LMFDB - Embedded newform 1350.2.q.b.1043.2

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			1043.2
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.1043
Dual form			1350.2.q.b.1007.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(1.67303 + 0.448288i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(1.67303 + 0.448288i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-3.00000 + 1.73205i) q^{11} +(-3.34607 + 0.896575i) q^{13} +(0.866025 - 1.50000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-4.24264 - 4.24264i) q^{17} -2.00000i q^{19} +(0.896575 + 3.34607i) q^{22} +(-0.776457 - 2.89778i) q^{23} +3.46410i q^{26} +(-1.22474 - 1.22474i) q^{28} +(-4.33013 - 7.50000i) q^{29} +(-5.00000 + 8.66025i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-5.19615 + 3.00000i) q^{34} +(2.44949 - 2.44949i) q^{37} +(-1.93185 - 0.517638i) q^{38} +(-7.50000 - 4.33013i) q^{41} +(2.68973 - 10.0382i) q^{43} +3.46410 q^{44} -3.00000 q^{46} +(0.776457 - 2.89778i) q^{47} +(-3.46410 - 2.00000i) q^{49} +(3.34607 + 0.896575i) q^{52} +(-1.50000 + 0.866025i) q^{56} +(-8.36516 + 2.24144i) q^{58} +(-3.46410 + 6.00000i) q^{59} +(6.50000 + 11.2583i) q^{61} +(7.07107 + 7.07107i) q^{62} -1.00000i q^{64} +(-3.13801 - 11.7112i) q^{67} +(1.55291 + 5.79555i) q^{68} +3.46410i q^{71} +(9.79796 + 9.79796i) q^{73} +(-1.73205 - 3.00000i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(-5.79555 + 1.55291i) q^{77} +(-3.46410 + 2.00000i) q^{79} +(-6.12372 + 6.12372i) q^{82} +(-2.89778 - 0.776457i) q^{83} +(-9.00000 - 5.19615i) q^{86} +(0.896575 - 3.34607i) q^{88} +1.73205 q^{89} -6.00000 q^{91} +(-0.776457 + 2.89778i) q^{92} +(-2.59808 - 1.50000i) q^{94} +(-6.69213 - 1.79315i) q^{97} +(-2.82843 + 2.82843i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 24 q^{11} + 4 q^{16} - 40 q^{31} - 60 q^{41} - 24 q^{46} - 12 q^{56} + 52 q^{61} - 8 q^{76} - 72 q^{86} - 48 q^{91}+O(q^{100}) $ 8 * q - 24 * q^11 + 4 * q^16 - 40 * q^31 - 60 * q^41 - 24 * q^46 - 12 * q^56 + 52 * q^61 - 8 * q^76 - 72 * q^86 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.67303	+	0.448288i	0.632347	+	0.169437i	0.560734	−	0.827996i	$-0.310519\pi$
$7$	1.67303	+	0.448288i	0.632347	+	0.169437i	0.0716124	+	0.997433i	$0.477186\pi$
$8$	−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
$13$	−3.34607	+	0.896575i	−0.928032	+	0.248665i	−0.691015	−	0.722840i	$-0.742836\pi$
$13$	−3.34607	+	0.896575i	−0.928032	+	0.248665i	−0.237016	+	0.971506i	$0.576170\pi$
$14$	0.866025	−	1.50000i	0.231455	−	0.400892i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−4.24264	−	4.24264i	−1.02899	−	1.02899i	−0.999567	−	0.0294245i	$-0.990633\pi$
$17$	−4.24264	−	4.24264i	−1.02899	−	1.02899i	−0.0294245	−	0.999567i	$-0.509367\pi$
$18$		0			0
$19$		−	2.00000i		−	0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$		−	2.00000i		−	0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$		0			0
$21$		0			0
$22$	0.896575	+	3.34607i	0.191151	+	0.713384i
$23$	−0.776457	−	2.89778i	−0.161903	−	0.604228i	−0.998415	−	0.0562805i	$-0.982076\pi$
$23$	−0.776457	−	2.89778i	−0.161903	−	0.604228i	0.836512	−	0.547948i	$-0.184591\pi$
$24$		0			0
$25$		0			0
$26$			3.46410i			0.679366i
$27$		0			0
$28$	−1.22474	−	1.22474i	−0.231455	−	0.231455i
$29$	−4.33013	−	7.50000i	−0.804084	−	1.39272i	−0.916907	−	0.399100i	$-0.869323\pi$
$29$	−4.33013	−	7.50000i	−0.804084	−	1.39272i	0.112823	−	0.993615i	$-0.464011\pi$
$30$		0			0
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.0680129	+	0.997684i	$0.521666\pi$
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.830014	+	0.557743i	$0.811667\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$		0			0
$34$	−5.19615	+	3.00000i	−0.891133	+	0.514496i
$35$		0			0
$36$		0			0
$37$	2.44949	−	2.44949i	0.402694	−	0.402694i	−0.476488	−	0.879181i	$-0.658090\pi$
$37$	2.44949	−	2.44949i	0.402694	−	0.402694i	0.879181	+	0.476488i	$0.158090\pi$
$38$	−1.93185	−	0.517638i	−0.313388	−	0.0839720i
$39$		0			0
$40$		0			0
$41$	−7.50000	−	4.33013i	−1.17130	−	0.676252i	−0.217317	−	0.976101i	$-0.569730\pi$
$41$	−7.50000	−	4.33013i	−1.17130	−	0.676252i	−0.953987	+	0.299849i	$0.903064\pi$
$42$		0			0
$43$	2.68973	−	10.0382i	0.410179	−	1.53081i	−0.384120	−	0.923283i	$-0.625495\pi$
$43$	2.68973	−	10.0382i	0.410179	−	1.53081i	0.794299	−	0.607527i	$-0.207838\pi$
$44$	3.46410			0.522233
$45$		0			0
$46$	−3.00000			−0.442326
$47$	0.776457	−	2.89778i	0.113258	−	0.422684i	−0.885893	−	0.463890i	$-0.846453\pi$
$47$	0.776457	−	2.89778i	0.113258	−	0.422684i	0.999151	+	0.0412058i	$0.0131199\pi$
$48$		0			0
$49$	−3.46410	−	2.00000i	−0.494872	−	0.285714i
$50$		0			0
$51$		0			0
$52$	3.34607	+	0.896575i	0.464016	+	0.124333i
$53$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$53$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$54$		0			0
$55$		0			0
$56$	−1.50000	+	0.866025i	−0.200446	+	0.115728i
$57$		0			0
$58$	−8.36516	+	2.24144i	−1.09840	+	0.294315i
$59$	−3.46410	+	6.00000i	−0.450988	+	0.781133i	−0.998448	−	0.0556984i	$-0.982261\pi$
$59$	−3.46410	+	6.00000i	−0.450988	+	0.781133i	0.547460	+	0.836832i	$0.315595\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	7.07107	+	7.07107i	0.898027	+	0.898027i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	−3.13801	−	11.7112i	−0.383369	−	1.43075i	−0.840721	−	0.541468i	$-0.817869\pi$
$67$	−3.13801	−	11.7112i	−0.383369	−	1.43075i	0.457352	−	0.889286i	$-0.348798\pi$
$68$	1.55291	+	5.79555i	0.188319	+	0.702814i
$69$		0			0
$70$		0			0
$71$			3.46410i			0.411113i	0.978645	+	0.205557i	$0.0659005\pi$
$71$			3.46410i			0.411113i	−0.978645	+	0.205557i	$0.934100\pi$
$72$		0			0
$73$	9.79796	+	9.79796i	1.14676	+	1.14676i	0.987185	+	0.159579i	$0.0510137\pi$
$73$	9.79796	+	9.79796i	1.14676	+	1.14676i	0.159579	+	0.987185i	$0.448986\pi$
$74$	−1.73205	−	3.00000i	−0.201347	−	0.348743i
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	−5.79555	+	1.55291i	−0.660465	+	0.176971i
$78$		0			0
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	−0.682048	−	0.731307i	$-0.738911\pi$
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	0.292306	+	0.956325i	$0.405577\pi$
$80$		0			0
$81$		0			0
$82$	−6.12372	+	6.12372i	−0.676252	+	0.676252i
$83$	−2.89778	−	0.776457i	−0.318072	−	0.0852272i	0.0962507	−	0.995357i	$-0.469315\pi$
$83$	−2.89778	−	0.776457i	−0.318072	−	0.0852272i	−0.414323	+	0.910130i	$0.635982\pi$
$84$		0			0
$85$		0			0
