LMFDB - Embedded newform 441.2.u.c.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			127.4
Character	$\chi$	$=$	441.127
Dual form			441.2.u.c.316.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.06977 + 0.996749i) q^{2} +(2.04346 + 2.56242i) q^{4} +(0.349558 + 1.53152i) q^{5} +(-0.354322 + 2.62192i) q^{7} +(0.653025 + 2.86109i) q^{8} +O(q^{10})$	\(q+(2.06977 + 0.996749i) q^{2} +(2.04346 + 2.56242i) q^{4} +(0.349558 + 1.53152i) q^{5} +(-0.354322 + 2.62192i) q^{7} +(0.653025 + 2.86109i) q^{8} +(-0.803031 + 3.51831i) q^{10} +(-4.49332 - 2.16387i) q^{11} +(1.84222 + 0.887167i) q^{13} +(-3.34676 + 5.07360i) q^{14} +(-0.0415703 + 0.182131i) q^{16} +(1.20696 - 1.51349i) q^{17} +6.63276 q^{19} +(-3.21008 + 4.02531i) q^{20} +(-7.14330 - 8.95742i) q^{22} +(-1.01258 - 1.26973i) q^{23} +(2.28150 - 1.09871i) q^{25} +(2.92869 + 3.67246i) q^{26} +(-7.44250 + 4.44987i) q^{28} +(3.96658 - 4.97393i) q^{29} -6.35646 q^{31} +(3.39189 - 4.25330i) q^{32} +(4.00670 - 1.92953i) q^{34} +(-4.13936 + 0.373864i) q^{35} +(-3.87938 + 4.86459i) q^{37} +(13.7283 + 6.61120i) q^{38} +(-4.15353 + 2.00024i) q^{40} +(1.76255 + 7.72224i) q^{41} +(1.23475 - 5.40977i) q^{43} +(-3.63718 - 15.9355i) q^{44} +(-0.830200 - 3.63734i) q^{46} +(0.138094 + 0.0665024i) q^{47} +(-6.74891 - 1.85801i) q^{49} +5.81731 q^{50} +(1.49121 + 6.53344i) q^{52} +(-2.44815 - 3.06989i) q^{53} +(1.74332 - 7.63798i) q^{55} +(-7.73293 + 0.698432i) q^{56} +(13.1677 - 6.34121i) q^{58} +(-2.33810 + 10.2439i) q^{59} +(5.14458 - 6.45110i) q^{61} +(-13.1564 - 6.33579i) q^{62} +(11.5965 - 5.58460i) q^{64} +(-0.714746 + 3.13151i) q^{65} -15.5318 q^{67} +6.34457 q^{68} +(-8.94018 - 3.35209i) q^{70} +(-5.76688 - 7.23144i) q^{71} +(4.80479 - 2.31387i) q^{73} +(-12.8782 + 6.20181i) q^{74} +(13.5538 + 16.9959i) q^{76} +(7.26557 - 11.0144i) q^{77} +8.93772 q^{79} -0.293468 q^{80} +(-4.04906 + 17.7401i) q^{82} +(6.94067 - 3.34245i) q^{83} +(2.73983 + 1.31943i) q^{85} +(7.94783 - 9.96626i) q^{86} +(3.25677 - 14.2688i) q^{88} +(-0.997768 + 0.480500i) q^{89} +(-2.97882 + 4.51581i) q^{91} +(1.18442 - 5.18930i) q^{92} +(0.219536 + 0.275289i) q^{94} +(2.31854 + 10.1582i) q^{95} -15.4355 q^{97} +(-12.1167 - 10.5726i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8	$ 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) $ 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

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 $

$2$	2.06977	+	0.996749i	1.46355	+	0.704808i	0.984888	−	0.173192i	$-0.0554081\pi$
$2$	2.06977	+	0.996749i	1.46355	+	0.704808i	0.478661	+	0.878000i	$0.341122\pi$
$3$		0			0
$3$		0			0
$4$	2.04346	+	2.56242i	1.02173	+	1.28121i
$5$	0.349558	+	1.53152i	0.156327	+	0.684914i	0.990966	+	0.134116i	$0.0428195\pi$
$5$	0.349558	+	1.53152i	0.156327	+	0.684914i	−0.834638	+	0.550798i	$0.814323\pi$
$6$		0			0
$7$	−0.354322	+	2.62192i	−0.133921	+	0.990992i
$7$	−0.354322	+	2.62192i	−0.133921	+	0.990992i
$8$	0.653025	+	2.86109i	0.230879	+	1.01155i
$9$		0			0
$10$	−0.803031	+	3.51831i	−0.253941	+	1.11259i
$11$	−4.49332	−	2.16387i	−1.35479	−	0.652431i	−0.391319	−	0.920255i	$-0.627981\pi$
$11$	−4.49332	−	2.16387i	−1.35479	−	0.652431i	−0.963468	+	0.267825i	$0.913695\pi$
$12$		0			0
$13$	1.84222	+	0.887167i	0.510940	+	0.246056i	0.671546	−	0.740963i	$-0.265631\pi$
$13$	1.84222	+	0.887167i	0.510940	+	0.246056i	−0.160606	+	0.987019i	$0.551345\pi$
$14$	−3.34676	+	5.07360i	−0.894459	+	1.35598i
$15$		0			0
$16$	−0.0415703	+	0.182131i	−0.0103926	+	0.0455328i
$17$	1.20696	−	1.51349i	0.292732	−	0.367074i	−0.613617	−	0.789604i	$-0.710286\pi$
$17$	1.20696	−	1.51349i	0.292732	−	0.367074i	0.906349	+	0.422529i	$0.138858\pi$
$18$		0			0
$19$	6.63276			1.52166			0.760830	−	0.648951i	$-0.224792\pi$
$19$	6.63276			1.52166			0.760830	+	0.648951i	$0.224792\pi$
$20$	−3.21008	+	4.02531i	−0.717795	+	0.900086i
$21$		0			0
$22$	−7.14330	−	8.95742i	−1.52296	−	1.90973i
$23$	−1.01258	−	1.26973i	−0.211137	−	0.264758i	0.664974	−	0.746866i	$-0.268442\pi$
$23$	−1.01258	−	1.26973i	−0.211137	−	0.264758i	−0.876111	+	0.482109i	$0.839871\pi$
$24$		0			0
$25$	2.28150	−	1.09871i	0.456299	−	0.219742i
$26$	2.92869	+	3.67246i	0.574364	+	0.720229i
$27$		0			0
$28$	−7.44250	+	4.44987i	−1.40650	+	0.840946i
$29$	3.96658	−	4.97393i	0.736574	−	0.923635i	−0.262573	−	0.964912i	$-0.584571\pi$
$29$	3.96658	−	4.97393i	0.736574	−	0.923635i	0.999148	+	0.0412769i	$0.0131426\pi$
$30$		0			0
$31$	−6.35646			−1.14165			−0.570827	−	0.821070i	$-0.693377\pi$
$31$	−6.35646			−1.14165			−0.570827	+	0.821070i	$0.693377\pi$
$32$	3.39189	−	4.25330i	0.599607	−	0.751884i
$33$		0			0
$34$	4.00670	−	1.92953i	0.687144	−	0.330911i
$35$	−4.13936	+	0.373864i	−0.699680	+	0.0631946i
$36$		0			0
$37$	−3.87938	+	4.86459i	−0.637766	+	0.799733i	−0.990722	−	0.135907i	$-0.956605\pi$
$37$	−3.87938	+	4.86459i	−0.637766	+	0.799733i	0.352956	+	0.935640i	$0.385177\pi$
$38$	13.7283	+	6.61120i	2.22702	+	1.07248i
$39$		0			0
$40$	−4.15353	+	2.00024i	−0.656731	+	0.316265i
$41$	1.76255	+	7.72224i	0.275264	+	1.20601i	0.903706	+	0.428154i	$0.140836\pi$
$41$	1.76255	+	7.72224i	0.275264	+	1.20601i	−0.628441	+	0.777857i	$0.716307\pi$
$42$		0			0
$43$	1.23475	−	5.40977i	0.188297	−	0.824983i	−0.789217	−	0.614114i	$-0.789514\pi$
$43$	1.23475	−	5.40977i	0.188297	−	0.824983i	0.977514	−	0.210869i	$-0.0676293\pi$
$44$	−3.63718	−	15.9355i	−0.548326	−	2.40237i
$45$		0			0
$46$	−0.830200	−	3.63734i	−0.122406	−	0.536297i
$47$	0.138094	+	0.0665024i	0.0201430	+	0.00970037i	0.443928	−	0.896062i	$-0.353585\pi$
$47$	0.138094	+	0.0665024i	0.0201430	+	0.00970037i	−0.423785	+	0.905763i	$0.639299\pi$
$48$		0			0
$49$	−6.74891	−	1.85801i	−0.964130	−	0.265429i
$50$	5.81731			0.822692
$51$		0			0
$52$	1.49121	+	6.53344i	0.206794	+	0.906025i
$53$	−2.44815	−	3.06989i	−0.336280	−	0.421681i	0.584726	−	0.811231i	$-0.301202\pi$
$53$	−2.44815	−	3.06989i	−0.336280	−	0.421681i	−0.921005	+	0.389550i	$0.872631\pi$
$54$		0			0
$55$	1.74332	−	7.63798i	0.235069	−	1.02991i
$56$	−7.73293	+	0.698432i	−1.03336	+	0.0933319i
$57$		0			0
$58$	13.1677	−	6.34121i	1.72900	−	0.832642i
$59$	−2.33810	+	10.2439i	−0.304395	+	1.33364i	0.559023	+	0.829152i	$0.311176\pi$
$59$	−2.33810	+	10.2439i	−0.304395	+	1.33364i	−0.863418	+	0.504489i	$0.831681\pi$
$60$		0			0
$61$	5.14458	−	6.45110i	0.658696	−	0.825979i	−0.334505	−	0.942394i	$-0.608569\pi$
$61$	5.14458	−	6.45110i	0.658696	−	0.825979i	0.993201	+	0.116415i	$0.0371404\pi$
$62$	−13.1564	−	6.33579i	−1.67087	−	0.804647i
$63$		0			0
$64$	11.5965	−	5.58460i	1.44957	−	0.698075i
$65$	−0.714746	+	3.13151i	−0.0886533	+	0.388416i
$66$		0			0
$67$	−15.5318			−1.89752			−0.948758	−	0.316003i	$-0.897659\pi$
$67$	−15.5318			−1.89752			−0.948758	+	0.316003i	$0.897659\pi$
$68$	6.34457			0.769392
$69$		0			0
$70$	−8.94018	−	3.35209i	−1.06856	−	0.400652i
$71$	−5.76688	−	7.23144i	−0.684402	−	0.858214i	0.311349	−	0.950296i	$-0.399219\pi$
$71$	−5.76688	−	7.23144i	−0.684402	−	0.858214i	−0.995751	+	0.0920821i	$0.970648\pi$
$72$		0			0
$73$	4.80479	−	2.31387i	0.562358	−	0.270817i	−0.131034	−	0.991378i	$-0.541830\pi$
$73$	4.80479	−	2.31387i	0.562358	−	0.270817i	0.693392	+	0.720560i	$0.256115\pi$
$74$	−12.8782	+	6.20181i	−1.49706	+	0.720946i
$75$		0			0
$76$	13.5538	+	16.9959i	1.55473	+	1.94957i
$77$	7.26557	−	11.0144i	0.827988	−	1.25521i
$78$		0			0
$79$	8.93772			1.00557			0.502786	−	0.864411i	$-0.332308\pi$
$79$	8.93772			1.00557			0.502786	+	0.864411i	$0.332308\pi$
$80$	−0.293468			−0.0328107
$81$		0			0
$82$	−4.04906	+	17.7401i	−0.447144	+	1.95906i
