LMFDB - Embedded newform 819.2.et.d.145.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.8
Character	$\chi$	$=$	819.145
Dual form			819.2.et.d.514.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22934 - 1.22934i) q^{2} -1.02253i q^{4} +(1.95691 - 0.524353i) q^{5} +(-1.82011 - 1.92021i) q^{7} +(1.20163 + 1.20163i) q^{8} +O(q^{10})$	\(q+(1.22934 - 1.22934i) q^{2} -1.02253i q^{4} +(1.95691 - 0.524353i) q^{5} +(-1.82011 - 1.92021i) q^{7} +(1.20163 + 1.20163i) q^{8} +(1.76110 - 3.05031i) q^{10} +(3.50126 - 0.938159i) q^{11} +(-1.78841 - 3.13075i) q^{13} +(-4.59811 - 0.123058i) q^{14} +4.99949 q^{16} +1.50579 q^{17} +(-1.07053 + 3.99526i) q^{19} +(-0.536169 - 2.00101i) q^{20} +(3.15091 - 5.45753i) q^{22} -3.71137i q^{23} +(-0.775564 + 0.447772i) q^{25} +(-6.04730 - 1.65018i) q^{26} +(-1.96348 + 1.86112i) q^{28} +(1.84505 + 3.19572i) q^{29} +(1.89117 - 7.05794i) q^{31} +(3.74279 - 3.74279i) q^{32} +(1.85112 - 1.85112i) q^{34} +(-4.56866 - 2.80330i) q^{35} +(1.85150 + 1.85150i) q^{37} +(3.59548 + 6.22755i) q^{38} +(2.98158 + 1.72141i) q^{40} +(1.33248 - 4.97288i) q^{41} +(-4.51217 - 2.60510i) q^{43} +(-0.959299 - 3.58015i) q^{44} +(-4.56251 - 4.56251i) q^{46} +(-0.0684756 - 0.255554i) q^{47} +(-0.374411 + 6.98998i) q^{49} +(-0.402966 + 1.50389i) q^{50} +(-3.20130 + 1.82871i) q^{52} +(2.63938 + 4.57154i) q^{53} +(6.35973 - 3.67179i) q^{55} +(0.120285 - 4.49450i) q^{56} +(6.19679 + 1.66043i) q^{58} +(-0.912817 + 0.912817i) q^{59} +(-9.19565 + 5.30911i) q^{61} +(-6.35170 - 11.0015i) q^{62} +0.796700i q^{64} +(-5.14139 - 5.18884i) q^{65} +(3.47221 + 12.9585i) q^{67} -1.53972i q^{68} +(-9.06262 + 2.17022i) q^{70} +(-3.11400 - 11.6216i) q^{71} +(-2.77707 - 0.744113i) q^{73} +4.55224 q^{74} +(4.08528 + 1.09465i) q^{76} +(-8.17413 - 5.01560i) q^{77} +(-8.09801 + 14.0262i) q^{79} +(9.78357 - 2.62150i) q^{80} +(-4.47528 - 7.75141i) q^{82} +(10.3721 + 10.3721i) q^{83} +(2.94671 - 0.789567i) q^{85} +(-8.74952 + 2.34443i) q^{86} +(5.33456 + 3.07991i) q^{88} +(-7.11661 + 7.11661i) q^{89} +(-2.75659 + 9.13243i) q^{91} -3.79500 q^{92} +(-0.398342 - 0.229983i) q^{94} +8.37970i q^{95} +(-0.645956 + 0.173083i) q^{97} +(8.13276 + 9.05331i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{7}+O(q^{10}) $ 40 * q - 2 * q^7	$ 40 q - 2 q^{7} + 8 q^{11} + 18 q^{14} - 64 q^{16} - 8 q^{17} - 14 q^{19} + 14 q^{20} + 4 q^{22} - 24 q^{25} + 10 q^{26} - 2 q^{28} - 8 q^{29} - 8 q^{31} - 10 q^{32} + 24 q^{34} + 22 q^{35} + 12 q^{37} - 8 q^{38} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 28 q^{44} + 40 q^{46} - 10 q^{47} + 38 q^{49} + 20 q^{50} + 40 q^{52} + 8 q^{53} + 42 q^{55} - 20 q^{56} - 48 q^{58} + 26 q^{59} - 12 q^{61} + 24 q^{62} + 44 q^{65} + 46 q^{67} + 32 q^{70} + 6 q^{71} + 10 q^{73} - 40 q^{74} + 64 q^{76} + 24 q^{77} - 34 q^{80} + 24 q^{82} - 12 q^{83} + 2 q^{85} - 12 q^{86} - 84 q^{88} + 16 q^{89} + 26 q^{91} - 236 q^{92} + 30 q^{94} + 62 q^{97} + 14 q^{98}+O(q^{100}) $ 40 * q - 2 * q^7 + 8 * q^11 + 18 * q^14 - 64 * q^16 - 8 * q^17 - 14 * q^19 + 14 * q^20 + 4 * q^22 - 24 * q^25 + 10 * q^26 - 2 * q^28 - 8 * q^29 - 8 * q^31 - 10 * q^32 + 24 * q^34 + 22 * q^35 + 12 * q^37 - 8 * q^38 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 28 * q^44 + 40 * q^46 - 10 * q^47 + 38 * q^49 + 20 * q^50 + 40 * q^52 + 8 * q^53 + 42 * q^55 - 20 * q^56 - 48 * q^58 + 26 * q^59 - 12 * q^61 + 24 * q^62 + 44 * q^65 + 46 * q^67 + 32 * q^70 + 6 * q^71 + 10 * q^73 - 40 * q^74 + 64 * q^76 + 24 * q^77 - 34 * q^80 + 24 * q^82 - 12 * q^83 + 2 * q^85 - 12 * q^86 - 84 * q^88 + 16 * q^89 + 26 * q^91 - 236 * q^92 + 30 * q^94 + 62 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.22934	−	1.22934i	0.869272	−	0.869272i	−0.123120	−	0.992392i	$-0.539290\pi$
$2$	1.22934	−	1.22934i	0.869272	−	0.869272i	0.992392	+	0.123120i	$0.0392900\pi$
$3$		0			0
$3$		0			0
$4$		−	1.02253i		−	0.511267i
$5$	1.95691	−	0.524353i	0.875158	−	0.234498i	0.206841	−	0.978375i	$-0.433682\pi$
$5$	1.95691	−	0.524353i	0.875158	−	0.234498i	0.668317	+	0.743877i	$0.267015\pi$
$6$		0			0
$7$	−1.82011	−	1.92021i	−0.687936	−	0.725771i
$7$	−1.82011	−	1.92021i	−0.687936	−	0.725771i
$8$	1.20163	+	1.20163i	0.424842	+	0.424842i
$9$		0			0
$10$	1.76110	−	3.05031i	0.556908	−	0.964593i
$11$	3.50126	−	0.938159i	1.05567	−	0.282866i	0.311076	−	0.950385i	$-0.399311\pi$
$11$	3.50126	−	0.938159i	1.05567	−	0.282866i	0.744592	+	0.667519i	$0.232644\pi$
$12$		0			0
$13$	−1.78841	−	3.13075i	−0.496016	−	0.868313i
$13$	−1.78841	−	3.13075i	−0.496016	−	0.868313i
$14$	−4.59811	−	0.123058i	−1.22890	−	0.0328887i
$15$		0			0
$16$	4.99949			1.24987
$17$	1.50579			0.365208			0.182604	−	0.983187i	$-0.441547\pi$
$17$	1.50579			0.365208			0.182604	+	0.983187i	$0.441547\pi$
$18$		0			0
$19$	−1.07053	+	3.99526i	−0.245595	+	0.916575i	0.727488	+	0.686121i	$0.240688\pi$
$19$	−1.07053	+	3.99526i	−0.245595	+	0.916575i	−0.973083	+	0.230454i	$0.925979\pi$
$20$	−0.536169	−	2.00101i	−0.119891	−	0.447439i
$21$		0			0
$22$	3.15091	−	5.45753i	0.671776	−	1.16355i
$23$		−	3.71137i		−	0.773873i	−0.922106	−	0.386937i	$-0.873533\pi$
$23$		−	3.71137i		−	0.773873i	0.922106	−	0.386937i	$-0.126467\pi$
$24$		0			0
$25$	−0.775564	+	0.447772i	−0.155113	+	0.0895544i
$26$	−6.04730	−	1.65018i	−1.18597	−	0.323627i
$27$		0			0
$28$	−1.96348	+	1.86112i	−0.371063	+	0.351719i
$29$	1.84505	+	3.19572i	0.342617	+	0.593430i	0.984918	−	0.173023i	$-0.0553534\pi$
$29$	1.84505	+	3.19572i	0.342617	+	0.593430i	−0.642301	+	0.766452i	$0.722020\pi$
$30$		0			0
$31$	1.89117	−	7.05794i	0.339664	−	1.26764i	−0.559059	−	0.829128i	$-0.688838\pi$
$31$	1.89117	−	7.05794i	0.339664	−	1.26764i	0.898723	−	0.438516i	$-0.144496\pi$
$32$	3.74279	−	3.74279i	0.661637	−	0.661637i
$33$		0			0
$34$	1.85112	−	1.85112i	0.317465	−	0.317465i
$35$	−4.56866	−	2.80330i	−0.772245	−	0.473845i
$36$		0			0
$37$	1.85150	+	1.85150i	0.304385	+	0.304385i	0.842727	−	0.538342i	$-0.180949\pi$
$37$	1.85150	+	1.85150i	0.304385	+	0.304385i	−0.538342	+	0.842727i	$0.680949\pi$
$38$	3.59548	+	6.22755i	0.583263	+	1.01024i
$39$		0			0
$40$	2.98158	+	1.72141i	0.471428	+	0.272179i
$41$	1.33248	−	4.97288i	0.208098	−	0.776634i	−0.780384	−	0.625300i	$-0.784977\pi$
$41$	1.33248	−	4.97288i	0.208098	−	0.776634i	0.988483	−	0.151334i	$-0.0483568\pi$
$42$		0			0
$43$	−4.51217	−	2.60510i	−0.688099	−	0.397274i	0.114800	−	0.993389i	$-0.463377\pi$
$43$	−4.51217	−	2.60510i	−0.688099	−	0.397274i	−0.802900	+	0.596114i	$0.796711\pi$
$44$	−0.959299	−	3.58015i	−0.144620	−	0.539728i
$45$		0			0
$46$	−4.56251	−	4.56251i	−0.672706	−	0.672706i
$47$	−0.0684756	−	0.255554i	−0.00998819	−	0.0372764i	0.960752	−	0.277409i	$-0.0894757\pi$
$47$	−0.0684756	−	0.255554i	−0.00998819	−	0.0372764i	−0.970740	+	0.240133i	$0.922809\pi$
$48$		0			0
$49$	−0.374411	+	6.98998i	−0.0534873	+	0.998569i
$50$	−0.402966	+	1.50389i	−0.0569881	+	0.212682i
$51$		0			0
$52$	−3.20130	+	1.82871i	−0.443940	+	0.253597i
$53$	2.63938	+	4.57154i	0.362547	+	0.627949i	0.988379	−	0.152008i	$-0.0485740\pi$
$53$	2.63938	+	4.57154i	0.362547	+	0.627949i	−0.625832	+	0.779958i	$0.715241\pi$
$54$		0			0
$55$	6.35973	−	3.67179i	0.857546	−	0.495104i
$56$	0.120285	−	4.49450i	0.0160738	−	0.600602i
$57$		0			0
$58$	6.19679	+	1.66043i	0.813679	+	0.218025i
$59$	−0.912817	+	0.912817i	−0.118839	+	0.118839i	−0.764025	−	0.645186i	$-0.776780\pi$
$59$	−0.912817	+	0.912817i	−0.118839	+	0.118839i	0.645186	+	0.764025i	$0.276780\pi$
$60$		0			0
$61$	−9.19565	+	5.30911i	−1.17738	+	0.679762i	−0.955408	−	0.295290i	$-0.904584\pi$
$61$	−9.19565	+	5.30911i	−1.17738	+	0.679762i	−0.221975	+	0.975052i	$0.571250\pi$
$62$	−6.35170	−	11.0015i	−0.806667	−	1.39719i
$63$		0			0
$64$			0.796700i			0.0995875i
$65$	−5.14139	−	5.18884i	−0.637710	−	0.643597i
$66$		0			0