$86$	−9.00000	−	5.19615i	−0.970495	−	0.560316i
$87$		0			0
$88$	0.896575	−	3.34607i	0.0955753	−	0.356692i
$89$	1.73205			0.183597			0.0917985	−	0.995778i	$-0.470738\pi$
$89$	1.73205			0.183597			0.0917985	+	0.995778i	$0.470738\pi$
$90$		0			0
$91$	−6.00000			−0.628971
$92$	−0.776457	+	2.89778i	−0.0809513	+	0.302114i
$93$		0			0
$94$	−2.59808	−	1.50000i	−0.267971	−	0.154713i
$95$		0			0
$96$		0			0
$97$	−6.69213	−	1.79315i	−0.679483	−	0.182067i	−0.0974602	−	0.995239i	$-0.531072\pi$
$97$	−6.69213	−	1.79315i	−0.679483	−	0.182067i	−0.582023	+	0.813173i	$0.697739\pi$
$98$	−2.82843	+	2.82843i	−0.285714	+	0.285714i
$99$		0			0
$100$		0			0
$101$	−12.0000	+	6.92820i	−1.19404	+	0.689382i	−0.959221	−	0.282656i	$-0.908784\pi$
$101$	−12.0000	+	6.92820i	−1.19404	+	0.689382i	−0.234823	+	0.972038i	$0.575451\pi$
$102$		0			0
$103$	3.34607	−	0.896575i	0.329698	−	0.0883422i	−0.0901732	−	0.995926i	$-0.528742\pi$
$103$	3.34607	−	0.896575i	0.329698	−	0.0883422i	0.419871	+	0.907584i	$0.362075\pi$
$104$	1.73205	−	3.00000i	0.169842	−	0.294174i
$105$		0			0
$106$		0			0
$107$	2.12132	+	2.12132i	0.205076	+	0.205076i	0.802171	−	0.597095i	$-0.203678\pi$
$107$	2.12132	+	2.12132i	0.205076	+	0.205076i	−0.597095	+	0.802171i	$0.703678\pi$
$108$		0			0
$109$			5.00000i			0.478913i	0.970907	+	0.239457i	$0.0769693\pi$
$109$			5.00000i			0.478913i	−0.970907	+	0.239457i	$0.923031\pi$
$110$		0			0
$111$		0			0
$112$	0.448288	+	1.67303i	0.0423592	+	0.158087i
$113$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$113$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$114$		0			0
$115$		0			0
$116$			8.66025i			0.804084i
$117$		0			0
$118$	4.89898	+	4.89898i	0.450988	+	0.450988i
$119$	−5.19615	−	9.00000i	−0.476331	−	0.825029i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	12.5570	−	3.36465i	1.13686	−	0.304621i
$123$		0			0
$124$	8.66025	−	5.00000i	0.777714	−	0.449013i
$125$		0			0
$126$		0			0
$127$	−3.67423	+	3.67423i	−0.326036	+	0.326036i	−0.851077	−	0.525041i	$-0.824050\pi$
$127$	−3.67423	+	3.67423i	−0.326036	+	0.326036i	0.525041	+	0.851077i	$0.324050\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$		0			0
$130$		0			0
$131$	6.00000	+	3.46410i	0.524222	+	0.302660i	0.738661	−	0.674078i	$-0.235459\pi$
$131$	6.00000	+	3.46410i	0.524222	+	0.302660i	−0.214438	+	0.976738i	$0.568792\pi$
$132$		0			0
$133$	0.896575	−	3.34607i	0.0777430	−	0.290141i
$134$	−12.1244			−1.04738
$135$		0			0
$136$	6.00000			0.514496
$137$	−3.10583	+	11.5911i	−0.265349	+	0.990295i	0.696688	+	0.717375i	$0.254656\pi$
$137$	−3.10583	+	11.5911i	−0.265349	+	0.990295i	−0.962037	+	0.272921i	$0.912010\pi$
$138$		0			0
$139$	−3.46410	−	2.00000i	−0.293821	−	0.169638i	0.345843	−	0.938293i	$-0.387593\pi$
$139$	−3.46410	−	2.00000i	−0.293821	−	0.169638i	−0.639664	+	0.768655i	$0.720926\pi$
$140$		0			0
$141$		0			0
$142$	3.34607	+	0.896575i	0.280796	+	0.0752389i
$143$	8.48528	−	8.48528i	0.709575	−	0.709575i
$144$		0			0
$145$		0			0
$146$	12.0000	−	6.92820i	0.993127	−	0.573382i
$147$		0			0
$148$	−3.34607	+	0.896575i	−0.275045	+	0.0736980i
$149$	2.59808	−	4.50000i	0.212843	−	0.368654i	−0.739760	−	0.672870i	$-0.765061\pi$
$149$	2.59808	−	4.50000i	0.212843	−	0.368654i	0.952603	+	0.304216i	$0.0983945\pi$
$150$		0			0
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	0.587646	−	0.809118i	$-0.300055\pi$
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	−0.994540	+	0.104357i	$0.966722\pi$
$152$	1.41421	+	1.41421i	0.114708	+	0.114708i
$153$		0			0
$154$			6.00000i			0.483494i
$155$		0			0
$156$		0			0
$157$	−5.37945	−	20.0764i	−0.429327	−	1.60227i	−0.754288	−	0.656543i	$-0.772018\pi$
$157$	−5.37945	−	20.0764i	−0.429327	−	1.60227i	0.324961	−	0.945727i	$-0.394649\pi$
$158$	1.03528	+	3.86370i	0.0823622	+	0.307380i
$159$		0			0
$160$		0			0
$161$		−	5.19615i		−	0.409514i
$162$		0			0
$163$	12.2474	+	12.2474i	0.959294	+	0.959294i	0.999203	−	0.0399091i	$-0.0127068\pi$
$163$	12.2474	+	12.2474i	0.959294	+	0.959294i	−0.0399091	+	0.999203i	$0.512707\pi$
$164$	4.33013	+	7.50000i	0.338126	+	0.585652i
$165$		0			0
$166$	−1.50000	+	2.59808i	−0.116423	+	0.201650i
$167$	−8.69333	+	2.32937i	−0.672710	+	0.180252i	−0.578975	−	0.815345i	$-0.696547\pi$
$167$	−8.69333	+	2.32937i	−0.672710	+	0.180252i	−0.0937349	+	0.995597i	$0.529881\pi$
$168$		0			0
$169$	−0.866025	+	0.500000i	−0.0666173	+	0.0384615i
$170$		0			0
$171$		0			0
$172$	−7.34847	+	7.34847i	−0.560316	+	0.560316i
$173$	23.1822	+	6.21166i	1.76251	+	0.472264i	0.987223	−	0.159344i	$-0.0509379\pi$
$173$	23.1822	+	6.21166i	1.76251	+	0.472264i	0.775288	+	0.631607i	$0.217605\pi$
$174$		0			0
$175$		0			0
$176$	−3.00000	−	1.73205i	−0.226134	−	0.130558i
$177$		0			0
$178$	0.448288	−	1.67303i	0.0336006	−	0.125399i
$179$	24.2487			1.81243			0.906217	−	0.422813i	$-0.138957\pi$
$179$	24.2487			1.81243			0.906217	+	0.422813i	$0.138957\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$	−1.55291	+	5.79555i	−0.115110	+	0.429595i
$183$		0			0
$184$	2.59808	+	1.50000i	0.191533	+	0.110581i
$185$		0			0
$186$		0			0
$187$	20.0764	+	5.37945i	1.46813	+	0.393385i
$188$	−2.12132	+	2.12132i	−0.154713	+	0.154713i
$189$		0			0
$190$		0			0
$191$	15.0000	−	8.66025i	1.08536	−	0.626634i	0.153024	−	0.988222i	$-0.451099\pi$
$191$	15.0000	−	8.66025i	1.08536	−	0.626634i	0.932338	+	0.361588i	$0.117765\pi$
$192$		0			0
$193$	−16.7303	+	4.48288i	−1.20428	+	0.322685i	−0.804513	−	0.593934i	$-0.797574\pi$
$193$	−16.7303	+	4.48288i	−1.20428	+	0.322685i	−0.399762	+	0.916619i	$0.630907\pi$
$194$	−3.46410	+	6.00000i	−0.248708	+	0.430775i
$195$		0			0
$196$	2.00000	+	3.46410i	0.142857	+	0.247436i
$197$	−8.48528	−	8.48528i	−0.604551	−	0.604551i	0.336966	−	0.941517i	$-0.390599\pi$
$197$	−8.48528	−	8.48528i	−0.604551	−	0.604551i	−0.941517	+	0.336966i	$0.890599\pi$
$198$		0			0
$199$		−	10.0000i		−	0.708881i	−0.935079	−	0.354441i	$-0.884671\pi$
$199$		−	10.0000i		−	0.708881i	0.935079	−	0.354441i	$-0.115329\pi$
$200$		0			0
$201$		0			0
$202$	3.58630	+	13.3843i	0.252331	+	0.941713i
$203$	−3.88229	−	14.4889i	−0.272483	−	1.01692i
$204$		0			0
$205$		0			0
$206$		−	3.46410i		−	0.241355i
$207$		0			0
$208$	−2.44949	−	2.44949i	−0.169842	−	0.169842i
$209$	3.46410	+	6.00000i	0.239617	+	0.415029i
$210$		0			0
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	−0.186966	−	0.982366i	$-0.559865\pi$
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	0.944237	−	0.329266i	$-0.106801\pi$
