LMFDB - Embedded newform 396.2.r.b.271.5

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			271.5
Character	$\chi$	$=$	396.271
Dual form			396.2.r.b.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.140058 - 1.40726i) q^{2} +(-1.96077 + 0.394195i) q^{4} +(0.213696 - 0.155259i) q^{5} +(1.03321 + 3.17989i) q^{7} +(0.829356 + 2.70410i) q^{8} +O(q^{10})$	\(q+(-0.140058 - 1.40726i) q^{2} +(-1.96077 + 0.394195i) q^{4} +(0.213696 - 0.155259i) q^{5} +(1.03321 + 3.17989i) q^{7} +(0.829356 + 2.70410i) q^{8} +(-0.248420 - 0.278981i) q^{10} +(1.85745 - 2.74771i) q^{11} +(3.89823 - 5.36545i) q^{13} +(4.33023 - 1.89936i) q^{14} +(3.68922 - 1.54585i) q^{16} +(2.74676 + 3.78059i) q^{17} +(1.27559 - 3.92586i) q^{19} +(-0.357806 + 0.388665i) q^{20} +(-4.12689 - 2.22908i) q^{22} +0.765361i q^{23} +(-1.52352 + 4.68893i) q^{25} +(-8.09657 - 4.73436i) q^{26} +(-3.27938 - 5.82774i) q^{28} +(-3.67765 + 1.19494i) q^{29} +(2.37677 - 3.27135i) q^{31} +(-2.69212 - 4.97519i) q^{32} +(4.93558 - 4.39491i) q^{34} +(0.714499 + 0.519114i) q^{35} +(0.274094 + 0.843576i) q^{37} +(-5.70337 - 1.24524i) q^{38} +(0.597067 + 0.449091i) q^{40} +(5.66025 + 1.83913i) q^{41} -2.10908 q^{43} +(-2.55889 + 6.11981i) q^{44} +(1.07706 - 0.107195i) q^{46} +(4.91501 + 1.59698i) q^{47} +(-3.38106 + 2.45648i) q^{49} +(6.81192 + 1.48728i) q^{50} +(-5.52849 + 12.0571i) q^{52} +(-4.59637 - 3.33946i) q^{53} +(-0.0296780 - 0.875559i) q^{55} +(-7.74185 + 5.43116i) q^{56} +(2.19667 + 5.00805i) q^{58} +(9.46770 - 3.07624i) q^{59} +(1.87298 + 2.57794i) q^{61} +(-4.93652 - 2.88656i) q^{62} +(-6.62434 + 4.48532i) q^{64} -1.75181i q^{65} +5.99397i q^{67} +(-6.87605 - 6.33011i) q^{68} +(0.630458 - 1.07819i) q^{70} +(-2.69549 - 3.71003i) q^{71} +(-14.3347 + 4.65764i) q^{73} +(1.14874 - 0.503872i) q^{74} +(-0.953581 + 8.20054i) q^{76} +(10.6565 + 3.06752i) q^{77} +(-11.6701 - 8.47885i) q^{79} +(0.548364 - 0.903127i) q^{80} +(1.79537 - 8.22304i) q^{82} +(-0.496492 + 0.360722i) q^{83} +(1.17394 + 0.381437i) q^{85} +(0.295392 + 2.96802i) q^{86} +(8.97056 + 2.74390i) q^{88} -2.78024 q^{89} +(21.0892 + 6.85231i) q^{91} +(-0.301701 - 1.50070i) q^{92} +(1.55899 - 7.14037i) q^{94} +(-0.336938 - 1.03699i) q^{95} +(8.14034 + 5.91430i) q^{97} +(3.93046 + 4.41398i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

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 $

$2$	−0.140058	−	1.40726i	−0.0990356	−	0.995084i
$2$	−0.140058	−	1.40726i	−0.0990356	−	0.995084i
$3$		0			0
$3$		0			0
$4$	−1.96077	+	0.394195i	−0.980384	+	0.197097i
$5$	0.213696	−	0.155259i	0.0955677	−	0.0694340i	−0.538975	−	0.842322i	$-0.681188\pi$
$5$	0.213696	−	0.155259i	0.0955677	−	0.0694340i	0.634543	+	0.772888i	$0.281188\pi$
$6$		0			0
$7$	1.03321	+	3.17989i	0.390516	+	1.20189i	0.932399	+	0.361431i	$0.117712\pi$
$7$	1.03321	+	3.17989i	0.390516	+	1.20189i	−0.541883	+	0.840454i	$0.682288\pi$
$8$	0.829356	+	2.70410i	0.293221	+	0.956045i
$9$		0			0
$10$	−0.248420	−	0.278981i	−0.0785573	−	0.0882214i
$11$	1.85745	−	2.74771i	0.560041	−	0.828465i
$11$	1.85745	−	2.74771i	0.560041	−	0.828465i
$12$		0			0
$13$	3.89823	−	5.36545i	1.08117	−	1.48811i	0.222953	−	0.974829i	$-0.428430\pi$
$13$	3.89823	−	5.36545i	1.08117	−	1.48811i	0.858221	−	0.513280i	$-0.171570\pi$
$14$	4.33023	−	1.89936i	1.15730	−	0.507626i
$15$		0			0
$16$	3.68922	−	1.54585i	0.922305	−	0.386462i
$17$	2.74676	+	3.78059i	0.666188	+	0.916929i	0.999666	−	0.0258289i	$-0.00822250\pi$
$17$	2.74676	+	3.78059i	0.666188	+	0.916929i	−0.333479	+	0.942758i	$0.608223\pi$
$18$		0			0
$19$	1.27559	−	3.92586i	0.292640	−	0.900655i	−0.691363	−	0.722507i	$-0.742990\pi$
$19$	1.27559	−	3.92586i	0.292640	−	0.900655i	0.984004	−	0.178147i	$-0.0570104\pi$
$20$	−0.357806	+	0.388665i	−0.0800078	+	0.0869081i
$21$		0			0
$22$	−4.12689	−	2.22908i	−0.879856	−	0.475240i
$23$			0.765361i			0.159589i	0.996811	+	0.0797944i	$0.0254264\pi$
$23$			0.765361i			0.159589i	−0.996811	+	0.0797944i	$0.974574\pi$
$24$		0			0
$25$	−1.52352	+	4.68893i	−0.304705	+	0.937785i
$26$	−8.09657	−	4.73436i	−1.58787	−	0.928483i
$27$		0			0
$28$	−3.27938	−	5.82774i	−0.619744	−	1.10134i
$29$	−3.67765	+	1.19494i	−0.682922	+	0.221895i	−0.629874	−	0.776697i	$-0.716894\pi$
$29$	−3.67765	+	1.19494i	−0.682922	+	0.221895i	−0.0530476	+	0.998592i	$0.516894\pi$
$30$		0			0
$31$	2.37677	−	3.27135i	0.426881	−	0.587551i	−0.540353	−	0.841439i	$-0.681709\pi$
$31$	2.37677	−	3.27135i	0.426881	−	0.587551i	0.967234	+	0.253887i	$0.0817092\pi$
$32$	−2.69212	−	4.97519i	−0.475904	−	0.879497i
$33$		0			0
$34$	4.93558	−	4.39491i	0.846445	−	0.753721i
$35$	0.714499	+	0.519114i	0.120772	+	0.0877463i
$36$		0			0
$37$	0.274094	+	0.843576i	0.0450608	+	0.138683i	0.971056	−	0.238853i	$-0.0767714\pi$
$37$	0.274094	+	0.843576i	0.0450608	+	0.138683i	−0.925995	+	0.377536i	$0.876771\pi$
$38$	−5.70337	−	1.24524i	−0.925209	−	0.202005i
$39$		0			0
$40$	0.597067	+	0.449091i	0.0944045	+	0.0710074i
$41$	5.66025	+	1.83913i	0.883983	+	0.287223i	0.715610	−	0.698500i	$-0.246149\pi$
$41$	5.66025	+	1.83913i	0.883983	+	0.287223i	0.168373	+	0.985723i	$0.446149\pi$
$42$		0			0
$43$	−2.10908			−0.321631			−0.160816	−	0.986984i	$-0.551412\pi$
$43$	−2.10908			−0.321631			−0.160816	+	0.986984i	$0.551412\pi$
$44$	−2.55889	+	6.11981i	−0.385767	+	0.922596i
$45$		0			0
$46$	1.07706	−	0.107195i	0.158804	−	0.0158050i
$47$	4.91501	+	1.59698i	0.716928	+	0.232944i	0.644691	−	0.764444i	$-0.276986\pi$
$47$	4.91501	+	1.59698i	0.716928	+	0.232944i	0.0722371	+	0.997387i	$0.476986\pi$
$48$		0			0
$49$	−3.38106	+	2.45648i	−0.483008	+	0.350926i
$50$	6.81192	+	1.48728i	0.963352	+	0.210333i
$51$		0			0
$52$	−5.52849	+	12.0571i	−0.766663	+	1.67201i
$53$	−4.59637	−	3.33946i	−0.631360	−	0.458710i	0.225511	−	0.974241i	$-0.427595\pi$
$53$	−4.59637	−	3.33946i	−0.631360	−	0.458710i	−0.856871	+	0.515531i	$0.827595\pi$
$54$		0			0
$55$	−0.0296780	−	0.875559i	−0.00400178	−	0.118060i
$56$	−7.74185	+	5.43116i	−1.03455	+	0.725769i
$57$		0			0
$58$	2.19667	+	5.00805i	0.288437	+	0.657589i
$59$	9.46770	−	3.07624i	1.23259	−	0.400493i	0.380938	−	0.924601i	$-0.375601\pi$
$59$	9.46770	−	3.07624i	1.23259	−	0.400493i	0.851652	+	0.524108i	$0.175601\pi$
$60$		0			0
$61$	1.87298	+	2.57794i	0.239811	+	0.330071i	0.911910	−	0.410390i	$-0.134607\pi$
$61$	1.87298	+	2.57794i	0.239811	+	0.330071i	−0.672100	+	0.740461i	$0.734607\pi$
$62$	−4.93652	−	2.88656i	−0.626939	−	0.366594i
$63$		0			0
$64$	−6.62434	+	4.48532i	−0.828042	+	0.560666i
$65$		−	1.75181i		−	0.217285i
$66$		0			0
$67$			5.99397i			0.732280i	0.930560	+	0.366140i	$0.119321\pi$
$67$			5.99397i			0.732280i	−0.930560	+	0.366140i	$0.880679\pi$
$68$	−6.87605	−	6.33011i	−0.833844	−	0.767638i
$69$		0			0
$70$	0.630458	−	1.07819i	0.0753542	−	0.128869i
$71$	−2.69549	−	3.71003i	−0.319896	−	0.440299i	0.618539	−	0.785754i	$-0.287725\pi$
$71$	−2.69549	−	3.71003i	−0.319896	−	0.440299i	−0.938435	+	0.345455i	$0.887725\pi$
$72$		0			0
$73$	−14.3347	+	4.65764i	−1.67775	+	0.545135i	−0.984473	−	0.175534i	$-0.943835\pi$
$73$	−14.3347	+	4.65764i	−1.67775	+	0.545135i	−0.693280	+	0.720669i	$0.743835\pi$
$74$	1.14874	−	0.503872i	0.133539	−	0.0585739i
$75$		0			0
$76$	−0.953581	+	8.20054i	−0.109383	+	0.940666i
$77$	10.6565	+	3.06752i	1.21442	+	0.349576i
$78$		0			0
$79$	−11.6701	−	8.47885i	−1.31299	−	0.953945i	−0.999991	−	0.00419263i	$-0.998665\pi$
$79$	−11.6701	−	8.47885i	−1.31299	−	0.953945i	−0.313002	−	0.949753i	$-0.601335\pi$
$80$	0.548364	−	0.903127i	0.0613090	−	0.100973i
$81$		0			0
$82$	1.79537	−	8.22304i	0.198266	−	0.908083i
