LMFDB - Embedded newform 450.2.h.e.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			271.1
Root			$1.17421 - 0.0566033i$ of defining polynomial
Character	$\chi$	$=$	450.271
Dual form			450.2.h.e.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-2.15743 - 0.587785i) q^{5} +1.83337 q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-2.15743 - 0.587785i) q^{5} +1.83337 q^{7} +(0.809017 - 0.587785i) q^{8} +(1.22570 - 1.87020i) q^{10} +(0.566541 - 1.74363i) q^{11} +(-0.747156 - 2.29951i) q^{13} +(-0.566541 + 1.74363i) q^{14} +(0.309017 + 0.951057i) q^{16} +(2.25284 - 1.63679i) q^{17} +(1.35294 - 0.982966i) q^{19} +(1.39991 + 1.74363i) q^{20} +(1.48322 + 1.07763i) q^{22} +(2.39991 - 7.38615i) q^{23} +(4.30902 + 2.53621i) q^{25} +2.41785 q^{26} +(-1.48322 - 1.07763i) q^{28} +(6.13597 + 4.45805i) q^{29} +(4.28304 - 3.11181i) q^{31} -1.00000 q^{32} +(0.860510 + 2.64838i) q^{34} +(-3.95536 - 1.07763i) q^{35} +(-0.406315 - 1.25051i) q^{37} +(0.516776 + 1.59047i) q^{38} +(-2.09089 + 0.792578i) q^{40} +(-1.08621 - 3.34301i) q^{41} -4.30550 q^{43} +(-1.48322 + 1.07763i) q^{44} +(6.28304 + 4.56489i) q^{46} +(1.48322 + 1.07763i) q^{47} -3.63877 q^{49} +(-3.74364 + 3.31439i) q^{50} +(-0.747156 + 2.29951i) q^{52} +(-5.27267 - 3.83082i) q^{53} +(-2.24716 + 3.42877i) q^{55} +(1.48322 - 1.07763i) q^{56} +(-6.13597 + 4.45805i) q^{58} +(2.79981 + 8.61694i) q^{59} +(0.799717 - 2.46127i) q^{61} +(1.63597 + 5.03501i) q^{62} +(0.309017 - 0.951057i) q^{64} +(0.260320 + 5.40020i) q^{65} +(-7.68574 + 5.58402i) q^{67} -2.78467 q^{68} +(2.24716 - 3.42877i) q^{70} +(0.247156 + 0.179569i) q^{71} +(4.61920 - 14.2164i) q^{73} +1.31486 q^{74} -1.67232 q^{76} +(1.03868 - 3.19672i) q^{77} +(2.79981 + 2.03418i) q^{79} +(-0.107666 - 2.23347i) q^{80} +3.51505 q^{82} +(-5.15555 + 3.74572i) q^{83} +(-5.82243 + 2.20707i) q^{85} +(1.33047 - 4.09478i) q^{86} +(-0.566541 - 1.74363i) q^{88} +(1.02608 - 3.15794i) q^{89} +(-1.36981 - 4.21584i) q^{91} +(-6.28304 + 4.56489i) q^{92} +(-1.48322 + 1.07763i) q^{94} +(-3.49664 + 1.32545i) q^{95} +(-8.97214 - 6.51864i) q^{97} +(1.12444 - 3.46068i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8	$ 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8} - q^{11} - 13 q^{13} + q^{14} - 2 q^{16} + 11 q^{17} + 20 q^{19} - 5 q^{20} + q^{22} + 3 q^{23} + 30 q^{25} - 22 q^{26} - q^{28} + 15 q^{29} - 9 q^{31} - 8 q^{32} - q^{34} + 15 q^{35} - 6 q^{37} + 15 q^{38} - 5 q^{40} + 9 q^{41} + 12 q^{43} - q^{44} + 7 q^{46} + q^{47} - 4 q^{49} + 5 q^{50} - 13 q^{52} - 7 q^{53} - 25 q^{55} + q^{56} - 15 q^{58} - 10 q^{59} + 6 q^{61} - 21 q^{62} - 2 q^{64} + 10 q^{65} - 11 q^{67} - 24 q^{68} + 25 q^{70} + 9 q^{71} - 8 q^{73} - 24 q^{74} - 10 q^{76} - 33 q^{77} - 10 q^{79} + 26 q^{82} - 27 q^{83} + 5 q^{85} + 23 q^{86} + q^{88} + 15 q^{89} + q^{91} - 7 q^{92} - q^{94} + 30 q^{95} - 36 q^{97} + 19 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8 - q^11 - 13 * q^13 + q^14 - 2 * q^16 + 11 * q^17 + 20 * q^19 - 5 * q^20 + q^22 + 3 * q^23 + 30 * q^25 - 22 * q^26 - q^28 + 15 * q^29 - 9 * q^31 - 8 * q^32 - q^34 + 15 * q^35 - 6 * q^37 + 15 * q^38 - 5 * q^40 + 9 * q^41 + 12 * q^43 - q^44 + 7 * q^46 + q^47 - 4 * q^49 + 5 * q^50 - 13 * q^52 - 7 * q^53 - 25 * q^55 + q^56 - 15 * q^58 - 10 * q^59 + 6 * q^61 - 21 * q^62 - 2 * q^64 + 10 * q^65 - 11 * q^67 - 24 * q^68 + 25 * q^70 + 9 * q^71 - 8 * q^73 - 24 * q^74 - 10 * q^76 - 33 * q^77 - 10 * q^79 + 26 * q^82 - 27 * q^83 + 5 * q^85 + 23 * q^86 + q^88 + 15 * q^89 + q^91 - 7 * q^92 - q^94 + 30 * q^95 - 36 * q^97 + 19 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−2.15743	−	0.587785i	−0.964832	−	0.262866i
$5$	−2.15743	−	0.587785i	−0.964832	−	0.262866i
$6$		0			0
$7$	1.83337			0.692947			0.346474	−	0.938060i	$-0.387379\pi$
$7$	1.83337			0.692947			0.346474	+	0.938060i	$0.387379\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$		0			0
$10$	1.22570	−	1.87020i	0.387600	−	0.591410i
$11$	0.566541	−	1.74363i	0.170819	−	0.525726i	−0.828599	−	0.559842i	$-0.810862\pi$
$11$	0.566541	−	1.74363i	0.170819	−	0.525726i	0.999418	+	0.0341166i	$0.0108618\pi$
$12$		0			0
$13$	−0.747156	−	2.29951i	−0.207224	−	0.637769i	−0.999615	−	0.0277557i	$-0.991164\pi$
$13$	−0.747156	−	2.29951i	−0.207224	−	0.637769i	0.792391	−	0.610014i	$-0.208836\pi$
$14$	−0.566541	+	1.74363i	−0.151414	+	0.466006i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.25284	−	1.63679i	0.546395	−	0.396979i	−0.280060	−	0.959983i	$-0.590354\pi$
$17$	2.25284	−	1.63679i	0.546395	−	0.396979i	0.826455	+	0.563003i	$0.190354\pi$
$18$		0			0
$19$	1.35294	−	0.982966i	0.310385	−	0.225508i	−0.421677	−	0.906746i	$-0.638558\pi$
$19$	1.35294	−	0.982966i	0.310385	−	0.225508i	0.732062	+	0.681238i	$0.238558\pi$
$20$	1.39991	+	1.74363i	0.313029	+	0.389889i
$21$		0			0
$22$	1.48322	+	1.07763i	0.316224	+	0.229750i
$23$	2.39991	−	7.38615i	0.500415	−	1.54012i	−0.307929	−	0.951409i	$-0.599636\pi$
$23$	2.39991	−	7.38615i	0.500415	−	1.54012i	0.808344	−	0.588710i	$-0.200364\pi$
$24$		0			0
$25$	4.30902	+	2.53621i	0.861803	+	0.507242i
$26$	2.41785			0.474179
$27$		0			0
$28$	−1.48322	−	1.07763i	−0.280303	−	0.203652i
$29$	6.13597	+	4.45805i	1.13942	+	0.827838i	0.987039	−	0.160483i	$-0.0513052\pi$
$29$	6.13597	+	4.45805i	1.13942	+	0.827838i	0.152383	+	0.988321i	$0.451305\pi$
$30$		0			0
$31$	4.28304	−	3.11181i	0.769256	−	0.558897i	−0.132479	−	0.991186i	$-0.542294\pi$
$31$	4.28304	−	3.11181i	0.769256	−	0.558897i	0.901735	+	0.432288i	$0.142294\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	0.860510	+	2.64838i	0.147576	+	0.454193i
$35$	−3.95536	−	1.07763i	−0.668578	−	0.182152i
$36$		0			0
$37$	−0.406315	−	1.25051i	−0.0667977	−	0.205582i	0.912086	−	0.409998i	$-0.134471\pi$
$37$	−0.406315	−	1.25051i	−0.0667977	−	0.205582i	−0.978884	+	0.204416i	$0.934471\pi$
$38$	0.516776	+	1.59047i	0.0838321	+	0.258009i
$39$		0			0
$40$	−2.09089	+	0.792578i	−0.330599	+	0.125318i
$41$	−1.08621	−	3.34301i	−0.169637	−	0.522090i	0.829711	−	0.558194i	$-0.188505\pi$
$41$	−1.08621	−	3.34301i	−0.169637	−	0.522090i	−0.999348	+	0.0361034i	$0.988505\pi$
$42$		0			0
$43$	−4.30550			−0.656583			−0.328291	−	0.944576i	$-0.606473\pi$
$43$	−4.30550			−0.656583			−0.328291	+	0.944576i	$0.606473\pi$
$44$	−1.48322	+	1.07763i	−0.223604	+	0.162458i
$45$		0			0
$46$	6.28304	+	4.56489i	0.926383	+	0.673057i
$47$	1.48322	+	1.07763i	0.216350	+	0.157188i	0.690682	−	0.723158i	$-0.257310\pi$
$47$	1.48322	+	1.07763i	0.216350	+	0.157188i	−0.474332	+	0.880346i	$0.657310\pi$
$48$		0			0
$49$	−3.63877			−0.519824
$50$	−3.74364	+	3.31439i	−0.529431	+	0.468725i
$51$		0			0
$52$	−0.747156	+	2.29951i	−0.103612	+	0.318885i
$53$	−5.27267	−	3.83082i	−0.724257	−	0.526203i	0.163485	−	0.986546i	$-0.447727\pi$
$53$	−5.27267	−	3.83082i	−0.724257	−	0.526203i	−0.887741	+	0.460342i	$0.847727\pi$
$54$		0			0
$55$	−2.24716	+	3.42877i	−0.303006	+	0.462335i
$56$	1.48322	−	1.07763i	0.198204	−	0.144004i
$57$		0			0
$58$	−6.13597	+	4.45805i	−0.805693	+	0.585370i
$59$	2.79981	+	8.61694i	0.364505	+	1.12183i	0.950291	+	0.311364i	$0.100786\pi$
$59$	2.79981	+	8.61694i	0.364505	+	1.12183i	−0.585786	+	0.810466i	$0.699214\pi$
$60$		0			0
$61$	0.799717	−	2.46127i	0.102393	−	0.315134i	−0.886717	−	0.462313i	$-0.847019\pi$
$61$	0.799717	−	2.46127i	0.102393	−	0.315134i	0.989110	+	0.147180i	$0.0470195\pi$
$62$	1.63597	+	5.03501i	0.207769	+	0.639447i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.260320	+	5.40020i	0.0322887	+	0.669812i
$66$		0			0
$67$	−7.68574	+	5.58402i	−0.938963	+	0.682196i	−0.948171	−	0.317761i	$-0.897069\pi$
$67$	−7.68574	+	5.58402i	−0.938963	+	0.682196i	0.00920814	+	0.999958i	$0.497069\pi$
$68$	−2.78467			−0.337691
$69$		0			0
$70$	2.24716	−	3.42877i	0.268587	−	0.409816i
