LMFDB - Embedded newform 1470.2.m.d.97.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(97,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1470.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.m (of order $4$, degree $2$, 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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.8
Root			$-1.09227 + 0.838128i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.d.1273.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.62401 - 1.53707i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.62401 - 1.53707i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(2.23522 + 0.0614757i) q^{10} -4.55445 q^{11} +(0.707107 - 0.707107i) q^{12} +(-1.77772 - 1.77772i) q^{13} +(-2.23522 - 0.0614757i) q^{15} -1.00000 q^{16} +(2.91639 - 2.91639i) q^{17} +(-0.707107 + 0.707107i) q^{18} +3.77912 q^{19} +(1.53707 + 1.62401i) q^{20} +(-3.22048 - 3.22048i) q^{22} +(5.69431 - 5.69431i) q^{23} +1.00000 q^{24} +(0.274824 - 4.99244i) q^{25} -2.51408i q^{26} +(0.707107 - 0.707107i) q^{27} +1.55563i q^{29} +(-1.53707 - 1.62401i) q^{30} +3.89374i q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.22048 + 3.22048i) q^{33} +4.12440 q^{34} -1.00000 q^{36} +(-8.08634 - 8.08634i) q^{37} +(2.67224 + 2.67224i) q^{38} +2.51408i q^{39} +(-0.0614757 + 2.23522i) q^{40} -11.3796i q^{41} +(0.367260 - 0.367260i) q^{43} -4.55445i q^{44} +(1.53707 + 1.62401i) q^{45} +8.05297 q^{46} +(3.57116 - 3.57116i) q^{47} +(0.707107 + 0.707107i) q^{48} +(3.72452 - 3.33586i) q^{50} -4.12440 q^{51} +(1.77772 - 1.77772i) q^{52} +(-5.96425 + 5.96425i) q^{53} +1.00000 q^{54} +(-7.39647 + 7.00051i) q^{55} +(-2.67224 - 2.67224i) q^{57} +(-1.09999 + 1.09999i) q^{58} -0.443022 q^{59} +(0.0614757 - 2.23522i) q^{60} -8.19194i q^{61} +(-2.75329 + 2.75329i) q^{62} -1.00000i q^{64} +(-5.61952 - 0.154555i) q^{65} +4.55445i q^{66} +(6.58705 + 6.58705i) q^{67} +(2.91639 + 2.91639i) q^{68} -8.05297 q^{69} -6.68403 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-3.07520 - 3.07520i) q^{73} -11.4358i q^{74} +(-3.72452 + 3.33586i) q^{75} +3.77912i q^{76} +(-1.77772 + 1.77772i) q^{78} -4.71445i q^{79} +(-1.62401 + 1.53707i) q^{80} -1.00000 q^{81} +(8.04662 - 8.04662i) q^{82} +(3.21718 + 3.21718i) q^{83} +(0.253550 - 9.21894i) q^{85} +0.519384 q^{86} +(1.09999 - 1.09999i) q^{87} +(3.22048 - 3.22048i) q^{88} +6.04851 q^{89} +(-0.0614757 + 2.23522i) q^{90} +(5.69431 + 5.69431i) q^{92} +(2.75329 - 2.75329i) q^{93} +5.05038 q^{94} +(6.13733 - 5.80877i) q^{95} +1.00000i q^{96} +(-0.462652 + 0.462652i) q^{97} -4.55445i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{10} - 8 q^{11} - 16 q^{13} + 4 q^{15} - 16 q^{16} + 24 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{22} + 8 q^{23} + 16 q^{24} + 16 q^{25} + 8 q^{30} - 4 q^{33} + 16 q^{34} - 16 q^{36} + 16 q^{37} + 8 q^{38} - 24 q^{43} - 8 q^{45} + 8 q^{46} + 24 q^{47} - 16 q^{51} + 16 q^{52} - 16 q^{53} + 16 q^{54} - 56 q^{55} - 8 q^{57} - 36 q^{58} - 16 q^{59} + 8 q^{62} - 32 q^{65} + 48 q^{67} + 24 q^{68} - 8 q^{69} - 32 q^{71} + 56 q^{73} - 16 q^{78} - 16 q^{81} + 24 q^{82} - 16 q^{83} + 8 q^{85} + 16 q^{86} + 36 q^{87} - 4 q^{88} + 32 q^{89} + 8 q^{92} - 8 q^{93} - 16 q^{94} - 24 q^{95} + 44 q^{97}+O(q^{100}) $ 16 * q - 4 * q^10 - 8 * q^11 - 16 * q^13 + 4 * q^15 - 16 * q^16 + 24 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^22 + 8 * q^23 + 16 * q^24 + 16 * q^25 + 8 * q^30 - 4 * q^33 + 16 * q^34 - 16 * q^36 + 16 * q^37 + 8 * q^38 - 24 * q^43 - 8 * q^45 + 8 * q^46 + 24 * q^47 - 16 * q^51 + 16 * q^52 - 16 * q^53 + 16 * q^54 - 56 * q^55 - 8 * q^57 - 36 * q^58 - 16 * q^59 + 8 * q^62 - 32 * q^65 + 48 * q^67 + 24 * q^68 - 8 * q^69 - 32 * q^71 + 56 * q^73 - 16 * q^78 - 16 * q^81 + 24 * q^82 - 16 * q^83 + 8 * q^85 + 16 * q^86 + 36 * q^87 - 4 * q^88 + 32 * q^89 + 8 * q^92 - 8 * q^93 - 16 * q^94 - 24 * q^95 + 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$			1.00000i			0.500000i
$5$	1.62401	−	1.53707i	0.726280	−	0.687399i
$5$	1.62401	−	1.53707i	0.726280	−	0.687399i
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	2.23522	+	0.0614757i	0.706839	+	0.0194403i
$11$	−4.55445			−1.37322			−0.686609	−	0.727027i	$-0.740901\pi$
$11$	−4.55445			−1.37322			−0.686609	+	0.727027i	$0.740901\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−1.77772	−	1.77772i	−0.493051	−	0.493051i	0.416215	−	0.909266i	$-0.363356\pi$
$13$	−1.77772	−	1.77772i	−0.493051	−	0.493051i	−0.909266	+	0.416215i	$0.863356\pi$
$14$		0			0
$15$	−2.23522	−	0.0614757i	−0.577132	−	0.0158730i
$16$	−1.00000			−0.250000
$17$	2.91639	−	2.91639i	0.707328	−	0.707328i	−0.258645	−	0.965973i	$-0.583276\pi$
$17$	2.91639	−	2.91639i	0.707328	−	0.707328i	0.965973	+	0.258645i	$0.0832759\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	3.77912			0.866989			0.433494	−	0.901156i	$-0.357280\pi$
$19$	3.77912			0.866989			0.433494	+	0.901156i	$0.357280\pi$
$20$	1.53707	+	1.62401i	0.343700	+	0.363140i
$21$		0			0
$22$	−3.22048	−	3.22048i	−0.686609	−	0.686609i
$23$	5.69431	−	5.69431i	1.18735	−	1.18735i	0.209547	−	0.977799i	$-0.432801\pi$
$23$	5.69431	−	5.69431i	1.18735	−	1.18735i	0.977799	−	0.209547i	$-0.0671989\pi$
$24$	1.00000			0.204124
$25$	0.274824	−	4.99244i	0.0549647	−	0.998488i
$26$		−	2.51408i		−	0.493051i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$			1.55563i			0.288873i	0.989514	+	0.144436i	$0.0461369\pi$
$29$			1.55563i			0.288873i	−0.989514	+	0.144436i	$0.953863\pi$
$30$	−1.53707	−	1.62401i	−0.280630	−	0.296502i
$31$			3.89374i			0.699336i	0.936874	+	0.349668i	$0.113706\pi$
$31$			3.89374i			0.699336i	−0.936874	+	0.349668i	$0.886294\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	3.22048	+	3.22048i	0.560614	+	0.560614i
$34$	4.12440			0.707328
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−8.08634	−	8.08634i	−1.32939	−	1.32939i	−0.905905	−	0.423480i	$-0.860808\pi$
$37$	−8.08634	−	8.08634i	−1.32939	−	1.32939i	−0.423480	−	0.905905i	$-0.639192\pi$
$38$	2.67224	+	2.67224i	0.433494	+	0.433494i
$39$			2.51408i			0.402574i
$40$	−0.0614757	+	2.23522i	−0.00972016	+	0.353420i
$41$		−	11.3796i		−	1.77720i	−0.458682	−	0.888600i	$-0.651678\pi$
$41$		−	11.3796i		−	1.77720i	0.458682	−	0.888600i	$-0.348322\pi$
$42$		0			0
$43$	0.367260	−	0.367260i	0.0560066	−	0.0560066i	−0.678549	−	0.734555i	$-0.737391\pi$
$43$	0.367260	−	0.367260i	0.0560066	−	0.0560066i	0.734555	+	0.678549i	$0.237391\pi$
$44$		−	4.55445i		−	0.686609i
$45$	1.53707	+	1.62401i	0.229133	+	0.242093i
$46$	8.05297			1.18735
$47$	3.57116	−	3.57116i	0.520907	−	0.520907i	−0.396939	−	0.917845i	$-0.629927\pi$
$47$	3.57116	−	3.57116i	0.520907	−	0.520907i	0.917845	+	0.396939i	$0.129927\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		0			0
$50$	3.72452	−	3.33586i	0.526727	−	0.471762i
$51$	−4.12440			−0.577531
$52$	1.77772	−	1.77772i	0.246525	−	0.246525i
$53$	−5.96425	+	5.96425i	−0.819253	+	0.819253i	−0.986000	−	0.166746i	$-0.946674\pi$
$53$	−5.96425	+	5.96425i	−0.819253	+	0.819253i	0.166746	+	0.986000i	$0.446674\pi$
$54$	1.00000			0.136083
$55$	−7.39647	+	7.00051i	−0.997340	+	0.943949i
$56$		0			0
$57$	−2.67224	−	2.67224i	−0.353947	−	0.353947i
$58$	−1.09999	+	1.09999i	−0.144436	+	0.144436i
$59$	−0.443022			−0.0576765			−0.0288383	−	0.999584i	$-0.509181\pi$
$59$	−0.443022			−0.0576765			−0.0288383	+	0.999584i	$0.509181\pi$
$60$	0.0614757	−	2.23522i	0.00793648	−	0.288566i
$61$		−	8.19194i		−	1.04887i	−0.851451	−	0.524435i	$-0.824277\pi$
$61$		−	8.19194i		−	1.04887i	0.851451	−	0.524435i	$-0.175723\pi$
$62$	−2.75329	+	2.75329i	−0.349668	+	0.349668i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−5.61952	−	0.154555i	−0.697016	−	0.0191701i
$66$			4.55445i			0.560614i
$67$	6.58705	+	6.58705i	0.804737	+	0.804737i	0.983832	−	0.179095i	$-0.0573170\pi$
$67$	6.58705	+	6.58705i	0.804737	+	0.804737i	−0.179095	+	0.983832i	$0.557317\pi$
$68$	2.91639	+	2.91639i	0.353664	+	0.353664i
$69$	−8.05297			−0.969464
