.24035i	−0.177055	−	0.306668i
$293$	2.83219	+	0.228638i	0.165458	+	0.0133572i	0.162918	−	0.986640i	$-0.447909\pi$
$293$	2.83219	+	0.228638i	0.165458	+	0.0133572i	0.00254009	+	0.999997i	$0.499191\pi$
$294$	−4.31719	+	0.701612i	−0.251784	+	0.0409189i
$295$	−9.85361	+	48.2662i	−0.573699	+	2.81017i
$296$	−0.101354	−	0.496463i	−0.00589106	−	0.0288563i
$297$	0.576174	−	0.432967i	0.0334330	−	0.0251233i
$298$	−24.4455	−	35.4154i	−1.41609	−	2.05156i
$299$	3.46044	−	0.279356i	0.200123	−	0.0161556i
$300$	−16.8452	+	4.15197i	−0.972559	+	0.239714i
$301$	−7.68319	+	13.3077i	−0.442852	+	0.767042i
$302$	16.4782	+	28.5411i	0.948214	+	1.64236i
$303$	−1.46817	−	1.52852i	−0.0843440	−	0.0878114i
$304$	23.8764	−	10.1728i	1.36941	−	0.583449i
$305$	−11.8563	−	24.9866i	−0.678888	−	1.43073i
$306$	−0.730816	−	0.647447i	−0.0417780	−	0.0370121i
$307$	10.9291	−	5.73603i	0.623756	−	0.327372i	−0.123064	−	0.992399i	$-0.539272\pi$
$307$	10.9291	−	5.73603i	0.623756	−	0.327372i	0.746820	+	0.665026i	$0.231580\pi$
$308$	−2.93109	−	3.05159i	−0.167015	−	0.173881i
$309$	−7.29422	+	5.48125i	−0.414954	+	0.311817i
$310$	−66.8028	−	35.0608i	−3.79415	−	1.99132i
$311$	−13.8827	−	8.77889i	−0.787216	−	0.497805i	0.0793627	−	0.996846i	$-0.474711\pi$
$311$	−13.8827	−	8.77889i	−0.787216	−	0.497805i	−0.866579	+	0.499041i	$0.833686\pi$
$312$	−0.110131	−	0.0271449i	−0.00623495	−	0.00153678i
$313$	−29.3186			−1.65719			−0.828593	−	0.559852i	$-0.810858\pi$
$313$	−29.3186			−1.65719			−0.828593	+	0.559852i	$0.810858\pi$
$314$	−18.0717	+	17.0651i	−1.01985	+	0.963038i
$315$	11.3382			0.638833
$316$	−16.6166	−	4.09562i	−0.934755	−	0.230396i
$317$	14.4662	+	9.14789i	0.812505	+	0.513797i	0.874928	−	0.484253i	$-0.160909\pi$
$317$	14.4662	+	9.14789i	0.812505	+	0.513797i	−0.0624233	+	0.998050i	$0.519883\pi$
$318$	21.1783	+	11.1152i	1.18762	+	0.623311i
$319$	−1.59633	+	1.19956i	−0.0893771	+	0.0671625i
$320$	19.3441	+	20.1393i	1.08137	+	1.12582i
$321$	5.83490	−	3.06239i	0.325673	−	0.170926i
$322$	17.7628	+	15.7365i	0.989882	+	0.876959i
$323$	−1.32732	−	2.79728i	−0.0738543	−	0.155645i
$324$	−1.78021	+	0.758478i	−0.0989007	+	0.0421377i
$325$	5.46844	+	5.69325i	0.303335	+	0.315805i
$326$	8.84480	+	15.3197i	0.489868	+	0.848477i
$327$	7.61420	−	13.1882i	0.421066	−	0.729308i
$328$	−0.0750035	+	0.0184867i	−0.00414137	+	0.00102076i
$329$	−2.93133	+	0.236641i	−0.161609	+	0.0130465i
$330$	3.03510	+	4.39710i	0.167077	+	0.242052i
$331$	9.61393	−	7.22440i	0.528429	−	0.397089i	−0.302770	−	0.953064i	$-0.597911\pi$
$331$	9.61393	−	7.22440i	0.528429	−	0.397089i	0.831199	+	0.555975i	$0.187655\pi$
$332$	0.802842	+	3.93258i	0.0440617	+	0.215828i
$333$	−0.786749	+	3.85375i	−0.0431136	+	0.211184i
$334$	2.28096	−	0.370692i	0.124808	−	0.0202834i
$335$	16.6755	+	1.34619i	0.911082	+	0.0735502i
$336$	−6.25855	−	10.8401i	−0.341432	−	0.591377i
$337$	11.2770	+	16.3376i	0.614300	+	0.889967i	0.999459	−	0.0328834i	$-0.0104690\pi$
$337$	11.2770	+	16.3376i	0.614300	+	0.889967i	−0.385160	+	0.922850i	$0.625854\pi$
$338$	6.74685	+	23.2928i	0.366980	+	1.26696i
$339$	0.184733	−	0.637771i	0.0100333	−	0.0346389i
$340$	2.46560	−	2.56696i	0.133716	−	0.139213i
$341$	−0.884107	+	7.28128i	−0.0478771	+	0.394303i
$342$	−12.4788			−0.674775
$343$	1.75359	−	14.4421i	0.0946848	−	0.779799i
$344$	−0.644028	−	0.104665i	−0.0347237	−	0.00564314i
$345$	−9.31933	−	11.4141i	−0.501736	−	0.614515i
$346$	11.7550	+	30.9954i	0.631953	+	1.66632i
$347$	−1.44456	−	7.07592i	−0.0775480	−	0.379855i	0.922432	−	0.386159i	$-0.126199\pi$
$347$	−1.44456	−	7.07592i	−0.0775480	−	0.379855i	−0.999980	+	0.00630395i	$0.997993\pi$
$348$	4.93219	−	2.10141i	0.264393	−	0.112647i
$349$	−7.02037	+	14.7951i	−0.375792	+	0.791964i	0.624151	+	0.781303i	$0.285445\pi$
$349$	−7.02037	+	14.7951i	−0.375792	+	0.791964i	−0.999943	+	0.0106610i	$0.996606\pi$
$350$	−2.17276	+	53.9165i	−0.116139	+	2.88196i
$351$	0.703884	+	0.528934i	0.0375705	+	0.0282324i
$352$	2.44900	−	5.16117i	0.130532	−	0.275091i
$353$	6.98710	−	3.66711i	0.371886	−	0.195181i	−0.268418	−	0.963303i	$-0.586501\pi$
$353$	6.98710	−	3.66711i	0.371886	−	0.195181i	0.640304	+	0.768122i	$0.278808\pi$
$354$	−26.0640	−	2.10411i	−1.38529	−	0.111832i
$355$	0.474156	−	0.686933i	0.0251656	−	0.0364586i
$356$	−33.9712	−	11.3413i	−1.80047	−	0.601086i
$357$	−1.26211	+	0.798112i	−0.0667981	+	0.0422406i
$358$	10.8664	+	37.5152i	0.574308	+	1.98274i
$359$	14.3669	+	7.54031i	0.758254	+	0.397962i	0.799096	−	0.601203i	$-0.205312\pi$
$359$	14.3669	+	7.54031i	0.758254	+	0.397962i	−0.0408421	+	0.999166i	$0.513004\pi$
$360$	0.170719	+	0.450148i	0.00899766	+	0.0237249i
$361$	−18.9263	−	8.06372i	−0.996119	−	0.424406i
$362$	−0.355532	−	8.82244i	−0.0186864	−	0.463697i
$363$	−5.95364	+	8.62533i	−0.312485	+	0.452713i
$364$	2.58456	−	4.47659i	0.135468	−	0.234637i
$365$	11.6482	−	0.940339i	0.609694	−	0.0492196i
$366$	12.4079	−	7.84630i	0.648573	−	0.410133i
$367$	−22.7827	+	7.60599i	−1.18925	+	0.397029i	−0.841344	−	0.540501i	$-0.818235\pi$
$367$	−22.7827	+	7.60599i	−1.18925	+	0.397029i	−0.347904	+	0.937530i	$0.613107\pi$
$368$	−5.76856	+	15.2104i	−0.300707	+	0.792899i
$369$	0.591867	+	0.0961878i	0.0308114	+	0.00500734i
$370$	−28.3108	−	6.97798i	−1.47181	−	0.362768i
$371$	25.3407	−	26.3824i	1.31562	−	1.36971i
$372$	6.98326	−	18.4133i	0.362065	−	0.954687i
$373$	11.6553	−	10.3257i	0.603490	−	0.534646i	−0.305108	−	0.952318i	$-0.598692\pi$
$373$	11.6553	−	10.3257i	0.603490	−	0.534646i	0.908598	+	0.417672i	$0.137154\pi$
$374$	−0.647373	−	0.275820i	−0.0334748	−	0.0142623i
$375$	2.96449	−	14.5211i	0.153086	−	0.749864i
$376$	−0.0535322	−	0.112817i	−0.00276071	−	0.00581808i
$377$	−1.95015	−	1.46545i	−0.100438	−	0.0754743i
$378$	0.725444	+	5.97457i	0.0373128	+	0.307299i
$379$	3.54285	+	29.1780i	0.181984	+	1.49877i	0.742060	+	0.670333i	$0.233849\pi$
$379$	3.54285	+	29.1780i	0.181984	+	1.49877i	−0.560076	+	0.828441i	$0.689228\pi$
$380$	1.83173	−	45.4539i	0.0939658	−	2.33174i
$381$	−13.5342	−	11.9902i	−0.693376	−	0.614278i
$382$	−44.5217	+	7.23548i	−2.27793	+	0.370199i
$383$	0.520140	+	12.9072i	0.0265779	+	0.659525i	0.956494	+	0.291752i	$0.0942384\pi$
$383$	0.520140	+	12.9072i	0.0265779	+	0.659525i	−0.929916	+	0.367772i	$0.880121\pi$
$384$	0.651459	−	0.797893i	0.0332446	−	0.0407173i
$385$	7.75109	−	2.58769i	0.395032	−	0.131881i
$386$	9.28257	−	32.0472i	0.472470	−	1.63116i
