LMFDB - Embedded newform 171.2.x.a.110.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(14,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

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

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

chi := DirichletCharacter("171.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			110.10
Character	$\chi$	$=$	171.110
Dual form			171.2.x.a.14.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.103187 - 0.0865845i) q^{2} +(-1.73169 + 0.0351497i) q^{3} +(-0.344146 + 1.95175i) q^{4} +(0.862577 - 2.36991i) q^{5} +(-0.175646 + 0.153565i) q^{6} +(1.62680 + 2.81770i) q^{7} +(0.268181 + 0.464503i) q^{8} +(2.99753 - 0.121737i) q^{9} +O(q^{10})$	\(q+(0.103187 - 0.0865845i) q^{2} +(-1.73169 + 0.0351497i) q^{3} +(-0.344146 + 1.95175i) q^{4} +(0.862577 - 2.36991i) q^{5} +(-0.175646 + 0.153565i) q^{6} +(1.62680 + 2.81770i) q^{7} +(0.268181 + 0.464503i) q^{8} +(2.99753 - 0.121737i) q^{9} +(-0.116191 - 0.319231i) q^{10} +5.59201i q^{11} +(0.527352 - 3.39192i) q^{12} +(1.44664 + 3.97461i) q^{13} +(0.411835 + 0.149896i) q^{14} +(-1.41042 + 4.13428i) q^{15} +(-3.65678 - 1.33096i) q^{16} +(1.48046 - 4.06752i) q^{17} +(0.298767 - 0.272101i) q^{18} +(-2.66309 - 3.45079i) q^{19} +(4.32861 + 2.49913i) q^{20} +(-2.91617 - 4.82222i) q^{21} +(0.484182 + 0.577025i) q^{22} +(3.14450 + 0.554460i) q^{23} +(-0.480735 - 0.794951i) q^{24} +(-1.04222 - 0.874524i) q^{25} +(0.493415 + 0.284873i) q^{26} +(-5.18652 + 0.316173i) q^{27} +(-6.05930 + 2.20541i) q^{28} +(1.06770 - 6.05526i) q^{29} +(0.212427 + 0.548726i) q^{30} -6.64743i q^{31} +(-1.50061 + 0.546176i) q^{32} +(-0.196557 - 9.68366i) q^{33} +(-0.199420 - 0.547902i) q^{34} +(8.08095 - 1.42489i) q^{35} +(-0.793987 + 5.89231i) q^{36} +4.71492i q^{37} +(-0.573582 - 0.125497i) q^{38} +(-2.64485 - 6.83196i) q^{39} +(1.33216 - 0.234896i) q^{40} +(-4.53739 + 3.80732i) q^{41} +(-0.718441 - 0.245098i) q^{42} +(1.19499 + 6.77712i) q^{43} +(-10.9142 - 1.92447i) q^{44} +(2.29709 - 7.20888i) q^{45} +(0.372480 - 0.215052i) q^{46} +(-0.139535 - 0.0246038i) q^{47} +(6.37920 + 2.17628i) q^{48} +(-1.79297 + 3.10552i) q^{49} -0.183264 q^{50} +(-2.42073 + 7.09574i) q^{51} +(-8.25529 + 1.45563i) q^{52} +(-4.63584 - 3.88993i) q^{53} +(-0.507808 + 0.481698i) q^{54} +(13.2526 + 4.82354i) q^{55} +(-0.872555 + 1.51131i) q^{56} +(4.73294 + 5.88211i) q^{57} +(-0.414118 - 0.717273i) q^{58} +(-0.831759 - 4.71714i) q^{59} +(-7.58368 - 4.17557i) q^{60} +(4.55261 - 1.65702i) q^{61} +(-0.575565 - 0.685931i) q^{62} +(5.21941 + 8.24811i) q^{63} +(3.78391 - 6.55392i) q^{64} +10.6673 q^{65} +(-0.858737 - 0.982212i) q^{66} +(-2.35074 + 2.80150i) q^{67} +(7.42928 + 4.28930i) q^{68} +(-5.46480 - 0.849627i) q^{69} +(0.710479 - 0.846716i) q^{70} +(4.47532 - 3.75524i) q^{71} +(0.860428 + 1.35971i) q^{72} +(-1.71133 - 9.70541i) q^{73} +(0.408239 + 0.486520i) q^{74} +(1.83554 + 1.47777i) q^{75} +(7.65156 - 4.01009i) q^{76} +(-15.7566 + 9.09710i) q^{77} +(-0.864457 - 0.475970i) q^{78} +(3.30685 - 9.08549i) q^{79} +(-6.30851 + 7.51819i) q^{80} +(8.97036 - 0.729820i) q^{81} +(-0.138546 + 0.785736i) q^{82} +(3.95513 - 2.28350i) q^{83} +(10.4153 - 4.03207i) q^{84} +(-8.36266 - 7.01710i) q^{85} +(0.710101 + 0.595846i) q^{86} +(-1.63610 + 10.5234i) q^{87} +(-2.59751 + 1.49967i) q^{88} +(2.35153 - 13.3362i) q^{89} +(-0.387147 - 0.942759i) q^{90} +(-8.84589 + 10.5421i) q^{91} +(-2.16433 + 5.94645i) q^{92} +(0.233655 + 11.5113i) q^{93} +(-0.0165286 + 0.00954276i) q^{94} +(-10.4752 + 3.33470i) q^{95} +(2.57939 - 0.998555i) q^{96} +(2.21552 + 2.64035i) q^{97} +(0.0838777 + 0.475694i) q^{98} +(0.680755 + 16.7622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.103187	−	0.0865845i	0.0729645	−	0.0612245i	−0.605576	−	0.795787i	$-0.707057\pi$
$2$	0.103187	−	0.0865845i	0.0729645	−	0.0612245i	0.678541	+	0.734563i	$0.262613\pi$
$3$	−1.73169	+	0.0351497i	−0.999794	+	0.0202937i
$3$	−1.73169	+	0.0351497i	−0.999794	+	0.0202937i
$4$	−0.344146	+	1.95175i	−0.172073	+	0.975873i
$5$	0.862577	−	2.36991i	0.385756	−	1.05986i	−0.583136	−	0.812374i	$-0.698175\pi$
$5$	0.862577	−	2.36991i	0.385756	−	1.05986i	0.968892	−	0.247482i	$-0.0796031\pi$
$6$	−0.175646	+	0.153565i	−0.0717070	+	0.0626926i
$7$	1.62680	+	2.81770i	0.614873	+	1.06499i	0.990407	+	0.138183i	$0.0441263\pi$
$7$	1.62680	+	2.81770i	0.614873	+	1.06499i	−0.375533	+	0.926809i	$0.622540\pi$
$8$	0.268181	+	0.464503i	0.0948163	+	0.164227i
$9$	2.99753	−	0.121737i	0.999176	−	0.0405790i
$10$	−0.116191	−	0.319231i	−0.0367427	−	0.100950i
$11$			5.59201i			1.68606i	0.537870	+	0.843028i	$0.319229\pi$
$11$			5.59201i			1.68606i	−0.537870	+	0.843028i	$0.680771\pi$
$12$	0.527352	−	3.39192i	0.152233	−	0.979164i
$13$	1.44664	+	3.97461i	0.401226	+	1.10236i	0.961680	+	0.274174i	$0.0884044\pi$
$13$	1.44664	+	3.97461i	0.401226	+	1.10236i	−0.560454	+	0.828185i	$0.689373\pi$
$14$	0.411835	+	0.149896i	0.110068	+	0.0400613i
$15$	−1.41042	+	4.13428i	−0.364168	+	1.06747i
$16$	−3.65678	−	1.33096i	−0.914195	−	0.332740i
$17$	1.48046	−	4.06752i	0.359064	−	0.986519i	−0.620291	−	0.784371i	$-0.712986\pi$
$17$	1.48046	−	4.06752i	0.359064	−	0.986519i	0.979355	−	0.202148i	$-0.0647921\pi$
$18$	0.298767	−	0.272101i	0.0704200	−	0.0641349i
$19$	−2.66309	−	3.45079i	−0.610954	−	0.791666i
$19$	−2.66309	−	3.45079i	−0.610954	−	0.791666i
$20$	4.32861	+	2.49913i	0.967908	+	0.558822i
$21$	−2.91617	−	4.82222i	−0.636359	−	1.05229i
$22$	0.484182	+	0.577025i	0.103228	+	0.123022i
$23$	3.14450	+	0.554460i	0.655673	+	0.115613i	0.491581	−	0.870832i	$-0.336419\pi$
$23$	3.14450	+	0.554460i	0.655673	+	0.115613i	0.164093	+	0.986445i	$0.447530\pi$
$24$	−0.480735	−	0.794951i	−0.0981296	−	0.162269i
$25$	−1.04222	−	0.874524i	−0.208443	−	0.174905i
$26$	0.493415	+	0.284873i	0.0967667	+	0.0558683i
$27$	−5.18652	+	0.316173i	−0.998147	+	0.0608476i
$28$	−6.05930	+	2.20541i	−1.14510	+	0.416782i
$29$	1.06770	−	6.05526i	0.198268	−	1.12443i	−0.709420	−	0.704786i	$-0.751043\pi$
$29$	1.06770	−	6.05526i	0.198268	−	1.12443i	0.907688	−	0.419647i	$-0.137846\pi$
$30$	0.212427	+	0.548726i	0.0387837	+	0.100183i
$31$		−	6.64743i		−	1.19391i	−0.802273	−	0.596957i	$-0.796376\pi$
$31$		−	6.64743i		−	1.19391i	0.802273	−	0.596957i	$-0.203624\pi$
$32$	−1.50061	+	0.546176i	−0.265272	+	0.0965511i
$33$	−0.196557	−	9.68366i	−0.0342163	−	1.68571i
$34$	−0.199420	−	0.547902i	−0.0342002	−	0.0939644i
$35$	8.08095	−	1.42489i	1.36593	−	0.240850i
$36$	−0.793987	+	5.89231i	−0.132331	+	0.982052i
$37$			4.71492i			0.775127i	0.921843	+	0.387564i	$0.126683\pi$
$37$			4.71492i			0.775127i	−0.921843	+	0.387564i	$0.873317\pi$
$38$	−0.573582	−	0.125497i	−0.0930473	−	0.0203582i
$39$	−2.64485	−	6.83196i	−0.423514	−	1.09399i
$40$	1.33216	−	0.234896i	0.210633	−	0.0371402i
$41$	−4.53739	+	3.80732i	−0.708622	+	0.594604i	−0.924212	−	0.381880i	$-0.875277\pi$
$41$	−4.53739	+	3.80732i	−0.708622	+	0.594604i	0.215590	+	0.976484i	$0.430832\pi$
$42$	−0.718441	−	0.245098i	−0.110858	−	0.0378194i
$43$	1.19499	+	6.77712i	0.182234	+	1.03350i	0.929458	+	0.368928i	$0.120275\pi$
$43$	1.19499	+	6.77712i	0.182234	+	1.03350i	−0.747224	+	0.664573i	$0.768614\pi$
$44$	−10.9142	−	1.92447i	−1.64538	−	0.290124i
$45$	2.29709	−	7.20888i	0.342431	−	1.07464i
$46$	0.372480	−	0.215052i	0.0549192	−	0.0317076i
$47$	−0.139535	−	0.0246038i	−0.0203533	−	0.00358883i	0.163462	−	0.986550i	$-0.447734\pi$
$47$	−0.139535	−	0.0246038i	−0.0203533	−	0.00358883i	−0.183816	+	0.982961i	$0.558845\pi$
$48$	6.37920	+	2.17628i	0.920759	+	0.314119i
$49$	−1.79297	+	3.10552i	−0.256139	+	0.443645i
$50$	−0.183264			−0.0259174
$51$	−2.42073	+	7.09574i	−0.338970	+	0.993603i
$52$	−8.25529	+	1.45563i	−1.14480	+	0.201860i
$53$	−4.63584	−	3.88993i	−0.636782	−	0.534324i	0.266246	−	0.963905i	$-0.414217\pi$
$53$	−4.63584	−	3.88993i	−0.636782	−	0.534324i	−0.903028	+	0.429582i	$0.858661\pi$
$54$	−0.507808	+	0.481698i	−0.0691040	+	0.0655508i
$55$	13.2526	+	4.82354i	1.78698	+	0.650406i
$56$	−0.872555	+	1.51131i	−0.116600	+	0.201957i
$57$	4.73294	+	5.88211i	0.626894	+	0.779105i
$58$	−0.414118	−	0.717273i	−0.0543763	−	0.0941825i
$59$	−0.831759	−	4.71714i	−0.108286	−	0.614119i	−0.989857	−	0.142068i	$-0.954625\pi$
$59$	−0.831759	−	4.71714i	−0.108286	−	0.614119i	0.881571	−	0.472051i	$-0.156486\pi$
$60$	−7.58368	−	4.17557i	−0.979049	−	0.539064i
$61$	4.55261	−	1.65702i	0.582903	−	0.212159i	−0.0337024	−	0.999432i	$-0.510730\pi$
$61$	4.55261	−	1.65702i	0.582903	−	0.212159i	0.616605	+	0.787273i	$0.288508\pi$
$62$	−0.575565	−	0.685931i	−0.0730968	−	0.0871134i
$63$	5.21941	+	8.24811i	0.657583	+	1.03916i
$64$	3.78391	−	6.55392i	0.472989	−	0.819240i
$65$	10.6673			1.32312
$66$	−0.858737	−	0.982212i	−0.105703	−	0.120902i
$67$	−2.35074	+	2.80150i	−0.287189	+	0.342258i	−0.890280	−	0.455414i	$-0.849491\pi$
$67$	−2.35074	+	2.80150i	−0.287189	+	0.342258i	0.603091	+	0.797672i	$0.293936\pi$
$68$	7.42928	+	4.28930i	0.900933	+	0.520154i
$69$	−5.46480	−	0.849627i	−0.657885	−	0.102283i
$70$	0.710479	−	0.846716i	0.0849185	−	0.101202i
$71$	4.47532	−	3.75524i	0.531122	−	0.445665i	−0.337366	−	0.941373i	$-0.609536\pi$
$71$	4.47532	−	3.75524i	0.531122	−	0.445665i	0.868489	+	0.495709i	$0.165092\pi$
$72$	0.860428	+	1.35971i	0.101402	+	0.160244i
$73$	−1.71133	−	9.70541i	−0.200296	−	1.13593i	−0.904673	−	0.426107i	$-0.859885\pi$
$73$	−1.71133	−	9.70541i	−0.200296	−	1.13593i	0.704377	−	0.709826i	$-0.251226\pi$