$67$	3.47221	+	12.9585i	0.424198	+	1.58313i	0.765668	+	0.643237i	$0.222409\pi$
$67$	3.47221	+	12.9585i	0.424198	+	1.58313i	−0.341469	+	0.939893i	$0.610925\pi$
$68$		−	1.53972i		−	0.186719i
$69$		0			0
$70$	−9.06262	+	2.17022i	−1.08319	+	0.259391i
$71$	−3.11400	−	11.6216i	−0.369564	−	1.37923i	−0.861127	−	0.508390i	$-0.830241\pi$
$71$	−3.11400	−	11.6216i	−0.369564	−	1.37923i	0.491562	−	0.870842i	$-0.336426\pi$
$72$		0			0
$73$	−2.77707	−	0.744113i	−0.325031	−	0.0870919i	0.0926138	−	0.995702i	$-0.470478\pi$
$73$	−2.77707	−	0.744113i	−0.325031	−	0.0870919i	−0.417645	+	0.908610i	$0.637144\pi$
$74$	4.55224			0.529187
$75$		0			0
$76$	4.08528	+	1.09465i	0.468614	+	0.125565i
$77$	−8.17413	−	5.01560i	−0.931528	−	0.571580i
$78$		0			0
$79$	−8.09801	+	14.0262i	−0.911098	+	1.57807i	−0.0985815	+	0.995129i	$0.531431\pi$
$79$	−8.09801	+	14.0262i	−0.911098	+	1.57807i	−0.812516	+	0.582939i	$0.801903\pi$
$80$	9.78357	−	2.62150i	1.09384	−	0.293093i
$81$		0			0
$82$	−4.47528	−	7.75141i	−0.494212	−	0.856000i
$83$	10.3721	+	10.3721i	1.13849	+	1.13849i	0.988722	+	0.149764i	$0.0478513\pi$
$83$	10.3721	+	10.3721i	1.13849	+	1.13849i	0.149764	+	0.988722i	$0.452149\pi$
$84$		0			0
$85$	2.94671	−	0.789567i	0.319615	−	0.0856406i
$86$	−8.74952	+	2.34443i	−0.943485	+	0.252806i
$87$		0			0
$88$	5.33456	+	3.07991i	0.568665	+	0.328319i
$89$	−7.11661	+	7.11661i	−0.754359	+	0.754359i	−0.975290	−	0.220931i	$-0.929091\pi$
$89$	−7.11661	+	7.11661i	−0.754359	+	0.754359i	0.220931	+	0.975290i	$0.429091\pi$
$90$		0			0
$91$	−2.75659	+	9.13243i	−0.288969	+	0.957338i
$92$	−3.79500			−0.395656
$93$		0			0
$94$	−0.398342	−	0.229983i	−0.0410858	−	0.0237209i
$95$			8.37970i			0.859739i
$96$		0			0
$97$	−0.645956	+	0.173083i	−0.0655869	+	0.0175739i	−0.291463	−	0.956582i	$-0.594142\pi$
$97$	−0.645956	+	0.173083i	−0.0655869	+	0.0175739i	0.225876	+	0.974156i	$0.427475\pi$
$98$	8.13276	+	9.05331i	0.821532	+	0.914522i
$99$		0			0
$100$	0.457862	+	0.793041i	0.0457862	+	0.0793041i
$101$	−3.62609	+	6.28058i	−0.360810	+	0.624941i	−0.988094	−	0.153849i	$-0.950833\pi$
$101$	−3.62609	+	6.28058i	−0.360810	+	0.624941i	0.627285	+	0.778790i	$0.284166\pi$
$102$		0			0
$103$	7.23449	−	12.5305i	0.712835	−	1.23467i	−0.250954	−	0.967999i	$-0.580744\pi$
$103$	7.23449	−	12.5305i	0.712835	−	1.23467i	0.963789	−	0.266667i	$-0.0859225\pi$
$104$	1.61300	−	5.91103i	0.158167	−	0.579624i
$105$		0			0
$106$	8.86465	+	2.37527i	0.861010	+	0.230707i
$107$	5.88078			0.568516			0.284258	−	0.958748i	$-0.408253\pi$
$107$	5.88078			0.568516			0.284258	+	0.958748i	$0.408253\pi$
$108$		0			0
$109$	0.496935	+	0.133153i	0.0475977	+	0.0127538i	0.282539	−	0.959256i	$-0.408823\pi$
$109$	0.496935	+	0.133153i	0.0475977	+	0.0127538i	−0.234942	+	0.972009i	$0.575490\pi$
$110$	3.30438	−	12.3321i	0.315060	−	1.17582i
$111$		0			0
$112$	−9.09962	−	9.60007i	−0.859833	−	0.907122i
$113$	−3.88416	+	6.72757i	−0.365391	+	0.632876i	−0.988839	−	0.148989i	$-0.952398\pi$
$113$	−3.88416	+	6.72757i	−0.365391	+	0.632876i	0.623448	+	0.781865i	$0.285731\pi$
$114$		0			0
$115$	−1.94607	−	7.26282i	−0.181472	−	0.677261i
$116$	3.26773	−	1.88662i	0.303401	−	0.175169i
$117$		0			0
$118$			2.24432i			0.206606i
$119$	−2.74071	−	2.89144i	−0.251240	−	0.265058i
$120$		0			0
$121$	1.85238	−	1.06947i	0.168398	−	0.0972247i
$122$	−4.77786	+	17.8312i	−0.432567	+	1.61436i
$123$		0			0
$124$	−7.21698	−	1.93379i	−0.648104	−	0.173659i
$125$	−8.44572	+	8.44572i	−0.755408	+	0.755408i
$126$		0			0
$127$	16.4913	−	9.52126i	1.46337	−	0.844875i	0.464201	−	0.885730i	$-0.346341\pi$
$127$	16.4913	−	9.52126i	1.46337	−	0.844875i	0.999165	+	0.0408546i	$0.0130081\pi$
$128$	8.46499	+	8.46499i	0.748206	+	0.748206i
$129$		0			0
$130$	−12.6993	−	0.0583404i	−1.11380	−	0.00511680i
$131$	−15.7198	−	9.07584i	−1.37345	−	0.792960i	−0.382087	−	0.924127i	$-0.624794\pi$
$131$	−15.7198	−	9.07584i	−1.37345	−	0.792960i	−0.991360	+	0.131167i	$0.958128\pi$
$132$		0			0
$133$	9.62020	−	5.21617i	0.834177	−	0.452299i
$134$	20.1988	+	11.6618i	1.74491	+	1.00743i
$135$		0			0
$136$	1.80941	+	1.80941i	0.155156	+	0.155156i
$137$	14.2350	+	14.2350i	1.21618	+	1.21618i	0.968960	+	0.247217i	$0.0795161\pi$
$137$	14.2350	+	14.2350i	1.21618	+	1.21618i	0.247217	+	0.968960i	$0.420484\pi$
$138$		0			0
$139$	−17.7595	−	10.2535i	−1.50634	−	0.869687i	−0.999973	−	0.00736980i	$-0.997654\pi$
$139$	−17.7595	−	10.2535i	−1.50634	−	0.869687i	−0.506369	−	0.862317i	$-0.669013\pi$
$140$	−2.86647	+	4.67161i	−0.242261	+	0.394823i
$141$		0			0
$142$	−18.1150	−	10.4587i	−1.52018	−	0.877676i
$143$	−9.19883	−	9.28374i	−0.769245	−	0.776345i
$144$		0			0
$145$	5.28628	+	5.28628i	0.439002	+	0.439002i
$146$	−4.32872	+	2.49919i	−0.358247	+	0.206834i
$147$		0			0
$148$	1.89322	−	1.89322i	0.155622	−	0.155622i
$149$	12.1748	+	3.26223i	0.997399	+	0.267252i	0.720356	−	0.693605i	$-0.243979\pi$
$149$	12.1748	+	3.26223i	0.997399	+	0.267252i	0.277044	+	0.960857i	$0.410645\pi$
$150$		0			0
$151$	−5.46323	+	20.3890i	−0.444591	+	1.65924i	0.272422	+	0.962178i	$0.412175\pi$
$151$	−5.46323	+	20.3890i	−0.444591	+	1.65924i	−0.717014	+	0.697059i	$0.754491\pi$
$152$	−6.08722	+	3.51446i	−0.493739	+	0.285060i
$153$		0			0
$154$	−16.2146	+	3.88290i	−1.30661	+	0.312893i
$155$		−	14.8034i		−	1.18904i
$156$		0			0
$157$	−3.20707	+	1.85160i	−0.255952	+	0.147774i	−0.622487	−	0.782630i	$-0.713877\pi$
$157$	−3.20707	+	1.85160i	−0.255952	+	0.147774i	0.366535	+	0.930404i	$0.380544\pi$
$158$	7.28770	+	27.1981i	0.579778	+	2.16376i
$159$		0			0
$160$	5.36177	−	9.28685i	0.423885	−	0.734190i
$161$	−7.12660	+	6.75509i	−0.561655	+	0.532375i
$162$		0			0
$163$	−2.55543	+	9.53701i	−0.200157	+	0.746996i	0.790714	+	0.612185i	$0.209709\pi$
$163$	−2.55543	+	9.53701i	−0.200157	+	0.746996i	−0.990871	+	0.134811i	$0.956957\pi$
$164$	−5.08494	−	1.36251i	−0.397067	−	0.106394i
$165$		0			0
$166$	25.5016			1.97931
$167$	−20.4714	−	5.48528i	−1.58412	−	0.424464i	−0.643922	−	0.765091i	$-0.722694\pi$
$167$	−20.4714	−	5.48528i	−1.58412	−	0.424464i	−0.940199	+	0.340627i	$0.889361\pi$
$168$		0			0
$169$	−6.60316	+	11.1981i	−0.507936	+	0.861395i
$170$	2.65185	−	4.59313i	0.203387	−	0.352277i
$171$		0			0
$172$	−2.66380	+	4.61384i	−0.203113	+	0.351802i
$173$	6.65526	+	11.5272i	0.505990	+	0.876400i	0.999976	+	0.00693041i	$0.00220604\pi$
$173$	6.65526	+	11.5272i	0.505990	+	0.876400i	−0.493986	+	0.869470i	$0.664461\pi$
$174$		0			0
$175$	2.27143	+	0.674252i	0.171704	+	0.0509687i
$176$	17.5045	−	4.69032i	1.31945	−	0.353546i
$177$		0			0
$178$			17.4974i			1.31149i
$179$	−4.04205	−	2.33368i	−0.302117	−	0.174427i	0.341277	−	0.939963i	$-0.389141\pi$
$179$	−4.04205	−	2.33368i	−0.302117	−	0.174427i	−0.643393	+	0.765536i	$0.722474\pi$
$180$		0			0
$181$	1.72036			0.127874			0.0639368	−	0.997954i	$-0.479634\pi$
$181$	1.72036			0.127874			0.0639368	+	0.997954i	$0.479634\pi$
$182$	7.83805	+	14.6156i	0.580995	+	1.08338i
$183$		0			0
$184$	4.45970	−	4.45970i	0.328774	−	0.328774i
$185$	4.59407	+	2.65239i	0.337763	+	0.195007i
$186$		0			0
$187$	5.27217	−	1.41267i	0.385539	−	0.103305i
$188$	−0.261313	+	0.0700186i	−0.0190582	+	0.00510663i
$189$		0			0
$190$	10.3015	+	10.3015i	0.747347	+	0.747347i
$191$	4.85830	+	8.41483i	0.351535	+	0.608876i	0.986519	−	0.163650i	$-0.0523266\pi$
$191$	4.85830	+	8.41483i	0.351535	+	0.608876i	−0.634984	+	0.772525i	$0.718993\pi$
$192$		0			0
$193$	7.12897	−	1.91020i	0.513155	−	0.137499i	0.00705630	−	0.999975i	$-0.497754\pi$
$193$	7.12897	−	1.91020i	0.513155	−	0.137499i	0.506098	+	0.862476i	$0.331087\pi$
$194$	−0.581319	+	1.00687i	−0.0417363	+	0.0722894i
$195$		0			0
$196$	7.14749	+	0.382848i	0.510535	+	0.0273463i
$197$	−0.502809	−	0.134727i	−0.0358236	−	0.00959892i	0.240863	−	0.970559i	$-0.422570\pi$
$197$	−0.502809	−	0.134727i	−0.0358236	−	0.00959892i	−0.276686	+	0.960960i	$0.589236\pi$
