LMFDB - Embedded newform 792.2.br.b.685.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [792,2,Mod(37,792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(792, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 0, 2]))

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

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

chi := DirichletCharacter("792.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.br (of order $10$, 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:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			685.4
Character	$\chi$	$=$	792.685
Dual form			792.2.br.b.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.210425 - 1.39847i) q^{2} +(-1.91144 + 0.588548i) q^{4} +(0.117836 - 0.162187i) q^{5} +(-0.725001 + 2.23132i) q^{7} +(1.22528 + 2.54925i) q^{8} +O(q^{10})$	\(q+(-0.210425 - 1.39847i) q^{2} +(-1.91144 + 0.588548i) q^{4} +(0.117836 - 0.162187i) q^{5} +(-0.725001 + 2.23132i) q^{7} +(1.22528 + 2.54925i) q^{8} +(-0.251609 - 0.130662i) q^{10} +(-1.47592 - 2.97013i) q^{11} +(0.959026 + 1.31999i) q^{13} +(3.27300 + 0.544366i) q^{14} +(3.30722 - 2.24995i) q^{16} +(-2.69920 - 1.96108i) q^{17} +(4.68224 - 1.52135i) q^{19} +(-0.129781 + 0.379363i) q^{20} +(-3.84307 + 2.68902i) q^{22} +9.25109 q^{23} +(1.53267 + 4.71706i) q^{25} +(1.64416 - 1.61893i) q^{26} +(0.0725573 - 4.69175i) q^{28} +(5.88863 + 1.91333i) q^{29} +(6.68182 - 4.85463i) q^{31} +(-3.84241 - 4.15161i) q^{32} +(-2.17453 + 4.18741i) q^{34} +(0.276461 + 0.380516i) q^{35} +(1.21740 + 0.395559i) q^{37} +(-3.11283 - 6.22784i) q^{38} +(0.557837 + 0.101668i) q^{40} +(1.86354 + 5.73540i) q^{41} -2.47184i q^{43} +(4.56919 + 4.80859i) q^{44} +(-1.94666 - 12.9374i) q^{46} +(-1.47060 - 4.52605i) q^{47} +(1.20994 + 0.879070i) q^{49} +(6.27416 - 3.13598i) q^{50} +(-2.61000 - 1.95864i) q^{52} +(-5.14997 - 7.08833i) q^{53} +(-0.655632 - 0.110613i) q^{55} +(-6.57654 + 0.885793i) q^{56} +(1.43662 - 8.63770i) q^{58} +(-1.81173 - 0.588668i) q^{59} +(-3.75888 + 5.17366i) q^{61} +(-8.19508 - 8.32280i) q^{62} +(-4.99736 + 6.24711i) q^{64} +0.327092 q^{65} +8.27349i q^{67} +(6.31354 + 2.15989i) q^{68} +(0.473966 - 0.466692i) q^{70} +(-1.00994 - 0.733765i) q^{71} +(2.13073 - 6.55770i) q^{73} +(0.297005 - 1.78574i) q^{74} +(-8.05444 + 5.66370i) q^{76} +(7.69737 - 1.13990i) q^{77} +(11.8293 - 8.59451i) q^{79} +(0.0247966 - 0.801513i) q^{80} +(7.62865 - 3.81298i) q^{82} +(-5.50905 + 7.58255i) q^{83} +(-0.636123 + 0.206689i) q^{85} +(-3.45680 + 0.520139i) q^{86} +(5.76319 - 7.40173i) q^{88} -5.11129 q^{89} +(-3.64061 + 1.18291i) q^{91} +(-17.6829 + 5.44471i) q^{92} +(-6.02010 + 3.00899i) q^{94} +(0.304992 - 0.938668i) q^{95} +(-0.242496 + 0.176183i) q^{97} +(0.974753 - 1.87704i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - q^{4} - 10 q^{7} + 5 q^{8}+O(q^{10}) $ 40 * q + 5 * q^2 - q^4 - 10 * q^7 + 5 * q^8	$ 40 q + 5 q^{2} - q^{4} - 10 q^{7} + 5 q^{8} - 20 q^{10} - 2 q^{14} + 15 q^{16} + 6 q^{17} - 8 q^{20} - 35 q^{22} + 8 q^{23} - 4 q^{25} + 10 q^{26} + 32 q^{28} - 6 q^{31} - 20 q^{32} + 10 q^{34} - 12 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 18 q^{46} + 6 q^{47} - 4 q^{49} - 61 q^{50} + 20 q^{52} - 2 q^{55} + 32 q^{56} + 4 q^{58} - 48 q^{62} - 49 q^{64} + 36 q^{65} + 42 q^{68} - 8 q^{70} - 22 q^{71} - 6 q^{73} - 54 q^{74} - 134 q^{76} + 74 q^{79} + 44 q^{80} - 31 q^{82} + 15 q^{86} - 73 q^{88} + 16 q^{89} + 4 q^{92} - 100 q^{94} - 66 q^{95} + 10 q^{97} + 144 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 - q^4 - 10 * q^7 + 5 * q^8 - 20 * q^10 - 2 * q^14 + 15 * q^16 + 6 * q^17 - 8 * q^20 - 35 * q^22 + 8 * q^23 - 4 * q^25 + 10 * q^26 + 32 * q^28 - 6 * q^31 - 20 * q^32 + 10 * q^34 - 12 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 18 * q^46 + 6 * q^47 - 4 * q^49 - 61 * q^50 + 20 * q^52 - 2 * q^55 + 32 * q^56 + 4 * q^58 - 48 * q^62 - 49 * q^64 + 36 * q^65 + 42 * q^68 - 8 * q^70 - 22 * q^71 - 6 * q^73 - 54 * q^74 - 134 * q^76 + 74 * q^79 + 44 * q^80 - 31 * q^82 + 15 * q^86 - 73 * q^88 + 16 * q^89 + 4 * q^92 - 100 * q^94 - 66 * q^95 + 10 * q^97 + 144 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.210425	−	1.39847i	−0.148793	−	0.988868i
$2$	−0.210425	−	1.39847i	−0.148793	−	0.988868i
$3$		0			0
$3$		0			0
$4$	−1.91144	+	0.588548i	−0.955721	+	0.294274i
$5$	0.117836	−	0.162187i	0.0526977	−	0.0725322i	−0.781855	−	0.623460i	$-0.785726\pi$
$5$	0.117836	−	0.162187i	0.0526977	−	0.0725322i	0.834553	+	0.550928i	$0.185726\pi$
$6$		0			0
$7$	−0.725001	+	2.23132i	−0.274025	+	0.843361i	0.715451	+	0.698663i	$0.246221\pi$
$7$	−0.725001	+	2.23132i	−0.274025	+	0.843361i	−0.989476	+	0.144699i	$0.953779\pi$
$8$	1.22528	+	2.54925i	0.433203	+	0.901296i
$9$		0			0
$10$	−0.251609	−	0.130662i	−0.0795659	−	0.0413188i
$11$	−1.47592	−	2.97013i	−0.445005	−	0.895528i
$11$	−1.47592	−	2.97013i	−0.445005	−	0.895528i
$12$		0			0
$13$	0.959026	+	1.31999i	0.265986	+	0.366098i	0.921029	−	0.389493i	$-0.127350\pi$
$13$	0.959026	+	1.31999i	0.265986	+	0.366098i	−0.655044	+	0.755591i	$0.727350\pi$
$14$	3.27300	+	0.544366i	0.874746	+	0.145488i
$15$		0			0
$16$	3.30722	−	2.24995i	0.826806	−	0.562487i
$17$	−2.69920	−	1.96108i	−0.654651	−	0.475632i	0.210201	−	0.977658i	$-0.432588\pi$
$17$	−2.69920	−	1.96108i	−0.654651	−	0.475632i	−0.864852	+	0.502026i	$0.832588\pi$
$18$		0			0
$19$	4.68224	−	1.52135i	1.07418	−	0.349022i	0.282065	−	0.959395i	$-0.408981\pi$
$19$	4.68224	−	1.52135i	1.07418	−	0.349022i	0.792114	+	0.610373i	$0.208981\pi$
$20$	−0.129781	+	0.379363i	−0.0290200	+	0.0848281i
$21$		0			0
$22$	−3.84307	+	2.68902i	−0.819345	+	0.573300i
$23$	9.25109			1.92899			0.964493	−	0.264108i	$-0.0850776\pi$
$23$	9.25109			1.92899			0.964493	+	0.264108i	$0.0850776\pi$
$24$		0			0
$25$	1.53267	+	4.71706i	0.306533	+	0.943412i
$26$	1.64416	−	1.61893i	0.322446	−	0.317498i
$27$		0			0
$28$	0.0725573	−	4.69175i	0.0137120	−	0.886657i
$29$	5.88863	+	1.91333i	1.09349	+	0.355297i	0.799595	−	0.600540i	$-0.205048\pi$
$29$	5.88863	+	1.91333i	1.09349	+	0.355297i	0.293897	+	0.955837i	$0.405048\pi$
$30$		0			0
$31$	6.68182	−	4.85463i	1.20009	−	0.871917i	0.205797	−	0.978595i	$-0.434021\pi$
$31$	6.68182	−	4.85463i	1.20009	−	0.871917i	0.994294	+	0.106678i	$0.0340214\pi$
$32$	−3.84241	−	4.15161i	−0.679249	−	0.733908i
$33$		0			0
$34$	−2.17453	+	4.18741i	−0.372930	+	0.718134i
$35$	0.276461	+	0.380516i	0.0467304	+	0.0643189i
$36$		0			0
$37$	1.21740	+	0.395559i	0.200140	+	0.0650295i	0.407372	−	0.913262i	$-0.366445\pi$
$37$	1.21740	+	0.395559i	0.200140	+	0.0650295i	−0.207232	+	0.978292i	$0.566445\pi$
$38$	−3.11283	−	6.22784i	−0.504967	−	1.01029i
$39$		0			0
$40$	0.557837	+	0.101668i	0.0882019	+	0.0160751i
$41$	1.86354	+	5.73540i	0.291037	+	0.895718i	0.984524	+	0.175250i	$0.0560733\pi$
$41$	1.86354	+	5.73540i	0.291037	+	0.895718i	−0.693487	+	0.720469i	$0.743927\pi$
$42$		0			0
$43$		−	2.47184i		−	0.376952i	−0.982078	−	0.188476i	$-0.939645\pi$
$43$		−	2.47184i		−	0.376952i	0.982078	−	0.188476i	$-0.0603549\pi$
$44$	4.56919	+	4.80859i	0.688831	+	0.724922i
$45$		0			0
$46$	−1.94666	−	12.9374i	−0.287020	−	1.90751i
$47$	−1.47060	−	4.52605i	−0.214509	−	0.660192i	−0.999188	−	0.0402894i	$-0.987172\pi$
$47$	−1.47060	−	4.52605i	−0.214509	−	0.660192i	0.784679	−	0.619903i	$-0.212828\pi$
$48$		0			0
$49$	1.20994	+	0.879070i	0.172848	+	0.125581i
$50$	6.27416	−	3.13598i	0.887300	−	0.443494i
$51$		0			0
$52$	−2.61000	−	1.95864i	−0.361942	−	0.271615i
$53$	−5.14997	−	7.08833i	−0.707403	−	0.973657i	−0.999849	−	0.0173746i	$-0.994469\pi$
$53$	−5.14997	−	7.08833i	−0.707403	−	0.973657i	0.292446	−	0.956282i	$-0.405531\pi$
$54$		0			0
$55$	−0.655632	−	0.110613i	−0.0884054	−	0.0149151i
$56$	−6.57654	+	0.885793i	−0.878827	+	0.118369i
$57$		0			0
$58$	1.43662	−	8.63770i	0.188638	−	1.13418i
$59$	−1.81173	−	0.588668i	−0.235868	−	0.0766381i	0.188698	−	0.982035i	$-0.439573\pi$
$59$	−1.81173	−	0.588668i	−0.235868	−	0.0766381i	−0.424566	+	0.905397i	$0.639573\pi$
$60$		0			0
$61$	−3.75888	+	5.17366i	−0.481276	+	0.662419i	−0.978749	−	0.205060i	$-0.934261\pi$
$61$	−3.75888	+	5.17366i	−0.481276	+	0.662419i	0.497474	+	0.867479i	$0.334261\pi$
$62$	−8.19508	−	8.32280i	−1.04078	−	1.05700i
