LMFDB - Embedded newform 396.2.r.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,2,Mod(19,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("396.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.r (of order $10$, 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:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	396.19
Dual form			396.2.r.b.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16623 + 0.799941i) q^{2} +(0.720190 - 1.86583i) q^{4} +(1.53251 + 1.11343i) q^{5} +(-1.07196 + 3.29914i) q^{7} +(0.652646 + 2.75210i) q^{8} +O(q^{10})$	\(q+(-1.16623 + 0.799941i) q^{2} +(0.720190 - 1.86583i) q^{4} +(1.53251 + 1.11343i) q^{5} +(-1.07196 + 3.29914i) q^{7} +(0.652646 + 2.75210i) q^{8} +(-2.67794 - 0.0726042i) q^{10} +(0.210969 - 3.30991i) q^{11} +(1.06787 + 1.46980i) q^{13} +(-1.38897 - 4.70507i) q^{14} +(-2.96265 - 2.68751i) q^{16} +(-1.74921 + 2.40759i) q^{17} +(1.34636 + 4.14366i) q^{19} +(3.18118 - 2.05752i) q^{20} +(2.40169 + 4.02888i) q^{22} +3.82341i q^{23} +(-0.436233 - 1.34259i) q^{25} +(-2.42114 - 0.859894i) q^{26} +(5.38363 + 4.37610i) q^{28} +(8.48417 + 2.75668i) q^{29} +(-1.65449 - 2.27721i) q^{31} +(5.60498 + 0.764309i) q^{32} +(0.114062 - 4.20707i) q^{34} +(-5.31616 + 3.86242i) q^{35} +(-3.51620 + 10.8218i) q^{37} +(-4.88484 - 3.75546i) q^{38} +(-2.06409 + 4.94430i) q^{40} +(-7.37845 + 2.39740i) q^{41} -2.35165 q^{43} +(-6.02379 - 2.77740i) q^{44} +(-3.05850 - 4.45898i) q^{46} +(2.66757 - 0.866745i) q^{47} +(-4.07214 - 2.95858i) q^{49} +(1.58274 + 1.21681i) q^{50} +(3.51148 - 0.933936i) q^{52} +(-5.05557 + 3.67309i) q^{53} +(4.00867 - 4.83757i) q^{55} +(-9.77918 - 0.796961i) q^{56} +(-12.0997 + 3.57191i) q^{58} +(7.68642 + 2.49747i) q^{59} +(4.57345 - 6.29481i) q^{61} +(3.75115 + 1.33226i) q^{62} +(-7.14811 + 3.59229i) q^{64} +3.44150i q^{65} -15.0787i q^{67} +(3.23238 + 4.99766i) q^{68} +(3.11017 - 8.75708i) q^{70} +(3.24129 - 4.46126i) q^{71} +(11.1487 + 3.62244i) q^{73} +(-4.55606 - 15.4334i) q^{74} +(8.70100 + 0.472149i) q^{76} +(10.6937 + 4.24410i) q^{77} +(4.34223 - 3.15482i) q^{79} +(-1.54793 - 7.41735i) q^{80} +(6.68720 - 8.69825i) q^{82} +(-6.10662 - 4.43672i) q^{83} +(-5.36138 + 1.74202i) q^{85} +(2.74257 - 1.88118i) q^{86} +(9.24689 - 1.57959i) q^{88} +5.20905 q^{89} +(-5.99381 + 1.94751i) q^{91} +(7.13384 + 2.75358i) q^{92} +(-2.41765 + 3.14472i) q^{94} +(-2.55038 + 7.84928i) q^{95} +(6.72491 - 4.88593i) q^{97} +(7.11574 + 0.192922i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} + 14 q^{14} - 24 q^{16} + 22 q^{20} - 26 q^{22} - 20 q^{25} + 38 q^{26} - 10 q^{28} - 48 q^{37} - 58 q^{38} + 70 q^{40} + 40 q^{41} - 34 q^{44} + 70 q^{46} - 28 q^{49} - 70 q^{50} + 30 q^{52} + 64 q^{53} - 60 q^{56} - 54 q^{58} - 40 q^{64} + 4 q^{70} + 20 q^{73} - 50 q^{74} + 8 q^{77} - 58 q^{80} + 62 q^{82} + 40 q^{85} - 8 q^{86} + 8 q^{88} - 48 q^{89} - 42 q^{92} - 10 q^{94} + 48 q^{97}+O(q^{100}) $ 48 * q - 4 * q^4 + 14 * q^14 - 24 * q^16 + 22 * q^20 - 26 * q^22 - 20 * q^25 + 38 * q^26 - 10 * q^28 - 48 * q^37 - 58 * q^38 + 70 * q^40 + 40 * q^41 - 34 * q^44 + 70 * q^46 - 28 * q^49 - 70 * q^50 + 30 * q^52 + 64 * q^53 - 60 * q^56 - 54 * q^58 - 40 * q^64 + 4 * q^70 + 20 * q^73 - 50 * q^74 + 8 * q^77 - 58 * q^80 + 62 * q^82 + 40 * q^85 - 8 * q^86 + 8 * q^88 - 48 * q^89 - 42 * q^92 - 10 * q^94 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.16623	+	0.799941i	−0.824650	+	0.565643i
$2$	−1.16623	+	0.799941i	−0.824650	+	0.565643i
$3$		0			0
$3$		0			0
$4$	0.720190	−	1.86583i	0.360095	−	0.932916i
$5$	1.53251	+	1.11343i	0.685359	+	0.497943i	0.875131	−	0.483886i	$-0.160775\pi$
$5$	1.53251	+	1.11343i	0.685359	+	0.497943i	−0.189772	+	0.981828i	$0.560775\pi$
$6$		0			0
$7$	−1.07196	+	3.29914i	−0.405162	+	1.24696i	0.515599	+	0.856830i	$0.327570\pi$
$7$	−1.07196	+	3.29914i	−0.405162	+	1.24696i	−0.920760	+	0.390129i	$0.872430\pi$
$8$	0.652646	+	2.75210i	0.230745	+	0.973014i
$9$		0			0
$10$	−2.67794	−	0.0726042i	−0.846839	−	0.0229595i
$11$	0.210969	−	3.30991i	0.0636096	−	0.997975i
$11$	0.210969	−	3.30991i	0.0636096	−	0.997975i
$12$		0			0
$13$	1.06787	+	1.46980i	0.296175	+	0.407650i	0.931008	−	0.365000i	$-0.118931\pi$
$13$	1.06787	+	1.46980i	0.296175	+	0.407650i	−0.634833	+	0.772650i	$0.718931\pi$
$14$	−1.38897	−	4.70507i	−0.371218	−	1.25748i
$15$		0			0
$16$	−2.96265	−	2.68751i	−0.740663	−	0.671877i
$17$	−1.74921	+	2.40759i	−0.424247	+	0.583926i	−0.966621	−	0.256212i	$-0.917526\pi$
$17$	−1.74921	+	2.40759i	−0.424247	+	0.583926i	0.542374	+	0.840137i	$0.317526\pi$
$18$		0			0
$19$	1.34636	+	4.14366i	0.308875	+	0.950621i	0.978203	+	0.207653i	$0.0665825\pi$
$19$	1.34636	+	4.14366i	0.308875	+	0.950621i	−0.669327	+	0.742968i	$0.733418\pi$
$20$	3.18118	−	2.05752i	0.711333	−	0.460076i
$21$		0			0
$22$	2.40169	+	4.02888i	0.512042	+	0.858960i
$23$			3.82341i			0.797236i	0.917117	+	0.398618i	$0.130510\pi$
$23$			3.82341i			0.797236i	−0.917117	+	0.398618i	$0.869490\pi$
$24$		0			0
$25$	−0.436233	−	1.34259i	−0.0872466	−	0.268517i
$26$	−2.42114	−	0.859894i	−0.474825	−	0.168639i
$27$		0			0
$28$	5.38363	+	4.37610i	1.01741	+	0.827005i
$29$	8.48417	+	2.75668i	1.57547	+	0.511902i	0.960885	−	0.276948i	$-0.0893228\pi$
$29$	8.48417	+	2.75668i	1.57547	+	0.511902i	0.614587	+	0.788849i	$0.289323\pi$
$30$		0			0
$31$	−1.65449	−	2.27721i	−0.297155	−	0.408999i	0.634167	−	0.773196i	$-0.281343\pi$
$31$	−1.65449	−	2.27721i	−0.297155	−	0.408999i	−0.931322	+	0.364197i	$0.881343\pi$
$32$	5.60498	+	0.764309i	0.990830	+	0.135112i
$33$		0			0
$34$	0.114062	−	4.20707i	0.0195615	−	0.721507i
$35$	−5.31616	+	3.86242i	−0.898595	+	0.652868i
$36$		0			0
$37$	−3.51620	+	10.8218i	−0.578060	+	1.77909i	0.0474530	+	0.998873i	$0.484890\pi$
$37$	−3.51620	+	10.8218i	−0.578060	+	1.77909i	−0.625513	+	0.780213i	$0.715110\pi$
$38$	−4.88484	−	3.75546i	−0.792426	−	0.609216i
$39$		0			0
$40$	−2.06409	+	4.94430i	−0.326362	+	0.781762i
$41$	−7.37845	+	2.39740i	−1.15232	+	0.374412i	−0.822017	−	0.569463i	$-0.807151\pi$
$41$	−7.37845	+	2.39740i	−1.15232	+	0.374412i	−0.330304	+	0.943875i	$0.607151\pi$
$42$		0			0
$43$	−2.35165			−0.358623			−0.179312	−	0.983792i	$-0.557387\pi$
$43$	−2.35165			−0.358623			−0.179312	+	0.983792i	$0.557387\pi$
$44$	−6.02379	−	2.77740i	−0.908121	−	0.418708i
$45$		0			0
$46$	−3.05850	−	4.45898i	−0.450951	−	0.657441i
$47$	2.66757	−	0.866745i	0.389104	−	0.126428i	−0.107930	−	0.994158i	$-0.534422\pi$
$47$	2.66757	−	0.866745i	0.389104	−	0.126428i	0.497034	+	0.867731i	$0.334422\pi$
$48$		0			0
$49$	−4.07214	−	2.95858i	−0.581734	−	0.422654i
$50$	1.58274	+	1.21681i	0.223833	+	0.172082i
$51$		0			0
$52$	3.51148	−	0.933936i	0.486954	−	0.129514i
$53$	−5.05557	+	3.67309i	−0.694437	+	0.504538i	−0.878116	−	0.478449i	$-0.841199\pi$
$53$	−5.05557	+	3.67309i	−0.694437	+	0.504538i	0.183679	+	0.982986i	$0.441199\pi$
$54$		0			0
$55$	4.00867	−	4.83757i	0.540530	−	0.652297i
$56$	−9.77918	−	0.796961i	−1.30680	−	0.106498i
$57$		0			0
$58$	−12.0997	+	3.57191i	−1.58877	+	0.469015i
$59$	7.68642	+	2.49747i	1.00069	+	0.325143i	0.763140	−	0.646233i	$-0.223657\pi$
$59$	7.68642	+	2.49747i	1.00069	+	0.325143i	0.237547	+	0.971376i	$0.423657\pi$
$60$		0			0
$61$	4.57345	−	6.29481i	0.585570	−	0.805968i	−0.408722	−	0.912659i	$-0.634025\pi$
$61$	4.57345	−	6.29481i	0.585570	−	0.805968i	0.994292	+	0.106691i	$0.0340255\pi$
$62$	3.75115	+	1.33226i	0.476396	+	0.169197i
$63$		0			0
$64$	−7.14811	+	3.59229i	−0.893513	+	0.449036i
$65$			3.44150i			0.426865i
$66$		0			0
$67$		−	15.0787i		−	1.84216i	−0.389377	−	0.921079i	$-0.627310\pi$
$67$		−	15.0787i		−	1.84216i	0.389377	−	0.921079i	$-0.372690\pi$
$68$	3.23238	+	4.99766i	0.391984	+	0.606055i
$69$		0			0
$70$	3.11017	−	8.75708i	0.371736	−	1.04667i