$198$		0			0
$199$	15.6835			1.11177			0.555887	−	0.831258i	$-0.312379\pi$
$199$	15.6835			1.11177			0.555887	+	0.831258i	$0.312379\pi$
$200$	−1.47000	−	0.393886i	−0.103945	−	0.0278520i
$201$		0			0
$202$	3.26325	+	12.1786i	0.229602	+	0.856885i
$203$	2.77826	−	9.35943i	0.194996	−	0.656903i
$204$		0			0
$205$		−	10.4302i		−	0.728476i
$206$	−6.51058	−	24.2978i	−0.453613	−	1.69291i
$207$		0			0
$208$	−8.94115	−	15.6521i	−0.619957	−	1.08528i
$209$			14.9927i			1.03707i
$210$		0			0
$211$	−2.58812	−	4.48276i	−0.178174	−	0.308606i	0.763081	−	0.646302i	$-0.223686\pi$
$211$	−2.58812	−	4.48276i	−0.178174	−	0.308606i	−0.941255	+	0.337697i	$0.890352\pi$
$212$	4.67455	−	2.69886i	0.321050	−	0.185358i
$213$		0			0
$214$	7.22945	−	7.22945i	0.494195	−	0.494195i
$215$	−10.1959	−	2.73199i	−0.695356	−	0.186320i
$216$		0			0
$217$	−16.9949	+	9.21478i	−1.15369	+	0.625540i
$218$	0.774590	−	0.447210i	0.0524618	−	0.0302889i
$219$		0			0
$220$	−3.75453	−	6.50304i	−0.253130	−	0.438435i
$221$	−2.69298	−	4.71426i	−0.181149	−	0.317115i
$222$		0			0
$223$	3.25346	−	12.1421i	0.217868	−	0.813093i	−0.767270	−	0.641325i	$-0.778385\pi$
$223$	3.25346	−	12.1421i	0.217868	−	0.813093i	0.985137	−	0.171769i	$-0.0549482\pi$
$224$	−13.9992	−	0.374658i	−0.935362	−	0.0250329i
$225$		0			0
$226$	3.49550	+	13.0454i	0.232517	+	0.867766i
$227$	−4.65410	−	4.65410i	−0.308904	−	0.308904i	0.535581	−	0.844484i	$-0.320093\pi$
$227$	−4.65410	−	4.65410i	−0.308904	−	0.308904i	−0.844484	+	0.535581i	$0.820093\pi$
$228$		0			0
$229$	−2.36710	−	8.83413i	−0.156422	−	0.583776i	−0.998979	−	0.0451689i	$-0.985617\pi$
$229$	−2.36710	−	8.83413i	−0.156422	−	0.583776i	0.842557	−	0.538607i	$-0.181049\pi$
$230$	−11.3208	−	6.53608i	−0.746472	−	0.430976i
$231$		0			0
$232$	−1.62301	+	6.05716i	−0.106556	+	0.397672i
$233$	−6.66005	−	3.84518i	−0.436315	−	0.251906i	0.265719	−	0.964051i	$-0.414391\pi$
$233$	−6.66005	−	3.84518i	−0.436315	−	0.251906i	−0.702033	+	0.712144i	$0.747724\pi$
$234$		0			0
$235$	−0.268002	−	0.464192i	−0.0174825	−	0.0302806i
$236$	0.933386	+	0.933386i	0.0607583	+	0.0607583i
$237$		0			0
$238$	−6.92380	−	0.185300i	−0.448803	−	0.0120112i
$239$	14.4981	−	14.4981i	0.937806	−	0.937806i	−0.0603699	−	0.998176i	$-0.519228\pi$
$239$	14.4981	−	14.4981i	0.937806	−	0.937806i	0.998176	+	0.0603699i	$0.0192280\pi$
$240$		0			0
$241$	7.05015	−	7.05015i	0.454140	−	0.454140i	−0.442586	−	0.896726i	$-0.645939\pi$
$241$	7.05015	−	7.05015i	0.454140	−	0.454140i	0.896726	+	0.442586i	$0.145939\pi$
$242$	0.962456	−	3.59194i	0.0618690	−	0.230898i
$243$		0			0
$244$	5.42875	+	9.40286i	0.347540	+	0.601957i
$245$	2.93253	+	13.8751i	0.187352	+	0.886448i
$246$		0			0
$247$	14.4227	−	3.79362i	0.917693	−	0.241382i
$248$	10.7536	−	6.20857i	0.682852	−	0.394245i
$249$		0			0
$250$			20.7653i			1.31331i
$251$	3.38103	−	5.85611i	0.213409	−	0.369635i	−0.739371	−	0.673299i	$-0.764877\pi$
$251$	3.38103	−	5.85611i	0.213409	−	0.369635i	0.952779	+	0.303664i	$0.0982101\pi$
$252$		0			0
$253$	−3.48185	−	12.9944i	−0.218902	−	0.816954i
$254$	8.56853	−	31.9782i	0.537637	−	2.00649i
$255$		0			0
$256$	19.2192			1.20120
$257$	19.3062			1.20429			0.602143	−	0.798388i	$-0.294314\pi$
$257$	19.3062			1.20429			0.602143	+	0.798388i	$0.294314\pi$
$258$		0			0
$259$	0.185338	−	6.92521i	0.0115163	−	0.430311i
$260$	−5.30577	+	5.25724i	−0.329050	+	0.326040i
$261$		0			0
$262$	−30.4822	+	8.16768i	−1.88320	+	0.504601i
$263$	14.0880	−	24.4011i	0.868701	−	1.50464i	0.00537709	−	0.999986i	$-0.498288\pi$
$263$	14.0880	−	24.4011i	0.868701	−	1.50464i	0.863324	−	0.504649i	$-0.168378\pi$
$264$		0			0
$265$	7.56214	+	7.56214i	0.464539	+	0.464539i
$266$	5.41404	−	18.2389i	0.331956	−	1.11830i
$267$		0			0
$268$	13.2505	−	3.55045i	0.809402	−	0.216879i
$269$			17.4840i			1.06602i	0.846110	+	0.533008i	$0.178939\pi$
$269$			17.4840i			1.06602i	−0.846110	+	0.533008i	$0.821061\pi$
$270$		0			0
$271$	5.83971	−	5.83971i	0.354737	−	0.354737i	−0.507132	−	0.861869i	$-0.669294\pi$
$271$	5.83971	−	5.83971i	0.354737	−	0.354737i	0.861869	+	0.507132i	$0.169294\pi$
$272$	7.52820			0.456464
$273$		0			0
$274$	34.9992			2.11438
$275$	−2.29537	+	2.29537i	−0.138416	+	0.138416i
$276$		0			0
$277$		−	20.6373i		−	1.23997i	−0.784612	−	0.619987i	$-0.787138\pi$
$277$		−	20.6373i		−	1.23997i	0.784612	−	0.619987i	$-0.212862\pi$
$278$	−34.4373	+	9.22746i	−2.06541	+	0.553426i
$279$		0			0
$280$	−2.12132	−	8.85841i	−0.126773	−	0.529391i
$281$	−3.70317	−	3.70317i	−0.220913	−	0.220913i	0.587970	−	0.808883i	$-0.299927\pi$
$281$	−3.70317	−	3.70317i	−0.220913	−	0.220913i	−0.808883	+	0.587970i	$0.799927\pi$
$282$		0			0
$283$	0.421973	−	0.730879i	0.0250837	−	0.0434463i	−0.853211	−	0.521566i	$-0.825348\pi$
$283$	0.421973	−	0.730879i	0.0250837	−	0.0434463i	0.878295	+	0.478120i	$0.158681\pi$
$284$	−11.8835	+	3.18417i	−0.705156	+	0.188946i
$285$		0			0
$286$	−22.7213	−	0.104381i	−1.34354	−	0.00617219i
$287$	−11.9742	+	6.49254i	−0.706817	+	0.383243i
$288$		0			0
$289$	−14.7326			−0.866623
$290$	12.9972			0.763224
$291$		0			0
$292$	−0.760881	+	2.83965i	−0.0445272	+	0.166178i
$293$	4.34707	+	16.2235i	0.253959	+	0.947787i	0.968667	+	0.248364i	$0.0798929\pi$
$293$	4.34707	+	16.2235i	0.253959	+	0.947787i	−0.714708	+	0.699423i	$0.753440\pi$
$294$		0			0
$295$	−1.30767	+	2.26494i	−0.0761352	+	0.131870i
$296$			4.44966i			0.258631i
$297$		0			0
$298$	18.9773	−	10.9566i	1.09933	−	0.634696i
$299$	−11.6193	+	6.63745i	−0.671964	+	0.383854i
$300$		0			0
$301$	3.21029	+	13.4059i	0.185038	+	0.772702i
$302$	18.3488	+	31.7811i	1.05586	+	1.82880i
$303$		0			0
$304$	−5.35208	+	19.9743i	−0.306963	+	1.14560i
$305$	−15.2112	+	15.2112i	−0.870993	+	0.870993i
$306$		0			0
$307$	−19.8317	+	19.8317i	−1.13185	+	1.13185i	−0.141986	+	0.989869i	$0.545349\pi$
$307$	−19.8317	+	19.8317i	−1.13185	+	1.13185i	−0.989869	+	0.141986i	$0.954651\pi$
$308$	−5.12862	+	8.35832i	−0.292230	+	0.476260i
$309$		0			0
$310$	−18.1984	−	18.1984i	−1.03360	−	1.03360i
$311$	−11.9512	−	20.7001i	−0.677690	−	1.17379i	−0.975675	−	0.219223i	$-0.929648\pi$
$311$	−11.9512	−	20.7001i	−0.677690	−	1.17379i	0.297985	−	0.954571i	$-0.403686\pi$
$312$		0			0
$313$	−21.1920	−	12.2352i	−1.19784	−	0.691576i	−0.237770	−	0.971321i	$-0.576417\pi$
$313$	−21.1920	−	12.2352i	−1.19784	−	0.691576i	−0.960074	+	0.279746i	$0.909750\pi$
$314$	−1.66632	+	6.21881i	−0.0940361	+	0.350948i
$315$		0			0
$316$	14.3422	+	8.28049i	0.806814	+	0.465814i
$317$	−6.44215	−	24.0424i	−0.361827	−	1.35036i	−0.871671	−	0.490091i	$-0.836963\pi$
$317$	−6.44215	−	24.0424i	−0.361827	−	1.35036i	0.509844	−	0.860267i	$-0.329703\pi$
$318$		0			0
$319$	9.45808	+	9.45808i	0.529551	+	0.529551i
$320$	0.417752	+	1.55907i	0.0233531	+	0.0871548i
$321$		0			0
$322$	−0.456714	+	17.0653i	−0.0254517	+	0.951010i
$323$	−1.61199	+	6.01603i	−0.0896935	+	0.334741i
$324$		0			0
$325$	2.78889	+	1.62729i	0.154700	+	0.0902661i
$326$	8.58270	+	14.8657i	0.475352	+	0.823334i
$327$		0			0
$328$	7.57674	−	4.37443i	0.418355	−	0.241538i
$329$	−0.366085	+	0.596624i	−0.0201829	+	0.0328930i
$330$		0			0
$331$	−4.76996	−	1.27811i	−0.262181	−	0.0702511i	0.125334	−	0.992115i	$-0.460000\pi$
$331$	−4.76996	−	1.27811i	−0.262181	−	0.0702511i	−0.387515	+	0.921863i	$0.626666\pi$
$332$	10.6058	−	10.6058i	0.582070	−	0.582070i
$333$		0			0
$334$	−31.9094	+	18.4229i	−1.74601	+	1.00806i
$335$	13.5896	+	23.5379i	0.742481	+	1.28602i
$336$		0			0
$337$			4.37276i			0.238200i	0.992882	+	0.119100i	$0.0380009\pi$
$337$			4.37276i			0.238200i	−0.992882	+	0.119100i	$0.961999\pi$
$338$	5.64876	+	21.8838i	0.307252	+	1.19032i
$339$		0			0
$340$	−0.807359	−	3.01311i	−0.0437852	−	0.163409i
$341$		−	26.4859i		−	1.43429i
$342$		0			0
$343$	14.1037	−	12.0036i	0.761528	−	0.648132i
