LMFDB - Embedded newform 450.2.h.b.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(91,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.h (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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			271.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	450.271
Dual form			450.2.h.b.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.80902 + 1.31433i) q^{5} +2.00000 q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.80902 + 1.31433i) q^{5} +2.00000 q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.690983 + 2.12663i) q^{10} +(1.61803 - 4.97980i) q^{11} +(-1.50000 - 4.61653i) q^{13} +(0.618034 - 1.90211i) q^{14} +(0.309017 + 0.951057i) q^{16} +(6.35410 - 4.61653i) q^{17} +(2.23607 - 1.62460i) q^{19} +2.23607 q^{20} +(-4.23607 - 3.07768i) q^{22} +(-1.85410 + 5.70634i) q^{23} +(1.54508 - 4.75528i) q^{25} -4.85410 q^{26} +(-1.61803 - 1.17557i) q^{28} +(-1.11803 - 0.812299i) q^{29} +(-3.00000 + 2.17963i) q^{31} +1.00000 q^{32} +(-2.42705 - 7.46969i) q^{34} +(-3.61803 + 2.62866i) q^{35} +(-0.663119 - 2.04087i) q^{37} +(-0.854102 - 2.62866i) q^{38} +(0.690983 - 2.12663i) q^{40} +(1.88197 + 5.79210i) q^{41} -1.23607 q^{43} +(-4.23607 + 3.07768i) q^{44} +(4.85410 + 3.52671i) q^{46} +(3.85410 + 2.80017i) q^{47} -3.00000 q^{49} +(-4.04508 - 2.93893i) q^{50} +(-1.50000 + 4.61653i) q^{52} +(6.92705 + 5.03280i) q^{53} +(3.61803 + 11.1352i) q^{55} +(-1.61803 + 1.17557i) q^{56} +(-1.11803 + 0.812299i) q^{58} +(-2.76393 - 8.50651i) q^{59} +(-2.73607 + 8.42075i) q^{61} +(1.14590 + 3.52671i) q^{62} +(0.309017 - 0.951057i) q^{64} +(8.78115 + 6.37988i) q^{65} +(7.85410 - 5.70634i) q^{67} -7.85410 q^{68} +(1.38197 + 4.25325i) q^{70} +(-11.4721 - 8.33499i) q^{71} +(-0.972136 + 2.99193i) q^{73} -2.14590 q^{74} -2.76393 q^{76} +(3.23607 - 9.95959i) q^{77} +(-1.80902 - 1.31433i) q^{80} +6.09017 q^{82} +(4.85410 - 3.52671i) q^{83} +(-5.42705 + 16.7027i) q^{85} +(-0.381966 + 1.17557i) q^{86} +(1.61803 + 4.97980i) q^{88} +(-0.427051 + 1.31433i) q^{89} +(-3.00000 - 9.23305i) q^{91} +(4.85410 - 3.52671i) q^{92} +(3.85410 - 2.80017i) q^{94} +(-1.90983 + 5.87785i) q^{95} +(11.2082 + 8.14324i) q^{97} +(-0.927051 + 2.85317i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} - 5 q^{5} + 8 q^{7} - q^{8}+O(q^{10}) $ 4 * q - q^2 - q^4 - 5 * q^5 + 8 * q^7 - q^8	$ 4 q - q^{2} - q^{4} - 5 q^{5} + 8 q^{7} - q^{8} + 5 q^{10} + 2 q^{11} - 6 q^{13} - 2 q^{14} - q^{16} + 12 q^{17} - 8 q^{22} + 6 q^{23} - 5 q^{25} - 6 q^{26} - 2 q^{28} - 12 q^{31} + 4 q^{32} - 3 q^{34} - 10 q^{35} + 13 q^{37} + 10 q^{38} + 5 q^{40} + 12 q^{41} + 4 q^{43} - 8 q^{44} + 6 q^{46} + 2 q^{47} - 12 q^{49} - 5 q^{50} - 6 q^{52} + 21 q^{53} + 10 q^{55} - 2 q^{56} - 20 q^{59} - 2 q^{61} + 18 q^{62} - q^{64} + 15 q^{65} + 18 q^{67} - 18 q^{68} + 10 q^{70} - 28 q^{71} + 14 q^{73} - 22 q^{74} - 20 q^{76} + 4 q^{77} - 5 q^{80} + 2 q^{82} + 6 q^{83} - 15 q^{85} - 6 q^{86} + 2 q^{88} + 5 q^{89} - 12 q^{91} + 6 q^{92} + 2 q^{94} - 30 q^{95} + 18 q^{97} + 3 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 - 5 * q^5 + 8 * q^7 - q^8 + 5 * q^10 + 2 * q^11 - 6 * q^13 - 2 * q^14 - q^16 + 12 * q^17 - 8 * q^22 + 6 * q^23 - 5 * q^25 - 6 * q^26 - 2 * q^28 - 12 * q^31 + 4 * q^32 - 3 * q^34 - 10 * q^35 + 13 * q^37 + 10 * q^38 + 5 * q^40 + 12 * q^41 + 4 * q^43 - 8 * q^44 + 6 * q^46 + 2 * q^47 - 12 * q^49 - 5 * q^50 - 6 * q^52 + 21 * q^53 + 10 * q^55 - 2 * q^56 - 20 * q^59 - 2 * q^61 + 18 * q^62 - q^64 + 15 * q^65 + 18 * q^67 - 18 * q^68 + 10 * q^70 - 28 * q^71 + 14 * q^73 - 22 * q^74 - 20 * q^76 + 4 * q^77 - 5 * q^80 + 2 * q^82 + 6 * q^83 - 15 * q^85 - 6 * q^86 + 2 * q^88 + 5 * q^89 - 12 * q^91 + 6 * q^92 + 2 * q^94 - 30 * q^95 + 18 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$6$		0			0
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$	0.690983	+	2.12663i	0.218508	+	0.672499i
$11$	1.61803	−	4.97980i	0.487856	−	1.50147i	−0.339946	−	0.940445i	$-0.610409\pi$
$11$	1.61803	−	4.97980i	0.487856	−	1.50147i	0.827802	−	0.561020i	$-0.189591\pi$
$12$		0			0
$13$	−1.50000	−	4.61653i	−0.416025	−	1.28039i	−0.911331	−	0.411675i	$-0.864944\pi$
$13$	−1.50000	−	4.61653i	−0.416025	−	1.28039i	0.495306	−	0.868719i	$-0.335056\pi$
$14$	0.618034	−	1.90211i	0.165177	−	0.508361i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	6.35410	−	4.61653i	1.54110	−	1.11967i	0.591452	−	0.806340i	$-0.298555\pi$
$17$	6.35410	−	4.61653i	1.54110	−	1.11967i	0.949644	−	0.313332i	$-0.101445\pi$
$18$		0			0
$19$	2.23607	−	1.62460i	0.512989	−	0.372708i	−0.300967	−	0.953635i	$-0.597309\pi$
$19$	2.23607	−	1.62460i	0.512989	−	0.372708i	0.813956	+	0.580926i	$0.197309\pi$
$20$	2.23607			0.500000
$21$		0			0
$22$	−4.23607	−	3.07768i	−0.903133	−	0.656164i
$23$	−1.85410	+	5.70634i	−0.386607	+	1.18985i	0.548701	+	0.836019i	$0.315123\pi$
$23$	−1.85410	+	5.70634i	−0.386607	+	1.18985i	−0.935308	+	0.353835i	$0.884877\pi$
$24$		0			0
$25$	1.54508	−	4.75528i	0.309017	−	0.951057i
$26$	−4.85410			−0.951968
$27$		0			0
$28$	−1.61803	−	1.17557i	−0.305780	−	0.222162i
$29$	−1.11803	−	0.812299i	−0.207614	−	0.150840i	0.479120	−	0.877750i	$-0.340956\pi$
$29$	−1.11803	−	0.812299i	−0.207614	−	0.150840i	−0.686733	+	0.726909i	$0.740956\pi$
$30$		0			0
$31$	−3.00000	+	2.17963i	−0.538816	+	0.391473i	−0.823645	−	0.567106i	$-0.808063\pi$
$31$	−3.00000	+	2.17963i	−0.538816	+	0.391473i	0.284829	+	0.958578i	$0.408063\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−2.42705	−	7.46969i	−0.416236	−	1.28104i
$35$	−3.61803	+	2.62866i	−0.611559	+	0.444324i
$36$		0			0
$37$	−0.663119	−	2.04087i	−0.109016	−	0.335517i	0.881636	−	0.471930i	$-0.156443\pi$
$37$	−0.663119	−	2.04087i	−0.109016	−	0.335517i	−0.990652	+	0.136413i	$0.956443\pi$
$38$	−0.854102	−	2.62866i	−0.138554	−	0.426424i
$39$		0			0
$40$	0.690983	−	2.12663i	0.109254	−	0.336249i
$41$	1.88197	+	5.79210i	0.293914	+	0.904573i	0.983584	+	0.180450i	$0.0577554\pi$
$41$	1.88197	+	5.79210i	0.293914	+	0.904573i	−0.689670	+	0.724123i	$0.742245\pi$
$42$		0			0
$43$	−1.23607			−0.188499			−0.0942493	−	0.995549i	$-0.530045\pi$
$43$	−1.23607			−0.188499			−0.0942493	+	0.995549i	$0.530045\pi$
$44$	−4.23607	+	3.07768i	−0.638611	+	0.463978i
$45$		0			0
$46$	4.85410	+	3.52671i	0.715698	+	0.519985i
$47$	3.85410	+	2.80017i	0.562179	+	0.408447i	0.832256	−	0.554392i	$-0.187049\pi$
$47$	3.85410	+	2.80017i	0.562179	+	0.408447i	−0.270077	+	0.962839i	$0.587049\pi$
$48$		0			0
$49$	−3.00000			−0.428571
$50$	−4.04508	−	2.93893i	−0.572061	−	0.415627i
$51$		0			0
$52$	−1.50000	+	4.61653i	−0.208013	+	0.640197i
$53$	6.92705	+	5.03280i	0.951504	+	0.691308i	0.951162	−	0.308692i	$-0.0998913\pi$
$53$	6.92705	+	5.03280i	0.951504	+	0.691308i	0.000341607		1.00000i	$0.499891\pi$
$54$		0			0
$55$	3.61803	+	11.1352i	0.487856	+	1.50147i
$56$	−1.61803	+	1.17557i	−0.216219	+	0.157092i
$57$		0			0
$58$	−1.11803	+	0.812299i	−0.146805	+	0.106660i
$59$	−2.76393	−	8.50651i	−0.359833	−	1.10745i	−0.953154	−	0.302487i	$-0.902183\pi$
$59$	−2.76393	−	8.50651i	−0.359833	−	1.10745i	0.593320	−	0.804966i	$-0.297817\pi$
$60$		0			0
$61$	−2.73607	+	8.42075i	−0.350318	+	1.07817i	0.608357	+	0.793663i	$0.291829\pi$
$61$	−2.73607	+	8.42075i	−0.350318	+	1.07817i	−0.958675	+	0.284504i	$0.908171\pi$
$62$	1.14590	+	3.52671i	0.145529	+	0.447893i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	8.78115	+	6.37988i	1.08917	+	0.791327i
$66$		0			0
$67$	7.85410	−	5.70634i	0.959531	−	0.697140i	0.00648944	−	0.999979i	$-0.497934\pi$
$67$	7.85410	−	5.70634i	0.959531	−	0.697140i	0.953042	+	0.302839i	$0.0979343\pi$
