LMFDB - Embedded newform 819.2.fm.g.496.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			496.7
Character	$\chi$	$=$	819.496
Dual form			819.2.fm.g.748.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.47996 + 0.664504i) q^{2} +(3.97660 + 2.29589i) q^{4} +(-0.281686 - 0.281686i) q^{5} +(1.14426 + 2.38551i) q^{7} +(4.70528 + 4.70528i) q^{8} +O(q^{10})$	\(q+(2.47996 + 0.664504i) q^{2} +(3.97660 + 2.29589i) q^{4} +(-0.281686 - 0.281686i) q^{5} +(1.14426 + 2.38551i) q^{7} +(4.70528 + 4.70528i) q^{8} +(-0.511390 - 0.885754i) q^{10} +(-0.939666 + 3.50688i) q^{11} +(-3.44571 - 1.06165i) q^{13} +(1.25253 + 6.67635i) q^{14} +(3.95046 + 6.84240i) q^{16} +(2.04856 - 3.54822i) q^{17} +(-0.777996 + 0.208463i) q^{19} +(-0.473433 - 1.76688i) q^{20} +(-4.66067 + 8.07252i) q^{22} +(4.41149 - 2.54698i) q^{23} -4.84131i q^{25} +(-7.83976 - 4.92254i) q^{26} +(-0.926631 + 12.1133i) q^{28} +(-1.00735 - 1.74478i) q^{29} +(4.44176 + 4.44176i) q^{31} +(1.80569 + 6.73893i) q^{32} +(7.43817 - 7.43817i) q^{34} +(0.349645 - 0.994288i) q^{35} +(0.463819 - 1.73100i) q^{37} -2.06793 q^{38} -2.65083i q^{40} +(0.578490 - 2.15895i) q^{41} +(-2.65096 - 1.53053i) q^{43} +(-11.7881 + 11.7881i) q^{44} +(12.6328 - 3.38495i) q^{46} +(5.99945 - 5.99945i) q^{47} +(-4.38135 + 5.45928i) q^{49} +(3.21707 - 12.0063i) q^{50} +(-11.2648 - 12.1327i) q^{52} -9.09347 q^{53} +(1.25253 - 0.723149i) q^{55} +(-5.84047 + 16.6086i) q^{56} +(-1.33878 - 4.99638i) q^{58} +(1.92316 + 7.17731i) q^{59} +(-2.40353 - 1.38768i) q^{61} +(8.06384 + 13.9670i) q^{62} +2.11035i q^{64} +(0.671556 + 1.26966i) q^{65} +(-4.85858 - 1.30185i) q^{67} +(16.2926 - 9.40656i) q^{68} +(1.52782 - 2.23346i) q^{70} +(0.582978 + 2.17570i) q^{71} +(3.50176 - 3.50176i) q^{73} +(2.30051 - 3.98460i) q^{74} +(-3.57239 - 0.957219i) q^{76} +(-9.44093 + 1.77118i) q^{77} -3.61967 q^{79} +(0.814620 - 3.04020i) q^{80} +(2.86927 - 4.96972i) q^{82} +(5.36774 + 5.36774i) q^{83} +(-1.57654 + 0.422432i) q^{85} +(-5.55723 - 5.55723i) q^{86} +(-20.9222 + 12.0795i) q^{88} +(-11.5425 - 3.09280i) q^{89} +(-1.41019 - 9.43458i) q^{91} +23.3903 q^{92} +(18.8651 - 10.8918i) q^{94} +(0.277872 + 0.160430i) q^{95} +(7.71975 - 2.06850i) q^{97} +(-14.4933 + 10.6274i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8}+O(q^{10}) $ 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8	$ 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50} - 72 q^{53} - 60 q^{56} - 16 q^{58} - 4 q^{65} - 56 q^{67} + 56 q^{70} - 84 q^{71} + 24 q^{74} - 80 q^{79} + 36 q^{85} + 48 q^{86} - 228 q^{88} - 48 q^{91} - 24 q^{92} + 84 q^{95} + 32 q^{98}+O(q^{100}) $ 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8 + 4 * q^11 + 32 * q^14 + 12 * q^16 + 4 * q^22 + 12 * q^23 + 24 * q^28 - 4 * q^29 - 4 * q^32 + 20 * q^35 + 4 * q^37 - 48 * q^43 - 24 * q^44 + 84 * q^46 + 24 * q^49 + 44 * q^50 - 72 * q^53 - 60 * q^56 - 16 * q^58 - 4 * q^65 - 56 * q^67 + 56 * q^70 - 84 * q^71 + 24 * q^74 - 80 * q^79 + 36 * q^85 + 48 * q^86 - 228 * q^88 - 48 * q^91 - 24 * q^92 + 84 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.47996	+	0.664504i	1.75360	+	0.469875i	0.985388	−	0.170322i	$-0.0544807\pi$
$2$	2.47996	+	0.664504i	1.75360	+	0.469875i	0.768211	+	0.640197i	$0.221147\pi$
$3$		0			0
$3$		0			0
$4$	3.97660	+	2.29589i	1.98830	+	1.14795i
$5$	−0.281686	−	0.281686i	−0.125974	−	0.125974i	0.641309	−	0.767283i	$-0.278392\pi$
$5$	−0.281686	−	0.281686i	−0.125974	−	0.125974i	−0.767283	+	0.641309i	$0.778392\pi$
$6$		0			0
$7$	1.14426	+	2.38551i	0.432488	+	0.901640i
$7$	1.14426	+	2.38551i	0.432488	+	0.901640i
$8$	4.70528	+	4.70528i	1.66357	+	1.66357i
$9$		0			0
$10$	−0.511390	−	0.885754i	−0.161716	−	0.280100i
$11$	−0.939666	+	3.50688i	−0.283320	+	1.05736i	0.666738	+	0.745292i	$0.267690\pi$
$11$	−0.939666	+	3.50688i	−0.283320	+	1.05736i	−0.950058	+	0.312072i	$0.898977\pi$
$12$		0			0
$13$	−3.44571	−	1.06165i	−0.955667	−	0.294449i
$13$	−3.44571	−	1.06165i	−0.955667	−	0.294449i
$14$	1.25253	+	6.67635i	0.334753	+	1.78433i
$15$		0			0
$16$	3.95046	+	6.84240i	0.987615	+	1.71060i
$17$	2.04856	−	3.54822i	0.496850	−	0.860569i	−0.503144	−	0.864203i	$-0.667823\pi$
$17$	2.04856	−	3.54822i	0.496850	−	0.860569i	0.999993	+	0.00363405i	$0.00115676\pi$
$18$		0			0
$19$	−0.777996	+	0.208463i	−0.178484	+	0.0478248i	−0.346954	−	0.937882i	$-0.612784\pi$
$19$	−0.777996	+	0.208463i	−0.178484	+	0.0478248i	0.168470	+	0.985707i	$0.446117\pi$
$20$	−0.473433	−	1.76688i	−0.105863	−	0.395086i
$21$		0			0
$22$	−4.66067	+	8.07252i	−0.993659	+	1.72107i
$23$	4.41149	−	2.54698i	0.919860	−	0.531081i	0.0362693	−	0.999342i	$-0.488453\pi$
$23$	4.41149	−	2.54698i	0.919860	−	0.531081i	0.883590	+	0.468261i	$0.155119\pi$
$24$		0			0
$25$		−	4.84131i		−	0.968261i
$26$	−7.83976	−	4.92254i	−1.53750	−	0.965390i
$27$		0			0
$28$	−0.926631	+	12.1133i	−0.175117	+	2.28920i
$29$	−1.00735	−	1.74478i	−0.187060	−	0.323998i	0.757209	−	0.653173i	$-0.226563\pi$
$29$	−1.00735	−	1.74478i	−0.187060	−	0.323998i	−0.944269	+	0.329175i	$0.893229\pi$
$30$		0			0
$31$	4.44176	+	4.44176i	0.797764	+	0.797764i	0.982743	−	0.184978i	$-0.0592214\pi$
$31$	4.44176	+	4.44176i	0.797764	+	0.797764i	−0.184978	+	0.982743i	$0.559221\pi$
$32$	1.80569	+	6.73893i	0.319204	+	1.19129i
$33$		0			0
$34$	7.43817	−	7.43817i	1.27563	−	1.27563i
$35$	0.349645	−	0.994288i	0.0591009	−	0.168065i
$36$		0			0
$37$	0.463819	−	1.73100i	0.0762514	−	0.284574i	−0.917263	−	0.398283i	$-0.869606\pi$
$37$	0.463819	−	1.73100i	0.0762514	−	0.284574i	0.993514	+	0.113708i	$0.0362730\pi$
$38$	−2.06793			−0.335462
$39$		0			0
$40$		−	2.65083i		−	0.419133i
$41$	0.578490	−	2.15895i	0.0903449	−	0.337172i	−0.905928	−	0.423432i	$-0.860825\pi$
$41$	0.578490	−	2.15895i	0.0903449	−	0.337172i	0.996273	+	0.0862606i	$0.0274918\pi$
$42$		0			0
$43$	−2.65096	−	1.53053i	−0.404267	−	0.233404i	0.284057	−	0.958808i	$-0.408320\pi$
$43$	−2.65096	−	1.53053i	−0.404267	−	0.233404i	−0.688323	+	0.725404i	$0.741653\pi$
$44$	−11.7881	+	11.7881i	−1.77712	+	1.77712i
$45$		0			0
$46$	12.6328	−	3.38495i	1.86261	−	0.499084i
$47$	5.99945	−	5.99945i	0.875109	−	0.875109i	−0.117914	−	0.993024i	$-0.537621\pi$
$47$	5.99945	−	5.99945i	0.875109	−	0.875109i	0.993024	+	0.117914i	$0.0376209\pi$
$48$		0			0
$49$	−4.38135	+	5.45928i	−0.625908	+	0.779897i
$50$	3.21707	−	12.0063i	0.454962	−	1.69794i
$51$		0			0
$52$	−11.2648	−	12.1327i	−1.56214	−	1.68251i
$53$	−9.09347			−1.24908			−0.624542	−	0.780991i	$-0.714714\pi$
$53$	−9.09347			−1.24908			−0.624542	+	0.780991i	$0.714714\pi$
$54$		0			0
$55$	1.25253	−	0.723149i	0.168891	−	0.0975094i
$56$	−5.84047	+	16.6086i	−0.780465	+	2.21941i
$57$		0			0
$58$	−1.33878	−	4.99638i	−0.175790	−	0.656057i
$59$	1.92316	+	7.17731i	0.250374	+	0.934407i	0.970606	+	0.240674i	$0.0773685\pi$
$59$	1.92316	+	7.17731i	0.250374	+	0.934407i	−0.720232	+	0.693733i	$0.755965\pi$
$60$		0			0
$61$	−2.40353	−	1.38768i	−0.307741	−	0.177674i	0.338174	−	0.941084i	$-0.390191\pi$
$61$	−2.40353	−	1.38768i	−0.307741	−	0.177674i	−0.645915	+	0.763409i	$0.723524\pi$
$62$	8.06384	+	13.9670i	1.02411	+	1.77381i
$63$		0			0
$64$			2.11035i			0.263794i
$65$	0.671556	+	1.26966i	0.0832963	+	0.157482i
$66$		0			0
$67$	−4.85858	−	1.30185i	−0.593570	−	0.159046i	−0.0504855	−	0.998725i	$-0.516077\pi$
$67$	−4.85858	−	1.30185i	−0.593570	−	0.159046i	−0.543084	+	0.839678i	$0.682744\pi$
$68$	16.2926	−	9.40656i	1.97577	−	1.14071i
$69$		0			0
$70$	1.52782	−	2.23346i	0.182609	−	0.266949i
$71$	0.582978	+	2.17570i	0.0691867	+	0.258208i	0.991852	−	0.127393i	$-0.0406608\pi$
$71$	0.582978	+	2.17570i	0.0691867	+	0.258208i	−0.922666	+	0.385601i	$0.873994\pi$
$72$		0			0
$73$	3.50176	−	3.50176i	0.409850	−	0.409850i	−0.471836	−	0.881686i	$-0.656409\pi$