$83$	6.94067	−	3.34245i	0.761838	−	0.366882i	−0.0122790	−	0.999925i	$-0.503909\pi$
$83$	6.94067	−	3.34245i	0.761838	−	0.366882i	0.774117	+	0.633043i	$0.218194\pi$
$84$		0			0
$85$	2.73983	+	1.31943i	0.297176	+	0.143113i
$86$	7.94783	−	9.96626i	0.857036	−	1.07469i
$87$		0			0
$88$	3.25677	−	14.2688i	0.347173	−	1.52106i
$89$	−0.997768	+	0.480500i	−0.105763	+	0.0509329i	−0.486017	−	0.873949i	$-0.661551\pi$
$89$	−0.997768	+	0.480500i	−0.105763	+	0.0509329i	0.380254	+	0.924882i	$0.375837\pi$
$90$		0			0
$91$	−2.97882	+	4.51581i	−0.312265	+	0.473386i
$92$	1.18442	−	5.18930i	0.123485	−	0.541022i
$93$		0			0
$94$	0.219536	+	0.275289i	0.0226434	+	0.0283939i
$95$	2.31854	+	10.1582i	0.237877	+	1.04221i
$96$		0			0
$97$	−15.4355			−1.56724			−0.783621	−	0.621240i	$-0.786629\pi$
$97$	−15.4355			−1.56724			−0.783621	+	0.621240i	$0.786629\pi$
$98$	−12.1167	−	10.5726i	−1.22397	−	1.06800i
$99$		0			0
$100$	7.47751	+	3.60098i	0.747751	+	0.360098i
$101$	−1.70584	−	7.47379i	−0.169738	−	0.743670i	−0.986103	−	0.166134i	$-0.946872\pi$
$101$	−1.70584	−	7.47379i	−0.169738	−	0.743670i	0.816365	−	0.577536i	$-0.195986\pi$
$102$		0			0
$103$	−2.51904	−	11.0366i	−0.248209	−	1.08747i	−0.933323	−	0.359038i	$-0.883105\pi$
$103$	−2.51904	−	11.0366i	−0.248209	−	1.08747i	0.685114	−	0.728436i	$-0.259752\pi$
$104$	−1.33525	+	5.85010i	−0.130932	+	0.573650i
$105$		0			0
$106$	−2.00721	−	8.79415i	−0.194957	−	0.854164i
$107$	−15.7962	+	7.60703i	−1.52707	+	0.735400i	−0.993867	−	0.110585i	$-0.964728\pi$
$107$	−15.7962	+	7.60703i	−1.52707	+	0.735400i	−0.533207	+	0.845985i	$0.679013\pi$
$108$		0			0
$109$	3.15450	+	1.51913i	0.302146	+	0.145506i	0.578814	−	0.815460i	$-0.303516\pi$
$109$	3.15450	+	1.51913i	0.302146	+	0.145506i	−0.276668	+	0.960966i	$0.589230\pi$
$110$	11.2214	−	14.0712i	1.06992	−	1.34164i
$111$		0			0
$112$	−0.462804	−	0.173527i	−0.0437309	−	0.0163968i
$113$	−11.0454	+	5.31919i	−1.03906	+	0.500387i	−0.874015	−	0.485898i	$-0.838493\pi$
$113$	−11.0454	+	5.31919i	−1.03906	+	0.500387i	−0.165049	+	0.986285i	$0.552778\pi$
$114$		0			0
$115$	1.59066	−	1.99462i	0.148330	−	0.186000i
$116$	20.8508			1.93595
$117$		0			0
$118$	−15.0499	+	18.8720i	−1.38546	+	1.73731i
$119$	3.54058	+	3.70082i	0.324565	+	0.339254i
$120$		0			0
$121$	8.64919	+	10.8457i	0.786290	+	0.985977i
$122$	17.0782	−	8.22444i	1.54619	−	0.744606i
$123$		0			0
$124$	−12.9892	−	16.2879i	−1.16646	−	1.46270i
$125$	7.37741	+	9.25098i	0.659856	+	0.827433i
$126$		0			0
$127$	−0.634871	+	0.796103i	−0.0563357	+	0.0706427i	−0.809201	−	0.587532i	$-0.800100\pi$
$127$	−0.634871	+	0.796103i	−0.0563357	+	0.0706427i	0.752865	+	0.658175i	$0.228671\pi$
$128$	18.6883			1.65182
$129$		0			0
$130$	−4.60069	+	5.76908i	−0.403507	+	0.505982i
$131$	−2.96256	+	12.9798i	−0.258840	+	1.13405i	0.663653	+	0.748041i	$0.269005\pi$
$131$	−2.96256	+	12.9798i	−0.258840	+	1.13405i	−0.922493	+	0.386013i	$0.873852\pi$
$132$		0			0
$133$	−2.35013	+	17.3906i	−0.203782	+	1.50795i
$134$	−32.1473	−	15.4813i	−2.77711	−	1.33738i
$135$		0			0
$136$	5.11840	+	2.46489i	0.438899	+	0.211363i
$137$	−0.754302	+	3.30481i	−0.0644443	+	0.282349i	−0.996875	−	0.0790011i	$-0.974827\pi$
$137$	−0.754302	+	3.30481i	−0.0644443	+	0.282349i	0.932430	+	0.361350i	$0.117684\pi$
$138$		0			0
$139$	0.237631	+	1.04113i	0.0201556	+	0.0883074i	0.984005	−	0.178139i	$-0.0570076\pi$
$139$	0.237631	+	1.04113i	0.0201556	+	0.0883074i	−0.963850	+	0.266446i	$0.914150\pi$
$140$	−9.41663	−	9.84281i	−0.795850	−	0.831869i
$141$		0			0
$142$	−4.72819	−	20.7155i	−0.396781	−	1.73841i
$143$	−6.35797	−	7.97265i	−0.531680	−	0.666706i
$144$		0			0
$145$	9.00420	+	4.33619i	0.747758	+	0.360101i
$146$	12.2512			1.01391
$147$		0			0
$148$	−20.3925			−1.67625
$149$	18.9384	+	9.12026i	1.55150	+	0.747161i	0.996412	−	0.0846337i	$-0.0269720\pi$
$149$	18.9384	+	9.12026i	1.55150	+	0.747161i	0.555083	+	0.831795i	$0.312686\pi$
$150$		0			0
$151$	9.99499	+	12.5333i	0.813381	+	1.01995i	0.999301	+	0.0373828i	$0.0119021\pi$
$151$	9.99499	+	12.5333i	0.813381	+	1.01995i	−0.185920	+	0.982565i	$0.559526\pi$
$152$	4.33136	+	18.9769i	0.351320	+	1.53923i
$153$		0			0
$154$	26.0167	−	15.5553i	2.09648	−	1.25349i
$155$	−2.22195	−	9.73502i	−0.178472	−	0.781935i
$156$		0			0
$157$	0.190806	−	0.835975i	0.0152280	−	0.0667181i	−0.966743	−	0.255750i	$-0.917678\pi$
$157$	0.190806	−	0.835975i	0.0152280	−	0.0667181i	0.981971	+	0.189032i	$0.0605349\pi$
$158$	18.4990	+	8.90866i	1.47170	+	0.708735i
$159$		0			0
$160$	7.69965	+	3.70796i	0.608711	+	0.293140i
$161$	3.68791	−	2.20500i	0.290648	−	0.173779i
$162$		0			0
$163$	0.842710	−	3.69216i	0.0660062	−	0.289192i	−0.931142	−	0.364656i	$-0.881187\pi$
$163$	0.842710	−	3.69216i	0.0660062	−	0.289192i	0.997149	+	0.0754639i	$0.0240438\pi$
$164$	−16.1859	+	20.2965i	−1.26391	+	1.58489i
$165$		0			0
$166$	17.6972			1.37357
$167$	−12.0871	+	15.1568i	−0.935331	+	1.17287i	0.0493989	+	0.998779i	$0.484269\pi$
$167$	−12.0871	+	15.1568i	−0.935331	+	1.17287i	−0.984730	+	0.174089i	$0.944302\pi$
$168$		0			0
$169$	−5.49865	−	6.89509i	−0.422973	−	0.530392i
$170$	4.35568	+	5.46185i	0.334065	+	0.418904i
$171$		0			0
$172$	16.3853	−	7.89073i	1.24936	−	0.601662i
$173$	1.84382	+	2.31208i	0.140183	+	0.175784i	0.846967	−	0.531645i	$-0.178426\pi$
$173$	1.84382	+	2.31208i	0.140183	+	0.175784i	−0.706784	+	0.707430i	$0.749855\pi$
$174$		0			0
$175$	2.07235	+	6.37119i	0.156655	+	0.481617i
$176$	0.580897	−	0.728421i	0.0437867	−	0.0549068i
$177$		0			0
$178$	−2.54409			−0.190688
$179$	6.38129	−	8.00188i	0.476960	−	0.598089i	−0.483900	−	0.875123i	$-0.660780\pi$
$179$	6.38129	−	8.00188i	0.476960	−	0.598089i	0.960860	+	0.277034i	$0.0893516\pi$
$180$		0			0
$181$	−21.0794	+	10.1513i	−1.56682	+	0.754540i	−0.997704	−	0.0677188i	$-0.978428\pi$
$181$	−21.0794	+	10.1513i	−1.56682	+	0.754540i	−0.569114	+	0.822259i	$0.692714\pi$
$182$	−10.6666	+	6.37756i	−0.790661	+	0.472736i
$183$		0			0
$184$	2.97158	−	3.72625i	0.219068	−	0.274702i
$185$	−8.80626	−	4.24087i	−0.647449	−	0.311795i
$186$		0			0
$187$	−8.69826	+	4.18886i	−0.636080	+	0.306320i
$188$	0.111782	+	0.489749i	0.00815254	+	0.0357186i
$189$		0			0
$190$	−5.32631	+	23.3361i	−0.386411	+	1.69298i
$191$	−0.620056	−	2.71664i	−0.0448657	−	0.196569i	0.947528	−	0.319672i	$-0.103573\pi$
$191$	−0.620056	−	2.71664i	−0.0448657	−	0.196569i	−0.992394	+	0.123103i	$0.960716\pi$
$192$		0			0
$193$	1.92406	+	8.42986i	0.138497	+	0.606795i	0.995766	+	0.0919259i	$0.0293023\pi$
$193$	1.92406	+	8.42986i	0.138497	+	0.606795i	−0.857269	+	0.514869i	$0.827841\pi$
$194$	−31.9480	−	15.3854i	−2.29373	−	1.10460i
$195$		0			0
$196$	−9.03015	−	21.0903i	−0.645011	−	1.50645i
$197$	13.1270			0.935259			0.467629	−	0.883925i	$-0.345108\pi$
$197$	13.1270			0.935259			0.467629	+	0.883925i	$0.345108\pi$
$198$		0			0
$199$	−4.80460	−	21.0503i	−0.340589	−	1.49222i	−0.797834	−	0.602877i	$-0.794021\pi$
$199$	−4.80460	−	21.0503i	−0.340589	−	1.49222i	0.457246	−	0.889340i	$-0.348836\pi$
$200$	4.63338	+	5.81008i	0.327630	+	0.410835i
$201$		0			0
$202$	3.91879	−	17.1693i	0.275725	−	1.20803i
$203$	11.6358	+	12.1624i	0.816672	+	0.853634i
$204$		0			0
$205$	−11.2106	+	5.39875i	−0.782983	+	0.377065i
$206$	5.78693	−	25.3542i	0.403194	−	1.76651i
$207$		0			0
$208$	−0.238163	+	0.298646i	−0.0165136	+	0.0207074i
$209$	−29.8031	−	14.3524i	−2.06152	−	0.992778i
$210$		0			0
$211$	−6.25590	+	3.01268i	−0.430674	+	0.207402i	−0.636646	−	0.771156i	$-0.719679\pi$
$211$	−6.25590	+	3.01268i	−0.430674	+	0.207402i	0.205972	+	0.978558i	$0.433964\pi$