$71$	0.247156	+	0.179569i	0.0293320	+	0.0213110i	0.602355	−	0.798229i	$-0.294229\pi$
$71$	0.247156	+	0.179569i	0.0293320	+	0.0213110i	−0.573023	+	0.819540i	$0.694229\pi$
$72$		0			0
$73$	4.61920	−	14.2164i	0.540636	−	1.66391i	−0.190509	−	0.981685i	$-0.561014\pi$
$73$	4.61920	−	14.2164i	0.540636	−	1.66391i	0.731145	−	0.682222i	$-0.238986\pi$
$74$	1.31486			0.152850
$75$		0			0
$76$	−1.67232			−0.191829
$77$	1.03868	−	3.19672i	0.118368	−	0.364300i
$78$		0			0
$79$	2.79981	+	2.03418i	0.315004	+	0.228864i	0.734041	−	0.679106i	$-0.237632\pi$
$79$	2.79981	+	2.03418i	0.315004	+	0.228864i	−0.419037	+	0.907969i	$0.637632\pi$
$80$	−0.107666	−	2.23347i	−0.0120374	−	0.249710i
$81$		0			0
$82$	3.51505			0.388172
$83$	−5.15555	+	3.74572i	−0.565895	+	0.411147i	−0.833612	−	0.552351i	$-0.813731\pi$
$83$	−5.15555	+	3.74572i	−0.565895	+	0.411147i	0.267717	+	0.963498i	$0.413731\pi$
$84$		0			0
$85$	−5.82243	+	2.20707i	−0.631532	+	0.239390i
$86$	1.33047	−	4.09478i	0.143469	−	0.441551i
$87$		0			0
$88$	−0.566541	−	1.74363i	−0.0603935	−	0.185872i
$89$	1.02608	−	3.15794i	0.108764	−	0.334741i	−0.881832	−	0.471565i	$-0.843689\pi$
$89$	1.02608	−	3.15794i	0.108764	−	0.334741i	0.990595	+	0.136824i	$0.0436894\pi$
$90$		0			0
$91$	−1.36981	−	4.21584i	−0.143595	−	0.441940i
$92$	−6.28304	+	4.56489i	−0.655052	+	0.475923i
$93$		0			0
$94$	−1.48322	+	1.07763i	−0.152983	+	0.111149i
$95$	−3.49664	+	1.32545i	−0.358748	+	0.135988i
$96$		0			0
$97$	−8.97214	−	6.51864i	−0.910982	−	0.661867i	0.0302807	−	0.999541i	$-0.490360\pi$
$97$	−8.97214	−	6.51864i	−0.910982	−	0.661867i	−0.941263	+	0.337674i	$0.890360\pi$
$98$	1.12444	−	3.46068i	0.113586	−	0.349581i
$99$		0			0
$100$	−1.99532	−	4.58462i	−0.199532	−	0.458462i
$101$	13.1807			1.31152			0.655762	−	0.754968i	$-0.272347\pi$
$101$	13.1807			1.31152			0.655762	+	0.754968i	$0.272347\pi$
$102$		0			0
$103$	2.13029	+	1.54774i	0.209903	+	0.152504i	0.687770	−	0.725929i	$-0.258590\pi$
$103$	2.13029	+	1.54774i	0.209903	+	0.152504i	−0.477867	+	0.878432i	$0.658590\pi$
$104$	−1.95608	−	1.42118i	−0.191809	−	0.139358i
$105$		0			0
$106$	5.27267	−	3.83082i	0.512127	−	0.372082i
$107$	−18.8045			−1.81790			−0.908949	−	0.416908i	$-0.863114\pi$
$107$	−18.8045			−1.81790			−0.908949	+	0.416908i	$0.863114\pi$
$108$		0			0
$109$	3.18574	+	9.80470i	0.305139	+	0.939120i	0.979625	+	0.200833i	$0.0643649\pi$
$109$	3.18574	+	9.80470i	0.305139	+	0.939120i	−0.674487	+	0.738287i	$0.735635\pi$
$110$	−2.56654	−	3.19672i	−0.244710	−	0.304795i
$111$		0			0
$112$	0.566541	+	1.74363i	0.0535331	+	0.164758i
$113$	−1.87160	−	5.76019i	−0.176065	−	0.541873i	0.823615	−	0.567149i	$-0.191954\pi$
$113$	−1.87160	−	5.76019i	−0.176065	−	0.541873i	−0.999681	+	0.0252760i	$0.991954\pi$
$114$		0			0
$115$	−9.51911	+	14.5245i	−0.887661	+	1.35442i
$116$	−2.34373	−	7.21327i	−0.217610	−	0.669735i
$117$		0			0
$118$	−9.06039			−0.834076
$119$	4.13029	−	3.00083i	0.378623	−	0.275086i
$120$		0			0
$121$	6.17989	+	4.48996i	0.561809	+	0.408178i
$122$	2.09369	+	1.52115i	0.189553	+	0.137719i
$123$		0			0
$124$	−5.29413			−0.475427
$125$	−7.80566	−	8.00448i	−0.698159	−	0.715942i
$126$		0			0
$127$	0.102986	−	0.316957i	0.00913850	−	0.0281254i	−0.946383	−	0.323046i	$-0.895293\pi$
$127$	0.102986	−	0.316957i	0.00913850	−	0.0281254i	0.955522	+	0.294921i	$0.0952932\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$		0			0
$130$	−5.21634	−	1.42118i	−0.457503	−	0.124645i
$131$	−4.18910	+	3.04356i	−0.366003	+	0.265917i	−0.755552	−	0.655089i	$-0.772631\pi$
$131$	−4.18910	+	3.04356i	−0.366003	+	0.265917i	0.389548	+	0.921006i	$0.372631\pi$
$132$		0			0
$133$	2.48043	−	1.80214i	0.215080	−	0.156265i
$134$	−2.93569	−	9.03513i	−0.253605	−	0.780516i
$135$		0			0
$136$	0.860510	−	2.64838i	0.0737881	−	0.227096i
$137$	6.03299	+	18.5676i	0.515433	+	1.58634i	0.782493	+	0.622660i	$0.213948\pi$
$137$	6.03299	+	18.5676i	0.515433	+	1.58634i	−0.267060	+	0.963680i	$0.586052\pi$
$138$		0			0
$139$	−2.45825	+	7.56572i	−0.208506	+	0.641716i	0.791045	+	0.611758i	$0.209537\pi$
$139$	−2.45825	+	7.56572i	−0.208506	+	0.641716i	−0.999551	+	0.0299582i	$0.990463\pi$
$140$	2.56654	+	3.19672i	0.216912	+	0.270172i
$141$		0			0
$142$	−0.247156	+	0.179569i	−0.0207409	+	0.0150691i
$143$	−4.43280			−0.370689
$144$		0			0
$145$	−10.6176	−	13.2246i	−0.881741	−	1.09824i
$146$	12.0932	+	8.78624i	1.00084	+	0.727154i
$147$		0			0
$148$	−0.406315	+	1.25051i	−0.0333989	+	0.102791i
$149$	1.67955			0.137594			0.0687969	−	0.997631i	$-0.478084\pi$
$149$	1.67955			0.137594			0.0687969	+	0.997631i	$0.478084\pi$
$150$		0			0
$151$	−21.2664			−1.73063			−0.865316	−	0.501227i	$-0.832882\pi$
$151$	−21.2664			−1.73063			−0.865316	+	0.501227i	$0.832882\pi$
$152$	0.516776	−	1.59047i	0.0419161	−	0.129004i
$153$		0			0
$154$	2.71929	+	1.97568i	0.219127	+	0.159205i
$155$	−11.0694	+	4.19601i	−0.889118	+	0.337031i
$156$		0			0
$157$	10.4514			0.834113			0.417056	−	0.908881i	$-0.363062\pi$
$157$	10.4514			0.834113			0.417056	+	0.908881i	$0.363062\pi$
$158$	−2.79981	+	2.03418i	−0.222741	+	0.161831i
$159$		0			0
$160$	2.15743	+	0.587785i	0.170560	+	0.0464685i
$161$	4.39991	−	13.5415i	0.346761	−	1.06722i
$162$		0			0
$163$	3.21706	+	9.90109i	0.251980	+	0.775513i	0.994410	+	0.105590i	$0.0336731\pi$
$163$	3.21706	+	9.90109i	0.251980	+	0.775513i	−0.742430	+	0.669923i	$0.766327\pi$
$164$	−1.08621	+	3.34301i	−0.0848187	+	0.261045i
$165$		0			0
$166$	−1.96924	−	6.06071i	−0.152843	−	0.470402i
$167$	1.71650	−	1.24711i	0.132826	−	0.0965041i	−0.519388	−	0.854538i	$-0.673840\pi$
$167$	1.71650	−	1.24711i	0.132826	−	0.0965041i	0.652215	+	0.758034i	$0.273840\pi$
$168$		0			0
$169$	5.78772	−	4.20502i	0.445209	−	0.323463i
$170$	−0.299814	−	6.21949i	−0.0229947	−	0.477013i
$171$		0			0
$172$	3.48322	+	2.53071i	0.265593	+	0.192965i
$173$	5.59774	−	17.2281i	0.425588	−	1.30983i	−0.476841	−	0.878989i	$-0.658218\pi$
$173$	5.59774	−	17.2281i	0.425588	−	1.30983i	0.902430	−	0.430837i	$-0.141782\pi$
$174$		0			0
$175$	7.90000	+	4.64980i	0.597184	+	0.351492i
$176$	1.83337			0.138195
$177$		0			0
$178$	2.68630	+	1.95171i	0.201347	+	0.146287i
$179$	8.54361	+	6.20730i	0.638579	+	0.463955i	0.859362	−	0.511368i	$-0.170861\pi$
$179$	8.54361	+	6.20730i	0.638579	+	0.463955i	−0.220782	+	0.975323i	$0.570861\pi$
$180$		0			0
$181$	−14.6886	+	10.6719i	−1.09180	+	0.793237i	−0.979702	−	0.200460i	$-0.935756\pi$
$181$	−14.6886	+	10.6719i	−1.09180	+	0.793237i	−0.112096	+	0.993697i	$0.535756\pi$
$182$	4.43280			0.328581
$183$		0			0
$184$	−2.39991	−	7.38615i	−0.176923	−	0.544514i
$185$	0.141566	+	2.93671i	0.0104081	+	0.215911i
$186$		0			0
$187$	−1.57763	−	4.85544i	−0.115368	−	0.355065i
$188$	−0.566541	−	1.74363i	−0.0413193	−	0.127168i
$189$		0			0
$190$	−0.180052	−	3.73509i	−0.0130623	−	0.270972i
$191$	6.76906	+	20.8330i	0.489792	+	1.50742i	0.824919	+	0.565251i	$0.191221\pi$
$191$	6.76906	+	20.8330i	0.489792	+	1.50742i	−0.335127	+	0.942173i	$0.608779\pi$
$192$		0			0
$193$	27.4248			1.97408			0.987041	−	0.160465i	$-0.0512995\pi$
$193$	27.4248			1.97408			0.987041	+	0.160465i	$0.0512995\pi$
$194$	8.97214	−	6.51864i	0.644162	−	0.468011i
$195$		0			0
$196$	2.94383	+	2.13882i	0.210273	+	0.152773i
$197$	−0.909110	−	0.660507i	−0.0647714	−	0.0470592i	0.554928	−	0.831898i	$-0.312746\pi$
$197$	−0.909110	−	0.660507i	−0.0647714	−	0.0470592i	−0.619700	+	0.784839i	$0.712746\pi$
$198$		0			0
$199$	25.4992			1.80759			0.903794	−	0.427968i	$-0.140770\pi$
$199$	25.4992			1.80759			0.903794	+	0.427968i	$0.140770\pi$
$200$	4.97682	−	0.480938i	0.351914	−	0.0340074i
$201$		0			0
$202$	−4.07305	+	12.5355i	−0.286579	+	0.881998i
$203$	11.2495	+	8.17323i	0.789559	+	0.573648i
$204$		0			0
$205$	0.378451	+	7.85077i	0.0264321	+	0.548322i
