LMFDB - Embedded newform 819.2.fm.e.748.8

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 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			748.8
Character	$\chi$	$=$	819.748
Dual form			819.2.fm.e.496.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.16866 - 0.581092i) q^{2} +(2.63339 - 1.52039i) q^{4} +(-1.87790 + 1.87790i) q^{5} +(1.25762 + 2.32774i) q^{7} +(1.65230 - 1.65230i) q^{8} +O(q^{10})$	\(q+(2.16866 - 0.581092i) q^{2} +(2.63339 - 1.52039i) q^{4} +(-1.87790 + 1.87790i) q^{5} +(1.25762 + 2.32774i) q^{7} +(1.65230 - 1.65230i) q^{8} +(-2.98130 + 5.16377i) q^{10} +(1.20979 + 4.51499i) q^{11} +(1.52548 - 3.26694i) q^{13} +(4.07999 + 4.31730i) q^{14} +(-0.417624 + 0.723346i) q^{16} +(2.18729 + 3.78849i) q^{17} +(0.194491 + 0.0521138i) q^{19} +(-2.09010 + 7.80037i) q^{20} +(5.24724 + 9.08849i) q^{22} +(-7.20237 - 4.15829i) q^{23} -2.05302i q^{25} +(1.40986 - 7.97134i) q^{26} +(6.85087 + 4.21777i) q^{28} +(5.20380 - 9.01325i) q^{29} +(6.75799 - 6.75799i) q^{31} +(-1.69492 + 6.32554i) q^{32} +(6.94495 + 6.94495i) q^{34} +(-6.73296 - 2.00958i) q^{35} +(1.22755 + 4.58128i) q^{37} +0.452070 q^{38} +6.20572i q^{40} +(0.136339 + 0.508825i) q^{41} +(2.49507 - 1.44053i) q^{43} +(10.0504 + 10.0504i) q^{44} +(-18.0359 - 4.83270i) q^{46} +(0.928461 + 0.928461i) q^{47} +(-3.83677 + 5.85484i) q^{49} +(-1.19299 - 4.45231i) q^{50} +(-0.949833 - 10.9224i) q^{52} -1.95082 q^{53} +(-10.7506 - 6.20683i) q^{55} +(5.92410 + 1.76816i) q^{56} +(6.04777 - 22.5706i) q^{58} +(1.76081 - 6.57142i) q^{59} +(-2.13306 + 1.23152i) q^{61} +(10.7288 - 18.5828i) q^{62} +13.0324i q^{64} +(3.27029 + 8.99969i) q^{65} +(-1.40878 + 0.377482i) q^{67} +(11.5199 + 6.65104i) q^{68} +(-15.7693 - 0.445637i) q^{70} +(1.44014 - 5.37468i) q^{71} +(-8.75032 - 8.75032i) q^{73} +(5.32429 + 9.22194i) q^{74} +(0.591404 - 0.158466i) q^{76} +(-8.98827 + 8.49422i) q^{77} -4.46495 q^{79} +(-0.574115 - 2.14263i) q^{80} +(0.591348 + 1.02425i) q^{82} +(-5.42187 + 5.42187i) q^{83} +(-11.2219 - 3.00690i) q^{85} +(4.57389 - 4.57389i) q^{86} +(9.45905 + 5.46119i) q^{88} +(15.0461 - 4.03159i) q^{89} +(9.52308 - 0.557652i) q^{91} -25.2888 q^{92} +(2.55304 + 1.47400i) q^{94} +(-0.463100 + 0.267371i) q^{95} +(2.84925 + 0.763454i) q^{97} +(-4.91847 + 14.9267i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 2 * q^10 + 4 * q^11 + 6 * q^13 - 34 * q^14 + 14 * q^16 + 8 * q^17 + 2 * q^19 - 44 * q^20 - 4 * q^22 + 18 * q^23 + 28 * q^26 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * q^70 + 4 * q^71 + 12 * q^73 + 18 * q^74 - 48 * q^76 - 28 * q^77 - 4 * q^79 + 98 * q^80 + 20 * q^82 + 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 + 54 * q^89 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

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 $

$2$	2.16866	−	0.581092i	1.53348	−	0.410894i	0.609326	−	0.792920i	$-0.291440\pi$
$2$	2.16866	−	0.581092i	1.53348	−	0.410894i	0.924152	+	0.382026i	$0.124774\pi$
$3$		0			0
$3$		0			0
$4$	2.63339	−	1.52039i	1.31669	−	0.760193i
$5$	−1.87790	+	1.87790i	−0.839823	+	0.839823i	−0.988835	−	0.149013i	$-0.952390\pi$
$5$	−1.87790	+	1.87790i	−0.839823	+	0.839823i	0.149013	+	0.988835i	$0.452390\pi$
$6$		0			0
$7$	1.25762	+	2.32774i	0.475337	+	0.879804i
$7$	1.25762	+	2.32774i	0.475337	+	0.879804i
$8$	1.65230	−	1.65230i	0.584177	−	0.584177i
$9$		0			0
$10$	−2.98130	+	5.16377i	−0.942771	+	1.63293i
$11$	1.20979	+	4.51499i	0.364764	+	1.36132i	0.867740	+	0.497019i	$0.165572\pi$
$11$	1.20979	+	4.51499i	0.364764	+	1.36132i	−0.502975	+	0.864301i	$0.667761\pi$
$12$		0			0
$13$	1.52548	−	3.26694i	0.423092	−	0.906087i
$13$	1.52548	−	3.26694i	0.423092	−	0.906087i
$14$	4.07999	+	4.31730i	1.09042	+	1.15385i
$15$		0			0
$16$	−0.417624	+	0.723346i	−0.104406	+	0.180836i
$17$	2.18729	+	3.78849i	0.530495	+	0.918845i	0.999367	+	0.0355783i	$0.0113273\pi$
$17$	2.18729	+	3.78849i	0.530495	+	0.918845i	−0.468872	+	0.883266i	$0.655339\pi$
$18$		0			0
$19$	0.194491	+	0.0521138i	0.0446194	+	0.0119557i	0.281060	−	0.959690i	$-0.409314\pi$
$19$	0.194491	+	0.0521138i	0.0446194	+	0.0119557i	−0.236440	+	0.971646i	$0.575981\pi$
$20$	−2.09010	+	7.80037i	−0.467361	+	1.74422i
$21$		0			0
$22$	5.24724	+	9.08849i	1.11872	+	1.93767i
$23$	−7.20237	−	4.15829i	−1.50180	−	0.867064i	−0.999998	−	0.00208060i	$-0.999338\pi$
$23$	−7.20237	−	4.15829i	−1.50180	−	0.867064i	−0.501801	−	0.864983i	$-0.667329\pi$
$24$		0			0
$25$		−	2.05302i		−	0.410604i
$26$	1.40986	−	7.97134i	0.276497	−	1.56331i
$27$		0			0
$28$	6.85087	+	4.21777i	1.29469	+	0.797084i
$29$	5.20380	−	9.01325i	0.966322	−	1.67372i	0.260300	−	0.965528i	$-0.416179\pi$
$29$	5.20380	−	9.01325i	0.966322	−	1.67372i	0.706022	−	0.708190i	$-0.250488\pi$
$30$		0			0
$31$	6.75799	−	6.75799i	1.21377	−	1.21377i	0.243995	−	0.969777i	$-0.421542\pi$
$31$	6.75799	−	6.75799i	1.21377	−	1.21377i	0.969777	−	0.243995i	$-0.0784579\pi$
$32$	−1.69492	+	6.32554i	−0.299623	+	1.11821i
$33$		0			0
$34$	6.94495	+	6.94495i	1.19105	+	1.19105i
$35$	−6.73296	−	2.00958i	−1.13808	−	0.339681i
$36$		0			0
$37$	1.22755	+	4.58128i	0.201808	+	0.753158i	0.990399	+	0.138240i	$0.0441444\pi$
$37$	1.22755	+	4.58128i	0.201808	+	0.753158i	−0.788591	+	0.614919i	$0.789189\pi$
$38$	0.452070			0.0733354
$39$		0			0
$40$			6.20572i			0.981210i
$41$	0.136339	+	0.508825i	0.0212926	+	0.0794651i	0.975755	−	0.218867i	$-0.0702362\pi$
$41$	0.136339	+	0.508825i	0.0212926	+	0.0794651i	−0.954462	+	0.298333i	$0.903570\pi$
$42$		0			0
$43$	2.49507	−	1.44053i	0.380494	−	0.219678i	−0.297539	−	0.954710i	$-0.596166\pi$
$43$	2.49507	−	1.44053i	0.380494	−	0.219678i	0.678033	+	0.735031i	$0.262832\pi$
$44$	10.0504	+	10.0504i	1.51515	+	1.51515i
$45$		0			0
$46$	−18.0359	−	4.83270i	−2.65925	−	0.712543i
$47$	0.928461	+	0.928461i	0.135430	+	0.135430i	0.771572	−	0.636142i	$-0.219471\pi$
$47$	0.928461	+	0.928461i	0.135430	+	0.135430i	−0.636142	+	0.771572i	$0.719471\pi$
$48$		0			0
$49$	−3.83677	+	5.85484i	−0.548110	+	0.836406i
$50$	−1.19299	−	4.45231i	−0.168715	−	0.629651i
$51$		0			0
$52$	−0.949833	−	10.9224i	−0.131718	−	1.51467i
$53$	−1.95082			−0.267966			−0.133983	−	0.990984i	$-0.542777\pi$
$53$	−1.95082			−0.267966			−0.133983	+	0.990984i	$0.542777\pi$
$54$		0			0
$55$	−10.7506	−	6.20683i	−1.44960	−	0.836929i
$56$	5.92410	+	1.76816i	0.791642	+	0.236281i
$57$		0			0
$58$	6.04777	−	22.5706i	0.794111	−	2.96366i
$59$	1.76081	−	6.57142i	0.229237	−	0.855526i	−0.751425	−	0.659819i	$-0.770633\pi$
$59$	1.76081	−	6.57142i	0.229237	−	0.855526i	0.980662	−	0.195707i	$-0.0627002\pi$
$60$		0			0
$61$	−2.13306	+	1.23152i	−0.273111	+	0.157681i	−0.630300	−	0.776351i	$-0.717068\pi$
$61$	−2.13306	+	1.23152i	−0.273111	+	0.157681i	0.357190	+	0.934032i	$0.383735\pi$
$62$	10.7288	−	18.5828i	1.36256	−	2.36002i
$63$		0			0
$64$			13.0324i			1.62905i
$65$	3.27029	+	8.99969i	0.405630	+	1.11627i
$66$		0			0
$67$	−1.40878	+	0.377482i	−0.172110	+	0.0461168i	−0.343845	−	0.939026i	$-0.611729\pi$
$67$	−1.40878	+	0.377482i	−0.172110	+	0.0461168i	0.171735	+	0.985143i	$0.445063\pi$
$68$	11.5199	+	6.65104i	1.39700	+	0.806558i
$69$		0			0
$70$	−15.7693	−	0.445637i	−1.88479	−	0.0532638i
$71$	1.44014	−	5.37468i	0.170913	−	0.637857i	−0.826299	−	0.563232i	$-0.809558\pi$
$71$	1.44014	−	5.37468i	0.170913	−	0.637857i	0.997212	−	0.0746244i	$-0.0237758\pi$
$72$		0			0
$73$	−8.75032	−	8.75032i	−1.02415	−	1.02415i	−0.999701	−	0.0244465i	$-0.992218\pi$
$73$	−8.75032	−	8.75032i	−1.02415	−	1.02415i	−0.0244465	−	0.999701i	$-0.507782\pi$
$74$	5.32429	+	9.22194i	0.618936	+	1.07203i
$75$		0			0