$212$		0			0
$213$		0			0
$214$	2.59808	−	1.50000i	0.177601	−	0.102538i
$215$		0			0
$216$		0			0
$217$	−12.2474	+	12.2474i	−0.831411	+	0.831411i
$218$	4.82963	+	1.29410i	0.327104	+	0.0876472i
$219$		0			0
$220$		0			0
$221$	18.0000	+	10.3923i	1.21081	+	0.699062i
$222$		0			0
$223$	4.03459	−	15.0573i	0.270176	−	1.00831i	−0.688829	−	0.724923i	$-0.741875\pi$
$223$	4.03459	−	15.0573i	0.270176	−	1.00831i	0.959005	−	0.283387i	$-0.0914582\pi$
$224$	1.73205			0.115728
$225$		0			0
$226$		0			0
$227$	6.21166	−	23.1822i	0.412282	−	1.53866i	−0.377936	−	0.925832i	$-0.623366\pi$
$227$	6.21166	−	23.1822i	0.412282	−	1.53866i	0.790218	−	0.612826i	$-0.209967\pi$
$228$		0			0
$229$	4.33013	+	2.50000i	0.286143	+	0.165205i	0.636201	−	0.771523i	$-0.280505\pi$
$229$	4.33013	+	2.50000i	0.286143	+	0.165205i	−0.350058	+	0.936728i	$0.613838\pi$
$230$		0			0
$231$		0			0
$232$	8.36516	+	2.24144i	0.549200	+	0.147158i
$233$	4.24264	−	4.24264i	0.277945	−	0.277945i	−0.554343	−	0.832288i	$-0.687031\pi$
$233$	4.24264	−	4.24264i	0.277945	−	0.277945i	0.832288	+	0.554343i	$0.187031\pi$
$234$		0			0
$235$		0			0
$236$	6.00000	−	3.46410i	0.390567	−	0.225494i
$237$		0			0
$238$	−10.0382	+	2.68973i	−0.650680	+	0.174349i
$239$	−10.3923	+	18.0000i	−0.672222	+	1.16432i	0.305050	+	0.952336i	$0.401327\pi$
$239$	−10.3923	+	18.0000i	−0.672222	+	1.16432i	−0.977273	+	0.211987i	$0.932007\pi$
$240$		0			0
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	0.450910	−	0.892570i	$-0.351100\pi$
$242$	−0.707107	−	0.707107i	−0.0454545	−	0.0454545i
$243$		0			0
$244$		−	13.0000i		−	0.832240i
$245$		0			0
$246$		0			0
$247$	1.79315	+	6.69213i	0.114095	+	0.425810i
$248$	−2.58819	−	9.65926i	−0.164350	−	0.613364i
$249$		0			0
$250$		0			0
$251$		−	10.3923i		−	0.655956i	−0.944685	−	0.327978i	$-0.893633\pi$
$251$		−	10.3923i		−	0.655956i	0.944685	−	0.327978i	$-0.106367\pi$
$252$		0			0
$253$	7.34847	+	7.34847i	0.461994	+	0.461994i
$254$	2.59808	+	4.50000i	0.163018	+	0.282355i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$257$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$258$		0			0
$259$	5.19615	−	3.00000i	0.322873	−	0.186411i
$260$		0			0
$261$		0			0
$262$	4.89898	−	4.89898i	0.302660	−	0.302660i
$263$	−23.1822	−	6.21166i	−1.42948	−	0.383027i	−0.540641	−	0.841253i	$-0.681818\pi$
$263$	−23.1822	−	6.21166i	−1.42948	−	0.383027i	−0.888836	+	0.458226i	$0.848485\pi$
$264$		0			0
$265$		0			0
$266$	−3.00000	−	1.73205i	−0.183942	−	0.106199i
$267$		0			0
$268$	−3.13801	+	11.7112i	−0.191685	+	0.715377i
$269$	1.73205			0.105605			0.0528025	−	0.998605i	$-0.483185\pi$
$269$	1.73205			0.105605			0.0528025	+	0.998605i	$0.483185\pi$
$270$		0			0
$271$	−10.0000			−0.607457			−0.303728	−	0.952759i	$-0.598232\pi$
$271$	−10.0000			−0.607457			−0.303728	+	0.952759i	$0.598232\pi$
$272$	1.55291	−	5.79555i	0.0941593	−	0.351407i
$273$		0			0
$274$	10.3923	+	6.00000i	0.627822	+	0.362473i
$275$		0			0
$276$		0			0
$277$	10.0382	+	2.68973i	0.603137	+	0.161610i	0.547450	−	0.836838i	$-0.315599\pi$
$277$	10.0382	+	2.68973i	0.603137	+	0.161610i	0.0556866	+	0.998448i	$0.482265\pi$
$278$	−2.82843	+	2.82843i	−0.169638	+	0.169638i
$279$		0			0
$280$		0			0
$281$	−4.50000	+	2.59808i	−0.268447	+	0.154988i	−0.628182	−	0.778067i	$-0.716201\pi$
$281$	−4.50000	+	2.59808i	−0.268447	+	0.154988i	0.359734	+	0.933055i	$0.382867\pi$
$282$		0			0
$283$	−5.01910	+	1.34486i	−0.298354	+	0.0799438i	−0.404891	−	0.914365i	$-0.632691\pi$
$283$	−5.01910	+	1.34486i	−0.298354	+	0.0799438i	0.106537	+	0.994309i	$0.466024\pi$
$284$	1.73205	−	3.00000i	0.102778	−	0.178017i
$285$		0			0
$286$	−6.00000	−	10.3923i	−0.354787	−	0.614510i
$287$	−10.6066	−	10.6066i	−0.626088	−	0.626088i
$288$		0			0
$289$			19.0000i			1.11765i
$290$		0			0
$291$		0			0
$292$	−3.58630	−	13.3843i	−0.209872	−	0.783255i
$293$	7.76457	+	28.9778i	0.453611	+	1.69290i	0.692139	+	0.721764i	$0.256668\pi$
$293$	7.76457	+	28.9778i	0.453611	+	1.69290i	−0.238528	+	0.971136i	$0.576665\pi$
$294$		0			0
$295$		0			0
$296$			3.46410i			0.201347i
$297$		0			0
$298$	−3.67423	−	3.67423i	−0.212843	−	0.212843i
$299$	5.19615	+	9.00000i	0.300501	+	0.520483i
$300$		0			0
$301$	9.00000	−	15.5885i	0.518751	−	0.898504i
$302$	−9.65926	+	2.58819i	−0.555828	+	0.148934i
$303$		0			0
$304$	1.73205	−	1.00000i	0.0993399	−	0.0573539i
$305$		0			0
$306$		0			0
$307$	3.67423	−	3.67423i	0.209700	−	0.209700i	−0.594440	−	0.804140i	$-0.702626\pi$
$307$	3.67423	−	3.67423i	0.209700	−	0.209700i	0.804140	+	0.594440i	$0.202626\pi$
$308$	5.79555	+	1.55291i	0.330232	+	0.0884855i
$309$		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
$313$	−0.896575	+	3.34607i	−0.0506774	+	0.189131i	−0.986624	−	0.163010i	$-0.947880\pi$
$313$	−0.896575	+	3.34607i	−0.0506774	+	0.189131i	0.935947	+	0.352141i	$0.114546\pi$
$314$	−20.7846			−1.17294
$315$		0			0
$316$	4.00000			0.225018
$317$	−1.55291	+	5.79555i	−0.0872204	+	0.325511i	−0.995725	−	0.0923631i	$-0.970558\pi$
$317$	−1.55291	+	5.79555i	−0.0872204	+	0.325511i	0.908505	+	0.417874i	$0.137225\pi$
$318$		0			0
$319$	25.9808	+	15.0000i	1.45464	+	0.839839i
$320$		0			0
$321$		0			0
$322$	−5.01910	−	1.34486i	−0.279703	−	0.0749463i
$323$	−8.48528	+	8.48528i	−0.472134	+	0.472134i
$324$		0			0
$325$		0			0
$326$	15.0000	−	8.66025i	0.830773	−	0.479647i
$327$		0			0
$328$	8.36516	−	2.24144i	0.461889	−	0.123763i
$329$	2.59808	−	4.50000i	0.143237	−	0.248093i
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$	2.12132	+	2.12132i	0.116423	+	0.116423i
$333$		0			0
$334$			9.00000i			0.492458i
$335$		0			0
$336$		0			0
$337$	−3.58630	−	13.3843i	−0.195358	−	0.729087i	−0.992174	−	0.124864i	$-0.960150\pi$
$337$	−3.58630	−	13.3843i	−0.195358	−	0.729087i	0.796815	−	0.604223i	$-0.206516\pi$
$338$	0.258819	+	0.965926i	0.0140779	+	0.0525394i
$339$		0			0
$340$		0			0
$341$		−	34.6410i		−	1.87592i
$342$		0			0
$343$	−13.4722	−	13.4722i	−0.727430	−	0.727430i
$344$	5.19615	+	9.00000i	0.280158	+	0.485247i
$345$		0			0
$346$	12.0000	−	20.7846i	0.645124	−	1.11739i
$347$	11.5911	−	3.10583i	0.622243	−	0.166730i	0.0660960	−	0.997813i	$-0.478946\pi$
$347$	11.5911	−	3.10583i	0.622243	−	0.166730i	0.556147	+	0.831084i	$0.312279\pi$
$348$		0			0
$349$	0.866025	−	0.500000i	0.0463573	−	0.0267644i	−0.476642	−	0.879097i	$-0.658146\pi$
$349$	0.866025	−	0.500000i	0.0463573	−	0.0267644i	0.523000	+	0.852333i	$0.324813\pi$
$350$		0			0