$212$	2.86363	−	12.5464i	0.196675	−	0.861690i
$213$		0			0
$214$	−40.2768			−2.75326
$215$	8.71677			0.594479
$216$		0			0
$217$	2.25223	−	16.6661i	0.152892	−	1.13137i
$218$	5.01490	+	6.28848i	0.339652	+	0.425910i
$219$		0			0
$220$	23.1341	−	11.1408i	1.55970	−	0.751113i
$221$	3.56621	−	1.71740i	0.239889	−	0.115525i
$222$		0			0
$223$	0.905061	+	1.13491i	0.0606073	+	0.0759992i	0.811211	−	0.584753i	$-0.198809\pi$
$223$	0.905061	+	1.13491i	0.0606073	+	0.0759992i	−0.750604	+	0.660753i	$0.770237\pi$
$224$	9.94998	+	10.4003i	0.664811	+	0.694899i
$225$		0			0
$226$	−28.1633			−1.87340
$227$	−6.73983			−0.447338			−0.223669	−	0.974665i	$-0.571804\pi$
$227$	−6.73983			−0.447338			−0.223669	+	0.974665i	$0.571804\pi$
$228$		0			0
$229$	0.664901	−	2.91312i	0.0439379	−	0.192504i	−0.948196	−	0.317686i	$-0.897094\pi$
$229$	0.664901	−	2.91312i	0.0439379	−	0.192504i	0.992134	+	0.125182i	$0.0399514\pi$
$230$	5.28044	−	2.54293i	0.348182	−	0.167676i
$231$		0			0
$232$	16.8211	+	8.10063i	1.10436	+	0.531832i
$233$	1.74903	−	2.19321i	0.114583	−	0.143682i	−0.721233	−	0.692693i	$-0.756424\pi$
$233$	1.74903	−	2.19321i	0.114583	−	0.143682i	0.835815	+	0.549011i	$0.184995\pi$
$234$		0			0
$235$	−0.0535777	+	0.234739i	−0.00349502	+	0.0153127i
$236$	−31.0270	+	14.9418i	−2.01968	+	0.972628i
$237$		0			0
$238$	3.63940	+	11.1889i	0.235907	+	0.725270i
$239$	2.92146	−	12.7998i	0.188974	−	0.827948i	−0.788185	−	0.615438i	$-0.788979\pi$
$239$	2.92146	−	12.7998i	0.188974	−	0.827948i	0.977159	−	0.212510i	$-0.0681637\pi$
$240$		0			0
$241$	0.635232	+	0.796555i	0.0409189	+	0.0513106i	0.801870	−	0.597499i	$-0.203839\pi$
$241$	0.635232	+	0.796555i	0.0409189	+	0.0513106i	−0.760951	+	0.648809i	$0.775267\pi$
$242$	7.09136	+	31.0693i	0.455850	+	1.99721i
$243$		0			0
$244$	27.0432			1.73126
$245$	0.486426	−	10.9855i	0.0310766	−	0.701841i
$246$		0			0
$247$	12.2190	+	5.88437i	0.777477	+	0.374413i
$248$	−4.15093	−	18.1864i	−0.263584	−	1.15484i
$249$		0			0
$250$	6.04864	+	26.5008i	0.382550	+	1.67606i
$251$	−5.23743	+	22.9467i	−0.330584	+	1.44838i	0.487419	+	0.873168i	$0.337939\pi$
$251$	−5.23743	+	22.9467i	−0.330584	+	1.44838i	−0.818003	+	0.575215i	$0.804919\pi$
$252$		0			0
$253$	1.80230	+	7.89640i	0.113310	+	0.496442i
$254$	−2.10755	+	1.01494i	−0.132240	+	0.0636832i
$255$		0			0
$256$	15.4873	+	7.45831i	0.967959	+	0.466145i
$257$	6.24023	−	7.82500i	0.389255	−	0.488110i	−0.548136	−	0.836389i	$-0.684662\pi$
$257$	6.24023	−	7.82500i	0.389255	−	0.488110i	0.937391	+	0.348279i	$0.113234\pi$
$258$		0			0
$259$	−11.3800	−	11.8950i	−0.707119	−	0.739122i
$260$	−9.48479	+	4.56763i	−0.588222	+	0.283273i
$261$		0			0
$262$	−19.0695	+	23.9123i	−1.17812	+	1.47731i
$263$	−21.4916			−1.32523			−0.662613	−	0.748962i	$-0.730553\pi$
$263$	−21.4916			−1.32523			−0.662613	+	0.748962i	$0.730553\pi$
$264$		0			0
$265$	3.84581	−	4.82249i	0.236246	−	0.296243i
$266$	−22.1983	+	33.6520i	−1.36106	+	2.06333i
$267$		0			0
$268$	−31.7387	−	39.7991i	−1.93875	−	2.43112i
$269$	7.91070	−	3.80959i	0.482324	−	0.232275i	−0.176890	−	0.984231i	$-0.556604\pi$
$269$	7.91070	−	3.80959i	0.482324	−	0.232275i	0.659214	+	0.751956i	$0.270889\pi$
$270$		0			0
$271$	5.31614	+	6.66623i	0.322932	+	0.404944i	0.916625	−	0.399747i	$-0.130902\pi$
$271$	5.31614	+	6.66623i	0.322932	+	0.404944i	−0.593693	+	0.804692i	$0.702331\pi$
$272$	0.225479	+	0.282742i	0.0136717	+	0.0171438i
$273$		0			0
$274$	−4.85530	+	6.08835i	−0.293319	+	0.367811i
$275$	−12.6290			−0.761554
$276$		0			0
$277$	17.1470	−	21.5017i	1.03026	−	1.29191i	0.0746739	−	0.997208i	$-0.476208\pi$
$277$	17.1470	−	21.5017i	1.03026	−	1.29191i	0.955589	−	0.294701i	$-0.0952202\pi$
$278$	−0.545903	+	2.39176i	−0.0327411	+	0.143448i
$279$		0			0
$280$	−3.77277	−	11.5990i	−0.225466	−	0.693170i
$281$	11.0825	+	5.33707i	0.661129	+	0.318383i	0.734190	−	0.678945i	$-0.237562\pi$
$281$	11.0825	+	5.33707i	0.661129	+	0.318383i	−0.0730605	+	0.997328i	$0.523277\pi$
$282$		0			0
$283$	27.9732	+	13.4712i	1.66283	+	0.800778i	0.998580	+	0.0532703i	$0.0169645\pi$
$283$	27.9732	+	13.4712i	1.66283	+	0.800778i	0.664253	+	0.747508i	$0.268750\pi$
$284$	6.74558	−	29.5543i	0.400277	−	1.75373i
$285$		0			0
$286$	−5.21282	−	22.8389i	−0.308240	−	1.35049i
$287$	−20.8716	+	1.88511i	−1.23201	+	0.111274i
$288$		0			0
$289$	2.94898	+	12.9203i	0.173469	+	0.760019i
$290$	14.3145	+	17.9498i	0.840578	+	1.05405i
$291$		0			0
$292$	15.7475	+	7.58360i	0.921553	+	0.443796i
$293$	8.47409			0.495062			0.247531	−	0.968880i	$-0.420381\pi$
$293$	8.47409			0.495062			0.247531	+	0.968880i	$0.420381\pi$
$294$		0			0
$295$	−16.5060			−0.961015
$296$	−16.4514	−	7.92255i	−0.956215	−	0.460489i
$297$		0			0
$298$	30.1076	+	37.7537i	1.74408	+	2.18701i
$299$	−0.738928	−	3.23746i	−0.0427333	−	0.187227i
$300$		0			0
$301$	13.7465	+	5.15420i	0.792334	+	0.297083i
$302$	8.19476	+	35.9036i	0.471556	+	2.06602i
$303$		0			0
$304$	−0.275726	+	1.20803i	−0.0158140	+	0.0692855i
$305$	11.6783	+	5.62397i	0.668697	+	0.322027i
$306$		0			0
$307$	−25.2380	−	12.1540i	−1.44041	−	0.693665i	−0.459510	−	0.888173i	$-0.651975\pi$
$307$	−25.2380	−	12.1540i	−1.44041	−	0.693665i	−0.980901	+	0.194507i	$0.937689\pi$
$308$	43.0704	−	3.89009i	2.45417	−	0.221658i
$309$		0			0
$310$	5.10443	−	22.3640i	0.289912	−	1.27019i
$311$	15.6980	−	19.6846i	0.890150	−	1.11621i	−0.102445	−	0.994739i	$-0.532667\pi$
$311$	15.6980	−	19.6846i	0.890150	−	1.11621i	0.992595	−	0.121474i	$-0.0387620\pi$
$312$		0			0
$313$	10.8336			0.612353			0.306177	−	0.951975i	$-0.400950\pi$
$313$	10.8336			0.612353			0.306177	+	0.951975i	$0.400950\pi$
$314$	1.22818	−	1.54009i	0.0693103	−	0.0869124i
$315$		0			0
$316$	18.2639	+	22.9022i	1.02742	+	1.28835i
$317$	16.6493	+	20.8776i	0.935118	+	1.17260i	0.984775	+	0.173835i	$0.0556158\pi$
$317$	16.6493	+	20.8776i	0.935118	+	1.17260i	−0.0496567	+	0.998766i	$0.515813\pi$
$318$		0			0
$319$	−28.5860	+	13.7663i	−1.60051	+	0.770765i
$320$	12.6066	+	15.8081i	0.704728	+	0.883701i
$321$		0			0
$322$	9.83097	−	0.887926i	0.547859	−	0.0494822i
$323$	8.00551	−	10.0386i	0.445438	−	0.558562i
$324$		0			0
$325$	5.17776			0.287210
$326$	5.42437	−	6.80194i	0.300428	−	0.376725i
$327$		0			0
$328$	−20.9430	+	10.0856i	−1.15639	+	0.556886i
$329$	−0.223293	+	0.338507i	−0.0123106	+	0.0186625i
$330$		0			0
$331$	−15.2046	+	19.0660i	−0.835720	+	1.04796i	0.162403	+	0.986724i	$0.448075\pi$
$331$	−15.2046	+	19.0660i	−0.835720	+	1.04796i	−0.998123	+	0.0612355i	$0.980496\pi$
$332$	22.7478	+	10.9547i	1.24845	+	0.601220i
$333$		0			0
$334$	−40.1251	+	19.3232i	−2.19555	+	1.05732i
$335$	−5.42929	−	23.7873i	−0.296634	−	1.29964i
$336$		0			0
$337$	2.16074	−	9.46681i	0.117703	−	0.515690i	−0.881362	−	0.472442i	$-0.843372\pi$
$337$	2.16074	−	9.46681i	0.117703	−	0.515690i	0.999064	−	0.0432474i	$-0.0137704\pi$
$338$	−4.50827	−	19.7520i	−0.245218	−	1.07437i
$339$		0			0
$340$	2.21780	+	9.71681i	0.120277	+	0.526968i
$341$	28.5616	+	13.7545i	1.54670	+	0.744850i
$342$		0			0
$343$	7.26283	−	17.0368i	0.392156	−	0.919899i
$344$	16.2842			0.877984
$345$		0			0
$346$	1.51172	+	6.62330i	0.0812708	+	0.356071i
$347$	−2.71489	−	3.40436i	−0.145743	−	0.182756i	0.703602	−	0.710594i	$-0.251574\pi$
$347$	−2.71489	−	3.40436i	−0.145743	−	0.182756i	−0.849345	+	0.527839i	$0.823002\pi$
$348$		0			0
$349$	−1.27027	+	5.56541i	−0.0679959	+	0.297909i	−0.997480	−	0.0709537i	$-0.977396\pi$
$349$	−1.27027	+	5.56541i	−0.0679959	+	0.297909i	0.929484	+	0.368863i	$0.120253\pi$
$350$	−2.06120	+	15.2525i	−0.110176	+	0.815281i
$351$		0			0
