LMFDB - Embedded newform 495.2.n.h.91.4

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			91.4
Root			$0.431051 - 1.32664i$ of defining polynomial
Character	$\chi$	$=$	495.91
Dual form			495.2.n.h.136.4

$q$-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 $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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	0.372302	−	0.928112i	$-0.378569\pi$
$2$	1.93752	−	1.40769i	1.37004	−	0.995390i	0.997734	−	0.0672778i	$-0.0214314\pi$
$3$		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	−0.767664	−	0.640852i	$-0.778581\pi$
$7$	0.608715	−	1.87343i	0.230073	−	0.708091i	0.997737	−	0.0672388i	$-0.0214189\pi$
$8$	−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	−0.865053	−	0.501681i	$-0.832715\pi$
$13$	−2.36251	+	1.71646i	−0.655241	+	0.476061i	0.209811	+	0.977742i	$0.432715\pi$
$14$	−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	0.999945	−	0.0104529i	$-0.00332731\pi$
$17$	5.35593	+	3.89131i	1.29900	+	0.943782i	0.299059	+	0.954235i	$0.403327\pi$
$18$		0			0
$19$	−1.10014	−	3.38588i	−0.252389	−	0.776775i	−0.994333	−	0.106312i	$-0.966096\pi$
$19$	−1.10014	−	3.38588i	−0.252389	−	0.776775i	0.741943	−	0.670463i	$-0.233904\pi$
$20$	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	0.797982	+	0.602682i	$0.205901\pi$
$29$	−1.08698	+	3.34537i	−0.201846	+	0.621219i	−0.999828	+	0.0185376i	$0.994099\pi$
$30$		0			0
$31$	−6.56916	+	4.77277i	−1.17986	+	0.857215i	−0.992155	−	0.125011i	$-0.960103\pi$
$31$	−6.56916	+	4.77277i	−1.17986	+	0.857215i	−0.187700	+	0.982226i	$0.560103\pi$
$32$	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	−0.773238	−	0.634116i	$-0.781364\pi$
$37$	1.36892	−	4.21310i	0.225049	−	0.692629i	0.998287	−	0.0585129i	$-0.0186359\pi$
$38$	−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	0.963383	+	0.268129i	$0.0864054\pi$
$41$	2.18726	+	6.73169i	0.341592	+	1.05131i	−0.621791	+	0.783183i	$0.713595\pi$
$42$		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	0.950443	−	0.310900i	$-0.100630\pi$
$47$	−0.00839056	−	0.0258235i	−0.00122389	−	0.00376674i	−0.951667	+	0.307133i	$0.900630\pi$
$48$		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	−0.792225	−	0.610229i	$-0.791078\pi$
$53$	−3.32464	+	2.41549i	−0.456675	+	0.331794i	0.335551	+	0.942022i	$0.391078\pi$
$54$		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	0.555315	+	0.831640i	$0.312598\pi$
$59$	−2.94011	+	9.04874i	−0.382770	+	1.17805i	−0.938085	+	0.346405i	$0.887402\pi$
$60$		0			0
$61$	−2.50982	−	1.82349i	−0.321349	−	0.233474i	0.415402	−	0.909638i	$-0.363641\pi$
$61$	−2.50982	−	1.82349i	−0.321349	−	0.233474i	−0.736751	+	0.676164i	$0.763641\pi$
$62$	−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	0.839330	−	0.543623i	$-0.182948\pi$
$71$	4.90133	+	3.56102i	0.581680	+	0.422616i	−0.257649	+	0.966239i	$0.582948\pi$
$72$		0			0
$73$	−0.733271	+	2.25678i	−0.0858229	+	0.264136i	−0.984754	−	0.173955i	$-0.944345\pi$
$73$	−0.733271	+	2.25678i	−0.0858229	+	0.264136i	0.898931	+	0.438091i	$0.144345\pi$
$74$	−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	0.154010	−	0.988069i	$-0.450781\pi$
