LMFDB - Embedded newform 495.2.n.h.91.3

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			91.3
Root			$0.0698401 - 0.214946i$ of defining polynomial
Character	$\chi$	$=$	495.91
Dual form			495.2.n.h.136.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.991861 - 0.720629i) q^{2} +(-0.153553 + 0.472586i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.139581 + 0.429587i) q^{7} +(0.945971 + 2.91140i) q^{8} +O(q^{10})$	\(q+(0.991861 - 0.720629i) q^{2} +(-0.153553 + 0.472586i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.139581 + 0.429587i) q^{7} +(0.945971 + 2.91140i) q^{8} +1.22601 q^{10} +(-1.55234 + 2.93091i) q^{11} +(3.91592 - 2.84508i) q^{13} +(0.171128 + 0.526677i) q^{14} +(2.23230 + 1.62186i) q^{16} +(-0.598736 - 0.435007i) q^{17} +(2.10247 + 6.47075i) q^{19} +(-0.402006 + 0.292074i) q^{20} +(0.572395 + 4.02572i) q^{22} -0.00634166 q^{23} +(0.309017 + 0.951057i) q^{25} +(1.83380 - 5.64385i) q^{26} +(-0.181584 - 0.131928i) q^{28} +(-0.100091 + 0.308048i) q^{29} +(4.53521 - 3.29503i) q^{31} -2.73956 q^{32} -0.907341 q^{34} +(-0.365429 + 0.265500i) q^{35} +(2.27713 - 7.00828i) q^{37} +(6.74837 + 4.90298i) q^{38} +(-0.945971 + 2.91140i) q^{40} +(-3.39006 - 10.4335i) q^{41} -1.80668 q^{43} +(-1.14674 - 1.18366i) q^{44} +(-0.00629004 + 0.00456998i) q^{46} +(-0.518988 - 1.59728i) q^{47} +(5.49806 + 3.99457i) q^{49} +(0.991861 + 0.720629i) q^{50} +(0.743247 + 2.28748i) q^{52} +(-6.98948 + 5.07816i) q^{53} +(-2.97862 + 1.45871i) q^{55} -1.38274 q^{56} +(0.122712 + 0.377669i) q^{58} +(-0.463691 + 1.42709i) q^{59} +(-10.5540 - 7.66790i) q^{61} +(2.12381 - 6.53641i) q^{62} +(-7.18186 + 5.21793i) q^{64} +4.84034 q^{65} +9.60773 q^{67} +(0.297516 - 0.216158i) q^{68} +(-0.171128 + 0.526677i) q^{70} +(-9.23296 - 6.70814i) q^{71} +(3.16430 - 9.73870i) q^{73} +(-2.79178 - 8.59220i) q^{74} -3.38083 q^{76} +(-1.04241 - 1.07597i) q^{77} +(1.69866 - 1.23415i) q^{79} +(0.852662 + 2.62422i) q^{80} +(-10.8812 - 7.90563i) q^{82} +(12.8589 + 9.34255i) q^{83} +(-0.228697 - 0.703856i) q^{85} +(-1.79197 + 1.30194i) q^{86} +(-10.0015 - 1.74692i) q^{88} -9.36925 q^{89} +(0.675622 + 2.07935i) q^{91} +(0.000973778 - 0.00299698i) q^{92} +(-1.66581 - 1.21028i) q^{94} +(-2.10247 + 6.47075i) q^{95} +(-4.75689 + 3.45608i) q^{97} +8.33191 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.991861	−	0.720629i	0.701351	−	0.509562i	−0.179021	−	0.983845i	$-0.557293\pi$
$2$	0.991861	−	0.720629i	0.701351	−	0.509562i	0.880372	+	0.474284i	$0.157293\pi$
$3$		0			0
$3$		0			0
$4$	−0.153553	+	0.472586i	−0.0767763	+	0.236293i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	−0.139581	+	0.429587i	−0.0527568	+	0.162369i	−0.973964	−	0.226705i	$-0.927205\pi$
$7$	−0.139581	+	0.429587i	−0.0527568	+	0.162369i	0.921207	+	0.389073i	$0.127205\pi$
$8$	0.945971	+	2.91140i	0.334451	+	1.02933i
$9$		0			0
$10$	1.22601			0.387698
$11$	−1.55234	+	2.93091i	−0.468048	+	0.883703i
$11$	−1.55234	+	2.93091i	−0.468048	+	0.883703i
$12$		0			0
$13$	3.91592	−	2.84508i	1.08608	−	0.789084i	0.107348	−	0.994222i	$-0.465764\pi$
$13$	3.91592	−	2.84508i	1.08608	−	0.789084i	0.978733	+	0.205138i	$0.0657643\pi$
$14$	0.171128	+	0.526677i	0.0457358	+	0.140760i
$15$		0			0
$16$	2.23230	+	1.62186i	0.558074	+	0.405465i
$17$	−0.598736	−	0.435007i	−0.145215	−	0.105505i	0.512806	−	0.858505i	$-0.328606\pi$
$17$	−0.598736	−	0.435007i	−0.145215	−	0.105505i	−0.658021	+	0.753000i	$0.728606\pi$
$18$		0			0
$19$	2.10247	+	6.47075i	0.482340	+	1.48449i	0.835796	+	0.549040i	$0.185007\pi$
$19$	2.10247	+	6.47075i	0.482340	+	1.48449i	−0.353456	+	0.935451i	$0.614993\pi$
$20$	−0.402006	+	0.292074i	−0.0898912	+	0.0653098i
$21$		0			0
$22$	0.572395	+	4.02572i	0.122035	+	0.858286i
$23$	−0.00634166			−0.00132233			−0.000661164	−	1.00000i	$-0.500210\pi$
$23$	−0.00634166			−0.00132233			−0.000661164		1.00000i	$0.500210\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	1.83380	−	5.64385i	0.359637	−	1.10685i
$27$		0			0
$28$	−0.181584	−	0.131928i	−0.0343162	−	0.0249321i
$29$	−0.100091	+	0.308048i	−0.0185864	+	0.0572030i	−0.959920	−	0.280276i	$-0.909574\pi$
$29$	−0.100091	+	0.308048i	−0.0185864	+	0.0572030i	0.941333	+	0.337479i	$0.109574\pi$
$30$		0			0
$31$	4.53521	−	3.29503i	0.814548	−	0.591804i	−0.100597	−	0.994927i	$-0.532075\pi$
$31$	4.53521	−	3.29503i	0.814548	−	0.591804i	0.915146	+	0.403123i	$0.132075\pi$
$32$	−2.73956			−0.484291
$33$		0			0
$34$	−0.907341			−0.155608
$35$	−0.365429	+	0.265500i	−0.0617688	+	0.0448776i
$36$		0			0
$37$	2.27713	−	7.00828i	0.374358	−	1.15215i	−0.569553	−	0.821954i	$-0.692884\pi$
$37$	2.27713	−	7.00828i	0.374358	−	1.15215i	0.943911	−	0.330200i	$-0.107116\pi$
$38$	6.74837	+	4.90298i	1.09473	+	0.795368i
$39$		0			0
$40$	−0.945971	+	2.91140i	−0.149571	+	0.460332i
$41$	−3.39006	−	10.4335i	−0.529438	−	1.62944i	−0.755369	−	0.655299i	$-0.772543\pi$
$41$	−3.39006	−	10.4335i	−0.529438	−	1.62944i	0.225931	−	0.974143i	$-0.427457\pi$
$42$		0			0
$43$	−1.80668			−0.275516			−0.137758	−	0.990466i	$-0.543990\pi$
$43$	−1.80668			−0.275516			−0.137758	+	0.990466i	$0.543990\pi$
$44$	−1.14674	−	1.18366i	−0.172878	−	0.178444i
$45$		0			0
$46$	−0.00629004	+	0.00456998i	−0.000927416	+	0.000673807i
$47$	−0.518988	−	1.59728i	−0.0757022	−	0.232987i	0.906044	−	0.423184i	$-0.139088\pi$
$47$	−0.518988	−	1.59728i	−0.0757022	−	0.232987i	−0.981746	+	0.190196i	$0.939088\pi$
$48$		0			0
$49$	5.49806	+	3.99457i	0.785437	+	0.570653i
$50$	0.991861	+	0.720629i	0.140270	+	0.101912i
$51$		0			0
$52$	0.743247	+	2.28748i	0.103070	+	0.317216i
$53$	−6.98948	+	5.07816i	−0.960079	+	0.697539i	−0.953169	−	0.302438i	$-0.902200\pi$
$53$	−6.98948	+	5.07816i	−0.960079	+	0.697539i	−0.00691024	+	0.999976i	$0.502200\pi$
$54$		0			0
$55$	−2.97862	+	1.45871i	−0.401636	+	0.196693i
$56$	−1.38274			−0.184776
$57$		0			0
$58$	0.122712	+	0.377669i	0.0161129	+	0.0495903i
$59$	−0.463691	+	1.42709i	−0.0603674	+	0.185792i	−0.976692	−	0.214643i	$-0.931141\pi$
$59$	−0.463691	+	1.42709i	−0.0603674	+	0.185792i	0.916325	+	0.400435i	$0.131141\pi$
$60$		0			0
$61$	−10.5540	−	7.66790i	−1.35130	−	0.981774i	−0.998946	−	0.0459057i	$-0.985383\pi$
$61$	−10.5540	−	7.66790i	−1.35130	−	0.981774i	−0.352350	−	0.935868i	$-0.614617\pi$
$62$	2.12381	−	6.53641i	0.269724	−	0.830125i
$63$		0			0
$64$	−7.18186	+	5.21793i	−0.897733	+	0.652241i
$65$	4.84034			0.600371
$66$		0			0
$67$	9.60773			1.17377			0.586885	−	0.809670i	$-0.300354\pi$
$67$	9.60773			1.17377			0.586885	+	0.809670i	$0.300354\pi$
$68$	0.297516	−	0.216158i	0.0360791	−	0.0262130i
$69$		0			0
$70$	−0.171128	+	0.526677i	−0.0204537	+	0.0629500i
$71$	−9.23296	−	6.70814i	−1.09575	−	0.796110i	−0.115390	−	0.993320i	$-0.536812\pi$
$71$	−9.23296	−	6.70814i	−1.09575	−	0.796110i	−0.980361	+	0.197211i	$0.936812\pi$
$72$		0			0
$73$	3.16430	−	9.73870i	0.370353	−	1.13983i	−0.576208	−	0.817303i	$-0.695468\pi$
$73$	3.16430	−	9.73870i	0.370353	−	1.13983i	0.946561	−	0.322526i	$-0.104532\pi$
$74$	−2.79178	−	8.59220i	−0.324537	−	0.998823i
$75$		0			0
$76$	−3.38083			−0.387807
$77$	−1.04241	−	1.07597i	−0.118793	−	0.122618i
$78$		0			0
$79$	1.69866	−	1.23415i	0.191114	−	0.138852i	−0.488114	−	0.872780i	$-0.662315\pi$
$79$	1.69866	−	1.23415i	0.191114	−	0.138852i	0.679228	+	0.733928i	$0.262315\pi$
$80$	0.852662	+	2.62422i	0.0953305	+	0.293397i
$81$		0			0
$82$	−10.8812	−	7.90563i	−1.20162	−	0.873030i