$351$		0			0
$352$	−2.44949	+	2.44949i	−0.130558	+	0.130558i
$353$	−23.1822	−	6.21166i	−1.23387	−	0.330613i	−0.417782	−	0.908547i	$-0.637192\pi$
$353$	−23.1822	−	6.21166i	−1.23387	−	0.330613i	−0.816083	+	0.577934i	$0.803859\pi$
$354$		0			0
$355$		0			0
$356$	−1.50000	−	0.866025i	−0.0794998	−	0.0458993i
$357$		0			0
$358$	6.27603	−	23.4225i	0.331698	−	1.23792i
$359$	−17.3205			−0.914141			−0.457071	−	0.889430i	$-0.651101\pi$
$359$	−17.3205			−0.914141			−0.457071	+	0.889430i	$0.651101\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$	1.81173	−	6.76148i	0.0952226	−	0.355376i
$363$		0			0
$364$	5.19615	+	3.00000i	0.272352	+	0.157243i
$365$		0			0
$366$		0			0
$367$	3.34607	+	0.896575i	0.174663	+	0.0468009i	0.345091	−	0.938569i	$-0.387848\pi$
$367$	3.34607	+	0.896575i	0.174663	+	0.0468009i	−0.170427	+	0.985370i	$0.554515\pi$
$368$	2.12132	−	2.12132i	0.110581	−	0.110581i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−13.3843	+	3.58630i	−0.693011	+	0.185692i	−0.588098	−	0.808790i	$-0.700123\pi$
$373$	−13.3843	+	3.58630i	−0.693011	+	0.185692i	−0.104913	+	0.994481i	$0.533456\pi$
$374$	10.3923	−	18.0000i	0.537373	−	0.930758i
$375$		0			0
$376$	1.50000	+	2.59808i	0.0773566	+	0.133986i
$377$	21.2132	+	21.2132i	1.09254	+	1.09254i
$378$		0			0
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$		0			0
$381$		0			0
$382$	−4.48288	−	16.7303i	−0.229364	−	0.855998i
$383$	−6.21166	−	23.1822i	−0.317401	−	1.18456i	−0.921733	−	0.387824i	$-0.873227\pi$
$383$	−6.21166	−	23.1822i	−0.317401	−	1.18456i	0.604333	−	0.796732i	$-0.293440\pi$
$384$		0			0
$385$		0			0
$386$			17.3205i			0.881591i
$387$		0			0
$388$	4.89898	+	4.89898i	0.248708	+	0.248708i
$389$	12.9904	+	22.5000i	0.658638	+	1.14080i	0.980968	+	0.194168i	$0.0622006\pi$
$389$	12.9904	+	22.5000i	0.658638	+	1.14080i	−0.322330	+	0.946627i	$0.604466\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.455150	+	0.788342i
$392$	3.86370	−	1.03528i	0.195146	−	0.0522893i
$393$		0			0
$394$	−10.3923	+	6.00000i	−0.523557	+	0.302276i
$395$		0			0
$396$		0			0
$397$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$397$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$398$	−9.65926	−	2.58819i	−0.484175	−	0.129734i
$399$		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
$403$	8.96575	−	33.4607i	0.446616	−	1.66679i
$404$	13.8564			0.689382
$405$		0			0
$406$	−15.0000			−0.744438
$407$	−3.10583	+	11.5911i	−0.153950	+	0.574550i
$408$		0			0
$409$	1.73205	+	1.00000i	0.0856444	+	0.0494468i	0.542211	−	0.840243i	$-0.317588\pi$
$409$	1.73205	+	1.00000i	0.0856444	+	0.0494468i	−0.456566	+	0.889689i	$0.650921\pi$
$410$		0			0
$411$		0			0
$412$	−3.34607	−	0.896575i	−0.164849	−	0.0441711i
$413$	−8.48528	+	8.48528i	−0.417533	+	0.417533i
$414$		0			0
$415$		0			0
$416$	−3.00000	+	1.73205i	−0.147087	+	0.0849208i
$417$		0			0
$418$	6.69213	−	1.79315i	0.327323	−	0.0877059i
$419$	−5.19615	+	9.00000i	−0.253849	+	0.439679i	−0.964582	−	0.263783i	$-0.915030\pi$
$419$	−5.19615	+	9.00000i	−0.253849	+	0.439679i	0.710734	+	0.703461i	$0.248363\pi$
$420$		0			0
$421$	−5.00000	−	8.66025i	−0.243685	−	0.422075i	0.718076	−	0.695965i	$-0.245023\pi$
$421$	−5.00000	−	8.66025i	−0.243685	−	0.422075i	−0.961761	+	0.273890i	$0.911690\pi$
$422$	−15.5563	−	15.5563i	−0.757271	−	0.757271i
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	5.82774	+	21.7494i	0.282024	+	1.05253i
$428$	−0.776457	−	2.89778i	−0.0375315	−	0.140069i
$429$		0			0
$430$		0			0
$431$		−	6.92820i		−	0.333720i	−0.985981	−	0.166860i	$-0.946637\pi$
$431$		−	6.92820i		−	0.333720i	0.985981	−	0.166860i	$-0.0533628\pi$
$432$		0			0
$433$	−7.34847	−	7.34847i	−0.353145	−	0.353145i	0.508133	−	0.861278i	$-0.330336\pi$
$433$	−7.34847	−	7.34847i	−0.353145	−	0.353145i	−0.861278	+	0.508133i	$0.830336\pi$
$434$	8.66025	+	15.0000i	0.415705	+	0.720023i
$435$		0			0
$436$	2.50000	−	4.33013i	0.119728	−	0.207375i
$437$	−5.79555	+	1.55291i	−0.277239	+	0.0742860i
$438$		0			0
$439$	17.3205	−	10.0000i	0.826663	−	0.477274i	−0.0260459	−	0.999661i	$-0.508292\pi$
$439$	17.3205	−	10.0000i	0.826663	−	0.477274i	0.852709	+	0.522387i	$0.174958\pi$
$440$		0			0
$441$		0			0
$442$	14.6969	−	14.6969i	0.699062	−	0.699062i
$443$	8.69333	+	2.32937i	0.413033	+	0.110672i	0.459351	−	0.888255i	$-0.348082\pi$
$443$	8.69333	+	2.32937i	0.413033	+	0.110672i	−0.0463181	+	0.998927i	$0.514749\pi$
$444$		0			0
$445$		0			0
$446$	−13.5000	−	7.79423i	−0.639244	−	0.369067i
$447$		0			0
$448$	0.448288	−	1.67303i	0.0211796	−	0.0790434i
$449$	−13.8564			−0.653924			−0.326962	−	0.945037i	$-0.606025\pi$
$449$	−13.8564			−0.653924			−0.326962	+	0.945037i	$0.606025\pi$
$450$		0			0
$451$	30.0000			1.41264
$452$		0			0
$453$		0			0
$454$	−20.7846	−	12.0000i	−0.975470	−	0.563188i
$455$		0			0
$456$		0			0
$457$	−30.1146	−	8.06918i	−1.40870	−	0.377460i	−0.527240	−	0.849717i	$-0.676773\pi$
$457$	−30.1146	−	8.06918i	−1.40870	−	0.377460i	−0.881461	+	0.472256i	$0.843440\pi$
$458$	3.53553	−	3.53553i	0.165205	−	0.165205i
$459$		0			0
$460$		0			0
$461$	−10.5000	+	6.06218i	−0.489034	+	0.282344i	−0.724174	−	0.689618i	$-0.757779\pi$
$461$	−10.5000	+	6.06218i	−0.489034	+	0.282344i	0.235140	+	0.971962i	$0.424445\pi$
$462$		0			0
$463$	16.7303	−	4.48288i	0.777524	−	0.208337i	0.151831	−	0.988406i	$-0.451483\pi$
$463$	16.7303	−	4.48288i	0.777524	−	0.208337i	0.625693	+	0.780069i	$0.284816\pi$
$464$	4.33013	−	7.50000i	0.201021	−	0.348179i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	25.4558	+	25.4558i	1.17796	+	1.17796i	0.980264	+	0.197692i	$0.0633445\pi$
$467$	25.4558	+	25.4558i	1.17796	+	1.17796i	0.197692	+	0.980264i	$0.436655\pi$
$468$		0			0
$469$		−	21.0000i		−	0.969690i
$470$		0			0
$471$		0			0
$472$	−1.79315	−	6.69213i	−0.0825365	−	0.308030i
$473$	9.31749	+	34.7733i	0.428418	+	1.59888i
$474$		0			0
$475$		0			0
$476$			10.3923i			0.476331i
$477$		0			0
$478$	14.6969	+	14.6969i	0.672222	+	0.672222i
$479$	−13.8564	−	24.0000i	−0.633115	−	1.09659i	−0.986911	−	0.161265i	$-0.948443\pi$
$479$	−13.8564	−	24.0000i	−0.633115	−	1.09659i	0.353796	−	0.935323i	$-0.384891\pi$
$480$		0			0
$481$	−6.00000	+	10.3923i	−0.273576	+	0.473848i
$482$	−16.4207	+	4.39992i	−0.747944	+	0.200411i
$483$		0			0
$484$	−0.866025	+	0.500000i	−0.0393648	+	0.0227273i
$485$		0			0
$486$		0			0
$487$	17.1464	−	17.1464i	0.776979	−	0.776979i	−0.202337	−	0.979316i	$-0.564854\pi$