$70$		0			0
$71$	−6.68403			−0.793248			−0.396624	−	0.917981i	$-0.629818\pi$
$71$	−6.68403			−0.793248			−0.396624	+	0.917981i	$0.629818\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	−3.07520	−	3.07520i	−0.359925	−	0.359925i	0.503861	−	0.863785i	$-0.331913\pi$
$73$	−3.07520	−	3.07520i	−0.359925	−	0.359925i	−0.863785	+	0.503861i	$0.831913\pi$
$74$		−	11.4358i		−	1.32939i
$75$	−3.72452	+	3.33586i	−0.430070	+	0.385192i
$76$			3.77912i			0.433494i
$77$		0			0
$78$	−1.77772	+	1.77772i	−0.201287	+	0.201287i
$79$		−	4.71445i		−	0.530417i	−0.964191	−	0.265208i	$-0.914559\pi$
$79$		−	4.71445i		−	0.530417i	0.964191	−	0.265208i	$-0.0854408\pi$
$80$	−1.62401	+	1.53707i	−0.181570	+	0.171850i
$81$	−1.00000			−0.111111
$82$	8.04662	−	8.04662i	0.888600	−	0.888600i
$83$	3.21718	+	3.21718i	0.353131	+	0.353131i	0.861273	−	0.508142i	$-0.169668\pi$
$83$	3.21718	+	3.21718i	0.353131	+	0.353131i	−0.508142	+	0.861273i	$0.669668\pi$
$84$		0			0
$85$	0.253550	−	9.21894i	0.0275014	−	0.999935i
$86$	0.519384			0.0560066
$87$	1.09999	−	1.09999i	0.117932	−	0.117932i
$88$	3.22048	−	3.22048i	0.343304	−	0.343304i
$89$	6.04851			0.641141			0.320570	−	0.947225i	$-0.396125\pi$
$89$	6.04851			0.641141			0.320570	+	0.947225i	$0.396125\pi$
$90$	−0.0614757	+	2.23522i	−0.00648011	+	0.235613i
$91$		0			0
$92$	5.69431	+	5.69431i	0.593673	+	0.593673i
$93$	2.75329	−	2.75329i	0.285503	−	0.285503i
$94$	5.05038			0.520907
$95$	6.13733	−	5.80877i	0.629676	−	0.595967i
$96$			1.00000i			0.102062i
$97$	−0.462652	+	0.462652i	−0.0469752	+	0.0469752i	−0.730204	−	0.683229i	$-0.760575\pi$
$97$	−0.462652	+	0.462652i	−0.0469752	+	0.0469752i	0.683229	+	0.730204i	$0.260575\pi$
$98$		0			0
$99$		−	4.55445i		−	0.457739i
$100$	4.99244	+	0.274824i	0.499244	+	0.0274824i
$101$		−	5.60204i		−	0.557423i	−0.960375	−	0.278712i	$-0.910093\pi$
$101$		−	5.60204i		−	0.557423i	0.960375	−	0.278712i	$-0.0899074\pi$
$102$	−2.91639	−	2.91639i	−0.288765	−	0.288765i
$103$	3.93011	+	3.93011i	0.387245	+	0.387245i	0.873704	−	0.486458i	$-0.161711\pi$
$103$	3.93011	+	3.93011i	0.387245	+	0.387245i	−0.486458	+	0.873704i	$0.661711\pi$
$104$	2.51408			0.246525
$105$		0			0
$106$	−8.43473			−0.819253
$107$	5.29649	+	5.29649i	0.512031	+	0.512031i	0.915148	−	0.403118i	$-0.132073\pi$
$107$	5.29649	+	5.29649i	0.512031	+	0.512031i	−0.403118	+	0.915148i	$0.632073\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$		−	1.46687i		−	0.140500i	−0.997529	−	0.0702501i	$-0.977620\pi$
$109$		−	1.46687i		−	0.140500i	0.997529	−	0.0702501i	$-0.0223797\pi$
$110$	−10.1802	−	0.279988i	−0.970644	−	0.0266958i
$111$			11.4358i			1.08544i
$112$		0			0
$113$	7.08834	−	7.08834i	0.666815	−	0.666815i	−0.290163	−	0.956977i	$-0.593709\pi$
$113$	7.08834	−	7.08834i	0.666815	−	0.666815i	0.956977	+	0.290163i	$0.0937094\pi$
$114$		−	3.77912i		−	0.353947i
$115$	0.495062	−	18.0002i	0.0461648	−	1.67853i
$116$	−1.55563			−0.144436
$117$	1.77772	−	1.77772i	0.164350	−	0.164350i
$118$	−0.313264	−	0.313264i	−0.0288383	−	0.0288383i
$119$		0			0
$120$	1.62401	−	1.53707i	0.148251	−	0.140315i
$121$	9.74299			0.885727
$122$	5.79257	−	5.79257i	0.524435	−	0.524435i
$123$	−8.04662	+	8.04662i	−0.725539	+	0.725539i
$124$	−3.89374			−0.349668
$125$	−7.22742	−	8.53020i	−0.646440	−	0.762965i
$126$		0			0
$127$	12.9176	+	12.9176i	1.14625	+	1.14625i	0.987283	+	0.158971i	$0.0508176\pi$
$127$	12.9176	+	12.9176i	1.14625	+	1.14625i	0.158971	+	0.987283i	$0.449182\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−0.519384			−0.0457292
$130$	−3.86431	−	4.08289i	−0.338923	−	0.358093i
$131$		−	0.373725i		−	0.0326525i	−0.999867	−	0.0163262i	$-0.994803\pi$
$131$		−	0.373725i		−	0.0326525i	0.999867	−	0.0163262i	$-0.00519704\pi$
$132$	−3.22048	+	3.22048i	−0.280307	+	0.280307i
$133$		0			0
$134$			9.31550i			0.804737i
$135$	0.0614757	−	2.23522i	0.00529099	−	0.192377i
$136$			4.12440i			0.353664i
$137$	−1.87991	−	1.87991i	−0.160611	−	0.160611i	0.622226	−	0.782837i	$-0.286228\pi$
$137$	−1.87991	−	1.87991i	−0.160611	−	0.160611i	−0.782837	+	0.622226i	$0.786228\pi$
$138$	−5.69431	−	5.69431i	−0.484732	−	0.484732i
$139$	−4.58070			−0.388530			−0.194265	−	0.980949i	$-0.562232\pi$
$139$	−4.58070			−0.388530			−0.194265	+	0.980949i	$0.562232\pi$
$140$		0			0
$141$	−5.05038			−0.425319
$142$	−4.72632	−	4.72632i	−0.396624	−	0.396624i
$143$	8.09653	+	8.09653i	0.677066	+	0.677066i
$144$		−	1.00000i		−	0.0833333i
$145$	2.39111	+	2.52636i	0.198571	+	0.209802i
$146$		−	4.34898i		−	0.359925i
$147$		0			0
$148$	8.08634	−	8.08634i	0.664693	−	0.664693i
$149$			17.2441i			1.41269i	0.707869	+	0.706344i	$0.249657\pi$
$149$			17.2441i			1.41269i	−0.707869	+	0.706344i	$0.750343\pi$
$150$	−4.99244	−	0.274824i	−0.407631	−	0.0224393i
$151$	−5.56770			−0.453093			−0.226546	−	0.974000i	$-0.572744\pi$
$151$	−5.56770			−0.453093			−0.226546	+	0.974000i	$0.572744\pi$
$152$	−2.67224	+	2.67224i	−0.216747	+	0.216747i
$153$	2.91639	+	2.91639i	0.235776	+	0.235776i
$154$		0			0
$155$	5.98495	+	6.32347i	0.480723	+	0.507914i
$156$	−2.51408			−0.201287
$157$	2.92099	−	2.92099i	0.233120	−	0.233120i	−0.580874	−	0.813994i	$-0.697289\pi$
$157$	2.92099	−	2.92099i	0.233120	−	0.233120i	0.813994	+	0.580874i	$0.197289\pi$
$158$	3.33362	−	3.33362i	0.265208	−	0.265208i
$159$	8.43473			0.668918
$160$	−2.23522	−	0.0614757i	−0.176710	−	0.00486008i
$161$		0			0
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−15.3717	+	15.3717i	−1.20401	+	1.20401i	−0.231069	+	0.972937i	$0.574222\pi$
$163$	−15.3717	+	15.3717i	−1.20401	+	1.20401i	−0.972937	+	0.231069i	$0.925778\pi$
$164$	11.3796			0.888600
$165$	10.1802	+	0.279988i	0.792528	+	0.0217970i
$166$			4.54978i			0.353131i
$167$	17.4949	−	17.4949i	1.35380	−	1.35380i	0.472425	−	0.881371i	$-0.343379\pi$
$167$	17.4949	−	17.4949i	1.35380	−	1.35380i	0.881371	−	0.472425i	$-0.156621\pi$
$168$		0			0
$169$		−	6.67942i		−	0.513802i
$170$	6.69806	−	6.33949i	0.513718	−	0.486217i
$171$			3.77912i			0.288996i
$172$	0.367260	+	0.367260i	0.0280033	+	0.0280033i
$173$	11.7140	+	11.7140i	0.890601	+	0.890601i	0.994580	−	0.103979i	$-0.0331574\pi$
$173$	11.7140	+	11.7140i	0.890601	+	0.890601i	−0.103979	+	0.994580i	$0.533157\pi$
$174$	1.55563			0.117932
$175$		0			0
$176$	4.55445			0.343304
$177$	0.313264	+	0.313264i	0.0235463	+	0.0235463i
$178$	4.27694	+	4.27694i	0.320570	+	0.320570i
$179$			12.7273i			0.951285i	0.879639	+	0.475643i	$0.157784\pi$
$179$			12.7273i			0.951285i	−0.879639	+	0.475643i	$0.842216\pi$
$180$	−1.62401	+	1.53707i	−0.121047	+	0.114567i
$181$			9.09951i			0.676361i	0.941081	+	0.338180i	$0.109811\pi$
$181$			9.09951i			0.676361i	−0.941081	+	0.338180i	$0.890189\pi$
$182$		0			0
$183$	−5.79257	+	5.79257i	−0.428199	+	0.428199i
$184$			8.05297i			0.593673i
$185$	−25.5616	−	0.703024i	−1.87932	−	0.0516874i
$186$	3.89374			0.285503
$187$	−13.2825	+	13.2825i	−0.971315	+	0.971315i
$188$	3.57116	+	3.57116i	0.260453	+	0.260453i
$189$		0			0
$190$	8.44717	+	0.232324i	0.612822	+	0.0168545i
$191$	18.2062			1.31735			0.658676	−	0.752427i	$-0.271117\pi$
$191$	18.2062			1.31735			0.658676	+	0.752427i	$0.271117\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−7.12147	+	7.12147i	−0.512614	+	0.512614i	−0.915327	−	0.402712i	$-0.868068\pi$
$193$	−7.12147	+	7.12147i	−0.512614	+	0.512614i	0.402712	+	0.915327i	$0.368068\pi$
$194$	−0.654289			−0.0469752
$195$	3.86431	+	4.08289i	0.276729	+	0.292382i
$196$		0			0
$197$	16.2439	+	16.2439i	1.15733	+	1.15733i	0.985048	+	0.172283i	$0.0551142\pi$
$197$	16.2439	+	16.2439i	1.15733	+	1.15733i	0.172283	+	0.985048i	$0.444886\pi$
$198$	3.22048	−	3.22048i	0.228870	−	0.228870i
$199$	−25.3969			−1.80034			−0.900168	−	0.435542i	$-0.856557\pi$
$199$	−25.3969			−1.80034			−0.900168	+	0.435542i	$0.856557\pi$
$200$	3.33586	+	3.72452i	0.235881	+	0.263363i
$201$		−	9.31550i		−	0.657065i
$202$	3.96124	−	3.96124i	0.278712	−	0.278712i
$203$		0			0
$204$		−	4.12440i		−	0.288765i
$205$	−17.4913	−	18.4807i	−1.22165	−	1.29075i
