LMFDB - Embedded newform 819.2.fn.f.775.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(73,819)]

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, 3]))

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

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

chi := DirichletCharacter("819.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fn (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			775.1
Character	$\chi$	$=$	819.775
Dual form			819.2.fn.f.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.52924 + 0.677708i) q^{2} +(4.20573 - 2.42818i) q^{4} +(-1.05058 - 3.92082i) q^{5} +(-2.39518 - 1.12389i) q^{7} +(-5.28864 + 5.28864i) q^{8} +O(q^{10})$	\(q+(-2.52924 + 0.677708i) q^{2} +(4.20573 - 2.42818i) q^{4} +(-1.05058 - 3.92082i) q^{5} +(-2.39518 - 1.12389i) q^{7} +(-5.28864 + 5.28864i) q^{8} +(5.31435 + 9.20472i) q^{10} +(-0.560897 - 0.150292i) q^{11} +(-2.59678 - 2.50134i) q^{13} +(6.81965 + 1.21935i) q^{14} +(4.93574 - 8.54896i) q^{16} +(-0.229516 - 0.397534i) q^{17} +(-1.99360 - 7.44023i) q^{19} +(-13.9389 - 13.9389i) q^{20} +1.52050 q^{22} +(0.0405237 + 0.0233964i) q^{23} +(-9.93900 + 5.73828i) q^{25} +(8.26308 + 4.56664i) q^{26} +(-12.8025 + 1.08917i) q^{28} +1.08136 q^{29} +(4.88993 + 1.31025i) q^{31} +(-2.81843 + 10.5185i) q^{32} +(0.849915 + 0.849915i) q^{34} +(-1.89022 + 10.5718i) q^{35} +(1.13412 + 4.23261i) q^{37} +(10.0846 + 17.4671i) q^{38} +(26.2920 + 15.1797i) q^{40} +(4.50540 - 4.50540i) q^{41} +0.884530i q^{43} +(-2.72392 + 0.729872i) q^{44} +(-0.118350 - 0.0317118i) q^{46} +(-3.18059 + 0.852236i) q^{47} +(4.47376 + 5.38381i) q^{49} +(21.2493 - 21.2493i) q^{50} +(-16.9951 - 4.21450i) q^{52} +(-0.253079 - 0.438345i) q^{53} +2.35707i q^{55} +(18.6111 - 6.72342i) q^{56} +(-2.73501 + 0.732844i) q^{58} +(-0.577611 + 2.15568i) q^{59} +(0.165995 + 0.0958371i) q^{61} -13.2558 q^{62} -8.77105i q^{64} +(-7.07918 + 12.8094i) q^{65} +(-2.31148 + 8.62657i) q^{67} +(-1.93057 - 1.11461i) q^{68} +(-2.38377 - 28.0197i) q^{70} +(4.23807 + 4.23807i) q^{71} +(-1.87486 + 6.99707i) q^{73} +(-5.73695 - 9.93669i) q^{74} +(-26.4507 - 26.4507i) q^{76} +(1.17454 + 0.990361i) q^{77} +(2.92382 - 5.06421i) q^{79} +(-38.7043 - 10.3708i) q^{80} +(-8.34191 + 14.4486i) q^{82} +(9.67812 - 9.67812i) q^{83} +(-1.31754 + 1.31754i) q^{85} +(-0.599453 - 2.23719i) q^{86} +(3.76123 - 2.17154i) q^{88} +(-18.2195 + 4.88190i) q^{89} +(3.40854 + 8.90965i) q^{91} +0.227242 q^{92} +(7.46691 - 4.31102i) q^{94} +(-27.0774 + 15.6331i) q^{95} +(-5.63729 + 5.63729i) q^{97} +(-14.9639 - 10.5851i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{7}+O(q^{10}) $ 36 * q - 6 * q^7	$ 36 q - 6 q^{7} - 4 q^{11} + 36 q^{14} + 12 q^{16} - 4 q^{17} - 18 q^{19} - 44 q^{20} - 8 q^{22} + 12 q^{23} - 48 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{29} - 6 q^{31} - 76 q^{32} - 48 q^{34} - 8 q^{35} - 8 q^{37} - 16 q^{38} + 60 q^{40} + 32 q^{41} - 4 q^{44} + 28 q^{46} - 14 q^{47} + 6 q^{49} + 68 q^{50} - 62 q^{52} + 8 q^{53} + 8 q^{56} + 36 q^{58} - 26 q^{59} + 36 q^{61} - 48 q^{62} + 8 q^{65} - 40 q^{67} - 36 q^{68} - 64 q^{70} + 36 q^{71} - 8 q^{73} - 40 q^{74} - 60 q^{76} - 60 q^{77} - 26 q^{80} - 24 q^{83} + 44 q^{85} - 48 q^{86} + 168 q^{88} - 10 q^{89} + 4 q^{91} + 40 q^{92} + 36 q^{97} - 38 q^{98}+O(q^{100}) $ 36 * q - 6 * q^7 - 4 * q^11 + 36 * q^14 + 12 * q^16 - 4 * q^17 - 18 * q^19 - 44 * q^20 - 8 * q^22 + 12 * q^23 - 48 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^29 - 6 * q^31 - 76 * q^32 - 48 * q^34 - 8 * q^35 - 8 * q^37 - 16 * q^38 + 60 * q^40 + 32 * q^41 - 4 * q^44 + 28 * q^46 - 14 * q^47 + 6 * q^49 + 68 * q^50 - 62 * q^52 + 8 * q^53 + 8 * q^56 + 36 * q^58 - 26 * q^59 + 36 * q^61 - 48 * q^62 + 8 * q^65 - 40 * q^67 - 36 * q^68 - 64 * q^70 + 36 * q^71 - 8 * q^73 - 40 * q^74 - 60 * q^76 - 60 * q^77 - 26 * q^80 - 24 * q^83 + 44 * q^85 - 48 * q^86 + 168 * q^88 - 10 * q^89 + 4 * q^91 + 40 * q^92 + 36 * q^97 - 38 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.52924	+	0.677708i	−1.78844	+	0.479212i	−0.992080	−	0.125605i	$-0.959913\pi$
$2$	−2.52924	+	0.677708i	−1.78844	+	0.479212i	−0.796364	+	0.604817i	$0.793246\pi$
$3$		0			0
$3$		0			0
$4$	4.20573	−	2.42818i	2.10286	−	1.21409i
$5$	−1.05058	−	3.92082i	−0.469834	−	1.75344i	−0.640343	−	0.768089i	$-0.721208\pi$
$5$	−1.05058	−	3.92082i	−0.469834	−	1.75344i	0.170509	−	0.985356i	$-0.445459\pi$
$6$		0			0
$7$	−2.39518	−	1.12389i	−0.905293	−	0.424789i
$7$	−2.39518	−	1.12389i	−0.905293	−	0.424789i
$8$	−5.28864	+	5.28864i	−1.86982	+	1.86982i
$9$		0			0
$10$	5.31435	+	9.20472i	1.68054	+	2.91079i
$11$	−0.560897	−	0.150292i	−0.169117	−	0.0453148i	0.173267	−	0.984875i	$-0.444568\pi$
$11$	−0.560897	−	0.150292i	−0.169117	−	0.0453148i	−0.342384	+	0.939560i	$0.611234\pi$
$12$		0			0
$13$	−2.59678	−	2.50134i	−0.720219	−	0.693747i
$13$	−2.59678	−	2.50134i	−0.720219	−	0.693747i
$14$	6.81965	+	1.21935i	1.82263	+	0.325884i
$15$		0			0
$16$	4.93574	−	8.54896i	1.23394	−	2.13724i
$17$	−0.229516	−	0.397534i	−0.0556659	−	0.0964162i	0.836850	−	0.547433i	$-0.184395\pi$
$17$	−0.229516	−	0.397534i	−0.0556659	−	0.0964162i	−0.892516	+	0.451017i	$0.851062\pi$
$18$		0			0
$19$	−1.99360	−	7.44023i	−0.457364	−	1.70691i	−0.681044	−	0.732243i	$-0.738474\pi$
$19$	−1.99360	−	7.44023i	−0.457364	−	1.70691i	0.223680	−	0.974663i	$-0.428193\pi$
$20$	−13.9389	−	13.9389i	−3.11684	−	3.11684i
$21$		0			0
$22$	1.52050			0.324172
$23$	0.0405237	+	0.0233964i	0.00844978	+	0.00487848i	0.504219	−	0.863576i	$-0.331780\pi$
$23$	0.0405237	+	0.0233964i	0.00844978	+	0.00487848i	−0.495769	+	0.868454i	$0.665114\pi$
$24$		0			0
$25$	−9.93900	+	5.73828i	−1.98780	+	1.14766i
$26$	8.26308	+	4.56664i	1.62052	+	0.895591i
$27$		0			0
$28$	−12.8025	+	1.08917i	−2.41944	+	0.205833i
$29$	1.08136			0.200803			0.100401	−	0.994947i	$-0.467987\pi$
$29$	1.08136			0.200803			0.100401	+	0.994947i	$0.467987\pi$
$30$		0			0
$31$	4.88993	+	1.31025i	0.878258	+	0.235328i	0.669655	−	0.742672i	$-0.266442\pi$
$31$	4.88993	+	1.31025i	0.878258	+	0.235328i	0.208602	+	0.978001i	$0.433109\pi$
$32$	−2.81843	+	10.5185i	−0.498234	+	1.85943i
$33$		0			0
$34$	0.849915	+	0.849915i	0.145759	+	0.145759i
$35$	−1.89022	+	10.5718i	−0.319506	+	1.78696i
$36$		0			0
$37$	1.13412	+	4.23261i	0.186449	+	0.695836i	0.994316	+	0.106471i	$0.0339553\pi$
$37$	1.13412	+	4.23261i	0.186449	+	0.695836i	−0.807867	+	0.589365i	$0.799378\pi$
$38$	10.0846	+	17.4671i	1.63594	+	2.83353i
$39$		0			0
$40$	26.2920	+	15.1797i	4.15712	+	2.40012i
$41$	4.50540	−	4.50540i	0.703626	−	0.703626i	−0.261561	−	0.965187i	$-0.584237\pi$
$41$	4.50540	−	4.50540i	0.703626	−	0.703626i	0.965187	+	0.261561i	$0.0842373\pi$
$42$		0			0
$43$			0.884530i			0.134890i	0.997723	+	0.0674448i	$0.0214846\pi$
$43$			0.884530i			0.134890i	−0.997723	+	0.0674448i	$0.978515\pi$
$44$	−2.72392	+	0.729872i	−0.410646	+	0.110032i
$45$		0			0
$46$	−0.118350	−	0.0317118i	−0.0174498	−	0.00467566i
$47$	−3.18059	+	0.852236i	−0.463936	+	0.124311i	−0.483213	−	0.875503i	$-0.660530\pi$
$47$	−3.18059	+	0.852236i	−0.463936	+	0.124311i	0.0192766	+	0.999814i	$0.493864\pi$
$48$		0			0
$49$	4.47376	+	5.38381i	0.639109	+	0.769116i
$50$	21.2493	−	21.2493i	3.00510	−	3.00510i
$51$		0			0
$52$	−16.9951	−	4.21450i	−2.35679	−	0.584447i
$53$	−0.253079	−	0.438345i	−0.0347630	−	0.0602113i	0.848120	−	0.529803i	$-0.177734\pi$
$53$	−0.253079	−	0.438345i	−0.0347630	−	0.0602113i	−0.882883	+	0.469592i	$0.844401\pi$
$54$		0			0
$55$			2.35707i			0.317828i
$56$	18.6111	−	6.72342i	2.48701	−	0.898454i
$57$		0			0
$58$	−2.73501	+	0.732844i	−0.359124	+	0.0962271i
$59$	−0.577611	+	2.15568i	−0.0751986	+	0.280645i	−0.993278	−	0.115751i	$-0.963073\pi$
$59$	−0.577611	+	2.15568i	−0.0751986	+	0.280645i	0.918080	+	0.396396i	$0.129739\pi$
$60$		0			0
