LMFDB - Embedded newform 1323.2.g.c.667.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(361,1323)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("1323.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	1323.667
Dual form			1323.2.g.c.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.119562 - 0.207087i) q^{2} +(0.971410 - 1.68253i) q^{4} -1.18194 q^{5} -0.942820 q^{8} +O(q^{10})$	\(q+(-0.119562 - 0.207087i) q^{2} +(0.971410 - 1.68253i) q^{4} -1.18194 q^{5} -0.942820 q^{8} +(0.141315 + 0.244765i) q^{10} +3.70370 q^{11} +(-0.500000 - 0.866025i) q^{13} +(-1.83009 - 3.16982i) q^{16} +(-3.47141 - 6.01266i) q^{17} +(-0.971410 + 1.68253i) q^{19} +(-1.14815 + 1.98866i) q^{20} +(-0.442820 - 0.766987i) q^{22} +5.60301 q^{23} -3.60301 q^{25} +(-0.119562 + 0.207087i) q^{26} +(0.119562 - 0.207087i) q^{29} +(-0.830095 + 1.43777i) q^{31} +(-1.38044 + 2.39099i) q^{32} +(-0.830095 + 1.43777i) q^{34} +(4.77292 - 8.26693i) q^{37} +0.464574 q^{38} +1.11436 q^{40} +(-5.09097 - 8.81782i) q^{41} +(-1.11273 + 1.92730i) q^{43} +(3.59781 - 6.23159i) q^{44} +(-0.669905 - 1.16031i) q^{46} +(2.91423 + 5.04759i) q^{47} +(0.430782 + 0.746136i) q^{50} -1.94282 q^{52} +(-5.80150 - 10.0485i) q^{53} -4.37756 q^{55} -0.0571799 q^{58} +(1.30150 - 2.25427i) q^{59} +(3.80150 + 6.58440i) q^{61} +0.396990 q^{62} -6.66019 q^{64} +(0.590972 + 1.02359i) q^{65} +(-1.75404 + 3.03809i) q^{67} -13.4887 q^{68} -8.60301 q^{71} +(-7.57442 - 13.1193i) q^{73} -2.28263 q^{74} +(1.88727 + 3.26886i) q^{76} +(-3.68878 - 6.38915i) q^{79} +(2.16307 + 3.74654i) q^{80} +(-1.21737 + 2.10855i) q^{82} +(-3.47141 + 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} +0.532157 q^{86} -3.49192 q^{88} +(1.37360 - 2.37915i) q^{89} +(5.44282 - 9.42724i) q^{92} +(0.696860 - 1.20700i) q^{94} +(1.14815 - 1.98866i) q^{95} +(-3.58414 + 6.20790i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 3 q^{4} + 10 q^{5} + 12 q^{8}+O(q^{10}) $ 6 * q - q^2 - 3 * q^4 + 10 * q^5 + 12 * q^8	$ 6 q - q^{2} - 3 q^{4} + 10 q^{5} + 12 q^{8} + 4 q^{11} - 3 q^{13} - 3 q^{16} - 12 q^{17} + 3 q^{19} - 16 q^{20} + 15 q^{22} + 12 q^{25} - q^{26} + q^{29} + 3 q^{31} - 8 q^{32} + 3 q^{34} + 3 q^{37} - 16 q^{38} + 42 q^{40} - 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} - 9 q^{47} + 10 q^{50} + 6 q^{52} - 18 q^{53} - 12 q^{55} - 18 q^{58} - 9 q^{59} + 6 q^{61} + 36 q^{62} - 24 q^{64} - 5 q^{65} - 12 q^{68} - 18 q^{71} - 3 q^{73} - 12 q^{74} + 21 q^{76} - 15 q^{79} + 11 q^{80} - 9 q^{82} - 12 q^{83} - 9 q^{85} - 68 q^{86} - 42 q^{88} - 2 q^{89} + 15 q^{92} - 24 q^{94} + 16 q^{95} - 3 q^{97}+O(q^{100}) $ 6 * q - q^2 - 3 * q^4 + 10 * q^5 + 12 * q^8 + 4 * q^11 - 3 * q^13 - 3 * q^16 - 12 * q^17 + 3 * q^19 - 16 * q^20 + 15 * q^22 + 12 * q^25 - q^26 + q^29 + 3 * q^31 - 8 * q^32 + 3 * q^34 + 3 * q^37 - 16 * q^38 + 42 * q^40 - 22 * q^41 + 3 * q^43 + 23 * q^44 - 12 * q^46 - 9 * q^47 + 10 * q^50 + 6 * q^52 - 18 * q^53 - 12 * q^55 - 18 * q^58 - 9 * q^59 + 6 * q^61 + 36 * q^62 - 24 * q^64 - 5 * q^65 - 12 * q^68 - 18 * q^71 - 3 * q^73 - 12 * q^74 + 21 * q^76 - 15 * q^79 + 11 * q^80 - 9 * q^82 - 12 * q^83 - 9 * q^85 - 68 * q^86 - 42 * q^88 - 2 * q^89 + 15 * q^92 - 24 * q^94 + 16 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.119562	−	0.207087i	−0.0845428	−	0.146433i	0.820653	−	0.571426i	$-0.193610\pi$
$2$	−0.119562	−	0.207087i	−0.0845428	−	0.146433i	−0.905196	+	0.424994i	$0.860276\pi$
$3$		0			0
$3$		0			0
$4$	0.971410	−	1.68253i	0.485705	−	0.841266i
$5$	−1.18194			−0.528581			−0.264291	−	0.964443i	$-0.585138\pi$
$5$	−1.18194			−0.528581			−0.264291	+	0.964443i	$0.585138\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−0.942820			−0.333337
$9$		0			0
$10$	0.141315	+	0.244765i	0.0446878	+	0.0774015i
$11$	3.70370			1.11671			0.558353	−	0.829603i	$-0.311433\pi$
$11$	3.70370			1.11671			0.558353	+	0.829603i	$0.311433\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$		0			0
$16$	−1.83009	−	3.16982i	−0.457524	−	0.792454i
$17$	−3.47141	−	6.01266i	−0.841941	−	1.45828i	−0.888252	−	0.459357i	$-0.848080\pi$
$17$	−3.47141	−	6.01266i	−0.841941	−	1.45828i	0.0463112	−	0.998927i	$-0.485253\pi$
$18$		0			0
$19$	−0.971410	+	1.68253i	−0.222857	+	0.385999i	−0.955674	−	0.294426i	$-0.904872\pi$
$19$	−0.971410	+	1.68253i	−0.222857	+	0.385999i	0.732818	+	0.680425i	$0.238205\pi$
$20$	−1.14815	+	1.98866i	−0.256735	+	0.444677i
$21$		0			0
$22$	−0.442820	−	0.766987i	−0.0944096	−	0.163522i
$23$	5.60301			1.16831			0.584154	−	0.811643i	$-0.301426\pi$
$23$	5.60301			1.16831			0.584154	+	0.811643i	$0.301426\pi$
$24$		0			0
$25$	−3.60301			−0.720602
$26$	−0.119562	+	0.207087i	−0.0234480	+	0.0406131i
$27$		0			0
$28$		0			0
$29$	0.119562	−	0.207087i	0.0222020	−	0.0384551i	−0.854711	−	0.519104i	$-0.826266\pi$
$29$	0.119562	−	0.207087i	0.0222020	−	0.0384551i	0.876913	+	0.480649i	$0.159599\pi$
$30$		0			0
$31$	−0.830095	+	1.43777i	−0.149089	+	0.258231i	−0.930891	−	0.365297i	$-0.880968\pi$
$31$	−0.830095	+	1.43777i	−0.149089	+	0.258231i	0.781802	+	0.623527i	$0.214301\pi$
$32$	−1.38044	+	2.39099i	−0.244029	+	0.422671i
$33$		0			0
$34$	−0.830095	+	1.43777i	−0.142360	+	0.246575i
$35$		0			0
$36$		0			0
$37$	4.77292	−	8.26693i	0.784662	−	1.35908i	−0.144538	−	0.989499i	$-0.546170\pi$
$37$	4.77292	−	8.26693i	0.784662	−	1.35908i	0.929201	−	0.369576i	$-0.120497\pi$
$38$	0.464574			0.0753638
$39$		0			0
$40$	1.11436			0.176196
$41$	−5.09097	−	8.81782i	−0.795076	−	1.37711i	−0.922791	−	0.385301i	$-0.874097\pi$
$41$	−5.09097	−	8.81782i	−0.795076	−	1.37711i	0.127715	−	0.991811i	$-0.459236\pi$
$42$		0			0
$43$	−1.11273	+	1.92730i	−0.169689	+	0.293910i	−0.938311	−	0.345794i	$-0.887610\pi$
$43$	−1.11273	+	1.92730i	−0.169689	+	0.293910i	0.768622	+	0.639704i	$0.220943\pi$
$44$	3.59781	−	6.23159i	0.542390	−	0.939447i
$45$		0			0
$46$	−0.669905	−	1.16031i	−0.0987721	−	0.171078i
$47$	2.91423	+	5.04759i	0.425084	+	0.736267i	0.996428	−	0.0844432i	$-0.0269112\pi$
$47$	2.91423	+	5.04759i	0.425084	+	0.736267i	−0.571344	+	0.820711i	$0.693578\pi$
$48$		0			0
$49$		0			0
$50$	0.430782	+	0.746136i	0.0609217	+	0.105520i
$51$		0			0
$52$	−1.94282			−0.269421
$53$	−5.80150	−	10.0485i	−0.796898	−	1.38027i	−0.921627	−	0.388077i	$-0.873139\pi$
$53$	−5.80150	−	10.0485i	−0.796898	−	1.38027i	0.124729	−	0.992191i	$-0.460194\pi$
$54$		0			0
$55$	−4.37756			−0.590270
$56$		0			0
$57$		0			0
$58$	−0.0571799			−0.00750809
$59$	1.30150	−	2.25427i	0.169442	−	0.293481i	−0.768782	−	0.639511i	$-0.779137\pi$
$59$	1.30150	−	2.25427i	0.169442	−	0.293481i	0.938224	+	0.346029i	$0.112470\pi$
$60$		0			0
$61$	3.80150	+	6.58440i	0.486733	+	0.843046i	0.999884	−	0.0152524i	$-0.00485519\pi$
$61$	3.80150	+	6.58440i	0.486733	+	0.843046i	−0.513151	+	0.858298i	$0.671522\pi$
$62$	0.396990			0.0504178
$63$		0			0
$64$	−6.66019			−0.832524
$65$	0.590972	+	1.02359i	0.0733010	+	0.126961i
$66$		0			0
$67$	−1.75404	+	3.03809i	−0.214290	+	0.371161i	−0.953053	−	0.302804i	$-0.902077\pi$
$67$	−1.75404	+	3.03809i	−0.214290	+	0.371161i	0.738763	+	0.673966i	$0.235410\pi$
$68$	−13.4887			−1.63574
$69$		0			0
$70$		0			0
