LMFDB - Embedded newform 450.2.h.f.181.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
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} - x^{11} + 6 x^{10} - 26 x^{9} + 61 x^{8} - 120 x^{7} + 465 x^{6} - 600 x^{5} + 1525 x^{4} + \cdots + 15625 $ x^12 - x^11 + 6x^10 - 26x^9 + 61x^8 - 120x^7 + 465x^6 - 600x^5 + 1525x^4 - 3250x^3 + 3750x^2 - 3125x + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.3
Root			$1.95382 - 1.08748i$ of defining polynomial
Character	$\chi$	$=$	450.181
Dual form			450.2.h.f.271.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(1.95382 - 1.08748i) q^{5} +0.757055 q^{7} +(-0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(1.95382 - 1.08748i) q^{5} +0.757055 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.63801 + 1.52214i) q^{10} +(1.05531 + 3.24790i) q^{11} +(1.64480 - 5.06217i) q^{13} +(0.233943 + 0.720002i) q^{14} +(0.309017 - 0.951057i) q^{16} +(3.87565 + 2.81582i) q^{17} +(-0.298039 - 0.216538i) q^{19} +(-0.941467 + 2.02821i) q^{20} +(-2.76283 + 2.00732i) q^{22} +(1.43384 + 4.41289i) q^{23} +(2.63479 - 4.24946i) q^{25} +5.32268 q^{26} +(-0.612470 + 0.444986i) q^{28} +(0.127036 - 0.0922973i) q^{29} +(-3.70430 - 2.69133i) q^{31} +1.00000 q^{32} +(-1.48037 + 4.55610i) q^{34} +(1.47915 - 0.823279i) q^{35} +(-2.49762 + 7.68689i) q^{37} +(0.113841 - 0.350366i) q^{38} +(-2.21987 - 0.268637i) q^{40} +(0.678849 - 2.08928i) q^{41} +7.65386 q^{43} +(-2.76283 - 2.00732i) q^{44} +(-3.75383 + 2.72732i) q^{46} +(-9.14961 + 6.64758i) q^{47} -6.42687 q^{49} +(4.85567 + 1.19268i) q^{50} +(1.64480 + 5.06217i) q^{52} +(-4.41541 + 3.20798i) q^{53} +(5.59390 + 5.19818i) q^{55} +(-0.612470 - 0.444986i) q^{56} +(0.127036 + 0.0922973i) q^{58} +(2.79557 - 8.60388i) q^{59} +(-4.05146 - 12.4691i) q^{61} +(1.41492 - 4.35467i) q^{62} +(0.309017 + 0.951057i) q^{64} +(-2.29136 - 11.6792i) q^{65} +(2.28438 + 1.65970i) q^{67} -4.79056 q^{68} +(1.24007 + 1.15234i) q^{70} +(5.67313 - 4.12177i) q^{71} +(-3.80108 - 11.6985i) q^{73} -8.08248 q^{74} +0.368397 q^{76} +(0.798926 + 2.45884i) q^{77} +(-12.2665 + 8.91212i) q^{79} +(-0.430490 - 2.19424i) q^{80} +2.19680 q^{82} +(-5.60559 - 4.07270i) q^{83} +(10.6344 + 1.28692i) q^{85} +(2.36517 + 7.27925i) q^{86} +(1.05531 - 3.24790i) q^{88} +(-0.281367 - 0.865958i) q^{89} +(1.24520 - 3.83234i) q^{91} +(-3.75383 - 2.72732i) q^{92} +(-9.14961 - 6.64758i) q^{94} +(-0.817795 - 0.0989650i) q^{95} +(2.80543 - 2.03826i) q^{97} +(-1.98601 - 6.11231i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} + q^{5} - 2 q^{7} - 3 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 + q^5 - 2 * q^7 - 3 * q^8	$ 12 q - 3 q^{2} - 3 q^{4} + q^{5} - 2 q^{7} - 3 q^{8} + q^{10} + q^{11} + 4 q^{13} + 8 q^{14} - 3 q^{16} - 8 q^{17} - 8 q^{19} + q^{20} - 4 q^{22} - 11 q^{25} - 16 q^{26} - 7 q^{28} - 6 q^{29} - 3 q^{31} + 12 q^{32} + 2 q^{34} - 18 q^{35} - 8 q^{37} + 2 q^{38} + q^{40} + 20 q^{41} + 32 q^{43} - 4 q^{44} - 10 q^{46} + 34 q^{49} + 9 q^{50} + 4 q^{52} + 2 q^{53} + 44 q^{55} - 7 q^{56} - 6 q^{58} - 19 q^{59} - 26 q^{61} + 2 q^{62} - 3 q^{64} + 16 q^{65} - 16 q^{67} + 12 q^{68} - 23 q^{70} + 48 q^{71} - 30 q^{73} - 8 q^{74} + 12 q^{76} - 39 q^{77} - 18 q^{79} - 4 q^{80} - 40 q^{82} - 29 q^{83} - 4 q^{85} + 12 q^{86} + q^{88} + 62 q^{89} - 26 q^{91} - 10 q^{92} + 6 q^{95} + 23 q^{97} - 6 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 + q^5 - 2 * q^7 - 3 * q^8 + q^10 + q^11 + 4 * q^13 + 8 * q^14 - 3 * q^16 - 8 * q^17 - 8 * q^19 + q^20 - 4 * q^22 - 11 * q^25 - 16 * q^26 - 7 * q^28 - 6 * q^29 - 3 * q^31 + 12 * q^32 + 2 * q^34 - 18 * q^35 - 8 * q^37 + 2 * q^38 + q^40 + 20 * q^41 + 32 * q^43 - 4 * q^44 - 10 * q^46 + 34 * q^49 + 9 * q^50 + 4 * q^52 + 2 * q^53 + 44 * q^55 - 7 * q^56 - 6 * q^58 - 19 * q^59 - 26 * q^61 + 2 * q^62 - 3 * q^64 + 16 * q^65 - 16 * q^67 + 12 * q^68 - 23 * q^70 + 48 * q^71 - 30 * q^73 - 8 * q^74 + 12 * q^76 - 39 * q^77 - 18 * q^79 - 4 * q^80 - 40 * q^82 - 29 * q^83 - 4 * q^85 + 12 * q^86 + q^88 + 62 * q^89 - 26 * q^91 - 10 * q^92 + 6 * q^95 + 23 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.95382	−	1.08748i	0.873773	−	0.486334i
$5$	1.95382	−	1.08748i	0.873773	−	0.486334i
$6$		0			0
$7$	0.757055			0.286140			0.143070	−	0.989713i	$-0.454303\pi$
$7$	0.757055			0.286140			0.143070	+	0.989713i	$0.454303\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$		0			0
$10$	1.63801	+	1.52214i	0.517985	+	0.481343i
$11$	1.05531	+	3.24790i	0.318187	+	0.979280i	0.974423	+	0.224724i	$0.0721479\pi$
$11$	1.05531	+	3.24790i	0.318187	+	0.979280i	−0.656235	+	0.754556i	$0.727852\pi$
$12$		0			0
$13$	1.64480	−	5.06217i	0.456185	−	1.40399i	−0.413553	−	0.910480i	$-0.635712\pi$
$13$	1.64480	−	5.06217i	0.456185	−	1.40399i	0.869738	−	0.493513i	$-0.164288\pi$
$14$	0.233943	+	0.720002i	0.0625238	+	0.192429i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	3.87565	+	2.81582i	0.939983	+	0.682937i	0.948417	−	0.317027i	$-0.102685\pi$
$17$	3.87565	+	2.81582i	0.939983	+	0.682937i	−0.00843371	+	0.999964i	$0.502685\pi$
$18$		0			0
$19$	−0.298039	−	0.216538i	−0.0683749	−	0.0496773i	0.553073	−	0.833133i	$-0.313455\pi$
$19$	−0.298039	−	0.216538i	−0.0683749	−	0.0496773i	−0.621448	+	0.783456i	$0.713455\pi$
$20$	−0.941467	+	2.02821i	−0.210518	+	0.453522i
$21$		0			0
$22$	−2.76283	+	2.00732i	−0.589038	+	0.427961i
$23$	1.43384	+	4.41289i	0.298975	+	0.920152i	0.981857	+	0.189623i	$0.0607264\pi$
$23$	1.43384	+	4.41289i	0.298975	+	0.920152i	−0.682882	+	0.730529i	$0.739274\pi$
$24$		0			0
$25$	2.63479	−	4.24946i	0.526958	−	0.849891i
$26$	5.32268			1.04386
$27$		0			0
$28$	−0.612470	+	0.444986i	−0.115746	+	0.0840944i
$29$	0.127036	−	0.0922973i	0.0235901	−	0.0171392i	−0.575928	−	0.817501i	$-0.695359\pi$
$29$	0.127036	−	0.0922973i	0.0235901	−	0.0171392i	0.599518	+	0.800361i	$0.295359\pi$
$30$		0			0
$31$	−3.70430	−	2.69133i	−0.665312	−	0.483377i	0.203141	−	0.979150i	$-0.434885\pi$
$31$	−3.70430	−	2.69133i	−0.665312	−	0.483377i	−0.868453	+	0.495772i	$0.834885\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−1.48037	+	4.55610i	−0.253881	+	0.781364i
$35$	1.47915	−	0.823279i	0.250021	−	0.139160i
$36$		0			0
$37$	−2.49762	+	7.68689i	−0.410607	+	1.26372i	0.505515	+	0.862818i	$0.331302\pi$
$37$	−2.49762	+	7.68689i	−0.410607	+	1.26372i	−0.916122	+	0.400900i	$0.868698\pi$
$38$	0.113841	−	0.350366i	0.0184674	−	0.0568369i
$39$		0			0
$40$	−2.21987	−	0.268637i	−0.350993	−	0.0424752i
$41$	0.678849	−	2.08928i	0.106018	−	0.326291i	−0.883950	−	0.467582i	$-0.845125\pi$
$41$	0.678849	−	2.08928i	0.106018	−	0.326291i	0.989968	+	0.141291i	$0.0451253\pi$
$42$		0			0
$43$	7.65386			1.16720			0.583601	−	0.812040i	$-0.301643\pi$
$43$	7.65386			1.16720			0.583601	+	0.812040i	$0.301643\pi$
$44$	−2.76283	−	2.00732i	−0.416513	−	0.302614i
$45$		0			0
$46$	−3.75383	+	2.72732i	−0.553472	+	0.402121i
$47$	−9.14961	+	6.64758i	−1.33461	+	0.969649i	−0.334984	+	0.942224i	$0.608731\pi$
$47$	−9.14961	+	6.64758i	−1.33461	+	0.969649i	−0.999624	+	0.0274252i	$0.991269\pi$
$48$		0			0
$49$	−6.42687			−0.918124
$50$	4.85567	+	1.19268i	0.686695	+	0.168670i
$51$		0			0
$52$	1.64480	+	5.06217i	0.228092	+	0.701997i
$53$	−4.41541	+	3.20798i	−0.606504	+	0.440651i	−0.848181	−	0.529706i	$-0.822302\pi$
$53$	−4.41541	+	3.20798i	−0.606504	+	0.440651i	0.241678	+	0.970357i	$0.422302\pi$
$54$		0			0
$55$	5.59390	+	5.19818i	0.754281	+	0.700923i
$56$	−0.612470	−	0.444986i	−0.0818448	−	0.0594637i
$57$		0			0
$58$	0.127036	+	0.0922973i	0.0166807	+	0.0121192i
$59$	2.79557	−	8.60388i	0.363952	−	1.12013i	−0.586683	−	0.809817i	$-0.699566\pi$
$59$	2.79557	−	8.60388i	0.363952	−	1.12013i	0.950635	−	0.310312i	$-0.100434\pi$
$60$		0			0