$387$	4.28072	+	2.70696i	0.217601	+	0.137603i
$388$	5.65548	+	6.92671i	0.287114	+	0.351650i
$389$	−12.1305	+	10.7467i	−0.615040	+	0.544878i	−0.912093	−	0.409983i	$-0.865535\pi$
$389$	−12.1305	+	10.7467i	−0.615040	+	0.544878i	0.297053	+	0.954861i	$0.403996\pi$
$390$	−4.12805	+	5.05595i	−0.209032	+	0.256018i
$391$	1.84084	+	0.614564i	0.0930955	+	0.0310798i
$392$	−0.275793	+	0.0679768i	−0.0139296	+	0.00343335i
$393$	10.3784	−	2.55805i	0.523521	−	0.129036i
$394$	−0.311755	−	0.104079i	−0.0157060	−	0.00524343i
$395$	20.9031	−	25.6016i	1.05175	−	1.28816i
$396$	−1.04390	+	0.924813i	−0.0524579	+	0.0464736i
$397$	−8.06066	−	9.87252i	−0.404553	−	0.495488i	0.531642	−	0.846969i	$-0.321575\pi$
$397$	−8.06066	−	9.87252i	−0.404553	−	0.495488i	−0.936195	+	0.351482i	$0.885678\pi$
$398$	15.4372	+	9.76191i	0.773798	+	0.489320i
$399$	−5.30995	+	18.3321i	−0.265830	+	0.917751i
$400$	−35.0863	+	11.7135i	−1.75432	+	0.585677i
$401$	12.4666	−	15.2688i	0.622551	−	0.762486i	−0.363014	−	0.931784i	$-0.618252\pi$
$401$	12.4666	−	15.2688i	0.622551	−	0.762486i	0.985565	+	0.169297i	$0.0541499\pi$
$402$	0.357578	+	8.87321i	0.0178344	+	0.442556i
$403$	−8.84448	+	1.43737i	−0.440575	+	0.0716004i
$404$	3.06978	+	2.71958i	0.152727	+	0.135304i
$405$	0.150477	−	3.73405i	0.00747728	−	0.185547i
$406$	−2.00989	−	16.5529i	−0.0997491	−	0.821508i
$407$	0.341693	+	2.81409i	0.0169371	+	0.139489i
$408$	−0.0506903	−	0.0380913i	−0.00250954	−	0.00188580i
$409$	−12.0718	−	25.4408i	−0.596914	−	1.25797i	−0.946995	−	0.321249i	$-0.895897\pi$
$409$	−12.0718	−	25.4408i	−0.596914	−	1.25797i	0.350081	−	0.936719i	$-0.386154\pi$
$410$	−0.889159	+	4.35539i	−0.0439124	+	0.215097i
$411$	1.71240	+	0.729583i	0.0844662	+	0.0359877i
$412$	13.2155	−	11.7079i	0.651080	−	0.576807i
$413$	−14.1818	+	37.3943i	−0.697839	+	1.84005i
$414$	5.41832	−	5.64107i	0.266296	−	0.277243i
$415$	−7.52622	−	1.85505i	−0.369447	−	0.0910606i
$416$	6.88859	+	1.11950i	0.337741	+	0.0548882i
$417$	7.35789	−	19.4012i	0.360317	−	0.950079i
$418$	−8.53085	+	2.84802i	−0.417258	+	0.139301i
$419$	−19.8381	+	12.5449i	−0.969155	+	0.612857i	−0.922476	−	0.386053i	$-0.873838\pi$
$419$	−19.8381	+	12.5449i	−0.969155	+	0.612857i	−0.0466787	+	0.998910i	$0.514864\pi$
$420$	−21.8688	+	1.76543i	−1.06709	+	0.0861444i
$421$	7.32724	−	12.6912i	0.357108	−	0.618529i	−0.630368	−	0.776296i	$-0.717096\pi$
$421$	7.32724	−	12.6912i	0.357108	−	0.618529i	0.987476	+	0.157767i	$0.0504295\pi$
$422$	31.9369	−	46.2686i	1.55466	−	2.25232i
$423$	0.0390305	+	0.968531i	0.00189773	+	0.0470916i
$424$	1.42899	+	0.608836i	0.0693979	+	0.0295677i
$425$	1.56484	+	4.12613i	0.0759057	+	0.200147i
$426$	0.392313	+	0.205902i	0.0190076	+	0.00997597i
$427$	−6.24688	−	21.5667i	−0.302308	−	1.04369i
$428$	−10.7774	+	6.81523i	−0.520947	+	0.329427i
$429$	0.601913	+	0.200948i	0.0290606	+	0.00970187i
$430$	−21.3289	+	30.9003i	−1.02857	+	1.49014i
$431$	23.7145	+	1.91443i	1.14229	+	0.0922148i	0.637089	−	0.770790i	$-0.280138\pi$
$431$	23.7145	+	1.91443i	1.14229	+	0.0922148i	0.505196	+	0.863005i	$0.331420\pi$
$432$	−3.65310	+	1.91729i	−0.175760	+	0.0922458i
$433$	−3.30784	+	6.97113i	−0.158965	+	0.335011i	−0.967269	−	0.253754i	$-0.918335\pi$
$433$	−3.30784	+	6.97113i	−0.158965	+	0.335011i	0.808304	+	0.588766i	$0.200386\pi$
$434$	−48.9657	−	36.7953i	−2.35043	−	1.76623i
$435$	−0.416907	+	10.3454i	−0.0199891	+	0.496026i
$436$	−12.6326	+	26.6227i	−0.604994	+	1.27500i
$437$	22.8194	−	9.72242i	1.09160	−	0.465086i
$438$	1.24079	+	6.07777i	0.0592871	+	0.290407i
$439$	4.90286	+	12.9278i	0.234001	+	0.617010i	0.999656	−	0.0262421i	$-0.00835406\pi$
$439$	4.90286	+	12.9278i	0.234001	+	0.617010i	−0.765655	+	0.643252i	$0.777585\pi$
$440$	0.219445	+	0.268771i	0.0104616	+	0.0128132i
$441$	2.17634	+	0.353689i	0.103635	+	0.0168423i
$442$	0.103620	−	0.853386i	0.00492869	−	0.0405914i
$443$	15.1751			0.720993			0.360496	−	0.932761i	$-0.382607\pi$
$443$	15.1751			0.720993			0.360496	+	0.932761i	$0.382607\pi$
$444$	0.917410	−	7.55555i	0.0435383	−	0.358570i
$445$	47.9134	−	49.8831i	2.27131	−	2.36469i
$446$	10.2809	−	35.4937i	0.486814	−	1.68068i
$447$	6.03546	+	20.8368i	0.285467	+	0.985548i
$448$	12.8784	+	18.6576i	0.608447	+	0.881487i
$449$	0.843326	+	1.46068i	0.0397990	+	0.0689340i	0.885239	−	0.465137i	$-0.153995\pi$
$449$	0.843326	+	1.46068i	0.0397990	+	0.0689340i	−0.845440	+	0.534071i	$0.820662\pi$
$450$	17.7278	+	1.43113i	0.835696	+	0.0674643i
$451$	0.426570	−	0.0693244i	0.0200864	−	0.00326436i
$452$	−0.257003	+	1.25889i	−0.0120884	+	0.0592130i
$453$	−3.32315	−	16.2779i	−0.156135	−	0.764801i
$454$	43.5153	−	32.6996i	2.04228	−	1.53467i
$455$	5.67092	+	8.21575i	0.265857	+	0.385160i
$456$	−0.807773	+	0.0652102i	−0.0378274	+	0.00305375i
$457$	14.0467	−	3.46219i	0.657075	−	0.161954i	0.103338	−	0.994646i	$-0.467048\pi$
$457$	14.0467	−	3.46219i	0.657075	−	0.161954i	0.553737	+	0.832692i	$0.313201\pi$
$458$	13.8276	−	23.9502i	0.646123	−	1.11912i
$459$	0.246096	+	0.426251i	0.0114868	+	0.0198957i
$460$	19.7522	+	20.5642i	0.920952	+	0.958813i
$461$	−7.14890	+	3.04586i	−0.332958	+	0.141860i	−0.551974	−	0.833861i	$-0.686125\pi$
$461$	−7.14890	+	3.04586i	−0.332958	+	0.141860i	0.219017	+	0.975721i	$0.429715\pi$
$462$	1.85950	+	3.91882i	0.0865119	+	0.182320i
$463$	9.83028	+	8.70887i	0.456852	+	0.404735i	0.859915	−	0.510437i	$-0.170516\pi$
$463$	9.83028	+	8.70887i	0.456852	+	0.404735i	−0.403064	+	0.915172i	$0.632055\pi$
$464$	10.1211	−	5.31198i	0.469862	−	0.246603i
$465$	26.3459	+	27.4290i	1.22176	+	1.27199i
$466$	32.9843	−	24.7861i	1.52797	−	1.14819i
$467$	23.8403	+	12.5123i	1.10320	+	0.579002i	0.915132	−	0.403154i	$-0.132086\pi$
$467$	23.8403	+	12.5123i	1.10320	+	0.579002i	0.188065	+	0.982157i	$0.439779\pi$
$468$	−1.44000	−	0.910600i	−0.0665639	−	0.0420925i
$469$	13.1874	+	3.25041i	0.608939	+	0.150090i
$470$	−7.18579			−0.331456
$471$	11.3655	−	5.27506i	0.523693	−	0.243062i
$472$	−1.69816			−0.0781643
$473$	3.54423	+	0.873574i	0.162964	+	0.0401670i
$474$	14.8281	+	9.37670i	0.681075	+	0.430686i
$475$	49.9405	+	26.2108i	2.29143	+	1.20263i
$476$	2.31007	−	1.73590i	0.105882	−	0.0795651i
$477$	−8.35235	−	8.69572i	−0.382428	−	0.398150i
$478$	44.0302	−	23.1088i	2.01389	−	1.05697i
$479$	25.9153	+	22.9589i	1.18410	+	1.04902i	0.997784	+	0.0665296i	$0.0211927\pi$
