LMFDB - Embedded newform 324.2.p.a.83.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			83.48
Character	$\chi$	$=$	324.83
Dual form			324.2.p.a.203.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38565 + 0.282806i) q^{2} +(-1.57425 - 0.722316i) q^{3} +(1.84004 + 0.783738i) q^{4} +(-0.187018 - 0.789092i) q^{5} +(-1.97708 - 1.44608i) q^{6} +(1.71428 - 1.27624i) q^{7} +(2.32801 + 1.60636i) q^{8} +(1.95652 + 2.27421i) q^{9} +O(q^{10})$	\(q+(1.38565 + 0.282806i) q^{2} +(-1.57425 - 0.722316i) q^{3} +(1.84004 + 0.783738i) q^{4} +(-0.187018 - 0.789092i) q^{5} +(-1.97708 - 1.44608i) q^{6} +(1.71428 - 1.27624i) q^{7} +(2.32801 + 1.60636i) q^{8} +(1.95652 + 2.27421i) q^{9} +(-0.0359818 - 1.14629i) q^{10} +(2.24280 - 2.37723i) q^{11} +(-2.33058 - 2.56289i) q^{12} +(-3.56685 - 1.79134i) q^{13} +(2.73632 - 1.28361i) q^{14} +(-0.275560 + 1.37731i) q^{15} +(2.77151 + 2.88422i) q^{16} +(1.53626 - 4.22084i) q^{17} +(2.06789 + 3.70457i) q^{18} +(2.53116 + 6.95430i) q^{19} +(0.274320 - 1.59854i) q^{20} +(-3.62056 + 0.770860i) q^{21} +(3.78003 - 2.65973i) q^{22} +(2.00970 - 2.69949i) q^{23} +(-2.50456 - 4.21037i) q^{24} +(3.88047 - 1.94885i) q^{25} +(-4.43580 - 3.49089i) q^{26} +(-1.43735 - 4.99340i) q^{27} +(4.15459 - 1.00478i) q^{28} +(-3.77265 + 5.73604i) q^{29} +(-0.771342 + 1.83054i) q^{30} +(-3.39428 + 1.46415i) q^{31} +(3.02466 + 4.78032i) q^{32} +(-5.24784 + 2.12234i) q^{33} +(3.32239 - 5.41413i) q^{34} +(-1.32767 - 1.11405i) q^{35} +(1.81769 + 5.71804i) q^{36} +(-6.90854 + 5.79695i) q^{37} +(1.54058 + 10.3520i) q^{38} +(4.32120 + 5.39641i) q^{39} +(0.832186 - 2.13743i) q^{40} +(-6.86170 + 0.399649i) q^{41} +(-5.23482 + 0.0442268i) q^{42} +(-9.84330 + 2.94689i) q^{43} +(5.98998 - 2.61644i) q^{44} +(1.42866 - 1.96919i) q^{45} +(3.54816 - 3.17219i) q^{46} +(0.646240 - 1.49815i) q^{47} +(-2.27972 - 6.54239i) q^{48} +(-0.697634 + 2.33026i) q^{49} +(5.92812 - 1.60300i) q^{50} +(-5.46723 + 5.53498i) q^{51} +(-5.15921 - 6.09162i) q^{52} +(0.992359 - 0.572939i) q^{53} +(-0.579498 - 7.32558i) q^{54} +(-2.29530 - 1.32519i) q^{55} +(6.04096 - 0.217329i) q^{56} +(1.03853 - 12.7761i) q^{57} +(-6.84975 + 6.88121i) q^{58} +(-3.20784 - 3.40011i) q^{59} +(-1.58650 + 2.31835i) q^{60} +(3.21966 - 0.376324i) q^{61} +(-5.11735 + 1.06887i) q^{62} +(6.25646 + 1.40166i) q^{63} +(2.83922 + 7.47923i) q^{64} +(-0.746466 + 3.14959i) q^{65} +(-7.87187 + 1.45670i) q^{66} +(5.13628 + 7.80933i) q^{67} +(6.13481 - 6.56249i) q^{68} +(-5.11365 + 2.79803i) q^{69} +(-1.52463 - 1.91915i) q^{70} +(-0.409541 - 2.32262i) q^{71} +(0.901585 + 8.43725i) q^{72} +(0.538577 - 3.05442i) q^{73} +(-11.2122 + 6.07876i) q^{74} +(-7.51651 + 0.265042i) q^{75} +(-0.792915 + 14.7800i) q^{76} +(0.810889 - 6.93760i) q^{77} +(4.46152 + 8.69958i) q^{78} +(3.28438 + 0.191293i) q^{79} +(1.75759 - 2.72638i) q^{80} +(-1.34407 + 8.89907i) q^{81} +(-9.62093 - 1.38676i) q^{82} +(0.0672270 - 1.15424i) q^{83} +(-7.26613 - 1.41915i) q^{84} +(-3.61793 - 0.422876i) q^{85} +(-14.4727 + 1.29961i) q^{86} +(10.0823 - 6.30491i) q^{87} +(9.03995 - 1.93146i) q^{88} +(0.349419 + 0.0616119i) q^{89} +(2.53651 - 2.32457i) q^{90} +(-8.40077 + 1.48128i) q^{91} +(5.81362 - 3.39210i) q^{92} +(6.40102 + 0.146807i) q^{93} +(1.31915 - 1.89315i) q^{94} +(5.01421 - 3.29790i) q^{95} +(-1.30867 - 9.71017i) q^{96} +(16.8774 + 4.00002i) q^{97} +(-1.62569 + 3.03163i) q^{98} +(9.79441 + 0.449506i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{1}{54}\right)$

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 $

$2$	1.38565	+	0.282806i	0.979801	+	0.199974i
$2$	1.38565	+	0.282806i	0.979801	+	0.199974i
$3$	−1.57425	−	0.722316i	−0.908893	−	0.417029i
$3$	−1.57425	−	0.722316i	−0.908893	−	0.417029i
$4$	1.84004	+	0.783738i	0.920021	+	0.391869i
$5$	−0.187018	−	0.789092i	−0.0836371	−	0.352893i	0.915095	−	0.403239i	$-0.132116\pi$
$5$	−0.187018	−	0.789092i	−0.0836371	−	0.352893i	−0.998732	+	0.0503464i	$0.983967\pi$
$6$	−1.97708	−	1.44608i	−0.807140	−	0.590361i
$7$	1.71428	−	1.27624i	0.647939	−	0.482372i	−0.222316	−	0.974975i	$-0.571362\pi$
$7$	1.71428	−	1.27624i	0.647939	−	0.482372i	0.870255	+	0.492602i	$0.163954\pi$
$8$	2.32801	+	1.60636i	0.823074	+	0.567934i
$9$	1.95652	+	2.27421i	0.652173	+	0.758070i
$10$	−0.0359818	−	1.14629i	−0.0113784	−	0.362490i
$11$	2.24280	−	2.37723i	0.676231	−	0.716762i	−0.294842	−	0.955546i	$-0.595267\pi$
$11$	2.24280	−	2.37723i	0.676231	−	0.716762i	0.971073	+	0.238783i	$0.0767486\pi$
$12$	−2.33058	−	2.56289i	−0.672780	−	0.739843i
$13$	−3.56685	−	1.79134i	−0.989267	−	0.496828i	−0.120854	−	0.992670i	$-0.538563\pi$
$13$	−3.56685	−	1.79134i	−0.989267	−	0.496828i	−0.868413	+	0.495842i	$0.834860\pi$
$14$	2.73632	−	1.28361i	0.731313	−	0.343058i
$15$	−0.275560	+	1.37731i	−0.0711494	+	0.355621i
$16$	2.77151	+	2.88422i	0.692877	+	0.721056i
$17$	1.53626	−	4.22084i	0.372597	−	1.02370i	−0.601756	−	0.798680i	$-0.705532\pi$
$17$	1.53626	−	4.22084i	0.372597	−	1.02370i	0.974353	−	0.225023i	$-0.0722458\pi$
$18$	2.06789	+	3.70457i	0.487406	+	0.873176i
$19$	2.53116	+	6.95430i	0.580687	+	1.59543i	0.787009	+	0.616941i	$0.211628\pi$
$19$	2.53116	+	6.95430i	0.580687	+	1.59543i	−0.206322	+	0.978484i	$0.566149\pi$
$20$	0.274320	−	1.59854i	0.0613399	−	0.357443i
$21$	−3.62056	+	0.770860i	−0.790070	+	0.168215i
$22$	3.78003	−	2.65973i	0.805905	−	0.567056i
$23$	2.00970	−	2.69949i	0.419050	−	0.562882i	−0.541602	−	0.840635i	$-0.682182\pi$
$23$	2.00970	−	2.69949i	0.419050	−	0.562882i	0.960653	+	0.277752i	$0.0895895\pi$
$24$	−2.50456	−	4.21037i	−0.511241	−	0.859437i
$25$	3.88047	−	1.94885i	0.776095	−	0.389769i
$26$	−4.43580	−	3.49089i	−0.869932	−	0.684620i
$27$	−1.43735	−	4.99340i	−0.276618	−	0.960980i
$28$	4.15459	−	1.00478i	0.785144	−	0.189886i
$29$	−3.77265	+	5.73604i	−0.700564	+	1.06516i	0.293458	+	0.955972i	$0.405194\pi$
$29$	−3.77265	+	5.73604i	−0.700564	+	1.06516i	−0.994022	+	0.109184i	$0.965176\pi$
$30$	−0.771342	+	1.83054i	−0.140827	+	0.334210i
$31$	−3.39428	+	1.46415i	−0.609631	+	0.262969i	−0.678434	−	0.734661i	$-0.737341\pi$
$31$	−3.39428	+	1.46415i	−0.609631	+	0.262969i	0.0688034	+	0.997630i	$0.478082\pi$
$32$	3.02466	+	4.78032i	0.534690	+	0.845049i
$33$	−5.24784	+	2.12234i	−0.913532	+	0.369452i
$34$	3.32239	−	5.41413i	0.569785	−	0.928516i
$35$	−1.32767	−	1.11405i	−0.224417	−	0.188308i
$36$	1.81769	+	5.71804i	0.302948	+	0.953007i
$37$	−6.90854	+	5.79695i	−1.13576	+	0.953013i	−0.999292	−	0.0376316i	$-0.988019\pi$
$37$	−6.90854	+	5.79695i	−1.13576	+	0.953013i	−0.136465	+	0.990645i	$0.543574\pi$
$38$	1.54058	+	10.3520i	0.249915	+	1.67932i
$39$	4.32120	+	5.39641i	0.691945	+	0.864117i
$40$	0.832186	−	2.13743i	0.131580	−	0.337957i
$41$	−6.86170	+	0.399649i	−1.07162	+	0.0624146i	−0.584869	−	0.811128i	$-0.698854\pi$
$41$	−6.86170	+	0.399649i	−1.07162	+	0.0624146i	−0.486748	+	0.873542i	$0.661817\pi$
$42$	−5.23482	+	0.0442268i	−0.807750	+	0.00682435i
$43$	−9.84330	+	2.94689i	−1.50109	+	0.449396i	−0.928777	−	0.370640i	$-0.879139\pi$
$43$	−9.84330	+	2.94689i	−1.50109	+	0.449396i	−0.572312	+	0.820036i	$0.693953\pi$
$44$	5.98998	−	2.61644i	0.903023	−	0.394443i
$45$	1.42866	−	1.96919i	0.212971	−	0.293550i
$46$	3.54816	−	3.17219i	0.523148	−	0.467714i
$47$	0.646240	−	1.49815i	0.0942638	−	0.218528i	−0.864560	−	0.502530i	$-0.832403\pi$
$47$	0.646240	−	1.49815i	0.0942638	−	0.218528i	0.958824	+	0.284001i	$0.0916621\pi$
$48$	−2.27972	−	6.54239i	−0.329050	−	0.944313i
$49$	−0.697634	+	2.33026i	−0.0996620	+	0.332894i
$50$	5.92812	−	1.60300i	0.838362	−	0.226698i
$51$	−5.46723	+	5.53498i	−0.765565	+	0.775052i
$52$	−5.15921	−	6.09162i	−0.715454	−	0.844756i
$53$	0.992359	−	0.572939i	0.136311	−	0.0786992i	−0.430294	−	0.902689i	$-0.641590\pi$
$53$	0.992359	−	0.572939i	0.136311	−	0.0786992i	0.566605	+	0.823990i	$0.308257\pi$
$54$	−0.579498	−	7.32558i	−0.0788597	−	0.996886i
$55$	−2.29530	−	1.32519i	−0.309498	−	0.178689i
$56$	6.04096	−	0.217329i	0.807257	−	0.0290418i
$57$	1.03853	−	12.7761i	0.137557	−	1.69223i
$58$	−6.84975	+	6.88121i	−0.899417	+	0.903547i
$59$	−3.20784	−	3.40011i	−0.417625	−	0.442657i	0.484070	−	0.875029i	$-0.339158\pi$
$59$	−3.20784	−	3.40011i	−0.417625	−	0.442657i	−0.901695	+	0.432372i	$0.857677\pi$
$60$	−1.58650	+	2.31835i	−0.204816	+	0.299297i
$61$	3.21966	−	0.376324i	0.412235	−	0.0481833i	0.0925518	−	0.995708i	$-0.470498\pi$
$61$	3.21966	−	0.376324i	0.412235	−	0.0481833i	0.319683	+	0.947525i	$0.396424\pi$
$62$	−5.11735	+	1.06887i	−0.649904	+	0.135747i
$63$	6.25646	+	1.40166i	0.788240	+	0.176593i
$64$	2.83922	+	7.47923i	0.354902	+	0.934904i
$65$	−0.746466	+	3.14959i	−0.0925877	+	0.390658i
$66$	−7.87187	+	1.45670i	−0.968961	+	0.179307i
$67$	5.13628	+	7.80933i	0.627496	+	0.954062i	0.999665	+	0.0258966i	$0.00824405\pi$
$67$	5.13628	+	7.80933i	0.627496	+	0.954062i	−0.372168	+	0.928165i	$0.621386\pi$
$68$	6.13481	−	6.56249i	0.743955	−	0.795819i
$69$	−5.11365	+	2.79803i	−0.615611	+	0.336844i
$70$	−1.52463	−	1.91915i	−0.182228	−	0.229382i
$71$	−0.409541	−	2.32262i	−0.0486035	−	0.275644i	0.950814	−	0.309761i	$-0.100249\pi$
$71$	−0.409541	−	2.32262i	−0.0486035	−	0.275644i	−0.999418	+	0.0341171i	$0.989138\pi$
$72$	0.901585	+	8.43725i	0.106253	+	0.994339i
$73$	0.538577	−	3.05442i	0.0630357	−	0.357493i	−0.936932	−	0.349511i	$-0.886348\pi$
$73$	0.538577	−	3.05442i	0.0630357	−	0.357493i	0.999968	−	0.00798267i	$-0.00254099\pi$
$74$	−11.2122	+	6.07876i	−1.30339	+	0.706642i
$75$	−7.51651	+	0.265042i	−0.867932	+	0.0306044i