$63$		0			0
$64$	−4.99736	+	6.24711i	−0.624671	+	0.780888i
$65$	0.327092			0.0405708
$66$		0			0
$67$			8.27349i			1.01077i	0.862895	+	0.505384i	$0.168649\pi$
$67$			8.27349i			1.01077i	−0.862895	+	0.505384i	$0.831351\pi$
$68$	6.31354	+	2.15989i	0.765630	+	0.261925i
$69$		0			0
$70$	0.473966	−	0.466692i	0.0566497	−	0.0557804i
$71$	−1.00994	−	0.733765i	−0.119858	−	0.0870819i	0.526241	−	0.850335i	$-0.323601\pi$
$71$	−1.00994	−	0.733765i	−0.119858	−	0.0870819i	−0.646099	+	0.763253i	$0.723601\pi$
$72$		0			0
$73$	2.13073	−	6.55770i	0.249383	−	0.767521i	−0.745502	−	0.666503i	$-0.767790\pi$
$73$	2.13073	−	6.55770i	0.249383	−	0.767521i	0.994885	−	0.101017i	$-0.0322098\pi$
$74$	0.297005	−	1.78574i	0.0345261	−	0.207588i
$75$		0			0
$76$	−8.05444	+	5.66370i	−0.923908	+	0.649670i
$77$	7.69737	−	1.13990i	0.877196	−	0.129904i
$78$		0			0
$79$	11.8293	−	8.59451i	1.33090	−	0.966958i	0.331177	−	0.943569i	$-0.392554\pi$
$79$	11.8293	−	8.59451i	1.33090	−	0.966958i	0.999726	−	0.0233897i	$-0.00744585\pi$
$80$	0.0247966	−	0.801513i	0.00277234	−	0.0896119i
$81$		0			0
$82$	7.62865	−	3.81298i	0.842443	−	0.421074i
$83$	−5.50905	+	7.58255i	−0.604697	+	0.832293i	−0.996128	−	0.0879138i	$-0.971980\pi$
$83$	−5.50905	+	7.58255i	−0.604697	+	0.832293i	0.391432	+	0.920207i	$0.371980\pi$
$84$		0			0
$85$	−0.636123	+	0.206689i	−0.0689973	+	0.0224186i
$86$	−3.45680	+	0.520139i	−0.372756	+	0.0560880i
$87$		0			0
$88$	5.76319	−	7.40173i	0.614358	−	0.789027i
$89$	−5.11129			−0.541795			−0.270898	−	0.962608i	$-0.587320\pi$
$89$	−5.11129			−0.541795			−0.270898	+	0.962608i	$0.587320\pi$
$90$		0			0
$91$	−3.64061	+	1.18291i	−0.381640	+	0.124002i
$92$	−17.6829	+	5.44471i	−1.84357	+	0.567650i
$93$		0			0
$94$	−6.02010	+	3.00899i	−0.620926	+	0.310354i
$95$	0.304992	−	0.938668i	0.0312915	−	0.0963053i
$96$		0			0
$97$	−0.242496	+	0.176183i	−0.0246217	+	0.0178887i	−0.600028	−	0.799979i	$-0.704844\pi$
$97$	−0.242496	+	0.176183i	−0.0246217	+	0.0178887i	0.575406	+	0.817868i	$0.304844\pi$
$98$	0.974753	−	1.87704i	0.0984649	−	0.189610i
$99$		0			0
$100$	−5.70582	−	8.11434i	−0.570582	−	0.811434i
$101$	8.82844	+	12.1513i	0.878462	+	1.20910i	0.976844	+	0.213951i	$0.0686332\pi$
$101$	8.82844	+	12.1513i	0.878462	+	1.20910i	−0.0983822	+	0.995149i	$0.531367\pi$
$102$		0			0
$103$	0.872910	−	2.68654i	0.0860104	−	0.264713i	−0.898796	−	0.438366i	$-0.855557\pi$
$103$	0.872910	−	2.68654i	0.0860104	−	0.264713i	0.984807	+	0.173653i	$0.0555573\pi$
$104$	−2.18990	+	4.06215i	−0.214737	+	0.398327i
$105$		0			0
$106$	−8.82914	+	8.69365i	−0.857561	+	0.844402i
$107$	−0.849631	+	0.276062i	−0.0821369	+	0.0266879i	−0.349797	−	0.936825i	$-0.613750\pi$
$107$	−0.849631	+	0.276062i	−0.0821369	+	0.0266879i	0.267660	+	0.963513i	$0.413750\pi$
$108$		0			0
$109$			1.35318i			0.129611i	0.997898	+	0.0648057i	$0.0206428\pi$
$109$			1.35318i			0.129611i	−0.997898	+	0.0648057i	$0.979357\pi$
$110$	−0.0167276	+	0.940158i	−0.00159492	+	0.0896406i
$111$		0			0
$112$	2.62263	+	9.01071i	0.247815	+	0.851432i
$113$	1.16461	+	3.58429i	0.109557	+	0.337182i	0.990773	−	0.135532i	$-0.0432744\pi$
$113$	1.16461	+	3.58429i	0.109557	+	0.337182i	−0.881216	+	0.472714i	$0.843274\pi$
$114$		0			0
$115$	1.09011	−	1.50041i	0.101653	−	0.139914i
$116$	−12.3819	−	0.191484i	−1.14963	−	0.0177789i
$117$		0			0
$118$	−0.442000	+	2.65753i	−0.0406894	+	0.244645i
$119$	6.33273	−	4.60099i	0.580520	−	0.421772i
$120$		0			0
$121$	−6.64335	+	8.76732i	−0.603940	+	0.797029i
$122$	8.02618	+	4.16802i	0.726656	+	0.377355i
$123$		0			0
$124$	−9.91474	+	13.2119i	−0.890370	+	1.18646i
$125$	1.89896	+	0.617009i	0.169848	+	0.0551870i
$126$		0			0
$127$	−5.94849	−	4.32183i	−0.527843	−	0.383500i	0.291707	−	0.956508i	$-0.405777\pi$
$127$	−5.94849	−	4.32183i	−0.527843	−	0.383500i	−0.819550	+	0.573007i	$0.805777\pi$
$128$	9.78797	+	5.67412i	0.865143	+	0.501526i
$129$		0			0
$130$	−0.0688285	−	0.457429i	−0.00603666	−	0.0401192i
$131$		−	6.85311i		−	0.598759i	−0.954134	−	0.299380i	$-0.903220\pi$
$131$		−	6.85311i		−	0.598759i	0.954134	−	0.299380i	$-0.0967797\pi$
$132$		0			0
$133$			11.5506i			1.00156i
$134$	11.5702	−	1.74095i	0.999516	−	0.150395i
$135$		0			0
$136$	1.69201	−	9.28380i	0.145089	−	0.796080i
$137$	2.26770	+	1.64758i	0.193743	+	0.140762i	0.680428	−	0.732815i	$-0.261794\pi$
$137$	2.26770	+	1.64758i	0.193743	+	0.140762i	−0.486685	+	0.873578i	$0.661794\pi$
$138$		0			0
$139$	−8.46925	−	2.75183i	−0.718352	−	0.233407i	−0.0730436	−	0.997329i	$-0.523271\pi$
$139$	−8.46925	−	2.75183i	−0.718352	−	0.233407i	−0.645309	+	0.763922i	$0.723271\pi$
$140$	−0.752390	−	0.564623i	−0.0635886	−	0.0477194i
$141$		0			0
$142$	−0.813632	+	1.56678i	−0.0682785	+	0.131481i
$143$	2.50509	−	4.79662i	0.209486	−	0.401114i
$144$		0			0
$145$	1.00421	−	0.729601i	0.0833950	−	0.0605900i
$146$	−9.61911	−	1.59985i	−0.796083	−	0.132405i
$147$		0			0
$148$	−2.55980	−	0.0395871i	−0.210415	−	0.00325404i
$149$	−7.08039	+	9.74532i	−0.580048	+	0.798368i	−0.993701	−	0.112067i	$-0.964253\pi$
$149$	−7.08039	+	9.74532i	−0.580048	+	0.798368i	0.413653	+	0.910435i	$0.364253\pi$
$150$		0			0
$151$	1.63679	+	5.03752i	0.133200	+	0.409947i	0.995306	−	0.0967811i	$-0.0308547\pi$
$151$	1.63679	+	5.03752i	0.133200	+	0.409947i	−0.862106	+	0.506728i	$0.830855\pi$
$152$	9.61537	+	10.0721i	0.779910	+	0.816957i
$153$		0			0
$154$	−3.21384	−	10.5247i	−0.258978	−	0.848103i
$155$		−	1.65575i		−	0.132993i
$156$		0			0
$157$	3.75714	−	1.22077i	0.299853	−	0.0974281i	−0.155227	−	0.987879i	$-0.549611\pi$
$157$	3.75714	−	1.22077i	0.299853	−	0.0974281i	0.455080	+	0.890451i	$0.349611\pi$
$158$	−14.5084	−	14.7345i	−1.15422	−	1.17221i
$159$		0			0
$160$	−1.12611	+	0.133981i	−0.0890269	+	0.0105922i
$161$	−6.70705	+	20.6422i	−0.528590	+	1.62683i
$162$		0			0
$163$	−9.43913	−	12.9918i	−0.739330	−	1.01760i	−0.998657	−	0.0518106i	$-0.983501\pi$
$163$	−9.43913	−	12.9918i	−0.739330	−	1.01760i	0.259327	−	0.965790i	$-0.416499\pi$
$164$	−6.93761	−	9.86609i	−0.541736	−	0.770413i
$165$		0			0
$166$	11.7632	+	6.10868i	0.913003	+	0.474126i
$167$	7.50715	−	5.45426i	0.580921	−	0.422064i	−0.258135	−	0.966109i	$-0.583108\pi$
$167$	7.50715	−	5.45426i	0.580921	−	0.422064i	0.839056	+	0.544045i	$0.183108\pi$
$168$		0			0
$169$	3.19459	−	9.83193i	0.245738	−	0.756303i
$170$	0.422905	+	0.846107i	0.0324353	+	0.0648935i
$171$		0			0
$172$	1.45480	+	4.72478i	0.110927	+	0.360261i
$173$	−8.40944	+	2.73239i	−0.639358	+	0.207740i	−0.610716	−	0.791850i	$-0.709118\pi$
$173$	−8.40944	+	2.73239i	−0.639358	+	0.207740i	−0.0286420	+	0.999590i	$0.509118\pi$
$174$		0			0
$175$	−11.6365			−0.879635
$176$	−11.5638	−	6.50215i	−0.871656	−	0.490118i
$177$		0			0
$178$	1.07554	+	7.14798i	0.0806154	+	0.535764i
$179$	10.1324	−	3.29223i	0.757334	−	0.246073i	0.0952002	−	0.995458i	$-0.469651\pi$
$179$	10.1324	−	3.29223i	0.757334	−	0.246073i	0.662134	+	0.749385i	$0.269651\pi$
$180$		0			0
$181$	7.88600	−	10.8542i	0.586162	−	0.806783i	−0.408192	−	0.912896i	$-0.633841\pi$
$181$	7.88600	−	10.8542i	0.586162	−	0.806783i	0.994354	+	0.106113i	$0.0338407\pi$
$182$	2.42034	+	4.84238i	0.179407	+	0.358941i
$183$		0			0
$184$	11.3352	+	23.5834i	0.835642	+	1.73859i
$185$	0.207608	−	0.150836i	0.0152637	−	0.0110897i
$186$		0			0
$187$	−1.84088	+	10.9113i	−0.134618	+	0.797917i
$188$	5.47477	+	7.78576i	0.399289	+	0.567835i
$189$		0			0
$190$	−1.37688	−	0.229002i	−0.0998892	−	0.0166136i
$191$	4.57929	−	14.0936i	0.331346	−	1.01978i	−0.637148	−	0.770741i	$-0.719886\pi$
$191$	4.57929	−	14.0936i	0.331346	−	1.01978i	0.968494	−	0.249036i	$-0.0801139\pi$
$192$		0			0
$193$	3.61949	+	2.62972i	0.260537	+	0.189291i	0.710384	−	0.703815i	$-0.248521\pi$
$193$	3.61949	+	2.62972i	0.260537	+	0.189291i	−0.449847	+	0.893106i	$0.648521\pi$
$194$	0.297415	+	0.302050i	0.0213531	+	0.0216859i
$195$		0			0
$196$	−2.83010	−	0.968187i	−0.202150	−	0.0691562i
$197$			20.3350i			1.44881i	0.689373	+	0.724406i	$0.257886\pi$
$197$			20.3350i			1.44881i	−0.689373	+	0.724406i	$0.742114\pi$
$198$		0			0
$199$	10.4142			0.738245			0.369122	−	0.929381i	$-0.379658\pi$
$199$	10.4142			0.738245			0.369122	+	0.929381i	$0.379658\pi$
$200$	−10.1470	+	9.68688i	−0.717503	+	0.684966i