$71$	−8.60301			−1.02099			−0.510495	−	0.859881i	$-0.670538\pi$
$71$	−8.60301			−1.02099			−0.510495	+	0.859881i	$0.670538\pi$
$72$		0			0
$73$	−7.57442	−	13.1193i	−0.886519	−	1.53550i	−0.843963	−	0.536402i	$-0.819783\pi$
$73$	−7.57442	−	13.1193i	−0.886519	−	1.53550i	−0.0425559	−	0.999094i	$-0.513550\pi$
$74$	−2.28263			−0.265350
$75$		0			0
$76$	1.88727	+	3.26886i	0.216485	+	0.374963i
$77$		0			0
$78$		0			0
$79$	−3.68878	−	6.38915i	−0.415020	−	0.718836i	0.580410	−	0.814324i	$-0.302892\pi$
$79$	−3.68878	−	6.38915i	−0.415020	−	0.718836i	−0.995431	+	0.0954881i	$0.969559\pi$
$80$	2.16307	+	3.74654i	0.241838	+	0.418876i
$81$		0			0
$82$	−1.21737	+	2.10855i	−0.134436	+	0.232850i
$83$	−3.47141	+	6.01266i	−0.381037	+	0.659975i	−0.991211	−	0.132292i	$-0.957766\pi$
$83$	−3.47141	+	6.01266i	−0.381037	+	0.659975i	0.610174	+	0.792267i	$0.291100\pi$
$84$		0			0
$85$	4.10301	+	7.10662i	0.445034	+	0.770821i
$86$	0.532157			0.0573840
$87$		0			0
$88$	−3.49192			−0.372240
$89$	1.37360	−	2.37915i	0.145602	−	0.252189i	−0.783996	−	0.620766i	$-0.786822\pi$
$89$	1.37360	−	2.37915i	0.145602	−	0.252189i	0.929597	+	0.368577i	$0.120155\pi$
$90$		0			0
$91$		0			0
$92$	5.44282	−	9.42724i	0.567453	−	0.982858i
$93$		0			0
$94$	0.696860	−	1.20700i	0.0718756	−	0.124492i
$95$	1.14815	−	1.98866i	0.117798	−	0.204032i
$96$		0			0
$97$	−3.58414	+	6.20790i	−0.363914	+	0.630317i	−0.988601	−	0.150558i	$-0.951893\pi$
$97$	−3.58414	+	6.20790i	−0.363914	+	0.630317i	0.624687	+	0.780875i	$0.285226\pi$
$98$		0			0
$99$		0			0
$100$	−3.50000	+	6.06218i	−0.350000	+	0.606218i
$101$	12.7850			1.27215			0.636075	−	0.771627i	$-0.280557\pi$
$101$	12.7850			1.27215			0.636075	+	0.771627i	$0.280557\pi$
$102$		0			0
$103$	−4.39699			−0.433248			−0.216624	−	0.976255i	$-0.569505\pi$
$103$	−4.39699			−0.433248			−0.216624	+	0.976255i	$0.569505\pi$
$104$	0.471410	+	0.816506i	0.0462256	+	0.0800650i
$105$		0			0
$106$	−1.38727	+	2.40283i	−0.134744	+	0.233384i
$107$	6.86389	−	11.8886i	0.663557	−	1.14931i	−0.316117	−	0.948720i	$-0.602379\pi$
$107$	6.86389	−	11.8886i	0.663557	−	1.14931i	0.979674	−	0.200594i	$-0.0642873\pi$
$108$		0			0
$109$	−0.631600	−	1.09396i	−0.0604963	−	0.104783i	0.834191	−	0.551476i	$-0.185935\pi$
$109$	−0.631600	−	1.09396i	−0.0604963	−	0.104783i	−0.894687	+	0.446693i	$0.852602\pi$
$110$	0.523388	+	0.906535i	0.0499031	+	0.0864347i
$111$		0			0
$112$		0			0
$113$	6.08126	+	10.5330i	0.572076	+	0.990866i	0.996353	+	0.0853326i	$0.0271953\pi$
$113$	6.08126	+	10.5330i	0.572076	+	0.990866i	−0.424276	+	0.905533i	$0.639471\pi$
$114$		0			0
$115$	−6.62244			−0.617546
$116$	−0.232287	−	0.402332i	−0.0215673	−	0.0373556i
$117$		0			0
$118$	−0.622440			−0.0573003
$119$		0			0
$120$		0			0
$121$	2.71737			0.247034
$122$	0.909028	−	1.57448i	0.0822996	−	0.142547i
$123$		0			0
$124$	1.61273	+	2.79332i	0.144827	+	0.250848i
$125$	10.1683			0.909478
$126$		0			0
$127$	1.33981			0.118889			0.0594445	−	0.998232i	$-0.481067\pi$
$127$	1.33981			0.118889			0.0594445	+	0.998232i	$0.481067\pi$
$128$	3.55718	+	6.16122i	0.314413	+	0.544580i
$129$		0			0
$130$	0.141315	−	0.244765i	0.0123942	−	0.0214673i
$131$	4.96690			0.433960			0.216980	−	0.976176i	$-0.430379\pi$
$131$	4.96690			0.433960			0.216980	+	0.976176i	$0.430379\pi$
$132$		0			0
$133$		0			0
$134$	0.838864			0.0724668
$135$		0			0
$136$	3.27292	+	5.66886i	0.280650	+	0.486100i
$137$	4.33981			0.370775			0.185387	−	0.982665i	$-0.440646\pi$
$137$	4.33981			0.370775			0.185387	+	0.982665i	$0.440646\pi$
$138$		0			0
$139$	−1.97141	−	3.41458i	−0.167213	−	0.289621i	0.770226	−	0.637771i	$-0.220143\pi$
$139$	−1.97141	−	3.41458i	−0.167213	−	0.289621i	−0.937439	+	0.348150i	$0.886810\pi$
$140$		0			0
$141$		0			0
$142$	1.02859	+	1.78157i	0.0863174	+	0.149506i
$143$	−1.85185	−	3.20750i	−0.154859	−	0.268224i
$144$		0			0
$145$	−0.141315	+	0.244765i	−0.0117356	+	0.0203266i
$146$	−1.81122	+	3.13713i	−0.149898	+	0.259630i
$147$		0			0
$148$	−9.27292	−	16.0612i	−0.762229	−	1.32022i
$149$	−11.1111			−0.910256			−0.455128	−	0.890426i	$-0.650406\pi$
$149$	−11.1111			−0.910256			−0.455128	+	0.890426i	$0.650406\pi$
$150$		0			0
$151$	13.9234			1.13307			0.566535	−	0.824038i	$-0.308284\pi$
$151$	13.9234			1.13307			0.566535	+	0.824038i	$0.308284\pi$
$152$	0.915865	−	1.58632i	0.0742864	−	0.128668i
$153$		0			0
$154$		0			0
$155$	0.981125	−	1.69936i	0.0788059	−	0.136496i
$156$		0			0
$157$	−0.0285900	+	0.0495193i	−0.00228173	+	0.00395207i	−0.867164	−	0.498023i	$-0.834060\pi$
$157$	−0.0285900	+	0.0495193i	−0.00228173	+	0.00395207i	0.864882	+	0.501975i	$0.167393\pi$
$158$	−0.882073	+	1.52780i	−0.0701740	+	0.121545i
$159$		0			0
$160$	1.63160	−	2.82601i	0.128989	−	0.223416i
$161$		0			0
$162$		0			0
$163$	0.754040	−	1.30604i	0.0590610	−	0.102297i	−0.834983	−	0.550276i	$-0.814523\pi$
$163$	0.754040	−	1.30604i	0.0590610	−	0.102297i	0.894044	+	0.447979i	$0.147856\pi$
$164$	−19.7817			−1.54469
$165$		0			0
$166$	1.66019			0.128856
$167$	−7.34213	−	12.7169i	−0.568151	−	0.984067i	−0.996749	−	0.0805714i	$-0.974325\pi$
$167$	−7.34213	−	12.7169i	−0.568151	−	0.984067i	0.428598	−	0.903496i	$-0.359008\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	0.981125	−	1.69936i	0.0752489	−	0.130335i
$171$		0			0
$172$	2.16182	+	3.74439i	0.164838	+	0.285507i
$173$	0.126398	+	0.218928i	0.00960987	+	0.0166448i	0.870790	−	0.491655i	$-0.163608\pi$
$173$	0.126398	+	0.218928i	0.00960987	+	0.0166448i	−0.861180	+	0.508299i	$0.830274\pi$
$174$		0			0
$175$		0			0
$176$	−6.77812	−	11.7400i	−0.510920	−	0.884939i
$177$		0			0
$178$	−0.656920			−0.0492383
$179$	7.09617	+	12.2909i	0.530393	+	0.918667i	0.999371	+	0.0354578i	$0.0112889\pi$
$179$	7.09617	+	12.2909i	0.530393	+	0.918667i	−0.468978	+	0.883210i	$0.655378\pi$
$180$		0			0
$181$	−1.43147			−0.106400			−0.0532002	−	0.998584i	$-0.516942\pi$
$181$	−1.43147			−0.106400			−0.0532002	+	0.998584i	$0.516942\pi$
$182$		0			0
$183$		0			0
$184$	−5.28263			−0.389441
$185$	−5.64132	+	9.77104i	−0.414758	+	0.718381i
$186$		0			0
$187$	−12.8571	−	22.2691i	−0.940201	−	1.62848i
$188$	11.3236			0.825862
$189$		0			0
$190$	−0.549100			−0.0398359
$191$	7.53379	+	13.0489i	0.545126	+	0.944186i	0.998599	+	0.0529159i	$0.0168515\pi$
$191$	7.53379	+	13.0489i	0.545126	+	0.944186i	−0.453473	+	0.891270i	$0.649815\pi$
$192$		0			0
$193$	3.92395	−	6.79647i	0.282452	−	0.489221i	−0.689536	−	0.724251i	$-0.742186\pi$
$193$	3.92395	−	6.79647i	0.282452	−	0.489221i	0.971988	+	0.235030i	$0.0755190\pi$
$194$	1.71410			0.123065
$195$		0			0
$196$		0			0
$197$	−6.69002			−0.476644			−0.238322	−	0.971186i	$-0.576597\pi$
$197$	−6.69002			−0.476644			−0.238322	+	0.971186i	$0.576597\pi$
$198$		0			0
$199$	9.96978	+	17.2682i	0.706739	+	1.22411i	0.966060	+	0.258316i	$0.0831677\pi$
$199$	9.96978	+	17.2682i	0.706739	+	1.22411i	−0.259322	+	0.965791i	$0.583499\pi$
$200$	3.39699			0.240203
$201$		0			0
$202$	−1.52859	−	2.64760i	−0.107551	−	0.186284i
$203$		0			0
$204$		0			0
$205$	6.01724	+	10.4222i	0.420262	+	0.727916i
$206$	0.525711	+	0.910559i	0.0366280	+	0.0634416i
$207$		0			0
$208$	−1.83009	+	3.16982i	−0.126894	+	0.219787i