$74$	0.408239	+	0.486520i	0.0474568	+	0.0565568i
$75$	1.83554	+	1.47777i	0.211950	+	0.170639i
$76$	7.65156	−	4.01009i	0.877695	−	0.459989i
$77$	−15.7566	+	9.09710i	−1.79564	+	1.03671i
$78$	−0.864457	−	0.475970i	−0.0978805	−	0.0538930i
$79$	3.30685	−	9.08549i	0.372049	−	1.02220i	−0.602518	−	0.798105i	$-0.705836\pi$
$79$	3.30685	−	9.08549i	0.372049	−	1.02220i	0.974568	−	0.224092i	$-0.0719418\pi$
$80$	−6.30851	+	7.51819i	−0.705312	+	0.840559i
$81$	8.97036	−	0.729820i	0.996707	−	0.0810912i
$82$	−0.138546	+	0.785736i	−0.0152999	+	0.0867700i
$83$	3.95513	−	2.28350i	0.434132	−	0.250646i	−0.266973	−	0.963704i	$-0.586024\pi$
$83$	3.95513	−	2.28350i	0.434132	−	0.250646i	0.701105	+	0.713058i	$0.252690\pi$
$84$	10.4153	−	4.03207i	1.13641	−	0.439935i
$85$	−8.36266	−	7.01710i	−0.907058	−	0.761112i
$86$	0.710101	+	0.595846i	0.0765722	+	0.0642517i
$87$	−1.63610	+	10.5234i	−0.175408	+	1.12822i
$88$	−2.59751	+	1.49967i	−0.276895	+	0.159866i
$89$	2.35153	−	13.3362i	0.249262	−	1.41364i	−0.561120	−	0.827734i	$-0.689629\pi$
$89$	2.35153	−	13.3362i	0.249262	−	1.41364i	0.810382	−	0.585902i	$-0.199259\pi$
$90$	−0.387147	−	0.942759i	−0.0408088	−	0.0993755i
$91$	−8.84589	+	10.5421i	−0.927301	+	1.10511i
$92$	−2.16433	+	5.94645i	−0.225647	+	0.619960i
$93$	0.233655	+	11.5113i	0.0242289	+	1.19367i
$94$	−0.0165286	+	0.00954276i	−0.00170479	+	0.000984261i
$95$	−10.4752	+	3.33470i	−1.07473	+	0.342133i
$96$	2.57939	−	0.998555i	0.263258	−	0.101915i
$97$	2.21552	+	2.64035i	0.224952	+	0.268087i	0.866702	−	0.498827i	$-0.166236\pi$
$97$	2.21552	+	2.64035i	0.224952	+	0.268087i	−0.641750	+	0.766914i	$0.721791\pi$
$98$	0.0838777	+	0.475694i	0.00847293	+	0.0480523i
$99$	0.680755	+	16.7622i	0.0684184	+	1.68467i
$100$	2.06552	−	1.73318i	0.206552	−	0.173318i
$101$	−7.01849	+	8.36431i	−0.698366	+	0.832280i	−0.992340	−	0.123533i	$-0.960577\pi$
$101$	−7.01849	+	8.36431i	−0.698366	+	0.832280i	0.293975	+	0.955813i	$0.405022\pi$
$102$	0.364593	+	0.941789i	0.0361001	+	0.0932510i
$103$	12.9051	+	7.45078i	1.27158	+	0.734147i	0.975285	−	0.220950i	$-0.0709156\pi$
$103$	12.9051	+	7.45078i	1.27158	+	0.734147i	0.296295	+	0.955097i	$0.404249\pi$
$104$	−1.45826	+	1.73789i	−0.142994	+	0.170414i
$105$	−13.9437	+	2.75152i	−1.36076	+	0.268520i
$106$	−0.815169			−0.0791762
$107$	0.768615	−	1.33128i	0.0743048	−	0.128700i	−0.826479	−	0.562968i	$-0.809660\pi$
$107$	0.768615	−	1.33128i	0.0743048	−	0.128700i	0.900784	+	0.434268i	$0.142993\pi$
$108$	1.16783	−	10.2316i	0.112374	−	0.984535i
$109$	5.52240	+	6.58135i	0.528950	+	0.630379i	0.962673	−	0.270668i	$-0.0872446\pi$
$109$	5.52240	+	6.58135i	0.528950	+	0.630379i	−0.433722	+	0.901047i	$0.642800\pi$
$110$	1.78514	−	0.649739i	0.170207	−	0.0619502i
$111$	−0.165728	−	8.16479i	−0.0157302	−	0.774968i
$112$	−2.19861	−	12.4689i	−0.207749	−	1.17820i
$113$	−3.11821	−	5.40090i	−0.293336	−	0.508074i	0.681260	−	0.732041i	$-0.261432\pi$
$113$	−3.11821	−	5.40090i	−0.293336	−	0.508074i	−0.974597	+	0.223968i	$0.928099\pi$
$114$	0.997680	+	0.197160i	0.0934413	+	0.0184658i
$115$	4.02639	−	6.97392i	0.375463	−	0.650321i
$116$	11.4509	+	4.16778i	1.06319	+	0.386969i
$117$	4.82021	+	11.7379i	0.445628	+	1.08517i
$118$	−0.494258	−	0.414732i	−0.0455002	−	0.0381792i
$119$	13.8695	−	2.44556i	1.27141	−	0.224185i
$120$	−2.29863	+	0.453592i	−0.209836	+	0.0414071i
$121$	−20.2706			−1.84278
$122$	0.326301	−	0.565169i	0.0295419	−	0.0511680i
$123$	7.72355	−	6.75261i	0.696409	−	0.608862i
$124$	12.9741	+	2.28768i	1.16511	+	0.205440i
$125$	7.94907	−	4.58940i	0.710987	−	0.410488i
$126$	1.25274	+	0.399181i	0.111603	+	0.0355619i
$127$	4.03172	+	0.710901i	0.357757	+	0.0630822i	0.349638	−	0.936885i	$-0.386305\pi$
$127$	4.03172	+	0.710901i	0.357757	+	0.0630822i	0.00811892	+	0.999967i	$0.497416\pi$
$128$	−0.731618	−	4.14921i	−0.0646665	−	0.366742i
$129$	−2.30757	−	11.6939i	−0.203170	−	1.02959i
$130$	1.10073	−	0.923625i	0.0965407	−	0.0810072i
$131$	−16.7482	+	2.95316i	−1.46330	+	0.258019i	−0.847883	−	0.530183i	$-0.822123\pi$
$131$	−16.7482	+	2.95316i	−1.46330	+	0.258019i	−0.615416	+	0.788202i	$0.711012\pi$
$132$	18.9677	+	2.94896i	1.65093	+	0.256674i
$133$	5.39100	−	13.1175i	0.467459	−	1.13744i
$134$			0.492618i			0.0425557i
$135$	−3.72447	+	12.5643i	−0.320552	+	1.08136i
$136$	2.28641	−	0.403156i	0.196058	−	0.0345703i
$137$	0.142507	+	0.391534i	0.0121752	+	0.0334510i	0.945631	−	0.325240i	$-0.105445\pi$
$137$	0.142507	+	0.391534i	0.0121752	+	0.0334510i	−0.933456	+	0.358691i	$0.883223\pi$
$138$	−0.637463	+	0.385496i	−0.0542645	+	0.0328156i
$139$	1.78161	−	0.648453i	0.151114	−	0.0550011i	−0.265356	−	0.964151i	$-0.585489\pi$
$139$	1.78161	−	0.648453i	0.151114	−	0.0550011i	0.416470	+	0.909150i	$0.363267\pi$
$140$			16.2623i			1.37442i
$141$	0.242497	+	0.0377016i	0.0204219	+	0.00317505i
$142$	0.136651	−	0.774986i	0.0114675	−	0.0650354i
$143$	−22.2261	+	8.08963i	−1.85864	+	0.676489i
$144$	−11.1233	−	3.54442i	−0.926944	−	0.295368i
$145$	−13.4294	−	7.75349i	−1.11525	−	0.643892i
$146$	−1.01693	−	0.853302i	−0.0841614	−	0.0706198i
$147$	2.99572	−	5.44083i	0.247083	−	0.448752i
$148$	−9.20232	−	1.62262i	−0.756426	−	0.133378i
$149$	−4.87697	−	5.81215i	−0.399537	−	0.476150i	0.528342	−	0.849032i	$-0.322814\pi$
$149$	−4.87697	−	5.81215i	−0.399537	−	0.476150i	−0.927879	+	0.372882i	$0.878370\pi$
$150$	0.317357	−	0.00644167i	0.0259121	−	0.000525960i
$151$	−10.9434	−	6.31816i	−0.890559	−	0.514165i	−0.0164340	−	0.999865i	$-0.505231\pi$
$151$	−10.9434	−	6.31816i	−0.890559	−	0.514165i	−0.874125	+	0.485700i	$0.838565\pi$
$152$	0.888716	−	2.16245i	0.0720844	−	0.175398i
$153$	3.94255	−	12.3727i	0.318736	−	1.00028i
$154$	−0.838219	+	2.30299i	−0.0675456	+	0.185580i
$155$	−15.7538	−	5.73392i	−1.26538	−	0.460560i
$156$	14.2445	−	2.81088i	1.14047	−	0.225050i
$157$	15.8179	+	5.75724i	1.26240	+	0.459478i	0.884575	−	0.466398i	$-0.154448\pi$
$157$	15.8179	+	5.75724i	1.26240	+	0.459478i	0.377829	+	0.925875i	$0.376671\pi$
$158$	−0.445438	−	1.22383i	−0.0354371	−	0.0973627i
$159$	8.16459	+	6.57323i	0.647494	+	0.521291i
$160$			4.02742i			0.318395i
$161$	3.55317	+	9.76227i	0.280029	+	0.769374i
$162$	0.862437	−	0.852003i	0.0677595	−	0.0669396i
$163$	−4.08627	−	7.07762i	−0.320061	−	0.554362i	0.660439	−	0.750879i	$-0.270370\pi$
$163$	−4.08627	−	7.07762i	−0.320061	−	0.554362i	−0.980500	+	0.196517i	$0.937037\pi$
$164$	−5.86941	−	10.1661i	−0.458324	−	0.793840i
$165$	−23.1189	−	7.88708i	−1.79981	−	0.614008i
$166$	0.210404	−	0.578081i	0.0163305	−	0.0448678i
$167$	0.222299	−	1.26072i	0.0172020	−	0.0975576i	−0.974998	−	0.222214i	$-0.928672\pi$
$167$	0.222299	−	1.26072i	0.0172020	−	0.0975576i	0.992200	+	0.124656i	$0.0397828\pi$
$168$	1.45788	−	2.64780i	0.112478	−	0.204282i
$169$	−3.74620	+	3.14344i	−0.288169	+	0.241803i
$170$	−1.47049			−0.112782
$171$	−8.40276	−	10.0197i	−0.642575	−	0.766222i
$172$	−13.6385			−1.03992
$173$	−10.0744	+	8.45341i	−0.765941	+	0.642701i	−0.939666	−	0.342093i	$-0.888864\pi$
$173$	−10.0744	+	8.45341i	−0.765941	+	0.642701i	0.173725	+	0.984794i	$0.444420\pi$
$174$	0.742337	+	1.22754i	0.0562764	+	0.0930596i
$175$	0.768669	−	4.35934i	0.0581059	−	0.329535i
$176$	7.44274	−	20.4488i	0.561017	−	1.54138i
$177$	1.60616	+	8.13941i	0.120726	+	0.611795i
$178$	−0.912061	−	1.57974i	−0.0683619	−	0.118406i
$179$	−2.69199	−	4.66266i	−0.201209	−	0.348504i	0.747710	−	0.664026i	$-0.231154\pi$
$179$	−2.69199	−	4.66266i	−0.201209	−	0.348504i	−0.948918	+	0.315522i	$0.897820\pi$
$180$	13.2794	+	6.96425i	0.989787	+	0.519085i
$181$	2.71075	+	7.44773i	0.201489	+	0.553586i	0.998747	−	0.0500533i	$-0.0159391\pi$
$181$	2.71075	+	7.44773i	0.201489	+	0.553586i	−0.797258	+	0.603639i	$0.793717\pi$
$182$			1.85373i			0.137408i
$183$	−7.82549	+	3.02947i	−0.578477	+	0.223945i
$184$	0.585747	+	1.60933i	0.0431818	+	0.118641i
$185$	11.1739	+	4.06698i	0.821524	+	0.299010i
$186$	1.02081	+	1.16759i	0.0748496	+	0.0856120i
$187$	22.7456	+	8.27874i	1.66333	+	0.605401i
$188$	0.0960407	−	0.263870i	0.00700448	−	0.0192447i
$189$	−9.32833	−	14.0997i	−0.678536	−	1.02561i
$190$	−0.792174	+	1.25109i	−0.0574704	+	0.0907635i
$191$	−11.9444	−	6.89608i	−0.864263	−	0.498983i	0.00117451	−	0.999999i	$-0.499626\pi$
$191$	−11.9444	−	6.89608i	−0.864263	−	0.498983i	−0.865438	+	0.501017i	$0.832959\pi$
$192$	−6.32220	+	11.4824i	−0.456266	+	0.828670i
$193$	7.28513	+	8.68208i	0.524395	+	0.624950i	0.961614	−	0.274405i	$-0.0884809\pi$
$193$	7.28513	+	8.68208i	0.524395	+	0.624950i	−0.437219	+	0.899355i	$0.644036\pi$
$194$	0.457227	+	0.0806215i	0.0328270	+	0.00578829i
$195$	−18.4725	+	0.374953i	−1.32285	+	0.0268509i
$196$	−5.44414	−	4.56818i	−0.388867	−	0.326298i
$197$	−4.19971	−	2.42471i	−0.299217	−	0.172753i	0.342874	−	0.939381i	$-0.388600\pi$
$197$	−4.19971	−	2.42471i	−0.299217	−	0.172753i	−0.642091	+	0.766628i	$0.721933\pi$
$198$	1.52159	+	1.67071i	0.108135	+	0.118732i
$199$	7.72995	−	2.81347i	0.547962	−	0.199442i	−0.0531789	−	0.998585i	$-0.516935\pi$
$199$	7.72995	−	2.81347i	0.547962	−	0.199442i	0.601141	+	0.799143i	$0.294713\pi$
$200$	0.126716	−	0.718644i	0.00896020	−	0.0508158i
$201$	3.97229	−	4.93398i	0.280184	−	0.348016i
$202$			1.47078i			0.103484i
$203$	18.7989	−	6.84223i	1.31942	−	0.480230i
$204$	−13.0160	−	7.16661i	−0.911303	−	0.501763i
$205$	5.10917	+	14.0373i	0.356840	+	0.980410i
$206$	1.97677	−	0.348558i	0.137728	−	0.0242852i
$207$	9.49323	+	1.27921i	0.659825	+	0.0889111i