$73$	3.50176	−	3.50176i	0.409850	−	0.409850i	0.881686	+	0.471836i	$0.156409\pi$
$74$	2.30051	−	3.98460i	0.267429	−	0.463200i
$75$		0			0
$76$	−3.57239	−	0.957219i	−0.409781	−	0.109801i
$77$	−9.44093	+	1.77118i	−1.07589	+	0.201845i
$78$		0			0
$79$	−3.61967			−0.407245			−0.203622	−	0.979050i	$-0.565271\pi$
$79$	−3.61967			−0.407245			−0.203622	+	0.979050i	$0.565271\pi$
$80$	0.814620	−	3.04020i	0.0910772	−	0.339905i
$81$		0			0
$82$	2.86927	−	4.96972i	0.316857	−	0.548813i
$83$	5.36774	+	5.36774i	0.589186	+	0.589186i	0.937411	−	0.348225i	$-0.113215\pi$
$83$	5.36774	+	5.36774i	0.589186	+	0.589186i	−0.348225	+	0.937411i	$0.613215\pi$
$84$		0			0
$85$	−1.57654	+	0.422432i	−0.170999	+	0.0458191i
$86$	−5.55723	−	5.55723i	−0.599251	−	0.599251i
$87$		0			0
$88$	−20.9222	+	12.0795i	−2.23032	+	1.28768i
$89$	−11.5425	−	3.09280i	−1.22350	−	0.327836i	−0.411454	−	0.911430i	$-0.634979\pi$
$89$	−11.5425	−	3.09280i	−1.22350	−	0.327836i	−0.812045	+	0.583595i	$0.801646\pi$
$90$		0			0
$91$	−1.41019	−	9.43458i	−0.147828	−	0.989013i
$92$	23.3903			2.43861
$93$		0			0
$94$	18.8651	−	10.8918i	1.94578	−	1.12340i
$95$	0.277872	+	0.160430i	0.0285091	+	0.0164597i
$96$		0			0
$97$	7.71975	−	2.06850i	0.783822	−	0.210024i	0.155353	−	0.987859i	$-0.450349\pi$
$97$	7.71975	−	2.06850i	0.783822	−	0.210024i	0.628469	+	0.777835i	$0.283682\pi$
$98$	−14.4933	+	10.6274i	−1.46405	+	1.07353i
$99$		0			0
$100$	11.1151	−	19.2519i	1.11151	−	1.92519i
$101$	−2.25123	−	3.89924i	−0.224005	−	0.387989i	0.732015	−	0.681288i	$-0.238580\pi$
$101$	−2.25123	−	3.89924i	−0.224005	−	0.387989i	−0.956021	+	0.293300i	$0.905247\pi$
$102$		0			0
$103$	−16.1000			−1.58638			−0.793192	−	0.608971i	$-0.791582\pi$
$103$	−16.1000			−1.58638			−0.793192	+	0.608971i	$0.791582\pi$
$104$	−11.2177	−	21.2084i	−1.09998	−	2.07965i
$105$		0			0
$106$	−22.5515	−	6.04265i	−2.19039	−	0.586914i
$107$	−5.40840	−	9.36762i	−0.522850	−	0.905602i	−0.999646	−	0.0265887i	$-0.991536\pi$
$107$	−5.40840	−	9.36762i	−0.522850	−	0.905602i	0.476797	−	0.879014i	$-0.341798\pi$
$108$		0			0
$109$	2.35784	−	2.35784i	0.225841	−	0.225841i	−0.585112	−	0.810953i	$-0.698949\pi$
$109$	2.35784	−	2.35784i	0.225841	−	0.225841i	0.810953	+	0.585112i	$0.198949\pi$
$110$	3.58677	−	0.961072i	0.341985	−	0.0916346i
$111$		0			0
$112$	−11.8023	+	17.2533i	−1.11521	+	1.63029i
$113$	−3.82032	+	6.61699i	−0.359386	+	0.622474i	−0.987858	−	0.155357i	$-0.950347\pi$
$113$	−3.82032	+	6.61699i	−0.359386	+	0.622474i	0.628473	+	0.777832i	$0.283680\pi$
$114$		0			0
$115$	−1.96011	−	0.525209i	−0.182781	−	0.0489760i
$116$		−	9.25107i		−	0.858940i
$117$		0			0
$118$			19.0774i			1.75622i
$119$	10.8084	+	0.826808i	0.990804	+	0.0757934i
$120$		0			0
$121$	−1.88896	−	1.09059i	−0.171723	−	0.0991446i
$122$	−5.03856	−	5.03856i	−0.456169	−	0.456169i
$123$		0			0
$124$	7.46532	+	27.8609i	0.670405	+	2.50199i
$125$	−2.77216	+	2.77216i	−0.247950	+	0.247950i
$126$		0			0
$127$	10.8931	−	6.28911i	0.966602	−	0.558068i	0.0684037	−	0.997658i	$-0.478209\pi$
$127$	10.8931	−	6.28911i	0.966602	−	0.558068i	0.898199	+	0.439590i	$0.144876\pi$
$128$	2.20905	−	8.24427i	0.195254	−	0.728697i
$129$		0			0
$130$	0.821740	+	3.59497i	0.0720713	+	0.315299i
$131$			11.7715i			1.02848i	0.857646	+	0.514241i	$0.171926\pi$
$131$			11.7715i			1.02848i	−0.857646	+	0.514241i	$0.828074\pi$
$132$		0			0
$133$	−1.38752	−	1.61738i	−0.120313	−	0.140245i
$134$	−11.1840	−	6.45709i	−0.966151	−	0.557808i
$135$		0			0
$136$	26.3344	−	7.05628i	2.25816	−	0.605071i
$137$	12.5772	−	3.37005i	1.07454	−	0.287923i	0.322184	−	0.946677i	$-0.395583\pi$
$137$	12.5772	−	3.37005i	1.07454	−	0.287923i	0.752358	+	0.658754i	$0.228916\pi$
$138$		0			0
$139$	−7.49780	−	4.32886i	−0.635955	−	0.367169i	0.147099	−	0.989122i	$-0.453006\pi$
$139$	−7.49780	−	4.32886i	−0.635955	−	0.367169i	−0.783055	+	0.621953i	$0.786340\pi$
$140$	3.67318	−	3.15114i	0.310440	−	0.266320i
$141$		0			0
$142$			5.78305i			0.485303i
$143$	6.96090	−	11.0861i	0.582099	−	0.927065i
$144$		0			0
$145$	−0.207724	+	0.775238i	−0.0172506	+	0.0643800i
$146$	11.0112	−	6.35730i	0.911291	−	0.526134i
$147$		0			0
$148$	5.81861	−	5.81861i	0.478287	−	0.478287i
$149$	4.83483	+	18.0438i	0.396085	+	1.47821i	0.819925	+	0.572471i	$0.194015\pi$
$149$	4.83483	+	18.0438i	0.396085	+	1.47821i	−0.423840	+	0.905737i	$0.639318\pi$
$150$		0			0
$151$	9.94985	+	9.94985i	0.809707	+	0.809707i	0.984589	−	0.174882i	$-0.0559544\pi$
$151$	9.94985	+	9.94985i	0.809707	+	0.809707i	−0.174882	+	0.984589i	$0.555954\pi$
$152$	−4.64157	−	2.67981i	−0.376481	−	0.217361i
$153$		0			0
$154$	−24.5901	−	1.88107i	−1.98153	−	0.151581i
$155$		−	2.50237i		−	0.200995i
$156$		0			0
$157$		−	14.0101i		−	1.11813i	−0.829124	−	0.559064i	$-0.811160\pi$
$157$		−	14.0101i		−	1.11813i	0.829124	−	0.559064i	$-0.188840\pi$
$158$	−8.97665	−	2.40529i	−0.714144	−	0.191354i
$159$		0			0
$160$	1.38963	−	2.40690i	0.109860	−	0.190282i
$161$	11.1237	+	7.60928i	0.876672	+	0.599695i
$162$		0			0
$163$	−9.15502	+	2.45308i	−0.717076	+	0.192140i	−0.598867	−	0.800849i	$-0.704382\pi$
$163$	−9.15502	+	2.45308i	−0.717076	+	0.192140i	−0.118210	+	0.992989i	$0.537715\pi$
$164$	7.25715	−	7.25715i	0.566688	−	0.566688i
$165$		0			0
$166$	9.74492	+	16.8787i	0.756353	+	1.31004i
$167$	−9.41229	−	2.52202i	−0.728345	−	0.195159i	−0.124453	−	0.992226i	$-0.539718\pi$
$167$	−9.41229	−	2.52202i	−0.728345	−	0.195159i	−0.603892	+	0.797066i	$0.706384\pi$
$168$		0			0
$169$	10.7458	+	7.31628i	0.826600	+	0.562790i
$170$	−4.19046			−0.321394
$171$		0			0
$172$	−7.02786	−	12.1726i	−0.535870	−	0.928153i
$173$	−8.50332	+	14.7282i	−0.646496	+	1.11976i	0.337458	+	0.941341i	$0.390433\pi$
$173$	−8.50332	+	14.7282i	−0.646496	+	1.11976i	−0.983954	+	0.178423i	$0.942900\pi$
$174$		0			0
$175$	11.5490	−	5.53969i	0.873023	−	0.418762i
$176$	−27.7076	+	7.42423i	−2.08854	+	0.559622i
$177$		0			0
$178$	−26.5697	−	15.3400i	−1.99149	−	1.14978i
$179$	−9.41215	+	5.43411i	−0.703497	+	0.406164i	−0.808649	−	0.588292i	$-0.799801\pi$
$179$	−9.41215	+	5.43411i	−0.703497	+	0.406164i	0.105152	+	0.994456i	$0.466467\pi$
$180$		0			0
$181$	20.7716			1.54394			0.771969	−	0.635661i	$-0.219272\pi$
$181$	20.7716			1.54394			0.771969	+	0.635661i	$0.219272\pi$
$182$	2.77210	−	24.3345i	0.205482	−	1.80379i
$183$		0			0
$184$	32.7415	+	8.77307i	2.41374	+	0.646759i
$185$	−0.618250	+	0.356947i	−0.0454546	+	0.0262432i
$186$		0			0
$187$	10.5182	+	10.5182i	0.769167	+	0.769167i
$188$	37.6315	−	10.0833i	2.74456	−	0.735402i
$189$		0			0
$190$	0.582507	+	0.582507i	0.0422595	+	0.0422595i
$191$	0.742192	−	1.28551i	0.0537031	−	0.0930165i	−0.837924	−	0.545787i	$-0.816231\pi$
$191$	0.742192	−	1.28551i	0.0537031	−	0.0930165i	0.891627	+	0.452770i	$0.149564\pi$
$192$		0			0
$193$	−1.90039	+	7.09237i	−0.136793	+	0.510520i	0.863191	+	0.504878i	$0.168463\pi$
$193$	−1.90039	+	7.09237i	−0.136793	+	0.510520i	−0.999984	+	0.00564177i	$0.998204\pi$
$194$	20.5192			1.47319
$195$		0			0
$196$	−29.9568	+	11.6503i	−2.13977	+	0.832162i
$197$	−17.4416	−	4.67347i	−1.24266	−	0.332971i	−0.423166	−	0.906052i	$-0.639081\pi$
$197$	−17.4416	−	4.67347i	−1.24266	−	0.332971i	−0.819499	+	0.573081i	$0.805748\pi$
$198$		0			0
$199$	−1.63076	+	2.82456i	−0.115602	+	0.200228i	−0.918020	−	0.396534i	$-0.870213\pi$
$199$	−1.63076	+	2.82456i	−0.115602	+	0.200228i	0.802418	+	0.596762i	$0.203546\pi$
$200$	22.7797	−	22.7797i	1.61077	−	1.61077i
$201$		0			0
$202$	−2.99190	−	11.1659i	−0.210509	−	0.785631i
$203$	3.00953	−	4.39952i	0.211228	−	0.308786i
$204$		0			0
$205$	−0.771100	+	0.445195i	−0.0538560	+	0.0310938i
$206$	−39.9275	−	10.6985i	−2.78188	−	0.745403i
$207$		0			0
$208$	−6.34789	−	27.7709i	−0.440147	−	1.92557i