$83$	12.8589	+	9.34255i	1.41145	+	1.02548i	0.993110	+	0.117187i	$0.0373876\pi$
$83$	12.8589	+	9.34255i	1.41145	+	1.02548i	0.418339	+	0.908291i	$0.362612\pi$
$84$		0			0
$85$	−0.228697	−	0.703856i	−0.0248056	−	0.0763439i
$86$	−1.79197	+	1.30194i	−0.193233	+	0.140392i
$87$		0			0
$88$	−10.0015	−	1.74692i	−1.06617	−	0.186223i
$89$	−9.36925			−0.993138			−0.496569	−	0.867997i	$-0.665407\pi$
$89$	−9.36925			−0.993138			−0.496569	+	0.867997i	$0.665407\pi$
$90$		0			0
$91$	0.675622	+	2.07935i	0.0708244	+	0.217975i
$92$	0.000973778	−	0.00299698i	0.000101523	−	0.000312457i
$93$		0			0
$94$	−1.66581	−	1.21028i	−0.171815	−	0.124831i
$95$	−2.10247	+	6.47075i	−0.215709	+	0.663885i
$96$		0			0
$97$	−4.75689	+	3.45608i	−0.482989	+	0.350912i	−0.802482	−	0.596677i	$-0.796487\pi$
$97$	−4.75689	+	3.45608i	−0.482989	+	0.350912i	0.319493	+	0.947589i	$0.396487\pi$
$98$	8.33191			0.841650
$99$		0			0
$100$	−0.496906			−0.0496906
$101$	1.78628	−	1.29781i	0.177742	−	0.129137i	−0.495357	−	0.868689i	$-0.664963\pi$
$101$	1.78628	−	1.29781i	0.177742	−	0.129137i	0.673099	+	0.739552i	$0.264963\pi$
$102$		0			0
$103$	2.99111	−	9.20568i	0.294723	−	0.907063i	−0.688592	−	0.725149i	$-0.741771\pi$
$103$	2.99111	−	9.20568i	0.294723	−	0.907063i	0.983314	−	0.181914i	$-0.0582292\pi$
$104$	11.9875	+	8.70944i	1.17547	+	0.854031i
$105$		0			0
$106$	−3.27313	+	10.0736i	−0.317914	+	0.978439i
$107$	−3.63294	−	11.1810i	−0.351210	−	1.08091i	−0.958175	−	0.286184i	$-0.907613\pi$
$107$	−3.63294	−	11.1810i	−0.351210	−	1.08091i	0.606965	−	0.794729i	$-0.292387\pi$
$108$		0			0
$109$	−12.5091			−1.19816			−0.599078	−	0.800691i	$-0.704466\pi$
$109$	−12.5091			−1.19816			−0.599078	+	0.800691i	$0.704466\pi$
$110$	−1.90318	+	3.59332i	−0.181461	+	0.342609i
$111$		0			0
$112$	−1.00832	+	0.732586i	−0.0952771	+	0.0692228i
$113$	3.06115	+	9.42124i	0.287968	+	0.886276i	0.985493	+	0.169715i	$0.0542847\pi$
$113$	3.06115	+	9.42124i	0.287968	+	0.886276i	−0.697525	+	0.716561i	$0.745715\pi$
$114$		0			0
$115$	−0.00513051	−	0.00372753i	−0.000478422	−	0.000347594i
$116$	−0.130210	−	0.0946030i	−0.0120897	−	0.00878367i
$117$		0			0
$118$	0.568489	+	1.74963i	0.0523336	+	0.161066i
$119$	0.270446	−	0.196491i	0.0247917	−	0.0180123i
$120$		0			0
$121$	−6.18048	−	9.09954i	−0.561862	−	0.827231i
$122$	−15.9938			−1.44801
$123$		0			0
$124$	0.860790	+	2.64924i	0.0773012	+	0.237909i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	0.454312	+	0.330077i	0.0403137	+	0.0292896i	0.607760	−	0.794121i	$-0.292068\pi$
$127$	0.454312	+	0.330077i	0.0403137	+	0.0292896i	−0.567446	+	0.823411i	$0.692068\pi$
$128$	−1.67007	+	5.13995i	−0.147615	+	0.454312i
$129$		0			0
$130$	4.80095	−	3.48809i	0.421071	−	0.305926i
$131$	3.03500			0.265170			0.132585	−	0.991172i	$-0.457672\pi$
$131$	3.03500			0.265170			0.132585	+	0.991172i	$0.457672\pi$
$132$		0			0
$133$	−3.07322			−0.266482
$134$	9.52953	−	6.92361i	0.823226	−	0.598108i
$135$		0			0
$136$	0.700092	−	2.15466i	0.0600324	−	0.184761i
$137$	16.7469	+	12.1674i	1.43079	+	1.03953i	0.989869	+	0.141981i	$0.0453471\pi$
$137$	16.7469	+	12.1674i	1.43079	+	1.03953i	0.440918	+	0.897547i	$0.354653\pi$
$138$		0			0
$139$	1.09662	−	3.37504i	0.0930139	−	0.286267i	−0.893717	−	0.448631i	$-0.851912\pi$
$139$	1.09662	−	3.37504i	0.0930139	−	0.286267i	0.986731	+	0.162364i	$0.0519117\pi$
$140$	−0.0693589	−	0.213465i	−0.00586190	−	0.0180411i
$141$		0			0
$142$	−13.9919			−1.17417
$143$	2.25985	+	15.8937i	0.188978	+	1.32910i
$144$		0			0
$145$	−0.262041	+	0.190384i	−0.0217613	+	0.0158105i
$146$	−3.87945	−	11.9397i	−0.321065	−	0.988138i
$147$		0			0
$148$	2.96236	+	2.15228i	0.243504	+	0.176916i
$149$	−5.10052	−	3.70575i	−0.417851	−	0.303587i	0.358921	−	0.933368i	$-0.383145\pi$
$149$	−5.10052	−	3.70575i	−0.417851	−	0.303587i	−0.776773	+	0.629781i	$0.783145\pi$
$150$		0			0
$151$	−1.13852	−	3.50400i	−0.0926512	−	0.285151i	0.893983	−	0.448100i	$-0.147899\pi$
$151$	−1.13852	−	3.50400i	−0.0926512	−	0.285151i	−0.986634	+	0.162949i	$0.947899\pi$
$152$	−16.8500	+	12.2423i	−1.36672	+	0.992980i
$153$		0			0
$154$	−1.80929	−	0.316022i	−0.145797	−	0.0254657i
$155$	5.60583			0.450271
$156$		0			0
$157$	0.874113	+	2.69024i	0.0697618	+	0.214705i	0.979859	−	0.199690i	$-0.0639934\pi$
$157$	0.874113	+	2.69024i	0.0697618	+	0.214705i	−0.910097	+	0.414394i	$0.863993\pi$
$158$	0.795469	−	2.44820i	0.0632841	−	0.194768i
$159$		0			0
$160$	−2.21635	−	1.61028i	−0.175218	−	0.127303i
$161$	0.000885178	−	0.00272430i	6.97618e−5	−	0.000214705i
$162$		0			0
$163$	−7.16094	+	5.20273i	−0.560888	+	0.407509i	−0.831784	−	0.555099i	$-0.812680\pi$
$163$	−7.16094	+	5.20273i	−0.560888	+	0.407509i	0.270896	+	0.962609i	$0.412680\pi$
$164$	5.45129			0.425674
$165$		0			0
$166$	19.4868			1.51247
$167$	15.9249	−	11.5701i	1.23230	−	0.895320i	0.235241	−	0.971937i	$-0.424412\pi$
$167$	15.9249	−	11.5701i	1.23230	−	0.895320i	0.997061	+	0.0766171i	$0.0244119\pi$
$168$		0			0
$169$	3.22271	−	9.91849i	0.247901	−	0.762961i
$170$	−0.734054	−	0.533322i	−0.0562994	−	0.0409039i
$171$		0			0
$172$	0.277420	−	0.853811i	0.0211531	−	0.0651025i
$173$	−0.899661	−	2.76887i	−0.0684000	−	0.210513i	0.911014	−	0.412375i	$-0.135301\pi$
$173$	−0.899661	−	2.76887i	−0.0684000	−	0.210513i	−0.979414	+	0.201862i	$0.935301\pi$
$174$		0			0
$175$	−0.451695			−0.0341449
$176$	−8.21881	+	4.02499i	−0.619516	+	0.303395i
$177$		0			0
$178$	−9.29299	+	6.75175i	−0.696539	+	0.506065i
$179$	1.94467	+	5.98508i	0.145352	+	0.447346i	0.997056	−	0.0766763i	$-0.0244308\pi$
$179$	1.94467	+	5.98508i	0.145352	+	0.447346i	−0.851704	+	0.524022i	$0.824431\pi$
$180$		0			0
$181$	9.03200	+	6.56213i	0.671343	+	0.487759i	0.870475	−	0.492213i	$-0.163812\pi$
$181$	9.03200	+	6.56213i	0.671343	+	0.487759i	−0.199131	+	0.979973i	$0.563812\pi$
$182$	2.16856	+	1.57555i	0.160745	+	0.116788i
$183$		0			0
$184$	−0.00599902	−	0.0184631i	−0.000442254	−	0.00136112i
$185$	5.96160	−	4.33136i	0.438306	−	0.318448i
$186$		0			0
$187$	2.20441	−	1.07956i	0.161202	−	0.0789455i
$188$	0.834545			0.0608655
$189$		0			0
$190$	2.57765	+	7.93318i	0.187002	+	0.575534i
$191$	6.30228	−	19.3964i	0.456017	−	1.40348i	−0.413920	−	0.910313i	$-0.635841\pi$
$191$	6.30228	−	19.3964i	0.456017	−	1.40348i	0.869937	−	0.493163i	$-0.164159\pi$
$192$		0			0
$193$	2.40629	+	1.74827i	0.173208	+	0.125843i	0.671012	−	0.741447i	$-0.265860\pi$
$193$	2.40629	+	1.74827i	0.173208	+	0.125843i	−0.497804	+	0.867290i	$0.665860\pi$
$194$	−2.22762	+	6.85590i	−0.159934	+	0.492225i
$195$		0			0
$196$	−2.73202	+	1.98493i	−0.195144	+	0.141781i
$197$	−5.20127			−0.370575			−0.185288	−	0.982684i	$-0.559322\pi$
$197$	−5.20127			−0.370575			−0.185288	+	0.982684i	$0.559322\pi$
$198$		0			0
$199$	8.10264			0.574381			0.287191	−	0.957873i	$-0.407279\pi$
$199$	8.10264			0.574381			0.287191	+	0.957873i	$0.407279\pi$
$200$	−2.47658	+	1.79934i	−0.175121	+	0.127233i
$201$		0			0
$202$	0.836505	−	2.57450i	0.0588563	−	0.181141i
$203$	−0.118363	−	0.0859955i	−0.00830743	−	0.00603570i
$204$		0			0
$205$	3.39006	−	10.4335i	0.236772	−	0.728709i
$206$	−3.66712	−	11.2862i	−0.255500	−	0.786349i
$207$		0			0
$208$	13.3558			0.926059
$209$	−22.2289	−	3.88264i	−1.53761	−	0.268568i
$210$		0			0
$211$	1.06252	−	0.771967i	0.0731470	−	0.0531444i	−0.550611	−	0.834762i	$-0.685605\pi$
$211$	1.06252	−	0.771967i	0.0731470	−	0.0531444i	0.623758	+	0.781618i	$0.285605\pi$