$201$		0			0
$202$	15.1355	−	14.9033i	1.06493	−	1.04859i
$203$	−8.53853	+	11.7523i	−0.599287	+	0.824848i
$204$		0			0
$205$	1.14980	+	0.373592i	0.0803054	+	0.0260928i
$206$	−3.94073	−	0.655423i	−0.274564	−	0.0456655i
$207$		0			0
$208$	6.14162	+	2.20773i	0.425844	+	0.153078i
$209$	−11.4292	−	11.6615i	−0.790574	−	0.806641i
$210$		0			0
$211$	11.0079	+	15.1511i	0.757817	+	1.04305i	0.997393	+	0.0721675i	$0.0229916\pi$
$211$	11.0079	+	15.1511i	0.757817	+	1.04305i	−0.239576	+	0.970878i	$0.577008\pi$
$212$	14.0157	+	10.5179i	0.962602	+	0.722374i
$213$		0			0
$214$	0.564848	+	1.13009i	0.0386122	+	0.0772516i
$215$	−0.400901	−	0.291271i	−0.0273412	−	0.0198645i
$216$		0			0
$217$	5.98792	+	18.4289i	0.406486	+	1.25104i
$218$	1.89239	−	0.284744i	0.128169	−	0.0192853i
$219$		0			0
$220$	1.31830	−	0.174440i	0.0888800	−	0.0117607i
$221$		−	5.44363i		−	0.366178i
$222$		0			0
$223$	4.50465	+	13.8639i	0.301654	+	0.928394i	0.980905	+	0.194488i	$0.0623047\pi$
$223$	4.50465	+	13.8639i	0.301654	+	0.928394i	−0.679251	+	0.733906i	$0.737695\pi$
$224$	12.0493	−	5.56375i	0.805081	−	0.371744i
$225$		0			0
$226$	4.76747	−	2.38290i	0.317127	−	0.158508i
$227$	−3.97727	−	1.29229i	−0.263981	−	0.0857725i	0.174036	−	0.984739i	$-0.444319\pi$
$227$	−3.97727	−	1.29229i	−0.263981	−	0.0857725i	−0.438017	+	0.898967i	$0.644319\pi$
$228$		0			0
$229$	13.6608	+	18.8025i	0.902733	+	1.24251i	0.969588	+	0.244743i	$0.0787037\pi$
$229$	13.6608	+	18.8025i	0.902733	+	1.24251i	−0.0668544	+	0.997763i	$0.521296\pi$
$230$	−2.32766	−	1.20876i	−0.153481	−	0.0797034i
$231$		0			0
$232$	2.33767	+	17.3560i	0.153476	+	1.13948i
$233$	−11.3120	+	8.21868i	−0.741077	+	0.538424i	−0.893048	−	0.449961i	$-0.851438\pi$
$233$	−11.3120	+	8.21868i	−0.741077	+	0.538424i	0.151971	+	0.988385i	$0.451438\pi$
$234$		0			0
$235$	−0.907356	−	0.294818i	−0.0591894	−	0.0192318i
$236$	3.80948	+	0.0589133i	0.247976	+	0.00383493i
$237$		0			0
$238$	−7.76692	−	7.88797i	−0.503455	−	0.511301i
$239$	7.39672	+	22.7648i	0.478454	+	1.47253i	0.841242	+	0.540659i	$0.181825\pi$
$239$	7.39672	+	22.7648i	0.478454	+	1.47253i	−0.362788	+	0.931872i	$0.618175\pi$
$240$		0			0
$241$	−26.1842			−1.68667			−0.843336	−	0.537387i	$-0.819412\pi$
$241$	−26.1842			−1.68667			−0.843336	+	0.537387i	$0.819412\pi$
$242$	13.6588	+	7.44566i	0.878019	+	0.478625i
$243$		0			0
$244$	4.13994	−	12.1014i	0.265033	−	0.774715i
$245$	0.285148	−	0.0926500i	0.0182174	−	0.00591919i
$246$		0			0
$247$	6.49855	+	4.72147i	0.413493	+	0.300420i
$248$	20.5628	+	11.0853i	1.30574	+	0.703920i
$249$		0			0
$250$	0.463280	−	2.78547i	0.0293004	−	0.176169i
$251$	−11.3303	−	15.5948i	−0.715161	−	0.984335i	−0.999671	−	0.0256619i	$-0.991831\pi$
$251$	−11.3303	−	15.5948i	−0.715161	−	0.984335i	0.284509	−	0.958673i	$-0.408169\pi$
$252$		0			0
$253$	−13.6538	−	27.4769i	−0.858409	−	1.72746i
$254$	−4.79224	+	9.22821i	−0.300692	+	0.579029i
$255$		0			0
$256$	5.87545	−	14.8822i	0.367216	−	0.930136i
$257$	−2.27691	+	7.00760i	−0.142030	+	0.437122i	−0.996617	−	0.0821853i	$-0.973810\pi$
$257$	−2.27691	+	7.00760i	−0.142030	+	0.437122i	0.854587	+	0.519308i	$0.173810\pi$
$258$		0			0
$259$	−1.76524	+	2.42964i	−0.109687	+	0.150971i
$260$	−0.625218	+	0.192509i	−0.0387744	+	0.0119389i
$261$		0			0
$262$	−9.58388	+	1.44207i	−0.592094	+	0.0890913i
$263$	−2.69244			−0.166023			−0.0830114	−	0.996549i	$-0.526454\pi$
$263$	−2.69244			−0.166023			−0.0830114	+	0.996549i	$0.526454\pi$
$264$		0			0
$265$	−1.75649			−0.107900
$266$	16.1531	−	2.43053i	0.990413	−	0.149026i
$267$		0			0
$268$	−4.86934	−	15.8143i	−0.297442	−	0.966012i
$269$	9.14422	−	12.5859i	0.557533	−	0.767378i	−0.433477	−	0.901164i	$-0.642714\pi$
$269$	9.14422	−	12.5859i	0.557533	−	0.767378i	0.991010	+	0.133786i	$0.0427136\pi$
$270$		0			0
$271$	−0.288637	+	0.888332i	−0.0175334	+	0.0539623i	−0.959440	−	0.281911i	$-0.909032\pi$
$271$	−0.288637	+	0.888332i	−0.0175334	+	0.0539623i	0.941907	+	0.335874i	$0.109032\pi$
$272$	−13.3392	−	0.412676i	−0.808806	−	0.0250222i
$273$		0			0
$274$	1.82691	−	3.51800i	0.110368	−	0.212530i
$275$	11.7482	−	11.5142i	0.708443	−	0.694332i
$276$		0			0
$277$	−7.97055	−	10.9705i	−0.478904	−	0.659155i	0.499390	−	0.866377i	$-0.333558\pi$
$277$	−7.97055	−	10.9705i	−0.478904	−	0.659155i	−0.978294	+	0.207223i	$0.933558\pi$
$278$	−2.06620	+	12.4231i	−0.123923	+	0.745085i
$279$		0			0
$280$	−0.631287	+	1.17101i	−0.0377266	+	0.0699811i
$281$	−12.5780	−	9.13844i	−0.750339	−	0.545153i	0.145593	−	0.989345i	$-0.453491\pi$
$281$	−12.5780	−	9.13844i	−0.750339	−	0.545153i	−0.895932	+	0.444191i	$0.853491\pi$
$282$		0			0
$283$	−2.22890	+	0.724213i	−0.132494	+	0.0430500i	−0.374514	−	0.927221i	$-0.622190\pi$
$283$	−2.22890	+	0.724213i	−0.132494	+	0.0430500i	0.242019	+	0.970271i	$0.422190\pi$
$284$	2.36230	+	0.808151i	0.140177	+	0.0479550i
$285$		0			0
$286$	−7.23507	−	2.49396i	−0.427819	−	0.147471i
$287$	−14.1486			−0.835166
$288$		0			0
$289$	−1.81347	−	5.58129i	−0.106675	−	0.328311i
$290$	−1.23164	−	1.25083i	−0.0723242	−	0.0734513i
$291$		0			0
$292$	−0.213241	+	13.7887i	−0.0124790	+	0.806923i
$293$	−17.4944	−	5.68428i	−1.02203	−	0.332079i	−0.250398	−	0.968143i	$-0.580562\pi$
$293$	−17.4944	−	5.68428i	−1.02203	−	0.332079i	−0.771637	+	0.636064i	$0.780562\pi$
$294$		0			0
$295$	−0.308961	+	0.224474i	−0.0179884	+	0.0130694i
$296$	0.483286	+	3.58814i	0.0280905	+	0.208557i
$297$		0			0
$298$	15.1184	+	7.85106i	0.875788	+	0.454800i
$299$	8.87204	+	12.2113i	0.513083	+	0.706198i
$300$		0			0
$301$	5.51548	+	1.79209i	0.317907	+	0.103294i
$302$	6.70040	−	3.34902i	0.385565	−	0.192715i
$303$		0			0
$304$	12.0622	−	15.5663i	0.691817	−	0.892786i
$305$	0.396169	+	1.21928i	0.0226846	+	0.0698160i
$306$		0			0
$307$		−	20.3704i		−	1.16260i	−0.813690	−	0.581299i	$-0.802545\pi$
$307$		−	20.3704i		−	1.16260i	0.813690	−	0.581299i	$-0.197455\pi$
$308$	−14.0422	+	6.70912i	−0.800128	+	0.382287i
$309$		0			0
$310$	−2.31552	+	0.348412i	−0.131513	+	0.0197885i
$311$	−6.70833	−	20.6461i	−0.380395	−	1.17073i	−0.939766	−	0.341818i	$-0.888957\pi$
$311$	−6.70833	−	20.6461i	−0.380395	−	1.17073i	0.559372	−	0.828917i	$-0.311043\pi$
$312$		0			0
$313$	−21.7038	−	15.7687i	−1.22677	−	0.891301i	−0.230127	−	0.973161i	$-0.573914\pi$
$313$	−21.7038	−	15.7687i	−1.22677	−	0.891301i	−0.996644	+	0.0818590i	$0.973914\pi$
$314$	−2.49781	−	4.99738i	−0.140960	−	0.282018i
$315$		0			0
$316$	−17.5528	+	23.3900i	−0.987422	+	1.31579i
$317$	−2.23951	−	3.08242i	−0.125783	−	0.173126i	0.741481	−	0.670974i	$-0.234124\pi$
$317$	−2.23951	−	3.08242i	−0.125783	−	0.173126i	−0.867264	+	0.497848i	$0.834124\pi$
$318$		0			0
$319$	−3.00828	−	20.3139i	−0.168431	−	1.13736i
$320$	0.424331	+	1.54664i	0.0237208	+	0.0864598i
$321$		0			0
$322$	30.2788	+	5.03598i	1.68737	+	0.280644i
$323$	−15.6218	−	5.07582i	−0.869218	−	0.282426i
$324$		0			0
$325$	−4.75659	+	6.54688i	−0.263848	+	0.363156i
$326$	−16.1825	+	15.9342i	−0.896265	+	0.882512i
$327$		0			0
$328$	−12.3376	+	11.7781i	−0.681230	+	0.650338i
$329$	11.1653			0.615562
$330$		0			0
$331$		−	28.2300i		−	1.55166i	−0.630941	−	0.775831i	$-0.717331\pi$
$331$		−	28.2300i		−	1.55166i	0.630941	−	0.775831i	$-0.282669\pi$
$332$	6.06753	−	17.7360i	0.332999	−	0.973387i
$333$		0			0
$334$	−9.20732	−	9.35081i	−0.503802	−	0.511654i
$335$	1.34185	+	0.974912i	0.0733132	+	0.0532652i
$336$		0			0
$337$	−6.34988	+	19.5429i	−0.345900	+	1.06457i	0.615200	+	0.788371i	$0.289075\pi$
$337$	−6.34988	+	19.5429i	−0.345900	+	1.06457i	−0.961100	+	0.276200i	$0.910925\pi$
$338$	−14.4219	−	2.39865i	−0.784448	−	0.130469i
$339$		0			0
$340$	1.09427	−	0.769463i	0.0593449	−	0.0417300i
$341$	−24.2807	−	12.6809i	−1.31487	−	0.686707i
$342$		0			0
$343$	−16.1252	+	11.7157i	−0.870681	+	0.632587i
$344$	6.30135	−	3.02871i	0.339746	−	0.163297i
$345$		0			0
$346$	5.59073	+	11.1854i	0.300560	+	0.601331i
$347$	2.21490	−	3.04855i	0.118902	−	0.163655i	−0.745417	−	0.666598i	$-0.767750\pi$
$347$	2.21490	−	3.04855i	0.118902	−	0.163655i	0.864319	+	0.502944i	$0.167750\pi$
$348$		0			0
$349$	29.9260	−	9.72356i	1.60190	−	0.520490i	0.634326	−	0.773065i	$-0.281278\pi$
$349$	29.9260	−	9.72356i	1.60190	−	0.520490i	0.967577	+	0.252575i	$0.0812776\pi$
