LMFDB - Embedded newform 396.2.r.b.19.5

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			19.5
Character	$\chi$	$=$	396.19
Dual form			396.2.r.b.271.5

$q$-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 $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

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

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 $

$2$	−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	0.634543	−	0.772888i	$-0.281188\pi$
$5$	0.213696	+	0.155259i	0.0955677	+	0.0694340i	−0.538975	+	0.842322i	$0.681188\pi$
$6$		0			0
$7$	1.03321	−	3.17989i	0.390516	−	1.20189i	−0.541883	−	0.840454i	$-0.682288\pi$
$7$	1.03321	−	3.17989i	0.390516	−	1.20189i	0.932399	−	0.361431i	$-0.117712\pi$
$8$	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	0.858221	+	0.513280i	$0.171570\pi$
$13$	3.89823	+	5.36545i	1.08117	+	1.48811i	0.222953	+	0.974829i	$0.428430\pi$
$14$	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	−0.333479	−	0.942758i	$-0.608223\pi$
$17$	2.74676	−	3.78059i	0.666188	−	0.916929i	0.999666	+	0.0258289i	$0.00822250\pi$
$18$		0			0
$19$	1.27559	+	3.92586i	0.292640	+	0.900655i	0.984004	+	0.178147i	$0.0570104\pi$
$19$	1.27559	+	3.92586i	0.292640	+	0.900655i	−0.691363	+	0.722507i	$0.742990\pi$
$20$	−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	$-0.974574\pi$
$23$		−	0.765361i		−	0.159589i	0.996811	−	0.0797944i	$-0.0254264\pi$
$24$		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	−0.0530476	−	0.998592i	$-0.516894\pi$
$29$	−3.67765	−	1.19494i	−0.682922	−	0.221895i	−0.629874	+	0.776697i	$0.716894\pi$
$30$		0			0
$31$	2.37677	+	3.27135i	0.426881	+	0.587551i	0.967234	−	0.253887i	$-0.0817092\pi$
$31$	2.37677	+	3.27135i	0.426881	+	0.587551i	−0.540353	+	0.841439i	$0.681709\pi$
$32$	−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	−0.925995	−	0.377536i	$-0.876771\pi$
$37$	0.274094	−	0.843576i	0.0450608	−	0.138683i	0.971056	+	0.238853i	$0.0767714\pi$
$38$	−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	0.168373	−	0.985723i	$-0.446149\pi$
$41$	5.66025	−	1.83913i	0.883983	−	0.287223i	0.715610	+	0.698500i	$0.246149\pi$
$42$		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	0.0722371	−	0.997387i	$-0.476986\pi$
$47$	4.91501	−	1.59698i	0.716928	−	0.232944i	0.644691	+	0.764444i	$0.276986\pi$
$48$		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	−0.856871	−	0.515531i	$-0.827595\pi$
$53$	−4.59637	+	3.33946i	−0.631360	+	0.458710i	0.225511	+	0.974241i	$0.427595\pi$
$54$		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	0.851652	−	0.524108i	$-0.175601\pi$
$59$	9.46770	+	3.07624i	1.23259	+	0.400493i	0.380938	+	0.924601i	$0.375601\pi$
$60$		0			0
$61$	1.87298	−	2.57794i	0.239811	−	0.330071i	−0.672100	−	0.740461i	$-0.734607\pi$
$61$	1.87298	−	2.57794i	0.239811	−	0.330071i	0.911910	+	0.410390i	$0.134607\pi$
$62$	−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	$-0.880679\pi$
$67$		−	5.99397i		−	0.732280i	0.930560	−	0.366140i	$-0.119321\pi$
$68$	−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	−0.938435	−	0.345455i	$-0.887725\pi$
$71$	−2.69549	+	3.71003i	−0.319896	+	0.440299i	0.618539	+	0.785754i	$0.287725\pi$
$72$		0			0
$73$	−14.3347	−	4.65764i	−1.67775	−	0.545135i	−0.693280	−	0.720669i	$-0.743835\pi$
$73$	−14.3347	−	4.65764i	−1.67775	−	0.545135i	−0.984473	+	0.175534i	$0.943835\pi$
$74$	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	−0.313002	+	0.949753i	$0.601335\pi$
