LMFDB - Embedded newform 117.2.bc.a.110.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(20,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 11]))

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

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

chi := DirichletCharacter("117.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.bc (of order $12$, degree $4$, 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			110.7
Character	$\chi$	$=$	117.110
Dual form			117.2.bc.a.50.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0178736 - 0.0667051i) q^{2} +(-1.73062 + 0.0702708i) q^{3} +(1.72792 + 0.997615i) q^{4} +(0.690628 - 2.57746i) q^{5} +(-0.0262450 + 0.116698i) q^{6} +(1.75672 + 1.75672i) q^{7} +(0.195093 - 0.195093i) q^{8} +(2.99012 - 0.243225i) q^{9} +O(q^{10})$	\(q+(0.0178736 - 0.0667051i) q^{2} +(-1.73062 + 0.0702708i) q^{3} +(1.72792 + 0.997615i) q^{4} +(0.690628 - 2.57746i) q^{5} +(-0.0262450 + 0.116698i) q^{6} +(1.75672 + 1.75672i) q^{7} +(0.195093 - 0.195093i) q^{8} +(2.99012 - 0.243225i) q^{9} +(-0.159586 - 0.0921368i) q^{10} +(2.94182 + 0.788259i) q^{11} +(-3.06049 - 1.60508i) q^{12} +(-3.20340 - 1.65477i) q^{13} +(0.148582 - 0.0857836i) q^{14} +(-1.01410 + 4.50914i) q^{15} +(1.98570 + 3.43934i) q^{16} +(-0.757582 - 1.31217i) q^{17} +(0.0372199 - 0.203804i) q^{18} +(-5.08773 - 1.36325i) q^{19} +(3.76466 - 3.76466i) q^{20} +(-3.16368 - 2.91679i) q^{21} +(0.105162 - 0.182146i) q^{22} -6.17236 q^{23} +(-0.323924 + 0.351343i) q^{24} +(-1.83620 - 1.06013i) q^{25} +(-0.167638 + 0.184106i) q^{26} +(-5.15769 + 0.631049i) q^{27} +(1.28295 + 4.78802i) q^{28} +(-6.73536 + 3.88866i) q^{29} +(0.282657 + 0.148240i) q^{30} +(6.99365 + 1.87394i) q^{31} +(0.797918 - 0.213802i) q^{32} +(-5.14658 - 1.15746i) q^{33} +(-0.101069 + 0.0270814i) q^{34} +(5.74113 - 3.31464i) q^{35} +(5.40934 + 2.56272i) q^{36} +(1.73614 - 0.465197i) q^{37} +(-0.181872 + 0.315012i) q^{38} +(5.66016 + 2.63867i) q^{39} +(-0.368108 - 0.637582i) q^{40} +(-4.20290 - 4.20290i) q^{41} +(-0.251111 + 0.158900i) q^{42} -1.45159i q^{43} +(4.29686 + 4.29686i) q^{44} +(1.43816 - 7.87490i) q^{45} +(-0.110322 + 0.411728i) q^{46} +(2.96979 + 11.0834i) q^{47} +(-3.67819 - 5.81267i) q^{48} -0.827835i q^{49} +(-0.103535 + 0.103535i) q^{50} +(1.40330 + 2.21764i) q^{51} +(-3.88440 - 6.05506i) q^{52} -9.11286i q^{53} +(-0.0500922 + 0.355324i) q^{54} +(4.06341 - 7.03803i) q^{55} +0.685450 q^{56} +(8.90076 + 2.00176i) q^{57} +(0.139009 + 0.518788i) q^{58} +(-0.222038 - 0.828658i) q^{59} +(-6.25067 + 6.77976i) q^{60} -5.50190 q^{61} +(0.250003 - 0.433018i) q^{62} +(5.68010 + 4.82555i) q^{63} +7.88577i q^{64} +(-6.47744 + 7.11379i) q^{65} +(-0.169196 + 0.322616i) q^{66} +(-3.08710 + 3.08710i) q^{67} -3.02310i q^{68} +(10.6820 - 0.433736i) q^{69} +(-0.118489 - 0.442207i) q^{70} +(-0.849841 + 3.17165i) q^{71} +(0.535902 - 0.630805i) q^{72} +(0.551749 + 0.551749i) q^{73} -0.124124i q^{74} +(3.25226 + 1.70565i) q^{75} +(-7.43120 - 7.43120i) q^{76} +(3.78322 + 6.55273i) q^{77} +(0.277180 - 0.330399i) q^{78} +(6.40258 - 11.0896i) q^{79} +(10.2361 - 2.74277i) q^{80} +(8.88168 - 1.45454i) q^{81} +(-0.355476 + 0.205234i) q^{82} +(-3.03557 + 0.813378i) q^{83} +(-2.55675 - 8.19611i) q^{84} +(-3.90527 + 1.04641i) q^{85} +(-0.0968284 - 0.0259451i) q^{86} +(11.3831 - 7.20312i) q^{87} +(0.727714 - 0.420146i) q^{88} +(3.38089 + 12.6176i) q^{89} +(-0.499591 - 0.236685i) q^{90} +(-2.72052 - 8.53446i) q^{91} +(-10.6653 - 6.15764i) q^{92} +(-12.2351 - 2.75164i) q^{93} +0.792402 q^{94} +(-7.02746 + 12.1719i) q^{95} +(-1.36587 + 0.426081i) q^{96} +(-2.03610 + 2.03610i) q^{97} +(-0.0552209 - 0.0147964i) q^{98} +(8.98814 + 1.64147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21} + 2 q^{22} - 12 q^{23} - 18 q^{24} + 48 q^{26} - 32 q^{27} - 6 q^{29} + 66 q^{30} + 6 q^{31} + 30 q^{32} - 56 q^{33} - 6 q^{34} - 6 q^{35} - 6 q^{36} - 6 q^{37} - 36 q^{38} - 32 q^{39} - 12 q^{40} + 18 q^{41} + 80 q^{42} - 12 q^{44} + 34 q^{45} - 12 q^{46} + 30 q^{47} + 22 q^{48} - 12 q^{50} - 16 q^{52} - 56 q^{54} - 4 q^{55} - 12 q^{56} - 2 q^{57} - 28 q^{58} + 30 q^{59} - 58 q^{60} - 4 q^{61} - 18 q^{62} - 2 q^{63} + 30 q^{65} + 32 q^{66} - 16 q^{67} - 48 q^{69} - 46 q^{70} + 48 q^{71} + 126 q^{72} - 22 q^{73} + 24 q^{75} - 18 q^{76} - 72 q^{77} + 94 q^{78} + 8 q^{79} + 54 q^{80} - 14 q^{81} - 12 q^{82} + 72 q^{83} - 110 q^{84} + 78 q^{85} + 102 q^{86} + 14 q^{87} - 6 q^{88} + 114 q^{90} - 16 q^{91} + 120 q^{92} - 44 q^{93} - 52 q^{94} - 6 q^{95} + 16 q^{96} + 48 q^{97} - 36 q^{98} - 32 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9 - 12 * q^10 + 6 * q^11 - 18 * q^12 - 2 * q^13 - 12 * q^14 + 4 * q^15 + 14 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^20 + 22 * q^21 + 2 * q^22 - 12 * q^23 - 18 * q^24 + 48 * q^26 - 32 * q^27 - 6 * q^29 + 66 * q^30 + 6 * q^31 + 30 * q^32 - 56 * q^33 - 6 * q^34 - 6 * q^35 - 6 * q^36 - 6 * q^37 - 36 * q^38 - 32 * q^39 - 12 * q^40 + 18 * q^41 + 80 * q^42 - 12 * q^44 + 34 * q^45 - 12 * q^46 + 30 * q^47 + 22 * q^48 - 12 * q^50 - 16 * q^52 - 56 * q^54 - 4 * q^55 - 12 * q^56 - 2 * q^57 - 28 * q^58 + 30 * q^59 - 58 * q^60 - 4 * q^61 - 18 * q^62 - 2 * q^63 + 30 * q^65 + 32 * q^66 - 16 * q^67 - 48 * q^69 - 46 * q^70 + 48 * q^71 + 126 * q^72 - 22 * q^73 + 24 * q^75 - 18 * q^76 - 72 * q^77 + 94 * q^78 + 8 * q^79 + 54 * q^80 - 14 * q^81 - 12 * q^82 + 72 * q^83 - 110 * q^84 + 78 * q^85 + 102 * q^86 + 14 * q^87 - 6 * q^88 + 114 * q^90 - 16 * q^91 + 120 * q^92 - 44 * q^93 - 52 * q^94 - 6 * q^95 + 16 * q^96 + 48 * q^97 - 36 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.0178736	−	0.0667051i	0.0126385	−	0.0471676i	−0.959319	−	0.282326i	$-0.908894\pi$
$2$	0.0178736	−	0.0667051i	0.0126385	−	0.0471676i	0.971957	+	0.235158i	$0.0755608\pi$
$3$	−1.73062	+	0.0702708i	−0.999177	+	0.0405709i
$3$	−1.73062	+	0.0702708i	−0.999177	+	0.0405709i
$4$	1.72792	+	0.997615i	0.863960	+	0.498808i
$5$	0.690628	−	2.57746i	0.308858	−	1.15267i	−0.620715	−	0.784036i	$-0.713158\pi$
$5$	0.690628	−	2.57746i	0.308858	−	1.15267i	0.929573	−	0.368638i	$-0.120176\pi$
$6$	−0.0262450	+	0.116698i	−0.0107145	+	0.0476416i
$7$	1.75672	+	1.75672i	0.663980	+	0.663980i	0.956316	−	0.292336i	$-0.0944326\pi$
$7$	1.75672	+	1.75672i	0.663980	+	0.663980i	−0.292336	+	0.956316i	$0.594433\pi$
$8$	0.195093	−	0.195093i	0.0689759	−	0.0689759i
$9$	2.99012	−	0.243225i	0.996708	−	0.0810749i
$10$	−0.159586	−	0.0921368i	−0.0504654	−	0.0291362i
$11$	2.94182	+	0.788259i	0.886993	+	0.237669i	0.673422	−	0.739258i	$-0.264824\pi$
$11$	2.94182	+	0.788259i	0.886993	+	0.237669i	0.213571	+	0.976927i	$0.431490\pi$
$12$	−3.06049	−	1.60508i	−0.883486	−	0.463345i
$13$	−3.20340	−	1.65477i	−0.888462	−	0.458949i
$13$	−3.20340	−	1.65477i	−0.888462	−	0.458949i
$14$	0.148582	−	0.0857836i	0.0397101	−	0.0229266i
$15$	−1.01410	+	4.50914i	−0.261839	+	1.16426i
$16$	1.98570	+	3.43934i	0.496426	+	0.859835i
$17$	−0.757582	−	1.31217i	−0.183741	−	0.318248i	0.759411	−	0.650611i	$-0.225487\pi$
$17$	−0.757582	−	1.31217i	−0.183741	−	0.318248i	−0.943151	+	0.332363i	$0.892154\pi$
$18$	0.0372199	−	0.203804i	0.00877281	−	0.0480370i
$19$	−5.08773	−	1.36325i	−1.16721	−	0.312752i	−0.377366	−	0.926064i	$-0.623170\pi$
$19$	−5.08773	−	1.36325i	−1.16721	−	0.312752i	−0.789841	+	0.613312i	$0.789837\pi$
$20$	3.76466	−	3.76466i	0.841804	−	0.841804i
$21$	−3.16368	−	2.91679i	−0.690371	−	0.636495i
$22$	0.105162	−	0.182146i	0.0224206	−	0.0388336i
$23$	−6.17236			−1.28703			−0.643513	−	0.765435i	$-0.722524\pi$
$23$	−6.17236			−1.28703			−0.643513	+	0.765435i	$0.722524\pi$
$24$	−0.323924	+	0.351343i	−0.0661207	+	0.0717175i
$25$	−1.83620	−	1.06013i	−0.367239	−	0.212026i
$26$	−0.167638	+	0.184106i	−0.0328764	+	0.0361062i
$27$	−5.15769	+	0.631049i	−0.992598	+	0.121445i
$28$	1.28295	+	4.78802i	0.242454	+	0.904850i
$29$	−6.73536	+	3.88866i	−1.25073	+	0.722107i	−0.971254	−	0.238047i	$-0.923493\pi$
$29$	−6.73536	+	3.88866i	−1.25073	+	0.722107i	−0.279472	+	0.960154i	$0.590159\pi$
$30$	0.282657	+	0.148240i	0.0516060	+	0.0270648i
$31$	6.99365	+	1.87394i	1.25610	+	0.336570i	0.824689	−	0.565587i	$-0.191350\pi$
$31$	6.99365	+	1.87394i	1.25610	+	0.336570i	0.431408	+	0.902157i	$0.358017\pi$
$32$	0.797918	−	0.213802i	0.141053	−	0.0377951i
$33$	−5.14658	−	1.15746i	−0.895905	−	0.201487i
$34$	−0.101069	+	0.0270814i	−0.0173332	+	0.00464442i
$35$	5.74113	−	3.31464i	0.970428	−	0.560277i
$36$	5.40934	+	2.56272i	0.901557	+	0.427120i
$37$	1.73614	−	0.465197i	0.285420	−	0.0764780i	−0.113269	−	0.993564i	$-0.536132\pi$
$37$	1.73614	−	0.465197i	0.285420	−	0.0764780i	0.398689	+	0.917086i	$0.369465\pi$
$38$	−0.181872	+	0.315012i	−0.0295036	+	0.0511017i
$39$	5.66016	+	2.63867i	0.906351	+	0.422526i
$40$	−0.368108	−	0.637582i	−0.0582030	−	0.100811i
$41$	−4.20290	−	4.20290i	−0.656383	−	0.656383i	0.298140	−	0.954522i	$-0.403634\pi$
$41$	−4.20290	−	4.20290i	−0.656383	−	0.656383i	−0.954522	+	0.298140i	$0.903634\pi$
$42$	−0.251111	+	0.158900i	−0.0387472	+	0.0245188i
$43$		−	1.45159i		−	0.221365i	−0.993856	−	0.110683i	$-0.964696\pi$
$43$		−	1.45159i		−	0.221365i	0.993856	−	0.110683i	$-0.0353037\pi$
$44$	4.29686	+	4.29686i	0.647776	+	0.647776i
$45$	1.43816	−	7.87490i	0.214388	−	1.17392i
$46$	−0.110322	+	0.411728i	−0.0162661	+	0.0607060i
$47$	2.96979	+	11.0834i	0.433189	+	1.61668i	0.745363	+	0.666659i	$0.232276\pi$
$47$	2.96979	+	11.0834i	0.433189	+	1.61668i	−0.312174	+	0.950025i	$0.601057\pi$
$48$	−3.67819	−	5.81267i	−0.530902	−	0.838987i
$49$		−	0.827835i		−	0.118262i
$50$	−0.103535	+	0.103535i	−0.0146421	+	0.0146421i
$51$	1.40330	+	2.21764i	0.196501	+	0.310532i
$52$	−3.88440	−	6.05506i	−0.538669	−	0.839686i
$53$		−	9.11286i		−	1.25175i	−0.779924	−	0.625874i	$-0.784742\pi$
$53$		−	9.11286i		−	1.25175i	0.779924	−	0.625874i	$-0.215258\pi$