$350$	2.44861	+	16.2733i	0.130884	+	0.869843i
$351$		0			0
$352$	−6.65974	+	17.5399i	−0.354965	+	0.934879i
$353$	30.7625			1.63732			0.818662	−	0.574276i	$-0.194716\pi$
$353$	30.7625			1.63732			0.818662	+	0.574276i	$0.194716\pi$
$354$		0			0
$355$	−0.238014	+	0.0773355i	−0.0126325	+	0.00410454i
$356$	9.76993	−	3.00823i	0.517805	−	0.159436i
$357$		0			0
$358$	−6.73621	−	13.4772i	−0.356020	−	0.712290i
$359$	3.84845	−	11.8443i	0.203113	−	0.625118i	−0.796672	−	0.604411i	$-0.793408\pi$
$359$	3.84845	−	11.8443i	0.203113	−	0.625118i	0.999786	−	0.0207068i	$-0.00659164\pi$
$360$		0			0
$361$	4.23752	−	3.07874i	0.223028	−	0.162039i
$362$	−16.8386	−	8.74436i	−0.885019	−	0.459593i
$363$		0			0
$364$	6.26262	−	4.40373i	0.328251	−	0.230818i
$365$	−0.812498	−	1.11831i	−0.0425281	−	0.0585349i
$366$		0			0
$367$	−1.43633	+	4.42056i	−0.0749757	+	0.230752i	−0.981520	−	0.191359i	$-0.938711\pi$
$367$	−1.43633	+	4.42056i	−0.0749757	+	0.230752i	0.906544	+	0.422110i	$0.138711\pi$
$368$	30.5954	−	20.8145i	1.59490	−	1.08503i
$369$		0			0
$370$	−0.254626	−	0.258594i	−0.0132374	−	0.0134437i
$371$	19.5501	−	6.35221i	1.01499	−	0.329790i
$372$		0			0
$373$			18.0242i			0.933256i	0.884454	+	0.466628i	$0.154531\pi$
$373$			18.0242i			0.933256i	−0.884454	+	0.466628i	$0.845469\pi$
$374$	15.6466	+	0.278390i	0.809065	+	0.0143952i
$375$		0			0
$376$	9.73613	−	9.29463i	0.502103	−	0.479334i
$377$	3.12178	+	9.60785i	0.160780	+	0.494829i
$378$		0			0
$379$	−8.17433	+	11.2510i	−0.419887	+	0.577925i	−0.965595	−	0.260050i	$-0.916261\pi$
$379$	−8.17433	+	11.2510i	−0.419887	+	0.577925i	0.545708	+	0.837975i	$0.316261\pi$
$380$	−0.0305232	+	1.97371i	−0.00156581	+	0.101249i
$381$		0			0
$382$	−20.6731	−	3.43835i	−1.05773	−	0.175921i
$383$	−18.2628	+	13.2687i	−0.933184	+	0.677998i	−0.946770	−	0.321910i	$-0.895675\pi$
$383$	−18.2628	+	13.2687i	−0.933184	+	0.677998i	0.0135866	+	0.999908i	$0.495675\pi$
$384$		0			0
$385$	0.722148	−	1.38273i	0.0368041	−	0.0704706i
$386$	2.91595	−	5.61512i	0.148418	−	0.285802i
$387$		0			0
$388$	0.359824	−	0.479485i	0.0182673	−	0.0243421i
$389$	22.3165	+	7.25108i	1.13149	+	0.367644i	0.814143	−	0.580665i	$-0.197207\pi$
$389$	22.3165	+	7.25108i	1.13149	+	0.367644i	0.317349	+	0.948309i	$0.397207\pi$
$390$		0			0
$391$	−24.9705	−	18.1421i	−1.26281	−	0.917487i
$392$	−0.758457	+	4.16154i	−0.0383078	+	0.210190i
$393$		0			0
$394$	28.4380	−	4.27901i	1.43268	−	0.215573i
$395$		−	2.93130i		−	0.147490i
$396$		0			0
$397$		−	29.9901i		−	1.50516i	−0.658500	−	0.752581i	$-0.728809\pi$
$397$		−	29.9901i		−	1.50516i	0.658500	−	0.752581i	$-0.271191\pi$
$398$	−2.19142	−	14.5640i	−0.109846	−	0.730027i
$399$		0			0
$400$	15.6820	+	12.1519i	0.784101	+	0.607597i
$401$	−16.3663	−	11.8908i	−0.817292	−	0.593797i	0.0986435	−	0.995123i	$-0.468550\pi$
$401$	−16.3663	−	11.8908i	−0.817292	−	0.593797i	−0.915936	+	0.401325i	$0.868550\pi$
$402$		0			0
$403$	12.8161	+	4.16420i	0.638414	+	0.207433i
$404$	−24.0267	−	18.0306i	−1.19537	−	0.897054i
$405$		0			0
$406$	18.2319	+	9.46791i	0.904836	+	0.469885i
$407$	−0.621926	−	4.19966i	−0.0308277	−	0.208170i
$408$		0			0
$409$	−3.58977	+	2.60812i	−0.177503	+	0.128963i	−0.672989	−	0.739652i	$-0.734990\pi$
$409$	−3.58977	+	2.60812i	−0.177503	+	0.128963i	0.495486	+	0.868616i	$0.334990\pi$
$410$	0.280511	−	1.68657i	0.0138535	−	0.0832939i
$411$		0			0
$412$	−0.0873599	+	5.64892i	−0.00430391	+	0.278302i
$413$	2.62702	−	3.61578i	0.129267	−	0.177921i
$414$		0			0
$415$	0.580629	+	1.78699i	0.0285019	+	0.0877200i
$416$	1.79509	−	9.05343i	0.0880116	−	0.443881i
$417$		0			0
$418$	−13.9032	+	18.4373i	−0.680029	+	0.901797i
$419$		−	6.01641i		−	0.293921i	−0.989142	−	0.146960i	$-0.953051\pi$
$419$		−	6.01641i		−	0.293921i	0.989142	−	0.146960i	$-0.0469490\pi$
$420$		0			0
$421$	−26.1104	+	8.48380i	−1.27254	+	0.413475i	−0.865949	−	0.500133i	$-0.833284\pi$
$421$	−26.1104	+	8.48380i	−1.27254	+	0.413475i	−0.406596	+	0.913608i	$0.633284\pi$
$422$	18.8720	−	18.5824i	0.918676	−	0.904579i
$423$		0			0
$424$	11.7598	−	21.8138i	0.571104	−	1.05937i
$425$	5.11357	−	15.7379i	0.248044	−	0.763402i
$426$		0			0
$427$	−8.81892	−	12.1382i	−0.426777	−	0.587409i
$428$	1.46154	−	1.02772i	0.0706464	−	0.0496769i
$429$		0			0
$430$	−0.322975	+	0.621939i	−0.0155752	+	0.0299926i
$431$	−20.1455	+	14.6365i	−0.970373	+	0.705017i	−0.955537	−	0.294873i	$-0.904723\pi$
$431$	−20.1455	+	14.6365i	−0.970373	+	0.705017i	−0.0148364	+	0.999890i	$0.504723\pi$
$432$		0			0
$433$	4.18538	−	12.8813i	0.201137	−	0.619035i	−0.798713	−	0.601712i	$-0.794486\pi$
$433$	4.18538	−	12.8813i	0.201137	−	0.619035i	0.999850	−	0.0173233i	$-0.00551447\pi$
$434$	24.5123	−	12.2518i	1.17663	−	0.588107i
$435$		0			0
$436$	−0.796413	−	2.58653i	−0.0381413	−	0.123872i
$437$	43.3158	−	14.0742i	2.07208	−	0.673259i
$438$		0			0
$439$	−30.1967			−1.44121			−0.720606	−	0.693345i	$-0.756136\pi$
$439$	−30.1967			−1.44121			−0.720606	+	0.693345i	$0.756136\pi$
$440$	−0.521354	−	1.80690i	−0.0248546	−	0.0861407i
$441$		0			0
$442$	−7.61275	+	1.14548i	−0.362102	+	0.0544848i
$443$	13.2565	−	4.30729i	0.629835	−	0.204646i	0.0233328	−	0.999728i	$-0.492572\pi$
$443$	13.2565	−	4.30729i	0.629835	−	0.204646i	0.606502	+	0.795082i	$0.292572\pi$
$444$		0			0
$445$	−0.602292	+	0.828984i	−0.0285514	+	0.0392976i
$446$	18.4403	−	9.21693i	0.873176	−	0.436434i
$447$		0			0
$448$	−10.3162	−	15.6799i	−0.487396	−	0.740806i
$449$	5.70957	−	4.14825i	0.269451	−	0.195768i	−0.444852	−	0.895604i	$-0.646744\pi$
$449$	5.70957	−	4.14825i	0.269451	−	0.195768i	0.714303	+	0.699836i	$0.246744\pi$
$450$		0			0
$451$	14.2844	−	13.9999i	0.672628	−	0.659231i
$452$	−4.33561	−	6.16574i	−0.203930	−	0.290012i
$453$		0			0
$454$	−0.970316	+	5.83403i	−0.0455392	+	0.273805i
$455$	−0.237142	+	0.729849i	−0.0111174	+	0.0342158i
$456$		0			0
$457$	−5.07195	−	3.68499i	−0.237256	−	0.172377i	0.462804	−	0.886461i	$-0.346843\pi$
$457$	−5.07195	−	3.68499i	−0.237256	−	0.172377i	−0.700060	+	0.714084i	$0.746843\pi$
$458$	23.4202	−	23.0608i	1.09435	−	1.07756i
$459$		0			0
$460$	−1.20062	+	3.50952i	−0.0559792	+	0.163632i
$461$		−	18.0857i		−	0.842334i	−0.906983	−	0.421167i	$-0.861621\pi$
$461$		−	18.0857i		−	0.842334i	0.906983	−	0.421167i	$-0.138379\pi$
$462$		0			0
$463$	9.95458			0.462628			0.231314	−	0.972879i	$-0.425697\pi$
$463$	9.95458			0.462628			0.231314	+	0.972879i	$0.425697\pi$
$464$	23.7799	−	6.92131i	1.10396	−	0.321314i
$465$		0			0
$466$	13.8739	+	14.0901i	0.642697	+	0.652713i
$467$	−19.1724	+	26.3885i	−0.887191	+	1.22111i	0.0871856	+	0.996192i	$0.472213\pi$
$467$	−19.1724	+	26.3885i	−0.887191	+	1.22111i	−0.974377	+	0.224922i	$0.927787\pi$
$468$		0			0
$469$	−18.4608	−	5.99829i	−0.852442	−	0.276975i
$470$	−0.221363	+	1.33095i	−0.0102107	+	0.0613921i
$471$		0			0
$472$	−0.719224	−	5.33985i	−0.0331050	−	0.245787i
$473$	−7.34169	+	3.64823i	−0.337571	+	0.167746i
$474$		0			0
$475$	14.3526	+	19.7547i	0.658543	+	0.906407i
$476$	−9.39674	+	12.5216i	−0.430699	+	0.573929i
$477$		0			0
$478$	30.2794	−	15.1344i	1.38495	−	0.692231i
$479$	6.88599	+	5.00296i	0.314629	+	0.228591i	0.733880	−	0.679279i	$-0.237707\pi$
$479$	6.88599	+	5.00296i	0.314629	+	0.228591i	−0.419251	+	0.907870i	$0.637707\pi$
$480$		0			0
$481$	0.645391	+	1.98631i	0.0294273	+	0.0905679i
$482$	5.50982	+	36.6178i	0.250965	+	1.66790i
$483$		0			0
$484$	7.53838	−	20.6682i	0.342654	−	0.939462i
$485$			0.0600903i			0.00272856i
$486$		0			0
$487$	2.20485	+	6.78582i	0.0999112	+	0.307495i	0.988502	−	0.151205i	$-0.0483153\pi$
$487$	2.20485	+	6.78582i	0.0999112	+	0.307495i	−0.888591	+	0.458700i	$0.848315\pi$
$488$	−17.7947	−	3.24314i	−0.805526	−	0.146810i
$489$		0			0
$490$	−0.189571	−	0.379275i	−0.00856393	−	0.0171339i
$491$	−11.5079	−	3.73913i	−0.519343	−	0.168745i	0.0376042	−	0.999293i	$-0.488027\pi$
$491$	−11.5079	−	3.73913i	−0.519343	−	0.168745i	−0.556947	+	0.830548i	$0.688027\pi$
$492$		0			0
$493$	−12.1424	−	16.7125i	−0.546865	−	0.752695i
$494$	5.23538	−	10.0816i	0.235551	−	0.453591i
$495$		0			0
$496$	11.1756	−	31.0891i	0.501800	−	1.39594i
$497$	2.36948	−	1.72153i	0.106286	−	0.0772210i
$498$		0			0