$209$		−	2.92422i		−	0.202273i
$210$		0			0
$211$	1.10904	+	1.92091i	0.0763492	+	0.132241i	0.901672	−	0.432420i	$-0.142340\pi$
$211$	1.10904	+	1.92091i	0.0763492	+	0.132241i	−0.825323	+	0.564661i	$0.809007\pi$
$212$	−36.1611	−	20.8776i	−2.48356	−	1.43388i
$213$		0			0
$214$	−7.18781	−	26.8253i	−0.491348	−	1.83374i
$215$	0.315609	+	1.17787i	0.0215243	+	0.0803299i
$216$		0			0
$217$	−5.51337	+	15.6784i	−0.374272	+	1.06432i
$218$	7.41417	−	4.28057i	0.502151	−	0.289917i
$219$		0			0
$220$	6.64109			0.447742
$221$	−10.8257	+	10.0513i	−0.728216	+	0.676120i
$222$		0			0
$223$	−1.40793	+	5.25448i	−0.0942823	+	0.351866i	−0.996910	−	0.0785566i	$-0.974969\pi$
$223$	−1.40793	+	5.25448i	−0.0942823	+	0.351866i	0.902627	+	0.430423i	$0.141636\pi$
$224$	−14.0096	+	12.0186i	−0.936059	+	0.803024i
$225$		0			0
$226$	−13.8713	+	13.8713i	−0.922704	+	0.922704i
$227$	−0.334926	+	0.0897430i	−0.0222298	+	0.00595646i	−0.269917	−	0.962884i	$-0.586996\pi$
$227$	−0.334926	+	0.0897430i	−0.0222298	+	0.00595646i	0.247687	+	0.968840i	$0.420330\pi$
$228$		0			0
$229$	−18.7465	+	18.7465i	−1.23880	+	1.23880i	−0.278312	+	0.960491i	$0.589775\pi$
$229$	−18.7465	+	18.7465i	−1.23880	+	1.23880i	−0.960491	+	0.278312i	$0.910225\pi$
$230$	−4.51199	−	2.60500i	−0.297512	−	0.171768i
$231$		0			0
$232$	3.46982	−	12.9496i	0.227805	−	0.850180i
$233$			21.8266i			1.42991i	0.699173	+	0.714953i	$0.253552\pi$
$233$			21.8266i			1.42991i	−0.699173	+	0.714953i	$0.746448\pi$
$234$		0			0
$235$	−3.37993			−0.220482
$236$	−8.83072	+	32.9567i	−0.574831	+	2.14530i
$237$		0			0
$238$	26.2550	+	9.23268i	1.70186	+	0.598466i
$239$	−2.02192	+	2.02192i	−0.130787	+	0.130787i	−0.769470	−	0.638683i	$-0.779480\pi$
$239$	−2.02192	+	2.02192i	−0.130787	+	0.130787i	0.638683	+	0.769470i	$0.279480\pi$
$240$		0			0
$241$	−7.81005	−	29.1475i	−0.503090	−	1.87756i	−0.478938	−	0.877849i	$-0.658978\pi$
$241$	−7.81005	−	29.1475i	−0.503090	−	1.87756i	−0.0241515	−	0.999708i	$-0.507688\pi$
$242$	−3.95985	−	3.95985i	−0.254549	−	0.254549i
$243$		0			0
$244$	−6.37193	−	11.0365i	−0.407921	−	0.706540i
$245$	2.77197	−	0.303637i	0.177095	−	0.0193986i
$246$		0			0
$247$	2.90206	+	0.107656i	0.184654	+	0.00685001i
$248$			41.7995i			2.65427i
$249$		0			0
$250$	−8.71697	+	5.03275i	−0.551310	+	0.318299i
$251$	8.33953	−	14.4445i	0.526386	−	0.911728i	−0.473141	−	0.880987i	$-0.656880\pi$
$251$	8.33953	−	14.4445i	0.526386	−	0.911728i	0.999527	−	0.0307412i	$-0.00978676\pi$
$252$		0			0
$253$	4.78661	+	17.8639i	0.300932	+	1.12309i
$254$	31.1935	−	8.35828i	1.95726	−	0.524445i
$255$		0			0
$256$	13.0671	−	22.6328i	0.816691	−	1.41455i
$257$	6.10569	+	10.5754i	0.380863	+	0.659674i	0.991186	−	0.132479i	$-0.0422937\pi$
$257$	6.10569	+	10.5754i	0.380863	+	0.659674i	−0.610323	+	0.792153i	$0.708960\pi$
$258$		0			0
$259$	4.66005	−	0.874257i	0.289561	−	0.0543237i
$260$	−0.244494	+	6.59076i	−0.0151629	+	0.408742i
$261$		0			0
$262$	−7.82222	+	29.1929i	−0.483258	+	1.80354i
$263$	7.30314	+	12.6494i	0.450331	+	0.779996i	0.998406	−	0.0564328i	$-0.0179727\pi$
$263$	7.30314	+	12.6494i	0.450331	+	0.779996i	−0.548075	+	0.836429i	$0.684639\pi$
$264$		0			0
$265$	2.56151	+	2.56151i	0.157352	+	0.157352i
$266$	−2.36624	−	4.93307i	−0.145083	−	0.302466i
$267$		0			0
$268$	−16.3317	−	16.3317i	−0.997618	−	0.997618i
$269$	4.31634	+	2.49204i	0.263172	+	0.151942i	0.625781	−	0.779999i	$-0.284781\pi$
$269$	4.31634	+	2.49204i	0.263172	+	0.151942i	−0.362609	+	0.931941i	$0.618114\pi$
$270$		0			0
$271$	−25.5915	−	6.85721i	−1.55457	−	0.416546i	−0.623631	−	0.781719i	$-0.714343\pi$
$271$	−25.5915	−	6.85721i	−1.55457	−	0.416546i	−0.930940	+	0.365173i	$0.881010\pi$
$272$	32.3711			1.96278
$273$		0			0
$274$	33.4304			2.01960
$275$	16.9779	+	4.54921i	1.02380	+	0.274328i
$276$		0			0
$277$	17.6881	+	10.2122i	1.06277	+	0.613592i	0.926198	−	0.377038i	$-0.123057\pi$
$277$	17.6881	+	10.2122i	1.06277	+	0.613592i	0.136574	+	0.990630i	$0.456391\pi$
$278$	−15.7177	−	15.7177i	−0.942687	−	0.942687i
$279$		0			0
$280$	6.32359	−	3.03323i	0.377907	−	0.181270i
$281$	3.86728	+	3.86728i	0.230703	+	0.230703i	0.812986	−	0.582283i	$-0.197841\pi$
$281$	3.86728	+	3.86728i	0.230703	+	0.230703i	−0.582283	+	0.812986i	$0.697841\pi$
$282$		0			0
$283$	12.5189	+	21.6835i	0.744174	+	1.28895i	0.950580	+	0.310481i	$0.100490\pi$
$283$	12.5189	+	21.6835i	0.744174	+	1.28895i	−0.206405	+	0.978467i	$0.566177\pi$
$284$	−2.67691	+	9.99036i	−0.158845	+	0.592819i
$285$		0			0
$286$	24.6295	−	22.8675i	1.45637	−	1.35219i
$287$	5.81215	−	1.09040i	0.343081	−	0.0643643i
$288$		0			0
$289$	0.106779	+	0.184946i	0.00628111	+	0.0108792i
$290$	−1.03030	+	1.78453i	−0.0605012	+	0.104791i
$291$		0			0
$292$	21.9648	−	5.88544i	1.28539	−	0.344420i
$293$	−4.77690	−	17.8276i	−0.279069	−	1.04150i	−0.953065	−	0.302766i	$-0.902090\pi$
$293$	−4.77690	−	17.8276i	−0.279069	−	1.04150i	0.673996	−	0.738735i	$-0.264577\pi$
$294$		0			0
$295$	1.48003	−	2.56348i	0.0861704	−	0.149251i
$296$	10.3272	−	5.96243i	0.600258	−	0.346559i
$297$		0			0
$298$			47.9608i			2.77829i
$299$	−17.9047	+	4.09267i	−1.03546	+	0.236685i
$300$		0			0
$301$	0.617728	−	8.07521i	0.0356052	−	0.465447i
$302$	18.0636	+	31.2870i	1.03944	+	1.80036i
$303$		0			0
$304$	−4.49983	−	4.49983i	−0.258083	−	0.258083i
$305$	0.286152	+	1.06793i	0.0163850	+	0.0611497i
$306$		0			0
$307$	14.6697	−	14.6697i	0.837243	−	0.837243i	−0.151252	−	0.988495i	$-0.548330\pi$
$307$	14.6697	−	14.6697i	0.837243	−	0.837243i	0.988495	+	0.151252i	$0.0483305\pi$
$308$	−41.6093	−	14.6321i	−2.37091	−	0.833739i
$309$		0			0
$310$	1.66284	−	6.20579i	0.0944427	−	0.352465i
$311$	5.86149			0.332374			0.166187	−	0.986094i	$-0.446854\pi$
$311$	5.86149			0.332374			0.166187	+	0.986094i	$0.446854\pi$
$312$		0			0
$313$			20.4076i			1.15351i	0.816918	+	0.576754i	$0.195681\pi$
$313$			20.4076i			1.15351i	−0.816918	+	0.576754i	$0.804319\pi$
$314$	9.30978	−	34.7446i	0.525381	−	1.96075i
$315$		0			0
$316$	−14.3940	−	8.31037i	−0.809725	−	0.467495i
$317$	5.42384	−	5.42384i	0.304633	−	0.304633i	−0.538190	−	0.842824i	$-0.680892\pi$
$317$	5.42384	−	5.42384i	0.304633	−	0.304633i	0.842824	+	0.538190i	$0.180892\pi$
$318$		0			0
$319$	7.06531	−	1.89314i	0.395582	−	0.105996i
$320$	0.594457	−	0.594457i	0.0332312	−	0.0332312i
$321$		0			0
$322$	22.5300	+	26.2625i	1.25555	+	1.46355i
$323$	−0.854101	+	3.18755i	−0.0475234	+	0.177360i
$324$		0			0
$325$	−5.13978	+	16.6817i	−0.285103	+	0.925335i
$326$	−24.3342			−1.34775
$327$		0			0
$328$	12.8804	−	7.43652i	0.711203	−	0.410613i
$329$	21.1767	+	7.44686i	1.16751	+	0.410559i
$330$		0			0
$331$	6.52453	+	24.3499i	0.358621	+	1.33839i	0.875866	+	0.482554i	$0.160291\pi$
$331$	6.52453	+	24.3499i	0.358621	+	1.33839i	−0.517246	+	0.855837i	$0.673043\pi$
$332$	9.02162	+	33.6691i	0.495126	+	1.84783i
$333$		0			0
$334$	−21.6662	−	12.5090i	−1.18552	−	0.684463i
$335$	1.00188	+	1.73531i	0.0547386	+	0.0948100i
$336$		0			0
$337$		−	30.1306i		−	1.64132i	−0.571417	−	0.820660i	$-0.693606\pi$
$337$		−	30.1306i		−	1.64132i	0.571417	−	0.820660i	$-0.306394\pi$
$338$	21.7875	+	25.2847i	1.18508	+	1.37531i
$339$		0			0
$340$	−7.23912	−	1.93972i	−0.392596	−	0.105196i
$341$	−19.7505	+	11.4030i	−1.06955	+	0.617505i
$342$		0			0
$343$	−18.0366	−	4.20497i	−0.973884	−	0.227047i
$344$	−5.27192	−	19.6751i	−0.284243	−	1.06081i
$345$		0			0
$346$	−30.8749	+	30.8749i	−1.65984	+	1.65984i
$347$	17.2300	−	29.8433i	0.924957	−	1.60207i	0.133326	−	0.991072i	$-0.457434\pi$
$347$	17.2300	−	29.8433i	0.924957	−	1.60207i	0.791631	−	0.611000i	$-0.209232\pi$
$348$		0			0
$349$	−3.97028	−	1.06383i	−0.212524	−	0.0569457i	0.150986	−	0.988536i	$-0.451755\pi$
$349$	−3.97028	−	1.06383i	−0.212524	−	0.0569457i	−0.363510	+	0.931590i	$0.618422\pi$