$71$	3.24129	−	4.46126i	0.384671	−	0.529454i	−0.572144	−	0.820153i	$-0.693888\pi$
$71$	3.24129	−	4.46126i	0.384671	−	0.529454i	0.956814	+	0.290700i	$0.0938880\pi$
$72$		0			0
$73$	11.1487	+	3.62244i	1.30486	+	0.423974i	0.877269	−	0.479999i	$-0.159363\pi$
$73$	11.1487	+	3.62244i	1.30486	+	0.423974i	0.427589	+	0.903973i	$0.359363\pi$
$74$	−4.55606	−	15.4334i	−0.529631	−	1.79410i
$75$		0			0
$76$	8.70100	+	0.472149i	0.998073	+	0.0541593i
$77$	10.6937	+	4.24410i	1.21866	+	0.483660i
$78$		0			0
$79$	4.34223	−	3.15482i	0.488539	−	0.354945i	−0.316083	−	0.948732i	$-0.602368\pi$
$79$	4.34223	−	3.15482i	0.488539	−	0.354945i	0.804622	+	0.593787i	$0.202368\pi$
$80$	−1.54793	−	7.41735i	−0.173064	−	0.829285i
$81$		0			0
$82$	6.68720	−	8.69825i	0.738478	−	0.960561i
$83$	−6.10662	−	4.43672i	−0.670288	−	0.486993i	0.199833	−	0.979830i	$-0.435960\pi$
$83$	−6.10662	−	4.43672i	−0.670288	−	0.486993i	−0.870122	+	0.492837i	$0.835960\pi$
$84$		0			0
$85$	−5.36138	+	1.74202i	−0.581523	+	0.188948i
$86$	2.74257	−	1.88118i	0.295738	−	0.202853i
$87$		0			0
$88$	9.24689	−	1.57959i	0.985721	−	0.168385i
$89$	5.20905			0.552158			0.276079	−	0.961135i	$-0.410965\pi$
$89$	5.20905			0.552158			0.276079	+	0.961135i	$0.410965\pi$
$90$		0			0
$91$	−5.99381	+	1.94751i	−0.628322	+	0.204154i
$92$	7.13384	+	2.75358i	0.743754	+	0.287081i
$93$		0			0
$94$	−2.41765	+	3.14472i	−0.249362	+	0.324353i
$95$	−2.55038	+	7.84928i	−0.261664	+	0.805319i
$96$		0			0
$97$	6.72491	−	4.88593i	0.682811	−	0.496091i	−0.191478	−	0.981497i	$-0.561328\pi$
$97$	6.72491	−	4.88593i	0.682811	−	0.496091i	0.874289	+	0.485406i	$0.161328\pi$
$98$	7.11574	+	0.192922i	0.718799	+	0.0194880i
$99$		0			0
$100$	−2.81921	−	0.152981i	−0.281921	−	0.0152981i
$101$	−7.18085	−	9.88359i	−0.714521	−	0.983454i	−0.999688	−	0.0249764i	$-0.992049\pi$
$101$	−7.18085	−	9.88359i	−0.714521	−	0.983454i	0.285167	−	0.958478i	$-0.407951\pi$
$102$		0			0
$103$	13.0192	+	4.23019i	1.28282	+	0.416813i	0.869572	−	0.493806i	$-0.164395\pi$
$103$	13.0192	+	4.23019i	1.28282	+	0.416813i	0.413246	+	0.910619i	$0.364395\pi$
$104$	−3.34810	+	3.89816i	−0.328308	+	0.382246i
$105$		0			0
$106$	2.95772	−	8.32783i	0.287279	−	0.808870i
$107$	−1.16180	−	3.57564i	−0.112315	−	0.345670i	0.879062	−	0.476707i	$-0.158170\pi$
$107$	−1.16180	−	3.57564i	−0.112315	−	0.345670i	−0.991378	+	0.131036i	$0.958170\pi$
$108$		0			0
$109$		−	1.43350i		−	0.137305i	−0.997641	−	0.0686524i	$-0.978130\pi$
$109$		−	1.43350i		−	0.137305i	0.997641	−	0.0686524i	$-0.0218699\pi$
$110$	−0.805276	+	8.84842i	−0.0767801	+	0.843664i
$111$		0			0
$112$	12.0423	−	6.89332i	1.13789	−	0.651358i
$113$	−3.77854	−	11.6292i	−0.355455	−	1.09398i	−0.955745	−	0.294196i	$-0.904948\pi$
$113$	−3.77854	−	11.6292i	−0.355455	−	1.09398i	0.600290	−	0.799783i	$-0.295052\pi$
$114$		0			0
$115$	−4.25711	+	5.85941i	−0.396978	+	0.546393i
$116$	11.2537	−	13.8447i	1.04488	−	1.28545i
$117$		0			0
$118$	−10.9620	+	3.23605i	−1.00913	+	0.297903i
$119$	−6.06789	−	8.35174i	−0.556243	−	0.765603i
$120$		0			0
$121$	−10.9110	−	1.39658i	−0.991908	−	0.126962i
$122$	−0.298223	+	10.9997i	−0.0269999	+	0.995866i
$123$		0			0
$124$	−5.44044	+	1.44697i	−0.488566	+	0.129942i
$125$	3.75318	−	11.5511i	0.335695	−	1.03316i
$126$		0			0
$127$	−4.15959	−	3.02212i	−0.369104	−	0.268170i	0.387735	−	0.921771i	$-0.373258\pi$
$127$	−4.15959	−	3.02212i	−0.369104	−	0.268170i	−0.756839	+	0.653601i	$0.773258\pi$
$128$	5.46273	−	9.90750i	0.482841	−	0.875708i
$129$		0			0
$130$	−2.75299	−	4.01358i	−0.241453	−	0.352014i
$131$	3.48536			0.304517			0.152259	−	0.988341i	$-0.451345\pi$
$131$	3.48536			0.304517			0.152259	+	0.988341i	$0.451345\pi$
$132$		0			0
$133$	−15.1138			−1.31053
$134$	12.0621	+	17.5853i	1.04200	+	1.51913i
$135$		0			0
$136$	−7.76754	−	3.24271i	−0.666061	−	0.278060i
$137$	2.73135	+	1.98444i	0.233355	+	0.169542i	0.698318	−	0.715788i	$-0.253932\pi$
$137$	2.73135	+	1.98444i	0.233355	+	0.169542i	−0.464963	+	0.885330i	$0.653932\pi$
$138$		0			0
$139$	−7.02174	+	21.6107i	−0.595577	+	1.83300i	−0.0437412	+	0.999043i	$0.513928\pi$
$139$	−7.02174	+	21.6107i	−0.595577	+	1.83300i	−0.551835	+	0.833953i	$0.686072\pi$
$140$	3.37797	+	12.7007i	0.285491	+	1.07341i
$141$		0			0
$142$	−0.211357	+	7.79570i	−0.0177367	+	0.654201i
$143$	5.09020	−	3.22448i	0.425664	−	0.269645i
$144$		0			0
$145$	9.93271	+	13.6712i	0.824866	+	1.13533i
$146$	−15.8997	+	4.69371i	−1.31587	+	0.388454i
$147$		0			0
$148$	17.6592	+	14.3544i	1.45158	+	1.17992i
$149$	8.22015	−	11.3141i	0.673421	−	0.926884i	−0.326411	−	0.945228i	$-0.605839\pi$
$149$	8.22015	−	11.3141i	0.673421	−	0.926884i	0.999832	+	0.0183440i	$0.00583941\pi$
$150$		0			0
$151$	−2.51556	−	7.74210i	−0.204713	−	0.630043i	−0.999725	−	0.0234490i	$-0.992535\pi$
$151$	−2.51556	−	7.74210i	−0.204713	−	0.630043i	0.795012	−	0.606594i	$-0.207465\pi$
$152$	−10.5251	+	6.40965i	−0.853696	+	0.519891i
$153$		0			0
$154$	−15.8664	+	3.60474i	−1.27855	+	0.290478i
$155$		−	5.33201i		−	0.428277i
$156$		0			0
$157$	−5.73392	−	17.6472i	−0.457617	−	1.40840i	−0.868036	−	0.496502i	$-0.834618\pi$
$157$	−5.73392	−	17.6472i	−0.457617	−	1.40840i	0.410419	−	0.911897i	$-0.365382\pi$
$158$	−2.54038	+	7.15277i	−0.202102	+	0.569044i
$159$		0			0
$160$	7.73868	+	7.41209i	0.611797	+	0.585977i
$161$	−12.6140	−	4.09853i	−0.994121	−	0.323009i
$162$		0			0
$163$	0.374651	+	0.515663i	0.0293450	+	0.0403899i	0.823437	−	0.567407i	$-0.192053\pi$
$163$	0.374651	+	0.515663i	0.0293450	+	0.0403899i	−0.794092	+	0.607797i	$0.792053\pi$
$164$	−0.840738	+	15.4935i	−0.0656506	+	1.20984i
$165$		0			0
$166$	10.6708	+	0.289307i	0.828218	+	0.0224546i
$167$	7.36364	−	5.35000i	0.569816	−	0.413995i	−0.265223	−	0.964187i	$-0.585445\pi$
$167$	7.36364	−	5.35000i	0.569816	−	0.413995i	0.835038	+	0.550192i	$0.185445\pi$
$168$		0			0
$169$	2.99726	−	9.22460i	0.230558	−	0.709585i
$170$	4.85910	−	6.32038i	0.372676	−	0.484751i
$171$		0			0
$172$	−1.69363	+	4.38778i	−0.129138	+	0.334565i
$173$	−15.6017	+	5.06931i	−1.18618	+	0.385412i	−0.834658	−	0.550769i	$-0.814335\pi$
$173$	−15.6017	+	5.06931i	−1.18618	+	0.385412i	−0.351519	+	0.936181i	$0.614335\pi$
$174$		0			0
$175$	4.89701			0.370179
$176$	−9.52043	+	9.23912i	−0.717629	+	0.696425i
$177$		0			0
$178$	−6.07496	+	4.16693i	−0.455337	+	0.312325i
$179$	−0.513988	+	0.167005i	−0.0384172	+	0.0124825i	−0.328163	−	0.944621i	$-0.606429\pi$
$179$	−0.513988	+	0.167005i	−0.0384172	+	0.0124825i	0.289745	+	0.957104i	$0.406429\pi$
$180$		0			0
$181$	4.07479	+	2.96051i	0.302877	+	0.220053i	0.728834	−	0.684690i	$-0.240063\pi$
$181$	4.07479	+	2.96051i	0.302877	+	0.220053i	−0.425957	+	0.904743i	$0.640063\pi$
$182$	5.43228	−	7.06593i	0.402667	−	0.523762i
$183$		0			0
$184$	−10.5224	+	2.49533i	−0.775722	+	0.183958i
$185$	−17.4379	+	12.6694i	−1.28206	+	0.931473i
$186$		0			0
$187$	7.59986	+	6.29767i	0.555757	+	0.460531i
$188$	0.303956	−	5.60145i	0.0221683	−	0.408528i
$189$		0			0
$190$	−3.30462	−	11.1942i	−0.239742	−	0.812115i
$191$	2.78876	+	0.906124i	0.201788	+	0.0655648i	0.408167	−	0.912907i	$-0.366168\pi$
$191$	2.78876	+	0.906124i	0.201788	+	0.0655648i	−0.206379	+	0.978472i	$0.566168\pi$
$192$		0			0
$193$	6.51760	−	8.97070i	0.469147	−	0.645725i	−0.507227	−	0.861812i	$-0.669329\pi$
$193$	6.51760	−	8.97070i	0.469147	−	0.645725i	0.976374	+	0.216087i	$0.0693295\pi$
$194$	−3.93434	+	11.0777i	−0.282469	+	0.795329i
$195$		0			0
$196$	−8.45293	+	5.46718i	−0.603780	+	0.390513i
$197$		−	5.97699i		−	0.425843i	−0.977069	−	0.212921i	$-0.931702\pi$
$197$		−	5.97699i		−	0.425843i	0.977069	−	0.212921i	$-0.0682978\pi$
$198$		0			0
$199$		−	2.73310i		−	0.193745i	−0.995297	−	0.0968723i	$-0.969116\pi$
$199$		−	2.73310i		−	0.193745i	0.995297	−	0.0968723i	$-0.0308838\pi$
