LMFDB - Embedded newform 1014.2.g.d.239.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1014,2,Mod(239,1014)] 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("1014.239"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1014, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.9349208943630483456.9
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.8
Root			$0.500000 + 0.410882i$ of defining polynomial
Character	$\chi$	$=$	1014.239
Dual form			1014.2.g.d.437.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +(1.53819 + 0.796225i) q^{3} +1.00000i q^{4} +(-2.02097 - 2.02097i) q^{5} +(0.524648 + 1.65068i) q^{6} +(2.53819 + 2.53819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.73205 + 2.44949i) q^{9} -2.85808i q^{10} +(-2.97155 + 2.97155i) q^{11} +(-0.796225 + 1.53819i) q^{12} +3.58954i q^{14} +(-1.49949 - 4.71778i) q^{15} -1.00000 q^{16} +3.45408 q^{17} +(-0.507306 + 2.95680i) q^{18} +(-1.58784 + 1.58784i) q^{19} +(2.02097 - 2.02097i) q^{20} +(1.88324 + 5.92518i) q^{21} -4.20241 q^{22} +3.03237 q^{23} +(-1.65068 + 0.524648i) q^{24} +3.16864i q^{25} +(0.713876 + 5.14688i) q^{27} +(-2.53819 + 2.53819i) q^{28} +2.01416i q^{29} +(2.27568 - 4.39627i) q^{30} +(-1.21829 + 1.21829i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-6.93684 + 2.20478i) q^{33} +(2.44240 + 2.44240i) q^{34} -10.2592i q^{35} +(-2.44949 + 1.73205i) q^{36} +(3.42423 + 3.42423i) q^{37} -2.24555 q^{38} +2.85808 q^{40} +(-5.61494 - 5.61494i) q^{41} +(-2.85808 + 5.52139i) q^{42} +1.95035i q^{43} +(-2.97155 - 2.97155i) q^{44} +(1.44992 - 8.45077i) q^{45} +(2.14421 + 2.14421i) q^{46} +(0.957390 - 0.957390i) q^{47} +(-1.53819 - 0.796225i) q^{48} +5.88481i q^{49} +(-2.24057 + 2.24057i) q^{50} +(5.31303 + 2.75023i) q^{51} +7.22186i q^{53} +(-3.13461 + 4.14418i) q^{54} +12.0108 q^{55} -3.58954 q^{56} +(-3.70668 + 1.17812i) q^{57} +(-1.42423 + 1.42423i) q^{58} +(7.27501 - 7.27501i) q^{59} +(4.71778 - 1.49949i) q^{60} +0.274207 q^{61} -1.72293 q^{62} +(-1.82100 + 10.6135i) q^{63} -1.00000i q^{64} +(-6.46410 - 3.34607i) q^{66} +(3.00229 - 3.00229i) q^{67} +3.45408i q^{68} +(4.66435 + 2.41445i) q^{69} +(7.25436 - 7.25436i) q^{70} +(7.80205 + 7.80205i) q^{71} +(-2.95680 - 0.507306i) q^{72} +(-10.0822 - 10.0822i) q^{73} +4.84259i q^{74} +(-2.52295 + 4.87397i) q^{75} +(-1.58784 - 1.58784i) q^{76} -15.0847 q^{77} +1.58051 q^{79} +(2.02097 + 2.02097i) q^{80} +(-3.00000 + 8.48528i) q^{81} -7.94072i q^{82} +(2.58938 + 2.58938i) q^{83} +(-5.92518 + 1.88324i) q^{84} +(-6.98059 - 6.98059i) q^{85} +(-1.37910 + 1.37910i) q^{86} +(-1.60373 + 3.09816i) q^{87} -4.20241i q^{88} +(6.96131 - 6.96131i) q^{89} +(7.00085 - 4.95035i) q^{90} +3.03237i q^{92} +(-2.84400 + 0.903931i) q^{93} +1.35395 q^{94} +6.41797 q^{95} +(-0.524648 - 1.65068i) q^{96} +(5.67277 - 5.67277i) q^{97} +(-4.16119 + 4.16119i) q^{98} +(-12.4257 - 2.13191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{7} + 24 q^{15} - 16 q^{16} - 32 q^{19} + 24 q^{21} - 16 q^{28} - 16 q^{31} - 24 q^{33} - 24 q^{34} + 8 q^{37} + 48 q^{45} + 48 q^{55} + 24 q^{57} + 24 q^{58} + 24 q^{60} + 48 q^{61} - 48 q^{66}+ \cdots - 16 q^{97}+O(q^{100}) $ 16 * q + 16 * q^7 + 24 * q^15 - 16 * q^16 - 32 * q^19 + 24 * q^21 - 16 * q^28 - 16 * q^31 - 24 * q^33 - 24 * q^34 + 8 * q^37 + 48 * q^45 + 48 * q^55 + 24 * q^57 + 24 * q^58 + 24 * q^60 + 48 * q^61 - 48 * q^66 - 32 * q^67 - 56 * q^73 - 32 * q^76 - 96 * q^79 - 48 * q^81 - 24 * q^84 - 24 * q^85 - 96 * q^87 - 48 * q^93 + 48 * q^94 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.53819	+	0.796225i	0.888074	+	0.459701i
$3$	1.53819	+	0.796225i	0.888074	+	0.459701i
$4$			1.00000i			0.500000i
$5$	−2.02097	−	2.02097i	−0.903805	−	0.903805i	0.0919576	−	0.995763i	$-0.470688\pi$
$5$	−2.02097	−	2.02097i	−0.903805	−	0.903805i	−0.995763	+	0.0919576i	$0.970688\pi$
$6$	0.524648	+	1.65068i	0.214186	+	0.673887i
$7$	2.53819	+	2.53819i	0.959345	+	0.959345i	0.999205	−	0.0398600i	$-0.0126912\pi$
$7$	2.53819	+	2.53819i	0.959345	+	0.959345i	−0.0398600	+	0.999205i	$0.512691\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.73205	+	2.44949i	0.577350	+	0.816497i
$10$		−	2.85808i		−	0.903805i
$11$	−2.97155	+	2.97155i	−0.895957	+	0.895957i	−0.995076	−	0.0991187i	$-0.968398\pi$
$11$	−2.97155	+	2.97155i	−0.895957	+	0.895957i	0.0991187	+	0.995076i	$0.468398\pi$
$12$	−0.796225	+	1.53819i	−0.229850	+	0.444037i
$13$		0			0
$13$		0			0
$14$			3.58954i			0.959345i
$15$	−1.49949	−	4.71778i	−0.387166	−	1.21813i
$16$	−1.00000			−0.250000
$17$	3.45408			0.837737			0.418869	−	0.908047i	$-0.362427\pi$
$17$	3.45408			0.837737			0.418869	+	0.908047i	$0.362427\pi$
$18$	−0.507306	+	2.95680i	−0.119573	+	0.696923i
$19$	−1.58784	+	1.58784i	−0.364276	+	0.364276i	−0.865385	−	0.501108i	$-0.832926\pi$
$19$	−1.58784	+	1.58784i	−0.364276	+	0.364276i	0.501108	+	0.865385i	$0.332926\pi$
$20$	2.02097	−	2.02097i	0.451903	−	0.451903i
$21$	1.88324	+	5.92518i	0.410958	+	1.29298i
$22$	−4.20241			−0.895957
$23$	3.03237			0.632292			0.316146	−	0.948711i	$-0.397611\pi$
$23$	3.03237			0.632292			0.316146	+	0.948711i	$0.397611\pi$
$24$	−1.65068	+	0.524648i	−0.336944	+	0.107093i
$25$			3.16864i			0.633728i
$26$		0			0
$27$	0.713876	+	5.14688i	0.137386	+	0.990518i
$28$	−2.53819	+	2.53819i	−0.479673	+	0.479673i
$29$			2.01416i			0.374021i	0.982358	+	0.187010i	$0.0598798\pi$
$29$			2.01416i			0.374021i	−0.982358	+	0.187010i	$0.940120\pi$
$30$	2.27568	−	4.39627i	0.415480	−	0.802646i
$31$	−1.21829	+	1.21829i	−0.218812	+	0.218812i	−0.807998	−	0.589186i	$-0.799449\pi$
$31$	−1.21829	+	1.21829i	−0.218812	+	0.218812i	0.589186	+	0.807998i	$0.299449\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−6.93684	+	2.20478i	−1.20755	+	0.383804i
$34$	2.44240	+	2.44240i	0.418869	+	0.418869i
$35$		−	10.2592i		−	1.73412i
$36$	−2.44949	+	1.73205i	−0.408248	+	0.288675i
$37$	3.42423	+	3.42423i	0.562940	+	0.562940i	0.930141	−	0.367202i	$-0.119684\pi$
$37$	3.42423	+	3.42423i	0.562940	+	0.562940i	−0.367202	+	0.930141i	$0.619684\pi$
$38$	−2.24555			−0.364276
$39$		0			0
$40$	2.85808			0.451903
$41$	−5.61494	−	5.61494i	−0.876906	−	0.876906i	0.116307	−	0.993213i	$-0.462894\pi$
$41$	−5.61494	−	5.61494i	−0.876906	−	0.876906i	−0.993213	+	0.116307i	$0.962894\pi$
$42$	−2.85808	+	5.52139i	−0.441012	+	0.851969i
$43$			1.95035i			0.297425i	0.988880	+	0.148712i	$0.0475129\pi$
$43$			1.95035i			0.297425i	−0.988880	+	0.148712i	$0.952487\pi$
$44$	−2.97155	−	2.97155i	−0.447978	−	0.447978i
$45$	1.44992	−	8.45077i	0.216142	−	1.25977i
$46$	2.14421	+	2.14421i	0.316146	+	0.316146i
$47$	0.957390	−	0.957390i	0.139650	−	0.139650i	−0.633826	−	0.773476i	$-0.718516\pi$
$47$	0.957390	−	0.957390i	0.139650	−	0.139650i	0.773476	+	0.633826i	$0.218516\pi$
$48$	−1.53819	−	0.796225i	−0.222018	−	0.114925i
$49$			5.88481i			0.840687i
$50$	−2.24057	+	2.24057i	−0.316864	+	0.316864i
$51$	5.31303	+	2.75023i	0.743973	+	0.385109i
$52$		0			0
$53$			7.22186i			0.991999i	0.868323	+	0.495999i	$0.165198\pi$
$53$			7.22186i			0.991999i	−0.868323	+	0.495999i	$0.834802\pi$
$54$	−3.13461	+	4.14418i	−0.426566	+	0.563952i
$55$	12.0108			1.61954
$56$	−3.58954			−0.479673
$57$	−3.70668	+	1.17812i	−0.490962	+	0.156046i
$58$	−1.42423	+	1.42423i	−0.187010	+	0.187010i
$59$	7.27501	−	7.27501i	0.947125	−	0.947125i	−0.0515453	−	0.998671i	$-0.516415\pi$
$59$	7.27501	−	7.27501i	0.947125	−	0.947125i	0.998671	+	0.0515453i	$0.0164147\pi$
$60$	4.71778	−	1.49949i	0.609063	−	0.193583i
$61$	0.274207			0.0351086			0.0175543	−	0.999846i	$-0.494412\pi$
$61$	0.274207			0.0351086			0.0175543	+	0.999846i	$0.494412\pi$
$62$	−1.72293			−0.218812
$63$	−1.82100	+	10.6135i	−0.229424	+	1.33718i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−6.46410	−	3.34607i	−0.795676	−	0.411872i
$67$	3.00229	−	3.00229i	0.366788	−	0.366788i	−0.499516	−	0.866304i	$-0.666489\pi$
$67$	3.00229	−	3.00229i	0.366788	−	0.366788i	0.866304	+	0.499516i	$0.166489\pi$
$68$			3.45408i			0.418869i
$69$	4.66435	+	2.41445i	0.561522	+	0.290665i
$70$	7.25436	−	7.25436i	0.867061	−	0.867061i
$71$	7.80205	+	7.80205i	0.925933	+	0.925933i	0.997440	−	0.0715067i	$-0.0227807\pi$
$71$	7.80205	+	7.80205i	0.925933	+	0.925933i	−0.0715067	+	0.997440i	$0.522781\pi$