$83$	−0.496492	+	0.360722i	−0.0544971	+	0.0395944i	−0.614700	−	0.788761i	$-0.710723\pi$
$83$	−0.496492	+	0.360722i	−0.0544971	+	0.0395944i	0.560203	+	0.828355i	$0.310723\pi$
$84$		0			0
$85$	1.17394	+	0.381437i	0.127332	+	0.0413727i
$86$	0.295392	+	2.96802i	0.0318529	+	0.320050i
$87$		0			0
$88$	8.97056	+	2.74390i	0.956265	+	0.292501i
$89$	−2.78024			−0.294705			−0.147353	−	0.989084i	$-0.547075\pi$
$89$	−2.78024			−0.294705			−0.147353	+	0.989084i	$0.547075\pi$
$90$		0			0
$91$	21.0892	+	6.85231i	2.21075	+	0.718317i
$92$	−0.301701	−	1.50070i	−0.0314546	−	0.156458i
$93$		0			0
$94$	1.55899	−	7.14037i	0.160797	−	0.736473i
$95$	−0.336938	−	1.03699i	−0.0345691	−	0.106393i
$96$		0			0
$97$	8.14034	+	5.91430i	0.826526	+	0.600506i	0.918574	−	0.395248i	$-0.129341\pi$
$97$	8.14034	+	5.91430i	0.826526	+	0.600506i	−0.0920484	+	0.995755i	$0.529341\pi$
$98$	3.93046	+	4.41398i	0.397036	+	0.445880i
$99$		0			0
$100$	1.13893	−	9.79446i	0.113893	−	0.979446i
$101$	−11.6323	+	16.0105i	−1.15746	+	1.59310i	−0.437260	+	0.899335i	$0.644051\pi$
$101$	−11.6323	+	16.0105i	−1.15746	+	1.59310i	−0.720198	+	0.693769i	$0.755949\pi$
$102$		0			0
$103$	−6.38362	+	2.07416i	−0.628997	+	0.204373i	−0.606131	−	0.795365i	$-0.707279\pi$
$103$	−6.38362	+	2.07416i	−0.628997	+	0.204373i	−0.0228662	+	0.999739i	$0.507279\pi$
$104$	17.7418	+	6.09134i	1.73972	+	0.597305i
$105$		0			0
$106$	−4.05573	+	6.93601i	−0.393928	+	0.673685i
$107$	−3.77667	+	11.6234i	−0.365104	+	1.12368i	0.584811	+	0.811169i	$0.301168\pi$
$107$	−3.77667	+	11.6234i	−0.365104	+	1.12368i	−0.949916	+	0.312506i	$0.898832\pi$
$108$		0			0
$109$			2.09407i			0.200576i	0.994958	+	0.100288i	$0.0319764\pi$
$109$			2.09407i			0.200576i	−0.994958	+	0.100288i	$0.968024\pi$
$110$	−1.22798	+	0.164393i	−0.117084	+	0.0156743i
$111$		0			0
$112$	8.72737	+	10.1341i	0.824659	+	0.957585i
$113$	3.72590	−	11.4671i	0.350503	−	1.07874i	−0.608068	−	0.793885i	$-0.708055\pi$
$113$	3.72590	−	11.4671i	0.350503	−	1.07874i	0.958571	−	0.284853i	$-0.0919448\pi$
$114$		0			0
$115$	0.118829	+	0.163555i	0.0110809	+	0.0152515i
$116$	6.73997	−	3.79271i	0.625791	−	0.352144i
$117$		0			0
$118$	−5.65510	−	12.8927i	−0.520594	−	1.18687i
$119$	−9.18389	+	12.6405i	−0.841886	+	1.15876i
$120$		0			0
$121$	−4.09979	−	10.2074i	−0.372708	−	0.927949i
$122$	3.36550	−	2.99683i	0.304698	−	0.271320i
$123$		0			0
$124$	−3.37075	+	7.35126i	−0.302702	+	0.660163i
$125$	0.810551	+	2.49462i	0.0724979	+	0.223125i
$126$		0			0
$127$	−1.89867	+	1.37946i	−0.168480	+	0.122408i	−0.668830	−	0.743415i	$-0.733205\pi$
$127$	−1.89867	+	1.37946i	−0.168480	+	0.122408i	0.500350	+	0.865823i	$0.333205\pi$
$128$	7.23981	+	8.69397i	0.639915	+	0.768446i
$129$		0			0
$130$	−2.46526	+	0.245354i	−0.216217	+	0.0215190i
$131$	−13.7656			−1.20271			−0.601353	−	0.798983i	$-0.705372\pi$
$131$	−13.7656			−1.20271			−0.601353	+	0.798983i	$0.705372\pi$
$132$		0			0
$133$	13.8018			1.19676
$134$	8.43508	−	0.839501i	0.728680	−	0.0725218i
$135$		0			0
$136$	−7.94507	+	10.5630i	−0.681284	+	0.905768i
$137$	4.81224	−	3.49630i	0.411138	−	0.298709i	−0.362925	−	0.931819i	$-0.618222\pi$
$137$	4.81224	−	3.49630i	0.411138	−	0.298709i	0.774062	+	0.633110i	$0.218222\pi$
$138$		0			0
$139$	−2.33565	−	7.18840i	−0.198107	−	0.609712i	−0.999926	−	0.0121448i	$-0.996134\pi$
$139$	−2.33565	−	7.18840i	−0.198107	−	0.609712i	0.801819	−	0.597567i	$-0.203866\pi$
$140$	−1.60560	−	0.736210i	−0.135698	−	0.0622211i
$141$		0			0
$142$	−4.84345	+	4.31288i	−0.406453	+	0.361929i
$143$	−7.50194	−	20.6772i	−0.627344	−	1.72912i
$144$		0			0
$145$	−0.600373	+	0.826342i	−0.0498582	+	0.0686240i
$146$	8.56220	+	19.5204i	0.708612	+	1.61552i
$147$		0			0
$148$	−0.869969	−	1.54601i	−0.0715110	−	0.127081i
$149$	−10.4316	−	14.3578i	−0.854588	−	1.17624i	−0.982833	−	0.184497i	$-0.940934\pi$
$149$	−10.4316	−	14.3578i	−0.854588	−	1.17624i	0.128245	−	0.991743i	$-0.459066\pi$
$150$		0			0
$151$	−4.19328	+	12.9056i	−0.341245	+	1.05024i	0.622319	+	0.782764i	$0.286191\pi$
$151$	−4.19328	+	12.9056i	−0.341245	+	1.05024i	−0.963564	+	0.267479i	$0.913809\pi$
$152$	11.6739	+	0.193390i	0.946875	+	0.0156860i
$153$		0			0
$154$	2.82427	−	15.4262i	0.227586	−	1.24308i
$155$		−	1.06809i		−	0.0857910i
$156$		0			0
$157$	4.46673	−	13.7472i	0.356484	−	1.09714i	−0.598660	−	0.801003i	$-0.704300\pi$
$157$	4.46673	−	13.7472i	0.356484	−	1.09714i	0.955144	−	0.296141i	$-0.0957000\pi$
$158$	−10.2975	+	17.6105i	−0.819222	+	1.40101i
$159$		0			0
$160$	−1.34774	−	0.645202i	−0.106548	−	0.0510077i
$161$	−2.43376	+	0.790778i	−0.191807	+	0.0623220i
$162$		0			0
$163$	3.68738	−	5.07524i	0.288818	−	0.397523i	−0.639812	−	0.768531i	$-0.720988\pi$
$163$	3.68738	−	5.07524i	0.288818	−	0.397523i	0.928630	+	0.371008i	$0.120988\pi$
$164$	−11.8234	−	1.37486i	−0.923254	−	0.107358i
$165$		0			0
$166$	0.577168	+	0.648172i	0.0447969	+	0.0503079i
$167$	−1.90114	−	1.38126i	−0.147115	−	0.106885i	0.511793	−	0.859109i	$-0.328981\pi$
$167$	−1.90114	−	1.38126i	−0.147115	−	0.106885i	−0.658908	+	0.752223i	$0.728981\pi$
$168$		0			0
$169$	−9.57467	−	29.4678i	−0.736513	−	2.26675i
$170$	0.372362	−	1.70547i	0.0285589	−	0.130803i
$171$		0			0
$172$	4.13541	−	0.831388i	0.315322	−	0.0633927i
$173$	−15.5257	−	5.04461i	−1.18040	−	0.383534i	−0.347883	−	0.937538i	$-0.613099\pi$
$173$	−15.5257	−	5.04461i	−1.18040	−	0.383534i	−0.832514	+	0.554004i	$0.813099\pi$
$174$		0			0
$175$	−16.4844			−1.24610
$176$	2.60499	−	13.0082i	0.196358	−	0.980532i
$177$		0			0
$178$	0.389394	+	3.91253i	0.0291863	+	0.293256i
$179$	23.3391	+	7.58332i	1.74444	+	0.566804i	0.995408	−	0.0957267i	$-0.0305175\pi$
$179$	23.3391	+	7.58332i	1.74444	+	0.566804i	0.749035	+	0.662530i	$0.230517\pi$
$180$		0			0
$181$	−10.6410	+	7.73114i	−0.790939	+	0.574651i	−0.908242	−	0.418445i	$-0.862575\pi$
$181$	−10.6410	+	7.73114i	−0.790939	+	0.574651i	0.117303	+	0.993096i	$0.462575\pi$
$182$	6.68928	−	30.6378i	0.495842	−	2.27102i
$183$		0			0
$184$	−2.06961	+	0.634756i	−0.152574	+	0.0467949i
$185$	0.189546	+	0.137713i	0.0139357	+	0.0101249i
$186$		0			0
$187$	15.4899	−	0.525047i	1.13274	−	0.0383952i
$188$	−10.2667	−	1.19384i	−0.748777	−	0.0870698i
$189$		0			0
$190$	−1.41212	+	0.619397i	−0.102446	+	0.0449358i
$191$	−10.5402	+	3.42473i	−0.762665	+	0.247805i	−0.664422	−	0.747358i	$-0.731322\pi$
$191$	−10.5402	+	3.42473i	−0.762665	+	0.247805i	−0.0982428	+	0.995162i	$0.531322\pi$
$192$		0			0
$193$	8.15394	+	11.2229i	0.586933	+	0.807844i	0.994434	−	0.105361i	$-0.0335997\pi$
$193$	8.15394	+	11.2229i	0.586933	+	0.807844i	−0.407501	+	0.913205i	$0.633600\pi$
$194$	7.18285	−	12.2839i	0.515699	−	0.881934i
$195$		0			0
$196$	5.66114	−	6.14939i	0.404367	−	0.439242i
$197$		−	6.04339i		−	0.430574i	−0.976551	−	0.215287i	$-0.930931\pi$
$197$		−	6.04339i		−	0.430574i	0.976551	−	0.215287i	$-0.0690686\pi$
$198$		0			0
$199$			17.1475i			1.21556i	0.794107	+	0.607778i	$0.207939\pi$
$199$			17.1475i			1.21556i	−0.794107	+	0.607778i	$0.792061\pi$
$200$	−13.9429	−	0.230979i	−0.985910	−	0.0163327i
$201$		0			0
$202$	24.1601	+	14.1273i	1.69990	+	0.993994i
$203$	−7.59955	−	10.4599i	−0.533384	−	0.734140i
$204$		0			0
$205$	1.49511	−	0.485792i	0.104423	−	0.0339292i
$206$	3.81297	+	8.69292i	0.265662	+	0.605664i
$207$		0			0
$208$	6.08725	−	25.8204i	0.422075	−	1.79032i
$209$	−8.41778	−	10.7970i	−0.582270	−	0.746846i
$210$		0			0
$211$	−10.3629	−	7.52909i	−0.713411	−	0.518324i	0.170861	−	0.985295i	$-0.445345\pi$
$211$	−10.3629	−	7.52909i	−0.713411	−	0.518324i	−0.884272	+	0.466972i	$0.845345\pi$