$68$	−7.85410			−0.952450
$69$		0			0
$70$	1.38197	+	4.25325i	0.165177	+	0.508361i
$71$	−11.4721	−	8.33499i	−1.36149	−	0.989182i	−0.998348	−	0.0574487i	$-0.981703\pi$
$71$	−11.4721	−	8.33499i	−1.36149	−	0.989182i	−0.363144	−	0.931733i	$-0.618297\pi$
$72$		0			0
$73$	−0.972136	+	2.99193i	−0.113780	+	0.350179i	−0.991691	−	0.128646i	$-0.958937\pi$
$73$	−0.972136	+	2.99193i	−0.113780	+	0.350179i	0.877911	+	0.478824i	$0.158937\pi$
$74$	−2.14590			−0.249456
$75$		0			0
$76$	−2.76393			−0.317045
$77$	3.23607	−	9.95959i	0.368784	−	1.13500i
$78$		0			0
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$	−1.80902	−	1.31433i	−0.202254	−	0.146946i
$81$		0			0
$82$	6.09017			0.672547
$83$	4.85410	−	3.52671i	0.532807	−	0.387107i	−0.288600	−	0.957450i	$-0.593190\pi$
$83$	4.85410	−	3.52671i	0.532807	−	0.387107i	0.821407	+	0.570343i	$0.193190\pi$
$84$		0			0
$85$	−5.42705	+	16.7027i	−0.588646	+	1.81167i
$86$	−0.381966	+	1.17557i	−0.0411885	+	0.126765i
$87$		0			0
$88$	1.61803	+	4.97980i	0.172483	+	0.530848i
$89$	−0.427051	+	1.31433i	−0.0452673	+	0.139318i	−0.971136	−	0.238528i	$-0.923335\pi$
$89$	−0.427051	+	1.31433i	−0.0452673	+	0.139318i	0.925868	+	0.377846i	$0.123335\pi$
$90$		0			0
$91$	−3.00000	−	9.23305i	−0.314485	−	0.967887i
$92$	4.85410	−	3.52671i	0.506075	−	0.367685i
$93$		0			0
$94$	3.85410	−	2.80017i	0.397520	−	0.288815i
$95$	−1.90983	+	5.87785i	−0.195944	+	0.603055i
$96$		0			0
$97$	11.2082	+	8.14324i	1.13802	+	0.826820i	0.986842	−	0.161686i	$-0.0516932\pi$
$97$	11.2082	+	8.14324i	1.13802	+	0.826820i	0.151178	+	0.988506i	$0.451693\pi$
$98$	−0.927051	+	2.85317i	−0.0936463	+	0.288214i
$99$		0			0
$100$	−4.04508	+	2.93893i	−0.404508	+	0.293893i
$101$	−1.67376			−0.166546			−0.0832728	−	0.996527i	$-0.526537\pi$
$101$	−1.67376			−0.166546			−0.0832728	+	0.996527i	$0.526537\pi$
$102$		0			0
$103$	1.85410	+	1.34708i	0.182690	+	0.132732i	0.675372	−	0.737478i	$-0.263983\pi$
$103$	1.85410	+	1.34708i	0.182690	+	0.132732i	−0.492682	+	0.870210i	$0.663983\pi$
$104$	3.92705	+	2.85317i	0.385079	+	0.279776i
$105$		0			0
$106$	6.92705	−	5.03280i	0.672815	−	0.488828i
$107$	−10.9443			−1.05802			−0.529011	−	0.848615i	$-0.677437\pi$
$107$	−10.9443			−1.05802			−0.529011	+	0.848615i	$0.677437\pi$
$108$		0			0
$109$	0.791796	+	2.43690i	0.0758403	+	0.233412i	0.981789	−	0.189975i	$-0.0608408\pi$
$109$	0.791796	+	2.43690i	0.0758403	+	0.233412i	−0.905949	+	0.423388i	$0.860841\pi$
$110$	11.7082			1.11633
$111$		0			0
$112$	0.618034	+	1.90211i	0.0583987	+	0.179733i
$113$	3.57295	+	10.9964i	0.336115	+	1.03445i	0.966170	+	0.257905i	$0.0830321\pi$
$113$	3.57295	+	10.9964i	0.336115	+	1.03445i	−0.630056	+	0.776550i	$0.716968\pi$
$114$		0			0
$115$	−4.14590	−	12.7598i	−0.386607	−	1.18985i
$116$	0.427051	+	1.31433i	0.0396507	+	0.122032i
$117$		0			0
$118$	−8.94427			−0.823387
$119$	12.7082	−	9.23305i	1.16496	−	0.846392i
$120$		0			0
$121$	−13.2812	−	9.64932i	−1.20738	−	0.877211i
$122$	7.16312	+	5.20431i	0.648518	+	0.471176i
$123$		0			0
$124$	3.70820			0.333007
$125$	3.45492	+	10.6331i	0.309017	+	0.951057i
$126$		0			0
$127$	0.0901699	−	0.277515i	0.00800129	−	0.0246254i	−0.946976	−	0.321304i	$-0.895879\pi$
$127$	0.0901699	−	0.277515i	0.00800129	−	0.0246254i	0.954977	+	0.296678i	$0.0958789\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	8.78115	−	6.37988i	0.770158	−	0.559553i
$131$	−0.618034	+	0.449028i	−0.0539979	+	0.0392318i	−0.614457	−	0.788950i	$-0.710625\pi$
$131$	−0.618034	+	0.449028i	−0.0539979	+	0.0392318i	0.560459	+	0.828182i	$0.310625\pi$
$132$		0			0
$133$	4.47214	−	3.24920i	0.387783	−	0.281741i
$134$	−3.00000	−	9.23305i	−0.259161	−	0.797614i
$135$		0			0
$136$	−2.42705	+	7.46969i	−0.208118	+	0.640521i
$137$	4.64590	+	14.2986i	0.396926	+	1.22161i	0.927452	+	0.373943i	$0.121995\pi$
$137$	4.64590	+	14.2986i	0.396926	+	1.22161i	−0.530526	+	0.847669i	$0.678005\pi$
$138$		0			0
$139$	−4.14590	+	12.7598i	−0.351650	+	1.08227i	0.606276	+	0.795254i	$0.292663\pi$
$139$	−4.14590	+	12.7598i	−0.351650	+	1.08227i	−0.957926	+	0.287014i	$0.907337\pi$
$140$	4.47214			0.377964
$141$		0			0
$142$	−11.4721	+	8.33499i	−0.962720	+	0.699457i
$143$	−25.4164			−2.12543
$144$		0			0
$145$	3.09017			0.256625
$146$	2.54508	+	1.84911i	0.210633	+	0.153034i
$147$		0			0
$148$	−0.663119	+	2.04087i	−0.0545080	+	0.167759i
$149$	−7.03444			−0.576284			−0.288142	−	0.957588i	$-0.593038\pi$
$149$	−7.03444			−0.576284			−0.288142	+	0.957588i	$0.593038\pi$
$150$		0			0
$151$	−6.94427			−0.565117			−0.282558	−	0.959250i	$-0.591183\pi$
$151$	−6.94427			−0.565117			−0.282558	+	0.959250i	$0.591183\pi$
$152$	−0.854102	+	2.62866i	−0.0692768	+	0.213212i
$153$		0			0
$154$	−8.47214	−	6.15537i	−0.682704	−	0.496014i
$155$	2.56231	−	7.88597i	0.205809	−	0.633416i
$156$		0			0
$157$	17.8541			1.42491			0.712456	−	0.701717i	$-0.247583\pi$
$157$	17.8541			1.42491			0.712456	+	0.701717i	$0.247583\pi$
$158$		0			0
$159$		0			0
$160$	−1.80902	+	1.31433i	−0.143015	+	0.103907i
$161$	−3.70820	+	11.4127i	−0.292247	+	0.899445i
$162$		0			0
$163$	6.32624	+	19.4702i	0.495509	+	1.52502i	0.816162	+	0.577824i	$0.196098\pi$
$163$	6.32624	+	19.4702i	0.495509	+	1.52502i	−0.320652	+	0.947197i	$0.603902\pi$
$164$	1.88197	−	5.79210i	0.146957	−	0.452287i
$165$		0			0
$166$	−1.85410	−	5.70634i	−0.143906	−	0.442898i
$167$	5.23607	−	3.80423i	0.405179	−	0.294380i	−0.366468	−	0.930431i	$-0.619433\pi$
$167$	5.23607	−	3.80423i	0.405179	−	0.294380i	0.771647	+	0.636051i	$0.219433\pi$
$168$		0			0
$169$	−8.54508	+	6.20837i	−0.657314	+	0.477567i
$170$	14.2082	+	10.3229i	1.08972	+	0.791728i
$171$		0			0
$172$	1.00000	+	0.726543i	0.0762493	+	0.0553983i
$173$	3.37132	−	10.3759i	0.256317	−	0.788862i	−0.737250	−	0.675620i	$-0.763876\pi$
$173$	3.37132	−	10.3759i	0.256317	−	0.788862i	0.993567	−	0.113243i	$-0.0361238\pi$
$174$		0			0
$175$	3.09017	−	9.51057i	0.233595	−	0.718931i
$176$	5.23607			0.394683
$177$		0			0
$178$	1.11803	+	0.812299i	0.0838002	+	0.0608844i
$179$	−3.09017	−	2.24514i	−0.230970	−	0.167810i	0.466281	−	0.884637i	$-0.345594\pi$
$179$	−3.09017	−	2.24514i	−0.230970	−	0.167810i	−0.697251	+	0.716827i	$0.745594\pi$
$180$		0			0
$181$	16.2082	−	11.7759i	1.20475	−	0.875299i	0.210003	−	0.977701i	$-0.432653\pi$
$181$	16.2082	−	11.7759i	1.20475	−	0.875299i	0.994743	+	0.102401i	$0.0326526\pi$
$182$	−9.70820			−0.719620
$183$		0			0
$184$	−1.85410	−	5.70634i	−0.136686	−	0.420677i
$185$	3.88197	+	2.82041i	0.285408	+	0.207361i
$186$		0			0
$187$	−12.7082	−	39.1118i	−0.929316	−	2.86014i
$188$	−1.47214	−	4.53077i	−0.107367	−	0.330440i
$189$		0			0
$190$	5.00000	+	3.63271i	0.362738	+	0.263545i
$191$	0.236068	+	0.726543i	0.0170813	+	0.0525708i	0.959234	−	0.282614i	$-0.0912014\pi$
$191$	0.236068	+	0.726543i	0.0170813	+	0.0525708i	−0.942153	+	0.335184i	$0.891201\pi$
$192$		0			0
$193$	2.38197			0.171458			0.0857288	−	0.996319i	$-0.472678\pi$
$193$	2.38197			0.171458			0.0857288	+	0.996319i	$0.472678\pi$
$194$	11.2082	−	8.14324i	0.804702	−	0.584650i
$195$		0			0
$196$	2.42705	+	1.76336i	0.173361	+	0.125954i
$197$	−10.7812	−	7.83297i	−0.768125	−	0.558076i	0.133266	−	0.991080i	$-0.457453\pi$
$197$	−10.7812	−	7.83297i	−0.768125	−	0.558076i	−0.901392	+	0.433005i	$0.857453\pi$
$198$		0			0
$199$	−6.18034			−0.438113			−0.219056	−	0.975712i	$-0.570298\pi$
$199$	−6.18034			−0.438113			−0.219056	+	0.975712i	$0.570298\pi$
$200$	1.54508	+	4.75528i	0.109254	+	0.336249i
$201$		0			0
$202$	−0.517221	+	1.59184i	−0.0363915	+	0.112002i
$203$	−2.23607	−	1.62460i	−0.156941	−	0.114024i
$204$		0			0