$209$	−3.59781	+	6.23159i	−0.248866	+	0.431048i
$210$		0			0
$211$	9.04583	+	15.6678i	0.622741	+	1.07862i	0.988973	+	0.148095i	$0.0473141\pi$
$211$	9.04583	+	15.6678i	0.622741	+	1.07862i	−0.366233	+	0.930523i	$0.619353\pi$
$212$	−22.5426			−1.54823
$213$		0			0
$214$	−3.28263			−0.224396
$215$	1.31518	−	2.27796i	0.0896944	−	0.155355i
$216$		0			0
$217$		0			0
$218$	−0.151030	+	0.261592i	−0.0102291	+	0.0177172i
$219$		0			0
$220$	−4.25241	+	7.36538i	−0.286697	+	0.496574i
$221$	−3.47141	+	6.01266i	−0.233512	+	0.404455i
$222$		0			0
$223$	11.3285	−	19.6215i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$223$	11.3285	−	19.6215i	0.758610	−	1.31395i	0.943560	−	0.331203i	$-0.107454\pi$
$224$		0			0
$225$		0			0
$226$	1.45417	−	2.51870i	0.0967299	−	0.167541i
$227$	5.28263			0.350620			0.175310	−	0.984513i	$-0.443907\pi$
$227$	5.28263			0.350620			0.175310	+	0.984513i	$0.443907\pi$
$228$		0			0
$229$	19.3365			1.27779			0.638897	−	0.769292i	$-0.279391\pi$
$229$	19.3365			1.27779			0.638897	+	0.769292i	$0.279391\pi$
$230$	0.791790	+	1.37142i	0.0522091	+	0.0904288i
$231$		0			0
$232$	−0.112725	+	0.195246i	−0.00740077	+	0.0128185i
$233$	−8.49028	+	14.7056i	−0.556217	+	0.963396i	0.441591	+	0.897217i	$0.354414\pi$
$233$	−8.49028	+	14.7056i	−0.556217	+	0.963396i	−0.997808	+	0.0661796i	$0.978919\pi$
$234$		0			0
$235$	−3.44445	−	5.96597i	−0.224691	−	0.389177i
$236$	−2.52859	−	4.37965i	−0.164597	−	0.285091i
$237$		0			0
$238$		0			0
$239$	8.44282	+	14.6234i	0.546121	+	0.945909i	0.998535	+	0.0541011i	$0.0172293\pi$
$239$	8.44282	+	14.6234i	0.546121	+	0.945909i	−0.452415	+	0.891808i	$0.649437\pi$
$240$		0			0
$241$	27.1456			1.74860			0.874300	−	0.485386i	$-0.161321\pi$
$241$	27.1456			1.74860			0.874300	+	0.485386i	$0.161321\pi$
$242$	−0.324893	−	0.562732i	−0.0208849	−	0.0361738i
$243$		0			0
$244$	14.7713			0.945634
$245$		0			0
$246$		0			0
$247$	1.94282			0.123619
$248$	0.782630	−	1.35556i	0.0496971	−	0.0860778i
$249$		0			0
$250$	−1.21574	−	2.10571i	−0.0768898	−	0.133177i
$251$	19.0780			1.20419			0.602096	−	0.798424i	$-0.294332\pi$
$251$	19.0780			1.20419			0.602096	+	0.798424i	$0.294332\pi$
$252$		0			0
$253$	20.7518			1.30466
$254$	−0.160190	−	0.277457i	−0.0100512	−	0.0174092i
$255$		0			0
$256$	−5.80959	+	10.0625i	−0.363099	+	0.628906i
$257$	14.8421			0.925827			0.462913	−	0.886404i	$-0.346804\pi$
$257$	14.8421			0.925827			0.462913	+	0.886404i	$0.346804\pi$
$258$		0			0
$259$		0			0
$260$	2.29630			0.142411
$261$		0			0
$262$	−0.593850	−	1.02858i	−0.0366882	−	0.0635458i
$263$	7.74145			0.477358			0.238679	−	0.971099i	$-0.423286\pi$
$263$	7.74145			0.477358			0.238679	+	0.971099i	$0.423286\pi$
$264$		0			0
$265$	6.85705	+	11.8768i	0.421225	+	0.729584i
$266$		0			0
$267$		0			0
$268$	3.40778	+	5.90246i	0.208164	+	0.360550i
$269$	−0.755675	−	1.30887i	−0.0460743	−	0.0798031i	0.842069	−	0.539371i	$-0.181338\pi$
$269$	−0.755675	−	1.30887i	−0.0460743	−	0.0798031i	−0.888143	+	0.459567i	$0.848004\pi$
$270$		0			0
$271$	10.9903	−	19.0357i	0.667612	−	1.15634i	−0.310958	−	0.950424i	$-0.600650\pi$
$271$	10.9903	−	19.0357i	0.667612	−	1.15634i	0.978570	−	0.205915i	$-0.0660169\pi$
$272$	−12.7060	+	22.0075i	−0.770416	+	1.33440i
$273$		0			0
$274$	−0.518875	−	0.898718i	−0.0313464	−	0.0542935i
$275$	−13.3445			−0.804701
$276$		0			0
$277$	−10.8285			−0.650619			−0.325310	−	0.945608i	$-0.605469\pi$
$277$	−10.8285			−0.650619			−0.325310	+	0.945608i	$0.605469\pi$
$278$	−0.471410	+	0.816506i	−0.0282733	+	0.0489708i
$279$		0			0
$280$		0			0
$281$	−8.43831	+	14.6156i	−0.503387	+	0.871892i	0.496605	+	0.867977i	$0.334580\pi$
$281$	−8.43831	+	14.6156i	−0.503387	+	0.871892i	−0.999992	+	0.00391559i	$0.998754\pi$
$282$		0			0
$283$	7.65856	−	13.2650i	0.455254	−	0.788523i	−0.543449	−	0.839442i	$-0.682882\pi$
$283$	7.65856	−	13.2650i	0.455254	−	0.788523i	0.998703	+	0.0509194i	$0.0162152\pi$
$284$	−8.35705	+	14.4748i	−0.495900	+	0.858923i
$285$		0			0
$286$	−0.442820	+	0.766987i	−0.0261845	+	0.0453529i
$287$		0			0
$288$		0			0
$289$	−15.6014	+	27.0224i	−0.917728	+	1.58955i
$290$	0.0675835			0.00396864
$291$		0			0
$292$	−29.4315			−1.72235
$293$	−4.68482	−	8.11435i	−0.273690	−	0.474045i	0.696114	−	0.717932i	$-0.254911\pi$
$293$	−4.68482	−	8.11435i	−0.273690	−	0.474045i	−0.969804	+	0.243886i	$0.921578\pi$
$294$		0			0
$295$	−1.53831	+	2.66442i	−0.0895636	+	0.155129i
$296$	−4.50000	+	7.79423i	−0.261557	+	0.453030i
$297$		0			0
$298$	1.32846	+	2.30096i	0.0769556	+	0.133291i
$299$	−2.80150	−	4.85235i	−0.162015	−	0.280619i
$300$		0			0
$301$		0			0
$302$	−1.66470	−	2.88335i	−0.0957929	−	0.165918i
$303$		0			0
$304$	7.11109			0.407849
$305$	−4.49316	−	7.78239i	−0.257278	−	0.445618i
$306$		0			0
$307$	2.71410			0.154902			0.0774509	−	0.996996i	$-0.475322\pi$
$307$	2.71410			0.154902			0.0774509	+	0.996996i	$0.475322\pi$
$308$		0			0
$309$		0			0
$310$	−0.469220			−0.0266499
$311$	−6.99028	+	12.1075i	−0.396383	+	0.686555i	−0.993277	−	0.115765i	$-0.963068\pi$
$311$	−6.99028	+	12.1075i	−0.396383	+	0.686555i	0.596894	+	0.802320i	$0.296401\pi$
$312$		0			0
$313$	9.52696	+	16.5012i	0.538495	+	0.932701i	0.998985	+	0.0450364i	$0.0143404\pi$
$313$	9.52696	+	16.5012i	0.538495	+	0.932701i	−0.460490	+	0.887665i	$0.652326\pi$
$314$	0.0136731			0.000771615
$315$		0			0
$316$	−14.3333			−0.806309
$317$	−2.00972	−	3.48093i	−0.112877	−	0.195508i	0.804052	−	0.594559i	$-0.202673\pi$
$317$	−2.00972	−	3.48093i	−0.112877	−	0.195508i	−0.916929	+	0.399050i	$0.869340\pi$
$318$		0			0
$319$	0.442820	−	0.766987i	0.0247932	−	0.0429430i
$320$	7.87197			0.440056
$321$		0			0
$322$		0			0
$323$	13.4887			0.750529
$324$		0			0
$325$	1.80150	+	3.12030i	0.0999295	+	0.173083i
$326$	−0.360617			−0.0199727
$327$		0			0
$328$	4.79987	+	8.31362i	0.265028	+	0.459043i
$329$		0			0
$330$		0			0
$331$	6.18878	+	10.7193i	0.340166	+	0.589185i	0.984463	−	0.175590i	$-0.0561834\pi$
$331$	6.18878	+	10.7193i	0.340166	+	0.589185i	−0.644297	+	0.764775i	$0.722850\pi$
$332$	6.74433	+	11.6815i	0.370143	+	0.641106i
$333$		0			0
$334$	−1.75567	+	3.04092i	−0.0960663	+	0.166392i
$335$	2.07318	−	3.59085i	0.113270	−	0.196189i
$336$		0			0
$337$	−6.12997	−	10.6174i	−0.333920	−	0.578367i	0.649356	−	0.760484i	$-0.275038\pi$
$337$	−6.12997	−	10.6174i	−0.333920	−	0.578367i	−0.983277	+	0.182117i	$0.941705\pi$
$338$	−2.86948			−0.156079
$339$		0			0
$340$	15.9428			0.864621
$341$	−3.07442	+	5.32505i	−0.166489	+	0.288368i
$342$		0			0
$343$		0			0
$344$	1.04910	−	1.81709i	0.0565637	−	0.0979711i
$345$		0			0
$346$	0.0302247	−	0.0523508i	0.00162489	−	0.00281440i
$347$	3.32489	−	5.75888i	0.178490	−	0.309153i	−0.762874	−	0.646547i	$-0.776212\pi$
$347$	3.32489	−	5.75888i	0.178490	−	0.309153i	0.941363	+	0.337394i	$0.109546\pi$
$348$		0			0
$349$	−5.71737	+	9.90278i	−0.306044	+	0.530083i	−0.977493	−	0.210967i	$-0.932339\pi$
$349$	−5.71737	+	9.90278i	−0.306044	+	0.530083i	0.671449	+	0.741050i	$0.265672\pi$
$350$		0			0
$351$		0			0
$352$	−5.11273	+	8.85550i	−0.272509	+	0.472000i
$353$	22.1956			1.18135			0.590677	−	0.806908i	$-0.298861\pi$
