LMFDB - Embedded newform 450.2.h.d.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.1064390625.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 3x^{6} - 5x^{5} + 36x^{4} - 35x^{3} + 23x^{2} - 171x + 361 $ x^8 - 2x^7 - 3x^6 - 5x^5 + 36x^4 - 35x^3 + 23x^2 - 171*x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-0.815575 + 1.64827i$ of defining polynomial
Character	$\chi$	$=$	450.181
Dual form			450.2.h.d.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-0.00655751 - 2.23606i) q^{5} +2.63925 q^{7} +(-0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-0.00655751 - 2.23606i) q^{5} +2.63925 q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.12459 - 0.697217i) q^{10} +(-1.93766 - 5.96351i) q^{11} +(0.697541 - 2.14681i) q^{13} +(0.815575 + 2.51008i) q^{14} +(0.309017 - 0.951057i) q^{16} +(1.31557 + 0.955821i) q^{17} +(1.00000 + 0.726543i) q^{19} +(1.31963 + 1.80515i) q^{20} +(5.07286 - 3.68565i) q^{22} +(1.38197 + 4.25325i) q^{23} +(-4.99991 + 0.0293259i) q^{25} +2.25729 q^{26} +(-2.13520 + 1.55131i) q^{28} +(5.55164 - 4.03350i) q^{29} +(4.75324 + 3.45343i) q^{31} +1.00000 q^{32} +(-0.502505 + 1.54655i) q^{34} +(-0.0173069 - 5.90153i) q^{35} +(2.49750 - 7.68650i) q^{37} +(-0.381966 + 1.17557i) q^{38} +(-1.30902 + 1.81286i) q^{40} +(-3.55164 + 10.9308i) q^{41} -1.97377 q^{43} +(5.07286 + 3.68565i) q^{44} +(-3.61803 + 2.62866i) q^{46} +(5.25729 - 3.81964i) q^{47} -0.0343355 q^{49} +(-1.57295 - 4.74614i) q^{50} +(0.697541 + 2.14681i) q^{52} +(-5.66298 + 4.11440i) q^{53} +(-13.3220 + 4.37183i) q^{55} +(-2.13520 - 1.55131i) q^{56} +(5.55164 + 4.03350i) q^{58} +(-2.79176 + 8.59216i) q^{59} +(-0.933608 - 2.87335i) q^{61} +(-1.81557 + 5.58776i) q^{62} +(0.309017 + 0.951057i) q^{64} +(-4.80496 - 1.54566i) q^{65} +(8.12451 + 5.90280i) q^{67} -1.62614 q^{68} +(5.60734 - 1.84013i) q^{70} +(-7.90966 + 5.74670i) q^{71} +(-3.70565 - 11.4048i) q^{73} +8.08206 q^{74} -1.23607 q^{76} +(-5.11398 - 15.7392i) q^{77} +(-3.03853 + 2.20762i) q^{79} +(-2.12864 - 0.684743i) q^{80} -11.4934 q^{82} +(-6.77446 - 4.92193i) q^{83} +(2.12864 - 2.94797i) q^{85} +(-0.609928 - 1.87717i) q^{86} +(-1.93766 + 5.96351i) q^{88} +(0.120539 + 0.370980i) q^{89} +(1.84099 - 5.66598i) q^{91} +(-3.61803 - 2.62866i) q^{92} +(5.25729 + 3.81964i) q^{94} +(1.61803 - 2.24082i) q^{95} +(-1.21471 + 0.882537i) q^{97} +(-0.0106103 - 0.0326550i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 2 * q^8	$ 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8} + 4 q^{10} + 5 q^{11} + 6 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{17} + 8 q^{19} - q^{20} + 20 q^{23} + 14 q^{25} - 14 q^{26} + 3 q^{28} + 18 q^{29} + 9 q^{31} + 8 q^{32} - 3 q^{34} + 4 q^{35} + 21 q^{37} - 12 q^{38} - 6 q^{40} - 2 q^{41} - 32 q^{43} - 20 q^{46} + 10 q^{47} + 22 q^{49} - 26 q^{50} + 6 q^{52} - 7 q^{53} - 40 q^{55} + 3 q^{56} + 18 q^{58} + 25 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{64} - 37 q^{65} - 2 q^{67} + 2 q^{68} - 11 q^{70} - 24 q^{73} + 26 q^{74} + 8 q^{76} - 35 q^{77} - 6 q^{79} - q^{80} - 42 q^{82} - 11 q^{83} + q^{85} - 2 q^{86} + 5 q^{88} - 9 q^{89} - 4 q^{91} - 20 q^{92} + 10 q^{94} + 4 q^{95} + q^{97} + 7 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 2 * q^8 + 4 * q^10 + 5 * q^11 + 6 * q^13 - 2 * q^14 - 2 * q^16 + 2 * q^17 + 8 * q^19 - q^20 + 20 * q^23 + 14 * q^25 - 14 * q^26 + 3 * q^28 + 18 * q^29 + 9 * q^31 + 8 * q^32 - 3 * q^34 + 4 * q^35 + 21 * q^37 - 12 * q^38 - 6 * q^40 - 2 * q^41 - 32 * q^43 - 20 * q^46 + 10 * q^47 + 22 * q^49 - 26 * q^50 + 6 * q^52 - 7 * q^53 - 40 * q^55 + 3 * q^56 + 18 * q^58 + 25 * q^59 + 10 * q^61 - 6 * q^62 - 2 * q^64 - 37 * q^65 - 2 * q^67 + 2 * q^68 - 11 * q^70 - 24 * q^73 + 26 * q^74 + 8 * q^76 - 35 * q^77 - 6 * q^79 - q^80 - 42 * q^82 - 11 * q^83 + q^85 - 2 * q^86 + 5 * q^88 - 9 * q^89 - 4 * q^91 - 20 * q^92 + 10 * q^94 + 4 * q^95 + q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.00655751	−	2.23606i	−0.00293261	−	0.999996i
$5$	−0.00655751	−	2.23606i	−0.00293261	−	0.999996i
$6$		0			0
$7$	2.63925			0.997544			0.498772	−	0.866733i	$-0.333784\pi$
$7$	2.63925			0.997544			0.498772	+	0.866733i	$0.333784\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$		0			0
$10$	2.12459	−	0.697217i	0.671855	−	0.220479i
$11$	−1.93766	−	5.96351i	−0.584227	−	1.79807i	−0.602353	−	0.798230i	$-0.705770\pi$
$11$	−1.93766	−	5.96351i	−0.584227	−	1.79807i	0.0181264	−	0.999836i	$-0.494230\pi$
$12$		0			0
$13$	0.697541	−	2.14681i	0.193463	−	0.595418i	−0.806528	−	0.591196i	$-0.798656\pi$
$13$	0.697541	−	2.14681i	0.193463	−	0.595418i	0.999991	−	0.00422199i	$-0.00134391\pi$
$14$	0.815575	+	2.51008i	0.217971	+	0.670847i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.31557	+	0.955821i	0.319074	+	0.231821i	0.735780	−	0.677221i	$-0.236816\pi$
$17$	1.31557	+	0.955821i	0.319074	+	0.231821i	−0.416706	+	0.909041i	$0.636816\pi$
$18$		0			0
$19$	1.00000	+	0.726543i	0.229416	+	0.166680i	0.696555	−	0.717504i	$-0.254715\pi$
$19$	1.00000	+	0.726543i	0.229416	+	0.166680i	−0.467139	+	0.884184i	$0.654715\pi$
$20$	1.31963	+	1.80515i	0.295078	+	0.403645i
$21$		0			0
$22$	5.07286	−	3.68565i	1.08154	−	0.785783i
$23$	1.38197	+	4.25325i	0.288160	+	0.886865i	0.985434	+	0.170060i	$0.0543961\pi$
$23$	1.38197	+	4.25325i	0.288160	+	0.886865i	−0.697274	+	0.716805i	$0.745604\pi$
$24$		0			0
$25$	−4.99991	+	0.0293259i	−0.999983	+	0.00586519i
$26$	2.25729			0.442691
$27$		0			0
$28$	−2.13520	+	1.55131i	−0.403515	+	0.293171i
$29$	5.55164	−	4.03350i	1.03091	−	0.749003i	0.0624227	−	0.998050i	$-0.480117\pi$
$29$	5.55164	−	4.03350i	1.03091	−	0.749003i	0.968491	+	0.249047i	$0.0801173\pi$
$30$		0			0
$31$	4.75324	+	3.45343i	0.853706	+	0.620254i	0.926165	−	0.377117i	$-0.123085\pi$
$31$	4.75324	+	3.45343i	0.853706	+	0.620254i	−0.0724591	+	0.997371i	$0.523085\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.502505	+	1.54655i	−0.0861789	+	0.265231i
$35$	−0.0173069	−	5.90153i	−0.00292540	−	0.997540i
$36$		0			0
$37$	2.49750	−	7.68650i	0.410586	−	1.26365i	−0.505554	−	0.862795i	$-0.668712\pi$
$37$	2.49750	−	7.68650i	0.410586	−	1.26365i	0.916140	−	0.400858i	$-0.131288\pi$
$38$	−0.381966	+	1.17557i	−0.0619631	+	0.190703i
$39$		0			0
$40$	−1.30902	+	1.81286i	−0.206974	+	0.286639i
$41$	−3.55164	+	10.9308i	−0.554673	+	1.70711i	0.142131	+	0.989848i	$0.454605\pi$
$41$	−3.55164	+	10.9308i	−0.554673	+	1.70711i	−0.696804	+	0.717261i	$0.745395\pi$
$42$		0			0
$43$	−1.97377			−0.300997			−0.150499	−	0.988610i	$-0.548088\pi$
$43$	−1.97377			−0.300997			−0.150499	+	0.988610i	$0.548088\pi$
$44$	5.07286	+	3.68565i	0.764763	+	0.555633i
$45$		0			0
$46$	−3.61803	+	2.62866i	−0.533450	+	0.387574i
$47$	5.25729	−	3.81964i	0.766854	−	0.557152i	−0.134151	−	0.990961i	$-0.542831\pi$
$47$	5.25729	−	3.81964i	0.766854	−	0.557152i	0.901005	+	0.433809i	$0.142831\pi$
$48$		0			0
$49$	−0.0343355			−0.00490508
$50$	−1.57295	−	4.74614i	−0.222449	−	0.671205i
$51$		0			0
$52$	0.697541	+	2.14681i	0.0967315	+	0.297709i
$53$	−5.66298	+	4.11440i	−0.777870	+	0.565156i	−0.904339	−	0.426815i	$-0.859636\pi$
$53$	−5.66298	+	4.11440i	−0.777870	+	0.565156i	0.126469	+	0.991971i	$0.459636\pi$
$54$		0			0
$55$	−13.3220	+	4.37183i	−1.79634	+	0.589497i
$56$	−2.13520	−	1.55131i	−0.285328	−	0.207303i
$57$		0			0
$58$	5.55164	+	4.03350i	0.728966	+	0.529625i
$59$	−2.79176	+	8.59216i	−0.363457	+	1.11860i	0.587485	+	0.809235i	$0.300118\pi$
$59$	−2.79176	+	8.59216i	−0.363457	+	1.11860i	−0.950942	+	0.309370i	$0.899882\pi$
$60$		0			0
$61$	−0.933608	−	2.87335i	−0.119536	−	0.367895i	0.873330	−	0.487129i	$-0.161956\pi$
$61$	−0.933608	−	2.87335i	−0.119536	−	0.367895i	−0.992866	+	0.119234i	$0.961956\pi$
$62$	−1.81557	+	5.58776i	−0.230578	+	0.709647i
$63$		0			0