$61$	0.165995	+	0.0958371i	0.0212535	+	0.0122707i	0.510589	−	0.859825i	$-0.329427\pi$
$61$	0.165995	+	0.0958371i	0.0212535	+	0.0122707i	−0.489336	+	0.872096i	$0.662761\pi$
$62$	−13.2558			−1.68349
$63$		0			0
$64$		−	8.77105i		−	1.09638i
$65$	−7.07918	+	12.8094i	−0.878064	+	1.58881i
$66$		0			0
$67$	−2.31148	+	8.62657i	−0.282392	+	1.05390i	0.668331	+	0.743864i	$0.267009\pi$
$67$	−2.31148	+	8.62657i	−0.282392	+	1.05390i	−0.950724	+	0.310039i	$0.899658\pi$
$68$	−1.93057	−	1.11461i	−0.234116	−	0.135167i
$69$		0			0
$70$	−2.38377	−	28.0197i	−0.284914	−	3.34899i
$71$	4.23807	+	4.23807i	0.502966	+	0.502966i	0.912358	−	0.409392i	$-0.134259\pi$
$71$	4.23807	+	4.23807i	0.502966	+	0.502966i	−0.409392	+	0.912358i	$0.634259\pi$
$72$		0			0
$73$	−1.87486	+	6.99707i	−0.219436	+	0.818945i	0.765122	+	0.643885i	$0.222678\pi$
$73$	−1.87486	+	6.99707i	−0.219436	+	0.818945i	−0.984558	+	0.175060i	$0.943988\pi$
$74$	−5.73695	−	9.93669i	−0.666907	−	1.15512i
$75$		0			0
$76$	−26.4507	−	26.4507i	−3.03411	−	3.03411i
$77$	1.17454	+	0.990361i	0.133851	+	0.112862i
$78$		0			0
$79$	2.92382	−	5.06421i	0.328956	−	0.569768i	−0.653349	−	0.757057i	$-0.726637\pi$
$79$	2.92382	−	5.06421i	0.328956	−	0.569768i	0.982305	+	0.187289i	$0.0599699\pi$
$80$	−38.7043	−	10.3708i	−4.32728	−	1.15949i
$81$		0			0
$82$	−8.34191	+	14.4486i	−0.921210	+	1.59558i
$83$	9.67812	−	9.67812i	1.06231	−	1.06231i	0.0643872	−	0.997925i	$-0.479491\pi$
$83$	9.67812	−	9.67812i	1.06231	−	1.06231i	0.997925	−	0.0643872i	$-0.0205093\pi$
$84$		0			0
$85$	−1.31754	+	1.31754i	−0.142907	+	0.142907i
$86$	−0.599453	−	2.23719i	−0.0646407	−	0.241242i
$87$		0			0
$88$	3.76123	−	2.17154i	0.400948	−	0.231487i
$89$	−18.2195	+	4.88190i	−1.93126	+	0.517481i	−0.959247	+	0.282568i	$0.908814\pi$
$89$	−18.2195	+	4.88190i	−1.93126	+	0.517481i	−0.972016	+	0.234913i	$0.924520\pi$
$90$		0			0
$91$	3.40854	+	8.90965i	0.357313	+	0.933985i
$92$	0.227242			0.0236916
$93$		0			0
$94$	7.46691	−	4.31102i	0.770153	−	0.444648i
$95$	−27.0774	+	15.6331i	−2.77808	+	1.60392i
$96$		0			0
$97$	−5.63729	+	5.63729i	−0.572380	+	0.572380i	−0.932793	−	0.360413i	$-0.882636\pi$
$97$	−5.63729	+	5.63729i	−0.572380	+	0.572380i	0.360413	+	0.932793i	$0.382636\pi$
$98$	−14.9639	−	10.5851i	−1.51158	−	1.06925i
$99$		0			0
$100$	−27.8671	+	48.2673i	−2.78671	+	4.82673i
$101$	3.16376	+	5.47980i	0.314806	+	0.545261i	0.979396	−	0.201948i	$-0.0647271\pi$
$101$	3.16376	+	5.47980i	0.314806	+	0.545261i	−0.664590	+	0.747208i	$0.731394\pi$
$102$		0			0
$103$	8.07204	−	13.9812i	0.795361	−	1.37761i	−0.127248	−	0.991871i	$-0.540614\pi$
$103$	8.07204	−	13.9812i	0.795361	−	1.37761i	0.922609	−	0.385736i	$-0.126052\pi$
$104$	26.9622	−	0.504767i	2.64386	−	0.0494965i
$105$		0			0
$106$	0.937167	+	0.937167i	0.0910257	+	0.0910257i
$107$	−0.476396	+	0.825143i	−0.0460550	+	0.0797695i	−0.888134	−	0.459585i	$-0.847998\pi$
$107$	−0.476396	+	0.825143i	−0.0460550	+	0.0797695i	0.842079	+	0.539354i	$0.181332\pi$
$108$		0			0
$109$	1.83505	−	6.84849i	0.175766	−	0.655967i	−0.820654	−	0.571425i	$-0.806391\pi$
$109$	1.83505	−	6.84849i	0.175766	−	0.655967i	0.996420	−	0.0845416i	$-0.0269426\pi$
$110$	−1.59741	−	5.96161i	−0.152307	−	0.568417i
$111$		0			0
$112$	−21.4300	+	14.9291i	−2.02495	+	1.41066i
$113$	−18.2692			−1.71862			−0.859309	−	0.511457i	$-0.829106\pi$
$113$	−18.2692			−1.71862			−0.859309	+	0.511457i	$0.829106\pi$
$114$		0			0
$115$	0.0491596	−	0.183466i	0.00458415	−	0.0171083i
$116$	4.54789	−	2.62572i	0.422261	−	0.243792i
$117$		0			0
$118$		−	5.84368i		−	0.537954i
$119$	0.102950	+	1.21012i	0.00943743	+	0.110931i
$120$		0			0
$121$	−9.23426	−	5.33140i	−0.839478	−	0.484673i
$122$	−0.484791	−	0.129899i	−0.0438909	−	0.0117605i
$123$		0			0
$124$	23.7472	−	6.36306i	2.13257	−	0.571419i
$125$	18.5893	+	18.5893i	1.66268	+	1.66268i
$126$		0			0
$127$		−	5.46783i		−	0.485192i	−0.970127	−	0.242596i	$-0.922001\pi$
$127$		−	5.46783i		−	0.485192i	0.970127	−	0.242596i	$-0.0779989\pi$
$128$	0.307346	+	1.14703i	0.0271658	+	0.101384i
$129$		0			0
$130$	9.22393	−	37.1957i	0.808992	−	3.26228i
$131$	5.30476	+	3.06270i	0.463479	+	0.267590i	0.713506	−	0.700649i	$-0.247106\pi$
$131$	5.30476	+	3.06270i	0.463479	+	0.267590i	−0.250027	+	0.968239i	$0.580440\pi$
$132$		0			0
$133$	−3.58693	+	20.0613i	−0.311026	+	1.73953i
$134$		−	23.3852i		−	2.02017i
$135$		0			0
$136$	3.31625	+	0.888585i	0.284366	+	0.0761956i
$137$	3.77164	+	1.01061i	0.322233	+	0.0863420i	0.416310	−	0.909223i	$-0.363323\pi$
$137$	3.77164	+	1.01061i	0.322233	+	0.0863420i	−0.0940768	+	0.995565i	$0.529990\pi$
$138$		0			0
$139$		−	8.41346i		−	0.713620i	−0.934177	−	0.356810i	$-0.883864\pi$
$139$		−	8.41346i		−	0.713620i	0.934177	−	0.356810i	$-0.116136\pi$
$140$	17.7205	+	49.0519i	1.49765	+	4.14564i
$141$		0			0
$142$	−13.5913	−	7.84692i	−1.14055	−	0.658499i
$143$	1.08060	+	1.79327i	0.0903642	+	0.149961i
$144$		0			0
$145$	−1.13605	−	4.23980i	−0.0943439	−	0.352096i
$146$		−	18.9679i		−	1.56979i
$147$		0			0
$148$	15.0473	+	15.0473i	1.23688	+	1.23688i
$149$	−13.9051	+	3.72585i	−1.13915	+	0.305234i	−0.778608	−	0.627511i	$-0.784074\pi$
$149$	−13.9051	+	3.72585i	−1.13915	+	0.305234i	−0.360539	+	0.932744i	$0.617407\pi$
$150$		0			0
$151$	7.19436	+	1.92772i	0.585469	+	0.156876i	0.539381	−	0.842062i	$-0.318658\pi$
$151$	7.19436	+	1.92772i	0.585469	+	0.156876i	0.0460873	+	0.998937i	$0.485325\pi$
$152$	49.8921	+	28.8052i	4.04679	+	2.33641i
$153$		0			0
$154$	−3.64187	−	1.70887i	−0.293470	−	0.137704i
$155$		−	20.5491i		−	1.65054i
$156$		0			0
$157$	−18.1293	+	10.4670i	−1.44688	+	0.835355i	−0.998294	−	0.0583857i	$-0.981405\pi$
$157$	−18.1293	+	10.4670i	−1.44688	+	0.835355i	−0.448584	+	0.893741i	$0.648071\pi$
$158$	−3.96300	+	14.7901i	−0.315279	+	1.17664i
$159$		0			0
$160$	44.2023			3.49450
$161$	−0.0707667	−	0.101583i	−0.00557720	−	0.00800582i
$162$		0			0
$163$	2.92277	+	10.9079i	0.228929	+	0.854375i	0.980792	+	0.195055i	$0.0624887\pi$
$163$	2.92277	+	10.9079i	0.228929	+	0.854375i	−0.751863	+	0.659319i	$0.770845\pi$
$164$	8.00858	−	29.8884i	0.625365	−	2.33389i
$165$		0			0
$166$	−17.9194	+	31.0373i	−1.39081	+	2.40896i
$167$	−9.38835	−	9.38835i	−0.726492	−	0.726492i	0.243427	−	0.969919i	$-0.421728\pi$
$167$	−9.38835	−	9.38835i	−0.726492	−	0.726492i	−0.969919	+	0.243427i	$0.921728\pi$
$168$		0			0
$169$	0.486584	+	12.9909i	0.0374295	+	0.999299i
$170$	2.43946	−	4.22527i	0.187098	−	0.324063i
$171$		0			0
$172$	2.14780	+	3.72009i	0.163768	+	0.283654i
$173$	3.19038	−	5.52590i	0.242560	−	0.420127i	−0.718883	−	0.695131i	$-0.755346\pi$
$173$	3.19038	−	5.52590i	0.242560	−	0.420127i	0.961443	+	0.275005i	$0.0886795\pi$
$174$		0			0
$175$	30.2548	−	2.57392i	2.28705	−	0.194570i
$176$	−4.05329	+	4.05329i	−0.305528	+	0.305528i
$177$		0			0
$178$	42.7730	−	24.6950i	3.20598	−	1.85097i
$179$	16.2954	−	9.40817i	1.21798	−	0.703200i	0.253493	−	0.967337i	$-0.418421\pi$
$179$	16.2954	−	9.40817i	1.21798	−	0.703200i	0.964485	+	0.264137i	$0.0850872\pi$
$180$		0			0
$181$	15.0820			1.12104			0.560519	−	0.828141i	$-0.310602\pi$
$181$	15.0820			1.12104			0.560519	+	0.828141i	$0.310602\pi$
$182$	−14.6592	−	20.2247i	−1.08661	−	1.49915i
$183$		0			0
$184$	−0.338050	+	0.0905803i	−0.0249214	+	0.00667767i
$185$	15.4038	−	8.89339i	1.13251	−	0.653855i
$186$		0			0
$187$	0.0689890	+	0.257470i	0.00504497	+	0.0188281i
$188$	−11.3073	+	11.3073i	−0.824670	+	0.824670i
$189$		0			0
$190$	57.8905	−	57.8905i	4.19982	−	4.19982i
$191$	−0.485364	+	0.840675i	−0.0351197	+	0.0608291i	−0.883051	−	0.469277i	$-0.844515\pi$
$191$	−0.485364	+	0.840675i	−0.0351197	+	0.0608291i	0.847931	+	0.530106i	$0.177848\pi$
$192$		0			0
$193$	−11.7370	−	3.14492i	−0.844847	−	0.226376i	−0.189667	−	0.981849i	$-0.560741\pi$
$193$	−11.7370	−	3.14492i	−0.844847	−	0.226376i	−0.655181	+	0.755472i	$0.727407\pi$
$194$	10.4376	−	18.0785i	0.749378	−	1.29796i