$76$	0.591404	−	0.158466i	0.0678387	−	0.0181773i
$77$	−8.98827	+	8.49422i	−1.02431	+	0.968006i
$78$		0			0
$79$	−4.46495			−0.502346			−0.251173	−	0.967942i	$-0.580816\pi$
$79$	−4.46495			−0.502346			−0.251173	+	0.967942i	$0.580816\pi$
$80$	−0.574115	−	2.14263i	−0.0641880	−	0.239553i
$81$		0			0
$82$	0.591348	+	1.02425i	0.0653035	+	0.113109i
$83$	−5.42187	+	5.42187i	−0.595128	+	0.595128i	−0.939012	−	0.343884i	$-0.888257\pi$
$83$	−5.42187	+	5.42187i	−0.595128	+	0.595128i	0.343884	+	0.939012i	$0.388257\pi$
$84$		0			0
$85$	−11.2219	−	3.00690i	−1.21719	−	0.326145i
$86$	4.57389	−	4.57389i	0.493215	−	0.493215i
$87$		0			0
$88$	9.45905	+	5.46119i	1.00834	+	0.582164i
$89$	15.0461	−	4.03159i	1.59488	−	0.427347i	0.651390	−	0.758743i	$-0.274186\pi$
$89$	15.0461	−	4.03159i	1.59488	−	0.427347i	0.943492	+	0.331396i	$0.107520\pi$
$90$		0			0
$91$	9.52308	−	0.557652i	0.998290	−	0.0584578i
$92$	−25.2888			−2.63654
$93$		0			0
$94$	2.55304	+	1.47400i	0.263326	+	0.152031i
$95$	−0.463100	+	0.267371i	−0.0475131	+	0.0274317i
$96$		0			0
$97$	2.84925	+	0.763454i	0.289297	+	0.0775170i	0.400549	−	0.916275i	$-0.368819\pi$
$97$	2.84925	+	0.763454i	0.289297	+	0.0775170i	−0.111252	+	0.993792i	$0.535486\pi$
$98$	−4.91847	+	14.9267i	−0.496841	+	1.50782i
$99$		0			0
$100$	−3.12138	−	5.40639i	−0.312138	−	0.540639i
$101$	0.316767	−	0.548657i	0.0315195	−	0.0545934i	−0.849835	−	0.527048i	$-0.823299\pi$
$101$	0.316767	−	0.548657i	0.0315195	−	0.0545934i	0.881355	+	0.472455i	$0.156632\pi$
$102$		0			0
$103$	−1.95716			−0.192845			−0.0964223	−	0.995341i	$-0.530740\pi$
$103$	−1.95716			−0.192845			−0.0964223	+	0.995341i	$0.530740\pi$
$104$	−2.87742	−	7.91853i	−0.282154	−	0.776475i
$105$		0			0
$106$	−4.23068	+	1.13361i	−0.410920	+	0.110106i
$107$	3.59988	−	6.23517i	0.348013	−	0.602777i	−0.637883	−	0.770133i	$-0.720190\pi$
$107$	3.59988	−	6.23517i	0.348013	−	0.602777i	0.985896	+	0.167357i	$0.0535231\pi$
$108$		0			0
$109$	−2.42207	−	2.42207i	−0.231992	−	0.231992i	0.581531	−	0.813524i	$-0.302454\pi$
$109$	−2.42207	−	2.42207i	−0.231992	−	0.231992i	−0.813524	+	0.581531i	$0.802454\pi$
$110$	−26.9211	−	7.21348i	−2.56682	−	0.687778i
$111$		0			0
$112$	−2.20898	−	0.0624252i	−0.208729	−	0.00589863i
$113$	−0.379755	−	0.657754i	−0.0357243	−	0.0618763i	0.847610	−	0.530619i	$-0.178040\pi$
$113$	−0.379755	−	0.657754i	−0.0357243	−	0.0618763i	−0.883335	+	0.468743i	$0.844707\pi$
$114$		0			0
$115$	21.3342	−	5.71648i	1.98942	−	0.533065i
$116$		−	31.6471i		−	2.93836i
$117$		0			0
$118$		−	15.2744i		−	1.40612i
$119$	−6.06786	+	9.85594i	−0.556239	+	0.903492i
$120$		0			0
$121$	−9.39523	+	5.42434i	−0.854112	+	0.493122i
$122$	−3.91027	+	3.91027i	−0.354019	+	0.354019i
$123$		0			0
$124$	7.52164	−	28.0712i	0.675464	−	2.52086i
$125$	−5.53414	−	5.53414i	−0.494988	−	0.494988i
$126$		0			0
$127$	−1.04032	−	0.600626i	−0.0923131	−	0.0532970i	0.453133	−	0.891443i	$-0.350306\pi$
$127$	−1.04032	−	0.600626i	−0.0923131	−	0.0532970i	−0.545446	+	0.838146i	$0.683640\pi$
$128$	4.18317	+	15.6118i	0.369743	+	1.37990i
$129$		0			0
$130$	12.3218	+	17.6170i	1.08069	+	1.54511i
$131$		−	3.03417i		−	0.265097i	−0.991177	−	0.132548i	$-0.957684\pi$
$131$		−	3.03417i		−	0.265097i	0.991177	−	0.132548i	$-0.0423160\pi$
$132$		0			0
$133$	0.123289	+	0.518266i	0.0106905	+	0.0449393i
$134$	−2.83582	+	1.63726i	−0.244978	+	0.141438i
$135$		0			0
$136$	9.87379	+	2.64567i	0.846671	+	0.226865i
$137$	11.2793	+	3.02227i	0.963654	+	0.258210i	0.706146	−	0.708066i	$-0.250432\pi$
$137$	11.2793	+	3.02227i	0.963654	+	0.258210i	0.257508	+	0.966276i	$0.417099\pi$
$138$		0			0
$139$	−5.80746	+	3.35294i	−0.492582	+	0.284393i	−0.725645	−	0.688069i	$-0.758459\pi$
$139$	−5.80746	+	3.35294i	−0.492582	+	0.284393i	0.233063	+	0.972462i	$0.425125\pi$
$140$	−20.7858	+	4.94470i	−1.75672	+	0.417903i
$141$		0			0
$142$		−	12.4927i		−	1.04837i
$143$	16.5957	+	2.93522i	1.38780	+	0.245455i
$144$		0			0
$145$	7.15376	+	26.6982i	0.594087	+	2.21716i
$146$	−24.0612	−	13.8918i	−1.99132	−	1.14969i
$147$		0			0
$148$	10.1979	+	10.1979i	0.838265	+	0.838265i
$149$	1.23932	−	4.62521i	0.101529	−	0.378912i	−0.896399	−	0.443248i	$-0.853826\pi$
$149$	1.23932	−	4.62521i	0.101529	−	0.378912i	0.997928	+	0.0643356i	$0.0204928\pi$
$150$		0			0
$151$	−7.66300	+	7.66300i	−0.623606	+	0.623606i	−0.946452	−	0.322845i	$-0.895361\pi$
$151$	−7.66300	+	7.66300i	−0.623606	+	0.623606i	0.322845	+	0.946452i	$0.395361\pi$
$152$	0.407466	−	0.235251i	0.0330499	−	0.0190814i
$153$		0			0
$154$	−14.5566	+	23.6441i	−1.17301	+	1.90530i
$155$			25.3817i			2.03870i
$156$		0			0
$157$			8.00601i			0.638949i	0.947595	+	0.319475i	$0.103506\pi$
$157$			8.00601i			0.638949i	−0.947595	+	0.319475i	$0.896494\pi$
$158$	−9.68297	+	2.59455i	−0.770336	+	0.206411i
$159$		0			0
$160$	−8.69584	−	15.0616i	−0.687467	−	1.19073i
$161$	0.621570	−	21.9948i	0.0489865	−	1.73344i
$162$		0			0
$163$	18.3794	+	4.92475i	1.43959	+	0.385736i	0.892389	−	0.451266i	$-0.149028\pi$
$163$	18.3794	+	4.92475i	1.43959	+	0.385736i	0.547199	+	0.837003i	$0.315694\pi$
$164$	1.13264	+	1.13264i	0.0884447	+	0.0884447i
$165$		0			0
$166$	−8.60761	+	14.9088i	−0.668080	+	1.15715i
$167$	10.5127	−	2.81688i	0.813500	−	0.217977i	0.171997	−	0.985097i	$-0.444978\pi$
$167$	10.5127	−	2.81688i	0.813500	−	0.217977i	0.641503	+	0.767121i	$0.278311\pi$
$168$		0			0
$169$	−8.34582	−	9.96731i	−0.641986	−	0.766716i
$170$	−26.0839			−2.00054
$171$		0			0
$172$	4.38032	−	7.58693i	0.333996	−	0.578498i
$173$	4.07283	+	7.05435i	0.309651	+	0.536332i	0.978286	−	0.207259i	$-0.0664543\pi$
$173$	4.07283	+	7.05435i	0.309651	+	0.536332i	−0.668635	+	0.743591i	$0.733121\pi$
$174$		0			0
$175$	4.77890	−	2.58192i	0.361251	−	0.195175i
$176$	−3.77113	−	1.01047i	−0.284260	−	0.0761672i
$177$		0			0
$178$	30.2872	−	17.4863i	2.27012	−	1.31065i
$179$	−10.2340	−	5.90863i	−0.764928	−	0.441631i	0.0661342	−	0.997811i	$-0.478933\pi$
$179$	−10.2340	−	5.90863i	−0.764928	−	0.441631i	−0.831062	+	0.556179i	$0.812267\pi$
$180$		0			0
$181$	10.4995			0.780423			0.390212	−	0.920725i	$-0.372402\pi$
$181$	10.4995			0.780423			0.390212	+	0.920725i	$0.372402\pi$
$182$	20.3283	−	6.74314i	1.50683	−	0.499835i
$183$		0			0
$184$	−18.7712	+	5.02974i	−1.38383	+	0.370797i
$185$	−10.9084	−	6.29797i	−0.802002	−	0.463036i
$186$		0			0
$187$	−14.4588	+	14.4588i	−1.05734	+	1.05734i
$188$	3.85661	+	1.03338i	0.281272	+	0.0753667i
$189$		0			0
$190$	−0.848942	+	0.848942i	−0.0615887	+	0.0615887i
$191$	6.67464	+	11.5608i	0.482960	+	0.836511i	0.999809	−	0.0195655i	$-0.00622830\pi$
$191$	6.67464	+	11.5608i	0.482960	+	0.836511i	−0.516849	+	0.856077i	$0.672895\pi$
$192$		0			0
$193$	−2.08783	−	7.79189i	−0.150285	−	0.560872i	−0.999463	−	0.0327652i	$-0.989569\pi$
$193$	−2.08783	−	7.79189i	−0.150285	−	0.560872i	0.849178	−	0.528107i	$-0.177098\pi$
$194$	6.62270			0.475482
$195$		0			0
$196$	−1.20208	+	21.2514i	−0.0858631	+	1.51796i
$197$	12.2629	−	3.28585i	0.873699	−	0.234107i	0.206012	−	0.978549i	$-0.433951\pi$
$197$	12.2629	−	3.28585i	0.873699	−	0.234107i	0.667686	+	0.744443i	$0.267285\pi$
$198$		0			0
$199$	−10.8366	−	18.7696i	−0.768188	−	1.33054i	−0.938544	−	0.345158i	$-0.887825\pi$
$199$	−10.8366	−	18.7696i	−0.768188	−	1.33054i	0.170356	−	0.985383i	$-0.445508\pi$
$200$	−3.39221	−	3.39221i	−0.239865	−	0.239865i
$201$		0			0
$202$	0.368142	−	1.37392i	0.0259024	−	0.0966689i
$203$	27.5249	+	0.777849i	1.93187	+	0.0545943i
$204$		0			0
$205$	−1.21155	−	0.699491i	−0.0846186	−	0.0488546i
$206$	−4.24442	+	1.13729i	−0.295723	+	0.0792387i
$207$		0			0