$487$	17.1464	−	17.1464i	0.776979	−	0.776979i	0.979316	+	0.202337i	$0.0648537\pi$
$488$	−12.5570	−	3.36465i	−0.568430	−	0.152310i
$489$		0			0
$490$		0			0
$491$	−12.0000	−	6.92820i	−0.541552	−	0.312665i	0.204155	−	0.978938i	$-0.434555\pi$
$491$	−12.0000	−	6.92820i	−0.541552	−	0.312665i	−0.745708	+	0.666273i	$0.767889\pi$
$492$		0			0
$493$	−13.4486	+	50.1910i	−0.605696	+	2.26049i
$494$	6.92820			0.311715
$495$		0			0
$496$	−10.0000			−0.449013
$497$	−1.55291	+	5.79555i	−0.0696577	+	0.259966i
$498$		0			0
$499$	−38.1051	−	22.0000i	−1.70582	−	0.984855i	−0.939599	−	0.342277i	$-0.888802\pi$
$499$	−38.1051	−	22.0000i	−1.70582	−	0.984855i	−0.766220	−	0.642578i	$-0.777865\pi$
$500$		0			0
$501$		0			0
$502$	−10.0382	−	2.68973i	−0.448027	−	0.120048i
$503$	−6.36396	+	6.36396i	−0.283755	+	0.283755i	−0.834605	−	0.550850i	$-0.814304\pi$
$503$	−6.36396	+	6.36396i	−0.283755	+	0.283755i	0.550850	+	0.834605i	$0.314304\pi$
$504$		0			0
$505$		0			0
$506$	9.00000	−	5.19615i	0.400099	−	0.230997i
$507$		0			0
$508$	5.01910	−	1.34486i	0.222686	−	0.0596687i
$509$	2.59808	−	4.50000i	0.115158	−	0.199459i	−0.802685	−	0.596403i	$-0.796596\pi$
$509$	2.59808	−	4.50000i	0.115158	−	0.199459i	0.917843	+	0.396944i	$0.129929\pi$
$510$		0			0
$511$	12.0000	+	20.7846i	0.530849	+	0.919457i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$	2.68973	+	10.0382i	0.118294	+	0.441479i
$518$	−1.55291	−	5.79555i	−0.0682311	−	0.254642i
$519$		0			0
$520$		0			0
$521$		−	5.19615i		−	0.227648i	−0.993501	−	0.113824i	$-0.963690\pi$
$521$		−	5.19615i		−	0.227648i	0.993501	−	0.113824i	$-0.0363099\pi$
$522$		0			0
$523$	−8.57321	−	8.57321i	−0.374880	−	0.374880i	0.494371	−	0.869251i	$-0.335399\pi$
$523$	−8.57321	−	8.57321i	−0.374880	−	0.374880i	−0.869251	+	0.494371i	$0.835399\pi$
$524$	−3.46410	−	6.00000i	−0.151330	−	0.262111i
$525$		0			0
$526$	−12.0000	+	20.7846i	−0.523225	+	0.906252i
$527$	57.9555	−	15.5291i	2.52458	−	0.676460i
$528$		0			0
$529$	12.1244	−	7.00000i	0.527146	−	0.304348i
$530$		0			0
$531$		0			0
$532$	−2.44949	+	2.44949i	−0.106199	+	0.106199i
$533$	28.9778	+	7.76457i	1.25517	+	0.336321i
$534$		0			0
$535$		0			0
$536$	10.5000	+	6.06218i	0.453531	+	0.261846i
$537$		0			0
$538$	0.448288	−	1.67303i	0.0193271	−	0.0721296i
$539$	13.8564			0.596838
$540$		0			0
$541$	−43.0000			−1.84871			−0.924357	−	0.381528i	$-0.875398\pi$
$541$	−43.0000			−1.84871			−0.924357	+	0.381528i	$0.875398\pi$
$542$	−2.58819	+	9.65926i	−0.111172	+	0.414901i
$543$		0			0
$544$	−5.19615	−	3.00000i	−0.222783	−	0.128624i
$545$		0			0
$546$		0			0
$547$	−1.67303	−	0.448288i	−0.0715337	−	0.0191674i	0.222875	−	0.974847i	$-0.428456\pi$
$547$	−1.67303	−	0.448288i	−0.0715337	−	0.0191674i	−0.294408	+	0.955680i	$0.595123\pi$
$548$	8.48528	−	8.48528i	0.362473	−	0.362473i
$549$		0			0
$550$		0			0
$551$	−15.0000	+	8.66025i	−0.639021	+	0.368939i
$552$		0			0
$553$	−6.69213	+	1.79315i	−0.284578	+	0.0762525i
$554$	5.19615	−	9.00000i	0.220763	−	0.382373i
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−25.4558	−	25.4558i	−1.07860	−	1.07860i	−0.996635	−	0.0819634i	$-0.973881\pi$
$557$	−25.4558	−	25.4558i	−1.07860	−	1.07860i	−0.0819634	−	0.996635i	$-0.526119\pi$
$558$		0			0
$559$			36.0000i			1.52264i
$560$		0			0
$561$		0			0
$562$	1.34486	+	5.01910i	0.0567296	+	0.211718i
$563$	−5.43520	−	20.2844i	−0.229066	−	0.854887i	−0.980734	−	0.195346i	$-0.937417\pi$
$563$	−5.43520	−	20.2844i	−0.229066	−	0.854887i	0.751668	−	0.659542i	$-0.229250\pi$
$564$		0			0
$565$		0			0
$566$			5.19615i			0.218411i
$567$		0			0
$568$	−2.44949	−	2.44949i	−0.102778	−	0.102778i
$569$	−3.46410	−	6.00000i	−0.145223	−	0.251533i	0.784233	−	0.620466i	$-0.213057\pi$
$569$	−3.46410	−	6.00000i	−0.145223	−	0.251533i	−0.929456	+	0.368933i	$0.879723\pi$
$570$		0			0
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$	−11.5911	+	3.10583i	−0.484649	+	0.129861i
$573$		0			0
$574$	−12.9904	+	7.50000i	−0.542208	+	0.313044i
$575$		0			0
$576$		0			0
$577$	−24.4949	+	24.4949i	−1.01974	+	1.01974i	−0.0199346	+	0.999801i	$0.506346\pi$
$577$	−24.4949	+	24.4949i	−1.01974	+	1.01974i	−0.999801	+	0.0199346i	$0.993654\pi$
$578$	18.3526	+	4.91756i	0.763367	+	0.204544i
$579$		0			0
$580$		0			0
$581$	−4.50000	−	2.59808i	−0.186691	−	0.107786i
$582$		0			0
$583$		0			0
$584$	−13.8564			−0.573382
$585$		0			0
$586$	30.0000			1.23929
$587$	−0.776457	+	2.89778i	−0.0320478	+	0.119604i	−0.980097	−	0.198520i	$-0.936386\pi$
$587$	−0.776457	+	2.89778i	−0.0320478	+	0.119604i	0.948049	+	0.318125i	$0.103053\pi$
$588$		0			0
$589$	17.3205	+	10.0000i	0.713679	+	0.412043i
$590$		0			0
$591$		0			0
$592$	3.34607	+	0.896575i	0.137522	+	0.0368490i
$593$	−12.7279	+	12.7279i	−0.522673	+	0.522673i	−0.918378	−	0.395705i	$-0.870500\pi$
$593$	−12.7279	+	12.7279i	−0.522673	+	0.522673i	0.395705	+	0.918378i	$0.370500\pi$
$594$		0			0
$595$		0			0
$596$	−4.50000	+	2.59808i	−0.184327	+	0.106421i
$597$		0			0
$598$	10.0382	−	2.68973i	0.410492	−	0.109991i
$599$	13.8564	−	24.0000i	0.566157	−	0.980613i	−0.430784	−	0.902455i	$-0.641763\pi$
$599$	13.8564	−	24.0000i	0.566157	−	0.980613i	0.996941	−	0.0781581i	$-0.0249039\pi$
$600$		0			0
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	0.934780	+	0.355228i	$0.115597\pi$
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	−0.159754	+	0.987157i	$0.551070\pi$
$602$	−12.7279	−	12.7279i	−0.518751	−	0.518751i
$603$		0			0
$604$			10.0000i			0.406894i
$605$		0			0
$606$		0			0
$607$	10.3106	+	38.4797i	0.418495	+	1.56184i	0.777730	+	0.628598i	$0.216371\pi$
$607$	10.3106	+	38.4797i	0.418495	+	1.56184i	−0.359235	+	0.933247i	$0.616962\pi$
$608$	−0.517638	−	1.93185i	−0.0209930	−	0.0783469i
$609$		0			0
$610$		0			0
$611$			10.3923i			0.420428i
$612$		0			0
$613$	12.2474	+	12.2474i	0.494670	+	0.494670i	0.909774	−	0.415104i	$-0.136255\pi$
$613$	12.2474	+	12.2474i	0.494670	+	0.494670i	−0.415104	+	0.909774i	$0.636255\pi$
$614$	−2.59808	−	4.50000i	−0.104850	−	0.181605i
$615$		0			0
$616$	3.00000	−	5.19615i	0.120873	−	0.209359i
$617$	−34.7733	+	9.31749i	−1.39992	+	0.375108i	−0.878317	−	0.478079i	$-0.841333\pi$
$617$	−34.7733	+	9.31749i	−1.39992	+	0.375108i	−0.521605	+	0.853187i	$0.674666\pi$
$618$		0			0
$619$	−19.0526	+	11.0000i	−0.765787	+	0.442127i	−0.831370	−	0.555720i	$-0.812443\pi$
$619$	−19.0526	+	11.0000i	−0.765787	+	0.442127i	0.0655827	+	0.997847i	$0.479109\pi$
$620$		0			0
$621$		0			0
$622$	17.1464	−	17.1464i	0.687509	−	0.687509i