$79$	10.1442	−	7.37019i	1.14131	−	0.829212i	0.987301	+	0.158858i	$0.0507811\pi$
$80$	−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	0.788748	−	0.614717i	$-0.210730\pi$
$83$	4.08014	+	2.96440i	0.447854	+	0.325385i	−0.340894	+	0.940102i	$0.610730\pi$
$84$		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	−0.926543	−	0.376189i	$-0.877234\pi$
$97$	−8.42159	+	6.11864i	−0.855083	+	0.621254i	0.0714597	+	0.997443i	$0.477234\pi$
$98$	7.47144			0.754729
$99$		0			0
$100$	3.73560			0.373560
$101$	13.9285	−	10.1196i	1.38594	−	1.00694i	0.389639	−	0.920968i	$-0.372600\pi$
$101$	13.9285	−	10.1196i	1.38594	−	1.00694i	0.996297	−	0.0859743i	$-0.0274003\pi$
$102$		0			0
$103$	2.06114	−	6.34353i	0.203090	−	0.625047i	−0.796696	−	0.604380i	$-0.793421\pi$
$103$	2.06114	−	6.34353i	0.203090	−	0.625047i	0.999786	−	0.0206671i	$-0.00657902\pi$
$104$	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	−0.985682	−	0.168616i	$-0.946070\pi$
$107$	−2.97246	−	9.14829i	−0.287359	−	0.884399i	0.698323	−	0.715783i	$-0.253930\pi$
$108$		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	0.885821	−	0.464026i	$-0.153596\pi$
$113$	−1.10098	−	3.38846i	−0.103571	−	0.318759i	−0.989392	+	0.145267i	$0.953596\pi$
$114$		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	−0.996207	−	0.0870147i	$-0.972267\pi$
$127$	−15.6285	−	11.3548i	−1.38681	−	1.00757i	−0.390601	−	0.920560i	$-0.627733\pi$
$128$	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	−0.926323	−	0.376730i	$-0.877049\pi$
$137$	−18.3865	−	13.3586i	−1.57086	−	1.14130i	−0.644541	−	0.764570i	$-0.722951\pi$
$138$		0			0
$139$	3.92759	−	12.0879i	0.333134	−	1.02528i	−0.634500	−	0.772923i	$-0.718794\pi$
$139$	3.92759	−	12.0879i	0.333134	−	1.02528i	0.967634	−	0.252358i	$-0.0812062\pi$
$140$	−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	0.435997	−	0.899948i	$-0.356396\pi$
$149$	−3.48099	−	2.52909i	−0.285174	−	0.207191i	−0.721171	+	0.692757i	$0.756396\pi$
$150$		0			0
$151$	5.43388	+	16.7238i	0.442203	+	1.36096i	0.885522	+	0.464597i	$0.153801\pi$
$151$	5.43388	+	16.7238i	0.442203	+	1.36096i	−0.443320	+	0.896364i	$0.646199\pi$
$152$	−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	−0.590088	−	0.807339i	$-0.700907\pi$
$157$	−7.35808	−	22.6458i	−0.587239	−	1.80733i	0.00284976	−	0.999996i	$-0.499093\pi$
$158$	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	0.258899	−	0.965904i	$-0.416640\pi$
$163$	16.0551	−	11.6647i	1.25753	−	0.913651i	0.998634	+	0.0522532i	$0.0166403\pi$
$164$	26.4410			2.06469
$165$		0			0
$166$	12.0783			0.937460
$167$	−11.7113	+	8.50878i	−0.906250	+	0.658429i	−0.940064	−	0.340999i	$-0.889235\pi$
$167$	−11.7113	+	8.50878i	−0.906250	+	0.658429i	0.0338134	+	0.999428i	$0.489235\pi$
$168$		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	0.887414	−	0.460973i	$-0.152500\pi$
$173$	−1.33466	−	4.10765i	−0.101472	−	0.312299i	−0.988886	+	0.148674i	$0.952500\pi$
$174$		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	0.999499	−	0.0316512i	$-0.0100766\pi$
$179$	2.30499	+	7.09404i	0.172283	+	0.530233i	−0.827216	+	0.561884i	$0.810077\pi$
$180$		0			0
$181$	16.5553	+	12.0281i	1.23054	+	0.894043i	0.996931	−	0.0782870i	$-0.0249450\pi$