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−4.80496	−	1.54566i	−0.595982	−	0.191716i
$66$		0			0
$67$	8.12451	+	5.90280i	0.992566	+	0.721142i	0.960482	−	0.278344i	$-0.0897854\pi$
$67$	8.12451	+	5.90280i	0.992566	+	0.721142i	0.0320847	+	0.999485i	$0.489785\pi$
$68$	−1.62614			−0.197198
$69$		0			0
$70$	5.60734	−	1.84013i	0.670205	−	0.219938i
$71$	−7.90966	+	5.74670i	−0.938704	+	0.682008i	−0.948108	−	0.317948i	$-0.897006\pi$
$71$	−7.90966	+	5.74670i	−0.938704	+	0.682008i	0.00940457	+	0.999956i	$0.497006\pi$
$72$		0			0
$73$	−3.70565	−	11.4048i	−0.433713	−	1.33483i	−0.894400	−	0.447269i	$-0.852397\pi$
$73$	−3.70565	−	11.4048i	−0.433713	−	1.33483i	0.460687	−	0.887563i	$-0.347603\pi$
$74$	8.08206			0.939521
$75$		0			0
$76$	−1.23607			−0.141787
$77$	−5.11398	−	15.7392i	−0.582792	−	1.79365i
$78$		0			0
$79$	−3.03853	+	2.20762i	−0.341861	+	0.248377i	−0.745447	−	0.666565i	$-0.767764\pi$
$79$	−3.03853	+	2.20762i	−0.341861	+	0.248377i	0.403586	+	0.914942i	$0.367764\pi$
$80$	−2.12864	−	0.684743i	−0.237990	−	0.0765566i
$81$		0			0
$82$	−11.4934			−1.26923
$83$	−6.77446	−	4.92193i	−0.743593	−	0.540252i	0.150241	−	0.988649i	$-0.451995\pi$
$83$	−6.77446	−	4.92193i	−0.743593	−	0.540252i	−0.893834	+	0.448397i	$0.851995\pi$
$84$		0			0
$85$	2.12864	−	2.94797i	0.230884	−	0.319752i
$86$	−0.609928	−	1.87717i	−0.0657703	−	0.202420i
$87$		0			0
$88$	−1.93766	+	5.96351i	−0.206555	+	0.635712i
$89$	0.120539	+	0.370980i	0.0127771	+	0.0393238i	0.957242	−	0.289289i	$-0.0934189\pi$
$89$	0.120539	+	0.370980i	0.0127771	+	0.0393238i	−0.944465	+	0.328613i	$0.893419\pi$
$90$		0			0
$91$	1.84099	−	5.66598i	0.192988	−	0.593956i
$92$	−3.61803	−	2.62866i	−0.377206	−	0.274056i
$93$		0			0
$94$	5.25729	+	3.81964i	0.542248	+	0.393966i
$95$	1.61803	−	2.24082i	0.166007	−	0.229904i
$96$		0			0
$97$	−1.21471	+	0.882537i	−0.123335	+	0.0896081i	−0.647743	−	0.761859i	$-0.724287\pi$
$97$	−1.21471	+	0.882537i	−0.123335	+	0.0896081i	0.524408	+	0.851467i	$0.324287\pi$
$98$	−0.0106103	−	0.0326550i	−0.00107180	−	0.00329866i
$99$		0			0
$100$	4.02778	−	2.96260i	0.402778	−	0.296260i
$101$	−4.68671			−0.466345			−0.233172	−	0.972435i	$-0.574911\pi$
$101$	−4.68671			−0.466345			−0.233172	+	0.972435i	$0.574911\pi$
$102$		0			0
$103$	3.46161	−	2.51501i	0.341083	−	0.247811i	−0.404036	−	0.914743i	$-0.632393\pi$
$103$	3.46161	−	2.51501i	0.341083	−	0.247811i	0.745119	+	0.666932i	$0.232393\pi$
$104$	−1.82618	+	1.32680i	−0.179072	+	0.130104i
$105$		0			0
$106$	−5.66298	−	4.11440i	−0.550037	−	0.399625i
$107$	18.7850			1.81601			0.908006	−	0.418956i	$-0.137604\pi$
$107$	18.7850			1.81601			0.908006	+	0.418956i	$0.137604\pi$
$108$		0			0
$109$	−4.94982	+	15.2340i	−0.474107	+	1.45915i	0.373052	+	0.927810i	$0.378311\pi$
$109$	−4.94982	+	15.2340i	−0.474107	+	1.45915i	−0.847159	+	0.531340i	$0.821689\pi$
$110$	−8.27460	−	11.3190i	−0.788952	−	1.07923i
$111$		0			0
$112$	0.815575	−	2.51008i	0.0770645	−	0.237180i
$113$	2.98776	−	9.19537i	0.281064	−	0.865027i	−0.706486	−	0.707727i	$-0.749721\pi$
$113$	2.98776	−	9.19537i	0.281064	−	0.865027i	0.987551	−	0.157301i	$-0.0502792\pi$
$114$		0			0
$115$	9.50146	−	3.11805i	0.886016	−	0.290759i
$116$	−2.12054	+	6.52635i	−0.196887	+	0.605956i
$117$		0			0
$118$	−9.03434			−0.831678
$119$	3.47214	+	2.52265i	0.318290	+	0.231251i
$120$		0			0
$121$	−22.9097	+	16.6449i	−2.08270	+	1.51317i
$122$	2.44422	−	1.77583i	0.221289	−	0.160776i
$123$		0			0
$124$	−5.87532			−0.527620
$125$	0.0983615	+	11.1799i	0.00879772	+	0.999961i
$126$		0			0
$127$	2.30651	+	7.09871i	0.204670	+	0.629909i	0.999727	+	0.0233743i	$0.00744093\pi$
$127$	2.30651	+	7.09871i	0.204670	+	0.629909i	−0.795057	+	0.606535i	$0.792559\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$		0			0
$130$	−0.0148022	−	5.04743i	−0.00129824	−	0.442689i
$131$	16.5966	+	12.0582i	1.45006	+	1.05353i	0.985818	+	0.167816i	$0.0536714\pi$
$131$	16.5966	+	12.0582i	1.45006	+	1.05353i	0.464237	+	0.885711i	$0.346329\pi$
$132$		0			0
$133$	2.63925	+	1.91753i	0.228852	+	0.166271i
$134$	−3.10328	+	9.55093i	−0.268083	+	0.825075i
$135$		0			0
$136$	−0.502505	−	1.54655i	−0.0430894	−	0.132616i
$137$	0.946724	−	2.91372i	0.0808840	−	0.248936i	−0.902435	−	0.430827i	$-0.858222\pi$
$137$	0.946724	−	2.91372i	0.0808840	−	0.248936i	0.983319	+	0.181891i	$0.0582219\pi$
$138$		0			0
$139$	−5.15400	−	15.8624i	−0.437157	−	1.34543i	−0.890860	−	0.454278i	$-0.849897\pi$
$139$	−5.15400	−	15.8624i	−0.437157	−	1.34543i	0.453703	−	0.891153i	$-0.350103\pi$
$140$	3.48283	+	4.76426i	0.294353	+	0.402654i
$141$		0			0
$142$	−7.90966	−	5.74670i	−0.663764	−	0.482253i
$143$	−14.1541			−1.18363
$144$		0			0
$145$	−9.05556	−	12.3873i	−0.752023	−	1.02871i
$146$	9.70151	−	7.04856i	0.802902	−	0.583343i
$147$		0			0
$148$	2.49750	+	7.68650i	0.205293	+	0.631826i
$149$	−14.4853			−1.18668			−0.593339	−	0.804953i	$-0.702191\pi$
$149$	−14.4853			−1.18668			−0.593339	+	0.804953i	$0.702191\pi$
$150$		0			0
$151$	10.3050			0.838610			0.419305	−	0.907845i	$-0.362274\pi$
$151$	10.3050			0.838610			0.419305	+	0.907845i	$0.362274\pi$
$152$	−0.381966	−	1.17557i	−0.0309815	−	0.0953514i
$153$		0			0
$154$	13.3886	−	9.72737i	1.07888	−	0.783854i
$155$	7.69090	−	10.6512i	0.617748	−	0.855522i
$156$		0			0
$157$	−7.58370			−0.605245			−0.302623	−	0.953110i	$-0.597862\pi$
$157$	−7.58370			−0.605245			−0.302623	+	0.953110i	$0.597862\pi$
$158$	−3.03853	−	2.20762i	−0.241732	−	0.175629i
$159$		0			0
$160$	−0.00655751	−	2.23606i	−0.000518416	−	0.176776i
$161$	3.64736	+	11.2254i	0.287452	+	0.884687i
$162$		0			0
$163$	−4.32624	+	13.3148i	−0.338857	+	1.04289i	0.625934	+	0.779876i	$0.284718\pi$
$163$	−4.32624	+	13.3148i	−0.338857	+	1.04289i	−0.964791	+	0.263019i	$0.915282\pi$
$164$	−3.55164	−	10.9308i	−0.277337	−	0.853555i
$165$		0			0
$166$	2.58761	−	7.96385i	0.200838	−	0.618115i
$167$	14.0210	+	10.1869i	1.08498	+	0.788285i	0.978545	−	0.206034i	$-0.0660559\pi$
$167$	14.0210	+	10.1869i	1.08498	+	0.788285i	0.106437	+	0.994319i	$0.466056\pi$
$168$		0			0
$169$	6.39500	+	4.64624i	0.491923	+	0.357403i
$170$	3.46147	+	1.11349i	0.265483	+	0.0854007i
$171$		0			0
$172$	1.59681	−	1.16015i	0.121756	−	0.0884608i
$173$	−1.17528	−	3.61713i	−0.0893547	−	0.275005i	0.896387	−	0.443273i	$-0.146183\pi$
$173$	−1.17528	−	3.61713i	−0.0893547	−	0.275005i	−0.985741	+	0.168268i	$0.946183\pi$
$174$		0			0
$175$	−13.1960	+	0.0773986i	−0.997527	+	0.00585078i
$176$	−6.27040			−0.472649
$177$		0			0
$178$	−0.315575	+	0.229278i	−0.0236533	+	0.0171851i
$179$	0.100866	−	0.0732836i	0.00753909	−	0.00547747i	−0.584009	−	0.811747i	$-0.698517\pi$
$179$	0.100866	−	0.0732836i	0.00753909	−	0.00547747i	0.591548	+	0.806269i	$0.298517\pi$
$180$		0			0
$181$	7.53853	+	5.47706i	0.560334	+	0.407107i	0.831581	−	0.555403i	$-0.187436\pi$
$181$	7.53853	+	5.47706i	0.560334	+	0.407107i	−0.271247	+	0.962510i	$0.587436\pi$
$182$	5.95756			0.441604
$183$		0			0
$184$	1.38197	−	4.25325i	0.101880	−	0.313554i
$185$	−17.2038	−	5.53414i	−1.26485	−	0.406878i
$186$		0			0
$187$	3.15091	−	9.69750i	0.230417	−	0.709151i
$188$	−2.00811	+	6.18031i	−0.146456	+	0.450746i
$189$		0			0
$190$	2.63115	+	0.846389i	0.190884	+	0.0614035i
$191$	−1.00000	+	3.07768i	−0.0723575	+	0.222693i	−0.980695	−	0.195545i	$-0.937352\pi$
$191$	−1.00000	+	3.07768i	−0.0723575	+	0.222693i	0.908337	+	0.418239i	$0.137352\pi$
$192$		0			0
$193$	−10.8641			−0.782017			−0.391008	−	0.920387i	$-0.627874\pi$
$193$	−10.8641			−0.782017			−0.391008	+	0.920387i	$0.627874\pi$
$194$	−1.21471	−	0.882537i	−0.0872110	−	0.0633625i
$195$		0			0
$196$	0.0277780	−	0.0201819i	0.00198415	−	0.00144157i
$197$	−7.34335	+	5.33526i	−0.523192	+	0.380121i	−0.817805	−	0.575495i	$-0.804809\pi$
$197$	−7.34335	+	5.33526i	−0.523192	+	0.380121i	0.294613	+	0.955617i	$0.404809\pi$