$479$	25.9153	+	22.9589i	1.18410	+	1.04902i	0.186314	+	0.982490i	$0.440346\pi$
$480$	−12.6986	−	26.7618i	−0.579610	−	1.22150i
$481$	−3.18597	+	1.35742i	−0.145268	+	0.0618928i
$482$	−21.9894	−	22.8934i	−1.00159	−	1.04277i
$483$	−5.98147	−	10.3602i	−0.272166	−	0.471406i
$484$	10.1402	−	17.5634i	0.460920	−	0.798337i
$485$	−16.7679	+	4.13292i	−0.761392	+	0.187666i
$486$	1.97727	−	0.159621i	0.0896906	−	0.00724057i
$487$	3.26398	+	4.72870i	0.147905	+	0.214278i	0.889933	−	0.456092i	$-0.150751\pi$
$487$	3.26398	+	4.72870i	0.147905	+	0.214278i	−0.742028	+	0.670369i	$0.766136\pi$
$488$	0.762184	−	0.572744i	0.0345024	−	0.0259269i
$489$	−1.78373	−	8.73727i	−0.0806629	−	0.395113i
$490$	−3.26950	+	16.0151i	−0.147701	+	0.723487i
$491$	9.60122	−	1.56035i	0.433297	−	0.0704176i	0.0601490	−	0.998189i	$-0.480842\pi$
$491$	9.60122	−	1.56035i	0.433297	−	0.0704176i	0.373148	+	0.927772i	$0.378278\pi$
$492$	−1.15656	−	0.0933672i	−0.0521418	−	0.00420932i
$493$	−0.681824	−	1.18095i	−0.0307078	−	0.0531875i
$494$	−6.24142	−	9.04226i	−0.280815	−	0.406831i
$495$	−0.749348	−	2.58705i	−0.0336807	−	0.116279i
$496$	11.6815	−	40.3292i	0.524514	−	1.81083i
$497$	0.469418	−	0.488716i	0.0210563	−	0.0219219i
$498$	0.495958	−	4.08458i	0.0222244	−	0.183035i
$499$	20.3382			0.910463			0.455231	−	0.890373i	$-0.349557\pi$
$499$	20.3382			0.910463			0.455231	+	0.890373i	$0.349557\pi$
$500$	−3.45683	+	28.4695i	−0.154594	+	1.27320i
$501$	−1.14985	−	0.186869i	−0.0513716	−	0.00834870i
$502$	−1.70314	−	2.08596i	−0.0760147	−	0.0931011i
$503$	0.202076	+	0.532830i	0.00901012	+	0.0237577i	0.939446	−	0.342697i	$-0.111341\pi$
$503$	0.202076	+	0.532830i	0.00901012	+	0.0237577i	−0.930436	+	0.366455i	$0.880571\pi$
$504$	0.0781805	+	0.382953i	0.00348243	+	0.0170581i
$505$	−7.28662	+	3.10454i	−0.324250	+	0.138150i
$506$	2.41666	−	5.09301i	0.107434	−	0.226412i
$507$	0.492242	−	12.2149i	0.0218612	−	0.542481i
$508$	27.9714	+	21.0192i	1.24103	+	0.932575i
$509$	6.30361	−	13.2846i	0.279403	−	0.588829i	−0.714432	−	0.699705i	$-0.753315\pi$
$509$	6.30361	−	13.2846i	0.279403	−	0.588829i	0.993834	+	0.110877i	$0.0353659\pi$
$510$	−3.23080	+	1.69565i	−0.143062	+	0.0750849i
$511$	9.45659	+	0.763415i	0.418335	+	0.0337715i
$512$	−17.9729	+	26.0382i	−0.794297	+	1.15074i
$513$	5.96693	+	1.99205i	0.263446	+	0.0879513i
$514$	−29.2434	+	18.4924i	−1.28987	+	0.815665i
$515$	9.48656	+	32.7514i	0.418028	+	1.44320i
$516$	−8.67807	−	4.55460i	−0.382031	−	0.200505i
$517$	0.247729	+	0.653208i	0.0108951	+	0.0287280i
$518$	−21.7778	−	9.27863i	−0.956860	−	0.407680i
$519$	−0.672885	−	16.6975i	−0.0295364	−	0.732937i
$520$	−0.240795	+	0.348852i	−0.0105596	+	0.0152982i
$521$	−1.67704	+	2.90471i	−0.0734724	+	0.127258i	−0.900421	−	0.435020i	$-0.856741\pi$
$521$	−1.67704	+	2.90471i	−0.0734724	+	0.127258i	0.826949	+	0.562278i	$0.190075\pi$
$522$	−5.47814	+	0.442241i	−0.239772	+	0.0193564i
$523$	14.5955	−	9.22964i	0.638217	−	0.403584i	−0.175799	−	0.984426i	$-0.556251\pi$
$523$	14.5955	−	9.22964i	0.638217	−	0.403584i	0.814016	+	0.580842i	$0.197277\pi$
$524$	−19.6194	+	6.54991i	−0.857077	+	0.286134i
$525$	9.64591	−	25.4342i	0.420982	−	1.11004i
$526$	−26.6634	−	4.33323i	−1.16258	−	0.188938i
$527$	−4.86348	−	1.19874i	−0.211856	−	0.0522179i
$528$	−2.05978	+	2.14446i	−0.0896404	+	0.0933256i
$529$	2.64274	−	6.96832i	0.114902	−	0.302970i
$530$	66.9044	−	59.2722i	2.90614	−	2.57462i
$531$	12.1270	+	5.16685i	0.526268	+	0.224222i
$532$	7.38730	−	36.1854i	0.320280	−	1.56883i
$533$	0.226331	+	0.476983i	0.00980349	+	0.0206604i
$534$	29.3512	+	22.0560i	1.27015	+	0.954458i
$535$	−2.96838	−	24.4468i	−0.128334	−	1.05693i
$536$	0.0695152	+	0.572509i	0.00300260	+	0.0247286i
$537$	0.792801	−	19.6732i	0.0342119	−	0.848959i
$538$	15.4887	+	13.7218i	0.667766	+	0.591589i
$539$	1.56853	−	0.254911i	0.0675613	−	0.0109798i
$540$	0.291182	+	7.22561i	0.0125305	+	0.310941i
$541$	−16.6819	+	20.4316i	−0.717212	+	0.878425i	−0.996654	−	0.0817376i	$-0.973953\pi$
$541$	−16.6819	+	20.4316i	−0.717212	+	0.878425i	0.279442	+	0.960163i	$0.409851\pi$
$542$	−44.1071	+	14.7251i	−1.89456	+	0.632498i
$543$	−1.23837	+	4.27535i	−0.0531435	+	0.183473i
$544$	3.29736	+	2.08512i	0.141373	+	0.0893989i
$545$	−35.9924	−	44.0826i	−1.54174	−	1.88829i
$546$	−3.96640	+	3.51392i	−0.169746	+	0.150382i
$547$	−8.76098	+	10.7303i	−0.374592	+	0.458792i	−0.927154	−	0.374679i	$-0.877753\pi$
$547$	−8.76098	+	10.7303i	−0.374592	+	0.458792i	0.552562	+	0.833472i	$0.313650\pi$
$548$	−3.41644	−	1.14058i	−0.145943	−	0.0487230i
$549$	−7.18559	+	1.77109i	−0.306674	+	0.0755882i
$550$	12.4458	−	3.06763i	0.530693	−	0.130804i
$551$	−16.5317	−	5.51911i	−0.704276	−	0.235122i
$552$	0.321259	−	0.393470i	0.0136737	−	0.0167472i
$553$	20.0845	−	17.7933i	0.854081	−	0.756650i
$554$	10.7741	+	13.1959i	0.457748	+	0.560639i
$555$	12.4233	+	7.85603i	0.527340	+	0.333470i
$556$	−11.1709	+	38.5663i	−0.473750	+	1.63558i
$557$	−22.6586	+	7.56456i	−0.960077	+	0.320521i	−0.753160	−	0.657838i	$-0.771471\pi$
$557$	−22.6586	+	7.56456i	−0.960077	+	0.320521i	−0.206917	+	0.978358i	$0.566343\pi$
$558$	−12.7679	+	15.6378i	−0.540506	+	0.662000i
$559$	0.179562	+	4.45578i	0.00759465	+	0.188459i
$560$	−46.1717	+	7.50363i	−1.95111	+	0.317086i
$561$	0.265521	+	0.235231i	0.0112103	+	0.00993146i
$562$	2.19671	−	54.5108i	0.0926626	−	2.29940i
$563$	−4.58794	−	37.7851i	−0.193358	−	1.59245i	−0.689550	−	0.724238i	$-0.742192\pi$
$563$	−4.58794	−	37.7851i	−0.193358	−	1.59245i	0.496192	−	0.868213i	$-0.334731\pi$
$564$	−0.226089	−	1.86201i	−0.00952006	−	0.0784047i
$565$	−1.98372	−	1.49067i	−0.0834555	−	0.0627128i
$566$	10.8678	+	22.9033i	0.456806	+	0.962698i
$567$	0.606869	−	2.97264i	0.0254861	−	0.124839i
$568$	0.0264711	+	0.0112783i	0.00111070	+	0.000473226i
$569$	14.3128	−	12.6800i	0.600022	−	0.531573i	−0.307516	−	0.951543i	$-0.599498\pi$
$569$	14.3128	−	12.6800i	0.600022	−	0.531573i	0.907538	+	0.419970i	$0.137959\pi$
$570$	−16.5367	+	43.6038i	−0.692648	+	1.82636i
$571$	−9.20838	+	9.58694i	−0.385359	+	0.401201i	−0.885422	−	0.464788i	$-0.846131\pi$
$571$	−9.20838	+	9.58694i	−0.385359	+	0.401201i	0.500063	+	0.865989i	$0.333310\pi$
$572$	−1.19225	−	0.293863i	−0.0498504	−	0.0122870i
$573$	22.4438	+	3.64747i	0.937603	+	0.152375i
$574$	−1.27972	+	3.37434i	−0.0534144	+	0.140842i
$575$	−33.5330	+	11.1950i	−1.39842	+	0.466862i
$576$	6.31551	−	3.99369i	0.263146	−	0.166404i
