LMFDB - Embedded newform 198.2.f.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,2,Mod(37,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, 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("198.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	198.f (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:	$1.58103796002$
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 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	198.37
Dual form			198.2.f.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(1.11803 - 0.812299i) q^{5} +(-0.500000 - 1.53884i) q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(1.11803 - 0.812299i) q^{5} +(-0.500000 - 1.53884i) q^{7} +(0.309017 - 0.951057i) q^{8} -1.38197 q^{10} +(3.23607 - 0.726543i) q^{11} +(1.00000 + 0.726543i) q^{13} +(-0.500000 + 1.53884i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(3.23607 - 2.35114i) q^{17} +(2.38197 - 7.33094i) q^{19} +(1.11803 + 0.812299i) q^{20} +(-3.04508 - 1.31433i) q^{22} -7.70820 q^{23} +(-0.954915 + 2.93893i) q^{25} +(-0.381966 - 1.17557i) q^{26} +(1.30902 - 0.951057i) q^{28} +(-0.0450850 - 0.138757i) q^{29} +(4.54508 + 3.30220i) q^{31} +1.00000 q^{32} -4.00000 q^{34} +(-1.80902 - 1.31433i) q^{35} +(2.76393 + 8.50651i) q^{37} +(-6.23607 + 4.53077i) q^{38} +(-0.427051 - 1.31433i) q^{40} +(-2.38197 + 7.33094i) q^{41} -9.23607 q^{43} +(1.69098 + 2.85317i) q^{44} +(6.23607 + 4.53077i) q^{46} +(-1.23607 + 3.80423i) q^{47} +(3.54508 - 2.57565i) q^{49} +(2.50000 - 1.81636i) q^{50} +(-0.381966 + 1.17557i) q^{52} +(2.92705 + 2.12663i) q^{53} +(3.02786 - 3.44095i) q^{55} -1.61803 q^{56} +(-0.0450850 + 0.138757i) q^{58} +(1.64590 + 5.06555i) q^{59} +(-7.85410 + 5.70634i) q^{61} +(-1.73607 - 5.34307i) q^{62} +(-0.809017 - 0.587785i) q^{64} +1.70820 q^{65} -12.9443 q^{67} +(3.23607 + 2.35114i) q^{68} +(0.690983 + 2.12663i) q^{70} +(4.85410 - 3.52671i) q^{71} +(-1.71885 - 5.29007i) q^{73} +(2.76393 - 8.50651i) q^{74} +7.70820 q^{76} +(-2.73607 - 4.61653i) q^{77} +(0.118034 + 0.0857567i) q^{79} +(-0.427051 + 1.31433i) q^{80} +(6.23607 - 4.53077i) q^{82} +(-0.500000 + 0.363271i) q^{83} +(1.70820 - 5.25731i) q^{85} +(7.47214 + 5.42882i) q^{86} +(0.309017 - 3.30220i) q^{88} -11.2361 q^{89} +(0.618034 - 1.90211i) q^{91} +(-2.38197 - 7.33094i) q^{92} +(3.23607 - 2.35114i) q^{94} +(-3.29180 - 10.1311i) q^{95} +(5.97214 + 4.33901i) q^{97} -4.38197 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} - 2 q^{7} - q^{8}+O(q^{10}) $ 4 * q - q^2 - q^4 - 2 * q^7 - q^8	$ 4 q - q^{2} - q^{4} - 2 q^{7} - q^{8} - 10 q^{10} + 4 q^{11} + 4 q^{13} - 2 q^{14} - q^{16} + 4 q^{17} + 14 q^{19} - q^{22} - 4 q^{23} - 15 q^{25} - 6 q^{26} + 3 q^{28} + 11 q^{29} + 7 q^{31} + 4 q^{32} - 16 q^{34} - 5 q^{35} + 20 q^{37} - 16 q^{38} + 5 q^{40} - 14 q^{41} - 28 q^{43} + 9 q^{44} + 16 q^{46} + 4 q^{47} + 3 q^{49} + 10 q^{50} - 6 q^{52} + 5 q^{53} + 30 q^{55} - 2 q^{56} + 11 q^{58} + 20 q^{59} - 18 q^{61} + 2 q^{62} - q^{64} - 20 q^{65} - 16 q^{67} + 4 q^{68} + 5 q^{70} + 6 q^{71} - 27 q^{73} + 20 q^{74} + 4 q^{76} - 2 q^{77} - 4 q^{79} + 5 q^{80} + 16 q^{82} - 2 q^{83} - 20 q^{85} + 12 q^{86} - q^{88} - 36 q^{89} - 2 q^{91} - 14 q^{92} + 4 q^{94} - 40 q^{95} + 6 q^{97} - 22 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 - 2 * q^7 - q^8 - 10 * q^10 + 4 * q^11 + 4 * q^13 - 2 * q^14 - q^16 + 4 * q^17 + 14 * q^19 - q^22 - 4 * q^23 - 15 * q^25 - 6 * q^26 + 3 * q^28 + 11 * q^29 + 7 * q^31 + 4 * q^32 - 16 * q^34 - 5 * q^35 + 20 * q^37 - 16 * q^38 + 5 * q^40 - 14 * q^41 - 28 * q^43 + 9 * q^44 + 16 * q^46 + 4 * q^47 + 3 * q^49 + 10 * q^50 - 6 * q^52 + 5 * q^53 + 30 * q^55 - 2 * q^56 + 11 * q^58 + 20 * q^59 - 18 * q^61 + 2 * q^62 - q^64 - 20 * q^65 - 16 * q^67 + 4 * q^68 + 5 * q^70 + 6 * q^71 - 27 * q^73 + 20 * q^74 + 4 * q^76 - 2 * q^77 - 4 * q^79 + 5 * q^80 + 16 * q^82 - 2 * q^83 - 20 * q^85 + 12 * q^86 - q^88 - 36 * q^89 - 2 * q^91 - 14 * q^92 + 4 * q^94 - 40 * q^95 + 6 * q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.11803	−	0.812299i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$5$	1.11803	−	0.812299i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$6$		0			0
$7$	−0.500000	−	1.53884i	−0.188982	−	0.581628i	0.811012	−	0.585030i	$-0.198917\pi$
$7$	−0.500000	−	1.53884i	−0.188982	−	0.581628i	−0.999994	+	0.00340203i	$0.998917\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$		0			0
$10$	−1.38197			−0.437016
$11$	3.23607	−	0.726543i	0.975711	−	0.219061i
$11$	3.23607	−	0.726543i	0.975711	−	0.219061i
$12$		0			0
$13$	1.00000	+	0.726543i	0.277350	+	0.201507i	0.717761	−	0.696290i	$-0.245167\pi$
$13$	1.00000	+	0.726543i	0.277350	+	0.201507i	−0.440411	+	0.897796i	$0.645167\pi$
$14$	−0.500000	+	1.53884i	−0.133631	+	0.411273i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	3.23607	−	2.35114i	0.784862	−	0.570235i	−0.121572	−	0.992583i	$-0.538794\pi$
$17$	3.23607	−	2.35114i	0.784862	−	0.570235i	0.906434	+	0.422347i	$0.138794\pi$
$18$		0			0
$19$	2.38197	−	7.33094i	0.546460	−	1.68183i	−0.171031	−	0.985266i	$-0.554710\pi$
$19$	2.38197	−	7.33094i	0.546460	−	1.68183i	0.717492	−	0.696567i	$-0.245290\pi$
$20$	1.11803	+	0.812299i	0.250000	+	0.181636i
$21$		0			0
$22$	−3.04508	−	1.31433i	−0.649214	−	0.280216i
$23$	−7.70820			−1.60727			−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−7.70820			−1.60727			−0.803636	+	0.595121i	$0.797104\pi$
$24$		0			0
$25$	−0.954915	+	2.93893i	−0.190983	+	0.587785i
$26$	−0.381966	−	1.17557i	−0.0749097	−	0.230548i
$27$		0			0
$28$	1.30902	−	0.951057i	0.247381	−	0.179733i
$29$	−0.0450850	−	0.138757i	−0.00837207	−	0.0257666i	0.946783	−	0.321872i	$-0.104312\pi$
$29$	−0.0450850	−	0.138757i	−0.00837207	−	0.0257666i	−0.955155	+	0.296105i	$0.904312\pi$
$30$		0			0
$31$	4.54508	+	3.30220i	0.816321	+	0.593092i	0.915656	−	0.401962i	$-0.131672\pi$
$31$	4.54508	+	3.30220i	0.816321	+	0.593092i	−0.0993351	+	0.995054i	$0.531672\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−4.00000			−0.685994
$35$	−1.80902	−	1.31433i	−0.305780	−	0.222162i
$36$		0			0
$37$	2.76393	+	8.50651i	0.454388	+	1.39846i	0.871853	+	0.489768i	$0.162919\pi$
$37$	2.76393	+	8.50651i	0.454388	+	1.39846i	−0.417465	+	0.908693i	$0.637081\pi$
$38$	−6.23607	+	4.53077i	−1.01162	+	0.734988i
$39$		0			0
$40$	−0.427051	−	1.31433i	−0.0675227	−	0.207813i
$41$	−2.38197	+	7.33094i	−0.372001	+	1.14490i	0.573479	+	0.819220i	$0.305593\pi$
$41$	−2.38197	+	7.33094i	−0.372001	+	1.14490i	−0.945480	+	0.325680i	$0.894407\pi$
$42$		0			0
$43$	−9.23607			−1.40849			−0.704244	−	0.709958i	$-0.748714\pi$
$43$	−9.23607			−1.40849			−0.704244	+	0.709958i	$0.748714\pi$
$44$	1.69098	+	2.85317i	0.254925	+	0.430131i
$45$		0			0
$46$	6.23607	+	4.53077i	0.919458	+	0.668025i
$47$	−1.23607	+	3.80423i	−0.180299	+	0.554903i	−0.999836	−	0.0181233i	$-0.994231\pi$
$47$	−1.23607	+	3.80423i	−0.180299	+	0.554903i	0.819537	+	0.573027i	$0.194231\pi$
$48$		0			0
$49$	3.54508	−	2.57565i	0.506441	−	0.367951i
$50$	2.50000	−	1.81636i	0.353553	−	0.256872i
$51$		0			0
$52$	−0.381966	+	1.17557i	−0.0529692	+	0.163022i
$53$	2.92705	+	2.12663i	0.402061	+	0.292115i	0.770380	−	0.637585i	$-0.220066\pi$
$53$	2.92705	+	2.12663i	0.402061	+	0.292115i	−0.368319	+	0.929700i	$0.620066\pi$
$54$		0			0
$55$	3.02786	−	3.44095i	0.408277	−	0.463978i
$56$	−1.61803			−0.216219
$57$		0			0
$58$	−0.0450850	+	0.138757i	−0.00591995	+	0.0182197i
$59$	1.64590	+	5.06555i	0.214278	+	0.659479i	0.999204	+	0.0398899i	$0.0127007\pi$
$59$	1.64590	+	5.06555i	0.214278	+	0.659479i	−0.784926	+	0.619589i	$0.787299\pi$
$60$		0			0
$61$	−7.85410	+	5.70634i	−1.00561	+	0.730622i	−0.963285	−	0.268482i	$-0.913478\pi$
$61$	−7.85410	+	5.70634i	−1.00561	+	0.730622i	−0.0423300	+	0.999104i	$0.513478\pi$
