LMFDB - Embedded newform 1350.2.q.c.557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(143,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("1350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.q (of order $12$, degree $4$, 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:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 450)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.557
Dual form			1350.2.q.c.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{8} +(-3.00000 + 1.73205i) q^{11} +(-0.896575 - 3.34607i) q^{13} +(0.500000 + 0.866025i) q^{16} +(4.24264 - 4.24264i) q^{17} +5.00000i q^{19} +(3.34607 - 0.896575i) q^{22} +(-5.79555 + 1.55291i) q^{23} +3.46410i q^{26} +(-3.46410 - 6.00000i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-5.19615 + 3.00000i) q^{34} +(-4.89898 - 4.89898i) q^{37} +(1.29410 - 4.82963i) q^{38} +(1.50000 + 0.866025i) q^{41} +(-11.7112 - 3.13801i) q^{43} -3.46410 q^{44} +6.00000 q^{46} +(5.79555 + 1.55291i) q^{47} +(6.06218 + 3.50000i) q^{49} +(0.896575 - 3.34607i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(1.79315 + 6.69213i) q^{58} +(0.866025 - 1.50000i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(2.82843 - 2.82843i) q^{62} +1.00000i q^{64} +(8.36516 - 2.24144i) q^{67} +(5.79555 - 1.55291i) q^{68} -6.92820i q^{71} +(-8.57321 + 8.57321i) q^{73} +(3.46410 + 6.00000i) q^{74} +(-2.50000 + 4.33013i) q^{76} +(-12.1244 + 7.00000i) q^{79} +(-1.22474 - 1.22474i) q^{82} +(2.32937 - 8.69333i) q^{83} +(10.5000 + 6.06218i) q^{86} +(3.34607 + 0.896575i) q^{88} -12.1244 q^{89} +(-5.79555 - 1.55291i) q^{92} +(-5.19615 - 3.00000i) q^{94} +(-1.34486 + 5.01910i) q^{97} +(-4.94975 - 4.94975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 24 q^{11} + 4 q^{16} - 16 q^{31} + 12 q^{41} + 48 q^{46} - 32 q^{61} - 20 q^{76} + 84 q^{86}+O(q^{100}) $ 8 * q - 24 * q^11 + 4 * q^16 - 16 * q^31 + 12 * q^41 + 48 * q^46 - 32 * q^61 - 20 * q^76 + 84 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$7$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.878668	−	0.477432i	$-0.841568\pi$
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.0258656	+	0.999665i	$0.508234\pi$
$12$		0			0
$13$	−0.896575	−	3.34607i	−0.248665	−	0.928032i	−0.971506	−	0.237016i	$-0.923830\pi$
$13$	−0.896575	−	3.34607i	−0.248665	−	0.928032i	0.722840	−	0.691015i	$-0.242836\pi$
$14$		0			0
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	4.24264	−	4.24264i	1.02899	−	1.02899i	0.0294245	−	0.999567i	$-0.490633\pi$
$17$	4.24264	−	4.24264i	1.02899	−	1.02899i	0.999567	−	0.0294245i	$-0.00936746\pi$
$18$		0			0
$19$			5.00000i			1.14708i	0.819178	+	0.573539i	$0.194430\pi$
$19$			5.00000i			1.14708i	−0.819178	+	0.573539i	$0.805570\pi$
$20$		0			0
$21$		0			0
$22$	3.34607	−	0.896575i	0.713384	−	0.191151i
$23$	−5.79555	+	1.55291i	−1.20846	+	0.323805i	−0.806156	−	0.591703i	$-0.798456\pi$
$23$	−5.79555	+	1.55291i	−1.20846	+	0.323805i	−0.402300	+	0.915508i	$0.631789\pi$
$24$		0			0
$25$		0			0
$26$			3.46410i			0.679366i
$27$		0			0
$28$		0			0
$29$	−3.46410	−	6.00000i	−0.643268	−	1.11417i	−0.984699	−	0.174265i	$-0.944245\pi$
$29$	−3.46410	−	6.00000i	−0.643268	−	1.11417i	0.341431	−	0.939907i	$-0.389088\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$		0			0
$34$	−5.19615	+	3.00000i	−0.891133	+	0.514496i
$35$		0			0
$36$		0			0
$37$	−4.89898	−	4.89898i	−0.805387	−	0.805387i	0.178545	−	0.983932i	$-0.442861\pi$
$37$	−4.89898	−	4.89898i	−0.805387	−	0.805387i	−0.983932	+	0.178545i	$0.942861\pi$
$38$	1.29410	−	4.82963i	0.209930	−	0.783469i
$39$		0			0
$40$		0			0
$41$	1.50000	+	0.866025i	0.234261	+	0.135250i	0.612536	−	0.790443i	$-0.290149\pi$
$41$	1.50000	+	0.866025i	0.234261	+	0.135250i	−0.378275	+	0.925693i	$0.623483\pi$
$42$		0			0
$43$	−11.7112	−	3.13801i	−1.78595	−	0.478543i	−0.794299	−	0.607527i	$-0.792162\pi$
$43$	−11.7112	−	3.13801i	−1.78595	−	0.478543i	−0.991647	+	0.128984i	$0.958828\pi$
$44$	−3.46410			−0.522233
$45$		0			0
$46$	6.00000			0.884652
$47$	5.79555	+	1.55291i	0.845369	+	0.226516i	0.655407	−	0.755276i	$-0.272497\pi$
$47$	5.79555	+	1.55291i	0.845369	+	0.226516i	0.189961	+	0.981792i	$0.439164\pi$
$48$		0			0
$49$	6.06218	+	3.50000i	0.866025	+	0.500000i
$50$		0			0
$51$		0			0
$52$	0.896575	−	3.34607i	0.124333	−	0.464016i
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	0.352892	−	0.935664i	$-0.385198\pi$
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	−0.935664	+	0.352892i	$0.885198\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	1.79315	+	6.69213i	0.235452	+	0.878720i
$59$	0.866025	−	1.50000i	0.112747	−	0.195283i	−0.804130	−	0.594454i	$-0.797368\pi$
$59$	0.866025	−	1.50000i	0.112747	−	0.195283i	0.916877	+	0.399170i	$0.130702\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	2.82843	−	2.82843i	0.359211	−	0.359211i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	8.36516	−	2.24144i	1.02197	−	0.273835i	0.291346	−	0.956618i	$-0.405897\pi$
$67$	8.36516	−	2.24144i	1.02197	−	0.273835i	0.730622	+	0.682783i	$0.239230\pi$
$68$	5.79555	−	1.55291i	0.702814	−	0.188319i
$69$		0			0
$70$		0			0
$71$		−	6.92820i		−	0.822226i	−0.911584	−	0.411113i	$-0.865140\pi$
$71$		−	6.92820i		−	0.822226i	0.911584	−	0.411113i	$-0.134860\pi$
$72$		0			0
$73$	−8.57321	+	8.57321i	−1.00342	+	1.00342i	−0.00342468	+	0.999994i	$0.501090\pi$
$73$	−8.57321	+	8.57321i	−1.00342	+	1.00342i	−0.999994	+	0.00342468i	$0.998910\pi$
$74$	3.46410	+	6.00000i	0.402694	+	0.697486i
$75$		0			0
$76$	−2.50000	+	4.33013i	−0.286770	+	0.496700i
$77$		0			0
$78$		0			0
$79$	−12.1244	+	7.00000i	−1.36410	+	0.787562i	−0.990166	−	0.139895i	$-0.955323\pi$
$79$	−12.1244	+	7.00000i	−1.36410	+	0.787562i	−0.373930	+	0.927457i	$0.621990\pi$
$80$		0			0
$81$		0			0
$82$	−1.22474	−	1.22474i	−0.135250	−	0.135250i
$83$	2.32937	−	8.69333i	0.255682	−	0.954217i	−0.712028	−	0.702151i	$-0.752223\pi$
$83$	2.32937	−	8.69333i	0.255682	−	0.954217i	0.967710	−	0.252066i	$-0.0811101\pi$
$84$		0			0
$85$		0			0
$86$	10.5000	+	6.06218i	1.13224	+	0.653701i
$87$		0			0
$88$	3.34607	+	0.896575i	0.356692	+	0.0955753i
$89$	−12.1244			−1.28518			−0.642590	−	0.766211i	$-0.722140\pi$
$89$	−12.1244			−1.28518			−0.642590	+	0.766211i	$0.722140\pi$
$90$		0			0
$91$		0			0
$92$	−5.79555	−	1.55291i	−0.604228	−	0.161903i
$93$		0			0
