LMFDB - Embedded newform 495.2.n.h.136.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (of order $5$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 5x^14 - 8x^13 + 47x^12 + 32x^11 + 171x^10 + 26x^9 + 360x^8 - 172x^7 + 471x^6 - 430x^5 + 383x^4 + 70x^3 + 17x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.4
Root			$0.431051 + 1.32664i$ of defining polynomial
Character	$\chi$	$=$	495.136
Dual form			495.2.n.h.91.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93752 + 1.40769i) q^{2} +(1.15436 + 3.55277i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.608715 + 1.87343i) q^{7} +(-1.28446 + 3.95317i) q^{8} +O(q^{10})$	\(q+(1.93752 + 1.40769i) q^{2} +(1.15436 + 3.55277i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.608715 + 1.87343i) q^{7} +(-1.28446 + 3.95317i) q^{8} +2.39491 q^{10} +(-1.69771 + 2.84917i) q^{11} +(-2.36251 - 1.71646i) q^{13} +(-1.45782 + 4.48671i) q^{14} +(-2.00919 + 1.45977i) q^{16} +(5.35593 - 3.89131i) q^{17} +(-1.10014 + 3.38588i) q^{19} +(3.02216 + 2.19573i) q^{20} +(-7.30012 + 3.13048i) q^{22} +2.78918 q^{23} +(0.309017 - 0.951057i) q^{25} +(-2.16116 - 6.65137i) q^{26} +(-5.95319 + 4.32525i) q^{28} +(-1.08698 - 3.34537i) q^{29} +(-6.56916 - 4.77277i) q^{31} +2.36545 q^{32} +15.8550 q^{34} +(1.59364 + 1.15785i) q^{35} +(1.36892 + 4.21310i) q^{37} +(-6.89783 + 5.01157i) q^{38} +(1.28446 + 3.95317i) q^{40} +(2.18726 - 6.73169i) q^{41} -10.8914 q^{43} +(-12.0822 - 2.74260i) q^{44} +(5.40411 + 3.92631i) q^{46} +(-0.00839056 + 0.0258235i) q^{47} +(2.52390 - 1.83372i) q^{49} +(1.93752 - 1.40769i) q^{50} +(3.37099 - 10.3749i) q^{52} +(-3.32464 - 2.41549i) q^{53} +(0.301222 + 3.30292i) q^{55} -8.18786 q^{56} +(2.60321 - 8.01186i) q^{58} +(-2.94011 - 9.04874i) q^{59} +(-2.50982 + 1.82349i) q^{61} +(-6.00930 - 18.4947i) q^{62} +(8.60150 + 6.24935i) q^{64} -2.92022 q^{65} +1.58295 q^{67} +(20.0076 + 14.5364i) q^{68} +(1.45782 + 4.48671i) q^{70} +(4.90133 - 3.56102i) q^{71} +(-0.733271 - 2.25678i) q^{73} +(-3.27844 + 10.0900i) q^{74} -13.2992 q^{76} +(-6.37115 - 1.44622i) q^{77} +(10.1442 + 7.37019i) q^{79} +(-0.767444 + 2.36195i) q^{80} +(13.7140 - 9.96381i) q^{82} +(4.08014 - 2.96440i) q^{83} +(2.04578 - 6.29628i) q^{85} +(-21.1024 - 15.3318i) q^{86} +(-9.08260 - 10.3710i) q^{88} +12.0573 q^{89} +(1.77758 - 5.47084i) q^{91} +(3.21973 + 9.90931i) q^{92} +(-0.0526085 + 0.0382223i) q^{94} +(1.10014 + 3.38588i) q^{95} +(-8.42159 - 6.11864i) q^{97} +7.47144 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) $ 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8	$ 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} + 8 q^{10} - 4 q^{11} + 2 q^{13} + 22 q^{14} + 8 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 28 q^{22} - 8 q^{23} - 4 q^{25} - 6 q^{26} - 2 q^{28} + 26 q^{29} - 10 q^{31} - 56 q^{32} - 4 q^{34} + 4 q^{35} + 22 q^{37} + 30 q^{38} - 6 q^{40} + 6 q^{41} + 28 q^{43} - 68 q^{44} + 16 q^{46} + 20 q^{47} + 10 q^{49} + 2 q^{50} + 30 q^{52} - 14 q^{53} - 6 q^{55} - 68 q^{56} - 6 q^{58} + 16 q^{59} - 38 q^{61} + 20 q^{62} + 10 q^{64} - 12 q^{65} + 20 q^{67} + 48 q^{68} - 22 q^{70} + 54 q^{71} + 2 q^{73} - 28 q^{74} - 44 q^{76} - 34 q^{77} - 12 q^{79} + 22 q^{80} + 30 q^{82} + 28 q^{83} - 4 q^{85} - 74 q^{86} + 46 q^{88} - 76 q^{89} - 34 q^{91} + 8 q^{92} - 10 q^{94} + 4 q^{95} - 18 q^{97} - 8 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8 + 8 * q^10 - 4 * q^11 + 2 * q^13 + 22 * q^14 + 8 * q^16 + 4 * q^17 - 4 * q^19 - 2 * q^20 - 28 * q^22 - 8 * q^23 - 4 * q^25 - 6 * q^26 - 2 * q^28 + 26 * q^29 - 10 * q^31 - 56 * q^32 - 4 * q^34 + 4 * q^35 + 22 * q^37 + 30 * q^38 - 6 * q^40 + 6 * q^41 + 28 * q^43 - 68 * q^44 + 16 * q^46 + 20 * q^47 + 10 * q^49 + 2 * q^50 + 30 * q^52 - 14 * q^53 - 6 * q^55 - 68 * q^56 - 6 * q^58 + 16 * q^59 - 38 * q^61 + 20 * q^62 + 10 * q^64 - 12 * q^65 + 20 * q^67 + 48 * q^68 - 22 * q^70 + 54 * q^71 + 2 * q^73 - 28 * q^74 - 44 * q^76 - 34 * q^77 - 12 * q^79 + 22 * q^80 + 30 * q^82 + 28 * q^83 - 4 * q^85 - 74 * q^86 + 46 * q^88 - 76 * q^89 - 34 * q^91 + 8 * q^92 - 10 * q^94 + 4 * q^95 - 18 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	1.93752	+	1.40769i	1.37004	+	0.995390i	0.997734	+	0.0672778i	$0.0214314\pi$
$2$	1.93752	+	1.40769i	1.37004	+	0.995390i	0.372302	+	0.928112i	$0.378569\pi$
$3$		0			0
$3$		0			0
$4$	1.15436	+	3.55277i	0.577182	+	1.77638i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	0.608715	+	1.87343i	0.230073	+	0.708091i	0.997737	+	0.0672388i	$0.0214189\pi$
$7$	0.608715	+	1.87343i	0.230073	+	0.708091i	−0.767664	+	0.640852i	$0.778581\pi$
$8$	−1.28446	+	3.95317i	−0.454126	+	1.39766i
$9$		0			0
$10$	2.39491			0.757337
$11$	−1.69771	+	2.84917i	−0.511880	+	0.859057i
$11$	−1.69771	+	2.84917i	−0.511880	+	0.859057i
$12$		0			0
$13$	−2.36251	−	1.71646i	−0.655241	−	0.476061i	0.209811	−	0.977742i	$-0.432715\pi$
$13$	−2.36251	−	1.71646i	−0.655241	−	0.476061i	−0.865053	+	0.501681i	$0.832715\pi$
$14$	−1.45782	+	4.48671i	−0.389619	+	1.19912i
$15$		0			0
$16$	−2.00919	+	1.45977i	−0.502299	+	0.364941i
$17$	5.35593	−	3.89131i	1.29900	−	0.943782i	0.299059	−	0.954235i	$-0.403327\pi$
$17$	5.35593	−	3.89131i	1.29900	−	0.943782i	0.999945	+	0.0104529i	$0.00332731\pi$
$18$		0			0
$19$	−1.10014	+	3.38588i	−0.252389	+	0.776775i	0.741943	+	0.670463i	$0.233904\pi$
$19$	−1.10014	+	3.38588i	−0.252389	+	0.776775i	−0.994333	+	0.106312i	$0.966096\pi$
$20$	3.02216	+	2.19573i	0.675776	+	0.490980i
$21$		0			0
$22$	−7.30012	+	3.13048i	−1.55639	+	0.667420i
$23$	2.78918			0.581585			0.290792	−	0.956786i	$-0.406081\pi$
$23$	2.78918			0.581585			0.290792	+	0.956786i	$0.406081\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−2.16116	−	6.65137i	−0.423839	−	1.30444i
$27$		0			0
$28$	−5.95319	+	4.32525i	−1.12505	+	0.817395i
$29$	−1.08698	−	3.34537i	−0.201846	−	0.621219i	−0.999828	−	0.0185376i	$-0.994099\pi$
$29$	−1.08698	−	3.34537i	−0.201846	−	0.621219i	0.797982	−	0.602682i	$-0.205901\pi$
$30$		0			0
$31$	−6.56916	−	4.77277i	−1.17986	−	0.857215i	−0.187700	−	0.982226i	$-0.560103\pi$
$31$	−6.56916	−	4.77277i	−1.17986	−	0.857215i	−0.992155	+	0.125011i	$0.960103\pi$
$32$	2.36545			0.418156
$33$		0			0
$34$	15.8550			2.71911
$35$	1.59364	+	1.15785i	0.269374	+	0.195712i
$36$		0			0
$37$	1.36892	+	4.21310i	0.225049	+	0.692629i	0.998287	+	0.0585129i	$0.0186359\pi$
$37$	1.36892	+	4.21310i	0.225049	+	0.692629i	−0.773238	+	0.634116i	$0.781364\pi$
$38$	−6.89783	+	5.01157i	−1.11898	+	0.812984i
$39$		0			0
$40$	1.28446	+	3.95317i	0.203091	+	0.625050i
$41$	2.18726	−	6.73169i	0.341592	−	1.05131i	−0.621791	−	0.783183i	$-0.713595\pi$
$41$	2.18726	−	6.73169i	0.341592	−	1.05131i	0.963383	−	0.268129i	$-0.0864054\pi$
$42$		0			0
$43$	−10.8914			−1.66092			−0.830462	−	0.557075i	$-0.811924\pi$
$43$	−10.8914			−1.66092			−0.830462	+	0.557075i	$0.811924\pi$
$44$	−12.0822	−	2.74260i	−1.82146	−	0.413462i
$45$		0			0
$46$	5.40411	+	3.92631i	0.796792	+	0.578903i
$47$	−0.00839056	+	0.0258235i	−0.00122389	+	0.00376674i	−0.951667	−	0.307133i	$-0.900630\pi$
$47$	−0.00839056	+	0.0258235i	−0.00122389	+	0.00376674i	0.950443	+	0.310900i	$0.100630\pi$
$48$		0			0
$49$	2.52390	−	1.83372i	0.360557	−	0.261960i
$50$	1.93752	−	1.40769i	0.274007	−	0.199078i
$51$		0			0
$52$	3.37099	−	10.3749i	0.467473	−	1.43873i
$53$	−3.32464	−	2.41549i	−0.456675	−	0.331794i	0.335551	−	0.942022i	$-0.391078\pi$
$53$	−3.32464	−	2.41549i	−0.456675	−	0.331794i	−0.792225	+	0.610229i	$0.791078\pi$
$54$		0			0
$55$	0.301222	+	3.30292i	0.0406167	+	0.445365i
$56$	−8.18786			−1.09415
$57$		0			0
$58$	2.60321	−	8.01186i	0.341818	−	1.05201i
$59$	−2.94011	−	9.04874i	−0.382770	−	1.17805i	−0.938085	−	0.346405i	$-0.887402\pi$