$205$	−11.0172	−	8.00448i	−0.769476	−	0.559057i
$206$	1.85410	−	1.34708i	0.129181	−	0.0938558i
$207$		0			0
$208$	3.92705	−	2.85317i	0.272292	−	0.197832i
$209$	−4.47214	−	13.7638i	−0.309344	−	0.952063i
$210$		0			0
$211$	−2.47214	+	7.60845i	−0.170189	+	0.523787i	−0.999381	−	0.0351760i	$-0.988801\pi$
$211$	−2.47214	+	7.60845i	−0.170189	+	0.523787i	0.829192	+	0.558963i	$0.188801\pi$
$212$	−2.64590	−	8.14324i	−0.181721	−	0.559280i
$213$		0			0
$214$	−3.38197	+	10.4086i	−0.231186	+	0.711519i
$215$	2.23607	−	1.62460i	0.152499	−	0.110797i
$216$		0			0
$217$	−6.00000	+	4.35926i	−0.407307	+	0.295926i
$218$	2.56231			0.173541
$219$		0			0
$220$	3.61803	−	11.1352i	0.243928	−	0.750733i
$221$	−30.8435	−	22.4091i	−2.07476	−	1.50740i
$222$		0			0
$223$	−0.708204	+	2.17963i	−0.0474248	+	0.145959i	−0.971965	−	0.235127i	$-0.924450\pi$
$223$	−0.708204	+	2.17963i	−0.0474248	+	0.145959i	0.924540	+	0.381085i	$0.124450\pi$
$224$	2.00000			0.133631
$225$		0			0
$226$	11.5623			0.769113
$227$	5.23607	−	16.1150i	0.347530	−	1.06959i	−0.612685	−	0.790327i	$-0.709911\pi$
$227$	5.23607	−	16.1150i	0.347530	−	1.06959i	0.960215	−	0.279261i	$-0.0900893\pi$
$228$		0			0
$229$	19.6353	+	14.2658i	1.29753	+	0.942714i	0.999928	−	0.0119751i	$-0.00381187\pi$
$229$	19.6353	+	14.2658i	1.29753	+	0.942714i	0.297606	+	0.954689i	$0.403812\pi$
$230$	−13.4164			−0.884652
$231$		0			0
$232$	1.38197			0.0907305
$233$	−17.8713	+	12.9843i	−1.17079	+	0.850628i	−0.991103	−	0.133096i	$-0.957508\pi$
$233$	−17.8713	+	12.9843i	−1.17079	+	0.850628i	−0.179686	+	0.983724i	$0.557508\pi$
$234$		0			0
$235$	−10.6525			−0.694891
$236$	−2.76393	+	8.50651i	−0.179917	+	0.553727i
$237$		0			0
$238$	−4.85410	−	14.9394i	−0.314645	−	0.968377i
$239$	−8.29180	+	25.5195i	−0.536352	+	1.65072i	0.204358	+	0.978896i	$0.434489\pi$
$239$	−8.29180	+	25.5195i	−0.536352	+	1.65072i	−0.740710	+	0.671825i	$0.765511\pi$
$240$		0			0
$241$	−4.28115	−	13.1760i	−0.275773	−	0.848743i	−0.989014	−	0.147824i	$-0.952773\pi$
$241$	−4.28115	−	13.1760i	−0.275773	−	0.848743i	0.713240	−	0.700919i	$-0.247227\pi$
$242$	−13.2812	+	9.64932i	−0.853745	+	0.620282i
$243$		0			0
$244$	7.16312	−	5.20431i	0.458572	−	0.333172i
$245$	5.42705	−	3.94298i	0.346722	−	0.251908i
$246$		0			0
$247$	−10.8541	−	7.88597i	−0.690630	−	0.501772i
$248$	1.14590	−	3.52671i	0.0727646	−	0.223946i
$249$		0			0
$250$	11.1803			0.707107
$251$	12.4721			0.787234			0.393617	−	0.919274i	$-0.371224\pi$
$251$	12.4721			0.787234			0.393617	+	0.919274i	$0.371224\pi$
$252$		0			0
$253$	25.4164	+	18.4661i	1.59792	+	1.16095i
$254$	−0.236068	−	0.171513i	−0.0148122	−	0.0107617i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	11.6180			0.724713			0.362357	−	0.932040i	$-0.381972\pi$
$257$	11.6180			0.724713			0.362357	+	0.932040i	$0.381972\pi$
$258$		0			0
$259$	−1.32624	−	4.08174i	−0.0824084	−	0.253627i
$260$	−3.35410	−	10.3229i	−0.208013	−	0.640197i
$261$		0			0
$262$	0.236068	+	0.726543i	0.0145843	+	0.0448859i
$263$	−0.145898	−	0.449028i	−0.00899646	−	0.0276883i	0.946458	−	0.322828i	$-0.104634\pi$
$263$	−0.145898	−	0.449028i	−0.00899646	−	0.0276883i	−0.955454	+	0.295140i	$0.904634\pi$
$264$		0			0
$265$	−19.1459			−1.17612
$266$	−1.70820	−	5.25731i	−0.104737	−	0.322346i
$267$		0			0
$268$	−9.70820			−0.593023
$269$	−1.54508	+	1.12257i	−0.0942055	+	0.0684443i	−0.633891	−	0.773422i	$-0.718543\pi$
$269$	−1.54508	+	1.12257i	−0.0942055	+	0.0684443i	0.539685	+	0.841867i	$0.318543\pi$
$270$		0			0
$271$	−22.7984	−	16.5640i	−1.38490	−	1.00619i	−0.996403	−	0.0847417i	$-0.972993\pi$
$271$	−22.7984	−	16.5640i	−1.38490	−	1.00619i	−0.388500	−	0.921449i	$-0.627007\pi$
$272$	6.35410	+	4.61653i	0.385274	+	0.279918i
$273$		0			0
$274$	15.0344			0.908264
$275$	−21.1803	−	15.3884i	−1.27722	−	0.927957i
$276$		0			0
$277$	−6.84346	+	21.0620i	−0.411184	+	1.26549i	0.504437	+	0.863449i	$0.331700\pi$
$277$	−6.84346	+	21.0620i	−0.411184	+	1.26549i	−0.915620	+	0.402044i	$0.868300\pi$
$278$	10.8541	+	7.88597i	0.650986	+	0.472969i
$279$		0			0
$280$	1.38197	−	4.25325i	0.0825883	−	0.254181i
$281$	−4.92705	+	3.57971i	−0.293923	+	0.213548i	−0.724968	−	0.688783i	$-0.758145\pi$
$281$	−4.92705	+	3.57971i	−0.293923	+	0.213548i	0.431044	+	0.902331i	$0.358145\pi$
$282$		0			0
$283$	−2.61803	+	1.90211i	−0.155626	+	0.113069i	−0.662873	−	0.748732i	$-0.730663\pi$
$283$	−2.61803	+	1.90211i	−0.155626	+	0.113069i	0.507247	+	0.861801i	$0.330663\pi$
$284$	4.38197	+	13.4863i	0.260022	+	0.800265i
$285$		0			0
$286$	−7.85410	+	24.1724i	−0.464423	+	1.42935i
$287$	3.76393	+	11.5842i	0.222178	+	0.683793i
$288$		0			0
$289$	13.8090	−	42.4998i	0.812295	−	2.49999i
$290$	0.954915	−	2.93893i	0.0560745	−	0.172580i
$291$		0			0
$292$	2.54508	−	1.84911i	0.148940	−	0.108211i
$293$	28.7984			1.68242			0.841209	−	0.540709i	$-0.181844\pi$
$293$	28.7984			1.68242			0.841209	+	0.540709i	$0.181844\pi$
$294$		0			0
$295$	16.1803	+	11.7557i	0.942056	+	0.684444i
$296$	1.73607	+	1.26133i	0.100907	+	0.0733132i
$297$		0			0
$298$	−2.17376	+	6.69015i	−0.125923	+	0.387550i
$299$	29.1246			1.68432
$300$		0			0
$301$	−2.47214			−0.142492
$302$	−2.14590	+	6.60440i	−0.123483	+	0.380040i
$303$		0			0
$304$	2.23607	+	1.62460i	0.128247	+	0.0931771i
$305$	−6.11803	−	18.8294i	−0.350318	−	1.07817i
$306$		0			0
$307$	−16.2918			−0.929822			−0.464911	−	0.885357i	$-0.653914\pi$
$307$	−16.2918			−0.929822			−0.464911	+	0.885357i	$0.653914\pi$
$308$	−8.47214	+	6.15537i	−0.482745	+	0.350735i
$309$		0			0
$310$	−6.70820	−	4.87380i	−0.381000	−	0.276813i
$311$	5.76393	−	17.7396i	0.326843	−	1.00592i	−0.643759	−	0.765228i	$-0.722626\pi$
$311$	5.76393	−	17.7396i	0.326843	−	1.00592i	0.970602	−	0.240690i	$-0.0773738\pi$
$312$		0			0
$313$	−8.14590	−	25.0705i	−0.460433	−	1.41707i	−0.864636	−	0.502399i	$-0.832451\pi$
$313$	−8.14590	−	25.0705i	−0.460433	−	1.41707i	0.404203	−	0.914669i	$-0.367549\pi$
$314$	5.51722	−	16.9803i	0.311355	−	0.958252i
$315$		0			0
$316$		0			0
$317$	−5.61803	+	4.08174i	−0.315540	+	0.229253i	−0.734270	−	0.678857i	$-0.762475\pi$
$317$	−5.61803	+	4.08174i	−0.315540	+	0.229253i	0.418730	+	0.908111i	$0.362475\pi$
$318$		0			0
$319$	−5.85410	+	4.25325i	−0.327767	+	0.238137i
$320$	0.690983	+	2.12663i	0.0386271	+	0.118882i
$321$		0			0
$322$	9.70820	+	7.05342i	0.541017	+	0.393072i
$323$	6.70820	−	20.6457i	0.373254	−	1.14876i
$324$		0			0
$325$	−24.2705			−1.34629
$326$	20.4721			1.13385
$327$		0			0
$328$	−4.92705	−	3.57971i	−0.272051	−	0.197657i
$329$	7.70820	+	5.60034i	0.424967	+	0.308757i
$330$		0			0
$331$	26.2705	−	19.0866i	1.44396	−	1.04910i	0.456761	−	0.889589i	$-0.349009\pi$
$331$	26.2705	−	19.0866i	1.44396	−	1.04910i	0.987197	−	0.159507i	$-0.0509906\pi$
$332$	−6.00000			−0.329293
$333$		0			0
$334$	−2.00000	−	6.15537i	−0.109435	−	0.336807i
$335$	−6.70820	+	20.6457i	−0.366508	+	1.12800i
$336$		0			0
$337$	8.90983	+	27.4216i	0.485349	+	1.49375i	0.831474	+	0.555563i	$0.187497\pi$
$337$	8.90983	+	27.4216i	0.485349	+	1.49375i	−0.346125	+	0.938188i	$0.612503\pi$
$338$	3.26393	+	10.0453i	0.177534	+	0.546395i
$339$		0			0
$340$	14.2082	−	10.3229i	0.770548	−	0.559836i
$341$	6.00000	+	18.4661i	0.324918	+	0.999995i
$342$		0			0
$343$	−20.0000			−1.07990
$344$	1.00000	−	0.726543i	0.0539164	−	0.0391725i
$345$		0			0
$346$	−8.82624	−	6.41264i	−0.474501	−	0.344746i
$347$	−4.23607	−	3.07768i	−0.227404	−	0.165219i	0.468249	−	0.883596i	$-0.344885\pi$
$347$	−4.23607	−	3.07768i	−0.227404	−	0.165219i	−0.695653	+	0.718378i	$0.744885\pi$
$348$		0			0
$349$	14.7984			0.792139			0.396069	−	0.918221i	$-0.370374\pi$