$344$	−2.29160	−	8.55236i	−0.123555	−	0.461112i
$345$		0			0
$346$	22.3524	+	5.98931i	1.20167	+	0.321987i
$347$	−27.2839			−1.46468			−0.732338	−	0.680941i	$-0.761571\pi$
$347$	−27.2839			−1.46468			−0.732338	+	0.680941i	$0.761571\pi$
$348$		0			0
$349$	−4.48654	−	1.20217i	−0.240159	−	0.0643505i	0.136732	−	0.990608i	$-0.456340\pi$
$349$	−4.48654	−	1.20217i	−0.240159	−	0.0643505i	−0.376891	+	0.926258i	$0.623007\pi$
$350$	3.62123	−	1.96346i	0.193563	−	0.104952i
$351$		0			0
$352$	9.59313	−	16.6158i	0.511315	−	0.885624i
$353$	4.05220	−	1.08578i	0.215677	−	0.0577905i	−0.149363	−	0.988782i	$-0.547722\pi$
$353$	4.05220	−	1.08578i	0.215677	−	0.0577905i	0.365039	+	0.930992i	$0.381055\pi$
$354$		0			0
$355$	−12.1877	−	21.1097i	−0.646854	−	1.12038i
$356$	7.27697	+	7.27697i	0.385679	+	0.385679i
$357$		0			0
$358$	−7.83790	+	2.10016i	−0.414246	+	0.110997i
$359$	−6.88575	+	1.84503i	−0.363416	+	0.0973770i	−0.435906	−	0.899992i	$-0.643572\pi$
$359$	−6.88575	+	1.84503i	−0.363416	+	0.0973770i	0.0724902	+	0.997369i	$0.476905\pi$
$360$		0			0
$361$	1.63844	+	0.945951i	0.0862334	+	0.0497869i
$362$	2.11490	−	2.11490i	0.111157	−	0.111157i
$363$		0			0
$364$	9.33821	+	2.81871i	0.489455	+	0.147740i
$365$	−5.82466			−0.304877
$366$		0			0
$367$	2.69586	+	1.55645i	0.140723	+	0.0812462i	0.568708	−	0.822539i	$-0.307443\pi$
$367$	2.69586	+	1.55645i	0.140723	+	0.0812462i	−0.427986	+	0.903785i	$0.640777\pi$
$368$		−	18.5549i		−	0.967243i
$369$		0			0
$370$	8.90833	−	2.38698i	0.463122	−	0.124093i
$371$	3.97436	−	13.3889i	0.206338	−	0.695115i
$372$		0			0
$373$	−6.10678	−	10.5773i	−0.316197	−	0.547670i	0.663494	−	0.748182i	$-0.269073\pi$
$373$	−6.10678	−	10.5773i	−0.316197	−	0.547670i	−0.979691	+	0.200512i	$0.935740\pi$
$374$	4.74461	−	8.21791i	0.245338	−	0.424938i
$375$		0			0
$376$	0.224800	−	0.389366i	0.0115932	−	0.0200800i
$377$	6.70528	−	11.4916i	0.345339	−	0.591849i
$378$		0			0
$379$	−24.7492	−	6.63154i	−1.27128	−	0.340639i	−0.440760	−	0.897625i	$-0.645291\pi$
$379$	−24.7492	−	6.63154i	−1.27128	−	0.340639i	−0.830522	+	0.556986i	$0.811958\pi$
$380$	8.56853			0.439556
$381$		0			0
$382$	16.3171	+	4.37217i	0.834858	+	0.223699i
$383$	9.35075	−	34.8975i	0.477801	−	1.78318i	−0.132692	−	0.991157i	$-0.542362\pi$
$383$	9.35075	−	34.8975i	0.477801	−	1.78318i	0.610493	−	0.792021i	$-0.290971\pi$
$384$		0			0
$385$	−18.6260	−	5.52896i	−0.949269	−	0.281782i
$386$	6.41562	−	11.1122i	0.326547	−	0.565595i
$387$		0			0
$388$	0.176984	+	0.660512i	0.00898498	+	0.0335324i
$389$	−10.5275	+	6.07805i	−0.533765	+	0.308170i	−0.742548	−	0.669792i	$-0.766383\pi$
$389$	−10.5275	+	6.07805i	−0.533765	+	0.308170i	0.208783	+	0.977962i	$0.433050\pi$
$390$		0			0
$391$		−	5.58855i		−	0.282625i
$392$	−8.84931	+	7.94949i	−0.446957	+	0.401510i
$393$		0			0
$394$	−0.783746	+	0.452496i	−0.0394846	+	0.0227964i
$395$	−8.49244	+	31.6942i	−0.427301	+	1.59471i
$396$		0			0
$397$	−14.4162	−	3.86281i	−0.723529	−	0.193869i	−0.121783	−	0.992557i	$-0.538861\pi$
$397$	−14.4162	−	3.86281i	−0.723529	−	0.193869i	−0.601746	+	0.798688i	$0.705528\pi$
$398$	19.2803	−	19.2803i	0.966434	−	0.966434i
$399$		0			0
$400$	−3.87743	+	2.23863i	−0.193871	+	0.111932i
$401$	−3.16078	−	3.16078i	−0.157842	−	0.157842i	0.623768	−	0.781610i	$-0.285601\pi$
$401$	−3.16078	−	3.16078i	−0.157842	−	0.157842i	−0.781610	+	0.623768i	$0.785601\pi$
$402$		0			0
$403$	−25.4788	+	6.70173i	−1.26919	+	0.333837i
$404$	6.42210	+	3.70780i	0.319512	+	0.184470i
$405$		0			0
$406$	−8.09047	−	14.9213i	−0.401523	−	0.740532i
$407$	8.21959	+	4.74558i	0.407430	+	0.235230i
$408$		0			0
$409$	0.391611	+	0.391611i	0.0193639	+	0.0193639i	0.716722	−	0.697359i	$-0.245641\pi$
$409$	0.391611	+	0.391611i	0.0193639	+	0.0193639i	−0.697359	+	0.716722i	$0.745641\pi$
$410$	−12.8222	−	12.8222i	−0.633244	−	0.633244i
$411$		0			0
$412$	−12.8129	−	7.39751i	−0.631244	−	0.364449i
$413$	3.41423	+	0.0913743i	0.168003	+	0.00449624i
$414$		0			0
$415$	25.7359	+	14.8587i	1.26333	+	0.729383i
$416$	−18.4114	−	5.02408i	−0.902691	−	0.246326i
$417$		0			0
$418$	18.4311	+	18.4311i	0.901495	+	0.901495i
$419$	20.1383	−	11.6268i	0.983819	−	0.568008i	0.0803983	−	0.996763i	$-0.474381\pi$
$419$	20.1383	−	11.6268i	0.983819	−	0.568008i	0.903421	+	0.428754i	$0.141047\pi$
$420$		0			0
$421$	−19.0536	+	19.0536i	−0.928614	+	0.928614i	−0.997617	−	0.0690021i	$-0.978018\pi$
$421$	−19.0536	+	19.0536i	−0.928614	+	0.928614i	0.0690021	+	0.997617i	$0.478018\pi$
$422$	−8.69249	−	2.32914i	−0.423144	−	0.113381i
$423$		0			0
$424$	−2.32175	+	8.66489i	−0.112754	+	0.420804i
$425$	−1.16784	+	0.674252i	−0.0566485	+	0.0327060i
$426$		0			0
$427$	26.9317	+	7.99442i	1.30332	+	0.386877i
$428$		−	6.01330i		−	0.290664i
$429$		0			0
$430$	−15.8927	+	9.17568i	−0.766416	+	0.442490i
$431$	5.29920	+	19.7769i	0.255253	+	0.952619i	0.967949	+	0.251146i	$0.0808073\pi$
$431$	5.29920	+	19.7769i	0.255253	+	0.952619i	−0.712696	+	0.701473i	$0.752526\pi$
$432$		0			0
$433$	−13.7982	+	23.8993i	−0.663101	+	1.14852i	0.316695	+	0.948527i	$0.397427\pi$
$433$	−13.7982	+	23.8993i	−0.663101	+	1.14852i	−0.979796	+	0.199997i	$0.935907\pi$
$434$	−9.56434	+	32.2205i	−0.459103	+	1.54663i
$435$		0			0
$436$	0.136154	−	0.508132i	0.00652058	−	0.0243351i
$437$	14.8279	+	3.97311i	0.709313	+	0.190060i
$438$		0			0
$439$	−18.0551			−0.861721			−0.430860	−	0.902419i	$-0.641790\pi$
$439$	−18.0551			−0.861721			−0.430860	+	0.902419i	$0.641790\pi$
$440$	12.0542	+	3.22992i	0.574662	+	0.153980i
$441$		0			0
$442$	−9.10598	−	2.48483i	−0.433127	−	0.118191i
$443$	19.5401	−	33.8445i	0.928380	−	1.60800i	0.142348	−	0.989817i	$-0.454535\pi$
$443$	19.5401	−	33.8445i	0.928380	−	1.60800i	0.786033	−	0.618185i	$-0.212132\pi$
$444$		0			0
$445$	−10.1950	+	17.6582i	−0.483288	+	0.837079i
$446$	−10.9271	−	18.9263i	−0.517413	−	0.896185i
$447$		0			0
$448$	1.52983	−	1.45008i	0.0722777	−	0.0685099i
$449$	−21.8252	+	5.84805i	−1.03000	+	0.275987i	−0.733962	−	0.679191i	$-0.762331\pi$
$449$	−21.8252	+	5.84805i	−1.03000	+	0.275987i	−0.296034	+	0.955177i	$0.595664\pi$
$450$		0			0
$451$		−	18.6614i		−	0.878732i
$452$	6.87917	+	3.97169i	0.323569	+	0.186812i
$453$		0			0
$454$	−11.4429			−0.537042
$455$	−0.605787	+	19.3168i	−0.0283997	+	0.905585i
$456$		0			0
$457$	13.8930	−	13.8930i	0.649886	−	0.649886i	−0.303080	−	0.952965i	$-0.598015\pi$
$457$	13.8930	−	13.8930i	0.649886	−	0.649886i	0.952965	+	0.303080i	$0.0980148\pi$
$458$	−13.7701	−	7.95016i	−0.643433	−	0.371486i
$459$		0			0
$460$	−7.42648	+	1.98992i	−0.346261	+	0.0927804i
$461$	−14.3331	+	3.84054i	−0.667559	+	0.178872i	−0.576655	−	0.816988i	$-0.695642\pi$
$461$	−14.3331	+	3.84054i	−0.667559	+	0.178872i	−0.0909042	+	0.995860i	$0.528976\pi$
$462$		0			0
$463$	−21.6764	−	21.6764i	−1.00739	−	1.00739i	−0.999972	−	0.00741751i	$-0.997639\pi$
$463$	−21.6764	−	21.6764i	−1.00739	−	1.00739i	−0.00741751	−	0.999972i	$-0.502361\pi$
$464$	9.22430	+	15.9770i	0.428228	+	0.741712i
$465$		0			0
$466$	−12.9145	+	3.46042i	−0.598251	+	0.160301i
$467$	10.6105	−	18.3780i	0.490996	−	0.850431i	−0.508950	−	0.860796i	$-0.669966\pi$
$467$	10.6105	−	18.3780i	0.490996	−	0.850431i	0.999946	+	0.0103654i	$0.00329948\pi$
$468$		0			0
$469$	18.5632	−	30.2532i	0.857168	−	1.39696i
$470$	−0.900112	−	0.241184i	−0.0415191	−	0.0111250i
$471$		0			0
$472$	−2.19375			−0.100975
$473$	−18.2423	−	4.88800i	−0.838780	−	0.224750i
$474$		0			0
$475$	−0.958703	−	3.57793i	−0.0439883	−	0.164167i
$476$	−2.95659	+	2.80246i	−0.135515	+	0.128451i
$477$		0			0
$478$		−	35.6461i		−	1.63042i
$479$	2.76842	+	10.3319i	0.126492	+	0.472075i	0.999888	−	0.0149350i	$-0.00475415\pi$
$479$	2.76842	+	10.3319i	0.126492	+	0.472075i	−0.873396	+	0.487010i	$0.838087\pi$
$480$		0			0
$481$	2.48534	−	9.10784i	0.113322	−	0.415282i
$482$		−	17.3340i		−	0.789542i
