LMFDB - Embedded newform 833.2.j.a.373.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [833,2,Mod(67,833)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("833.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(833, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,-2,0,-10,0,0,0,0,0,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 15 x^{18} + 158 x^{16} - 789 x^{14} + 2811 x^{12} - 5497 x^{10} + 7763 x^{8} - 6130 x^{6} + \cdots + 1 $ x^20 - 15x^18 + 158x^16 - 789x^14 + 2811x^12 - 5497x^10 + 7763x^8 - 6130x^6 + 3256x^4 - 58*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.7
Root			$1.69010 - 0.975779i$ of defining polynomial
Character	$\chi$	$=$	833.373
Dual form			833.2.j.a.67.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.558220 - 0.966865i) q^{2} +(-1.69010 + 0.975779i) q^{3} +(0.376781 + 0.652604i) q^{4} +(1.29801 + 0.749406i) q^{5} +2.17880i q^{6} +3.07419 q^{8} +(0.404290 - 0.700250i) q^{9} +(1.44915 - 0.836667i) q^{10} +(-0.854248 + 0.493200i) q^{11} +(-1.27360 - 0.735310i) q^{12} +5.99921 q^{13} -2.92502 q^{15} +(0.962509 - 1.66712i) q^{16} +(-4.12016 + 0.155952i) q^{17} +(-0.451365 - 0.781787i) q^{18} +(-2.38637 + 4.13331i) q^{19} +1.12945i q^{20} +1.10126i q^{22} +(0.807250 + 0.466066i) q^{23} +(-5.19568 + 2.99973i) q^{24} +(-1.37678 - 2.38465i) q^{25} +(3.34888 - 5.80042i) q^{26} -4.27669i q^{27} +4.13364i q^{29} +(-1.63280 + 2.82810i) q^{30} +(1.49480 - 0.863025i) q^{31} +(1.99960 + 3.46341i) q^{32} +(0.962509 - 1.66712i) q^{33} +(-2.14917 + 4.07069i) q^{34} +0.609315 q^{36} +(6.78631 + 3.91808i) q^{37} +(2.66423 + 4.61459i) q^{38} +(-10.1393 + 5.85390i) q^{39} +(3.99032 + 2.30381i) q^{40} +9.93404i q^{41} -5.60852 q^{43} +(-0.643729 - 0.371657i) q^{44} +(1.04954 - 0.605954i) q^{45} +(0.901246 - 0.520335i) q^{46} +(-1.68782 + 2.92339i) q^{47} +3.75679i q^{48} -3.07419 q^{50} +(6.81129 - 4.28394i) q^{51} +(2.26039 + 3.91511i) q^{52} +(3.06460 + 5.30805i) q^{53} +(-4.13498 - 2.38733i) q^{54} -1.47843 q^{55} -9.31426i q^{57} +(3.99667 + 2.30748i) q^{58} +(3.33497 + 5.77634i) q^{59} +(-1.10209 - 1.90888i) q^{60} +(0.508145 + 0.293377i) q^{61} -1.92703i q^{62} +8.31491 q^{64} +(7.78702 + 4.49584i) q^{65} +(-1.07458 - 1.86123i) q^{66} +(0.414272 + 0.717540i) q^{67} +(-1.65417 - 2.63007i) q^{68} -1.81911 q^{69} -15.0439i q^{71} +(1.24286 - 2.15270i) q^{72} +(6.04993 - 3.49293i) q^{73} +(7.57651 - 4.37430i) q^{74} +(4.65379 + 2.68687i) q^{75} -3.59655 q^{76} +13.0711i q^{78} +(-12.0106 - 6.93432i) q^{79} +(2.49869 - 1.44262i) q^{80} +(5.38597 + 9.32877i) q^{81} +(9.60488 + 5.54538i) q^{82} -0.776646 q^{83} +(-5.46487 - 2.88524i) q^{85} +(-3.13079 + 5.42268i) q^{86} +(-4.03352 - 6.98626i) q^{87} +(-2.62612 + 1.51619i) q^{88} +(2.05100 - 3.55243i) q^{89} -1.35302i q^{90} +0.702420i q^{92} +(-1.68424 + 2.91720i) q^{93} +(1.88435 + 3.26379i) q^{94} +(-6.19505 + 3.57671i) q^{95} +(-6.75905 - 3.90234i) q^{96} -11.1720i q^{97} +0.797583i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 10 q^{4} + 16 q^{13} - 16 q^{15} - 2 q^{16} + 2 q^{17} + 18 q^{18} + 10 q^{19} - 10 q^{25} - 12 q^{26} - 10 q^{30} - 12 q^{32} - 2 q^{33} - 24 q^{34} + 56 q^{36} + 2 q^{38} - 52 q^{43}+ \cdots - 50 q^{94}+O(q^{100}) $ 20 * q - 2 * q^2 - 10 * q^4 + 16 * q^13 - 16 * q^15 - 2 * q^16 + 2 * q^17 + 18 * q^18 + 10 * q^19 - 10 * q^25 - 12 * q^26 - 10 * q^30 - 12 * q^32 - 2 * q^33 - 24 * q^34 + 56 * q^36 + 2 * q^38 - 52 * q^43 - 30 * q^47 + 6 * q^51 + 2 * q^52 + 40 * q^53 - 12 * q^55 + 14 * q^59 - 22 * q^60 - 24 * q^64 - 12 * q^66 + 12 * q^67 + 32 * q^68 + 88 * q^69 - 16 * q^72 - 132 * q^76 - 2 * q^81 - 96 * q^83 - 4 * q^85 - 10 * q^86 + 26 * q^87 - 16 * q^89 + 46 * q^93 - 50 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.558220	−	0.966865i	0.394721	−	0.683677i	−0.598344	−	0.801239i	$-0.704175\pi$
$2$	0.558220	−	0.966865i	0.394721	−	0.683677i	0.993066	+	0.117562i	$0.0375079\pi$
$3$	−1.69010	+	0.975779i	−0.975779	+	0.563366i	−0.900993	−	0.433833i	$-0.857161\pi$
$3$	−1.69010	+	0.975779i	−0.975779	+	0.563366i	−0.0747859	+	0.997200i	$0.523827\pi$
$4$	0.376781	+	0.652604i	0.188391	+	0.326302i
$5$	1.29801	+	0.749406i	0.580487	+	0.335145i	0.761327	−	0.648368i	$-0.224548\pi$
$5$	1.29801	+	0.749406i	0.580487	+	0.335145i	−0.180840	+	0.983513i	$0.557882\pi$
$6$			2.17880i			0.889490i
$7$		0			0
$7$		0			0
$8$	3.07419			1.08689
$9$	0.404290	−	0.700250i	0.134763	−	0.233417i
$10$	1.44915	−	0.836667i	0.458261	−	0.264577i
$11$	−0.854248	+	0.493200i	−0.257566	+	0.148706i	−0.623224	−	0.782044i	$-0.714177\pi$
$11$	−0.854248	+	0.493200i	−0.257566	+	0.148706i	0.365658	+	0.930749i	$0.380844\pi$
$12$	−1.27360	−	0.735310i	−0.367655	−	0.212266i
$13$	5.99921			1.66388			0.831940	−	0.554865i	$-0.187230\pi$
$13$	5.99921			1.66388			0.831940	+	0.554865i	$0.187230\pi$
$14$		0			0
$15$	−2.92502			−0.755237
$16$	0.962509	−	1.66712i	0.240627	−	0.416779i
$17$	−4.12016	+	0.155952i	−0.999284	+	0.0378240i
$17$	−4.12016	+	0.155952i	−0.999284	+	0.0378240i
$18$	−0.451365	−	0.781787i	−0.106388	−	0.184269i
$19$	−2.38637	+	4.13331i	−0.547470	+	0.948246i	0.450977	+	0.892536i	$0.351076\pi$
$19$	−2.38637	+	4.13331i	−0.547470	+	0.948246i	−0.998447	+	0.0557102i	$0.982258\pi$
$20$			1.12945i			0.252552i
$21$		0			0
$22$			1.10126i			0.234789i
$23$	0.807250	+	0.466066i	0.168323	+	0.0971815i	0.581795	−	0.813335i	$-0.302351\pi$
$23$	0.807250	+	0.466066i	0.168323	+	0.0971815i	−0.413472	+	0.910517i	$0.635684\pi$
$24$	−5.19568	+	2.99973i	−1.06056	+	0.612317i
$25$	−1.37678	−	2.38465i	−0.275356	−	0.476931i
$26$	3.34888	−	5.80042i	0.656769	−	1.13756i
$27$		−	4.27669i		−	0.823048i
$28$		0			0
$29$			4.13364i			0.767597i	0.923417	+	0.383799i	$0.125384\pi$
$29$			4.13364i			0.767597i	−0.923417	+	0.383799i	$0.874616\pi$
$30$	−1.63280	+	2.82810i	−0.298108	+	0.516338i
$31$	1.49480	−	0.863025i	0.268475	−	0.155004i	−0.359720	−	0.933060i	$-0.617128\pi$
$31$	1.49480	−	0.863025i	0.268475	−	0.155004i	0.628194	+	0.778057i	$0.283794\pi$
$32$	1.99960	+	3.46341i	0.353483	+	0.612251i
$33$	0.962509	−	1.66712i	0.167551	−	0.290208i
$34$	−2.14917	+	4.07069i	−0.368579	+	0.698118i
$35$		0			0
$36$	0.609315			0.101552
$37$	6.78631	+	3.91808i	1.11566	+	0.644128i	0.940290	−	0.340374i	$-0.110554\pi$
$37$	6.78631	+	3.91808i	1.11566	+	0.644128i	0.175372	+	0.984502i	$0.443887\pi$
$38$	2.66423	+	4.61459i	0.432196	+	0.748585i
$39$	−10.1393	+	5.85390i	−1.62358	+	0.937374i
$40$	3.99032	+	2.30381i	0.630925	+	0.364265i
$41$			9.93404i			1.55144i	0.631079	+	0.775718i	$0.282612\pi$
$41$			9.93404i			1.55144i	−0.631079	+	0.775718i	$0.717388\pi$
$42$		0			0
$43$	−5.60852			−0.855291			−0.427646	−	0.903946i	$-0.640657\pi$
$43$	−5.60852			−0.855291			−0.427646	+	0.903946i	$0.640657\pi$
$44$	−0.643729	−	0.371657i	−0.0970459	−	0.0560295i
$45$	1.04954	−	0.605954i	0.156457	−	0.0903303i
$46$	0.901246	−	0.520335i	0.132882	−	0.0767192i
$47$	−1.68782	+	2.92339i	−0.246194	+	0.426420i	−0.962467	−	0.271400i	$-0.912513\pi$
$47$	−1.68782	+	2.92339i	−0.246194	+	0.426420i	0.716273	+	0.697820i	$0.245847\pi$
$48$			3.75679i			0.542245i
$49$		0			0
$50$	−3.07419			−0.434756
$51$	6.81129	−	4.28394i	0.953772	−	0.599871i
$52$	2.26039	+	3.91511i	0.313459	+	0.542928i
$53$	3.06460	+	5.30805i	0.420955	+	0.729116i	0.996033	−	0.0889826i	$-0.0283616\pi$
$53$	3.06460	+	5.30805i	0.420955	+	0.729116i	−0.575078	+	0.818099i	$0.695028\pi$
$54$	−4.13498	−	2.38733i	−0.562699	−	0.324875i
$55$	−1.47843			−0.199351
$56$		0			0
$57$		−	9.31426i		−	1.23370i
$58$	3.99667	+	2.30748i	0.524789	+	0.302987i
$59$	3.33497	+	5.77634i	0.434176	+	0.752015i	0.997228	−	0.0744062i	$-0.0237062\pi$
$59$	3.33497	+	5.77634i	0.434176	+	0.752015i	−0.563052	+	0.826422i	$0.690373\pi$
$60$	−1.10209	−	1.90888i	−0.142279	−	0.246435i
$61$	0.508145	+	0.293377i	0.0650612	+	0.0375631i	0.532178	−	0.846633i	$-0.321374\pi$
$61$	0.508145	+	0.293377i	0.0650612	+	0.0375631i	−0.467117	+	0.884196i	$0.654707\pi$
$62$		−	1.92703i		−	0.244733i
$63$		0			0
$64$	8.31491			1.03936
$65$	7.78702	+	4.49584i	0.965861	+	0.557640i
$66$	−1.07458	−	1.86123i	−0.132272	−	0.229102i