$350$	32.3223	−	6.06388i	1.72770	−	0.324128i
$351$		0			0
$352$	−25.3294			−1.35006
$353$	−2.81747	+	10.5149i	−0.149959	+	0.559653i	0.849526	+	0.527547i	$0.176888\pi$
$353$	−2.81747	+	10.5149i	−0.149959	+	0.559653i	−0.999484	+	0.0321060i	$0.989779\pi$
$354$		0			0
$355$	0.448649	−	0.777083i	0.0238118	−	0.0412433i
$356$	−38.7991	−	38.7991i	−2.05635	−	2.05635i
$357$		0			0
$358$	−26.9528	+	7.22197i	−1.42450	+	0.381693i
$359$	−21.7659	−	21.7659i	−1.14876	−	1.14876i	−0.986797	−	0.161963i	$-0.948218\pi$
$359$	−21.7659	−	21.7659i	−1.14876	−	1.14876i	−0.161963	−	0.986797i	$-0.551782\pi$
$360$		0			0
$361$	−15.8927	+	9.17563i	−0.836456	+	0.482928i
$362$	51.5127	+	13.8028i	2.70745	+	0.725458i
$363$		0			0
$364$	16.0530	−	40.7552i	0.841407	−	2.13615i
$365$	−1.97280			−0.103261
$366$		0			0
$367$	−21.5968	+	12.4689i	−1.12734	+	0.650873i	−0.943266	−	0.332039i	$-0.892263\pi$
$367$	−21.5968	+	12.4689i	−1.12734	+	0.650873i	−0.184079	+	0.982912i	$0.558930\pi$
$368$	34.8548	+	20.1235i	1.81693	+	1.04901i
$369$		0			0
$370$	−1.77043	+	0.474385i	−0.0920403	+	0.0246621i
$371$	−10.4053	−	21.6926i	−0.540214	−	1.12622i
$372$		0			0
$373$	−9.09462	+	15.7523i	−0.470902	+	0.815626i	−0.999446	−	0.0332801i	$-0.989405\pi$
$373$	−9.09462	+	15.7523i	−0.470902	+	0.815626i	0.528544	+	0.848906i	$0.322738\pi$
$374$	19.0954	+	33.0741i	0.987398	+	1.71022i
$375$		0			0
$376$	56.4582			2.91161
$377$	1.61868	+	7.08146i	0.0833665	+	0.364714i
$378$		0			0
$379$	−0.810924	−	0.217286i	−0.0416544	−	0.0111613i	0.237932	−	0.971282i	$-0.423531\pi$
$379$	−0.810924	−	0.217286i	−0.0416544	−	0.0111613i	−0.279586	+	0.960121i	$0.590197\pi$
$380$	0.736658	+	1.27593i	0.0377898	+	0.0654538i
$381$		0			0
$382$	2.69484	−	2.69484i	0.137880	−	0.137880i
$383$	5.60755	−	1.50254i	0.286532	−	0.0767761i	−0.112690	−	0.993630i	$-0.535947\pi$
$383$	5.60755	−	1.50254i	0.286532	−	0.0767761i	0.399223	+	0.916854i	$0.369280\pi$
$384$		0			0
$385$	3.15830	+	2.16046i	0.160962	+	0.110107i
$386$	−9.42582	+	16.3260i	−0.479761	+	0.830971i
$387$		0			0
$388$	35.4474	+	9.49811i	1.79957	+	0.482194i
$389$			8.72624i			0.442438i	0.975224	+	0.221219i	$0.0710036\pi$
$389$			8.72624i			0.442438i	−0.975224	+	0.221219i	$0.928996\pi$
$390$		0			0
$391$		−	20.8706i		−	1.05547i
$392$	−46.3029	+	5.07194i	−2.33865	+	0.256172i
$393$		0			0
$394$	−40.1491	−	23.1801i	−2.02268	−	1.16780i
$395$	1.01961	+	1.01961i	0.0513022	+	0.0513022i
$396$		0			0
$397$	−0.0550441	−	0.205427i	−0.00276258	−	0.0103101i	0.964531	−	0.263970i	$-0.0850321\pi$
$397$	−0.0550441	−	0.205427i	−0.00276258	−	0.0103101i	−0.967293	+	0.253660i	$0.918365\pi$
$398$	−5.92117	+	5.92117i	−0.296801	+	0.296801i
$399$		0			0
$400$	33.1261	−	19.1254i	1.65631	−	0.956269i
$401$	1.81652	−	6.77934i	0.0907126	−	0.338544i	−0.905622	−	0.424086i	$-0.860595\pi$
$401$	1.81652	−	6.77934i	0.0907126	−	0.338544i	0.996335	+	0.0855419i	$0.0272622\pi$
$402$		0			0
$403$	−10.5894	−	20.0206i	−0.527496	−	0.997298i
$404$		−	20.6743i		−	1.02858i
$405$		0			0
$406$	10.3870	−	8.91081i	0.515500	−	0.442236i
$407$	5.63456	+	3.25312i	0.279295	+	0.161251i
$408$		0			0
$409$	10.3417	−	2.77106i	0.511366	−	0.137020i	0.00609589	−	0.999981i	$-0.498060\pi$
$409$	10.3417	−	2.77106i	0.511366	−	0.137020i	0.505270	+	0.862961i	$0.331393\pi$
$410$	−2.20813	+	0.591668i	−0.109052	+	0.0292204i
$411$		0			0
$412$	−64.0235	−	36.9640i	−3.15421	−	1.82108i
$413$	−14.9210	+	12.8004i	−0.734214	+	0.629867i
$414$		0			0
$415$		−	3.02404i		−	0.148444i
$416$	0.932509	−	25.1374i	0.0457200	−	1.23246i
$417$		0			0
$418$	1.94316	−	7.25197i	0.0950430	−	0.354705i
$419$	−0.903448	+	0.521606i	−0.0441363	+	0.0254821i	−0.521906	−	0.853003i	$-0.674779\pi$
$419$	−0.903448	+	0.521606i	−0.0441363	+	0.0254821i	0.477769	+	0.878485i	$0.341445\pi$
$420$		0			0
$421$	−22.9876	+	22.9876i	−1.12035	+	1.12035i	−0.128658	+	0.991689i	$0.541067\pi$
$421$	−22.9876	+	22.9876i	−1.12035	+	1.12035i	−0.991689	+	0.128658i	$0.958933\pi$
$422$	1.47392	+	5.50074i	0.0717492	+	0.267772i
$423$		0			0
$424$	−42.7873	−	42.7873i	−2.07794	−	2.07794i
$425$	−17.1780	−	9.91772i	−0.833255	−	0.481080i
$426$		0			0
$427$	0.560073	−	7.32152i	0.0271038	−	0.354313i
$428$		−	49.6684i		−	2.40081i
$429$		0			0
$430$			3.13079i			0.150980i
$431$	−7.90477	−	2.11808i	−0.380760	−	0.102024i	0.0633623	−	0.997991i	$-0.479818\pi$
$431$	−7.90477	−	2.11808i	−0.380760	−	0.102024i	−0.444122	+	0.895966i	$0.646484\pi$
$432$		0			0
$433$	9.95068	−	17.2351i	0.478199	−	0.828266i	−0.521488	−	0.853258i	$-0.674623\pi$
$433$	9.95068	−	17.2351i	0.478199	−	0.828266i	0.999688	+	0.0249929i	$0.00795632\pi$
$434$	−24.0913	+	35.2182i	−1.15642	+	1.69053i
$435$		0			0
$436$	14.7896	−	3.96285i	0.708292	−	0.189786i
$437$	−2.90117	+	2.90117i	−0.138782	+	0.138782i
$438$		0			0
$439$	−3.63272	−	6.29205i	−0.173380	−	0.300303i	0.766219	−	0.642579i	$-0.222136\pi$
$439$	−3.63272	−	6.29205i	−0.173380	−	0.300303i	−0.939599	+	0.342276i	$0.888802\pi$
$440$	9.29613	+	2.49089i	0.443176	+	0.118749i
$441$		0			0
$442$	−33.5265	+	17.7330i	−1.59469	+	0.843473i
$443$	−26.5617			−1.26198			−0.630992	−	0.775789i	$-0.717352\pi$
$443$	−26.5617			−1.26198			−0.630992	+	0.775789i	$0.717352\pi$
$444$		0			0
$445$	2.38016	+	4.12255i	0.112830	+	0.195428i
$446$	−6.98325	+	12.0954i	−0.330667	+	0.572731i
$447$		0			0
$448$	−5.03427	+	2.41478i	−0.237847	+	0.114088i
$449$	−19.1518	+	5.13170i	−0.903828	+	0.242180i	−0.680659	−	0.732600i	$-0.738307\pi$
$449$	−19.1518	+	5.13170i	−0.903828	+	0.242180i	−0.223168	+	0.974780i	$0.571640\pi$
$450$		0			0
$451$	7.02760	+	4.05739i	0.330917	+	0.191055i
$452$	−30.3838	+	17.5421i	−1.42913	+	0.825111i
$453$		0			0
$454$	−0.890238			−0.0417809
$455$	−2.26036	+	3.05483i	−0.105967	+	0.143212i
$456$		0			0
$457$	24.2444	+	6.49628i	1.13411	+	0.303883i	0.776579	−	0.630019i	$-0.216953\pi$
$457$	24.2444	+	6.49628i	1.13411	+	0.303883i	0.357528	+	0.933903i	$0.383620\pi$
$458$	−58.9477	+	34.0335i	−2.75445	+	1.59028i
$459$		0			0
$460$	−6.58874	−	6.58874i	−0.307201	−	0.307201i
$461$	32.6719	−	8.75440i	1.52168	−	0.407733i	0.601386	−	0.798959i	$-0.294615\pi$
$461$	32.6719	−	8.75440i	1.52168	−	0.407733i	0.920295	+	0.391226i	$0.127949\pi$
$462$		0			0
$463$	13.6651	+	13.6651i	0.635073	+	0.635073i	0.949336	−	0.314263i	$-0.101757\pi$
$463$	13.6651	+	13.6651i	0.635073	+	0.635073i	−0.314263	+	0.949336i	$0.601757\pi$
$464$	7.95899	−	13.7854i	0.369487	−	0.639970i
$465$		0			0
$466$	−14.5038	+	54.1291i	−0.671877	+	2.50748i
$467$	−15.1526			−0.701178			−0.350589	−	0.936529i	$-0.614019\pi$
$467$	−15.1526			−0.701178			−0.350589	+	0.936529i	$0.614019\pi$
$468$		0			0
$469$	−2.45387	−	13.0799i	−0.113309	−	0.603972i
$470$	−8.38209	−	2.24597i	−0.386637	−	0.103599i
$471$		0			0
$472$	−24.7223	+	42.8203i	−1.13794	+	1.97096i
$473$	7.85840	−	7.85840i	0.361329	−	0.361329i
$474$		0			0
$475$	1.00923	+	3.76652i	0.0463069	+	0.172820i
$476$	41.0824	+	28.1028i	1.88301	+	1.28809i
$477$		0			0
$478$	−6.35787	+	3.67072i	−0.290802	+	0.167895i
$479$	24.2829	+	6.50658i	1.10951	+	0.297293i	0.766633	−	0.642086i	$-0.221931\pi$
$479$	24.2829	+	6.50658i	1.10951	+	0.297293i	0.342881	+	0.939379i	$0.388597\pi$
$480$		0			0
$481$	−3.43590	+	5.47209i	−0.156664	+	0.249506i
$482$		−	77.4746i		−	3.52887i
$483$		0			0
$484$	−5.00776	−	8.67369i	−0.227625	−	0.394259i
$485$	−2.75722	−	1.59188i	−0.125199	−	0.0722836i
$486$		0			0
$487$	−6.68642	−	24.9540i	−0.302990	−	1.13078i	−0.934661	−	0.355539i	$-0.884297\pi$
$487$	−6.68642	−	24.9540i	−0.302990	−	1.13078i	0.631671	−	0.775237i	$-0.282369\pi$
$488$	−4.77987	−	17.8387i	−0.216375	−	0.807521i
$489$		0			0
$490$	7.07616	+	1.08898i	0.319668	+	0.0491951i