$577$	−42.6149	+	3.44023i	−1.77408	+	0.143219i	−0.923743	−	0.383014i	$-0.874886\pi$
$577$	−42.6149	+	3.44023i	−1.77408	+	0.143219i	−0.850341	+	0.526232i	$0.823604\pi$
$578$	−16.6212	+	28.7887i	−0.691349	+	1.19745i
$579$	−9.55446	+	13.8420i	−0.397070	+	0.575255i
$580$	−0.806739	−	20.0190i	−0.0334980	−	0.831244i
$581$	−5.78946	−	2.46666i	−0.240187	−	0.102334i
$582$	−3.25067	−	8.57131i	−0.134745	−	0.355292i
$583$	−7.69452	−	4.03840i	−0.318674	−	0.167253i
$584$	0.112079	+	0.386941i	0.00463785	+	0.0160117i
$585$	2.78100	−	1.75860i	0.114980	−	0.0727091i
$586$	5.34640	+	1.78489i	0.220858	+	0.0737332i
$587$	−5.56558	+	8.06313i	−0.229716	+	0.332801i	−0.920844	−	0.389931i	$-0.872499\pi$
$587$	−5.56558	+	8.06313i	−0.229716	+	0.332801i	0.691128	+	0.722732i	$0.257114\pi$
$588$	−4.25275	−	0.343318i	−0.175381	−	0.0141582i
$589$	−56.6869	+	29.7516i	−2.33574	+	1.22589i
$590$	−41.8920	+	88.2855i	−1.72467	+	3.63466i
$591$	0.132456	+	0.0995340i	0.00544850	+	0.00409428i
$592$	0.653405	−	16.2141i	0.0268548	−	0.666394i
$593$	−15.4047	+	32.4648i	−0.632597	+	1.33317i	0.293528	+	0.955951i	$0.405171\pi$
$593$	−15.4047	+	32.4648i	−0.632597	+	1.33317i	−0.926124	+	0.377219i	$0.876881\pi$
$594$	1.31529	−	0.560391i	0.0539668	−	0.0229931i
$595$	1.11625	+	5.46777i	0.0457619	+	0.224157i
$596$	−14.8855	−	39.2499i	−0.609735	−	1.60774i
$597$	−5.82321	−	7.13213i	−0.238328	−	0.291899i
$598$	6.79762	+	1.10472i	0.277975	+	0.0451754i
$599$	0.804223	−	6.62337i	0.0328596	−	0.270624i	−0.967014	−	0.254723i	$-0.918016\pi$
$599$	0.804223	−	6.62337i	0.0328596	−	0.270624i	0.999874	−	0.0159001i	$-0.00506137\pi$
$600$	1.15503			0.0471538
$601$	−0.856301	+	7.05227i	−0.0349293	+	0.287668i	0.964769	+	0.263099i	$0.0847445\pi$
$601$	−0.856301	+	7.05227i	−0.0349293	+	0.287668i	−0.999698	+	0.0245694i	$0.992179\pi$
$602$	−21.1158	+	21.9839i	−0.860616	+	0.895996i
$603$	1.24549	−	4.29995i	0.0507205	−	0.175107i
$604$	8.94423	+	30.8791i	0.363935	+	1.25645i
$605$	22.2493	+	32.2336i	0.904561	+	1.31048i
$606$	−2.10213	−	3.64100i	−0.0853934	−	0.147906i
$607$	−42.0515	−	3.39475i	−1.70682	−	0.137789i	−0.811834	−	0.583888i	$-0.801531\pi$
$607$	−42.0515	−	3.39475i	−1.70682	−	0.137789i	−0.894983	+	0.446100i	$0.852813\pi$
$608$	49.2168	−	7.99851i	1.99600	−	0.324382i
$609$	−1.68137	+	8.23589i	−0.0681325	+	0.333735i
$610$	−10.9740	−	53.7540i	−0.444323	−	2.17644i
$611$	−0.682287	+	0.512705i	−0.0276024	+	0.0207418i
$612$	−0.541036	−	0.783826i	−0.0218701	−	0.0316843i
$613$	35.3532	−	2.85401i	1.42790	−	0.115272i	0.657801	−	0.753192i	$-0.271487\pi$
$613$	35.3532	−	2.85401i	1.42790	−	0.115272i	0.770103	+	0.637920i	$0.220205\pi$
$614$	23.7731	−	5.85954i	0.959404	−	0.236472i
$615$	1.12044	−	1.94066i	0.0451804	−	0.0782548i
$616$	0.140847	+	0.243955i	0.00567490	+	0.00982922i
$617$	7.22377	+	7.52075i	0.290818	+	0.302774i	0.850544	−	0.525904i	$-0.176273\pi$
$617$	7.22377	+	7.52075i	0.290818	+	0.302774i	−0.559726	+	0.828678i	$0.689093\pi$
$618$	−16.6512	+	7.09440i	−0.669809	+	0.285379i
$619$	−6.39373	−	13.4745i	−0.256986	−	0.541586i	0.733420	−	0.679776i	$-0.237923\pi$
$619$	−6.39373	−	13.4745i	−0.256986	−	0.541586i	−0.990406	+	0.138190i	$0.955872\pi$
$620$	−55.0864	−	48.8023i	−2.21232	−	1.95995i
$621$	−3.49137	+	1.83241i	−0.140104	+	0.0735321i
$622$	−22.5713	−	23.4992i	−0.905025	−	0.942231i
$623$	44.8911	−	33.7335i	1.79852	−	1.35150i
$624$	−3.21644	−	1.68812i	−0.128760	−	0.0675787i
$625$	−8.92240	−	5.64218i	−0.356896	−	0.225687i
$626$	−56.4692	−	13.9184i	−2.25696	−	0.556292i
$627$	4.53380			0.181063
$628$	−21.1001	+	11.9441i	−0.841988	+	0.476623i
$629$	−1.93591			−0.0771897
$630$	21.8379	+	5.38256i	0.870043	+	0.214446i
$631$	17.6243	+	11.1450i	0.701614	+	0.443674i	0.837060	−	0.547111i	$-0.184272\pi$
$631$	17.6243	+	11.1450i	0.701614	+	0.443674i	−0.135446	+	0.990785i	$0.543247\pi$
$632$	1.00885	+	0.529483i	0.0401297	+	0.0210617i
$633$	−22.6572	+	17.0258i	−0.900544	+	0.676715i
$634$	23.5200	+	24.4869i	0.934098	+	0.972499i
$635$	−59.8320	+	31.4023i	−2.37436	+	1.24616i
$636$	17.4639	+	15.4716i	0.692487	+	0.613490i
$637$	0.832235	+	1.75390i	0.0329744	+	0.0694920i
$638$	−3.64408	+	1.55260i	−0.144271	+	0.0614679i
$639$	−0.154721	−	0.161082i	−0.00612069	−	0.00637231i
$640$	−1.92472	−	3.33371i	−0.0760812	−	0.131776i
$641$	16.5611	−	28.6847i	0.654124	−	1.13298i	−0.327988	−	0.944682i	$-0.606371\pi$
$641$	16.5611	−	28.6847i	0.654124	−	1.13298i	0.982113	−	0.188295i	$-0.0602960\pi$
$642$	12.6922	−	3.12834i	0.500920	−	0.123466i
$643$	13.6791	−	1.10429i	0.539450	−	0.0435489i	0.192260	−	0.981344i	$-0.438418\pi$
$643$	13.6791	−	1.10429i	0.539450	−	0.0435489i	0.347189	+	0.937795i	$0.387136\pi$
$644$	13.1501	+	19.0512i	0.518187	+	0.750724i
$645$	15.1315	−	11.3706i	0.595803	−	0.447717i
$646$	−1.22855	−	6.01783i	−0.0483366	−	0.236768i
$647$	5.78075	−	28.3160i	0.227265	−	1.11322i	−0.692703	−	0.721223i	$-0.743580\pi$
$647$	5.78075	−	28.3160i	0.227265	−	1.11322i	0.919968	−	0.391994i	$-0.128214\pi$
$648$	0.127158	−	0.0206651i	0.00499522	−	0.000811803i
$649$	9.46961	+	0.764466i	0.371715	+	0.0300079i
$650$	7.82976	+	13.5615i	0.307109	+	0.531928i
$651$	17.5399	+	25.4109i	0.687442	+	0.995931i
$652$	4.80088	+	16.5746i	0.188017	+	0.649110i
$653$	−9.94998	+	34.3513i	−0.389373	+	1.34427i	0.491484	+	0.870887i	$0.336455\pi$
$653$	−9.94998	+	34.3513i	−0.389373	+	1.34427i	−0.880856	+	0.473384i	$0.843032\pi$
$654$	20.9262	−	21.7865i	0.818279	−	0.851919i
$655$	4.81493	−	39.6545i	0.188135	−	1.54943i
$656$	−2.47388			−0.0965889
$657$	0.376925	−	3.10426i	0.0147052	−	0.121109i
$658$	−5.75824	−	0.935806i	−0.224480	−	0.0364815i
$659$	22.0064	+	26.9530i	0.857249	+	1.04994i	0.998203	+	0.0599232i	$0.0190856\pi$
$659$	22.0064	+	26.9530i	0.857249	+	1.04994i	−0.140954	+	0.990016i	$0.545017\pi$
$660$	1.84815	+	4.87318i	0.0719393	+	0.189688i
$661$	5.57218	+	27.2943i	0.216733	+	1.06163i	0.931912	+	0.362685i	$0.118140\pi$
$661$	5.57218	+	27.2943i	0.216733	+	1.06163i	−0.715179	+	0.698941i	$0.753655\pi$
$662$	21.9466	−	9.35057i	0.852979	−	0.363420i
$663$	−0.185778	+	0.391519i	−0.00721502	+	0.0152053i
$664$	0.0107595	−	0.266994i	0.000417549	−	0.0103614i
$665$	57.0199	+	42.8477i	2.21114	+	1.66156i
$666$	−3.34481	+	7.04904i	−0.129609	+	0.273145i
$667$	9.67305	−	5.07681i	0.374542	−	0.196575i
$668$	2.24691	+	0.181389i	0.0869356	+	0.00701817i