$79$	−11.6701	+	8.47885i	−1.31299	+	0.953945i	−0.999991	+	0.00419263i	$0.998665\pi$
$80$	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	0.560203	−	0.828355i	$-0.310723\pi$
$83$	−0.496492	−	0.360722i	−0.0544971	−	0.0395944i	−0.614700	+	0.788761i	$0.710723\pi$
$84$		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	−0.0920484	−	0.995755i	$-0.529341\pi$
$97$	8.14034	−	5.91430i	0.826526	−	0.600506i	0.918574	+	0.395248i	$0.129341\pi$
$98$	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	−0.720198	−	0.693769i	$-0.755949\pi$
$101$	−11.6323	−	16.0105i	−1.15746	−	1.59310i	−0.437260	−	0.899335i	$-0.644051\pi$
$102$		0			0
$103$	−6.38362	−	2.07416i	−0.628997	−	0.204373i	−0.0228662	−	0.999739i	$-0.507279\pi$
$103$	−6.38362	−	2.07416i	−0.628997	−	0.204373i	−0.606131	+	0.795365i	$0.707279\pi$
$104$	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	−0.949916	−	0.312506i	$-0.898832\pi$
$107$	−3.77667	−	11.6234i	−0.365104	−	1.12368i	0.584811	−	0.811169i	$-0.301168\pi$
$108$		0			0
$109$		−	2.09407i		−	0.200576i	−0.994958	−	0.100288i	$-0.968024\pi$
$109$		−	2.09407i		−	0.200576i	0.994958	−	0.100288i	$-0.0319764\pi$
$110$	−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	0.958571	+	0.284853i	$0.0919448\pi$
$113$	3.72590	+	11.4671i	0.350503	+	1.07874i	−0.608068	+	0.793885i	$0.708055\pi$
$114$		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	0.500350	−	0.865823i	$-0.333205\pi$
$127$	−1.89867	−	1.37946i	−0.168480	−	0.122408i	−0.668830	+	0.743415i	$0.733205\pi$
$128$	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	0.774062	−	0.633110i	$-0.218222\pi$
$137$	4.81224	+	3.49630i	0.411138	+	0.298709i	−0.362925	+	0.931819i	$0.618222\pi$
$138$		0			0
$139$	−2.33565	+	7.18840i	−0.198107	+	0.609712i	0.801819	+	0.597567i	$0.203866\pi$
$139$	−2.33565	+	7.18840i	−0.198107	+	0.609712i	−0.999926	+	0.0121448i	$0.996134\pi$
$140$	−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	0.128245	+	0.991743i	$0.459066\pi$
$149$	−10.4316	+	14.3578i	−0.854588	+	1.17624i	−0.982833	+	0.184497i	$0.940934\pi$
$150$		0			0
$151$	−4.19328	−	12.9056i	−0.341245	−	1.05024i	−0.963564	−	0.267479i	$-0.913809\pi$
$151$	−4.19328	−	12.9056i	−0.341245	−	1.05024i	0.622319	−	0.782764i	$-0.286191\pi$
$152$	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	0.955144	+	0.296141i	$0.0957000\pi$
$157$	4.46673	+	13.7472i	0.356484	+	1.09714i	−0.598660	+	0.801003i	$0.704300\pi$
$158$	−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	0.928630	−	0.371008i	$-0.120988\pi$
$163$	3.68738	+	5.07524i	0.288818	+	0.397523i	−0.639812	+	0.768531i	$0.720988\pi$
$164$	−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	−0.658908	−	0.752223i	$-0.728981\pi$
$167$	−1.90114	+	1.38126i	−0.147115	+	0.106885i	0.511793	+	0.859109i	$0.328981\pi$
$168$		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	−0.832514	−	0.554004i	$-0.813099\pi$
$173$	−15.5257	+	5.04461i	−1.18040	+	0.383534i	−0.347883	+	0.937538i	$0.613099\pi$
$174$		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	0.749035	−	0.662530i	$-0.230517\pi$
$179$	23.3391	−	7.58332i	1.74444	−	0.566804i	0.995408	+	0.0957267i	$0.0305175\pi$
$180$		0			0
$181$	−10.6410	−	7.73114i	−0.790939	−	0.574651i	0.117303	−	0.993096i	$-0.462575\pi$
$181$	−10.6410	−	7.73114i	−0.790939	−	0.574651i	−0.908242	+	0.418445i	$0.862575\pi$
$182$	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	−0.0982428	−	0.995162i	$-0.531322\pi$
$191$	−10.5402	−	3.42473i	−0.762665	−	0.247805i	−0.664422	+	0.747358i	$0.731322\pi$
