LMFDB - Embedded newform 1050.2.j.c.743.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(407,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1050.407");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.j (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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 86x^{8} + 196x^{6} + 185x^{4} + 60x^{2} + 4 $ x^12 + 16x^10 + 86x^8 + 196x^6 + 185x^4 + 60*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			743.4
Root			$1.12212i$ of defining polynomial
Character	$\chi$	$=$	1050.743
Dual form			1050.2.j.c.407.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.46025 + 0.931481i) q^{3} +1.00000i q^{4} +(-1.69121 - 0.373900i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.26469 - 2.72040i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.46025 + 0.931481i) q^{3} +1.00000i q^{4} +(-1.69121 - 0.373900i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.26469 - 2.72040i) q^{9} -6.30293i q^{11} +(-0.931481 - 1.46025i) q^{12} +(0.977522 + 0.977522i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-4.86992 - 4.86992i) q^{17} +(2.81788 - 1.02934i) q^{18} -0.285884i q^{19} +(0.373900 - 1.69121i) q^{21} +(4.45685 - 4.45685i) q^{22} +(4.26030 - 4.26030i) q^{23} +(0.373900 - 1.69121i) q^{24} +1.38242i q^{26} +(0.687232 + 5.15051i) q^{27} +(-0.707107 - 0.707107i) q^{28} -3.84102 q^{29} +6.64835 q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.87106 + 9.20389i) q^{33} -6.88711i q^{34} +(2.72040 + 1.26469i) q^{36} +(-0.317848 + 0.317848i) q^{37} +(0.202151 - 0.202151i) q^{38} +(-2.33797 - 0.516888i) q^{39} +4.55435i q^{41} +(1.46025 - 0.931481i) q^{42} +(-2.07154 - 2.07154i) q^{43} +6.30293 q^{44} +6.02497 q^{46} +(-6.69331 - 6.69331i) q^{47} +(1.46025 - 0.931481i) q^{48} -1.00000i q^{49} +(11.6476 + 2.57509i) q^{51} +(-0.977522 + 0.977522i) q^{52} +(3.12501 - 3.12501i) q^{53} +(-3.15601 + 4.12790i) q^{54} -1.00000i q^{56} +(0.266296 + 0.417464i) q^{57} +(-2.71601 - 2.71601i) q^{58} +13.0634 q^{59} +1.09215 q^{61} +(4.70110 + 4.70110i) q^{62} +(1.02934 + 2.81788i) q^{63} -1.00000i q^{64} +(-2.35667 + 10.6596i) q^{66} +(5.63576 - 5.63576i) q^{67} +(4.86992 - 4.86992i) q^{68} +(-2.25274 + 10.1895i) q^{69} -5.42814i q^{71} +(1.02934 + 2.81788i) q^{72} +(3.69101 + 3.69101i) q^{73} -0.449505 q^{74} +0.285884 q^{76} +(4.45685 + 4.45685i) q^{77} +(-1.28770 - 2.01869i) q^{78} -4.38280i q^{79} +(-5.80113 - 6.88091i) q^{81} +(-3.22041 + 3.22041i) q^{82} +(-1.52991 + 1.52991i) q^{83} +(1.69121 + 0.373900i) q^{84} -2.92960i q^{86} +(5.60887 - 3.57783i) q^{87} +(4.45685 + 4.45685i) q^{88} -8.96370 q^{89} -1.38242 q^{91} +(4.26030 + 4.26030i) q^{92} +(-9.70829 + 6.19281i) q^{93} -9.46577i q^{94} +(1.69121 + 0.373900i) q^{96} +(-1.50962 + 1.50962i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-17.1465 - 7.97124i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3}+O(q^{10}) $ 12 * q - 4 * q^3	$ 12 q - 4 q^{3} + 4 q^{12} - 12 q^{14} - 12 q^{16} - 28 q^{17} - 4 q^{21} - 4 q^{22} + 24 q^{23} - 4 q^{24} + 20 q^{27} + 8 q^{29} - 8 q^{31} - 4 q^{33} + 4 q^{36} + 20 q^{37} + 4 q^{38} - 40 q^{39} + 4 q^{42} - 8 q^{43} + 8 q^{44} + 8 q^{46} - 16 q^{47} + 4 q^{48} + 8 q^{51} + 24 q^{53} - 4 q^{54} + 12 q^{57} + 8 q^{58} + 32 q^{59} - 28 q^{62} - 8 q^{63} - 8 q^{66} + 28 q^{68} - 32 q^{69} - 8 q^{72} + 24 q^{73} + 8 q^{74} - 4 q^{77} - 36 q^{81} - 32 q^{82} + 24 q^{83} + 64 q^{87} - 4 q^{88} + 48 q^{89} + 24 q^{91} + 24 q^{92} - 76 q^{93} - 8 q^{97} - 40 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 + 4 * q^12 - 12 * q^14 - 12 * q^16 - 28 * q^17 - 4 * q^21 - 4 * q^22 + 24 * q^23 - 4 * q^24 + 20 * q^27 + 8 * q^29 - 8 * q^31 - 4 * q^33 + 4 * q^36 + 20 * q^37 + 4 * q^38 - 40 * q^39 + 4 * q^42 - 8 * q^43 + 8 * q^44 + 8 * q^46 - 16 * q^47 + 4 * q^48 + 8 * q^51 + 24 * q^53 - 4 * q^54 + 12 * q^57 + 8 * q^58 + 32 * q^59 - 28 * q^62 - 8 * q^63 - 8 * q^66 + 28 * q^68 - 32 * q^69 - 8 * q^72 + 24 * q^73 + 8 * q^74 - 4 * q^77 - 36 * q^81 - 32 * q^82 + 24 * q^83 + 64 * q^87 - 4 * q^88 + 48 * q^89 + 24 * q^91 + 24 * q^92 - 76 * q^93 - 8 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.46025	+	0.931481i	−0.843078	+	0.537791i
$3$	−1.46025	+	0.931481i	−0.843078	+	0.537791i
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−1.69121	−	0.373900i	−0.690435	−	0.152644i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.26469	−	2.72040i	0.421563	−	0.906799i
$10$		0			0
$11$		−	6.30293i		−	1.90041i	−0.311631	−	0.950203i	$-0.600875\pi$
$11$		−	6.30293i		−	1.90041i	0.311631	−	0.950203i	$-0.399125\pi$
$12$	−0.931481	−	1.46025i	−0.268895	−	0.421539i
$13$	0.977522	+	0.977522i	0.271116	+	0.271116i	0.829549	−	0.558434i	$-0.188597\pi$
$13$	0.977522	+	0.977522i	0.271116	+	0.271116i	−0.558434	+	0.829549i	$0.688597\pi$
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.86992	−	4.86992i	−1.18113	−	1.18113i	−0.979452	−	0.201678i	$-0.935360\pi$
$17$	−4.86992	−	4.86992i	−1.18113	−	1.18113i	−0.201678	−	0.979452i	$-0.564640\pi$
$18$	2.81788	−	1.02934i	0.664181	−	0.242618i
$19$		−	0.285884i		−	0.0655864i	−0.999462	−	0.0327932i	$-0.989560\pi$
$19$		−	0.285884i		−	0.0655864i	0.999462	−	0.0327932i	$-0.0104403\pi$
$20$		0			0
$21$	0.373900	−	1.69121i	0.0815916	−	0.369053i
$22$	4.45685	−	4.45685i	0.950203	−	0.950203i
$23$	4.26030	−	4.26030i	0.888334	−	0.888334i	−0.106029	−	0.994363i	$-0.533814\pi$
$23$	4.26030	−	4.26030i	0.888334	−	0.888334i	0.994363	+	0.106029i	$0.0338136\pi$
$24$	0.373900	−	1.69121i	0.0763220	−	0.345217i
$25$		0			0
$26$			1.38242i			0.271116i
$27$	0.687232	+	5.15051i	0.132258	+	0.991215i
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$	−3.84102			−0.713259			−0.356630	−	0.934246i	$-0.616074\pi$
$29$	−3.84102			−0.713259			−0.356630	+	0.934246i	$0.616074\pi$
$30$		0			0
$31$	6.64835			1.19408			0.597040	−	0.802212i	$-0.296343\pi$
$31$	6.64835			1.19408			0.597040	+	0.802212i	$0.296343\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	5.87106	+	9.20389i	1.02202	+	1.60219i
$34$		−	6.88711i		−	1.18113i
$35$		0			0
$36$	2.72040	+	1.26469i	0.453400	+	0.210781i
$37$	−0.317848	+	0.317848i	−0.0522539	+	0.0522539i	−0.732751	−	0.680497i	$-0.761764\pi$
$37$	−0.317848	+	0.317848i	−0.0522539	+	0.0522539i	0.680497	+	0.732751i	$0.261764\pi$
$38$	0.202151	−	0.202151i	0.0327932	−	0.0327932i
$39$	−2.33797	−	0.516888i	−0.374375	−	0.0827684i
$40$		0			0
$41$			4.55435i			0.711270i	0.934625	+	0.355635i	$0.115735\pi$
$41$			4.55435i			0.711270i	−0.934625	+	0.355635i	$0.884265\pi$
$42$	1.46025	−	0.931481i	0.225322	−	0.143731i
$43$	−2.07154	−	2.07154i	−0.315907	−	0.315907i	0.531286	−	0.847193i	$-0.321709\pi$
$43$	−2.07154	−	2.07154i	−0.315907	−	0.315907i	−0.847193	+	0.531286i	$0.821709\pi$
$44$	6.30293			0.950203
$45$		0			0
$46$	6.02497			0.888334
$47$	−6.69331	−	6.69331i	−0.976320	−	0.976320i	0.0234064	−	0.999726i	$-0.492549\pi$
$47$	−6.69331	−	6.69331i	−0.976320	−	0.976320i	−0.999726	+	0.0234064i	$0.992549\pi$
$48$	1.46025	−	0.931481i	0.210770	−	0.134448i
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	11.6476	+	2.57509i	1.63099	+	0.360585i
$52$	−0.977522	+	0.977522i	−0.135558	+	0.135558i
$53$	3.12501	−	3.12501i	0.429253	−	0.429253i	−0.459121	−	0.888374i	$-0.651836\pi$
$53$	3.12501	−	3.12501i	0.429253	−	0.429253i	0.888374	+	0.459121i	$0.151836\pi$
$54$	−3.15601	+	4.12790i	−0.429479	+	0.561737i
$55$		0			0
$56$		−	1.00000i		−	0.133631i
$57$	0.266296	+	0.417464i	0.0352717	+	0.0552945i
$58$	−2.71601	−	2.71601i	−0.356630	−	0.356630i
$59$	13.0634			1.70071			0.850354	−	0.526211i	$-0.176388\pi$
$59$	13.0634			1.70071			0.850354	+	0.526211i	$0.176388\pi$
$60$		0			0
$61$	1.09215			0.139835			0.0699176	−	0.997553i	$-0.477726\pi$
$61$	1.09215			0.139835			0.0699176	+	0.997553i	$0.477726\pi$
$62$	4.70110	+	4.70110i	0.597040	+	0.597040i