$54$	−0.0500922	+	0.355324i	−0.00681669	+	0.0483534i
$55$	4.06341	−	7.03803i	0.547910	−	0.949008i
$56$	0.685450			0.0915972
$57$	8.90076	+	2.00176i	1.17893	+	0.265140i
$58$	0.139009	+	0.518788i	0.0182527	+	0.0681202i
$59$	−0.222038	−	0.828658i	−0.0289069	−	0.107882i	0.949965	−	0.312356i	$-0.101118\pi$
$59$	−0.222038	−	0.828658i	−0.0289069	−	0.107882i	−0.978872	+	0.204474i	$0.934452\pi$
$60$	−6.25067	+	6.77976i	−0.806958	+	0.875264i
$61$	−5.50190			−0.704447			−0.352223	−	0.935916i	$-0.614574\pi$
$61$	−5.50190			−0.704447			−0.352223	+	0.935916i	$0.614574\pi$
$62$	0.250003	−	0.433018i	0.0317504	−	0.0549934i
$63$	5.68010	+	4.82555i	0.715626	+	0.607962i
$64$			7.88577i			0.985721i
$65$	−6.47744	+	7.11379i	−0.803428	+	0.882357i
$66$	−0.169196	+	0.322616i	−0.0208266	+	0.0397112i
$67$	−3.08710	+	3.08710i	−0.377149	+	0.377149i	−0.870073	−	0.492923i	$-0.835928\pi$
$67$	−3.08710	+	3.08710i	−0.377149	+	0.377149i	0.492923	+	0.870073i	$0.335928\pi$
$68$		−	3.02310i		−	0.366605i
$69$	10.6820	−	0.433736i	1.28597	−	0.0522157i
$70$	−0.118489	−	0.442207i	−0.0141622	−	0.0528539i
$71$	−0.849841	+	3.17165i	−0.100858	+	0.376406i	−0.997842	−	0.0656559i	$-0.979086\pi$
$71$	−0.849841	+	3.17165i	−0.100858	+	0.376406i	0.896985	+	0.442061i	$0.145753\pi$
$72$	0.535902	−	0.630805i	0.0631566	−	0.0743410i
$73$	0.551749	+	0.551749i	0.0645773	+	0.0645773i	0.738658	−	0.674081i	$-0.235460\pi$
$73$	0.551749	+	0.551749i	0.0645773	+	0.0645773i	−0.674081	+	0.738658i	$0.735460\pi$
$74$		−	0.124124i		−	0.0144291i
$75$	3.25226	+	1.70565i	0.375539	+	0.196952i
$76$	−7.43120	−	7.43120i	−0.852417	−	0.852417i
$77$	3.78322	+	6.55273i	0.431138	+	0.746753i
$78$	0.277180	−	0.330399i	0.0313845	−	0.0374103i
$79$	6.40258	−	11.0896i	0.720347	−	1.24768i	−0.240514	−	0.970646i	$-0.577316\pi$
$79$	6.40258	−	11.0896i	0.720347	−	1.24768i	0.960861	−	0.277032i	$-0.0893508\pi$
$80$	10.2361	−	2.74277i	1.14444	−	0.306650i
$81$	8.88168	−	1.45454i	0.986854	−	0.161616i
$82$	−0.355476	+	0.205234i	−0.0392557	+	0.0226643i
$83$	−3.03557	+	0.813378i	−0.333197	+	0.0892798i	−0.421539	−	0.906810i	$-0.638510\pi$
$83$	−3.03557	+	0.813378i	−0.333197	+	0.0892798i	0.0883420	+	0.996090i	$0.471843\pi$
$84$	−2.55675	−	8.19611i	−0.278965	−	0.894269i
$85$	−3.90527	+	1.04641i	−0.423586	+	0.113500i
$86$	−0.0968284	−	0.0259451i	−0.0104413	−	0.00279773i
$87$	11.3831	−	7.20312i	1.22040	−	0.772255i
$88$	0.727714	−	0.420146i	0.0775746	−	0.0447877i
$89$	3.38089	+	12.6176i	0.358373	+	1.33747i	0.876186	+	0.481973i	$0.160080\pi$
$89$	3.38089	+	12.6176i	0.358373	+	1.33747i	−0.517813	+	0.855494i	$0.673254\pi$
$90$	−0.499591	−	0.236685i	−0.0526615	−	0.0249488i
$91$	−2.72052	−	8.53446i	−0.285188	−	0.894654i
$92$	−10.6653	−	6.15764i	−1.11194	−	0.641978i
$93$	−12.2351	−	2.75164i	−1.26872	−	0.285332i
$94$	0.792402			0.0817300
$95$	−7.02746	+	12.1719i	−0.721002	+	1.24881i
$96$	−1.36587	+	0.426081i	−0.139404	+	0.0434867i
$97$	−2.03610	+	2.03610i	−0.206735	+	0.206735i	−0.802878	−	0.596143i	$-0.796699\pi$
$97$	−2.03610	+	2.03610i	−0.206735	+	0.206735i	0.596143	+	0.802878i	$0.296699\pi$
$98$	−0.0552209	−	0.0147964i	−0.00557815	−	0.00149466i
$99$	8.98814	+	1.64147i	0.903342	+	0.164974i
$100$	−2.11520	−	3.66363i	−0.211520	−	0.366363i
$101$	3.50847	+	6.07684i	0.349105	+	0.604668i	0.986091	−	0.166208i	$-0.0531522\pi$
$101$	3.50847	+	6.07684i	0.349105	+	0.604668i	−0.636985	+	0.770876i	$0.719819\pi$
$102$	0.173010	−	0.0539700i	0.0171305	−	0.00534382i
$103$	−3.56398	+	2.05766i	−0.351169	+	0.202748i	−0.665200	−	0.746665i	$-0.731654\pi$
$103$	−3.56398	+	2.05766i	−0.351169	+	0.202748i	0.314031	+	0.949413i	$0.398320\pi$
$104$	−0.947795	+	0.302127i	−0.0929389	+	0.0296260i
$105$	−9.70281	+	6.13983i	−0.946898	+	0.599186i
$106$	−0.607875	−	0.162880i	−0.0590420	−	0.0158203i
$107$	−3.71622	−	2.14556i	−0.359260	−	0.207419i	0.309496	−	0.950901i	$-0.399840\pi$
$107$	−3.71622	−	2.14556i	−0.359260	−	0.207419i	−0.668756	+	0.743482i	$0.733173\pi$
$108$	−9.54163	−	4.05499i	−0.918143	−	0.390192i
$109$	5.48305	−	5.48305i	0.525181	−	0.525181i	−0.393950	−	0.919132i	$-0.628892\pi$
$109$	5.48305	−	5.48305i	0.525181	−	0.525181i	0.919132	+	0.393950i	$0.128892\pi$
$110$	−0.396845	−	0.396845i	−0.0378377	−	0.0378377i
$111$	−2.97192	+	0.927082i	−0.282082	+	0.0879947i
$112$	−2.55364	+	9.53031i	−0.241296	+	0.900530i
$113$	−6.80555	−	3.92919i	−0.640212	−	0.369627i	0.144484	−	0.989507i	$-0.453848\pi$
$113$	−6.80555	−	3.92919i	−0.640212	−	0.369627i	−0.784696	+	0.619880i	$0.787181\pi$
$114$	0.292616	−	0.557947i	0.0274060	−	0.0522566i
$115$	−4.26280	+	15.9090i	−0.397508	+	1.48352i
$116$	−15.5176			−1.44077
$117$	−9.98103	−	4.16881i	−0.922747	−	0.385407i
$118$	−0.0592444			−0.00545389
$119$	0.974259	−	3.63599i	0.0893102	−	0.333310i
$120$	0.681860	+	1.07755i	0.0622450	+	0.0983662i
$121$	−1.49331	−	0.862160i	−0.135755	−	0.0783782i
$122$	−0.0983387	+	0.367005i	−0.00890317	+	0.0332271i
$123$	7.56898	+	6.97830i	0.682472	+	0.629212i
$124$	10.2150	+	10.2150i	0.917334	+	0.917334i
$125$	5.43359	−	5.43359i	0.485995	−	0.485995i
$126$	0.423413	−	0.292642i	0.0377206	−	0.0260706i
$127$	−5.60433	−	3.23566i	−0.497304	−	0.287119i	0.230295	−	0.973121i	$-0.426031\pi$
$127$	−5.60433	−	3.23566i	−0.497304	−	0.287119i	−0.727600	+	0.686002i	$0.759364\pi$
$128$	2.12186	+	0.568550i	0.187547	+	0.0502532i
$129$	0.102004	+	2.51215i	0.00898097	+	0.221183i
$130$	0.358751	+	0.559228i	0.0314646	+	0.0490475i
$131$	−3.71544	+	2.14511i	−0.324619	+	0.187419i	−0.653450	−	0.756970i	$-0.726679\pi$
$131$	−3.71544	+	2.14511i	−0.324619	+	0.187419i	0.328831	+	0.944389i	$0.393346\pi$
$132$	−7.73819	−	7.13431i	−0.673523	−	0.620962i
$133$	−6.54289	−	11.3326i	−0.567340	−	0.982662i
$134$	0.150748	+	0.261103i	0.0130226	+	0.0225559i
$135$	−1.93554	+	13.7296i	−0.166585	+	1.18165i
$136$	−0.403795	−	0.108196i	−0.0346251	−	0.00927777i
$137$	7.81077	−	7.81077i	0.667319	−	0.667319i	−0.289775	−	0.957095i	$-0.593581\pi$
$137$	7.81077	−	7.81077i	0.667319	−	0.667319i	0.957095	+	0.289775i	$0.0935806\pi$
$138$	0.161994	−	0.720299i	0.0137898	−	0.0613159i
$139$	11.4780	−	19.8805i	0.973554	−	1.68624i	0.288927	−	0.957351i	$-0.406702\pi$
$139$	11.4780	−	19.8805i	0.973554	−	1.68624i	0.684627	−	0.728894i	$-0.259965\pi$
$140$	13.2270			1.11788
$141$	−5.91844	−	18.9726i	−0.498423	−	1.59778i
$142$	0.196376	+	0.113377i	0.0164795	+	0.00951443i
$143$	−8.11944	−	7.39314i	−0.678982	−	0.618245i
$144$	6.77403	+	9.80108i	0.564503	+	0.816757i
$145$	5.37124	+	20.0457i	0.446057	+	1.66471i
$146$	0.0466662	−	0.0269427i	0.00386212	−	0.00222980i
$147$	0.0581726	+	1.43267i	0.00479800	+	0.118165i
$148$	3.46400	+	0.928176i	0.284739	+	0.0762956i
$149$	17.5139	−	4.69284i	1.43480	−	0.384453i	0.544088	−	0.839028i	$-0.316876\pi$
$149$	17.5139	−	4.69284i	1.43480	−	0.384453i	0.890708	+	0.454575i	$0.150209\pi$
$150$	0.171905	−	0.186456i	0.0140360	−	0.0152241i
$151$	4.20335	−	1.12628i	0.342064	−	0.0916557i	−0.0836977	−	0.996491i	$-0.526673\pi$
$151$	4.20335	−	1.12628i	0.342064	−	0.0916557i	0.425761	+	0.904836i	$0.360006\pi$
$152$	−1.25854	+	0.726621i	−0.102081	+	0.0589368i
$153$	−2.58442	−	3.73929i	−0.208938	−	0.302304i
$154$	0.504720	−	0.135239i	0.0406715	−	0.0108979i
$155$	9.66001	−	16.7316i	0.775911	−	1.34392i
$156$	7.14792	+	10.2061i	0.572292	+	0.817140i
$157$	7.99329	+	13.8448i	0.637934	+	1.10493i	0.985885	+	0.167422i	$0.0535442\pi$
$157$	7.99329	+	13.8448i	0.637934	+	1.10493i	−0.347951	+	0.937513i	$0.613122\pi$
$158$	−0.625296	−	0.625296i	−0.0497459	−	0.0497459i
$159$	0.640368	+	15.7709i	0.0507845	+	1.25072i
$160$		−	2.20426i		−	0.174262i
$161$	−10.8431	−	10.8431i	−0.854559	−	0.854559i
$162$	0.0617220	−	0.618452i	0.00484934	−	0.0485902i
$163$	−0.954155	+	3.56095i	−0.0747352	+	0.278915i	−0.993173	−	0.116650i	$-0.962785\pi$
$163$	−0.954155	+	3.56095i	−0.0747352	+	0.278915i	0.918438	+	0.395565i	$0.129451\pi$
$164$	−3.06940	−	11.4552i	−0.239680	−	0.894497i
$165$	−6.53767	+	12.4657i	−0.508957	+	0.970456i
$166$			0.217026i			0.0168445i
$167$	8.30121	−	8.30121i	0.642367	−	0.642367i	−0.308770	−	0.951137i	$-0.599917\pi$
$167$	8.30121	−	8.30121i	0.642367	−	0.642367i	0.951137	+	0.308770i	$0.0999173\pi$
$168$	−1.18626	+	0.0481671i	−0.0915218	+	0.00371618i
$169$	7.52350	+	10.6017i	0.578731	+	0.815519i
$170$			0.279205i			0.0214140i
$171$	−15.5445	−	2.83884i	−1.18872	−	0.217091i
$172$	1.44813	−	2.50823i	0.110419	−	0.191251i
$173$	23.9338			1.81965			0.909825	−	0.414993i	$-0.136216\pi$
$173$	23.9338			1.81965			0.909825	+	0.414993i	$0.136216\pi$
$174$	−0.277028	−	0.888059i	−0.0210014	−	0.0673236i
$175$	−1.36334	−	5.08804i	−0.103059	−	0.384620i
$176$	3.13050	+	11.6832i	0.235970	+	0.880653i
$177$	0.442495	+	1.41849i	0.0332600	+	0.106621i
$178$	0.902090			0.0676145
$179$	−10.4999	+	18.1864i	−0.784802	+	1.35932i	0.144316	+	0.989532i	$0.453902\pi$
$179$	−10.4999	+	18.1864i	−0.784802	+	1.35932i	−0.929118	+	0.369785i	$0.879431\pi$
$180$	10.3411	−	12.1725i	0.770784	−	0.907282i
$181$		−	1.43702i		−	0.106813i	−0.998573	−	0.0534065i	$-0.982992\pi$
$181$		−	1.43702i		−	0.106813i	0.998573	−	0.0534065i	$-0.0170079\pi$
$182$	−0.617917	+	0.0289312i	−0.0458031	+	0.00214452i
$183$	9.52173	−	0.386623i	0.703867	−	0.0285800i
$184$	−1.20419	+	1.20419i	−0.0887737	+	0.0887737i
$185$		−	4.79611i		−	0.352617i
$186$	−0.402233	+	0.766960i	−0.0294932	+	0.0562362i
$187$	−1.19434	−	4.45735i	−0.0873389	−	0.325953i
$188$	−5.92543	+	22.1140i	−0.432156	+	1.61283i
$189$	−10.1692	−	7.95206i	−0.739702	−	0.578428i
$190$	0.686324	+	0.686324i	0.0497911	+	0.0497911i
$191$			11.2587i			0.814650i	0.913283	+	0.407325i	$0.133538\pi$
$191$			11.2587i			0.814650i	−0.913283	+	0.407325i	$0.866462\pi$
$192$	−0.554139	−	13.6473i	−0.0399916	−	0.984910i
$193$	5.24277	+	5.24277i	0.377383	+	0.377383i	0.870157	−	0.492774i	$-0.164017\pi$