$499$	−13.3674	−	4.34332i	−0.598405	−	0.194434i	−0.00587615	−	0.999983i	$-0.501870\pi$
$499$	−13.3674	−	4.34332i	−0.598405	−	0.194434i	−0.592529	+	0.805549i	$0.701870\pi$
$500$	−3.99289	−	0.0617496i	−0.178568	−	0.00276153i
$501$		0			0
$502$	−19.4247	+	19.1266i	−0.866967	+	0.853663i
$503$	8.50938	+	26.1892i	0.379415	+	1.16772i	0.940452	+	0.339928i	$0.110403\pi$
$503$	8.50938	+	26.1892i	0.379415	+	1.16772i	−0.561037	+	0.827791i	$0.689597\pi$
$504$		0			0
$505$	3.01109			0.133992
$506$	−35.5526	+	24.8763i	−1.58051	+	1.10589i
$507$		0			0
$508$	13.9138	+	4.75996i	0.617325	+	0.211189i
$509$	−0.286361	+	0.0930445i	−0.0126927	+	0.00412412i	−0.315356	−	0.948973i	$-0.602124\pi$
$509$	−0.286361	+	0.0930445i	−0.0126927	+	0.00412412i	0.302664	+	0.953097i	$0.402124\pi$
$510$		0			0
$511$	13.0876	+	9.50868i	0.578960	+	0.420639i
$512$	−22.0486	−	5.08506i	−0.974421	−	0.224730i
$513$		0			0
$514$	10.2790	+	1.70961i	0.453389	+	0.0754078i
$515$	−0.332862	−	0.458145i	−0.0146677	−	0.0201883i
$516$		0			0
$517$	−11.2725	+	11.0480i	−0.495763	+	0.485888i
$518$	3.76924	+	1.95738i	0.165611	+	0.0860023i
$519$		0			0
$520$	0.400780	+	0.833840i	0.0175754	+	0.0365663i
$521$	5.15755	−	15.8733i	0.225956	−	0.695422i	−0.772237	−	0.635335i	$-0.780862\pi$
$521$	5.15755	−	15.8733i	0.225956	−	0.695422i	0.998193	−	0.0600874i	$-0.0191379\pi$
$522$		0			0
$523$	−3.37114	+	4.63997i	−0.147409	+	0.202892i	−0.876336	−	0.481700i	$-0.840019\pi$
$523$	−3.37114	+	4.63997i	−0.147409	+	0.202892i	0.728927	+	0.684592i	$0.240019\pi$
$524$	4.03338	+	13.0993i	0.176199	+	0.572247i
$525$		0			0
$526$	0.566557	+	3.76530i	0.0247031	+	0.164175i
$527$	−27.5559			−1.20035
$528$		0			0
$529$	62.5827			2.72099
$530$	0.369609	+	2.45639i	0.0160548	+	0.106699i
$531$		0			0
$532$	−6.79806	−	22.0783i	−0.294733	−	0.957214i
$533$	−5.78346	+	7.96024i	−0.250509	+	0.344796i
$534$		0			0
$535$	−0.0553432	+	0.170329i	−0.00239270	+	0.00736396i
$536$	−21.0912	+	10.1374i	−0.911001	+	0.437867i
$537$		0			0
$538$	−19.5252	−	10.1395i	−0.841793	−	0.437146i
$539$	0.825189	−	4.89110i	0.0355434	−	0.210675i
$540$		0			0
$541$	14.1771	+	19.5131i	0.609522	+	0.838935i	0.996538	−	0.0831377i	$-0.0264941\pi$
$541$	14.1771	+	19.5131i	0.609522	+	0.838935i	−0.387016	+	0.922073i	$0.626494\pi$
$542$	1.30304	+	0.216722i	0.0559705	+	0.00930902i
$543$		0			0
$544$	2.22978	+	18.7413i	0.0956012	+	0.803526i
$545$	0.219469	+	0.159453i	0.00940101	+	0.00683023i
$546$		0			0
$547$	−7.03428	+	2.28558i	−0.300764	+	0.0977241i	−0.455511	−	0.890230i	$-0.650544\pi$
$547$	−7.03428	+	2.28558i	−0.300764	+	0.0977241i	0.154747	+	0.987954i	$0.450544\pi$
$548$	−5.30426	−	1.81461i	−0.226587	−	0.0775161i
$549$		0			0
$550$	−18.5744	−	14.0066i	−0.792015	−	0.597245i
$551$	30.4828			1.29861
$552$		0			0
$553$	10.6009	+	32.6261i	0.450795	+	1.38740i
$554$	−13.6648	+	13.4551i	−0.580560	+	0.571651i
$555$		0			0
$556$	17.8081	+	0.275400i	0.755230	+	0.0116795i
$557$	−10.8601	−	3.52867i	−0.460158	−	0.149514i	0.0697589	−	0.997564i	$-0.477777\pi$
$557$	−10.8601	−	3.52867i	−0.460158	−	0.149514i	−0.529917	+	0.848049i	$0.677777\pi$
$558$		0			0
$559$	3.26280	−	2.37056i	0.138002	−	0.100264i
$560$	1.77046	+	0.636427i	0.0748155	+	0.0268940i
$561$		0			0
$562$	−10.1331	+	19.5129i	−0.427440	+	0.823102i
$563$	5.71080	+	7.86025i	0.240682	+	0.331270i	0.912221	−	0.409699i	$-0.134366\pi$
$563$	5.71080	+	7.86025i	0.240682	+	0.331270i	−0.671539	+	0.740969i	$0.734366\pi$
$564$		0			0
$565$	0.718558	+	0.233474i	0.0302300	+	0.00982231i
$566$	1.48181	+	2.96466i	0.0622850	+	0.124614i
$567$		0			0
$568$	0.633088	−	3.47366i	0.0265638	−	0.145752i
$569$	7.44871	+	22.9248i	0.312266	+	0.961057i	0.976865	+	0.213856i	$0.0686025\pi$
$569$	7.44871	+	22.9248i	0.312266	+	0.961057i	−0.664599	+	0.747200i	$0.731398\pi$
$570$		0			0
$571$		−	12.8180i		−	0.536415i	−0.963361	−	0.268207i	$-0.913569\pi$
$571$		−	12.8180i		−	0.536415i	0.963361	−	0.268207i	$-0.0864312\pi$
$572$	−1.96529	+	10.6428i	−0.0821730	+	0.444999i
$573$		0			0
$574$	2.97723	+	19.7864i	0.124267	+	0.825869i
$575$	14.1788	+	43.6380i	0.591298	+	1.81983i
$576$		0			0
$577$	−18.4866	−	13.4313i	−0.769608	−	0.559153i	0.132234	−	0.991219i	$-0.457785\pi$
$577$	−18.4866	−	13.4313i	−0.769608	−	0.559153i	−0.901842	+	0.432065i	$0.857785\pi$
$578$	−7.42367	+	3.71053i	−0.308784	+	0.154338i
$579$		0			0
$580$	−1.49008	+	1.98561i	−0.0618723	+	0.0824481i
$581$	−12.9251	−	17.7898i	−0.536222	−	0.738047i
$582$		0			0
$583$	−13.4523	+	25.7579i	−0.557139	+	1.06678i
$584$	19.3280	−	2.60328i	0.799797	−	0.107725i
$585$		0			0
$586$	−4.26803	+	25.6616i	−0.176311	+	1.06007i
$587$	27.8685	+	9.05504i	1.15026	+	0.373741i	0.821240	−	0.570583i	$-0.193283\pi$
$587$	27.8685	+	9.05504i	1.15026	+	0.373741i	0.329017	+	0.944324i	$0.393283\pi$
$588$		0			0
$589$	23.9003	−	32.8959i	0.984794	−	1.35545i
$590$	0.378933	+	0.384839i	0.0156004	+	0.0158436i
$591$		0			0
$592$	4.91622	−	1.43090i	0.202055	−	0.0588096i
$593$	−10.3694			−0.425820			−0.212910	−	0.977072i	$-0.568294\pi$
$593$	−10.3694			−0.425820			−0.212910	+	0.977072i	$0.568294\pi$
$594$		0			0
$595$		−	1.56925i		−	0.0643329i
$596$	7.79817	−	22.7948i	0.319426	−	0.933710i
$597$		0			0
$598$	15.2103	−	14.9769i	0.621994	−	0.612449i
$599$	−16.8754	−	12.2607i	−0.689508	−	0.500957i	0.186990	−	0.982362i	$-0.440127\pi$
$599$	−16.8754	−	12.2607i	−0.689508	−	0.500957i	−0.876498	+	0.481405i	$0.840127\pi$
$600$		0			0
$601$	12.1139	−	37.2827i	0.494135	−	1.52079i	−0.324164	−	0.946001i	$-0.605083\pi$
$601$	12.1139	−	37.2827i	0.494135	−	1.52079i	0.818300	−	0.574792i	$-0.194917\pi$
$602$	1.34559	−	8.09034i	0.0548420	−	0.329738i
$603$		0			0
$604$	−6.09345	−	8.66560i	−0.247939	−	0.352598i
$605$	0.639122	+	2.11057i	0.0259840	+	0.0858068i
$606$		0			0
$607$	21.5873	−	15.6841i	0.876203	−	0.636599i	−0.0560410	−	0.998428i	$-0.517848\pi$
$607$	21.5873	−	15.6841i	0.876203	−	0.636599i	0.932244	+	0.361830i	$0.117848\pi$
$608$	−24.3072	−	13.5932i	−0.985785	−	0.551276i
$609$		0			0
$610$	1.62177	−	0.810600i	0.0656635	−	0.0328202i
$611$	4.56398	−	6.28177i	0.184639	−	0.254133i
$612$		0			0
$613$	−29.2625	+	9.50796i	−1.18190	+	0.384023i	−0.833073	−	0.553164i	$-0.813420\pi$
$613$	−29.2625	+	9.50796i	−1.18190	+	0.384023i	−0.348828	+	0.937187i	$0.613420\pi$
$614$	−28.4874	+	4.28644i	−1.14966	+	0.172987i
$615$		0			0
$616$	12.3373	+	18.2258i	0.497086	+	0.734339i
$617$	−10.0183			−0.403323			−0.201662	−	0.979455i	$-0.564634\pi$
$617$	−10.0183			−0.403323			−0.201662	+	0.979455i	$0.564634\pi$
$618$		0			0
$619$	30.5262	−	9.91856i	1.22695	−	0.398660i	0.377342	−	0.926074i	$-0.376838\pi$
$619$	30.5262	−	9.91856i	1.22695	−	0.398660i	0.849609	+	0.527414i	$0.176838\pi$
$620$	0.974490	+	3.16488i	0.0391364	+	0.127104i
$621$		0			0
$622$	−27.4614	+	13.7259i	−1.10110	+	0.550358i
$623$	3.70569	−	11.4049i	0.148465	−	0.456929i
$624$		0			0
$625$	−19.7390	+	14.3412i	−0.789561	+	0.573649i
$626$	−17.4851	+	33.6703i	−0.698845	+	1.34573i
$627$		0			0
$628$	−6.46308	+	4.54469i	−0.257905	+	0.181353i
$629$	−2.51029	−	3.45512i	−0.100092	−	0.137765i
$630$		0			0
$631$	−0.865296	+	2.66311i	−0.0344469	+	0.106017i	−0.966802	−	0.255528i	$-0.917751\pi$
$631$	−0.865296	+	2.66311i	−0.0344469	+	0.106017i	0.932355	+	0.361545i	$0.117751\pi$
$632$	36.4038	+	19.6252i	1.44807	+	0.780650i
$633$		0			0
$634$	−3.83942	+	3.78051i	−0.152483	+	0.150143i
$635$	−1.40189	+	0.455501i	−0.0556322	+	0.0180760i
$636$		0			0
$637$			2.44015i			0.0966823i
$638$	−27.7754	+	8.48156i	−1.09964	+	0.335788i
$639$		0			0
$640$	2.07364	−	0.918868i	0.0819679	−	0.0363214i
$641$	−5.21567	−	16.0522i	−0.206007	−	0.634023i	−0.999671	−	0.0256668i	$-0.991829\pi$
$641$	−5.21567	−	16.0522i	−0.206007	−	0.634023i	0.793664	−	0.608356i	$-0.208171\pi$
$642$		0			0
$643$	−28.8449	+	39.7016i	−1.13753	+	1.56568i	−0.364630	+	0.931153i	$0.618804\pi$
$643$	−28.8449	+	39.7016i	−1.13753	+	1.56568i	−0.772902	+	0.634525i	$0.781196\pi$
$644$	0.671235	−	43.4038i	0.0264504	−	1.71035i
$645$		0			0
$646$	−3.81117	+	22.9147i	−0.149948	+	0.901566i
$647$	−28.5917	+	20.7731i	−1.12406	+	0.816675i	−0.984819	−	0.173585i	$-0.944465\pi$
$647$	−28.5917	+	20.7731i	−1.12406	+	0.816675i	−0.139237	+	0.990259i	$0.544465\pi$