$491$	31.2520	−	18.0433i	1.41038	−	0.814284i	0.414958	−	0.909841i	$-0.363796\pi$
$491$	31.2520	−	18.0433i	1.41038	−	0.814284i	0.995424	+	0.0955563i	$0.0304630\pi$
$492$		0			0
$493$	−8.25448			−0.371763
$494$	7.12547	+	2.19542i	0.320590	+	0.0987764i
$495$		0			0
$496$	−12.8453	+	47.9393i	−0.576771	+	2.15254i
$497$	−4.52309	+	3.88026i	−0.202888	+	0.174054i
$498$		0			0
$499$	19.9711	−	19.9711i	0.894029	−	0.894029i	−0.100871	−	0.994900i	$-0.532163\pi$
$499$	19.9711	−	19.9711i	0.894029	−	0.894029i	0.994900	+	0.100871i	$0.0321628\pi$
$500$	−17.3884	+	4.65920i	−0.777632	+	0.208366i
$501$		0			0
$502$	30.2801	−	30.2801i	1.35147	−	1.35147i
$503$	23.3796	+	13.4982i	1.04244	+	0.601855i	0.920525	−	0.390685i	$-0.127762\pi$
$503$	23.3796	+	13.4982i	1.04244	+	0.601855i	0.121920	+	0.992540i	$0.461095\pi$
$504$		0			0
$505$	−0.464223	+	1.73250i	−0.0206576	+	0.0770954i
$506$			47.4825i			2.11085i
$507$		0			0
$508$	57.7565			2.56253
$509$	−1.30100	+	4.85539i	−0.0576658	+	0.215212i	−0.988746	−	0.149602i	$-0.952201\pi$
$509$	−1.30100	+	4.85539i	−0.0576658	+	0.215212i	0.931081	+	0.364814i	$0.118867\pi$
$510$		0			0
$511$	12.3604	+	4.34659i	0.546792	+	0.192282i
$512$	35.3750	−	35.3750i	1.56337	−	1.56337i
$513$		0			0
$514$	8.11452	+	30.2838i	0.357916	+	1.33576i
$515$	4.53516	+	4.53516i	0.199843	+	0.199843i
$516$		0			0
$517$	15.4019	+	26.6768i	0.677373	+	1.17325i
$518$	12.1377	+	0.928495i	0.533300	+	0.0407957i
$519$		0			0
$520$	−2.81425	+	9.13397i	−0.123413	+	0.400551i
$521$		−	28.5686i		−	1.25161i	−0.779979	−	0.625806i	$-0.784770\pi$
$521$		−	28.5686i		−	1.25161i	0.779979	−	0.625806i	$-0.215230\pi$
$522$		0			0
$523$	−15.9700	+	9.22026i	−0.698318	+	0.403174i	−0.806720	−	0.590933i	$-0.798760\pi$
$523$	−15.9700	+	9.22026i	−0.698318	+	0.403174i	0.108403	+	0.994107i	$0.465426\pi$
$524$	−27.0261	+	46.8106i	−1.18064	+	2.04493i
$525$		0			0
$526$	9.70594	+	36.2230i	0.423199	+	1.57940i
$527$	24.8596	−	6.66110i	1.08290	−	0.290162i
$528$		0			0
$529$	1.47417	−	2.55334i	0.0640944	−	0.111015i
$530$	4.65031	+	8.05458i	0.201997	+	0.349868i
$531$		0			0
$532$	−1.80427	−	9.61729i	−0.0782250	−	0.416962i
$533$	−4.28536	+	6.82496i	−0.185620	+	0.295622i
$534$		0			0
$535$	−1.11526	+	4.16220i	−0.0482169	+	0.179948i
$536$	−16.7354	−	28.9865i	−0.722859	−	1.25203i
$537$		0			0
$538$	9.04840	+	9.04840i	0.390104	+	0.390104i
$539$	−15.0280	−	20.4948i	−0.647303	−	0.882773i
$540$		0			0
$541$	−4.67673	−	4.67673i	−0.201068	−	0.201068i	0.599389	−	0.800458i	$-0.295410\pi$
$541$	−4.67673	−	4.67673i	−0.201068	−	0.201068i	−0.800458	+	0.599389i	$0.795410\pi$
$542$	−58.9092	−	34.0113i	−2.53037	−	1.46091i
$543$		0			0
$544$	27.6103	+	7.39814i	1.18378	+	0.317193i
$545$	−1.32835			−0.0569001
$546$		0			0
$547$	33.8006			1.44521			0.722605	−	0.691261i	$-0.242944\pi$
$547$	33.8006			1.44521			0.722605	+	0.691261i	$0.242944\pi$
$548$	57.7518	+	15.4745i	2.46703	+	0.661040i
$549$		0			0
$550$	39.0816	+	22.5637i	1.66644	+	0.962121i
$551$	1.14744	+	1.14744i	0.0488825	+	0.0488825i
$552$		0			0
$553$	−4.14183	−	8.63478i	−0.176129	−	0.367188i
$554$	37.0797	+	37.0797i	1.57536	+	1.57536i
$555$		0			0
$556$	−19.8772	−	34.4283i	−0.842981	−	1.46009i
$557$	−6.41622	+	23.9457i	−0.271864	+	1.01461i	0.686050	+	0.727555i	$0.259343\pi$
$557$	−6.41622	+	23.9457i	−0.271864	+	1.01461i	−0.957914	+	0.287056i	$0.907323\pi$
$558$		0			0
$559$	7.50953	+	8.08815i	0.317619	+	0.342092i
$560$	8.18458	−	1.53548i	0.345862	−	0.0648860i
$561$		0			0
$562$	7.02090	+	12.1606i	0.296159	+	0.512962i
$563$	2.10194	−	3.64067i	0.0885863	−	0.153436i	−0.818327	−	0.574752i	$-0.805098\pi$
$563$	2.10194	−	3.64067i	0.0885863	−	0.153436i	0.906914	+	0.421316i	$0.138432\pi$
$564$		0			0
$565$	2.94005	−	0.787784i	0.123689	−	0.0331423i
$566$	16.6378	+	62.0931i	0.699338	+	2.60997i
$567$		0			0
$568$	−7.49422	+	12.9804i	−0.314450	+	0.544644i
$569$	0.733859	−	0.423694i	0.0307650	−	0.0177622i	−0.484539	−	0.874770i	$-0.661012\pi$
$569$	0.733859	−	0.423694i	0.0307650	−	0.0177622i	0.515304	+	0.857008i	$0.327679\pi$
$570$		0			0
$571$			17.8746i			0.748028i	0.927423	+	0.374014i	$0.122019\pi$
$571$			17.8746i			0.748028i	−0.927423	+	0.374014i	$0.877981\pi$
$572$	53.1332	−	28.1035i	2.22161	−	1.17507i
$573$		0			0
$574$	15.1385	+	1.15805i	0.631869	+	0.0483360i
$575$	−12.3307	−	21.3574i	−0.514225	−	0.890664i
$576$		0			0
$577$	6.04475	+	6.04475i	0.251646	+	0.251646i	0.821645	−	0.569999i	$-0.193056\pi$
$577$	6.04475	+	6.04475i	0.251646	+	0.251646i	−0.569999	+	0.821645i	$0.693056\pi$
$578$	0.141910	+	0.529615i	0.00590268	+	0.0220291i
$579$		0			0
$580$	−2.60590	+	2.60590i	−0.108204	+	0.108204i
$581$	−6.66275	+	18.9469i	−0.276418	+	0.786050i
$582$		0			0
$583$	8.54482	−	31.8897i	0.353890	−	1.32074i
$584$	32.9535			1.36363
$585$		0			0
$586$		−	47.3861i		−	1.95750i
$587$	−10.7910	+	40.2727i	−0.445394	+	1.66223i	0.269502	+	0.963000i	$0.413141\pi$
$587$	−10.7910	+	40.2727i	−0.445394	+	1.66223i	−0.714895	+	0.699231i	$0.753526\pi$
$588$		0			0
$589$	−4.38162	−	2.52973i	−0.180541	−	0.104236i
$590$	5.37385	−	5.37385i	0.221238	−	0.221238i
$591$		0			0
$592$	13.6765	−	3.66460i	0.562100	−	0.150614i
$593$	−6.50540	+	6.50540i	−0.267145	+	0.267145i	−0.827949	−	0.560804i	$-0.810492\pi$
$593$	−6.50540	+	6.50540i	−0.267145	+	0.267145i	0.560804	+	0.827949i	$0.310492\pi$
$594$		0			0
$595$	−2.81168	−	3.27748i	−0.115268	−	0.134364i
$596$	−22.2005	+	82.8534i	−0.909368	+	3.39381i
$597$		0			0
$598$	−47.1226	−	1.74808i	−1.92699	−	0.0714845i
$599$	41.5746			1.69869			0.849345	−	0.527838i	$-0.176997\pi$
$599$	41.5746			1.69869			0.849345	+	0.527838i	$0.176997\pi$
$600$		0			0
$601$	−22.6812	+	13.0950i	−0.925184	+	0.534155i	−0.885285	−	0.465049i	$-0.846037\pi$
$601$	−22.6812	+	13.0950i	−0.925184	+	0.534155i	−0.0398987	+	0.999204i	$0.512704\pi$
$602$	6.89795	−	19.6157i	0.281140	−	0.799478i
$603$		0			0
$604$	16.7228	+	62.4104i	0.680442	+	2.53944i
$605$	0.224889	+	0.839298i	0.00914305	+	0.0341223i
$606$		0			0
$607$	16.5683	+	9.56570i	0.672486	+	0.388260i	0.797018	−	0.603956i	$-0.206410\pi$
$607$	16.5683	+	9.56570i	0.672486	+	0.388260i	−0.124532	+	0.992216i	$0.539743\pi$
$608$	−2.80964	−	4.86644i	−0.113946	−	0.197360i
$609$		0			0
$610$			2.83859i			0.114931i
$611$	−27.0417	+	14.3030i	−1.09399	+	0.578638i
$612$		0			0
$613$	−10.7855	−	2.88996i	−0.435622	−	0.116725i	0.0343420	−	0.999410i	$-0.489066\pi$
$613$	−10.7855	−	2.88996i	−0.435622	−	0.116725i	−0.469964	+	0.882686i	$0.655733\pi$
$614$	46.1284	−	26.6322i	1.86159	−	1.07479i
$615$		0			0
$616$	−52.7561	−	36.0883i	−2.12561	−	1.45404i
$617$	2.84075	+	10.6018i	0.114364	+	0.426814i	0.999239	−	0.0390163i	$-0.0124224\pi$
$617$	2.84075	+	10.6018i	0.114364	+	0.426814i	−0.884874	+	0.465830i	$0.845756\pi$
$618$		0			0
$619$	18.7983	−	18.7983i	0.755567	−	0.755567i	−0.219945	−	0.975512i	$-0.570588\pi$
$619$	18.7983	−	18.7983i	0.755567	−	0.755567i	0.975512	+	0.219945i	$0.0705878\pi$
$620$	5.74517	−	9.95093i	0.230732	−	0.399639i
$621$		0			0
$622$	14.5363	+	3.89498i	0.582851	+	0.156175i
$623$	−5.82964	−	31.0737i	−0.233559	−	1.24494i
$624$		0			0
$625$	−22.6448			−0.905791
$626$	−13.5610	+	50.6102i	−0.542005	+	2.02279i
$627$		0			0
$628$	32.1657	−	55.7127i	1.28355	−	2.22318i
$629$	−5.19179	−	5.19179i	−0.207010	−	0.207010i
$630$		0			0
$631$	−34.9180	+	9.35626i	−1.39007	+	0.372467i	−0.874767	−	0.484544i	$-0.838986\pi$
$631$	−34.9180	+	9.35626i	−1.39007	+	0.372467i	−0.515298	+	0.857011i	$0.672319\pi$
$632$	−17.0316	−	17.0316i	−0.677479	−	0.677479i
$633$		0			0
$634$	17.0551	−	9.84677i	0.677345	−	0.391065i
$635$	−4.83998	−	1.29687i	−0.192069	−	0.0514647i
$636$		0			0
$637$	20.8927	−	14.1596i	0.827799	−	0.561024i
$638$	18.7797			0.743496
$639$		0			0