$212$	10.3288	+	4.73604i	0.709386	+	0.325272i
$213$		0			0
$214$	16.8861	+	3.68682i	1.15431	+	0.252025i
$215$	−0.450701	+	0.327453i	−0.0307376	+	0.0223321i
$216$		0			0
$217$	12.8582	+	4.17789i	0.872873	+	0.283614i
$218$	2.94691	−	0.293290i	0.199590	−	0.0198641i
$219$		0			0
$220$	0.403333	+	1.70507i	0.0271927	+	0.114956i
$221$	30.9921			2.08476
$222$		0			0
$223$	1.94261	+	0.631192i	0.130087	+	0.0422677i	0.373337	−	0.927696i	$-0.378214\pi$
$223$	1.94261	+	0.631192i	0.130087	+	0.0422677i	−0.243250	+	0.969964i	$0.578214\pi$
$224$	13.0390	−	13.7010i	0.871207	−	0.915440i
$225$		0			0
$226$	−16.6591	−	3.63726i	−1.10815	−	0.241947i
$227$	−5.65067	−	17.3910i	−0.375048	−	1.15428i	−0.943446	−	0.331526i	$-0.892436\pi$
$227$	−5.65067	−	17.3910i	−0.375048	−	1.15428i	0.568398	−	0.822754i	$-0.307564\pi$
$228$		0			0
$229$	−10.0961	−	7.33523i	−0.667168	−	0.484726i	0.201908	−	0.979404i	$-0.435286\pi$
$229$	−10.0961	−	7.33523i	−0.667168	−	0.484726i	−0.869076	+	0.494679i	$0.835286\pi$
$230$	0.213521	−	0.190131i	0.0140792	−	0.0125369i
$231$		0			0
$232$	−6.28132	−	8.95370i	−0.412389	−	0.587839i
$233$	7.79576	−	10.7299i	0.510717	−	0.702942i	−0.473323	−	0.880889i	$-0.656946\pi$
$233$	7.79576	−	10.7299i	0.510717	−	0.702942i	0.984040	+	0.177947i	$0.0569456\pi$
$234$		0			0
$235$	1.29826	−	0.421831i	0.0846894	−	0.0275172i
$236$	−17.3513	+	9.76392i	−1.12948	+	0.635577i
$237$		0			0
$238$	19.0748	+	11.1537i	1.23644	+	0.722989i
$239$	−6.21895	+	19.1400i	−0.402271	+	1.23806i	0.520882	+	0.853629i	$0.325603\pi$
$239$	−6.21895	+	19.1400i	−0.402271	+	1.23806i	−0.923153	+	0.384433i	$0.874397\pi$
$240$		0			0
$241$		−	10.0285i		−	0.645994i	−0.946400	−	0.322997i	$-0.895310\pi$
$241$		−	10.0285i		−	0.645994i	0.946400	−	0.322997i	$-0.104690\pi$
$242$	−13.7903	+	7.19910i	−0.886476	+	0.462776i
$243$		0			0
$244$	−4.68869	−	4.31641i	−0.300163	−	0.276330i
$245$	−0.341127	+	1.04988i	−0.0217938	+	0.0670744i
$246$		0			0
$247$	−16.0915	−	22.1480i	−1.02388	−	1.40925i
$248$	10.8172	+	3.71393i	0.686896	+	0.235835i
$249$		0			0
$250$	3.39706	−	1.49005i	0.214849	−	0.0942388i
$251$	−7.39146	+	10.1735i	−0.466545	+	0.642144i	−0.975850	−	0.218442i	$-0.929902\pi$
$251$	−7.39146	+	10.1735i	−0.466545	+	0.642144i	0.509305	+	0.860586i	$0.329902\pi$
$252$		0			0
$253$	2.10299	+	1.42162i	0.132214	+	0.0893763i
$254$	2.20719	+	2.47872i	0.138491	+	0.155529i
$255$		0			0
$256$	11.2207	−	11.4060i	0.701294	−	0.712873i
$257$	−0.311817	−	0.959673i	−0.0194506	−	0.0598628i	0.940860	−	0.338795i	$-0.110019\pi$
$257$	−0.311817	−	0.959673i	−0.0194506	−	0.0598628i	−0.960311	+	0.278933i	$0.910019\pi$
$258$		0			0
$259$	−2.39928	+	1.74318i	−0.149084	+	0.108316i
$260$	0.690555	+	3.43489i	0.0428264	+	0.213023i
$261$		0			0
$262$	1.92798	+	19.3718i	0.119111	+	1.19679i
$263$	14.7299			0.908282			0.454141	−	0.890930i	$-0.349946\pi$
$263$	14.7299			0.908282			0.454141	+	0.890930i	$0.349946\pi$
$264$		0			0
$265$	−1.50071			−0.0921877
$266$	−1.93304	−	19.4227i	−0.118522	−	1.19088i
$267$		0			0
$268$	−2.36279	−	11.7528i	−0.144331	−	0.717916i
$269$	−9.60330	+	6.97720i	−0.585523	+	0.425408i	−0.840711	−	0.541484i	$-0.817863\pi$
$269$	−9.60330	+	6.97720i	−0.585523	+	0.425408i	0.255188	+	0.966892i	$0.417863\pi$
$270$		0			0
$271$	−4.35634	−	13.4074i	−0.264629	−	0.814443i	−0.991779	−	0.127965i	$-0.959156\pi$
$271$	−4.35634	−	13.4074i	−0.264629	−	0.814443i	0.727150	−	0.686478i	$-0.240844\pi$
$272$	15.9776	+	9.70136i	0.968787	+	0.588232i
$273$		0			0
$274$	−5.59420	−	6.28240i	−0.337958	−	0.379534i
$275$	10.0539	+	12.8956i	0.606275	+	0.777636i
$276$		0			0
$277$	−12.0276	+	16.5545i	−0.722665	+	0.994664i	0.276766	+	0.960937i	$0.410737\pi$
$277$	−12.0276	+	16.5545i	−0.722665	+	0.994664i	−0.999431	+	0.0337262i	$0.989263\pi$
$278$	−9.78883	+	4.29366i	−0.587095	+	0.257517i
$279$		0			0
$280$	−0.811164	+	2.36261i	−0.0484763	+	0.141193i
$281$	7.74854	+	10.6650i	0.462239	+	0.636218i	0.974971	−	0.222331i	$-0.0713665\pi$
$281$	7.74854	+	10.6650i	0.462239	+	0.636218i	−0.512732	+	0.858549i	$0.671367\pi$
$282$		0			0
$283$	−1.28277	+	3.94797i	−0.0762529	+	0.234682i	−0.981916	−	0.189315i	$-0.939373\pi$
$283$	−1.28277	+	3.94797i	−0.0762529	+	0.234682i	0.905664	+	0.423997i	$0.139373\pi$
$284$	6.74771	+	6.21195i	0.400403	+	0.368611i
$285$		0			0
$286$	−28.0476	+	13.4532i	−1.65849	+	0.795504i
$287$			19.8992i			1.17461i
$288$		0			0
$289$	−1.49490	+	4.60083i	−0.0879353	+	0.270637i
$290$	1.24697	+	0.729146i	0.0732243	+	0.0428169i
$291$		0			0
$292$	26.2711	−	14.7832i	1.53740	−	0.865123i
$293$	7.59864	−	2.46895i	0.443917	−	0.144237i	−0.0785249	−	0.996912i	$-0.525021\pi$
$293$	7.59864	−	2.46895i	0.443917	−	0.144237i	0.522442	+	0.852675i	$0.325021\pi$
$294$		0			0
$295$	1.54559	−	2.12733i	0.0899880	−	0.123858i
$296$	−2.05379	+	1.44080i	−0.119374	+	0.0837450i
$297$		0			0
$298$	−18.7442	+	16.6909i	−1.08582	+	0.966876i
$299$	4.10651	+	2.98355i	0.237486	+	0.172543i
$300$		0			0
$301$	−2.17912	−	6.70663i	−0.125602	−	0.386564i
$302$	18.7488	+	4.09352i	1.07887	+	0.235556i
$303$		0			0
$304$	−1.36286	−	16.4552i	−0.0781654	−	0.943773i
$305$	0.800496	+	0.260097i	0.0458363	+	0.0148931i
$306$		0			0
$307$	28.2669			1.61328			0.806639	−	0.591044i	$-0.201284\pi$
$307$	28.2669			1.61328			0.806639	+	0.591044i	$0.201284\pi$
$308$	−22.1042	−	1.81394i	−1.25950	−	0.103359i
$309$		0			0
$310$	−1.50308	+	0.149594i	−0.0853692	+	0.00849636i
$311$	−12.2480	−	3.97962i	−0.694522	−	0.225664i	−0.0595796	−	0.998224i	$-0.518976\pi$
$311$	−12.2480	−	3.97962i	−0.694522	−	0.225664i	−0.634942	+	0.772560i	$0.718976\pi$
$312$		0			0
$313$	−7.79540	+	5.66369i	−0.440622	+	0.320131i	−0.785882	−	0.618376i	$-0.787791\pi$
$313$	−7.79540	+	5.66369i	−0.440622	+	0.320131i	0.345260	+	0.938507i	$0.387791\pi$
$314$	−19.9715	−	4.36046i	−1.12706	−	0.246075i
$315$		0			0
$316$	26.2247	+	12.0247i	1.47526	+	0.676445i
$317$	5.37930	+	3.90829i	0.302132	+	0.219512i	0.728513	−	0.685032i	$-0.240212\pi$
$317$	5.37930	+	3.90829i	0.302132	+	0.219512i	−0.426381	+	0.904544i	$0.640212\pi$
$318$		0			0
$319$	−3.54769	+	12.3246i	−0.198632	+	0.690047i
$320$	−0.719206	+	1.98698i	−0.0402049	+	0.111076i
$321$		0			0
$322$	1.45370	+	3.31419i	0.0810114	+	0.184692i
$323$	18.3458	−	5.96092i	1.02079	−	0.331675i
$324$		0			0
$325$	19.2192	+	26.4529i	1.06609	+	1.46734i
$326$	−7.65863	−	4.47827i	−0.424172	−	0.248029i
$327$		0			0
$328$	−0.278827	+	16.8312i	−0.0153957	+	0.929347i
$329$			17.2792i			0.952633i
$330$		0			0
$331$			4.25037i			0.233621i	0.993154	+	0.116811i	$0.0372671\pi$
$331$			4.25037i			0.233621i	−0.993154	+	0.116811i	$0.962733\pi$
$332$	0.831310	−	0.903007i	0.0456241	−	0.0495590i
$333$		0			0
$334$	−1.67753	+	2.86886i	−0.0917901	+	0.156977i
$335$	0.930619	+	1.28089i	0.0508451	+	0.0699823i
$336$		0			0
$337$	18.7683	−	6.09818i	1.02237	−	0.332189i	0.250602	−	0.968090i	$-0.419372\pi$
$337$	18.7683	−	6.09818i	1.02237	−	0.332189i	0.771770	+	0.635901i	$0.219372\pi$
$338$	−40.1279	+	17.6012i	−2.18267	+	0.957382i
$339$		0			0
$340$	−2.45219	−	0.285148i	−0.132989	−	0.0154643i
$341$	−4.57397	−	12.6070i	−0.247695	−	0.682709i
$342$		0			0
$343$	7.63014	+	5.54362i	0.411989	+	0.299328i
$344$	−1.74917	−	5.70316i	−0.0943092	−	0.307494i
$345$		0			0
$346$	−4.92459	+	22.5552i	−0.264747	+	1.21258i
$347$	7.87165	−	5.71909i	0.422572	−	0.307017i	−0.356100	−	0.934448i	$-0.615894\pi$
$347$	7.87165	−	5.71909i	0.422572	−	0.307017i	0.778672	+	0.627431i	$0.215894\pi$
$348$		0			0
$349$	−18.2493	−	5.92957i	−0.976865	−	0.317403i	−0.223281	−	0.974754i	$-0.571677\pi$