$208$		−	16.4597i		−	1.14127i
$209$	19.2969	−	14.8920i	1.33479	−	1.03010i
$210$	−1.20057	+	1.49123i	−0.0828472	+	0.102904i
$211$	−2.18267	+	0.384864i	−0.150261	+	0.0264951i	−0.248273	−	0.968690i	$-0.579863\pi$
$211$	−2.18267	+	0.384864i	−0.150261	+	0.0264951i	0.0980114	+	0.995185i	$0.468752\pi$
$212$	9.18757	−	7.70929i	0.631005	−	0.529476i
$213$	−7.61788	+	6.66023i	−0.521969	+	0.456351i
$214$	−0.0359569	−	0.203922i	−0.00245796	−	0.0139398i
$215$	17.0919	+	3.01377i	1.16566	+	0.205537i
$216$	−1.53779	−	2.32437i	−0.104633	−	0.158153i
$217$	18.7305	−	10.8141i	1.27151	−	0.734106i
$218$	1.13969	+	0.200957i	0.0771892	+	0.0136105i
$219$	3.30464	+	16.7467i	0.223307	+	1.13163i
$220$	−13.9751	+	24.2057i	−0.942204	+	1.63195i
$221$	18.3085			1.23156
$222$	−0.724046	−	0.828154i	−0.0485948	−	0.0555821i
$223$	−17.4612	+	3.07887i	−1.16929	+	0.206177i	−0.724380	−	0.689401i	$-0.757874\pi$
$223$	−17.4612	+	3.07887i	−1.16929	+	0.206177i	−0.444905	+	0.895578i	$0.646763\pi$
$224$	−3.98015	−	3.33974i	−0.265935	−	0.223146i
$225$	−3.23054	−	2.49454i	−0.215369	−	0.166302i
$226$	−0.789394	−	0.287316i	−0.0525097	−	0.0191120i
$227$	−11.6829	+	20.2354i	−0.775421	+	1.34307i	0.159136	+	0.987257i	$0.449129\pi$
$227$	−11.6829	+	20.2354i	−0.775421	+	1.34307i	−0.934557	+	0.355813i	$0.884204\pi$
$228$	−13.1092	+	7.21320i	−0.868179	+	0.477706i
$229$	−3.85869	−	6.68345i	−0.254989	−	0.441655i	0.709903	−	0.704299i	$-0.248739\pi$
$229$	−3.85869	−	6.68345i	−0.254989	−	0.441655i	−0.964893	+	0.262645i	$0.915405\pi$
$230$	−0.188360	−	1.06824i	−0.0124201	−	0.0704379i
$231$	26.9659	−	16.3072i	1.77423	−	1.07294i
$232$	3.09902	−	1.12795i	0.203461	−	0.0740537i
$233$	12.0936	+	14.4126i	0.792278	+	0.944200i	0.999418	−	0.0341109i	$-0.0108600\pi$
$233$	12.0936	+	14.4126i	0.792278	+	0.944200i	−0.207140	+	0.978311i	$0.566416\pi$
$234$	1.51371	+	0.793849i	0.0989540	+	0.0518955i
$235$	−0.178668	+	0.309463i	−0.0116550	+	0.0201871i
$236$	9.49291			0.617936
$237$	−5.40710	+	15.8495i	−0.351229	+	1.02954i
$238$	1.21941	−	1.45323i	0.0790425	−	0.0941992i
$239$	−2.35071	−	1.35718i	−0.152055	−	0.0877887i	0.422042	−	0.906576i	$-0.361313\pi$
$239$	−2.35071	−	1.35718i	−0.152055	−	0.0877887i	−0.574097	+	0.818787i	$0.694647\pi$
$240$	10.6601	−	13.2409i	0.688109	−	0.854699i
$241$	−12.5086	+	14.9072i	−0.805750	+	0.960255i	−0.999785	−	0.0207393i	$-0.993398\pi$
$241$	−12.5086	+	14.9072i	−0.805750	+	0.960255i	0.194035	+	0.980995i	$0.437842\pi$
$242$	−2.09167	+	1.75512i	−0.134458	+	0.112823i
$243$	−15.5083	+	1.57913i	−0.994856	+	0.101301i
$244$	1.66731	+	9.45581i	0.106739	+	0.605346i
$245$	5.81323	+	6.92793i	0.371393	+	0.442609i
$246$	0.212302	−	1.36552i	0.0135359	−	0.0870626i
$247$	9.86304	−	15.5768i	0.627570	−	0.991128i
$248$	3.08775	−	1.78272i	0.196073	−	0.113203i
$249$	−6.76881	+	4.09334i	−0.428956	+	0.259405i
$250$	0.422873	−	1.16183i	0.0267449	−	0.0734809i
$251$	1.06650	−	1.27100i	0.0673166	−	0.0802248i	−0.731335	−	0.682018i	$-0.761102\pi$
$251$	1.06650	−	1.27100i	0.0673166	−	0.0802248i	0.798652	+	0.601793i	$0.205547\pi$
$252$	−17.8945	+	7.34841i	−1.12724	+	0.462906i
$253$	−3.10055	+	17.5841i	−0.194930	+	1.10550i
$254$	0.477575	−	0.275728i	0.0299657	−	0.0173007i
$255$	14.7282	+	11.8575i	0.922317	+	0.742548i
$256$	11.1598	+	9.36420i	0.697489	+	0.585262i
$257$	8.68951	+	7.29137i	0.542037	+	0.454823i	0.872234	−	0.489089i	$-0.162671\pi$
$257$	8.68951	+	7.29137i	0.542037	+	0.454823i	−0.330197	+	0.943912i	$0.607115\pi$
$258$	−1.25062	−	1.00686i	−0.0778603	−	0.0626845i
$259$	−13.2852	+	7.67024i	−0.825505	+	0.476605i
$260$	−3.67111	+	20.8199i	−0.227673	+	1.29120i
$261$	2.46333	−	18.2808i	0.152476	−	1.13155i
$262$	−1.47251	+	1.75487i	−0.0909719	+	0.108416i
$263$	−1.34452	+	3.69404i	−0.0829066	+	0.227784i	−0.974218	−	0.225607i	$-0.927564\pi$
$263$	−1.34452	+	3.69404i	−0.0829066	+	0.227784i	0.891312	+	0.453391i	$0.149786\pi$
$264$	4.44538	−	2.68828i	0.273594	−	0.165452i
$265$	−13.2176	+	7.63117i	−0.811949	+	0.468779i
$266$	−0.579493	−	1.82034i	−0.0355310	−	0.111612i
$267$	−3.60337	+	23.1769i	−0.220523	+	1.41840i
$268$	−4.65883	−	5.55218i	−0.284583	−	0.339153i
$269$	0.440791	+	2.49985i	0.0268755	+	0.152419i	0.995292	−	0.0969181i	$-0.0308985\pi$
$269$	0.440791	+	2.49985i	0.0268755	+	0.152419i	−0.968417	+	0.249337i	$0.919787\pi$
$270$	0.703557	+	1.61896i	0.0428171	+	0.0985269i
$271$	−2.66821	+	2.23890i	−0.162082	+	0.136003i	−0.720222	−	0.693744i	$-0.755960\pi$
$271$	−2.66821	+	2.23890i	−0.162082	+	0.136003i	0.558139	+	0.829747i	$0.311515\pi$
$272$	−10.8274	+	12.9036i	−0.656508	+	0.782396i
$273$	14.9478	−	18.5667i	0.904683	−	1.12370i
$274$	0.0486056	+	0.0280625i	0.00293637	+	0.00169532i
$275$	4.89035	−	5.82809i	0.294899	−	0.351447i
$276$	3.53894	−	10.3735i	0.213019	−	0.624412i
$277$	−6.95207			−0.417709			−0.208855	−	0.977947i	$-0.566974\pi$
$277$	−6.95207			−0.417709			−0.208855	+	0.977947i	$0.566974\pi$
$278$	0.127694	−	0.221172i	0.00765856	−	0.0132650i
$279$	−0.809239	−	19.9259i	−0.0484478	−	1.19293i
$280$	2.82902	+	3.37150i	0.169067	+	0.201486i
$281$	20.7754	−	7.56162i	1.23936	−	0.451089i	0.362564	−	0.931959i	$-0.381901\pi$
$281$	20.7754	−	7.56162i	1.23936	−	0.451089i	0.876792	+	0.480870i	$0.159679\pi$
$282$	0.0282870	−	0.0171061i	0.00168446	−	0.00101865i
$283$	−1.68623	−	9.56307i	−0.100236	−	0.568466i	−0.993017	−	0.117974i	$-0.962360\pi$
$283$	−1.68623	−	9.56307i	−0.100236	−	0.568466i	0.892781	−	0.450491i	$-0.148751\pi$
$284$	5.78911	+	10.0270i	0.343520	+	0.594995i
$285$	18.0226	−	6.14288i	1.06757	−	0.363873i
$286$	−1.59302	+	2.75918i	−0.0941970	+	0.163154i
$287$	−18.1094	−	6.59127i	−1.06896	−	0.389070i
$288$	−4.43162	+	1.81986i	−0.261136	+	0.107236i
$289$	−1.33023	−	1.11620i	−0.0782490	−	0.0656587i
$290$	−2.05708	+	0.362719i	−0.120796	+	0.0212996i
$291$	−3.92941	−	4.49441i	−0.230346	−	0.263467i
$292$	19.5315			1.14299
$293$	7.50380	−	12.9970i	0.438377	−	0.759291i	−0.559188	−	0.829041i	$-0.688887\pi$
$293$	7.50380	−	12.9970i	0.438377	−	0.759291i	0.997564	+	0.0697501i	$0.0222202\pi$
$294$	−0.161971	−	0.820808i	−0.00944634	−	0.0478705i
$295$	−11.8967	−	2.09770i	−0.692650	−	0.122133i
$296$	−2.19009	+	1.26445i	−0.127297	+	0.0734947i
$297$	−1.76805	−	29.0031i	−0.102592	−	1.68293i
$298$	−1.00648	−	0.177470i	−0.0583040	−	0.0102806i
$299$	2.34520	+	13.3003i	0.135626	+	0.769175i
$300$	−3.51594	+	3.07394i	−0.202993	+	0.177474i
$301$	−17.1519	+	14.3922i	−0.988620	+	0.829550i
$302$	−1.67627	+	0.295572i	−0.0964587	+	0.0170083i
$303$	11.8599	−	14.7311i	0.681332	−	0.846281i
$304$	5.14545	+	16.1632i	0.295112	+	0.927026i
$305$		−	12.2186i		−	0.699635i
$306$	−0.664467	−	1.61807i	−0.0379851	−	0.0924992i
$307$	−23.6620	+	4.17224i	−1.35046	+	0.238122i	−0.801634	−	0.597815i	$-0.796036\pi$
$307$	−23.6620	+	4.17224i	−1.35046	+	0.238122i	−0.548825	+	0.835937i	$0.684925\pi$
$308$	−12.3327	−	33.8837i	−0.702718	−	1.93070i
$309$	−22.6096	−	12.4489i	−1.28622	−	0.708191i
$310$	−2.12207	+	0.772369i	−0.120525	+	0.0438676i
$311$			16.9267i			0.959825i	0.877316	+	0.479912i	$0.159332\pi$
$311$			16.9267i			0.959825i	−0.877316	+	0.479912i	$0.840668\pi$
$312$	2.46417	−	3.06074i	0.139506	−	0.173280i
$313$	1.95010	−	11.0596i	0.110226	−	0.625125i	−0.878777	−	0.477233i	$-0.841640\pi$
$313$	1.95010	−	11.0596i	0.110226	−	0.625125i	0.989003	−	0.147893i	$-0.0472490\pi$
$314$	2.13069	−	0.775509i	0.120242	−	0.0437645i
$315$	24.0494	−	5.25490i	1.35503	−	0.296080i
$316$	16.5945	+	9.58086i	0.933516	+	0.538966i
$317$	−0.731718	−	0.613984i	−0.0410974	−	0.0344848i	0.622008	−	0.783011i	$-0.286317\pi$
$317$	−0.731718	−	0.613984i	−0.0410974	−	0.0344848i	−0.663105	+	0.748526i	$0.730762\pi$
$318$	1.41162	−	0.0286529i	0.0791599	−	0.00160678i
$319$	33.8611	+	5.97062i	1.89586	+	0.334291i
$320$	−12.2683	−	14.6208i	−0.685819	−	0.817327i
$321$	−1.28421	+	2.33239i	−0.0716777	+	0.130181i
$322$	1.21190	+	0.699693i	0.0675368	+	0.0389924i
$323$	−17.9788	+	5.72341i	−1.00037	+	0.318459i
$324$	−1.66269	+	17.7590i	−0.0923714	+	0.986613i
$325$	1.96818	−	5.40753i	0.109175	−	0.299956i
$326$	−1.03446	−	0.376514i	−0.0572936	−	0.0208532i
$327$	−9.79445	−	11.2028i	−0.541634	−	0.619514i
$328$	−2.98536	−	1.08658i	−0.164839	−	0.0599964i
$329$	−0.157670	−	0.433194i	−0.00869261	−	0.0238827i
$330$	−3.06848	+	1.18790i	−0.168914	+	0.0653915i
$331$			0.710114i			0.0390314i	0.999810	+	0.0195157i	$0.00621244\pi$
$331$			0.710114i			0.0390314i	−0.999810	+	0.0195157i	$0.993788\pi$
$332$	3.09566	+	8.50527i	0.169897	+	0.466787i
$333$	0.573980	+	14.1331i	0.0314539	+	0.774489i
$334$	−0.0862205	−	0.149338i	−0.00471778	−	0.00817143i
$335$	4.61162	+	7.98756i	0.251960	+	0.436407i
$336$	4.24560	+	21.5151i	0.231616	+	1.17374i
$337$	−0.997763	+	2.74133i	−0.0543516	+	0.149330i	−0.963897	−	0.266274i	$-0.914207\pi$
$337$	−0.997763	+	2.74133i	−0.0543516	+	0.149330i	0.909546	+	0.415604i	$0.136430\pi$
$338$	−0.114388	+	0.648726i	−0.00622188	+	0.0352860i
$339$	5.58962	+	9.24310i	0.303587	+	0.502016i
$340$	16.5736	−	13.9069i	0.898829	−	0.754207i
$341$	37.1725			2.01301
$342$	−1.73461	−	0.306353i	−0.0937968	−	0.0165657i
$343$	11.1080			0.599775
$344$	−2.82752	+	2.37257i	−0.152450	+	0.127921i
$345$	−6.72735	+	12.2182i	−0.362188	+	0.657807i
$346$	−0.307615	+	1.74457i	−0.0165375	+	0.0937887i
$347$	10.0537	−	27.6224i	0.539712	−	1.48285i	−0.307478	−	0.951555i	$-0.599485\pi$