$59$	−2.94011	−	9.04874i	−0.382770	−	1.17805i	0.555315	−	0.831640i	$-0.312598\pi$
$60$		0			0
$61$	−2.50982	+	1.82349i	−0.321349	+	0.233474i	−0.736751	−	0.676164i	$-0.763641\pi$
$61$	−2.50982	+	1.82349i	−0.321349	+	0.233474i	0.415402	+	0.909638i	$0.363641\pi$
$62$	−6.00930	−	18.4947i	−0.763182	−	2.34883i
$63$		0			0
$64$	8.60150	+	6.24935i	1.07519	+	0.781169i
$65$	−2.92022			−0.362209
$66$		0			0
$67$	1.58295			0.193388			0.0966939	−	0.995314i	$-0.469173\pi$
$67$	1.58295			0.193388			0.0966939	+	0.995314i	$0.469173\pi$
$68$	20.0076	+	14.5364i	2.42628	+	1.76280i
$69$		0			0
$70$	1.45782	+	4.48671i	0.174243	+	0.536264i
$71$	4.90133	−	3.56102i	0.581680	−	0.422616i	−0.257649	−	0.966239i	$-0.582948\pi$
$71$	4.90133	−	3.56102i	0.581680	−	0.422616i	0.839330	+	0.543623i	$0.182948\pi$
$72$		0			0
$73$	−0.733271	−	2.25678i	−0.0858229	−	0.264136i	0.898931	−	0.438091i	$-0.144345\pi$
$73$	−0.733271	−	2.25678i	−0.0858229	−	0.264136i	−0.984754	+	0.173955i	$0.944345\pi$
$74$	−3.27844	+	10.0900i	−0.381111	+	1.17294i
$75$		0			0
$76$	−13.2992			−1.52552
$77$	−6.37115	−	1.44622i	−0.726060	−	0.164812i
$78$		0			0
$79$	10.1442	+	7.37019i	1.14131	+	0.829212i	0.987301	−	0.158858i	$-0.0507811\pi$
$79$	10.1442	+	7.37019i	1.14131	+	0.829212i	0.154010	+	0.988069i	$0.450781\pi$
$80$	−0.767444	+	2.36195i	−0.0858029	+	0.264074i
$81$		0			0
$82$	13.7140	−	9.96381i	1.51446	−	1.10032i
$83$	4.08014	−	2.96440i	0.447854	−	0.325385i	−0.340894	−	0.940102i	$-0.610730\pi$
$83$	4.08014	−	2.96440i	0.447854	−	0.325385i	0.788748	+	0.614717i	$0.210730\pi$
$84$		0			0
$85$	2.04578	−	6.29628i	0.221896	−	0.682927i
$86$	−21.1024	−	15.3318i	−2.27553	−	1.65327i
$87$		0			0
$88$	−9.08260	−	10.3710i	−0.968208	−	1.10555i
$89$	12.0573			1.27807			0.639035	−	0.769177i	$-0.279334\pi$
$89$	12.0573			1.27807			0.639035	+	0.769177i	$0.279334\pi$
$90$		0			0
$91$	1.77758	−	5.47084i	0.186341	−	0.573499i
$92$	3.21973	+	9.90931i	0.335680	+	1.03312i
$93$		0			0
$94$	−0.0526085	+	0.0382223i	−0.00542615	+	0.00394233i
$95$	1.10014	+	3.38588i	0.112872	+	0.347384i
$96$		0			0
$97$	−8.42159	−	6.11864i	−0.855083	−	0.621254i	0.0714597	−	0.997443i	$-0.477234\pi$
$97$	−8.42159	−	6.11864i	−0.855083	−	0.621254i	−0.926543	+	0.376189i	$0.877234\pi$
$98$	7.47144			0.754729
$99$		0			0
$100$	3.73560			0.373560
$101$	13.9285	+	10.1196i	1.38594	+	1.00694i	0.996297	+	0.0859743i	$0.0274003\pi$
$101$	13.9285	+	10.1196i	1.38594	+	1.00694i	0.389639	+	0.920968i	$0.372600\pi$
$102$		0			0
$103$	2.06114	+	6.34353i	0.203090	+	0.625047i	0.999786	+	0.0206671i	$0.00657902\pi$
$103$	2.06114	+	6.34353i	0.203090	+	0.625047i	−0.796696	+	0.604380i	$0.793421\pi$
$104$	9.82001	−	7.13465i	0.962931	−	0.699610i
$105$		0			0
$106$	−3.04130	−	9.36015i	−0.295397	−	0.909138i
$107$	−2.97246	+	9.14829i	−0.287359	+	0.884399i	0.698323	+	0.715783i	$0.253930\pi$
$107$	−2.97246	+	9.14829i	−0.287359	+	0.884399i	−0.985682	+	0.168616i	$0.946070\pi$
$108$		0			0
$109$	−19.2602			−1.84480			−0.922398	−	0.386240i	$-0.873773\pi$
$109$	−19.2602			−1.84480			−0.922398	+	0.386240i	$0.873773\pi$
$110$	−4.06587	+	6.82351i	−0.387666	+	0.650596i
$111$		0			0
$112$	−3.95780	−	2.87551i	−0.373977	−	0.271710i
$113$	−1.10098	+	3.38846i	−0.103571	+	0.318759i	−0.989392	−	0.145267i	$-0.953596\pi$
$113$	−1.10098	+	3.38846i	−0.103571	+	0.318759i	0.885821	+	0.464026i	$0.153596\pi$
$114$		0			0
$115$	2.25650	−	1.63944i	0.210419	−	0.152879i
$116$	10.6305	−	7.72354i	0.987021	−	0.717113i
$117$		0			0
$118$	7.04131	−	21.6709i	0.648205	−	1.99497i
$119$	10.5504	+	7.66528i	0.967149	+	0.702675i
$120$		0			0
$121$	−5.23554	−	9.67415i	−0.475958	−	0.879468i
$122$	−7.42975			−0.672658
$123$		0			0
$124$	9.37334	−	28.8482i	0.841751	−	2.59064i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	−15.6285	+	11.3548i	−1.38681	+	1.00757i	−0.390601	+	0.920560i	$0.627733\pi$
$127$	−15.6285	+	11.3548i	−1.38681	+	1.00757i	−0.996207	+	0.0870147i	$0.972267\pi$
$128$	6.40650	+	19.7172i	0.566260	+	1.74277i
$129$		0			0
$130$	−5.65799	−	4.11077i	−0.496239	−	0.360539i
$131$	−13.9027			−1.21468			−0.607341	−	0.794441i	$-0.707764\pi$
$131$	−13.9027			−1.21468			−0.607341	+	0.794441i	$0.707764\pi$
$132$		0			0
$133$	−7.01290			−0.608096
$134$	3.06700	+	2.22830i	0.264948	+	0.192496i
$135$		0			0
$136$	8.50351	+	26.1711i	0.729170	+	2.24416i
$137$	−18.3865	+	13.3586i	−1.57086	+	1.14130i	−0.644541	+	0.764570i	$0.722951\pi$
$137$	−18.3865	+	13.3586i	−1.57086	+	1.14130i	−0.926323	+	0.376730i	$0.877049\pi$
$138$		0			0
$139$	3.92759	+	12.0879i	0.333134	+	1.02528i	0.967634	+	0.252358i	$0.0812062\pi$
$139$	3.92759	+	12.0879i	0.333134	+	1.02528i	−0.634500	+	0.772923i	$0.718794\pi$
$140$	−2.27392	+	6.99840i	−0.192181	+	0.591472i
$141$		0			0
$142$	14.5093			1.21759
$143$	8.90135	−	3.81712i	0.744368	−	0.319204i
$144$		0			0
$145$	−2.84574	−	2.06755i	−0.236326	−	0.171701i
$146$	1.75612	−	5.40478i	0.145337	−	0.447303i
$147$		0			0
$148$	−13.3879	+	9.72689i	−1.10048	+	0.799546i
$149$	−3.48099	+	2.52909i	−0.285174	+	0.207191i	−0.721171	−	0.692757i	$-0.756396\pi$
$149$	−3.48099	+	2.52909i	−0.285174	+	0.207191i	0.435997	+	0.899948i	$0.356396\pi$
$150$		0			0
$151$	5.43388	−	16.7238i	0.442203	−	1.36096i	−0.443320	−	0.896364i	$-0.646199\pi$
$151$	5.43388	−	16.7238i	0.442203	−	1.36096i	0.885522	−	0.464597i	$-0.153801\pi$
$152$	−11.9719	−	8.69807i	−0.971047	−	0.705507i
$153$		0			0
$154$	−10.3084	−	11.7707i	−0.830677	−	0.948511i
$155$	−8.11992			−0.652208
$156$		0			0
$157$	−7.35808	+	22.6458i	−0.587239	+	1.80733i	0.00284976	+	0.999996i	$0.499093\pi$
$157$	−7.35808	+	22.6458i	−0.587239	+	1.80733i	−0.590088	+	0.807339i	$0.700907\pi$
$158$	9.27966	+	28.5598i	0.738250	+	2.27210i
$159$		0			0
$160$	1.91369	−	1.39037i	0.151290	−	0.109919i
$161$	1.69782	+	5.22535i	0.133807	+	0.411815i
$162$		0			0
$163$	16.0551	+	11.6647i	1.25753	+	0.913651i	0.998634	−	0.0522532i	$-0.0166403\pi$
$163$	16.0551	+	11.6647i	1.25753	+	0.913651i	0.258899	+	0.965904i	$0.416640\pi$
$164$	26.4410			2.06469
$165$		0			0
$166$	12.0783			0.937460
$167$	−11.7113	−	8.50878i	−0.906250	−	0.658429i	0.0338134	−	0.999428i	$-0.489235\pi$
$167$	−11.7113	−	8.50878i	−0.906250	−	0.658429i	−0.940064	+	0.340999i	$0.889235\pi$
$168$		0			0
$169$	−1.38202	−	4.25343i	−0.106310	−	0.327187i
$170$	12.8270	−	9.31935i	0.983784	−	0.714761i
$171$		0			0
$172$	−12.5726	−	38.6946i	−0.958655	−	2.95044i
$173$	−1.33466	+	4.10765i	−0.101472	+	0.312299i	−0.988886	−	0.148674i	$-0.952500\pi$
$173$	−1.33466	+	4.10765i	−0.101472	+	0.312299i	0.887414	+	0.460973i	$0.152500\pi$
$174$		0			0
$175$	1.96984			0.148906
$176$	−0.748084	−	8.20280i	−0.0563890	−	0.618309i
$177$		0			0
$178$	23.3613	+	16.9730i	1.75100	+	1.27218i
$179$	2.30499	−	7.09404i	0.172283	−	0.530233i	−0.827216	−	0.561884i	$-0.810077\pi$
$179$	2.30499	−	7.09404i	0.172283	−	0.530233i	0.999499	+	0.0316512i	$0.0100766\pi$
$180$		0			0
$181$	16.5553	−	12.0281i	1.23054	−	0.894043i	0.233613	−	0.972330i	$-0.424945\pi$
$181$	16.5553	−	12.0281i	1.23054	−	0.894043i	0.996931	+	0.0782870i	$0.0249450\pi$
$182$	11.1454	−	8.09758i	0.826149	−	0.600233i
$183$		0			0
$184$	−3.58260	+	11.0261i	−0.264113	+	0.812855i
$185$	3.58388	+	2.60384i	0.263492	+	0.191438i
$186$		0			0
$187$	1.99418	+	21.8663i	0.145829	+	1.59902i
$188$	−0.101431			−0.00739759
$189$		0			0
$190$	−2.63474	+	8.10889i	−0.191144	+	0.588281i
$191$	−2.02460	−	6.23107i	−0.146495	−	0.450865i	0.850705	−	0.525643i	$-0.176175\pi$
$191$	−2.02460	−	6.23107i	−0.146495	−	0.450865i	−0.997200	+	0.0747781i	$0.976175\pi$
$192$		0			0
$193$	5.52218	−	4.01210i	0.397495	−	0.288797i	−0.371025	−	0.928623i	$-0.620994\pi$
$193$	5.52218	−	4.01210i	0.397495	−	0.288797i	0.768520	+	0.639826i	$0.220994\pi$