$94$	−5.19615	−	3.00000i	−0.535942	−	0.309426i
$95$		0			0
$96$		0			0
$97$	−1.34486	+	5.01910i	−0.136550	+	0.509612i	0.863437	+	0.504457i	$0.168307\pi$
$97$	−1.34486	+	5.01910i	−0.136550	+	0.509612i	−0.999987	+	0.00515471i	$0.998359\pi$
$98$	−4.94975	−	4.94975i	−0.500000	−	0.500000i
$99$		0			0
$100$		0			0
$101$	−3.00000	+	1.73205i	−0.298511	+	0.172345i	−0.641774	−	0.766894i	$-0.721801\pi$
$101$	−3.00000	+	1.73205i	−0.298511	+	0.172345i	0.343263	+	0.939239i	$0.388468\pi$
$102$		0			0
$103$	−0.896575	−	3.34607i	−0.0883422	−	0.329698i	0.907584	−	0.419871i	$-0.137925\pi$
$103$	−0.896575	−	3.34607i	−0.0883422	−	0.329698i	−0.995926	+	0.0901732i	$0.971258\pi$
$104$	−1.73205	+	3.00000i	−0.169842	+	0.294174i
$105$		0			0
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	2.12132	−	2.12132i	0.205076	−	0.205076i	−0.597095	−	0.802171i	$-0.703678\pi$
$107$	2.12132	−	2.12132i	0.205076	−	0.205076i	0.802171	+	0.597095i	$0.203678\pi$
$108$		0			0
$109$		−	20.0000i		−	1.91565i	−0.287348	−	0.957826i	$-0.592774\pi$
$109$		−	20.0000i		−	1.91565i	0.287348	−	0.957826i	$-0.407226\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−14.4889	+	3.88229i	−1.36300	+	0.365215i	−0.864917	−	0.501915i	$-0.832629\pi$
$113$	−14.4889	+	3.88229i	−1.36300	+	0.365215i	−0.498083	+	0.867129i	$0.665962\pi$
$114$		0			0
$115$		0			0
$116$		−	6.92820i		−	0.643268i
$117$		0			0
$118$	−1.22474	+	1.22474i	−0.112747	+	0.112747i
$119$		0			0
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	2.07055	+	7.72741i	0.187459	+	0.699607i
$123$		0			0
$124$	−3.46410	+	2.00000i	−0.311086	+	0.179605i
$125$		0			0
$126$		0			0
$127$	−7.34847	−	7.34847i	−0.652071	−	0.652071i	0.301420	−	0.953491i	$-0.402539\pi$
$127$	−7.34847	−	7.34847i	−0.652071	−	0.652071i	−0.953491	+	0.301420i	$0.902539\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$		0			0
$130$		0			0
$131$	−3.00000	−	1.73205i	−0.262111	−	0.151330i	0.363186	−	0.931717i	$-0.381689\pi$
$131$	−3.00000	−	1.73205i	−0.262111	−	0.151330i	−0.625297	+	0.780387i	$0.715022\pi$
$132$		0			0
$133$		0			0
$134$	−8.66025			−0.748132
$135$		0			0
$136$	−6.00000			−0.514496
$137$	−8.69333	−	2.32937i	−0.742722	−	0.199012i	−0.132434	−	0.991192i	$-0.542279\pi$
$137$	−8.69333	−	2.32937i	−0.742722	−	0.199012i	−0.610287	+	0.792180i	$0.708946\pi$
$138$		0			0
$139$	3.46410	+	2.00000i	0.293821	+	0.169638i	0.639664	−	0.768655i	$-0.279074\pi$
$139$	3.46410	+	2.00000i	0.293821	+	0.169638i	−0.345843	+	0.938293i	$0.612407\pi$
$140$		0			0
$141$		0			0
$142$	−1.79315	+	6.69213i	−0.150478	+	0.561591i
$143$	8.48528	+	8.48528i	0.709575	+	0.709575i
$144$		0			0
$145$		0			0
$146$	10.5000	−	6.06218i	0.868986	−	0.501709i
$147$		0			0
$148$	−1.79315	−	6.69213i	−0.147396	−	0.550090i
$149$	−5.19615	+	9.00000i	−0.425685	+	0.737309i	−0.996484	−	0.0837813i	$-0.973300\pi$
$149$	−5.19615	+	9.00000i	−0.425685	+	0.737309i	0.570799	+	0.821090i	$0.306634\pi$
$150$		0			0
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	−0.982873	−	0.184284i	$-0.941004\pi$
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	0.331842	−	0.943335i	$-0.392330\pi$
$152$	3.53553	−	3.53553i	0.286770	−	0.286770i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.34607	+	0.896575i	−0.267045	+	0.0715545i	−0.389857	−	0.920875i	$-0.627476\pi$
$157$	−3.34607	+	0.896575i	−0.267045	+	0.0715545i	0.122812	+	0.992430i	$0.460809\pi$
$158$	13.5230	−	3.62347i	1.07583	−	0.288268i
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.22474	+	1.22474i	−0.0959294	+	0.0959294i	−0.753443	−	0.657513i	$-0.771608\pi$
$163$	−1.22474	+	1.22474i	−0.0959294	+	0.0959294i	0.657513	+	0.753443i	$0.271608\pi$
$164$	0.866025	+	1.50000i	0.0676252	+	0.117130i
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	3.10583	+	11.5911i	0.240336	+	0.896947i	0.975670	+	0.219242i	$0.0703585\pi$
$167$	3.10583	+	11.5911i	0.240336	+	0.896947i	−0.735334	+	0.677705i	$0.762975\pi$
$168$		0			0
$169$	0.866025	−	0.500000i	0.0666173	−	0.0384615i
$170$		0			0
$171$		0			0
$172$	−8.57321	−	8.57321i	−0.653701	−	0.653701i
$173$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$173$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$174$		0			0
$175$		0			0
$176$	−3.00000	−	1.73205i	−0.226134	−	0.130558i
$177$		0			0
$178$	11.7112	+	3.13801i	0.877794	+	0.235204i
$179$	22.5167			1.68297			0.841487	−	0.540277i	$-0.181681\pi$
$179$	22.5167			1.68297			0.841487	+	0.540277i	$0.181681\pi$
$180$		0			0
$181$	16.0000			1.18927			0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000			1.18927			0.594635	+	0.803996i	$0.297296\pi$
$182$		0			0
$183$		0			0
$184$	5.19615	+	3.00000i	0.383065	+	0.221163i
$185$		0			0
$186$		0			0
$187$	−5.37945	+	20.0764i	−0.393385	+	1.46813i
$188$	4.24264	+	4.24264i	0.309426	+	0.309426i
$189$		0			0
$190$		0			0
$191$	−21.0000	+	12.1244i	−1.51951	+	0.877288i	−0.519771	+	0.854306i	$0.673983\pi$
$191$	−21.0000	+	12.1244i	−1.51951	+	0.877288i	−0.999736	+	0.0229818i	$0.992684\pi$
$192$		0			0
$193$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$193$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$194$	2.59808	−	4.50000i	0.186531	−	0.323081i
$195$		0			0
$196$	3.50000	+	6.06218i	0.250000	+	0.433013i
$197$	−16.9706	+	16.9706i	−1.20910	+	1.20910i	−0.237785	+	0.971318i	$0.576421\pi$
$197$	−16.9706	+	16.9706i	−1.20910	+	1.20910i	−0.971318	+	0.237785i	$0.923579\pi$
$198$		0			0
$199$		−	8.00000i		−	0.567105i	−0.958957	−	0.283552i	$-0.908487\pi$
$199$		−	8.00000i		−	0.567105i	0.958957	−	0.283552i	$-0.0915130\pi$
$200$		0			0
$201$		0			0
$202$	3.34607	−	0.896575i	0.235428	−	0.0630828i
$203$		0			0
$204$		0			0
$205$		0			0
$206$			3.46410i			0.241355i
$207$		0			0
$208$	2.44949	−	2.44949i	0.169842	−	0.169842i
$209$	−8.66025	−	15.0000i	−0.599042	−	1.03757i
$210$		0			0
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	0.998221	+	0.0596196i	$0.0189888\pi$
$212$	−1.55291	−	5.79555i	−0.106655	−	0.398040i
$213$		0			0
$214$	−2.59808	+	1.50000i	−0.177601	+	0.102538i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−5.17638	+	19.3185i	−0.350589	+	1.30842i
$219$		0			0
$220$		0			0
$221$	−18.0000	−	10.3923i	−1.21081	−	0.699062i
$222$		0			0
$223$	6.69213	+	1.79315i	0.448138	+	0.120078i	0.475828	−	0.879538i	$-0.342148\pi$
$223$	6.69213	+	1.79315i	0.448138	+	0.120078i	−0.0276899	+	0.999617i	$0.508815\pi$