$648$		0			0
$649$	0.925546	+	6.24991i	0.0363309	+	0.245330i
$650$	10.1565	+	5.27432i	0.398372	+	0.206876i
$651$		0			0
$652$	25.6887	+	19.2778i	1.00605	+	0.754977i
$653$	−0.182805	−	0.0593970i	−0.00715372	−	0.00232438i	0.305438	−	0.952212i	$-0.401197\pi$
$653$	−0.182805	−	0.0593970i	−0.00715372	−	0.00232438i	−0.312592	+	0.949888i	$0.601197\pi$
$654$		0			0
$655$	−1.11149	−	0.807542i	−0.0434293	−	0.0315533i
$656$	19.0675	+	14.7754i	0.744461	+	0.576881i
$657$		0			0
$658$	−2.34946	−	15.6143i	−0.0915914	−	0.608709i
$659$			46.4826i			1.81071i	0.424660	+	0.905353i	$0.360394\pi$
$659$			46.4826i			1.81071i	−0.424660	+	0.905353i	$0.639606\pi$
$660$		0			0
$661$			24.0904i			0.937007i	0.883462	+	0.468503i	$0.155207\pi$
$661$			24.0904i			0.937007i	−0.883462	+	0.468503i	$0.844793\pi$
$662$	−39.4789	+	5.94031i	−1.53439	+	0.230877i
$663$		0			0
$664$	−26.0800	−	4.75317i	−1.01210	−	0.184459i
$665$	1.87335	+	1.36107i	0.0726455	+	0.0527801i
$666$		0			0
$667$	54.4763	+	17.7004i	2.10933	+	0.685363i
$668$	−11.1394	+	14.8438i	−0.430996	+	0.574325i
$669$		0			0
$670$	1.08103	−	2.08169i	0.0417637	−	0.0804226i
$671$	20.9142	+	3.52849i	0.807385	+	0.136216i
$672$		0			0
$673$	6.12494	−	4.45003i	0.236099	−	0.171536i	−0.463444	−	0.886126i	$-0.653387\pi$
$673$	6.12494	−	4.45003i	0.236099	−	0.171536i	0.699544	+	0.714590i	$0.253387\pi$
$674$	28.6664	+	4.76780i	1.10419	+	0.183649i
$675$		0			0
$676$	−0.319711	+	20.6733i	−0.0122966	+	0.795128i
$677$	−12.1390	+	16.7079i	−0.466540	+	0.642137i	−0.975849	−	0.218447i	$-0.929901\pi$
$677$	−12.1390	+	16.7079i	−0.466540	+	0.642137i	0.509309	+	0.860584i	$0.329901\pi$
$678$		0			0
$679$	−0.217313	−	0.668820i	−0.00833969	−	0.0256669i
$680$	−1.30633	−	1.36839i	−0.0500956	−	0.0524752i
$681$		0			0
$682$	−12.6245	+	36.6242i	−0.483419	+	1.40241i
$683$		−	14.6272i		−	0.559694i	−0.960045	−	0.279847i	$-0.909716\pi$
$683$		−	14.6272i		−	0.559694i	0.960045	−	0.279847i	$-0.0902837\pi$
$684$		0			0
$685$	0.534432	−	0.173648i	0.0204196	−	0.00663473i
$686$	19.7772	+	20.0854i	0.755097	+	0.766864i
$687$		0			0
$688$	−5.56152	−	8.17494i	−0.212031	−	0.311667i
$689$	4.41754	−	13.5958i	0.168295	−	0.517958i
$690$		0			0
$691$	13.4854	+	18.5610i	0.513008	+	0.706095i	0.984423	−	0.175817i	$-0.0562566\pi$
$691$	13.4854	+	18.5610i	0.513008	+	0.706095i	−0.471415	+	0.881911i	$0.656257\pi$
$692$	14.4660	−	10.1722i	0.549915	−	0.386688i
$693$		0			0
$694$	−4.72938	−	2.45598i	−0.179525	−	0.0932279i
$695$	−1.44429	+	1.04934i	−0.0547851	+	0.0398037i
$696$		0			0
$697$	6.21750	−	19.1355i	0.235505	−	0.724809i
$698$	−19.8953	−	39.8046i	−0.753048	−	1.50663i
$699$		0			0
$700$	22.2425	−	6.84862i	0.840686	−	0.258854i
$701$	−0.666479	+	0.216552i	−0.0251726	+	0.00817907i	−0.321576	−	0.946884i	$-0.604213\pi$
$701$	−0.666479	+	0.216552i	−0.0251726	+	0.00817907i	0.296404	+	0.955063i	$0.404213\pi$
$702$		0			0
$703$	6.30196			0.237683
$704$	25.9304	+	5.62262i	0.977289	+	0.211910i
$705$		0			0
$706$	−6.47321	−	43.0205i	−0.243623	−	1.61910i
$707$	−33.5141	+	10.8894i	−1.26043	+	0.409538i
$708$		0			0
$709$	−2.38215	+	3.27875i	−0.0894636	+	0.123136i	−0.851403	−	0.524513i	$-0.824248\pi$
$709$	−2.38215	+	3.27875i	−0.0894636	+	0.123136i	0.761939	+	0.647649i	$0.224248\pi$
$710$	0.158236	+	0.316583i	0.00593848	+	0.0118811i
$711$		0			0
$712$	−6.26277	−	13.0299i	−0.234707	−	0.488318i
$713$	61.8141	−	44.9106i	2.31496	−	1.68192i
$714$		0			0
$715$	−0.482760	−	0.971506i	−0.0180542	−	0.0363323i
$716$	−17.4299	+	12.2563i	−0.651388	+	0.458041i
$717$		0			0
$718$	−17.3737	−	2.88960i	−0.648381	−	0.107839i
$719$	−3.11822	+	9.59690i	−0.116290	+	0.357904i	−0.992214	−	0.124545i	$-0.960253\pi$
$719$	−3.11822	+	9.59690i	−0.116290	+	0.357904i	0.875924	+	0.482449i	$0.160253\pi$
$720$		0			0
$721$	5.36169	+	3.89549i	0.199680	+	0.145076i
$722$	−5.19721	−	5.27821i	−0.193420	−	0.196435i
$723$		0			0
$724$	−8.68545	+	25.3884i	−0.322792	+	0.943551i
$725$			30.7095i			1.14052i
$726$		0			0
$727$	−13.6615			−0.506675			−0.253338	−	0.967378i	$-0.581528\pi$
$727$	−13.6615			−0.506675			−0.253338	+	0.967378i	$0.581528\pi$
$728$	−7.47631	−	7.83144i	−0.277090	−	0.290252i
$729$		0			0
$730$	−1.39295	+	1.37158i	−0.0515554	+	0.0507643i
$731$	−4.84748	+	6.67199i	−0.179291	+	0.246772i
$732$		0			0
$733$	−17.0433	−	5.53772i	−0.629510	−	0.204540i	−0.0231521	−	0.999732i	$-0.507370\pi$
$733$	−17.0433	−	5.53772i	−0.629510	−	0.204540i	−0.606358	+	0.795192i	$0.707370\pi$
$734$	6.48427	+	1.07846i	0.239339	+	0.0398068i
$735$		0			0
$736$	−35.5465	−	38.4069i	−1.31026	−	1.41570i
$737$	24.5733	−	12.2110i	0.905170	−	0.449797i
$738$		0			0
$739$	−13.8476	−	19.0596i	−0.509393	−	0.701120i	0.474424	−	0.880297i	$-0.342656\pi$
$739$	−13.8476	−	19.0596i	−0.509393	−	0.701120i	−0.983817	+	0.179177i	$0.942656\pi$
$740$	−0.308057	+	0.410502i	−0.0113244	+	0.0150904i
$741$		0			0
$742$	−12.9972	−	26.0036i	−0.477143	−	0.954621i
$743$	−11.0265	−	8.01121i	−0.404523	−	0.293903i	0.366858	−	0.930277i	$-0.380434\pi$
$743$	−11.0265	−	8.01121i	−0.404523	−	0.293903i	−0.771381	+	0.636374i	$0.780434\pi$
$744$		0			0
$745$	0.746241	+	2.29669i	0.0273402	+	0.0841444i
$746$	25.2063	−	3.79274i	0.922868	−	0.138862i
$747$		0			0
$748$	−2.90312	−	21.9399i	−0.106148	−	0.802201i
$749$		−	2.09595i		−	0.0765842i
$750$		0			0
$751$	−3.77972	−	11.6328i	−0.137924	−	0.424486i	0.858110	−	0.513467i	$-0.171639\pi$
$751$	−3.77972	−	11.6328i	−0.137924	−	0.424486i	−0.996033	+	0.0889809i	$0.971639\pi$
$752$	−15.0470	−	11.6599i	−0.548708	−	0.425192i
$753$		0			0
$754$	12.7794	−	6.38745i	0.465398	−	0.232617i
$755$	1.00989	+	0.328134i	0.0367537	+	0.0119420i
$756$		0			0
$757$	12.5436	+	17.2648i	0.455906	+	0.627501i	0.973654	−	0.228033i	$-0.0732293\pi$
$757$	12.5436	+	17.2648i	0.455906	+	0.627501i	−0.517747	+	0.855534i	$0.673229\pi$
$758$	17.4543	+	9.06407i	0.633968	+	0.329222i
$759$		0			0
$760$	2.76660	−	0.372633i	0.100355	−	0.0135168i
$761$	9.57071	−	6.95353i	0.346938	−	0.252065i	−0.400645	−	0.916233i	$-0.631214\pi$
$761$	9.57071	−	6.95353i	0.346938	−	0.252065i	0.747583	+	0.664168i	$0.231214\pi$
$762$		0			0
$763$	−3.01939	−	0.981060i	−0.109309	−	0.0355167i
$764$	−0.458290	+	29.6343i	−0.0165804	+	1.07213i
$765$		0			0
$766$	22.3988	+	22.7479i	0.809302	+	0.821914i
$767$	−0.960466	−	2.95601i	−0.0346804	−	0.106735i
$768$		0			0
$769$	2.94327			0.106137			0.0530685	−	0.998591i	$-0.483100\pi$
$769$	2.94327			0.106137			0.0530685	+	0.998591i	$0.483100\pi$
$770$	−2.08567	−	0.718941i	−0.0751624	−	0.0259088i
$771$		0			0
$772$	−8.46617	−	2.89631i	−0.304704	−	0.104240i
$773$	−7.56561	+	2.45822i	−0.272116	+	0.0884159i	−0.441896	−	0.897066i	$-0.645694\pi$
$773$	−7.56561	+	2.45822i	−0.272116	+	0.0884159i	0.169780	+	0.985482i	$0.445694\pi$
$774$		0			0
$775$	33.1406	+	24.0780i	1.19044	+	0.864908i
$776$	−0.746261	−	0.402308i	−0.0267892	−	0.0144420i
$777$		0			0
$778$	5.44446	−	32.7348i	0.195193	−	1.17360i
$779$	17.4511	+	24.0194i	0.625251	+	0.860584i
$780$		0			0
$781$	−0.688790	+	4.08263i	−0.0246468	+	0.146088i
$782$	−20.1168	+	38.7381i	−0.719376	+	1.38527i
$783$		0			0
$784$	5.97939	+	0.184986i	0.213550	+	0.00660663i
$785$	0.244733	−	0.753210i	0.00873489	−	0.0268832i
$786$		0			0
$787$	−1.60061	+	2.20304i	−0.0570554	+	0.0785300i	−0.836591	−	0.547828i	$-0.815455\pi$
$787$	−1.60061	+	2.20304i	−0.0570554	+	0.0785300i	0.779536	+	0.626358i	$0.215455\pi$
$788$	−11.9681	−	38.8693i	−0.426348	−	1.38466i
$789$		0			0
$790$	−4.09934	+	0.616821i	−0.145848	+	0.0219455i
$791$	−8.84207			−0.314388
$792$		0			0
$793$	−10.4340			−0.370523
$794$	−41.9403	+	6.31069i	−1.48841	+	0.223958i
$795$		0			0
$796$	−19.9062	+	6.12926i	−0.705556	+	0.217246i
$797$	−16.4925	+	22.7000i	−0.584196	+	0.804077i	−0.994148	−	0.108031i	$-0.965546\pi$
$797$	−16.4925	+	22.7000i	−0.584196	+	0.804077i	0.409952	+	0.912107i	$0.365546\pi$
$798$		0			0
$799$	−4.90650	+	15.1007i	−0.173580	+	0.534223i
$800$	13.6943	−	24.4879i	0.484165	−	0.865779i
$801$		0			0
$802$	−13.1850	+	25.3899i	−0.465580	+	0.896547i
$803$	−22.6220	+	3.35008i	−0.798313	+	0.118222i
$804$		0			0
$805$	2.55756	+	3.52018i	0.0901423	+	0.124070i
$806$	3.12668	−	18.7992i	0.110133	−	0.662172i
