LMFDB - Embedded newform 225.2.h.b.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.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:	$1.79663404548$
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 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	225.91
Dual form			225.2.h.b.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.363271i) q^{2} +(-0.500000 - 1.53884i) q^{4} +(1.80902 - 1.31433i) q^{5} -1.61803 q^{7} +(0.690983 - 2.12663i) q^{8} +O(q^{10})$	\(q+(0.500000 + 0.363271i) q^{2} +(-0.500000 - 1.53884i) q^{4} +(1.80902 - 1.31433i) q^{5} -1.61803 q^{7} +(0.690983 - 2.12663i) q^{8} +1.38197 q^{10} +(-0.618034 - 0.449028i) q^{11} +(3.92705 - 2.85317i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-1.50000 + 1.08981i) q^{16} +(0.236068 - 0.726543i) q^{17} +(-1.80902 + 5.56758i) q^{19} +(-2.92705 - 2.12663i) q^{20} +(-0.145898 - 0.449028i) q^{22} +(6.66312 + 4.84104i) q^{23} +(1.54508 - 4.75528i) q^{25} +3.00000 q^{26} +(0.809017 + 2.48990i) q^{28} +(0.427051 + 1.31433i) q^{29} +(-0.927051 + 2.85317i) q^{31} -5.61803 q^{32} +(0.381966 - 0.277515i) q^{34} +(-2.92705 + 2.12663i) q^{35} +(-3.42705 + 2.48990i) q^{37} +(-2.92705 + 2.12663i) q^{38} +(-1.54508 - 4.75528i) q^{40} +(-4.23607 + 3.07768i) q^{41} +1.85410 q^{43} +(-0.381966 + 1.17557i) q^{44} +(1.57295 + 4.84104i) q^{46} +(0.500000 + 1.53884i) q^{47} -4.38197 q^{49} +(2.50000 - 1.81636i) q^{50} +(-6.35410 - 4.61653i) q^{52} +(-1.69098 - 5.20431i) q^{53} -1.70820 q^{55} +(-1.11803 + 3.44095i) q^{56} +(-0.263932 + 0.812299i) q^{58} +(-3.35410 + 2.43690i) q^{59} +(3.80902 + 2.76741i) q^{61} +(-1.50000 + 1.08981i) q^{62} +(0.190983 + 0.138757i) q^{64} +(3.35410 - 10.3229i) q^{65} +(2.85410 - 8.78402i) q^{67} -1.23607 q^{68} -2.23607 q^{70} +(1.35410 + 4.16750i) q^{71} +(7.28115 + 5.29007i) q^{73} -2.61803 q^{74} +9.47214 q^{76} +(1.00000 + 0.726543i) q^{77} +(0.954915 + 2.93893i) q^{79} +(-1.28115 + 3.94298i) q^{80} -3.23607 q^{82} +(0.545085 - 1.67760i) q^{83} +(-0.527864 - 1.62460i) q^{85} +(0.927051 + 0.673542i) q^{86} +(-1.38197 + 1.00406i) q^{88} +(7.23607 + 5.25731i) q^{89} +(-6.35410 + 4.61653i) q^{91} +(4.11803 - 12.6740i) q^{92} +(-0.309017 + 0.951057i) q^{94} +(4.04508 + 12.4495i) q^{95} +(0.881966 + 2.71441i) q^{97} +(-2.19098 - 1.59184i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 5 * q^5 - 2 * q^7 + 5 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8} + 10 q^{10} + 2 q^{11} + 9 q^{13} - q^{14} - 6 q^{16} - 8 q^{17} - 5 q^{19} - 5 q^{20} - 14 q^{22} + 11 q^{23} - 5 q^{25} + 12 q^{26} + q^{28} - 5 q^{29} + 3 q^{31} - 18 q^{32} + 6 q^{34} - 5 q^{35} - 7 q^{37} - 5 q^{38} + 5 q^{40} - 8 q^{41} - 6 q^{43} - 6 q^{44} + 13 q^{46} + 2 q^{47} - 22 q^{49} + 10 q^{50} - 12 q^{52} - 9 q^{53} + 20 q^{55} - 10 q^{58} + 13 q^{61} - 6 q^{62} + 3 q^{64} - 2 q^{67} + 4 q^{68} - 8 q^{71} + 9 q^{73} - 6 q^{74} + 20 q^{76} + 4 q^{77} + 15 q^{79} + 15 q^{80} - 4 q^{82} - 9 q^{83} - 20 q^{85} - 3 q^{86} - 10 q^{88} + 20 q^{89} - 12 q^{91} + 12 q^{92} + q^{94} + 5 q^{95} + 8 q^{97} - 11 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 5 * q^5 - 2 * q^7 + 5 * q^8 + 10 * q^10 + 2 * q^11 + 9 * q^13 - q^14 - 6 * q^16 - 8 * q^17 - 5 * q^19 - 5 * q^20 - 14 * q^22 + 11 * q^23 - 5 * q^25 + 12 * q^26 + q^28 - 5 * q^29 + 3 * q^31 - 18 * q^32 + 6 * q^34 - 5 * q^35 - 7 * q^37 - 5 * q^38 + 5 * q^40 - 8 * q^41 - 6 * q^43 - 6 * q^44 + 13 * q^46 + 2 * q^47 - 22 * q^49 + 10 * q^50 - 12 * q^52 - 9 * q^53 + 20 * q^55 - 10 * q^58 + 13 * q^61 - 6 * q^62 + 3 * q^64 - 2 * q^67 + 4 * q^68 - 8 * q^71 + 9 * q^73 - 6 * q^74 + 20 * q^76 + 4 * q^77 + 15 * q^79 + 15 * q^80 - 4 * q^82 - 9 * q^83 - 20 * q^85 - 3 * q^86 - 10 * q^88 + 20 * q^89 - 12 * q^91 + 12 * q^92 + q^94 + 5 * q^95 + 8 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.500000	+	0.363271i	0.353553	+	0.256872i	0.750358	−	0.661031i	$-0.229881\pi$
$2$	0.500000	+	0.363271i	0.353553	+	0.256872i	−0.396805	+	0.917903i	$0.629881\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	−	1.53884i	−0.250000	−	0.769421i
$5$	1.80902	−	1.31433i	0.809017	−	0.587785i
$5$	1.80902	−	1.31433i	0.809017	−	0.587785i
$6$		0			0
$7$	−1.61803			−0.611559			−0.305780	−	0.952102i	$-0.598917\pi$
$7$	−1.61803			−0.611559			−0.305780	+	0.952102i	$0.598917\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$		0			0
$10$	1.38197			0.437016
$11$	−0.618034	−	0.449028i	−0.186344	−	0.135387i	0.490702	−	0.871327i	$-0.336740\pi$
$11$	−0.618034	−	0.449028i	−0.186344	−	0.135387i	−0.677046	+	0.735940i	$0.736740\pi$
$12$		0			0
$13$	3.92705	−	2.85317i	1.08917	−	0.791327i	0.109909	−	0.993942i	$-0.464944\pi$
$13$	3.92705	−	2.85317i	1.08917	−	0.791327i	0.979259	+	0.202615i	$0.0649439\pi$
$14$	−0.809017	−	0.587785i	−0.216219	−	0.157092i
$15$		0			0
$16$	−1.50000	+	1.08981i	−0.375000	+	0.272453i
$17$	0.236068	−	0.726543i	0.0572549	−	0.176212i	−0.918339	−	0.395794i	$-0.870469\pi$
$17$	0.236068	−	0.726543i	0.0572549	−	0.176212i	0.975594	+	0.219582i	$0.0704693\pi$
$18$		0			0
$19$	−1.80902	+	5.56758i	−0.415017	+	1.27729i	0.497219	+	0.867625i	$0.334355\pi$
$19$	−1.80902	+	5.56758i	−0.415017	+	1.27729i	−0.912236	+	0.409666i	$0.865645\pi$
$20$	−2.92705	−	2.12663i	−0.654508	−	0.475528i
$21$		0			0
$22$	−0.145898	−	0.449028i	−0.0311056	−	0.0957331i
$23$	6.66312	+	4.84104i	1.38936	+	1.00943i	0.995936	+	0.0900679i	$0.0287084\pi$
$23$	6.66312	+	4.84104i	1.38936	+	1.00943i	0.393421	+	0.919359i	$0.371292\pi$
$24$		0			0
$25$	1.54508	−	4.75528i	0.309017	−	0.951057i
$26$	3.00000			0.588348
$27$		0			0
$28$	0.809017	+	2.48990i	0.152890	+	0.470547i
$29$	0.427051	+	1.31433i	0.0793014	+	0.244065i	0.982846	−	0.184430i	$-0.0590440\pi$
$29$	0.427051	+	1.31433i	0.0793014	+	0.244065i	−0.903544	+	0.428495i	$0.859044\pi$
$30$		0			0
$31$	−0.927051	+	2.85317i	−0.166503	+	0.512444i	−0.999144	−	0.0413693i	$-0.986828\pi$
$31$	−0.927051	+	2.85317i	−0.166503	+	0.512444i	0.832641	+	0.553814i	$0.186828\pi$
$32$	−5.61803			−0.993137
$33$		0			0
$34$	0.381966	−	0.277515i	0.0655066	−	0.0475934i
$35$	−2.92705	+	2.12663i	−0.494762	+	0.359466i
$36$		0			0
$37$	−3.42705	+	2.48990i	−0.563404	+	0.409337i	−0.832703	−	0.553720i	$-0.813208\pi$
$37$	−3.42705	+	2.48990i	−0.563404	+	0.409337i	0.269299	+	0.963057i	$0.413208\pi$
$38$	−2.92705	+	2.12663i	−0.474830	+	0.344984i
$39$		0			0
$40$	−1.54508	−	4.75528i	−0.244299	−	0.751876i
$41$	−4.23607	+	3.07768i	−0.661563	+	0.480653i	−0.867190	−	0.497977i	$-0.834076\pi$
$41$	−4.23607	+	3.07768i	−0.661563	+	0.480653i	0.205628	+	0.978630i	$0.434076\pi$
$42$		0			0
$43$	1.85410			0.282748			0.141374	−	0.989956i	$-0.454848\pi$
$43$	1.85410			0.282748			0.141374	+	0.989956i	$0.454848\pi$
$44$	−0.381966	+	1.17557i	−0.0575835	+	0.177224i
$45$		0			0
$46$	1.57295	+	4.84104i	0.231919	+	0.713772i
$47$	0.500000	+	1.53884i	0.0729325	+	0.224463i	0.980877	−	0.194626i	$-0.0623494\pi$
$47$	0.500000	+	1.53884i	0.0729325	+	0.224463i	−0.907945	+	0.419089i	$0.862349\pi$
$48$		0			0
$49$	−4.38197			−0.625995
$50$	2.50000	−	1.81636i	0.353553	−	0.256872i
$51$		0			0
$52$	−6.35410	−	4.61653i	−0.881155	−	0.640197i
$53$	−1.69098	−	5.20431i	−0.232274	−	0.714867i	−0.997471	−	0.0710707i	$-0.977358\pi$
$53$	−1.69098	−	5.20431i	−0.232274	−	0.714867i	0.765197	−	0.643796i	$-0.222642\pi$
$54$		0			0
$55$	−1.70820			−0.230334
$56$	−1.11803	+	3.44095i	−0.149404	+	0.459817i
$57$		0			0
$58$	−0.263932	+	0.812299i	−0.0346560	+	0.106660i
$59$	−3.35410	+	2.43690i	−0.436667	+	0.317257i	−0.784309	−	0.620370i	$-0.786982\pi$
$59$	−3.35410	+	2.43690i	−0.436667	+	0.317257i	0.347642	+	0.937627i	$0.386982\pi$
$60$		0			0
$61$	3.80902	+	2.76741i	0.487695	+	0.354331i	0.804297	−	0.594227i	$-0.202542\pi$
$61$	3.80902	+	2.76741i	0.487695	+	0.354331i	−0.316602	+	0.948558i	$0.602542\pi$
$62$	−1.50000	+	1.08981i	−0.190500	+	0.138406i