$72$	−2.95680	−	0.507306i	−0.348462	−	0.0597866i
$73$	−10.0822	−	10.0822i	−1.18003	−	1.18003i	−0.979735	−	0.200296i	$-0.935810\pi$
$73$	−10.0822	−	10.0822i	−1.18003	−	1.18003i	−0.200296	−	0.979735i	$-0.564190\pi$
$74$			4.84259i			0.562940i
$75$	−2.52295	+	4.87397i	−0.291325	+	0.562797i
$76$	−1.58784	−	1.58784i	−0.182138	−	0.182138i
$77$	−15.0847			−1.71906
$78$		0			0
$79$	1.58051			0.177821			0.0889105	−	0.996040i	$-0.471661\pi$
$79$	1.58051			0.177821			0.0889105	+	0.996040i	$0.471661\pi$
$80$	2.02097	+	2.02097i	0.225951	+	0.225951i
$81$	−3.00000	+	8.48528i	−0.333333	+	0.942809i
$82$		−	7.94072i		−	0.876906i
$83$	2.58938	+	2.58938i	0.284221	+	0.284221i	0.834790	−	0.550569i	$-0.185589\pi$
$83$	2.58938	+	2.58938i	0.284221	+	0.284221i	−0.550569	+	0.834790i	$0.685589\pi$
$84$	−5.92518	+	1.88324i	−0.646491	+	0.205479i
$85$	−6.98059	−	6.98059i	−0.757152	−	0.757152i
$86$	−1.37910	+	1.37910i	−0.148712	+	0.148712i
$87$	−1.60373	+	3.09816i	−0.171938	+	0.332158i
$88$		−	4.20241i		−	0.447978i
$89$	6.96131	−	6.96131i	0.737897	−	0.737897i	−0.234273	−	0.972171i	$-0.575271\pi$
$89$	6.96131	−	6.96131i	0.737897	−	0.737897i	0.972171	+	0.234273i	$0.0752711\pi$
$90$	7.00085	−	4.95035i	0.737954	−	0.521812i
$91$		0			0
$92$			3.03237i			0.316146i
$93$	−2.84400	+	0.903931i	−0.294910	+	0.0937332i
$94$	1.35395			0.139650
$95$	6.41797			0.658470
$96$	−0.524648	−	1.65068i	−0.0535466	−	0.168472i
$97$	5.67277	−	5.67277i	0.575983	−	0.575983i	−0.357811	−	0.933794i	$-0.616477\pi$
$97$	5.67277	−	5.67277i	0.575983	−	0.575983i	0.933794	+	0.357811i	$0.116477\pi$
$98$	−4.16119	+	4.16119i	−0.420343	+	0.420343i
$99$	−12.4257	−	2.13191i	−1.24883	−	0.214265i
$100$	−3.16864			−0.316864
$101$	−2.10685			−0.209639			−0.104820	−	0.994491i	$-0.533427\pi$
$101$	−2.10685			−0.209639			−0.104820	+	0.994491i	$0.533427\pi$
$102$	1.81217	+	5.70158i	0.179432	+	0.564541i
$103$		−	14.2629i		−	1.40537i	−0.711503	−	0.702683i	$-0.751985\pi$
$103$		−	14.2629i		−	1.40537i	0.711503	−	0.702683i	$-0.248015\pi$
$104$		0			0
$105$	8.16864	−	15.7806i	0.797178	−	1.54003i
$106$	−5.10662	+	5.10662i	−0.495999	+	0.495999i
$107$		−	13.8455i		−	1.33850i	−0.743039	−	0.669248i	$-0.766616\pi$
$107$		−	13.8455i		−	1.33850i	0.743039	−	0.669248i	$-0.233384\pi$
$108$	−5.14688	+	0.713876i	−0.495259	+	0.0686928i
$109$	−5.84220	+	5.84220i	−0.559581	+	0.559581i	−0.929188	−	0.369607i	$-0.879492\pi$
$109$	−5.84220	+	5.84220i	−0.559581	+	0.559581i	0.369607	+	0.929188i	$0.379492\pi$
$110$	8.49295	+	8.49295i	0.809771	+	0.809771i
$111$	2.54065	+	7.99357i	0.241148	+	0.758716i
$112$	−2.53819	−	2.53819i	−0.239836	−	0.239836i
$113$		−	18.0041i		−	1.69368i	−0.531845	−	0.846841i	$-0.678501\pi$
$113$		−	18.0041i		−	1.69368i	0.531845	−	0.846841i	$-0.321499\pi$
$114$	−3.45408	−	1.78796i	−0.323504	−	0.167458i
$115$	−6.12832	−	6.12832i	−0.571469	−	0.571469i
$116$	−2.01416			−0.187010
$117$		0			0
$118$	10.2884			0.947125
$119$	8.76711	+	8.76711i	0.803679	+	0.803679i
$120$	4.39627	+	2.27568i	0.401323	+	0.207740i
$121$		−	6.66025i		−	0.605478i
$122$	0.193894	+	0.193894i	0.0175543	+	0.0175543i
$123$	−4.16608	−	13.1076i	−0.375643	−	1.18187i
$124$	−1.21829	−	1.21829i	−0.109406	−	0.109406i
$125$	−3.70112	+	3.70112i	−0.331039	+	0.331039i
$126$	−8.79254	+	6.21727i	−0.783302	+	0.553878i
$127$		−	20.6932i		−	1.83623i	−0.396317	−	0.918114i	$-0.629712\pi$
$127$		−	20.6932i		−	1.83623i	0.396317	−	0.918114i	$-0.370288\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−1.55291	+	3.00000i	−0.136726	+	0.264135i
$130$		0			0
$131$			4.68295i			0.409151i	0.978851	+	0.204576i	$0.0655814\pi$
$131$			4.68295i			0.409151i	−0.978851	+	0.204576i	$0.934419\pi$
$132$	−2.20478	−	6.93684i	−0.191902	−	0.603774i
$133$	−8.06049			−0.698933
$134$	4.24588			0.366788
$135$	8.95897	−	11.8444i	0.771065	−	1.01940i
$136$	−2.44240	+	2.44240i	−0.209434	+	0.209434i
$137$	3.87494	−	3.87494i	0.331058	−	0.331058i	−0.521930	−	0.852988i	$-0.674788\pi$
$137$	3.87494	−	3.87494i	0.331058	−	0.331058i	0.852988	+	0.521930i	$0.174788\pi$
$138$	1.59092	+	5.00547i	0.135428	+	0.426094i
$139$	14.6932			1.24626			0.623132	−	0.782117i	$-0.285860\pi$
$139$	14.6932			1.24626			0.623132	+	0.782117i	$0.285860\pi$
$140$	10.2592			0.867061
$141$	2.23494	−	0.710348i	0.188216	−	0.0598221i
$142$			11.0338i			0.925933i
$143$		0			0
$144$	−1.73205	−	2.44949i	−0.144338	−	0.204124i
$145$	4.07056	−	4.07056i	0.338042	−	0.338042i
$146$		−	14.2584i		−	1.18003i
$147$	−4.68563	+	9.05195i	−0.386464	+	0.746592i
$148$	−3.42423	+	3.42423i	−0.281470	+	0.281470i
$149$	−7.30774	−	7.30774i	−0.598673	−	0.598673i	0.341286	−	0.939959i	$-0.389137\pi$
$149$	−7.30774	−	7.30774i	−0.598673	−	0.598673i	−0.939959	+	0.341286i	$0.889137\pi$
$150$	−5.23041	+	1.66242i	−0.427061	+	0.135736i
$151$	6.48932	+	6.48932i	0.528094	+	0.528094i	0.920004	−	0.391910i	$-0.128186\pi$
$151$	6.48932	+	6.48932i	0.528094	+	0.528094i	−0.391910	+	0.920004i	$0.628186\pi$
$152$		−	2.24555i		−	0.182138i
$153$	5.98264	+	8.46073i	0.483668	+	0.684010i
$154$	−10.6665	−	10.6665i	−0.859532	−	0.859532i
$155$	4.92427			0.395527
$156$		0			0
$157$	−14.1431			−1.12874			−0.564372	−	0.825520i	$-0.690882\pi$
$157$	−14.1431			−1.12874			−0.564372	+	0.825520i	$0.690882\pi$
$158$	1.11759	+	1.11759i	0.0889105	+	0.0889105i
$159$	−5.75023	+	11.1086i	−0.456023	+	0.880968i
$160$			2.85808i			0.225951i
$161$	7.69672	+	7.69672i	0.606587	+	0.606587i
$162$	−8.12132	+	3.87868i	−0.638071	+	0.304738i
$163$	0.787963	+	0.787963i	0.0617181	+	0.0617181i	0.737292	−	0.675574i	$-0.236104\pi$
$163$	0.787963	+	0.787963i	0.0617181	+	0.0617181i	−0.675574	+	0.737292i	$0.736104\pi$
$164$	5.61494	−	5.61494i	0.438453	−	0.438453i
$165$	18.4749	+	9.56333i	1.43827	+	0.744504i
$166$			3.66193i			0.284221i
$167$	3.94925	−	3.94925i	0.305602	−	0.305602i	−0.537598	−	0.843201i	$-0.680668\pi$
$167$	3.94925	−	3.94925i	0.305602	−	0.305602i	0.843201	+	0.537598i	$0.180668\pi$
$168$	−5.52139	−	2.85808i	−0.425985	−	0.220506i
$169$		0			0
$170$		−	9.87205i		−	0.757152i
$171$	−6.63963	−	1.13918i	−0.507745	−	0.0871153i
$172$	−1.95035			−0.148712
$173$	−17.4953			−1.33014			−0.665072	−	0.746779i	$-0.731599\pi$
$173$	−17.4953			−1.33014			−0.665072	+	0.746779i	$0.731599\pi$
$174$	−3.32474	+	1.05673i	−0.252048	+	0.0801102i
$175$	−8.04261	+	8.04261i	−0.607964	+	0.607964i
$176$	2.97155	−	2.97155i	0.223989	−	0.223989i
$177$	16.9829	−	5.39779i	1.27651	−	0.405723i
$178$	9.84478			0.737897
$179$	9.21508			0.688768			0.344384	−	0.938829i	$-0.388088\pi$
$179$	9.21508			0.688768			0.344384	+	0.938829i	$0.388088\pi$
$180$	8.45077	+	1.44992i	0.629883	+	0.108071i
$181$		−	13.8110i		−	1.02656i	−0.858220	−	0.513282i	$-0.828429\pi$
$181$		−	13.8110i		−	1.02656i	0.858220	−	0.513282i	$-0.171571\pi$
$182$		0			0
$183$	0.421783	+	0.218331i	0.0311791	+	0.0161395i
$184$	−2.14421	+	2.14421i	−0.158073	+	0.158073i
$185$		−	13.8405i		−	1.01758i
$186$	−2.65019	−	1.37184i	−0.194321	−	0.100588i
$187$	−10.2640	+	10.2640i	−0.750577	+	0.750577i
$188$	0.957390	+	0.957390i	0.0698248	+	0.0698248i
$189$	−11.2518	+	14.8757i	−0.818448	+	1.08205i
$190$	4.53819	+	4.53819i	0.329235	+	0.329235i
$191$			22.7030i			1.64273i	0.570402	+	0.821366i	$0.306788\pi$
$191$			22.7030i			1.64273i	−0.570402	+	0.821366i	$0.693212\pi$
$192$	0.796225	−	1.53819i	0.0574626	−	0.111009i
$193$	14.1745	+	14.1745i	1.02030	+	1.02030i	0.999790	+	0.0205099i	$0.00652896\pi$
$193$	14.1745	+	14.1745i	1.02030	+	1.02030i	0.0205099	+	0.999790i	$0.493471\pi$
$194$	8.02251			0.575983
$195$		0			0
$196$	−5.88481			−0.420343
$197$	13.1786	+	13.1786i	0.938935	+	0.938935i	0.998240	−	0.0593051i	$-0.0188885\pi$
$197$	13.1786	+	13.1786i	0.938935	+	0.938935i	−0.0593051	+	0.998240i	$0.518888\pi$
$198$	−7.27879	−	10.2938i	−0.517281	−	0.731546i
$199$			4.51039i			0.319733i	0.987139	+	0.159866i	$0.0511064\pi$
$199$			4.51039i			0.319733i	−0.987139	+	0.159866i	$0.948894\pi$
$200$	−2.24057	−	2.24057i	−0.158432	−	0.158432i
$201$	7.00859	−	2.22759i	0.494348	−	0.157122i
$202$	−1.48977	−	1.48977i	−0.104820	−	0.104820i
$203$	−5.11233	+	5.11233i	−0.358815	+	0.358815i
$204$	−2.75023	+	5.31303i	−0.192554	+	0.371986i
$205$			22.6952i			1.58510i
$206$	10.0854	−	10.0854i	0.702683	−	0.702683i