$193$	5.24277	+	5.24277i	0.377383	+	0.377383i	−0.492774	+	0.870157i	$0.664017\pi$
$194$	0.0994259	+	0.172211i	0.00713836	+	0.0123640i
$195$	10.7101	−	12.7665i	0.766969	−	0.914227i
$196$	0.825861	−	1.43043i	0.0589901	−	0.102174i
$197$	18.9257	−	5.07113i	1.34840	−	0.361303i	0.488856	−	0.872364i	$-0.337414\pi$
$197$	18.9257	−	5.07113i	1.34840	−	0.361303i	0.859544	+	0.511062i	$0.170748\pi$
$198$	0.270145	−	0.570216i	0.0191983	−	0.0405235i
$199$	−18.7031	+	10.7982i	−1.32583	+	0.765466i	−0.984651	−	0.174535i	$-0.944158\pi$
$199$	−18.7031	+	10.7982i	−1.32583	+	0.765466i	−0.341174	+	0.940000i	$0.610825\pi$
$200$	−0.565053	+	0.151406i	−0.0399553	+	0.0107060i
$201$	5.12568	−	5.55955i	0.361538	−	0.392140i
$202$	0.468065	−	0.125418i	0.0329330	−	0.00882436i
$203$	−18.6635	−	5.00087i	−1.30992	−	0.350992i
$204$	0.212436	+	5.23185i	0.0148735	+	0.366303i
$205$	−13.7354	+	7.93016i	−0.959325	+	0.553866i
$206$	0.0735557	+	0.274514i	0.00512487	+	0.0191263i
$207$	−18.4561	+	1.50127i	−1.28279	+	0.104345i
$208$	−0.669695	−	14.3034i	−0.0464350	−	0.991766i
$209$	−13.8926	−	8.02091i	−0.960973	−	0.554818i
$210$	0.236134	+	0.756968i	0.0162948	+	0.0522358i
$211$	−5.28566			−0.363880			−0.181940	−	0.983310i	$-0.558238\pi$
$211$	−5.28566			−0.363880			−0.181940	+	0.983310i	$0.558238\pi$
$212$	9.09113	−	15.7463i	0.624381	−	1.08146i
$213$	1.24788	−	5.54865i	0.0855034	−	0.380188i
$214$	−0.209542	+	0.209542i	−0.0143240	+	0.0143240i
$215$	−3.74141	−	1.00251i	−0.255162	−	0.0683704i
$216$	−0.883117	+	1.12934i	−0.0600885	+	0.0768422i
$217$	8.99391	+	15.5779i	0.610547	+	1.05750i
$218$	−0.267746	−	0.463750i	−0.0181340	−	0.0314091i
$219$	−0.993642	−	0.916098i	−0.0671441	−	0.0619042i
$220$	14.0425	−	8.10744i	0.946745	−	0.546604i
$221$	0.255501	+	5.45702i	0.0171868	+	0.367079i
$222$	0.00872231	+	0.214812i	0.000585403	+	0.0144173i
$223$	23.4774	+	6.29074i	1.57216	+	0.421259i	0.936488	−	0.350699i	$-0.114056\pi$
$223$	23.4774	+	6.29074i	1.57216	+	0.421259i	0.635673	+	0.771958i	$0.280723\pi$
$224$	1.77731	+	1.02613i	0.118752	+	0.0685613i
$225$	−5.74830	−	2.72331i	−0.383220	−	0.181554i
$226$	−0.383736	+	0.383736i	−0.0255258	+	0.0255258i
$227$	−6.42408	−	6.42408i	−0.426381	−	0.426381i	0.461012	−	0.887394i	$-0.347486\pi$
$227$	−6.42408	−	6.42408i	−0.426381	−	0.426381i	−0.887394	+	0.461012i	$0.847486\pi$
$228$	13.3828	+	12.3384i	0.886298	+	0.817132i
$229$	2.27629	−	8.49524i	0.150422	−	0.561382i	−0.849032	−	0.528341i	$-0.822814\pi$
$229$	2.27629	−	8.49524i	0.150422	−	0.561382i	0.999454	−	0.0330406i	$-0.0105191\pi$
$230$	0.985020	+	0.568701i	0.0649503	+	0.0374991i
$231$	−7.00780	−	11.0745i	−0.461079	−	0.728646i
$232$	−0.555372	+	2.07268i	−0.0364620	+	0.136078i
$233$	15.0989			0.989160			0.494580	−	0.869132i	$-0.335322\pi$
$233$	15.0989			0.989160			0.494580	+	0.869132i	$0.335322\pi$
$234$	−0.456478	+	0.591275i	−0.0298409	+	0.0386528i
$235$	30.6181			1.99730
$236$	0.443018	−	1.65336i	0.0288380	−	0.107625i
$237$	−10.3012	+	19.6419i	−0.669135	+	1.27588i
$238$	−0.225125	−	0.129976i	−0.0145927	−	0.00842511i
$239$	−0.900550	+	3.36090i	−0.0582518	+	0.217398i	−0.988916	−	0.148476i	$-0.952563\pi$
$239$	−0.900550	+	3.36090i	−0.0582518	+	0.217398i	0.930664	+	0.365874i	$0.119230\pi$
$240$	−17.5222	+	5.46600i	−1.13105	+	0.352829i
$241$	−13.1930	−	13.1930i	−0.849839	−	0.849839i	0.140274	−	0.990113i	$-0.455202\pi$
$241$	−13.1930	−	13.1930i	−0.849839	−	0.849839i	−0.990113	+	0.140274i	$0.955202\pi$
$242$	−0.0842012	+	0.0842012i	−0.00541266	+	0.00541266i
$243$	−15.2686	+	3.14139i	−0.979484	+	0.201520i
$244$	−9.50685	−	5.48878i	−0.608614	−	0.351383i
$245$	−2.13371	−	0.571726i	−0.136318	−	0.0365262i
$246$	0.600773	−	0.380163i	0.0383039	−	0.0242383i
$247$	14.0422	+	12.7861i	0.893482	+	0.813557i
$248$	1.73001	−	0.998820i	0.109856	−	0.0634251i
$249$	5.19627	−	1.62096i	0.329300	−	0.102724i
$250$	−0.265330	−	0.459566i	−0.0167810	−	0.0290655i
$251$	−4.80452	−	8.32168i	−0.303259	−	0.525260i	0.673613	−	0.739084i	$-0.264741\pi$
$251$	−4.80452	−	8.32168i	−0.303259	−	0.525260i	−0.976872	+	0.213824i	$0.931408\pi$
$252$	5.00073	+	14.0047i	0.315016	+	0.882215i
$253$	−18.1580	−	4.86542i	−1.14158	−	0.305886i
$254$	−0.316005	+	0.316005i	−0.0198279	+	0.0198279i
$255$	6.68503	−	2.08538i	0.418633	−	0.130591i
$256$	−7.80992	+	13.5272i	−0.488120	+	0.845449i
$257$	13.6508			0.851513			0.425757	−	0.904838i	$-0.360008\pi$
$257$	13.6508			0.851513			0.425757	+	0.904838i	$0.360008\pi$
$258$	0.169397	+	0.0380970i	0.0105462	+	0.00237182i
$259$	3.86714	+	2.23270i	0.240293	+	0.138733i
$260$	−18.2893	+	5.83007i	−1.13426	+	0.361566i
$261$	−19.1938	+	13.2658i	−1.18806	+	0.821132i
$262$	0.0766815	+	0.286179i	0.00473740	+	0.0176802i
$263$	−18.6839	+	10.7872i	−1.15210	+	0.665165i	−0.949398	−	0.314076i	$-0.898305\pi$
$263$	−18.6839	+	10.7872i	−1.15210	+	0.665165i	−0.202701	+	0.979241i	$0.564972\pi$
$264$	−1.22988	+	0.778252i	−0.0756936	+	0.0478981i
$265$	−23.4880	−	6.29360i	−1.44286	−	0.386612i
$266$	−0.872888	+	0.233890i	−0.0535202	+	0.0143407i
$267$	−6.73770	−	21.5988i	−0.412340	−	1.32183i
$268$	−8.41400	+	2.25453i	−0.513967	+	0.137717i
$269$	−4.14355	+	2.39228i	−0.252637	+	0.145860i	−0.620971	−	0.783834i	$-0.713262\pi$
$269$	−4.14355	+	2.39228i	−0.252637	+	0.145860i	0.368334	+	0.929693i	$0.379928\pi$
$270$	0.881236	+	0.374507i	0.0536303	+	0.0227918i
$271$	−25.9261	+	6.94689i	−1.57490	+	0.421993i	−0.937343	−	0.348409i	$-0.886722\pi$
$271$	−25.9261	+	6.94689i	−1.57490	+	0.421993i	−0.637558	+	0.770402i	$0.720055\pi$
$272$	3.00867	−	5.21116i	0.182427	−	0.315973i
$273$	5.30792	+	14.5788i	0.321250	+	0.882347i
$274$	−0.381412	−	0.660625i	−0.0230419	−	0.0399098i
$275$	−4.56611	−	4.56611i	−0.275347	−	0.275347i
$276$	18.8904	+	9.90710i	1.13707	+	0.596337i
$277$			6.74921i			0.405520i	0.979228	+	0.202760i	$0.0649912\pi$
$277$			6.74921i			0.405520i	−0.979228	+	0.202760i	$0.935009\pi$
$278$	−1.12098	−	1.12098i	−0.0672319	−	0.0672319i
$279$	21.3677	+	3.90229i	1.27925	+	0.233624i
$280$	0.473391	−	1.76672i	0.0282905	−	0.105582i
$281$	−6.69716	−	24.9941i	−0.399519	−	1.49102i	−0.813945	−	0.580942i	$-0.802684\pi$
$281$	−6.69716	−	24.9941i	−0.399519	−	1.49102i	0.414426	−	0.910083i	$-0.363982\pi$
$282$	−1.37135	+	0.0556827i	−0.0816627	+	0.00331586i
$283$		−	14.7417i		−	0.876304i	−0.898901	−	0.438152i	$-0.855633\pi$
$283$		−	14.7417i		−	0.876304i	0.898901	−	0.438152i	$-0.144367\pi$
$284$	−4.63254	+	4.63254i	−0.274891	+	0.274891i
$285$	11.3066	−	21.5589i	0.669743	−	1.27704i
$286$	−0.638284	+	0.409467i	−0.0377425	+	0.0242123i
$287$		−	14.7667i		−	0.871649i
$288$	2.33387	−	0.833366i	0.137525	−	0.0491066i
$289$	7.35214	−	12.7343i	0.432479	−	0.749075i
$290$	1.43316			0.0841579
$291$	3.38064	−	3.66680i	0.198177	−	0.214952i
$292$	0.402945	+	1.50381i	0.0235806	+	0.0880039i
$293$	4.38888	+	16.3795i	0.256401	+	0.956902i	0.967306	+	0.253613i	$0.0816190\pi$
$293$	4.38888	+	16.3795i	0.256401	+	0.956902i	−0.710905	+	0.703288i	$0.751714\pi$
$294$	0.0966063	+	0.0217266i	0.00563420	+	0.00126712i
$295$	−2.28918			−0.133281
$296$	0.247952	−	0.429466i	0.0144119	−	0.0249622i
$297$	−15.6704	−	2.20916i	−0.909292	−	0.128189i
$298$		−	1.25215i		−	0.0725349i
$299$	19.7725	+	10.2138i	1.14347	+	0.590680i
$300$	3.91806	+	6.19174i	0.226210	+	0.357480i
$301$	2.55004	−	2.55004i	0.146982	−	0.146982i
$302$		−	0.300516i		−	0.0172927i
$303$	−6.49886	−	10.2702i	−0.373350	−	0.590007i
$304$	−5.41404	−	20.2055i	−0.310517	−	1.15886i
$305$	−3.79977	+	14.1809i	−0.217574	+	0.811997i
$306$	−0.295623	+	0.105559i	−0.0168996	+	0.00603442i
$307$	2.71788	+	2.71788i	0.155118	+	0.155118i	0.780399	−	0.625282i	$-0.215016\pi$
$307$	2.71788	+	2.71788i	0.155118	+	0.155118i	−0.625282	+	0.780399i	$0.715016\pi$
$308$			15.0968i			0.860220i
$309$	6.02332	−	3.81149i	0.342655	−	0.216828i
$310$	−0.943427	−	0.943427i	−0.0535830	−	0.0535830i
$311$	2.89624	+	5.01644i	0.164231	+	0.284456i	0.936382	−	0.350983i	$-0.114152\pi$
$311$	2.89624	+	5.01644i	0.164231	+	0.284456i	−0.772151	+	0.635439i	$0.780819\pi$
$312$	1.61905	−	0.589472i	0.0916605	−	0.0333723i
$313$	1.55795	−	2.69845i	0.0880607	−	0.152526i	−0.818631	−	0.574320i	$-0.805266\pi$
$313$	1.55795	−	2.69845i	0.0880607	−	0.152526i	0.906691	+	0.421795i	$0.138600\pi$
$314$	1.06639	−	0.285738i	0.0601797	−	0.0161251i
$315$	16.3605	−	11.3076i	0.921809	−	0.637110i
$316$	22.1263	−	12.7746i	1.24470	−	0.718629i
$317$	−17.0394	+	4.56569i	−0.957027	+	0.256435i	−0.703341	−	0.710852i	$-0.748309\pi$
$317$	−17.0394	+	4.56569i	−0.957027	+	0.256435i	−0.253685	+	0.967287i	$0.581643\pi$
$318$	1.06345	+	0.239167i	0.0596352	+	0.0134118i
$319$	−22.8795	+	6.13055i	−1.28101	+	0.343245i
$320$	20.3252	+	5.44613i	1.13622	+	0.304448i
$321$	6.58215	+	3.45202i	0.367380	+	0.192673i
$322$	−0.917098	+	0.529487i	−0.0511079	+	0.0295071i
$323$	2.06555	+	7.70875i	0.114930	+	0.428926i
$324$	16.7979	+	6.34717i	0.933218	+	0.352620i
$325$	4.12780	+	6.43448i	0.228969	+	0.356921i
$326$	0.220480	+	0.127294i	0.0122112	+	0.00705017i
$327$	−9.10381	+	9.87441i	−0.503442	+	0.546056i
$328$	−1.63992			−0.0905492
$329$	−14.2534	+	24.6876i	−0.785816	+	1.36107i
$330$	0.714677	+	0.658903i	0.0393417	+	0.0362714i
$331$	8.00382	−	8.00382i	0.439930	−	0.439930i	−0.452058	−	0.891988i	$-0.649310\pi$
$331$	8.00382	−	8.00382i	0.439930	−	0.439930i	0.891988	+	0.452058i	$0.149310\pi$
$332$	−6.05666	−	1.62288i	−0.332402	−	0.0890669i
$333$	5.07813	−	1.81327i	0.278280	−	0.0993666i
$334$	−0.405361	−	0.702106i	−0.0221804	−	0.0384175i
$335$	5.82483	+	10.0889i	0.318245	+	0.551216i
$336$	3.74969	−	16.6728i	0.204562	−	0.909578i
$337$	−15.9475	+	9.20731i	−0.868717	+	0.501554i	−0.866922	−	0.498444i	$-0.833905\pi$
$337$	−15.9475	+	9.20731i	−0.868717	+	0.501554i	−0.00179550	+	0.999998i	$0.500572\pi$
$338$	0.841663	−	0.312365i	0.0457804	−	0.0169904i