$63$		0			0
$64$	0.190983	+	0.138757i	0.0238729	+	0.0173447i
$65$	3.35410	−	10.3229i	0.416025	−	1.28039i
$66$		0			0
$67$	2.85410	−	8.78402i	0.348684	−	1.07314i	−0.610898	−	0.791709i	$-0.709191\pi$
$67$	2.85410	−	8.78402i	0.348684	−	1.07314i	0.959582	−	0.281430i	$-0.0908086\pi$
$68$	−1.23607			−0.149895
$69$		0			0
$70$	−2.23607			−0.267261
$71$	1.35410	+	4.16750i	0.160702	+	0.494591i	0.998694	−	0.0510922i	$-0.0162702\pi$
$71$	1.35410	+	4.16750i	0.160702	+	0.494591i	−0.837992	+	0.545683i	$0.816270\pi$
$72$		0			0
$73$	7.28115	+	5.29007i	0.852194	+	0.619156i	0.925750	−	0.378136i	$-0.123435\pi$
$73$	7.28115	+	5.29007i	0.852194	+	0.619156i	−0.0735557	+	0.997291i	$0.523435\pi$
$74$	−2.61803			−0.304340
$75$		0			0
$76$	9.47214			1.08653
$77$	1.00000	+	0.726543i	0.113961	+	0.0827972i
$78$		0			0
$79$	0.954915	+	2.93893i	0.107436	+	0.330655i	0.990295	−	0.138985i	$-0.0443839\pi$
$79$	0.954915	+	2.93893i	0.107436	+	0.330655i	−0.882858	+	0.469640i	$0.844384\pi$
$80$	−1.28115	+	3.94298i	−0.143237	+	0.440839i
$81$		0			0
$82$	−3.23607			−0.357364
$83$	0.545085	−	1.67760i	0.0598308	−	0.184140i	−0.916674	−	0.399636i	$-0.869137\pi$
$83$	0.545085	−	1.67760i	0.0598308	−	0.184140i	0.976505	+	0.215495i	$0.0691366\pi$
$84$		0			0
$85$	−0.527864	−	1.62460i	−0.0572549	−	0.176212i
$86$	0.927051	+	0.673542i	0.0999665	+	0.0726299i
$87$		0			0
$88$	−1.38197	+	1.00406i	−0.147318	+	0.107033i
$89$	7.23607	+	5.25731i	0.767022	+	0.557274i	0.901056	−	0.433703i	$-0.142793\pi$
$89$	7.23607	+	5.25731i	0.767022	+	0.557274i	−0.134034	+	0.990977i	$0.542793\pi$
$90$		0			0
$91$	−6.35410	+	4.61653i	−0.666091	+	0.483943i
$92$	4.11803	−	12.6740i	0.429335	−	1.32136i
$93$		0			0
$94$	−0.309017	+	0.951057i	−0.0318727	+	0.0980940i
$95$	4.04508	+	12.4495i	0.415017	+	1.27729i
$96$		0			0
$97$	0.881966	+	2.71441i	0.0895501	+	0.275607i	0.985795	−	0.167953i	$-0.0537155\pi$
$97$	0.881966	+	2.71441i	0.0895501	+	0.275607i	−0.896245	+	0.443559i	$0.853716\pi$
$98$	−2.19098	−	1.59184i	−0.221323	−	0.160800i
$99$		0			0
$100$	−8.09017			−0.809017
$101$	7.47214			0.743505			0.371753	−	0.928332i	$-0.378757\pi$
$101$	7.47214			0.743505			0.371753	+	0.928332i	$0.378757\pi$
$102$		0			0
$103$	−3.57295	−	10.9964i	−0.352053	−	1.08351i	−0.957699	−	0.287773i	$-0.907085\pi$
$103$	−3.57295	−	10.9964i	−0.352053	−	1.08351i	0.605645	−	0.795735i	$-0.292915\pi$
$104$	−3.35410	−	10.3229i	−0.328897	−	1.01224i
$105$		0			0
$106$	1.04508	−	3.21644i	0.101508	−	0.312408i
$107$	−10.4164			−1.00699			−0.503496	−	0.863998i	$-0.667953\pi$
$107$	−10.4164			−1.00699			−0.503496	+	0.863998i	$0.667953\pi$
$108$		0			0
$109$	−8.09017	+	5.87785i	−0.774898	+	0.562996i	−0.903443	−	0.428707i	$-0.858969\pi$
$109$	−8.09017	+	5.87785i	−0.774898	+	0.562996i	0.128546	+	0.991704i	$0.458969\pi$
$110$	−0.854102	−	0.620541i	−0.0814354	−	0.0591663i
$111$		0			0
$112$	2.42705	−	1.76336i	0.229335	−	0.166621i
$113$	8.20820	−	5.96361i	0.772163	−	0.561009i	−0.130454	−	0.991454i	$-0.541643\pi$
$113$	8.20820	−	5.96361i	0.772163	−	0.561009i	0.902617	+	0.430445i	$0.141643\pi$
$114$		0			0
$115$	18.4164			1.71734
$116$	1.80902	−	1.31433i	0.167963	−	0.122032i
$117$		0			0
$118$	−2.56231			−0.235879
$119$	−0.381966	+	1.17557i	−0.0350148	+	0.107764i
$120$		0			0
$121$	−3.21885	−	9.90659i	−0.292622	−	0.900599i
$122$	0.899187	+	2.76741i	0.0814086	+	0.250550i
$123$		0			0
$124$	4.85410			0.435911
$125$	−3.45492	−	10.6331i	−0.309017	−	0.951057i
$126$		0			0
$127$	12.8541	+	9.33905i	1.14062	+	0.828707i	0.987205	−	0.159455i	$-0.0509738\pi$
$127$	12.8541	+	9.33905i	1.14062	+	0.828707i	0.153412	+	0.988162i	$0.450974\pi$
$128$	3.51722	+	10.8249i	0.310881	+	0.956794i
$129$		0			0
$130$	5.42705	−	3.94298i	0.475984	−	0.345823i
$131$	5.50000	−	16.9273i	0.480537	−	1.47894i	−0.357805	−	0.933797i	$-0.616475\pi$
$131$	5.50000	−	16.9273i	0.480537	−	1.47894i	0.838342	−	0.545145i	$-0.183525\pi$
$132$		0			0
$133$	2.92705	−	9.00854i	0.253808	−	0.781139i
$134$	4.61803	−	3.35520i	0.398937	−	0.289845i
$135$		0			0
$136$	−1.38197	−	1.00406i	−0.118503	−	0.0860972i
$137$	4.80902	−	3.49396i	0.410862	−	0.298509i	−0.363089	−	0.931755i	$-0.618278\pi$
$137$	4.80902	−	3.49396i	0.410862	−	0.298509i	0.773951	+	0.633246i	$0.218278\pi$
$138$		0			0
$139$	−4.04508	−	2.93893i	−0.343100	−	0.249276i	0.402869	−	0.915258i	$-0.368013\pi$
$139$	−4.04508	−	2.93893i	−0.343100	−	0.249276i	−0.745968	+	0.665981i	$0.768013\pi$
$140$	4.73607	+	3.44095i	0.400271	+	0.290814i
$141$		0			0
$142$	−0.836881	+	2.57565i	−0.0702295	+	0.216144i
$143$	−3.70820			−0.310096
$144$		0			0
$145$	2.50000	+	1.81636i	0.207614	+	0.150840i
$146$	1.71885	+	5.29007i	0.142253	+	0.437809i
$147$		0			0
$148$	5.54508	+	4.02874i	0.455803	+	0.331160i
$149$	−13.9443			−1.14236			−0.571180	−	0.820825i	$-0.693514\pi$
$149$	−13.9443			−1.14236			−0.571180	+	0.820825i	$0.693514\pi$
$150$		0			0
$151$	−5.56231			−0.452654			−0.226327	−	0.974051i	$-0.572672\pi$
$151$	−5.56231			−0.452654			−0.226327	+	0.974051i	$0.572672\pi$
$152$	10.5902	+	7.69421i	0.858976	+	0.624083i
$153$		0			0
$154$	0.236068	+	0.726543i	0.0190229	+	0.0585465i
$155$	2.07295	+	6.37988i	0.166503	+	0.512444i
$156$		0			0
$157$	−9.18034			−0.732671			−0.366335	−	0.930483i	$-0.619388\pi$
$157$	−9.18034			−0.732671			−0.366335	+	0.930483i	$0.619388\pi$
$158$	−0.590170	+	1.81636i	−0.0469514	+	0.144502i
$159$		0			0
$160$	−10.1631	+	7.38394i	−0.803465	+	0.583752i
$161$	−10.7812	−	7.83297i	−0.849674	−	0.617324i
$162$		0			0
$163$	−8.89919	+	6.46564i	−0.697038	+	0.506428i	−0.878966	−	0.476884i	$-0.841766\pi$
$163$	−8.89919	+	6.46564i	−0.697038	+	0.506428i	0.181928	+	0.983312i	$0.441766\pi$
$164$	6.85410	+	4.97980i	0.535215	+	0.388857i
$165$		0			0
$166$	0.881966	−	0.640786i	0.0684538	−	0.0497346i
$167$	1.71885	−	5.29007i	0.133008	−	0.409358i	−0.862267	−	0.506455i	$-0.830956\pi$
$167$	1.71885	−	5.29007i	0.133008	−	0.409358i	0.995275	+	0.0970971i	$0.0309557\pi$
$168$		0			0
$169$	3.26393	−	10.0453i	0.251072	−	0.772719i
$170$	0.326238	−	1.00406i	0.0250213	−	0.0770077i
$171$		0			0
$172$	−0.927051	−	2.85317i	−0.0706870	−	0.217552i
$173$	−13.6631	−	9.92684i	−1.03879	−	0.754723i	−0.0687392	−	0.997635i	$-0.521898\pi$
$173$	−13.6631	−	9.92684i	−1.03879	−	0.754723i	−0.970049	+	0.242911i	$0.921898\pi$
$174$		0			0
$175$	−2.50000	+	7.69421i	−0.188982	+	0.581628i
$176$	1.41641			0.106766
$177$		0			0
$178$	1.70820	+	5.25731i	0.128035	+	0.394052i
$179$	2.92705	+	9.00854i	0.218778	+	0.673330i	0.998864	+	0.0476570i	$0.0151754\pi$
$179$	2.92705	+	9.00854i	0.218778	+	0.673330i	−0.780086	+	0.625673i	$0.784825\pi$
$180$		0			0
$181$	4.23607	−	13.0373i	0.314864	−	0.969053i	−0.660946	−	0.750434i	$-0.729845\pi$
$181$	4.23607	−	13.0373i	0.314864	−	0.969053i	0.975810	−	0.218619i	$-0.0701553\pi$
$182$	−4.85410			−0.359810
$183$		0			0
$184$	14.8992	−	10.8249i	1.09838	−	0.798022i
$185$	−2.92705	+	9.00854i	−0.215201	+	0.662321i
$186$		0			0
$187$	−0.472136	+	0.343027i	−0.0345260	+	0.0250846i
$188$	2.11803	−	1.53884i	0.154474	−	0.112232i
$189$		0			0
$190$	−2.50000	+	7.69421i	−0.181369	+	0.558197i
$191$	−19.5623	+	14.2128i	−1.41548	+	1.02841i	−0.422982	+	0.906138i	$0.639016\pi$
$191$	−19.5623	+	14.2128i	−1.41548	+	1.02841i	−0.992497	+	0.122267i	$0.960984\pi$
$192$		0			0
$193$	−5.70820			−0.410886			−0.205443	−	0.978669i	$-0.565863\pi$
$193$	−5.70820			−0.410886			−0.205443	+	0.978669i	$0.565863\pi$
$194$	−0.545085	+	1.67760i	−0.0391348	+	0.120445i
$195$		0			0
$196$	2.19098	+	6.74315i	0.156499	+	0.481654i
$197$	3.00000	+	9.23305i	0.213741	+	0.657828i	0.999241	+	0.0389652i	$0.0124062\pi$
$197$	3.00000	+	9.23305i	0.213741	+	0.657828i	−0.785499	+	0.618862i	$0.787594\pi$
$198$		0			0
$199$	2.56231			0.181637			0.0908185	−	0.995867i	$-0.471052\pi$
$199$	2.56231			0.181637			0.0908185	+	0.995867i	$0.471052\pi$