$640$	−2.94456	+	1.70004i	−0.116394	+	0.0672000i
$641$	−21.5157	−	12.4221i	−0.849819	−	0.490643i	0.0107708	−	0.999942i	$-0.496571\pi$
$641$	−21.5157	−	12.4221i	−0.849819	−	0.490643i	−0.860590	+	0.509299i	$0.829905\pi$
$642$		0			0
$643$	28.7931	−	7.71509i	1.13549	−	0.304253i	0.358353	−	0.933586i	$-0.383338\pi$
$643$	28.7931	−	7.71509i	1.13549	−	0.304253i	0.777136	+	0.629333i	$0.216672\pi$
$644$	26.7645	+	55.7980i	1.05467	+	2.19875i
$645$		0			0
$646$	−4.23628	+	7.33745i	−0.166674	+	0.288688i
$647$	−6.87674	−	11.9109i	−0.270352	−	0.468264i	0.698600	−	0.715513i	$-0.253807\pi$
$647$	−6.87674	−	11.9109i	−0.270352	−	0.468264i	−0.968952	+	0.247249i	$0.920474\pi$
$648$		0			0
$649$	−26.9771			−1.05894
$650$	−23.8315	+	37.9547i	−0.934750	+	1.48870i
$651$		0			0
$652$	−42.0379	−	11.2640i	−1.64633	−	0.441133i
$653$	0.855193	+	1.48124i	0.0334663	+	0.0579653i	0.882273	−	0.470737i	$-0.156012\pi$
$653$	0.855193	+	1.48124i	0.0334663	+	0.0579653i	−0.848807	+	0.528703i	$0.822679\pi$
$654$		0			0
$655$	3.31587	−	3.31587i	0.129562	−	0.129562i
$656$	17.0577	−	4.57060i	0.665992	−	0.178452i
$657$		0			0
$658$	47.5689	+	32.5399i	1.85443	+	1.26854i
$659$	4.73353	−	8.19872i	0.184392	−	0.319377i	−0.758979	−	0.651115i	$-0.774302\pi$
$659$	4.73353	−	8.19872i	0.184392	−	0.319377i	0.943372	+	0.331738i	$0.107635\pi$
$660$		0			0
$661$	−8.52858	−	2.28523i	−0.331723	−	0.0888850i	0.0891132	−	0.996022i	$-0.471597\pi$
$661$	−8.52858	−	2.28523i	−0.331723	−	0.0888850i	−0.420836	+	0.907137i	$0.638263\pi$
$662$			64.7224i			2.51551i
$663$		0			0
$664$			50.5135i			1.96030i
$665$	−0.0647500	+	0.846440i	−0.00251090	+	0.0328236i
$666$		0			0
$667$	−8.88783	−	5.13139i	−0.344138	−	0.198688i
$668$	−31.6387	−	31.6387i	−1.22414	−	1.22414i
$669$		0			0
$670$	1.33151	+	4.96926i	0.0514407	+	0.191979i
$671$	7.12495	−	7.12495i	0.275056	−	0.275056i
$672$		0			0
$673$	15.2065	−	8.77951i	0.586169	−	0.338425i	−0.177412	−	0.984137i	$-0.556773\pi$
$673$	15.2065	−	8.77951i	0.586169	−	0.338425i	0.763581	+	0.645712i	$0.223439\pi$
$674$	20.0219	−	74.7228i	0.771216	−	2.87822i
$675$		0			0
$676$	25.9344	+	53.7651i	0.997476	+	2.06789i
$677$		−	23.4987i		−	0.903127i	−0.892239	−	0.451564i	$-0.850866\pi$
$677$		−	23.4987i		−	0.903127i	0.892239	−	0.451564i	$-0.149134\pi$
$678$		0			0
$679$	13.7678	+	16.0487i	0.528360	+	0.615892i
$680$	−9.40571	−	5.43039i	−0.360692	−	0.208246i
$681$		0			0
$682$	−56.5579	+	15.1546i	−2.16571	+	0.580301i
$683$	33.6607	−	9.01937i	1.28799	−	0.345117i	0.451095	−	0.892476i	$-0.351034\pi$
$683$	33.6607	−	9.01937i	1.28799	−	0.345117i	0.836898	+	0.547359i	$0.184367\pi$
$684$		0			0
$685$	−4.49212	−	2.59353i	−0.171635	−	0.0990936i
$686$	−41.9358	−	22.4136i	−1.60112	−	0.855753i
$687$		0			0
$688$		−	24.1852i		−	0.922052i
$689$	31.3334	+	9.65409i	1.19371	+	0.367792i
$690$		0			0
$691$	−12.0465	+	44.9582i	−0.458271	+	1.71029i	0.220019	+	0.975496i	$0.429388\pi$
$691$	−12.0465	+	44.9582i	−0.458271	+	1.71029i	−0.678290	+	0.734795i	$0.737279\pi$
$692$	−67.6287	+	39.0454i	−2.57086	+	1.48428i
$693$		0			0
$694$	62.5609	−	62.5609i	2.37478	−	2.37478i
$695$	0.892649	+	3.33141i	0.0338601	+	0.126368i
$696$		0			0
$697$	−6.47536	−	6.47536i	−0.245272	−	0.245272i
$698$	−9.13923	−	5.27654i	−0.345925	−	0.199720i
$699$		0			0
$700$	58.6443	+	4.48610i	2.21655	+	0.169559i
$701$		−	7.19399i		−	0.271713i	−0.990729	−	0.135857i	$-0.956621\pi$
$701$		−	7.19399i		−	0.271713i	0.990729	−	0.135857i	$-0.0433787\pi$
$702$		0			0
$703$			1.44340i			0.0544388i
$704$	−7.40075	−	1.98302i	−0.278926	−	0.0747380i
$705$		0			0
$706$	−13.9744	+	24.2044i	−0.525934	+	0.910945i
$707$	6.72571	−	9.83206i	0.252946	−	0.369773i
$708$		0			0
$709$	−0.150433	+	0.0403084i	−0.00564964	+	0.00151382i	−0.261643	−	0.965165i	$-0.584264\pi$
$709$	−0.150433	+	0.0403084i	−0.00564964	+	0.00151382i	0.255993	+	0.966679i	$0.417598\pi$
$710$	1.62901	−	1.62901i	0.0611356	−	0.0611356i
$711$		0			0
$712$	−39.7581	−	68.8630i	−1.49000	−	2.58075i
$713$	30.9079	+	8.28174i	1.15751	+	0.310154i
$714$		0			0
$715$	−5.08359	+	1.16201i	−0.190115	+	0.0434567i
$716$	−49.9045			−1.86502
$717$		0			0
$718$	−39.5151	−	68.4421i	−1.47469	−	2.55424i
$719$	6.48137	−	11.2261i	0.241714	−	0.418661i	−0.719488	−	0.694504i	$-0.755624\pi$
$719$	6.48137	−	11.2261i	0.241714	−	0.418661i	0.961203	+	0.275843i	$0.0889570\pi$
$720$		0			0
$721$	−18.4226	−	38.4069i	−0.686093	−	1.43035i
$722$	−45.5105	+	12.1945i	−1.69372	+	0.453832i
$723$		0			0
$724$	82.6002	+	47.6893i	3.06981	+	1.77236i
$725$	−8.44702	+	4.87689i	−0.313714	+	0.181123i
$726$		0			0
$727$	−49.4330			−1.83337			−0.916684	−	0.399614i	$-0.869144\pi$
$727$	−49.4330			−1.83337			−0.916684	+	0.399614i	$0.869144\pi$
$728$	37.7570	−	51.0277i	1.39937	−	1.89121i
$729$		0			0
$730$	−4.89246	−	1.31093i	−0.181078	−	0.0485198i
$731$	−10.8613	+	6.27077i	−0.401720	+	0.231933i
$732$		0			0
$733$	−24.1928	−	24.1928i	−0.893581	−	0.893581i	0.101277	−	0.994858i	$-0.467707\pi$
$733$	−24.1928	−	24.1928i	−0.893581	−	0.893581i	−0.994858	+	0.101277i	$0.967707\pi$
$734$	−61.8450	+	16.5713i	−2.28274	+	0.611658i
$735$		0			0
$736$	25.1297	+	25.1297i	0.926292	+	0.926292i
$737$	9.13088	−	15.8151i	0.336340	−	0.582558i
$738$		0			0
$739$	1.10636	−	4.12898i	0.0406980	−	0.151887i	−0.942587	−	0.333961i	$-0.891615\pi$
$739$	1.10636	−	4.12898i	0.0406980	−	0.151887i	0.983285	+	0.182074i	$0.0582812\pi$
$740$	−3.27805			−0.120503
$741$		0			0
$742$	−11.3898	−	60.7112i	−0.418134	−	2.22878i
$743$	−23.2815	−	6.23826i	−0.854115	−	0.228859i	−0.194909	−	0.980821i	$-0.562441\pi$
$743$	−23.2815	−	6.23826i	−0.854115	−	0.228859i	−0.659206	+	0.751962i	$0.729108\pi$
$744$		0			0
$745$	3.72080	−	6.44461i	0.136319	−	0.236112i
$746$	−33.0218	+	33.0218i	−1.20902	+	1.20902i
$747$		0			0
$748$	17.6780	+	65.9754i	0.646373	+	2.41230i
$749$	16.1580	−	23.6208i	0.590400	−	0.863084i
$750$		0			0
$751$	−11.3539	+	6.55518i	−0.414310	+	0.239202i	−0.692640	−	0.721283i	$-0.743553\pi$
$751$	−11.3539	+	6.55518i	−0.414310	+	0.239202i	0.278330	+	0.960486i	$0.410219\pi$
$752$	64.7512	+	17.3500i	2.36123	+	0.632690i
$753$		0			0
$754$	−0.691382	+	18.6374i	−0.0251786	+	0.678734i
$755$		−	5.60548i		−	0.204004i
$756$		0			0
$757$	7.95111	+	13.7717i	0.288988	+	0.500542i	0.973568	−	0.228395i	$-0.0733479\pi$
$757$	7.95111	+	13.7717i	0.288988	+	0.500542i	−0.684580	+	0.728937i	$0.740015\pi$
$758$	−1.86667	−	1.07772i	−0.0678007	−	0.0391447i
$759$		0			0
$760$	0.552600	+	2.06233i	0.0200449	+	0.0748087i
$761$	−10.2470	−	38.2424i	−0.371454	−	1.38629i	−0.858457	−	0.512886i	$-0.828576\pi$
$761$	−10.2470	−	38.2424i	−0.371454	−	1.38629i	0.487002	−	0.873401i	$-0.338090\pi$
$762$		0			0
$763$	8.32265	+	2.92669i	0.301300	+	0.105953i
$764$	5.90280	−	3.40799i	0.213556	−	0.123297i
$765$		0			0
$766$	14.9050			0.538538
$767$	0.993171	−	26.7726i	0.0358613	−	0.966704i
$768$		0			0
$769$	−1.28737	+	4.80452i	−0.0464236	+	0.173255i	−0.985245	−	0.171148i	$-0.945252\pi$
$769$	−1.28737	+	4.80452i	−0.0464236	+	0.173255i	0.938822	+	0.344404i	$0.111919\pi$
$770$	6.39683	+	7.45657i	0.230526	+	0.268716i
$771$		0			0
$772$	−23.8404	+	23.8404i	−0.858036	+	0.858036i
$773$	32.0473	−	8.58704i	1.15266	−	0.308855i	0.368630	−	0.929576i	$-0.379827\pi$
$773$	32.0473	−	8.58704i	1.15266	−	0.308855i	0.784031	+	0.620722i	$0.213160\pi$
$774$		0			0
$775$	21.5039	−	21.5039i	0.772444	−	0.772444i
$776$	46.0565	+	26.5907i	1.65333	+	0.954551i
$777$		0			0
$778$	−5.79862	+	21.6408i	−0.207891	+	0.775859i
$779$			1.80025i			0.0645007i
$780$		0			0
$781$	−8.17773			−0.292622
$782$	13.8686	−	51.7582i	0.495939	−	1.85087i
$783$		0			0
$784$	−54.6629	−	8.41231i	−1.95225	−	0.300440i
$785$	−3.94646	+	3.94646i	−0.140855	+	0.140855i