$483$		0			0
$484$	−1.09357	−	1.89412i	−0.0497078	−	0.0860964i
$485$	−1.17332	+	0.677418i	−0.0532778	+	0.0307600i
$486$		0			0
$487$	22.5829	−	22.5829i	1.02333	−	1.02333i	0.0236059	−	0.999721i	$-0.492485\pi$
$487$	22.5829	−	22.5829i	1.02333	−	1.02333i	0.999721	−	0.0236059i	$-0.00751470\pi$
$488$	−17.4294	−	4.67020i	−0.788993	−	0.211410i
$489$		0			0
$490$	20.6622	+	13.4521i	0.933424	+	0.607704i
$491$	−7.33827	+	4.23675i	−0.331171	+	0.191202i	−0.656361	−	0.754447i	$-0.727905\pi$
$491$	−7.33827	+	4.23675i	−0.331171	+	0.191202i	0.325190	+	0.945649i	$0.394572\pi$
$492$		0			0
$493$	2.77826	+	4.81209i	0.125127	+	0.216725i
$494$	13.0667	−	22.3940i	0.587898	−	1.00755i
$495$		0			0
$496$	9.45489	−	35.2861i	0.424537	−	1.58439i
$497$	−16.6481	+	27.1321i	−0.746770	+	1.21704i
$498$		0			0
$499$	6.55352	+	24.4581i	0.293376	+	1.09489i	0.942499	+	0.334210i	$0.108469\pi$
$499$	6.55352	+	24.4581i	0.293376	+	1.09489i	−0.649123	+	0.760684i	$0.724864\pi$
$500$	8.63603	+	8.63603i	0.386215	+	0.386215i
$501$		0			0
$502$	−3.04271	−	11.3555i	−0.135803	−	0.506823i
$503$	5.83735	+	3.37020i	0.260275	+	0.150270i	0.624460	−	0.781057i	$-0.285319\pi$
$503$	5.83735	+	3.37020i	0.260275	+	0.150270i	−0.364185	+	0.931327i	$0.618652\pi$
$504$		0			0
$505$	−3.80271	+	14.1919i	−0.169218	+	0.631531i
$506$	−20.2549	−	11.6942i	−0.900440	−	0.519869i
$507$		0			0
$508$	−9.73581	−	16.8629i	−0.431957	−	0.748171i
$509$	2.17639	+	2.17639i	0.0964669	+	0.0964669i	0.753693	−	0.657226i	$-0.228270\pi$
$509$	2.17639	+	2.17639i	0.0964669	+	0.0964669i	−0.657226	+	0.753693i	$0.728270\pi$
$510$		0			0
$511$	3.62571	+	6.68692i	0.160392	+	0.295812i
$512$	6.69691	−	6.69691i	0.295964	−	0.295964i
$513$		0			0
$514$	23.7338	−	23.7338i	1.04685	−	1.04685i
$515$	7.58685	−	28.3145i	0.334317	−	1.24769i
$516$		0			0
$517$	−0.479501	−	0.830521i	−0.0210884	−	0.0365263i
$518$	−8.28556	−	8.74125i	−0.364047	−	0.384068i
$519$		0			0
$520$	0.0570258	−	12.4132i	0.00250075	−	0.544353i
$521$	22.0369	−	12.7230i	0.965453	−	0.557405i	0.0676060	−	0.997712i	$-0.478464\pi$
$521$	22.0369	−	12.7230i	0.965453	−	0.557405i	0.897847	+	0.440308i	$0.145131\pi$
$522$		0			0
$523$			14.9240i			0.652581i	0.945270	+	0.326290i	$0.105799\pi$
$523$			14.9240i			0.652581i	−0.945270	+	0.326290i	$0.894201\pi$
$524$	−9.28035	+	16.0740i	−0.405414	+	0.702198i
$525$		0			0
$526$	−12.6783	−	47.3160i	−0.552799	−	2.06307i
$527$	2.84771	−	10.6278i	0.124048	−	0.462954i
$528$		0			0
$529$	9.22577			0.401120
$530$	18.5928			0.807621
$531$		0			0
$532$	−5.33370	−	9.83698i	−0.231245	−	0.426487i
$533$	−17.9519	+	4.72190i	−0.777581	+	0.204528i
$534$		0			0
$535$	11.5082	−	3.08361i	0.497542	−	0.133316i
$536$	−11.3990	+	19.7437i	−0.492363	+	0.852797i
$537$		0			0
$538$	21.4937	+	21.4937i	0.926658	+	0.926658i
$539$	5.24680	+	24.8250i	0.225996	+	1.06929i
$540$		0			0
$541$	−11.1755	+	2.99446i	−0.480471	+	0.128742i	−0.490922	−	0.871204i	$-0.663340\pi$
$541$	−11.1755	+	2.99446i	−0.480471	+	0.128742i	0.0104509	+	0.999945i	$0.496673\pi$
$542$		−	14.3579i		−	0.616726i
$543$		0			0
$544$	5.63586	−	5.63586i	0.241636	−	0.241636i
$545$	1.04228			0.0446463
$546$		0			0
$547$	−1.37820			−0.0589275			−0.0294637	−	0.999566i	$-0.509380\pi$
$547$	−1.37820			−0.0589275			−0.0294637	+	0.999566i	$0.509380\pi$
$548$	14.5558	−	14.5558i	0.621791	−	0.621791i
$549$		0			0
$550$			5.64356i			0.240642i
$551$	−14.7429	+	3.95034i	−0.628068	+	0.168290i
$552$		0			0
$553$	41.6725	−	9.97927i	1.77209	−	0.424362i
$554$	−25.3701	−	25.3701i	−1.07787	−	1.07787i
$555$		0			0
$556$	−10.4845	+	18.1597i	−0.444642	+	0.770143i
$557$	28.5094	−	7.63906i	1.20798	−	0.323677i	0.402011	−	0.915635i	$-0.368311\pi$
$557$	28.5094	−	7.63906i	1.20798	−	0.323677i	0.805969	+	0.591958i	$0.201645\pi$
$558$		0			0
$559$	−0.0863000	+	18.7855i	−0.00365010	+	0.794540i
$560$	−22.8410	−	14.0151i	−0.965208	−	0.592246i
$561$		0			0
$562$	−9.10488			−0.384066
$563$	34.8266			1.46776			0.733882	−	0.679277i	$-0.237706\pi$
$563$	34.8266			1.46776			0.733882	+	0.679277i	$0.237706\pi$
$564$		0			0
$565$	−4.07335	+	15.2019i	−0.171367	+	0.639550i
$566$	−0.379749	−	1.41724i	−0.0159620	−	0.0595712i
$567$		0			0
$568$	10.2230	−	17.7068i	0.428949	−	0.742962i
$569$		−	39.0510i		−	1.63711i	−0.574432	−	0.818553i	$-0.694777\pi$
$569$		−	39.0510i		−	1.63711i	0.574432	−	0.818553i	$-0.305223\pi$
$570$		0			0
$571$	10.3165	−	5.95625i	0.431733	−	0.249261i	−0.268351	−	0.963321i	$-0.586479\pi$
$571$	10.3165	−	5.95625i	0.431733	−	0.249261i	0.700085	+	0.714060i	$0.253146\pi$
$572$	−9.49294	+	9.40611i	−0.396920	+	0.393289i
$573$		0			0
$574$	−6.73884	+	22.7019i	−0.281274	+	0.947558i
$575$	1.66185	+	2.87840i	0.0693038	+	0.120038i
$576$		0			0
$577$	6.54951	−	24.4431i	0.272660	−	1.01758i	−0.684734	−	0.728793i	$-0.740082\pi$
$577$	6.54951	−	24.4431i	0.272660	−	1.01758i	0.957393	−	0.288787i	$-0.0932518\pi$
$578$	−18.1113	+	18.1113i	−0.753331	+	0.753331i
$579$		0			0
$580$	5.40540	−	5.40540i	0.224447	−	0.224447i
$581$	1.03826	−	38.7949i	0.0430744	−	1.60949i
$582$		0			0
$583$	13.5300	+	13.5300i	0.560355	+	0.560355i
$584$	−2.44287	−	4.23117i	−0.101087	−	0.175087i
$585$		0			0
$586$	25.2881	+	14.6001i	1.04464	+	0.603125i
$587$	0.718902	−	2.68298i	0.0296723	−	0.110738i	−0.949501	−	0.313763i	$-0.898410\pi$
$587$	0.718902	−	2.68298i	0.0296723	−	0.110738i	0.979174	+	0.203024i	$0.0650770\pi$
$588$		0			0
$589$	26.1737	+	15.1114i	1.07847	+	0.622655i
$590$	1.17682	+	4.39194i	0.0484487	+	0.180813i
$591$		0			0
$592$	9.25657	+	9.25657i	0.380443	+	0.380443i
$593$	6.94149	+	25.9060i	0.285053	+	1.06383i	0.948801	+	0.315875i	$0.102298\pi$
$593$	6.94149	+	25.9060i	0.285053	+	1.06383i	−0.663748	+	0.747956i	$0.731035\pi$
$594$		0			0
$595$	−6.87946	−	4.22119i	−0.282030	−	0.173052i
$596$	3.33574	−	12.4492i	0.136637	−	0.509937i
$597$		0			0
$598$	−6.12443	+	22.4437i	−0.250446	+	0.917793i
$599$	12.6948	+	21.9880i	0.518695	+	0.898407i	0.999764	+	0.0217238i	$0.00691543\pi$
$599$	12.6948	+	21.9880i	0.518695	+	0.898407i	−0.481069	+	0.876683i	$0.659751\pi$
$600$		0			0
$601$	27.2508	−	15.7333i	1.11158	−	0.641774i	0.172345	−	0.985037i	$-0.444866\pi$
$601$	27.2508	−	15.7333i	1.11158	−	0.641774i	0.939239	+	0.343263i	$0.111532\pi$
$602$	20.4269	+	12.5338i	0.832537	+	0.510839i
$603$		0			0
$604$	20.8485	+	5.58634i	0.848313	+	0.227305i
$605$	3.06416	−	3.06416i	0.124576	−	0.124576i
$606$		0			0
$607$	−29.0411	+	16.7669i	−1.17874	+	0.680548i	−0.955723	−	0.294266i	$-0.904925\pi$
$607$	−29.0411	+	16.7669i	−1.17874	+	0.680548i	−0.223020	+	0.974814i	$0.571591\pi$
$608$	10.9466	+	18.9601i	0.443945	+	0.768935i
$609$		0			0
$610$			37.3995i			1.51426i
$611$	−0.677614	+	0.671416i	−0.0274133	+	0.0271626i
$612$		0			0
$613$	8.29428	+	30.9547i	0.335003	+	1.25025i	0.903866	+	0.427815i	$0.140717\pi$
$613$	8.29428	+	30.9547i	0.335003	+	1.25025i	−0.568863	+	0.822432i	$0.692617\pi$
$614$			48.7596i			1.96778i
$615$		0			0
$616$	−3.79540	−	15.8492i	−0.152921	−	0.638584i
$617$	−1.63790	−	6.11271i	−0.0659392	−	0.246088i	0.925087	−	0.379755i	$-0.123992\pi$
$617$	−1.63790	−	6.11271i	−0.0659392	−	0.246088i	−0.991026	+	0.133666i	$0.957325\pi$
$618$		0			0
$619$	19.4896	+	5.22223i	0.783355	+	0.209899i	0.628263	−	0.778001i	$-0.283766\pi$
$619$	19.4896	+	5.22223i	0.783355	+	0.209899i	0.155092	+	0.987900i	$0.450433\pi$
$620$	−15.1370			−0.607916
$621$		0			0
$622$	−40.1394	−	10.7553i	−1.60944	−	0.431249i
$623$	26.6184	+	0.712383i	1.06644	+	0.0285410i
$624$		0			0
$625$	−9.86014	+	17.0783i	−0.394406	+	0.683130i
$626$	−41.0933	+	11.0109i	−1.64242	+	0.440085i
$627$		0			0
$628$	1.89333	+	3.27934i	0.0755519	+	0.130860i
$629$	2.78798	+	2.78798i	0.111164	+	0.111164i
$630$		0			0
$631$	−38.8147	+	10.4004i	−1.54519	+	0.414032i	−0.927938	−	0.372735i	$-0.878420\pi$