$194$	−7.70386	−	23.7100i	−0.553105	−	1.70228i
$195$		0			0
$196$	9.42828	+	6.85005i	0.673449	+	0.489289i
$197$	−3.45091			−0.245867			−0.122934	−	0.992415i	$-0.539230\pi$
$197$	−3.45091			−0.245867			−0.122934	+	0.992415i	$0.539230\pi$
$198$		0			0
$199$	−10.6742			−0.756671			−0.378336	−	0.925668i	$-0.623504\pi$
$199$	−10.6742			−0.756671			−0.378336	+	0.925668i	$0.623504\pi$
$200$	3.36276	+	2.44319i	0.237783	+	0.172760i
$201$		0			0
$202$	12.7414	+	39.2141i	0.896484	+	2.75909i
$203$	5.60566	−	4.07275i	0.393441	−	0.285851i
$204$		0			0
$205$	−2.18726	−	6.73169i	−0.152765	−	0.470161i
$206$	−4.93624	+	15.1922i	−0.343924	+	1.05849i
$207$		0			0
$208$	7.25237			0.502861
$209$	−7.77924	−	8.88275i	−0.538101	−	0.614432i
$210$		0			0
$211$	1.11582	+	0.810693i	0.0768164	+	0.0558104i	0.625531	−	0.780200i	$-0.284883\pi$
$211$	1.11582	+	0.810693i	0.0768164	+	0.0558104i	−0.548714	+	0.836010i	$0.684883\pi$
$212$	4.74384	−	14.6000i	0.325808	−	1.00273i
$213$		0			0
$214$	−18.6372	+	13.5407i	−1.27401	+	0.925624i
$215$	−8.81134	+	6.40181i	−0.600928	+	0.436600i
$216$		0			0
$217$	4.94272	−	15.2121i	0.335534	−	1.03267i
$218$	−37.3172	−	27.1125i	−2.52744	−	1.83629i
$219$		0			0
$220$	−11.3868	+	4.88294i	−0.767696	+	0.329208i
$221$	−19.3327			−1.30046
$222$		0			0
$223$	3.74028	−	11.5114i	0.250468	−	0.770861i	−0.744221	−	0.667933i	$-0.767179\pi$
$223$	3.74028	−	11.5114i	0.250468	−	0.770861i	0.994689	−	0.102927i	$-0.0328209\pi$
$224$	1.43988	+	4.43150i	0.0962062	+	0.296092i
$225$		0			0
$226$	−6.90307	+	5.01538i	−0.459186	+	0.333618i
$227$	5.35589	+	16.4837i	0.355483	+	1.09406i	0.955729	+	0.294248i	$0.0950692\pi$
$227$	5.35589	+	16.4837i	0.355483	+	1.09406i	−0.600246	+	0.799815i	$0.704931\pi$
$228$		0			0
$229$	0.677291	+	0.492081i	0.0447567	+	0.0325176i	0.609939	−	0.792449i	$-0.291194\pi$
$229$	0.677291	+	0.492081i	0.0447567	+	0.0325176i	−0.565182	+	0.824966i	$0.691194\pi$
$230$	6.67984			0.440456
$231$		0			0
$232$	14.6210			0.959914
$233$	−15.4102	−	11.1962i	−1.00956	−	0.733487i	−0.0454418	−	0.998967i	$-0.514470\pi$
$233$	−15.4102	−	11.1962i	−1.00956	−	0.733487i	−0.964116	+	0.265480i	$0.914470\pi$
$234$		0			0
$235$	0.00839056	+	0.0258235i	0.000547340	+	0.00168454i
$236$	28.7541	−	20.8911i	1.87173	−	1.35989i
$237$		0			0
$238$	9.65119	+	29.7033i	0.625594	+	1.92538i
$239$	−7.97065	+	24.5311i	−0.515578	+	1.58679i	0.266649	+	0.963794i	$0.414084\pi$
$239$	−7.97065	+	24.5311i	−0.515578	+	1.58679i	−0.782227	+	0.622993i	$0.785916\pi$
$240$		0			0
$241$	−17.0680			−1.09944			−0.549722	−	0.835348i	$-0.685266\pi$
$241$	−17.0680			−1.09944			−0.549722	+	0.835348i	$0.685266\pi$
$242$	3.47425	−	26.1139i	0.223333	−	1.67867i
$243$		0			0
$244$	−9.37568	−	6.81183i	−0.600216	−	0.436083i
$245$	0.964044	−	2.96702i	0.0615905	−	0.189556i
$246$		0			0
$247$	8.41083	−	6.11082i	0.535168	−	0.388822i
$248$	27.3054	−	19.8385i	1.73389	−	1.25975i
$249$		0			0
$250$	0.740068	−	2.27770i	0.0468060	−	0.144054i
$251$	−8.34630	−	6.06394i	−0.526814	−	0.382752i	0.292351	−	0.956311i	$-0.405562\pi$
$251$	−8.34630	−	6.06394i	−0.526814	−	0.382752i	−0.819164	+	0.573559i	$0.805562\pi$
$252$		0			0
$253$	−4.73523	+	7.94685i	−0.297701	+	0.499614i
$254$	−46.2647			−2.90291
$255$		0			0
$256$	−8.77205	+	26.9976i	−0.548253	+	1.68735i
$257$	3.48064	+	10.7123i	0.217117	+	0.668216i	0.998997	+	0.0447871i	$0.0142609\pi$
$257$	3.48064	+	10.7123i	0.217117	+	0.668216i	−0.781880	+	0.623429i	$0.785739\pi$
$258$		0			0
$259$	−7.05968	+	5.12916i	−0.438667	+	0.318710i
$260$	−3.37099	−	10.3749i	−0.209060	−	0.643421i
$261$		0			0
$262$	−26.9368	−	19.5707i	−1.66416	−	1.20908i
$263$	−5.15082			−0.317613			−0.158806	−	0.987310i	$-0.550765\pi$
$263$	−5.15082			−0.317613			−0.158806	+	0.987310i	$0.550765\pi$
$264$		0			0
$265$	−4.10948			−0.252444
$266$	−13.5877	−	9.87201i	−0.833113	−	0.605292i
$267$		0			0
$268$	1.82730	+	5.62384i	0.111620	+	0.343531i
$269$	18.7305	−	13.6085i	1.14202	−	0.829725i	0.154619	−	0.987974i	$-0.450585\pi$
$269$	18.7305	−	13.6085i	1.14202	−	0.829725i	0.987399	+	0.158249i	$0.0505849\pi$
$270$		0			0
$271$	4.06201	+	12.5016i	0.246749	+	0.759417i	0.995344	+	0.0963885i	$0.0307291\pi$
$271$	4.06201	+	12.5016i	0.246749	+	0.759417i	−0.748594	+	0.663028i	$0.769271\pi$
$272$	−5.08071	+	15.6368i	−0.308063	+	0.948121i
$273$		0			0
$274$	−54.4290			−3.28818
$275$	2.18510	+	2.49506i	0.131766	+	0.150458i
$276$		0			0
$277$	−8.37246	−	6.08295i	−0.503052	−	0.365489i	0.307129	−	0.951668i	$-0.400632\pi$
$277$	−8.37246	−	6.08295i	−0.503052	−	0.365489i	−0.810182	+	0.586179i	$0.800632\pi$
$278$	−9.40624	+	28.9494i	−0.564149	+	1.73627i
$279$		0			0
$280$	−6.62412	+	4.81271i	−0.395867	+	0.287614i
$281$	0.313106	−	0.227485i	0.0186783	−	0.0135706i	−0.578407	−	0.815748i	$-0.696325\pi$
$281$	0.313106	−	0.227485i	0.0186783	−	0.0135706i	0.597085	+	0.802178i	$0.296325\pi$
$282$		0			0
$283$	−4.48858	+	13.8144i	−0.266818	+	0.821182i	0.724451	+	0.689327i	$0.242094\pi$
$283$	−4.48858	+	13.8144i	−0.266818	+	0.821182i	−0.991269	+	0.131856i	$0.957906\pi$
$284$	18.3094	+	13.3026i	1.08646	+	0.789361i
$285$		0			0
$286$	22.6199	+	5.13460i	1.33754	+	0.303615i
$287$	13.9428			0.823016
$288$		0			0
$289$	8.29040	−	25.5152i	0.487671	−	1.50090i
$290$	−2.60321	−	8.01186i	−0.152866	−	0.470472i
$291$		0			0
$292$	7.17134	−	5.21028i	0.419671	−	0.304909i
$293$	4.57888	+	14.0923i	0.267501	+	0.823284i	0.991107	+	0.133070i	$0.0424835\pi$
$293$	4.57888	+	14.0923i	0.267501	+	0.823284i	−0.723606	+	0.690214i	$0.757517\pi$
$294$		0			0
$295$	−7.69732	−	5.59243i	−0.448155	−	0.325604i
$296$	−18.4134			−1.07026
$297$		0			0
$298$	−10.3047			−0.596934
$299$	−6.58946	−	4.78752i	−0.381078	−	0.276870i
$300$		0			0
$301$	−6.62977	−	20.4043i	−0.382134	−	1.17609i
$302$	34.0702	−	24.7534i	1.96052	−	1.42440i
$303$		0			0
$304$	−2.73220	−	8.40885i	−0.156702	−	0.482280i
$305$	−0.958666	+	2.95047i	−0.0548930	+	0.168943i
$306$		0			0
$307$	32.3539			1.84653			0.923266	−	0.384161i	$-0.125509\pi$
$307$	32.3539			1.84653			0.923266	+	0.384161i	$0.125509\pi$
$308$	−2.21655	−	24.3047i	−0.126300	−	1.38489i
$309$		0			0
$310$	−15.7325	−	11.4304i	−0.893549	−	0.649201i
$311$	−0.544966	+	1.67723i	−0.0309022	+	0.0951072i	−0.965318	−	0.261077i	$-0.915922\pi$
$311$	−0.544966	+	1.67723i	−0.0309022	+	0.0951072i	0.934416	+	0.356184i	$0.115922\pi$
$312$		0			0
$313$	21.1748	−	15.3844i	1.19687	−	0.869577i	0.202897	−	0.979200i	$-0.434964\pi$
$313$	21.1748	−	15.3844i	1.19687	−	0.869577i	0.993973	+	0.109623i	$0.0349643\pi$
$314$	−46.1348	+	33.5189i	−2.60354	+	1.89158i
$315$		0			0
$316$	−14.4745	+	44.5479i	−0.814253	+	2.50601i
$317$	8.39392	+	6.09854i	0.471450	+	0.342528i	0.798006	−	0.602650i	$-0.205888\pi$
$317$	8.39392	+	6.09854i	0.471450	+	0.342528i	−0.326556	+	0.945178i	$0.605888\pi$
$318$		0			0
$319$	11.3769	+	2.58249i	0.636984	+	0.144592i
$320$	10.6320			0.594349
$321$		0			0
$322$	−4.06612	+	12.5142i	−0.226596	+	0.697391i
$323$	7.28325	+	22.4156i	0.405251	+	1.24723i
$324$		0			0
$325$	−2.36251	+	1.71646i	−0.131048	+	0.0952122i
$326$	14.6868	+	45.2013i	0.813427	+	2.50347i
$327$		0			0
$328$	23.8020	+	17.2932i	1.31425	+	0.954856i
$329$	−0.0534861			−0.00294878
$330$		0			0
$331$	9.22380			0.506986			0.253493	−	0.967337i	$-0.418421\pi$
$331$	9.22380			0.506986			0.253493	+	0.967337i	$0.418421\pi$
$332$	15.2418	+	11.0738i	0.836501	+	0.607753i
$333$		0			0
$334$	−10.7132	−	32.9719i	−0.586202	−	1.80414i
$335$	1.28063	−	0.930433i	0.0699684	−	0.0508350i
$336$		0			0
$337$	8.81849	+	27.1405i	0.480374	+	1.47844i	0.838571	+	0.544792i	$0.183392\pi$
$337$	8.81849	+	27.1405i	0.480374	+	1.47844i	−0.358197	+	0.933646i	$0.616608\pi$