$352$	−24.4444	+	11.7718i	−1.30289	+	0.627440i
$353$	−1.48524	+	6.50726i	−0.0790513	+	0.346346i	−0.998950	−	0.0458092i	$-0.985413\pi$
$353$	−1.48524	+	6.50726i	−0.0790513	+	0.346346i	0.919899	+	0.392156i	$0.128271\pi$
$354$		0			0
$355$	9.05919	−	11.3599i	0.480812	−	0.602919i
$356$	−3.27014	−	1.57482i	−0.173317	−	0.0834652i
$357$		0			0
$358$	21.1837	−	10.2015i	1.11959	−	0.539167i
$359$	4.51541	−	19.7833i	0.238314	−	1.04412i	−0.704211	−	0.709990i	$-0.748699\pi$
$359$	4.51541	−	19.7833i	0.238314	−	1.04412i	0.942526	−	0.334133i	$-0.108444\pi$
$360$		0			0
$361$	24.9935			1.31545
$362$	−53.7478			−2.82492
$363$		0			0
$364$	−17.6585	+	1.59490i	−0.925557	+	0.0835956i
$365$	5.22327	+	6.54978i	0.273399	+	0.342831i
$366$		0			0
$367$	2.04223	−	0.983484i	0.106603	−	0.0513375i	−0.379822	−	0.925060i	$-0.624015\pi$
$367$	2.04223	−	0.983484i	0.106603	−	0.0513375i	0.486425	+	0.873722i	$0.338301\pi$
$368$	0.273351	−	0.131639i	0.0142494	−	0.00686216i
$369$		0			0
$370$	−13.9999	−	17.5553i	−0.727818	−	0.912654i
$371$	8.91643	−	5.33113i	0.462918	−	0.276778i
$372$		0			0
$373$	−17.5522			−0.908816			−0.454408	−	0.890794i	$-0.650149\pi$
$373$	−17.5522			−0.908816			−0.454408	+	0.890794i	$0.650149\pi$
$374$	−22.1786			−1.14683
$375$		0			0
$376$	−0.100091	+	0.438526i	−0.00516179	+	0.0226153i
$377$	11.7200	−	5.64406i	0.603611	−	0.290684i
$378$		0			0
$379$	8.85837	+	4.26596i	0.455024	+	0.219128i	0.647334	−	0.762206i	$-0.275884\pi$
$379$	8.85837	+	4.26596i	0.455024	+	0.219128i	−0.192311	+	0.981334i	$0.561598\pi$
$380$	−21.2917	+	26.6989i	−1.09224	+	1.36963i
$381$		0			0
$382$	1.42444	−	6.24086i	0.0728805	−	0.319310i
$383$	−15.6719	+	7.54718i	−0.800795	+	0.385643i	−0.789081	−	0.614289i	$-0.789443\pi$
$383$	−15.6719	+	7.54718i	−0.800795	+	0.385643i	−0.0117140	+	0.999931i	$0.503729\pi$
$384$		0			0
$385$	19.4085	+	7.27715i	0.989147	+	0.370878i
$386$	−4.42009	+	19.3657i	−0.224977	+	0.985688i
$387$		0			0
$388$	−31.5419	−	39.5523i	−1.60130	−	2.00797i
$389$	1.11030	+	4.86455i	0.0562945	+	0.246642i	0.995244	−	0.0974124i	$-0.0310566\pi$
$389$	1.11030	+	4.86455i	0.0562945	+	0.246642i	−0.938950	+	0.344055i	$0.888199\pi$
$390$		0			0
$391$	−3.14387			−0.158992
$392$	0.908714	−	20.5226i	0.0458970	−	1.03655i
$393$		0			0
$394$	27.1698	+	13.0843i	1.36880	+	0.659178i
$395$	3.12425	+	13.6882i	0.157198	+	0.688731i
$396$		0			0
$397$	0.738295	+	3.23468i	0.0370540	+	0.162344i	0.990070	−	0.140576i	$-0.0448955\pi$
$397$	0.738295	+	3.23468i	0.0370540	+	0.162344i	−0.953016	+	0.302920i	$0.902038\pi$
$398$	11.0375	−	48.3583i	0.553258	−	2.42398i
$399$		0			0
$400$	0.105267	+	0.461206i	0.00526336	+	0.0230603i
$401$	−12.8234	+	6.17544i	−0.640372	+	0.308387i	−0.725747	−	0.687962i	$-0.758505\pi$
$401$	−12.8234	+	6.17544i	−0.640372	+	0.308387i	0.0853750	+	0.996349i	$0.472791\pi$
$402$		0			0
$403$	−11.7100	−	5.63924i	−0.583317	−	0.280911i
$404$	15.6652	−	19.6435i	0.779371	−	0.977300i
$405$		0			0
$406$	11.9605	+	36.7714i	0.593592	+	1.82493i
$407$	27.9576	−	13.4637i	1.38581	−	0.667369i
$408$		0			0
$409$	−3.49663	+	4.38464i	−0.172897	+	0.216806i	−0.860728	−	0.509064i	$-0.829992\pi$
$409$	−3.49663	+	4.38464i	−0.172897	+	0.216806i	0.687831	+	0.725871i	$0.258563\pi$
$410$	−28.5846			−1.41169
$411$		0			0
$412$	23.1330	−	29.0078i	1.13968	−	1.42911i
$413$	−26.0302	−	9.75995i	−1.28086	−	0.480256i
$414$		0			0
$415$	7.54518	+	9.46136i	0.370379	+	0.464440i
$416$	10.0220	−	4.82634i	0.491369	−	0.236631i
$417$		0			0
$418$	−47.3798	−	59.4124i	−2.31742	−	2.90596i
$419$	−17.1005	−	21.4434i	−0.835417	−	1.04758i	−0.998143	−	0.0609080i	$-0.980600\pi$
$419$	−17.1005	−	21.4434i	−0.835417	−	1.04758i	0.162727	−	0.986671i	$-0.447971\pi$
$420$		0			0
$421$	13.1728	−	16.5181i	0.642002	−	0.805045i	−0.349250	−	0.937030i	$-0.613563\pi$
$421$	13.1728	−	16.5181i	0.642002	−	0.805045i	0.991252	+	0.131984i	$0.0421349\pi$
$422$	−15.9512			−0.776490
$423$		0			0
$424$	7.18452	−	9.00910i	0.348911	−	0.437521i
$425$	1.09080	−	4.77912i	0.0529117	−	0.231821i
$426$		0			0
$427$	15.0914	+	15.7744i	0.730325	+	0.763379i
$428$	−51.7713	−	24.9317i	−2.50246	−	1.20512i
$429$		0			0
$430$	18.0417	+	8.68843i	0.870048	+	0.418993i
$431$	5.33413	−	23.3704i	0.256936	−	1.12571i	−0.667571	−	0.744546i	$-0.732666\pi$
$431$	5.33413	−	23.3704i	0.256936	−	1.12571i	0.924507	−	0.381164i	$-0.124477\pi$
$432$		0			0
$433$	0.210679	+	0.923044i	0.0101246	+	0.0443587i	0.979738	−	0.200284i	$-0.0641865\pi$
$433$	0.210679	+	0.923044i	0.0101246	+	0.0443587i	−0.969613	+	0.244643i	$0.921329\pi$
$434$	21.2735	−	32.2501i	1.02116	−	1.54806i
$435$		0			0
$436$	2.55346	+	11.1874i	0.122288	+	0.535780i
$437$	−6.71619	−	8.42184i	−0.321279	−	0.402871i
$438$		0			0
$439$	−1.10279	−	0.531075i	−0.0526332	−	0.0253468i	0.407382	−	0.913258i	$-0.366442\pi$
$439$	−1.10279	−	0.531075i	−0.0526332	−	0.0253468i	−0.460015	+	0.887911i	$0.652156\pi$
$440$	22.9914			1.09607
$441$		0			0
$442$	9.09305			0.432512
$443$	−1.97912	−	0.953096i	−0.0940310	−	0.0452829i	0.386277	−	0.922383i	$-0.373761\pi$
$443$	−1.97912	−	0.953096i	−0.0940310	−	0.0452829i	−0.480308	+	0.877100i	$0.659475\pi$
$444$		0			0
$445$	−1.08467	−	1.36013i	−0.0514183	−	0.0644766i
$446$	0.742047	+	3.25112i	0.0351370	+	0.153945i
$447$		0			0
$448$	10.5335	+	32.3839i	0.497659	+	1.53000i
$449$	1.63742	+	7.17402i	0.0772748	+	0.338563i	0.998756	−	0.0498594i	$-0.0158773\pi$
$449$	1.63742	+	7.17402i	0.0772748	+	0.338563i	−0.921481	+	0.388422i	$0.873020\pi$
$450$		0			0
$451$	8.79021	−	38.5124i	0.413915	−	1.81348i
$452$	−36.2009	−	17.4334i	−1.70274	−	0.819999i
$453$		0			0
$454$	−13.9499	−	6.71792i	−0.654702	−	0.315288i
$455$	−7.95731	−	2.98357i	−0.373044	−	0.139872i
$456$		0			0
$457$	3.61569	−	15.8414i	0.169135	−	0.741027i	−0.817211	−	0.576339i	$-0.804481\pi$
$457$	3.61569	−	15.8414i	0.169135	−	0.741027i	0.986346	−	0.164689i	$-0.0526619\pi$
$458$	4.27984	−	5.36675i	0.199984	−	0.250772i
$459$		0			0
$460$	8.36152			0.389858
$461$	10.4171	−	13.0626i	0.485173	−	0.608388i	−0.477640	−	0.878556i	$-0.658508\pi$
$461$	10.4171	−	13.0626i	0.485173	−	0.608388i	0.962813	+	0.270168i	$0.0870792\pi$
$462$		0			0
$463$	1.04928	+	1.31575i	0.0487641	+	0.0611482i	0.805615	−	0.592439i	$-0.201835\pi$
$463$	1.04928	+	1.31575i	0.0487641	+	0.0611482i	−0.756851	+	0.653587i	$0.773263\pi$
$464$	0.741016	+	0.929205i	0.0344008	+	0.0431373i
$465$		0			0
$466$	5.80617	−	2.79610i	0.268965	−	0.129527i
$467$	8.10328	+	10.1612i	0.374975	+	0.470204i	0.933133	−	0.359531i	$-0.117063\pi$
$467$	8.10328	+	10.1612i	0.374975	+	0.470204i	−0.558158	+	0.829735i	$0.688492\pi$
$468$		0			0
$469$	5.50327	−	40.7232i	0.254117	−	1.88042i
$470$	−0.344869	+	0.432452i	−0.0159076	+	0.0199475i
$471$		0			0
$472$	−30.8355			−1.41932
$473$	−17.2541	+	21.6360i	−0.793346	+	0.994825i
$474$		0			0
$475$	15.1326	−	7.28749i	0.694332	−	0.334373i
$476$	−2.24802	+	16.6349i	−0.103038	+	0.762462i
$477$		0			0
$478$	18.8049	−	23.5806i	0.860116	−	1.07855i
$479$	−19.7464	−	9.50939i	−0.902238	−	0.434495i	−0.0755413	−	0.997143i	$-0.524068\pi$
$479$	−19.7464	−	9.50939i	−0.902238	−	0.434495i	−0.826697	+	0.562648i	$0.809783\pi$
$480$		0			0
$481$	−11.4624	+	5.51999i	−0.522639	+	0.251690i
$482$	0.520818	+	2.28185i	0.0237226	+	0.103936i
$483$		0			0
$484$	−10.1171	+	44.3257i	−0.459866	+	2.01481i
$485$	−5.39562	−	23.6398i	−0.245003	−	1.07343i
$486$		0			0
$487$	−7.02025	−	30.7577i	−0.318118	−	1.39377i	−0.840850	−	0.541269i	$-0.817944\pi$
$487$	−7.02025	−	30.7577i	−0.318118	−	1.39377i	0.522732	−	0.852497i	$-0.324913\pi$