$62$	−1.73607	−	5.34307i	−0.220481	−	0.678570i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.70820			0.211877
$66$		0			0
$67$	−12.9443			−1.58139			−0.790697	−	0.612207i	$-0.790282\pi$
$67$	−12.9443			−1.58139			−0.790697	+	0.612207i	$0.790282\pi$
$68$	3.23607	+	2.35114i	0.392431	+	0.285118i
$69$		0			0
$70$	0.690983	+	2.12663i	0.0825883	+	0.254181i
$71$	4.85410	−	3.52671i	0.576076	−	0.418544i	−0.261231	−	0.965276i	$-0.584129\pi$
$71$	4.85410	−	3.52671i	0.576076	−	0.418544i	0.837307	+	0.546733i	$0.184129\pi$
$72$		0			0
$73$	−1.71885	−	5.29007i	−0.201176	−	0.619156i	−0.999849	−	0.0173902i	$-0.994464\pi$
$73$	−1.71885	−	5.29007i	−0.201176	−	0.619156i	0.798673	−	0.601765i	$-0.205536\pi$
$74$	2.76393	−	8.50651i	0.321301	−	0.988861i
$75$		0			0
$76$	7.70820			0.884192
$77$	−2.73607	−	4.61653i	−0.311804	−	0.526102i
$78$		0			0
$79$	0.118034	+	0.0857567i	0.0132799	+	0.00964838i	0.594405	−	0.804166i	$-0.297387\pi$
$79$	0.118034	+	0.0857567i	0.0132799	+	0.00964838i	−0.581126	+	0.813814i	$0.697387\pi$
$80$	−0.427051	+	1.31433i	−0.0477458	+	0.146946i
$81$		0			0
$82$	6.23607	−	4.53077i	0.688659	−	0.500340i
$83$	−0.500000	+	0.363271i	−0.0548821	+	0.0398742i	−0.614888	−	0.788614i	$-0.710799\pi$
$83$	−0.500000	+	0.363271i	−0.0548821	+	0.0398742i	0.560006	+	0.828489i	$0.310799\pi$
$84$		0			0
$85$	1.70820	−	5.25731i	0.185281	−	0.570235i
$86$	7.47214	+	5.42882i	0.805741	+	0.585405i
$87$		0			0
$88$	0.309017	−	3.30220i	0.0329413	−	0.352015i
$89$	−11.2361			−1.19102			−0.595510	−	0.803348i	$-0.703050\pi$
$89$	−11.2361			−1.19102			−0.595510	+	0.803348i	$0.703050\pi$
$90$		0			0
$91$	0.618034	−	1.90211i	0.0647876	−	0.199396i
$92$	−2.38197	−	7.33094i	−0.248337	−	0.764303i
$93$		0			0
$94$	3.23607	−	2.35114i	0.333775	−	0.242502i
$95$	−3.29180	−	10.1311i	−0.337731	−	1.03943i
$96$		0			0
$97$	5.97214	+	4.33901i	0.606379	+	0.440560i	0.848137	−	0.529777i	$-0.177724\pi$
$97$	5.97214	+	4.33901i	0.606379	+	0.440560i	−0.241759	+	0.970336i	$0.577724\pi$
$98$	−4.38197			−0.442645
$99$		0			0
$100$	−3.09017			−0.309017
$101$	7.35410	+	5.34307i	0.731760	+	0.531655i	0.890120	−	0.455726i	$-0.150620\pi$
$101$	7.35410	+	5.34307i	0.731760	+	0.531655i	−0.158359	+	0.987382i	$0.550620\pi$
$102$		0			0
$103$	−0.972136	−	2.99193i	−0.0957874	−	0.294803i	0.891671	−	0.452685i	$-0.149534\pi$
$103$	−0.972136	−	2.99193i	−0.0957874	−	0.294803i	−0.987458	+	0.157881i	$0.949534\pi$
$104$	1.00000	−	0.726543i	0.0980581	−	0.0712434i
$105$		0			0
$106$	−1.11803	−	3.44095i	−0.108593	−	0.334215i
$107$	3.11803	−	9.59632i	0.301432	−	0.927711i	−0.679553	−	0.733626i	$-0.737826\pi$
$107$	3.11803	−	9.59632i	0.301432	−	0.927711i	0.980985	−	0.194085i	$-0.0621738\pi$
$108$		0			0
$109$	14.9443			1.43140			0.715701	−	0.698407i	$-0.246107\pi$
$109$	14.9443			1.43140			0.715701	+	0.698407i	$0.246107\pi$
$110$	−4.47214	+	1.00406i	−0.426401	+	0.0957331i
$111$		0			0
$112$	1.30902	+	0.951057i	0.123690	+	0.0898664i
$113$	3.38197	−	10.4086i	0.318149	−	0.979161i	−0.656290	−	0.754508i	$-0.727875\pi$
$113$	3.38197	−	10.4086i	0.318149	−	0.979161i	0.974439	−	0.224652i	$-0.0721246\pi$
$114$		0			0
$115$	−8.61803	+	6.26137i	−0.803636	+	0.583876i
$116$	0.118034	−	0.0857567i	0.0109592	−	0.00796231i
$117$		0			0
$118$	1.64590	−	5.06555i	0.151517	−	0.466322i
$119$	−5.23607	−	3.80423i	−0.479990	−	0.348733i
$120$		0			0
$121$	9.94427	−	4.70228i	0.904025	−	0.427480i
$122$	9.70820			0.878939
$123$		0			0
$124$	−1.73607	+	5.34307i	−0.155904	+	0.479822i
$125$	3.45492	+	10.6331i	0.309017	+	0.951057i
$126$		0			0
$127$	−3.23607	+	2.35114i	−0.287155	+	0.208630i	−0.722032	−	0.691860i	$-0.756792\pi$
$127$	−3.23607	+	2.35114i	−0.287155	+	0.208630i	0.434877	+	0.900490i	$0.356792\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	−1.38197	−	1.00406i	−0.121206	−	0.0880616i
$131$	2.85410			0.249364			0.124682	−	0.992197i	$-0.460209\pi$
$131$	2.85410			0.249364			0.124682	+	0.992197i	$0.460209\pi$
$132$		0			0
$133$	−12.4721			−1.08147
$134$	10.4721	+	7.60845i	0.904655	+	0.657270i
$135$		0			0
$136$	−1.23607	−	3.80423i	−0.105992	−	0.326210i
$137$	6.61803	−	4.80828i	0.565417	−	0.410799i	−0.268021	−	0.963413i	$-0.586370\pi$
$137$	6.61803	−	4.80828i	0.565417	−	0.410799i	0.833437	+	0.552614i	$0.186370\pi$
$138$		0			0
$139$	−0.708204	−	2.17963i	−0.0600691	−	0.184874i	0.916519	−	0.399991i	$-0.130987\pi$
$139$	−0.708204	−	2.17963i	−0.0600691	−	0.184874i	−0.976588	+	0.215117i	$0.930987\pi$
$140$	0.690983	−	2.12663i	0.0583987	−	0.179733i
$141$		0			0
$142$	−6.00000			−0.503509
$143$	3.76393	+	1.62460i	0.314756	+	0.135856i
$144$		0			0
$145$	−0.163119	−	0.118513i	−0.0135463	−	0.00984196i
$146$	−1.71885	+	5.29007i	−0.142253	+	0.437809i
$147$		0			0
$148$	−7.23607	+	5.25731i	−0.594801	+	0.432148i
$149$	−18.6353	+	13.5393i	−1.52666	+	1.10918i	−0.568600	+	0.822614i	$0.692515\pi$
$149$	−18.6353	+	13.5393i	−1.52666	+	1.10918i	−0.958060	+	0.286569i	$0.907485\pi$
$150$		0			0
$151$	−1.48278	+	4.56352i	−0.120667	+	0.371374i	−0.993087	−	0.117383i	$-0.962550\pi$
$151$	−1.48278	+	4.56352i	−0.120667	+	0.371374i	0.872420	+	0.488757i	$0.162550\pi$
$152$	−6.23607	−	4.53077i	−0.505812	−	0.367494i
$153$		0			0
$154$	−0.500000	+	5.34307i	−0.0402911	+	0.430557i
$155$	7.76393			0.623614
$156$		0			0
$157$	−5.56231	+	17.1190i	−0.443920	+	1.36625i	0.439743	+	0.898124i	$0.355069\pi$
$157$	−5.56231	+	17.1190i	−0.443920	+	1.36625i	−0.883663	+	0.468123i	$0.844931\pi$
$158$	−0.0450850	−	0.138757i	−0.00358677	−	0.0110389i
$159$		0			0
$160$	1.11803	−	0.812299i	0.0883883	−	0.0642179i
$161$	3.85410	+	11.8617i	0.303746	+	0.934833i
$162$		0			0
$163$	6.85410	+	4.97980i	0.536855	+	0.390048i	0.822916	−	0.568164i	$-0.192346\pi$
$163$	6.85410	+	4.97980i	0.536855	+	0.390048i	−0.286061	+	0.958211i	$0.592346\pi$
$164$	−7.70820			−0.601910
$165$		0			0
$166$	0.618034			0.0479687
$167$	−15.9443	−	11.5842i	−1.23380	−	0.896412i	−0.236635	−	0.971599i	$-0.576045\pi$
$167$	−15.9443	−	11.5842i	−1.23380	−	0.896412i	−0.997169	+	0.0751869i	$0.976045\pi$
$168$		0			0
$169$	−3.54508	−	10.9106i	−0.272699	−	0.839281i
$170$	−4.47214	+	3.24920i	−0.342997	+	0.249202i
$171$		0			0
$172$	−2.85410	−	8.78402i	−0.217623	−	0.669775i
$173$	−0.409830	+	1.26133i	−0.0311588	+	0.0958969i	−0.965426	−	0.260676i	$-0.916055\pi$
$173$	−0.409830	+	1.26133i	−0.0311588	+	0.0958969i	0.934268	+	0.356572i	$0.116055\pi$
$174$		0			0
$175$	5.00000			0.377964
$176$	−2.19098	+	2.48990i	−0.165152	+	0.187683i
$177$		0			0
$178$	9.09017	+	6.60440i	0.681337	+	0.495020i
$179$	−0.482779	+	1.48584i	−0.0360846	+	0.111057i	−0.967476	−	0.252961i	$-0.918595\pi$
$179$	−0.482779	+	1.48584i	−0.0360846	+	0.111057i	0.931392	+	0.364018i	$0.118595\pi$
$180$		0			0
$181$	4.38197	−	3.18368i	0.325709	−	0.236641i	−0.412899	−	0.910777i	$-0.635484\pi$
$181$	4.38197	−	3.18368i	0.325709	−	0.236641i	0.738608	+	0.674136i	$0.235484\pi$
$182$	−1.61803	+	1.17557i	−0.119937	+	0.0871391i
$183$		0			0
$184$	−2.38197	+	7.33094i	−0.175601	+	0.540444i
$185$	10.0000	+	7.26543i	0.735215	+	0.534165i
$186$		0			0
$187$	8.76393	−	9.95959i	0.640882	−	0.728318i
$188$	−4.00000			−0.291730
$189$		0			0
$190$	−3.29180	+	10.1311i	−0.238812	+	0.734988i
$191$	6.47214	+	19.9192i	0.468307	+	1.44130i	0.854775	+	0.518999i	$0.173695\pi$
$191$	6.47214	+	19.9192i	0.468307	+	1.44130i	−0.386468	+	0.922303i	$0.626305\pi$
$192$		0			0
$193$	1.92705	−	1.40008i	0.138712	−	0.100780i	−0.516265	−	0.856429i	$-0.672678\pi$
$193$	1.92705	−	1.40008i	0.138712	−	0.100780i	0.654977	+	0.755648i	$0.272678\pi$
$194$	−2.28115	−	7.02067i	−0.163777	−	0.504055i
$195$		0			0
$196$	3.54508	+	2.57565i	0.253220	+	0.183975i
$197$	−12.5066			−0.891057			−0.445528	−	0.895268i	$-0.646984\pi$
$197$	−12.5066			−0.891057			−0.445528	+	0.895268i	$0.646984\pi$