$63$	1.02934	+	2.81788i	0.129685	+	0.355020i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−2.35667	+	10.6596i	−0.290085	+	1.31211i
$67$	5.63576	−	5.63576i	0.688518	−	0.688518i	−0.273386	−	0.961904i	$-0.588144\pi$
$67$	5.63576	−	5.63576i	0.688518	−	0.688518i	0.961904	+	0.273386i	$0.0881438\pi$
$68$	4.86992	−	4.86992i	0.590565	−	0.590565i
$69$	−2.25274	+	10.1895i	−0.271198	+	1.22667i
$70$		0			0
$71$		−	5.42814i		−	0.644202i	−0.946705	−	0.322101i	$-0.895611\pi$
$71$		−	5.42814i		−	0.644202i	0.946705	−	0.322101i	$-0.104389\pi$
$72$	1.02934	+	2.81788i	0.121309	+	0.332090i
$73$	3.69101	+	3.69101i	0.432000	+	0.432000i	0.889308	−	0.457308i	$-0.151186\pi$
$73$	3.69101	+	3.69101i	0.432000	+	0.432000i	−0.457308	+	0.889308i	$0.651186\pi$
$74$	−0.449505			−0.0522539
$75$		0			0
$76$	0.285884			0.0327932
$77$	4.45685	+	4.45685i	0.507905	+	0.507905i
$78$	−1.28770	−	2.01869i	−0.145804	−	0.228572i
$79$		−	4.38280i		−	0.493104i	−0.969130	−	0.246552i	$-0.920702\pi$
$79$		−	4.38280i		−	0.493104i	0.969130	−	0.246552i	$-0.0792976\pi$
$80$		0			0
$81$	−5.80113	−	6.88091i	−0.644570	−	0.764545i
$82$	−3.22041	+	3.22041i	−0.355635	+	0.355635i
$83$	−1.52991	+	1.52991i	−0.167930	+	0.167930i	−0.786069	−	0.618139i	$-0.787887\pi$
$83$	−1.52991	+	1.52991i	−0.167930	+	0.167930i	0.618139	+	0.786069i	$0.287887\pi$
$84$	1.69121	+	0.373900i	0.184526	+	0.0407958i
$85$		0			0
$86$		−	2.92960i		−	0.315907i
$87$	5.60887	−	3.57783i	0.601334	−	0.383584i
$88$	4.45685	+	4.45685i	0.475102	+	0.475102i
$89$	−8.96370			−0.950150			−0.475075	−	0.879945i	$-0.657579\pi$
$89$	−8.96370			−0.950150			−0.475075	+	0.879945i	$0.657579\pi$
$90$		0			0
$91$	−1.38242			−0.144917
$92$	4.26030	+	4.26030i	0.444167	+	0.444167i
$93$	−9.70829	+	6.19281i	−1.00670	+	0.642165i
$94$		−	9.46577i		−	0.976320i
$95$		0			0
$96$	1.69121	+	0.373900i	0.172609	+	0.0381610i
$97$	−1.50962	+	1.50962i	−0.153278	+	0.153278i	−0.779580	−	0.626302i	$-0.784568\pi$
$97$	−1.50962	+	1.50962i	−0.153278	+	0.153278i	0.626302	+	0.779580i	$0.284568\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$	−17.1465	−	7.97124i	−1.72329	−	0.801140i
$100$		0			0
$101$			1.57944i			0.157160i	0.996908	+	0.0785802i	$0.0250387\pi$
$101$			1.57944i			0.157160i	−0.996908	+	0.0785802i	$0.974961\pi$
$102$	6.41521	+	10.0569i	0.635201	+	0.995785i
$103$	−4.29497	−	4.29497i	−0.423196	−	0.423196i	0.463106	−	0.886303i	$-0.346735\pi$
$103$	−4.29497	−	4.29497i	−0.423196	−	0.423196i	−0.886303	+	0.463106i	$0.846735\pi$
$104$	−1.38242			−0.135558
$105$		0			0
$106$	4.41943			0.429253
$107$	−7.11516	−	7.11516i	−0.687849	−	0.687849i	0.273907	−	0.961756i	$-0.411684\pi$
$107$	−7.11516	−	7.11516i	−0.687849	−	0.687849i	−0.961756	+	0.273907i	$0.911684\pi$
$108$	−5.15051	+	0.687232i	−0.495608	+	0.0661289i
$109$		−	4.12915i		−	0.395501i	−0.980252	−	0.197751i	$-0.936636\pi$
$109$		−	4.12915i		−	0.395501i	0.980252	−	0.197751i	$-0.0633636\pi$
$110$		0			0
$111$	0.168070	−	0.760209i	0.0159525	−	0.0721559i
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	−8.20404	+	8.20404i	−0.771771	+	0.771771i	−0.978416	−	0.206645i	$-0.933745\pi$
$113$	−8.20404	+	8.20404i	−0.771771	+	0.771771i	0.206645	+	0.978416i	$0.433745\pi$
$114$	−0.106892	+	0.483491i	−0.0100114	+	0.0452831i
$115$		0			0
$116$		−	3.84102i		−	0.356630i
$117$	3.89551	−	1.42299i	0.360140	−	0.131555i
$118$	9.23721	+	9.23721i	0.850354	+	0.850354i
$119$	6.88711			0.631341
$120$		0			0
$121$	−28.7270			−2.61154
$122$	0.772265	+	0.772265i	0.0699176	+	0.0699176i
$123$	−4.24229	−	6.65051i	−0.382514	−	0.599656i
$124$			6.64835i			0.597040i
$125$		0			0
$126$	−1.26469	+	2.72040i	−0.112667	+	0.242352i
$127$	6.41439	−	6.41439i	0.569185	−	0.569185i	−0.362715	−	0.931900i	$-0.618150\pi$
$127$	6.41439	−	6.41439i	0.569185	−	0.569185i	0.931900	+	0.362715i	$0.118150\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	4.95457	+	1.09538i	0.436226	+	0.0964425i
$130$		0			0
$131$		−	2.00357i		−	0.175053i	−0.996162	−	0.0875263i	$-0.972104\pi$
$131$		−	2.00357i		−	0.175053i	0.996162	−	0.0875263i	$-0.0278962\pi$
$132$	−9.20389	+	5.87106i	−0.801096	+	0.511010i
$133$	0.202151	+	0.202151i	0.0175287	+	0.0175287i
$134$	7.97017			0.688518
$135$		0			0
$136$	6.88711			0.590565
$137$	7.18005	+	7.18005i	0.613433	+	0.613433i	0.943839	−	0.330406i	$-0.107186\pi$
$137$	7.18005	+	7.18005i	0.613433	+	0.613433i	−0.330406	+	0.943839i	$0.607186\pi$
$138$	−8.79800	+	5.61215i	−0.748935	+	0.477738i
$139$			7.92412i			0.672115i	0.941842	+	0.336057i	$0.109094\pi$
$139$			7.92412i			0.672115i	−0.941842	+	0.336057i	$0.890906\pi$
$140$		0			0
$141$	16.0086	+	3.53925i	1.34817	+	0.298059i
$142$	3.83827	−	3.83827i	0.322101	−	0.322101i
$143$	6.16126	−	6.16126i	0.515230	−	0.515230i
$144$	−1.26469	+	2.72040i	−0.105391	+	0.226700i
$145$		0			0
$146$			5.21988i			0.432000i
$147$	0.931481	+	1.46025i	0.0768272	+	0.120440i
$148$	−0.317848	−	0.317848i	−0.0261270	−	0.0261270i
$149$	−4.88159			−0.399916			−0.199958	−	0.979805i	$-0.564081\pi$
$149$	−4.88159			−0.399916			−0.199958	+	0.979805i	$0.564081\pi$
$150$		0			0
$151$	−1.36645			−0.111200			−0.0555999	−	0.998453i	$-0.517707\pi$
$151$	−1.36645			−0.111200			−0.0555999	+	0.998453i	$0.517707\pi$
$152$	0.202151	+	0.202151i	0.0163966	+	0.0163966i
$153$	−19.4071	+	7.08920i	−1.56897	+	0.573128i
$154$			6.30293i			0.507905i
$155$		0			0
$156$	0.516888	−	2.33797i	0.0413842	−	0.187188i
$157$	8.22730	−	8.22730i	0.656610	−	0.656610i	−0.297966	−	0.954576i	$-0.596308\pi$
$157$	8.22730	−	8.22730i	0.656610	−	0.656610i	0.954576	+	0.297966i	$0.0963083\pi$
$158$	3.09911	−	3.09911i	0.246552	−	0.246552i
$159$	−1.65242	+	7.47419i	−0.131046	+	0.592742i
$160$		0			0
$161$			6.02497i			0.474834i
$162$	0.763518	−	8.96755i	0.0599876	−	0.704558i
$163$	13.7521	+	13.7521i	1.07714	+	1.07714i	0.996764	+	0.0803803i	$0.0256135\pi$
$163$	13.7521	+	13.7521i	1.07714	+	1.07714i	0.0803803	+	0.996764i	$0.474387\pi$
$164$	−4.55435			−0.355635
$165$		0			0
$166$	−2.16362			−0.167930
$167$	−10.5146	−	10.5146i	−0.813647	−	0.813647i	0.171532	−	0.985179i	$-0.445128\pi$
$167$	−10.5146	−	10.5146i	−0.813647	−	0.813647i	−0.985179	+	0.171532i	$0.945128\pi$
$168$	0.931481	+	1.46025i	0.0718653	+	0.112661i
$169$		−	11.0889i		−	0.852992i
$170$		0			0
$171$	−0.777719	−	0.361554i	−0.0594737	−	0.0276488i
$172$	2.07154	−	2.07154i	0.157953	−	0.157953i
$173$	3.15253	−	3.15253i	0.239682	−	0.239682i	−0.577036	−	0.816719i	$-0.695791\pi$
$173$	3.15253	−	3.15253i	0.239682	−	0.239682i	0.816719	+	0.577036i	$0.195791\pi$
$174$	6.49598	+	1.43616i	0.492459	+	0.108875i
$175$		0			0
$176$			6.30293i			0.475102i
$177$	−19.0759	+	12.1683i	−1.43383	+	0.914625i
$178$	−6.33829	−	6.33829i	−0.475075	−	0.475075i
$179$	−0.251416			−0.0187917			−0.00939584	−	0.999956i	$-0.502991\pi$
$179$	−0.251416			−0.0187917			−0.00939584	+	0.999956i	$0.502991\pi$
$180$		0			0
$181$	−12.8653			−0.956270			−0.478135	−	0.878286i	$-0.658687\pi$
$181$	−12.8653			−0.956270			−0.478135	+	0.878286i	$0.658687\pi$
$182$	−0.977522	−	0.977522i	−0.0724587	−	0.0724587i
$183$	−1.59481	+	1.01731i	−0.117892	+	0.0752020i
$184$			6.02497i			0.444167i
$185$		0			0
$186$	−11.2438	−	2.48582i	−0.824434	−	0.182269i
$187$	−30.6948	+	30.6948i	−2.24463	+	2.24463i
$188$	6.69331	−	6.69331i	0.488160	−	0.488160i
$189$	−4.12790	−	3.15601i	−0.300261	−	0.229566i
$190$		0			0
$191$		−	16.4695i		−	1.19169i	−0.803100	−	0.595845i	$-0.796817\pi$
$191$		−	16.4695i		−	1.19169i	0.803100	−	0.595845i	$-0.203183\pi$
$192$	0.931481	+	1.46025i	0.0672238	+	0.105385i
$193$	−13.9786	−	13.9786i	−1.00620	−	1.00620i	−0.999981	−	0.00621990i	$-0.998020\pi$
$193$	−13.9786	−	13.9786i	−1.00620	−	1.00620i	−0.00621990	−	0.999981i	$-0.501980\pi$
$194$	−2.13492			−0.153278
$195$		0			0
$196$	1.00000			0.0714286
$197$	−11.7072	−	11.7072i	−0.834104	−	0.834104i	0.153971	−	0.988075i	$-0.450794\pi$