$207$	5.25221	+	7.42775i	0.365054	+	0.516264i
$208$		0			0
$209$		−	9.43672i		−	0.652752i
$210$	16.9347	−	5.38247i	1.16860	−	0.371426i
$211$	−8.57683			−0.590453			−0.295227	−	0.955427i	$-0.595395\pi$
$211$	−8.57683			−0.590453			−0.295227	+	0.955427i	$0.595395\pi$
$212$	−7.22186			−0.495999
$213$	5.78884	+	18.2132i	0.396645	+	1.24795i
$214$	9.79025	−	9.79025i	0.669248	−	0.669248i
$215$	3.94159	−	3.94159i	0.268814	−	0.268814i
$216$	−4.14418	−	3.13461i	−0.281976	−	0.213283i
$217$	−6.18452			−0.419833
$218$	−8.26212			−0.559581
$219$	−7.48062	−	23.5360i	−0.505494	−	1.59042i
$220$			12.0108i			0.809771i
$221$		0			0
$222$	−3.85579	+	7.44882i	−0.258784	+	0.499932i
$223$	14.9027	−	14.9027i	0.997958	−	0.997958i	−0.00203979	−	0.999998i	$-0.500649\pi$
$223$	14.9027	−	14.9027i	0.997958	−	0.997958i	0.999998	+	0.00203979i	$0.000649285\pi$
$224$		−	3.58954i		−	0.239836i
$225$	−7.76155	+	5.48825i	−0.517437	+	0.365883i
$226$	12.7308	−	12.7308i	0.846841	−	0.846841i
$227$	3.55443	+	3.55443i	0.235916	+	0.235916i	0.815157	−	0.579241i	$-0.196651\pi$
$227$	3.55443	+	3.55443i	0.235916	+	0.235916i	−0.579241	+	0.815157i	$0.696651\pi$
$228$	−1.17812	−	3.70668i	−0.0780231	−	0.245481i
$229$	9.92484	+	9.92484i	0.655852	+	0.655852i	0.954396	−	0.298544i	$-0.0965010\pi$
$229$	9.92484	+	9.92484i	0.655852	+	0.655852i	−0.298544	+	0.954396i	$0.596501\pi$
$230$		−	8.66676i		−	0.571469i
$231$	−23.2032	−	12.0108i	−1.52666	−	0.790255i
$232$	−1.42423	−	1.42423i	−0.0935052	−	0.0935052i
$233$	18.7944			1.23126			0.615630	−	0.788035i	$-0.288902\pi$
$233$	18.7944			1.23126			0.615630	+	0.788035i	$0.288902\pi$
$234$		0			0
$235$	−3.86971			−0.252432
$236$	7.27501	+	7.27501i	0.473563	+	0.473563i
$237$	2.43112	+	1.25844i	0.157918	+	0.0817445i
$238$			12.3986i			0.803679i
$239$	−6.82142	−	6.82142i	−0.441241	−	0.441241i	0.451188	−	0.892429i	$-0.351000\pi$
$239$	−6.82142	−	6.82142i	−0.441241	−	0.441241i	−0.892429	+	0.451188i	$0.851000\pi$
$240$	1.49949	+	4.71778i	0.0967914	+	0.304531i
$241$	5.99419	+	5.99419i	0.386119	+	0.386119i	0.873301	−	0.487181i	$-0.161975\pi$
$241$	5.99419	+	5.99419i	0.386119	+	0.386119i	−0.487181	+	0.873301i	$0.661975\pi$
$242$	4.70951	−	4.70951i	0.302739	−	0.302739i
$243$	−11.3708	+	10.6633i	−0.729435	+	0.684050i
$244$			0.274207i			0.0175543i
$245$	11.8930	−	11.8930i	0.759817	−	0.759817i
$246$	6.32260	−	12.2143i	0.403114	−	0.778757i
$247$		0			0
$248$		−	1.72293i		−	0.109406i
$249$	1.92122	+	6.04468i	0.121753	+	0.383066i
$250$	−5.23418			−0.331039
$251$	7.03975			0.444345			0.222173	−	0.975007i	$-0.428685\pi$
$251$	7.03975			0.444345			0.222173	+	0.975007i	$0.428685\pi$
$252$	−10.6135	−	1.82100i	−0.668590	−	0.114712i
$253$	−9.01084	+	9.01084i	−0.566507	+	0.566507i
$254$	14.6323	−	14.6323i	0.918114	−	0.918114i
$255$	−5.17935	−	16.2956i	−0.324343	−	1.02047i
$256$	1.00000			0.0625000
$257$	1.63199			0.101801			0.0509003	−	0.998704i	$-0.483791\pi$
$257$	1.63199			0.101801			0.0509003	+	0.998704i	$0.483791\pi$
$258$	−3.21940	+	1.02324i	−0.200431	+	0.0637044i
$259$			17.3827i			1.08011i
$260$		0			0
$261$	−4.93367	+	3.48863i	−0.305387	+	0.215941i
$262$	−3.31135	+	3.31135i	−0.204576	+	0.204576i
$263$		−	10.5679i		−	0.651646i	−0.945431	−	0.325823i	$-0.894359\pi$
$263$		−	10.5679i		−	0.651646i	0.945431	−	0.325823i	$-0.105641\pi$
$264$	3.34607	−	6.46410i	0.205936	−	0.397838i
$265$	14.5952	−	14.5952i	0.896574	−	0.896574i
$266$	−5.69963	−	5.69963i	−0.349467	−	0.349467i
$267$	16.2506	−	5.16504i	0.994519	−	0.316095i
$268$	3.00229	+	3.00229i	0.183394	+	0.183394i
$269$			8.61859i			0.525485i	0.964866	+	0.262742i	$0.0846269\pi$
$269$			8.61859i			0.525485i	−0.964866	+	0.262742i	$0.915373\pi$
$270$	14.7102	−	2.04032i	0.895235	−	0.124170i
$271$	−14.0234	−	14.0234i	−0.851858	−	0.851858i	0.138504	−	0.990362i	$-0.455771\pi$
$271$	−14.0234	−	14.0234i	−0.851858	−	0.851858i	−0.990362	+	0.138504i	$0.955771\pi$
$272$	−3.45408			−0.209434
$273$		0			0
$274$	5.47999			0.331058
$275$	−9.41578	−	9.41578i	−0.567793	−	0.567793i
$276$	−2.41445	+	4.66435i	−0.145333	+	0.280761i
$277$			15.5025i			0.931452i	0.884929	+	0.465726i	$0.154207\pi$
$277$			15.5025i			0.931452i	−0.884929	+	0.465726i	$0.845793\pi$
$278$	10.3897	+	10.3897i	0.623132	+	0.623132i
$279$	−5.09435	−	0.874052i	−0.304991	−	0.0523281i
$280$	7.25436	+	7.25436i	0.433531	+	0.433531i
$281$	11.9452	−	11.9452i	0.712591	−	0.712591i	−0.254486	−	0.967077i	$-0.581906\pi$
$281$	11.9452	−	11.9452i	0.712591	−	0.712591i	0.967077	+	0.254486i	$0.0819061\pi$
$282$	2.08264	+	1.07805i	0.124019	+	0.0641970i
$283$		−	1.57972i		−	0.0939046i	−0.998897	−	0.0469523i	$-0.985049\pi$
$283$		−	1.57972i		−	0.0939046i	0.998897	−	0.0469523i	$-0.0149509\pi$
$284$	−7.80205	+	7.80205i	−0.462967	+	0.462967i
$285$	9.87205	+	5.11015i	0.584770	+	0.302699i
$286$		0			0
$287$		−	28.5035i		−	1.68251i
$288$	0.507306	−	2.95680i	0.0298933	−	0.174231i
$289$	−5.06933			−0.298196
$290$	5.75665			0.338042
$291$	13.2426	−	4.20899i	0.776295	−	0.246735i
$292$	10.0822	−	10.0822i	0.590016	−	0.590016i
$293$	2.76136	−	2.76136i	0.161321	−	0.161321i	−0.621831	−	0.783152i	$-0.713611\pi$
$293$	2.76136	−	2.76136i	0.161321	−	0.161321i	0.783152	+	0.621831i	$0.213611\pi$
$294$	−9.71393	+	3.08745i	−0.566528	+	0.180064i
$295$	−29.4051			−1.71203
$296$	−4.84259			−0.281470
$297$	−17.4155	−	13.1729i	−1.01055	−	0.764370i
$298$		−	10.3347i		−	0.598673i
$299$		0			0
$300$	−4.87397	−	2.52295i	−0.281399	−	0.145663i
$301$	−4.95035	+	4.95035i	−0.285333	+	0.285333i
$302$			9.17729i			0.528094i
$303$	−3.24073	−	1.67753i	−0.186175	−	0.0963714i
$304$	1.58784	−	1.58784i	0.0910691	−	0.0910691i
$305$	−0.554165	−	0.554165i	−0.0317314	−	0.0317314i
$306$	−1.75228	+	10.2130i	−0.100171	+	0.583839i
$307$	−21.7994	−	21.7994i	−1.24416	−	1.24416i	−0.958260	−	0.285899i	$-0.907708\pi$
$307$	−21.7994	−	21.7994i	−1.24416	−	1.24416i	−0.285899	−	0.958260i	$-0.592292\pi$
$308$		−	15.0847i		−	0.859532i
$309$	11.3565	−	21.9390i	0.646048	−	1.24807i
$310$	3.48199	+	3.48199i	0.197764	+	0.197764i
$311$	−20.9295			−1.18681			−0.593403	−	0.804906i	$-0.702216\pi$
$311$	−20.9295			−1.18681			−0.593403	+	0.804906i	$0.702216\pi$
$312$		0			0
$313$	−32.6685			−1.84653			−0.923267	−	0.384159i	$-0.874491\pi$
$313$	−32.6685			−1.84653			−0.923267	+	0.384159i	$0.874491\pi$
$314$	−10.0007	−	10.0007i	−0.564372	−	0.564372i
$315$	25.1298	−	17.7695i	1.41591	−	1.00120i
$316$			1.58051i			0.0889105i
$317$	−5.21085	−	5.21085i	−0.292671	−	0.292671i	0.545464	−	0.838134i	$-0.316354\pi$
$317$	−5.21085	−	5.21085i	−0.292671	−	0.292671i	−0.838134	+	0.545464i	$0.816354\pi$
$318$	−11.9210	+	3.78893i	−0.668495	+	0.212473i
$319$	−5.98519	−	5.98519i	−0.335106	−	0.335106i
$320$	−2.02097	+	2.02097i	−0.112976	+	0.112976i
$321$	11.0241	−	21.2970i	0.615308	−	1.18868i
$322$			10.8848i			0.606587i
$323$	−5.48454	+	5.48454i	−0.305168	+	0.305168i
$324$	−8.48528	−	3.00000i	−0.471405	−	0.166667i
$325$		0			0
$326$			1.11435i			0.0617181i
$327$	−13.6381	+	4.33470i	−0.754189	+	0.239709i
$328$	7.94072			0.438453
$329$	4.86007			0.267944
$330$	6.30146	+	19.8261i	0.346884	+	1.09139i
$331$	−12.8956	+	12.8956i	−0.708809	+	0.708809i	−0.966285	−	0.257476i	$-0.917109\pi$
$331$	−12.8956	+	12.8956i	−0.708809	+	0.708809i	0.257476	+	0.966285i	$0.417109\pi$
$332$	−2.58938	+	2.58938i	−0.142110	+	0.142110i
$333$	−2.45667	+	14.3186i	−0.134625	+	0.784652i
$334$	5.58509			0.305602
$335$	−12.1351			−0.663010
$336$	−1.88324	−	5.92518i	−0.102739	−	0.323245i
$337$			4.92484i			0.268273i	0.990963	+	0.134136i	$0.0428260\pi$
$337$			4.92484i			0.268273i	−0.990963	+	0.134136i	$0.957174\pi$
$338$		0			0
$339$	14.3353	−	27.6937i	0.778587	−	1.50412i
$340$	6.98059	−	6.98059i	0.378576	−	0.378576i
$341$		−	7.24045i		−	0.392093i
$342$	−3.88941	−	5.50045i	−0.210315	−	0.297430i
$343$	2.83057	−	2.83057i	0.152836	−	0.152836i
$344$	−1.37910	−	1.37910i	−0.0743562	−	0.0743562i
$345$	−4.54699	−	14.3060i	−0.244802	−	0.770212i
$346$	−12.3711	−	12.3711i	−0.665072	−	0.665072i
$347$		−	14.9422i		−	0.802137i	−0.916048	−	0.401069i	$-0.868639\pi$
$347$		−	14.9422i		−	0.802137i	0.916048	−	0.401069i	$-0.131361\pi$
$348$	−3.09816	−	1.60373i	−0.166079	−	0.0859688i
$349$	22.0872	+	22.0872i	1.18230	+	1.18230i	0.979147	+	0.203155i	$0.0651196\pi$