$198$		0			0
$199$	−2.61803			−0.185588			−0.0927938	−	0.995685i	$-0.529580\pi$
$199$	−2.61803			−0.185588			−0.0927938	+	0.995685i	$0.529580\pi$
$200$	2.50000	+	1.81636i	0.176777	+	0.128436i
$201$		0			0
$202$	−2.80902	−	8.64527i	−0.197642	−	0.608279i
$203$	−0.190983	+	0.138757i	−0.0134044	+	0.00973885i
$204$		0			0
$205$	3.29180	+	10.1311i	0.229909	+	0.707587i
$206$	−0.972136	+	2.99193i	−0.0677319	+	0.208457i
$207$		0			0
$208$	−1.23607			−0.0857059
$209$	2.38197	−	25.4540i	0.164764	−	1.76069i
$210$		0			0
$211$	3.85410	+	2.80017i	0.265327	+	0.192772i	0.712492	−	0.701680i	$-0.247566\pi$
$211$	3.85410	+	2.80017i	0.265327	+	0.192772i	−0.447165	+	0.894451i	$0.647566\pi$
$212$	−1.11803	+	3.44095i	−0.0767869	+	0.236326i
$213$		0			0
$214$	−8.16312	+	5.93085i	−0.558019	+	0.405425i
$215$	−10.3262	+	7.50245i	−0.704244	+	0.511663i
$216$		0			0
$217$	2.80902	−	8.64527i	0.190688	−	0.586879i
$218$	−12.0902	−	8.78402i	−0.818850	−	0.594929i
$219$		0			0
$220$	4.20820	+	1.81636i	0.283717	+	0.122459i
$221$	4.94427			0.332588
$222$		0			0
$223$	4.42705	−	13.6251i	0.296457	−	0.912402i	−0.686271	−	0.727346i	$-0.740754\pi$
$223$	4.42705	−	13.6251i	0.296457	−	0.912402i	0.982728	−	0.185056i	$-0.0592465\pi$
$224$	−0.500000	−	1.53884i	−0.0334077	−	0.102818i
$225$		0			0
$226$	−8.85410	+	6.43288i	−0.588966	+	0.427909i
$227$	7.42705	+	22.8581i	0.492951	+	1.51715i	0.820126	+	0.572183i	$0.193903\pi$
$227$	7.42705	+	22.8581i	0.492951	+	1.51715i	−0.327176	+	0.944964i	$0.606097\pi$
$228$		0			0
$229$	−17.3262	−	12.5882i	−1.14495	−	0.831855i	−0.157149	−	0.987575i	$-0.550230\pi$
$229$	−17.3262	−	12.5882i	−1.14495	−	0.831855i	−0.987801	+	0.155720i	$0.950230\pi$
$230$	10.6525			0.702403
$231$		0			0
$232$	−0.145898			−0.00957868
$233$	0.763932	+	0.555029i	0.0500469	+	0.0363612i	0.612527	−	0.790449i	$-0.290153\pi$
$233$	0.763932	+	0.555029i	0.0500469	+	0.0363612i	−0.562481	+	0.826810i	$0.690153\pi$
$234$		0			0
$235$	1.70820	+	5.25731i	0.111431	+	0.342949i
$236$	−4.30902	+	3.13068i	−0.280493	+	0.203790i
$237$		0			0
$238$	2.00000	+	6.15537i	0.129641	+	0.398993i
$239$	5.09017	−	15.6659i	0.329256	−	1.01334i	−0.640227	−	0.768186i	$-0.721160\pi$
$239$	5.09017	−	15.6659i	0.329256	−	1.01334i	0.969483	−	0.245159i	$-0.0788402\pi$
$240$		0			0
$241$	6.38197			0.411099			0.205549	−	0.978647i	$-0.434102\pi$
$241$	6.38197			0.411099			0.205549	+	0.978647i	$0.434102\pi$
$242$	−10.8090	−	2.04087i	−0.694830	−	0.131192i
$243$		0			0
$244$	−7.85410	−	5.70634i	−0.502807	−	0.365311i
$245$	1.87132	−	5.75934i	0.119554	−	0.367951i
$246$		0			0
$247$	7.70820	−	5.60034i	0.490461	−	0.356341i
$248$	4.54508	−	3.30220i	0.288613	−	0.209690i
$249$		0			0
$250$	3.45492	−	10.6331i	0.218508	−	0.672499i
$251$	−0.263932	−	0.191758i	−0.0166592	−	0.0121036i	0.579424	−	0.815026i	$-0.303277\pi$
$251$	−0.263932	−	0.191758i	−0.0166592	−	0.0121036i	−0.596084	+	0.802922i	$0.703277\pi$
$252$		0			0
$253$	−24.9443	+	5.60034i	−1.56823	+	0.352090i
$254$	4.00000			0.250982
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−6.70820	−	20.6457i	−0.418446	−	1.28785i	−0.909132	−	0.416508i	$-0.863254\pi$
$257$	−6.70820	−	20.6457i	−0.418446	−	1.28785i	0.490686	−	0.871337i	$-0.336746\pi$
$258$		0			0
$259$	11.7082	−	8.50651i	0.727512	−	0.528569i
$260$	0.527864	+	1.62460i	0.0327367	+	0.100753i
$261$		0			0
$262$	−2.30902	−	1.67760i	−0.142652	−	0.103642i
$263$	12.7639			0.787058			0.393529	−	0.919312i	$-0.371254\pi$
$263$	12.7639			0.787058			0.393529	+	0.919312i	$0.371254\pi$
$264$		0			0
$265$	5.00000			0.307148
$266$	10.0902	+	7.33094i	0.618668	+	0.449489i
$267$		0			0
$268$	−4.00000	−	12.3107i	−0.244339	−	0.751998i
$269$	4.85410	−	3.52671i	0.295960	−	0.215027i	−0.429889	−	0.902882i	$-0.641447\pi$
$269$	4.85410	−	3.52671i	0.295960	−	0.215027i	0.725849	+	0.687854i	$0.241447\pi$
$270$		0			0
$271$	5.41641	+	16.6700i	0.329023	+	1.01263i	0.969592	+	0.244729i	$0.0786988\pi$
$271$	5.41641	+	16.6700i	0.329023	+	1.01263i	−0.640568	+	0.767901i	$0.721301\pi$
$272$	−1.23607	+	3.80423i	−0.0749476	+	0.230665i
$273$		0			0
$274$	−8.18034			−0.494192
$275$	−0.954915	+	10.2044i	−0.0575835	+	0.615346i
$276$		0			0
$277$	−1.85410	−	1.34708i	−0.111402	−	0.0809384i	0.530689	−	0.847566i	$-0.321933\pi$
$277$	−1.85410	−	1.34708i	−0.111402	−	0.0809384i	−0.642092	+	0.766628i	$0.721933\pi$
$278$	−0.708204	+	2.17963i	−0.0424752	+	0.130725i
$279$		0			0
$280$	−1.80902	+	1.31433i	−0.108109	+	0.0785461i
$281$	13.5623	−	9.85359i	0.809059	−	0.587816i	−0.104498	−	0.994525i	$-0.533324\pi$
$281$	13.5623	−	9.85359i	0.809059	−	0.587816i	0.913558	+	0.406709i	$0.133324\pi$
$282$		0			0
$283$	−5.09017	+	15.6659i	−0.302579	+	0.931243i	0.677990	+	0.735071i	$0.262851\pi$
$283$	−5.09017	+	15.6659i	−0.302579	+	0.931243i	−0.980569	+	0.196172i	$0.937149\pi$
$284$	4.85410	+	3.52671i	0.288038	+	0.209272i
$285$		0			0
$286$	−2.09017	−	3.52671i	−0.123594	−	0.208539i
$287$	12.4721			0.736207
$288$		0			0
$289$	−0.309017	+	0.951057i	−0.0181775	+	0.0559445i
$290$	0.0623059	+	0.191758i	0.00365873	+	0.0112604i
$291$		0			0
$292$	4.50000	−	3.26944i	0.263343	−	0.191330i
$293$	−2.35410	−	7.24518i	−0.137528	−	0.423268i	0.858447	−	0.512903i	$-0.171430\pi$
$293$	−2.35410	−	7.24518i	−0.137528	−	0.423268i	−0.995975	+	0.0896350i	$0.971430\pi$
$294$		0			0
$295$	5.95492	+	4.32650i	0.346709	+	0.251899i
$296$	8.94427			0.519875
$297$		0			0
$298$	23.0344			1.33435
$299$	−7.70820	−	5.60034i	−0.445777	−	0.323876i
$300$		0			0
$301$	4.61803	+	14.2128i	0.266179	+	0.819215i
$302$	3.88197	−	2.82041i	0.223382	−	0.162297i
$303$		0			0
$304$	2.38197	+	7.33094i	0.136615	+	0.420458i
$305$	−4.14590	+	12.7598i	−0.237393	+	0.730622i
$306$		0			0
$307$	−12.7639			−0.728476			−0.364238	−	0.931306i	$-0.618671\pi$
$307$	−12.7639			−0.728476			−0.364238	+	0.931306i	$0.618671\pi$
$308$	3.54508	−	4.02874i	0.202000	−	0.229559i
$309$		0			0
$310$	−6.28115	−	4.56352i	−0.356746	−	0.259191i
$311$	−2.32624	+	7.15942i	−0.131909	+	0.405974i	−0.995096	−	0.0989097i	$-0.968465\pi$
$311$	−2.32624	+	7.15942i	−0.131909	+	0.405974i	0.863188	+	0.504883i	$0.168465\pi$
$312$		0			0
$313$	20.2082	−	14.6821i	1.14224	−	0.829882i	0.154806	−	0.987945i	$-0.450525\pi$
$313$	20.2082	−	14.6821i	1.14224	−	0.829882i	0.987429	+	0.158062i	$0.0505247\pi$
$314$	14.5623	−	10.5801i	0.821798	−	0.597072i
$315$		0			0
$316$	−0.0450850	+	0.138757i	−0.00253623	+	0.00780571i
$317$	−21.7984	−	15.8374i	−1.22432	−	0.889520i	−0.227867	−	0.973692i	$-0.573175\pi$
$317$	−21.7984	−	15.8374i	−1.22432	−	0.889520i	−0.996451	+	0.0841726i	$0.973175\pi$
$318$		0			0
$319$	−0.246711	−	0.416272i	−0.0138132	−	0.0233067i
$320$	−1.38197			−0.0772542
$321$		0			0
$322$	3.85410	−	11.8617i	0.214781	−	0.661027i
$323$	−9.52786	−	29.3238i	−0.530145	−	1.63162i
$324$		0			0
$325$	−3.09017	+	2.24514i	−0.171412	+	0.124538i
$326$	−2.61803	−	8.05748i	−0.144999	−	0.446263i
$327$		0			0
$328$	6.23607	+	4.53077i	0.344329	+	0.250170i
$329$	6.47214			0.356820
$330$		0			0
$331$	28.3607			1.55884			0.779422	−	0.626499i	$-0.215513\pi$
$331$	28.3607			1.55884			0.779422	+	0.626499i	$0.215513\pi$
$332$	−0.500000	−	0.363271i	−0.0274411	−	0.0199371i
$333$		0			0
$334$	6.09017	+	18.7436i	0.333239	+	1.02561i
$335$	−14.4721	+	10.5146i	−0.790697	+	0.574475i
$336$		0			0
$337$	−4.90983	−	15.1109i	−0.267455	−	0.823143i	−0.991118	−	0.132989i	$-0.957543\pi$
$337$	−4.90983	−	15.1109i	−0.267455	−	0.823143i	0.723662	−	0.690155i	$-0.242457\pi$
$338$	−3.54508	+	10.9106i	−0.192827	+	0.593461i
$339$		0			0
$340$	5.52786			0.299791
$341$	17.1074	+	7.38394i	0.926417	+	0.399863i
$342$		0			0
$343$	−14.8992	−	10.8249i	−0.804480	−	0.584489i
$344$	−2.85410	+	8.78402i	−0.153883	+	0.473603i
$345$		0			0
