LMFDB - Embedded newform 819.2.et.c.271.5

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:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.5
Character	$\chi$	$=$	819.271
Dual form			819.2.et.c.136.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.374685 - 0.374685i) q^{2} -1.71922i q^{4} +(0.545981 + 2.03763i) q^{5} +(-2.03549 - 1.69021i) q^{7} +(-1.39354 + 1.39354i) q^{8} +O(q^{10})$	\(q+(-0.374685 - 0.374685i) q^{2} -1.71922i q^{4} +(0.545981 + 2.03763i) q^{5} +(-2.03549 - 1.69021i) q^{7} +(-1.39354 + 1.39354i) q^{8} +(0.558898 - 0.968040i) q^{10} +(0.745933 + 2.78386i) q^{11} +(2.80107 + 2.27024i) q^{13} +(0.129371 + 1.39596i) q^{14} -2.39417 q^{16} +3.29760 q^{17} +(6.53354 + 1.75066i) q^{19} +(3.50314 - 0.938663i) q^{20} +(0.763581 - 1.32256i) q^{22} -7.84515i q^{23} +(0.476290 - 0.274986i) q^{25} +(-0.198893 - 1.90015i) q^{26} +(-2.90584 + 3.49945i) q^{28} +(-0.677462 - 1.17340i) q^{29} +(6.38499 + 1.71085i) q^{31} +(3.68413 + 3.68413i) q^{32} +(-1.23556 - 1.23556i) q^{34} +(2.33268 - 5.07039i) q^{35} +(2.87856 - 2.87856i) q^{37} +(-1.79207 - 3.10396i) q^{38} +(-3.60036 - 2.07867i) q^{40} +(-6.61712 - 1.77305i) q^{41} +(-4.36301 - 2.51899i) q^{43} +(4.78608 - 1.28243i) q^{44} +(-2.93946 + 2.93946i) q^{46} +(3.53471 - 0.947124i) q^{47} +(1.28640 + 6.88078i) q^{49} +(-0.281492 - 0.0754255i) q^{50} +(3.90305 - 4.81566i) q^{52} +(3.87961 + 6.71968i) q^{53} +(-5.26521 + 3.03987i) q^{55} +(5.19189 - 0.481159i) q^{56} +(-0.185820 + 0.693490i) q^{58} +(2.01369 + 2.01369i) q^{59} +(-3.14962 + 1.81843i) q^{61} +(-1.75133 - 3.03339i) q^{62} +2.02756i q^{64} +(-3.09658 + 6.94705i) q^{65} +(1.82619 - 0.489326i) q^{67} -5.66931i q^{68} +(-2.77382 + 1.02578i) q^{70} +(9.87427 - 2.64580i) q^{71} +(1.82296 - 6.80337i) q^{73} -2.15710 q^{74} +(3.00977 - 11.2326i) q^{76} +(3.18696 - 6.92729i) q^{77} +(-1.13108 + 1.95909i) q^{79} +(-1.30717 - 4.87843i) q^{80} +(1.81500 + 3.14367i) q^{82} +(3.97225 - 3.97225i) q^{83} +(1.80043 + 6.71929i) q^{85} +(0.690929 + 2.57858i) q^{86} +(-4.91890 - 2.83993i) q^{88} +(-8.73455 - 8.73455i) q^{89} +(-1.86436 - 9.35543i) q^{91} -13.4876 q^{92} +(-1.67928 - 0.969531i) q^{94} +14.2688i q^{95} +(3.94107 + 14.7083i) q^{97} +(2.09613 - 3.06012i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.374685	−	0.374685i	−0.264942	−	0.264942i	0.562116	−	0.827058i	$-0.309987\pi$
$2$	−0.374685	−	0.374685i	−0.264942	−	0.264942i	−0.827058	+	0.562116i	$0.809987\pi$
$3$		0			0
$3$		0			0
$4$		−	1.71922i		−	0.859611i
$5$	0.545981	+	2.03763i	0.244170	+	0.911255i	0.973799	+	0.227412i	$0.0730263\pi$
$5$	0.545981	+	2.03763i	0.244170	+	0.911255i	−0.729629	+	0.683844i	$0.760307\pi$
$6$		0			0
$7$	−2.03549	−	1.69021i	−0.769341	−	0.638838i
$7$	−2.03549	−	1.69021i	−0.769341	−	0.638838i
$8$	−1.39354	+	1.39354i	−0.492690	+	0.492690i
$9$		0			0
$10$	0.558898	−	0.968040i	0.176739	−	0.306121i
$11$	0.745933	+	2.78386i	0.224907	+	0.839366i	0.982442	+	0.186570i	$0.0597372\pi$
$11$	0.745933	+	2.78386i	0.224907	+	0.839366i	−0.757534	+	0.652795i	$0.773596\pi$
$12$		0			0
$13$	2.80107	+	2.27024i	0.776877	+	0.629652i
$13$	2.80107	+	2.27024i	0.776877	+	0.629652i
$14$	0.129371	+	1.39596i	0.0345758	+	0.373086i
$15$		0			0
$16$	−2.39417			−0.598543
$17$	3.29760			0.799786			0.399893	−	0.916562i	$-0.369047\pi$
$17$	3.29760			0.799786			0.399893	+	0.916562i	$0.369047\pi$
$18$		0			0
$19$	6.53354	+	1.75066i	1.49890	+	0.401628i	0.912730	−	0.408563i	$-0.133970\pi$
$19$	6.53354	+	1.75066i	1.49890	+	0.401628i	0.586166	+	0.810191i	$0.300637\pi$
$20$	3.50314	−	0.938663i	0.783325	−	0.209891i
$21$		0			0
$22$	0.763581	−	1.32256i	0.162796	−	0.281971i
$23$		−	7.84515i		−	1.63583i	−0.575341	−	0.817914i	$-0.695130\pi$
$23$		−	7.84515i		−	1.63583i	0.575341	−	0.817914i	$-0.304870\pi$
$24$		0			0
$25$	0.476290	−	0.274986i	0.0952579	−	0.0549972i
$26$	−0.198893	−	1.90015i	−0.0390061	−	0.372649i
$27$		0			0
$28$	−2.90584	+	3.49945i	−0.549152	+	0.661334i
$29$	−0.677462	−	1.17340i	−0.125802	−	0.217895i	0.796244	−	0.604975i	$-0.206817\pi$
$29$	−0.677462	−	1.17340i	−0.125802	−	0.217895i	−0.922046	+	0.387080i	$0.873484\pi$
$30$		0			0
$31$	6.38499	+	1.71085i	1.14678	+	0.307278i	0.781673	−	0.623688i	$-0.214366\pi$
$31$	6.38499	+	1.71085i	1.14678	+	0.307278i	0.365105	+	0.930966i	$0.381033\pi$
$32$	3.68413	+	3.68413i	0.651269	+	0.651269i
$33$		0			0
$34$	−1.23556	−	1.23556i	−0.211897	−	0.211897i
$35$	2.33268	−	5.07039i	0.394294	−	0.857052i
$36$		0			0
$37$	2.87856	−	2.87856i	0.473232	−	0.473232i	−0.429727	−	0.902959i	$-0.641390\pi$
$37$	2.87856	−	2.87856i	0.473232	−	0.473232i	0.902959	+	0.429727i	$0.141390\pi$
$38$	−1.79207	−	3.10396i	−0.290713	−	0.503529i
$39$		0			0
$40$	−3.60036	−	2.07867i	−0.569266	−	0.328666i
$41$	−6.61712	−	1.77305i	−1.03342	−	0.276904i	−0.298036	−	0.954555i	$-0.596332\pi$
$41$	−6.61712	−	1.77305i	−1.03342	−	0.276904i	−0.735384	+	0.677651i	$0.762998\pi$
$42$		0			0
$43$	−4.36301	−	2.51899i	−0.665353	−	0.384142i	0.128961	−	0.991650i	$-0.458836\pi$
$43$	−4.36301	−	2.51899i	−0.665353	−	0.384142i	−0.794314	+	0.607508i	$0.792169\pi$
$44$	4.78608	−	1.28243i	0.721528	−	0.193333i
$45$		0			0
$46$	−2.93946	+	2.93946i	−0.433400	+	0.433400i
$47$	3.53471	−	0.947124i	0.515591	−	0.138152i	0.00836456	−	0.999965i	$-0.497337\pi$
$47$	3.53471	−	0.947124i	0.515591	−	0.138152i	0.507226	+	0.861813i	$0.330671\pi$
$48$		0			0
$49$	1.28640	+	6.88078i	0.183772	+	0.982969i
$50$	−0.281492	−	0.0754255i	−0.0398089	−	0.0106668i
$51$		0			0
$52$	3.90305	−	4.81566i	0.541256	−	0.667812i
$53$	3.87961	+	6.71968i	0.532905	+	0.923019i	0.999262	+	0.0384223i	$0.0122332\pi$
$53$	3.87961	+	6.71968i	0.532905	+	0.923019i	−0.466356	+	0.884597i	$0.654433\pi$
$54$		0			0
$55$	−5.26521	+	3.03987i	−0.709961	+	0.409896i
$56$	5.19189	−	0.481159i	0.693795	−	0.0642976i
$57$		0			0
$58$	−0.185820	+	0.693490i	−0.0243994	+	0.0910597i
$59$	2.01369	+	2.01369i	0.262160	+	0.262160i	0.825931	−	0.563771i	$-0.190650\pi$
$59$	2.01369	+	2.01369i	0.262160	+	0.262160i	−0.563771	+	0.825931i	$0.690650\pi$
$60$		0			0
$61$	−3.14962	+	1.81843i	−0.403267	+	0.232827i	−0.687893	−	0.725812i	$-0.741464\pi$
$61$	−3.14962	+	1.81843i	−0.403267	+	0.232827i	0.284625	+	0.958639i	$0.408131\pi$
$62$	−1.75133	−	3.03339i	−0.222419	−	0.385241i
$63$		0			0
$64$			2.02756i			0.253445i
$65$	−3.09658	+	6.94705i	−0.384084	+	0.861676i
$66$		0			0
$67$	1.82619	−	0.489326i	0.223104	−	0.0597807i	−0.145535	−	0.989353i	$-0.546490\pi$
$67$	1.82619	−	0.489326i	0.223104	−	0.0597807i	0.368640	+	0.929572i	$0.379824\pi$
$68$		−	5.66931i		−	0.687505i
$69$		0			0
$70$	−2.77382	+	1.02578i	−0.331534	+	0.122604i
$71$	9.87427	−	2.64580i	1.17186	−	0.313999i	0.380167	−	0.924918i	$-0.375866\pi$
$71$	9.87427	−	2.64580i	1.17186	−	0.313999i	0.791693	+	0.610919i	$0.209200\pi$
$72$		0			0
$73$	1.82296	−	6.80337i	0.213361	−	0.796274i	−0.773376	−	0.633947i	$-0.781434\pi$
$73$	1.82296	−	6.80337i	0.213361	−	0.796274i	0.986737	−	0.162326i	$-0.0518997\pi$
$74$	−2.15710			−0.250758
$75$		0			0
$76$	3.00977	−	11.2326i	0.345244	−	1.28847i
$77$	3.18696	−	6.92729i	0.363188	−	0.789438i
$78$		0			0
$79$	−1.13108	+	1.95909i	−0.127256	+	0.220414i	−0.922613	−	0.385728i	$-0.873950\pi$
$79$	−1.13108	+	1.95909i	−0.127256	+	0.220414i	0.795356	+	0.606142i	$0.207284\pi$
$80$	−1.30717	−	4.87843i	−0.146146	−	0.545425i
$81$		0			0
$82$	1.81500	+	3.14367i	0.200433	+	0.347160i