$181$	16.5553	+	12.0281i	1.23054	+	0.894043i	0.233613	+	0.972330i	$0.424945\pi$
$182$	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	−0.997200	−	0.0747781i	$-0.976175\pi$
$191$	−2.02460	+	6.23107i	−0.146495	+	0.450865i	0.850705	+	0.525643i	$0.176175\pi$
$192$		0			0
$193$	5.52218	+	4.01210i	0.397495	+	0.288797i	0.768520	−	0.639826i	$-0.220994\pi$
$193$	5.52218	+	4.01210i	0.397495	+	0.288797i	−0.371025	+	0.928623i	$0.620994\pi$
$194$	−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	−0.548714	−	0.836010i	$-0.684883\pi$
$211$	1.11582	−	0.810693i	0.0768164	−	0.0558104i	0.625531	+	0.780200i	$0.284883\pi$
$212$	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	0.994689	+	0.102927i	$0.0328209\pi$
$223$	3.74028	+	11.5114i	0.250468	+	0.770861i	−0.744221	+	0.667933i	$0.767179\pi$
$224$	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	−0.600246	−	0.799815i	$-0.704931\pi$
$227$	5.35589	−	16.4837i	0.355483	−	1.09406i	0.955729	−	0.294248i	$-0.0950692\pi$
$228$		0			0
$229$	0.677291	−	0.492081i	0.0447567	−	0.0325176i	−0.565182	−	0.824966i	$-0.691194\pi$
$229$	0.677291	−	0.492081i	0.0447567	−	0.0325176i	0.609939	+	0.792449i	$0.291194\pi$
$230$	6.67984			0.440456
$231$		0			0
$232$	14.6210			0.959914
$233$	−15.4102	+	11.1962i	−1.00956	+	0.733487i	−0.964116	−	0.265480i	$-0.914470\pi$
$233$	−15.4102	+	11.1962i	−1.00956	+	0.733487i	−0.0454418	+	0.998967i	$0.514470\pi$
$234$		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	−0.782227	−	0.622993i	$-0.785916\pi$
$239$	−7.97065	−	24.5311i	−0.515578	−	1.58679i	0.266649	−	0.963794i	$-0.414084\pi$
$240$		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	−0.819164	−	0.573559i	$-0.805562\pi$
$251$	−8.34630	+	6.06394i	−0.526814	+	0.382752i	0.292351	+	0.956311i	$0.405562\pi$
$252$		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	−0.781880	−	0.623429i	$-0.785739\pi$
$257$	3.48064	−	10.7123i	0.217117	−	0.668216i	0.998997	−	0.0447871i	$-0.0142609\pi$
$258$		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	0.987399	−	0.158249i	$-0.0505849\pi$
$269$	18.7305	+	13.6085i	1.14202	+	0.829725i	0.154619	+	0.987974i	$0.450585\pi$
$270$		0			0
$271$	4.06201	−	12.5016i	0.246749	−	0.759417i	−0.748594	−	0.663028i	$-0.769271\pi$
$271$	4.06201	−	12.5016i	0.246749	−	0.759417i	0.995344	−	0.0963885i	$-0.0307291\pi$
$272$	−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	−0.810182	−	0.586179i	$-0.800632\pi$
$277$	−8.37246	+	6.08295i	−0.503052	+	0.365489i	0.307129	+	0.951668i	$0.400632\pi$
$278$	−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	0.597085	−	0.802178i	$-0.296325\pi$
$281$	0.313106	+	0.227485i	0.0186783	+	0.0135706i	−0.578407	+	0.815748i	$0.696325\pi$
$282$		0			0
$283$	−4.48858	−	13.8144i	−0.266818	−	0.821182i	−0.991269	−	0.131856i	$-0.957906\pi$
$283$	−4.48858	−	13.8144i	−0.266818	−	0.821182i	0.724451	−	0.689327i	$-0.242094\pi$
$284$	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	−0.723606	−	0.690214i	$-0.757517\pi$
$293$	4.57888	−	14.0923i	0.267501	−	0.823284i	0.991107	−	0.133070i	$-0.0424835\pi$
$294$		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	0.934416	−	0.356184i	$-0.115922\pi$