$197$	−11.7072	−	11.7072i	−0.834104	−	0.834104i	−0.988075	+	0.153971i	$0.950794\pi$
$198$	−6.48788	−	17.7609i	−0.461073	−	1.26221i
$199$			11.1512i			0.790487i	0.918576	+	0.395243i	$0.129340\pi$
$199$			11.1512i			0.790487i	−0.918576	+	0.395243i	$0.870660\pi$
$200$		0			0
$201$	−2.98004	+	13.4793i	−0.210196	+	0.950753i
$202$	−1.11683	+	1.11683i	−0.0785802	+	0.0785802i
$203$	2.71601	−	2.71601i	0.190627	−	0.190627i
$204$	−2.57509	+	11.6476i	−0.180292	+	0.815493i
$205$		0			0
$206$		−	6.07401i		−	0.423196i
$207$	−6.20176	−	16.9777i	−0.431052	−	1.18003i
$208$	−0.977522	−	0.977522i	−0.0677789	−	0.0677789i
$209$	−1.80191			−0.124641
$210$		0			0
$211$	0.766419			0.0527625			0.0263812	−	0.999652i	$-0.491602\pi$
$211$	0.766419			0.0527625			0.0263812	+	0.999652i	$0.491602\pi$
$212$	3.12501	+	3.12501i	0.214626	+	0.214626i
$213$	5.05621	+	7.92647i	0.346446	+	0.543112i
$214$		−	10.0624i		−	0.687849i
$215$		0			0
$216$	−4.12790	−	3.15601i	−0.280868	−	0.214739i
$217$	−4.70110	+	4.70110i	−0.319131	+	0.319131i
$218$	2.91975	−	2.91975i	0.197751	−	0.197751i
$219$	−8.82792	−	1.95171i	−0.596535	−	0.131884i
$220$		0			0
$221$		−	9.52091i		−	0.640446i
$222$	0.656392	−	0.418706i	0.0440542	−	0.0281017i
$223$	1.66559	+	1.66559i	0.111536	+	0.111536i	0.760672	−	0.649136i	$-0.224869\pi$
$223$	1.66559	+	1.66559i	0.111536	+	0.111536i	−0.649136	+	0.760672i	$0.724869\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−11.6023			−0.771771
$227$	5.55282	+	5.55282i	0.368554	+	0.368554i	0.866950	−	0.498396i	$-0.166077\pi$
$227$	5.55282	+	5.55282i	0.368554	+	0.368554i	−0.498396	+	0.866950i	$0.666077\pi$
$228$	−0.417464	+	0.266296i	−0.0276472	+	0.0176359i
$229$			7.79020i			0.514791i	0.966306	+	0.257396i	$0.0828643\pi$
$229$			7.79020i			0.514791i	−0.966306	+	0.257396i	$0.917136\pi$
$230$		0			0
$231$	−10.6596	−	2.35667i	−0.701350	−	0.155057i
$232$	2.71601	−	2.71601i	0.178315	−	0.178315i
$233$	5.53555	−	5.53555i	0.362646	−	0.362646i	−0.502140	−	0.864786i	$-0.667454\pi$
$233$	5.53555	−	5.53555i	0.362646	−	0.362646i	0.864786	+	0.502140i	$0.167454\pi$
$234$	3.76074	+	1.74834i	0.245848	+	0.114292i
$235$		0			0
$236$			13.0634i			0.850354i
$237$	4.08250	+	6.40001i	0.265187	+	0.415725i
$238$	4.86992	+	4.86992i	0.315670	+	0.315670i
$239$	25.9459			1.67830			0.839149	−	0.543901i	$-0.183053\pi$
$239$	25.9459			1.67830			0.839149	+	0.543901i	$0.183053\pi$
$240$		0			0
$241$	3.35854			0.216342			0.108171	−	0.994132i	$-0.465501\pi$
$241$	3.35854			0.216342			0.108171	+	0.994132i	$0.465501\pi$
$242$	−20.3130	−	20.3130i	−1.30577	−	1.30577i
$243$	14.8806	+	4.64424i	0.954588	+	0.297928i
$244$			1.09215i			0.0699176i
$245$		0			0
$246$	1.70287	−	7.70237i	0.108571	−	0.491085i
$247$	0.279458	−	0.279458i	0.0177815	−	0.0177815i
$248$	−4.70110	+	4.70110i	−0.298520	+	0.298520i
$249$	0.808977	−	3.65914i	0.0512669	−	0.231889i
$250$		0			0
$251$			18.4740i			1.16607i	0.812447	+	0.583035i	$0.198135\pi$
$251$			18.4740i			1.16607i	−0.812447	+	0.583035i	$0.801865\pi$
$252$	−2.81788	+	1.02934i	−0.177510	+	0.0648425i
$253$	−26.8524	−	26.8524i	−1.68820	−	1.68820i
$254$	9.07132			0.569185
$255$		0			0
$256$	1.00000			0.0625000
$257$	8.49575	+	8.49575i	0.529950	+	0.529950i	0.920557	−	0.390607i	$-0.127735\pi$
$257$	8.49575	+	8.49575i	0.529950	+	0.529950i	−0.390607	+	0.920557i	$0.627735\pi$
$258$	2.72886	+	4.27796i	0.169892	+	0.266334i
$259$		−	0.449505i		−	0.0279309i
$260$		0			0
$261$	−4.85769	+	10.4491i	−0.300683	+	0.646783i
$262$	1.41674	−	1.41674i	0.0875263	−	0.0875263i
$263$	3.09922	−	3.09922i	0.191106	−	0.191106i	−0.605068	−	0.796174i	$-0.706854\pi$
$263$	3.09922	−	3.09922i	0.191106	−	0.191106i	0.796174	+	0.605068i	$0.206854\pi$
$264$	−10.6596	−	2.35667i	−0.656053	−	0.145043i
$265$		0			0
$266$			0.285884i			0.0175287i
$267$	13.0893	−	8.34951i	0.801051	−	0.510982i
$268$	5.63576	+	5.63576i	0.344259	+	0.344259i
$269$	−9.23352			−0.562978			−0.281489	−	0.959564i	$-0.590828\pi$
$269$	−9.23352			−0.562978			−0.281489	+	0.959564i	$0.590828\pi$
$270$		0			0
$271$	−23.2360			−1.41149			−0.705745	−	0.708466i	$-0.749387\pi$
$271$	−23.2360			−1.41149			−0.705745	+	0.708466i	$0.749387\pi$
$272$	4.86992	+	4.86992i	0.295283	+	0.295283i
$273$	2.01869	−	1.28770i	0.122177	−	0.0779353i
$274$			10.1541i			0.613433i
$275$		0			0
$276$	−10.1895	−	2.25274i	−0.613336	−	0.135599i
$277$	−12.1601	+	12.1601i	−0.730628	+	0.730628i	−0.970744	−	0.240116i	$-0.922814\pi$
$277$	−12.1601	+	12.1601i	−0.730628	+	0.730628i	0.240116	+	0.970744i	$0.422814\pi$
$278$	−5.60320	+	5.60320i	−0.336057	+	0.336057i
$279$	8.40809	−	18.0862i	0.503379	−	1.08279i
$280$		0			0
$281$			16.0124i			0.955220i	0.878572	+	0.477610i	$0.158497\pi$
$281$			16.0124i			0.955220i	−0.878572	+	0.477610i	$0.841503\pi$
$282$	8.81718	+	13.8224i	0.525056	+	0.823114i
$283$	−19.8944	−	19.8944i	−1.18260	−	1.18260i	−0.979069	−	0.203527i	$-0.934759\pi$
$283$	−19.8944	−	19.8944i	−1.18260	−	1.18260i	−0.203527	−	0.979069i	$-0.565241\pi$
$284$	5.42814			0.322101
$285$		0			0
$286$	8.71333			0.515230
$287$	−3.22041	−	3.22041i	−0.190095	−	0.190095i
$288$	−2.81788	+	1.02934i	−0.166045	+	0.0606546i
$289$			30.4323i			1.79014i
$290$		0			0
$291$	0.798246	−	3.61060i	0.0467940	−	0.211657i
$292$	−3.69101	+	3.69101i	−0.216000	+	0.216000i
$293$	−6.63925	+	6.63925i	−0.387869	+	0.387869i	−0.873927	−	0.486058i	$-0.838434\pi$
$293$	−6.63925	+	6.63925i	−0.387869	+	0.387869i	0.486058	+	0.873927i	$0.338434\pi$
$294$	−0.373900	+	1.69121i	−0.0218063	+	0.0986335i
$295$		0			0
$296$		−	0.449505i		−	0.0261270i
$297$	32.4633	−	4.33158i	1.88371	−	0.251344i
$298$	−3.45181	−	3.45181i	−0.199958	−	0.199958i
$299$	8.32907			0.481683
$300$		0			0
$301$	2.92960			0.168859
$302$	−0.966224	−	0.966224i	−0.0555999	−	0.0555999i
$303$	−1.47122	−	2.30639i	−0.0845194	−	0.132499i
$304$			0.285884i			0.0163966i
$305$		0			0
$306$	−18.7357	−	8.71005i	−1.07105	−	0.497920i
$307$	−3.85359	+	3.85359i	−0.219936	+	0.219936i	−0.808471	−	0.588536i	$-0.799705\pi$
$307$	−3.85359	+	3.85359i	−0.219936	+	0.219936i	0.588536	+	0.808471i	$0.299705\pi$
$308$	−4.45685	+	4.45685i	−0.253952	+	0.253952i
$309$	10.2724	+	2.27107i	0.584379	+	0.129197i
$310$		0			0
$311$		−	28.2254i		−	1.60052i	−0.599655	−	0.800259i	$-0.704696\pi$
$311$		−	28.2254i		−	1.60052i	0.599655	−	0.800259i	$-0.295304\pi$
$312$	2.01869	−	1.28770i	0.114286	−	0.0729018i
$313$	5.27143	+	5.27143i	0.297959	+	0.297959i	0.840214	−	0.542255i	$-0.182429\pi$
$313$	5.27143	+	5.27143i	0.297959	+	0.297959i	−0.542255	+	0.840214i	$0.682429\pi$
$314$	11.6352			0.656610
$315$		0			0
$316$	4.38280			0.246552
$317$	22.4384	+	22.4384i	1.26027	+	1.26027i	0.950963	+	0.309306i	$0.100097\pi$
$317$	22.4384	+	22.4384i	1.26027	+	1.26027i	0.309306	+	0.950963i	$0.399903\pi$
$318$	−6.45349	+	4.11661i	−0.361894	+	0.230848i
$319$			24.2097i			1.35548i
$320$		0			0
$321$	17.0176	+	3.76231i	0.949829	+	0.209992i
$322$	−4.26030	+	4.26030i	−0.237417	+	0.237417i
$323$	−1.39224	+	1.39224i	−0.0774660	+	0.0774660i
$324$	6.88091	−	5.80113i	0.382273	−	0.322285i
$325$		0			0
$326$			19.4484i			1.07714i
$327$	3.84623	+	6.02961i	0.212697	+	0.333438i
$328$	−3.22041	−	3.22041i	−0.177817	−	0.177817i
$329$	9.46577			0.521865
$330$		0			0
$331$	23.8482			1.31082			0.655409	−	0.755274i	$-0.272496\pi$
$331$	23.8482			1.31082			0.655409	+	0.755274i	$0.272496\pi$
$332$	−1.52991	−	1.52991i	−0.0839648	−	0.0839648i
$333$	0.462695	+	1.26665i	0.0253555	+	0.0694122i
$334$		−	14.8699i		−	0.813647i
$335$		0			0
$336$	−0.373900	+	1.69121i	−0.0203979	+	0.0922632i
$337$	9.69647	−	9.69647i	0.528200	−	0.528200i	−0.391835	−	0.920035i	$-0.628160\pi$
$337$	9.69647	−	9.69647i	0.528200	−	0.528200i	0.920035	+	0.391835i	$0.128160\pi$
$338$	7.84104	−	7.84104i	0.426496	−	0.426496i
$339$	4.33808	−	19.6219i	0.235612	−	1.06571i
$340$		0			0
$341$		−	41.9041i		−	2.26924i