$200$	−9.04508	−	6.57164i	−0.639584	−	0.464685i
$201$		0			0
$202$	3.73607	+	2.71441i	0.262869	+	0.190985i
$203$	−0.690983	−	2.12663i	−0.0484975	−	0.149260i
$204$		0			0
$205$	−3.61803	+	11.1352i	−0.252694	+	0.777714i
$206$	2.20820	−	6.79615i	0.153853	−	0.473510i
$207$		0			0
$208$	−2.78115	+	8.55951i	−0.192838	+	0.593495i
$209$	3.61803	−	2.62866i	0.250265	−	0.181828i
$210$		0			0
$211$	−10.6631	−	7.74721i	−0.734079	−	0.533340i	0.156772	−	0.987635i	$-0.449891\pi$
$211$	−10.6631	−	7.74721i	−0.734079	−	0.533340i	−0.890851	+	0.454295i	$0.849891\pi$
$212$	−7.16312	+	5.20431i	−0.491965	+	0.357434i
$213$		0			0
$214$	−5.20820	−	3.78398i	−0.356025	−	0.258668i
$215$	3.35410	−	2.43690i	0.228748	−	0.166195i
$216$		0			0
$217$	1.50000	−	4.61653i	0.101827	−	0.313390i
$218$	−6.18034			−0.418585
$219$		0			0
$220$	0.854102	+	2.62866i	0.0575835	+	0.177224i
$221$	−1.14590	−	3.52671i	−0.0770814	−	0.237232i
$222$		0			0
$223$	−17.9443	−	13.0373i	−1.20164	−	0.873041i	−0.207193	−	0.978300i	$-0.566433\pi$
$223$	−17.9443	−	13.0373i	−1.20164	−	0.873041i	−0.994445	+	0.105260i	$0.966433\pi$
$224$	9.09017			0.607363
$225$		0			0
$226$	6.27051			0.417108
$227$	15.5623	+	11.3067i	1.03291	+	0.750451i	0.968888	−	0.247498i	$-0.0796084\pi$
$227$	15.5623	+	11.3067i	1.03291	+	0.750451i	0.0640182	+	0.997949i	$0.479608\pi$
$228$		0			0
$229$	2.56231	+	7.88597i	0.169322	+	0.521119i	0.999329	−	0.0366339i	$-0.0116635\pi$
$229$	2.56231	+	7.88597i	0.169322	+	0.521119i	−0.830007	+	0.557753i	$0.811664\pi$
$230$	9.20820	+	6.69015i	0.607171	+	0.441136i
$231$		0			0
$232$	3.09017			0.202880
$233$	−4.61803	+	14.2128i	−0.302537	+	0.931115i	0.678047	+	0.735018i	$0.262826\pi$
$233$	−4.61803	+	14.2128i	−0.302537	+	0.931115i	−0.980585	+	0.196096i	$0.937174\pi$
$234$		0			0
$235$	2.92705	+	2.12663i	0.190940	+	0.138726i
$236$	5.42705	+	3.94298i	0.353271	+	0.256666i
$237$		0			0
$238$	−0.618034	+	0.449028i	−0.0400612	+	0.0291062i
$239$	−23.8435	−	17.3233i	−1.54231	−	1.12055i	−0.948869	−	0.315669i	$-0.897771\pi$
$239$	−23.8435	−	17.3233i	−1.54231	−	1.12055i	−0.593436	−	0.804881i	$-0.702229\pi$
$240$		0			0
$241$	−9.28115	+	6.74315i	−0.597852	+	0.434365i	−0.845116	−	0.534584i	$-0.820468\pi$
$241$	−9.28115	+	6.74315i	−0.597852	+	0.434365i	0.247264	+	0.968948i	$0.420468\pi$
$242$	1.98936	−	6.12261i	0.127881	−	0.393576i
$243$		0			0
$244$	2.35410	−	7.24518i	0.150706	−	0.463825i
$245$	−7.92705	+	5.75934i	−0.506441	+	0.367951i
$246$		0			0
$247$	8.78115	+	27.0256i	0.558731	+	1.71960i
$248$	5.42705	+	3.94298i	0.344618	+	0.250380i
$249$		0			0
$250$	2.13525	−	6.57164i	0.135045	−	0.415627i
$251$	6.81966			0.430453			0.215227	−	0.976564i	$-0.430951\pi$
$251$	6.81966			0.430453			0.215227	+	0.976564i	$0.430951\pi$
$252$		0			0
$253$	−1.94427	−	5.98385i	−0.122235	−	0.376202i
$254$	3.03444	+	9.33905i	0.190398	+	0.585984i
$255$		0			0
$256$	−2.02786	+	6.24112i	−0.126742	+	0.390070i
$257$	−16.1459			−1.00715			−0.503577	−	0.863951i	$-0.667983\pi$
$257$	−16.1459			−1.00715			−0.503577	+	0.863951i	$0.667983\pi$
$258$		0			0
$259$	5.54508	−	4.02874i	0.344555	−	0.250334i
$260$	−17.5623			−1.08917
$261$		0			0
$262$	8.89919	−	6.46564i	0.549794	−	0.399448i
$263$	−17.8713	+	12.9843i	−1.10199	+	0.800645i	−0.981384	−	0.192055i	$-0.938485\pi$
$263$	−17.8713	+	12.9843i	−1.10199	+	0.800645i	−0.120609	+	0.992700i	$0.538485\pi$
$264$		0			0
$265$	−9.89919	−	7.19218i	−0.608102	−	0.441812i
$266$	4.73607	−	3.44095i	0.290387	−	0.210978i
$267$		0			0
$268$	−14.9443			−0.912867
$269$	5.32624	−	16.3925i	0.324746	−	0.999467i	−0.646808	−	0.762652i	$-0.723897\pi$
$269$	5.32624	−	16.3925i	0.324746	−	0.999467i	0.971555	−	0.236814i	$-0.0761033\pi$
$270$		0			0
$271$	−2.47214	−	7.60845i	−0.150172	−	0.462181i	0.847468	−	0.530846i	$-0.178126\pi$
$271$	−2.47214	−	7.60845i	−0.150172	−	0.462181i	−0.997640	+	0.0686657i	$0.978126\pi$
$272$	0.437694	+	1.34708i	0.0265391	+	0.0816790i
$273$		0			0
$274$	3.67376			0.221940
$275$	−3.09017	+	2.24514i	−0.186344	+	0.135387i
$276$		0			0
$277$	9.13525	+	6.63715i	0.548884	+	0.398788i	0.827374	−	0.561651i	$-0.189834\pi$
$277$	9.13525	+	6.63715i	0.548884	+	0.398788i	−0.278490	+	0.960439i	$0.589834\pi$
$278$	−0.954915	−	2.93893i	−0.0572720	−	0.176265i
$279$		0			0
$280$	2.50000	+	7.69421i	0.149404	+	0.459817i
$281$	0.336881	−	1.03681i	0.0200966	−	0.0618511i	−0.940505	−	0.339779i	$-0.889648\pi$
$281$	0.336881	−	1.03681i	0.0200966	−	0.0618511i	0.960602	+	0.277928i	$0.0896477\pi$
$282$		0			0
$283$	−7.15248	+	22.0131i	−0.425171	+	1.30854i	0.477660	+	0.878545i	$0.341485\pi$
$283$	−7.15248	+	22.0131i	−0.425171	+	1.30854i	−0.902831	+	0.429996i	$0.858515\pi$
$284$	5.73607	−	4.16750i	0.340373	−	0.247295i
$285$		0			0
$286$	−1.85410	−	1.34708i	−0.109635	−	0.0796547i
$287$	6.85410	−	4.97980i	0.404585	−	0.293948i
$288$		0			0
$289$	13.2812	+	9.64932i	0.781244	+	0.567607i
$290$	0.590170	+	1.81636i	0.0346560	+	0.106660i
$291$		0			0
$292$	4.50000	−	13.8496i	0.263343	−	0.810485i
$293$	28.4721			1.66336			0.831680	−	0.555255i	$-0.187379\pi$
$293$	28.4721			1.66336			0.831680	+	0.555255i	$0.187379\pi$
$294$		0			0
$295$	−2.86475	+	8.81678i	−0.166792	+	0.513333i
$296$	2.92705	+	9.00854i	0.170131	+	0.523611i
$297$		0			0
$298$	−6.97214	−	5.06555i	−0.403885	−	0.293440i
$299$	39.9787			2.31203
$300$		0			0
$301$	−3.00000			−0.172917
$302$	−2.78115	−	2.02063i	−0.160037	−	0.116274i
$303$		0			0
$304$	−3.35410	−	10.3229i	−0.192371	−	0.592057i
$305$	10.5279			0.602824
$306$		0			0
$307$	4.76393			0.271892			0.135946	−	0.990716i	$-0.456593\pi$
$307$	4.76393			0.271892			0.135946	+	0.990716i	$0.456593\pi$
$308$	0.618034	−	1.90211i	0.0352158	−	0.108383i
$309$		0			0
$310$	−1.28115	+	3.94298i	−0.0727646	+	0.223946i
$311$	−23.8713	−	17.3435i	−1.35362	−	0.983461i	−0.998822	−	0.0485178i	$-0.984550\pi$
$311$	−23.8713	−	17.3435i	−1.35362	−	0.983461i	−0.354796	−	0.934944i	$-0.615450\pi$
$312$		0			0
$313$	17.1803	−	12.4822i	0.971090	−	0.705538i	0.0153904	−	0.999882i	$-0.495101\pi$
$313$	17.1803	−	12.4822i	0.971090	−	0.705538i	0.955700	+	0.294343i	$0.0951009\pi$
$314$	−4.59017	−	3.33495i	−0.259038	−	0.188202i
$315$		0			0
$316$	4.04508	−	2.93893i	0.227554	−	0.165328i
$317$	7.30902	−	22.4948i	0.410515	−	1.26344i	−0.505686	−	0.862718i	$-0.668761\pi$
$317$	7.30902	−	22.4948i	0.410515	−	1.26344i	0.916201	−	0.400719i	$-0.131239\pi$
$318$		0			0
$319$	0.326238	−	1.00406i	0.0182658	−	0.0562164i
$320$	0.527864			0.0295085
$321$		0			0
$322$	−2.54508	−	7.83297i	−0.141832	−	0.436514i
$323$	3.61803	+	2.62866i	0.201313	+	0.146262i
$324$		0			0
$325$	−7.50000	−	23.0826i	−0.416025	−	1.28039i
$326$	−6.79837			−0.376527
$327$		0			0
$328$	3.61803	+	11.1352i	0.199773	+	0.614837i
$329$	−0.809017	−	2.48990i	−0.0446026	−	0.137273i
$330$		0			0
$331$	5.29180	−	16.2865i	0.290863	−	0.895186i	−0.693716	−	0.720248i	$-0.744028\pi$
$331$	5.29180	−	16.2865i	0.290863	−	0.895186i	0.984580	−	0.174937i	$-0.0559722\pi$
$332$	−2.85410			−0.156639
$333$		0			0
$334$	2.78115	−	2.02063i	0.152178	−	0.110564i
$335$	−6.38197	−	19.6417i	−0.348684	−	1.07314i
$336$		0			0
$337$	−0.927051	+	0.673542i	−0.0504997	+	0.0366902i	−0.612749	−	0.790278i	$-0.709936\pi$
$337$	−0.927051	+	0.673542i	−0.0504997	+	0.0366902i	0.562249	+	0.826968i	$0.309936\pi$
$338$	5.28115	−	3.83698i	0.287257	−	0.208704i
$339$		0			0
$340$	−2.23607	+	1.62460i	−0.121268	+	0.0881062i
$341$	1.85410	−	1.34708i	0.100405	−	0.0729487i
$342$		0			0
$343$	18.4164			0.994393
$344$	1.28115	−	3.94298i	0.0690751	−	0.212591i
$345$		0			0
$346$	−3.22542	−	9.92684i	−0.173400	−	0.533670i
$347$	9.60739	+	29.5685i	0.515752	+	1.58732i	0.781910	+	0.623391i	$0.214246\pi$
$347$	9.60739	+	29.5685i	0.515752	+	1.58732i	−0.266158	+	0.963929i	$0.585754\pi$
$348$		0			0
$349$	8.29180			0.443850			0.221925	−	0.975064i	$-0.428766\pi$