$67$	0.414272	+	0.717540i	0.0506114	+	0.0876614i	0.890221	−	0.455528i	$-0.150550\pi$
$67$	0.414272	+	0.717540i	0.0506114	+	0.0876614i	−0.839610	+	0.543190i	$0.817216\pi$
$68$	−1.65417	−	2.63007i	−0.200598	−	0.318943i
$69$	−1.81911			−0.218995
$70$		0			0
$71$		−	15.0439i		−	1.78538i	−0.450674	−	0.892688i	$-0.648816\pi$
$71$		−	15.0439i		−	1.78538i	0.450674	−	0.892688i	$-0.351184\pi$
$72$	1.24286	−	2.15270i	0.146473	−	0.253698i
$73$	6.04993	−	3.49293i	0.708090	−	0.408816i	−0.102263	−	0.994757i	$-0.532608\pi$
$73$	6.04993	−	3.49293i	0.708090	−	0.408816i	0.810354	+	0.585941i	$0.199275\pi$
$74$	7.57651	−	4.37430i	0.880751	−	0.508502i
$75$	4.65379	+	2.68687i	0.537374	+	0.310253i
$76$	−3.59655			−0.412553
$77$		0			0
$78$			13.0711i			1.48001i
$79$	−12.0106	−	6.93432i	−1.35130	−	0.780172i	−0.362866	−	0.931841i	$-0.618202\pi$
$79$	−12.0106	−	6.93432i	−1.35130	−	0.780172i	−0.988431	+	0.151670i	$0.951535\pi$
$80$	2.49869	−	1.44262i	0.279362	−	0.161290i
$81$	5.38597	+	9.32877i	0.598441	+	1.03653i
$82$	9.60488	+	5.54538i	1.06068	+	0.612385i
$83$	−0.776646			−0.0852480			−0.0426240	−	0.999091i	$-0.513572\pi$
$83$	−0.776646			−0.0852480			−0.0426240	+	0.999091i	$0.513572\pi$
$84$		0			0
$85$	−5.46487	−	2.88524i	−0.592749	−	0.312948i
$86$	−3.13079	+	5.42268i	−0.337601	+	0.584743i
$87$	−4.03352	−	6.98626i	−0.432438	−	0.749005i
$88$	−2.62612	+	1.51619i	−0.279945	+	0.161626i
$89$	2.05100	−	3.55243i	0.217405	−	0.376557i	−0.736609	−	0.676319i	$-0.763574\pi$
$89$	2.05100	−	3.55243i	0.217405	−	0.376557i	0.954014	+	0.299762i	$0.0969074\pi$
$90$		−	1.35302i		−	0.142621i
$91$		0			0
$92$			0.702420i			0.0732323i
$93$	−1.68424	+	2.91720i	−0.174648	+	0.302499i
$94$	1.88435	+	3.26379i	0.194356	+	0.336634i
$95$	−6.19505	+	3.57671i	−0.635599	+	0.366963i
$96$	−6.75905	−	3.90234i	−0.689843	−	0.398281i
$97$		−	11.1720i		−	1.13435i	−0.823598	−	0.567174i	$-0.808037\pi$
$97$		−	11.1720i		−	1.13435i	0.823598	−	0.567174i	$-0.191963\pi$
$98$		0			0
$99$			0.797583i			0.0801601i
$100$	1.03749	−	1.79699i	0.103749	−	0.179699i
$101$	−5.25999	−	9.11057i	−0.523389	−	0.906536i	−0.999629	−	0.0272208i	$-0.991334\pi$
$101$	−5.25999	−	9.11057i	−0.523389	−	0.906536i	0.476241	−	0.879315i	$-0.341999\pi$
$102$	−0.339789	−	8.97698i	−0.0336441	−	0.888854i
$103$	0.560282	−	0.970438i	0.0552063	−	0.0956201i	−0.837102	−	0.547048i	$-0.815752\pi$
$103$	0.560282	−	0.970438i	0.0552063	−	0.0956201i	0.892308	+	0.451427i	$0.149085\pi$
$104$	18.4427			1.80845
$105$		0			0
$106$	6.84289			0.664640
$107$	13.1108	+	7.56951i	1.26747	+	0.731772i	0.974508	−	0.224353i	$-0.0720270\pi$
$107$	13.1108	+	7.56951i	1.26747	+	0.731772i	0.292958	+	0.956125i	$0.405360\pi$
$108$	2.79098	−	1.61137i	0.268562	−	0.155055i
$109$	7.49409	−	4.32672i	0.717804	−	0.414424i	−0.0961400	−	0.995368i	$-0.530650\pi$
$109$	7.49409	−	4.32672i	0.717804	−	0.414424i	0.813944	+	0.580944i	$0.197316\pi$
$110$	−0.825289	+	1.42944i	−0.0786882	+	0.136292i
$111$	−15.2927			−1.45152
$112$		0			0
$113$			3.20782i			0.301767i	0.988552	+	0.150883i	$0.0482118\pi$
$113$			3.20782i			0.301767i	−0.988552	+	0.150883i	$0.951788\pi$
$114$	−9.00564	−	5.19941i	−0.843455	−	0.486969i
$115$	0.698546	+	1.20992i	0.0651397	+	0.112825i
$116$	−2.69763	+	1.55748i	−0.250469	+	0.144608i
$117$	2.42542	−	4.20094i	0.224230	−	0.388377i
$118$	7.44659			0.685514
$119$		0			0
$120$	−8.99205			−0.820858
$121$	−5.01351	+	8.68365i	−0.455773	+	0.789423i
$122$	0.567313	−	0.327538i	0.0513621	−	0.0296539i
$123$	−9.69343	−	16.7895i	−0.874027	−	1.51386i
$124$	1.12643	+	0.650344i	0.101156	+	0.0584026i
$125$		−	11.6211i		−	1.03943i
$126$		0			0
$127$	−13.5319			−1.20076			−0.600381	−	0.799714i	$-0.704984\pi$
$127$	−13.5319			−1.20076			−0.600381	+	0.799714i	$0.704984\pi$
$128$	0.642342	−	1.11257i	0.0567756	−	0.0983382i
$129$	9.47895	−	5.47268i	0.834575	−	0.481842i
$130$	8.69374	−	5.01933i	0.762492	−	0.440225i
$131$	−1.87938	−	1.08506i	−0.164202	−	0.0948020i	0.415647	−	0.909526i	$-0.363555\pi$
$131$	−1.87938	−	1.08506i	−0.164202	−	0.0948020i	−0.579849	+	0.814724i	$0.696888\pi$
$132$	1.45062			0.126260
$133$		0			0
$134$	0.925019			0.0799095
$135$	3.20497	−	5.55118i	0.275840	−	0.477769i
$136$	−12.6661	+	0.479427i	−1.08611	+	0.0411105i
$137$	4.15713	+	7.20037i	0.355168	+	0.615169i	0.987147	−	0.159817i	$-0.0510904\pi$
$137$	4.15713	+	7.20037i	0.355168	+	0.615169i	−0.631979	+	0.774986i	$0.717757\pi$
$138$	−1.01546	+	1.75883i	−0.0864420	+	0.149722i
$139$		−	0.897376i		−	0.0761144i	−0.999276	−	0.0380572i	$-0.987883\pi$
$139$		−	0.897376i		−	0.0761144i	0.999276	−	0.0380572i	$-0.0121169\pi$
$140$		0			0
$141$		−	6.58776i		−	0.554789i
$142$	−14.5454	−	8.39778i	−1.22062	−	0.704726i
$143$	−5.12481	+	2.95881i	−0.428558	+	0.247428i
$144$	−0.778265	−	1.34799i	−0.0648554	−	0.112333i
$145$	−3.09777	+	5.36550i	−0.257256	+	0.445581i
$146$		−	7.79929i		−	0.645473i
$147$		0			0
$148$			5.90503i			0.485391i
$149$	3.29386	−	5.70513i	0.269843	−	0.467383i	−0.698978	−	0.715143i	$-0.746361\pi$
$149$	3.29386	−	5.70513i	0.269843	−	0.467383i	0.968821	+	0.247761i	$0.0796947\pi$
$150$	5.19568	−	2.99973i	0.424225	−	0.244927i
$151$	−5.80180	−	10.0490i	−0.472144	−	0.817777i	0.527348	−	0.849649i	$-0.323186\pi$
$151$	−5.80180	−	10.0490i	−0.472144	−	0.817777i	−0.999492	+	0.0318723i	$0.989853\pi$
$152$	−7.33613	+	12.7066i	−0.595039	+	1.03064i
$153$	−1.55653	+	2.94819i	−0.125838	+	0.238347i
$154$		0			0
$155$	2.58703			0.207795
$156$	−7.64056	−	4.41128i	−0.611734	−	0.353185i
$157$	−11.2046	−	19.4070i	−0.894226	−	1.54885i	−0.834759	−	0.550615i	$-0.814393\pi$
$157$	−11.2046	−	19.4070i	−0.894226	−	1.54885i	−0.0594669	−	0.998230i	$-0.518940\pi$
$158$	−13.4091	+	7.74175i	−1.06677	+	0.615900i
$159$	−10.3590	−	5.98075i	−0.821519	−	0.474304i
$160$			5.99406i			0.473872i
$161$		0			0
$162$	12.0262			0.944869
$163$	−8.31491	−	4.80062i	−0.651274	−	0.376013i	0.137670	−	0.990478i	$-0.456039\pi$
$163$	−8.31491	−	4.80062i	−0.651274	−	0.376013i	−0.788944	+	0.614465i	$0.789372\pi$
$164$	−6.48300	+	3.74296i	−0.506237	+	0.292276i
$165$	2.49869	−	1.44262i	0.194523	−	0.112308i
$166$	−0.433539	+	0.750912i	−0.0336492	+	0.0582821i
$167$			7.80778i			0.604184i	0.953279	+	0.302092i	$0.0976851\pi$
$167$			7.80778i			0.604184i	−0.953279	+	0.302092i	$0.902315\pi$
$168$		0			0
$169$	22.9905			1.76850
$170$	−5.84024	+	3.67319i	−0.447926	+	0.281721i
$171$	1.92957	+	3.34211i	0.147558	+	0.255577i
$172$	−2.11318	−	3.66014i	−0.161129	−	0.279083i
$173$	7.17055	+	4.13992i	0.545167	+	0.314752i	0.747170	−	0.664633i	$-0.231412\pi$
$173$	7.17055	+	4.13992i	0.545167	+	0.314752i	−0.202003	+	0.979385i	$0.564745\pi$
$174$	−9.00636			−0.682770
$175$		0			0
$176$			1.89884i			0.143130i
$177$	−11.2729	−	6.50839i	−0.847320	−	0.489201i
$178$	−2.28981	−	3.96608i	−0.171629	−	0.297270i
$179$	7.28348	+	12.6154i	0.544393	+	0.942916i	0.998645	+	0.0520428i	$0.0165732\pi$
$179$	7.28348	+	12.6154i	0.544393	+	0.942916i	−0.454252	+	0.890873i	$0.650093\pi$
$180$	0.790896	+	0.456624i	0.0589499	+	0.0340348i
$181$		−	11.5908i		−	0.861539i	−0.902462	−	0.430770i	$-0.858242\pi$
$181$		−	11.5908i		−	0.861539i	0.902462	−	0.430770i	$-0.141758\pi$
$182$		0			0
$183$	−1.14509			−0.0846472
$184$	2.48164	+	1.43277i	0.182949	+	0.105626i
$185$	5.87246	+	10.1714i	0.431752	+	0.747816i
$186$	1.88036	+	3.25687i	0.137874	+	0.238806i
$187$	3.44272	−	2.16528i	0.251757	−	0.158341i
$188$	−2.54376			−0.185522
$189$		0			0
$190$			7.98637i			0.579392i
$191$	11.3485	−	19.6562i	0.821150	−	1.42227i	−0.0836758	−	0.996493i	$-0.526666\pi$
$191$	11.3485	−	19.6562i	0.821150	−	1.42227i	0.904826	−	0.425781i	$-0.140001\pi$
$192$	−14.0530	+	8.11351i	−1.01419	+	0.585542i
$193$	22.9877	−	13.2720i	1.65469	−	0.955337i	0.679586	−	0.733596i	$-0.262159\pi$
$193$	22.9877	−	13.2720i	1.65469	−	0.955337i	0.975106	−	0.221741i	$-0.0711739\pi$
$194$	−10.8018	−	6.23645i	−0.775527	−	0.447751i
$195$	−17.5478			−1.25662
$196$		0			0
$197$		−	2.97811i		−	0.212182i	−0.994356	−	0.106091i	$-0.966167\pi$
$197$		−	2.97811i		−	0.212182i	0.994356	−	0.106091i	$-0.0338334\pi$
$198$	0.771155	+	0.445227i	0.0548036	+	0.0316409i