$212$	−1.32661	−	4.08290i	−0.0911122	−	0.280415i
$213$		0			0
$214$	−11.6608	−	8.47204i	−0.797113	−	0.579137i
$215$	−1.46163	−	1.06194i	−0.0996826	−	0.0724236i
$216$		0			0
$217$	0.782470	+	2.40820i	0.0531175	+	0.163479i
$218$	−12.4073	+	9.01443i	−0.840328	+	0.610534i
$219$		0			0
$220$	−0.231994	−	1.63164i	−0.0156411	−	0.110005i
$221$	−3.58223			−0.240967
$222$		0			0
$223$	8.84861	+	27.2332i	0.592547	+	1.82367i	0.566577	+	0.824009i	$0.308267\pi$
$223$	8.84861	+	27.2332i	0.592547	+	1.82367i	0.0259701	+	0.999663i	$0.491733\pi$
$224$	0.382392	−	1.17688i	0.0255497	−	0.0786338i
$225$		0			0
$226$	9.82545	+	7.13861i	0.653579	+	0.474853i
$227$	2.43074	−	7.48104i	0.161334	−	0.496534i	−0.837414	−	0.546570i	$-0.815933\pi$
$227$	2.43074	−	7.48104i	0.161334	−	0.496534i	0.998747	+	0.0500354i	$0.0159334\pi$
$228$		0			0
$229$	13.0664	−	9.49331i	0.863453	−	0.627336i	−0.0653689	−	0.997861i	$-0.520822\pi$
$229$	13.0664	−	9.49331i	0.863453	−	0.627336i	0.928822	+	0.370526i	$0.120822\pi$
$230$	−0.00777492			−0.000512663
$231$		0			0
$232$	−0.991532			−0.0650973
$233$	14.9138	−	10.8355i	0.977035	−	0.709858i	0.0199914	−	0.999800i	$-0.493636\pi$
$233$	14.9138	−	10.8355i	0.977035	−	0.709858i	0.957044	+	0.289942i	$0.0936361\pi$
$234$		0			0
$235$	0.518988	−	1.59728i	0.0338551	−	0.104195i
$236$	−0.603224	−	0.438268i	−0.0392665	−	0.0285288i
$237$		0			0
$238$	0.126648	−	0.389782i	0.00820937	−	0.0252658i
$239$	−6.91081	−	21.2693i	−0.447023	−	1.37579i	−0.880250	−	0.474510i	$-0.842625\pi$
$239$	−6.91081	−	21.2693i	−0.447023	−	1.37579i	0.433227	−	0.901285i	$-0.357375\pi$
$240$		0			0
$241$	−13.2213			−0.851662			−0.425831	−	0.904803i	$-0.640018\pi$
$241$	−13.2213			−0.851662			−0.425831	+	0.904803i	$0.640018\pi$
$242$	−12.6876	−	4.57164i	−0.815588	−	0.293876i
$243$		0			0
$244$	5.24433	−	3.81023i	0.335734	−	0.243925i
$245$	2.10007	+	6.46335i	0.134169	+	0.412928i
$246$		0			0
$247$	26.6429	+	19.3572i	1.69525	+	1.23167i
$248$	13.8833	+	10.0868i	0.881591	+	0.640513i
$249$		0			0
$250$	0.378857	+	1.16600i	0.0239610	+	0.0737444i
$251$	−16.9919	+	12.3454i	−1.07252	+	0.779232i	−0.976364	−	0.216134i	$-0.930655\pi$
$251$	−16.9919	+	12.3454i	−1.07252	+	0.779232i	−0.0961569	+	0.995366i	$0.530655\pi$
$252$		0			0
$253$	0.00984441	−	0.0185868i	0.000618913	−	0.00116854i
$254$	0.688477			0.0431989
$255$		0			0
$256$	−3.43893	−	10.5839i	−0.214933	−	0.661497i
$257$	1.04068	−	3.20289i	0.0649160	−	0.199791i	−0.913338	−	0.407203i	$-0.866504\pi$
$257$	1.04068	−	3.20289i	0.0649160	−	0.199791i	0.978254	+	0.207412i	$0.0665041\pi$
$258$		0			0
$259$	2.69283	+	1.95645i	0.167324	+	0.121568i
$260$	−0.743247	+	2.28748i	−0.0460942	+	0.141863i
$261$		0			0
$262$	3.01030	−	2.18711i	0.185977	−	0.135120i
$263$	−21.0450			−1.29769			−0.648845	−	0.760920i	$-0.724748\pi$
$263$	−21.0450			−1.29769			−0.648845	+	0.760920i	$0.724748\pi$
$264$		0			0
$265$	−8.63948			−0.530719
$266$	−3.04820	+	2.21465i	−0.186897	+	0.135789i
$267$		0			0
$268$	−1.47529	+	4.54048i	−0.0901177	+	0.277354i
$269$	18.9161	+	13.7434i	1.15334	+	0.837947i	0.988921	−	0.148444i	$-0.0474265\pi$
$269$	18.9161	+	13.7434i	1.15334	+	0.837947i	0.164415	+	0.986391i	$0.447427\pi$
$270$		0			0
$271$	−6.34951	+	19.5418i	−0.385705	+	1.18708i	0.550262	+	0.834992i	$0.314528\pi$
$271$	−6.34951	+	19.5418i	−0.385705	+	1.18708i	−0.935967	+	0.352087i	$0.885472\pi$
$272$	−0.631036	−	1.94213i	−0.0382622	−	0.117759i
$273$		0			0
$274$	25.3788			1.53319
$275$	−3.26716	−	0.570661i	−0.197017	−	0.0344122i
$276$		0			0
$277$	15.8420	−	11.5099i	0.951856	−	0.691564i	0.000611096	−	1.00000i	$-0.499805\pi$
$277$	15.8420	−	11.5099i	0.951856	−	0.691564i	0.951245	+	0.308436i	$0.0998055\pi$
$278$	−1.34446	−	4.13783i	−0.0806354	−	0.248170i
$279$		0			0
$280$	−1.11866	−	0.812754i	−0.0668527	−	0.0485714i
$281$	11.1585	+	8.10711i	0.665659	+	0.483630i	0.868569	−	0.495567i	$-0.165040\pi$
$281$	11.1585	+	8.10711i	0.665659	+	0.483630i	−0.202910	+	0.979197i	$0.565040\pi$
$282$		0			0
$283$	9.73949	+	29.9751i	0.578953	+	1.78183i	0.622306	+	0.782774i	$0.286196\pi$
$283$	9.73949	+	29.9751i	0.578953	+	1.78183i	−0.0433533	+	0.999060i	$0.513804\pi$
$284$	4.58792	−	3.33332i	0.272243	−	0.197796i
$285$		0			0
$286$	13.6949	+	14.1359i	0.809799	+	0.835872i
$287$	4.95530			0.292502
$288$		0			0
$289$	−5.08404	−	15.6471i	−0.299061	−	0.920415i
$290$	−0.122712	+	0.377669i	−0.00720589	+	0.0221775i
$291$		0			0
$292$	4.11649	+	2.99080i	0.240899	+	0.175024i
$293$	7.20413	−	22.1720i	0.420870	−	1.29530i	−0.486024	−	0.873945i	$-0.661553\pi$
$293$	7.20413	−	22.1720i	0.420870	−	1.29530i	0.906894	−	0.421359i	$-0.138447\pi$
$294$		0			0
$295$	−1.21396	+	0.881993i	−0.0706794	+	0.0513516i
$296$	22.5580			1.31116
$297$		0			0
$298$	−7.72948			−0.447757
$299$	−0.0248334	+	0.0180425i	−0.00143615	+	0.00104343i
$300$		0			0
$301$	0.252179	−	0.776126i	0.0145353	−	0.0447352i
$302$	−3.65433	−	2.65503i	−0.210283	−	0.152780i
$303$		0			0
$304$	−5.80129	+	17.8545i	−0.332727	+	1.02403i
$305$	−4.03125	−	12.4069i	−0.230829	−	0.710418i
$306$		0			0
$307$	−10.0938			−0.576083			−0.288042	−	0.957618i	$-0.593004\pi$
$307$	−10.0938			−0.576083			−0.288042	+	0.957618i	$0.593004\pi$
$308$	0.668551	−	0.327409i	0.0380942	−	0.0186558i
$309$		0			0
$310$	5.56020	−	4.03972i	0.315798	−	0.229441i
$311$	4.11778	+	12.6732i	0.233498	+	0.718632i	0.997317	+	0.0732020i	$0.0233218\pi$
$311$	4.11778	+	12.6732i	0.233498	+	0.718632i	−0.763819	+	0.645430i	$0.776678\pi$
$312$		0			0
$313$	−18.7435	−	13.6180i	−1.05945	−	0.769732i	−0.0854599	−	0.996342i	$-0.527236\pi$
$313$	−18.7435	−	13.6180i	−1.05945	−	0.769732i	−0.973986	+	0.226609i	$0.927236\pi$
$314$	2.80566	+	2.03843i	0.158333	+	0.115036i
$315$		0			0
$316$	0.322407	+	0.992267i	0.0181368	+	0.0558194i
$317$	5.60802	−	4.07446i	0.314978	−	0.228845i	−0.419052	−	0.907962i	$-0.637637\pi$
$317$	5.60802	−	4.07446i	0.314978	−	0.228845i	0.734029	+	0.679118i	$0.237637\pi$
$318$		0			0
$319$	−0.747485	−	0.771552i	−0.0418512	−	0.0431986i
$320$	−8.87727			−0.496254
$321$		0			0
$322$	−0.00108523	−	0.00334001i	−6.04777e−5	−	0.000186131i
$323$	1.55599	−	4.78886i	0.0865779	−	0.266459i
$324$		0			0
$325$	3.91592	+	2.84508i	0.217216	+	0.157817i
$326$	−3.35342	+	10.3208i	−0.185729	+	0.571614i
$327$		0			0
$328$	27.1692	−	19.7396i	1.50017	−	1.08994i
$329$	0.758613			0.0418237
$330$		0			0
$331$	−10.5717			−0.581075			−0.290538	−	0.956864i	$-0.593834\pi$
$331$	−10.5717			−0.581075			−0.290538	+	0.956864i	$0.593834\pi$
$332$	−6.38968	+	4.64237i	−0.350679	+	0.254783i
$333$		0			0
$334$	7.45750	−	22.9518i	0.408056	−	1.25587i
$335$	7.77281	+	5.64728i	0.424674	+	0.308544i
$336$		0			0
$337$	−1.96123	+	6.03605i	−0.106835	+	0.328805i	−0.990157	−	0.139963i	$-0.955302\pi$
$337$	−1.96123	+	6.03605i	−0.106835	+	0.328805i	0.883322	+	0.468767i	$0.155302\pi$
$338$	−3.95107	−	12.1601i	−0.214910	−	0.661424i
$339$		0			0
$340$	0.367750			0.0199440
$341$	2.61724	+	18.4073i	0.141731	+	0.996811i
$342$		0			0
$343$	−5.04145	+	3.66283i	−0.272213	+	0.197774i
$344$	−1.70906	−	5.25996i	−0.0921466	−	0.283598i
$345$		0			0
$346$	−2.88767	−	2.09801i	−0.155242	−	0.112790i
$347$	20.4210	+	14.8367i	1.09626	+	0.796477i	0.980445	−	0.196794i	$-0.0630532\pi$
$347$	20.4210	+	14.8367i	1.09626	+	0.796477i	0.115811	+	0.993271i	$0.463053\pi$
$348$		0			0
$349$	−3.43118	−	10.5601i	−0.183667	−	0.565269i	0.816256	−	0.577691i	$-0.196046\pi$