$353$	22.1956			1.18135			0.590677	+	0.806908i	$0.298861\pi$
$354$		0			0
$355$	10.1683			0.539676
$356$	−2.66866	−	4.62226i	−0.141439	−	0.244979i
$357$		0			0
$358$	1.69686	−	2.93905i	0.0896819	−	0.155334i
$359$	−3.77812	+	6.54389i	−0.199401	+	0.345373i	−0.948334	−	0.317272i	$-0.897233\pi$
$359$	−3.77812	+	6.54389i	−0.199401	+	0.345373i	0.748933	+	0.662646i	$0.230566\pi$
$360$		0			0
$361$	7.61273	+	13.1856i	0.400670	+	0.693980i
$362$	0.171149	+	0.296439i	0.00899539	+	0.0155805i
$363$		0			0
$364$		0			0
$365$	8.95254	+	15.5062i	0.468597	+	0.811634i
$366$		0			0
$367$	−18.5231			−0.966900			−0.483450	−	0.875372i	$-0.660616\pi$
$367$	−18.5231			−0.966900			−0.483450	+	0.875372i	$0.660616\pi$
$368$	−10.2540	−	17.7605i	−0.534529	−	0.925831i
$369$		0			0
$370$	2.69794			0.140259
$371$		0			0
$372$		0			0
$373$	15.6602			0.810854			0.405427	−	0.914127i	$-0.367123\pi$
$373$	15.6602			0.810854			0.405427	+	0.914127i	$0.367123\pi$
$374$	−3.07442	+	5.32505i	−0.158974	+	0.275352i
$375$		0			0
$376$	−2.74759	−	4.75897i	−0.141696	−	0.245425i
$377$	−0.239123			−0.0123155
$378$		0			0
$379$	4.03775			0.207405			0.103703	−	0.994608i	$-0.466931\pi$
$379$	4.03775			0.207405			0.103703	+	0.994608i	$0.466931\pi$
$380$	−2.23065	−	3.86360i	−0.114430	−	0.198199i
$381$		0			0
$382$	1.80150	−	3.12030i	0.0921730	−	0.159648i
$383$	−0.225450			−0.0115200			−0.00575998	−	0.999983i	$-0.501833\pi$
$383$	−0.225450			−0.0115200			−0.00575998	+	0.999983i	$0.501833\pi$
$384$		0			0
$385$		0			0
$386$	−1.87661			−0.0955171
$387$		0			0
$388$	6.96333	+	12.0608i	0.353510	+	0.612296i
$389$	−25.2632			−1.28090			−0.640448	−	0.768002i	$-0.721251\pi$
$389$	−25.2632			−1.28090			−0.640448	+	0.768002i	$0.721251\pi$
$390$		0			0
$391$	−19.4503	−	33.6890i	−0.983646	−	1.70373i
$392$		0			0
$393$		0			0
$394$	0.799870	+	1.38542i	0.0402969	+	0.0697962i
$395$	4.35993	+	7.55162i	0.219372	+	0.379963i
$396$		0			0
$397$	10.1505	−	17.5811i	0.509438	−	0.882372i	−0.490503	−	0.871440i	$-0.663187\pi$
$397$	10.1505	−	17.5811i	0.509438	−	0.882372i	0.999940	−	0.0109322i	$-0.00347991\pi$
$398$	2.38401	−	4.12922i	0.119499	−	0.206979i
$399$		0			0
$400$	6.59385	+	11.4209i	0.329693	+	0.571044i
$401$	15.2255			0.760323			0.380161	−	0.924920i	$-0.375868\pi$
$401$	15.2255			0.760323			0.380161	+	0.924920i	$0.375868\pi$
$402$		0			0
$403$	1.66019			0.0826999
$404$	12.4194	−	21.5111i	0.617890	−	1.07022i
$405$		0			0
$406$		0			0
$407$	17.6774	−	30.6182i	0.876238	−	1.51769i
$408$		0			0
$409$	−0.828460	+	1.43494i	−0.0409647	+	0.0709530i	−0.885781	−	0.464104i	$-0.846376\pi$
$409$	−0.828460	+	1.43494i	−0.0409647	+	0.0709530i	0.844816	+	0.535057i	$0.179710\pi$
$410$	1.43886	−	2.49218i	0.0710603	−	0.123080i
$411$		0			0
$412$	−4.27128	+	7.39807i	−0.210431	+	0.364477i
$413$		0			0
$414$		0			0
$415$	4.10301	−	7.10662i	0.201409	−	0.348850i
$416$	2.76088			0.135363
$417$		0			0
$418$	1.72064			0.0841592
$419$	16.6871	+	28.9030i	0.815220	+	1.41200i	0.909170	+	0.416426i	$0.136718\pi$
$419$	16.6871	+	28.9030i	0.815220	+	1.41200i	−0.0939492	+	0.995577i	$0.529949\pi$
$420$		0			0
$421$	−9.12025	+	15.7967i	−0.444494	+	0.769886i	−0.998017	−	0.0629481i	$-0.979950\pi$
$421$	−9.12025	+	15.7967i	−0.444494	+	0.769886i	0.553523	+	0.832834i	$0.313283\pi$
$422$	2.16307	−	3.74654i	0.105297	−	0.182379i
$423$		0			0
$424$	5.46978	+	9.47393i	0.265636	+	0.460095i
$425$	12.5075	+	21.6637i	0.606704	+	1.05084i
$426$		0			0
$427$		0			0
$428$	−13.3353	−	23.0974i	−0.644586	−	1.11646i
$429$		0			0
$430$	−0.628979			−0.0303321
$431$	14.6413	+	25.3595i	0.705247	+	1.22152i	0.966602	+	0.256281i	$0.0824974\pi$
$431$	14.6413	+	25.3595i	0.705247	+	1.22152i	−0.261355	+	0.965243i	$0.584169\pi$
$432$		0			0
$433$	−12.2449			−0.588451			−0.294226	−	0.955736i	$-0.595062\pi$
$433$	−12.2449			−0.588451			−0.294226	+	0.955736i	$0.595062\pi$
$434$		0			0
$435$		0			0
$436$	−2.45417			−0.117533
$437$	−5.44282	+	9.42724i	−0.260365	+	0.450966i
$438$		0			0
$439$	2.41586	+	4.18440i	0.115303	+	0.199711i	0.917901	−	0.396810i	$-0.129883\pi$
$439$	2.41586	+	4.18440i	0.115303	+	0.199711i	−0.802598	+	0.596520i	$0.796549\pi$
$440$	4.12725			0.196759
$441$		0			0
$442$	1.66019			0.0789672
$443$	0.622440	+	1.07810i	0.0295730	+	0.0512220i	0.880433	−	0.474170i	$-0.157252\pi$
$443$	0.622440	+	1.07810i	0.0295730	+	0.0512220i	−0.850860	+	0.525392i	$0.823919\pi$
$444$		0			0
$445$	−1.62352	+	2.81202i	−0.0769622	+	0.133302i
$446$	−5.41780			−0.256540
$447$		0			0
$448$		0			0
$449$	−8.82846			−0.416641			−0.208320	−	0.978061i	$-0.566800\pi$
$449$	−8.82846			−0.416641			−0.208320	+	0.978061i	$0.566800\pi$
$450$		0			0
$451$	−18.8554	−	32.6585i	−0.887867	−	1.53783i
$452$	23.6296			1.11144
$453$		0			0
$454$	−0.631600	−	1.09396i	−0.0296425	−	0.0513422i
$455$		0			0
$456$		0			0
$457$	5.25404	+	9.10026i	0.245774	+	0.425692i	0.962349	−	0.271817i	$-0.0876247\pi$
$457$	5.25404	+	9.10026i	0.245774	+	0.425692i	−0.716575	+	0.697510i	$0.754291\pi$
$458$	−2.31191	−	4.00434i	−0.108028	−	0.187111i
$459$		0			0
$460$	−6.43310	+	11.1425i	−0.299945	+	0.519520i
$461$	11.2758	−	19.5302i	0.525166	−	0.909614i	−0.474404	−	0.880307i	$-0.657337\pi$
$461$	11.2758	−	19.5302i	0.525166	−	0.909614i	0.999570	−	0.0293073i	$-0.00933013\pi$
$462$		0			0
$463$	−5.19850	−	9.00406i	−0.241595	−	0.418454i	0.719574	−	0.694416i	$-0.244337\pi$
$463$	−5.19850	−	9.00406i	−0.241595	−	0.418454i	−0.961169	+	0.275962i	$0.911004\pi$
$464$	−0.875237			−0.0406318
$465$		0			0
$466$	4.06045			0.188097
$467$	6.65856	−	11.5330i	0.308121	−	0.533682i	−0.669830	−	0.742514i	$-0.733633\pi$
$467$	6.65856	−	11.5330i	0.308121	−	0.533682i	0.977951	+	0.208833i	$0.0669664\pi$
$468$		0			0
$469$		0			0
$470$	−0.823649	+	1.42660i	−0.0379921	+	0.0658043i
$471$		0			0
$472$	−1.22708	+	2.12537i	−0.0564812	+	0.0978282i
$473$	−4.12120	+	7.13812i	−0.189493	+	0.328211i
$474$		0			0
$475$	3.50000	−	6.06218i	0.160591	−	0.278152i
$476$		0			0
$477$		0			0
$478$	2.01887	−	3.49679i	0.0923412	−	0.159940i
$479$	−14.5354			−0.664141			−0.332070	−	0.943255i	$-0.607747\pi$
$479$	−14.5354			−0.664141			−0.332070	+	0.943255i	$0.607747\pi$
$480$		0			0
$481$	−9.54583			−0.435252
$482$	−3.24557	−	5.62149i	−0.147832	−	0.256052i
$483$		0			0
$484$	2.63968	−	4.57206i	0.119985	−	0.207821i
$485$	4.23624	−	7.33739i	0.192358	−	0.333174i
$486$		0			0
$487$	−6.52696	−	11.3050i	−0.295765	−	0.512279i	0.679398	−	0.733770i	$-0.262241\pi$
$487$	−6.52696	−	11.3050i	−0.295765	−	0.512279i	−0.975162	+	0.221491i	$0.928908\pi$
$488$	−3.58414	−	6.20790i	−0.162246	−	0.281019i
$489$		0			0
$490$		0			0
$491$	9.67223	+	16.7528i	0.436502	+	0.756043i	0.997417	−	0.0718303i	$-0.0228840\pi$
$491$	9.67223	+	16.7528i	0.436502	+	0.756043i	−0.560915	+	0.827873i	$0.689551\pi$
$492$		0			0
$493$	−1.66019			−0.0747712
$494$	−0.232287	−	0.402332i	−0.0104511	−	0.0181018i
$495$		0			0
$496$	6.07661			0.272848
$497$		0			0
$498$		0			0
$499$	−36.2222			−1.62153			−0.810764	−	0.585374i	$-0.800948\pi$
$499$	−36.2222			−1.62153			−0.810764	+	0.585374i	$0.800948\pi$
$500$	9.87756	−	17.1084i	0.441738	−	0.765112i