$349$	8.29180			0.443850			0.221925	+	0.975064i	$0.428766\pi$
$350$	−4.04508	+	2.93893i	−0.216219	+	0.157092i
$351$		0			0
$352$	3.47214	+	2.52265i	0.185065	+	0.134458i
$353$	−7.44427	−	22.9111i	−0.396219	−	1.21944i	−0.928008	−	0.372559i	$-0.878480\pi$
$353$	−7.44427	−	22.9111i	−0.396219	−	1.21944i	0.531790	−	0.846876i	$-0.321520\pi$
$354$		0			0
$355$	7.92705	+	5.75934i	0.420724	+	0.305674i
$356$	4.47214	−	13.7638i	0.237023	−	0.729481i
$357$		0			0
$358$	−1.80902	+	5.56758i	−0.0956095	+	0.294256i
$359$	−23.2533	+	16.8945i	−1.22726	+	0.891658i	−0.996682	−	0.0813956i	$-0.974062\pi$
$359$	−23.2533	+	16.8945i	−1.22726	+	0.891658i	−0.230580	+	0.973053i	$0.574062\pi$
$360$		0			0
$361$	−12.3541	−	8.97578i	−0.650216	−	0.472409i
$362$	6.85410	−	4.97980i	0.360244	−	0.261732i
$363$		0			0
$364$	10.2812	+	7.46969i	0.538879	+	0.391518i
$365$	20.1246			1.05337
$366$		0			0
$367$	−1.68034	+	5.17155i	−0.0877130	+	0.269953i	−0.985286	−	0.170913i	$-0.945328\pi$
$367$	−1.68034	+	5.17155i	−0.0877130	+	0.269953i	0.897573	+	0.440866i	$0.145328\pi$
$368$	−15.2705			−0.796030
$369$		0			0
$370$	−4.73607	+	3.44095i	−0.246216	+	0.178887i
$371$	2.73607	+	8.42075i	0.142050	+	0.437184i
$372$		0			0
$373$	−4.26393	−	3.09793i	−0.220778	−	0.160405i	0.471899	−	0.881653i	$-0.343569\pi$
$373$	−4.26393	−	3.09793i	−0.220778	−	0.160405i	−0.692677	+	0.721248i	$0.743569\pi$
$374$	−0.360680			−0.0186503
$375$		0			0
$376$	3.61803			0.186586
$377$	5.42705	+	3.94298i	0.279507	+	0.203074i
$378$		0			0
$379$	−10.6910	−	32.9035i	−0.549159	−	1.69014i	−0.710891	−	0.703303i	$-0.751708\pi$
$379$	−10.6910	−	32.9035i	−0.549159	−	1.69014i	0.161732	−	0.986835i	$-0.448292\pi$
$380$	17.1353	−	12.4495i	0.879020	−	0.638645i
$381$		0			0
$382$	−14.9443			−0.764615
$383$	3.51064	−	10.8046i	0.179385	−	0.552092i	−0.820421	−	0.571760i	$-0.806261\pi$
$383$	3.51064	−	10.8046i	0.179385	−	0.552092i	0.999807	+	0.0196680i	$0.00626093\pi$
$384$		0			0
$385$	2.76393			0.140863
$386$	−2.85410	−	2.07363i	−0.145270	−	0.105545i
$387$		0			0
$388$	3.73607	−	2.71441i	0.189670	−	0.137803i
$389$	12.1353	+	8.81678i	0.615282	+	0.447028i	0.851270	−	0.524727i	$-0.175833\pi$
$389$	12.1353	+	8.81678i	0.615282	+	0.447028i	−0.235988	+	0.971756i	$0.575833\pi$
$390$		0			0
$391$	5.09017	−	3.69822i	0.257421	−	0.187027i
$392$	−3.02786	+	9.31881i	−0.152930	+	0.470671i
$393$		0			0
$394$	−1.85410	+	5.70634i	−0.0934083	+	0.287481i
$395$	5.59017	+	4.06150i	0.281272	+	0.204356i
$396$		0			0
$397$	−0.0106431	−	0.0327561i	−0.000534163	−	0.00164398i	0.950789	−	0.309839i	$-0.100275\pi$
$397$	−0.0106431	−	0.0327561i	−0.000534163	−	0.00164398i	−0.951323	+	0.308195i	$0.900275\pi$
$398$	1.28115	+	0.930812i	0.0642184	+	0.0466574i
$399$		0			0
$400$	2.86475	+	8.81678i	0.143237	+	0.440839i
$401$	22.5967			1.12843			0.564214	−	0.825629i	$-0.309179\pi$
$401$	22.5967			1.12843			0.564214	+	0.825629i	$0.309179\pi$
$402$		0			0
$403$	4.50000	+	13.8496i	0.224161	+	0.689897i
$404$	−3.73607	−	11.4984i	−0.185876	−	0.572069i
$405$		0			0
$406$	0.427051	−	1.31433i	0.0211942	−	0.0652290i
$407$	3.23607			0.160406
$408$		0			0
$409$	−22.9894	+	16.7027i	−1.13675	+	0.825898i	−0.986663	−	0.162775i	$-0.947955\pi$
$409$	−22.9894	+	16.7027i	−1.13675	+	0.825898i	−0.150087	+	0.988673i	$0.547955\pi$
$410$	−5.85410	+	4.25325i	−0.289113	+	0.210053i
$411$		0			0
$412$	−15.1353	+	10.9964i	−0.745660	+	0.541754i
$413$	5.42705	−	3.94298i	0.267048	−	0.194022i
$414$		0			0
$415$	−1.21885	−	3.75123i	−0.0598308	−	0.184140i
$416$	−22.0623	+	16.0292i	−1.08169	+	0.785896i
$417$		0			0
$418$	2.76393			0.135188
$419$	0.163119	−	0.502029i	0.00796888	−	0.0245257i	−0.946993	−	0.321254i	$-0.895896\pi$
$419$	0.163119	−	0.502029i	0.00796888	−	0.0245257i	0.954962	+	0.296728i	$0.0958956\pi$
$420$		0			0
$421$	9.88854	+	30.4338i	0.481938	+	1.48325i	0.836367	+	0.548170i	$0.184675\pi$
$421$	9.88854	+	30.4338i	0.481938	+	1.48325i	−0.354429	+	0.935083i	$0.615325\pi$
$422$	−2.51722	−	7.74721i	−0.122536	−	0.377128i
$423$		0			0
$424$	−12.2361			−0.594236
$425$	−3.09017	−	2.24514i	−0.149895	−	0.108905i
$426$		0			0
$427$	−6.16312	−	4.47777i	−0.298254	−	0.216694i
$428$	5.20820	+	16.0292i	0.251748	+	0.774801i
$429$		0			0
$430$	2.56231			0.123565
$431$	−7.36475	+	22.6664i	−0.354747	+	1.09180i	0.601409	+	0.798942i	$0.294606\pi$
$431$	−7.36475	+	22.6664i	−0.354747	+	1.09180i	−0.956156	+	0.292858i	$0.905394\pi$
$432$		0			0
$433$	6.22542	−	19.1599i	0.299175	−	0.920765i	−0.682612	−	0.730781i	$-0.739156\pi$
$433$	6.22542	−	19.1599i	0.299175	−	0.920765i	0.981787	−	0.189985i	$-0.0608438\pi$
$434$	2.42705	−	1.76336i	0.116502	−	0.0846438i
$435$		0			0
$436$	13.0902	+	9.51057i	0.626905	+	0.455473i
$437$	−39.0066	+	28.3399i	−1.86594	+	1.35568i
$438$		0			0
$439$	−4.83688	−	3.51420i	−0.230852	−	0.167724i	0.466346	−	0.884602i	$-0.345570\pi$
$439$	−4.83688	−	3.51420i	−0.230852	−	0.167724i	−0.697198	+	0.716879i	$0.745570\pi$
$440$	−1.18034	+	3.63271i	−0.0562705	+	0.173183i
$441$		0			0
$442$	0.708204	−	2.17963i	0.0336858	−	0.103674i
$443$	−12.0557			−0.572785			−0.286392	−	0.958112i	$-0.592456\pi$
$443$	−12.0557			−0.572785			−0.286392	+	0.958112i	$0.592456\pi$
$444$		0			0
$445$	20.0000			0.948091
$446$	−4.23607	−	13.0373i	−0.200584	−	0.617333i
$447$		0			0
$448$	−0.309017	−	0.224514i	−0.0145997	−	0.0106073i
$449$	−20.3262			−0.959254			−0.479627	−	0.877472i	$-0.659228\pi$
$449$	−20.3262			−0.959254			−0.479627	+	0.877472i	$0.659228\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	−13.2812	−	9.64932i	−0.624693	−	0.453866i
$453$		0			0
$454$	3.67376	+	11.3067i	0.172418	+	0.530649i
$455$	−5.42705	+	16.7027i	−0.254424	+	0.783037i
$456$		0			0
$457$	5.41641			0.253369			0.126684	−	0.991943i	$-0.459566\pi$
$457$	5.41641			0.253369			0.126684	+	0.991943i	$0.459566\pi$
$458$	−1.58359	+	4.87380i	−0.0739964	+	0.227738i
$459$		0			0
$460$	−9.20820	−	28.3399i	−0.429335	−	1.32136i
$461$	18.7533	+	13.6251i	0.873428	+	0.634582i	0.931505	−	0.363730i	$-0.118497\pi$
$461$	18.7533	+	13.6251i	0.873428	+	0.634582i	−0.0580768	+	0.998312i	$0.518497\pi$
$462$		0			0
$463$	−13.0451	+	9.47781i	−0.606257	+	0.440471i	−0.848094	−	0.529846i	$-0.822250\pi$
$463$	−13.0451	+	9.47781i	−0.606257	+	0.440471i	0.241838	+	0.970317i	$0.422250\pi$
$464$	−2.07295	−	1.50609i	−0.0962342	−	0.0699183i
$465$		0			0
$466$	−7.47214	+	5.42882i	−0.346140	+	0.251485i
$467$	8.79180	−	27.0584i	0.406836	−	1.25211i	−0.512517	−	0.858677i	$-0.671287\pi$
$467$	8.79180	−	27.0584i	0.406836	−	1.25211i	0.919353	−	0.393435i	$-0.128713\pi$
$468$		0			0
$469$	−4.61803	+	14.2128i	−0.213241	+	0.656288i
$470$	0.690983	+	2.12663i	0.0318727	+	0.0980940i
$471$		0			0
$472$	2.86475	+	8.81678i	0.131861	+	0.405825i
$473$	−1.14590	−	0.832544i	−0.0526884	−	0.0382804i
$474$		0			0
$475$	23.6803	+	17.2048i	1.08653	+	0.789409i
$476$	2.00000			0.0916698
$477$		0			0
$478$	−5.62868	−	17.3233i	−0.257450	−	0.792349i
$479$	1.28115	+	3.94298i	0.0585374	+	0.180160i	0.976050	−	0.217548i	$-0.0698059\pi$
$479$	1.28115	+	3.94298i	0.0585374	+	0.180160i	−0.917512	+	0.397708i	$0.869806\pi$
$480$		0			0
$481$	−6.35410	+	19.5559i	−0.289722	+	0.891673i
$482$	−7.09017			−0.322948
$483$		0			0
$484$	−13.6353	+	9.90659i	−0.619784	+	0.450300i
$485$	5.16312	+	3.75123i	0.234445	+	0.170334i
$486$		0			0
$487$	7.75329	−	5.63309i	0.351335	−	0.255260i	−0.398094	−	0.917345i	$-0.630328\pi$
$487$	7.75329	−	5.63309i	0.351335	−	0.255260i	0.749429	+	0.662085i	$0.230328\pi$
$488$	8.51722	−	6.18812i	0.385556	−	0.280123i
$489$		0			0
$490$	−6.05573			−0.273570
$491$	30.1353	−	21.8945i	1.35999	−	0.988087i	0.361539	−	0.932357i	$-0.382251\pi$
$491$	30.1353	−	21.8945i	1.35999	−	0.988087i	0.998446	−	0.0557300i	$-0.0177486\pi$
$492$		0			0
$493$	1.05573			0.0475476
$494$	−5.42705	+	16.7027i	−0.244175	+	0.751492i
$495$		0			0
$496$	−1.71885	−	5.29007i	−0.0771785	−	0.237531i