$339$	12.0540	+	6.32171i	0.654681	+	0.343348i
$340$	−7.79192	−	2.08784i	−0.422576	−	0.113229i
$341$	19.0969	+	11.0256i	1.03416	+	0.597071i
$342$	−0.467202	+	0.986160i	−0.0252634	+	0.0533254i
$343$	13.7514	−	13.7514i	0.742503	−	0.742503i
$344$	−0.283195	−	0.283195i	−0.0152689	−	0.0152689i
$345$	6.25937	−	27.8320i	0.336993	−	1.49843i
$346$	0.427782	−	1.59650i	0.0229977	−	0.0858286i
$347$	1.06106	+	0.612601i	0.0569605	+	0.0328861i	0.528210	−	0.849114i	$-0.322863\pi$
$347$	1.06106	+	0.612601i	0.0569605	+	0.0328861i	−0.471249	+	0.882000i	$0.656197\pi$
$348$	26.8551	−	1.09043i	1.43958	−	0.0584533i
$349$	2.46587	−	9.20276i	0.131995	−	0.492613i	−0.867997	−	0.496569i	$-0.834593\pi$
$349$	2.46587	−	9.20276i	0.131995	−	0.492613i	0.999992	+	0.00395679i	$0.00125949\pi$
$350$	−0.363766			−0.0194441
$351$	17.5664	+	6.51327i	0.937623	+	0.347653i
$352$	2.51587			0.134096
$353$	4.68836	−	17.4972i	0.249536	−	0.931282i	−0.721513	−	0.692401i	$-0.756553\pi$
$353$	4.68836	−	17.4972i	0.249536	−	0.931282i	0.971049	−	0.238881i	$-0.0767806\pi$
$354$	0.102530	−	0.00416315i	0.00544940	−	0.000221269i
$355$	7.58787	+	4.38086i	0.402722	+	0.232512i
$356$	−6.74565	+	25.1751i	−0.357519	+	1.33428i
$357$	−1.43057	+	6.36099i	−0.0757140	+	0.336659i
$358$	1.02546	+	1.02546i	0.0541970	+	0.0541970i
$359$	−10.4633	+	10.4633i	−0.552233	+	0.552233i	−0.927085	−	0.374851i	$-0.877694\pi$
$359$	−10.4633	+	10.4633i	−0.552233	+	0.552233i	0.374851	+	0.927085i	$0.377694\pi$
$360$	−1.25576	−	1.81692i	−0.0661846	−	0.0957598i
$361$	7.57210	+	4.37175i	0.398532	+	0.230092i
$362$	−0.0958567	−	0.0256847i	−0.00503811	−	0.00134996i
$363$	2.64494	+	1.38714i	0.138823	+	0.0728060i
$364$	3.81326	−	17.4609i	0.199869	−	0.915199i
$365$	1.80316	−	1.04106i	0.0943818	−	0.0544914i
$366$	0.144398	−	0.642059i	0.00754779	−	0.0335609i
$367$	−0.378590	−	0.655738i	−0.0197623	−	0.0342292i	0.855975	−	0.517017i	$-0.172958\pi$
$367$	−0.378590	−	0.655738i	−0.0197623	−	0.0342292i	−0.875737	+	0.482788i	$0.839624\pi$
$368$	−12.2565	−	21.2288i	−0.638913	−	1.10663i
$369$	−13.5894	−	11.5449i	−0.707438	−	0.601006i
$370$	−0.319925	−	0.0857236i	−0.0166321	−	0.00445656i
$371$	16.0088	−	16.0088i	0.831135	−	0.831135i
$372$	−18.3961	−	16.9605i	−0.953795	−	0.879361i
$373$	−11.1919	+	19.3849i	−0.579494	+	1.00371i	0.416044	+	0.909345i	$0.363416\pi$
$373$	−11.1919	+	19.3849i	−0.579494	+	1.00371i	−0.995537	+	0.0943680i	$0.969917\pi$
$374$	−0.318675			−0.0164783
$375$	−9.02168	+	9.78532i	−0.465877	+	0.505312i
$376$	2.74169	+	1.58291i	0.141392	+	0.0816326i
$377$	28.0109	−	1.31148i	1.44263	−	0.0675448i
$378$	−0.712204	+	0.536207i	−0.0366318	+	0.0275795i
$379$	−5.60828	−	20.9304i	−0.288078	−	1.07512i	−0.946561	−	0.322526i	$-0.895468\pi$
$379$	−5.60828	−	20.9304i	−0.288078	−	1.07512i	0.658483	−	0.752596i	$-0.271199\pi$
$380$	−24.2858	+	14.0214i	−1.24583	+	0.719283i
$381$	9.92637	+	5.20590i	0.508543	+	0.266706i
$382$	0.751012	+	0.201233i	0.0384251	+	0.0102960i
$383$	−11.3242	+	3.03430i	−0.578638	+	0.155046i	−0.536255	−	0.844056i	$-0.680162\pi$
$383$	−11.3242	+	3.03430i	−0.578638	+	0.155046i	−0.0423829	+	0.999101i	$0.513495\pi$
$384$	−3.71209	−	0.834842i	−0.189432	−	0.0426029i
$385$	19.5022	−	5.22559i	0.993923	−	0.266321i
$386$	0.443427	−	0.256012i	0.0225698	−	0.0130307i
$387$	−0.353062	−	4.34043i	−0.0179472	−	0.220636i
$388$	−5.54946	+	1.48697i	−0.281731	+	0.0754896i
$389$	−5.55179	+	9.61598i	−0.281487	+	0.487550i	−0.971751	−	0.236008i	$-0.924161\pi$
$389$	−5.55179	+	9.61598i	−0.281487	+	0.487550i	0.690264	+	0.723557i	$0.257494\pi$
$390$	−0.660161	−	0.942604i	−0.0334286	−	0.0477306i
$391$	4.67607	+	8.09918i	0.236479	+	0.409593i
$392$	−0.161505	−	0.161505i	−0.00815724	−	0.00815724i
$393$	6.27929	−	3.97346i	0.316748	−	0.200435i
$394$		−	1.35308i		−	0.0681672i
$395$	−24.1612	−	24.1612i	−1.21568	−	1.21568i
$396$	13.8932	+	11.8030i	0.698162	+	0.593125i
$397$	−4.35209	+	16.2422i	−0.218425	+	0.815174i	0.766507	+	0.642236i	$0.221993\pi$
$397$	−4.35209	+	16.2422i	−0.218425	+	0.815174i	−0.984933	+	0.172939i	$0.944674\pi$
$398$	0.386006	+	1.44059i	0.0193487	+	0.0722104i
$399$	12.1196	+	19.1527i	0.606741	+	0.958836i
$400$		−	8.42040i		−	0.421020i
$401$	10.4514	−	10.4514i	0.521920	−	0.521920i	−0.396231	−	0.918151i	$-0.629682\pi$
$401$	10.4514	−	10.4514i	0.521920	−	0.521920i	0.918151	+	0.396231i	$0.129682\pi$
$402$	−0.279236	−	0.441278i	−0.0139270	−	0.0220090i
$403$	−19.3025	−	17.5758i	−0.961526	−	0.875514i
$404$			14.0004i			0.696546i
$405$	2.38491	−	23.8967i	0.118507	−	1.18744i
$406$	−0.667167	+	1.15557i	−0.0331110	+	0.0573499i
$407$	5.47411			0.271342
$408$	0.706420	+	0.158873i	0.0349730	+	0.00786536i
$409$	2.01210	+	7.50926i	0.0994919	+	0.371309i	0.997662	−	0.0683389i	$-0.0217699\pi$
$409$	2.01210	+	7.50926i	0.0994919	+	0.371309i	−0.898170	+	0.439648i	$0.855103\pi$
$410$	0.283481	+	1.05796i	0.0140001	+	0.0522491i
$411$	−12.9686	+	14.0664i	−0.639696	+	0.693844i
$412$	−8.21103			−0.404528
$413$	1.06566	−	1.84578i	0.0524379	−	0.0908251i
$414$	−0.229734	+	1.25795i	−0.0112908	+	0.0618249i
$415$			8.38579i			0.411642i
$416$	−2.90984	−	0.635477i	−0.142667	−	0.0311568i
$417$	−18.4671	+	35.2123i	−0.904340	+	1.72435i
$418$	−0.783347	+	0.783347i	−0.0383147	+	0.0383147i
$419$		−	38.6352i		−	1.88745i	−0.330726	−	0.943727i	$-0.607293\pi$
$419$		−	38.6352i		−	1.88745i	0.330726	−	0.943727i	$-0.392707\pi$
$420$	−22.8909	+	0.929468i	−1.11696	+	0.0453534i
$421$	5.66833	+	21.1545i	0.276258	+	1.03101i	0.954994	+	0.296625i	$0.0958613\pi$
$421$	5.66833	+	21.1545i	0.276258	+	1.03101i	−0.678736	+	0.734382i	$0.737472\pi$
$422$	−0.0944736	+	0.352580i	−0.00459890	+	0.0171633i
$423$	11.5758	+	32.4185i	0.562835	+	1.57624i
$424$	−1.77786	−	1.77786i	−0.0863404	−	0.0863404i
$425$			3.21254i			0.155831i
$426$	−0.347820	−	0.182414i	−0.0168519	−	0.00883801i
$427$	−9.66533	−	9.66533i	−0.467738	−	0.467738i
$428$	−4.28089	−	7.41471i	−0.206924	−	0.358404i
$429$	14.5712	+	12.2242i	0.703506	+	0.590189i
$430$	−0.133745	+	0.231653i	−0.00644974	+	0.0111713i
$431$	6.12425	−	1.64099i	0.294995	−	0.0790436i	−0.108286	−	0.994120i	$-0.534536\pi$
$431$	6.12425	−	1.64099i	0.294995	−	0.0790436i	0.403281	+	0.915076i	$0.367870\pi$
$432$	−12.4120	−	16.4860i	−0.597175	−	0.793182i
$433$	−15.1663	+	8.75626i	−0.728846	+	0.420799i	−0.818000	−	0.575219i	$-0.804917\pi$
$433$	−15.1663	+	8.75626i	−0.728846	+	0.420799i	0.0891542	+	0.996018i	$0.471584\pi$
$434$	1.19988	−	0.321507i	0.0575961	−	0.0154328i
$435$	−10.7042	−	34.3142i	−0.513229	−	1.64524i
$436$	14.9443	−	4.00430i	0.715700	−	0.191771i
$437$	31.4033	+	8.41449i	1.50222	+	0.402520i
$438$	−0.0788684	+	0.0499071i	−0.00376848	+	0.00238465i
$439$	−16.6592	+	9.61818i	−0.795099	+	0.459051i	−0.841755	−	0.539860i	$-0.818477\pi$
$439$	−16.6592	+	9.61818i	−0.795099	+	0.459051i	0.0466556	+	0.998911i	$0.485144\pi$
$440$	−0.580329	−	2.16582i	−0.0276661	−	0.103251i
$441$	−0.201350	−	2.47533i	−0.00958809	−	0.117873i
$442$	0.368578	+	0.0804934i	0.0175315	+	0.00382868i
$443$	10.3181	+	5.95715i	0.490227	+	0.283033i	0.724669	−	0.689097i	$-0.241993\pi$
$443$	10.3181	+	5.95715i	0.490227	+	0.283033i	−0.234442	+	0.972130i	$0.575326\pi$
$444$	−6.06011	−	1.36291i	−0.287600	−	0.0646807i
$445$	34.8564			1.65235
$446$	0.839250	−	1.45362i	0.0397396	−	0.0688311i
$447$	−29.9803	+	9.35227i	−1.41802	+	0.442347i
$448$	−13.8531	+	13.8531i	−0.654499	+	0.654499i
$449$	−2.87999	−	0.771691i	−0.135915	−	0.0364183i	0.190220	−	0.981741i	$-0.439080\pi$
$449$	−2.87999	−	0.771691i	−0.135915	−	0.0364183i	−0.326135	+	0.945323i	$0.605746\pi$
$450$	−0.284401	+	0.334766i	−0.0134068	+	0.0157810i
$451$	−9.05122	−	15.6772i	−0.426205	−	0.738209i
$452$	−7.83963	−	13.5786i	−0.368745	−	0.638686i
$453$	−7.19527	+	2.24455i	−0.338063	+	0.105458i
$454$	−0.543341	+	0.313698i	−0.0255002	+	0.0147226i
$455$	−23.8761	+	1.11789i	−1.11933	+	0.0524075i
$456$	2.12701	−	1.34595i	0.0996063	−	0.0630298i
$457$	6.87337	+	1.84171i	0.321522	+	0.0861517i	0.415971	−	0.909378i	$-0.363442\pi$
$457$	6.87337	+	1.84171i	0.321522	+	0.0861517i	−0.0944480	+	0.995530i	$0.530109\pi$
$458$	−0.525991	−	0.303681i	−0.0245779	−	0.0141901i
$459$	4.73542	+	6.28970i	0.221030	+	0.293578i
$460$	−23.2368	+	23.2368i	−1.08342	+	1.08342i
$461$	10.6342	+	10.6342i	0.495284	+	0.495284i	0.909966	−	0.414683i	$-0.136107\pi$
$461$	10.6342	+	10.6342i	0.495284	+	0.495284i	−0.414683	+	0.909966i	$0.636107\pi$
$462$	−0.863978	+	0.269516i	−0.0401959	+	0.0125390i
$463$	8.55785	−	31.9383i	0.397717	−	1.48430i	−0.419386	−	0.907808i	$-0.637755\pi$
$463$	8.55785	−	31.9383i	0.397717	−	1.48430i	0.817103	−	0.576492i	$-0.195579\pi$
$464$	−26.7489	−	15.4435i	−1.24179	−	0.716945i
$465$	−15.5421	+	29.6350i	−0.720748	+	1.37429i
$466$	0.269871	−	1.00717i	0.0125015	−	0.0466563i
$467$	17.4914			0.809406			0.404703	−	0.914448i	$-0.367375\pi$
$467$	17.4914			0.809406			0.404703	+	0.914448i	$0.367375\pi$
$468$	−13.0876	−	17.1606i	−0.604973	−	0.793249i
$469$	−10.8464			−0.500839
$470$	0.547255	−	2.04238i	0.0252430	−	0.0942081i
$471$	−14.8063	−	23.3984i	−0.682237	−	1.07814i
$472$	−0.204984	−	0.118347i	−0.00943515	−	0.00544738i
$473$	1.14423	−	4.27032i	0.0526117	−	0.196349i
$474$	1.12609	+	1.03821i	0.0517232	+	0.0476867i
$475$	7.89685	+	7.89685i	0.362332	+	0.362332i
$476$	5.31076	−	5.31076i	0.243418	−	0.243418i
$477$	−2.21647	−	27.2486i	−0.101485	−	1.24763i
$478$	0.208093	+	0.120143i	0.00951796	+	0.00549520i
$479$	−5.18747	−	1.38998i	−0.237022	−	0.0635098i	0.138353	−	0.990383i	$-0.455819\pi$
$479$	−5.18747	−	1.38998i	−0.237022	−	0.0635098i	−0.375374	+	0.926873i	$0.622486\pi$
$480$	0.154895	+	3.81474i	0.00706995	+	0.174118i
$481$	−6.33134	−	1.38269i	−0.288684	−	0.0630454i
$482$	−1.11585	+	0.644237i	−0.0508256	+	0.0293442i
$483$	19.5273	+	18.0034i	0.888525	+	0.819185i
$484$	−1.72021	−	2.97949i	−0.0781913	−	0.135431i