$338$	3.30982	−	10.1866i	0.180031	−	0.554077i
$339$		0			0
$340$	24.7308			1.34121
$341$	24.7510	−	10.6138i	1.34034	−	0.574772i
$342$		0			0
$343$	16.1272	+	11.7171i	0.870785	+	0.632662i
$344$	13.9896	−	43.0555i	0.754268	−	2.32140i
$345$		0			0
$346$	−8.36825	+	6.07989i	−0.449880	+	0.326857i
$347$	−8.22756	+	5.97767i	−0.441679	+	0.320898i	−0.786302	−	0.617843i	$-0.788007\pi$
$347$	−8.22756	+	5.97767i	−0.441679	+	0.320898i	0.344623	+	0.938741i	$0.388007\pi$
$348$		0			0
$349$	−7.32909	+	22.5566i	−0.392317	+	1.20743i	0.538714	+	0.842489i	$0.318910\pi$
$349$	−7.32909	+	22.5566i	−0.392317	+	1.20743i	−0.931031	+	0.364940i	$0.881090\pi$
$350$	3.81662	+	2.77294i	0.204007	+	0.148220i
$351$		0			0
$352$	−4.01585	+	6.73956i	−0.214045	+	0.359220i
$353$	−14.1383			−0.752504			−0.376252	−	0.926517i	$-0.622787\pi$
$353$	−14.1383			−0.752504			−0.376252	+	0.926517i	$0.622787\pi$
$354$		0			0
$355$	1.87214	−	5.76186i	0.0993629	−	0.305808i
$356$	13.9185	+	42.8367i	0.737679	+	2.27034i
$357$		0			0
$358$	14.4522	−	10.5001i	0.763823	−	0.554950i
$359$	−7.42661	−	22.8568i	−0.391962	−	1.20633i	−0.931303	−	0.364246i	$-0.881327\pi$
$359$	−7.42661	−	22.8568i	−0.391962	−	1.20633i	0.539341	−	0.842087i	$-0.318673\pi$
$360$		0			0
$361$	5.11742	+	3.71803i	0.269338	+	0.195686i
$362$	49.0081			2.57581
$363$		0			0
$364$	21.4886			1.12631
$365$	−1.91973	−	1.39476i	−0.100483	−	0.0730053i
$366$		0			0
$367$	−0.555320	−	1.70910i	−0.0289875	−	0.0892143i	0.935516	−	0.353284i	$-0.114935\pi$
$367$	−0.555320	−	1.70910i	−0.0289875	−	0.0892143i	−0.964504	+	0.264070i	$0.914935\pi$
$368$	−5.60401	+	4.07155i	−0.292129	+	0.212244i
$369$		0			0
$370$	3.27844	+	10.0900i	0.170438	+	0.524554i
$371$	2.50151	−	7.69884i	0.129872	−	0.399704i
$372$		0			0
$373$	−6.87802			−0.356131			−0.178065	−	0.984019i	$-0.556984\pi$
$373$	−6.87802			−0.356131			−0.178065	+	0.984019i	$0.556984\pi$
$374$	−26.9173	+	45.1736i	−1.39186	+	2.33587i
$375$		0			0
$376$	−0.0913072	−	0.0663386i	−0.00470881	−	0.00342115i
$377$	−3.17421	+	9.76920i	−0.163480	+	0.503140i
$378$		0			0
$379$	2.85849	−	2.07682i	0.146831	−	0.106679i	−0.511945	−	0.859018i	$-0.671075\pi$
$379$	2.85849	−	2.07682i	0.146831	−	0.106679i	0.658776	+	0.752340i	$0.271075\pi$
$380$	−10.7593	+	7.81708i	−0.551940	+	0.401008i
$381$		0			0
$382$	4.84873	−	14.9229i	0.248083	−	0.763520i
$383$	1.53984	+	1.11876i	0.0786821	+	0.0571659i	0.626431	−	0.779477i	$-0.284515\pi$
$383$	1.53984	+	1.11876i	0.0786821	+	0.0571659i	−0.547749	+	0.836643i	$0.684515\pi$
$384$		0			0
$385$	−6.00444	+	2.57486i	−0.306014	+	0.131227i
$386$	16.3472			0.832048
$387$		0			0
$388$	12.0165	−	36.9831i	0.610047	−	1.87753i
$389$	−2.16998	−	6.67850i	−0.110022	−	0.338613i	0.880854	−	0.473388i	$-0.156969\pi$
$389$	−2.16998	−	6.67850i	−0.110022	−	0.338613i	−0.990876	+	0.134774i	$0.956969\pi$
$390$		0			0
$391$	14.9387	−	10.8536i	0.755481	−	0.548889i
$392$	4.00715	+	12.3327i	0.202392	+	0.622898i
$393$		0			0
$394$	−6.68623	−	4.85783i	−0.336847	−	0.244734i
$395$	12.5389			0.630902
$396$		0			0
$397$	−12.5149			−0.628104			−0.314052	−	0.949406i	$-0.601687\pi$
$397$	−12.5149			−0.628104			−0.314052	+	0.949406i	$0.601687\pi$
$398$	−20.6814	−	15.0260i	−1.03667	−	0.753183i
$399$		0			0
$400$	0.767444	+	2.36195i	0.0383722	+	0.118097i
$401$	−22.1091	+	16.0632i	−1.10408	+	0.802160i	−0.981721	−	0.190326i	$-0.939045\pi$
$401$	−22.1091	+	16.0632i	−1.10408	+	0.802160i	−0.122357	+	0.992486i	$0.539045\pi$
$402$		0			0
$403$	7.32740	+	22.5514i	0.365004	+	1.12337i
$404$	−19.8742	+	61.1664i	−0.988777	+	3.04314i
$405$		0			0
$406$	16.5943			0.823561
$407$	−14.3279	−	3.25235i	−0.710206	−	0.161213i
$408$		0			0
$409$	9.38375	+	6.81769i	0.463997	+	0.337113i	0.795097	−	0.606482i	$-0.207420\pi$
$409$	9.38375	+	6.81769i	0.463997	+	0.337113i	−0.331100	+	0.943596i	$0.607420\pi$
$410$	5.23829	−	16.1218i	0.258701	−	0.796198i
$411$		0			0
$412$	−20.1578	+	14.6455i	−0.993103	+	0.721531i
$413$	15.1625	−	11.0162i	0.746099	−	0.542072i
$414$		0			0
$415$	1.55847	−	4.79649i	0.0765025	−	0.235451i
$416$	−5.58838	−	4.06020i	−0.273993	−	0.199067i
$417$		0			0
$418$	−2.56827	−	28.1613i	−0.125618	−	1.37741i
$419$	9.07542			0.443363			0.221682	−	0.975119i	$-0.428845\pi$
$419$	9.07542			0.443363			0.221682	+	0.975119i	$0.428845\pi$
$420$		0			0
$421$	5.72149	−	17.6089i	0.278848	−	0.858207i	−0.709327	−	0.704880i	$-0.751001\pi$
$421$	5.72149	−	17.6089i	0.278848	−	0.858207i	0.988175	−	0.153328i	$-0.0489989\pi$
$422$	1.02073	+	3.14147i	0.0496882	+	0.152925i
$423$		0			0
$424$	13.8192	−	10.0403i	0.671121	−	0.487598i
$425$	−2.04578	−	6.29628i	−0.0992351	−	0.305414i
$426$		0			0
$427$	−4.94395	−	3.59199i	−0.239255	−	0.173829i
$428$	−35.9330			−1.73689
$429$		0			0
$430$	−26.0840			−1.25788
$431$	20.0566	+	14.5719i	0.966091	+	0.701906i	0.954557	−	0.298028i	$-0.0963287\pi$
$431$	20.0566	+	14.5719i	0.966091	+	0.701906i	0.0115333	+	0.999933i	$0.496329\pi$
$432$		0			0
$433$	−10.9348	−	33.6539i	−0.525494	−	1.61730i	−0.763338	−	0.646000i	$-0.776441\pi$
$433$	−10.9348	−	33.6539i	−0.525494	−	1.61730i	0.237844	−	0.971303i	$-0.423559\pi$
$434$	30.9907	−	22.5160i	1.48760	−	1.08080i
$435$		0			0
$436$	−22.2333	−	68.4271i	−1.06478	−	3.27706i
$437$	−3.06849	+	9.44384i	−0.146786	+	0.451760i
$438$		0			0
$439$	−10.2916			−0.491192			−0.245596	−	0.969372i	$-0.578984\pi$
$439$	−10.2916			−0.491192			−0.245596	+	0.969372i	$0.578984\pi$
$440$	−13.4439	−	3.05169i	−0.640912	−	0.145484i
$441$		0			0
$442$	−37.4576	−	27.2145i	−1.78168	−	1.29446i
$443$	11.0783	−	34.0956i	0.526348	−	1.61993i	−0.235288	−	0.971926i	$-0.575603\pi$
$443$	11.0783	−	34.0956i	0.526348	−	1.61993i	0.761636	−	0.648006i	$-0.224397\pi$
$444$		0			0
$445$	9.75456	−	7.08710i	0.462410	−	0.335961i
$446$	23.4514	−	17.0384i	1.11046	−	0.806794i
$447$		0			0
$448$	−6.47188	+	19.9184i	−0.305768	+	0.941056i
$449$	21.7169	+	15.7783i	1.02489	+	0.744623i	0.967279	−	0.253716i	$-0.0816529\pi$
$449$	21.7169	+	15.7783i	1.02489	+	0.744623i	0.0576072	+	0.998339i	$0.481653\pi$
$450$		0			0
$451$	15.4664	+	17.6603i	0.728284	+	0.831593i
$452$	−13.3093			−0.626017
$453$		0			0
$454$	−12.8269	+	39.4771i	−0.601995	+	1.85275i
$455$	−1.77758	−	5.47084i	−0.0833343	−	0.256477i
$456$		0			0
$457$	15.8875	−	11.5429i	0.743185	−	0.539955i	−0.150522	−	0.988607i	$-0.548095\pi$
$457$	15.8875	−	11.5429i	0.743185	−	0.539955i	0.893707	+	0.448651i	$0.148095\pi$
$458$	0.619569	+	1.90684i	0.0289506	+	0.0891007i
$459$		0			0
$460$	8.42936	+	6.12429i	0.393021	+	0.285546i
$461$	19.5626			0.911122			0.455561	−	0.890205i	$-0.349439\pi$
$461$	19.5626			0.911122			0.455561	+	0.890205i	$0.349439\pi$
$462$		0			0
$463$	−14.7474			−0.685371			−0.342686	−	0.939450i	$-0.611337\pi$
$463$	−14.7474			−0.685371			−0.342686	+	0.939450i	$0.611337\pi$
$464$	7.06740	+	5.13476i	0.328096	+	0.238375i
$465$		0			0
$466$	−14.0969	−	43.3858i	−0.653026	−	2.00981i
$467$	8.33684	−	6.05707i	0.385783	−	0.280288i	−0.377942	−	0.925829i	$-0.623368\pi$
$467$	8.33684	−	6.05707i	0.385783	−	0.280288i	0.763725	+	0.645541i	$0.223368\pi$
$468$		0			0
$469$	0.963564	+	2.96555i	0.0444933	+	0.136936i
$470$	−0.0200947	+	0.0618450i	−0.000926897	+	0.00285270i
$471$		0			0
$472$	39.5476			1.82033
$473$	18.4905	−	31.0315i	0.850193	−	1.42683i
$474$		0			0
$475$	2.88020	+	2.09259i	0.132153	+	0.0960147i
$476$	−15.0540	+	46.3314i	−0.689999	+	2.12360i
$477$		0			0
$478$	−49.9756	+	36.3094i	−2.28583	+	1.66075i
$479$	9.22083	−	6.69932i	0.421310	−	0.306100i	−0.356854	−	0.934160i	$-0.616151\pi$
$479$	9.22083	−	6.69932i	0.421310	−	0.306100i	0.778165	+	0.628060i	$0.216151\pi$
$480$		0			0
$481$	3.99754	−	12.3032i	0.182272	−	0.560976i
$482$	−33.0696	−	24.0265i	−1.50628	−	1.09437i