$311$	−0.544966	−	1.67723i	−0.0309022	−	0.0951072i	−0.965318	+	0.261077i	$0.915922\pi$
$312$		0			0
$313$	21.1748	+	15.3844i	1.19687	+	0.869577i	0.993973	−	0.109623i	$-0.0349643\pi$
$313$	21.1748	+	15.3844i	1.19687	+	0.869577i	0.202897	+	0.979200i	$0.434964\pi$
$314$	−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	−0.326556	−	0.945178i	$-0.605888\pi$
$317$	8.39392	−	6.09854i	0.471450	−	0.342528i	0.798006	+	0.602650i	$0.205888\pi$
$318$		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	−0.358197	−	0.933646i	$-0.616608\pi$
$337$	8.81849	−	27.1405i	0.480374	−	1.47844i	0.838571	−	0.544792i	$-0.183392\pi$
$338$	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	0.344623	−	0.938741i	$-0.388007\pi$
$347$	−8.22756	−	5.97767i	−0.441679	−	0.320898i	−0.786302	+	0.617843i	$0.788007\pi$
$348$		0			0
$349$	−7.32909	−	22.5566i	−0.392317	−	1.20743i	−0.931031	−	0.364940i	$-0.881090\pi$
$349$	−7.32909	−	22.5566i	−0.392317	−	1.20743i	0.538714	−	0.842489i	$-0.318910\pi$
$350$	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	0.539341	+	0.842087i	$0.318673\pi$
$359$	−7.42661	+	22.8568i	−0.391962	+	1.20633i	−0.931303	+	0.364246i	$0.881327\pi$
$360$		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	−0.964504	−	0.264070i	$-0.914935\pi$
$367$	−0.555320	+	1.70910i	−0.0289875	+	0.0892143i	0.935516	+	0.353284i	$0.114935\pi$
$368$	−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	0.658776	−	0.752340i	$-0.271075\pi$
$379$	2.85849	+	2.07682i	0.146831	+	0.106679i	−0.511945	+	0.859018i	$0.671075\pi$
$380$	−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	−0.547749	−	0.836643i	$-0.684515\pi$
$383$	1.53984	−	1.11876i	0.0786821	−	0.0571659i	0.626431	+	0.779477i	$0.284515\pi$
$384$		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	−0.990876	−	0.134774i	$-0.956969\pi$
$389$	−2.16998	+	6.67850i	−0.110022	+	0.338613i	0.880854	+	0.473388i	$0.156969\pi$
$390$		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	−0.122357	−	0.992486i	$-0.539045\pi$
$401$	−22.1091	−	16.0632i	−1.10408	−	0.802160i	−0.981721	+	0.190326i	$0.939045\pi$
$402$		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	−0.331100	−	0.943596i	$-0.607420\pi$
$409$	9.38375	−	6.81769i	0.463997	−	0.337113i	0.795097	+	0.606482i	$0.207420\pi$
$410$	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	0.988175	+	0.153328i	$0.0489989\pi$
$421$	5.72149	+	17.6089i	0.278848	+	0.858207i	−0.709327	+	0.704880i	$0.751001\pi$
$422$	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	0.0115333	−	0.999933i	$-0.496329\pi$
$431$	20.0566	−	14.5719i	0.966091	−	0.701906i	0.954557	+	0.298028i	$0.0963287\pi$
$432$		0			0
$433$	−10.9348	+	33.6539i	−0.525494	+	1.61730i	0.237844	+	0.971303i	$0.423559\pi$
$433$	−10.9348	+	33.6539i	−0.525494	+	1.61730i	−0.763338	+	0.646000i	$0.776441\pi$
$434$	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	0.761636	+	0.648006i	$0.224397\pi$
$443$	11.0783	+	34.0956i	0.526348	+	1.61993i	−0.235288	+	0.971926i	$0.575603\pi$
$444$		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	0.0576072	−	0.998339i	$-0.481653\pi$
$449$	21.7169	−	15.7783i	1.02489	−	0.744623i	0.967279	+	0.253716i	$0.0816529\pi$