$192$		0			0
$193$	8.15394	−	11.2229i	0.586933	−	0.807844i	−0.407501	−	0.913205i	$-0.633600\pi$
$193$	8.15394	−	11.2229i	0.586933	−	0.807844i	0.994434	+	0.105361i	$0.0335997\pi$
$194$	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	$0.0690686\pi$
$197$			6.04339i			0.430574i	−0.976551	+	0.215287i	$0.930931\pi$
$198$		0			0
$199$		−	17.1475i		−	1.21556i	−0.794107	−	0.607778i	$-0.792061\pi$
$199$		−	17.1475i		−	1.21556i	0.794107	−	0.607778i	$-0.207939\pi$
$200$	−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	−0.884272	−	0.466972i	$-0.845345\pi$
$211$	−10.3629	+	7.52909i	−0.713411	+	0.518324i	0.170861	+	0.985295i	$0.445345\pi$
$212$	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	−0.243250	−	0.969964i	$-0.578214\pi$
$223$	1.94261	−	0.631192i	0.130087	−	0.0422677i	0.373337	+	0.927696i	$0.378214\pi$
$224$	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	0.568398	+	0.822754i	$0.307564\pi$
$227$	−5.65067	+	17.3910i	−0.375048	+	1.15428i	−0.943446	+	0.331526i	$0.892436\pi$
$228$		0			0
$229$	−10.0961	+	7.33523i	−0.667168	+	0.484726i	−0.869076	−	0.494679i	$-0.835286\pi$
$229$	−10.0961	+	7.33523i	−0.667168	+	0.484726i	0.201908	+	0.979404i	$0.435286\pi$
$230$	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	0.984040	−	0.177947i	$-0.0569456\pi$
$233$	7.79576	+	10.7299i	0.510717	+	0.702942i	−0.473323	+	0.880889i	$0.656946\pi$
$234$		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	−0.923153	−	0.384433i	$-0.874397\pi$
$239$	−6.21895	−	19.1400i	−0.402271	−	1.23806i	0.520882	−	0.853629i	$-0.325603\pi$
$240$		0			0
$241$			10.0285i			0.645994i	0.946400	+	0.322997i	$0.104690\pi$
$241$			10.0285i			0.645994i	−0.946400	+	0.322997i	$0.895310\pi$
$242$	−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	0.509305	−	0.860586i	$-0.329902\pi$
$251$	−7.39146	−	10.1735i	−0.466545	−	0.642144i	−0.975850	+	0.218442i	$0.929902\pi$
$252$		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	−0.960311	−	0.278933i	$-0.910019\pi$
$257$	−0.311817	+	0.959673i	−0.0194506	+	0.0598628i	0.940860	+	0.338795i	$0.110019\pi$
$258$		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	0.255188	−	0.966892i	$-0.417863\pi$
$269$	−9.60330	−	6.97720i	−0.585523	−	0.425408i	−0.840711	+	0.541484i	$0.817863\pi$
$270$		0			0
$271$	−4.35634	+	13.4074i	−0.264629	+	0.814443i	0.727150	+	0.686478i	$0.240844\pi$
$271$	−4.35634	+	13.4074i	−0.264629	+	0.814443i	−0.991779	+	0.127965i	$0.959156\pi$
$272$	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	−0.999431	−	0.0337262i	$-0.989263\pi$
$277$	−12.0276	−	16.5545i	−0.722665	−	0.994664i	0.276766	−	0.960937i	$-0.410737\pi$
$278$	−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	−0.512732	−	0.858549i	$-0.671367\pi$
$281$	7.74854	−	10.6650i	0.462239	−	0.636218i	0.974971	+	0.222331i	$0.0713665\pi$
$282$		0			0
$283$	−1.28277	−	3.94797i	−0.0762529	−	0.234682i	0.905664	−	0.423997i	$-0.139373\pi$
$283$	−1.28277	−	3.94797i	−0.0762529	−	0.234682i	−0.981916	+	0.189315i	$0.939373\pi$
$284$	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	0.522442	−	0.852675i	$-0.325021\pi$
$293$	7.59864	+	2.46895i	0.443917	+	0.144237i	−0.0785249	+	0.996912i	$0.525021\pi$
$294$		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	−0.634942	−	0.772560i	$-0.718976\pi$
$311$	−12.2480	+	3.97962i	−0.694522	+	0.225664i	−0.0595796	+	0.998224i	$0.518976\pi$
$312$		0			0
$313$	−7.79540	−	5.66369i	−0.440622	−	0.320131i	0.345260	−	0.938507i	$-0.387791\pi$