$195$		0			0
$196$	31.8883	+	11.7798i	2.27773	+	0.841411i
$197$	5.15273	+	5.15273i	0.367117	+	0.367117i	0.866425	−	0.499308i	$-0.166412\pi$
$197$	5.15273	+	5.15273i	0.367117	+	0.367117i	−0.499308	+	0.866425i	$0.666412\pi$
$198$		0			0
$199$	0.108027	+	0.187109i	0.00765787	+	0.0132638i	0.869829	−	0.493353i	$-0.164229\pi$
$199$	0.108027	+	0.187109i	0.00765787	+	0.0132638i	−0.862171	+	0.506617i	$0.830896\pi$
$200$	22.2161	−	82.9115i	1.57091	−	5.86273i
$201$		0			0
$202$	−11.7156	−	11.7156i	−0.824309	−	0.824309i
$203$	−2.59004	−	1.21532i	−0.181785	−	0.0852987i
$204$		0			0
$205$	−22.3982	−	12.9316i	−1.56436	−	0.903182i
$206$	−10.9410	+	40.8323i	−0.762294	+	2.84492i
$207$		0			0
$208$	−34.2009	+	9.85382i	−2.37141	+	0.683240i
$209$			4.47283i			0.309392i
$210$		0			0
$211$	−0.835450			−0.0575147			−0.0287574	−	0.999586i	$-0.509155\pi$
$211$	−0.835450			−0.0575147			−0.0287574	+	0.999586i	$0.509155\pi$
$212$	−2.12876	−	1.22904i	−0.146204	−	0.0844108i
$213$		0			0
$214$	0.645716	−	2.40984i	0.0441402	−	0.164734i
$215$	3.46808	−	0.929270i	0.236521	−	0.0633757i
$216$		0			0
$217$	−10.2397	−	8.63401i	−0.695115	−	0.586115i
$218$			18.5651i			1.25739i
$219$		0			0
$220$	5.72339	+	9.91321i	0.385871	+	0.668348i
$221$	−0.398364	+	1.60641i	−0.0267968	+	0.108059i
$222$		0			0
$223$	−0.345071	+	0.345071i	−0.0231077	+	0.0231077i	−0.718566	−	0.695459i	$-0.755201\pi$
$223$	−0.345071	+	0.345071i	−0.0231077	+	0.0231077i	0.695459	+	0.718566i	$0.255201\pi$
$224$	18.5723	−	22.0262i	1.24091	−	1.47169i
$225$		0			0
$226$	46.2071	−	12.3812i	3.07365	−	0.823583i
$227$	1.07196	+	0.287231i	0.0711485	+	0.0190642i	0.294218	−	0.955738i	$-0.404941\pi$
$227$	1.07196	+	0.287231i	0.0711485	+	0.0190642i	−0.223069	+	0.974803i	$0.571608\pi$
$228$		0			0
$229$	10.3710	−	2.77889i	0.685332	−	0.183634i	0.100681	−	0.994919i	$-0.467898\pi$
$229$	10.3710	−	2.77889i	0.685332	−	0.183634i	0.584651	+	0.811285i	$0.301231\pi$
$230$			0.497346i			0.0327940i
$231$		0			0
$232$	−5.71890	+	5.71890i	−0.375464	+	0.375464i
$233$	9.10406	+	5.25623i	0.596427	+	0.344347i	0.767635	−	0.640888i	$-0.221434\pi$
$233$	9.10406	+	5.25623i	0.596427	+	0.344347i	−0.171208	+	0.985235i	$0.554767\pi$
$234$		0			0
$235$	6.68293	+	11.5752i	0.435946	+	0.755081i
$236$	2.80509	+	10.4687i	0.182596	+	0.681456i
$237$		0			0
$238$	−1.08049	−	2.99091i	−0.0700379	−	0.193872i
$239$	−11.4260	−	11.4260i	−0.739090	−	0.739090i	0.233312	−	0.972402i	$-0.425044\pi$
$239$	−11.4260	−	11.4260i	−0.739090	−	0.739090i	−0.972402	+	0.233312i	$0.925044\pi$
$240$		0			0
$241$	−2.52547	+	9.42517i	−0.162680	+	0.607128i	0.835645	+	0.549270i	$0.185094\pi$
$241$	−2.52547	+	9.42517i	−0.162680	+	0.607128i	−0.998325	+	0.0578588i	$0.981573\pi$
$242$	26.9688	+	7.22627i	1.73362	+	0.464523i
$243$		0			0
$244$	0.930838			0.0595908
$245$	16.4089	−	23.1970i	1.04833	−	1.48200i
$246$		0			0
$247$	−13.4336	+	24.3074i	−0.854759	+	1.54664i
$248$	−32.7905	+	18.9316i	−2.08220	+	1.20216i
$249$		0			0
$250$	−59.6150	−	34.4187i	−3.77038	−	2.17683i
$251$	−15.5951			−0.984355			−0.492177	−	0.870495i	$-0.663799\pi$
$251$	−15.5951			−0.984355			−0.492177	+	0.870495i	$0.663799\pi$
$252$		0			0
$253$	−0.0192134	−	0.0192134i	−0.00120793	−	0.00120793i
$254$	3.70560	+	13.8295i	0.232510	+	0.867738i
$255$		0			0
$256$	7.21635	+	12.4991i	0.451022	+	0.781192i
$257$	−7.55731	+	13.0896i	−0.471412	+	0.816509i	−0.999465	−	0.0327020i	$-0.989589\pi$
$257$	−7.55731	+	13.0896i	−0.471412	+	0.816509i	0.528053	+	0.849211i	$0.322922\pi$
$258$		0			0
$259$	2.04054	−	11.4125i	0.126793	−	0.709137i
$260$	1.33038	+	71.0623i	0.0825067	+	4.40710i
$261$		0			0
$262$	−15.4926	−	4.15124i	−0.957138	−	0.256464i
$263$	13.1981	+	22.8598i	0.813832	+	1.40960i	0.910164	+	0.414249i	$0.135956\pi$
$263$	13.1981	+	22.8598i	0.813832	+	1.40960i	−0.0963317	+	0.995349i	$0.530711\pi$
$264$		0			0
$265$	−1.45279	+	1.45279i	−0.0892443	+	0.0892443i
$266$	−4.52348	−	53.1707i	−0.277352	−	3.26010i
$267$		0			0
$268$	11.2254	+	41.8937i	0.685699	+	2.55906i
$269$	11.5339	−	6.65909i	0.703234	−	0.406012i	−0.105317	−	0.994439i	$-0.533586\pi$
$269$	11.5339	−	6.65909i	0.703234	−	0.406012i	0.808551	+	0.588427i	$0.200252\pi$
$270$		0			0
$271$	−19.4735	+	5.21791i	−1.18293	+	0.316965i	−0.796089	−	0.605180i	$-0.793101\pi$
$271$	−19.4735	+	5.21791i	−1.18293	+	0.316965i	−0.386843	+	0.922146i	$0.626434\pi$
$272$	−4.53134			−0.274753
$273$		0			0
$274$	−10.2243			−0.617671
$275$	6.43718	−	1.72484i	0.388176	−	0.104012i
$276$		0			0
$277$	−3.53497	+	2.04092i	−0.212396	+	0.122627i	−0.602424	−	0.798176i	$-0.705798\pi$
$277$	−3.53497	+	2.04092i	−0.212396	+	0.122627i	0.390029	+	0.920803i	$0.372465\pi$
$278$	5.70187	+	21.2797i	0.341976	+	1.27627i
$279$		0			0
$280$	−45.9138	−	65.9072i	−2.74387	−	3.93871i
$281$	−0.558878	+	0.558878i	−0.0333399	+	0.0333399i	−0.723580	−	0.690240i	$-0.757505\pi$
$281$	−0.558878	+	0.558878i	−0.0333399	+	0.0333399i	0.690240	+	0.723580i	$0.257505\pi$
$282$		0			0
$283$	−11.3665	−	19.6873i	−0.675667	−	1.17029i	−0.976274	−	0.216541i	$-0.930523\pi$
$283$	−11.3665	−	19.6873i	−0.675667	−	1.17029i	0.300607	−	0.953748i	$-0.402811\pi$
$284$	28.1149	+	7.53337i	1.66831	+	0.447024i
$285$		0			0
$286$	−3.94841	−	3.80329i	−0.233474	−	0.224893i
$287$	−15.8548	+	5.72769i	−0.935880	+	0.338095i
$288$		0			0
$289$	8.39464	−	14.5400i	0.493803	−	0.855291i
$290$	5.74670	+	9.95357i	0.337458	+	0.584494i
$291$		0			0
$292$	9.10498	+	33.9802i	0.532829	+	1.98854i
$293$	−7.07914	−	7.07914i	−0.413568	−	0.413568i	0.469412	−	0.882979i	$-0.344466\pi$
$293$	−7.07914	−	7.07914i	−0.413568	−	0.413568i	−0.882979	+	0.469412i	$0.844466\pi$
$294$		0			0
$295$	9.05885			0.527426
$296$	−28.3827	−	16.3868i	−1.64971	−	0.952461i
$297$		0			0
$298$	32.6442	−	18.8472i	1.89103	−	1.09179i
$299$	−0.0467090	−	0.162119i	−0.00270125	−	0.00937558i
$300$		0			0
$301$	0.994110	−	2.11861i	0.0572995	−	0.122114i
$302$	−19.5027			−1.12226
$303$		0			0
$304$	−73.4461	−	19.6798i	−4.21242	−	1.12872i
$305$	0.201369	−	0.751521i	0.0115304	−	0.0430319i
$306$		0			0
$307$	−12.9630	−	12.9630i	−0.739837	−	0.739837i	0.232709	−	0.972546i	$-0.425241\pi$
$307$	−12.9630	−	12.9630i	−0.739837	−	0.739837i	−0.972546	+	0.232709i	$0.925241\pi$
$308$	7.34456	+	1.31320i	0.418495	+	0.0748264i
$309$		0			0
$310$	13.9263	+	51.9736i	0.790960	+	2.95190i
$311$	3.35745	+	5.81527i	0.190383	+	0.329753i	0.945377	−	0.325978i	$-0.105694\pi$
$311$	3.35745	+	5.81527i	0.190383	+	0.329753i	−0.754994	+	0.655732i	$0.772360\pi$
$312$		0			0
$313$	0.880023	+	0.508082i	0.0497418	+	0.0287185i	0.524665	−	0.851309i	$-0.324191\pi$
$313$	0.880023	+	0.508082i	0.0497418	+	0.0287185i	−0.474923	+	0.880027i	$0.657524\pi$
$314$	38.7599	−	38.7599i	2.18735	−	2.18735i
$315$		0			0
$316$		−	28.3983i		−	1.59753i
$317$	22.8613	−	6.12568i	1.28402	−	0.344052i	0.448634	−	0.893715i	$-0.351911\pi$
$317$	22.8613	−	6.12568i	1.28402	−	0.344052i	0.835387	+	0.549663i	$0.185244\pi$
$318$		0			0
$319$	−0.606529	−	0.162519i	−0.0339591	−	0.00909932i
$320$	−34.3897	+	9.21470i	−1.92244	+	0.515117i
$321$		0			0
$322$	0.247829	+	0.208968i	0.0138110	+	0.0116453i
$323$	−2.50018	+	2.50018i	−0.139114	+	0.139114i
$324$		0			0
$325$	40.1628	+	9.95974i	2.22783	+	0.552467i
$326$	−14.7848	−	25.6080i	−0.818854	−	1.41830i
$327$		0			0
$328$			47.6549i			2.63130i
$329$	8.57589	+	1.53336i	0.472804	+	0.0845368i
$330$		0			0
$331$	−15.6044	+	4.18120i	−0.857698	+	0.229819i	−0.660761	−	0.750597i	$-0.729766\pi$
$331$	−15.6044	+	4.18120i	−0.857698	+	0.229819i	−0.196937	+	0.980416i	$0.563099\pi$
$332$	17.2033	−	64.2038i	0.944156	−	3.52364i
$333$		0			0
$334$	30.1080	+	17.3828i	1.64743	+	0.951147i
$335$	36.2516			1.98064
$336$		0			0
$337$			9.93413i			0.541147i	0.962699	+	0.270573i	$0.0872132\pi$
$337$			9.93413i			0.541147i	−0.962699	+	0.270573i	$0.912787\pi$