$349$	−18.2493	−	5.92957i	−0.976865	−	0.317403i	−0.753584	+	0.657352i	$0.771677\pi$
$350$	2.30876	+	23.1978i	0.123409	+	1.23998i
$351$		0			0
$352$	−18.6708	−	1.84400i	−0.995158	−	0.0982854i
$353$	2.30703			0.122791			0.0613955	−	0.998114i	$-0.480445\pi$
$353$	2.30703			0.122791			0.0613955	+	0.998114i	$0.480445\pi$
$354$		0			0
$355$	−1.15203	−	0.374318i	−0.0611435	−	0.0198667i
$356$	5.45141	−	1.09596i	0.288924	−	0.0580857i
$357$		0			0
$358$	7.40290	−	33.9062i	0.391255	−	1.79200i
$359$	−5.45434	−	16.7867i	−0.287869	−	0.885971i	−0.985524	−	0.169536i	$-0.945773\pi$
$359$	−5.45434	−	16.7867i	−0.287869	−	0.885971i	0.697655	−	0.716434i	$-0.254227\pi$
$360$		0			0
$361$	1.58605	+	1.15233i	0.0834765	+	0.0606492i
$362$	12.3701	+	13.8919i	0.650157	+	0.730140i
$363$		0			0
$364$	−44.0522	−	5.12251i	−2.30896	−	0.268493i
$365$	−2.34013	+	3.22092i	−0.122488	+	0.168590i
$366$		0			0
$367$	5.96243	−	1.93731i	0.311236	−	0.101127i	−0.149234	−	0.988802i	$-0.547681\pi$
$367$	5.96243	−	1.93731i	0.311236	−	0.101127i	0.460470	+	0.887675i	$0.347681\pi$
$368$	1.18313	+	2.82359i	0.0616751	+	0.147190i
$369$		0			0
$370$	0.167251	−	0.286028i	0.00869496	−	0.0148699i
$371$	5.87010	−	18.0663i	0.304760	−	0.937956i
$372$		0			0
$373$		−	0.0244567i		−	0.00126632i	−1.00000		0.000633161i	$-0.999798\pi$
$373$		−	0.0244567i		−	0.00126632i	1.00000		0.000633161i	$-0.000201541\pi$
$374$	−2.90836	−	21.7248i	−0.150388	−	1.12336i
$375$		0			0
$376$	−0.242116	+	14.6152i	−0.0124862	+	0.753719i
$377$	−7.92492	+	24.3904i	−0.408154	+	1.25617i
$378$		0			0
$379$	18.8371	+	25.9270i	0.967596	+	1.33178i	0.943252	+	0.332078i	$0.107750\pi$
$379$	18.8371	+	25.9270i	0.967596	+	1.33178i	0.0243438	+	0.999704i	$0.492250\pi$
$380$	1.06943	+	1.90047i	0.0548607	+	0.0974922i
$381$		0			0
$382$	6.29573	+	14.3532i	0.322117	+	0.734374i
$383$	20.7395	−	28.5454i	1.05974	−	1.45860i	0.179685	−	0.983724i	$-0.442492\pi$
$383$	20.7395	−	28.5454i	1.05974	−	1.45860i	0.880052	−	0.474878i	$-0.157508\pi$
$384$		0			0
$385$	2.75352	−	0.999008i	0.140332	−	0.0509142i
$386$	14.6516	−	13.0466i	0.745745	−	0.664053i
$387$		0			0
$388$	−18.2927	−	8.38769i	−0.928671	−	0.425820i
$389$	−2.94817	−	9.07354i	−0.149478	−	0.460047i	0.848081	−	0.529866i	$-0.177758\pi$
$389$	−2.94817	−	9.07354i	−0.149478	−	0.460047i	−0.997560	+	0.0698193i	$0.977758\pi$
$390$		0			0
$391$	−2.89352	+	2.10226i	−0.146332	+	0.106316i
$392$	−9.44668	−	7.10543i	−0.477130	−	0.358879i
$393$		0			0
$394$	−8.50462	+	0.846422i	−0.428457	+	0.0426421i
$395$	−3.81028			−0.191716
$396$		0			0
$397$	−8.04088			−0.403560			−0.201780	−	0.979431i	$-0.564673\pi$
$397$	−8.04088			−0.403560			−0.201780	+	0.979431i	$0.564673\pi$
$398$	24.1310	−	2.40164i	1.20958	−	0.120383i
$399$		0			0
$400$	1.62776	+	19.6536i	0.0813878	+	0.982681i
$401$	−30.1047	+	21.8724i	−1.50336	+	1.09225i	−0.534338	+	0.845271i	$0.679439\pi$
$401$	−30.1047	+	21.8724i	−1.50336	+	1.09225i	−0.969020	+	0.246983i	$0.920561\pi$
$402$		0			0
$403$	−8.28705	−	25.5049i	−0.412807	−	1.27049i
$404$	16.4970	−	35.9783i	0.820756	−	1.78999i
$405$		0			0
$406$	−13.6554	+	12.1595i	−0.677707	+	0.603468i
$407$	2.82702	+	0.813766i	0.140130	+	0.0403369i
$408$		0			0
$409$	−6.07530	+	8.36194i	−0.300404	+	0.413471i	−0.932359	−	0.361534i	$-0.882253\pi$
$409$	−6.07530	+	8.36194i	−0.300404	+	0.413471i	0.631954	+	0.775006i	$0.282253\pi$
$410$	−0.893038	−	2.03598i	−0.0441040	−	0.100550i
$411$		0			0
$412$	11.6992	−	6.58335i	0.576377	−	0.324338i
$413$	19.5642	+	26.9279i	0.962693	+	1.32503i
$414$		0			0
$415$	−0.0500928	+	0.154170i	−0.00245896	+	0.00756790i
$416$	−37.1886	−	4.95000i	−1.82332	−	0.242694i
$417$		0			0
$418$	−14.0153	+	13.3582i	−0.685509	+	0.653372i
$419$		−	2.33902i		−	0.114269i	−0.998366	−	0.0571343i	$-0.981804\pi$
$419$		−	2.33902i		−	0.114269i	0.998366	−	0.0571343i	$-0.0181963\pi$
$420$		0			0
$421$	4.01513	−	12.3573i	0.195686	−	0.602258i	−0.804282	−	0.594247i	$-0.797450\pi$
$421$	4.01513	−	12.3573i	0.195686	−	0.602258i	0.999968	−	0.00801103i	$-0.00255002\pi$
$422$	−9.14399	+	15.6378i	−0.445122	+	0.761237i
$423$		0			0
$424$	5.21821	−	15.1987i	0.253419	−	0.738112i
$425$	−21.9117	+	7.11954i	−1.06287	+	0.345348i
$426$		0			0
$427$	−6.26237	+	8.61942i	−0.303057	+	0.417123i
$428$	2.82329	−	24.2795i	0.136469	−	1.17359i
$429$		0			0
$430$	0.523937	+	0.588392i	0.0252665	+	0.0283748i
$431$	−22.6258	−	16.4386i	−1.08985	−	0.791821i	−0.110474	−	0.993879i	$-0.535237\pi$
$431$	−22.6258	−	16.4386i	−1.08985	−	0.791821i	−0.979374	+	0.202058i	$0.935237\pi$
$432$		0			0
$433$	9.68478	+	29.8067i	0.465421	+	1.43242i	0.858453	+	0.512893i	$0.171426\pi$
$433$	9.68478	+	29.8067i	0.465421	+	1.43242i	−0.393032	+	0.919525i	$0.628574\pi$
$434$	4.07849	−	18.6800i	0.195774	−	0.896670i
$435$		0			0
$436$	−0.825472	−	4.10599i	−0.0395330	−	0.196641i
$437$	3.00470	+	0.976287i	0.143734	+	0.0467021i
$438$		0			0
$439$	1.92512			0.0918811			0.0459405	−	0.998944i	$-0.485372\pi$
$439$	1.92512			0.0918811			0.0459405	+	0.998944i	$0.485372\pi$
$440$	2.34299	−	0.806402i	0.111698	−	0.0384437i
$441$		0			0
$442$	−4.34068	−	43.6140i	−0.206465	−	2.07451i
$443$	25.8441	+	8.39727i	1.22789	+	0.398966i	0.849950	−	0.526863i	$-0.176632\pi$
$443$	25.8441	+	8.39727i	1.22789	+	0.398966i	0.377942	+	0.925829i	$0.376632\pi$
$444$		0			0
$445$	−0.594127	+	0.431658i	−0.0281643	+	0.0204626i
$446$	0.616175	−	2.82216i	0.0291767	−	0.133633i
$447$		0			0
$448$	−21.1072	−	16.4304i	−0.997220	−	0.776263i
$449$	−8.13130	−	5.90774i	−0.383740	−	0.278803i	0.379146	−	0.925337i	$-0.376218\pi$
$449$	−8.13130	−	5.90774i	−0.383740	−	0.278803i	−0.762885	+	0.646534i	$0.776218\pi$
$450$		0			0
$451$	15.5670	−	12.1366i	0.733021	−	0.571492i
$452$	−2.78534	+	23.9531i	−0.131011	+	1.12666i
$453$		0			0
$454$	−23.6822	+	10.3877i	−1.11146	+	0.487519i
$455$	5.57057	−	1.80999i	0.261152	−	0.0848535i
$456$		0			0
$457$	5.80668	+	7.99221i	0.271625	+	0.373860i	0.922937	−	0.384950i	$-0.125781\pi$
$457$	5.80668	+	7.99221i	0.271625	+	0.373860i	−0.651312	+	0.758810i	$0.725781\pi$
$458$	−8.90856	+	15.2352i	−0.416270	+	0.711893i
$459$		0			0
$460$	−0.297469	−	0.273850i	−0.0138696	−	0.0127683i
$461$			23.0867i			1.07526i	0.843182	+	0.537628i	$0.180679\pi$
$461$			23.0867i			1.07526i	−0.843182	+	0.537628i	$0.819321\pi$
$462$		0			0
$463$			5.87663i			0.273110i	0.990632	+	0.136555i	$0.0436031\pi$
$463$			5.87663i			0.273110i	−0.990632	+	0.136555i	$0.956397\pi$
$464$	−11.7205	+	10.0935i	−0.544108	+	0.468578i
$465$		0			0
$466$	−16.1917	−	9.46786i	−0.750065	−	0.438590i
$467$	−2.22211	−	3.05847i	−0.102827	−	0.141529i	0.754503	−	0.656297i	$-0.227878\pi$
$467$	−2.22211	−	3.05847i	−0.102827	−	0.141529i	−0.857330	+	0.514768i	$0.827878\pi$
$468$		0			0
$469$	−19.0602	+	6.19302i	−0.880117	+	0.285967i
$470$	−0.775458	−	1.76792i	−0.0357692	−	0.0815478i
$471$		0			0
$472$	16.1706	+	23.0503i	0.744311	+	1.06098i
$473$	−3.91750	+	5.79513i	−0.180127	+	0.266460i
$474$		0			0
$475$	16.4647	+	11.9623i	0.755452	+	0.548868i
$476$	13.0246	−	28.4054i	0.596984	−	1.30196i
$477$		0			0
$478$	27.8059	+	6.07099i	1.27181	+	0.277681i
$479$	−17.5590	+	12.7573i	−0.802290	+	0.582898i	−0.911585	−	0.411112i	$-0.865141\pi$
$479$	−17.5590	+	12.7573i	−0.802290	+	0.582898i	0.109295	+	0.994009i	$0.465141\pi$
$480$		0			0
$481$	5.59465	+	1.81781i	0.255094	+	0.0828851i
$482$	−14.1128	+	1.40457i	−0.642818	+	0.0639764i
$483$		0			0
$484$	12.0624	+	18.3983i	0.548293	+	0.836286i
$485$	2.65781			0.120685
$486$		0			0