$313$	−7.79540	−	5.66369i	−0.440622	−	0.320131i	−0.785882	+	0.618376i	$0.787791\pi$
$314$	−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	−0.426381	−	0.904544i	$-0.640212\pi$
$317$	5.37930	−	3.90829i	0.302132	−	0.219512i	0.728513	+	0.685032i	$0.240212\pi$
$318$		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	$-0.962733\pi$
$331$		−	4.25037i		−	0.233621i	0.993154	−	0.116811i	$-0.0372671\pi$
$332$	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	0.771770	−	0.635901i	$-0.219372\pi$
$337$	18.7683	+	6.09818i	1.02237	+	0.332189i	0.250602	+	0.968090i	$0.419372\pi$
$338$	−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	0.778672	−	0.627431i	$-0.215894\pi$
$347$	7.87165	+	5.71909i	0.422572	+	0.307017i	−0.356100	+	0.934448i	$0.615894\pi$
$348$		0			0
$349$	−18.2493	+	5.92957i	−0.976865	+	0.317403i	−0.753584	−	0.657352i	$-0.771677\pi$
$349$	−18.2493	+	5.92957i	−0.976865	+	0.317403i	−0.223281	+	0.974754i	$0.571677\pi$
$350$	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	0.697655	+	0.716434i	$0.254227\pi$
$359$	−5.45434	+	16.7867i	−0.287869	+	0.885971i	−0.985524	+	0.169536i	$0.945773\pi$
$360$		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	0.460470	−	0.887675i	$-0.347681\pi$
$367$	5.96243	+	1.93731i	0.311236	+	0.101127i	−0.149234	+	0.988802i	$0.547681\pi$
$368$	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	$0.000201541\pi$
$373$			0.0244567i			0.00126632i	−1.00000		0.000633161i	$0.999798\pi$
$374$	−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	0.0243438	−	0.999704i	$-0.492250\pi$
$379$	18.8371	−	25.9270i	0.967596	−	1.33178i	0.943252	−	0.332078i	$-0.107750\pi$
$380$	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	0.880052	+	0.474878i	$0.157508\pi$
$383$	20.7395	+	28.5454i	1.05974	+	1.45860i	0.179685	+	0.983724i	$0.442492\pi$
$384$		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	−0.997560	−	0.0698193i	$-0.977758\pi$
$389$	−2.94817	+	9.07354i	−0.149478	+	0.460047i	0.848081	+	0.529866i	$0.177758\pi$
$390$		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	−0.969020	−	0.246983i	$-0.920561\pi$
$401$	−30.1047	−	21.8724i	−1.50336	−	1.09225i	−0.534338	−	0.845271i	$-0.679439\pi$
$402$		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	0.631954	−	0.775006i	$-0.282253\pi$
$409$	−6.07530	−	8.36194i	−0.300404	−	0.413471i	−0.932359	+	0.361534i	$0.882253\pi$
$410$	−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	$0.0181963\pi$
$419$			2.33902i			0.114269i	−0.998366	+	0.0571343i	$0.981804\pi$
$420$		0			0
$421$	4.01513	+	12.3573i	0.195686	+	0.602258i	0.999968	+	0.00801103i	$0.00255002\pi$
$421$	4.01513	+	12.3573i	0.195686	+	0.602258i	−0.804282	+	0.594247i	$0.797450\pi$
$422$	−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	−0.979374	−	0.202058i	$-0.935237\pi$
$431$	−22.6258	+	16.4386i	−1.08985	+	0.791821i	−0.110474	+	0.993879i	$0.535237\pi$
$432$		0			0
$433$	9.68478	−	29.8067i	0.465421	−	1.43242i	−0.393032	−	0.919525i	$-0.628574\pi$
$433$	9.68478	−	29.8067i	0.465421	−	1.43242i	0.858453	−	0.512893i	$-0.171426\pi$
$434$	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	0.377942	−	0.925829i	$-0.376632\pi$
$443$	25.8441	−	8.39727i	1.22789	−	0.398966i	0.849950	+	0.526863i	$0.176632\pi$
$444$		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	−0.762885	−	0.646534i	$-0.776218\pi$
$449$	−8.13130	+	5.90774i	−0.383740	+	0.278803i	0.379146	+	0.925337i	$0.376218\pi$
$450$		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	−0.651312	−	0.758810i	$-0.725781\pi$