$338$	−10.0347	−	32.5274i	−0.545817	−	1.76925i
$339$		0			0
$340$	−2.34198	+	8.74040i	−0.127012	+	0.474015i
$341$	−2.54583	−	1.46984i	−0.137864	−	0.0795961i
$342$		0			0
$343$	−4.66468	−	17.9232i	−0.251869	−	0.967761i
$344$	−4.67796	−	4.67796i	−0.252219	−	0.252219i
$345$		0			0
$346$	−4.32430	+	16.1385i	−0.232476	+	0.867611i
$347$	−5.33134	−	9.23415i	−0.286201	−	0.495715i	0.686698	−	0.726942i	$-0.259059\pi$
$347$	−5.33134	−	9.23415i	−0.286201	−	0.495715i	−0.972900	+	0.231227i	$0.925726\pi$
$348$		0			0
$349$	14.7539	+	14.7539i	0.789757	+	0.789757i	0.981454	−	0.191697i	$-0.0613992\pi$
$349$	14.7539	+	14.7539i	0.789757	+	0.789757i	−0.191697	+	0.981454i	$0.561399\pi$
$350$	−74.7775	+	27.0140i	−3.99702	+	1.44396i
$351$		0			0
$352$	3.16171	−	5.47623i	0.168519	−	0.291884i
$353$	−28.2057	−	7.55771i	−1.50124	−	0.402256i	−0.587725	−	0.809061i	$-0.699976\pi$
$353$	−28.2057	−	7.55771i	−1.50124	−	0.402256i	−0.913515	+	0.406805i	$0.866643\pi$
$354$		0			0
$355$	12.1643	−	21.0691i	0.645613	−	1.11823i
$356$	−64.7722	+	64.7722i	−3.43292	+	3.43292i
$357$		0			0
$358$	−34.8391	+	34.8391i	−1.84130	+	1.84130i
$359$	4.92341	+	18.3744i	0.259847	+	0.969764i	0.965329	+	0.261036i	$0.0840640\pi$
$359$	4.92341	+	18.3744i	0.259847	+	0.969764i	−0.705482	+	0.708728i	$0.749269\pi$
$360$		0			0
$361$	−34.9280	+	20.1657i	−1.83832	+	1.06135i
$362$	−38.1461	+	10.2212i	−2.00492	+	0.537215i
$363$		0			0
$364$	35.9696	+	29.1950i	1.88532	+	1.53023i
$365$	29.4039			1.53907
$366$		0			0
$367$	21.7369	−	12.5498i	1.13466	−	0.655094i	0.189555	−	0.981870i	$-0.439296\pi$
$367$	21.7369	−	12.5498i	1.13466	−	0.655094i	0.945102	+	0.326776i	$0.105962\pi$
$368$	0.400029	−	0.230957i	0.0208530	−	0.0120395i
$369$		0			0
$370$	−32.9328	+	32.9328i	−1.71210	+	1.71210i
$371$	0.113519	+	1.33435i	0.00589361	+	0.0692758i
$372$		0			0
$373$	16.6168	−	28.7811i	0.860383	−	1.49023i	−0.0111767	−	0.999938i	$-0.503558\pi$
$373$	16.6168	−	28.7811i	0.860383	−	1.49023i	0.871560	−	0.490289i	$-0.163109\pi$
$374$	−0.348980	−	0.604451i	−0.0180453	−	0.0312554i
$375$		0			0
$376$	12.3138	−	21.3282i	0.635037	−	1.09992i
$377$	−2.80805	−	2.70484i	−0.144622	−	0.139306i
$378$		0			0
$379$	−21.2082	−	21.2082i	−1.08939	−	1.08939i	−0.995591	−	0.0938026i	$-0.970098\pi$
$379$	−21.2082	−	21.2082i	−1.08939	−	1.08939i	−0.0938026	−	0.995591i	$-0.529902\pi$
$380$	−75.9200	+	131.497i	−3.89462	+	6.74567i
$381$		0			0
$382$	0.657870	−	2.45521i	0.0336596	−	0.125619i
$383$	−5.16636	−	19.2811i	−0.263989	−	0.985220i	−0.962866	−	0.269978i	$-0.912983\pi$
$383$	−5.16636	−	19.2811i	−0.263989	−	0.985220i	0.698878	−	0.715241i	$-0.253683\pi$
$384$		0			0
$385$	2.64908	−	5.64561i	0.135010	−	0.287727i
$386$	31.8170			1.61944
$387$		0			0
$388$	−10.0206	+	37.3972i	−0.508717	+	1.89856i
$389$	−16.9603	+	9.79204i	−0.859922	+	0.496476i	−0.863986	−	0.503516i	$-0.832040\pi$
$389$	−16.9603	+	9.79204i	−0.859922	+	0.496476i	0.00406416	+	0.999992i	$0.498706\pi$
$390$		0			0
$391$		−	0.0214794i		−	0.00108626i
$392$	−52.1332	−	4.81292i	−2.63312	−	0.243089i
$393$		0			0
$394$	−16.5246	−	9.54046i	−0.832495	−	0.480641i
$395$	−22.9276	−	6.14343i	−1.15361	−	0.309109i
$396$		0			0
$397$	23.4483	−	6.28296i	1.17684	−	0.315333i	0.383166	−	0.923679i	$-0.374834\pi$
$397$	23.4483	−	6.28296i	1.17684	−	0.315333i	0.793671	+	0.608347i	$0.208167\pi$
$398$	−0.400033	−	0.400033i	−0.0200518	−	0.0200518i
$399$		0			0
$400$			113.291i			5.66454i
$401$	−6.63267	−	24.7535i	−0.331220	−	1.23613i	−0.907910	−	0.419166i	$-0.862323\pi$
$401$	−6.63267	−	24.7535i	−0.331220	−	1.23613i	0.576690	−	0.816963i	$-0.304344\pi$
$402$		0			0
$403$	−9.42071	−	15.6338i	−0.469279	−	0.778777i
$404$	26.6119	+	15.3644i	1.32399	+	0.764406i
$405$		0			0
$406$	7.37447	+	1.31855i	0.365989	+	0.0654383i
$407$		−	2.54451i		−	0.126127i
$408$		0			0
$409$	−9.84051	−	2.63676i	−0.486582	−	0.130379i	0.00718375	−	0.999974i	$-0.497713\pi$
$409$	−9.84051	−	2.63676i	−0.486582	−	0.130379i	−0.493766	+	0.869595i	$0.664380\pi$
$410$	65.4143	+	17.5277i	3.23058	+	0.865632i
$411$		0			0
$412$		−	78.4014i		−	3.86256i
$413$	3.80621	−	4.51406i	0.187292	−	0.222122i
$414$		0			0
$415$	−48.1139	−	27.7785i	−2.36182	−	1.36360i
$416$	33.6293	−	20.2645i	1.64881	−	0.993550i
$417$		0			0
$418$	−3.03127	−	11.3129i	−0.148264	−	0.553330i
$419$			20.6163i			1.00717i	0.863945	+	0.503586i	$0.167986\pi$
$419$			20.6163i			1.00717i	−0.863945	+	0.503586i	$0.832014\pi$
$420$		0			0
$421$	−10.3833	−	10.3833i	−0.506050	−	0.506050i	0.407262	−	0.913311i	$-0.366484\pi$
$421$	−10.3833	−	10.3833i	−0.506050	−	0.506050i	−0.913311	+	0.407262i	$0.866484\pi$
$422$	2.11306	−	0.566191i	0.102862	−	0.0275618i
$423$		0			0
$424$	3.65669	+	0.979807i	0.177585	+	0.0475836i
$425$	4.56233	+	2.63406i	0.221305	+	0.127771i
$426$		0			0
$427$	−0.289877	−	0.416106i	−0.0140281	−	0.0201368i
$428$			4.62710i			0.223659i
$429$		0			0
$430$	−8.14185	+	4.70070i	−0.392635	+	0.226688i
$431$	−1.26575	+	4.72385i	−0.0609691	+	0.227540i	−0.989687	−	0.143248i	$-0.954245\pi$
$431$	−1.26575	+	4.72385i	−0.0609691	+	0.227540i	0.928718	+	0.370787i	$0.120912\pi$
$432$		0			0
$433$	−24.5015			−1.17747			−0.588733	−	0.808328i	$-0.700373\pi$
$433$	−24.5015			−1.17747			−0.588733	+	0.808328i	$0.700373\pi$
$434$	31.7500	+	14.8980i	1.52405	+	0.715126i
$435$		0			0
$436$	−8.91165	−	33.2587i	−0.426791	−	1.59280i
$437$	0.0932862	−	0.348149i	0.00446248	−	0.0166542i
$438$		0			0
$439$	16.1929	−	28.0470i	0.772846	−	1.33861i	−0.163151	−	0.986601i	$-0.552166\pi$
$439$	16.1929	−	28.0470i	0.772846	−	1.33861i	0.935997	−	0.352008i	$-0.114501\pi$
$440$	−12.4657	−	12.4657i	−0.594280	−	0.594280i
$441$		0			0
$442$	−0.0811190	−	4.33297i	−0.00385844	−	0.206099i
$443$	17.6889	−	30.6380i	0.840423	−	1.45566i	−0.0491148	−	0.998793i	$-0.515640\pi$
$443$	17.6889	−	30.6380i	0.840423	−	1.45566i	0.889538	−	0.456862i	$-0.151027\pi$
$444$		0			0
$445$	38.2821	+	66.3066i	1.81475	+	3.14323i
$446$	0.638911	−	1.10663i	0.0302533	−	0.0524003i
$447$		0			0
$448$	−9.85765	+	21.0082i	−0.465730	+	0.992546i
$449$	−15.3334	+	15.3334i	−0.723628	+	0.723628i	−0.969342	−	0.245714i	$-0.920978\pi$
$449$	−15.3334	+	15.3334i	−0.723628	+	0.723628i	0.245714	+	0.969342i	$0.420978\pi$
$450$		0			0
$451$	−3.20420	+	1.84994i	−0.150880	+	0.0871104i
$452$	−76.8351	+	44.3608i	−3.61402	+	2.08656i
$453$		0			0
$454$	−2.90591			−0.136381
$455$	31.3522	−	22.7246i	1.46981	−	1.06535i
$456$		0			0
$457$	31.3312	−	8.39516i	1.46561	−	0.392709i	0.564187	−	0.825647i	$-0.309190\pi$
$457$	31.3312	−	8.39516i	1.46561	−	0.392709i	0.901424	+	0.432938i	$0.142523\pi$
$458$	−24.3474	+	14.0570i	−1.13768	+	0.656839i
$459$		0			0
$460$	−0.238736	−	0.890977i	−0.0111311	−	0.0415420i
$461$	−16.4874	+	16.4874i	−0.767896	+	0.767896i	−0.977736	−	0.209840i	$-0.932706\pi$
$461$	−16.4874	+	16.4874i	−0.767896	+	0.767896i	0.209840	+	0.977736i	$0.432706\pi$
$462$		0			0
$463$	−19.8546	+	19.8546i	−0.922722	+	0.922722i	−0.997221	−	0.0744988i	$-0.976264\pi$
$463$	−19.8546	+	19.8546i	−0.922722	+	0.922722i	0.0744988	+	0.997221i	$0.476264\pi$
$464$	5.33729	−	9.24446i	0.247777	−	0.429163i
$465$		0			0
$466$	−26.5886	−	7.12439i	−1.23169	−	0.330031i
$467$	−3.59024	+	6.21849i	−0.166137	+	0.287757i	−0.937058	−	0.349173i	$-0.886463\pi$
$467$	−3.59024	+	6.21849i	−0.166137	+	0.287757i	0.770922	+	0.636930i	$0.219796\pi$
$468$		0			0
$469$	15.2317	−	18.0643i	0.703334	−	0.834133i
$470$	−24.7474	−	24.7474i	−1.14151	−	1.14151i
$471$		0			0
$472$	−8.34581	−	14.4554i	−0.384147	−	0.665362i
$473$	0.132938	−	0.496130i	0.00611248	−	0.0228121i
$474$		0			0
$475$	62.5085	+	62.5085i	2.86809	+	2.86809i
$476$	3.37136	+	4.83944i	0.154526	+	0.221815i
$477$		0			0
$478$	36.6428	+	21.1557i	1.67600	+	0.967640i
$479$	7.46237	−	27.8499i	0.340964	−	1.27250i	−0.556292	−	0.830987i	$-0.687777\pi$