$208$	1.72605	+	2.46780i	0.119680	+	0.171111i
$209$			0.941173i			0.0651023i
$210$		0			0
$211$	6.50914	−	11.2742i	0.448108	−	0.776145i	−0.550155	−	0.835062i	$-0.685431\pi$
$211$	6.50914	−	11.2742i	0.448108	−	0.776145i	0.998263	+	0.0589170i	$0.0187647\pi$
$212$	−5.13727	+	2.96601i	−0.352829	+	0.203706i
$213$		0			0
$214$	4.18372	−	15.6138i	0.285993	−	1.06734i
$215$	−1.98032	+	7.39066i	−0.135057	+	0.504039i
$216$		0			0
$217$	24.2299	+	7.23187i	1.64483	+	0.490931i
$218$	−6.66011	−	3.84521i	−0.451079	−	0.260431i
$219$		0			0
$220$	−37.7471			−2.54491
$221$	15.7135	−	1.36647i	1.05700	−	0.0919186i
$222$		0			0
$223$	−4.38178	−	16.3530i	−0.293426	−	1.09508i	−0.942460	−	0.334320i	$-0.891493\pi$
$223$	−4.38178	−	16.3530i	−0.293426	−	1.09508i	0.649034	−	0.760759i	$-0.275173\pi$
$224$	−16.8558	+	4.00980i	−1.12623	+	0.267916i
$225$		0			0
$226$	−1.20578	−	1.20578i	−0.0802070	−	0.0802070i
$227$	−18.2910	−	4.90106i	−1.21402	−	0.325295i	−0.405679	−	0.914015i	$-0.632965\pi$
$227$	−18.2910	−	4.90106i	−1.21402	−	0.325295i	−0.808336	+	0.588721i	$0.799632\pi$
$228$		0			0
$229$	0.181433	+	0.181433i	0.0119894	+	0.0119894i	0.713076	−	0.701087i	$-0.247301\pi$
$229$	0.181433	+	0.181433i	0.0119894	+	0.0119894i	−0.701087	+	0.713076i	$0.747301\pi$
$230$	42.9449	−	24.7943i	2.83170	−	1.63488i
$231$		0			0
$232$	−6.29435	−	23.4909i	−0.413245	−	1.54225i
$233$		−	11.3848i		−	0.745842i	−0.927863	−	0.372921i	$-0.878356\pi$
$233$		−	11.3848i		−	0.745842i	0.927863	−	0.372921i	$-0.121644\pi$
$234$		0			0
$235$	−3.48711			−0.227474
$236$	−5.35421	−	19.9822i	−0.348529	−	1.30073i
$237$		0			0
$238$	−7.43194	+	24.9002i	−0.481741	+	1.61404i
$239$	12.2181	+	12.2181i	0.790322	+	0.790322i	0.981546	−	0.191224i	$-0.0612458\pi$
$239$	12.2181	+	12.2181i	0.790322	+	0.790322i	−0.191224	+	0.981546i	$0.561246\pi$
$240$		0			0
$241$	−7.89185	+	29.4528i	−0.508359	+	1.89722i	−0.0721047	+	0.997397i	$0.522972\pi$
$241$	−7.89185	+	29.4528i	−0.508359	+	1.89722i	−0.436254	+	0.899824i	$0.643695\pi$
$242$	−17.2231	+	17.2231i	−1.10714	+	1.10714i
$243$		0			0
$244$	−3.74479	+	6.48616i	−0.239735	+	0.415234i
$245$	−3.78973	−	18.1999i	−0.242117	−	1.16275i
$246$		0			0
$247$	0.466946	−	0.555894i	0.0297111	−	0.0353707i
$248$		−	22.3325i		−	1.41811i
$249$		0			0
$250$	−15.2175	−	8.78584i	−0.962441	−	0.555666i
$251$	−5.46171	−	9.45996i	−0.344740	−	0.597107i	0.640566	−	0.767903i	$-0.278700\pi$
$251$	−5.46171	−	9.45996i	−0.344740	−	0.597107i	−0.985307	+	0.170795i	$0.945366\pi$
$252$		0			0
$253$	10.0613	−	37.5493i	0.632548	−	2.36070i
$254$	−2.60511	−	0.698038i	−0.163459	−	0.0437988i
$255$		0			0
$256$	5.11138	+	8.85317i	0.319461	+	0.553323i
$257$	−14.2035	+	24.6012i	−0.885991	+	1.53458i	−0.0414174	+	0.999142i	$0.513187\pi$
$257$	−14.2035	+	24.6012i	−0.885991	+	1.53458i	−0.844574	+	0.535439i	$0.820146\pi$
$258$		0			0
$259$	−9.12025	+	8.61895i	−0.566705	+	0.535555i
$260$	22.2949	+	18.7276i	1.38267	+	1.16143i
$261$		0			0
$262$	−1.76313	−	6.58009i	−0.108927	−	0.406520i
$263$	−10.8579	+	18.8064i	−0.669526	+	1.15965i	0.308510	+	0.951221i	$0.400170\pi$
$263$	−10.8579	+	18.8064i	−0.669526	+	1.15965i	−0.978037	+	0.208433i	$0.933164\pi$
$264$		0			0
$265$	3.66345	−	3.66345i	0.225044	−	0.225044i
$266$	0.568533	+	1.05230i	0.0348590	+	0.0645208i
$267$		0			0
$268$	−3.13595	+	3.13595i	−0.191559	+	0.191559i
$269$	10.7149	−	6.18625i	0.653298	−	0.377182i	−0.136420	−	0.990651i	$-0.543560\pi$
$269$	10.7149	−	6.18625i	0.653298	−	0.377182i	0.789719	+	0.613469i	$0.210226\pi$
$270$		0			0
$271$	7.64449	−	2.04834i	0.464370	−	0.124427i	−0.0190456	−	0.999819i	$-0.506063\pi$
$271$	7.64449	−	2.04834i	0.464370	−	0.124427i	0.483415	+	0.875391i	$0.339396\pi$
$272$	−3.65385			−0.221547
$273$		0			0
$274$	26.2172			1.58384
$275$	9.26935	−	2.48371i	0.558963	−	0.149774i
$276$		0			0
$277$	9.70888	−	5.60543i	0.583350	−	0.336797i	−0.179113	−	0.983828i	$-0.557323\pi$
$277$	9.70888	−	5.60543i	0.583350	−	0.336797i	0.762464	+	0.647031i	$0.223990\pi$
$278$	−10.6461	+	10.6461i	−0.638509	+	0.638509i
$279$		0			0
$280$	−14.4453	+	7.80445i	−0.863272	+	0.466405i
$281$	15.1948	−	15.1948i	0.906448	−	0.906448i	−0.0895355	−	0.995984i	$-0.528538\pi$
$281$	15.1948	−	15.1948i	0.906448	−	0.906448i	0.995984	+	0.0895355i	$0.0285383\pi$
$282$		0			0
$283$	−7.64747	+	13.2458i	−0.454595	+	0.787382i	−0.998665	−	0.0516583i	$-0.983549\pi$
$283$	−7.64747	+	13.2458i	−0.454595	+	0.787382i	0.544070	+	0.839040i	$0.316883\pi$
$284$	−4.37914	−	16.3432i	−0.259854	−	0.969789i
$285$		0			0
$286$	37.6961	−	3.27812i	2.22902	−	0.193839i
$287$	−1.01295	+	0.957272i	−0.0597926	+	0.0565060i
$288$		0			0
$289$	−1.06845	+	1.85062i	−0.0628502	+	0.108860i
$290$	31.0282	+	53.7424i	1.82204	+	3.15586i
$291$		0			0
$292$	−36.3468	−	9.73911i	−2.12704	−	0.569938i
$293$	5.44000	−	20.3023i	0.317808	−	1.18608i	−0.603539	−	0.797334i	$-0.706243\pi$
$293$	5.44000	−	20.3023i	0.317808	−	1.18608i	0.921347	−	0.388742i	$-0.127090\pi$
$294$		0			0
$295$	9.03385	+	15.6471i	0.525971	+	0.911009i
$296$	9.59795	+	5.54138i	0.557869	+	0.322086i
$297$		0			0
$298$		−	10.7507i		−	0.622771i
$299$	−24.5720	+	17.1863i	−1.42103	+	0.993912i
$300$		0			0
$301$	6.49103	+	3.99624i	0.374137	+	0.230339i
$302$	−12.1656	+	21.0714i	−0.700050	+	1.21252i
$303$		0			0
$304$	−0.118921	+	0.118921i	−0.00682057	+	0.00682057i
$305$	1.69300	−	6.31836i	0.0969409	−	0.361788i
$306$		0			0
$307$	12.7905	+	12.7905i	0.729995	+	0.729995i	0.970618	−	0.240624i	$-0.0773520\pi$
$307$	12.7905	+	12.7905i	0.729995	+	0.729995i	−0.240624	+	0.970618i	$0.577352\pi$
$308$	−10.7551	+	36.0342i	−0.612828	+	2.05324i
$309$		0			0
$310$	14.7491	+	55.0443i	0.837692	+	3.12631i
$311$	−19.5517			−1.10868			−0.554338	−	0.832292i	$-0.687028\pi$
$311$	−19.5517			−1.10868			−0.554338	+	0.832292i	$0.687028\pi$
$312$		0			0
$313$			13.2495i			0.748904i	0.927246	+	0.374452i	$0.122169\pi$
$313$			13.2495i			0.748904i	−0.927246	+	0.374452i	$0.877831\pi$
$314$	4.65223	+	17.3624i	0.262540	+	0.979814i
$315$		0			0
$316$	−11.7579	+	6.78845i	−0.661435	+	0.381880i
$317$	−17.8861	−	17.8861i	−1.00458	−	1.00458i	−0.999989	−	0.00459262i	$-0.998538\pi$
$317$	−17.8861	−	17.8861i	−1.00458	−	1.00458i	−0.00459262	−	0.999989i	$-0.501462\pi$
$318$		0			0
$319$	46.9902	+	12.5910i	2.63094	+	0.704959i
$320$	−24.4735	−	24.4735i	−1.36811	−	1.36811i
$321$		0			0
$322$	−11.4330	−	48.0606i	−0.637139	−	2.67831i
$323$	0.227976	+	0.850818i	0.0126849	+	0.0473408i
$324$		0			0
$325$	−6.70709	−	3.13184i	−0.372043	−	0.173723i
$326$	42.7206			2.36607
$327$		0			0
$328$	1.06601	+	0.615459i	0.0588603	+	0.0339830i
$329$	−0.993565	+	3.32887i	−0.0547770	+	0.183527i
$330$		0			0
$331$	−3.51837	+	13.1307i	−0.193387	+	0.721731i	0.799291	+	0.600944i	$0.205208\pi$
$331$	−3.51837	+	13.1307i	−0.193387	+	0.721731i	−0.992678	+	0.120787i	$0.961458\pi$
$332$	−6.03454	+	22.5212i	−0.331189	+	1.23601i
$333$		0			0
$334$	21.1617	−	12.2177i	1.15792	−	0.668524i
$335$	1.93668	−	3.35443i	0.105812	−	0.183272i
$336$		0			0
$337$		−	1.75678i		−	0.0956980i	−0.998855	−	0.0478490i	$-0.984763\pi$
$337$		−	1.75678i		−	0.0956980i	0.998855	−	0.0478490i	$-0.0152366\pi$
$338$	−23.8912	−	16.7661i	−1.29951	−	0.911954i
$339$		0			0
$340$	−34.1233	+	9.14331i	−1.85060	+	0.495866i
$341$	38.6880	+	22.3365i	2.09507	+	1.20959i
$342$		0			0
$343$	−18.4538	−	1.56784i	−0.996410	−	0.0846554i
$344$	1.74242	−	6.50279i	0.0939449	−	0.350607i
$345$		0			0
$346$	12.9318	+	12.9318i	0.695219	+	0.695219i
$347$	−5.43920	−	9.42098i	−0.291992	−	0.505744i	0.682289	−	0.731083i	$-0.260985\pi$