$76$	−0.792915	+	14.7800i	−0.0909536	+	1.69538i
$77$	0.810889	−	6.93760i	0.0924094	−	0.790613i
$78$	4.46152	+	8.69958i	0.505168	+	0.985034i
$79$	3.28438	+	0.191293i	0.369521	+	0.0215222i	0.241901	−	0.970301i	$-0.422229\pi$
$79$	3.28438	+	0.191293i	0.369521	+	0.0215222i	0.127620	+	0.991823i	$0.459266\pi$
$80$	1.75759	−	2.72638i	0.196505	−	0.304818i
$81$	−1.34407	+	8.89907i	−0.149341	+	0.988786i
$82$	−9.62093	−	1.38676i	−1.06245	−	0.153142i
$83$	0.0672270	−	1.15424i	0.00737912	−	0.126695i	−0.992607	−	0.121375i	$-0.961270\pi$
$83$	0.0672270	−	1.15424i	0.00737912	−	0.126695i	0.999986	−	0.00531966i	$-0.00169331\pi$
$84$	−7.26613	−	1.41915i	−0.792800	−	0.154842i
$85$	−3.61793	−	0.422876i	−0.392420	−	0.0458673i
$86$	−14.4727	+	1.29961i	−1.56064	+	0.140141i
$87$	10.0823	−	6.30491i	1.08094	−	0.675957i
$88$	9.03995	−	1.93146i	0.963662	−	0.205894i
$89$	0.349419	+	0.0616119i	0.0370383	+	0.00653085i	0.192137	−	0.981368i	$-0.438458\pi$
$89$	0.349419	+	0.0616119i	0.0370383	+	0.00653085i	−0.155098	+	0.987899i	$0.549569\pi$
$90$	2.53651	−	2.32457i	0.267372	−	0.245032i
$91$	−8.40077	+	1.48128i	−0.880640	+	0.155281i
$92$	5.81362	−	3.39210i	0.606111	−	0.353651i
$93$	6.40102	+	0.146807i	0.663755	+	0.0152232i
$94$	1.31915	−	1.89315i	0.136060	−	0.195264i
$95$	5.01421	−	3.29790i	0.514447	−	0.338357i
$96$	−1.30867	−	9.71017i	−0.133565	−	0.991040i
$97$	16.8774	+	4.00002i	1.71364	+	0.406141i	0.966120	−	0.258094i	$-0.0830945\pi$
$97$	16.8774	+	4.00002i	1.71364	+	0.406141i	0.747524	+	0.664235i	$0.231243\pi$
$98$	−1.62569	+	3.03163i	−0.164219	+	0.306240i
$99$	9.79441	+	0.449506i	0.984376	+	0.0451771i
$100$	8.66762	−	0.544684i	0.866762	−	0.0544684i
$101$	0.786520	+	6.72911i	0.0782617	+	0.669571i	0.974246	+	0.225486i	$0.0723971\pi$
$101$	0.786520	+	6.72911i	0.0782617	+	0.669571i	−0.895985	+	0.444085i	$0.853529\pi$
$102$	−9.14098	+	6.12337i	−0.905092	+	0.606304i
$103$	−11.5923	+	10.9367i	−1.14222	+	1.07763i	−0.146132	+	0.989265i	$0.546682\pi$
$103$	−11.5923	+	10.9367i	−1.14222	+	1.07763i	−0.996088	+	0.0883637i	$0.971836\pi$
$104$	−5.42611	−	9.89990i	−0.532074	−	0.970765i
$105$	1.28539	+	2.71279i	0.125441	+	0.264741i
$106$	1.53709	−	0.513247i	0.149295	−	0.0498509i
$107$	9.58102	−	16.5948i	0.926232	−	1.60428i	0.136664	−	0.990617i	$-0.456362\pi$
$107$	9.58102	−	16.5948i	0.926232	−	1.60428i	0.789568	−	0.613663i	$-0.210305\pi$
$108$	1.26874	−	10.3146i	0.122084	−	0.992520i
$109$	−5.01287	−	8.68254i	−0.480146	−	0.831637i	0.519595	−	0.854413i	$-0.326083\pi$
$109$	−5.01287	−	8.68254i	−0.480146	−	0.831637i	−0.999741	+	0.0227760i	$0.992750\pi$
$110$	−2.80571	−	2.48537i	−0.267514	−	0.236971i
$111$	15.0630	−	4.13570i	1.42972	−	0.392543i
$112$	8.43211	+	1.40728i	0.796759	+	0.132975i
$113$	−3.35647	−	1.00486i	−0.315750	−	0.0945294i	0.125007	−	0.992156i	$-0.460105\pi$
$113$	−3.35647	−	1.00486i	−0.315750	−	0.0945294i	−0.440757	+	0.897626i	$0.645290\pi$
$114$	5.05219	−	17.4095i	0.473181	−	1.63055i
$115$	−2.50599	−	1.08098i	−0.233685	−	0.100802i
$116$	−11.4374	+	7.59778i	−1.06194	+	0.705436i
$117$	−2.90473	−	11.6166i	−0.268542	−	1.07395i
$118$	−3.48337	−	5.61856i	−0.320670	−	0.517230i
$119$	−2.75320	−	9.19634i	−0.252386	−	0.843027i
$120$	−2.85397	+	2.76374i	−0.260530	+	0.252294i
$121$	0.0185251	+	0.318063i	0.00168410	+	0.0289148i
$122$	4.56774	+	0.389085i	0.413544	+	0.0352261i
$123$	11.0907	+	4.32717i	1.00001	+	0.390168i
$124$	−7.39313	+	0.0338688i	−0.663923	+	0.00304151i
$125$	−4.86988	−	5.80370i	−0.435576	−	0.519099i
$126$	8.27286	+	3.71157i	0.737005	+	0.330653i
$127$	−0.373655	+	0.445305i	−0.0331565	+	0.0395144i	−0.782368	−	0.622817i	$-0.785988\pi$
$127$	−0.373655	+	0.445305i	−0.0331565	+	0.0395144i	0.749211	+	0.662331i	$0.230433\pi$
$128$	1.81898	+	11.1665i	0.160777	+	0.986991i
$129$	17.6244	+	2.47083i	1.55174	+	0.217545i
$130$	−1.92506	+	4.15311i	−0.168839	+	0.364252i
$131$	−1.86598	−	4.32584i	−0.163032	−	0.377950i	0.817044	−	0.576576i	$-0.195611\pi$
$131$	−1.86598	−	4.32584i	−0.163032	−	0.377950i	−0.980075	+	0.198626i	$0.936352\pi$
$132$	−11.3196	−	0.207737i	−0.985246	−	0.0180812i
$133$	13.2145	+	8.69129i	1.14584	+	0.753630i
$134$	4.90855	+	12.2736i	0.424034	+	1.06027i
$135$	−3.67144	+	2.06806i	−0.315987	+	0.177990i
$136$	10.3566	−	7.35834i	0.888071	−	0.630973i
$137$	6.38123	+	12.7061i	0.545185	+	1.08555i	0.982503	+	0.186246i	$0.0596320\pi$
$137$	6.38123	+	12.7061i	0.545185	+	1.08555i	−0.437318	+	0.899307i	$0.644072\pi$
$138$	−7.87701	+	2.43092i	−0.670536	+	0.206934i
$139$	−8.49662	−	6.32550i	−0.720674	−	0.536522i	0.173175	−	0.984891i	$-0.444597\pi$
$139$	−8.49662	−	6.32550i	−0.720674	−	0.536522i	−0.893848	+	0.448369i	$0.852005\pi$
$140$	−1.56985	−	3.09044i	−0.132676	−	0.261190i
$141$	−2.09948	+	1.89168i	−0.176808	+	0.159308i
$142$	0.0893710	−	3.33415i	0.00749985	−	0.279796i
$143$	−12.2582	+	4.46161i	−1.02508	+	0.373099i
$144$	−1.13682	+	11.9460i	−0.0947352	+	0.995503i
$145$	5.23182	+	1.90423i	0.434479	+	0.158137i
$146$	1.61009	−	4.08004i	0.133252	−	0.337667i
$147$	2.78143	−	3.16450i	0.229409	−	0.261003i
$148$	−17.2553	+	5.25215i	−1.41838	+	0.431724i
$149$	8.59748	−	17.1190i	0.704333	−	1.40244i	−0.201791	−	0.979429i	$-0.564676\pi$
$149$	8.59748	−	17.1190i	0.704333	−	1.40244i	0.906124	−	0.423013i	$-0.139028\pi$
$150$	−10.4902	−	1.75846i	−0.856521	−	0.143578i
$151$	10.8400	+	10.2270i	0.882147	+	0.832263i	0.986749	−	0.162251i	$-0.0518756\pi$
$151$	10.8400	+	10.2270i	0.882147	+	0.832263i	−0.104603	+	0.994514i	$0.533357\pi$
$152$	−5.27856	+	20.2556i	−0.428148	+	1.64295i
$153$	12.6048	−	4.76437i	1.01904	−	0.385176i
$154$	3.08560	−	9.38375i	0.248645	−	0.756164i
$155$	1.79014	+	2.40458i	0.143788	+	0.193140i
$156$	3.72181	+	13.3163i	0.297983	+	1.06616i
$157$	−2.21985	+	0.526113i	−0.177163	+	0.0419884i	−0.318240	−	0.948010i	$-0.603092\pi$
$157$	−2.21985	+	0.526113i	−0.177163	+	0.0419884i	0.141077	+	0.989999i	$0.454944\pi$
$158$	4.49689	+	1.19391i	0.357754	+	0.0949820i
$159$	−1.97606	+	0.185151i	−0.156712	+	0.0146834i
$160$	3.20644	−	3.28074i	0.253491	−	0.259365i
$161$		−	7.19254i		−	0.566852i
$162$	−4.37911	+	11.9509i	−0.344056	+	0.938949i
$163$			1.59696i			0.125083i	0.998042	+	0.0625416i	$0.0199206\pi$
$163$			1.59696i			0.125083i	−0.998042	+	0.0625416i	$0.980079\pi$
$164$	−12.9390	−	4.64241i	−1.01037	−	0.362511i
$165$	2.65616	+	3.74411i	0.206782	+	0.291479i
$166$	0.419579	−	1.58036i	0.0325657	−	0.122660i
$167$	−17.5496	+	4.15933i	−1.35803	+	0.321859i	−0.844197	−	0.536033i	$-0.819922\pi$
$167$	−17.5496	+	4.15933i	−1.35803	+	0.321859i	−0.513831	+	0.857891i	$0.671774\pi$
$168$	−9.66695	−	4.02135i	−0.745822	−	0.310254i
$169$	1.75047	+	2.35129i	0.134651	+	0.180868i
$170$	−4.89359	−	1.60913i	−0.375321	−	0.123415i
$171$	−10.8633	+	19.3626i	−0.830736	+	1.48070i
$172$	−20.4217	−	2.29217i	−1.55714	−	0.174776i
$173$	8.45837	+	7.98006i	0.643078	+	0.606712i	0.937089	−	0.349089i	$-0.113509\pi$
$173$	8.45837	+	7.98006i	0.643078	+	0.606712i	−0.294012	+	0.955802i	$0.594991\pi$
$174$	15.7536	−	5.88504i	1.19428	−	0.446144i
$175$	4.16504	−	8.29328i	0.314848	−	0.626913i
$176$	13.0724	−	0.119775i	0.985370	−	0.00902839i
$177$	2.59398	+	7.66970i	0.194976	+	0.576490i
$178$	0.466747	+	0.184190i	0.0349842	+	0.0138056i
$179$	−8.91243	−	3.24386i	−0.666146	−	0.242457i	−0.0132586	−	0.999912i	$-0.504220\pi$
$179$	−8.91243	−	3.24386i	−0.666146	−	0.242457i	−0.652888	+	0.757455i	$0.726443\pi$
$180$	4.17212	−	2.50370i	0.310971	−	0.186615i
$181$	−16.5014	+	6.00603i	−1.22654	+	0.446425i	−0.872412	−	0.488772i	$-0.837445\pi$
$181$	−16.5014	+	6.00603i	−1.22654	+	0.446425i	−0.354130	+	0.935196i	$0.615223\pi$
$182$	−12.0594	−	0.323249i	−0.893904	−	0.0239608i
$183$	−5.34037	−	1.73318i	−0.394771	−	0.128121i
$184$	9.01493	−	3.05613i	0.664590	−	0.225301i
$185$	5.86635	+	4.36734i	0.431303	+	0.321093i
$186$	8.82804	+	2.01367i	0.647304	+	0.147649i
$187$	−6.58838	−	13.1185i	−0.481790	−	0.959323i
$188$	2.36327	−	2.25018i	0.172359	−	0.164111i
$189$	−8.83679	−	6.72571i	−0.642782	−	0.489223i
$190$	7.88059	−	3.15168i	0.571718	−	0.228647i
$191$	4.48444	+	2.94947i	0.324483	+	0.213416i	0.701290	−	0.712876i	$-0.252608\pi$
$191$	4.48444	+	2.94947i	0.324483	+	0.213416i	−0.376807	+	0.926292i	$0.622978\pi$
$192$	0.932736	−	13.8250i	0.0673144	−	0.997732i
$193$	−6.87853	−	15.9462i	−0.495127	−	1.14783i	−0.964320	−	0.264738i	$-0.914714\pi$
$193$	−6.87853	−	15.9462i	−0.495127	−	1.14783i	0.469193	−	0.883096i	$-0.344545\pi$
$194$	22.2549	+	10.3157i	1.59781	+	0.740621i
$195$	3.45012	−	4.41905i	0.247068	−	0.316455i
$196$	−3.10999	+	3.74101i	−0.222142	+	0.267215i
$197$	5.50800	−	6.56418i	0.392429	−	0.467678i	−0.533267	−	0.845947i	$-0.679036\pi$
$197$	5.50800	−	6.56418i	0.392429	−	0.467678i	0.925696	+	0.378268i	$0.123480\pi$
$198$	13.4445	+	3.39277i	0.955458	+	0.241114i
$199$	−6.36811	−	7.58922i	−0.451424	−	0.537986i	0.491552	−	0.870848i	$-0.336430\pi$
$199$	−6.36811	−	7.58922i	−0.451424	−	0.537986i	−0.942975	+	0.332863i	$0.891985\pi$
$200$	12.1643	+	1.69651i	0.860147	+	0.119961i
$201$	−2.44497	−	16.0038i	−0.172455	−	1.12882i
$202$	−0.813190	+	9.54661i	−0.0572159	+	0.671697i
$203$	0.853149	+	14.6480i	0.0598793	+	1.02809i
$204$	−14.3979	+	5.89972i	−1.00806	+	0.413063i
$205$	1.59862	+	5.33977i	0.111653	+	0.372946i
$206$	−19.1558	+	11.8761i	−1.33465	+	0.827448i
$207$	10.0712	−	0.711132i	0.699998	−	0.0494271i
$208$	−4.71893	−	15.2523i	−0.327199	−	1.05756i
$209$	22.2089	+	9.57997i	1.53622	+	0.662661i