$631$	−38.8147	+	10.4004i	−1.54519	+	0.414032i	−0.617250	+	0.786767i	$0.711753\pi$
$632$	−26.5852	+	7.12348i	−1.05750	+	0.283357i
$633$		0			0
$634$	−37.4758	−	21.6367i	−1.48835	−	0.859302i
$635$	27.2795	−	27.2795i	1.08256	−	1.08256i
$636$		0			0
$637$	22.5535	−	11.3288i	0.893601	−	0.448862i
$638$	23.2543			0.920647
$639$		0			0
$640$	21.0039	+	12.1266i	0.830251	+	0.479346i
$641$			5.63886i			0.222722i	0.993780	+	0.111361i	$0.0355209\pi$
$641$			5.63886i			0.222722i	−0.993780	+	0.111361i	$0.964479\pi$
$642$		0			0
$643$	6.33945	−	1.69865i	0.250003	−	0.0669882i	−0.131641	−	0.991297i	$-0.542025\pi$
$643$	6.33945	−	1.69865i	0.250003	−	0.0669882i	0.381644	+	0.924309i	$0.375358\pi$
$644$	6.90730	+	7.28719i	0.272186	+	0.287155i
$645$		0			0
$646$	5.41404	+	9.37740i	0.213013	+	0.368949i
$647$	17.6460	−	30.5638i	0.693736	−	1.20159i	−0.276869	−	0.960908i	$-0.589297\pi$
$647$	17.6460	−	30.5638i	0.693736	−	1.20159i	0.970605	−	0.240678i	$-0.0773699\pi$
$648$		0			0
$649$	−2.33964	+	4.05238i	−0.0918389	+	0.159070i
$650$	5.42897	−	1.42799i	0.212942	−	0.0560104i
$651$		0			0
$652$	9.75192	+	2.61302i	0.381914	+	0.102334i
$653$	50.4143			1.97287			0.986433	−	0.164167i	$-0.0524936\pi$
$653$	50.4143			1.97287			0.986433	+	0.164167i	$0.0524936\pi$
$654$		0			0
$655$	−35.5213	−	9.51789i	−1.38793	−	0.371895i
$656$	6.66172	−	24.8619i	0.260097	−	0.970693i
$657$		0			0
$658$	0.283410	+	1.18349i	0.0110485	+	0.0461374i
$659$	−3.05790	+	5.29643i	−0.119119	+	0.206320i	−0.919419	−	0.393280i	$-0.871340\pi$
$659$	−3.05790	+	5.29643i	−0.119119	+	0.206320i	0.800300	+	0.599600i	$0.204674\pi$
$660$		0			0
$661$	1.42133	+	5.30446i	0.0552831	+	0.206320i	0.988043	−	0.154179i	$-0.0492732\pi$
$661$	1.42133	+	5.30446i	0.0552831	+	0.206320i	−0.932760	+	0.360499i	$0.882607\pi$
$662$	−7.43510	+	4.29266i	−0.288974	+	0.166839i
$663$		0			0
$664$			24.9269i			0.967353i
$665$	16.0908	−	15.2520i	0.623974	−	0.591446i
$666$		0			0
$667$	11.8605	−	6.84765i	0.459239	−	0.265142i
$668$	−5.60889	+	20.9326i	−0.217014	+	0.809908i
$669$		0			0
$670$	45.6423	+	12.2298i	1.76331	+	0.472479i
$671$	−27.2155	+	27.2155i	−1.05064	+	1.05064i
$672$		0			0
$673$	19.0175	−	10.9798i	0.733073	−	0.423240i	−0.0864726	−	0.996254i	$-0.527560\pi$
$673$	19.0175	−	10.9798i	0.733073	−	0.423240i	0.819545	+	0.573015i	$0.194226\pi$
$674$	5.37560	+	5.37560i	0.207060	+	0.207060i
$675$		0			0
$676$	11.4505	+	6.75196i	0.440403	+	0.259691i
$677$	−6.64801	−	3.83823i	−0.255504	−	0.147515i	0.366778	−	0.930308i	$-0.380461\pi$
$677$	−6.64801	−	3.83823i	−0.255504	−	0.147515i	−0.622282	+	0.782793i	$0.713794\pi$
$678$		0			0
$679$	1.50807	+	0.925340i	0.0578743	+	0.0355113i
$680$	4.48963	+	2.59209i	0.172170	+	0.0994022i
$681$		0			0
$682$	−32.5601	−	32.5601i	−1.24679	−	1.24679i
$683$	13.2436	+	13.2436i	0.506751	+	0.506751i	0.913528	−	0.406776i	$-0.133347\pi$
$683$	13.2436	+	13.2436i	0.506751	+	0.506751i	−0.406776	+	0.913528i	$0.633347\pi$
$684$		0			0
$685$	35.3208	+	20.3925i	1.34954	+	0.779156i
$686$	2.58176	−	32.0946i	0.0985720	−	1.22538i
$687$		0			0
$688$	−22.5586	−	13.0242i	−0.860037	−	0.496542i
$689$	9.59204	−	16.4390i	0.365428	−	0.626277i
$690$		0			0
$691$	16.0944	+	16.0944i	0.612261	+	0.612261i	0.943535	−	0.331274i	$-0.107478\pi$
$691$	16.0944	+	16.0944i	0.612261	+	0.612261i	−0.331274	+	0.943535i	$0.607478\pi$
$692$	11.7870	−	6.80523i	0.448074	−	0.258696i
$693$		0			0
$694$	−33.5411	+	33.5411i	−1.27320	+	1.27320i
$695$	−40.1302	−	10.7529i	−1.52223	−	0.407880i
$696$		0			0
$697$	2.00644	−	7.48813i	0.0759993	−	0.283633i
$698$	−6.99334	+	4.03760i	−0.264702	+	0.152826i
$699$		0			0
$700$	0.689445	−	2.32261i	0.0260586	−	0.0877864i
$701$			27.1008i			1.02358i	0.859110	+	0.511791i	$0.171018\pi$
$701$			27.1008i			1.02358i	−0.859110	+	0.511791i	$0.828982\pi$
$702$		0			0
$703$	−9.37931	+	5.41515i	−0.353747	+	0.204236i
$704$	0.747431	+	2.78945i	0.0281699	+	0.105131i
$705$		0			0
$706$	3.64672	−	6.31631i	0.137246	−	0.237717i
$707$	18.6599	−	4.46847i	0.701778	−	0.168054i
$708$		0			0
$709$	6.14500	−	22.9335i	0.230780	−	0.861284i	−0.749225	−	0.662315i	$-0.769574\pi$
$709$	6.14500	−	22.9335i	0.230780	−	0.861284i	0.980006	−	0.198969i	$-0.0637594\pi$
$710$	−40.9336	−	10.9681i	−1.53621	−	0.411627i
$711$		0			0
$712$	−17.1031			−0.640967
$713$	−26.1946	−	7.01882i	−0.980996	−	0.262857i
$714$		0			0
$715$	−22.8693	−	13.3440i	−0.855262	−	0.499039i
$716$	−2.38626	+	4.13313i	−0.0891788	+	0.154462i
$717$		0			0
$718$	−6.19674	+	10.7331i	−0.231260	+	0.400554i
$719$	7.10279	+	12.3024i	0.264890	+	0.458802i	0.967535	−	0.252738i	$-0.0813312\pi$
$719$	7.10279	+	12.3024i	0.264890	+	0.458802i	−0.702645	+	0.711540i	$0.747998\pi$
$720$		0			0
$721$	−37.2287	+	8.91513i	−1.38647	+	0.332017i
$722$	3.17708	−	0.851296i	0.118239	−	0.0316819i
$723$		0			0
$724$		−	1.75913i		−	0.0653775i
$725$	−2.86191	−	1.65232i	−0.106289	−	0.0613657i
$726$		0			0
$727$	30.9551			1.14806			0.574030	−	0.818834i	$-0.305379\pi$
$727$	30.9551			1.14806			0.574030	+	0.818834i	$0.305379\pi$
$728$	−14.2863	+	7.66143i	−0.529484	+	0.283951i
$729$		0			0
$730$	−7.16046	+	7.16046i	−0.265021	+	0.265021i
$731$	−6.79439	−	3.92274i	−0.251300	−	0.145088i
$732$		0			0
$733$	−10.4520	+	2.80061i	−0.386054	+	0.103443i	−0.446626	−	0.894721i	$-0.647374\pi$
$733$	−10.4520	+	2.80061i	−0.386054	+	0.103443i	0.0605714	+	0.998164i	$0.480708\pi$
$734$	5.22752	−	1.40071i	0.192951	−	0.0517011i
$735$		0			0
$736$	−13.8908	−	13.8908i	−0.512023	−	0.512023i
$737$	24.3142	+	42.1135i	0.895626	+	1.55127i
$738$		0			0
$739$	28.1179	−	7.53418i	1.03433	−	0.277149i	0.298571	−	0.954387i	$-0.403490\pi$
$739$	28.1179	−	7.53418i	1.03433	−	0.277149i	0.735764	+	0.677238i	$0.236823\pi$
$740$	2.71216	−	4.69759i	0.0997008	−	0.172687i
$741$		0			0
$742$	−11.5736	−	21.3452i	−0.424880	−	0.783608i
$743$	−50.7369	−	13.5949i	−1.86135	−	0.498749i	−0.861397	−	0.507932i	$-0.830410\pi$
$743$	−50.7369	−	13.5949i	−1.86135	−	0.498749i	−0.999958	+	0.00918346i	$0.997077\pi$
$744$		0			0
$745$	25.5356			0.935552
$746$	−20.5103	−	5.49572i	−0.750935	−	0.201213i
$747$		0			0
$748$	−1.44451	−	5.39097i	−0.0528164	−	0.197113i
$749$	−10.7037	−	11.2923i	−0.391103	−	0.412613i
$750$		0			0
$751$		−	42.8386i		−	1.56320i	−0.623779	−	0.781600i	$-0.714404\pi$
$751$		−	42.8386i		−	1.56320i	0.623779	−	0.781600i	$-0.285596\pi$
$752$	−0.342343	−	1.27764i	−0.0124840	−	0.0465908i
$753$		0			0
$754$	−5.88405	−	22.3701i	−0.214284	−	0.814672i
$755$			42.7643i			1.55635i
$756$		0			0
$757$	−3.86571	−	6.69561i	−0.140502	−	0.243356i	0.787184	−	0.616718i	$-0.211538\pi$
$757$	−3.86571	−	6.69561i	−0.140502	−	0.243356i	−0.927686	+	0.373362i	$0.878205\pi$
$758$	−38.5775	+	22.2727i	−1.40120	+	0.808982i
$759$		0			0
$760$	−10.0693	+	10.0693i	−0.365253	+	0.365253i
$761$	20.4285	+	5.47379i	0.740531	+	0.198425i	0.609314	−	0.792929i	$-0.291445\pi$
$761$	20.4285	+	5.47379i	0.740531	+	0.198425i	0.131217	+	0.991354i	$0.458112\pi$
$762$		0			0
$763$	−0.648793	−	1.19657i	−0.0234879	−	0.0433188i
$764$	8.60445	−	4.96778i	0.311298	−	0.179728i
$765$		0			0
$766$	−31.4055	−	54.3960i	−1.13473	−	1.96541i
$767$	4.49029	+	1.22531i	0.162135	+	0.0442433i
$768$		0			0
$769$	−8.37135	+	31.2423i	−0.301879	+	1.12663i	0.633720	+	0.773562i	$0.281527\pi$
$769$	−8.37135	+	31.2423i	−0.301879	+	1.12663i	−0.935599	+	0.353064i	$0.885140\pi$
$770$	−29.6946	+	16.1007i	−1.07012	+	0.580228i
$771$		0			0
$772$	−1.95325	−	7.28962i	−0.0702989	−	0.262359i
$773$	31.6179	+	31.6179i	1.13722	+	1.13722i	0.988947	+	0.148269i	$0.0473703\pi$
$773$	31.6179	+	31.6179i	1.13722	+	1.13722i	0.148269	+	0.988947i	$0.452630\pi$
$774$		0			0
$775$	1.69363	+	6.32070i	0.0608369	+	0.227046i
$776$	−0.984186	−	0.568220i	−0.0353302	−	0.0203979i
$777$		0			0
$778$	−5.46986	+	20.4138i	−0.196104	+	0.731870i