$199$	15.2825	−	8.82333i	1.08334	−	0.625469i	0.151548	−	0.988450i	$-0.451574\pi$
$199$	15.2825	−	8.82333i	1.08334	−	0.625469i	0.931797	+	0.362980i	$0.118241\pi$
$200$	−4.23248	−	7.33087i	−0.299282	−	0.518371i
$201$	−1.40032	−	0.808475i	−0.0987710	−	0.0570255i
$202$	−11.7449			−0.826370
$203$		0			0
$204$	5.36208	+	2.83097i	0.375421	+	0.198208i
$205$	−7.44463	+	12.8945i	−0.519956	+	0.900590i
$206$	−0.625522	−	1.08344i	−0.0435822	−	0.0754865i
$207$	0.652726	−	0.376851i	0.0453676	−	0.0261930i
$208$	5.77429	−	10.0014i	0.400375	−	0.693470i
$209$		−	4.70783i		−	0.325647i
$210$		0			0
$211$			8.38213i			0.577050i	0.957472	+	0.288525i	$0.0931648\pi$
$211$			8.38213i			0.577050i	−0.957472	+	0.288525i	$0.906835\pi$
$212$	−2.30937	+	3.99994i	−0.158608	+	0.274717i
$213$	14.6795	+	25.4256i	1.00582	+	1.74213i
$214$	14.6374	−	8.45090i	1.00059	−	0.577692i
$215$	−7.27991	−	4.20306i	−0.496486	−	0.286646i
$216$		−	13.1473i		−	0.894562i
$217$		0			0
$218$		−	9.66103i		−	0.654328i
$219$	−6.81665	+	11.8068i	−0.460627	+	0.797829i
$220$	−0.557045	−	0.964829i	−0.0375559	−	0.0650488i
$221$	−24.7177	+	0.935590i	−1.66269	+	0.0629346i
$222$	−8.53670	+	14.7860i	−0.572946	+	0.992371i
$223$	10.6244			0.711460			0.355730	−	0.934589i	$-0.384232\pi$
$223$	10.6244			0.711460			0.355730	+	0.934589i	$0.384232\pi$
$224$		0			0
$225$	−2.22647			−0.148432
$226$	3.10153	+	1.79067i	0.206311	+	0.119114i
$227$	4.53776	−	2.61988i	0.301182	−	0.173887i	−0.341792	−	0.939776i	$-0.611034\pi$
$227$	4.53776	−	2.61988i	0.301182	−	0.173887i	0.642974	+	0.765888i	$0.277701\pi$
$228$	6.07853	−	3.50944i	0.402560	−	0.232418i
$229$	9.72250	−	16.8399i	0.642481	−	1.11281i	−0.342396	−	0.939556i	$-0.611239\pi$
$229$	9.72250	−	16.8399i	0.642481	−	1.11281i	0.984877	−	0.173254i	$-0.0554281\pi$
$230$	1.55977			0.102848
$231$		0			0
$232$			12.7076i			0.834293i
$233$	−25.9286	−	14.9699i	−1.69864	−	0.980710i	−0.947054	−	0.321075i	$-0.895956\pi$
$233$	−25.9286	−	14.9699i	−1.69864	−	0.980710i	−0.751586	−	0.659635i	$-0.770711\pi$
$234$	−2.70783	−	4.69010i	−0.177016	−	0.306601i
$235$	−4.38161	+	2.52973i	−0.285825	+	0.165021i
$236$	−2.51311	+	4.35283i	−0.163589	+	0.283345i
$237$	27.0654			1.75809
$238$		0			0
$239$	−1.00794			−0.0651980			−0.0325990	−	0.999469i	$-0.510378\pi$
$239$	−1.00794			−0.0651980			−0.0325990	+	0.999469i	$0.510378\pi$
$240$	−2.81536	+	4.87634i	−0.181731	+	0.314767i
$241$	6.22988	−	3.59682i	0.401302	−	0.231692i	−0.285744	−	0.958306i	$-0.592241\pi$
$241$	6.22988	−	3.59682i	0.401302	−	0.231692i	0.687046	+	0.726614i	$0.258907\pi$
$242$	5.59728	+	9.69477i	0.359807	+	0.623203i
$243$	−7.09449	−	4.09600i	−0.455111	−	0.262759i
$244$			0.442156i			0.0283062i
$245$		0			0
$246$	−21.6443			−1.37999
$247$	−14.3163	+	24.7966i	−0.910924	+	1.57777i
$248$	4.59531	−	2.65310i	0.291802	−	0.168472i
$249$	1.31261	−	0.757835i	0.0831832	−	0.0480258i
$250$	−11.2361	−	6.48715i	−0.710631	−	0.410283i
$251$	−14.1491			−0.893084			−0.446542	−	0.894763i	$-0.647345\pi$
$251$	−14.1491			−0.893084			−0.446542	+	0.894763i	$0.647345\pi$
$252$		0			0
$253$	−0.919456			−0.0578057
$254$	−7.55378	+	13.0835i	−0.473966	+	0.820934i
$255$	12.0515	−	0.456164i	0.754696	−	0.0285661i
$256$	7.59777	+	13.1597i	0.474861	+	0.822483i
$257$	−12.5825	+	21.7935i	−0.784875	+	1.35944i	0.144199	+	0.989549i	$0.453939\pi$
$257$	−12.5825	+	21.7935i	−0.784875	+	1.35944i	−0.929074	+	0.369894i	$0.879394\pi$
$258$		−	12.2198i		−	0.760773i
$259$		0			0
$260$			6.77579i			0.420217i
$261$	2.89458	+	1.67119i	0.179170	+	0.103444i
$262$	−2.09821	+	1.21140i	−0.129628	+	0.0748407i
$263$	−4.05023	−	7.01521i	−0.249748	−	0.432576i	0.713708	−	0.700444i	$-0.247014\pi$
$263$	−4.05023	−	7.01521i	−0.249748	−	0.432576i	−0.963456	+	0.267867i	$0.913681\pi$
$264$	2.95893	−	5.12502i	0.182110	−	0.315423i
$265$			9.18652i			0.564324i
$266$		0			0
$267$			8.00528i			0.489915i
$268$	−0.312180	+	0.540711i	−0.0190694	+	0.0330292i
$269$	−19.2625	+	11.1212i	−1.17446	+	0.678074i	−0.954726	−	0.297487i	$-0.903852\pi$
$269$	−19.2625	+	11.1212i	−1.17446	+	0.678074i	−0.219732	+	0.975560i	$0.570518\pi$
$270$	−3.57816	−	6.19755i	−0.217760	−	0.377171i
$271$	3.46171	−	5.99587i	0.210284	−	0.364223i	−0.741519	−	0.670932i	$-0.765894\pi$
$271$	3.46171	−	5.99587i	0.210284	−	0.364223i	0.951803	+	0.306709i	$0.0992277\pi$
$272$	−3.70570	+	7.01888i	−0.224691	+	0.425582i
$273$		0			0
$274$	9.28238			0.560769
$275$	2.35223	+	1.35806i	0.141845	+	0.0818940i
$276$	−0.685407	−	1.18716i	−0.0412566	−	0.0714586i
$277$	21.2656	−	12.2777i	1.27773	−	0.737697i	0.301299	−	0.953530i	$-0.402580\pi$
$277$	21.2656	−	12.2777i	1.27773	−	0.737697i	0.976430	+	0.215833i	$0.0692466\pi$
$278$	−0.867642	−	0.500933i	−0.0520377	−	0.0300440i
$279$		−	1.39565i		−	0.0835553i
$280$		0			0
$281$	−7.25294			−0.432674			−0.216337	−	0.976319i	$-0.569411\pi$
$281$	−7.25294			−0.432674			−0.216337	+	0.976319i	$0.569411\pi$
$282$	−6.36947	−	3.67742i	−0.379297	−	0.218987i
$283$	7.93032	−	4.57857i	0.471408	−	0.272168i	−0.245421	−	0.969417i	$-0.578926\pi$
$283$	7.93032	−	4.57857i	0.471408	−	0.272168i	0.716829	+	0.697249i	$0.245593\pi$
$284$	9.81768	−	5.66824i	0.582572	−	0.336348i
$285$	6.98017	−	12.0900i	0.413469	−	0.716150i
$286$			6.60667i			0.390660i
$287$		0			0
$288$	3.23367			0.190546
$289$	16.9514	−	1.28510i	0.997139	−	0.0755939i
$290$	3.45848	+	5.99026i	0.203089	+	0.351760i
$291$	10.9014	+	18.8818i	0.639053	+	1.10687i
$292$	4.55900	+	2.63214i	0.266795	+	0.154034i
$293$	16.9412			0.989716			0.494858	−	0.868974i	$-0.335220\pi$
$293$	16.9412			0.989716			0.494858	+	0.868974i	$0.335220\pi$
$294$		0			0
$295$			9.99699i			0.582047i
$296$	20.8624	+	12.0449i	1.21260	+	0.700096i
$297$	2.10926	+	3.65335i	0.122392	+	0.211989i
$298$	−3.67739	−	6.36943i	−0.213026	−	0.368971i
$299$	4.84286	+	2.79603i	0.280070	+	0.161698i
$300$			4.04945i			0.233795i
$301$		0			0
$302$	−12.9547			−0.745460
$303$	17.7798	+	10.2652i	1.02142	+	0.589719i
$304$	4.59380	+	7.95669i	0.263472	+	0.456348i
$305$	0.439718	+	0.761613i	0.0251782	+	0.0436098i
$306$	1.98162	+	3.15069i	0.113281	+	0.180113i
$307$	18.9097			1.07923			0.539616	−	0.841911i	$-0.318569\pi$
$307$	18.9097			1.07923			0.539616	+	0.841911i	$0.318569\pi$
$308$		0			0
$309$			2.18685i			0.124405i
$310$	1.44413	−	2.50131i	0.0820210	−	0.142065i
$311$	−2.34802	+	1.35563i	−0.133144	+	0.0768707i	−0.565093	−	0.825028i	$-0.691160\pi$
$311$	−2.34802	+	1.35563i	−0.133144	+	0.0768707i	0.431949	+	0.901898i	$0.357826\pi$
$312$	−31.1699	+	17.9960i	−1.76465	+	1.01882i
$313$	23.6809	+	13.6722i	1.33852	+	0.772797i	0.986588	−	0.163228i	$-0.0521905\pi$
$313$	23.6809	+	13.6722i	1.33852	+	0.772797i	0.351935	+	0.936024i	$0.385524\pi$
$314$	−25.0186			−1.41188
$315$		0			0
$316$		−	10.4509i		−	0.587908i
$317$	4.85991	+	2.80587i	0.272960	+	0.157594i	0.630232	−	0.776407i	$-0.282960\pi$
$317$	4.85991	+	2.80587i	0.272960	+	0.157594i	−0.357272	+	0.934000i	$0.616293\pi$
$318$	−11.5652	+	6.67714i	−0.648542	+	0.374436i
$319$	−2.03871	−	3.53115i	−0.114146	−	0.197707i
$320$	10.7928	+	6.23124i	0.603338	+	0.348337i
$321$	−29.5447			−1.64902
$322$		0			0
$323$	9.18760	−	17.4020i	0.511212	−	0.968275i
$324$	−4.05866	+	7.02981i	−0.225481	+	0.390545i
$325$	−8.25959	−	14.3060i	−0.458160	−	0.793556i
$326$	−9.28310	+	5.35960i	−0.514143	+	0.296841i
$327$	−8.44384	+	14.6252i	−0.466945	+	0.808773i
$328$			30.5391i			1.68624i
$329$		0			0
$330$		−	3.22120i		−	0.177321i
$331$	13.6766	−	23.6886i	0.751735	−	1.30204i	−0.195246	−	0.980754i	$-0.562550\pi$
$331$	13.6766	−	23.6886i	0.751735	−	1.30204i	0.946981	−	0.321289i	$-0.104116\pi$
$332$	−0.292626	−	0.506843i	−0.0160599	−	0.0278166i
$333$	5.48727	−	3.16808i	0.300700	−	0.173609i
$334$	7.54907	+	4.35846i	0.413067	+	0.238484i
$335$			1.24183i			0.0678485i
$336$		0			0
$337$			21.0117i			1.14458i	0.820052	+	0.572289i	$0.193945\pi$
$337$			21.0117i			1.14458i	−0.820052	+	0.572289i	$0.806055\pi$
$338$	12.8337	−	22.2287i	0.698063	−	1.20908i
$339$	−3.13013	−	5.42154i	−0.170005	−	0.294458i
$340$	−0.176140	−	4.65350i	−0.00955254	−	0.252372i
$341$	−0.851289	+	1.47448i	−0.0460999	+	0.0798474i