$210$	1.01391	+	4.12248i	0.0699661	+	0.284478i
$211$	15.0443	+	4.50396i	1.03569	+	0.310065i	0.759136	−	0.650933i	$-0.225622\pi$
$211$	15.0443	+	4.50396i	1.03569	+	0.310065i	0.276555	+	0.960998i	$0.410807\pi$
$212$	2.27502	−	0.276481i	0.156249	−	0.0189888i
$213$	−1.03295	+	3.95220i	−0.0707764	+	0.270800i
$214$	17.9690	−	20.2850i	1.22834	−	1.38665i
$215$	4.16624	+	7.21614i	0.284135	+	0.492137i
$216$	4.67504	−	13.9336i	0.318096	−	0.948058i
$217$	−3.95016	+	6.84188i	−0.268154	+	0.464457i
$218$	−4.49060	−	13.4486i	−0.304142	−	0.910855i
$219$	−3.05411	+	4.41940i	−0.206378	+	0.298635i
$220$	−3.18484	−	4.23732i	−0.214722	−	0.285680i
$221$	−13.0406	+	12.3031i	−0.877203	+	0.827598i
$222$	22.0416	−	1.47072i	1.47934	−	0.0987084i
$223$	−3.02893	−	25.9142i	−0.202832	−	1.73534i	−0.584809	−	0.811171i	$-0.698831\pi$
$223$	−3.02893	−	25.9142i	−0.202832	−	1.73534i	0.381977	−	0.924172i	$-0.375243\pi$
$224$	11.2859	+	4.33464i	0.754074	+	0.289620i
$225$	12.0243	+	5.01206i	0.801621	+	0.334137i
$226$	−4.36671	−	2.34161i	−0.290469	−	0.155762i
$227$	26.5098	+	6.28294i	1.75952	+	0.417013i	0.978291	−	0.207236i	$-0.0664466\pi$
$227$	26.5098	+	6.28294i	1.75952	+	0.417013i	0.781226	+	0.624249i	$0.214595\pi$
$228$	11.9241	−	22.6946i	0.789690	−	1.50299i
$229$	14.3485	−	9.43713i	0.948173	−	0.623623i	0.0216116	−	0.999766i	$-0.493120\pi$
$229$	14.3485	−	9.43713i	0.948173	−	0.623623i	0.926562	+	0.376143i	$0.122750\pi$
$230$	−3.16672	−	2.20657i	−0.208807	−	0.145497i
$231$	−6.28768	+	10.3358i	−0.413699	+	0.680045i
$232$	−17.9969	+	7.29329i	−1.18155	+	0.478828i
$233$	7.38132	−	1.30153i	0.483567	−	0.0852658i	0.0734499	−	0.997299i	$-0.476599\pi$
$233$	7.38132	−	1.30153i	0.483567	−	0.0852658i	0.410117	+	0.912033i	$0.365488\pi$
$234$	−0.739701	−	16.9179i	−0.0483558	−	1.10596i
$235$	−1.30304	−	0.229761i	−0.0850009	−	0.0149880i
$236$	−3.23776	−	8.77046i	−0.210760	−	0.570908i
$237$	−5.03225	−	2.67350i	−0.326880	−	0.173663i
$238$	−1.21419	−	13.5215i	−0.0787045	−	0.876470i
$239$	−14.2122	−	1.66117i	−0.919311	−	0.107452i	−0.356743	−	0.934203i	$-0.616113\pi$
$239$	−14.2122	−	1.66117i	−0.919311	−	0.107452i	−0.562569	+	0.826751i	$0.690187\pi$
$240$	−4.73620	+	3.02246i	−0.305720	+	0.195099i
$241$	0.0402789	−	0.691562i	0.00259459	−	0.0445474i	−0.996762	−	0.0804041i	$-0.974379\pi$
$241$	0.0402789	−	0.691562i	0.00259459	−	0.0445474i	0.999357	+	0.0358566i	$0.0114160\pi$
$242$	−0.0642808	+	0.445962i	−0.00413213	+	0.0286675i
$243$	8.54384	−	13.0385i	0.548088	−	0.836421i
$244$	6.21924	+	1.83092i	0.398146	+	0.117212i
$245$	1.96926	+	0.114696i	0.125811	+	0.00732768i
$246$	14.1441	+	9.13245i	0.901792	+	0.582264i
$247$	3.42925	−	29.3391i	0.218198	−	1.86680i
$248$	−10.2539	−	2.04389i	−0.651120	−	0.129787i
$249$	−0.939560	+	1.76851i	−0.0595422	+	0.112075i
$250$	−5.10663	−	9.41912i	−0.322971	−	0.595717i
$251$	−4.85121	+	27.5126i	−0.306206	+	1.73658i	0.311567	+	0.950224i	$0.399146\pi$
$251$	−4.85121	+	27.5126i	−0.306206	+	1.73658i	−0.617773	+	0.786356i	$0.711965\pi$
$252$	10.4136	+	7.48254i	0.655996	+	0.471356i
$253$	−1.90996	−	10.8319i	−0.120078	−	0.680998i
$254$	−0.643689	+	0.511364i	−0.0403887	+	0.0320858i
$255$	5.39008	+	3.27900i	0.337540	+	0.205339i
$256$	−0.637484	+	15.9873i	−0.0398427	+	0.999206i
$257$	−2.61471	−	3.97547i	−0.163101	−	0.247983i	0.744685	−	0.667416i	$-0.232600\pi$
$257$	−2.61471	−	3.97547i	−0.163101	−	0.247983i	−0.907787	+	0.419432i	$0.862229\pi$
$258$	23.7224	+	8.40798i	1.47689	+	0.523458i
$259$	−4.44491	+	18.7546i	−0.276193	+	1.16535i
$260$	−3.84198	+	5.21034i	−0.238269	+	0.323131i
$261$	−20.4262	+	2.64286i	−1.26435	+	0.163589i
$262$	−1.36223	−	6.52180i	−0.0841586	−	0.402918i
$263$	−25.0703	+	2.93030i	−1.54590	+	0.180690i	−0.845858	−	0.533409i	$-0.820911\pi$
$263$	−25.0703	+	2.93030i	−1.54590	+	0.180690i	−0.700045	+	0.714099i	$0.746837\pi$
$264$	−15.6263	−	3.48910i	−0.961729	−	0.214739i
$265$	−0.637690	−	0.675912i	−0.0391730	−	0.0415209i
$266$	15.8526	+	15.7802i	0.971988	+	0.967546i
$267$	−0.505569	−	0.349383i	−0.0309403	−	0.0213819i
$268$	3.33049	+	18.3950i	0.203442	+	1.12365i
$269$	−17.8554	−	10.3088i	−1.08866	−	0.628539i	−0.155442	−	0.987845i	$-0.549680\pi$
$269$	−17.8554	−	10.3088i	−1.08866	−	0.628539i	−0.933220	+	0.359306i	$0.883014\pi$
$270$	−5.67218	+	1.82729i	−0.345198	+	0.111206i
$271$	9.80988	−	5.66373i	0.595908	−	0.344047i	−0.171522	−	0.985180i	$-0.554869\pi$
$271$	9.80988	−	5.66373i	0.595908	−	0.344047i	0.767430	+	0.641133i	$0.221535\pi$
$272$	16.4316	−	7.26717i	0.996311	−	0.440637i
$273$	14.2949	+	3.73610i	0.865164	+	0.226119i
$274$	5.24879	+	19.4108i	0.317091	+	1.17265i
$275$	4.07028	−	13.5957i	0.245447	−	0.819850i
$276$	−11.6022	+	1.14074i	−0.698373	+	0.0686643i
$277$	0.492012	−	1.14061i	0.0295621	−	0.0685328i	−0.902795	−	0.430070i	$-0.858489\pi$
$277$	0.492012	−	1.14061i	0.0295621	−	0.0685328i	0.932358	+	0.361537i	$0.117748\pi$
$278$	−9.98444	−	11.1678i	−0.598827	−	0.669800i
$279$	−9.97076	−	4.85467i	−0.596934	−	0.290642i
$280$	−1.30126	−	4.72623i	−0.0777653	−	0.282446i
$281$	−12.6216	+	3.77866i	−0.752943	+	0.225416i	−0.640200	−	0.768208i	$-0.721149\pi$
$281$	−12.6216	+	3.77866i	−0.752943	+	0.225416i	−0.112742	+	0.993624i	$0.535963\pi$
$282$	−3.44412	+	2.02745i	−0.205095	+	0.120733i
$283$	7.77855	−	0.453049i	0.462387	−	0.0269309i	0.174629	−	0.984634i	$-0.444127\pi$
$283$	7.77855	−	0.453049i	0.462387	−	0.0269309i	0.287757	+	0.957703i	$0.407090\pi$
$284$	1.06675	−	4.59469i	0.0633002	−	0.272645i
$285$	−10.2757	+	1.56987i	−0.608682	+	0.0929909i
$286$	−18.2473	+	2.71554i	−1.07898	+	0.160573i
$287$	−11.2529	+	9.44227i	−0.664235	+	0.557360i
$288$	−4.95364	+	16.2315i	−0.291896	+	0.956450i
$289$	−2.43261	−	2.04120i	−0.143095	−	0.120071i
$290$	6.71093	+	4.11817i	0.394079	+	0.241827i
$291$	−23.6800	−	18.4879i	−1.38815	−	1.08378i
$292$	3.38487	−	5.19816i	0.198085	−	0.304199i
$293$	−22.0919	+	9.52951i	−1.29062	+	0.556720i	−0.927082	−	0.374859i	$-0.877691\pi$
$293$	−22.0919	+	9.52951i	−1.29062	+	0.556720i	−0.363540	+	0.931579i	$0.618432\pi$
$294$	4.74903	−	3.59827i	0.276969	−	0.209856i
$295$	−2.08308	+	3.16716i	−0.121281	+	0.184399i
$296$	−25.3951	+	2.39773i	−1.47606	+	0.139365i
$297$	−15.0942	−	7.78230i	−0.875852	−	0.451575i
$298$	16.7544	−	21.2895i	0.970558	−	1.23327i
$299$	−12.0040	+	6.02863i	−0.694209	+	0.348645i
$300$	−14.0384	−	5.40329i	−0.810509	−	0.311959i
$301$	−13.1133	+	17.6142i	−0.755837	+	1.01526i
$302$	12.1282	+	17.2367i	0.697898	+	0.991858i
$303$	3.62237	−	11.1614i	0.208099	−	0.641206i
$304$	−13.0426	+	26.5743i	−0.748046	+	1.52414i
$305$	−0.899088	−	2.47022i	−0.0514816	−	0.141445i
$306$	18.8132	−	3.03703i	1.07548	−	0.173616i
$307$	4.78841	−	13.1560i	0.273289	−	0.750855i	−0.724794	−	0.688966i	$-0.758065\pi$
$307$	4.78841	−	13.1560i	0.273289	−	0.750855i	0.998083	−	0.0618896i	$-0.0197127\pi$
$308$	6.92933	−	12.1299i	0.394835	−	0.691168i
$309$	26.1489	−	8.84387i	1.48756	−	0.503110i
$310$	1.80048	+	3.83816i	0.102260	+	0.217993i
$311$	29.4820	+	14.8064i	1.67177	+	0.839595i	0.994602	+	0.103767i	$0.0330897\pi$
$311$	29.4820	+	14.8064i	1.67177	+	0.839595i	0.677169	+	0.735828i	$0.263207\pi$
$312$	1.39119	+	19.5043i	0.0787609	+	1.10421i
$313$	5.06497	−	5.36855i	0.286289	−	0.303449i	−0.568229	−	0.822871i	$-0.692371\pi$
$313$	5.06497	−	5.36855i	0.286289	−	0.303449i	0.854518	+	0.519422i	$0.173853\pi$
$314$	−3.22471	+	0.101223i	−0.181981	+	0.00571232i
$315$	−0.0640331	−	5.19906i	−0.00360786	−	0.292934i
$316$	5.89347	+	2.92608i	0.331533	+	0.164605i
$317$	−22.0258	+	16.3976i	−1.23709	+	0.920979i	−0.998739	−	0.0502001i	$-0.984014\pi$
$317$	−22.0258	+	16.3976i	−1.23709	+	0.920979i	−0.238350	+	0.971179i	$0.576607\pi$
$318$	−2.79049	−	0.302287i	−0.156483	−	0.0169514i
$319$	5.17458	+	21.8333i	0.289721	+	1.22243i
$320$	5.37081	−	3.63915i	0.300238	−	0.203435i
$321$	−27.0696	+	19.2038i	−1.51088	+	1.07185i
$322$	2.03409	−	9.96633i	0.113355	−	0.555402i
$323$	33.2415			1.84960
$324$	−9.44768	+	15.3213i	−0.524871	+	0.851182i
$325$	−17.3321			−0.961413
$326$	−0.451628	+	2.21282i	−0.0250134	+	0.122557i
$327$	1.61996	+	17.2894i	0.0895841	+	0.956104i
$328$	−16.6161	−	10.0920i	−0.917468	−	0.557236i
$329$	−0.804160	−	3.39302i	−0.0443348	−	0.187063i
$330$	2.62165	+	5.93920i	0.144317	+	0.326942i
$331$	13.1152	−	9.76391i	0.720877	−	0.536673i	−0.173035	−	0.984916i	$-0.555357\pi$
$331$	13.1152	−	9.76391i	0.720877	−	0.536673i	0.893912	+	0.448243i	$0.147950\pi$
$332$	1.02832	−	2.07117i	0.0564367	−	0.113670i
$333$	−26.7002	−	4.36963i	−1.46316	−	0.239454i
$334$	−25.4938	+	0.800243i	−1.39496	+	0.0437874i
$335$	5.20170	−	5.51348i	0.284199	−	0.301234i
$336$	−12.2577	−	8.30605i	−0.668714	−	0.453132i
$337$	−6.62911	−	3.32926i	−0.361111	−	0.181357i	0.258988	−	0.965881i	$-0.416611\pi$
$337$	−6.62911	−	3.32926i	−0.361111	−	0.181357i	−0.620098	+	0.784524i	$0.712907\pi$
$338$	1.76057	+	3.75310i	0.0957627	+	0.204142i
$339$	4.55809	+	4.00633i	0.247562	+	0.217594i
$340$	−6.32573	−	3.61362i	−0.343061	−	0.195976i
$341$	−4.13208	+	11.3528i	−0.223765	+	0.614788i
$342$	−20.5285	+	23.7576i	−1.11006	+	1.28466i
$343$	6.89474	+	18.9431i	0.372281	+	1.02283i
$344$	−27.6490	−	8.95150i	−1.49073	−	0.482633i
$345$	3.16425	+	3.51185i	0.170357	+	0.189072i
$346$	9.46351	+	13.4496i	0.508762	+	0.723056i
$347$	−9.33273	+	12.5360i	−0.501007	+	0.672969i	−0.978638	−	0.205591i	$-0.934088\pi$
$347$	−9.33273	+	12.5360i	−0.501007	+	0.672969i	0.477631	+	0.878561i	$0.341496\pi$
$348$	23.4933	−	3.69938i	1.25937	−	0.198308i