$342$	−0.294273	−	0.805588i	−0.0159125	−	0.0435612i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	2.92960			0.157953
$345$		0			0
$346$	4.45835			0.239682
$347$	2.11053	+	2.11053i	0.113299	+	0.113299i	0.761484	−	0.648184i	$-0.224471\pi$
$347$	2.11053	+	2.11053i	0.113299	+	0.113299i	−0.648184	+	0.761484i	$0.724471\pi$
$348$	3.57783	+	5.60887i	0.191792	+	0.300667i
$349$			15.3537i			0.821863i	0.911666	+	0.410931i	$0.134796\pi$
$349$			15.3537i			0.821863i	−0.911666	+	0.410931i	$0.865204\pi$
$350$		0			0
$351$	−4.36295	+	5.70652i	−0.232877	+	0.304591i
$352$	−4.45685	+	4.45685i	−0.237551	+	0.237551i
$353$	3.24802	−	3.24802i	0.172875	−	0.172875i	−0.615366	−	0.788241i	$-0.710992\pi$
$353$	3.24802	−	3.24802i	0.172875	−	0.172875i	0.788241	+	0.615366i	$0.210992\pi$
$354$	−22.0930	−	4.88440i	−1.17423	−	0.259603i
$355$		0			0
$356$		−	8.96370i		−	0.475075i
$357$	−10.0569	+	6.41521i	−0.532270	+	0.339529i
$358$	−0.177778	−	0.177778i	−0.00939584	−	0.00939584i
$359$	−10.4735			−0.552768			−0.276384	−	0.961047i	$-0.589136\pi$
$359$	−10.4735			−0.552768			−0.276384	+	0.961047i	$0.589136\pi$
$360$		0			0
$361$	18.9183			0.995698
$362$	−9.09714	−	9.09714i	−0.478135	−	0.478135i
$363$	41.9487	−	26.7586i	2.20174	−	1.40446i
$364$		−	1.38242i		−	0.0724587i
$365$		0			0
$366$	−1.84705	−	0.408354i	−0.0965470	−	0.0213450i
$367$	−1.44611	+	1.44611i	−0.0754862	+	0.0754862i	−0.743842	−	0.668356i	$-0.766998\pi$
$367$	−1.44611	+	1.44611i	−0.0754862	+	0.0754862i	0.668356	+	0.743842i	$0.266998\pi$
$368$	−4.26030	+	4.26030i	−0.222083	+	0.222083i
$369$	12.3896	+	5.75983i	0.644979	+	0.299845i
$370$		0			0
$371$			4.41943i			0.229445i
$372$	−6.19281	−	9.70829i	−0.321082	−	0.503351i
$373$	16.7299	+	16.7299i	0.866242	+	0.866242i	0.992054	−	0.125812i	$-0.0401536\pi$
$373$	16.7299	+	16.7299i	0.866242	+	0.866242i	−0.125812	+	0.992054i	$0.540154\pi$
$374$	−43.4090			−2.24463
$375$		0			0
$376$	9.46577			0.488160
$377$	−3.75468	−	3.75468i	−0.193376	−	0.193376i
$378$	−0.687232	−	5.15051i	−0.0353474	−	0.264913i
$379$		−	28.9831i		−	1.48876i	−0.667756	−	0.744380i	$-0.732745\pi$
$379$		−	28.9831i		−	1.48876i	0.667756	−	0.744380i	$-0.267255\pi$
$380$		0			0
$381$	−3.39176	+	15.3415i	−0.173765	+	0.785970i
$382$	11.6457	−	11.6457i	0.595845	−	0.595845i
$383$	17.6093	−	17.6093i	0.899792	−	0.899792i	−0.0956253	−	0.995417i	$-0.530485\pi$
$383$	17.6093	−	17.6093i	0.899792	−	0.899792i	0.995417	+	0.0956253i	$0.0304850\pi$
$384$	−0.373900	+	1.69121i	−0.0190805	+	0.0863043i
$385$		0			0
$386$		−	19.7687i		−	1.00620i
$387$	−8.25526	+	3.01556i	−0.419638	+	0.153290i
$388$	−1.50962	−	1.50962i	−0.0766392	−	0.0766392i
$389$	5.90624			0.299458			0.149729	−	0.988727i	$-0.452160\pi$
$389$	5.90624			0.299458			0.149729	+	0.988727i	$0.452160\pi$
$390$		0			0
$391$	−41.4947			−2.09848
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$	1.86629	+	2.92572i	0.0941416	+	0.147583i
$394$		−	16.5565i		−	0.834104i
$395$		0			0
$396$	7.97124	−	17.1465i	0.400570	−	0.861643i
$397$	17.8605	−	17.8605i	0.896395	−	0.896395i	−0.0987205	−	0.995115i	$-0.531475\pi$
$397$	17.8605	−	17.8605i	0.896395	−	0.896395i	0.995115	+	0.0987205i	$0.0314750\pi$
$398$	−7.88508	+	7.88508i	−0.395243	+	0.395243i
$399$	−0.483491	−	0.106892i	−0.0242048	−	0.00535130i
$400$		0			0
$401$			27.6315i			1.37985i	0.723880	+	0.689926i	$0.242357\pi$
$401$			27.6315i			1.37985i	−0.723880	+	0.689926i	$0.757643\pi$
$402$	−11.6385	+	7.42406i	−0.580475	+	0.370278i
$403$	6.49891	+	6.49891i	0.323734	+	0.323734i
$404$	−1.57944			−0.0785802
$405$		0			0
$406$	3.84102			0.190627
$407$	2.00338	+	2.00338i	0.0993037	+	0.0993037i
$408$	−10.0569	+	6.41521i	−0.497893	+	0.317600i
$409$		−	9.35480i		−	0.462565i	−0.972887	−	0.231282i	$-0.925708\pi$
$409$		−	9.35480i		−	0.462565i	0.972887	−	0.231282i	$-0.0742921\pi$
$410$		0			0
$411$	−17.1728	−	3.79663i	−0.847071	−	0.187274i
$412$	4.29497	−	4.29497i	0.211598	−	0.211598i
$413$	−9.23721	+	9.23721i	−0.454533	+	0.454533i
$414$	7.61971	−	16.3903i	0.374488	−	0.805541i
$415$		0			0
$416$		−	1.38242i		−	0.0677789i
$417$	−7.38116	−	11.5712i	−0.361457	−	0.566646i
$418$	−1.27414	−	1.27414i	−0.0623204	−	0.0623204i
$419$	8.34692			0.407774			0.203887	−	0.978994i	$-0.434643\pi$
$419$	8.34692			0.407774			0.203887	+	0.978994i	$0.434643\pi$
$420$		0			0
$421$	27.0969			1.32062			0.660312	−	0.750991i	$-0.270424\pi$
$421$	27.0969			1.32062			0.660312	+	0.750991i	$0.270424\pi$
$422$	0.541940	+	0.541940i	0.0263812	+	0.0263812i
$423$	−26.6734	+	9.74352i	−1.29691	+	0.473746i
$424$			4.41943i			0.214626i
$425$		0			0
$426$	−2.02958	+	9.18013i	−0.0983335	+	0.444779i
$427$	−0.772265	+	0.772265i	−0.0373725	+	0.0373725i
$428$	7.11516	−	7.11516i	0.343924	−	0.343924i
$429$	−3.25791	+	14.7361i	−0.157293	+	0.711465i
$430$		0			0
$431$			22.0104i			1.06020i	0.847935	+	0.530101i	$0.177846\pi$
$431$			22.0104i			1.06020i	−0.847935	+	0.530101i	$0.822154\pi$
$432$	−0.687232	−	5.15051i	−0.0330645	−	0.247804i
$433$	−3.04246	−	3.04246i	−0.146211	−	0.146211i	0.630212	−	0.776423i	$-0.282968\pi$
$433$	−3.04246	−	3.04246i	−0.146211	−	0.146211i	−0.776423	+	0.630212i	$0.782968\pi$
$434$	−6.64835			−0.319131
$435$		0			0
$436$	4.12915			0.197751
$437$	−1.21795	−	1.21795i	−0.0582626	−	0.0582626i
$438$	−4.86221	−	7.62235i	−0.232326	−	0.364210i
$439$			3.84848i			0.183678i	0.995774	+	0.0918390i	$0.0292745\pi$
$439$			3.84848i			0.183678i	−0.995774	+	0.0918390i	$0.970725\pi$
$440$		0			0
$441$	−2.72040	−	1.26469i	−0.129543	−	0.0602232i
$442$	6.73230	−	6.73230i	0.320223	−	0.320223i
$443$	−1.25470	+	1.25470i	−0.0596125	+	0.0596125i	−0.736285	−	0.676672i	$-0.763421\pi$
$443$	−1.25470	+	1.25470i	−0.0596125	+	0.0596125i	0.676672	+	0.736285i	$0.263421\pi$
$444$	0.760209	+	0.168070i	0.0360779	+	0.00797625i
$445$		0			0
$446$			2.35550i			0.111536i
$447$	7.12837	−	4.54711i	0.337160	−	0.215071i
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	−36.8518			−1.73914			−0.869571	−	0.493808i	$-0.835605\pi$
$449$	−36.8518			−1.73914			−0.869571	+	0.493808i	$0.835605\pi$
$450$		0			0
$451$	28.7058			1.35170
$452$	−8.20404	−	8.20404i	−0.385885	−	0.385885i
$453$	1.99536	−	1.27282i	0.0937502	−	0.0598022i
$454$			7.85287i			0.368554i
$455$		0			0
$456$	−0.483491	−	0.106892i	−0.0226415	−	0.00500568i
$457$	17.4336	−	17.4336i	0.815509	−	0.815509i	−0.169945	−	0.985454i	$-0.554359\pi$
$457$	17.4336	−	17.4336i	0.815509	−	0.815509i	0.985454	+	0.169945i	$0.0543590\pi$
$458$	−5.50851	+	5.50851i	−0.257396	+	0.257396i
$459$	21.7358	−	28.4293i	1.01454	−	1.32697i
$460$		0			0
$461$			22.2553i			1.03653i	0.855219	+	0.518267i	$0.173422\pi$
$461$			22.2553i			1.03653i	−0.855219	+	0.518267i	$0.826578\pi$
$462$	−5.87106	−	9.20389i	−0.273146	−	0.428204i
$463$	11.8397	+	11.8397i	0.550236	+	0.550236i	0.926509	−	0.376273i	$-0.122795\pi$
$463$	11.8397	+	11.8397i	0.550236	+	0.550236i	−0.376273	+	0.926509i	$0.622795\pi$
$464$	3.84102			0.178315
$465$		0			0
$466$	7.82845			0.362646
$467$	19.7958	+	19.7958i	0.916038	+	0.916038i	0.996738	−	0.0807000i	$-0.0257156\pi$
$467$	19.7958	+	19.7958i	0.916038	+	0.916038i	−0.0807000	+	0.996738i	$0.525716\pi$
$468$	1.42299	+	3.89551i	0.0657777	+	0.180070i
$469$			7.97017i			0.368028i
$470$		0			0
$471$	−4.35038	+	19.6775i	−0.200455	+	0.906692i
$472$	−9.23721	+	9.23721i	−0.425177	+	0.425177i
$473$	−13.0568	+	13.0568i	−0.600351	+	0.600351i
$474$	−1.63873	+	7.41225i	−0.0752693	+	0.340456i
$475$		0			0
$476$			6.88711i			0.315670i
$477$	−4.54911	−	12.4534i	−0.208289	−	0.570203i
$478$	18.3465	+	18.3465i	0.839149	+	0.839149i
$479$	−7.58779			−0.346695			−0.173347	−	0.984861i	$-0.555458\pi$
$479$	−7.58779			−0.346695			−0.173347	+	0.984861i	$0.555458\pi$
$480$		0			0
$481$	−0.621407			−0.0283337
$482$	2.37484	+	2.37484i	0.108171	+	0.108171i
$483$	−5.61215	−	8.79800i	−0.255362	−	0.400323i
$484$		−	28.7270i		−	1.30577i
$485$		0			0
$486$	7.23817	+	13.8061i	0.328330	+	0.626258i