$497$	−2.19098	−	6.74315i	−0.0982790	−	0.302472i
$498$		0			0
$499$	−12.5623			−0.562366			−0.281183	−	0.959654i	$-0.590727\pi$
$499$	−12.5623			−0.562366			−0.281183	+	0.959654i	$0.590727\pi$
$500$	−14.6353	+	10.6331i	−0.654508	+	0.475528i
$501$		0			0
$502$	3.40983	+	2.47739i	0.152188	+	0.110571i
$503$	3.27051	+	10.0656i	0.145825	+	0.448803i	0.997116	−	0.0758907i	$-0.0241800\pi$
$503$	3.27051	+	10.0656i	0.145825	+	0.448803i	−0.851291	+	0.524693i	$0.824180\pi$
$504$		0			0
$505$	13.5172	−	9.82084i	0.601508	−	0.437021i
$506$	1.20163	−	3.69822i	0.0534188	−	0.164406i
$507$		0			0
$508$	7.94427	−	24.4500i	0.352470	−	1.08479i
$509$	−3.78115	+	2.74717i	−0.167597	+	0.121766i	−0.668422	−	0.743782i	$-0.733030\pi$
$509$	−3.78115	+	2.74717i	−0.167597	+	0.121766i	0.500825	+	0.865548i	$0.333030\pi$
$510$		0			0
$511$	−11.7812	−	8.55951i	−0.521168	−	0.378650i
$512$	15.1353	−	10.9964i	0.668890	−	0.485977i
$513$		0			0
$514$	−8.07295	−	5.86534i	−0.356083	−	0.258709i
$515$	−20.9164	−	15.1967i	−0.921687	−	0.669645i
$516$		0			0
$517$	0.381966	−	1.17557i	0.0167988	−	0.0517015i
$518$	4.23607			0.186122
$519$		0			0
$520$	−19.6353	−	14.2658i	−0.861063	−	0.625599i
$521$	4.74671	+	14.6089i	0.207957	+	0.640026i	0.999579	+	0.0290150i	$0.00923706\pi$
$521$	4.74671	+	14.6089i	0.207957	+	0.640026i	−0.791622	+	0.611011i	$0.790763\pi$
$522$		0			0
$523$	16.0623	+	11.6699i	0.702356	+	0.510291i	0.880699	−	0.473677i	$-0.157074\pi$
$523$	16.0623	+	11.6699i	0.702356	+	0.510291i	−0.178343	+	0.983968i	$0.557074\pi$
$524$	−28.7984			−1.25806
$525$		0			0
$526$	−13.6525			−0.595276
$527$	1.85410	+	1.34708i	0.0807660	+	0.0586799i
$528$		0			0
$529$	13.8541	+	42.6385i	0.602352	+	1.85385i
$530$	−2.33688	−	7.19218i	−0.101508	−	0.312408i
$531$		0			0
$532$	−15.3262			−0.664477
$533$	−7.85410	+	24.1724i	−0.340199	+	1.04702i
$534$		0			0
$535$	−18.8435	+	13.6906i	−0.814674	+	0.591895i
$536$	−16.7082	−	12.1392i	−0.721684	−	0.524334i
$537$		0			0
$538$	8.61803	−	6.26137i	0.371550	−	0.269947i
$539$	2.70820	+	1.96763i	0.116651	+	0.0847516i
$540$		0			0
$541$	10.6180	−	7.71445i	0.456505	−	0.331670i	−0.335654	−	0.941985i	$-0.608957\pi$
$541$	10.6180	−	7.71445i	0.456505	−	0.331670i	0.792159	+	0.610315i	$0.208957\pi$
$542$	1.52786	−	4.70228i	0.0656274	−	0.201980i
$543$		0			0
$544$	−1.32624	+	4.08174i	−0.0568620	+	0.175003i
$545$	−6.90983	+	21.2663i	−0.295985	+	0.910947i
$546$		0			0
$547$	−10.7254	−	33.0095i	−0.458586	−	1.41138i	−0.866873	−	0.498529i	$-0.833874\pi$
$547$	−10.7254	−	33.0095i	−0.458586	−	1.41138i	0.408287	−	0.912854i	$-0.366126\pi$
$548$	−7.78115	−	5.65334i	−0.332394	−	0.241499i
$549$		0			0
$550$	−2.36068			−0.100660
$551$	−8.09017			−0.344653
$552$		0			0
$553$	−1.54508	−	4.75528i	−0.0657037	−	0.202215i
$554$	2.15654	+	6.63715i	0.0916227	+	0.281986i
$555$		0			0
$556$	−2.50000	+	7.69421i	−0.106024	+	0.326307i
$557$	−9.23607			−0.391345			−0.195672	−	0.980669i	$-0.562689\pi$
$557$	−9.23607			−0.391345			−0.195672	+	0.980669i	$0.562689\pi$
$558$		0			0
$559$	7.28115	−	5.29007i	0.307960	−	0.223746i
$560$	2.07295	−	6.37988i	0.0875981	−	0.269599i
$561$		0			0
$562$	0.545085	−	0.396027i	0.0229930	−	0.0167054i
$563$	7.78115	−	5.65334i	0.327936	−	0.238260i	−0.411618	−	0.911356i	$-0.635036\pi$
$563$	7.78115	−	5.65334i	0.327936	−	0.238260i	0.739555	+	0.673097i	$0.235036\pi$
$564$		0			0
$565$	7.01064	−	21.5765i	0.294940	−	0.907732i
$566$	−11.5729	+	8.40824i	−0.486447	+	0.353425i
$567$		0			0
$568$	9.79837			0.411131
$569$	−9.10739	+	28.0297i	−0.381802	+	1.17506i	0.556972	+	0.830531i	$0.311963\pi$
$569$	−9.10739	+	28.0297i	−0.381802	+	1.17506i	−0.938774	+	0.344534i	$0.888037\pi$
$570$		0			0
$571$	9.92705	+	30.5523i	0.415434	+	1.27857i	0.911862	+	0.410497i	$0.134645\pi$
$571$	9.92705	+	30.5523i	0.415434	+	1.27857i	−0.496428	+	0.868078i	$0.665355\pi$
$572$	1.85410	+	5.70634i	0.0775239	+	0.238594i
$573$		0			0
$574$	5.23607			0.218549
$575$	33.3156	−	24.2052i	1.38936	−	1.00943i
$576$		0			0
$577$	−30.5623	−	22.2048i	−1.27233	−	0.924399i	−0.273033	−	0.962005i	$-0.588027\pi$
$577$	−30.5623	−	22.2048i	−1.27233	−	0.924399i	−0.999293	+	0.0376062i	$0.988027\pi$
$578$	3.13525	+	9.64932i	0.130409	+	0.401359i
$579$		0			0
$580$	1.54508	−	4.75528i	0.0641562	−	0.197452i
$581$	−0.881966	+	2.71441i	−0.0365901	+	0.112613i
$582$		0			0
$583$	−1.29180	+	3.97574i	−0.0535007	+	0.164658i
$584$	16.2812	−	11.8290i	0.673719	−	0.489485i
$585$		0			0
$586$	14.2361	+	10.3431i	0.588087	+	0.427270i
$587$	15.1353	−	10.9964i	0.624699	−	0.453870i	−0.229861	−	0.973224i	$-0.573827\pi$
$587$	15.1353	−	10.9964i	0.624699	−	0.453870i	0.854560	+	0.519353i	$0.173827\pi$
$588$		0			0
$589$	−14.2082	−	10.3229i	−0.585439	−	0.425346i
$590$	−4.63525	+	3.36771i	−0.190830	+	0.138646i
$591$		0			0
$592$	2.42705	−	7.46969i	0.0997512	−	0.307003i
$593$	22.0902			0.907135			0.453567	−	0.891222i	$-0.350151\pi$
$593$	22.0902			0.907135			0.453567	+	0.891222i	$0.350151\pi$
$594$		0			0
$595$	0.854102	+	2.62866i	0.0350148	+	0.107764i
$596$	6.97214	+	21.4580i	0.285590	+	0.878955i
$597$		0			0
$598$	19.9894	+	14.5231i	0.817426	+	0.593894i
$599$	0.527864			0.0215679			0.0107840	−	0.999942i	$-0.496567\pi$
$599$	0.527864			0.0215679			0.0107840	+	0.999942i	$0.496567\pi$
$600$		0			0
$601$	36.2705			1.47950			0.739752	−	0.672879i	$-0.234943\pi$
$601$	36.2705			1.47950			0.739752	+	0.672879i	$0.234943\pi$
$602$	−1.50000	−	1.08981i	−0.0611354	−	0.0444175i
$603$		0			0
$604$	2.78115	+	8.55951i	0.113164	+	0.348281i
$605$	−18.8435	−	13.6906i	−0.766096	−	0.556601i
$606$		0			0
$607$	−15.4377			−0.626597			−0.313298	−	0.949655i	$-0.601434\pi$
$607$	−15.4377			−0.626597			−0.313298	+	0.949655i	$0.601434\pi$
$608$	10.1631	−	31.2789i	0.412169	−	1.26853i
$609$		0			0
$610$	5.26393	+	3.82447i	0.213130	+	0.154848i
$611$	6.35410	+	4.61653i	0.257059	+	0.186765i
$612$		0			0
$613$	−25.8713	+	18.7966i	−1.04493	+	0.759188i	−0.971242	−	0.238093i	$-0.923478\pi$
$613$	−25.8713	+	18.7966i	−1.04493	+	0.759188i	−0.0736905	+	0.997281i	$0.523478\pi$
$614$	2.38197	+	1.73060i	0.0961283	+	0.0698413i
$615$		0			0
$616$	2.23607	−	1.62460i	0.0900937	−	0.0654569i
$617$	−3.01722	+	9.28605i	−0.121469	+	0.373842i	−0.993241	−	0.116069i	$-0.962971\pi$
$617$	−3.01722	+	9.28605i	−0.121469	+	0.373842i	0.871772	+	0.489911i	$0.162971\pi$
$618$		0			0
$619$	12.1976	−	37.5402i	0.490261	−	1.50887i	−0.333952	−	0.942590i	$-0.608382\pi$
$619$	12.1976	−	37.5402i	0.490261	−	1.50887i	0.824213	−	0.566279i	$-0.191618\pi$
$620$	8.78115	−	6.37988i	0.352660	−	0.256222i
$621$		0			0
$622$	−5.63525	−	17.3435i	−0.225953	−	0.695412i
$623$	−11.7082	−	8.50651i	−0.469079	−	0.340806i
$624$		0			0
$625$	−20.2254	−	14.6946i	−0.809017	−	0.587785i
$626$	13.1246			0.524565
$627$		0			0
$628$	4.59017	+	14.1271i	0.183168	+	0.563732i
$629$	1.00000	+	3.07768i	0.0398726	+	0.122715i
$630$		0			0
$631$	−1.78115	+	5.48183i	−0.0709066	+	0.218228i	−0.980230	−	0.197862i	$-0.936600\pi$
$631$	−1.78115	+	5.48183i	−0.0709066	+	0.218228i	0.909323	+	0.416090i	$0.136600\pi$
$632$	6.90983			0.274858
$633$		0			0
$634$	11.8262	−	8.59226i	0.469680	−	0.341242i
$635$	35.5279			1.40988
$636$		0			0
$637$	−17.2082	+	12.5025i	−0.681814	+	0.495367i
$638$	0.527864	−	0.383516i	0.0208983	−	0.0151835i
$639$		0			0
$640$	20.5902	+	14.9596i	0.813898	+	0.591331i
$641$	8.16312	−	5.93085i	0.322424	−	0.234255i	−0.414785	−	0.909919i	$-0.636143\pi$
$641$	8.16312	−	5.93085i	0.322424	−	0.234255i	0.737209	+	0.675665i	$0.236143\pi$
$642$		0			0
$643$	22.8328			0.900438			0.450219	−	0.892918i	$-0.351346\pi$
$643$	22.8328			0.900438			0.450219	+	0.892918i	$0.351346\pi$
$644$	−6.66312	+	20.5070i	−0.262564	+	0.808088i
$645$		0			0
$646$	0.854102	+	2.62866i	0.0336042	+	0.103423i
$647$	−9.43769	−	29.0462i	−0.371034	−	1.14193i	−0.946116	−	0.323829i	$-0.895030\pi$