$349$	14.7984			0.792139			0.396069	+	0.918221i	$0.370374\pi$
$350$	−8.09017	−	5.87785i	−0.432438	−	0.314184i
$351$		0			0
$352$	1.61803	−	4.97980i	0.0862415	−	0.265424i
$353$	16.5623	+	12.0332i	0.881523	+	0.640464i	0.933654	−	0.358177i	$-0.116601\pi$
$353$	16.5623	+	12.0332i	0.881523	+	0.640464i	−0.0521313	+	0.998640i	$0.516601\pi$
$354$		0			0
$355$	31.7082			1.68290
$356$	1.11803	−	0.812299i	0.0592557	−	0.0430518i
$357$		0			0
$358$	−3.09017	+	2.24514i	−0.163321	+	0.118659i
$359$	8.61803	+	26.5236i	0.454842	+	1.39986i	0.871320	+	0.490715i	$0.163264\pi$
$359$	8.61803	+	26.5236i	0.454842	+	1.39986i	−0.416478	+	0.909146i	$0.636736\pi$
$360$		0			0
$361$	−3.51064	+	10.8046i	−0.184771	+	0.568666i
$362$	−6.19098	−	19.0539i	−0.325391	−	1.00145i
$363$		0			0
$364$	−3.00000	+	9.23305i	−0.157243	+	0.483943i
$365$	−2.17376	−	6.69015i	−0.113780	−	0.350179i
$366$		0			0
$367$	10.0902	−	7.33094i	0.526703	−	0.382672i	−0.292420	−	0.956290i	$-0.594461\pi$
$367$	10.0902	−	7.33094i	0.526703	−	0.382672i	0.819123	+	0.573618i	$0.194461\pi$
$368$	−6.00000			−0.312772
$369$		0			0
$370$	3.88197	−	2.82041i	0.201814	−	0.146626i
$371$	13.8541	+	10.0656i	0.719269	+	0.522580i
$372$		0			0
$373$	0.798374	−	2.45714i	0.0413382	−	0.127226i	−0.928258	−	0.371938i	$-0.878693\pi$
$373$	0.798374	−	2.45714i	0.0413382	−	0.127226i	0.969596	+	0.244712i	$0.0786934\pi$
$374$	−41.1246			−2.12650
$375$		0			0
$376$	−4.76393			−0.245681
$377$	−2.07295	+	6.37988i	−0.106762	+	0.328581i
$378$		0			0
$379$	2.76393	+	2.00811i	0.141974	+	0.103150i	0.656505	−	0.754322i	$-0.272034\pi$
$379$	2.76393	+	2.00811i	0.141974	+	0.103150i	−0.514531	+	0.857472i	$0.672034\pi$
$380$	5.00000	−	3.63271i	0.256495	−	0.186354i
$381$		0			0
$382$	0.763932			0.0390862
$383$	16.5623	−	12.0332i	0.846294	−	0.614869i	−0.0778275	−	0.996967i	$-0.524798\pi$
$383$	16.5623	−	12.0332i	0.846294	−	0.614869i	0.924122	+	0.382098i	$0.124798\pi$
$384$		0			0
$385$	7.23607	+	22.2703i	0.368784	+	1.13500i
$386$	0.736068	−	2.26538i	0.0374649	−	0.115305i
$387$		0			0
$388$	−4.28115	−	13.1760i	−0.217343	−	0.668912i
$389$	−4.93769	+	15.1967i	−0.250351	+	0.770501i	0.744359	+	0.667780i	$0.232755\pi$
$389$	−4.93769	+	15.1967i	−0.250351	+	0.770501i	−0.994710	+	0.102722i	$0.967245\pi$
$390$		0			0
$391$	14.5623	+	44.8182i	0.736447	+	2.26655i
$392$	2.42705	−	1.76336i	0.122585	−	0.0890629i
$393$		0			0
$394$	−10.7812	+	7.83297i	−0.543147	+	0.394619i
$395$		0			0
$396$		0			0
$397$	−23.3262	−	16.9475i	−1.17071	−	0.850571i	−0.179617	−	0.983737i	$-0.557486\pi$
$397$	−23.3262	−	16.9475i	−1.17071	−	0.850571i	−0.991094	+	0.133166i	$0.957486\pi$
$398$	−1.90983	+	5.87785i	−0.0957311	+	0.294630i
$399$		0			0
$400$	5.00000			0.250000
$401$	26.0902			1.30288			0.651440	−	0.758700i	$-0.274165\pi$
$401$	26.0902			1.30288			0.651440	+	0.758700i	$0.274165\pi$
$402$		0			0
$403$	14.5623	+	10.5801i	0.725400	+	0.527034i
$404$	1.35410	+	0.983813i	0.0673691	+	0.0489465i
$405$		0			0
$406$	−2.23607	+	1.62460i	−0.110974	+	0.0806275i
$407$	−11.2361			−0.556951
$408$		0			0
$409$	6.48278	+	19.9519i	0.320553	+	0.986560i	0.973408	+	0.229077i	$0.0735709\pi$
$409$	6.48278	+	19.9519i	0.320553	+	0.986560i	−0.652855	+	0.757483i	$0.726429\pi$
$410$	−11.0172	+	8.00448i	−0.544102	+	0.395313i
$411$		0			0
$412$	−0.708204	−	2.17963i	−0.0348907	−	0.107383i
$413$	−5.52786	−	17.0130i	−0.272008	−	0.837156i
$414$		0			0
$415$	−4.14590	+	12.7598i	−0.203514	+	0.626352i
$416$	−1.50000	−	4.61653i	−0.0735436	−	0.226344i
$417$		0			0
$418$	−14.4721			−0.707855
$419$	−30.6525	+	22.2703i	−1.49747	+	1.08798i	−0.526097	+	0.850425i	$0.676345\pi$
$419$	−30.6525	+	22.2703i	−1.49747	+	1.08798i	−0.971375	+	0.237552i	$0.923655\pi$
$420$		0			0
$421$	8.97214	+	6.51864i	0.437275	+	0.317699i	0.784551	−	0.620064i	$-0.212893\pi$
$421$	8.97214	+	6.51864i	0.437275	+	0.317699i	−0.347276	+	0.937763i	$0.612893\pi$
$422$	6.47214	+	4.70228i	0.315059	+	0.228904i
$423$		0			0
$424$	−8.56231			−0.415822
$425$	−12.1353	−	37.3485i	−0.588646	−	1.81167i
$426$		0			0
$427$	−5.47214	+	16.8415i	−0.264815	+	0.815017i
$428$	8.85410	+	6.43288i	0.427979	+	0.310945i
$429$		0			0
$430$	−0.854102	−	2.62866i	−0.0411885	−	0.126765i
$431$	3.00000	−	2.17963i	0.144505	−	0.104989i	−0.513184	−	0.858279i	$-0.671534\pi$
$431$	3.00000	−	2.17963i	0.144505	−	0.104989i	0.657689	+	0.753290i	$0.271534\pi$
$432$		0			0
$433$	18.7254	−	13.6048i	0.899886	−	0.653806i	−0.0385504	−	0.999257i	$-0.512274\pi$
$433$	18.7254	−	13.6048i	0.899886	−	0.653806i	0.938437	+	0.345451i	$0.112274\pi$
$434$	2.29180	+	7.05342i	0.110010	+	0.338575i
$435$		0			0
$436$	0.791796	−	2.43690i	0.0379202	−	0.116706i
$437$	5.12461	+	15.7719i	0.245143	+	0.754474i
$438$		0			0
$439$	−7.76393	+	23.8949i	−0.370552	+	1.14044i	0.575878	+	0.817535i	$0.304660\pi$
$439$	−7.76393	+	23.8949i	−0.370552	+	1.14044i	−0.946431	+	0.322907i	$0.895340\pi$
$440$	−9.47214	−	6.88191i	−0.451566	−	0.328082i
$441$		0			0
$442$	−30.8435	+	22.4091i	−1.46707	+	1.06589i
$443$	−30.0689			−1.42862			−0.714308	−	0.699832i	$-0.753258\pi$
$443$	−30.0689			−1.42862			−0.714308	+	0.699832i	$0.753258\pi$
$444$		0			0
$445$	−0.954915	−	2.93893i	−0.0452673	−	0.139318i
$446$	1.85410	+	1.34708i	0.0877943	+	0.0637863i
$447$		0			0
$448$	0.618034	−	1.90211i	0.0291994	−	0.0898664i
$449$	−4.79837			−0.226449			−0.113225	−	0.993569i	$-0.536118\pi$
$449$	−4.79837			−0.226449			−0.113225	+	0.993569i	$0.536118\pi$
$450$		0			0
$451$	31.8885			1.50157
$452$	3.57295	−	10.9964i	0.168057	−	0.517227i
$453$		0			0
$454$	−13.7082	−	9.95959i	−0.643358	−	0.467427i
$455$	17.5623	+	12.7598i	0.823334	+	0.598187i
$456$		0			0
$457$	−12.4721			−0.583422			−0.291711	−	0.956507i	$-0.594225\pi$
$457$	−12.4721			−0.583422			−0.291711	+	0.956507i	$0.594225\pi$
$458$	19.6353	−	14.2658i	0.917495	−	0.666599i
$459$		0			0
$460$	−4.14590	+	12.7598i	−0.193303	+	0.594927i
$461$	−7.75329	+	23.8622i	−0.361107	+	1.11137i	0.591277	+	0.806469i	$0.298624\pi$
$461$	−7.75329	+	23.8622i	−0.361107	+	1.11137i	−0.952383	+	0.304903i	$0.901376\pi$
$462$		0			0
$463$	−3.79837	−	11.6902i	−0.176525	−	0.543289i	0.823174	−	0.567789i	$-0.192201\pi$
$463$	−3.79837	−	11.6902i	−0.176525	−	0.543289i	−0.999700	+	0.0244992i	$0.992201\pi$
$464$	0.427051	−	1.31433i	0.0198253	−	0.0610161i
$465$		0			0
$466$	6.82624	+	21.0090i	0.316219	+	0.973223i
$467$	12.7984	−	9.29856i	0.592238	−	0.430286i	−0.250877	−	0.968019i	$-0.580719\pi$
$467$	12.7984	−	9.29856i	0.592238	−	0.430286i	0.843115	+	0.537733i	$0.180719\pi$
$468$		0			0
$469$	15.7082	−	11.4127i	0.725337	−	0.526989i
$470$	−3.29180	+	10.1311i	−0.151839	+	0.467313i
$471$		0			0
$472$	7.23607	+	5.25731i	0.333067	+	0.241987i
$473$	−2.00000	+	6.15537i	−0.0919601	+	0.283024i
$474$		0			0
$475$	−4.27051	−	13.1433i	−0.195944	−	0.603055i
$476$	−15.7082			−0.719984
$477$		0			0
$478$	21.7082	+	15.7719i	0.992910	+	0.721391i
$479$	3.61803	+	2.62866i	0.165312	+	0.120106i	0.667366	−	0.744730i	$-0.267422\pi$
$479$	3.61803	+	2.62866i	0.165312	+	0.120106i	−0.502053	+	0.864837i	$0.667422\pi$
$480$		0			0
$481$	−8.42705	+	6.12261i	−0.384240	+	0.279167i
$482$	−13.8541			−0.631037
$483$		0			0
$484$	5.07295	+	15.6129i	0.230589	+	0.709679i
$485$	−30.9787			−1.40667
$486$		0			0
$487$	3.18034	+	9.78808i	0.144115	+	0.443540i	0.996896	−	0.0787282i	$-0.0250859\pi$
$487$	3.18034	+	9.78808i	0.144115	+	0.443540i	−0.852781	+	0.522268i	$0.825086\pi$
$488$	−2.73607	−	8.42075i	−0.123856	−	0.381190i
$489$		0			0
$490$	−2.07295	−	6.37988i	−0.0936463	−	0.288214i
$491$	−9.23607	−	28.4257i	−0.416818	−	1.28283i	−0.910615	−	0.413256i	$-0.864391\pi$