$501$		0			0
$502$	−2.28100	−	3.95080i	−0.101806	−	0.176333i
$503$	−15.6764			−0.698974			−0.349487	−	0.936941i	$-0.613644\pi$
$503$	−15.6764			−0.698974			−0.349487	+	0.936941i	$0.613644\pi$
$504$		0			0
$505$	−15.1111			−0.672435
$506$	−2.48113	−	4.29743i	−0.110299	−	0.191044i
$507$		0			0
$508$	1.30150	−	2.25427i	0.0577449	−	0.100017i
$509$	−34.3034			−1.52047			−0.760237	−	0.649646i	$-0.774917\pi$
$509$	−34.3034			−1.52047			−0.760237	+	0.649646i	$0.774917\pi$
$510$		0			0
$511$		0			0
$512$	17.0071			0.751616
$513$		0			0
$514$	−1.77455	−	3.07361i	−0.0782720	−	0.135571i
$515$	5.19699			0.229007
$516$		0			0
$517$	10.7934	+	18.6948i	0.474694	+	0.822195i
$518$		0			0
$519$		0			0
$520$	−0.557180	−	0.965064i	−0.0244340	−	0.0423209i
$521$	−5.12244	−	8.87233i	−0.224418	−	0.388704i	0.731727	−	0.681598i	$-0.238715\pi$
$521$	−5.12244	−	8.87233i	−0.224418	−	0.388704i	−0.956145	+	0.292895i	$0.905381\pi$
$522$		0			0
$523$	−15.3015	+	26.5030i	−0.669088	+	1.15889i	0.309071	+	0.951039i	$0.399982\pi$
$523$	−15.3015	+	26.5030i	−0.669088	+	1.15889i	−0.978159	+	0.207856i	$0.933352\pi$
$524$	4.82489	−	8.35696i	0.210776	−	0.365075i
$525$		0			0
$526$	−0.925580	−	1.60315i	−0.0403572	−	0.0699007i
$527$	11.5264			0.502098
$528$		0			0
$529$	8.39372			0.364944
$530$	1.63968	−	2.84001i	0.0712232	−	0.123362i
$531$		0			0
$532$		0			0
$533$	−5.09097	+	8.81782i	−0.220514	+	0.381942i
$534$		0			0
$535$	−8.11273	+	14.0517i	−0.350744	+	0.607506i
$536$	1.65374	−	2.86437i	0.0714309	−	0.123722i
$537$		0			0
$538$	−0.180699	+	0.312981i	−0.00779051	+	0.0134936i
$539$		0			0
$540$		0			0
$541$	13.0458	−	22.5960i	0.560884	−	0.971480i	−0.436536	−	0.899687i	$-0.643795\pi$
$541$	13.0458	−	22.5960i	0.560884	−	0.971480i	0.997420	−	0.0717926i	$-0.0228720\pi$
$542$	−5.25607			−0.225767
$543$		0			0
$544$	19.1683			0.821833
$545$	0.746515	+	1.29300i	0.0319772	+	0.0553861i
$546$		0			0
$547$	5.46169	−	9.45993i	0.233525	−	0.404478i	−0.725318	−	0.688414i	$-0.758307\pi$
$547$	5.46169	−	9.45993i	0.233525	−	0.404478i	0.958843	+	0.283937i	$0.0916405\pi$
$548$	4.21574	−	7.30187i	0.180087	−	0.311920i
$549$		0			0
$550$	1.59549	+	2.76346i	0.0680317	+	0.117834i
$551$	0.232287	+	0.402332i	0.00989575	+	0.0171399i
$552$		0			0
$553$		0			0
$554$	1.29467	+	2.24243i	0.0550052	+	0.0952718i
$555$		0			0
$556$	−7.66019			−0.324864
$557$	−6.97210	−	12.0760i	−0.295417	−	0.511678i	0.679665	−	0.733523i	$-0.262125\pi$
$557$	−6.97210	−	12.0760i	−0.295417	−	0.511678i	−0.975082	+	0.221845i	$0.928792\pi$
$558$		0			0
$559$	2.22545			0.0941265
$560$		0			0
$561$		0			0
$562$	4.03559			0.170231
$563$	15.1287	−	26.2037i	0.637600	−	1.10435i	−0.348358	−	0.937361i	$-0.613261\pi$
$563$	15.1287	−	26.2037i	0.637600	−	1.10435i	0.985958	−	0.166993i	$-0.0534059\pi$
$564$		0			0
$565$	−7.18770	−	12.4495i	−0.302389	−	0.523753i
$566$	−3.66268			−0.153954
$567$		0			0
$568$	8.11109			0.340334
$569$	−10.5676	−	18.3036i	−0.443016	−	0.767326i	0.554896	−	0.831920i	$-0.312758\pi$
$569$	−10.5676	−	18.3036i	−0.443016	−	0.767326i	−0.997912	+	0.0645936i	$0.979425\pi$
$570$		0			0
$571$	16.3932	−	28.3938i	0.686033	−	1.18824i	−0.287078	−	0.957907i	$-0.592684\pi$
$571$	16.3932	−	28.3938i	0.686033	−	1.18824i	0.973111	−	0.230336i	$-0.0739826\pi$
$572$	−7.19562			−0.300864
$573$		0			0
$574$		0			0
$575$	−20.1877			−0.841885
$576$		0			0
$577$	8.68715	+	15.0466i	0.361651	+	0.626397i	0.988233	−	0.152958i	$-0.0488800\pi$
$577$	8.68715	+	15.0466i	0.361651	+	0.626397i	−0.626582	+	0.779355i	$0.715547\pi$
$578$	7.46130			0.310349
$579$		0			0
$580$	0.274550	+	0.475534i	0.0114001	+	0.0197455i
$581$		0			0
$582$		0			0
$583$	−21.4870	−	37.2166i	−0.889901	−	1.54135i
$584$	7.14132	+	12.3691i	0.295510	+	0.511838i
$585$		0			0
$586$	−1.12025	+	1.94033i	−0.0462771	+	0.0801543i
$587$	8.48796	−	14.7016i	0.350336	−	0.606799i	−0.635973	−	0.771712i	$-0.719401\pi$
$587$	8.48796	−	14.7016i	0.350336	−	0.606799i	0.986308	+	0.164913i	$0.0527342\pi$
$588$		0			0
$589$	−1.61273	−	2.79332i	−0.0664512	−	0.115097i
$590$	0.735689			0.0302878
$591$		0			0
$592$	−34.9396			−1.43601
$593$	−6.53667	+	11.3218i	−0.268429	+	0.464932i	−0.968456	−	0.249184i	$-0.919838\pi$
$593$	−6.53667	+	11.3218i	−0.268429	+	0.464932i	0.700027	+	0.714116i	$0.253171\pi$
$594$		0			0
$595$		0			0
$596$	−10.7934	+	18.6948i	−0.442116	+	0.765767i
$597$		0			0
$598$	−0.669905	+	1.16031i	−0.0273945	+	0.0474486i
$599$	14.6030	−	25.2932i	0.596663	−	1.03345i	−0.396647	−	0.917971i	$-0.629826\pi$
$599$	14.6030	−	25.2932i	0.596663	−	1.03345i	0.993310	−	0.115479i	$-0.0368403\pi$
$600$		0			0
$601$	−3.89536	+	6.74695i	−0.158895	+	0.275214i	−0.934470	−	0.356041i	$-0.884126\pi$
$601$	−3.89536	+	6.74695i	−0.158895	+	0.275214i	0.775576	+	0.631255i	$0.217460\pi$
$602$		0			0
$603$		0			0
$604$	13.5253	−	23.4265i	0.550337	−	0.953212i
$605$	−3.21178			−0.130577
$606$		0			0
$607$	−19.6408			−0.797194			−0.398597	−	0.917126i	$-0.630503\pi$
$607$	−19.6408			−0.797194			−0.398597	+	0.917126i	$0.630503\pi$
$608$	−2.68194	−	4.64526i	−0.108767	−	0.188390i
$609$		0			0
$610$	−1.07442	+	1.86095i	−0.0435020	+	0.0753477i
$611$	2.91423	−	5.04759i	0.117897	−	0.204204i
$612$		0			0
$613$	−11.7826	−	20.4081i	−0.475896	−	0.824276i	0.523723	−	0.851889i	$-0.324543\pi$
$613$	−11.7826	−	20.4081i	−0.475896	−	0.824276i	−0.999619	+	0.0276128i	$0.991209\pi$
$614$	−0.324502	−	0.562054i	−0.0130958	−	0.0226827i
$615$		0			0
$616$		0			0
$617$	−5.33009	−	9.23200i	−0.214582	−	0.371666i	0.738562	−	0.674186i	$-0.235505\pi$
$617$	−5.33009	−	9.23200i	−0.214582	−	0.371666i	−0.953143	+	0.302520i	$0.902172\pi$
$618$		0			0
$619$	−18.0150			−0.724086			−0.362043	−	0.932161i	$-0.617921\pi$
$619$	−18.0150			−0.724086			−0.362043	+	0.932161i	$0.617921\pi$
$620$	−1.90615	−	3.30155i	−0.0765528	−	0.132593i
$621$		0			0
$622$	3.34308			0.134045
$623$		0			0
$624$		0			0
$625$	5.99673			0.239869
$626$	2.27812	−	3.94581i	0.0910519	−	0.157706i
$627$		0			0
$628$	0.0555452	+	0.0962071i	0.00221649	+	0.00383908i
$629$	−66.2750			−2.64256
$630$		0			0
$631$	12.4703			0.496436			0.248218	−	0.968704i	$-0.420155\pi$
$631$	12.4703			0.496436			0.248218	+	0.968704i	$0.420155\pi$
$632$	3.47786	+	6.02382i	0.138342	+	0.239615i
$633$		0			0
$634$	−0.480570	+	0.832371i	−0.0190859	+	0.0330577i
$635$	−1.58358			−0.0628424
$636$		0			0
$637$		0			0
$638$	−0.211777			−0.00838434
$639$		0			0
$640$	−4.20439	−	7.28221i	−0.166193	−	0.287855i
$641$	−19.1456			−0.756205			−0.378102	−	0.925764i	$-0.623423\pi$
$641$	−19.1456			−0.756205			−0.378102	+	0.925764i	$0.623423\pi$
$642$		0			0
$643$	−3.24433	−	5.61934i	−0.127944	−	0.221605i	0.794936	−	0.606693i	$-0.207504\pi$
$643$	−3.24433	−	5.61934i	−0.127944	−	0.221605i	−0.922880	+	0.385088i	$0.874171\pi$
$644$		0			0
$645$		0			0
$646$	−1.61273	−	2.79332i	−0.0634518	−	0.109902i
$647$	−24.0494	−	41.6548i	−0.945479	−	1.63762i	−0.754789	−	0.655968i	$-0.772261\pi$
$647$	−24.0494	−	41.6548i	−0.945479	−	1.63762i	−0.190691	−	0.981650i	$-0.561073\pi$
$648$		0			0
$649$	4.82038	−	8.34914i	0.189216	−	0.327733i
$650$	0.430782	−	0.746136i	0.0168967	−	0.0292659i