$669$	−10.5820	+	15.3307i	−0.409124	+	0.592719i
$670$	31.4789	+	10.5092i	1.21614	+	0.406006i
$671$	−4.50806	+	2.85073i	−0.174032	+	0.110051i
$672$	−6.69069	−	23.0989i	−0.258099	−	0.891061i
$673$	−16.8837	−	8.86125i	−0.650819	−	0.341576i	0.106793	−	0.994281i	$-0.465942\pi$
$673$	−16.8837	−	8.86125i	−0.650819	−	0.341576i	−0.757612	+	0.652705i	$0.773634\pi$
$674$	13.9642	+	36.8207i	0.537883	+	1.41828i
$675$	−8.24836	−	3.51430i	−0.317479	−	0.135265i
$676$	0.952517	+	23.6365i	0.0366353	+	0.909095i
$677$	1.09045	−	1.57978i	0.0419092	−	0.0607160i	−0.801469	−	0.598036i	$-0.795948\pi$
$677$	1.09045	−	1.57978i	0.0419092	−	0.0607160i	0.843378	+	0.537320i	$0.180563\pi$
$678$	0.658574	−	1.14068i	0.0252924	−	0.0438077i
$679$	−13.9750	+	1.12818i	−0.536311	+	0.0432955i
$680$	−0.200274	+	0.126646i	−0.00768017	+	0.00485664i
$681$	−26.0276	+	8.68927i	−0.997378	+	0.332974i
$682$	−5.15948	+	13.6044i	−0.197567	+	0.520940i
$683$	−24.9512	−	4.05497i	−0.954732	−	0.155159i	−0.336963	−	0.941518i	$-0.609400\pi$
$683$	−24.9512	−	4.05497i	−0.954732	−	0.155159i	−0.617770	+	0.786359i	$0.711964\pi$
$684$	−11.8191	−	2.91314i	−0.451914	−	0.111387i
$685$	4.81858	−	5.01668i	0.184109	−	0.191677i
$686$	10.2336	−	26.9838i	0.390720	−	1.03025i
$687$	−10.4352	+	9.24477i	−0.398127	+	0.352710i
$688$	−19.2236	−	8.19041i	−0.732893	−	0.312256i
$689$	2.12348	−	10.4015i	0.0808981	−	0.396265i
$690$	−12.5309	−	26.4084i	−0.477044	−	1.00535i
$691$	6.57899	+	4.94379i	0.250277	+	0.188071i	0.718475	−	0.695553i	$-0.244840\pi$
$691$	6.57899	+	4.94379i	0.250277	+	0.188071i	−0.468199	+	0.883623i	$0.655097\pi$
$692$	3.89777	+	32.1010i	0.148171	+	1.22030i
$693$	−0.263569	−	2.17069i	−0.0100122	−	0.0824576i
$694$	0.576850	−	14.3144i	0.0218969	−	0.543367i
$695$	−58.0416	−	51.4204i	−2.20164	−	1.95049i
$696$	−0.352298	+	0.0572540i	−0.0133538	+	0.00217021i
$697$	0.0118839	+	0.294895i	0.000450133	+	0.0111699i
$698$	−20.5453	+	25.1634i	−0.777651	+	0.952450i
$699$	−19.7287	+	6.58641i	−0.746208	+	0.249121i
$700$	−14.6446	+	50.5590i	−0.553513	+	1.91095i
$701$	5.42571	+	3.43101i	0.204926	+	0.129588i	0.632987	−	0.774162i	$-0.281829\pi$
$701$	5.42571	+	3.43101i	0.204926	+	0.129588i	−0.428061	+	0.903750i	$0.640803\pi$
$702$	1.10462	+	1.35291i	0.0416911	+	0.0510624i
$703$	−18.5202	+	16.4074i	−0.698501	+	0.618818i
$704$	3.40599	−	4.17158i	0.128368	−	0.157222i
$705$	3.43600	+	1.14710i	0.129407	+	0.0432025i
$706$	15.1984	−	3.74608i	0.572001	−	0.140985i
$707$	−6.24334	+	1.53885i	−0.234805	+	0.0578743i
$708$	−24.1949	−	8.07746i	−0.909301	−	0.303569i
$709$	0.0357625	−	0.0438011i	0.00134309	−	0.00164498i	−0.773933	−	0.633268i	$-0.781713\pi$
$709$	0.0357625	−	0.0438011i	0.00134309	−	0.00164498i	0.775276	+	0.631623i	$0.217611\pi$
$710$	1.23936	−	1.09798i	0.0465123	−	0.0412063i
$711$	−5.59342	−	6.85069i	−0.209770	−	0.256921i
$712$	2.01521	+	1.27434i	0.0755233	+	0.0477581i
$713$	11.1643	−	38.5437i	0.418107	−	1.44347i
$714$	−2.80979	+	0.938045i	−0.105154	+	0.0351054i
$715$	1.49981	−	1.83693i	0.0560897	−	0.0686974i
$716$	1.53412	+	38.0687i	0.0573326	+	1.42269i
$717$	−24.7427	+	4.02108i	−0.924034	+	0.150170i
$718$	24.0918	+	21.3434i	0.899097	+	0.796530i
$719$	−1.01894	+	25.2846i	−0.0379999	+	0.942958i	0.861958	+	0.506980i	$0.169238\pi$
$719$	−1.01894	+	25.2846i	−0.0379999	+	0.942958i	−0.899958	+	0.435977i	$0.856403\pi$
$720$	1.85843	+	15.3056i	0.0692596	+	0.570404i
$721$	3.33672	+	27.4804i	0.124266	+	1.02342i
$722$	−32.6249	−	24.5160i	−1.21417	−	0.912392i
$723$	6.86000	+	14.4571i	0.255126	+	0.537667i
$724$	1.72284	−	8.43904i	0.0640289	−	0.313634i
$725$	22.8526	+	9.73658i	0.848724	+	0.361608i
$726$	−15.5617	+	13.7865i	−0.577550	+	0.511665i
$727$	−10.8642	+	28.6466i	−0.402932	+	1.06244i	0.567988	+	0.823037i	$0.307722\pi$
$727$	−10.8642	+	28.6466i	−0.402932	+	1.06244i	−0.970919	+	0.239406i	$0.923047\pi$
$728$	−0.238389	+	0.248189i	−0.00883529	+	0.00919851i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	22.8815	+	3.71860i	0.846881	+	0.137631i
$731$	−0.883978	+	2.33086i	−0.0326951	+	0.0862099i
$732$	13.5837	−	4.53490i	0.502067	−	0.167615i
$733$	−16.0863	+	10.1723i	−0.594160	+	0.375724i	−0.797442	−	0.603396i	$-0.793814\pi$
$733$	−16.0863	+	10.1723i	−0.594160	+	0.375724i	0.203281	+	0.979120i	$0.434839\pi$
$734$	−47.4916	+	3.83391i	−1.75295	+	0.141512i
$735$	4.11993	−	7.13593i	0.151966	−	0.263213i
$736$	−17.7543	+	25.7216i	−0.654433	+	0.948109i
$737$	−0.129916	−	3.22383i	−0.00478551	−	0.118751i
$738$	1.09431	+	0.466240i	0.0402819	+	0.0171625i
$739$	−15.6080	−	41.1549i	−0.574150	−	1.51391i	−0.835961	−	0.548789i	$-0.815089\pi$
$739$	−15.6080	−	41.1549i	−0.574150	−	1.51391i	0.261811	−	0.965119i	$-0.415680\pi$
$740$	−25.1851	−	13.2182i	−0.925824	−	0.485910i
$741$	1.54097	+	5.32005i	0.0566090	+	0.195437i
$742$	61.3320	−	38.7840i	2.25157	−	1.42381i
$743$	27.2105	+	9.08420i	0.998257	+	0.333267i	0.768409	−	0.639959i	$-0.221049\pi$
$743$	27.2105	+	9.08420i	0.998257	+	0.333267i	0.229848	+	0.973227i	$0.426177\pi$
$744$	−0.744767	+	1.07898i	−0.0273045	+	0.0395574i
$745$	80.8069	+	6.52341i	2.96053	+	0.238999i
$746$	27.3507	−	14.3548i	1.00138	−	0.525566i
$747$	−0.889194	+	1.87394i	−0.0325339	+	0.0685637i
$748$	−0.548759	−	0.412366i	−0.0200646	−	0.0150776i
$749$	0.805033	−	19.9767i	0.0294153	−	0.729933i
$750$	12.6034	−	26.5610i	0.460210	−	0.969871i
$751$	−42.2635	+	18.0068i	−1.54222	+	0.657077i	−0.984885	−	0.173212i	$-0.944585\pi$
$751$	−42.2635	+	18.0068i	−1.54222	+	0.657077i	−0.557332	+	0.830289i	$0.688175\pi$
$752$	−0.799919	−	3.91826i	−0.0291700	−	0.142884i
$753$	0.481388	+	1.26932i	0.0175428	+	0.0462565i
$754$	−3.06041	−	3.74833i	−0.111454	−	0.136506i
$755$	−61.2825	−	9.95938i	−2.23030	−	0.362459i
$756$	−0.707656	+	5.82807i	−0.0257372	+	0.211965i
$757$	−18.2864			−0.664631			−0.332316	−	0.943168i	$-0.607830\pi$
$757$	−18.2864			−0.664631			−0.332316	+	0.943168i	$0.607830\pi$
$758$	−7.02795	+	57.8804i	−0.255267	+	2.10231i
$759$	−1.96859	+	2.04952i	−0.0714553	+	0.0743928i
$760$	−0.842592	+	2.90896i	−0.0305640	+	0.105519i
$761$	−7.38256	−	25.4875i	−0.267618	−	0.923923i	−0.975941	−	0.218035i	$-0.930035\pi$
$761$	−7.38256	−	25.4875i	−0.267618	−	0.923923i	0.708323	−	0.705888i	$-0.249452\pi$
$762$	−20.3754	−	29.5189i	−0.738124	−	1.06936i
$763$	−23.1011	−	40.0124i	−0.836318	−	1.44854i
$764$	−43.8571	−	3.54051i	−1.58670	−	0.128091i