$483$		0			0
$484$	28.3263	−	29.7681i	1.28756	−	1.35310i
$485$	−10.4097			−0.472678
$486$		0			0
$487$	−10.7054	+	32.9479i	−0.485109	+	1.49301i	0.346715	+	0.937971i	$0.387297\pi$
$487$	−10.7054	+	32.9479i	−0.485109	+	1.49301i	−0.831823	+	0.555040i	$0.812703\pi$
$488$	−3.98479	−	12.2639i	−0.180383	−	0.555162i
$489$		0			0
$490$	6.04452	−	4.39160i	0.273063	−	0.198392i
$491$	−11.3147	−	34.8232i	−0.510627	−	1.57155i	−0.791100	−	0.611686i	$-0.790491\pi$
$491$	−11.3147	−	34.8232i	−0.510627	−	1.57155i	0.280473	−	0.959862i	$-0.409509\pi$
$492$		0			0
$493$	−18.8396	−	13.6878i	−0.848495	−	0.616467i
$494$	24.8983			1.12023
$495$		0			0
$496$	20.1658			0.905473
$497$	9.65485	+	7.01466i	0.433079	+	0.314651i
$498$		0			0
$499$	−6.59797	−	20.3065i	−0.295366	−	0.909042i	−0.983098	−	0.183078i	$-0.941394\pi$
$499$	−6.59797	−	20.3065i	−0.295366	−	0.909042i	0.687733	−	0.725964i	$-0.258606\pi$
$500$	3.02216	−	2.19573i	0.135155	−	0.0981960i
$501$		0			0
$502$	−7.63498	−	23.4980i	−0.340766	−	1.04877i
$503$	3.60237	−	11.0870i	0.160622	−	0.494343i	−0.838065	−	0.545570i	$-0.816313\pi$
$503$	3.60237	−	11.0870i	0.160622	−	0.494343i	0.998687	+	0.0512270i	$0.0163132\pi$
$504$		0			0
$505$	17.2166			0.766127
$506$	−20.3614	+	8.73147i	−0.905173	+	0.388161i
$507$		0			0
$508$	−58.3819	−	42.4169i	−2.59028	−	1.88195i
$509$	9.06760	−	27.9072i	0.401914	−	1.23697i	−0.521530	−	0.853233i	$-0.674639\pi$
$509$	9.06760	−	27.9072i	0.401914	−	1.23697i	0.923444	−	0.383732i	$-0.125361\pi$
$510$		0			0
$511$	3.78157	−	2.74747i	0.167287	−	0.121541i
$512$	−21.4555	+	15.5883i	−0.948208	+	0.688913i
$513$		0			0
$514$	−8.33583	+	25.6550i	−0.367678	+	1.13160i
$515$	5.39613	+	3.92052i	0.237782	+	0.172759i
$516$		0			0
$517$	−0.0593308	−	0.0677470i	−0.00260936	−	0.00297951i
$518$	−20.8986			−0.918230
$519$		0			0
$520$	3.75091	−	11.5441i	0.164488	−	0.506243i
$521$	1.23624	+	3.80477i	0.0541608	+	0.166690i	0.974478	−	0.224483i	$-0.0720694\pi$
$521$	1.23624	+	3.80477i	0.0541608	+	0.166690i	−0.920317	+	0.391173i	$0.872069\pi$
$522$		0			0
$523$	3.59665	−	2.61312i	0.157271	−	0.114264i	−0.506367	−	0.862318i	$-0.669012\pi$
$523$	3.59665	−	2.61312i	0.157271	−	0.114264i	0.663637	+	0.748054i	$0.269012\pi$
$524$	−16.0487	−	49.3930i	−0.701093	−	2.15774i
$525$		0			0
$526$	−9.97983	−	7.25077i	−0.435141	−	0.316149i
$527$	−53.7563			−2.34166
$528$		0			0
$529$	−15.2205			−0.661759
$530$	−7.96222	−	5.78489i	−0.345857	−	0.251280i
$531$		0			0
$532$	−8.09544	−	24.9152i	−0.350982	−	1.08021i
$533$	−16.7221	+	12.1493i	−0.724314	+	0.526245i
$534$		0			0
$535$	2.97246	+	9.14829i	0.128511	+	0.395515i
$536$	−2.03323	+	6.25765i	−0.0878224	+	0.270289i
$537$		0			0
$538$	55.4474			2.39051
$539$	0.939725	+	10.3042i	0.0404768	+	0.443831i
$540$		0			0
$541$	10.6676	+	7.75046i	0.458636	+	0.333218i	0.792996	−	0.609227i	$-0.208520\pi$
$541$	10.6676	+	7.75046i	0.458636	+	0.333218i	−0.334360	+	0.942445i	$0.608520\pi$
$542$	−9.72815	+	29.9402i	−0.417860	+	1.28604i
$543$		0			0
$544$	12.6692	−	9.20469i	0.543186	−	0.394648i
$545$	−15.5819	+	11.3209i	−0.667454	+	0.484933i
$546$		0			0
$547$	0.577321	−	1.77681i	0.0246845	−	0.0759710i	−0.937955	−	0.346756i	$-0.887283\pi$
$547$	0.577321	−	1.77681i	0.0246845	−	0.0759710i	0.962640	+	0.270785i	$0.0872832\pi$
$548$	−68.6846	−	49.9023i	−2.93406	−	2.13172i
$549$		0			0
$550$	0.721399	+	7.91019i	0.0307606	+	0.337292i
$551$	12.5229			0.533491
$552$		0			0
$553$	−7.63264	+	23.4908i	−0.324573	+	0.998932i
$554$	−7.65891	−	23.5717i	−0.325396	−	1.00147i
$555$		0			0
$556$	−38.4116	+	27.9076i	−1.62901	+	1.18355i
$557$	4.17820	+	12.8592i	0.177036	+	0.544861i	0.999721	−	0.0236374i	$-0.00752471\pi$
$557$	4.17820	+	12.8592i	0.177036	+	0.544861i	−0.822685	+	0.568498i	$0.807525\pi$
$558$		0			0
$559$	25.7310	+	18.6947i	1.08831	+	0.790701i
$560$	−4.89211			−0.206729
$561$		0			0
$562$	0.926879			0.0390980
$563$	24.7333	+	17.9698i	1.04238	+	0.757336i	0.970749	−	0.240095i	$-0.0771787\pi$
$563$	24.7333	+	17.9698i	1.04238	+	0.757336i	0.0716337	+	0.997431i	$0.477179\pi$
$564$		0			0
$565$	1.10098	+	3.38846i	0.0463184	+	0.142553i
$566$	−28.1432	+	20.4472i	−1.18295	+	0.859461i
$567$		0			0
$568$	7.78175	+	23.9498i	0.326515	+	1.00491i
$569$	11.2742	−	34.6984i	0.472638	−	1.45463i	−0.376478	−	0.926426i	$-0.622865\pi$
$569$	11.2742	−	34.6984i	0.472638	−	1.45463i	0.849116	−	0.528206i	$-0.177135\pi$
$570$		0			0
$571$	−19.9929			−0.836679			−0.418339	−	0.908291i	$-0.637388\pi$
$571$	−19.9929			−0.836679			−0.418339	+	0.908291i	$0.637388\pi$
$572$	23.8367	+	27.2181i	0.996664	+	1.13804i
$573$		0			0
$574$	27.0145	+	19.6272i	1.12756	+	0.819222i
$575$	0.861905	−	2.65267i	0.0359439	−	0.110624i
$576$		0			0
$577$	25.1775	−	18.2925i	1.04815	−	0.761527i	0.0762921	−	0.997086i	$-0.475692\pi$
$577$	25.1775	−	18.2925i	1.04815	−	0.761527i	0.971860	+	0.235558i	$0.0756919\pi$
$578$	51.9805	−	37.7660i	2.16210	−	1.57086i
$579$		0			0
$580$	4.06051	−	12.4970i	0.168603	−	0.518908i
$581$	8.03724	+	5.83940i	0.333441	+	0.242259i
$582$		0			0
$583$	12.5264	−	5.37165i	0.518792	−	0.222471i
$584$	9.86327			0.408145
$585$		0			0
$586$	−10.9660	+	33.7499i	−0.453002	+	1.39420i
$587$	−9.85974	−	30.3452i	−0.406955	−	1.25248i	−0.919252	−	0.393670i	$-0.871205\pi$
$587$	−9.85974	−	30.3452i	−0.406955	−	1.25248i	0.512297	−	0.858808i	$-0.328795\pi$
$588$		0			0
$589$	23.3870	−	16.9917i	0.963646	−	0.700130i
$590$	−7.04131	−	21.6709i	−0.289886	−	0.892178i
$591$		0			0
$592$	−8.90056	−	6.46663i	−0.365811	−	0.265777i
$593$	−34.5829			−1.42015			−0.710074	−	0.704127i	$-0.751338\pi$
$593$	−34.5829			−1.42015			−0.710074	+	0.704127i	$0.751338\pi$
$594$		0			0
$595$	13.0410			0.534627
$596$	−13.0036	−	9.44765i	−0.532647	−	0.386991i
$597$		0			0
$598$	−6.02787	−	18.5519i	−0.246498	−	0.758643i
$599$	14.3857	−	10.4519i	0.587785	−	0.427051i	−0.253737	−	0.967273i	$-0.581660\pi$
$599$	14.3857	−	10.4519i	0.587785	−	0.427051i	0.841522	+	0.540222i	$0.181660\pi$
$600$		0			0
$601$	−4.57989	−	14.0954i	−0.186818	−	0.574965i	0.813157	−	0.582044i	$-0.197747\pi$
$601$	−4.57989	−	14.0954i	−0.186818	−	0.574965i	−0.999975	+	0.00707858i	$0.997747\pi$
$602$	15.8777	−	48.8666i	0.647127	−	1.99165i
$603$		0			0
$604$	65.6883			2.67282
$605$	−9.92196	−	4.74917i	−0.403385	−	0.193081i
$606$		0			0
$607$	11.1672	+	8.11345i	0.453263	+	0.329315i	0.790883	−	0.611968i	$-0.209622\pi$
$607$	11.1672	+	8.11345i	0.453263	+	0.329315i	−0.337620	+	0.941283i	$0.609622\pi$
$608$	−2.60232	+	8.00912i	−0.105538	+	0.324813i
$609$		0			0
$610$	−6.01079	+	4.36710i	−0.243370	+	0.176819i
$611$	0.0641478	−	0.0466061i	0.00259514	−	0.00188548i
$612$		0			0
$613$	6.95138	−	21.3942i	0.280764	−	0.864102i	−0.706873	−	0.707341i	$-0.749895\pi$
$613$	6.95138	−	21.3942i	0.280764	−	0.864102i	0.987637	−	0.156761i	$-0.0501053\pi$
$614$	62.6864	+	45.5443i	2.52982	+	1.83802i
$615$		0			0
$616$	13.9006	−	23.3286i	0.560073	−	0.939937i
$617$	−10.6195			−0.427525			−0.213762	−	0.976886i	$-0.568572\pi$
$617$	−10.6195			−0.427525			−0.213762	+	0.976886i	$0.568572\pi$
$618$		0			0
$619$	−0.813488	+	2.50366i	−0.0326968	+	0.100630i	−0.966073	−	0.258269i	$-0.916848\pi$
$619$	−0.813488	+	2.50366i	−0.0326968	+	0.100630i	0.933376	+	0.358899i	$0.116848\pi$
$620$	−9.37334	−	28.8482i	−0.376443	−	1.15857i
$621$		0			0
$622$	−3.41692	+	2.48253i	−0.137006	+	0.0995406i
$623$	7.33946	+	22.5885i	0.294049	+	0.904991i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	62.6832			2.50532
$627$		0			0
$628$	−88.9493			−3.54946
$629$	23.7263	+	17.2382i	0.946030	+	0.687331i
$630$		0			0
$631$	7.45705	+	22.9504i	0.296860	+	0.913642i	0.982590	+	0.185786i	$0.0594831\pi$
$631$	7.45705	+	22.9504i	0.296860	+	0.913642i	−0.685730	+	0.727856i	$0.740517\pi$