$349$	−12.4063	+	6.23069i	−0.664095	+	0.333521i	−0.748715	−	0.662892i	$-0.769329\pi$
$349$	−12.4063	+	6.23069i	−0.664095	+	0.333521i	0.0846195	+	0.996413i	$0.473033\pi$
$350$	8.11667	−	10.3137i	0.433854	−	0.551289i
$351$	−3.81807	+	20.3855i	−0.203793	+	1.08810i
$352$	18.1476	+	3.53099i	0.967273	+	0.188202i
$353$	12.1666	−	18.4984i	0.647563	−	0.984572i	−0.351269	−	0.936274i	$-0.614250\pi$
$353$	12.1666	−	18.4984i	0.647563	−	0.984572i	0.998833	−	0.0482981i	$-0.0153797\pi$
$354$	1.42531	+	11.3611i	0.0757546	+	0.603836i
$355$	−1.75617	+	0.757537i	−0.0932077	+	0.0402059i
$356$	0.594657	+	0.387221i	0.0315168	+	0.0205227i
$357$	−2.30844	+	16.4660i	−0.122175	+	0.871474i
$358$	−11.4321	−	7.01533i	−0.604206	−	0.370772i
$359$	−6.98535	−	5.86140i	−0.368673	−	0.309353i	0.439564	−	0.898211i	$-0.355133\pi$
$359$	−6.98535	−	5.86140i	−0.368673	−	0.309353i	−0.808236	+	0.588858i	$0.799578\pi$
$360$	6.48915	−	2.28935i	0.342008	−	0.120659i
$361$	−27.4007	+	22.9919i	−1.44214	+	1.21010i
$362$	−24.5637	+	3.65555i	−1.29104	+	0.192131i
$363$	0.200579	−	0.514091i	0.0105277	−	0.0269828i
$364$	−16.6187	−	3.85839i	−0.871057	−	0.202234i
$365$	−2.51094	+	0.146246i	−0.131429	+	0.00765486i
$366$	−6.90971	−	3.91187i	−0.361177	−	0.204477i
$367$	3.28582	−	0.983711i	0.171519	−	0.0513493i	−0.199892	−	0.979818i	$-0.564059\pi$
$367$	3.28582	−	0.983711i	0.171519	−	0.0513493i	0.371411	+	0.928469i	$0.378874\pi$
$368$	13.3558	−	1.68525i	0.696220	−	0.0878496i
$369$	−14.3339	−	14.8230i	−0.746195	−	0.771656i
$370$	6.89359	+	7.71063i	0.358381	+	0.400856i
$371$	0.969979	−	2.24866i	0.0503588	−	0.116745i
$372$	11.6631	+	5.28686i	0.604703	+	0.274111i
$373$	8.43142	−	28.1629i	0.436562	−	1.45822i	−0.403122	−	0.915146i	$-0.632075\pi$
$373$	8.43142	−	28.1629i	0.436562	−	1.45822i	0.839685	−	0.543074i	$-0.182740\pi$
$374$	−5.41918	−	20.0409i	−0.280219	−	1.03629i
$375$	3.47430	+	12.6541i	0.179412	+	0.653453i
$376$	3.91102	−	2.44961i	0.201696	−	0.126329i
$377$	23.7317	−	13.7015i	1.22224	−	0.705663i
$378$	−10.3426	−	11.8186i	−0.531966	−	0.607881i
$379$	6.36794	+	3.67653i	0.327099	+	0.188851i	0.654552	−	0.756017i	$-0.272857\pi$
$379$	6.36794	+	3.67653i	0.327099	+	0.188851i	−0.327453	+	0.944867i	$0.606190\pi$
$380$	11.8110	−	2.13844i	0.605894	−	0.109700i
$381$	0.909877	−	0.431123i	0.0466144	−	0.0220871i
$382$	5.37974	+	5.35515i	0.275251	+	0.273993i
$383$	3.42702	+	3.63243i	0.175112	+	0.185608i	0.808985	−	0.587829i	$-0.200017\pi$
$383$	3.42702	+	3.63243i	0.175112	+	0.185608i	−0.633873	+	0.773437i	$0.718536\pi$
$384$	5.20223	−	18.8928i	0.265475	−	0.964118i
$385$	−5.62605	+	0.657591i	−0.286730	+	0.0335140i
$386$	−5.02154	−	24.0411i	−0.255589	−	1.22366i
$387$	−25.9604	−	16.6201i	−1.31964	−	0.844846i
$388$	27.9202	+	20.5877i	1.41743	+	1.04518i
$389$	3.86890	−	16.3242i	0.196161	−	0.827668i	−0.782577	−	0.622554i	$-0.786095\pi$
$389$	3.86890	−	16.3242i	0.196161	−	0.827668i	0.978738	−	0.205115i	$-0.0657567\pi$
$390$	6.03038	−	5.14753i	0.305360	−	0.260655i
$391$	−8.30669	−	12.6297i	−0.420087	−	0.638712i
$392$	−5.36733	+	4.30421i	−0.271091	+	0.217395i
$393$	−0.187099	+	8.15778i	−0.00943788	+	0.411505i
$394$	9.48854	−	7.53795i	0.478026	−	0.379756i
$395$	−0.463290	−	2.62745i	−0.0233107	−	0.132201i
$396$	17.6698	+	8.50337i	0.887943	+	0.427310i
$397$	2.41157	−	13.6767i	0.121033	−	0.686415i	−0.862551	−	0.505969i	$-0.831135\pi$
$397$	2.41157	−	13.6767i	0.121033	−	0.686415i	0.983585	−	0.180446i	$-0.0577540\pi$
$398$	−6.67769	−	12.3169i	−0.334722	−	0.617392i
$399$	−14.5250	−	23.2273i	−0.727159	−	1.16282i
$400$	16.3757	+	5.79090i	0.818784	+	0.289545i
$401$	−0.242603	+	2.07560i	−0.0121150	+	0.103651i	−0.997943	−	0.0641095i	$-0.979579\pi$
$401$	−0.242603	+	2.07560i	−0.0121150	+	0.103651i	0.985828	+	0.167760i	$0.0536534\pi$
$402$	1.13811	−	22.8672i	0.0567635	−	1.14051i
$403$	14.7297	+	0.857906i	0.733738	+	0.0427354i
$404$	−3.82663	+	12.9983i	−0.190382	+	0.646688i
$405$	7.27355	−	0.603696i	0.361426	−	0.0299979i
$406$	−2.96037	+	20.5383i	−0.146921	+	1.01930i
$407$	−1.71379	+	29.4246i	−0.0849494	+	1.45852i
$408$	−21.6189	+	4.10312i	−1.07030	+	0.203135i
$409$	21.0087	+	2.45557i	1.03881	+	0.121420i	0.618361	−	0.785894i	$-0.287797\pi$
$409$	21.0087	+	2.45557i	1.03881	+	0.121420i	0.420453	+	0.907314i	$0.361871\pi$
$410$	0.705011	+	7.85114i	0.0348180	+	0.387740i
$411$	−0.867842	−	24.6118i	−0.0428075	−	1.21401i
$412$	−29.9018	+	11.0388i	−1.47316	+	0.543840i
$413$	−9.83850	−	1.73479i	−0.484121	−	0.0853636i
$414$	14.1563	+	1.86282i	0.695743	+	0.0915525i
$415$	−0.923376	+	0.162816i	−0.0453267	+	0.00799233i
$416$	−2.22534	−	22.4689i	−0.109106	−	1.10163i
$417$	8.80678	+	16.0951i	0.431270	+	0.788183i
$418$	28.0644	+	19.5553i	1.37268	+	0.956479i
$419$	19.2914	−	12.6881i	0.942445	−	0.619856i	0.0174552	−	0.999848i	$-0.494444\pi$
$419$	19.2914	−	12.6881i	0.942445	−	0.619856i	0.924990	+	0.379992i	$0.124073\pi$
$420$	0.239055	+	5.99905i	0.0116647	+	0.292724i
$421$	−8.13315	−	1.92759i	−0.396385	−	0.0939450i	0.0275888	−	0.999619i	$-0.491217\pi$
$421$	−8.13315	−	1.92759i	−0.396385	−	0.0939450i	−0.423974	+	0.905674i	$0.639365\pi$
$422$	19.5723	+	10.4955i	0.952766	+	0.510914i
$423$	4.67150	−	1.46148i	0.227136	−	0.0710595i
$424$	3.23056	+	0.260281i	0.156890	+	0.0126404i
$425$	−2.26435	−	19.3728i	−0.109837	−	0.939718i
$426$	−2.54901	+	5.18423i	−0.123500	+	0.251177i
$427$	5.03913	−	4.75417i	0.243860	−	0.230071i
$428$	30.6355	−	23.0261i	1.48082	−	1.11301i
$429$	22.5201	+	1.83059i	1.08728	+	0.0883818i
$430$	3.73218	+	11.1773i	0.179982	+	0.539016i
$431$	2.58028	−	4.46918i	0.124288	−	0.215273i	−0.797167	−	0.603759i	$-0.793669\pi$
$431$	2.58028	−	4.46918i	0.124288	−	0.215273i	0.921454	+	0.388487i	$0.127002\pi$
$432$	10.4185	−	17.9849i	0.501258	−	0.865298i
$433$	11.4677	+	19.8626i	0.551101	+	0.954535i	0.998195	+	0.0600484i	$0.0191255\pi$
$433$	11.4677	+	19.8626i	0.551101	+	0.954535i	−0.447094	+	0.894487i	$0.647541\pi$
$434$	−7.40845	+	8.36331i	−0.355617	+	0.401451i
$435$	−6.86073	−	6.77675i	−0.328947	−	0.324920i
$436$	−2.41905	−	19.9050i	−0.115851	−	0.953278i
$437$	23.8599	+	7.14319i	1.14137	+	0.341705i
$438$	−5.48176	+	5.26001i	−0.261929	+	0.251333i
$439$	−1.61907	−	0.698400i	−0.0772742	−	0.0333328i	0.357092	−	0.934069i	$-0.383768\pi$
$439$	−1.61907	−	0.698400i	−0.0772742	−	0.0333328i	−0.434366	+	0.900736i	$0.643028\pi$
$440$	−3.21473	−	6.77213i	−0.153256	−	0.322849i
$441$	−6.66444	+	2.97263i	−0.317354	+	0.141554i
$442$	−21.5490	+	13.3599i	−1.02498	+	0.635464i
$443$	−11.9652	−	39.9666i	−0.568485	−	1.89887i	−0.411972	−	0.911197i	$-0.635160\pi$
$443$	−11.9652	−	39.9666i	−0.568485	−	1.89887i	−0.156513	−	0.987676i	$-0.550025\pi$
$444$	30.9578	+	4.19559i	1.46919	+	0.199114i
$445$	−0.0167302	−	0.287246i	−0.000793086	−	0.0136168i
$446$	3.13164	−	36.7646i	0.148288	−	1.74085i
$447$	−25.8999	+	20.7394i	−1.22502	+	0.980942i
$448$	14.4125	+	9.19801i	0.680926	+	0.434565i
$449$	6.20903	+	7.39963i	0.293022	+	0.349210i	0.892391	−	0.451263i	$-0.149026\pi$
$449$	6.20903	+	7.39963i	0.293022	+	0.349210i	−0.599369	+	0.800473i	$0.704582\pi$
$450$	15.2440	+	10.3455i	0.718610	+	0.487691i
$451$	−14.4394	+	17.2082i	−0.679924	+	0.810302i
$452$	−5.38850	−	4.47958i	−0.253454	−	0.210702i
$453$	−9.67772	−	23.9298i	−0.454699	−	1.12432i
$454$	34.9564	+	16.2031i	1.64059	+	0.760447i
$455$	2.73996	+	6.35195i	0.128452	+	0.297784i
$456$	22.9407	−	28.0746i	1.07430	−	1.31471i
$457$	−17.4488	−	11.4763i	−0.816222	−	0.536838i	0.0713797	−	0.997449i	$-0.477260\pi$
$457$	−17.4488	−	11.4763i	−0.816222	−	0.536838i	−0.887602	+	0.460611i	$0.847630\pi$
$458$	22.5508	−	9.01872i	1.05373	−	0.421417i
$459$	−23.2845	−	1.60434i	−1.08683	−	0.0748841i
$460$	−3.76393	−	3.95309i	−0.175494	−	0.184314i
$461$	5.38546	+	10.7233i	0.250826	+	0.499436i	0.983446	−	0.181202i	$-0.0579989\pi$
$461$	5.38546	+	10.7233i	0.250826	+	0.499436i	−0.732620	+	0.680638i	$0.761703\pi$
$462$	−11.6355	+	12.5436i	−0.541334	+	0.583580i
$463$	−19.2537	−	14.3339i	−0.894797	−	0.666152i	0.0482414	−	0.998836i	$-0.484638\pi$
$463$	−19.2537	−	14.3339i	−0.894797	−	0.666152i	−0.943038	+	0.332684i	$0.892046\pi$
$464$	−27.0000	+	5.01631i	−1.25344	+	0.232876i
$465$	−1.08126	−	5.07845i	−0.0501424	−	0.235507i
$466$	10.5960	+	0.284022i	0.490850	+	0.0131571i
$467$	1.89021	−	0.687979i	0.0874683	−	0.0318359i	−0.297915	−	0.954592i	$-0.596291\pi$
$467$	1.89021	−	0.687979i	0.0874683	−	0.0318359i	0.385384	+	0.922756i	$0.374069\pi$
$468$	3.75952	−	23.6515i	0.173784	−	1.09329i
$469$	18.7716	+	6.83230i	0.866792	+	0.315487i
$470$	−1.74058	−	0.686875i	−0.0802868	−	0.0316832i
$471$	3.87461	+	0.775197i	0.178533	+	0.0357192i
$472$	−2.00606	−	13.0684i	−0.0923366	−	0.601523i
$473$	−15.0711	+	30.0091i	−0.692972	+	1.37982i
$474$	−6.21685	−	5.12768i	−0.285549	−	0.235522i
$475$	23.3750	+	22.0531i	1.07252	+	1.01187i
$476$	2.14152	−	19.0794i	0.0981562	−	0.874505i
$477$	3.24455	+	1.13587i	0.148558	+	0.0520078i
$478$	−19.2233	−	6.32109i	−0.879255	−	0.289120i
$479$	19.6180	+	26.3515i	0.896368	+	1.20403i	0.978258	+	0.207389i	$0.0664967\pi$
$479$	19.6180	+	26.3515i	0.896368	+	1.20403i	−0.0818908	+	0.996641i	$0.526096\pi$
$480$	−7.41747	+	2.84864i	−0.338560	+	0.130022i
$481$	35.0260	−	8.30133i	1.59705	−	0.378508i
$482$	0.251390	−	0.946870i	0.0114505	−	0.0431288i
$483$	−5.19529	+	11.3228i	−0.236394	+	0.515207i
$484$	−0.215191	+	0.599768i	−0.00978142	+	0.0272622i
$485$		−	14.0659i		−	0.638700i
$486$	15.5261	−	15.6505i	0.704279	−	0.709923i