$198$		0			0
$199$	26.0735			1.84830			0.924151	−	0.382027i	$-0.124774\pi$
$199$	26.0735			1.84830			0.924151	+	0.382027i	$0.124774\pi$
$200$	4.06225	+	2.91515i	0.287245	+	0.206132i
$201$		0			0
$202$	−1.44827	−	4.45732i	−0.101900	−	0.313616i
$203$	14.6522	−	10.6454i	1.02838	−	0.747164i
$204$		0			0
$205$	24.4653	+	7.87000i	1.70873	+	0.549665i
$206$	3.46161	+	2.51501i	0.241182	+	0.175229i
$207$		0			0
$208$	−1.82618	−	1.32680i	−0.126623	−	0.0919971i
$209$	2.39508	−	7.37130i	0.165671	−	0.509884i
$210$		0			0
$211$	4.79016	+	14.7426i	0.329768	+	1.01492i	0.969242	+	0.246110i	$0.0791523\pi$
$211$	4.79016	+	14.7426i	0.329768	+	1.01492i	−0.639474	+	0.768813i	$0.720848\pi$
$212$	2.16307	−	6.65723i	0.148560	−	0.457221i
$213$		0			0
$214$	5.80488	+	17.8656i	0.396813	+	1.22127i
$215$	0.0129430	+	4.41346i	0.000882706	+	0.300996i
$216$		0			0
$217$	12.5450	+	9.11448i	0.851610	+	0.618731i
$218$	−16.0180			−1.08487
$219$		0			0
$220$	8.20806	−	11.3674i	0.553388	−	0.766389i
$221$	2.96963	−	2.15756i	0.199759	−	0.145133i
$222$		0			0
$223$	0.555695	+	1.71025i	0.0372121	+	0.114527i	0.967937	−	0.251193i	$-0.0808228\pi$
$223$	0.555695	+	1.71025i	0.0372121	+	0.114527i	−0.930725	+	0.365720i	$0.880823\pi$
$224$	2.63925			0.176343
$225$		0			0
$226$	9.66858			0.643144
$227$	0.319627	+	0.983712i	0.0212144	+	0.0652912i	0.961103	−	0.276189i	$-0.0890717\pi$
$227$	0.319627	+	0.983712i	0.0212144	+	0.0652912i	−0.939889	+	0.341481i	$0.889072\pi$
$228$		0			0
$229$	2.21626	−	1.61020i	0.146454	−	0.106405i	−0.512145	−	0.858899i	$-0.671149\pi$
$229$	2.21626	−	1.61020i	0.146454	−	0.106405i	0.658600	+	0.752493i	$0.271149\pi$
$230$	5.90155	+	8.07290i	0.389137	+	0.532311i
$231$		0			0
$232$	−6.86221			−0.450526
$233$	14.5768	+	10.5907i	0.954960	+	0.693819i	0.951975	−	0.306177i	$-0.0990498\pi$
$233$	14.5768	+	10.5907i	0.954960	+	0.693819i	0.00298513	+	0.999996i	$0.499050\pi$
$234$		0			0
$235$	−8.57542	−	11.7306i	−0.559399	−	0.765217i
$236$	−2.79176	−	8.59216i	−0.181728	−	0.559302i
$237$		0			0
$238$	−1.32624	+	4.08174i	−0.0859672	+	0.264580i
$239$	0.840987	+	2.58829i	0.0543989	+	0.167423i	0.974565	−	0.224106i	$-0.0719463\pi$
$239$	0.840987	+	2.58829i	0.0543989	+	0.167423i	−0.920166	+	0.391529i	$0.871946\pi$
$240$		0			0
$241$	0.463977	−	1.42798i	0.0298874	−	0.0919840i	−0.935000	−	0.354647i	$-0.884601\pi$
$241$	0.463977	−	1.42798i	0.0298874	−	0.0919840i	0.964888	+	0.262663i	$0.0846009\pi$
$242$	−22.9097	−	16.6449i	−1.47269	−	1.06997i
$243$		0			0
$244$	2.44422	+	1.77583i	0.156475	+	0.113686i
$245$	0.000225156		0.0767763i	1.43847e−5		0.00490506i
$246$		0			0
$247$	2.25729	−	1.64002i	0.143628	−	0.104352i
$248$	−1.81557	−	5.58776i	−0.115289	−	0.354823i
$249$		0			0
$250$	−10.6023	+	3.54833i	−0.670550	+	0.224416i
$251$	0.957281			0.0604230			0.0302115	−	0.999544i	$-0.490382\pi$
$251$	0.957281			0.0604230			0.0302115	+	0.999544i	$0.490382\pi$
$252$		0			0
$253$	22.6865	−	16.4827i	1.42629	−	1.03626i
$254$	−6.03853	+	4.38725i	−0.378891	+	0.275280i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	8.25729			0.515076			0.257538	−	0.966268i	$-0.417089\pi$
$257$	8.25729			0.515076			0.257538	+	0.966268i	$0.417089\pi$
$258$		0			0
$259$	6.59153	−	20.2866i	0.409577	−	1.26055i
$260$	4.79582	−	1.57382i	0.297424	−	0.0976041i
$261$		0			0
$262$	−6.33935	+	19.5105i	−0.391647	+	1.20536i
$263$	0.467126	−	1.43767i	0.0288043	−	0.0886504i	−0.935621	−	0.353006i	$-0.885159\pi$
$263$	0.467126	−	1.43767i	0.0288043	−	0.0886504i	0.964425	+	0.264356i	$0.0851594\pi$
$264$		0			0
$265$	9.23716	+	12.6358i	0.567434	+	0.776209i
$266$	−1.00811	+	3.10263i	−0.0618109	+	0.190234i
$267$		0			0
$268$	−10.0424			−0.613440
$269$	7.96139	+	5.78429i	0.485414	+	0.352674i	0.803418	−	0.595415i	$-0.203012\pi$
$269$	7.96139	+	5.78429i	0.485414	+	0.352674i	−0.318004	+	0.948089i	$0.603012\pi$
$270$		0			0
$271$	−6.96808	+	5.06261i	−0.423281	+	0.307532i	−0.778957	−	0.627078i	$-0.784251\pi$
$271$	−6.96808	+	5.06261i	−0.423281	+	0.307532i	0.355676	+	0.934609i	$0.384251\pi$
$272$	1.31557	−	0.955821i	0.0797684	−	0.0579552i
$273$		0			0
$274$	3.06366			0.185083
$275$	9.86303	+	29.7602i	0.594763	+	1.79461i
$276$		0			0
$277$	4.52373	+	13.9226i	0.271804	+	0.836528i	0.990047	+	0.140735i	$0.0449466\pi$
$277$	4.52373	+	13.9226i	0.271804	+	0.836528i	−0.718243	+	0.695792i	$0.755053\pi$
$278$	13.4934	−	9.80350i	0.809278	−	0.587975i
$279$		0			0
$280$	−3.45483	+	4.78461i	−0.206466	+	0.285935i
$281$	−1.56890	−	1.13987i	−0.0935925	−	0.0679989i	0.540005	−	0.841662i	$-0.318422\pi$
$281$	−1.56890	−	1.13987i	−0.0935925	−	0.0679989i	−0.633597	+	0.773663i	$0.718422\pi$
$282$		0			0
$283$	−1.69481	−	1.23135i	−0.100746	−	0.0731963i	0.536272	−	0.844045i	$-0.319832\pi$
$283$	−1.69481	−	1.23135i	−0.100746	−	0.0731963i	−0.637018	+	0.770849i	$0.719832\pi$
$284$	3.02122	−	9.29836i	0.179276	−	0.551756i
$285$		0			0
$286$	−4.37386	−	13.4614i	−0.258632	−	0.795987i
$287$	−9.37369	+	28.8492i	−0.553311	+	1.70292i
$288$		0			0
$289$	−4.43615	−	13.6531i	−0.260950	−	0.803121i
$290$	8.98275	−	12.4402i	0.527485	−	0.730516i
$291$		0			0
$292$	9.70151	+	7.04856i	0.567738	+	0.412486i
$293$	−24.1031			−1.40812			−0.704059	−	0.710141i	$-0.748631\pi$
$293$	−24.1031			−1.40812			−0.704059	+	0.710141i	$0.748631\pi$
$294$		0			0
$295$	19.2309	+	6.18620i	1.11967	+	0.360175i
$296$	−6.53853	+	4.75052i	−0.380044	+	0.276118i
$297$		0			0
$298$	−4.47619	−	13.7763i	−0.259299	−	0.798039i
$299$	10.0949			0.583803
$300$		0			0
$301$	−5.20928			−0.300258
$302$	3.18443	+	9.80065i	0.183243	+	0.563964i
$303$		0			0
$304$	1.00000	−	0.726543i	0.0573539	−	0.0416701i
$305$	−6.41886	+	2.10645i	−0.367543	+	0.120615i
$306$		0			0
$307$	−14.5670			−0.831385			−0.415692	−	0.909505i	$-0.636461\pi$
$307$	−14.5670			−0.831385			−0.415692	+	0.909505i	$0.636461\pi$
$308$	13.3886	+	9.72737i	0.762885	+	0.554268i
$309$		0			0
$310$	12.5065	+	4.02309i	0.710320	+	0.228496i
$311$	−2.37696	−	7.31552i	−0.134785	−	0.414825i	0.860772	−	0.508991i	$-0.169981\pi$
$311$	−2.37696	−	7.31552i	−0.134785	−	0.414825i	−0.995556	+	0.0941662i	$0.969981\pi$
$312$		0			0
$313$	7.42601	−	22.8549i	0.419743	−	1.29184i	−0.488196	−	0.872734i	$-0.662345\pi$
$313$	7.42601	−	22.8549i	0.419743	−	1.29184i	0.907939	−	0.419102i	$-0.137655\pi$
$314$	−2.34349	−	7.21253i	−0.132251	−	0.407026i
$315$		0			0
$316$	1.16061	−	3.57200i	0.0652897	−	0.200941i
$317$	−9.53161	−	6.92512i	−0.535348	−	0.388953i	0.287006	−	0.957929i	$-0.407340\pi$
$317$	−9.53161	−	6.92512i	−0.535348	−	0.388953i	−0.822355	+	0.568975i	$0.807340\pi$
$318$		0			0
$319$	−34.8110	−	25.2917i	−1.94904	−	1.41606i
$320$	2.12459	−	0.697217i	0.118768	−	0.0389756i
$321$		0			0
$322$	−9.54891	+	6.93769i	−0.532140	+	0.386622i
$323$	0.621130	+	1.91164i	0.0345606	+	0.106367i
$324$		0			0
$325$	−3.42469	+	10.7543i	−0.189967	+	0.596542i
$326$	−14.0000			−0.775388
$327$		0			0
$328$	9.29832	−	6.75563i	0.513414	−	0.373017i
$329$	13.8753	−	10.0810i	0.764971	−	0.555784i
$330$		0			0
$331$	10.9228	+	7.93586i	0.600370	+	0.436194i	0.846010	−	0.533167i	$-0.178998\pi$
$331$	10.9228	+	7.93586i	0.600370	+	0.436194i	−0.245640	+	0.969361i	$0.578998\pi$
$332$	8.37369			0.459566
$333$		0			0
$334$	−5.35556	+	16.4827i	−0.293043	+	0.901895i
$335$	13.1457	−	18.2056i	0.718228	−	0.994677i
$336$		0			0
$337$	7.91075	−	24.3468i	0.430926	−	1.32625i	−0.466278	−	0.884638i	$-0.654405\pi$
$337$	7.91075	−	24.3468i	0.430926	−	1.32625i	0.897204	−	0.441616i	$-0.145595\pi$
$338$	−2.44267	+	7.51777i	−0.132864	+	0.408913i
$339$		0			0
$340$	0.0106634	+	3.63614i	0.000578305	+	0.197198i
$341$	11.3844	−	35.0375i	0.616499	−	1.89739i
$342$		0			0
$343$	−18.5654			−1.00244
$344$	1.59681	+	1.16015i	0.0860944	+	0.0625513i
$345$		0			0
$346$	3.07692	−	2.23551i	0.165416	−	0.120182i