$491$	−9.23607	−	28.4257i	−0.416818	−	1.28283i	0.493797	−	0.869577i	$-0.335609\pi$
$492$		0			0
$493$	−10.8541			−0.488844
$494$	−10.8541	+	7.88597i	−0.488349	+	0.354806i
$495$		0			0
$496$	−3.00000	−	2.17963i	−0.134704	−	0.0978682i
$497$	−22.9443	−	16.6700i	−1.02919	−	0.747751i
$498$		0			0
$499$	−33.4164			−1.49592			−0.747962	−	0.663742i	$-0.768967\pi$
$499$	−33.4164			−1.49592			−0.747962	+	0.663742i	$0.768967\pi$
$500$	3.45492	−	10.6331i	0.154508	−	0.475528i
$501$		0			0
$502$	3.85410	−	11.8617i	0.172017	−	0.529414i
$503$	17.4164	+	12.6538i	0.776559	+	0.564203i	0.903944	−	0.427650i	$-0.140658\pi$
$503$	17.4164	+	12.6538i	0.776559	+	0.564203i	−0.127385	+	0.991853i	$0.540658\pi$
$504$		0			0
$505$	3.02786	−	2.19987i	0.134738	−	0.0978930i
$506$	25.4164	−	18.4661i	1.12990	−	0.820918i
$507$		0			0
$508$	−0.236068	+	0.171513i	−0.0104738	+	0.00760968i
$509$	4.24671	+	13.0700i	0.188232	+	0.579319i	0.999989	−	0.00467647i	$-0.00148857\pi$
$509$	4.24671	+	13.0700i	0.188232	+	0.579319i	−0.811757	+	0.583995i	$0.801489\pi$
$510$		0			0
$511$	−1.94427	+	5.98385i	−0.0860095	+	0.264710i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	3.59017	−	11.0494i	0.158356	−	0.487368i
$515$	−5.12461			−0.225817
$516$		0			0
$517$	20.1803	−	14.6619i	0.887530	−	0.644829i
$518$	−4.29180			−0.188571
$519$		0			0
$520$	−10.8541			−0.475984
$521$	5.07295	+	3.68571i	0.222250	+	0.161474i	0.693339	−	0.720612i	$-0.256139\pi$
$521$	5.07295	+	3.68571i	0.222250	+	0.161474i	−0.471089	+	0.882086i	$0.656139\pi$
$522$		0			0
$523$	−0.708204	+	2.17963i	−0.0309676	+	0.0953085i	−0.965346	−	0.260975i	$-0.915956\pi$
$523$	−0.708204	+	2.17963i	−0.0309676	+	0.0953085i	0.934378	+	0.356283i	$0.115956\pi$
$524$	0.763932			0.0333725
$525$		0			0
$526$	−0.472136			−0.0205861
$527$	−9.00000	+	27.6992i	−0.392046	+	1.20659i
$528$		0			0
$529$	−10.5172	−	7.64121i	−0.457270	−	0.332226i
$530$	−5.91641	+	18.2088i	−0.256992	+	0.790941i
$531$		0			0
$532$	−5.52786			−0.239663
$533$	23.9164	−	17.3763i	1.03593	−	0.752651i
$534$		0			0
$535$	19.7984	−	14.3844i	0.855958	−	0.621890i
$536$	−3.00000	+	9.23305i	−0.129580	+	0.398807i
$537$		0			0
$538$	0.590170	+	1.81636i	0.0254440	+	0.0783087i
$539$	−4.85410	+	14.9394i	−0.209081	+	0.643485i
$540$		0			0
$541$	6.57295	+	20.2295i	0.282593	+	0.869732i	0.987110	+	0.160045i	$0.0511639\pi$
$541$	6.57295	+	20.2295i	0.282593	+	0.869732i	−0.704517	+	0.709688i	$0.748836\pi$
$542$	−22.7984	+	16.5640i	−0.979274	+	0.711484i
$543$		0			0
$544$	6.35410	−	4.61653i	0.272430	−	0.197932i
$545$	−4.63525	−	3.36771i	−0.198553	−	0.144257i
$546$		0			0
$547$	−1.61803	−	1.17557i	−0.0691821	−	0.0502638i	0.552657	−	0.833409i	$-0.313614\pi$
$547$	−1.61803	−	1.17557i	−0.0691821	−	0.0502638i	−0.621839	+	0.783145i	$0.713614\pi$
$548$	4.64590	−	14.2986i	0.198463	−	0.610806i
$549$		0			0
$550$	−21.1803	+	15.3884i	−0.903133	+	0.656164i
$551$	−3.81966			−0.162723
$552$		0			0
$553$		0			0
$554$	17.9164	+	13.0170i	0.761195	+	0.553041i
$555$		0			0
$556$	10.8541	−	7.88597i	0.460316	−	0.334439i
$557$	27.2705			1.15549			0.577744	−	0.816218i	$-0.303933\pi$
$557$	27.2705			1.15549			0.577744	+	0.816218i	$0.303933\pi$
$558$		0			0
$559$	1.85410	+	5.70634i	0.0784202	+	0.241352i
$560$	−3.61803	−	2.62866i	−0.152890	−	0.111081i
$561$		0			0
$562$	1.88197	+	5.79210i	0.0793859	+	0.244325i
$563$	−3.23607	−	9.95959i	−0.136384	−	0.419747i	0.859419	−	0.511272i	$-0.170826\pi$
$563$	−3.23607	−	9.95959i	−0.136384	−	0.419747i	−0.995803	+	0.0915256i	$0.970826\pi$
$564$		0			0
$565$	−20.9164	−	15.1967i	−0.879960	−	0.639328i
$566$	1.00000	+	3.07768i	0.0420331	+	0.129365i
$567$		0			0
$568$	14.1803			0.594994
$569$	17.2984	−	12.5680i	0.725186	−	0.526878i	−0.162851	−	0.986651i	$-0.552069\pi$
$569$	17.2984	−	12.5680i	0.725186	−	0.526878i	0.888037	+	0.459772i	$0.152069\pi$
$570$		0			0
$571$	−27.2705	−	19.8132i	−1.14124	−	0.829156i	−0.153944	−	0.988080i	$-0.549198\pi$
$571$	−27.2705	−	19.8132i	−1.14124	−	0.829156i	−0.987291	+	0.158924i	$0.949198\pi$
$572$	20.5623	+	14.9394i	0.859753	+	0.624647i
$573$		0			0
$574$	12.1803			0.508398
$575$	24.2705	+	17.6336i	1.01215	+	0.735370i
$576$		0			0
$577$	8.90983	−	27.4216i	0.370921	−	1.14158i	−0.575268	−	0.817965i	$-0.695102\pi$
$577$	8.90983	−	27.4216i	0.370921	−	1.14158i	0.946190	−	0.323613i	$-0.104898\pi$
$578$	−36.1525	−	26.2663i	−1.50374	−	1.09253i
$579$		0			0
$580$	−2.50000	−	1.81636i	−0.103807	−	0.0754201i
$581$	9.70820	−	7.05342i	0.402764	−	0.292625i
$582$		0			0
$583$	36.2705	−	26.3521i	1.50217	−	1.09139i
$584$	−0.972136	−	2.99193i	−0.0402273	−	0.123807i
$585$		0			0
$586$	8.89919	−	27.3889i	0.367622	−	1.13142i
$587$	4.90983	+	15.1109i	0.202650	+	0.623694i	0.999802	+	0.0199141i	$0.00633929\pi$
$587$	4.90983	+	15.1109i	0.202650	+	0.623694i	−0.797151	+	0.603780i	$0.793661\pi$
$588$		0			0
$589$	−3.16718	+	9.74759i	−0.130502	+	0.401642i
$590$	16.1803	−	11.7557i	0.666134	−	0.483975i
$591$		0			0
$592$	1.73607	−	1.26133i	0.0713520	−	0.0518402i
$593$	6.03444			0.247805			0.123902	−	0.992294i	$-0.460459\pi$
$593$	6.03444			0.247805			0.123902	+	0.992294i	$0.460459\pi$
$594$		0			0
$595$	−10.8541	+	33.4055i	−0.444975	+	1.36949i
$596$	5.69098	+	4.13474i	0.233112	+	0.169366i
$597$		0			0
$598$	9.00000	−	27.6992i	0.368037	−	1.13270i
$599$	−1.05573			−0.0431359			−0.0215679	−	0.999767i	$-0.506866\pi$
$599$	−1.05573			−0.0431359			−0.0215679	+	0.999767i	$0.506866\pi$
$600$		0			0
$601$	7.32624			0.298843			0.149422	−	0.988774i	$-0.452259\pi$
$601$	7.32624			0.298843			0.149422	+	0.988774i	$0.452259\pi$
$602$	−0.763932	+	2.35114i	−0.0311355	+	0.0958254i
$603$		0			0
$604$	5.61803	+	4.08174i	0.228595	+	0.166084i
$605$	36.7082			1.49240
$606$		0			0
$607$	−1.81966			−0.0738577			−0.0369289	−	0.999318i	$-0.511757\pi$
$607$	−1.81966			−0.0738577			−0.0369289	+	0.999318i	$0.511757\pi$
$608$	2.23607	−	1.62460i	0.0906845	−	0.0658862i
$609$		0			0
$610$	−19.7984			−0.801613
$611$	7.14590	−	21.9928i	0.289092	−	0.889734i
$612$		0			0
$613$	−6.66312	−	20.5070i	−0.269121	−	0.828269i	−0.990715	−	0.135953i	$-0.956590\pi$
$613$	−6.66312	−	20.5070i	−0.269121	−	0.828269i	0.721594	−	0.692316i	$-0.243410\pi$
$614$	−5.03444	+	15.4944i	−0.203174	+	0.625304i
$615$		0			0
$616$	3.23607	+	9.95959i	0.130385	+	0.401283i
$617$	6.78115	−	4.92680i	0.272999	−	0.198345i	−0.442859	−	0.896591i	$-0.646036\pi$
$617$	6.78115	−	4.92680i	0.272999	−	0.198345i	0.715858	+	0.698246i	$0.246036\pi$
$618$		0			0
$619$	−2.76393	+	2.00811i	−0.111092	+	0.0807129i	−0.641944	−	0.766751i	$-0.721872\pi$
$619$	−2.76393	+	2.00811i	−0.111092	+	0.0807129i	0.530852	+	0.847464i	$0.321872\pi$
$620$	−6.70820	+	4.87380i	−0.269408	+	0.195736i
$621$		0			0
$622$	−15.0902	−	10.9637i	−0.605061	−	0.439602i
$623$	−0.854102	+	2.62866i	−0.0342189	+	0.105315i
$624$		0			0
$625$	−20.2254	−	14.6946i	−0.809017	−	0.587785i
$626$	−26.3607			−1.05358
$627$		0			0
$628$	−14.4443	−	10.4944i	−0.576389	−	0.418771i
$629$	−13.6353	−	9.90659i	−0.543673	−	0.395002i
$630$		0			0
$631$	34.8885	−	25.3480i	1.38889	−	1.00909i	0.392905	−	0.919579i	$-0.371470\pi$
$631$	34.8885	−	25.3480i	1.38889	−	1.00909i	0.995986	−	0.0895093i	$-0.0285299\pi$
$632$		0			0
$633$		0			0
$634$	2.14590	+	6.60440i	0.0852245	+	0.262294i
$635$	0.201626	+	0.620541i	0.00800129	+	0.0246254i
$636$		0			0
$637$	4.50000	+	13.8496i	0.178296	+	0.548740i
$638$	2.23607	+	6.88191i	0.0885268	+	0.272457i
$639$		0			0
$640$	2.23607			0.0883883
$641$	8.32624	+	25.6255i	0.328867	+	1.01215i	0.969665	+	0.244438i	$0.0786035\pi$