$83$	3.97225	−	3.97225i	0.436011	−	0.436011i	−0.454656	−	0.890667i	$-0.650238\pi$
$83$	3.97225	−	3.97225i	0.436011	−	0.436011i	0.890667	+	0.454656i	$0.150238\pi$
$84$		0			0
$85$	1.80043	+	6.71929i	0.195284	+	0.728810i
$86$	0.690929	+	2.57858i	0.0745048	+	0.278056i
$87$		0			0
$88$	−4.91890	−	2.83993i	−0.524356	−	0.302737i
$89$	−8.73455	−	8.73455i	−0.925861	−	0.925861i	0.0715743	−	0.997435i	$-0.477198\pi$
$89$	−8.73455	−	8.73455i	−0.925861	−	0.925861i	−0.997435	+	0.0715743i	$0.977198\pi$
$90$		0			0
$91$	−1.86436	−	9.35543i	−0.195438	−	0.980716i
$92$	−13.4876			−1.40618
$93$		0			0
$94$	−1.67928	−	0.969531i	−0.173204	−	0.0999995i
$95$			14.2688i			1.46394i
$96$		0			0
$97$	3.94107	+	14.7083i	0.400155	+	1.49340i	0.812819	+	0.582516i	$0.197932\pi$
$97$	3.94107	+	14.7083i	0.400155	+	1.49340i	−0.412664	+	0.910883i	$0.635402\pi$
$98$	2.09613	−	3.06012i	0.211741	−	0.309119i
$99$		0			0
$100$	−0.472762	−	0.818848i	−0.0472762	−	0.0818848i
$101$	−4.18736	+	7.25272i	−0.416658	+	0.721673i	−0.995601	−	0.0936951i	$-0.970132\pi$
$101$	−4.18736	+	7.25272i	−0.416658	+	0.721673i	0.578943	+	0.815368i	$0.303465\pi$
$102$		0			0
$103$	3.94643	−	6.83541i	0.388853	−	0.673513i	−0.603442	−	0.797407i	$-0.706205\pi$
$103$	3.94643	−	6.83541i	0.388853	−	0.673513i	0.992296	+	0.123893i	$0.0395380\pi$
$104$	−7.06706	+	0.739728i	−0.692982	+	0.0725363i
$105$		0			0
$106$	1.06413	−	3.97140i	0.103358	−	0.385736i
$107$	20.0157			1.93499			0.967497	−	0.252883i	$-0.0813786\pi$
$107$	20.0157			1.93499			0.967497	+	0.252883i	$0.0813786\pi$
$108$		0			0
$109$	−1.81100	+	6.75874i	−0.173462	+	0.647370i	0.823346	+	0.567539i	$0.192105\pi$
$109$	−1.81100	+	6.75874i	−0.173462	+	0.647370i	−0.996808	+	0.0798304i	$0.974562\pi$
$110$	3.11179	+	0.833802i	0.296698	+	0.0794999i
$111$		0			0
$112$	4.87330	+	4.04664i	0.460483	+	0.382372i
$113$	−2.05899	+	3.56627i	−0.193693	+	0.335486i	−0.946471	−	0.322788i	$-0.895380\pi$
$113$	−2.05899	+	3.56627i	−0.193693	+	0.335486i	0.752778	+	0.658274i	$0.228713\pi$
$114$		0			0
$115$	15.9855	−	4.28331i	1.49066	−	0.399420i
$116$	−2.01733	+	1.16471i	−0.187305	+	0.108140i
$117$		0			0
$118$		−	1.50900i		−	0.138914i
$119$	−6.71223	−	5.57363i	−0.615309	−	0.510934i
$120$		0			0
$121$	2.33281	−	1.34685i	0.212074	−	0.122441i
$122$	1.86145	+	0.498775i	0.168528	+	0.0451570i
$123$		0			0
$124$	2.94134	−	10.9772i	0.264140	−	0.985783i
$125$	8.27861	+	8.27861i	0.740461	+	0.740461i
$126$		0			0
$127$	−15.0417	+	8.68434i	−1.33474	+	0.770611i	−0.986022	−	0.166618i	$-0.946715\pi$
$127$	−15.0417	+	8.68434i	−1.33474	+	0.770611i	−0.348716	+	0.937229i	$0.613382\pi$
$128$	8.12796	−	8.12796i	0.718417	−	0.718417i
$129$		0			0
$130$	3.76320	−	1.44271i	0.330054	−	0.126534i
$131$	−6.59348	−	3.80675i	−0.576075	−	0.332597i	0.183497	−	0.983020i	$-0.441258\pi$
$131$	−6.59348	−	3.80675i	−0.576075	−	0.332597i	−0.759572	+	0.650423i	$0.774592\pi$
$132$		0			0
$133$	−10.3400	−	14.6065i	−0.896588	−	1.26654i
$134$	−0.867588	−	0.500902i	−0.0749482	−	0.0432714i
$135$		0			0
$136$	−4.59533	+	4.59533i	−0.394046	+	0.394046i
$137$	−11.1157	+	11.1157i	−0.949677	+	0.949677i	−0.998793	−	0.0491165i	$-0.984359\pi$
$137$	−11.1157	+	11.1157i	−0.949677	+	0.949677i	0.0491165	+	0.998793i	$0.484359\pi$
$138$		0			0
$139$	16.0562	+	9.27005i	1.36187	+	0.786275i	0.989873	−	0.141959i	$-0.0453402\pi$
$139$	16.0562	+	9.27005i	1.36187	+	0.786275i	0.371996	+	0.928234i	$0.378674\pi$
$140$	−8.71712	−	4.01039i	−0.736731	−	0.338940i
$141$		0			0
$142$	−4.69109	−	2.70840i	−0.393667	−	0.227284i
$143$	−4.23063	+	9.49124i	−0.353783	+	0.793698i
$144$		0			0
$145$	2.02107	−	2.02107i	0.167841	−	0.167841i
$146$	−3.23215	+	1.86608i	−0.267495	+	0.154438i
$147$		0			0
$148$	−4.94888	−	4.94888i	−0.406795	−	0.406795i
$149$	−5.71487	+	21.3282i	−0.468181	+	1.74727i	0.177943	+	0.984041i	$0.443056\pi$
$149$	−5.71487	+	21.3282i	−0.468181	+	1.74727i	−0.646124	+	0.763233i	$0.723611\pi$
$150$		0			0
$151$	−17.2088	−	4.61110i	−1.40044	−	0.375246i	−0.521935	−	0.852986i	$-0.674789\pi$
$151$	−17.2088	−	4.61110i	−1.40044	−	0.375246i	−0.878501	+	0.477740i	$0.841456\pi$
$152$	−11.5443	+	6.66512i	−0.936369	+	0.540613i
$153$		0			0
$154$	−3.78966	+	1.40144i	−0.305379	+	0.112932i
$155$			13.9443i			1.12004i
$156$		0			0
$157$	3.29871	−	1.90451i	0.263265	−	0.151996i	−0.362558	−	0.931961i	$-0.618096\pi$
$157$	3.29871	−	1.90451i	0.263265	−	0.151996i	0.625823	+	0.779965i	$0.284763\pi$
$158$	1.15784	−	0.310242i	0.0921127	−	0.0246815i
$159$		0			0
$160$	−5.49543	+	9.51836i	−0.434452	+	0.752493i
$161$	−13.2599	+	15.9687i	−1.04503	+	1.25851i
$162$		0			0
$163$	7.66571	+	2.05402i	0.600425	+	0.160883i	0.546213	−	0.837646i	$-0.316069\pi$
$163$	7.66571	+	2.05402i	0.600425	+	0.160883i	0.0542114	+	0.998529i	$0.482736\pi$
$164$	−3.04827	+	11.3763i	−0.238030	+	0.888339i
$165$		0			0
$166$	−2.97668			−0.231035
$167$	2.98897	−	11.1550i	0.231294	−	0.863200i	−0.748491	−	0.663145i	$-0.769221\pi$
$167$	2.98897	−	11.1550i	0.231294	−	0.863200i	0.979785	−	0.200055i	$-0.0641120\pi$
$168$		0			0
$169$	2.69199	+	12.7182i	0.207076	+	0.978325i
$170$	1.84302	−	3.19221i	0.141354	−	0.244832i
$171$		0			0
$172$	−4.33070	+	7.50099i	−0.330213	+	0.571945i
$173$	−9.52913	−	16.5049i	−0.724486	−	1.25485i	−0.959185	−	0.282779i	$-0.908744\pi$
$173$	−9.52913	−	16.5049i	−0.724486	−	1.25485i	0.234699	−	0.972068i	$-0.424589\pi$
$174$		0			0
$175$	−1.43426	−	0.245298i	−0.108420	−	0.0185428i
$176$	−1.78589	−	6.66504i	−0.134617	−	0.502396i
$177$		0			0
$178$			6.54541i			0.490599i
$179$	−9.39442	−	5.42387i	−0.702172	−	0.405399i	0.105984	−	0.994368i	$-0.466201\pi$
$179$	−9.39442	−	5.42387i	−0.702172	−	0.405399i	−0.808156	+	0.588969i	$0.799534\pi$
$180$		0			0
$181$	−5.71631			−0.424890			−0.212445	−	0.977173i	$-0.568143\pi$
$181$	−5.71631			−0.424890			−0.212445	+	0.977173i	$0.568143\pi$
$182$	−2.80679	+	4.20389i	−0.208053	+	0.311613i
$183$		0			0
$184$	10.9325	+	10.9325i	0.805955	+	0.805955i
$185$	7.43707	+	4.29379i	0.546784	+	0.315686i
$186$		0			0
$187$	2.45979	+	9.18007i	0.179878	+	0.671313i
$188$	−1.62832	−	6.07696i	−0.118757	−	0.443208i
$189$		0			0
$190$	5.34629	−	5.34629i	0.387860	−	0.387860i
$191$	−11.5025	−	19.9230i	−0.832294	−	1.44157i	−0.896215	−	0.443620i	$-0.853694\pi$
$191$	−11.5025	−	19.9230i	−0.832294	−	1.44157i	0.0639213	−	0.997955i	$-0.479639\pi$
$192$		0			0
$193$	−1.29072	−	4.81703i	−0.0929080	−	0.346737i	0.903786	−	0.427985i	$-0.140776\pi$
$193$	−1.29072	−	4.81703i	−0.0929080	−	0.346737i	−0.996694	+	0.0812474i	$0.974110\pi$
$194$	4.03431	−	6.98763i	0.289647	−	0.501683i
$195$		0			0
$196$	11.8296	−	2.21161i	0.844971	−	0.157972i
$197$	−1.17127	+	4.37125i	−0.0834496	+	0.311438i	−0.995016	−	0.0997145i	$-0.968207\pi$
$197$	−1.17127	+	4.37125i	−0.0834496	+	0.311438i	0.911566	+	0.411153i	$0.134874\pi$
$198$		0			0
$199$	−21.8071			−1.54587			−0.772934	−	0.634487i	$-0.781211\pi$
$199$	−21.8071			−1.54587			−0.772934	+	0.634487i	$0.781211\pi$
$200$	−0.280524	+	1.04693i	−0.0198361	+	0.0740292i
$201$		0			0
$202$	4.28643	−	1.14855i	0.301592	−	0.0808114i
$203$	−0.604322	+	3.53349i	−0.0424151	+	0.248002i
$204$		0			0
$205$		−	14.4513i		−	1.00932i
$206$	−4.03979	+	1.08246i	−0.281466	+	0.0754185i
$207$		0			0
$208$	−6.70624	−	5.43535i	−0.464994	−	0.376874i
$209$			19.4943i			1.34845i
$210$		0			0
$211$	5.12257	+	8.87255i	0.352652	+	0.610811i	0.986713	−	0.162472i	$-0.0519466\pi$
$211$	5.12257	+	8.87255i	0.352652	+	0.610811i	−0.634061	+	0.773283i	$0.718613\pi$