$206$			5.55802i			0.387245i
$207$	5.69431	+	5.69431i	0.395782	+	0.395782i
$208$	1.77772	+	1.77772i	0.123263	+	0.123263i
$209$	−17.2118			−1.19056
$210$		0			0
$211$	−13.6182			−0.937517			−0.468759	−	0.883326i	$-0.655299\pi$
$211$	−13.6182			−0.937517			−0.468759	+	0.883326i	$0.655299\pi$
$212$	−5.96425	−	5.96425i	−0.409627	−	0.409627i
$213$	4.72632	+	4.72632i	0.323842	+	0.323842i
$214$			7.49036i			0.512031i
$215$	0.0319295	−	1.16094i	0.00217757	−	0.0791753i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	1.03723	−	1.03723i	0.0702501	−	0.0702501i
$219$			4.34898i			0.293877i
$220$	−7.00051	−	7.39647i	−0.471974	−	0.498670i
$221$	−10.3690			−0.697497
$222$	−8.08634	+	8.08634i	−0.542719	+	0.542719i
$223$	−15.8412	−	15.8412i	−1.06081	−	1.06081i	−0.998027	−	0.0627803i	$-0.980003\pi$
$223$	−15.8412	−	15.8412i	−1.06081	−	1.06081i	−0.0627803	−	0.998027i	$-0.519997\pi$
$224$		0			0
$225$	4.99244	+	0.274824i	0.332829	+	0.0183216i
$226$	10.0244			0.666815
$227$	7.74471	−	7.74471i	0.514035	−	0.514035i	−0.401726	−	0.915760i	$-0.631589\pi$
$227$	7.74471	−	7.74471i	0.514035	−	0.514035i	0.915760	+	0.401726i	$0.131589\pi$
$228$	2.67224	−	2.67224i	0.176973	−	0.176973i
$229$	−28.9443			−1.91269			−0.956347	−	0.292233i	$-0.905602\pi$
$229$	−28.9443			−1.91269			−0.956347	+	0.292233i	$0.905602\pi$
$230$	13.0781	−	12.3780i	0.862345	−	0.816180i
$231$		0			0
$232$	−1.09999	−	1.09999i	−0.0722182	−	0.0722182i
$233$	0.998499	−	0.998499i	0.0654138	−	0.0654138i	−0.673643	−	0.739057i	$-0.735271\pi$
$233$	0.998499	−	0.998499i	0.0654138	−	0.0654138i	0.739057	+	0.673643i	$0.235271\pi$
$234$	2.51408			0.164350
$235$	0.310475	−	11.2887i	0.0202532	−	0.736395i
$236$		−	0.443022i		−	0.0288383i
$237$	−3.33362	+	3.33362i	−0.216542	+	0.216542i
$238$		0			0
$239$			4.36430i			0.282303i	0.989988	+	0.141152i	$0.0450805\pi$
$239$			4.36430i			0.282303i	−0.989988	+	0.141152i	$0.954920\pi$
$240$	2.23522	+	0.0614757i	0.144283	+	0.00396824i
$241$		−	3.06991i		−	0.197750i	−0.995100	−	0.0988752i	$-0.968476\pi$
$241$		−	3.06991i		−	0.197750i	0.995100	−	0.0988752i	$-0.0315245\pi$
$242$	6.88934	+	6.88934i	0.442863	+	0.442863i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	8.19194			0.524435
$245$		0			0
$246$	−11.3796			−0.725539
$247$	−6.71821	−	6.71821i	−0.427469	−	0.427469i
$248$	−2.75329	−	2.75329i	−0.174834	−	0.174834i
$249$		−	4.54978i		−	0.288330i
$250$	0.921206	−	11.1423i	0.0582622	−	0.704702i
$251$		−	1.25355i		−	0.0791234i	−0.999217	−	0.0395617i	$-0.987404\pi$
$251$		−	1.25355i		−	0.0791234i	0.999217	−	0.0395617i	$-0.0125962\pi$
$252$		0			0
$253$	−25.9344	+	25.9344i	−1.63048	+	1.63048i
$254$			18.2683i			1.14625i
$255$	−6.69806	+	6.33949i	−0.419449	+	0.396994i
$256$	1.00000			0.0625000
$257$	4.99100	−	4.99100i	0.311330	−	0.311330i	−0.534095	−	0.845425i	$-0.679347\pi$
$257$	4.99100	−	4.99100i	0.311330	−	0.311330i	0.845425	+	0.534095i	$0.179347\pi$
$258$	−0.367260	−	0.367260i	−0.0228646	−	0.0228646i
$259$		0			0
$260$	0.154555	−	5.61952i	0.00958507	−	0.348508i
$261$	−1.55563			−0.0962909
$262$	0.264263	−	0.264263i	0.0163262	−	0.0163262i
$263$	−4.02195	+	4.02195i	−0.248004	+	0.248004i	−0.820151	−	0.572147i	$-0.806111\pi$
$263$	−4.02195	+	4.02195i	−0.248004	+	0.248004i	0.572147	+	0.820151i	$0.306111\pi$
$264$	−4.55445			−0.280307
$265$	−0.518531	+	18.8535i	−0.0318531	+	1.15816i
$266$		0			0
$267$	−4.27694	−	4.27694i	−0.261745	−	0.261745i
$268$	−6.58705	+	6.58705i	−0.402368	+	0.402368i
$269$	7.70782			0.469954			0.234977	−	0.972001i	$-0.424499\pi$
$269$	7.70782			0.469954			0.234977	+	0.972001i	$0.424499\pi$
$270$	1.62401	−	1.53707i	0.0988342	−	0.0935432i
$271$			17.8863i			1.08652i	0.839566	+	0.543258i	$0.182810\pi$
$271$			17.8863i			1.08652i	−0.839566	+	0.543258i	$0.817190\pi$
$272$	−2.91639	+	2.91639i	−0.176832	+	0.176832i
$273$		0			0
$274$		−	2.65859i		−	0.160611i
$275$	−1.25167	+	22.7378i	−0.0754786	+	1.37114i
$276$		−	8.05297i		−	0.484732i
$277$	10.4272	+	10.4272i	0.626512	+	0.626512i	0.947189	−	0.320676i	$-0.103910\pi$
$277$	10.4272	+	10.4272i	0.626512	+	0.626512i	−0.320676	+	0.947189i	$0.603910\pi$
$278$	−3.23904	−	3.23904i	−0.194265	−	0.194265i
$279$	−3.89374			−0.233112
$280$		0			0
$281$	0.587402			0.0350415			0.0175207	−	0.999847i	$-0.494423\pi$
$281$	0.587402			0.0350415			0.0175207	+	0.999847i	$0.494423\pi$
$282$	−3.57116	−	3.57116i	−0.212659	−	0.212659i
$283$	13.1629	+	13.1629i	0.782453	+	0.782453i	0.980244	−	0.197791i	$-0.0633768\pi$
$283$	13.1629	+	13.1629i	0.782453	+	0.782453i	−0.197791	+	0.980244i	$0.563377\pi$
$284$		−	6.68403i		−	0.396624i
$285$	−8.44717	−	0.232324i	−0.500367	−	0.0137617i
$286$			11.4502i			0.677066i
$287$		0			0
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$		−	0.0106359i		−	0.000625638i
$290$	−0.0956333	+	3.47717i	−0.00561578	+	0.204187i
$291$	0.654289			0.0383551
$292$	3.07520	−	3.07520i	0.179962	−	0.179962i
$293$	20.6736	+	20.6736i	1.20777	+	1.20777i	0.971749	+	0.236018i	$0.0758423\pi$
$293$	20.6736	+	20.6736i	1.20777	+	1.20777i	0.236018	+	0.971749i	$0.424158\pi$
$294$		0			0
$295$	−0.719472	+	0.680956i	−0.0418893	+	0.0396468i
$296$	11.4358			0.664693
$297$	−3.22048	+	3.22048i	−0.186871	+	0.186871i
$298$	−12.1934	+	12.1934i	−0.706344	+	0.706344i
$299$	−20.2458			−1.17084
$300$	−3.33586	−	3.72452i	−0.192596	−	0.215035i
$301$		0			0
$302$	−3.93696	−	3.93696i	−0.226546	−	0.226546i
$303$	−3.96124	+	3.96124i	−0.227567	+	0.227567i
$304$	−3.77912			−0.216747
$305$	−12.5916	−	13.3038i	−0.720992	−	0.761773i
$306$			4.12440i			0.235776i
$307$	1.63464	−	1.63464i	0.0932937	−	0.0932937i	−0.658920	−	0.752213i	$-0.728986\pi$
$307$	1.63464	−	1.63464i	0.0932937	−	0.0932937i	0.752213	+	0.658920i	$0.228986\pi$
$308$		0			0
$309$		−	5.55802i		−	0.316185i
$310$	−0.239370	+	8.70337i	−0.0135953	+	0.494318i
$311$			13.8839i			0.787286i	0.919263	+	0.393643i	$0.128785\pi$
$311$			13.8839i			0.787286i	−0.919263	+	0.393643i	$0.871215\pi$
$312$	−1.77772	−	1.77772i	−0.100644	−	0.100644i
$313$	−9.53915	−	9.53915i	−0.539185	−	0.539185i	0.384105	−	0.923289i	$-0.374510\pi$
$313$	−9.53915	−	9.53915i	−0.539185	−	0.539185i	−0.923289	+	0.384105i	$0.874510\pi$
$314$	4.13090			0.233120
$315$		0			0
$316$	4.71445			0.265208
$317$	9.69943	+	9.69943i	0.544774	+	0.544774i	0.924925	−	0.380150i	$-0.124128\pi$
$317$	9.69943	+	9.69943i	0.544774	+	0.544774i	−0.380150	+	0.924925i	$0.624128\pi$
$318$	5.96425	+	5.96425i	0.334459	+	0.334459i
$319$		−	7.08502i		−	0.396685i
$320$	−1.53707	−	1.62401i	−0.0859249	−	0.0907850i
$321$		−	7.49036i		−	0.418071i
$322$		0			0
$323$	11.0214	−	11.0214i	0.613245	−	0.613245i
$324$		−	1.00000i		−	0.0555556i
$325$	−9.36372	+	8.38660i	−0.519406	+	0.465205i
$326$	−21.7389			−1.20401
$327$	−1.03723	+	1.03723i	−0.0573590	+	0.0573590i
$328$	8.04662	+	8.04662i	0.444300	+	0.444300i
$329$		0			0
$330$	7.00051	+	7.39647i	0.385365	+	0.407162i
$331$	33.2387			1.82697			0.913483	−	0.406878i	$-0.133383\pi$
$331$	33.2387			1.82697			0.913483	+	0.406878i	$0.133383\pi$
$332$	−3.21718	+	3.21718i	−0.176566	+	0.176566i
$333$	8.08634	−	8.08634i	0.443129	−	0.443129i
$334$	24.7415			1.35380
$335$	20.8222	+	0.572677i	1.13764	+	0.0312887i
$336$		0			0
$337$	−17.0329	−	17.0329i	−0.927842	−	0.927842i	0.0697246	−	0.997566i	$-0.477788\pi$
$337$	−17.0329	−	17.0329i	−0.927842	−	0.927842i	−0.997566	+	0.0697246i	$0.977788\pi$
$338$	4.72307	−	4.72307i	0.256901	−	0.256901i
$339$	−10.0244			−0.544452
$340$	9.21894	+	0.253550i	0.499967	+	0.0137507i
$341$		−	17.7338i		−	0.960341i
$342$	−2.67224	+	2.67224i	−0.144498	+	0.144498i
$343$		0			0
$344$			0.519384i			0.0280033i
$345$	−13.0781	+	12.3780i	−0.704102	+	0.666409i
$346$			16.5661i			0.890601i
$347$	1.45458	+	1.45458i	0.0780861	+	0.0780861i	0.745071	−	0.666985i	$-0.232416\pi$
$347$	1.45458	+	1.45458i	0.0780861	+	0.0780861i	−0.666985	+	0.745071i	$0.732416\pi$
$348$	1.09999	+	1.09999i	0.0589659	+	0.0589659i
$349$	11.7250			0.627627			0.313814	−	0.949485i	$-0.398393\pi$