$623$	2.89778	+	0.776457i	0.116097	+	0.0311081i
$624$		0			0
$625$		0			0
$626$	3.00000	+	1.73205i	0.119904	+	0.0692267i
$627$		0			0
$628$	−5.37945	+	20.0764i	−0.214664	+	0.801135i
$629$	−20.7846			−0.828737
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	1.03528	−	3.86370i	0.0411811	−	0.153690i
$633$		0			0
$634$	5.19615	+	3.00000i	0.206366	+	0.119145i
$635$		0			0
$636$		0			0
$637$	13.3843	+	3.58630i	0.530304	+	0.142094i
$638$	21.2132	−	21.2132i	0.839839	−	0.839839i
$639$		0			0
$640$		0			0
$641$	−28.5000	+	16.4545i	−1.12568	+	0.649913i	−0.942845	−	0.333230i	$-0.891861\pi$
$641$	−28.5000	+	16.4545i	−1.12568	+	0.649913i	−0.182837	+	0.983143i	$0.558528\pi$
$642$		0			0
$643$	5.01910	−	1.34486i	0.197934	−	0.0530362i	−0.158490	−	0.987361i	$-0.550663\pi$
$643$	5.01910	−	1.34486i	0.197934	−	0.0530362i	0.356424	+	0.934324i	$0.383996\pi$
$644$	−2.59808	+	4.50000i	−0.102379	+	0.177325i
$645$		0			0
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	14.8492	+	14.8492i	0.583784	+	0.583784i	0.935941	−	0.352157i	$-0.114552\pi$
$647$	14.8492	+	14.8492i	0.583784	+	0.583784i	−0.352157	+	0.935941i	$0.614552\pi$
$648$		0			0
$649$		−	24.0000i		−	0.942082i
$650$		0			0
$651$		0			0
$652$	−4.48288	−	16.7303i	−0.175563	−	0.655210i
$653$	−4.65874	−	17.3867i	−0.182311	−	0.680393i	−0.995190	−	0.0979610i	$-0.968768\pi$
$653$	−4.65874	−	17.3867i	−0.182311	−	0.680393i	0.812880	−	0.582432i	$-0.197899\pi$
$654$		0			0
$655$		0			0
$656$		−	8.66025i		−	0.338126i
$657$		0			0
$658$	−3.67423	−	3.67423i	−0.143237	−	0.143237i
$659$	−10.3923	−	18.0000i	−0.404827	−	0.701180i	0.589475	−	0.807787i	$-0.299335\pi$
$659$	−10.3923	−	18.0000i	−0.404827	−	0.701180i	−0.994301	+	0.106606i	$0.966001\pi$
$660$		0			0
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	−0.996682	−	0.0813955i	$-0.974062\pi$
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	0.568831	+	0.822454i	$0.307396\pi$
$662$	−7.72741	+	2.07055i	−0.300334	+	0.0804743i
$663$		0			0
$664$	2.59808	−	1.50000i	0.100825	−	0.0582113i
$665$		0			0
$666$		0			0
$667$	−18.3712	+	18.3712i	−0.711335	+	0.711335i
$668$	8.69333	+	2.32937i	0.336355	+	0.0901261i
$669$		0			0
$670$		0			0
$671$	−39.0000	−	22.5167i	−1.50558	−	0.869246i
$672$		0			0
$673$	−9.86233	+	36.8067i	−0.380165	+	1.41879i	0.465485	+	0.885056i	$0.345880\pi$
$673$	−9.86233	+	36.8067i	−0.380165	+	1.41879i	−0.845649	+	0.533739i	$0.820787\pi$
$674$	−13.8564			−0.533729
$675$		0			0
$676$	1.00000			0.0384615
$677$	1.55291	−	5.79555i	0.0596833	−	0.222741i	−0.929642	−	0.368464i	$-0.879884\pi$
$677$	1.55291	−	5.79555i	0.0596833	−	0.222741i	0.989326	+	0.145722i	$0.0465506\pi$
$678$		0			0
$679$	−10.3923	−	6.00000i	−0.398820	−	0.230259i
$680$		0			0
$681$		0			0
$682$	−33.4607	−	8.96575i	−1.28127	−	0.343316i
$683$	8.48528	−	8.48528i	0.324680	−	0.324680i	−0.525879	−	0.850559i	$-0.676264\pi$
$683$	8.48528	−	8.48528i	0.324680	−	0.324680i	0.850559	+	0.525879i	$0.176264\pi$
$684$		0			0
$685$		0			0
$686$	−16.5000	+	9.52628i	−0.629973	+	0.363715i
$687$		0			0
$688$	10.0382	−	2.68973i	0.382703	−	0.102545i
$689$		0			0
$690$		0			0
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	0.932024	−	0.362397i	$-0.118041\pi$
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	−0.779857	+	0.625958i	$0.784708\pi$
$692$	−16.9706	−	16.9706i	−0.645124	−	0.645124i
$693$		0			0
$694$		−	12.0000i		−	0.455514i
$695$		0			0
$696$		0			0
$697$	13.4486	+	50.1910i	0.509403	+	1.90112i
$698$	−0.258819	−	0.965926i	−0.00979645	−	0.0365608i
$699$		0			0
$700$		0			0
$701$			12.1244i			0.457931i	0.973435	+	0.228965i	$0.0735342\pi$
$701$			12.1244i			0.457931i	−0.973435	+	0.228965i	$0.926466\pi$
$702$		0			0
$703$	−4.89898	−	4.89898i	−0.184769	−	0.184769i
$704$	1.73205	+	3.00000i	0.0652791	+	0.113067i
$705$		0			0
$706$	−12.0000	+	20.7846i	−0.451626	+	0.782239i
$707$	−23.1822	+	6.21166i	−0.871857	+	0.233613i
$708$		0			0
$709$	−35.5070	+	20.5000i	−1.33349	+	0.769894i	−0.985834	−	0.167727i	$-0.946357\pi$
$709$	−35.5070	+	20.5000i	−1.33349	+	0.769894i	−0.347661	+	0.937620i	$0.613024\pi$
$710$		0			0
$711$		0			0
$712$	−1.22474	+	1.22474i	−0.0458993	+	0.0458993i
$713$	28.9778	+	7.76457i	1.08523	+	0.290785i
$714$		0			0
$715$		0			0
$716$	−21.0000	−	12.1244i	−0.784807	−	0.453108i
$717$		0			0
$718$	−4.48288	+	16.7303i	−0.167299	+	0.624370i
$719$	6.92820			0.258378			0.129189	−	0.991620i	$-0.458763\pi$
$719$	6.92820			0.258378			0.129189	+	0.991620i	$0.458763\pi$
$720$		0			0
$721$	6.00000			0.223452
$722$	3.88229	−	14.4889i	0.144484	−	0.539221i
$723$		0			0
$724$	−6.06218	−	3.50000i	−0.225299	−	0.130076i
$725$		0			0
$726$		0			0
$727$	5.01910	+	1.34486i	0.186148	+	0.0498782i	0.350689	−	0.936492i	$-0.385948\pi$
$727$	5.01910	+	1.34486i	0.186148	+	0.0498782i	−0.164541	+	0.986370i	$0.552614\pi$
$728$	4.24264	−	4.24264i	0.157243	−	0.157243i
$729$		0			0
$730$		0			0
$731$	−54.0000	+	31.1769i	−1.99726	+	1.15312i
$732$		0			0
$733$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$733$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$734$	1.73205	−	3.00000i	0.0639312	−	0.110732i
$735$		0			0
$736$	−1.50000	−	2.59808i	−0.0552907	−	0.0957664i
$737$	29.6985	+	29.6985i	1.09396	+	1.09396i
$738$		0			0
$739$			4.00000i			0.147142i	0.997290	+	0.0735712i	$0.0234396\pi$
$739$			4.00000i			0.147142i	−0.997290	+	0.0735712i	$0.976560\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	6.98811	+	26.0800i	0.256369	+	0.956782i	0.967324	+	0.253544i	$0.0815964\pi$
$743$	6.98811	+	26.0800i	0.256369	+	0.956782i	−0.710955	+	0.703238i	$0.751737\pi$
$744$		0			0
$745$		0			0
$746$			13.8564i			0.507319i
$747$		0			0
$748$	−14.6969	−	14.6969i	−0.537373	−	0.537373i
$749$	2.59808	+	4.50000i	0.0949316	+	0.164426i
$750$		0			0
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	−0.847203	−	0.531269i	$-0.821715\pi$
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	0.883694	+	0.468065i	$0.155049\pi$
$752$	2.89778	−	0.776457i	0.105671	−	0.0283145i
$753$		0			0
$754$	25.9808	−	15.0000i	0.946164	−	0.546268i
$755$		0			0
$756$		0			0
$757$	31.8434	−	31.8434i	1.15737	−	1.15737i	0.172327	−	0.985040i	$-0.444871\pi$
$757$	31.8434	−	31.8434i	1.15737	−	1.15737i	0.985040	−	0.172327i	$-0.0551286\pi$
$758$	−7.72741	−	2.07055i	−0.280672	−	0.0752058i
$759$		0			0
$760$		0			0
$761$	34.5000	+	19.9186i	1.25062	+	0.722048i	0.971233	−	0.238129i	$-0.0765342\pi$