$346$	1.07295	−	0.779543i	0.0576821	−	0.0419085i
$347$	−15.1074	+	10.9762i	−0.811007	+	0.589231i	−0.914122	−	0.405438i	$-0.867119\pi$
$347$	−15.1074	+	10.9762i	−0.811007	+	0.589231i	0.103115	+	0.994669i	$0.467119\pi$
$348$		0			0
$349$	−7.94427	+	24.4500i	−0.425247	+	1.30878i	0.477510	+	0.878626i	$0.341539\pi$
$349$	−7.94427	+	24.4500i	−0.425247	+	1.30878i	−0.902757	+	0.430150i	$0.858461\pi$
$350$	−4.04508	−	2.93893i	−0.216219	−	0.157092i
$351$		0			0
$352$	3.23607	−	0.726543i	0.172483	−	0.0387248i
$353$	−11.2361			−0.598036			−0.299018	−	0.954248i	$-0.596659\pi$
$353$	−11.2361			−0.598036			−0.299018	+	0.954248i	$0.596659\pi$
$354$		0			0
$355$	2.56231	−	7.88597i	0.135993	−	0.418544i
$356$	−3.47214	−	10.6861i	−0.184023	−	0.566364i
$357$		0			0
$358$	1.26393	−	0.918300i	0.0668009	−	0.0485337i
$359$	1.79837	+	5.53483i	0.0949145	+	0.292117i	0.987231	−	0.159293i	$-0.0509213\pi$
$359$	1.79837	+	5.53483i	0.0949145	+	0.292117i	−0.892317	+	0.451410i	$0.850921\pi$
$360$		0			0
$361$	−32.6976	−	23.7562i	−1.72092	−	1.25032i
$362$	−5.41641			−0.284680
$363$		0			0
$364$	2.00000			0.104828
$365$	−6.21885	−	4.51826i	−0.325509	−	0.236496i
$366$		0			0
$367$	3.10081	+	9.54332i	0.161861	+	0.498157i	0.998791	−	0.0491524i	$-0.0156520\pi$
$367$	3.10081	+	9.54332i	0.161861	+	0.498157i	−0.836930	+	0.547310i	$0.815652\pi$
$368$	6.23607	−	4.53077i	0.325078	−	0.236183i
$369$		0			0
$370$	−3.81966	−	11.7557i	−0.198575	−	0.611150i
$371$	1.80902	−	5.56758i	0.0939195	−	0.289054i
$372$		0			0
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$	−12.9443	+	2.90617i	−0.669332	+	0.150274i
$375$		0			0
$376$	3.23607	+	2.35114i	0.166887	+	0.121251i
$377$	0.0557281	−	0.171513i	0.00287014	−	0.00883339i
$378$		0			0
$379$	−3.09017	+	2.24514i	−0.158731	+	0.115325i	−0.664316	−	0.747452i	$-0.731277\pi$
$379$	−3.09017	+	2.24514i	−0.158731	+	0.115325i	0.505584	+	0.862777i	$0.331277\pi$
$380$	8.61803	−	6.26137i	0.442096	−	0.321201i
$381$		0			0
$382$	6.47214	−	19.9192i	0.331143	−	1.01915i
$383$	30.5066	+	22.1643i	1.55881	+	1.13254i	0.936974	+	0.349399i	$0.113614\pi$
$383$	30.5066	+	22.1643i	1.55881	+	1.13254i	0.621839	+	0.783145i	$0.286386\pi$
$384$		0			0
$385$	−6.80902	−	2.93893i	−0.347020	−	0.149782i
$386$	−2.38197			−0.121239
$387$		0			0
$388$	−2.28115	+	7.02067i	−0.115808	+	0.356420i
$389$	−0.326238	−	1.00406i	−0.0165409	−	0.0509077i	0.942445	−	0.334360i	$-0.108520\pi$
$389$	−0.326238	−	1.00406i	−0.0165409	−	0.0509077i	−0.958986	+	0.283452i	$0.908520\pi$
$390$		0			0
$391$	−24.9443	+	18.1231i	−1.26149	+	0.916523i
$392$	−1.35410	−	4.16750i	−0.0683925	−	0.210490i
$393$		0			0
$394$	10.1180	+	7.35118i	0.509739	+	0.370347i
$395$	0.201626			0.0101449
$396$		0			0
$397$	−12.9443			−0.649654			−0.324827	−	0.945773i	$-0.605306\pi$
$397$	−12.9443			−0.649654			−0.324827	+	0.945773i	$0.605306\pi$
$398$	2.11803	+	1.53884i	0.106167	+	0.0771352i
$399$		0			0
$400$	−0.954915	−	2.93893i	−0.0477458	−	0.146946i
$401$	9.47214	−	6.88191i	0.473016	−	0.343666i	−0.325600	−	0.945508i	$-0.605566\pi$
$401$	9.47214	−	6.88191i	0.473016	−	0.343666i	0.798615	+	0.601842i	$0.205566\pi$
$402$		0			0
$403$	2.14590	+	6.60440i	0.106895	+	0.328988i
$404$	−2.80902	+	8.64527i	−0.139754	+	0.430118i
$405$		0			0
$406$	0.236068			0.0117159
$407$	15.1246	+	25.5195i	0.749699	+	1.26496i
$408$		0			0
$409$	−13.7361	−	9.97984i	−0.679205	−	0.493471i	0.193889	−	0.981023i	$-0.437890\pi$
$409$	−13.7361	−	9.97984i	−0.679205	−	0.493471i	−0.873094	+	0.487552i	$0.837890\pi$
$410$	3.29180	−	10.1311i	0.162570	−	0.500340i
$411$		0			0
$412$	2.54508	−	1.84911i	0.125387	−	0.0910992i
$413$	6.97214	−	5.06555i	0.343076	−	0.249260i
$414$		0			0
$415$	−0.263932	+	0.812299i	−0.0129559	+	0.0398742i
$416$	1.00000	+	0.726543i	0.0490290	+	0.0356217i
$417$		0			0
$418$	−16.8885	+	19.1926i	−0.826046	+	0.938743i
$419$	−0.909830			−0.0444481			−0.0222241	−	0.999753i	$-0.507075\pi$
$419$	−0.909830			−0.0444481			−0.0222241	+	0.999753i	$0.507075\pi$
$420$		0			0
$421$	12.2361	−	37.6587i	0.596349	−	1.83537i	0.0484585	−	0.998825i	$-0.484569\pi$
$421$	12.2361	−	37.6587i	0.596349	−	1.83537i	0.547891	−	0.836550i	$-0.315431\pi$
$422$	−1.47214	−	4.53077i	−0.0716625	−	0.220554i
$423$		0			0
$424$	2.92705	−	2.12663i	0.142150	−	0.103278i
$425$	3.81966	+	11.7557i	0.185281	+	0.570235i
$426$		0			0
$427$	12.7082	+	9.23305i	0.614993	+	0.446819i
$428$	10.0902			0.487727
$429$		0			0
$430$	12.7639			0.615531
$431$	−19.4721	−	14.1473i	−0.937940	−	0.681453i	0.00998408	−	0.999950i	$-0.496822\pi$
$431$	−19.4721	−	14.1473i	−0.937940	−	0.681453i	−0.947924	+	0.318497i	$0.896822\pi$
$432$		0			0
$433$	2.97214	+	9.14729i	0.142832	+	0.439591i	0.996726	−	0.0808560i	$-0.0257654\pi$
$433$	2.97214	+	9.14729i	0.142832	+	0.439591i	−0.853894	+	0.520447i	$0.825765\pi$
$434$	−7.35410	+	5.34307i	−0.353008	+	0.256475i
$435$		0			0
$436$	4.61803	+	14.2128i	0.221164	+	0.680672i
$437$	−18.3607	+	56.5084i	−0.878310	+	2.70316i
$438$		0			0
$439$	−34.9230			−1.66678			−0.833392	−	0.552683i	$-0.813604\pi$
$439$	−34.9230			−1.66678			−0.833392	+	0.552683i	$0.813604\pi$
$440$	−2.33688	−	3.94298i	−0.111406	−	0.187974i
$441$		0			0
$442$	−4.00000	−	2.90617i	−0.190261	−	0.138232i
$443$	−2.11803	+	6.51864i	−0.100631	+	0.309710i	−0.988680	−	0.150038i	$-0.952060\pi$
$443$	−2.11803	+	6.51864i	−0.100631	+	0.309710i	0.888049	+	0.459748i	$0.152060\pi$
$444$		0			0
$445$	−12.5623	+	9.12705i	−0.595510	+	0.432664i
$446$	−11.5902	+	8.42075i	−0.548810	+	0.398734i
$447$		0			0
$448$	−0.500000	+	1.53884i	−0.0236228	+	0.0727034i
$449$	−6.85410	−	4.97980i	−0.323465	−	0.235011i	0.414188	−	0.910192i	$-0.364066\pi$
$449$	−6.85410	−	4.97980i	−0.323465	−	0.235011i	−0.737653	+	0.675180i	$0.764066\pi$
$450$		0			0
$451$	−2.38197	+	25.4540i	−0.112162	+	1.19858i
$452$	10.9443			0.514775
$453$		0			0
$454$	7.42705	−	22.8581i	0.348569	−	1.07278i
$455$	−0.854102	−	2.62866i	−0.0400409	−	0.123233i
$456$		0			0
$457$	13.6803	−	9.93935i	0.639939	−	0.464943i	−0.219890	−	0.975525i	$-0.570570\pi$
$457$	13.6803	−	9.93935i	0.639939	−	0.464943i	0.859829	+	0.510582i	$0.170570\pi$
$458$	6.61803	+	20.3682i	0.309240	+	0.951744i
$459$		0			0
$460$	−8.61803	−	6.26137i	−0.401818	−	0.291938i
$461$	−22.0000			−1.02464			−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000			−1.02464			−0.512321	+	0.858794i	$0.671214\pi$
$462$		0			0
$463$	34.7426			1.61463			0.807314	−	0.590122i	$-0.200920\pi$
$463$	34.7426			1.61463			0.807314	+	0.590122i	$0.200920\pi$
$464$	0.118034	+	0.0857567i	0.00547959	+	0.00398116i
$465$		0			0
$466$	−0.291796	−	0.898056i	−0.0135172	−	0.0416016i
$467$	−9.54508	+	6.93491i	−0.441694	+	0.320909i	−0.786308	−	0.617835i	$-0.788010\pi$
$467$	−9.54508	+	6.93491i	−0.441694	+	0.320909i	0.344614	+	0.938745i	$0.388010\pi$
$468$		0			0
$469$	6.47214	+	19.9192i	0.298855	+	0.919783i
$470$	1.70820	−	5.25731i	0.0787936	−	0.242502i
$471$		0			0
$472$	5.32624			0.245160
$473$	−29.8885	+	6.71040i	−1.37428	+	0.308544i
$474$		0			0
$475$	19.2705	+	14.0008i	0.884192	+	0.642403i
$476$	2.00000	−	6.15537i	0.0916698	−	0.282131i
$477$		0			0
$478$	−13.3262	+	9.68208i	−0.609528	+	0.442848i
$479$	10.7082	−	7.77997i	0.489270	−	0.355476i	−0.315633	−	0.948881i	$-0.602217\pi$
$479$	10.7082	−	7.77997i	0.489270	−	0.355476i	0.804904	+	0.593406i	$0.202217\pi$
$480$		0			0
$481$	−3.41641	+	10.5146i	−0.155775	+	0.479426i
$482$	−5.16312	−	3.75123i	−0.235174	−	0.170864i
$483$		0			0
$484$	7.54508	+	8.00448i	0.342958	+	0.363840i
$485$	10.2016			0.463232
$486$		0			0
$487$	−2.50000	+	7.69421i	−0.113286	+	0.348658i	−0.991586	−	0.129452i	$-0.958678\pi$
$487$	−2.50000	+	7.69421i	−0.113286	+	0.348658i	0.878300	+	0.478110i	$0.158678\pi$
$488$	3.00000	+	9.23305i	0.135804	+	0.417961i
$489$		0			0