$479$	7.46237	−	27.8499i	0.340964	−	1.27250i	0.897257	−	0.441509i	$-0.145557\pi$
$480$		0			0
$481$	7.64212	−	13.8280i	0.348451	−	0.630503i
$482$		−	25.5501i		−	1.16377i
$483$		0			0
$484$	−51.7824			−2.35374
$485$	28.0252	+	16.1804i	1.27256	+	0.734713i
$486$		0			0
$487$	−0.0179567	+	0.0670152i	−0.000813694	+	0.00303675i	−0.966331	−	0.257300i	$-0.917167\pi$
$487$	−0.0179567	+	0.0670152i	−0.000813694	+	0.00303675i	0.965518	+	0.260337i	$0.0838337\pi$
$488$	−1.38473	+	0.371039i	−0.0626840	+	0.0167961i
$489$		0			0
$490$	−25.7814	+	69.7912i	−1.16468	+	3.15285i
$491$		−	29.0806i		−	1.31239i	−0.754592	−	0.656195i	$-0.772165\pi$
$491$		−	29.0806i		−	1.31239i	0.754592	−	0.656195i	$-0.227835\pi$
$492$		0			0
$493$	−0.248189	−	0.429876i	−0.0111779	−	0.0193606i
$494$	17.5035	−	70.5832i	0.787520	−	3.17569i
$495$		0			0
$496$	35.3367	−	35.3367i	1.58667	−	1.58667i
$497$	−5.38783	−	14.9140i	−0.241677	−	0.668986i
$498$		0			0
$499$	19.4710	−	5.21725i	0.871644	−	0.233556i	0.204845	−	0.978794i	$-0.434331\pi$
$499$	19.4710	−	5.21725i	0.871644	−	0.233556i	0.666798	+	0.745238i	$0.267664\pi$
$500$	123.320	+	33.0434i	5.51502	+	1.47775i
$501$		0			0
$502$	39.4438	−	10.5689i	1.76046	−	0.471715i
$503$			34.9296i			1.55743i	0.627376	+	0.778716i	$0.284129\pi$
$503$			34.9296i			1.55743i	−0.627376	+	0.778716i	$0.715871\pi$
$504$		0			0
$505$	18.1615	−	18.1615i	0.808178	−	0.808178i
$506$	0.0616163	+	0.0355742i	0.00273918	+	0.00158147i
$507$		0			0
$508$	−13.2769	−	22.9962i	−0.589066	−	1.02029i
$509$	6.48888	+	24.2168i	0.287615	+	1.07339i	0.946907	+	0.321506i	$0.104189\pi$
$509$	6.48888	+	24.2168i	0.287615	+	1.07339i	−0.659293	+	0.751886i	$0.729144\pi$
$510$		0			0
$511$	12.3545	−	14.6521i	0.546532	−	0.648171i
$512$	−28.4020	−	28.4020i	−1.25520	−	1.25520i
$513$		0			0
$514$	10.2433	−	38.2285i	0.451813	−	1.68619i
$515$	−63.2980	−	16.9607i	−2.78925	−	0.747376i
$516$		0			0
$517$	1.91207			0.0840927
$518$	2.57332	+	30.2478i	0.113065	+	1.32901i
$519$		0			0
$520$	−30.3050	−	105.184i	−1.32896	−	4.61260i
$521$	3.25185	−	1.87746i	0.142466	−	0.0822528i	−0.427073	−	0.904217i	$-0.640455\pi$
$521$	3.25185	−	1.87746i	0.142466	−	0.0822528i	0.569539	+	0.821964i	$0.307122\pi$
$522$		0			0
$523$	−0.279523	−	0.161383i	−0.0122227	−	0.00705678i	0.493876	−	0.869532i	$-0.335580\pi$
$523$	−0.279523	−	0.161383i	−0.0122227	−	0.00705678i	−0.506099	+	0.862475i	$0.668913\pi$
$524$	29.7471			1.29951
$525$		0			0
$526$	−48.8736	−	48.8736i	−2.13099	−	2.13099i
$527$	−0.601449	−	2.24464i	−0.0261995	−	0.0977780i
$528$		0			0
$529$	−11.4989	−	19.9167i	−0.499952	−	0.865943i
$530$	2.68990	−	4.65903i	0.116842	−	0.202376i
$531$		0			0
$532$	33.6267	+	93.0819i	1.45790	+	4.03561i
$533$	−22.9691	+	0.430012i	−0.994903	+	0.0186259i
$534$		0			0
$535$	3.73573	+	1.00099i	0.161510	+	0.0432764i
$536$	−33.3982	−	57.8474i	−1.44258	−	2.49863i
$537$		0			0
$538$	−24.6591	+	24.6591i	−1.06313	+	1.06313i
$539$	−1.70018	−	3.69214i	−0.0732319	−	0.159032i
$540$		0			0
$541$	6.41652	+	23.9468i	0.275868	+	1.02955i	0.955258	+	0.295775i	$0.0955777\pi$
$541$	6.41652	+	23.9468i	0.275868	+	1.02955i	−0.679390	+	0.733777i	$0.737756\pi$
$542$	45.7170	−	26.3947i	1.96371	−	1.13375i
$543$		0			0
$544$	4.82836	−	1.29375i	0.207014	−	0.0554693i
$545$	−28.7796			−1.23278
$546$		0			0
$547$	−2.96777			−0.126893			−0.0634464	−	0.997985i	$-0.520209\pi$
$547$	−2.96777			−0.126893			−0.0634464	+	0.997985i	$0.520209\pi$
$548$	18.3164	−	4.90787i	0.782438	−	0.209654i
$549$		0			0
$550$	−15.1122	+	8.72506i	−0.644388	+	0.372038i
$551$	−2.15579	−	8.04553i	−0.0918399	−	0.342751i
$552$		0			0
$553$	−12.6947	+	8.84365i	−0.539832	+	0.376070i
$554$	7.55765	−	7.55765i	0.321094	−	0.321094i
$555$		0			0
$556$	−20.4294	−	35.3847i	−0.866399	−	1.50065i
$557$	5.99869	+	1.60734i	0.254173	+	0.0681054i	0.383656	−	0.923476i	$-0.374665\pi$
$557$	5.99869	+	1.60734i	0.254173	+	0.0681054i	−0.129483	+	0.991582i	$0.541332\pi$
$558$		0			0
$559$	2.21251	−	2.29693i	0.0935792	−	0.0971499i
$560$	81.0482	+	68.3391i	3.42491	+	2.88786i
$561$		0			0
$562$	1.03478	−	1.79230i	0.0436497	−	0.0756034i
$563$	−9.09381	−	15.7509i	−0.383259	−	0.663823i	0.608267	−	0.793732i	$-0.291865\pi$
$563$	−9.09381	−	15.7509i	−0.383259	−	0.663823i	−0.991526	+	0.129909i	$0.958532\pi$
$564$		0			0
$565$	19.1932	+	71.6301i	0.807465	+	3.01350i
$566$	42.0908	+	42.0908i	1.76921	+	1.76921i
$567$		0			0
$568$	−44.8272			−1.88091
$569$	−26.1342	−	15.0886i	−1.09560	−	0.632547i	−0.160541	−	0.987029i	$-0.551324\pi$
$569$	−26.1342	−	15.0886i	−1.09560	−	0.632547i	−0.935063	+	0.354482i	$0.884657\pi$
$570$		0			0
$571$	−34.6783	+	20.0215i	−1.45124	+	0.837876i	−0.998552	−	0.0537918i	$-0.982869\pi$
$571$	−34.6783	+	20.0215i	−1.45124	+	0.837876i	−0.452691	+	0.891667i	$0.649536\pi$
$572$	8.89909	+	4.91813i	0.372090	+	0.205637i
$573$		0			0
$574$	36.2189	−	25.2317i	1.51175	−	1.05315i
$575$	−0.537020			−0.0223953
$576$		0			0
$577$	−2.72677	−	0.730637i	−0.113517	−	0.0304168i	0.201613	−	0.979465i	$-0.435382\pi$
$577$	−2.72677	−	0.730637i	−0.113517	−	0.0304168i	−0.315130	+	0.949048i	$0.602048\pi$
$578$	−11.3782	+	42.4642i	−0.473273	+	1.76628i
$579$		0			0
$580$	−15.0729	−	15.0729i	−0.625869	−	0.625869i
$581$	−34.0579	+	12.3037i	−1.41296	+	0.510445i
$582$		0			0
$583$	0.0760714	+	0.283902i	0.00315055	+	0.0117580i
$584$	−27.0895	−	46.9204i	−1.12097	−	1.94158i
$585$		0			0
$586$	22.7024	+	13.1073i	0.937829	+	0.541456i
$587$	24.8081	−	24.8081i	1.02394	−	1.02394i	0.0242353	−	0.999706i	$-0.492285\pi$
$587$	24.8081	−	24.8081i	1.02394	−	1.02394i	0.999706	−	0.0242353i	$-0.00771510\pi$
$588$		0			0
$589$		−	38.9943i		−	1.60673i
$590$	−22.9120	+	6.13926i	−0.943273	+	0.252749i
$591$		0			0
$592$	41.7821	+	11.1955i	1.71723	+	0.460132i
$593$	−14.0874	+	3.77472i	−0.578501	+	0.155009i	−0.536193	−	0.844096i	$-0.680138\pi$
$593$	−14.0874	+	3.77472i	−0.578501	+	0.155009i	−0.0423087	+	0.999105i	$0.513471\pi$
$594$		0			0
$595$	4.63649	−	1.67497i	0.190078	−	0.0686672i
$596$	−49.4339	+	49.4339i	−2.02489	+	2.02489i
$597$		0			0
$598$	0.228008	+	0.378383i	0.00932394	+	0.0154732i
$599$	14.5135	+	25.1381i	0.593006	+	1.02712i	0.993825	+	0.110959i	$0.0353924\pi$
$599$	14.5135	+	25.1381i	0.593006	+	1.02712i	−0.400819	+	0.916157i	$0.631274\pi$
$600$		0			0
$601$		−	4.85980i		−	0.198235i	−0.995076	−	0.0991176i	$-0.968398\pi$
$601$		−	4.85980i		−	0.198235i	0.995076	−	0.0991176i	$-0.0316020\pi$
$602$	−1.07855	+	6.03219i	−0.0439583	+	0.245854i
$603$		0			0
$604$	34.9384	−	9.36171i	1.42162	−	0.380923i
$605$	−11.2021	+	41.8070i	−0.455432	+	1.69969i
$606$		0			0
$607$	−27.0785	−	15.6338i	−1.09908	−	0.634557i	−0.163104	−	0.986609i	$-0.552151\pi$
$607$	−27.0785	−	15.6338i	−1.09908	−	0.634557i	−0.935980	+	0.352052i	$0.885484\pi$
$608$	83.8792			3.40175
$609$		0			0
$610$			2.03725i			0.0824857i
$611$	10.3910	+	5.74266i	0.420376	+	0.232323i
$612$		0			0
$613$	8.58499	−	32.0396i	0.346744	−	1.29407i	−0.543817	−	0.839204i	$-0.683021\pi$
$613$	8.58499	−	32.0396i	0.346744	−	1.29407i	0.890561	−	0.454864i	$-0.150312\pi$
$614$	41.5717	+	24.0014i	1.67770	+	0.968619i
$615$		0			0
$616$	−11.4494	+	0.974052i	−0.461309	+	0.0392457i
$617$	13.6876	+	13.6876i	0.551042	+	0.551042i	0.926741	−	0.375700i	$-0.122598\pi$
$617$	13.6876	+	13.6876i	0.551042	+	0.551042i	−0.375700	+	0.926741i	$0.622598\pi$
$618$		0			0
$619$	−3.13330	+	11.6936i	−0.125938	+	0.470007i	−0.999871	−	0.0160389i	$-0.994894\pi$
$619$	−3.13330	+	11.6936i	−0.125938	+	0.470007i	0.873933	+	0.486046i	$0.161561\pi$
$620$	−49.8968	−	86.4238i	−2.00390	−	3.47086i
$621$		0			0
$622$	−12.4328	−	12.4328i	−0.498512	−	0.498512i
$623$	49.1257	+	8.78360i	1.96818	+	0.351908i
$624$		0			0
$625$	24.6644	−	42.7199i	0.986575	−	1.70880i
$626$	−2.57012	−	0.688662i	−0.102723	−	0.0275245i
$627$		0			0
$628$	−50.8313	+	88.0425i	−2.02839	+	3.51328i