$807$		0			0
$808$	−20.1594	+	37.3947i	−0.709205	+	1.31554i
$809$	−26.3156	−	19.1194i	−0.925207	−	0.672202i	0.0196074	−	0.999808i	$-0.493758\pi$
$809$	−26.3156	−	19.1194i	−0.925207	−	0.672202i	−0.944815	+	0.327605i	$0.893758\pi$
$810$		0			0
$811$	−8.46947	+	2.75190i	−0.297403	+	0.0966322i	−0.453918	−	0.891043i	$-0.649974\pi$
$811$	−8.46947	+	2.75190i	−0.297403	+	0.0966322i	0.156515	+	0.987676i	$0.449974\pi$
$812$	9.40413	−	27.4891i	0.330020	−	0.964680i
$813$		0			0
$814$	−5.74224	+	1.75346i	−0.201265	+	0.0614588i
$815$	−3.21938			−0.112770
$816$		0			0
$817$	−3.76054	−	11.5738i	−0.131565	−	0.404915i
$818$	4.40276	+	4.47137i	0.153939	+	0.156338i
$819$		0			0
$820$	−2.41765	−	0.0373887i	−0.0844280	−	0.00130567i
$821$	13.6833	+	4.44597i	0.477550	+	0.155165i	0.537895	−	0.843012i	$-0.319220\pi$
$821$	13.6833	+	4.44597i	0.477550	+	0.155165i	−0.0603443	+	0.998178i	$0.519220\pi$
$822$		0			0
$823$	28.5715	−	20.7584i	0.995940	−	0.723593i	0.0347264	−	0.999397i	$-0.488944\pi$
$823$	28.5715	−	20.7584i	0.995940	−	0.723593i	0.961214	+	0.275804i	$0.0889440\pi$
$824$	7.91823	−	1.06651i	0.275845	−	0.0371535i
$825$		0			0
$826$	−5.60936	−	2.91296i	−0.195175	−	0.101355i
$827$	7.54322	+	10.3823i	0.262303	+	0.361030i	0.919773	−	0.392452i	$-0.128373\pi$
$827$	7.54322	+	10.3823i	0.262303	+	0.361030i	−0.657469	+	0.753481i	$0.728373\pi$
$828$		0			0
$829$	22.7234	+	7.38328i	0.789216	+	0.256432i	0.675770	−	0.737112i	$-0.263811\pi$
$829$	22.7234	+	7.38328i	0.789216	+	0.256432i	0.113446	+	0.993544i	$0.463811\pi$
$830$	2.37688	−	1.18802i	0.0825026	−	0.0412368i
$831$		0			0
$832$	−13.0387	−	0.605312i	−0.452035	−	0.0209854i
$833$	−1.54193	−	4.74556i	−0.0534246	−	0.164424i
$834$		0			0
$835$		−	1.86027i		−	0.0643773i
$836$	28.7096	+	15.5636i	0.992942	+	0.538278i
$837$		0			0
$838$	−8.41378	+	1.26601i	−0.290649	+	0.0437334i
$839$	−7.29937	−	22.4652i	−0.252002	−	0.775583i	−0.994406	−	0.105630i	$-0.966314\pi$
$839$	−7.29937	−	22.4652i	−0.252002	−	0.775583i	0.742403	−	0.669953i	$-0.233686\pi$
$840$		0			0
$841$	7.55366	+	5.48805i	0.260471	+	0.189243i
$842$	17.3586	+	34.7295i	0.598218	+	1.19686i
$843$		0			0
$844$	−29.9582	−	22.4818i	−1.03120	−	0.773855i
$845$	−1.21817	−	1.67667i	−0.0419065	−	0.0576793i
$846$		0			0
$847$	−14.7463	−	21.1798i	−0.506689	−	0.727746i
$848$	−32.9805	−	11.8555i	−1.13255	−	0.407120i
$849$		0			0
$850$	−23.0851	−	3.83951i	−0.791812	−	0.131694i
$851$	11.2623	+	3.65935i	0.386068	+	0.125441i
$852$		0			0
$853$	−24.5116	+	33.7374i	−0.839262	+	1.15515i	0.146865	+	0.989156i	$0.453082\pi$
$853$	−24.5116	+	33.7374i	−0.839262	+	1.15515i	−0.986128	+	0.165989i	$0.946918\pi$
$854$	−15.1192	+	14.8872i	−0.517368	+	0.509429i
$855$		0			0
$856$	−1.74479	−	1.82767i	−0.0596356	−	0.0624684i
$857$	4.35256			0.148680			0.0743402	−	0.997233i	$-0.476315\pi$
$857$	4.35256			0.148680			0.0743402	+	0.997233i	$0.476315\pi$
$858$		0			0
$859$			7.91648i			0.270107i	0.990838	+	0.135053i	$0.0431206\pi$
$859$			7.91648i			0.270107i	−0.990838	+	0.135053i	$0.956879\pi$
$860$	0.937726	+	0.320799i	0.0319762	+	0.0109392i
$861$		0			0
$862$	24.7079	+	25.0929i	0.841554	+	0.854669i
$863$	−9.98178	−	7.25219i	−0.339784	−	0.246867i	0.404787	−	0.914411i	$-0.367346\pi$
$863$	−9.98178	−	7.25219i	−0.339784	−	0.246867i	−0.744571	+	0.667544i	$0.767346\pi$
$864$		0			0
$865$	−0.547774	+	1.68588i	−0.0186249	+	0.0573215i
$866$	−18.8948	−	3.14259i	−0.642072	−	0.106790i
$867$		0			0
$868$	−22.2919	−	31.7016i	−0.756635	−	1.07602i
$869$	−42.9859	−	22.4499i	−1.45820	−	0.761560i
$870$		0			0
$871$	−10.9209	+	7.93449i	−0.370040	+	0.268850i
$872$	−3.44960	+	1.65803i	−0.116818	+	0.0561481i
$873$		0			0
$874$	−28.7971	−	57.6144i	−0.974075	−	1.94883i
$875$	−2.75350	+	3.78986i	−0.0930852	+	0.128121i
$876$		0			0
$877$	55.4714	−	18.0237i	1.87314	−	0.608619i	0.882834	−	0.469686i	$-0.155633\pi$
$877$	55.4714	−	18.0237i	1.87314	−	0.608619i	0.990302	−	0.138933i	$-0.0443671\pi$
$878$	6.35416	+	42.2292i	0.214442	+	1.42517i
$879$		0			0
$880$	−2.41720	+	1.10932i	−0.0814837	+	0.0373951i
$881$	25.8106			0.869581			0.434791	−	0.900532i	$-0.356822\pi$
$881$	25.8106			0.869581			0.434791	+	0.900532i	$0.356822\pi$
$882$		0			0
$883$	−34.8110	+	11.3108i	−1.17148	+	0.380638i	−0.829196	−	0.558958i	$-0.811201\pi$
$883$	−34.8110	+	11.3108i	−1.17148	+	0.380638i	−0.342287	+	0.939596i	$0.611201\pi$
$884$	3.20383	+	10.4052i	0.107757	+	0.349964i
$885$		0			0
$886$	−8.81313	−	17.6324i	−0.296083	−	0.592374i
$887$	−6.76505	+	20.8207i	−0.227148	+	0.699091i	0.770918	+	0.636934i	$0.219798\pi$
$887$	−6.76505	+	20.8207i	−0.227148	+	0.699091i	−0.998066	+	0.0621563i	$0.980202\pi$
$888$		0			0
$889$	13.9561	−	10.1397i	0.468071	−	0.340074i
$890$	1.28605	+	0.667849i	0.0431084	+	0.0223863i
$891$		0			0
$892$	−16.7699	−	23.8488i	−0.561499	−	0.798517i
$893$	−13.7714	−	18.9547i	−0.460843	−	0.634296i
$894$		0			0
$895$	0.660007	−	2.03129i	0.0220616	−	0.0678986i
$896$	−19.7571	+	17.7264i	−0.660038	+	0.592197i
$897$		0			0
$898$	−7.00264	−	7.11178i	−0.233681	−	0.237323i
$899$	48.6353	−	15.8026i	1.62208	−	0.527045i
$900$		0			0
$901$			29.2323i			0.973869i
$902$	−22.5843	−	17.0304i	−0.751975	−	0.567051i
$903$		0			0
$904$	−7.71029	+	7.36065i	−0.256441	+	0.244812i
$905$	−0.831149	−	2.55801i	−0.0276283	−	0.0850313i
$906$		0			0
$907$	−16.9320	+	23.3049i	−0.562218	+	0.773827i	−0.991606	−	0.129293i	$-0.958729\pi$
$907$	−16.9320	+	23.3049i	−0.562218	+	0.773827i	0.429388	+	0.903120i	$0.358729\pi$
$908$	8.36290	+	0.129331i	0.277533	+	0.00429201i
$909$		0			0
$910$	1.07057	+	0.178058i	0.0354891	+	0.00590256i
$911$	35.7732	−	25.9908i	1.18522	−	0.861113i	0.192469	−	0.981303i	$-0.438351\pi$
$911$	35.7732	−	25.9908i	1.18522	−	0.861113i	0.992751	+	0.120191i	$0.0383505\pi$
$912$		0			0
$913$	30.6521	+	5.17138i	1.01444	+	0.171148i
$914$	−4.08608	+	7.86840i	−0.135156	+	0.260263i
$915$		0			0
$916$	−37.1781	−	27.8999i	−1.22840	−	0.921838i
$917$	15.2915	+	4.96852i	0.504970	+	0.164075i
$918$		0			0
$919$	15.3711	+	11.1678i	0.507046	+	0.368390i	0.811702	−	0.584072i	$-0.198541\pi$
$919$	15.3711	+	11.1678i	0.507046	+	0.368390i	−0.304656	+	0.952462i	$0.598541\pi$
$920$	5.16061	+	0.940540i	0.170140	+	0.0310087i
$921$		0			0
$922$	−25.2923	+	3.80568i	−0.832957	+	0.125334i
$923$		−	2.03681i		−	0.0670423i
$924$		0			0
$925$			6.34883i			0.208748i
$926$	−2.09470	−	13.9212i	−0.0688360	−	0.457479i
$927$		0			0
$928$	−14.6831	−	31.7991i	−0.481998	−	1.04386i
$929$	22.7067	+	16.4974i	0.744983	+	0.541262i	0.894268	−	0.447532i	$-0.147697\pi$
$929$	22.7067	+	16.4974i	0.744983	+	0.541262i	−0.149285	+	0.988794i	$0.547697\pi$
$930$		0			0
$931$	7.00259	+	2.27528i	0.229500	+	0.0745692i
$932$	16.7852	−	22.3672i	0.549819	−	0.732662i
$933$		0			0
$934$	40.9379	+	21.2592i	1.33953	+	0.695622i
$935$	1.55276	+	1.58431i	0.0507806	+	0.0518126i
$936$		0			0
$937$	−0.237551	+	0.172591i	−0.00776046	+	0.00563830i	−0.591659	−	0.806189i	$-0.701527\pi$
$937$	−0.237551	+	0.172591i	−0.00776046	+	0.00563830i	0.583898	+	0.811827i	$0.301527\pi$
$938$	−4.50380	+	27.0791i	−0.147054	+	0.884165i
$939$		0			0
$940$	1.90787	+	0.0295051i	0.0622280	+	0.000962349i
$941$	−9.48051	+	13.0488i	−0.309056	+	0.425379i	−0.935087	−	0.354420i	$-0.884678\pi$
$941$	−9.48051	+	13.0488i	−0.309056	+	0.425379i	0.626031	+	0.779798i	$0.284678\pi$
$942$		0			0
$943$	17.2398	+	53.0587i	0.561405	+	1.72783i
$944$	−7.31628	+	2.12945i	−0.238125	+	0.0693078i
$945$		0			0
$946$	6.64683	+	9.49947i	0.216107	+	0.308854i
$947$		−	29.0812i		−	0.945011i	−0.881328	−	0.472505i	$-0.843350\pi$
$947$		−	29.0812i		−	0.945011i	0.881328	−	0.472505i	$-0.156650\pi$
$948$		0			0
$949$	10.6995	−	3.47648i	0.347320	−	0.112851i
$950$	24.6062	−	24.2286i	0.798330	−	0.786079i
$951$		0			0
$952$	19.4885	+	10.5062i	0.631625	+	0.340508i
$953$	−12.5355	+	38.5803i	−0.406065	+	1.24974i	0.513937	+	0.857828i	$0.328186\pi$
$953$	−12.5355	+	38.5803i	−0.406065	+	1.24974i	−0.920003	+	0.391912i	$0.871814\pi$
$954$		0			0
$955$	−1.74620	−	2.40343i	−0.0565056	−	0.0777732i
$956$	−27.5366	−	39.1602i	−0.890596	−	1.26653i
$957$		0			0
$958$	5.54751	−	10.6826i	0.179232	−	0.345139i
$959$	−5.32037	+	3.86548i	−0.171804	+	0.124823i