$347$	−0.205646	+	0.149411i	−0.0110397	+	0.00802078i	−0.593291	−	0.804988i	$-0.702172\pi$
$347$	−0.205646	+	0.149411i	−0.0110397	+	0.00802078i	0.582252	+	0.813009i	$0.302172\pi$
$348$		0			0
$349$	−31.6783			−1.69570			−0.847849	−	0.530238i	$-0.822103\pi$
$349$	−31.6783			−1.69570			−0.847849	+	0.530238i	$0.822103\pi$
$350$	−4.15141	−	12.5263i	−0.221902	−	0.669557i
$351$		0			0
$352$	−1.93766	−	5.96351i	−0.103278	−	0.317856i
$353$	23.4295	−	17.0225i	1.24703	−	0.906019i	0.248982	−	0.968508i	$-0.419904\pi$
$353$	23.4295	−	17.0225i	1.24703	−	0.906019i	0.998046	+	0.0624895i	$0.0199040\pi$
$354$		0			0
$355$	12.9018	+	17.6488i	0.684758	+	0.936700i
$356$	−0.315575	−	0.229278i	−0.0167254	−	0.0121517i
$357$		0			0
$358$	0.100866	+	0.0732836i	0.00533095	+	0.00387316i
$359$	2.47715	−	7.62387i	0.130739	−	0.402372i	−0.864164	−	0.503210i	$-0.832152\pi$
$359$	2.47715	−	7.62387i	0.130739	−	0.402372i	0.994903	+	0.100838i	$0.0321522\pi$
$360$		0			0
$361$	−5.39919	−	16.6170i	−0.284168	−	0.874578i
$362$	−2.87946	+	8.86207i	−0.151341	+	0.465780i
$363$		0			0
$364$	1.84099	+	5.66598i	0.0964939	+	0.296978i
$365$	−25.4775	+	8.36083i	−1.33355	+	0.437626i
$366$		0			0
$367$	−12.4056	−	9.01320i	−0.647567	−	0.470485i	0.214874	−	0.976642i	$-0.431066\pi$
$367$	−12.4056	−	9.01320i	−0.647567	−	0.470485i	−0.862442	+	0.506157i	$0.831066\pi$
$368$	4.47214			0.233126
$369$		0			0
$370$	−0.0529982	−	18.0720i	−0.00275524	−	0.939517i
$371$	−14.9460	+	10.8589i	−0.775960	+	0.563768i
$372$		0			0
$373$	5.13261	+	15.7966i	0.265757	+	0.817914i	0.991518	+	0.129968i	$0.0414875\pi$
$373$	5.13261	+	15.7966i	0.265757	+	0.817914i	−0.725762	+	0.687946i	$0.758512\pi$
$374$	10.1966			0.527251
$375$		0			0
$376$	−6.49837			−0.335128
$377$	−4.78667	−	14.7318i	−0.246526	−	0.758729i
$378$		0			0
$379$	−15.8539	+	11.5186i	−0.814362	+	0.591668i	−0.915092	−	0.403245i	$-0.867882\pi$
$379$	−15.8539	+	11.5186i	−0.814362	+	0.591668i	0.100730	+	0.994914i	$0.467882\pi$
$380$	0.00810552	+	2.76392i	0.000415805	+	0.141786i
$381$		0			0
$382$	−3.23607			−0.165572
$383$	−15.5620	−	11.3065i	−0.795182	−	0.577734i	0.114314	−	0.993445i	$-0.463533\pi$
$383$	−15.5620	−	11.3065i	−0.795182	−	0.577734i	−0.909497	+	0.415711i	$0.863533\pi$
$384$		0			0
$385$	−35.1603	+	11.5384i	−1.79193	+	0.588050i
$386$	−3.35720	−	10.3324i	−0.170877	−	0.525905i
$387$		0			0
$388$	0.463977	−	1.42798i	0.0235549	−	0.0724945i
$389$	0.510524	+	1.57123i	0.0258846	+	0.0796646i	0.963164	−	0.268914i	$-0.0866646\pi$
$389$	0.510524	+	1.57123i	0.0258846	+	0.0796646i	−0.937280	+	0.348578i	$0.886665\pi$
$390$		0			0
$391$	−2.24727	+	6.91638i	−0.113649	+	0.349777i
$392$	0.0277780	+	0.0201819i	0.00140300	+	0.00101934i
$393$		0			0
$394$	−7.34335	−	5.33526i	−0.369953	−	0.268786i
$395$	4.95629	+	6.77985i	0.249378	+	0.341131i
$396$		0			0
$397$	6.55392	−	4.76170i	0.328932	−	0.238983i	−0.411045	−	0.911615i	$-0.634836\pi$
$397$	6.55392	−	4.76170i	0.328932	−	0.238983i	0.739977	+	0.672632i	$0.234836\pi$
$398$	8.05716	+	24.7974i	0.403869	+	1.24298i
$399$		0			0
$400$	−1.51717	+	4.76426i	−0.0758584	+	0.238213i
$401$	24.0079			1.19890			0.599449	−	0.800413i	$-0.295386\pi$
$401$	24.0079			1.19890			0.599449	+	0.800413i	$0.295386\pi$
$402$		0			0
$403$	10.7294	−	7.79538i	0.534471	−	0.388316i
$404$	3.79162	−	2.75478i	0.188640	−	0.137055i
$405$		0			0
$406$	14.6522	+	10.6454i	0.727176	+	0.528325i
$407$	−50.6778			−2.51201
$408$		0			0
$409$	−3.50101	+	10.7750i	−0.173114	+	0.532789i	−0.999542	−	0.0302522i	$-0.990369\pi$
$409$	−3.50101	+	10.7750i	−0.173114	+	0.532789i	0.826429	+	0.563042i	$0.190369\pi$
$410$	0.0753678	+	25.6998i	0.00372215	+	1.26922i
$411$		0			0
$412$	−1.32222	+	4.06937i	−0.0651410	+	0.200483i
$413$	−7.36817	+	22.6769i	−0.362564	+	1.11586i
$414$		0			0
$415$	−10.9613	+	15.1804i	−0.538069	+	0.745174i
$416$	0.697541	−	2.14681i	0.0341997	−	0.105256i
$417$		0			0
$418$	7.75065			0.379096
$419$	−18.5382	−	13.4688i	−0.905651	−	0.657994i	0.0342601	−	0.999413i	$-0.489093\pi$
$419$	−18.5382	−	13.4688i	−0.905651	−	0.657994i	−0.939911	+	0.341419i	$0.889093\pi$
$420$		0			0
$421$	−23.7532	+	17.2577i	−1.15766	+	0.841089i	−0.989480	−	0.144667i	$-0.953789\pi$
$421$	−23.7532	+	17.2577i	−1.15766	+	0.841089i	−0.168180	+	0.985756i	$0.553789\pi$
$422$	−12.5408	+	9.11143i	−0.610477	+	0.443537i
$423$		0			0
$424$	6.99983			0.339942
$425$	−6.60579	−	4.74044i	−0.320428	−	0.229945i
$426$		0			0
$427$	−2.46403	−	7.58351i	−0.119243	−	0.366992i
$428$	−15.1974	+	11.0415i	−0.734593	+	0.533713i
$429$		0			0
$430$	−4.19345	+	1.37615i	−0.202226	+	0.0663636i
$431$	3.20173	+	2.32619i	0.154222	+	0.112049i	0.662220	−	0.749309i	$-0.269614\pi$
$431$	3.20173	+	2.32619i	0.154222	+	0.112049i	−0.507998	+	0.861358i	$0.669614\pi$
$432$		0			0
$433$	−0.328915	−	0.238970i	−0.0158066	−	0.0114842i	0.579854	−	0.814720i	$-0.303110\pi$
$433$	−0.328915	−	0.238970i	−0.0158066	−	0.0114842i	−0.595661	+	0.803236i	$0.703110\pi$
$434$	−4.79176	+	14.7475i	−0.230012	+	0.707904i
$435$		0			0
$436$	−4.94982	−	15.2340i	−0.237053	−	0.729575i
$437$	−1.70820	+	5.25731i	−0.0817145	+	0.251491i
$438$		0			0
$439$	−1.76233	−	5.42390i	−0.0841115	−	0.258868i	0.900152	−	0.435576i	$-0.143455\pi$
$439$	−1.76233	−	5.42390i	−0.0841115	−	0.258868i	−0.984263	+	0.176708i	$0.943455\pi$
$440$	13.3475	+	4.29362i	0.636315	+	0.204690i
$441$		0			0
$442$	2.96963	+	2.15756i	0.141251	+	0.102625i
$443$	22.7666			1.08167			0.540836	−	0.841128i	$-0.318108\pi$
$443$	22.7666			1.08167			0.540836	+	0.841128i	$0.318108\pi$
$444$		0			0
$445$	0.828743	−	0.271964i	0.0392862	−	0.0128923i
$446$	−1.45483	+	1.05700i	−0.0688882	+	0.0500502i
$447$		0			0
$448$	0.815575	+	2.51008i	0.0385323	+	0.118590i
$449$	−34.7078			−1.63796			−0.818980	−	0.573822i	$-0.805460\pi$
$449$	−34.7078			−1.63796			−0.818980	+	0.573822i	$0.805460\pi$
$450$		0			0
$451$	72.0680			3.39355
$452$	2.98776	+	9.19537i	0.140532	+	0.432514i
$453$		0			0
$454$	−0.836795	+	0.607967i	−0.0392727	+	0.0285333i
$455$	−12.6815	−	4.07940i	−0.594519	−	0.191245i
$456$		0			0
$457$	36.5194			1.70831			0.854153	−	0.520022i	$-0.174076\pi$
$457$	36.5194			1.70831			0.854153	+	0.520022i	$0.174076\pi$
$458$	2.21626	+	1.61020i	0.103559	+	0.0752399i
$459$		0			0
$460$	−5.85410	+	8.10737i	−0.272949	+	0.378008i
$461$	−9.21772	−	28.3692i	−0.429312	−	1.32129i	−0.898804	−	0.438350i	$-0.855563\pi$
$461$	−9.21772	−	28.3692i	−0.429312	−	1.32129i	0.469492	−	0.882936i	$-0.344437\pi$
$462$		0			0
$463$	−11.3555	+	34.9485i	−0.527733	+	1.62419i	0.231115	+	0.972927i	$0.425763\pi$
$463$	−11.3555	+	34.9485i	−0.527733	+	1.62419i	−0.758848	+	0.651268i	$0.774237\pi$
$464$	−2.12054	−	6.52635i	−0.0984435	−	0.302978i
$465$		0			0
$466$	−5.56785	+	17.1361i	−0.257926	+	0.793814i
$467$	17.7336	+	12.8842i	0.820614	+	0.596211i	0.916888	−	0.399144i	$-0.130693\pi$
$467$	17.7336	+	12.8842i	0.820614	+	0.596211i	−0.0962744	+	0.995355i	$0.530693\pi$
$468$		0			0
$469$	21.4426	+	15.5790i	0.990129	+	0.719371i
$470$	8.50647	−	11.7807i	0.392374	−	0.543401i
$471$		0			0
$472$	7.30893	−	5.31025i	0.336421	−	0.244424i
$473$	3.82450	+	11.7706i	0.175851	+	0.541212i
$474$		0			0
$475$	−5.02122	−	3.60332i	−0.230389	−	0.165332i
$476$	−4.29180			−0.196714
$477$		0			0
$478$	−2.20173	+	1.59965i	−0.100705	+	0.0731664i
$479$	−5.88844	+	4.27820i	−0.269050	+	0.195476i	−0.714127	−	0.700016i	$-0.753176\pi$
$479$	−5.88844	+	4.27820i	−0.269050	+	0.195476i	0.445077	+	0.895492i	$0.353176\pi$
$480$		0			0
$481$	−14.7593	−	10.7233i	−0.672968	−	0.488940i
$482$	1.50146			0.0683897
$483$		0			0
$484$	8.75073	−	26.9320i	0.397761	−	1.22418i
$485$	1.98137	+	2.71037i	0.0899694	+	0.123072i
$486$		0			0
$487$	−9.70333	+	29.8638i	−0.439700	+	1.35326i	0.448493	+	0.893787i	$0.351961\pi$