$347$	10.0537	−	27.6224i	0.539712	−	1.48285i	0.847190	−	0.531291i	$-0.178293\pi$
$348$	−19.9759	−	6.81482i	−1.07082	−	0.365313i
$349$	−8.53800	−	14.7882i	−0.457028	−	0.791597i	0.541774	−	0.840524i	$-0.317753\pi$
$349$	−8.53800	−	14.7882i	−0.457028	−	0.791597i	−0.998802	+	0.0489277i	$0.984420\pi$
$350$	−0.298134	−	0.516384i	−0.0159359	−	0.0276019i
$351$	−8.75970	−	20.1570i	−0.467558	−	1.07590i
$352$	−3.05422	−	8.39140i	−0.162791	−	0.447263i
$353$			16.8199i			0.895235i	0.894225	+	0.447618i	$0.147727\pi$
$353$			16.8199i			0.895235i	−0.894225	+	0.447618i	$0.852273\pi$
$354$	0.870482	+	0.700816i	0.0462656	+	0.0372479i
$355$	−5.03927	−	13.8453i	−0.267457	−	0.734831i
$356$	25.2196	+	9.17920i	1.33664	+	0.486497i
$357$	−23.9318	+	4.72248i	−1.26660	+	0.249940i
$358$	−0.681493	−	0.248043i	−0.0360180	−	0.0131095i
$359$	−5.55151	+	15.2527i	−0.292998	+	0.805004i	0.702627	+	0.711559i	$0.252010\pi$
$359$	−5.55151	+	15.2527i	−0.292998	+	0.805004i	−0.995624	+	0.0934457i	$0.970212\pi$
$360$	3.96459	−	0.866279i	0.208952	−	0.0456569i
$361$	−4.81596	+	18.3795i	−0.253471	+	0.967343i
$362$	0.924574	+	0.533803i	0.0485945	+	0.0280561i
$363$	35.1025	−	0.712506i	1.84240	−	0.0373968i
$364$	−17.5313	−	20.8930i	−0.918888	−	1.09509i
$365$	−24.4771	−	4.31598i	−1.28119	−	0.225909i
$366$	−0.545187	+	0.990169i	−0.0284974	+	0.0517570i
$367$	−9.78337	−	8.20922i	−0.510688	−	0.428518i	0.350683	−	0.936494i	$-0.385949\pi$
$367$	−9.78337	−	8.20922i	−0.510688	−	0.428518i	−0.861371	+	0.507976i	$0.830394\pi$
$368$	−10.7608	−	6.21274i	−0.560944	−	0.323861i
$369$	−13.1375	+	11.9649i	−0.683910	+	0.622870i
$370$	1.50515	−	0.547828i	0.0782488	−	0.0284802i
$371$	3.41908	−	19.3906i	0.177510	−	1.00671i
$372$	−22.5476	−	3.50553i	−1.16904	−	0.181753i
$373$			8.95828i			0.463842i	0.972735	+	0.231921i	$0.0745011\pi$
$373$			8.95828i			0.463842i	−0.972735	+	0.231921i	$0.925499\pi$
$374$	3.06387	−	1.11516i	0.158429	−	0.0576635i
$375$	−13.6040	+	8.22684i	−0.702510	+	0.424832i
$376$	−0.0259921	−	0.0714127i	−0.00134044	−	0.00368283i
$377$	25.6119	−	4.51607i	1.31908	−	0.232589i
$378$	−2.18339	−	0.647226i	−0.112301	−	0.0332897i
$379$		−	13.5552i		−	0.696283i	−0.937442	−	0.348142i	$-0.886813\pi$
$379$		−	13.5552i		−	0.696283i	0.937442	−	0.348142i	$-0.113187\pi$
$380$	−2.90350	−	21.5925i	−0.148946	−	1.10767i
$381$	−7.00669	−	1.08935i	−0.358964	−	0.0558090i
$382$	−1.82960	+	0.322608i	−0.0936105	+	0.0165061i
$383$	−23.1176	+	19.3980i	−1.18125	+	0.991190i	−0.181284	+	0.983431i	$0.558025\pi$
$383$	−23.1176	+	19.3980i	−1.18125	+	0.991190i	−0.999970	+	0.00775906i	$0.997530\pi$
$384$	1.41278	+	7.15945i	0.0720957	+	0.365354i
$385$	7.96800	+	45.1888i	0.406087	+	2.30303i
$386$	1.50347	+	0.265102i	0.0765245	+	0.0134933i
$387$	4.40704	+	20.1691i	0.224022	+	1.02525i
$388$	−5.91576	+	3.41547i	−0.300327	+	0.173394i
$389$	−32.7269	−	5.77063i	−1.65932	−	0.292582i	−0.736104	−	0.676869i	$-0.763336\pi$
$389$	−32.7269	−	5.77063i	−1.65932	−	0.292582i	−0.923214	+	0.384286i	$0.874448\pi$
$390$	−1.87367	+	1.63813i	−0.0948769	+	0.0829497i
$391$	6.91058	−	11.9695i	0.349483	−	0.605322i
$392$	−1.92336			−0.0971446
$393$	28.8990	−	5.70267i	1.45776	−	0.287662i
$394$	−0.643300	+	0.113431i	−0.0324090	+	0.00571458i
$395$	−18.6794	−	15.6739i	−0.939862	−	0.788638i
$396$	−32.9499	−	4.43998i	−1.65579	−	0.223118i
$397$	−7.21012	−	2.62427i	−0.361865	−	0.131708i	0.154688	−	0.987963i	$-0.450563\pi$
$397$	−7.21012	−	2.62427i	−0.361865	−	0.131708i	−0.516553	+	0.856255i	$0.672785\pi$
$398$	0.554030	−	0.959609i	0.0277710	−	0.0481008i
$399$	−8.87449	+	22.9051i	−0.444280	+	1.14669i
$400$	2.64720	+	4.58509i	0.132360	+	0.229254i
$401$	0.731594	+	4.14908i	0.0365341	+	0.207195i	0.997611	−	0.0690872i	$-0.0220087\pi$
$401$	0.731594	+	4.14908i	0.0365341	+	0.207195i	−0.961077	+	0.276282i	$0.910898\pi$
$402$	−0.0173154	−	0.853063i	−0.000863612	−	0.0425469i
$403$	26.4210	−	9.61645i	1.31612	−	0.479029i
$404$	−13.9096	−	16.5769i	−0.692030	−	0.824729i
$405$	6.00802	−	21.8885i	0.298541	−	1.08765i
$406$	1.34738	−	2.33372i	0.0668691	−	0.115821i
$407$	−26.3659			−1.30691
$408$	−3.94519	+	0.778509i	−0.195316	+	0.0385419i
$409$	16.5354	−	19.7061i	0.817622	−	0.974403i	−0.182339	−	0.983236i	$-0.558367\pi$
$409$	16.5354	−	19.7061i	0.817622	−	0.974403i	0.999961	+	0.00883223i	$0.00281142\pi$
$410$	1.74262	+	1.00610i	0.0860617	+	0.0496878i
$411$	−0.260540	−	0.673007i	−0.0128515	−	0.0331970i
$412$	−18.9833	+	22.6234i	−0.935239	+	1.11457i
$413$	11.9384	−	10.0175i	0.587450	−	0.492929i
$414$	1.09034	−	0.689968i	0.0535873	−	0.0339101i
$415$	−2.00008	−	11.3430i	−0.0981799	−	0.556806i
$416$	−4.34167	−	5.17420i	−0.212868	−	0.253686i
$417$	−3.06241	+	1.18555i	−0.149967	+	0.0580564i
$418$	0.701778	−	3.20748i	0.0343251	−	0.156883i
$419$	31.5553	−	18.2185i	1.54158	−	0.890030i	0.542837	−	0.839838i	$-0.317350\pi$
$419$	31.5553	−	18.2185i	1.54158	−	0.890030i	0.998740	−	0.0501919i	$-0.0159833\pi$
$420$	−0.571616	−	28.1614i	−0.0278920	−	1.37414i
$421$	7.85109	−	21.5707i	0.382639	−	1.05129i	−0.587602	−	0.809150i	$-0.699928\pi$
$421$	7.85109	−	21.5707i	0.382639	−	1.05129i	0.970241	−	0.242141i	$-0.0778498\pi$
$422$	−0.191901	+	0.228699i	−0.00934160	+	0.0111329i
$423$	−0.421255	−	0.0567640i	−0.0204821	−	0.00275996i
$424$	0.563642	−	3.19657i	0.0273729	−	0.155239i
$425$	−5.10011	+	2.94455i	−0.247391	+	0.142832i
$426$	−0.209397	+	1.34684i	−0.0101453	+	0.0652547i
$427$	12.0752	+	10.1323i	0.584359	+	0.490336i
$428$	2.33381	+	1.95830i	0.112809	+	0.0946578i
$429$	38.2044	−	14.7900i	1.84453	−	0.714068i
$430$	2.02462	−	1.16891i	0.0976358	−	0.0563701i
$431$	−1.78163	+	10.1041i	−0.0858180	+	0.486698i	0.911359	+	0.411612i	$0.135034\pi$
$431$	−1.78163	+	10.1041i	−0.0858180	+	0.486698i	−0.997177	+	0.0750858i	$0.976077\pi$
$432$	19.3868	+	5.74687i	0.932747	+	0.276497i
$433$	19.5271	−	23.2715i	0.938412	−	1.11836i	−0.0543821	−	0.998520i	$-0.517319\pi$
$433$	19.5271	−	23.2715i	0.938412	−	1.11836i	0.992794	−	0.119835i	$-0.0382367\pi$
$434$	0.996422	−	2.73765i	0.0478298	−	0.131411i
$435$	23.5282	+	12.9546i	1.12809	+	0.621127i
$436$	−14.7456	+	8.51339i	−0.706188	+	0.407718i
$437$	−6.46074	−	12.3276i	−0.309059	−	0.589709i
$438$	1.79100	+	1.44191i	0.0855772	+	0.0688973i
$439$	1.64359	+	1.95875i	0.0784443	+	0.0934862i	0.803839	−	0.594847i	$-0.202787\pi$
$439$	1.64359	+	1.95875i	0.0784443	+	0.0934862i	−0.725395	+	0.688333i	$0.758343\pi$
$440$	1.31354	+	7.44945i	0.0626205	+	0.355138i
$441$	−4.99643	+	9.52715i	−0.237925	+	0.453674i
$442$	1.88921	−	1.58523i	0.0898605	−	0.0754019i
$443$	13.3813	−	15.9472i	0.635764	−	0.757675i	−0.347930	−	0.937520i	$-0.613115\pi$
$443$	13.3813	−	15.9472i	0.635764	−	0.757675i	0.983695	+	0.179846i	$0.0575599\pi$
$444$	15.9926	+	2.48642i	0.758977	+	0.118000i
$445$	−29.5773	−	17.0764i	−1.40210	−	0.809501i
$446$	−1.53519	+	1.82957i	−0.0726933	+	0.0866325i
$447$	8.64972	+	9.89344i	0.409118	+	0.467944i
$448$	24.6227			1.16331
$449$	−18.2631	+	31.6327i	−0.861890	+	1.49284i	0.00821237	+	0.999966i	$0.497386\pi$
$449$	−18.2631	+	31.6327i	−0.861890	+	1.49284i	−0.870102	+	0.492871i	$0.835947\pi$
$450$	−0.549339	+	0.0223100i	−0.0258961	+	0.00105170i
$451$	−21.2906	−	25.3732i	−1.00254	−	1.19478i
$452$	11.6143	−	4.22726i	0.546291	−	0.198834i
$453$	19.1727	+	10.5565i	0.900810	+	0.495986i
$454$	0.546542	+	3.09959i	0.0256505	+	0.145471i
$455$	17.3536	+	30.0574i	0.813550	+	1.40911i
$456$	−1.46297	+	3.77594i	−0.0685101	+	0.176825i
$457$	11.6182	−	20.1233i	0.543477	−	0.941330i	−0.455224	−	0.890377i	$-0.650441\pi$
$457$	11.6182	−	20.1233i	0.543477	−	0.941330i	0.998701	−	0.0509530i	$-0.0162259\pi$
$458$	−0.976852	−	0.355545i	−0.0456453	−	0.0166135i
$459$	−6.39238	+	21.5644i	−0.298371	+	1.00654i
$460$	12.2257	+	10.2585i	0.570024	+	0.478307i
$461$	−11.2368	+	1.98135i	−0.523349	+	0.0922806i	−0.429081	−	0.903266i	$-0.641162\pi$
$461$	−11.2368	+	1.98135i	−0.523349	+	0.0922806i	−0.0942687	+	0.995547i	$0.530051\pi$
$462$	1.37059	−	4.01753i	0.0637656	−	0.186913i
$463$	−33.6219			−1.56254			−0.781272	−	0.624191i	$-0.785429\pi$
$463$	−33.6219			−1.56254			−0.781272	+	0.624191i	$0.785429\pi$
$464$	−11.9637	+	20.7217i	−0.555399	+	0.961979i
$465$	27.4824	+	9.37566i	1.27446	+	0.434786i
$466$	2.49581	+	0.440079i	0.115616	+	0.0203863i
$467$	−24.9139	+	14.3841i	−1.15288	+	0.665615i	−0.949587	−	0.313503i	$-0.898497\pi$
$467$	−24.9139	+	14.3841i	−1.15288	+	0.665615i	−0.203292	+	0.979118i	$0.565164\pi$
$468$	−24.5683	+	5.36827i	−1.13567	+	0.248148i
$469$	−11.7180	−	2.06620i	−0.541087	−	0.0954083i
$470$	0.00835835	+	0.0474026i	0.000385542	+	0.00218652i
$471$	−27.5941	−	9.41378i	−1.27147	−	0.433764i
$472$	1.96807	−	1.65140i	0.0905875	−	0.0760120i
$473$	−37.8977	+	6.68239i	−1.74254	+	0.307257i
$474$	0.814379	+	2.10364i	0.0374057	+	0.0966235i
$475$	−0.242289	+	5.92541i	−0.0111170	+	0.271876i
$476$			27.9114i			1.27931i
$477$	−14.3696	−	11.0958i	−0.657940	−	0.508044i
$478$	−0.360074	+	0.0634908i	−0.0164694	+	0.00290400i
$479$	13.0939	+	35.9753i	0.598277	+	1.64375i	0.754707	+	0.656062i	$0.227779\pi$
$479$	13.0939	+	35.9753i	0.598277	+	1.64375i	−0.156430	+	0.987689i	$0.549999\pi$
$480$	−0.141563	−	6.97426i	−0.00646142	−	0.318330i
$481$	−18.7400	+	6.82079i	−0.854469	+	0.311001i
$482$			2.62128i			0.119396i
$483$	−6.49615	−	16.7804i	−0.295585	−	0.763533i
$484$	6.97604	−	39.5631i	0.317093	−	1.79832i
$485$	8.16846	−	2.97308i	0.370911	−	0.135000i
$486$	−1.46353	+	1.50572i	−0.0663870	+	0.0683009i