$488$	21.8167	+	10.5064i	0.987597	+	0.475601i
$489$		0			0
$490$	11.9566	−	22.2527i	0.540145	−	1.00527i
$491$	−8.99979			−0.406155			−0.203077	−	0.979163i	$-0.565094\pi$
$491$	−8.99979			−0.406155			−0.203077	+	0.979163i	$0.565094\pi$
$492$		0			0
$493$	−2.74045	−	12.0067i	−0.123424	−	0.540755i
$494$	19.4253	+	24.3586i	0.873986	+	1.09594i
$495$		0			0
$496$	0.264240	−	1.15771i	0.0118647	−	0.0519827i
$497$	21.0036	−	12.5580i	0.942139	−	0.563304i
$498$		0			0
$499$	8.54514	−	4.11512i	0.382533	−	0.184218i	−0.232728	−	0.972542i	$-0.574765\pi$
$499$	8.54514	−	4.11512i	0.382533	−	0.184218i	0.615261	+	0.788324i	$0.289051\pi$
$500$	−8.62944	+	37.8081i	−0.385920	+	1.69083i
$501$		0			0
$502$	−33.7124	+	42.2740i	−1.50466	+	1.88678i
$503$	−2.01166	−	0.968763i	−0.0896953	−	0.0431950i	0.388498	−	0.921449i	$-0.372994\pi$
$503$	−2.01166	−	0.968763i	−0.0896953	−	0.0431950i	−0.478194	+	0.878254i	$0.658708\pi$
$504$		0			0
$505$	10.8499	−	5.22505i	0.482815	−	0.232512i
$506$	−4.14038	+	18.1402i	−0.184062	+	0.806429i
$507$		0			0
$508$	−3.33728			−0.148068
$509$	30.2034			1.33874			0.669372	−	0.742928i	$-0.266563\pi$
$509$	30.2034			1.33874			0.669372	+	0.742928i	$0.266563\pi$
$510$		0			0
$511$	4.36432	+	13.4176i	0.193066	+	0.593561i
$512$	1.31730	+	1.65184i	0.0582171	+	0.0730019i
$513$		0			0
$514$	20.7154	−	9.97602i	0.913718	−	0.440023i
$515$	16.0222	−	7.71591i	0.706024	−	0.340003i
$516$		0			0
$517$	−0.476596	−	0.597633i	−0.0209607	−	0.0262839i
$518$	−11.6976	−	35.9630i	−0.513964	−	1.58012i
$519$		0			0
$520$	−9.42627			−0.413369
$521$	−19.3686			−0.848552			−0.424276	−	0.905533i	$-0.639471\pi$
$521$	−19.3686			−0.848552			−0.424276	+	0.905533i	$0.639471\pi$
$522$		0			0
$523$	−8.82216	+	38.6524i	−0.385766	+	1.69015i	0.293257	+	0.956034i	$0.405261\pi$
$523$	−8.82216	+	38.6524i	−0.385766	+	1.69015i	−0.679023	+	0.734117i	$0.737596\pi$
$524$	−39.3137	+	18.9325i	−1.71743	+	0.827069i
$525$		0			0
$526$	−44.4826	−	21.4217i	−1.93953	−	0.934030i
$527$	−7.67202	+	9.62041i	−0.334198	+	0.419072i
$528$		0			0
$529$	4.53107	−	19.8519i	0.197003	−	0.863128i
$530$	12.7667	−	6.14814i	0.554552	−	0.267058i
$531$		0			0
$532$	−49.3643	+	29.5149i	−2.14021	+	1.27963i
$533$	−3.60391	+	15.7898i	−0.156103	+	0.683930i
$534$		0			0
$535$	−17.1720	−	21.5330i	−0.742409	−	0.930952i
$536$	−10.1427	−	44.4380i	−0.438097	−	1.91943i
$537$		0			0
$538$	20.1705			0.869614
$539$	26.3045	+	22.9524i	1.13302	+	0.988628i
$540$		0			0
$541$	−13.9084	−	6.69793i	−0.597969	−	0.287967i	0.110312	−	0.993897i	$-0.464815\pi$
$541$	−13.9084	−	6.69793i	−0.597969	−	0.287967i	−0.708281	+	0.705930i	$0.750529\pi$
$542$	4.35863	+	19.0964i	0.187219	+	0.820261i
$543$		0			0
$544$	−2.34341	−	10.2672i	−0.100473	−	0.440201i
$545$	−1.22388	+	5.36218i	−0.0524254	+	0.229691i
$546$		0			0
$547$	2.62241	+	11.4895i	0.112126	+	0.491256i	0.999541	+	0.0302855i	$0.00964164\pi$
$547$	2.62241	+	11.4895i	0.112126	+	0.491256i	−0.887415	+	0.460971i	$0.847501\pi$
$548$	−10.0097	+	4.82042i	−0.427593	+	0.205918i
$549$		0			0
$550$	−26.1390	−	12.5879i	−1.11457	−	0.536750i
$551$	26.3093	−	32.9909i	1.12082	−	1.40546i
$552$		0			0
$553$	−3.16683	+	23.4340i	−0.134667	+	0.996513i
$554$	56.9221	−	27.4122i	2.41839	−	1.16463i
$555$		0			0
$556$	−2.18222	+	2.73642i	−0.0925468	+	0.116050i
$557$	−5.03902			−0.213510			−0.106755	−	0.994285i	$-0.534046\pi$
$557$	−5.03902			−0.213510			−0.106755	+	0.994285i	$0.534046\pi$
$558$		0			0
$559$	7.07405	−	8.87057i	0.299200	−	0.375185i
$560$	0.103982	−	0.769449i	0.00439405	−	0.0325152i
$561$		0			0
$562$	17.6186	+	22.0930i	0.743196	+	0.931938i
$563$	9.92548	−	4.77986i	0.418309	−	0.201447i	−0.212876	−	0.977079i	$-0.568283\pi$
$563$	9.92548	−	4.77986i	0.418309	−	0.201447i	0.631185	+	0.775632i	$0.282569\pi$
$564$		0			0
$565$	−12.0074	−	15.0568i	−0.505156	−	0.633446i
$566$	44.4707	+	55.7645i	1.86924	+	2.34396i
$567$		0			0
$568$	16.9239	−	21.2219i	0.710110	−	0.890450i
$569$	2.99100			0.125389			0.0626946	−	0.998033i	$-0.480031\pi$
$569$	2.99100			0.125389			0.0626946	+	0.998033i	$0.480031\pi$
$570$		0			0
$571$	7.97618	−	10.0018i	0.333793	−	0.418563i	−0.586404	−	0.810019i	$-0.699457\pi$
$571$	7.97618	−	10.0018i	0.333793	−	0.418563i	0.920197	+	0.391456i	$0.128028\pi$
$572$	7.43699	−	32.5836i	0.310956	−	1.36239i
$573$		0			0
$574$	−45.0784	−	16.9020i	−1.88154	−	0.705476i
$575$	−3.70526	−	1.78436i	−0.154520	−	0.0744130i
$576$		0			0
$577$	17.2094	+	8.28761i	0.716437	+	0.345018i	0.756334	−	0.654186i	$-0.226989\pi$
$577$	17.2094	+	8.28761i	0.716437	+	0.345018i	−0.0398970	+	0.999204i	$0.512703\pi$
$578$	−6.77461	+	29.6815i	−0.281787	+	1.23459i
$579$		0			0
$580$	7.28858	+	31.9334i	0.302642	+	1.32596i
$581$	6.30440	+	19.3822i	0.261551	+	0.804108i
$582$		0			0
$583$	4.35750	+	19.0915i	0.180469	+	0.790687i
$584$	9.75783	+	12.2359i	0.403782	+	0.506326i
$585$		0			0
$586$	17.5394	+	8.44654i	0.724547	+	0.348923i
$587$	−0.124741			−0.00514863			−0.00257431	−	0.999997i	$-0.500819\pi$
$587$	−0.124741			−0.00514863			−0.00257431	+	0.999997i	$0.500819\pi$
$588$		0			0
$589$	−42.1609			−1.73721
$590$	−34.1636	−	16.4523i	−1.40649	−	0.677331i
$591$		0			0
$592$	−0.724727	−	0.908779i	−0.0297861	−	0.0373506i
$593$	5.49188	+	24.0615i	0.225525	+	0.988088i	0.953241	+	0.302210i	$0.0977244\pi$
$593$	5.49188	+	24.0615i	0.225525	+	0.988088i	−0.727717	+	0.685878i	$0.759418\pi$
$594$		0			0
$595$	−4.43023	+	6.71611i	−0.181622	+	0.275334i
$596$	15.3300	+	67.1651i	0.627941	+	2.75119i
$597$		0			0
$598$	1.69752	−	7.43731i	0.0694167	−	0.304134i
$599$	18.3688	+	8.84594i	0.750528	+	0.361435i	0.769721	−	0.638380i	$-0.220395\pi$
$599$	18.3688	+	8.84594i	0.750528	+	0.361435i	−0.0191928	+	0.999816i	$0.506110\pi$
$600$		0			0
$601$	19.9569	+	9.61076i	0.814061	+	0.392031i	0.794113	−	0.607770i	$-0.207936\pi$
$601$	19.9569	+	9.61076i	0.814061	+	0.392031i	0.0199478	+	0.999801i	$0.493650\pi$
$602$	23.3146	+	24.3698i	0.950233	+	0.993239i
$603$		0			0
$604$	−11.6913	+	51.2227i	−0.475711	+	2.08422i
$605$	−13.5870	+	17.0376i	−0.552391	+	0.692677i
$606$		0			0
$607$	10.3803			0.421325			0.210663	−	0.977559i	$-0.432438\pi$
$607$	10.3803			0.421325			0.210663	+	0.977559i	$0.432438\pi$
$608$	22.4976	−	28.2111i	0.912398	−	1.14411i
$609$		0			0
$610$	18.5657	+	23.2806i	0.751703	+	0.942606i
$611$	0.195400	+	0.245024i	0.00790505	+	0.00991262i
$612$		0			0
$613$	−20.4376	+	9.84224i	−0.825467	+	0.397524i	−0.798413	−	0.602110i	$-0.794327\pi$
$613$	−20.4376	+	9.84224i	−0.825467	+	0.397524i	−0.0270541	+	0.999634i	$0.508613\pi$
$614$	−40.1225	−	50.3120i	−1.61921	−	2.03043i
$615$		0			0
$616$	36.2578	+	13.5948i	1.46087	+	0.547748i
$617$	0.440020	−	0.551767i	0.0177145	−	0.0222133i	−0.772895	−	0.634534i	$-0.781192\pi$
$617$	0.440020	−	0.551767i	0.0177145	−	0.0222133i	0.790610	+	0.612320i	$0.209764\pi$
$618$		0			0
$619$	−11.7990			−0.474243			−0.237122	−	0.971480i	$-0.576204\pi$
$619$	−11.7990			−0.474243			−0.237122	+	0.971480i	$0.576204\pi$
$620$	20.4047	−	25.5867i	0.819473	−	1.02759i
$621$		0			0
$622$	52.1118	−	25.0957i	2.08949	−	1.00625i
$623$	−0.906300	−	2.78632i	−0.0363102	−	0.111631i
$624$		0			0
$625$	−3.69496	+	4.63334i	−0.147799	+	0.185333i
$626$	22.4231	+	10.7984i	0.896209	+	0.431592i
$627$		0			0
$628$	2.53202	−	1.21936i	0.101039	−	0.0486577i
$629$	2.68021	+	11.7428i	0.106867	+	0.468215i
$630$		0			0
$631$	3.85749	−	16.9008i	0.153564	−	0.672809i	−0.838268	−	0.545259i	$-0.816431\pi$
$631$	3.85749	−	16.9008i	0.153564	−	0.672809i	0.991832	−	0.127550i	$-0.0407114\pi$