$487$		−	22.1324i		−	1.00291i	−0.865183	−	0.501457i	$-0.832798\pi$
$487$		−	22.1324i		−	1.00291i	0.865183	−	0.501457i	$-0.167202\pi$
$488$	8.09989	+	4.29584i	0.366665	+	0.194464i
$489$	1.15351	−	2.51401i	0.0521634	−	0.113687i
$490$	2.69626	+	0.715846i	0.121805	+	0.0323386i
$491$	17.8323	−	4.22634i	0.804761	−	0.190732i	0.192407	−	0.981315i	$-0.438371\pi$
$491$	17.8323	−	4.22634i	0.804761	−	0.190732i	0.612354	+	0.790583i	$0.290223\pi$
$492$	17.0160	+	16.6544i	0.767139	+	0.750837i
$493$	18.4151	+	24.7358i	0.829375	+	1.11404i
$494$	13.0490	−	39.6839i	0.587102	−	1.78546i
$495$	−1.47703	−	7.81276i	−0.0663876	−	0.351157i
$496$	−13.6302	−	5.73196i	−0.612014	−	0.257373i
$497$	−3.66628	−	3.45896i	−0.164455	−	0.155156i
$498$	−1.80204	+	2.18481i	−0.0807515	+	0.0979039i
$499$	−14.5822	+	29.0355i	−0.652788	+	1.29981i	0.286961	+	0.957942i	$0.407355\pi$
$499$	−14.5822	+	29.0355i	−0.652788	+	1.29981i	−0.939749	+	0.341865i	$0.888941\pi$
$500$	−4.41221	−	14.4958i	−0.197320	−	0.648271i
$501$	30.6318	+	6.12853i	1.36853	+	0.273803i
$502$	−14.5028	+	36.7508i	−0.647292	+	1.64027i
$503$	−26.0278	−	9.47334i	−1.16052	−	0.422395i	−0.311238	−	0.950332i	$-0.600743\pi$
$503$	−26.0278	−	9.47334i	−1.16052	−	0.422395i	−0.849284	+	0.527937i	$0.822966\pi$
$504$	12.3135	+	13.3132i	0.548487	+	0.593017i
$505$	5.16279	−	1.87910i	0.229741	−	0.0836189i
$506$	0.416797	−	15.5494i	0.0185289	−	0.691255i
$507$	−1.05730	−	4.96590i	−0.0469563	−	0.220543i
$508$	−1.03654	+	0.526532i	−0.0459892	+	0.0233611i
$509$	−22.1661	−	16.5021i	−0.982497	−	0.731442i	−0.0191824	−	0.999816i	$-0.506106\pi$
$509$	−22.1661	−	16.5021i	−0.982497	−	0.731442i	−0.963315	+	0.268374i	$0.913514\pi$
$510$	6.54143	+	6.06789i	0.289660	+	0.268691i
$511$	−2.97489	−	5.92350i	−0.131602	−	0.262040i
$512$	−5.40463	+	21.9725i	−0.238853	+	0.971056i
$513$	31.0874	−	22.6348i	1.37254	−	0.999352i
$514$	−2.49878	−	6.24806i	−0.110217	−	0.275590i
$515$	10.7981	+	7.10199i	0.475819	+	0.312951i
$516$	30.4931	+	18.3593i	1.34238	+	0.808225i
$517$	−2.11207	−	4.89633i	−0.0928887	−	0.215340i
$518$	−11.4630	+	24.7302i	−0.503655	+	1.08658i
$519$	−7.55145	−	18.6722i	−0.331472	−	0.819619i
$520$	−6.79714	+	6.13316i	−0.298074	+	0.268957i
$521$	8.94361	−	10.6586i	0.391827	−	0.466961i	−0.533683	−	0.845685i	$-0.679192\pi$
$521$	8.94361	−	10.6586i	0.391827	−	0.466961i	0.925510	+	0.378724i	$0.123637\pi$
$522$	−29.0510	−	2.11457i	−1.27153	−	0.0925524i
$523$	12.8788	+	15.3484i	0.563151	+	0.671137i	0.970210	−	0.242265i	$-0.0778902\pi$
$523$	12.8788	+	15.3484i	0.563151	+	0.671137i	−0.407059	+	0.913402i	$0.633446\pi$
$524$	−0.0431641	−	9.42217i	−0.00188563	−	0.411609i
$525$	−12.5472	+	10.0472i	−0.547604	+	0.438496i
$526$	−35.5674	−	3.02967i	−1.55081	−	0.132100i
$527$	0.965443	+	16.5760i	0.0420553	+	0.722062i
$528$	−20.6657	−	9.25386i	−0.899361	−	0.402723i
$529$	3.34811	+	11.1835i	0.145570	+	0.486237i
$530$	−0.692462	−	1.11692i	−0.0300786	−	0.0485158i
$531$	1.45637	−	13.9477i	0.0632011	−	0.605278i
$532$	17.5035	+	26.3490i	0.758871	+	1.14237i
$533$	25.1906	+	10.8662i	1.09112	+	0.470665i
$534$	−0.601733	−	0.627100i	−0.0260395	−	0.0271373i
$535$	−14.8866	−	4.45677i	−0.643606	−	0.192683i
$536$	−0.587316	+	26.4309i	−0.0253682	+	1.14164i
$537$	11.6873	+	11.5442i	0.504344	+	0.498170i
$538$	−21.8259	−	19.3340i	−0.940981	−	0.833547i
$539$	3.97491	+	6.88475i	0.171212	+	0.296547i
$540$	−8.37642	+	0.927862i	−0.360464	+	0.0399288i
$541$	6.17071	−	10.6880i	0.265300	−	0.459512i	−0.702342	−	0.711839i	$-0.747862\pi$
$541$	6.17071	−	10.6880i	0.265300	−	0.459512i	0.967642	+	0.252327i	$0.0811958\pi$
$542$	15.1948	−	5.07365i	0.652671	−	0.217932i
$543$	30.3156	+	2.46426i	1.30097	+	0.105752i
$544$	24.8236	−	5.42279i	1.06430	−	0.232500i
$545$	−5.91382	+	5.57941i	−0.253320	+	0.238995i
$546$	18.7511	+	9.21959i	0.802471	+	0.394562i
$547$	−1.35398	−	11.5840i	−0.0578920	−	0.495298i	−0.990815	−	0.135223i	$-0.956825\pi$
$547$	−1.35398	−	11.5840i	−0.0578920	−	0.495298i	0.932923	−	0.360075i	$-0.117249\pi$
$548$	1.78349	+	28.3809i	0.0761870	+	1.21237i
$549$	7.15516	+	6.58589i	0.305375	+	0.281079i
$550$	9.48490	−	17.6877i	0.404438	−	0.754207i
$551$	−49.4393	−	11.7173i	−2.10619	−	0.499175i
$552$	−16.3992	−	1.70052i	−0.697998	−	0.0723790i
$553$	5.87449	−	3.86371i	0.249809	−	0.164302i
$554$	1.00433	−	1.44134i	0.0426698	−	0.0612368i
$555$	−6.08050	−	11.1126i	−0.258103	−	0.471705i
$556$	−10.6766	−	18.2983i	−0.452789	−	0.776021i
$557$	13.7525	−	2.42494i	0.582713	−	0.102748i	0.125482	−	0.992096i	$-0.459952\pi$
$557$	13.7525	−	2.42494i	0.582713	−	0.102748i	0.457231	+	0.889348i	$0.348841\pi$
$558$	−12.4430	−	9.54665i	−0.526756	−	0.404142i
$559$	40.3885	+	7.12158i	1.70825	+	0.301211i
$560$	−0.466487	−	6.91689i	−0.0197127	−	0.292292i
$561$	0.896015	+	25.4108i	0.0378298	+	1.07284i
$562$	−18.5578	+	1.66643i	−0.782811	+	0.0702943i
$563$	−19.7650	−	2.31019i	−0.832994	−	0.0973630i	−0.311104	−	0.950376i	$-0.600699\pi$
$563$	−19.7650	−	2.31019i	−0.832994	−	0.0973630i	−0.521890	+	0.853013i	$0.674773\pi$
$564$	−5.34572	+	1.83532i	−0.225095	+	0.0772808i
$565$	−0.165207	+	2.83649i	−0.00695030	+	0.119332i
$566$	10.9065	+	1.57205i	0.458432	+	0.0660782i
$567$	9.05321	+	16.9709i	0.380199	+	0.712710i
$568$	2.77755	−	6.06494i	0.116543	−	0.254479i
$569$	−20.7396	−	1.20795i	−0.869450	−	0.0506397i	−0.382383	−	0.924004i	$-0.624896\pi$
$569$	−20.7396	−	1.20795i	−0.869450	−	0.0506397i	−0.487067	+	0.873364i	$0.661933\pi$
$570$	−14.6825	−	0.730753i	−0.614983	−	0.0306079i
$571$	2.84606	−	24.3496i	0.119104	−	1.01900i	−0.793051	−	0.609155i	$-0.791509\pi$
$571$	2.84606	−	24.3496i	0.119104	−	1.01900i	0.912155	−	0.409845i	$-0.134417\pi$
$572$	−26.0523	−	1.39765i	−1.08930	−	0.0584388i
$573$	−4.92919	−	7.88238i	−0.205920	−	0.329291i
$574$	−18.2628	+	9.90129i	−0.762276	+	0.413272i
$575$	2.53768	−	14.3919i	0.105828	−	0.600183i
$576$	−11.4544	+	21.0902i	−0.477265	+	0.878759i
$577$	−3.47506	−	19.7080i	−0.144668	−	0.820456i	−0.967633	−	0.252363i	$-0.918792\pi$
$577$	−3.47506	−	19.7080i	−0.144668	−	0.820456i	0.822964	−	0.568093i	$-0.192319\pi$
$578$	−2.79348	−	3.51634i	−0.116193	−	0.146261i
$579$	−0.689696	+	30.0718i	−0.0286628	+	1.24974i
$580$	8.13435	+	7.60423i	0.337760	+	0.315748i
$581$	−1.35784	−	2.06450i	−0.0563328	−	0.0856498i
$582$	−27.5837	−	32.3145i	−1.14338	−	1.33948i
$583$	0.863657	−	3.64406i	0.0357690	−	0.150921i
$584$	6.16031	−	6.24556i	0.254916	−	0.258443i
$585$	−8.62330	+	4.46460i	−0.356529	+	0.184589i
$586$	−33.3066	+	6.95683i	−1.37588	+	0.287384i
$587$	25.1617	−	2.94098i	1.03853	−	0.121387i	0.420302	−	0.907384i	$-0.361924\pi$
$587$	25.1617	−	2.94098i	1.03853	−	0.121387i	0.618230	+	0.785997i	$0.287850\pi$
$588$	7.59809	−	3.64289i	0.313340	−	0.150230i
$589$	−18.7736	−	19.8988i	−0.773552	−	0.819918i
$590$	−3.78210	+	3.79947i	−0.155707	+	0.156422i
$591$	−13.4124	+	6.35514i	−0.551712	+	0.261415i
$592$	−35.8668	−	3.85947i	−1.47412	−	0.158623i
$593$	26.3073	+	15.1885i	1.08031	+	0.623717i	0.930980	−	0.365071i	$-0.118955\pi$
$593$	26.3073	+	15.1885i	1.08031	+	0.623717i	0.149330	+	0.988787i	$0.452288\pi$
$594$	−18.7143	−	15.0522i	−0.767858	−	0.617601i
$595$	−6.74186	+	3.89241i	−0.276389	+	0.159573i
$596$	29.2365	−	24.7615i	1.19757	−	1.01427i
$597$	4.54318	+	16.5471i	0.185940	+	0.677228i
$598$	−18.3382	+	4.95876i	−0.749906	+	0.202779i
$599$	1.22380	−	4.08776i	0.0500030	−	0.167022i	−0.929341	−	0.369222i	$-0.879624\pi$
$599$	1.22380	−	4.08776i	0.0500030	−	0.167022i	0.979344	+	0.202201i	$0.0648093\pi$
$600$	−17.9242	−	11.4572i	−0.731754	−	0.467739i
$601$	1.45527	−	3.37370i	0.0593618	−	0.137616i	−0.885953	−	0.463774i	$-0.846495\pi$
$601$	1.45527	−	3.37370i	0.0593618	−	0.137616i	0.945315	+	0.326158i	$0.105754\pi$
$602$	−23.1518	+	20.6986i	−0.943596	+	0.843610i
$603$	−7.71084	+	26.9601i	−0.314010	+	1.09790i
$604$	11.9308	+	27.3139i	0.485455	+	1.11139i
$605$	0.247516	−	0.0741015i	0.0100630	−	0.00301266i
$606$	8.17583	−	14.4414i	0.332121	−	0.586640i
$607$	23.4927	−	1.36829i	0.953538	−	0.0555373i	0.425684	−	0.904872i	$-0.360034\pi$
$607$	23.4927	−	1.36829i	0.953538	−	0.0555373i	0.527855	+	0.849335i	$0.322997\pi$
$608$	−25.5879	+	33.1341i	−1.03772	+	1.34377i
$609$	9.23742	−	23.6758i	0.374319	−	0.959394i
$610$	−0.547226	−	3.67713i	−0.0221566	−	0.148883i
$611$	−4.98875	+	4.18605i	−0.201823	+	0.169350i
$612$	26.9274	+	1.11222i	1.08847	+	0.0449587i
$613$	34.3015	+	28.7824i	1.38543	+	1.16251i	0.967155	+	0.254188i	$0.0818080\pi$
$613$	34.3015	+	28.7824i	1.38543	+	1.16251i	0.418271	+	0.908323i	$0.362636\pi$
$614$	10.3557	−	16.8755i	0.417920	−	0.681038i
$615$	1.34037	−	9.56084i	0.0540490	−	0.385530i
$616$	13.0320	−	14.8482i	0.525076	−	0.598251i
$617$	6.96956	−	3.00637i	0.280584	−	0.121032i	−0.251138	−	0.967951i	$-0.580805\pi$
$617$	6.96956	−	3.00637i	0.280584	−	0.121032i	0.531721	+	0.846919i	$0.321545\pi$
$618$	38.7343	−	4.85943i	1.55812	−	0.195475i
$619$	−14.4070	+	21.9047i	−0.579065	+	0.880425i	−0.999640	−	0.0268327i	$-0.991458\pi$
$619$	−14.4070	+	21.9047i	−0.579065	+	0.880425i	0.420575	+	0.907258i	$0.361828\pi$
$620$	1.40937	+	5.82752i	0.0566019	+	0.234039i
$621$	−16.3683	−	6.15510i	−0.656836	−	0.246996i
$622$	36.6643	+	28.8542i	1.47011	+	1.15695i
$623$	0.677634	−	0.340321i	0.0271488	−	0.0136347i
$624$	−3.58821	+	27.4195i	−0.143643	+	1.09766i
$625$	9.29649	−	12.4873i	0.371860	−	0.499494i
$626$	8.53652	−	6.00653i	0.341188	−	0.240069i
$627$	−28.0425	−	31.1231i	−1.11991	−	1.24294i