$487$	10.4152	+	6.01323i	0.471959	+	0.272486i	0.717059	−	0.697012i	$-0.245488\pi$
$487$	10.4152	+	6.01323i	0.471959	+	0.272486i	−0.245100	+	0.969498i	$0.578821\pi$
$488$	1.99062	+	1.67032i	0.0901109	+	0.0756120i
$489$	7.32494	+	12.1126i	0.331245	+	0.547753i
$490$	1.19970	+	0.211540i	0.0541971	+	0.00955641i
$491$	−17.7421	−	21.1442i	−0.800688	−	0.954222i	0.198980	−	0.980004i	$-0.436237\pi$
$491$	−17.7421	−	21.1442i	−0.800688	−	0.954222i	−0.999668	+	0.0257812i	$0.991793\pi$
$492$	10.5214	+	17.3983i	0.474339	+	0.784376i
$493$	−23.0492	−	13.3075i	−1.03808	−	0.599338i
$494$	−0.330967	−	2.46132i	−0.0148909	−	0.110740i
$495$	40.3122	+	12.8454i	1.81190	+	0.577357i
$496$	−8.84746	+	24.3082i	−0.397263	+	1.09147i
$497$	17.8616	+	6.50109i	0.801202	+	0.291614i
$498$	−0.344036	+	1.00846i	−0.0154166	+	0.0451900i
$499$	39.9561	+	14.5428i	1.78868	+	0.651027i	0.999311	+	0.0371090i	$0.0118149\pi$
$499$	39.9561	+	14.5428i	1.78868	+	0.651027i	0.789370	+	0.613918i	$0.210407\pi$
$500$	6.22171	+	17.0940i	0.278243	+	0.764467i
$501$	−0.340640	+	2.19100i	−0.0152187	+	0.0978866i
$502$		−	0.223493i		−	0.00997499i
$503$	−1.07189	−	2.94500i	−0.0477934	−	0.131311i	0.913499	−	0.406840i	$-0.133369\pi$
$503$	−1.07189	−	2.94500i	−0.0477934	−	0.131311i	−0.961293	+	0.275529i	$0.911147\pi$
$504$	−2.43153	+	4.63642i	−0.108309	+	0.206523i
$505$	13.7687	+	23.8481i	0.612698	+	1.06122i
$506$	1.20257	+	2.08292i	0.0534608	+	0.0925969i
$507$	6.37678	−	5.57515i	0.283203	−	0.247601i
$508$	−2.77500	+	7.62424i	−0.123121	+	0.338271i
$509$	−2.36932	+	13.4371i	−0.105018	+	0.595587i	0.886195	+	0.463312i	$0.153339\pi$
$509$	−2.36932	+	13.4371i	−0.105018	+	0.595587i	−0.991213	+	0.132275i	$0.957772\pi$
$510$	2.54645	−	0.0516874i	0.112758	−	0.00228876i
$511$	24.5630	−	20.6108i	1.08660	−	0.911768i
$512$	10.3888			0.459124
$513$	14.9032	+	17.0556i	0.657993	+	0.753024i
$514$	1.52797			0.0673958
$515$	28.7893	−	24.1571i	1.26861	−	1.06449i
$516$	23.6177	−	0.479388i	1.03971	−	0.0211039i
$517$	0.137585	−	0.780281i	0.00605096	−	0.0343167i
$518$	−0.706746	+	1.94177i	−0.0310526	+	0.0853164i
$519$	17.1486	−	14.9928i	0.752740	−	0.658112i
$520$	2.86077	+	4.95501i	0.125453	+	0.217291i
$521$	12.4453	+	21.5558i	0.545237	+	0.944377i	0.998592	+	0.0530476i	$0.0168935\pi$
$521$	12.4453	+	21.5558i	0.545237	+	0.944377i	−0.453355	+	0.891330i	$0.649773\pi$
$522$	−1.32865	−	2.09963i	−0.0581534	−	0.0918984i
$523$	5.92536	+	16.2798i	0.259098	+	0.711866i	0.999224	+	0.0393974i	$0.0125438\pi$
$523$	5.92536	+	16.2798i	0.259098	+	0.711866i	−0.740126	+	0.672469i	$0.765234\pi$
$524$		−	33.7046i		−	1.47239i
$525$	−1.17787	+	7.57606i	−0.0514065	+	0.330646i
$526$	0.181109	+	0.497593i	0.00789672	+	0.0216961i
$527$	−27.0386	−	9.84124i	−1.17782	−	0.428691i
$528$	−12.1698	+	35.6726i	−0.529622	+	1.55245i
$529$	−12.0325	−	4.37946i	−0.523151	−	0.190412i
$530$	−0.703146	+	1.93188i	−0.0305427	+	0.0839154i
$531$	−3.06747	−	14.0385i	−0.133117	−	0.609219i
$532$	23.7468	+	15.0362i	1.02956	+	0.651903i
$533$	−21.6966	−	12.5265i	−0.939785	−	0.542585i
$534$	1.63494	+	2.70356i	0.0707507	+	0.116995i
$535$	−2.49203	−	2.96988i	−0.107740	−	0.128399i
$536$	−1.93173	−	0.340617i	−0.0834381	−	0.0147124i
$537$	4.82559	+	7.97968i	0.208240	+	0.344348i
$538$	0.261933	+	0.219788i	0.0112927	+	0.00947571i
$539$	−17.3661	−	10.0263i	−0.748011	−	0.431864i
$540$	−23.2406	−	11.5932i	−1.00012	−	0.498891i
$541$	−22.9418	+	8.35015i	−0.986347	+	0.359001i	−0.784305	−	0.620376i	$-0.786980\pi$
$541$	−22.9418	+	8.35015i	−0.986347	+	0.359001i	−0.202042	+	0.979377i	$0.564758\pi$
$542$	−0.0814722	+	0.462052i	−0.00349953	+	0.0198468i
$543$	−4.95598	−	12.8019i	−0.212681	−	0.549383i
$544$			6.91234i			0.296364i
$545$	20.3607	−	7.41069i	0.872157	−	0.317439i
$546$	−0.0651580	−	3.21009i	−0.00278851	−	0.137379i
$547$	12.3945	+	34.0536i	0.529951	+	1.45603i	0.859128	+	0.511761i	$0.171006\pi$
$547$	12.3945	+	34.0536i	0.529951	+	1.45603i	−0.329177	+	0.944268i	$0.606771\pi$
$548$	−0.813217	+	0.143392i	−0.0347389	+	0.00612541i
$549$	13.4449	−	5.52118i	0.573813	−	0.235638i
$550$		−	1.02481i		−	0.0436982i
$551$	−23.7388	+	12.4412i	−1.01131	+	0.530014i
$552$	−1.07090	−	2.76627i	−0.0455806	−	0.117740i
$553$	30.9798	−	5.46258i	1.31740	−	0.232292i
$554$	−0.717366	+	0.601941i	−0.0304780	+	0.0255740i
$555$	−19.4928	−	6.65000i	−0.827423	−	0.282277i
$556$	0.652483	+	3.70041i	0.0276714	+	0.156933i
$557$	28.5484	+	5.03385i	1.20963	+	0.213291i	0.741858	−	0.670557i	$-0.233945\pi$
$557$	28.5484	+	5.03385i	1.20963	+	0.213291i	0.467775	+	0.883848i	$0.345056\pi$
$558$	−1.80878	−	1.98603i	−0.0765716	−	0.0840754i
$559$	−25.2077	+	14.5537i	−1.06617	+	0.615555i
$560$	−31.4467	−	5.54490i	−1.32887	−	0.234315i
$561$	−39.6795	−	13.5367i	−1.67527	−	0.571521i
$562$	1.48904	−	2.57909i	0.0628113	−	0.108792i
$563$	24.4247			1.02938			0.514689	−	0.857377i	$-0.327907\pi$
$563$	24.4247			1.02938			0.514689	+	0.857377i	$0.327907\pi$
$564$	−0.157038	+	0.460317i	−0.00661250	+	0.0193828i
$565$	−15.4893	+	2.73119i	−0.651641	+	0.114902i
$566$	−1.00201	−	0.840787i	−0.0421177	−	0.0353409i
$567$	16.6494	+	24.0885i	0.699210	+	1.01162i
$568$	2.94452	+	1.07172i	0.123549	+	0.0449682i
$569$	−14.7212	+	25.4978i	−0.617144	+	1.06893i	0.372860	+	0.927888i	$0.378377\pi$
$569$	−14.7212	+	25.4978i	−0.617144	+	1.06893i	−0.990004	+	0.141038i	$0.954956\pi$
$570$	1.32783	−	2.19435i	0.0556166	−	0.0919111i
$571$	−1.77107	−	3.06758i	−0.0741170	−	0.128374i	0.826585	−	0.562812i	$-0.190280\pi$
$571$	−1.77107	−	3.06758i	−0.0741170	−	0.128374i	−0.900702	+	0.434438i	$0.856947\pi$
$572$	−8.13991	−	46.1637i	−0.340347	−	1.93020i
$573$	20.9264	+	11.5221i	0.874211	+	0.481341i
$574$	−2.43936	+	0.887854i	−0.101817	+	0.0370583i
$575$	−2.79236	−	3.32781i	−0.116450	−	0.138779i
$576$	10.5445	−	20.1062i	0.439355	−	0.837759i
$577$	12.1224	−	20.9967i	0.504664	−	0.874103i	−0.495322	−	0.868710i	$-0.664950\pi$
$577$	12.1224	−	20.9967i	0.504664	−	0.874103i	0.999985	−	0.00539373i	$-0.00171688\pi$
$578$	−0.233909			−0.00972932
$579$	−12.9208	−	14.7786i	−0.536970	−	0.614179i
$580$	19.7545	−	23.5425i	0.820262	−	0.977551i
$581$	12.8684	+	7.42959i	0.533872	+	0.308231i
$582$	−0.794612	−	0.123540i	−0.0329377	−	0.00512091i
$583$	21.7526	−	25.9237i	0.900899	−	1.07365i
$584$	4.04925	−	3.39773i	0.167559	−	0.140599i
$585$	31.9756	−	1.29861i	1.32203	−	0.0536908i
$586$	−0.351038	−	1.99084i	−0.0145013	−	0.0822407i
$587$	−16.7138	−	19.9187i	−0.689853	−	0.822135i	0.301485	−	0.953471i	$-0.402518\pi$
$587$	−16.7138	−	19.9187i	−0.689853	−	0.822135i	−0.991338	+	0.131336i	$0.958073\pi$
$588$	9.58816	+	7.71933i	0.395409	+	0.318340i
$589$	−22.9389	+	17.7027i	−0.945182	+	0.729426i
$590$	−1.40921	+	0.813610i	−0.0580164	+	0.0334958i
$591$	7.35785	+	4.05123i	0.302661	+	0.166645i
$592$	6.27536	−	17.2414i	0.257916	−	0.708617i
$593$	−1.71132	+	2.03947i	−0.0702756	+	0.0837511i	−0.800037	−	0.599951i	$-0.795187\pi$
$593$	−1.71132	+	2.03947i	−0.0702756	+	0.0837511i	0.729761	+	0.683702i	$0.239631\pi$
$594$	−2.69366	−	2.83967i	−0.110522	−	0.116513i
$595$	6.16773	−	34.9789i	0.252852	−	1.43400i
$596$	13.0222	−	7.51839i	0.533411	−	0.307965i
$597$	−13.2870	+	5.14378i	−0.543801	+	0.210521i
$598$	1.39359	+	1.16936i	0.0569882	+	0.0478188i
$599$	−26.8814	−	22.5562i	−1.09835	−	0.921621i	−0.101033	−	0.994883i	$-0.532215\pi$
$599$	−26.8814	−	22.5562i	−1.09835	−	0.921621i	−0.997313	+	0.0732620i	$0.976659\pi$
$600$	−0.194174	+	1.24893i	−0.00792712	+	0.0509872i
$601$	9.86553	−	5.69586i	0.402423	−	0.232339i	−0.285106	−	0.958496i	$-0.592029\pi$
$601$	9.86553	−	5.69586i	0.402423	−	0.232339i	0.687529	+	0.726157i	$0.258695\pi$
$602$	−0.523723	+	2.97018i	−0.0213453	+	0.121055i
$603$	−6.70537	+	8.68376i	−0.273064	+	0.353630i
$604$	16.0976	−	19.1843i	0.655001	−	0.780599i
$605$	−17.4850	+	48.0395i	−0.710865	+	1.95309i
$606$	−0.0516976	−	2.54695i	−0.00210007	−	0.103463i
$607$	−15.8849	+	9.17116i	−0.644749	+	0.372246i	−0.786441	−	0.617665i	$-0.788079\pi$
$607$	−15.8849	+	9.17116i	−0.644749	+	0.372246i	0.141693	+	0.989911i	$0.454745\pi$
$608$	5.88098	+	3.72377i	0.238505	+	0.151019i
$609$	−32.3134	+	12.5094i	−1.30940	+	0.506907i
$610$	−1.05794	−	1.26081i	−0.0428348	−	0.0510485i
$611$	−0.104066	−	0.590190i	−0.00421008	−	0.0238765i
$612$	22.7917	+	11.9529i	0.921298	+	0.483166i
$613$	−22.9981	+	19.2977i	−0.928884	+	0.779426i	−0.975617	−	0.219481i	$-0.929564\pi$
$613$	−22.9981	+	19.2977i	−0.928884	+	0.779426i	0.0467327	+	0.998907i	$0.485119\pi$
$614$	−2.08036	+	2.47928i	−0.0839567	+	0.100056i
$615$	−9.34093	−	24.1288i	−0.376663	−	0.972966i
$616$	−8.45127	−	4.87934i	−0.340511	−	0.196594i
$617$	7.03442	−	8.38330i	0.283195	−	0.337499i	−0.605629	−	0.795747i	$-0.707078\pi$
$617$	7.03442	−	8.38330i	0.283195	−	0.337499i	0.888824	+	0.458248i	$0.151523\pi$
$618$	−3.41091	+	0.673078i	−0.137207	+	0.0270752i
$619$	−47.4285			−1.90631			−0.953156	−	0.302480i	$-0.902185\pi$
$619$	−47.4285			−1.90631			−0.953156	+	0.302480i	$0.902185\pi$
$620$	16.6128	−	28.7742i	0.667185	−	1.15560i
$621$	−16.4843	−	1.88151i	−0.661493	−	0.0755025i
$622$	1.46559	+	1.74662i	0.0587648	+	0.0700331i
$623$	41.4030	−	15.0695i	1.65878	−	0.603745i
$624$	0.578553	+	28.5032i	0.0231607	+	1.14104i
$625$	−5.20104	−	29.4965i	−0.208042	−	1.17986i
$626$	−0.756363	−	1.31006i	−0.0302304	−	0.0523605i
$627$	−32.8928	+	26.4667i	−1.31361	+	1.05698i