$61$	−4.05146	−	12.4691i	−0.518736	−	1.59651i	−0.776379	−	0.630266i	$-0.782946\pi$
$61$	−4.05146	−	12.4691i	−0.518736	−	1.59651i	0.257643	−	0.966240i	$-0.417054\pi$
$62$	1.41492	−	4.35467i	0.179695	−	0.553043i
$63$		0			0
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−2.29136	−	11.6792i	−0.284208	−	1.44863i
$66$		0			0
$67$	2.28438	+	1.65970i	0.279081	+	0.202764i	0.718517	−	0.695510i	$-0.244821\pi$
$67$	2.28438	+	1.65970i	0.279081	+	0.202764i	−0.439435	+	0.898274i	$0.644821\pi$
$68$	−4.79056			−0.580941
$69$		0			0
$70$	1.24007	+	1.15234i	0.148216	+	0.137731i
$71$	5.67313	−	4.12177i	0.673276	−	0.489164i	−0.197844	−	0.980234i	$-0.563394\pi$
$71$	5.67313	−	4.12177i	0.673276	−	0.489164i	0.871120	+	0.491070i	$0.163394\pi$
$72$		0			0
$73$	−3.80108	−	11.6985i	−0.444882	−	1.36921i	−0.882613	−	0.470101i	$-0.844218\pi$
$73$	−3.80108	−	11.6985i	−0.444882	−	1.36921i	0.437731	−	0.899106i	$-0.355782\pi$
$74$	−8.08248			−0.939569
$75$		0			0
$76$	0.368397			0.0422580
$77$	0.798926	+	2.45884i	0.0910461	+	0.280211i
$78$		0			0
$79$	−12.2665	+	8.91212i	−1.38009	+	1.00269i	−0.383215	+	0.923659i	$0.625183\pi$
$79$	−12.2665	+	8.91212i	−1.38009	+	1.00269i	−0.996872	+	0.0790332i	$0.974817\pi$
$80$	−0.430490	−	2.19424i	−0.0481302	−	0.245323i
$81$		0			0
$82$	2.19680			0.242596
$83$	−5.60559	−	4.07270i	−0.615294	−	0.447037i	0.235981	−	0.971758i	$-0.424170\pi$
$83$	−5.60559	−	4.07270i	−0.615294	−	0.447037i	−0.851274	+	0.524721i	$0.824170\pi$
$84$		0			0
$85$	10.6344	+	1.28692i	1.15347	+	0.139586i
$86$	2.36517	+	7.27925i	0.255043	+	0.784942i
$87$		0			0
$88$	1.05531	−	3.24790i	0.112496	−	0.346228i
$89$	−0.281367	−	0.865958i	−0.0298248	−	0.0917913i	0.935036	−	0.354553i	$-0.115367\pi$
$89$	−0.281367	−	0.865958i	−0.0298248	−	0.0917913i	−0.964861	+	0.262761i	$0.915367\pi$
$90$		0			0
$91$	1.24520	−	3.83234i	0.130533	−	0.401738i
$92$	−3.75383	−	2.72732i	−0.391364	−	0.284342i
$93$		0			0
$94$	−9.14961	−	6.64758i	−0.943710	−	0.685645i
$95$	−0.817795	−	0.0989650i	−0.0839039	−	0.0101536i
$96$		0			0
$97$	2.80543	−	2.03826i	0.284848	−	0.206954i	−0.436181	−	0.899859i	$-0.643669\pi$
$97$	2.80543	−	2.03826i	0.284848	−	0.206954i	0.721029	+	0.692905i	$0.243669\pi$
$98$	−1.98601	−	6.11231i	−0.200617	−	0.617437i
$99$		0			0
$100$	0.366179	+	4.98657i	0.0366179	+	0.498657i
$101$	−14.2056			−1.41351			−0.706756	−	0.707458i	$-0.749842\pi$
$101$	−14.2056			−1.41351			−0.706756	+	0.707458i	$0.749842\pi$
$102$		0			0
$103$	4.20080	−	3.05206i	0.413917	−	0.300728i	−0.361269	−	0.932462i	$-0.617656\pi$
$103$	4.20080	−	3.05206i	0.413917	−	0.300728i	0.775186	+	0.631733i	$0.217656\pi$
$104$	−4.30614	+	3.12859i	−0.422252	+	0.306784i
$105$		0			0
$106$	−4.41541	−	3.20798i	−0.428863	−	0.311587i
$107$	0.635311			0.0614178			0.0307089	−	0.999528i	$-0.490224\pi$
$107$	0.635311			0.0614178			0.0307089	+	0.999528i	$0.490224\pi$
$108$		0			0
$109$	2.09912	−	6.46041i	0.201059	−	0.618795i	−0.798793	−	0.601605i	$-0.794528\pi$
$109$	2.09912	−	6.46041i	0.201059	−	0.618795i	0.999852	−	0.0171899i	$-0.00547198\pi$
$110$	−3.21516	+	6.92644i	−0.306553	+	0.660410i
$111$		0			0
$112$	0.233943	−	0.720002i	0.0221055	−	0.0680338i
$113$	0.528020	−	1.62508i	0.0496720	−	0.152875i	−0.923144	−	0.384455i	$-0.874390\pi$
$113$	0.528020	−	1.62508i	0.0496720	−	0.152875i	0.972816	+	0.231580i	$0.0743895\pi$
$114$		0			0
$115$	7.60037	+	7.06271i	0.708738	+	0.658601i
$116$	−0.0485236	+	0.149340i	−0.00450530	+	0.0138659i
$117$		0			0
$118$	9.04665			0.832812
$119$	2.93408	+	2.13173i	0.268967	+	0.195416i
$120$		0			0
$121$	−0.536020	+	0.389441i	−0.0487291	+	0.0354038i
$122$	10.6069	−	7.70634i	0.960300	−	0.697699i
$123$		0			0
$124$	4.57877			0.411185
$125$	0.526706	−	11.1679i	0.0471100	−	0.998890i
$126$		0			0
$127$	4.81950	+	14.8329i	0.427662	+	1.31621i	0.900422	+	0.435017i	$0.143258\pi$
$127$	4.81950	+	14.8329i	0.427662	+	1.31621i	−0.472760	+	0.881191i	$0.656742\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$		0			0
$130$	10.3995	−	5.78829i	0.912099	−	0.507667i
$131$	−13.2991	−	9.66234i	−1.16194	−	0.844202i	−0.171922	−	0.985111i	$-0.554998\pi$
$131$	−13.2991	−	9.66234i	−1.16194	−	0.844202i	−0.990023	+	0.140908i	$0.954998\pi$
$132$		0			0
$133$	−0.225632	−	0.163931i	−0.0195648	−	0.0142147i
$134$	−0.872555	+	2.68545i	−0.0753773	+	0.231987i
$135$		0			0
$136$	−1.48037	−	4.55610i	−0.126940	−	0.390682i
$137$	−2.38994	+	7.35549i	−0.204187	+	0.628422i	0.795559	+	0.605876i	$0.207177\pi$
$137$	−2.38994	+	7.35549i	−0.204187	+	0.628422i	−0.999746	+	0.0225460i	$0.992823\pi$
$138$		0			0
$139$	3.44740	+	10.6100i	0.292405	+	0.899930i	0.984081	+	0.177722i	$0.0568728\pi$
$139$	3.44740	+	10.6100i	0.292405	+	0.899930i	−0.691676	+	0.722208i	$0.743127\pi$
$140$	−0.712742	+	1.53547i	−0.0602377	+	0.129771i
$141$		0			0
$142$	5.67313	+	4.12177i	0.476078	+	0.345891i
$143$	18.1772			1.52005
$144$		0			0
$145$	0.147834	−	0.318481i	0.0122770	−	0.0264484i
$146$	9.95134	−	7.23008i	0.823579	−	0.598365i
$147$		0			0
$148$	−2.49762	−	7.68689i	−0.205303	−	0.631859i
$149$	−2.23707			−0.183268			−0.0916340	−	0.995793i	$-0.529209\pi$
$149$	−2.23707			−0.183268			−0.0916340	+	0.995793i	$0.529209\pi$
$150$		0			0
$151$	−18.8597			−1.53478			−0.767391	−	0.641180i	$-0.778445\pi$
$151$	−18.8597			−1.53478			−0.767391	+	0.641180i	$0.778445\pi$
$152$	0.113841	+	0.350366i	0.00923372	+	0.0284185i
$153$		0			0
$154$	−2.09162	+	1.51965i	−0.168547	+	0.122457i
$155$	−10.1643	−	1.23002i	−0.816414	−	0.0987980i
$156$		0			0
$157$	−3.08881			−0.246514			−0.123257	−	0.992375i	$-0.539334\pi$
$157$	−3.08881			−0.246514			−0.123257	+	0.992375i	$0.539334\pi$
$158$	−12.2665	−	8.91212i	−0.975869	−	0.709010i
$159$		0			0
$160$	1.95382	−	1.08748i	0.154463	−	0.0859726i
$161$	1.08549	+	3.34080i	0.0855488	+	0.263292i
$162$		0			0
$163$	−4.06026	+	12.4962i	−0.318024	+	0.978776i	0.656468	+	0.754354i	$0.272050\pi$
$163$	−4.06026	+	12.4962i	−0.318024	+	0.978776i	−0.974492	+	0.224423i	$0.927950\pi$
$164$	0.678849	+	2.08928i	0.0530092	+	0.163145i
$165$		0			0
$166$	2.14115	−	6.58977i	0.166185	−	0.511465i
$167$	−13.1244	−	9.53541i	−1.01559	−	0.737873i	−0.0502193	−	0.998738i	$-0.515992\pi$
$167$	−13.1244	−	9.53541i	−1.01559	−	0.737873i	−0.965375	+	0.260866i	$0.915992\pi$
$168$		0			0
$169$	−12.4030	−	9.01129i	−0.954075	−	0.693176i
$170$	2.06229	+	10.5116i	0.158170	+	0.806206i
$171$		0			0
$172$	−6.19210	+	4.49882i	−0.472143	+	0.343032i
$173$	6.93923	+	21.3567i	0.527580	+	1.62372i	0.759157	+	0.650907i	$0.225611\pi$
$173$	6.93923	+	21.3567i	0.527580	+	1.62372i	−0.231578	+	0.972816i	$0.574389\pi$
$174$		0			0
$175$	1.99468	−	3.21707i	0.150784	−	0.243188i
$176$	3.41505			0.257419
$177$		0			0
$178$	0.736628	−	0.535191i	0.0552126	−	0.0401143i
$179$	15.2206	−	11.0584i	1.13764	−	0.826542i	0.150849	−	0.988557i	$-0.451799\pi$
$179$	15.2206	−	11.0584i	1.13764	−	0.826542i	0.986788	+	0.162015i	$0.0517992\pi$
$180$		0			0
$181$	−6.94947	−	5.04909i	−0.516550	−	0.375296i	0.298753	−	0.954331i	$-0.403429\pi$
$181$	−6.94947	−	5.04909i	−0.516550	−	0.375296i	−0.815303	+	0.579035i	$0.803429\pi$
$182$	4.02956			0.298691
$183$		0			0
$184$	1.43384	−	4.41289i	0.105704	−	0.325323i
$185$	3.47942	+	17.7349i	0.255812	+	1.30389i
$186$		0			0
$187$	−5.05552	+	15.5593i	−0.369696	+	1.13781i
$188$	3.49484	−	10.7560i	0.254887	−	0.784463i
$189$		0			0
$190$	−0.158591	−	0.808351i	−0.0115054	−	0.0586439i
$191$	−6.85405	+	21.0946i	−0.495941	+	1.52635i	0.319543	+	0.947572i	$0.396471\pi$
$191$	−6.85405	+	21.0946i	−0.495941	+	1.52635i	−0.815485	+	0.578779i	$0.803529\pi$
$192$		0			0
$193$	14.8635			1.06990			0.534948	−	0.844885i	$-0.320331\pi$
$193$	14.8635			1.06990			0.534948	+	0.844885i	$0.320331\pi$
$194$	2.80543	+	2.03826i	0.201418	+	0.146339i