$342$	4.30849			0.232976
$343$		0			0
$344$	−17.2416			−0.929607
$345$	−2.36122	−	1.36325i	−0.127124	−	0.0733950i
$346$	8.00549	−	4.62197i	0.430378	−	0.248479i
$347$	−19.3773	+	11.1875i	−1.04023	+	0.600574i	−0.919897	−	0.392160i	$-0.871728\pi$
$347$	−19.3773	+	11.1875i	−1.04023	+	0.600574i	−0.120328	+	0.992734i	$0.538395\pi$
$348$	3.03951	−	5.26458i	0.162935	−	0.282211i
$349$	7.84612			0.419993			0.209997	−	0.977702i	$-0.432655\pi$
$349$	7.84612			0.419993			0.209997	+	0.977702i	$0.432655\pi$
$350$		0			0
$351$		−	25.6567i		−	1.36945i
$352$	−3.41631	−	1.97241i	−0.182090	−	0.105130i
$353$	−3.24994	−	5.62906i	−0.172977	−	0.299605i	0.766482	−	0.642265i	$-0.222005\pi$
$353$	−3.24994	−	5.62906i	−0.172977	−	0.299605i	−0.939459	+	0.342661i	$0.888672\pi$
$354$	−12.5855	+	7.26623i	−0.668910	+	0.386196i
$355$	11.2740	−	19.5271i	0.598359	−	1.03639i
$356$	3.09111			0.163828
$357$		0			0
$358$	16.2631			0.859533
$359$	11.3648	−	19.6844i	0.599812	−	1.03890i	−0.393037	−	0.919523i	$-0.628575\pi$
$359$	11.3648	−	19.6844i	0.599812	−	1.03890i	0.992848	−	0.119382i	$-0.0380912\pi$
$360$	3.22649	−	1.86282i	0.170051	−	0.0981790i
$361$	−1.88949	−	3.27268i	−0.0994466	−	0.172247i
$362$	−11.2068	−	6.47023i	−0.589015	−	0.340068i
$363$		−	19.5683i		−	1.02707i
$364$		0			0
$365$	10.4705			0.548050
$366$	−0.639210	+	1.10714i	−0.0334120	+	0.0578713i
$367$	−24.4483	+	14.1152i	−1.27619	+	0.736808i	−0.976145	−	0.217118i	$-0.930334\pi$
$367$	−24.4483	+	14.1152i	−1.27619	+	0.736808i	−0.300043	+	0.953926i	$0.597001\pi$
$368$	1.55397	−	0.897186i	0.0810064	−	0.0467691i
$369$	6.95632	+	4.01623i	0.362131	+	0.209077i
$370$	13.1125			0.681686
$371$		0			0
$372$	−2.53837			−0.131608
$373$	4.69067	−	8.12448i	0.242874	−	0.420670i	−0.718658	−	0.695364i	$-0.755243\pi$
$373$	4.69067	−	8.12448i	0.242874	−	0.420670i	0.961532	+	0.274694i	$0.0885766\pi$
$374$	−0.171744	−	4.53735i	−0.00888065	−	0.234621i
$375$	11.3397	+	19.6409i	0.585577	+	1.01425i
$376$	−5.18867	+	8.98705i	−0.267585	+	0.463472i
$377$			24.7985i			1.27719i
$378$		0			0
$379$		−	21.1109i		−	1.08439i	−0.840251	−	0.542197i	$-0.817593\pi$
$379$		−	21.1109i		−	1.08439i	0.840251	−	0.542197i	$-0.182407\pi$
$380$	−4.66836	−	2.69528i	−0.239482	−	0.138265i
$381$	22.8703	−	13.2042i	1.17168	−	0.676469i
$382$	−12.6699	−	21.9450i	−0.648251	−	1.12280i
$383$	8.72018	−	15.1038i	0.445580	−	0.771767i	−0.552512	−	0.833505i	$-0.686331\pi$
$383$	8.72018	−	15.1038i	0.445580	−	0.771767i	0.998092	+	0.0617373i	$0.0196641\pi$
$384$			2.50714i			0.127942i
$385$		0			0
$386$		−	29.6347i		−	1.50837i
$387$	−2.26747	+	3.92737i	−0.115262	+	0.199639i
$388$	7.29091	−	4.20941i	0.370140	−	0.213700i
$389$	−12.2819	−	21.2729i	−0.622718	−	1.07858i	−0.988977	−	0.148066i	$-0.952695\pi$
$389$	−12.2819	−	21.2729i	−0.622718	−	1.07858i	0.366259	−	0.930513i	$-0.380638\pi$
$390$	−9.79552	+	16.9663i	−0.496016	+	0.859124i
$391$	−3.39868	−	1.79437i	−0.171879	−	0.0907453i
$392$		0			0
$393$	4.23511			0.213633
$394$	−2.87943	−	1.66244i	−0.145064	−	0.0837526i
$395$	−10.3932	−	18.0016i	−0.522941	−	0.905760i
$396$	−0.520506	+	0.300514i	−0.0261564	+	0.0151014i
$397$	−1.65447	−	0.955210i	−0.0830356	−	0.0479406i	0.457907	−	0.889000i	$-0.348599\pi$
$397$	−1.65447	−	0.955210i	−0.0830356	−	0.0479406i	−0.540943	+	0.841059i	$0.681932\pi$
$398$		−	19.7014i		−	0.987544i
$399$		0			0
$400$	−5.30066			−0.265033
$401$	12.1985	+	7.04283i	0.609166	+	0.351702i	0.772639	−	0.634846i	$-0.218936\pi$
$401$	12.1985	+	7.04283i	0.609166	+	0.351702i	−0.163473	+	0.986548i	$0.552270\pi$
$402$	−1.56337	+	0.902614i	−0.0779740	+	0.0450183i
$403$	8.96764	−	5.17747i	0.446710	−	0.257908i
$404$	3.96373	−	6.86538i	0.197203	−	0.341566i
$405$			16.1451i			0.802257i
$406$		0			0
$407$	−7.72959			−0.383142
$408$	20.9392	−	13.1696i	1.03664	−	0.651993i
$409$	1.96938	+	3.41107i	0.0973796	+	0.168666i	0.910599	−	0.413290i	$-0.135621\pi$
$409$	1.96938	+	3.41107i	0.0973796	+	0.168666i	−0.813220	+	0.581957i	$0.802287\pi$
$410$	8.31148	+	14.3959i	0.410475	+	0.710963i
$411$	−14.0519	−	8.11289i	−0.693131	−	0.400179i
$412$	0.844416			0.0416014
$413$		0			0
$414$		−	0.841464i		−	0.0413557i
$415$	−1.00809	−	0.582023i	−0.0494854	−	0.0285704i
$416$	11.9960	+	20.7777i	0.588154	+	1.01871i
$417$	0.875641	+	1.51665i	0.0428803	+	0.0742709i
$418$	−4.55183	−	2.62800i	−0.222637	−	0.128540i
$419$		−	10.3202i		−	0.504174i	−0.967705	−	0.252087i	$-0.918883\pi$
$419$		−	10.3202i		−	0.504174i	0.967705	−	0.252087i	$-0.0811169\pi$
$420$		0			0
$421$	2.25685			0.109992			0.0549961	−	0.998487i	$-0.482485\pi$
$421$	2.25685			0.109992			0.0549961	+	0.998487i	$0.482485\pi$
$422$	8.10439	+	4.67907i	0.394516	+	0.227774i
$423$	1.36474	+	2.36379i	0.0663558	+	0.114932i
$424$	9.42116	+	16.3179i	0.457532	+	0.792468i
$425$	6.04444	+	9.61044i	0.293199	+	0.466175i
$426$	32.7775			1.58808
$427$		0			0
$428$			11.4082i			0.551436i
$429$	5.77429	−	10.0014i	0.278785	−	0.482871i
$430$	−8.12758	+	4.69246i	−0.391947	+	0.226291i
$431$	−1.71655	+	0.991053i	−0.0826835	+	0.0477374i	−0.540772	−	0.841169i	$-0.681868\pi$
$431$	−1.71655	+	0.991053i	−0.0826835	+	0.0477374i	0.458088	+	0.888907i	$0.348534\pi$
$432$	−7.12973	−	4.11635i	−0.343029	−	0.198048i
$433$	−33.9841			−1.63317			−0.816586	−	0.577224i	$-0.804136\pi$
$433$	−33.9841			−1.63317			−0.816586	+	0.577224i	$0.804136\pi$
$434$		0			0
$435$		−	12.0910i		−	0.579718i
$436$	5.64727	+	3.26045i	0.270455	+	0.156147i
$437$	−3.85279	+	2.22441i	−0.184304	+	0.106408i
$438$	7.61038	+	13.1816i	0.363638	+	0.629839i
$439$	−13.2715	−	7.66229i	−0.633413	−	0.365701i	0.148660	−	0.988888i	$-0.452504\pi$
$439$	−13.2715	−	7.66229i	−0.633413	−	0.365701i	−0.782073	+	0.623187i	$0.785837\pi$
$440$	−4.54497			−0.216673
$441$		0			0
$442$	−12.8933	+	24.4209i	−0.613272	+	1.16158i
$443$	−16.2680	+	28.1769i	−0.772914	+	1.33873i	0.163045	+	0.986619i	$0.447868\pi$
$443$	−16.2680	+	28.1769i	−0.772914	+	1.33873i	−0.935959	+	0.352108i	$0.885465\pi$
$444$	−5.76201	−	9.98009i	−0.273453	−	0.473634i
$445$	5.32443	−	3.07406i	0.252402	−	0.145724i
$446$	5.93073	−	10.2723i	0.280828	−	0.486409i
$447$			12.8563i			0.608083i
$448$		0			0
$449$			2.31105i			0.109065i	0.998512	+	0.0545326i	$0.0173669\pi$
$449$			2.31105i			0.109065i	−0.998512	+	0.0545326i	$0.982633\pi$
$450$	−1.24286	+	2.15270i	−0.0585891	+	0.101479i
$451$	−4.89948	−	8.48614i	−0.230707	−	0.399597i
$452$	−2.09344	+	1.20865i	−0.0984671	+	0.0568500i
$453$	19.6112	+	11.3226i	0.921416	+	0.531980i
$454$		−	5.84987i		−	0.274548i
$455$		0			0
$456$		−	28.6338i		−	1.34090i
$457$	4.51441	−	7.81918i	0.211175	−	0.365766i	−0.740908	−	0.671607i	$-0.765604\pi$
$457$	4.51441	−	7.81918i	0.211175	−	0.365766i	0.952083	+	0.305841i	$0.0989377\pi$
$458$	−10.8546	−	18.8007i	−0.507201	−	0.878499i
$459$	0.666959	+	17.6206i	0.0311310	+	0.822459i
$460$	−0.526398	+	0.911748i	−0.0245434	+	0.0425105i
$461$	38.6386			1.79958			0.899789	−	0.436324i	$-0.143720\pi$
$461$	38.6386			1.79958			0.899789	+	0.436324i	$0.143720\pi$
$462$		0			0
$463$	25.1396			1.16834			0.584168	−	0.811633i	$-0.301421\pi$
$463$	25.1396			1.16834			0.584168	+	0.811633i	$0.301421\pi$
$464$	6.89125	+	3.97867i	0.319918	+	0.184705i
$465$	−4.37233	+	2.52437i	−0.202762	+	0.117065i
$466$	−28.9477	+	16.7130i	−1.34098	+	0.774214i
$467$	8.67496	−	15.0255i	0.401429	−	0.695296i	−0.592469	−	0.805593i	$-0.701847\pi$
$467$	8.67496	−	15.0255i	0.401429	−	0.695296i	0.993899	+	0.110297i	$0.0351802\pi$
$468$	3.65541			0.168971
$469$		0			0
$470$			5.64857i			0.260549i
$471$	37.8738	+	21.8665i	1.74513	+	1.00755i
$472$	10.2523	+	17.7575i	0.471901	+	0.817357i
$473$	4.79107	−	2.76612i	0.220294	−	0.127187i
$474$	15.1085	−	26.1686i	0.693955	−	1.20197i
$475$	13.1420			0.602997
$476$		0			0
$477$	4.95595			0.226917
$478$	−0.562650	+	0.974538i	−0.0257350	+	0.0445743i
$479$	−22.2296	+	12.8343i	−1.01570	+	0.586413i	−0.912854	−	0.408285i	$-0.866127\pi$
$479$	−22.2296	+	12.8343i	−1.01570	+	0.586413i	−0.102842	+	0.994698i	$0.532794\pi$
$480$	−5.84888	−	10.1305i	−0.266963	−	0.462394i
$481$	40.7125	+	23.5054i	1.85633	+	1.07175i
$482$		−	8.03127i		−	0.365814i
$483$		0			0