$765$	1.81554	−	0.295055i	0.0656411	−	0.0106677i
$766$	−5.12559	+	25.1068i	−0.185195	+	0.907146i
$767$	2.32154	+	11.3716i	0.0838259	+	0.410606i
$768$	13.5809	−	10.2054i	0.490058	−	0.368255i
$769$	−4.46129	−	6.46329i	−0.160878	−	0.233072i	0.734252	−	0.678877i	$-0.237533\pi$
$769$	−4.46129	−	6.46329i	−0.160878	−	0.233072i	−0.895130	+	0.445805i	$0.852918\pi$
$770$	16.1575	−	1.30437i	0.582275	−	0.0470061i
$771$	16.9352	−	4.17416i	0.609908	−	0.150329i
$772$	16.2732	−	28.1860i	0.585684	−	1.01444i
$773$	5.85336	+	10.1383i	0.210531	+	0.364650i	0.951881	−	0.306468i	$-0.0991474\pi$
$773$	5.85336	+	10.1383i	0.210531	+	0.364650i	−0.741350	+	0.671119i	$0.765814\pi$
$774$	6.95982	+	7.24594i	0.250166	+	0.260450i
$775$	83.9435	−	35.7650i	3.01534	−	1.28472i
$776$	−0.255212	−	0.537849i	−0.00916159	−	0.0193076i
$777$	8.93218	+	7.91322i	0.320440	+	0.283885i
$778$	−28.4657	+	14.9400i	−1.02055	+	0.535624i
$779$	2.61302	+	2.72044i	0.0936210	+	0.0974698i
$780$	−5.09012	+	3.82498i	−0.182256	+	0.136956i
$781$	−0.142536	−	0.0748085i	−0.00510032	−	0.00267686i
$782$	3.25382	+	2.05759i	0.116356	+	0.0735792i
$783$	2.69006	+	0.663039i	0.0961347	+	0.0236951i
$784$	−9.09664			−0.324880
$785$	−3.37091	−	46.7041i	−0.120313	−	1.66694i
$786$	21.2038			0.756313
$787$	15.7990	+	3.89411i	0.563174	+	0.138810i	0.510618	−	0.859808i	$-0.329417\pi$
$787$	15.7990	+	3.89411i	0.563174	+	0.138810i	0.0525567	+	0.998618i	$0.483263\pi$
$788$	−0.270977	−	0.171355i	−0.00965314	−	0.00610428i
$789$	12.0578	+	6.32843i	0.429269	+	0.225298i
$790$	52.4144	−	39.3868i	1.86482	−	1.40132i
$791$	−1.39550	−	1.45287i	−0.0496181	−	0.0516580i
$792$	0.0822122	−	0.0431483i	0.00292128	−	0.00153321i
$793$	−4.87732	−	4.32093i	−0.173199	−	0.153441i
$794$	−10.8385	−	22.8417i	−0.384644	−	0.810620i
$795$	−41.4533	+	17.6616i	−1.47020	+	0.626393i
$796$	12.3422	+	12.8496i	0.437459	+	0.455443i
$797$	9.22375	+	15.9760i	0.326722	+	0.565899i	0.981859	−	0.189611i	$-0.0607226\pi$
$797$	9.22375	+	15.9760i	0.326722	+	0.565899i	−0.655137	+	0.755510i	$0.727389\pi$
$798$	−18.9300	+	32.7878i	−0.670116	+	1.16067i
$799$	−0.463227	+	0.114175i	−0.0163878	+	0.00403923i
$800$	−70.8364	+	5.71850i	−2.50444	+	0.202180i
$801$	−10.5138	−	15.2319i	−0.371488	−	0.538194i
$802$	31.2598	−	23.4902i	1.10382	−	0.829469i
$803$	−0.450804	−	2.20818i	−0.0159085	−	0.0779251i
$804$	−1.73276	+	8.48760i	−0.0611096	+	0.299334i
$805$	−44.1276	+	7.17143i	−1.55529	+	0.252760i
$806$	−17.7173	−	1.43029i	−0.624066	−	0.0503798i
$807$	−5.21569	−	9.03384i	−0.183601	−	0.318006i
$808$	−0.155101	−	0.224703i	−0.00545645	−	0.00790503i
$809$	0.775643	+	2.67783i	0.0272701	+	0.0941474i	0.972999	−	0.230809i	$-0.0741374\pi$
$809$	0.775643	+	2.67783i	0.0272701	+	0.0941474i	−0.945729	+	0.324957i	$0.894650\pi$
$810$	2.06250	−	7.12056i	0.0724687	−	0.250191i
$811$	−21.7102	+	22.6027i	−0.762347	+	0.793687i	−0.983376	−	0.181580i	$-0.941879\pi$
$811$	−21.7102	+	22.6027i	−0.762347	+	0.793687i	0.221029	+	0.975267i	$0.429058\pi$
$812$	1.96061	−	16.1470i	0.0688038	−	0.566650i
$813$	23.4412			0.822118
$814$	−0.677815	+	5.58231i	−0.0237574	+	0.195660i
$815$	−32.8939	−	5.34577i	−1.15222	−	0.187254i
$816$	−1.28426	−	1.57293i	−0.0449580	−	0.0550635i
$817$	11.2981	+	29.7905i	0.395269	+	1.04224i
$818$	−11.1735	−	54.7313i	−0.390672	−	1.91364i
$819$	2.45754	−	1.04706i	0.0858735	−	0.0365873i
$820$	−1.85891	+	3.91757i	−0.0649159	+	0.136807i
$821$	−1.63903	+	40.6722i	−0.0572027	+	1.41947i	0.674716	+	0.738078i	$0.264266\pi$
$821$	−1.63903	+	40.6722i	−0.0572027	+	1.41947i	−0.731918	+	0.681392i	$0.761375\pi$
$822$	2.95181	+	2.21814i	0.102956	+	0.0773666i
$823$	19.9722	−	42.0905i	0.696188	−	1.46718i	−0.179225	−	0.983808i	$-0.557359\pi$
$823$	19.9722	−	42.0905i	0.696188	−	1.46718i	0.875413	−	0.483376i	$-0.160590\pi$
$824$	−1.04079	+	0.546247i	−0.0362575	+	0.0190294i
$825$	−6.44088	−	0.519961i	−0.224243	−	0.0181027i
$826$	−45.0671	+	65.2909i	−1.56808	+	2.27176i
$827$	−22.5401	−	7.52500i	−0.783797	−	0.261670i	−0.103522	−	0.994627i	$-0.533011\pi$
$827$	−22.5401	−	7.52500i	−0.783797	−	0.261670i	−0.680275	+	0.732957i	$0.738139\pi$
$828$	6.44877	−	4.07796i	0.224110	−	0.141719i
$829$	13.5773	+	46.8743i	0.471560	+	1.62801i	0.745671	+	0.666315i	$0.232129\pi$
$829$	13.5773	+	46.8743i	0.471560	+	1.62801i	−0.274111	+	0.961698i	$0.588384\pi$
$830$	−13.6153	−	7.14584i	−0.472593	−	0.248036i
$831$	−3.04528	−	8.02975i	−0.105640	−	0.278549i
$832$	6.05266	+	2.57880i	0.209838	+	0.0894037i
$833$	0.0436977	+	1.08435i	0.00151404	+	0.0375704i
$834$	23.3820	−	33.8747i	0.809653	−	1.17298i
$835$	−2.17674	+	3.77022i	−0.0753290	+	0.130474i
$836$	−8.74473	+	0.705947i	−0.302443	+	0.0244157i
$837$	8.60149	−	5.43925i	0.297311	−	0.188008i
$838$	−44.1647	+	14.7444i	−1.52565	+	0.509335i
$839$	12.7643	−	33.6568i	0.440674	−	1.16196i	−0.512273	−	0.858823i	$-0.671196\pi$
$839$	12.7643	−	33.6568i	0.440674	−	1.16196i	0.952947	−	0.303138i	$-0.0980344\pi$
$840$	1.44173	+	0.234304i	0.0497445	+	0.00808427i
$841$	20.7043	+	5.10316i	0.713943	+	0.175971i
$842$	20.1376	−	20.9654i	0.693986	−	0.722516i
$843$	−9.75223	+	25.7145i	−0.335884	+	0.885655i
$844$	41.0498	−	36.3670i	1.41299	−	1.25180i
$845$	−42.0293	−	17.9070i	−1.44585	−	0.616020i
$846$	−0.384616	+	1.88397i	−0.0132234	+	0.0647723i
$847$	13.6314	+	28.7275i	0.468380	+	0.987089i
$848$	39.7676	+	29.8834i	1.36563	+	1.02620i
$849$	−1.54041	−	12.6865i	−0.0528669	−	0.435398i
$850$	1.05516	+	8.69003i	0.0361917	+	0.298066i
$851$	0.624477	−	15.4962i	0.0214068	−	0.531204i
$852$	0.323506	+	0.286601i	0.0110831	+	0.00981879i
$853$	14.6451	−	2.38005i	0.501437	−	0.0814915i	0.0955684	−	0.995423i	$-0.469533\pi$
$853$	14.6451	−	2.38005i	0.501437	−	0.0814915i	0.405869	+	0.913931i	$0.366969\pi$
$854$	−1.79346	−	44.5043i	−0.0613710	−	1.52291i
$855$	14.8680	−	18.2100i	0.508475	−	0.622769i
$856$	0.805237	−	0.268828i	0.0275224	−	0.00918834i
$857$	−11.9938	+	41.4073i	−0.409699	+	1.41445i	0.445097	+	0.895482i	$0.353169\pi$
$857$	−11.9938	+	41.4073i	−0.409699	+	1.41445i	−0.854796	+	0.518963i	$0.826318\pi$
$858$	1.06392	+	0.672784i	0.0363217	+	0.0229685i
$859$	0.0861078	+	0.105463i	0.00293796	+	0.00359835i	0.776072	−	0.630644i	$-0.217209\pi$
$859$	0.0861078	+	0.105463i	0.00293796	+	0.00359835i	−0.773134	+	0.634243i	$0.781312\pi$
$860$	−27.4149	+	24.2875i	−0.934842	+	0.828197i