$641$	8.32624	+	25.6255i	0.328867	+	1.01215i	−0.640798	+	0.767709i	$0.721397\pi$
$642$		0			0
$643$	−39.7771			−1.56866			−0.784328	−	0.620347i	$-0.786992\pi$
$643$	−39.7771			−1.56866			−0.784328	+	0.620347i	$0.786992\pi$
$644$	9.70820	−	7.05342i	0.382557	−	0.277944i
$645$		0			0
$646$	−17.5623	−	12.7598i	−0.690980	−	0.502026i
$647$	−29.0344	−	21.0948i	−1.14146	−	0.829320i	−0.154139	−	0.988049i	$-0.549261\pi$
$647$	−29.0344	−	21.0948i	−1.14146	−	0.829320i	−0.987322	+	0.158729i	$0.949261\pi$
$648$		0			0
$649$	−46.8328			−1.83835
$650$	−7.50000	+	23.0826i	−0.294174	+	0.905375i
$651$		0			0
$652$	6.32624	−	19.4702i	0.247755	−	0.762510i
$653$	−26.0623	−	18.9354i	−1.01990	−	0.740998i	−0.0536351	−	0.998561i	$-0.517081\pi$
$653$	−26.0623	−	18.9354i	−1.01990	−	0.740998i	−0.966262	+	0.257562i	$0.917081\pi$
$654$		0			0
$655$	0.527864	−	1.62460i	0.0206254	−	0.0634783i
$656$	−4.92705	+	3.57971i	−0.192369	+	0.139764i
$657$		0			0
$658$	7.70820	−	5.60034i	0.300497	−	0.218324i
$659$	−12.0344	−	37.0382i	−0.468795	−	1.44280i	−0.854146	−	0.520033i	$-0.825920\pi$
$659$	−12.0344	−	37.0382i	−0.468795	−	1.44280i	0.385351	−	0.922770i	$-0.374080\pi$
$660$		0			0
$661$	−7.27051	+	22.3763i	−0.282790	+	0.870338i	0.704262	+	0.709940i	$0.251278\pi$
$661$	−7.27051	+	22.3763i	−0.282790	+	0.870338i	−0.987052	+	0.160398i	$0.948722\pi$
$662$	−10.0344	−	30.8828i	−0.390000	−	1.20030i
$663$		0			0
$664$	−1.85410	+	5.70634i	−0.0719531	+	0.221449i
$665$	−3.81966	+	11.7557i	−0.148120	+	0.455867i
$666$		0			0
$667$	6.70820	−	4.87380i	0.259743	−	0.188714i
$668$	−6.47214			−0.250414
$669$		0			0
$670$	17.5623	+	12.7598i	0.678491	+	0.492953i
$671$	37.5066	+	27.2501i	1.44793	+	1.05198i
$672$		0			0
$673$	−5.80902	+	17.8783i	−0.223921	+	0.689158i	0.774478	+	0.632601i	$0.218013\pi$
$673$	−5.80902	+	17.8783i	−0.223921	+	0.689158i	−0.998399	+	0.0565578i	$0.981987\pi$
$674$	28.8328			1.11060
$675$		0			0
$676$	10.5623			0.406243
$677$	−11.2705	+	34.6871i	−0.433161	+	1.33313i	0.461799	+	0.886985i	$0.347204\pi$
$677$	−11.2705	+	34.6871i	−0.433161	+	1.33313i	−0.894960	+	0.446147i	$0.852796\pi$
$678$		0			0
$679$	22.4164	+	16.2865i	0.860263	+	0.625017i
$680$	−5.42705	−	16.7027i	−0.208118	−	0.640521i
$681$		0			0
$682$	19.4164			0.743493
$683$	15.7082	−	11.4127i	0.601058	−	0.436694i	−0.245196	−	0.969473i	$-0.578852\pi$
$683$	15.7082	−	11.4127i	0.601058	−	0.436694i	0.846254	+	0.532779i	$0.178852\pi$
$684$		0			0
$685$	−27.1976	−	19.7602i	−1.03917	−	0.754998i
$686$	−6.18034	+	19.0211i	−0.235966	+	0.726230i
$687$		0			0
$688$	−0.381966	−	1.17557i	−0.0145623	−	0.0448182i
$689$	12.8435	−	39.5281i	0.489297	−	1.50590i
$690$		0			0
$691$	−7.47214	−	22.9969i	−0.284253	−	0.874842i	−0.986621	−	0.163028i	$-0.947874\pi$
$691$	−7.47214	−	22.9969i	−0.284253	−	0.874842i	0.702368	−	0.711814i	$-0.252126\pi$
$692$	−8.82624	+	6.41264i	−0.335523	+	0.243772i
$693$		0			0
$694$	−4.23607	+	3.07768i	−0.160799	+	0.116827i
$695$	−9.27051	−	28.5317i	−0.351650	−	1.08227i
$696$		0			0
$697$	38.6976	+	28.1154i	1.46577	+	1.06495i
$698$	4.57295	−	14.0741i	0.173089	−	0.532712i
$699$		0			0
$700$	−8.09017	+	5.87785i	−0.305780	+	0.222162i
$701$	20.1591			0.761397			0.380698	−	0.924699i	$-0.375684\pi$
$701$	20.1591			0.761397			0.380698	+	0.924699i	$0.375684\pi$
$702$		0			0
$703$	−4.79837	−	3.48622i	−0.180974	−	0.131485i
$704$	−4.23607	−	3.07768i	−0.159653	−	0.115995i
$705$		0			0
$706$	16.5623	−	12.0332i	0.623331	−	0.452876i
$707$	−3.34752			−0.125897
$708$		0			0
$709$	−9.20820	−	28.3399i	−0.345821	−	1.06433i	−0.961143	−	0.276052i	$-0.910974\pi$
$709$	−9.20820	−	28.3399i	−0.345821	−	1.06433i	0.615321	−	0.788276i	$-0.289026\pi$
$710$	9.79837	−	30.1563i	0.367726	−	1.13175i
$711$		0			0
$712$	−0.427051	−	1.31433i	−0.0160044	−	0.0492565i
$713$	−6.87539	−	21.1603i	−0.257485	−	0.792458i
$714$		0			0
$715$	45.9787	−	33.4055i	1.71951	−	1.24929i
$716$	1.18034	+	3.63271i	0.0441114	+	0.135761i
$717$		0			0
$718$	27.8885			1.04079
$719$	18.0902	−	13.1433i	0.674649	−	0.490162i	−0.196929	−	0.980418i	$-0.563097\pi$
$719$	18.0902	−	13.1433i	0.674649	−	0.490162i	0.871578	+	0.490256i	$0.163097\pi$
$720$		0			0
$721$	3.70820	+	2.69417i	0.138101	+	0.100336i
$722$	9.19098	+	6.67764i	0.342053	+	0.248516i
$723$		0			0
$724$	−20.0344			−0.744574
$725$	−5.59017	+	4.06150i	−0.207614	+	0.150840i
$726$		0			0
$727$	3.18034	−	9.78808i	0.117952	−	0.363020i	−0.874599	−	0.484847i	$-0.838875\pi$
$727$	3.18034	−	9.78808i	0.117952	−	0.363020i	0.992551	+	0.121827i	$0.0388753\pi$
$728$	7.85410	+	5.70634i	0.291092	+	0.211491i
$729$		0			0
$730$	−7.03444			−0.260356
$731$	−7.85410	+	5.70634i	−0.290494	+	0.211057i
$732$		0			0
$733$	5.14590	−	3.73871i	0.190068	−	0.138093i	−0.488682	−	0.872462i	$-0.662522\pi$
$733$	5.14590	−	3.73871i	0.190068	−	0.138093i	0.678750	+	0.734370i	$0.262522\pi$
$734$	−3.85410	−	11.8617i	−0.142257	−	0.437824i
$735$		0			0
$736$	−1.85410	+	5.70634i	−0.0683431	+	0.210338i
$737$	−15.7082	−	48.3449i	−0.578619	−	1.78081i
$738$		0			0
$739$	2.56231	−	7.88597i	0.0942559	−	0.290090i	−0.892803	−	0.450447i	$-0.851265\pi$
$739$	2.56231	−	7.88597i	0.0942559	−	0.290090i	0.987059	+	0.160357i	$0.0512646\pi$
$740$	−1.48278	−	4.56352i	−0.0545080	−	0.167759i
$741$		0			0
$742$	13.8541	−	10.0656i	0.508600	−	0.369520i
$743$	−6.65248			−0.244056			−0.122028	−	0.992527i	$-0.538940\pi$
$743$	−6.65248			−0.244056			−0.122028	+	0.992527i	$0.538940\pi$
$744$		0			0
$745$	12.7254	−	9.24556i	0.466223	−	0.338731i
$746$	−2.09017	−	1.51860i	−0.0765266	−	0.0555998i
$747$		0			0
$748$	−12.7082	+	39.1118i	−0.464658	+	1.43007i
$749$	−21.8885			−0.799790
$750$		0			0
$751$	14.7639			0.538744			0.269372	−	0.963036i	$-0.413184\pi$
$751$	14.7639			0.538744			0.269372	+	0.963036i	$0.413184\pi$
$752$	−1.47214	+	4.53077i	−0.0536833	+	0.165220i
$753$		0			0
$754$	5.42705	+	3.94298i	0.197642	+	0.143595i
$755$	12.5623	−	9.12705i	0.457189	−	0.332167i
$756$		0			0
$757$	−28.8541			−1.04872			−0.524360	−	0.851497i	$-0.675695\pi$
$757$	−28.8541			−1.04872			−0.524360	+	0.851497i	$0.675695\pi$
$758$	2.76393	−	2.00811i	0.100391	−	0.0729380i
$759$		0			0
$760$	−1.90983	−	5.87785i	−0.0692768	−	0.213212i
$761$	−7.46556	+	22.9766i	−0.270626	+	0.832902i	0.719717	+	0.694267i	$0.244271\pi$
$761$	−7.46556	+	22.9766i	−0.270626	+	0.832902i	−0.990344	+	0.138635i	$0.955729\pi$
$762$		0			0
$763$	1.58359	+	4.87380i	0.0573299	+	0.176443i
$764$	0.236068	−	0.726543i	0.00854064	−	0.0262854i
$765$		0			0
$766$	−6.32624	−	19.4702i	−0.228576	−	0.703485i
$767$	−35.1246	+	25.5195i	−1.26828	+	0.921457i
$768$		0			0
$769$	1.90983	−	1.38757i	0.0688702	−	0.0500372i	−0.552817	−	0.833302i	$-0.686447\pi$
$769$	1.90983	−	1.38757i	0.0688702	−	0.0500372i	0.621688	+	0.783265i	$0.286447\pi$
$770$	23.4164			0.843869
$771$		0			0
$772$	−1.92705	−	1.40008i	−0.0693561	−	0.0503901i
$773$	−4.35410	+	13.4005i	−0.156606	+	0.481984i	−0.998320	−	0.0579395i	$-0.981547\pi$
$773$	−4.35410	+	13.4005i	−0.156606	+	0.481984i	0.841714	+	0.539924i	$0.181547\pi$
$774$		0			0
$775$	5.72949	+	17.6336i	0.205809	+	0.633416i
$776$	−13.8541			−0.497333
$777$		0			0
$778$	12.9271	+	9.39205i	0.463457	+	0.336721i
$779$	13.6180	+	9.89408i	0.487917	+	0.354492i
$780$		0			0
$781$	−60.0689	+	43.6426i	−2.14943	+	1.56165i
$782$	47.1246			1.68517
$783$		0			0
$784$	−0.927051	−	2.85317i	−0.0331090	−	0.101899i
$785$	−32.2984	+	23.4661i	−1.15278	+	0.837543i
$786$		0			0
$787$	9.43769	+	29.0462i	0.336417	+	1.03539i	0.966020	+	0.258469i	$0.0832179\pi$
$787$	9.43769	+	29.0462i	0.336417	+	1.03539i	−0.629602	+	0.776918i	$0.716782\pi$