$347$	−5.43920	−	9.42098i	−0.291992	−	0.505744i	−0.974281	+	0.225338i	$0.927651\pi$
$348$		0			0
$349$	11.9450	−	3.20064i	0.639399	−	0.171326i	0.0754676	−	0.997148i	$-0.475955\pi$
$349$	11.9450	−	3.20064i	0.639399	−	0.171326i	0.563931	+	0.825822i	$0.309288\pi$
$350$	8.86349	−	8.37630i	0.473774	−	0.447732i
$351$		0			0
$352$	−30.6102			−1.63153
$353$	4.55715	+	17.0075i	0.242552	+	0.905218i	0.974598	+	0.223962i	$0.0718992\pi$
$353$	4.55715	+	17.0075i	0.242552	+	0.905218i	−0.732045	+	0.681256i	$0.761434\pi$
$354$		0			0
$355$	7.38867	+	12.7975i	0.392150	+	0.679223i
$356$	33.4926	−	33.4926i	1.77510	−	1.77510i
$357$		0			0
$358$	−25.6277	−	6.86691i	−1.35446	−	0.362927i
$359$	−11.4993	+	11.4993i	−0.606911	+	0.606911i	−0.942137	−	0.335227i	$-0.891187\pi$
$359$	−11.4993	+	11.4993i	−0.606911	+	0.606911i	0.335227	+	0.942137i	$0.391187\pi$
$360$		0			0
$361$	−16.4194	−	9.47973i	−0.864177	−	0.498933i
$362$	22.7699	−	6.10119i	1.19676	−	0.320671i
$363$		0			0
$364$	24.2301	−	15.9473i	1.27000	−	0.835864i
$365$	32.8645			1.72020
$366$		0			0
$367$	11.3884	+	6.57510i	0.594470	+	0.343217i	0.766863	−	0.641811i	$-0.221817\pi$
$367$	11.3884	+	6.57510i	0.594470	+	0.343217i	−0.172393	+	0.985028i	$0.555150\pi$
$368$	6.01577	−	3.47320i	0.313594	−	0.181053i
$369$		0			0
$370$	−27.3164	−	7.31940i	−1.42011	−	0.380518i
$371$	−2.45340	−	4.54102i	−0.127374	−	0.235758i
$372$		0			0
$373$	4.81532	+	8.34037i	0.249328	+	0.431848i	0.963339	−	0.268286i	$-0.0864571\pi$
$373$	4.81532	+	8.34037i	0.249328	+	0.431848i	−0.714012	+	0.700134i	$0.753124\pi$
$374$	−22.9545	+	39.7583i	−1.18695	+	2.05585i
$375$		0			0
$376$	3.06819			0.158230
$377$	−21.5075	−	30.7500i	−1.10769	−	1.58371i
$378$		0			0
$379$	−32.1516	+	8.61500i	−1.65152	+	0.442523i	−0.960037	−	0.279872i	$-0.909708\pi$
$379$	−32.1516	+	8.61500i	−1.65152	+	0.442523i	−0.691481	+	0.722395i	$0.743041\pi$
$380$	−0.813014	+	1.40818i	−0.0417068	+	0.0722382i
$381$		0			0
$382$	21.1930	+	21.1930i	1.08433	+	1.08433i
$383$	−3.73221	−	1.00004i	−0.190707	−	0.0510998i	0.162201	−	0.986758i	$-0.448141\pi$
$383$	−3.73221	−	1.00004i	−0.190707	−	0.0510998i	−0.352908	+	0.935658i	$0.614807\pi$
$384$		0			0
$385$	0.927780	−	32.8304i	0.0472840	−	1.67319i
$386$	−9.05560	−	15.6848i	−0.460918	−	0.798334i
$387$		0			0
$388$	8.66392	−	2.32149i	0.439844	−	0.117856i
$389$		−	12.5816i		−	0.637911i	−0.947770	−	0.318955i	$-0.896668\pi$
$389$		−	12.5816i		−	0.637911i	0.947770	−	0.318955i	$-0.103332\pi$
$390$		0			0
$391$		−	36.3815i		−	1.83989i
$392$	3.33446	+	16.0135i	0.168416	+	0.808802i
$393$		0			0
$394$	24.6848	−	14.2518i	1.24360	−	0.717995i
$395$	8.38473	−	8.38473i	0.421881	−	0.421881i
$396$		0			0
$397$	6.87160	−	25.6452i	0.344876	−	1.28709i	−0.547882	−	0.836556i	$-0.684566\pi$
$397$	6.87160	−	25.6452i	0.344876	−	1.28709i	0.892757	−	0.450538i	$-0.148768\pi$
$398$	−34.4079	−	34.4079i	−1.72471	−	1.72471i
$399$		0			0
$400$	1.48504	+	0.857390i	0.0742521	+	0.0428695i
$401$	3.89519	+	14.5370i	0.194517	+	0.725946i	0.992391	+	0.123123i	$0.0392908\pi$
$401$	3.89519	+	14.5370i	0.194517	+	0.725946i	−0.797875	+	0.602823i	$0.794043\pi$
$402$		0			0
$403$	−11.7688	−	32.3872i	−0.586245	−	1.61332i
$404$		−	1.92643i		−	0.0958437i
$405$		0			0
$406$	60.1443	−	14.3076i	2.98491	−	0.710075i
$407$	−19.1994	+	11.0848i	−0.951676	+	0.549451i
$408$		0			0
$409$	−23.9970	−	6.42996i	−1.18657	−	0.317941i	−0.389042	−	0.921220i	$-0.627194\pi$
$409$	−23.9970	−	6.42996i	−1.18657	−	0.317941i	−0.797531	+	0.603279i	$0.793861\pi$
$410$	−3.03392	−	0.812937i	−0.149835	−	0.0401481i
$411$		0			0
$412$	−5.15395	+	2.97564i	−0.253917	+	0.146599i
$413$	17.5110	−	4.16566i	0.861660	−	0.204979i
$414$		0			0
$415$		−	20.3635i		−	0.999603i
$416$	18.0796	+	15.1867i	0.886426	+	0.744590i
$417$		0			0
$418$	0.546908	+	2.04109i	0.0267501	+	0.0998329i
$419$	15.5289	+	8.96562i	0.758637	+	0.437999i	0.828806	−	0.559536i	$-0.189021\pi$
$419$	15.5289	+	8.96562i	0.758637	+	0.437999i	−0.0701691	+	0.997535i	$0.522354\pi$
$420$		0			0
$421$	0.833811	+	0.833811i	0.0406375	+	0.0406375i	0.727134	−	0.686496i	$-0.240852\pi$
$421$	0.833811	+	0.833811i	0.0406375	+	0.0406375i	−0.686496	+	0.727134i	$0.740852\pi$
$422$	7.56482	−	28.2323i	0.368250	−	1.37433i
$423$		0			0
$424$	−3.22335	+	3.22335i	−0.156540	+	0.156540i
$425$	7.77785	−	4.49054i	0.377281	−	0.217823i
$426$		0			0
$427$	−5.54926	−	3.41643i	−0.268547	−	0.165333i
$428$		−	21.8928i		−	1.05823i
$429$		0			0
$430$			17.1786i			0.828426i
$431$	−13.4572	+	3.60584i	−0.648209	+	0.173687i	−0.567919	−	0.823085i	$-0.692251\pi$
$431$	−13.4572	+	3.60584i	−0.648209	+	0.173687i	−0.0802899	+	0.996772i	$0.525585\pi$
$432$		0			0
$433$	0.380141	+	0.658423i	0.0182684	+	0.0316418i	0.875015	−	0.484096i	$-0.160851\pi$
$433$	0.380141	+	0.658423i	0.0182684	+	0.0316418i	−0.856747	+	0.515737i	$0.827518\pi$
$434$	56.7488	+	1.60371i	2.72403	+	0.0769806i
$435$		0			0
$436$	−10.0607	−	2.69577i	−0.481822	−	0.129104i
$437$	−1.18410	−	1.18410i	−0.0566430	−	0.0566430i
$438$		0			0
$439$	−15.9560	+	27.6366i	−0.761539	+	1.31902i	0.180518	+	0.983572i	$0.442223\pi$
$439$	−15.9560	+	27.6366i	−0.761539	+	1.31902i	−0.942057	+	0.335453i	$0.891111\pi$
$440$	−28.0187	+	7.50759i	−1.33574	+	0.357910i
$441$		0			0
$442$	33.2832	−	12.0944i	1.58312	−	0.575270i
$443$	−13.9082			−0.660799			−0.330399	−	0.943841i	$-0.607183\pi$
$443$	−13.9082			−0.660799			−0.330399	+	0.943841i	$0.607183\pi$
$444$		0			0
$445$	−20.6841	+	35.8260i	−0.980522	+	1.69831i
$446$	−19.0052	−	32.9180i	−0.899923	−	1.55871i
$447$		0			0
$448$	−30.3361	+	16.3898i	−1.43324	+	0.774347i
$449$	−37.3413	−	10.0056i	−1.76224	−	0.472192i	−0.775075	−	0.631869i	$-0.782288\pi$
$449$	−37.3413	−	10.0056i	−1.76224	−	0.472192i	−0.987169	+	0.159677i	$0.948955\pi$
$450$		0			0
$451$	−2.13240	+	1.23114i	−0.100411	+	0.0579721i
$452$	−2.00008	−	1.15475i	−0.0940759	−	0.0543148i
$453$		0			0
$454$	−42.5150			−1.99533
$455$	−16.8362	+	18.9306i	−0.789292	+	0.887481i
$456$		0			0
$457$	−11.2913	+	3.02549i	−0.528183	+	0.141526i	−0.513049	−	0.858359i	$-0.671484\pi$
$457$	−11.2913	+	3.02549i	−0.528183	+	0.141526i	−0.0151341	+	0.999885i	$0.504818\pi$
$458$	0.498897	+	0.288038i	0.0233119	+	0.0134591i
$459$		0			0
$460$	47.4899	−	47.4899i	2.21423	−	2.21423i
$461$	33.0727	+	8.86180i	1.54035	+	0.412735i	0.926379	−	0.376594i	$-0.122905\pi$
$461$	33.0727	+	8.86180i	1.54035	+	0.412735i	0.613971	+	0.789329i	$0.289571\pi$
$462$		0			0
$463$	−18.1263	+	18.1263i	−0.842399	+	0.842399i	−0.989170	−	0.146772i	$-0.953112\pi$
$463$	−18.1263	+	18.1263i	−0.842399	+	0.842399i	0.146772	+	0.989170i	$0.453112\pi$
$464$	4.34646	+	7.52830i	0.201780	+	0.349492i
$465$		0			0
$466$	−6.61561	−	24.6898i	−0.306462	−	1.14373i
$467$	−20.4427			−0.945975			−0.472988	−	0.881069i	$-0.656824\pi$
$467$	−20.4427			−0.945975			−0.472988	+	0.881069i	$0.656824\pi$
$468$		0			0
$469$	−2.65040	−	2.80455i	−0.122384	−	0.129502i
$470$	−7.56238	+	2.02633i	−0.348826	+	0.0934678i
$471$		0			0
$472$	−7.94858	−	13.7673i	−0.365863	−	0.633694i
$473$	9.52246	+	9.52246i	0.437843	+	0.437843i
$474$		0			0
$475$	0.106991	−	0.399295i	0.00490907	−	0.0183209i
$476$	−0.994179	+	35.1800i	−0.0455681	+	1.61247i
$477$		0			0
$478$	33.5967	+	19.3971i	1.53668	+	0.887202i
$479$	−11.4241	+	3.06108i	−0.521980	+	0.139864i	−0.510182	−	0.860066i	$-0.670422\pi$
$479$	−11.4241	+	3.06108i	−0.521980	+	0.139864i	−0.0117979	+	0.999930i	$0.503755\pi$
$480$		0			0
$481$	16.8394	+	2.97832i	0.767810	+	0.135800i
$482$			68.4591i			3.11823i
$483$		0			0
$484$	−16.4942	+	28.5688i	−0.749736	+	1.29858i