$450$		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	0.893707	−	0.448651i	$-0.148095\pi$
$457$	15.8875	+	11.5429i	0.743185	+	0.539955i	−0.150522	+	0.988607i	$0.548095\pi$
$458$	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	0.763725	−	0.645541i	$-0.223368\pi$
$467$	8.33684	+	6.05707i	0.385783	+	0.280288i	−0.377942	+	0.925829i	$0.623368\pi$
$468$		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	0.778165	−	0.628060i	$-0.216151\pi$
$479$	9.22083	+	6.69932i	0.421310	+	0.306100i	−0.356854	+	0.934160i	$0.616151\pi$
$480$		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	−0.831823	−	0.555040i	$-0.812703\pi$
$487$	−10.7054	−	32.9479i	−0.485109	−	1.49301i	0.346715	−	0.937971i	$-0.387297\pi$
$488$	−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	0.280473	+	0.959862i	$0.409509\pi$
$491$	−11.3147	+	34.8232i	−0.510627	+	1.57155i	−0.791100	+	0.611686i	$0.790491\pi$
$492$		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	0.687733	+	0.725964i	$0.258606\pi$
$499$	−6.59797	+	20.3065i	−0.295366	+	0.909042i	−0.983098	+	0.183078i	$0.941394\pi$
$500$	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	0.998687	−	0.0512270i	$-0.0163132\pi$
$503$	3.60237	+	11.0870i	0.160622	+	0.494343i	−0.838065	+	0.545570i	$0.816313\pi$
$504$		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	0.923444	+	0.383732i	$0.125361\pi$
$509$	9.06760	+	27.9072i	0.401914	+	1.23697i	−0.521530	+	0.853233i	$0.674639\pi$
$510$		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	−0.920317	−	0.391173i	$-0.872069\pi$
$521$	1.23624	−	3.80477i	0.0541608	−	0.166690i	0.974478	+	0.224483i	$0.0720694\pi$
$522$		0			0
$523$	3.59665	+	2.61312i	0.157271	+	0.114264i	0.663637	−	0.748054i	$-0.269012\pi$
$523$	3.59665	+	2.61312i	0.157271	+	0.114264i	−0.506367	+	0.862318i	$0.669012\pi$
$524$	−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	−0.334360	−	0.942445i	$-0.608520\pi$
$541$	10.6676	−	7.75046i	0.458636	−	0.333218i	0.792996	+	0.609227i	$0.208520\pi$
$542$	−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	0.962640	−	0.270785i	$-0.0872832\pi$
$547$	0.577321	+	1.77681i	0.0246845	+	0.0759710i	−0.937955	+	0.346756i	$0.887283\pi$
$548$	−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	−0.822685	−	0.568498i	$-0.807525\pi$
$557$	4.17820	−	12.8592i	0.177036	−	0.544861i	0.999721	+	0.0236374i	$0.00752471\pi$
$558$		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	0.0716337	−	0.997431i	$-0.477179\pi$
$563$	24.7333	−	17.9698i	1.04238	−	0.757336i	0.970749	+	0.240095i	$0.0771787\pi$
$564$		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	0.849116	+	0.528206i	$0.177135\pi$
$569$	11.2742	+	34.6984i	0.472638	+	1.45463i	−0.376478	+	0.926426i	$0.622865\pi$
$570$		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	0.971860	−	0.235558i	$-0.0756919\pi$
$577$	25.1775	+	18.2925i	1.04815	+	0.761527i	0.0762921	+	0.997086i	$0.475692\pi$
$578$	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	0.512297	+	0.858808i	$0.328795\pi$
$587$	−9.85974	+	30.3452i	−0.406955	+	1.25248i	−0.919252	+	0.393670i	$0.871205\pi$
$588$		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	0.841522	−	0.540222i	$-0.181660\pi$