$212$	11.5526	−	6.66991i	0.793438	−	0.458091i
$213$		0			0
$214$	−7.49959	−	7.49959i	−0.512662	−	0.512662i
$215$	2.75064	−	10.2655i	0.187592	−	0.700103i
$216$		0			0
$217$	−10.1049	−	14.2744i	−0.685963	−	0.969007i
$218$	3.21095	−	1.85384i	0.217473	−	0.125558i
$219$		0			0
$220$	5.22621	+	9.05207i	0.352351	+	0.610290i
$221$	9.23682	+	7.48636i	0.621336	+	0.503587i
$222$		0			0
$223$	−20.9821	−	5.62213i	−1.40506	−	0.376486i	−0.524904	−	0.851161i	$-0.675899\pi$
$223$	−20.9821	−	5.62213i	−1.40506	−	0.376486i	−0.880161	+	0.474675i	$0.842565\pi$
$224$	−1.27205	−	13.7259i	−0.0849927	−	0.917103i
$225$		0			0
$226$	2.10770	−	0.564756i	0.140202	−	0.0375670i
$227$	8.25938	−	8.25938i	0.548194	−	0.548194i	−0.377724	−	0.925918i	$-0.623293\pi$
$227$	8.25938	−	8.25938i	0.548194	−	0.548194i	0.925918	+	0.377724i	$0.123293\pi$
$228$		0			0
$229$	−4.69053	+	1.25682i	−0.309959	+	0.0830532i	−0.410445	−	0.911885i	$-0.634627\pi$
$229$	−4.69053	+	1.25682i	−0.309959	+	0.0830532i	0.100487	+	0.994938i	$0.467960\pi$
$230$	−7.59442	−	4.38464i	−0.500761	−	0.289115i
$231$		0			0
$232$	2.57924	+	0.691106i	0.169336	+	0.0453733i
$233$	−1.91696	−	1.10676i	−0.125584	−	0.0725060i	0.435892	−	0.899999i	$-0.356433\pi$
$233$	−1.91696	−	1.10676i	−0.125584	−	0.0725060i	−0.561476	+	0.827493i	$0.689766\pi$
$234$		0			0
$235$	3.85977	+	6.68532i	0.251784	+	0.436102i
$236$	3.46198	−	3.46198i	0.225355	−	0.225355i
$237$		0			0
$238$	0.426614	+	4.60333i	0.0276533	+	0.298389i
$239$	5.82013	+	5.82013i	0.376473	+	0.376473i	0.869828	−	0.493355i	$-0.164230\pi$
$239$	5.82013	+	5.82013i	0.376473	+	0.376473i	−0.493355	+	0.869828i	$0.664230\pi$
$240$		0			0
$241$	−10.2858	−	10.2858i	−0.662564	−	0.662564i	0.293420	−	0.955984i	$-0.405207\pi$
$241$	−10.2858	−	10.2858i	−0.662564	−	0.662564i	−0.955984	+	0.293420i	$0.905207\pi$
$242$	−1.37871	−	0.369425i	−0.0886271	−	0.0237476i
$243$		0			0
$244$	3.12629	+	5.41490i	0.200140	+	0.346653i
$245$	−13.3181	+	6.37799i	−0.850864	+	0.407475i
$246$		0			0
$247$	14.3265	+	19.7364i	0.911572	+	1.25580i
$248$	−11.2819	+	6.51358i	−0.716399	+	0.413613i
$249$		0			0
$250$		−	6.20374i		−	0.392359i
$251$	−10.7479	+	18.6160i	−0.678403	+	1.17503i	0.297058	+	0.954859i	$0.403994\pi$
$251$	−10.7479	+	18.6160i	−0.678403	+	1.17503i	−0.975462	+	0.220169i	$0.929339\pi$
$252$		0			0
$253$	21.8398	−	5.85196i	1.37306	−	0.367910i
$254$	8.88980	+	2.38201i	0.557796	+	0.149461i
$255$		0			0
$256$	−2.03573			−0.127233
$257$	7.54278			0.470506			0.235253	−	0.971934i	$-0.424408\pi$
$257$	7.54278			0.470506			0.235253	+	0.971934i	$0.424408\pi$
$258$		0			0
$259$	−10.7246	+	0.993906i	−0.666395	+	0.0617583i
$260$	11.9435	+	5.32371i	0.740706	+	0.330163i
$261$		0			0
$262$	1.04415	+	3.89681i	0.0645076	+	0.240746i
$263$	11.9190	−	20.6443i	0.734955	−	1.27298i	−0.219787	−	0.975548i	$-0.570536\pi$
$263$	11.9190	−	20.6443i	0.734955	−	1.27298i	0.954743	−	0.297432i	$-0.0961303\pi$
$264$		0			0
$265$	−11.5740	+	11.5740i	−0.710987	+	0.710987i
$266$	−1.59860	+	9.34705i	−0.0980163	+	0.573104i
$267$		0			0
$268$	−0.841260	−	3.13962i	−0.0513881	−	0.191783i
$269$		−	27.6300i		−	1.68463i	−0.538985	−	0.842316i	$-0.681192\pi$
$269$		−	27.6300i		−	1.68463i	0.538985	−	0.842316i	$-0.318808\pi$
$270$		0			0
$271$	−14.6246	−	14.6246i	−0.888382	−	0.888382i	0.105986	−	0.994368i	$-0.466200\pi$
$271$	−14.6246	−	14.6246i	−0.888382	−	0.888382i	−0.994368	+	0.105986i	$0.966200\pi$
$272$	−7.89502			−0.478706
$273$		0			0
$274$	8.32976			0.503219
$275$	1.12080	+	1.12080i	0.0675870	+	0.0675870i
$276$		0			0
$277$			8.98397i			0.539795i	0.962889	+	0.269897i	$0.0869898\pi$
$277$			8.98397i			0.539795i	−0.962889	+	0.269897i	$0.913010\pi$
$278$	−2.54267	−	9.48936i	−0.152499	−	0.569134i
$279$		0			0
$280$	3.81510	+	10.3164i	0.227996	+	0.616525i
$281$	−13.3221	+	13.3221i	−0.794731	+	0.794731i	−0.982259	−	0.187528i	$-0.939952\pi$
$281$	−13.3221	+	13.3221i	−0.794731	+	0.794731i	0.187528	+	0.982259i	$0.439952\pi$
$282$		0			0
$283$	−9.69865	+	16.7985i	−0.576525	+	0.998570i	0.419349	+	0.907825i	$0.362258\pi$
$283$	−9.69865	+	16.7985i	−0.576525	+	0.998570i	−0.995874	+	0.0907452i	$0.971075\pi$
$284$	−4.54873	−	16.9761i	−0.269917	−	1.00734i
$285$		0			0
$286$	5.14138	−	1.97107i	0.304016	−	0.116552i
$287$	10.4722	+	14.7933i	0.618156	+	0.873222i
$288$		0			0
$289$	−6.12581			−0.360342
$290$	−1.51453			−0.0889362
$291$		0			0
$292$	−11.6965	−	3.13407i	−0.684486	−	0.183407i
$293$	25.2467	−	6.76482i	1.47493	−	0.395205i	0.570309	−	0.821431i	$-0.306824\pi$
$293$	25.2467	−	6.76482i	1.47493	−	0.395205i	0.904617	+	0.426225i	$0.140157\pi$
$294$		0			0
$295$	−3.00371	+	5.20258i	−0.174883	+	0.302906i
$296$			8.02275i			0.466313i
$297$		0			0
$298$	10.1326	−	5.85008i	0.586967	−	0.338886i
$299$	17.8104	−	21.9748i	1.03000	−	1.27084i
$300$		0			0
$301$	4.62324	+	12.5018i	0.266479	+	0.720589i
$302$	4.72019	+	8.17560i	0.271616	+	0.470453i
$303$		0			0
$304$	−15.6424	−	4.19137i	−0.897153	−	0.240391i
$305$	−5.42493	−	5.42493i	−0.310630	−	0.310630i
$306$		0			0
$307$	1.58354	+	1.58354i	0.0903771	+	0.0903771i	0.750850	−	0.660473i	$-0.229644\pi$
$307$	1.58354	+	1.58354i	0.0903771	+	0.0903771i	−0.660473	+	0.750850i	$0.729644\pi$
$308$	−11.9096	−	5.47910i	−0.678610	−	0.312201i
$309$		0			0
$310$	5.22473	−	5.22473i	0.296745	−	0.296745i
$311$	7.59574	+	13.1562i	0.430715	+	0.746020i	0.996935	−	0.0782342i	$-0.0249282\pi$
$311$	7.59574	+	13.1562i	0.430715	+	0.746020i	−0.566220	+	0.824254i	$0.691595\pi$
$312$		0			0
$313$	−2.66705	−	1.53982i	−0.150750	−	0.0870358i	0.422727	−	0.906257i	$-0.361073\pi$
$313$	−2.66705	−	1.53982i	−0.150750	−	0.0870358i	−0.573478	+	0.819221i	$0.694406\pi$
$314$	−1.94957	−	0.522385i	−0.110020	−	0.0294799i
$315$		0			0
$316$	3.36810	+	1.94458i	0.189471	+	0.109391i
$317$	7.94761	−	2.12956i	0.446382	−	0.119608i	−0.0286238	−	0.999590i	$-0.509112\pi$
$317$	7.94761	−	2.12956i	0.446382	−	0.119608i	0.475006	+	0.879982i	$0.342446\pi$
$318$		0			0
$319$	2.76124	−	2.76124i	0.154600	−	0.154600i
$320$	−4.13142	+	1.10701i	−0.230953	+	0.0618838i
$321$		0			0
$322$	10.9515	−	1.01494i	0.610305	−	0.0565601i
$323$	21.5450	+	5.77297i	1.19880	+	0.321217i
$324$		0			0
$325$	1.95841	+	0.311038i	0.108633	+	0.0172533i
$326$	−2.10261	−	3.64184i	−0.116453	−	0.201703i
$327$		0			0
$328$	11.6920	−	6.75038i	0.645583	−	0.372728i
$329$	−8.79569	−	4.04654i	−0.484922	−	0.223093i
$330$		0			0
$331$	5.70505	−	21.2915i	0.313578	−	1.17029i	−0.611728	−	0.791068i	$-0.709525\pi$
$331$	5.70505	−	21.2915i	0.313578	−	1.17029i	0.925306	−	0.379221i	$-0.123808\pi$
$332$	−6.82918	−	6.82918i	−0.374800	−	0.374800i
$333$		0			0
$334$	−5.29953	+	3.05969i	−0.289978	+	0.167419i
$335$	1.99413	+	3.45393i	0.108951	+	0.188709i
$336$		0			0
$337$			6.60942i			0.360038i	0.983663	+	0.180019i	$0.0576159\pi$
$337$			6.60942i			0.360038i	−0.983663	+	0.180019i	$0.942384\pi$
$338$	3.75668	−	5.77398i	0.204336	−	0.314063i
$339$		0			0
$340$	11.5520	−	3.09534i	0.626493	−	0.167868i
$341$			19.0511i			1.03168i
$342$		0			0
$343$	9.01149	−	16.1800i	0.486574	−	0.873639i
$344$	9.59032	−	2.56972i	0.517075	−	0.138550i
$345$		0			0
$346$	−2.61373	+	9.75457i	−0.140515	+	0.524409i
$347$	−15.4106			−0.827285			−0.413642	−	0.910439i	$-0.635744\pi$
$347$	−15.4106			−0.827285			−0.413642	+	0.910439i	$0.635744\pi$
$348$		0			0
$349$	0.658426	−	2.45728i	0.0352447	−	0.131535i	−0.946062	−	0.323986i	$-0.894977\pi$