$647$	−9.43769	−	29.0462i	−0.371034	−	1.14193i	0.575082	−	0.818096i	$-0.304970\pi$
$648$		0			0
$649$	3.16718			0.124323
$650$	4.63525	−	14.2658i	0.181810	−	0.559553i
$651$		0			0
$652$	14.3992	+	10.4616i	0.563916	+	0.409709i
$653$	−2.44427	−	7.52270i	−0.0956518	−	0.294386i	0.891771	−	0.452487i	$-0.149463\pi$
$653$	−2.44427	−	7.52270i	−0.0956518	−	0.294386i	−0.987423	+	0.158101i	$0.949463\pi$
$654$		0			0
$655$	−12.2984	−	37.8505i	−0.480537	−	1.47894i
$656$	3.00000	−	9.23305i	0.117130	−	0.360490i
$657$		0			0
$658$	0.500000	−	1.53884i	0.0194920	−	0.0599903i
$659$	19.7984	−	14.3844i	0.771235	−	0.560335i	−0.131101	−	0.991369i	$-0.541851\pi$
$659$	19.7984	−	14.3844i	0.771235	−	0.560335i	0.902336	+	0.431034i	$0.141851\pi$
$660$		0			0
$661$	32.9164	+	23.9152i	1.28030	+	0.930192i	0.999562	−	0.0295922i	$-0.00942086\pi$
$661$	32.9164	+	23.9152i	1.28030	+	0.930192i	0.280738	+	0.959784i	$0.409421\pi$
$662$	8.56231	−	6.22088i	0.332783	−	0.241781i
$663$		0			0
$664$	−3.19098	−	2.31838i	−0.123834	−	0.0899708i
$665$	−6.54508	−	20.1437i	−0.253808	−	0.781139i
$666$		0			0
$667$	−3.51722	+	10.8249i	−0.136187	+	0.419142i
$668$	−9.00000			−0.348220
$669$		0			0
$670$	3.94427	−	12.1392i	0.152381	−	0.468979i
$671$	−1.11146	−	3.42071i	−0.0429073	−	0.132055i
$672$		0			0
$673$	8.23607	+	5.98385i	0.317477	+	0.230661i	0.735098	−	0.677961i	$-0.237136\pi$
$673$	8.23607	+	5.98385i	0.317477	+	0.230661i	−0.417621	+	0.908621i	$0.637136\pi$
$674$	−0.708204			−0.0272790
$675$		0			0
$676$	−17.0902			−0.657314
$677$	6.78115	+	4.92680i	0.260621	+	0.189352i	0.710421	−	0.703777i	$-0.248505\pi$
$677$	6.78115	+	4.92680i	0.260621	+	0.189352i	−0.449800	+	0.893129i	$0.648505\pi$
$678$		0			0
$679$	−1.42705	−	4.39201i	−0.0547652	−	0.168550i
$680$	−3.81966			−0.146477
$681$		0			0
$682$	1.41641			0.0542371
$683$	1.39919	−	4.30625i	0.0535384	−	0.164774i	−0.920712	−	0.390242i	$-0.872391\pi$
$683$	1.39919	−	4.30625i	0.0535384	−	0.164774i	0.974251	+	0.225468i	$0.0723912\pi$
$684$		0			0
$685$	4.10739	−	12.6412i	0.156935	−	0.482997i
$686$	9.20820	+	6.69015i	0.351571	+	0.255431i
$687$		0			0
$688$	−2.78115	+	2.02063i	−0.106030	+	0.0770356i
$689$	−21.4894	−	15.6129i	−0.818679	−	0.594805i
$690$		0			0
$691$	−2.20820	+	1.60435i	−0.0840040	+	0.0610325i	−0.628995	−	0.777410i	$-0.716533\pi$
$691$	−2.20820	+	1.60435i	−0.0840040	+	0.0610325i	0.544991	+	0.838442i	$0.316533\pi$
$692$	−8.44427	+	25.9888i	−0.321003	+	0.987946i
$693$		0			0
$694$	−5.93769	+	18.2743i	−0.225392	+	0.693685i
$695$	−11.1803			−0.424094
$696$		0			0
$697$	1.23607	+	3.80423i	0.0468194	+	0.144095i
$698$	4.14590	+	3.01217i	0.156925	+	0.114012i
$699$		0			0
$700$	13.0902			0.494762
$701$	−35.0132			−1.32243			−0.661214	−	0.750197i	$-0.729959\pi$
$701$	−35.0132			−1.32243			−0.661214	+	0.750197i	$0.729959\pi$
$702$		0			0
$703$	−7.66312	−	23.5847i	−0.289020	−	0.889512i
$704$	−0.0557281	−	0.171513i	−0.00210033	−	0.00646416i
$705$		0			0
$706$	4.60081	−	14.1598i	0.173154	−	0.532913i
$707$	−12.0902			−0.454698
$708$		0			0
$709$	−27.1353	+	19.7149i	−1.01909	+	0.740409i	−0.966095	−	0.258186i	$-0.916875\pi$
$709$	−27.1353	+	19.7149i	−1.01909	+	0.740409i	−0.0529906	+	0.998595i	$0.516875\pi$
$710$	1.87132	+	5.75934i	0.0702295	+	0.216144i
$711$		0			0
$712$	16.1803	−	11.7557i	0.606384	−	0.440564i
$713$	−19.9894	+	14.5231i	−0.748607	+	0.543895i
$714$		0			0
$715$	−6.70820	+	4.87380i	−0.250873	+	0.182270i
$716$	12.3992	−	9.00854i	0.463379	−	0.336665i
$717$		0			0
$718$	−17.7639			−0.662944
$719$	11.3435	−	34.9116i	0.423040	−	1.30198i	−0.481819	−	0.876271i	$-0.660024\pi$
$719$	11.3435	−	34.9116i	0.423040	−	1.30198i	0.904859	−	0.425712i	$-0.139976\pi$
$720$		0			0
$721$	5.78115	+	17.7926i	0.215301	+	0.662630i
$722$	−2.91641	−	8.97578i	−0.108537	−	0.334044i
$723$		0			0
$724$	−22.1803			−0.824326
$725$	6.90983			0.256625
$726$		0			0
$727$	−3.59017	−	2.60841i	−0.133152	−	0.0967406i	0.519216	−	0.854643i	$-0.326224\pi$
$727$	−3.59017	−	2.60841i	−0.133152	−	0.0967406i	−0.652368	+	0.757903i	$0.726224\pi$
$728$	5.42705	+	16.7027i	0.201140	+	0.619045i
$729$		0			0
$730$	10.0623	+	7.31069i	0.372423	+	0.270581i
$731$	0.437694	−	1.34708i	0.0161887	−	0.0498237i
$732$		0			0
$733$	8.33688	−	25.6583i	0.307930	−	0.947710i	−0.670638	−	0.741785i	$-0.733980\pi$
$733$	8.33688	−	25.6583i	0.307930	−	0.947710i	0.978568	−	0.205925i	$-0.0660204\pi$
$734$	−2.71885	+	1.97536i	−0.100354	+	0.0729118i
$735$		0			0
$736$	−37.4336	−	27.1971i	−1.37982	−	1.00250i
$737$	−5.70820	+	4.14725i	−0.210264	+	0.152766i
$738$		0			0
$739$	25.0623	+	18.2088i	0.921932	+	0.669823i	0.944004	−	0.329934i	$-0.107026\pi$
$739$	25.0623	+	18.2088i	0.921932	+	0.669823i	−0.0220723	+	0.999756i	$0.507026\pi$
$740$	15.3262			0.563404
$741$		0			0
$742$	−1.69098	+	5.20431i	−0.0620779	+	0.191056i
$743$	16.3607			0.600215			0.300108	−	0.953905i	$-0.402977\pi$
$743$	16.3607			0.600215			0.300108	+	0.953905i	$0.402977\pi$
$744$		0			0
$745$	−25.2254	+	18.3273i	−0.924188	+	0.671462i
$746$	−1.00658	−	3.09793i	−0.0368534	−	0.113423i
$747$		0			0
$748$	0.763932	+	0.555029i	0.0279321	+	0.0202939i
$749$	16.8541			0.615835
$750$		0			0
$751$	−40.8885			−1.49204			−0.746022	−	0.665921i	$-0.768039\pi$
$751$	−40.8885			−1.49204			−0.746022	+	0.665921i	$0.768039\pi$
$752$	−2.42705	−	1.76336i	−0.0885054	−	0.0643030i
$753$		0			0
$754$	1.28115	+	3.94298i	0.0466568	+	0.143595i
$755$	−10.0623	+	7.31069i	−0.366205	+	0.266063i
$756$		0			0
$757$	3.58359			0.130248			0.0651239	−	0.997877i	$-0.479256\pi$
$757$	3.58359			0.130248			0.0651239	+	0.997877i	$0.479256\pi$
$758$	6.60739	−	20.3355i	0.239991	−	0.738617i
$759$		0			0
$760$	29.2705			1.06175
$761$	30.2984	+	22.0131i	1.09832	+	0.797973i	0.980784	−	0.195096i	$-0.0625020\pi$
$761$	30.2984	+	22.0131i	1.09832	+	0.797973i	0.117531	+	0.993069i	$0.462502\pi$
$762$		0			0
$763$	13.0902	−	9.51057i	0.473896	−	0.344306i
$764$	31.6525	+	22.9969i	1.14515	+	0.831998i
$765$		0			0
$766$	5.68034	−	4.12701i	0.205239	−	0.149115i
$767$	−6.21885	+	19.1396i	−0.224550	+	0.691092i
$768$		0			0
$769$	−4.14590	+	12.7598i	−0.149505	+	0.460129i	−0.997563	−	0.0697749i	$-0.977772\pi$
$769$	−4.14590	+	12.7598i	−0.149505	+	0.460129i	0.848058	+	0.529904i	$0.177772\pi$
$770$	1.38197	+	1.00406i	0.0498026	+	0.0361837i
$771$		0			0
$772$	2.85410	+	8.78402i	0.102721	+	0.316144i
$773$	26.8262	+	19.4904i	0.964873	+	0.701021i	0.954277	−	0.298923i	$-0.0966273\pi$
$773$	26.8262	+	19.4904i	0.964873	+	0.701021i	0.0105954	+	0.999944i	$0.496627\pi$
$774$		0			0
$775$	12.1353	+	8.81678i	0.435911	+	0.316708i
$776$	6.38197			0.229099
$777$		0			0
$778$	2.86475	+	8.81678i	0.102706	+	0.316097i
$779$	−9.47214	−	29.1522i	−0.339374	−	1.04449i
$780$		0			0
$781$	1.03444	−	3.18368i	0.0370152	−	0.113921i
$782$	3.88854			0.139054
$783$		0			0
$784$	6.57295	−	4.77553i	0.234748	−	0.170555i
$785$	−16.6074	+	12.0660i	−0.592743	+	0.430653i
$786$		0			0
$787$	27.6525	−	20.0907i	0.985704	−	0.716156i	0.0267281	−	0.999643i	$-0.491491\pi$
$787$	27.6525	−	20.0907i	0.985704	−	0.716156i	0.958976	+	0.283487i	$0.0914912\pi$
$788$	12.7082	−	9.23305i	0.452711	−	0.328914i
$789$		0			0
$790$	1.31966	+	4.06150i	0.0469514	+	0.144502i
$791$	−13.2812	+	9.64932i	−0.472223	+	0.343090i
$792$		0			0
$793$	22.8541			0.811573
$794$	0.00657781	−	0.0202444i	0.000233438	−	0.000718447i
$795$		0			0
$796$	−1.28115	−	3.94298i	−0.0454093	−	0.139755i
$797$	−4.39919	−	13.5393i	−0.155827	−	0.479587i	0.842417	−	0.538827i	$-0.181132\pi$
$797$	−4.39919	−	13.5393i	−0.155827	−	0.479587i	−0.998244	+	0.0592400i	$0.981132\pi$
$798$		0			0
$799$	1.23607			0.0437289
$800$	−8.68034	+	26.7153i	−0.306896	+	0.944530i
$801$		0			0
$802$	11.2984	+	8.20875i	0.398959	+	0.289861i
$803$	−2.12461	−	6.53888i	−0.0749759	−	0.230752i
$804$		0			0
$805$	−29.7984			−1.05025