$224$		0			0
$225$		0			0
$226$	15.0000			0.997785
$227$	−2.89778	−	0.776457i	−0.192332	−	0.0515353i	0.161367	−	0.986894i	$-0.448410\pi$
$227$	−2.89778	−	0.776457i	−0.192332	−	0.0515353i	−0.353699	+	0.935359i	$0.615076\pi$
$228$		0			0
$229$	13.8564	+	8.00000i	0.915657	+	0.528655i	0.882247	−	0.470787i	$-0.156030\pi$
$229$	13.8564	+	8.00000i	0.915657	+	0.528655i	0.0334101	+	0.999442i	$0.489363\pi$
$230$		0			0
$231$		0			0
$232$	−1.79315	+	6.69213i	−0.117726	+	0.439360i
$233$	6.36396	+	6.36396i	0.416917	+	0.416917i	0.884140	−	0.467223i	$-0.154745\pi$
$233$	6.36396	+	6.36396i	0.416917	+	0.416917i	−0.467223	+	0.884140i	$0.654745\pi$
$234$		0			0
$235$		0			0
$236$	1.50000	−	0.866025i	0.0976417	−	0.0563735i
$237$		0			0
$238$		0			0
$239$	5.19615	−	9.00000i	0.336111	−	0.582162i	−0.647586	−	0.761992i	$-0.724222\pi$
$239$	5.19615	−	9.00000i	0.336111	−	0.582162i	0.983698	+	0.179830i	$0.0575549\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$	−0.707107	+	0.707107i	−0.0454545	+	0.0454545i
$243$		0			0
$244$		−	8.00000i		−	0.512148i
$245$		0			0
$246$		0			0
$247$	16.7303	−	4.48288i	1.06453	−	0.285239i
$248$	3.86370	−	1.03528i	0.245345	−	0.0657401i
$249$		0			0
$250$		0			0
$251$			5.19615i			0.327978i	0.986462	+	0.163989i	$0.0524362\pi$
$251$			5.19615i			0.327978i	−0.986462	+	0.163989i	$0.947564\pi$
$252$		0			0
$253$	14.6969	−	14.6969i	0.923989	−	0.923989i
$254$	5.19615	+	9.00000i	0.326036	+	0.564710i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.88229	−	14.4889i	−0.242170	−	0.903792i	−0.974785	−	0.223148i	$-0.928367\pi$
$257$	−3.88229	−	14.4889i	−0.242170	−	0.903792i	0.732614	−	0.680644i	$-0.238300\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	2.44949	+	2.44949i	0.151330	+	0.151330i
$263$	−3.10583	+	11.5911i	−0.191514	+	0.714738i	0.801628	+	0.597823i	$0.203967\pi$
$263$	−3.10583	+	11.5911i	−0.191514	+	0.714738i	−0.993142	+	0.116916i	$0.962699\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	8.36516	+	2.24144i	0.510984	+	0.136918i
$269$	13.8564			0.844840			0.422420	−	0.906400i	$-0.361181\pi$
$269$	13.8564			0.844840			0.422420	+	0.906400i	$0.361181\pi$
$270$		0			0
$271$	−10.0000			−0.607457			−0.303728	−	0.952759i	$-0.598232\pi$
$271$	−10.0000			−0.607457			−0.303728	+	0.952759i	$0.598232\pi$
$272$	5.79555	+	1.55291i	0.351407	+	0.0941593i
$273$		0			0
$274$	7.79423	+	4.50000i	0.470867	+	0.271855i
$275$		0			0
$276$		0			0
$277$	1.79315	−	6.69213i	0.107740	−	0.402091i	−0.890902	−	0.454196i	$-0.849926\pi$
$277$	1.79315	−	6.69213i	0.107740	−	0.402091i	0.998642	+	0.0521052i	$0.0165931\pi$
$278$	−2.82843	−	2.82843i	−0.169638	−	0.169638i
$279$		0			0
$280$		0			0
$281$	18.0000	−	10.3923i	1.07379	−	0.619953i	0.144575	−	0.989494i	$-0.453818\pi$
$281$	18.0000	−	10.3923i	1.07379	−	0.619953i	0.929214	+	0.369541i	$0.120485\pi$
$282$		0			0
$283$	−3.13801	−	11.7112i	−0.186536	−	0.696160i	−0.994297	−	0.106650i	$-0.965988\pi$
$283$	−3.13801	−	11.7112i	−0.186536	−	0.696160i	0.807761	−	0.589510i	$-0.200679\pi$
$284$	3.46410	−	6.00000i	0.205557	−	0.356034i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.354787	−	0.614510i
$287$		0			0
$288$		0			0
$289$		−	19.0000i		−	1.11765i
$290$		0			0
$291$		0			0
$292$	−11.7112	+	3.13801i	−0.685348	+	0.183638i
$293$	−5.79555	+	1.55291i	−0.338580	+	0.0907222i	−0.424103	−	0.905614i	$-0.639411\pi$
$293$	−5.79555	+	1.55291i	−0.338580	+	0.0907222i	0.0855230	+	0.996336i	$0.472744\pi$
$294$		0			0
$295$		0			0
$296$			6.92820i			0.402694i
$297$		0			0
$298$	7.34847	−	7.34847i	0.425685	−	0.425685i
$299$	10.3923	+	18.0000i	0.601003	+	1.04097i
$300$		0			0
$301$		0			0
$302$	4.14110	+	15.4548i	0.238294	+	0.889325i
$303$		0			0
$304$	−4.33013	+	2.50000i	−0.248350	+	0.143385i
$305$		0			0
$306$		0			0
$307$	17.1464	+	17.1464i	0.978598	+	0.978598i	0.999776	−	0.0211774i	$-0.00674148\pi$
$307$	17.1464	+	17.1464i	0.978598	+	0.978598i	−0.0211774	+	0.999776i	$0.506741\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	21.0000	+	12.1244i	1.19080	+	0.687509i	0.958488	−	0.285132i	$-0.0920375\pi$
$311$	21.0000	+	12.1244i	1.19080	+	0.687509i	0.232313	+	0.972641i	$0.425371\pi$
$312$		0			0
$313$	31.7876	+	8.51747i	1.79674	+	0.481436i	0.993462	−	0.114165i	$-0.0364192\pi$
$313$	31.7876	+	8.51747i	1.79674	+	0.481436i	0.803281	+	0.595601i	$0.203086\pi$
$314$	3.46410			0.195491
$315$		0			0
$316$	−14.0000			−0.787562
$317$	11.5911	+	3.10583i	0.651022	+	0.174441i	0.569191	−	0.822206i	$-0.307257\pi$
$317$	11.5911	+	3.10583i	0.651022	+	0.174441i	0.0818309	+	0.996646i	$0.473923\pi$
$318$		0			0
$319$	20.7846	+	12.0000i	1.16371	+	0.671871i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	21.2132	+	21.2132i	1.18033	+	1.18033i
$324$		0			0
$325$		0			0
$326$	1.50000	−	0.866025i	0.0830773	−	0.0479647i
$327$		0			0
$328$	−0.448288	−	1.67303i	−0.0247525	−	0.0923778i
$329$		0			0
$330$		0			0
$331$	0.500000	+	0.866025i	0.0274825	+	0.0476011i	0.879440	−	0.476011i	$-0.157918\pi$
$331$	0.500000	+	0.866025i	0.0274825	+	0.0476011i	−0.851957	+	0.523612i	$0.824584\pi$
$332$	6.36396	−	6.36396i	0.349268	−	0.349268i
$333$		0			0
$334$		−	12.0000i		−	0.656611i
$335$		0			0
$336$		0			0
$337$	6.69213	−	1.79315i	0.364544	−	0.0976792i	−0.0718974	−	0.997412i	$-0.522905\pi$
$337$	6.69213	−	1.79315i	0.364544	−	0.0976792i	0.436441	+	0.899733i	$0.356239\pi$
$338$	−0.965926	+	0.258819i	−0.0525394	+	0.0140779i
$339$		0			0
$340$		0			0
$341$		−	13.8564i		−	0.750366i
$342$		0			0
$343$		0			0
$344$	6.06218	+	10.5000i	0.326851	+	0.566122i
$345$		0			0
$346$		0			0
$347$	−3.10583	−	11.5911i	−0.166730	−	0.622243i	−0.997813	−	0.0660960i	$-0.978946\pi$
$347$	−3.10583	−	11.5911i	−0.166730	−	0.622243i	0.831084	−	0.556147i	$-0.187721\pi$
$348$		0			0
$349$	22.5167	−	13.0000i	1.20529	−	0.695874i	0.243563	−	0.969885i	$-0.421684\pi$
$349$	22.5167	−	13.0000i	1.20529	−	0.695874i	0.961727	+	0.274011i	$0.0883505\pi$
$350$		0			0
$351$		0			0
$352$	2.44949	+	2.44949i	0.130558	+	0.130558i
$353$	−2.32937	+	8.69333i	−0.123980	+	0.462699i	−0.999801	−	0.0199361i	$-0.993654\pi$
$353$	−2.32937	+	8.69333i	−0.123980	+	0.462699i	0.875821	+	0.482635i	$0.160320\pi$
$354$		0			0
$355$		0			0
$356$	−10.5000	−	6.06218i	−0.556499	−	0.321295i
$357$		0			0
$358$	−21.7494	−	5.82774i	−1.14949	−	0.308006i
$359$	27.7128			1.46263			0.731313	−	0.682042i	$-0.238908\pi$