$487$	−7.27475	−	2.36371i	−0.329651	−	0.107110i	0.139516	−	0.990220i	$-0.455445\pi$
$487$	−7.27475	−	2.36371i	−0.329651	−	0.107110i	−0.469166	+	0.883110i	$0.655445\pi$
$488$	−5.41764	+	7.20276i	−0.245245	+	0.326053i
$489$		0			0
$490$	1.52523	+	0.333011i	0.0689030	+	0.0150439i
$491$	7.07668	+	21.7798i	0.319366	+	0.982908i	0.973920	+	0.226893i	$0.0728567\pi$
$491$	7.07668	+	21.7798i	0.319366	+	0.982908i	−0.654553	+	0.756016i	$0.727143\pi$
$492$		0			0
$493$	−14.6192	−	10.6215i	−0.658416	−	0.478367i
$494$	−28.9143	+	25.7469i	−1.30092	+	1.15841i
$495$		0			0
$496$	3.71143	−	15.7429i	0.166648	−	0.706875i
$497$	9.01247	−	12.4046i	0.404264	−	0.556422i
$498$		0			0
$499$	36.2914	−	11.7918i	1.62462	−	0.527873i	0.651598	−	0.758564i	$-0.274099\pi$
$499$	36.2914	−	11.7918i	1.62462	−	0.527873i	0.973027	+	0.230692i	$0.0740989\pi$
$500$	−2.57267	−	4.57185i	−0.115053	−	0.204459i
$501$		0			0
$502$	15.3520	+	8.97684i	0.685192	+	0.400656i
$503$	−0.902960	+	2.77903i	−0.0402610	+	0.123911i	−0.969167	−	0.246405i	$-0.920751\pi$
$503$	−0.902960	+	2.77903i	−0.0402610	+	0.123911i	0.928906	+	0.370316i	$0.120751\pi$
$504$		0			0
$505$			5.22740i			0.232616i
$506$	1.70605	−	3.15856i	0.0758430	−	0.140415i
$507$		0			0
$508$	3.17907	−	3.45325i	0.141048	−	0.153213i
$509$	9.59462	−	29.5292i	0.425274	−	1.30886i	−0.477457	−	0.878655i	$-0.658442\pi$
$509$	9.59462	−	29.5292i	0.425274	−	1.30886i	0.902732	−	0.430204i	$-0.141558\pi$
$510$		0			0
$511$	−29.6215	−	40.7705i	−1.31038	−	1.80358i
$512$	−17.6227	−	14.1930i	−0.778821	−	0.627246i
$513$		0			0
$514$	−1.30684	+	0.573217i	−0.0576422	+	0.0252835i
$515$	−1.04212	+	1.43436i	−0.0459213	+	0.0632053i
$516$		0			0
$517$	13.5174	−	10.5387i	0.594495	−	0.463491i
$518$	2.78915	+	3.13227i	0.122548	+	0.137624i
$519$		0			0
$520$	4.73708	−	1.45287i	0.207735	−	0.0637128i
$521$	−0.962822	−	2.96326i	−0.0421820	−	0.129823i	0.927748	−	0.373208i	$-0.121742\pi$
$521$	−0.962822	−	2.96326i	−0.0421820	−	0.129823i	−0.969930	+	0.243385i	$0.921742\pi$
$522$		0			0
$523$	−31.4971	+	22.8840i	−1.37727	+	1.00065i	−0.380142	+	0.924928i	$0.624125\pi$
$523$	−31.4971	+	22.8840i	−1.37727	+	1.00065i	−0.997129	+	0.0757180i	$0.975875\pi$
$524$	26.9912	−	5.42633i	1.17911	−	0.237050i
$525$		0			0
$526$	−2.06303	−	20.7288i	−0.0899523	−	0.903817i
$527$	18.8961			0.823126
$528$		0			0
$529$	22.4142			0.974531
$530$	0.210185	+	2.11189i	0.00912986	+	0.0917345i
$531$		0			0
$532$	−27.0621	+	5.44059i	−1.17329	+	0.235879i
$533$	31.9327	−	23.2005i	1.38316	−	1.00492i
$534$		0			0
$535$	0.997579	+	3.07023i	0.0431291	+	0.132738i
$536$	−16.2083	+	4.97113i	−0.700093	+	0.214720i
$537$		0			0
$538$	11.1638	+	12.5371i	0.481304	+	0.540514i
$539$	0.469560	+	13.8529i	0.0202254	+	0.596689i
$540$		0			0
$541$	−3.61016	+	4.96896i	−0.155213	+	0.213632i	−0.879541	−	0.475823i	$-0.842150\pi$
$541$	−3.61016	+	4.96896i	−0.155213	+	0.213632i	0.724328	+	0.689456i	$0.242150\pi$
$542$	−18.2576	+	8.00831i	−0.784231	+	0.343986i
$543$		0			0
$544$	11.4146	−	23.8435i	0.489395	−	1.02228i
$545$	0.325124	+	0.447494i	0.0139268	+	0.0191686i
$546$		0			0
$547$	7.06160	−	21.7334i	0.301932	−	0.929252i	−0.678872	−	0.734257i	$-0.737531\pi$
$547$	7.06160	−	21.7334i	0.301932	−	0.929252i	0.980804	−	0.194996i	$-0.0624692\pi$
$548$	−8.05747	+	8.75239i	−0.344198	+	0.373884i
$549$		0			0
$550$	16.7394	−	15.9546i	0.713770	−	0.680308i
$551$			15.9622i			0.680012i
$552$		0			0
$553$	14.9041	−	45.8702i	0.633788	−	1.95060i
$554$	24.9811	+	14.6073i	1.06134	+	0.620606i
$555$		0			0
$556$	7.41330	+	13.1741i	0.314394	+	0.558705i
$557$	17.3847	−	5.64864i	0.736615	−	0.239341i	0.0834032	−	0.996516i	$-0.473421\pi$
$557$	17.3847	−	5.64864i	0.736615	−	0.239341i	0.653212	+	0.757175i	$0.273421\pi$
$558$		0			0
$559$	−8.22167	+	11.3162i	−0.347739	+	0.478622i
$560$	3.43842	+	0.810618i	0.145300	+	0.0342549i
$561$		0			0
$562$	13.9231	−	12.3979i	0.587312	−	0.522975i
$563$	−13.4244	−	9.75341i	−0.565772	−	0.411057i	0.267795	−	0.963476i	$-0.413705\pi$
$563$	−13.4244	−	9.75341i	−0.565772	−	0.411057i	−0.833567	+	0.552419i	$0.813705\pi$
$564$		0			0
$565$	−0.984169	−	3.02896i	−0.0414043	−	0.127429i
$566$	5.73548	+	1.25225i	0.241080	+	0.0526361i
$567$		0			0
$568$	7.79677	−	10.3658i	0.327145	−	0.434940i
$569$	39.2099	+	12.7401i	1.64376	+	0.534091i	0.977375	−	0.211513i	$-0.0678389\pi$
$569$	39.2099	+	12.7401i	1.64376	+	0.534091i	0.666389	+	0.745604i	$0.267839\pi$
$570$		0			0
$571$	−8.89753			−0.372350			−0.186175	−	0.982517i	$-0.559609\pi$
$571$	−8.89753			−0.372350			−0.186175	+	0.982517i	$0.559609\pi$
$572$	22.8604	+	37.5860i	0.955842	+	1.57155i
$573$		0			0
$574$	28.0033	−	2.78703i	1.16884	−	0.116328i
$575$	−3.58872	−	1.16605i	−0.149660	−	0.0486275i
$576$		0			0
$577$	−16.3150	+	11.8536i	−0.679204	+	0.493470i	−0.873093	−	0.487553i	$-0.837890\pi$
$577$	−16.3150	+	11.8536i	−0.679204	+	0.493470i	0.193890	+	0.981023i	$0.437890\pi$
$578$	6.68394	+	1.45933i	0.278015	+	0.0607003i
$579$		0			0
$580$	0.851451	−	1.85693i	0.0353546	−	0.0771048i
$581$	−1.66004	−	1.20609i	−0.0688699	−	0.0500369i
$582$		0			0
$583$	−17.7134	+	6.42661i	−0.733612	+	0.266163i
$584$	−24.4833	−	34.8997i	−1.01313	−	1.44416i
$585$		0			0
$586$	−4.53870	−	10.3475i	−0.187492	−	0.427450i
$587$	0.526749	−	0.171151i	0.0217413	−	0.00706417i	−0.298126	−	0.954526i	$-0.596362\pi$
$587$	0.526749	−	0.171151i	0.0217413	−	0.00706417i	0.319867	+	0.947462i	$0.396362\pi$
$588$		0			0
$589$	−9.81107	−	13.5038i	−0.404258	−	0.556414i
$590$	−3.21018	−	1.87711i	−0.132161	−	0.0772793i
$591$		0			0
$592$	2.31524	+	2.68843i	0.0951556	+	0.110494i
$593$		−	34.6597i		−	1.42330i	−0.702533	−	0.711651i	$-0.747948\pi$
$593$		−	34.6597i		−	1.42330i	0.702533	−	0.711651i	$-0.252052\pi$
$594$		0			0
$595$			4.12712i			0.169195i
$596$	26.1137	+	24.0403i	1.06966	+	0.984729i
$597$		0			0
$598$	3.62349	−	6.19680i	0.148176	−	0.253406i
$599$	19.4341	+	26.7488i	0.794057	+	1.09293i	0.993591	+	0.113034i	$0.0360570\pi$
$599$	19.4341	+	26.7488i	0.794057	+	1.09293i	−0.199535	+	0.979891i	$0.563943\pi$
$600$		0			0
$601$	−10.1517	+	3.29847i	−0.414095	+	0.134548i	−0.508653	−	0.860972i	$-0.669856\pi$
$601$	−10.1517	+	3.29847i	−0.414095	+	0.134548i	0.0945579	+	0.995519i	$0.469856\pi$
$602$	−9.13278	+	4.00590i	−0.372224	+	0.163268i
$603$		0			0
$604$	3.13473	−	26.9579i	0.127550	−	1.09690i
$605$	−2.46091	−	1.54476i	−0.100050	−	0.0628033i
$606$		0			0
$607$	−6.00393	−	4.36211i	−0.243692	−	0.177053i	0.459235	−	0.888315i	$-0.348124\pi$
$607$	−6.00393	−	4.36211i	−0.243692	−	0.177053i	−0.702927	+	0.711262i	$0.748124\pi$
$608$	−22.9659	+	4.22258i	−0.931392	+	0.171248i
$609$		0			0
$610$	0.253909	−	1.16294i	0.0102805	−	0.0470859i
$611$	27.7284	−	20.1458i	1.12177	−	0.815014i
$612$		0			0
$613$	8.38874	+	2.72567i	0.338818	+	0.110089i	0.473484	−	0.880802i	$-0.342996\pi$
$613$	8.38874	+	2.72567i	0.338818	+	0.110089i	−0.134666	+	0.990891i	$0.542996\pi$
$614$	−3.95899	−	39.7789i	−0.159772	−	1.60535i
$615$		0			0
$616$	0.543169	+	31.3604i	0.0218849	+	1.26355i
$617$	−30.1412			−1.21344			−0.606719	−	0.794917i	$-0.707515\pi$
$617$	−30.1412			−1.21344			−0.606719	+	0.794917i	$0.707515\pi$
$618$		0			0
$619$	7.17057	+	2.32986i	0.288210	+	0.0936450i	0.449554	−	0.893253i	$-0.351583\pi$
$619$	7.17057	+	2.32986i	0.288210	+	0.0936450i	−0.161344	+	0.986898i	$0.551583\pi$
$620$	0.421035	+	2.09427i	0.0169092	+	0.0841081i
$621$		0			0
$622$	−3.88494	+	17.7935i	−0.155772	+	0.713456i
$623$	−2.87257	−	8.84087i	−0.115087	−	0.354202i
$624$		0			0
$625$	−19.3827	−	14.0823i	−0.775307	−	0.563293i