$206$	−2.13029	+	1.54774i	−0.148424	+	0.107836i
$207$		0			0
$208$	1.95608	−	1.42118i	0.135630	−	0.0985408i
$209$	−0.947439	−	2.91592i	−0.0655358	−	0.201698i
$210$		0			0
$211$	6.58341	−	20.2617i	0.453221	−	1.39487i	−0.419990	−	0.907529i	$-0.637967\pi$
$211$	6.58341	−	20.2617i	0.453221	−	1.39487i	0.873211	−	0.487342i	$-0.162033\pi$
$212$	2.01398	+	6.19839i	0.138321	+	0.425708i
$213$		0			0
$214$	5.81090	−	17.8841i	0.397225	−	1.22253i
$215$	9.28882	+	2.53071i	0.633492	+	0.172593i
$216$		0			0
$217$	7.85237	−	5.70508i	0.533054	−	0.387286i
$218$	−10.3093			−0.698232
$219$		0			0
$220$	3.83337	−	1.45309i	0.258445	−	0.0979670i
$221$	−5.44703	−	3.95750i	−0.366407	−	0.266210i
$222$		0			0
$223$	1.00280	−	3.08629i	0.0671522	−	0.206673i	−0.911850	−	0.410524i	$-0.865346\pi$
$223$	1.00280	−	3.08629i	0.0671522	−	0.206673i	0.979002	+	0.203851i	$0.0653458\pi$
$224$	−1.83337			−0.122497
$225$		0			0
$226$	6.05662			0.402880
$227$	−5.06085	+	15.5757i	−0.335901	+	1.03380i	0.630376	+	0.776290i	$0.282901\pi$
$227$	−5.06085	+	15.5757i	−0.335901	+	1.03380i	−0.966277	+	0.257506i	$0.917099\pi$
$228$		0			0
$229$	4.11788	+	2.99181i	0.272117	+	0.197705i	0.715472	−	0.698642i	$-0.246212\pi$
$229$	4.11788	+	2.99181i	0.272117	+	0.197705i	−0.443355	+	0.896346i	$0.646212\pi$
$230$	−10.8720	−	13.5415i	−0.716881	−	0.892901i
$231$		0			0
$232$	7.58448			0.497946
$233$	−1.34536	+	0.977464i	−0.0881378	+	0.0640358i	−0.630981	−	0.775798i	$-0.717348\pi$
$233$	−1.34536	+	0.977464i	−0.0881378	+	0.0640358i	0.542844	+	0.839834i	$0.317348\pi$
$234$		0			0
$235$	−2.56654	−	3.19672i	−0.167423	−	0.208531i
$236$	2.79981	−	8.61694i	0.182252	−	0.560915i
$237$		0			0
$238$	1.57763	+	4.85544i	0.102263	+	0.314732i
$239$	−3.95536	+	12.1733i	−0.255851	+	0.787428i	0.737810	+	0.675009i	$0.235860\pi$
$239$	−3.95536	+	12.1733i	−0.255851	+	0.787428i	−0.993661	+	0.112420i	$0.964140\pi$
$240$		0			0
$241$	0.122209	+	0.376121i	0.00787219	+	0.0242281i	0.954915	−	0.296878i	$-0.0959454\pi$
$241$	0.122209	+	0.376121i	0.00787219	+	0.0242281i	−0.947043	+	0.321106i	$0.895945\pi$
$242$	−6.17989	+	4.48996i	−0.397259	+	0.288625i
$243$		0			0
$244$	−2.09369	+	1.52115i	−0.134034	+	0.0973817i
$245$	7.85040	+	2.13882i	0.501543	+	0.136644i
$246$		0			0
$247$	−3.27120	−	2.37666i	−0.208141	−	0.151223i
$248$	1.63597	−	5.03501i	0.103885	−	0.319724i
$249$		0			0
$250$	10.0248	−	4.95010i	0.634024	−	0.313072i
$251$	−9.36589			−0.591170			−0.295585	−	0.955316i	$-0.595515\pi$
$251$	−9.36589			−0.591170			−0.295585	+	0.955316i	$0.595515\pi$
$252$		0			0
$253$	−11.5191	−	8.36912i	−0.724200	−	0.526162i
$254$	0.269620	+	0.195890i	0.0169175	+	0.0122913i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	4.97926			0.310598			0.155299	−	0.987868i	$-0.450366\pi$
$257$	4.97926			0.310598			0.155299	+	0.987868i	$0.450366\pi$
$258$		0			0
$259$	−0.744923	−	2.29264i	−0.0462873	−	0.142458i
$260$	2.96356	−	4.52187i	0.183792	−	0.280434i
$261$		0			0
$262$	−1.60009	−	4.92458i	−0.0988541	−	0.304242i
$263$	6.12199	+	18.8416i	0.377498	+	1.16182i	0.941778	+	0.336236i	$0.109154\pi$
$263$	6.12199	+	18.8416i	0.377498	+	1.16182i	−0.564279	+	0.825584i	$0.690846\pi$
$264$		0			0
$265$	9.12372	+	11.3639i	0.560466	+	0.698080i
$266$	0.947439	+	2.91592i	0.0580912	+	0.178786i
$267$		0			0
$268$	9.50010			0.580311
$269$	11.9685	−	8.69564i	0.729734	−	0.530183i	−0.159745	−	0.987158i	$-0.551067\pi$
$269$	11.9685	−	8.69564i	0.729734	−	0.530183i	0.889479	+	0.456976i	$0.151067\pi$
$270$		0			0
$271$	10.1583	+	7.38047i	0.617075	+	0.448331i	0.851899	−	0.523707i	$-0.175451\pi$
$271$	10.1583	+	7.38047i	0.617075	+	0.448331i	−0.234823	+	0.972038i	$0.575451\pi$
$272$	2.25284	+	1.63679i	0.136599	+	0.0992448i
$273$		0			0
$274$	−19.5232			−1.17944
$275$	6.86346	−	6.07648i	0.413882	−	0.366426i
$276$		0			0
$277$	−1.95664	+	6.02193i	−0.117563	+	0.361823i	−0.992473	−	0.122463i	$-0.960921\pi$
$277$	−1.95664	+	6.02193i	−0.117563	+	0.361823i	0.874910	+	0.484286i	$0.160921\pi$
$278$	−6.43579	−	4.67587i	−0.385993	−	0.280440i
$279$		0			0
$280$	−3.83337	+	1.45309i	−0.229087	+	0.0868384i
$281$	−16.2525	+	11.8082i	−0.969545	+	0.704416i	−0.955348	−	0.295484i	$-0.904519\pi$
$281$	−16.2525	+	11.8082i	−0.969545	+	0.704416i	−0.0141971	+	0.999899i	$0.504519\pi$
$282$		0			0
$283$	−1.46981	+	1.06788i	−0.0873709	+	0.0634787i	−0.630613	−	0.776097i	$-0.717197\pi$
$283$	−1.46981	+	1.06788i	−0.0873709	+	0.0634787i	0.543242	+	0.839576i	$0.317197\pi$
$284$	−0.0944052	−	0.290549i	−0.00560192	−	0.0172409i
$285$		0			0
$286$	1.36981	−	4.21584i	0.0809986	−	0.249288i
$287$	−1.99142	−	6.12896i	−0.117550	−	0.361781i
$288$		0			0
$289$	−2.85705	+	8.79311i	−0.168062	+	0.517242i
$290$	15.8583	−	6.01129i	0.931232	−	0.352995i
$291$		0			0
$292$	−12.0932	+	8.78624i	−0.707702	+	0.514176i
$293$	6.85931			0.400725			0.200363	−	0.979722i	$-0.435788\pi$
$293$	6.85931			0.400725			0.200363	+	0.979722i	$0.435788\pi$
$294$		0			0
$295$	−0.975494	−	20.2361i	−0.0567955	−	1.17819i
$296$	−1.06375	−	0.772856i	−0.0618290	−	0.0449214i
$297$		0			0
$298$	−0.519009	+	1.59734i	−0.0300654	+	0.0925317i
$299$	−18.7776			−1.08594
$300$		0			0
$301$	−7.89356			−0.454977
$302$	6.57167	−	20.2255i	0.378157	−	1.16385i
$303$		0			0
$304$	1.35294	+	0.982966i	0.0775963	+	0.0563770i
$305$	−3.17203	+	4.83997i	−0.181630	+	0.277136i
$306$		0			0
$307$	−2.89526			−0.165241			−0.0826206	−	0.996581i	$-0.526329\pi$
$307$	−2.89526			−0.165241			−0.0826206	+	0.996581i	$0.526329\pi$
$308$	−2.71929	+	1.97568i	−0.154946	+	0.112575i
$309$		0			0
$310$	−0.569997	−	11.8243i	−0.0323736	−	0.671575i
$311$	6.38090	−	19.6384i	0.361828	−	1.11359i	−0.590116	−	0.807318i	$-0.700918\pi$
$311$	6.38090	−	19.6384i	0.361828	−	1.11359i	0.951944	−	0.306272i	$-0.0990819\pi$
$312$		0			0
$313$	5.07629	+	15.6232i	0.286929	+	0.883076i	0.985814	+	0.167842i	$0.0536798\pi$
$313$	5.07629	+	15.6232i	0.286929	+	0.883076i	−0.698885	+	0.715234i	$0.746320\pi$
$314$	−3.22966	+	9.93987i	−0.182260	+	0.560939i
$315$		0			0
$316$	−1.06943	−	3.29138i	−0.0601603	−	0.185154i
$317$	13.3535	−	9.70191i	0.750009	−	0.544914i	−0.145820	−	0.989311i	$-0.546582\pi$
$317$	13.3535	−	9.70191i	0.750009	−	0.544914i	0.895830	+	0.444397i	$0.146582\pi$
$318$		0			0
$319$	11.2495	−	8.17323i	0.629850	−	0.457613i
$320$	−1.22570	+	1.87020i	−0.0685187	+	0.104548i
$321$		0			0
$322$	11.5191	+	8.36912i	0.641935	+	0.466393i
$323$	1.43905	−	4.42894i	0.0800709	−	0.246433i
$324$		0			0
$325$	2.61254	−	11.8036i	0.144917	−	0.654744i
$326$	−10.4106			−0.576591
$327$		0			0
$328$	−2.84373	−	2.06609i	−0.157019	−	0.114081i
$329$	2.71929	+	1.97568i	0.149919	+	0.108923i
$330$		0			0
$331$	−22.2245	+	16.1471i	−1.22157	+	0.887522i	−0.996229	−	0.0867577i	$-0.972349\pi$
$331$	−22.2245	+	16.1471i	−1.22157	+	0.887522i	−0.225340	+	0.974280i	$0.572349\pi$
$332$	6.37261			0.349742
$333$		0			0
$334$	0.655643	+	2.01786i	0.0358752	+	0.110413i
$335$	19.8637	−	7.52957i	1.08527	−	0.411384i
$336$		0			0
$337$	−0.848317	−	2.61085i	−0.0462108	−	0.142222i	0.925289	−	0.379263i	$-0.123822\pi$
$337$	−0.848317	−	2.61085i	−0.0462108	−	0.142222i	−0.971500	+	0.237041i	$0.923822\pi$
$338$	2.21071	+	6.80387i	0.120247	+	0.370082i
$339$		0			0
$340$	6.00773	+	1.63679i	0.325815	+	0.0887672i
$341$	−2.99934	−	9.23102i	−0.162423	−	0.499888i
$342$		0			0
$343$	−19.5048			−1.05316
$344$	−3.48322	+	2.53071i	−0.187803	+	0.136447i
$345$		0			0
$346$	14.6551	+	10.6475i	0.787862	+	0.572415i
$347$	−17.2637	−	12.5428i	−0.926762	−	0.673332i	0.0184361	−	0.999830i	$-0.494131\pi$
$347$	−17.2637	−	12.5428i	−0.926762	−	0.673332i	−0.945198	+	0.326498i	$0.894131\pi$
$348$		0			0
$349$	−16.7650			−0.897411			−0.448705	−	0.893680i	$-0.648115\pi$
$349$	−16.7650			−0.897411			−0.448705	+	0.893680i	$0.648115\pi$