$788$	4.11803	+	12.6740i	0.146699	+	0.451493i
$789$		0			0
$790$		0			0
$791$	7.14590	+	21.9928i	0.254079	+	0.781974i
$792$		0			0
$793$	42.9787			1.52622
$794$	−23.3262	+	16.9475i	−0.827817	+	0.601444i
$795$		0			0
$796$	5.00000	+	3.63271i	0.177220	+	0.128758i
$797$	−10.7812	−	7.83297i	−0.381888	−	0.277458i	0.380235	−	0.924890i	$-0.375843\pi$
$797$	−10.7812	−	7.83297i	−0.381888	−	0.277458i	−0.762123	+	0.647432i	$0.775843\pi$
$798$		0			0
$799$	37.4164			1.32370
$800$	1.54508	−	4.75528i	0.0546270	−	0.168125i
$801$		0			0
$802$	8.06231	−	24.8132i	0.284690	−	0.876185i
$803$	13.3262	+	9.68208i	0.470273	+	0.341673i
$804$		0			0
$805$	−8.29180	−	25.5195i	−0.292247	−	0.899445i
$806$	14.5623	−	10.5801i	0.512935	−	0.372669i
$807$		0			0
$808$	1.35410	−	0.983813i	0.0476371	−	0.0346104i
$809$	−2.53851	−	7.81272i	−0.0892492	−	0.274681i	0.896463	−	0.443118i	$-0.146128\pi$
$809$	−2.53851	−	7.81272i	−0.0892492	−	0.274681i	−0.985712	+	0.168438i	$0.946128\pi$
$810$		0			0
$811$	3.18034	−	9.78808i	0.111677	−	0.343706i	−0.879563	−	0.475783i	$-0.842165\pi$
$811$	3.18034	−	9.78808i	0.111677	−	0.343706i	0.991239	+	0.132077i	$0.0421647\pi$
$812$	0.854102	+	2.62866i	0.0299731	+	0.0922477i
$813$		0			0
$814$	−3.47214	+	10.6861i	−0.121698	+	0.374549i
$815$	−37.0344	−	26.9071i	−1.29726	−	0.942514i
$816$		0			0
$817$	−2.76393	+	2.00811i	−0.0966977	+	0.0702550i
$818$	20.9787			0.733504
$819$		0			0
$820$	4.20820	+	12.9515i	0.146957	+	0.452287i
$821$	−36.2705	−	26.3521i	−1.26585	−	0.919694i	−0.266820	−	0.963746i	$-0.585973\pi$
$821$	−36.2705	−	26.3521i	−1.26585	−	0.919694i	−0.999029	+	0.0440528i	$0.985973\pi$
$822$		0			0
$823$	−7.29180	+	22.4418i	−0.254176	+	0.782273i	0.739815	+	0.672811i	$0.234913\pi$
$823$	−7.29180	+	22.4418i	−0.254176	+	0.782273i	−0.993991	+	0.109463i	$0.965087\pi$
$824$	−2.29180			−0.0798385
$825$		0			0
$826$	−17.8885			−0.622422
$827$	−4.56231	+	14.0413i	−0.158647	+	0.488265i	−0.998512	−	0.0545300i	$-0.982634\pi$
$827$	−4.56231	+	14.0413i	−0.158647	+	0.488265i	0.839865	+	0.542795i	$0.182634\pi$
$828$		0			0
$829$	−31.6697	−	23.0094i	−1.09993	−	0.799149i	−0.118885	−	0.992908i	$-0.537932\pi$
$829$	−31.6697	−	23.0094i	−1.09993	−	0.799149i	−0.981049	+	0.193759i	$0.937932\pi$
$830$	10.8541	+	7.88597i	0.376751	+	0.273726i
$831$		0			0
$832$	−4.85410			−0.168286
$833$	−19.0623	+	13.8496i	−0.660470	+	0.479859i
$834$		0			0
$835$	−4.47214	+	13.7638i	−0.154765	+	0.476317i
$836$	−4.47214	+	13.7638i	−0.154672	+	0.476032i
$837$		0			0
$838$	11.7082	+	36.0341i	0.404453	+	1.24478i
$839$	1.58359	−	4.87380i	0.0546717	−	0.168262i	−0.919992	−	0.391937i	$-0.871805\pi$
$839$	1.58359	−	4.87380i	0.0546717	−	0.168262i	0.974664	+	0.223674i	$0.0718053\pi$
$840$		0			0
$841$	−8.37132	−	25.7643i	−0.288666	−	0.888424i
$842$	8.97214	−	6.51864i	0.309200	−	0.224647i
$843$		0			0
$844$	6.47214	−	4.70228i	0.222780	−	0.161859i
$845$	7.29837	−	22.4621i	0.251072	−	0.772719i
$846$		0			0
$847$	−26.5623	−	19.2986i	−0.912692	−	0.663109i
$848$	−2.64590	+	8.14324i	−0.0908605	+	0.279640i
$849$		0			0
$850$	−39.2705			−1.34697
$851$	12.8754			0.441363
$852$		0			0
$853$	−13.3090	−	9.66957i	−0.455692	−	0.331080i	0.336147	−	0.941810i	$-0.390876\pi$
$853$	−13.3090	−	9.66957i	−0.455692	−	0.331080i	−0.791839	+	0.610730i	$0.790876\pi$
$854$	14.3262	+	10.4086i	0.490234	+	0.356176i
$855$		0			0
$856$	8.85410	−	6.43288i	0.302627	−	0.219871i
$857$	−23.3050			−0.796082			−0.398041	−	0.917368i	$-0.630310\pi$
$857$	−23.3050			−0.796082			−0.398041	+	0.917368i	$0.630310\pi$
$858$		0			0
$859$	14.0689	+	43.2996i	0.480024	+	1.47736i	0.839060	+	0.544039i	$0.183106\pi$
$859$	14.0689	+	43.2996i	0.480024	+	1.47736i	−0.359036	+	0.933324i	$0.616894\pi$
$860$	−2.76393			−0.0942493
$861$		0			0
$862$	−1.14590	−	3.52671i	−0.0390294	−	0.120120i
$863$	−3.76393	−	11.5842i	−0.128126	−	0.394330i	0.866332	−	0.499469i	$-0.166471\pi$
$863$	−3.76393	−	11.5842i	−0.128126	−	0.394330i	−0.994458	+	0.105138i	$0.966471\pi$
$864$		0			0
$865$	7.53851	+	23.2011i	0.256317	+	0.788862i
$866$	−7.15248	−	22.0131i	−0.243051	−	0.748034i
$867$		0			0
$868$	7.41641			0.251729
$869$		0			0
$870$		0			0
$871$	−38.1246	−	27.6992i	−1.29180	−	0.938550i
$872$	−2.07295	−	1.50609i	−0.0701989	−	0.0510025i
$873$		0			0
$874$	16.5836			0.560948
$875$	6.90983	+	21.2663i	0.233595	+	0.718931i
$876$		0			0
$877$	5.55573	−	17.0988i	0.187604	−	0.577385i	−0.812380	−	0.583129i	$-0.801828\pi$
$877$	5.55573	−	17.0988i	0.187604	−	0.577385i	0.999984	+	0.00574402i	$0.00182839\pi$
$878$	20.3262	+	14.7679i	0.685977	+	0.498392i
$879$		0			0
$880$	−9.47214	+	6.88191i	−0.319306	+	0.231989i
$881$	37.7984	−	27.4621i	1.27346	−	0.925223i	0.274125	−	0.961694i	$-0.411612\pi$
$881$	37.7984	−	27.4621i	1.27346	−	0.925223i	0.999335	+	0.0364716i	$0.0116118\pi$
$882$		0			0
$883$	−34.1246	+	24.7930i	−1.14838	+	0.834350i	−0.988265	−	0.152747i	$-0.951188\pi$
$883$	−34.1246	+	24.7930i	−1.14838	+	0.834350i	−0.160119	+	0.987098i	$0.551188\pi$
$884$	11.7812	+	36.2587i	0.396243	+	1.21951i
$885$		0			0
$886$	−9.29180	+	28.5972i	−0.312164	+	0.960742i
$887$	−7.97871	−	24.5560i	−0.267899	−	0.824508i	−0.991011	−	0.133778i	$-0.957289\pi$
$887$	−7.97871	−	24.5560i	−0.267899	−	0.824508i	0.723112	−	0.690730i	$-0.242711\pi$
$888$		0			0
$889$	0.180340	−	0.555029i	0.00604841	−	0.0186151i
$890$	−3.09017			−0.103583
$891$		0			0
$892$	1.85410	−	1.34708i	0.0620799	−	0.0451037i
$893$	13.1672			0.440623
$894$		0			0
$895$	8.54102			0.285495
$896$	−1.61803	−	1.17557i	−0.0540547	−	0.0392731i
$897$		0			0
$898$	−1.48278	+	4.56352i	−0.0494810	+	0.152287i
$899$	5.12461			0.170915
$900$		0			0
$901$	67.2492			2.24040
$902$	9.85410	−	30.3278i	0.328106	−	1.00981i
$903$		0			0
$904$	−9.35410	−	6.79615i	−0.311113	−	0.226037i
$905$	−13.8435	+	42.6058i	−0.460172	+	1.41626i
$906$		0			0
$907$	20.2918			0.673778			0.336889	−	0.941544i	$-0.390625\pi$
$907$	20.2918			0.673778			0.336889	+	0.941544i	$0.390625\pi$
$908$	−13.7082	+	9.95959i	−0.454923	+	0.330521i
$909$		0			0
$910$	17.5623	−	12.7598i	0.582185	−	0.422982i
$911$	−17.3262	+	53.3247i	−0.574044	+	1.76673i	0.0653683	+	0.997861i	$0.479178\pi$
$911$	−17.3262	+	53.3247i	−0.574044	+	1.76673i	−0.639412	+	0.768864i	$0.720822\pi$
$912$		0			0
$913$	−9.70820	−	29.8788i	−0.321295	−	0.988843i
$914$	−3.85410	+	11.8617i	−0.127482	+	0.392350i
$915$		0			0
$916$	−7.50000	−	23.0826i	−0.247807	−	0.762671i
$917$	−1.23607	+	0.898056i	−0.0408186	+	0.0296564i
$918$		0			0
$919$	0.854102	−	0.620541i	0.0281742	−	0.0204698i	−0.573609	−	0.819129i	$-0.694457\pi$
$919$	0.854102	−	0.620541i	0.0281742	−	0.0204698i	0.601783	+	0.798659i	$0.294457\pi$
$920$	10.8541	+	7.88597i	0.357849	+	0.259993i
$921$		0			0
$922$	20.2984	+	14.7476i	0.668491	+	0.485687i
$923$	−21.2705	+	65.4639i	−0.700127	+	2.15477i
$924$		0			0
$925$	−10.7295			−0.352783
$926$	−12.2918			−0.403933
$927$		0			0
$928$	−1.11803	−	0.812299i	−0.0367013	−	0.0266650i
$929$	−25.0623	−	18.2088i	−0.822268	−	0.597412i	0.0950935	−	0.995468i	$-0.469685\pi$
$929$	−25.0623	−	18.2088i	−0.822268	−	0.597412i	−0.917361	+	0.398056i	$0.869685\pi$
$930$		0			0
$931$	−6.70820	+	4.87380i	−0.219853	+	0.159732i
$932$	22.0902			0.723588
$933$		0			0
$934$	−4.88854	−	15.0454i	−0.159958	−	0.492300i
$935$	74.3951	+	54.0512i	2.43298	+	1.76766i
$936$		0			0
$937$	10.8435	+	33.3727i	0.354240	+	1.09024i	0.956449	+	0.291901i	$0.0942877\pi$
$937$	10.8435	+	33.3727i	0.354240	+	1.09024i	−0.602208	+	0.798339i	$0.705712\pi$
$938$	−6.00000	−	18.4661i	−0.195907	−	0.602940i
$939$		0			0
$940$	8.61803	+	6.26137i	0.281089	+	0.204223i