$349$	−3.43118	−	10.5601i	−0.183667	−	0.565269i	−0.999923	+	0.0124217i	$0.996046\pi$
$350$	−0.448019	+	0.325504i	−0.0239476	+	0.0173989i
$351$		0			0
$352$	4.25273	−	8.02942i	0.226672	−	0.427970i
$353$	−18.8552			−1.00356			−0.501780	−	0.864996i	$-0.667321\pi$
$353$	−18.8552			−1.00356			−0.501780	+	0.864996i	$0.667321\pi$
$354$		0			0
$355$	−3.52668	−	10.8540i	−0.187177	−	0.576070i
$356$	1.43867	−	4.42778i	0.0762494	−	0.234672i
$357$		0			0
$358$	6.24187	+	4.53498i	0.329893	+	0.239681i
$359$	−6.57983	+	20.2506i	−0.347270	+	1.06879i	0.613087	+	0.790016i	$0.289928\pi$
$359$	−6.57983	+	20.2506i	−0.347270	+	1.06879i	−0.960357	+	0.278773i	$0.910072\pi$
$360$		0			0
$361$	−22.0789	+	16.0412i	−1.16205	+	0.844275i
$362$	13.6873			0.719391
$363$		0			0
$364$	−1.08642			−0.0569437
$365$	8.28423	−	6.01885i	0.433617	−	0.315041i
$366$		0			0
$367$	−9.66781	+	29.7545i	−0.504656	+	1.55317i	0.296693	+	0.954973i	$0.404116\pi$
$367$	−9.66781	+	29.7545i	−0.504656	+	1.55317i	−0.801349	+	0.598197i	$0.795884\pi$
$368$	−0.0141565	−	0.0102853i	−0.000737957	−	0.000536157i
$369$		0			0
$370$	2.79178	−	8.59220i	0.145138	−	0.446687i
$371$	−1.20591	−	3.71141i	−0.0626078	−	0.192687i
$372$		0			0
$373$	9.39368			0.486386			0.243193	−	0.969978i	$-0.421805\pi$
$373$	9.39368			0.486386			0.243193	+	0.969978i	$0.421805\pi$
$374$	1.40850	−	2.65934i	0.0728319	−	0.137511i
$375$		0			0
$376$	4.15938	−	3.02196i	0.214503	−	0.155846i
$377$	0.484473	+	1.49106i	0.0249517	+	0.0767933i
$378$		0			0
$379$	6.63173	+	4.81823i	0.340649	+	0.247496i	0.744936	−	0.667136i	$-0.232480\pi$
$379$	6.63173	+	4.81823i	0.340649	+	0.247496i	−0.404287	+	0.914632i	$0.632480\pi$
$380$	−2.73515	−	1.98720i	−0.140310	−	0.101941i
$381$		0			0
$382$	−7.72664	−	23.7802i	−0.395329	−	1.21670i
$383$	−27.2501	+	19.7984i	−1.39242	+	1.01165i	−0.396820	+	0.917897i	$0.629886\pi$
$383$	−27.2501	+	19.7984i	−1.39242	+	1.01165i	−0.995596	+	0.0937524i	$0.970114\pi$
$384$		0			0
$385$	−0.210886	−	1.48319i	−0.0107478	−	0.0755901i
$386$	3.64656			0.185605
$387$		0			0
$388$	−0.902863	−	2.77873i	−0.0458359	−	0.141069i
$389$	−10.1771	+	31.3219i	−0.515999	+	1.58808i	0.265457	+	0.964123i	$0.414477\pi$
$389$	−10.1771	+	31.3219i	−0.515999	+	1.58808i	−0.781456	+	0.623960i	$0.785523\pi$
$390$		0			0
$391$	0.00379698	+	0.00275867i	0.000192021	+	0.000139512i
$392$	−6.42879	+	19.7858i	−0.324703	+	0.999333i
$393$		0			0
$394$	−5.15894	+	3.74819i	−0.259904	+	0.188831i
$395$	2.09965			0.105645
$396$		0			0
$397$	−15.3865			−0.772228			−0.386114	−	0.922451i	$-0.626183\pi$
$397$	−15.3865			−0.772228			−0.386114	+	0.922451i	$0.626183\pi$
$398$	8.03669	−	5.83900i	0.402843	−	0.292683i
$399$		0			0
$400$	−0.852662	+	2.62422i	−0.0426331	+	0.131211i
$401$	5.37426	+	3.90463i	0.268378	+	0.194988i	0.713832	−	0.700317i	$-0.246958\pi$
$401$	5.37426	+	3.90463i	0.268378	+	0.194988i	−0.445455	+	0.895305i	$0.646958\pi$
$402$		0			0
$403$	8.38491	−	25.8061i	0.417682	−	1.28549i
$404$	0.339039	+	1.04346i	0.0168678	+	0.0519138i
$405$		0			0
$406$	−0.179370			−0.00890198
$407$	17.0058	+	17.5533i	0.842945	+	0.870085i
$408$		0			0
$409$	−19.8088	+	14.3919i	−0.979482	+	0.711636i	−0.957593	−	0.288125i	$-0.906968\pi$
$409$	−19.8088	+	14.3919i	−0.979482	+	0.711636i	−0.0218895	+	0.999760i	$0.506968\pi$
$410$	−4.15623	−	12.7916i	−0.205262	−	0.631731i
$411$		0			0
$412$	3.89119	+	2.82711i	0.191705	+	0.139282i
$413$	−0.548339	−	0.398392i	−0.0269820	−	0.0196036i
$414$		0			0
$415$	4.91167	+	15.1166i	0.241104	+	0.742043i
$416$	−10.7279	+	7.79428i	−0.525979	+	0.382146i
$417$		0			0
$418$	−24.8459	+	12.1678i	−1.21526	+	0.595146i
$419$	−20.8656			−1.01935			−0.509676	−	0.860367i	$-0.670235\pi$
$419$	−20.8656			−1.01935			−0.509676	+	0.860367i	$0.670235\pi$
$420$		0			0
$421$	−5.23200	−	16.1025i	−0.254992	−	0.784785i	−0.993831	−	0.110903i	$-0.964626\pi$
$421$	−5.23200	−	16.1025i	−0.254992	−	0.784785i	0.738839	−	0.673882i	$-0.235374\pi$
$422$	0.497571	−	1.53137i	0.0242214	−	0.0745458i
$423$		0			0
$424$	−21.3964	−	15.5454i	−1.03910	−	0.754951i
$425$	0.228697	−	0.703856i	0.0110934	−	0.0341420i
$426$		0			0
$427$	4.76717	−	3.46355i	0.230700	−	0.167613i
$428$	5.84186			0.282377
$429$		0			0
$430$	−2.21500			−0.106817
$431$	21.1677	−	15.3792i	1.01961	−	0.740791i	0.0534080	−	0.998573i	$-0.482992\pi$
$431$	21.1677	−	15.3792i	1.01961	−	0.740791i	0.966203	+	0.257782i	$0.0829916\pi$
$432$		0			0
$433$	−7.74375	+	23.8328i	−0.372141	+	1.14533i	0.573246	+	0.819383i	$0.305684\pi$
$433$	−7.74375	+	23.8328i	−0.372141	+	1.14533i	−0.945387	+	0.325949i	$0.894316\pi$
$434$	2.51152	+	1.82472i	0.120557	+	0.0875895i
$435$		0			0
$436$	1.92081	−	5.91163i	0.0919899	−	0.283116i
$437$	−0.0133332	−	0.0410353i	−0.000637812	−	0.00196298i
$438$		0			0
$439$	5.11234			0.243999			0.121999	−	0.992530i	$-0.461069\pi$
$439$	5.11234			0.243999			0.121999	+	0.992530i	$0.461069\pi$
$440$	−7.06458	−	7.29203i	−0.336791	−	0.347634i
$441$		0			0
$442$	−3.55307	+	2.58146i	−0.169003	+	0.122788i
$443$	−8.67635	−	26.7031i	−0.412226	−	1.26870i	−0.914709	−	0.404113i	$-0.867580\pi$
$443$	−8.67635	−	26.7031i	−0.412226	−	1.26870i	0.502483	−	0.864587i	$-0.332420\pi$
$444$		0			0
$445$	−7.57988	−	5.50711i	−0.359321	−	0.261062i
$446$	28.4016	+	20.6350i	1.34486	+	0.977096i
$447$		0			0
$448$	−1.23910	−	3.81356i	−0.0585421	−	0.180174i
$449$	29.9297	−	21.7452i	1.41247	−	1.02622i	0.419510	−	0.907751i	$-0.362202\pi$
$449$	29.9297	−	21.7452i	1.41247	−	1.02622i	0.992958	−	0.118467i	$-0.0377981\pi$
$450$		0			0
$451$	35.8422	+	6.26041i	1.68775	+	0.294791i
$452$	−4.92239			−0.231530
$453$		0			0
$454$	−2.98010	−	9.17181i	−0.139863	−	0.430454i
$455$	−0.675622	+	2.07935i	−0.0316736	+	0.0974815i
$456$		0			0
$457$	−29.8092	−	21.6576i	−1.39441	−	1.01310i	−0.995365	−	0.0961719i	$-0.969340\pi$
$457$	−29.8092	−	21.6576i	−1.39441	−	1.01310i	−0.399050	−	0.916929i	$-0.630660\pi$
$458$	6.11891	−	18.8321i	0.285918	−	0.879965i
$459$		0			0
$460$	0.00254938	−	0.00185224i	0.000118866	−	8.63609e-5i
$461$	−23.0013			−1.07128			−0.535640	−	0.844447i	$-0.679929\pi$
$461$	−23.0013			−1.07128			−0.535640	+	0.844447i	$0.679929\pi$
$462$		0			0
$463$	−36.1571			−1.68036			−0.840181	−	0.542306i	$-0.817551\pi$
$463$	−36.1571			−1.68036			−0.840181	+	0.542306i	$0.817551\pi$
$464$	−0.723042	+	0.525321i	−0.0335664	+	0.0243874i
$465$		0			0
$466$	6.98403	−	21.4946i	0.323529	−	0.995720i
$467$	−1.83240	−	1.33132i	−0.0847935	−	0.0616061i	0.544581	−	0.838708i	$-0.316689\pi$
$467$	−1.83240	−	1.33132i	−0.0847935	−	0.0616061i	−0.629374	+	0.777102i	$0.716689\pi$
$468$		0			0
$469$	−1.34106	+	4.12736i	−0.0619244	+	0.190584i
$470$	−0.636283	−	1.95828i	−0.0293496	−	0.0903287i
$471$		0			0
$472$	−4.59348			−0.211432
$473$	2.80458	−	5.29521i	0.128955	−	0.243474i
$474$		0			0
$475$	−5.50435	+	3.99914i	−0.252557	+	0.183493i
$476$	0.0513310	+	0.157981i	0.00235275	+	0.00724103i
$477$		0			0
$478$	−22.1818	−	16.1160i	−1.01457	−	0.737130i
$479$	−24.7000	−	17.9456i	−1.12857	−	0.819954i	−0.143084	−	0.989711i	$-0.545702\pi$
$479$	−24.7000	−	17.9456i	−1.12857	−	0.819954i	−0.985486	+	0.169756i	$0.945702\pi$
$480$		0			0
$481$	−11.0221	−	33.9225i	−0.502564	−	1.54673i
$482$	−13.1137	+	9.52768i	−0.597314	+	0.433974i
$483$		0			0
$484$	5.24935	−	1.52355i	0.238607	−	0.0692524i
$485$	−5.87983			−0.266989
$486$		0			0