$349$	11.7250			0.627627			0.313814	+	0.949485i	$0.398393\pi$
$350$		0			0
$351$	−2.51408			−0.134191
$352$	3.22048	+	3.22048i	0.171652	+	0.171652i
$353$	−8.07703	−	8.07703i	−0.429897	−	0.429897i	0.458696	−	0.888593i	$-0.348317\pi$
$353$	−8.07703	−	8.07703i	−0.429897	−	0.429897i	−0.888593	+	0.458696i	$0.848317\pi$
$354$			0.443022i			0.0235463i
$355$	−10.8549	+	10.2738i	−0.576120	+	0.545278i
$356$			6.04851i			0.320570i
$357$		0			0
$358$	−8.99958	+	8.99958i	−0.475643	+	0.475643i
$359$			2.41155i			0.127277i	0.997973	+	0.0636383i	$0.0202704\pi$
$359$			2.41155i			0.127277i	−0.997973	+	0.0636383i	$0.979730\pi$
$360$	−2.23522	−	0.0614757i	−0.117807	−	0.00324005i
$361$	−4.71828			−0.248331
$362$	−6.43432	+	6.43432i	−0.338180	+	0.338180i
$363$	−6.88934	−	6.88934i	−0.361596	−	0.361596i
$364$		0			0
$365$	−9.72095	−	0.267357i	−0.508818	−	0.0139941i
$366$	−8.19194			−0.428199
$367$	−3.68321	+	3.68321i	−0.192262	+	0.192262i	−0.796673	−	0.604411i	$-0.793409\pi$
$367$	−3.68321	+	3.68321i	−0.192262	+	0.192262i	0.604411	+	0.796673i	$0.293409\pi$
$368$	−5.69431	+	5.69431i	−0.296836	+	0.296836i
$369$	11.3796			0.592400
$370$	−17.5777	−	18.5719i	−0.913819	−	0.965506i
$371$		0			0
$372$	2.75329	+	2.75329i	0.142751	+	0.142751i
$373$	−0.103701	+	0.103701i	−0.00536945	+	0.00536945i	−0.709786	−	0.704417i	$-0.751209\pi$
$373$	−0.103701	+	0.103701i	−0.00536945	+	0.00536945i	0.704417	+	0.709786i	$0.251209\pi$
$374$	−18.7843			−0.971315
$375$	−0.921206	+	11.1423i	−0.0475709	+	0.575387i
$376$			5.05038i			0.260453i
$377$	2.76547	−	2.76547i	0.142429	−	0.142429i
$378$		0			0
$379$		−	18.5438i		−	0.952530i	−0.879302	−	0.476265i	$-0.841990\pi$
$379$		−	18.5438i		−	0.952530i	0.879302	−	0.476265i	$-0.158010\pi$
$380$	5.80877	+	6.13733i	0.297984	+	0.314838i
$381$		−	18.2683i		−	0.935913i
$382$	12.8737	+	12.8737i	0.658676	+	0.658676i
$383$	2.72208	+	2.72208i	0.139092	+	0.139092i	0.773224	−	0.634132i	$-0.218643\pi$
$383$	2.72208	+	2.72208i	0.139092	+	0.139092i	−0.634132	+	0.773224i	$0.718643\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−10.0713			−0.512614
$387$	0.367260	+	0.367260i	0.0186689	+	0.0186689i
$388$	−0.462652	−	0.462652i	−0.0234876	−	0.0234876i
$389$			17.8217i			0.903596i	0.892120	+	0.451798i	$0.149217\pi$
$389$			17.8217i			0.903596i	−0.892120	+	0.451798i	$0.850783\pi$
$390$	−0.154555	+	5.61952i	−0.00782617	+	0.284555i
$391$		−	33.2136i		−	1.67969i
$392$		0			0
$393$	−0.264263	+	0.264263i	−0.0133303	+	0.0133303i
$394$			22.9723i			1.15733i
$395$	−7.24644	−	7.65631i	−0.364608	−	0.385231i
$396$	4.55445			0.228870
$397$	18.1348	−	18.1348i	0.910157	−	0.910157i	−0.0861268	−	0.996284i	$-0.527449\pi$
$397$	18.1348	−	18.1348i	0.910157	−	0.910157i	0.996284	+	0.0861268i	$0.0274490\pi$
$398$	−17.9583	−	17.9583i	−0.900168	−	0.900168i
$399$		0			0
$400$	−0.274824	+	4.99244i	−0.0137412	+	0.249622i
$401$	−5.26119			−0.262731			−0.131366	−	0.991334i	$-0.541936\pi$
$401$	−5.26119			−0.262731			−0.131366	+	0.991334i	$0.541936\pi$
$402$	6.58705	−	6.58705i	0.328532	−	0.328532i
$403$	6.92198	−	6.92198i	0.344808	−	0.344808i
$404$	5.60204			0.278712
$405$	−1.62401	+	1.53707i	−0.0806978	+	0.0763777i
$406$		0			0
$407$	36.8288	+	36.8288i	1.82554	+	1.82554i
$408$	2.91639	−	2.91639i	0.144383	−	0.144383i
$409$	−8.37545			−0.414140			−0.207070	−	0.978326i	$-0.566393\pi$
$409$	−8.37545			−0.414140			−0.207070	+	0.978326i	$0.566393\pi$
$410$	0.699571	−	25.4360i	0.0345494	−	1.25620i
$411$			2.65859i			0.131139i
$412$	−3.93011	+	3.93011i	−0.193623	+	0.193623i
$413$		0			0
$414$			8.05297i			0.395782i
$415$	10.1698	+	0.279701i	0.499214	+	0.0137300i
$416$			2.51408i			0.123263i
$417$	3.23904	+	3.23904i	0.158617	+	0.158617i
$418$	−12.1706	−	12.1706i	−0.595282	−	0.595282i
$419$	9.53078			0.465609			0.232805	−	0.972524i	$-0.425210\pi$
$419$	9.53078			0.465609			0.232805	+	0.972524i	$0.425210\pi$
$420$		0			0
$421$	16.8461			0.821027			0.410514	−	0.911854i	$-0.365349\pi$
$421$	16.8461			0.821027			0.410514	+	0.911854i	$0.365349\pi$
$422$	−9.62954	−	9.62954i	−0.468759	−	0.468759i
$423$	3.57116	+	3.57116i	0.173636	+	0.173636i
$424$		−	8.43473i		−	0.409627i
$425$	−13.7584	−	15.3614i	−0.667381	−	0.745137i
$426$			6.68403i			0.323842i
$427$		0			0
$428$	−5.29649	+	5.29649i	−0.256015	+	0.256015i
$429$		−	11.4502i		−	0.552822i
$430$	0.843485	−	0.798330i	0.0406764	−	0.0384989i
$431$	21.5581			1.03842			0.519209	−	0.854647i	$-0.326226\pi$
$431$	21.5581			1.03842			0.519209	+	0.854647i	$0.326226\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	25.8823	+	25.8823i	1.24382	+	1.24382i	0.958402	+	0.285422i	$0.0921338\pi$
$433$	25.8823	+	25.8823i	1.24382	+	1.24382i	0.285422	+	0.958402i	$0.407866\pi$
$434$		0			0
$435$	0.0956333	−	3.47717i	0.00458526	−	0.166718i
$436$	1.46687			0.0702501
$437$	21.5195	−	21.5195i	1.02942	−	1.02942i
$438$	−3.07520	+	3.07520i	−0.146939	+	0.146939i
$439$	−21.1797			−1.01085			−0.505426	−	0.862870i	$-0.668665\pi$
$439$	−21.1797			−1.01085			−0.505426	+	0.862870i	$0.668665\pi$
$440$	0.279988	−	10.1802i	0.0133479	−	0.485322i
$441$		0			0
$442$	−7.33202	−	7.33202i	−0.348749	−	0.348749i
$443$	−2.93476	+	2.93476i	−0.139435	+	0.139435i	−0.773379	−	0.633944i	$-0.781435\pi$
$443$	−2.93476	+	2.93476i	−0.139435	+	0.139435i	0.633944	+	0.773379i	$0.281435\pi$
$444$	−11.4358			−0.542719
$445$	9.82285	−	9.29699i	0.465648	−	0.440720i
$446$		−	22.4029i		−	1.06081i
$447$	12.1934	−	12.1934i	0.576728	−	0.576728i
$448$		0			0
$449$		−	29.3795i		−	1.38651i	−0.720694	−	0.693253i	$-0.756177\pi$
$449$		−	29.3795i		−	1.38651i	0.720694	−	0.693253i	$-0.243823\pi$
$450$	3.33586	+	3.72452i	0.157254	+	0.175576i
$451$			51.8280i			2.44048i
$452$	7.08834	+	7.08834i	0.333407	+	0.333407i
$453$	3.93696	+	3.93696i	0.184974	+	0.184974i
$454$	10.9527			0.514035
$455$		0			0
$456$	3.77912			0.176973
$457$	−0.333296	−	0.333296i	−0.0155909	−	0.0155909i	0.699268	−	0.714859i	$-0.253509\pi$
$457$	−0.333296	−	0.333296i	−0.0155909	−	0.0155909i	−0.714859	+	0.699268i	$0.753509\pi$
$458$	−20.4667	−	20.4667i	−0.956347	−	0.956347i
$459$		−	4.12440i		−	0.192510i
$460$	18.0002	+	0.495062i	0.839263	+	0.0230824i
$461$		−	26.3199i		−	1.22584i	−0.790145	−	0.612920i	$-0.789995\pi$
$461$		−	26.3199i		−	1.22584i	0.790145	−	0.612920i	$-0.210005\pi$
$462$		0			0
$463$	−1.02619	+	1.02619i	−0.0476909	+	0.0476909i	−0.730550	−	0.682859i	$-0.760736\pi$
$463$	−1.02619	+	1.02619i	−0.0476909	+	0.0476909i	0.682859	+	0.730550i	$0.260736\pi$
$464$		−	1.55563i		−	0.0722182i
$465$	0.239370	−	8.70337i	0.0111005	−	0.403609i
$466$	1.41209			0.0654138
$467$	−21.9300	+	21.9300i	−1.01480	+	1.01480i	−0.0149091	+	0.999889i	$0.504746\pi$
$467$	−21.9300	+	21.9300i	−1.01480	+	1.01480i	−0.999889	+	0.0149091i	$0.995254\pi$
$468$	1.77772	+	1.77772i	0.0821751	+	0.0821751i
$469$		0			0
$470$	8.20187	−	7.76279i	0.378324	−	0.358071i
$471$	−4.13090			−0.190342
$472$	0.313264	−	0.313264i	0.0144191	−	0.0144191i
$473$	−1.67267	+	1.67267i	−0.0769092	+	0.0769092i
$474$	−4.71445			−0.216542
$475$	1.03859	−	18.8670i	0.0476538	−	0.865678i
$476$		0			0
$477$	−5.96425	−	5.96425i	−0.273084	−	0.273084i
$478$	−3.08603	+	3.08603i	−0.141152	+	0.141152i
$479$	−33.3520			−1.52389			−0.761945	−	0.647642i	$-0.775755\pi$
$479$	−33.3520			−1.52389			−0.761945	+	0.647642i	$0.775755\pi$
$480$	1.53707	+	1.62401i	0.0701574	+	0.0741256i
$481$			28.7505i			1.31091i
$482$	2.17075	−	2.17075i	0.0988752	−	0.0988752i
$483$		0			0
$484$			9.74299i			0.442863i
$485$	−0.0402229	+	1.46248i	−0.00182643	+	0.0664078i
$486$			1.00000i			0.0453609i
$487$	−2.33606	−	2.33606i	−0.105857	−	0.105857i	0.652195	−	0.758052i	$-0.273848\pi$
$487$	−2.33606	−	2.33606i	−0.105857	−	0.105857i	−0.758052	+	0.652195i	$0.773848\pi$
$488$	5.79257	+	5.79257i	0.262217	+	0.262217i
$489$	21.7389			0.983067
$490$		0			0
$491$	3.61649			0.163210			0.0816051	−	0.996665i	$-0.473995\pi$
$491$	3.61649			0.163210			0.0816051	+	0.996665i	$0.473995\pi$