$779$	18.4415	+	10.6472i	0.660735	+	0.381475i
$780$		0			0
$781$	−21.8059	−	37.7688i	−0.780275	−	1.35148i
$782$	−6.87020	−	6.87020i	−0.245678	−	0.245678i
$783$		0			0
$784$	−1.87187	+	34.9463i	−0.0668524	+	1.24808i
$785$	−5.30506	+	5.30506i	−0.189346	+	0.189346i
$786$		0			0
$787$	−5.32189	+	5.32189i	−0.189705	+	0.189705i	−0.795569	−	0.605864i	$-0.792828\pi$
$787$	−5.32189	+	5.32189i	−0.189705	+	0.189705i	0.605864	+	0.795569i	$0.292828\pi$
$788$	−0.137763	+	0.514139i	−0.00490761	+	0.0183154i
$789$		0			0
$790$	28.5228	+	49.4029i	1.01480	+	1.75768i
$791$	19.9879	−	4.78649i	0.710689	−	0.170188i
$792$		0			0
$793$	33.0671	+	19.2944i	1.17425	+	0.685164i
$794$	−22.4711	+	12.9737i	−0.797468	+	0.460418i
$795$		0			0
$796$		−	16.0369i		−	0.568414i
$797$	5.44428	−	9.42978i	0.192846	−	0.334020i	−0.753346	−	0.657624i	$-0.771561\pi$
$797$	5.44428	−	9.42978i	0.192846	−	0.334020i	0.946192	+	0.323605i	$0.104895\pi$
$798$		0			0
$799$	−0.103110	−	0.384812i	−0.00364777	−	0.0136137i
$800$	−1.22686	+	4.57869i	−0.0433759	+	0.161881i
$801$		0			0
$802$	−7.77132			−0.274415
$803$	−10.4213			−0.367761
$804$		0			0
$805$	−10.4041	+	16.9560i	−0.366696	+	0.597620i
$806$	−23.0834	+	39.5607i	−0.813077	+	1.39347i
$807$		0			0
$808$	−11.9042	+	3.18972i	−0.418788	+	0.112214i
$809$	4.19351	−	7.26337i	0.147436	−	0.255366i	−0.782843	−	0.622219i	$-0.786231\pi$
$809$	4.19351	−	7.26337i	0.147436	−	0.255366i	0.930279	+	0.366853i	$0.119565\pi$
$810$		0			0
$811$	−24.6534	−	24.6534i	−0.865699	−	0.865699i	0.126294	−	0.991993i	$-0.459692\pi$
$811$	−24.6534	−	24.6534i	−0.865699	−	0.865699i	−0.991993	+	0.126294i	$0.959692\pi$
$812$	−9.57033	−	2.84086i	−0.335853	−	0.0996948i
$813$		0			0
$814$	15.9386	−	4.27072i	0.558646	−	0.149689i
$815$			20.0031i			0.700676i
$816$		0			0
$817$	15.2384	−	15.2384i	0.533126	−	0.533126i
$818$	0.962843			0.0336650
$819$		0			0
$820$	−10.6652			−0.372446
$821$	4.43825	−	4.43825i	0.154896	−	0.154896i	−0.625405	−	0.780301i	$-0.715066\pi$
$821$	4.43825	−	4.43825i	0.154896	−	0.154896i	0.780301	+	0.625405i	$0.215066\pi$
$822$		0			0
$823$			25.2689i			0.880818i	0.897797	+	0.440409i	$0.145167\pi$
$823$			25.2689i			0.880818i	−0.897797	+	0.440409i	$0.854833\pi$
$824$	23.7503	−	6.36387i	0.827380	−	0.221696i
$825$		0			0
$826$	4.30956	−	4.08490i	0.149949	−	0.142132i
$827$	−34.6333	−	34.6333i	−1.20432	−	1.20432i	−0.972840	−	0.231479i	$-0.925644\pi$
$827$	−34.6333	−	34.6333i	−1.20432	−	1.20432i	−0.231479	−	0.972840i	$-0.574356\pi$
$828$		0			0
$829$	−11.7777	+	20.3995i	−0.409056	+	0.708505i	−0.994784	−	0.102002i	$-0.967475\pi$
$829$	−11.7777	+	20.3995i	−0.409056	+	0.708505i	0.585729	+	0.810507i	$0.300808\pi$
$830$	49.9044	−	13.3718i	1.73221	−	0.464143i
$831$		0			0
$832$	2.49427	−	1.42483i	0.0864732	−	0.0493970i
$833$	−0.563786	+	10.5255i	−0.0195340	+	0.364686i
$834$		0			0
$835$	−42.9369			−1.48589
$836$	15.3306			0.530219
$837$		0			0
$838$	10.4634	−	39.0500i	0.361453	−	1.34896i
$839$	−1.73270	−	6.46654i	−0.0598196	−	0.223250i	0.929545	−	0.368710i	$-0.120200\pi$
$839$	−1.73270	−	6.46654i	−0.0598196	−	0.223250i	−0.989364	+	0.145460i	$0.953534\pi$
$840$		0			0
$841$	7.69160	−	13.3222i	0.265227	−	0.459387i
$842$			46.8465i			1.61444i
$843$		0			0
$844$	−4.58377	+	2.64644i	−0.157780	+	0.0910943i
$845$	−7.05004	+	25.3762i	−0.242529	+	0.872967i
$846$		0			0
$847$	−5.42514	−	1.61040i	−0.186410	−	0.0553341i
$848$	13.1956	+	22.8554i	0.453137	+	0.784857i
$849$		0			0
$850$	−0.606784	+	2.26455i	−0.0208125	+	0.0776734i
$851$	6.87160	−	6.87160i	0.235555	−	0.235555i
$852$		0			0
$853$	−12.3363	+	12.3363i	−0.422386	+	0.422386i	−0.886025	−	0.463638i	$-0.846544\pi$
$853$	−12.3363	+	12.3363i	−0.422386	+	0.422386i	0.463638	+	0.886025i	$0.346544\pi$
$854$	42.9359	−	23.2803i	1.46924	−	0.796634i
$855$		0			0
$856$	7.06655	+	7.06655i	0.241530	+	0.241530i
$857$	−11.7995	−	20.4373i	−0.403062	−	0.698123i	0.591032	−	0.806648i	$-0.298721\pi$
$857$	−11.7995	−	20.4373i	−0.403062	−	0.698123i	−0.994094	+	0.108525i	$0.965387\pi$
$858$		0			0
$859$	8.42384	+	4.86350i	0.287418	+	0.165941i	0.636777	−	0.771048i	$-0.280267\pi$
$859$	8.42384	+	4.86350i	0.287418	+	0.165941i	−0.349359	+	0.936989i	$0.613601\pi$
$860$	−2.79355	+	10.4257i	−0.0952592	+	0.355512i
$861$		0			0
$862$	30.8269	+	17.7979i	1.04997	+	0.606200i
$863$	11.3423	+	42.3300i	0.386096	+	1.44093i	0.836431	+	0.548072i	$0.184638\pi$
$863$	11.3423	+	42.3300i	0.386096	+	1.44093i	−0.450335	+	0.892860i	$0.648695\pi$
$864$		0			0
$865$	19.0681	+	19.0681i	0.648335	+	0.648335i
$866$	12.4175	+	46.3429i	0.421965	+	1.57480i
$867$		0			0
$868$	9.42242	+	17.3778i	0.319818	+	0.589842i
$869$	−15.1944	+	56.7065i	−0.515436	+	1.92363i
$870$		0			0
$871$	34.3600	−	34.0457i	1.16424	−	1.15359i
$872$	0.437132	+	0.757135i	0.0148032	+	0.0256398i
$873$		0			0
$874$	23.1127	−	13.3441i	0.781799	−	0.451372i
$875$	31.5897	+	0.845429i	1.06793	+	0.0285807i
$876$		0			0
$877$	−44.4001	−	11.8970i	−1.49928	−	0.401732i	−0.586424	−	0.810004i	$-0.699465\pi$
$877$	−44.4001	−	11.8970i	−1.49928	−	0.401732i	−0.912860	+	0.408272i	$0.866132\pi$
$878$	−22.1957	+	22.1957i	−0.749069	+	0.749069i
$879$		0			0
$880$	31.7954	−	18.3571i	1.07182	−	0.618817i
$881$	−0.277040	−	0.479848i	−0.00933373	−	0.0161665i	0.861321	−	0.508061i	$-0.169638\pi$
$881$	−0.277040	−	0.479848i	−0.00933373	−	0.0161665i	−0.870655	+	0.491895i	$0.836304\pi$
$882$		0			0
$883$			21.2142i			0.713914i	0.934121	+	0.356957i	$0.116186\pi$
$883$			21.2142i			0.713914i	−0.934121	+	0.356957i	$0.883814\pi$
$884$	−4.82049	+	2.75366i	−0.162131	+	0.0926156i
$885$		0			0
$886$	−17.5849	−	65.6277i	−0.590776	−	2.20481i
$887$			30.6428i			1.02888i	0.857525	+	0.514442i	$0.172001\pi$
$887$			30.6428i			1.02888i	−0.857525	+	0.514442i	$0.827999\pi$
$888$		0			0
$889$	−48.2988	−	14.3370i	−1.61989	−	0.480849i
$890$	9.17482	+	34.2409i	0.307541	+	1.14776i
$891$		0			0
$892$	−12.4157	−	3.32677i	−0.415708	−	0.111389i
$893$	1.09431			0.0366197
$894$		0			0
$895$	−9.13360	−	2.44734i	−0.305303	−	0.0818056i
$896$	0.847357	−	31.6617i	0.0283082	−	1.05774i
$897$		0			0
$898$	−19.6413	+	34.0198i	−0.655439	+	1.13525i
$899$	26.0445	−	6.97860i	0.868632	−	0.232749i
$900$		0			0
$901$	3.97436	+	6.88379i	0.132405	+	0.229332i
$902$	−22.9411	−	22.9411i	−0.763857	−	0.763857i
$903$		0			0
$904$	−12.7514	+	3.41673i	−0.424106	+	0.113639i
$905$	3.36660	−	0.902078i	0.111910	−	0.0299861i
$906$		0			0
$907$	−8.08859	−	4.66995i	−0.268577	−	0.155063i	0.359664	−	0.933082i	$-0.382891\pi$
$907$	−8.08859	−	4.66995i	−0.268577	−	0.155063i	−0.628241	+	0.778019i	$0.716225\pi$
$908$	−4.75898	+	4.75898i	−0.157932	+	0.157932i
$909$		0			0
$910$	23.0021	+	24.4915i	0.762513	+	0.811887i
$911$	23.5831			0.781342			0.390671	−	0.920530i	$-0.372243\pi$
$911$	23.5831			0.781342			0.390671	+	0.920530i	$0.372243\pi$
$912$		0			0
$913$	46.0461	+	26.5847i	1.52390	+	0.879825i
$914$		−	34.1583i		−	1.12985i
$915$		0			0
$916$	−9.03320	+	2.42044i	−0.298465	+	0.0799735i
$917$	11.1843	+	46.7044i	0.369337	+	1.54231i
$918$		0			0
$919$	−0.985346	−	1.70667i	−0.0325036	−	0.0562978i	0.849316	−	0.527885i	$-0.177015\pi$
$919$	−0.985346	−	1.70667i	−0.0325036	−	0.0562978i	−0.881820	+	0.471587i	$0.843681\pi$
$920$	6.38879	−	11.0657i	0.210632	−	0.364826i
$921$		0			0
$922$	−12.8989	+	22.3415i	−0.424802	+	0.735779i
$923$	−30.8152	+	30.5334i	−1.01430	+	1.00502i
$924$		0			0
$925$	−2.26501	−	0.606908i	−0.0744731	−	0.0199550i
$926$	−53.2953			−1.75139
$927$		0			0
$928$	18.8665	+	5.05527i	0.619323	+	0.165947i
$929$	−15.2849	+	57.0441i	−0.501482	+	1.87156i	−0.0112985	+	0.999936i	$0.503597\pi$
$929$	−15.2849	+	57.0441i	−0.501482	+	1.87156i	−0.490183	+	0.871619i	$0.663070\pi$
$930$		0			0
$931$	−27.5259	−	8.97882i	−0.902126	−	0.294269i