$485$	−6.78430	+	3.91692i	−0.308059	+	0.177858i
$486$		0			0
$487$	0.0483236	−	0.180346i	0.00218975	−	0.00817226i	−0.964822	−	0.262903i	$-0.915320\pi$
$487$	0.0483236	−	0.180346i	0.00218975	−	0.00817226i	0.967012	+	0.254731i	$0.0819868\pi$
$488$	−1.48961	+	5.55931i	−0.0674316	+	0.251658i
$489$		0			0
$490$	−18.7945	−	37.2673i	−0.849047	−	1.68356i
$491$	2.43785	+	1.40749i	0.110019	+	0.0635193i	0.554000	−	0.832517i	$-0.313101\pi$
$491$	2.43785	+	1.40749i	0.110019	+	0.0635193i	−0.443981	+	0.896036i	$0.646434\pi$
$492$		0			0
$493$	45.5288			2.05052
$494$	0.689624	−	1.47689i	0.0310276	−	0.0664482i
$495$		0			0
$496$	2.06607	+	7.71067i	0.0927691	+	0.346219i
$497$	14.3220	−	3.40704i	0.642430	−	0.152826i
$498$		0			0
$499$	1.80207	+	1.80207i	0.0806719	+	0.0806719i	0.746291	−	0.665619i	$-0.231833\pi$
$499$	1.80207	+	1.80207i	0.0806719	+	0.0806719i	−0.665619	+	0.746291i	$0.731833\pi$
$500$	−22.9875	−	6.15949i	−1.02803	−	0.275461i
$501$		0			0
$502$	−17.3417	−	17.3417i	−0.773999	−	0.773999i
$503$	6.33177	−	3.65565i	0.282320	−	0.162997i	−0.352153	−	0.935942i	$-0.614550\pi$
$503$	6.33177	−	3.65565i	0.282320	−	0.162997i	0.634473	+	0.772945i	$0.281217\pi$
$504$		0			0
$505$	0.435466	+	1.62518i	0.0193780	+	0.0723196i
$506$		−	87.2783i		−	3.87999i
$507$		0			0
$508$	−3.65274			−0.162064
$509$	6.75398	+	25.2062i	0.299365	+	1.11724i	0.937689	+	0.347477i	$0.112961\pi$
$509$	6.75398	+	25.2062i	0.299365	+	1.11724i	−0.638324	+	0.769768i	$0.720372\pi$
$510$		0			0
$511$	9.36390	−	31.3731i	0.414234	−	1.38786i
$512$	−6.62788	−	6.62788i	−0.292914	−	0.292914i
$513$		0			0
$514$	−16.5071	+	61.6053i	−0.728097	+	2.71729i
$515$	3.67535	−	3.67535i	0.161955	−	0.161955i
$516$		0			0
$517$	−3.06875	+	5.31523i	−0.134963	+	0.233763i
$518$	−14.7704	+	23.9913i	−0.648973	+	1.05412i
$519$		0			0
$520$	20.2737	+	9.46670i	0.889061	+	0.415142i
$521$			5.50223i			0.241057i	0.992710	+	0.120529i	$0.0384589\pi$
$521$			5.50223i			0.241057i	−0.992710	+	0.120529i	$0.961541\pi$
$522$		0			0
$523$	35.0507	+	20.2365i	1.53266	+	0.884882i	0.999238	+	0.0390336i	$0.0124279\pi$
$523$	35.0507	+	20.2365i	1.53266	+	0.884882i	0.533423	+	0.845849i	$0.320905\pi$
$524$	−4.61311	−	7.99014i	−0.201525	−	0.349051i
$525$		0			0
$526$	−12.6189	+	47.0943i	−0.550209	+	2.05341i
$527$	40.3843	+	10.8209i	1.75917	+	0.471367i
$528$		0			0
$529$	23.0828	+	39.9806i	1.00360	+	1.73829i
$530$	5.81600	−	10.0736i	0.252631	−	0.437569i
$531$		0			0
$532$	1.11263	+	1.17735i	0.0482387	+	0.0510444i
$533$	1.87028	+	0.330790i	0.0810110	+	0.0143281i
$534$		0			0
$535$	4.94882	+	18.4692i	0.213956	+	0.798495i
$536$	−1.70402	+	2.95145i	−0.0736024	+	0.127483i
$537$		0			0
$538$	19.6422	−	19.6422i	0.846836	−	0.846836i
$539$	−31.0762	−	10.2399i	−1.33855	−	0.441062i
$540$		0			0
$541$	25.7367	−	25.7367i	1.10651	−	1.10651i	0.112900	−	0.993606i	$-0.463986\pi$
$541$	25.7367	−	25.7367i	1.10651	−	1.10651i	0.993606	−	0.112900i	$-0.0360139\pi$
$542$	15.3881	−	8.88430i	0.660974	−	0.381613i
$543$		0			0
$544$	−27.6716	+	7.41457i	−1.18641	+	0.317897i
$545$	9.09682			0.389665
$546$		0			0
$547$	31.3852			1.34193			0.670967	−	0.741487i	$-0.265879\pi$
$547$	31.3852			1.34193			0.670967	+	0.741487i	$0.265879\pi$
$548$	34.2977	−	9.19005i	1.46513	−	0.392579i
$549$		0			0
$550$	18.6588	−	10.7727i	0.795616	−	0.459349i
$551$	1.48181	−	1.48181i	0.0631272	−	0.0631272i
$552$		0			0
$553$	−5.61522	−	10.3933i	−0.238783	−	0.441966i
$554$	17.7980	−	17.7980i	0.756166	−	0.756166i
$555$		0			0
$556$	−10.1955	+	17.6592i	−0.432387	+	0.748916i
$557$	0.169733	+	0.633453i	0.00719183	+	0.0268403i	0.969429	−	0.245374i	$-0.0789107\pi$
$557$	0.169733	+	0.633453i	0.00719183	+	0.0268403i	−0.962237	+	0.272214i	$0.912244\pi$
$558$		0			0
$559$	−0.899944	−	10.3487i	−0.0380636	−	0.437705i
$560$	4.26547	−	4.03101i	0.180249	−	0.170341i
$561$		0			0
$562$	24.1229	−	41.7821i	1.01756	−	1.76247i
$563$	−12.5830	−	21.7944i	−0.530309	−	0.918523i	−0.999375	−	0.0353593i	$-0.988742\pi$
$563$	−12.5830	−	21.7944i	−0.530309	−	0.918523i	0.469065	−	0.883164i	$-0.344591\pi$
$564$		0			0
$565$	1.94834	+	0.522056i	0.0819672	+	0.0219630i
$566$	−8.88777	+	33.1696i	−0.373581	+	1.39422i
$567$		0			0
$568$	−6.50104	−	11.2601i	−0.272778	−	0.472465i
$569$	3.46005	+	1.99766i	0.145053	+	0.0837463i	0.570770	−	0.821110i	$-0.306645\pi$
$569$	3.46005	+	1.99766i	0.145053	+	0.0837463i	−0.425717	+	0.904856i	$0.639978\pi$
$570$		0			0
$571$		−	17.9370i		−	0.750640i	−0.926895	−	0.375320i	$-0.877533\pi$
$571$		−	17.9370i		−	0.750640i	0.926895	−	0.375320i	$-0.122467\pi$
$572$	48.1656	−	17.5023i	2.01390	−	0.731808i
$573$		0			0
$574$	−1.64049	+	2.66462i	−0.0684726	+	0.111219i
$575$	−8.53705	+	14.7866i	−0.356020	+	0.616644i
$576$		0			0
$577$	−29.6210	+	29.6210i	−1.23314	+	1.23314i	−0.270389	+	0.962751i	$0.587152\pi$
$577$	−29.6210	+	29.6210i	−1.23314	+	1.23314i	−0.962751	+	0.270389i	$0.912848\pi$
$578$	−1.24174	+	4.63424i	−0.0516496	+	0.192759i
$579$		0			0
$580$	59.4302	+	59.4302i	2.46770	+	2.46770i
$581$	−19.4394	−	5.80206i	−0.806482	−	0.240710i
$582$		0			0
$583$	−2.36008	−	8.80794i	−0.0977446	−	0.364788i
$584$	−28.9163			−1.19657
$585$		0			0
$586$		−	47.1901i		−	1.94941i
$587$	−0.571868	−	2.13424i	−0.0236035	−	0.0880895i	0.953119	−	0.302595i	$-0.0978528\pi$
$587$	−0.571868	−	2.13424i	−0.0236035	−	0.0880895i	−0.976723	+	0.214505i	$0.931186\pi$
$588$		0			0
$589$	1.66656	−	0.962187i	0.0686693	−	0.0396462i
$590$	28.6838	+	28.6838i	1.18089	+	1.18089i
$591$		0			0
$592$	−3.82651	−	1.02531i	−0.157268	−	0.0421400i
$593$	1.48928	+	1.48928i	0.0611573	+	0.0611573i	0.737024	−	0.675867i	$-0.236230\pi$
$593$	1.48928	+	1.48928i	0.0611573	+	0.0611573i	−0.675867	+	0.737024i	$0.736230\pi$
$594$		0			0
$595$	−7.11364	−	29.9033i	−0.291631	−	1.22592i
$596$	−3.76850	−	14.0642i	−0.154364	−	0.576093i
$597$		0			0
$598$	−43.3015	+	51.5500i	−1.77073	+	2.10804i
$599$	−13.9002			−0.567945			−0.283973	−	0.958832i	$-0.591653\pi$
$599$	−13.9002			−0.567945			−0.283973	+	0.958832i	$0.591653\pi$
$600$		0			0
$601$	8.59776	+	4.96392i	0.350710	+	0.202482i	0.664998	−	0.746845i	$-0.268432\pi$
$601$	8.59776	+	4.96392i	0.350710	+	0.202482i	−0.314288	+	0.949328i	$0.601766\pi$
$602$	16.3991	+	4.89461i	0.668375	+	0.199489i
$603$		0			0
$604$	−8.52892	+	31.8304i	−0.347037	+	1.29516i
$605$	7.45694	−	27.8297i	0.303168	−	1.13144i
$606$		0			0
$607$	−26.6015	+	15.3584i	−1.07972	+	0.623378i	−0.930821	−	0.365475i	$-0.880907\pi$
$607$	−26.6015	+	15.3584i	−1.07972	+	0.623378i	−0.148900	+	0.988852i	$0.547573\pi$
$608$	−0.659297	+	1.14194i	−0.0267380	+	0.0463116i
$609$		0			0
$610$		−	14.6862i		−	0.594626i
$611$	4.44958	−	1.61688i	0.180011	−	0.0654119i
$612$		0			0
$613$	9.42794	−	2.52621i	0.380791	−	0.102033i	−0.0633459	−	0.997992i	$-0.520177\pi$
$613$	9.42794	−	2.52621i	0.380791	−	0.102033i	0.444137	+	0.895959i	$0.353510\pi$
$614$	35.1709	+	20.3059i	1.41938	+	0.819480i
$615$		0			0
$616$	−0.816322	+	28.8863i	−0.0328906	+	1.16386i
$617$	−6.69956	+	25.0031i	−0.269714	+	1.00659i	0.689587	+	0.724203i	$0.257792\pi$
$617$	−6.69956	+	25.0031i	−0.269714	+	1.00659i	−0.959301	+	0.282384i	$0.908875\pi$
$618$		0			0
$619$	−25.5525	−	25.5525i	−1.02704	−	1.02704i	−0.999624	−	0.0274172i	$-0.991272\pi$
$619$	−25.5525	−	25.5525i	−1.02704	−	1.02704i	−0.0274172	−	0.999624i	$-0.508728\pi$
$620$	38.5899	+	66.8397i	1.54981	+	2.68435i
$621$		0			0
$622$	−42.4011	+	11.3613i	−1.70013	+	0.455548i
$623$	28.3068	+	29.9532i	1.13409	+	1.20005i
$624$		0			0
$625$	31.0502			1.24201
$626$	7.69915	+	28.7336i	0.307720	+	1.14843i