$492$	−8.04662	−	8.04662i	−0.362770	−	0.362770i
$493$	4.53681	+	4.53681i	0.204328	+	0.204328i
$494$		−	9.50098i		−	0.427469i
$495$	−7.00051	−	7.39647i	−0.314650	−	0.332447i
$496$		−	3.89374i		−	0.174834i
$497$		0			0
$498$	3.21718	−	3.21718i	0.144165	−	0.144165i
$499$			0.647791i			0.0289991i	0.999895	+	0.0144996i	$0.00461551\pi$
$499$			0.647791i			0.0289991i	−0.999895	+	0.0144996i	$0.995384\pi$
$500$	8.53020	−	7.22742i	0.381482	−	0.323220i
$501$	−24.7415			−1.10537
$502$	0.886395	−	0.886395i	0.0395617	−	0.0395617i
$503$	−12.9189	−	12.9189i	−0.576027	−	0.576027i	0.357779	−	0.933806i	$-0.383534\pi$
$503$	−12.9189	−	12.9189i	−0.576027	−	0.576027i	−0.933806	+	0.357779i	$0.883534\pi$
$504$		0			0
$505$	−8.61073	−	9.09777i	−0.383172	−	0.404845i
$506$	−36.6768			−1.63048
$507$	−4.72307	+	4.72307i	−0.209759	+	0.209759i
$508$	−12.9176	+	12.9176i	−0.573127	+	0.573127i
$509$	20.3107			0.900256			0.450128	−	0.892964i	$-0.351378\pi$
$509$	20.3107			0.900256			0.450128	+	0.892964i	$0.351378\pi$
$510$	−9.21894	−	0.253550i	−0.408222	−	0.0112274i
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.67224	−	2.67224i	0.117982	−	0.117982i
$514$	7.05834			0.311330
$515$	12.4234	+	0.341683i	0.547441	+	0.0150563i
$516$		−	0.519384i		−	0.0228646i
$517$	−16.2646	+	16.2646i	−0.715318	+	0.715318i
$518$		0			0
$519$		−	16.5661i		−	0.727172i
$520$	4.08289	−	3.86431i	0.179046	−	0.169461i
$521$			1.24563i			0.0545720i	0.999628	+	0.0272860i	$0.00868648\pi$
$521$			1.24563i			0.0545720i	−0.999628	+	0.0272860i	$0.991314\pi$
$522$	−1.09999	−	1.09999i	−0.0481455	−	0.0481455i
$523$	−14.3494	−	14.3494i	−0.627454	−	0.627454i	0.319972	−	0.947427i	$-0.396326\pi$
$523$	−14.3494	−	14.3494i	−0.627454	−	0.627454i	−0.947427	+	0.319972i	$0.896326\pi$
$524$	0.373725			0.0163262
$525$		0			0
$526$	−5.68790			−0.248004
$527$	11.3557	+	11.3557i	0.494660	+	0.494660i
$528$	−3.22048	−	3.22048i	−0.140153	−	0.140153i
$529$		−	41.8503i		−	1.81958i
$530$	−13.6981	+	12.9648i	−0.595007	+	0.563154i
$531$		−	0.443022i		−	0.0192255i
$532$		0			0
$533$	−20.2298	+	20.2298i	−0.876250	+	0.876250i
$534$		−	6.04851i		−	0.261745i
$535$	16.7426	+	0.460475i	0.723847	+	0.0199081i
$536$	−9.31550			−0.402368
$537$	8.99958	−	8.99958i	0.388361	−	0.388361i
$538$	5.45025	+	5.45025i	0.234977	+	0.234977i
$539$		0			0
$540$	2.23522	+	0.0614757i	0.0961887	+	0.00264549i
$541$	−34.0135			−1.46236			−0.731178	−	0.682187i	$-0.761029\pi$
$541$	−34.0135			−1.46236			−0.731178	+	0.682187i	$0.761029\pi$
$542$	−12.6475	+	12.6475i	−0.543258	+	0.543258i
$543$	6.43432	−	6.43432i	0.276123	−	0.276123i
$544$	−4.12440			−0.176832
$545$	−2.25468	−	2.38221i	−0.0965798	−	0.102043i
$546$		0			0
$547$	27.8171	+	27.8171i	1.18937	+	1.18937i	0.977241	+	0.212132i	$0.0680407\pi$
$547$	27.8171	+	27.8171i	1.18937	+	1.18937i	0.212132	+	0.977241i	$0.431959\pi$
$548$	1.87991	−	1.87991i	0.0803056	−	0.0803056i
$549$	8.19194			0.349623
$550$	−16.9631	+	15.1930i	−0.723310	+	0.647832i
$551$			5.87890i			0.250449i
$552$	5.69431	−	5.69431i	0.242366	−	0.242366i
$553$		0			0
$554$			14.7464i			0.626512i
$555$	17.5777	+	18.5719i	0.746130	+	0.788332i
$556$		−	4.58070i		−	0.194265i
$557$	0.999336	+	0.999336i	0.0423432	+	0.0423432i	0.727961	−	0.685618i	$-0.240468\pi$
$557$	0.999336	+	0.999336i	0.0423432	+	0.0423432i	−0.685618	+	0.727961i	$0.740468\pi$
$558$	−2.75329	−	2.75329i	−0.116556	−	0.116556i
$559$	−1.30577			−0.0552282
$560$		0			0
$561$	18.7843			0.793076
$562$	0.415356	+	0.415356i	0.0175207	+	0.0175207i
$563$	27.0515	+	27.0515i	1.14008	+	1.14008i	0.988435	+	0.151648i	$0.0484581\pi$
$563$	27.0515	+	27.0515i	1.14008	+	1.14008i	0.151648	+	0.988435i	$0.451542\pi$
$564$		−	5.05038i		−	0.212659i
$565$	0.616258	−	22.4068i	0.0259262	−	0.942662i
$566$			18.6151i			0.782453i
$567$		0			0
$568$	4.72632	−	4.72632i	0.198312	−	0.198312i
$569$		−	36.0059i		−	1.50945i	−0.656044	−	0.754723i	$-0.727771\pi$
$569$		−	36.0059i		−	1.50945i	0.656044	−	0.754723i	$-0.272229\pi$
$570$	−5.80877	−	6.13733i	−0.243303	−	0.257064i
$571$	−34.3980			−1.43951			−0.719756	−	0.694228i	$-0.755746\pi$
$571$	−34.3980			−1.43951			−0.719756	+	0.694228i	$0.755746\pi$
$572$	−8.09653	+	8.09653i	−0.338533	+	0.338533i
$573$	−12.8737	−	12.8737i	−0.537806	−	0.537806i
$574$		0			0
$575$	−26.8636	−	29.9934i	−1.12029	−	1.25081i
$576$	1.00000			0.0416667
$577$	31.6173	−	31.6173i	1.31624	−	1.31624i	0.399518	−	0.916725i	$-0.369178\pi$
$577$	31.6173	−	31.6173i	1.31624	−	1.31624i	0.916725	−	0.399518i	$-0.130822\pi$
$578$	0.00752068	−	0.00752068i	0.000312819	−	0.000312819i
$579$	10.0713			0.418548
$580$	−2.52636	+	2.39111i	−0.104901	+	0.0992854i
$581$		0			0
$582$	0.462652	+	0.462652i	0.0191775	+	0.0191775i
$583$	27.1639	−	27.1639i	1.12501	−	1.12501i
$584$	4.34898			0.179962
$585$	0.154555	−	5.61952i	0.00639004	−	0.232339i
$586$			29.2369i			1.20777i
$587$	−19.7182	+	19.7182i	−0.813859	+	0.813859i	−0.985210	−	0.171351i	$-0.945187\pi$
$587$	−19.7182	+	19.7182i	−0.813859	+	0.813859i	0.171351	+	0.985210i	$0.445187\pi$
$588$		0			0
$589$			14.7149i			0.606316i
$590$	−0.990253	−	0.0272351i	−0.0407681	−	0.00112125i
$591$		−	22.9723i		−	0.944956i
$592$	8.08634	+	8.08634i	0.332346	+	0.332346i
$593$	7.04763	+	7.04763i	0.289411	+	0.289411i	0.836847	−	0.547436i	$-0.184396\pi$
$593$	7.04763	+	7.04763i	0.289411	+	0.289411i	−0.547436	+	0.836847i	$0.684396\pi$
$594$	−4.55445			−0.186871
$595$		0			0
$596$	−17.2441			−0.706344
$597$	17.9583	+	17.9583i	0.734984	+	0.734984i
$598$	−14.3159	−	14.3159i	−0.585422	−	0.585422i
$599$		−	16.4610i		−	0.672577i	−0.941759	−	0.336288i	$-0.890828\pi$
$599$		−	16.4610i		−	0.672577i	0.941759	−	0.336288i	$-0.109172\pi$
$600$	0.274824	−	4.99244i	0.0112196	−	0.203816i
$601$			34.0216i			1.38777i	0.720086	+	0.693885i	$0.244102\pi$
$601$			34.0216i			1.38777i	−0.720086	+	0.693885i	$0.755898\pi$
$602$		0			0
$603$	−6.58705	+	6.58705i	−0.268246	+	0.268246i
$604$		−	5.56770i		−	0.226546i
$605$	15.8227	−	14.9757i	0.643285	−	0.608848i
$606$	−5.60204			−0.227567
$607$	25.4539	−	25.4539i	1.03314	−	1.03314i	0.0337108	−	0.999432i	$-0.489267\pi$
$607$	25.4539	−	25.4539i	1.03314	−	1.03314i	0.999432	−	0.0337108i	$-0.0107325\pi$
$608$	−2.67224	−	2.67224i	−0.108374	−	0.108374i
$609$		0			0
$610$	0.503605	−	18.3108i	0.0203904	−	0.741383i
$611$	−12.6970			−0.513667
$612$	−2.91639	+	2.91639i	−0.117888	+	0.117888i
$613$	−23.2805	+	23.2805i	−0.940290	+	0.940290i	−0.998315	−	0.0580254i	$-0.981520\pi$
$613$	−23.2805	+	23.2805i	−0.940290	+	0.940290i	0.0580254	+	0.998315i	$0.481520\pi$
$614$	2.31173			0.0932937
$615$	−0.699571	+	25.4360i	−0.0282094	+	1.02568i
$616$		0			0
$617$	−10.3705	−	10.3705i	−0.417499	−	0.417499i	0.466842	−	0.884341i	$-0.345392\pi$
$617$	−10.3705	−	10.3705i	−0.417499	−	0.417499i	−0.884341	+	0.466842i	$0.845392\pi$
$618$	3.93011	−	3.93011i	0.158092	−	0.158092i
$619$	−5.17657			−0.208064			−0.104032	−	0.994574i	$-0.533174\pi$
$619$	−5.17657			−0.208064			−0.104032	+	0.994574i	$0.533174\pi$
$620$	−6.32347	+	5.98495i	−0.253957	+	0.240362i
$621$		−	8.05297i		−	0.323155i
$622$	−9.81743	+	9.81743i	−0.393643	+	0.393643i
$623$		0			0
$624$		−	2.51408i		−	0.100644i
$625$	−24.8489	−	2.74408i	−0.993958	−	0.109763i
$626$		−	13.4904i		−	0.539185i
$627$	12.1706	+	12.1706i	0.486046	+	0.486046i
$628$	2.92099	+	2.92099i	0.116560	+	0.116560i
$629$	−47.1658			−1.88062
$630$		0			0
$631$	14.5385			0.578769			0.289384	−	0.957213i	$-0.406549\pi$
$631$	14.5385			0.578769			0.289384	+	0.957213i	$0.406549\pi$
$632$	3.33362	+	3.33362i	0.132604	+	0.132604i
$633$	9.62954	+	9.62954i	0.382740	+	0.382740i
$634$			13.7171i			0.544774i
$635$	40.8337	+	1.12306i	1.62044	+	0.0445671i
$636$			8.43473i			0.334459i
$637$		0			0
$638$	5.00987	−	5.00987i	0.198343	−	0.198343i
$639$		−	6.68403i		−	0.264416i
$640$	0.0614757	−	2.23522i	0.00243004	−	0.0883549i
$641$	41.7486			1.64897			0.824484	−	0.565885i	$-0.191465\pi$