$485$	3.84177	+	6.65415i	0.174446	+	0.302149i
$486$	−0.0633585	+	1.07465i	−0.00287400	+	0.0487469i
$487$	28.6358	+	7.67295i	1.29761	+	0.347694i	0.840547	−	0.541738i	$-0.182234\pi$
$487$	28.6358	+	7.67295i	1.29761	+	0.347694i	0.457066	+	0.889433i	$0.348900\pi$
$488$	−1.07338	+	1.07338i	−0.0485898	+	0.0485898i
$489$	1.40105	−	6.22973i	0.0633578	−	0.281718i
$490$	−0.0762741	+	0.132111i	−0.00344571	+	0.00596815i
$491$	−23.8262			−1.07526			−0.537631	−	0.843180i	$-0.680681\pi$
$491$	−23.8262			−1.07526			−0.537631	+	0.843180i	$0.680681\pi$
$492$	6.11694	+	19.6089i	0.275773	+	0.884037i
$493$	10.2052	+	5.89196i	0.459618	+	0.265361i
$494$	1.10388	−	0.708152i	0.0496659	−	0.0318613i
$495$	10.4383	−	22.0329i	0.469166	−	0.990306i
$496$	7.44219	+	27.7746i	0.334164	+	1.24712i
$497$	−7.06465	+	4.07878i	−0.316893	+	0.182958i
$498$	−0.0152506	−	0.375590i	−0.000683395	−	0.0168306i
$499$	15.3923	+	4.12436i	0.689054	+	0.184632i	0.586323	−	0.810078i	$-0.300575\pi$
$499$	15.3923	+	4.12436i	0.689054	+	0.184632i	0.102732	+	0.994709i	$0.467242\pi$
$500$	14.8094	−	3.96818i	0.662298	−	0.177462i
$501$	−13.7829	+	14.9496i	−0.615777	+	0.667899i
$502$	−0.640973	+	0.171748i	−0.0286080	+	0.00766549i
$503$	16.3090	−	9.41599i	0.727182	−	0.419838i	−0.0902087	−	0.995923i	$-0.528753\pi$
$503$	16.3090	−	9.41599i	0.727182	−	0.419838i	0.817390	+	0.576084i	$0.195420\pi$
$504$	2.04958	−	0.166719i	0.0912956	−	0.00742623i
$505$	18.0858	−	4.84609i	0.804810	−	0.215648i
$506$	−0.649097	+	1.12427i	−0.0288559	+	0.0499798i
$507$	−13.7653	−	17.8190i	−0.611341	−	0.791368i
$508$	−6.45590	−	11.1819i	−0.286434	−	0.496118i
$509$	−18.1384	−	18.1384i	−0.803969	−	0.803969i	0.179744	−	0.983713i	$-0.442473\pi$
$509$	−18.1384	−	18.1384i	−0.803969	−	0.803969i	−0.983713	+	0.179744i	$0.942473\pi$
$510$	−0.0196199	−	0.483199i	−0.000868786	−	0.0213964i
$511$			1.93854i			0.0857560i
$512$	3.86936	+	3.86936i	0.171003	+	0.171003i
$513$	27.1012	+	3.82063i	1.19655	+	0.168685i
$514$	0.243989	−	0.910578i	0.0107619	−	0.0401639i
$515$	2.84216	+	10.6071i	0.125241	+	0.467404i
$516$	−2.32991	+	4.44256i	−0.102569	+	0.195573i
$517$			34.9464i			1.53694i
$518$	0.218052	−	0.218052i	0.00958066	−	0.00958066i
$519$	−41.4203	+	1.68184i	−1.81815	+	0.0738247i
$520$	0.124147	+	2.65156i	0.00544422	+	0.116279i
$521$		−	0.0536058i		−	0.00234851i	−0.999999	−	0.00117426i	$-0.999626\pi$
$521$		−	0.0536058i		−	0.00234851i	0.999999	−	0.00117426i	$-0.000373777\pi$
$522$	0.541835	+	1.51743i	0.0237155	+	0.0664161i
$523$	−7.40582	+	12.8273i	−0.323834	+	0.560897i	−0.981276	−	0.192608i	$-0.938305\pi$
$523$	−7.40582	+	12.8273i	−0.323834	+	0.560897i	0.657442	+	0.753505i	$0.271639\pi$
$524$	−8.55997			−0.373944
$525$	2.71697	+	8.70969i	0.118578	+	0.380122i
$526$	0.385610	+	1.43912i	0.0168134	+	0.0627485i
$527$	−2.83933	−	10.5965i	−0.123683	−	0.461592i
$528$	−6.23871	−	19.9992i	−0.271505	−	0.870355i
$529$	15.0980			0.656434
$530$	−0.839630	+	1.45428i	−0.0364712	+	0.0631700i
$531$	−0.865472	−	2.42379i	−0.0375583	−	0.105183i
$532$		−	26.1091i		−	1.13197i
$533$	6.50874	+	20.4184i	0.281925	+	0.884418i
$534$	−1.56118	+	0.0633906i	−0.0675588	+	0.00274318i
$535$	−8.09661	+	8.09661i	−0.350047	+	0.350047i
$536$			1.20455i			0.0520284i
$537$	16.8935	−	32.2117i	0.729007	−	1.39004i
$538$	0.0855173	+	0.319155i	0.00368691	+	0.0137597i
$539$	0.652549	−	2.43535i	0.0281073	−	0.104898i
$540$	−17.0413	+	21.7926i	−0.733340	+	0.937806i
$541$	−6.00591	−	6.00591i	−0.258214	−	0.258214i	0.566113	−	0.824328i	$-0.308447\pi$
$541$	−6.00591	−	6.00591i	−0.258214	−	0.258214i	−0.824328	+	0.566113i	$0.808447\pi$
$542$			1.85357i			0.0796177i
$543$	0.100981	+	2.48694i	0.00433349	+	0.106725i
$544$	−0.885032	−	0.885032i	−0.0379454	−	0.0379454i
$545$	−10.3456	−	17.9191i	−0.443156	−	0.767569i
$546$	1.06735	−	0.0934906i	0.0456784	−	0.00400103i
$547$	−8.68966	+	15.0509i	−0.371543	+	0.643532i	−0.989803	−	0.142442i	$-0.954505\pi$
$547$	−8.68966	+	15.0509i	−0.371543	+	0.643532i	0.618260	+	0.785974i	$0.287838\pi$
$548$	21.2885	−	5.70425i	0.909402	−	0.243673i
$549$	−16.4514	+	1.33820i	−0.702128	+	0.0571129i
$550$	−0.386196	+	0.222970i	−0.0164674	+	0.00950748i
$551$	39.5690	−	10.6025i	1.68570	−	0.451681i
$552$	1.99937	−	2.16861i	0.0850990	−	0.0923023i
$553$	30.7290	−	8.23380i	1.30673	−	0.350137i
$554$	0.450207	+	0.120633i	0.0191274	+	0.00512518i
$555$	0.337026	+	8.30026i	0.0143060	+	0.352326i
$556$	39.6663	−	22.9013i	1.68222	−	0.971232i
$557$	−1.51385	−	5.64977i	−0.0641440	−	0.239389i	0.926409	−	0.376518i	$-0.122879\pi$
$557$	−1.51385	−	5.64977i	−0.0641440	−	0.239389i	−0.990553	+	0.137130i	$0.956212\pi$
$558$	0.642220	−	1.35558i	0.0271873	−	0.0573865i
$559$	−2.40204	+	4.65001i	−0.101595	+	0.196675i
$560$	22.8004	+	13.1638i	0.963491	+	0.556272i
$561$	2.38018	+	7.63006i	0.100491	+	0.322142i
$562$	−1.78694			−0.0753775
$563$	−10.0522	+	17.4108i	−0.423648	+	0.733780i	−0.996293	−	0.0860237i	$-0.972584\pi$
$563$	−10.0522	+	17.4108i	−0.423648	+	0.733780i	0.572645	+	0.819803i	$0.305917\pi$
$564$	8.70072	−	38.6874i	0.366366	−	1.62903i
$565$	−14.8274	+	14.8274i	−0.623794	+	0.623794i
$566$	−0.983348	−	0.263487i	−0.0413332	−	0.0110752i
$567$	18.1579	+	13.0474i	0.762560	+	0.547941i
$568$	0.452969	+	0.784566i	0.0190062	+	0.0329196i
$569$	−13.8515	−	23.9916i	−0.580687	−	1.00578i	−0.995398	−	0.0958264i	$-0.969451\pi$
$569$	−13.8515	−	23.9916i	−0.580687	−	1.00578i	0.414711	−	0.909953i	$-0.363883\pi$
$570$	−1.23600	−	1.13954i	−0.0517702	−	0.0477301i
$571$	12.3582	−	7.13501i	0.517174	−	0.298591i	−0.218603	−	0.975814i	$-0.570150\pi$
$571$	12.3582	−	7.13501i	0.517174	−	0.298591i	0.735778	+	0.677223i	$0.236817\pi$
$572$	−6.65425	−	20.8748i	−0.278228	−	0.872821i
$573$	−0.791157	−	19.4846i	−0.0330510	−	0.813979i
$574$	−0.985013	−	0.263933i	−0.0411137	−	0.0110164i
$575$	11.3337	+	6.54349i	0.472646	+	0.272882i
$576$	1.91801	+	23.5794i	0.0799173	+	0.982476i
$577$	5.31921	−	5.31921i	0.221442	−	0.221442i	−0.587664	−	0.809105i	$-0.699952\pi$
$577$	5.31921	−	5.31921i	0.221442	−	0.221442i	0.809105	+	0.587664i	$0.199952\pi$
$578$	−0.718033	−	0.718033i	−0.0298662	−	0.0298662i
$579$	−9.44168	−	8.70485i	−0.392383	−	0.361761i
$580$	−10.7169	+	39.9959i	−0.444994	+	1.66074i
$581$	−6.76154	−	3.90377i	−0.280516	−	0.161956i
$582$	−0.184170	−	0.291045i	−0.00763410	−	0.0120642i
$583$	7.18330	−	26.8084i	0.297502	−	1.11029i
$584$	0.215285			0.00890856
$585$	−17.6381	+	22.8466i	−0.729246	+	0.944591i
$586$	1.17104			0.0483753
$587$	−6.90691	+	25.7769i	−0.285079	+	1.06393i	0.663703	+	0.747996i	$0.268984\pi$
$587$	−6.90691	+	25.7769i	−0.285079	+	1.06393i	−0.948782	+	0.315932i	$0.897683\pi$
$588$	−1.32874	+	2.53358i	−0.0547962	+	0.104483i
$589$	−33.0272	−	19.0682i	−1.36086	−	0.785693i
$590$	−0.0409158	+	0.152700i	−0.00168448	+	0.00628655i
$591$	−32.3969	+	10.1061i	−1.33263	+	0.415711i
$592$	5.04743	+	5.04743i	0.207448	+	0.207448i
$593$	−30.8664	+	30.8664i	−1.26753	+	1.26753i	−0.320173	+	0.947359i	$0.603741\pi$
$593$	−30.8664	+	30.8664i	−1.26753	+	1.26753i	−0.947359	+	0.320173i	$0.896259\pi$
$594$	−0.427450	+	1.00581i	−0.0175385	+	0.0412690i
$595$	−8.69875	−	5.02223i	−0.356614	−	0.205891i
$596$	34.9443	+	9.36330i	1.43138	+	0.383536i
$597$	31.6092	−	20.0019i	1.29368	−	0.818625i
$598$	1.03472	−	1.13637i	0.0423128	−	0.0464696i
$599$	15.8006	−	9.12248i	0.645595	−	0.372735i	−0.141171	−	0.989985i	$-0.545087\pi$
$599$	15.8006	−	9.12248i	0.645595	−	0.372735i	0.786767	+	0.617251i	$0.211754\pi$
$600$	0.967256	−	0.301733i	0.0394881	−	0.0123182i
$601$	11.9056	+	20.6211i	0.485641	+	0.841154i	0.999864	−	0.0165023i	$-0.00525308\pi$
$601$	11.9056	+	20.6211i	0.485641	+	0.841154i	−0.514223	+	0.857656i	$0.671920\pi$
$602$	−0.124522	−	0.215679i	−0.00507516	−	0.00879043i
$603$	−8.47995	+	9.98167i	−0.345330	+	0.406485i
$604$	8.38665	+	2.24720i	0.341248	+	0.0914371i
$605$	−3.25350	+	3.25350i	−0.132274	+	0.132274i
$606$	−0.801232	+	0.249942i	−0.0325478	+	0.0101532i
$607$	−4.78300	+	8.28439i	−0.194136	+	0.336253i	−0.946617	−	0.322361i	$-0.895524\pi$
$607$	−4.78300	+	8.28439i	−0.194136	+	0.336253i	0.752481	+	0.658614i	$0.228857\pi$
$608$	−4.35106			−0.176459
$609$	32.6509	+	7.34313i	1.32308	+	0.297559i
$610$	0.878025	+	0.506928i	0.0355502	+	0.0205249i
$611$	8.82704	−	40.4189i	0.357104	−	1.63517i
$612$	−0.735293	−	9.03945i	−0.0297225	−	0.365398i
$613$	−6.31167	−	23.5555i	−0.254926	−	0.951396i	−0.968132	−	0.250442i	$-0.919424\pi$
$613$	−6.31167	−	23.5555i	−0.254926	−	0.951396i	0.713206	−	0.700955i	$-0.247243\pi$
$614$	0.229875	−	0.132718i	0.00927699	−	0.00535607i
$615$	23.2136	−	14.6893i	0.936064	−	0.592331i
$616$	2.01647	+	0.540313i	0.0812461	+	0.0217698i
$617$	46.4824	−	12.4549i	1.87131	−	0.501416i	0.871368	−	0.490629i	$-0.163233\pi$
$617$	46.4824	−	12.4549i	1.87131	−	0.501416i	0.999942	−	0.0107866i	$-0.00343354\pi$
$618$	−0.146588	−	0.469911i	−0.00589662	−	0.0189026i
$619$	−9.20307	+	2.46596i	−0.369903	+	0.0991152i	−0.438982	−	0.898496i	$-0.644661\pi$
$619$	−9.20307	+	2.46596i	−0.369903	+	0.0991152i	0.0690788	+	0.997611i	$0.477994\pi$
$620$	33.3835	−	19.2740i	1.34071	−	0.774061i
$621$	31.8351	−	3.89506i	1.27750	−	0.156303i
$622$	0.386388	−	0.103532i	0.0154928	−	0.00415127i
$623$	−16.2264	+	28.1050i	−0.650098	+	1.12600i
$624$	2.16410	+	24.7068i	0.0866335	+	0.989065i
$625$	−15.5529	−	26.9384i	−0.622116	−	1.07754i
$626$	−0.152155	−	0.152155i	−0.00608132	−	0.00608132i
$627$	24.6065	+	12.9049i	0.982691	+	0.515374i
$628$			31.8969i			1.27283i
$629$	−1.92569	−	1.92569i	−0.0767822	−	0.0767822i
$630$	−0.461853	−	1.29343i	−0.0184007	−	0.0515317i
$631$	−4.48760	+	16.7479i	−0.178648	+	0.666725i	0.817253	+	0.576279i	$0.195496\pi$
$631$	−4.48760	+	16.7479i	−0.178648	+	0.666725i	−0.995901	+	0.0904459i	$0.971171\pi$
$632$	−0.914406	−	3.41261i	−0.0363731	−	0.135746i