$349$	22.0872	+	22.0872i	1.18230	+	1.18230i	0.203155	+	0.979147i	$0.434880\pi$
$350$	−11.3740			−0.607964
$351$		0			0
$352$	4.20241			0.223989
$353$	7.31540	+	7.31540i	0.389360	+	0.389360i	0.874459	−	0.485099i	$-0.161217\pi$
$353$	7.31540	+	7.31540i	0.389360	+	0.389360i	−0.485099	+	0.874459i	$0.661217\pi$
$354$	15.8255	+	8.19190i	0.841117	+	0.435394i
$355$		−	31.5354i		−	1.67373i
$356$	6.96131	+	6.96131i	0.368949	+	0.368949i
$357$	6.50488	+	20.4661i	0.344275	+	1.08318i
$358$	6.51605	+	6.51605i	0.344384	+	0.344384i
$359$	9.08944	−	9.08944i	0.479722	−	0.479722i	−0.425321	−	0.905043i	$-0.639839\pi$
$359$	9.08944	−	9.08944i	0.479722	−	0.479722i	0.905043	+	0.425321i	$0.139839\pi$
$360$	4.95035	+	7.00085i	0.260906	+	0.368977i
$361$			13.9575i			0.734606i
$362$	9.76586	−	9.76586i	0.513282	−	0.513282i
$363$	5.30306	−	10.2447i	0.278339	−	0.537709i
$364$		0			0
$365$			40.7516i			2.13304i
$366$	0.143862	+	0.452628i	0.00751980	+	0.0236593i
$367$	1.64695			0.0859700			0.0429850	−	0.999076i	$-0.486313\pi$
$367$	1.64695			0.0859700			0.0429850	+	0.999076i	$0.486313\pi$
$368$	−3.03237			−0.158073
$369$	4.02837	−	23.4791i	0.209709	−	1.22227i
$370$	9.78673	−	9.78673i	0.508788	−	0.508788i
$371$	−18.3304	+	18.3304i	−0.951669	+	0.951669i
$372$	−0.903931	−	2.84400i	−0.0468666	−	0.147455i
$373$	−19.9516			−1.03305			−0.516526	−	0.856271i	$-0.672775\pi$
$373$	−19.9516			−1.03305			−0.516526	+	0.856271i	$0.672775\pi$
$374$	−14.5155			−0.750577
$375$	−8.63996	+	2.74610i	−0.446165	+	0.141808i
$376$			1.35395i			0.0698248i
$377$		0			0
$378$	−18.4749	+	2.56249i	−0.950248	+	0.131800i
$379$	−8.70575	+	8.70575i	−0.447184	+	0.447184i	−0.894417	−	0.447233i	$-0.852409\pi$
$379$	−8.70575	+	8.70575i	−0.447184	+	0.447184i	0.447233	+	0.894417i	$0.352409\pi$
$380$			6.41797i			0.329235i
$381$	16.4765	−	31.8301i	0.844115	−	1.63071i
$382$	−16.0534	+	16.0534i	−0.821366	+	0.821366i
$383$	20.0436	+	20.0436i	1.02418	+	1.02418i	0.999700	+	0.0244774i	$0.00779217\pi$
$383$	20.0436	+	20.0436i	1.02418	+	1.02418i	0.0244774	+	0.999700i	$0.492208\pi$
$384$	1.65068	−	0.524648i	0.0842359	−	0.0267733i
$385$	30.4858	+	30.4858i	1.55370	+	1.55370i
$386$			20.0457i			1.02030i
$387$	−4.77735	+	3.37810i	−0.242846	+	0.171718i
$388$	5.67277	+	5.67277i	0.287991	+	0.287991i
$389$	15.9504			0.808717			0.404359	−	0.914601i	$-0.367495\pi$
$389$	15.9504			0.808717			0.404359	+	0.914601i	$0.367495\pi$
$390$		0			0
$391$	10.4740			0.529695
$392$	−4.16119	−	4.16119i	−0.210172	−	0.210172i
$393$	−3.72868	+	7.20326i	−0.188087	+	0.363357i
$394$			18.6373i			0.938935i
$395$	−3.19416	−	3.19416i	−0.160716	−	0.160716i
$396$	2.13191	−	12.4257i	0.107132	−	0.624413i
$397$	−8.97449	−	8.97449i	−0.450417	−	0.450417i	0.445076	−	0.895493i	$-0.353177\pi$
$397$	−8.97449	−	8.97449i	−0.450417	−	0.450417i	−0.895493	+	0.445076i	$0.853177\pi$
$398$	−3.18933	+	3.18933i	−0.159866	+	0.159866i
$399$	−12.3986	−	6.41797i	−0.620705	−	0.321300i
$400$		−	3.16864i		−	0.158432i
$401$	−11.6106	+	11.6106i	−0.579804	+	0.579804i	−0.934849	−	0.355045i	$-0.884465\pi$
$401$	−11.6106	+	11.6106i	−0.579804	+	0.579804i	0.355045	+	0.934849i	$0.384465\pi$
$402$	6.53097	+	3.38068i	0.325735	+	0.168613i
$403$		0			0
$404$		−	2.10685i		−	0.104820i
$405$	23.2114	−	11.0856i	1.15338	−	0.550847i
$406$	−7.22992			−0.358815
$407$	−20.3506			−1.00874
$408$	−5.70158	+	1.81217i	−0.282270	+	0.0897160i
$409$	24.0968	−	24.0968i	1.19151	−	1.19151i	0.214868	−	0.976643i	$-0.431068\pi$
$409$	24.0968	−	24.0968i	1.19151	−	1.19151i	0.976643	−	0.214868i	$-0.0689322\pi$
$410$	−16.0480	+	16.0480i	−0.792552	+	0.792552i
$411$	9.04570	−	2.87506i	0.446192	−	0.141816i
$412$	14.2629			0.702683
$413$	36.9307			1.81724
$414$	−1.53834	+	8.96609i	−0.0756052	+	0.440659i
$415$		−	10.4661i		−	0.513761i
$416$		0			0
$417$	22.6010	+	11.6991i	1.10677	+	0.572909i
$418$	6.67277	−	6.67277i	0.326376	−	0.326376i
$419$			32.9024i			1.60739i	0.595044	+	0.803693i	$0.297134\pi$
$419$			32.9024i			1.60739i	−0.595044	+	0.803693i	$0.702866\pi$
$420$	15.7806	+	8.16864i	0.770014	+	0.398589i
$421$	−17.0945	+	17.0945i	−0.833137	+	0.833137i	−0.987945	−	0.154808i	$-0.950524\pi$
$421$	−17.0945	+	17.0945i	−0.833137	+	0.833137i	0.154808	+	0.987945i	$0.450524\pi$
$422$	−6.06473	−	6.06473i	−0.295227	−	0.295227i
$423$	4.00336	+	0.686869i	0.194650	+	0.0333967i
$424$	−5.10662	−	5.10662i	−0.248000	−	0.248000i
$425$			10.9447i			0.530898i
$426$	−8.78537	+	16.9720i	−0.425652	+	0.822297i
$427$	0.695990	+	0.695990i	0.0336813	+	0.0336813i
$428$	13.8455			0.669248
$429$		0			0
$430$	5.57425			0.268814
$431$	1.24152	+	1.24152i	0.0598018	+	0.0598018i	0.736375	−	0.676573i	$-0.236536\pi$
$431$	1.24152	+	1.24152i	0.0598018	+	0.0598018i	−0.676573	+	0.736375i	$0.736536\pi$
$432$	−0.713876	−	5.14688i	−0.0343464	−	0.247629i
$433$			10.2438i			0.492286i	0.969234	+	0.246143i	$0.0791633\pi$
$433$			10.2438i			0.492286i	−0.969234	+	0.246143i	$0.920837\pi$
$434$	−4.37312	−	4.37312i	−0.209916	−	0.209916i
$435$	9.50238	−	3.02021i	0.455604	−	0.144808i
$436$	−5.84220	−	5.84220i	−0.279791	−	0.279791i
$437$	−4.81492	+	4.81492i	−0.230329	+	0.230329i
$438$	11.3529	−	21.9321i	0.542461	−	1.04795i
$439$		−	5.40224i		−	0.257835i	−0.991655	−	0.128917i	$-0.958850\pi$
$439$		−	5.40224i		−	0.257835i	0.991655	−	0.128917i	$-0.0411502\pi$
$440$	−8.49295	+	8.49295i	−0.404885	+	0.404885i
$441$	−14.4148	+	10.1928i	−0.686418	+	0.485371i
$442$		0			0
$443$			13.5731i			0.644876i	0.946591	+	0.322438i	$0.104502\pi$
$443$			13.5731i			0.644876i	−0.946591	+	0.322438i	$0.895498\pi$
$444$	−7.99357	+	2.54065i	−0.379358	+	0.120574i
$445$	−28.1372			−1.33383
$446$	21.0756			0.997958
$447$	−5.42208	−	17.0593i	−0.256455	−	0.806877i
$448$	2.53819	−	2.53819i	0.119918	−	0.119918i
$449$	1.43493	−	1.43493i	0.0677187	−	0.0677187i	−0.672436	−	0.740155i	$-0.734752\pi$
$449$	1.43493	−	1.43493i	0.0677187	−	0.0677187i	0.740155	+	0.672436i	$0.234752\pi$
$450$	−9.36902	−	1.60747i	−0.441660	−	0.0757769i
$451$	33.3702			1.57134
$452$	18.0041			0.846841
$453$	4.81484	+	15.1488i	0.226221	+	0.711751i
$454$			5.02672i			0.235916i
$455$		0			0
$456$	1.78796	−	3.45408i	0.0837291	−	0.161752i
$457$	−21.1802	+	21.1802i	−0.990770	+	0.990770i	−0.999958	−	0.00918755i	$-0.997075\pi$
$457$	−21.1802	+	21.1802i	−0.990770	+	0.990770i	0.00918755	+	0.999958i	$0.497075\pi$
$458$			14.0358i			0.655852i
$459$	2.46578	+	17.7777i	0.115093	+	0.829794i
$460$	6.12832	−	6.12832i	0.285735	−	0.285735i
$461$	−11.3922	−	11.3922i	−0.530589	−	0.530589i	0.390159	−	0.920748i	$-0.372420\pi$
$461$	−11.3922	−	11.3922i	−0.530589	−	0.530589i	−0.920748	+	0.390159i	$0.872420\pi$
$462$	−7.91417	−	24.9001i	−0.368200	−	1.15846i
$463$	4.07041	+	4.07041i	0.189168	+	0.189168i	0.795336	−	0.606168i	$-0.207294\pi$
$463$	4.07041	+	4.07041i	0.189168	+	0.189168i	−0.606168	+	0.795336i	$0.707294\pi$
$464$		−	2.01416i		−	0.0935052i
$465$	7.57446	+	3.92083i	0.351257	+	0.181824i
$466$	13.2896	+	13.2896i	0.615630	+	0.615630i
$467$	−36.8536			−1.70538			−0.852690	−	0.522417i	$-0.825030\pi$
$467$	−36.8536			−1.70538			−0.852690	+	0.522417i	$0.825030\pi$
$468$		0			0
$469$	15.2408			0.703753
$470$	−2.73630	−	2.73630i	−0.126216	−	0.126216i
$471$	−21.7548	−	11.2611i	−1.00241	−	0.518885i
$472$			10.2884i			0.473563i
$473$	−5.79555	−	5.79555i	−0.266480	−	0.266480i
$474$	0.829210	+	2.60891i	0.0380869	+	0.119831i
$475$	−5.03130	−	5.03130i	−0.230852	−	0.230852i
$476$	−8.76711	+	8.76711i	−0.401840	+	0.401840i
$477$	−17.6899	+	12.5086i	−0.809963	+	0.572731i
$478$		−	9.64695i		−	0.441241i
$479$	−10.6370	+	10.6370i	−0.486018	+	0.486018i	−0.907047	−	0.421029i	$-0.861669\pi$
$479$	−10.6370	+	10.6370i	−0.486018	+	0.486018i	0.421029	+	0.907047i	$0.361669\pi$
$480$	−2.27568	+	4.39627i	−0.103870	+	0.200661i
$481$		0			0
$482$			8.47706i			0.386119i
$483$	5.71069	+	17.9673i	0.259845	+	0.817542i
$484$	6.66025			0.302739
$485$	−22.9290			−1.04115
$486$	−15.5804	−	0.500258i	−0.706743	−	0.0226921i
$487$	−11.8303	+	11.8303i	−0.536081	+	0.536081i	−0.922376	−	0.386294i	$-0.873755\pi$
$487$	−11.8303	+	11.8303i	−0.536081	+	0.536081i	0.386294	+	0.922376i	$0.373755\pi$
$488$	−0.193894	+	0.193894i	−0.00877716	+	0.00877716i