$195$		0			0
$196$	5.19945	−	3.77762i	0.371389	−	0.269830i
$197$	2.07042	−	1.50425i	0.147511	−	0.107173i	−0.511582	−	0.859234i	$-0.670940\pi$
$197$	2.07042	−	1.50425i	0.147511	−	0.107173i	0.659093	+	0.752061i	$0.270940\pi$
$198$		0			0
$199$	1.87380			0.132830			0.0664151	−	0.997792i	$-0.478844\pi$
$199$	1.87380			0.132830			0.0664151	+	0.997792i	$0.478844\pi$
$200$	−4.62936	+	1.88919i	−0.327345	+	0.133586i
$201$		0			0
$202$	−4.38978	−	13.5103i	−0.308864	−	0.950584i
$203$	0.0961735	−	0.0698741i	0.00675006	−	0.00490420i
$204$		0			0
$205$	−0.945700	−	4.82030i	−0.0660505	−	0.336664i
$206$	4.20080	+	3.05206i	0.292683	+	0.212647i
$207$		0			0
$208$	−4.30614	−	3.12859i	−0.298577	−	0.216929i
$209$	0.388772	−	1.19652i	0.0268919	−	0.0827649i
$210$		0			0
$211$	5.40860	+	16.6460i	0.372343	+	1.14595i	0.945254	+	0.326337i	$0.105814\pi$
$211$	5.40860	+	16.6460i	0.372343	+	1.14595i	−0.572910	+	0.819618i	$0.694186\pi$
$212$	1.68654	−	5.19063i	0.115832	−	0.356494i
$213$		0			0
$214$	0.196322	+	0.604217i	0.0134203	+	0.0413034i
$215$	14.9542	−	8.32339i	1.01987	−	0.567651i
$216$		0			0
$217$	−2.80436	−	2.03749i	−0.190372	−	0.138314i
$218$	6.79288			0.460072
$219$		0			0
$220$	−7.58097	−	0.917408i	−0.511109	−	0.0618516i
$221$	20.6288	−	14.9877i	1.38765	−	1.00818i
$222$		0			0
$223$	−6.96128	−	21.4246i	−0.466162	−	1.43470i	−0.857516	−	0.514458i	$-0.827993\pi$
$223$	−6.96128	−	21.4246i	−0.466162	−	1.43470i	0.391354	−	0.920240i	$-0.372007\pi$
$224$	0.757055			0.0505829
$225$		0			0
$226$	1.70871			0.113662
$227$	3.07802	+	9.47318i	0.204296	+	0.628757i	0.999742	+	0.0227328i	$0.00723670\pi$
$227$	3.07802	+	9.47318i	0.204296	+	0.628757i	−0.795446	+	0.606025i	$0.792763\pi$
$228$		0			0
$229$	−8.49555	+	6.17238i	−0.561402	+	0.407882i	−0.831972	−	0.554818i	$-0.812788\pi$
$229$	−8.49555	+	6.17238i	−0.561402	+	0.407882i	0.270570	+	0.962700i	$0.412788\pi$
$230$	−4.36840	+	9.41088i	−0.288044	+	0.620535i
$231$		0			0
$232$	−0.157026			−0.0103092
$233$	17.2663	+	12.5447i	1.13115	+	0.821829i	0.985862	−	0.167560i	$-0.0535887\pi$
$233$	17.2663	+	12.5447i	1.13115	+	0.821829i	0.145289	+	0.989389i	$0.453589\pi$
$234$		0			0
$235$	−10.6476	+	22.9381i	−0.694570	+	1.49632i
$236$	2.79557	+	8.60388i	0.181976	+	0.560065i
$237$		0			0
$238$	−1.12072	+	3.44922i	−0.0726454	+	0.223579i
$239$	7.75624	+	23.8712i	0.501709	+	1.54410i	0.806233	+	0.591598i	$0.201503\pi$
$239$	7.75624	+	23.8712i	0.501709	+	1.54410i	−0.304524	+	0.952505i	$0.598497\pi$
$240$		0			0
$241$	−2.89974	+	8.92448i	−0.186789	+	0.574876i	−0.999975	−	0.00712767i	$-0.997731\pi$
$241$	−2.89974	+	8.92448i	−0.186789	+	0.574876i	0.813186	+	0.582004i	$0.197731\pi$
$242$	−0.536020	−	0.389441i	−0.0344567	−	0.0250342i
$243$		0			0
$244$	10.6069	+	7.70634i	0.679035	+	0.493348i
$245$	−12.5569	+	6.98907i	−0.802232	+	0.446515i
$246$		0			0
$247$	−1.58637	+	1.15256i	−0.100938	+	0.0733359i
$248$	1.41492	+	4.35467i	0.0898473	+	0.276522i
$249$		0			0
$250$	10.7841	−	2.95015i	0.682046	−	0.186584i
$251$	−26.3827			−1.66526			−0.832630	−	0.553829i	$-0.813166\pi$
$251$	−26.3827			−1.66526			−0.832630	+	0.553829i	$0.813166\pi$
$252$		0			0
$253$	−12.8195	+	9.31392i	−0.805956	+	0.585561i
$254$	−12.6176	+	9.16724i	−0.791700	+	0.575204i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	3.70789			0.231292			0.115646	−	0.993290i	$-0.463106\pi$
$257$	3.70789			0.231292			0.115646	+	0.993290i	$0.463106\pi$
$258$		0			0
$259$	−1.89084	+	5.81940i	−0.117491	+	0.361600i
$260$	8.71862	+	8.10186i	0.540706	+	0.502456i
$261$		0			0
$262$	5.07979	−	15.6340i	0.313831	−	0.965871i
$263$	4.66990	−	14.3725i	0.287959	−	0.886245i	−0.697538	−	0.716548i	$-0.745721\pi$
$263$	4.66990	−	14.3725i	0.287959	−	0.886245i	0.985496	−	0.169697i	$-0.0542790\pi$
$264$		0			0
$265$	−5.13829	+	11.0695i	−0.315643	+	0.679992i
$266$	0.0861838	−	0.265247i	0.00528427	−	0.0162633i
$267$		0			0
$268$	−2.82365			−0.172482
$269$	14.8677	+	10.8020i	0.906498	+	0.658609i	0.940127	−	0.340825i	$-0.110706\pi$
$269$	14.8677	+	10.8020i	0.906498	+	0.658609i	−0.0336287	+	0.999434i	$0.510706\pi$
$270$		0			0
$271$	19.1346	−	13.9021i	1.16235	−	0.844494i	0.172273	−	0.985049i	$-0.444889\pi$
$271$	19.1346	−	13.9021i	1.16235	−	0.844494i	0.990073	+	0.140555i	$0.0448887\pi$
$272$	3.87565	−	2.81582i	0.234996	−	0.170734i
$273$		0			0
$274$	−7.73402			−0.467229
$275$	16.5823	+	4.07306i	0.999953	+	0.245615i
$276$		0			0
$277$	−1.77153	−	5.45220i	−0.106441	−	0.327591i	0.883625	−	0.468195i	$-0.155096\pi$
$277$	−1.77153	−	5.45220i	−0.106441	−	0.327591i	−0.990066	+	0.140604i	$0.955096\pi$
$278$	−9.02542	+	6.55735i	−0.541309	+	0.393284i
$279$		0			0
$280$	−1.68057	−	0.203373i	−0.100433	−	0.0121538i
$281$	−26.0953	−	18.9593i	−1.55671	−	1.13102i	−0.938639	−	0.344900i	$-0.887913\pi$
$281$	−26.0953	−	18.9593i	−1.55671	−	1.13102i	−0.618075	−	0.786119i	$-0.712087\pi$
$282$		0			0
$283$	14.6401	+	10.6367i	0.870266	+	0.632285i	0.930658	−	0.365889i	$-0.119235\pi$
$283$	14.6401	+	10.6367i	0.870266	+	0.632285i	−0.0603923	+	0.998175i	$0.519235\pi$
$284$	−2.16694	+	6.66916i	−0.128584	+	0.395742i
$285$		0			0
$286$	5.61707	+	17.2876i	0.332144	+	1.02223i
$287$	0.513926	−	1.58170i	0.0303361	−	0.0933648i
$288$		0			0
$289$	1.83850	+	5.65832i	0.108147	+	0.332843i
$290$	0.348577	+	0.0421829i	0.0204691	+	0.00247706i
$291$		0			0
$292$	9.95134	+	7.23008i	0.582358	+	0.423108i
$293$	12.2210			0.713959			0.356979	−	0.934112i	$-0.383807\pi$
$293$	12.2210			0.713959			0.356979	+	0.934112i	$0.383807\pi$
$294$		0			0
$295$	−3.89449	−	19.8505i	−0.226746	−	1.15574i
$296$	6.53886	−	4.75076i	0.380064	−	0.276132i
$297$		0			0
$298$	−0.691293	−	2.12758i	−0.0400455	−	0.123247i
$299$	24.6972			1.42827
$300$		0			0
$301$	5.79439			0.333983
$302$	−5.82797	−	17.9367i	−0.335362	−	1.03214i
$303$		0			0
$304$	−0.298039	+	0.216538i	−0.0170937	+	0.0124193i
$305$	−21.4757	−	19.9565i	−1.22969	−	1.14270i
$306$		0			0
$307$	6.68293			0.381415			0.190708	−	0.981647i	$-0.438922\pi$
$307$	6.68293			0.381415			0.190708	+	0.981647i	$0.438922\pi$
$308$	−2.09162	−	1.51965i	−0.119181	−	0.0865900i
$309$		0			0
$310$	−1.97111	−	10.0469i	−0.111952	−	0.570626i
$311$	6.76848	+	20.8312i	0.383805	+	1.18123i	0.937343	+	0.348407i	$0.113277\pi$
$311$	6.76848	+	20.8312i	0.383805	+	1.18123i	−0.553538	+	0.832824i	$0.686723\pi$
$312$		0			0
$313$	1.86393	−	5.73660i	0.105356	−	0.324252i	−0.884458	−	0.466620i	$-0.845472\pi$
$313$	1.86393	−	5.73660i	0.105356	−	0.324252i	0.989814	+	0.142368i	$0.0454717\pi$
$314$	−0.954495	−	2.93763i	−0.0538653	−	0.165780i
$315$		0			0
$316$	4.68538	−	14.4201i	0.263573	−	0.811195i
$317$	4.55828	+	3.31179i	0.256019	+	0.186008i	0.708390	−	0.705821i	$-0.249422\pi$
$317$	4.55828	+	3.31179i	0.256019	+	0.186008i	−0.452371	+	0.891830i	$0.649422\pi$
$318$		0			0
$319$	0.433835	+	0.315200i	0.0242901	+	0.0176478i
$320$	1.63801	+	1.52214i	0.0915678	+	0.0850902i
$321$		0			0
$322$	−2.84185	+	2.06473i	−0.158370	+	0.115063i
$323$	−0.545362	−	1.67845i	−0.0303448	−	0.0933916i
$324$		0			0
$325$	−17.1778	−	20.3272i	−0.952851	−	1.12755i
$326$	−13.1393			−0.727716
$327$		0			0
$328$	−1.77725	+	1.29125i	−0.0981321	+	0.0712972i
$329$	−6.92675	+	5.03258i	−0.381884	+	0.277455i
$330$		0			0
$331$	21.8782	+	15.8954i	1.20253	+	0.873693i	0.994532	−	0.104436i	$-0.0333036\pi$
$331$	21.8782	+	15.8954i	1.20253	+	0.873693i	0.208003	+	0.978128i	$0.433304\pi$
$332$	6.92889			0.380272
$333$		0			0
$334$	5.01306	−	15.4286i	0.274303	−	0.844217i
$335$	6.26814	+	0.758536i	0.342465	+	0.0414432i
$336$		0			0
$337$	5.76296	−	17.7366i	0.313929	−	0.966173i	−0.662265	−	0.749270i	$-0.730405\pi$
$337$	5.76296	−	17.7366i	0.313929	−	0.966173i	0.976193	−	0.216903i	$-0.0695954\pi$