$633$	9.14749	−	0.371427i	0.363580	−	0.0147629i
$634$			1.21822i			0.0483817i
$635$	−12.2103	+	12.2103i	−0.484551	+	0.484551i
$636$	−14.6268	+	27.8898i	−0.579992	+	1.10590i
$637$	−1.36987	+	2.65188i	−0.0542764	+	0.105071i
$638$			1.63576i			0.0647602i
$639$	−1.76971	+	9.69033i	−0.0700085	+	0.383343i
$640$	2.93083	−	5.07634i	0.115851	−	0.200660i
$641$	−14.3272			−0.565892			−0.282946	−	0.959136i	$-0.591312\pi$
$641$	−14.3272			−0.565892			−0.282946	+	0.959136i	$0.591312\pi$
$642$	0.347914	−	0.377363i	0.0137311	−	0.0148933i
$643$	−6.38765	−	23.8390i	−0.251904	−	0.940120i	−0.969787	−	0.243955i	$-0.921555\pi$
$643$	−6.38765	−	23.8390i	−0.251904	−	0.940120i	0.717882	−	0.696165i	$-0.245112\pi$
$644$	−7.91880	−	29.5533i	−0.312044	−	1.16457i
$645$	6.54542	+	1.47205i	0.257726	+	0.0579620i
$646$	0.551132			0.0216840
$647$	11.3450	−	19.6501i	0.446017	−	0.772524i	−0.552106	−	0.833774i	$-0.686176\pi$
$647$	11.3450	−	19.6501i	0.446017	−	0.772524i	0.998122	+	0.0612504i	$0.0195088\pi$
$648$	1.44899	−	2.01653i	0.0569215	−	0.0792167i
$649$		−	2.61279i		−	0.102561i
$650$	0.502992	−	0.160338i	0.0197290	−	0.00628898i
$651$	−16.6598	−	26.3275i	−0.652948	−	1.03186i
$652$	−5.20117	+	5.20117i	−0.203693	+	0.203693i
$653$		−	0.251261i		−	0.00983260i	−0.999988	−	0.00491630i	$-0.998435\pi$
$653$		−	0.251261i		−	0.00983260i	0.999988	−	0.00491630i	$-0.00156491\pi$
$654$	0.495956	+	0.783762i	0.0193934	+	0.0306475i
$655$	2.96294	+	11.0578i	0.115772	+	0.432066i
$656$	6.10949	−	22.8009i	0.238535	−	0.890226i
$657$	1.78400	+	1.51560i	0.0696003	+	0.0591291i
$658$	1.39203	+	1.39203i	0.0542671	+	0.0542671i
$659$			26.9100i			1.04827i	0.851637	+	0.524133i	$0.175610\pi$
$659$			26.9100i			1.04827i	−0.851637	+	0.524133i	$0.824390\pi$
$660$	−23.7326	+	15.0177i	−0.923790	+	0.584564i
$661$	24.5144	+	24.5144i	0.953500	+	0.953500i	0.998966	−	0.0454661i	$-0.0144773\pi$
$661$	24.5144	+	24.5144i	0.953500	+	0.953500i	−0.0454661	+	0.998966i	$0.514477\pi$
$662$	−0.390839	−	0.676953i	−0.0151904	−	0.0263105i
$663$	−0.825645	−	9.42610i	−0.0320654	−	0.366080i
$664$	−0.433534	+	0.750903i	−0.0168244	+	0.0291407i
$665$	−33.7280	+	9.03740i	−1.30792	+	0.350455i
$666$	−0.0301901	−	0.371147i	−0.00116984	−	0.0143816i
$667$	41.5731	−	24.0022i	1.60972	−	0.929370i
$668$	22.6252	−	6.06242i	0.875397	−	0.234562i
$669$	−41.0726	−	9.23714i	−1.58796	−	0.357129i
$670$	0.777093	−	0.208221i	0.0300217	−	0.00804429i
$671$	−16.1856	−	4.33693i	−0.624839	−	0.167425i
$672$	−3.14797	−	1.65096i	−0.121436	−	0.0636870i
$673$	17.7006	−	10.2194i	0.682306	−	0.393930i	−0.118417	−	0.992964i	$-0.537782\pi$
$673$	17.7006	−	10.2194i	0.682306	−	0.393930i	0.800723	+	0.599034i	$0.204449\pi$
$674$	0.329135	+	1.22835i	0.0126778	+	0.0473143i
$675$	10.1395	+	4.30908i	0.390270	+	0.165857i
$676$	2.42355	+	25.8245i	0.0932134	+	0.993251i
$677$	−11.4569	−	6.61467i	−0.440326	−	0.254222i	0.263410	−	0.964684i	$-0.415153\pi$
$677$	−11.4569	−	6.61467i	−0.440326	−	0.254222i	−0.703736	+	0.710462i	$0.748486\pi$
$678$	0.637138	−	0.691069i	0.0244691	−	0.0265403i
$679$	−7.15373			−0.274535
$680$	−0.557744	+	0.966041i	−0.0213885	+	0.0370460i
$681$	11.5691	+	10.6662i	0.443329	+	0.408732i
$682$	1.07680	−	1.07680i	0.0412326	−	0.0412326i
$683$	−13.5168	−	3.62181i	−0.517205	−	0.138585i	−0.00923131	−	0.999957i	$-0.502938\pi$
$683$	−13.5168	−	3.62181i	−0.517205	−	0.138585i	−0.507973	+	0.861373i	$0.669605\pi$
$684$	−24.0277	−	20.4128i	−0.918720	−	0.780501i
$685$	−14.7376	−	25.5263i	−0.563095	−	0.975309i
$686$	−0.671500	−	1.16307i	−0.0256380	−	0.0444063i
$687$	−3.34244	+	14.8620i	−0.127522	+	0.567022i
$688$	4.99251	−	2.88242i	0.190338	−	0.109891i
$689$	−15.0797	+	29.1921i	−0.574489	+	1.11213i
$690$	−1.74466	−	0.914991i	−0.0664182	−	0.0348331i
$691$	−39.9295	−	10.6991i	−1.51899	−	0.407012i	−0.599580	−	0.800315i	$-0.704666\pi$
$691$	−39.9295	−	10.6991i	−1.51899	−	0.407012i	−0.919409	+	0.393303i	$0.871332\pi$
$692$	41.3556	+	23.8767i	1.57211	+	0.907655i
$693$	12.9061	+	18.6733i	0.490262	+	0.709340i
$694$	0.0598285	−	0.0598285i	0.00227106	−	0.00227106i
$695$	−43.3142	−	43.3142i	−1.64300	−	1.64300i
$696$	0.815492	−	3.62605i	0.0309111	−	0.137445i
$697$	−2.33088	+	8.69896i	−0.0882884	+	0.329497i
$698$	−0.569797	−	0.328973i	−0.0215672	−	0.0124518i
$699$	−26.1305	+	1.06101i	−0.988345	+	0.0401311i
$700$	2.72017	−	10.1518i	0.102813	−	0.383703i
$701$	−23.7308			−0.896298			−0.448149	−	0.893959i	$-0.647917\pi$
$701$	−23.7308			−0.896298			−0.448149	+	0.893959i	$0.647917\pi$
$702$	0.748443	−	1.05535i	0.0282481	−	0.0398317i
$703$	−9.46720			−0.357062
$704$	−6.21603	+	23.1985i	−0.234276	+	0.874328i
$705$	−52.9884	+	2.15156i	−1.99566	+	0.0810323i
$706$	−1.08336	−	0.625476i	−0.0407726	−	0.0235401i
$707$	−4.51193	+	16.8387i	−0.169689	+	0.633286i
$708$	−0.650514	+	2.89248i	−0.0244478	+	0.108706i
$709$	−27.0913	−	27.0913i	−1.01744	−	1.01744i	−0.999845	−	0.0175911i	$-0.994400\pi$
$709$	−27.0913	−	27.0913i	−1.01744	−	1.01744i	−0.0175911	−	0.999845i	$-0.505600\pi$
$710$	0.427848	−	0.427848i	0.0160569	−	0.0160569i
$711$	16.4473	−	34.7165i	0.616820	−	1.30197i
$712$	3.12121	+	1.80203i	0.116972	+	0.0675339i
$713$	−43.1673	−	11.5666i	−1.61663	−	0.433174i
$714$	0.398741	+	0.209120i	0.0149225	+	0.00782613i
$715$	−24.6630	+	15.8216i	−0.922344	+	0.591695i
$716$	−36.2861	+	20.9498i	−1.35607	+	0.782930i
$717$	1.32234	−	5.87974i	0.0493837	−	0.219583i
$718$	0.510940	+	0.884975i	0.0190681	+	0.0330270i
$719$	21.1677	+	36.6636i	0.789423	+	1.36732i	0.926321	+	0.376735i	$0.122953\pi$
$719$	21.1677	+	36.6636i	0.789423	+	1.36732i	−0.136898	+	0.990585i	$0.543713\pi$
$720$	29.9402	−	10.6909i	1.11581	−	0.398426i
$721$	−9.87568	−	2.64618i	−0.367790	−	0.0985489i
$722$	0.426959	−	0.426959i	0.0158898	−	0.0158898i
$723$	23.7593	+	21.9051i	0.883618	+	0.814660i
$724$	1.43359	−	2.48306i	0.0532791	−	0.0922821i
$725$	16.4899			0.612421
$726$	0.139804	−	0.151638i	0.00518861	−	0.00562780i
$727$	−25.4774	−	14.7094i	−0.944904	−	0.545541i	−0.0534100	−	0.998573i	$-0.517009\pi$
$727$	−25.4774	−	14.7094i	−0.944904	−	0.545541i	−0.891494	+	0.453032i	$0.850342\pi$
$728$	−2.19577	−	1.13426i	−0.0813806	−	0.0420385i
$729$	26.2036	−	6.50951i	0.970502	−	0.241093i
$730$	−0.0372148	−	0.138888i	−0.00137738	−	0.00514046i
$731$	−1.90473	+	1.09970i	−0.0704490	+	0.0406738i
$732$	16.8385	+	8.83097i	0.622369	+	0.326402i
$733$	7.32806	+	1.96355i	0.270668	+	0.0725253i	0.391600	−	0.920135i	$-0.371922\pi$
$733$	7.32806	+	1.96355i	0.270668	+	0.0725253i	−0.120932	+	0.992661i	$0.538588\pi$
$734$	−0.0505078	+	0.0135335i	−0.00186428	+	0.000499532i
$735$	3.73283	+	0.839506i	0.137687	+	0.0309656i
$736$	−4.92503	+	1.31966i	−0.181539	+	0.0486433i
$737$	−11.5151	+	6.64827i	−0.424166	+	0.244892i
$738$	−1.01300	+	0.700136i	−0.0372890	+	0.0257724i
$739$	−6.96809	+	1.86709i	−0.256325	+	0.0686822i	−0.384693	−	0.923044i	$-0.625693\pi$
$739$	−6.96809	+	1.86709i	−0.256325	+	0.0686822i	0.128368	+	0.991727i	$0.459026\pi$
$740$	4.78467	−	8.28729i	0.175888	−	0.304647i
$741$	−25.2002	−	21.1411i	−0.925753	−	0.776638i
$742$	−0.781734	−	1.35400i	−0.0286984	−	0.0497070i
$743$	30.9424	+	30.9424i	1.13516	+	1.13516i	0.989305	+	0.145860i	$0.0465948\pi$
$743$	30.9424	+	30.9424i	1.13516	+	1.13516i	0.145860	+	0.989305i	$0.453405\pi$
$744$	−2.92381	+	1.85015i	−0.107192	+	0.0678299i
$745$		−	48.3824i		−	1.77259i
$746$	1.09303	+	1.09303i	0.0400188	+	0.0400188i
$747$	−8.87889	+	3.17042i	−0.324862	+	0.116000i
$748$	2.38299	−	8.89343i	0.0871307	−	0.325176i
$749$	−2.75921	−	10.2975i	−0.100820	−	0.376264i
$750$	0.491482	+	0.776691i	0.0179464	+	0.0283607i
$751$		−	15.1950i		−	0.554473i	−0.960802	−	0.277236i	$-0.910582\pi$
$751$		−	15.1950i		−	0.554473i	0.960802	−	0.277236i	$-0.0894185\pi$
$752$	−32.2225	+	32.2225i	−1.17503	+	1.17503i
$753$	8.89960	+	14.0641i	0.324319	+	0.512524i
$754$	0.413172	−	1.89191i	0.0150468	−	0.0688993i
$755$		−	11.6118i		−	0.422597i
$756$	−9.63851	−	23.8855i	−0.350549	−	0.868708i
$757$	−23.4618	+	40.6370i	−0.852732	+	1.47698i	0.0260003	+	0.999662i	$0.491723\pi$
$757$	−23.4618	+	40.6370i	−0.852732	+	1.47698i	−0.878733	+	0.477314i	$0.841610\pi$
$758$	−1.49640			−0.0543519
$759$	31.7666	+	7.14424i	1.15305	+	0.259319i
$760$	1.00365	+	3.74567i	0.0364062	+	0.135870i
$761$	5.90347	+	22.0320i	0.214001	+	0.798661i	0.986516	+	0.163665i	$0.0523316\pi$
$761$	5.90347	+	22.0320i	0.214001	+	0.798661i	−0.772515	+	0.634996i	$0.781002\pi$
$762$	0.524680	−	0.569092i	0.0190072	−	0.0206160i
$763$	19.2644			0.697419
$764$	−11.2318	+	19.4541i	−0.406354	+	0.703825i
$765$	−11.4227	+	4.07877i	−0.412990	+	0.147468i
$766$			0.809614i			0.0292526i
$767$	−0.659959	+	3.02194i	−0.0238297	+	0.109116i
$768$	12.5655	−	23.9593i	0.453418	−	0.864556i
$769$	23.8804	−	23.8804i	0.861150	−	0.861150i	−0.130321	−	0.991472i	$-0.541601\pi$
$769$	23.8804	−	23.8804i	0.861150	−	0.861150i	0.991472	+	0.130321i	$0.0416009\pi$
$770$		−	1.39430i		−	0.0502469i
$771$	−23.6244	+	0.959252i	−0.850812	+	0.0345466i
$772$	3.82882	+	14.2894i	0.137802	+	0.514285i
$773$	−11.9731	+	44.6843i	−0.430643	+	1.60718i	0.320640	+	0.947201i	$0.396102\pi$
$773$	−11.9731	+	44.6843i	−0.430643	+	1.60718i	−0.751283	+	0.659981i	$0.770565\pi$
$774$	−0.295839	−	0.0540280i	−0.0106337	−	0.00194200i
$775$	−10.8551	−	10.8551i	−0.389926	−	0.389926i
$776$			0.794458i			0.0285194i
$777$	−6.84947	−	3.59221i	−0.245723	−	0.128870i
$778$	0.542205	+	0.542205i	0.0194390	+	0.0194390i
$779$	15.6536	+	27.1129i	0.560849	+	0.971419i
$780$	31.2423	−	11.3749i	1.11865	−	0.407286i
$781$	−5.00016	+	8.66054i	−0.178920	+	0.309898i
$782$	0.623835	−	0.167156i	0.0223083	−	0.00597749i
$783$	32.2850	−	24.3069i	1.15377	−	0.868657i
$784$	2.84721	−	1.64384i	0.101686	−	0.0587084i
$785$	41.2048	−	11.0408i	1.47066	−	0.394062i
$786$	−0.152817	−	0.489881i	−0.00545080	−	0.0174735i