$651$		0			0
$652$	−1.46496	−	2.53739i	−0.0573724	−	0.0993720i
$653$	43.2405			1.69213			0.846066	−	0.533079i	$-0.178965\pi$
$653$	43.2405			1.69213			0.846066	+	0.533079i	$0.178965\pi$
$654$		0			0
$655$	−5.87059			−0.229383
$656$	−18.6339	+	32.2749i	−0.727532	+	1.26012i
$657$		0			0
$658$		0			0
$659$	−1.25404	+	2.17206i	−0.0488505	+	0.0846115i	−0.889417	−	0.457097i	$-0.848889\pi$
$659$	−1.25404	+	2.17206i	−0.0488505	+	0.0846115i	0.840566	+	0.541709i	$0.182222\pi$
$660$		0			0
$661$	21.1677	−	36.6636i	0.823329	−	1.42605i	−0.0798613	−	0.996806i	$-0.525448\pi$
$661$	21.1677	−	36.6636i	0.823329	−	1.42605i	0.903190	−	0.429241i	$-0.141219\pi$
$662$	1.47988	−	2.56323i	0.0575172	−	0.0996227i
$663$		0			0
$664$	3.27292	−	5.66886i	0.127014	−	0.219994i
$665$		0			0
$666$		0			0
$667$	0.669905	−	1.16031i	0.0259388	−	0.0449274i
$668$	−28.5289			−1.10382
$669$		0			0
$670$	−0.991489			−0.0383046
$671$	14.0796	+	24.3866i	0.543538	+	0.941435i
$672$		0			0
$673$	−6.70765	+	11.6180i	−0.258561	+	0.447841i	−0.965857	−	0.259077i	$-0.916582\pi$
$673$	−6.70765	+	11.6180i	−0.258561	+	0.447841i	0.707296	+	0.706918i	$0.249915\pi$
$674$	−1.46582	+	2.53887i	−0.0564612	+	0.0977936i
$675$		0			0
$676$	−11.6569	−	20.1904i	−0.448343	−	0.776553i
$677$	0.981125	+	1.69936i	0.0377077	+	0.0653117i	0.884263	−	0.466989i	$-0.154661\pi$
$677$	0.981125	+	1.69936i	0.0377077	+	0.0653117i	−0.846556	+	0.532300i	$0.821328\pi$
$678$		0			0
$679$		0			0
$680$	−3.86840	−	6.70027i	−0.148346	−	0.256943i
$681$		0			0
$682$	1.47033			0.0563019
$683$	13.5836	+	23.5275i	0.519761	+	0.900253i	0.999736	+	0.0229706i	$0.00731243\pi$
$683$	13.5836	+	23.5275i	0.519761	+	0.900253i	−0.479975	+	0.877282i	$0.659354\pi$
$684$		0			0
$685$	−5.12941			−0.195985
$686$		0			0
$687$		0			0
$688$	8.14557			0.310547
$689$	−5.80150	+	10.0485i	−0.221020	+	0.382817i
$690$		0			0
$691$	25.1586	+	43.5759i	0.957077	+	1.65771i	0.729543	+	0.683935i	$0.239733\pi$
$691$	25.1586	+	43.5759i	0.957077	+	1.65771i	0.227534	+	0.973770i	$0.426934\pi$
$692$	0.491138			0.0186703
$693$		0			0
$694$	−1.59012			−0.0603601
$695$	2.33009	+	4.03584i	0.0883855	+	0.153088i
$696$		0			0
$697$	−35.3457	+	61.2205i	−1.33881	+	2.31889i
$698$	2.73431			0.103495
$699$		0			0
$700$		0			0
$701$	−45.1672			−1.70594			−0.852970	−	0.521960i	$-0.825201\pi$
$701$	−45.1672			−1.70594			−0.852970	+	0.521960i	$0.825201\pi$
$702$		0			0
$703$	9.27292	+	16.0612i	0.349735	+	0.605758i
$704$	−24.6673			−0.929685
$705$		0			0
$706$	−2.65374	−	4.59642i	−0.0998750	−	0.172989i
$707$		0			0
$708$		0			0
$709$	−19.8090	−	34.3102i	−0.743944	−	1.28855i	−0.950687	−	0.310153i	$-0.899620\pi$
$709$	−19.8090	−	34.3102i	−0.743944	−	1.28855i	0.206743	−	0.978395i	$-0.433714\pi$
$710$	−1.21574	−	2.10571i	−0.0456257	−	0.0790261i
$711$		0			0
$712$	−1.29506	+	2.24311i	−0.0485344	+	0.0840640i
$713$	−4.65103	+	8.05582i	−0.174182	+	0.301693i
$714$		0			0
$715$	2.18878	+	3.79108i	0.0818557	+	0.141778i
$716$	27.5732			1.03046
$717$		0			0
$718$	1.80687			0.0674318
$719$	−11.0189	+	19.0853i	−0.410935	+	0.711760i	−0.994992	−	0.0999525i	$-0.968131\pi$
$719$	−11.0189	+	19.0853i	−0.410935	+	0.711760i	0.584058	+	0.811712i	$0.301464\pi$
$720$		0			0
$721$		0			0
$722$	1.82038	−	3.15299i	0.0677475	−	0.117342i
$723$		0			0
$724$	−1.39054	+	2.40849i	−0.0516792	+	0.0895110i
$725$	−0.430782	+	0.746136i	−0.0159988	+	0.0277108i
$726$		0			0
$727$	−14.0555	+	24.3449i	−0.521291	+	0.902903i	0.478402	+	0.878141i	$0.341216\pi$
$727$	−14.0555	+	24.3449i	−0.521291	+	0.902903i	−0.999693	+	0.0247621i	$0.992117\pi$
$728$		0			0
$729$		0			0
$730$	2.14076	−	3.70790i	0.0792331	−	0.137236i
$731$	15.4509			0.571472
$732$		0			0
$733$	11.8695			0.438409			0.219205	−	0.975679i	$-0.429654\pi$
$733$	11.8695			0.438409			0.219205	+	0.975679i	$0.429654\pi$
$734$	2.21466	+	3.83590i	0.0817444	+	0.141586i
$735$		0			0
$736$	−7.73461	+	13.3967i	−0.285102	+	0.493810i
$737$	−6.49643	+	11.2522i	−0.239299	+	0.414478i
$738$		0			0
$739$	6.09222	+	10.5520i	0.224106	+	0.388163i	0.956051	−	0.293201i	$-0.0947206\pi$
$739$	6.09222	+	10.5520i	0.224106	+	0.388163i	−0.731945	+	0.681364i	$0.761387\pi$
$740$	10.9601	+	18.9834i	0.402900	+	0.697843i
$741$		0			0
$742$		0			0
$743$	−22.2427	−	38.5255i	−0.816005	−	1.41336i	−0.908604	−	0.417659i	$-0.862851\pi$
$743$	−22.2427	−	38.5255i	−0.816005	−	1.41336i	0.0925987	−	0.995704i	$-0.470483\pi$
$744$		0			0
$745$	13.1327			0.481144
$746$	−1.87236	−	3.24302i	−0.0685519	−	0.118735i
$747$		0			0
$748$	−49.9579			−1.82664
$749$		0			0
$750$		0			0
$751$	42.8058			1.56200			0.781002	−	0.624528i	$-0.214709\pi$
$751$	42.8058			1.56200			0.781002	+	0.624528i	$0.214709\pi$
$752$	10.6666	−	18.4752i	0.388972	−	0.673720i
$753$		0			0
$754$	0.0285900	+	0.0495193i	0.00104119	+	0.00180339i
$755$	−16.4567			−0.598919
$756$		0			0
$757$	−22.4919			−0.817483			−0.408741	−	0.912650i	$-0.634032\pi$
$757$	−22.4919			−0.817483			−0.408741	+	0.912650i	$0.634032\pi$
$758$	−0.482760	−	0.836165i	−0.0175346	−	0.0303709i
$759$		0			0
$760$	−1.08250	+	1.87495i	−0.0392664	+	0.0680114i
$761$	14.3365			0.519699			0.259850	−	0.965649i	$-0.416327\pi$
$761$	14.3365			0.519699			0.259850	+	0.965649i	$0.416327\pi$
$762$		0			0
$763$		0			0
$764$	29.2736			1.05908
$765$		0			0
$766$	0.0269552	+	0.0466878i	0.000973931	+	0.00168690i
$767$	−2.60301			−0.0939892
$768$		0			0
$769$	15.6105	+	27.0382i	0.562930	+	0.975024i	0.997239	+	0.0742597i	$0.0236594\pi$
$769$	15.6105	+	27.0382i	0.562930	+	0.975024i	−0.434309	+	0.900764i	$0.643007\pi$
$770$		0			0
$771$		0			0
$772$	−7.62352	−	13.2043i	−0.274376	−	0.475234i
$773$	2.19002	+	3.79323i	0.0787697	+	0.136433i	0.902719	−	0.430230i	$-0.141567\pi$
$773$	2.19002	+	3.79323i	0.0787697	+	0.136433i	−0.823950	+	0.566663i	$0.808234\pi$
$774$		0			0
$775$	2.99084	−	5.18029i	0.107434	−	0.186081i
$776$	3.37919	−	5.85294i	0.121306	−	0.210108i
$777$		0			0
$778$	3.02051	+	5.23168i	0.108291	+	0.187565i
$779$	19.7817			0.708752
$780$		0			0
$781$	−31.8629			−1.14015
$782$	−4.65103	+	8.05582i	−0.166321	+	0.288076i
$783$		0			0
$784$		0			0
$785$	0.0337917	−	0.0585290i	0.00120608	−	0.00208899i
$786$		0			0
$787$	−13.8107	+	23.9208i	−0.492297	+	0.852683i	−0.999961	−	0.00887191i	$-0.997176\pi$
$787$	−13.8107	+	23.9208i	−0.492297	+	0.852683i	0.507664	+	0.861555i	$0.330509\pi$
$788$	−6.49876	+	11.2562i	−0.231509	+	0.400985i
$789$		0			0
$790$	1.04256	−	1.80577i	0.0370926	−	0.0642463i
$791$		0			0
$792$		0			0
$793$	3.80150	−	6.58440i	0.134995	−	0.233819i
$794$	−4.85443			−0.172277
$795$		0			0
$796$	38.7390			1.37307
$797$	−1.48181	−	2.56658i	−0.0524885	−	0.0909128i	0.838587	−	0.544767i	$-0.183382\pi$
$797$	−1.48181	−	2.56658i	−0.0524885	−	0.0909128i	−0.891076	+	0.453854i	$0.850049\pi$
$798$		0			0
$799$	20.2330	−	35.0445i	0.715791	−	1.23979i
$800$	4.97373	−	8.61476i	0.175848	−	0.304578i
$801$		0			0
$802$	−1.82038	−	3.15299i	−0.0642798	−	0.111336i
$803$	−28.0534	−	48.5898i	−0.989981	−	1.71470i
$804$		0			0
$805$		0			0
$806$	−0.198495	−	0.343803i	−0.00699169	−	0.0121100i
$807$		0			0
$808$	−12.0539			−0.424055