$806$	−2.78115	+	8.55951i	−0.0979619	+	0.301496i
$807$		0			0
$808$	5.16312	−	15.8904i	0.181638	−	0.559024i
$809$	−12.9271	+	9.39205i	−0.454491	+	0.330207i	−0.791366	−	0.611342i	$-0.790630\pi$
$809$	−12.9271	+	9.39205i	−0.454491	+	0.330207i	0.336875	+	0.941549i	$0.390630\pi$
$810$		0			0
$811$	1.04508	+	0.759299i	0.0366979	+	0.0266626i	0.605983	−	0.795478i	$-0.292780\pi$
$811$	1.04508	+	0.759299i	0.0366979	+	0.0266626i	−0.569285	+	0.822140i	$0.692780\pi$
$812$	−2.92705	+	2.12663i	−0.102719	+	0.0746300i
$813$		0			0
$814$	1.61803	+	1.17557i	0.0567121	+	0.0412037i
$815$	−7.60081	+	23.3929i	−0.266245	+	0.819417i
$816$		0			0
$817$	−3.35410	+	10.3229i	−0.117345	+	0.361151i
$818$	−17.5623			−0.614052
$819$		0			0
$820$	18.9443			0.661563
$821$	−6.08359	−	18.7234i	−0.212319	−	0.653450i	−0.999333	−	0.0365154i	$-0.988374\pi$
$821$	−6.08359	−	18.7234i	−0.212319	−	0.653450i	0.787014	−	0.616935i	$-0.211626\pi$
$822$		0			0
$823$	−27.7426	−	20.1562i	−0.967048	−	0.702601i	−0.0122710	−	0.999925i	$-0.503906\pi$
$823$	−27.7426	−	20.1562i	−0.967048	−	0.702601i	−0.954777	+	0.297323i	$0.903906\pi$
$824$	−25.8541			−0.900670
$825$		0			0
$826$	4.14590			0.144254
$827$	−24.2984	−	17.6538i	−0.844937	−	0.613883i	0.0788082	−	0.996890i	$-0.474889\pi$
$827$	−24.2984	−	17.6538i	−0.844937	−	0.613883i	−0.923745	+	0.383007i	$0.874889\pi$
$828$		0			0
$829$	−9.00658	−	27.7194i	−0.312811	−	0.962734i	−0.976646	−	0.214855i	$-0.931072\pi$
$829$	−9.00658	−	27.7194i	−0.312811	−	0.962734i	0.663835	−	0.747879i	$-0.268928\pi$
$830$	0.753289	−	2.31838i	0.0261470	−	0.0804723i
$831$		0			0
$832$	1.14590			0.0397269
$833$	−1.03444	+	3.18368i	−0.0358413	+	0.110308i
$834$		0			0
$835$	−3.84346	−	11.8290i	−0.133008	−	0.409358i
$836$	−5.85410	−	4.25325i	−0.202468	−	0.147102i
$837$		0			0
$838$	0.263932	−	0.191758i	0.00911738	−	0.00662416i
$839$	3.35410	+	2.43690i	0.115796	+	0.0841311i	0.644176	−	0.764877i	$-0.277200\pi$
$839$	3.35410	+	2.43690i	0.115796	+	0.0841311i	−0.528380	+	0.849008i	$0.677200\pi$
$840$		0			0
$841$	21.9164	−	15.9232i	0.755738	−	0.549076i
$842$	−6.11146	+	18.8091i	−0.210615	+	0.648205i
$843$		0			0
$844$	−6.59017	+	20.2825i	−0.226843	+	0.698151i
$845$	−7.29837	−	22.4621i	−0.251072	−	0.772719i
$846$		0			0
$847$	5.20820	+	16.0292i	0.178956	+	0.550770i
$848$	8.20820	+	5.96361i	0.281871	+	0.204791i
$849$		0			0
$850$	−0.729490	−	2.24514i	−0.0250213	−	0.0770077i
$851$	−34.8885			−1.19596
$852$		0			0
$853$	14.6180	+	44.9897i	0.500512	+	1.54042i	0.808187	+	0.588926i	$0.200449\pi$
$853$	14.6180	+	44.9897i	0.500512	+	1.54042i	−0.307675	+	0.951491i	$0.599551\pi$
$854$	−1.45492	−	4.47777i	−0.0497862	−	0.153226i
$855$		0			0
$856$	−7.19756	+	22.1518i	−0.246008	+	0.757133i
$857$	40.6869			1.38984			0.694919	−	0.719088i	$-0.255440\pi$
$857$	40.6869			1.38984			0.694919	+	0.719088i	$0.255440\pi$
$858$		0			0
$859$	22.9894	−	16.7027i	0.784387	−	0.569890i	−0.121906	−	0.992542i	$-0.538901\pi$
$859$	22.9894	−	16.7027i	0.784387	−	0.569890i	0.906292	+	0.422651i	$0.138901\pi$
$860$	−5.42705	−	3.94298i	−0.185061	−	0.134455i
$861$		0			0
$862$	−11.9164	+	8.65778i	−0.405874	+	0.294885i
$863$	−33.6246	+	24.4297i	−1.14460	+	0.831597i	−0.987753	−	0.156027i	$-0.950131\pi$
$863$	−33.6246	+	24.4297i	−1.14460	+	0.831597i	−0.156842	+	0.987624i	$0.550131\pi$
$864$		0			0
$865$	−37.7639			−1.28401
$866$	10.0729	−	7.31843i	0.342293	−	0.248690i
$867$		0			0
$868$	−7.85410			−0.266586
$869$	0.729490	−	2.24514i	0.0247463	−	0.0761612i
$870$		0			0
$871$	−13.8541	−	42.6385i	−0.469428	−	1.44475i
$872$	6.90983	+	21.2663i	0.233996	+	0.720167i
$873$		0			0
$874$	−29.7984			−1.00795
$875$	5.59017	+	17.2048i	0.188982	+	0.581628i
$876$		0			0
$877$	−24.7082	−	17.9516i	−0.834337	−	0.606181i	0.0864462	−	0.996257i	$-0.472449\pi$
$877$	−24.7082	−	17.9516i	−0.834337	−	0.606181i	−0.920783	+	0.390075i	$0.872449\pi$
$878$	−1.14183	−	3.51420i	−0.0385350	−	0.118598i
$879$		0			0
$880$	2.56231	−	1.86162i	0.0863753	−	0.0627553i
$881$	−1.34752	+	4.14725i	−0.0453992	+	0.139725i	−0.971187	−	0.238320i	$-0.923403\pi$
$881$	−1.34752	+	4.14725i	−0.0453992	+	0.139725i	0.925787	+	0.378044i	$0.123403\pi$
$882$		0			0
$883$	−14.6525	+	45.0957i	−0.493095	+	1.51759i	0.326809	+	0.945090i	$0.394026\pi$
$883$	−14.6525	+	45.0957i	−0.493095	+	1.51759i	−0.819904	+	0.572500i	$0.805974\pi$
$884$	−4.85410	+	3.52671i	−0.163261	+	0.118616i
$885$		0			0
$886$	−6.02786	−	4.37950i	−0.202510	−	0.147132i
$887$	−4.76393	+	3.46120i	−0.159957	+	0.116216i	−0.664885	−	0.746946i	$-0.731519\pi$
$887$	−4.76393	+	3.46120i	−0.159957	+	0.116216i	0.504927	+	0.863162i	$0.331519\pi$
$888$		0			0
$889$	−20.7984	−	15.1109i	−0.697555	−	0.506803i
$890$	10.0000	+	7.26543i	0.335201	+	0.243538i
$891$		0			0
$892$	−11.0902	+	34.1320i	−0.371326	+	1.14283i
$893$	−9.47214			−0.316973
$894$		0			0
$895$	17.1353	+	12.4495i	0.572768	+	0.416141i
$896$	−5.69098	−	17.5150i	−0.190122	−	0.585137i
$897$		0			0
$898$	−10.1631	−	7.38394i	−0.339148	−	0.246405i
$899$	−4.14590			−0.138273
$900$		0			0
$901$	−4.18034			−0.139267
$902$	2.00000	+	1.45309i	0.0665927	+	0.0483824i
$903$		0			0
$904$	−7.01064	−	21.5765i	−0.233171	−	0.717625i
$905$	−9.47214	−	29.1522i	−0.314864	−	0.969053i
$906$		0			0
$907$	47.2492			1.56888			0.784442	−	0.620202i	$-0.212949\pi$
$907$	47.2492			1.56888			0.784442	+	0.620202i	$0.212949\pi$
$908$	9.61803	−	29.6013i	0.319186	−	0.982352i
$909$		0			0
$910$	−8.78115	+	6.37988i	−0.291092	+	0.211491i
$911$	−28.9336	−	21.0215i	−0.958614	−	0.696474i	−0.00578548	−	0.999983i	$-0.501842\pi$
$911$	−28.9336	−	21.0215i	−0.958614	−	0.696474i	−0.952828	+	0.303510i	$0.901842\pi$
$912$		0			0
$913$	−1.09017	+	0.792055i	−0.0360794	+	0.0262132i
$914$	2.70820	+	1.96763i	0.0895794	+	0.0650833i
$915$		0			0
$916$	10.8541	−	7.88597i	0.358630	−	0.260560i
$917$	−8.89919	+	27.3889i	−0.293877	+	0.904461i
$918$		0			0
$919$	−0.551663	+	1.69784i	−0.0181977	+	0.0560067i	−0.959743	−	0.280880i	$-0.909374\pi$
$919$	−0.551663	+	1.69784i	−0.0181977	+	0.0560067i	0.941545	+	0.336886i	$0.109374\pi$
$920$	12.7254	−	39.1648i	0.419545	−	1.29123i
$921$		0			0
$922$	4.42705	+	13.6251i	0.145797	+	0.448718i
$923$	17.2082	+	12.5025i	0.566415	+	0.411525i
$924$		0			0
$925$	6.54508	+	20.1437i	0.215201	+	0.662321i
$926$	−9.96556			−0.327489
$927$		0			0
$928$	−2.39919	−	7.38394i	−0.0787572	−	0.242390i
$929$	11.3197	+	34.8383i	0.371386	+	1.14301i	0.945885	+	0.324503i	$0.105197\pi$
$929$	11.3197	+	34.8383i	0.371386	+	1.14301i	−0.574499	+	0.818506i	$0.694803\pi$
$930$		0			0
$931$	7.92705	−	24.3970i	0.259799	−	0.799578i
$932$	24.1803			0.792053
$933$		0			0
$934$	14.2254	−	10.3354i	0.465470	−	0.338184i
$935$	−0.403252	+	1.24108i	−0.0131878	+	0.0405877i
$936$		0			0
$937$	−41.4787	+	30.1360i	−1.35505	+	0.984502i	−0.356308	+	0.934369i	$0.615965\pi$
$937$	−41.4787	+	30.1360i	−1.35505	+	0.984502i	−0.998743	+	0.0501333i	$0.984035\pi$
$938$	−7.47214	+	5.42882i	−0.243974	+	0.177257i
$939$		0			0
$940$	1.80902	−	5.56758i	0.0590036	−	0.181594i
$941$	−15.8435	+	11.5109i	−0.516482	+	0.375246i	−0.815277	−	0.579071i	$-0.803415\pi$
$941$	−15.8435	+	11.5109i	−0.516482	+	0.375246i	0.298795	+	0.954317i	$0.403415\pi$
$942$		0			0
$943$	−43.1246			−1.40433
$944$	2.37539	−	7.31069i	0.0773123	−	0.237943i
$945$		0			0
$946$	−0.270510	−	0.832544i	−0.00879503	−	0.0270683i
$947$	8.85410	+	27.2501i	0.287720	+	0.885510i	0.985570	+	0.169267i	$0.0541399\pi$
$947$	8.85410	+	27.2501i	0.287720	+	0.885510i	−0.697851	+	0.716243i	$0.745860\pi$
$948$		0			0
$949$	43.6869			1.41814
$950$	5.59017	+	17.2048i	0.181369	+	0.558197i
$951$		0			0
$952$	2.23607	+	1.62460i	0.0724714	+	0.0526535i
$953$	−10.7361	−	33.0422i	−0.347775	−	1.07034i	−0.960081	−	0.279721i	$-0.909758\pi$
$953$	−10.7361	−	33.0422i	−0.347775	−	1.07034i	0.612306	−	0.790621i	$-0.290242\pi$
$954$		0			0