$349$	0.658426	−	2.45728i	0.0352447	−	0.131535i	0.981307	+	0.192451i	$0.0616436\pi$
$350$	0.445488	+	0.629307i	0.0238123	+	0.0336379i
$351$		0			0
$352$	−7.50800	+	13.0042i	−0.400178	+	0.693128i
$353$	1.30540	+	4.87182i	0.0694794	+	0.259301i	0.991925	−	0.126827i	$-0.0404792\pi$
$353$	1.30540	+	4.87182i	0.0694794	+	0.259301i	−0.922445	+	0.386127i	$0.873813\pi$
$354$		0			0
$355$	10.7823	+	18.6756i	0.572267	+	0.991195i
$356$	−15.0166	+	15.0166i	−0.795880	+	0.795880i
$357$		0			0
$358$	1.48771	+	5.55219i	0.0786277	+	0.293443i
$359$	2.50899	+	9.36366i	0.132419	+	0.494195i	0.999995	−	0.00310948i	$-0.000989781\pi$
$359$	2.50899	+	9.36366i	0.132419	+	0.494195i	−0.867576	+	0.497305i	$0.834323\pi$
$360$		0			0
$361$	23.1678	+	13.3760i	1.21936	+	0.703998i
$362$	2.14181	+	2.14181i	0.112571	+	0.112571i
$363$		0			0
$364$	−16.0841	+	3.20525i	−0.843034	+	0.168001i
$365$	14.8580			0.777705
$366$		0			0
$367$	−6.48275	−	3.74282i	−0.338397	−	0.195373i	0.321166	−	0.947023i	$-0.395925\pi$
$367$	−6.48275	−	3.74282i	−0.338397	−	0.195373i	−0.659563	+	0.751649i	$0.729259\pi$
$368$			18.7826i			0.979113i
$369$		0			0
$370$	−1.17774	−	4.39538i	−0.0612277	−	0.228505i
$371$	3.46076	−	20.2352i	0.179674	−	1.05056i
$372$		0			0
$373$	−9.46898	−	16.4008i	−0.490285	−	0.849199i	0.509652	−	0.860381i	$-0.329774\pi$
$373$	−9.46898	−	16.4008i	−0.490285	−	0.849199i	−0.999937	+	0.0111813i	$0.996441\pi$
$374$	2.51799	−	4.36128i	0.130202	−	0.225517i
$375$		0			0
$376$	−3.60590	+	6.24561i	−0.185960	+	0.322092i
$377$	0.766281	−	4.82478i	0.0394655	−	0.248489i
$378$		0			0
$379$	6.61698	−	24.6949i	0.339891	−	1.26849i	−0.558577	−	0.829453i	$-0.688652\pi$
$379$	6.61698	−	24.6949i	0.339891	−	1.26849i	0.898468	−	0.439039i	$-0.144681\pi$
$380$	24.5312			1.25842
$381$		0			0
$382$	−3.15501	+	11.7747i	−0.161424	+	0.602444i
$383$	−8.70527	−	2.33257i	−0.444819	−	0.119189i	0.0294554	−	0.999566i	$-0.490623\pi$
$383$	−8.70527	−	2.33257i	−0.444819	−	0.119189i	−0.474274	+	0.880377i	$0.657289\pi$
$384$		0			0
$385$	15.8553	+	2.71168i	0.808060	+	0.138200i
$386$	−1.32126	+	2.28848i	−0.0672501	+	0.116481i
$387$		0			0
$388$	25.2868	−	6.77558i	1.28374	−	0.343978i
$389$	−24.4866	+	14.1373i	−1.24152	+	0.716792i	−0.969404	−	0.245472i	$-0.921057\pi$
$389$	−24.4866	+	14.1373i	−1.24152	+	0.716792i	−0.272116	+	0.962264i	$0.587724\pi$
$390$		0			0
$391$		−	25.8702i		−	1.30831i
$392$	−11.3813	−	7.79597i	−0.574841	−	0.393756i
$393$		0			0
$394$	2.07670	−	1.19898i	0.104623	−	0.0604038i
$395$	−4.60944	−	1.23510i	−0.231926	−	0.0621444i
$396$		0			0
$397$	4.40344	−	16.4338i	0.221002	−	0.824791i	−0.762965	−	0.646440i	$-0.776257\pi$
$397$	4.40344	−	16.4338i	0.221002	−	0.824791i	0.983967	−	0.178351i	$-0.0570763\pi$
$398$	8.17081	+	8.17081i	0.409566	+	0.409566i
$399$		0			0
$400$	−1.14032	+	0.658363i	−0.0570159	+	0.0329182i
$401$	−4.03016	+	4.03016i	−0.201256	+	0.201256i	−0.800538	−	0.599282i	$-0.795453\pi$
$401$	−4.03016	+	4.03016i	−0.201256	+	0.201256i	0.599282	+	0.800538i	$0.295453\pi$
$402$		0			0
$403$	14.0008	+	19.2877i	0.697427	+	0.960789i
$404$	12.4690	+	7.19901i	0.620358	+	0.358164i
$405$		0			0
$406$	1.55038	−	1.09751i	0.0769438	−	0.0544687i
$407$	10.1607	+	5.86629i	0.503648	+	0.290781i
$408$		0			0
$409$	−8.37498	+	8.37498i	−0.414116	+	0.414116i	−0.883170	−	0.469054i	$-0.844595\pi$
$409$	−8.37498	+	8.37498i	−0.414116	+	0.414116i	0.469054	+	0.883170i	$0.344595\pi$
$410$	−5.41468	+	5.41468i	−0.267412	+	0.267412i
$411$		0			0
$412$	−11.7516	−	6.78479i	−0.578960	−	0.334262i
$413$	−0.695284	−	7.50238i	−0.0342127	−	0.369168i
$414$		0			0
$415$	10.2627	+	5.92519i	0.503778	+	0.290856i
$416$	1.95564	+	18.6834i	0.0958831	+	0.916029i
$417$		0			0
$418$	7.30424	−	7.30424i	0.357262	−	0.357262i
$419$	9.24123	−	5.33542i	0.451463	−	0.260653i	−0.256985	−	0.966415i	$-0.582729\pi$
$419$	9.24123	−	5.33542i	0.451463	−	0.260653i	0.708448	+	0.705763i	$0.249396\pi$
$420$		0			0
$421$	−7.86566	−	7.86566i	−0.383349	−	0.383349i	0.488958	−	0.872307i	$-0.337377\pi$
$421$	−7.86566	−	7.86566i	−0.383349	−	0.383349i	−0.872307	+	0.488958i	$0.837377\pi$
$422$	1.40506	−	5.24376i	0.0683973	−	0.255262i
$423$		0			0
$424$	−14.7705	−	3.95774i	−0.717319	−	0.192205i
$425$	1.57061	−	0.906795i	0.0761860	−	0.0439860i
$426$		0			0
$427$	9.48453	+	1.62211i	0.458989	+	0.0784995i
$428$		−	34.4115i		−	1.66334i
$429$		0			0
$430$	−4.87696	+	2.81571i	−0.235188	+	0.135786i
$431$	−6.29747	+	1.68740i	−0.303338	+	0.0812793i	−0.407278	−	0.913304i	$-0.633522\pi$
$431$	−6.29747	+	1.68740i	−0.303338	+	0.0812793i	0.103939	+	0.994584i	$0.466855\pi$
$432$		0			0
$433$	11.6587	−	20.1934i	0.560281	−	0.970435i	−0.437191	−	0.899369i	$-0.644026\pi$
$433$	11.6587	−	20.1934i	0.560281	−	0.970435i	0.997472	−	0.0710664i	$-0.0226402\pi$
$434$	−1.56225	+	9.13453i	−0.0749905	+	0.438472i
$435$		0			0
$436$	11.6198	+	3.11351i	0.556486	+	0.149110i
$437$	13.7342	−	51.2566i	0.656994	−	2.45194i
$438$		0			0
$439$	5.87248			0.280278			0.140139	−	0.990132i	$-0.455245\pi$
$439$	5.87248			0.280278			0.140139	+	0.990132i	$0.455245\pi$
$440$	3.10109	−	11.5734i	0.147839	−	0.551742i
$441$		0			0
$442$	−0.655871	−	6.26593i	−0.0311966	−	0.298040i
$443$	11.2685	−	19.5176i	0.535381	−	0.927308i	−0.463763	−	0.885959i	$-0.653501\pi$
$443$	11.2685	−	19.5176i	0.535381	−	0.927308i	0.999145	−	0.0413488i	$-0.0131655\pi$
$444$		0			0
$445$	13.0289	−	22.5667i	0.617628	−	1.06976i
$446$	5.75515	+	9.96820i	0.272514	+	0.472008i
$447$		0			0
$448$	3.42700	−	4.12707i	0.161910	−	0.194986i
$449$	1.20603	+	4.50095i	0.0569159	+	0.212413i	0.988527	−	0.151043i	$-0.0482632\pi$
$449$	1.20603	+	4.50095i	0.0569159	+	0.212413i	−0.931611	+	0.363456i	$0.881597\pi$
$450$		0			0
$451$		−	19.7437i		−	0.929695i
$452$	6.13121	+	3.53986i	0.288388	+	0.166501i
$453$		0			0
$454$	−6.18933			−0.290480
$455$	18.0450	−	8.90676i	0.845963	−	0.417556i
$456$		0			0
$457$	−19.2757	−	19.2757i	−0.901678	−	0.901678i	0.0939032	−	0.995581i	$-0.470066\pi$
$457$	−19.2757	−	19.2757i	−0.901678	−	0.901678i	−0.995581	+	0.0939032i	$0.970066\pi$
$458$	2.22838	+	1.28656i	0.104125	+	0.0601169i
$459$		0			0
$460$	−7.36396	−	27.4827i	−0.343346	−	1.28139i
$461$	5.21155	+	19.4498i	0.242726	+	0.905866i	0.974513	+	0.224332i	$0.0720200\pi$
$461$	5.21155	+	19.4498i	0.242726	+	0.905866i	−0.731787	+	0.681534i	$0.761313\pi$
$462$		0			0
$463$	6.95272	−	6.95272i	0.323120	−	0.323120i	−0.526843	−	0.849963i	$-0.676624\pi$
$463$	6.95272	−	6.95272i	0.323120	−	0.323120i	0.849963	+	0.526843i	$0.176624\pi$
$464$	1.62196	+	2.80932i	0.0752976	+	0.130419i
$465$		0			0
$466$	0.303570	+	1.13294i	0.0140626	+	0.0524824i
$467$	−7.90161	+	13.6860i	−0.365643	+	0.633312i	−0.988879	−	0.148722i	$-0.952484\pi$
$467$	−7.90161	+	13.6860i	−0.365643	+	0.633312i	0.623236	+	0.782034i	$0.285817\pi$
$468$		0			0
$469$	−4.54424	−	2.09062i	−0.209834	−	0.0965359i
$470$	1.05869	−	3.95109i	0.0488338	−	0.182250i
$471$		0			0
$472$	−5.61229			−0.258327
$473$	3.75799	−	14.0250i	0.172793	−	0.644871i
$474$		0			0
$475$	3.59326	−	0.962812i	0.164870	−	0.0441768i
$476$	−9.58231	+	11.5398i	−0.439205	+	0.528926i
$477$		0			0
$478$		−	4.36143i		−	0.199487i
$479$	31.8547	−	8.53543i	1.45548	−	0.389994i	0.557552	−	0.830142i	$-0.311741\pi$
$479$	31.8547	−	8.53543i	1.45548	−	0.389994i	0.897925	+	0.440148i	$0.145074\pi$
$480$		0			0
$481$	14.5981	−	1.52802i	0.665615	−	0.0696716i
$482$			7.70784i			0.351082i
$483$		0			0