$786$		0			0
$787$	−3.27477	−	12.2216i	−0.116733	−	0.435653i	0.882678	−	0.469978i	$-0.155738\pi$
$787$	−3.27477	−	12.2216i	−0.116733	−	0.435653i	−0.999411	+	0.0343257i	$0.989072\pi$
$788$	−58.6286	−	58.6286i	−2.08856	−	2.08856i
$789$		0			0
$790$	1.85106	+	3.20614i	0.0658579	+	0.114069i
$791$	−20.1564	−	1.54190i	−0.716678	−	0.0548235i
$792$		0			0
$793$	6.80864	+	7.33325i	0.241782	+	0.260411i
$794$		−	0.546029i		−	0.0193779i
$795$		0			0
$796$	−12.9698	+	7.48811i	−0.459702	+	0.265409i
$797$	−3.71613	+	6.43653i	−0.131632	+	0.227994i	−0.924306	−	0.381652i	$-0.875355\pi$
$797$	−3.71613	+	6.43653i	−0.131632	+	0.227994i	0.792674	+	0.609646i	$0.208688\pi$
$798$		0			0
$799$	−8.99708	−	33.5776i	−0.318294	−	1.18789i
$800$	32.6252	−	8.74190i	1.15348	−	0.309073i
$801$		0			0
$802$	9.00980	−	15.6054i	0.318147	−	0.551047i
$803$	8.98977	+	15.5707i	0.317242	+	0.549479i
$804$		0			0
$805$	−0.989970	−	5.27683i	−0.0348919	−	0.185984i
$806$	−12.9576	−	56.6871i	−0.456411	−	1.99672i
$807$		0			0
$808$	7.75436	−	28.9397i	0.272797	−	1.01809i
$809$	−26.9123	−	46.6134i	−0.946185	−	1.63884i	−0.753361	−	0.657607i	$-0.771569\pi$
$809$	−26.9123	−	46.6134i	−0.946185	−	1.63884i	−0.192824	−	0.981233i	$-0.561765\pi$
$810$		0			0
$811$	19.2534	+	19.2534i	0.676078	+	0.676078i	0.959110	−	0.283032i	$-0.0913404\pi$
$811$	19.2534	+	19.2534i	0.676078	+	0.676078i	−0.283032	+	0.959110i	$0.591340\pi$
$812$	22.0686	−	10.5856i	0.774455	−	0.371482i
$813$		0			0
$814$	11.8118	+	11.8118i	0.414004	+	0.414004i
$815$	3.26984	+	1.88784i	0.114538	+	0.0661283i
$816$		0			0
$817$	2.38149	+	0.638119i	0.0833178	+	0.0223249i
$818$	27.4885			0.961113
$819$		0			0
$820$	−4.08848			−0.142776
$821$	−9.07220	−	2.43089i	−0.316622	−	0.0848386i	0.0970082	−	0.995284i	$-0.469073\pi$
$821$	−9.07220	−	2.43089i	−0.316622	−	0.0848386i	−0.413630	+	0.910445i	$0.635739\pi$
$822$		0			0
$823$	−37.1775	−	21.4644i	−1.29592	−	0.748202i	−0.316227	−	0.948684i	$-0.602416\pi$
$823$	−37.1775	−	21.4644i	−1.29592	−	0.748202i	−0.979698	+	0.200481i	$0.935749\pi$
$824$	−75.7552	−	75.7552i	−2.63906	−	2.63906i
$825$		0			0
$826$	−45.5095	+	21.8295i	−1.58348	+	0.759544i
$827$	2.53773	+	2.53773i	0.0882457	+	0.0882457i	0.749852	−	0.661606i	$-0.230125\pi$
$827$	2.53773	+	2.53773i	0.0882457	+	0.0882457i	−0.661606	+	0.749852i	$0.730125\pi$
$828$		0			0
$829$	25.3747	+	43.9503i	0.881301	+	1.52646i	0.849896	+	0.526951i	$0.176665\pi$
$829$	25.3747	+	43.9503i	0.881301	+	1.52646i	0.0314050	+	0.999507i	$0.490002\pi$
$830$	2.00949	−	7.49951i	0.0697503	−	0.260312i
$831$		0			0
$832$	2.24046	−	7.27165i	0.0776738	−	0.252099i
$833$	10.3952	+	26.7297i	0.360173	+	0.926128i
$834$		0			0
$835$	1.94090	+	3.36173i	0.0671675	+	0.116338i
$836$	6.71370	−	11.6285i	0.232198	−	0.402179i
$837$		0			0
$838$	−2.58713	+	0.693219i	−0.0893709	+	0.0239469i
$839$	−3.51172	−	13.1059i	−0.121238	−	0.452466i	0.878440	−	0.477853i	$-0.158585\pi$
$839$	−3.51172	−	13.1059i	−0.121238	−	0.452466i	−0.999678	+	0.0253868i	$0.991918\pi$
$840$		0			0
$841$	12.4705	−	21.5995i	0.430017	−	0.744811i
$842$	−72.2838	+	41.7331i	−2.49106	+	1.43822i
$843$		0			0
$844$			10.1849i			0.350579i
$845$	−0.966049	−	5.08784i	−0.0332331	−	0.175027i
$846$		0			0
$847$	0.440167	−	5.75405i	0.0151243	−	0.197712i
$848$	−35.9234	−	62.2212i	−1.23361	−	2.13668i
$849$		0			0
$850$	−36.0104	−	36.0104i	−1.23515	−	1.23515i
$851$	−2.36267	−	8.81761i	−0.0809914	−	0.302264i
$852$		0			0
$853$	35.8111	−	35.8111i	1.22615	−	1.22615i	0.260737	−	0.965410i	$-0.416034\pi$
$853$	35.8111	−	35.8111i	1.22615	−	1.22615i	0.965410	−	0.260737i	$-0.0839656\pi$
$854$	6.25415	−	17.7849i	0.214012	−	0.608588i
$855$		0			0
$856$	18.6293	−	69.5253i	0.636735	−	2.37633i
$857$	−30.8652			−1.05433			−0.527167	−	0.849761i	$-0.676746\pi$
$857$	−30.8652			−1.05433			−0.527167	+	0.849761i	$0.676746\pi$
$858$		0			0
$859$		−	32.4866i		−	1.10843i	−0.832374	−	0.554215i	$-0.813019\pi$
$859$		−	32.4866i		−	1.10843i	0.832374	−	0.554215i	$-0.186981\pi$
$860$	−1.44921	+	5.40851i	−0.0494175	+	0.184429i
$861$		0			0
$862$	−18.1961	−	10.5055i	−0.619761	−	0.357819i
$863$	5.35457	−	5.35457i	0.182272	−	0.182272i	−0.610073	−	0.792345i	$-0.708860\pi$
$863$	5.35457	−	5.35457i	0.182272	−	0.182272i	0.792345	+	0.610073i	$0.208860\pi$
$864$		0			0
$865$	6.54400	−	1.75346i	0.222503	−	0.0596194i
$866$	36.1301	−	36.1301i	1.22775	−	1.22775i
$867$		0			0
$868$	−57.9204	+	49.6887i	−1.96595	+	1.68654i
$869$	3.40128	−	12.6938i	0.115381	−	0.430606i
$870$		0			0
$871$	15.3591	+	9.64391i	0.520424	+	0.326771i
$872$	22.1886			0.751402
$873$		0			0
$874$	−9.12264	+	5.26696i	−0.308578	+	0.178158i
$875$	−9.78510	−	3.44097i	−0.330797	−	0.116326i
$876$		0			0
$877$	−4.95841	−	18.5050i	−0.167433	−	0.624870i	−0.997717	−	0.0675294i	$-0.978488\pi$
$877$	−4.95841	−	18.5050i	−0.167433	−	0.624870i	0.830284	−	0.557341i	$-0.188178\pi$
$878$	−4.82791	−	18.0180i	−0.162934	−	0.608078i
$879$		0			0
$880$	9.89615	+	5.71355i	0.333599	+	0.192604i
$881$	−3.37117	−	5.83904i	−0.113578	−	0.196722i	0.803633	−	0.595126i	$-0.202898\pi$
$881$	−3.37117	−	5.83904i	−0.113578	−	0.196722i	−0.917210	+	0.398403i	$0.869564\pi$
$882$		0			0
$883$		−	41.6349i		−	1.40112i	−0.713591	−	0.700562i	$-0.752933\pi$
$883$		−	41.6349i		−	1.40112i	0.713591	−	0.700562i	$-0.247067\pi$
$884$	−66.1262	+	15.1152i	−2.22406	+	0.508378i
$885$		0			0
$886$	−65.8720	−	17.6504i	−2.21301	−	0.592975i
$887$	−16.4801	+	9.51479i	−0.553348	+	0.319475i	−0.750471	−	0.660903i	$-0.770173\pi$
$887$	−16.4801	+	9.51479i	−0.553348	+	0.319475i	0.197123	+	0.980379i	$0.436840\pi$
$888$		0			0
$889$	27.4672	+	18.7892i	0.921221	+	0.630169i
$890$	3.16325	+	11.8054i	0.106032	+	0.395718i
$891$		0			0
$892$	−17.6625	+	17.6625i	−0.591385	+	0.591385i
$893$	−3.41688	+	5.91821i	−0.114342	+	0.198045i
$894$		0			0
$895$	4.18199	+	1.12056i	0.139788	+	0.0374562i
$896$	22.1945	−	4.16385i	0.741467	−	0.139104i
$897$		0			0
$898$	−50.9057			−1.69875
$899$	3.27550	−	12.2243i	0.109244	−	0.407704i
$900$		0			0
$901$	−18.6285	+	32.2656i	−0.620607	+	1.07492i
$902$	14.7320	+	14.7320i	0.490523	+	0.490523i
$903$		0			0
$904$	−49.1105	+	13.1591i	−1.63339	+	0.437666i
$905$	−5.85106	−	5.85106i	−0.194496	−	0.194496i
$906$		0			0
$907$	−4.78340	+	2.76169i	−0.158830	+	0.0917006i	−0.577308	−	0.816526i	$-0.695897\pi$
$907$	−4.78340	+	2.76169i	−0.158830	+	0.0917006i	0.418478	+	0.908227i	$0.362564\pi$
$908$	−1.53791	−	0.412081i	−0.0510372	−	0.0136754i
$909$		0			0
$910$	−7.63556	+	6.07383i	−0.253116	+	0.201346i
$911$	23.9393			0.793146			0.396573	−	0.918003i	$-0.370199\pi$
$911$	23.9393			0.793146			0.396573	+	0.918003i	$0.370199\pi$
$912$		0			0
$913$	−23.8679	+	13.7801i	−0.789913	+	0.456056i
$914$	55.8085	+	32.2211i	1.84598	+	1.06578i
$915$		0			0
$916$	−117.587	+	31.5074i	−3.88519	+	1.04103i
$917$	−28.0811	+	13.4696i	−0.927320	+	0.444806i
$918$		0			0
$919$	21.7832	−	37.7297i	0.718562	−	1.24459i	−0.243007	−	0.970025i	$-0.578134\pi$
$919$	21.7832	−	37.7297i	0.718562	−	1.24459i	0.961569	−	0.274562i	$-0.0885329\pi$
$920$	−6.75159	−	11.6941i	−0.222593	−	0.385543i
$921$		0			0
$922$	86.8424			2.86000
$923$	0.301066	−	8.11575i	0.00990971	−	0.267133i
$924$		0			0
$925$	−8.38029	−	2.24549i	−0.275542	−	0.0738313i
$926$	24.8085	+	42.9696i	0.815258	+	1.41207i
$927$		0			0
$928$	9.93900	−	9.93900i	0.326264	−	0.326264i
$929$	−32.5120	+	8.71157i	−1.06669	+	0.285817i	−0.749130	−	0.662423i	$-0.769528\pi$
$929$	−32.5120	+	8.71157i	−1.06669	+	0.285817i	−0.317555	+	0.948240i	$0.602862\pi$
$930$		0			0
$931$	2.27062	−	5.16065i	0.0744164	−	0.169133i
$932$	−50.1114	+	86.7955i	−1.64145	+	2.84308i
$933$		0			0
$934$	−37.5779	−	10.0690i	−1.22959	−	0.329466i
$935$		−	5.92567i		−	0.193790i