$809$	−12.3948	−	21.4684i	−0.435778	−	0.754790i	0.561581	−	0.827422i	$-0.310193\pi$
$809$	−12.3948	−	21.4684i	−0.435778	−	0.754790i	−0.997359	+	0.0726323i	$0.976860\pi$
$810$		0			0
$811$	8.24377			0.289478			0.144739	−	0.989470i	$-0.453766\pi$
$811$	8.24377			0.289478			0.144739	+	0.989470i	$0.453766\pi$
$812$		0			0
$813$		0			0
$814$	−8.45417			−0.296319
$815$	−0.891233	+	1.54366i	−0.0312185	+	0.0540721i
$816$		0			0
$817$	−2.16182	−	3.74439i	−0.0756327	−	0.131000i
$818$	0.396208			0.0138531
$819$		0			0
$820$	23.3808			0.816494
$821$	−14.4497	−	25.0275i	−0.504296	−	0.873467i	−0.999988	−	0.00496829i	$-0.998419\pi$
$821$	−14.4497	−	25.0275i	−0.504296	−	0.873467i	0.495691	−	0.868499i	$-0.334915\pi$
$822$		0			0
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	−0.360623	−	0.932712i	$-0.617436\pi$
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	0.988063	−	0.154047i	$-0.0492308\pi$
$824$	4.14557			0.144418
$825$		0			0
$826$		0			0
$827$	50.7108			1.76339			0.881694	−	0.471821i	$-0.156403\pi$
$827$	50.7108			1.76339			0.881694	+	0.471821i	$0.156403\pi$
$828$		0			0
$829$	−7.40615	−	12.8278i	−0.257226	−	0.445529i	0.708272	−	0.705940i	$-0.249475\pi$
$829$	−7.40615	−	12.8278i	−0.257226	−	0.445529i	−0.965498	+	0.260411i	$0.916142\pi$
$830$	−1.96225			−0.0681107
$831$		0			0
$832$	3.33009	+	5.76789i	0.115450	+	0.199966i
$833$		0			0
$834$		0			0
$835$	8.67799	+	15.0307i	0.300314	+	0.520159i
$836$	6.98989	+	12.1069i	0.241751	+	0.418724i
$837$		0			0
$838$	3.99028	−	6.91138i	0.137842	−	0.238750i
$839$	16.8606	−	29.2034i	0.582093	−	1.00821i	−0.413138	−	0.910669i	$-0.635567\pi$
$839$	16.8606	−	29.2034i	0.582093	−	1.00821i	0.995231	−	0.0975464i	$-0.0310994\pi$
$840$		0			0
$841$	14.4714	+	25.0652i	0.499014	+	0.864318i
$842$	4.36173			0.150315
$843$		0			0
$844$	35.1488			1.20987
$845$	−7.09166	+	12.2831i	−0.243961	+	0.422552i
$846$		0			0
$847$		0			0
$848$	−21.2346	+	36.7794i	−0.729199	+	1.26301i
$849$		0			0
$850$	2.99084	−	5.18029i	0.102585	−	0.177682i
$851$	26.7427	−	46.3197i	0.916728	−	1.58782i
$852$		0			0
$853$	−5.89480	+	10.2101i	−0.201834	+	0.349587i	−0.949119	−	0.314916i	$-0.898024\pi$
$853$	−5.89480	+	10.2101i	−0.201834	+	0.349587i	0.747285	+	0.664503i	$0.231357\pi$
$854$		0			0
$855$		0			0
$856$	−6.47141	+	11.2088i	−0.221188	+	0.383109i
$857$	31.3261			1.07008			0.535040	−	0.844827i	$-0.320296\pi$
$857$	31.3261			1.07008			0.535040	+	0.844827i	$0.320296\pi$
$858$		0			0
$859$	−50.3893			−1.71926			−0.859631	−	0.510915i	$-0.829307\pi$
$859$	−50.3893			−1.71926			−0.859631	+	0.510915i	$0.829307\pi$
$860$	−2.55515	−	4.42566i	−0.0871300	−	0.150914i
$861$		0			0
$862$	3.50108	−	6.06405i	0.119247	−	0.206542i
$863$	0.566340	−	0.980929i	0.0192784	−	0.0333912i	−0.856225	−	0.516603i	$-0.827196\pi$
$863$	0.566340	−	0.980929i	0.0192784	−	0.0333912i	0.875504	+	0.483211i	$0.160530\pi$
$864$		0			0
$865$	−0.149395	−	0.258761i	−0.00507960	−	0.00879812i
$866$	1.46402	+	2.53575i	0.0497494	+	0.0861684i
$867$		0			0
$868$		0			0
$869$	−13.6621	−	23.6635i	−0.463456	−	0.802729i
$870$		0			0
$871$	3.50808			0.118867
$872$	0.595485	+	1.03141i	0.0201657	+	0.0349280i
$873$		0			0
$874$	2.60301			0.0880481
$875$		0			0
$876$		0			0
$877$	−27.3937			−0.925020			−0.462510	−	0.886614i	$-0.653051\pi$
$877$	−27.3937			−0.925020			−0.462510	+	0.886614i	$0.653051\pi$
$878$	0.577690	−	1.00059i	0.0194961	−	0.0337682i
$879$		0			0
$880$	8.01135	+	13.8761i	0.270063	+	0.467762i
$881$	−1.20929			−0.0407420			−0.0203710	−	0.999792i	$-0.506485\pi$
$881$	−1.20929			−0.0407420			−0.0203710	+	0.999792i	$0.506485\pi$
$882$		0			0
$883$	−51.0884			−1.71926			−0.859631	−	0.510916i	$-0.829306\pi$
$883$	−51.0884			−1.71926			−0.859631	+	0.510916i	$0.829306\pi$
$884$	6.74433	+	11.6815i	0.226836	+	0.392892i
$885$		0			0
$886$	0.148840	−	0.257798i	0.00500038	−	0.00866091i
$887$	41.5757			1.39597			0.697987	−	0.716110i	$-0.254079\pi$
$887$	41.5757			1.39597			0.697987	+	0.716110i	$0.254079\pi$
$888$		0			0
$889$		0			0
$890$	0.776443			0.0260264
$891$		0			0
$892$	−22.0092	−	38.1210i	−0.736921	−	1.27638i
$893$	−11.3236			−0.378931
$894$		0			0
$895$	−8.38727	−	14.5272i	−0.280356	−	0.485590i
$896$		0			0
$897$		0			0
$898$	1.05555	+	1.82826i	0.0352240	+	0.0610098i
$899$	0.198495	+	0.343803i	0.00662018	+	0.0114665i
$900$		0			0
$901$	−40.2788	+	69.7649i	−1.34188	+	2.32421i
$902$	−4.50877	+	7.80942i	−0.150126	+	0.260025i
$903$		0			0
$904$	−5.73353	−	9.93077i	−0.190694	−	0.330292i
$905$	1.69192			0.0562412
$906$		0			0
$907$	35.4509			1.17713			0.588564	−	0.808451i	$-0.299694\pi$
$907$	35.4509			1.17713			0.588564	+	0.808451i	$0.299694\pi$
$908$	5.13160	−	8.88819i	0.170298	−	0.294965i
$909$		0			0
$910$		0			0
$911$	−10.3554	+	17.9361i	−0.343090	+	0.594250i	−0.985005	−	0.172526i	$-0.944807\pi$
$911$	−10.3554	+	17.9361i	−0.343090	+	0.594250i	0.641915	+	0.766776i	$0.278140\pi$
$912$		0			0
$913$	−12.8571	+	22.2691i	−0.425506	+	0.736998i
$914$	1.25636	−	2.17609i	0.0415568	−	0.0719785i
$915$		0			0
$916$	18.7837	−	32.5343i	0.620631	−	1.07496i
$917$		0			0
$918$		0			0
$919$	−7.19630	+	12.4644i	−0.237384	+	0.411161i	−0.959963	−	0.280127i	$-0.909623\pi$
$919$	−7.19630	+	12.4644i	−0.237384	+	0.411161i	0.722579	+	0.691289i	$0.242957\pi$
$920$	6.24377			0.205851
$921$		0			0
$922$	−5.39261			−0.177596
$923$	4.30150	+	7.45043i	0.141586	+	0.245234i
$924$		0			0
$925$	−17.1969	+	29.7858i	−0.565429	+	0.979352i
$926$	−1.24308	+	2.15308i	−0.0408502	+	0.0707546i
$927$		0			0
$928$	0.330095	+	0.571741i	0.0108359	+	0.0187683i
$929$	−20.8714	−	36.1503i	−0.684769	−	1.18605i	−0.973509	−	0.228647i	$-0.926570\pi$
$929$	−20.8714	−	36.1503i	−0.684769	−	1.18605i	0.288741	−	0.957407i	$-0.406763\pi$
$930$		0			0
$931$		0			0
$932$	16.4951	+	28.5703i	0.540315	+	0.935853i
$933$		0			0
$934$	−3.18443			−0.104198
$935$	15.1963	+	26.3208i	0.496972	+	0.860781i
$936$		0			0
$937$	3.17154			0.103610			0.0518048	−	0.998657i	$-0.483503\pi$
$937$	3.17154			0.103610			0.0518048	+	0.998657i	$0.483503\pi$
$938$		0			0
$939$		0			0
$940$	−13.3839			−0.436535
$941$	−1.61040	+	2.78930i	−0.0524976	+	0.0909285i	−0.891080	−	0.453846i	$-0.850052\pi$
$941$	−1.61040	+	2.78930i	−0.0524976	+	0.0909285i	0.838582	+	0.544775i	$0.183385\pi$
$942$		0			0
$943$	−28.5248	−	49.4063i	−0.928894	−	1.60889i
$944$	−9.52751			−0.310094
$945$		0			0
$946$	1.97095			0.0640810
$947$	−22.6735	−	39.2716i	−0.736789	−	1.27616i	−0.953934	−	0.300016i	$-0.903008\pi$
$947$	−22.6735	−	39.2716i	−0.736789	−	1.27616i	0.217145	−	0.976139i	$-0.430325\pi$
$948$		0			0
$949$	−7.57442	+	13.1193i	−0.245876	+	0.425870i
$950$	−1.67386			−0.0543073
$951$		0			0
$952$		0			0
$953$	54.2703			1.75799			0.878994	−	0.476832i	$-0.158215\pi$
$953$	54.2703			1.75799			0.878994	+	0.476832i	$0.158215\pi$
$954$		0			0
$955$	−8.90451	−	15.4231i	−0.288143	−	0.499079i
$956$	32.8058			1.06101
$957$		0			0
$958$	1.73788	+	3.01010i	0.0561483	+	0.0972518i
$959$		0			0
$960$		0			0
$961$	14.1219	+	24.4598i	0.455545	+	0.789027i
$962$	1.14132	+	1.97682i	0.0367975	+	0.0637351i
$963$		0			0