$941$	−6.69756	−	20.6130i	−0.218334	−	0.671964i	−0.998900	−	0.0468901i	$-0.985069\pi$
$941$	−6.69756	−	20.6130i	−0.218334	−	0.671964i	0.780566	−	0.625074i	$-0.214931\pi$
$942$		0			0
$943$	−36.5410			−1.18994
$944$	7.23607	−	5.25731i	0.235514	−	0.171111i
$945$		0			0
$946$	5.23607	+	3.80423i	0.170239	+	0.123686i
$947$	8.85410	+	6.43288i	0.287720	+	0.209041i	0.722278	−	0.691603i	$-0.243095\pi$
$947$	8.85410	+	6.43288i	0.287720	+	0.209041i	−0.434558	+	0.900644i	$0.643095\pi$
$948$		0			0
$949$	15.2705			0.495702
$950$	−13.8197			−0.448369
$951$		0			0
$952$	−4.85410	+	14.9394i	−0.157322	+	0.484188i
$953$	−26.5902	−	19.3189i	−0.861340	−	0.625800i	0.0669091	−	0.997759i	$-0.478686\pi$
$953$	−26.5902	−	19.3189i	−0.861340	−	0.625800i	−0.928249	+	0.371959i	$0.878686\pi$
$954$		0			0
$955$	−1.38197	−	1.00406i	−0.0447194	−	0.0324905i
$956$	21.7082	−	15.7719i	0.702093	−	0.510101i
$957$		0			0
$958$	3.61803	−	2.62866i	0.116893	−	0.0849280i
$959$	9.29180	+	28.5972i	0.300048	+	0.923452i
$960$		0			0
$961$	−5.33030	+	16.4050i	−0.171945	+	0.529193i
$962$	3.21885	+	9.90659i	0.103780	+	0.319401i
$963$		0			0
$964$	−4.28115	+	13.1760i	−0.137887	+	0.424371i
$965$	−4.30902	+	3.13068i	−0.138712	+	0.100780i
$966$		0			0
$967$	−33.1246	+	24.0664i	−1.06522	+	0.773925i	−0.975046	−	0.222002i	$-0.928741\pi$
$967$	−33.1246	+	24.0664i	−1.06522	+	0.773925i	−0.0901695	+	0.995926i	$0.528741\pi$
$968$	16.4164			0.527643
$969$		0			0
$970$	−9.57295	+	29.4625i	−0.307369	+	0.945984i
$971$	−27.3262	−	19.8537i	−0.876941	−	0.637135i	0.0554996	−	0.998459i	$-0.482325\pi$
$971$	−27.3262	−	19.8537i	−0.876941	−	0.637135i	−0.932440	+	0.361324i	$0.882325\pi$
$972$		0			0
$973$	−8.29180	+	25.5195i	−0.265823	+	0.818118i
$974$	10.2918			0.329770
$975$		0			0
$976$	−8.85410			−0.283413
$977$	6.35410	−	19.5559i	0.203286	−	0.625649i	−0.796494	−	0.604647i	$-0.793314\pi$
$977$	6.35410	−	19.5559i	0.203286	−	0.625649i	0.999779	−	0.0210023i	$-0.00668574\pi$
$978$		0			0
$979$	5.85410	+	4.25325i	0.187098	+	0.135935i
$980$	−6.70820			−0.214286
$981$		0			0
$982$	−29.8885			−0.953782
$983$	−34.4164	+	25.0050i	−1.09771	+	0.797535i	−0.980685	−	0.195594i	$-0.937337\pi$
$983$	−34.4164	+	25.0050i	−1.09771	+	0.797535i	−0.117028	+	0.993129i	$0.537337\pi$
$984$		0			0
$985$	29.7984			0.949455
$986$	−3.35410	+	10.3229i	−0.106816	+	0.328747i
$987$		0			0
$988$	4.14590	+	12.7598i	0.131899	+	0.405942i
$989$	2.29180	−	7.05342i	0.0728749	−	0.224286i
$990$		0			0
$991$	18.7082	+	57.5779i	0.594286	+	1.82902i	0.558250	+	0.829673i	$0.311473\pi$
$991$	18.7082	+	57.5779i	0.594286	+	1.82902i	0.0360356	+	0.999351i	$0.488527\pi$
$992$	−3.00000	+	2.17963i	−0.0952501	+	0.0692032i
$993$		0			0
$994$	−22.9443	+	16.6700i	−0.727748	+	0.528740i
$995$	11.1803	−	8.12299i	0.354441	−	0.257516i
$996$		0			0
$997$	1.14590	+	0.832544i	0.0362910	+	0.0263669i	0.605783	−	0.795630i	$-0.292860\pi$
$997$	1.14590	+	0.832544i	0.0362910	+	0.0263669i	−0.569492	+	0.821997i	$0.692860\pi$
$998$	−10.3262	+	31.7809i	−0.326871	+	1.00601i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.b.271.1		4
3.2	odd	2		150.2.g.b.121.1	yes	4
15.2	even	4		750.2.h.a.649.1		8
15.8	even	4		750.2.h.a.649.2		8
15.14	odd	2		750.2.g.a.601.1		4
25.6	even	5	inner	450.2.h.b.181.1		4
75.8	even	20		750.2.h.a.349.1		8
75.17	even	20		750.2.h.a.349.2		8
75.38	even	20		3750.2.c.c.1249.3		4
75.41	odd	10		3750.2.a.b.1.1		2
75.44	odd	10		750.2.g.a.151.1		4
75.56	odd	10		150.2.g.b.31.1	✓	4
75.59	odd	10		3750.2.a.g.1.1		2
75.62	even	20		3750.2.c.c.1249.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.b.31.1	✓	4	75.56	odd	10
150.2.g.b.121.1	yes	4	3.2	odd	2
450.2.h.b.181.1		4	25.6	even	5	inner
450.2.h.b.271.1		4	1.1	even	1	trivial
750.2.g.a.151.1		4	75.44	odd	10
750.2.g.a.601.1		4	15.14	odd	2
750.2.h.a.349.1		8	75.8	even	20
750.2.h.a.349.2		8	75.17	even	20
750.2.h.a.649.1		8	15.2	even	4
750.2.h.a.649.2		8	15.8	even	4
3750.2.a.b.1.1		2	75.41	odd	10
3750.2.a.g.1.1		2	75.59	odd	10
3750.2.c.c.1249.1		4	75.62	even	20
3750.2.c.c.1249.3		4	75.38	even	20

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.80902 + 1.31433i) q^{5} +2.00000 q^{7} +(-0.809017 + 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-1.80902 + 1.31433i) q^{5} +2.00000 q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.690983 + 2.12663i) q^{10} +(1.61803 - 4.97980i) q^{11} +(-1.50000 - 4.61653i) q^{13} +(0.618034 - 1.90211i) q^{14} +(0.309017 + 0.951057i) q^{16} +(6.35410 - 4.61653i) q^{17} +(2.23607 - 1.62460i) q^{19} +2.23607 q^{20} +(-4.23607 - 3.07768i) q^{22} +(-1.85410 + 5.70634i) q^{23} +(1.54508 - 4.75528i) q^{25} -4.85410 q^{26} +(-1.61803 - 1.17557i) q^{28} +(-1.11803 - 0.812299i) q^{29} +(-3.00000 + 2.17963i) q^{31} +1.00000 q^{32} +(-2.42705 - 7.46969i) q^{34} +(-3.61803 + 2.62866i) q^{35} +(-0.663119 - 2.04087i) q^{37} +(-0.854102 - 2.62866i) q^{38} +(0.690983 - 2.12663i) q^{40} +(1.88197 + 5.79210i) q^{41} -1.23607 q^{43} +(-4.23607 + 3.07768i) q^{44} +(4.85410 + 3.52671i) q^{46} +(3.85410 + 2.80017i) q^{47} -3.00000 q^{49} +(-4.04508 - 2.93893i) q^{50} +(-1.50000 + 4.61653i) q^{52} +(6.92705 + 5.03280i) q^{53} +(3.61803 + 11.1352i) q^{55} +(-1.61803 + 1.17557i) q^{56} +(-1.11803 + 0.812299i) q^{58} +(-2.76393 - 8.50651i) q^{59} +(-2.73607 + 8.42075i) q^{61} +(1.14590 + 3.52671i) q^{62} +(0.309017 - 0.951057i) q^{64} +(8.78115 + 6.37988i) q^{65} +(7.85410 - 5.70634i) q^{67} -7.85410 q^{68} +(1.38197 + 4.25325i) q^{70} +(-11.4721 - 8.33499i) q^{71} +(-0.972136 + 2.99193i) q^{73} -2.14590 q^{74} -2.76393 q^{76} +(3.23607 - 9.95959i) q^{77} +(-1.80902 - 1.31433i) q^{80} +6.09017 q^{82} +(4.85410 - 3.52671i) q^{83} +(-5.42705 + 16.7027i) q^{85} +(-0.381966 + 1.17557i) q^{86} +(1.61803 + 4.97980i) q^{88} +(-0.427051 + 1.31433i) q^{89} +(-3.00000 - 9.23305i) q^{91} +(4.85410 - 3.52671i) q^{92} +(3.85410 - 2.80017i) q^{94} +(-1.90983 + 5.87785i) q^{95} +(11.2082 + 8.14324i) q^{97} +(-0.927051 + 2.85317i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - 5 q^{5} + 8 q^{7} - q^{8}+O(q^{10}) \) 4 * q - q^2 - q^4 - 5 * q^5 + 8 * q^7 - q^8	\( 4 q - q^{2} - q^{4} - 5 q^{5} + 8 q^{7} - q^{8} + 5 q^{10} + 2 q^{11} - 6 q^{13} - 2 q^{14} - q^{16} + 12 q^{17} - 8 q^{22} + 6 q^{23} - 5 q^{25} - 6 q^{26} - 2 q^{28} - 12 q^{31} + 4 q^{32} - 3 q^{34} - 10 q^{35} + 13 q^{37} + 10 q^{38} + 5 q^{40} + 12 q^{41} + 4 q^{43} - 8 q^{44} + 6 q^{46} + 2 q^{47} - 12 q^{49} - 5 q^{50} - 6 q^{52} + 21 q^{53} + 10 q^{55} - 2 q^{56} - 20 q^{59} - 2 q^{61} + 18 q^{62} - q^{64} + 15 q^{65} + 18 q^{67} - 18 q^{68} + 10 q^{70} - 28 q^{71} + 14 q^{73} - 22 q^{74} - 20 q^{76} + 4 q^{77} - 5 q^{80} + 2 q^{82} + 6 q^{83} - 15 q^{85} - 6 q^{86} + 2 q^{88} + 5 q^{89} - 12 q^{91} + 6 q^{92} + 2 q^{94} - 30 q^{95} + 18 q^{97} + 3 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 - 5 * q^5 + 8 * q^7 - q^8 + 5 * q^10 + 2 * q^11 - 6 * q^13 - 2 * q^14 - q^16 + 12 * q^17 - 8 * q^22 + 6 * q^23 - 5 * q^25 - 6 * q^26 - 2 * q^28 - 12 * q^31 + 4 * q^32 - 3 * q^34 - 10 * q^35 + 13 * q^37 + 10 * q^38 + 5 * q^40 + 12 * q^41 + 4 * q^43 - 8 * q^44 + 6 * q^46 + 2 * q^47 - 12 * q^49 - 5 * q^50 - 6 * q^52 + 21 * q^53 + 10 * q^55 - 2 * q^56 - 20 * q^59 - 2 * q^61 + 18 * q^62 - q^64 + 15 * q^65 + 18 * q^67 - 18 * q^68 + 10 * q^70 - 28 * q^71 + 14 * q^73 - 22 * q^74 - 20 * q^76 + 4 * q^77 - 5 * q^80 + 2 * q^82 + 6 * q^83 - 15 * q^85 - 6 * q^86 + 2 * q^88 + 5 * q^89 - 12 * q^91 + 6 * q^92 + 2 * q^94 - 30 * q^95 + 18 * q^97 + 3 * q^98

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