$627$		0			0
$628$	12.1722	+	21.0829i	0.485725	+	0.841300i
$629$	−14.6712	+	14.6712i	−0.584977	+	0.584977i
$630$		0			0
$631$	9.92759	+	2.66009i	0.395211	+	0.105897i	0.450951	−	0.892549i	$-0.351085\pi$
$631$	9.92759	+	2.66009i	0.395211	+	0.105897i	−0.0557396	+	0.998445i	$0.517752\pi$
$632$	−7.37744	+	7.37744i	−0.293459	+	0.293459i
$633$		0			0
$634$	−49.1823	−	28.3954i	−1.95328	−	1.12773i
$635$	3.08153	−	0.825692i	0.122287	−	0.0327666i
$636$		0			0
$637$	13.2745	+	21.4660i	0.525955	+	0.850512i
$638$	109.222			4.32416
$639$		0			0
$640$	−37.1730	−	21.4618i	−1.46939	−	0.848353i
$641$	26.2509	−	15.1559i	1.03685	−	0.598624i	0.117908	−	0.993025i	$-0.462381\pi$
$641$	26.2509	−	15.1559i	1.03685	−	0.598624i	0.918939	+	0.394401i	$0.129048\pi$
$642$		0			0
$643$	−35.0393	−	9.38876i	−1.38182	−	0.370256i	−0.510035	−	0.860153i	$-0.670368\pi$
$643$	−35.0393	−	9.38876i	−1.38182	−	0.370256i	−0.871780	+	0.489897i	$0.837034\pi$
$644$	−31.8038	−	58.8659i	−1.25325	−	2.31964i
$645$		0			0
$646$	0.988806	+	1.71266i	0.0389041	+	0.0673838i
$647$	−9.62979	+	16.6793i	−0.378586	+	0.655730i	−0.990857	−	0.134918i	$-0.956923\pi$
$647$	−9.62979	+	16.6793i	−0.378586	+	0.655730i	0.612271	+	0.790648i	$0.290256\pi$
$648$		0			0
$649$	31.8001			1.24826
$650$	−16.3653	−	2.89447i	−0.641901	−	0.113531i
$651$		0			0
$652$	55.8877	−	14.9751i	2.18873	−	0.586468i
$653$	0.0312823	−	0.0541825i	0.00122417	−	0.00212033i	−0.865413	−	0.501060i	$-0.832944\pi$
$653$	0.0312823	−	0.0541825i	0.00122417	−	0.00212033i	0.866637	+	0.498939i	$0.166277\pi$
$654$		0			0
$655$	5.69787	+	5.69787i	0.222634	+	0.222634i
$656$	−0.424995	−	0.113877i	−0.0165933	−	0.00444615i
$657$		0			0
$658$	−0.220329	+	7.79655i	−0.00858932	+	0.303941i
$659$	−3.09067	−	5.35320i	−0.120395	−	0.208531i	0.799528	−	0.600628i	$-0.205083\pi$
$659$	−3.09067	−	5.35320i	−0.120395	−	0.208531i	−0.919924	+	0.392098i	$0.871750\pi$
$660$		0			0
$661$	6.90812	−	1.85103i	0.268695	−	0.0719965i	−0.121956	−	0.992536i	$-0.538917\pi$
$661$	6.90812	−	1.85103i	0.268695	−	0.0719965i	0.390651	+	0.920539i	$0.372250\pi$
$662$			30.5207i			1.18622i
$663$		0			0
$664$			17.9171i			0.695320i
$665$	−1.20478	−	0.741726i	−0.0467192	−	0.0287629i
$666$		0			0
$667$	−74.9594	+	43.2778i	−2.90244	+	1.67572i
$668$	23.4013	−	23.4013i	0.905425	−	0.905425i
$669$		0			0
$670$	2.25078	−	8.40001i	0.0869551	−	0.324521i
$671$	−8.14087	−	8.14087i	−0.314275	−	0.314275i
$672$		0			0
$673$	−4.05354	−	2.34031i	−0.156253	−	0.0902125i	0.419835	−	0.907600i	$-0.362088\pi$
$673$	−4.05354	−	2.34031i	−0.156253	−	0.0902125i	−0.576088	+	0.817388i	$0.695421\pi$
$674$	−1.02085	−	3.80987i	−0.0393217	−	0.146751i
$675$		0			0
$676$	−37.1319	−	13.5589i	−1.42815	−	0.521497i
$677$		−	31.1590i		−	1.19754i	−0.800922	−	0.598769i	$-0.795657\pi$
$677$		−	31.1590i		−	1.19754i	0.800922	−	0.598769i	$-0.204343\pi$
$678$		0			0
$679$	1.80615	+	7.59246i	0.0693139	+	0.291372i
$680$	−23.5103	+	13.5737i	−0.901579	+	0.520527i
$681$		0			0
$682$	96.8808	+	25.9591i	3.70976	+	0.994026i
$683$	−41.3109	−	11.0692i	−1.58072	−	0.423552i	−0.641570	−	0.767064i	$-0.721717\pi$
$683$	−41.3109	−	11.0692i	−1.58072	−	0.423552i	−0.939148	+	0.343512i	$0.888383\pi$
$684$		0			0
$685$	−26.8569	+	15.5058i	−1.02615	+	0.592447i
$686$	−40.9311	+	7.32322i	−1.56276	+	0.279602i
$687$		0			0
$688$			2.40640i			0.0917430i
$689$	−2.97595	+	6.37323i	−0.113374	+	0.242801i
$690$		0			0
$691$	−4.65384	−	17.3684i	−0.177040	−	0.660724i	−0.996195	−	0.0871512i	$-0.972224\pi$
$691$	−4.65384	−	17.3684i	−0.177040	−	0.660724i	0.819155	−	0.573573i	$-0.194443\pi$
$692$	21.4507	+	12.3845i	0.815432	+	0.470790i
$693$		0			0
$694$	−17.2703	−	17.2703i	−0.655570	−	0.655570i
$695$	4.60935	−	17.2023i	0.174843	−	0.652521i
$696$		0			0
$697$	−1.62947	+	1.62947i	−0.0617205	+	0.0617205i
$698$	24.0447	−	13.8822i	0.910106	−	0.525450i
$699$		0			0
$700$	8.65917	−	14.0650i	0.327286	−	0.531606i
$701$			34.0110i			1.28458i	0.766462	+	0.642290i	$0.222015\pi$
$701$			34.0110i			1.28458i	−0.766462	+	0.642290i	$0.777985\pi$
$702$		0			0
$703$			0.954993i			0.0360182i
$704$	−58.8411	+	15.7664i	−2.21766	+	0.594219i
$705$		0			0
$706$	19.7658	+	34.2354i	0.743897	+	1.28847i
$707$	1.67551	+	0.0473495i	0.0630139	+	0.00178076i
$708$		0			0
$709$	−2.70932	−	0.725960i	−0.101751	−	0.0272640i	0.207584	−	0.978217i	$-0.433440\pi$
$709$	−2.70932	−	0.725960i	−0.101751	−	0.0272640i	−0.309335	+	0.950953i	$0.600106\pi$
$710$	23.4601	+	23.4601i	0.880441	+	0.880441i
$711$		0			0
$712$	18.1993	−	31.5221i	0.682047	−	1.18134i
$713$	−76.7753	+	20.5719i	−2.87526	+	0.770423i
$714$		0			0
$715$	−36.6771	+	25.6530i	−1.37165	+	0.959369i
$716$	−35.9336			−1.34290
$717$		0			0
$718$	−18.2560	+	31.6203i	−0.681308	+	1.18006i
$719$	−10.7719	−	18.6575i	−0.401725	−	0.695809i	0.592209	−	0.805784i	$-0.298256\pi$
$719$	−10.7719	−	18.6575i	−0.401725	−	0.695809i	−0.993934	+	0.109976i	$0.964923\pi$
$720$		0			0
$721$	−2.46137	−	4.55576i	−0.0916661	−	0.169665i
$722$	−41.1167	−	11.0172i	−1.53021	−	0.410017i
$723$		0			0
$724$	27.6493	−	15.9633i	1.02758	−	0.593272i
$725$	−18.5044	−	10.6835i	−0.687235	−	0.396775i
$726$		0			0
$727$	−25.2656			−0.937048			−0.468524	−	0.883451i	$-0.655214\pi$
$727$	−25.2656			−0.937048			−0.468524	+	0.883451i	$0.655214\pi$
$728$	14.8136	−	16.6564i	0.549028	−	0.617328i
$729$		0			0
$730$	71.2720	−	19.0973i	2.63789	−	0.706822i
$731$	10.9149	+	6.30170i	0.403701	+	0.233077i
$732$		0			0
$733$	22.8545	−	22.8545i	0.844152	−	0.844152i	−0.145244	−	0.989396i	$-0.546397\pi$
$733$	22.8545	−	22.8545i	0.844152	−	0.844152i	0.989396	+	0.145244i	$0.0463967\pi$
$734$	28.5184	+	7.64147i	1.05263	+	0.282052i
$735$		0			0
$736$	38.5109	−	38.5109i	1.41953	−	1.41953i
$737$	−3.40865	−	5.90396i	−0.125559	−	0.217475i
$738$		0			0
$739$	3.35655	+	12.5268i	0.123473	+	0.460806i	0.999781	−	0.0209450i	$-0.00666750\pi$
$739$	3.35655	+	12.5268i	0.123473	+	0.460806i	−0.876308	+	0.481751i	$0.840001\pi$
$740$	−38.3014			−1.40799
$741$		0			0
$742$	−7.95935	−	8.42229i	−0.292197	−	0.309192i
$743$	−31.0606	+	8.32266i	−1.13950	+	0.305329i	−0.778751	−	0.627333i	$-0.784146\pi$
$743$	−31.0606	+	8.32266i	−1.13950	+	0.305329i	−0.360751	+	0.932662i	$0.617480\pi$
$744$		0			0
$745$	6.35837	+	11.0130i	0.232953	+	0.403486i
$746$	15.2893	+	15.2893i	0.559782	+	0.559782i
$747$		0			0
$748$	−16.0927	+	60.0587i	−0.588407	+	2.19596i
$749$	19.0412	+	0.538099i	0.695749	+	0.0196617i
$750$		0			0
$751$	−13.1305	−	7.58091i	−0.479140	−	0.276631i	0.240918	−	0.970545i	$-0.422551\pi$
$751$	−13.1305	−	7.58091i	−0.479140	−	0.276631i	−0.720058	+	0.693914i	$0.755885\pi$
$752$	−1.05935	+	0.283851i	−0.0386304	+	0.0103510i
$753$		0			0
$754$	−64.5111	−	54.1887i	−2.34935	−	1.97344i
$755$		−	28.7807i		−	1.04744i
$756$		0			0
$757$	−17.8529	+	30.9221i	−0.648875	+	1.12388i	0.334517	+	0.942390i	$0.391427\pi$
$757$	−17.8529	+	30.9221i	−0.648875	+	1.12388i	−0.983392	+	0.181494i	$0.941907\pi$
$758$	−64.7200	+	37.3661i	−2.35074	+	1.35720i
$759$		0			0
$760$	−0.323404	+	1.20696i	−0.0117311	+	0.0437810i
$761$	−0.802382	+	2.99453i	−0.0290863	+	0.108552i	−0.978943	−	0.204134i	$-0.934562\pi$
$761$	−0.802382	+	2.99453i	−0.0290863	+	0.108552i	0.949857	+	0.312686i	$0.101229\pi$
$762$		0			0
$763$	2.59191	−	8.68401i	0.0938334	−	0.314382i
$764$	35.1538	+	20.2961i	1.27182	+	0.734286i
$765$		0			0
$766$	−8.67503			−0.313442
$767$	−18.7824	−	15.7770i	−0.678192	−	0.569675i
$768$		0			0
$769$	−8.07284	−	30.1282i	−0.291114	−	1.08645i	−0.944255	−	0.329216i	$-0.893216\pi$