$350$	−6.86346	+	6.07648i	−0.366867	+	0.324802i
$351$		0			0
$352$	−0.566541	+	1.74363i	−0.0301967	+	0.0929360i
$353$	2.41785	+	1.75667i	0.128689	+	0.0934981i	0.650268	−	0.759705i	$-0.274657\pi$
$353$	2.41785	+	1.75667i	0.128689	+	0.0934981i	−0.521579	+	0.853203i	$0.674657\pi$
$354$		0			0
$355$	−0.427674	−	0.532683i	−0.0226986	−	0.0282719i
$356$	−2.68630	+	1.95171i	−0.142374	+	0.103441i
$357$		0			0
$358$	−8.54361	+	6.20730i	−0.451544	+	0.328066i
$359$	−2.07194	−	6.37678i	−0.109353	−	0.336554i	0.881375	−	0.472418i	$-0.156619\pi$
$359$	−2.07194	−	6.37678i	−0.109353	−	0.336554i	−0.990727	+	0.135865i	$0.956619\pi$
$360$		0			0
$361$	−5.00711	+	15.4103i	−0.263532	+	0.811068i
$362$	−5.61056	−	17.2675i	−0.294884	−	0.907561i
$363$		0			0
$364$	−1.36981	+	4.21584i	−0.0717976	+	0.220970i
$365$	−18.3218	+	27.9559i	−0.959007	+	1.46328i
$366$		0			0
$367$	−3.24949	+	2.36089i	−0.169622	+	0.123237i	−0.669357	−	0.742941i	$-0.733430\pi$
$367$	−3.24949	+	2.36089i	−0.169622	+	0.123237i	0.499736	+	0.866178i	$0.333430\pi$
$368$	7.76626			0.404844
$369$		0			0
$370$	−2.83672	−	0.772856i	−0.147474	−	0.0401789i
$371$	−9.66673	−	7.02329i	−0.501872	−	0.364631i
$372$		0			0
$373$	8.21467	−	25.2822i	0.425340	−	1.30906i	−0.477329	−	0.878725i	$-0.658395\pi$
$373$	8.21467	−	25.2822i	0.425340	−	1.30906i	0.902669	−	0.430336i	$-0.141605\pi$
$374$	5.10532			0.263990
$375$		0			0
$376$	1.83337			0.0945486
$377$	5.66679	−	17.4406i	0.291855	−	0.898236i
$378$		0			0
$379$	12.6431	+	9.18578i	0.649435	+	0.471842i	0.863079	−	0.505070i	$-0.168533\pi$
$379$	12.6431	+	9.18578i	0.649435	+	0.471842i	−0.213644	+	0.976912i	$0.568533\pi$
$380$	3.60792	+	0.982966i	0.185082	+	0.0504251i
$381$		0			0
$382$	−21.9051			−1.12076
$383$	10.8776	−	7.90306i	0.555821	−	0.403828i	−0.274106	−	0.961699i	$-0.588382\pi$
$383$	10.8776	−	7.90306i	0.555821	−	0.403828i	0.829927	+	0.557872i	$0.188382\pi$
$384$		0			0
$385$	−4.11986	+	6.28618i	−0.209967	+	0.320374i
$386$	−8.47474	+	26.0826i	−0.431353	+	1.32757i
$387$		0			0
$388$	3.42705	+	10.5474i	0.173982	+	0.535462i
$389$	7.75991	−	23.8826i	0.393443	−	1.21089i	−0.536724	−	0.843758i	$-0.680338\pi$
$389$	7.75991	−	23.8826i	0.393443	−	1.21089i	0.930167	−	0.367136i	$-0.119662\pi$
$390$		0			0
$391$	−6.68294	−	20.5680i	−0.337971	−	1.04017i
$392$	−2.94383	+	2.13882i	−0.148686	+	0.108026i
$393$		0			0
$394$	0.909110	−	0.660507i	0.0458003	−	0.0332759i
$395$	−4.84474	−	6.03430i	−0.243765	−	0.303619i
$396$		0			0
$397$	−2.84628	−	2.06794i	−0.142850	−	0.103787i	0.514065	−	0.857751i	$-0.328139\pi$
$397$	−2.84628	−	2.06794i	−0.142850	−	0.103787i	−0.656915	+	0.753964i	$0.728139\pi$
$398$	−7.87968	+	24.2511i	−0.394972	+	1.21560i
$399$		0			0
$400$	−1.08052	+	4.88185i	−0.0540261	+	0.244093i
$401$	−29.8696			−1.49161			−0.745807	−	0.666162i	$-0.767936\pi$
$401$	−29.8696			−1.49161			−0.745807	+	0.666162i	$0.767936\pi$
$402$		0			0
$403$	−10.3557	−	7.52388i	−0.515856	−	0.374791i
$404$	−10.6634	−	7.74739i	−0.530523	−	0.385447i
$405$		0			0
$406$	−11.2495	+	8.17323i	−0.558303	+	0.405631i
$407$	−2.41062			−0.119490
$408$		0			0
$409$	−11.9784	−	36.8656i	−0.592291	−	1.82289i	−0.567771	−	0.823186i	$-0.692194\pi$
$409$	−11.9784	−	36.8656i	−0.592291	−	1.82289i	−0.0245200	−	0.999699i	$-0.507806\pi$
$410$	−7.58347	−	2.06609i	−0.374521	−	0.102037i
$411$		0			0
$412$	−0.813697	−	2.50430i	−0.0400880	−	0.123378i
$413$	5.13308	+	15.7980i	0.252582	+	0.777369i
$414$		0			0
$415$	13.3244	−	5.05079i	0.654070	−	0.247933i
$416$	0.747156	+	2.29951i	0.0366323	+	0.112743i
$417$		0			0
$418$	3.06598			0.149962
$419$	−15.2988	+	11.1152i	−0.747395	+	0.543014i	−0.895018	−	0.446030i	$-0.852838\pi$
$419$	−15.2988	+	11.1152i	−0.747395	+	0.543014i	0.147624	+	0.989044i	$0.452838\pi$
$420$		0			0
$421$	17.8414	+	12.9625i	0.869536	+	0.631755i	0.930462	−	0.366388i	$-0.119406\pi$
$421$	17.8414	+	12.9625i	0.869536	+	0.631755i	−0.0609265	+	0.998142i	$0.519406\pi$
$422$	17.2356	+	12.5224i	0.839016	+	0.609581i
$423$		0			0
$424$	−6.51738			−0.316512
$425$	13.8588	−	1.33925i	0.672250	−	0.0649633i
$426$		0			0
$427$	1.46617	−	4.51242i	0.0709531	−	0.218371i
$428$	15.2131	+	11.0530i	0.735355	+	0.534267i
$429$		0			0
$430$	−5.27725	+	8.05216i	−0.254492	+	0.388310i
$431$	−7.44763	+	5.41102i	−0.358740	+	0.260640i	−0.752526	−	0.658562i	$-0.771165\pi$
$431$	−7.44763	+	5.41102i	−0.358740	+	0.260640i	0.393787	+	0.919202i	$0.371165\pi$
$432$		0			0
$433$	−28.1516	+	20.4533i	−1.35288	+	0.982923i	−0.354015	+	0.935240i	$0.615184\pi$
$433$	−28.1516	+	20.4533i	−1.35288	+	0.982923i	−0.998862	+	0.0476837i	$0.984816\pi$
$434$	2.99934	+	9.23102i	0.143973	+	0.443103i
$435$		0			0
$436$	3.18574	−	9.80470i	0.152569	−	0.469560i
$437$	−4.01342	−	12.3520i	−0.191988	−	0.590878i
$438$		0			0
$439$	−2.58025	+	7.94118i	−0.123148	+	0.379012i	−0.993559	−	0.113314i	$-0.963853\pi$
$439$	−2.58025	+	7.94118i	−0.123148	+	0.379012i	0.870411	+	0.492326i	$0.163853\pi$
$440$	0.197391	+	4.09478i	0.00941024	+	0.195211i
$441$		0			0
$442$	5.44703	−	3.95750i	0.259089	−	0.188239i
$443$	1.19887			0.0569599			0.0284799	−	0.999594i	$-0.490933\pi$
$443$	1.19887			0.0569599			0.0284799	+	0.999594i	$0.490933\pi$
$444$		0			0
$445$	−4.06988	+	6.20992i	−0.192931	+	0.294379i
$446$	2.62535	+	1.90743i	0.124314	+	0.0903194i
$447$		0			0
$448$	0.566541	−	1.74363i	0.0267666	−	0.0823790i
$449$	−32.7953			−1.54771			−0.773853	−	0.633365i	$-0.781673\pi$
$449$	−32.7953			−1.54771			−0.773853	+	0.633365i	$0.781673\pi$
$450$		0			0
$451$	−6.44437			−0.303453
$452$	−1.87160	+	5.76019i	−0.0880326	+	0.270936i
$453$		0			0
$454$	−13.2495	−	9.62631i	−0.621829	−	0.451785i
$455$	0.477261	+	9.90054i	0.0223743	+	0.464145i
$456$		0			0
$457$	19.7884			0.925664			0.462832	−	0.886446i	$-0.346833\pi$
$457$	19.7884			0.925664			0.462832	+	0.886446i	$0.346833\pi$
$458$	−4.11788	+	2.99181i	−0.192416	+	0.139798i
$459$		0			0
$460$	16.2384	−	6.15537i	0.757119	−	0.286995i
$461$	−2.90468	+	8.93970i	−0.135285	+	0.416363i	−0.995634	−	0.0933412i	$-0.970245\pi$
$461$	−2.90468	+	8.93970i	−0.135285	+	0.416363i	0.860350	+	0.509704i	$0.170245\pi$
$462$		0			0
$463$	5.47977	+	16.8650i	0.254666	+	0.783783i	0.993895	+	0.110328i	$0.0351902\pi$
$463$	5.47977	+	16.8650i	0.254666	+	0.783783i	−0.739229	+	0.673454i	$0.764810\pi$
$464$	−2.34373	+	7.21327i	−0.108805	+	0.334868i
$465$		0			0
$466$	−0.513883	−	1.58157i	−0.0238052	−	0.0732649i
$467$	17.6857	−	12.8494i	0.818398	−	0.594601i	−0.0978549	−	0.995201i	$-0.531198\pi$
$467$	17.6857	−	12.8494i	0.818398	−	0.594601i	0.916253	+	0.400599i	$0.131198\pi$
$468$		0			0
$469$	−14.0908	+	10.2375i	−0.650651	+	0.472726i
$470$	3.83337	−	1.45309i	0.176820	−	0.0670258i
$471$		0			0
$472$	7.33001	+	5.32556i	0.337391	+	0.245129i
$473$	−2.43924	+	7.50722i	−0.112157	+	0.345182i
$474$		0			0
$475$	8.32284	−	0.804283i	0.381878	−	0.0369030i
$476$	−5.10532			−0.234002
$477$		0			0
$478$	−10.3553	−	7.52354i	−0.473639	−	0.344119i
$479$	−4.94352	−	3.59168i	−0.225875	−	0.164108i	0.469092	−	0.883149i	$-0.344581\pi$
$479$	−4.94352	−	3.59168i	−0.225875	−	0.164108i	−0.694967	+	0.719041i	$0.744581\pi$
$480$		0			0
$481$	−2.57198	+	1.86865i	−0.117272	+	0.0852031i
$482$	−0.395477			−0.0180135
$483$		0			0
$484$	−2.36051	−	7.26490i	−0.107296	−	0.330223i
$485$	15.5252	+	19.3372i	0.704963	+	0.878057i
$486$		0			0
$487$	1.56421	+	4.81415i	0.0708812	+	0.218150i	0.980222	−	0.197903i	$-0.0634131\pi$
$487$	1.56421	+	4.81415i	0.0708812	+	0.218150i	−0.909340	+	0.416053i	$0.863413\pi$
$488$	−0.799717	−	2.46127i	−0.0362015	−	0.111417i
$489$		0			0
$490$	−4.46004	+	6.80524i	−0.201484	+	0.307429i
$491$	−0.736165	−	2.26568i	−0.0332227	−	0.102249i	0.933070	−	0.359695i	$-0.117119\pi$