$599$	14.3857	+	10.4519i	0.587785	+	0.427051i	−0.253737	+	0.967273i	$0.581660\pi$
$600$		0			0
$601$	−4.57989	+	14.0954i	−0.186818	+	0.574965i	−0.999975	−	0.00707858i	$-0.997747\pi$
$601$	−4.57989	+	14.0954i	−0.186818	+	0.574965i	0.813157	+	0.582044i	$0.197747\pi$
$602$	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	−0.337620	−	0.941283i	$-0.609622\pi$
$607$	11.1672	−	8.11345i	0.453263	−	0.329315i	0.790883	+	0.611968i	$0.209622\pi$
$608$	−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	0.987637	+	0.156761i	$0.0501053\pi$
$613$	6.95138	+	21.3942i	0.280764	+	0.864102i	−0.706873	+	0.707341i	$0.749895\pi$
$614$	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	0.933376	−	0.358899i	$-0.116848\pi$
$619$	−0.813488	−	2.50366i	−0.0326968	−	0.100630i	−0.966073	+	0.258269i	$0.916848\pi$
$620$	−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	−0.685730	−	0.727856i	$-0.740517\pi$
$631$	7.45705	−	22.9504i	0.296860	−	0.913642i	0.982590	−	0.185786i	$-0.0594831\pi$
$632$	−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	0.686770	+	0.726875i	$0.259028\pi$
$641$	14.1378	+	43.5115i	0.558408	+	1.71860i	−0.128362	+	0.991727i	$0.540972\pi$
$642$		0			0
$643$	5.34699	+	3.88482i	0.210865	+	0.153202i	0.688205	−	0.725516i	$-0.258399\pi$
$643$	5.34699	+	3.88482i	0.210865	+	0.153202i	−0.477340	+	0.878719i	$0.658399\pi$
$644$	−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	−0.616995	−	0.786967i	$-0.711650\pi$
$647$	−1.50597	+	1.09415i	−0.0592058	+	0.0430155i	0.557789	+	0.829983i	$0.311650\pi$
$648$		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	0.549589	+	0.835435i	$0.314784\pi$
$653$	−9.86620	+	30.3650i	−0.386094	+	1.18828i	−0.935683	+	0.352841i	$0.885216\pi$
$654$		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	−0.555075	−	0.831800i	$-0.687310\pi$
$673$	1.67294	−	1.21546i	0.0644870	−	0.0468525i	0.619562	+	0.784948i	$0.287310\pi$
$674$	−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	0.832369	−	0.554222i	$-0.186984\pi$
$677$	14.6355	+	10.6333i	0.562489	+	0.408672i	−0.269880	+	0.962894i	$0.586984\pi$
$678$		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	−0.804311	−	0.594208i	$-0.797465\pi$
$691$	−12.8209	+	9.31495i	−0.487731	+	0.354358i	0.316580	+	0.948566i	$0.397465\pi$
$692$	−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	−0.978913	−	0.204277i	$-0.934516\pi$
$701$	−8.12897	−	25.0184i	−0.307027	−	0.944932i	0.671886	−	0.740655i	$-0.265484\pi$
$702$		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	0.0108444	−	0.999941i	$-0.496548\pi$
$709$	−24.9444	−	18.1231i	−0.936805	−	0.680629i	−0.947649	+	0.319312i	$0.896548\pi$
$710$	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	0.177841	+	0.984059i	$0.443089\pi$
$719$	−14.5990	+	44.9311i	−0.544451	+	1.67565i	−0.722292	+	0.691588i	$0.756911\pi$
$720$		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	−0.654443	−	0.756111i	$-0.727097\pi$
$733$	8.64860	−	26.6177i	0.319443	−	0.983146i	0.973887	−	0.227035i	$-0.0729031\pi$
$734$	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	−0.546802	−	0.837262i	$-0.684155\pi$
$739$	2.18866	−	1.59015i	0.0805111	−	0.0584947i	0.627313	+	0.778767i	$0.284155\pi$