$487$	−4.99195	−	15.3636i	−0.226207	−	0.696193i	−0.998167	−	0.0605221i	$-0.980723\pi$
$487$	−4.99195	−	15.3636i	−0.226207	−	0.696193i	0.771960	−	0.635671i	$-0.219277\pi$
$488$	12.3406	−	37.9804i	0.558632	−	1.71929i
$489$		0			0
$490$	6.74066	+	4.89737i	0.304512	+	0.221241i
$491$	3.60828	−	11.1051i	0.162839	−	0.501168i	−0.836031	−	0.548682i	$-0.815130\pi$
$491$	3.60828	−	11.1051i	0.162839	−	0.501168i	0.998871	+	0.0475137i	$0.0151298\pi$
$492$		0			0
$493$	0.193931	−	0.140899i	0.00873420	−	0.00634577i
$494$	40.3754			1.81658
$495$		0			0
$496$	15.4680			0.694534
$497$	4.17048	−	3.03003i	0.187072	−	0.135916i
$498$		0			0
$499$	−12.6501	+	38.9330i	−0.566296	+	1.74288i	0.0977712	+	0.995209i	$0.468829\pi$
$499$	−12.6501	+	38.9330i	−0.566296	+	1.74288i	−0.664068	+	0.747672i	$0.731171\pi$
$500$	−0.402006	−	0.292074i	−0.0179782	−	0.0130620i
$501$		0			0
$502$	−7.95720	+	24.4897i	−0.355147	+	1.09303i
$503$	0.131171	+	0.403703i	0.00584863	+	0.0180002i	0.953938	−	0.300003i	$-0.0969877\pi$
$503$	0.131171	+	0.403703i	0.00584863	+	0.0180002i	−0.948090	+	0.318003i	$0.896988\pi$
$504$		0			0
$505$	2.20797			0.0982533
$506$	−0.00362993	−	0.0255297i	−0.000161370	−	0.00113493i
$507$		0			0
$508$	−0.225751	+	0.164017i	−0.0100161	+	0.00727710i
$509$	6.12017	+	18.8360i	0.271272	+	0.834889i	0.990182	+	0.139786i	$0.0446414\pi$
$509$	6.12017	+	18.8360i	0.271272	+	0.834889i	−0.718910	+	0.695103i	$0.755359\pi$
$510$		0			0
$511$	3.74195	+	2.71868i	0.165534	+	0.120267i
$512$	−19.7827	−	14.3729i	−0.874278	−	0.635200i
$513$		0			0
$514$	−1.27588	−	3.92677i	−0.0562769	−	0.173202i
$515$	7.83082	−	5.68943i	0.345067	−	0.250706i
$516$		0			0
$517$	5.48714	+	0.958415i	0.241324	+	0.0421510i
$518$	4.08078			0.179299
$519$		0			0
$520$	4.57882	+	14.0922i	0.200795	+	0.617982i
$521$	−11.3748	+	35.0079i	−0.498337	+	1.53372i	0.313353	+	0.949637i	$0.398548\pi$
$521$	−11.3748	+	35.0079i	−0.498337	+	1.53372i	−0.811690	+	0.584088i	$0.801452\pi$
$522$		0			0
$523$	8.49589	+	6.17262i	0.371499	+	0.269910i	0.757832	−	0.652449i	$-0.226258\pi$
$523$	8.49589	+	6.17262i	0.371499	+	0.269910i	−0.386333	+	0.922359i	$0.626258\pi$
$524$	−0.466033	+	1.43430i	−0.0203587	+	0.0626577i
$525$		0			0
$526$	−20.8737	+	15.1656i	−0.910137	+	0.661253i
$527$	−4.14875			−0.180723
$528$		0			0
$529$	−23.0000			−0.999998
$530$	−8.56916	+	6.22586i	−0.372220	+	0.270434i
$531$		0			0
$532$	0.471900	−	1.45236i	0.0204595	−	0.0629678i
$533$	−42.9594	−	31.2118i	−1.86078	−	1.35193i
$534$		0			0
$535$	3.63294	−	11.1810i	0.157066	−	0.483399i
$536$	9.08863	+	27.9719i	0.392569	+	1.20820i
$537$		0			0
$538$	28.6660			1.23588
$539$	−20.2426	+	9.91338i	−0.871910	+	0.427000i
$540$		0			0
$541$	−0.529593	+	0.384772i	−0.0227690	+	0.0165426i	−0.599112	−	0.800666i	$-0.704479\pi$
$541$	−0.529593	+	0.384772i	−0.0227690	+	0.0165426i	0.576343	+	0.817208i	$0.304479\pi$
$542$	7.78454	+	23.9584i	0.334375	+	1.02910i
$543$		0			0
$544$	1.64028	+	1.19173i	0.0703262	+	0.0510950i
$545$	−10.1201	−	7.35267i	−0.433497	−	0.314954i
$546$		0			0
$547$	−4.14573	−	12.7592i	−0.177259	−	0.545546i	0.822471	−	0.568807i	$-0.192595\pi$
$547$	−4.14573	−	12.7592i	−0.177259	−	0.545546i	−0.999729	+	0.0232616i	$0.992595\pi$
$548$	−8.32166	+	6.04604i	−0.355484	+	0.258274i
$549$		0			0
$550$	−3.65180	+	1.78839i	−0.155713	+	0.0762574i
$551$	−2.20374			−0.0938823
$552$		0			0
$553$	0.293073	+	0.901985i	0.0124627	+	0.0383563i
$554$	7.41872	−	22.8325i	0.315191	−	0.970059i
$555$		0			0
$556$	1.42661	+	1.03649i	0.0605017	+	0.0439571i
$557$	4.09205	−	12.5940i	0.173386	−	0.533626i	−0.826171	−	0.563420i	$-0.809485\pi$
$557$	4.09205	−	12.5940i	0.173386	−	0.533626i	0.999556	+	0.0297943i	$0.00948523\pi$
$558$		0			0
$559$	−7.07481	+	5.14015i	−0.299232	+	0.217405i
$560$	−1.24635			−0.0526679
$561$		0			0
$562$	16.9099			0.713300
$563$	−17.2822	+	12.5562i	−0.728356	+	0.529182i	−0.889043	−	0.457824i	$-0.848629\pi$
$563$	−17.2822	+	12.5562i	−0.728356	+	0.529182i	0.160687	+	0.987005i	$0.448629\pi$
$564$		0			0
$565$	−3.06115	+	9.42124i	−0.128783	+	0.396355i
$566$	31.2611	+	22.7125i	1.31400	+	0.954679i
$567$		0			0
$568$	10.7960	−	33.2265i	0.452988	−	1.39415i
$569$	−14.0100	−	43.1185i	−0.587332	−	1.80762i	−0.589698	−	0.807624i	$-0.700753\pi$
$569$	−14.0100	−	43.1185i	−0.587332	−	1.80762i	0.00236662	−	0.999997i	$-0.499247\pi$
$570$		0			0
$571$	−25.1544			−1.05268			−0.526339	−	0.850275i	$-0.676436\pi$
$571$	−25.1544			−1.05268			−0.526339	+	0.850275i	$0.676436\pi$
$572$	−7.85817	−	1.37255i	−0.328567	−	0.0573893i
$573$		0			0
$574$	4.91497	−	3.57093i	0.205147	−	0.149048i
$575$	−0.00195968	−	0.00603127i	−8.17243e−5	−	0.000251522i
$576$		0			0
$577$	−6.16999	−	4.48276i	−0.256860	−	0.186620i	0.451902	−	0.892068i	$-0.350746\pi$
$577$	−6.16999	−	4.48276i	−0.256860	−	0.186620i	−0.708762	+	0.705448i	$0.750746\pi$
$578$	−16.3184	−	11.8560i	−0.678755	−	0.493144i
$579$		0			0
$580$	−0.0497357	−	0.153071i	−0.00206516	−	0.00635592i
$581$	−5.80831	+	4.21998i	−0.240969	+	0.175074i
$582$		0			0
$583$	−4.03358	−	28.3686i	−0.167054	−	1.17491i
$584$	31.3466			1.29713
$585$		0			0
$586$	−8.83232	−	27.1831i	−0.364860	−	1.12292i
$587$	2.43760	−	7.50217i	0.100611	−	0.309648i	−0.888065	−	0.459719i	$-0.847950\pi$
$587$	2.43760	−	7.50217i	0.100611	−	0.309648i	0.988675	+	0.150071i	$0.0479502\pi$
$588$		0			0
$589$	30.8564	+	22.4185i	1.27142	+	0.923739i
$590$	−0.568489	+	1.74963i	−0.0234043	+	0.0720310i
$591$		0			0
$592$	16.4497	−	11.9514i	0.676077	−	0.491199i
$593$	−8.68507			−0.356653			−0.178327	−	0.983971i	$-0.557068\pi$
$593$	−8.68507			−0.356653			−0.178327	+	0.983971i	$0.557068\pi$
$594$		0			0
$595$	0.334290			0.0137045
$596$	2.53448	−	1.84141i	0.103816	−	0.0754271i
$597$		0			0
$598$	−0.0116293	+	0.0357914i	−0.000475558	+	0.00146362i
$599$	11.3275	+	8.22991i	0.462829	+	0.336265i	0.794640	−	0.607081i	$-0.207660\pi$
$599$	11.3275	+	8.22991i	0.462829	+	0.336265i	−0.331811	+	0.943346i	$0.607660\pi$
$600$		0			0
$601$	−3.18091	+	9.78983i	−0.129752	+	0.399335i	−0.994737	−	0.102462i	$-0.967328\pi$
$601$	−3.18091	+	9.78983i	−0.129752	+	0.399335i	0.864985	+	0.501798i	$0.167328\pi$
$602$	−0.309173	−	0.951537i	−0.0126010	−	0.0387817i
$603$		0			0
$604$	1.83076			0.0744927
$605$	0.348460	−	10.9945i	0.0141669	−	0.446989i
$606$		0			0
$607$	−22.2282	+	16.1497i	−0.902214	+	0.655497i	−0.939034	−	0.343825i	$-0.888277\pi$
$607$	−22.2282	+	16.1497i	−0.902214	+	0.655497i	0.0368195	+	0.999322i	$0.488277\pi$
$608$	−5.75986	−	17.7270i	−0.233593	−	0.718926i
$609$		0			0
$610$	−12.9392	−	9.40090i	−0.523894	−	0.380631i
$611$	−6.57671	−	4.77826i	−0.266065	−	0.193308i
$612$		0			0
$613$	−3.35530	−	10.3266i	−0.135519	−	0.417086i	0.860151	−	0.510039i	$-0.170369\pi$
$613$	−3.35530	−	10.3266i	−0.135519	−	0.417086i	−0.995670	+	0.0929536i	$0.970369\pi$
$614$	−10.0116	+	7.27388i	−0.404037	+	0.293550i
$615$		0			0
$616$	2.14648	−	4.05269i	0.0864842	−	0.163287i
$617$	18.2404			0.734330			0.367165	−	0.930156i	$-0.380329\pi$
$617$	18.2404			0.734330			0.367165	+	0.930156i	$0.380329\pi$
$618$		0			0
$619$	6.08144	+	18.7167i	0.244434	+	0.752289i	0.995729	+	0.0923233i	$0.0294293\pi$
$619$	6.08144	+	18.7167i	0.244434	+	0.752289i	−0.751295	+	0.659966i	$0.770571\pi$
$620$	−0.860790	+	2.64924i	−0.0345701	+	0.106396i
$621$		0			0
$622$	13.2169	+	9.60267i	0.529951	+	0.385032i