$489$	0.584640	+	1.83943i	0.0264383	+	0.0831820i
$490$	16.8193			0.759817
$491$	−25.2666			−1.14026			−0.570132	−	0.821553i	$-0.693108\pi$
$491$	−25.2666			−1.14026			−0.570132	+	0.821553i	$0.693108\pi$
$492$	13.1076	−	4.16608i	0.590936	−	0.187821i
$493$			6.95708i			0.313331i
$494$		0			0
$495$	20.8034	+	29.4204i	0.935043	+	1.32235i
$496$	1.21829	−	1.21829i	0.0547030	−	0.0547030i
$497$			39.6062i			1.77658i
$498$	−2.91572	+	5.63274i	−0.130657	+	0.252409i
$499$	−1.37946	+	1.37946i	−0.0617533	+	0.0617533i	−0.737309	−	0.675556i	$-0.763904\pi$
$499$	−1.37946	+	1.37946i	−0.0617533	+	0.0617533i	0.675556	+	0.737309i	$0.263904\pi$
$500$	−3.70112	−	3.70112i	−0.165519	−	0.165519i
$501$	9.21920	−	2.93020i	0.411883	−	0.130912i
$502$	4.97786	+	4.97786i	0.222173	+	0.222173i
$503$			11.2904i			0.503414i	0.967803	+	0.251707i	$0.0809919\pi$
$503$			11.2904i			0.503414i	−0.967803	+	0.251707i	$0.919008\pi$
$504$	−6.21727	−	8.79254i	−0.276939	−	0.391651i
$505$	4.25788	+	4.25788i	0.189473	+	0.189473i
$506$	−12.7433			−0.566507
$507$		0			0
$508$	20.6932			0.918114
$509$	−26.5900	−	26.5900i	−1.17858	−	1.17858i	−0.980106	−	0.198473i	$-0.936402\pi$
$509$	−26.5900	−	26.5900i	−1.17858	−	1.17858i	−0.198473	−	0.980106i	$-0.563598\pi$
$510$	7.86037	−	15.1851i	0.348063	−	0.672406i
$511$		−	51.1810i		−	2.26411i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−9.30596	−	7.03892i	−0.410868	−	0.310776i
$514$	1.15399	+	1.15399i	0.0509003	+	0.0509003i
$515$	−28.8249	+	28.8249i	−1.27018	+	1.27018i
$516$	−3.00000	−	1.55291i	−0.132068	−	0.0683632i
$517$			5.68987i			0.250240i
$518$	−12.2914	+	12.2914i	−0.540054	+	0.540054i
$519$	−26.9111	−	13.9302i	−1.18127	−	0.611468i
$520$		0			0
$521$		−	18.2111i		−	0.797843i	−0.916985	−	0.398922i	$-0.869385\pi$
$521$		−	18.2111i		−	0.797843i	0.916985	−	0.398922i	$-0.130615\pi$
$522$	−5.95547	−	1.02180i	−0.260664	−	0.0447228i
$523$	33.8098			1.47840			0.739199	−	0.673487i	$-0.235204\pi$
$523$	33.8098			1.47840			0.739199	+	0.673487i	$0.235204\pi$
$524$	−4.68295			−0.204576
$525$	−18.7748	+	5.96732i	−0.819398	+	0.260435i
$526$	7.47265	−	7.47265i	0.325823	−	0.325823i
$527$	−4.20809	+	4.20809i	−0.183307	+	0.183307i
$528$	6.93684	−	2.20478i	0.301887	−	0.0959509i
$529$	−13.8048			−0.600207
$530$	20.6407			0.896574
$531$	30.4207	+	5.21937i	1.32015	+	0.226502i
$532$		−	8.06049i		−	0.349467i
$533$		0			0
$534$	15.1431	+	7.83866i	0.655307	+	0.339212i
$535$	−27.9814	+	27.9814i	−1.20974	+	1.20974i
$536$			4.24588i			0.183394i
$537$	14.1745	+	7.33728i	0.611676	+	0.316627i
$538$	−6.09426	+	6.09426i	−0.262742	+	0.262742i
$539$	−17.4870	−	17.4870i	−0.753219	−	0.753219i
$540$	11.8444	+	8.95897i	0.509702	+	0.385533i
$541$	4.97355	+	4.97355i	0.213829	+	0.213829i	0.805892	−	0.592063i	$-0.201686\pi$
$541$	4.97355	+	4.97355i	0.213829	+	0.213829i	−0.592063	+	0.805892i	$0.701686\pi$
$542$		−	19.8320i		−	0.851858i
$543$	10.9967	−	21.2439i	0.471912	−	0.911665i
$544$	−2.44240	−	2.44240i	−0.104717	−	0.104717i
$545$	23.6138			1.01150
$546$		0			0
$547$	−2.15870			−0.0922995			−0.0461497	−	0.998935i	$-0.514695\pi$
$547$	−2.15870			−0.0922995			−0.0461497	+	0.998935i	$0.514695\pi$
$548$	3.87494	+	3.87494i	0.165529	+	0.165529i
$549$	0.474941	+	0.671668i	0.0202700	+	0.0286661i
$550$		−	13.3159i		−	0.567793i
$551$	−3.19818	−	3.19818i	−0.136247	−	0.136247i
$552$	−5.00547	+	1.59092i	−0.213047	+	0.0677142i
$553$	4.01163	+	4.01163i	0.170592	+	0.170592i
$554$	−10.9619	+	10.9619i	−0.465726	+	0.465726i
$555$	11.0202	−	21.2893i	0.467780	−	0.903682i
$556$			14.6932i			0.623132i
$557$	−1.59427	+	1.59427i	−0.0675516	+	0.0675516i	−0.740075	−	0.672524i	$-0.765210\pi$
$557$	−1.59427	+	1.59427i	−0.0675516	+	0.0675516i	0.672524	+	0.740075i	$0.265210\pi$
$558$	−2.98420	−	4.22030i	−0.126331	−	0.178659i
$559$		0			0
$560$			10.2592i			0.433531i
$561$	−23.9604	+	7.61550i	−1.01161	+	0.321527i
$562$	16.8931			0.712591
$563$	36.2979			1.52978			0.764888	−	0.644164i	$-0.222794\pi$
$563$	36.2979			1.52978			0.764888	+	0.644164i	$0.222794\pi$
$564$	0.710348	+	2.23494i	0.0299111	+	0.0941081i
$565$	−36.3857	+	36.3857i	−1.53076	+	1.53076i
$566$	1.11703	−	1.11703i	0.0469523	−	0.0469523i
$567$	−29.1518	+	13.9227i	−1.22426	+	0.584698i
$568$	−11.0338			−0.462967
$569$	−39.0751			−1.63811			−0.819057	−	0.573712i	$-0.805503\pi$
$569$	−39.0751			−1.63811			−0.819057	+	0.573712i	$0.805503\pi$
$570$	3.36717	+	10.5940i	0.141035	+	0.443734i
$571$		−	31.9061i		−	1.33523i	−0.744508	−	0.667614i	$-0.767316\pi$
$571$		−	31.9061i		−	1.33523i	0.744508	−	0.667614i	$-0.232684\pi$
$572$		0			0
$573$	−18.0767	+	34.9215i	−0.755165	+	1.45887i
$574$	20.1550	−	20.1550i	0.841255	−	0.841255i
$575$			9.60848i			0.400701i
$576$	2.44949	−	1.73205i	0.102062	−	0.0721688i
$577$	−9.31011	+	9.31011i	−0.387585	+	0.387585i	−0.873825	−	0.486240i	$-0.838368\pi$
$577$	−9.31011	+	9.31011i	−0.387585	+	0.387585i	0.486240	+	0.873825i	$0.338368\pi$
$578$	−3.58456	−	3.58456i	−0.149098	−	0.149098i
$579$	10.5169	+	33.0890i	0.437069	+	1.37513i
$580$	4.07056	+	4.07056i	0.169021	+	0.169021i
$581$			13.1447i			0.545332i
$582$	12.3401	+	6.38772i	0.511515	+	0.264780i
$583$	−21.4601	−	21.4601i	−0.888788	−	0.888788i
$584$	14.2584			0.590016
$585$		0			0
$586$	3.90516			0.161321
$587$	−20.7092	−	20.7092i	−0.854758	−	0.854758i	0.135957	−	0.990715i	$-0.456589\pi$
$587$	−20.7092	−	20.7092i	−0.854758	−	0.854758i	−0.990715	+	0.135957i	$0.956589\pi$
$588$	−9.05195	−	4.68563i	−0.373296	−	0.193232i
$589$		−	3.86892i		−	0.159416i
$590$	−20.7926	−	20.7926i	−0.856017	−	0.856017i
$591$	9.77803	+	30.7643i	0.402214	+	1.26547i
$592$	−3.42423	−	3.42423i	−0.140735	−	0.140735i
$593$	12.7368	−	12.7368i	0.523037	−	0.523037i	−0.395450	−	0.918487i	$-0.629411\pi$
$593$	12.7368	−	12.7368i	0.523037	−	0.523037i	0.918487	+	0.395450i	$0.129411\pi$
$594$	−3.00000	−	21.6293i	−0.123091	−	0.887461i
$595$		−	35.4361i		−	1.45274i
$596$	7.30774	−	7.30774i	0.299337	−	0.299337i
$597$	−3.59128	+	6.93783i	−0.146981	+	0.283946i
$598$		0			0
$599$			15.6579i			0.639764i	0.947457	+	0.319882i	$0.103643\pi$
$599$			15.6579i			0.639764i	−0.947457	+	0.319882i	$0.896357\pi$
$600$	−1.66242	−	5.23041i	−0.0678680	−	0.213531i
$601$	7.99663			0.326189			0.163095	−	0.986610i	$-0.447852\pi$
$601$	7.99663			0.326189			0.163095	+	0.986610i	$0.447852\pi$
$602$	−7.00085			−0.285333
$603$	12.5542	+	2.15396i	0.511247	+	0.0877160i
$604$	−6.48932	+	6.48932i	−0.264047	+	0.264047i
$605$	−13.4602	+	13.4602i	−0.547234	+	0.547234i
$606$	−1.10535	−	3.47773i	−0.0449019	−	0.141273i
$607$	4.49161			0.182309			0.0911545	−	0.995837i	$-0.470944\pi$
$607$	4.49161			0.182309			0.0911545	+	0.995837i	$0.470944\pi$
$608$	2.24555			0.0910691
$609$	−11.9343	+	3.79316i	−0.483602	+	0.153707i
$610$		−	0.783707i		−	0.0317314i
$611$		0			0
$612$	−8.46073	+	5.98264i	−0.342005	+	0.241834i
$613$	22.3358	−	22.3358i	0.902133	−	0.902133i	−0.0934876	−	0.995620i	$-0.529802\pi$
$613$	22.3358	−	22.3358i	0.902133	−	0.902133i	0.995620	+	0.0934876i	$0.0298016\pi$
$614$		−	30.8290i		−	1.24416i
$615$	−18.0705	+	34.9096i	−0.728674	+	1.40769i
$616$	10.6665	−	10.6665i	0.429766	−	0.429766i
$617$	−3.83238	−	3.83238i	−0.154286	−	0.154286i	0.625743	−	0.780029i	$-0.284796\pi$
$617$	−3.83238	−	3.83238i	−0.154286	−	0.154286i	−0.780029	+	0.625743i	$0.784796\pi$
$618$	23.5435	−	7.48300i	0.947058	−	0.301010i
$619$	−7.22455	−	7.22455i	−0.290379	−	0.290379i	0.546851	−	0.837230i	$-0.315826\pi$
$619$	−7.22455	−	7.22455i	−0.290379	−	0.290379i	−0.837230	+	0.546851i	$0.815826\pi$
$620$			4.92427i			0.197764i
$621$	2.16473	+	15.6072i	0.0868678	+	0.626297i
$622$	−14.7994	−	14.7994i	−0.593403	−	0.593403i
$623$	35.3382			1.41580
$624$		0			0
$625$	30.8029			1.23212
$626$	−23.1001	−	23.1001i	−0.923267	−	0.923267i
$627$	7.51376	−	14.5155i	0.300071	−	0.579692i
$628$		−	14.1431i		−	0.564372i
$629$	11.8276	+	11.8276i	0.471596	+	0.471596i
$630$	30.3344	+	5.20456i	1.20855	+	0.207355i
$631$	−14.8492	−	14.8492i	−0.591139	−	0.591139i	0.346800	−	0.937939i	$-0.387268\pi$
$631$	−14.8492	−	14.8492i	−0.591139	−	0.591139i	−0.937939	+	0.346800i	$0.887268\pi$
$632$	−1.11759	+	1.11759i	−0.0444553	+	0.0444553i
$633$	−13.1928	−	6.82909i	−0.524366	−	0.271432i
$634$		−	7.36926i		−	0.292671i