$484$	−2.31553	−	4.01062i	−0.105252	−	0.182301i
$485$	−27.8183	+	16.0609i	−1.26316	+	0.729287i
$486$		0			0
$487$	19.1464	+	19.1464i	0.867606	+	0.867606i	0.992207	−	0.124601i	$-0.0397651\pi$
$487$	19.1464	+	19.1464i	0.867606	+	0.867606i	−0.124601	+	0.992207i	$0.539765\pi$
$488$	1.85506	−	6.92316i	0.0839745	−	0.313397i
$489$		0			0
$490$	7.37984	+	2.60037i	0.333387	+	0.117473i
$491$	10.9028	−	6.29476i	0.492038	−	0.284078i	−0.233381	−	0.972385i	$-0.574979\pi$
$491$	10.9028	−	6.29476i	0.492038	−	0.284078i	0.725420	+	0.688307i	$0.241646\pi$
$492$		0			0
$493$	−2.23400	−	3.86941i	−0.100614	−	0.174269i
$494$	2.02703	−	12.7629i	0.0912002	−	0.574228i
$495$		0			0
$496$	−15.2868	−	4.09607i	−0.686396	−	0.183919i
$497$	−24.5709	−	11.3041i	−1.10216	−	0.507057i
$498$		0			0
$499$	24.0438	−	6.44253i	1.07635	−	0.288407i	0.323251	−	0.946313i	$-0.395224\pi$
$499$	24.0438	−	6.44253i	1.07635	−	0.288407i	0.753100	+	0.657906i	$0.228558\pi$
$500$	14.2328	−	14.2328i	0.636509	−	0.636509i
$501$		0			0
$502$	11.0022	−	2.94803i	0.491052	−	0.131577i
$503$	−22.2573	−	12.8503i	−0.992404	−	0.572965i	−0.0864120	−	0.996259i	$-0.527540\pi$
$503$	−22.2573	−	12.8503i	−0.992404	−	0.572965i	−0.905992	+	0.423295i	$0.860873\pi$
$504$		0			0
$505$	−17.0646	−	4.57244i	−0.759364	−	0.203471i
$506$	−10.3757	−	5.99041i	−0.461256	−	0.266306i
$507$		0			0
$508$	14.9303	+	25.8601i	0.662426	+	1.14735i
$509$	−6.37261	+	6.37261i	−0.282461	+	0.282461i	−0.834090	−	0.551629i	$-0.814007\pi$
$509$	−6.37261	+	6.37261i	−0.282461	+	0.282461i	0.551629	+	0.834090i	$0.314007\pi$
$510$		0			0
$511$	−15.2097	+	10.7670i	−0.672837	+	0.476303i
$512$	−15.4932	−	15.4932i	−0.684708	−	0.684708i
$513$		0			0
$514$	−2.82617	−	2.82617i	−0.124657	−	0.124657i
$515$	16.0827	+	4.30935i	0.708689	+	0.189893i
$516$		0			0
$517$	5.27332	+	9.13366i	0.231920	+	0.401698i
$518$	4.39076	+	3.64595i	0.192919	+	0.160194i
$519$		0			0
$520$	−5.36577	−	13.9962i	−0.235305	−	0.613773i
$521$	10.2174	−	5.89904i	0.447634	−	0.258442i	−0.259196	−	0.965825i	$-0.583458\pi$
$521$	10.2174	−	5.89904i	0.447634	−	0.258442i	0.706831	+	0.707383i	$0.250124\pi$
$522$		0			0
$523$			28.6286i			1.25184i	0.779888	+	0.625920i	$0.215276\pi$
$523$			28.6286i			1.25184i	−0.779888	+	0.625920i	$0.784724\pi$
$524$	−6.54464	+	11.3357i	−0.285904	+	0.495200i
$525$		0			0
$526$	−12.2010	+	3.26924i	−0.531987	+	0.142545i
$527$	21.0552	+	5.64172i	0.917178	+	0.245757i
$528$		0			0
$529$	−38.5465			−1.67593
$530$	8.67323			0.376741
$531$		0			0
$532$	−25.1118	+	17.7767i	−1.08873	+	0.770717i
$533$	−14.5098	−	19.9889i	−0.628487	−	0.865815i
$534$		0			0
$535$	10.9282	+	40.7846i	0.472468	+	1.76327i
$536$	−1.86297	+	3.22675i	−0.0804679	+	0.139375i
$537$		0			0
$538$	−10.3525	+	10.3525i	−0.446330	+	0.446330i
$539$	−18.1956	+	8.71378i	−0.783739	+	0.375329i
$540$		0			0
$541$	5.54336	+	20.6881i	0.238328	+	0.889451i	0.976621	+	0.214971i	$0.0689655\pi$
$541$	5.54336	+	20.6881i	0.238328	+	0.889451i	−0.738293	+	0.674480i	$0.764368\pi$
$542$			10.9592i			0.470740i
$543$		0			0
$544$	12.1488	+	12.1488i	0.520876	+	0.520876i
$545$	−14.7606			−0.632273
$546$		0			0
$547$	−26.1223			−1.11691			−0.558455	−	0.829535i	$-0.688606\pi$
$547$	−26.1223			−1.11691			−0.558455	+	0.829535i	$0.688606\pi$
$548$	19.1103	+	19.1103i	0.816353	+	0.816353i
$549$		0			0
$550$		−	0.839896i		−	0.0358133i
$551$	−2.37201	−	8.85245i	−0.101051	−	0.377127i
$552$		0			0
$553$	5.61355	−	2.07593i	0.238713	−	0.0882777i
$554$	3.36616	−	3.36616i	0.143014	−	0.143014i
$555$		0			0
$556$	15.9373	−	27.6042i	0.675891	−	1.17068i
$557$	−8.92401	−	33.3049i	−0.378123	−	1.41117i	−0.848728	−	0.528829i	$-0.822631\pi$
$557$	−8.92401	−	33.3049i	−0.378123	−	1.41117i	0.470606	−	0.882344i	$-0.344035\pi$
$558$		0			0
$559$	−6.50239	−	16.9610i	−0.275022	−	0.717372i
$560$	−5.58483	+	12.1394i	−0.236002	+	0.512982i
$561$		0			0
$562$	9.98320			0.421116
$563$	−16.0219			−0.675243			−0.337622	−	0.941282i	$-0.609622\pi$
$563$	−16.0219			−0.675243			−0.337622	+	0.941282i	$0.609622\pi$
$564$		0			0
$565$	−8.39090	−	2.24834i	−0.353008	−	0.0945882i
$566$	9.92810	−	2.66023i	0.417309	−	0.111818i
$567$		0			0
$568$	−10.0731	+	17.4472i	−0.422660	+	0.732068i
$569$		−	26.4737i		−	1.10983i	−0.831906	−	0.554917i	$-0.812750\pi$
$569$		−	26.4737i		−	1.10983i	0.831906	−	0.554917i	$-0.187250\pi$
$570$		0			0
$571$	−13.5784	+	7.83948i	−0.568237	+	0.328072i	−0.756445	−	0.654057i	$-0.773065\pi$
$571$	−13.5784	+	7.83948i	−0.568237	+	0.328072i	0.188208	+	0.982129i	$0.439732\pi$
$572$	16.3176	+	7.27339i	0.682271	+	0.304116i
$573$		0			0
$574$	1.61905	−	9.46662i	0.0675777	−	0.395129i
$575$	−2.15731	−	3.73657i	−0.0899660	−	0.155826i
$576$		0			0
$577$	28.1675	+	7.54746i	1.17263	+	0.314205i	0.791999	−	0.610523i	$-0.209041\pi$
$577$	28.1675	+	7.54746i	1.17263	+	0.314205i	0.380630	+	0.924728i	$0.375707\pi$
$578$	2.29525	+	2.29525i	0.0954698	+	0.0954698i
$579$		0			0
$580$	−3.47467	−	3.47467i	−0.144278	−	0.144278i
$581$	−14.7994	+	1.37153i	−0.613981	+	0.0569008i
$582$		0			0
$583$	−15.8127	+	15.8127i	−0.654896	+	0.654896i
$584$	6.94038	+	12.0211i	0.287195	+	0.497436i
$585$		0			0
$586$	−11.9942	−	6.92487i	−0.495477	−	0.286064i
$587$	−7.40030	−	1.98290i	−0.305443	−	0.0818432i	0.102842	−	0.994698i	$-0.467206\pi$
$587$	−7.40030	−	1.98290i	−0.305443	−	0.0818432i	−0.408285	+	0.912854i	$0.633873\pi$
$588$		0			0
$589$	38.7215	+	22.3558i	1.59549	+	0.921157i
$590$	3.07478	−	0.823884i	0.126587	−	0.0339188i
$591$		0			0
$592$	−6.89176	+	6.89176i	−0.283249	+	0.283249i
$593$	17.5955	−	4.71470i	0.722561	−	0.193610i	0.121247	−	0.992622i	$-0.461311\pi$
$593$	17.5955	−	4.71470i	0.722561	−	0.193610i	0.601314	+	0.799013i	$0.294644\pi$
$594$		0			0
$595$	7.69225	−	16.7201i	0.315351	−	0.685458i
$596$	36.6679	+	9.82514i	1.50198	+	0.402453i
$597$		0			0
$598$	−14.9069	+	1.56035i	−0.609590	+	0.0638073i
$599$	7.09934	+	12.2964i	0.290071	+	0.502418i	0.973826	−	0.227293i	$-0.0729876\pi$
$599$	7.09934	+	12.2964i	0.290071	+	0.502418i	−0.683755	+	0.729712i	$0.739654\pi$
$600$		0			0
$601$	11.4194	−	6.59300i	0.465807	−	0.268934i	−0.248676	−	0.968587i	$-0.579995\pi$
$601$	11.4194	−	6.59300i	0.465807	−	0.268934i	0.714483	+	0.699653i	$0.246662\pi$
$602$	2.95196	−	6.41648i	0.120313	−	0.261516i
$603$		0			0
$604$	−7.92750	+	29.5858i	−0.322565	+	1.20383i
$605$	4.01805	+	4.01805i	0.163357	+	0.163357i
$606$		0			0
$607$	9.77151	−	5.64158i	0.396613	−	0.228985i	−0.288408	−	0.957508i	$-0.593126\pi$
$607$	9.77151	−	5.64158i	0.396613	−	0.228985i	0.685022	+	0.728523i	$0.259793\pi$
$608$	17.6208	+	30.5201i	0.714617	+	1.23775i
$609$		0			0
$610$			4.06528i			0.164598i
$611$	12.0512	+	5.37170i	0.487539	+	0.217316i
$612$		0			0
$613$	−9.62690	+	2.57952i	−0.388827	+	0.104186i	−0.447936	−	0.894066i	$-0.647841\pi$
$613$	−9.62690	+	2.57952i	−0.388827	+	0.104186i	0.0591091	+	0.998252i	$0.481174\pi$
$614$		−	1.18665i		−	0.0478894i
$615$		0			0
$616$	5.21228	+	14.0946i	0.210009	+	0.567887i
$617$	−37.7991	+	10.1282i	−1.52173	+	0.407747i	−0.920312	−	0.391184i	$-0.872065\pi$
$617$	−37.7991	+	10.1282i	−1.52173	+	0.407747i	−0.601422	+	0.798932i	$0.705399\pi$
$618$		0			0
$619$	−5.02957	+	18.7706i	−0.202156	+	0.754455i	0.788142	+	0.615493i	$0.211043\pi$
$619$	−5.02957	+	18.7706i	−0.202156	+	0.754455i	−0.990298	+	0.138962i	$0.955624\pi$
$620$	23.9734			0.962795
$621$		0			0
$622$	2.08342	−	7.77544i	0.0835376	−	0.311767i
$623$	3.01586	+	32.5423i	0.120828	+	1.30378i