$359$	27.7128			1.46263			0.731313	+	0.682042i	$0.238908\pi$
$360$		0			0
$361$	−6.00000			−0.315789
$362$	−15.4548	−	4.14110i	−0.812287	−	0.217652i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−4.48288	+	16.7303i	−0.234004	+	0.873316i	0.744591	+	0.667521i	$0.232645\pi$
$367$	−4.48288	+	16.7303i	−0.234004	+	0.873316i	−0.978595	+	0.205795i	$0.934022\pi$
$368$	−4.24264	−	4.24264i	−0.221163	−	0.221163i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	5.37945	+	20.0764i	0.278538	+	1.03952i	0.953434	+	0.301603i	$0.0975218\pi$
$373$	5.37945	+	20.0764i	0.278538	+	1.03952i	−0.674896	+	0.737913i	$0.735812\pi$
$374$	10.3923	−	18.0000i	0.537373	−	0.930758i
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	−16.9706	+	16.9706i	−0.874028	+	0.874028i
$378$		0			0
$379$			8.00000i			0.410932i	0.978664	+	0.205466i	$0.0658711\pi$
$379$			8.00000i			0.410932i	−0.978664	+	0.205466i	$0.934129\pi$
$380$		0			0
$381$		0			0
$382$	23.4225	−	6.27603i	1.19840	−	0.321110i
$383$	5.79555	−	1.55291i	0.296139	−	0.0793502i	−0.107691	−	0.994184i	$-0.534346\pi$
$383$	5.79555	−	1.55291i	0.296139	−	0.0793502i	0.403830	+	0.914834i	$0.367679\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−3.67423	+	3.67423i	−0.186531	+	0.186531i
$389$	−5.19615	−	9.00000i	−0.263455	−	0.456318i	0.703702	−	0.710495i	$-0.251529\pi$
$389$	−5.19615	−	9.00000i	−0.263455	−	0.456318i	−0.967158	+	0.254177i	$0.918196\pi$
$390$		0			0
$391$	−18.0000	+	31.1769i	−0.910299	+	1.57668i
$392$	−1.81173	−	6.76148i	−0.0915064	−	0.341506i
$393$		0			0
$394$	20.7846	−	12.0000i	1.04711	−	0.604551i
$395$		0			0
$396$		0			0
$397$	−17.1464	−	17.1464i	−0.860555	−	0.860555i	0.130848	−	0.991402i	$-0.458230\pi$
$397$	−17.1464	−	17.1464i	−0.860555	−	0.860555i	−0.991402	+	0.130848i	$0.958230\pi$
$398$	−2.07055	+	7.72741i	−0.103787	+	0.387340i
$399$		0			0
$400$		0			0
$401$	18.0000	+	10.3923i	0.898877	+	0.518967i	0.876836	−	0.480790i	$-0.159650\pi$
$401$	18.0000	+	10.3923i	0.898877	+	0.518967i	0.0220414	+	0.999757i	$0.492983\pi$
$402$		0			0
$403$	13.3843	+	3.58630i	0.666718	+	0.178646i
$404$	−3.46410			−0.172345
$405$		0			0
$406$		0			0
$407$	23.1822	+	6.21166i	1.14910	+	0.307900i
$408$		0			0
$409$	−25.1147	−	14.5000i	−1.24184	−	0.716979i	−0.272374	−	0.962191i	$-0.587809\pi$
$409$	−25.1147	−	14.5000i	−1.24184	−	0.716979i	−0.969469	+	0.245212i	$0.921142\pi$
$410$		0			0
$411$		0			0
$412$	0.896575	−	3.34607i	0.0441711	−	0.164849i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−3.00000	+	1.73205i	−0.147087	+	0.0849208i
$417$		0			0
$418$	4.48288	+	16.7303i	0.219265	+	0.818307i
$419$	−12.9904	+	22.5000i	−0.634622	+	1.09920i	0.351974	+	0.936010i	$0.385511\pi$
$419$	−12.9904	+	22.5000i	−0.634622	+	1.09920i	−0.986595	+	0.163187i	$0.947823\pi$
$420$		0			0
$421$	4.00000	+	6.92820i	0.194948	+	0.337660i	0.946883	−	0.321577i	$-0.104213\pi$
$421$	4.00000	+	6.92820i	0.194948	+	0.337660i	−0.751935	+	0.659237i	$0.770879\pi$
$422$	−9.19239	+	9.19239i	−0.447478	+	0.447478i
$423$		0			0
$424$			6.00000i			0.291386i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	2.89778	−	0.776457i	0.140069	−	0.0375315i
$429$		0			0
$430$		0			0
$431$			13.8564i			0.667440i	0.942672	+	0.333720i	$0.108304\pi$
$431$			13.8564i			0.667440i	−0.942672	+	0.333720i	$0.891696\pi$
$432$		0			0
$433$	−4.89898	+	4.89898i	−0.235430	+	0.235430i	−0.814955	−	0.579525i	$-0.803238\pi$
$433$	−4.89898	+	4.89898i	−0.235430	+	0.235430i	0.579525	+	0.814955i	$0.303238\pi$
$434$		0			0
$435$		0			0
$436$	10.0000	−	17.3205i	0.478913	−	0.829502i
$437$	−7.76457	−	28.9778i	−0.371430	−	1.38619i
$438$		0			0
$439$	−22.5167	+	13.0000i	−1.07466	+	0.620456i	−0.929451	−	0.368945i	$-0.879719\pi$
$439$	−22.5167	+	13.0000i	−1.07466	+	0.620456i	−0.145210	+	0.989401i	$0.546386\pi$
$440$		0			0
$441$		0			0
$442$	14.6969	+	14.6969i	0.699062	+	0.699062i
$443$	9.31749	−	34.7733i	0.442687	−	1.65213i	−0.279285	−	0.960208i	$-0.590097\pi$
$443$	9.31749	−	34.7733i	0.442687	−	1.65213i	0.721972	−	0.691922i	$-0.243236\pi$
$444$		0			0
$445$		0			0
$446$	−6.00000	−	3.46410i	−0.284108	−	0.164030i
$447$		0			0
$448$		0			0
$449$	8.66025			0.408703			0.204351	−	0.978898i	$-0.434492\pi$
$449$	8.66025			0.408703			0.204351	+	0.978898i	$0.434492\pi$
$450$		0			0
$451$	−6.00000			−0.282529
$452$	−14.4889	−	3.88229i	−0.681500	−	0.182607i
$453$		0			0
$454$	2.59808	+	1.50000i	0.121934	+	0.0703985i
$455$		0			0
$456$		0			0
$457$	−1.34486	+	5.01910i	−0.0629100	+	0.234783i	−0.990221	−	0.139509i	$-0.955448\pi$
$457$	−1.34486	+	5.01910i	−0.0629100	+	0.234783i	0.927311	+	0.374292i	$0.122114\pi$
$458$	−11.3137	−	11.3137i	−0.528655	−	0.528655i
$459$		0			0
$460$		0			0
$461$	30.0000	−	17.3205i	1.39724	−	0.806696i	0.403137	−	0.915140i	$-0.367920\pi$
$461$	30.0000	−	17.3205i	1.39724	−	0.806696i	0.994103	+	0.108443i	$0.0345866\pi$
$462$		0			0
$463$	−1.79315	−	6.69213i	−0.0833348	−	0.311010i	0.911659	−	0.410948i	$-0.134802\pi$
$463$	−1.79315	−	6.69213i	−0.0833348	−	0.311010i	−0.994994	+	0.0999382i	$0.968136\pi$
$464$	3.46410	−	6.00000i	0.160817	−	0.278543i
$465$		0			0
$466$	−4.50000	−	7.79423i	−0.208458	−	0.361061i
$467$	14.8492	−	14.8492i	0.687141	−	0.687141i	−0.274458	−	0.961599i	$-0.588498\pi$
$467$	14.8492	−	14.8492i	0.687141	−	0.687141i	0.961599	+	0.274458i	$0.0884985\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.67303	+	0.448288i	−0.0770076	+	0.0206341i
$473$	40.5689	−	10.8704i	1.86536	−	0.499822i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−7.34847	+	7.34847i	−0.336111	+	0.336111i
$479$	8.66025	+	15.0000i	0.395697	+	0.685367i	0.993190	−	0.116507i	$-0.0371697\pi$
$479$	8.66025	+	15.0000i	0.395697	+	0.685367i	−0.597493	+	0.801874i	$0.703836\pi$
$480$		0			0
$481$	−12.0000	+	20.7846i	−0.547153	+	0.947697i
$482$	−0.258819	−	0.965926i	−0.0117889	−	0.0439967i
$483$		0			0
$484$	0.866025	−	0.500000i	0.0393648	−	0.0227273i
$485$		0			0
$486$		0			0
$487$	4.89898	+	4.89898i	0.221994	+	0.221994i	0.809338	−	0.587344i	$-0.199826\pi$
$487$	4.89898	+	4.89898i	0.221994	+	0.221994i	−0.587344	+	0.809338i	$0.699826\pi$
$488$	−2.07055	+	7.72741i	−0.0937295	+	0.349803i
$489$		0			0
$490$		0			0
$491$	−25.5000	−	14.7224i	−1.15080	−	0.664414i	−0.201717	−	0.979444i	$-0.564652\pi$
$491$	−25.5000	−	14.7224i	−1.15080	−	0.664414i	−0.949082	+	0.315030i	$0.897985\pi$