$960$		0			0
$961$	11.4998	−	35.3927i	0.370961	−	1.14170i
$962$	2.64199	−	1.32053i	0.0851811	−	0.0425756i
$963$		0			0
$964$	50.0496	−	15.4106i	1.61199	−	0.496343i
$965$	0.853011	−	0.277160i	0.0274594	−	0.00892210i
$966$		0			0
$967$	6.42732			0.206689			0.103344	−	0.994646i	$-0.467046\pi$
$967$	6.42732			0.206689			0.103344	+	0.994646i	$0.467046\pi$
$968$	−30.4901	−	6.19311i	−0.979989	−	0.199054i
$969$		0			0
$970$	0.0840346	−	0.0126445i	0.00269819	−	0.000405991i
$971$	−48.2270	+	15.6699i	−1.54768	+	0.502871i	−0.953482	−	0.301450i	$-0.902529\pi$
$971$	−48.2270	+	15.6699i	−1.54768	+	0.502871i	−0.594195	+	0.804321i	$0.702529\pi$
$972$		0			0
$973$	12.2804	−	16.9026i	0.393693	−	0.541871i
$974$	9.02582	−	4.51133i	0.289206	−	0.144552i
$975$		0			0
$976$	−0.790994	+	25.5677i	−0.0253191	+	0.818404i
$977$	−0.0813429	+	0.0590991i	−0.00260239	+	0.00189075i	−0.589086	−	0.808071i	$-0.700512\pi$
$977$	−0.0813429	+	0.0590991i	−0.00260239	+	0.00189075i	0.586483	+	0.809961i	$0.300512\pi$
$978$		0			0
$979$	7.54383	+	15.1812i	0.241102	+	0.485193i
$980$	−0.490514	+	0.344918i	−0.0156689	+	0.0110180i
$981$		0			0
$982$	−2.80752	+	16.8802i	−0.0895916	+	0.538670i
$983$	−8.13927	+	25.0501i	−0.259603	+	0.798974i	0.733285	+	0.679921i	$0.237986\pi$
$983$	−8.13927	+	25.0501i	−0.259603	+	0.798974i	−0.992888	+	0.119053i	$0.962014\pi$
$984$		0			0
$985$	3.29808	+	2.39620i	0.105086	+	0.0763491i
$986$	−20.8169	+	20.4975i	−0.662946	+	0.652773i
$987$		0			0
$988$	−15.2004	−	5.20012i	−0.483590	−	0.165438i
$989$		−	22.8672i		−	0.727136i
$990$		0			0
$991$	−27.9640			−0.888306			−0.444153	−	0.895951i	$-0.646495\pi$
$991$	−27.9640			−0.888306			−0.444153	+	0.895951i	$0.646495\pi$
$992$	−45.8288	−	9.08683i	−1.45507	−	0.288507i
$993$		0			0
$994$	−2.90610	−	2.95139i	−0.0921760	−	0.0936125i
$995$	1.22717	−	1.68905i	0.0389038	−	0.0535465i
$996$		0			0
$997$	−54.4887	−	17.7045i	−1.72567	−	0.560706i	−0.732861	−	0.680378i	$-0.761815\pi$
$997$	−54.4887	−	17.7045i	−1.72567	−	0.560706i	−0.992813	+	0.119673i	$0.961815\pi$
$998$	−3.26117	+	19.6078i	−0.103231	+	0.620674i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.br.b.685.4		40
3.2	odd	2		88.2.o.a.69.7	yes	40
8.5	even	2	inner	792.2.br.b.685.9		40
11.4	even	5	inner	792.2.br.b.37.9		40
12.11	even	2		352.2.w.a.113.9		40
24.5	odd	2		88.2.o.a.69.2	yes	40
24.11	even	2		352.2.w.a.113.2		40
33.2	even	10		968.2.c.i.485.8		20
33.5	odd	10		968.2.o.j.493.2		40
33.8	even	10		968.2.o.d.269.1		40
33.14	odd	10		968.2.o.j.269.10		40
33.17	even	10		968.2.o.d.493.9		40
33.20	odd	10		968.2.c.h.485.13		20
33.26	odd	10		88.2.o.a.37.2	✓	40
33.29	even	10		968.2.o.i.565.9		40
33.32	even	2		968.2.o.i.245.4		40
88.37	even	10	inner	792.2.br.b.37.4		40
132.35	odd	10		3872.2.c.i.1937.4		20
132.59	even	10		352.2.w.a.81.2		40
132.119	even	10		3872.2.c.h.1937.4		20
264.5	odd	10		968.2.o.j.493.10		40
264.29	even	10		968.2.o.i.565.4		40
264.35	odd	10		3872.2.c.i.1937.17		20
264.53	odd	10		968.2.c.h.485.14		20
264.59	even	10		352.2.w.a.81.9		40
264.101	even	10		968.2.c.i.485.7		20
264.125	odd	10		88.2.o.a.37.7	yes	40
264.149	even	10		968.2.o.d.493.1		40
264.173	even	10		968.2.o.d.269.9		40
264.197	even	2		968.2.o.i.245.9		40
264.245	odd	10		968.2.o.j.269.2		40
264.251	even	10		3872.2.c.h.1937.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.37.2	✓	40	33.26	odd	10
88.2.o.a.37.7	yes	40	264.125	odd	10
88.2.o.a.69.2	yes	40	24.5	odd	2
88.2.o.a.69.7	yes	40	3.2	odd	2
352.2.w.a.81.2		40	132.59	even	10
352.2.w.a.81.9		40	264.59	even	10
352.2.w.a.113.2		40	24.11	even	2
352.2.w.a.113.9		40	12.11	even	2
792.2.br.b.37.4		40	88.37	even	10	inner
792.2.br.b.37.9		40	11.4	even	5	inner
792.2.br.b.685.4		40	1.1	even	1	trivial
792.2.br.b.685.9		40	8.5	even	2	inner
968.2.c.h.485.13		20	33.20	odd	10
968.2.c.h.485.14		20	264.53	odd	10
968.2.c.i.485.7		20	264.101	even	10
968.2.c.i.485.8		20	33.2	even	10
968.2.o.d.269.1		40	33.8	even	10
968.2.o.d.269.9		40	264.173	even	10
968.2.o.d.493.1		40	264.149	even	10
968.2.o.d.493.9		40	33.17	even	10
968.2.o.i.245.4		40	33.32	even	2
968.2.o.i.245.9		40	264.197	even	2
968.2.o.i.565.4		40	264.29	even	10
968.2.o.i.565.9		40	33.29	even	10
968.2.o.j.269.2		40	264.245	odd	10
968.2.o.j.269.10		40	33.14	odd	10
968.2.o.j.493.2		40	33.5	odd	10
968.2.o.j.493.10		40	264.5	odd	10
3872.2.c.h.1937.4		20	132.119	even	10
3872.2.c.h.1937.17		20	264.251	even	10
3872.2.c.i.1937.4		20	132.35	odd	10
3872.2.c.i.1937.17		20	264.35	odd	10

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:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.br (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.210425 - 1.39847i) q^{2} +(-1.91144 + 0.588548i) q^{4} +(0.117836 - 0.162187i) q^{5} +(-0.725001 + 2.23132i) q^{7} +(1.22528 + 2.54925i) q^{8} +O(q^{10})\)	\(q+(-0.210425 - 1.39847i) q^{2} +(-1.91144 + 0.588548i) q^{4} +(0.117836 - 0.162187i) q^{5} +(-0.725001 + 2.23132i) q^{7} +(1.22528 + 2.54925i) q^{8} +(-0.251609 - 0.130662i) q^{10} +(-1.47592 - 2.97013i) q^{11} +(0.959026 + 1.31999i) q^{13} +(3.27300 + 0.544366i) q^{14} +(3.30722 - 2.24995i) q^{16} +(-2.69920 - 1.96108i) q^{17} +(4.68224 - 1.52135i) q^{19} +(-0.129781 + 0.379363i) q^{20} +(-3.84307 + 2.68902i) q^{22} +9.25109 q^{23} +(1.53267 + 4.71706i) q^{25} +(1.64416 - 1.61893i) q^{26} +(0.0725573 - 4.69175i) q^{28} +(5.88863 + 1.91333i) q^{29} +(6.68182 - 4.85463i) q^{31} +(-3.84241 - 4.15161i) q^{32} +(-2.17453 + 4.18741i) q^{34} +(0.276461 + 0.380516i) q^{35} +(1.21740 + 0.395559i) q^{37} +(-3.11283 - 6.22784i) q^{38} +(0.557837 + 0.101668i) q^{40} +(1.86354 + 5.73540i) q^{41} -2.47184i q^{43} +(4.56919 + 4.80859i) q^{44} +(-1.94666 - 12.9374i) q^{46} +(-1.47060 - 4.52605i) q^{47} +(1.20994 + 0.879070i) q^{49} +(6.27416 - 3.13598i) q^{50} +(-2.61000 - 1.95864i) q^{52} +(-5.14997 - 7.08833i) q^{53} +(-0.655632 - 0.110613i) q^{55} +(-6.57654 + 0.885793i) q^{56} +(1.43662 - 8.63770i) q^{58} +(-1.81173 - 0.588668i) q^{59} +(-3.75888 + 5.17366i) q^{61} +(-8.19508 - 8.32280i) q^{62} +(-4.99736 + 6.24711i) q^{64} +0.327092 q^{65} +8.27349i q^{67} +(6.31354 + 2.15989i) q^{68} +(0.473966 - 0.466692i) q^{70} +(-1.00994 - 0.733765i) q^{71} +(2.13073 - 6.55770i) q^{73} +(0.297005 - 1.78574i) q^{74} +(-8.05444 + 5.66370i) q^{76} +(7.69737 - 1.13990i) q^{77} +(11.8293 - 8.59451i) q^{79} +(0.0247966 - 0.801513i) q^{80} +(7.62865 - 3.81298i) q^{82} +(-5.50905 + 7.58255i) q^{83} +(-0.636123 + 0.206689i) q^{85} +(-3.45680 + 0.520139i) q^{86} +(5.76319 - 7.40173i) q^{88} -5.11129 q^{89} +(-3.64061 + 1.18291i) q^{91} +(-17.6829 + 5.44471i) q^{92} +(-6.02010 + 3.00899i) q^{94} +(0.304992 - 0.938668i) q^{95} +(-0.242496 + 0.176183i) q^{97} +(0.974753 - 1.87704i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - q^{4} - 10 q^{7} + 5 q^{8}+O(q^{10}) \) 40 * q + 5 * q^2 - q^4 - 10 * q^7 + 5 * q^8	\( 40 q + 5 q^{2} - q^{4} - 10 q^{7} + 5 q^{8} - 20 q^{10} - 2 q^{14} + 15 q^{16} + 6 q^{17} - 8 q^{20} - 35 q^{22} + 8 q^{23} - 4 q^{25} + 10 q^{26} + 32 q^{28} - 6 q^{31} - 20 q^{32} + 10 q^{34} - 12 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 18 q^{46} + 6 q^{47} - 4 q^{49} - 61 q^{50} + 20 q^{52} - 2 q^{55} + 32 q^{56} + 4 q^{58} - 48 q^{62} - 49 q^{64} + 36 q^{65} + 42 q^{68} - 8 q^{70} - 22 q^{71} - 6 q^{73} - 54 q^{74} - 134 q^{76} + 74 q^{79} + 44 q^{80} - 31 q^{82} + 15 q^{86} - 73 q^{88} + 16 q^{89} + 4 q^{92} - 100 q^{94} - 66 q^{95} + 10 q^{97} + 144 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 - q^4 - 10 * q^7 + 5 * q^8 - 20 * q^10 - 2 * q^14 + 15 * q^16 + 6 * q^17 - 8 * q^20 - 35 * q^22 + 8 * q^23 - 4 * q^25 + 10 * q^26 + 32 * q^28 - 6 * q^31 - 20 * q^32 + 10 * q^34 - 12 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 18 * q^46 + 6 * q^47 - 4 * q^49 - 61 * q^50 + 20 * q^52 - 2 * q^55 + 32 * q^56 + 4 * q^58 - 48 * q^62 - 49 * q^64 + 36 * q^65 + 42 * q^68 - 8 * q^70 - 22 * q^71 - 6 * q^73 - 54 * q^74 - 134 * q^76 + 74 * q^79 + 44 * q^80 - 31 * q^82 + 15 * q^86 - 73 * q^88 + 16 * q^89 + 4 * q^92 - 100 * q^94 - 66 * q^95 + 10 * q^97 + 144 * q^98

Introduction

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