$200$	3.41023	−	2.07679i	0.241140	−	0.146851i
$201$		0			0
$202$	16.2808	+	5.78230i	1.14551	+	0.406841i
$203$	−18.1893	+	25.0355i	−1.27664	+	1.75715i
$204$		0			0
$205$	−13.9769	−	4.54137i	−0.976189	−	0.317183i
$206$	−18.5673	+	5.48119i	−1.29364	+	0.381893i
$207$		0			0
$208$	0.786366	−	7.22444i	0.0545247	−	0.500925i
$209$	13.9992	−	3.58213i	0.968343	−	0.247781i
$210$		0			0
$211$	−20.5281	+	14.9146i	−1.41321	+	1.02676i	−0.420370	+	0.907353i	$0.638100\pi$
$211$	−20.5281	+	14.9146i	−1.41321	+	1.02676i	−0.992845	+	0.119408i	$0.961900\pi$
$212$	3.21239	+	12.0782i	0.220628	+	0.829532i
$213$		0			0
$214$	4.21522	+	3.24066i	0.288147	+	0.221527i
$215$	−3.60392	−	2.61840i	−0.245786	−	0.178574i
$216$		0			0
$217$	9.28638	−	3.01733i	0.630401	−	0.204830i
$218$	1.14672	+	1.67180i	0.0776655	+	0.113228i
$219$		0			0
$220$	−6.13907	−	10.9635i	−0.413896	−	0.739158i
$221$	−5.40662			−0.363689
$222$		0			0
$223$	19.2234	−	6.24606i	1.28729	−	0.418267i	0.416150	−	0.909296i	$-0.363379\pi$
$223$	19.2234	−	6.24606i	1.28729	−	0.418267i	0.871143	+	0.491029i	$0.163379\pi$
$224$	−8.52986	+	17.6723i	−0.569926	+	1.18078i
$225$		0			0
$226$	13.7093	+	10.5397i	0.911928	+	0.701089i
$227$	−1.06125	+	3.26618i	−0.0704373	+	0.216784i	−0.980078	−	0.198612i	$-0.936357\pi$
$227$	−1.06125	+	3.26618i	−0.0704373	+	0.216784i	0.909641	+	0.415395i	$0.136357\pi$
$228$		0			0
$229$	−4.73582	+	3.44077i	−0.312952	+	0.227373i	−0.733162	−	0.680054i	$-0.761956\pi$
$229$	−4.73582	+	3.44077i	−0.312952	+	0.227373i	0.420210	+	0.907427i	$0.361956\pi$
$230$	0.277596	−	10.2389i	0.0183041	−	0.675131i
$231$		0			0
$232$	−2.04949	+	25.1484i	−0.134555	+	1.65108i
$233$	5.80493	+	7.98980i	0.380294	+	0.523429i	0.955662	−	0.294465i	$-0.0951414\pi$
$233$	5.80493	+	7.98980i	0.380294	+	0.523429i	−0.575369	+	0.817894i	$0.695141\pi$
$234$		0			0
$235$	5.05313	+	1.64186i	0.329630	+	0.107103i
$236$	10.1955	−	12.5429i	0.663673	−	0.816474i
$237$		0			0
$238$	13.7575	+	4.88611i	0.891764	+	0.316719i
$239$	6.05813	+	18.6450i	0.391868	+	1.20605i	0.931374	+	0.364064i	$0.118611\pi$
$239$	6.05813	+	18.6450i	0.391868	+	1.20605i	−0.539506	+	0.841982i	$0.681389\pi$
$240$		0			0
$241$			12.1924i			0.785384i	0.919670	+	0.392692i	$0.128456\pi$
$241$			12.1924i			0.785384i	−0.919670	+	0.392692i	$0.871544\pi$
$242$	13.8419	−	7.09941i	0.889792	−	0.456367i
$243$		0			0
$244$	−8.45130	−	13.0667i	−0.541039	−	0.836513i
$245$	−2.94641	−	9.06811i	−0.188239	−	0.579340i
$246$		0			0
$247$	−4.65262	+	6.40379i	−0.296039	+	0.407463i
$248$	5.18731	−	6.03953i	0.329395	−	0.383511i
$249$		0			0
$250$	4.86312	+	16.4736i	0.307571	+	1.04188i
$251$	13.7792	+	18.9654i	0.869733	+	1.19708i	0.979160	+	0.203090i	$0.0650983\pi$
$251$	13.7792	+	18.9654i	0.869733	+	1.19708i	−0.109427	+	0.993995i	$0.534902\pi$
$252$		0			0
$253$	12.6551	+	0.806622i	0.795622	+	0.0507119i
$254$	7.26857	+	0.197065i	0.456070	+	0.0123650i
$255$		0			0
$256$	1.55461	+	15.9243i	0.0971632	+	0.995268i
$257$	4.56819	−	14.0594i	0.284956	−	0.877004i	−0.701456	−	0.712713i	$-0.747466\pi$
$257$	4.56819	−	14.0594i	0.284956	−	0.877004i	0.986412	−	0.164291i	$-0.0525336\pi$
$258$		0			0
$259$	−31.9333	−	23.2009i	−1.98424	−	1.44164i
$260$	6.42125	+	2.47853i	0.398229	+	0.153712i
$261$		0			0
$262$	−4.06474	+	2.78808i	−0.251120	+	0.172248i
$263$	−10.3241			−0.636611			−0.318306	−	0.947988i	$-0.603114\pi$
$263$	−10.3241			−0.636611			−0.318306	+	0.947988i	$0.603114\pi$
$264$		0			0
$265$	−11.8375			−0.727169
$266$	17.6261	−	12.0901i	1.08073	−	0.741292i
$267$		0			0
$268$	−28.1343	−	10.8595i	−1.71858	−	0.663352i
$269$	4.14874	+	3.01423i	0.252953	+	0.183781i	0.707034	−	0.707179i	$-0.250033\pi$
$269$	4.14874	+	3.01423i	0.252953	+	0.183781i	−0.454082	+	0.890960i	$0.650033\pi$
$270$		0			0
$271$	3.21618	−	9.89839i	0.195369	−	0.601284i	−0.804603	−	0.593813i	$-0.797622\pi$
$271$	3.21618	−	9.89839i	0.195369	−	0.601284i	0.999972	−	0.00747111i	$-0.00237815\pi$
$272$	11.6527	−	2.43182i	0.706550	−	0.147451i
$273$		0			0
$274$	−4.77282	−	0.129401i	−0.288337	−	0.00781737i
$275$	−4.53587	+	1.16065i	−0.273523	+	0.0699896i
$276$		0			0
$277$	10.9032	+	15.0070i	0.655110	+	0.901681i	0.999307	−	0.0372160i	$-0.0118490\pi$
$277$	10.9032	+	15.0070i	0.655110	+	0.901681i	−0.344197	+	0.938897i	$0.611849\pi$
$278$	−9.09830	−	30.8201i	−0.545680	−	1.84846i
$279$		0			0
$280$	−14.0993	−	12.1098i	−0.842596	−	0.723700i
$281$	7.89816	−	10.8709i	0.471165	−	0.648503i	−0.505612	−	0.862761i	$-0.668733\pi$
$281$	7.89816	−	10.8709i	0.471165	−	0.648503i	0.976777	+	0.214258i	$0.0687334\pi$
$282$		0			0
$283$	−0.130142	−	0.400534i	−0.00773611	−	0.0238093i	0.947114	−	0.320897i	$-0.103984\pi$
$283$	−0.130142	−	0.400534i	−0.00773611	−	0.0238093i	−0.954850	+	0.297088i	$0.903984\pi$
$284$	−5.98961	−	9.26066i	−0.355418	−	0.549519i
$285$		0			0
$286$	−3.35696	+	7.83235i	−0.198501	+	0.463137i
$287$		−	26.9125i		−	1.58859i
$288$		0			0
$289$	2.51656	+	7.74519i	0.148033	+	0.455599i
$290$	−22.5200	−	7.99820i	−1.32242	−	0.469671i
$291$		0			0
$292$	14.7881	−	18.1928i	0.865405	−	1.06465i
$293$	17.0553	+	5.54161i	0.996382	+	0.323744i	0.761419	−	0.648260i	$-0.224503\pi$
$293$	17.0553	+	5.54161i	0.996382	+	0.323744i	0.234963	+	0.972004i	$0.424503\pi$
$294$		0			0
$295$	8.99875	+	12.3857i	0.523928	+	0.721124i
$296$	−32.0774	−	2.61417i	−1.86446	−	0.151945i
$297$		0			0
$298$	−0.536015	+	19.7704i	−0.0310505	+	1.14527i
$299$	−5.61966	+	4.08292i	−0.324993	+	0.236122i
$300$		0			0
$301$	2.52087	−	7.75843i	0.145300	−	0.447188i
$302$	9.12695	+	7.01678i	0.525197	+	0.403770i
$303$		0			0
$304$	7.14733	−	15.8946i	0.409927	−	0.911616i
$305$	14.0177	−	4.55463i	0.802652	−	0.260797i
$306$		0			0
$307$	9.77664			0.557983			0.278991	−	0.960294i	$-0.410000\pi$
$307$	9.77664			0.557983			0.278991	+	0.960294i	$0.410000\pi$
$308$	15.6203	−	16.8961i	0.890048	−	0.962745i
$309$		0			0
$310$	4.26529	+	6.21836i	0.242252	+	0.353179i
$311$	10.8311	−	3.51925i	0.614178	−	0.199558i	0.0146241	−	0.999893i	$-0.495345\pi$
$311$	10.8311	−	3.51925i	0.614178	−	0.199558i	0.599554	+	0.800335i	$0.295345\pi$
$312$		0			0
$313$	−10.8009	−	7.84731i	−0.610503	−	0.443556i	0.239089	−	0.970998i	$-0.423151\pi$
$313$	−10.8009	−	7.84731i	−0.610503	−	0.443556i	−0.849591	+	0.527442i	$0.823151\pi$
$314$	20.8038	+	15.9939i	1.17403	+	0.902588i
$315$		0			0
$316$	−2.75912	−	10.3739i	−0.155213	−	0.583580i
$317$	−9.51230	+	6.91109i	−0.534264	+	0.388165i	−0.821950	−	0.569559i	$-0.807114\pi$
$317$	−9.51230	+	6.91109i	−0.534264	+	0.388165i	0.287686	+	0.957725i	$0.407114\pi$
$318$		0			0
$319$	10.9142	−	27.5003i	0.611080	−	1.53972i
$320$	−14.9543	−	2.45372i	−0.835972	−	0.137167i
$321$		0			0
$322$	17.9894	−	5.31060i	1.00251	−	0.295948i
$323$	−12.3313	−	4.00668i	−0.686131	−	0.222938i
$324$		0			0
$325$	1.50750	−	2.07489i	0.0836209	−	0.115094i
$326$	−0.849430	−	0.301684i	−0.0470456	−	0.0167087i
$327$		0			0
$328$	−11.4134	−	18.7416i	−0.630200	−	1.03483i
$329$			9.72980i			0.536421i
$330$		0			0
$331$			0.109341i			0.00600991i	0.999995	+	0.00300496i	$0.000956508\pi$
$331$			0.109341i			0.00600991i	−0.999995	+	0.00300496i	$0.999043\pi$
$332$	−12.6761	+	8.19864i	−0.695691	+	0.449959i
$333$		0			0
$334$	−4.30803	+	12.1298i	−0.235725	+	0.663714i
$335$	16.7891	−	23.1083i	0.917288	−	1.26254i
$336$		0			0
$337$	−19.3456	−	6.28577i	−1.05382	−	0.342408i	−0.269655	−	0.962957i	$-0.586910\pi$
$337$	−19.3456	−	6.28577i	−1.05382	−	0.342408i	−0.784167	+	0.620549i	$0.786910\pi$
$338$	3.88364	+	13.1556i	0.211242	+	0.715573i
$339$		0			0
$340$	−0.610902	+	11.2580i	−0.0331308	+	0.610551i
$341$	−7.88640	+	4.99579i	−0.427073	+	0.270537i
$342$		0			0
$343$	−5.51899	+	4.00978i	−0.297998	+	0.216508i
$344$	−1.53479	−	6.47197i	−0.0827505	−	0.348945i
$345$		0			0