$769$	−8.07284	−	30.1282i	−0.291114	−	1.08645i	0.653141	−	0.757237i	$-0.273451\pi$
$770$	−17.0654	−	71.7372i	−0.614995	−	2.58523i
$771$		0			0
$772$	−17.3447	−	17.3447i	−0.624251	−	0.624251i
$773$	5.18000	+	1.38798i	0.186312	+	0.0499220i	0.350768	−	0.936462i	$-0.385920\pi$
$773$	5.18000	+	1.38798i	0.186312	+	0.0499220i	−0.164457	+	0.986384i	$0.552587\pi$
$774$		0			0
$775$	−13.8743	−	13.8743i	−0.498379	−	0.498379i
$776$	5.96928	−	3.44636i	0.214284	−	0.123717i
$777$		0			0
$778$	−7.31105	−	27.2852i	−0.262114	−	0.978222i
$779$			0.106067i			0.00380026i
$780$		0			0
$781$	26.0089			0.930670
$782$	−21.1410	−	78.8993i	−0.756001	−	2.82143i
$783$		0			0
$784$	−2.63275	−	5.22044i	−0.0940267	−	0.186444i
$785$	−15.0345	−	15.0345i	−0.536604	−	0.536604i
$786$		0			0
$787$	3.63938	−	13.5824i	0.129730	−	0.484159i	−0.870234	−	0.492638i	$-0.836033\pi$
$787$	3.63938	−	13.5824i	0.129730	−	0.484159i	0.999964	+	0.00847973i	$0.00269922\pi$
$788$	27.2973	−	27.2973i	0.972426	−	0.972426i
$789$		0			0
$790$	13.3114	−	23.0560i	0.473597	−	0.820294i
$791$	1.05350	−	1.71118i	0.0374580	−	0.0608425i
$792$		0			0
$793$	0.769372	+	8.84726i	0.0273212	+	0.314175i
$794$		−	59.6088i		−	2.11544i
$795$		0			0
$796$	−57.0740	−	32.9517i	−2.02294	−	1.16794i
$797$	14.0098	+	24.2657i	0.496252	+	0.859534i	0.999991	−	0.00432247i	$-0.00137589\pi$
$797$	14.0098	+	24.2657i	0.496252	+	0.859534i	−0.503739	+	0.863856i	$0.668043\pi$
$798$		0			0
$799$	−1.48666	+	5.54828i	−0.0525941	+	0.196284i
$800$	12.9865	+	3.47971i	0.459141	+	0.123026i
$801$		0			0
$802$	16.8947	+	29.2625i	0.596573	+	1.03330i
$803$	28.9216	−	50.0936i	1.02062	−	1.76776i
$804$		0			0
$805$	40.1369	+	42.4713i	1.41464	+	1.49692i
$806$	−44.3424	−	63.3981i	−1.56190	−	2.23310i
$807$		0			0
$808$	−0.383152	−	1.42994i	−0.0134792	−	0.0503052i
$809$	−22.8429	+	39.5651i	−0.803115	+	1.39104i	0.114441	+	0.993430i	$0.463492\pi$
$809$	−22.8429	+	39.5651i	−0.803115	+	1.39104i	−0.917556	+	0.397606i	$0.869841\pi$
$810$		0			0
$811$	7.85623	−	7.85623i	0.275870	−	0.275870i	−0.555588	−	0.831458i	$-0.687507\pi$
$811$	7.85623	−	7.85623i	0.275870	−	0.275870i	0.831458	+	0.555588i	$0.187507\pi$
$812$	73.6664	−	39.8002i	2.58518	−	1.39671i
$813$		0			0
$814$	−35.1957	+	35.1957i	−1.23361	+	1.23361i
$815$	−43.7629	+	25.2665i	−1.53295	+	0.885048i
$816$		0			0
$817$	0.560341	−	0.150143i	0.0196038	−	0.00525284i
$818$	−55.7777			−1.95022
$819$		0			0
$820$	−4.25399			−0.148556
$821$	−25.7120	+	6.88952i	−0.897356	+	0.240446i	−0.677881	−	0.735172i	$-0.737101\pi$
$821$	−25.7120	+	6.88952i	−0.897356	+	0.240446i	−0.219476	+	0.975618i	$0.570435\pi$
$822$		0			0
$823$	38.5488	−	22.2561i	1.34373	−	0.775800i	0.356373	−	0.934344i	$-0.384013\pi$
$823$	38.5488	−	22.2561i	1.34373	−	0.775800i	0.987352	+	0.158543i	$0.0506798\pi$
$824$	−3.23382	+	3.23382i	−0.112655	+	0.112655i
$825$		0			0
$826$	35.5549	−	19.2094i	1.23711	−	0.668381i
$827$	10.7544	−	10.7544i	0.373966	−	0.373966i	−0.494953	−	0.868920i	$-0.664815\pi$
$827$	10.7544	−	10.7544i	0.373966	−	0.373966i	0.868920	+	0.494953i	$0.164815\pi$
$828$		0			0
$829$	22.8384	−	39.5572i	0.793209	−	1.37388i	−0.130761	−	0.991414i	$-0.541742\pi$
$829$	22.8384	−	39.5572i	0.793209	−	1.37388i	0.923970	−	0.382464i	$-0.124924\pi$
$830$	−11.8330	−	44.1615i	−0.410731	−	1.53287i
$831$		0			0
$832$	42.5761	+	19.8807i	1.47606	+	0.689238i
$833$	−30.5732	−	1.72936i	−1.05930	−	0.0599189i
$834$		0			0
$835$	−14.4521	+	25.0317i	−0.500134	+	0.866257i
$836$	1.43095	+	2.47847i	0.0494903	+	0.0857197i
$837$		0			0
$838$	38.8869	+	10.4197i	1.34332	+	0.359943i
$839$	−0.546041	+	2.03785i	−0.0188514	+	0.0703546i	−0.974711	−	0.223470i	$-0.928262\pi$
$839$	−0.546041	+	2.03785i	−0.0188514	+	0.0703546i	0.955859	+	0.293825i	$0.0949282\pi$
$840$		0			0
$841$	−39.6591	−	68.6916i	−1.36755	−	2.36867i
$842$	2.29278	+	1.32374i	0.0790144	+	0.0456190i
$843$		0			0
$844$		−	39.5856i		−	1.36259i
$845$	34.3902	+	3.04501i	1.18306	+	0.104751i
$846$		0			0
$847$	−24.4421	−	15.0479i	−0.839841	−	0.517052i
$848$	0.814711	−	1.41112i	0.0279773	−	0.0484581i
$849$		0			0
$850$	14.2581	−	14.2581i	0.489050	−	0.489050i
$851$	10.2090	−	38.1006i	0.349961	−	1.30607i
$852$		0			0
$853$	−31.7998	−	31.7998i	−1.08881	−	1.08881i	−0.995652	−	0.0931541i	$-0.970305\pi$
$853$	−31.7998	−	31.7998i	−1.08881	−	1.08881i	−0.0931541	−	0.995652i	$-0.529695\pi$
$854$	−14.0197	−	4.18446i	−0.479746	−	0.143189i
$855$		0			0
$856$	−4.35430	−	16.2505i	−0.148827	−	0.555429i
$857$	−0.314991			−0.0107599			−0.00537994	−	0.999986i	$-0.501712\pi$
$857$	−0.314991			−0.0107599			−0.00537994	+	0.999986i	$0.501712\pi$
$858$		0			0
$859$			11.6151i			0.396303i	0.980171	+	0.198151i	$0.0634938\pi$
$859$			11.6151i			0.396303i	−0.980171	+	0.198151i	$0.936506\pi$
$860$	6.02170	+	22.4733i	0.205338	+	0.766333i
$861$		0			0
$862$	−27.0887	+	15.6397i	−0.922646	+	0.532690i
$863$	10.5474	+	10.5474i	0.359038	+	0.359038i	0.863458	−	0.504420i	$-0.168294\pi$
$863$	10.5474	+	10.5474i	0.359038	+	0.359038i	−0.504420	+	0.863458i	$0.668294\pi$
$864$		0			0
$865$	−20.8957	−	5.59899i	−0.710476	−	0.190371i
$866$	1.20700	+	1.20700i	0.0410156	+	0.0410156i
$867$		0			0
$868$	74.8018	−	17.7945i	2.53894	−	0.603983i
$869$	−5.40164	−	20.1592i	−0.183238	−	0.683853i
$870$		0			0
$871$	−0.915858	+	5.17825i	−0.0310327	+	0.175458i
$872$	−8.00399			−0.271049
$873$		0			0
$874$	−3.25597	−	1.87984i	−0.110135	−	0.0635865i
$875$	5.92219	−	19.8419i	0.200207	−	0.670779i
$876$		0			0
$877$	13.5647	−	50.6241i	0.458047	−	1.70945i	−0.220925	−	0.975291i	$-0.570908\pi$
$877$	13.5647	−	50.6241i	0.458047	−	1.70945i	0.678972	−	0.734164i	$-0.262426\pi$
$878$	−18.5438	+	69.2065i	−0.625824	+	2.33561i
$879$		0			0
$880$	8.97938	−	5.18425i	0.302695	−	0.174761i
$881$	−2.13878	+	3.70447i	−0.0720572	+	0.124807i	−0.899803	−	0.436297i	$-0.856290\pi$
$881$	−2.13878	+	3.70447i	−0.0720572	+	0.124807i	0.827746	+	0.561104i	$0.189623\pi$
$882$		0			0
$883$			33.8768i			1.14004i	0.821630	+	0.570022i	$0.193065\pi$
$883$			33.8768i			1.14004i	−0.821630	+	0.570022i	$0.806935\pi$
$884$	39.3020	−	27.4890i	1.32187	−	0.924554i
$885$		0			0
$886$	−30.1622	+	8.08195i	−1.01332	+	0.271518i
$887$	3.88879	+	2.24520i	0.130573	+	0.0753863i	0.563864	−	0.825868i	$-0.309314\pi$
$887$	3.88879	+	2.24520i	0.130573	+	0.0753863i	−0.433291	+	0.901254i	$0.642648\pi$
$888$		0			0
$889$	0.0897799	−	3.17695i	0.00301112	−	0.106551i
$890$	−24.0388	+	89.7139i	−0.805781	+	3.00722i
$891$		0			0
$892$	−36.4018	−	36.4018i	−1.21882	−	1.21882i
$893$	0.132192	+	0.228963i	0.00442364	+	0.00766197i
$894$		0			0
$895$	30.3143	−	8.12270i	1.01330	−	0.271512i
$896$	−31.0794	+	29.3711i	−1.03829	+	0.981219i
$897$		0			0
$898$	−86.7949			−2.89638
$899$	−25.7442	−	96.0787i	−0.858617	−	3.20440i
$900$		0			0
$901$	−4.26701	−	7.39069i	−0.142155	−	0.246219i
$902$	−3.90905	+	3.90905i	−0.130157	+	0.130157i
$903$		0			0
$904$	−1.71428	−	0.459339i	−0.0570160	−	0.0152774i
$905$	−19.7171	+	19.7171i	−0.655417	+	0.655417i
$906$		0			0
$907$	13.2542	+	7.65232i	0.440099	+	0.254091i	0.703640	−	0.710557i	$-0.251557\pi$
$907$	13.2542	+	7.65232i	0.440099	+	0.254091i	−0.263541	+	0.964648i	$0.584890\pi$
$908$	−55.6187	+	14.9030i	−1.84577	+	0.494573i
$909$		0			0
$910$	−25.5116	+	50.8375i	−0.845701	+	1.68525i
$911$	−15.6790			−0.519470			−0.259735	−	0.965680i	$-0.583635\pi$
$911$	−15.6790			−0.519470			−0.259735	+	0.965680i	$0.583635\pi$
$912$		0			0
$913$	−31.0390	−	17.9204i	−1.02724	−	0.593077i
$914$	−22.7289	+	13.1225i	−0.751805	+	0.434055i
$915$		0			0
$916$	0.753632	+	0.201935i	0.0249007	+	0.00667212i