$861$	1.15058	−	1.40921i	0.0392117	−	0.0480256i
$862$	44.7665	+	14.9453i	1.52475	+	0.509038i
$863$	19.8222	−	4.88573i	0.674755	−	0.166312i	0.112973	−	0.993598i	$-0.463962\pi$
$863$	19.8222	−	4.88573i	0.674755	−	0.166312i	0.561781	+	0.827286i	$0.310116\pi$
$864$	−7.69610	+	1.89692i	−0.261827	+	0.0645345i
$865$	−59.2366	−	19.7761i	−2.01410	−	0.672407i
$866$	−9.68050	+	11.8565i	−0.328957	+	0.402899i
$867$	12.5434	−	11.1124i	0.425995	−	0.377398i
$868$	−37.7873	−	46.2810i	−1.28258	−	1.57088i
$869$	−5.38735	−	3.40675i	−0.182753	−	0.115566i
$870$	−5.71427	+	19.7280i	−0.193732	+	0.668840i
$871$	3.73874	−	1.24817i	0.126682	−	0.0422928i
$872$	1.24074	−	1.51963i	0.0420167	−	0.0514611i
$873$	0.186076	+	4.61743i	0.00629772	+	0.156276i
$874$	48.5669	−	7.89288i	1.64280	−	0.266981i
$875$	−33.6567	−	29.8173i	−1.13781	−	1.00801i
$876$	−0.243651	+	6.04613i	−0.00823219	+	0.204280i
$877$	1.48388	+	12.2209i	0.0501072	+	0.412670i	0.996082	+	0.0884308i	$0.0281852\pi$
$877$	1.48388	+	12.2209i	0.0501072	+	0.412670i	−0.945975	+	0.324239i	$0.894892\pi$
$878$	3.30598	+	27.2272i	0.111571	+	0.918873i
$879$	−2.27154	−	1.70695i	−0.0766170	−	0.0575739i
$880$	4.76365	+	10.0392i	0.160582	+	0.338420i
$881$	0.469559	−	2.30005i	0.0158198	−	0.0774907i	−0.971114	−	0.238615i	$-0.923307\pi$
$881$	0.469559	−	2.30005i	0.0158198	−	0.0774907i	0.986934	+	0.161124i	$0.0515119\pi$
$882$	4.02384	+	1.71440i	0.135490	+	0.0577267i
$883$	−26.5860	+	23.5531i	−0.894690	+	0.792626i	−0.979010	−	0.203813i	$-0.934667\pi$
$883$	−26.5860	+	23.5531i	−0.894690	+	0.792626i	0.0843200	+	0.996439i	$0.473128\pi$
$884$	0.297363	−	0.784081i	0.0100014	−	0.0263715i
$885$	34.1248	−	35.5277i	1.14709	−	1.19425i
$886$	29.2282	+	7.20410i	0.981939	+	0.242026i
$887$	4.16415	+	0.676741i	0.139819	+	0.0227227i	0.229918	−	0.973210i	$-0.426154\pi$
$887$	4.16415	+	0.676741i	0.139819	+	0.0227227i	−0.0900991	+	0.995933i	$0.528718\pi$
$888$	−0.179679	+	0.473775i	−0.00602964	+	0.0158989i
$889$	−52.0351	+	17.3719i	−1.74520	+	0.582634i
$890$	115.965	−	73.3318i	3.88715	−	2.45809i
$891$	−0.718382	+	0.0579938i	−0.0240667	+	0.00194287i
$892$	18.0233	−	31.2173i	0.603465	−	1.04523i
$893$	−3.46386	+	5.01827i	−0.115914	+	0.167930i
$894$	1.73276	+	42.9981i	0.0579523	+	1.43807i
$895$	−67.6920	−	28.8409i	−2.26269	−	0.964044i
$896$	−1.10820	−	2.92208i	−0.0370224	−	0.0976199i
$897$	−3.07404	−	1.61338i	−0.102639	−	0.0538692i
$898$	0.930863	+	3.21371i	0.0310633	+	0.107243i
$899$	−23.8310	+	15.0698i	−0.794807	+	0.502606i
$900$	16.4565	+	5.49399i	0.548550	+	0.183133i
$901$	3.37117	−	4.88398i	0.112310	−	0.162709i
$902$	0.854508	+	0.0689830i	0.0284520	+	0.00229688i
$903$	13.6063	−	7.14111i	0.452788	−	0.237641i
$904$	0.0366698	−	0.0772799i	0.00121962	−	0.00257029i
$905$	13.2980	+	9.99279i	0.442040	+	0.332172i
$906$	1.32702	−	32.9297i	0.0440873	−	1.09402i
$907$	−1.21296	+	2.55625i	−0.0402755	+	0.0848789i	−0.922591	−	0.385780i	$-0.873932\pi$
$907$	−1.21296	+	2.55625i	−0.0402755	+	0.0848789i	0.882315	+	0.470659i	$0.155984\pi$
$908$	48.8485	−	20.8124i	1.62109	−	0.690684i
$909$	0.423936	+	2.07658i	0.0140611	+	0.0688757i
$910$	7.02225	+	18.5161i	0.232785	+	0.613804i
$911$	−10.7486	−	13.1647i	−0.356117	−	0.436165i	0.565213	−	0.824945i	$-0.308794\pi$
$911$	−10.7486	−	13.1647i	−0.356117	−	0.436165i	−0.921331	+	0.388780i	$0.872897\pi$
$912$	−25.6171	−	4.16318i	−0.848267	−	0.137857i
$913$	−0.180192	+	1.48402i	−0.00596349	+	0.0491138i
$914$	28.6982			0.949253
$915$	−3.33366	+	27.4552i	−0.110207	+	0.907640i
$916$	18.6877	−	19.4560i	0.617460	−	0.642844i
$917$	9.02259	−	31.1496i	0.297952	−	1.02865i
$918$	0.271640	+	0.937812i	0.00896547	+	0.0309524i
$919$	−26.8188	−	38.8538i	−0.884671	−	1.28167i	−0.958702	−	0.284411i	$-0.908202\pi$
$919$	−26.8188	−	38.8538i	−0.884671	−	1.28167i	0.0740312	−	0.997256i	$-0.476414\pi$
$920$	−0.949150	−	1.64398i	−0.0312925	−	0.0542003i
$921$	−12.3029	−	0.993190i	−0.405393	−	0.0327267i
$922$	−15.2151	+	2.47270i	−0.501084	+	0.0814341i
$923$	0.0393359	−	0.192680i	0.00129476	−	0.00634215i
$924$	0.846360	+	4.14575i	0.0278432	+	0.136385i
$925$	28.1921	−	21.1850i	0.926950	−	0.696557i
$926$	14.7993	+	21.4405i	0.486335	+	0.704578i
$927$	9.09454	−	0.734187i	0.298704	−	0.0241139i
$928$	21.3225	−	5.25553i	0.699946	−	0.172521i
$929$	−8.81293	+	15.2644i	−0.289143	+	0.500810i	−0.973605	−	0.228238i	$-0.926704\pi$
$929$	−8.81293	+	15.2644i	−0.289143	+	0.500810i	0.684462	+	0.729048i	$0.260037\pi$
$930$	37.7223	+	65.3369i	1.23696	+	2.14248i
$931$	9.60824	+	10.0032i	0.314897	+	0.327843i
$932$	37.0268	−	15.7757i	1.21285	−	0.516749i
$933$	7.04151	+	14.8397i	0.230529	+	0.485829i
$934$	39.9777	+	35.4172i	1.30811	+	1.15888i
$935$	1.17382	−	0.616067i	0.0383880	−	0.0201476i
$936$	0.0785737	+	0.0818039i	0.00256826	+	0.00267384i
$937$	−27.1550	+	20.4057i	−0.887115	+	0.666624i	−0.943352	−	0.331794i	$-0.892346\pi$
$937$	−27.1550	+	20.4057i	−0.887115	+	0.666624i	0.0562370	+	0.998417i	$0.482090\pi$
$938$	23.8566	+	12.5209i	0.778947	+	0.408823i
$939$	24.7798	+	15.6698i	0.808658	+	0.511364i
$940$	−6.80591	−	1.67751i	−0.221984	−	0.0547142i
$941$	26.5272			0.864761			0.432380	−	0.901691i	$-0.357674\pi$
$941$	26.5272			0.864761			0.432380	+	0.901691i	$0.357674\pi$
$942$	24.3947	−	4.76453i	0.794824	−	0.155237i
$943$	−2.36436			−0.0769941
$944$	−52.8036	−	13.0149i	−1.71861	−	0.423600i
$945$	−9.58289	−	6.05986i	−0.311732	−	0.197127i
$946$	6.41167	+	3.36510i	0.208461	+	0.109409i
$947$	−45.2583	+	34.0094i	−1.47070	+	1.10516i	−0.499661	+	0.866221i	$0.666542\pi$
$947$	−45.2583	+	34.0094i	−1.47070	+	1.10516i	−0.971035	+	0.238935i	$0.923202\pi$
$948$	11.8552	+	12.3426i	0.385039	+	0.400868i
$949$	2.43790	−	1.27951i	0.0791377	−	0.0415347i
$950$	83.7451	+	74.1917i	2.71705	+	2.40710i
$951$	−7.33748	−	15.4634i	−0.237934	−	0.501436i
$952$	−0.176980	+	0.0754043i	−0.00573597	+	0.00244387i
$953$	−22.6445	−	23.5754i	−0.733527	−	0.763683i	0.245062	−	0.969507i	$-0.421192\pi$
$953$	−22.6445	−	23.5754i	−0.733527	−	0.763683i	−0.978589	+	0.205825i	$0.934012\pi$
$954$	−11.9590	−	20.7135i	−0.387186	−	0.670626i
$955$	42.4874	−	73.5903i	1.37486	−	2.38133i
$956$	47.0972	−	11.6084i	1.52323	−	0.375443i
$957$	1.99032	−	0.160676i	0.0643380	−	0.00519390i
$958$	39.0149	+	56.5229i	1.26052	+	1.82617i
$959$	4.51463	−	3.39253i	0.145785	−	0.109550i
$960$	−5.58564	−	27.3603i	−0.180276	−	0.883049i