$624$		0			0
$625$	−10.9738	+	19.0072i	−0.438953	+	0.760290i
$626$	0.422355	+	1.57625i	0.0168807	+	0.0629996i
$627$		0			0
$628$	−3.27427	−	5.67121i	−0.130658	−	0.226306i
$629$	9.49234	−	9.49234i	0.378484	−	0.378484i
$630$		0			0
$631$	−2.13268	−	7.95928i	−0.0849008	−	0.316854i	0.910395	−	0.413741i	$-0.135778\pi$
$631$	−2.13268	−	7.95928i	−0.0849008	−	0.316854i	−0.995295	+	0.0968871i	$0.969111\pi$
$632$	−1.15386	−	4.30626i	−0.0458980	−	0.171294i
$633$		0			0
$634$	−3.77576	−	2.17994i	−0.149955	−	0.0865764i
$635$	−25.9080	−	25.9080i	−1.02813	−	1.02813i
$636$		0			0
$637$	−12.0177	+	22.1940i	−0.476160	+	0.879359i
$638$	−2.06919			−0.0819200
$639$		0			0
$640$	20.9995	+	12.1241i	0.830078	+	0.479246i
$641$			39.9291i			1.57710i	0.614968	+	0.788552i	$0.289169\pi$
$641$			39.9291i			1.57710i	−0.614968	+	0.788552i	$0.710831\pi$
$642$		0			0
$643$	3.71724	+	13.8729i	0.146594	+	0.547095i	0.999679	+	0.0253239i	$0.00806170\pi$
$643$	3.71724	+	13.8729i	0.146594	+	0.547095i	−0.853086	+	0.521771i	$0.825272\pi$
$644$	27.4537	+	22.7968i	1.08183	+	0.898319i
$645$		0			0
$646$	−5.90955	−	10.2356i	−0.232508	−	0.402716i
$647$	−4.52657	+	7.84025i	−0.177958	+	0.308232i	−0.941181	−	0.337903i	$-0.890282\pi$
$647$	−4.52657	+	7.84025i	−0.177958	+	0.308232i	0.763223	+	0.646135i	$0.223616\pi$
$648$		0			0
$649$	−4.10375	+	7.10790i	−0.161086	+	0.279010i
$650$	−0.617244	−	0.850327i	−0.0242103	−	0.0333526i
$651$		0			0
$652$	3.53132	−	13.1791i	0.138297	−	0.516132i
$653$	−33.8493			−1.32462			−0.662312	−	0.749228i	$-0.730425\pi$
$653$	−33.8493			−1.32462			−0.662312	+	0.749228i	$0.730425\pi$
$654$		0			0
$655$	4.15682	−	15.5135i	0.162420	−	0.606161i
$656$	15.8425	+	4.24499i	0.618546	+	0.165739i
$657$		0			0
$658$	1.77944	+	4.81179i	0.0693697	+	0.187583i
$659$	−14.7702	+	25.5827i	−0.575365	+	0.996561i	0.420637	+	0.907229i	$0.361807\pi$
$659$	−14.7702	+	25.5827i	−0.575365	+	0.996561i	−0.996002	+	0.0893323i	$0.971527\pi$
$660$		0			0
$661$	−20.8758	+	5.59365i	−0.811973	+	0.217568i	−0.640834	−	0.767679i	$-0.721411\pi$
$661$	−20.8758	+	5.59365i	−0.811973	+	0.217568i	−0.171139	+	0.985247i	$0.554745\pi$
$662$	−10.1152	+	5.84002i	−0.393139	+	0.226979i
$663$		0			0
$664$			11.0709i			0.429636i
$665$	24.1171	−	29.0438i	0.935223	−	1.12627i
$666$		0			0
$667$	−9.20550	+	5.31480i	−0.356438	+	0.205790i
$668$	−19.1779	−	5.13871i	−0.742016	−	0.198823i
$669$		0			0
$670$	0.546967	−	2.04131i	0.0211312	−	0.0788626i
$671$	−7.41167	−	7.41167i	−0.286124	−	0.286124i
$672$		0			0
$673$	−40.0862	+	23.1438i	−1.54521	+	0.892126i	−0.546711	+	0.837321i	$0.684120\pi$
$673$	−40.0862	+	23.1438i	−1.54521	+	0.892126i	−0.998497	+	0.0548050i	$0.982546\pi$
$674$	2.47645	−	2.47645i	0.0953893	−	0.0953893i
$675$		0			0
$676$	21.8655	−	4.62813i	0.840979	−	0.178005i
$677$	−3.29683	−	1.90343i	−0.126707	−	0.0731546i	0.435307	−	0.900282i	$-0.356640\pi$
$677$	−3.29683	−	1.90343i	−0.126707	−	0.0731546i	−0.562014	+	0.827128i	$0.689973\pi$
$678$		0			0
$679$	16.8380	−	36.5997i	0.646184	−	1.40457i
$680$	−11.8725	−	6.85462i	−0.455291	−	0.262863i
$681$		0			0
$682$	7.13816	−	7.13816i	0.273334	−	0.273334i
$683$	7.72051	−	7.72051i	0.295417	−	0.295417i	−0.543799	−	0.839216i	$-0.683015\pi$
$683$	7.72051	−	7.72051i	0.295417	−	0.295417i	0.839216	+	0.543799i	$0.183015\pi$
$684$		0			0
$685$	−28.7186	−	16.5807i	−1.09728	−	0.633515i
$686$	−9.43888	+	2.68594i	−0.360378	+	0.102550i
$687$		0			0
$688$	10.4458	+	6.03088i	0.398242	+	0.229925i
$689$	−4.38825	+	27.6300i	−0.167179	+	1.05262i
$690$		0			0
$691$	−16.3121	+	16.3121i	−0.620541	+	0.620541i	−0.945670	−	0.325129i	$-0.894592\pi$
$691$	−16.3121	+	16.3121i	−0.620541	+	0.620541i	0.325129	+	0.945670i	$0.394592\pi$
$692$	−28.3756	+	16.3827i	−1.07868	+	0.622776i
$693$		0			0
$694$	5.77412	+	5.77412i	0.219183	+	0.219183i
$695$	−10.1225	+	37.7778i	−0.383970	+	1.43300i
$696$		0			0
$697$	−21.8206	−	5.84682i	−0.826515	−	0.221464i
$698$	−1.16741	+	0.674003i	−0.0441870	+	0.0255114i
$699$		0			0
$700$	−0.421722	+	2.46582i	−0.0159396	+	0.0931992i
$701$		−	12.3895i		−	0.467945i	−0.972243	−	0.233973i	$-0.924827\pi$
$701$		−	12.3895i		−	0.467945i	0.972243	−	0.233973i	$-0.0751726\pi$
$702$		0			0
$703$	23.8465	−	13.7678i	0.899389	−	0.519262i
$704$	−5.64445	+	1.51243i	−0.212733	+	0.0570017i
$705$		0			0
$706$	1.33628	−	2.31451i	0.0502917	−	0.0871077i
$707$	20.7819	−	7.68531i	0.781584	−	0.289036i
$708$		0			0
$709$	23.0444	+	6.17472i	0.865449	+	0.231896i	0.664119	−	0.747627i	$-0.268807\pi$
$709$	23.0444	+	6.17472i	0.865449	+	0.231896i	0.201330	+	0.979523i	$0.435474\pi$
$710$	2.95747	−	11.0374i	0.110992	−	0.414227i
$711$		0			0
$712$	24.3438			0.912324
$713$	13.4219	−	50.0912i	0.502654	−	1.87593i
$714$		0			0
$715$	−21.6495	−	3.43842i	−0.809645	−	0.128589i
$716$	−9.32484	+	16.1511i	−0.348486	+	0.603595i
$717$		0			0
$718$	2.56834	−	4.44850i	0.0958498	−	0.166017i
$719$	−20.8277	−	36.0747i	−0.776744	−	1.34536i	−0.933809	−	0.357771i	$-0.883537\pi$
$719$	−20.8277	−	36.0747i	−0.776744	−	1.34536i	0.157065	−	0.987588i	$-0.449797\pi$
$720$		0			0
$721$	−19.5862	+	7.24311i	−0.729427	+	0.269747i
$722$	−3.66887	−	13.6924i	−0.136541	−	0.509579i
$723$		0			0
$724$			9.82760i			0.365240i
$725$	−0.645337	−	0.372585i	−0.0239672	−	0.0138375i
$726$		0			0
$727$	31.5386			1.16970			0.584851	−	0.811141i	$-0.301153\pi$
$727$	31.5386			1.16970			0.584851	+	0.811141i	$0.301153\pi$
$728$	15.6352	+	10.4391i	0.579479	+	0.386898i
$729$		0			0
$730$	−5.56708	−	5.56708i	−0.206047	−	0.206047i
$731$	−14.3875	−	8.30662i	−0.532140	−	0.307231i
$732$		0			0
$733$	−8.44436	−	31.5148i	−0.311899	−	1.16402i	−0.926842	−	0.375452i	$-0.877487\pi$
$733$	−8.44436	−	31.5148i	−0.311899	−	1.16402i	0.614942	−	0.788572i	$-0.289179\pi$
$734$	1.02661	+	3.83137i	0.0378929	+	0.141418i
$735$		0			0
$736$	28.9026	−	28.9026i	1.06536	−	1.06536i
$737$	2.72443	+	4.71885i	0.100356	+	0.173821i
$738$		0			0
$739$	8.60509	+	32.1146i	0.316543	+	1.18136i	0.922544	+	0.385892i	$0.126106\pi$
$739$	8.60509	+	32.1146i	0.316543	+	1.18136i	−0.606001	+	0.795464i	$0.707227\pi$
$740$	7.38199	−	12.7860i	0.271367	−	0.470022i
$741$		0			0
$742$	−8.87850	+	6.28512i	−0.325940	+	0.230734i
$743$	−8.41303	+	31.3979i	−0.308644	+	1.15188i	0.621118	+	0.783717i	$0.286679\pi$
$743$	−8.41303	+	31.3979i	−0.308644	+	1.15188i	−0.929763	+	0.368159i	$0.879988\pi$
$744$		0			0
$745$	−46.5792			−1.70653
$746$	−2.59723	+	9.69301i	−0.0950915	+	0.354886i
$747$		0			0
$748$	15.7826	−	4.22893i	0.577068	−	0.154625i
$749$	−40.7417	−	33.8307i	−1.48867	−	1.23615i
$750$		0			0
$751$		−	42.9234i		−	1.56630i	−0.621835	−	0.783148i	$-0.713613\pi$
$751$		−	42.9234i		−	1.56630i	0.621835	−	0.783148i	$-0.286387\pi$
$752$	−8.46271	+	2.26758i	−0.308603	+	0.0826900i
$753$		0			0
$754$	−2.09489	+	1.52066i	−0.0762912	+	0.0553791i
$755$		−	37.5828i		−	1.36778i
$756$		0			0
$757$	6.45620	+	11.1825i	0.234654	+	0.406433i	0.959172	−	0.282823i	$-0.0912708\pi$
$757$	6.45620	+	11.1825i	0.234654	+	0.406433i	−0.724518	+	0.689256i	$0.757937\pi$
$758$	−11.7321	+	6.77353i	−0.426129	+	0.246026i
$759$		0			0
$760$	−19.8840	−	19.8840i	−0.721270	−	0.721270i
$761$	−9.87024	+	36.8362i	−0.357796	+	1.33531i	0.519134	+	0.854693i	$0.326255\pi$
$761$	−9.87024	+	36.8362i	−0.357796	+	1.33531i	−0.876929	+	0.480619i	$0.840412\pi$
$762$		0			0
$763$	15.1099	−	10.6964i	0.547016	−	0.387234i
$764$	−34.2520	+	19.7754i	−1.23919	+	0.715449i
$765$		0			0