$457$	5.80668	−	7.99221i	0.271625	−	0.373860i	0.922937	+	0.384950i	$0.125781\pi$
$458$	−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	$-0.819321\pi$
$461$		−	23.0867i		−	1.07526i	0.843182	−	0.537628i	$-0.180679\pi$
$462$		0			0
$463$		−	5.87663i		−	0.273110i	−0.990632	−	0.136555i	$-0.956397\pi$
$463$		−	5.87663i		−	0.273110i	0.990632	−	0.136555i	$-0.0436031\pi$
$464$	−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	−0.857330	−	0.514768i	$-0.827878\pi$
$467$	−2.22211	+	3.05847i	−0.102827	+	0.141529i	0.754503	+	0.656297i	$0.227878\pi$
$468$		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	0.109295	−	0.994009i	$-0.465141\pi$
$479$	−17.5590	−	12.7573i	−0.802290	−	0.582898i	−0.911585	+	0.411112i	$0.865141\pi$
$480$		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	−0.469166	−	0.883110i	$-0.655445\pi$
$487$	−7.27475	+	2.36371i	−0.329651	+	0.107110i	0.139516	+	0.990220i	$0.455445\pi$
$488$	−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	−0.654553	−	0.756016i	$-0.727143\pi$
$491$	7.07668	−	21.7798i	0.319366	−	0.982908i	0.973920	−	0.226893i	$-0.0728567\pi$
$492$		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	0.973027	−	0.230692i	$-0.0740989\pi$
$499$	36.2914	+	11.7918i	1.62462	+	0.527873i	0.651598	+	0.758564i	$0.274099\pi$
$500$	−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	0.928906	−	0.370316i	$-0.120751\pi$
$503$	−0.902960	−	2.77903i	−0.0402610	−	0.123911i	−0.969167	+	0.246405i	$0.920751\pi$
$504$		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	0.902732	+	0.430204i	$0.141558\pi$
$509$	9.59462	+	29.5292i	0.425274	+	1.30886i	−0.477457	+	0.878655i	$0.658442\pi$
$510$		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	−0.969930	−	0.243385i	$-0.921742\pi$
$521$	−0.962822	+	2.96326i	−0.0421820	+	0.129823i	0.927748	+	0.373208i	$0.121742\pi$
$522$		0			0
$523$	−31.4971	−	22.8840i	−1.37727	−	1.00065i	−0.997129	−	0.0757180i	$-0.975875\pi$
$523$	−31.4971	−	22.8840i	−1.37727	−	1.00065i	−0.380142	−	0.924928i	$-0.624125\pi$
$524$	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	0.724328	−	0.689456i	$-0.242150\pi$
$541$	−3.61016	−	4.96896i	−0.155213	−	0.213632i	−0.879541	+	0.475823i	$0.842150\pi$
$542$	−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	0.980804	+	0.194996i	$0.0624692\pi$
$547$	7.06160	+	21.7334i	0.301932	+	0.929252i	−0.678872	+	0.734257i	$0.737531\pi$
$548$	−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	0.653212	−	0.757175i	$-0.273421\pi$
$557$	17.3847	+	5.64864i	0.736615	+	0.239341i	0.0834032	+	0.996516i	$0.473421\pi$
$558$		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	−0.833567	−	0.552419i	$-0.813705\pi$
$563$	−13.4244	+	9.75341i	−0.565772	+	0.411057i	0.267795	+	0.963476i	$0.413705\pi$
$564$		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	0.666389	−	0.745604i	$-0.267839\pi$
$569$	39.2099	−	12.7401i	1.64376	−	0.534091i	0.977375	+	0.211513i	$0.0678389\pi$
$570$		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	0.193890	−	0.981023i	$-0.437890\pi$
$577$	−16.3150	−	11.8536i	−0.679204	−	0.493470i	−0.873093	+	0.487553i	$0.837890\pi$
$578$	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	0.319867	−	0.947462i	$-0.396362\pi$
$587$	0.526749	+	0.171151i	0.0217413	+	0.00706417i	−0.298126	+	0.954526i	$0.596362\pi$
$588$		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	$0.252052\pi$
$593$			34.6597i			1.42330i	−0.702533	+	0.711651i	$0.747948\pi$