$623$	1.30777	−	4.02491i	0.0523948	−	0.161255i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−28.4044			−1.13527
$627$		0			0
$628$	−1.40559			−0.0560893
$629$	−4.41205	+	3.20554i	−0.175920	+	0.127813i
$630$		0			0
$631$	−9.40181	+	28.9358i	−0.374280	+	1.15192i	0.569683	+	0.821865i	$0.307066\pi$
$631$	−9.40181	+	28.9358i	−0.374280	+	1.15192i	−0.943963	+	0.330051i	$0.892934\pi$
$632$	5.19997	+	3.77800i	0.206844	+	0.150281i
$633$		0			0
$634$	2.62619	−	8.08260i	0.104300	−	0.321001i
$635$	0.173532	+	0.534076i	0.00688640	+	0.0211942i
$636$		0			0
$637$	32.8948			1.30334
$638$	−1.29740	−	0.226612i	−0.0513647	−	0.00897166i
$639$		0			0
$640$	−4.37230	+	3.17666i	−0.172830	+	0.125569i
$641$	11.5427	+	35.5247i	0.455908	+	1.40314i	0.870066	+	0.492935i	$0.164076\pi$
$641$	11.5427	+	35.5247i	0.455908	+	1.40314i	−0.414159	+	0.910205i	$0.635924\pi$
$642$		0			0
$643$	−0.861554	−	0.625956i	−0.0339764	−	0.0246853i	0.570667	−	0.821181i	$-0.306685\pi$
$643$	−0.861554	−	0.625956i	−0.0339764	−	0.0246853i	−0.604644	+	0.796496i	$0.706685\pi$
$644$	0.00115154		0.000836645i	4.53772e−5		3.29684e-5i
$645$		0			0
$646$	−1.90766	−	5.87118i	−0.0750559	−	0.230998i
$647$	12.7864	−	9.28987i	0.502686	−	0.365223i	−0.307356	−	0.951595i	$-0.599444\pi$
$647$	12.7864	−	9.28987i	0.502686	−	0.365223i	0.810042	+	0.586372i	$0.199444\pi$
$648$		0			0
$649$	−3.46288	−	3.57437i	−0.135930	−	0.140306i
$650$	5.93429			0.232762
$651$		0			0
$652$	−1.35916	−	4.18305i	−0.0532287	−	0.163821i
$653$	10.9241	−	33.6210i	0.427495	−	1.31569i	−0.473091	−	0.881014i	$-0.656862\pi$
$653$	10.9241	−	33.6210i	0.427495	−	1.31569i	0.900585	−	0.434679i	$-0.143138\pi$
$654$		0			0
$655$	2.45537	+	1.78393i	0.0959393	+	0.0697040i
$656$	9.35409	−	28.7889i	0.365216	−	1.12402i
$657$		0			0
$658$	0.752439	−	0.546679i	0.0293331	−	0.0213118i
$659$	−28.4474			−1.10815			−0.554077	−	0.832465i	$-0.686929\pi$
$659$	−28.4474			−1.10815			−0.554077	+	0.832465i	$0.686929\pi$
$660$		0			0
$661$	39.5989			1.54022			0.770110	−	0.637911i	$-0.220201\pi$
$661$	39.5989			1.54022			0.770110	+	0.637911i	$0.220201\pi$
$662$	−10.4857	+	7.61830i	−0.407538	+	0.296094i
$663$		0			0
$664$	−15.0357	+	46.2752i	−0.583499	+	1.79583i
$665$	−2.48629	−	1.80639i	−0.0964140	−	0.0700489i
$666$		0			0
$667$	0.000634741	−	0.00195353i	2.45773e−5	−	7.56411e-5i
$668$	3.02256	+	9.30248i	0.116946	+	0.359924i
$669$		0			0
$670$	11.7791			0.455068
$671$	38.8573	−	19.0295i	1.50007	−	0.734627i
$672$		0			0
$673$	14.2080	−	10.3227i	0.547679	−	0.397912i	−0.279250	−	0.960218i	$-0.590086\pi$
$673$	14.2080	−	10.3227i	0.547679	−	0.397912i	0.826929	+	0.562306i	$0.190086\pi$
$674$	2.40448	+	7.40024i	0.0926173	+	0.285047i
$675$		0			0
$676$	4.19248	+	3.04602i	0.161249	+	0.117155i
$677$	36.4616	+	26.4909i	1.40133	+	1.01813i	0.994512	+	0.104619i	$0.0333622\pi$
$677$	36.4616	+	26.4909i	1.40133	+	1.01813i	0.406819	+	0.913509i	$0.366638\pi$
$678$		0			0
$679$	−0.820716	−	2.52590i	−0.0314962	−	0.0969353i
$680$	1.83287	−	1.33165i	0.0702872	−	0.0510666i
$681$		0			0
$682$	15.8608	+	16.3714i	0.607340	+	0.626894i
$683$	15.7677			0.603334			0.301667	−	0.953413i	$-0.402457\pi$
$683$	15.7677			0.603334			0.301667	+	0.953413i	$0.402457\pi$
$684$		0			0
$685$	6.39676	+	19.6872i	0.244408	+	0.752210i
$686$	−2.36087	+	7.26603i	−0.0901386	+	0.277418i
$687$		0			0
$688$	−4.03304	−	2.93018i	−0.153758	−	0.111712i
$689$	−12.9225	+	39.7713i	−0.492307	+	1.51517i
$690$		0			0
$691$	−2.39970	+	1.74348i	−0.0912889	+	0.0663253i	−0.632493	−	0.774566i	$-0.717968\pi$
$691$	−2.39970	+	1.74348i	−0.0912889	+	0.0663253i	0.541205	+	0.840891i	$0.317968\pi$
$692$	1.44668			0.0549944
$693$		0			0
$694$	30.9465			1.17471
$695$	2.87098	−	2.08589i	0.108903	−	0.0791224i
$696$		0			0
$697$	−2.50891	+	7.72162i	−0.0950316	+	0.292477i
$698$	−11.0132	−	8.00153i	−0.416854	−	0.302862i
$699$		0			0
$700$	0.0693589	−	0.213465i	0.00262152	−	0.00806821i
$701$	11.4738	+	35.3128i	0.433360	+	1.33375i	0.894757	+	0.446553i	$0.147348\pi$
$701$	11.4738	+	35.3128i	0.433360	+	1.33375i	−0.461397	+	0.887194i	$0.652652\pi$
$702$		0			0
$703$	50.1364			1.89093
$704$	−4.14459	−	29.1494i	−0.156205	−	1.09861i
$705$		0			0
$706$	−18.7017	+	13.5876i	−0.703848	+	0.511375i
$707$	0.308191	+	0.948516i	0.0115907	+	0.0356726i
$708$		0			0
$709$	25.6867	+	18.6625i	0.964683	+	0.700883i	0.954234	−	0.299062i	$-0.0966738\pi$
$709$	25.6867	+	18.6625i	0.964683	+	0.700883i	0.0104495	+	0.999945i	$0.496674\pi$
$710$	−11.3197	−	8.22423i	−0.424820	−	0.308650i
$711$		0			0
$712$	−8.86303	−	27.2776i	−0.332156	−	1.02227i
$713$	−0.0287608	+	0.0208959i	−0.00107710	+	0.000782558i
$714$		0			0
$715$	−7.51386	+	14.1866i	−0.281002	+	0.530549i
$716$	−3.12708			−0.116864
$717$		0			0
$718$	8.06692	+	24.8274i	0.301055	+	0.926552i
$719$	−9.85059	+	30.3170i	−0.367365	+	1.13063i	0.581122	+	0.813816i	$0.302614\pi$
$719$	−9.85059	+	30.3170i	−0.367365	+	1.13063i	−0.948487	+	0.316816i	$0.897386\pi$
$720$		0			0
$721$	3.53714	+	2.56989i	0.131730	+	0.0957075i
$722$	−10.3394	+	31.8213i	−0.384792	+	1.18427i
$723$		0			0
$724$	−4.48806	+	3.26077i	−0.166797	+	0.121185i
$725$	−0.323900			−0.0120294
$726$		0			0
$727$	41.4129			1.53592			0.767959	−	0.640499i	$-0.221272\pi$
$727$	41.4129			1.53592			0.767959	+	0.640499i	$0.221272\pi$
$728$	−5.41470	+	3.93401i	−0.200682	+	0.145804i
$729$		0			0
$730$	3.87945	−	11.9397i	0.143585	−	0.441909i
$731$	1.08172	+	0.785918i	0.0400090	+	0.0290682i
$732$		0			0
$733$	14.7376	−	45.3578i	0.544347	−	1.67533i	−0.178189	−	0.983996i	$-0.557024\pi$
$733$	14.7376	−	45.3578i	0.544347	−	1.67533i	0.722537	−	0.691333i	$-0.242976\pi$
$734$	11.8528	+	36.4792i	0.437495	+	1.34647i
$735$		0			0
$736$	0.0173734			0.000640391
$737$	−14.9145	+	28.1594i	−0.549381	+	1.03726i
$738$		0			0
$739$	10.0777	−	7.32187i	0.370714	−	0.269339i	−0.386793	−	0.922167i	$-0.626417\pi$
$739$	10.0777	−	7.32187i	0.370714	−	0.269339i	0.757507	+	0.652827i	$0.226417\pi$
$740$	1.13152	+	3.48246i	0.0415955	+	0.128018i
$741$		0			0
$742$	−3.87065	−	2.81219i	−0.142096	−	0.103239i
$743$	22.1446	+	16.0890i	0.812407	+	0.590249i	0.914528	−	0.404524i	$-0.132563\pi$
$743$	22.1446	+	16.0890i	0.812407	+	0.590249i	−0.102120	+	0.994772i	$0.532563\pi$
$744$		0			0
$745$	−1.94823	−	5.99603i	−0.0713775	−	0.219677i
$746$	9.31722	−	6.76936i	0.341128	−	0.247844i
$747$		0			0
$748$	0.171694	+	1.20754i	0.00627775	+	0.0441521i
$749$	5.31033			0.194035
$750$		0			0
$751$	−12.9393	−	39.8231i	−0.472162	−	1.45317i	−0.849747	−	0.527191i	$-0.823245\pi$
$751$	−12.9393	−	39.8231i	−0.472162	−	1.45317i	0.377585	−	0.925975i	$-0.376755\pi$
$752$	1.43203	−	4.40733i	0.0522207	−	0.160719i
$753$		0			0
$754$	1.55503	+	1.12979i	0.0566308	+	0.0411447i
$755$	1.13852	−	3.50400i	0.0414349	−	0.127523i
$756$		0			0
$757$	−13.0407	+	9.47464i	−0.473973	+	0.344362i	−0.798988	−	0.601347i	$-0.794631\pi$
$757$	−13.0407	+	9.47464i	−0.473973	+	0.344362i	0.325015	+	0.945709i	$0.394631\pi$
$758$	10.0499			0.365029
$759$		0			0
$760$	−20.8278			−0.755504
$761$	−8.83760	+	6.42090i	−0.320363	+	0.232757i	−0.736330	−	0.676622i	$-0.763443\pi$
$761$	−8.83760	+	6.42090i	−0.320363	+	0.232757i	0.415967	+	0.909380i	$0.363443\pi$
$762$		0			0
$763$	1.74604	−	5.37376i	0.0632109	−	0.194543i
$764$	8.19875	+	5.95674i	0.296620	+	0.215507i
$765$		0			0
$766$	−12.7610	+	39.2744i	−0.461075	+	1.41904i
$767$	2.24442	+	6.90762i	0.0810414	+	0.249420i