$632$	5.83655	+	25.5716i	0.232166	+	1.01718i
$633$		0			0
$634$	13.6505	+	59.8069i	0.542132	+	2.37524i
$635$	−1.44117	−	0.694030i	−0.0571910	−	0.0275417i
$636$		0			0
$637$	−10.7846	−	9.41027i	−0.427303	−	0.372848i
$638$	−72.8880			−2.88566
$639$		0			0
$640$	6.53264	+	28.6214i	0.258225	+	1.13136i
$641$	5.54815	+	6.95716i	0.219139	+	0.274791i	0.879234	−	0.476391i	$-0.158055\pi$
$641$	5.54815	+	6.95716i	0.219139	+	0.274791i	−0.660095	+	0.751182i	$0.729484\pi$
$642$		0			0
$643$	−9.71297	+	42.5553i	−0.383042	+	1.67822i	0.304846	+	0.952402i	$0.401395\pi$
$643$	−9.71297	+	42.5553i	−0.383042	+	1.67822i	−0.687889	+	0.725816i	$0.741462\pi$
$644$	13.1863	+	4.94415i	0.519611	+	0.194827i
$645$		0			0
$646$	26.5755	−	12.7981i	1.04560	−	0.503534i
$647$	−3.89226	+	17.0531i	−0.153020	+	0.670426i	0.838977	+	0.544167i	$0.183154\pi$
$647$	−3.89226	+	17.0531i	−0.153020	+	0.670426i	−0.991997	+	0.126259i	$0.959703\pi$
$648$		0			0
$649$	32.6723	−	40.9697i	1.28250	−	1.60820i
$650$	10.7168	+	5.16093i	0.420347	+	0.202428i
$651$		0			0
$652$	11.1829	−	5.38540i	0.437956	−	0.210909i
$653$	−5.64841	+	24.7473i	−0.221039	+	0.968436i	0.735658	+	0.677353i	$0.236873\pi$
$653$	−5.64841	+	24.7473i	−0.221039	+	0.968436i	−0.956698	+	0.291083i	$0.905984\pi$
$654$		0			0
$655$	−20.9144			−0.817193
$656$	−1.47973			−0.0577738
$657$		0			0
$658$	−0.799573	+	0.478064i	−0.0311706	+	0.0186369i
$659$	15.7614	+	19.7642i	0.613978	+	0.769904i	0.987483	−	0.157724i	$-0.0504157\pi$
$659$	15.7614	+	19.7642i	0.613978	+	0.769904i	−0.373505	+	0.927628i	$0.621844\pi$
$660$		0			0
$661$	−26.7045	+	12.8602i	−1.03869	+	0.500205i	−0.873891	−	0.486123i	$-0.838411\pi$
$661$	−26.7045	+	12.8602i	−1.03869	+	0.500205i	−0.164796	+	0.986328i	$0.552696\pi$
$662$	−50.4740	+	24.3070i	−1.96173	+	0.944718i
$663$		0			0
$664$	14.0955	+	17.6752i	0.547011	+	0.685930i
$665$	−27.4554	+	2.47975i	−1.06468	+	0.0961606i
$666$		0			0
$667$	−10.3320			−0.400058
$668$	−63.5377			−2.45835
$669$		0			0
$670$	12.4725	−	54.6458i	0.481856	−	2.11115i
$671$	−37.0756	+	17.8547i	−1.43129	+	0.689271i
$672$		0			0
$673$	−2.95923	−	1.42509i	−0.114070	−	0.0549331i	0.375979	−	0.926628i	$-0.377307\pi$
$673$	−2.95923	−	1.42509i	−0.114070	−	0.0549331i	−0.490048	+	0.871695i	$0.663021\pi$
$674$	13.9083	−	17.4404i	0.535726	−	0.671779i
$675$		0			0
$676$	6.43184	−	28.1797i	0.247378	−	1.08384i
$677$	−16.6001	+	7.99418i	−0.637993	+	0.307241i	−0.724775	−	0.688986i	$-0.758056\pi$
$677$	−16.6001	+	7.99418i	−0.637993	+	0.307241i	0.0867815	+	0.996227i	$0.472342\pi$
$678$		0			0
$679$	5.46915	−	40.4707i	0.209887	−	1.55312i
$680$	−1.98584	+	8.70053i	−0.0761534	+	0.333650i
$681$		0			0
$682$	45.4061	+	56.9375i	1.73869	+	2.18025i
$683$	−10.6955	−	46.8599i	−0.409251	−	1.79304i	−0.587682	−	0.809092i	$-0.699959\pi$
$683$	−10.6955	−	46.8599i	−0.409251	−	1.79304i	0.178431	−	0.983952i	$-0.442898\pi$
$684$		0			0
$685$	−5.32504			−0.203459
$686$	32.0138	−	28.0230i	1.22229	−	1.06992i
$687$		0			0
$688$	0.933960	+	0.449772i	0.0356069	+	0.0171474i
$689$	−1.78654	−	7.82733i	−0.0680616	−	0.298198i
$690$		0			0
$691$	8.89180	+	38.9575i	0.338260	+	1.48201i	0.802686	+	0.596402i	$0.203403\pi$
$691$	8.89180	+	38.9575i	0.338260	+	1.48201i	−0.464426	+	0.885612i	$0.653739\pi$
$692$	−2.15674	+	9.44928i	−0.0819869	+	0.359208i
$693$		0			0
$694$	−2.22590	−	9.75230i	−0.0844940	−	0.370192i
$695$	−1.51144	+	0.727871i	−0.0573322	+	0.0276097i
$696$		0			0
$697$	13.8148	+	6.65287i	0.523274	+	0.251996i
$698$	−8.17648	+	10.2530i	−0.309484	+	0.388081i
$699$		0			0
$700$	−12.0909	+	18.3295i	−0.456994	+	0.692790i
$701$	−27.5787	+	13.2812i	−1.04163	+	0.501625i	−0.874863	−	0.484371i	$-0.839049\pi$
$701$	−27.5787	+	13.2812i	−1.04163	+	0.501625i	−0.166772	+	0.985996i	$0.553334\pi$
$702$		0			0
$703$	−25.7310	+	32.2656i	−0.970463	+	1.21692i
$704$	−64.1913			−2.41930
$705$		0			0
$706$	−9.56021	+	11.9881i	−0.359803	+	0.451179i
$707$	20.2001	−	1.82446i	0.759702	−	0.0686157i
$708$		0			0
$709$	20.0076	+	25.0887i	0.751401	+	0.942226i	0.999650	−	0.0264698i	$-0.00842658\pi$
$709$	20.0076	+	25.0887i	0.751401	+	0.942226i	−0.248249	+	0.968696i	$0.579855\pi$
$710$	30.0734	−	14.4826i	1.12863	−	0.543522i
$711$		0			0
$712$	−2.02632	−	2.54093i	−0.0759396	−	0.0952252i
$713$	6.43641	+	8.07101i	0.241046	+	0.302262i
$714$		0			0
$715$	9.98775	−	12.5242i	0.373521	−	0.468380i
$716$	33.5441			1.25360
$717$		0			0
$718$	29.0649	−	36.4462i	1.08469	−	1.36016i
$719$	4.71408	−	20.6537i	0.175805	−	0.770254i	−0.807732	−	0.589550i	$-0.799305\pi$
$719$	4.71408	−	20.6537i	0.175805	−	0.770254i	0.983537	−	0.180704i	$-0.0578377\pi$
$720$		0			0
$721$	29.8297	−	2.69420i	1.11092	−	0.100337i
$722$	51.7309	+	24.9123i	1.92522	+	0.927139i
$723$		0			0
$724$	−69.0868	−	33.2704i	−2.56759	−	1.23649i
$725$	3.58482	−	15.7061i	0.133137	−	0.583311i
$726$		0			0
$727$	−2.66916	−	11.6943i	−0.0989936	−	0.433719i	0.901006	−	0.433806i	$-0.142830\pi$
$727$	−2.66916	−	11.6943i	−0.0989936	−	0.433719i	−1.00000		8.65026e-5i	$0.999972\pi$
$728$	−14.8654	−	5.57373i	−0.550948	−	0.206576i
$729$		0			0
$730$	4.28249	+	18.7628i	0.158502	+	0.694444i
$731$	−6.69732	−	8.39817i	−0.247709	−	0.310618i
$732$		0			0
$733$	−1.32402	−	0.637613i	−0.0489037	−	0.0235508i	0.409272	−	0.912412i	$-0.365783\pi$
$733$	−1.32402	−	0.637613i	−0.0489037	−	0.0235508i	−0.458176	+	0.888862i	$0.651497\pi$
$734$	5.20723			0.192202
$735$		0			0
$736$	−8.83511			−0.325666
$737$	69.7895	+	33.6089i	2.57073	+	1.23800i
$738$		0			0
$739$	−13.0323	−	16.3420i	−0.479401	−	0.601150i	0.482044	−	0.876147i	$-0.339895\pi$
$739$	−13.0323	−	16.3420i	−0.479401	−	0.601150i	−0.961445	+	0.274997i	$0.911323\pi$
$740$	−7.12836	−	31.2314i	−0.262044	−	1.14809i
$741$		0			0
$742$	23.7688	−	2.14678i	0.872578	−	0.0788106i
$743$	7.22250	+	31.6438i	0.264968	+	1.16090i	0.915786	+	0.401666i	$0.131569\pi$
$743$	7.22250	+	31.6438i	0.264968	+	1.16090i	−0.650818	+	0.759233i	$0.725574\pi$
$744$		0			0
$745$	−7.34774	+	32.1925i	−0.269200	+	1.17944i
$746$	−36.3289	−	17.4951i	−1.33010	−	0.640541i
$747$		0			0
$748$	−28.5082	−	13.7288i	−1.04236	−	0.501975i
$749$	−14.3481	−	44.1116i	−0.524268	−	1.61180i
$750$		0			0
$751$	5.35617	−	23.4669i	0.195450	−	0.856320i	−0.778154	−	0.628074i	$-0.783844\pi$
$751$	5.35617	−	23.4669i	0.195450	−	0.856320i	0.973603	−	0.228247i	$-0.0732992\pi$
$752$	−0.0178528	+	0.0223867i	−0.000651023	+	0.000816357i
$753$		0			0
$754$	29.8835			1.08829
$755$	−15.7011	+	19.6886i	−0.571423	+	0.716542i
$756$		0			0
$757$	−9.64428	−	12.0935i	−0.350527	−	0.439547i	0.575043	−	0.818123i	$-0.304985\pi$
$757$	−9.64428	−	12.0935i	−0.350527	−	0.439547i	−0.925570	+	0.378576i	$0.876414\pi$
$758$	14.0827	+	17.6591i	0.511506	+	0.641409i
$759$		0			0
$760$	−27.5494	+	13.2671i	−0.999322	+	0.481248i
$761$	−11.1414	−	13.9708i	−0.403874	−	0.506442i	0.537752	−	0.843103i	$-0.319274\pi$
$761$	−11.1414	−	13.9708i	−0.403874	−	0.506442i	−0.941626	+	0.336661i	$0.890702\pi$
$762$		0			0
$763$	−5.10073	+	7.73257i	−0.184659	+	0.279938i
$764$	5.69412	−	7.14020i	0.206006	−	0.258323i
$765$		0			0
$766$	−39.9598			−1.44381
$767$	−13.3953	+	16.7972i	−0.483678	+	0.606513i
$768$		0			0
$769$	−17.4147	+	8.38649i	−0.627991	+	0.302425i	−0.720677	−	0.693271i	$-0.756169\pi$
$769$	−17.4147	+	8.38649i	−0.627991	+	0.302425i	0.0926860	+	0.995695i	$0.470455\pi$
$770$	32.9176	+	34.4074i	1.18627	+	1.23996i
$771$		0			0
$772$	−17.6691	+	22.1564i	−0.635925	+	0.797425i
$773$	−30.6431	−	14.7570i	−1.10216	−	0.530771i	−0.207821	−	0.978167i	$-0.566637\pi$