$964$	26.3695	−	45.6733i	0.849304	−	1.47104i
$965$	−4.63788	+	8.03305i	−0.149299	+	0.258593i
$966$		0			0
$967$	−12.8295	−	22.2214i	−0.412570	−	0.714593i	0.582600	−	0.812759i	$-0.302036\pi$
$967$	−12.8295	−	22.2214i	−0.412570	−	0.714593i	−0.995170	+	0.0981667i	$0.968702\pi$
$968$	−2.56199			−0.0823455
$969$		0			0
$970$	−2.02597			−0.0650500
$971$	−10.5092	+	18.2024i	−0.337255	+	0.584143i	−0.983915	−	0.178635i	$-0.942832\pi$
$971$	−10.5092	+	18.2024i	−0.337255	+	0.584143i	0.646660	+	0.762778i	$0.276165\pi$
$972$		0			0
$973$		0			0
$974$	−1.56075	+	2.70329i	−0.0500096	+	0.0866191i
$975$		0			0
$976$	13.9142	−	24.1002i	0.445384	−	0.771427i
$977$	−1.04910	+	1.81709i	−0.0335637	+	0.0581340i	−0.882319	−	0.470651i	$-0.844019\pi$
$977$	−1.04910	+	1.81709i	−0.0335637	+	0.0581340i	0.848756	+	0.528785i	$0.177352\pi$
$978$		0			0
$979$	5.08740	−	8.81164i	0.162594	−	0.281621i
$980$		0			0
$981$		0			0
$982$	2.31285	−	4.00598i	0.0738062	−	0.127836i
$983$	−42.9923			−1.37124			−0.685622	−	0.727958i	$-0.740469\pi$
$983$	−42.9923			−1.37124			−0.685622	+	0.727958i	$0.740469\pi$
$984$		0			0
$985$	7.90723			0.251945
$986$	0.198495	+	0.343803i	0.00632137	+	0.0109489i
$987$		0			0
$988$	1.88727	−	3.26886i	0.0600422	−	0.103996i
$989$	−6.23461	+	10.7987i	−0.198249	+	0.343377i
$990$		0			0
$991$	8.63160	+	14.9504i	0.274192	+	0.474914i	0.969931	−	0.243380i	$-0.0782564\pi$
$991$	8.63160	+	14.9504i	0.274192	+	0.474914i	−0.695739	+	0.718295i	$0.744923\pi$
$992$	−2.29179	−	3.96950i	−0.0727644	−	0.126032i
$993$		0			0
$994$		0			0
$995$	−11.7837	−	20.4100i	−0.373569	−	0.647040i
$996$		0			0
$997$	−38.9018			−1.23203			−0.616016	−	0.787733i	$-0.711254\pi$
$997$	−38.9018			−1.23203			−0.616016	+	0.787733i	$0.711254\pi$
$998$	4.33078	+	7.50114i	0.137089	+	0.237444i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.g.c.667.2		6
3.2	odd	2		441.2.g.e.79.2		6
7.2	even	3		189.2.f.a.127.2		6
7.3	odd	6		1323.2.h.e.802.2		6
7.4	even	3		1323.2.h.d.802.2		6
7.5	odd	6		1323.2.f.c.883.2		6
7.6	odd	2		1323.2.g.b.667.2		6
9.4	even	3		1323.2.h.d.226.2		6
9.5	odd	6		441.2.h.c.373.2		6
21.2	odd	6		63.2.f.b.43.2	yes	6
21.5	even	6		441.2.f.d.295.2		6
21.11	odd	6		441.2.h.c.214.2		6
21.17	even	6		441.2.h.b.214.2		6
21.20	even	2		441.2.g.d.79.2		6
28.23	odd	6		3024.2.r.g.2017.3		6
63.2	odd	6		567.2.a.d.1.2		3
63.4	even	3	inner	1323.2.g.c.361.2		6
63.5	even	6		441.2.f.d.148.2		6
63.13	odd	6		1323.2.h.e.226.2		6
63.16	even	3		567.2.a.g.1.2		3
63.23	odd	6		63.2.f.b.22.2	✓	6
63.31	odd	6		1323.2.g.b.361.2		6
63.32	odd	6		441.2.g.e.67.2		6
63.40	odd	6		1323.2.f.c.442.2		6
63.41	even	6		441.2.h.b.373.2		6
63.47	even	6		3969.2.a.m.1.2		3
63.58	even	3		189.2.f.a.64.2		6
63.59	even	6		441.2.g.d.67.2		6
63.61	odd	6		3969.2.a.p.1.2		3
84.23	even	6		1008.2.r.k.673.2		6
252.23	even	6		1008.2.r.k.337.2		6
252.79	odd	6		9072.2.a.cd.1.1		3
252.191	even	6		9072.2.a.bq.1.3		3
252.247	odd	6		3024.2.r.g.1009.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.2	✓	6	63.23	odd	6
63.2.f.b.43.2	yes	6	21.2	odd	6
189.2.f.a.64.2		6	63.58	even	3
189.2.f.a.127.2		6	7.2	even	3
441.2.f.d.148.2		6	63.5	even	6
441.2.f.d.295.2		6	21.5	even	6
441.2.g.d.67.2		6	63.59	even	6
441.2.g.d.79.2		6	21.20	even	2
441.2.g.e.67.2		6	63.32	odd	6
441.2.g.e.79.2		6	3.2	odd	2
441.2.h.b.214.2		6	21.17	even	6
441.2.h.b.373.2		6	63.41	even	6
441.2.h.c.214.2		6	21.11	odd	6
441.2.h.c.373.2		6	9.5	odd	6
567.2.a.d.1.2		3	63.2	odd	6
567.2.a.g.1.2		3	63.16	even	3
1008.2.r.k.337.2		6	252.23	even	6
1008.2.r.k.673.2		6	84.23	even	6
1323.2.f.c.442.2		6	63.40	odd	6
1323.2.f.c.883.2		6	7.5	odd	6
1323.2.g.b.361.2		6	63.31	odd	6
1323.2.g.b.667.2		6	7.6	odd	2
1323.2.g.c.361.2		6	63.4	even	3	inner
1323.2.g.c.667.2		6	1.1	even	1	trivial
1323.2.h.d.226.2		6	9.4	even	3
1323.2.h.d.802.2		6	7.4	even	3
1323.2.h.e.226.2		6	63.13	odd	6
1323.2.h.e.802.2		6	7.3	odd	6
3024.2.r.g.1009.3		6	252.247	odd	6
3024.2.r.g.2017.3		6	28.23	odd	6
3969.2.a.m.1.2		3	63.47	even	6
3969.2.a.p.1.2		3	63.61	odd	6
9072.2.a.bq.1.3		3	252.191	even	6
9072.2.a.cd.1.1		3	252.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.119562 - 0.207087i) q^{2} +(0.971410 - 1.68253i) q^{4} -1.18194 q^{5} -0.942820 q^{8} +O(q^{10})\)	\(q+(-0.119562 - 0.207087i) q^{2} +(0.971410 - 1.68253i) q^{4} -1.18194 q^{5} -0.942820 q^{8} +(0.141315 + 0.244765i) q^{10} +3.70370 q^{11} +(-0.500000 - 0.866025i) q^{13} +(-1.83009 - 3.16982i) q^{16} +(-3.47141 - 6.01266i) q^{17} +(-0.971410 + 1.68253i) q^{19} +(-1.14815 + 1.98866i) q^{20} +(-0.442820 - 0.766987i) q^{22} +5.60301 q^{23} -3.60301 q^{25} +(-0.119562 + 0.207087i) q^{26} +(0.119562 - 0.207087i) q^{29} +(-0.830095 + 1.43777i) q^{31} +(-1.38044 + 2.39099i) q^{32} +(-0.830095 + 1.43777i) q^{34} +(4.77292 - 8.26693i) q^{37} +0.464574 q^{38} +1.11436 q^{40} +(-5.09097 - 8.81782i) q^{41} +(-1.11273 + 1.92730i) q^{43} +(3.59781 - 6.23159i) q^{44} +(-0.669905 - 1.16031i) q^{46} +(2.91423 + 5.04759i) q^{47} +(0.430782 + 0.746136i) q^{50} -1.94282 q^{52} +(-5.80150 - 10.0485i) q^{53} -4.37756 q^{55} -0.0571799 q^{58} +(1.30150 - 2.25427i) q^{59} +(3.80150 + 6.58440i) q^{61} +0.396990 q^{62} -6.66019 q^{64} +(0.590972 + 1.02359i) q^{65} +(-1.75404 + 3.03809i) q^{67} -13.4887 q^{68} -8.60301 q^{71} +(-7.57442 - 13.1193i) q^{73} -2.28263 q^{74} +(1.88727 + 3.26886i) q^{76} +(-3.68878 - 6.38915i) q^{79} +(2.16307 + 3.74654i) q^{80} +(-1.21737 + 2.10855i) q^{82} +(-3.47141 + 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} +0.532157 q^{86} -3.49192 q^{88} +(1.37360 - 2.37915i) q^{89} +(5.44282 - 9.42724i) q^{92} +(0.696860 - 1.20700i) q^{94} +(1.14815 - 1.98866i) q^{95} +(-3.58414 + 6.20790i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{4} + 10 q^{5} + 12 q^{8}+O(q^{10}) \) 6 * q - q^2 - 3 * q^4 + 10 * q^5 + 12 * q^8	\( 6 q - q^{2} - 3 q^{4} + 10 q^{5} + 12 q^{8} + 4 q^{11} - 3 q^{13} - 3 q^{16} - 12 q^{17} + 3 q^{19} - 16 q^{20} + 15 q^{22} + 12 q^{25} - q^{26} + q^{29} + 3 q^{31} - 8 q^{32} + 3 q^{34} + 3 q^{37} - 16 q^{38} + 42 q^{40} - 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} - 9 q^{47} + 10 q^{50} + 6 q^{52} - 18 q^{53} - 12 q^{55} - 18 q^{58} - 9 q^{59} + 6 q^{61} + 36 q^{62} - 24 q^{64} - 5 q^{65} - 12 q^{68} - 18 q^{71} - 3 q^{73} - 12 q^{74} + 21 q^{76} - 15 q^{79} + 11 q^{80} - 9 q^{82} - 12 q^{83} - 9 q^{85} - 68 q^{86} - 42 q^{88} - 2 q^{89} + 15 q^{92} - 24 q^{94} + 16 q^{95} - 3 q^{97}+O(q^{100}) \) 6 * q - q^2 - 3 * q^4 + 10 * q^5 + 12 * q^8 + 4 * q^11 - 3 * q^13 - 3 * q^16 - 12 * q^17 + 3 * q^19 - 16 * q^20 + 15 * q^22 + 12 * q^25 - q^26 + q^29 + 3 * q^31 - 8 * q^32 + 3 * q^34 + 3 * q^37 - 16 * q^38 + 42 * q^40 - 22 * q^41 + 3 * q^43 + 23 * q^44 - 12 * q^46 - 9 * q^47 + 10 * q^50 + 6 * q^52 - 18 * q^53 - 12 * q^55 - 18 * q^58 - 9 * q^59 + 6 * q^61 + 36 * q^62 - 24 * q^64 - 5 * q^65 - 12 * q^68 - 18 * q^71 - 3 * q^73 - 12 * q^74 + 21 * q^76 - 15 * q^79 + 11 * q^80 - 9 * q^82 - 12 * q^83 - 9 * q^85 - 68 * q^86 - 42 * q^88 - 2 * q^89 + 15 * q^92 - 24 * q^94 + 16 * q^95 - 3 * q^97

Introduction

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