$635$	−41.8204	+	41.8204i	−1.65959	+	1.65959i
$636$	−11.1086	−	5.75023i	−0.440484	−	0.228011i
$637$		0			0
$638$		−	8.46434i		−	0.335106i
$639$	−5.59750	+	32.6246i	−0.221434	+	1.29061i
$640$	−2.85808			−0.112976
$641$	42.6873			1.68605			0.843024	−	0.537876i	$-0.180773\pi$
$641$	42.6873			1.68605			0.843024	+	0.537876i	$0.180773\pi$
$642$	22.8545	−	7.26401i	0.901995	−	0.286688i
$643$	2.22166	−	2.22166i	0.0876138	−	0.0876138i	−0.661942	−	0.749555i	$-0.730267\pi$
$643$	2.22166	−	2.22166i	0.0876138	−	0.0876138i	0.749555	+	0.661942i	$0.230267\pi$
$644$	−7.69672	+	7.69672i	−0.303293	+	0.303293i
$645$	9.20130	−	2.92452i	0.362301	−	0.115153i
$646$	−7.75631			−0.305168
$647$	−36.4701			−1.43379			−0.716895	−	0.697181i	$-0.754437\pi$
$647$	−36.4701			−1.43379			−0.716895	+	0.697181i	$0.754437\pi$
$648$	−3.87868	−	8.12132i	−0.152369	−	0.319036i
$649$			43.2361i			1.69717i
$650$		0			0
$651$	−9.51297	−	4.92427i	−0.372843	−	0.192998i
$652$	−0.787963	+	0.787963i	−0.0308590	+	0.0308590i
$653$			45.4283i			1.77775i	0.458152	+	0.888874i	$0.348512\pi$
$653$			45.4283i			1.77775i	−0.458152	+	0.888874i	$0.651488\pi$
$654$	−12.7087	−	6.57851i	−0.496949	−	0.257240i
$655$	9.46410	−	9.46410i	0.369793	−	0.369793i
$656$	5.61494	+	5.61494i	0.219226	+	0.219226i
$657$	7.23336	−	42.1591i	0.282200	−	1.64478i
$658$	3.43659	+	3.43659i	0.133972	+	0.133972i
$659$		−	13.2626i		−	0.516639i	−0.966060	−	0.258319i	$-0.916831\pi$
$659$		−	13.2626i		−	0.516639i	0.966060	−	0.258319i	$-0.0831687\pi$
$660$	−9.56333	+	18.4749i	−0.372252	+	0.719136i
$661$	−6.57777	−	6.57777i	−0.255846	−	0.255846i	0.567516	−	0.823362i	$-0.307904\pi$
$661$	−6.57777	−	6.57777i	−0.255846	−	0.255846i	−0.823362	+	0.567516i	$0.807904\pi$
$662$	−18.2372			−0.708809
$663$		0			0
$664$	−3.66193			−0.142110
$665$	16.2900	+	16.2900i	0.631700	+	0.631700i
$666$	−11.8619	+	8.38761i	−0.459638	+	0.325013i
$667$			6.10768i			0.236490i
$668$	3.94925	+	3.94925i	0.152801	+	0.152801i
$669$	34.7891	−	11.0573i	1.34502	−	0.427498i
$670$	−8.58080	−	8.58080i	−0.331505	−	0.331505i
$671$	−0.814821	+	0.814821i	−0.0314558	+	0.0314558i
$672$	2.85808	−	5.52139i	0.110253	−	0.212992i
$673$		−	26.4742i		−	1.02050i	−0.860025	−	0.510252i	$-0.829552\pi$
$673$		−	26.4742i		−	1.02050i	0.860025	−	0.510252i	$-0.170448\pi$
$674$	−3.48238	+	3.48238i	−0.134136	+	0.134136i
$675$	−16.3086	+	2.26202i	−0.627719	+	0.0870650i
$676$		0			0
$677$		−	41.0789i		−	1.57879i	−0.613885	−	0.789396i	$-0.710394\pi$
$677$		−	41.0789i		−	1.57879i	0.613885	−	0.789396i	$-0.289606\pi$
$678$	29.7190	−	9.44581i	1.14135	−	0.362764i
$679$	28.7971			1.10513
$680$	9.87205			0.378576
$681$	2.63726	+	8.29751i	0.101060	+	0.317961i
$682$	5.11977	−	5.11977i	0.196046	−	0.196046i
$683$	−4.21174	+	4.21174i	−0.161158	+	0.161158i	−0.783079	−	0.621922i	$-0.786352\pi$
$683$	−4.21174	+	4.21174i	−0.161158	+	0.161158i	0.621922	+	0.783079i	$0.286352\pi$
$684$	1.13918	−	6.63963i	0.0435577	−	0.253873i
$685$	−15.6623			−0.598424
$686$	4.00303			0.152836
$687$	7.36387	+	23.1687i	0.280949	+	0.883940i
$688$		−	1.95035i		−	0.0743562i
$689$		0			0
$690$	6.90069	−	13.3311i	0.262705	−	0.507507i
$691$	20.2360	−	20.2360i	0.769814	−	0.769814i	−0.208260	−	0.978074i	$-0.566780\pi$
$691$	20.2360	−	20.2360i	0.769814	−	0.769814i	0.978074	+	0.208260i	$0.0667799\pi$
$692$		−	17.4953i		−	0.665072i
$693$	−26.1275	−	36.9499i	−0.992502	−	1.40361i
$694$	10.5657	−	10.5657i	0.401069	−	0.401069i
$695$	−29.6946	−	29.6946i	−1.12638	−	1.12638i
$696$	−1.05673	−	3.32474i	−0.0400551	−	0.126024i
$697$	−19.3944	−	19.3944i	−0.734617	−	0.734617i
$698$			31.2360i			1.18230i
$699$	28.9093	+	14.9646i	1.09345	+	0.566011i
$700$	−8.04261	−	8.04261i	−0.303982	−	0.303982i
$701$	−0.672924			−0.0254160			−0.0127080	−	0.999919i	$-0.504045\pi$
$701$	−0.672924			−0.0254160			−0.0127080	+	0.999919i	$0.504045\pi$
$702$		0			0
$703$	−10.8743			−0.410131
$704$	2.97155	+	2.97155i	0.111995	+	0.111995i
$705$	−5.95235	−	3.08116i	−0.224178	−	0.116043i
$706$			10.3455i			0.389360i
$707$	−5.34758	−	5.34758i	−0.201116	−	0.201116i
$708$	5.39779	+	16.9829i	0.202861	+	0.638256i
$709$	21.6346	+	21.6346i	0.812504	+	0.812504i	0.985009	−	0.172505i	$-0.0551860\pi$
$709$	21.6346	+	21.6346i	0.812504	+	0.812504i	−0.172505	+	0.985009i	$0.555186\pi$
$710$	22.2989	−	22.2989i	0.836864	−	0.836864i
$711$	2.73752	+	3.87144i	0.102665	+	0.145190i
$712$			9.84478i			0.368949i
$713$	−3.69432	+	3.69432i	−0.138353	+	0.138353i
$714$	−9.87205	+	19.0713i	−0.369452	+	0.713727i
$715$		0			0
$716$			9.21508i			0.344384i
$717$	−5.06125	−	15.9240i	−0.189016	−	0.594694i
$718$	12.8544			0.479722
$719$	−23.1131			−0.861974			−0.430987	−	0.902358i	$-0.641834\pi$
$719$	−23.1131			−0.861974			−0.430987	+	0.902358i	$0.641834\pi$
$720$	−1.44992	+	8.45077i	−0.0540354	+	0.314942i
$721$	36.2019	−	36.2019i	1.34823	−	1.34823i
$722$	−9.86945	+	9.86945i	−0.367303	+	0.367303i
$723$	4.44747	+	13.9929i	0.165403	+	0.520402i
$724$	13.8110			0.513282
$725$	−6.38216			−0.237027
$726$	10.9939	−	3.49429i	0.408024	−	0.129685i
$727$			11.5379i			0.427917i	0.976843	+	0.213959i	$0.0686357\pi$
$727$			11.5379i			0.427917i	−0.976843	+	0.213959i	$0.931364\pi$
$728$		0			0
$729$	−25.9808	+	7.34847i	−0.962250	+	0.272166i
$730$	−28.8157	+	28.8157i	−1.06652	+	1.06652i
$731$			6.73665i			0.249164i
$732$	−0.218331	+	0.421783i	−0.00806974	+	0.0155895i
$733$	0.910162	−	0.910162i	0.0336176	−	0.0336176i	−0.690098	−	0.723716i	$-0.742433\pi$
$733$	0.910162	−	0.910162i	0.0336176	−	0.0336176i	0.723716	+	0.690098i	$0.242433\pi$
$734$	1.16457	+	1.16457i	0.0429850	+	0.0429850i
$735$	27.7632	−	8.82419i	1.02406	−	0.325485i
$736$	−2.14421	−	2.14421i	−0.0790365	−	0.0790365i
$737$			17.8429i			0.657253i
$738$	19.4507	−	13.7537i	0.715991	−	0.506282i
$739$	8.82889	+	8.82889i	0.324776	+	0.324776i	0.850596	−	0.525820i	$-0.176241\pi$
$739$	8.82889	+	8.82889i	0.324776	+	0.324776i	−0.525820	+	0.850596i	$0.676241\pi$
$740$	13.8405			0.508788
$741$		0			0
$742$	−25.9232			−0.951669
$743$	32.3947	+	32.3947i	1.18844	+	1.18844i	0.977497	+	0.210948i	$0.0676549\pi$
$743$	32.3947	+	32.3947i	1.18844	+	1.18844i	0.210948	+	0.977497i	$0.432345\pi$
$744$	1.37184	−	2.65019i	0.0502941	−	0.0971607i
$745$			29.5374i			1.08217i
$746$	−14.1079	−	14.1079i	−0.516526	−	0.516526i
$747$	−1.85772	+	10.8276i	−0.0679704	+	0.396160i
$748$	−10.2640	−	10.2640i	−0.375288	−	0.375288i
$749$	35.1425	−	35.1425i	1.28408	−	1.28408i
$750$	−8.05116	−	4.16759i	−0.293987	−	0.152179i
$751$			16.0234i			0.584701i	0.956311	+	0.292350i	$0.0944373\pi$
$751$			16.0234i			0.584701i	−0.956311	+	0.292350i	$0.905563\pi$
$752$	−0.957390	+	0.957390i	−0.0349124	+	0.0349124i
$753$	10.8285	+	5.60523i	0.394611	+	0.204266i
$754$		0			0
$755$		−	26.2295i		−	0.954588i
$756$	−14.8757	−	11.2518i	−0.541024	−	0.409224i
$757$	−31.2554			−1.13600			−0.567998	−	0.823030i	$-0.692282\pi$
$757$	−31.2554			−1.13600			−0.567998	+	0.823030i	$0.692282\pi$
$758$	−12.3118			−0.447184
$759$	−21.0350	+	6.68572i	−0.763523	+	0.242676i
$760$	−4.53819	+	4.53819i	−0.164617	+	0.164617i
$761$	−12.1654	+	12.1654i	−0.440994	+	0.440994i	−0.892346	−	0.451352i	$-0.850942\pi$
$761$	−12.1654	+	12.1654i	−0.440994	+	0.440994i	0.451352	+	0.892346i	$0.350942\pi$
$762$	34.1579	−	10.8567i	1.23741	−	0.393295i
$763$	−29.6572			−1.07366
$764$	−22.7030			−0.821366
$765$	5.00815	−	29.1896i	0.181070	−	1.05535i
$766$			28.3459i			1.02418i
$767$		0			0
$768$	1.53819	+	0.796225i	0.0555046	+	0.0287313i
$769$	0.164384	−	0.164384i	0.00592784	−	0.00592784i	−0.704137	−	0.710064i	$-0.748666\pi$
$769$	0.164384	−	0.164384i	0.00592784	−	0.00592784i	0.710064	+	0.704137i	$0.248666\pi$
$770$			43.1134i			1.55370i
$771$	2.51030	+	1.29943i	0.0904064	+	0.0467978i
$772$	−14.1745	+	14.1745i	−0.510150	+	0.510150i
$773$	31.2927	+	31.2927i	1.12552	+	1.12552i	0.990897	+	0.134621i	$0.0429818\pi$
$773$	31.2927	+	31.2927i	1.12552	+	1.12552i	0.134621	+	0.990897i	$0.457018\pi$
$774$	−5.76677	−	0.989422i	−0.207282	−	0.0355640i
$775$	−3.86034	−	3.86034i	−0.138667	−	0.138667i
$776$			8.02251i			0.287991i
$777$	−13.8405	+	26.7378i	−0.496526	+	0.959215i
$778$	11.2786	+	11.2786i	0.404359	+	0.404359i
$779$	17.8313			0.638872
$780$		0			0
$781$	−46.3684			−1.65919