$773$	−30.6431	−	14.7570i	−1.10216	−	0.530771i	−0.894336	+	0.447396i	$0.852351\pi$
$774$		0			0
$775$	−14.5022	+	6.98391i	−0.520936	+	0.250869i
$776$	−10.0798	−	44.1625i	−0.361844	−	1.58534i
$777$		0			0
$778$	−2.55066	+	11.1752i	−0.0914457	+	0.400650i
$779$	11.6906	+	51.2198i	0.418858	+	1.83514i
$780$		0			0
$781$	10.2645	+	44.9719i	0.367294	+	1.60922i
$782$	−6.50709	−	3.13365i	−0.232693	−	0.112059i
$783$		0			0
$784$	0.618955	−	1.15195i	0.0221055	−	0.0411411i
$785$	1.34701			0.0480767
$786$		0			0
$787$	9.95904	+	43.6334i	0.355002	+	1.55536i	0.765459	+	0.643484i	$0.222512\pi$
$787$	9.95904	+	43.6334i	0.355002	+	1.55536i	−0.410458	+	0.911880i	$0.634631\pi$
$788$	26.8245	+	33.6368i	0.955583	+	1.19826i
$789$		0			0
$790$	−7.17726	+	31.4456i	−0.255355	+	1.11879i
$791$	−10.0328	−	30.8449i	−0.356727	−	1.09672i
$792$		0			0
$793$	15.2007	−	7.32025i	0.539791	−	0.259950i
$794$	−1.69606	+	7.43094i	−0.0601911	+	0.263714i
$795$		0			0
$796$	44.1217	−	55.3269i	1.56385	−	1.96101i
$797$	38.0586	+	18.3281i	1.34810	+	0.649213i	0.961951	−	0.273222i	$-0.0880892\pi$
$797$	38.0586	+	18.3281i	1.34810	+	0.649213i	0.386153	+	0.922435i	$0.373804\pi$
$798$		0			0
$799$	0.267325	−	0.128737i	0.00945726	−	0.00455438i
$800$	3.06544	−	13.4306i	0.108380	−	0.474843i
$801$		0			0
$802$	−32.6969			−1.15457
$803$	−26.5964			−0.938565
$804$		0			0
$805$	4.66614	+	4.87732i	0.164460	+	0.171903i
$806$	−18.6161	−	23.3439i	−0.655725	−	0.822253i
$807$		0			0
$808$	20.2692	−	9.76114i	0.713069	−	0.343396i
$809$	17.1277	−	8.24826i	0.602177	−	0.289993i	−0.107850	−	0.994167i	$-0.534397\pi$
$809$	17.1277	−	8.24826i	0.602177	−	0.289993i	0.710028	+	0.704174i	$0.248682\pi$
$810$		0			0
$811$	9.44695	+	11.8461i	0.331727	+	0.415973i	0.919523	−	0.393037i	$-0.128575\pi$
$811$	9.44695	+	11.8461i	0.331727	+	0.415973i	−0.587795	+	0.809010i	$0.700004\pi$
$812$	−7.38791	+	54.6692i	−0.259265	+	1.91851i
$813$		0			0
$814$	71.2857			2.49856
$815$	5.94917			0.208390
$816$		0			0
$817$	8.18977	−	35.8817i	0.286524	−	1.25534i
$818$	−11.6076	+	5.58993i	−0.405851	+	0.195447i
$819$		0			0
$820$	−36.7423	−	17.6942i	−1.28310	−	0.617907i
$821$	29.4654	−	36.9484i	1.02835	−	1.28951i	0.0719616	−	0.997407i	$-0.477074\pi$
$821$	29.4654	−	36.9484i	1.02835	−	1.28951i	0.956387	−	0.292101i	$-0.0943545\pi$
$822$		0			0
$823$	−1.80084	+	7.89001i	−0.0627734	+	0.275028i	−0.996568	−	0.0827821i	$-0.973619\pi$
$823$	−1.80084	+	7.89001i	−0.0627734	+	0.275028i	0.933794	+	0.357810i	$0.116477\pi$
$824$	29.9319	−	14.4144i	1.04273	−	0.502150i
$825$		0			0
$826$	−44.1483	−	46.1464i	−1.53612	−	1.60564i
$827$	10.4572	−	45.8159i	0.363631	−	1.59317i	−0.380264	−	0.924878i	$-0.624167\pi$
$827$	10.4572	−	45.8159i	0.363631	−	1.59317i	0.743896	−	0.668296i	$-0.232976\pi$
$828$		0			0
$829$	7.96554	+	9.98847i	0.276655	+	0.346914i	0.900674	−	0.434495i	$-0.143073\pi$
$829$	7.96554	+	9.98847i	0.276655	+	0.346914i	−0.624020	+	0.781409i	$0.714502\pi$
$830$	6.18620	+	27.1035i	0.214726	+	0.940776i
$831$		0			0
$832$	26.3179			0.912407
$833$	−10.9578	+	7.97183i	−0.379664	+	0.276208i
$834$		0			0
$835$	−27.4380	−	13.2135i	−0.949532	−	0.457271i
$836$	−24.1246	−	105.697i	−0.834366	−	3.65560i
$837$		0			0
$838$	−14.0205	−	61.4279i	−0.484331	−	2.12199i
$839$	−5.89972	+	25.8484i	−0.203681	+	0.892384i	0.764991	+	0.644041i	$0.222743\pi$
$839$	−5.89972	+	25.8484i	−0.203681	+	0.892384i	−0.968672	+	0.248344i	$0.920114\pi$
$840$		0			0
$841$	−2.55313	−	11.1860i	−0.0880391	−	0.385724i
$842$	43.7291	−	21.0588i	1.50700	−	0.725735i
$843$		0			0
$844$	−20.5034	−	9.87394i	−0.705758	−	0.339875i
$845$	8.63784	−	10.8315i	0.297151	−	0.372615i
$846$		0			0
$847$	−31.5013	+	18.8346i	−1.08240	+	0.647164i
$848$	0.660893	−	0.318269i	0.0226952	−	0.0109294i
$849$		0			0
$850$	7.02129	−	8.80442i	0.240828	−	0.301989i
$851$	10.1049			0.346392
$852$		0			0
$853$	16.8667	−	21.1501i	0.577503	−	0.724166i	−0.404182	−	0.914679i	$-0.632444\pi$
$853$	16.8667	−	21.1501i	0.577503	−	0.724166i	0.981685	+	0.190513i	$0.0610150\pi$
$854$	15.5126	+	47.6918i	0.530831	+	1.63198i
$855$		0			0
$856$	−32.0797	−	40.2267i	−1.09646	−	1.37492i
$857$	−5.26554	+	2.53575i	−0.179868	+	0.0866196i	−0.521651	−	0.853159i	$-0.674684\pi$
$857$	−5.26554	+	2.53575i	−0.179868	+	0.0866196i	0.341783	+	0.939779i	$0.388969\pi$
$858$		0			0
$859$	24.7644	+	31.0536i	0.844950	+	1.05953i	0.997460	+	0.0712323i	$0.0226932\pi$
$859$	24.7644	+	31.0536i	0.844950	+	1.05953i	−0.152509	+	0.988302i	$0.548735\pi$
$860$	17.8124	+	22.3360i	0.607397	+	0.761652i
$861$		0			0
$862$	34.3348	−	43.0545i	1.16945	−	1.46644i
$863$	−24.8211			−0.844921			−0.422461	−	0.906381i	$-0.638834\pi$
$863$	−24.8211			−0.844921			−0.422461	+	0.906381i	$0.638834\pi$
$864$		0			0
$865$	−2.89646	+	3.63205i	−0.0984826	+	0.123493i
$866$	−0.483986	+	2.12048i	−0.0164465	+	0.0720569i
$867$		0			0
$868$	47.3079	−	28.2854i	1.60574	−	0.960069i
$869$	−40.1600	−	19.3400i	−1.36233	−	0.656066i
$870$		0			0
$871$	−28.6131	−	13.7793i	−0.969518	−	0.466895i
$872$	−2.28639	+	10.0173i	−0.0774269	+	0.339229i
$873$		0			0
$874$	−5.50652	−	24.1256i	−0.186261	−	0.816061i
$875$	−26.8693	+	16.0651i	−0.908348	+	0.543101i
$876$		0			0
$877$	0.0307207	+	0.134596i	0.00103736	+	0.00454498i	0.975444	−	0.220248i	$-0.0706866\pi$
$877$	0.0307207	+	0.134596i	0.00103736	+	0.00454498i	−0.974407	+	0.224793i	$0.927829\pi$
$878$	−1.75317	−	2.19840i	−0.0591666	−	0.0741926i
$879$		0			0
$880$	1.31865	+	0.635026i	0.0444515	+	0.0214067i
$881$	−24.1130			−0.812387			−0.406193	−	0.913787i	$-0.633144\pi$
$881$	−24.1130			−0.812387			−0.406193	+	0.913787i	$0.633144\pi$
$882$		0			0
$883$	40.7803			1.37237			0.686183	−	0.727429i	$-0.259285\pi$
$883$	40.7803			1.37237			0.686183	+	0.727429i	$0.259285\pi$
$884$	11.6881	+	5.62869i	0.393113	+	0.189313i
$885$		0			0
$886$	−3.14633	−	3.94538i	−0.105703	−	0.132548i
$887$	1.55125	+	6.79648i	0.0520859	+	0.228203i	0.994271	−	0.106890i	$-0.0340893\pi$
$887$	1.55125	+	6.79648i	0.0520859	+	0.228203i	−0.942185	+	0.335093i	$0.891232\pi$
$888$		0			0
$889$	−1.86237	−	1.94666i	−0.0624618	−	0.0652887i
$890$	−0.889308	−	3.89631i	−0.0298097	−	0.130605i
$891$		0			0
$892$	−1.05866	+	4.63829i	−0.0354465	+	0.155301i
$893$	0.915942	+	0.441095i	0.0306508	+	0.0147607i
$894$		0			0
$895$	14.4856	+	6.97592i	0.484202	+	0.233179i
$896$	−6.62166	+	48.9991i	−0.221214	+	1.63695i
$897$		0			0
$898$	−3.76161	+	16.4807i	−0.125526	+	0.549967i
$899$	−25.2134	+	31.6166i	−0.840913	+	1.05447i
$900$		0			0
$901$	−7.60106			−0.253228
$902$	56.5809	−	70.9502i	1.88394	−	2.36238i
$903$		0			0
$904$	−22.4316	−	28.1283i	−0.746064	−	0.935535i
$905$	−22.9153	−	28.7349i	−0.761732	−	0.955181i
$906$		0			0
$907$	−48.6275	+	23.4178i	−1.61465	+	0.777574i	−0.999938	−	0.0111774i	$-0.996442\pi$
$907$	−48.6275	+	23.4178i	−1.61465	+	0.777574i	−0.614712	+	0.788752i	$0.710728\pi$
$908$	−13.7726	−	17.2703i	−0.457059	−	0.573134i
$909$		0			0
$910$	−13.4959	−	14.1067i	−0.447386	−	0.467634i
$911$	1.22963	−	1.54191i	0.0407396	−	0.0510858i	−0.761044	−	0.648700i	$-0.775313\pi$
$911$	1.22963	−	1.54191i	0.0407396	−	0.0510858i	0.801784	+	0.597614i	$0.203884\pi$
$912$		0			0
$913$	−38.4193			−1.27149
$914$	23.2735	−	29.1840i	0.769819	−	0.965322i
$915$		0			0
$916$	8.82334	−	4.24910i	0.291531	−	0.140394i
$917$	−32.9824	−	12.3666i	−1.08917	−	0.408382i
$918$		0			0
$919$	12.1418	−	15.2254i	0.400522	−	0.502238i	−0.540144	−	0.841572i	$-0.681630\pi$
$919$	12.1418	−	15.2254i	0.400522	−	0.502238i	0.940666	+	0.339334i	$0.110202\pi$