$628$	−4.49694	−	0.771708i	−0.179448	−	0.0307945i
$629$	13.8547	+	38.0654i	0.552422	+	1.51777i
$630$	1.38160	−	7.22217i	0.0550441	−	0.287738i
$631$	15.6485	−	42.9938i	0.622956	−	1.71156i	−0.0766781	−	0.997056i	$-0.524431\pi$
$631$	15.6485	−	42.9938i	0.622956	−	1.71156i	0.699634	−	0.714501i	$-0.253346\pi$
$632$	7.33876	+	5.72122i	0.291920	+	0.227578i
$633$	−20.4302	−	17.9571i	−0.812026	−	0.713730i
$634$	−35.1573	+	16.4922i	−1.39627	+	0.654991i
$635$	0.421267	+	0.211568i	0.0167175	+	0.00839582i
$636$	−3.78115	−	1.20803i	−0.149932	−	0.0479015i
$637$	6.66264	−	7.06199i	0.263984	−	0.279806i
$638$	0.995575	+	31.7166i	0.0394152	+	1.25567i
$639$	4.48085	−	5.47563i	0.177260	−	0.216613i
$640$	8.47123	−	3.52369i	0.334855	−	0.139286i
$641$	−14.9690	+	11.1440i	−0.591240	+	0.440162i	−0.850744	−	0.525580i	$-0.823848\pi$
$641$	−14.9690	+	11.1440i	−0.591240	+	0.440162i	0.259504	+	0.965742i	$0.416441\pi$
$642$	−42.9399	+	18.9543i	−1.69470	+	0.748067i
$643$	10.2662	+	43.3164i	0.404859	+	1.70823i	0.668585	+	0.743636i	$0.266900\pi$
$643$	10.2662	+	43.3164i	0.404859	+	1.70823i	−0.263726	+	0.964598i	$0.584952\pi$
$644$	5.63707	−	13.2346i	0.222132	−	0.521515i
$645$	−1.34637	−	14.3693i	−0.0530131	−	0.565792i
$646$	46.0610	+	9.40088i	1.81225	+	0.369873i
$647$	35.4204			1.39252			0.696259	−	0.717790i	$-0.254846\pi$
$647$	35.4204			1.39252			0.696259	+	0.717790i	$0.254846\pi$
$648$	−17.4241	+	18.5580i	−0.684484	+	0.729028i
$649$	−15.2774			−0.599691
$650$	−24.0162	−	4.90162i	−0.941994	−	0.192257i
$651$	11.1605	−	7.91755i	0.437416	−	0.310313i
$652$	−1.25160	+	2.93847i	−0.0490163	+	0.115079i
$653$	−9.32350	−	39.3389i	−0.364857	−	1.53945i	−0.777692	−	0.628646i	$-0.783610\pi$
$653$	−9.32350	−	39.3389i	−0.364857	−	1.53945i	0.412835	−	0.910806i	$-0.364539\pi$
$654$	−2.64483	+	24.4151i	−0.103421	+	0.954706i
$655$	−3.06451	+	2.28144i	−0.119740	+	0.0891434i
$656$	−20.1699	−	18.6830i	−0.787504	−	0.729450i
$657$	8.00014	−	4.75120i	0.312115	−	0.185362i
$658$	−0.154718	−	4.92895i	−0.00603154	−	0.192150i
$659$	33.9663	−	36.0022i	1.32314	−	1.40245i	0.468288	−	0.883576i	$-0.344871\pi$
$659$	33.9663	−	36.0022i	1.32314	−	1.40245i	0.854852	−	0.518872i	$-0.173648\pi$
$660$	1.95305	+	8.97106i	0.0760223	+	0.349198i
$661$	−39.6598	−	19.9179i	−1.54259	−	0.774717i	−0.544636	−	0.838672i	$-0.683332\pi$
$661$	−39.6598	−	19.9179i	−1.54259	−	0.774717i	−0.997953	+	0.0639548i	$0.979629\pi$
$662$	20.9344	−	9.82029i	0.813637	−	0.381676i
$663$	29.4158	−	9.94879i	1.14242	−	0.386379i
$664$	2.01063	−	2.57909i	0.0780277	−	0.100088i
$665$	4.38688	−	12.0528i	0.170116	−	0.467389i
$666$	−35.7613	−	13.6057i	−1.38572	−	0.527211i
$667$	7.90250	+	21.7119i	0.305986	+	0.840689i
$668$	−35.5518	−	6.10095i	−1.37554	−	0.236053i
$669$	−13.9499	+	42.9832i	−0.539336	+	1.66183i
$670$	8.76697	−	6.16868i	0.338698	−	0.238317i
$671$	6.32645	−	8.49789i	0.244230	−	0.328057i
$672$	−14.6359	−	14.9758i	−0.564593	−	0.577705i
$673$	21.2113	−	10.6527i	0.817634	−	0.410631i	0.00973536	−	0.999953i	$-0.496901\pi$
$673$	21.2113	−	10.6527i	0.817634	−	0.410631i	0.807899	+	0.589321i	$0.200605\pi$
$674$	−8.24408	−	6.48794i	−0.317550	−	0.249906i
$675$	−15.3090	−	16.5756i	−0.589242	−	0.637994i
$676$	1.37814	+	5.69837i	0.0530054	+	0.219168i
$677$	19.6133	−	29.8206i	0.753801	−	1.14610i	−0.231091	−	0.972932i	$-0.574230\pi$
$677$	19.6133	−	29.8206i	0.753801	−	1.14610i	0.984893	−	0.173167i	$-0.0554000\pi$
$678$	5.18290	+	6.84042i	0.199048	+	0.262705i
$679$	34.0377	−	14.6824i	1.30625	−	0.563460i
$680$	−7.74328	−	6.79616i	−0.296941	−	0.260621i
$681$	−37.1947	−	29.0394i	−1.42531	−	1.11279i
$682$	−8.93624	+	14.5624i	−0.342186	+	0.557623i
$683$	8.30371	+	6.96764i	0.317733	+	0.266609i	0.787679	−	0.616086i	$-0.211282\pi$
$683$	8.30371	+	6.96764i	0.317733	+	0.266609i	−0.469947	+	0.882695i	$0.655727\pi$
$684$	−35.1641	+	27.1140i	−1.34453	+	1.03673i
$685$	8.83284	−	7.41164i	0.337486	−	0.283184i
$686$	4.19646	+	28.1984i	0.160221	+	1.07662i
$687$	−29.4046	+	4.49227i	−1.12186	+	0.171391i
$688$	−35.7803	−	20.2229i	−1.36411	−	0.770992i
$689$	−4.56592	+	0.265935i	−0.173948	+	0.0101313i
$690$	3.39136	+	5.76106i	0.129107	+	0.219320i
$691$	11.6538	−	3.48891i	0.443330	−	0.132724i	−0.0573548	−	0.998354i	$-0.518267\pi$
$691$	11.6538	−	3.48891i	0.443330	−	0.132724i	0.500685	+	0.865629i	$0.333081\pi$
$692$	9.30947	+	21.3128i	0.353893	+	0.810190i
$693$	17.3641	−	11.7294i	0.659607	−	0.445564i
$694$	−16.4771	+	14.7312i	−0.625464	+	0.559188i
$695$	−3.40238	+	7.88759i	−0.129059	+	0.299193i
$696$	33.5997	+	1.51799i	1.27359	+	0.0575394i
$697$	−8.85450	+	29.5761i	−0.335388	+	1.12027i
$698$	−18.9529	+	5.12497i	−0.717377	+	0.193983i
$699$	−12.5602	−	3.28272i	−0.475069	−	0.124164i
$700$	14.1636	−	11.9957i	0.535334	−	0.453394i
$701$	−18.8411	+	10.8779i	−0.711620	+	0.410854i	−0.811660	−	0.584130i	$-0.801436\pi$
$701$	−18.8411	+	10.8779i	−0.711620	+	0.410854i	0.100041	+	0.994983i	$0.468103\pi$
$702$	−11.0556	+	27.1673i	−0.417268	+	1.02537i
$703$	−57.8004	−	33.3711i	−2.17998	−	1.25861i
$704$	24.1477	+	10.0250i	0.910099	+	0.377830i
$705$	1.88535	+	1.30291i	0.0710063	+	0.0490703i
$706$	22.0901	−	22.1915i	0.831372	−	0.835190i
$707$	9.93626	+	10.5318i	0.373691	+	0.396090i
$708$	−1.23800	+	16.1456i	−0.0465268	+	0.606788i
$709$	3.04466	−	0.355870i	0.114345	−	0.0133650i	−0.0587281	−	0.998274i	$-0.518704\pi$
$709$	3.04466	−	0.355870i	0.114345	−	0.0133650i	0.173073	+	0.984909i	$0.444630\pi$
$710$	−2.64767	+	0.553026i	−0.0993652	+	0.0207547i
$711$	5.99091	+	7.84363i	0.224676	+	0.294159i
$712$	0.714477	+	0.704725i	0.0267762	+	0.0264107i
$713$	−2.86901	+	12.1053i	−0.107445	+	0.453348i
$714$	−7.85537	+	22.1633i	−0.293980	+	0.829439i
$715$	5.81312	+	8.83842i	0.217398	+	0.330538i
$716$	−13.8569	−	12.9539i	−0.517857	−	0.484108i
$717$	21.1737	+	12.8808i	0.790745	+	0.481042i
$718$	−8.02160	−	10.0973i	−0.299363	−	0.376829i
$719$	1.87960	+	10.6598i	0.0700974	+	0.397542i	0.999588	+	0.0286967i	$0.00913571\pi$
$719$	1.87960	+	10.6598i	0.0700974	+	0.397542i	−0.929491	+	0.368845i	$0.879753\pi$
$720$	9.63912	−	1.33707i	0.359229	−	0.0498296i
$721$	−5.91456	+	33.5432i	−0.220270	+	1.24921i
$722$	−44.4699	+	24.1096i	−1.65500	+	0.897267i
$723$	−0.562935	+	1.05960i	−0.0209358	+	0.0394068i
$724$	−35.0705	−	1.88146i	−1.30338	−	0.0699239i
$725$	−3.46101	+	29.6109i	−0.128539	+	1.09972i
$726$	0.423320	−	0.655625i	0.0157109	−	0.0243325i
$727$	−16.2782	−	0.948097i	−0.603725	−	0.0351630i	−0.246439	−	0.969158i	$-0.579261\pi$
$727$	−16.2782	−	0.948097i	−0.603725	−	0.0351630i	−0.357285	+	0.933995i	$0.616298\pi$
$728$	−21.9365	−	10.0462i	−0.813021	−	0.372338i
$729$	−22.8681	+	14.3545i	−0.846965	+	0.531649i
$730$	−3.52064	−	0.507464i	−0.130305	−	0.0187821i
$731$	−2.68351	+	46.0741i	−0.0992533	+	1.70411i
$732$	−8.46814	−	7.37458i	−0.312991	−	0.272572i
$733$	−18.9461	−	2.21448i	−0.699791	−	0.0817938i	−0.241244	−	0.970464i	$-0.577556\pi$
$733$	−18.9461	−	2.21448i	−0.699791	−	0.0817938i	−0.458546	+	0.888671i	$0.651630\pi$
$734$	4.83120	−	0.433828i	0.178323	−	0.0160129i
$735$	−3.01726	−	1.60299i	−0.111293	−	0.0591271i
$736$	18.9831	+	1.44194i	0.699725	+	0.0531506i
$737$	30.0843	+	5.30467i	1.10817	+	0.195400i
$738$	−15.6697	−	24.5932i	−0.576811	−	0.905289i
$739$	19.6768	−	3.46955i	0.723822	−	0.127629i	0.200414	−	0.979711i	$-0.435771\pi$
$739$	19.6768	−	3.46955i	0.723822	−	0.127629i	0.523408	+	0.852082i	$0.324660\pi$
$740$	7.37148	+	12.6338i	0.270981	+	0.464426i
$741$	−26.5906	+	43.7101i	−0.976830	+	1.60573i
$742$	1.97999	−	2.84154i	0.0726875	−	0.104316i
$743$	−41.8291	+	27.5115i	−1.53456	+	1.00930i	−0.549820	+	0.835283i	$0.685304\pi$
$743$	−41.8291	+	27.5115i	−1.53456	+	1.00930i	−0.984743	+	0.174014i	$0.944326\pi$
$744$	14.6658	+	10.6241i	0.537674	+	0.389499i
$745$	−15.1163	−	3.58264i	−0.553820	−	0.131258i
$746$	19.6476	−	36.6394i	0.719350	−	1.34146i
$747$	2.75652	−	2.10541i	0.100856	−	0.0770329i
$748$	−1.84139	−	29.3022i	−0.0673279	−	1.07140i
$749$	−4.75433	−	40.6759i	−0.173719	−	1.48626i
$750$	1.23552	+	18.5166i	0.0451148	+	0.676132i
$751$	−3.76064	+	3.54798i	−0.137228	+	0.129468i	−0.751796	−	0.659396i	$-0.770812\pi$
$751$	−3.76064	+	3.54798i	−0.137228	+	0.129468i	0.614568	+	0.788864i	$0.289330\pi$
$752$	6.11207	−	2.28824i	0.222884	−	0.0834437i
$753$	27.5098	−	39.8076i	1.00251	−	1.45067i
$754$	36.7586	−	12.2740i	1.33867	−	0.446993i
$755$	6.04277	−	10.4664i	0.219919	−	0.380911i
$756$	−10.9889	−	19.3013i	−0.399661	−	0.701982i
$757$	15.9040	+	27.5465i	0.578040	+	1.00119i	0.995704	+	0.0925932i	$0.0295156\pi$
$757$	15.9040	+	27.5465i	0.578040	+	1.00119i	−0.417664	+	0.908602i	$0.637151\pi$
$758$	7.78398	+	6.89527i	0.282727	+	0.250447i
$759$	−4.81732	+	18.4318i	−0.174858	+	0.669030i
$760$	16.9707	+	0.377103i	0.615592	+	0.0136790i
$761$	−31.4395	−	9.41237i	−1.13968	−	0.341198i	−0.339293	−	0.940681i	$-0.610188\pi$
$761$	−31.4395	−	9.41237i	−1.13968	−	0.341198i	−0.800388	+	0.599483i	$0.795373\pi$
$762$	1.38269	−	0.340067i	0.0500897	−	0.0123193i
$763$	−19.6745	−	8.48674i	−0.712263	−	0.307240i
$764$	5.93996	+	8.94177i	0.214900	+	0.323502i
$765$	−6.11685	−	9.05531i	−0.221155	−	0.327395i
$766$	3.72137	+	6.00244i	0.134459	+	0.216877i
$767$	5.35113	+	17.8740i	0.193218	+	0.645394i
$768$	12.5514	−	24.7075i	0.452911	−	0.891556i
$769$	3.01844	+	51.8246i	0.108848	+	1.86884i	0.405815	+	0.913955i	$0.366988\pi$
$769$	3.01844	+	51.8246i	0.108848	+	1.86884i	−0.296967	+	0.954888i	$0.595975\pi$
$770$	−7.98170	−	0.679890i	−0.287641	−	0.0245015i