$740$	−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	0.647583	−	0.761995i	$-0.275780\pi$
$743$	3.35268	+	2.43586i	0.122998	+	0.0893631i	−0.524586	+	0.851358i	$0.675780\pi$
$744$		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	−0.807361	−	0.590058i	$-0.799105\pi$
$751$	−13.7301	−	42.2570i	−0.501019	−	1.54198i	0.306342	−	0.951922i	$-0.400895\pi$
$752$	−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	−0.933736	−	0.357961i	$-0.883472\pi$
$757$	−24.2625	+	17.6277i	−0.881835	+	0.640691i	0.0519011	+	0.998652i	$0.483472\pi$
$758$	8.46192			0.307351
$759$		0			0
$760$	−14.7980			−0.536782
$761$	32.2328	−	23.4185i	1.16844	−	0.848921i	0.177618	−	0.984099i	$-0.443161\pi$
$761$	32.2328	−	23.4185i	1.16844	−	0.848921i	0.990821	+	0.135178i	$0.0431607\pi$
$762$		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	0.818354	−	0.574715i	$-0.194887\pi$
$773$	−5.04670	−	15.5321i	−0.181517	−	0.558652i	−0.999871	+	0.0160625i	$0.994887\pi$
$774$		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	0.689192	−	0.724579i	$-0.257966\pi$
$787$	5.97674	+	4.34236i	0.213048	+	0.154788i	−0.476144	+	0.879367i	$0.657966\pi$
$788$	−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	0.867864	−	0.496802i	$-0.165492\pi$
$797$	18.7331	+	13.6104i	0.663562	+	0.482106i	−0.204302	+	0.978908i	$0.565492\pi$
$798$		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	0.354535	−	0.935043i	$-0.384639\pi$
$809$	−12.0935	−	8.78647i	−0.425186	−	0.308916i	−0.779721	+	0.626127i	$0.784639\pi$
$810$		0			0
$811$	−7.76050	−	23.8844i	−0.272508	−	0.838694i	−0.989868	−	0.141991i	$-0.954650\pi$
$811$	−7.76050	−	23.8844i	−0.272508	−	0.838694i	0.717360	−	0.696703i	$-0.245350\pi$
$812$	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	−0.855201	−	0.518296i	$-0.826566\pi$
$821$	4.04920	−	12.4622i	0.141318	−	0.434932i	0.996519	+	0.0833641i	$0.0265664\pi$
$822$		0			0
$823$	16.6448	−	12.0932i	0.580202	−	0.421541i	−0.258595	−	0.965986i	$-0.583259\pi$
$823$	16.6448	−	12.0932i	0.580202	−	0.421541i	0.838797	+	0.544444i	$0.183259\pi$
$824$	−27.7245			−0.965828
$825$		0			0
$826$	44.8852			1.56176
$827$	10.2214	−	7.42627i	0.355432	−	0.258237i	−0.395712	−	0.918375i	$-0.629502\pi$
$827$	10.2214	−	7.42627i	0.355432	−	0.258237i	0.751144	+	0.660138i	$0.229502\pi$
$828$		0			0
$829$	2.40686	−	7.40755i	0.0835937	−	0.257275i	−0.900520	−	0.434815i	$-0.856814\pi$
$829$	2.40686	−	7.40755i	0.0835937	−	0.257275i	0.984114	+	0.177540i	$0.0568139\pi$
$830$	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	−0.971013	−	0.239028i	$-0.923171\pi$
$839$	−9.44113	−	29.0568i	−0.325944	−	1.00315i	0.645068	−	0.764125i	$-0.276829\pi$
$840$		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	0.172383	−	0.985030i	$-0.444853\pi$
$853$	−20.7705	−	15.0906i	−0.711167	−	0.516693i	−0.883550	+	0.468337i	$0.844853\pi$
$854$	−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	0.391847	−	0.920030i	$-0.371836\pi$
$863$	−10.6364	−	7.72777i	−0.362066	−	0.263056i	−0.753913	+	0.656974i	$0.771836\pi$
$864$		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	−0.824751	−	0.565496i	$-0.808685\pi$