$492$		0			0
$493$	−40.1528	−	10.7589i	−1.80839	−	0.484557i
$494$	−17.3205			−0.779287
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	−11.2583	−	6.50000i	−0.503992	−	0.290980i	0.226369	−	0.974042i	$-0.427315\pi$
$499$	−11.2583	−	6.50000i	−0.503992	−	0.290980i	−0.730361	+	0.683062i	$0.760648\pi$
$500$		0			0
$501$		0			0
$502$	1.34486	−	5.01910i	0.0600242	−	0.224013i
$503$	−29.6985	−	29.6985i	−1.32419	−	1.32419i	−0.910349	−	0.413841i	$-0.864187\pi$
$503$	−29.6985	−	29.6985i	−1.32419	−	1.32419i	−0.413841	−	0.910349i	$-0.635813\pi$
$504$		0			0
$505$		0			0
$506$	−18.0000	+	10.3923i	−0.800198	+	0.461994i
$507$		0			0
$508$	−2.68973	−	10.0382i	−0.119337	−	0.445373i
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			15.0000i			0.661622i
$515$		0			0
$516$		0			0
$517$	−20.0764	+	5.37945i	−0.882959	+	0.236588i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			20.7846i			0.910590i	0.890341	+	0.455295i	$0.150466\pi$
$521$			20.7846i			0.910590i	−0.890341	+	0.455295i	$0.849534\pi$
$522$		0			0
$523$	3.67423	−	3.67423i	0.160663	−	0.160663i	−0.622197	−	0.782860i	$-0.713760\pi$
$523$	3.67423	−	3.67423i	0.160663	−	0.160663i	0.782860	+	0.622197i	$0.213760\pi$
$524$	−1.73205	−	3.00000i	−0.0756650	−	0.131056i
$525$		0			0
$526$	6.00000	−	10.3923i	0.261612	−	0.453126i
$527$	6.21166	+	23.1822i	0.270584	+	1.00983i
$528$		0			0
$529$	11.2583	−	6.50000i	0.489493	−	0.282609i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.55291	−	5.79555i	0.0672642	−	0.251033i
$534$		0			0
$535$		0			0
$536$	−7.50000	−	4.33013i	−0.323951	−	0.187033i
$537$		0			0
$538$	−13.3843	−	3.58630i	−0.577036	−	0.154616i
$539$	−24.2487			−1.04447
$540$		0			0
$541$	32.0000			1.37579			0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000			1.37579			0.687894	+	0.725811i	$0.258536\pi$
$542$	9.65926	+	2.58819i	0.414901	+	0.111172i
$543$		0			0
$544$	−5.19615	−	3.00000i	−0.222783	−	0.128624i
$545$		0			0
$546$		0			0
$547$	5.82774	−	21.7494i	0.249176	−	0.929938i	−0.722062	−	0.691828i	$-0.756805\pi$
$547$	5.82774	−	21.7494i	0.249176	−	0.929938i	0.971238	−	0.238110i	$-0.0765278\pi$
$548$	−6.36396	−	6.36396i	−0.271855	−	0.271855i
$549$		0			0
$550$		0			0
$551$	30.0000	−	17.3205i	1.27804	−	0.737878i
$552$		0			0
$553$		0			0
$554$	−3.46410	+	6.00000i	−0.147176	+	0.254916i
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−16.9706	+	16.9706i	−0.719066	+	0.719066i	−0.968414	−	0.249348i	$-0.919784\pi$
$557$	−16.9706	+	16.9706i	−0.719066	+	0.719066i	0.249348	+	0.968414i	$0.419784\pi$
$558$		0			0
$559$			42.0000i			1.77641i
$560$		0			0
$561$		0			0
$562$	−20.0764	+	5.37945i	−0.846871	+	0.226919i
$563$	−20.2844	+	5.43520i	−0.854887	+	0.229066i	−0.659542	−	0.751668i	$-0.729250\pi$
$563$	−20.2844	+	5.43520i	−0.854887	+	0.229066i	−0.195346	+	0.980734i	$0.562583\pi$
$564$		0			0
$565$		0			0
$566$			12.1244i			0.509625i
$567$		0			0
$568$	−4.89898	+	4.89898i	−0.205557	+	0.205557i
$569$	−17.3205	−	30.0000i	−0.726113	−	1.25767i	−0.958514	−	0.285045i	$-0.907991\pi$
$569$	−17.3205	−	30.0000i	−0.726113	−	1.25767i	0.232401	−	0.972620i	$-0.425342\pi$
$570$		0			0
$571$	0.500000	−	0.866025i	0.0209243	−	0.0362420i	−0.855374	−	0.518012i	$-0.826672\pi$
$571$	0.500000	−	0.866025i	0.0209243	−	0.0362420i	0.876298	+	0.481770i	$0.160006\pi$
$572$	3.10583	+	11.5911i	0.129861	+	0.484649i
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−25.7196	−	25.7196i	−1.07072	−	1.07072i	−0.997301	−	0.0734217i	$-0.976608\pi$
$577$	−25.7196	−	25.7196i	−1.07072	−	1.07072i	−0.0734217	−	0.997301i	$-0.523392\pi$
$578$	−4.91756	+	18.3526i	−0.204544	+	0.763367i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	20.0764	+	5.37945i	0.831479	+	0.222794i
$584$	12.1244			0.501709
$585$		0			0
$586$	6.00000			0.247858
$587$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$587$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$588$		0			0
$589$	−17.3205	−	10.0000i	−0.713679	−	0.412043i
$590$		0			0
$591$		0			0
$592$	1.79315	−	6.69213i	0.0736980	−	0.275045i
$593$	23.3345	+	23.3345i	0.958234	+	0.958234i	0.999162	−	0.0409281i	$-0.0130314\pi$
$593$	23.3345	+	23.3345i	0.958234	+	0.958234i	−0.0409281	+	0.999162i	$0.513031\pi$
$594$		0			0
$595$		0			0
$596$	−9.00000	+	5.19615i	−0.368654	+	0.212843i
$597$		0			0
$598$	−5.37945	−	20.0764i	−0.219982	−	0.820985i
$599$	−13.8564	+	24.0000i	−0.566157	+	0.980613i	0.430784	+	0.902455i	$0.358237\pi$
$599$	−13.8564	+	24.0000i	−0.566157	+	0.980613i	−0.996941	+	0.0781581i	$0.975096\pi$
$600$		0			0
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$	13.0000	+	22.5167i	0.530281	+	0.918474i	−0.469095	+	0.883148i	$0.655420\pi$
$602$		0			0
$603$		0			0
$604$		−	16.0000i		−	0.651031i
$605$		0			0
$606$		0			0
$607$	−23.4225	+	6.27603i	−0.950688	+	0.254736i	−0.700654	−	0.713501i	$-0.747108\pi$
$607$	−23.4225	+	6.27603i	−0.950688	+	0.254736i	−0.250034	+	0.968237i	$0.580442\pi$
$608$	4.82963	−	1.29410i	0.195867	−	0.0524825i
$609$		0			0
$610$		0			0
$611$		−	20.7846i		−	0.840855i
$612$		0			0
$613$	−2.44949	+	2.44949i	−0.0989340	+	0.0989340i	−0.754841	−	0.655907i	$-0.772286\pi$
$613$	−2.44949	+	2.44949i	−0.0989340	+	0.0989340i	0.655907	+	0.754841i	$0.272286\pi$
$614$	−12.1244	−	21.0000i	−0.489299	−	0.847491i
$615$		0			0
$616$		0			0
$617$	−2.32937	−	8.69333i	−0.0937770	−	0.349980i	0.903054	−	0.429527i	$-0.141320\pi$
$617$	−2.32937	−	8.69333i	−0.0937770	−	0.349980i	−0.996831	+	0.0795462i	$0.974653\pi$
$618$		0			0
$619$	−14.7224	+	8.50000i	−0.591744	+	0.341644i	−0.765787	−	0.643094i	$-0.777650\pi$
$619$	−14.7224	+	8.50000i	−0.591744	+	0.341644i	0.174042	+	0.984738i	$0.444317\pi$
$620$		0			0
$621$		0			0
$622$	−17.1464	−	17.1464i	−0.687509	−	0.687509i
$623$		0			0
$624$		0			0
$625$		0			0
$626$	−28.5000	−	16.4545i	−1.13909	−	0.657653i
$627$		0			0
$628$	−3.34607	−	0.896575i	−0.133523	−	0.0357773i
$629$	−41.5692			−1.65747
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	13.5230	+	3.62347i	0.537915	+	0.144134i
$633$		0			0
$634$	−10.3923	−	6.00000i	−0.412731	−	0.238290i
$635$		0			0
$636$		0			0
$637$	6.27603	−	23.4225i	0.248665	−	0.928032i
$638$	−16.9706	−	16.9706i	−0.671871	−	0.671871i
$639$		0			0
$640$		0			0
$641$	−19.5000	+	11.2583i	−0.770204	+	0.444677i	−0.832947	−	0.553352i	$-0.813348\pi$