$641$	41.7486			1.64897			0.824484	+	0.565885i	$0.191465\pi$
$642$	5.29649	−	5.29649i	0.209036	−	0.209036i
$643$	15.5128	+	15.5128i	0.611766	+	0.611766i	0.943406	−	0.331640i	$-0.107602\pi$
$643$	15.5128	+	15.5128i	0.611766	+	0.611766i	−0.331640	+	0.943406i	$0.607602\pi$
$644$		0			0
$645$	−0.843485	+	0.798330i	−0.0332122	+	0.0314342i
$646$	15.5866			0.613245
$647$	10.1126	−	10.1126i	0.397569	−	0.397569i	−0.479806	−	0.877375i	$-0.659293\pi$
$647$	10.1126	−	10.1126i	0.397569	−	0.397569i	0.877375	+	0.479806i	$0.159293\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	2.01772			0.0792024
$650$	−12.5514	−	0.690928i	−0.492305	−	0.0271004i
$651$		0			0
$652$	−15.3717	−	15.3717i	−0.602003	−	0.602003i
$653$	10.7942	−	10.7942i	0.422408	−	0.422408i	−0.463624	−	0.886032i	$-0.653451\pi$
$653$	10.7942	−	10.7942i	0.422408	−	0.422408i	0.886032	+	0.463624i	$0.153451\pi$
$654$	−1.46687			−0.0573590
$655$	−0.574442	−	0.606933i	−0.0224453	−	0.0237148i
$656$			11.3796i			0.444300i
$657$	3.07520	−	3.07520i	0.119975	−	0.119975i
$658$		0			0
$659$		−	18.9116i		−	0.736690i	−0.929689	−	0.368345i	$-0.879924\pi$
$659$		−	18.9116i		−	0.736690i	0.929689	−	0.368345i	$-0.120076\pi$
$660$	−0.279988	+	10.1802i	−0.0108985	+	0.396264i
$661$			22.6108i			0.879457i	0.898131	+	0.439728i	$0.144925\pi$
$661$			22.6108i			0.879457i	−0.898131	+	0.439728i	$0.855075\pi$
$662$	23.5033	+	23.5033i	0.913483	+	0.913483i
$663$	7.33202	+	7.33202i	0.284752	+	0.284752i
$664$	−4.54978			−0.176566
$665$		0			0
$666$	11.4358			0.443129
$667$	8.85822	+	8.85822i	0.342992	+	0.342992i
$668$	17.4949	+	17.4949i	0.676898	+	0.676898i
$669$			22.4029i			0.866146i
$670$	14.3186	+	15.1285i	0.553175	+	0.584464i
$671$			37.3097i			1.44033i
$672$		0			0
$673$	−24.2623	+	24.2623i	−0.935243	+	0.935243i	−0.998027	−	0.0627838i	$-0.980002\pi$
$673$	−24.2623	+	24.2623i	−0.935243	+	0.935243i	0.0627838	+	0.998027i	$0.480002\pi$
$674$		−	24.0882i		−	0.927842i
$675$	−3.33586	−	3.72452i	−0.128397	−	0.143357i
$676$	6.67942			0.256901
$677$	6.29469	−	6.29469i	0.241925	−	0.241925i	−0.575721	−	0.817646i	$-0.695279\pi$
$677$	6.29469	−	6.29469i	0.241925	−	0.241925i	0.817646	+	0.575721i	$0.195279\pi$
$678$	−7.08834	−	7.08834i	−0.272226	−	0.272226i
$679$		0			0
$680$	6.33949	+	6.69806i	0.243108	+	0.256859i
$681$	−10.9527			−0.419707
$682$	12.5397	−	12.5397i	0.480170	−	0.480170i
$683$	33.8718	−	33.8718i	1.29607	−	1.29607i	0.365099	−	0.930969i	$-0.381035\pi$
$683$	33.8718	−	33.8718i	1.29607	−	1.29607i	0.930969	−	0.365099i	$-0.118965\pi$
$684$	−3.77912			−0.144498
$685$	−5.94254	−	0.163439i	−0.227053	−	0.00624467i
$686$		0			0
$687$	20.4667	+	20.4667i	0.780854	+	0.780854i
$688$	−0.367260	+	0.367260i	−0.0140016	+	0.0140016i
$689$	21.2055			0.807867
$690$	−18.0002	−	0.495062i	−0.685255	−	0.0188467i
$691$			25.8478i			0.983296i	0.870794	+	0.491648i	$0.163605\pi$
$691$			25.8478i			0.983296i	−0.870794	+	0.491648i	$0.836395\pi$
$692$	−11.7140	+	11.7140i	−0.445300	+	0.445300i
$693$		0			0
$694$			2.05709i			0.0780861i
$695$	−7.43910	+	7.04086i	−0.282181	+	0.267075i
$696$			1.55563i			0.0589659i
$697$	−33.1874	−	33.1874i	−1.25706	−	1.25706i
$698$	8.29086	+	8.29086i	0.313814	+	0.313814i
$699$	−1.41209			−0.0534102
$700$		0			0
$701$	3.95788			0.149487			0.0747435	−	0.997203i	$-0.476186\pi$
$701$	3.95788			0.149487			0.0747435	+	0.997203i	$0.476186\pi$
$702$	−1.77772	−	1.77772i	−0.0670957	−	0.0670957i
$703$	−30.5592	−	30.5592i	−1.15256	−	1.15256i
$704$			4.55445i			0.171652i
$705$	−8.20187	+	7.76279i	−0.308900	+	0.292364i
$706$		−	11.4227i		−	0.429897i
$707$		0			0
$708$	−0.313264	+	0.313264i	−0.0117732	+	0.0117732i
$709$		−	29.0598i		−	1.09136i	−0.837993	−	0.545682i	$-0.816271\pi$
$709$		−	29.0598i		−	1.09136i	0.837993	−	0.545682i	$-0.183729\pi$
$710$	−14.9403	−	0.410905i	−0.560699	−	0.0154210i
$711$	4.71445			0.176806
$712$	−4.27694	+	4.27694i	−0.160285	+	0.160285i
$713$	22.1722	+	22.1722i	0.830354	+	0.830354i
$714$		0			0
$715$	25.5938	+	0.703911i	0.957154	+	0.0263248i
$716$	−12.7273			−0.475643
$717$	3.08603	−	3.08603i	0.115250	−	0.115250i
$718$	−1.70522	+	1.70522i	−0.0636383	+	0.0636383i
$719$	−20.2638			−0.755713			−0.377857	−	0.925864i	$-0.623339\pi$
$719$	−20.2638			−0.755713			−0.377857	+	0.925864i	$0.623339\pi$
$720$	−1.53707	−	1.62401i	−0.0572833	−	0.0605233i
$721$		0			0
$722$	−3.33633	−	3.33633i	−0.124165	−	0.124165i
$723$	−2.17075	+	2.17075i	−0.0807312	+	0.0807312i
$724$	−9.09951			−0.338180
$725$	7.76638	+	0.427523i	0.288436	+	0.0158778i
$726$		−	9.74299i		−	0.361596i
$727$	2.80940	−	2.80940i	0.104195	−	0.104195i	−0.653088	−	0.757282i	$-0.726527\pi$
$727$	2.80940	−	2.80940i	0.104195	−	0.104195i	0.757282	+	0.653088i	$0.226527\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−6.68470	−	7.06280i	−0.247412	−	0.261406i
$731$		−	2.14214i		−	0.0792300i
$732$	−5.79257	−	5.79257i	−0.214100	−	0.214100i
$733$	1.23291	+	1.23291i	0.0455384	+	0.0455384i	0.729509	−	0.683971i	$-0.239748\pi$
$733$	1.23291	+	1.23291i	0.0455384	+	0.0455384i	−0.683971	+	0.729509i	$0.739748\pi$
$734$	−5.20884			−0.192262
$735$		0			0
$736$	−8.05297			−0.296836
$737$	−30.0004	−	30.0004i	−1.10508	−	1.10508i
$738$	8.04662	+	8.04662i	0.296200	+	0.296200i
$739$			23.4049i			0.860962i	0.902600	+	0.430481i	$0.141656\pi$
$739$			23.4049i			0.860962i	−0.902600	+	0.430481i	$0.858344\pi$
$740$	0.703024	−	25.5616i	0.0258437	−	0.939662i
$741$			9.50098i			0.349027i
$742$		0			0
$743$	1.84057	−	1.84057i	0.0675240	−	0.0675240i	−0.672538	−	0.740062i	$-0.734796\pi$
$743$	1.84057	−	1.84057i	0.0675240	−	0.0675240i	0.740062	+	0.672538i	$0.234796\pi$
$744$			3.89374i			0.142751i
$745$	26.5053	+	28.0045i	0.971081	+	1.02601i
$746$	−0.146656			−0.00536945
$747$	−3.21718	+	3.21718i	−0.117710	+	0.117710i
$748$	−13.2825	−	13.2825i	−0.485658	−	0.485658i
$749$		0			0
$750$	−8.53020	+	7.22742i	−0.311479	+	0.263908i
$751$	42.3724			1.54619			0.773096	−	0.634289i	$-0.218707\pi$
$751$	42.3724			1.54619			0.773096	+	0.634289i	$0.218707\pi$
$752$	−3.57116	+	3.57116i	−0.130227	+	0.130227i
$753$	−0.886395	+	0.886395i	−0.0323020	+	0.0323020i
$754$	3.91096			0.142429
$755$	−9.04201	+	8.55795i	−0.329072	+	0.311456i
$756$		0			0
$757$	10.2470	+	10.2470i	0.372434	+	0.372434i	0.868363	−	0.495929i	$-0.165172\pi$
$757$	10.2470	+	10.2470i	0.372434	+	0.372434i	−0.495929	+	0.868363i	$0.665172\pi$
$758$	13.1124	−	13.1124i	0.476265	−	0.476265i
$759$	36.6768			1.33128
$760$	−0.232324	+	8.44717i	−0.00842727	+	0.306411i
$761$		−	15.4825i		−	0.561239i	−0.959819	−	0.280620i	$-0.909460\pi$
$761$		−	15.4825i		−	0.561239i	0.959819	−	0.280620i	$-0.0905400\pi$
$762$	12.9176	−	12.9176i	0.467956	−	0.467956i
$763$		0			0
$764$			18.2062i			0.658676i
$765$	9.21894	+	0.253550i	0.333312	+	0.00916712i
$766$			3.84961i			0.139092i
$767$	0.787569	+	0.787569i	0.0284375	+	0.0284375i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−15.9644			−0.575691			−0.287846	−	0.957677i	$-0.592939\pi$
$769$	−15.9644			−0.575691			−0.287846	+	0.957677i	$0.592939\pi$
$770$		0			0
$771$	−7.05834			−0.254200
$772$	−7.12147	−	7.12147i	−0.256307	−	0.256307i
$773$	16.3831	+	16.3831i	0.589258	+	0.589258i	0.937430	−	0.348172i	$-0.113198\pi$
$773$	16.3831	+	16.3831i	0.589258	+	0.589258i	−0.348172	+	0.937430i	$0.613198\pi$
$774$			0.519384i			0.0186689i
$775$	19.4393	+	1.07009i	0.698279	+	0.0384388i
$776$		−	0.654289i		−	0.0234876i
$777$		0			0
$778$	−12.6018	+	12.6018i	−0.451798	+	0.451798i
$779$		−	43.0050i		−	1.54081i
$780$	−4.08289	+	3.86431i	−0.146191	+	0.138365i
$781$	30.4420			1.08930
$782$	23.4856	−	23.4856i	0.839843	−	0.839843i
$783$	1.09999	+	1.09999i	0.0393106	+	0.0393106i
$784$		0			0
$785$	0.253950	−	9.23348i	0.00906386	−	0.329557i
$786$	−0.373725			−0.0133303
$787$	1.48872	−	1.48872i	0.0530672	−	0.0530672i	−0.680075	−	0.733142i	$-0.738053\pi$
$787$	1.48872	−	1.48872i	0.0530672	−	0.0530672i	0.733142	+	0.680075i	$0.238053\pi$
$788$	−16.2439	+	16.2439i	−0.578665	+	0.578665i