$491$	−0.736165	−	2.26568i	−0.0332227	−	0.102249i	−0.966293	+	0.257446i	$0.917119\pi$
$492$		0			0
$493$	21.1203			0.951209
$494$	3.27120	−	2.37666i	0.147178	−	0.106931i
$495$		0			0
$496$	4.28304	+	3.11181i	0.192314	+	0.139724i
$497$	0.453127	+	0.329216i	0.0203255	+	0.0147674i
$498$		0			0
$499$	−0.0503313			−0.00225314			−0.00112657	−	0.999999i	$-0.500359\pi$
$499$	−0.0503313			−0.00225314			−0.00112657	+	0.999999i	$0.500359\pi$
$500$	1.61000	+	11.0638i	0.0720012	+	0.494789i
$501$		0			0
$502$	2.89422	−	8.90749i	0.129175	−	0.397561i
$503$	−4.37744	−	3.18040i	−0.195181	−	0.141807i	0.485903	−	0.874013i	$-0.338491\pi$
$503$	−4.37744	−	3.18040i	−0.195181	−	0.141807i	−0.681083	+	0.732206i	$0.738491\pi$
$504$		0			0
$505$	−28.4364	−	7.74739i	−1.26540	−	0.344755i
$506$	11.5191	−	8.36912i	0.512087	−	0.372053i
$507$		0			0
$508$	−0.269620	+	0.195890i	−0.0119625	+	0.00869123i
$509$	−5.85472	−	18.0190i	−0.259506	−	0.798678i	−0.992908	−	0.118883i	$-0.962069\pi$
$509$	−5.85472	−	18.0190i	−0.259506	−	0.798678i	0.733402	−	0.679795i	$-0.237931\pi$
$510$		0			0
$511$	8.46868	−	26.0639i	0.374632	−	1.15300i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	−1.53868	+	4.73556i	−0.0678681	+	0.208877i
$515$	−3.68621	−	4.59130i	−0.162434	−	0.202317i
$516$		0			0
$517$	2.71929	−	1.97568i	0.119594	−	0.0868904i
$518$	2.41062			0.105917
$519$		0			0
$520$	3.38476	+	4.21584i	0.148432	+	0.184877i
$521$	31.0817	+	22.5822i	1.36171	+	0.989342i	0.998334	+	0.0577005i	$0.0183768\pi$
$521$	31.0817	+	22.5822i	1.36171	+	0.989342i	0.363379	+	0.931642i	$0.381623\pi$
$522$		0			0
$523$	−3.79057	+	11.6662i	−0.165750	+	0.510127i	−0.999091	−	0.0426332i	$-0.986425\pi$
$523$	−3.79057	+	11.6662i	−0.165750	+	0.510127i	0.833341	+	0.552760i	$0.186425\pi$
$524$	5.17801			0.226202
$525$		0			0
$526$	−19.8112			−0.863809
$527$	4.55565	−	14.0208i	0.198447	−	0.610757i
$528$		0			0
$529$	−30.1883	−	21.9331i	−1.31254	−	0.953613i
$530$	−13.6271	+	5.16553i	−0.591924	+	0.224376i
$531$		0			0
$532$	−3.06598			−0.132927
$533$	−6.87572	+	4.99550i	−0.297820	+	0.216379i
$534$		0			0
$535$	40.5694	+	11.0530i	1.75397	+	0.477863i
$536$	−2.93569	+	9.03513i	−0.126803	+	0.390258i
$537$		0			0
$538$	4.57157	+	14.0698i	0.197094	+	0.606594i
$539$	−2.06151	+	6.34468i	−0.0887957	+	0.273285i
$540$		0			0
$541$	12.9872	+	39.9704i	0.558362	+	1.71846i	0.686896	+	0.726756i	$0.258973\pi$
$541$	12.9872	+	39.9704i	0.558362	+	1.71846i	−0.128534	+	0.991705i	$0.541027\pi$
$542$	−10.1583	+	7.38047i	−0.436338	+	0.317018i
$543$		0			0
$544$	−2.25284	+	1.63679i	−0.0965899	+	0.0701767i
$545$	−1.10996	−	23.0255i	−0.0475453	−	0.986304i
$546$		0			0
$547$	−15.6719	−	11.3863i	−0.670080	−	0.486842i	0.199972	−	0.979802i	$-0.435915\pi$
$547$	−15.6719	−	11.3863i	−0.670080	−	0.486842i	−0.870052	+	0.492960i	$0.835915\pi$
$548$	6.03299	−	18.5676i	0.257717	−	0.793170i
$549$		0			0
$550$	3.65815	+	8.40528i	0.155984	+	0.358402i
$551$	12.6837			0.540344
$552$		0			0
$553$	5.13308	+	3.72940i	0.218281	+	0.158590i
$554$	−5.12256	−	3.72176i	−0.217637	−	0.158122i
$555$		0			0
$556$	6.43579	−	4.67587i	0.272938	−	0.198301i
$557$	−8.54685			−0.362142			−0.181071	−	0.983470i	$-0.557956\pi$
$557$	−8.54685			−0.362142			−0.181071	+	0.983470i	$0.557956\pi$
$558$		0			0
$559$	3.21688	+	9.90054i	0.136060	+	0.418748i
$560$	−0.197391	−	4.09478i	−0.00834129	−	0.173036i
$561$		0			0
$562$	−6.20792	−	19.1060i	−0.261865	−	0.805938i
$563$	7.24949	+	22.3116i	0.305529	+	0.940323i	0.979479	+	0.201546i	$0.0645964\pi$
$563$	7.24949	+	22.3116i	0.305529	+	0.940323i	−0.673950	+	0.738777i	$0.735404\pi$
$564$		0			0
$565$	0.652091	+	13.5273i	0.0274337	+	0.569098i
$566$	−0.561416	−	1.72786i	−0.0235981	−	0.0726274i
$567$		0			0
$568$	0.305502			0.0128186
$569$	−5.74445	+	4.17359i	−0.240820	+	0.174966i	−0.701649	−	0.712523i	$-0.747552\pi$
$569$	−5.74445	+	4.17359i	−0.240820	+	0.174966i	0.460829	+	0.887489i	$0.347552\pi$
$570$		0			0
$571$	9.67745	+	7.03108i	0.404989	+	0.294241i	0.771570	−	0.636145i	$-0.219472\pi$
$571$	9.67745	+	7.03108i	0.404989	+	0.294241i	−0.366581	+	0.930386i	$0.619472\pi$
$572$	3.58621	+	2.60553i	0.149947	+	0.108943i
$573$		0			0
$574$	6.44437			0.268983
$575$	29.0741	−	25.7404i	1.21247	−	1.07345i
$576$		0			0
$577$	12.8457	−	39.5350i	0.534774	−	1.64587i	−0.209362	−	0.977838i	$-0.567139\pi$
$577$	12.8457	−	39.5350i	0.534774	−	1.64587i	0.744137	−	0.668027i	$-0.232861\pi$
$578$	−7.47987	−	5.43444i	−0.311121	−	0.226043i
$579$		0			0
$580$	0.816590	+	16.9397i	0.0339070	+	0.703385i
$581$	−9.45200	+	6.86728i	−0.392135	+	0.284903i
$582$		0			0
$583$	−9.66673	+	7.02329i	−0.400355	+	0.290875i
$584$	−4.61920	−	14.2164i	−0.191144	−	0.588280i
$585$		0			0
$586$	−2.11964	+	6.52359i	−0.0875617	+	0.269487i
$587$	−5.91072	−	18.1913i	−0.243962	−	0.750836i	−0.995806	−	0.0914953i	$-0.970835\pi$
$587$	−5.91072	−	18.1913i	−0.243962	−	0.750836i	0.751844	−	0.659341i	$-0.229165\pi$
$588$		0			0
$589$	2.73588	−	8.42016i	0.112730	−	0.346947i
$590$	19.5472	+	5.32556i	0.804744	+	0.219250i
$591$		0			0
$592$	1.06375	−	0.772856i	0.0437197	−	0.0317642i
$593$	−0.538428			−0.0221106			−0.0110553	−	0.999939i	$-0.503519\pi$
$593$	−0.538428			−0.0221106			−0.0110553	+	0.999939i	$0.503519\pi$
$594$		0			0
$595$	−10.6747	+	4.04636i	−0.437618	+	0.165885i
$596$	−1.35878	−	0.987213i	−0.0556579	−	0.0404378i
$597$		0			0
$598$	5.80261	−	17.8586i	0.237286	−	0.730292i
$599$	38.4209			1.56983			0.784917	−	0.619601i	$-0.212705\pi$
$599$	38.4209			1.56983			0.784917	+	0.619601i	$0.212705\pi$
$600$		0			0
$601$	19.6034			0.799639			0.399820	−	0.916594i	$-0.369073\pi$
$601$	19.6034			0.799639			0.399820	+	0.916594i	$0.369073\pi$
$602$	2.43924	−	7.50722i	0.0994162	−	0.305971i
$603$		0			0
$604$	17.2048	+	12.5001i	0.700055	+	0.508620i
$605$	−10.6936	−	13.3192i	−0.434755	−	0.541503i
$606$		0			0
$607$	−32.4415			−1.31676			−0.658381	−	0.752685i	$-0.728758\pi$
$607$	−32.4415			−1.31676			−0.658381	+	0.752685i	$0.728758\pi$
$608$	−1.35294	+	0.982966i	−0.0548688	+	0.0398646i
$609$		0			0
$610$	−3.62287	−	4.51242i	−0.146686	−	0.182702i
$611$	1.36981	−	4.21584i	0.0554166	−	0.170555i
$612$		0			0
$613$	−7.25273	−	22.3216i	−0.292935	−	0.901561i	−0.983907	−	0.178680i	$-0.942817\pi$
$613$	−7.25273	−	22.3216i	−0.292935	−	0.901561i	0.690972	−	0.722881i	$-0.257183\pi$
$614$	0.894685	−	2.75356i	0.0361065	−	0.111124i
$615$		0			0
$616$	−1.03868	−	3.19672i	−0.0418495	−	0.128799i
$617$	14.0876	−	10.2353i	0.567147	−	0.412056i	−0.266921	−	0.963718i	$-0.586006\pi$
$617$	14.0876	−	10.2353i	0.567147	−	0.412056i	0.834068	+	0.551662i	$0.186006\pi$
$618$		0			0
$619$	−10.1801	+	7.39624i	−0.409171	+	0.297280i	−0.773266	−	0.634082i	$-0.781378\pi$
$619$	−10.1801	+	7.39624i	−0.409171	+	0.297280i	0.364095	+	0.931362i	$0.381378\pi$
$620$	11.4217	+	3.11181i	0.458707	+	0.124973i
$621$		0			0
$622$	16.7054	+	12.1372i	0.669826	+	0.486657i
$623$	1.88117	−	5.78966i	0.0753676	−	0.231958i
$624$		0			0
$625$	12.1353	+	21.8572i	0.485410	+	0.874287i
$626$	−16.4272			−0.656563
$627$		0			0
$628$	−8.45536	−	6.14318i	−0.337406	−	0.245140i
$629$	−2.96218	−	2.15215i	−0.118110	−	0.0858118i
$630$		0			0
$631$	−33.7653	+	24.5319i	−1.34418	+	0.976601i	−0.344897	+	0.938640i	$0.612086\pi$
$631$	−33.7653	+	24.5319i	−1.34418	+	0.976601i	−0.999279	+	0.0379610i	$0.987914\pi$
$632$	3.46076			0.137662
$633$		0			0
$634$	5.10060	+	15.6980i	0.202571	+	0.623448i
$635$	−0.408487	+	0.623280i	−0.0162103	+	0.0247341i
$636$		0			0
$637$	2.71873	+	8.36739i	0.107720	+	0.331528i
$638$	4.29692	+	13.2246i	0.170117	+	0.523565i
$639$		0			0
$640$	−1.39991	−	1.74363i	−0.0553362	−	0.0689232i
$641$	4.44926	+	13.6934i	0.175735	+	0.540858i	0.999666	−	0.0258324i	$-0.00822362\pi$
$641$	4.44926	+	13.6934i	0.175735	+	0.540858i	−0.823931	+	0.566690i	$0.808224\pi$