$484$	−7.55598			−0.343454
$485$	8.37239	−	14.5014i	0.380170	−	0.658475i
$486$	−7.92057	+	4.57294i	−0.359284	+	0.207433i
$487$	−26.6590	+	15.3916i	−1.20803	+	0.697458i	−0.962329	−	0.271887i	$-0.912352\pi$
$487$	−26.6590	+	15.3916i	−1.20803	+	0.697458i	−0.245704	+	0.969345i	$0.579019\pi$
$488$	1.56213	+	0.901897i	0.0707143	+	0.0408269i
$489$	18.7374			0.847333
$490$		0			0
$491$	−34.0328			−1.53588			−0.767938	−	0.640524i	$-0.778717\pi$
$491$	−34.0328			−1.53588			−0.767938	+	0.640524i	$0.778717\pi$
$492$	7.30461	−	12.6519i	0.329317	−	0.570394i
$493$	−0.644651	−	17.0312i	−0.0290336	−	0.767048i
$494$	15.9833	+	27.6839i	0.719122	+	1.24556i
$495$	−0.597714	+	1.03527i	−0.0268652	+	0.0465320i
$496$		−	3.32268i		−	0.149193i
$497$		0			0
$498$		−	1.69215i		−	0.0758272i
$499$	−16.3514	−	9.44046i	−0.731987	−	0.422613i	0.0871615	−	0.996194i	$-0.472220\pi$
$499$	−16.3514	−	9.44046i	−0.731987	−	0.422613i	−0.819149	+	0.573581i	$0.805554\pi$
$500$	7.58400	−	4.37862i	0.339167	−	0.195818i
$501$	−7.61867	−	13.1959i	−0.340377	−	0.589551i
$502$	−7.89831	+	13.6803i	−0.352519	+	0.610581i
$503$			29.9077i			1.33352i	0.745274	+	0.666759i	$0.232319\pi$
$503$			29.9077i			1.33352i	−0.745274	+	0.666759i	$0.767681\pi$
$504$		0			0
$505$		−	15.7675i		−	0.701643i
$506$	−0.513259	+	0.888990i	−0.0228171	+	0.0395204i
$507$	−38.8562	+	22.4336i	−1.72566	+	0.996312i
$508$	−5.09857	−	8.83098i	−0.226212	−	0.391811i
$509$	−8.78865	+	15.2224i	−0.389550	+	0.674721i	−0.992389	−	0.123142i	$-0.960703\pi$
$509$	−8.78865	+	15.2224i	−0.389550	+	0.674721i	0.602839	+	0.797863i	$0.294036\pi$
$510$	6.28636	−	11.9068i	0.278365	−	0.527244i
$511$		0			0
$512$	19.5343			0.863301
$513$	17.6769	+	10.2057i	0.780452	+	0.450594i
$514$	14.0476	+	24.3312i	0.619613	+	1.07320i
$515$	1.45450	−	0.839758i	0.0640931	−	0.0370042i
$516$	7.14298	+	4.12400i	0.314452	+	0.181549i
$517$		−	3.32974i		−	0.146442i
$518$		0			0
$519$	−16.1586			−0.709283
$520$	23.9388	+	13.8211i	1.04978	+	0.606093i
$521$	21.3384	−	12.3197i	0.934853	−	0.539738i	0.0465100	−	0.998918i	$-0.485190\pi$
$521$	21.3384	−	12.3197i	0.934853	−	0.539738i	0.888343	+	0.459180i	$0.151857\pi$
$522$	3.23162	−	1.86578i	0.141444	−	0.0816629i
$523$	−14.1347	+	24.4820i	−0.618068	+	1.07053i	0.371770	+	0.928325i	$0.378751\pi$
$523$	−14.1347	+	24.4820i	−0.618068	+	1.07053i	−0.989838	+	0.142200i	$0.954582\pi$
$524$		−	1.63532i		−	0.0714393i
$525$		0			0
$526$	−9.04368			−0.394323
$527$	−6.02423	+	3.78892i	−0.262420	+	0.165048i
$528$	−1.85285	−	3.20923i	−0.0806349	−	0.139664i
$529$	−11.0656	−	19.1661i	−0.481112	−	0.833310i
$530$	8.88213	+	5.12810i	0.385815	+	0.222750i
$531$	5.39318			0.234044
$532$		0			0
$533$			59.5964i			2.58141i
$534$	7.74003	+	4.46871i	0.334944	+	0.193380i
$535$	11.3453	+	19.6506i	0.490499	+	0.849569i
$536$	1.27355	+	2.20585i	0.0550089	+	0.0952782i
$537$	−24.6196	−	14.2141i	−1.06241	−	0.613385i
$538$			24.8324i			1.07060i
$539$		0			0
$540$	4.83030			0.207863
$541$	−27.4382	−	15.8414i	−1.17966	−	0.681077i	−0.223723	−	0.974653i	$-0.571821\pi$
$541$	−27.4382	−	15.8414i	−1.17966	−	0.681077i	−0.955936	+	0.293576i	$0.905155\pi$
$542$	−3.86480	−	6.69402i	−0.166007	−	0.287533i
$543$	11.3101	+	19.5896i	0.485362	+	0.840672i
$544$	−8.77880	−	13.9580i	−0.376388	−	0.598443i
$545$	12.9699			0.555568
$546$		0			0
$547$			35.5388i			1.51953i	0.650197	+	0.759766i	$0.274686\pi$
$547$			35.5388i			1.51953i	−0.650197	+	0.759766i	$0.725314\pi$
$548$	−3.13266	+	5.42593i	−0.133821	+	0.231784i
$549$	0.410875	−	0.237219i	0.0175357	−	0.0101243i
$550$	2.62612	−	1.51619i	0.111978	−	0.0646506i
$551$	−17.0856	−	9.86437i	−0.727871	−	0.420236i
$552$	−5.59228			−0.238023
$553$		0			0
$554$		−	27.4147i		−	1.16474i
$555$	−19.8501	−	11.4605i	−0.842589	−	0.486469i
$556$	0.585631	−	0.338114i	0.0248363	−	0.0143392i
$557$	−3.16066	−	5.47442i	−0.133921	−	0.231959i	0.791264	−	0.611475i	$-0.209424\pi$
$557$	−3.16066	−	5.47442i	−0.133921	−	0.231959i	−0.925185	+	0.379517i	$0.876090\pi$
$558$	−1.34940	−	0.779079i	−0.0571248	−	0.0329810i
$559$	−33.6467			−1.42310
$560$		0			0
$561$	−3.70570	+	7.01888i	−0.156455	+	0.296337i
$562$	−4.04873	+	7.01261i	−0.170785	+	0.295809i
$563$	4.70295	+	8.14574i	0.198206	+	0.343302i	0.947947	−	0.318429i	$-0.103155\pi$
$563$	4.70295	+	8.14574i	0.198206	+	0.343302i	−0.749741	+	0.661731i	$0.769822\pi$
$564$	4.29920	−	2.48214i	0.181029	−	0.104517i
$565$	−2.40396	+	4.16379i	−0.101135	+	0.175172i
$566$		−	10.2234i		−	0.429721i
$567$		0			0
$568$		−	46.2476i		−	1.94051i
$569$	−8.44752	+	14.6315i	−0.354138	+	0.613386i	−0.986970	−	0.160904i	$-0.948559\pi$
$569$	−8.44752	+	14.6315i	−0.354138	+	0.613386i	0.632832	+	0.774289i	$0.281892\pi$
$570$	−7.79293	−	13.4978i	−0.326410	−	0.565359i
$571$	−0.390415	+	0.225406i	−0.0163384	+	0.00943297i	−0.508147	−	0.861270i	$-0.669669\pi$
$571$	−0.390415	+	0.225406i	−0.0163384	+	0.00943297i	0.491809	+	0.870703i	$0.336336\pi$
$572$	−3.86186	−	2.22965i	−0.161473	−	0.0932263i
$573$			44.2946i			1.85043i
$574$		0			0
$575$		−	2.56668i		−	0.107038i
$576$	3.36163	−	5.82252i	0.140068	−	0.242605i
$577$	10.1309	+	17.5472i	0.421755	+	0.730500i	0.996111	−	0.0881048i	$-0.0280810\pi$
$577$	10.1309	+	17.5472i	0.421755	+	0.730500i	−0.574357	+	0.818605i	$0.694748\pi$
$578$	8.22007	−	17.1070i	0.341910	−	0.711559i
$579$	−25.9010	+	44.8619i	−1.07641	+	1.86440i
$580$	−4.66873			−0.193858
$581$		0			0
$582$	24.3416			1.00899
$583$	−5.23586	−	3.02293i	−0.216847	−	0.125197i
$584$	18.5986	−	10.7379i	0.769616	−	0.444338i
$585$	6.29643	−	3.63524i	0.260325	−	0.150299i
$586$	9.45692	−	16.3799i	0.390662	−	0.676646i
$587$	−36.5831			−1.50995			−0.754973	−	0.655756i	$-0.772350\pi$
$587$	−36.5831			−1.50995			−0.754973	+	0.655756i	$0.772350\pi$
$588$		0			0
$589$			8.23798i			0.339440i
$590$	9.66574	+	5.58052i	0.397932	+	0.229746i
$591$	2.90598	+	5.03330i	0.119536	+	0.207042i
$592$	13.0638	−	7.54237i	0.536918	−	0.309990i
$593$	2.14224	−	3.71046i	0.0879711	−	0.152370i	−0.818682	−	0.574247i	$-0.805295\pi$
$593$	2.14224	−	3.71046i	0.0879711	−	0.152370i	0.906653	+	0.421876i	$0.138628\pi$
$594$	4.70973			0.193243
$595$		0			0
$596$	4.96426			0.203344
$597$	−17.2192	+	29.8246i	−0.704737	+	1.22064i
$598$	5.40676	−	3.12160i	0.221099	−	0.127652i
$599$	−7.50569	−	13.0002i	−0.306674	−	0.531175i	0.670959	−	0.741495i	$-0.265883\pi$
$599$	−7.50569	−	13.0002i	−0.306674	−	0.531175i	−0.977633	+	0.210320i	$0.932549\pi$
$600$	14.3066	+	8.25993i	0.584066	+	0.337210i
$601$			23.4374i			0.956033i	0.878351	+	0.478017i	$0.158644\pi$
$601$			23.4374i			0.956033i	−0.878351	+	0.478017i	$0.841356\pi$
$602$		0			0
$603$	0.669943			0.0272822
$604$	4.37202	−	7.57256i	0.177895	−	0.308123i
$605$	−13.0152	+	7.51430i	−0.529141	+	0.305500i
$606$	19.8501	−	11.4605i	0.806355	−	0.465549i
$607$	9.52983	+	5.50205i	0.386804	+	0.223321i	0.680774	−	0.732493i	$-0.261643\pi$
$607$	9.52983	+	5.50205i	0.386804	+	0.223321i	−0.293971	+	0.955814i	$0.594977\pi$
$608$	−19.0871			−0.774086
$609$		0			0
$610$	0.981836			0.0397534
$611$	−10.1256	+	17.5380i	−0.409637	+	0.709512i
$612$	−2.51047	+	0.0950241i	−0.101480	+	0.00384112i
$613$	3.14915	+	5.45448i	0.127193	+	0.220304i	0.922588	−	0.385787i	$-0.126070\pi$
$613$	3.14915	+	5.45448i	0.127193	+	0.220304i	−0.795395	+	0.606091i	$0.792737\pi$
$614$	10.5558	−	18.2831i	0.425996	−	0.737847i
$615$		−	29.0573i		−	1.17170i
$616$		0			0
$617$			24.1377i			0.971748i	0.874029	+	0.485874i	$0.161499\pi$
$617$			24.1377i			0.971748i	−0.874029	+	0.485874i	$0.838501\pi$
$618$	2.11439	+	1.22074i	0.0850531	+	0.0491054i
$619$	3.11966	−	1.80114i	0.125390	−	0.0723939i	−0.435993	−	0.899950i	$-0.643603\pi$
$619$	3.11966	−	1.80114i	0.125390	−	0.0723939i	0.561383	+	0.827556i	$0.310269\pi$
$620$	0.974743	+	1.68830i	0.0391466	+	0.0678039i
$621$	1.99322	−	3.45236i	0.0799851	−	0.138538i
$622$			3.02696i			0.121370i
$623$		0			0
$624$			22.5377i			0.902231i
$625$	1.82504	−	3.16106i	0.0730016	−	0.126443i
$626$	26.4383	−	15.2642i	1.05669	−	0.610078i
$627$	4.59380	+	7.95669i	0.183459	+	0.317760i
$628$	8.44338	−	14.6244i	0.336928	−	0.583576i
$629$	−28.5717	−	15.0847i	−1.13923	−	0.601468i