$338$	4.73751	−	14.5806i	0.257687	−	0.793078i
$339$		0			0
$340$	−9.35988	+	5.20963i	−0.507611	+	0.282532i
$341$	4.83201	−	14.8714i	0.261668	−	0.805331i
$342$		0			0
$343$	−10.1649			−0.548852
$344$	−6.19210	−	4.49882i	−0.333856	−	0.242560i
$345$		0			0
$346$	−18.1671	+	13.1992i	−0.976671	+	0.709593i
$347$	−3.98201	+	2.89310i	−0.213766	+	0.155310i	−0.689516	−	0.724271i	$-0.742177\pi$
$347$	−3.98201	+	2.89310i	−0.213766	+	0.155310i	0.475750	+	0.879580i	$0.342177\pi$
$348$		0			0
$349$	36.8722			1.97372			0.986861	−	0.161572i	$-0.0516565\pi$
$349$	36.8722			1.97372			0.986861	+	0.161572i	$0.0516565\pi$
$350$	3.67601	+	0.902923i	0.196491	+	0.0482633i
$351$		0			0
$352$	1.05531	+	3.24790i	0.0562481	+	0.173114i
$353$	−16.4117	+	11.9238i	−0.873508	+	0.634641i	−0.931526	−	0.363675i	$-0.881522\pi$
$353$	−16.4117	+	11.9238i	−0.873508	+	0.634641i	0.0580178	+	0.998316i	$0.481522\pi$
$354$		0			0
$355$	6.60192	−	14.2226i	0.350393	−	0.754856i
$356$	0.736628	+	0.535191i	0.0390412	+	0.0283651i
$357$		0			0
$358$	15.2206	+	11.0584i	0.804431	+	0.584454i
$359$	0.740055	−	2.27765i	0.0390586	−	0.120210i	−0.929626	−	0.368504i	$-0.879870\pi$
$359$	0.740055	−	2.27765i	0.0390586	−	0.120210i	0.968685	+	0.248294i	$0.0798700\pi$
$360$		0			0
$361$	−5.82938	−	17.9410i	−0.306810	−	0.944263i
$362$	2.65446	−	8.16960i	0.139515	−	0.429384i
$363$		0			0
$364$	1.24520	+	3.83234i	0.0652663	+	0.200869i
$365$	−20.1485	−	18.7231i	−1.05462	−	0.980014i
$366$		0			0
$367$	−27.6443	−	20.0848i	−1.44302	−	1.04842i	−0.987401	−	0.158241i	$-0.949418\pi$
$367$	−27.6443	−	20.0848i	−1.44302	−	1.04842i	−0.455620	−	0.890175i	$-0.650582\pi$
$368$	4.63999			0.241876
$369$		0			0
$370$	−15.7917	+	8.78950i	−0.820970	+	0.456945i
$371$	−3.34271	+	2.42862i	−0.173545	+	0.126088i
$372$		0			0
$373$	5.50140	+	16.9316i	0.284851	+	0.876683i	0.986443	+	0.164103i	$0.0524731\pi$
$373$	5.50140	+	16.9316i	0.284851	+	0.876683i	−0.701592	+	0.712579i	$0.747527\pi$
$374$	−16.3600			−0.845956
$375$		0			0
$376$	11.3095			0.583245
$377$	−0.258275	−	0.794890i	−0.0133019	−	0.0409389i
$378$		0			0
$379$	29.1852	−	21.2043i	1.49914	−	1.08919i	0.528422	−	0.848982i	$-0.322784\pi$
$379$	29.1852	−	21.2043i	1.49914	−	1.08919i	0.970721	−	0.240210i	$-0.0772162\pi$
$380$	0.719780	−	0.400623i	0.0369239	−	0.0205515i
$381$		0			0
$382$	−22.1802			−1.13484
$383$	−31.1901	−	22.6609i	−1.59374	−	1.15792i	−0.898348	−	0.439285i	$-0.855232\pi$
$383$	−31.1901	−	22.6609i	−1.59374	−	1.15792i	−0.695389	−	0.718633i	$-0.744768\pi$
$384$		0			0
$385$	4.23489	+	3.93531i	0.215830	+	0.200562i
$386$	4.59306	+	14.1360i	0.233781	+	0.719503i
$387$		0			0
$388$	−1.07158	+	3.29798i	−0.0544011	+	0.167430i
$389$	−10.4673	−	32.2151i	−0.530715	−	1.63337i	−0.752730	−	0.658329i	$-0.771263\pi$
$389$	−10.4673	−	32.2151i	−0.530715	−	1.63337i	0.222015	−	0.975043i	$-0.428737\pi$
$390$		0			0
$391$	−6.86888	+	21.1402i	−0.347374	+	1.06911i
$392$	5.19945	+	3.77762i	0.262612	+	0.190799i
$393$		0			0
$394$	2.07042	+	1.50425i	0.104306	+	0.0757828i
$395$	−14.2747	+	30.7522i	−0.718239	+	1.54731i
$396$		0			0
$397$	17.1368	−	12.4506i	0.860072	−	0.624879i	−0.0678323	−	0.997697i	$-0.521608\pi$
$397$	17.1368	−	12.4506i	0.860072	−	0.624879i	0.927905	+	0.372818i	$0.121608\pi$
$398$	0.579036	+	1.78209i	0.0290245	+	0.0893281i
$399$		0			0
$400$	−3.22728	−	3.81899i	−0.161364	−	0.190949i
$401$	14.3575			0.716979			0.358490	−	0.933534i	$-0.383292\pi$
$401$	14.3575			0.716979			0.358490	+	0.933534i	$0.383292\pi$
$402$		0			0
$403$	−19.7168	+	14.3251i	−0.982164	+	0.713584i
$404$	11.4926	−	8.34985i	0.571777	−	0.415421i
$405$		0			0
$406$	0.0961735	+	0.0698741i	0.00477301	+	0.00346780i
$407$	−27.6020			−1.36818
$408$		0			0
$409$	0.681893	−	2.09865i	0.0337174	−	0.103772i	−0.932781	−	0.360443i	$-0.882626\pi$
$409$	0.681893	−	2.09865i	0.0337174	−	0.103772i	0.966499	+	0.256671i	$0.0826257\pi$
$410$	4.29214	−	2.38897i	0.211974	−	0.117983i
$411$		0			0
$412$	−1.60456	+	4.93833i	−0.0790511	+	0.243294i
$413$	2.11640	−	6.51361i	0.104141	−	0.320514i
$414$		0			0
$415$	−15.3813	−	1.86136i	−0.755036	−	0.0913704i
$416$	1.64480	−	5.06217i	0.0806429	−	0.248193i
$417$		0			0
$418$	1.25809			0.0615354
$419$	−13.3964	−	9.73303i	−0.654455	−	0.475490i	0.210331	−	0.977630i	$-0.432546\pi$
$419$	−13.3964	−	9.73303i	−0.654455	−	0.475490i	−0.864786	+	0.502141i	$0.832546\pi$
$420$		0			0
$421$	−3.44049	+	2.49966i	−0.167679	+	0.121826i	−0.668460	−	0.743748i	$-0.733046\pi$
$421$	−3.44049	+	2.49966i	−0.167679	+	0.121826i	0.500781	+	0.865574i	$0.333046\pi$
$422$	−14.1599	+	10.2878i	−0.689293	+	0.500801i
$423$		0			0
$424$	5.45775			0.265052
$425$	22.1772	−	9.05030i	1.07575	−	0.439004i
$426$		0			0
$427$	−3.06718	−	9.43980i	−0.148431	−	0.456824i
$428$	−0.513977	+	0.373426i	−0.0248440	+	0.0180503i
$429$		0			0
$430$	12.5371	+	11.6502i	0.604594	+	0.561825i
$431$	−25.9543	−	18.8569i	−1.25018	−	0.908306i	−0.251944	−	0.967742i	$-0.581070\pi$
$431$	−25.9543	−	18.8569i	−1.25018	−	0.908306i	−0.998232	+	0.0594352i	$0.981070\pi$
$432$		0			0
$433$	−9.94229	−	7.22350i	−0.477796	−	0.347139i	0.322676	−	0.946510i	$-0.395418\pi$
$433$	−9.94229	−	7.22350i	−0.477796	−	0.347139i	−0.800472	+	0.599371i	$0.795418\pi$
$434$	1.07117	−	3.29672i	0.0514178	−	0.158248i
$435$		0			0
$436$	2.09912	+	6.46041i	0.100529	+	0.309398i
$437$	0.528221	−	1.62570i	0.0252682	−	0.0777676i
$438$		0			0
$439$	−4.95483	−	15.2494i	−0.236481	−	0.727814i	−0.996921	−	0.0784063i	$-0.975017\pi$
$439$	−4.95483	−	15.2494i	−0.236481	−	0.727814i	0.760440	−	0.649408i	$-0.224983\pi$
$440$	−1.47014	−	7.49343i	−0.0700863	−	0.357235i
$441$		0			0
$442$	20.6288	+	14.9877i	0.981214	+	0.712893i
$443$	21.4037			1.01692			0.508461	−	0.861085i	$-0.330215\pi$
$443$	21.4037			1.01692			0.508461	+	0.861085i	$0.330215\pi$
$444$		0			0
$445$	−1.49145	−	1.38594i	−0.0707014	−	0.0656999i
$446$	18.2249	−	13.2411i	0.862972	−	0.626986i
$447$		0			0
$448$	0.233943	+	0.720002i	0.0110528	+	0.0340169i
$449$	−23.4862			−1.10838			−0.554190	−	0.832390i	$-0.686972\pi$
$449$	−23.4862			−1.10838			−0.554190	+	0.832390i	$0.686972\pi$
$450$		0			0
$451$	7.50218			0.353264
$452$	0.528020	+	1.62508i	0.0248360	+	0.0764373i
$453$		0			0
$454$	−8.05837	+	5.85475i	−0.378198	+	0.274777i
$455$	−1.73468	−	8.84181i	−0.0813232	−	0.414511i
$456$		0			0
$457$	9.67236			0.452454			0.226227	−	0.974075i	$-0.427361\pi$
$457$	9.67236			0.452454			0.226227	+	0.974075i	$0.427361\pi$
$458$	−8.49555	−	6.17238i	−0.396971	−	0.288416i
$459$		0			0
$460$	−10.3002	−	1.24647i	−0.480249	−	0.0581170i
$461$	9.01431	+	27.7432i	0.419838	+	1.29213i	0.907851	+	0.419293i	$0.137722\pi$
$461$	9.01431	+	27.7432i	0.419838	+	1.29213i	−0.488013	+	0.872836i	$0.662278\pi$
$462$		0			0
$463$	−9.74107	+	29.9799i	−0.452706	+	1.39329i	0.421102	+	0.907013i	$0.361644\pi$
$463$	−9.74107	+	29.9799i	−0.452706	+	1.39329i	−0.873808	+	0.486272i	$0.838356\pi$
$464$	−0.0485236	−	0.149340i	−0.00225265	−	0.00693295i
$465$		0			0
$466$	−6.59513	+	20.2977i	−0.305513	+	0.940274i
$467$	6.70921	+	4.87453i	0.310465	+	0.225566i	0.732096	−	0.681201i	$-0.238542\pi$
$467$	6.70921	+	4.87453i	0.310465	+	0.225566i	−0.421631	+	0.906768i	$0.638542\pi$
$468$		0			0
$469$	1.72940	+	1.25648i	0.0798563	+	0.0580190i
$470$	−25.1057	−	3.03816i	−1.15804	−	0.140140i
$471$		0			0
$472$	−7.31889	+	5.31749i	−0.336879	+	0.244757i
$473$	8.07718	+	24.8590i	0.371389	+	1.14302i
$474$		0			0
$475$	−1.70544	+	0.695973i	−0.0782510	+	0.0319334i
$476$	−3.62672			−0.166230
$477$		0			0
$478$	−20.3061	+	14.7532i	−0.928779	+	0.674798i
$479$	9.94974	−	7.22891i	0.454615	−	0.330297i	−0.336800	−	0.941576i	$-0.609345\pi$
$479$	9.94974	−	7.22891i	0.454615	−	0.330297i	0.791415	+	0.611279i	$0.209345\pi$
$480$		0			0