$632$	−42.1654	+	30.6350i	−1.67725	+	1.21859i
$633$		0			0
$634$	7.67855	+	23.6321i	0.304954	+	0.938552i
$635$	−5.96957	+	18.3724i	−0.236895	+	0.729088i
$636$		0			0
$637$	−9.11024			−0.360961
$638$	18.4076	+	21.0188i	0.728766	+	0.832143i
$639$		0			0
$640$	16.7724	+	12.1859i	0.662989	+	0.481690i
$641$	14.1378	−	43.5115i	0.558408	−	1.71860i	−0.128362	−	0.991727i	$-0.540972\pi$
$641$	14.1378	−	43.5115i	0.558408	−	1.71860i	0.686770	−	0.726875i	$-0.259028\pi$
$642$		0			0
$643$	5.34699	−	3.88482i	0.210865	−	0.153202i	−0.477340	−	0.878719i	$-0.658399\pi$
$643$	5.34699	−	3.88482i	0.210865	−	0.153202i	0.688205	+	0.725516i	$0.258399\pi$
$644$	−16.6045	+	12.0639i	−0.654310	+	0.475384i
$645$		0			0
$646$	−17.4427	+	53.6832i	−0.686276	+	2.11214i
$647$	−1.50597	−	1.09415i	−0.0592058	−	0.0430155i	0.557789	−	0.829983i	$-0.311650\pi$
$647$	−1.50597	−	1.09415i	−0.0592058	−	0.0430155i	−0.616995	+	0.786967i	$0.711650\pi$
$648$		0			0
$649$	30.7729	+	6.98528i	1.20794	+	0.274196i
$650$	−6.99366			−0.274314
$651$		0			0
$652$	−22.9086	+	70.5054i	−0.897169	+	2.76120i
$653$	−9.86620	−	30.3650i	−0.386094	−	1.18828i	−0.935683	−	0.352841i	$-0.885216\pi$
$653$	−9.86620	−	30.3650i	−0.386094	−	1.18828i	0.549589	−	0.835435i	$-0.314784\pi$
$654$		0			0
$655$	−11.2475	+	8.17179i	−0.439476	+	0.319298i
$656$	5.43206	+	16.7181i	0.212086	+	0.652734i
$657$		0			0
$658$	−0.103631	−	0.0752920i	−0.00403994	−	0.00293519i
$659$	8.36924			0.326019			0.163010	−	0.986624i	$-0.447880\pi$
$659$	8.36924			0.326019			0.163010	+	0.986624i	$0.447880\pi$
$660$		0			0
$661$	−34.0773			−1.32545			−0.662726	−	0.748862i	$-0.730601\pi$
$661$	−34.0773			−1.32545			−0.662726	+	0.748862i	$0.730601\pi$
$662$	17.8713	+	12.9843i	0.694589	+	0.504648i
$663$		0			0
$664$	6.47796	+	19.9371i	0.251394	+	0.773710i
$665$	−5.67356	+	4.12208i	−0.220011	+	0.159847i
$666$		0			0
$667$	−3.03177	−	9.33084i	−0.117391	−	0.361291i
$668$	16.7106	−	51.4299i	0.646552	−	1.98988i
$669$		0			0
$670$	3.79102			0.146460
$671$	−0.934482	−	10.2467i	−0.0360753	−	0.395568i
$672$		0			0
$673$	1.67294	+	1.21546i	0.0644870	+	0.0468525i	0.619562	−	0.784948i	$-0.287310\pi$
$673$	1.67294	+	1.21546i	0.0644870	+	0.0468525i	−0.555075	+	0.831800i	$0.687310\pi$
$674$	−21.1195	+	64.9991i	−0.813493	+	2.50367i
$675$		0			0
$676$	13.5161	−	9.82001i	0.519850	−	0.377693i
$677$	14.6355	−	10.6333i	0.562489	−	0.408672i	−0.269880	−	0.962894i	$-0.586984\pi$
$677$	14.6355	−	10.6333i	0.562489	−	0.408672i	0.832369	+	0.554222i	$0.186984\pi$
$678$		0			0
$679$	6.33652	−	19.5018i	0.243173	−	0.748411i
$680$	22.2625	+	16.1746i	0.853728	+	0.620269i
$681$		0			0
$682$	62.8967	+	14.2772i	2.40844	+	0.546703i
$683$	47.3828			1.81305			0.906526	−	0.422149i	$-0.138724\pi$
$683$	47.3828			1.81305			0.906526	+	0.422149i	$0.138724\pi$
$684$		0			0
$685$	−7.02301	+	21.6146i	−0.268336	+	0.825852i
$686$	14.7527	+	45.4042i	0.563261	+	1.73354i
$687$		0			0
$688$	21.8830	−	15.8989i	0.834280	−	0.606140i
$689$	3.70839	+	11.4132i	0.141278	+	0.434810i
$690$		0			0
$691$	−12.8209	−	9.31495i	−0.487731	−	0.354358i	0.316580	−	0.948566i	$-0.397465\pi$
$691$	−12.8209	−	9.31495i	−0.487731	−	0.354358i	−0.804311	+	0.594208i	$0.797465\pi$
$692$	−16.1342			−0.613331
$693$		0			0
$694$	−24.3558			−0.924534
$695$	10.2826	+	7.47073i	0.390040	+	0.283381i
$696$		0			0
$697$	−14.4803	−	44.5657i	−0.548480	−	1.68805i
$698$	−45.9531	+	33.3869i	−1.73935	+	1.26371i
$699$		0			0
$700$	2.27392	+	6.99840i	0.0859460	+	0.264514i
$701$	−8.12897	+	25.0184i	−0.307027	+	0.944932i	0.671886	+	0.740655i	$0.265484\pi$
$701$	−8.12897	+	25.0184i	−0.307027	+	0.944932i	−0.978913	+	0.204277i	$0.934516\pi$
$702$		0			0
$703$	−15.7711			−0.594817
$704$	−32.4083	+	13.8975i	−1.22144	+	0.523782i
$705$		0			0
$706$	−27.3932	−	19.9024i	−1.03096	−	0.749035i
$707$	−10.4800	+	32.2541i	−0.394140	+	1.21304i
$708$		0			0
$709$	−24.9444	+	18.1231i	−0.936805	+	0.680629i	−0.947649	−	0.319312i	$-0.896548\pi$
$709$	−24.9444	+	18.1231i	−0.936805	+	0.680629i	0.0108444	+	0.999941i	$0.496548\pi$
$710$	11.7382	−	8.52833i	0.440528	−	0.320063i
$711$		0			0
$712$	−15.4871	+	47.6645i	−0.580405	+	1.78630i
$713$	−18.3226	−	13.3121i	−0.686186	−	0.498543i
$714$		0			0
$715$	4.95769	−	8.32020i	0.185407	−	0.311158i
$716$	27.8643			1.04134
$717$		0			0
$718$	17.7861	−	54.7399i	0.663770	−	2.04288i
$719$	−14.5990	−	44.9311i	−0.544451	−	1.67565i	−0.722292	−	0.691588i	$-0.756911\pi$
$719$	−14.5990	−	44.9311i	−0.544451	−	1.67565i	0.177841	−	0.984059i	$-0.443089\pi$
$720$		0			0
$721$	−10.6295	+	7.72281i	−0.395865	+	0.287613i
$722$	4.68129	+	14.4075i	0.174220	+	0.536193i
$723$		0			0
$724$	61.8439	+	44.9322i	2.29841	+	1.66989i
$725$	−3.51753			−0.130638
$726$		0			0
$727$	−24.4299			−0.906054			−0.453027	−	0.891497i	$-0.649656\pi$
$727$	−24.4299			−0.906054			−0.453027	+	0.891497i	$0.649656\pi$
$728$	19.3439	+	14.0542i	0.716932	+	0.520882i
$729$		0			0
$730$	−1.75612	−	5.40478i	−0.0649969	−	0.200040i
$731$	−58.3336	+	42.3819i	−2.15755	+	1.56755i
$732$		0			0
$733$	8.64860	+	26.6177i	0.319443	+	0.983146i	0.973887	+	0.227035i	$0.0729031\pi$
$733$	8.64860	+	26.6177i	0.319443	+	0.983146i	−0.654443	+	0.756111i	$0.727097\pi$
$734$	1.32994	−	4.09314i	0.0490891	−	0.151081i
$735$		0			0
$736$	6.59766			0.243193
$737$	−2.68739	+	4.51009i	−0.0989913	+	0.166131i
$738$		0			0
$739$	2.18866	+	1.59015i	0.0805111	+	0.0584947i	0.627313	−	0.778767i	$-0.284155\pi$
$739$	2.18866	+	1.59015i	0.0805111	+	0.0584947i	−0.546802	+	0.837262i	$0.684155\pi$
$740$	−5.11373	+	15.7384i	−0.187984	+	0.578557i
$741$		0			0
$742$	15.6843	−	11.3953i	0.575790	−	0.418336i
$743$	3.35268	−	2.43586i	0.122998	−	0.0893631i	−0.524586	−	0.851358i	$-0.675780\pi$
$743$	3.35268	−	2.43586i	0.122998	−	0.0893631i	0.647583	+	0.761995i	$0.275780\pi$
$744$		0			0
$745$	−1.32962	+	4.09215i	−0.0487135	+	0.149925i
$746$	−13.3263	−	9.68215i	−0.487912	−	0.354489i
$747$		0			0
$748$	−75.3838	+	32.3265i	−2.75630	+	1.18197i
$749$	−18.9481			−0.692348
$750$		0			0
$751$	−13.7301	+	42.2570i	−0.501019	+	1.54198i	0.306342	+	0.951922i	$0.400895\pi$
$751$	−13.7301	+	42.2570i	−0.501019	+	1.54198i	−0.807361	+	0.590058i	$0.799105\pi$
$752$	−0.0208380	−	0.0641327i	−0.000759883	−	0.00233868i
$753$		0			0
$754$	−19.9021	+	14.4598i	−0.724793	+	0.526593i
$755$	−5.43388	−	16.7238i	−0.197759	−	0.608640i
$756$		0			0
$757$	−24.2625	−	17.6277i	−0.881835	−	0.640691i	0.0519011	−	0.998652i	$-0.483472\pi$
$757$	−24.2625	−	17.6277i	−0.881835	−	0.640691i	−0.933736	+	0.357961i	$0.883472\pi$
$758$	8.46192			0.307351
$759$		0			0
$760$	−14.7980			−0.536782
$761$	32.2328	+	23.4185i	1.16844	+	0.848921i	0.990821	−	0.135178i	$-0.0431607\pi$
$761$	32.2328	+	23.4185i	1.16844	+	0.848921i	0.177618	+	0.984099i	$0.443161\pi$
$762$		0			0
$763$	−11.7240	−	36.0828i	−0.424437	−	1.30628i
$764$	19.8004	−	14.3859i	0.716354	−	0.520462i
$765$		0			0
$766$	1.40861	+	4.33524i	0.0508950	+	0.156639i
$767$	−8.58577	+	26.4243i	−0.310014	+	0.954126i
$768$		0			0
$769$	20.5304			0.740346			0.370173	−	0.928963i	$-0.379298\pi$
$769$	20.5304			0.740346			0.370173	+	0.928963i	$0.379298\pi$
$770$	−15.2583	−	3.46356i	−0.549873	−	0.124818i
$771$		0			0
$772$	20.6286	+	14.9876i	0.742441	+	0.539415i
$773$	−5.04670	+	15.5321i	−0.181517	+	0.558652i	−0.999871	−	0.0160625i	$-0.994887\pi$
$773$	−5.04670	+	15.5321i	−0.181517	+	0.558652i	0.818354	+	0.574715i	$0.194887\pi$
$774$		0			0
$775$	−6.56916	+	4.77277i	−0.235971	+	0.171443i
$776$	35.0052	−	25.4328i	1.25661	−	0.912984i
$777$		0			0
$778$	5.19690	−	15.9944i	0.186318	−	0.573428i
$779$	20.3864	+	14.8116i	0.730419	+	0.530681i
$780$		0			0
$781$	1.82491	+	20.0103i	0.0653005	+	0.716025i