$629$	1.42231	−	1.42231i	0.0567111	−	0.0567111i
$630$		0			0
$631$	19.1930	−	19.1930i	0.764060	−	0.764060i	−0.212993	−	0.977054i	$-0.568321\pi$
$631$	19.1930	−	19.1930i	0.764060	−	0.764060i	0.977054	+	0.212993i	$0.0683212\pi$
$632$	11.3197	+	42.2458i	0.450275	+	1.68045i
$633$		0			0
$634$	−53.6705	+	30.9867i	−2.13153	+	1.23064i
$635$	−21.4384	+	5.74440i	−0.850757	+	0.227960i
$636$		0			0
$637$	1.84935	−	25.1710i	0.0732739	−	0.997312i
$638$	1.64420			0.0650945
$639$		0			0
$640$	4.17441	−	2.41010i	0.165008	−	0.0952674i
$641$	−11.0951	+	6.40575i	−0.438229	+	0.253012i	−0.702846	−	0.711342i	$-0.748088\pi$
$641$	−11.0951	+	6.40575i	−0.438229	+	0.253012i	0.264617	+	0.964354i	$0.414754\pi$
$642$		0			0
$643$	3.85306	−	3.85306i	0.151950	−	0.151950i	−0.627038	−	0.778988i	$-0.715733\pi$
$643$	3.85306	−	3.85306i	0.151950	−	0.151950i	0.778988	+	0.627038i	$0.215733\pi$
$644$	−0.544286	−	0.255394i	−0.0214479	−	0.0100639i
$645$		0			0
$646$	4.62917	−	8.01796i	0.182132	−	0.315462i
$647$	12.4892	+	21.6319i	0.491001	+	0.850438i	0.999946	−	0.0103604i	$-0.00329786\pi$
$647$	12.4892	+	21.6319i	0.491001	+	0.850438i	−0.508945	+	0.860799i	$0.669965\pi$
$648$		0			0
$649$	0.647962	−	1.12230i	0.0254347	−	0.0440542i
$650$	−108.331	+	2.02811i	−4.24911	+	0.0795489i
$651$		0			0
$652$	38.7788	+	38.7788i	1.51869	+	1.51869i
$653$	15.4392	−	26.7415i	0.604183	−	1.04648i	−0.387997	−	0.921660i	$-0.626833\pi$
$653$	15.4392	−	26.7415i	0.604183	−	1.04648i	0.992180	−	0.124815i	$-0.0398336\pi$
$654$		0			0
$655$	6.43523	−	24.0166i	0.251445	−	0.938407i
$656$	−16.2790	−	60.7540i	−0.635588	−	2.37205i
$657$		0			0
$658$	−22.7297	+	1.93372i	−0.886095	+	0.0753843i
$659$	−14.7700			−0.575357			−0.287678	−	0.957727i	$-0.592883\pi$
$659$	−14.7700			−0.575357			−0.287678	+	0.957727i	$0.592883\pi$
$660$		0			0
$661$	−7.35076	+	27.4334i	−0.285912	+	1.06704i	0.662259	+	0.749275i	$0.269598\pi$
$661$	−7.35076	+	27.4334i	−0.285912	+	1.06704i	−0.948171	+	0.317762i	$0.897069\pi$
$662$	36.6338	−	21.1505i	1.42381	−	0.822038i
$663$		0			0
$664$			102.368i			3.97266i
$665$	82.4250	−	7.01228i	3.19630	−	0.271925i
$666$		0			0
$667$	0.0438205	+	0.0252998i	0.00169674	+	0.000979612i
$668$	−62.2814	−	16.6883i	−2.40974	−	0.645688i
$669$		0			0
$670$	−91.6892	+	24.5680i	−3.54226	+	0.949146i
$671$	−0.0787025	−	0.0787025i	−0.00303828	−	0.00303828i
$672$		0			0
$673$			25.3723i			0.978030i	0.872275	+	0.489015i	$0.162644\pi$
$673$			25.3723i			0.978030i	−0.872275	+	0.489015i	$0.837356\pi$
$674$	−6.73244	−	25.1258i	−0.259324	−	0.967811i
$675$		0			0
$676$	33.5906	+	53.4546i	1.29195	+	2.05595i
$677$	27.0806	+	15.6350i	1.04079	+	0.600902i	0.920058	−	0.391783i	$-0.128142\pi$
$677$	27.0806	+	15.6350i	1.04079	+	0.600902i	0.120735	+	0.992685i	$0.461475\pi$
$678$		0			0
$679$	19.8380	−	7.16665i	0.761311	−	0.275031i
$680$		−	13.9359i		−	0.534419i
$681$		0			0
$682$	7.43514	+	1.99224i	0.284706	+	0.0762868i
$683$	0.831182	+	0.222715i	0.0318043	+	0.00852193i	0.274686	−	0.961534i	$-0.411426\pi$
$683$	0.831182	+	0.222715i	0.0318043	+	0.00852193i	−0.242882	+	0.970056i	$0.578093\pi$
$684$		0			0
$685$		−	15.8496i		−	0.605584i
$686$	23.9448	+	42.1708i	0.914217	+	1.61009i
$687$		0			0
$688$	7.56180	+	4.36581i	0.288291	+	0.166445i
$689$	−0.439260	+	1.77132i	−0.0167345	+	0.0674820i
$690$		0			0
$691$	8.72057	+	32.5456i	0.331746	+	1.23809i	0.907354	+	0.420368i	$0.138099\pi$
$691$	8.72057	+	32.5456i	0.331746	+	1.23809i	−0.575608	+	0.817726i	$0.695234\pi$
$692$		−	30.9873i		−	1.17796i
$693$		0			0
$694$	19.7423	+	19.7423i	0.749408	+	0.749408i
$695$	−32.9877	+	8.83902i	−1.25129	+	0.335283i
$696$		0			0
$697$	−2.82512	−	0.756988i	−0.107009	−	0.0286730i
$698$	−47.3149	−	27.3173i	−1.79090	−	1.03397i
$699$		0			0
$700$	120.994	−	84.2894i	4.57313	−	3.18584i
$701$			4.56454i			0.172400i	0.996278	+	0.0862002i	$0.0274725\pi$
$701$			4.56454i			0.172400i	−0.996278	+	0.0862002i	$0.972528\pi$
$702$		0			0
$703$	29.2306	−	16.8763i	1.10245	−	0.636501i
$704$	−1.31822	+	4.91966i	−0.0496822	+	0.185417i
$705$		0			0
$706$	76.4611			2.87765
$707$	−1.41911	−	16.6808i	−0.0533713	−	0.627346i
$708$		0			0
$709$	−6.92558	−	25.8466i	−0.260096	−	0.970690i	−0.965184	−	0.261571i	$-0.915760\pi$
$709$	−6.92558	−	25.8466i	−0.260096	−	0.970690i	0.705089	−	0.709119i	$-0.250907\pi$
$710$	−16.4877	+	61.5328i	−0.618771	+	2.30928i
$711$		0			0
$712$	70.5378	−	122.175i	2.64352	−	4.57870i
$713$	0.167503	+	0.167503i	0.00627304	+	0.00627304i
$714$		0			0
$715$	5.89584	−	6.12081i	0.220492	−	0.228905i
$716$	45.6894	−	79.1364i	1.70749	−	2.95747i
$717$		0			0
$718$	−24.9050	−	43.1367i	−0.929445	−	1.60985i
$719$	12.4067	−	21.4890i	0.462690	−	0.801403i	−0.536404	−	0.843962i	$-0.680218\pi$
$719$	12.4067	−	21.4890i	0.462690	−	0.801403i	0.999094	+	0.0425584i	$0.0135509\pi$
$720$		0			0
$721$	−35.0472	+	24.4154i	−1.30523	+	0.909276i
$722$	74.6750	−	74.6750i	2.77912	−	2.77912i
$723$		0			0
$724$	63.4309	−	36.6219i	2.35739	−	1.36104i
$725$	−10.7476	+	6.20512i	−0.399155	+	0.230452i
$726$		0			0
$727$	−15.9619			−0.591993			−0.295997	−	0.955189i	$-0.595652\pi$
$727$	−15.9619			−0.591993			−0.295997	+	0.955189i	$0.595652\pi$
$728$	−65.1465	−	29.0934i	−2.41449	−	1.07827i
$729$		0			0
$730$	−74.3697	+	19.9273i	−2.75255	+	0.737542i
$731$	0.351631	−	0.203014i	0.0130055	−	0.00750875i
$732$		0			0
$733$	7.62589	+	28.4602i	0.281669	+	1.05120i	0.951240	+	0.308453i	$0.0998113\pi$
$733$	7.62589	+	28.4602i	0.281669	+	1.05120i	−0.669571	+	0.742748i	$0.733522\pi$
$734$	−46.4728	+	46.4728i	−1.71534	+	1.71534i
$735$		0			0
$736$	−0.360309	+	0.360309i	−0.0132812	+	0.0132812i
$737$	2.59301	−	4.49122i	0.0955147	−	0.165436i
$738$		0			0
$739$	7.27300	+	1.94879i	0.267542	+	0.0716876i	0.390096	−	0.920774i	$-0.372442\pi$
$739$	7.27300	+	1.94879i	0.267542	+	0.0716876i	−0.122554	+	0.992462i	$0.539109\pi$
$740$	43.1895	−	74.8064i	1.58768	−	2.74994i
$741$		0			0
$742$	−1.19141	−	3.29795i	−0.0437382	−	0.121072i
$743$	−16.2100	−	16.2100i	−0.594686	−	0.594686i	0.344207	−	0.938894i	$-0.388148\pi$
$743$	−16.2100	−	16.2100i	−0.594686	−	0.594686i	−0.938894	+	0.344207i	$0.888148\pi$
$744$		0			0
$745$	29.2168	+	50.6050i	1.07042	+	1.85402i
$746$	−22.5226	+	84.0556i	−0.824612	+	3.07749i
$747$		0			0
$748$	0.915333	+	0.915333i	0.0334679	+	0.0334679i
$749$	2.06842	−	1.44095i	0.0755784	−	0.0526511i
$750$		0			0
$751$	0.625628	+	0.361207i	0.0228295	+	0.0131806i	0.511371	−	0.859360i	$-0.329138\pi$
$751$	0.625628	+	0.361207i	0.0228295	+	0.0131806i	−0.488542	+	0.872540i	$0.662471\pi$
$752$	−8.41283	+	31.3971i	−0.306785	+	1.14494i
$753$		0			0
$754$	8.93532	+	4.93816i	0.325405	+	0.179837i
$755$		−	30.2330i		−	1.10029i
$756$		0			0
$757$	−16.2792			−0.591679			−0.295839	−	0.955238i	$-0.595599\pi$
$757$	−16.2792			−0.591679			−0.295839	+	0.955238i	$0.595599\pi$
$758$	68.0137	+	39.2678i	2.47037	+	1.42627i
$759$		0			0
$760$	60.5245	−	225.880i	2.19545	−	8.19354i
$761$	−1.26328	+	0.338495i	−0.0457939	+	0.0122704i	−0.281643	−	0.959519i	$-0.590879\pi$
$761$	−1.26328	+	0.338495i	−0.0457939	+	0.0122704i	0.235849	+	0.971790i	$0.424213\pi$
$762$		0			0
$763$	−12.0922	+	14.3410i	−0.437767	+	0.519178i
$764$			4.71420i			0.170554i
$765$		0			0
$766$	26.1340	+	45.2654i	0.944259	+	1.63550i
$767$	6.89201	−	4.15302i	0.248856	−	0.149957i
$768$		0			0
$769$	20.7983	−	20.7983i	0.750007	−	0.750007i	−0.224473	−	0.974480i	$-0.572066\pi$
$769$	20.7983	−	20.7983i	0.750007	−	0.750007i	0.974480	+	0.224473i	$0.0720660\pi$
$770$	−2.87409	+	16.0744i	−0.103575	+	0.579282i
$771$		0			0
$772$	−56.9990	+	15.2728i	−2.05144	+	0.549682i
$773$	10.6687	+	2.85866i	0.383725	+	0.102819i	0.445524	−	0.895270i	$-0.353017\pi$
$773$	10.6687	+	2.85866i	0.383725	+	0.102819i	−0.0617995	+	0.998089i	$0.519684\pi$
$774$		0			0
$775$	−56.1196	+	15.0372i	−2.01588	+	0.540152i
$776$		−	59.6272i		−	2.14049i