$487$	−9.70333	+	29.8638i	−0.439700	+	1.35326i	−0.888193	+	0.459471i	$0.848039\pi$
$488$	−0.933608	+	2.87335i	−0.0422625	+	0.130071i
$489$		0			0
$490$	−0.0729490	+	0.0239393i	−0.00329550	+	0.00108147i
$491$	8.18133	−	25.1795i	0.369218	−	1.13634i	−0.578079	−	0.815981i	$-0.696197\pi$
$491$	8.18133	−	25.1795i	0.369218	−	1.13634i	0.947297	−	0.320356i	$-0.103803\pi$
$492$		0			0
$493$	11.1589			0.502572
$494$	2.25729	+	1.64002i	0.101560	+	0.0737878i
$495$		0			0
$496$	4.75324	−	3.45343i	0.213427	−	0.155063i
$497$	−20.8756	+	15.1670i	−0.936399	+	0.680333i
$498$		0			0
$499$	−28.1904			−1.26197			−0.630987	−	0.775793i	$-0.717350\pi$
$499$	−28.1904			−1.26197			−0.630987	+	0.775793i	$0.717350\pi$
$500$	−6.65096	−	8.98692i	−0.297440	−	0.401907i
$501$		0			0
$502$	0.295816	+	0.910428i	0.0132029	+	0.0406344i
$503$	5.76421	−	4.18794i	0.257013	−	0.186731i	−0.451816	−	0.892111i	$-0.649224\pi$
$503$	5.76421	−	4.18794i	0.257013	−	0.186731i	0.708829	+	0.705380i	$0.249224\pi$
$504$		0			0
$505$	0.0307331	+	10.4797i	0.00136760	+	0.466343i
$506$	22.6865	+	16.4827i	1.00854	+	0.732747i
$507$		0			0
$508$	−6.03853	−	4.38725i	−0.267916	−	0.194653i
$509$	2.61038	−	8.03393i	0.115703	−	0.356097i	−0.876390	−	0.481602i	$-0.840055\pi$
$509$	2.61038	−	8.03393i	0.115703	−	0.356097i	0.992093	+	0.125505i	$0.0400550\pi$
$510$		0			0
$511$	−9.78014	−	30.1002i	−0.432648	−	1.33155i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$		0			0
$514$	2.55164	+	7.85315i	0.112548	+	0.346388i
$515$	−5.64640	−	7.72387i	−0.248810	−	0.340355i
$516$		0			0
$517$	−32.9653	−	23.9507i	−1.44981	−	1.05335i
$518$	21.3306			0.937214
$519$		0			0
$520$	2.97878	+	4.07476i	0.130628	+	0.178690i
$521$	−11.4788	+	8.33986i	−0.502897	+	0.365376i	−0.810122	−	0.586261i	$-0.800599\pi$
$521$	−11.4788	+	8.33986i	−0.502897	+	0.365376i	0.307226	+	0.951637i	$0.400599\pi$
$522$		0			0
$523$	−5.88343	−	18.1073i	−0.257264	−	0.791778i	−0.993375	−	0.114917i	$-0.963340\pi$
$523$	−5.88343	−	18.1073i	−0.257264	−	0.791778i	0.736111	−	0.676861i	$-0.236660\pi$
$524$	−20.5146			−0.896183
$525$		0			0
$526$	1.51165			0.0659112
$527$	2.95238	+	9.08648i	0.128608	+	0.395813i
$528$		0			0
$529$	2.42705	−	1.76336i	0.105524	−	0.0766676i
$530$	−9.16289	+	12.6897i	−0.398011	+	0.551207i
$531$		0			0
$532$	−3.26230			−0.141439
$533$	20.9890	+	15.2494i	0.909134	+	0.660525i
$534$		0			0
$535$	−0.123183	−	42.0043i	−0.00532565	−	1.81600i
$536$	−3.10328	−	9.55093i	−0.134041	−	0.412537i
$537$		0			0
$538$	−3.04098	+	9.35917i	−0.131106	+	0.403503i
$539$	0.0665307	+	0.204760i	0.00286568	+	0.00881965i
$540$		0			0
$541$	4.88256	−	15.0270i	0.209918	−	0.646060i	−0.789558	−	0.613676i	$-0.789690\pi$
$541$	4.88256	−	15.0270i	0.209918	−	0.646060i	0.999476	−	0.0323838i	$-0.0103099\pi$
$542$	−6.96808	−	5.06261i	−0.299305	−	0.217458i
$543$		0			0
$544$	1.31557	+	0.955821i	0.0564048	+	0.0409805i
$545$	34.0965	+	10.9682i	1.46053	+	0.469826i
$546$		0			0
$547$	−17.0558	+	12.3918i	−0.729255	+	0.529835i	−0.889328	−	0.457271i	$-0.848827\pi$
$547$	−17.0558	+	12.3918i	−0.729255	+	0.529835i	0.160073	+	0.987105i	$0.448827\pi$
$548$	0.946724	+	2.91372i	0.0404420	+	0.124468i
$549$		0			0
$550$	−25.2558	+	18.5767i	−1.07691	+	0.792113i
$551$	8.48215			0.361352
$552$		0			0
$553$	−8.01945	+	5.82647i	−0.341022	+	0.247767i
$554$	−11.8433	+	8.60464i	−0.503172	+	0.365576i
$555$		0			0
$556$	13.4934	+	9.80350i	0.572246	+	0.415761i
$557$	−10.1705			−0.430938			−0.215469	−	0.976511i	$-0.569128\pi$
$557$	−10.1705			−0.430938			−0.215469	+	0.976511i	$0.569128\pi$
$558$		0			0
$559$	−1.37678	+	4.23731i	−0.0582318	+	0.179219i
$560$	−5.61803	−	1.80721i	−0.237405	−	0.0763687i
$561$		0			0
$562$	0.599265	−	1.84435i	0.0252785	−	0.0777991i
$563$	6.12049	−	18.8369i	0.257948	−	0.793881i	−0.735287	−	0.677756i	$-0.762953\pi$
$563$	6.12049	−	18.8369i	0.257948	−	0.793881i	0.993235	−	0.116125i	$-0.0370474\pi$
$564$		0			0
$565$	−20.5810	−	6.62050i	−0.865848	−	0.278526i
$566$	0.647360	−	1.99237i	0.0272106	−	0.0837455i
$567$		0			0
$568$	9.77688			0.410229
$569$	8.34991	+	6.06656i	0.350046	+	0.254324i	0.748889	−	0.662696i	$-0.230588\pi$
$569$	8.34991	+	6.06656i	0.350046	+	0.254324i	−0.398842	+	0.917020i	$0.630588\pi$
$570$		0			0
$571$	−9.50146	+	6.90322i	−0.397624	+	0.288891i	−0.768572	−	0.639763i	$-0.779033\pi$
$571$	−9.50146	+	6.90322i	−0.397624	+	0.288891i	0.370949	+	0.928653i	$0.379033\pi$
$572$	11.4509	−	8.31958i	0.478787	−	0.347859i
$573$		0			0
$574$	−30.3339			−1.26611
$575$	−7.03444	−	21.2254i	−0.293357	−	0.885159i
$576$		0			0
$577$	3.30910	+	10.1844i	0.137760	+	0.423981i	0.996009	−	0.0892521i	$-0.0284477\pi$
$577$	3.30910	+	10.1844i	0.137760	+	0.423981i	−0.858249	+	0.513233i	$0.828448\pi$
$578$	11.6140	−	8.43805i	0.483078	−	0.350977i
$579$		0			0
$580$	14.6072	+	4.69885i	0.606531	+	0.195109i
$581$	−17.8795	−	12.9902i	−0.741767	−	0.538925i
$582$		0			0
$583$	35.5092	+	25.7989i	1.47064	+	1.06848i
$584$	−3.70565	+	11.4048i	−0.153341	+	0.471934i
$585$		0			0
$586$	−7.44827	−	22.9234i	−0.307685	−	0.946958i
$587$	11.4736	−	35.3122i	0.473567	−	1.45749i	−0.374313	−	0.927303i	$-0.622121\pi$
$587$	11.4736	−	35.3122i	0.473567	−	1.45749i	0.847880	−	0.530188i	$-0.177879\pi$
$588$		0			0
$589$	2.24417	+	6.90686i	0.0924696	+	0.284592i
$590$	0.0592427	+	20.2013i	0.00243898	+	0.831674i
$591$		0			0
$592$	−6.53853	−	4.75052i	−0.268732	−	0.195245i
$593$	16.5966			0.681542			0.340771	−	0.940146i	$-0.389312\pi$
$593$	16.5966			0.681542			0.340771	+	0.940146i	$0.389312\pi$
$594$		0			0
$595$	5.61803	−	7.78044i	0.230317	−	0.318967i
$596$	11.7188	−	8.51422i	0.480021	−	0.348756i
$597$		0			0
$598$	3.11950	+	9.60082i	0.127566	+	0.392607i
$599$	−45.8295			−1.87254			−0.936272	−	0.351275i	$-0.885748\pi$
$599$	−45.8295			−1.87254			−0.936272	+	0.351275i	$0.885748\pi$
$600$		0			0
$601$	−23.3609			−0.952909			−0.476455	−	0.879199i	$-0.658078\pi$
$601$	−23.3609			−0.952909			−0.476455	+	0.879199i	$0.658078\pi$
$602$	−1.60976	−	4.95432i	−0.0656088	−	0.201923i
$603$		0			0
$604$	−8.33693	+	6.05714i	−0.339225	+	0.246461i
$605$	37.3692	+	51.1183i	1.51927	+	2.07825i
$606$		0			0
$607$	21.3526			0.866674			0.433337	−	0.901232i	$-0.357336\pi$
$607$	21.3526			0.866674			0.433337	+	0.901232i	$0.357336\pi$
$608$	1.00000	+	0.726543i	0.0405554	+	0.0294652i
$609$		0			0
$610$	−3.98688	−	5.45377i	−0.161424	−	0.220817i
$611$	−4.53287	−	13.9508i	−0.183380	−	0.564387i
$612$		0			0
$613$	10.4761	−	32.2421i	0.423126	−	1.30225i	−0.481652	−	0.876363i	$-0.659963\pi$
$613$	10.4761	−	32.2421i	0.423126	−	1.30225i	0.904777	−	0.425885i	$-0.140037\pi$
$614$	−4.50146	−	13.8541i	−0.181664	−	0.559105i
$615$		0			0
$616$	−5.11398	+	15.7392i	−0.206048	+	0.634151i
$617$	5.59850	+	4.06755i	0.225387	+	0.163753i	0.694748	−	0.719253i	$-0.255516\pi$
$617$	5.59850	+	4.06755i	0.225387	+	0.163753i	−0.469361	+	0.883006i	$0.655516\pi$
$618$		0			0
$619$	11.1538	+	8.10373i	0.448310	+	0.325717i	0.788928	−	0.614485i	$-0.210636\pi$
$619$	11.1538	+	8.10373i	0.448310	+	0.325717i	−0.340618	+	0.940202i	$0.610636\pi$
$620$	0.0385275	+	13.1376i	0.00154730	+	0.527617i
$621$		0			0
$622$	6.22295	−	4.52124i	0.249518	−	0.181285i
$623$	0.318132	+	0.979111i	0.0127457	+	0.0392272i
$624$		0			0
$625$	24.9983	−	0.293254i	0.999931	−	0.0117302i
$626$	24.0311			0.960475
$627$		0			0
$628$	6.13534	−	4.45759i	0.244827	−	0.177877i
$629$	10.6326	−	7.72501i	0.423948	−	0.308016i
$630$		0			0
$631$	−9.03461	−	6.56403i	−0.359662	−	0.261310i	0.393249	−	0.919432i	$-0.371351\pi$
$631$	−9.03461	−	6.56403i	−0.359662	−	0.261310i	−0.752911	+	0.658122i	$0.771351\pi$
$632$	3.75583			0.149399
$633$		0			0
$634$	3.64075	−	11.2051i	0.144593	−	0.445010i
$635$	15.8580	−	5.20405i	0.629306	−	0.206516i
$636$		0			0
$637$	−0.0239504	+	0.0737119i	−0.000948951	+	0.00292057i