$955$	−16.7082	+	51.4226i	−0.540665	+	1.66400i
$956$	−14.7361	+	45.3530i	−0.476598	+	1.46682i
$957$		0			0
$958$	−0.791796	+	2.43690i	−0.0255818	+	0.0787326i
$959$	−7.78115	+	5.65334i	−0.251267	+	0.182556i
$960$		0			0
$961$	17.7984	+	12.9313i	0.574141	+	0.417138i
$962$	−10.2812	+	7.46969i	−0.331478	+	0.240833i
$963$		0			0
$964$	15.0172	+	10.9106i	0.483672	+	0.351408i
$965$	−10.3262	+	7.50245i	−0.332413	+	0.241512i
$966$		0			0
$967$	12.3262	−	37.9363i	0.396385	−	1.21995i	−0.531493	−	0.847063i	$-0.678369\pi$
$967$	12.3262	−	37.9363i	0.396385	−	1.21995i	0.927878	−	0.372885i	$-0.121631\pi$
$968$	−23.2918			−0.748627
$969$		0			0
$970$	1.21885	+	3.75123i	0.0391348	+	0.120445i
$971$	−1.04508	−	3.21644i	−0.0335384	−	0.103220i	0.932886	−	0.360172i	$-0.117282\pi$
$971$	−1.04508	−	3.21644i	−0.0335384	−	0.103220i	−0.966424	+	0.256951i	$0.917282\pi$
$972$		0			0
$973$	6.54508	+	4.75528i	0.209826	+	0.152447i
$974$	5.92299			0.189785
$975$		0			0
$976$	−8.72949			−0.279424
$977$	−27.2254	−	19.7804i	−0.871019	−	0.632832i	0.0598416	−	0.998208i	$-0.480940\pi$
$977$	−27.2254	−	19.7804i	−0.871019	−	0.632832i	−0.930860	+	0.365376i	$0.880940\pi$
$978$		0			0
$979$	−2.11146	−	6.49839i	−0.0674824	−	0.207690i
$980$	12.8262	+	9.31881i	0.409719	+	0.297678i
$981$		0			0
$982$	23.0213			0.734639
$983$	−2.28115	+	7.02067i	−0.0727575	+	0.223924i	−0.980822	−	0.194906i	$-0.937560\pi$
$983$	−2.28115	+	7.02067i	−0.0727575	+	0.223924i	0.908064	+	0.418830i	$0.137560\pi$
$984$		0			0
$985$	17.5623	+	12.7598i	0.559582	+	0.406560i
$986$	0.527864	+	0.383516i	0.0168106	+	0.0122136i
$987$		0			0
$988$	37.1976	−	27.0256i	1.18341	−	0.859799i
$989$	12.3541	+	8.97578i	0.392838	+	0.285413i
$990$		0			0
$991$	−23.7533	+	17.2578i	−0.754548	+	0.548211i	−0.897233	−	0.441557i	$-0.854426\pi$
$991$	−23.7533	+	17.2578i	−0.754548	+	0.548211i	0.142685	+	0.989768i	$0.454426\pi$
$992$	5.20820	−	16.0292i	0.165361	−	0.508928i
$993$		0			0
$994$	1.35410	−	4.16750i	0.0429495	−	0.132185i
$995$	4.63525	−	3.36771i	0.146947	−	0.106764i
$996$		0			0
$997$	−3.36475	−	10.3556i	−0.106563	−	0.327966i	0.883531	−	0.468372i	$-0.155159\pi$
$997$	−3.36475	−	10.3556i	−0.106563	−	0.327966i	−0.990094	+	0.140406i	$0.955159\pi$
$998$	−6.28115	−	4.56352i	−0.198826	−	0.144456i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.b.91.1		4
3.2	odd	2		25.2.d.a.16.1	yes	4
12.11	even	2		400.2.u.b.241.1		4
15.2	even	4		125.2.e.a.49.2		8
15.8	even	4		125.2.e.a.49.1		8
15.14	odd	2		125.2.d.a.76.1		4
25.6	even	5		5625.2.a.f.1.1		2
25.11	even	5	inner	225.2.h.b.136.1		4
25.19	even	10		5625.2.a.d.1.2		2
75.2	even	20		125.2.e.a.74.1		8
75.8	even	20		625.2.b.a.624.2		4
75.11	odd	10		25.2.d.a.11.1	✓	4
75.14	odd	10		125.2.d.a.51.1		4
75.17	even	20		625.2.b.a.624.3		4
75.23	even	20		125.2.e.a.74.2		8
75.29	odd	10		625.2.d.b.126.1		4
75.38	even	20		625.2.e.c.124.1		8
75.41	odd	10		625.2.d.h.501.1		4
75.44	odd	10		625.2.a.c.1.1		2
75.47	even	20		625.2.e.c.499.1		8
75.53	even	20		625.2.e.c.499.2		8
75.56	odd	10		625.2.a.b.1.2		2
75.59	odd	10		625.2.d.b.501.1		4
75.62	even	20		625.2.e.c.124.2		8
75.71	odd	10		625.2.d.h.126.1		4
300.11	even	10		400.2.u.b.161.1		4
300.119	even	10		10000.2.a.l.1.1		2
300.131	even	10		10000.2.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.11.1	✓	4	75.11	odd	10
25.2.d.a.16.1	yes	4	3.2	odd	2
125.2.d.a.51.1		4	75.14	odd	10
125.2.d.a.76.1		4	15.14	odd	2
125.2.e.a.49.1		8	15.8	even	4
125.2.e.a.49.2		8	15.2	even	4
125.2.e.a.74.1		8	75.2	even	20
125.2.e.a.74.2		8	75.23	even	20
225.2.h.b.91.1		4	1.1	even	1	trivial
225.2.h.b.136.1		4	25.11	even	5	inner
400.2.u.b.161.1		4	300.11	even	10
400.2.u.b.241.1		4	12.11	even	2
625.2.a.b.1.2		2	75.56	odd	10
625.2.a.c.1.1		2	75.44	odd	10
625.2.b.a.624.2		4	75.8	even	20
625.2.b.a.624.3		4	75.17	even	20
625.2.d.b.126.1		4	75.29	odd	10
625.2.d.b.501.1		4	75.59	odd	10
625.2.d.h.126.1		4	75.71	odd	10
625.2.d.h.501.1		4	75.41	odd	10
625.2.e.c.124.1		8	75.38	even	20
625.2.e.c.124.2		8	75.62	even	20
625.2.e.c.499.1		8	75.47	even	20
625.2.e.c.499.2		8	75.53	even	20
5625.2.a.d.1.2		2	25.19	even	10
5625.2.a.f.1.1		2	25.6	even	5
10000.2.a.c.1.2		2	300.131	even	10
10000.2.a.l.1.1		2	300.119	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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.363271i) q^{2} +(-0.500000 - 1.53884i) q^{4} +(1.80902 - 1.31433i) q^{5} -1.61803 q^{7} +(0.690983 - 2.12663i) q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.363271i) q^{2} +(-0.500000 - 1.53884i) q^{4} +(1.80902 - 1.31433i) q^{5} -1.61803 q^{7} +(0.690983 - 2.12663i) q^{8} +1.38197 q^{10} +(-0.618034 - 0.449028i) q^{11} +(3.92705 - 2.85317i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-1.50000 + 1.08981i) q^{16} +(0.236068 - 0.726543i) q^{17} +(-1.80902 + 5.56758i) q^{19} +(-2.92705 - 2.12663i) q^{20} +(-0.145898 - 0.449028i) q^{22} +(6.66312 + 4.84104i) q^{23} +(1.54508 - 4.75528i) q^{25} +3.00000 q^{26} +(0.809017 + 2.48990i) q^{28} +(0.427051 + 1.31433i) q^{29} +(-0.927051 + 2.85317i) q^{31} -5.61803 q^{32} +(0.381966 - 0.277515i) q^{34} +(-2.92705 + 2.12663i) q^{35} +(-3.42705 + 2.48990i) q^{37} +(-2.92705 + 2.12663i) q^{38} +(-1.54508 - 4.75528i) q^{40} +(-4.23607 + 3.07768i) q^{41} +1.85410 q^{43} +(-0.381966 + 1.17557i) q^{44} +(1.57295 + 4.84104i) q^{46} +(0.500000 + 1.53884i) q^{47} -4.38197 q^{49} +(2.50000 - 1.81636i) q^{50} +(-6.35410 - 4.61653i) q^{52} +(-1.69098 - 5.20431i) q^{53} -1.70820 q^{55} +(-1.11803 + 3.44095i) q^{56} +(-0.263932 + 0.812299i) q^{58} +(-3.35410 + 2.43690i) q^{59} +(3.80902 + 2.76741i) q^{61} +(-1.50000 + 1.08981i) q^{62} +(0.190983 + 0.138757i) q^{64} +(3.35410 - 10.3229i) q^{65} +(2.85410 - 8.78402i) q^{67} -1.23607 q^{68} -2.23607 q^{70} +(1.35410 + 4.16750i) q^{71} +(7.28115 + 5.29007i) q^{73} -2.61803 q^{74} +9.47214 q^{76} +(1.00000 + 0.726543i) q^{77} +(0.954915 + 2.93893i) q^{79} +(-1.28115 + 3.94298i) q^{80} -3.23607 q^{82} +(0.545085 - 1.67760i) q^{83} +(-0.527864 - 1.62460i) q^{85} +(0.927051 + 0.673542i) q^{86} +(-1.38197 + 1.00406i) q^{88} +(7.23607 + 5.25731i) q^{89} +(-6.35410 + 4.61653i) q^{91} +(4.11803 - 12.6740i) q^{92} +(-0.309017 + 0.951057i) q^{94} +(4.04508 + 12.4495i) q^{95} +(0.881966 + 2.71441i) q^{97} +(-2.19098 - 1.59184i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 5 * q^5 - 2 * q^7 + 5 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8} + 10 q^{10} + 2 q^{11} + 9 q^{13} - q^{14} - 6 q^{16} - 8 q^{17} - 5 q^{19} - 5 q^{20} - 14 q^{22} + 11 q^{23} - 5 q^{25} + 12 q^{26} + q^{28} - 5 q^{29} + 3 q^{31} - 18 q^{32} + 6 q^{34} - 5 q^{35} - 7 q^{37} - 5 q^{38} + 5 q^{40} - 8 q^{41} - 6 q^{43} - 6 q^{44} + 13 q^{46} + 2 q^{47} - 22 q^{49} + 10 q^{50} - 12 q^{52} - 9 q^{53} + 20 q^{55} - 10 q^{58} + 13 q^{61} - 6 q^{62} + 3 q^{64} - 2 q^{67} + 4 q^{68} - 8 q^{71} + 9 q^{73} - 6 q^{74} + 20 q^{76} + 4 q^{77} + 15 q^{79} + 15 q^{80} - 4 q^{82} - 9 q^{83} - 20 q^{85} - 3 q^{86} - 10 q^{88} + 20 q^{89} - 12 q^{91} + 12 q^{92} + q^{94} + 5 q^{95} + 8 q^{97} - 11 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 5 * q^5 - 2 * q^7 + 5 * q^8 + 10 * q^10 + 2 * q^11 + 9 * q^13 - q^14 - 6 * q^16 - 8 * q^17 - 5 * q^19 - 5 * q^20 - 14 * q^22 + 11 * q^23 - 5 * q^25 + 12 * q^26 + q^28 - 5 * q^29 + 3 * q^31 - 18 * q^32 + 6 * q^34 - 5 * q^35 - 7 * q^37 - 5 * q^38 + 5 * q^40 - 8 * q^41 - 6 * q^43 - 6 * q^44 + 13 * q^46 + 2 * q^47 - 22 * q^49 + 10 * q^50 - 12 * q^52 - 9 * q^53 + 20 * q^55 - 10 * q^58 + 13 * q^61 - 6 * q^62 + 3 * q^64 - 2 * q^67 + 4 * q^68 - 8 * q^71 + 9 * q^73 - 6 * q^74 + 20 * q^76 + 4 * q^77 + 15 * q^79 + 15 * q^80 - 4 * q^82 - 9 * q^83 - 20 * q^85 - 3 * q^86 - 10 * q^88 + 20 * q^89 - 12 * q^91 + 12 * q^92 + q^94 + 5 * q^95 + 8 * q^97 - 11 * q^98

Introduction

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