$961$	−14.5161	+	71.1045i	−0.468261	+	2.29369i
$962$	−6.78076	+	1.10198i	−0.218621	+	0.0355293i
$963$	−6.56835	−	0.530252i	−0.211662	−	0.0170871i
$964$	−15.4825	−	26.8165i	−0.498659	−	0.863702i
$965$	35.7058	+	51.7288i	1.14941	+	1.66521i
$966$	−6.60234	−	22.7939i	−0.212427	−	0.733382i
$967$	8.01659	−	27.6765i	0.257796	−	0.890016i	−0.722315	−	0.691565i	$-0.756922\pi$
$967$	8.01659	−	27.6765i	0.257796	−	0.890016i	0.980111	−	0.198451i	$-0.0635911\pi$
$968$	−0.935294	+	0.973744i	−0.0300615	+	0.0312973i
$969$	−0.373207	+	3.07364i	−0.0119892	+	0.0987395i
$970$	−34.2579			−1.09996
$971$	−5.00380	+	41.2100i	−0.160580	+	1.32249i	0.660132	+	0.751150i	$0.270500\pi$
$971$	−5.00380	+	41.2100i	−0.160580	+	1.32249i	−0.820711	+	0.571343i	$0.806423\pi$
$972$	1.91000	+	0.310405i	0.0612633	+	0.00995625i
$973$	−39.8145	−	48.7639i	−1.27639	−	1.56330i
$974$	4.04176	+	10.6572i	0.129506	+	0.341480i
$975$	−1.57902	−	7.73457i	−0.0505693	−	0.247705i
$976$	28.0893	−	11.9678i	0.899118	−	0.383078i
$977$	13.3713	−	28.1794i	0.427785	−	0.901537i	−0.569070	−	0.822289i	$-0.692697\pi$
$977$	13.3713	−	28.1794i	0.427785	−	0.901537i	0.996855	−	0.0792484i	$-0.0252520\pi$
$978$	0.712289	−	17.6753i	0.0227765	−	0.565193i
$979$	−10.6639	−	8.01342i	−0.340821	−	0.256110i
$980$	−6.83533	+	14.4052i	−0.218347	+	0.460156i
$981$	−13.4841	+	7.07699i	−0.430513	+	0.225951i
$982$	19.2332	+	1.55267i	0.613757	+	0.0495476i
$983$	7.69131	−	11.1428i	0.245315	−	0.355400i	−0.680913	−	0.732364i	$-0.738417\pi$
$983$	7.69131	−	11.1428i	0.245315	−	0.355400i	0.926228	+	0.376965i	$0.123032\pi$
$984$	0.0732727	+	0.0244620i	0.00233585	+	0.000779821i
$985$	0.523324	−	0.330930i	0.0166745	−	0.0105443i
$986$	−0.752597	−	2.59827i	−0.0239676	−	0.0827456i
$987$	2.60401	+	1.36669i	0.0828865	+	0.0435022i
$988$	−3.80057	−	10.0213i	−0.120912	−	0.318819i
$989$	−18.3725	−	7.82780i	−0.584212	−	0.248910i
$990$	−0.215136	−	5.33854i	−0.00683746	−	0.169670i
$991$	−23.0572	+	33.4041i	−0.732436	+	1.06112i	0.262916	+	0.964819i	$0.415316\pi$
$991$	−23.0572	+	33.4041i	−0.732436	+	1.06112i	−0.995353	+	0.0962984i	$0.969300\pi$
$992$	40.3336	−	69.8598i	1.28059	−	2.21805i
$993$	−11.9868	+	0.967674i	−0.380389	+	0.0307082i
$994$	1.13613	−	0.718447i	0.0360360	−	0.0227878i
$995$	−32.6382	+	10.8962i	−1.03470	+	0.345434i
$996$	1.42328	−	3.75287i	0.0450982	−	0.118914i
$997$	27.9289	+	4.53888i	0.884516	+	0.143748i	0.585666	−	0.810552i	$-0.300833\pi$
$997$	27.9289	+	4.53888i	0.884516	+	0.143748i	0.298850	+	0.954300i	$0.403397\pi$
$998$	39.1725	+	9.65515i	1.23998	+	0.305629i
$999$	2.72465	−	2.83666i	0.0862041	−	0.0897480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.q.b.19.11	✓	336
157.124	even	39	inner	471.2.q.b.124.11	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.q.b.19.11	✓	336	1.1	even	1	trivial
471.2.q.b.124.11	yes	336	157.124	even	39	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.92606 + 0.474730i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.71341 + 0.899266i) q^{4} +(-2.98759 + 2.24503i) q^{5} +(-1.37416 - 1.43065i) q^{6} +(-2.68643 + 1.40995i) q^{7} +(-0.0964276 - 0.0854274i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(1.92606 + 0.474730i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(1.71341 + 0.899266i) q^{4} +(-2.98759 + 2.24503i) q^{5} +(-1.37416 - 1.43065i) q^{6} +(-2.68643 + 1.40995i) q^{7} +(-0.0964276 - 0.0854274i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-6.82004 + 2.90575i) q^{10} +(0.499260 + 0.519785i) q^{11} +(-0.967529 - 1.67581i) q^{12} +(-0.440234 + 0.762508i) q^{13} +(-5.84357 + 1.44031i) q^{14} +(3.72497 - 0.300710i) q^{15} +(-2.34365 - 3.39536i) q^{16} +(-0.393479 + 0.295680i) q^{17} +(0.396791 + 1.94361i) q^{18} +(-1.25829 + 6.16354i) q^{19} +(-7.13783 + 1.16001i) q^{20} +(3.02412 + 0.244132i) q^{21} +(0.714845 + 1.23815i) q^{22} +(-2.23989 - 3.24504i) q^{23} +(0.0358416 + 0.123740i) q^{24} +(2.49444 - 8.61182i) q^{25} +(-1.20990 + 1.25964i) q^{26} +(0.120537 - 0.992709i) q^{27} -5.87088 q^{28} +(-0.333954 + 2.75036i) q^{29} +(7.31725 + 1.18917i) q^{30} +(6.43639 + 7.88315i) q^{31} +(-2.81075 - 7.41134i) q^{32} +(-0.144162 - 0.706154i) q^{33} +(-0.898231 + 0.382701i) q^{34} +(4.86058 - 10.2435i) q^{35} +(-0.0779169 + 1.93349i) q^{36} +(3.14440 + 2.36286i) q^{37} +(-5.34956 + 11.2740i) q^{38} +(0.779616 - 0.409174i) q^{39} +(0.479872 + 0.0387393i) q^{40} +(0.340630 - 0.493488i) q^{41} +(5.70872 + 1.90585i) q^{42} +(4.28072 - 2.70696i) q^{43} +(0.388011 + 1.33957i) q^{44} +(-3.30902 - 1.73671i) q^{45} +(-2.77363 - 7.31347i) q^{46} +(0.891752 + 0.379940i) q^{47} +(0.166124 + 4.12232i) q^{48} +(1.25252 - 1.81459i) q^{49} +(8.89273 - 15.4027i) q^{50} +(0.490596 - 0.0396050i) q^{51} +(-1.44000 + 0.910600i) q^{52} +(-11.4367 + 3.81815i) q^{53} +(0.703429 - 1.85479i) q^{54} +(-2.65851 - 0.432050i) q^{55} +(0.379495 + 0.0935370i) q^{56} +(4.35770 - 4.53684i) q^{57} +(-1.94889 + 5.13881i) q^{58} +(9.86676 - 8.74119i) q^{59} +(6.65281 + 2.83450i) q^{60} +(-1.48032 + 7.25108i) q^{61} +(8.65448 + 18.2389i) q^{62} +(-2.42547 - 1.82263i) q^{63} +(-0.900686 - 7.41782i) q^{64} +(-0.396612 - 3.26639i) q^{65} +(0.0575678 - 1.42853i) q^{66} +(-3.35085 - 2.96860i) q^{67} +(-0.940086 + 0.152779i) q^{68} +(0.158769 + 3.93982i) q^{69} +(14.2246 - 17.4220i) q^{70} +(-0.211858 + 0.0707285i) q^{71} +(0.0358416 - 0.123740i) q^{72} +(-2.64296 - 1.67130i) q^{73} +(4.93456 + 6.04374i) q^{74} +(-6.71100 + 5.94543i) q^{75} +(-7.69863 + 9.42911i) q^{76} +(-2.07410 - 0.692436i) q^{77} +(1.69583 - 0.417985i) q^{78} +(-8.58712 + 2.11653i) q^{79} +(14.6245 + 4.88238i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(0.890345 - 0.788777i) q^{82} +(1.31182 + 1.60668i) q^{83} +(4.96201 + 3.13778i) q^{84} +(0.511743 - 1.76674i) q^{85} +(9.52998 - 3.18157i) q^{86} +(1.75223 - 2.14609i) q^{87} +(-0.00373858 - 0.0927720i) q^{88} +(-18.2685 + 2.96892i) q^{89} +(-5.54890 - 4.91589i) q^{90} +(0.107562 - 2.66914i) q^{91} +(-0.919691 - 7.57433i) q^{92} +(-1.22670 - 10.1028i) q^{93} +(1.53719 + 1.15513i) q^{94} +(-10.0780 - 21.2390i) q^{95} +(-1.58549 + 7.76624i) q^{96} +(4.25139 + 1.81135i) q^{97} +(3.27386 - 2.90039i) q^{98} +(-0.255571 + 0.673884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Introduction

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