$481$	34.8043	+	25.2868i	1.58694	+	1.15298i
$482$	−9.38375			−0.427418
$483$		0			0
$484$	0.204741	−	0.630129i	0.00930643	−	0.0286422i
$485$	3.26473	−	7.03323i	0.148244	−	0.319362i
$486$		0			0
$487$	6.83776	−	21.0445i	0.309849	−	0.953616i	−0.667975	−	0.744184i	$-0.732839\pi$
$487$	6.83776	−	21.0445i	0.309849	−	0.953616i	0.977823	−	0.209432i	$-0.0671615\pi$
$488$	−4.05146	+	12.4691i	−0.183401	+	0.564450i
$489$		0			0
$490$	−10.5273	−	9.78259i	−0.475575	−	0.441933i
$491$	−2.03450	+	6.26156i	−0.0918158	+	0.282580i	−0.986411	−	0.164298i	$-0.947464\pi$
$491$	−2.03450	+	6.26156i	−0.0918158	+	0.282580i	0.894595	+	0.446878i	$0.147464\pi$
$492$		0			0
$493$	0.752241			0.0338792
$494$	−1.58637	−	1.15256i	−0.0713741	−	0.0518563i
$495$		0			0
$496$	−3.70430	+	2.69133i	−0.166328	+	0.120844i
$497$	4.29487	−	3.12040i	0.192651	−	0.139969i
$498$		0			0
$499$	3.16838			0.141836			0.0709182	−	0.997482i	$-0.477407\pi$
$499$	3.16838			0.141836			0.0709182	+	0.997482i	$0.477407\pi$
$500$	6.13823	+	9.34463i	0.274510	+	0.417905i
$501$		0			0
$502$	−8.15270	−	25.0914i	−0.363873	−	1.11989i
$503$	−16.2211	+	11.7853i	−0.723264	+	0.525482i	−0.887425	−	0.460951i	$-0.847508\pi$
$503$	−16.2211	+	11.7853i	−0.723264	+	0.525482i	0.164161	+	0.986433i	$0.447508\pi$
$504$		0			0
$505$	−27.7551	+	15.4483i	−1.23509	+	0.687439i
$506$	−12.8195	−	9.31392i	−0.569897	−	0.414054i
$507$		0			0
$508$	−12.6176	−	9.16724i	−0.559817	−	0.406731i
$509$	−7.64644	+	23.5333i	−0.338922	+	1.04310i	0.625835	+	0.779955i	$0.284758\pi$
$509$	−7.64644	+	23.5333i	−0.338922	+	1.04310i	−0.964757	+	0.263141i	$0.915242\pi$
$510$		0			0
$511$	−2.87762	−	8.85641i	−0.127299	−	0.391785i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$		0			0
$514$	1.14580	+	3.52641i	0.0505391	+	0.155543i
$515$	4.88854	−	10.5314i	0.215415	−	0.464070i
$516$		0			0
$517$	−31.2464	−	22.7018i	−1.37421	−	0.998424i
$518$	−6.11888			−0.268848
$519$		0			0
$520$	−5.01113	+	10.7955i	−0.219752	+	0.473415i
$521$	33.3030	−	24.1960i	1.45903	−	1.06005i	0.475414	−	0.879762i	$-0.342298\pi$
$521$	33.3030	−	24.1960i	1.45903	−	1.06005i	0.983615	−	0.180284i	$-0.0577018\pi$
$522$		0			0
$523$	−2.82203	−	8.68532i	−0.123399	−	0.379783i	0.870207	−	0.492686i	$-0.163985\pi$
$523$	−2.82203	−	8.68532i	−0.123399	−	0.379783i	−0.993606	+	0.112903i	$0.963985\pi$
$524$	16.4385			0.718121
$525$		0			0
$526$	15.1121			0.658920
$527$	−6.77825	−	20.8613i	−0.295265	−	0.908733i
$528$		0			0
$529$	1.18966	−	0.864339i	0.0517244	−	0.0375800i
$530$	−12.1155	−	1.46615i	−0.526264	−	0.0636856i
$531$		0			0
$532$	0.278897			0.0120917
$533$	−9.45972	−	6.87289i	−0.409746	−	0.297698i
$534$		0			0
$535$	1.24128	−	0.690886i	0.0536652	−	0.0298696i
$536$	−0.872555	−	2.68545i	−0.0376886	−	0.115994i
$537$		0			0
$538$	−5.67895	+	17.4780i	−0.244837	+	0.753530i
$539$	−6.78233	−	20.8739i	−0.292135	−	0.899100i
$540$		0			0
$541$	−2.14537	+	6.60278i	−0.0922368	+	0.283876i	−0.986524	−	0.163618i	$-0.947683\pi$
$541$	−2.14537	+	6.60278i	−0.0922368	+	0.283876i	0.894287	+	0.447494i	$0.147683\pi$
$542$	19.1346	+	13.9021i	0.821903	+	0.597147i
$543$		0			0
$544$	3.87565	+	2.81582i	0.166167	+	0.120727i
$545$	−2.92426	−	14.9052i	−0.125262	−	0.638468i
$546$		0			0
$547$	33.2583	−	24.1635i	1.42202	−	1.03316i	0.430587	−	0.902549i	$-0.358307\pi$
$547$	33.2583	−	24.1635i	1.42202	−	1.03316i	0.991434	−	0.130610i	$-0.0416934\pi$
$548$	−2.38994	−	7.35549i	−0.102093	−	0.314211i
$549$		0			0
$550$	1.25052	+	17.0294i	0.0533223	+	0.726136i
$551$	−0.0578478			−0.00246440
$552$		0			0
$553$	−9.28640	+	6.74697i	−0.394898	+	0.286910i
$554$	4.63792	−	3.36965i	0.197046	−	0.143163i
$555$		0			0
$556$	−9.02542	−	6.55735i	−0.382763	−	0.278094i
$557$	11.3965			0.482884			0.241442	−	0.970415i	$-0.422380\pi$
$557$	11.3965			0.482884			0.241442	+	0.970415i	$0.422380\pi$
$558$		0			0
$559$	12.5891	−	38.7451i	0.532460	−	1.63874i
$560$	−0.325904	−	1.66116i	−0.0137720	−	0.0701967i
$561$		0			0
$562$	9.96751	−	30.6768i	0.420454	−	1.29402i
$563$	4.01128	−	12.3455i	0.169055	−	0.520299i	−0.830257	−	0.557381i	$-0.811806\pi$
$563$	4.01128	−	12.3455i	0.169055	−	0.520299i	0.999312	+	0.0370821i	$0.0118063\pi$
$564$		0			0
$565$	−0.735581	−	3.74931i	−0.0309461	−	0.157735i
$566$	−5.59204	+	17.2105i	−0.235051	+	0.723412i
$567$		0			0
$568$	−7.01237			−0.294233
$569$	−9.93141	−	7.21559i	−0.416347	−	0.302493i	0.359820	−	0.933022i	$-0.382838\pi$
$569$	−9.93141	−	7.21559i	−0.416347	−	0.302493i	−0.776166	+	0.630528i	$0.782838\pi$
$570$		0			0
$571$	−3.54421	+	2.57502i	−0.148321	+	0.107761i	−0.659471	−	0.751730i	$-0.729220\pi$
$571$	−3.54421	+	2.57502i	−0.148321	+	0.107761i	0.511150	+	0.859491i	$0.329220\pi$
$572$	−14.7057	+	10.6843i	−0.614875	+	0.446733i
$573$		0			0
$574$	1.66310			0.0694164
$575$	22.5302	+	5.53402i	0.939576	+	0.230784i
$576$		0			0
$577$	5.60242	+	17.2425i	0.233232	+	0.717814i	0.997351	+	0.0727386i	$0.0231739\pi$
$577$	5.60242	+	17.2425i	0.233232	+	0.717814i	−0.764119	+	0.645075i	$0.776826\pi$
$578$	−4.81326	+	3.49704i	−0.200205	+	0.145458i
$579$		0			0
$580$	0.0675979	+	0.344552i	0.00280685	+	0.0143067i
$581$	−4.24374	−	3.08326i	−0.176060	−	0.127915i
$582$		0			0
$583$	−15.0788	−	10.9554i	−0.624502	−	0.453727i
$584$	−3.80108	+	11.6985i	−0.157290	+	0.484088i
$585$		0			0
$586$	3.77650	+	11.6229i	0.156006	+	0.480136i
$587$	−5.23334	+	16.1066i	−0.216003	+	0.664789i	0.783078	+	0.621924i	$0.213649\pi$
$587$	−5.23334	+	16.1066i	−0.216003	+	0.664789i	−0.999081	+	0.0428655i	$0.986351\pi$
$588$		0			0
$589$	0.521251	+	1.60425i	0.0214778	+	0.0661018i
$590$	17.6755	−	9.83802i	0.727688	−	0.405025i
$591$		0			0
$592$	6.53886	+	4.75076i	0.268745	+	0.195255i
$593$	−3.07662			−0.126342			−0.0631709	−	0.998003i	$-0.520121\pi$
$593$	−3.07662			−0.126342			−0.0631709	+	0.998003i	$0.520121\pi$
$594$		0			0
$595$	8.05086	+	0.974270i	0.330053	+	0.0399412i
$596$	1.80983	−	1.31492i	0.0741334	−	0.0538611i
$597$		0			0
$598$	7.63185	+	23.4884i	0.312089	+	0.960512i
$599$	17.6867			0.722659			0.361329	−	0.932438i	$-0.382323\pi$
$599$	17.6867			0.722659			0.361329	+	0.932438i	$0.382323\pi$
$600$		0			0
$601$	4.35491			0.177640			0.0888202	−	0.996048i	$-0.471690\pi$
$601$	4.35491			0.177640			0.0888202	+	0.996048i	$0.471690\pi$
$602$	1.79056	+	5.51079i	0.0729780	+	0.224603i
$603$		0			0
$604$	15.2578	−	11.0855i	0.620832	−	0.451061i
$605$	−0.623776	+	1.34381i	−0.0253601	+	0.0546335i
$606$		0			0
$607$	1.39480			0.0566131			0.0283066	−	0.999599i	$-0.490989\pi$
$607$	1.39480			0.0566131			0.0283066	+	0.999599i	$0.490989\pi$
$608$	−0.298039	−	0.216538i	−0.0120871	−	0.00878179i
$609$		0			0
$610$	12.3434	−	26.5915i	0.499769	−	1.07666i
$611$	18.6019	+	57.2508i	0.752553	+	2.31612i
$612$		0			0
$613$	−0.252641	+	0.777550i	−0.0102041	+	0.0314049i	−0.956029	−	0.293272i	$-0.905256\pi$
$613$	−0.252641	+	0.777550i	−0.0102041	+	0.0314049i	0.945825	+	0.324677i	$0.105256\pi$
$614$	2.06514	+	6.35585i	0.0833423	+	0.256501i
$615$		0			0
$616$	0.798926	−	2.45884i	0.0321896	−	0.0990695i
$617$	28.1657	+	20.4636i	1.13391	+	0.823833i	0.986259	−	0.165207i	$-0.0528292\pi$
$617$	28.1657	+	20.4636i	1.13391	+	0.823833i	0.147650	+	0.989040i	$0.452829\pi$
$618$		0			0
$619$	1.81990	+	1.32223i	0.0731480	+	0.0531451i	0.623758	−	0.781617i	$-0.285605\pi$
$619$	1.81990	+	1.32223i	0.0731480	+	0.0531451i	−0.550610	+	0.834762i	$0.685605\pi$
$620$	8.94606	−	4.97930i	0.359283	−	0.199974i
$621$		0			0
$622$	−17.7201	+	12.8744i	−0.710512	+	0.516217i
$623$	−0.213010	−	0.655577i	−0.00853407	−	0.0262652i
$624$		0			0
$625$	−11.1158	−	22.3928i	−0.444631	−	0.895714i
$626$	6.03182			0.241080
$627$		0			0
$628$	2.49890	−	1.81556i	0.0997170	−	0.0724486i
$629$	−31.3248	+	22.7588i	−1.24900	+	0.907454i