$771$	1.24466	+	8.14703i	0.0448252	+	0.293408i
$772$	−0.159115	−	34.7327i	−0.00572666	−	1.25006i
$773$	11.9457	+	14.2364i	0.429659	+	0.512047i	0.936824	−	0.349802i	$-0.113751\pi$
$773$	11.9457	+	14.2364i	0.429659	+	0.512047i	−0.507165	+	0.861849i	$0.669307\pi$
$774$	−31.2718	−	30.3714i	−1.12404	−	1.09168i
$775$	−10.3180	+	12.2965i	−0.370634	+	0.441704i
$776$	32.8653	+	36.4233i	1.17979	+	1.30752i
$777$	20.5441	−	26.3137i	0.737016	−	0.943999i
$778$	9.97750	−	21.5254i	0.357711	−	0.771724i
$779$	−20.1473	−	46.7067i	−0.721853	−	1.67344i
$780$	9.81174	−	5.42724i	0.351317	−	0.194326i
$781$	−6.43993	−	4.23561i	−0.230439	−	0.151562i
$782$	−7.93840	−	19.8495i	−0.283876	−	0.709817i
$783$	34.0650	+	10.5937i	1.21738	+	0.378587i
$784$	−8.65449	+	4.44620i	−0.309089	+	0.158793i
$785$	0.830303	+	1.65327i	0.0296348	+	0.0590077i
$786$	−2.56632	+	11.2509i	−0.0915375	+	0.401306i
$787$	−14.9636	−	11.1400i	−0.533394	−	0.397097i	0.296488	−	0.955037i	$-0.404185\pi$
$787$	−14.9636	−	11.1400i	−0.533394	−	0.397097i	−0.829881	+	0.557940i	$0.811592\pi$
$788$	15.2796	−	7.76153i	0.544312	−	0.276493i
$789$	41.5835	+	13.4957i	1.48041	+	0.480459i
$790$	0.101100	−	3.77174i	0.00359699	−	0.134193i
$791$	−7.03639	+	2.56103i	−0.250185	+	0.0910599i
$792$	22.0794	+	16.7798i	0.784556	+	0.596244i
$793$	−12.1582	−	4.42521i	−0.431749	−	0.157144i
$794$	7.20945	−	18.2691i	0.255854	−	0.648347i
$795$	0.515661	+	1.52467i	0.0182886	+	0.0540744i
$796$	−5.76963	−	18.9554i	−0.204499	−	0.671857i
$797$	5.25916	−	10.4719i	0.186289	−	0.370932i	−0.781030	−	0.624493i	$-0.785306\pi$
$797$	5.25916	−	10.4719i	0.186289	−	0.370932i	0.967319	+	0.253561i	$0.0816019\pi$
$798$	−13.5577	−	36.2926i	−0.479938	−	1.28474i
$799$	−5.33067	−	5.02923i	−0.188585	−	0.177921i
$800$	21.0532	+	12.6553i	0.744344	+	0.447432i
$801$	0.543526	+	0.915196i	0.0192045	+	0.0323369i
$802$	−0.923154	+	2.80744i	−0.0325977	+	0.0991342i
$803$	−6.05315	−	8.13079i	−0.213611	−	0.286929i
$804$	8.04398	−	31.3640i	0.283689	−	1.10612i
$805$	−5.67557	+	1.34514i	−0.200038	+	0.0474098i
$806$	20.1675	+	5.35439i	0.710371	+	0.188601i
$807$	20.6626	+	29.1259i	0.727358	+	1.02528i
$808$	−8.97835	+	16.9288i	−0.315857	+	0.595554i
$809$			4.84049i			0.170183i	0.996373	+	0.0850913i	$0.0271182\pi$
$809$			4.84049i			0.170183i	−0.996373	+	0.0850913i	$0.972882\pi$
$810$	10.2493	+	1.22049i	0.360124	+	0.0428837i
$811$			1.26610i			0.0444587i	0.999753	+	0.0222293i	$0.00707640\pi$
$811$			1.26610i			0.0444587i	−0.999753	+	0.0222293i	$0.992924\pi$
$812$	−9.91037	+	27.6216i	−0.347786	+	0.969328i
$813$	−19.5342	+	1.83030i	−0.685094	+	0.0641913i
$814$	−10.6962	+	40.2875i	−0.374900	+	1.41208i
$815$	1.26014	−	0.298660i	0.0441409	−	0.0104616i
$816$	−31.1166	−	0.428466i	−1.08930	−	0.0149993i
$817$	−45.4085	−	60.9942i	−1.58864	−	2.13392i
$818$	28.4162	+	9.34393i	0.993550	+	0.326703i
$819$	−19.8050	−	16.2070i	−0.692043	−	0.566317i
$820$	−1.24345	+	11.0783i	−0.0434232	+	0.386871i
$821$	5.56822	+	5.25335i	0.194332	+	0.183343i	0.777257	−	0.629183i	$-0.216610\pi$
$821$	5.56822	+	5.25335i	0.194332	+	0.183343i	−0.582925	+	0.812526i	$0.698092\pi$
$822$	5.75782	−	34.3487i	0.200827	−	1.19805i
$823$	−3.48383	+	6.93688i	−0.121439	+	0.241805i	−0.946136	−	0.323770i	$-0.895049\pi$
$823$	−3.48383	+	6.93688i	−0.121439	+	0.241805i	0.824697	+	0.565575i	$0.191346\pi$
$824$	−44.5552	+	6.83943i	−1.55215	+	0.238263i
$825$	−16.2280	+	18.4629i	−0.564986	+	0.642797i
$826$	−13.1421	−	5.18620i	−0.457272	−	0.180451i
$827$	4.63744	+	1.68789i	0.161259	+	0.0586936i	0.421388	−	0.906880i	$-0.361543\pi$
$827$	4.63744	+	1.68789i	0.161259	+	0.0586936i	−0.260129	+	0.965574i	$0.583765\pi$
$828$	19.0888	+	6.58469i	0.663382	+	0.228834i
$829$	30.9838	−	11.2772i	1.07611	−	0.391673i	0.257653	−	0.966237i	$-0.417051\pi$
$829$	30.9838	−	11.2772i	1.07611	−	0.391673i	0.818459	+	0.574565i	$0.194829\pi$
$830$	−1.32552	−	0.0355302i	−0.0460095	−	0.00123327i
$831$	−1.59843	+	1.44022i	−0.0554490	+	0.0499607i
$832$	3.27078	−	31.7633i	0.113394	−	1.10119i
$833$	8.76390	+	6.52448i	0.303651	+	0.226060i
$834$	7.65130	+	24.7928i	0.264943	+	0.858505i
$835$	6.56418	+	13.0704i	0.227163	+	0.452319i
$836$	33.3571	+	35.0335i	1.15368	+	1.21166i
$837$	12.1898	+	14.8445i	0.421343	+	0.513101i
$838$	30.3193	−	12.1256i	1.04736	−	0.418871i
$839$	−30.9040	−	20.3259i	−1.06692	−	0.701727i	−0.110550	−	0.993871i	$-0.535261\pi$
$839$	−30.9040	−	20.3259i	−1.06692	−	0.701727i	−0.956375	+	0.292143i	$0.905632\pi$
$840$	−1.36532	+	8.38018i	−0.0471080	+	0.289144i
$841$	−7.18293	−	16.6519i	−0.247687	−	0.574204i
$842$	−10.7245	−	4.97106i	−0.369592	−	0.171314i
$843$	22.5990	+	3.16824i	0.778349	+	0.109120i
$844$	24.1522	+	20.0783i	0.831352	+	0.691122i
$845$	1.52801	−	1.82101i	0.0525652	−	0.0626447i
$846$	6.88637	−	0.703970i	0.236758	−	0.0242030i
$847$	0.437681	+	0.521608i	0.0150389	+	0.0179227i
$848$	4.40281	+	1.27428i	0.151193	+	0.0437589i
$849$	−12.5726	−	4.90536i	−0.431491	−	0.168351i
$850$	2.34113	−	27.4842i	0.0803003	−	0.942701i
$851$	1.76475	+	30.2996i	0.0604950	+	1.03866i
$852$	−4.99816	+	6.46265i	−0.171234	+	0.221407i
$853$	0.0284590	+	0.0950598i	0.000974419	+	0.00325479i	0.958475	−	0.285175i	$-0.0920519\pi$
$853$	0.0284590	+	0.0950598i	0.000974419	+	0.00325479i	−0.957501	+	0.288430i	$0.906867\pi$
$854$	8.32697	−	5.16252i	0.284943	−	0.176658i
$855$	17.3105	+	4.95097i	0.592007	+	0.169319i
$856$	48.9619	−	23.2422i	1.67348	−	0.794403i
$857$	−30.6167	−	13.2068i	−1.04585	−	0.451134i	−0.197349	−	0.980333i	$-0.563233\pi$
$857$	−30.6167	−	13.2068i	−1.04585	−	0.451134i	−0.848498	+	0.529199i	$0.822492\pi$
$858$	30.6873	+	8.90537i	1.04765	+	0.304024i
$859$	−18.3557	−	5.49535i	−0.626290	−	0.187499i	−0.0420967	−	0.999114i	$-0.513404\pi$
$859$	−18.3557	−	5.49535i	−0.626290	−	0.187499i	−0.584193	+	0.811615i	$0.698589\pi$
$860$	2.01049	+	16.5432i	0.0685572	+	0.564120i
$861$	24.5351	−	6.73636i	0.836154	−	0.229575i
$862$	4.83927	−	5.46299i	0.164826	−	0.186070i
$863$	−17.3432	−	30.0393i	−0.590368	−	1.02255i	−0.994183	−	0.107707i	$-0.965649\pi$
$863$	−17.3432	−	30.0393i	−0.590368	−	1.02255i	0.403814	−	0.914841i	$-0.367684\pi$
$864$	19.5225	−	21.9743i	0.664170	−	0.747582i
$865$	4.71513	−	8.16684i	0.160319	−	0.277681i
$866$	10.2729	+	30.7657i	0.349088	+	1.04546i
$867$	2.35514	+	4.97047i	0.0799848	+	0.168806i
$868$	−12.6307	+	9.49345i	−0.428714	+	0.322229i
$869$	7.82096	−	7.37869i	0.265308	−	0.250305i
$870$	−7.59005	−	11.3304i	−0.257327	−	0.384138i
$871$	−4.33117	−	37.0555i	−0.146756	−	1.25558i
$872$	2.27731	−	28.2655i	0.0771193	−	0.957190i
$873$	23.9241	+	46.2090i	0.809709	+	1.56394i
$874$	31.0413	+	16.6457i	1.04999	+	0.563048i
$875$	−15.7553	−	3.73407i	−0.532625	−	0.126234i
$876$	−9.08335	+	5.73825i	−0.306898	+	0.193878i
$877$	44.8178	−	29.4771i	1.51339	−	0.995373i	0.523739	−	0.851879i	$-0.324537\pi$
$877$	44.8178	−	29.4771i	1.51339	−	0.995373i	0.989651	−	0.143494i	$-0.0458338\pi$
$878$	−2.04596	−	1.42562i	−0.0690476	−	0.0481124i
$879$	41.6614	+	0.955505i	1.40521	+	0.0322284i
$880$	−2.53929	−	10.2929i	−0.0855995	−	0.346975i
$881$	−16.7049	+	2.94553i	−0.562804	+	0.0992375i	−0.447810	−	0.894129i	$-0.647796\pi$
$881$	−16.7049	+	2.94553i	−0.562804	+	0.0992375i	−0.114994	+	0.993366i	$0.536685\pi$
$882$	−10.0752	+	2.23428i	−0.339251	+	0.0752321i
$883$	−35.1995	−	6.20662i	−1.18456	−	0.208869i	−0.453544	−	0.891234i	$-0.649841\pi$
$883$	−35.1995	−	6.20662i	−1.18456	−	0.208869i	−0.731012	+	0.682364i	$0.760952\pi$
$884$	−33.6376	+	12.4179i	−1.13136	+	0.417659i
$885$	5.56697	−	3.48126i	0.187132	−	0.117021i
$886$	−5.27680	−	58.7635i	−0.177278	−	1.97420i
$887$	−34.7117	−	4.05721i	−1.16550	−	0.136228i	−0.488741	−	0.872429i	$-0.662544\pi$
$887$	−34.7117	−	4.05721i	−1.16550	−	0.136228i	−0.676763	+	0.736201i	$0.736618\pi$
$888$	41.7101	+	14.5687i	1.39970	+	0.488892i
$889$	−0.0722364	+	1.24025i	−0.00242273	+	0.0415967i
$890$	0.0580526	−	0.402753i	0.00194593	−	0.0135003i
$891$	18.1407	+	23.1540i	0.607736	+	0.775689i
$892$	14.7366	−	50.0571i	0.493417	−	1.67604i
$893$	12.0543	+	0.702086i	0.403383	+	0.0234944i
$894$	−41.7534	+	21.4129i	−1.39644	+	0.716156i
$895$	−0.892916	+	7.63939i	−0.0298469	+	0.255356i
$896$	17.3694	+	16.8211i	0.580271	+	0.561955i
$897$	23.2518	−	0.819889i	0.776356	−	0.0273753i
$898$	6.51087	+	12.0092i	0.217271	+	0.400753i
$899$	4.40702	−	24.9935i	0.146982	−	0.833578i
$900$	18.1971	+	18.6463i	0.606570	+	0.621544i
$901$	−0.893760	−	5.06877i	−0.0297755	−	0.168865i
$902$	−24.8745	+	19.7610i	−0.828230	+	0.657968i
$903$	33.3666	−	18.2572i	1.11037	−	0.607561i
$904$	−6.19971	−	7.73102i	−0.206199	−	0.257130i
$905$	7.82538	+	11.8979i	0.260124	+	0.395500i
$906$	−6.64244	−	35.8952i	−0.220680	−	1.19254i
$907$	−4.97436	+	20.9885i	−0.165171	+	0.696911i	0.825927	+	0.563777i	$0.190652\pi$
$907$	−4.97436	+	20.9885i	−0.165171	+	0.696911i	−0.991098	+	0.133134i	$0.957496\pi$
$908$	43.8550	+	32.3376i	1.45538	+	1.07316i
$909$	−13.7646	+	14.9543i	−0.456542	+	0.496004i
$910$	2.00026	+	9.57645i	0.0663079	+	0.317456i
$911$	45.8977	−	5.36467i	1.52066	−	0.177739i	0.685631	−	0.727949i	$-0.259526\pi$
$911$	45.8977	−	5.36467i	1.52066	−	0.177739i	0.835026	+	0.550210i	$0.185452\pi$
$912$	39.7274	−	32.4137i	1.31551	−	1.07332i
$913$	−2.59313	−	2.74855i	−0.0858200	−	0.0909638i
$914$	−20.9324	−	20.8367i	−0.692382	−	0.689217i
$915$	−0.368894	+	4.53817i	−0.0121953	+	0.150027i
$916$	33.7980	−	6.11928i	1.11672	−	0.202187i
$917$	−8.71962	−	5.03428i	−0.287947	−	0.166246i