$641$	−19.5000	+	11.2583i	−0.770204	+	0.444677i	0.0627436	+	0.998030i	$0.480015\pi$
$642$		0			0
$643$	12.1038	+	45.1719i	0.477326	+	1.78141i	0.612376	+	0.790566i	$0.290214\pi$
$643$	12.1038	+	45.1719i	0.477326	+	1.78141i	−0.135050	+	0.990839i	$0.543120\pi$
$644$		0			0
$645$		0			0
$646$	−15.0000	−	25.9808i	−0.590167	−	1.02220i
$647$	29.6985	−	29.6985i	1.16757	−	1.16757i	0.184790	−	0.982778i	$-0.440840\pi$
$647$	29.6985	−	29.6985i	1.16757	−	1.16757i	0.982778	−	0.184790i	$-0.0591604\pi$
$648$		0			0
$649$			6.00000i			0.235521i
$650$		0			0
$651$		0			0
$652$	−1.67303	+	0.448288i	−0.0655210	+	0.0175563i
$653$	−28.9778	+	7.76457i	−1.13399	+	0.303851i	−0.776531	−	0.630079i	$-0.783023\pi$
$653$	−28.9778	+	7.76457i	−1.13399	+	0.303851i	−0.357457	+	0.933930i	$0.616356\pi$
$654$		0			0
$655$		0			0
$656$			1.73205i			0.0676252i
$657$		0			0
$658$		0			0
$659$	−7.79423	−	13.5000i	−0.303620	−	0.525885i	0.673333	−	0.739339i	$-0.264862\pi$
$659$	−7.79423	−	13.5000i	−0.303620	−	0.525885i	−0.976953	+	0.213454i	$0.931529\pi$
$660$		0			0
$661$	25.0000	−	43.3013i	0.972387	−	1.68422i	0.284087	−	0.958799i	$-0.408310\pi$
$661$	25.0000	−	43.3013i	0.972387	−	1.68422i	0.688301	−	0.725426i	$-0.258357\pi$
$662$	−0.258819	−	0.965926i	−0.0100593	−	0.0375418i
$663$		0			0
$664$	−7.79423	+	4.50000i	−0.302475	+	0.174634i
$665$		0			0
$666$		0			0
$667$	29.3939	+	29.3939i	1.13814	+	1.13814i
$668$	−3.10583	+	11.5911i	−0.120168	+	0.448474i
$669$		0			0
$670$		0			0
$671$	24.0000	+	13.8564i	0.926510	+	0.534921i
$672$		0			0
$673$	−33.4607	−	8.96575i	−1.28981	−	0.345604i	−0.452224	−	0.891904i	$-0.649369\pi$
$673$	−33.4607	−	8.96575i	−1.28981	−	0.345604i	−0.837590	+	0.546300i	$0.816036\pi$
$674$	−6.92820			−0.266864
$675$		0			0
$676$	1.00000			0.0384615
$677$	5.79555	+	1.55291i	0.222741	+	0.0596833i	0.368464	−	0.929642i	$-0.379884\pi$
$677$	5.79555	+	1.55291i	0.222741	+	0.0596833i	−0.145722	+	0.989326i	$0.546551\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−3.58630	+	13.3843i	−0.137327	+	0.512510i
$683$	2.12132	+	2.12132i	0.0811701	+	0.0811701i	0.746526	−	0.665356i	$-0.231720\pi$
$683$	2.12132	+	2.12132i	0.0811701	+	0.0811701i	−0.665356	+	0.746526i	$0.731720\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−3.13801	−	11.7112i	−0.119636	−	0.446486i
$689$	−10.3923	+	18.0000i	−0.395915	+	0.685745i
$690$		0			0
$691$	17.5000	+	30.3109i	0.665731	+	1.15308i	0.979086	+	0.203445i	$0.0652137\pi$
$691$	17.5000	+	30.3109i	0.665731	+	1.15308i	−0.313355	+	0.949636i	$0.601453\pi$
$692$		0			0
$693$		0			0
$694$			12.0000i			0.455514i
$695$		0			0
$696$		0			0
$697$	10.0382	−	2.68973i	0.380224	−	0.101881i
$698$	−25.1141	+	6.72930i	−0.950582	+	0.254708i
$699$		0			0
$700$		0			0
$701$			6.92820i			0.261675i	0.991404	+	0.130837i	$0.0417666\pi$
$701$			6.92820i			0.261675i	−0.991404	+	0.130837i	$0.958233\pi$
$702$		0			0
$703$	24.4949	−	24.4949i	0.923843	−	0.923843i
$704$	−1.73205	−	3.00000i	−0.0652791	−	0.113067i
$705$		0			0
$706$	4.50000	−	7.79423i	0.169360	−	0.293340i
$707$		0			0
$708$		0			0
$709$	−39.8372	+	23.0000i	−1.49612	+	0.863783i	−0.999990	−	0.00446726i	$-0.998578\pi$
$709$	−39.8372	+	23.0000i	−1.49612	+	0.863783i	−0.496126	+	0.868250i	$0.665245\pi$
$710$		0			0
$711$		0			0
$712$	8.57321	+	8.57321i	0.321295	+	0.321295i
$713$	6.21166	−	23.1822i	0.232628	−	0.868181i
$714$		0			0
$715$		0			0
$716$	19.5000	+	11.2583i	0.728749	+	0.420744i
$717$		0			0
$718$	−26.7685	−	7.17260i	−0.998992	−	0.267679i
$719$	−6.92820			−0.258378			−0.129189	−	0.991620i	$-0.541237\pi$
$719$	−6.92820			−0.258378			−0.129189	+	0.991620i	$0.541237\pi$
$720$		0			0
$721$		0			0
$722$	5.79555	+	1.55291i	0.215688	+	0.0577935i
$723$		0			0
$724$	13.8564	+	8.00000i	0.514969	+	0.297318i
$725$		0			0
$726$		0			0
$727$	8.96575	−	33.4607i	0.332521	−	1.24099i	−0.574010	−	0.818848i	$-0.694613\pi$
$727$	8.96575	−	33.4607i	0.332521	−	1.24099i	0.906531	−	0.422139i	$-0.138720\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−63.0000	+	36.3731i	−2.33014	+	1.34531i
$732$		0			0
$733$	−8.06918	−	30.1146i	−0.298042	−	1.11231i	−0.938771	−	0.344541i	$-0.888035\pi$
$733$	−8.06918	−	30.1146i	−0.298042	−	1.11231i	0.640729	−	0.767767i	$-0.278632\pi$
$734$	8.66025	−	15.0000i	0.319656	−	0.553660i
$735$		0			0
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	−21.2132	+	21.2132i	−0.781398	+	0.781398i
$738$		0			0
$739$			23.0000i			0.846069i	0.906114	+	0.423034i	$0.139035\pi$
$739$			23.0000i			0.846069i	−0.906114	+	0.423034i	$0.860965\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.5911	+	3.10583i	−0.425237	+	0.113942i	−0.465089	−	0.885264i	$-0.653978\pi$
$743$	−11.5911	+	3.10583i	−0.425237	+	0.113942i	0.0398527	+	0.999206i	$0.487311\pi$
$744$		0			0
$745$		0			0
$746$		−	20.7846i		−	0.760979i
$747$		0			0
$748$	−14.6969	+	14.6969i	−0.537373	+	0.537373i
$749$		0			0
$750$		0			0
$751$	19.0000	−	32.9090i	0.693320	−	1.20087i	−0.277424	−	0.960748i	$-0.589481\pi$
$751$	19.0000	−	32.9090i	0.693320	−	1.20087i	0.970744	−	0.240118i	$-0.0771860\pi$
$752$	1.55291	+	5.79555i	0.0566290	+	0.211342i
$753$		0			0
$754$	20.7846	−	12.0000i	0.756931	−	0.437014i
$755$		0			0
$756$		0			0
$757$	14.6969	+	14.6969i	0.534169	+	0.534169i	0.921810	−	0.387641i	$-0.126710\pi$
$757$	14.6969	+	14.6969i	0.534169	+	0.534169i	−0.387641	+	0.921810i	$0.626710\pi$
$758$	2.07055	−	7.72741i	0.0752058	−	0.280672i
$759$		0			0
$760$		0			0
$761$	−1.50000	−	0.866025i	−0.0543750	−	0.0313934i	0.472566	−	0.881295i	$-0.343328\pi$
$761$	−1.50000	−	0.866025i	−0.0543750	−	0.0313934i	−0.526941	+	0.849902i	$0.676661\pi$
$762$		0			0
$763$		0			0
$764$	−24.2487			−0.877288
$765$		0			0
$766$	−6.00000			−0.216789
$767$	−5.79555	−	1.55291i	−0.209265	−	0.0560725i
$768$		0			0
$769$	−42.4352	−	24.5000i	−1.53025	−	0.883493i	−0.999350	−	0.0360609i	$-0.988519\pi$
$769$	−42.4352	−	24.5000i	−1.53025	−	0.883493i	−0.530904	−	0.847432i	$-0.678148\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−29.6985	−	29.6985i	−1.06818	−	1.06818i	−0.997499	−	0.0706813i	$-0.977483\pi$
$773$	−29.6985	−	29.6985i	−1.06818	−	1.06818i	−0.0706813	−	0.997499i	$-0.522517\pi$
$774$		0			0
$775$		0			0
$776$	4.50000	−	2.59808i	0.161541	−	0.0932655i
$777$		0			0
$778$	2.68973	+	10.0382i	0.0964314	+	0.359887i
$779$	−4.33013	+	7.50000i	−0.155143	+	0.268715i
$780$		0			0