$630$		0			0
$631$	−13.8717	−	10.0784i	−0.552225	−	0.401215i	0.276380	−	0.961048i	$-0.410865\pi$
$631$	−13.8717	−	10.0784i	−0.552225	−	0.401215i	−0.828605	+	0.559833i	$0.810865\pi$
$632$	15.1622			0.603120
$633$		0			0
$634$	−1.74111	+	5.35858i	−0.0691483	+	0.212816i
$635$	25.5469	+	23.7397i	1.01380	+	0.942080i
$636$		0			0
$637$	−10.5709	+	32.5339i	−0.418834	+	1.28904i
$638$	−0.165710	+	0.510004i	−0.00656054	+	0.0201913i
$639$		0			0
$640$	−0.941467	+	2.02821i	−0.0372148	+	0.0801721i
$641$	1.05804	−	3.25632i	0.0417902	−	0.128617i	−0.927985	−	0.372618i	$-0.878460\pi$
$641$	1.05804	−	3.25632i	0.0417902	−	0.128617i	0.969775	+	0.244001i	$0.0784601\pi$
$642$		0			0
$643$	35.7348			1.40924			0.704622	−	0.709583i	$-0.251117\pi$
$643$	35.7348			1.40924			0.704622	+	0.709583i	$0.251117\pi$
$644$	−2.84185	−	2.06473i	−0.111985	−	0.0813617i
$645$		0			0
$646$	1.42778	−	1.03734i	0.0561752	−	0.0408136i
$647$	7.28879	−	5.29562i	0.286552	−	0.208192i	−0.435218	−	0.900325i	$-0.643329\pi$
$647$	7.28879	−	5.29562i	0.286552	−	0.208192i	0.721770	+	0.692133i	$0.243329\pi$
$648$		0			0
$649$	30.8948			1.21273
$650$	14.0241	−	22.6185i	0.550072	−	0.887170i
$651$		0			0
$652$	−4.06026	−	12.4962i	−0.159012	−	0.489388i
$653$	−32.6076	+	23.6908i	−1.27603	+	0.927092i	−0.999426	−	0.0338908i	$-0.989210\pi$
$653$	−32.6076	+	23.6908i	−1.27603	+	0.927092i	−0.276607	+	0.960983i	$0.589210\pi$
$654$		0			0
$655$	−36.4915	−	4.41600i	−1.42584	−	0.172547i
$656$	−1.77725	−	1.29125i	−0.0693899	−	0.0504147i
$657$		0			0
$658$	−6.92675	−	5.03258i	−0.270033	−	0.196190i
$659$	6.89337	−	21.2156i	0.268527	−	0.826443i	−0.722332	−	0.691546i	$-0.756930\pi$
$659$	6.89337	−	21.2156i	0.268527	−	0.826443i	0.990860	−	0.134896i	$-0.0430702\pi$
$660$		0			0
$661$	7.53432	+	23.1882i	0.293051	+	0.901918i	0.983869	+	0.178889i	$0.0572505\pi$
$661$	7.53432	+	23.1882i	0.293051	+	0.901918i	−0.690818	+	0.723028i	$0.742750\pi$
$662$	−8.35673	+	25.7194i	−0.324794	+	0.999612i
$663$		0			0
$664$	2.14115	+	6.58977i	0.0830926	+	0.255733i
$665$	−0.619115	−	0.0749219i	−0.0240083	−	0.00290535i
$666$		0			0
$667$	0.589447	+	0.428259i	0.0228235	+	0.0165822i
$668$	16.2226			0.627672
$669$		0			0
$670$	1.21555	+	6.19575i	0.0469608	+	0.239363i
$671$	36.2230	−	26.3175i	1.39837	−	1.01598i
$672$		0			0
$673$	13.3741	+	41.1612i	0.515533	+	1.58665i	0.782311	+	0.622889i	$0.214041\pi$
$673$	13.3741	+	41.1612i	0.515533	+	1.58665i	−0.266778	+	0.963758i	$0.585959\pi$
$674$	18.6493			0.718346
$675$		0			0
$676$	15.3309			0.589651
$677$	13.0504	+	40.1649i	0.501566	+	1.54366i	0.806468	+	0.591278i	$0.201377\pi$
$677$	13.0504	+	40.1649i	0.501566	+	1.54366i	−0.304901	+	0.952384i	$0.598623\pi$
$678$		0			0
$679$	2.12386	−	1.54308i	0.0815064	−	0.0592179i
$680$	−7.84701	−	7.29191i	−0.300919	−	0.279632i
$681$		0			0
$682$	15.6367			0.598761
$683$	−11.8307	−	8.59550i	−0.452689	−	0.328898i	0.337968	−	0.941158i	$-0.390261\pi$
$683$	−11.8307	−	8.59550i	−0.452689	−	0.328898i	−0.790656	+	0.612260i	$0.790261\pi$
$684$		0			0
$685$	3.32942	+	16.9703i	0.127210	+	0.648401i
$686$	−3.14112	−	9.66737i	−0.119928	−	0.369102i
$687$		0			0
$688$	2.36517	−	7.27925i	0.0901713	−	0.277519i
$689$	8.97690	+	27.6281i	0.341993	+	1.05254i
$690$		0			0
$691$	1.08250	−	3.33158i	0.0411801	−	0.126739i	−0.928353	−	0.371700i	$-0.878775\pi$
$691$	1.08250	−	3.33158i	0.0411801	−	0.126739i	0.969533	+	0.244961i	$0.0787750\pi$
$692$	−18.1671	−	13.1992i	−0.690611	−	0.501758i
$693$		0			0
$694$	−3.98201	−	2.89310i	−0.151155	−	0.109821i
$695$	18.2737	+	16.9810i	0.693162	+	0.644128i
$696$		0			0
$697$	8.51402	−	6.18580i	0.322492	−	0.234304i
$698$	11.3941	+	35.0675i	0.431274	+	1.32732i
$699$		0			0
$700$	0.277218	+	3.77511i	0.0104778	+	0.142686i
$701$	−9.02395			−0.340830			−0.170415	−	0.985372i	$-0.554511\pi$
$701$	−9.02395			−0.340830			−0.170415	+	0.985372i	$0.554511\pi$
$702$		0			0
$703$	2.40890	−	1.75017i	0.0908533	−	0.0660088i
$704$	−2.76283	+	2.00732i	−0.104128	+	0.0756535i
$705$		0			0
$706$	−16.4117	−	11.9238i	−0.617664	−	0.448759i
$707$	−10.7544			−0.404462
$708$		0			0
$709$	−1.02371	+	3.15066i	−0.0384462	+	0.118325i	−0.968438	−	0.249256i	$-0.919814\pi$
$709$	−1.02371	+	3.15066i	−0.0384462	+	0.118325i	0.929991	+	0.367581i	$0.119814\pi$
$710$	15.5666	+	1.88378i	0.584203	+	0.0706970i
$711$		0			0
$712$	−0.281367	+	0.865958i	−0.0105447	+	0.0324531i
$713$	6.56520	−	20.2056i	0.245869	−	0.756706i
$714$		0			0
$715$	35.5149	−	19.7673i	1.32818	−	0.739255i
$716$	−5.81373	+	17.8928i	−0.217269	+	0.668687i
$717$		0			0
$718$	2.39487			0.0893757
$719$	6.42008	+	4.66446i	0.239429	+	0.173955i	0.701029	−	0.713133i	$-0.252724\pi$
$719$	6.42008	+	4.66446i	0.239429	+	0.173955i	−0.461600	+	0.887088i	$0.652724\pi$
$720$		0			0
$721$	3.18023	−	2.31058i	0.118438	−	0.0860503i
$722$	15.2615	−	11.0881i	0.567975	−	0.412658i
$723$		0			0
$724$	8.59002			0.319246
$725$	−0.0574995	−	0.783020i	−0.00213548	−	0.0290806i
$726$		0			0
$727$	−9.98054	−	30.7170i	−0.370158	−	1.13923i	−0.946688	−	0.322153i	$-0.895594\pi$
$727$	−9.98054	−	30.7170i	−0.370158	−	1.13923i	0.576530	−	0.817076i	$-0.304406\pi$
$728$	−3.25998	+	2.36852i	−0.120823	+	0.0877830i
$729$		0			0
$730$	11.5806	−	24.9481i	0.428615	−	0.923370i
$731$	29.6637	+	21.5519i	1.09715	+	0.797126i
$732$		0			0
$733$	15.3898	+	11.1813i	0.568434	+	0.412991i	0.834536	−	0.550954i	$-0.185736\pi$
$733$	15.3898	+	11.1813i	0.568434	+	0.412991i	−0.266102	+	0.963945i	$0.585736\pi$
$734$	10.5592	−	32.4978i	0.389746	−	1.19952i
$735$		0			0
$736$	1.43384	+	4.41289i	0.0528519	+	0.162661i
$737$	−2.97982	+	9.17094i	−0.109763	+	0.337816i
$738$		0			0
$739$	4.78189	+	14.7172i	0.175905	+	0.541379i	0.999674	−	0.0255466i	$-0.00813261\pi$
$739$	4.78189	+	14.7172i	0.175905	+	0.541379i	−0.823769	+	0.566926i	$0.808133\pi$
$740$	−13.2392	−	12.3027i	−0.486683	−	0.452255i
$741$		0			0
$742$	−3.34271	−	2.42862i	−0.122715	−	0.0891575i
$743$	−6.45309			−0.236741			−0.118370	−	0.992970i	$-0.537767\pi$
$743$	−6.45309			−0.236741			−0.118370	+	0.992970i	$0.537767\pi$
$744$		0			0
$745$	−4.37082	+	2.43276i	−0.160135	+	0.0891295i
$746$	−14.4028	+	10.4643i	−0.527325	+	0.383124i
$747$		0			0
$748$	−5.05552	−	15.5593i	−0.184848	−	0.568904i
$749$	0.480965			0.0175741
$750$		0			0
$751$	−10.3545			−0.377842			−0.188921	−	0.981992i	$-0.560499\pi$
$751$	−10.3545			−0.377842			−0.188921	+	0.981992i	$0.560499\pi$
$752$	3.49484	+	10.7560i	0.127444	+	0.392231i
$753$		0			0
$754$	0.676174	−	0.491269i	0.0246248	−	0.0178910i
$755$	−36.8484	+	20.5095i	−1.34105	+	0.746417i
$756$		0			0
$757$	0.883693			0.0321184			0.0160592	−	0.999871i	$-0.494888\pi$
$757$	0.883693			0.0321184			0.0160592	+	0.999871i	$0.494888\pi$
$758$	29.1852	+	21.2043i	1.06005	+	0.770175i
$759$		0			0
$760$	0.603440	+	0.560752i	0.0218891	+	0.0203406i
$761$	1.21638	+	3.74363i	0.0440937	+	0.135706i	0.970680	−	0.240376i	$-0.0772708\pi$
$761$	1.21638	+	3.74363i	0.0440937	+	0.135706i	−0.926586	+	0.376083i	$0.877271\pi$
$762$		0			0
$763$	1.58915	−	4.89089i	0.0575309	−	0.177062i
$764$	−6.85405	−	21.0946i	−0.247971	−	0.763175i
$765$		0			0
$766$	11.9135	−	36.6661i	0.430454	−	1.32480i
$767$	−38.9561	−	28.3033i	−1.40662	−	1.02197i
$768$		0			0
$769$	3.49330	+	2.53803i	0.125972	+	0.0915237i	0.648987	−	0.760800i	$-0.275193\pi$
$769$	3.49330	+	2.53803i	0.125972	+	0.0915237i	−0.523015	+	0.852323i	$0.675193\pi$
$770$	−2.43405	+	5.24369i	−0.0877170	+	0.188970i
$771$		0			0
$772$	−12.0248	+	8.73652i	−0.432782	+	0.314434i
$773$	8.28955	+	25.5126i	0.298154	+	0.917625i	0.982144	+	0.188133i	$0.0602435\pi$
$773$	8.28955	+	25.5126i	0.298154	+	0.917625i	−0.683989	+	0.729492i	$0.739756\pi$
$774$		0			0
$775$	−21.1967	+	8.65017i	−0.761410	+	0.310723i