$490$	−4.89919	+	3.55947i	−0.221323	+	0.160800i
$491$	−10.2918	−	31.6749i	−0.464462	−	1.42947i	−0.859658	−	0.510871i	$-0.829323\pi$
$491$	−10.2918	−	31.6749i	−0.464462	−	1.42947i	0.395195	−	0.918597i	$-0.370677\pi$
$492$		0			0
$493$	−0.472136	−	0.343027i	−0.0212639	−	0.0154492i
$494$	−9.52786			−0.428679
$495$		0			0
$496$	−5.61803			−0.252257
$497$	−7.85410	−	5.70634i	−0.352305	−	0.255964i
$498$		0			0
$499$	−7.81966	−	24.0664i	−0.350056	−	1.07736i	−0.958821	−	0.284011i	$-0.908335\pi$
$499$	−7.81966	−	24.0664i	−0.350056	−	1.07736i	0.608765	−	0.793351i	$-0.291665\pi$
$500$	−9.04508	+	6.57164i	−0.404508	+	0.293893i
$501$		0			0
$502$	0.100813	+	0.310271i	0.00449951	+	0.0138481i
$503$	9.70820	−	29.8788i	0.432867	−	1.33223i	−0.462389	−	0.886677i	$-0.653008\pi$
$503$	9.70820	−	29.8788i	0.432867	−	1.33223i	0.895256	−	0.445552i	$-0.146992\pi$
$504$		0			0
$505$	12.5623			0.559015
$506$	23.4721	+	10.1311i	1.04346	+	0.450383i
$507$		0			0
$508$	−3.23607	−	2.35114i	−0.143577	−	0.104315i
$509$	3.17376	−	9.76784i	0.140675	−	0.432952i	−0.855755	−	0.517381i	$-0.826907\pi$
$509$	3.17376	−	9.76784i	0.140675	−	0.432952i	0.996429	+	0.0844297i	$0.0269069\pi$
$510$		0			0
$511$	−7.28115	+	5.29007i	−0.322099	+	0.234019i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	−6.70820	+	20.6457i	−0.295886	+	0.910644i
$515$	−3.51722	−	2.55541i	−0.154987	−	0.112605i
$516$		0			0
$517$	−1.23607	+	13.2088i	−0.0543622	+	0.580922i
$518$	−14.4721			−0.635869
$519$		0			0
$520$	0.527864	−	1.62460i	0.0231484	−	0.0712434i
$521$	8.65248	+	26.6296i	0.379072	+	1.16666i	0.940690	+	0.339267i	$0.110179\pi$
$521$	8.65248	+	26.6296i	0.379072	+	1.16666i	−0.561618	+	0.827396i	$0.689821\pi$
$522$		0			0
$523$	13.4721	−	9.78808i	0.589095	−	0.428003i	−0.252896	−	0.967493i	$-0.581383\pi$
$523$	13.4721	−	9.78808i	0.589095	−	0.428003i	0.841992	+	0.539491i	$0.181383\pi$
$524$	0.881966	+	2.71441i	0.0385289	+	0.118580i
$525$		0			0
$526$	−10.3262	−	7.50245i	−0.450245	−	0.327122i
$527$	22.4721			0.978902
$528$		0			0
$529$	36.4164			1.58332
$530$	−4.04508	−	2.93893i	−0.175707	−	0.127659i
$531$		0			0
$532$	−3.85410	−	11.8617i	−0.167097	−	0.514270i
$533$	−7.70820	+	5.60034i	−0.333879	+	0.242578i
$534$		0			0
$535$	−4.30902	−	13.2618i	−0.186295	−	0.573357i
$536$	−4.00000	+	12.3107i	−0.172774	+	0.531743i
$537$		0			0
$538$	−6.00000			−0.258678
$539$	9.60081	−	10.9106i	0.413536	−	0.469955i
$540$		0			0
$541$	−3.61803	−	2.62866i	−0.155551	−	0.113015i	0.507287	−	0.861777i	$-0.330648\pi$
$541$	−3.61803	−	2.62866i	−0.155551	−	0.113015i	−0.662838	+	0.748762i	$0.730648\pi$
$542$	5.41641	−	16.6700i	0.232655	−	0.716037i
$543$		0			0
$544$	3.23607	−	2.35114i	0.138745	−	0.100804i
$545$	16.7082	−	12.1392i	0.715701	−	0.519987i
$546$		0			0
$547$	−0.888544	+	2.73466i	−0.0379914	+	0.116925i	−0.968254	−	0.249970i	$-0.919579\pi$
$547$	−0.888544	+	2.73466i	−0.0379914	+	0.116925i	0.930262	+	0.366895i	$0.119579\pi$
$548$	6.61803	+	4.80828i	0.282708	+	0.205400i
$549$		0			0
$550$	6.77051	−	7.69421i	0.288696	−	0.328082i
$551$	−1.12461			−0.0479101
$552$		0			0
$553$	0.0729490	−	0.224514i	0.00310211	−	0.00954731i
$554$	0.708204	+	2.17963i	0.0300887	+	0.0926035i
$555$		0			0
$556$	1.85410	−	1.34708i	0.0786314	−	0.0571291i
$557$	−4.11803	−	12.6740i	−0.174487	−	0.537015i	0.825123	−	0.564953i	$-0.191106\pi$
$557$	−4.11803	−	12.6740i	−0.174487	−	0.537015i	−0.999610	+	0.0279384i	$0.991106\pi$
$558$		0			0
$559$	−9.23607	−	6.71040i	−0.390644	−	0.283820i
$560$	2.23607			0.0944911
$561$		0			0
$562$	−16.7639			−0.707144
$563$	6.47214	+	4.70228i	0.272768	+	0.198178i	0.715757	−	0.698350i	$-0.246082\pi$
$563$	6.47214	+	4.70228i	0.272768	+	0.198178i	−0.442989	+	0.896527i	$0.646082\pi$
$564$		0			0
$565$	−4.67376	−	14.3844i	−0.196627	−	0.605155i
$566$	13.3262	−	9.68208i	0.560144	−	0.406968i
$567$		0			0
$568$	−1.85410	−	5.70634i	−0.0777964	−	0.239433i
$569$	5.09017	−	15.6659i	0.213391	−	0.656750i	−0.785873	−	0.618388i	$-0.787786\pi$
$569$	5.09017	−	15.6659i	0.213391	−	0.656750i	0.999264	−	0.0383620i	$-0.0122140\pi$
$570$		0			0
$571$	1.34752			0.0563921			0.0281961	−	0.999602i	$-0.491024\pi$
$571$	1.34752			0.0563921			0.0281961	+	0.999602i	$0.491024\pi$
$572$	−0.381966	+	4.08174i	−0.0159708	+	0.170666i
$573$		0			0
$574$	−10.0902	−	7.33094i	−0.421156	−	0.305987i
$575$	7.36068	−	22.6538i	0.306962	−	0.944731i
$576$		0			0
$577$	4.25329	−	3.09020i	0.177067	−	0.128647i	−0.495722	−	0.868481i	$-0.665096\pi$
$577$	4.25329	−	3.09020i	0.177067	−	0.128647i	0.672788	+	0.739835i	$0.265096\pi$
$578$	0.809017	−	0.587785i	0.0336507	−	0.0244486i
$579$		0			0
$580$	0.0623059	−	0.191758i	0.00258711	−	0.00796231i
$581$	0.809017	+	0.587785i	0.0335637	+	0.0243854i
$582$		0			0
$583$	11.0172	+	4.75528i	0.456287	+	0.196944i
$584$	−5.56231			−0.230170
$585$		0			0
$586$	−2.35410	+	7.24518i	−0.0972471	+	0.299296i
$587$	6.55166	+	20.1639i	0.270416	+	0.832255i	0.990396	+	0.138260i	$0.0441510\pi$
$587$	6.55166	+	20.1639i	0.270416	+	0.832255i	−0.719980	+	0.693995i	$0.755849\pi$
$588$		0			0
$589$	35.0344	−	25.4540i	1.44357	−	1.04881i
$590$	−2.27458	−	7.00042i	−0.0936428	−	0.288203i
$591$		0			0
$592$	−7.23607	−	5.25731i	−0.297401	−	0.216074i
$593$	7.88854			0.323944			0.161972	−	0.986795i	$-0.448215\pi$
$593$	7.88854			0.323944			0.161972	+	0.986795i	$0.448215\pi$
$594$		0			0
$595$	−8.94427			−0.366679
$596$	−18.6353	−	13.5393i	−0.763330	−	0.554592i
$597$		0			0
$598$	2.94427	+	9.06154i	0.120400	+	0.370554i
$599$	26.1803	−	19.0211i	1.06970	−	0.777182i	0.0938414	−	0.995587i	$-0.470085\pi$
$599$	26.1803	−	19.0211i	1.06970	−	0.777182i	0.975858	+	0.218405i	$0.0700853\pi$
$600$		0			0
$601$	−6.20820	−	19.1069i	−0.253238	−	0.779386i	−0.994172	−	0.107808i	$-0.965617\pi$
$601$	−6.20820	−	19.1069i	−0.253238	−	0.779386i	0.740934	−	0.671578i	$-0.234383\pi$
$602$	4.61803	−	14.2128i	0.188217	−	0.579272i
$603$		0			0
$604$	−4.79837			−0.195243
$605$	7.29837	−	13.3350i	0.296721	−	0.542146i
$606$		0			0
$607$	−12.1803	−	8.84953i	−0.494385	−	0.359192i	0.312483	−	0.949923i	$-0.398839\pi$
$607$	−12.1803	−	8.84953i	−0.494385	−	0.359192i	−0.806868	+	0.590732i	$0.798839\pi$
$608$	2.38197	−	7.33094i	0.0966015	−	0.297309i
$609$		0			0
$610$	10.8541	−	7.88597i	0.439470	−	0.319293i
$611$	−4.00000	+	2.90617i	−0.161823	+	0.117571i
$612$		0			0
$613$	1.03444	−	3.18368i	0.0417807	−	0.128588i	−0.927990	−	0.372604i	$-0.878465\pi$
$613$	1.03444	−	3.18368i	0.0417807	−	0.128588i	0.969771	+	0.244016i	$0.0784650\pi$
$614$	10.3262	+	7.50245i	0.416733	+	0.302774i
$615$		0			0
$616$	−5.23607	+	1.17557i	−0.210967	+	0.0473651i
$617$	15.1246			0.608894			0.304447	−	0.952529i	$-0.401528\pi$
$617$	15.1246			0.608894			0.304447	+	0.952529i	$0.401528\pi$
$618$		0			0
$619$	1.23607	−	3.80423i	0.0496818	−	0.152905i	−0.923138	−	0.384469i	$-0.874384\pi$
$619$	1.23607	−	3.80423i	0.0496818	−	0.152905i	0.972820	+	0.231565i	$0.0743845\pi$
$620$	2.39919	+	7.38394i	0.0963537	+	0.296546i
$621$		0			0
$622$	6.09017	−	4.42477i	0.244194	−	0.177417i
$623$	5.61803	+	17.2905i	0.225082	+	0.692730i
$624$		0			0
$625$		0			0
$626$	−24.9787			−0.998350
$627$		0			0
$628$	−18.0000			−0.718278
$629$	28.9443	+	21.0292i	1.15408	+	0.838491i
$630$		0			0
$631$	−7.48278	−	23.0296i	−0.297885	−	0.916795i	−0.982237	−	0.187644i	$-0.939915\pi$
$631$	−7.48278	−	23.0296i	−0.297885	−	0.916795i	0.684352	−	0.729151i	$-0.260085\pi$
$632$	0.118034	−	0.0857567i	0.00469514	−	0.00341122i
$633$		0			0
$634$	8.32624	+	25.6255i	0.330677	+	1.01772i
$635$	−1.70820	+	5.25731i	−0.0677880	+	0.208630i
$636$		0			0
$637$	5.41641			0.214606
$638$	−0.0450850	+	0.481784i	−0.00178493	+	0.0190740i
$639$		0			0
$640$	1.11803	+	0.812299i	0.0441942	+	0.0321089i
$641$	6.23607	−	19.1926i	0.246310	−	0.758064i	−0.749108	−	0.662447i	$-0.769518\pi$