$781$	12.0000	+	20.7846i	0.429394	+	0.743732i
$782$	25.4558	−	25.4558i	0.910299	−	0.910299i
$783$		0			0
$784$			7.00000i			0.250000i
$785$		0			0
$786$		0			0
$787$	−30.1146	+	8.06918i	−1.07347	+	0.287635i	−0.751918	−	0.659257i	$-0.770871\pi$
$787$	−30.1146	+	8.06918i	−1.07347	+	0.287635i	−0.321551	+	0.946892i	$0.604204\pi$
$788$	−23.1822	+	6.21166i	−0.825832	+	0.221281i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−19.5959	+	19.5959i	−0.695871	+	0.695871i
$794$	12.1244	+	21.0000i	0.430277	+	0.745262i
$795$		0			0
$796$	4.00000	−	6.92820i	0.141776	−	0.245564i
$797$	−1.55291	−	5.79555i	−0.0550070	−	0.205289i	0.932953	−	0.359998i	$-0.117223\pi$
$797$	−1.55291	−	5.79555i	−0.0550070	−	0.205289i	−0.987960	+	0.154709i	$0.950556\pi$
$798$		0			0
$799$	31.1769	−	18.0000i	1.10296	−	0.636794i
$800$		0			0
$801$		0			0
$802$	−14.6969	−	14.6969i	−0.518967	−	0.518967i
$803$	10.8704	−	40.5689i	0.383608	−	1.43164i
$804$		0			0
$805$		0			0
$806$	−12.0000	−	6.92820i	−0.422682	−	0.244036i
$807$		0			0
$808$	3.34607	+	0.896575i	0.117714	+	0.0315414i
$809$	−29.4449			−1.03523			−0.517613	−	0.855615i	$-0.673179\pi$
$809$	−29.4449			−1.03523			−0.517613	+	0.855615i	$0.673179\pi$
$810$		0			0
$811$	25.0000			0.877869			0.438934	−	0.898519i	$-0.355356\pi$
$811$	25.0000			0.877869			0.438934	+	0.898519i	$0.355356\pi$
$812$		0			0
$813$		0			0
$814$	−20.7846	−	12.0000i	−0.728500	−	0.420600i
$815$		0			0
$816$		0			0
$817$	15.6901	−	58.5561i	0.548926	−	2.04862i
$818$	20.5061	+	20.5061i	0.716979	+	0.716979i
$819$		0			0
$820$		0			0
$821$	48.0000	−	27.7128i	1.67521	−	0.967184i	0.710567	−	0.703630i	$-0.248439\pi$
$821$	48.0000	−	27.7128i	1.67521	−	0.967184i	0.964645	−	0.263554i	$-0.0848948\pi$
$822$		0			0
$823$	0.896575	+	3.34607i	0.0312527	+	0.116637i	0.979790	−	0.200029i	$-0.0641035\pi$
$823$	0.896575	+	3.34607i	0.0312527	+	0.116637i	−0.948537	+	0.316665i	$0.897437\pi$
$824$	−1.73205	+	3.00000i	−0.0603388	+	0.104510i
$825$		0			0
$826$		0			0
$827$	10.6066	−	10.6066i	0.368828	−	0.368828i	−0.498222	−	0.867050i	$-0.666014\pi$
$827$	10.6066	−	10.6066i	0.368828	−	0.368828i	0.867050	+	0.498222i	$0.166014\pi$
$828$		0			0
$829$			38.0000i			1.31979i	0.751356	+	0.659897i	$0.229400\pi$
$829$			38.0000i			1.31979i	−0.751356	+	0.659897i	$0.770600\pi$
$830$		0			0
$831$		0			0
$832$	3.34607	−	0.896575i	0.116004	−	0.0310832i
$833$	40.5689	−	10.8704i	1.40563	−	0.376637i
$834$		0			0
$835$		0			0
$836$		−	17.3205i		−	0.599042i
$837$		0			0
$838$	18.3712	−	18.3712i	0.634622	−	0.634622i
$839$	−6.92820	−	12.0000i	−0.239188	−	0.414286i	0.721293	−	0.692630i	$-0.243548\pi$
$839$	−6.92820	−	12.0000i	−0.239188	−	0.414286i	−0.960482	+	0.278344i	$0.910215\pi$
$840$		0			0
$841$	−9.50000	+	16.4545i	−0.327586	+	0.567396i
$842$	−2.07055	−	7.72741i	−0.0713559	−	0.266304i
$843$		0			0
$844$	11.2583	−	6.50000i	0.387528	−	0.223739i
$845$		0			0
$846$		0			0
$847$		0			0
$848$	1.55291	−	5.79555i	0.0533273	−	0.199020i
$849$		0			0
$850$		0			0
$851$	36.0000	+	20.7846i	1.23406	+	0.712487i
$852$		0			0
$853$	3.34607	+	0.896575i	0.114567	+	0.0306982i	0.315647	−	0.948877i	$-0.397778\pi$
$853$	3.34607	+	0.896575i	0.114567	+	0.0306982i	−0.201080	+	0.979575i	$0.564445\pi$
$854$		0			0
$855$		0			0
$856$	−3.00000			−0.102538
$857$	14.4889	+	3.88229i	0.494931	+	0.132616i	0.497646	−	0.867380i	$-0.334198\pi$
$857$	14.4889	+	3.88229i	0.494931	+	0.132616i	−0.00271550	+	0.999996i	$0.500864\pi$
$858$		0			0
$859$	−11.2583	−	6.50000i	−0.384129	−	0.221777i	0.295484	−	0.955348i	$-0.404519\pi$
$859$	−11.2583	−	6.50000i	−0.384129	−	0.221777i	−0.679613	+	0.733571i	$0.737852\pi$
$860$		0			0
$861$		0			0
$862$	3.58630	−	13.3843i	0.122150	−	0.455870i
$863$	−4.24264	−	4.24264i	−0.144421	−	0.144421i	0.631199	−	0.775621i	$-0.282563\pi$
$863$	−4.24264	−	4.24264i	−0.144421	−	0.144421i	−0.775621	+	0.631199i	$0.782563\pi$
$864$		0			0
$865$		0			0
$866$	6.00000	−	3.46410i	0.203888	−	0.117715i
$867$		0			0
$868$		0			0
$869$	24.2487	−	42.0000i	0.822581	−	1.42475i
$870$		0			0
$871$	−15.0000	−	25.9808i	−0.508256	−	0.880325i
$872$	−14.1421	+	14.1421i	−0.478913	+	0.478913i
$873$		0			0
$874$			30.0000i			1.01477i
$875$		0			0
$876$		0			0
$877$	10.0382	−	2.68973i	0.338966	−	0.0908256i	−0.0853209	−	0.996354i	$-0.527192\pi$
$877$	10.0382	−	2.68973i	0.338966	−	0.0908256i	0.424287	+	0.905528i	$0.360525\pi$
$878$	25.1141	−	6.72930i	0.847559	−	0.227103i
$879$		0			0
$880$		0			0
$881$			6.92820i			0.233417i	0.993166	+	0.116709i	$0.0372343\pi$
$881$			6.92820i			0.233417i	−0.993166	+	0.116709i	$0.962766\pi$
$882$		0			0
$883$	−36.7423	+	36.7423i	−1.23648	+	1.23648i	−0.275048	+	0.961431i	$0.588694\pi$
$883$	−36.7423	+	36.7423i	−1.23648	+	1.23648i	−0.961431	+	0.275048i	$0.911306\pi$
$884$	−10.3923	−	18.0000i	−0.349531	−	0.605406i
$885$		0			0
$886$	−18.0000	+	31.1769i	−0.604722	+	1.04741i
$887$	1.55291	+	5.79555i	0.0521418	+	0.194596i	0.987084	−	0.160205i	$-0.0512155\pi$
$887$	1.55291	+	5.79555i	0.0521418	+	0.194596i	−0.934942	+	0.354800i	$0.884549\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	4.89898	+	4.89898i	0.164030	+	0.164030i
$893$	−7.76457	+	28.9778i	−0.259831	+	0.969704i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−8.36516	−	2.24144i	−0.279149	−	0.0747978i
$899$	27.7128			0.924274
$900$		0			0
$901$	−36.0000			−1.19933
$902$	5.79555	+	1.55291i	0.192971	+	0.0517064i
$903$		0			0
$904$	12.9904	+	7.50000i	0.432054	+	0.249446i
$905$		0			0
$906$		0			0
$907$	−8.51747	+	31.7876i	−0.282818	+	1.05549i	0.667601	+	0.744519i	$0.267321\pi$
$907$	−8.51747	+	31.7876i	−0.282818	+	1.05549i	−0.950419	+	0.310972i	$0.899346\pi$
$908$	−2.12132	−	2.12132i	−0.0703985	−	0.0703985i
$909$		0			0
$910$		0			0
$911$	−15.0000	+	8.66025i	−0.496972	+	0.286927i	−0.727462	−	0.686148i	$-0.759300\pi$
$911$	−15.0000	+	8.66025i	−0.496972	+	0.286927i	0.230490	+	0.973075i	$0.425967\pi$
$912$		0			0
$913$	8.06918	+	30.1146i	0.267051	+	0.996647i
$914$	2.59808	−	4.50000i	0.0859367	−	0.148847i
$915$		0			0
$916$	8.00000	+	13.8564i	0.264327	+	0.457829i
$917$		0			0
$918$		0			0
$919$			2.00000i			0.0659739i	0.999456	+	0.0329870i	$0.0105020\pi$
$919$			2.00000i			0.0659739i	−0.999456	+	0.0329870i	$0.989498\pi$
$920$		0			0
$921$		0			0
$922$	−33.4607	+	8.96575i	−1.10197	+	0.295271i
$923$	−23.1822	+	6.21166i	−0.763052	+	0.204459i