$761$	34.5000	+	19.9186i	1.25062	+	0.722048i	0.279391	+	0.960178i	$0.409868\pi$
$762$		0			0
$763$	−2.24144	+	8.36516i	−0.0811455	+	0.302839i
$764$	−17.3205			−0.626634
$765$		0			0
$766$	−24.0000			−0.867155
$767$	6.21166	−	23.1822i	0.224290	−	0.837061i
$768$		0			0
$769$	−19.9186	−	11.5000i	−0.718283	−	0.414701i	0.0958377	−	0.995397i	$-0.469447\pi$
$769$	−19.9186	−	11.5000i	−0.718283	−	0.414701i	−0.814120	+	0.580696i	$0.802780\pi$
$770$		0			0
$771$		0			0
$772$	16.7303	+	4.48288i	0.602138	+	0.161342i
$773$	25.4558	−	25.4558i	0.915583	−	0.915583i	−0.0811212	−	0.996704i	$-0.525850\pi$
$773$	25.4558	−	25.4558i	0.915583	−	0.915583i	0.996704	+	0.0811212i	$0.0258501\pi$
$774$		0			0
$775$		0			0
$776$	6.00000	−	3.46410i	0.215387	−	0.124354i
$777$		0			0
$778$	25.0955	−	6.72432i	0.899717	−	0.241078i
$779$	−8.66025	+	15.0000i	−0.310286	+	0.537431i
$780$		0			0
$781$	−6.00000	−	10.3923i	−0.214697	−	0.371866i
$782$	12.7279	+	12.7279i	0.455150	+	0.455150i
$783$		0			0
$784$		−	4.00000i		−	0.142857i
$785$		0			0
$786$		0			0
$787$	0.896575	+	3.34607i	0.0319595	+	0.119274i	0.980063	−	0.198688i	$-0.0636681\pi$
$787$	0.896575	+	3.34607i	0.0319595	+	0.119274i	−0.948103	+	0.317962i	$0.897001\pi$
$788$	3.10583	+	11.5911i	0.110641	+	0.412916i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−31.8434	−	31.8434i	−1.13079	−	1.13079i
$794$		0			0
$795$		0			0
$796$	−5.00000	+	8.66025i	−0.177220	+	0.306955i
$797$	40.5689	−	10.8704i	1.43702	−	0.385049i	0.545533	−	0.838089i	$-0.316327\pi$
$797$	40.5689	−	10.8704i	1.43702	−	0.385049i	0.891490	+	0.453040i	$0.149660\pi$
$798$		0			0
$799$	−15.5885	+	9.00000i	−0.551480	+	0.318397i
$800$		0			0
$801$		0			0
$802$	14.6969	−	14.6969i	0.518967	−	0.518967i
$803$	−46.3644	−	12.4233i	−1.63617	−	0.438409i
$804$		0			0
$805$		0			0
$806$	−30.0000	−	17.3205i	−1.05670	−	0.610089i
$807$		0			0
$808$	3.58630	−	13.3843i	0.126166	−	0.470857i
$809$	−6.92820			−0.243583			−0.121791	−	0.992556i	$-0.538864\pi$
$809$	−6.92820			−0.243583			−0.121791	+	0.992556i	$0.538864\pi$
$810$		0			0
$811$	4.00000			0.140459			0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000			0.140459			0.0702295	+	0.997531i	$0.477627\pi$
$812$	−3.88229	+	14.4889i	−0.136242	+	0.508460i
$813$		0			0
$814$	10.3923	+	6.00000i	0.364250	+	0.210300i
$815$		0			0
$816$		0			0
$817$	−20.0764	−	5.37945i	−0.702384	−	0.188203i
$818$	1.41421	−	1.41421i	0.0494468	−	0.0494468i
$819$		0			0
$820$		0			0
$821$	16.5000	−	9.52628i	0.575854	−	0.332469i	−0.183630	−	0.982995i	$-0.558785\pi$
$821$	16.5000	−	9.52628i	0.575854	−	0.332469i	0.759484	+	0.650526i	$0.225452\pi$
$822$		0			0
$823$	28.4416	−	7.62089i	0.991410	−	0.265648i	0.273567	−	0.961853i	$-0.411796\pi$
$823$	28.4416	−	7.62089i	0.991410	−	0.265648i	0.717843	+	0.696205i	$0.245130\pi$
$824$	−1.73205	+	3.00000i	−0.0603388	+	0.104510i
$825$		0			0
$826$	6.00000	+	10.3923i	0.208767	+	0.361595i
$827$	−31.8198	−	31.8198i	−1.10648	−	1.10648i	−0.993609	−	0.112874i	$-0.963994\pi$
$827$	−31.8198	−	31.8198i	−1.10648	−	1.10648i	−0.112874	−	0.993609i	$-0.536006\pi$
$828$		0			0
$829$		−	29.0000i		−	1.00721i	−0.863934	−	0.503606i	$-0.832006\pi$
$829$		−	29.0000i		−	1.00721i	0.863934	−	0.503606i	$-0.167994\pi$
$830$		0			0
$831$		0			0
$832$	0.896575	+	3.34607i	0.0310832	+	0.116004i
$833$	6.21166	+	23.1822i	0.215221	+	0.803216i
$834$		0			0
$835$		0			0
$836$		−	6.92820i		−	0.239617i
$837$		0			0
$838$	7.34847	+	7.34847i	0.253849	+	0.253849i
$839$	−19.0526	−	33.0000i	−0.657767	−	1.13929i	−0.981192	−	0.193033i	$-0.938168\pi$
$839$	−19.0526	−	33.0000i	−0.657767	−	1.13929i	0.323425	−	0.946254i	$-0.395166\pi$
$840$		0			0
$841$	−23.0000	+	39.8372i	−0.793103	+	1.37370i
$842$	−9.65926	+	2.58819i	−0.332880	+	0.0891949i
$843$		0			0
$844$	−19.0526	+	11.0000i	−0.655816	+	0.378636i
$845$		0			0
$846$		0			0
$847$	1.22474	−	1.22474i	0.0420827	−	0.0420827i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−9.00000	−	5.19615i	−0.308516	−	0.178122i
$852$		0			0
$853$	−4.48288	+	16.7303i	−0.153491	+	0.572835i	0.845739	+	0.533597i	$0.179160\pi$
$853$	−4.48288	+	16.7303i	−0.153491	+	0.572835i	−0.999230	+	0.0392388i	$0.987507\pi$
$854$	22.5167			0.770504
$855$		0			0
$856$	−3.00000			−0.102538
$857$	−10.8704	+	40.5689i	−0.371326	+	1.38581i	0.487314	+	0.873227i	$0.337977\pi$
$857$	−10.8704	+	40.5689i	−0.371326	+	1.38581i	−0.858640	+	0.512580i	$0.828690\pi$
$858$		0			0
$859$	19.0526	+	11.0000i	0.650065	+	0.375315i	0.788481	−	0.615059i	$-0.210868\pi$
$859$	19.0526	+	11.0000i	0.650065	+	0.375315i	−0.138416	+	0.990374i	$0.544201\pi$
$860$		0			0
$861$		0			0
$862$	−6.69213	−	1.79315i	−0.227935	−	0.0610750i
$863$	−10.6066	+	10.6066i	−0.361053	+	0.361053i	−0.864201	−	0.503148i	$-0.832175\pi$
$863$	−10.6066	+	10.6066i	−0.361053	+	0.361053i	0.503148	+	0.864201i	$0.332175\pi$
$864$		0			0
$865$		0			0
$866$	−9.00000	+	5.19615i	−0.305832	+	0.176572i
$867$		0			0
$868$	16.7303	−	4.48288i	0.567864	−	0.152159i
$869$	6.92820	−	12.0000i	0.235023	−	0.407072i
$870$		0			0
$871$	21.0000	+	36.3731i	0.711558	+	1.23245i
$872$	−3.53553	−	3.53553i	−0.119728	−	0.119728i
$873$		0			0
$874$			6.00000i			0.202953i
$875$		0			0
$876$		0			0
$877$	−4.48288	−	16.7303i	−0.151376	−	0.564943i	−0.999388	−	0.0349667i	$-0.988867\pi$
$877$	−4.48288	−	16.7303i	−0.151376	−	0.564943i	0.848012	−	0.529976i	$-0.177799\pi$
$878$	−5.17638	−	19.3185i	−0.174694	−	0.651968i
$879$		0			0
$880$		0			0
$881$			1.73205i			0.0583543i	0.999574	+	0.0291771i	$0.00928869\pi$
$881$			1.73205i			0.0583543i	−0.999574	+	0.0291771i	$0.990711\pi$
$882$		0			0
$883$	−30.6186	−	30.6186i	−1.03040	−	1.03040i	−0.999523	−	0.0308754i	$-0.990170\pi$
$883$	−30.6186	−	30.6186i	−1.03040	−	1.03040i	−0.0308754	−	0.999523i	$-0.509830\pi$
$884$	−10.3923	−	18.0000i	−0.349531	−	0.605406i
$885$		0			0
$886$	4.50000	−	7.79423i	0.151180	−	0.261852i
$887$	23.1822	−	6.21166i	0.778383	−	0.208567i	0.152311	−	0.988333i	$-0.451328\pi$
$887$	23.1822	−	6.21166i	0.778383	−	0.208567i	0.626072	+	0.779766i	$0.284662\pi$
$888$		0			0
$889$	−7.79423	+	4.50000i	−0.261410	+	0.150925i
$890$		0			0
$891$		0			0
$892$	−11.0227	+	11.0227i	−0.369067	+	0.369067i
$893$	−5.79555	−	1.55291i	−0.193941	−	0.0519663i
$894$		0			0
$895$		0			0
$896$	−1.50000	−	0.866025i	−0.0501115	−	0.0289319i
$897$		0			0
$898$	−3.58630	+	13.3843i	−0.119676	+	0.446639i
$899$	86.6025			2.88836
$900$		0			0
$901$		0			0