$918$	−31.8103	−	8.80802i	−1.04990	−	0.290708i
$919$	−2.25487	+	1.30185i	−0.0743813	+	0.0429440i	−0.536729	−	0.843754i	$-0.680340\pi$
$919$	−2.25487	+	1.30185i	−0.0743813	+	0.0429440i	0.462348	+	0.886698i	$0.347007\pi$
$920$	−4.09752	−	6.54206i	−0.135091	−	0.215685i
$921$	−17.0410	+	17.2521i	−0.561519	+	0.568478i
$922$	4.42974	+	16.3818i	0.145886	+	0.539506i
$923$	−2.69983	+	9.01807i	−0.0888660	+	0.296833i
$924$	−19.6702	+	14.0904i	−0.647101	+	0.463540i
$925$	−15.5110	+	35.9586i	−0.510000	+	1.18231i
$926$	−22.6252	−	25.3068i	−0.743510	−	0.831632i
$927$	−47.5529	−	4.96532i	−1.56184	−	0.163082i
$928$	−38.8311	−	0.684900i	−1.27469	−	0.0224829i
$929$	−17.2461	+	5.16313i	−0.565825	+	0.169397i	−0.556924	−	0.830564i	$-0.688018\pi$
$929$	−17.2461	+	5.16313i	−0.565825	+	0.169397i	−0.00890083	+	0.999960i	$0.502833\pi$
$930$	−0.0620357	−	7.34273i	−0.00203423	−	0.240778i
$931$	−17.9711	+	1.04670i	−0.588981	+	0.0343042i
$932$	14.6020	+	3.39016i	0.478304	+	0.111048i
$933$	−35.7171	−	44.6043i	−1.16932	−	1.46028i
$934$	2.81372	−	0.418735i	0.0920679	−	0.0137014i
$935$	−9.11959	+	7.65224i	−0.298242	+	0.250255i
$936$	11.8982	−	31.7095i	0.388904	−	1.03646i
$937$	1.48601	+	1.24691i	0.0485457	+	0.0407347i	0.666738	−	0.745292i	$-0.267690\pi$
$937$	1.48601	+	1.24691i	0.0485457	+	0.0407347i	−0.618192	+	0.786027i	$0.712135\pi$
$938$	24.0786	+	14.7759i	0.786195	+	0.482450i
$939$	−11.8513	+	4.79293i	−0.386753	+	0.156411i
$940$	−2.21757	−	1.44401i	−0.0723293	−	0.0470985i
$941$	22.4728	−	9.69380i	0.732591	−	0.316009i	0.00309618	−	0.999995i	$-0.499014\pi$
$941$	22.4728	−	9.69380i	0.732591	−	0.316009i	0.729495	+	0.683986i	$0.239755\pi$
$942$	5.14961	+	2.16991i	0.167784	+	0.0706996i
$943$	−12.7111	+	19.3263i	−0.413930	+	0.629350i
$944$	0.916126	−	18.6756i	0.0298173	−	0.607838i
$945$	−3.65456	+	8.23086i	−0.118883	+	0.267750i
$946$	−29.3700	+	37.3198i	−0.954902	+	1.21337i
$947$	−40.5746	+	20.3773i	−1.31850	+	0.662174i	−0.962237	−	0.272213i	$-0.912245\pi$
$947$	−40.5746	+	20.3773i	−1.31850	+	0.662174i	−0.356260	+	0.934387i	$0.615948\pi$
$948$	−7.16423	−	8.86332i	−0.232683	−	0.287867i
$949$	−7.39254	+	9.92990i	−0.239972	+	0.322338i
$950$	26.1527	+	37.1685i	0.848506	+	1.20590i
$951$	46.5182	−	9.90429i	1.50846	−	0.321169i
$952$	8.36316	−	25.8318i	0.271052	−	0.837212i
$953$	−11.4604	−	31.4873i	−0.371239	−	1.01997i	−0.974883	−	0.222718i	$-0.928507\pi$
$953$	−11.4604	−	31.4873i	−0.371239	−	1.01997i	0.603643	−	0.797254i	$-0.293715\pi$
$954$	4.17458	+	2.49149i	0.135157	+	0.0806650i
$955$	1.48873	−	4.09024i	0.0481741	−	0.132357i
$956$	−24.8491	−	14.1953i	−0.803679	−	0.459108i
$957$	7.62445	−	38.1087i	0.246463	−	1.23188i
$958$	19.7312	+	42.0620i	0.637488	+	1.35896i
$959$	27.1552	+	13.6378i	0.876887	+	0.440389i
$960$	−11.0836	+	1.84951i	−0.357722	+	0.0596926i
$961$	−11.8961	+	12.6091i	−0.383745	+	0.406746i
$962$	50.8814	−	1.59715i	1.64048	−	0.0514942i
$963$	56.4855	−	10.6788i	1.82022	−	0.344120i
$964$	0.616118	−	1.24093i	0.0198438	−	0.0399678i
$965$	−11.2966	+	8.41002i	−0.363651	+	0.270728i
$966$	−10.4010	+	14.2202i	−0.334647	+	0.457528i
$967$	−8.91819	−	37.6288i	−0.286790	−	1.21006i	−0.905468	−	0.424416i	$-0.860480\pi$
$967$	−8.91819	−	37.6288i	−0.286790	−	1.21006i	0.618678	−	0.785645i	$-0.287669\pi$
$968$	−0.467797	+	0.770210i	−0.0150356	+	0.0247555i
$969$	−52.3303	−	24.0108i	−1.68109	−	0.771340i
$970$	3.97792	−	19.4904i	0.127723	−	0.625799i
$971$	−32.0716			−1.02923			−0.514614	−	0.857422i	$-0.672065\pi$
$971$	−32.0716			−1.02923			−0.514614	+	0.857422i	$0.672065\pi$
$972$	25.9398	−	17.2953i	0.832020	−	0.554746i
$973$	−22.6385			−0.725755
$974$	6.25916	−	30.6677i	0.200556	−	0.982656i
$975$	27.2851	+	12.5193i	0.873822	+	0.400937i
$976$	10.0087	+	8.24322i	0.320371	+	0.263859i
$977$	11.7290	+	49.4883i	0.375242	+	1.58327i	0.753420	+	0.657539i	$0.228403\pi$
$977$	11.7290	+	49.4883i	0.375242	+	1.58327i	−0.378178	+	0.925733i	$0.623449\pi$
$978$	2.30933	−	3.15731i	0.0738442	−	0.100960i
$979$	0.930143	−	0.692466i	0.0297275	−	0.0221313i
$980$	3.53363	+	1.75443i	0.112878	+	0.0560432i
$981$	9.93816	−	28.3879i	0.317301	−	0.906355i
$982$	25.9045	−	0.813135i	0.826647	−	0.0259482i
$983$	−1.29446	+	1.37205i	−0.0412870	+	0.0437617i	−0.747688	−	0.664050i	$-0.768836\pi$
$983$	−1.29446	+	1.37205i	−0.0412870	+	0.0437617i	0.706401	+	0.707812i	$0.250318\pi$
$984$	18.8682	+	27.8893i	0.601496	+	0.889079i
$985$	−6.20984	−	3.11870i	−0.197862	−	0.0993700i
$986$	18.5214	+	39.4830i	0.589843	+	1.25739i
$987$	−1.18488	+	5.92231i	−0.0377152	+	0.188509i
$988$	29.3042	−	51.2976i	0.932289	−	1.63199i
$989$	−11.8269	+	32.4942i	−0.376075	+	1.03326i
$990$	0.162846	−	11.2434i	0.00517558	−	0.357340i
$991$	11.4282	+	31.3986i	0.363028	+	0.997411i	0.977953	+	0.208825i	$0.0669640\pi$
$991$	11.4282	+	31.3986i	0.363028	+	0.997411i	−0.614925	+	0.788586i	$0.710814\pi$
$992$	−17.2656	−	11.7972i	−0.548185	−	0.374561i
$993$	−27.6992	+	5.89750i	−0.879009	+	0.187151i
$994$	−4.10196	−	5.82975i	−0.130106	−	0.184908i
$995$	−4.79764	+	6.44435i	−0.152095	+	0.204300i
$996$	−3.11488	+	2.51776i	−0.0986986	+	0.0797782i
$997$	−13.6163	+	6.83839i	−0.431234	+	0.216574i	−0.651157	−	0.758943i	$-0.725716\pi$
$997$	−13.6163	+	6.83839i	−0.431234	+	0.216574i	0.219922	+	0.975517i	$0.429420\pi$
$998$	−28.4172	+	36.1091i	−0.899530	+	1.14301i
$999$	38.8765	+	26.1648i	1.23000	+	0.827819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.83.48	✓	936
3.2	odd	2		972.2.p.a.251.5		936
4.3	odd	2	inner	324.2.p.a.83.51	yes	936
12.11	even	2		972.2.p.a.251.2		936
81.40	even	27		972.2.p.a.395.2		936
81.41	odd	54	inner	324.2.p.a.203.51	yes	936
324.203	even	54	inner	324.2.p.a.203.48	yes	936
324.283	odd	54		972.2.p.a.395.5		936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.83.48	✓	936	1.1	even	1	trivial
324.2.p.a.83.51	yes	936	4.3	odd	2	inner
324.2.p.a.203.48	yes	936	324.203	even	54	inner
324.2.p.a.203.51	yes	936	81.41	odd	54	inner
972.2.p.a.251.2		936	12.11	even	2
972.2.p.a.251.5		936	3.2	odd	2
972.2.p.a.395.2		936	81.40	even	27
972.2.p.a.395.5		936	324.283	odd	54

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38565 + 0.282806i) q^{2} +(-1.57425 - 0.722316i) q^{3} +(1.84004 + 0.783738i) q^{4} +(-0.187018 - 0.789092i) q^{5} +(-1.97708 - 1.44608i) q^{6} +(1.71428 - 1.27624i) q^{7} +(2.32801 + 1.60636i) q^{8} +(1.95652 + 2.27421i) q^{9} +O(q^{10})\)	\(q+(1.38565 + 0.282806i) q^{2} +(-1.57425 - 0.722316i) q^{3} +(1.84004 + 0.783738i) q^{4} +(-0.187018 - 0.789092i) q^{5} +(-1.97708 - 1.44608i) q^{6} +(1.71428 - 1.27624i) q^{7} +(2.32801 + 1.60636i) q^{8} +(1.95652 + 2.27421i) q^{9} +(-0.0359818 - 1.14629i) q^{10} +(2.24280 - 2.37723i) q^{11} +(-2.33058 - 2.56289i) q^{12} +(-3.56685 - 1.79134i) q^{13} +(2.73632 - 1.28361i) q^{14} +(-0.275560 + 1.37731i) q^{15} +(2.77151 + 2.88422i) q^{16} +(1.53626 - 4.22084i) q^{17} +(2.06789 + 3.70457i) q^{18} +(2.53116 + 6.95430i) q^{19} +(0.274320 - 1.59854i) q^{20} +(-3.62056 + 0.770860i) q^{21} +(3.78003 - 2.65973i) q^{22} +(2.00970 - 2.69949i) q^{23} +(-2.50456 - 4.21037i) q^{24} +(3.88047 - 1.94885i) q^{25} +(-4.43580 - 3.49089i) q^{26} +(-1.43735 - 4.99340i) q^{27} +(4.15459 - 1.00478i) q^{28} +(-3.77265 + 5.73604i) q^{29} +(-0.771342 + 1.83054i) q^{30} +(-3.39428 + 1.46415i) q^{31} +(3.02466 + 4.78032i) q^{32} +(-5.24784 + 2.12234i) q^{33} +(3.32239 - 5.41413i) q^{34} +(-1.32767 - 1.11405i) q^{35} +(1.81769 + 5.71804i) q^{36} +(-6.90854 + 5.79695i) q^{37} +(1.54058 + 10.3520i) q^{38} +(4.32120 + 5.39641i) q^{39} +(0.832186 - 2.13743i) q^{40} +(-6.86170 + 0.399649i) q^{41} +(-5.23482 + 0.0442268i) q^{42} +(-9.84330 + 2.94689i) q^{43} +(5.98998 - 2.61644i) q^{44} +(1.42866 - 1.96919i) q^{45} +(3.54816 - 3.17219i) q^{46} +(0.646240 - 1.49815i) q^{47} +(-2.27972 - 6.54239i) q^{48} +(-0.697634 + 2.33026i) q^{49} +(5.92812 - 1.60300i) q^{50} +(-5.46723 + 5.53498i) q^{51} +(-5.15921 - 6.09162i) q^{52} +(0.992359 - 0.572939i) q^{53} +(-0.579498 - 7.32558i) q^{54} +(-2.29530 - 1.32519i) q^{55} +(6.04096 - 0.217329i) q^{56} +(1.03853 - 12.7761i) q^{57} +(-6.84975 + 6.88121i) q^{58} +(-3.20784 - 3.40011i) q^{59} +(-1.58650 + 2.31835i) q^{60} +(3.21966 - 0.376324i) q^{61} +(-5.11735 + 1.06887i) q^{62} +(6.25646 + 1.40166i) q^{63} +(2.83922 + 7.47923i) q^{64} +(-0.746466 + 3.14959i) q^{65} +(-7.87187 + 1.45670i) q^{66} +(5.13628 + 7.80933i) q^{67} +(6.13481 - 6.56249i) q^{68} +(-5.11365 + 2.79803i) q^{69} +(-1.52463 - 1.91915i) q^{70} +(-0.409541 - 2.32262i) q^{71} +(0.901585 + 8.43725i) q^{72} +(0.538577 - 3.05442i) q^{73} +(-11.2122 + 6.07876i) q^{74} +(-7.51651 + 0.265042i) q^{75} +(-0.792915 + 14.7800i) q^{76} +(0.810889 - 6.93760i) q^{77} +(4.46152 + 8.69958i) q^{78} +(3.28438 + 0.191293i) q^{79} +(1.75759 - 2.72638i) q^{80} +(-1.34407 + 8.89907i) q^{81} +(-9.62093 - 1.38676i) q^{82} +(0.0672270 - 1.15424i) q^{83} +(-7.26613 - 1.41915i) q^{84} +(-3.61793 - 0.422876i) q^{85} +(-14.4727 + 1.29961i) q^{86} +(10.0823 - 6.30491i) q^{87} +(9.03995 - 1.93146i) q^{88} +(0.349419 + 0.0616119i) q^{89} +(2.53651 - 2.32457i) q^{90} +(-8.40077 + 1.48128i) q^{91} +(5.81362 - 3.39210i) q^{92} +(6.40102 + 0.146807i) q^{93} +(1.31915 - 1.89315i) q^{94} +(5.01421 - 3.29790i) q^{95} +(-1.30867 - 9.71017i) q^{96} +(16.8774 + 4.00002i) q^{97} +(-1.62569 + 3.03163i) q^{98} +(9.79441 + 0.449506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

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