$924$		0			0
$925$		0			0
$926$			6.92820i			0.227675i
$927$		0			0
$928$	−4.89898	+	4.89898i	−0.160817	+	0.160817i
$929$	27.7128	+	48.0000i	0.909228	+	1.57483i	0.815139	+	0.579265i	$0.196660\pi$
$929$	27.7128	+	48.0000i	0.909228	+	1.57483i	0.0940887	+	0.995564i	$0.470006\pi$
$930$		0			0
$931$	−17.5000	+	30.3109i	−0.573539	+	0.993399i
$932$	2.32937	+	8.69333i	0.0763011	+	0.284760i
$933$		0			0
$934$	−18.1865	+	10.5000i	−0.595082	+	0.343570i
$935$		0			0
$936$		0			0
$937$	−3.67423	−	3.67423i	−0.120032	−	0.120032i	0.644539	−	0.764571i	$-0.277049\pi$
$937$	−3.67423	−	3.67423i	−0.120032	−	0.120032i	−0.764571	+	0.644539i	$0.777049\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−36.0000	−	20.7846i	−1.17357	−	0.677559i	−0.219049	−	0.975714i	$-0.570295\pi$
$941$	−36.0000	−	20.7846i	−1.17357	−	0.677559i	−0.954517	+	0.298155i	$0.903629\pi$
$942$		0			0
$943$	−10.0382	−	2.68973i	−0.326889	−	0.0875895i
$944$	1.73205			0.0563735
$945$		0			0
$946$	−42.0000			−1.36554
$947$	−14.4889	−	3.88229i	−0.470826	−	0.126157i	0.0156019	−	0.999878i	$-0.495034\pi$
$947$	−14.4889	−	3.88229i	−0.470826	−	0.126157i	−0.486427	+	0.873721i	$0.661700\pi$
$948$		0			0
$949$	36.3731	+	21.0000i	1.18072	+	0.681689i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−4.24264	−	4.24264i	−0.137433	−	0.137433i	0.635044	−	0.772476i	$-0.280982\pi$
$953$	−4.24264	−	4.24264i	−0.137433	−	0.137433i	−0.772476	+	0.635044i	$0.780982\pi$
$954$		0			0
$955$		0			0
$956$	9.00000	−	5.19615i	0.291081	−	0.168056i
$957$		0			0
$958$	−4.48288	−	16.7303i	−0.144835	−	0.540532i
$959$		0			0
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	16.9706	−	16.9706i	0.547153	−	0.547153i
$963$		0			0
$964$			1.00000i			0.0322078i
$965$		0			0
$966$		0			0
$967$	6.69213	−	1.79315i	0.215204	−	0.0576638i	−0.149606	−	0.988746i	$-0.547800\pi$
$967$	6.69213	−	1.79315i	0.215204	−	0.0576638i	0.364810	+	0.931082i	$0.381134\pi$
$968$	−0.965926	+	0.258819i	−0.0310460	+	0.00831876i
$969$		0			0
$970$		0			0
$971$			22.5167i			0.722594i	0.932451	+	0.361297i	$0.117666\pi$
$971$			22.5167i			0.722594i	−0.932451	+	0.361297i	$0.882334\pi$
$972$		0			0
$973$		0			0
$974$	−3.46410	−	6.00000i	−0.110997	−	0.192252i
$975$		0			0
$976$	4.00000	−	6.92820i	0.128037	−	0.221766i
$977$	−0.776457	−	2.89778i	−0.0248411	−	0.0927081i	0.952392	−	0.304875i	$-0.0986147\pi$
$977$	−0.776457	−	2.89778i	−0.0248411	−	0.0927081i	−0.977233	+	0.212167i	$0.931948\pi$
$978$		0			0
$979$	36.3731	−	21.0000i	1.16249	−	0.671163i
$980$		0			0
$981$		0			0
$982$	20.8207	+	20.8207i	0.664414	+	0.664414i
$983$	10.8704	−	40.5689i	0.346712	−	1.29395i	−0.543888	−	0.839158i	$-0.683048\pi$
$983$	10.8704	−	40.5689i	0.346712	−	1.29395i	0.890600	−	0.454788i	$-0.150285\pi$
$984$		0			0
$985$		0			0
$986$	36.0000	+	20.7846i	1.14647	+	0.661917i
$987$		0			0
$988$	16.7303	+	4.48288i	0.532263	+	0.142619i
$989$	72.7461			2.31319
$990$		0			0
$991$	−40.0000			−1.27064			−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000			−1.27064			−0.635321	+	0.772248i	$0.719132\pi$
$992$	3.86370	+	1.03528i	0.122673	+	0.0328701i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−2.68973	+	10.0382i	−0.0851845	+	0.317913i	−0.995349	−	0.0963340i	$-0.969288\pi$
$997$	−2.68973	+	10.0382i	−0.0851845	+	0.317913i	0.910165	+	0.414247i	$0.135955\pi$
$998$	9.19239	+	9.19239i	0.290980	+	0.290980i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.q.c.557.1		8
3.2	odd	2		450.2.p.g.257.2	yes	8
5.2	odd	4	inner	1350.2.q.c.1043.2		8
5.3	odd	4	inner	1350.2.q.c.1043.1		8
5.4	even	2	inner	1350.2.q.c.557.2		8
9.2	odd	6	inner	1350.2.q.c.1007.1		8
9.7	even	3		450.2.p.g.407.2	yes	8
15.2	even	4		450.2.p.g.293.1	yes	8
15.8	even	4		450.2.p.g.293.2	yes	8
15.14	odd	2		450.2.p.g.257.1	✓	8
45.2	even	12	inner	1350.2.q.c.143.2		8
45.7	odd	12		450.2.p.g.443.1	yes	8
45.29	odd	6	inner	1350.2.q.c.1007.2		8
45.34	even	6		450.2.p.g.407.1	yes	8
45.38	even	12	inner	1350.2.q.c.143.1		8
45.43	odd	12		450.2.p.g.443.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.p.g.257.1	✓	8	15.14	odd	2
450.2.p.g.257.2	yes	8	3.2	odd	2
450.2.p.g.293.1	yes	8	15.2	even	4
450.2.p.g.293.2	yes	8	15.8	even	4
450.2.p.g.407.1	yes	8	45.34	even	6
450.2.p.g.407.2	yes	8	9.7	even	3
450.2.p.g.443.1	yes	8	45.7	odd	12
450.2.p.g.443.2	yes	8	45.43	odd	12
1350.2.q.c.143.1		8	45.38	even	12	inner
1350.2.q.c.143.2		8	45.2	even	12	inner
1350.2.q.c.557.1		8	1.1	even	1	trivial
1350.2.q.c.557.2		8	5.4	even	2	inner
1350.2.q.c.1007.1		8	9.2	odd	6	inner
1350.2.q.c.1007.2		8	45.29	odd	6	inner
1350.2.q.c.1043.1		8	5.3	odd	4	inner
1350.2.q.c.1043.2		8	5.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.q (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-0.707107 - 0.707107i) q^{8} +(-3.00000 + 1.73205i) q^{11} +(-0.896575 - 3.34607i) q^{13} +(0.500000 + 0.866025i) q^{16} +(4.24264 - 4.24264i) q^{17} +5.00000i q^{19} +(3.34607 - 0.896575i) q^{22} +(-5.79555 + 1.55291i) q^{23} +3.46410i q^{26} +(-3.46410 - 6.00000i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-5.19615 + 3.00000i) q^{34} +(-4.89898 - 4.89898i) q^{37} +(1.29410 - 4.82963i) q^{38} +(1.50000 + 0.866025i) q^{41} +(-11.7112 - 3.13801i) q^{43} -3.46410 q^{44} +6.00000 q^{46} +(5.79555 + 1.55291i) q^{47} +(6.06218 + 3.50000i) q^{49} +(0.896575 - 3.34607i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(1.79315 + 6.69213i) q^{58} +(0.866025 - 1.50000i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(2.82843 - 2.82843i) q^{62} +1.00000i q^{64} +(8.36516 - 2.24144i) q^{67} +(5.79555 - 1.55291i) q^{68} -6.92820i q^{71} +(-8.57321 + 8.57321i) q^{73} +(3.46410 + 6.00000i) q^{74} +(-2.50000 + 4.33013i) q^{76} +(-12.1244 + 7.00000i) q^{79} +(-1.22474 - 1.22474i) q^{82} +(2.32937 - 8.69333i) q^{83} +(10.5000 + 6.06218i) q^{86} +(3.34607 + 0.896575i) q^{88} -12.1244 q^{89} +(-5.79555 - 1.55291i) q^{92} +(-5.19615 - 3.00000i) q^{94} +(-1.34486 + 5.01910i) q^{97} +(-4.94975 - 4.94975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 24 q^{11} + 4 q^{16} - 16 q^{31} + 12 q^{41} + 48 q^{46} - 32 q^{61} - 20 q^{76} + 84 q^{86}+O(q^{100}) \) 8 * q - 24 * q^11 + 4 * q^16 - 16 * q^31 + 12 * q^41 + 48 * q^46 - 32 * q^61 - 20 * q^76 + 84 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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