$594$		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	−0.199535	−	0.979891i	$-0.563943\pi$
$599$	19.4341	−	26.7488i	0.794057	−	1.09293i	0.993591	−	0.113034i	$-0.0360570\pi$
$600$		0			0
$601$	−10.1517	−	3.29847i	−0.414095	−	0.134548i	0.0945579	−	0.995519i	$-0.469856\pi$
$601$	−10.1517	−	3.29847i	−0.414095	−	0.134548i	−0.508653	+	0.860972i	$0.669856\pi$
$602$	−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	−0.702927	−	0.711262i	$-0.748124\pi$
$607$	−6.00393	+	4.36211i	−0.243692	+	0.177053i	0.459235	+	0.888315i	$0.348124\pi$
$608$	−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	−0.134666	−	0.990891i	$-0.542996\pi$
$613$	8.38874	−	2.72567i	0.338818	−	0.110089i	0.473484	+	0.880802i	$0.342996\pi$
$614$	−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	−0.161344	−	0.986898i	$-0.551583\pi$
$619$	7.17057	−	2.32986i	0.288210	−	0.0936450i	0.449554	+	0.893253i	$0.351583\pi$
$620$	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	0.960431	−	0.278516i	$-0.0898427\pi$
$631$	39.5316	+	12.8446i	1.57373	+	0.511336i	0.613297	+	0.789852i	$0.289843\pi$
$632$	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	0.971003	+	0.239066i	$0.0768413\pi$
$641$	8.25277	+	25.3994i	0.325965	+	1.00322i	−0.645039	+	0.764150i	$0.723159\pi$
$642$		0			0
$643$	−9.57732	+	13.1820i	−0.377693	+	0.519849i	−0.954971	−	0.296698i	$-0.904115\pi$
$643$	−9.57732	+	13.1820i	−0.377693	+	0.519849i	0.577279	+	0.816547i	$0.304115\pi$
$644$	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	0.749252	−	0.662285i	$-0.230413\pi$
$647$	−2.85269	−	3.92639i	−0.112151	−	0.154362i	−0.861402	+	0.507923i	$0.830413\pi$
$648$		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	−0.980673	−	0.195654i	$-0.937317\pi$
$653$	−1.84727	+	5.68532i	−0.0722893	+	0.222484i	0.908384	+	0.418138i	$0.137317\pi$
$654$		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	0.886644	−	0.462452i	$-0.153030\pi$
$673$	4.48381	+	6.17144i	0.172838	+	0.237891i	−0.713806	+	0.700343i	$0.753030\pi$
$674$	−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	−0.715244	−	0.698875i	$-0.753685\pi$
$677$	4.43491	−	6.10413i	0.170448	−	0.234601i	0.885692	+	0.464274i	$0.153685\pi$
$678$		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	$-0.933846\pi$
$683$		−	10.7849i		−	0.412674i	0.978481	−	0.206337i	$-0.0661543\pi$
$684$		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	0.386065	−	0.922471i	$-0.373834\pi$
$691$	−16.0497	−	22.0905i	−0.610558	−	0.840361i	−0.996623	+	0.0821106i	$0.973834\pi$
$692$	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	−0.476776	−	0.879025i	$-0.658195\pi$
$701$	−9.15601	+	2.97497i	−0.345818	+	0.112363i	0.130958	+	0.991388i	$0.458195\pi$
$702$		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	0.826961	−	0.562260i	$-0.190068\pi$
$709$	14.5854	+	10.5969i	0.547765	+	0.397974i	−0.279196	+	0.960234i	$0.590068\pi$
$710$	−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	−0.714882	−	0.699245i	$-0.753520\pi$
$719$	−45.6978	−	14.8481i	−1.70424	−	0.553741i	−0.989358	+	0.145504i	$0.953520\pi$
$720$		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	$-0.832919\pi$
$727$		−	27.0238i		−	1.00226i	0.865373	−	0.501128i	$-0.167081\pi$
$728$	−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	−0.366759	−	0.930316i	$-0.619532\pi$
$733$	−32.7676	−	10.6468i	−1.21030	−	0.393250i	−0.843540	+	0.537066i	$0.819532\pi$
$734$	−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	−0.932346	−	0.361568i	$-0.882242\pi$
$739$	−23.8296	+	17.3132i	−0.876585	+	0.636876i	0.0557608	+	0.998444i	$0.482242\pi$