$630$		0			0
$631$	−11.4191			−0.454587			−0.227293	−	0.973826i	$-0.572988\pi$
$631$	−11.4191			−0.454587			−0.227293	+	0.973826i	$0.572988\pi$
$632$	−36.9228	−	21.3174i	−1.46871	−	0.847960i
$633$	−8.17911	−	14.1666i	−0.325090	−	0.563073i
$634$	5.42580	−	3.13259i	0.215486	−	0.124411i
$635$	−17.5645	−	10.1409i	−0.697028	−	0.402429i
$636$		−	9.01373i		−	0.357418i
$637$		0			0
$638$	−4.55220			−0.180223
$639$	−10.5345	−	6.08207i	−0.416737	−	0.240603i
$640$	1.66753	−	0.962750i	0.0659150	−	0.0380560i
$641$	4.90140	−	2.82983i	0.193594	−	0.111771i	−0.400070	−	0.916485i	$-0.631014\pi$
$641$	4.90140	−	2.82983i	0.193594	−	0.111771i	0.593664	+	0.804713i	$0.297681\pi$
$642$	−16.4924	+	28.5657i	−0.650904	+	1.12740i
$643$		−	15.2852i		−	0.602791i	−0.953499	−	0.301395i	$-0.902548\pi$
$643$		−	15.2852i		−	0.602791i	0.953499	−	0.301395i	$-0.0974524\pi$
$644$		0			0
$645$	16.4050			0.645947
$646$	−11.6967	−	18.5973i	−0.460201	−	0.731702i
$647$	14.3719	+	24.8929i	0.565018	+	0.978640i	0.997048	+	0.0767810i	$0.0244642\pi$
$647$	14.3719	+	24.8929i	0.565018	+	0.978640i	−0.432030	+	0.901859i	$0.642202\pi$
$648$	16.5575	+	28.6784i	0.650439	+	1.12659i
$649$	−5.69779	−	3.28962i	−0.223658	−	0.129129i
$650$	−18.4427			−0.723381
$651$		0			0
$652$		−	7.23513i		−	0.283349i
$653$	−18.0039	−	10.3946i	−0.704547	−	0.406770i	0.104492	−	0.994526i	$-0.466678\pi$
$653$	−18.0039	−	10.3946i	−0.704547	−	0.406770i	−0.809039	+	0.587755i	$0.800012\pi$
$654$	9.42704	+	16.3281i	0.368626	+	0.638479i
$655$	−1.62630	−	2.81683i	−0.0635448	−	0.110063i
$656$	16.5612	+	9.56161i	0.646606	+	0.373318i
$657$		−	5.64862i		−	0.220374i
$658$		0			0
$659$	47.0480			1.83273			0.916365	−	0.400343i	$-0.131109\pi$
$659$	47.0480			1.83273			0.916365	+	0.400343i	$0.131109\pi$
$660$	1.88292	+	1.08710i	0.0732926	+	0.0423155i
$661$	2.94057	+	5.09322i	0.114375	+	0.198103i	0.917530	−	0.397667i	$-0.130180\pi$
$661$	2.94057	+	5.09322i	0.114375	+	0.198103i	−0.803155	+	0.595770i	$0.796847\pi$
$662$	−15.2691	−	26.4469i	−0.593451	−	1.02789i
$663$	40.8624	−	25.7002i	1.58696	−	0.998114i
$664$	−2.38755			−0.0926551
$665$		0			0
$666$		−	7.07393i		−	0.274109i
$667$	−1.92655	+	3.33688i	−0.0745963	+	0.129205i
$668$	−5.09539	+	2.94183i	−0.197147	+	0.113823i
$669$	−17.9562	+	10.3670i	−0.694228	+	0.400812i
$670$	1.20068	+	0.693215i	0.0463864	+	0.0267812i
$671$	−0.578775			−0.0223434
$672$		0			0
$673$			25.3750i			0.978135i	0.872246	+	0.489068i	$0.162663\pi$
$673$			25.3750i			0.978135i	−0.872246	+	0.489068i	$0.837337\pi$
$674$	20.3155	+	11.7291i	0.782522	+	0.451789i
$675$	−10.1984	+	5.88806i	−0.392537	+	0.226632i
$676$	8.66237	+	15.0037i	0.333168	+	0.577064i
$677$	−36.9800	−	21.3504i	−1.42126	−	0.820562i	−0.424849	−	0.905264i	$-0.639673\pi$
$677$	−36.9800	−	21.3504i	−1.42126	−	0.820562i	−0.996406	+	0.0847023i	$0.973006\pi$
$678$	−6.98920			−0.268419
$679$		0			0
$680$	−16.8000	−	8.86977i	−0.644252	−	0.340140i
$681$	−5.11284	+	8.85570i	−0.195924	+	0.339351i
$682$	0.950413	+	1.64616i	0.0363932	+	0.0630349i
$683$	17.2620	−	9.96620i	0.660511	−	0.381346i	−0.131961	−	0.991255i	$-0.542127\pi$
$683$	17.2620	−	9.96620i	0.660511	−	0.381346i	0.792472	+	0.609909i	$0.208794\pi$
$684$	−1.45405	+	2.51849i	−0.0555969	+	0.0962967i
$685$			12.4615i			0.476130i
$686$		0			0
$687$			37.9480i			1.44781i
$688$	−5.39825	+	9.35005i	−0.205806	+	0.356467i
$689$	18.3852	+	31.8441i	0.700419	+	1.21316i
$690$	−2.63616	+	1.52199i	−0.100357	+	0.0579411i
$691$	−6.86111	−	3.96126i	−0.261009	−	0.150693i	0.363786	−	0.931483i	$-0.381484\pi$
$691$	−6.86111	−	3.96126i	−0.261009	−	0.150693i	−0.624795	+	0.780789i	$0.714817\pi$
$692$			6.23938i			0.237186i
$693$		0			0
$694$			24.9803i			0.948238i
$695$	0.672499	−	1.16480i	0.0255093	−	0.0441835i
$696$	−12.3998	−	21.4771i	−0.470013	−	0.814086i
$697$	−1.54924	−	40.9298i	−0.0586816	−	1.55033i
$698$	4.37986	−	7.58614i	0.165780	−	0.287140i
$699$	58.4292			2.21000
$700$		0			0
$701$	−18.6458			−0.704240			−0.352120	−	0.935955i	$-0.614539\pi$
$701$	−18.6458			−0.704240			−0.352120	+	0.935955i	$0.614539\pi$
$702$	−24.8066	−	14.3221i	−0.936264	−	0.540552i
$703$	−32.3892	+	18.6999i	−1.22158	+	0.705281i
$704$	−7.10300	+	4.10092i	−0.267704	+	0.154559i
$705$	4.93691	−	8.55097i	0.185935	−	0.322048i
$706$	−7.25672			−0.273110
$707$		0			0
$708$		−	9.80896i		−	0.368643i
$709$	−4.73118	−	2.73155i	−0.177683	−	0.102585i	0.408520	−	0.912749i	$-0.366045\pi$
$709$	−4.73118	−	2.73155i	−0.177683	−	0.102585i	−0.586204	+	0.810164i	$0.699378\pi$
$710$	−12.5867	−	21.8008i	−0.472370	−	0.818169i
$711$	−9.71151	+	5.60694i	−0.364210	+	0.210277i
$712$	6.30515	−	10.9208i	0.236295	−	0.409276i
$713$	1.60891			0.0602541
$714$		0			0
$715$	−8.86940			−0.331697
$716$	−5.48856	+	9.50646i	−0.205117	+	0.355273i
$717$	1.70351	−	0.983523i	0.0636188	−	0.0367303i
$718$	−12.6881	−	21.9765i	−0.473517	−	0.820155i
$719$	−36.0496	−	20.8132i	−1.34442	−	0.776203i	−0.356970	−	0.934116i	$-0.616190\pi$
$719$	−36.0496	−	20.8132i	−1.34442	−	0.776203i	−0.987453	+	0.157913i	$0.949524\pi$
$720$		−	2.33295i		−	0.0869438i
$721$		0			0
$722$	−4.21899			−0.157015
$723$	−7.01941	+	12.1580i	−0.261055	+	0.452160i
$724$	7.56422	−	4.36721i	0.281122	−	0.162306i
$725$	9.85730	−	5.69111i	0.366091	−	0.211363i
$726$	−18.9199	−	10.9234i	−0.702184	−	0.405406i
$727$	21.8552			0.810565			0.405283	−	0.914191i	$-0.367173\pi$
$727$	21.8552			0.810565			0.405283	+	0.914191i	$0.367173\pi$
$728$		0			0
$729$	−16.3286			−0.604764
$730$	5.84483	−	10.1235i	0.216327	−	0.374689i
$731$	23.1080	−	0.874662i	0.854679	−	0.0323505i
$732$	−0.431447	−	0.747288i	−0.0159467	−	0.0276206i
$733$	−13.5132	+	23.4056i	−0.499123	+	0.864506i	−0.999999	−	0.00101295i	$-0.999678\pi$
$733$	−13.5132	+	23.4056i	−0.499123	+	0.864506i	0.500877	+	0.865518i	$0.333011\pi$
$734$			31.5175i			1.16333i
$735$		0			0
$736$			3.72779i			0.137408i
$737$	−0.707782	−	0.408638i	−0.0260715	−	0.0150524i
$738$	7.76631	−	4.48388i	0.285882	−	0.165054i
$739$	−7.24918	−	12.5560i	−0.266666	−	0.461878i	0.701333	−	0.712834i	$-0.252589\pi$
$739$	−7.24918	−	12.5560i	−0.266666	−	0.461878i	−0.967999	+	0.250955i	$0.919255\pi$
$740$	−4.42527	+	7.66479i	−0.162676	+	0.281763i
$741$		−	55.8782i		−	2.05274i
$742$		0			0
$743$			2.58568i			0.0948596i	0.998875	+	0.0474298i	$0.0151030\pi$
$743$			2.58568i			0.0948596i	−0.998875	+	0.0474298i	$0.984897\pi$
$744$	−5.17768	+	8.96801i	−0.189823	+	0.328783i
$745$	8.55092	−	4.93688i	0.313281	−	0.180873i
$746$	−5.23685	−	9.07050i	−0.191735	−	0.332094i
$747$	−0.313990	+	0.543847i	−0.0114883	+	0.0198983i
$748$	2.71023	+	1.43089i	0.0990957	+	0.0523187i
$749$		0			0
$750$	25.3201			0.924559
$751$	16.5966	+	9.58206i	0.605619	+	0.349654i	0.771249	−	0.636534i	$-0.219632\pi$
$751$	16.5966	+	9.58206i	0.605619	+	0.349654i	−0.165630	+	0.986188i	$0.552966\pi$
$752$	3.24909	+	5.62758i	0.118482	+	0.205217i
$753$	23.9134	−	13.8064i	0.871452	−	0.503133i
$754$	23.9768	+	13.8430i	0.873185	+	0.504134i
$755$		−	17.3916i		−	0.632946i
$756$		0			0
$757$	−2.81660			−0.102371			−0.0511855	−	0.998689i	$-0.516300\pi$
$757$	−2.81660			−0.102371			−0.0511855	+	0.998689i	$0.516300\pi$
$758$	−20.4114	−	11.7845i	−0.741375	−	0.428033i
$759$	1.55397	−	0.897186i	0.0564056	−	0.0325658i
$760$	−19.0447	+	10.9955i	−0.690825	+	0.398848i
$761$	2.52804	−	4.37870i	0.0916415	−	0.158728i	−0.816560	−	0.577260i	$-0.804122\pi$
$761$	2.52804	−	4.37870i	0.0916415	−	0.158728i	0.908202	+	0.418532i	$0.137455\pi$
$762$		−	29.4833i		−	1.06807i
$763$		0			0
$764$	17.1036			0.618788
$765$	−4.22978	+	2.66030i	−0.152928	+	0.0961835i
$766$	−9.73555	−	16.8625i	−0.351760	−	0.609266i
$767$	20.0072	+	34.6535i	0.722417	+	1.25126i
$768$	−25.6820	−	14.8275i	−0.926718	−	0.535041i
$769$	−11.9647			−0.431460			−0.215730	−	0.976453i	$-0.569213\pi$
$769$	−11.9647			−0.431460			−0.215730	+	0.976453i	$0.569213\pi$
$770$		0			0
$771$		−	49.1110i		−	1.76869i
$772$	17.3227	+	10.0013i	0.623457	+	0.359953i
$773$	−17.1472	−	29.6998i	−0.616741	−	1.06823i	−0.990076	−	0.140531i	$-0.955119\pi$
$773$	−17.1472	−	29.6998i	−0.616741	−	1.06823i	0.373335	−	0.927697i	$-0.378214\pi$