$641$	6.23607	−	19.1926i	0.246310	−	0.758064i	0.995418	−	0.0956164i	$-0.0304822\pi$
$642$		0			0
$643$	−4.85410	+	3.52671i	−0.191427	+	0.139080i	−0.679371	−	0.733795i	$-0.737747\pi$
$643$	−4.85410	+	3.52671i	−0.191427	+	0.139080i	0.487944	+	0.872875i	$0.337747\pi$
$644$	−10.0902	+	7.33094i	−0.397608	+	0.288879i
$645$		0			0
$646$	−9.52786	+	29.3238i	−0.374869	+	1.15373i
$647$	−17.1803	−	12.4822i	−0.675429	−	0.490728i	0.196409	−	0.980522i	$-0.437072\pi$
$647$	−17.1803	−	12.4822i	−0.675429	−	0.490728i	−0.871838	+	0.489794i	$0.837072\pi$
$648$		0			0
$649$	9.00658	+	15.1967i	0.353539	+	0.596521i
$650$	3.81966			0.149819
$651$		0			0
$652$	−2.61803	+	8.05748i	−0.102530	+	0.315555i
$653$	1.10081	+	3.38795i	0.0430781	+	0.132581i	0.970282	−	0.241975i	$-0.0777952\pi$
$653$	1.10081	+	3.38795i	0.0430781	+	0.132581i	−0.927204	+	0.374556i	$0.877795\pi$
$654$		0			0
$655$	3.19098	−	2.31838i	0.124682	−	0.0905868i
$656$	−2.38197	−	7.33094i	−0.0930001	−	0.286225i
$657$		0			0
$658$	−5.23607	−	3.80423i	−0.204123	−	0.148304i
$659$	−45.9230			−1.78891			−0.894453	−	0.447162i	$-0.852435\pi$
$659$	−45.9230			−1.78891			−0.894453	+	0.447162i	$0.852435\pi$
$660$		0			0
$661$	−11.5967			−0.451061			−0.225531	−	0.974236i	$-0.572412\pi$
$661$	−11.5967			−0.451061			−0.225531	+	0.974236i	$0.572412\pi$
$662$	−22.9443	−	16.6700i	−0.891754	−	0.647898i
$663$		0			0
$664$	0.190983	+	0.587785i	0.00741158	+	0.0228105i
$665$	−13.9443	+	10.1311i	−0.540736	+	0.392867i
$666$		0			0
$667$	0.347524	+	1.06957i	0.0134562	+	0.0414139i
$668$	6.09017	−	18.7436i	0.235636	−	0.725212i
$669$		0			0
$670$	17.8885			0.691095
$671$	−21.2705	+	24.1724i	−0.821139	+	0.933167i
$672$		0			0
$673$	−6.26393	−	4.55101i	−0.241457	−	0.175429i	0.460475	−	0.887673i	$-0.347679\pi$
$673$	−6.26393	−	4.55101i	−0.241457	−	0.175429i	−0.701932	+	0.712244i	$0.747679\pi$
$674$	−4.90983	+	15.1109i	−0.189120	+	0.582050i
$675$		0			0
$676$	9.28115	−	6.74315i	0.356967	−	0.259352i
$677$	41.1418	−	29.8913i	1.58121	−	1.14882i	0.665916	−	0.746026i	$-0.268041\pi$
$677$	41.1418	−	29.8913i	1.58121	−	1.14882i	0.915293	−	0.402789i	$-0.131959\pi$
$678$		0			0
$679$	3.69098	−	11.3597i	0.141647	−	0.435944i
$680$	−4.47214	−	3.24920i	−0.171499	−	0.124601i
$681$		0			0
$682$	−9.50000	−	16.0292i	−0.363774	−	0.613790i
$683$	14.4508			0.552946			0.276473	−	0.961022i	$-0.410834\pi$
$683$	14.4508			0.552946			0.276473	+	0.961022i	$0.410834\pi$
$684$		0			0
$685$	3.49342	−	10.7516i	0.133477	−	0.410799i
$686$	5.69098	+	17.5150i	0.217283	+	0.668728i
$687$		0			0
$688$	7.47214	−	5.42882i	0.284873	−	0.206972i
$689$	1.38197	+	4.25325i	0.0526487	+	0.162036i
$690$		0			0
$691$	−4.14590	−	3.01217i	−0.157717	−	0.114588i	0.506128	−	0.862459i	$-0.331077\pi$
$691$	−4.14590	−	3.01217i	−0.157717	−	0.114588i	−0.663845	+	0.747870i	$0.731077\pi$
$692$	−1.32624			−0.0504160
$693$		0			0
$694$	18.6738			0.708846
$695$	−2.56231	−	1.86162i	−0.0971938	−	0.0706154i
$696$		0			0
$697$	9.52786	+	29.3238i	0.360894	+	1.11072i
$698$	20.7984	−	15.1109i	0.787230	−	0.571956i
$699$		0			0
$700$	1.54508	+	4.75528i	0.0583987	+	0.179733i
$701$	−4.97871	+	15.3229i	−0.188043	+	0.578738i	−0.999988	−	0.00499706i	$-0.998409\pi$
$701$	−4.97871	+	15.3229i	−0.188043	+	0.578738i	0.811944	+	0.583735i	$0.198409\pi$
$702$		0			0
$703$	68.9443			2.60028
$704$	−3.04508	−	1.31433i	−0.114766	−	0.0495356i
$705$		0			0
$706$	9.09017	+	6.60440i	0.342113	+	0.248560i
$707$	4.54508	−	13.9883i	0.170936	−	0.526085i
$708$		0			0
$709$	−27.9443	+	20.3027i	−1.04947	+	0.762484i	−0.972111	−	0.234519i	$-0.924648\pi$
$709$	−27.9443	+	20.3027i	−1.04947	+	0.762484i	−0.0773577	+	0.997003i	$0.524648\pi$
$710$	−6.70820	+	4.87380i	−0.251754	+	0.182910i
$711$		0			0
$712$	−3.47214	+	10.6861i	−0.130124	+	0.400480i
$713$	−35.0344	−	25.4540i	−1.31205	−	0.953260i
$714$		0			0
$715$	5.52786	−	1.24108i	0.206730	−	0.0464139i
$716$	−1.56231			−0.0583861
$717$		0			0
$718$	1.79837	−	5.53483i	0.0671147	−	0.206558i
$719$	−0.326238	−	1.00406i	−0.0121666	−	0.0374450i	0.944789	−	0.327680i	$-0.106267\pi$
$719$	−0.326238	−	1.00406i	−0.0121666	−	0.0374450i	−0.956956	+	0.290235i	$0.906267\pi$
$720$		0			0
$721$	−4.11803	+	2.99193i	−0.153364	+	0.111425i
$722$	12.4894	+	38.4383i	0.464806	+	1.43052i
$723$		0			0
$724$	4.38197	+	3.18368i	0.162854	+	0.118321i
$725$	0.450850			0.0167441
$726$		0			0
$727$	−31.4164			−1.16517			−0.582585	−	0.812770i	$-0.697959\pi$
$727$	−31.4164			−1.16517			−0.582585	+	0.812770i	$0.697959\pi$
$728$	−1.61803	−	1.17557i	−0.0599683	−	0.0435695i
$729$		0			0
$730$	2.37539	+	7.31069i	0.0879171	+	0.270581i
$731$	−29.8885	+	21.7153i	−1.10547	+	0.803169i
$732$		0			0
$733$	7.18034	+	22.0988i	0.265212	+	0.816238i	0.991645	+	0.129001i	$0.0411769\pi$
$733$	7.18034	+	22.0988i	0.265212	+	0.816238i	−0.726433	+	0.687238i	$0.758823\pi$
$734$	3.10081	−	9.54332i	0.114453	−	0.352250i
$735$		0			0
$736$	−7.70820			−0.284128
$737$	−41.8885	+	9.40456i	−1.54298	+	0.346422i
$738$		0			0
$739$	−27.1246	−	19.7072i	−0.997795	−	0.724940i	−0.0361807	−	0.999345i	$-0.511519\pi$
$739$	−27.1246	−	19.7072i	−0.997795	−	0.724940i	−0.961614	+	0.274405i	$0.911519\pi$
$740$	−3.81966	+	11.7557i	−0.140413	+	0.432148i
$741$		0			0
$742$	−4.73607	+	3.44095i	−0.173867	+	0.126321i
$743$	−20.2705	+	14.7274i	−0.743653	+	0.540295i	−0.893853	−	0.448360i	$-0.852008\pi$
$743$	−20.2705	+	14.7274i	−0.743653	+	0.540295i	0.150200	+	0.988656i	$0.452008\pi$
$744$		0			0
$745$	−9.83688	+	30.2748i	−0.360395	+	1.10918i
$746$		0			0
$747$		0			0
$748$	12.1803	+	5.25731i	0.445357	+	0.192226i
$749$	−16.3262			−0.596548
$750$		0			0
$751$	−5.81966	+	17.9111i	−0.212362	+	0.653584i	0.786968	+	0.616994i	$0.211650\pi$
$751$	−5.81966	+	17.9111i	−0.212362	+	0.653584i	−0.999330	+	0.0365904i	$0.988350\pi$
$752$	−1.23607	−	3.80423i	−0.0450748	−	0.138726i
$753$		0			0
$754$	−0.145898	+	0.106001i	−0.00531329	+	0.00386033i
$755$	2.04915	+	6.30664i	0.0745762	+	0.229522i
$756$		0			0
$757$	44.2148	+	32.1239i	1.60701	+	1.16756i	0.871992	+	0.489520i	$0.162828\pi$
$757$	44.2148	+	32.1239i	1.60701	+	1.16756i	0.735021	+	0.678044i	$0.237172\pi$
$758$	3.81966			0.138736
$759$		0			0
$760$	−10.6525			−0.386406
$761$	43.8328	+	31.8464i	1.58894	+	1.15443i	0.905436	+	0.424483i	$0.139544\pi$
$761$	43.8328	+	31.8464i	1.58894	+	1.15443i	0.683502	+	0.729948i	$0.260456\pi$
$762$		0			0
$763$	−7.47214	−	22.9969i	−0.270509	−	0.832543i
$764$	−16.9443	+	12.3107i	−0.613022	+	0.445387i
$765$		0			0
$766$	−11.6525	−	35.8626i	−0.421021	−	1.29577i
$767$	−2.03444	+	6.26137i	−0.0734594	+	0.226085i
$768$		0			0
$769$	−41.5623			−1.49878			−0.749388	−	0.662132i	$-0.769652\pi$
$769$	−41.5623			−1.49878			−0.749388	+	0.662132i	$0.769652\pi$
$770$	3.78115	+	6.37988i	0.136263	+	0.229915i
$771$		0			0
$772$	1.92705	+	1.40008i	0.0693561	+	0.0503901i
$773$	−12.9894	+	39.9771i	−0.467195	+	1.43788i	0.389007	+	0.921235i	$0.372818\pi$
$773$	−12.9894	+	39.9771i	−0.467195	+	1.43788i	−0.856201	+	0.516642i	$0.827182\pi$
$774$		0			0
$775$	−14.0451	+	10.2044i	−0.504514	+	0.366551i
$776$	5.97214	−	4.33901i	0.214387	−	0.155761i
$777$		0			0
$778$	−0.326238	+	1.00406i	−0.0116962	+	0.0359972i
$779$	48.0689	+	34.9241i	1.72225	+	1.25129i
$780$		0			0
$781$	13.1459	−	14.9394i	0.470397	−	0.534573i
$782$	30.8328			1.10258
$783$		0			0
$784$	−1.35410	+	4.16750i	−0.0483608	+	0.148839i
$785$	7.68692	+	23.6579i	0.274358	+	0.844387i
$786$		0			0
$787$	−16.4164	+	11.9272i	−0.585182	+	0.425159i	−0.840588	−	0.541674i	$-0.817791\pi$
$787$	−16.4164	+	11.9272i	−0.585182	+	0.425159i	0.255407	+	0.966834i	$0.417791\pi$
$788$	−3.86475	−	11.8945i	−0.137676	−	0.423723i
$789$		0			0
$790$	−0.163119	−	0.118513i	−0.00580351	−	0.00421650i