$638$	13.2966	−	40.9228i	0.526419	−	1.62015i
$639$		0			0
$640$	1.31963	+	1.80515i	0.0521628	+	0.0713550i
$641$	−4.97551	+	15.3130i	−0.196521	+	0.604829i	0.803435	+	0.595393i	$0.203004\pi$
$641$	−4.97551	+	15.3130i	−0.196521	+	0.604829i	−0.999955	+	0.00943607i	$0.996996\pi$
$642$		0			0
$643$	−2.52460			−0.0995603			−0.0497802	−	0.998760i	$-0.515852\pi$
$643$	−2.52460			−0.0995603			−0.0497802	+	0.998760i	$0.515852\pi$
$644$	−9.54891	−	6.93769i	−0.376280	−	0.273383i
$645$		0			0
$646$	−1.62614	+	1.18146i	−0.0639796	+	0.0464839i
$647$	−0.896543	+	0.651377i	−0.0352467	+	0.0256083i	−0.605269	−	0.796021i	$-0.706935\pi$
$647$	−0.896543	+	0.651377i	−0.0352467	+	0.0256083i	0.570022	+	0.821629i	$0.306935\pi$
$648$		0			0
$649$	56.6489			2.22366
$650$	−11.2862	+	0.0661971i	−0.442683	+	0.00259646i
$651$		0			0
$652$	−4.32624	−	13.3148i	−0.169429	−	0.521447i
$653$	26.1323	−	18.9862i	1.02264	−	0.742988i	0.0558144	−	0.998441i	$-0.482225\pi$
$653$	26.1323	−	18.9862i	1.02264	−	0.742988i	0.966822	+	0.255453i	$0.0822245\pi$
$654$		0			0
$655$	26.8539	−	37.1901i	1.04927	−	1.45314i
$656$	9.29832	+	6.75563i	0.363038	+	0.263763i
$657$		0			0
$658$	13.8753	+	10.0810i	0.540916	+	0.392999i
$659$	0.654648	−	2.01480i	0.0255015	−	0.0784854i	−0.937496	−	0.347997i	$-0.886862\pi$
$659$	0.654648	−	2.01480i	0.0255015	−	0.0784854i	0.962997	+	0.269511i	$0.0868621\pi$
$660$		0			0
$661$	−15.3606	−	47.2750i	−0.597457	−	1.83878i	−0.542095	−	0.840317i	$-0.682369\pi$
$661$	−15.3606	−	47.2750i	−0.597457	−	1.83878i	−0.0553624	−	0.998466i	$-0.517631\pi$
$662$	−4.17213	+	12.8405i	−0.162154	+	0.499060i
$663$		0			0
$664$	2.58761	+	7.96385i	0.100419	+	0.309057i
$665$	4.27040	−	5.91410i	0.165599	−	0.229339i
$666$		0			0
$667$	24.8277	+	18.0384i	0.961332	+	0.698449i
$668$	−17.3310			−0.670555
$669$		0			0
$670$	21.3768	+	6.87650i	0.825857	+	0.265662i
$671$	−15.3262	+	11.1352i	−0.591663	+	0.429868i
$672$		0			0
$673$	−2.85916	−	8.79960i	−0.110213	−	0.339200i	0.880706	−	0.473664i	$-0.157069\pi$
$673$	−2.85916	−	8.79960i	−0.110213	−	0.339200i	−0.990918	+	0.134464i	$0.957069\pi$
$674$	25.5997			0.986065
$675$		0			0
$676$	−7.90465			−0.304025
$677$	10.8742	+	33.4674i	0.417930	+	1.28626i	0.909603	+	0.415478i	$0.136386\pi$
$677$	10.8742	+	33.4674i	0.417930	+	1.28626i	−0.491673	+	0.870780i	$0.663614\pi$
$678$		0			0
$679$	−3.20592	+	2.32924i	−0.123032	+	0.0893880i
$680$	−3.45488	+	1.13377i	−0.132489	+	0.0434782i
$681$		0			0
$682$	36.8406			1.41070
$683$	16.1761	+	11.7527i	0.618963	+	0.449703i	0.852559	−	0.522631i	$-0.175049\pi$
$683$	16.1761	+	11.7527i	0.618963	+	0.449703i	−0.233596	+	0.972334i	$0.575049\pi$
$684$		0			0
$685$	−6.52145	−	2.09782i	−0.249172	−	0.0801537i
$686$	−5.73702	−	17.6567i	−0.219041	−	0.674138i
$687$		0			0
$688$	−0.609928	+	1.87717i	−0.0232533	+	0.0715663i
$689$	4.88266	+	15.0273i	0.186015	+	0.572494i
$690$		0			0
$691$	4.81448	−	14.8174i	0.183151	−	0.563682i	−0.816760	−	0.576977i	$-0.804232\pi$
$691$	4.81448	−	14.8174i	0.183151	−	0.563682i	0.999912	+	0.0132952i	$0.00423212\pi$
$692$	3.07692	+	2.23551i	0.116967	+	0.0849813i
$693$		0			0
$694$	−0.205646	−	0.149411i	−0.00780622	−	0.00567155i
$695$	−35.4354	+	11.6287i	−1.34414	+	0.441101i
$696$		0			0
$697$	−15.1204	+	10.9856i	−0.572725	+	0.416109i
$698$	−9.78912	−	30.1278i	−0.370524	−	1.14035i
$699$		0			0
$700$	10.6303	−	7.81906i	0.401789	−	0.295533i
$701$	28.2932			1.06862			0.534310	−	0.845289i	$-0.320572\pi$
$701$	28.2932			1.06862			0.534310	+	0.845289i	$0.320572\pi$
$702$		0			0
$703$	8.08206	−	5.87196i	0.304821	−	0.221465i
$704$	5.07286	−	3.68565i	0.191191	−	0.138908i
$705$		0			0
$706$	23.4295	+	17.0225i	0.881782	+	0.640652i
$707$	−12.3694			−0.465199
$708$		0			0
$709$	4.10591	−	12.6367i	0.154201	−	0.474581i	−0.843878	−	0.536534i	$-0.819733\pi$
$709$	4.10591	−	12.6367i	0.154201	−	0.474581i	0.998079	+	0.0619537i	$0.0197331\pi$
$710$	−12.7981	+	17.7241i	−0.480304	+	0.665175i
$711$		0			0
$712$	0.120539	−	0.370980i	0.00451738	−	0.0139031i
$713$	−8.11950	+	24.9892i	−0.304078	+	0.935854i
$714$		0			0
$715$	0.0928157	+	31.6494i	0.00347111	+	1.18362i
$716$	−0.0385275	+	0.118575i	−0.00143984	+	0.00443137i
$717$		0			0
$718$	8.01621			0.299162
$719$	−38.2407	−	27.7835i	−1.42614	−	1.03615i	−0.990719	−	0.135923i	$-0.956600\pi$
$719$	−38.2407	−	27.7835i	−1.42614	−	1.03615i	−0.435419	−	0.900228i	$-0.643400\pi$
$720$		0			0
$721$	9.13607	−	6.63775i	0.340245	−	0.247203i
$722$	14.1353	−	10.2699i	0.526060	−	0.382205i
$723$		0			0
$724$	−9.31813			−0.346306
$725$	−27.6394	+	20.3300i	−1.02650	+	0.755037i
$726$		0			0
$727$	−4.33935	−	13.3552i	−0.160938	−	0.495315i	0.837776	−	0.546014i	$-0.183855\pi$
$727$	−4.33935	−	13.3552i	−0.160938	−	0.495315i	−0.998714	+	0.0506983i	$0.983855\pi$
$728$	−4.81977	+	3.50177i	−0.178632	+	0.129784i
$729$		0			0
$730$	−15.8246	−	21.6469i	−0.585695	−	0.801188i
$731$	−2.59664	−	1.88657i	−0.0960403	−	0.0697773i
$732$		0			0
$733$	37.7288	+	27.4116i	1.39355	+	1.01247i	0.995466	+	0.0951187i	$0.0303231\pi$
$733$	37.7288	+	27.4116i	1.39355	+	1.01247i	0.398079	+	0.917351i	$0.369677\pi$
$734$	4.73852	−	14.5837i	0.174902	−	0.538293i
$735$		0			0
$736$	1.38197	+	4.25325i	0.0509399	+	0.156777i
$737$	19.4588	−	59.8882i	0.716776	−	2.20601i
$738$		0			0
$739$	2.84791	+	8.76497i	0.104762	+	0.322424i	0.989675	−	0.143333i	$-0.0457820\pi$
$739$	2.84791	+	8.76497i	0.104762	+	0.322424i	−0.884912	+	0.465757i	$0.845782\pi$
$740$	17.1711	−	5.63495i	0.631222	−	0.207145i
$741$		0			0
$742$	−14.9460	−	10.8589i	−0.548687	−	0.398644i
$743$	−17.7239			−0.650225			−0.325113	−	0.945675i	$-0.605402\pi$
$743$	−17.7239			−0.650225			−0.325113	+	0.945675i	$0.605402\pi$
$744$		0			0
$745$	0.0949871	+	32.3899i	0.00348006	+	1.18667i
$746$	−13.4374	+	9.76281i	−0.491976	+	0.357442i
$747$		0			0
$748$	3.15091	+	9.69750i	0.115209	+	0.354576i
$749$	49.5783			1.81155
$750$		0			0
$751$	−24.1305			−0.880535			−0.440268	−	0.897867i	$-0.645116\pi$
$751$	−24.1305			−0.880535			−0.440268	+	0.897867i	$0.645116\pi$
$752$	−2.00811	−	6.18031i	−0.0732281	−	0.225373i
$753$		0			0
$754$	12.5317	−	9.10478i	0.456376	−	0.331577i
$755$	−0.0675752	−	23.0426i	−0.00245931	−	0.838607i
$756$		0			0
$757$	−46.8140			−1.70148			−0.850741	−	0.525585i	$-0.823847\pi$
$757$	−46.8140			−1.70148			−0.850741	+	0.525585i	$0.823847\pi$
$758$	−15.8539	−	11.5186i	−0.575841	−	0.418373i
$759$		0			0
$760$	−2.62614	+	0.861807i	−0.0952601	+	0.0312610i
$761$	14.3023	+	44.0179i	0.518458	+	1.59565i	0.776902	+	0.629622i	$0.216790\pi$
$761$	14.3023	+	44.0179i	0.518458	+	1.59565i	−0.258444	+	0.966026i	$0.583210\pi$
$762$		0			0
$763$	−13.0638	+	40.2063i	−0.472943	+	1.45557i
$764$	−1.00000	−	3.07768i	−0.0361787	−	0.111347i
$765$		0			0
$766$	5.94417	−	18.2943i	0.214771	−	0.660999i
$767$	16.4984	+	11.9868i	0.595721	+	0.432817i
$768$		0			0
$769$	30.7054	+	22.3088i	1.10727	+	0.804476i	0.982231	−	0.187676i	$-0.0600955\pi$
$769$	30.7054	+	22.3088i	1.10727	+	0.804476i	0.125036	+	0.992152i	$0.460096\pi$
$770$	−21.8388	−	29.8739i	−0.787014	−	1.07658i
$771$		0			0
$772$	8.78926	−	6.38577i	0.316332	−	0.229829i
$773$	−16.3878	−	50.4363i	−0.589427	−	1.81407i	−0.580715	−	0.814107i	$-0.697227\pi$
$773$	−16.3878	−	50.4363i	−0.589427	−	1.81407i	−0.00871188	−	0.999962i	$-0.502773\pi$
$774$		0			0
$775$	−23.8670	−	17.1274i	−0.857330	−	0.615236i
$776$	1.50146			0.0538993
$777$		0			0
$778$	−1.33657	+	0.971075i	−0.0479184	+	0.0348147i
$779$	−11.4934	+	8.35041i	−0.411792	+	0.299185i
$780$		0			0
$781$	49.5967	+	36.0341i	1.77471	+	1.28940i
$782$	−7.27232			−0.260058
$783$		0			0
$784$	−0.0106103	+	0.0326550i	−0.000378938	+	0.00116625i
$785$	0.0497302	+	16.9576i	0.00177495	+	0.605242i
$786$		0			0