$642$		0			0
$643$	30.1666			1.18966			0.594828	−	0.803853i	$-0.297220\pi$
$643$	30.1666			1.18966			0.594828	+	0.803853i	$0.297220\pi$
$644$	−11.5191	+	8.36912i	−0.453916	+	0.329790i
$645$		0			0
$646$	3.76748	+	2.73724i	0.148230	+	0.107695i
$647$	−8.64660	−	6.28212i	−0.339933	−	0.246976i	0.404701	−	0.914449i	$-0.367376\pi$
$647$	−8.64660	−	6.28212i	−0.339933	−	0.246976i	−0.744633	+	0.667474i	$0.767376\pi$
$648$		0			0
$649$	16.6110			0.652039
$650$	10.4185	+	6.13217i	0.408649	+	0.240524i
$651$		0			0
$652$	3.21706	−	9.90109i	0.125990	−	0.387757i
$653$	8.22432	+	5.97532i	0.321843	+	0.233832i	0.736961	−	0.675935i	$-0.236260\pi$
$653$	8.22432	+	5.97532i	0.321843	+	0.233832i	−0.415119	+	0.909767i	$0.636260\pi$
$654$		0			0
$655$	10.8266	−	4.10398i	0.423032	−	0.160356i
$656$	2.84373	−	2.06609i	0.111029	−	0.0806674i
$657$		0			0
$658$	−2.71929	+	1.97568i	−0.106009	+	0.0770201i
$659$	−9.61668	−	29.5971i	−0.374613	−	1.15294i	−0.943740	−	0.330689i	$-0.892719\pi$
$659$	−9.61668	−	29.5971i	−0.374613	−	1.15294i	0.569127	−	0.822250i	$-0.307281\pi$
$660$		0			0
$661$	12.8131	−	39.4347i	0.498372	−	1.53383i	−0.313262	−	0.949667i	$-0.601422\pi$
$661$	12.8131	−	39.4347i	0.498372	−	1.53383i	0.811635	−	0.584165i	$-0.198578\pi$
$662$	−8.48901	−	26.1265i	−0.329935	−	1.01543i
$663$		0			0
$664$	−1.96924	+	6.06071i	−0.0764215	+	0.235201i
$665$	−6.41062	+	2.43003i	−0.248593	+	0.0942324i
$666$		0			0
$667$	47.6536	−	34.6224i	1.84515	−	1.34058i
$668$	−2.12171			−0.0820913
$669$		0			0
$670$	1.02284	+	21.2182i	0.0395156	+	0.819732i
$671$	−3.83849	−	2.78883i	−0.148183	−	0.107661i
$672$		0			0
$673$	0.662831	−	2.03998i	0.0255503	−	0.0786356i	−0.937468	−	0.348071i	$-0.886837\pi$
$673$	0.662831	−	2.03998i	0.0255503	−	0.0786356i	0.963019	+	0.269435i	$0.0868369\pi$
$674$	2.74521			0.105742
$675$		0			0
$676$	−7.15401			−0.275154
$677$	−12.8391	+	39.5147i	−0.493446	+	1.51867i	0.325918	+	0.945398i	$0.394327\pi$
$677$	−12.8391	+	39.5147i	−0.493446	+	1.51867i	−0.819364	+	0.573274i	$0.805673\pi$
$678$		0			0
$679$	−16.4492	−	11.9510i	−0.631263	−	0.458639i
$680$	−3.41317	+	5.20790i	−0.130889	+	0.199714i
$681$		0			0
$682$	9.70607			0.371665
$683$	−23.3247	+	16.9464i	−0.892495	+	0.648436i	−0.936527	−	0.350595i	$-0.885980\pi$
$683$	−23.3247	+	16.9464i	−0.892495	+	0.648436i	0.0440323	+	0.999030i	$0.485980\pi$
$684$		0			0
$685$	−2.10198	−	43.6045i	−0.0803124	−	1.66604i
$686$	6.02730	−	18.5501i	0.230123	−	0.708247i
$687$		0			0
$688$	−1.33047	−	4.09478i	−0.0507238	−	0.156112i
$689$	−4.86950	+	14.9868i	−0.185513	+	0.570951i
$690$		0			0
$691$	−15.2050	−	46.7963i	−0.578426	−	1.78021i	−0.624204	−	0.781262i	$-0.714576\pi$
$691$	−15.2050	−	46.7963i	−0.578426	−	1.78021i	0.0457774	−	0.998952i	$-0.485424\pi$
$692$	−14.6551	+	10.6475i	−0.557103	+	0.404759i
$693$		0			0
$694$	17.2637	−	12.5428i	0.655319	−	0.476117i
$695$	9.75053	−	14.8776i	0.369859	−	0.564340i
$696$		0			0
$697$	−7.91886	−	5.75339i	−0.299948	−	0.217925i
$698$	5.18067	−	15.9445i	0.196091	−	0.603507i
$699$		0			0
$700$	−3.65815	−	8.40528i	−0.138265	−	0.317690i
$701$	24.9783			0.943419			0.471709	−	0.881754i	$-0.343637\pi$
$701$	24.9783			0.943419			0.471709	+	0.881754i	$0.343637\pi$
$702$		0			0
$703$	−1.77893	−	1.29247i	−0.0670935	−	0.0487462i
$704$	−1.48322	−	1.07763i	−0.0559011	−	0.0406145i
$705$		0			0
$706$	−2.41785	+	1.75667i	−0.0909969	+	0.0661131i
$707$	24.1650			0.908817
$708$		0			0
$709$	3.02602	+	9.31312i	0.113644	+	0.349762i	0.991662	−	0.128867i	$-0.0411340\pi$
$709$	3.02602	+	9.31312i	0.113644	+	0.349762i	−0.878017	+	0.478629i	$0.841134\pi$
$710$	0.638770	−	0.242134i	0.0239726	−	0.00908712i
$711$		0			0
$712$	−1.02608	−	3.15794i	−0.0384538	−	0.118349i
$713$	−12.7054	−	39.1032i	−0.475821	−	1.46443i
$714$		0			0
$715$	9.56346	+	2.60553i	0.357653	+	0.0974414i
$716$	−3.26337	−	10.0436i	−0.121958	−	0.375348i
$717$		0			0
$718$	6.70494			0.250226
$719$	−6.94474	+	5.04565i	−0.258995	+	0.188171i	−0.709704	−	0.704500i	$-0.751171\pi$
$719$	−6.94474	+	5.04565i	−0.258995	+	0.188171i	0.450709	+	0.892671i	$0.351171\pi$
$720$		0			0
$721$	3.90559	+	2.83758i	0.145452	+	0.105677i
$722$	−13.1088	−	9.52408i	−0.487858	−	0.354450i
$723$		0			0
$724$	18.1561			0.674768
$725$	15.1335	+	34.7719i	0.562043	+	1.29140i
$726$		0			0
$727$	−7.42142	+	22.8408i	−0.275245	+	0.847118i	0.713909	+	0.700238i	$0.246923\pi$
$727$	−7.42142	+	22.8408i	−0.275245	+	0.847118i	−0.989154	+	0.146880i	$0.953077\pi$
$728$	−3.58621	−	2.60553i	−0.132914	−	0.0965675i
$729$		0			0
$730$	−20.9259	−	26.0639i	−0.774501	−	0.964669i
$731$	−9.69962	+	7.04719i	−0.358754	+	0.260650i
$732$		0			0
$733$	15.3787	−	11.1733i	0.568025	−	0.412695i	−0.266362	−	0.963873i	$-0.585822\pi$
$733$	15.3787	−	11.1733i	0.568025	−	0.412695i	0.834387	+	0.551178i	$0.185822\pi$
$734$	−1.24119	−	3.82000i	−0.0458133	−	0.140999i
$735$		0			0
$736$	−2.39991	+	7.38615i	−0.0884617	+	0.272257i
$737$	5.38220	+	16.5647i	0.198256	+	0.610168i
$738$		0			0
$739$	−6.42507	+	19.7743i	−0.236350	+	0.727411i	0.760589	+	0.649233i	$0.224910\pi$
$739$	−6.42507	+	19.7743i	−0.236350	+	0.727411i	−0.996939	+	0.0781776i	$0.975090\pi$
$740$	1.61163	−	2.45906i	0.0592446	−	0.0903968i
$741$		0			0
$742$	9.66673	−	7.02329i	0.354877	−	0.257833i
$743$	−6.53365			−0.239696			−0.119848	−	0.992792i	$-0.538241\pi$
$743$	−6.53365			−0.239696			−0.119848	+	0.992792i	$0.538241\pi$
$744$		0			0
$745$	−3.62351	−	0.987213i	−0.132755	−	0.0361687i
$746$	21.5063	+	15.6252i	0.787401	+	0.572080i
$747$		0			0
$748$	−1.57763	+	4.85544i	−0.0576838	+	0.177533i
$749$	−34.4755			−1.25971
$750$		0			0
$751$	27.9879			1.02129			0.510646	−	0.859791i	$-0.329406\pi$
$751$	27.9879			1.02129			0.510646	+	0.859791i	$0.329406\pi$
$752$	−0.566541	+	1.74363i	−0.0206596	+	0.0635838i
$753$		0			0
$754$	14.8359	+	10.7789i	0.540290	+	0.392544i
$755$	45.8807	+	12.5001i	1.66977	+	0.454923i
$756$		0			0
$757$	4.48558			0.163031			0.0815156	−	0.996672i	$-0.474024\pi$
$757$	4.48558			0.163031			0.0815156	+	0.996672i	$0.474024\pi$
$758$	−12.6431	+	9.18578i	−0.459220	+	0.333643i
$759$		0			0
$760$	−2.04977	+	3.12758i	−0.0743528	+	0.113449i
$761$	−0.138770	+	0.427091i	−0.00503042	+	0.0154820i	−0.953540	−	0.301266i	$-0.902591\pi$
$761$	−0.138770	+	0.427091i	−0.00503042	+	0.0154820i	0.948510	+	0.316748i	$0.102591\pi$
$762$		0			0
$763$	5.84063	+	17.9756i	0.211445	+	0.650760i
$764$	6.76906	−	20.8330i	0.244896	−	0.753712i
$765$		0			0
$766$	4.15489	+	12.7874i	0.150122	+	0.462028i
$767$	17.7228	−	12.8764i	0.639935	−	0.464940i
$768$		0			0
$769$	−16.9783	+	12.3355i	−0.612254	+	0.444829i	−0.850207	−	0.526448i	$-0.823524\pi$
$769$	−16.9783	+	12.3355i	−0.612254	+	0.444829i	0.237953	+	0.971277i	$0.423524\pi$
$770$	−4.70541	−	5.86076i	−0.169571	−	0.211207i
$771$		0			0
$772$	−22.1872	−	16.1199i	−0.798533	−	0.580168i
$773$	−10.8283	+	33.3262i	−0.389468	+	1.19866i	0.543718	+	0.839268i	$0.317016\pi$
$773$	−10.8283	+	33.3262i	−0.389468	+	1.19866i	−0.933187	+	0.359392i	$0.882984\pi$
$774$		0			0
$775$	26.3479	−	2.54615i	0.946444	−	0.0914602i
$776$	−11.0902			−0.398114
$777$		0			0
$778$	20.3157	+	14.7602i	0.728354	+	0.529180i
$779$	−4.75564	−	3.45517i	−0.170388	−	0.123794i
$780$		0			0
$781$	0.453127	−	0.329216i	0.0162142	−	0.0117803i
$782$	21.6265			0.773361
$783$		0			0
$784$	−1.12444	−	3.46068i	−0.0401586	−	0.123596i
$785$	−22.5482	−	6.14318i	−0.804779	−	0.219259i
$786$		0			0
$787$	12.1132	+	37.2807i	0.431790	+	1.32891i	0.896340	+	0.443367i	$0.146216\pi$
$787$	12.1132	+	37.2807i	0.431790	+	1.32891i	−0.464550	+	0.885547i	$0.653784\pi$
$788$	0.347249	+	1.06872i	0.0123702	+	0.0380717i
$789$		0			0
$790$	7.23607	−	2.74292i	0.257448	−	0.0975888i
$791$	−3.43132	−	10.5605i	−0.122004	−	0.375489i