$877$	−14.5081	−	44.6513i	−0.489904	−	1.50777i	0.334847	−	0.942273i	$-0.391315\pi$
$878$	−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	0.882387	−	0.470525i	$-0.155936\pi$
$883$	−3.21065	−	9.88136i	−0.108047	−	0.332534i	−0.990433	+	0.137991i	$0.955936\pi$
$884$	−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	−0.969031	−	0.246938i	$-0.920576\pi$
$887$	−1.18899	+	3.65932i	−0.0399222	+	0.122868i	0.929109	+	0.369806i	$0.120576\pi$
$888$		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	0.571491	−	0.820608i	$-0.306365\pi$
$907$	−0.974354	−	0.707910i	−0.0323529	−	0.0235058i	−0.603844	+	0.797102i	$0.706365\pi$
$908$	−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	−0.970965	−	0.239223i	$-0.923107\pi$
$911$	−31.4956	+	22.8829i	−1.04349	+	0.758143i	−0.0725299	+	0.997366i	$0.523107\pi$
$912$		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	0.708086	−	0.706127i	$-0.249559\pi$
$919$	7.74032	+	5.62368i	0.255330	+	0.185508i	−0.452756	+	0.891635i	$0.649559\pi$
$920$	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	0.670161	−	0.742216i	$-0.266225\pi$
$929$	5.22304	+	3.79476i	0.171362	+	0.124502i	−0.498798	+	0.866718i	$0.666225\pi$
$930$		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	−0.594091	−	0.804398i	$-0.702488\pi$
$937$	−0.387158	+	0.281287i	−0.0126479	+	0.00918924i	0.581443	+	0.813587i	$0.302488\pi$
$938$	−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	0.319154	−	0.947703i	$-0.396601\pi$
$941$	−14.8330	−	10.7768i	−0.483541	−	0.351313i	−0.802695	+	0.596390i	$0.796601\pi$
$942$		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	−0.804666	−	0.593728i	$-0.797656\pi$
$953$	6.02925	−	18.5561i	0.195307	−	0.601092i	0.999973	−	0.00736474i	$-0.00234429\pi$
$954$		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	0.705325	+	0.708884i	$0.250801\pi$
$971$	17.1814	+	52.8788i	0.551377	+	1.69696i	−0.153948	+	0.988079i	$0.549199\pi$
$972$		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	0.127796	−	0.991800i	$-0.459210\pi$
$977$	34.7123	−	25.2200i	1.11055	−	0.806858i	0.982749	+	0.184942i	$0.0592098\pi$
$978$		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	−0.622976	−	0.782241i	$-0.714076\pi$
$983$	10.6854	−	32.8864i	0.340812	−	1.04891i	0.963788	−	0.266671i	$-0.0859236\pi$
$984$		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	−0.929335	−	0.369238i	$-0.879619\pi$
$997$	1.24866	−	3.84297i	0.0395454	−	0.121708i	0.968880	+	0.247530i	$0.0796188\pi$
$998$	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.91.4	yes	16
3.2	odd	2		495.2.n.g.91.1	✓	16
11.2	odd	10		5445.2.a.cc.1.7		8
11.4	even	5	inner	495.2.n.h.136.4	yes	16
11.9	even	5		5445.2.a.ca.1.2		8
33.2	even	10		5445.2.a.cb.1.2		8
33.20	odd	10		5445.2.a.cd.1.7		8
33.26	odd	10		495.2.n.g.136.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.n.g.91.1	✓	16	3.2	odd	2
495.2.n.g.136.1	yes	16	33.26	odd	10
495.2.n.h.91.4	yes	16	1.1	even	1	trivial
495.2.n.h.136.4	yes	16	11.4	even	5	inner
5445.2.a.ca.1.2		8	11.9	even	5
5445.2.a.cb.1.2		8	33.2	even	10
5445.2.a.cc.1.7		8	11.2	odd	10
5445.2.a.cd.1.7		8	33.20	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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