$774$	2.53149	+	4.38467i	0.0909925	+	0.157604i
$775$	−4.11604	−	2.37639i	−0.147852	−	0.0853626i
$776$		−	34.3449i		−	1.23291i
$777$		0			0
$778$	−27.4240			−0.983200
$779$	−41.0605	−	23.7063i	−1.47114	−	0.849365i
$780$	−6.61168	−	11.4518i	−0.236736	−	0.410039i
$781$	7.41964	+	12.8512i	0.265495	+	0.459852i
$782$	−3.63213	+	2.28441i	−0.129885	+	0.0816904i
$783$	17.6783			0.631770
$784$		0			0
$785$		−	33.5872i		−	1.19878i
$786$	2.36412	−	4.09478i	0.0843255	−	0.146056i
$787$	23.1487	−	13.3649i	0.825164	−	0.476408i	−0.0270303	−	0.999635i	$-0.508605\pi$
$787$	23.1487	−	13.3649i	0.825164	−	0.476408i	0.852194	+	0.523226i	$0.175272\pi$
$788$	1.94353	−	1.12210i	0.0692353	−	0.0399730i
$789$	13.6906	+	7.90426i	0.487398	+	0.281399i
$790$	−23.2068			−0.825663
$791$		0			0
$792$			2.45192i			0.0871252i
$793$	3.04846	+	1.76003i	0.108254	+	0.0625005i
$794$	−1.84712	+	1.06643i	−0.0655518	+	0.0378463i
$795$	−8.96402	−	15.5261i	−0.317921	−	0.550655i
$796$	11.5163	+	6.64893i	0.408184	+	0.235665i
$797$	−8.74810			−0.309874			−0.154937	−	0.987924i	$-0.549517\pi$
$797$	−8.74810			−0.309874			−0.154937	+	0.987924i	$0.549517\pi$
$798$		0			0
$799$	6.49817	−	12.3080i	0.229889	−	0.435427i
$800$	5.50603	−	9.53672i	0.194668	−	0.337174i
$801$	−1.65839	−	2.87242i	−0.0585965	−	0.101492i
$802$	13.6189	−	7.86290i	0.480901	−	0.277649i
$803$	−3.44543	+	5.96765i	−0.121586	+	0.210594i
$804$		−	1.21847i		−	0.0429722i
$805$		0			0
$806$		−	11.5607i		−	0.407207i
$807$	21.7037	−	37.5920i	0.764008	−	1.32330i
$808$	−16.1702	−	28.0076i	−0.568865	−	0.985304i
$809$	−11.8416	+	6.83675i	−0.416328	+	0.240367i	−0.693505	−	0.720452i	$-0.743935\pi$
$809$	−11.8416	+	6.83675i	−0.416328	+	0.240367i	0.277177	+	0.960819i	$0.410601\pi$
$810$	15.6101	+	9.01252i	0.548485	+	0.316668i
$811$		−	22.3364i		−	0.784338i	−0.919893	−	0.392169i	$-0.871725\pi$
$811$		−	22.3364i		−	0.784338i	0.919893	−	0.392169i	$-0.128275\pi$
$812$		0			0
$813$			13.5115i			0.473868i
$814$	−4.31481	+	7.47347i	−0.151234	+	0.261945i
$815$	−7.19522	−	12.4625i	−0.252038	−	0.436542i
$816$	−0.585880	−	15.4785i	−0.0205099	−	0.541857i
$817$	13.3840	−	23.1817i	0.468246	−	0.811026i
$818$	4.39739			0.153751
$819$		0			0
$820$	−11.2200			−0.391819
$821$	−17.8233	−	10.2903i	−0.622037	−	0.359133i	0.155625	−	0.987816i	$-0.450261\pi$
$821$	−17.8233	−	10.2903i	−0.622037	−	0.359133i	−0.777662	+	0.628683i	$0.783594\pi$
$822$	−15.6881	+	9.05755i	−0.547187	+	0.315918i
$823$	6.61541	−	3.81941i	0.230599	−	0.133136i	−0.380250	−	0.924884i	$-0.624162\pi$
$823$	6.61541	−	3.81941i	0.230599	−	0.133136i	0.610848	+	0.791748i	$0.290829\pi$
$824$	1.72241	−	2.98331i	0.0600031	−	0.103928i
$825$	−5.30066			−0.184545
$826$		0			0
$827$		−	15.4126i		−	0.535949i	−0.963426	−	0.267974i	$-0.913646\pi$
$827$		−	15.4126i		−	0.535949i	0.963426	−	0.267974i	$-0.0863543\pi$
$828$	0.491870	+	0.283981i	0.0170937	+	0.00986902i
$829$	−19.2365	−	33.3185i	−0.668110	−	1.15720i	−0.978432	−	0.206569i	$-0.933770\pi$
$829$	−19.2365	−	33.3185i	−0.668110	−	1.15720i	0.310322	−	0.950631i	$-0.399563\pi$
$830$	−1.12548	+	0.649794i	−0.0390658	+	0.0225547i
$831$	−23.9607	+	41.5011i	−0.831187	+	1.43966i
$832$	49.8828			1.72938
$833$		0			0
$834$	1.95520			0.0677030
$835$	−5.85120	+	10.1346i	−0.202489	+	0.350721i
$836$	3.07235	−	1.77382i	0.106259	−	0.0613489i
$837$	−3.69089	−	6.39281i	−0.127576	−	0.220968i
$838$	−9.97822	−	5.76093i	−0.344692	−	0.199008i
$839$			16.1818i			0.558658i	0.960195	+	0.279329i	$0.0901120\pi$
$839$			16.1818i			0.558658i	−0.960195	+	0.279329i	$0.909888\pi$
$840$		0			0
$841$	11.9130			0.410794
$842$	1.25982	−	2.18207i	0.0434162	−	0.0751991i
$843$	12.2582	−	7.07726i	0.422194	−	0.243754i
$844$	−5.47021	+	3.15823i	−0.188293	+	0.108711i
$845$	29.8418	+	17.2292i	1.02659	+	0.592702i
$846$	3.04729			0.104768
$847$		0			0
$848$	11.7988			0.405174
$849$	−8.93535	+	15.4765i	−0.306660	+	0.531151i
$850$	12.6661	−	0.479427i	0.434445	−	0.0164442i
$851$	3.65217	+	6.32574i	0.125195	+	0.216844i
$852$	−11.0619	+	19.1598i	−0.378974	+	0.656403i
$853$		−	12.8634i		−	0.440435i	−0.975451	−	0.220217i	$-0.929323\pi$
$853$		−	12.8634i		−	0.440435i	0.975451	−	0.220217i	$-0.0706767\pi$
$854$		0			0
$855$			5.78411i			0.197812i
$856$	40.3050	+	23.2701i	1.37760	+	0.795355i
$857$	−41.9623	+	24.2269i	−1.43340	+	0.827576i	−0.997379	−	0.0723591i	$-0.976947\pi$
$857$	−41.9623	+	24.2269i	−1.43340	+	0.827576i	−0.436025	+	0.899935i	$0.643614\pi$
$858$	−6.44665	−	11.1659i	−0.220085	−	0.381198i
$859$	−17.5817	+	30.4524i	−0.599879	+	1.03902i	0.392959	+	0.919556i	$0.371451\pi$
$859$	−17.5817	+	30.4524i	−0.599879	+	1.03902i	−0.992838	+	0.119465i	$0.961882\pi$
$860$		−	6.33453i		−	0.216006i
$861$		0			0
$862$			2.21290i			0.0753718i
$863$	−7.85420	+	13.6039i	−0.267360	+	0.463081i	−0.968179	−	0.250258i	$-0.919485\pi$
$863$	−7.85420	+	13.6039i	−0.267360	+	0.463081i	0.700819	+	0.713339i	$0.252818\pi$
$864$	14.8119	−	8.55167i	0.503912	−	0.290934i
$865$	6.20496	+	10.7473i	0.210975	+	0.365419i
$866$	−18.9706	+	32.8580i	−0.644647	+	1.11656i
$867$	−27.3955	+	18.7127i	−0.930400	+	0.635517i
$868$		0			0
$869$	13.6800			0.464063
$870$	−11.6903	−	6.74942i	−0.396340	−	0.228827i
$871$	2.48530	+	4.30467i	0.0842112	+	0.145858i
$872$	23.0382	−	13.3011i	0.780173	−	0.450433i
$873$	−7.82321	−	4.51674i	−0.264776	−	0.152868i
$874$			4.96684i			0.168006i
$875$		0			0
$876$	−10.2735			−0.347111
$877$	−3.54827	−	2.04860i	−0.119817	−	0.0691762i	0.438894	−	0.898539i	$-0.355370\pi$
$877$	−3.54827	−	2.04860i	−0.119817	−	0.0691762i	−0.558711	+	0.829363i	$0.688704\pi$
$878$	−14.8168	+	8.55448i	−0.500043	+	0.288700i
$879$	−28.6323	+	16.5309i	−0.965744	+	0.557573i
$880$	−1.42300	+	2.46471i	−0.0479694	+	0.0830854i
$881$		−	23.1066i		−	0.778480i	−0.921136	−	0.389240i	$-0.872738\pi$
$881$		−	23.1066i		−	0.778480i	0.921136	−	0.389240i	$-0.127262\pi$
$882$		0			0
$883$	21.3780			0.719425			0.359713	−	0.933063i	$-0.382875\pi$
$883$	21.3780			0.719425			0.359713	+	0.933063i	$0.382875\pi$
$884$	−9.92372	−	15.7783i	−0.333771	−	0.530683i
$885$	−9.75485	−	16.8959i	−0.327906	−	0.567950i
$886$	18.1622	+	31.4579i	0.610171	+	1.05685i
$887$	34.9061	+	20.1531i	1.17203	+	0.676673i	0.954158	−	0.299303i	$-0.0967542\pi$
$887$	34.9061	+	20.1531i	1.17203	+	0.676673i	0.217875	+	0.975977i	$0.430088\pi$
$888$	−47.0126			−1.57764
$889$		0			0
$890$		−	6.86400i		−	0.230082i
$891$	−9.20191	−	5.31272i	−0.308276	−	0.177983i
$892$	4.00306	+	6.93350i	0.134032	+	0.232151i
$893$	−8.05551	−	13.9526i	−0.269568	−	0.466905i
$894$	12.4303	+	7.17665i	0.415732	+	0.240023i
$895$			21.8331i			0.729801i
$896$		0			0
$897$	−10.9132			−0.364382
$898$	2.23448	+	1.29007i	0.0745654	+	0.0430504i
$899$	3.56743	+	6.17898i	0.118981	+	0.206080i
$900$	−0.838893	−	1.45301i	−0.0279631	−	0.0484335i
$901$	−13.4544	−	21.3920i	−0.448232	−	0.712672i
$902$	−10.9399			−0.364260
$903$		0			0
$904$			9.86145i			0.327987i
$905$	8.68624	−	15.0450i	0.288740	−	0.500113i
$906$	21.8948	−	12.6409i	0.727405	−	0.419967i
$907$	0.826212	−	0.477013i	0.0274339	−	0.0158390i	−0.486220	−	0.873836i	$-0.661625\pi$
$907$	0.826212	−	0.477013i	0.0274339	−	0.0158390i	0.513654	+	0.857997i	$0.328291\pi$
$908$	3.41948	+	1.97424i	0.113480	+	0.0655174i
$909$	−8.50624			−0.282134
$910$		0			0
$911$			13.7884i			0.456829i	0.973564	+	0.228414i	$0.0733541\pi$
$911$			13.7884i			0.456829i	−0.973564	+	0.228414i	$0.926646\pi$
$912$	−15.5280	−	8.96507i	−0.514182	−	0.296863i
$913$	0.663449	−	0.383042i	0.0219569	−	0.0126768i
$914$	−5.04006	−	8.72965i	−0.166710	−	0.288751i
$915$	−1.48633	−	0.858134i	−0.0491366	−	0.0283690i
$916$	14.6530			0.484149
$917$		0			0
$918$	17.4091	+	9.19131i	0.574585	+	0.303359i
$919$	20.2231	−	35.0274i	0.667097	−	1.15545i	−0.311615	−	0.950208i	$-0.600870\pi$
$919$	20.2231	−	35.0274i	0.667097	−	1.15545i	0.978712	−	0.205238i	$-0.0657967\pi$
$920$	2.14746	+	3.71951i	0.0707996	+	0.122629i
$921$	−31.9592	+	18.4517i	−1.05309	+	0.608003i
$922$	21.5688	−	37.3583i	0.710332	−	1.23033i
$923$		−	90.2512i		−	2.97065i
$924$		0			0
$925$		−	21.5773i		−	0.709459i