$487$	−2.74204	+	2.74204i	−0.124254	+	0.124254i	−0.766499	−	0.642245i	$-0.778003\pi$
$487$	−2.74204	+	2.74204i	−0.124254	+	0.124254i	0.642245	+	0.766499i	$0.278003\pi$
$488$	−0.772265	+	0.772265i	−0.0349588	+	0.0349588i
$489$	−32.8913	−	7.27173i	−1.48740	−	0.328839i
$490$		0			0
$491$			41.2178i			1.86013i	0.367390	+	0.930067i	$0.380251\pi$
$491$			41.2178i			1.86013i	−0.367390	+	0.930067i	$0.619749\pi$
$492$	6.65051	−	4.24229i	0.299828	−	0.191257i
$493$	18.7055	+	18.7055i	0.842452	+	0.842452i
$494$	0.395214			0.0177815
$495$		0			0
$496$	−6.64835			−0.298520
$497$	3.83827	+	3.83827i	0.172170	+	0.172170i
$498$	3.15944	−	2.01537i	0.141578	−	0.0903109i
$499$			16.1619i			0.723505i	0.932274	+	0.361753i	$0.117821\pi$
$499$			16.1619i			0.723505i	−0.932274	+	0.361753i	$0.882179\pi$
$500$		0			0
$501$	25.1482	+	5.55987i	1.12354	+	0.248397i
$502$	−13.0631	+	13.0631i	−0.583035	+	0.583035i
$503$	−21.1438	+	21.1438i	−0.942754	+	0.942754i	−0.998448	−	0.0556938i	$-0.982263\pi$
$503$	−21.1438	+	21.1438i	−0.942754	+	0.942754i	0.0556938	+	0.998448i	$0.482263\pi$
$504$	−2.72040	−	1.26469i	−0.121176	−	0.0563337i
$505$		0			0
$506$		−	37.9750i		−	1.68820i
$507$	10.3291	+	16.1926i	0.458731	+	0.719140i
$508$	6.41439	+	6.41439i	0.284592	+	0.284592i
$509$	31.1749			1.38180			0.690901	−	0.722949i	$-0.257214\pi$
$509$	31.1749			1.38180			0.690901	+	0.722949i	$0.257214\pi$
$510$		0			0
$511$	−5.21988			−0.230914
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.47245	−	0.196469i	0.0650102	−	0.00867431i
$514$			12.0148i			0.529950i
$515$		0			0
$516$	−1.09538	+	4.95457i	−0.0482212	+	0.218113i
$517$	−42.1875	+	42.1875i	−1.85540	+	1.85540i
$518$	0.317848	−	0.317848i	0.0139655	−	0.0139655i
$519$	−1.66697	+	7.54001i	−0.0731721	+	0.330970i
$520$		0			0
$521$		−	25.1391i		−	1.10136i	−0.834715	−	0.550682i	$-0.814368\pi$
$521$		−	25.1391i		−	1.10136i	0.834715	−	0.550682i	$-0.185632\pi$
$522$	−10.8235	+	3.95372i	−0.473733	+	0.173050i
$523$	−8.35714	−	8.35714i	−0.365432	−	0.365432i	0.500376	−	0.865808i	$-0.333195\pi$
$523$	−8.35714	−	8.35714i	−0.365432	−	0.365432i	−0.865808	+	0.500376i	$0.833195\pi$
$524$	2.00357			0.0875263
$525$		0			0
$526$	4.38296			0.191106
$527$	−32.3770	−	32.3770i	−1.41036	−	1.41036i
$528$	−5.87106	−	9.20389i	−0.255505	−	0.400548i
$529$		−	13.3003i		−	0.578275i
$530$		0			0
$531$	16.5211	−	35.5376i	0.716955	−	1.54220i
$532$	−0.202151	+	0.202151i	−0.00876435	+	0.00876435i
$533$	−4.45198	+	4.45198i	−0.192836	+	0.192836i
$534$	15.1595	+	3.35152i	0.656016	+	0.145035i
$535$		0			0
$536$			7.97017i			0.344259i
$537$	0.367131	−	0.234189i	0.0158429	−	0.0101060i
$538$	−6.52909	−	6.52909i	−0.281489	−	0.281489i
$539$	−6.30293			−0.271487
$540$		0			0
$541$	15.9353			0.685111			0.342555	−	0.939498i	$-0.388708\pi$
$541$	15.9353			0.685111			0.342555	+	0.939498i	$0.388708\pi$
$542$	−16.4304	−	16.4304i	−0.705745	−	0.705745i
$543$	18.7866	−	11.9838i	0.806211	−	0.514273i
$544$			6.88711i			0.295283i
$545$		0			0
$546$	2.33797	+	0.516888i	0.100056	+	0.0221208i
$547$	23.5457	−	23.5457i	1.00674	−	1.00674i	0.00676436	−	0.999977i	$-0.497847\pi$
$547$	23.5457	−	23.5457i	1.00674	−	1.00674i	0.999977	−	0.00676436i	$-0.00215318\pi$
$548$	−7.18005	+	7.18005i	−0.306717	+	0.306717i
$549$	1.38123	−	2.97108i	0.0589493	−	0.126802i
$550$		0			0
$551$			1.09809i			0.0467801i
$552$	−5.61215	−	8.79800i	−0.238869	−	0.374468i
$553$	3.09911	+	3.09911i	0.131788	+	0.131788i
$554$	−17.1969			−0.730628
$555$		0			0
$556$	−7.92412			−0.336057
$557$	19.6460	+	19.6460i	0.832429	+	0.832429i	0.987849	−	0.155419i	$-0.0496729\pi$
$557$	19.6460	+	19.6460i	0.832429	+	0.832429i	−0.155419	+	0.987849i	$0.549673\pi$
$558$	18.7343	−	6.84343i	0.793085	−	0.289706i
$559$		−	4.04995i		−	0.171295i
$560$		0			0
$561$	16.2306	−	73.4139i	0.685257	−	3.09954i
$562$	−11.3225	+	11.3225i	−0.477610	+	0.477610i
$563$	25.9632	−	25.9632i	1.09422	−	1.09422i	0.0991442	−	0.995073i	$-0.468389\pi$
$563$	25.9632	−	25.9632i	1.09422	−	1.09422i	0.995073	−	0.0991442i	$-0.0316105\pi$
$564$	−3.53925	+	16.0086i	−0.149029	+	0.674085i
$565$		0			0
$566$		−	28.1349i		−	1.18260i
$567$	8.96755	+	0.763518i	0.376602	+	0.0320647i
$568$	3.83827	+	3.83827i	0.161050	+	0.161050i
$569$	−45.5655			−1.91020			−0.955102	−	0.296277i	$-0.904255\pi$
$569$	−45.5655			−1.91020			−0.955102	+	0.296277i	$0.904255\pi$
$570$		0			0
$571$	−17.3897			−0.727734			−0.363867	−	0.931451i	$-0.618544\pi$
$571$	−17.3897			−0.727734			−0.363867	+	0.931451i	$0.618544\pi$
$572$	6.16126	+	6.16126i	0.257615	+	0.257615i
$573$	15.3410	+	24.0496i	0.640879	+	1.00469i
$574$		−	4.55435i		−	0.190095i
$575$		0			0
$576$	−2.72040	−	1.26469i	−0.113350	−	0.0526953i
$577$	14.7414	−	14.7414i	0.613693	−	0.613693i	−0.330214	−	0.943906i	$-0.607121\pi$
$577$	14.7414	−	14.7414i	0.613693	−	0.613693i	0.943906	+	0.330214i	$0.107121\pi$
$578$	−21.5189	+	21.5189i	−0.895068	+	0.895068i
$579$	33.4331	+	7.39151i	1.38943	+	0.307181i
$580$		0			0
$581$		−	2.16362i		−	0.0897621i
$582$	3.11753	−	1.98864i	0.129226	−	0.0824317i
$583$	−19.6967	−	19.6967i	−0.815755	−	0.815755i
$584$	−5.21988			−0.216000
$585$		0			0
$586$	−9.38931			−0.387869
$587$	15.1380	+	15.1380i	0.624811	+	0.624811i	0.946758	−	0.321947i	$-0.104337\pi$
$587$	15.1380	+	15.1380i	0.624811	+	0.624811i	−0.321947	+	0.946758i	$0.604337\pi$
$588$	−1.46025	+	0.931481i	−0.0602199	+	0.0384136i
$589$		−	1.90066i		−	0.0783153i
$590$		0			0
$591$	28.0005	+	6.19047i	1.15179	+	0.254642i
$592$	0.317848	−	0.317848i	0.0130635	−	0.0130635i
$593$	−16.1719	+	16.1719i	−0.664098	+	0.664098i	−0.956343	−	0.292245i	$-0.905598\pi$
$593$	−16.1719	+	16.1719i	−0.664098	+	0.664098i	0.292245	+	0.956343i	$0.405598\pi$
$594$	26.0179	+	19.8921i	1.06753	+	0.816184i
$595$		0			0
$596$		−	4.88159i		−	0.199958i
$597$	−10.3871	−	16.2836i	−0.425116	−	0.666442i
$598$	5.88954	+	5.88954i	0.240841	+	0.240841i
$599$	−28.5725			−1.16744			−0.583720	−	0.811955i	$-0.698404\pi$
$599$	−28.5725			−1.16744			−0.583720	+	0.811955i	$0.698404\pi$
$600$		0			0
$601$	6.29448			0.256757			0.128378	−	0.991725i	$-0.459023\pi$
$601$	6.29448			0.256757			0.128378	+	0.991725i	$0.459023\pi$
$602$	2.07154	+	2.07154i	0.0844296	+	0.0844296i
$603$	−8.20404	−	22.4590i	−0.334094	−	0.914601i
$604$		−	1.36645i		−	0.0555999i
$605$		0			0
$606$	0.590553	−	2.67117i	0.0239896	−	0.108509i
$607$	0.368490	−	0.368490i	0.0149566	−	0.0149566i	−0.699589	−	0.714546i	$-0.746634\pi$
$607$	0.368490	−	0.368490i	0.0149566	−	0.0149566i	0.714546	+	0.699589i	$0.246634\pi$
$608$	−0.202151	+	0.202151i	−0.00819830	+	0.00819830i
$609$	−1.43616	+	6.49598i	−0.0581960	+	0.263230i
$610$		0			0
$611$		−	13.0857i		−	0.529391i
$612$	−7.08920	−	19.4071i	−0.286564	−	0.784484i
$613$	27.1118	+	27.1118i	1.09504	+	1.09504i	0.994982	+	0.100053i	$0.0319013\pi$
$613$	27.1118	+	27.1118i	1.09504	+	1.09504i	0.100053	+	0.994982i	$0.468099\pi$
$614$	−5.44979			−0.219936
$615$		0			0
$616$	−6.30293			−0.253952
$617$	18.2218	+	18.2218i	0.733582	+	0.733582i	0.971328	−	0.237745i	$-0.0764083\pi$
$617$	18.2218	+	18.2218i	0.733582	+	0.733582i	−0.237745	+	0.971328i	$0.576408\pi$
$618$	5.65782	+	8.86960i	0.227591	+	0.356788i
$619$		−	15.1105i		−	0.607341i	−0.952777	−	0.303670i	$-0.901788\pi$
$619$		−	15.1105i		−	0.607341i	0.952777	−	0.303670i	$-0.0982121\pi$
$620$		0			0
$621$	24.8705	+	19.0149i	0.998019	+	0.763041i
$622$	19.9584	−	19.9584i	0.800259	−	0.800259i
$623$	6.33829	−	6.33829i	0.253938	−	0.253938i
$624$	2.33797	+	0.516888i	0.0935938	+	0.0206921i
$625$		0			0
$626$			7.45493i			0.297959i
$627$	2.63125	−	1.67844i	0.105082	−	0.0670306i
$628$	8.22730	+	8.22730i	0.328305	+	0.328305i
$629$	3.09579			0.123437
$630$		0			0
$631$	18.7681			0.747148			0.373574	−	0.927600i	$-0.378132\pi$
$631$	18.7681			0.747148			0.373574	+	0.927600i	$0.378132\pi$
$632$	3.09911	+	3.09911i	0.123276	+	0.123276i