$782$	44.2225			1.58139
$783$		0			0
$784$	−2.39421	+	7.36861i	−0.0855073	+	0.263164i
$785$	7.35808	+	22.6458i	0.262621	+	0.808265i
$786$		0			0
$787$	5.97674	−	4.34236i	0.213048	−	0.154788i	−0.476144	−	0.879367i	$-0.657966\pi$
$787$	5.97674	−	4.34236i	0.213048	−	0.154788i	0.689192	+	0.724579i	$0.257966\pi$
$788$	−3.98361	−	12.2603i	−0.141910	−	0.436755i
$789$		0			0
$790$	24.2945	+	17.6510i	0.864358	+	0.627993i
$791$	−7.01823			−0.249539
$792$		0			0
$793$	9.05941			0.321709
$794$	−24.2479	−	17.6171i	−0.860525	−	0.625208i
$795$		0			0
$796$	−12.3219	−	37.9228i	−0.436737	−	1.34414i
$797$	18.7331	−	13.6104i	0.663562	−	0.482106i	−0.204302	−	0.978908i	$-0.565492\pi$
$797$	18.7331	−	13.6104i	0.663562	−	0.482106i	0.867864	+	0.496802i	$0.165492\pi$
$798$		0			0
$799$	0.0555480	+	0.170959i	0.00196515	+	0.00604810i
$800$	0.730963	−	2.24967i	0.0258434	−	0.0795379i
$801$		0			0
$802$	−65.4491			−2.31109
$803$	7.67482	+	1.74214i	0.270839	+	0.0614789i
$804$		0			0
$805$	4.44494	+	3.22944i	0.156664	+	0.113823i
$806$	−17.5485	+	54.0086i	−0.618118	+	1.90237i
$807$		0			0
$808$	−57.8952	+	42.0633i	−2.03675	+	1.47978i
$809$	−12.0935	+	8.78647i	−0.425186	+	0.308916i	−0.779721	−	0.626127i	$-0.784639\pi$
$809$	−12.0935	+	8.78647i	−0.425186	+	0.308916i	0.354535	+	0.935043i	$0.384639\pi$
$810$		0			0
$811$	−7.76050	+	23.8844i	−0.272508	+	0.838694i	0.717360	+	0.696703i	$0.245350\pi$
$811$	−7.76050	+	23.8844i	−0.272508	+	0.838694i	−0.989868	+	0.141991i	$0.954650\pi$
$812$	20.9405	+	15.2142i	0.734868	+	0.533913i
$813$		0			0
$814$	−23.1823	−	26.4707i	−0.812538	−	0.927799i
$815$	19.8452			0.695147
$816$		0			0
$817$	11.9821	−	36.8770i	0.419200	−	1.29016i
$818$	8.58402	+	26.4189i	0.300133	+	0.923715i
$819$		0			0
$820$	21.3912	−	15.5416i	0.747013	−	0.542737i
$821$	4.04920	+	12.4622i	0.141318	+	0.434932i	0.996519	−	0.0833641i	$-0.0265664\pi$
$821$	4.04920	+	12.4622i	0.141318	+	0.434932i	−0.855201	+	0.518296i	$0.826566\pi$
$822$		0			0
$823$	16.6448	+	12.0932i	0.580202	+	0.421541i	0.838797	−	0.544444i	$-0.183259\pi$
$823$	16.6448	+	12.0932i	0.580202	+	0.421541i	−0.258595	+	0.965986i	$0.583259\pi$
$824$	−27.7245			−0.965828
$825$		0			0
$826$	44.8852			1.56176
$827$	10.2214	+	7.42627i	0.355432	+	0.258237i	0.751144	−	0.660138i	$-0.229502\pi$
$827$	10.2214	+	7.42627i	0.355432	+	0.258237i	−0.395712	+	0.918375i	$0.629502\pi$
$828$		0			0
$829$	2.40686	+	7.40755i	0.0835937	+	0.257275i	0.984114	−	0.177540i	$-0.0568139\pi$
$829$	2.40686	+	7.40755i	0.0835937	+	0.257275i	−0.900520	+	0.434815i	$0.856814\pi$
$830$	9.77157	−	7.09946i	0.339176	−	0.246426i
$831$		0			0
$832$	−9.59432	−	29.5283i	−0.332623	−	1.02371i
$833$	6.38226	−	19.6426i	0.221132	−	0.680575i
$834$		0			0
$835$	−14.4760			−0.500963
$836$	22.5782	−	37.8917i	0.780885	−	1.31051i
$837$		0			0
$838$	17.5838	+	12.7754i	0.607424	+	0.441319i
$839$	−9.44113	+	29.0568i	−0.325944	+	1.00315i	0.645068	+	0.764125i	$0.276829\pi$
$839$	−9.44113	+	29.0568i	−0.325944	+	1.00315i	−0.971013	+	0.239028i	$0.923171\pi$
$840$		0			0
$841$	13.4515	−	9.77311i	0.463846	−	0.337004i
$842$	35.8735	−	26.0636i	1.23628	−	0.898212i
$843$		0			0
$844$	−1.59214	+	4.90009i	−0.0548036	+	0.168668i
$845$	−3.61819	−	2.62877i	−0.124469	−	0.0904323i
$846$		0			0
$847$	14.9369	−	15.6972i	0.513238	−	0.539364i
$848$	10.2059			0.350472
$849$		0			0
$850$	4.89947	−	15.0790i	0.168050	−	0.517206i
$851$	3.81816	+	11.7511i	0.130885	+	0.402822i
$852$		0			0
$853$	−20.7705	+	15.0906i	−0.711167	+	0.516693i	−0.883550	−	0.468337i	$-0.844853\pi$
$853$	−20.7705	+	15.0906i	−0.711167	+	0.516693i	0.172383	+	0.985030i	$0.444853\pi$
$854$	−4.52260	−	13.9191i	−0.154760	−	0.476303i
$855$		0			0
$856$	−32.3467	−	23.5013i	−1.10559	−	0.803256i
$857$	−14.7370			−0.503407			−0.251703	−	0.967804i	$-0.580991\pi$
$857$	−14.7370			−0.503407			−0.251703	+	0.967804i	$0.580991\pi$
$858$		0			0
$859$	−1.68741			−0.0575738			−0.0287869	−	0.999586i	$-0.509164\pi$
$859$	−1.68741			−0.0575738			−0.0287869	+	0.999586i	$0.509164\pi$
$860$	−32.9156	−	23.9146i	−1.12241	−	0.815481i
$861$		0			0
$862$	18.3472	+	56.4670i	0.624909	+	1.92327i
$863$	−10.6364	+	7.72777i	−0.362066	+	0.263056i	−0.753913	−	0.656974i	$-0.771836\pi$
$863$	−10.6364	+	7.72777i	−0.362066	+	0.263056i	0.391847	+	0.920030i	$0.371836\pi$
$864$		0			0
$865$	1.33466	+	4.10765i	0.0453797	+	0.139664i
$866$	26.1879	−	80.5981i	0.889901	−	2.73883i
$867$		0			0
$868$	59.7509			2.02808
$869$	−38.2209	+	16.3901i	−1.29655	+	0.555995i
$870$		0			0
$871$	−3.73972	−	2.71707i	−0.126716	−	0.0920643i
$872$	24.7390	−	76.1389i	0.837769	−	2.57839i
$873$		0			0
$874$	−19.2393	+	13.9782i	−0.650779	+	0.472819i
$875$	1.59364	−	1.15785i	0.0538748	−	0.0391423i
$876$		0			0
$877$	−14.5081	+	44.6513i	−0.489904	+	1.50777i	0.334847	+	0.942273i	$0.391315\pi$
$877$	−14.5081	+	44.6513i	−0.489904	+	1.50777i	−0.824751	+	0.565496i	$0.808685\pi$
$878$	−19.9402	−	14.4874i	−0.672950	−	0.488927i
$879$		0			0
$880$	−5.42670	−	6.19649i	−0.182934	−	0.208884i
$881$	14.1843			0.477880			0.238940	−	0.971034i	$-0.423200\pi$
$881$	14.1843			0.477880			0.238940	+	0.971034i	$0.423200\pi$
$882$		0			0
$883$	−3.21065	+	9.88136i	−0.108047	+	0.332534i	−0.990433	−	0.137991i	$-0.955936\pi$
$883$	−3.21065	+	9.88136i	−0.108047	+	0.332534i	0.882387	+	0.470525i	$0.155936\pi$
$884$	−22.3170	−	68.6846i	−0.750601	−	2.31011i
$885$		0			0
$886$	69.4607	−	50.4662i	2.33358	−	1.69544i
$887$	−1.18899	−	3.65932i	−0.0399222	−	0.122868i	0.929109	−	0.369806i	$-0.120576\pi$
$887$	−1.18899	−	3.65932i	−0.0399222	−	0.122868i	−0.969031	+	0.246938i	$0.920576\pi$
$888$		0			0
$889$	−30.7858	−	22.3672i	−1.03252	−	0.750171i
$890$	28.8761			0.967931
$891$		0			0
$892$	45.2150			1.51391
$893$	−0.0782046	−	0.0568189i	−0.00261702	−	0.00190137i
$894$		0			0
$895$	−2.30499	−	7.09404i	−0.0770474	−	0.237128i
$896$	−33.0391	+	24.0043i	−1.10376	+	0.801928i
$897$		0			0
$898$	19.8661	+	61.1416i	0.662941	+	2.04032i
$899$	−8.82616	+	27.1641i	−0.294369	+	0.905974i
$900$		0			0
$901$	−27.2060			−0.906363
$902$	5.10614	+	55.9892i	0.170016	+	1.86424i
$903$		0			0
$904$	−11.9810	−	8.70468i	−0.398481	−	0.289513i
$905$	6.32355	−	19.4619i	0.210202	−	0.646935i
$906$		0			0
$907$	−0.974354	+	0.707910i	−0.0323529	+	0.0235058i	−0.603844	−	0.797102i	$-0.706365\pi$
$907$	−0.974354	+	0.707910i	−0.0323529	+	0.0235058i	0.571491	+	0.820608i	$0.306365\pi$
$908$	−52.3802	+	38.0564i	−1.73830	+	1.26295i
$909$		0			0
$910$	4.25715	−	13.1022i	0.141123	−	0.434332i
$911$	−31.4956	−	22.8829i	−1.04349	−	0.758143i	−0.0725299	−	0.997366i	$-0.523107\pi$
$911$	−31.4956	−	22.8829i	−1.04349	−	0.758143i	−0.970965	+	0.239223i	$0.923107\pi$
$912$		0			0
$913$	1.51916	+	16.6577i	0.0502769	+	0.551290i
$914$	47.0313			1.55566
$915$		0			0
$916$	−0.966408	+	2.97430i	−0.0319310	+	0.0982736i
$917$	−8.46278	−	26.0457i	−0.279465	−	0.860106i
$918$		0			0
$919$	7.74032	−	5.62368i	0.255330	−	0.185508i	−0.452756	−	0.891635i	$-0.649559\pi$
$919$	7.74032	−	5.62368i	0.255330	−	0.185508i	0.708086	+	0.706127i	$0.249559\pi$
$920$	3.58260	+	11.0261i	0.118115	+	0.363520i
$921$		0			0
$922$	37.9030	+	27.5382i	1.24827	+	0.906921i
$923$	−17.6918			−0.582332
$924$		0			0
$925$	4.42991			0.145655
$926$	−28.5735	−	20.7599i	−0.938983	−	0.682211i
$927$		0			0
$928$	−2.57118	−	7.91329i	−0.0844032	−	0.259766i
$929$	5.22304	−	3.79476i	0.171362	−	0.124502i	−0.498798	−	0.866718i	$-0.666225\pi$
$929$	5.22304	−	3.79476i	0.171362	−	0.124502i	0.670161	+	0.742216i	$0.266225\pi$
$930$		0			0
$931$	3.43212	+	10.5630i	0.112483	+	0.346188i
$932$	21.9884	−	67.6734i	0.720255	−	2.21672i
$933$		0			0
$934$	24.6793			0.807532
$935$	14.4660	+	16.5181i	0.473089	+	0.540198i