$789$	5.68790			0.202495
$790$	0.289824	−	10.5378i	0.0103115	−	0.374920i
$791$		0			0
$792$	3.22048	+	3.22048i	0.114435	+	0.114435i
$793$	−14.5630	+	14.5630i	−0.517146	+	0.517146i
$794$	25.6464			0.910157
$795$	13.6981	−	12.9648i	0.485821	−	0.459813i
$796$		−	25.3969i		−	0.900168i
$797$	23.6759	−	23.6759i	0.838642	−	0.838642i	−0.150038	−	0.988680i	$-0.547940\pi$
$797$	23.6759	−	23.6759i	0.838642	−	0.838642i	0.988680	+	0.150038i	$0.0479397\pi$
$798$		0			0
$799$		−	20.8298i		−	0.736904i
$800$	−3.72452	+	3.33586i	−0.131682	+	0.117940i
$801$			6.04851i			0.213714i
$802$	−3.72022	−	3.72022i	−0.131366	−	0.131366i
$803$	14.0058	+	14.0058i	0.494255	+	0.494255i
$804$	9.31550			0.328532
$805$		0			0
$806$	9.78915			0.344808
$807$	−5.45025	−	5.45025i	−0.191858	−	0.191858i
$808$	3.96124	+	3.96124i	0.139356	+	0.139356i
$809$		−	1.33300i		−	0.0468658i	−0.999725	−	0.0234329i	$-0.992540\pi$
$809$		−	1.33300i		−	0.0468658i	0.999725	−	0.0234329i	$-0.00745960\pi$
$810$	−2.23522	−	0.0614757i	−0.0785377	−	0.00216004i
$811$		−	41.6705i		−	1.46325i	−0.681708	−	0.731624i	$-0.738763\pi$
$811$		−	41.6705i		−	1.46325i	0.681708	−	0.731624i	$-0.261237\pi$
$812$		0			0
$813$	12.6475	−	12.6475i	0.443568	−	0.443568i
$814$			52.0838i			1.82554i
$815$	−1.33641	+	48.5913i	−0.0468125	+	1.70208i
$816$	4.12440			0.144383
$817$	1.38792	−	1.38792i	0.0485571	−	0.0485571i
$818$	−5.92234	−	5.92234i	−0.207070	−	0.207070i
$819$		0			0
$820$	18.4807	−	17.4913i	0.645373	−	0.610823i
$821$	−32.1667			−1.12262			−0.561312	−	0.827604i	$-0.689703\pi$
$821$	−32.1667			−1.12262			−0.561312	+	0.827604i	$0.689703\pi$
$822$	−1.87991	+	1.87991i	−0.0655693	+	0.0655693i
$823$	10.4634	−	10.4634i	0.364732	−	0.364732i	−0.500820	−	0.865552i	$-0.666968\pi$
$823$	10.4634	−	10.4634i	0.364732	−	0.364732i	0.865552	+	0.500820i	$0.166968\pi$
$824$	−5.55802			−0.193623
$825$	16.9631	−	15.1930i	0.590580	−	0.528952i
$826$		0			0
$827$	−34.2632	−	34.2632i	−1.19145	−	1.19145i	−0.976661	−	0.214788i	$-0.931094\pi$
$827$	−34.2632	−	34.2632i	−1.19145	−	1.19145i	−0.214788	−	0.976661i	$-0.568906\pi$
$828$	−5.69431	+	5.69431i	−0.197891	+	0.197891i
$829$	50.4913			1.75363			0.876817	−	0.480824i	$-0.159662\pi$
$829$	50.4913			1.75363			0.876817	+	0.480824i	$0.159662\pi$
$830$	6.99333	+	7.38889i	0.242742	+	0.256472i
$831$		−	14.7464i		−	0.511545i
$832$	−1.77772	+	1.77772i	−0.0616313	+	0.0616313i
$833$		0			0
$834$			4.58070i			0.158617i
$835$	1.52100	−	55.3028i	0.0526365	−	1.91383i
$836$		−	17.2118i		−	0.595282i
$837$	2.75329	+	2.75329i	0.0951676	+	0.0951676i
$838$	6.73928	+	6.73928i	0.232805	+	0.232805i
$839$	22.4313			0.774414			0.387207	−	0.921993i	$-0.373440\pi$
$839$	22.4313			0.774414			0.387207	+	0.921993i	$0.373440\pi$
$840$		0			0
$841$	26.5800			0.916553
$842$	11.9120	+	11.9120i	0.410514	+	0.410514i
$843$	−0.415356	−	0.415356i	−0.0143056	−	0.0143056i
$844$		−	13.6182i		−	0.468759i
$845$	−10.2668	−	10.8475i	−0.353187	−	0.373164i
$846$			5.05038i			0.173636i
$847$		0			0
$848$	5.96425	−	5.96425i	0.204813	−	0.204813i
$849$		−	18.6151i		−	0.638870i
$850$	1.13348	−	20.5908i	0.0388781	−	0.706259i
$851$	−92.0922			−3.15688
$852$	−4.72632	+	4.72632i	−0.161921	+	0.161921i
$853$	−24.4497	−	24.4497i	−0.837140	−	0.837140i	0.151341	−	0.988482i	$-0.451641\pi$
$853$	−24.4497	−	24.4497i	−0.837140	−	0.837140i	−0.988482	+	0.151341i	$0.951641\pi$
$854$		0			0
$855$	5.80877	+	6.13733i	0.198656	+	0.209892i
$856$	−7.49036			−0.256015
$857$	−10.2631	+	10.2631i	−0.350580	+	0.350580i	−0.860325	−	0.509745i	$-0.829740\pi$
$857$	−10.2631	+	10.2631i	−0.350580	+	0.350580i	0.509745	+	0.860325i	$0.329740\pi$
$858$	8.09653	−	8.09653i	0.276411	−	0.276411i
$859$	17.3100			0.590611			0.295306	−	0.955403i	$-0.404579\pi$
$859$	17.3100			0.590611			0.295306	+	0.955403i	$0.404579\pi$
$860$	1.16094	+	0.0319295i	0.0395877	+	0.00108879i
$861$		0			0
$862$	15.2439	+	15.2439i	0.519209	+	0.519209i
$863$	−6.62117	+	6.62117i	−0.225387	+	0.225387i	−0.810763	−	0.585375i	$-0.800947\pi$
$863$	−6.62117	+	6.62117i	−0.225387	+	0.225387i	0.585375	+	0.810763i	$0.300947\pi$
$864$	−1.00000			−0.0340207
$865$	37.0290	+	1.01841i	1.25902	+	0.0346271i
$866$			36.6031i			1.24382i
$867$	−0.00752068	+	0.00752068i	−0.000255416	+	0.000255416i
$868$		0			0
$869$			21.4717i			0.728378i
$870$	2.52636	−	2.39111i	0.0856515	−	0.0810662i
$871$		−	23.4199i		−	0.793552i
$872$	1.03723	+	1.03723i	0.0351251	+	0.0351251i
$873$	−0.462652	−	0.462652i	−0.0156584	−	0.0156584i
$874$	30.4331			1.02942
$875$		0			0
$876$	−4.34898			−0.146939
$877$	−26.4634	−	26.4634i	−0.893604	−	0.893604i	0.101256	−	0.994860i	$-0.467714\pi$
$877$	−26.4634	−	26.4634i	−0.893604	−	0.893604i	−0.994860	+	0.101256i	$0.967714\pi$
$878$	−14.9763	−	14.9763i	−0.505426	−	0.505426i
$879$		−	29.2369i		−	0.986137i
$880$	7.39647	−	7.00051i	0.249335	−	0.235987i
$881$			49.1425i			1.65565i	0.560984	+	0.827827i	$0.310423\pi$
$881$			49.1425i			1.65565i	−0.560984	+	0.827827i	$0.689577\pi$
$882$		0			0
$883$	22.9167	−	22.9167i	0.771207	−	0.771207i	−0.207110	−	0.978318i	$-0.566406\pi$
$883$	22.9167	−	22.9167i	0.771207	−	0.771207i	0.978318	+	0.207110i	$0.0664060\pi$
$884$		−	10.3690i		−	0.348749i
$885$	0.990253	+	0.0272351i	0.0332870	+	0.000915497i
$886$	−4.15037			−0.139435
$887$	−18.5496	+	18.5496i	−0.622833	+	0.622833i	−0.946255	−	0.323422i	$-0.895167\pi$
$887$	−18.5496	+	18.5496i	−0.622833	+	0.622833i	0.323422	+	0.946255i	$0.395167\pi$
$888$	−8.08634	−	8.08634i	−0.271360	−	0.271360i
$889$		0			0
$890$	13.5198	+	0.371836i	0.453184	+	0.0124640i
$891$	4.55445			0.152580
$892$	15.8412	−	15.8412i	0.530404	−	0.530404i
$893$	13.4958	−	13.4958i	0.451620	−	0.451620i
$894$	17.2441			0.576728
$895$	19.5628	+	20.6693i	0.653913	+	0.690899i
$896$		0			0
$897$	14.3159	+	14.3159i	0.477995	+	0.477995i
$898$	20.7745	−	20.7745i	0.693253	−	0.693253i
$899$	−6.05721			−0.202019
$900$	−0.274824	+	4.99244i	−0.00916079	+	0.166415i
$901$			34.7882i			1.15896i
$902$	−36.6479	+	36.6479i	−1.22024	+	1.22024i
$903$		0			0
$904$			10.0244i			0.333407i
$905$	13.9866	+	14.7777i	0.464930	+	0.491227i
$906$			5.56770i			0.184974i
$907$	0.894517	+	0.894517i	0.0297019	+	0.0297019i	0.721802	−	0.692100i	$-0.243314\pi$
$907$	0.894517	+	0.894517i	0.0297019	+	0.0297019i	−0.692100	+	0.721802i	$0.743314\pi$
$908$	7.74471	+	7.74471i	0.257017	+	0.257017i
$909$	5.60204			0.185808
$910$		0			0
$911$	−49.7996			−1.64993			−0.824967	−	0.565182i	$-0.808806\pi$
$911$	−49.7996			−1.64993			−0.824967	+	0.565182i	$0.808806\pi$
$912$	2.67224	+	2.67224i	0.0884867	+	0.0884867i
$913$	−14.6525	−	14.6525i	−0.484926	−	0.484926i
$914$		−	0.471352i		−	0.0155909i
$915$	−0.503605	+	18.3108i	−0.0166487	+	0.605336i
$916$		−	28.9443i		−	0.956347i
$917$		0			0
$918$	2.91639	−	2.91639i	0.0962551	−	0.0962551i
$919$			50.3704i			1.66157i	0.556595	+	0.830784i	$0.312107\pi$
$919$			50.3704i			1.66157i	−0.556595	+	0.830784i	$0.687893\pi$
$920$	12.3780	+	13.0781i	0.408090	+	0.431173i
$921$	−2.31173			−0.0761740
$922$	18.6110	−	18.6110i	0.612920	−	0.612920i
$923$	11.8823	+	11.8823i	0.391112	+	0.391112i
$924$		0			0
$925$	−42.5929	+	38.1482i	−1.40045	+	1.25431i
$926$	−1.45125			−0.0476909
$927$	−3.93011	+	3.93011i	−0.129082	+	0.129082i
$928$	1.09999	−	1.09999i	0.0361091	−	0.0361091i
$929$	22.8229			0.748796			0.374398	−	0.927268i	$-0.377849\pi$
$929$	22.8229			0.748796			0.374398	+	0.927268i	$0.377849\pi$
$930$	6.32347	−	5.98495i	0.207355	−	0.196254i
$931$		0			0
$932$	0.998499	+	0.998499i	0.0327069	+	0.0327069i
$933$	9.81743	−	9.81743i	0.321408	−	0.321408i
$934$	−31.0137			−1.01480
$935$	−1.15478	+	41.9872i	−0.0377654	+	1.37313i
$936$			2.51408i			0.0821751i
$937$	24.9461	−	24.9461i	0.814954	−	0.814954i	−0.170418	−	0.985372i	$-0.554512\pi$
$937$	24.9461	−	24.9461i	0.814954	−	0.814954i	0.985372	+	0.170418i	$0.0545117\pi$
$938$		0			0
$939$			13.4904i			0.440242i
$940$	11.2887	+	0.310475i	0.368197	+	0.0101266i
$941$		−	18.6379i		−	0.607579i	−0.952739	−	0.303789i	$-0.901748\pi$