$902$	7.76457	−	28.9778i	0.258532	−	0.964854i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−8.36516	−	2.24144i	−0.277761	−	0.0744257i	0.117250	−	0.993102i	$-0.462592\pi$
$907$	−8.36516	−	2.24144i	−0.277761	−	0.0744257i	−0.395010	+	0.918677i	$0.629259\pi$
$908$	−16.9706	+	16.9706i	−0.563188	+	0.563188i
$909$		0			0
$910$		0			0
$911$	48.0000	−	27.7128i	1.59031	−	0.918166i	0.597058	−	0.802198i	$-0.296336\pi$
$911$	48.0000	−	27.7128i	1.59031	−	0.918166i	0.993253	−	0.115968i	$-0.0369971\pi$
$912$		0			0
$913$	10.0382	−	2.68973i	0.332216	−	0.0890170i
$914$	−15.5885	+	27.0000i	−0.515620	+	0.893081i
$915$		0			0
$916$	−2.50000	−	4.33013i	−0.0826023	−	0.143071i
$917$	8.48528	+	8.48528i	0.280209	+	0.280209i
$918$		0			0
$919$			40.0000i			1.31948i	0.751495	+	0.659739i	$0.229333\pi$
$919$			40.0000i			1.31948i	−0.751495	+	0.659739i	$0.770667\pi$
$920$		0			0
$921$		0			0
$922$	3.13801	+	11.7112i	0.103345	+	0.385689i
$923$	−3.10583	−	11.5911i	−0.102230	−	0.381526i
$924$		0			0
$925$		0			0
$926$		−	17.3205i		−	0.569187i
$927$		0			0
$928$	−6.12372	−	6.12372i	−0.201021	−	0.201021i
$929$	3.46410	+	6.00000i	0.113653	+	0.196854i	0.917241	−	0.398333i	$-0.130411\pi$
$929$	3.46410	+	6.00000i	0.113653	+	0.196854i	−0.803587	+	0.595187i	$0.797078\pi$
$930$		0			0
$931$	−4.00000	+	6.92820i	−0.131095	+	0.227063i
$932$	−5.79555	+	1.55291i	−0.189840	+	0.0508674i
$933$		0			0
$934$	31.1769	−	18.0000i	1.02014	−	0.588978i
$935$		0			0
$936$		0			0
$937$	9.79796	−	9.79796i	0.320085	−	0.320085i	−0.528714	−	0.848800i	$-0.677326\pi$
$937$	9.79796	−	9.79796i	0.320085	−	0.320085i	0.848800	+	0.528714i	$0.177326\pi$
$938$	−20.2844	−	5.43520i	−0.662311	−	0.177466i
$939$		0			0
$940$		0			0
$941$	4.50000	+	2.59808i	0.146696	+	0.0846949i	0.571551	−	0.820566i	$-0.306342\pi$
$941$	4.50000	+	2.59808i	0.146696	+	0.0846949i	−0.424856	+	0.905261i	$0.639675\pi$
$942$		0			0
$943$	−6.72432	+	25.0955i	−0.218974	+	0.817222i
$944$	−6.92820			−0.225494
$945$		0			0
$946$	36.0000			1.17046
$947$	−6.98811	+	26.0800i	−0.227083	+	0.847486i	0.754476	+	0.656328i	$0.227891\pi$
$947$	−6.98811	+	26.0800i	−0.227083	+	0.847486i	−0.981559	+	0.191158i	$0.938776\pi$
$948$		0			0
$949$	−41.5692	−	24.0000i	−1.34939	−	0.779073i
$950$		0			0
$951$		0			0
$952$	10.0382	+	2.68973i	0.325340	+	0.0871745i
$953$	−29.6985	+	29.6985i	−0.962028	+	0.962028i	−0.999305	−	0.0372767i	$-0.988132\pi$
$953$	−29.6985	+	29.6985i	−0.962028	+	0.962028i	0.0372767	+	0.999305i	$0.488132\pi$
$954$		0			0
$955$		0			0
$956$	18.0000	−	10.3923i	0.582162	−	0.336111i
$957$		0			0
$958$	−26.7685	+	7.17260i	−0.864852	+	0.231736i
$959$	−10.3923	+	18.0000i	−0.335585	+	0.581250i
$960$		0			0
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	8.48528	+	8.48528i	0.273576	+	0.273576i
$963$		0			0
$964$			17.0000i			0.547533i
$965$		0			0
$966$		0			0
$967$	−13.8969	−	51.8640i	−0.446895	−	1.66783i	−0.710885	−	0.703309i	$-0.751705\pi$
$967$	−13.8969	−	51.8640i	−0.446895	−	1.66783i	0.263990	−	0.964525i	$-0.414961\pi$
$968$	0.258819	+	0.965926i	0.00831876	+	0.0310460i
$969$		0			0
$970$		0			0
$971$			38.1051i			1.22285i	0.791302	+	0.611426i	$0.209404\pi$
$971$			38.1051i			1.22285i	−0.791302	+	0.611426i	$0.790596\pi$
$972$		0			0
$973$	−4.89898	−	4.89898i	−0.157054	−	0.157054i
$974$	−12.1244	−	21.0000i	−0.388489	−	0.672883i
$975$		0			0
$976$	−6.50000	+	11.2583i	−0.208060	+	0.360370i
$977$	−40.5689	+	10.8704i	−1.29791	+	0.347775i	−0.840661	−	0.541562i	$-0.817833\pi$
$977$	−40.5689	+	10.8704i	−1.29791	+	0.347775i	−0.457253	+	0.889337i	$0.651167\pi$
$978$		0			0
$979$	−5.19615	+	3.00000i	−0.166070	+	0.0958804i
$980$		0			0
$981$		0			0
$982$	−9.79796	+	9.79796i	−0.312665	+	0.312665i
$983$	−8.69333	−	2.32937i	−0.277274	−	0.0742954i	0.117502	−	0.993073i	$-0.462511\pi$
$983$	−8.69333	−	2.32937i	−0.277274	−	0.0742954i	−0.394776	+	0.918777i	$0.629178\pi$
$984$		0			0
$985$		0			0
$986$	45.0000	+	25.9808i	1.43309	+	0.827396i
$987$		0			0
$988$	1.79315	−	6.69213i	0.0570477	−	0.212905i
$989$	−31.1769			−0.991368
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	−2.58819	+	9.65926i	−0.0821751	+	0.306682i
$993$		0			0
$994$	5.19615	+	3.00000i	0.164812	+	0.0951542i
$995$		0			0
$996$		0			0
$997$	−40.1528	−	10.7589i	−1.27165	−	0.340738i	−0.440988	−	0.897513i	$-0.645372\pi$
$997$	−40.1528	−	10.7589i	−1.27165	−	0.340738i	−0.830663	+	0.556775i	$0.812039\pi$
$998$	−31.1127	+	31.1127i	−0.984855	+	0.984855i
$999$		0			0

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(1.67303 + 0.448288i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(1.67303 + 0.448288i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-3.00000 + 1.73205i) q^{11} +(-3.34607 + 0.896575i) q^{13} +(0.866025 - 1.50000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-4.24264 - 4.24264i) q^{17} -2.00000i q^{19} +(0.896575 + 3.34607i) q^{22} +(-0.776457 - 2.89778i) q^{23} +3.46410i q^{26} +(-1.22474 - 1.22474i) q^{28} +(-4.33013 - 7.50000i) q^{29} +(-5.00000 + 8.66025i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-5.19615 + 3.00000i) q^{34} +(2.44949 - 2.44949i) q^{37} +(-1.93185 - 0.517638i) q^{38} +(-7.50000 - 4.33013i) q^{41} +(2.68973 - 10.0382i) q^{43} +3.46410 q^{44} -3.00000 q^{46} +(0.776457 - 2.89778i) q^{47} +(-3.46410 - 2.00000i) q^{49} +(3.34607 + 0.896575i) q^{52} +(-1.50000 + 0.866025i) q^{56} +(-8.36516 + 2.24144i) q^{58} +(-3.46410 + 6.00000i) q^{59} +(6.50000 + 11.2583i) q^{61} +(7.07107 + 7.07107i) q^{62} -1.00000i q^{64} +(-3.13801 - 11.7112i) q^{67} +(1.55291 + 5.79555i) q^{68} +3.46410i q^{71} +(9.79796 + 9.79796i) q^{73} +(-1.73205 - 3.00000i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(-5.79555 + 1.55291i) q^{77} +(-3.46410 + 2.00000i) q^{79} +(-6.12372 + 6.12372i) q^{82} +(-2.89778 - 0.776457i) q^{83} +(-9.00000 - 5.19615i) q^{86} +(0.896575 - 3.34607i) q^{88} +1.73205 q^{89} -6.00000 q^{91} +(-0.776457 + 2.89778i) q^{92} +(-2.59808 - 1.50000i) q^{94} +(-6.69213 - 1.79315i) q^{97} +(-2.82843 + 2.82843i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 24 q^{11} + 4 q^{16} - 40 q^{31} - 60 q^{41} - 24 q^{46} - 12 q^{56} + 52 q^{61} - 8 q^{76} - 72 q^{86} - 48 q^{91}+O(q^{100}) \) 8 * q - 24 * q^11 + 4 * q^16 - 40 * q^31 - 60 * q^41 - 24 * q^46 - 12 * q^56 + 52 * q^61 - 8 * q^76 - 72 * q^86 - 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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