$936$		0			0
$937$	−0.387158	−	0.281287i	−0.0126479	−	0.00918924i	0.581443	−	0.813587i	$-0.302488\pi$
$937$	−0.387158	−	0.281287i	−0.0126479	−	0.00918924i	−0.594091	+	0.804398i	$0.702488\pi$
$938$	−2.30765	+	7.10222i	−0.0753475	+	0.231896i
$939$		0			0
$940$	−0.0820591	+	0.0596194i	−0.00267647	+	0.00194457i
$941$	−14.8330	+	10.7768i	−0.483541	+	0.351313i	−0.802695	−	0.596390i	$-0.796601\pi$
$941$	−14.8330	+	10.7768i	−0.483541	+	0.351313i	0.319154	+	0.947703i	$0.396601\pi$
$942$		0			0
$943$	6.10066	−	18.7759i	0.198665	−	0.611427i
$944$	19.1163	+	13.8888i	0.622182	+	0.452042i
$945$		0			0
$946$	79.5086	−	34.0953i	2.58505	−	1.10853i
$947$	−23.6619			−0.768908			−0.384454	−	0.923144i	$-0.625610\pi$
$947$	−23.6619			−0.768908			−0.384454	+	0.923144i	$0.625610\pi$
$948$		0			0
$949$	−2.14131	+	6.59028i	−0.0695099	+	0.213930i
$950$	2.63474	+	8.10889i	0.0854822	+	0.263087i
$951$		0			0
$952$	−43.8536	+	31.8615i	−1.42130	+	1.03264i
$953$	6.02925	+	18.5561i	0.195307	+	0.601092i	0.999973	+	0.00736474i	$0.00234429\pi$
$953$	6.02925	+	18.5561i	0.195307	+	0.601092i	−0.804666	+	0.593728i	$0.797656\pi$
$954$		0			0
$955$	−5.30047	−	3.85102i	−0.171519	−	0.124616i
$956$	−96.3544			−3.11632
$957$		0			0
$958$	27.2962			0.881899
$959$	−36.2185	−	26.3143i	−1.16956	−	0.849733i
$960$		0			0
$961$	10.7949	+	33.2234i	0.348224	+	1.07172i
$962$	25.0644	−	18.2104i	0.808109	−	0.587126i
$963$		0			0
$964$	−19.7026	−	60.6385i	−0.634579	−	1.95303i
$965$	2.10928	−	6.49171i	0.0679003	−	0.208976i
$966$		0			0
$967$	−13.3686			−0.429905			−0.214953	−	0.976624i	$-0.568960\pi$
$967$	−13.3686			−0.429905			−0.214953	+	0.976624i	$0.568960\pi$
$968$	44.9684	−	8.27090i	1.44534	−	0.265837i
$969$		0			0
$970$	−20.1690	−	14.6536i	−0.647586	−	0.470499i
$971$	17.1814	−	52.8788i	0.551377	−	1.69696i	−0.153948	−	0.988079i	$-0.549199\pi$
$971$	17.1814	−	52.8788i	0.551377	−	1.69696i	0.705325	−	0.708884i	$-0.250801\pi$
$972$		0			0
$973$	−20.2551	+	14.7162i	−0.649348	+	0.471779i
$974$	−67.1225	+	48.7674i	−2.15074	+	1.56261i
$975$		0			0
$976$	2.38085	−	7.32749i	0.0762090	−	0.234547i
$977$	34.7123	+	25.2200i	1.11055	+	0.806858i	0.982749	−	0.184942i	$-0.0592098\pi$
$977$	34.7123	+	25.2200i	1.11055	+	0.806858i	0.127796	+	0.991800i	$0.459210\pi$
$978$		0			0
$979$	−20.4698	+	34.3533i	−0.654218	+	1.09794i
$980$	11.6540			0.372273
$981$		0			0
$982$	27.0978	−	83.3984i	0.864725	−	2.66135i
$983$	10.6854	+	32.8864i	0.340812	+	1.04891i	0.963788	+	0.266671i	$0.0859236\pi$
$983$	10.6854	+	32.8864i	0.340812	+	1.04891i	−0.622976	+	0.782241i	$0.714076\pi$
$984$		0			0
$985$	−2.79185	+	2.02840i	−0.0889557	+	0.0646301i
$986$	−17.2340	−	53.0409i	−0.548843	−	1.68917i
$987$		0			0
$988$	31.4195	+	22.8276i	0.999587	+	0.726242i
$989$	−30.3781			−0.965968
$990$		0			0
$991$	15.5839			0.495038			0.247519	−	0.968883i	$-0.420385\pi$
$991$	15.5839			0.495038			0.247519	+	0.968883i	$0.420385\pi$
$992$	−15.5390	−	11.2897i	−0.493363	−	0.358449i
$993$		0			0
$994$	8.83201	+	27.1821i	0.280134	+	0.862165i
$995$	−8.63558	+	6.27412i	−0.273766	+	0.198903i
$996$		0			0
$997$	1.24866	+	3.84297i	0.0395454	+	0.121708i	0.968880	−	0.247530i	$-0.0796188\pi$
$997$	1.24866	+	3.84297i	0.0395454	+	0.121708i	−0.929335	+	0.369238i	$0.879619\pi$
$998$	15.8016	−	48.6322i	0.500190	−	1.53943i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.h.136.4	yes	16
3.2	odd	2		495.2.n.g.136.1	yes	16
11.3	even	5	inner	495.2.n.h.91.4	yes	16
11.5	even	5		5445.2.a.ca.1.2		8
11.6	odd	10		5445.2.a.cc.1.7		8
33.5	odd	10		5445.2.a.cd.1.7		8
33.14	odd	10		495.2.n.g.91.1	✓	16
33.17	even	10		5445.2.a.cb.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.n.g.91.1	✓	16	33.14	odd	10
495.2.n.g.136.1	yes	16	3.2	odd	2
495.2.n.h.91.4	yes	16	11.3	even	5	inner
495.2.n.h.136.4	yes	16	1.1	even	1	trivial
5445.2.a.ca.1.2		8	11.5	even	5
5445.2.a.cb.1.2		8	33.17	even	10
5445.2.a.cc.1.7		8	11.6	odd	10
5445.2.a.cd.1.7		8	33.5	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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.93752 + 1.40769i) q^{2} +(1.15436 + 3.55277i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.608715 + 1.87343i) q^{7} +(-1.28446 + 3.95317i) q^{8} +O(q^{10})\)	\(q+(1.93752 + 1.40769i) q^{2} +(1.15436 + 3.55277i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.608715 + 1.87343i) q^{7} +(-1.28446 + 3.95317i) q^{8} +2.39491 q^{10} +(-1.69771 + 2.84917i) q^{11} +(-2.36251 - 1.71646i) q^{13} +(-1.45782 + 4.48671i) q^{14} +(-2.00919 + 1.45977i) q^{16} +(5.35593 - 3.89131i) q^{17} +(-1.10014 + 3.38588i) q^{19} +(3.02216 + 2.19573i) q^{20} +(-7.30012 + 3.13048i) q^{22} +2.78918 q^{23} +(0.309017 - 0.951057i) q^{25} +(-2.16116 - 6.65137i) q^{26} +(-5.95319 + 4.32525i) q^{28} +(-1.08698 - 3.34537i) q^{29} +(-6.56916 - 4.77277i) q^{31} +2.36545 q^{32} +15.8550 q^{34} +(1.59364 + 1.15785i) q^{35} +(1.36892 + 4.21310i) q^{37} +(-6.89783 + 5.01157i) q^{38} +(1.28446 + 3.95317i) q^{40} +(2.18726 - 6.73169i) q^{41} -10.8914 q^{43} +(-12.0822 - 2.74260i) q^{44} +(5.40411 + 3.92631i) q^{46} +(-0.00839056 + 0.0258235i) q^{47} +(2.52390 - 1.83372i) q^{49} +(1.93752 - 1.40769i) q^{50} +(3.37099 - 10.3749i) q^{52} +(-3.32464 - 2.41549i) q^{53} +(0.301222 + 3.30292i) q^{55} -8.18786 q^{56} +(2.60321 - 8.01186i) q^{58} +(-2.94011 - 9.04874i) q^{59} +(-2.50982 + 1.82349i) q^{61} +(-6.00930 - 18.4947i) q^{62} +(8.60150 + 6.24935i) q^{64} -2.92022 q^{65} +1.58295 q^{67} +(20.0076 + 14.5364i) q^{68} +(1.45782 + 4.48671i) q^{70} +(4.90133 - 3.56102i) q^{71} +(-0.733271 - 2.25678i) q^{73} +(-3.27844 + 10.0900i) q^{74} -13.2992 q^{76} +(-6.37115 - 1.44622i) q^{77} +(10.1442 + 7.37019i) q^{79} +(-0.767444 + 2.36195i) q^{80} +(13.7140 - 9.96381i) q^{82} +(4.08014 - 2.96440i) q^{83} +(2.04578 - 6.29628i) q^{85} +(-21.1024 - 15.3318i) q^{86} +(-9.08260 - 10.3710i) q^{88} +12.0573 q^{89} +(1.77758 - 5.47084i) q^{91} +(3.21973 + 9.90931i) q^{92} +(-0.0526085 + 0.0382223i) q^{94} +(1.10014 + 3.38588i) q^{95} +(-8.42159 - 6.11864i) q^{97} +7.47144 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8	\( 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} + 8 q^{10} - 4 q^{11} + 2 q^{13} + 22 q^{14} + 8 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 28 q^{22} - 8 q^{23} - 4 q^{25} - 6 q^{26} - 2 q^{28} + 26 q^{29} - 10 q^{31} - 56 q^{32} - 4 q^{34} + 4 q^{35} + 22 q^{37} + 30 q^{38} - 6 q^{40} + 6 q^{41} + 28 q^{43} - 68 q^{44} + 16 q^{46} + 20 q^{47} + 10 q^{49} + 2 q^{50} + 30 q^{52} - 14 q^{53} - 6 q^{55} - 68 q^{56} - 6 q^{58} + 16 q^{59} - 38 q^{61} + 20 q^{62} + 10 q^{64} - 12 q^{65} + 20 q^{67} + 48 q^{68} - 22 q^{70} + 54 q^{71} + 2 q^{73} - 28 q^{74} - 44 q^{76} - 34 q^{77} - 12 q^{79} + 22 q^{80} + 30 q^{82} + 28 q^{83} - 4 q^{85} - 74 q^{86} + 46 q^{88} - 76 q^{89} - 34 q^{91} + 8 q^{92} - 10 q^{94} + 4 q^{95} - 18 q^{97} - 8 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8 + 8 * q^10 - 4 * q^11 + 2 * q^13 + 22 * q^14 + 8 * q^16 + 4 * q^17 - 4 * q^19 - 2 * q^20 - 28 * q^22 - 8 * q^23 - 4 * q^25 - 6 * q^26 - 2 * q^28 + 26 * q^29 - 10 * q^31 - 56 * q^32 - 4 * q^34 + 4 * q^35 + 22 * q^37 + 30 * q^38 - 6 * q^40 + 6 * q^41 + 28 * q^43 - 68 * q^44 + 16 * q^46 + 20 * q^47 + 10 * q^49 + 2 * q^50 + 30 * q^52 - 14 * q^53 - 6 * q^55 - 68 * q^56 - 6 * q^58 + 16 * q^59 - 38 * q^61 + 20 * q^62 + 10 * q^64 - 12 * q^65 + 20 * q^67 + 48 * q^68 - 22 * q^70 + 54 * q^71 + 2 * q^73 - 28 * q^74 - 44 * q^76 - 34 * q^77 - 12 * q^79 + 22 * q^80 + 30 * q^82 + 28 * q^83 - 4 * q^85 - 74 * q^86 + 46 * q^88 - 76 * q^89 - 34 * q^91 + 8 * q^92 - 10 * q^94 + 4 * q^95 - 18 * q^97 - 8 * q^98

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