$626$	9.06209	+	10.1769i	0.362194	+	0.406752i
$627$		0			0
$628$	−3.33915	+	28.7158i	−0.133247	+	1.14588i
$629$	−2.43635	+	3.35334i	−0.0971435	+	0.133707i
$630$		0			0
$631$	39.5316	−	12.8446i	1.57373	−	0.511336i	0.613297	−	0.789852i	$-0.289843\pi$
$631$	39.5316	−	12.8446i	1.57373	−	0.511336i	0.960431	+	0.278516i	$0.0898427\pi$
$632$	13.2490	−	38.5892i	0.527016	−	1.53500i
$633$		0			0
$634$	4.74658	−	8.11747i	0.188511	−	0.322386i
$635$	−0.191563	+	0.589571i	−0.00760196	+	0.0233964i
$636$		0			0
$637$			27.7169i			1.09818i
$638$	17.8409	+	3.26636i	0.706326	+	0.129317i
$639$		0			0
$640$	2.89694	+	0.733819i	0.114511	+	0.0290067i
$641$	8.25277	−	25.3994i	0.325965	−	1.00322i	−0.645039	−	0.764150i	$-0.723159\pi$
$641$	8.25277	−	25.3994i	0.325965	−	1.00322i	0.971003	−	0.239066i	$-0.0768413\pi$
$642$		0			0
$643$	−9.57732	−	13.1820i	−0.377693	−	0.519849i	0.577279	−	0.816547i	$-0.304115\pi$
$643$	−9.57732	−	13.1820i	−0.377693	−	0.519849i	−0.954971	+	0.296698i	$0.904115\pi$
$644$	4.46032	−	2.50991i	0.175761	−	0.0989043i
$645$		0			0
$646$	−10.9580	−	24.9825i	−0.431139	−	0.982924i
$647$	−2.85269	+	3.92639i	−0.112151	+	0.154362i	−0.861402	−	0.507923i	$-0.830413\pi$
$647$	−2.85269	+	3.92639i	−0.112151	+	0.154362i	0.749252	+	0.662285i	$0.230413\pi$
$648$		0			0
$649$	9.13314	−	31.7284i	0.358507	−	1.24545i
$650$	34.5344	−	30.7513i	1.35455	−	1.20617i
$651$		0			0
$652$	−5.22945	+	11.4049i	−0.204801	+	0.446651i
$653$	−1.84727	−	5.68532i	−0.0722893	−	0.222484i	0.908384	−	0.418138i	$-0.137317\pi$
$653$	−1.84727	−	5.68532i	−0.0722893	−	0.222484i	−0.980673	+	0.195654i	$0.937317\pi$
$654$		0			0
$655$	−2.94165	+	2.13724i	−0.114940	+	0.0835087i
$656$	23.7249	−	1.96495i	0.926303	−	0.0767185i
$657$		0			0
$658$	24.3164	−	2.42008i	0.947950	−	0.0943446i
$659$	−38.6071			−1.50392			−0.751959	−	0.659209i	$-0.770891\pi$
$659$	−38.6071			−1.50392			−0.751959	+	0.659209i	$0.770891\pi$
$660$		0			0
$661$	38.4608			1.49595			0.747975	−	0.663727i	$-0.231026\pi$
$661$	38.4608			1.49595			0.747975	+	0.663727i	$0.231026\pi$
$662$	5.98138	−	0.595296i	0.232473	−	0.0231368i
$663$		0			0
$664$	−1.38720	−	1.04340i	−0.0538337	−	0.0404917i
$665$	2.94938	−	2.14285i	0.114372	−	0.0830962i
$666$		0			0
$667$	−0.914560	−	2.81473i	−0.0354119	−	0.108987i
$668$	4.27219	+	1.95891i	0.165296	+	0.0757926i
$669$		0			0
$670$	1.67220	−	1.48902i	0.0646028	−	0.0575259i
$671$	10.5624	−	0.358023i	0.407756	−	0.0138213i
$672$		0			0
$673$	4.48381	−	6.17144i	0.172838	−	0.237891i	−0.713806	−	0.700343i	$-0.753030\pi$
$673$	4.48381	−	6.17144i	0.172838	−	0.237891i	0.886644	+	0.462452i	$0.153030\pi$
$674$	−11.2104	−	25.5577i	−0.431807	−	0.984447i
$675$		0			0
$676$	30.3898	+	54.0052i	1.16884	+	2.07712i
$677$	4.43491	+	6.10413i	0.170448	+	0.234601i	0.885692	−	0.464274i	$-0.153685\pi$
$677$	4.43491	+	6.10413i	0.170448	+	0.234601i	−0.715244	+	0.698875i	$0.753685\pi$
$678$		0			0
$679$	−10.3962	+	31.9961i	−0.398968	+	1.22790i
$680$	−0.0578292	+	3.49081i	−0.00221765	+	0.133866i
$681$		0			0
$682$	−17.1008	+	8.20249i	−0.654822	+	0.314089i
$683$			10.7849i			0.412674i	0.978481	+	0.206337i	$0.0661543\pi$
$683$			10.7849i			0.412674i	−0.978481	+	0.206337i	$0.933846\pi$
$684$		0			0
$685$	0.485524	−	1.49429i	0.0185509	−	0.0570939i
$686$	6.73267	−	11.5140i	0.257054	−	0.439608i
$687$		0			0
$688$	−7.78085	+	3.26032i	−0.296642	+	0.124298i
$689$	−35.8354	+	11.6436i	−1.36522	+	0.443587i
$690$		0			0
$691$	−16.0497	+	22.0905i	−0.610558	+	0.840361i	−0.996623	−	0.0821106i	$-0.973834\pi$
$691$	−16.0497	+	22.0905i	−0.610558	+	0.840361i	0.386065	+	0.922471i	$0.373834\pi$
$692$	32.4308	+	3.77115i	1.23284	+	0.143358i
$693$		0			0
$694$	−9.15074	−	10.2765i	−0.347357	−	0.390089i
$695$	−1.61518	−	1.17350i	−0.0612674	−	0.0445134i
$696$		0			0
$697$	8.59437	+	26.4508i	0.325535	+	1.00189i
$698$	−5.78850	+	26.5121i	−0.219098	+	1.00350i
$699$		0			0
$700$	32.3221	−	6.49806i	1.22166	−	0.245604i
$701$	−9.15601	−	2.97497i	−0.345818	−	0.112363i	0.130958	−	0.991388i	$-0.458195\pi$
$701$	−9.15601	−	2.97497i	−0.345818	−	0.112363i	−0.476776	+	0.879025i	$0.658195\pi$
$702$		0			0
$703$	3.66140			0.138092
$704$	0.0200024	+	26.5330i	0.000753867	+	1.00000i
$705$		0			0
$706$	−0.323117	−	3.24660i	−0.0121607	−	0.122187i
$707$	−62.9302	−	20.4473i	−2.36673	−	0.768999i
$708$		0			0
$709$	14.5854	−	10.5969i	0.547765	−	0.397974i	−0.279196	−	0.960234i	$-0.590068\pi$
$709$	14.5854	−	10.5969i	0.547765	−	0.397974i	0.826961	+	0.562260i	$0.190068\pi$
$710$	−0.365412	+	1.67363i	−0.0137137	+	0.0628104i
$711$		0			0
$712$	−2.30581	−	7.51806i	−0.0864139	−	0.281751i
$713$	2.50376	+	1.81909i	0.0937666	+	0.0681254i
$714$		0			0
$715$	−4.81346	−	3.25390i	−0.180013	−	0.121689i
$716$	−48.7518	−	5.66899i	−1.82194	−	0.211860i
$717$		0			0
$718$	−22.8594	+	10.0268i	−0.853106	+	0.374197i
$719$	−45.6978	+	14.8481i	−1.70424	+	0.553741i	−0.989358	−	0.145504i	$-0.953520\pi$
$719$	−45.6978	+	14.8481i	−1.70424	+	0.553741i	−0.714882	+	0.699245i	$0.753520\pi$
$720$		0			0
$721$	−13.1912	−	18.1562i	−0.491267	−	0.676171i
$722$	1.39950	−	2.39338i	0.0520839	−	0.0890725i
$723$		0			0
$724$	17.8169	−	19.3536i	0.662162	−	0.719271i
$725$		−	19.0647i		−	0.708046i
$726$		0			0
$727$			27.0238i			1.00226i	0.865373	+	0.501128i	$0.167081\pi$
$727$			27.0238i			1.00226i	−0.865373	+	0.501128i	$0.832919\pi$
$728$	−1.03887	+	62.7104i	−0.0385030	+	2.32420i
$729$		0			0
$730$	4.86042	+	2.84206i	0.179892	+	0.105189i
$731$	−5.79313	−	7.97356i	−0.214267	−	0.294913i
$732$		0			0
$733$	−32.7676	+	10.6468i	−1.21030	+	0.393250i	−0.843540	−	0.537066i	$-0.819532\pi$
$733$	−32.7676	+	10.6468i	−1.21030	+	0.393250i	−0.366759	+	0.930316i	$0.619532\pi$
$734$	−3.56139	−	8.11936i	−0.131453	−	0.299691i
$735$		0			0
$736$	3.80782	−	2.06044i	0.140358	−	0.0759489i
$737$	16.4697	+	11.1335i	0.606668	+	0.410107i
$738$		0			0
$739$	−23.8296	−	17.3132i	−0.876585	−	0.636876i	0.0557608	−	0.998444i	$-0.482242\pi$
$739$	−23.8296	−	17.3132i	−0.876585	−	0.636876i	−0.932346	+	0.361568i	$0.882242\pi$
$740$	−0.425941	−	0.195305i	−0.0156579	−	0.00717957i
$741$		0			0
$742$	−26.2462	−	5.73044i	−0.963527	−	0.210371i
$743$	−35.7350	+	25.9630i	−1.31099	+	0.952491i	−0.310994	+	0.950412i	$0.600662\pi$
$743$	−35.7350	+	25.9630i	−1.31099	+	0.952491i	−0.999998	+	0.00207936i	$0.999338\pi$
$744$		0			0
$745$	−4.45837	−	1.44861i	−0.163342	−	0.0530731i
$746$	−0.0344170	+	0.00342535i	−0.00126010	+	0.000125411i
$747$		0			0
$748$	−30.1652	+	7.13555i	−1.10295	+	0.260901i
$749$	−40.8632			−1.49311
$750$		0			0
$751$	−11.6991	−	3.80126i	−0.426905	−	0.138710i	0.0876808	−	0.996149i	$-0.472054\pi$
$751$	−11.6991	−	3.80126i	−0.426905	−	0.138710i	−0.514586	+	0.857439i	$0.672054\pi$
$752$	20.6012	−	1.70624i	0.751250	−	0.0622202i
$753$		0			0
$754$	35.4336	+	7.73637i	1.29042	+	0.281742i
$755$	1.10762	+	3.40892i	0.0403106	+	0.124063i
$756$		0			0
$757$	−9.30726	−	6.76212i	−0.338278	−	0.245773i	0.405657	−	0.914025i	$-0.367043\pi$
$757$	−9.30726	−	6.76212i	−0.338278	−	0.245773i	−0.743935	+	0.668252i	$0.767043\pi$
$758$	33.8478	−	30.1400i	1.22941	−	1.09473i
$759$		0			0
$760$	2.52468	−	1.77115i	0.0915798	−	0.0642462i
$761$	7.53101	−	10.3655i	0.272999	−	0.375751i	−0.650400	−	0.759591i	$-0.725399\pi$
$761$	7.53101	−	10.3655i	0.272999	−	0.375751i	0.923399	+	0.383841i	$0.125399\pi$
$762$		0			0
$763$	−6.65892	+	2.16361i	−0.241069	+	0.0783280i
$764$	19.3169	−	10.8700i	0.698862	−	0.393263i
$765$		0			0
$766$	−43.0756	−	25.1878i	−1.55638	−	0.910073i