$932$	−3.93183	+	6.81013i	−0.128791	+	0.223073i
$933$		0			0
$934$	−9.54879	−	35.6366i	−0.312446	−	1.16606i
$935$	9.57643	−	5.52896i	0.313183	−	0.180816i
$936$		0			0
$937$			49.8381i			1.62814i	0.580767	+	0.814070i	$0.302753\pi$
$937$			49.8381i			1.62814i	−0.580767	+	0.814070i	$0.697247\pi$
$938$	−14.3710	−	60.0117i	−0.469228	−	1.95945i
$939$		0			0
$940$	−0.474652	+	0.274041i	−0.0154815	+	0.00893822i
$941$	3.26950	−	12.2019i	0.106583	−	0.397771i	−0.891937	−	0.452159i	$-0.850654\pi$
$941$	3.26950	−	12.2019i	0.106583	−	0.397771i	0.998520	+	0.0543875i	$0.0173206\pi$
$942$		0			0
$943$	−18.4562	−	4.94532i	−0.601016	−	0.161042i
$944$	−4.56362	+	4.56362i	−0.148533	+	0.148533i
$945$		0			0
$946$	−28.4349	+	16.4169i	−0.924497	+	0.533759i
$947$	−22.5249	−	22.5249i	−0.731962	−	0.731962i	0.239046	−	0.971008i	$-0.423165\pi$
$947$	−22.5249	−	22.5249i	−0.731962	−	0.731962i	−0.971008	+	0.239046i	$0.923165\pi$
$948$		0			0
$949$	2.63691	+	10.0251i	0.0855978	+	0.325428i
$950$	−5.57705	−	3.21991i	−0.180943	−	0.104468i
$951$		0			0
$952$	0.181125	−	6.76778i	0.00587029	−	0.219345i
$953$	−30.8939	−	17.8366i	−1.00075	−	0.577784i	−0.0922803	−	0.995733i	$-0.529416\pi$
$953$	−30.8939	−	17.8366i	−1.00075	−	0.577784i	−0.908470	+	0.417949i	$0.862749\pi$
$954$		0			0
$955$	13.9196	+	13.9196i	0.450429	+	0.450429i
$956$	−14.8248	−	14.8248i	−0.479469	−	0.479469i
$957$		0			0
$958$	16.1046	+	9.29802i	0.520318	+	0.300405i
$959$	1.42494	−	53.2434i	0.0460138	−	1.71932i
$960$		0			0
$961$	−19.3912	−	11.1955i	−0.625524	−	0.361146i
$962$	−8.14128	−	14.2519i	−0.262485	−	0.459500i
$963$		0			0
$964$	−7.20901	−	7.20901i	−0.232187	−	0.232187i
$965$	12.9492	−	7.47620i	0.416848	−	0.240667i
$966$		0			0
$967$	23.3410	−	23.3410i	0.750597	−	0.750597i	−0.223994	−	0.974591i	$-0.571910\pi$
$967$	23.3410	−	23.3410i	0.750597	−	0.750597i	0.974591	+	0.223994i	$0.0719096\pi$
$968$	3.51100	+	0.940768i	0.112848	+	0.0302374i
$969$		0			0
$970$	−0.609633	+	2.27518i	−0.0195741	+	0.0730517i
$971$	−8.62278	+	4.97836i	−0.276718	+	0.159763i	−0.631937	−	0.775020i	$-0.717740\pi$
$971$	−8.62278	+	4.97836i	−0.276718	+	0.159763i	0.355219	+	0.934783i	$0.384406\pi$
$972$		0			0
$973$	12.6354	+	52.7644i	0.405074	+	1.69155i
$974$		−	55.5239i		−	1.77910i
$975$		0			0
$976$	−45.9736	+	26.5429i	−1.47158	+	0.849616i
$977$	−4.08620	−	15.2499i	−0.130729	−	0.487887i	0.869250	−	0.494373i	$-0.164602\pi$
$977$	−4.08620	−	15.2499i	−0.130729	−	0.487887i	−0.999979	+	0.00648549i	$0.997936\pi$
$978$		0			0
$979$	−18.2406	+	31.5936i	−0.582971	+	1.00974i
$980$	14.1878	−	2.99861i	0.453212	−	0.0957871i
$981$		0			0
$982$	−3.81281	+	14.2296i	−0.121672	+	0.454084i
$983$	1.62207	+	0.434633i	0.0517361	+	0.0138626i	0.284594	−	0.958648i	$-0.408141\pi$
$983$	1.62207	+	0.434633i	0.0517361	+	0.0138626i	−0.232858	+	0.972511i	$0.574808\pi$
$984$		0			0
$985$	−1.05460			−0.0336023
$986$	9.33109	+	2.50026i	0.297162	+	0.0796244i
$987$		0			0
$988$	−3.87910	−	14.7477i	−0.123411	−	0.469186i
$989$	−9.66848	+	16.7463i	−0.307440	+	0.532502i
$990$		0			0
$991$	8.18227	−	14.1721i	0.259918	−	0.450192i	−0.706302	−	0.707911i	$-0.749638\pi$
$991$	8.18227	−	14.1721i	0.259918	−	0.450192i	0.966220	+	0.257719i	$0.0829710\pi$
$992$	−19.3381	−	33.4946i	−0.613986	−	1.06346i
$993$		0			0
$994$	12.8884	+	53.8207i	0.408795	+	1.70709i
$995$	30.6913	−	8.22370i	0.972979	−	0.260709i
$996$		0			0
$997$			18.9696i			0.600774i	0.953817	+	0.300387i	$0.0971158\pi$
$997$			18.9696i			0.600774i	−0.953817	+	0.300387i	$0.902884\pi$
$998$	38.1237	+	22.0107i	1.20678	+	0.696737i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.d.145.8		40
3.2	odd	2		273.2.bt.b.145.3	✓	40
7.3	odd	6		819.2.gh.d.262.8		40
13.7	odd	12		819.2.gh.d.397.8		40
21.17	even	6		273.2.cg.b.262.3	yes	40
39.20	even	12		273.2.cg.b.124.3	yes	40
91.59	even	12	inner	819.2.et.d.514.8		40
273.59	odd	12		273.2.bt.b.241.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.3	✓	40	3.2	odd	2
273.2.bt.b.241.3	yes	40	273.59	odd	12
273.2.cg.b.124.3	yes	40	39.20	even	12
273.2.cg.b.262.3	yes	40	21.17	even	6
819.2.et.d.145.8		40	1.1	even	1	trivial
819.2.et.d.514.8		40	91.59	even	12	inner
819.2.gh.d.262.8		40	7.3	odd	6
819.2.gh.d.397.8		40	13.7	odd	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22934 - 1.22934i) q^{2} -1.02253i q^{4} +(1.95691 - 0.524353i) q^{5} +(-1.82011 - 1.92021i) q^{7} +(1.20163 + 1.20163i) q^{8} +O(q^{10})\)	\(q+(1.22934 - 1.22934i) q^{2} -1.02253i q^{4} +(1.95691 - 0.524353i) q^{5} +(-1.82011 - 1.92021i) q^{7} +(1.20163 + 1.20163i) q^{8} +(1.76110 - 3.05031i) q^{10} +(3.50126 - 0.938159i) q^{11} +(-1.78841 - 3.13075i) q^{13} +(-4.59811 - 0.123058i) q^{14} +4.99949 q^{16} +1.50579 q^{17} +(-1.07053 + 3.99526i) q^{19} +(-0.536169 - 2.00101i) q^{20} +(3.15091 - 5.45753i) q^{22} -3.71137i q^{23} +(-0.775564 + 0.447772i) q^{25} +(-6.04730 - 1.65018i) q^{26} +(-1.96348 + 1.86112i) q^{28} +(1.84505 + 3.19572i) q^{29} +(1.89117 - 7.05794i) q^{31} +(3.74279 - 3.74279i) q^{32} +(1.85112 - 1.85112i) q^{34} +(-4.56866 - 2.80330i) q^{35} +(1.85150 + 1.85150i) q^{37} +(3.59548 + 6.22755i) q^{38} +(2.98158 + 1.72141i) q^{40} +(1.33248 - 4.97288i) q^{41} +(-4.51217 - 2.60510i) q^{43} +(-0.959299 - 3.58015i) q^{44} +(-4.56251 - 4.56251i) q^{46} +(-0.0684756 - 0.255554i) q^{47} +(-0.374411 + 6.98998i) q^{49} +(-0.402966 + 1.50389i) q^{50} +(-3.20130 + 1.82871i) q^{52} +(2.63938 + 4.57154i) q^{53} +(6.35973 - 3.67179i) q^{55} +(0.120285 - 4.49450i) q^{56} +(6.19679 + 1.66043i) q^{58} +(-0.912817 + 0.912817i) q^{59} +(-9.19565 + 5.30911i) q^{61} +(-6.35170 - 11.0015i) q^{62} +0.796700i q^{64} +(-5.14139 - 5.18884i) q^{65} +(3.47221 + 12.9585i) q^{67} -1.53972i q^{68} +(-9.06262 + 2.17022i) q^{70} +(-3.11400 - 11.6216i) q^{71} +(-2.77707 - 0.744113i) q^{73} +4.55224 q^{74} +(4.08528 + 1.09465i) q^{76} +(-8.17413 - 5.01560i) q^{77} +(-8.09801 + 14.0262i) q^{79} +(9.78357 - 2.62150i) q^{80} +(-4.47528 - 7.75141i) q^{82} +(10.3721 + 10.3721i) q^{83} +(2.94671 - 0.789567i) q^{85} +(-8.74952 + 2.34443i) q^{86} +(5.33456 + 3.07991i) q^{88} +(-7.11661 + 7.11661i) q^{89} +(-2.75659 + 9.13243i) q^{91} -3.79500 q^{92} +(-0.398342 - 0.229983i) q^{94} +8.37970i q^{95} +(-0.645956 + 0.173083i) q^{97} +(8.13276 + 9.05331i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{7}+O(q^{10}) \) 40 * q - 2 * q^7	\( 40 q - 2 q^{7} + 8 q^{11} + 18 q^{14} - 64 q^{16} - 8 q^{17} - 14 q^{19} + 14 q^{20} + 4 q^{22} - 24 q^{25} + 10 q^{26} - 2 q^{28} - 8 q^{29} - 8 q^{31} - 10 q^{32} + 24 q^{34} + 22 q^{35} + 12 q^{37} - 8 q^{38} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 28 q^{44} + 40 q^{46} - 10 q^{47} + 38 q^{49} + 20 q^{50} + 40 q^{52} + 8 q^{53} + 42 q^{55} - 20 q^{56} - 48 q^{58} + 26 q^{59} - 12 q^{61} + 24 q^{62} + 44 q^{65} + 46 q^{67} + 32 q^{70} + 6 q^{71} + 10 q^{73} - 40 q^{74} + 64 q^{76} + 24 q^{77} - 34 q^{80} + 24 q^{82} - 12 q^{83} + 2 q^{85} - 12 q^{86} - 84 q^{88} + 16 q^{89} + 26 q^{91} - 236 q^{92} + 30 q^{94} + 62 q^{97} + 14 q^{98}+O(q^{100}) \) 40 * q - 2 * q^7 + 8 * q^11 + 18 * q^14 - 64 * q^16 - 8 * q^17 - 14 * q^19 + 14 * q^20 + 4 * q^22 - 24 * q^25 + 10 * q^26 - 2 * q^28 - 8 * q^29 - 8 * q^31 - 10 * q^32 + 24 * q^34 + 22 * q^35 + 12 * q^37 - 8 * q^38 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 28 * q^44 + 40 * q^46 - 10 * q^47 + 38 * q^49 + 20 * q^50 + 40 * q^52 + 8 * q^53 + 42 * q^55 - 20 * q^56 - 48 * q^58 + 26 * q^59 - 12 * q^61 + 24 * q^62 + 44 * q^65 + 46 * q^67 + 32 * q^70 + 6 * q^71 + 10 * q^73 - 40 * q^74 + 64 * q^76 + 24 * q^77 - 34 * q^80 + 24 * q^82 - 12 * q^83 + 2 * q^85 - 12 * q^86 - 84 * q^88 + 16 * q^89 + 26 * q^91 - 236 * q^92 + 30 * q^94 + 62 * q^97 + 14 * q^98

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