$628$	−16.6803	+	28.8912i	−0.665617	+	1.15288i
$629$	19.1780	+	6.98023i	0.764678	+	0.278320i
$630$	2.02660	−	2.62455i	0.0807419	−	0.104564i
$631$	−17.0532	−	14.3094i	−0.678878	−	0.569646i	0.236800	−	0.971558i	$-0.423901\pi$
$631$	−17.0532	−	14.3094i	−0.678878	−	0.569646i	−0.915678	+	0.401912i	$0.868346\pi$
$632$	5.10707	−	0.900515i	0.203149	−	0.0358206i
$633$	3.76619	−	0.743187i	0.149693	−	0.0295390i
$634$	−0.128666			−0.00510996
$635$	5.16244	−	8.94161i	0.204865	−	0.354837i
$636$	−15.6391	+	13.6731i	−0.620130	+	0.542172i
$637$	−14.9370	−	2.63380i	−0.591826	−	0.104355i
$638$	4.01100	−	2.31575i	0.158797	−	0.0916815i
$639$	12.9577	−	11.8012i	0.512600	−	0.466850i
$640$	−10.4643	−	1.84514i	−0.413639	−	0.0729358i
$641$	7.66945	+	43.4956i	0.302925	+	1.71797i	0.633115	+	0.774058i	$0.281776\pi$
$641$	7.66945	+	43.4956i	0.302925	+	1.71797i	−0.330190	+	0.943915i	$0.607113\pi$
$642$	0.0694341	+	0.351866i	0.00274034	+	0.0138870i
$643$	25.4969	−	21.3944i	1.00550	−	0.843714i	0.0177628	−	0.999842i	$-0.494346\pi$
$643$	25.4969	−	21.3944i	1.00550	−	0.843714i	0.987737	+	0.156128i	$0.0499012\pi$
$644$	−20.2763	+	3.57526i	−0.798997	+	0.140885i
$645$	−29.7039	−	4.61815i	−1.16959	−	0.181840i
$646$	−1.35962	+	2.14727i	−0.0534937	+	0.0844831i
$647$		−	22.4865i		−	0.884037i	−0.897006	−	0.442019i	$-0.854263\pi$
$647$		−	22.4865i		−	0.884037i	0.897006	−	0.442019i	$-0.145737\pi$
$648$	2.74469	+	3.97104i	0.107821	+	0.155997i
$649$	26.3783	−	4.65121i	1.03544	−	0.182576i
$650$	−0.265117	−	0.728403i	−0.0103987	−	0.0285703i
$651$	−32.0554	+	19.3850i	−1.25635	+	0.759759i
$652$	15.2200	−	5.53962i	0.596061	−	0.216948i
$653$			43.4613i			1.70077i	0.526158	+	0.850387i	$0.323632\pi$
$653$			43.4613i			1.70077i	−0.526158	+	0.850387i	$0.676368\pi$
$654$	−1.98065	−	0.307937i	−0.0774495	−	0.0120413i
$655$	−7.44790	+	42.2391i	−0.291014	+	1.65042i
$656$	21.6596	−	7.88346i	0.845666	−	0.307797i
$657$	−6.31126	−	28.8839i	−0.246226	−	1.12687i
$658$	−0.0537774	−	0.0310484i	−0.00209646	−	0.00121039i
$659$	−10.0769	−	8.45551i	−0.392540	−	0.329380i	0.425062	−	0.905164i	$-0.360252\pi$
$659$	−10.0769	−	8.45551i	−0.392540	−	0.329380i	−0.817602	+	0.575784i	$0.804697\pi$
$660$	23.3499	−	42.4080i	0.908892	−	1.65073i
$661$	−19.4264	−	3.42540i	−0.755599	−	0.133233i	−0.217438	−	0.976074i	$-0.569770\pi$
$661$	−19.4264	−	3.42540i	−0.755599	−	0.133233i	−0.538162	+	0.842842i	$0.680881\pi$
$662$	0.0614849	+	0.0732748i	0.00238968	+	0.00284791i
$663$	−31.7048	+	0.643539i	−1.23131	+	0.0249930i
$664$	2.12138	+	1.22478i	0.0823256	+	0.0475307i
$665$	−26.4373	−	24.0911i	−1.02519	−	0.934213i
$666$	1.28293	+	1.40866i	0.0497127	+	0.0545845i
$667$	6.71479	−	18.4487i	0.259998	−	0.714338i
$668$	2.38411	+	0.867744i	0.0922438	+	0.0335740i
$669$	30.1292	−	5.94542i	1.16486	−	0.229863i
$670$	1.16746	+	0.424921i	0.0451029	+	0.0164161i
$671$	9.26606	+	25.4583i	0.357712	+	0.982806i
$672$	7.00979	+	5.64351i	0.270409	+	0.217703i
$673$			33.8762i			1.30583i	0.757430	+	0.652916i	$0.226455\pi$
$673$			33.8762i			1.30583i	−0.757430	+	0.652916i	$0.773545\pi$
$674$	0.134400	+	0.369262i	0.00517690	+	0.0142234i
$675$	5.68199	+	4.20622i	0.218700	+	0.161897i
$676$	−4.84595	−	8.39343i	−0.186383	−	0.322824i
$677$	8.20002	+	14.2028i	0.315152	+	0.545860i	0.979470	−	0.201591i	$-0.0646111\pi$
$677$	8.20002	+	14.2028i	0.315152	+	0.545860i	−0.664318	+	0.747450i	$0.731278\pi$
$678$	1.37709	+	0.469796i	0.0528867	+	0.0180424i
$679$	−3.83552	+	10.5380i	−0.147194	+	0.404412i
$680$	1.01676	−	5.76634i	0.0389910	−	0.221129i
$681$	19.5199	−	35.4521i	0.748006	−	1.35853i
$682$	3.83574	−	3.21857i	0.146878	−	0.123245i
$683$	8.67073			0.331776			0.165888	−	0.986145i	$-0.446951\pi$
$683$	8.67073			0.331776			0.165888	+	0.986145i	$0.446951\pi$
$684$	22.4476	−	12.9518i	0.858306	−	0.495226i
$685$	1.05082			0.0401499
$686$	1.14620	−	0.961780i	0.0437623	−	0.0367209i
$687$	6.91699	+	11.4381i	0.263900	+	0.436389i
$688$	4.65025	−	26.3729i	0.177289	−	1.00546i
$689$	8.75458	−	24.0530i	0.333523	−	0.916347i
$690$	0.363731	+	1.84325i	0.0138470	+	0.0701714i
$691$	−7.27516	−	12.6009i	−0.276760	−	0.479363i	0.693818	−	0.720151i	$-0.255927\pi$
$691$	−7.27516	−	12.6009i	−0.276760	−	0.479363i	−0.970578	+	0.240788i	$0.922594\pi$
$692$	−13.0319	−	22.5718i	−0.495397	−	0.858053i
$693$	−46.1235	+	29.1870i	−1.75209	+	1.10872i
$694$	−1.35425	−	3.72078i	−0.0514067	−	0.141239i
$695$		−	4.78160i		−	0.181376i
$696$	−5.32692	+	2.06220i	−0.201916	+	0.0781674i
$697$	8.76896	+	24.0925i	0.332148	+	0.912570i
$698$	−2.16145	−	0.786702i	−0.0818120	−	0.0297771i
$699$	−21.4490	−	24.5331i	−0.811276	−	0.927928i
$700$	8.24379	+	3.00049i	0.311586	+	0.113408i
$701$	13.4491	−	36.9510i	0.507965	−	1.39562i	−0.375368	−	0.926876i	$-0.622484\pi$
$701$	13.4491	−	36.9510i	0.507965	−	1.39562i	0.883333	−	0.468746i	$-0.155294\pi$
$702$	−2.64918	−	1.32150i	−0.0999868	−	0.0498767i
$703$	16.2702	−	12.5562i	0.613642	−	0.473567i
$704$	36.6496	+	21.1597i	1.38128	+	0.797485i
$705$	0.298521	−	0.542175i	0.0112430	−	0.0204195i
$706$	1.45635	+	1.73561i	0.0548103	+	0.0653204i
$707$	−34.9858	−	6.16895i	−1.31578	−	0.232007i
$708$	−16.4388	+	0.333673i	−0.617808	+	0.0125402i
$709$	24.0739	+	20.2004i	0.904114	+	0.758642i	0.970990	−	0.239120i	$-0.0768588\pi$
$709$	24.0739	+	20.2004i	0.904114	+	0.758642i	−0.0668761	+	0.997761i	$0.521303\pi$
$710$	−1.71878	−	0.992336i	−0.0645045	−	0.0372417i
$711$	8.80633	−	27.6366i	0.330263	−	1.03645i
$712$	6.82535	−	2.48423i	0.255791	−	0.0931003i
$713$	3.68574	−	20.9028i	0.138032	−	0.782818i
$714$	−2.06056	+	2.55942i	−0.0771146	+	0.0957839i
$715$			59.6518i			2.23085i
$716$	10.0268	−	3.64944i	0.374718	−	0.136386i
$717$	4.11841	+	2.26760i	0.153805	+	0.0846849i
$718$	0.747798	+	2.05456i	0.0279076	+	0.0766754i
$719$	−27.1608	+	4.78918i	−1.01293	+	0.178606i	−0.655388	−	0.755292i	$-0.727495\pi$
$719$	−27.1608	+	4.78918i	−1.01293	+	0.178606i	−0.357538	+	0.933898i	$0.616384\pi$
$720$	−17.9947	+	23.3040i	−0.670622	+	0.868487i
$721$			48.4838i			1.80563i
$722$	1.09444	+	2.31352i	0.0407307	+	0.0861004i
$723$	21.1371	−	26.2543i	0.786097	−	0.976409i
$724$	−15.4690	+	2.72760i	−0.574900	+	0.101370i
$725$	−6.40825	+	5.37716i	−0.237996	+	0.199703i
$726$	3.56044	−	3.11285i	0.132140	−	0.115529i
$727$	−7.10634	−	40.3020i	−0.263559	−	1.49472i	−0.773106	−	0.634277i	$-0.781298\pi$
$727$	−7.10634	−	40.3020i	−0.263559	−	1.49472i	0.509547	−	0.860443i	$-0.329813\pi$
$728$	−7.26915	−	1.28175i	−0.269413	−	0.0475047i
$729$	26.8001	−	3.27968i	0.992595	−	0.121470i
$730$	−2.89943	+	1.67399i	−0.107313	+	0.0619570i
$731$	29.3352	+	5.17259i	1.08500	+	0.191315i
$732$	−3.21965	−	16.3160i	−0.119002	−	0.603055i
$733$	10.5580	−	18.2871i	0.389970	−	0.675448i	−0.602475	−	0.798138i	$-0.705819\pi$
$733$	10.5580	−	18.2871i	0.389970	−	0.675448i	0.992445	+	0.122690i	$0.0391521\pi$
$734$	−1.72031			−0.0634979
$735$	−10.3102	−	11.7927i	−0.380299	−	0.434981i
$736$	−5.02148	+	0.885423i	−0.185094	+	0.0326371i
$737$	−15.6660	−	13.1454i	−0.577066	−	0.484216i
$738$	−0.319644	+	2.37213i	−0.0117663	+	0.0873194i
$739$	−7.84938	−	2.85694i	−0.288744	−	0.105094i	0.193587	−	0.981083i	$-0.437988\pi$
$739$	−7.84938	−	2.85694i	−0.288744	−	0.105094i	−0.482331	+	0.875989i	$0.660210\pi$
$740$	−11.7832	+	20.4091i	−0.433158	+	0.750252i
$741$	−16.5323	+	27.3209i	−0.607327	+	1.00366i
$742$	−1.32612	−	2.29690i	−0.0486833	−	0.0843220i
$743$	6.94687	+	39.3976i	0.254856	+	1.44536i	0.796443	+	0.604714i	$0.206713\pi$
$743$	6.94687	+	39.3976i	0.254856	+	1.44536i	−0.541587	+	0.840645i	$0.682176\pi$
$744$	−5.28438	+	3.19565i	−0.193735	+	0.117158i
$745$	−17.9810	+	6.54456i	−0.658774	+	0.239774i
$746$	0.775648	+	0.924382i	0.0283985	+	0.0338440i
$747$	11.5776	−	7.32633i	0.423603	−	0.268056i
$748$	−23.9858	+	41.5446i	−0.877008	+	1.51902i
$749$	5.00154			0.182752
$750$	−0.691449	+	2.02681i	−0.0252481	+	0.0740085i
$751$	−12.8097	+	15.2660i	−0.467432	+	0.557064i	−0.947329	−	0.320261i	$-0.896229\pi$
$751$	−12.8097	+	15.2660i	−0.467432	+	0.557064i	0.479897	+	0.877325i	$0.340674\pi$
$752$	0.477502	+	0.275686i	0.0174127	+	0.0100532i
$753$	−1.80217	+	2.23847i	−0.0656747	+	0.0815744i
$754$	2.25180	−	2.68359i	0.0820058	−	0.0977307i
$755$	−24.4130	+	20.4849i	−0.888480	+	0.745523i
$756$	30.7294	−	13.3542i	1.11762	−	0.485687i
$757$	−0.389864	−	2.21103i	−0.0141699	−	0.0803612i	0.976903	−	0.213684i	$-0.0685464\pi$
$757$	−0.389864	−	2.21103i	−0.0141699	−	0.0803612i	−0.991073	+	0.133323i	$0.957435\pi$
$758$	−1.17367	−	1.39872i	−0.0426296	−	0.0508040i
$759$	4.75113	−	30.5592i	0.172455	−	1.10923i
$760$	−4.35823	−	3.97146i	−0.158090	−	0.144060i
$761$	−17.3649	+	10.0256i	−0.629477	+	0.363429i	−0.780550	−	0.625094i	$-0.785061\pi$
$761$	−17.3649	+	10.0256i	−0.629477	+	0.363429i	0.151072	+	0.988523i	$0.451727\pi$
$762$	−0.817323	+	0.494264i	−0.0296085	+	0.0179053i
$763$	−9.56042	+	26.2670i	−0.346111	+	0.950931i
$764$	17.5700	−	20.9391i	0.635660	−	0.757550i
$765$	−25.9216	−	20.0159i	−0.937196	−	0.723677i
$766$	−0.705881	+	4.00325i	−0.0255045	+	0.144643i
$767$	17.5455	−	10.1299i	0.633533	−	0.365770i
$768$	−19.6545	−	15.8237i	−0.709222	−	0.570987i
$769$	−10.8423	−	9.09779i	−0.390984	−	0.328075i	0.426012	−	0.904717i	$-0.359918\pi$
$769$	−10.8423	−	9.09779i	−0.390984	−	0.328075i	−0.816996	+	0.576643i	$0.804362\pi$
$770$	4.73485	+	3.97301i	0.170632	+	0.143177i
$771$	−15.3039	−	12.3210i	−0.551155	−	0.443729i