$633$	−1.11917	+	0.713904i	−0.0444829	+	0.0283751i
$634$			31.7327i			1.26027i
$635$		0			0
$636$	−7.47419	−	1.65242i	−0.296371	−	0.0655229i
$637$	0.977522	−	0.977522i	0.0387308	−	0.0387308i
$638$	−17.1188	+	17.1188i	−0.677741	+	0.677741i
$639$	−14.7667	−	6.86490i	−0.584162	−	0.271571i
$640$		0			0
$641$			21.9502i			0.866979i	0.901159	+	0.433489i	$0.142718\pi$
$641$			21.9502i			0.866979i	−0.901159	+	0.433489i	$0.857282\pi$
$642$	9.37289	+	14.6936i	0.369919	+	0.579910i
$643$	29.9588	+	29.9588i	1.18146	+	1.18146i	0.979367	+	0.202091i	$0.0647737\pi$
$643$	29.9588	+	29.9588i	1.18146	+	1.18146i	0.202091	+	0.979367i	$0.435226\pi$
$644$	−6.02497			−0.237417
$645$		0			0
$646$	−1.96892			−0.0774660
$647$	−20.4792	−	20.4792i	−0.805120	−	0.805120i	0.178771	−	0.983891i	$-0.442788\pi$
$647$	−20.4792	−	20.4792i	−0.805120	−	0.805120i	−0.983891	+	0.178771i	$0.942788\pi$
$648$	8.96755	+	0.763518i	0.352279	+	0.0299938i
$649$		−	82.3377i		−	3.23204i
$650$		0			0
$651$	2.48582	−	11.2438i	0.0974269	−	0.440678i
$652$	−13.7521	+	13.7521i	−0.538572	+	0.538572i
$653$	−16.2736	+	16.2736i	−0.636835	+	0.636835i	−0.949773	−	0.312939i	$-0.898687\pi$
$653$	−16.2736	+	16.2736i	−0.636835	+	0.636835i	0.312939	+	0.949773i	$0.398687\pi$
$654$	−1.54389	+	6.98327i	−0.0603708	+	0.273068i
$655$		0			0
$656$		−	4.55435i		−	0.177817i
$657$	14.7090	−	5.37304i	0.573852	−	0.209622i
$658$	6.69331	+	6.69331i	0.260932	+	0.260932i
$659$	43.5045			1.69469			0.847347	−	0.531040i	$-0.178199\pi$
$659$	43.5045			1.69469			0.847347	+	0.531040i	$0.178199\pi$
$660$		0			0
$661$	−45.7539			−1.77962			−0.889811	−	0.456330i	$-0.849164\pi$
$661$	−45.7539			−1.77962			−0.889811	+	0.456330i	$0.849164\pi$
$662$	16.8632	+	16.8632i	0.655409	+	0.655409i
$663$	8.86855	+	13.9030i	0.344426	+	0.539946i
$664$		−	2.16362i		−	0.0839648i
$665$		0			0
$666$	−0.568484	+	1.22283i	−0.0220283	+	0.0473838i
$667$	−16.3639	+	16.3639i	−0.633612	+	0.633612i
$668$	10.5146	−	10.5146i	0.406823	−	0.406823i
$669$	−3.98365	−	0.880721i	−0.154017	−	0.0340507i
$670$		0			0
$671$		−	6.88374i		−	0.265744i
$672$	−1.46025	+	0.931481i	−0.0563305	+	0.0359326i
$673$	−17.9013	−	17.9013i	−0.690044	−	0.690044i	0.272198	−	0.962241i	$-0.412250\pi$
$673$	−17.9013	−	17.9013i	−0.690044	−	0.690044i	−0.962241	+	0.272198i	$0.912250\pi$
$674$	13.7129			0.528200
$675$		0			0
$676$	11.0889			0.426496
$677$	21.4226	+	21.4226i	0.823337	+	0.823337i	0.986585	−	0.163248i	$-0.0521971\pi$
$677$	21.4226	+	21.4226i	0.823337	+	0.823337i	−0.163248	+	0.986585i	$0.552197\pi$
$678$	16.9423	−	10.8073i	0.650663	−	0.415051i
$679$		−	2.13492i		−	0.0819307i
$680$		0			0
$681$	−13.2809	−	2.93619i	−0.508924	−	0.112515i
$682$	29.6307	−	29.6307i	1.13462	−	1.13462i
$683$	−16.7015	+	16.7015i	−0.639067	+	0.639067i	−0.950325	−	0.311258i	$-0.899250\pi$
$683$	−16.7015	+	16.7015i	−0.639067	+	0.639067i	0.311258	+	0.950325i	$0.399250\pi$
$684$	0.361554	−	0.777719i	0.0138244	−	0.0297368i
$685$		0			0
$686$			1.00000i			0.0381802i
$687$	−7.25642	−	11.3757i	−0.276850	−	0.434009i
$688$	2.07154	+	2.07154i	0.0789767	+	0.0789767i
$689$	6.10953			0.232754
$690$		0			0
$691$	2.98394			0.113514			0.0567572	−	0.998388i	$-0.481924\pi$
$691$	2.98394			0.113514			0.0567572	+	0.998388i	$0.481924\pi$
$692$	3.15253	+	3.15253i	0.119841	+	0.119841i
$693$	17.7609	−	6.48788i	0.674682	−	0.246454i
$694$			2.98474i			0.113299i
$695$		0			0
$696$	−1.43616	+	6.49598i	−0.0544374	+	0.246229i
$697$	22.1793	−	22.1793i	0.840102	−	0.840102i
$698$	−10.8567	+	10.8567i	−0.410931	+	0.410931i
$699$	−2.92706	+	13.2396i	−0.110711	+	0.500767i
$700$		0			0
$701$		−	14.7851i		−	0.558425i	−0.960229	−	0.279213i	$-0.909927\pi$
$701$		−	14.7851i		−	0.558425i	0.960229	−	0.279213i	$-0.0900734\pi$
$702$	−7.12019	+	0.950046i	−0.268734	+	0.0358572i
$703$	0.0908679	+	0.0908679i	0.00342715	+	0.00342715i
$704$	−6.30293			−0.237551
$705$		0			0
$706$	4.59340			0.172875
$707$	−1.11683	−	1.11683i	−0.0420029	−	0.0420029i
$708$	−12.1683	−	19.0759i	−0.457313	−	0.716915i
$709$		−	30.1615i		−	1.13274i	−0.824152	−	0.566369i	$-0.808348\pi$
$709$		−	30.1615i		−	1.13274i	0.824152	−	0.566369i	$-0.191652\pi$
$710$		0			0
$711$	−11.9230	−	5.54288i	−0.447146	−	0.207874i
$712$	6.33829	−	6.33829i	0.237538	−	0.237538i
$713$	28.3240	−	28.3240i	1.06074	−	1.06074i
$714$	−11.6476	−	2.57509i	−0.435899	−	0.0963703i
$715$		0			0
$716$		−	0.251416i		−	0.00939584i
$717$	−37.8876	+	24.1681i	−1.41494	+	0.902573i
$718$	−7.40585	−	7.40585i	−0.276384	−	0.276384i
$719$	0.144200			0.00537777			0.00268888	−	0.999996i	$-0.499144\pi$
$719$	0.144200			0.00537777			0.00268888	+	0.999996i	$0.499144\pi$
$720$		0			0
$721$	6.07401			0.226208
$722$	13.3772	+	13.3772i	0.497849	+	0.497849i
$723$	−4.90432	+	3.12841i	−0.182394	+	0.116347i
$724$		−	12.8653i		−	0.478135i
$725$		0			0
$726$	48.5834	+	10.7410i	1.80310	+	0.398636i
$727$	−21.5446	+	21.5446i	−0.799045	+	0.799045i	−0.982945	−	0.183900i	$-0.941128\pi$
$727$	−21.5446	+	21.5446i	−0.799045	+	0.799045i	0.183900	+	0.982945i	$0.441128\pi$
$728$	0.977522	−	0.977522i	0.0362294	−	0.0362294i
$729$	−26.0554	+	7.07918i	−0.965016	+	0.262192i
$730$		0			0
$731$			20.1765i			0.746254i
$732$	−1.01731	−	1.59481i	−0.0376010	−	0.0589460i
$733$	−37.1546	−	37.1546i	−1.37233	−	1.37233i	−0.856972	−	0.515362i	$-0.827657\pi$
$733$	−37.1546	−	37.1546i	−1.37233	−	1.37233i	−0.515362	−	0.856972i	$-0.672343\pi$
$734$	−2.04510			−0.0754862
$735$		0			0
$736$	−6.02497			−0.222083
$737$	−35.5218	−	35.5218i	−1.30846	−	1.30846i
$738$	4.68799	+	12.8336i	0.172567	+	0.472412i
$739$		−	14.3549i		−	0.528053i	−0.964515	−	0.264027i	$-0.914949\pi$
$739$		−	14.3549i		−	0.528053i	0.964515	−	0.264027i	$-0.0850507\pi$
$740$		0			0
$741$	−0.147770	+	0.668390i	−0.00542848	+	0.0245539i
$742$	−3.12501	+	3.12501i	−0.114723	+	0.114723i
$743$	−8.55425	+	8.55425i	−0.313825	+	0.313825i	−0.846389	−	0.532564i	$-0.821228\pi$
$743$	−8.55425	+	8.55425i	−0.313825	+	0.313825i	0.532564	+	0.846389i	$0.321228\pi$
$744$	2.48582	−	11.2438i	0.0911345	−	0.412217i
$745$		0			0
$746$			23.6597i			0.866242i
$747$	2.22711	+	6.09683i	0.0814856	+	0.223071i
$748$	−30.6948	−	30.6948i	−1.12231	−	1.12231i
$749$	10.0624			0.367671
$750$		0			0
$751$	14.1560			0.516561			0.258281	−	0.966070i	$-0.416844\pi$
$751$	14.1560			0.516561			0.258281	+	0.966070i	$0.416844\pi$
$752$	6.69331	+	6.69331i	0.244080	+	0.244080i
$753$	−17.2082	−	26.9768i	−0.627101	−	0.983088i
$754$		−	5.30992i		−	0.193376i
$755$		0			0
$756$	3.15601	−	4.12790i	0.114783	−	0.150130i
$757$	20.8958	−	20.8958i	0.759471	−	0.759471i	−0.216755	−	0.976226i	$-0.569547\pi$
$757$	20.8958	−	20.8958i	0.759471	−	0.759471i	0.976226	+	0.216755i	$0.0695472\pi$
$758$	20.4941	−	20.4941i	0.744380	−	0.744380i
$759$	64.2238	+	14.1988i	2.33118	+	0.515386i
$760$		0			0
$761$			40.0280i			1.45101i	0.688214	+	0.725507i	$0.258395\pi$
$761$			40.0280i			1.45101i	−0.688214	+	0.725507i	$0.741605\pi$
$762$	−13.2464	+	8.44975i	−0.479868	+	0.306102i
$763$	2.91975	+	2.91975i	0.105702	+	0.105702i
$764$	16.4695			0.595845
$765$		0			0
$766$	24.9033			0.899792
$767$	12.7697	+	12.7697i	0.461089	+	0.461089i
$768$	−1.46025	+	0.931481i	−0.0526924	+	0.0336119i
$769$		−	42.4533i		−	1.53090i	−0.643493	−	0.765452i	$-0.722515\pi$
$769$		−	42.4533i		−	1.53090i	0.643493	−	0.765452i	$-0.277485\pi$
$770$		0			0
$771$	−20.3196	−	4.49233i	−0.731792	−	0.161787i
$772$	13.9786	−	13.9786i	0.503100	−	0.503100i
$773$	16.8991	−	16.8991i	0.607820	−	0.607820i	−0.334556	−	0.942376i	$-0.608586\pi$
$773$	16.8991	−	16.8991i	0.607820	−	0.607820i	0.942376	+	0.334556i	$0.108586\pi$
$774$	−7.96967	−	3.70503i	−0.286464	−	0.133174i
$775$		0			0
$776$		−	2.13492i		−	0.0766392i
$777$	0.418706	+	0.656392i	0.0150210	+	0.0235479i
$778$	4.17634	+	4.17634i	0.149729	+	0.149729i
$779$	1.30202			0.0466496
$780$		0			0
$781$	−34.2132			−1.22424