$776$	−3.46770			−0.124483
$777$		0			0
$778$	27.4038	−	19.9101i	0.982475	−	0.713810i
$779$	−0.654733	+	0.475691i	−0.0234582	+	0.0170434i
$780$		0			0
$781$	19.3740	+	14.0760i	0.693257	+	0.503680i
$782$	−22.2282			−0.794878
$783$		0			0
$784$	−1.98601	+	6.11231i	−0.0709290	+	0.218297i
$785$	−6.03497	+	3.35901i	−0.215397	+	0.119888i
$786$		0			0
$787$	−9.33947	+	28.7439i	−0.332916	+	1.02461i	0.634823	+	0.772658i	$0.281073\pi$
$787$	−9.33947	+	28.7439i	−0.332916	+	1.02461i	−0.967739	+	0.251953i	$0.918927\pi$
$788$	−0.790829	+	2.43392i	−0.0281721	+	0.0867048i
$789$		0			0
$790$	−33.6582	−	4.07313i	−1.19750	−	0.144915i
$791$	0.399740	−	1.23027i	0.0142131	−	0.0437435i
$792$		0			0
$793$	−69.7846			−2.47812
$794$	17.1368	+	12.4506i	0.608163	+	0.441856i
$795$		0			0
$796$	−1.51594	+	1.10139i	−0.0537310	+	0.0390378i
$797$	40.0204	−	29.0765i	1.41760	−	1.02994i	0.425434	−	0.904990i	$-0.360122\pi$
$797$	40.0204	−	29.0765i	1.41760	−	1.02994i	0.992163	−	0.124954i	$-0.0398784\pi$
$798$		0			0
$799$	−54.1791			−1.91672
$800$	2.63479	−	4.24946i	0.0931539	−	0.150241i
$801$		0			0
$802$	4.43671	+	13.6548i	0.156666	+	0.482167i
$803$	33.9843	−	24.6911i	1.19928	−	0.871329i
$804$		0			0
$805$	5.75389	+	5.34686i	0.202798	+	0.188452i
$806$	−19.7168	−	14.3251i	−0.694495	−	0.504580i
$807$		0			0
$808$	11.4926	+	8.34985i	0.404308	+	0.293747i
$809$	−10.3694	+	31.9136i	−0.364567	+	1.12202i	0.585684	+	0.810539i	$0.300826\pi$
$809$	−10.3694	+	31.9136i	−0.364567	+	1.12202i	−0.950252	+	0.311483i	$0.899174\pi$
$810$		0			0
$811$	−6.06842	−	18.6767i	−0.213091	−	0.655827i	−0.999284	−	0.0378454i	$-0.987951\pi$
$811$	−6.06842	−	18.6767i	−0.213091	−	0.655827i	0.786192	−	0.617982i	$-0.212049\pi$
$812$	−0.0367350	+	0.113059i	−0.00128915	+	0.00396758i
$813$		0			0
$814$	−8.52950	−	26.2511i	−0.298959	−	0.920101i
$815$	5.65632	+	28.8307i	0.198132	+	1.00989i
$816$		0			0
$817$	−2.28115	−	1.65735i	−0.0798074	−	0.0579835i
$818$	2.20665			0.0771538
$819$		0			0
$820$	3.59839	+	3.34384i	0.125661	+	0.116772i
$821$	43.1724	−	31.3666i	1.50673	−	1.09470i	0.539122	−	0.842228i	$-0.318756\pi$
$821$	43.1724	−	31.3666i	1.50673	−	1.09470i	0.967604	−	0.252473i	$-0.0812439\pi$
$822$		0			0
$823$	−5.26586	−	16.2067i	−0.183556	−	0.564928i	0.816364	−	0.577538i	$-0.195986\pi$
$823$	−5.26586	−	16.2067i	−0.183556	−	0.564928i	−0.999921	+	0.0126091i	$0.995986\pi$
$824$	−5.19247			−0.180888
$825$		0			0
$826$	6.84881			0.238301
$827$	−7.45044	−	22.9301i	−0.259077	−	0.797358i	−0.992999	−	0.118124i	$-0.962312\pi$
$827$	−7.45044	−	22.9301i	−0.259077	−	0.797358i	0.733922	−	0.679234i	$-0.237688\pi$
$828$		0			0
$829$	−11.4314	+	8.30540i	−0.397029	+	0.288459i	−0.768330	−	0.640054i	$-0.778912\pi$
$829$	−11.4314	+	8.30540i	−0.397029	+	0.288459i	0.371301	+	0.928513i	$0.378912\pi$
$830$	−2.98282	−	15.2036i	−0.103535	−	0.527726i
$831$		0			0
$832$	5.32268			0.184531
$833$	−24.9083	−	18.0969i	−0.863021	−	0.627021i
$834$		0			0
$835$	−36.0121	−	4.35799i	−1.24625	−	0.150815i
$836$	0.388772	+	1.19652i	0.0134460	+	0.0413825i
$837$		0			0
$838$	5.11696	−	15.7484i	0.176762	−	0.544019i
$839$	−6.91404	−	21.2792i	−0.238699	−	0.734640i	−0.996609	−	0.0822812i	$-0.973779\pi$
$839$	−6.91404	−	21.2792i	−0.238699	−	0.734640i	0.757910	−	0.652359i	$-0.226221\pi$
$840$		0			0
$841$	−8.95387	+	27.5572i	−0.308754	+	0.950248i
$842$	−3.44049	−	2.49966i	−0.118567	−	0.0861441i
$843$		0			0
$844$	−14.1599	−	10.2878i	−0.487404	−	0.354120i
$845$	−34.0327	−	4.11845i	−1.17076	−	0.141679i
$846$		0			0
$847$	−0.405796	+	0.294828i	−0.0139433	+	0.0101304i
$848$	1.68654	+	5.19063i	0.0579159	+	0.178247i
$849$		0			0
$850$	15.4605	+	18.2951i	0.530290	+	0.627517i
$851$	−37.5026			−1.28557
$852$		0			0
$853$	17.1397	−	12.4527i	0.586852	−	0.426373i	−0.254336	−	0.967116i	$-0.581857\pi$
$853$	17.1397	−	12.4527i	0.586852	−	0.426373i	0.841188	+	0.540743i	$0.181857\pi$
$854$	8.02998	−	5.83412i	0.274780	−	0.199639i
$855$		0			0
$856$	−0.513977	−	0.373426i	−0.0175674	−	0.0127635i
$857$	40.7978			1.39363			0.696813	−	0.717253i	$-0.254601\pi$
$857$	40.7978			1.39363			0.696813	+	0.717253i	$0.254601\pi$
$858$		0			0
$859$	−17.3408	+	53.3694i	−0.591659	+	1.82094i	−0.0209604	+	0.999780i	$0.506672\pi$
$859$	−17.3408	+	53.3694i	−0.591659	+	1.82094i	−0.570699	+	0.821159i	$0.693328\pi$
$860$	−7.20586	+	15.5236i	−0.245718	+	0.529352i
$861$		0			0
$862$	9.91368	−	30.5112i	0.337661	−	1.03921i
$863$	4.26345	−	13.1215i	0.145130	−	0.446663i	−0.851898	−	0.523708i	$-0.824548\pi$
$863$	4.26345	−	13.1215i	0.145130	−	0.446663i	0.997028	+	0.0770449i	$0.0245485\pi$
$864$		0			0
$865$	36.7829	+	34.1809i	1.25066	+	1.16219i
$866$	3.79762	−	11.6879i	0.129048	−	0.397170i
$867$		0			0
$868$	3.46638			0.117656
$869$	−41.8906	−	30.4353i	−1.42104	−	1.03245i
$870$		0			0
$871$	12.1590	−	8.83404i	0.411993	−	0.299330i
$872$	−5.49555	+	3.99275i	−0.186103	+	0.135212i
$873$		0			0
$874$	1.70936			0.0578199
$875$	0.398745	−	8.45473i	0.0134801	−	0.285822i
$876$		0			0
$877$	4.94954	+	15.2331i	0.167134	+	0.514386i	0.999187	−	0.0403099i	$-0.0128345\pi$
$877$	4.94954	+	15.2331i	0.167134	+	0.514386i	−0.832053	+	0.554696i	$0.812835\pi$
$878$	12.9719	−	9.42465i	0.437781	−	0.318066i
$879$		0			0
$880$	6.67237	−	3.71379i	0.224926	−	0.125192i
$881$	−3.32564	−	2.41622i	−0.112044	−	0.0814044i	0.530353	−	0.847777i	$-0.322060\pi$
$881$	−3.32564	−	2.41622i	−0.112044	−	0.0814044i	−0.642396	+	0.766373i	$0.722060\pi$
$882$		0			0
$883$	−19.5667	−	14.2160i	−0.658471	−	0.478407i	0.207675	−	0.978198i	$-0.433410\pi$
$883$	−19.5667	−	14.2160i	−0.658471	−	0.478407i	−0.866146	+	0.499790i	$0.833410\pi$
$884$	−7.87951	+	24.2506i	−0.265017	+	0.815638i
$885$		0			0
$886$	6.61411	+	20.3561i	0.222206	+	0.683878i
$887$	5.44908	−	16.7705i	0.182962	−	0.563100i	−0.816945	−	0.576715i	$-0.804334\pi$
$887$	5.44908	−	16.7705i	0.182962	−	0.563100i	0.999907	+	0.0136158i	$0.00433418\pi$
$888$		0			0
$889$	3.64863	+	11.2293i	0.122371	+	0.376619i
$890$	0.857226	−	1.84673i	0.0287343	−	0.0619025i
$891$		0			0
$892$	18.2249	+	13.2411i	0.610214	+	0.443346i
$893$	4.16640			0.139423
$894$		0			0
$895$	17.7124	−	38.1580i	0.592061	−	1.27548i
$896$	−0.612470	+	0.444986i	−0.0204612	+	0.0148659i
$897$		0			0
$898$	−7.25763	−	22.3367i	−0.242190	−	0.745385i
$899$	−0.718984			−0.0239794
$900$		0			0
$901$	−26.1457			−0.871040
$902$	2.31830	+	7.13500i	0.0771910	+	0.237569i
$903$		0			0
$904$	−1.38237	+	1.00435i	−0.0459771	+	0.0334043i
$905$	−19.0688	−	2.30760i	−0.633867	−	0.0767071i
$906$		0			0
$907$	−11.6990			−0.388459			−0.194229	−	0.980956i	$-0.562221\pi$
$907$	−11.6990			−0.388459			−0.194229	+	0.980956i	$0.562221\pi$
$908$	−8.05837	−	5.85475i	−0.267426	−	0.194297i
$909$		0			0
$910$	7.87302	−	4.38205i	0.260988	−	0.145264i
$911$	−1.30687	−	4.02212i	−0.0432984	−	0.133259i	0.927070	−	0.374887i	$-0.122319\pi$
$911$	−1.30687	−	4.02212i	−0.0432984	−	0.133259i	−0.970369	+	0.241628i	$0.922319\pi$
$912$		0			0
$913$	7.31212	−	22.5044i	0.241996	−	0.744786i
$914$	2.98892	+	9.19896i	0.0988648	+	0.304275i
$915$		0			0
$916$	3.24501	−	9.98712i	0.107218	−	0.329984i
$917$	−10.0681	−	7.31492i	−0.332479	−	0.241560i
$918$		0			0
$919$	39.6608	+	28.8153i	1.30829	+	0.950528i	1.00000		0.000764639i	$-0.000243392\pi$
$919$	39.6608	+	28.8153i	1.30829	+	0.950528i	0.308290	+	0.951293i	$0.400243\pi$
$920$	−1.99747	−	10.1812i	−0.0658545	−	0.335665i
$921$		0			0
$922$	−23.5998	+	17.1462i	−0.777217	+	0.564681i
$923$	−11.5339	−	35.4978i	−0.379644	−	1.16842i
$924$		0			0
$925$	26.0844	+	30.8669i	0.857650	+	1.01490i
$926$	−31.5228			−1.03590
$927$		0			0
$928$	0.127036	−	0.0922973i	0.00417017	−	0.00302981i
$929$	8.96621	−	6.51433i	0.294172	−	0.213728i	−0.430903	−	0.902398i	$-0.641805\pi$