$346$	14.1401	−	18.3924i	0.760175	−	0.988783i
$347$	0.0735503	+	0.0534374i	0.00394839	+	0.00286867i	0.589758	−	0.807580i	$-0.299223\pi$
$347$	0.0735503	+	0.0534374i	0.00394839	+	0.00286867i	−0.585809	+	0.810449i	$0.699223\pi$
$348$		0			0
$349$	3.99941	−	1.29949i	0.214083	−	0.0695599i	−0.200012	−	0.979793i	$-0.564098\pi$
$349$	3.99941	−	1.29949i	0.214083	−	0.0695599i	0.414095	+	0.910234i	$0.364098\pi$
$350$	−5.71105	+	3.91732i	−0.305268	+	0.209389i
$351$		0			0
$352$	3.71227	−	18.3907i	0.197865	−	0.980229i
$353$	−22.5015			−1.19764			−0.598818	−	0.800885i	$-0.704363\pi$
$353$	−22.5015			−1.19764			−0.598818	+	0.800885i	$0.704363\pi$
$354$		0			0
$355$	9.93463	−	3.22796i	0.527275	−	0.171322i
$356$	3.75151	−	9.71921i	0.198829	−	0.515117i
$357$		0			0
$358$	0.465835	−	0.605926i	0.0246201	−	0.0320242i
$359$	−0.804066	+	2.47466i	−0.0424370	+	0.130608i	−0.970030	−	0.242984i	$-0.921874\pi$
$359$	−0.804066	+	2.47466i	−0.0424370	+	0.130608i	0.927593	+	0.373591i	$0.121874\pi$
$360$		0			0
$361$	0.0140835	−	0.0102322i	0.000741236	−	0.000538539i
$362$	−7.12038	−	0.193047i	−0.374239	−	0.0101463i
$363$		0			0
$364$	−0.682965	+	12.5860i	−0.0357971	+	0.659686i
$365$	13.0522	+	17.9648i	0.683182	+	0.940319i
$366$		0			0
$367$	14.6886	+	4.77262i	0.766739	+	0.249129i	0.666169	−	0.745801i	$-0.267933\pi$
$367$	14.6886	+	4.77262i	0.766739	+	0.249129i	0.100571	+	0.994930i	$0.467933\pi$
$368$	10.2754	−	11.3274i	0.535644	−	0.590483i
$369$		0			0
$370$	10.2019	−	28.7248i	0.530371	−	1.49333i
$371$	−6.69869	−	20.6165i	−0.347779	−	1.07035i
$372$		0			0
$373$			5.55960i			0.287865i	0.989587	+	0.143933i	$0.0459749\pi$
$373$			5.55960i			0.287865i	−0.989587	+	0.143933i	$0.954025\pi$
$374$	−13.9010	−	1.26510i	−0.718801	−	0.0654166i
$375$		0			0
$376$	4.12634	+	6.77573i	0.212800	+	0.349432i
$377$	5.00826	+	15.4139i	0.257939	+	0.793854i
$378$		0			0
$379$	−15.1814	+	20.8954i	−0.779818	+	1.07333i	0.215484	+	0.976507i	$0.430867\pi$
$379$	−15.1814	+	20.8954i	−0.779818	+	1.07333i	−0.995302	+	0.0968197i	$0.969133\pi$
$380$	12.8087	+	10.4116i	0.657071	+	0.534102i
$381$		0			0
$382$	−3.97719	+	1.17409i	−0.203491	+	0.0600719i
$383$	0.0646313	+	0.0889574i	0.00330251	+	0.00454551i	0.810665	−	0.585510i	$-0.199106\pi$
$383$	0.0646313	+	0.0889574i	0.00330251	+	0.00454551i	−0.807363	+	0.590056i	$0.799106\pi$
$384$		0			0
$385$	11.6627	+	18.4109i	0.594386	+	0.938304i
$386$	−0.424996	+	15.6756i	−0.0216317	+	0.797867i
$387$		0			0
$388$	−4.27311	−	16.0664i	−0.216934	−	0.815645i
$389$	−6.06738	+	18.6735i	−0.307628	+	0.946782i	0.671055	+	0.741407i	$0.265841\pi$
$389$	−6.06738	+	18.6735i	−0.307628	+	0.946782i	−0.978683	+	0.205375i	$0.934159\pi$
$390$		0			0
$391$	−9.20520	−	6.68797i	−0.465527	−	0.338225i
$392$	5.48465	−	13.1378i	0.277017	−	0.663561i
$393$		0			0
$394$	4.78123	+	6.97055i	0.240875	+	0.351171i
$395$	10.1672			0.511567
$396$		0			0
$397$	30.2146			1.51643			0.758215	−	0.652005i	$-0.226072\pi$
$397$	30.2146			1.51643			0.758215	+	0.652005i	$0.226072\pi$
$398$	2.18632	+	3.18743i	0.109590	+	0.159771i
$399$		0			0
$400$	−2.31581	+	5.15000i	−0.115790	+	0.257500i
$401$	0.155811	+	0.113203i	0.00778083	+	0.00565310i	0.591669	−	0.806181i	$-0.298469\pi$
$401$	0.155811	+	0.113203i	0.00778083	+	0.00565310i	−0.583888	+	0.811834i	$0.698469\pi$
$402$		0			0
$403$	1.58026	−	4.86355i	0.0787185	−	0.242271i
$404$	−23.6127	+	6.28019i	−1.17478	+	0.312451i
$405$		0			0
$406$	1.18608	−	43.7475i	0.0588642	−	2.17115i
$407$	35.0772	+	13.9214i	1.73871	+	0.690057i
$408$		0			0
$409$	−18.2103	−	25.0644i	−0.900443	−	1.23935i	−0.970326	−	0.241799i	$-0.922263\pi$
$409$	−18.2103	−	25.0644i	−0.900443	−	1.23935i	0.0698831	−	0.997555i	$-0.477737\pi$
$410$	19.9331	−	5.88440i	0.984427	−	0.290610i
$411$		0			0
$412$	17.2691	−	21.2451i	0.850788	−	1.04667i
$413$	−16.4790	+	22.6814i	−0.810880	+	1.11608i
$414$		0			0
$415$	−4.41846	−	13.5986i	−0.216894	−	0.667530i
$416$	4.86203	+	9.05441i	0.238381	+	0.443929i
$417$		0			0
$418$	−13.4608	+	15.3761i	−0.658388	+	0.752070i
$419$		−	28.8010i		−	1.40702i	−0.710686	−	0.703510i	$-0.751615\pi$
$419$		−	28.8010i		−	1.40702i	0.710686	−	0.703510i	$-0.248385\pi$
$420$		0			0
$421$	−0.977355	−	3.00799i	−0.0476334	−	0.146601i	0.924411	−	0.381398i	$-0.124557\pi$
$421$	−0.977355	−	3.00799i	−0.0476334	−	0.146601i	−0.972044	+	0.234798i	$0.924557\pi$
$422$	12.0098	−	33.8151i	0.584627	−	1.64609i
$423$		0			0
$424$	−13.4082	−	11.5162i	−0.651160	−	0.559277i
$425$	3.99546	+	1.29820i	0.193808	+	0.0629721i
$426$		0			0
$427$	15.8650	+	21.8362i	0.767759	+	1.05673i
$428$	−7.50826	−	0.407427i	−0.362925	−	0.0196937i
$429$		0			0
$430$	6.29758	+	0.170740i	0.303696	+	0.00823379i
$431$	−2.16293	+	1.57146i	−0.104185	+	0.0756947i	−0.638658	−	0.769491i	$-0.720510\pi$
$431$	−2.16293	+	1.57146i	−0.104185	+	0.0756947i	0.534473	+	0.845185i	$0.320510\pi$
$432$		0			0
$433$	−6.48467	+	19.9578i	−0.311634	+	0.959110i	0.665484	+	0.746412i	$0.268225\pi$
$433$	−6.48467	+	19.9578i	−0.311634	+	0.959110i	−0.977118	+	0.212698i	$0.931775\pi$
$434$	−8.41638	+	10.9475i	−0.403999	+	0.525495i
$435$		0			0
$436$	−2.67468	−	1.03240i	−0.128094	−	0.0494428i
$437$	−15.8429	+	5.14767i	−0.757869	+	0.246247i
$438$		0			0
$439$	−9.75312			−0.465491			−0.232746	−	0.972538i	$-0.574771\pi$
$439$	−9.75312			−0.465491			−0.232746	+	0.972538i	$0.574771\pi$
$440$	15.9297	+	7.87506i	0.759419	+	0.375429i
$441$		0			0
$442$	6.30537	−	4.32498i	0.299916	−	0.205718i
$443$	−19.6000	+	6.36841i	−0.931222	+	0.302572i	−0.735062	−	0.678000i	$-0.762847\pi$
$443$	−19.6000	+	6.36841i	−0.931222	+	0.302572i	−0.196160	+	0.980572i	$0.562847\pi$
$444$		0			0
$445$	7.98292	+	5.79993i	0.378427	+	0.274943i
$446$	−17.4224	+	22.6619i	−0.824976	+	1.07307i
$447$		0			0
$448$	−4.18902	−	27.4334i	−0.197913	−	1.29611i
$449$	32.3068	−	23.4722i	1.52465	−	1.10772i	0.565529	−	0.824728i	$-0.308672\pi$
$449$	32.3068	−	23.4722i	1.52465	−	1.10772i	0.959121	−	0.282995i	$-0.0913281\pi$
$450$		0			0
$451$	6.37856	+	24.9278i	0.300355	+	1.17380i
$452$	−24.4193	−	1.32508i	−1.14859	−	0.0623267i
$453$		0			0
$454$	−1.37509	−	4.65805i	−0.0645362	−	0.218613i
$455$	−11.3540	−	3.68913i	−0.532283	−	0.172949i
$456$		0			0
$457$	−19.8109	+	27.2674i	−0.926716	+	1.27552i	0.0344108	+	0.999408i	$0.489045\pi$
$457$	−19.8109	+	27.2674i	−0.926716	+	1.27552i	−0.961127	+	0.276107i	$0.910955\pi$
$458$	2.77065	−	7.80111i	0.129464	−	0.364522i
$459$		0			0
$460$	7.86675	+	12.1629i	0.366789	+	0.567100i
$461$			18.4692i			0.860196i	0.902782	+	0.430098i	$0.141521\pi$
$461$			18.4692i			0.860196i	−0.902782	+	0.430098i	$0.858479\pi$
$462$		0			0
$463$		−	21.9821i		−	1.02159i	−0.859701	−	0.510797i	$-0.829350\pi$
$463$		−	21.9821i		−	1.02159i	0.859701	−	0.510797i	$-0.170650\pi$
$464$	−17.7271	−	30.9683i	−0.822959	−	1.43767i
$465$		0			0
$466$	−13.1613	−	4.67435i	−0.609683	−	0.216535i
$467$	−21.5485	+	29.6590i	−0.997147	+	1.37245i	−0.0700868	+	0.997541i	$0.522328\pi$
$467$	−21.5485	+	29.6590i	−0.997147	+	1.37245i	−0.927060	+	0.374914i	$0.877672\pi$
$468$		0			0
$469$	49.7468	+	16.1637i	2.29709	+	0.746371i
$470$	−7.20651	+	2.12741i	−0.332412	+	0.0981303i
$471$		0			0
$472$	−1.85678	+	22.7838i	−0.0854651	+	1.04871i
$473$	−0.496125	+	7.78374i	−0.0228119	+	0.357897i
$474$		0			0
$475$	4.97590	−	3.61520i	0.228310	−	0.165877i
$476$	−19.9530	+	5.30682i	−0.914543	+	0.243238i
$477$		0			0
$478$	−21.9801	−	16.8982i	−1.00535	−	0.772908i
$479$	−19.1217	−	13.8928i	−0.873695	−	0.634776i	0.0578810	−	0.998323i	$-0.481566\pi$
$479$	−19.1217	−	13.8928i	−0.873695	−	0.634776i	−0.931576	+	0.363547i	$0.881566\pi$
$480$		0			0
$481$	−19.6607	+	6.38816i	−0.896452	+	0.291275i
$482$	−9.75322	−	14.2192i	−0.444247	−	0.647667i
$483$		0			0