$767$	20.4018	−	62.7904i	0.736668	−	2.26723i
$768$		0			0
$769$		−	6.41973i		−	0.231501i	−0.993278	−	0.115751i	$-0.963073\pi$
$769$		−	6.41973i		−	0.231501i	0.993278	−	0.115751i	$-0.0369274\pi$
$770$	−1.79152	−	3.73500i	−0.0645618	−	0.134600i
$771$		0			0
$772$	−20.4120	−	18.7913i	−0.734644	−	0.676314i
$773$	−8.70055	+	26.7775i	−0.312937	+	0.963121i	0.663658	+	0.748036i	$0.269003\pi$
$773$	−8.70055	+	26.7775i	−0.312937	+	0.963121i	−0.976595	+	0.215085i	$0.930997\pi$
$774$		0			0
$775$	11.7180	+	16.1285i	0.420924	+	0.579352i
$776$	−9.24164	+	26.9174i	−0.331756	+	0.966277i
$777$		0			0
$778$	−12.3559	+	5.41966i	−0.442981	+	0.194304i
$779$	14.4403	−	19.8754i	0.517378	−	0.712110i
$780$		0			0
$781$	−15.2008	+	0.515247i	−0.543927	+	0.0184370i
$782$	3.36369	+	3.77750i	0.120285	+	0.135083i
$783$		0			0
$784$	−8.67612	+	14.2891i	−0.309861	+	0.510326i
$785$	−1.17985	−	3.63122i	−0.0421108	−	0.129604i
$786$		0			0
$787$	−10.3223	+	7.49956i	−0.367949	+	0.267330i	−0.756360	−	0.654156i	$-0.773024\pi$
$787$	−10.3223	+	7.49956i	−0.367949	+	0.267330i	0.388411	+	0.921486i	$0.373024\pi$
$788$	2.38227	+	11.8497i	0.0848650	+	0.422127i
$789$		0			0
$790$	0.533658	+	5.36206i	0.0189867	+	0.190773i
$791$	40.3139			1.43340
$792$		0			0
$793$	21.1331			0.750459
$794$	1.12619	+	11.3156i	0.0399669	+	0.401576i
$795$		0			0
$796$	−6.75946	−	33.6223i	−0.239583	−	1.19171i
$797$	−32.4990	+	23.6119i	−1.15117	+	0.836376i	−0.988636	−	0.150327i	$-0.951967\pi$
$797$	−32.4990	+	23.6119i	−1.15117	+	0.836376i	−0.162536	+	0.986703i	$0.551967\pi$
$798$		0			0
$799$	7.46282	+	22.9682i	0.264015	+	0.812556i
$800$	27.4298	−	5.04332i	0.969790	−	0.178308i
$801$		0			0
$802$	34.9965	+	39.3018i	1.23577	+	1.38780i
$803$	−13.8282	+	48.0389i	−0.487986	+	1.69526i
$804$		0			0
$805$	−0.397310	+	0.546850i	−0.0140033	+	0.0192739i
$806$	−34.7314	+	15.2342i	−1.22336	+	0.536602i
$807$		0			0
$808$	−52.9413	−	18.1766i	−1.86247	−	0.639449i
$809$	−11.8866	−	16.3605i	−0.417910	−	0.575204i	0.547215	−	0.836992i	$-0.315688\pi$
$809$	−11.8866	−	16.3605i	−0.417910	−	0.575204i	−0.965125	+	0.261788i	$0.915688\pi$
$810$		0			0
$811$	8.62836	−	26.5554i	0.302983	−	0.932485i	−0.677439	−	0.735579i	$-0.736910\pi$
$811$	8.62836	−	26.5554i	0.302983	−	0.932485i	0.980422	−	0.196907i	$-0.0630896\pi$
$812$	19.0242	+	17.5137i	0.667618	+	0.614611i
$813$		0			0
$814$	0.749236	−	4.09232i	0.0262607	−	0.143436i
$815$		−	1.65706i		−	0.0580441i
$816$		0			0
$817$	−2.69032	+	8.27995i	−0.0941223	+	0.289679i
$818$	12.6183	+	7.37839i	0.441189	+	0.257979i
$819$		0			0
$820$	−2.74007	+	1.54189i	−0.0956876	+	0.0538452i
$821$	25.0864	−	8.15107i	0.875522	−	0.284474i	0.163425	−	0.986556i	$-0.447746\pi$
$821$	25.0864	−	8.15107i	0.875522	−	0.284474i	0.712097	+	0.702081i	$0.247746\pi$
$822$		0			0
$823$	25.1235	−	34.5796i	0.875752	−	1.20537i	−0.101828	−	0.994802i	$-0.532469\pi$
$823$	25.1235	−	34.5796i	0.875752	−	1.20537i	0.977579	−	0.210567i	$-0.0675309\pi$
$824$	−10.9030	−	15.5417i	−0.379826	−	0.541422i
$825$		0			0
$826$	35.1544	−	31.3034i	1.22318	−	1.08919i
$827$	10.1906	+	7.40391i	0.354362	+	0.257459i	0.750697	−	0.660647i	$-0.229718\pi$
$827$	10.1906	+	7.40391i	0.354362	+	0.257459i	−0.396334	+	0.918106i	$0.629718\pi$
$828$		0			0
$829$	−3.42053	−	10.5273i	−0.118800	−	0.365628i	0.873921	−	0.486068i	$-0.161569\pi$
$829$	−3.42053	−	10.5273i	−0.118800	−	0.365628i	−0.992721	+	0.120440i	$0.961569\pi$
$830$	0.223973	+	0.0489010i	0.00777422	+	0.00169738i
$831$		0			0
$832$	−1.75740	+	53.0274i	−0.0609268	+	1.83839i
$833$	−18.5739	−	6.03504i	−0.643549	−	0.209102i
$834$		0			0
$835$	−0.620720			−0.0214809
$836$	20.7614	+	17.8522i	0.718050	+	0.617432i
$837$		0			0
$838$	−3.29161	+	0.327598i	−0.113707	+	0.0113167i
$839$	0.759442	+	0.246758i	0.0262189	+	0.00851902i	0.322097	−	0.946707i	$-0.395612\pi$
$839$	0.759442	+	0.246758i	0.0262189	+	0.00851902i	−0.295878	+	0.955226i	$0.595612\pi$
$840$		0			0
$841$	−11.3643	+	8.25664i	−0.391872	+	0.284712i
$842$	−17.9523	−	3.91961i	−0.618678	−	0.135079i
$843$		0			0
$844$	23.2872	+	10.6778i	0.801577	+	0.367545i
$845$	−6.62121	−	4.81059i	−0.227777	−	0.165489i
$846$		0			0
$847$	28.2226	−	23.5833i	0.969740	−	0.810331i
$848$	−22.1193	−	5.21470i	−0.759581	−	0.179074i
$849$		0			0
$850$	13.0879	+	29.8383i	0.448913	+	1.02345i
$851$	−0.645640	+	0.209781i	−0.0221323	+	0.00719121i
$852$		0			0
$853$	9.71467	+	13.3711i	0.332624	+	0.457818i	0.942269	−	0.334857i	$-0.108688\pi$
$853$	9.71467	+	13.3711i	0.332624	+	0.457818i	−0.609645	+	0.792675i	$0.708688\pi$
$854$	13.0069	+	7.60558i	0.445086	+	0.260258i
$855$		0			0
$856$	−34.5630	−	0.572575i	−1.18134	−	0.0195702i
$857$			4.04192i			0.138069i	0.997614	+	0.0690347i	$0.0219919\pi$
$857$			4.04192i			0.138069i	−0.997614	+	0.0690347i	$0.978008\pi$
$858$		0			0
$859$		−	13.5474i		−	0.462231i	−0.972926	−	0.231115i	$-0.925762\pi$
$859$		−	13.5474i		−	0.462231i	0.972926	−	0.231115i	$-0.0742375\pi$
$860$	0.754640	−	0.819724i	0.0257330	−	0.0279524i
$861$		0			0
$862$	−19.9645	+	34.1428i	−0.679994	+	1.16291i
$863$	−9.44467	−	12.9995i	−0.321500	−	0.442507i	0.617424	−	0.786630i	$-0.288176\pi$
$863$	−9.44467	−	12.9995i	−0.321500	−	0.442507i	−0.938925	+	0.344123i	$0.888176\pi$
$864$		0			0
$865$	−4.10100	+	1.33250i	−0.139438	+	0.0453062i
$866$	40.5894	−	17.8037i	1.37928	−	0.604993i
$867$		0			0
$868$	−26.8589	−	3.12323i	−0.911650	−	0.106009i
$869$	−44.9740	+	16.3171i	−1.52564	+	0.553520i
$870$		0			0
$871$	32.1604	+	23.3659i	1.08971	+	0.791723i
$872$	−5.66258	+	1.73673i	−0.191759	+	0.0588131i
$873$		0			0
$874$	0.953060	−	4.36514i	0.0322377	−	0.147653i
$875$	−7.09514	+	5.15492i	−0.239860	+	0.174268i
$876$		0			0
$877$	−8.88213	−	2.88598i	−0.299928	−	0.0974526i	0.155187	−	0.987885i	$-0.450402\pi$
$877$	−8.88213	−	2.88598i	−0.299928	−	0.0974526i	−0.455115	+	0.890432i	$0.650402\pi$
$878$	−0.269628	−	2.70915i	−0.00909950	−	0.0914294i
$879$		0			0
$880$	−1.46297	−	3.18425i	−0.0493168	−	0.107341i
$881$	27.4351			0.924312			0.462156	−	0.886799i	$-0.347076\pi$
$881$	27.4351			0.924312			0.462156	+	0.886799i	$0.347076\pi$
$882$		0			0
$883$	−24.6985	−	8.02501i	−0.831169	−	0.270063i	−0.137631	−	0.990484i	$-0.543949\pi$
$883$	−24.6985	−	8.02501i	−0.831169	−	0.270063i	−0.693538	+	0.720420i	$0.743949\pi$
$884$	−60.7683	+	12.2169i	−2.04386	+	0.410900i
$885$		0			0
$886$	8.19748	−	37.5455i	0.275400	−	1.26137i
$887$	6.60250	+	20.3204i	0.221690	+	0.682292i	0.998611	+	0.0526937i	$0.0167807\pi$
$887$	6.60250	+	20.3204i	0.221690	+	0.682292i	−0.776920	+	0.629599i	$0.783219\pi$
$888$		0			0
$889$	−6.34826	−	4.61228i	−0.212914	−	0.154691i
$890$	0.690668	+	0.775634i	0.0231512	+	0.0259993i
$891$		0			0
$892$	−4.05782	−	0.471854i	−0.135866	−	0.0157988i
$893$	12.5391	−	17.2586i	0.419604	−	0.577536i
$894$		0			0
$895$	6.16484	−	2.00308i	0.206068	−	0.0669555i
$896$	−20.1656	+	32.0045i	−0.673687	+	1.06919i
$897$		0			0
$898$	−7.17488	+	12.2703i	−0.239429	+	0.409465i
$899$	−4.83187	+	14.8710i	−0.161152	+	0.495974i
$900$		0			0
$901$		−	26.5497i		−	0.884499i
$902$	−19.2597	−	20.2070i	−0.641277	−	0.672820i
$903$		0			0
$904$	34.0984	+	0.564878i	1.13410	+	0.0187876i
$905$	−1.07361	+	3.30422i	−0.0356879	+	0.109836i
$906$		0			0
$907$	11.6618	+	16.0511i	0.387223	+	0.532967i	0.957480	−	0.288499i	$-0.0931563\pi$
$907$	11.6618	+	16.0511i	0.387223	+	0.532967i	−0.570257	+	0.821467i	$0.693156\pi$
$908$	17.9351	+	31.8722i	0.595197	+	1.05772i
$909$		0			0
$910$	−3.32732	−	7.58574i	−0.110300	−	0.251465i
$911$	6.00261	−	8.26188i	0.198875	−	0.273728i	−0.697918	−	0.716177i	$-0.745890\pi$