$766$	2.38776	+	4.13571i	0.0862731	+	0.149429i
$767$	1.06892	+	10.2120i	0.0385965	+	0.368735i
$768$		0			0
$769$	0.0137463	+	0.00368331i	0.000495704	+	0.000132824i	0.259067	−	0.965859i	$-0.416585\pi$
$769$	0.0137463	+	0.00368331i	0.000495704	+	0.000132824i	−0.258571	+	0.965992i	$0.583252\pi$
$770$	−4.92471	−	6.95676i	−0.177474	−	0.250704i
$771$		0			0
$772$	−8.28154	+	2.21903i	−0.298059	+	0.0798647i
$773$	−12.1599	+	12.1599i	−0.437360	+	0.437360i	−0.891123	−	0.453763i	$-0.850081\pi$
$773$	−12.1599	+	12.1599i	−0.437360	+	0.437360i	0.453763	+	0.891123i	$0.350081\pi$
$774$		0			0
$775$	3.51157	−	0.940921i	0.126139	−	0.0337989i
$776$	−25.9886	−	15.0045i	−0.932935	−	0.538630i
$777$		0			0
$778$	14.4718	+	3.87771i	0.518840	+	0.139023i
$779$	−40.1292	−	23.1686i	−1.43778	−	0.830101i
$780$		0			0
$781$	14.7311	+	25.5150i	0.527120	+	0.912999i
$782$	−9.69318	+	9.69318i	−0.346627	+	0.346627i
$783$		0			0
$784$	−3.07987	−	16.4738i	−0.109995	−	0.588349i
$785$	5.68171	+	5.68171i	0.202789	+	0.202789i
$786$		0			0
$787$	−23.9249	−	23.9249i	−0.852829	−	0.852829i	0.137652	−	0.990481i	$-0.456045\pi$
$787$	−23.9249	−	23.9249i	−0.852829	−	0.852829i	−0.990481	+	0.137652i	$0.956045\pi$
$788$	7.51514	+	2.01368i	0.267716	+	0.0717343i
$789$		0			0
$790$	1.26432	+	2.18986i	0.0449823	+	0.0779117i
$791$	10.2188	−	3.77898i	0.363338	−	0.134365i
$792$		0			0
$793$	−12.9506	−	2.05684i	−0.459889	−	0.0730406i
$794$	−7.80742	+	4.50761i	−0.277075	+	0.159969i
$795$		0			0
$796$			37.4913i			1.32884i
$797$	10.7585	−	18.6343i	0.381087	−	0.660062i	−0.610131	−	0.792300i	$-0.708883\pi$
$797$	10.7585	−	18.6343i	0.381087	−	0.660062i	0.991218	+	0.132239i	$0.0422166\pi$
$798$		0			0
$799$	11.6561	−	3.12324i	0.412363	−	0.110492i
$800$	2.76780	+	0.741630i	0.0978565	+	0.0262206i
$801$		0			0
$802$	3.02008			0.106643
$803$	20.2994			0.716351
$804$		0			0
$805$	−39.7780	−	18.3002i	−1.40199	−	0.644998i
$806$	1.98094	−	12.4727i	0.0697756	−	0.439332i
$807$		0			0
$808$	−4.27169	−	15.9422i	−0.150278	−	0.560844i
$809$	−1.69452	+	2.93499i	−0.0595761	+	0.103189i	−0.894275	−	0.447518i	$-0.852308\pi$
$809$	−1.69452	+	2.93499i	−0.0595761	+	0.103189i	0.834699	+	0.550706i	$0.185642\pi$
$810$		0			0
$811$	−10.1944	+	10.1944i	−0.357974	+	0.357974i	−0.863066	−	0.505092i	$-0.831459\pi$
$811$	−10.1944	+	10.1944i	−0.357974	+	0.357974i	0.505092	+	0.863066i	$0.331459\pi$
$812$	6.07485	+	1.03896i	0.213186	+	0.0364605i
$813$		0			0
$814$	−1.60906	−	6.00508i	−0.0563974	−	0.210478i
$815$			16.7413i			0.586423i
$816$		0			0
$817$	−24.0960	−	24.0960i	−0.843013	−	0.843013i
$818$	6.27596			0.219434
$819$		0			0
$820$	−24.8450			−0.867624
$821$	−2.93440	−	2.93440i	−0.102411	−	0.102411i	0.654045	−	0.756456i	$-0.273071\pi$
$821$	−2.93440	−	2.93440i	−0.102411	−	0.102411i	−0.756456	+	0.654045i	$0.773071\pi$
$822$		0			0
$823$		−	50.1952i		−	1.74969i	−0.484399	−	0.874847i	$-0.660962\pi$
$823$		−	50.1952i		−	1.74969i	0.484399	−	0.874847i	$-0.339038\pi$
$824$	4.02591	+	15.0249i	0.140249	+	0.523417i
$825$		0			0
$826$	−2.55052	+	3.07154i	−0.0887438	+	0.106873i
$827$	−17.6628	+	17.6628i	−0.614195	+	0.614195i	−0.944036	−	0.329842i	$-0.893005\pi$
$827$	−17.6628	+	17.6628i	−0.614195	+	0.614195i	0.329842	+	0.944036i	$0.393005\pi$
$828$		0			0
$829$	16.4016	−	28.4085i	0.569652	−	0.986667i	−0.426948	−	0.904276i	$-0.640411\pi$
$829$	16.4016	−	28.4085i	0.569652	−	0.986667i	0.996600	−	0.0823905i	$-0.0262555\pi$
$830$	−1.62521	−	6.06538i	−0.0564119	−	0.210532i
$831$		0			0
$832$	−4.60306	+	5.67934i	−0.159582	+	0.196896i
$833$	4.24205	+	22.6901i	0.146978	+	0.786165i
$834$		0			0
$835$	24.3617			0.843071
$836$	33.5151			1.15914
$837$		0			0
$838$	−5.46165	−	1.46345i	−0.188670	−	0.0505539i
$839$	12.9458	−	3.46880i	0.446937	−	0.119756i	−0.0283288	−	0.999599i	$-0.509019\pi$
$839$	12.9458	−	3.46880i	0.446937	−	0.119756i	0.475266	+	0.879842i	$0.342352\pi$
$840$		0			0
$841$	13.5821	−	23.5249i	0.468348	−	0.811202i
$842$			5.89429i			0.203131i
$843$		0			0
$844$	15.2539	−	8.80683i	0.525060	−	0.303144i
$845$	−24.4452	+	12.4292i	−0.840942	+	0.427577i
$846$		0			0
$847$	−7.02486	−	1.20144i	−0.241377	−	0.0412820i
$848$	−9.28845	−	16.0881i	−0.318967	−	0.552466i
$849$		0			0
$850$	−0.928248	−	0.248723i	−0.0318387	−	0.00853114i
$851$	−22.5827	−	22.5827i	−0.774126	−	0.774126i
$852$		0			0
$853$	26.6788	+	26.6788i	0.913466	+	0.913466i	0.996543	−	0.0830772i	$-0.0264748\pi$
$853$	26.6788	+	26.6788i	0.913466	+	0.913466i	−0.0830772	+	0.996543i	$0.526475\pi$
$854$	−2.94593	−	4.16149i	−0.100808	−	0.142403i
$855$		0			0
$856$	−27.8927	+	27.8927i	−0.953351	+	0.953351i
$857$	23.1022	+	40.0142i	0.789156	+	1.36686i	0.926484	+	0.376333i	$0.122815\pi$
$857$	23.1022	+	40.0142i	0.789156	+	1.36686i	−0.137328	+	0.990526i	$0.543852\pi$
$858$		0			0
$859$	23.6394	+	13.6482i	0.806565	+	0.465671i	0.845762	−	0.533561i	$-0.179147\pi$
$859$	23.6394	+	13.6482i	0.806565	+	0.465671i	−0.0391966	+	0.999232i	$0.512480\pi$
$860$	−17.6487	−	4.72896i	−0.601816	−	0.161256i
$861$		0			0
$862$	2.99181	+	1.72732i	0.101902	+	0.0588329i
$863$	17.4947	−	4.68768i	0.595525	−	0.159570i	0.0515479	−	0.998671i	$-0.483585\pi$
$863$	17.4947	−	4.68768i	0.595525	−	0.159570i	0.543977	+	0.839100i	$0.316918\pi$
$864$		0			0
$865$	28.4282	−	28.4282i	0.966588	−	0.966588i
$866$	−11.9345	+	3.19784i	−0.405551	+	0.108667i
$867$		0			0
$868$	−24.5408	+	17.3725i	−0.832970	+	0.589661i
$869$	−6.29753	−	1.68742i	−0.213629	−	0.0572418i
$870$		0			0
$871$	6.22617	+	2.77526i	0.210966	+	0.0940360i
$872$	−6.89486	−	11.9422i	−0.233489	−	0.404415i
$873$		0			0
$874$	−24.3511	+	14.0591i	−0.823687	+	0.475556i
$875$	−2.85843	−	30.8435i	−0.0966326	−	1.04270i
$876$		0			0
$877$	−2.86898	+	10.7072i	−0.0968786	+	0.361556i	−0.997298	−	0.0734680i	$-0.976593\pi$
$877$	−2.86898	+	10.7072i	−0.0968786	+	0.361556i	0.900419	+	0.435024i	$0.143260\pi$
$878$	−2.20033	−	2.20033i	−0.0742576	−	0.0742576i
$879$		0			0
$880$	12.6058	−	7.27797i	0.424942	−	0.245340i
$881$	5.59477	+	9.69042i	0.188492	+	0.326479i	0.944748	−	0.327798i	$-0.106307\pi$
$881$	5.59477	+	9.69042i	0.188492	+	0.326479i	−0.756255	+	0.654277i	$0.772973\pi$
$882$		0			0
$883$		−	45.3449i		−	1.52598i	−0.646411	−	0.762989i	$-0.723731\pi$
$883$		−	45.3449i		−	1.52598i	0.646411	−	0.762989i	$-0.276269\pi$
$884$	12.8707	−	15.8801i	0.432889	−	0.534107i
$885$		0			0
$886$	−11.5351	+	3.09081i	−0.387528	+	0.103838i
$887$			37.1402i			1.24704i	0.781805	+	0.623522i	$0.214299\pi$
$887$			37.1402i			1.24704i	−0.781805	+	0.623522i	$0.785701\pi$
$888$		0			0
$889$	45.2955	+	7.74676i	1.51916	+	0.259818i
$890$	−13.3371	+	3.57367i	−0.447061	+	0.119790i
$891$		0			0
$892$	−9.66570	+	36.0729i	−0.323632	+	1.20781i
$893$	24.7523			0.828303
$894$		0			0
$895$	5.92266	−	22.1037i	0.197973	−	0.738845i
$896$	−30.2823	+	2.80642i	−1.01166	+	0.0937558i
$897$		0			0
$898$	1.23456	−	2.13832i	0.0411978	−	0.0713567i
$899$	−2.31808	−	8.65118i	−0.0773122	−	0.288533i
$900$		0			0
$901$	12.7934	+	22.1588i	0.426211	+	0.738218i
$902$	−7.39767	+	7.39767i	−0.246316	+	0.246316i
$903$		0			0
$904$	−2.10045	−	7.83900i	−0.0698601	−	0.260721i
$905$	−3.12100	−	11.6477i	−0.103745	−	0.387183i
$906$		0			0
$907$	−40.5915	−	23.4355i	−1.34782	−	0.778163i	−0.359877	−	0.933000i	$-0.617181\pi$
$907$	−40.5915	−	23.4355i	−1.34782	−	0.778163i	−0.987940	+	0.154837i	$0.950515\pi$
$908$	−14.1997	−	14.1997i	−0.471234	−	0.471234i
$909$		0			0