$484$	−10.4638	+	19.3523i	−0.475626	+	0.879648i
$485$	15.7462			0.714996
$486$		0			0
$487$	35.0909	−	11.4017i	1.59012	−	0.516661i	0.625482	−	0.780238i	$-0.284902\pi$
$487$	35.0909	−	11.4017i	1.59012	−	0.516661i	0.964638	+	0.263577i	$0.0849023\pi$
$488$	20.3088	+	8.47831i	0.919336	+	0.383795i
$489$		0			0
$490$	10.6901	+	8.21856i	0.482931	+	0.371277i
$491$	5.75631	−	17.7161i	0.259779	−	0.799517i	−0.733072	−	0.680151i	$-0.761914\pi$
$491$	5.75631	−	17.7161i	0.259779	−	0.799517i	0.992850	−	0.119365i	$-0.0380860\pi$
$492$		0			0
$493$	−21.4776	+	15.6044i	−0.967302	+	0.702786i
$494$	0.303386	−	11.1901i	0.0136500	−	0.503467i
$495$		0			0
$496$	−1.21834	+	11.1930i	−0.0547051	+	0.502582i
$497$	11.2438	+	15.4758i	0.504353	+	0.694183i
$498$		0			0
$499$	−32.6136	−	10.5968i	−1.45998	−	0.474377i	−0.531919	−	0.846795i	$-0.678529\pi$
$499$	−32.6136	−	10.5968i	−1.45998	−	0.474377i	−0.928065	+	0.372418i	$0.878529\pi$
$500$	−18.8494	−	15.3218i	−0.842972	−	0.685212i
$501$		0			0
$502$	−31.2409	−	11.0955i	−1.39435	−	0.495217i
$503$	−1.01615	−	3.12740i	−0.0453080	−	0.139444i	0.925843	−	0.377907i	$-0.123356\pi$
$503$	−1.01615	−	3.12740i	−0.0453080	−	0.139444i	−0.971151	+	0.238464i	$0.923356\pi$
$504$		0			0
$505$		−	23.1421i		−	1.02981i
$506$	−15.4041	+	9.18265i	−0.684794	+	0.408219i
$507$		0			0
$508$	−8.63447	+	5.58460i	−0.383093	+	0.247776i
$509$	−10.4865	−	32.2741i	−0.464806	−	1.43052i	−0.859227	−	0.511595i	$-0.829055\pi$
$509$	−10.4865	−	32.2741i	−0.464806	−	1.43052i	0.394421	−	0.918930i	$-0.370945\pi$
$510$		0			0
$511$	−23.9019	+	32.8981i	−1.05736	+	1.45533i
$512$	−14.5515	−	17.3278i	−0.643093	−	0.765788i
$513$		0			0
$514$	5.91915	+	20.0508i	0.261083	+	0.884404i
$515$	15.2420	+	20.9788i	0.671642	+	0.924436i
$516$		0			0
$517$	−2.30607	−	9.01225i	−0.101421	−	0.396358i
$518$	55.8010	+	1.51287i	2.45176	+	0.0664719i
$519$		0			0
$520$	−9.47134	+	2.24608i	−0.415346	+	0.0984970i
$521$	−6.93119	+	21.3320i	−0.303661	+	0.934572i	0.676513	+	0.736431i	$0.263490\pi$
$521$	−6.93119	+	21.3320i	−0.303661	+	0.934572i	−0.980174	+	0.198141i	$0.936510\pi$
$522$		0			0
$523$	−21.7656	−	15.8137i	−0.951744	−	0.691483i	−0.000525638	−	1.00000i	$-0.500167\pi$
$523$	−21.7656	−	15.8137i	−0.951744	−	0.691483i	−0.951219	+	0.308517i	$0.900167\pi$
$524$	2.51012	−	6.50309i	0.109655	−	0.284089i
$525$		0			0
$526$	12.0403	−	8.25867i	0.524982	−	0.360095i
$527$	8.37664			0.364892
$528$		0			0
$529$	8.38153			0.364414
$530$	13.8052	−	9.46926i	0.599660	−	0.411319i
$531$		0			0
$532$	−10.8848	+	28.1997i	−0.471915	+	1.22261i
$533$	−11.4030	−	8.28475i	−0.493918	−	0.358852i
$534$		0			0
$535$	2.20078	−	6.77329i	0.0951478	−	0.292835i
$536$	41.4981	−	9.84105i	1.79245	−	0.425069i
$537$		0			0
$538$	−7.24959	−	0.196551i	−0.312552	−	0.00847390i
$539$	−10.6517	+	12.8542i	−0.458802	+	0.553671i
$540$		0			0
$541$	−8.91106	−	12.2650i	−0.383116	−	0.527315i	0.573290	−	0.819352i	$-0.305667\pi$
$541$	−8.91106	−	12.2650i	−0.383116	−	0.527315i	−0.956407	+	0.292038i	$0.905667\pi$
$542$	4.16731	+	14.1166i	0.179001	+	0.606358i
$543$		0			0
$544$	−11.6445	+	12.1575i	−0.499252	+	0.521250i
$545$	1.59611	−	2.19686i	0.0683699	−	0.0941031i
$546$		0			0
$547$	2.14142	+	6.59062i	0.0915606	+	0.281795i	0.986342	−	0.164710i	$-0.0526687\pi$
$547$	2.14142	+	6.59062i	0.0915606	+	0.281795i	−0.894781	+	0.446504i	$0.852669\pi$
$548$	5.66973	−	3.66706i	0.242199	−	0.156649i
$549$		0			0
$550$	4.36143	−	4.98201i	0.185972	−	0.212434i
$551$			38.8670i			1.65579i
$552$		0			0
$553$	5.75351	+	17.7075i	0.244664	+	0.752998i
$554$	−24.7203	−	8.77968i	−1.05027	−	0.373013i
$555$		0			0
$556$	35.2649	+	28.6652i	1.49557	+	1.21568i
$557$	0.278322	+	0.0904324i	0.0117929	+	0.00383174i	0.314908	−	0.949122i	$-0.398027\pi$
$557$	0.278322	+	0.0904324i	0.0117929	+	0.00383174i	−0.303115	+	0.952954i	$0.598027\pi$
$558$		0			0
$559$	−2.51127	−	3.45646i	−0.106215	−	0.146193i
$560$	26.1302	+	2.84422i	1.10420	+	0.120190i
$561$		0			0
$562$	−0.515019	+	18.9960i	−0.0217248	+	0.801299i
$563$	15.4345	−	11.2138i	0.650486	−	0.472606i	−0.212951	−	0.977063i	$-0.568307\pi$
$563$	15.4345	−	11.2138i	0.650486	−	0.472606i	0.863437	+	0.504457i	$0.168307\pi$
$564$		0			0
$565$	7.15764	−	22.0290i	0.301124	−	0.926765i
$566$	0.472179	+	0.363010i	0.0198472	+	0.0152585i
$567$		0			0
$568$	14.3932	+	6.00874i	0.603927	+	0.252121i
$569$	29.4110	−	9.55621i	1.23297	−	0.400617i	0.381183	−	0.924500i	$-0.375517\pi$
$569$	29.4110	−	9.55621i	1.23297	−	0.400617i	0.851791	+	0.523882i	$0.175517\pi$
$570$		0			0
$571$	14.7169			0.615883			0.307942	−	0.951405i	$-0.400360\pi$
$571$	14.7169			0.615883			0.307942	+	0.951405i	$0.400360\pi$
$572$	−2.35043	−	11.8197i	−0.0982763	−	0.494207i
$573$		0			0
$574$	21.5284	+	31.3862i	0.898578	+	1.31003i
$575$	5.13326	−	1.66790i	0.214072	−	0.0695561i
$576$		0			0
$577$	5.09251	+	3.69993i	0.212004	+	0.154030i	0.688720	−	0.725027i	$-0.258173\pi$
$577$	5.09251	+	3.69993i	0.212004	+	0.154030i	−0.476716	+	0.879057i	$0.658173\pi$
$578$	−9.13058	−	7.01958i	−0.379782	−	0.291976i
$579$		0			0
$580$	32.6616	−	8.68689i	1.35620	−	0.360703i
$581$	21.1834	−	15.3906i	0.878835	−	0.638511i
$582$		0			0
$583$	11.0910	+	17.5084i	0.459343	+	0.725124i
$584$	−2.69315	+	33.0465i	−0.111443	+	1.36748i
$585$		0			0
$586$	−24.3234	+	7.18044i	−1.00479	+	0.296621i
$587$	40.0307	+	13.0068i	1.65224	+	0.536847i	0.979225	−	0.202778i	$-0.0649968\pi$
$587$	40.0307	+	13.0068i	1.65224	+	0.536847i	0.673020	+	0.739624i	$0.264997\pi$
$588$		0			0
$589$	7.20845	−	9.92158i	0.297019	−	0.408811i
$590$	−20.4025	−	7.24614i	−0.839956	−	0.298319i
$591$		0			0
$592$	39.5009	−	22.6113i	1.62348	−	0.929318i
$593$		−	19.2298i		−	0.789675i	−0.918751	−	0.394837i	$-0.870801\pi$
$593$		−	19.2298i		−	0.789675i	0.918751	−	0.394837i	$-0.129199\pi$
$594$		0			0
$595$		−	19.5553i		−	0.801690i
$596$	−15.1901	−	23.4857i	−0.622209	−	0.962011i
$597$		0			0
$598$	3.28773	−	9.25703i	0.134445	−	0.378548i
$599$	−9.14751	+	12.5905i	−0.373757	+	0.514433i	−0.953917	−	0.300070i	$-0.902990\pi$
$599$	−9.14751	+	12.5905i	−0.373757	+	0.514433i	0.580160	+	0.814502i	$0.302990\pi$
$600$		0			0
$601$	−4.94174	−	1.60567i	−0.201578	−	0.0654966i	0.206488	−	0.978449i	$-0.433797\pi$
$601$	−4.94174	−	1.60567i	−0.201578	−	0.0654966i	−0.408066	+	0.912953i	$0.633797\pi$
$602$	3.26637	+	11.0647i	0.133127	+	0.450962i
$603$		0			0
$604$	−16.2571	−	0.882174i	−0.661494	−	0.0358951i
$605$	−15.1662	−	14.2889i	−0.616593	−	0.580927i
$606$		0			0
$607$	−4.32559	+	3.14273i	−0.175570	+	0.127559i	−0.672100	−	0.740460i	$-0.734607\pi$
$607$	−4.32559	+	3.14273i	−0.175570	+	0.127559i	0.496529	+	0.868020i	$0.334607\pi$
$608$	4.37927	+	24.2542i	0.177603	+	0.983637i
$609$		0			0
$610$	−12.7045	+	16.5251i	−0.514389	+	0.669081i
$611$	4.12257	+	2.99522i	0.166781	+	0.121174i
$612$		0			0
$613$	−20.2178	+	6.56916i	−0.816590	+	0.265326i	−0.687386	−	0.726292i	$-0.741242\pi$
$613$	−20.2178	+	6.56916i	−0.816590	+	0.265326i	−0.129203	+	0.991618i	$0.541242\pi$
$614$	−11.4018	+	7.82073i	−0.460140	+	0.315619i
$615$		0			0
$616$	−4.70097	+	32.2001i	−0.189408	+	1.29738i
$617$	−5.45994			−0.219809			−0.109905	−	0.993942i	$-0.535055\pi$
$617$	−5.45994			−0.219809			−0.109905	+	0.993942i	$0.535055\pi$
$618$		0			0
$619$	−6.31236	+	2.05101i	−0.253715	+	0.0824371i	−0.433113	−	0.901339i	$-0.642585\pi$
$619$	−6.31236	+	2.05101i	−0.253715	+	0.0824371i	0.179398	+	0.983777i	$0.442585\pi$
$620$	−9.94863	−	3.84006i	−0.399547	−	0.154221i
$621$		0			0
$622$	−9.81642	+	12.7685i	−0.393603	+	0.511971i
$623$	−5.58387	+	17.1854i	−0.223713	+	0.688519i
$624$		0			0
$625$	12.9028	−	9.37445i	0.516113	−	0.374978i
$626$	18.8737	+	0.511704i	0.754346	+	0.0204518i
$627$		0			0
$628$	−37.0562	−	2.01081i	−1.47870	−	0.0802400i