$782$	−29.3412	−	29.3412i	−1.04924	−	1.04924i
$783$	−2.63967	−	19.7832i	−0.0943341	−	0.706994i
$784$			1.00000i			0.0357143i
$785$		0			0
$786$	−0.749134	+	3.38846i	−0.0267207	+	0.120862i
$787$	−8.08931	+	8.08931i	−0.288353	+	0.288353i	−0.836429	−	0.548076i	$-0.815360\pi$
$787$	−8.08931	+	8.08931i	−0.288353	+	0.288353i	0.548076	+	0.836429i	$0.315360\pi$
$788$	11.7072	−	11.7072i	0.417052	−	0.417052i
$789$	−1.63879	+	7.41251i	−0.0583424	+	0.263892i
$790$		0			0
$791$		−	11.6023i		−	0.412529i
$792$	17.7609	−	6.48788i	0.631107	−	0.230537i
$793$	1.06760	+	1.06760i	0.0379115	+	0.0379115i
$794$	25.2586			0.896395
$795$		0			0
$796$	−11.1512			−0.395243
$797$	3.04716	+	3.04716i	0.107936	+	0.107936i	0.759012	−	0.651076i	$-0.225682\pi$
$797$	3.04716	+	3.04716i	0.107936	+	0.107936i	−0.651076	+	0.759012i	$0.725682\pi$
$798$	−0.266296	−	0.417464i	−0.00942677	−	0.0147781i
$799$			65.1918i			2.30632i
$800$		0			0
$801$	−11.3363	+	24.3848i	−0.400548	+	0.861595i
$802$	−19.5384	+	19.5384i	−0.689926	+	0.689926i
$803$	23.2642	−	23.2642i	0.820975	−	0.820975i
$804$	−13.4793	−	2.98004i	−0.475377	−	0.105098i
$805$		0			0
$806$			9.19085i			0.323734i
$807$	13.4833	−	8.60085i	0.474635	−	0.302764i
$808$	−1.11683	−	1.11683i	−0.0392901	−	0.0392901i
$809$	10.4944			0.368962			0.184481	−	0.982836i	$-0.440940\pi$
$809$	10.4944			0.368962			0.184481	+	0.982836i	$0.440940\pi$
$810$		0			0
$811$	10.8699			0.381692			0.190846	−	0.981620i	$-0.438877\pi$
$811$	10.8699			0.381692			0.190846	+	0.981620i	$0.438877\pi$
$812$	2.71601	+	2.71601i	0.0953133	+	0.0953133i
$813$	33.9305	−	21.6439i	1.19000	−	0.759086i
$814$			2.83320i			0.0993037i
$815$		0			0
$816$	−11.6476	−	2.57509i	−0.407746	−	0.0901462i
$817$	−0.592221	+	0.592221i	−0.0207192	+	0.0207192i
$818$	6.61484	−	6.61484i	0.231282	−	0.231282i
$819$	−1.74834	+	3.76074i	−0.0610918	+	0.131411i
$820$		0			0
$821$			47.8291i			1.66925i	0.550820	+	0.834624i	$0.314315\pi$
$821$			47.8291i			1.66925i	−0.550820	+	0.834624i	$0.685685\pi$
$822$	−9.45837	−	14.8276i	−0.329899	−	0.517172i
$823$	−12.5787	−	12.5787i	−0.438466	−	0.438466i	0.453030	−	0.891495i	$-0.350343\pi$
$823$	−12.5787	−	12.5787i	−0.438466	−	0.438466i	−0.891495	+	0.453030i	$0.850343\pi$
$824$	6.07401			0.211598
$825$		0			0
$826$	−13.0634			−0.454533
$827$	0.598351	+	0.598351i	0.0208067	+	0.0208067i	0.717434	−	0.696627i	$-0.245317\pi$
$827$	0.598351	+	0.598351i	0.0208067	+	0.0208067i	−0.696627	+	0.717434i	$0.745317\pi$
$828$	16.9777	−	6.20176i	0.590015	−	0.215526i
$829$			32.5297i			1.12980i	0.825159	+	0.564901i	$0.191086\pi$
$829$			32.5297i			1.12980i	−0.825159	+	0.564901i	$0.808914\pi$
$830$		0			0
$831$	6.42993	−	29.0837i	0.223052	−	1.00890i
$832$	0.977522	−	0.977522i	0.0338895	−	0.0338895i
$833$	−4.86992	+	4.86992i	−0.168733	+	0.168733i
$834$	2.96283	−	13.4014i	0.102594	−	0.464051i
$835$		0			0
$836$		−	1.80191i		−	0.0623204i
$837$	4.56896	+	34.2424i	0.157926	+	1.18359i
$838$	5.90217	+	5.90217i	0.203887	+	0.203887i
$839$	−50.4871			−1.74301			−0.871505	−	0.490387i	$-0.836855\pi$
$839$	−50.4871			−1.74301			−0.871505	+	0.490387i	$0.836855\pi$
$840$		0			0
$841$	−14.2466			−0.491261
$842$	19.1604	+	19.1604i	0.660312	+	0.660312i
$843$	−14.9152	−	23.3822i	−0.513708	−	0.805326i
$844$			0.766419i			0.0263812i
$845$		0			0
$846$	−25.7507	−	11.9712i	−0.885326	−	0.411580i
$847$	20.3130	−	20.3130i	0.697964	−	0.697964i
$848$	−3.12501	+	3.12501i	−0.107313	+	0.107313i
$849$	47.5820	+	10.5196i	1.63301	+	0.361032i
$850$		0			0
$851$			2.70826i			0.0928379i
$852$	−7.92647	+	5.05621i	−0.271556	+	0.173223i
$853$	−1.16052	−	1.16052i	−0.0397356	−	0.0397356i	0.686960	−	0.726695i	$-0.258945\pi$
$853$	−1.16052	−	1.16052i	−0.0397356	−	0.0397356i	−0.726695	+	0.686960i	$0.758945\pi$
$854$	−1.09215			−0.0373725
$855$		0			0
$856$	10.0624			0.343924
$857$	−24.7253	−	24.7253i	−0.844600	−	0.844600i	0.144853	−	0.989453i	$-0.453729\pi$
$857$	−24.7253	−	24.7253i	−0.844600	−	0.844600i	−0.989453	+	0.144853i	$0.953729\pi$
$858$	−12.7237	+	8.11630i	−0.434379	+	0.277086i
$859$			48.4452i			1.65293i	0.562989	+	0.826464i	$0.309651\pi$
$859$			48.4452i			1.65293i	−0.562989	+	0.826464i	$0.690349\pi$
$860$		0			0
$861$	7.70237	+	1.70287i	0.262496	+	0.0580337i
$862$	−15.5637	+	15.5637i	−0.530101	+	0.530101i
$863$	−31.1904	+	31.1904i	−1.06173	+	1.06173i	−0.0637701	+	0.997965i	$0.520312\pi$
$863$	−31.1904	+	31.1904i	−1.06173	+	1.06173i	−0.997965	+	0.0637701i	$0.979688\pi$
$864$	3.15601	−	4.12790i	0.107370	−	0.140434i
$865$		0			0
$866$		−	4.30269i		−	0.146211i
$867$	−28.3471	−	44.4389i	−0.962718	−	1.50923i
$868$	−4.70110	−	4.70110i	−0.159566	−	0.159566i
$869$	−27.6245			−0.937098
$870$		0			0
$871$	11.0182			0.373336
$872$	2.91975	+	2.91975i	0.0988753	+	0.0988753i
$873$	2.19756	+	6.01595i	0.0743763	+	0.203609i
$874$		−	1.72245i		−	0.0582626i
$875$		0			0
$876$	1.95171	−	8.82792i	0.0659422	−	0.298268i
$877$	−8.70402	+	8.70402i	−0.293914	+	0.293914i	−0.838624	−	0.544710i	$-0.816640\pi$
$877$	−8.70402	+	8.70402i	−0.293914	+	0.293914i	0.544710	+	0.838624i	$0.316640\pi$
$878$	−2.72129	+	2.72129i	−0.0918390	+	0.0918390i
$879$	3.51066	−	15.8793i	0.118412	−	0.535596i
$880$		0			0
$881$		−	0.355501i		−	0.0119771i	−0.999982	−	0.00598857i	$-0.998094\pi$
$881$		−	0.355501i		−	0.0119771i	0.999982	−	0.00598857i	$-0.00190623\pi$
$882$	−1.02934	−	2.81788i	−0.0346598	−	0.0948830i
$883$	−8.48174	−	8.48174i	−0.285433	−	0.285433i	0.549838	−	0.835271i	$-0.314689\pi$
$883$	−8.48174	−	8.48174i	−0.285433	−	0.285433i	−0.835271	+	0.549838i	$0.814689\pi$
$884$	9.52091			0.320223
$885$		0			0
$886$	−1.77441			−0.0596125
$887$	−2.65437	−	2.65437i	−0.0891249	−	0.0891249i	0.661139	−	0.750264i	$-0.270073\pi$
$887$	−2.65437	−	2.65437i	−0.0891249	−	0.0891249i	−0.750264	+	0.661139i	$0.770073\pi$
$888$	0.418706	+	0.656392i	0.0140508	+	0.0220271i
$889$			9.07132i			0.304242i
$890$		0			0
$891$	−43.3699	+	36.5641i	−1.45295	+	1.22494i
$892$	−1.66559	+	1.66559i	−0.0557681	+	0.0557681i
$893$	−1.91351	+	1.91351i	−0.0640333	+	0.0640333i
$894$	8.25581	+	1.82523i	0.276116	+	0.0610447i
$895$		0			0
$896$			1.00000i			0.0334077i
$897$	−12.1626	+	7.75837i	−0.406096	+	0.259044i
$898$	−26.0581	−	26.0581i	−0.869571	−	0.869571i
$899$	−25.5365			−0.851688
$900$		0			0
$901$	−30.4371			−1.01401
$902$	20.2980	+	20.2980i	0.675851	+	0.675851i
$903$	−4.27796	+	2.72886i	−0.142362	+	0.0908109i
$904$		−	11.6023i		−	0.385885i
$905$		0			0
$906$	2.31095	+	0.510914i	0.0767762	+	0.0169740i
$907$	21.5594	−	21.5594i	0.715870	−	0.715870i	−0.251887	−	0.967757i	$-0.581051\pi$
$907$	21.5594	−	21.5594i	0.715870	−	0.715870i	0.967757	+	0.251887i	$0.0810512\pi$
$908$	−5.55282	+	5.55282i	−0.184277	+	0.184277i
$909$	4.29671	+	1.99750i	0.142513	+	0.0662530i
$910$		0			0
$911$		−	18.6500i		−	0.617902i	−0.951078	−	0.308951i	$-0.900022\pi$
$911$		−	18.6500i		−	0.617902i	0.951078	−	0.308951i	$-0.0999778\pi$
$912$	−0.266296	−	0.417464i	−0.00881793	−	0.0138236i
$913$	9.64293	+	9.64293i	0.319134	+	0.319134i
$914$	24.6548			0.815509
$915$		0			0
$916$	−7.79020			−0.257396
$917$	1.41674	+	1.41674i	0.0467848	+	0.0467848i
$918$	35.4721	−	4.73304i	1.17075	−	0.156214i
$919$			6.56474i			0.216551i	0.994121	+	0.108275i	$0.0345329\pi$
$919$			6.56474i			0.216551i	−0.994121	+	0.108275i	$0.965467\pi$
$920$		0			0
$921$	2.03768	−	9.21676i	0.0671437	−	0.303702i
$922$	−15.7369	+	15.7369i	−0.518267	+	0.518267i
$923$	5.30612	−	5.30612i	0.174653	−	0.174653i
$924$	2.35667	−	10.6596i	0.0775286	−	0.350675i
$925$		0			0
$926$			16.7438i			0.550236i
$927$	−17.1158	+	6.25224i	−0.562158	+	0.205350i
$928$	2.71601	+	2.71601i	0.0891574	+	0.0891574i
$929$	9.96590			0.326971			0.163485	−	0.986546i	$-0.447726\pi$
$929$	9.96590			0.326971			0.163485	+	0.986546i	$0.447726\pi$
$930$		0			0
$931$	−0.285884			−0.00936948
$932$	5.53555	+	5.53555i	0.181323	+	0.181323i