$772$	−19.4524	+	11.2308i	−0.700106	+	0.404207i
$773$	−3.71753	+	21.0832i	−0.133710	+	0.758309i	0.842039	+	0.539417i	$0.181355\pi$
$773$	−3.71753	+	21.0832i	−0.133710	+	0.758309i	−0.975749	+	0.218892i	$0.929756\pi$
$774$	2.20109	+	1.69962i	0.0791164	+	0.0610916i
$775$	−5.81334	+	6.92807i	−0.208821	+	0.248864i
$776$	−0.632292	+	1.73721i	−0.0226980	+	0.0623622i
$777$	22.7364	−	13.7495i	0.815662	−	0.493260i
$778$	−3.87665	+	2.23818i	−0.138985	+	0.0802428i
$779$	25.2218	+	5.51838i	0.903663	+	0.197716i
$780$	5.62543	−	36.1827i	0.201423	−	1.29555i
$781$	20.9993	+	25.0260i	0.751415	+	0.895502i
$782$	−0.323286	−	1.83345i	−0.0115607	−	0.0655639i
$783$	−3.62317	+	31.7433i	−0.129481	+	1.13441i
$784$	10.6898	−	8.96982i	0.381779	−	0.320351i
$785$	27.2883	−	32.5209i	0.973961	−	1.16072i
$786$	2.48825	−	3.09065i	0.0887530	−	0.110240i
$787$	0.139304	+	0.0804270i	0.00496564	+	0.00286691i	0.502481	−	0.864588i	$-0.332421\pi$
$787$	0.139304	+	0.0804270i	0.00496564	+	0.00286691i	−0.497515	+	0.867455i	$0.665754\pi$
$788$	6.17773	−	7.36233i	0.220072	−	0.262272i
$789$	2.19845	−	6.44420i	0.0782670	−	0.229420i
$790$	−3.28459			−0.116861
$791$	10.1454	−	17.5724i	0.360730	−	0.624802i
$792$	−7.60354	+	4.81152i	−0.270180	+	0.170970i
$793$	13.1720	+	15.6978i	0.467751	+	0.557444i
$794$	−0.971214	+	0.353493i	−0.0344671	+	0.0125450i
$795$	22.6206	−	13.6794i	0.802269	−	0.485160i
$796$	2.83096	+	16.0551i	0.100341	+	0.569060i
$797$	−25.4455	−	44.0729i	−0.901325	−	1.56114i	−0.825776	−	0.563999i	$-0.809262\pi$
$797$	−25.4455	−	44.0729i	−0.901325	−	1.56114i	−0.0755495	−	0.997142i	$-0.524071\pi$
$798$	1.06749	+	3.13191i	0.0377887	+	0.110868i
$799$	−0.306652	+	0.531137i	−0.0108486	+	0.0187903i
$800$	2.04160	+	0.743082i	0.0721815	+	0.0262719i
$801$	5.42528	−	40.2620i	0.191693	−	1.42259i
$802$	0.434737	+	0.364788i	0.0153511	+	0.0128811i
$803$	54.2728	−	9.56976i	1.91525	−	0.337709i
$804$	8.26282	+	9.45092i	0.291407	+	0.333308i
$805$	26.2006			0.923450
$806$	1.89368	−	3.27994i	0.0667019	−	0.115531i
$807$	−0.851185	−	4.31349i	−0.0299631	−	0.151842i
$808$	−5.76748	−	1.01696i	−0.202899	−	0.0357766i
$809$	20.3468	−	11.7473i	0.715357	−	0.413012i	−0.0976843	−	0.995217i	$-0.531144\pi$
$809$	20.3468	−	11.7473i	0.715357	−	0.413012i	0.813041	+	0.582206i	$0.197810\pi$
$810$	−1.27525	−	2.77882i	−0.0448078	−	0.0976377i
$811$	41.1088	+	7.24859i	1.44352	+	0.254532i	0.839902	−	0.542738i	$-0.182612\pi$
$811$	41.1088	+	7.24859i	1.44352	+	0.254532i	0.603623	+	0.797270i	$0.293723\pi$
$812$	6.88475	+	39.0453i	0.241607	+	1.37022i
$813$	4.54183	−	3.97087i	0.159289	−	0.139265i
$814$	−2.72063	+	2.28288i	−0.0953579	+	0.0800148i
$815$	−20.2981	+	3.57909i	−0.711010	+	0.125370i
$816$	18.2962	−	22.7257i	0.640495	−	0.795558i
$817$	20.2041	−	22.1717i	0.706851	−	0.775690i
$818$		−	3.46513i		−	0.121155i
$819$	−25.2324	+	32.6772i	−0.881693	+	1.14183i
$820$	−29.1556	+	5.14092i	−1.01816	+	0.179529i
$821$	2.29358	+	6.30157i	0.0800467	+	0.219926i	0.973260	−	0.229707i	$-0.0737768\pi$
$821$	2.29358	+	6.30157i	0.0800467	+	0.219926i	−0.893213	+	0.449633i	$0.851555\pi$
$822$	−0.0851565	−	0.0468871i	−0.00297017	−	0.00163538i
$823$	−27.6680	+	10.0703i	−0.964446	+	0.351030i	−0.775774	−	0.631011i	$-0.782640\pi$
$823$	−27.6680	+	10.0703i	−0.964446	+	0.351030i	−0.188672	+	0.982040i	$0.560418\pi$
$824$			7.99263i			0.278437i
$825$	−8.26374	+	10.2644i	−0.287706	+	0.357359i
$826$	0.364532	−	2.06736i	0.0126837	−	0.0719327i
$827$	−14.2722	+	5.19465i	−0.496292	+	0.180636i	−0.578026	−	0.816019i	$-0.696177\pi$
$827$	−14.2722	+	5.19465i	−0.496292	+	0.180636i	0.0817334	+	0.996654i	$0.473954\pi$
$828$	−5.76374	+	18.0881i	−0.200304	+	0.628606i
$829$	−17.8437	−	10.3021i	−0.619738	−	0.357806i	0.157029	−	0.987594i	$-0.449808\pi$
$829$	−17.8437	−	10.3021i	−0.619738	−	0.357806i	−0.776767	+	0.629788i	$0.783142\pi$
$830$	−1.18851	−	0.997279i	−0.0412538	−	0.0346161i
$831$	12.0389	−	0.244363i	0.417623	−	0.00847686i
$832$	31.5233	+	5.55840i	1.09287	+	0.192703i
$833$	9.97735	+	11.8905i	0.345695	+	0.411983i
$834$	−0.213352	+	0.387491i	−0.00738779	+	0.0134177i
$835$	−2.79605	−	1.61430i	−0.0967612	−	0.0558651i
$836$	22.4245	+	42.7876i	0.775567	+	1.47984i
$837$	2.10174	+	34.4771i	0.0726468	+	1.19170i
$838$	1.67867	−	4.61211i	0.0579888	−	0.159323i
$839$	−21.3034	−	7.75381i	−0.735476	−	0.267691i	−0.0529949	−	0.998595i	$-0.516877\pi$
$839$	−21.3034	−	7.75381i	−0.735476	−	0.267691i	−0.682481	+	0.730903i	$0.739099\pi$
$840$	−5.01751	−	5.73897i	−0.173121	−	0.198013i
$841$	−8.27504	−	3.01187i	−0.285346	−	0.103858i
$842$	−1.05755	−	2.90561i	−0.0364457	−	0.100134i
$843$	−35.7108	+	13.8247i	−1.22995	+	0.476147i
$844$		−	4.39247i		−	0.151195i
$845$	4.21828	+	11.5896i	0.145113	+	0.398695i
$846$	−0.0483831	+	0.0306168i	−0.00166345	+	0.00105263i
$847$	−32.9763	−	57.1166i	−1.13308	−	1.96255i
$848$	11.7749	+	20.3947i	0.404352	+	0.700358i
$849$	3.25617	+	16.5010i	0.111751	+	0.566314i
$850$	−0.271314	+	0.745430i	−0.00930601	+	0.0255681i
$851$	−2.61423	+	14.8260i	−0.0896147	+	0.508230i
$852$	−10.3774	−	17.1603i	−0.355524	−	0.587901i
$853$	0.267661	−	0.224595i	0.00916455	−	0.00768997i	−0.638194	−	0.769876i	$-0.720318\pi$
$853$	0.267661	−	0.224595i	0.00916455	−	0.00768997i	0.647358	+	0.762186i	$0.275874\pi$
$854$	2.12331			0.0726580
$855$	−30.9937	+	11.2711i	−1.05996	+	0.385463i
$856$	0.824512			0.0281812
$857$	−18.6042	+	15.6108i	−0.635507	+	0.533254i	−0.902635	−	0.430407i	$-0.858370\pi$
$857$	−18.6042	+	15.6108i	−0.635507	+	0.533254i	0.267127	+	0.963661i	$0.413926\pi$
$858$	2.66163	−	4.83406i	0.0908666	−	0.165032i
$859$	0.784594	−	4.44965i	0.0267700	−	0.151820i	−0.968493	−	0.249042i	$-0.919884\pi$
$859$	0.784594	−	4.44965i	0.0267700	−	0.151820i	0.995263	+	0.0972214i	$0.0309955\pi$
$860$	−11.7642	+	32.3220i	−0.401157	+	1.10217i
$861$	31.5915	+	10.7775i	1.07664	+	0.367297i
$862$	0.691018	+	1.19688i	0.0235362	+	0.0407658i
$863$	−13.2541	−	22.9567i	−0.451174	−	0.781456i	0.547285	−	0.836946i	$-0.315661\pi$
$863$	−13.2541	−	22.9567i	−0.451174	−	0.781456i	−0.998459	+	0.0554900i	$0.982328\pi$
$864$	7.61024	−	3.30720i	0.258906	−	0.112513i
$865$	11.3439	+	31.1671i	0.385704	+	1.05971i
$866$		−	4.09207i		−	0.139054i
$867$	2.34279	+	1.88616i	0.0795653	+	0.0640572i
$868$	14.6603	+	40.2788i	0.497602	+	1.36715i
$869$	50.8062	+	18.4919i	1.72348	+	0.627296i
$870$	3.54949	−	0.700424i	0.120339	−	0.0237466i
$871$	−14.5356	−	5.29052i	−0.492519	−	0.179262i
$872$	−1.57605	+	4.33017i	−0.0533719	+	0.146638i
$873$	6.96251	+	7.64482i	0.235645	+	0.258738i
$874$	−1.73405	−	0.712652i	−0.0586550	−	0.0241058i
$875$	25.8631	+	14.9321i	0.874334	+	0.504797i
$876$	−33.8225	+	0.686525i	−1.14276	+	0.0231955i
$877$	17.3692	+	20.6998i	0.586516	+	0.698983i	0.974932	−	0.222501i	$-0.0714221\pi$
$877$	17.3692	+	20.6998i	0.586516	+	0.698983i	−0.388416	+	0.921484i	$0.626978\pi$
$878$	0.339196	+	0.0598093i	0.0114473	+	0.00201847i
$879$	−12.5375	+	22.7705i	−0.422878	+	0.768031i
$880$	−42.0418	−	35.2772i	−1.41723	−	1.18920i
$881$	15.1297	+	8.73514i	0.509733	+	0.294294i	0.732724	−	0.680526i	$-0.238249\pi$
$881$	15.1297	+	8.73514i	0.509733	+	0.294294i	−0.222991	+	0.974821i	$0.571582\pi$
$882$	0.309335	+	1.41570i	0.0104159	+	0.0476689i
$883$	17.5899	−	6.40220i	0.591947	−	0.215451i	−0.0286383	−	0.999590i	$-0.509117\pi$
$883$	17.5899	−	6.40220i	0.591947	−	0.215451i	0.620586	+	0.784139i	$0.286895\pi$
$884$	−6.30080	+	35.7336i	−0.211919	+	1.20185i
$885$	20.6751	+	3.21441i	0.694986	+	0.108051i
$886$		−	2.80416i		−	0.0942077i
$887$	41.0582	−	14.9440i	1.37860	−	0.501770i	0.456847	−	0.889545i	$-0.348979\pi$
$887$	41.0582	−	14.9440i	1.37860	−	0.501770i	0.921754	+	0.387776i	$0.126756\pi$
$888$	3.74813	−	2.26662i	0.125779	−	0.0760629i
$889$	4.55570	+	12.5167i	0.152793	+	0.419796i
$890$	−4.53056	+	0.798859i	−0.151865	+	0.0267778i
$891$	4.08117	+	50.1624i	0.136724	+	1.68050i
$892$		−	35.1393i		−	1.17655i
$893$	0.286691	+	0.547028i	0.00959374	+	0.0183056i
$894$	1.74916	+	0.271947i	0.0585007	+	0.00909526i
$895$	−13.3721	+	2.35787i	−0.446981	+	0.0788148i
$896$	10.5011	−	8.81143i	0.350815	−	0.294369i
$897$	−4.52866	−	22.9496i	−0.151208	−	0.766264i
$898$	0.854374	+	4.84540i	0.0285108	+	0.161693i
$899$	−40.2519	−	7.09750i	−1.34248	−	0.236715i
$900$	5.98048	−	5.44671i	0.199349	−	0.181557i
$901$	−22.6856	+	13.0975i	−0.755766	+	0.436342i
$902$	−4.39385	−	0.774753i	−0.146299	−	0.0257965i
$903$	29.1960	−	25.5257i	0.971581	−	0.849442i
$904$	1.67249	−	2.89684i	0.0556262	−	0.0963474i
$905$	19.9887			0.664447
$906$	2.89240	−	0.570761i	0.0960937	−	0.0189623i
$907$	18.6623	−	3.29066i	0.619670	−	0.109265i	0.145005	−	0.989431i	$-0.453680\pi$
$907$	18.6623	−	3.29066i	0.619670	−	0.109265i	0.474665	+	0.880166i	$0.342569\pi$
$908$	−35.4737	−	29.7660i	−1.17724	−	0.987819i
$909$	−20.0199	+	25.9267i	−0.664017	+	0.859933i
$910$	4.39318	+	1.59899i	0.145632	+	0.0530058i
$911$	11.2307	−	19.4521i	0.372090	−	0.644478i	−0.617797	−	0.786337i	$-0.711975\pi$
$911$	11.2307	−	19.4521i	0.372090	−	0.644478i	0.989887	+	0.141859i	$0.0453081\pi$
$912$	−9.47848	−	27.8089i	−0.313864	−	0.920846i
$913$	12.7693	+	22.1171i	0.422603	+	0.731970i
$914$	−0.543516	−	3.08243i	−0.0179779	−	0.101958i
$915$	0.429480	+	21.1589i	0.0141982	+	0.699491i
$916$	14.3724	−	5.23111i	0.474876	−	0.172841i
$917$	−35.5672	−	42.3873i	−1.17453	−	1.39975i
$918$	1.20753	+	2.77865i	0.0398544	+	0.0917093i