$787$	7.33514	−	1.96544i	0.261469	−	0.0700605i	−0.125703	−	0.992068i	$-0.540119\pi$
$787$	7.33514	−	1.96544i	0.261469	−	0.0700605i	0.387172	+	0.922007i	$0.373452\pi$
$788$	37.7611	+	10.1181i	1.34519	+	0.360441i
$789$	31.5768	−	19.9815i	1.12416	−	0.711359i
$790$	−2.04352	+	1.17983i	−0.0727052	+	0.0419764i
$791$	−5.05298	−	18.8580i	−0.179663	−	0.670512i
$792$	2.07377	−	1.43329i	0.0736881	−	0.0509296i
$793$	17.6248	+	9.10436i	0.625874	+	0.323305i
$794$	1.00565	+	0.580614i	0.0356893	+	0.0206052i
$795$	41.0912	+	9.24133i	1.45735	+	0.327756i
$796$	−43.0899			−1.52728
$797$	18.8135	−	32.5859i	0.666407	−	1.15425i	−0.312494	−	0.949920i	$-0.601165\pi$
$797$	18.8135	−	32.5859i	0.666407	−	1.15425i	0.978902	−	0.204332i	$-0.0655021\pi$
$798$	1.49421	−	0.466114i	0.0528943	−	0.0165003i
$799$	12.2935	−	12.2935i	0.434912	−	0.434912i
$800$	−1.69179	−	0.453314i	−0.0598138	−	0.0160271i
$801$	13.1782	+	36.9060i	0.465629	+	1.30401i
$802$	−0.510360	−	0.883970i	−0.0180214	−	0.0312141i
$803$	1.18823	+	2.05807i	0.0419316	+	0.0726277i
$804$	14.4031	−	4.49300i	0.507957	−	0.158456i
$805$	−35.4363	+	20.4591i	−1.24896	+	0.721090i
$806$	−1.51740	+	0.973432i	−0.0534482	+	0.0342877i
$807$	7.00282	−	4.43131i	0.246511	−	0.155990i
$808$	1.87003	+	0.501073i	0.0657874	+	0.0176277i
$809$	−19.7137	−	11.3817i	−0.693096	−	0.400159i	0.111675	−	0.993745i	$-0.464379\pi$
$809$	−19.7137	−	11.3817i	−0.693096	−	0.400159i	−0.804771	+	0.593586i	$0.797712\pi$
$810$	−1.55141	−	0.586206i	−0.0545109	−	0.0205972i
$811$	10.9550	−	10.9550i	0.384681	−	0.384681i	−0.488104	−	0.872785i	$-0.662312\pi$
$811$	10.9550	−	10.9550i	0.384681	−	0.384681i	0.872785	+	0.488104i	$0.162312\pi$
$812$	−27.2601	−	27.2601i	−0.956642	−	0.956642i
$813$	44.3802	−	13.8443i	1.55648	−	0.485541i
$814$	0.0978421	−	0.365152i	0.00342936	−	0.0127986i
$815$	8.51924	+	4.91859i	0.298416	+	0.172291i
$816$	−4.84068	+	9.22999i	−0.169458	+	0.323114i
$817$	−1.97888	+	7.38530i	−0.0692324	+	0.258379i
$818$	0.536869			0.0187712
$819$	−10.2105	−	24.8574i	−0.356783	−	0.868587i
$820$	−31.6450			−1.10509
$821$	−12.2905	+	45.8687i	−0.428941	+	1.60083i	0.326223	+	0.945293i	$0.394224\pi$
$821$	−12.2905	+	45.8687i	−0.428941	+	1.60083i	−0.755164	+	0.655536i	$0.772443\pi$
$822$	0.706504	+	1.11649i	0.0246422	+	0.0389421i
$823$	−10.6238	−	6.13367i	−0.370323	−	0.213806i	0.303276	−	0.952903i	$-0.401919\pi$
$823$	−10.6238	−	6.13367i	−0.370323	−	0.213806i	−0.673600	+	0.739096i	$0.735253\pi$
$824$	−0.293872	+	1.09674i	−0.0102375	+	0.0382069i
$825$	8.22308	+	7.58136i	0.286291	+	0.263949i
$826$	−0.104076	−	0.104076i	−0.00362127	−	0.00362127i
$827$	−6.58424	+	6.58424i	−0.228957	+	0.228957i	−0.812257	−	0.583300i	$-0.801761\pi$
$827$	−6.58424	+	6.58424i	−0.228957	+	0.228957i	0.583300	+	0.812257i	$0.301761\pi$
$828$	−33.3884	−	15.8180i	−1.16033	−	0.549714i
$829$	28.6973	+	16.5684i	0.996698	+	0.575444i	0.907270	−	0.420549i	$-0.138163\pi$
$829$	28.6973	+	16.5684i	0.996698	+	0.575444i	0.0894284	+	0.995993i	$0.471496\pi$
$830$	0.559375	+	0.149884i	0.0194162	+	0.00520255i
$831$	−0.474272	−	11.6803i	−0.0164523	−	0.405187i
$832$	13.0491	−	25.2613i	0.452396	−	0.875776i
$833$	−1.08626	+	0.627153i	−0.0376367	+	0.0217296i
$834$	2.01877	+	1.86122i	0.0699042	+	0.0644489i
$835$	−15.6630	−	27.1291i	−0.542040	−	0.938840i
$836$	−16.0036	−	27.7190i	−0.553495	−	0.958681i
$837$	−37.2536	−	5.25188i	−1.28767	−	0.181532i
$838$	−2.57717	−	0.690550i	−0.0890268	−	0.0238546i
$839$	−5.63483	+	5.63483i	−0.194536	+	0.194536i	−0.797653	−	0.603117i	$-0.793925\pi$
$839$	−5.63483	+	5.63483i	−0.194536	+	0.194536i	0.603117	+	0.797653i	$0.293925\pi$
$840$	−0.695114	+	3.09079i	−0.0239837	+	0.106643i
$841$	15.7434	−	27.2684i	0.542877	−	0.940290i
$842$	1.51243			0.0521217
$843$	13.3466	+	42.7848i	0.459682	+	1.47359i
$844$	−9.13319	−	5.27305i	−0.314378	−	0.181506i
$845$	32.5215	−	12.0696i	1.11877	−	0.415208i
$846$	2.36938	−	0.192732i	0.0814610	−	0.00662625i
$847$	−1.10875	−	4.13790i	−0.0380970	−	0.142180i
$848$	31.3422	−	18.0954i	1.07630	−	0.621400i
$849$	1.03591	+	25.5124i	0.0355524	+	0.875583i
$850$	0.214293	+	0.0574195i	0.00735018	+	0.00196947i
$851$	−10.7161	+	2.87136i	−0.367342	+	0.0984291i
$852$	7.69166	−	8.34273i	0.263512	−	0.285817i
$853$	−41.2070	+	11.0414i	−1.41090	+	0.378050i	−0.882247	−	0.470788i	$-0.843970\pi$
$853$	−41.2070	+	11.0414i	−1.41090	+	0.378050i	−0.528654	+	0.848837i	$0.677303\pi$
$854$	−0.817481	+	0.471973i	−0.0279736	+	0.0161506i
$855$	−18.0525	+	38.1048i	−0.617381	+	1.30316i
$856$	−1.14359	+	0.306425i	−0.0390872	+	0.0104734i
$857$	−2.75969	+	4.77993i	−0.0942693	+	0.163279i	−0.909303	−	0.416134i	$-0.863385\pi$
$857$	−2.75969	+	4.77993i	−0.0942693	+	0.163279i	0.815034	+	0.579413i	$0.196718\pi$
$858$	1.07586	−	0.753486i	0.0367291	−	0.0257236i
$859$	3.49427	+	6.05226i	0.119223	+	0.206500i	0.919460	−	0.393184i	$-0.128626\pi$
$859$	3.49427	+	6.05226i	0.119223	+	0.206500i	−0.800237	+	0.599684i	$0.795293\pi$
$860$	−5.46474	−	5.46474i	−0.186346	−	0.186346i
$861$	1.03767	+	25.5556i	0.0353636	+	0.870932i
$862$		−	0.437849i		−	0.0149132i
$863$	15.2638	+	15.2638i	0.519587	+	0.519587i	0.917446	−	0.397859i	$-0.130247\pi$
$863$	15.2638	+	15.2638i	0.519587	+	0.519587i	−0.397859	+	0.917446i	$0.630247\pi$
$864$	−3.98050	+	1.60625i	−0.135419	+	0.0546457i
$865$	16.5293	−	61.6882i	0.562014	−	2.09746i
$866$	0.313012	+	1.16818i	0.0106366	+	0.0396962i
$867$	−11.8289	+	22.5549i	−0.401732	+	0.766005i
$868$			35.8899i			1.21818i
$869$	27.5768	−	27.5768i	0.935477	−	0.935477i
$870$	−2.48026	+	0.100709i	−0.0840886	+	0.00341436i
$871$	14.9976	−	4.78078i	0.508175	−	0.161990i
$872$		−	2.13941i		−	0.0724497i
$873$	−5.59296	+	6.58342i	−0.189293	+	0.222815i
$874$	1.12258	−	1.94436i	0.0379718	−	0.0657691i
$875$	19.0906			0.645381
$876$	−0.803021	−	2.57422i	−0.0271316	−	0.0869748i
$877$	−0.940359	−	3.50947i	−0.0317537	−	0.118506i	0.948230	−	0.317585i	$-0.102872\pi$
$877$	−0.940359	−	3.50947i	−0.0317537	−	0.118506i	−0.979984	+	0.199078i	$0.936205\pi$
$878$	0.343823	+	1.28316i	0.0116035	+	0.0433047i
$879$	−8.74650	−	28.0384i	−0.295012	−	0.945711i
$880$	32.2749			1.08799
$881$	−2.80287	+	4.85471i	−0.0944310	+	0.163559i	−0.909371	−	0.415986i	$-0.863437\pi$
$881$	−2.80287	+	4.85471i	−0.0944310	+	0.163559i	0.814940	+	0.579545i	$0.196770\pi$
$882$	−0.168716	−	0.0308119i	−0.00568096	−	0.00103749i
$883$			34.2767i			1.15350i	0.816920	+	0.576751i	$0.195680\pi$
$883$			34.2767i			1.15350i	−0.816920	+	0.576751i	$0.804320\pi$
$884$	−5.00253	+	9.68419i	−0.168253	+	0.325715i
$885$	3.96171	−	0.160862i	0.133171	−	0.00540733i
$886$	0.581794	−	0.581794i	0.0195457	−	0.0195457i
$887$		−	19.9446i		−	0.669675i	−0.942276	−	0.334837i	$-0.891319\pi$
$887$		−	19.9446i		−	0.669675i	0.942276	−	0.334837i	$-0.108681\pi$
$888$	−0.398934	+	0.760669i	−0.0133873	+	0.0255264i
$889$	−4.16110	−	15.5294i	−0.139559	−	0.520841i
$890$	0.623008	−	2.32510i	0.0208833	−	0.0779375i
$891$	27.2749	+	2.72206i	0.913744	+	0.0911923i
$892$	34.2913	+	34.2913i	1.14816	+	1.14816i
$893$		−	60.4381i		−	2.02248i
$894$	0.0879893	+	2.16700i	0.00294280	+	0.0724752i
$895$	39.6232	+	39.6232i	1.32446	+	1.32446i
$896$	2.72873	+	4.72631i	0.0911606	+	0.157895i
$897$	−34.9365	−	16.2868i	−1.16650	−	0.543802i
$898$	−0.102951	+	0.178317i	−0.00343553	+	0.00595052i
$899$	−54.3919	+	14.5743i	−1.81407	+	0.486079i
$900$	−7.21580	−	10.4403i	−0.240527	−	0.348008i
$901$	−11.9576	+	6.90374i	−0.398366	+	0.229997i
$902$	−1.20752	+	0.323555i	−0.0402062	+	0.0107732i
$903$	−4.23397	+	4.59236i	−0.140898	+	0.152824i
$904$	−2.09427	+	0.561159i	−0.0696545	+	0.0186639i
$905$	−3.70386	−	0.992447i	−0.123121	−	0.0329900i
$906$	0.0211175	+	0.520080i	0.000701581	+	0.0172785i
$907$	0.167407	−	0.0966525i	0.00555866	−	0.00320929i	−0.497218	−	0.867626i	$-0.665645\pi$
$907$	0.167407	−	0.0966525i	0.00555866	−	0.00320929i	0.502777	+	0.864416i	$0.332312\pi$
$908$	−4.69154	−	17.5091i	−0.155694	−	0.581059i
$909$	11.9688	+	17.3172i	0.396980	+	0.574374i
$910$	−0.352182	+	1.61264i	−0.0116747	+	0.0534584i
$911$	50.8660	+	29.3675i	1.68526	+	0.972988i	0.958060	+	0.286567i	$0.0925142\pi$
$911$	50.8660	+	29.3675i	1.68526	+	0.972988i	0.727205	+	0.686421i	$0.240819\pi$
$912$	10.7895	+	34.5876i	0.357277	+	1.14531i
$913$	−9.57125			−0.316762
$914$	0.245703	−	0.425571i	0.00812714	−	0.0140766i
$915$	5.57947	−	24.8089i	0.184451	−	0.820156i
$916$	12.4082	−	12.4082i	0.409980	−	0.409980i
$917$	−10.2954	−	2.75863i	−0.339983	−	0.0910981i
$918$	0.504194	−	0.203457i	0.0166409	−	0.00671509i
$919$	1.01215	+	1.75309i	0.0333876	+	0.0578290i	0.882236	−	0.470807i	$-0.156037\pi$
$919$	1.01215	+	1.75309i	0.0333876	+	0.0578290i	−0.848849	+	0.528636i	$0.822704\pi$
$920$	2.27209	+	3.93538i	0.0749087	+	0.129746i
$921$	−4.89462	−	4.51264i	−0.161283	−	0.148697i
$922$	0.899426	−	0.519284i	0.0296210	−	0.0171017i
$923$	7.97071	−	8.75376i	0.262359	−	0.288134i
$924$	−1.06086	−	26.1269i	−0.0348999	−	0.859512i
$925$	−3.68106	−	0.986338i	−0.121033	−	0.0324306i
$926$	−1.97749	−	1.14170i	−0.0649844	−	0.0375188i
$927$	−10.1563	+	7.01952i	−0.333575	+	0.230551i
$928$	−4.54287	+	4.54287i	−0.149127	+	0.149127i
$929$	−18.2727	−	18.2727i	−0.599509	−	0.599509i	0.340673	−	0.940182i	$-0.389345\pi$
$929$	−18.2727	−	18.2727i	−0.599509	−	0.599509i	−0.940182	+	0.340673i	$0.889345\pi$
$930$	1.69901	+	1.56642i	0.0557128	+	0.0513650i
$931$	−1.12855	+	4.21181i	−0.0369867	+	0.138036i
$932$	26.0896	+	15.0629i	0.854595	+	0.493401i
$933$	−5.36482	−	8.47805i	−0.175636	−	0.277559i
$934$	0.312634	−	1.16677i	0.0102297	−	0.0381778i
$935$	−12.3135			−0.402693
$936$	−2.76054	+	1.13393i	−0.0902311	+	0.0370635i
$937$	−48.9912			−1.60047			−0.800237	−	0.599684i	$-0.795293\pi$
$937$	−48.9912			−1.60047			−0.800237	+	0.599684i	$0.795293\pi$
$938$	−0.193864	+	0.723509i	−0.00632987	+	0.0236234i