$740$	−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	−0.999998	−	0.00207936i	$-0.999338\pi$
$743$	−35.7350	−	25.9630i	−1.31099	−	0.952491i	−0.310994	−	0.950412i	$-0.600662\pi$
$744$		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	−0.514586	−	0.857439i	$-0.672054\pi$
$751$	−11.6991	+	3.80126i	−0.426905	+	0.138710i	0.0876808	+	0.996149i	$0.472054\pi$
$752$	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	−0.743935	−	0.668252i	$-0.767043\pi$
$757$	−9.30726	+	6.76212i	−0.338278	+	0.245773i	0.405657	+	0.914025i	$0.367043\pi$
$758$	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	0.923399	−	0.383841i	$-0.125399\pi$
$761$	7.53101	+	10.3655i	0.272999	+	0.375751i	−0.650400	+	0.759591i	$0.725399\pi$
$762$		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	$0.0369274\pi$
$769$			6.41973i			0.231501i	−0.993278	+	0.115751i	$0.963073\pi$
$770$	−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	−0.976595	−	0.215085i	$-0.930997\pi$
$773$	−8.70055	−	26.7775i	−0.312937	−	0.963121i	0.663658	−	0.748036i	$-0.269003\pi$
$774$		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	0.388411	−	0.921486i	$-0.373024\pi$
$787$	−10.3223	−	7.49956i	−0.367949	−	0.267330i	−0.756360	+	0.654156i	$0.773024\pi$
$788$	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	−0.162536	−	0.986703i	$-0.551967\pi$
$797$	−32.4990	−	23.6119i	−1.15117	−	0.836376i	−0.988636	+	0.150327i	$0.951967\pi$
$798$		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	−0.965125	−	0.261788i	$-0.915688\pi$
$809$	−11.8866	+	16.3605i	−0.417910	+	0.575204i	0.547215	+	0.836992i	$0.315688\pi$
$810$		0			0
$811$	8.62836	+	26.5554i	0.302983	+	0.932485i	0.980422	+	0.196907i	$0.0630896\pi$
$811$	8.62836	+	26.5554i	0.302983	+	0.932485i	−0.677439	+	0.735579i	$0.736910\pi$
$812$	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	0.712097	−	0.702081i	$-0.247746\pi$
$821$	25.0864	+	8.15107i	0.875522	+	0.284474i	0.163425	+	0.986556i	$0.447746\pi$
$822$		0			0
$823$	25.1235	+	34.5796i	0.875752	+	1.20537i	0.977579	+	0.210567i	$0.0675309\pi$
$823$	25.1235	+	34.5796i	0.875752	+	1.20537i	−0.101828	+	0.994802i	$0.532469\pi$
$824$	−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	−0.396334	−	0.918106i	$-0.629718\pi$
$827$	10.1906	−	7.40391i	0.354362	−	0.257459i	0.750697	+	0.660647i	$0.229718\pi$
$828$		0			0
$829$	−3.42053	+	10.5273i	−0.118800	+	0.365628i	−0.992721	−	0.120440i	$-0.961569\pi$
$829$	−3.42053	+	10.5273i	−0.118800	+	0.365628i	0.873921	+	0.486068i	$0.161569\pi$
$830$	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	−0.295878	−	0.955226i	$-0.595612\pi$
$839$	0.759442	−	0.246758i	0.0262189	−	0.00851902i	0.322097	+	0.946707i	$0.395612\pi$
$840$		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	−0.609645	−	0.792675i	$-0.708688\pi$
$853$	9.71467	−	13.3711i	0.332624	−	0.457818i	0.942269	+	0.334857i	$0.108688\pi$
$854$	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	$-0.978008\pi$
$857$		−	4.04192i		−	0.138069i	0.997614	−	0.0690347i	$-0.0219919\pi$
$858$		0			0
$859$			13.5474i			0.462231i	0.972926	+	0.231115i	$0.0742375\pi$
$859$			13.5474i			0.462231i	−0.972926	+	0.231115i	$0.925762\pi$
$860$	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	−0.938925	−	0.344123i	$-0.888176\pi$
$863$	−9.44467	+	12.9995i	−0.321500	+	0.442507i	0.617424	+	0.786630i	$0.288176\pi$
$864$		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	−0.455115	−	0.890432i	$-0.650402\pi$