$792$		0			0
$793$	−6.25724			−0.222201
$794$	2.84628	−	2.06794i	0.101011	−	0.0733884i
$795$		0			0
$796$	−20.6293	−	14.9880i	−0.731185	−	0.531237i
$797$	−6.98479	−	5.07475i	−0.247414	−	0.179757i	0.457166	−	0.889381i	$-0.348865\pi$
$797$	−6.98479	−	5.07475i	−0.247414	−	0.179757i	−0.704580	+	0.709625i	$0.748865\pi$
$798$		0			0
$799$	5.10532			0.180613
$800$	−4.30902	−	2.53621i	−0.152347	−	0.0896686i
$801$		0			0
$802$	9.23020	−	28.4076i	0.325930	−	1.00311i
$803$	−22.1713	−	16.1084i	−0.782408	−	0.568453i
$804$		0			0
$805$	−17.4520	+	26.6287i	−0.615102	+	0.938538i
$806$	10.3557	−	7.52388i	0.364765	−	0.265017i
$807$		0			0
$808$	10.6634	−	7.74739i	0.375136	−	0.272552i
$809$	14.1830	+	43.6508i	0.498648	+	1.53468i	0.811194	+	0.584778i	$0.198818\pi$
$809$	14.1830	+	43.6508i	0.498648	+	1.53468i	−0.312546	+	0.949903i	$0.601182\pi$
$810$		0			0
$811$	12.1734	−	37.4660i	0.427467	−	1.31561i	−0.473145	−	0.880984i	$-0.656881\pi$
$811$	12.1734	−	37.4660i	0.427467	−	1.31561i	0.900612	−	0.434623i	$-0.143119\pi$
$812$	−4.29692	−	13.2246i	−0.150792	−	0.464091i
$813$		0			0
$814$	0.744923	−	2.29264i	0.0261096	−	0.0803569i
$815$	−1.12087	−	23.2519i	−0.0392623	−	0.814477i
$816$		0			0
$817$	−5.82507	+	4.23216i	−0.203794	+	0.148065i
$818$	38.7628			1.35531
$819$		0			0
$820$	4.30839	−	6.57385i	0.150456	−	0.229569i
$821$	22.0672	+	16.0328i	0.770152	+	0.559548i	0.902007	−	0.431721i	$-0.142093\pi$
$821$	22.0672	+	16.0328i	0.770152	+	0.559548i	−0.131855	+	0.991269i	$0.542093\pi$
$822$		0			0
$823$	1.89701	−	5.83841i	0.0661258	−	0.203514i	−0.912534	−	0.409000i	$-0.865878\pi$
$823$	1.89701	−	5.83841i	0.0661258	−	0.203514i	0.978660	+	0.205486i	$0.0658775\pi$
$824$	2.63318			0.0917311
$825$		0			0
$826$	−16.6110			−0.577971
$827$	−13.6170	+	41.9087i	−0.473508	+	1.45731i	0.374451	+	0.927247i	$0.377831\pi$
$827$	−13.6170	+	41.9087i	−0.473508	+	1.45731i	−0.847959	+	0.530062i	$0.822169\pi$
$828$		0			0
$829$	−3.80236	−	2.76257i	−0.132061	−	0.0959481i	0.519794	−	0.854292i	$-0.326009\pi$
$829$	−3.80236	−	2.76257i	−0.132061	−	0.0959481i	−0.651855	+	0.758344i	$0.726009\pi$
$830$	0.686112	+	14.2331i	0.0238153	+	0.494036i
$831$		0			0
$832$	−2.41785			−0.0838238
$833$	−8.19758	+	5.95589i	−0.284029	+	0.206359i
$834$		0			0
$835$	−4.43625	+	1.68162i	−0.153523	+	0.0581948i
$836$	−0.947439	+	2.91592i	−0.0327679	+	0.100849i
$837$		0			0
$838$	−5.84362	−	17.9848i	−0.201864	−	0.621275i
$839$	14.2747	−	43.9331i	0.492819	−	1.51674i	−0.327509	−	0.944848i	$-0.606209\pi$
$839$	14.2747	−	43.9331i	0.492819	−	1.51674i	0.820328	−	0.571893i	$-0.193791\pi$
$840$		0			0
$841$	8.81451	+	27.1283i	0.303949	+	0.935458i
$842$	−17.8414	+	12.9625i	−0.614855	+	0.446718i
$843$		0			0
$844$	−17.2356	+	12.5224i	−0.593274	+	0.431039i
$845$	−14.9583	+	5.67011i	−0.514580	+	0.195058i
$846$		0			0
$847$	11.3300	+	8.23173i	0.389304	+	0.282846i
$848$	2.01398	−	6.19839i	0.0691604	−	0.212854i
$849$		0			0
$850$	−3.00889	+	13.5943i	−0.103204	+	0.466282i
$851$	−10.2116			−0.350048
$852$		0			0
$853$	−10.2282	−	7.43121i	−0.350206	−	0.254440i	0.398749	−	0.917060i	$-0.369444\pi$
$853$	−10.2282	−	7.43121i	−0.350206	−	0.254440i	−0.748956	+	0.662620i	$0.769444\pi$
$854$	3.83849	+	2.78883i	0.131350	+	0.0954317i
$855$		0			0
$856$	−15.2131	+	11.0530i	−0.519974	+	0.377783i
$857$	19.4162			0.663245			0.331623	−	0.943412i	$-0.392404\pi$
$857$	19.4162			0.663245			0.331623	+	0.943412i	$0.392404\pi$
$858$		0			0
$859$	2.88593	+	8.88197i	0.0984665	+	0.303049i	0.988142	−	0.153545i	$-0.0490691\pi$
$859$	2.88593	+	8.88197i	0.0984665	+	0.303049i	−0.889675	+	0.456594i	$0.849069\pi$
$860$	−6.02730	−	7.50722i	−0.205529	−	0.255994i
$861$		0			0
$862$	−2.84474	−	8.75521i	−0.0968923	−	0.298204i
$863$	5.05071	+	15.5445i	0.171928	+	0.529141i	0.999480	−	0.0322489i	$-0.0102669\pi$
$863$	5.05071	+	15.5445i	0.171928	+	0.529141i	−0.827552	+	0.561390i	$0.810267\pi$
$864$		0			0
$865$	−22.2032	+	33.8781i	−0.754930	+	1.15189i
$866$	−10.7529	−	33.0941i	−0.365400	−	1.12458i
$867$		0			0
$868$	−9.70607			−0.329445
$869$	5.13308	−	3.72940i	0.174128	−	0.126511i
$870$		0			0
$871$	18.5829	+	13.5013i	0.629659	+	0.457474i
$872$	8.34038	+	6.05964i	0.282441	+	0.205205i
$873$		0			0
$874$	12.9877			0.439315
$875$	−14.3106	−	14.6751i	−0.483787	−	0.496110i
$876$		0			0
$877$	−10.9717	+	33.7673i	−0.370487	+	1.14024i	0.575986	+	0.817459i	$0.304618\pi$
$877$	−10.9717	+	33.7673i	−0.370487	+	1.14024i	−0.946473	+	0.322782i	$0.895382\pi$
$878$	−6.75517	−	4.90792i	−0.227976	−	0.165634i
$879$		0			0
$880$	−3.95536	−	1.07763i	−0.133335	−	0.0363267i
$881$	−25.5378	+	18.5543i	−0.860390	+	0.625110i	−0.927991	−	0.372602i	$-0.878466\pi$
$881$	−25.5378	+	18.5543i	−0.860390	+	0.625110i	0.0676008	+	0.997712i	$0.478466\pi$
$882$		0			0
$883$	−28.2592	+	20.5315i	−0.950997	+	0.690940i	−0.951042	−	0.309060i	$-0.899986\pi$
$883$	−28.2592	+	20.5315i	−0.950997	+	0.690940i	4.54670e−5		1.00000i	$0.499986\pi$
$884$	2.08058	+	6.40337i	0.0699775	+	0.215369i
$885$		0			0
$886$	−0.370470	+	1.14019i	−0.0124462	+	0.0383054i
$887$	13.2668	+	40.8311i	0.445456	+	1.37097i	0.881982	+	0.471282i	$0.156209\pi$
$887$	13.2668	+	40.8311i	0.445456	+	1.37097i	−0.436526	+	0.899692i	$0.643791\pi$
$888$		0			0
$889$	0.188810	−	0.581099i	0.00633250	−	0.0194894i
$890$	−4.64832	−	5.78966i	−0.155812	−	0.194070i
$891$		0			0
$892$	−2.62535	+	1.90743i	−0.0879033	+	0.0638655i
$893$	3.06598			0.102599
$894$		0			0
$895$	−14.7837	−	18.4136i	−0.494164	−	0.615500i
$896$	1.48322	+	1.07763i	0.0495510	+	0.0360009i
$897$		0			0
$898$	10.1343	−	31.1902i	0.338186	−	1.04083i
$899$	40.1532			1.33918
$900$		0			0
$901$	−18.1487			−0.604622
$902$	1.99142	−	6.12896i	0.0663070	−	0.204072i
$903$		0			0
$904$	−4.89991	−	3.55999i	−0.162968	−	0.118404i
$905$	37.9625	−	14.3902i	1.26192	−	0.478345i
$906$		0			0
$907$	−39.8259			−1.32240			−0.661199	−	0.750211i	$-0.729952\pi$
$907$	−39.8259			−1.32240			−0.661199	+	0.750211i	$0.729952\pi$
$908$	13.2495	−	9.62631i	0.439700	−	0.319460i
$909$		0			0
$910$	−9.56346	−	2.60553i	−0.317026	−	0.0863726i
$911$	0.522189	−	1.60713i	0.0173009	−	0.0532467i	−0.942033	−	0.335519i	$-0.891088\pi$
$911$	0.522189	−	1.60713i	0.0173009	−	0.0532467i	0.959334	+	0.282273i	$0.0910882\pi$
$912$		0			0
$913$	3.61034	+	11.1115i	0.119485	+	0.367737i
$914$	−6.11496	+	18.8199i	−0.202265	+	0.622508i
$915$		0			0
$916$	−1.57289	−	4.84085i	−0.0519697	−	0.159946i
$917$	−7.68015	+	5.57995i	−0.253621	+	0.184266i
$918$		0			0
$919$	24.2013	−	17.5833i	0.798327	−	0.580019i	−0.112096	−	0.993697i	$-0.535756\pi$
$919$	24.2013	−	17.5833i	0.798327	−	0.580019i	0.910423	+	0.413679i	$0.135756\pi$
$920$	0.836161	+	17.3457i	0.0275674	+	0.571872i
$921$		0			0
$922$	−7.60456	−	5.52504i	−0.250443	−	0.181957i
$923$	0.228257	−	0.702504i	0.00751318	−	0.0231232i
$924$		0			0
$925$	1.42074	−	6.41896i	0.0467135	−	0.211054i
$926$	−17.7329			−0.582739
$927$		0			0
$928$	−6.13597	−	4.45805i	−0.201423	−	0.146343i
$929$	−12.8664	−	9.34795i	−0.422131	−	0.306696i	0.356363	−	0.934347i	$-0.384017\pi$
$929$	−12.8664	−	9.34795i	−0.422131	−	0.306696i	−0.778495	+	0.627651i	$0.784017\pi$
$930$		0			0
$931$	−4.92303	+	3.57679i	−0.161346	+	0.117225i
$932$	1.66296			0.0544721
$933$		0			0
$934$	6.75535	+	20.7908i	0.221042	+	0.680297i
$935$	0.549668	+	11.4026i	0.0179761	+	0.372905i
$936$		0			0
$937$	14.2973	+	44.0026i	0.467073	+	1.43750i	0.856357	+	0.516384i	$0.172722\pi$
$937$	14.2973	+	44.0026i	0.467073	+	1.43750i	−0.389284	+	0.921118i	$0.627278\pi$
$938$	−5.38220	−	16.5647i	−0.175735	−	0.540856i
$939$		0			0
$940$	0.197391	+	4.09478i	0.00643818	+	0.133557i
$941$	3.60650	+	11.0997i	0.117569	+	0.361839i	0.992474	−	0.122455i	$-0.0390766\pi$