$791$	−17.7082			−0.629631
$792$		0			0
$793$	−12.0000			−0.426132
$794$	10.4721	+	7.60845i	0.371642	+	0.270014i
$795$		0			0
$796$	−0.809017	−	2.48990i	−0.0286748	−	0.0882521i
$797$	37.7254	−	27.4091i	1.33630	−	0.970881i	0.336732	−	0.941601i	$-0.390678\pi$
$797$	37.7254	−	27.4091i	1.33630	−	0.970881i	0.999571	−	0.0292805i	$-0.00932159\pi$
$798$		0			0
$799$	4.94427	+	15.2169i	0.174916	+	0.538335i
$800$	−0.954915	+	2.93893i	−0.0337613	+	0.103907i
$801$		0			0
$802$	−11.7082			−0.413431
$803$	−9.40576	−	15.8702i	−0.331922	−	0.560047i
$804$		0			0
$805$	13.9443	+	10.1311i	0.491471	+	0.357075i
$806$	2.14590	−	6.60440i	0.0755860	−	0.232630i
$807$		0			0
$808$	7.35410	−	5.34307i	0.258716	−	0.187968i
$809$	−2.47214	+	1.79611i	−0.0869157	+	0.0631479i	−0.630394	−	0.776275i	$-0.717107\pi$
$809$	−2.47214	+	1.79611i	−0.0869157	+	0.0631479i	0.543479	+	0.839423i	$0.317107\pi$
$810$		0			0
$811$	6.74265	−	20.7517i	0.236766	−	0.728692i	−0.760116	−	0.649788i	$-0.774858\pi$
$811$	6.74265	−	20.7517i	0.236766	−	0.728692i	0.996882	−	0.0789043i	$-0.0251421\pi$
$812$	−0.190983	−	0.138757i	−0.00670219	−	0.00486943i
$813$		0			0
$814$	2.76393	−	29.5358i	0.0968758	−	1.03523i
$815$	11.7082			0.410120
$816$		0			0
$817$	−22.0000	+	67.7090i	−0.769683	+	2.36884i
$818$	5.24671	+	16.1477i	0.183447	+	0.564592i
$819$		0			0
$820$	−8.61803	+	6.26137i	−0.300955	+	0.218656i
$821$	−13.7705	−	42.3813i	−0.480594	−	1.47912i	−0.838262	−	0.545268i	$-0.816428\pi$
$821$	−13.7705	−	42.3813i	−0.480594	−	1.47912i	0.357668	−	0.933849i	$-0.383572\pi$
$822$		0			0
$823$	−19.2984	−	14.0211i	−0.672699	−	0.488744i	0.198229	−	0.980156i	$-0.436481\pi$
$823$	−19.2984	−	14.0211i	−0.672699	−	0.488744i	−0.870928	+	0.491411i	$0.836481\pi$
$824$	−3.14590			−0.109593
$825$		0			0
$826$	−8.61803			−0.299860
$827$	5.25329	+	3.81674i	0.182675	+	0.132721i	0.675365	−	0.737484i	$-0.263986\pi$
$827$	5.25329	+	3.81674i	0.182675	+	0.132721i	−0.492690	+	0.870205i	$0.663986\pi$
$828$		0			0
$829$	−6.72949	−	20.7112i	−0.233725	−	0.719331i	−0.997288	−	0.0735980i	$-0.976552\pi$
$829$	−6.72949	−	20.7112i	−0.233725	−	0.719331i	0.763563	−	0.645733i	$-0.223448\pi$
$830$	0.690983	−	0.502029i	0.0239844	−	0.0174257i
$831$		0			0
$832$	−0.381966	−	1.17557i	−0.0132423	−	0.0407556i
$833$	5.41641	−	16.6700i	0.187667	−	0.577581i
$834$		0			0
$835$	−27.2361			−0.942543
$836$	24.9443	−	5.60034i	0.862716	−	0.193692i
$837$		0			0
$838$	0.736068	+	0.534785i	0.0254270	+	0.0184738i
$839$	−15.7639	+	48.5164i	−0.544231	+	1.67497i	0.178579	+	0.983926i	$0.442850\pi$
$839$	−15.7639	+	48.5164i	−0.544231	+	1.67497i	−0.722810	+	0.691046i	$0.757150\pi$
$840$		0			0
$841$	23.4443	−	17.0333i	0.808423	−	0.587354i
$842$	−32.0344	+	23.2744i	−1.10398	+	0.802088i
$843$		0			0
$844$	−1.47214	+	4.53077i	−0.0506730	+	0.155955i
$845$	−12.8262	−	9.31881i	−0.441236	−	0.320577i
$846$		0			0
$847$	−12.2082	−	12.9515i	−0.419479	−	0.445019i
$848$	−3.61803			−0.124244
$849$		0			0
$850$	3.81966	−	11.7557i	0.131013	−	0.403217i
$851$	−21.3050	−	65.5699i	−0.730324	−	2.24771i
$852$		0			0
$853$	−18.1803	+	13.2088i	−0.622483	+	0.452260i	−0.853788	−	0.520621i	$-0.825700\pi$
$853$	−18.1803	+	13.2088i	−0.622483	+	0.452260i	0.231305	+	0.972881i	$0.425700\pi$
$854$	−4.85410	−	14.9394i	−0.166104	−	0.511215i
$855$		0			0
$856$	−8.16312	−	5.93085i	−0.279010	−	0.202712i
$857$	2.18034			0.0744790			0.0372395	−	0.999306i	$-0.488144\pi$
$857$	2.18034			0.0744790			0.0372395	+	0.999306i	$0.488144\pi$
$858$		0			0
$859$	41.9574			1.43157			0.715784	−	0.698321i	$-0.246069\pi$
$859$	41.9574			1.43157			0.715784	+	0.698321i	$0.246069\pi$
$860$	−10.3262	−	7.50245i	−0.352122	−	0.255831i
$861$		0			0
$862$	7.43769	+	22.8909i	0.253329	+	0.779666i
$863$	−26.7984	+	19.4702i	−0.912227	+	0.662772i	−0.941577	−	0.336797i	$-0.890656\pi$
$863$	−26.7984	+	19.4702i	−0.912227	+	0.662772i	0.0293499	+	0.999569i	$0.490656\pi$
$864$		0			0
$865$	0.566371	+	1.74311i	0.0192572	+	0.0592676i
$866$	2.97214	−	9.14729i	0.100997	−	0.310838i
$867$		0			0
$868$	9.09017			0.308540
$869$	0.444272	+	0.191758i	0.0150709	+	0.00650494i
$870$		0			0
$871$	−12.9443	−	9.40456i	−0.438600	−	0.318661i
$872$	4.61803	−	14.2128i	0.156386	−	0.481308i
$873$		0			0
$874$	48.0689	−	34.9241i	1.62595	−	1.18132i
$875$	14.6353	−	10.6331i	0.494762	−	0.359466i
$876$		0			0
$877$	7.67376	−	23.6174i	0.259125	−	0.797503i	−0.733864	−	0.679296i	$-0.762285\pi$
$877$	7.67376	−	23.6174i	0.259125	−	0.797503i	0.992989	−	0.118207i	$-0.0377147\pi$
$878$	28.2533	+	20.5272i	0.953502	+	0.692760i
$879$		0			0
$880$	−0.427051	+	4.56352i	−0.0143959	+	0.153836i
$881$	−34.0689			−1.14781			−0.573905	−	0.818922i	$-0.694572\pi$
$881$	−34.0689			−1.14781			−0.573905	+	0.818922i	$0.694572\pi$
$882$		0			0
$883$	3.25735	−	10.0251i	0.109619	−	0.337372i	−0.881168	−	0.472803i	$-0.843242\pi$
$883$	3.25735	−	10.0251i	0.109619	−	0.337372i	0.990787	+	0.135432i	$0.0432421\pi$
$884$	1.52786	+	4.70228i	0.0513876	+	0.158155i
$885$		0			0
$886$	5.54508	−	4.02874i	0.186291	−	0.135348i
$887$	−5.25735	−	16.1805i	−0.176525	−	0.543287i	0.823175	−	0.567788i	$-0.192200\pi$
$887$	−5.25735	−	16.1805i	−0.176525	−	0.543287i	−0.999700	+	0.0245004i	$0.992200\pi$
$888$		0			0
$889$	5.23607	+	3.80423i	0.175612	+	0.127590i
$890$	15.5279			0.520495
$891$		0			0
$892$	14.3262			0.479678
$893$	24.9443	+	18.1231i	0.834728	+	0.606466i
$894$		0			0
$895$	0.667184	+	2.05338i	0.0223015	+	0.0686370i
$896$	1.30902	−	0.951057i	0.0437312	−	0.0317726i
$897$		0			0
$898$	2.61803	+	8.05748i	0.0873649	+	0.268882i
$899$	0.253289	−	0.779543i	0.00844766	−	0.0259992i
$900$		0			0
$901$	14.4721			0.482137
$902$	16.8885	−	19.1926i	0.562327	−	0.639045i
$903$		0			0
$904$	−8.85410	−	6.43288i	−0.294483	−	0.213954i
$905$	2.31308	−	7.11894i	0.0768895	−	0.236641i
$906$		0			0
$907$	−9.47214	+	6.88191i	−0.314517	+	0.228510i	−0.733832	−	0.679331i	$-0.762270\pi$
$907$	−9.47214	+	6.88191i	−0.314517	+	0.228510i	0.419315	+	0.907841i	$0.362270\pi$
$908$	−19.4443	+	14.1271i	−0.645281	+	0.468824i
$909$		0			0
$910$	−0.854102	+	2.62866i	−0.0283132	+	0.0871391i
$911$	−32.7984	−	23.8294i	−1.08666	−	0.789504i	−0.107827	−	0.994170i	$-0.534389\pi$
$911$	−32.7984	−	23.8294i	−1.08666	−	0.789504i	−0.978832	+	0.204666i	$0.934389\pi$
$912$		0			0
$913$	−1.35410	+	1.53884i	−0.0448142	+	0.0509282i
$914$	−16.9098			−0.559327
$915$		0			0
$916$	6.61803	−	20.3682i	0.218666	−	0.672985i
$917$	−1.42705	−	4.39201i	−0.0471254	−	0.145037i
$918$		0			0
$919$	8.64590	−	6.28161i	0.285202	−	0.207211i	−0.435981	−	0.899956i	$-0.643599\pi$
$919$	8.64590	−	6.28161i	0.285202	−	0.207211i	0.721183	+	0.692744i	$0.243599\pi$
$920$	3.29180	+	10.1311i	0.108527	+	0.334013i
$921$		0			0
$922$	17.7984	+	12.9313i	0.586158	+	0.425869i
$923$	7.41641			0.244114
$924$		0			0
$925$	−27.6393			−0.908775
$926$	−28.1074	−	20.4212i	−0.923666	−	0.671083i
$927$		0			0
$928$	−0.0450850	−	0.138757i	−0.00147999	−	0.00455493i
$929$	3.09017	−	2.24514i	0.101385	−	0.0736607i	−0.535938	−	0.844258i	$-0.680042\pi$
$929$	3.09017	−	2.24514i	0.101385	−	0.0736607i	0.637323	+	0.770597i	$0.280042\pi$
$930$		0			0
$931$	−10.4377	−	32.1239i	−0.342082	−	1.05282i
$932$	−0.291796	+	0.898056i	−0.00955810	+	0.0294168i
$933$		0			0
$934$	11.7984			0.386055
$935$	1.70820	−	18.2541i	0.0558642	−	0.596973i
$936$		0			0
$937$	42.4336	+	30.8298i	1.38625	+	1.00717i	0.996265	+	0.0863439i	$0.0275184\pi$
$937$	42.4336	+	30.8298i	1.38625	+	1.00717i	0.389981	+	0.920823i	$0.372482\pi$
$938$	6.47214	−	19.9192i	0.211323	−	0.650384i
$939$		0			0
$940$	−4.47214	+	3.24920i	−0.145865	+	0.105977i
$941$	−27.3262	+	19.8537i	−0.890810	+	0.647211i	−0.936089	−	0.351763i	$-0.885582\pi$
$941$	−27.3262	+	19.8537i	−0.890810	+	0.647211i	0.0452792	+	0.998974i	$0.485582\pi$