$941$		−	18.6379i		−	0.607579i	0.952739	−	0.303789i	$-0.0982519\pi$
$942$	−2.92099	−	2.92099i	−0.0951709	−	0.0951709i
$943$	−64.7992	−	64.7992i	−2.11015	−	2.11015i
$944$	0.443022			0.0144191
$945$		0			0
$946$	−2.36551			−0.0769092
$947$	1.79497	+	1.79497i	0.0583288	+	0.0583288i	0.735669	−	0.677341i	$-0.236868\pi$
$947$	1.79497	+	1.79497i	0.0583288	+	0.0583288i	−0.677341	+	0.735669i	$0.736868\pi$
$948$	−3.33362	−	3.33362i	−0.108271	−	0.108271i
$949$			10.9337i			0.354922i
$950$	14.0754	−	12.6066i	0.456666	−	0.409012i
$951$		−	13.7171i		−	0.444806i
$952$		0			0
$953$	31.1031	−	31.1031i	1.00753	−	1.00753i	0.00755624	−	0.999971i	$-0.497595\pi$
$953$	31.1031	−	31.1031i	1.00753	−	1.00753i	0.999971	−	0.00755624i	$-0.00240525\pi$
$954$		−	8.43473i		−	0.273084i
$955$	29.5670	−	27.9842i	0.956766	−	0.905546i
$956$	−4.36430			−0.141152
$957$	−5.00987	+	5.00987i	−0.161946	+	0.161946i
$958$	−23.5834	−	23.5834i	−0.761945	−	0.761945i
$959$		0			0
$960$	−0.0614757	+	2.23522i	−0.00198412	+	0.0721415i
$961$	15.8388			0.510929
$962$	−20.3297	+	20.3297i	−0.655455	+	0.655455i
$963$	−5.29649	+	5.29649i	−0.170677	+	0.170677i
$964$	3.06991			0.0988752
$965$	−0.619139	+	22.5115i	−0.0199308	+	0.724672i
$966$		0			0
$967$	−14.7707	−	14.7707i	−0.474993	−	0.474993i	0.428533	−	0.903526i	$-0.359031\pi$
$967$	−14.7707	−	14.7707i	−0.474993	−	0.474993i	−0.903526	+	0.428533i	$0.859031\pi$
$968$	−6.88934	+	6.88934i	−0.221432	+	0.221432i
$969$	−15.5866			−0.500713
$970$	−1.06257	+	1.00569i	−0.0341171	+	0.0322907i
$971$		−	10.8449i		−	0.348029i	−0.984743	−	0.174014i	$-0.944326\pi$
$971$		−	10.8449i		−	0.348029i	0.984743	−	0.174014i	$-0.0556739\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$		0			0
$974$		−	3.30368i		−	0.105857i
$975$	12.5514	+	0.690928i	0.401966	+	0.0221274i
$976$			8.19194i			0.262217i
$977$	12.1198	+	12.1198i	0.387747	+	0.387747i	0.873883	−	0.486136i	$-0.161594\pi$
$977$	12.1198	+	12.1198i	0.387747	+	0.387747i	−0.486136	+	0.873883i	$0.661594\pi$
$978$	15.3717	+	15.3717i	0.491533	+	0.491533i
$979$	−27.5476			−0.880426
$980$		0			0
$981$	1.46687			0.0468334
$982$	2.55725	+	2.55725i	0.0816051	+	0.0816051i
$983$	−1.18835	−	1.18835i	−0.0379024	−	0.0379024i	0.687902	−	0.725804i	$-0.258532\pi$
$983$	−1.18835	−	1.18835i	−0.0379024	−	0.0379024i	−0.725804	+	0.687902i	$0.758532\pi$
$984$		−	11.3796i		−	0.362770i
$985$	51.3483	+	1.41224i	1.63609	+	0.0449977i
$986$			6.41602i			0.204328i
$987$		0			0
$988$	6.71821	−	6.71821i	0.213735	−	0.213735i
$989$		−	4.18258i		−	0.132998i
$990$	0.279988	−	10.1802i	0.00889860	−	0.323548i
$991$	−16.8078			−0.533918			−0.266959	−	0.963708i	$-0.586019\pi$
$991$	−16.8078			−0.533918			−0.266959	+	0.963708i	$0.586019\pi$
$992$	2.75329	−	2.75329i	0.0874170	−	0.0874170i
$993$	−23.5033	−	23.5033i	−0.745855	−	0.745855i
$994$		0			0
$995$	−41.2448	+	39.0368i	−1.30755	+	1.23755i
$996$	4.54978			0.144165
$997$	−12.3483	+	12.3483i	−0.391074	+	0.391074i	−0.875070	−	0.483996i	$-0.839185\pi$
$997$	−12.3483	+	12.3483i	−0.391074	+	0.391074i	0.483996	+	0.875070i	$0.339185\pi$
$998$	−0.458058	+	0.458058i	−0.0144996	+	0.0144996i
$999$	−11.4358			−0.361813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.d.97.8		16
5.3	odd	4		1470.2.m.e.1273.5		16
7.4	even	3		210.2.u.a.187.2	yes	16
7.5	odd	6		210.2.u.b.157.4	yes	16
7.6	odd	2		1470.2.m.e.97.5		16
21.5	even	6		630.2.bv.b.577.1		16
21.11	odd	6		630.2.bv.a.397.3		16
35.4	even	6		1050.2.bc.h.607.4		16
35.12	even	12		1050.2.bc.h.493.4		16
35.13	even	4	inner	1470.2.m.d.1273.8		16
35.18	odd	12		210.2.u.b.103.4	yes	16
35.19	odd	6		1050.2.bc.g.157.1		16
35.32	odd	12		1050.2.bc.g.943.1		16
35.33	even	12		210.2.u.a.73.2	✓	16
105.53	even	12		630.2.bv.b.523.1		16
105.68	odd	12		630.2.bv.a.73.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.2	✓	16	35.33	even	12
210.2.u.a.187.2	yes	16	7.4	even	3
210.2.u.b.103.4	yes	16	35.18	odd	12
210.2.u.b.157.4	yes	16	7.5	odd	6
630.2.bv.a.73.3		16	105.68	odd	12
630.2.bv.a.397.3		16	21.11	odd	6
630.2.bv.b.523.1		16	105.53	even	12
630.2.bv.b.577.1		16	21.5	even	6
1050.2.bc.g.157.1		16	35.19	odd	6
1050.2.bc.g.943.1		16	35.32	odd	12
1050.2.bc.h.493.4		16	35.12	even	12
1050.2.bc.h.607.4		16	35.4	even	6
1470.2.m.d.97.8		16	1.1	even	1	trivial
1470.2.m.d.1273.8		16	35.13	even	4	inner
1470.2.m.e.97.5		16	7.6	odd	2
1470.2.m.e.1273.5		16	5.3	odd	4

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.62401 - 1.53707i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.62401 - 1.53707i) q^{5} -1.00000i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(2.23522 + 0.0614757i) q^{10} -4.55445 q^{11} +(0.707107 - 0.707107i) q^{12} +(-1.77772 - 1.77772i) q^{13} +(-2.23522 - 0.0614757i) q^{15} -1.00000 q^{16} +(2.91639 - 2.91639i) q^{17} +(-0.707107 + 0.707107i) q^{18} +3.77912 q^{19} +(1.53707 + 1.62401i) q^{20} +(-3.22048 - 3.22048i) q^{22} +(5.69431 - 5.69431i) q^{23} +1.00000 q^{24} +(0.274824 - 4.99244i) q^{25} -2.51408i q^{26} +(0.707107 - 0.707107i) q^{27} +1.55563i q^{29} +(-1.53707 - 1.62401i) q^{30} +3.89374i q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.22048 + 3.22048i) q^{33} +4.12440 q^{34} -1.00000 q^{36} +(-8.08634 - 8.08634i) q^{37} +(2.67224 + 2.67224i) q^{38} +2.51408i q^{39} +(-0.0614757 + 2.23522i) q^{40} -11.3796i q^{41} +(0.367260 - 0.367260i) q^{43} -4.55445i q^{44} +(1.53707 + 1.62401i) q^{45} +8.05297 q^{46} +(3.57116 - 3.57116i) q^{47} +(0.707107 + 0.707107i) q^{48} +(3.72452 - 3.33586i) q^{50} -4.12440 q^{51} +(1.77772 - 1.77772i) q^{52} +(-5.96425 + 5.96425i) q^{53} +1.00000 q^{54} +(-7.39647 + 7.00051i) q^{55} +(-2.67224 - 2.67224i) q^{57} +(-1.09999 + 1.09999i) q^{58} -0.443022 q^{59} +(0.0614757 - 2.23522i) q^{60} -8.19194i q^{61} +(-2.75329 + 2.75329i) q^{62} -1.00000i q^{64} +(-5.61952 - 0.154555i) q^{65} +4.55445i q^{66} +(6.58705 + 6.58705i) q^{67} +(2.91639 + 2.91639i) q^{68} -8.05297 q^{69} -6.68403 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-3.07520 - 3.07520i) q^{73} -11.4358i q^{74} +(-3.72452 + 3.33586i) q^{75} +3.77912i q^{76} +(-1.77772 + 1.77772i) q^{78} -4.71445i q^{79} +(-1.62401 + 1.53707i) q^{80} -1.00000 q^{81} +(8.04662 - 8.04662i) q^{82} +(3.21718 + 3.21718i) q^{83} +(0.253550 - 9.21894i) q^{85} +0.519384 q^{86} +(1.09999 - 1.09999i) q^{87} +(3.22048 - 3.22048i) q^{88} +6.04851 q^{89} +(-0.0614757 + 2.23522i) q^{90} +(5.69431 + 5.69431i) q^{92} +(2.75329 - 2.75329i) q^{93} +5.05038 q^{94} +(6.13733 - 5.80877i) q^{95} +1.00000i q^{96} +(-0.462652 + 0.462652i) q^{97} -4.55445i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 4 q^{10} - 8 q^{11} - 16 q^{13} + 4 q^{15} - 16 q^{16} + 24 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{22} + 8 q^{23} + 16 q^{24} + 16 q^{25} + 8 q^{30} - 4 q^{33} + 16 q^{34} - 16 q^{36} + 16 q^{37} + 8 q^{38} - 24 q^{43} - 8 q^{45} + 8 q^{46} + 24 q^{47} - 16 q^{51} + 16 q^{52} - 16 q^{53} + 16 q^{54} - 56 q^{55} - 8 q^{57} - 36 q^{58} - 16 q^{59} + 8 q^{62} - 32 q^{65} + 48 q^{67} + 24 q^{68} - 8 q^{69} - 32 q^{71} + 56 q^{73} - 16 q^{78} - 16 q^{81} + 24 q^{82} - 16 q^{83} + 8 q^{85} + 16 q^{86} + 36 q^{87} - 4 q^{88} + 32 q^{89} + 8 q^{92} - 8 q^{93} - 16 q^{94} - 24 q^{95} + 44 q^{97}+O(q^{100}) \) 16 * q - 4 * q^10 - 8 * q^11 - 16 * q^13 + 4 * q^15 - 16 * q^16 + 24 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^22 + 8 * q^23 + 16 * q^24 + 16 * q^25 + 8 * q^30 - 4 * q^33 + 16 * q^34 - 16 * q^36 + 16 * q^37 + 8 * q^38 - 24 * q^43 - 8 * q^45 + 8 * q^46 + 24 * q^47 - 16 * q^51 + 16 * q^52 - 16 * q^53 + 16 * q^54 - 56 * q^55 - 8 * q^57 - 36 * q^58 - 16 * q^59 + 8 * q^62 - 32 * q^65 + 48 * q^67 + 24 * q^68 - 8 * q^69 - 32 * q^71 + 56 * q^73 - 16 * q^78 - 16 * q^81 + 24 * q^82 - 16 * q^83 + 8 * q^85 + 16 * q^86 + 36 * q^87 - 4 * q^88 + 32 * q^89 + 8 * q^92 - 8 * q^93 - 16 * q^94 - 24 * q^95 + 44 * q^97

Introduction

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