$911$	6.00261	−	8.26188i	0.198875	−	0.273728i	0.896794	+	0.442449i	$0.145890\pi$
$912$		0			0
$913$	0.0689525	+	2.03424i	0.00228200	+	0.0673234i
$914$	10.4339	−	9.29088i	0.345121	−	0.307315i
$915$		0			0
$916$	22.6876	+	10.4029i	0.749619	+	0.343720i
$917$	−14.2227	−	43.7731i	−0.469676	−	1.44552i
$918$		0			0
$919$	−24.3478	+	17.6897i	−0.803159	+	0.583529i	−0.911839	−	0.410548i	$-0.865338\pi$
$919$	−24.3478	+	17.6897i	−0.803159	+	0.583529i	0.108680	+	0.994077i	$0.465338\pi$
$920$	−0.343716	+	0.456971i	−0.0113320	+	0.0150659i
$921$		0			0
$922$	32.4890	−	3.23347i	1.06997	−	0.106489i
$923$	−30.4136			−1.00108
$924$		0			0
$925$	−4.37305			−0.143785
$926$	8.26996	−	0.823067i	0.271768	−	0.0270476i
$927$		0			0
$928$	15.8457	+	15.0801i	0.520161	+	0.495027i
$929$	−13.9833	+	10.1594i	−0.458776	+	0.333321i	−0.793051	−	0.609155i	$-0.791509\pi$
$929$	−13.9833	+	10.1594i	−0.458776	+	0.333321i	0.334275	+	0.942476i	$0.391509\pi$
$930$		0			0
$931$	5.33097	+	16.4070i	0.174716	+	0.537719i
$932$	−11.0560	+	24.1120i	−0.362151	+	0.789814i
$933$		0			0
$934$	−3.99285	+	3.55545i	−0.130650	+	0.116338i
$935$	3.22862	−	2.51715i	0.105587	−	0.0823197i
$936$		0			0
$937$	−4.26015	+	5.86359i	−0.139173	+	0.191555i	−0.872914	−	0.487874i	$-0.837773\pi$
$937$	−4.26015	+	5.86359i	−0.139173	+	0.191555i	0.733741	+	0.679429i	$0.237773\pi$
$938$	11.3847	+	25.9553i	0.371724	+	0.847469i
$939$		0			0
$940$	−2.37931	+	1.33888i	−0.0776045	+	0.0436695i
$941$	22.6672	+	31.1987i	0.738930	+	1.01705i	0.998680	+	0.0513733i	$0.0163598\pi$
$941$	22.6672	+	31.1987i	0.738930	+	1.01705i	−0.259750	+	0.965676i	$0.583640\pi$
$942$		0			0
$943$	−1.40760	+	4.33214i	−0.0458377	+	0.141074i
$944$	30.1730	−	25.9846i	0.982049	−	0.845726i
$945$		0			0
$946$	8.70393	+	4.70129i	0.282989	+	0.152852i
$947$		−	25.4572i		−	0.827247i	−0.910448	−	0.413624i	$-0.864263\pi$
$947$		−	25.4572i		−	0.827247i	0.910448	−	0.413624i	$-0.135737\pi$
$948$		0			0
$949$	−30.8897	+	95.0689i	−1.00272	+	3.08607i
$950$	14.5281	−	24.8455i	0.471353	−	0.806095i
$951$		0			0
$952$	−41.7980	−	14.3507i	−1.35468	−	0.465108i
$953$	28.3146	−	9.19996i	0.917198	−	0.298016i	0.187881	−	0.982192i	$-0.439838\pi$
$953$	28.3146	−	9.19996i	0.917198	−	0.298016i	0.729317	+	0.684176i	$0.239838\pi$
$954$		0			0
$955$	−1.72068	+	2.36832i	−0.0556800	+	0.0766370i
$956$	4.64904	−	39.9805i	0.150361	−	1.29306i
$957$		0			0
$958$	20.4122	+	22.9233i	0.659488	+	0.740618i
$959$	16.0899	+	11.6900i	0.519570	+	0.377490i
$960$		0			0
$961$	4.52686	+	13.9323i	0.146028	+	0.449428i
$962$	1.77456	−	8.12773i	0.0572142	−	0.262049i
$963$		0			0
$964$	3.95320	+	19.6636i	0.127324	+	0.633322i
$965$	3.48493	+	1.13232i	0.112184	+	0.0364507i
$966$		0			0
$967$	−27.0950			−0.871316			−0.435658	−	0.900112i	$-0.643484\pi$
$967$	−27.0950			−0.871316			−0.435658	+	0.900112i	$0.643484\pi$
$968$	24.2018	−	19.5518i	0.777874	−	0.628420i
$969$		0			0
$970$	−0.372246	−	3.74023i	−0.0119521	−	0.120091i
$971$	−0.248827	−	0.0808487i	−0.00798523	−	0.00259456i	0.305022	−	0.952345i	$-0.401336\pi$
$971$	−0.248827	−	0.0808487i	−0.00798523	−	0.00259456i	−0.313007	+	0.949751i	$0.601336\pi$
$972$		0			0
$973$	20.4451	−	14.8542i	0.655440	−	0.476205i
$974$	−2.30747	+	10.5685i	−0.0739363	+	0.338638i
$975$		0			0
$976$	10.8949	+	6.61523i	0.348739	+	0.211748i
$977$	41.1035	+	29.8634i	1.31502	+	0.955416i	0.999980	+	0.00633607i	$0.00201685\pi$
$977$	41.1035	+	29.8634i	1.31502	+	0.955416i	0.315037	+	0.949079i	$0.397983\pi$
$978$		0			0
$979$	−5.16415	+	7.63929i	−0.165047	+	0.244153i
$980$	0.255013	−	2.19304i	0.00814609	−	0.0700542i
$981$		0			0
$982$	29.6587	−	13.0092i	0.946448	−	0.415139i
$983$	9.50959	−	3.08985i	0.303309	−	0.0985510i	−0.153409	−	0.988163i	$-0.549025\pi$
$983$	9.50959	−	3.08985i	0.303309	−	0.0985510i	0.456717	+	0.889612i	$0.349025\pi$
$984$		0			0
$985$	−0.938291	−	1.29145i	−0.0298964	−	0.0411489i
$986$	−12.8997	+	22.0607i	−0.410809	+	0.702554i
$987$		0			0
$988$	40.2823	+	37.0840i	1.28155	+	1.17980i
$989$		−	1.61421i		−	0.0513287i
$990$		0			0
$991$		−	55.4443i		−	1.76125i	−0.473816	−	0.880624i	$-0.657124\pi$
$991$		−	55.4443i		−	1.76125i	0.473816	−	0.880624i	$-0.342876\pi$
$992$	−22.6741	−	3.01804i	−0.719904	−	0.0958230i
$993$		0			0
$994$	−18.7188	−	10.9455i	−0.593723	−	0.347171i
$995$	2.66231	+	3.66435i	0.0844009	+	0.116168i
$996$		0			0
$997$	53.9438	−	17.5274i	1.70842	−	0.555098i	0.718349	−	0.695683i	$-0.244898\pi$
$997$	53.9438	−	17.5274i	1.70842	−	0.555098i	0.990069	+	0.140585i	$0.0448983\pi$
$998$	−21.6770	−	49.4199i	−0.686173	−	1.56436i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.r.b.271.5		48
3.2	odd	2		132.2.j.a.7.8	yes	48
4.3	odd	2	inner	396.2.r.b.271.12		48
11.8	odd	10	inner	396.2.r.b.19.12		48
12.11	even	2		132.2.j.a.7.1	✓	48
33.8	even	10		132.2.j.a.19.1	yes	48
44.19	even	10	inner	396.2.r.b.19.5		48
132.107	odd	10		132.2.j.a.19.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.7.1	✓	48	12.11	even	2
132.2.j.a.7.8	yes	48	3.2	odd	2
132.2.j.a.19.1	yes	48	33.8	even	10
132.2.j.a.19.8	yes	48	132.107	odd	10
396.2.r.b.19.5		48	44.19	even	10	inner
396.2.r.b.19.12		48	11.8	odd	10	inner
396.2.r.b.271.5		48	1.1	even	1	trivial
396.2.r.b.271.12		48	4.3	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.140058 - 1.40726i) q^{2} +(-1.96077 + 0.394195i) q^{4} +(0.213696 - 0.155259i) q^{5} +(1.03321 + 3.17989i) q^{7} +(0.829356 + 2.70410i) q^{8} +O(q^{10})\)	\(q+(-0.140058 - 1.40726i) q^{2} +(-1.96077 + 0.394195i) q^{4} +(0.213696 - 0.155259i) q^{5} +(1.03321 + 3.17989i) q^{7} +(0.829356 + 2.70410i) q^{8} +(-0.248420 - 0.278981i) q^{10} +(1.85745 - 2.74771i) q^{11} +(3.89823 - 5.36545i) q^{13} +(4.33023 - 1.89936i) q^{14} +(3.68922 - 1.54585i) q^{16} +(2.74676 + 3.78059i) q^{17} +(1.27559 - 3.92586i) q^{19} +(-0.357806 + 0.388665i) q^{20} +(-4.12689 - 2.22908i) q^{22} +0.765361i q^{23} +(-1.52352 + 4.68893i) q^{25} +(-8.09657 - 4.73436i) q^{26} +(-3.27938 - 5.82774i) q^{28} +(-3.67765 + 1.19494i) q^{29} +(2.37677 - 3.27135i) q^{31} +(-2.69212 - 4.97519i) q^{32} +(4.93558 - 4.39491i) q^{34} +(0.714499 + 0.519114i) q^{35} +(0.274094 + 0.843576i) q^{37} +(-5.70337 - 1.24524i) q^{38} +(0.597067 + 0.449091i) q^{40} +(5.66025 + 1.83913i) q^{41} -2.10908 q^{43} +(-2.55889 + 6.11981i) q^{44} +(1.07706 - 0.107195i) q^{46} +(4.91501 + 1.59698i) q^{47} +(-3.38106 + 2.45648i) q^{49} +(6.81192 + 1.48728i) q^{50} +(-5.52849 + 12.0571i) q^{52} +(-4.59637 - 3.33946i) q^{53} +(-0.0296780 - 0.875559i) q^{55} +(-7.74185 + 5.43116i) q^{56} +(2.19667 + 5.00805i) q^{58} +(9.46770 - 3.07624i) q^{59} +(1.87298 + 2.57794i) q^{61} +(-4.93652 - 2.88656i) q^{62} +(-6.62434 + 4.48532i) q^{64} -1.75181i q^{65} +5.99397i q^{67} +(-6.87605 - 6.33011i) q^{68} +(0.630458 - 1.07819i) q^{70} +(-2.69549 - 3.71003i) q^{71} +(-14.3347 + 4.65764i) q^{73} +(1.14874 - 0.503872i) q^{74} +(-0.953581 + 8.20054i) q^{76} +(10.6565 + 3.06752i) q^{77} +(-11.6701 - 8.47885i) q^{79} +(0.548364 - 0.903127i) q^{80} +(1.79537 - 8.22304i) q^{82} +(-0.496492 + 0.360722i) q^{83} +(1.17394 + 0.381437i) q^{85} +(0.295392 + 2.96802i) q^{86} +(8.97056 + 2.74390i) q^{88} -2.78024 q^{89} +(21.0892 + 6.85231i) q^{91} +(-0.301701 - 1.50070i) q^{92} +(1.55899 - 7.14037i) q^{94} +(-0.336938 - 1.03699i) q^{95} +(8.14034 + 5.91430i) q^{97} +(3.93046 + 4.41398i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 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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