$933$	26.2914	+	41.2163i	0.860743	+	1.34936i
$934$			27.9954i			0.916038i
$935$		0			0
$936$	−1.74834	+	3.76074i	−0.0571461	+	0.122924i
$937$	21.4995	−	21.4995i	0.702357	−	0.702357i	−0.262559	−	0.964916i	$-0.584566\pi$
$937$	21.4995	−	21.4995i	0.702357	−	0.702357i	0.964916	+	0.262559i	$0.0845665\pi$
$938$	−5.63576	+	5.63576i	−0.184014	+	0.184014i
$939$	−12.6079	−	2.78740i	−0.411442	−	0.0909632i
$940$		0			0
$941$		−	60.1796i		−	1.96180i	−0.194518	−	0.980899i	$-0.562314\pi$
$941$		−	60.1796i		−	1.96180i	0.194518	−	0.980899i	$-0.437686\pi$
$942$	−16.9903	+	10.8379i	−0.553574	+	0.353119i
$943$	19.4029	+	19.4029i	0.631845	+	0.631845i
$944$	−13.0634			−0.425177
$945$		0			0
$946$	−18.4651			−0.600351
$947$	31.0571	+	31.0571i	1.00922	+	1.00922i	0.999957	+	0.00926262i	$0.00294843\pi$
$947$	31.0571	+	31.0571i	1.00922	+	1.00922i	0.00926262	+	0.999957i	$0.497052\pi$
$948$	−6.40001	+	4.08250i	−0.207863	+	0.132593i
$949$			7.21608i			0.234244i
$950$		0			0
$951$	−53.6668	−	11.8649i	−1.74027	−	0.384745i
$952$	−4.86992	+	4.86992i	−0.157835	+	0.157835i
$953$	5.02499	−	5.02499i	0.162775	−	0.162775i	−0.621020	−	0.783795i	$-0.713281\pi$
$953$	5.02499	−	5.02499i	0.162775	−	0.162775i	0.783795	+	0.621020i	$0.213281\pi$
$954$	5.58920	−	12.0226i	0.180957	−	0.389246i
$955$		0			0
$956$			25.9459i			0.839149i
$957$	−22.5509	−	35.3523i	−0.728966	−	1.14278i
$958$	−5.36537	−	5.36537i	−0.173347	−	0.173347i
$959$	−10.1541			−0.327894
$960$		0			0
$961$	13.2006			0.425826
$962$	−0.439401	−	0.439401i	−0.0141669	−	0.0141669i
$963$	−28.3545	+	10.3576i	−0.913712	+	0.333769i
$964$			3.35854i			0.108171i
$965$		0			0
$966$	2.25274	−	10.1895i	0.0724806	−	0.327842i
$967$	−43.4004	+	43.4004i	−1.39566	+	1.39566i	−0.583679	+	0.811984i	$0.698388\pi$
$967$	−43.4004	+	43.4004i	−1.39566	+	1.39566i	−0.811984	+	0.583679i	$0.801612\pi$
$968$	20.3130	−	20.3130i	0.652886	−	0.652886i
$969$	0.736178	−	3.32986i	0.0236494	−	0.106970i
$970$		0			0
$971$		−	18.7579i		−	0.601969i	−0.953629	−	0.300985i	$-0.902685\pi$
$971$		−	18.7579i		−	0.601969i	0.953629	−	0.300985i	$-0.0973153\pi$
$972$	−4.64424	+	14.8806i	−0.148964	+	0.477294i
$973$	−5.60320	−	5.60320i	−0.179630	−	0.179630i
$974$	−3.87783			−0.124254
$975$		0			0
$976$	−1.09215			−0.0349588
$977$	1.97273	+	1.97273i	0.0631133	+	0.0631133i	0.737959	−	0.674846i	$-0.235790\pi$
$977$	1.97273	+	1.97273i	0.0631133	+	0.0631133i	−0.674846	+	0.737959i	$0.735790\pi$
$978$	−18.1158	−	28.3995i	−0.579278	−	0.908117i
$979$			56.4976i			1.80567i
$980$		0			0
$981$	−11.2329	−	5.22209i	−0.358640	−	0.166728i
$982$	−29.1454	+	29.1454i	−0.930067	+	0.930067i
$983$	−25.3760	+	25.3760i	−0.809369	+	0.809369i	−0.984538	−	0.175169i	$-0.943953\pi$
$983$	−25.3760	+	25.3760i	−0.809369	+	0.809369i	0.175169	+	0.984538i	$0.443953\pi$
$984$	7.70237	+	1.70287i	0.245543	+	0.0542855i
$985$		0			0
$986$			26.4535i			0.842452i
$987$	−13.8224	+	8.81718i	−0.439973	+	0.280654i
$988$	0.279458	+	0.279458i	0.00889075	+	0.00889075i
$989$	−17.6508			−0.561261
$990$		0			0
$991$	38.4444			1.22123			0.610614	−	0.791928i	$-0.290923\pi$
$991$	38.4444			1.22123			0.610614	+	0.791928i	$0.290923\pi$
$992$	−4.70110	−	4.70110i	−0.149260	−	0.149260i
$993$	−34.8245	+	22.2142i	−1.10512	+	0.704945i
$994$			5.42814i			0.172170i
$995$		0			0
$996$	3.65914	+	0.808977i	0.115944	+	0.0256334i
$997$	2.86440	−	2.86440i	0.0907166	−	0.0907166i	−0.660292	−	0.751009i	$-0.729568\pi$
$997$	2.86440	−	2.86440i	0.0907166	−	0.0907166i	0.751009	+	0.660292i	$0.229568\pi$
$998$	−11.4282	+	11.4282i	−0.361753	+	0.361753i
$999$	−1.85552	−	1.41864i	−0.0587059	−	0.0448839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.j.c.743.4		12
3.2	odd	2		1050.2.j.d.743.3		12
5.2	odd	4		1050.2.j.d.407.3		12
5.3	odd	4		210.2.j.b.197.4	yes	12
5.4	even	2		210.2.j.a.113.3	✓	12
15.2	even	4	inner	1050.2.j.c.407.4		12
15.8	even	4		210.2.j.a.197.3	yes	12
15.14	odd	2		210.2.j.b.113.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.j.a.113.3	✓	12	5.4	even	2
210.2.j.a.197.3	yes	12	15.8	even	4
210.2.j.b.113.4	yes	12	15.14	odd	2
210.2.j.b.197.4	yes	12	5.3	odd	4
1050.2.j.c.407.4		12	15.2	even	4	inner
1050.2.j.c.743.4		12	1.1	even	1	trivial
1050.2.j.d.407.3		12	5.2	odd	4
1050.2.j.d.743.3		12	3.2	odd	2

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.46025 + 0.931481i) q^{3} +1.00000i q^{4} +(-1.69121 - 0.373900i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.26469 - 2.72040i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.46025 + 0.931481i) q^{3} +1.00000i q^{4} +(-1.69121 - 0.373900i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.26469 - 2.72040i) q^{9} -6.30293i q^{11} +(-0.931481 - 1.46025i) q^{12} +(0.977522 + 0.977522i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-4.86992 - 4.86992i) q^{17} +(2.81788 - 1.02934i) q^{18} -0.285884i q^{19} +(0.373900 - 1.69121i) q^{21} +(4.45685 - 4.45685i) q^{22} +(4.26030 - 4.26030i) q^{23} +(0.373900 - 1.69121i) q^{24} +1.38242i q^{26} +(0.687232 + 5.15051i) q^{27} +(-0.707107 - 0.707107i) q^{28} -3.84102 q^{29} +6.64835 q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.87106 + 9.20389i) q^{33} -6.88711i q^{34} +(2.72040 + 1.26469i) q^{36} +(-0.317848 + 0.317848i) q^{37} +(0.202151 - 0.202151i) q^{38} +(-2.33797 - 0.516888i) q^{39} +4.55435i q^{41} +(1.46025 - 0.931481i) q^{42} +(-2.07154 - 2.07154i) q^{43} +6.30293 q^{44} +6.02497 q^{46} +(-6.69331 - 6.69331i) q^{47} +(1.46025 - 0.931481i) q^{48} -1.00000i q^{49} +(11.6476 + 2.57509i) q^{51} +(-0.977522 + 0.977522i) q^{52} +(3.12501 - 3.12501i) q^{53} +(-3.15601 + 4.12790i) q^{54} -1.00000i q^{56} +(0.266296 + 0.417464i) q^{57} +(-2.71601 - 2.71601i) q^{58} +13.0634 q^{59} +1.09215 q^{61} +(4.70110 + 4.70110i) q^{62} +(1.02934 + 2.81788i) q^{63} -1.00000i q^{64} +(-2.35667 + 10.6596i) q^{66} +(5.63576 - 5.63576i) q^{67} +(4.86992 - 4.86992i) q^{68} +(-2.25274 + 10.1895i) q^{69} -5.42814i q^{71} +(1.02934 + 2.81788i) q^{72} +(3.69101 + 3.69101i) q^{73} -0.449505 q^{74} +0.285884 q^{76} +(4.45685 + 4.45685i) q^{77} +(-1.28770 - 2.01869i) q^{78} -4.38280i q^{79} +(-5.80113 - 6.88091i) q^{81} +(-3.22041 + 3.22041i) q^{82} +(-1.52991 + 1.52991i) q^{83} +(1.69121 + 0.373900i) q^{84} -2.92960i q^{86} +(5.60887 - 3.57783i) q^{87} +(4.45685 + 4.45685i) q^{88} -8.96370 q^{89} -1.38242 q^{91} +(4.26030 + 4.26030i) q^{92} +(-9.70829 + 6.19281i) q^{93} -9.46577i q^{94} +(1.69121 + 0.373900i) q^{96} +(-1.50962 + 1.50962i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-17.1465 - 7.97124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3}+O(q^{10}) \) 12 * q - 4 * q^3	\( 12 q - 4 q^{3} + 4 q^{12} - 12 q^{14} - 12 q^{16} - 28 q^{17} - 4 q^{21} - 4 q^{22} + 24 q^{23} - 4 q^{24} + 20 q^{27} + 8 q^{29} - 8 q^{31} - 4 q^{33} + 4 q^{36} + 20 q^{37} + 4 q^{38} - 40 q^{39} + 4 q^{42} - 8 q^{43} + 8 q^{44} + 8 q^{46} - 16 q^{47} + 4 q^{48} + 8 q^{51} + 24 q^{53} - 4 q^{54} + 12 q^{57} + 8 q^{58} + 32 q^{59} - 28 q^{62} - 8 q^{63} - 8 q^{66} + 28 q^{68} - 32 q^{69} - 8 q^{72} + 24 q^{73} + 8 q^{74} - 4 q^{77} - 36 q^{81} - 32 q^{82} + 24 q^{83} + 64 q^{87} - 4 q^{88} + 48 q^{89} + 24 q^{91} + 24 q^{92} - 76 q^{93} - 8 q^{97} - 40 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 + 4 * q^12 - 12 * q^14 - 12 * q^16 - 28 * q^17 - 4 * q^21 - 4 * q^22 + 24 * q^23 - 4 * q^24 + 20 * q^27 + 8 * q^29 - 8 * q^31 - 4 * q^33 + 4 * q^36 + 20 * q^37 + 4 * q^38 - 40 * q^39 + 4 * q^42 - 8 * q^43 + 8 * q^44 + 8 * q^46 - 16 * q^47 + 4 * q^48 + 8 * q^51 + 24 * q^53 - 4 * q^54 + 12 * q^57 + 8 * q^58 + 32 * q^59 - 28 * q^62 - 8 * q^63 - 8 * q^66 + 28 * q^68 - 32 * q^69 - 8 * q^72 + 24 * q^73 + 8 * q^74 - 4 * q^77 - 36 * q^81 - 32 * q^82 + 24 * q^83 + 64 * q^87 - 4 * q^88 + 48 * q^89 + 24 * q^91 + 24 * q^92 - 76 * q^93 - 8 * q^97 - 40 * q^99

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