$929$	8.96621	−	6.51433i	0.294172	−	0.213728i	0.725075	+	0.688670i	$0.241805\pi$
$930$		0			0
$931$	1.91546	+	1.39166i	0.0627767	+	0.0456099i
$932$	−21.3423			−0.699090
$933$		0			0
$934$	−2.56269	+	7.88715i	−0.0838538	+	0.258075i
$935$	7.04282	+	35.8978i	0.230325	+	1.17398i
$936$		0			0
$937$	−18.1912	+	55.9868i	−0.594281	+	1.82901i	−0.0360074	+	0.999352i	$0.511464\pi$
$937$	−18.1912	+	55.9868i	−0.594281	+	1.82901i	−0.558274	+	0.829657i	$0.688536\pi$
$938$	−0.660572	+	2.03303i	−0.0215684	+	0.0663808i
$939$		0			0
$940$	−4.86864	−	24.8158i	−0.158797	−	0.809403i
$941$	−6.92122	+	21.3013i	−0.225625	+	0.694404i	0.772602	+	0.634891i	$0.218955\pi$
$941$	−6.92122	+	21.3013i	−0.225625	+	0.694404i	−0.998228	+	0.0595131i	$0.981045\pi$
$942$		0			0
$943$	10.1931			0.331934
$944$	−7.31889	−	5.31749i	−0.238210	−	0.173070i
$945$		0			0
$946$	−21.1463	+	15.3637i	−0.687526	+	0.499517i
$947$	−17.1876	+	12.4875i	−0.558522	+	0.405790i	−0.830918	−	0.556395i	$-0.812184\pi$
$947$	−17.1876	+	12.4875i	−0.558522	+	0.405790i	0.272396	+	0.962185i	$0.412184\pi$
$948$		0			0
$949$	−65.4718			−2.12531
$950$	−1.18892	−	1.40690i	−0.0385737	−	0.0456460i
$951$		0			0
$952$	−1.12072	−	3.44922i	−0.0363227	−	0.111790i
$953$	−0.328756	+	0.238856i	−0.0106495	+	0.00773729i	−0.593097	−	0.805131i	$-0.702095\pi$
$953$	−0.328756	+	0.238856i	−0.0106495	+	0.00773729i	0.582448	+	0.812868i	$0.302095\pi$
$954$		0			0
$955$	9.54833	+	48.6685i	0.308977	+	1.57488i
$956$	−20.3061	−	14.7532i	−0.656746	−	0.477154i
$957$		0			0
$958$	9.94974	+	7.22891i	0.321461	+	0.233555i
$959$	−1.80932	+	5.56851i	−0.0584259	+	0.179817i
$960$		0			0
$961$	−3.10096	−	9.54376i	−0.100031	−	0.307863i
$962$	−13.2940	+	40.9149i	−0.428617	+	1.31915i
$963$		0			0
$964$	−2.89974	−	8.92448i	−0.0933943	−	0.287438i
$965$	29.0405	−	16.1637i	0.934845	−	0.520327i
$966$		0			0
$967$	−33.4953	−	24.3358i	−1.07714	−	0.782586i	−0.0999553	−	0.994992i	$-0.531870\pi$
$967$	−33.4953	−	24.3358i	−1.07714	−	0.782586i	−0.977181	+	0.212406i	$0.931870\pi$
$968$	0.662557			0.0212954
$969$		0			0
$970$	7.69785	+	0.931552i	0.247163	+	0.0299103i
$971$	−30.5279	+	22.1798i	−0.979687	+	0.711785i	−0.957639	−	0.287972i	$-0.907019\pi$
$971$	−30.5279	+	22.1798i	−0.979687	+	0.711785i	−0.0220486	+	0.999757i	$0.507019\pi$
$972$		0			0
$973$	2.60987	+	8.03237i	0.0836687	+	0.257506i
$974$	22.1275			0.709010
$975$		0			0
$976$	−13.1108			−0.419667
$977$	−15.7373	−	48.4343i	−0.503479	−	1.54955i	−0.803312	−	0.595558i	$-0.796931\pi$
$977$	−15.7373	−	48.4343i	−0.503479	−	1.54955i	0.299833	−	0.953992i	$-0.403069\pi$
$978$		0			0
$979$	2.51562	−	1.82770i	0.0803995	−	0.0584137i
$980$	6.05068	−	13.0350i	0.193282	−	0.416389i
$981$		0			0
$982$	−6.58379			−0.210097
$983$	−30.1830	−	21.9293i	−0.962689	−	0.699435i	−0.00891538	−	0.999960i	$-0.502838\pi$
$983$	−30.1830	−	21.9293i	−0.962689	−	0.699435i	−0.953774	+	0.300526i	$0.902838\pi$
$984$		0			0
$985$	2.40938	−	5.19055i	0.0767692	−	0.165385i
$986$	0.232455	+	0.715424i	0.00740289	+	0.0227837i
$987$		0			0
$988$	0.605939	−	1.86489i	0.0192775	−	0.0593300i
$989$	10.9744	+	33.7756i	0.348965	+	1.07400i
$990$		0			0
$991$	9.68847	−	29.8180i	0.307764	−	0.947201i	−0.670867	−	0.741578i	$-0.734078\pi$
$991$	9.68847	−	29.8180i	0.307764	−	0.947201i	0.978631	−	0.205623i	$-0.0659222\pi$
$992$	−3.70430	−	2.69133i	−0.117612	−	0.0854498i
$993$		0			0
$994$	4.29487	+	3.12040i	0.136225	+	0.0989732i
$995$	3.66106	−	2.03771i	0.116063	−	0.0645999i
$996$		0			0
$997$	4.02084	−	2.92131i	0.127341	−	0.0925188i	−0.522292	−	0.852767i	$-0.674923\pi$
$997$	4.02084	−	2.92131i	0.127341	−	0.0925188i	0.649633	+	0.760248i	$0.274923\pi$
$998$	0.979085	+	3.01331i	0.0309924	+	0.0953848i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.f.181.3	✓	12
3.2	odd	2		450.2.h.g.181.1	yes	12
25.21	even	5	inner	450.2.h.f.271.3	yes	12
75.71	odd	10		450.2.h.g.271.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.h.f.181.3	✓	12	1.1	even	1	trivial
450.2.h.f.271.3	yes	12	25.21	even	5	inner
450.2.h.g.181.1	yes	12	3.2	odd	2
450.2.h.g.271.1	yes	12	75.71	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(1.95382 - 1.08748i) q^{5} +0.757055 q^{7} +(-0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(1.95382 - 1.08748i) q^{5} +0.757055 q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.63801 + 1.52214i) q^{10} +(1.05531 + 3.24790i) q^{11} +(1.64480 - 5.06217i) q^{13} +(0.233943 + 0.720002i) q^{14} +(0.309017 - 0.951057i) q^{16} +(3.87565 + 2.81582i) q^{17} +(-0.298039 - 0.216538i) q^{19} +(-0.941467 + 2.02821i) q^{20} +(-2.76283 + 2.00732i) q^{22} +(1.43384 + 4.41289i) q^{23} +(2.63479 - 4.24946i) q^{25} +5.32268 q^{26} +(-0.612470 + 0.444986i) q^{28} +(0.127036 - 0.0922973i) q^{29} +(-3.70430 - 2.69133i) q^{31} +1.00000 q^{32} +(-1.48037 + 4.55610i) q^{34} +(1.47915 - 0.823279i) q^{35} +(-2.49762 + 7.68689i) q^{37} +(0.113841 - 0.350366i) q^{38} +(-2.21987 - 0.268637i) q^{40} +(0.678849 - 2.08928i) q^{41} +7.65386 q^{43} +(-2.76283 - 2.00732i) q^{44} +(-3.75383 + 2.72732i) q^{46} +(-9.14961 + 6.64758i) q^{47} -6.42687 q^{49} +(4.85567 + 1.19268i) q^{50} +(1.64480 + 5.06217i) q^{52} +(-4.41541 + 3.20798i) q^{53} +(5.59390 + 5.19818i) q^{55} +(-0.612470 - 0.444986i) q^{56} +(0.127036 + 0.0922973i) q^{58} +(2.79557 - 8.60388i) q^{59} +(-4.05146 - 12.4691i) q^{61} +(1.41492 - 4.35467i) q^{62} +(0.309017 + 0.951057i) q^{64} +(-2.29136 - 11.6792i) q^{65} +(2.28438 + 1.65970i) q^{67} -4.79056 q^{68} +(1.24007 + 1.15234i) q^{70} +(5.67313 - 4.12177i) q^{71} +(-3.80108 - 11.6985i) q^{73} -8.08248 q^{74} +0.368397 q^{76} +(0.798926 + 2.45884i) q^{77} +(-12.2665 + 8.91212i) q^{79} +(-0.430490 - 2.19424i) q^{80} +2.19680 q^{82} +(-5.60559 - 4.07270i) q^{83} +(10.6344 + 1.28692i) q^{85} +(2.36517 + 7.27925i) q^{86} +(1.05531 - 3.24790i) q^{88} +(-0.281367 - 0.865958i) q^{89} +(1.24520 - 3.83234i) q^{91} +(-3.75383 - 2.72732i) q^{92} +(-9.14961 - 6.64758i) q^{94} +(-0.817795 - 0.0989650i) q^{95} +(2.80543 - 2.03826i) q^{97} +(-1.98601 - 6.11231i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + q^{5} - 2 q^{7} - 3 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 + q^5 - 2 * q^7 - 3 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} + q^{5} - 2 q^{7} - 3 q^{8} + q^{10} + q^{11} + 4 q^{13} + 8 q^{14} - 3 q^{16} - 8 q^{17} - 8 q^{19} + q^{20} - 4 q^{22} - 11 q^{25} - 16 q^{26} - 7 q^{28} - 6 q^{29} - 3 q^{31} + 12 q^{32} + 2 q^{34} - 18 q^{35} - 8 q^{37} + 2 q^{38} + q^{40} + 20 q^{41} + 32 q^{43} - 4 q^{44} - 10 q^{46} + 34 q^{49} + 9 q^{50} + 4 q^{52} + 2 q^{53} + 44 q^{55} - 7 q^{56} - 6 q^{58} - 19 q^{59} - 26 q^{61} + 2 q^{62} - 3 q^{64} + 16 q^{65} - 16 q^{67} + 12 q^{68} - 23 q^{70} + 48 q^{71} - 30 q^{73} - 8 q^{74} + 12 q^{76} - 39 q^{77} - 18 q^{79} - 4 q^{80} - 40 q^{82} - 29 q^{83} - 4 q^{85} + 12 q^{86} + q^{88} + 62 q^{89} - 26 q^{91} - 10 q^{92} + 6 q^{95} + 23 q^{97} - 6 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + q^5 - 2 * q^7 - 3 * q^8 + q^10 + q^11 + 4 * q^13 + 8 * q^14 - 3 * q^16 - 8 * q^17 - 8 * q^19 + q^20 - 4 * q^22 - 11 * q^25 - 16 * q^26 - 7 * q^28 - 6 * q^29 - 3 * q^31 + 12 * q^32 + 2 * q^34 - 18 * q^35 - 8 * q^37 + 2 * q^38 + q^40 + 20 * q^41 + 32 * q^43 - 4 * q^44 - 10 * q^46 + 34 * q^49 + 9 * q^50 + 4 * q^52 + 2 * q^53 + 44 * q^55 - 7 * q^56 - 6 * q^58 - 19 * q^59 - 26 * q^61 + 2 * q^62 - 3 * q^64 + 16 * q^65 - 16 * q^67 + 12 * q^68 - 23 * q^70 + 48 * q^71 - 30 * q^73 - 8 * q^74 + 12 * q^76 - 39 * q^77 - 18 * q^79 - 4 * q^80 - 40 * q^82 - 29 * q^83 - 4 * q^85 + 12 * q^86 + q^88 + 62 * q^89 - 26 * q^91 - 10 * q^92 + 6 * q^95 + 23 * q^97 - 6 * q^98

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