$629$	−19.9037	−	27.3952i	−0.793614	−	1.09232i
$630$		0			0
$631$	19.5656	+	6.35725i	0.778894	+	0.253078i	0.671368	−	0.741124i	$-0.265707\pi$
$631$	19.5656	+	6.35725i	0.778894	+	0.253078i	0.107526	+	0.994202i	$0.465707\pi$
$632$	11.5163	+	9.89128i	0.458094	+	0.393454i
$633$		0			0
$634$	5.56508	−	15.6692i	0.221017	−	0.622303i
$635$	−3.00969	−	9.26286i	−0.119436	−	0.367585i
$636$		0			0
$637$		−	9.14464i		−	0.362324i
$638$	9.27005	+	40.8024i	0.367005	+	1.61538i
$639$		0			0
$640$	19.4030	−	9.10096i	0.766972	−	0.359747i
$641$	6.24661	+	19.2251i	0.246726	+	0.759346i	0.995348	+	0.0963480i	$0.0307162\pi$
$641$	6.24661	+	19.2251i	0.246726	+	0.759346i	−0.748621	+	0.662998i	$0.769284\pi$
$642$		0			0
$643$	12.0086	−	16.5284i	0.473573	−	0.651817i	−0.503681	−	0.863890i	$-0.668021\pi$
$643$	12.0086	−	16.5284i	0.473573	−	0.651817i	0.977254	+	0.212072i	$0.0680213\pi$
$644$	−16.7316	+	20.5838i	−0.659319	+	0.811117i
$645$		0			0
$646$	17.5862	−	5.19158i	0.691921	−	0.204260i
$647$	−8.24593	−	11.3496i	−0.324181	−	0.446197i	0.615557	−	0.788092i	$-0.288931\pi$
$647$	−8.24593	−	11.3496i	−0.324181	−	0.446197i	−0.939738	+	0.341896i	$0.888931\pi$
$648$		0			0
$649$	9.88799	−	24.9145i	0.388138	−	0.977978i
$650$	−0.0983001	+	3.62571i	−0.00385565	+	0.142212i
$651$		0			0
$652$	1.23196	−	0.327660i	0.0482473	−	0.0128322i
$653$	−13.1470	+	40.4622i	−0.514480	+	1.58341i	0.269745	+	0.962932i	$0.413060\pi$
$653$	−13.1470	+	40.4622i	−0.514480	+	1.58341i	−0.784226	+	0.620476i	$0.786940\pi$
$654$		0			0
$655$	5.34135	+	3.88072i	0.208704	+	0.151632i
$656$	28.3028	+	12.7270i	1.10504	+	0.496905i
$657$		0			0
$658$	−7.78326	−	11.3472i	−0.303423	−	0.442360i
$659$	−35.3651			−1.37763			−0.688815	−	0.724937i	$-0.741869\pi$
$659$	−35.3651			−1.37763			−0.688815	+	0.724937i	$0.741869\pi$
$660$		0			0
$661$	−6.75994			−0.262931			−0.131466	−	0.991321i	$-0.541968\pi$
$661$	−6.75994			−0.262931			−0.131466	+	0.991321i	$0.541968\pi$
$662$	−0.0874661	−	0.127517i	−0.00339947	−	0.00495607i
$663$		0			0
$664$	8.22483	−	19.7016i	0.319185	−	0.764571i
$665$	−23.1620	−	16.8282i	−0.898183	−	0.652569i
$666$		0			0
$667$	−10.5399	+	32.4385i	−0.408107	+	1.25602i
$668$	−4.67897	−	17.5923i	−0.181035	−	0.680667i
$669$		0			0
$670$	−1.09478	+	40.3799i	−0.0422950	+	1.56001i
$671$	−19.8704	−	16.4657i	−0.767088	−	0.635652i
$672$		0			0
$673$	−21.9062	−	30.1512i	−0.844420	−	1.16224i	−0.985065	−	0.172184i	$-0.944917\pi$
$673$	−21.9062	−	30.1512i	−0.844420	−	1.16224i	0.140645	−	0.990060i	$-0.455083\pi$
$674$	27.5897	−	8.14468i	1.06272	−	0.313721i
$675$		0			0
$676$	−15.0530	−	12.2358i	−0.578960	−	0.470609i
$677$	20.6777	−	28.4604i	0.794709	−	1.09382i	−0.198797	−	0.980041i	$-0.563703\pi$
$677$	20.6777	−	28.4604i	0.794709	−	1.09382i	0.993506	−	0.113782i	$-0.0362967\pi$
$678$		0			0
$679$	8.91058	+	27.4240i	0.341957	+	1.05243i
$680$	−8.29328	−	13.6181i	−0.318033	−	0.522231i
$681$		0			0
$682$	5.20103	−	12.1349i	0.199158	−	0.464669i
$683$			6.86049i			0.262509i	0.991349	+	0.131255i	$0.0419005\pi$
$683$			6.86049i			0.262509i	−0.991349	+	0.131255i	$0.958099\pi$
$684$		0			0
$685$	1.97628	+	6.08235i	0.0755096	+	0.232395i
$686$	3.22883	−	9.09120i	0.123277	−	0.347104i
$687$		0			0
$688$	6.96712	+	6.32007i	0.265619	+	0.240950i
$689$	−10.7974	−	3.50830i	−0.411350	−	0.133656i
$690$		0			0
$691$	−17.7244	−	24.3956i	−0.674270	−	0.928053i	0.325578	−	0.945515i	$-0.394441\pi$
$691$	−17.7244	−	24.3956i	−0.674270	−	0.928053i	−0.999848	+	0.0174625i	$0.994441\pi$
$692$	−1.77774	+	32.7610i	−0.0675795	+	1.24539i
$693$		0			0
$694$	−0.128523	−	0.00348452i	−0.00487868	−	0.000132271i
$695$	−34.8230	+	25.3004i	−1.32091	+	0.959698i
$696$		0			0
$697$	7.13454	−	21.9578i	0.270240	−	0.831713i
$698$	−3.62472	+	4.71479i	−0.137198	+	0.178457i
$699$		0			0
$700$	3.52678	−	9.13699i	0.133300	−	0.345346i
$701$	−2.65130	+	0.861459i	−0.100138	+	0.0325369i	−0.358658	−	0.933469i	$-0.616765\pi$
$701$	−2.65130	+	0.861459i	−0.100138	+	0.0325369i	0.258519	+	0.966006i	$0.416765\pi$
$702$		0			0
$703$	−49.5758			−1.86979
$704$	10.3821	+	24.4174i	0.391291	+	0.920267i
$705$		0			0
$706$	26.2420	−	17.9999i	0.987630	−	0.677435i
$707$	40.3050	−	13.0959i	1.51582	−	0.492521i
$708$		0			0
$709$	19.9662	+	14.5063i	0.749846	+	0.544795i	0.895779	−	0.444499i	$-0.146618\pi$
$709$	19.9662	+	14.5063i	0.749846	+	0.544795i	−0.145933	+	0.989294i	$0.546618\pi$
$710$	−9.00390	+	11.7117i	−0.337910	+	0.439531i
$711$		0			0
$712$	3.39966	+	14.3358i	0.127408	+	0.537258i
$713$	8.70671	−	6.32579i	0.326069	−	0.236903i
$714$		0			0
$715$	11.3910	+	0.726049i	0.426001	+	0.0271527i
$716$	−0.0585663	+	1.07929i	−0.00218873	+	0.0403349i
$717$		0			0
$718$	−1.04185	−	3.52923i	−0.0388817	−	0.131710i
$719$	17.1274	+	5.56504i	0.638745	+	0.207541i	0.610445	−	0.792059i	$-0.290991\pi$
$719$	17.1274	+	5.56504i	0.638745	+	0.207541i	0.0283002	+	0.999599i	$0.490991\pi$
$720$		0			0
$721$	−27.9120	+	38.4176i	−1.03950	+	1.43075i
$722$	−0.00823940	+	0.0231991i	−0.000306639	+	0.000863381i
$723$		0			0
$724$	8.45843	−	5.47074i	0.314355	−	0.203318i
$725$		−	12.5933i		−	0.467703i
$726$		0			0
$727$		−	3.09840i		−	0.114913i	−0.998348	−	0.0574566i	$-0.981701\pi$
$727$		−	3.09840i		−	0.114913i	0.998348	−	0.0574566i	$-0.0182991\pi$
$728$	−9.27156	−	15.2245i	−0.343627	−	0.564258i
$729$		0			0
$730$	−29.5926	−	10.5101i	−1.09527	−	0.388997i
$731$	4.11354	−	5.66180i	0.152145	−	0.209409i
$732$		0			0
$733$	−5.56847	−	1.80931i	−0.205676	−	0.0668283i	0.204367	−	0.978894i	$-0.434486\pi$
$733$	−5.56847	−	1.80931i	−0.205676	−	0.0668283i	−0.410043	+	0.912066i	$0.634486\pi$
$734$	−20.9481	+	6.18404i	−0.773210	+	0.228257i
$735$		0			0
$736$	−2.92227	+	21.4301i	−0.107716	+	0.789926i
$737$	−49.9091	−	3.18114i	−1.83843	−	0.117179i
$738$		0			0
$739$	3.46213	−	2.51539i	0.127357	−	0.0925300i	−0.522283	−	0.852772i	$-0.674920\pi$
$739$	3.46213	−	2.51539i	0.127357	−	0.0925300i	0.649640	+	0.760242i	$0.274920\pi$
$740$	11.0803	+	41.6606i	0.407321	+	1.53147i
$741$		0			0
$742$	24.3042	+	18.6850i	0.892234	+	0.685948i
$743$	−34.1318	−	24.7982i	−1.25217	−	0.909757i	−0.253827	−	0.967250i	$-0.581690\pi$
$743$	−34.1318	−	24.7982i	−1.25217	−	0.909757i	−0.998346	+	0.0574923i	$0.981690\pi$
$744$		0			0
$745$	25.1949	−	8.18632i	0.923070	−	0.299924i
$746$	−4.44735	−	6.48378i	−0.162829	−	0.237388i
$747$		0			0
$748$	17.2237	−	9.64454i	0.629762	−	0.352639i
$749$	13.0420			0.476543
$750$		0			0
$751$	−10.4683	+	3.40134i	−0.381992	+	0.124117i	−0.493718	−	0.869622i	$-0.664362\pi$
$751$	−10.4683	+	3.40134i	−0.381992	+	0.124117i	0.111725	+	0.993739i	$0.464362\pi$
$752$	−10.2325	−	4.60124i	−0.373139	−	0.167790i
$753$		0			0
$754$	−18.1710	−	13.9698i	−0.661747	−	0.508750i
$755$	4.76519	−	14.6658i	0.173423	−	0.533742i
$756$		0			0
$757$	−17.6019	+	12.7886i	−0.639753	+	0.464808i	−0.859765	−	0.510689i	$-0.829390\pi$
$757$	−17.6019	+	12.7886i	−0.639753	+	0.464808i	0.220012	+	0.975497i	$0.429390\pi$
$758$	0.989943	−	36.5132i	0.0359564	−	1.32622i
$759$		0			0
$760$	−23.2665	−	1.89612i	−0.843964	−	0.0687794i
$761$	−4.47259	−	6.15599i	−0.162131	−	0.223154i	0.720220	−	0.693745i	$-0.244041\pi$
$761$	−4.47259	−	6.15599i	−0.162131	−	0.223154i	−0.882351	+	0.470591i	$0.844041\pi$
$762$		0			0
$763$	4.72934	+	1.53665i	0.171213	+	0.0556306i
$764$	3.69911	−	4.55078i	0.133829	−	0.164641i
$765$		0			0
$766$	−0.146536	−	0.0520437i	−0.00529455	−	0.00188041i
$767$	4.53735	+	13.9645i	0.163834	+	0.504229i
$768$		0			0
$769$			12.9034i			0.465307i	0.972560	+	0.232653i	$0.0747408\pi$
$769$			12.9034i			0.465307i	−0.972560	+	0.232653i	$0.925259\pi$
$770$	−28.3290	−	12.1418i	−1.02091	−	0.437562i
$771$		0			0
$772$	−12.0439	−	18.6214i	−0.433470	−	0.670197i