$941$	3.60650	+	11.0997i	0.117569	+	0.361839i	−0.874906	+	0.484294i	$0.839077\pi$
$942$		0			0
$943$	−27.2988			−0.888971
$944$	−7.33001	+	5.32556i	−0.238571	+	0.173332i
$945$		0			0
$946$	−6.38602	−	4.63972i	−0.207628	−	0.150850i
$947$	−2.37336	−	1.72435i	−0.0771238	−	0.0560337i	0.548555	−	0.836114i	$-0.315178\pi$
$947$	−2.37336	−	1.72435i	−0.0771238	−	0.0560337i	−0.625679	+	0.780081i	$0.715178\pi$
$948$		0			0
$949$	−36.1421			−1.17322
$950$	−1.80698	+	8.16403i	−0.0586262	+	0.264876i
$951$		0			0
$952$	1.57763	−	4.85544i	0.0511313	−	0.157366i
$953$	−8.03924	−	5.84085i	−0.260417	−	0.189204i	0.449914	−	0.893072i	$-0.351455\pi$
$953$	−8.03924	−	5.84085i	−0.260417	−	0.189204i	−0.710331	+	0.703868i	$0.751455\pi$
$954$		0			0
$955$	−2.35843	−	48.9245i	−0.0763171	−	1.58316i
$956$	10.3553	−	7.52354i	0.334913	−	0.243329i
$957$		0			0
$958$	4.94352	−	3.59168i	0.159718	−	0.116042i
$959$	11.0607	+	34.0413i	0.357168	+	1.09925i
$960$		0			0
$961$	−0.918471	+	2.82676i	−0.0296281	+	0.0911859i
$962$	−0.982407	−	3.02354i	−0.0316741	−	0.0974828i
$963$		0			0
$964$	0.122209	−	0.376121i	0.00393610	−	0.0121141i
$965$	−59.1672	−	16.1199i	−1.90466	−	0.518918i
$966$		0			0
$967$	−36.7193	+	26.6781i	−1.18081	+	0.857910i	−0.992263	−	0.124153i	$-0.960379\pi$
$967$	−36.7193	+	26.6781i	−1.18081	+	0.857910i	−0.188549	+	0.982064i	$0.560379\pi$
$968$	7.63877			0.245519
$969$		0			0
$970$	−23.1883	+	8.78982i	−0.744532	+	0.282224i
$971$	−3.78844	−	2.75246i	−0.121577	−	0.0883307i	0.525335	−	0.850895i	$-0.323940\pi$
$971$	−3.78844	−	2.75246i	−0.121577	−	0.0883307i	−0.646912	+	0.762565i	$0.723940\pi$
$972$		0			0
$973$	−4.50688	+	13.8707i	−0.144484	+	0.444675i
$974$	−5.06189			−0.162194
$975$		0			0
$976$	2.58794			0.0828379
$977$	−0.991339	+	3.05103i	−0.0317157	+	0.0976110i	−0.965661	−	0.259804i	$-0.916342\pi$
$977$	−0.991339	+	3.05103i	−0.0317157	+	0.0976110i	0.933946	+	0.357415i	$0.116342\pi$
$978$		0			0
$979$	−4.92498	−	3.57820i	−0.157403	−	0.114360i
$980$	−5.09394	−	6.34468i	−0.162720	−	0.202674i
$981$		0			0
$982$	2.38228			0.0760216
$983$	15.8337	−	11.5038i	0.505015	−	0.366915i	−0.305914	−	0.952059i	$-0.598962\pi$
$983$	15.8337	−	11.5038i	0.505015	−	0.366915i	0.810929	+	0.585144i	$0.198962\pi$
$984$		0			0
$985$	1.57311	+	1.95936i	0.0501233	+	0.0624304i
$986$	−6.52652	+	20.0866i	−0.207847	+	0.639687i
$987$		0			0
$988$	1.24949	+	3.84552i	0.0397514	+	0.122342i
$989$	−10.3328	+	31.8011i	−0.328564	+	1.01122i
$990$		0			0
$991$	13.9762	+	43.0144i	0.443969	+	1.36640i	0.883610	+	0.468223i	$0.155106\pi$
$991$	13.9762	+	43.0144i	0.443969	+	1.36640i	−0.439641	+	0.898173i	$0.644894\pi$
$992$	−4.28304	+	3.11181i	−0.135987	+	0.0988000i
$993$		0			0
$994$	−0.453127	+	0.329216i	−0.0143723	+	0.0104421i
$995$	−55.0127	−	14.9880i	−1.74402	−	0.475153i
$996$		0			0
$997$	46.9808	+	34.1335i	1.48790	+	1.08102i	0.974904	+	0.222626i	$0.0714627\pi$
$997$	46.9808	+	34.1335i	1.48790	+	1.08102i	0.512991	+	0.858394i	$0.328537\pi$
$998$	0.0155532	−	0.0478679i	0.000492329	−	0.00151523i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.e.271.1		8
3.2	odd	2		50.2.d.b.21.1	✓	8
12.11	even	2		400.2.u.d.321.2		8
15.2	even	4		250.2.e.c.149.3		16
15.8	even	4		250.2.e.c.149.2		16
15.14	odd	2		250.2.d.d.101.2		8
25.6	even	5	inner	450.2.h.e.181.1		8
75.8	even	20		250.2.e.c.99.3		16
75.17	even	20		250.2.e.c.99.2		16
75.38	even	20		1250.2.b.e.1249.4		8
75.41	odd	10		1250.2.a.l.1.4		4
75.44	odd	10		250.2.d.d.151.2		8
75.56	odd	10		50.2.d.b.31.1	yes	8
75.59	odd	10		1250.2.a.f.1.1		4
75.62	even	20		1250.2.b.e.1249.5		8
300.59	even	10		10000.2.a.x.1.4		4
300.131	even	10		400.2.u.d.81.2		8
300.191	even	10		10000.2.a.t.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.21.1	✓	8	3.2	odd	2
50.2.d.b.31.1	yes	8	75.56	odd	10
250.2.d.d.101.2		8	15.14	odd	2
250.2.d.d.151.2		8	75.44	odd	10
250.2.e.c.99.2		16	75.17	even	20
250.2.e.c.99.3		16	75.8	even	20
250.2.e.c.149.2		16	15.8	even	4
250.2.e.c.149.3		16	15.2	even	4
400.2.u.d.81.2		8	300.131	even	10
400.2.u.d.321.2		8	12.11	even	2
450.2.h.e.181.1		8	25.6	even	5	inner
450.2.h.e.271.1		8	1.1	even	1	trivial
1250.2.a.f.1.1		4	75.59	odd	10
1250.2.a.l.1.4		4	75.41	odd	10
1250.2.b.e.1249.4		8	75.38	even	20
1250.2.b.e.1249.5		8	75.62	even	20
10000.2.a.t.1.1		4	300.191	even	10
10000.2.a.x.1.4		4	300.59	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-2.15743 - 0.587785i) q^{5} +1.83337 q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-2.15743 - 0.587785i) q^{5} +1.83337 q^{7} +(0.809017 - 0.587785i) q^{8} +(1.22570 - 1.87020i) q^{10} +(0.566541 - 1.74363i) q^{11} +(-0.747156 - 2.29951i) q^{13} +(-0.566541 + 1.74363i) q^{14} +(0.309017 + 0.951057i) q^{16} +(2.25284 - 1.63679i) q^{17} +(1.35294 - 0.982966i) q^{19} +(1.39991 + 1.74363i) q^{20} +(1.48322 + 1.07763i) q^{22} +(2.39991 - 7.38615i) q^{23} +(4.30902 + 2.53621i) q^{25} +2.41785 q^{26} +(-1.48322 - 1.07763i) q^{28} +(6.13597 + 4.45805i) q^{29} +(4.28304 - 3.11181i) q^{31} -1.00000 q^{32} +(0.860510 + 2.64838i) q^{34} +(-3.95536 - 1.07763i) q^{35} +(-0.406315 - 1.25051i) q^{37} +(0.516776 + 1.59047i) q^{38} +(-2.09089 + 0.792578i) q^{40} +(-1.08621 - 3.34301i) q^{41} -4.30550 q^{43} +(-1.48322 + 1.07763i) q^{44} +(6.28304 + 4.56489i) q^{46} +(1.48322 + 1.07763i) q^{47} -3.63877 q^{49} +(-3.74364 + 3.31439i) q^{50} +(-0.747156 + 2.29951i) q^{52} +(-5.27267 - 3.83082i) q^{53} +(-2.24716 + 3.42877i) q^{55} +(1.48322 - 1.07763i) q^{56} +(-6.13597 + 4.45805i) q^{58} +(2.79981 + 8.61694i) q^{59} +(0.799717 - 2.46127i) q^{61} +(1.63597 + 5.03501i) q^{62} +(0.309017 - 0.951057i) q^{64} +(0.260320 + 5.40020i) q^{65} +(-7.68574 + 5.58402i) q^{67} -2.78467 q^{68} +(2.24716 - 3.42877i) q^{70} +(0.247156 + 0.179569i) q^{71} +(4.61920 - 14.2164i) q^{73} +1.31486 q^{74} -1.67232 q^{76} +(1.03868 - 3.19672i) q^{77} +(2.79981 + 2.03418i) q^{79} +(-0.107666 - 2.23347i) q^{80} +3.51505 q^{82} +(-5.15555 + 3.74572i) q^{83} +(-5.82243 + 2.20707i) q^{85} +(1.33047 - 4.09478i) q^{86} +(-0.566541 - 1.74363i) q^{88} +(1.02608 - 3.15794i) q^{89} +(-1.36981 - 4.21584i) q^{91} +(-6.28304 + 4.56489i) q^{92} +(-1.48322 + 1.07763i) q^{94} +(-3.49664 + 1.32545i) q^{95} +(-8.97214 - 6.51864i) q^{97} +(1.12444 - 3.46068i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8	\( 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8} - q^{11} - 13 q^{13} + q^{14} - 2 q^{16} + 11 q^{17} + 20 q^{19} - 5 q^{20} + q^{22} + 3 q^{23} + 30 q^{25} - 22 q^{26} - q^{28} + 15 q^{29} - 9 q^{31} - 8 q^{32} - q^{34} + 15 q^{35} - 6 q^{37} + 15 q^{38} - 5 q^{40} + 9 q^{41} + 12 q^{43} - q^{44} + 7 q^{46} + q^{47} - 4 q^{49} + 5 q^{50} - 13 q^{52} - 7 q^{53} - 25 q^{55} + q^{56} - 15 q^{58} - 10 q^{59} + 6 q^{61} - 21 q^{62} - 2 q^{64} + 10 q^{65} - 11 q^{67} - 24 q^{68} + 25 q^{70} + 9 q^{71} - 8 q^{73} - 24 q^{74} - 10 q^{76} - 33 q^{77} - 10 q^{79} + 26 q^{82} - 27 q^{83} + 5 q^{85} + 23 q^{86} + q^{88} + 15 q^{89} + q^{91} - 7 q^{92} - q^{94} + 30 q^{95} - 36 q^{97} + 19 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 + 4 * q^7 + 2 * q^8 - q^11 - 13 * q^13 + q^14 - 2 * q^16 + 11 * q^17 + 20 * q^19 - 5 * q^20 + q^22 + 3 * q^23 + 30 * q^25 - 22 * q^26 - q^28 + 15 * q^29 - 9 * q^31 - 8 * q^32 - q^34 + 15 * q^35 - 6 * q^37 + 15 * q^38 - 5 * q^40 + 9 * q^41 + 12 * q^43 - q^44 + 7 * q^46 + q^47 - 4 * q^49 + 5 * q^50 - 13 * q^52 - 7 * q^53 - 25 * q^55 + q^56 - 15 * q^58 - 10 * q^59 + 6 * q^61 - 21 * q^62 - 2 * q^64 + 10 * q^65 - 11 * q^67 - 24 * q^68 + 25 * q^70 + 9 * q^71 - 8 * q^73 - 24 * q^74 - 10 * q^76 - 33 * q^77 - 10 * q^79 + 26 * q^82 - 27 * q^83 + 5 * q^85 + 23 * q^86 + q^88 + 15 * q^89 + q^91 - 7 * q^92 - q^94 + 30 * q^95 - 36 * q^97 + 19 * q^98

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