$768$		0			0
$769$	−34.2074			−1.23355			−0.616775	−	0.787139i	$-0.711561\pi$
$769$	−34.2074			−1.23355			−0.616775	+	0.787139i	$0.711561\pi$
$770$	−1.27800	−	1.31914i	−0.0460558	−	0.0475386i
$771$		0			0
$772$	−1.19570	+	0.868727i	−0.0430342	+	0.0312662i
$773$	−2.66894	−	8.21416i	−0.0959952	−	0.295443i	0.891517	−	0.452988i	$-0.149642\pi$
$773$	−2.66894	−	8.21416i	−0.0959952	−	0.295443i	−0.987512	+	0.157545i	$0.949642\pi$
$774$		0			0
$775$	4.53521	+	3.29503i	0.162910	+	0.118361i
$776$	−14.5619	−	10.5798i	−0.522742	−	0.379794i
$777$		0			0
$778$	12.4772	+	38.4009i	0.447329	+	1.37674i
$779$	60.3852	−	43.8724i	2.16352	−	1.57189i
$780$		0			0
$781$	33.9937	−	16.6477i	1.21639	−	0.595701i
$782$	0.00575405			0.000205764
$783$		0			0
$784$	5.79466	+	17.8341i	0.206952	+	0.636934i
$785$	−0.874113	+	2.69024i	−0.0311984	+	0.0960189i
$786$		0			0
$787$	18.6918	+	13.5804i	0.666291	+	0.484089i	0.868781	−	0.495196i	$-0.164904\pi$
$787$	18.6918	+	13.5804i	0.666291	+	0.484089i	−0.202491	+	0.979284i	$0.564904\pi$
$788$	0.798669	−	2.45805i	0.0284514	−	0.0875644i
$789$		0			0
$790$	2.08256	−	1.51307i	0.0740943	−	0.0538327i
$791$	−4.47453			−0.159096
$792$		0			0
$793$	−63.1443			−2.24232
$794$	−15.2613	+	11.0880i	−0.541603	+	0.393498i
$795$		0			0
$796$	−1.24418	+	3.82920i	−0.0440988	+	0.135722i
$797$	−32.1449	−	23.3547i	−1.13863	−	0.827265i	−0.151704	−	0.988426i	$-0.548476\pi$
$797$	−32.1449	−	23.3547i	−1.13863	−	0.827265i	−0.986928	+	0.161161i	$0.948476\pi$
$798$		0			0
$799$	−0.384092	+	1.18211i	−0.0135882	+	0.0418202i
$800$	−0.846572	−	2.60548i	−0.0299308	−	0.0921176i
$801$		0			0
$802$	8.14430			0.287585
$803$	23.6312	+	24.3920i	0.833927	+	0.860776i
$804$		0			0
$805$	0.00231743	−	0.00168371i	8.16785e−5	−	5.93429e-5i
$806$	−10.2800	−	31.6385i	−0.362096	−	1.11442i
$807$		0			0
$808$	5.46822	+	3.97289i	0.192371	+	0.139766i
$809$	−25.0908	−	18.2296i	−0.882147	−	0.640917i	0.0516716	−	0.998664i	$-0.483545\pi$
$809$	−25.0908	−	18.2296i	−0.882147	−	0.640917i	−0.933819	+	0.357747i	$0.883545\pi$
$810$		0			0
$811$	2.30503	+	7.09414i	0.0809404	+	0.249109i	0.983335	−	0.181801i	$-0.0581927\pi$
$811$	2.30503	+	7.09414i	0.0809404	+	0.249109i	−0.902395	+	0.430910i	$0.858193\pi$
$812$	0.0588151	−	0.0427317i	0.00206401	−	0.00149959i
$813$		0			0
$814$	29.5168	+	5.15557i	1.03456	+	0.180703i
$815$	−8.85141			−0.310051
$816$		0			0
$817$	−3.79849	−	11.6906i	−0.132892	−	0.409001i
$818$	−9.27633	+	28.5496i	−0.324339	+	0.998213i
$819$		0			0
$820$	4.41019	+	3.20419i	0.154010	+	0.111895i
$821$	3.91079	−	12.0362i	0.136488	−	0.420065i	−0.859331	−	0.511420i	$-0.829120\pi$
$821$	3.91079	−	12.0362i	0.136488	−	0.420065i	0.995818	+	0.0913546i	$0.0291197\pi$
$822$		0			0
$823$	22.0772	−	16.0401i	0.769564	−	0.559121i	−0.132265	−	0.991214i	$-0.542225\pi$
$823$	22.0772	−	16.0401i	0.769564	−	0.559121i	0.901829	+	0.432093i	$0.142225\pi$
$824$	29.6309			1.03224
$825$		0			0
$826$	−0.830969			−0.0289131
$827$	−13.7164	+	9.96556i	−0.476966	+	0.346536i	−0.800150	−	0.599800i	$-0.795247\pi$
$827$	−13.7164	+	9.96556i	−0.476966	+	0.346536i	0.323184	+	0.946336i	$0.395247\pi$
$828$		0			0
$829$	6.11217	−	18.8113i	0.212284	−	0.653344i	−0.787051	−	0.616888i	$-0.788393\pi$
$829$	6.11217	−	18.8113i	0.212284	−	0.653344i	0.999335	−	0.0364562i	$-0.0116069\pi$
$830$	15.7651	+	11.4540i	0.547215	+	0.397575i
$831$		0			0
$832$	−13.2782	+	40.8660i	−0.460337	+	1.41677i
$833$	−1.55422	−	4.78339i	−0.0538504	−	0.165735i
$834$		0			0
$835$	19.6842			0.681200
$836$	5.24819	−	9.90890i	0.181512	−	0.342706i
$837$		0			0
$838$	−20.6958	+	15.0364i	−0.714923	+	0.519422i
$839$	1.53882	+	4.73601i	0.0531261	+	0.163505i	0.974099	−	0.226121i	$-0.0726043\pi$
$839$	1.53882	+	4.73601i	0.0531261	+	0.163505i	−0.920973	+	0.389626i	$0.872604\pi$
$840$		0			0
$841$	23.3766	+	16.9841i	0.806090	+	0.585659i
$842$	−16.7933	−	12.2011i	−0.578736	−	0.420476i
$843$		0			0
$844$	0.201668	+	0.620670i	0.00694170	+	0.0213643i
$845$	8.43717	−	6.12996i	0.290247	−	0.210877i
$846$		0			0
$847$	4.77173	−	1.38493i	0.163959	−	0.0475868i
$848$	−23.8387			−0.818623
$849$		0			0
$850$	−0.280384	−	0.862933i	−0.00961709	−	0.0295983i
$851$	−0.0144408	+	0.0444441i	−0.000495023	+	0.00152353i
$852$		0			0
$853$	18.8068	+	13.6639i	0.643931	+	0.467843i	0.861199	−	0.508269i	$-0.169714\pi$
$853$	18.8068	+	13.6639i	0.643931	+	0.467843i	−0.217267	+	0.976112i	$0.569714\pi$
$854$	2.23243	−	6.87072i	0.0763923	−	0.235111i
$855$		0			0
$856$	29.1158	−	21.1539i	0.995158	−	0.723025i
$857$	30.6976			1.04861			0.524306	−	0.851530i	$-0.324325\pi$
$857$	30.6976			1.04861			0.524306	+	0.851530i	$0.324325\pi$
$858$		0			0
$859$	−11.1830			−0.381560			−0.190780	−	0.981633i	$-0.561102\pi$
$859$	−11.1830			−0.381560			−0.190780	+	0.981633i	$0.561102\pi$
$860$	0.726295	−	0.527684i	0.0247665	−	0.0179939i
$861$		0			0
$862$	9.91268	−	30.5081i	0.337627	−	1.03911i
$863$	−2.96371	−	2.15326i	−0.100886	−	0.0732980i	0.536199	−	0.844092i	$-0.319860\pi$
$863$	−2.96371	−	2.15326i	−0.100886	−	0.0732980i	−0.637085	+	0.770794i	$0.719860\pi$
$864$		0			0
$865$	0.899661	−	2.76887i	0.0305894	−	0.0941445i
$866$	9.49389	+	29.2192i	0.322616	+	0.992909i
$867$		0			0
$868$	−1.25823			−0.0427071
$869$	0.980280	+	6.89442i	0.0332537	+	0.233877i
$870$		0			0
$871$	37.6231	−	27.3348i	1.27481	−	0.926203i
$872$	−11.8333	−	36.4190i	−0.400725	−	1.23330i
$873$		0			0
$874$	−0.0427958	−	0.0310930i	−0.00144759	−	0.00105174i
$875$	−0.365429	−	0.265500i	−0.0123538	−	0.00897553i
$876$		0			0
$877$	2.27520	+	7.00235i	0.0768281	+	0.236453i	0.982094	−	0.188394i	$-0.0603281\pi$
$877$	2.27520	+	7.00235i	0.0768281	+	0.236453i	−0.905265	+	0.424846i	$0.860328\pi$
$878$	5.07073	−	3.68410i	0.171129	−	0.124332i
$879$		0			0
$880$	−9.01498	−	1.57461i	−0.303895	−	0.0530801i
$881$	−6.07165			−0.204559			−0.102280	−	0.994756i	$-0.532614\pi$
$881$	−6.07165			−0.204559			−0.102280	+	0.994756i	$0.532614\pi$
$882$		0			0
$883$	9.63412	+	29.6508i	0.324214	+	0.997828i	0.971794	+	0.235830i	$0.0757810\pi$
$883$	9.63412	+	29.6508i	0.324214	+	0.997828i	−0.647580	+	0.761997i	$0.724219\pi$
$884$	0.550061	−	1.69291i	0.0185005	−	0.0569388i
$885$		0			0
$886$	−27.8487	−	20.2333i	−0.935596	−	0.679750i
$887$	1.75830	−	5.41150i	0.0590380	−	0.181700i	−0.917188	−	0.398454i	$-0.869547\pi$
$887$	1.75830	−	5.41150i	0.0590380	−	0.181700i	0.976226	+	0.216754i	$0.0695468\pi$
$888$		0			0
$889$	−0.205210	+	0.149094i	−0.00688254	+	0.00500046i
$890$	−11.4868			−0.385037
$891$		0			0
$892$	−14.2288			−0.476414
$893$	9.24445	−	6.71648i	0.309354	−	0.224759i
$894$		0			0
$895$	−1.94467	+	5.98508i	−0.0650032	+	0.200059i
$896$	−1.97495	−	1.43488i	−0.0659784	−	0.0479361i
$897$		0			0
$898$	14.0159	−	43.1364i	0.467715	−	1.43948i
$899$	0.561092	+	1.72686i	0.0187135	+	0.0575941i
$900$		0			0
$901$	6.39389			0.213011
$902$	40.0620	−	19.6195i	1.33392	−	0.653258i
$903$		0			0
$904$	−24.5332	+	17.8244i	−0.815963	+	0.592832i
$905$	3.44992	+	10.6178i	0.114679	+	0.352946i
$906$		0			0
$907$	−34.3765	−	24.9760i	−1.14145	−	0.829313i	−0.154131	−	0.988050i	$-0.549258\pi$
$907$	−34.3765	−	24.9760i	−1.14145	−	0.829313i	−0.987321	+	0.158737i	$0.949258\pi$
$908$	3.16219	+	2.29747i	0.104941	+	0.0762441i
$909$		0			0
$910$	0.828317	+	2.54930i	0.0274585	+	0.0845084i
$911$	−1.73457	+	1.26024i	−0.0574690	+	0.0417537i	−0.616149	−	0.787630i	$-0.711308\pi$