$777$		0			0
$778$	36.2606	−	36.2606i	1.30001	−	1.30001i
$779$	−42.5032	−	24.5392i	−1.52284	−	0.879210i
$780$		0			0
$781$	−1.74017	−	3.01407i	−0.0622683	−	0.107852i
$782$	0.0145568	+	0.0543267i	0.000520549	+	0.00194272i
$783$		0			0
$784$	68.1073	−	11.6729i	2.43240	−	0.416889i
$785$	60.0855	+	60.0855i	2.14454	+	2.14454i
$786$		0			0
$787$	−10.1818	+	37.9988i	−0.362940	+	1.35451i	0.507251	+	0.861798i	$0.330662\pi$
$787$	−10.1818	+	37.9988i	−0.362940	+	1.35451i	−0.870192	+	0.492714i	$0.836005\pi$
$788$	34.1827	+	9.15923i	1.21771	+	0.326284i
$789$		0			0
$790$	62.1529			2.21130
$791$	43.7579	+	20.5324i	1.55585	+	0.730049i
$792$		0			0
$793$	−0.191331	−	0.664078i	−0.00679438	−	0.0235821i
$794$	−55.0485	+	31.7822i	−1.95360	+	1.12791i
$795$		0			0
$796$	0.908668	+	0.524620i	0.0322069	+	0.0185947i
$797$	35.8509			1.26990			0.634952	−	0.772552i	$-0.281020\pi$
$797$	35.8509			1.26990			0.634952	+	0.772552i	$0.281020\pi$
$798$		0			0
$799$	1.06879	+	1.06879i	0.0378111	+	0.0378111i
$800$	−32.3460	−	120.717i	−1.14360	−	4.26798i
$801$		0			0
$802$	33.5513	+	58.1125i	1.18474	+	2.05202i
$803$	2.10321	−	3.64286i	0.0742205	−	0.128554i
$804$		0			0
$805$	−0.323941	+	0.384184i	−0.0114174	+	0.0135407i
$806$	34.4224	+	33.1573i	1.21248	+	1.16791i
$807$		0			0
$808$	−45.7127	−	12.2487i	−1.60817	−	0.430907i
$809$	−19.4427	−	33.6758i	−0.683570	−	1.18398i	−0.973884	−	0.227046i	$-0.927093\pi$
$809$	−19.4427	−	33.6758i	−0.683570	−	1.18398i	0.290315	−	0.956931i	$-0.406240\pi$
$810$		0			0
$811$	−25.4440	+	25.4440i	−0.893460	+	0.893460i	−0.994847	−	0.101387i	$-0.967672\pi$
$811$	−25.4440	+	25.4440i	−0.893460	+	0.893460i	0.101387	+	0.994847i	$0.467672\pi$
$812$	−13.8440	+	1.17778i	−0.485830	+	0.0413318i
$813$		0			0
$814$	1.72444	+	6.43568i	0.0604414	+	0.225570i
$815$	39.6974	−	22.9193i	1.39054	−	0.802829i
$816$		0			0
$817$	6.58110	−	1.76340i	0.230244	−	0.0616936i
$818$	26.6760			0.932704
$819$		0			0
$820$	−125.601			−4.38617
$821$	−47.7830	+	12.8034i	−1.66764	+	0.446842i	−0.964472	−	0.264184i	$-0.914897\pi$
$821$	−47.7830	+	12.8034i	−1.66764	+	0.446842i	−0.703165	+	0.711027i	$0.748231\pi$
$822$		0			0
$823$	−45.1357	+	26.0591i	−1.57333	+	0.908363i	−0.577574	+	0.816338i	$0.696000\pi$
$823$	−45.1357	+	26.0591i	−1.57333	+	0.908363i	−0.995757	+	0.0920243i	$0.970666\pi$
$824$	31.2513	+	116.632i	1.08869	+	4.06305i
$825$		0			0
$826$	−6.56762	+	13.9967i	−0.228517	+	0.487006i
$827$	−23.0612	+	23.0612i	−0.801917	+	0.801917i	−0.983395	−	0.181478i	$-0.941912\pi$
$827$	−23.0612	+	23.0612i	−0.801917	+	0.801917i	0.181478	+	0.983395i	$0.441912\pi$
$828$		0			0
$829$	11.2371	+	19.4633i	0.390282	+	0.675989i	0.992487	−	0.122353i	$-0.0390441\pi$
$829$	11.2371	+	19.4633i	0.390282	+	0.675989i	−0.602204	+	0.798342i	$0.705711\pi$
$830$	140.517	+	37.6515i	4.87743	+	1.30690i
$831$		0			0
$832$	−21.9394	+	22.7765i	−0.760611	+	0.789634i
$833$	1.11345	−	3.01415i	0.0385787	−	0.104434i
$834$		0			0
$835$	−26.9468	+	46.6733i	−0.932533	+	1.61519i
$836$	10.8608	+	18.8115i	0.375629	+	0.650609i
$837$		0			0
$838$	−13.9718	−	52.1436i	−0.482649	−	1.80127i
$839$	−2.56768	−	2.56768i	−0.0886463	−	0.0886463i	0.661393	−	0.750039i	$-0.269966\pi$
$839$	−2.56768	−	2.56768i	−0.0886463	−	0.0886463i	−0.750039	+	0.661393i	$0.769966\pi$
$840$		0			0
$841$	−27.8307			−0.959678
$842$	33.2986	+	19.2250i	1.14755	+	0.662536i
$843$		0			0
$844$	−3.51367	+	2.02862i	−0.120946	+	0.0698280i
$845$	50.4238	−	15.5558i	1.73463	−	0.535136i
$846$		0			0
$847$	16.1258	+	23.1479i	0.554090	+	0.795372i
$848$	−4.99652			−0.171581
$849$		0			0
$850$	−13.3244	−	3.57025i	−0.457022	−	0.122459i
$851$	−0.0530688	+	0.198055i	−0.00181917	+	0.00678925i
$852$		0			0
$853$	−1.75869	−	1.75869i	−0.0602165	−	0.0602165i	0.676357	−	0.736574i	$-0.263558\pi$
$853$	−1.75869	−	1.75869i	−0.0602165	−	0.0602165i	−0.736574	+	0.676357i	$0.763558\pi$
$854$	1.01517	+	0.855981i	0.0347383	+	0.0292911i
$855$		0			0
$856$	−1.84439	−	6.88337i	−0.0630401	−	0.235269i
$857$	5.72312	+	9.91273i	0.195498	+	0.338613i	0.947064	−	0.321046i	$-0.104034\pi$
$857$	5.72312	+	9.91273i	0.195498	+	0.338613i	−0.751566	+	0.659658i	$0.770701\pi$
$858$		0			0
$859$	−35.5016	−	20.4969i	−1.21130	−	0.699344i	−0.248257	−	0.968694i	$-0.579858\pi$
$859$	−35.5016	−	20.4969i	−1.21130	−	0.699344i	−0.963042	+	0.269351i	$0.913191\pi$
$860$	12.3294	−	12.3294i	0.420428	−	0.420428i
$861$		0			0
$862$		−	12.8056i		−	0.436159i
$863$	−36.0090	+	9.64858i	−1.22576	+	0.328441i	−0.812927	−	0.582365i	$-0.802127\pi$
$863$	−36.0090	+	9.64858i	−1.22576	+	0.328441i	−0.412833	+	0.910807i	$0.635461\pi$
$864$		0			0
$865$	−25.0178	−	6.70351i	−0.850632	−	0.227926i
$866$	61.9702	−	16.6049i	2.10583	−	0.564256i
$867$		0			0
$868$	−64.0303	−	11.4485i	−2.17333	−	0.388588i
$869$	−2.40108	+	2.40108i	−0.0814509	+	0.0814509i
$870$		0			0
$871$	27.5804	−	16.6195i	0.934526	−	0.563131i
$872$	26.5143	+	45.9241i	0.897888	+	1.55519i
$873$		0			0
$874$			0.943773i			0.0319236i
$875$	−23.6325	−	65.4170i	−0.798923	−	2.21150i
$876$		0			0
$877$	−35.1735	+	9.42472i	−1.18773	+	0.318250i	−0.797986	−	0.602675i	$-0.794101\pi$
$877$	−35.1735	+	9.42472i	−1.18773	+	0.318250i	−0.389739	+	0.920925i	$0.627435\pi$
$878$	−21.9482	+	81.9117i	−0.740715	+	2.76438i
$879$		0			0
$880$	20.1505	+	11.6339i	0.679274	+	0.392179i
$881$	−44.0473			−1.48399			−0.741995	−	0.670406i	$-0.766120\pi$
$881$	−44.0473			−1.48399			−0.741995	+	0.670406i	$0.766120\pi$
$882$		0			0
$883$			4.14168i			0.139379i	0.997569	+	0.0696894i	$0.0222008\pi$
$883$			4.14168i			0.139379i	−0.997569	+	0.0696894i	$0.977799\pi$
$884$	2.22524	+	7.72342i	0.0748429	+	0.259767i
$885$		0			0
$886$	−23.9758	+	89.4788i	−0.805482	+	3.00610i
$887$	−43.3054	−	25.0024i	−1.45405	−	0.839497i	−0.455344	−	0.890316i	$-0.650484\pi$
$887$	−43.3054	−	25.0024i	−1.45405	−	0.839497i	−0.998708	+	0.0508183i	$0.983817\pi$
$888$		0			0
$889$	−6.14522	+	13.0964i	−0.206104	+	0.439240i
$890$	−141.761	−	141.761i	−4.75185	−	4.75185i
$891$		0			0
$892$	−0.613381	+	2.28917i	−0.0205375	+	0.0766471i
$893$	12.6817	+	21.9653i	0.424376	+	0.735040i
$894$		0			0
$895$	−54.0075	−	54.0075i	−1.80527	−	1.80527i
$896$	0.552982	−	3.09276i	0.0184738	−	0.103322i
$897$		0			0
$898$	28.3903	−	49.1735i	0.947397	−	1.64094i
$899$	5.28775	+	1.41685i	0.176356	+	0.0472546i
$900$		0			0
$901$	−0.116171	+	0.201215i	−0.00387023	+	0.00670343i
$902$	6.85047	−	6.85047i	0.228096	−	0.228096i
$903$		0			0
$904$	96.6190	−	96.6190i	3.21350	−	3.21350i
$905$	−15.8449	−	59.1340i	−0.526702	−	1.96568i
$906$		0			0
$907$	18.9852	−	10.9611i	0.630393	−	0.363958i	−0.150511	−	0.988608i	$-0.548092\pi$
$907$	18.9852	−	10.9611i	0.630393	−	0.363958i	0.780904	+	0.624651i	$0.214759\pi$
$908$	5.20582	−	1.39490i	0.172761	−	0.0462912i
$909$		0			0
$910$	−63.8966	+	78.7237i	−2.11815	+	2.60966i
$911$	−18.0264			−0.597240			−0.298620	−	0.954372i	$-0.596526\pi$
$911$	−18.0264			−0.597240			−0.298620	+	0.954372i	$0.596526\pi$
$912$		0			0
$913$	−6.88298	+	3.97389i	−0.227793	+	0.131517i
$914$	−73.5547	+	42.4668i	−2.43297	+	1.40468i
$915$		0			0
$916$	36.8698	−	36.8698i	1.21821	−	1.21821i
$917$	−9.26371	−	13.2977i	−0.305915	−	0.439127i
$918$		0			0
$919$	−9.95304	+	17.2392i	−0.328321	+	0.568668i	−0.982179	−	0.187949i	$-0.939816\pi$
$919$	−9.95304	+	17.2392i	−0.328321	+	0.568668i	0.653858	+	0.756617i	$0.273149\pi$
$920$	0.710299	+	1.23027i	0.0234179	+	0.0405609i
$921$		0			0
$922$	30.5270	−	52.8744i	1.00535	−	1.74133i
$923$	−0.404497	−	21.6062i	−0.0133142	−	0.711177i
$924$		0			0
$925$	−35.5600	−	35.5600i	−1.16920	−	1.16920i
$926$	36.7615	−	63.6728i	1.20806	−	2.09242i
$927$		0			0
$928$	−3.04773	+	11.3743i	−0.100047	+	0.373379i
$929$	12.8638	+	48.0085i	0.422049	+	1.57511i	0.770285	+	0.637700i	$0.220114\pi$
$929$	12.8638	+	48.0085i	0.422049	+	1.57511i	−0.348236	+	0.937407i	$0.613219\pi$