$877$	−8.88213	+	2.88598i	−0.299928	+	0.0974526i	0.155187	+	0.987885i	$0.450402\pi$
$878$	−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	−0.693538	−	0.720420i	$-0.743949\pi$
$883$	−24.6985	+	8.02501i	−0.831169	+	0.270063i	−0.137631	+	0.990484i	$0.543949\pi$
$884$	−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	−0.776920	−	0.629599i	$-0.783219\pi$
$887$	6.60250	−	20.3204i	0.221690	−	0.682292i	0.998611	−	0.0526937i	$-0.0167807\pi$
$888$		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	−0.570257	−	0.821467i	$-0.693156\pi$
$907$	11.6618	−	16.0511i	0.387223	−	0.532967i	0.957480	+	0.288499i	$0.0931563\pi$
$908$	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	0.896794	−	0.442449i	$-0.145890\pi$
$911$	6.00261	+	8.26188i	0.198875	+	0.273728i	−0.697918	+	0.716177i	$0.745890\pi$
$912$		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	0.108680	−	0.994077i	$-0.465338\pi$
$919$	−24.3478	−	17.6897i	−0.803159	−	0.583529i	−0.911839	+	0.410548i	$0.865338\pi$
$920$	−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	0.334275	−	0.942476i	$-0.391509\pi$
$929$	−13.9833	−	10.1594i	−0.458776	−	0.333321i	−0.793051	+	0.609155i	$0.791509\pi$
$930$		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	0.733741	−	0.679429i	$-0.237773\pi$
$937$	−4.26015	−	5.86359i	−0.139173	−	0.191555i	−0.872914	+	0.487874i	$0.837773\pi$
$938$	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	−0.259750	−	0.965676i	$-0.583640\pi$
$941$	22.6672	−	31.1987i	0.738930	−	1.01705i	0.998680	−	0.0513733i	$-0.0163598\pi$
$942$		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	$0.135737\pi$
$947$			25.4572i			0.827247i	−0.910448	+	0.413624i	$0.864263\pi$
$948$		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	0.729317	−	0.684176i	$-0.239838\pi$
$953$	28.3146	+	9.19996i	0.917198	+	0.298016i	0.187881	+	0.982192i	$0.439838\pi$
$954$		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	−0.313007	−	0.949751i	$-0.601336\pi$
$971$	−0.248827	+	0.0808487i	−0.00798523	+	0.00259456i	0.305022	+	0.952345i	$0.401336\pi$
$972$		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	0.315037	−	0.949079i	$-0.397983\pi$
$977$	41.1035	−	29.8634i	1.31502	−	0.955416i	0.999980	−	0.00633607i	$-0.00201685\pi$
$978$		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	0.456717	−	0.889612i	$-0.349025\pi$
$983$	9.50959	+	3.08985i	0.303309	+	0.0985510i	−0.153409	+	0.988163i	$0.549025\pi$
$984$		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	$0.342876\pi$
$991$			55.4443i			1.76125i	−0.473816	+	0.880624i	$0.657124\pi$
$992$	−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	0.990069	−	0.140585i	$-0.0448983\pi$
$997$	53.9438	+	17.5274i	1.70842	+	0.555098i	0.718349	+	0.695683i	$0.244898\pi$
$998$	−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.19.5		48
3.2	odd	2		132.2.j.a.19.8	yes	48
4.3	odd	2	inner	396.2.r.b.19.12		48
11.7	odd	10	inner	396.2.r.b.271.12		48
12.11	even	2		132.2.j.a.19.1	yes	48
33.29	even	10		132.2.j.a.7.1	✓	48
44.7	even	10	inner	396.2.r.b.271.5		48
132.95	odd	10		132.2.j.a.7.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.j.a.7.1	✓	48	33.29	even	10
132.2.j.a.7.8	yes	48	132.95	odd	10
132.2.j.a.19.1	yes	48	12.11	even	2
132.2.j.a.19.8	yes	48	3.2	odd	2
396.2.r.b.19.5		48	1.1	even	1	trivial
396.2.r.b.19.12		48	4.3	odd	2	inner
396.2.r.b.271.5		48	44.7	even	10	inner
396.2.r.b.271.12		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)

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