$782$	7.40626	+	7.40626i	0.264847	+	0.264847i
$783$	−10.3667	+	1.43786i	−0.370474	+	0.0513850i
$784$		−	5.88481i		−	0.210172i
$785$	28.5828	+	28.5828i	1.02017	+	1.02017i
$786$	−7.73005	+	2.45690i	−0.275722	+	0.0876347i
$787$	14.9399	+	14.9399i	0.532551	+	0.532551i	0.921331	−	0.388780i	$-0.127103\pi$
$787$	14.9399	+	14.9399i	0.532551	+	0.532551i	−0.388780	+	0.921331i	$0.627103\pi$
$788$	−13.1786	+	13.1786i	−0.469467	+	0.469467i
$789$	8.41445	−	16.2555i	0.299562	−	0.578710i
$790$		−	4.51722i		−	0.160716i
$791$	45.6978	−	45.6978i	1.62483	−	1.62483i
$792$	10.2938	−	7.27879i	0.365773	−	0.258640i
$793$		0			0
$794$		−	12.6918i		−	0.450417i
$795$	34.0711	−	10.8291i	1.20838	−	0.384068i
$796$	−4.51039			−0.159866
$797$	24.0741			0.852747			0.426373	−	0.904547i	$-0.359791\pi$
$797$	24.0741			0.852747			0.426373	+	0.904547i	$0.359791\pi$
$798$	−4.22892	−	13.3053i	−0.149702	−	0.471002i
$799$	3.30690	−	3.30690i	0.116990	−	0.116990i
$800$	2.24057	−	2.24057i	0.0792160	−	0.0792160i
$801$	29.1090	+	4.99431i	1.02852	+	0.176465i
$802$	−16.4198			−0.579804
$803$	59.9195			2.11451
$804$	2.22759	+	7.00859i	0.0785611	+	0.247174i
$805$		−	31.1097i		−	1.09647i
$806$		0			0
$807$	−6.86234	+	13.2570i	−0.241566	+	0.466669i
$808$	1.48977	−	1.48977i	0.0524098	−	0.0524098i
$809$		−	25.7155i		−	0.904109i	−0.891990	−	0.452055i	$-0.850691\pi$
$809$		−	25.7155i		−	0.904109i	0.891990	−	0.452055i	$-0.149309\pi$
$810$	24.2516	+	8.57425i	0.852116	+	0.301268i
$811$	−5.99463	+	5.99463i	−0.210500	+	0.210500i	−0.804480	−	0.593980i	$-0.797556\pi$
$811$	−5.99463	+	5.99463i	−0.210500	+	0.210500i	0.593980	+	0.804480i	$0.297556\pi$
$812$	−5.11233	−	5.11233i	−0.179408	−	0.179408i
$813$	−10.4048	−	32.7363i	−0.364913	−	1.14811i
$814$	−14.3900	−	14.3900i	−0.504370	−	0.504370i
$815$		−	3.18490i		−	0.111562i
$816$	−5.31303	−	2.75023i	−0.185993	−	0.0962772i
$817$	−3.09684	−	3.09684i	−0.108345	−	0.108345i
$818$	34.0781			1.19151
$819$		0			0
$820$	−22.6952			−0.792552
$821$	−37.5734	−	37.5734i	−1.31132	−	1.31132i	−0.920442	−	0.390879i	$-0.872171\pi$
$821$	−37.5734	−	37.5734i	−1.31132	−	1.31132i	−0.390879	−	0.920442i	$-0.627829\pi$
$822$	8.42925	+	4.36330i	0.294004	+	0.152188i
$823$			11.4619i			0.399538i	0.979843	+	0.199769i	$0.0640192\pi$
$823$			11.4619i			0.399538i	−0.979843	+	0.199769i	$0.935981\pi$
$824$	10.0854	+	10.0854i	0.351341	+	0.351341i
$825$	−6.98617	−	21.9803i	−0.243227	−	0.765257i
$826$	26.1139	+	26.1139i	0.908620	+	0.908620i
$827$	4.57665	−	4.57665i	0.159146	−	0.159146i	−0.623042	−	0.782188i	$-0.714104\pi$
$827$	4.57665	−	4.57665i	0.159146	−	0.159146i	0.782188	+	0.623042i	$0.214104\pi$
$828$	−7.42775	+	5.25221i	−0.258132	+	0.182527i
$829$			49.9553i			1.73502i	0.497422	+	0.867509i	$0.334280\pi$
$829$			49.9553i			1.73502i	−0.497422	+	0.867509i	$0.665720\pi$
$830$	7.40065	−	7.40065i	0.256880	−	0.256880i
$831$	−12.3434	+	23.8457i	−0.428189	+	0.827198i
$832$		0			0
$833$			20.3266i			0.704275i
$834$	7.70877	+	24.2538i	0.266933	+	0.839842i
$835$	−15.9627			−0.552410
$836$	9.43672			0.326376
$837$	−7.14013	−	5.40071i	−0.246799	−	0.186676i
$838$	−23.2655	+	23.2655i	−0.803693	+	0.803693i
$839$	8.20115	−	8.20115i	0.283135	−	0.283135i	−0.551223	−	0.834358i	$-0.685839\pi$
$839$	8.20115	−	8.20115i	0.283135	−	0.283135i	0.834358	+	0.551223i	$0.185839\pi$
$840$	5.38247	+	16.9347i	0.185713	+	0.584302i
$841$	24.9431			0.860108
$842$	−24.1753			−0.833137
$843$	27.8850	−	8.86291i	0.960412	−	0.305255i
$844$		−	8.57683i		−	0.295227i
$845$		0			0
$846$	2.34512	+	3.31649i	0.0806267	+	0.114023i
$847$	16.9050	−	16.9050i	0.580862	−	0.580862i
$848$		−	7.22186i		−	0.248000i
$849$	1.25781	−	2.42991i	0.0431680	−	0.0833942i
$850$	−7.73910	+	7.73910i	−0.265449	+	0.265449i
$851$	10.3835	+	10.3835i	0.355942	+	0.355942i
$852$	−18.2132	+	5.78884i	−0.623975	+	0.198322i
$853$	1.56247	+	1.56247i	0.0534978	+	0.0534978i	0.733350	−	0.679852i	$-0.237956\pi$
$853$	1.56247	+	1.56247i	0.0534978	+	0.0534978i	−0.679852	+	0.733350i	$0.737956\pi$
$854$			0.984278i			0.0336813i
$855$	11.1162	+	15.7207i	0.380168	+	0.537638i
$856$	9.79025	+	9.79025i	0.334624	+	0.334624i
$857$	−21.5804			−0.737174			−0.368587	−	0.929593i	$-0.620158\pi$
$857$	−21.5804			−0.737174			−0.368587	+	0.929593i	$0.620158\pi$
$858$		0			0
$859$	10.5544			0.360110			0.180055	−	0.983657i	$-0.442372\pi$
$859$	10.5544			0.360110			0.180055	+	0.983657i	$0.442372\pi$
$860$	3.94159	+	3.94159i	0.134407	+	0.134407i
$861$	22.6952	−	43.8438i	0.773452	−	1.49419i
$862$			1.75577i			0.0598018i
$863$	21.4177	+	21.4177i	0.729066	+	0.729066i	0.970434	−	0.241368i	$-0.0775960\pi$
$863$	21.4177	+	21.4177i	0.729066	+	0.729066i	−0.241368	+	0.970434i	$0.577596\pi$
$864$	3.13461	−	4.14418i	0.106642	−	0.140988i
$865$	35.3575	+	35.3575i	1.20219	+	1.20219i
$866$	−7.24346	+	7.24346i	−0.246143	+	0.246143i
$867$	−7.79759	−	4.03633i	−0.264820	−	0.137081i
$868$		−	6.18452i		−	0.209916i
$869$	−4.69656	+	4.69656i	−0.159320	+	0.159320i
$870$	8.85481	+	4.58359i	0.300206	+	0.155398i
$871$		0			0
$872$		−	8.26212i		−	0.279791i
$873$	23.7209	+	4.06987i	0.802831	+	0.137744i
$874$	−6.80933			−0.230329
$875$	−18.7883			−0.635161
$876$	23.5360	−	7.48062i	0.795208	−	0.252747i
$877$	−27.6234	+	27.6234i	−0.932775	+	0.932775i	−0.997879	−	0.0651031i	$-0.979262\pi$
$877$	−27.6234	+	27.6234i	−0.932775	+	0.932775i	0.0651031	+	0.997879i	$0.479262\pi$
$878$	3.81996	−	3.81996i	0.128917	−	0.128917i
$879$	6.44617	−	2.04883i	0.217424	−	0.0691054i
$880$	−12.0108			−0.404885
$881$	6.79415			0.228901			0.114450	−	0.993429i	$-0.463489\pi$
$881$	6.79415			0.228901			0.114450	+	0.993429i	$0.463489\pi$
$882$	−17.4002	−	2.98540i	−0.585894	−	0.100524i
$883$		−	40.6560i		−	1.36818i	−0.729397	−	0.684091i	$-0.760199\pi$
$883$		−	40.6560i		−	1.36818i	0.729397	−	0.684091i	$-0.239801\pi$
$884$		0			0
$885$	−45.2307	−	23.4131i	−1.52041	−	0.787023i
$886$	−9.59761	+	9.59761i	−0.322438	+	0.322438i
$887$		−	10.4419i		−	0.350606i	−0.984515	−	0.175303i	$-0.943909\pi$
$887$		−	10.4419i		−	0.350606i	0.984515	−	0.175303i	$-0.0560905\pi$
$888$	−7.44882	−	3.85579i	−0.249966	−	0.129392i
$889$	52.5233	−	52.5233i	1.76158	−	1.76158i
$890$	−19.8960	−	19.8960i	−0.666916	−	0.666916i
$891$	−16.2998	−	34.1291i	−0.546064	−	1.14337i
$892$	14.9027	+	14.9027i	0.498979	+	0.498979i
$893$			3.04037i			0.101742i
$894$	8.22875	−	15.8967i	0.275211	−	0.531666i
$895$	−18.6234	−	18.6234i	−0.622512	−	0.622512i
$896$	3.58954			0.119918
$897$		0			0
$898$	2.02930			0.0677187
$899$	−2.45384	−	2.45384i	−0.0818403	−	0.0818403i
$900$	−5.48825	−	7.76155i	−0.182942	−	0.258718i
$901$			24.9449i			0.831034i
$902$	23.5963	+	23.5963i	0.785670	+	0.785670i
$903$	−11.5562	+	3.67298i	−0.384565	+	0.122229i
$904$	12.7308	+	12.7308i	0.423421	+	0.423421i
$905$	−27.9116	+	27.9116i	−0.927814	+	0.927814i
$906$	−7.30719	+	14.1164i	−0.242765	+	0.468986i
$907$		−	39.2319i		−	1.30268i	−0.758788	−	0.651338i	$-0.774208\pi$
$907$		−	39.2319i		−	1.30268i	0.758788	−	0.651338i	$-0.225792\pi$
$908$	−3.55443	+	3.55443i	−0.117958	+	0.117958i
$909$	−3.64917	−	5.16071i	−0.121035	−	0.171170i
$910$		0			0
$911$		−	32.0923i		−	1.06326i	−0.846975	−	0.531632i	$-0.821579\pi$
$911$		−	32.0923i		−	1.06326i	0.846975	−	0.531632i	$-0.178421\pi$
$912$	3.70668	−	1.17812i	0.122741	−	0.0390115i
$913$	−15.3889			−0.509299
$914$	−29.9534			−0.990770
$915$	−0.411170	−	1.29365i	−0.0135929	−	0.0427667i
$916$	−9.92484	+	9.92484i	−0.327926	+	0.327926i
$917$	−11.8862	+	11.8862i	−0.392517	+	0.392517i
$918$	−10.8272	+	14.3143i	−0.357350	+	0.472443i
$919$	33.2842			1.09794			0.548972	−	0.835841i	$-0.315020\pi$
$919$	33.2842			1.09794			0.548972	+	0.835841i	$0.315020\pi$
$920$	8.66676			0.285735
$921$	−16.1744	−	50.8889i	−0.532964	−	1.67685i
$922$		−	16.1111i		−	0.530589i
$923$		0			0
$924$	12.0108	−	23.2032i	0.395128	−	0.763328i
$925$	−10.8501	+	10.8501i	−0.356751	+	0.356751i
$926$			5.75643i			0.189168i
$927$	34.9368	−	24.7041i	1.14748	−	0.811388i
$928$	1.42423	−	1.42423i	0.0467526	−	0.0467526i
$929$	−15.5309	−	15.5309i	−0.509552	−	0.509552i	0.404837	−	0.914389i	$-0.367328\pi$
$929$	−15.5309	−	15.5309i	−0.509552	−	0.509552i	−0.914389	+	0.404837i	$0.867328\pi$
$930$	2.58351	+	8.12840i	0.0847166	+	0.266541i