$920$	6.74554	+	3.24848i	0.222394	+	0.107099i
$921$		0			0
$922$	34.5812	−	16.6534i	1.13887	−	0.548451i
$923$	−4.20837	−	18.4381i	−0.138520	−	0.606897i
$924$		0			0
$925$	−3.50601	+	15.3609i	−0.115277	+	0.505062i
$926$	0.860289	+	3.76917i	0.0282709	+	0.123863i
$927$		0			0
$928$	−7.70140	−	33.7420i	−0.252811	−	1.10764i
$929$	−34.0961	−	16.4198i	−1.11866	−	0.538717i	−0.219180	−	0.975685i	$-0.570338\pi$
$929$	−34.0961	−	16.4198i	−1.11866	−	0.538717i	−0.899477	+	0.436968i	$0.856052\pi$
$930$		0			0
$931$	−44.7639	−	12.3237i	−1.46708	−	0.403893i
$932$	9.19400			0.301159
$933$		0			0
$934$	6.64378	+	29.1083i	0.217391	+	0.952452i
$935$	−9.45585	−	11.8573i	−0.309239	−	0.387774i
$936$		0			0
$937$	−7.81175	+	34.2255i	−0.255199	+	1.11810i	0.671117	+	0.741351i	$0.265815\pi$
$937$	−7.81175	+	34.2255i	−0.255199	+	1.11810i	−0.926316	+	0.376747i	$0.877043\pi$
$938$	51.9813	−	78.8023i	1.69725	−	2.57299i
$939$		0			0
$940$	−0.710984	+	0.342392i	−0.0231897	+	0.0111676i
$941$	3.33214	−	14.5990i	0.108625	−	0.475915i	−0.891130	−	0.453749i	$-0.850086\pi$
$941$	3.33214	−	14.5990i	0.108625	−	0.475915i	0.999754	−	0.0221667i	$-0.00705647\pi$
$942$		0			0
$943$	8.02046	−	10.0573i	0.261182	−	0.327512i
$944$	−1.76854	−	0.851683i	−0.0575610	−	0.0277199i
$945$		0			0
$946$	−57.2778	+	27.5835i	−1.86226	+	0.896818i
$947$	−11.5265	+	50.5008i	−0.374560	+	1.64105i	0.339237	+	0.940701i	$0.389831\pi$
$947$	−11.5265	+	50.5008i	−0.374560	+	1.64105i	−0.713797	+	0.700353i	$0.753026\pi$
$948$		0			0
$949$	10.9043			0.353968
$950$	38.5848			1.25186
$951$		0			0
$952$	−8.27630	+	12.5467i	−0.268236	+	0.406639i
$953$	4.63329	+	5.80996i	0.150087	+	0.188203i	0.851191	−	0.524856i	$-0.175881\pi$
$953$	4.63329	+	5.80996i	0.150087	+	0.188203i	−0.701104	+	0.713059i	$0.747309\pi$
$954$		0			0
$955$	3.94383	−	1.89925i	0.127619	−	0.0614583i
$956$	38.7682	−	18.6698i	1.25385	−	0.603825i
$957$		0			0
$958$	−31.3921	−	39.3645i	−1.01423	−	1.27181i
$959$	−8.39768	−	3.14868i	−0.271175	−	0.101676i
$960$		0			0
$961$	9.40459			0.303374
$962$	−29.2265			−0.942301
$963$		0			0
$964$	−0.743038	+	3.25546i	−0.0239316	+	0.104851i
$965$	−12.2379	+	5.89346i	−0.393952	+	0.189717i
$966$		0			0
$967$	33.0396	+	15.9110i	1.06248	+	0.511664i	0.881676	−	0.471854i	$-0.156415\pi$
$967$	33.0396	+	15.9110i	1.06248	+	0.511664i	0.180806	+	0.983519i	$0.442130\pi$
$968$	−25.3825	+	31.8287i	−0.815825	+	1.02301i
$969$		0			0
$970$	12.3952	−	54.3070i	0.397986	−	1.74369i
$971$	7.97989	−	3.84291i	0.256087	−	0.123325i	−0.301436	−	0.953486i	$-0.597466\pi$
$971$	7.97989	−	3.84291i	0.256087	−	0.123325i	0.557523	+	0.830161i	$0.311752\pi$
$972$		0			0
$973$	−2.81395	+	0.254154i	−0.0902112	+	0.00814781i
$974$	16.1274	−	70.6589i	0.516756	−	2.26406i
$975$		0			0
$976$	0.961086	+	1.20516i	0.0307636	+	0.0385763i
$977$	−8.72852	−	38.2421i	−0.279250	−	1.22347i	−0.898744	−	0.438473i	$-0.855519\pi$
$977$	−8.72852	−	38.2421i	−0.279250	−	1.22347i	0.619494	−	0.785001i	$-0.287338\pi$
$978$		0			0
$979$	5.52303			0.176517
$980$	29.1436	−	21.2021i	0.930957	−	0.677277i
$981$		0			0
$982$	−18.6275	−	8.97053i	−0.594428	−	0.286261i
$983$	9.94921	+	43.5904i	0.317331	+	1.39032i	0.842215	+	0.539142i	$0.181252\pi$
$983$	9.94921	+	43.5904i	0.317331	+	1.39032i	−0.524884	+	0.851174i	$0.675891\pi$
$984$		0			0
$985$	4.58865	+	20.1042i	0.146206	+	0.640572i
$986$	6.29556	−	27.5827i	0.200492	−	0.878411i
$987$		0			0
$988$	9.89087	+	43.3347i	0.314670	+	1.37866i
$989$	−8.11924	+	3.91002i	−0.258177	+	0.124331i
$990$		0			0
$991$	16.1939	+	7.79855i	0.514415	+	0.247729i	0.673035	−	0.739610i	$-0.264990\pi$
$991$	16.1939	+	7.79855i	0.514415	+	0.247729i	−0.158620	+	0.987340i	$0.550705\pi$
$992$	−21.5604	+	27.0359i	−0.684544	+	0.858391i
$993$		0			0
$994$	55.9898	−	5.05695i	1.77589	−	0.160397i
$995$	30.5594	−	14.7166i	0.968798	−	0.466548i
$996$		0			0
$997$	5.06625	−	6.35288i	0.160450	−	0.201198i	−0.695107	−	0.718906i	$-0.744643\pi$
$997$	5.06625	−	6.35288i	0.160450	−	0.201198i	0.855557	+	0.517708i	$0.173215\pi$
$998$	21.7882			0.689694
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.c.127.4		24
3.2	odd	2		147.2.i.a.127.1	yes	24
49.22	even	7	inner	441.2.u.c.316.4		24
147.62	even	14		7203.2.a.b.1.12		12
147.71	odd	14		147.2.i.a.22.1	✓	24
147.134	odd	14		7203.2.a.a.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.a.22.1	✓	24	147.71	odd	14
147.2.i.a.127.1	yes	24	3.2	odd	2
441.2.u.c.127.4		24	1.1	even	1	trivial
441.2.u.c.316.4		24	49.22	even	7	inner
7203.2.a.a.1.12		12	147.134	odd	14
7203.2.a.b.1.12		12	147.62	even	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.06977 + 0.996749i) q^{2} +(2.04346 + 2.56242i) q^{4} +(0.349558 + 1.53152i) q^{5} +(-0.354322 + 2.62192i) q^{7} +(0.653025 + 2.86109i) q^{8} +O(q^{10})\)	\(q+(2.06977 + 0.996749i) q^{2} +(2.04346 + 2.56242i) q^{4} +(0.349558 + 1.53152i) q^{5} +(-0.354322 + 2.62192i) q^{7} +(0.653025 + 2.86109i) q^{8} +(-0.803031 + 3.51831i) q^{10} +(-4.49332 - 2.16387i) q^{11} +(1.84222 + 0.887167i) q^{13} +(-3.34676 + 5.07360i) q^{14} +(-0.0415703 + 0.182131i) q^{16} +(1.20696 - 1.51349i) q^{17} +6.63276 q^{19} +(-3.21008 + 4.02531i) q^{20} +(-7.14330 - 8.95742i) q^{22} +(-1.01258 - 1.26973i) q^{23} +(2.28150 - 1.09871i) q^{25} +(2.92869 + 3.67246i) q^{26} +(-7.44250 + 4.44987i) q^{28} +(3.96658 - 4.97393i) q^{29} -6.35646 q^{31} +(3.39189 - 4.25330i) q^{32} +(4.00670 - 1.92953i) q^{34} +(-4.13936 + 0.373864i) q^{35} +(-3.87938 + 4.86459i) q^{37} +(13.7283 + 6.61120i) q^{38} +(-4.15353 + 2.00024i) q^{40} +(1.76255 + 7.72224i) q^{41} +(1.23475 - 5.40977i) q^{43} +(-3.63718 - 15.9355i) q^{44} +(-0.830200 - 3.63734i) q^{46} +(0.138094 + 0.0665024i) q^{47} +(-6.74891 - 1.85801i) q^{49} +5.81731 q^{50} +(1.49121 + 6.53344i) q^{52} +(-2.44815 - 3.06989i) q^{53} +(1.74332 - 7.63798i) q^{55} +(-7.73293 + 0.698432i) q^{56} +(13.1677 - 6.34121i) q^{58} +(-2.33810 + 10.2439i) q^{59} +(5.14458 - 6.45110i) q^{61} +(-13.1564 - 6.33579i) q^{62} +(11.5965 - 5.58460i) q^{64} +(-0.714746 + 3.13151i) q^{65} -15.5318 q^{67} +6.34457 q^{68} +(-8.94018 - 3.35209i) q^{70} +(-5.76688 - 7.23144i) q^{71} +(4.80479 - 2.31387i) q^{73} +(-12.8782 + 6.20181i) q^{74} +(13.5538 + 16.9959i) q^{76} +(7.26557 - 11.0144i) q^{77} +8.93772 q^{79} -0.293468 q^{80} +(-4.04906 + 17.7401i) q^{82} +(6.94067 - 3.34245i) q^{83} +(2.73983 + 1.31943i) q^{85} +(7.94783 - 9.96626i) q^{86} +(3.25677 - 14.2688i) q^{88} +(-0.997768 + 0.480500i) q^{89} +(-2.97882 + 4.51581i) q^{91} +(1.18442 - 5.18930i) q^{92} +(0.219536 + 0.275289i) q^{94} +(2.31854 + 10.1582i) q^{95} -15.4355 q^{97} +(-12.1167 - 10.5726i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8	\( 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) \) 24 * q - q^2 - 3 * q^4 - 3 * q^8 - 30 * q^10 - 9 * q^11 + 21 * q^14 - 29 * q^16 - 5 * q^17 + 26 * q^19 + 13 * q^20 + 11 * q^22 - 4 * q^23 - 28 * q^25 + 22 * q^26 - 7 * q^28 - 6 * q^29 + 36 * q^31 - 14 * q^32 + 46 * q^34 + 7 * q^35 - 22 * q^37 + 45 * q^38 + 35 * q^40 + 11 * q^41 + 6 * q^43 - 82 * q^44 - 16 * q^46 - 29 * q^47 - 42 * q^49 + 48 * q^50 - 50 * q^52 - 28 * q^53 + 23 * q^55 - 21 * q^56 + 39 * q^58 + 15 * q^59 - 32 * q^61 + 8 * q^62 + 29 * q^64 + 21 * q^65 - 34 * q^67 + 22 * q^68 - 24 * q^71 - 15 * q^73 - 6 * q^74 + 7 * q^76 + 21 * q^77 - 34 * q^79 - 8 * q^80 + 14 * q^82 - 14 * q^83 + 20 * q^85 + 100 * q^86 - 108 * q^88 - 10 * q^89 + 84 * q^91 + 21 * q^92 + 99 * q^94 - 18 * q^95 - 64 * q^97 - 91 * q^98

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