$936$		0			0
$937$			9.65419i			0.315389i	0.987488	+	0.157694i	$0.0504061\pi$
$937$			9.65419i			0.315389i	−0.987488	+	0.157694i	$0.949594\pi$
$938$	2.60611	−	34.0682i	0.0850924	−	1.11237i
$939$		0			0
$940$	−13.4406	−	7.75995i	−0.438385	−	0.253102i
$941$	8.69399	+	8.69399i	0.283416	+	0.283416i	0.834470	−	0.551054i	$-0.185774\pi$
$941$	8.69399	+	8.69399i	0.283416	+	0.283416i	−0.551054	+	0.834470i	$0.685774\pi$
$942$		0			0
$943$	−2.94680	−	10.9976i	−0.0959609	−	0.358131i
$944$	−41.5127	+	41.5127i	−1.35112	+	1.35112i
$945$		0			0
$946$	24.7105	−	14.2666i	0.803407	−	0.463847i
$947$	7.16842	−	26.7529i	0.232942	−	0.869353i	−0.746123	−	0.665808i	$-0.768087\pi$
$947$	7.16842	−	26.7529i	0.232942	−	0.869353i	0.979066	−	0.203545i	$-0.0652463\pi$
$948$		0			0
$949$	−15.7837	+	8.34839i	−0.512360	+	0.271000i
$950$			10.0115i			0.324815i
$951$		0			0
$952$	46.9662	+	54.7469i	1.52218	+	1.77436i
$953$	19.2186	+	11.0958i	0.622550	+	0.359430i	0.777861	−	0.628436i	$-0.216305\pi$
$953$	19.2186	+	11.0958i	0.622550	+	0.359430i	−0.155311	+	0.987866i	$0.549638\pi$
$954$		0			0
$955$	−0.571177	+	0.153046i	−0.0184829	+	0.00495247i
$956$	−12.6825	+	3.39826i	−0.410181	+	0.109908i
$957$		0			0
$958$	55.8970	+	32.2722i	1.80595	+	1.04267i
$959$	22.4308	+	26.1469i	0.724329	+	0.844326i
$960$		0			0
$961$			8.45855i			0.272856i
$962$	−12.1571	+	11.2874i	−0.391962	+	0.363921i
$963$		0			0
$964$	35.8621	−	133.839i	1.15504	−	4.31067i
$965$	2.53314	−	1.46251i	0.0815446	−	0.0470798i
$966$		0			0
$967$	−14.2351	+	14.2351i	−0.457769	+	0.457769i	−0.897923	−	0.440153i	$-0.854924\pi$
$967$	−14.2351	+	14.2351i	−0.457769	+	0.457769i	0.440153	+	0.897923i	$0.354924\pi$
$968$	−3.75654	−	14.0196i	−0.120740	−	0.450607i
$969$		0			0
$970$	−5.77999	−	5.77999i	−0.185584	−	0.185584i
$971$	39.5485	+	22.8334i	1.26917	+	0.732758i	0.974832	−	0.222943i	$-0.0715663\pi$
$971$	39.5485	+	22.8334i	1.26917	+	0.732758i	0.294342	+	0.955700i	$0.404900\pi$
$972$		0			0
$973$	1.74714	−	22.8394i	0.0560109	−	0.732199i
$974$		−	66.3283i		−	2.12529i
$975$		0			0
$976$		−	21.9279i		−	0.701895i
$977$	32.7282	+	8.76950i	1.04707	+	0.280561i	0.741040	−	0.671461i	$-0.234333\pi$
$977$	32.7282	+	8.76950i	1.04707	+	0.280561i	0.306029	+	0.952022i	$0.401000\pi$
$978$		0			0
$979$	21.6921	−	37.5719i	0.693283	−	1.20080i
$980$	11.7202	+	5.15671i	0.374387	+	0.164725i
$981$		0			0
$982$	89.4936	−	23.9797i	2.85586	−	0.765224i
$983$	25.1769	−	25.1769i	0.803017	−	0.803017i	−0.180549	−	0.983566i	$-0.557787\pi$
$983$	25.1769	−	25.1769i	0.803017	−	0.803017i	0.983566	+	0.180549i	$0.0577874\pi$
$984$		0			0
$985$	3.59662	+	6.22952i	0.114598	+	0.198489i
$986$	−20.4708	−	5.48514i	−0.651923	−	0.174682i
$987$		0			0
$988$	11.2932	+	7.09093i	0.359284	+	0.225592i
$989$	−15.5929			−0.495825
$990$		0			0
$991$	−24.8147	−	42.9803i	−0.788265	−	1.36532i	−0.927029	−	0.374990i	$-0.877646\pi$
$991$	−24.8147	−	42.9803i	−0.788265	−	1.36532i	0.138764	−	0.990326i	$-0.455687\pi$
$992$	−21.9123	+	37.9532i	−0.695716	+	1.20502i
$993$		0			0
$994$	−13.7956	+	6.61730i	−0.437568	+	0.209888i
$995$	1.25500	−	0.336278i	0.0397863	−	0.0106607i
$996$		0			0
$997$	−6.36471	−	3.67467i	−0.201572	−	0.116378i	0.395816	−	0.918330i	$-0.370462\pi$
$997$	−6.36471	−	3.67467i	−0.201572	−	0.116378i	−0.597389	+	0.801952i	$0.703795\pi$
$998$	62.7985	−	36.2567i	1.98785	−	1.14769i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.g.496.7		32
3.2	odd	2		91.2.bc.a.41.2	yes	32
7.6	odd	2	inner	819.2.fm.g.496.8		32
13.7	odd	12	inner	819.2.fm.g.748.8		32
21.2	odd	6		637.2.x.b.80.8		32
21.5	even	6		637.2.x.b.80.7		32
21.11	odd	6		637.2.bb.b.509.7		32
21.17	even	6		637.2.bb.b.509.8		32
21.20	even	2		91.2.bc.a.41.1	yes	32
39.20	even	12		91.2.bc.a.20.1	✓	32
91.20	even	12	inner	819.2.fm.g.748.7		32
273.20	odd	12		91.2.bc.a.20.2	yes	32
273.59	odd	12		637.2.x.b.215.7		32
273.137	even	12		637.2.x.b.215.8		32
273.215	odd	12		637.2.bb.b.423.7		32
273.254	even	12		637.2.bb.b.423.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.20.1	✓	32	39.20	even	12
91.2.bc.a.20.2	yes	32	273.20	odd	12
91.2.bc.a.41.1	yes	32	21.20	even	2
91.2.bc.a.41.2	yes	32	3.2	odd	2
637.2.x.b.80.7		32	21.5	even	6
637.2.x.b.80.8		32	21.2	odd	6
637.2.x.b.215.7		32	273.59	odd	12
637.2.x.b.215.8		32	273.137	even	12
637.2.bb.b.423.7		32	273.215	odd	12
637.2.bb.b.423.8		32	273.254	even	12
637.2.bb.b.509.7		32	21.11	odd	6
637.2.bb.b.509.8		32	21.17	even	6
819.2.fm.g.496.7		32	1.1	even	1	trivial
819.2.fm.g.496.8		32	7.6	odd	2	inner
819.2.fm.g.748.7		32	91.20	even	12	inner
819.2.fm.g.748.8		32	13.7	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(2.47996 + 0.664504i) q^{2} +(3.97660 + 2.29589i) q^{4} +(-0.281686 - 0.281686i) q^{5} +(1.14426 + 2.38551i) q^{7} +(4.70528 + 4.70528i) q^{8} +O(q^{10})\)	\(q+(2.47996 + 0.664504i) q^{2} +(3.97660 + 2.29589i) q^{4} +(-0.281686 - 0.281686i) q^{5} +(1.14426 + 2.38551i) q^{7} +(4.70528 + 4.70528i) q^{8} +(-0.511390 - 0.885754i) q^{10} +(-0.939666 + 3.50688i) q^{11} +(-3.44571 - 1.06165i) q^{13} +(1.25253 + 6.67635i) q^{14} +(3.95046 + 6.84240i) q^{16} +(2.04856 - 3.54822i) q^{17} +(-0.777996 + 0.208463i) q^{19} +(-0.473433 - 1.76688i) q^{20} +(-4.66067 + 8.07252i) q^{22} +(4.41149 - 2.54698i) q^{23} -4.84131i q^{25} +(-7.83976 - 4.92254i) q^{26} +(-0.926631 + 12.1133i) q^{28} +(-1.00735 - 1.74478i) q^{29} +(4.44176 + 4.44176i) q^{31} +(1.80569 + 6.73893i) q^{32} +(7.43817 - 7.43817i) q^{34} +(0.349645 - 0.994288i) q^{35} +(0.463819 - 1.73100i) q^{37} -2.06793 q^{38} -2.65083i q^{40} +(0.578490 - 2.15895i) q^{41} +(-2.65096 - 1.53053i) q^{43} +(-11.7881 + 11.7881i) q^{44} +(12.6328 - 3.38495i) q^{46} +(5.99945 - 5.99945i) q^{47} +(-4.38135 + 5.45928i) q^{49} +(3.21707 - 12.0063i) q^{50} +(-11.2648 - 12.1327i) q^{52} -9.09347 q^{53} +(1.25253 - 0.723149i) q^{55} +(-5.84047 + 16.6086i) q^{56} +(-1.33878 - 4.99638i) q^{58} +(1.92316 + 7.17731i) q^{59} +(-2.40353 - 1.38768i) q^{61} +(8.06384 + 13.9670i) q^{62} +2.11035i q^{64} +(0.671556 + 1.26966i) q^{65} +(-4.85858 - 1.30185i) q^{67} +(16.2926 - 9.40656i) q^{68} +(1.52782 - 2.23346i) q^{70} +(0.582978 + 2.17570i) q^{71} +(3.50176 - 3.50176i) q^{73} +(2.30051 - 3.98460i) q^{74} +(-3.57239 - 0.957219i) q^{76} +(-9.44093 + 1.77118i) q^{77} -3.61967 q^{79} +(0.814620 - 3.04020i) q^{80} +(2.86927 - 4.96972i) q^{82} +(5.36774 + 5.36774i) q^{83} +(-1.57654 + 0.422432i) q^{85} +(-5.55723 - 5.55723i) q^{86} +(-20.9222 + 12.0795i) q^{88} +(-11.5425 - 3.09280i) q^{89} +(-1.41019 - 9.43458i) q^{91} +23.3903 q^{92} +(18.8651 - 10.8918i) q^{94} +(0.277872 + 0.160430i) q^{95} +(7.71975 - 2.06850i) q^{97} +(-14.4933 + 10.6274i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8}+O(q^{10}) \) 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8	\( 32 q + 8 q^{2} - 12 q^{4} + 16 q^{8} + 4 q^{11} + 32 q^{14} + 12 q^{16} + 4 q^{22} + 12 q^{23} + 24 q^{28} - 4 q^{29} - 4 q^{32} + 20 q^{35} + 4 q^{37} - 48 q^{43} - 24 q^{44} + 84 q^{46} + 24 q^{49} + 44 q^{50} - 72 q^{53} - 60 q^{56} - 16 q^{58} - 4 q^{65} - 56 q^{67} + 56 q^{70} - 84 q^{71} + 24 q^{74} - 80 q^{79} + 36 q^{85} + 48 q^{86} - 228 q^{88} - 48 q^{91} - 24 q^{92} + 84 q^{95} + 32 q^{98}+O(q^{100}) \) 32 * q + 8 * q^2 - 12 * q^4 + 16 * q^8 + 4 * q^11 + 32 * q^14 + 12 * q^16 + 4 * q^22 + 12 * q^23 + 24 * q^28 - 4 * q^29 - 4 * q^32 + 20 * q^35 + 4 * q^37 - 48 * q^43 - 24 * q^44 + 84 * q^46 + 24 * q^49 + 44 * q^50 - 72 * q^53 - 60 * q^56 - 16 * q^58 - 4 * q^65 - 56 * q^67 + 56 * q^70 - 84 * q^71 + 24 * q^74 - 80 * q^79 + 36 * q^85 + 48 * q^86 - 228 * q^88 - 48 * q^91 - 24 * q^92 + 84 * q^95 + 32 * q^98

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