$939$	−2.50661	+	4.77949i	−0.0818001	+	0.155973i
$940$	52.9056	+	30.5451i	1.72559	+	0.996270i
$941$	−3.70184	+	13.8154i	−0.120676	+	0.450371i	−0.999649	−	0.0265022i	$-0.991563\pi$
$941$	−3.70184	+	13.8154i	−0.120676	+	0.450371i	0.878972	+	0.476873i	$0.158230\pi$
$942$	−1.82544	+	0.569440i	−0.0594760	+	0.0185534i
$943$	25.9418	+	25.9418i	0.844781	+	0.844781i
$944$	2.40914	−	2.40914i	0.0784107	−	0.0784107i
$945$	−27.5193	+	20.7188i	−0.895202	+	0.673984i
$946$	−0.264401	−	0.152652i	−0.00859640	−	0.00496314i
$947$	−31.8187	−	8.52579i	−1.03397	−	0.277051i	−0.298357	−	0.954454i	$-0.596438\pi$
$947$	−31.8187	−	8.52579i	−1.03397	−	0.277051i	−0.735612	+	0.677403i	$0.763105\pi$
$948$	−37.3947	+	23.6629i	−1.21452	+	0.768536i
$949$	−0.854455	−	2.68049i	−0.0277368	−	0.0870122i
$950$	0.667906	−	0.385616i	0.0216697	−	0.0125110i
$951$	29.1679	−	9.09886i	0.945835	−	0.295051i
$952$	−0.519285	−	0.899428i	−0.0168301	−	0.0291506i
$953$	−3.71729	−	6.43853i	−0.120415	−	0.208564i	0.799517	−	0.600644i	$-0.205089\pi$
$953$	−3.71729	−	6.43853i	−0.120415	−	0.208564i	−0.919931	+	0.392080i	$0.871756\pi$
$954$	−1.85724	−	0.339180i	−0.0601303	−	0.0109814i
$955$	29.0188	+	7.77556i	0.939026	+	0.251611i
$956$	−4.90896	+	4.90896i	−0.158767	+	0.158767i
$957$	39.1651	−	12.2174i	1.26603	−	0.394934i
$958$	−0.185437	+	0.321187i	−0.00599121	+	0.0103771i
$959$	27.4428			0.886173
$960$	−35.5581	−	7.99694i	−1.14763	−	0.258100i
$961$	18.5527	+	10.7114i	0.598473	+	0.345528i
$962$	−0.205396	+	0.397619i	−0.00662225	+	0.0128198i
$963$	−11.6338	−	5.51161i	−0.374894	−	0.177609i
$964$	−9.63495	−	35.9581i	−0.310321	−	1.15813i
$965$	17.1338	−	9.89221i	0.551557	−	0.318442i
$966$	1.54995	−	0.980788i	0.0498687	−	0.0315563i
$967$	22.5276	+	6.03626i	0.724440	+	0.194113i	0.602152	−	0.798382i	$-0.294310\pi$
$967$	22.5276	+	6.03626i	0.724440	+	0.194113i	0.122288	+	0.992495i	$0.460977\pi$
$968$	−0.459536	+	0.123132i	−0.0147700	+	0.00395762i
$969$	−4.11640	−	13.1958i	−0.132238	−	0.423910i
$970$	0.512532	−	0.137333i	0.0164564	−	0.00440948i
$971$	14.4605	−	8.34875i	0.464058	−	0.267924i	−0.249691	−	0.968326i	$-0.580329\pi$
$971$	14.4605	−	8.34875i	0.464058	−	0.267924i	0.713749	+	0.700401i	$0.246996\pi$
$972$	−29.5169	−	9.80416i	−0.946756	−	0.314469i
$973$	55.0884	−	14.7609i	1.76605	−	0.473212i
$974$	1.02365	−	1.77301i	0.0327999	−	0.0568110i
$975$	−7.59583	−	10.8456i	−0.243261	−	0.347338i
$976$	−10.9252	−	18.9229i	−0.349706	−	0.605708i
$977$	−27.2678	−	27.2678i	−0.872376	−	0.872376i	0.120355	−	0.992731i	$-0.461597\pi$
$977$	−27.2678	−	27.2678i	−0.872376	−	0.872376i	−0.992731	+	0.120355i	$0.961597\pi$
$978$	−0.390513	−	0.204805i	−0.0124872	−	0.00654894i
$979$			39.7839i			1.27150i
$980$	−3.11652	−	3.11652i	−0.0995536	−	0.0995536i
$981$	15.0614	−	17.7286i	0.480873	−	0.566031i
$982$	−0.425860	+	1.58933i	−0.0135897	+	0.0507176i
$983$	−14.6373	−	54.6271i	−0.466857	−	1.74234i	−0.650657	−	0.759372i	$-0.725506\pi$
$983$	−14.6373	−	54.6271i	−0.466857	−	1.74234i	0.183800	−	0.982964i	$-0.441160\pi$
$984$	2.83808	−	0.115238i	0.0904746	−	0.00367366i
$985$		−	52.2825i		−	1.66586i
$986$	0.575427	−	0.575427i	0.0183253	−	0.0183253i
$987$	22.9325	−	43.7266i	0.729949	−	1.39183i
$988$	11.5082	+	36.1020i	0.366124	+	1.14856i
$989$			8.95972i			0.284902i
$990$	−1.28314	−	1.09009i	−0.0407808	−	0.0346455i
$991$	−0.778818	+	1.34895i	−0.0247400	+	0.0428509i	−0.878130	−	0.478422i	$-0.841209\pi$
$991$	−0.778818	+	1.34895i	−0.0247400	+	0.0428509i	0.853390	+	0.521272i	$0.174542\pi$
$992$	5.98101			0.189897
$993$	−13.2892	+	14.4141i	−0.421719	+	0.457416i
$994$	0.145805	+	0.544151i	0.00462465	+	0.0172594i
$995$	14.9151	+	55.6639i	0.472841	+	1.76466i
$996$	10.5958	+	2.38298i	0.335742	+	0.0755077i
$997$	−4.19686			−0.132916			−0.0664580	−	0.997789i	$-0.521170\pi$
$997$	−4.19686			−0.132916			−0.0664580	+	0.997789i	$0.521170\pi$
$998$	0.550231	−	0.953029i	0.0174173	−	0.0301676i
$999$	−8.66091	+	3.49493i	−0.274019	+	0.110575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.bc.a.110.7	yes	48
3.2	odd	2		351.2.bf.a.305.6		48
9.4	even	3		351.2.ba.a.71.7		48
9.5	odd	6		117.2.x.a.32.6	yes	48
13.11	odd	12		117.2.x.a.11.6	✓	48
39.11	even	12		351.2.ba.a.89.7		48
117.50	even	12	inner	117.2.bc.a.50.7	yes	48
117.76	odd	12		351.2.bf.a.206.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.6	✓	48	13.11	odd	12
117.2.x.a.32.6	yes	48	9.5	odd	6
117.2.bc.a.50.7	yes	48	117.50	even	12	inner
117.2.bc.a.110.7	yes	48	1.1	even	1	trivial
351.2.ba.a.71.7		48	9.4	even	3
351.2.ba.a.89.7		48	39.11	even	12
351.2.bf.a.206.6		48	117.76	odd	12
351.2.bf.a.305.6		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0178736 - 0.0667051i) q^{2} +(-1.73062 + 0.0702708i) q^{3} +(1.72792 + 0.997615i) q^{4} +(0.690628 - 2.57746i) q^{5} +(-0.0262450 + 0.116698i) q^{6} +(1.75672 + 1.75672i) q^{7} +(0.195093 - 0.195093i) q^{8} +(2.99012 - 0.243225i) q^{9} +O(q^{10})\)	\(q+(0.0178736 - 0.0667051i) q^{2} +(-1.73062 + 0.0702708i) q^{3} +(1.72792 + 0.997615i) q^{4} +(0.690628 - 2.57746i) q^{5} +(-0.0262450 + 0.116698i) q^{6} +(1.75672 + 1.75672i) q^{7} +(0.195093 - 0.195093i) q^{8} +(2.99012 - 0.243225i) q^{9} +(-0.159586 - 0.0921368i) q^{10} +(2.94182 + 0.788259i) q^{11} +(-3.06049 - 1.60508i) q^{12} +(-3.20340 - 1.65477i) q^{13} +(0.148582 - 0.0857836i) q^{14} +(-1.01410 + 4.50914i) q^{15} +(1.98570 + 3.43934i) q^{16} +(-0.757582 - 1.31217i) q^{17} +(0.0372199 - 0.203804i) q^{18} +(-5.08773 - 1.36325i) q^{19} +(3.76466 - 3.76466i) q^{20} +(-3.16368 - 2.91679i) q^{21} +(0.105162 - 0.182146i) q^{22} -6.17236 q^{23} +(-0.323924 + 0.351343i) q^{24} +(-1.83620 - 1.06013i) q^{25} +(-0.167638 + 0.184106i) q^{26} +(-5.15769 + 0.631049i) q^{27} +(1.28295 + 4.78802i) q^{28} +(-6.73536 + 3.88866i) q^{29} +(0.282657 + 0.148240i) q^{30} +(6.99365 + 1.87394i) q^{31} +(0.797918 - 0.213802i) q^{32} +(-5.14658 - 1.15746i) q^{33} +(-0.101069 + 0.0270814i) q^{34} +(5.74113 - 3.31464i) q^{35} +(5.40934 + 2.56272i) q^{36} +(1.73614 - 0.465197i) q^{37} +(-0.181872 + 0.315012i) q^{38} +(5.66016 + 2.63867i) q^{39} +(-0.368108 - 0.637582i) q^{40} +(-4.20290 - 4.20290i) q^{41} +(-0.251111 + 0.158900i) q^{42} -1.45159i q^{43} +(4.29686 + 4.29686i) q^{44} +(1.43816 - 7.87490i) q^{45} +(-0.110322 + 0.411728i) q^{46} +(2.96979 + 11.0834i) q^{47} +(-3.67819 - 5.81267i) q^{48} -0.827835i q^{49} +(-0.103535 + 0.103535i) q^{50} +(1.40330 + 2.21764i) q^{51} +(-3.88440 - 6.05506i) q^{52} -9.11286i q^{53} +(-0.0500922 + 0.355324i) q^{54} +(4.06341 - 7.03803i) q^{55} +0.685450 q^{56} +(8.90076 + 2.00176i) q^{57} +(0.139009 + 0.518788i) q^{58} +(-0.222038 - 0.828658i) q^{59} +(-6.25067 + 6.77976i) q^{60} -5.50190 q^{61} +(0.250003 - 0.433018i) q^{62} +(5.68010 + 4.82555i) q^{63} +7.88577i q^{64} +(-6.47744 + 7.11379i) q^{65} +(-0.169196 + 0.322616i) q^{66} +(-3.08710 + 3.08710i) q^{67} -3.02310i q^{68} +(10.6820 - 0.433736i) q^{69} +(-0.118489 - 0.442207i) q^{70} +(-0.849841 + 3.17165i) q^{71} +(0.535902 - 0.630805i) q^{72} +(0.551749 + 0.551749i) q^{73} -0.124124i q^{74} +(3.25226 + 1.70565i) q^{75} +(-7.43120 - 7.43120i) q^{76} +(3.78322 + 6.55273i) q^{77} +(0.277180 - 0.330399i) q^{78} +(6.40258 - 11.0896i) q^{79} +(10.2361 - 2.74277i) q^{80} +(8.88168 - 1.45454i) q^{81} +(-0.355476 + 0.205234i) q^{82} +(-3.03557 + 0.813378i) q^{83} +(-2.55675 - 8.19611i) q^{84} +(-3.90527 + 1.04641i) q^{85} +(-0.0968284 - 0.0259451i) q^{86} +(11.3831 - 7.20312i) q^{87} +(0.727714 - 0.420146i) q^{88} +(3.38089 + 12.6176i) q^{89} +(-0.499591 - 0.236685i) q^{90} +(-2.72052 - 8.53446i) q^{91} +(-10.6653 - 6.15764i) q^{92} +(-12.2351 - 2.75164i) q^{93} +0.792402 q^{94} +(-7.02746 + 12.1719i) q^{95} +(-1.36587 + 0.426081i) q^{96} +(-2.03610 + 2.03610i) q^{97} +(-0.0552209 - 0.0147964i) q^{98} +(8.98814 + 1.64147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21} + 2 q^{22} - 12 q^{23} - 18 q^{24} + 48 q^{26} - 32 q^{27} - 6 q^{29} + 66 q^{30} + 6 q^{31} + 30 q^{32} - 56 q^{33} - 6 q^{34} - 6 q^{35} - 6 q^{36} - 6 q^{37} - 36 q^{38} - 32 q^{39} - 12 q^{40} + 18 q^{41} + 80 q^{42} - 12 q^{44} + 34 q^{45} - 12 q^{46} + 30 q^{47} + 22 q^{48} - 12 q^{50} - 16 q^{52} - 56 q^{54} - 4 q^{55} - 12 q^{56} - 2 q^{57} - 28 q^{58} + 30 q^{59} - 58 q^{60} - 4 q^{61} - 18 q^{62} - 2 q^{63} + 30 q^{65} + 32 q^{66} - 16 q^{67} - 48 q^{69} - 46 q^{70} + 48 q^{71} + 126 q^{72} - 22 q^{73} + 24 q^{75} - 18 q^{76} - 72 q^{77} + 94 q^{78} + 8 q^{79} + 54 q^{80} - 14 q^{81} - 12 q^{82} + 72 q^{83} - 110 q^{84} + 78 q^{85} + 102 q^{86} + 14 q^{87} - 6 q^{88} + 114 q^{90} - 16 q^{91} + 120 q^{92} - 44 q^{93} - 52 q^{94} - 6 q^{95} + 16 q^{96} + 48 q^{97} - 36 q^{98} - 32 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9 - 12 * q^10 + 6 * q^11 - 18 * q^12 - 2 * q^13 - 12 * q^14 + 4 * q^15 + 14 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^20 + 22 * q^21 + 2 * q^22 - 12 * q^23 - 18 * q^24 + 48 * q^26 - 32 * q^27 - 6 * q^29 + 66 * q^30 + 6 * q^31 + 30 * q^32 - 56 * q^33 - 6 * q^34 - 6 * q^35 - 6 * q^36 - 6 * q^37 - 36 * q^38 - 32 * q^39 - 12 * q^40 + 18 * q^41 + 80 * q^42 - 12 * q^44 + 34 * q^45 - 12 * q^46 + 30 * q^47 + 22 * q^48 - 12 * q^50 - 16 * q^52 - 56 * q^54 - 4 * q^55 - 12 * q^56 - 2 * q^57 - 28 * q^58 + 30 * q^59 - 58 * q^60 - 4 * q^61 - 18 * q^62 - 2 * q^63 + 30 * q^65 + 32 * q^66 - 16 * q^67 - 48 * q^69 - 46 * q^70 + 48 * q^71 + 126 * q^72 - 22 * q^73 + 24 * q^75 - 18 * q^76 - 72 * q^77 + 94 * q^78 + 8 * q^79 + 54 * q^80 - 14 * q^81 - 12 * q^82 + 72 * q^83 - 110 * q^84 + 78 * q^85 + 102 * q^86 + 14 * q^87 - 6 * q^88 + 114 * q^90 - 16 * q^91 + 120 * q^92 - 44 * q^93 - 52 * q^94 - 6 * q^95 + 16 * q^96 + 48 * q^97 - 36 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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