$910$	−10.0984	−	3.42396i	−0.334759	−	0.113503i
$911$	29.2953			0.970596			0.485298	−	0.874349i	$-0.338711\pi$
$911$	29.2953			0.970596			0.485298	+	0.874349i	$0.338711\pi$
$912$		0			0
$913$	14.0212	+	8.09515i	0.464035	+	0.267910i
$914$			14.4446i			0.477785i
$915$		0			0
$916$	2.16076	+	8.06406i	0.0713934	+	0.266444i
$917$	6.98674	+	18.8929i	0.230723	+	0.623899i
$918$		0			0
$919$	11.4671	+	19.8616i	0.378265	+	0.655173i	0.990810	−	0.135262i	$-0.0431876\pi$
$919$	11.4671	+	19.8616i	0.378265	+	0.655173i	−0.612545	+	0.790435i	$0.709854\pi$
$920$	−16.3075	+	28.2453i	−0.537641	+	0.931222i
$921$		0			0
$922$	5.33484	−	9.24022i	0.175694	−	0.304311i
$923$	33.6652	+	15.0059i	1.10810	+	0.493926i
$924$		0			0
$925$	0.579464	−	2.16259i	0.0190527	−	0.0711055i
$926$	−5.21016			−0.171217
$927$		0			0
$928$	1.82710	−	6.81882i	0.0599774	−	0.223839i
$929$	16.2916	+	4.36533i	0.534511	+	0.143222i	0.515971	−	0.856606i	$-0.327431\pi$
$929$	16.2916	+	4.36533i	0.534511	+	0.143222i	0.0185406	+	0.999828i	$0.494098\pi$
$930$		0			0
$931$	−3.64111	+	47.2079i	−0.119333	+	1.54718i
$932$	−1.90276	+	3.29568i	−0.0623270	+	0.107953i
$933$		0			0
$934$	8.08855	−	2.16732i	0.264665	−	0.0709169i
$935$	−17.3626	+	10.0243i	−0.567817	+	0.327829i
$936$		0			0
$937$			42.9957i			1.40461i	0.711877	+	0.702304i	$0.247845\pi$
$937$			42.9957i			1.40461i	−0.711877	+	0.702304i	$0.752155\pi$
$938$	0.919335	+	2.48598i	0.0300174	+	0.0811702i
$939$		0			0
$940$	11.4936	−	6.63581i	0.374879	−	0.216436i
$941$	−53.4286	−	14.3161i	−1.74172	−	0.466693i	−0.758893	−	0.651215i	$-0.774260\pi$
$941$	−53.4286	−	14.3161i	−1.74172	−	0.466693i	−0.982828	+	0.184522i	$0.940926\pi$
$942$		0			0
$943$	−13.9099	+	51.9123i	−0.452967	+	1.69050i
$944$	−4.82111	−	4.82111i	−0.156914	−	0.156914i
$945$		0			0
$946$	−6.66303	+	3.84690i	−0.216634	+	0.125074i
$947$	−20.1687	+	20.1687i	−0.655394	+	0.655394i	−0.954287	−	0.298893i	$-0.903383\pi$
$947$	−20.1687	+	20.1687i	−0.655394	+	0.655394i	0.298893	+	0.954287i	$0.403383\pi$
$948$		0			0
$949$	20.5515	−	14.9182i	0.667131	−	0.484264i
$950$	−1.70709	−	0.985590i	−0.0553854	−	0.0319768i
$951$		0			0
$952$	17.1208	−	1.58667i	0.554888	−	0.0514244i
$953$	−15.2652	−	8.81337i	−0.494488	−	0.285493i	0.231946	−	0.972729i	$-0.425491\pi$
$953$	−15.2652	−	8.81337i	−0.494488	−	0.285493i	−0.726435	+	0.687236i	$0.758824\pi$
$954$		0			0
$955$	34.3154	−	34.3154i	1.11042	−	1.11042i
$956$	10.0061	−	10.0061i	0.323620	−	0.323620i
$957$		0			0
$958$	−15.1336	−	8.73737i	−0.488943	−	0.282292i
$959$	41.4136	−	3.83801i	1.33731	−	0.123936i
$960$		0			0
$961$	10.9943	+	6.34756i	0.354655	+	0.204760i
$962$	−6.04220	−	4.89715i	−0.194808	−	0.157891i
$963$		0			0
$964$	−17.6835	+	17.6835i	−0.569547	+	0.569547i
$965$	9.11061	−	5.26001i	0.293281	−	0.169326i
$966$		0			0
$967$	−0.451783	−	0.451783i	−0.0145284	−	0.0145284i	0.699805	−	0.714334i	$-0.253270\pi$
$967$	−0.451783	−	0.451783i	−0.0145284	−	0.0145284i	−0.714334	+	0.699805i	$0.753270\pi$
$968$	−1.37397	+	5.12774i	−0.0441612	+	0.164812i
$969$		0			0
$970$	16.4409	+	4.40531i	0.527884	+	0.141446i
$971$	−41.6003	+	24.0179i	−1.33502	+	0.770772i	−0.986064	−	0.166368i	$-0.946796\pi$
$971$	−41.6003	+	24.0179i	−1.33502	+	0.770772i	−0.348953	+	0.937140i	$0.613463\pi$
$972$		0			0
$973$	−17.0139	−	46.0073i	−0.545439	−	1.47493i
$974$		−	14.3477i		−	0.459731i
$975$		0			0
$976$	7.54072	−	4.35364i	0.241373	−	0.139357i
$977$	52.7381	−	14.1311i	1.68724	−	0.452095i	0.717565	−	0.696491i	$-0.245257\pi$
$977$	52.7381	−	14.1311i	1.68724	−	0.452095i	0.969675	+	0.244397i	$0.0785899\pi$
$978$		0			0
$979$	17.8004	−	30.8312i	0.568903	−	0.985369i
$980$	10.9652	+	22.8968i	0.350270	+	0.731412i
$981$		0			0
$982$	−6.44368	−	1.72658i	−0.205626	−	0.0550974i
$983$	11.7532	−	43.8637i	0.374870	−	1.39903i	−0.478664	−	0.877998i	$-0.658879\pi$
$983$	11.7532	−	43.8637i	0.374870	−	1.39903i	0.853534	−	0.521036i	$-0.174454\pi$
$984$		0			0
$985$	−9.54647			−0.304176
$986$	−0.612761	+	2.28686i	−0.0195143	+	0.0728283i
$987$		0			0
$988$	33.9313	−	24.6304i	1.07950	−	0.783598i
$989$	−19.7618	+	34.2285i	−0.628390	+	1.08840i
$990$		0			0
$991$	−21.3076	+	36.9058i	−0.676858	+	1.17235i	0.299064	+	0.954233i	$0.403325\pi$
$991$	−21.3076	+	36.9058i	−0.676858	+	1.17235i	−0.975922	+	0.218119i	$0.930008\pi$
$992$	17.2201	+	29.8262i	0.546740	+	0.946982i
$993$		0			0
$994$	4.97088	+	13.4418i	0.157667	+	0.426348i
$995$	−11.9063	−	44.4349i	−0.377455	−	1.40868i
$996$		0			0
$997$			30.0295i			0.951045i	0.879704	+	0.475523i	$0.157741\pi$
$997$			30.0295i			0.951045i	−0.879704	+	0.475523i	$0.842259\pi$
$998$	−11.4228	−	6.59495i	−0.361582	−	0.208759i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.271.5		36
3.2	odd	2		273.2.bt.a.271.5	yes	36
7.3	odd	6		819.2.gh.c.388.5		36
13.6	odd	12		819.2.gh.c.19.5		36
21.17	even	6		273.2.cg.a.115.5	yes	36
39.32	even	12		273.2.cg.a.19.5	yes	36
91.45	even	12	inner	819.2.et.c.136.5		36
273.227	odd	12		273.2.bt.a.136.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.5	✓	36	273.227	odd	12
273.2.bt.a.271.5	yes	36	3.2	odd	2
273.2.cg.a.19.5	yes	36	39.32	even	12
273.2.cg.a.115.5	yes	36	21.17	even	6
819.2.et.c.136.5		36	91.45	even	12	inner
819.2.et.c.271.5		36	1.1	even	1	trivial
819.2.gh.c.19.5		36	13.6	odd	12
819.2.gh.c.388.5		36	7.3	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.374685 - 0.374685i) q^{2} -1.71922i q^{4} +(0.545981 + 2.03763i) q^{5} +(-2.03549 - 1.69021i) q^{7} +(-1.39354 + 1.39354i) q^{8} +O(q^{10})\)	\(q+(-0.374685 - 0.374685i) q^{2} -1.71922i q^{4} +(0.545981 + 2.03763i) q^{5} +(-2.03549 - 1.69021i) q^{7} +(-1.39354 + 1.39354i) q^{8} +(0.558898 - 0.968040i) q^{10} +(0.745933 + 2.78386i) q^{11} +(2.80107 + 2.27024i) q^{13} +(0.129371 + 1.39596i) q^{14} -2.39417 q^{16} +3.29760 q^{17} +(6.53354 + 1.75066i) q^{19} +(3.50314 - 0.938663i) q^{20} +(0.763581 - 1.32256i) q^{22} -7.84515i q^{23} +(0.476290 - 0.274986i) q^{25} +(-0.198893 - 1.90015i) q^{26} +(-2.90584 + 3.49945i) q^{28} +(-0.677462 - 1.17340i) q^{29} +(6.38499 + 1.71085i) q^{31} +(3.68413 + 3.68413i) q^{32} +(-1.23556 - 1.23556i) q^{34} +(2.33268 - 5.07039i) q^{35} +(2.87856 - 2.87856i) q^{37} +(-1.79207 - 3.10396i) q^{38} +(-3.60036 - 2.07867i) q^{40} +(-6.61712 - 1.77305i) q^{41} +(-4.36301 - 2.51899i) q^{43} +(4.78608 - 1.28243i) q^{44} +(-2.93946 + 2.93946i) q^{46} +(3.53471 - 0.947124i) q^{47} +(1.28640 + 6.88078i) q^{49} +(-0.281492 - 0.0754255i) q^{50} +(3.90305 - 4.81566i) q^{52} +(3.87961 + 6.71968i) q^{53} +(-5.26521 + 3.03987i) q^{55} +(5.19189 - 0.481159i) q^{56} +(-0.185820 + 0.693490i) q^{58} +(2.01369 + 2.01369i) q^{59} +(-3.14962 + 1.81843i) q^{61} +(-1.75133 - 3.03339i) q^{62} +2.02756i q^{64} +(-3.09658 + 6.94705i) q^{65} +(1.82619 - 0.489326i) q^{67} -5.66931i q^{68} +(-2.77382 + 1.02578i) q^{70} +(9.87427 - 2.64580i) q^{71} +(1.82296 - 6.80337i) q^{73} -2.15710 q^{74} +(3.00977 - 11.2326i) q^{76} +(3.18696 - 6.92729i) q^{77} +(-1.13108 + 1.95909i) q^{79} +(-1.30717 - 4.87843i) q^{80} +(1.81500 + 3.14367i) q^{82} +(3.97225 - 3.97225i) q^{83} +(1.80043 + 6.71929i) q^{85} +(0.690929 + 2.57858i) q^{86} +(-4.91890 - 2.83993i) q^{88} +(-8.73455 - 8.73455i) q^{89} +(-1.86436 - 9.35543i) q^{91} -13.4876 q^{92} +(-1.67928 - 0.969531i) q^{94} +14.2688i q^{95} +(3.94107 + 14.7083i) q^{97} +(2.09613 - 3.06012i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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