$926$	14.0334	−	24.3066i	0.461167	−	0.798764i
$927$	−0.453033	−	0.784676i	−0.0148795	−	0.0257721i
$928$	−14.3165	+	8.26563i	−0.469962	+	0.271333i
$929$	−28.1206	−	16.2355i	−0.922608	−	0.532668i	−0.0381421	−	0.999272i	$-0.512144\pi$
$929$	−28.1206	−	16.2355i	−0.922608	−	0.532668i	−0.884466	+	0.466604i	$0.845477\pi$
$930$			5.63660i			0.184832i
$931$		0			0
$932$		−	22.5615i		−	0.739026i
$933$	2.64559	−	4.58230i	0.0866128	−	0.150018i
$934$	−9.68507	−	16.7750i	−0.316905	−	0.548896i
$935$	6.09136	−	0.230565i	0.199209	−	0.00754027i
$936$	7.45618	−	12.9145i	0.243713	−	0.422123i
$937$	−16.4485			−0.537348			−0.268674	−	0.963231i	$-0.586585\pi$
$937$	−16.4485			−0.537348			−0.268674	+	0.963231i	$0.586585\pi$
$938$		0			0
$939$	−53.3641			−1.74147
$940$	−3.30182	−	1.90631i	−0.107693	−	0.0621768i
$941$	−15.0216	+	8.67273i	−0.489691	+	0.282723i	−0.724446	−	0.689331i	$-0.757904\pi$
$941$	−15.0216	+	8.67273i	−0.489691	+	0.282723i	0.234755	+	0.972054i	$0.424571\pi$
$942$	42.2839	−	24.4126i	1.37768	−	0.795405i
$943$	−4.62992	+	8.01926i	−0.150771	+	0.261143i
$944$	12.8398			0.417899
$945$		0			0
$946$		−	6.17642i		−	0.200813i
$947$	−15.2205	−	8.78759i	−0.494601	−	0.285558i	0.231880	−	0.972744i	$-0.425512\pi$
$947$	−15.2205	−	8.78759i	−0.494601	−	0.285558i	−0.726481	+	0.687186i	$0.758846\pi$
$948$	10.1978	+	17.6630i	0.331208	+	0.573668i
$949$	36.2948	−	20.9548i	1.17818	−	0.680221i
$950$	7.33613	−	12.7066i	0.238016	−	0.412255i
$951$	−10.9516			−0.355132
$952$		0			0
$953$	31.3803			1.01651			0.508254	−	0.861207i	$-0.330291\pi$
$953$	31.3803			1.01651			0.508254	+	0.861207i	$0.330291\pi$
$954$	2.76651	−	4.79173i	0.0895690	−	0.155138i
$955$	29.4610	−	17.0093i	0.953335	−	0.550408i
$956$	−0.379771	−	0.657783i	−0.0122827	−	0.0212742i
$957$	6.89125	+	3.97867i	0.222762	+	0.128612i
$958$			28.6574i			0.925878i
$959$		0			0
$960$	−24.3213			−0.784966
$961$	−14.0104	+	24.2667i	−0.451948	+	0.782796i
$962$	45.4530	−	26.2423i	1.46546	−	0.846086i
$963$	10.6011	−	6.12055i	0.341616	−	0.197232i
$964$	4.69460	+	2.71043i	0.151203	+	0.0872971i
$965$	39.7844			1.28070
$966$		0			0
$967$	20.9476			0.673630			0.336815	−	0.941571i	$-0.390650\pi$
$967$	20.9476			0.673630			0.336815	+	0.941571i	$0.390650\pi$
$968$	−15.4125	+	26.6952i	−0.495375	+	0.858015i
$969$	1.45258	+	38.3762i	0.0466636	+	1.23282i
$970$	−9.34726	−	16.1899i	−0.300123	−	0.519828i
$971$	−13.1596	+	22.7931i	−0.422312	+	0.731466i	−0.996165	−	0.0874923i	$-0.972115\pi$
$971$	−13.1596	+	22.7931i	−0.422312	+	0.731466i	0.573853	+	0.818958i	$0.305448\pi$
$972$		−	6.17319i		−	0.198005i
$973$		0			0
$974$			34.3675i			1.10121i
$975$	27.9191	+	16.1191i	0.894125	+	0.516224i
$976$	0.978188	−	0.564757i	0.0313110	−	0.0180774i
$977$	−8.26069	−	14.3079i	−0.264283	−	0.457751i	0.703093	−	0.711098i	$-0.251802\pi$
$977$	−8.26069	−	14.3079i	−0.264283	−	0.457751i	−0.967375	+	0.253347i	$0.918469\pi$
$978$	10.4596	−	18.1165i	0.334460	−	0.579302i
$979$			4.04621i			0.129317i
$980$		0			0
$981$		−	6.99698i		−	0.223397i
$982$	−18.9978	+	32.9051i	−0.606243	+	1.05004i
$983$	31.8214	−	18.3721i	1.01495	−	0.585979i	0.102309	−	0.994753i	$-0.467377\pi$
$983$	31.8214	−	18.3721i	1.01495	−	0.585979i	0.912636	+	0.408774i	$0.134043\pi$
$984$	−29.7994	−	51.6141i	−0.949971	−	1.64540i
$985$	2.23181	−	3.86562i	0.0711115	−	0.123169i
$986$	−16.8268	−	8.88388i	−0.535873	−	0.282920i
$987$		0			0
$988$	−21.5765			−0.686438
$989$	−4.52748	−	2.61394i	−0.143965	−	0.0831185i
$990$	0.667311	+	1.15582i	0.0212085	+	0.0367343i
$991$	−25.1909	+	14.5440i	−0.800215	+	0.462004i	−0.843546	−	0.537056i	$-0.819536\pi$
$991$	−25.1909	+	14.5440i	−0.800215	+	0.462004i	0.0433314	+	0.999061i	$0.486203\pi$
$992$	5.97803	+	3.45142i	0.189803	+	0.109583i
$993$			53.3815i			1.69401i
$994$		0			0
$995$	26.4490			0.838491
$996$	0.989133	+	0.571076i	0.0313419	+	0.0180952i
$997$	−27.5486	+	15.9052i	−0.872472	+	0.503722i	−0.868169	−	0.496269i	$-0.834703\pi$
$997$	−27.5486	+	15.9052i	−0.872472	+	0.503722i	−0.00430279	+	0.999991i	$0.501370\pi$
$998$	−18.2553	+	10.5397i	−0.577861	+	0.333628i
$999$	16.7564	−	29.0229i	0.530149	−	0.918244i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.j.a.373.7		20
7.2	even	3		833.2.b.d.50.3		10
7.3	odd	6		119.2.j.a.67.7	yes	20
7.4	even	3	inner	833.2.j.a.67.8		20
7.5	odd	6		833.2.b.c.50.4		10
7.6	odd	2		119.2.j.a.16.8	yes	20
17.16	even	2	inner	833.2.j.a.373.8		20
119.16	even	6		833.2.b.d.50.4		10
119.33	odd	6		833.2.b.c.50.3		10
119.67	even	6	inner	833.2.j.a.67.7		20
119.101	odd	6		119.2.j.a.67.8	yes	20
119.118	odd	2		119.2.j.a.16.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.j.a.16.7	✓	20	119.118	odd	2
119.2.j.a.16.8	yes	20	7.6	odd	2
119.2.j.a.67.7	yes	20	7.3	odd	6
119.2.j.a.67.8	yes	20	119.101	odd	6
833.2.b.c.50.3		10	119.33	odd	6
833.2.b.c.50.4		10	7.5	odd	6
833.2.b.d.50.3		10	7.2	even	3
833.2.b.d.50.4		10	119.16	even	6
833.2.j.a.67.7		20	119.67	even	6	inner
833.2.j.a.67.8		20	7.4	even	3	inner
833.2.j.a.373.7		20	1.1	even	1	trivial
833.2.j.a.373.8		20	17.16	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.558220 - 0.966865i) q^{2} +(-1.69010 + 0.975779i) q^{3} +(0.376781 + 0.652604i) q^{4} +(1.29801 + 0.749406i) q^{5} +2.17880i q^{6} +3.07419 q^{8} +(0.404290 - 0.700250i) q^{9} +(1.44915 - 0.836667i) q^{10} +(-0.854248 + 0.493200i) q^{11} +(-1.27360 - 0.735310i) q^{12} +5.99921 q^{13} -2.92502 q^{15} +(0.962509 - 1.66712i) q^{16} +(-4.12016 + 0.155952i) q^{17} +(-0.451365 - 0.781787i) q^{18} +(-2.38637 + 4.13331i) q^{19} +1.12945i q^{20} +1.10126i q^{22} +(0.807250 + 0.466066i) q^{23} +(-5.19568 + 2.99973i) q^{24} +(-1.37678 - 2.38465i) q^{25} +(3.34888 - 5.80042i) q^{26} -4.27669i q^{27} +4.13364i q^{29} +(-1.63280 + 2.82810i) q^{30} +(1.49480 - 0.863025i) q^{31} +(1.99960 + 3.46341i) q^{32} +(0.962509 - 1.66712i) q^{33} +(-2.14917 + 4.07069i) q^{34} +0.609315 q^{36} +(6.78631 + 3.91808i) q^{37} +(2.66423 + 4.61459i) q^{38} +(-10.1393 + 5.85390i) q^{39} +(3.99032 + 2.30381i) q^{40} +9.93404i q^{41} -5.60852 q^{43} +(-0.643729 - 0.371657i) q^{44} +(1.04954 - 0.605954i) q^{45} +(0.901246 - 0.520335i) q^{46} +(-1.68782 + 2.92339i) q^{47} +3.75679i q^{48} -3.07419 q^{50} +(6.81129 - 4.28394i) q^{51} +(2.26039 + 3.91511i) q^{52} +(3.06460 + 5.30805i) q^{53} +(-4.13498 - 2.38733i) q^{54} -1.47843 q^{55} -9.31426i q^{57} +(3.99667 + 2.30748i) q^{58} +(3.33497 + 5.77634i) q^{59} +(-1.10209 - 1.90888i) q^{60} +(0.508145 + 0.293377i) q^{61} -1.92703i q^{62} +8.31491 q^{64} +(7.78702 + 4.49584i) q^{65} +(-1.07458 - 1.86123i) q^{66} +(0.414272 + 0.717540i) q^{67} +(-1.65417 - 2.63007i) q^{68} -1.81911 q^{69} -15.0439i q^{71} +(1.24286 - 2.15270i) q^{72} +(6.04993 - 3.49293i) q^{73} +(7.57651 - 4.37430i) q^{74} +(4.65379 + 2.68687i) q^{75} -3.59655 q^{76} +13.0711i q^{78} +(-12.0106 - 6.93432i) q^{79} +(2.49869 - 1.44262i) q^{80} +(5.38597 + 9.32877i) q^{81} +(9.60488 + 5.54538i) q^{82} -0.776646 q^{83} +(-5.46487 - 2.88524i) q^{85} +(-3.13079 + 5.42268i) q^{86} +(-4.03352 - 6.98626i) q^{87} +(-2.62612 + 1.51619i) q^{88} +(2.05100 - 3.55243i) q^{89} -1.35302i q^{90} +0.702420i q^{92} +(-1.68424 + 2.91720i) q^{93} +(1.88435 + 3.26379i) q^{94} +(-6.19505 + 3.57671i) q^{95} +(-6.75905 - 3.90234i) q^{96} -11.1720i q^{97} +0.797583i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 10 q^{4} + 16 q^{13} - 16 q^{15} - 2 q^{16} + 2 q^{17} + 18 q^{18} + 10 q^{19} - 10 q^{25} - 12 q^{26} - 10 q^{30} - 12 q^{32} - 2 q^{33} - 24 q^{34} + 56 q^{36} + 2 q^{38} - 52 q^{43}+ \cdots - 50 q^{94}+O(q^{100}) \) 20 * q - 2 * q^2 - 10 * q^4 + 16 * q^13 - 16 * q^15 - 2 * q^16 + 2 * q^17 + 18 * q^18 + 10 * q^19 - 10 * q^25 - 12 * q^26 - 10 * q^30 - 12 * q^32 - 2 * q^33 - 24 * q^34 + 56 * q^36 + 2 * q^38 - 52 * q^43 - 30 * q^47 + 6 * q^51 + 2 * q^52 + 40 * q^53 - 12 * q^55 + 14 * q^59 - 22 * q^60 - 24 * q^64 - 12 * q^66 + 12 * q^67 + 32 * q^68 + 88 * q^69 - 16 * q^72 - 132 * q^76 - 2 * q^81 - 96 * q^83 - 4 * q^85 - 10 * q^86 + 26 * q^87 - 16 * q^89 + 46 * q^93 - 50 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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