$931$	−9.34415	−	9.34415i	−0.306242	−	0.306242i
$932$			18.7944i			0.615630i
$933$	−32.1936	−	16.6646i	−1.05397	−	0.545575i
$934$	−26.0594	−	26.0594i	−0.852690	−	0.852690i
$935$	41.4864			1.35675
$936$		0			0
$937$	55.9423			1.82755			0.913777	−	0.406216i	$-0.133152\pi$
$937$	55.9423			1.82755			0.913777	+	0.406216i	$0.133152\pi$
$938$	10.7768	+	10.7768i	0.351877	+	0.351877i
$939$	−50.2503	−	26.0115i	−1.63986	−	0.848853i
$940$		−	3.86971i		−	0.126216i
$941$	−17.1600	−	17.1600i	−0.559401	−	0.559401i	0.369736	−	0.929137i	$-0.379448\pi$
$941$	−17.1600	−	17.1600i	−0.559401	−	0.559401i	−0.929137	+	0.369736i	$0.879448\pi$
$942$	−7.42016	−	23.3458i	−0.241762	−	0.760647i
$943$	−17.0265	−	17.0265i	−0.554461	−	0.554461i
$944$	−7.27501	+	7.27501i	−0.236781	+	0.236781i
$945$	52.8029	−	7.32380i	1.71768	−	0.238243i
$946$		−	8.19615i		−	0.266480i
$947$	33.7186	−	33.7186i	1.09571	−	1.09571i	0.100799	−	0.994907i	$-0.467860\pi$
$947$	33.7186	−	33.7186i	1.09571	−	1.09571i	0.994907	−	0.100799i	$-0.0321400\pi$
$948$	−1.25844	+	2.43112i	−0.0408722	+	0.0789591i
$949$		0			0
$950$		−	7.11534i		−	0.230852i
$951$	−3.86626	−	12.1643i	−0.125372	−	0.394454i
$952$	−12.3986			−0.401840
$953$	−43.0555			−1.39471			−0.697353	−	0.716728i	$-0.745639\pi$
$953$	−43.0555			−1.39471			−0.697353	+	0.716728i	$0.745639\pi$
$954$	−21.3536	−	3.66369i	−0.691347	−	0.118616i
$955$	45.8821	−	45.8821i	1.48471	−	1.48471i
$956$	6.82142	−	6.82142i	0.220621	−	0.220621i
$957$	−4.44080	−	13.9719i	−0.143551	−	0.451648i
$958$	−15.0430			−0.486018
$959$	19.6706			0.635198
$960$	−4.71778	+	1.49949i	−0.152266	+	0.0483957i
$961$			28.0315i			0.904242i
$962$		0			0
$963$	33.9144	−	23.9811i	1.09288	−	0.772781i
$964$	−5.99419	+	5.99419i	−0.193060	+	0.193060i
$965$		−	57.2923i		−	1.84430i
$966$	−8.66676	+	16.7429i	−0.278848	+	0.538694i
$967$	4.96226	−	4.96226i	0.159576	−	0.159576i	−0.622803	−	0.782379i	$-0.714006\pi$
$967$	4.96226	−	4.96226i	0.159576	−	0.159576i	0.782379	+	0.622803i	$0.214006\pi$
$968$	4.70951	+	4.70951i	0.151369	+	0.151369i
$969$	−12.8032	+	4.06933i	−0.411298	+	0.130726i
$970$	−16.2132	−	16.2132i	−0.520576	−	0.520576i
$971$			31.7872i			1.02010i	0.860145	+	0.510050i	$0.170373\pi$
$971$			31.7872i			1.02010i	−0.860145	+	0.510050i	$0.829627\pi$
$972$	−10.6633	−	11.3708i	−0.342025	−	0.364717i
$973$	37.2942	+	37.2942i	1.19560	+	1.19560i
$974$	−16.7305			−0.536081
$975$		0			0
$976$	−0.274207			−0.00877716
$977$	−4.92840	−	4.92840i	−0.157673	−	0.157673i	0.623861	−	0.781535i	$-0.285563\pi$
$977$	−4.92840	−	4.92840i	−0.157673	−	0.157673i	−0.781535	+	0.623861i	$0.785563\pi$
$978$	−0.887272	+	1.71408i	−0.0283718	+	0.0548102i
$979$			41.3718i			1.32225i
$980$	11.8930	+	11.8930i	0.379909	+	0.379909i
$981$	−24.4294	−	4.19142i	−0.779970	−	0.133822i
$982$	−17.8662	−	17.8662i	−0.570132	−	0.570132i
$983$	−10.5636	+	10.5636i	−0.336926	+	0.336926i	−0.855209	−	0.518283i	$-0.826571\pi$
$983$	−10.5636	+	10.5636i	−0.336926	+	0.336926i	0.518283	+	0.855209i	$0.326571\pi$
$984$	12.2143	+	6.32260i	0.389379	+	0.201557i
$985$		−	53.2670i		−	1.69723i
$986$	−4.91940	+	4.91940i	−0.156666	+	0.156666i
$987$	7.47571	+	3.86971i	0.237954	+	0.123174i
$988$		0			0
$989$			5.91416i			0.188059i
$990$	−6.09317	+	35.5136i	−0.193654	+	1.12870i
$991$	26.3855			0.838162			0.419081	−	0.907949i	$-0.362352\pi$
$991$	26.3855			0.838162			0.419081	+	0.907949i	$0.362352\pi$
$992$	1.72293			0.0547030
$993$	−30.1038	+	9.56810i	−0.955315	+	0.303635i
$994$	−28.0058	+	28.0058i	−0.888290	+	0.888290i
$995$	9.11536	−	9.11536i	0.288976	−	0.288976i
$996$	−6.04468	+	1.92122i	−0.191533	+	0.0608763i
$997$	29.2650			0.926832			0.463416	−	0.886141i	$-0.346623\pi$
$997$	29.2650			0.926832			0.463416	+	0.886141i	$0.346623\pi$
$998$	−1.95086			−0.0617533
$999$	−15.1796	+	20.0686i	−0.480262	+	0.634941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.d.239.8		16
3.2	odd	2	inner	1014.2.g.d.239.4		16
13.2	odd	12		78.2.k.a.59.3	yes	16
13.4	even	6		78.2.k.a.41.1	✓	16
13.5	odd	4		1014.2.g.c.437.8		16
13.8	odd	4	inner	1014.2.g.d.437.4		16
13.12	even	2		1014.2.g.c.239.4		16
39.2	even	12		78.2.k.a.59.1	yes	16
39.5	even	4		1014.2.g.c.437.4		16
39.8	even	4	inner	1014.2.g.d.437.8		16
39.17	odd	6		78.2.k.a.41.3	yes	16
39.38	odd	2		1014.2.g.c.239.8		16
52.15	even	12		624.2.cn.d.449.4		16
52.43	odd	6		624.2.cn.d.353.3		16
156.95	even	6		624.2.cn.d.353.4		16
156.119	odd	12		624.2.cn.d.449.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.41.1	✓	16	13.4	even	6
78.2.k.a.41.3	yes	16	39.17	odd	6
78.2.k.a.59.1	yes	16	39.2	even	12
78.2.k.a.59.3	yes	16	13.2	odd	12
624.2.cn.d.353.3		16	52.43	odd	6
624.2.cn.d.353.4		16	156.95	even	6
624.2.cn.d.449.3		16	156.119	odd	12
624.2.cn.d.449.4		16	52.15	even	12
1014.2.g.c.239.4		16	13.12	even	2
1014.2.g.c.239.8		16	39.38	odd	2
1014.2.g.c.437.4		16	39.5	even	4
1014.2.g.c.437.8		16	13.5	odd	4
1014.2.g.d.239.4		16	3.2	odd	2	inner
1014.2.g.d.239.8		16	1.1	even	1	trivial
1014.2.g.d.437.4		16	13.8	odd	4	inner
1014.2.g.d.437.8		16	39.8	even	4	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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.53819 + 0.796225i) q^{3} +1.00000i q^{4} +(-2.02097 - 2.02097i) q^{5} +(0.524648 + 1.65068i) q^{6} +(2.53819 + 2.53819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.73205 + 2.44949i) q^{9} -2.85808i q^{10} +(-2.97155 + 2.97155i) q^{11} +(-0.796225 + 1.53819i) q^{12} +3.58954i q^{14} +(-1.49949 - 4.71778i) q^{15} -1.00000 q^{16} +3.45408 q^{17} +(-0.507306 + 2.95680i) q^{18} +(-1.58784 + 1.58784i) q^{19} +(2.02097 - 2.02097i) q^{20} +(1.88324 + 5.92518i) q^{21} -4.20241 q^{22} +3.03237 q^{23} +(-1.65068 + 0.524648i) q^{24} +3.16864i q^{25} +(0.713876 + 5.14688i) q^{27} +(-2.53819 + 2.53819i) q^{28} +2.01416i q^{29} +(2.27568 - 4.39627i) q^{30} +(-1.21829 + 1.21829i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-6.93684 + 2.20478i) q^{33} +(2.44240 + 2.44240i) q^{34} -10.2592i q^{35} +(-2.44949 + 1.73205i) q^{36} +(3.42423 + 3.42423i) q^{37} -2.24555 q^{38} +2.85808 q^{40} +(-5.61494 - 5.61494i) q^{41} +(-2.85808 + 5.52139i) q^{42} +1.95035i q^{43} +(-2.97155 - 2.97155i) q^{44} +(1.44992 - 8.45077i) q^{45} +(2.14421 + 2.14421i) q^{46} +(0.957390 - 0.957390i) q^{47} +(-1.53819 - 0.796225i) q^{48} +5.88481i q^{49} +(-2.24057 + 2.24057i) q^{50} +(5.31303 + 2.75023i) q^{51} +7.22186i q^{53} +(-3.13461 + 4.14418i) q^{54} +12.0108 q^{55} -3.58954 q^{56} +(-3.70668 + 1.17812i) q^{57} +(-1.42423 + 1.42423i) q^{58} +(7.27501 - 7.27501i) q^{59} +(4.71778 - 1.49949i) q^{60} +0.274207 q^{61} -1.72293 q^{62} +(-1.82100 + 10.6135i) q^{63} -1.00000i q^{64} +(-6.46410 - 3.34607i) q^{66} +(3.00229 - 3.00229i) q^{67} +3.45408i q^{68} +(4.66435 + 2.41445i) q^{69} +(7.25436 - 7.25436i) q^{70} +(7.80205 + 7.80205i) q^{71} +(-2.95680 - 0.507306i) q^{72} +(-10.0822 - 10.0822i) q^{73} +4.84259i q^{74} +(-2.52295 + 4.87397i) q^{75} +(-1.58784 - 1.58784i) q^{76} -15.0847 q^{77} +1.58051 q^{79} +(2.02097 + 2.02097i) q^{80} +(-3.00000 + 8.48528i) q^{81} -7.94072i q^{82} +(2.58938 + 2.58938i) q^{83} +(-5.92518 + 1.88324i) q^{84} +(-6.98059 - 6.98059i) q^{85} +(-1.37910 + 1.37910i) q^{86} +(-1.60373 + 3.09816i) q^{87} -4.20241i q^{88} +(6.96131 - 6.96131i) q^{89} +(7.00085 - 4.95035i) q^{90} +3.03237i q^{92} +(-2.84400 + 0.903931i) q^{93} +1.35395 q^{94} +6.41797 q^{95} +(-0.524648 - 1.65068i) q^{96} +(5.67277 - 5.67277i) q^{97} +(-4.16119 + 4.16119i) q^{98} +(-12.4257 - 2.13191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{7} + 24 q^{15} - 16 q^{16} - 32 q^{19} + 24 q^{21} - 16 q^{28} - 16 q^{31} - 24 q^{33} - 24 q^{34} + 8 q^{37} + 48 q^{45} + 48 q^{55} + 24 q^{57} + 24 q^{58} + 24 q^{60} + 48 q^{61} - 48 q^{66}+ \cdots - 16 q^{97}+O(q^{100}) \) 16 * q + 16 * q^7 + 24 * q^15 - 16 * q^16 - 32 * q^19 + 24 * q^21 - 16 * q^28 - 16 * q^31 - 24 * q^33 - 24 * q^34 + 8 * q^37 + 48 * q^45 + 48 * q^55 + 24 * q^57 + 24 * q^58 + 24 * q^60 + 48 * q^61 - 48 * q^66 - 32 * q^67 - 56 * q^73 - 32 * q^76 - 96 * q^79 - 48 * q^81 - 24 * q^84 - 24 * q^85 - 96 * q^87 - 48 * q^93 + 48 * q^94 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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