$942$		0			0
$943$	18.3607	−	56.5084i	0.597906	−	1.84017i
$944$	−4.30902	−	3.13068i	−0.140247	−	0.101895i
$945$		0			0
$946$	28.1246	+	12.1392i	0.914410	+	0.394680i
$947$	32.9230			1.06985			0.534927	−	0.844899i	$-0.320339\pi$
$947$	32.9230			1.06985			0.534927	+	0.844899i	$0.320339\pi$
$948$		0			0
$949$	2.12461	−	6.53888i	0.0689678	−	0.212261i
$950$	−7.36068	−	22.6538i	−0.238812	−	0.734988i
$951$		0			0
$952$	−5.23607	+	3.80423i	−0.169702	+	0.123296i
$953$	8.18034	+	25.1765i	0.264987	+	0.815547i	0.991696	+	0.128601i	$0.0410488\pi$
$953$	8.18034	+	25.1765i	0.264987	+	0.815547i	−0.726709	+	0.686945i	$0.758951\pi$
$954$		0			0
$955$	23.4164	+	17.0130i	0.757737	+	0.550528i
$956$	16.4721			0.532747
$957$		0			0
$958$	−13.2361			−0.427638
$959$	−10.7082	−	7.77997i	−0.345786	−	0.251228i
$960$		0			0
$961$	0.173762	+	0.534785i	0.00560523	+	0.0172511i
$962$	8.94427	−	6.49839i	0.288375	−	0.209517i
$963$		0			0
$964$	1.97214	+	6.06961i	0.0635182	+	0.195489i
$965$	1.01722	−	3.13068i	0.0327455	−	0.100780i
$966$		0			0
$967$	−17.3820			−0.558966			−0.279483	−	0.960151i	$-0.590163\pi$
$967$	−17.3820			−0.558966			−0.279483	+	0.960151i	$0.590163\pi$
$968$	−1.39919	−	10.9106i	−0.0449716	−	0.350682i
$969$		0			0
$970$	−8.25329	−	5.99637i	−0.264997	−	0.192532i
$971$	4.47214	−	13.7638i	0.143518	−	0.441702i	−0.853300	−	0.521421i	$-0.825402\pi$
$971$	4.47214	−	13.7638i	0.143518	−	0.441702i	0.996817	+	0.0797188i	$0.0254022\pi$
$972$		0			0
$973$	−3.00000	+	2.17963i	−0.0961756	+	0.0698757i
$974$	6.54508	−	4.75528i	0.209718	−	0.152369i
$975$		0			0
$976$	3.00000	−	9.23305i	0.0960277	−	0.295543i
$977$	46.1246	+	33.5115i	1.47566	+	1.07213i	0.978924	+	0.204224i	$0.0654671\pi$
$977$	46.1246	+	33.5115i	1.47566	+	1.07213i	0.496733	+	0.867903i	$0.334533\pi$
$978$		0			0
$979$	−36.3607	+	8.16348i	−1.16209	+	0.260906i
$980$	6.05573			0.193443
$981$		0			0
$982$	−10.2918	+	31.6749i	−0.328424	+	1.01079i
$983$	−9.14590	−	28.1482i	−0.291709	−	0.897788i	−0.984307	−	0.176464i	$-0.943534\pi$
$983$	−9.14590	−	28.1482i	−0.291709	−	0.897788i	0.692598	−	0.721324i	$-0.256466\pi$
$984$		0			0
$985$	−13.9828	+	10.1591i	−0.445528	+	0.323695i
$986$	0.180340	+	0.555029i	0.00574319	+	0.0176757i
$987$		0			0
$988$	7.70820	+	5.60034i	0.245231	+	0.178170i
$989$	71.1935			2.26382
$990$		0			0
$991$	−18.3951			−0.584340			−0.292170	−	0.956366i	$-0.594377\pi$
$991$	−18.3951			−0.584340			−0.292170	+	0.956366i	$0.594377\pi$
$992$	4.54508	+	3.30220i	0.144307	+	0.104845i
$993$		0			0
$994$	3.00000	+	9.23305i	0.0951542	+	0.292855i
$995$	−2.92705	+	2.12663i	−0.0927938	+	0.0674186i
$996$		0			0
$997$	−2.05573	−	6.32688i	−0.0651056	−	0.200374i	0.913212	−	0.407485i	$-0.133594\pi$
$997$	−2.05573	−	6.32688i	−0.0651056	−	0.200374i	−0.978318	+	0.207110i	$0.933594\pi$
$998$	−7.81966	+	24.0664i	−0.247527	+	0.761810i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.2.f.a.37.1		4
3.2	odd	2		66.2.e.b.37.1	yes	4
11.3	even	5	inner	198.2.f.a.91.1		4
11.5	even	5		2178.2.a.v.1.2		2
11.6	odd	10		2178.2.a.o.1.2		2
12.11	even	2		528.2.y.g.433.1		4
33.2	even	10		726.2.e.a.511.1		4
33.5	odd	10		726.2.a.k.1.1		2
33.8	even	10		726.2.e.c.487.1		4
33.14	odd	10		66.2.e.b.25.1	✓	4
33.17	even	10		726.2.a.m.1.1		2
33.20	odd	10		726.2.e.j.511.1		4
33.26	odd	10		726.2.e.j.493.1		4
33.29	even	10		726.2.e.a.493.1		4
33.32	even	2		726.2.e.c.565.1		4
132.47	even	10		528.2.y.g.289.1		4
132.71	even	10		5808.2.a.bz.1.1		2
132.83	odd	10		5808.2.a.by.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.b.25.1	✓	4	33.14	odd	10
66.2.e.b.37.1	yes	4	3.2	odd	2
198.2.f.a.37.1		4	1.1	even	1	trivial
198.2.f.a.91.1		4	11.3	even	5	inner
528.2.y.g.289.1		4	132.47	even	10
528.2.y.g.433.1		4	12.11	even	2
726.2.a.k.1.1		2	33.5	odd	10
726.2.a.m.1.1		2	33.17	even	10
726.2.e.a.493.1		4	33.29	even	10
726.2.e.a.511.1		4	33.2	even	10
726.2.e.c.487.1		4	33.8	even	10
726.2.e.c.565.1		4	33.32	even	2
726.2.e.j.493.1		4	33.26	odd	10
726.2.e.j.511.1		4	33.20	odd	10
2178.2.a.o.1.2		2	11.6	odd	10
2178.2.a.v.1.2		2	11.5	even	5
5808.2.a.by.1.1		2	132.83	odd	10
5808.2.a.bz.1.1		2	132.71	even	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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(1.11803 - 0.812299i) q^{5} +(-0.500000 - 1.53884i) q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(1.11803 - 0.812299i) q^{5} +(-0.500000 - 1.53884i) q^{7} +(0.309017 - 0.951057i) q^{8} -1.38197 q^{10} +(3.23607 - 0.726543i) q^{11} +(1.00000 + 0.726543i) q^{13} +(-0.500000 + 1.53884i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(3.23607 - 2.35114i) q^{17} +(2.38197 - 7.33094i) q^{19} +(1.11803 + 0.812299i) q^{20} +(-3.04508 - 1.31433i) q^{22} -7.70820 q^{23} +(-0.954915 + 2.93893i) q^{25} +(-0.381966 - 1.17557i) q^{26} +(1.30902 - 0.951057i) q^{28} +(-0.0450850 - 0.138757i) q^{29} +(4.54508 + 3.30220i) q^{31} +1.00000 q^{32} -4.00000 q^{34} +(-1.80902 - 1.31433i) q^{35} +(2.76393 + 8.50651i) q^{37} +(-6.23607 + 4.53077i) q^{38} +(-0.427051 - 1.31433i) q^{40} +(-2.38197 + 7.33094i) q^{41} -9.23607 q^{43} +(1.69098 + 2.85317i) q^{44} +(6.23607 + 4.53077i) q^{46} +(-1.23607 + 3.80423i) q^{47} +(3.54508 - 2.57565i) q^{49} +(2.50000 - 1.81636i) q^{50} +(-0.381966 + 1.17557i) q^{52} +(2.92705 + 2.12663i) q^{53} +(3.02786 - 3.44095i) q^{55} -1.61803 q^{56} +(-0.0450850 + 0.138757i) q^{58} +(1.64590 + 5.06555i) q^{59} +(-7.85410 + 5.70634i) q^{61} +(-1.73607 - 5.34307i) q^{62} +(-0.809017 - 0.587785i) q^{64} +1.70820 q^{65} -12.9443 q^{67} +(3.23607 + 2.35114i) q^{68} +(0.690983 + 2.12663i) q^{70} +(4.85410 - 3.52671i) q^{71} +(-1.71885 - 5.29007i) q^{73} +(2.76393 - 8.50651i) q^{74} +7.70820 q^{76} +(-2.73607 - 4.61653i) q^{77} +(0.118034 + 0.0857567i) q^{79} +(-0.427051 + 1.31433i) q^{80} +(6.23607 - 4.53077i) q^{82} +(-0.500000 + 0.363271i) q^{83} +(1.70820 - 5.25731i) q^{85} +(7.47214 + 5.42882i) q^{86} +(0.309017 - 3.30220i) q^{88} -11.2361 q^{89} +(0.618034 - 1.90211i) q^{91} +(-2.38197 - 7.33094i) q^{92} +(3.23607 - 2.35114i) q^{94} +(-3.29180 - 10.1311i) q^{95} +(5.97214 + 4.33901i) q^{97} -4.38197 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - 2 q^{7} - q^{8}+O(q^{10}) \) 4 * q - q^2 - q^4 - 2 * q^7 - q^8	\( 4 q - q^{2} - q^{4} - 2 q^{7} - q^{8} - 10 q^{10} + 4 q^{11} + 4 q^{13} - 2 q^{14} - q^{16} + 4 q^{17} + 14 q^{19} - q^{22} - 4 q^{23} - 15 q^{25} - 6 q^{26} + 3 q^{28} + 11 q^{29} + 7 q^{31} + 4 q^{32} - 16 q^{34} - 5 q^{35} + 20 q^{37} - 16 q^{38} + 5 q^{40} - 14 q^{41} - 28 q^{43} + 9 q^{44} + 16 q^{46} + 4 q^{47} + 3 q^{49} + 10 q^{50} - 6 q^{52} + 5 q^{53} + 30 q^{55} - 2 q^{56} + 11 q^{58} + 20 q^{59} - 18 q^{61} + 2 q^{62} - q^{64} - 20 q^{65} - 16 q^{67} + 4 q^{68} + 5 q^{70} + 6 q^{71} - 27 q^{73} + 20 q^{74} + 4 q^{76} - 2 q^{77} - 4 q^{79} + 5 q^{80} + 16 q^{82} - 2 q^{83} - 20 q^{85} + 12 q^{86} - q^{88} - 36 q^{89} - 2 q^{91} - 14 q^{92} + 4 q^{94} - 40 q^{95} + 6 q^{97} - 22 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 - 2 * q^7 - q^8 - 10 * q^10 + 4 * q^11 + 4 * q^13 - 2 * q^14 - q^16 + 4 * q^17 + 14 * q^19 - q^22 - 4 * q^23 - 15 * q^25 - 6 * q^26 + 3 * q^28 + 11 * q^29 + 7 * q^31 + 4 * q^32 - 16 * q^34 - 5 * q^35 + 20 * q^37 - 16 * q^38 + 5 * q^40 - 14 * q^41 - 28 * q^43 + 9 * q^44 + 16 * q^46 + 4 * q^47 + 3 * q^49 + 10 * q^50 - 6 * q^52 + 5 * q^53 + 30 * q^55 - 2 * q^56 + 11 * q^58 + 20 * q^59 - 18 * q^61 + 2 * q^62 - q^64 - 20 * q^65 - 16 * q^67 + 4 * q^68 + 5 * q^70 + 6 * q^71 - 27 * q^73 + 20 * q^74 + 4 * q^76 - 2 * q^77 - 4 * q^79 + 5 * q^80 + 16 * q^82 - 2 * q^83 - 20 * q^85 + 12 * q^86 - q^88 - 36 * q^89 - 2 * q^91 - 14 * q^92 + 4 * q^94 - 40 * q^95 + 6 * q^97 - 22 * q^98

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