$919$	2.17988	−	3.77567i	0.0719077	−	0.124548i	−0.827830	−	0.560980i	$-0.810425\pi$
$919$	2.17988	−	3.77567i	0.0719077	−	0.124548i	0.899737	+	0.436432i	$0.143758\pi$
$920$	4.31921			0.142400
$921$	40.8286	−	8.05676i	1.34535	−	0.265479i
$922$	−0.987941	+	1.17738i	−0.0325361	+	0.0387750i
$923$	21.3998	+	12.3552i	0.704383	+	0.406675i
$924$	22.5474	+	58.2427i	0.741755	+	1.91604i
$925$	4.12331	−	4.91397i	0.135574	−	0.161570i
$926$	−3.46936	+	2.91114i	−0.114010	+	0.0956660i
$927$	39.5905	+	20.7629i	1.30032	+	0.681943i
$928$	1.70503	+	9.66970i	0.0559703	+	0.317424i
$929$	1.88095	+	2.24163i	0.0617121	+	0.0735456i	0.796017	−	0.605274i	$-0.206936\pi$
$929$	1.88095	+	2.24163i	0.0617121	+	0.0735456i	−0.734305	+	0.678819i	$0.762492\pi$
$930$	3.64762	−	1.41210i	0.119610	−	0.0463045i
$931$	15.4913	−	2.08308i	0.507708	−	0.0682703i
$932$	−32.2917	+	18.6436i	−1.05775	+	0.610692i
$933$	−0.594968	−	29.3118i	−0.0194784	−	0.959627i
$934$	−1.32537	+	3.64141i	−0.0433673	+	0.119151i
$935$	39.2397	−	46.7641i	1.28328	−	1.52935i
$936$	−4.15961	+	5.38689i	−0.135961	+	0.176076i
$937$	1.22378	−	6.94041i	0.0399792	−	0.226733i	−0.958271	−	0.285860i	$-0.907721\pi$
$937$	1.22378	−	6.94041i	0.0399792	−	0.226733i	0.998250	+	0.0591271i	$0.0188317\pi$
$938$	−1.38805	+	0.801392i	−0.0453215	+	0.0261664i
$939$	−2.98824	+	19.2204i	−0.0975177	+	0.627233i
$940$	−0.542505	−	0.455216i	−0.0176946	−	0.0148475i
$941$	−40.8715	−	34.2952i	−1.33237	−	1.11799i	−0.983517	−	0.180816i	$-0.942126\pi$
$941$	−40.8715	−	34.2952i	−1.33237	−	1.11799i	−0.348855	−	0.937177i	$-0.613429\pi$
$942$	−3.66245	+	1.41784i	−0.119329	+	0.0461957i
$943$	−16.3788	+	9.45633i	−0.533368	+	0.307940i
$944$	−3.23676	+	18.3566i	−0.105348	+	0.597456i
$945$	−41.4615	+	9.94521i	−1.34874	+	0.323518i
$946$	−3.33198	+	3.97090i	−0.108332	+	0.129105i
$947$	−6.48403	+	17.8147i	−0.210703	+	0.578901i	−0.999354	−	0.0359398i	$-0.988558\pi$
$947$	−6.48403	+	17.8147i	−0.210703	+	0.578901i	0.788651	+	0.614841i	$0.210780\pi$
$948$	−29.0734	−	16.0078i	−0.944261	−	0.519910i
$949$	36.0996	−	20.8421i	1.17184	−	0.676563i
$950$	0.488048	+	0.632406i	0.0158344	+	0.0205180i
$951$	1.28869	+	1.03751i	0.0417887	+	0.0336437i
$952$	4.85551	+	5.78657i	0.157368	+	0.187544i
$953$	−4.50116	−	25.5273i	−0.145807	−	0.826912i	−0.966716	−	0.255853i	$-0.917644\pi$
$953$	−4.50116	−	25.5273i	−0.145807	−	0.826912i	0.820909	−	0.571059i	$-0.193467\pi$
$954$	−2.44349	+	0.0992362i	−0.0791110	+	0.00321289i
$955$	−26.6460	+	22.3587i	−0.862245	+	0.723509i
$956$	3.45786	−	4.12092i	0.111835	−	0.133280i
$957$	−58.8469	−	9.14908i	−1.90225	−	0.295748i
$958$	4.46603	+	2.57846i	0.144291	+	0.0833063i
$959$	−0.871396	+	1.03849i	−0.0281388	+	0.0335346i
$960$	21.7589	+	24.8875i	0.702264	+	0.803241i
$961$	−13.1884			−0.425431
$962$	−1.34315	+	2.32641i	−0.0433050	+	0.0750065i
$963$	2.14188	−	4.08412i	0.0690211	−	0.131609i
$964$	−24.7902	−	29.5439i	−0.798440	−	0.951544i
$965$	26.8598	−	9.77615i	0.864646	−	0.314705i
$966$	−2.12324	−	1.16906i	−0.0683142	−	0.0376138i
$967$	−6.59286	−	37.3900i	−0.212012	−	1.20238i	−0.886017	−	0.463654i	$-0.846538\pi$
$967$	−6.59286	−	37.3900i	−0.212012	−	1.20238i	0.674004	−	0.738727i	$-0.264573\pi$
$968$	−5.43619	−	9.41577i	−0.174726	−	0.302634i
$969$	30.9325	−	10.5431i	0.993697	−	0.338694i
$970$	0.585460	−	1.01405i	0.0187980	−	0.0325591i
$971$	44.6559	+	16.2534i	1.43307	+	0.521596i	0.937811	−	0.347146i	$-0.112849\pi$
$971$	44.6559	+	16.2534i	1.43307	+	0.521596i	0.495264	+	0.868743i	$0.335071\pi$
$972$	2.25504	−	30.8117i	0.0723304	−	0.988284i
$973$	4.72548	+	3.96515i	0.151492	+	0.127117i
$974$	1.59537	−	0.281307i	0.0511191	−	0.00901367i
$975$	−3.21821	+	9.43337i	−0.103065	+	0.302110i
$976$	−18.8533			−0.603480
$977$	−22.3582	+	38.7256i	−0.715304	+	1.23894i	0.247538	+	0.968878i	$0.420378\pi$
$977$	−22.3582	+	38.7256i	−0.715304	+	1.23894i	−0.962842	+	0.270064i	$0.912955\pi$
$978$	1.80461	+	0.615646i	0.0577050	+	0.0196862i
$979$	74.5763	+	13.1498i	2.38347	+	0.420270i
$980$	−15.5222	+	8.96173i	−0.495837	+	0.286272i
$981$	17.3548	+	19.0555i	0.554095	+	0.608395i
$982$	−3.66151	−	0.645623i	−0.116844	−	0.0206027i
$983$	−8.20062	−	46.5080i	−0.261559	−	1.48337i	−0.778658	−	0.627449i	$-0.784099\pi$
$983$	−8.20062	−	46.5080i	−0.261559	−	1.48337i	0.517099	−	0.855926i	$-0.327012\pi$
$984$	5.20792	+	1.77669i	0.166022	+	0.0566389i
$985$	−9.36892	+	7.86145i	−0.298519	+	0.250487i
$986$	−3.53061	+	0.622541i	−0.112437	+	0.0198258i
$987$	0.288262	+	0.744617i	0.00917548	+	0.0237014i
$988$	27.0076	+	24.6108i	0.859227	+	0.782975i
$989$			21.9732i			0.698708i
$990$	5.27192	−	2.16493i	0.167553	−	0.0688060i
$991$	44.8459	−	7.90753i	1.42458	−	0.251191i	0.592373	−	0.805664i	$-0.298191\pi$
$991$	44.8459	−	7.90753i	1.42458	−	0.251191i	0.832202	+	0.554472i	$0.187080\pi$
$992$	3.63067	+	9.97517i	0.115274	+	0.316712i
$993$	−0.0249603	−	1.22970i	−0.000792091	−	0.0390234i
$994$	2.40599	−	0.875707i	0.0763132	−	0.0277758i
$995$		−	20.7461i		−	0.657697i
$996$	−5.65970	−	14.6197i	−0.179334	−	0.463243i
$997$	6.34051	−	35.9588i	0.200806	−	1.13883i	−0.703099	−	0.711092i	$-0.748201\pi$
$997$	6.34051	−	35.9588i	0.200806	−	1.13883i	0.903904	−	0.427734i	$-0.140688\pi$
$998$	5.38215	−	1.95894i	0.170369	−	0.0620093i
$999$	−1.49073	−	24.4540i	−0.0471646	−	0.773691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.110.10	yes	108
3.2	odd	2		513.2.bo.a.224.9		108
9.4	even	3		513.2.cd.a.395.10		108
9.5	odd	6		171.2.bd.a.167.9	yes	108
19.14	odd	18		171.2.bd.a.128.9	yes	108
57.14	even	18		513.2.cd.a.413.10		108
171.14	even	18	inner	171.2.x.a.14.10	✓	108
171.166	odd	18		513.2.bo.a.71.9		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.10	✓	108	171.14	even	18	inner
171.2.x.a.110.10	yes	108	1.1	even	1	trivial
171.2.bd.a.128.9	yes	108	19.14	odd	18
171.2.bd.a.167.9	yes	108	9.5	odd	6
513.2.bo.a.71.9		108	171.166	odd	18
513.2.bo.a.224.9		108	3.2	odd	2
513.2.cd.a.395.10		108	9.4	even	3
513.2.cd.a.413.10		108	57.14	even	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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.103187 - 0.0865845i) q^{2} +(-1.73169 + 0.0351497i) q^{3} +(-0.344146 + 1.95175i) q^{4} +(0.862577 - 2.36991i) q^{5} +(-0.175646 + 0.153565i) q^{6} +(1.62680 + 2.81770i) q^{7} +(0.268181 + 0.464503i) q^{8} +(2.99753 - 0.121737i) q^{9} +O(q^{10})\)	\(q+(0.103187 - 0.0865845i) q^{2} +(-1.73169 + 0.0351497i) q^{3} +(-0.344146 + 1.95175i) q^{4} +(0.862577 - 2.36991i) q^{5} +(-0.175646 + 0.153565i) q^{6} +(1.62680 + 2.81770i) q^{7} +(0.268181 + 0.464503i) q^{8} +(2.99753 - 0.121737i) q^{9} +(-0.116191 - 0.319231i) q^{10} +5.59201i q^{11} +(0.527352 - 3.39192i) q^{12} +(1.44664 + 3.97461i) q^{13} +(0.411835 + 0.149896i) q^{14} +(-1.41042 + 4.13428i) q^{15} +(-3.65678 - 1.33096i) q^{16} +(1.48046 - 4.06752i) q^{17} +(0.298767 - 0.272101i) q^{18} +(-2.66309 - 3.45079i) q^{19} +(4.32861 + 2.49913i) q^{20} +(-2.91617 - 4.82222i) q^{21} +(0.484182 + 0.577025i) q^{22} +(3.14450 + 0.554460i) q^{23} +(-0.480735 - 0.794951i) q^{24} +(-1.04222 - 0.874524i) q^{25} +(0.493415 + 0.284873i) q^{26} +(-5.18652 + 0.316173i) q^{27} +(-6.05930 + 2.20541i) q^{28} +(1.06770 - 6.05526i) q^{29} +(0.212427 + 0.548726i) q^{30} -6.64743i q^{31} +(-1.50061 + 0.546176i) q^{32} +(-0.196557 - 9.68366i) q^{33} +(-0.199420 - 0.547902i) q^{34} +(8.08095 - 1.42489i) q^{35} +(-0.793987 + 5.89231i) q^{36} +4.71492i q^{37} +(-0.573582 - 0.125497i) q^{38} +(-2.64485 - 6.83196i) q^{39} +(1.33216 - 0.234896i) q^{40} +(-4.53739 + 3.80732i) q^{41} +(-0.718441 - 0.245098i) q^{42} +(1.19499 + 6.77712i) q^{43} +(-10.9142 - 1.92447i) q^{44} +(2.29709 - 7.20888i) q^{45} +(0.372480 - 0.215052i) q^{46} +(-0.139535 - 0.0246038i) q^{47} +(6.37920 + 2.17628i) q^{48} +(-1.79297 + 3.10552i) q^{49} -0.183264 q^{50} +(-2.42073 + 7.09574i) q^{51} +(-8.25529 + 1.45563i) q^{52} +(-4.63584 - 3.88993i) q^{53} +(-0.507808 + 0.481698i) q^{54} +(13.2526 + 4.82354i) q^{55} +(-0.872555 + 1.51131i) q^{56} +(4.73294 + 5.88211i) q^{57} +(-0.414118 - 0.717273i) q^{58} +(-0.831759 - 4.71714i) q^{59} +(-7.58368 - 4.17557i) q^{60} +(4.55261 - 1.65702i) q^{61} +(-0.575565 - 0.685931i) q^{62} +(5.21941 + 8.24811i) q^{63} +(3.78391 - 6.55392i) q^{64} +10.6673 q^{65} +(-0.858737 - 0.982212i) q^{66} +(-2.35074 + 2.80150i) q^{67} +(7.42928 + 4.28930i) q^{68} +(-5.46480 - 0.849627i) q^{69} +(0.710479 - 0.846716i) q^{70} +(4.47532 - 3.75524i) q^{71} +(0.860428 + 1.35971i) q^{72} +(-1.71133 - 9.70541i) q^{73} +(0.408239 + 0.486520i) q^{74} +(1.83554 + 1.47777i) q^{75} +(7.65156 - 4.01009i) q^{76} +(-15.7566 + 9.09710i) q^{77} +(-0.864457 - 0.475970i) q^{78} +(3.30685 - 9.08549i) q^{79} +(-6.30851 + 7.51819i) q^{80} +(8.97036 - 0.729820i) q^{81} +(-0.138546 + 0.785736i) q^{82} +(3.95513 - 2.28350i) q^{83} +(10.4153 - 4.03207i) q^{84} +(-8.36266 - 7.01710i) q^{85} +(0.710101 + 0.595846i) q^{86} +(-1.63610 + 10.5234i) q^{87} +(-2.59751 + 1.49967i) q^{88} +(2.35153 - 13.3362i) q^{89} +(-0.387147 - 0.942759i) q^{90} +(-8.84589 + 10.5421i) q^{91} +(-2.16433 + 5.94645i) q^{92} +(0.233655 + 11.5113i) q^{93} +(-0.0165286 + 0.00954276i) q^{94} +(-10.4752 + 3.33470i) q^{95} +(2.57939 - 0.998555i) q^{96} +(2.21552 + 2.64035i) q^{97} +(0.0838777 + 0.475694i) q^{98} +(0.680755 + 16.7622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

L-functions

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