$787$	3.52776	−	10.8573i	0.125751	−	0.387022i	−0.868286	−	0.496064i	$-0.834778\pi$
$787$	3.52776	−	10.8573i	0.125751	−	0.387022i	0.994037	+	0.109042i	$0.0347783\pi$
$788$	2.80491	−	8.63263i	0.0999208	−	0.307525i
$789$		0			0
$790$	−4.91644	+	6.80880i	−0.174919	+	0.242246i
$791$	7.88545	−	24.2689i	0.280374	−	0.862903i
$792$		0			0
$793$	−6.81977			−0.242177
$794$	6.55392	+	4.76170i	0.232590	+	0.168987i
$795$		0			0
$796$	−21.0939	+	15.3256i	−0.747654	+	0.543202i
$797$	20.1910	−	14.6696i	0.715200	−	0.519623i	−0.169647	−	0.985505i	$-0.554263\pi$
$797$	20.1910	−	14.6696i	0.715200	−	0.519623i	0.884847	+	0.465882i	$0.154263\pi$
$798$		0			0
$799$	10.5672			0.373842
$800$	−4.99991	+	0.0293259i	−0.176774	+	0.00103683i
$801$		0			0
$802$	7.41886	+	22.8329i	0.261969	+	0.806258i
$803$	−60.8324	+	44.1973i	−2.14673	+	1.55969i
$804$		0			0
$805$	25.0768	−	8.22932i	0.883840	−	0.290045i
$806$	10.7294	+	7.79538i	0.377928	+	0.274581i
$807$		0			0
$808$	3.79162	+	2.75478i	0.133389	+	0.0969127i
$809$	−6.13985	+	18.8965i	−0.215865	+	0.664366i	0.783226	+	0.621738i	$0.213573\pi$
$809$	−6.13985	+	18.8965i	−0.215865	+	0.664366i	−0.999091	+	0.0426279i	$0.986427\pi$
$810$		0			0
$811$	−1.19554	−	3.67949i	−0.0419811	−	0.129205i	0.927869	−	0.372906i	$-0.121638\pi$
$811$	−1.19554	−	3.67949i	−0.0419811	−	0.129205i	−0.969850	+	0.243701i	$0.921638\pi$
$812$	−5.59664	+	17.2247i	−0.196404	+	0.604468i
$813$		0			0
$814$	−15.6603	−	48.1975i	−0.548893	−	1.68932i
$815$	29.8010	+	9.58641i	1.04388	+	0.335797i
$816$		0			0
$817$	−1.97377	−	1.43403i	−0.0690535	−	0.0501703i
$818$	−11.3295			−0.396127
$819$		0			0
$820$	−24.4187	+	8.01336i	−0.852738	+	0.279839i
$821$	−8.80907	+	6.40016i	−0.307439	+	0.223367i	−0.730797	−	0.682595i	$-0.760851\pi$
$821$	−8.80907	+	6.40016i	−0.307439	+	0.223367i	0.423358	+	0.905962i	$0.360851\pi$
$822$		0			0
$823$	−3.17874	−	9.78315i	−0.110804	−	0.341019i	0.880245	−	0.474520i	$-0.157378\pi$
$823$	−3.17874	−	9.78315i	−0.110804	−	0.341019i	−0.991049	+	0.133500i	$0.957378\pi$
$824$	−4.27879			−0.149059
$825$		0			0
$826$	−23.8439			−0.829636
$827$	−5.23497	−	16.1116i	−0.182038	−	0.560255i	0.817847	−	0.575436i	$-0.195168\pi$
$827$	−5.23497	−	16.1116i	−0.182038	−	0.560255i	−0.999885	+	0.0151810i	$0.995168\pi$
$828$		0			0
$829$	12.2855	−	8.92593i	0.426692	−	0.310010i	−0.353633	−	0.935384i	$-0.615054\pi$
$829$	12.2855	−	8.92593i	0.426692	−	0.310010i	0.780325	+	0.625374i	$0.215054\pi$
$830$	−17.8246	−	5.73383i	−0.618701	−	0.199024i
$831$		0			0
$832$	2.25729			0.0782574
$833$	−0.0451710	−	0.0328186i	−0.00156508	−	0.00113710i
$834$		0			0
$835$	22.6865	−	31.4187i	0.785100	−	1.08729i
$836$	2.39508	+	7.37130i	0.0828356	+	0.254942i
$837$		0			0
$838$	7.08097	−	21.7930i	0.244608	−	0.752826i
$839$	−1.70827	−	5.25751i	−0.0589760	−	0.181510i	0.917228	−	0.398362i	$-0.130421\pi$
$839$	−1.70827	−	5.25751i	−0.0589760	−	0.181510i	−0.976204	+	0.216852i	$0.930421\pi$
$840$		0			0
$841$	5.59008	−	17.2045i	0.192762	−	0.593259i
$842$	−23.7532	−	17.2577i	−0.818589	−	0.594740i
$843$		0			0
$844$	−12.5408	−	9.11143i	−0.431672	−	0.313628i
$845$	10.3473	−	14.3300i	0.355959	−	0.492969i
$846$		0			0
$847$	−60.4646	+	43.9301i	−2.07759	+	1.50946i
$848$	2.16307	+	6.65723i	0.0742800	+	0.228610i
$849$		0			0
$850$	2.46713	−	7.74736i	0.0846217	−	0.265732i
$851$	36.1441			1.23900
$852$		0			0
$853$	−11.5422	+	8.38591i	−0.395198	+	0.287128i	−0.767582	−	0.640951i	$-0.778540\pi$
$853$	−11.5422	+	8.38591i	−0.395198	+	0.287128i	0.372384	+	0.928079i	$0.378540\pi$
$854$	6.45092	−	4.68686i	0.220746	−	0.160381i
$855$		0			0
$856$	−15.1974	−	11.0415i	−0.519435	−	0.377392i
$857$	−9.45919			−0.323120			−0.161560	−	0.986863i	$-0.551653\pi$
$857$	−9.45919			−0.323120			−0.161560	+	0.986863i	$0.551653\pi$
$858$		0			0
$859$	−7.59355	+	23.3705i	−0.259088	+	0.797392i	0.733908	+	0.679249i	$0.237694\pi$
$859$	−7.59355	+	23.3705i	−0.259088	+	0.797392i	−0.992997	+	0.118143i	$0.962306\pi$
$860$	−2.60464	−	3.56296i	−0.0888175	−	0.121496i
$861$		0			0
$862$	−1.22295	+	3.76386i	−0.0416539	+	0.128198i
$863$	−7.80637	+	24.0255i	−0.265732	+	0.817839i	0.725792	+	0.687914i	$0.241474\pi$
$863$	−7.80637	+	24.0255i	−0.265732	+	0.817839i	−0.991524	+	0.129925i	$0.958526\pi$
$864$		0			0
$865$	−8.08041	+	2.65171i	−0.274742	+	0.0901608i
$866$	0.125634	−	0.386662i	0.00426922	−	0.0131393i
$867$		0			0
$868$	−15.5065			−0.526324
$869$	19.0528	+	13.8427i	0.646322	+	0.469580i
$870$		0			0
$871$	18.3394	−	13.3243i	0.621405	−	0.451477i
$872$	12.9588	−	9.41512i	0.438840	−	0.318836i
$873$		0			0
$874$	−5.52786			−0.186983
$875$	0.259601	+	29.5066i	0.00877611	+	0.997506i
$876$		0			0
$877$	−10.6956	−	32.9178i	−0.361166	−	1.11155i	−0.952347	−	0.305015i	$-0.901338\pi$
$877$	−10.6956	−	32.9178i	−0.361166	−	1.11155i	0.591182	−	0.806538i	$-0.298662\pi$
$878$	4.61384	−	3.35215i	0.155710	−	0.113130i
$879$		0			0
$880$	0.0411182	+	14.0210i	0.00138609	+	0.472647i
$881$	−33.4160	−	24.2781i	−1.12581	−	0.817950i	−0.140732	−	0.990048i	$-0.544946\pi$
$881$	−33.4160	−	24.2781i	−1.12581	−	0.817950i	−0.985080	+	0.172097i	$0.944946\pi$
$882$		0			0
$883$	−33.7636	−	24.5307i	−1.13624	−	0.825523i	−0.149645	−	0.988740i	$-0.547813\pi$
$883$	−33.7636	−	24.5307i	−1.13624	−	0.825523i	−0.986590	+	0.163217i	$0.947813\pi$
$884$	−1.13430	+	3.49101i	−0.0381506	+	0.117415i
$885$		0			0
$886$	7.03526	+	21.6523i	0.236354	+	0.727423i
$887$	7.17533	−	22.0834i	0.240924	−	0.741488i	−0.755356	−	0.655315i	$-0.772536\pi$
$887$	7.17533	−	22.0834i	0.240924	−	0.741488i	0.996280	−	0.0861734i	$-0.0274639\pi$
$888$		0			0
$889$	6.08747	+	18.7353i	0.204167	+	0.628362i
$890$	0.514749	+	0.704140i	0.0172544	+	0.0236028i
$891$		0			0
$892$	−1.45483	−	1.05700i	−0.0487113	−	0.0353908i
$893$	8.03242			0.268795
$894$		0			0
$895$	−0.164528	−	0.225062i	−0.00549956	−	0.00752300i
$896$	−2.13520	+	1.55131i	−0.0713321	+	0.0518258i
$897$		0			0
$898$	−10.7253	−	33.0090i	−0.357907	−	1.10153i
$899$	40.3177			1.34467
$900$		0			0
$901$	−11.3827			−0.379213
$902$	22.2702	+	68.5407i	0.741518	+	2.28216i
$903$		0			0
$904$	−7.82205	+	5.68305i	−0.260157	+	0.189015i
$905$	12.1976	−	16.8925i	0.405462	−	0.561526i
$906$		0			0
$907$	33.4166			1.10958			0.554790	−	0.831990i	$-0.312798\pi$
$907$	33.4166			1.10958			0.554790	+	0.831990i	$0.312798\pi$
$908$	−0.836795	−	0.607967i	−0.0277700	−	0.0201761i
$909$		0			0
$910$	−0.0390667	−	13.3214i	−0.00129505	−	0.441602i
$911$	10.6524	+	32.7846i	0.352929	+	1.08620i	0.957201	+	0.289425i	$0.0934640\pi$
$911$	10.6524	+	32.7846i	0.352929	+	1.08620i	−0.604272	+	0.796778i	$0.706536\pi$
$912$		0			0
$913$	−16.2254	+	49.9366i	−0.536981	+	1.65266i
$914$	11.2851	+	34.7320i	0.373279	+	1.14883i
$915$		0			0
$916$	−0.846535	+	2.60537i	−0.0279703	+	0.0860837i
$917$	43.8028	+	31.8246i	1.44649	+	1.05094i
$918$		0			0
$919$	0.617756	+	0.448826i	0.0203779	+	0.0148054i	0.597928	−	0.801550i	$-0.295991\pi$
$919$	0.617756	+	0.448826i	0.0203779	+	0.0148054i	−0.577550	+	0.816356i	$0.695991\pi$
$920$	−9.51959	−	3.06227i	−0.313851	−	0.100960i
$921$		0			0
$922$	24.1323	−	17.5331i	0.794755	−	0.577423i
$923$	6.81977	+	20.9891i	0.224475	+	0.690864i
$924$		0			0
$925$	−12.2618	+	38.5051i	−0.403167	+	1.26604i
$926$	−36.7470			−1.20758
$927$		0			0
$928$	5.55164	−	4.03350i	0.182242	−	0.132406i
$929$	−12.2680	+	8.91319i	−0.402498	+	0.292432i	−0.770558	−	0.637370i	$-0.780022\pi$
$929$	−12.2680	+	8.91319i	−0.402498	+	0.292432i	0.368059	+	0.929802i	$0.380022\pi$
$930$		0			0
$931$	−0.0343355	−	0.0249462i	−0.00112530	−	0.000817580i
$932$	−18.0180			−0.590198
$933$		0			0
$934$	−6.77364	+	20.8471i	−0.221640	+	0.682138i
$935$	−21.7048	−	6.98202i	−0.709824	−	0.228337i
$936$		0			0
$937$	−8.61798	+	26.5234i	−0.281537	+	0.866482i	0.705878	+	0.708333i	$0.250553\pi$