$773$	7.73840	+	23.8163i	0.278331	+	0.856614i	0.988319	+	0.152401i	$0.0487004\pi$
$773$	7.73840	+	23.8163i	0.278331	+	0.856614i	−0.709988	+	0.704214i	$0.751300\pi$
$774$		0			0
$775$	−2.33561	+	3.21469i	−0.0838976	+	0.115475i
$776$	17.8356	+	15.3188i	0.640259	+	0.549914i
$777$		0			0
$778$	−7.86170	−	26.6311i	−0.281855	−	0.954772i
$779$	−19.8681	−	27.3460i	−0.711847	−	0.979773i
$780$		0			0
$781$	−14.0825	−	11.6696i	−0.503913	−	0.417570i
$782$	16.0854	+	0.436106i	0.575211	+	0.0155951i
$783$		0			0
$784$	4.11312	+	19.7091i	0.146897	+	0.703898i
$785$	10.8617	−	33.4288i	0.387670	−	1.19313i
$786$		0			0
$787$	3.63457	+	2.64067i	0.129558	+	0.0941296i	0.650677	−	0.759355i	$-0.274485\pi$
$787$	3.63457	+	2.64067i	0.129558	+	0.0941296i	−0.521119	+	0.853484i	$0.674485\pi$
$788$	−11.1520	−	4.30457i	−0.397275	−	0.153344i
$789$		0			0
$790$	−11.8573	+	8.13315i	−0.421864	+	0.289364i
$791$	42.4167			1.50816
$792$		0			0
$793$	14.1360			0.501984
$794$	−35.2373	+	24.1699i	−1.25052	+	0.857758i
$795$		0			0
$796$	−5.09951	−	1.96835i	−0.180747	−	0.0697665i
$797$	−3.79132	−	2.75456i	−0.134296	−	0.0975714i	0.518609	−	0.855011i	$-0.326450\pi$
$797$	−3.79132	−	2.75456i	−0.134296	−	0.0975714i	−0.652905	+	0.757440i	$0.726450\pi$
$798$		0			0
$799$	−2.57938	+	7.93852i	−0.0912520	+	0.280845i
$800$	−1.41893	−	7.85859i	−0.0501666	−	0.277843i
$801$		0			0
$802$	−0.272268	−	0.00738171i	−0.00961410	−	0.000260657i
$803$	14.3420	−	36.1370i	0.506117	−	1.27525i
$804$		0			0
$805$	−14.7676	−	20.3259i	−0.520490	−	0.716393i
$806$	2.04760	+	6.93614i	0.0721236	+	0.244315i
$807$		0			0
$808$	22.5141	−	26.2129i	0.792043	−	0.922167i
$809$	−5.40400	+	7.43797i	−0.189995	+	0.261505i	−0.893378	−	0.449305i	$-0.851672\pi$
$809$	−5.40400	+	7.43797i	−0.189995	+	0.261505i	0.703384	+	0.710810i	$0.251672\pi$
$810$		0			0
$811$	−0.540273	−	1.66279i	−0.0189716	−	0.0583884i	0.941123	−	0.338066i	$-0.109773\pi$
$811$	−0.540273	−	1.66279i	−0.0189716	−	0.0583884i	−0.960094	+	0.279677i	$0.909773\pi$
$812$	33.6122	+	51.9685i	1.17956	+	1.82374i
$813$		0			0
$814$	−52.0444	+	11.8242i	−1.82416	+	0.414437i
$815$			1.20741i			0.0422937i
$816$		0			0
$817$	−3.16616	−	9.74443i	−0.110770	−	0.340914i
$818$	41.2875	+	14.6637i	1.44358	+	0.512703i
$819$		0			0
$820$	−18.5395	+	22.8079i	−0.647426	+	0.796486i
$821$	−21.3086	−	6.92358i	−0.743675	−	0.241635i	−0.0874178	−	0.996172i	$-0.527862\pi$
$821$	−21.3086	−	6.92358i	−0.743675	−	0.241635i	−0.656258	+	0.754537i	$0.727862\pi$
$822$		0			0
$823$	16.2633	+	22.3844i	0.566901	+	0.780273i	0.992183	−	0.124788i	$-0.0398251\pi$
$823$	16.2633	+	22.3844i	0.566901	+	0.780273i	−0.425282	+	0.905061i	$0.639825\pi$
$824$	−3.14499	+	38.5909i	−0.109561	+	1.34438i
$825$		0			0
$826$	1.07456	−	39.6340i	0.0373886	−	1.37904i
$827$	−5.02913	+	3.65387i	−0.174880	+	0.127058i	−0.671782	−	0.740749i	$-0.734471\pi$
$827$	−5.02913	+	3.65387i	−0.174880	+	0.127058i	0.496902	+	0.867807i	$0.334471\pi$
$828$		0			0
$829$	−5.92631	+	18.2393i	−0.205829	+	0.633477i	0.793849	+	0.608115i	$0.208074\pi$
$829$	−5.92631	+	18.2393i	−0.205829	+	0.633477i	−0.999678	+	0.0253622i	$0.991926\pi$
$830$	16.0310	+	12.3246i	0.556445	+	0.427794i
$831$		0			0
$832$	−12.9132	−	6.67020i	−0.447686	−	0.231247i
$833$	14.2461	−	4.62883i	0.493598	−	0.160380i
$834$		0			0
$835$	17.2417			0.596674
$836$	3.39841	−	28.6999i	0.117537	−	0.992607i
$837$		0			0
$838$	23.0391	+	33.5886i	0.795871	+	1.16030i
$839$	39.6524	−	12.8838i	1.36895	−	0.444800i	0.469931	−	0.882703i	$-0.344279\pi$
$839$	39.6524	−	12.8838i	1.36895	−	0.444800i	0.899022	+	0.437904i	$0.144279\pi$
$840$		0			0
$841$	40.9205	+	29.7305i	1.41105	+	1.02519i
$842$	3.54604	+	2.72619i	0.122204	+	0.0939506i
$843$		0			0
$844$	13.0439	+	49.0433i	0.448989	+	1.68814i
$845$	14.8643	−	10.7996i	0.511348	−	0.371516i
$846$		0			0
$847$	16.3036	−	34.4998i	0.560199	−	1.18543i
$848$	24.8494	+	2.70481i	0.853331	+	0.0928834i
$849$		0			0
$850$	−5.69812	+	1.68213i	−0.195444	+	0.0576964i
$851$	−41.3760	−	13.4439i	−1.41835	−	0.460851i
$852$		0			0
$853$	14.8390	−	20.4241i	0.508078	−	0.699309i	−0.475516	−	0.879707i	$-0.657738\pi$
$853$	14.8390	−	20.4241i	0.508078	−	0.699309i	0.983594	+	0.180398i	$0.0577385\pi$
$854$	−35.9699	−	12.7751i	−1.23086	−	0.437154i
$855$		0			0
$856$	9.08228	−	5.53101i	0.310426	−	0.189046i
$857$		−	20.1558i		−	0.688510i	−0.938876	−	0.344255i	$-0.888132\pi$
$857$		−	20.1558i		−	0.688510i	0.938876	−	0.344255i	$-0.111868\pi$
$858$		0			0
$859$			2.64305i			0.0901798i	0.998983	+	0.0450899i	$0.0143574\pi$
$859$			2.64305i			0.0901798i	−0.998983	+	0.0450899i	$0.985643\pi$
$860$	−7.48101	+	4.83856i	−0.255100	+	0.164994i
$861$		0			0
$862$	1.26540	−	3.56291i	0.0430998	−	0.121353i
$863$	18.9266	−	26.0502i	0.644267	−	0.886758i	−0.354567	−	0.935031i	$-0.615372\pi$
$863$	18.9266	−	26.0502i	0.644267	−	0.886758i	0.998834	+	0.0482726i	$0.0153716\pi$
$864$		0			0
$865$	−29.5541	−	9.60272i	−1.00487	−	0.326502i
$866$	−8.40240	−	28.4627i	−0.285525	−	0.967203i
$867$		0			0
$868$	1.05814	−	19.4999i	0.0359155	−	0.661869i
$869$	−9.52608	−	15.0380i	−0.323150	−	0.510128i
$870$		0			0
$871$	22.1627	−	16.1022i	0.750955	−	0.545601i
$872$	3.94515	−	0.935570i	0.133600	−	0.0316824i
$873$		0			0
$874$	14.3587	−	18.6768i	0.485689	−	0.631751i
$875$	34.0855	+	24.7646i	1.15230	+	0.837196i
$876$		0			0
$877$	−32.3463	+	10.5100i	−1.09226	+	0.354896i	−0.799118	−	0.601174i	$-0.794700\pi$
$877$	−32.3463	+	10.5100i	−1.09226	+	0.354896i	−0.293139	+	0.956070i	$0.594700\pi$
$878$	11.3744	−	7.80192i	0.383867	−	0.263302i
$879$		0			0
$880$	−24.8773	+	3.55868i	−0.838614	+	0.119963i
$881$	4.53963			0.152944			0.0764719	−	0.997072i	$-0.475634\pi$
$881$	4.53963			0.152944			0.0764719	+	0.997072i	$0.475634\pi$
$882$		0			0
$883$	2.08769	−	0.678332i	0.0702564	−	0.0228277i	−0.273678	−	0.961821i	$-0.588240\pi$
$883$	2.08769	−	0.678332i	0.0702564	−	0.0228277i	0.343934	+	0.938994i	$0.388240\pi$
$884$	−3.89380	+	10.0878i	−0.130963	+	0.339291i
$885$		0			0
$886$	17.7637	−	23.1058i	0.596784	−	0.776256i
$887$	−6.21007	+	19.1126i	−0.208514	+	0.641739i	0.791037	+	0.611768i	$0.209541\pi$
$887$	−6.21007	+	19.1126i	−0.208514	+	0.641739i	−0.999551	+	0.0299709i	$0.990459\pi$
$888$		0			0
$889$	14.4293	−	10.4835i	0.483944	−	0.351606i
$890$	−13.9495	−	0.378199i	−0.467589	−	0.0126773i
$891$		0			0
$892$	2.19041	−	40.3659i	0.0733403	−	1.35155i
$893$	7.18299	+	9.88654i	0.240370	+	0.330840i
$894$		0			0
$895$	−0.973640	−	0.316355i	−0.0325452	−	0.0105746i
$896$	26.8305	+	28.6427i	0.896343	+	0.956887i
$897$		0			0
$898$	−18.9008	+	53.2176i	−0.630727	+	1.77589i
$899$	−7.75945	−	23.8811i	−0.258792	−	0.796480i
$900$		0			0
$901$		−	18.5968i		−	0.619548i
$902$	−27.3796	−	23.9691i	−0.911642	−	0.798083i
$903$		0			0
$904$	29.5386	−	17.9886i	0.982438	−	0.598293i
$905$	2.94833	+	9.07401i	0.0980057	+	0.301630i
$906$		0			0
$907$	25.2363	−	34.7347i	0.837957	−	1.15335i	−0.148433	−	0.988922i	$-0.547423\pi$
$907$	25.2363	−	34.7347i	0.837957	−	1.15335i	0.986389	−	0.164426i	$-0.0525771\pi$
$908$	5.32984	+	4.33237i	0.176877	+	0.143775i
$909$		0			0
$910$	16.1925	−	4.78013i	0.536775	−	0.158460i
$911$	−13.7521	−	18.9282i	−0.455628	−	0.627118i	0.517967	−	0.855401i	$-0.326689\pi$
$911$	−13.7521	−	18.9282i	−0.455628	−	0.627118i	−0.973595	+	0.228283i	$0.926689\pi$
$912$		0			0
$913$	−15.9734	+	19.2763i	−0.528643	+	0.637953i
$914$	1.29182	−	47.6477i	0.0427296	−	1.57604i
$915$		0			0
$916$	3.00921	+	11.3143i	0.0994272	+	0.373833i
$917$	−3.73615	+	11.4987i	−0.123379	+	0.379721i
$918$		0			0
$919$	13.0131	+	9.45455i	0.429261	+	0.311877i	0.781354	−	0.624089i	$-0.214530\pi$
$919$	13.0131	+	9.45455i	0.429261	+	0.311877i	−0.352092	+	0.935965i	$0.614530\pi$
$920$	−18.9041	−	7.89188i	−0.623249	−	0.260188i
$921$		0			0