$930$		0			0
$931$	31.1379	−	44.0190i	1.02050	−	1.44266i
$932$	51.0523			1.67227
$933$		0			0
$934$	4.86628	−	18.1612i	0.159229	−	0.594252i
$935$	0.937017	−	0.540987i	0.0306437	−	0.0176922i
$936$		0			0
$937$		−	7.64256i		−	0.249672i	−0.992177	−	0.124836i	$-0.960160\pi$
$937$		−	7.64256i		−	0.249672i	0.992177	−	0.124836i	$-0.0398404\pi$
$938$	−26.2823	+	56.0117i	−0.858146	+	1.82885i
$939$		0			0
$940$	56.2132	+	32.4547i	1.83347	+	1.05856i
$941$	15.6879	+	4.20355i	0.511410	+	0.137032i	0.505290	−	0.862949i	$-0.331385\pi$
$941$	15.6879	+	4.20355i	0.511410	+	0.137032i	0.00611953	+	0.999981i	$0.498052\pi$
$942$		0			0
$943$	0.287986	−	0.0771656i	0.00937811	−	0.00251286i
$944$	15.5778	+	15.5778i	0.507015	+	0.507015i
$945$		0			0
$946$			1.34493i			0.0437274i
$947$	−4.86048	−	18.1395i	−0.157944	−	0.589456i	−0.998835	−	0.0482515i	$-0.984635\pi$
$947$	−4.86048	−	18.1395i	−0.157944	−	0.589456i	0.840891	−	0.541205i	$-0.182032\pi$
$948$		0			0
$949$	22.3707	−	13.4802i	0.726182	−	0.437586i
$950$	−200.462	−	115.737i	−6.50384	−	3.75499i
$951$		0			0
$952$	−6.94433	−	5.85540i	−0.225067	−	0.189775i
$953$			37.5539i			1.21649i	0.793749	+	0.608246i	$0.208126\pi$
$953$			37.5539i			1.21649i	−0.793749	+	0.608246i	$0.791874\pi$
$954$		0			0
$955$	3.80605	+	1.01983i	0.123161	+	0.0330009i
$956$	−75.7993	−	20.3104i	−2.45153	−	0.656884i
$957$		0			0
$958$			75.4965i			2.43918i
$959$	−7.89794	−	6.65947i	−0.255038	−	0.215046i
$960$		0			0
$961$	−4.65212	−	2.68590i	−0.150068	−	0.0866421i
$962$	−9.95742	+	40.1535i	−0.321040	+	1.29460i
$963$		0			0
$964$	12.2646	+	45.7720i	0.395015	+	1.47422i
$965$			49.3227i			1.58775i
$966$		0			0
$967$	6.79849	+	6.79849i	0.218625	+	0.218625i	0.807919	−	0.589294i	$-0.200594\pi$
$967$	6.79849	+	6.79849i	0.218625	+	0.218625i	−0.589294	+	0.807919i	$0.700594\pi$
$968$	77.0326	−	20.6408i	2.47592	−	0.663421i
$969$		0			0
$970$	−81.8482	−	21.9311i	−2.62799	−	0.704167i
$971$	−9.79864	−	5.65725i	−0.314453	−	0.181550i	0.334464	−	0.942408i	$-0.391445\pi$
$971$	−9.79864	−	5.65725i	−0.314453	−	0.181550i	−0.648918	+	0.760859i	$0.724778\pi$
$972$		0			0
$973$	−9.45576	+	20.1517i	−0.303138	+	0.646035i
$974$		−	0.181667i		−	0.00582099i
$975$		0			0
$976$	1.63861	−	0.946055i	0.0524508	−	0.0302825i
$977$	8.82482	−	32.9347i	0.282331	−	1.05367i	−0.668437	−	0.743769i	$-0.733036\pi$
$977$	8.82482	−	32.9347i	0.282331	−	1.05367i	0.950768	−	0.309904i	$-0.100297\pi$
$978$		0			0
$979$	10.9530			0.350059
$980$	12.6851	−	137.404i	0.405210	−	4.38921i
$981$		0			0
$982$	19.7082	+	73.5519i	0.628913	+	2.34714i
$983$	11.4743	−	42.8226i	0.365973	−	1.36583i	−0.500124	−	0.865954i	$-0.666712\pi$
$983$	11.4743	−	42.8226i	0.365973	−	1.36583i	0.866097	−	0.499876i	$-0.166621\pi$
$984$		0			0
$985$	14.7896	−	25.6163i	0.471235	−	0.816203i
$986$	0.919060	+	0.919060i	0.0292688	+	0.0292688i
$987$		0			0
$988$	2.52456	+	134.849i	0.0803168	+	4.29013i
$989$	−0.0206948	+	0.0358444i	−0.000658056	+	0.00113979i
$990$		0			0
$991$	−9.99638	−	17.3142i	−0.317546	−	0.550005i	0.662430	−	0.749124i	$-0.269525\pi$
$991$	−9.99638	−	17.3142i	−0.317546	−	0.550005i	−0.979975	+	0.199119i	$0.936192\pi$
$992$	−27.5639	+	47.7421i	−0.875155	+	1.51581i
$993$		0			0
$994$	23.7345	+	34.0698i	0.752812	+	1.08063i
$995$	0.620130	−	0.620130i	0.0196594	−	0.0196594i
$996$		0			0
$997$	5.32624	−	3.07511i	0.168684	−	0.0973897i	−0.413281	−	0.910603i	$-0.635617\pi$
$997$	5.32624	−	3.07511i	0.168684	−	0.0973897i	0.581965	+	0.813214i	$0.302284\pi$
$998$	−45.7112	+	26.3914i	−1.44696	+	0.835405i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fn.f.775.1		36
3.2	odd	2		273.2.bz.a.229.9	yes	36
7.3	odd	6		819.2.fn.g.73.9		36
13.5	odd	4		819.2.fn.g.460.9		36
21.17	even	6		273.2.bz.b.73.1	yes	36
39.5	even	4		273.2.bz.b.187.1	yes	36
91.31	even	12	inner	819.2.fn.f.577.1		36
273.122	odd	12		273.2.bz.a.31.9	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.31.9	✓	36	273.122	odd	12
273.2.bz.a.229.9	yes	36	3.2	odd	2
273.2.bz.b.73.1	yes	36	21.17	even	6
273.2.bz.b.187.1	yes	36	39.5	even	4
819.2.fn.f.577.1		36	91.31	even	12	inner
819.2.fn.f.775.1		36	1.1	even	1	trivial
819.2.fn.g.73.9		36	7.3	odd	6
819.2.fn.g.460.9		36	13.5	odd	4

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.fn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.52924 + 0.677708i) q^{2} +(4.20573 - 2.42818i) q^{4} +(-1.05058 - 3.92082i) q^{5} +(-2.39518 - 1.12389i) q^{7} +(-5.28864 + 5.28864i) q^{8} +O(q^{10})\)	\(q+(-2.52924 + 0.677708i) q^{2} +(4.20573 - 2.42818i) q^{4} +(-1.05058 - 3.92082i) q^{5} +(-2.39518 - 1.12389i) q^{7} +(-5.28864 + 5.28864i) q^{8} +(5.31435 + 9.20472i) q^{10} +(-0.560897 - 0.150292i) q^{11} +(-2.59678 - 2.50134i) q^{13} +(6.81965 + 1.21935i) q^{14} +(4.93574 - 8.54896i) q^{16} +(-0.229516 - 0.397534i) q^{17} +(-1.99360 - 7.44023i) q^{19} +(-13.9389 - 13.9389i) q^{20} +1.52050 q^{22} +(0.0405237 + 0.0233964i) q^{23} +(-9.93900 + 5.73828i) q^{25} +(8.26308 + 4.56664i) q^{26} +(-12.8025 + 1.08917i) q^{28} +1.08136 q^{29} +(4.88993 + 1.31025i) q^{31} +(-2.81843 + 10.5185i) q^{32} +(0.849915 + 0.849915i) q^{34} +(-1.89022 + 10.5718i) q^{35} +(1.13412 + 4.23261i) q^{37} +(10.0846 + 17.4671i) q^{38} +(26.2920 + 15.1797i) q^{40} +(4.50540 - 4.50540i) q^{41} +0.884530i q^{43} +(-2.72392 + 0.729872i) q^{44} +(-0.118350 - 0.0317118i) q^{46} +(-3.18059 + 0.852236i) q^{47} +(4.47376 + 5.38381i) q^{49} +(21.2493 - 21.2493i) q^{50} +(-16.9951 - 4.21450i) q^{52} +(-0.253079 - 0.438345i) q^{53} +2.35707i q^{55} +(18.6111 - 6.72342i) q^{56} +(-2.73501 + 0.732844i) q^{58} +(-0.577611 + 2.15568i) q^{59} +(0.165995 + 0.0958371i) q^{61} -13.2558 q^{62} -8.77105i q^{64} +(-7.07918 + 12.8094i) q^{65} +(-2.31148 + 8.62657i) q^{67} +(-1.93057 - 1.11461i) q^{68} +(-2.38377 - 28.0197i) q^{70} +(4.23807 + 4.23807i) q^{71} +(-1.87486 + 6.99707i) q^{73} +(-5.73695 - 9.93669i) q^{74} +(-26.4507 - 26.4507i) q^{76} +(1.17454 + 0.990361i) q^{77} +(2.92382 - 5.06421i) q^{79} +(-38.7043 - 10.3708i) q^{80} +(-8.34191 + 14.4486i) q^{82} +(9.67812 - 9.67812i) q^{83} +(-1.31754 + 1.31754i) q^{85} +(-0.599453 - 2.23719i) q^{86} +(3.76123 - 2.17154i) q^{88} +(-18.2195 + 4.88190i) q^{89} +(3.40854 + 8.90965i) q^{91} +0.227242 q^{92} +(7.46691 - 4.31102i) q^{94} +(-27.0774 + 15.6331i) q^{95} +(-5.63729 + 5.63729i) q^{97} +(-14.9639 - 10.5851i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{7}+O(q^{10}) \) 36 * q - 6 * q^7	\( 36 q - 6 q^{7} - 4 q^{11} + 36 q^{14} + 12 q^{16} - 4 q^{17} - 18 q^{19} - 44 q^{20} - 8 q^{22} + 12 q^{23} - 48 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{29} - 6 q^{31} - 76 q^{32} - 48 q^{34} - 8 q^{35} - 8 q^{37} - 16 q^{38} + 60 q^{40} + 32 q^{41} - 4 q^{44} + 28 q^{46} - 14 q^{47} + 6 q^{49} + 68 q^{50} - 62 q^{52} + 8 q^{53} + 8 q^{56} + 36 q^{58} - 26 q^{59} + 36 q^{61} - 48 q^{62} + 8 q^{65} - 40 q^{67} - 36 q^{68} - 64 q^{70} + 36 q^{71} - 8 q^{73} - 40 q^{74} - 60 q^{76} - 60 q^{77} - 26 q^{80} - 24 q^{83} + 44 q^{85} - 48 q^{86} + 168 q^{88} - 10 q^{89} + 4 q^{91} + 40 q^{92} + 36 q^{97} - 38 q^{98}+O(q^{100}) \) 36 * q - 6 * q^7 - 4 * q^11 + 36 * q^14 + 12 * q^16 - 4 * q^17 - 18 * q^19 - 44 * q^20 - 8 * q^22 + 12 * q^23 - 48 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^29 - 6 * q^31 - 76 * q^32 - 48 * q^34 - 8 * q^35 - 8 * q^37 - 16 * q^38 + 60 * q^40 + 32 * q^41 - 4 * q^44 + 28 * q^46 - 14 * q^47 + 6 * q^49 + 68 * q^50 - 62 * q^52 + 8 * q^53 + 8 * q^56 + 36 * q^58 - 26 * q^59 + 36 * q^61 - 48 * q^62 + 8 * q^65 - 40 * q^67 - 36 * q^68 - 64 * q^70 + 36 * q^71 - 8 * q^73 - 40 * q^74 - 60 * q^76 - 60 * q^77 - 26 * q^80 - 24 * q^83 + 44 * q^85 - 48 * q^86 + 168 * q^88 - 10 * q^89 + 4 * q^91 + 40 * q^92 + 36 * q^97 - 38 * q^98

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