$937$	−8.61798	+	26.5234i	−0.281537	+	0.866482i	−0.987415	+	0.158149i	$0.949447\pi$
$938$	−8.19036	+	25.2073i	−0.267425	+	0.823049i
$939$		0			0
$940$	13.8327	+	4.44971i	0.451173	+	0.145134i
$941$	−11.4347	+	35.1922i	−0.372759	+	1.14723i	0.572219	+	0.820101i	$0.306083\pi$
$941$	−11.4347	+	35.1922i	−0.372759	+	1.14723i	−0.944978	+	0.327133i	$0.893917\pi$
$942$		0			0
$943$	−51.3999			−1.67381
$944$	7.30893	+	5.31025i	0.237885	+	0.172834i
$945$		0			0
$946$	−10.0127	+	7.27463i	−0.325540	+	0.236519i
$947$	−31.1403	+	22.6248i	−1.01192	+	0.735206i	−0.964612	−	0.263674i	$-0.915066\pi$
$947$	−31.1403	+	22.6248i	−1.01192	+	0.735206i	−0.0473125	+	0.998880i	$0.515066\pi$
$948$		0			0
$949$	−27.0688			−0.878690
$950$	1.87532	−	5.88895i	0.0608435	−	0.191063i
$951$		0			0
$952$	−1.32624	−	4.08174i	−0.0429836	−	0.132290i
$953$	−3.38452	+	2.45900i	−0.109635	+	0.0796548i	−0.641252	−	0.767330i	$-0.721585\pi$
$953$	−3.38452	+	2.45900i	−0.109635	+	0.0796548i	0.531617	+	0.846985i	$0.321585\pi$
$954$		0			0
$955$	6.88844	+	2.21588i	0.222905	+	0.0717041i
$956$	−2.20173	−	1.59965i	−0.0712091	−	0.0517365i
$957$		0			0
$958$	−5.88844	−	4.27820i	−0.190247	−	0.138222i
$959$	2.49864	−	7.69004i	0.0806854	−	0.248324i
$960$		0			0
$961$	1.08756	+	3.34716i	0.0350825	+	0.107973i
$962$	5.63757	−	17.3506i	0.181762	−	0.559407i
$963$		0			0
$964$	0.463977	+	1.42798i	0.0149437	+	0.0459920i
$965$	0.0712415	+	24.2928i	0.00229335	+	0.782013i
$966$		0			0
$967$	10.0583	+	7.30775i	0.323452	+	0.235001i	0.737647	−	0.675187i	$-0.235937\pi$
$967$	10.0583	+	7.30775i	0.323452	+	0.235001i	−0.414195	+	0.910188i	$0.635937\pi$
$968$	28.3180			0.910174
$969$		0			0
$970$	−1.96544	+	2.72195i	−0.0631065	+	0.0873964i
$971$	13.0873	−	9.50848i	0.419991	−	0.305142i	−0.357643	−	0.933858i	$-0.616420\pi$
$971$	13.0873	−	9.50848i	0.419991	−	0.305142i	0.777634	+	0.628717i	$0.216420\pi$
$972$		0			0
$973$	−13.6027	−	41.8649i	−0.436083	−	1.34213i
$974$	−31.4007			−1.00614
$975$		0			0
$976$	−3.02122			−0.0967069
$977$	−9.00047	−	27.7006i	−0.287951	−	0.886221i	−0.985499	−	0.169683i	$-0.945726\pi$
$977$	−9.00047	−	27.7006i	−0.287951	−	0.886221i	0.697548	−	0.716538i	$-0.254274\pi$
$978$		0			0
$979$	1.97878	−	1.43767i	0.0632421	−	0.0459481i
$980$	−0.0453101	−	0.0619810i	−0.00144738	−	0.00197991i
$981$		0			0
$982$	26.4753			0.844862
$983$	16.8455	+	12.2390i	0.537289	+	0.390364i	0.823077	−	0.567929i	$-0.192255\pi$
$983$	16.8455	+	12.2390i	0.537289	+	0.390364i	−0.285788	+	0.958293i	$0.592255\pi$
$984$		0			0
$985$	11.9781	+	16.3852i	0.381654	+	0.522075i
$986$	3.44829	+	10.6128i	0.109816	+	0.337979i
$987$		0			0
$988$	−0.862207	+	2.65360i	−0.0274305	+	0.0844223i
$989$	−2.72768	−	8.39495i	−0.0867353	−	0.266944i
$990$		0			0
$991$	−4.52367	+	13.9224i	−0.143699	+	0.442261i	−0.996841	−	0.0794178i	$-0.974694\pi$
$991$	−4.52367	+	13.9224i	−0.143699	+	0.442261i	0.853142	+	0.521678i	$0.174694\pi$
$992$	4.75324	+	3.45343i	0.150915	+	0.109646i
$993$		0			0
$994$	−20.8756	−	15.1670i	−0.662134	−	0.481068i
$995$	−0.170977	−	58.3019i	−0.00542034	−	1.84829i
$996$		0			0
$997$	3.36030	−	2.44140i	0.106422	−	0.0773198i	−0.533302	−	0.845925i	$-0.679049\pi$
$997$	3.36030	−	2.44140i	0.106422	−	0.0773198i	0.639723	+	0.768605i	$0.279049\pi$
$998$	−8.71130	−	26.8106i	−0.275751	−	0.848675i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.d.181.1		8
3.2	odd	2		150.2.g.c.31.2	✓	8
15.2	even	4		750.2.h.e.349.4		16
15.8	even	4		750.2.h.e.349.1		16
15.14	odd	2		750.2.g.d.151.1		8
25.21	even	5	inner	450.2.h.d.271.1		8
75.2	even	20		3750.2.c.h.1249.3		8
75.11	odd	10		3750.2.a.l.1.3		4
75.14	odd	10		3750.2.a.q.1.2		4
75.23	even	20		3750.2.c.h.1249.6		8
75.29	odd	10		750.2.g.d.601.1		8
75.47	even	20		750.2.h.e.649.2		16
75.53	even	20		750.2.h.e.649.3		16
75.71	odd	10		150.2.g.c.121.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.c.31.2	✓	8	3.2	odd	2
150.2.g.c.121.2	yes	8	75.71	odd	10
450.2.h.d.181.1		8	1.1	even	1	trivial
450.2.h.d.271.1		8	25.21	even	5	inner
750.2.g.d.151.1		8	15.14	odd	2
750.2.g.d.601.1		8	75.29	odd	10
750.2.h.e.349.1		16	15.8	even	4
750.2.h.e.349.4		16	15.2	even	4
750.2.h.e.649.2		16	75.47	even	20
750.2.h.e.649.3		16	75.53	even	20
3750.2.a.l.1.3		4	75.11	odd	10
3750.2.a.q.1.2		4	75.14	odd	10
3750.2.c.h.1249.3		8	75.2	even	20
3750.2.c.h.1249.6		8	75.23	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-0.00655751 - 2.23606i) q^{5} +2.63925 q^{7} +(-0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-0.00655751 - 2.23606i) q^{5} +2.63925 q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.12459 - 0.697217i) q^{10} +(-1.93766 - 5.96351i) q^{11} +(0.697541 - 2.14681i) q^{13} +(0.815575 + 2.51008i) q^{14} +(0.309017 - 0.951057i) q^{16} +(1.31557 + 0.955821i) q^{17} +(1.00000 + 0.726543i) q^{19} +(1.31963 + 1.80515i) q^{20} +(5.07286 - 3.68565i) q^{22} +(1.38197 + 4.25325i) q^{23} +(-4.99991 + 0.0293259i) q^{25} +2.25729 q^{26} +(-2.13520 + 1.55131i) q^{28} +(5.55164 - 4.03350i) q^{29} +(4.75324 + 3.45343i) q^{31} +1.00000 q^{32} +(-0.502505 + 1.54655i) q^{34} +(-0.0173069 - 5.90153i) q^{35} +(2.49750 - 7.68650i) q^{37} +(-0.381966 + 1.17557i) q^{38} +(-1.30902 + 1.81286i) q^{40} +(-3.55164 + 10.9308i) q^{41} -1.97377 q^{43} +(5.07286 + 3.68565i) q^{44} +(-3.61803 + 2.62866i) q^{46} +(5.25729 - 3.81964i) q^{47} -0.0343355 q^{49} +(-1.57295 - 4.74614i) q^{50} +(0.697541 + 2.14681i) q^{52} +(-5.66298 + 4.11440i) q^{53} +(-13.3220 + 4.37183i) q^{55} +(-2.13520 - 1.55131i) q^{56} +(5.55164 + 4.03350i) q^{58} +(-2.79176 + 8.59216i) q^{59} +(-0.933608 - 2.87335i) q^{61} +(-1.81557 + 5.58776i) q^{62} +(0.309017 + 0.951057i) q^{64} +(-4.80496 - 1.54566i) q^{65} +(8.12451 + 5.90280i) q^{67} -1.62614 q^{68} +(5.60734 - 1.84013i) q^{70} +(-7.90966 + 5.74670i) q^{71} +(-3.70565 - 11.4048i) q^{73} +8.08206 q^{74} -1.23607 q^{76} +(-5.11398 - 15.7392i) q^{77} +(-3.03853 + 2.20762i) q^{79} +(-2.12864 - 0.684743i) q^{80} -11.4934 q^{82} +(-6.77446 - 4.92193i) q^{83} +(2.12864 - 2.94797i) q^{85} +(-0.609928 - 1.87717i) q^{86} +(-1.93766 + 5.96351i) q^{88} +(0.120539 + 0.370980i) q^{89} +(1.84099 - 5.66598i) q^{91} +(-3.61803 - 2.62866i) q^{92} +(5.25729 + 3.81964i) q^{94} +(1.61803 - 2.24082i) q^{95} +(-1.21471 + 0.882537i) q^{97} +(-0.0106103 - 0.0326550i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8} + 4 q^{10} + 5 q^{11} + 6 q^{13} - 2 q^{14} - 2 q^{16} + 2 q^{17} + 8 q^{19} - q^{20} + 20 q^{23} + 14 q^{25} - 14 q^{26} + 3 q^{28} + 18 q^{29} + 9 q^{31} + 8 q^{32} - 3 q^{34} + 4 q^{35} + 21 q^{37} - 12 q^{38} - 6 q^{40} - 2 q^{41} - 32 q^{43} - 20 q^{46} + 10 q^{47} + 22 q^{49} - 26 q^{50} + 6 q^{52} - 7 q^{53} - 40 q^{55} + 3 q^{56} + 18 q^{58} + 25 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{64} - 37 q^{65} - 2 q^{67} + 2 q^{68} - 11 q^{70} - 24 q^{73} + 26 q^{74} + 8 q^{76} - 35 q^{77} - 6 q^{79} - q^{80} - 42 q^{82} - 11 q^{83} + q^{85} - 2 q^{86} + 5 q^{88} - 9 q^{89} - 4 q^{91} - 20 q^{92} + 10 q^{94} + 4 q^{95} + q^{97} + 7 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 2 * q^8 + 4 * q^10 + 5 * q^11 + 6 * q^13 - 2 * q^14 - 2 * q^16 + 2 * q^17 + 8 * q^19 - q^20 + 20 * q^23 + 14 * q^25 - 14 * q^26 + 3 * q^28 + 18 * q^29 + 9 * q^31 + 8 * q^32 - 3 * q^34 + 4 * q^35 + 21 * q^37 - 12 * q^38 - 6 * q^40 - 2 * q^41 - 32 * q^43 - 20 * q^46 + 10 * q^47 + 22 * q^49 - 26 * q^50 + 6 * q^52 - 7 * q^53 - 40 * q^55 + 3 * q^56 + 18 * q^58 + 25 * q^59 + 10 * q^61 - 6 * q^62 - 2 * q^64 - 37 * q^65 - 2 * q^67 + 2 * q^68 - 11 * q^70 - 24 * q^73 + 26 * q^74 + 8 * q^76 - 35 * q^77 - 6 * q^79 - q^80 - 42 * q^82 - 11 * q^83 + q^85 - 2 * q^86 + 5 * q^88 - 9 * q^89 - 4 * q^91 - 20 * q^92 + 10 * q^94 + 4 * q^95 + q^97 + 7 * q^98

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