$922$	−14.7743	−	21.5394i	−0.486564	−	0.709361i
$923$	10.0185			0.329762
$924$		0			0
$925$	16.0630			0.528150
$926$	17.5844	+	25.6362i	0.577858	+	0.842457i
$927$		0			0
$928$	45.4467	+	21.9357i	1.49186	+	0.720073i
$929$	5.33225	+	3.87411i	0.174945	+	0.127105i	0.671812	−	0.740722i	$-0.265516\pi$
$929$	5.33225	+	3.87411i	0.174945	+	0.127105i	−0.496867	+	0.867827i	$0.665516\pi$
$930$		0			0
$931$	6.77680	−	20.8569i	0.222101	−	0.683556i
$932$	19.0883	−	5.07684i	0.625257	−	0.166297i
$933$		0			0
$934$	1.40513	−	51.8268i	0.0459771	−	1.69582i
$935$	4.63483	+	18.1132i	0.151575	+	0.592364i
$936$		0			0
$937$	6.99890	+	9.63316i	0.228644	+	0.314702i	0.907889	−	0.419210i	$-0.137693\pi$
$937$	6.99890	+	9.63316i	0.228644	+	0.314702i	−0.679245	+	0.733911i	$0.737693\pi$
$938$	−70.9463	+	20.9439i	−2.31648	+	0.683841i
$939$		0			0
$940$	6.70266	−	8.24584i	0.218617	−	0.268950i
$941$	6.88516	−	9.47660i	0.224450	−	0.308928i	−0.681909	−	0.731437i	$-0.738850\pi$
$941$	6.88516	−	9.47660i	0.224450	−	0.308928i	0.906359	+	0.422508i	$0.138850\pi$
$942$		0			0
$943$	−9.16626	−	28.2109i	−0.298495	−	0.918672i
$944$	−16.0602	−	28.0564i	−0.522716	−	0.913160i
$945$		0			0
$946$	−5.64793	−	9.47451i	−0.183630	−	0.308043i
$947$			34.4025i			1.11793i	0.829191	+	0.558966i	$0.188802\pi$
$947$			34.4025i			1.11793i	−0.829191	+	0.558966i	$0.811198\pi$
$948$		0			0
$949$	6.58116	+	20.2547i	0.213634	+	0.657496i
$950$	−2.91110	+	8.19658i	−0.0944486	+	0.265932i
$951$		0			0
$952$	19.0246	−	22.1502i	0.616592	−	0.717891i
$953$	−19.7117	−	6.40471i	−0.638523	−	0.207469i	−0.0281762	−	0.999603i	$-0.508970\pi$
$953$	−19.7117	−	6.40471i	−0.638523	−	0.207469i	−0.610347	+	0.792134i	$0.708970\pi$
$954$		0			0
$955$	3.26490	+	4.49375i	0.105650	+	0.145414i
$956$	39.1514	+	2.12451i	1.26625	+	0.0687114i
$957$		0			0
$958$	33.4138	+	0.905912i	1.07955	+	0.0292687i
$959$	−9.47485	+	6.88388i	−0.305959	+	0.222292i
$960$		0			0
$961$	7.13118	−	21.9475i	0.230038	−	0.707984i
$962$	17.8188	−	23.1775i	0.574501	−	0.747272i
$963$		0			0
$964$	22.7490	+	8.78087i	0.732697	+	0.282813i
$965$	19.9766	−	6.49078i	0.643068	−	0.208946i
$966$		0			0
$967$	−55.9913			−1.80056			−0.900280	−	0.435312i	$-0.856638\pi$
$967$	−55.9913			−1.80056			−0.900280	+	0.435312i	$0.856638\pi$
$968$	−3.27749	−	30.9396i	−0.105342	−	0.994436i
$969$		0			0
$970$	−18.3637	+	12.5960i	−0.589621	+	0.404433i
$971$	−48.0716	+	15.6194i	−1.54269	+	0.501251i	−0.952118	−	0.305732i	$-0.901099\pi$
$971$	−48.0716	+	15.6194i	−1.54269	+	0.501251i	−0.590575	+	0.806983i	$0.701099\pi$
$972$		0			0
$973$	−63.7698	−	46.3315i	−2.04437	−	1.48532i
$974$	−31.8034	+	41.3677i	−1.01905	+	1.32551i
$975$		0			0
$976$	−30.4669	+	6.35816i	−0.975221	+	0.203520i
$977$	−17.4903	+	12.7074i	−0.559563	+	0.406546i	−0.831299	−	0.555826i	$-0.812402\pi$
$977$	−17.4903	+	12.7074i	−0.559563	+	0.406546i	0.271736	+	0.962372i	$0.412402\pi$
$978$		0			0
$979$	1.09895	−	17.2415i	0.0351225	−	0.551040i
$980$	−19.0415	−	1.03327i	−0.608260	−	0.0330065i
$981$		0			0
$982$	7.45864	+	25.2658i	0.238015	+	0.806264i
$983$	1.27749	+	0.415082i	0.0407456	+	0.0132391i	0.329319	−	0.944219i	$-0.393181\pi$
$983$	1.27749	+	0.415082i	0.0407456	+	0.0132391i	−0.288573	+	0.957458i	$0.593181\pi$
$984$		0			0
$985$	6.65498	−	9.15979i	0.212045	−	0.291855i
$986$	12.5653	−	35.3791i	0.400159	−	1.12670i
$987$		0			0
$988$	8.59761	+	13.2930i	0.273527	+	0.422905i
$989$		−	8.99132i		−	0.285907i
$990$		0			0
$991$		−	18.7949i		−	0.597039i	−0.954404	−	0.298520i	$-0.903507\pi$
$991$		−	18.7949i		−	0.597039i	0.954404	−	0.298520i	$-0.0964928\pi$
$992$	−7.53289	−	14.0283i	−0.239170	−	0.445398i
$993$		0			0
$994$	−25.4926	−	9.05395i	−0.808575	−	0.287174i
$995$	3.04313	−	4.18851i	0.0964737	−	0.132785i
$996$		0			0
$997$	−14.1935	−	4.61173i	−0.449511	−	0.146055i	0.0755083	−	0.997145i	$-0.475942\pi$
$997$	−14.1935	−	4.61173i	−0.449511	−	0.146055i	−0.525020	+	0.851090i	$0.675942\pi$
$998$	46.5118	−	13.7306i	1.47230	−	0.434635i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.r.b.19.2		48
3.2	odd	2		132.2.j.a.19.11	yes	48
4.3	odd	2	inner	396.2.r.b.19.10		48
11.7	odd	10	inner	396.2.r.b.271.10		48
12.11	even	2		132.2.j.a.19.3	yes	48
33.29	even	10		132.2.j.a.7.3	✓	48
44.7	even	10	inner	396.2.r.b.271.2		48
132.95	odd	10		132.2.j.a.7.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.7.3	✓	48	33.29	even	10
132.2.j.a.7.11	yes	48	132.95	odd	10
132.2.j.a.19.3	yes	48	12.11	even	2
132.2.j.a.19.11	yes	48	3.2	odd	2
396.2.r.b.19.2		48	1.1	even	1	trivial
396.2.r.b.19.10		48	4.3	odd	2	inner
396.2.r.b.271.2		48	44.7	even	10	inner
396.2.r.b.271.10		48	11.7	odd	10	inner

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:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16623 + 0.799941i) q^{2} +(0.720190 - 1.86583i) q^{4} +(1.53251 + 1.11343i) q^{5} +(-1.07196 + 3.29914i) q^{7} +(0.652646 + 2.75210i) q^{8} +O(q^{10})\)	\(q+(-1.16623 + 0.799941i) q^{2} +(0.720190 - 1.86583i) q^{4} +(1.53251 + 1.11343i) q^{5} +(-1.07196 + 3.29914i) q^{7} +(0.652646 + 2.75210i) q^{8} +(-2.67794 - 0.0726042i) q^{10} +(0.210969 - 3.30991i) q^{11} +(1.06787 + 1.46980i) q^{13} +(-1.38897 - 4.70507i) q^{14} +(-2.96265 - 2.68751i) q^{16} +(-1.74921 + 2.40759i) q^{17} +(1.34636 + 4.14366i) q^{19} +(3.18118 - 2.05752i) q^{20} +(2.40169 + 4.02888i) q^{22} +3.82341i q^{23} +(-0.436233 - 1.34259i) q^{25} +(-2.42114 - 0.859894i) q^{26} +(5.38363 + 4.37610i) q^{28} +(8.48417 + 2.75668i) q^{29} +(-1.65449 - 2.27721i) q^{31} +(5.60498 + 0.764309i) q^{32} +(0.114062 - 4.20707i) q^{34} +(-5.31616 + 3.86242i) q^{35} +(-3.51620 + 10.8218i) q^{37} +(-4.88484 - 3.75546i) q^{38} +(-2.06409 + 4.94430i) q^{40} +(-7.37845 + 2.39740i) q^{41} -2.35165 q^{43} +(-6.02379 - 2.77740i) q^{44} +(-3.05850 - 4.45898i) q^{46} +(2.66757 - 0.866745i) q^{47} +(-4.07214 - 2.95858i) q^{49} +(1.58274 + 1.21681i) q^{50} +(3.51148 - 0.933936i) q^{52} +(-5.05557 + 3.67309i) q^{53} +(4.00867 - 4.83757i) q^{55} +(-9.77918 - 0.796961i) q^{56} +(-12.0997 + 3.57191i) q^{58} +(7.68642 + 2.49747i) q^{59} +(4.57345 - 6.29481i) q^{61} +(3.75115 + 1.33226i) q^{62} +(-7.14811 + 3.59229i) q^{64} +3.44150i q^{65} -15.0787i q^{67} +(3.23238 + 4.99766i) q^{68} +(3.11017 - 8.75708i) q^{70} +(3.24129 - 4.46126i) q^{71} +(11.1487 + 3.62244i) q^{73} +(-4.55606 - 15.4334i) q^{74} +(8.70100 + 0.472149i) q^{76} +(10.6937 + 4.24410i) q^{77} +(4.34223 - 3.15482i) q^{79} +(-1.54793 - 7.41735i) q^{80} +(6.68720 - 8.69825i) q^{82} +(-6.10662 - 4.43672i) q^{83} +(-5.36138 + 1.74202i) q^{85} +(2.74257 - 1.88118i) q^{86} +(9.24689 - 1.57959i) q^{88} +5.20905 q^{89} +(-5.99381 + 1.94751i) q^{91} +(7.13384 + 2.75358i) q^{92} +(-2.41765 + 3.14472i) q^{94} +(-2.55038 + 7.84928i) q^{95} +(6.72491 - 4.88593i) q^{97} +(7.11574 + 0.192922i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} + 14 q^{14} - 24 q^{16} + 22 q^{20} - 26 q^{22} - 20 q^{25} + 38 q^{26} - 10 q^{28} - 48 q^{37} - 58 q^{38} + 70 q^{40} + 40 q^{41} - 34 q^{44} + 70 q^{46} - 28 q^{49} - 70 q^{50} + 30 q^{52} + 64 q^{53} - 60 q^{56} - 54 q^{58} - 40 q^{64} + 4 q^{70} + 20 q^{73} - 50 q^{74} + 8 q^{77} - 58 q^{80} + 62 q^{82} + 40 q^{85} - 8 q^{86} + 8 q^{88} - 48 q^{89} - 42 q^{92} - 10 q^{94} + 48 q^{97}+O(q^{100}) \) 48 * q - 4 * q^4 + 14 * q^14 - 24 * q^16 + 22 * q^20 - 26 * q^22 - 20 * q^25 + 38 * q^26 - 10 * q^28 - 48 * q^37 - 58 * q^38 + 70 * q^40 + 40 * q^41 - 34 * q^44 + 70 * q^46 - 28 * q^49 - 70 * q^50 + 30 * q^52 + 64 * q^53 - 60 * q^56 - 54 * q^58 - 40 * q^64 + 4 * q^70 + 20 * q^73 - 50 * q^74 + 8 * q^77 - 58 * q^80 + 62 * q^82 + 40 * q^85 - 8 * q^86 + 8 * q^88 - 48 * q^89 - 42 * q^92 - 10 * q^94 + 48 * q^97

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