$911$	−1.73457	+	1.26024i	−0.0574690	+	0.0417537i	0.558680	+	0.829383i	$0.311308\pi$
$912$		0			0
$913$	−47.3436	+	23.1855i	−1.56684	+	0.767329i
$914$	−45.1737			−1.49421
$915$		0			0
$916$	2.48002	+	7.63273i	0.0819423	+	0.252193i
$917$	−0.423630	+	1.30380i	−0.0139895	+	0.0430553i
$918$		0			0
$919$	−12.9995	−	9.44470i	−0.428815	−	0.311552i	0.352360	−	0.935864i	$-0.385379\pi$
$919$	−12.9995	−	9.44470i	−0.428815	−	0.311552i	−0.781175	+	0.624312i	$0.785379\pi$
$920$	0.00599902	−	0.0184631i	0.000197782	−	0.000608710i
$921$		0			0
$922$	−22.8141	+	16.5754i	−0.751343	+	0.545883i
$923$	−55.2407			−1.81827
$924$		0			0
$925$	7.36894			0.242289
$926$	−35.8628	+	26.0558i	−1.17852	+	0.856248i
$927$		0			0
$928$	0.274205	−	0.843916i	0.00900122	−	0.0277029i
$929$	−30.3196	−	22.0285i	−0.994753	−	0.722730i	−0.0337960	−	0.999429i	$-0.510760\pi$
$929$	−30.3196	−	22.0285i	−0.994753	−	0.722730i	−0.960957	+	0.276699i	$0.910760\pi$
$930$		0			0
$931$	−14.2883	+	43.9750i	−0.468282	+	1.44122i
$932$	2.83066	+	8.71187i	0.0927213	+	0.285367i
$933$		0			0
$934$	−2.77688			−0.0908621
$935$	2.41796	+	0.422334i	0.0790756	+	0.0138118i
$936$		0			0
$937$	21.0388	−	15.2856i	0.687308	−	0.499359i	−0.188466	−	0.982080i	$-0.560351\pi$
$937$	21.0388	−	15.2856i	0.687308	−	0.499359i	0.875774	+	0.482721i	$0.160351\pi$
$938$	1.64415	+	5.06017i	0.0536834	+	0.165220i
$939$		0			0
$940$	0.675161	+	0.490533i	0.0220213	+	0.0159994i
$941$	6.94527	+	5.04603i	0.226409	+	0.164496i	0.695207	−	0.718810i	$-0.255313\pi$
$941$	6.94527	+	5.04603i	0.226409	+	0.164496i	−0.468798	+	0.883306i	$0.655313\pi$
$942$		0			0
$943$	0.0214986	+	0.0661658i	0.000700090	+	0.00215466i
$944$	−3.34964	+	2.43366i	−0.109022	+	0.0792088i
$945$		0			0
$946$	−1.03413	−	7.27318i	−0.0336226	−	0.236471i
$947$	36.0304			1.17083			0.585416	−	0.810733i	$-0.300931\pi$
$947$	36.0304			1.17083			0.585416	+	0.810733i	$0.300931\pi$
$948$		0			0
$949$	−15.3163	−	47.1386i	−0.497187	−	1.53019i
$950$	−2.57765	+	7.93318i	−0.0836299	+	0.257386i
$951$		0			0
$952$	0.827896	+	0.601502i	0.0268323	+	0.0194948i
$953$	13.5512	−	41.7062i	0.438965	−	1.35100i	−0.450003	−	0.893027i	$-0.648577\pi$
$953$	13.5512	−	41.7062i	0.438965	−	1.35100i	0.888968	−	0.457969i	$-0.151423\pi$
$954$		0			0
$955$	16.4996	−	11.9876i	0.533914	−	0.387911i
$956$	11.1127			0.359412
$957$		0			0
$958$	−37.4310			−1.20934
$959$	−7.56451	+	5.49594i	−0.244271	+	0.177473i
$960$		0			0
$961$	0.131439	−	0.404529i	0.00423998	−	0.0130493i
$962$	−35.3779	−	25.7035i	−1.14063	−	0.828716i
$963$		0			0
$964$	2.03017	−	6.24822i	0.0653874	−	0.201242i
$965$	0.919120	+	2.82876i	0.0295875	+	0.0910610i
$966$		0			0
$967$	−48.1271			−1.54766			−0.773831	−	0.633392i	$-0.781662\pi$
$967$	−48.1271			−1.54766			−0.773831	+	0.633392i	$0.781662\pi$
$968$	20.6458	−	26.6017i	0.663582	−	0.855012i
$969$		0			0
$970$	−5.83198	+	4.23718i	−0.187253	+	0.136048i
$971$	−9.80617	−	30.1803i	−0.314695	−	0.968531i	−0.975880	−	0.218308i	$-0.929946\pi$
$971$	−9.80617	−	30.1803i	−0.314695	−	0.968531i	0.661185	−	0.750223i	$-0.270054\pi$
$972$		0			0
$973$	1.29681	+	0.942187i	0.0415738	+	0.0302051i
$974$	−16.0228	−	11.6413i	−0.513404	−	0.373010i
$975$		0			0
$976$	−11.1233	−	34.2341i	−0.356049	−	1.09581i
$977$	34.8913	−	25.3500i	1.11627	−	0.811018i	0.132631	−	0.991166i	$-0.457658\pi$
$977$	34.8913	−	25.3500i	1.11627	−	0.811018i	0.983640	+	0.180148i	$0.0576575\pi$
$978$		0			0
$979$	14.5443	−	27.4604i	0.464836	−	0.877639i
$980$	−3.37696			−0.107873
$981$		0			0
$982$	−4.42378	−	13.6150i	−0.141168	−	0.434472i
$983$	−13.8106	+	42.5048i	−0.440491	+	1.35569i	0.446863	+	0.894602i	$0.352541\pi$
$983$	−13.8106	+	42.5048i	−0.440491	+	1.35569i	−0.887354	+	0.461089i	$0.847459\pi$
$984$		0			0
$985$	−4.20792	−	3.05723i	−0.134075	−	0.0974115i
$986$	0.0908164	−	0.279504i	0.00289218	−	0.00890123i
$987$		0			0
$988$	−13.2390	+	9.61873i	−0.421190	+	0.306012i
$989$	0.0114573			0.000364322
$990$		0			0
$991$	13.7657			0.437282			0.218641	−	0.975805i	$-0.429838\pi$
$991$	13.7657			0.437282			0.218641	+	0.975805i	$0.429838\pi$
$992$	−12.4245	+	9.02693i	−0.394479	+	0.286605i
$993$		0			0
$994$	1.95301	−	6.01074i	0.0619457	−	0.190649i
$995$	6.55518	+	4.76261i	0.207813	+	0.150985i
$996$		0			0
$997$	1.51297	−	4.65646i	0.0479164	−	0.147471i	−0.924236	−	0.381823i	$-0.875297\pi$
$997$	1.51297	−	4.65646i	0.0479164	−	0.147471i	0.972152	+	0.234351i	$0.0752965\pi$
$998$	15.5091	+	47.7322i	0.490933	+	1.51094i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.h.91.3	yes	16
3.2	odd	2		495.2.n.g.91.2	✓	16
11.2	odd	10		5445.2.a.cc.1.6		8
11.4	even	5	inner	495.2.n.h.136.3	yes	16
11.9	even	5		5445.2.a.ca.1.3		8
33.2	even	10		5445.2.a.cb.1.3		8
33.20	odd	10		5445.2.a.cd.1.6		8
33.26	odd	10		495.2.n.g.136.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.n.g.91.2	✓	16	3.2	odd	2
495.2.n.g.136.2	yes	16	33.26	odd	10
495.2.n.h.91.3	yes	16	1.1	even	1	trivial
495.2.n.h.136.3	yes	16	11.4	even	5	inner
5445.2.a.ca.1.3		8	11.9	even	5
5445.2.a.cb.1.3		8	33.2	even	10
5445.2.a.cc.1.6		8	11.2	odd	10
5445.2.a.cd.1.6		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)

\(f(q)\)	\(=\)	\(q+(0.991861 - 0.720629i) q^{2} +(-0.153553 + 0.472586i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.139581 + 0.429587i) q^{7} +(0.945971 + 2.91140i) q^{8} +O(q^{10})\)	\(q+(0.991861 - 0.720629i) q^{2} +(-0.153553 + 0.472586i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.139581 + 0.429587i) q^{7} +(0.945971 + 2.91140i) q^{8} +1.22601 q^{10} +(-1.55234 + 2.93091i) q^{11} +(3.91592 - 2.84508i) q^{13} +(0.171128 + 0.526677i) q^{14} +(2.23230 + 1.62186i) q^{16} +(-0.598736 - 0.435007i) q^{17} +(2.10247 + 6.47075i) q^{19} +(-0.402006 + 0.292074i) q^{20} +(0.572395 + 4.02572i) q^{22} -0.00634166 q^{23} +(0.309017 + 0.951057i) q^{25} +(1.83380 - 5.64385i) q^{26} +(-0.181584 - 0.131928i) q^{28} +(-0.100091 + 0.308048i) q^{29} +(4.53521 - 3.29503i) q^{31} -2.73956 q^{32} -0.907341 q^{34} +(-0.365429 + 0.265500i) q^{35} +(2.27713 - 7.00828i) q^{37} +(6.74837 + 4.90298i) q^{38} +(-0.945971 + 2.91140i) q^{40} +(-3.39006 - 10.4335i) q^{41} -1.80668 q^{43} +(-1.14674 - 1.18366i) q^{44} +(-0.00629004 + 0.00456998i) q^{46} +(-0.518988 - 1.59728i) q^{47} +(5.49806 + 3.99457i) q^{49} +(0.991861 + 0.720629i) q^{50} +(0.743247 + 2.28748i) q^{52} +(-6.98948 + 5.07816i) q^{53} +(-2.97862 + 1.45871i) q^{55} -1.38274 q^{56} +(0.122712 + 0.377669i) q^{58} +(-0.463691 + 1.42709i) q^{59} +(-10.5540 - 7.66790i) q^{61} +(2.12381 - 6.53641i) q^{62} +(-7.18186 + 5.21793i) q^{64} +4.84034 q^{65} +9.60773 q^{67} +(0.297516 - 0.216158i) q^{68} +(-0.171128 + 0.526677i) q^{70} +(-9.23296 - 6.70814i) q^{71} +(3.16430 - 9.73870i) q^{73} +(-2.79178 - 8.59220i) q^{74} -3.38083 q^{76} +(-1.04241 - 1.07597i) q^{77} +(1.69866 - 1.23415i) q^{79} +(0.852662 + 2.62422i) q^{80} +(-10.8812 - 7.90563i) q^{82} +(12.8589 + 9.34255i) q^{83} +(-0.228697 - 0.703856i) q^{85} +(-1.79197 + 1.30194i) q^{86} +(-10.0015 - 1.74692i) q^{88} -9.36925 q^{89} +(0.675622 + 2.07935i) q^{91} +(0.000973778 - 0.00299698i) q^{92} +(-1.66581 - 1.21028i) q^{94} +(-2.10247 + 6.47075i) q^{95} +(-4.75689 + 3.45608i) q^{97} +8.33191 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) 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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