$917$	7.06277	−	3.81584i	0.233233	−	0.126010i
$918$		0			0
$919$	−26.1402	−	45.2762i	−0.862287	−	1.49352i	−0.869716	−	0.493552i	$-0.835698\pi$
$919$	−26.1402	−	45.2762i	−0.862287	−	1.49352i	0.00742976	−	0.999972i	$-0.497635\pi$
$920$	25.8052	−	44.6959i	0.850771	−	1.47358i
$921$		0			0
$922$	76.8731			2.53168
$923$	−15.3619	−	12.9038i	−0.505641	−	0.424734i
$924$		0			0
$925$	9.40546	−	2.52019i	0.309250	−	0.0828632i
$926$	−28.7768	+	49.8428i	−0.945663	+	1.63794i
$927$		0			0
$928$	48.1936	+	48.1936i	1.58203	+	1.58203i
$929$	−19.0687	−	5.10945i	−0.625625	−	0.167636i	−0.0679414	−	0.997689i	$-0.521643\pi$
$929$	−19.0687	−	5.10945i	−0.625625	−	0.167636i	−0.557684	+	0.830054i	$0.688310\pi$
$930$		0			0
$931$	−1.05134	+	0.938768i	−0.0344562	+	0.0307669i
$932$	−17.3093	−	29.9806i	−0.566984	−	0.982046i
$933$		0			0
$934$	−44.3333	+	11.8791i	−1.45063	+	0.388696i
$935$		−	54.3045i		−	1.77595i
$936$		0			0
$937$		−	32.0301i		−	1.04638i	−0.852217	−	0.523189i	$-0.824742\pi$
$937$		−	32.0301i		−	1.04638i	0.852217	−	0.523189i	$-0.175258\pi$
$938$	−7.37752	−	4.54201i	−0.240885	−	0.148302i
$939$		0			0
$940$	−9.18291	+	5.30176i	−0.299514	+	0.172924i
$941$	16.4141	−	16.4141i	0.535083	−	0.535083i	−0.386998	−	0.922081i	$-0.626488\pi$
$941$	16.4141	−	16.4141i	0.535083	−	0.535083i	0.922081	+	0.386998i	$0.126488\pi$
$942$		0			0
$943$	1.13388	−	4.23169i	0.0369241	−	0.137803i
$944$	4.01805	+	4.01805i	0.130777	+	0.130777i
$945$		0			0
$946$	26.1845	+	15.1176i	0.851330	+	0.491516i
$947$	11.1001	+	41.4261i	0.360704	+	1.34617i	0.873152	+	0.487449i	$0.162072\pi$
$947$	11.1001	+	41.4261i	0.360704	+	1.34617i	−0.512447	+	0.858719i	$0.671261\pi$
$948$		0			0
$949$	−41.9352	+	15.2383i	−1.36128	+	0.494658i
$950$		−	0.928107i		−	0.0301118i
$951$		0			0
$952$	6.25905	+	26.3109i	0.202857	+	0.852741i
$953$	10.3745	−	5.98973i	0.336064	−	0.194026i	−0.322466	−	0.946581i	$-0.604512\pi$
$953$	10.3745	−	5.98973i	0.336064	−	0.194026i	0.658530	+	0.752554i	$0.271179\pi$
$954$		0			0
$955$	−34.2444	−	9.17575i	−1.10812	−	0.296920i
$956$	50.7511	+	13.5987i	1.64141	+	0.439814i
$957$		0			0
$958$	−22.9963	+	13.2769i	−0.742976	+	0.428957i
$959$	7.15000	+	30.0561i	0.230885	+	0.970563i
$960$		0			0
$961$		−	60.3409i		−	1.94648i
$962$	38.2497	−	3.32625i	1.23322	−	0.107243i
$963$		0			0
$964$	23.9973	+	89.5592i	0.772902	+	2.88451i
$965$	18.5531	+	10.7117i	0.597246	+	0.344820i
$966$		0			0
$967$	3.08553	+	3.08553i	0.0992241	+	0.0992241i	0.754976	−	0.655752i	$-0.227648\pi$
$967$	3.08553	+	3.08553i	0.0992241	+	0.0992241i	−0.655752	+	0.754976i	$0.727648\pi$
$968$	−6.56111	+	24.4864i	−0.210882	+	0.787023i
$969$		0			0
$970$	−12.4368	+	12.4368i	−0.399321	+	0.399321i
$971$	−25.8972	+	14.9518i	−0.831081	+	0.479825i	−0.854223	−	0.519907i	$-0.825967\pi$
$971$	−25.8972	+	14.9518i	−0.831081	+	0.479825i	0.0231414	+	0.999732i	$0.492633\pi$
$972$		0			0
$973$	−15.1084	−	9.30154i	−0.484352	−	0.298194i
$974$		−	0.419190i		−	0.0134317i
$975$		0			0
$976$		−	2.05726i		−	0.0658512i
$977$	9.78075	−	2.62074i	0.312914	−	0.0838450i	−0.0989443	−	0.995093i	$-0.531547\pi$
$977$	9.78075	−	2.62074i	0.312914	−	0.0838450i	0.411858	+	0.911248i	$0.364880\pi$
$978$		0			0
$979$	36.4051	+	63.0555i	1.16351	+	2.01526i
$980$	−37.6507	−	42.1655i	−1.20271	−	1.34693i
$981$		0			0
$982$	6.10476	+	1.63577i	0.194811	+	0.0521994i
$983$	5.97019	+	5.97019i	0.190419	+	0.190419i	0.795877	−	0.605458i	$-0.207010\pi$
$983$	5.97019	+	5.97019i	0.190419	+	0.190419i	−0.605458	+	0.795877i	$0.707010\pi$
$984$		0			0
$985$	−16.8581	+	29.1991i	−0.537144	+	0.930360i
$986$	98.7368	−	26.4564i	3.14442	−	0.842545i
$987$		0			0
$988$	0.384476	−	2.17382i	0.0122318	−	0.0691585i
$989$	−23.9605			−0.761901
$990$		0			0
$991$	−27.8012	+	48.1532i	−0.883136	+	1.52964i	−0.0353002	+	0.999377i	$0.511239\pi$
$991$	−27.8012	+	48.1532i	−0.883136	+	1.52964i	−0.847836	+	0.530259i	$0.822095\pi$
$992$	31.2937	+	54.2023i	0.993576	+	1.72092i
$993$		0			0
$994$	29.0798	−	15.7111i	0.922357	−	0.498327i
$995$	55.5975	+	14.8973i	1.76256	+	0.472277i
$996$		0			0
$997$	9.66852	−	5.58213i	0.306205	−	0.176788i	−0.339022	−	0.940778i	$-0.610096\pi$
$997$	9.66852	−	5.58213i	0.306205	−	0.176788i	0.645227	+	0.763991i	$0.276763\pi$
$998$	4.95526	+	2.86092i	0.156856	+	0.0905609i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.e.748.8		32
3.2	odd	2		273.2.by.d.202.1	yes	32
7.6	odd	2		819.2.fm.f.748.8		32
13.2	odd	12		819.2.fm.f.496.8		32
21.20	even	2		273.2.by.c.202.1	✓	32
39.2	even	12		273.2.by.c.223.1	yes	32
91.41	even	12	inner	819.2.fm.e.496.8		32
273.41	odd	12		273.2.by.d.223.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.1	✓	32	21.20	even	2
273.2.by.c.223.1	yes	32	39.2	even	12
273.2.by.d.202.1	yes	32	3.2	odd	2
273.2.by.d.223.1	yes	32	273.41	odd	12
819.2.fm.e.496.8		32	91.41	even	12	inner
819.2.fm.e.748.8		32	1.1	even	1	trivial
819.2.fm.f.496.8		32	13.2	odd	12
819.2.fm.f.748.8		32	7.6	odd	2

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)

\(f(q)\)	\(=\)	\(q+(2.16866 - 0.581092i) q^{2} +(2.63339 - 1.52039i) q^{4} +(-1.87790 + 1.87790i) q^{5} +(1.25762 + 2.32774i) q^{7} +(1.65230 - 1.65230i) q^{8} +O(q^{10})\)	\(q+(2.16866 - 0.581092i) q^{2} +(2.63339 - 1.52039i) q^{4} +(-1.87790 + 1.87790i) q^{5} +(1.25762 + 2.32774i) q^{7} +(1.65230 - 1.65230i) q^{8} +(-2.98130 + 5.16377i) q^{10} +(1.20979 + 4.51499i) q^{11} +(1.52548 - 3.26694i) q^{13} +(4.07999 + 4.31730i) q^{14} +(-0.417624 + 0.723346i) q^{16} +(2.18729 + 3.78849i) q^{17} +(0.194491 + 0.0521138i) q^{19} +(-2.09010 + 7.80037i) q^{20} +(5.24724 + 9.08849i) q^{22} +(-7.20237 - 4.15829i) q^{23} -2.05302i q^{25} +(1.40986 - 7.97134i) q^{26} +(6.85087 + 4.21777i) q^{28} +(5.20380 - 9.01325i) q^{29} +(6.75799 - 6.75799i) q^{31} +(-1.69492 + 6.32554i) q^{32} +(6.94495 + 6.94495i) q^{34} +(-6.73296 - 2.00958i) q^{35} +(1.22755 + 4.58128i) q^{37} +0.452070 q^{38} +6.20572i q^{40} +(0.136339 + 0.508825i) q^{41} +(2.49507 - 1.44053i) q^{43} +(10.0504 + 10.0504i) q^{44} +(-18.0359 - 4.83270i) q^{46} +(0.928461 + 0.928461i) q^{47} +(-3.83677 + 5.85484i) q^{49} +(-1.19299 - 4.45231i) q^{50} +(-0.949833 - 10.9224i) q^{52} -1.95082 q^{53} +(-10.7506 - 6.20683i) q^{55} +(5.92410 + 1.76816i) q^{56} +(6.04777 - 22.5706i) q^{58} +(1.76081 - 6.57142i) q^{59} +(-2.13306 + 1.23152i) q^{61} +(10.7288 - 18.5828i) q^{62} +13.0324i q^{64} +(3.27029 + 8.99969i) q^{65} +(-1.40878 + 0.377482i) q^{67} +(11.5199 + 6.65104i) q^{68} +(-15.7693 - 0.445637i) q^{70} +(1.44014 - 5.37468i) q^{71} +(-8.75032 - 8.75032i) q^{73} +(5.32429 + 9.22194i) q^{74} +(0.591404 - 0.158466i) q^{76} +(-8.98827 + 8.49422i) q^{77} -4.46495 q^{79} +(-0.574115 - 2.14263i) q^{80} +(0.591348 + 1.02425i) q^{82} +(-5.42187 + 5.42187i) q^{83} +(-11.2219 - 3.00690i) q^{85} +(4.57389 - 4.57389i) q^{86} +(9.45905 + 5.46119i) q^{88} +(15.0461 - 4.03159i) q^{89} +(9.52308 - 0.557652i) q^{91} -25.2888 q^{92} +(2.55304 + 1.47400i) q^{94} +(-0.463100 + 0.267371i) q^{95} +(2.84925 + 0.763454i) q^{97} +(-4.91847 + 14.9267i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 2 * q^10 + 4 * q^11 + 6 * q^13 - 34 * q^14 + 14 * q^16 + 8 * q^17 + 2 * q^19 - 44 * q^20 - 4 * q^22 + 18 * q^23 + 28 * q^26 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * q^70 + 4 * q^71 + 12 * q^73 + 18 * q^74 - 48 * q^76 - 28 * q^77 - 4 * q^79 + 98 * q^80 + 20 * q^82 + 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 + 54 * q^89 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

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